diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/-Q6j1jdwl4c_raw.srt b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/-Q6j1jdwl4c_raw.srt
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index 0000000000000000000000000000000000000000..26a075d1ddf38177418d02812fe3959ce5c46ae8
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/-Q6j1jdwl4c_raw.srt
@@ -0,0 +1,2428 @@
+1
+00:00:21,280 --> 00:00:25,240
+بسم الله الرحمن الرحيم اليوم إن شاء الله سوف نكمل
+
+2
+00:00:25,240 --> 00:00:30,080
+حديثنا عن الاختلافات في الأخيرين الاثنين من
+
+3
+00:00:30,080 --> 00:00:34,820
+الدراسات نحكي عن الاختلافات المختلفة في السلاسة
+
+4
+00:00:34,820 --> 00:00:39,840
+الأخيرة إذا تتذكرين أننا قد درسنا الاختلافات
+
+5
+00:00:39,840 --> 00:00:45,060
+الأولى التي هي الاختلافات المخاطرة للإستعمال
+
+6
+00:00:45,060 --> 00:00:47,780
+وقررنا
+
+7
+00:00:49,760 --> 00:00:51,600
+أو الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+8
+00:00:51,600 --> 00:00:55,160
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+9
+00:00:55,160 --> 00:00:58,940
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+10
+00:00:58,940 --> 00:00:59,600
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+11
+00:00:59,600 --> 00:01:00,700
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+12
+00:01:00,700 --> 00:01:00,780
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+13
+00:01:00,780 --> 00:01:01,540
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+14
+00:01:01,540 --> 00:01:02,580
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+15
+00:01:02,580 --> 00:01:10,700
+الانتجار الاجتماعي أو الانتجار الاجتماعي أو
+
+16
+00:01:10,700 --> 00:01:18,530
+الانتجار السأعلمك شيء مرتبط بالطبع كيف يمكننا أن
+
+17
+00:01:18,530 --> 00:01:23,650
+نقوم بتأكيد الاختلاف الموتى أو اهتمام الحصول على
+
+18
+00:01:23,650 --> 00:01:24,610
+الحصول على الحصول على الحصول على الحصول على الحصول
+
+19
+00:01:24,610 --> 00:01:25,250
+على الحصول على الحصول على الحصول على الحصول على
+
+20
+00:01:25,250 --> 00:01:25,990
+الحصول على الحصول على الحصول على الحصول على الحصول
+
+21
+00:01:25,990 --> 00:01:26,490
+على الحصول على الحصول على الحصول على الحصول على
+
+22
+00:01:26,490 --> 00:01:28,110
+الحصول على الحصول على الحصول على الحصول على الحصول
+
+23
+00:01:28,110 --> 00:01:28,230
+على الحصول على الحصول على الحصول على الحصول على
+
+24
+00:01:28,230 --> 00:01:28,270
+الحصول على الحصول على الحصول على الحصول على الحصول
+
+25
+00:01:28,270 --> 00:01:28,790
+على الحصول على الحصول على الحصول على الحصول على
+
+26
+00:01:28,790 --> 00:01:31,250
+الحصول على الحصول على الحصول على الحصول على الحصول
+
+27
+00:01:31,250 --> 00:01:40,030
+على الحصول على الحصول على الحصول على الحصولكما
+
+28
+00:01:40,030 --> 00:01:44,870
+ذكرنا في السلسلة الأولى لـ Externalities لدينا
+
+29
+00:01:44,870 --> 00:01:48,050
+أربع مرات أول مرة هي الـ Negative Externalities of
+
+30
+00:01:48,050 --> 00:01:52,830
+Consumption Positive Externalities of Consumption
+
+31
+00:01:52,830 --> 00:01:57,830
+Negative Externalities of a Production Positive
+
+32
+00:01:57,830 --> 00:02:03,830
+Externalities of a Production الأمثلة التي
+
+33
+00:02:03,830 --> 00:02:08,150
+استخدمناها أو استخدمناها كانت
+
+34
+00:02:12,690 --> 00:02:17,550
+والخارجات الخارجية المستخدمة، الهيالت كير، وهي
+
+35
+00:02:17,550 --> 00:02:23,350
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+36
+00:02:23,350 --> 00:02:26,710
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+37
+00:02:26,710 --> 00:02:28,830
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+38
+00:02:28,830 --> 00:02:28,890
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+39
+00:02:28,890 --> 00:02:28,890
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+40
+00:02:28,890 --> 00:02:29,650
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+41
+00:02:29,650 --> 00:02:32,050
+مرتبطة بـVaccination وهي مرتبطة بـVaccination وهي
+
+42
+00:02:32,050 --> 00:02:32,770
+مرتبطة بـVaccination وهي مرتبطة
+
+43
+00:02:35,860 --> 00:02:40,320
+والفكتوريات التي تخلص من المخلوقات، أفسنات أفسنة
+
+44
+00:02:40,320 --> 00:02:49,560
+من الوصول للإنتاج، هذه هي الصورة الكبيرة في
+
+45
+00:02:49,560 --> 00:02:56,900
+الوضع عام، عندما نتحدث عن استخدام، هنا نتحدث عن
+
+46
+00:02:56,900 --> 00:02:57,460
+استخدام
+
+47
+00:03:00,510 --> 00:03:04,670
+في البرنامج يجب أن يكون هناك اتجارات اتجارات
+
+48
+00:03:04,670 --> 00:03:05,870
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+49
+00:03:05,870 --> 00:03:05,870
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+50
+00:03:05,870 --> 00:03:07,030
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+51
+00:03:07,030 --> 00:03:10,290
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+52
+00:03:10,290 --> 00:03:10,330
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+53
+00:03:10,330 --> 00:03:10,770
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+54
+00:03:10,770 --> 00:03:10,770
+اتجارات اتجارات اتجارات اتجارات
+
+55
+00:03:27,980 --> 00:03:30,460
+على سبيل المثال، هناك اتجارات مصالحية و اتجارات
+
+56
+00:03:30,460 --> 00:03:33,560
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+57
+00:03:33,560 --> 00:03:36,120
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+58
+00:03:36,120 --> 00:03:39,020
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+59
+00:03:39,020 --> 00:03:39,900
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+60
+00:03:39,900 --> 00:03:40,020
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+61
+00:03:40,020 --> 00:03:42,200
+اتجارات اتجارات اتجارات اتجارات اتجارات اتجارات
+
+62
+00:03:42,200 --> 00:03:55,500
+اتجارات اتجارات اتجارات ات
+
+63
+00:03:55,570 --> 00:04:01,910
+هذا المجلد الاجتماعي هو أقل من المجلد الاجتماعي
+
+64
+00:04:01,910 --> 00:04:02,010
+الخاص
+
+65
+00:04:06,810 --> 00:04:10,710
+والاستخلاصات المناسبة للإستخلاص هنا عندما يكون شخص
+
+66
+00:04:10,710 --> 00:04:16,390
+موازن و يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل
+
+67
+00:04:16,390 --> 00:04:16,750
+يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل
+
+68
+00:04:16,750 --> 00:04:17,530
+يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل
+
+69
+00:04:17,530 --> 00:04:18,010
+يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل
+
+70
+00:04:18,010 --> 00:04:20,050
+يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل يصبح أفضل
+
+71
+00:04:20,050 --> 00:04:27,990
+يصبح أفضل يصبح أفضل يصبح
+
+72
+00:04:27,990 --> 00:04:30,170
+أفضل يصبح
+
+73
+00:04:35,790 --> 00:04:40,670
+عن المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+74
+00:04:40,670 --> 00:04:42,270
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+75
+00:04:42,270 --> 00:04:45,130
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+76
+00:04:45,130 --> 00:04:45,550
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+77
+00:04:45,550 --> 00:04:45,550
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+78
+00:04:45,550 --> 00:04:45,710
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+79
+00:04:45,710 --> 00:04:46,230
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+80
+00:04:46,230 --> 00:04:46,610
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+81
+00:04:46,610 --> 00:04:49,570
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+82
+00:04:49,570 --> 00:04:55,590
+المخلوقات الموجودة هنا، المخلوقات الموجودة هنا،
+
+83
+00:04:55,590 --> 00:05:00,490
+المخو تصنع عاملين عاملين عاملين عاملين عاملين
+
+84
+00:05:00,490 --> 00:05:01,790
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+85
+00:05:01,790 --> 00:05:02,430
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+86
+00:05:02,430 --> 00:05:05,210
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+87
+00:05:05,210 --> 00:05:05,630
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+88
+00:05:05,630 --> 00:05:07,670
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+89
+00:05:07,670 --> 00:05:10,390
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+90
+00:05:10,390 --> 00:05:14,610
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+91
+00:05:14,610 --> 00:05:26,470
+عامل
+
+92
+00:05:26,950 --> 00:05:35,570
+والسيجارات الكوانوترية دي واحد ودي اتس ودي اتس ودي
+
+93
+00:05:35,570 --> 00:05:37,450
+اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي
+
+94
+00:05:37,450 --> 00:05:40,610
+اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي
+
+95
+00:05:40,610 --> 00:05:40,870
+اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي
+
+96
+00:05:40,870 --> 00:05:40,870
+اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي
+
+97
+00:05:40,870 --> 00:05:41,310
+اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي
+
+98
+00:05:41,310 --> 00:05:48,370
+اتس ودي اتس ودي اتس ودي اتس ودي اتس ودي
+
+99
+00:05:48,370 --> 00:05:54,190
+اتس ودي اتس ودي ات
+
+100
+00:05:56,020 --> 00:05:59,040
+قطع الوصول للوصول للوصول للوصول للوصول للوصول
+
+101
+00:05:59,040 --> 00:06:01,520
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+102
+00:06:01,520 --> 00:06:03,960
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+103
+00:06:03,960 --> 00:06:04,640
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+104
+00:06:04,640 --> 00:06:07,160
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+105
+00:06:07,160 --> 00:06:10,240
+للوصول
+
+106
+00:06:10,240 --> 00:06:13,500
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+107
+00:06:13,500 --> 00:06:16,320
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+108
+00:06:16,320 --> 00:06:26,240
+للوصول للوصول للوصول للوصول للوصول للوصول للتعامل
+
+109
+00:06:26,240 --> 00:06:31,780
+مع الـ two supply curves and one demand تعامل
+
+110
+00:06:31,780 --> 00:06:39,160
+مع الـ two supply curves and one demand تعامل مع
+
+111
+00:06:39,160 --> 00:06:39,240
+الـ two supply curves and one demand تعامل مع الـ
+
+112
+00:06:39,240 --> 00:06:44,480
+two
+
+113
+00:06:44,480 --> 00:06:48,620
+supply curves and one demand تعامل مع الـ two
+
+114
+00:06:48,620 --> 00:06:53,300
+supply curves and one demand تعامل مع الـ two
+
+115
+00:06:53,300 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+116
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+117
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+118
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+119
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+120
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+121
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+122
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+123
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+124
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+125
+00:06:53,320 --> 00:06:53,320
+supply curves and one demand تعامل مع الـ two
+
+126
+00:06:53,320 --> 00:06:56,400
+supply curves and one demand تعامتعامل مع اتفاقات
+
+127
+00:06:56,400 --> 00:07:03,860
+اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق
+
+128
+00:07:03,860 --> 00:07:08,360
+اتفاق اتفاق
+
+129
+00:07:08,360 --> 00:07:10,140
+اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق
+
+130
+00:07:10,140 --> 00:07:12,740
+اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق
+
+131
+00:07:12,740 --> 00:07:12,780
+اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق
+
+132
+00:07:12,780 --> 00:07:14,640
+اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق اتفاق
+
+133
+00:07:14,640 --> 00:07:20,880
+اتف
+
+134
+00:07:21,250 --> 00:07:24,670
+وهنا مجموعة الاحتياطات الخاصة مجموعة الاحتياطات
+
+135
+00:07:24,670 --> 00:07:28,390
+الاجتماعية هي أكتر من مجموعة الاحتياطات الخاصة
+
+136
+00:07:28,390 --> 00:07:34,250
+وهذه المطاولة ستمثل
+
+137
+00:07:34,250 --> 00:07:38,850
+كلاهما مجموعة الاحتياطات الاجتماعية ومجموعة
+
+138
+00:07:38,850 --> 00:07:41,550
+الاحتياطات الخاصة مجموعة الاحتياطات الاجتماعية
+
+139
+00:07:41,550 --> 00:07:48,250
+ومجموعة الاحتياطات الخاصة لأن
+
+140
+00:07:48,250 --> 00:07:50,650
+المطاولة تمثل مجموعة الاحتياطات الخاصة
+
+141
+00:07:55,570 --> 00:08:01,250
+هذا المثال هنا المجال الخاص أو الواجهة هنا، المجال
+
+142
+00:08:01,250 --> 00:08:04,450
+الخاص الاجتماعي،
+
+143
+00:08:04,450 --> 00:08:09,250
+أسف، هنا المجال الخاص الاجتماعي،
+
+144
+00:08:09,250 --> 00:08:12,510
+المجال الخاص الاجتماعي هي أكتر من المجال الخاص
+
+145
+00:08:12,510 --> 00:08:17,070
+الاجتماعي، أكتر
+
+146
+00:08:17,070 --> 00:08:17,550
+من المجال الخاص الاجتماعي، أكتر من المجال الخاص
+
+147
+00:08:17,550 --> 00:08:17,550
+الاجتماعي، أكتر من المجال الخاص الاجتماعي، أكتر من
+
+148
+00:08:17,550 --> 00:08:17,650
+المجال الخاص الاجتماعي، أكتر من المجال الخاص
+
+149
+00:08:17,650 --> 00:08:17,650
+الاجتماعي، أكتر من المجال الخاص الاجتماعي، أكتر من
+
+150
+00:08:17,650 --> 00:08:17,650
+المجال الخاص الاجتماعي، أكتر من المجال الخاص
+
+151
+00:08:17,650 --> 00:08:22,460
+الاجتماعي، أكتر من المجال الخاص الفي هذه الحالة،
+
+152
+00:08:22,460 --> 00:08:26,660
+انا اشتغل هنا، فالفائعات الاجتماعية الاجتماعية
+
+153
+00:08:26,660 --> 00:08:27,680
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+154
+00:08:27,680 --> 00:08:31,380
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+155
+00:08:31,380 --> 00:08:38,560
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+156
+00:08:38,560 --> 00:08:41,180
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+157
+00:08:41,180 --> 00:08:41,620
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+158
+00:08:41,620 --> 00:08:41,660
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+159
+00:08:41,660 --> 00:08:41,840
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+160
+00:08:41,840 --> 00:08:47,160
+الاجتماعية الاجتماعية الاجتماعية الاجتماع
+
+161
+00:08:48,490 --> 00:08:51,870
+وهذا هو مراجعات السياسة المفيدة مقارنة مع مراجعة
+
+162
+00:08:51,870 --> 00:08:55,910
+السياسة الخاصة مقارنة مع مراجعة السياسة الخاصة
+
+163
+00:08:55,910 --> 00:08:56,170
+مقارنة مع مراجعة السياسة الخاصة مقارنة مع مراجعة
+
+164
+00:08:56,170 --> 00:08:56,630
+السياسة الخاصة مقارنة مع مراجعة السياسة الخاصة
+
+165
+00:09:08,480 --> 00:09:12,420
+الخطوط الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+166
+00:09:12,420 --> 00:09:16,140
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+167
+00:09:16,140 --> 00:09:17,520
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+168
+00:09:17,520 --> 00:09:18,060
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+169
+00:09:18,060 --> 00:09:18,520
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+170
+00:09:18,520 --> 00:09:21,640
+الاجتماعية
+
+171
+00:09:21,640 --> 00:09:25,780
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+172
+00:09:25,780 --> 00:09:29,220
+الاجتماعية
+
+173
+00:09:29,220 --> 00:09:30,360
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+174
+00:09:30,360 --> 00:09:30,360
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+175
+00:09:30,360 --> 00:09:32,500
+الاجتماعية الاجتماعية الاجت
+
+176
+00:09:35,270 --> 00:09:40,010
+ماذا عن حالته هنا؟ مجموعات المجارات السياسية تحت
+
+177
+00:09:40,010 --> 00:09:41,690
+مجموعات المجارات السياسية تحت مجموعات المجارات
+
+178
+00:09:41,690 --> 00:09:45,090
+السياسية تحت
+
+179
+00:09:45,090 --> 00:09:46,610
+مجموعات المجارات السياسية تحت مجموعات المجارات
+
+180
+00:09:46,610 --> 00:09:48,890
+السياسية تحت مجموعات المجارات السياسية تحت مجموعات
+
+181
+00:09:48,890 --> 00:09:49,170
+المجارات السياسية تحت مجموعات المجارات السياسية
+
+182
+00:09:49,170 --> 00:09:51,030
+تحت مجموعات المجارات السياسية تحت مجموعات المجارات
+
+183
+00:09:51,030 --> 00:09:52,130
+السياسية تحت مجموعات المجارات السياسية تحت مجموعات
+
+184
+00:09:52,130 --> 00:09:54,230
+المجارات السياسية تحت مجموعات المجارات السياسية
+
+185
+00:09:54,230 --> 00:10:00,490
+تحت مجموعات المجارات السياسية تحت مجموعات
+
+186
+00:10:02,370 --> 00:10:07,070
+كمان؟ طيب where is the private equilibrium in all
+
+187
+00:10:07,070 --> 00:10:11,650
+these cases؟ I'm not asking about the social
+
+188
+00:10:11,650 --> 00:10:16,250
+equilibrium, the social efficient point in these
+
+189
+00:10:16,250 --> 00:10:20,470
+four cases I'm asking about the private efficient
+
+190
+00:10:20,470 --> 00:10:25,930
+point the private efficient point occurs when the
+
+191
+00:10:25,930 --> 00:10:30,030
+marginal private benefits equals the marginal
+
+192
+00:10:30,030 --> 00:10:39,690
+private costهذا هو الـ E1 هنا للمجال
+
+193
+00:10:39,690 --> 00:10:45,370
+السليماني، المجال السليماني، نعم، المقاومة الأفضل
+
+194
+00:10:45,370 --> 00:10:51,990
+أو المقاومة الأفضل هي المقاومة E هنا، وعن قيمة P1
+
+195
+00:10:51,990 --> 00:10:53,690
+وQ1
+
+196
+00:10:56,640 --> 00:11:02,300
+وهو يعني أن الشركات ستحاول تحرير في هذا النقطة، في
+
+197
+00:11:02,300 --> 00:11:09,360
+الـ Secure، حسنًا؟ ما رأيك في هذا النقطة؟ لتحرير
+
+198
+00:11:09,360 --> 00:11:15,280
+قيمة الاختلاف الأساسي أو اهتمام الشباب الاجتماعي
+
+199
+00:11:15,280 --> 00:11:19,960
+أو اهتمام الشباب الاجتماعي الممكن، يجب أن نأخذ
+
+200
+00:11:19,960 --> 00:11:29,800
+فرصة عضوية من A1، دائما من A1من A1 إلى Marginal
+
+201
+00:11:29,800 --> 00:11:38,520
+Social من A1 إلى Marginal Social من A1 إلى
+
+202
+00:11:38,520 --> 00:11:44,740
+Marginal Social من A1 إلى Marginal Social من A1
+
+203
+00:11:44,740 --> 00:11:48,600
+إلى Marginal Social من A1 إلى Marginal Social من
+
+204
+00:11:48,600 --> 00:11:54,440
+A1 إلى Marginal Socialعن طريق A1 إلى مجلس
+
+205
+00:11:54,440 --> 00:12:03,100
+الاجتماعي والطريق المشروع هنا يعني ماذا؟loss or
+
+206
+00:12:03,100 --> 00:12:06,700
+gains؟ welfare loss or gains؟ it's loss here
+
+207
+00:12:06,700 --> 00:12:09,600
+because we are talking about negative
+
+208
+00:12:09,600 --> 00:12:13,800
+externalities of consumption so this shaded
+
+209
+00:12:13,800 --> 00:12:18,860
+triangle here is or represents the dead weight
+
+210
+00:12:18,860 --> 00:12:21,980
+loss or the social welfare loss
+
+211
+00:12:26,500 --> 00:12:31,220
+ماذا عن .. دعنا نذهب إلى الانتجارات الخارقة من
+
+212
+00:12:31,220 --> 00:12:35,440
+انتجارات الانتجارات في هذا المثال الواجهة الواجهة
+
+213
+00:12:35,440 --> 00:12:37,420
+الواجهة الواجهة الواجهة الواجهة الواجهة الواجهة
+
+214
+00:12:37,420 --> 00:12:37,440
+الواجهة الواجهة الواجهة الواجهة الواجهة الواجهة
+
+215
+00:12:37,440 --> 00:12:37,800
+الواجهة الواجهة الواجهة الواجهة الواجهة الواجهة
+
+216
+00:12:37,800 --> 00:12:38,340
+الواجهة الواجهة الواجهة الواجهة الواجهة الواجهة
+
+217
+00:12:38,340 --> 00:12:39,020
+الواجهة الواجهة الواجهة الواجهة الواجهة الواجهة
+
+218
+00:12:39,020 --> 00:12:39,880
+الواجهة الواجهة الواجهة الواجهة الواجهة ال
+
+219
+00:12:55,760 --> 00:13:00,120
+هذا هو النقطة الانقلابية السياسية أو النقطة
+
+220
+00:13:00,120 --> 00:13:03,460
+الانقلابية السياسية هذا هو النقطة الانقلابية
+
+221
+00:13:03,460 --> 00:13:08,860
+السياسية النقطة الانقلابية السياسية هنا في P*)
+
+222
+00:13:08,860 --> 00:13:19,620
+وQ*) يعني أن المجتمع يجب أن يشرب سيجارة في Q*)
+
+223
+00:13:19,620 --> 00:13:27,570
+وليس Q1 يعني أن هناك تشربةو المجتمع، فالنقطة
+
+224
+00:13:27,570 --> 00:13:32,410
+الاجتماعية الاجتماعية هي QSAR في النقطة التي تقل
+
+225
+00:13:32,410 --> 00:13:35,070
+مجموعة الاجتماعات الاجتماعية تقل مجموعة الاجتماعات
+
+226
+00:13:35,070 --> 00:13:35,810
+الاجتماعية تقل مجموعة الاجتماعات الاجتماعية تقل
+
+227
+00:13:35,810 --> 00:13:36,170
+مجموعة الاجتماعات الاجتماعية تقل مجموعة الاجتماعات
+
+228
+00:13:36,170 --> 00:13:37,470
+الاجتماعية تقل مجموعة الاجتماعات الاجتماعية تقل
+
+229
+00:13:37,470 --> 00:13:39,390
+مجموعة الاجتماعات الاجتماعية تقل مجموعة الاجتماعات
+
+230
+00:13:39,390 --> 00:13:43,970
+الاجتماعية تقل مجموعة الاجتماعات الاجتماعية تقل
+
+231
+00:13:43,970 --> 00:13:48,050
+مجموعة الاجتما
+
+232
+00:13:50,350 --> 00:13:53,290
+الـ private efficient point with marginal private
+
+233
+00:13:53,290 --> 00:14:00,210
+benefits equals the marginal private cost هنا أين
+
+234
+00:14:00,210 --> 00:14:07,010
+الـ marginal private equals private فهذا
+
+235
+00:14:07,010 --> 00:14:13,530
+هو A1 وهذا
+
+236
+00:14:13,530 --> 00:14:19,580
+هو P1 و Q1كيف نستطيع أن نتأكد إذا كان هناك خسارة
+
+237
+00:14:19,580 --> 00:14:23,580
+أساسية أو خسارة البيئة الاجتماعية أو إيجارات أو
+
+238
+00:14:23,580 --> 00:14:28,880
+إيجارات ممكنة؟ علينا أن نأخذ مقارنة من A1 إلى
+
+239
+00:14:28,880 --> 00:14:31,480
+مقارنة الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+240
+00:14:31,480 --> 00:14:35,300
+الاجتماعية
+
+241
+00:14:35,300 --> 00:14:39,520
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+242
+00:14:39,520 --> 00:14:40,100
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+243
+00:14:40,100 --> 00:14:43,220
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+244
+00:14:43,220 --> 00:14:43,360
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+245
+00:14:43,360 --> 00:14:43,500
+الاجتماعية الاجتماعية الاجتماعية الاجت
+
+246
+00:14:46,460 --> 00:14:55,500
+الصورة المصادرة هنا تمثل
+
+247
+00:14:55,500 --> 00:14:58,620
+ماذا؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل
+
+248
+00:14:58,620 --> 00:15:00,920
+ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل
+
+249
+00:15:00,920 --> 00:15:05,220
+ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل
+
+250
+00:15:05,220 --> 00:15:08,380
+ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل
+
+251
+00:15:08,380 --> 00:15:09,080
+ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل ايه؟ تمثل
+
+252
+00:15:09,080 --> 00:15:16,990
+ايه؟ تمثل ايههذا يعني أننا قادرين على زيادة
+
+253
+00:15:16,990 --> 00:15:25,030
+أفضلاتنا إذا تحركنا من هنا إلى هنا أو تزيد تكلفتنا
+
+254
+00:15:25,030 --> 00:15:30,430
+ماهو الوضع الواقعي الاجتماعي هنا هو الوضع
+
+255
+00:15:30,430 --> 00:15:37,050
+الاجتماعي الواقعي الاجتماعي الاجتماعي الاجتماعي
+
+256
+00:15:37,050 --> 00:15:40,070
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+257
+00:15:40,070 --> 00:15:47,570
+الاجتماعي الاجتماعيهذا هو قيمة قيمة قيمة قيمة قيمة
+
+258
+00:15:47,570 --> 00:15:51,450
+قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة
+
+259
+00:15:51,450 --> 00:15:56,170
+قيمة قيمة قيمة قيمة قيمة
+
+260
+00:15:56,170 --> 00:15:56,170
+قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة
+
+261
+00:15:56,170 --> 00:15:56,310
+قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة
+
+262
+00:15:56,310 --> 00:15:56,310
+قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة
+
+263
+00:15:56,310 --> 00:15:56,310
+قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة
+
+264
+00:15:56,310 --> 00:15:56,450
+قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة قيمة
+
+265
+00:15:56,450 --> 00:16:02,010
+قيمة قيمة قيمة قيمة قيمة
+
+266
+00:16:02,010 --> 00:16:10,890
+قيم
+
+267
+00:16:11,070 --> 00:16:16,330
+هنا لدينا خاطئة هنا هنا هنا هنا هنا هنا هنا هنا
+
+268
+00:16:16,330 --> 00:16:16,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+269
+00:16:16,330 --> 00:16:16,890
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+270
+00:16:16,890 --> 00:16:18,150
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+271
+00:16:18,150 --> 00:16:18,170
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+272
+00:16:18,170 --> 00:16:18,170
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+273
+00:16:18,170 --> 00:16:18,230
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+274
+00:16:18,230 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+275
+00:16:18,330 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+276
+00:16:18,330 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+277
+00:16:18,330 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+278
+00:16:18,330 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+279
+00:16:18,330 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+280
+00:16:18,330 --> 00:16:18,330
+هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا
+
+281
+00:16:18,330 --> 00:16:27,170
+هنا هنا هن هن هن هن
+
+282
+00:16:27,170 --> 00:16:30,410
+هن هن هن هن هن هن هن هن هن هن هن هن هن هن هن هن هن
+
+283
+00:16:30,410 --> 00:16:37,680
+هن هن هن هعلى المدارس المجانية الاجتماعية المجانية
+
+284
+00:16:37,680 --> 00:16:42,680
+المجانية المجانية المجانية المجانية المجانية
+
+285
+00:16:42,680 --> 00:16:43,680
+المجانية المجانية المجانية المجانية المجانية
+
+286
+00:16:43,680 --> 00:16:43,820
+المجانية المجانية المجانية المجانية المجانية
+
+287
+00:16:43,820 --> 00:16:44,340
+المجانية المجانية المجانية المجانية المجانية
+
+288
+00:16:44,340 --> 00:16:44,420
+المجانية المجانية المجانية المجانية المجانية
+
+289
+00:16:44,420 --> 00:16:44,440
+المجانية المجانية المجانية المجانية المجانية
+
+290
+00:16:44,440 --> 00:16:47,200
+المجانية المجانية المجانية المجانية المجانية
+
+291
+00:16:47,200 --> 00:16:47,620
+المجانية المجانية المجانية المجانية المجانية
+
+292
+00:16:47,620 --> 00:16:47,620
+المجانية المجانية المجانية المجانية المجانية
+
+293
+00:16:47,620 --> 00:16:51,020
+المجانية المجانية المجانية المجانية المجانية
+
+294
+00:16:51,020 --> 00:16:54,180
+المجانية
+
+295
+00:16:58,010 --> 00:17:00,570
+المجلد الاجتماعي هو أكتر من المجلد الاجتماعي
+
+296
+00:17:00,570 --> 00:17:02,590
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+297
+00:17:02,590 --> 00:17:04,970
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+298
+00:17:04,970 --> 00:17:08,550
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+299
+00:17:08,550 --> 00:17:09,150
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+300
+00:17:09,150 --> 00:17:12,790
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+301
+00:17:12,790 --> 00:17:13,770
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+302
+00:17:13,770 --> 00:17:15,550
+والمجلد الاجتماعي هو اكتر من المجلد الاجتماعي
+
+303
+00:17:15,550 --> 00:17:18,990
+والمجلد الاجتما
+
+304
+00:17:21,350 --> 00:17:26,630
+كيون هذا هو الوضع أفضل بالنسبة للعاملين وليس
+
+305
+00:17:26,630 --> 00:17:33,950
+للمجتمع وهو يعني أن المجتمع يصنع او أسف المجتمع
+
+306
+00:17:33,950 --> 00:17:43,030
+يصنع في كيون وهو يحفظ أرباحهم هذا الوضع يحفظ
+
+307
+00:17:43,030 --> 00:17:50,470
+الأرباح للمجتمع ليس للمجتمع حسنا؟
+
+308
+00:17:52,690 --> 00:17:58,070
+أين هو؟ كيف يمكننا أن نقرر إذا كان هناك خسارة أو
+
+309
+00:17:58,070 --> 00:18:01,730
+فوائد قادمة؟
+
+310
+00:18:01,730 --> 00:18:14,850
+من A1 إلى Social، لذلك هذا هو الخسارة أو الخسارة
+
+311
+00:18:14,850 --> 00:18:21,620
+الموتىالشيطان الوحيد هنا يمثل الاختلاف الوحيد
+
+312
+00:18:21,620 --> 00:18:29,880
+لأننا لدينا هنا تكوين مجموعة من الهواتف التي تجعل
+
+313
+00:18:29,880 --> 00:18:37,620
+المجتمع يتعامل مع مشكلتها في المجتمع، حتى لو كانت
+
+314
+00:18:37,620 --> 00:18:41,100
+المجتمع متعامل مع المجتمع متعامل مع المجتمع متعامل
+
+315
+00:18:41,100 --> 00:18:43,440
+مع المجتمع متعامل مع المجتمع متعامل مع المجتمع
+
+316
+00:18:43,440 --> 00:18:44,400
+متعامل مع المجتمع متعامل مع المجتمع متعامل مع
+
+317
+00:18:44,400 --> 00:18:44,860
+المجتمع متعامل مع المجتمع متعامل مع المجتمع متعامل
+
+318
+00:18:44,860 --> 00:18:45,080
+مع المجتمع متعامل مع المجتمع متعامل مع المجتمع
+
+319
+00:18:45,080 --> 00:18:47,020
+متعامل مع المجتمع متعامل مع المجتمع متعامل مع
+
+320
+00:18:47,020 --> 00:18:55,080
+المجتمع متعP-star وQ-star وهو يعني أن هناك تكوين
+
+321
+00:18:55,080 --> 00:18:59,720
+من هنا للملوك اللي يخلص من المجتمع من المجتمع من
+
+322
+00:18:59,720 --> 00:18:59,760
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+323
+00:18:59,760 --> 00:19:00,020
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+324
+00:19:00,020 --> 00:19:01,960
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+325
+00:19:01,960 --> 00:19:03,420
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+326
+00:19:03,420 --> 00:19:04,340
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+327
+00:19:04,340 --> 00:19:04,640
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+328
+00:19:04,640 --> 00:19:06,500
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+329
+00:19:06,500 --> 00:19:06,500
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+330
+00:19:06,500 --> 00:19:13,400
+المجتمع من المجتمع من المجتمع من المجتمع من
+
+331
+00:19:13,400 --> 00:19:18,220
+المجفالحكومة يجب أن تتعامل لإنقاذ الـ Quanta من
+
+332
+00:19:18,220 --> 00:19:21,960
+الـ Q1 إلى الـ Q★ هنا، فالحكومة يجب أن تتعامل
+
+333
+00:19:21,960 --> 00:19:26,420
+لإنقاذ الـ Quanta المتخزن من السيجارة من الـ Q1
+
+334
+00:19:26,420 --> 00:19:30,840
+إلى الـ Q★ هنا، فالحكومة يجب أن تتعامل لإنقاذ
+
+335
+00:19:30,840 --> 00:19:36,760
+المجتمع من الـ Q1 إلى الـ Q★ ما هو الحالة الأخيرة
+
+336
+00:19:36,760 --> 00:19:38,160
+هنا؟
+
+337
+00:19:40,200 --> 00:19:44,040
+أين الـ private equilibrium؟ الـ marginal private
+
+338
+00:19:44,040 --> 00:19:50,500
+يقوم بالـ private. هذا .. أسف، هنا الـ deadweight
+
+339
+00:19:50,500 --> 00:19:56,060
+loss. الشيطان الوضعي هو الـ deadweight loss. ماذا
+
+340
+00:19:56,060 --> 00:19:59,340
+عن الحالة الأخيرة؟ الـ private equilibrium يحدث
+
+341
+00:19:59,340 --> 00:20:03,380
+عندما الـ marginal social marginal private cost
+
+342
+00:20:03,380 --> 00:20:07,580
+يقوم بالـ marginal private benefits. لذلك، هنا E1
+
+343
+00:20:12,270 --> 00:20:20,010
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+344
+00:20:20,010 --> 00:20:21,790
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+345
+00:20:21,790 --> 00:20:22,530
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+346
+00:20:22,530 --> 00:20:23,590
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+347
+00:20:23,590 --> 00:20:23,590
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+348
+00:20:23,590 --> 00:20:25,750
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+349
+00:20:25,750 --> 00:20:30,790
+P1 P1 P1 P1 P1 P1 P1 P1 P1 P1
+
+350
+00:20:42,820 --> 00:20:44,320
+أو مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+351
+00:20:44,320 --> 00:20:45,340
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+352
+00:20:45,340 --> 00:20:46,640
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+353
+00:20:46,640 --> 00:20:47,580
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+354
+00:20:47,580 --> 00:20:48,360
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+355
+00:20:48,360 --> 00:20:58,600
+مجلد مجلد مجلد مجلد مجلد
+
+356
+00:20:58,600 --> 00:21:02,820
+مجلد مج
+
+357
+00:21:07,410 --> 00:21:16,250
+هذا يمثل اهتمام الوظيفة لأن هناك اهتمام لإزالة
+
+358
+00:21:16,250 --> 00:21:24,290
+اهتمامنا إذا أزالت مصالحنا من Q1 لQSAR اهتمام هنا
+
+359
+00:21:24,290 --> 00:21:32,650
+يحدث عندما يكون هناك اهتمام لإزالة اهتمامنا اهتمام
+
+360
+00:21:32,650 --> 00:21:35,250
+الوظيفة السياسية إذا أزالت مصالحنا
+
+361
+00:21:39,490 --> 00:21:45,330
+from Q1 to Q star and the optimal price should be
+
+362
+00:21:45,330 --> 00:21:53,350
+P star at least should be P star okay تمام؟
+
+363
+00:21:53,350 --> 00:21:59,410
+من أموره بدت عوم؟ و لا واضحة اللي هو؟ إعادة إعادة
+
+364
+00:21:59,410 --> 00:22:02,990
+طب بدنا نخش هال gate بس تثبيت لأنها بدنا نروح على
+
+365
+00:22:02,990 --> 00:22:05,530
+التحليل هال gate okay طيب
+
+366
+00:22:16,530 --> 00:22:23,630
+لنذهب هنا الى الـ private equilibrium أين الـ
+
+367
+00:22:23,630 --> 00:22:33,190
+private هنا؟ سنرى أيه أكبر من واحد؟ أيه؟ في أي
+
+368
+00:22:33,190 --> 00:22:40,910
+واحد من هنا؟ المفاتيح الخاصة المخصصة هي أكبر من
+
+369
+00:22:40,910 --> 00:22:43,510
+المفاتيح الاجتماعية المخصصة، صح؟
+
+370
+00:22:46,480 --> 00:22:51,320
+وهذا الوضع يمثل ماذا؟ مجموعات السياسة ومجموعات
+
+371
+00:22:51,320 --> 00:22:55,360
+الشخصية ومجموعات الشخصية ومجموعات الشخصية ومجموعات
+
+372
+00:22:55,360 --> 00:23:00,640
+الشخصية ومجموعات الشخصية ومجموعات
+
+373
+00:23:00,640 --> 00:23:05,040
+الشخصية ومجموعات الشخصية ومجموعات الشخصية ومجموعات
+
+374
+00:23:05,040 --> 00:23:05,320
+الشخصية ومجموعات الشخصية ومجموعات الشخصية ومجموعات
+
+375
+00:23:05,320 --> 00:23:05,540
+الشخصية ومجموعات الشخصية ومجموعات الشخصية ومجموعات
+
+376
+00:23:05,540 --> 00:23:05,560
+الشخصية ومجموعات الشخصية ومجموعات الشخصية ومجموعات
+
+377
+00:23:05,560 --> 00:23:05,860
+الشخصية ومجموعات الشخصية ومجموعات الشخصية
+
+378
+00:23:14,970 --> 00:23:20,970
+هي أكتر من ميزات الاجتماع الاجتماعي و ميزات
+
+379
+00:23:20,970 --> 00:23:24,910
+الاجتماع الاجتماعي هي أكتر من ميزات الاجتماع
+
+380
+00:23:24,910 --> 00:23:30,110
+الاجتماعي و ميزات الاجتماع الاجتماعي هي أكتر من
+
+381
+00:23:30,110 --> 00:23:31,270
+ميزات الاجتماع الاجتماعي و ميزات الاجتماع
+
+382
+00:23:31,270 --> 00:23:31,650
+الاجتماعي هي أكتر من ميزات الاجتماع الاجتماعي و
+
+383
+00:23:31,650 --> 00:23:35,550
+ميزات الاجتماع الاجتماعي هي أكتر من ميزات الاجتماع
+
+384
+00:23:35,550 --> 00:23:38,350
+الاجتماعي و ميزات الاجتماع الاجتماعي هي أكتر من
+
+385
+00:23:38,350 --> 00:23:41,890
+ميزات الاجتماع الاجتماعي و ميزات الاجتماع
+
+386
+00:23:41,890 --> 00:23:47,700
+الاجتماعي هيالفائعات أكتر من الفائعات الاجتماعية
+
+387
+00:23:47,700 --> 00:23:53,800
+الاجتماعية الاجتماعية
+
+388
+00:23:53,800 --> 00:23:57,600
+الاجتماعية
+
+389
+00:23:57,600 --> 00:23:58,700
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+390
+00:23:58,700 --> 00:24:01,900
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+391
+00:24:01,900 --> 00:24:04,840
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+392
+00:24:04,840 --> 00:24:09,580
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+393
+00:24:14,450 --> 00:24:25,570
+هي نقطتين مهمات هدول انا عارفهم احنا at private
+
+394
+00:24:25,570 --> 00:24:28,750
+equilibrium where is the private equilibrium here
+
+395
+00:24:28,750 --> 00:24:38,830
+E1 let's compare at E1 and this point at the
+
+396
+00:24:38,830 --> 00:24:46,570
+marginal social at E1 here atA1 و الـ Private
+
+397
+00:24:46,570 --> 00:24:53,030
+Equilibrium ماذا نرى؟ هذا الوضع يمثل ثلاثة أشياء
+
+398
+00:24:53,030 --> 00:24:57,730
+مجنون الـ social cost مجنون الـ private cost و
+
+399
+00:24:57,730 --> 00:25:03,730
+مجنون الـ private benefits صح؟ لذلك مجنون الـ
+
+400
+00:25:03,730 --> 00:25:09,050
+private benefits هنا هو
+
+401
+00:25:09,050 --> 00:25:14,130
+أقل من مجنون الـ social benefits صح؟
+
+402
+00:25:15,800 --> 00:25:18,980
+هي marginal private benefits is less than the
+
+403
+00:25:18,980 --> 00:25:22,220
+marginal social benefits and the marginal private
+
+404
+00:25:22,220 --> 00:25:28,540
+benefits is less than or smaller than the marginal
+
+405
+00:25:28,540 --> 00:25:34,460
+.. okay .. marginal social .. اه okay .. here the
+
+406
+00:25:34,460 --> 00:25:40,000
+marginal social cost .. احكي ده .. marginal social
+
+407
+00:25:40,000 --> 00:25:42,260
+cost at A1 here
+
+408
+00:25:45,480 --> 00:25:52,040
+marginal social cost is
+
+409
+00:25:52,040 --> 00:25:58,620
+less than the marginal social benefits صح؟
+
+410
+00:25:58,620 --> 00:26:07,380
+اثبوت؟ تبنيش الحق هيك؟ at E1، this represents
+
+411
+00:26:07,380 --> 00:26:10,660
+three things marginal private cost, marginal
+
+412
+00:26:10,660 --> 00:26:15,250
+social benefits, marginal private benefitsمارجنال
+
+413
+00:26:15,250 --> 00:26:20,130
+الاختصار الاجتماعي والاختصار الاجتماعي الاختصار
+
+414
+00:26:20,130 --> 00:26:23,330
+الاجتماعي الاختصار الاجتماعي الاختصار الاختصار
+
+415
+00:26:23,330 --> 00:26:25,630
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+416
+00:26:25,630 --> 00:26:27,630
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+417
+00:26:27,630 --> 00:26:35,710
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+418
+00:26:35,710 --> 00:26:38,390
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+419
+00:26:38,390 --> 00:26:42,590
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+420
+00:26:42,590 --> 00:26:42,590
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+421
+00:26:42,590 --> 00:26:45,180
+الاختصار الاختصار الاختصاربعمل ليه؟ ما بين الـ
+
+422
+00:26:45,180 --> 00:26:48,200
+Marginal Private Cost و Marginal Social Cost
+
+423
+00:26:48,200 --> 00:26:52,220
+Marginal Private Cost is less than Marginal Social
+
+424
+00:26:52,220 --> 00:26:56,120
+Cost Marginal
+
+425
+00:26:56,120 --> 00:27:02,080
+Social Benefits is less than Marginal Social Cost
+
+426
+00:27:02,080 --> 00:27:04,820
+خلّي ال comparison ع المارجينال سوشال كوست
+
+427
+00:27:04,820 --> 00:27:06,940
+Marginal Social Cost and Marginal Private Benefits
+
+428
+00:27:06,940 --> 00:27:10,400
+is
+
+429
+00:27:10,400 --> 00:27:12,940
+less than Marginal Social Cost
+
+430
+00:27:24,940 --> 00:27:30,480
+مع الـ Marginal
+
+431
+00:27:30,480 --> 00:27:34,980
+Private Benefits و Marginal Social Benefits
+
+432
+00:27:46,190 --> 00:27:55,630
+على هذا النقطة ات اي وان مجنون مجانون مجانون
+
+433
+00:27:55,630 --> 00:27:56,190
+مجانون مجانون مجانون مجانون مجانون مجانون مجانون
+
+434
+00:27:56,190 --> 00:27:56,830
+مجانون مجانون مجانون مجانون مجانون مجانون مجانون
+
+435
+00:27:56,830 --> 00:27:56,970
+مجانون مجانون مجانون مجانون مجانون مجانون مجانون
+
+436
+00:27:56,970 --> 00:27:57,090
+مجانون مجانون مجانون مجانون مجانون مجانون مجانون
+
+437
+00:27:57,090 --> 00:27:57,370
+مجانون مجانون مجانون مجانون
+
+438
+00:28:18,960 --> 00:28:26,700
+هو أكتر من مجموعة الاجتماعات الاجتماعية طبعا
+
+439
+00:28:26,700 --> 00:28:35,680
+كيف يمكن للحكومة أن تتعامل في أربع حالات لتحقيق حل
+
+440
+00:28:35,680 --> 00:28:46,300
+أو لتحرير حالة أو لتصل إلى نقطة أفضل للاجتماع؟ في
+
+441
+00:28:46,300 --> 00:28:52,220
+هذه الحالةأين هو الـ Social Optimism؟ في الـ Q1،
+
+442
+00:28:52,220 --> 00:28:56,260
+هنا، هذا هو الانتجار الخاص، كيف يمكن أن الحكومة
+
+443
+00:28:56,260 --> 00:29:05,380
+تتعامل لإدخال الموضوع أو لإنقاذ الـ Q*) من مقاطع
+
+444
+00:29:05,380 --> 00:29:09,860
+السيجارات من الـ Q1 إلى الـ Q*)؟ لديها اختيارين
+
+445
+00:29:09,860 --> 00:29:14,780
+مختلفة، تستطيع تحكم الـ Demand
+
+446
+00:29:17,510 --> 00:29:23,130
+محرك أو تغيير حركة التطبيق عن مستخدمات خاصة
+
+447
+00:29:23,130 --> 00:29:27,190
+لمستخدمات مجانية الاجتماعية لمستخدمات مجانية
+
+448
+00:29:27,190 --> 00:29:27,190
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+449
+00:29:27,190 --> 00:29:29,310
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+450
+00:29:29,310 --> 00:29:29,970
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+451
+00:29:29,970 --> 00:29:29,970
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+452
+00:29:29,970 --> 00:29:30,070
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+453
+00:29:30,070 --> 00:29:30,270
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+454
+00:29:30,270 --> 00:29:35,530
+الاجتماعية الاجتماعية الاجتماعية
+
+455
+00:29:35,530 --> 00:29:40,570
+الاجتماعية الاجتماعية
+
+456
+00:29:47,970 --> 00:29:52,450
+أعمل تاكسيس و سبرايهيشيفت موجودة، لذلك لدينا
+
+457
+00:29:52,450 --> 00:29:59,430
+اتفاقين او اتفاقين تقليل الميزانيات الحقيقية تقليل
+
+458
+00:29:59,430 --> 00:30:01,290
+الميزانيات الحقيقية تقليل الميزانيات الحقيقية
+
+459
+00:30:01,290 --> 00:30:07,390
+تقليل الميزانيات الحقيقية تقليل
+
+460
+00:30:07,390 --> 00:30:13,540
+الميزانيات الحقيقيةالفرصة الأولى وهذا يعتمد على
+
+461
+00:30:13,540 --> 00:30:19,740
+إفعالة الانترنت وإنها إفعالة أو ليست إفعالة هذا
+
+462
+00:30:19,740 --> 00:30:25,720
+يعتمد على السلسلة نفسها وكيفية إدعاء الشمالين
+
+463
+00:30:25,720 --> 00:30:33,420
+لإيقاف الشمالين لذلك يمكن الحكومة أن تنفذ إفعالة
+
+464
+00:30:33,420 --> 00:30:37,180
+السلسلة الخاصة إذا اقتنع أن الإفعالات ليست عالية
+
+465
+00:30:37,820 --> 00:30:42,680
+طبعا اذا سموكتك وانت راح ينزل من ال Q وانت وانت
+
+466
+00:30:42,680 --> 00:30:48,140
+تذهب الى Q Star او تقوم بتعريف التعريف وتعريف
+
+467
+00:30:48,140 --> 00:30:49,320
+التعريف تقوم بتعريف التعريف تقوم بتعريف التعريف
+
+468
+00:30:49,320 --> 00:30:50,180
+تقوم بتعريف التعريف تقوم بتعريف التعريف تقوم
+
+469
+00:30:50,180 --> 00:30:51,080
+بتعريف التعريف تقوم بتعريف التعريف تقوم بتعريف
+
+470
+00:30:51,080 --> 00:30:52,000
+التعريف تقوم بتعريف التعريف تقوم بتعريف التعريف
+
+471
+00:30:52,000 --> 00:30:52,840
+تقوم بتعريف التعريف تقوم بتعريف التعريف تقوم
+
+472
+00:30:52,840 --> 00:30:54,420
+بتعريف التعريف تقوم بتعريف التعريف تقوم بتعريف
+
+473
+00:30:54,420 --> 00:31:04,860
+التعريف تقوم بتعريف التعريف
+
+474
+00:31:04,860 --> 00:31:13,410
+تطبعا ال price will go up تمام؟
+
+475
+00:31:13,410 --> 00:31:20,990
+let's go here ال second case ال vaccination
+
+476
+00:31:23,960 --> 00:31:29,500
+الحكومة تشعر بأن الوزيارة جيدة للمجتمع و يصبح
+
+477
+00:31:29,500 --> 00:31:36,440
+عملية العمل أفضل و يكونوا أفضل من بعض و يكونوا
+
+478
+00:31:36,440 --> 00:31:38,200
+أفضل من بعض و يكونوا أفضل من بعض و يكونوا أفضل من
+
+479
+00:31:38,200 --> 00:31:38,440
+بعض و يكونوا أفضل من بعض و يكونوا أفضل من بعض و
+
+480
+00:31:38,440 --> 00:31:38,720
+يكونوا أفضل من بعض و يكونوا أفضل من بعض و يكونوا
+
+481
+00:31:38,720 --> 00:31:38,860
+أفضل من بعض و يكونوا أفضل من بعض و يكونوا أفضل من
+
+482
+00:31:38,860 --> 00:31:39,180
+بعض و يكونوا أفضل من بعض و يكونوا أفضل من بعض و
+
+483
+00:31:39,180 --> 00:31:47,880
+يكونوا أفضل من بعض و يكونوا أفضل من بعض و
+
+484
+00:31:47,880 --> 00:31:54,380
+يكونوا أفضل من بعض و يكونوا أفضل من بعفي الـ E1،
+
+485
+00:31:54,380 --> 00:32:02,040
+هذا هو الانتصار الخاص أو الانتصار الواضح للشخصين
+
+486
+00:32:02,040 --> 00:32:04,900
+الذين يتواجدوا الواجهة للواجهة للواجهة للواجهة
+
+487
+00:32:04,900 --> 00:32:08,200
+للواجهة للواجهة للواجهة للواجهة للواجهة للواجهة
+
+488
+00:32:08,200 --> 00:32:09,260
+للواجهة للواجهة للواجهة للواجهة للواجهة للواجهة
+
+489
+00:32:09,260 --> 00:32:13,540
+للواجهة للواجهة للواجهة للواجهة للواجهة للواجهة
+
+490
+00:32:13,540 --> 00:32:17,860
+للواجهة للواجهة للواجهة للواجهة
+
+491
+00:32:22,870 --> 00:32:28,350
+أو ان تزيد رقم الناس المقاومة من الـ Q1 إلى الـ Q
+
+492
+00:32:28,350 --> 00:32:36,270
+Star لديها اختصارين اختصار واحد لتحكم التطبيقات
+
+493
+00:32:36,270 --> 00:32:42,010
+تزيد التطبيقات للتطبيقات
+
+494
+00:32:42,010 --> 00:32:50,510
+في هذه الحالة يجب أن يكون الحكومةوهي تعمل إعلامات
+
+495
+00:32:50,510 --> 00:32:55,030
+لتشجيعهم للوصول للوصول للوصول للوصول للوصول للوصول
+
+496
+00:32:55,030 --> 00:33:04,790
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+497
+00:33:04,790 --> 00:33:07,590
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+498
+00:33:07,590 --> 00:33:08,410
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+499
+00:33:08,410 --> 00:33:09,790
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+500
+00:33:09,790 --> 00:33:11,130
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+501
+00:33:11,130 --> 00:33:11,130
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+502
+00:33:11,130 --> 00:33:16,870
+للوصول للوصول للوصول للوصول
+
+503
+00:33:19,310 --> 00:33:26,090
+either either by advertising or legislations حط
+
+504
+00:33:26,090 --> 00:33:29,350
+conditions على الناس ان خاص بدك تستفيد من ال
+
+505
+00:33:29,350 --> 00:33:36,750
+benefits من انها مثلا من ال social compensation
+
+506
+00:33:36,750 --> 00:33:39,670
+سبعة العاملين و ال retirement هذا بيقوله روح على
+
+507
+00:33:39,670 --> 00:33:44,830
+ال vaccination طعم هذا condition okay here how can
+
+508
+00:33:44,830 --> 00:33:45,430
+the government
+
+509
+00:33:48,940 --> 00:33:57,360
+لتحقيق المعيار المميز للمجتمع بإزالة المقاومة من
+
+510
+00:33:57,360 --> 00:34:02,940
+مقاومة واحدة إلى مقاومة أكتر أو كيف يمكن الحكومة
+
+511
+00:34:02,940 --> 00:34:07,840
+أن تدعم مجتمعها لتحقيق المعيار؟ هذا يمكن أن يدعم
+
+512
+00:34:07,840 --> 00:34:14,240
+المطالب أو المساعدة تدعم المطالب لتحقيق المعيار
+
+513
+00:34:15,930 --> 00:34:18,430
+يقوم بإضافة الاحتياطات الخاصة إلى الاحتياطات
+
+514
+00:34:18,430 --> 00:34:27,630
+الاجتماعية بمعلومات كما ذكرنا بمعالجات بمصطلحات
+
+515
+00:34:27,630 --> 00:34:32,270
+مختلفة لشركات أخرى لذلك الاحتياطات الخاصة المجانية
+
+516
+00:34:32,270 --> 00:34:35,970
+ستزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+517
+00:34:35,970 --> 00:34:37,050
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+518
+00:34:37,050 --> 00:34:39,330
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+519
+00:34:39,330 --> 00:34:42,890
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+520
+00:34:42,890 --> 00:34:47,060
+تزال تزال تزال تزال تزال تزال تزال تزال تزبإزالة
+
+521
+00:34:47,060 --> 00:34:50,960
+المصادر بمعالجة
+
+522
+00:34:50,960 --> 00:34:58,700
+المصادر للمصادر الذين يصنعوا المعالجة، فهذا يؤدي
+
+523
+00:34:58,700 --> 00:35:05,400
+إلى تغيير الطريقة الصحيحة للجزء الصحيح أو الجزء
+
+524
+00:35:05,400 --> 00:35:07,800
+الصحيح أو الجزء الصحيح أو الجزء الصحيح أو الجزء
+
+525
+00:35:07,800 --> 00:35:07,800
+الصحيح أو الجزء الصحيح أو الجزء الصحيح أو الجزء
+
+526
+00:35:07,800 --> 00:35:08,360
+الصحيح أو الجزء الصحيح أو الجزء الصحيح أو الجزء
+
+527
+00:35:08,360 --> 00:35:08,360
+الصحيح أو الجزء الصحيح أو الجزء الصحيح أو الجزء
+
+528
+00:35:08,360 --> 00:35:11,560
+الصحيح أو الجزء الصحيح أو الجزء الصحيح أو الجزء
+
+529
+00:35:11,560 --> 00:35:14,040
+الصحيح أو الجزء الصحيح أو الجزء الصحيح أو الجزء
+
+530
+00:35:14,040 --> 00:35:19,050
+الصحيح أو الجزء الصحأقل قيمة تزيد هذه هي قيمة
+
+531
+00:35:19,050 --> 00:35:23,350
+التجارب الاجتماعية باستخدام تجارب تجارب تجارب
+
+532
+00:35:23,350 --> 00:35:30,850
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+533
+00:35:30,850 --> 00:35:30,890
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+534
+00:35:30,890 --> 00:35:31,290
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+535
+00:35:31,290 --> 00:35:31,290
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+536
+00:35:31,290 --> 00:35:31,330
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+537
+00:35:31,330 --> 00:35:42,190
+تجارب تجارب تجارب تجارب تجارب تج
+
+538
+00:35:43,890 --> 00:35:48,010
+للقمع الهيالتكيرية من مشكلة الهيالتكير، ستتخلص
+
+539
+00:35:48,010 --> 00:35:56,270
+أسعار المساعدة وهنا هو السعر الجديد P2 ستتخلص
+
+540
+00:35:56,270 --> 00:36:01,750
+الأسعار من P2 إلى P2 وهذا هو الانقلاب الجديد
+
+541
+00:36:01,750 --> 00:36:07,330
+والقمع الهيالتكيري يصبح Q1
+
+542
+00:36:10,830 --> 00:36:18,290
+ولكن بشكل عام، إذا كان الحكومة ترغب في إجراء عملية
+
+543
+00:36:18,290 --> 00:36:19,710
+إجراء عملية إجراء عملية إجراء عملية إجراء عملية
+
+544
+00:36:19,710 --> 00:36:22,370
+إجراء عملية إجراء عملية إجراء عملية إجراء عملية
+
+545
+00:36:22,370 --> 00:36:24,770
+إجراء عملية إجراء عملية إجراء عملية إجراء عملية
+
+546
+00:36:24,770 --> 00:36:28,070
+إجراء عملية إجراء عملية إجراء عملية إجراء عملية
+
+547
+00:36:28,070 --> 00:36:28,070
+إجراء عملية إجراء عملية إجراء عملية إجراء عملية
+
+548
+00:36:28,070 --> 00:36:28,150
+إجراء عملية إجراء عملية إجراء عملية إجراء عملية
+
+549
+00:36:28,150 --> 00:36:32,850
+إجراء عملية إجراء عملية إجراء عملية إجراء
+
+550
+00:36:32,850 --> 00:36:39,350
+عملية
+
+551
+00:36:39,350 --> 00:36:43,480
+إالتنمية أو التحكم في المصادر التي تخلص منها
+
+552
+00:36:43,480 --> 00:36:43,980
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+553
+00:36:43,980 --> 00:36:45,920
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+554
+00:36:45,920 --> 00:36:47,100
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+555
+00:36:47,100 --> 00:36:47,560
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+556
+00:36:47,560 --> 00:36:47,980
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+557
+00:36:47,980 --> 00:36:50,160
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+558
+00:36:50,160 --> 00:36:51,320
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+559
+00:36:51,320 --> 00:36:52,780
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+560
+00:36:52,780 --> 00:36:58,840
+المصادر التي تخلص منها المصادر التي تخلص منها
+
+561
+00:36:58,840 --> 00:37:05,260
+المصادر التي
+
+562
+00:37:06,590 --> 00:37:15,610
+والتقنية الأفضل للإنتاج هنا هي QSAR كيف يمكننا أن
+
+563
+00:37:15,610 --> 00:37:23,630
+نتقل قيمة من Q1 إلى QSAR؟ هذا يمكن أن يتم إيقافه
+
+564
+00:37:23,630 --> 00:37:31,750
+بإزالة قيمة الـ private cost كيف نجعل مصنع تكلفة
+
+565
+00:37:31,750 --> 00:37:33,450
+إنتاجه تبعته عالية؟
+
+566
+00:37:41,440 --> 00:37:44,960
+بالتالي، تأخذ المجالات المجانية المجانية المجانية
+
+567
+00:37:44,960 --> 00:37:45,340
+المجانية المجانية المجانية المجانية المجانية
+
+568
+00:37:45,340 --> 00:37:45,880
+المجانية المجانية المجانية المجانية المجانية
+
+569
+00:37:45,880 --> 00:37:46,680
+المجانية المجانية المجانية المجانية المجانية
+
+570
+00:37:46,680 --> 00:37:51,760
+المجانية المجانية
+
+571
+00:37:51,760 --> 00:37:57,880
+المجانية المجانية المجانية المجانية المجانية
+
+572
+00:37:57,880 --> 00:38:02,440
+المجانية المجانية المجانية المجانية المجانية
+
+573
+00:38:02,440 --> 00:38:04,080
+المجانية المجانية المجانية المجانية المجانية
+
+574
+00:38:04,080 --> 00:38:04,080
+المجانية المجانية المجانية المجانية المجانية
+
+575
+00:38:04,080 --> 00:38:04,080
+المجانية المجانية المجانية المجانية المجانية
+
+576
+00:38:04,080 --> 00:38:04,080
+المجانية المجانية المجانية المجانية المجانية
+
+577
+00:38:04,080 --> 00:38:07,810
+المجانية المجانية المجإذا كانت المالية تقلل
+
+578
+00:38:07,810 --> 00:38:13,270
+الإجتماع المفقود هنا في هذه الحالة، فسيتم إيقاف
+
+579
+00:38:13,270 --> 00:38:19,750
+المشكلة أو تصبحها أزرع اي
+
+580
+00:38:19,750 --> 00:38:25,450
+انقل هكذا
+
+581
+00:38:25,450 --> 00:38:33,290
+ماذا بيحصل؟ مفقودة هكذا و أخيرًا تقلل 0 بسبب المال
+
+582
+00:38:33,290 --> 00:38:42,170
+هناماذا عن الحلقه الأخيرة؟ البرنامج الموجودة هنا
+
+583
+00:38:42,170 --> 00:38:50,190
+تصنع مطالبات عامة للمجتمع هذا هو الانتجار الأساسي
+
+584
+00:38:50,190 --> 00:38:55,750
+للجزء السليماني E1
+
+585
+00:39:01,220 --> 00:39:07,380
+الذين يرغبون في إزالة عدد العاملين الذين يتعاملون
+
+586
+00:39:07,380 --> 00:39:15,200
+مع بعضهم البعض للعمل في المجتمع بإنشاء عاملين
+
+587
+00:39:15,200 --> 00:39:17,600
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+588
+00:39:17,600 --> 00:39:18,520
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+589
+00:39:18,520 --> 00:39:20,040
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+590
+00:39:20,040 --> 00:39:21,300
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+591
+00:39:21,300 --> 00:39:21,300
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+592
+00:39:21,300 --> 00:39:21,300
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+593
+00:39:21,300 --> 00:39:28,060
+عاملين
+
+594
+00:39:29,820 --> 00:39:34,440
+or to train more workers for the community so it
+
+595
+00:39:34,440 --> 00:39:39,760
+should decrease private cost يعني العام اللي
+
+596
+00:39:39,760 --> 00:39:43,940
+بنجيبه و ندربه في المقبعة الكبيرة هذا تمام بدل ما
+
+597
+00:39:43,940 --> 00:39:47,740
+يكلفني ألف دولار خليه يكلف متين كي بده يخليه هيك
+
+598
+00:39:47,740 --> 00:39:51,880
+اعمل subsidies مافيش
+
+599
+00:39:51,880 --> 00:39:57,370
+تانسة يعني انت هيك بدك تعمله subsidizingصح قبل
+
+600
+00:39:57,370 --> 00:40:02,850
+subsidies شو بيصير؟ private cost عليه بتقل فبيصير
+
+601
+00:40:02,850 --> 00:40:07,470
+يفرخ أكتر، ينتج أكتر skilled workers، so here the
+
+602
+00:40:07,470 --> 00:40:12,010
+new equilibrium or the number of skilled workers
+
+603
+00:40:12,010 --> 00:40:18,890
+will increase and this is the new equilibrium so
+
+604
+00:40:18,890 --> 00:40:23,350
+the cost here the marginal social cost equals the
+
+605
+00:40:23,350 --> 00:40:31,740
+marginal private costplus subsidies كوانتي
+
+606
+00:40:31,740 --> 00:40:36,020
+ون increase تمام؟
+
+607
+00:40:36,020 --> 00:40:40,180
+let's go home يطلق الألف
+
diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/AtVPLyho-zo.srt b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/AtVPLyho-zo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d7e183757bdbac8f150a1d1a949bb83620ce4524
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/AtVPLyho-zo.srt
@@ -0,0 +1,1030 @@
+1
+00:00:20,700 --> 00:00:24,600
+Okay, بسم الله الرحمن الرحيم اليوم إن شاء الله سوف
+
+2
+00:00:24,600 --> 00:00:30,540
+نكمل حديثنا عن مقاومة الميزانيات وعلاقاتها مع
+
+3
+00:00:30,540 --> 00:00:35,300
+الميزانيات، الميزانية مثل الاستثمارات والميزانيات 
+
+4
+00:00:35,300 --> 00:00:39,560
+المالية والاستثمارات
+
+5
+00:00:39,560 --> 00:00:42,420
+والميزانيات، الميزانية والميزانيات، الميزانية 
+
+6
+00:00:42,420 --> 00:00:42,780
+والميزانيات، الميزانية والميزانيات، الميزانية
+
+7
+00:00:42,780 --> 00:00:46,020
+والميزانيات
+
+8
+00:00:46,020 --> 00:00:47,540
+الميزانية والميزانيات، الميزانية والميزانيات
+
+9
+00:00:47,540 --> 00:00:48,540
+الميزانية والميزانيات، الميزانية والميزانيات
+
+10
+00:00:48,540 --> 00:00:49,840
+الميزانية والميزانيات، الميزانية والميزانيات
+
+11
+00:00:49,840 --> 00:00:52,380
+الميزانية والميزانيات، الميزانية، الحفاظ الوطنية
+
+12
+00:00:52,380 --> 00:01:00,020
+مختلطة
+
+13
+00:01:00,020 --> 00:01:11,180
+إلى اتنين أماكن، حفاظ خاص وحفاظ
+
+14
+00:01:11,180 --> 00:01:13,300
+مجتمعي أو حفاظ مجتمعي
+
+15
+00:01:19,870 --> 00:01:25,050
+الخاصية السعيدة هي الخصوصية للعائلات والمؤسسات
+
+16
+00:01:25,050 --> 00:01:28,950
+والخاصية السعيدة هي الخصوصية الحكومية والخصوصية
+
+17
+00:01:28,950 --> 00:01:34,070
+الحكومية هي الفرق بين المجالات والخصوصية الحكومية
+
+18
+00:01:34,070 --> 00:01:44,250
+والخصوصية الحكومية، خصوصية الحكومية هي المجالات
+
+19
+00:01:44,250 --> 00:01:51,470
+مع الخصوصية الحكومية إذا كانت المجالات أو أكثر من 
+
+20
+00:01:51,470 --> 00:01:53,550
+المستخدم اللي يستخدمه، السيارة هنا لدينا مقاومة
+
+21
+00:01:53,550 --> 00:02:02,430
+أفضل، هنا لدينا مقاومة أفضل، مقاومة أفضل، مقاومة عامة
+
+22
+00:02:02,430 --> 00:02:04,430
+عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة
+
+23
+00:02:04,430 --> 00:02:04,690
+عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة
+
+24
+00:02:04,690 --> 00:02:06,290
+عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة
+
+25
+00:02:06,290 --> 00:02:07,090
+عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة، عامة
+
+26
+00:02:07,090 --> 00:02:07,550
+عامة، عامة، عامة
+
+27
+00:02:19,960 --> 00:02:28,420
+والاستخدام الوطني يزداد، تمام؟ حسناً، دعنا نذهب إلى
+
+28
+00:02:28,420 --> 00:02:35,760
+شيء آخر هنا،
+
+29
+00:02:35,760 --> 00:02:44,260
+شيء آخر يتم إزالته هو أن الاستخدام الوطني يمثل
+
+30
+00:02:44,260 --> 00:02:49,850
+إعطاء مصنع، مصنع، مصنع، مصنع، مصنع، مصنع، الحماية الوطنية
+
+31
+00:02:49,850 --> 00:02:59,250
+موظفة
+
+32
+00:02:59,250 --> 00:03:08,950
+مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر
+
+33
+00:03:17,840 --> 00:03:23,020
+هو الانفصارات الحيوانية أو الانفصارات الحيوانية
+
+34
+00:03:23,020 --> 00:03:28,800
+الانفصارات
+
+35
+00:03:28,800 --> 00:03:33,480
+الانفصارات، الانفصارات، الانفصارات، الانفصارات
+
+36
+00:03:33,480 --> 00:03:44,080
+الانفصارات، الانفصارات، الانفصارات، الانفصارات
+
+37
+00:03:48,350 --> 00:03:54,350
+عندما يكون هناك نقل مجلس أو مجلس
+
+38
+00:03:54,350 --> 00:04:00,750
+نقل مجلس
+
+39
+00:04:00,750 --> 00:04:05,170
+يعني أن قيمة المال عالية
+
+40
+00:04:14,630 --> 00:04:17,270
+هو أكثر من المجالات المجاورة للمجالات المجاورة
+
+41
+00:04:17,270 --> 00:04:23,190
+للمجالات المجاورة، للمجالات المجاورة، للمجالات
+
+42
+00:04:23,190 --> 00:04:28,070
+المجاورة، للمجالات المجاورة، للمجالات المجاورة
+
+43
+00:04:28,070 --> 00:04:32,150
+للمجالات
+
+44
+00:04:32,150 --> 00:04:32,230
+المجاورة، للمجالات المجاورة، للمجالات المجاورة
+
+45
+00:04:32,230 --> 00:04:37,730
+للمجالات المجاورة، للمجالات
+
+46
+00:04:39,720 --> 00:04:44,540
+بيعملوا issuing لمن؟ لـ bonds أو بيرفع ال interest
+
+47
+00:04:44,540 --> 00:04:49,140
+rate عشان بدهم بيعملوا issuing لمن؟ لـ bonds أو
+
+48
+00:04:49,140 --> 00:04:52,720
+لمن؟ لـ bonds with
+
+49
+00:04:52,720 --> 00:04:56,540
+higher interest
+
+50
+00:04:56,540 --> 00:04:57,360
+rate عشان بدهم بيعملوا issuing لمن؟ لـ bonds with
+
+51
+00:04:57,360 --> 00:04:59,260
+higher interest rate عشان بدهم بيعملوا issuing
+
+52
+00:04:59,260 --> 00:05:01,540
+لمن؟ لـ bonds with higher interest rate عشان بدهم
+
+53
+00:05:01,540 --> 00:05:01,660
+rate عشان بدهم بيعملوا issuing لمن؟ لـ bonds with
+
+54
+00:05:01,660 --> 00:05:03,300
+rate عشان بدهم بيعملوا issuing لمن؟ لـ bonds with
+
+55
+00:05:03,300 --> 00:05:09,540
+higher interest rate عشان بدهم بيعملوا
+
+56
+00:05:14,050 --> 00:05:17,010
+الحيوانات، طبعاً هذا بيضغط على ال interest rate
+
+57
+00:05:17,010 --> 00:05:20,150
+interest rate لأنه هذا بيعمل borrowing  ال
+
+58
+00:05:20,150 --> 00:05:25,510
+government بدها تعمل increasing لل borrowing بدها
+
+59
+00:05:25,510 --> 00:05:28,710
+يغطي مين؟ ال budget deficit عشان يغطي ال borrowing
+
+60
+00:05:28,710 --> 00:05:32,810
+عشان يغطي ال budget deficit بيعمل increasing لل
+
+61
+00:05:32,810 --> 00:05:37,010
+borrowing بيعمل increasing لل interest rate هذا ال
+
+62
+00:05:37,010 --> 00:05:43,970
+saving shifts left interest rate goes up، شو يعمل في
+
+63
+00:05:43,970 --> 00:05:48,770
+ال investment؟ goes down، حد اللي قولنا عنه
+
+64
+00:05:48,770 --> 00:05:52,350
+crowding out المرة اللي فاتت، ان اذا حدا كان موجود
+
+65
+00:05:52,350 --> 00:05:56,530
+انه ال increasing في ال borrowing بيعمل increasing
+
+66
+00:05:56,530 --> 00:06:03,570
+في ال interest rate تمام؟ وبيعمل crowding out ال
+
+67
+00:06:03,570 --> 00:06:03,990
+borrowing
+
+68
+00:06:14,440 --> 00:06:18,100
+بتزايد الـ Budget Deficit بتزايد الـ Borrowing و
+
+69
+00:06:18,100 --> 00:06:22,700
+بتزايد الـ Interest Rate بتزايد أو تقلل
+
+70
+00:06:22,700 --> 00:06:33,860
+الinvestment هذا يعني أننا لدينا مجموعة خارقة لأن
+
+71
+00:06:33,860 --> 00:06:39,940
+انتقال ال Interest Rate بتزايد الinvestment
+
+72
+00:06:39,940 --> 00:06:46,000
+الاجتماعي أو الinvestment المخطط، هذا يعني أنه يتقل
+
+73
+00:06:46,000 --> 00:06:50,740
+الأسعار المجاورة أو الأسعار المجاورة أو الأسعار
+
+74
+00:06:50,740 --> 00:06:52,980
+المجاورة أو الأسعار المجاورة أو الأسعار المجاورة
+
+75
+00:06:52,980 --> 00:06:53,400
+أو الأسعار المجاورة أو الأسعار المجاورة أو الأسعار
+
+76
+00:06:53,400 --> 00:06:53,740
+المجاورة أو الأسعار المجاورة أو الأسعار المجاورة
+
+77
+00:06:53,740 --> 00:06:54,100
+المجاورة أو الأسعار المجاورة أو الأسعار المجاورة
+
+78
+00:06:54,100 --> 00:06:55,360
+أو الأسعار المجاورة أو الأسعار المجاورة أو الأسعار
+
+79
+00:06:55,360 --> 00:06:56,880
+المجاورة أو الأسعار المجاورة أو الأسعار المجاورة
+
+80
+00:06:56,880 --> 00:07:03,200
+أو الأسعار المجاورة أو الأسعار
+
+81
+00:07:17,900 --> 00:07:20,920
+something related to the economic growth, saving
+
+82
+00:07:20,920 --> 00:07:35,000
+and interest rates, International
+
+83
+00:07:35,000 --> 00:07:40,240
+Capital Markets، وإن إشي ثاني اسمه Recurrent
+
+84
+00:07:40,240 --> 00:07:45,360
+Equivalence وExpectations about the future
+
+85
+00:07:45,360 --> 00:07:49,100
+interest rates، الـ three points من النقشة and its
+
+86
+00:07:49,100 --> 00:07:53,100
+relationship with the crowding out with the
+
+87
+00:07:53,100 --> 00:07:56,860
+economic growth مع ال public finance و ال budget
+
+88
+00:07:56,860 --> 00:08:04,840
+deficit، طبعاً
+
+89
+00:08:04,840 --> 00:08:10,120
+بالالـ American references بيعطيك عقول هيك بدون
+
+90
+00:08:10,120 --> 00:08:12,640
+يعني بدون analysis بيقولك إن ال international
+
+91
+00:08:12,640 --> 00:08:15,740
+capital markets make supply curve more elastic
+
+92
+00:08:15,740 --> 00:08:18,500
+thus lowering the ethics of the U.S. government
+
+93
+00:08:18,500 --> 00:08:21,320
+borrowing on the interest rate، أنا متأكد، ما عليش
+
+94
+00:08:21,320 --> 00:08:27,060
+فاهم شي، مش فاهمين
+
+95
+00:08:27,060 --> 00:08:31,280
+بدأ أشرح طبعاً
+
+96
+00:08:31,280 --> 00:08:34,620
+this leads to less crowding out of private capital
+
+97
+00:08:36,640 --> 00:08:45,200
+شوف، in general زمان، اسمته في ايش اسمه؟
+
+98
+00:08:45,200 --> 00:08:52,960
+Bretton Woods، Bretton Woods حد صار تفقيه بالعالم
+
+99
+00:08:52,960 --> 00:08:58,120
+كانوا زمان باعتمدوا على الدهب، البلد اللي معها دهب
+
+100
+00:08:58,120 --> 00:09:03,660
+أكثر، تمام، ال gold كما هو بس يهو كان عملتها
+
+101
+00:09:03,660 --> 00:09:09,780
+عملتها في الـ .. في الـ .. ال link صار مع مين بالـ ..
+
+102
+00:09:09,780 --> 00:09:14,200
+أعتقد بالستراتة أو قبل .. قبل اللي هي الربط صار مع
+
+103
+00:09:14,200 --> 00:09:17,940
+الـ U.S. dollar يعني الـ .. الـ .. ال local currencies
+
+104
+00:09:17,940 --> 00:09:23,120
+في كل العالم، كل بلد تقيم الـ .. ال values تبع الـ ..
+
+105
+00:09:23,120 --> 00:09:26,480
+ال local currency تبعها بالـ U.S. dollar وهذا فرض
+
+106
+00:09:26,480 --> 00:09:32,900
+أعطى يعني سلطة للـ U.S. انه يتحكم في أمور كثيرة، تمام؟
+
+107
+00:09:32,900 --> 00:09:46,010
+طيب الـ U.S. Government عنده
+
+108
+00:09:46,010 --> 00:09:51,950
+Budget دا، فسأك شو بيعمل؟ في الـ Open Market
+
+109
+00:09:51,950 --> 00:09:58,010
+Operations بيروح بيعمل Selling of Bonds، بدا أفترض
+
+110
+00:09:58,010 --> 00:10:02,830
+هيك، لأن واحد من ال tools to solve the budget
+
+111
+00:10:02,830 --> 00:10:07,670
+deficit، يا بيعمل increasing ال money supply تمام؟
+
+112
+00:10:07,670 --> 00:10:15,390
+يا بيعمل .. بيعمل selling لل bonds تمام؟ يا بيرفع
+
+113
+00:10:15,390 --> 00:10:24,210
+interest rate تمام؟ طيب هلأ بالـ U.S. أسهل حاجة يروح
+
+114
+00:10:24,210 --> 00:10:26,750
+يعمل open market operations بيعمل selling of bonds
+
+115
+00:10:26,750 --> 00:10:30,810
+وهي يعني على السريع هذا بيعمل شو معاه؟ liquidity
+
+116
+00:10:30,810 --> 00:10:35,450
+اللي، let us assume that the government or the U.S.
+
+117
+00:10:35,450 --> 00:10:40,110
+government faces a budget deficit، بيعمل selling of
+
+118
+00:10:40,110 --> 00:10:47,850
+bonds في
+
+119
+00:10:47,850 --> 00:10:53,570
+ميزة في الـ U.S. مش موجودة عند أي بلد ثانية، انه الـ ..
+
+120
+00:10:53,570 --> 00:10:57,090
+ال foreign governments و ال private sector من برا
+
+121
+00:10:57,090 --> 00:11:03,270
+rest of the world بيقدر يشتري يتداول في الـ U.S. هذا
+
+122
+00:11:03,270 --> 00:11:13,130
+بيعمل طبعاً with higher interest rates عنده
+
+123
+00:11:13,130 --> 00:11:14,750
+ميزة هو انه
+
+124
+00:11:16,890 --> 00:11:20,470
+انت بايع ال bonds طبعاً، بفترض ان الـ U.S. dollar أكثر
+
+125
+00:11:20,470 --> 00:11:25,710
+استقراراً، ان هو ده اللي ماسك العالم كله طبعاً، تروح 
+
+126
+00:11:25,710 --> 00:11:29,770
+تشتري عملة الصومالية مالك فيها بصبط هذا تشتري
+
+127
+00:11:29,770 --> 00:11:33,870
+تداول على ال US dollar كمان حتى ال values وكأنه 
+
+128
+00:11:33,870 --> 00:11:37,430
+فيه prosperity فيه stability في ال US dollar في
+
+129
+00:11:37,430 --> 00:11:40,310
+الاستقرار في ال high يعني أي تحريك في ال interest
+
+130
+00:11:40,310 --> 00:11:43,590
+rates كمان بيبقى لها تأثيراتها على موضوعات ال
+
+131
+00:11:43,590 --> 00:11:44,850
+international investment
+
+132
+00:11:47,740 --> 00:11:52,280
+الآن بين selling ال bonds with higher interest
+
+133
+00:11:52,280 --> 00:11:58,520
+rates ال foreign governments بيقدر
+
+134
+00:11:58,520 --> 00:12:02,800
+يشتري private .. international private sectors من 
+
+135
+00:12:02,800 --> 00:12:05,840
+فره from the rest of the world private sector
+
+136
+00:12:05,840 --> 00:12:15,760
+بيشتري شو بيصير في ال liquidity في داخل ال US؟ بسيط
+
+137
+00:12:15,760 --> 00:12:22,080
+طبعا لأن أنت جايب فلوس من برا ودخلت جوا هذا بيعمل
+
+138
+00:12:22,080 --> 00:12:27,980
+increasing ال liquidity inside
+
+139
+00:12:27,980 --> 00:12:33,080
+the US طبعا
+
+140
+00:12:33,080 --> 00:12:41,640
+هو مقطع interest rate عالي عالمين ال bonds ال
+
+141
+00:12:41,640 --> 00:12:44,740
+liquidity اللي اجى هنا ودخل ال US 
+
+142
+00:12:49,330 --> 00:12:57,350
+فعلياً Saving، فعلياً Investment صح؟ حد بيعمل شو؟
+
+143
+00:12:57,350 --> 00:13:05,130
+بيعمل lowering لـ crowding out lowering
+
+144
+00:13:05,130 --> 00:13:08,490
+لميه؟ لـ crowding out، لأن هو أصلاً crowding out
+
+145
+00:13:08,490 --> 00:13:13,970
+شدر عن شو؟ Interest rate طلع، Investment نزل بال U
+
+146
+00:13:13,970 --> 00:13:19,270
+.S. interest rate and interest paying bonds تلقى
+
+147
+00:13:19,270 --> 00:13:25,670
+صح الناس اشترت من برا و من جوا liquidity زاد عندهم
+
+148
+00:13:25,670 --> 00:13:32,610
+تمام شو عمل investment زاد هذا بيعمل keeping على 
+
+149
+00:13:32,610 --> 00:13:35,810
+أنه long line and crowding out
+
+150
+00:13:38,520 --> 00:13:41,960
+إذا نهانا هيك ال international capital markets
+
+151
+00:13:41,960 --> 00:13:47,000
+فلنجيلوها ال gate this
+
+152
+00:13:47,000 --> 00:13:50,120
+leads to لسه crowding out of private capital هذا
+
+153
+00:13:50,120 --> 00:13:56,000
+واضح يمكن جثية أنه لسه crowding out liquidity
+
+154
+00:13:56,000 --> 00:14:03,960
+increased طبعا
+
+155
+00:14:03,960 --> 00:14:10,650
+يعني بدي تفهموا هذا الجزء تمام ما بدي أدخل في موضوع
+
+156
+00:14:10,650 --> 00:14:14,250
+ال aggregate supply أنه should be more elastic
+
+157
+00:14:14,250 --> 00:14:17,310
+less elastic بدي تفهم هذا الجزء just في الموضوع
+
+158
+00:14:17,310 --> 00:14:28,370
+الجسم تمام طيب واضح خلاص هذا البدأ تمام طيب
+
+159
+00:14:28,370 --> 00:14:34,690
+let's go to some or another point or term which is
+
+160
+00:14:35,910 --> 00:14:39,190
+Ricardian equivalence تشوف you are the consumers
+
+161
+00:14:39,190 --> 00:14:44,270
+you are the households and let us assume that the
+
+162
+00:14:44,270 --> 00:14:50,490
+government even the private sector the government
+
+163
+00:14:50,490 --> 00:14:56,370
+decided to decrease or reduce taxes or income
+
+164
+00:14:56,370 --> 00:15:01,130
+taxes وانت
+
+165
+00:15:01,130 --> 00:15:06,860
+ال income تبعك equals one thousand dollar هذا ال
+
+166
+00:15:06,860 --> 00:15:13,060
+income بتاخد one thousand dollar هذا monthly
+
+167
+00:15:13,060 --> 00:15:18,920
+income monthly salary تمام بتقيمه أنت يعني three
+
+168
+00:15:18,920 --> 00:15:22,100
+divided into three parts دعنا نقول consumption
+
+169
+00:15:22,100 --> 00:15:32,070
+seven hundred بتقيمه saving خلّيني أعمل نقول tax
+
+170
+00:15:32,070 --> 00:15:40,510
+rate 10% بيسبب تفعيل ال taxes 100 بيبقى
+
+171
+00:15:40,510 --> 00:15:48,090
+لإنك سايفنجر 200 صح؟
+
+172
+00:15:48,090 --> 00:15:52,150
+هاي ال 1000 دره هذا
+
+173
+00:15:52,150 --> 00:15:54,050
+ال margin of profit بتconsume كدهش عنده في
+
+174
+00:15:54,050 --> 00:16:02,540
+الاقتناء 70% بفترض أنه أي علاوة بتيجي بيعمل عليها
+
+175
+00:16:02,540 --> 00:16:10,240
+spending أو consumption يعني 70% السؤال لو ال
+
+176
+00:16:10,240 --> 00:16:16,220
+government أنا بافترض انه tax rate 10
+
+177
+00:16:16,220 --> 00:16:21,440
+% سؤال لو ال government
+
+178
+00:16:25,730 --> 00:16:33,830
+عملت decreasing بال tax rate to
+
+179
+00:16:33,830 --> 00:16:43,570
+5% كل
+
+180
+00:16:43,570 --> 00:16:47,710
+حاجة فيها ال logic يعني في منطق أن أنت هاي اللي
+
+181
+00:16:47,710 --> 00:16:55,500
+هيصير يعني هاي ال tax, taxes هيصير fifty صح؟ مصبوط؟
+
+182
+00:16:55,500 --> 00:17:03,680
+ضال عندنا كده؟ eight hundred fifty شو
+
+183
+00:17:03,680 --> 00:17:14,320
+التوزيع تبعتك؟ يعني لو أنت rational consumer طيب
+
+184
+00:17:14,320 --> 00:17:19,120
+سبعين في المية consumption؟
+
+185
+00:17:20,980 --> 00:17:25,200
+طب عارف ايش الدراسات هي؟ Ricardo عرف اعمل دراسة
+
+186
+00:17:25,200 --> 00:17:29,620
+قالك الحكومة ما تضمنش .. ما تضمنش .. ما فيش
+
+187
+00:17:29,620 --> 00:17:33,200
+guarantee أن الحكومة ترجع تعمل increasing the
+
+188
+00:17:33,200 --> 00:17:38,500
+taxes .. اه فإيش .. ايش حكاية؟ هيبقى يعمل .. يعمل
+
+189
+00:17:38,500 --> 00:17:44,180
+دراسة؟ لأ .. اه طبعا .. قالك الحكومة مش مضمونة
+
+190
+00:17:44,840 --> 00:17:48,160
+والظروف مش مضمونة كمان زي الموضوع اللي بنعيشه
+
+191
+00:17:48,160 --> 00:17:51,360
+حالياً واحد كان بياخد income مال جدا تمام اليوم
+
+192
+00:17:51,360 --> 00:17:56,300
+الجامعة كدهش متجبض كدهش الأمور تمام فقال لك بيثبت
+
+193
+00:17:56,300 --> 00:18:02,400
+ال consumption بودّي الجزء الثاني هذا ال 250 صغير
+
+194
+00:18:02,400 --> 00:18:07,160
+علوين ال saving لما التكافؤ في الظروف في الظروف
+
+195
+00:18:07,160 --> 00:18:10,100
+اللي هي هذا اللي هو Ricardian equivalence اللي هو
+
+196
+00:18:10,100 --> 00:18:15,620
+means that individuals upset the governmental
+
+197
+00:18:15,620 --> 00:18:21,780
+actions by saving and leaving larger pay quests
+
+198
+00:18:21,780 --> 00:18:28,000
+يعني بيخلي الوسيط تبع ال saving أعلى، هاي باختصار
+
+199
+00:18:33,890 --> 00:18:37,530
+مش منطقي، أي دراسة، هذا theory، هذا theory، طالع
+
+200
+00:18:37,530 --> 00:18:41,890
+فيه، طب
+
+201
+00:18:41,890 --> 00:18:47,970
+خلينا نشوف كمان شوية السلطة الفلسطينية وموضوع
+
+202
+00:18:47,970 --> 00:18:51,970
+التعديلات في ال tax وموضوع ال tax rate و ال income
+
+203
+00:18:51,970 --> 00:18:56,070
+tax و ال .. و ال .. هذا، راح نشوف هل فينا نروح ..
+
+204
+00:18:56,070 --> 00:18:59,030
+يعني أي تعديلات .. كيف ي .. نعم؟ النسبة بتنزل
+
+205
+00:18:59,030 --> 00:19:01,230
+القانون، و لو دمعاتهم عليها لسه، هم بتعرضوها ثاني
+
+206
+00:19:01,230 --> 00:19:04,730
+على المجلس التشريعي؟ طبعا بتعرض، ولا .. اه؟ مش واحد
+
+207
+00:19:04,730 --> 00:19:07,370
+بيغيرها اليوم هو بيقول .. لأ، لأ مش .. طبعا، ولا
+
+208
+00:19:07,370 --> 00:19:11,790
+.. ده بتدخل في ايش اسمه؟ legislations و هيك، ده
+
+209
+00:19:11,790 --> 00:19:15,470
+راح نناقشه ب details يعني بعد ال .. بعد شوية يعني،
+
+210
+00:19:15,470 --> 00:19:19,670
+تمام؟ لكن أي رؤية، يعني أحد ال theories اللي بت ..
+
+211
+00:19:19,670 --> 00:19:23,630
+المطروحة أنه .. مزاج الجوانب مش مضمون، يعني بعد
+
+212
+00:19:23,630 --> 00:19:28,210
+شوية راح تلاقي فجأة اللي هو تخلي ال taxes 20%، شو
+
+213
+00:19:28,210 --> 00:19:33,670
+سويه ده؟ شو سويه؟ فبه بيحاولوا إنه يعملوا keep the
+
+214
+00:19:33,670 --> 00:19:39,490
+same consumption ومواعي saving، here's the idea،
+
+215
+00:19:39,490 --> 00:19:40,630
+تمام؟ طيب
+
+216
+00:19:50,920 --> 00:19:54,920
+Long term interest rates reflect expectations
+
+217
+00:19:54,920 --> 00:19:56,440
+about the future
+
+218
+00:20:15,370 --> 00:20:19,370
+بتوقع .. اه .. بتوقع .. بيعمل reflections على ميه؟
+
+219
+00:20:19,370 --> 00:20:21,250
+ال expectation تبع ال future تبعا على ال
+
+220
+00:20:21,250 --> 00:20:26,750
+investment وبتالي على ال resources اللي .. يعني
+
+221
+00:20:26,750 --> 00:20:31,750
+هذا اللي راح يجينا في ال future تمام؟ خليني أشوف
+
+222
+00:20:31,750 --> 00:20:33,790
+بعض الشغلات المهمة بالله
+
+223
+00:20:37,330 --> 00:20:40,650
+طبعاً entire path of surplus and deficit matter
+
+224
+00:20:40,650 --> 00:20:44,670
+for these rates which are important for the
+
+225
+00:20:44,670 --> 00:20:47,150
+business making طبعا احنا عارفين ان ال interest
+
+226
+00:20:47,150 --> 00:20:53,550
+rate affect investment وبالتالي affect على مين؟
+
+227
+00:20:53,550 --> 00:20:56,890
+على ال capital طبعا ال investment تبع ال business
+
+228
+00:20:56,890 --> 00:20:59,610
+وبالتالي ال business sector و ال private sector
+
+229
+00:20:59,610 --> 00:21:03,050
+لازم يكونوا دوريين بموضوع ال changes في ال
+
+230
+00:21:03,050 --> 00:21:03,930
+interest rates
+
+231
+00:21:18,250 --> 00:21:23,810
+مهم لل government ان ال budget deficit خلّيني نحكي
+
+232
+00:21:23,810 --> 00:21:33,090
+في ال long term budget deficit long
+
+233
+00:21:33,090 --> 00:21:39,110
+term budget deficits وين رح يودينا على debts عالي
+
+234
+00:21:39,110 --> 00:21:44,130
+مصبوط أن كل budget ايش budget deficit في السنة
+
+235
+00:21:44,130 --> 00:21:52,640
+هذه رح يترحل ويترتب على long term debts تمام
+
+236
+00:21:52,640 --> 00:21:58,380
+زي كل العالم صح
+
+237
+00:21:58,380 --> 00:22:05,080
+هذا born in عالمين مش بس على الدولة، على future
+
+238
+00:22:05,080 --> 00:22:09,570
+generations على الجيارة اللي جاية، يعني أنا شو زم
+
+239
+00:22:09,570 --> 00:22:14,270
+بولدادي بكرا اشيلوا الدين تبع مين؟ ال debts تبع
+
+240
+00:22:14,270 --> 00:22:18,550
+مين؟ تبع ال generations اللي قبله وبالتالي الأمور ده
+
+241
+00:22:18,550 --> 00:22:21,830
+تمشي parallel، يعني ما تحمل كتير على ال future
+
+242
+00:22:21,830 --> 00:22:25,030
+generations، ضالك أنت وكأنه فيه هندك، أنت هالجيته،
+
+243
+00:22:25,030 --> 00:22:28,290
+تقدر تسحب دين، تسحب دين، تسحب دين، طب بعدين هتحمل
+
+244
+00:22:28,290 --> 00:22:32,230
+أولادك بكرا، على ال future generations، تمام؟
+
+245
+00:22:32,230 --> 00:22:35,990
+ويقولك أن ال government should match، يعني الأمور
+
+246
+00:22:35,990 --> 00:22:43,680
+تمشي بشكل rational، تمام؟ لأنه يقضي يعني final
+
+247
+00:22:43,680 --> 00:22:48,600
+deficit مطر بكوز of intergenerational equity بمعنى
+
+248
+00:22:48,600 --> 00:22:53,620
+بنمشي فيه عدالة في توزيع ال budget deficit مش هلجي
+
+249
+00:22:53,620 --> 00:22:59,280
+تمشي في إطار توسع كثير لأن هدوا راح يحملك على ال
+
+250
+00:22:59,280 --> 00:23:02,980
+debts لاحقاً تمام؟ ومو بتلجي ال future generations
+
+251
+00:23:02,980 --> 00:23:07,120
+يكون worse
+
+252
+00:23:07,120 --> 00:23:07,480
+off
+
+253
+00:23:16,760 --> 00:23:23,900
+تمام The continual increase in productivity 
+
+254
+00:23:23,900 --> 00:23:27,680
+and rising standard of living means طبعا  الfuture
+
+255
+00:23:27,680 --> 00:23:32,320
+generations have more resources at their disposal
+
+256
+00:23:32,320 --> 00:23:35,400
+than
+
+257
+00:23:35,400 --> 00:23:39,760
+current ones? okay we have finished يعطيكم 
+258
+00:23:39,760 --> 00:23:40,180
+العافية 
diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/BJCp34BXfzE.srt b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/BJCp34BXfzE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fe138a01cff01bfec14965f226bb77557fde7575
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/BJCp34BXfzE.srt
@@ -0,0 +1,1387 @@
+1
+00:00:21,040 --> 00:00:24,500
+Okay, بسم الله الرحمن الرحيم، اليوم إن شاء الله سوف 
+
+2
+00:00:24,500 --> 00:00:27,440
+نكمل ونتكلم عن الوحدات المجتمعية الواحدة
+
+3
+00:00:27,440 --> 00:00:30,960
+المجتمعية الواحدة المجتمعية الواحدة الواحدة
+
+4
+00:00:30,960 --> 00:00:36,660
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+5
+00:00:36,660 --> 00:00:38,380
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+6
+00:00:38,380 --> 00:00:38,560
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+7
+00:00:38,560 --> 00:00:38,600
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+8
+00:00:38,600 --> 00:00:49,440
+الواحدة الواحدة الواحدة الواحدة الوا
+
+9
+00:00:50,370 --> 00:00:57,870
+the two characteristics like rival and excludable
+
+10
+00:00:57,870 --> 00:01:03,810
+and in between we have impure goods, sometimes we
+
+11
+00:01:03,810 --> 00:01:06,350
+can say
+
+12
+00:01:09,170 --> 00:01:15,970
+الجودة ستكون مقارنة وليست مستخدمة مستخدمة وليست 
+
+13
+00:01:15,970 --> 00:01:21,090
+مقارنة، وكانت لدينا بعض الأمثلة مرتبطة مع هذه
+
+14
+00:01:21,090 --> 00:01:27,490
+النقطة، اليوم سنقوم بالتحقق من أفضل أموال خاصة و
+
+15
+00:01:27,490 --> 00:01:37,250
+أفضل أموال مجتمع، أفضل أموال خاصة و أفضل أموال
+
+16
+00:01:37,250 --> 00:01:45,030
+مجتمع، بالنسبة للجامعات العامة، قبل أن نذكر أن
+
+17
+00:01:45,030 --> 00:01:50,610
+الانتاج الشبكي يحدث
+
+18
+00:01:50,610 --> 00:01:53,690
+عندما يتساوي المساعدات الاجتماعية الاجتماعية
+
+19
+00:01:53,690 --> 00:01:56,730
+الاجتماعية الاجتماعية هي المساعدة الاجتماعية، هذا
+
+20
+00:01:56,730 --> 00:02:00,370
+يتعامل مع المساعدات الشبكية أو بمعرفة أفعال
+
+21
+00:02:00,370 --> 00:02:01,930
+المساعدات الشبكية
+
+22
+00:02:05,350 --> 00:02:11,730
+سأعود إلى الأموال الخاصة، وبعدها سنذهب للجمهور
+
+23
+00:02:11,730 --> 00:02:19,450
+لفهم أفضل مصالح الأموال الخاصة، لدينا مثلًا مثلًا
+
+24
+00:02:19,450 --> 00:02:25,690
+هنا تعتبر أموال خاصة، مثل آيس كريم، الشخص هنا يظهر
+
+25
+00:02:27,710 --> 00:02:32,750
+المطالب، يحصل على آيس كريم لكتير أو لكتير أو لكتر
+
+26
+00:02:32,750 --> 00:02:34,730
+أو لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو 
+
+27
+00:02:34,730 --> 00:02:39,150
+لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو
+
+28
+00:02:39,150 --> 00:02:39,650
+لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو
+
+29
+00:02:39,650 --> 00:02:39,890
+لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو
+
+30
+00:02:39,890 --> 00:02:42,730
+لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو لكتر أو
+
+31
+00:02:42,730 --> 00:02:54,110
+لكتر أو لكتر أو 
+
+32
+00:02:54,110 --> 00:02:54,130
+ل
+
+33
+00:02:57,320 --> 00:03:05,290
+هذا هو أسعار الحلو والقوات المطلوبة من الحلو، هذا هو
+
+34
+00:03:05,290 --> 00:03:07,390
+حرارة التطبيق المساعد للبنزين، وهو تسلسل للأسفل
+
+35
+00:03:07,390 --> 00:03:13,010
+لل بنزين، كفاية اكتشاف واحد هنا يمكنه أن يشتري أو
+
+36
+00:03:13,010 --> 00:03:17,530
+إذا كان السعر خمسة، يمكنه أن يشتري واحد عامة، وعندما
+
+37
+00:03:17,530 --> 00:03:22,610
+يتسلسل السعر لأربعة، أو لعامة، يمكنه أن يشتري اثنين
+
+38
+00:03:22,610 --> 00:03:27,330
+عامة، وهذا يعني تسلسل التطبيق المساعد للبنزين
+
+39
+00:03:34,180 --> 00:03:40,200
+مستر جيري هو أيضًا لديه
+
+40
+00:03:40,200 --> 00:03:47,000
+طريقة طلبية، طريقة طلبية واحدة تسلسل بالأسفل أيضًا
+
+41
+00:03:47,000 --> 00:03:55,500
+ولكنها أعلى... آسف، تحت الطريقة الطلبية لبن الآن
+
+42
+00:03:55,500 --> 00:04:03,800
+سوف نحصل على ما التطبيق التطبيق التطبيق التطبيق
+
+43
+00:04:03,800 --> 00:04:05,260
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+44
+00:04:05,260 --> 00:04:08,320
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+45
+00:04:08,320 --> 00:04:09,360
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+46
+00:04:09,360 --> 00:04:12,600
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+47
+00:04:12,600 --> 00:04:12,920
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+48
+00:04:12,920 --> 00:04:16,480
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+49
+00:04:16,480 --> 00:04:17,880
+التطبيق التطبيق التطبيق التطبيق التطبيق التطبيق
+
+50
+00:04:17,880 --> 00:04:24,300
+التطبيق التطبيق التطبيق
+
+51
+00:04:24,300 --> 00:04:29,180
+التطبي
+
+52
+00:04:33,440 --> 00:04:38,280
+هذا لـ Jerry، يستطيع أن يشتغل أو يشتغل في هذه
+
+53
+00:04:38,280 --> 00:04:43,820
+المجموعة، في هذه المجموعة، في نفس السعر هنا في ثلاثة
+
+54
+00:04:43,820 --> 00:04:46,780
+دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة
+
+55
+00:04:46,780 --> 00:04:46,820
+دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة
+
+56
+00:04:46,820 --> 00:04:54,460
+دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة
+
+57
+00:04:54,460 --> 00:04:58,600
+دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة
+
+58
+00:04:58,600 --> 00:05:02,230
+دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة دقيقة على ثلاثة
+
+59
+00:05:02,230 --> 00:05:05,270
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+60
+00:05:05,270 --> 00:05:10,810
+المجتمع
+
+61
+00:05:10,810 --> 00:05:12,550
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+62
+00:05:12,550 --> 00:05:12,570
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+63
+00:05:12,570 --> 00:05:18,930
+المجتمع المجتمع المجتمع المجتمع
+
+64
+00:05:18,930 --> 00:05:18,970
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+65
+00:05:18,970 --> 00:05:22,850
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+66
+00:05:22,850 --> 00:05:26,110
+المجتمع
+
+67
+00:05:26,110 --> 00:05:28,810
+الم
+
+68
+00:05:33,400 --> 00:05:39,660
+على سعر أكثر من أكثر
+
+69
+00:05:39,660 --> 00:05:47,080
+من أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+70
+00:05:47,080 --> 00:05:47,400
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+71
+00:05:47,400 --> 00:05:47,860
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+72
+00:05:47,860 --> 00:05:54,780
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر 
+
+73
+00:06:04,090 --> 00:06:09,590
+يجب أن يكون 8، لذلك يمكننا أن نكتشف طريقة طلب
+
+74
+00:06:09,590 --> 00:06:17,510
+المجتمع لجري وPin بإتصال
+
+75
+00:06:17,510 --> 00:06:22,830
+هذه النقطة هنا، هذا هو طريقة طلب المجتمع للمجتمع
+
+76
+00:06:22,830 --> 00:06:29,150
+هنا، أو مفيدات الاجتماعية كما ذكرنا سابقًا،
+
+77
+00:06:32,610 --> 00:06:38,150
+إذا إضافة مطالب بنزا وجوري إلى كل قيمة تجعل
+
+78
+00:06:38,150 --> 00:06:45,970
+المجتمع يطلب منها مطالب كامل من المجتمع المجاني
+
+79
+00:06:45,970 --> 00:06:49,390
+المجاني المجاني المجاني المجاني المجاني المجاني
+
+80
+00:06:49,390 --> 00:06:49,490
+المجاني المجاني المجاني المجاني المجاني المجاني
+
+81
+00:06:49,490 --> 00:06:53,890
+المجاني المجاني المجاني المجاني المجاني
+
+82
+00:06:53,890 --> 00:06:54,390
+المجاني المجاني المجاني المجاني المجاني المجاني
+
+83
+00:06:54,390 --> 00:06:58,750
+المجاني المجاني المجاني المجاني المجاني المجاني
+
+84
+00:06:58,750 --> 00:06:59,150
+المجاني المجاني المجاني المجاني المجاني المجاني
+
+85
+00:06:59,150 --> 00:07:02,710
+المجاني المجاني المجاني، هذا هو قيمة التجارب الاجتماعية
+
+86
+00:07:02,710 --> 00:07:06,010
+وهذا
+
+87
+00:07:06,010 --> 00:07:09,110
+هو مجموعة السوق المشتركة المشتركة المشتركة
+
+88
+00:07:09,110 --> 00:07:10,010
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+89
+00:07:10,010 --> 00:07:10,770
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+90
+00:07:10,770 --> 00:07:13,730
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+91
+00:07:13,730 --> 00:07:13,950
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+92
+00:07:13,950 --> 00:07:20,370
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+93
+00:07:20,370 --> 00:07:20,810
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+94
+00:07:20,810 --> 00:07:21,890
+المشتركة المشتركة المشتركة المشتركة المشتركة
+
+95
+00:07:21,890 --> 00:07:30,170
+المشتركة المشت
+
+96
+00:07:31,780 --> 00:07:38,460
+مقال نفسه لجري و بن و أحمد و علي، مقال نفسه، وهذا
+
+97
+00:07:38,460 --> 00:07:44,200
+هو الواقع الواقعي الاجتماعي هنا، حسنًا؟
+
+98
+00:07:44,200 --> 00:07:47,540
+لذلك، يؤدي إلى مقارنة مقارنة مقارنة مقارنة مقارنة
+
+99
+00:07:47,540 --> 00:07:48,200
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+100
+00:07:48,200 --> 00:07:58,760
+مقارنة مقارنة مقارنة مقارنة
+
+101
+00:07:58,760 --> 00:08:01,520
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+102
+00:08:01,520 --> 00:08:01,540
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+103
+00:08:01,540 --> 00:08:01,660
+مقارنة مقارنة مقارنة مقارنة
+
+104
+00:08:04,600 --> 00:08:13,080
+بن تشتري في هذا الوضع، وجيري تشتري في هذا الوضع
+
+105
+00:08:13,080 --> 00:08:16,860
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+106
+00:08:16,860 --> 00:08:16,980
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+107
+00:08:16,980 --> 00:08:17,560
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+108
+00:08:17,560 --> 00:08:17,900
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+109
+00:08:17,900 --> 00:08:19,440
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+110
+00:08:19,440 --> 00:08:25,080
+كمية كمية كمية كمية كمية
+
+111
+00:08:25,080 --> 00:08:26,680
+كمية
+
+112
+00:08:34,940 --> 00:08:40,020
+كما ترى هنا في هذا الفيديو، كما اقترح الأسعار، كل 
+
+113
+00:08:40,020 --> 00:08:48,300
+شخص تغيّر استخدامه كمان كمان كمان كمان
+
+114
+00:08:48,300 --> 00:08:53,520
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+115
+00:08:53,520 --> 00:08:53,620
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+116
+00:08:53,620 --> 00:08:58,080
+كمان كمان كمان كمان كمان كمان كمان
+
+117
+00:09:01,670 --> 00:09:05,430
+the market price، حسنًا، هنا للمواطنين الخاص بهم
+
+118
+00:09:05,430 --> 00:09:11,070
+المستخدمين يطلبون مواقع مختلفة في نفس السوق market
+
+119
+00:09:11,070 --> 00:09:19,890
+price، وهو صحيح هنا في هذا المثال، يمكننا
+
+120
+00:09:19,890 --> 00:09:25,010
+أيضًا أن نقدم هذه العلاقة المثالي بأنه لديه
+
+121
+00:09:25,010 --> 00:09:31,190
+احتياطات عن كوكيز وأعشاب، ما هي الاحتياطات؟ هل تتذكر
+
+122
+00:09:31,190 --> 00:09:34,450
+الـ Utility، الـ Total Utility، و Indifference
+
+123
+00:09:34,450 --> 00:09:40,470
+Curve؟ وهذا يعني أن هناك الاختيارات لكي تشتري
+
+124
+00:09:40,470 --> 00:09:44,930
+مجموعات مختلفة من الأموال. سأعود إلى الفكرة هنا عن
+
+125
+00:09:44,930 --> 00:09:48,950
+الـ Total Utility، معالجة المستخدم ومعالجة المستخدم
+
+126
+00:09:48,950 --> 00:09:50,130
+ومعالجة المستخدم ومعالجة المستخدم ومعالجة المستخدم
+
+127
+00:09:50,130 --> 00:09:51,950
+ومعالجة المستخدم ومعالجة المستخدم ومعالجة المستخدم
+
+128
+00:09:51,950 --> 00:09:54,510
+ومعالجة المستخدم ومعالجة المستخدم ومعالجة المستخدم
+
+129
+00:09:54,510 --> 00:09:54,790
+ومعالجة المستخدم ومعالجة المستخدم ومعالجة المستخدم
+
+130
+00:09:54,790 --> 00:09:56,450
+ومعالجة المستخدم ومعالجة المستخدم ومعالجة المستخدم
+
+131
+00:09:56,450 --> 00:10:00,430
+ومعالجة المستخدم ومعالجة المستخدم ومعالجة المستخدم
+
+132
+00:10:00,430 --> 00:10:14,950
+ومعالجة المستخدم ومعالجة المستخدم ومعالج
+
+133
+00:10:15,560 --> 00:10:24,360
+Cookies and ice cream وهنا كشخص يستخدم الكوكيز
+
+134
+00:10:24,360 --> 00:10:28,180
+والآيس كريم وهو كشخص يستخدم الكوكيز والآيس كريم
+
+135
+00:10:28,180 --> 00:10:33,560
+وهو كشخص يستخدم
+
+136
+00:10:33,560 --> 00:10:33,920
+الكوكيز والآيس كريم وهو كشخص يستخدم الكوكيز والآيس
+
+137
+00:10:33,920 --> 00:10:34,600
+كريم وهو كشخص يستخدم الكوكيز والآيس كريم وهو كشخص
+
+138
+00:10:34,600 --> 00:10:35,160
+يستخدم الكوكيز والآيس كريم وهو كشخص يستخدم الكوكيز
+
+139
+00:10:35,160 --> 00:10:37,580
+وهو كشخص يستخدم الكوكيز والآيس كريم وهو كشخص
+
+140
+00:10:37,580 --> 00:10:39,300
+يستخدم ال
+
+141
+00:10:45,010 --> 00:10:50,230
+لتحسين أفضلياتهم أو تحسين إيجارهم ونذهب إلى التحسين
+
+142
+00:10:50,230 --> 00:10:55,550
+الاجتماعي باستخدام إيجار مجالاتها لتفهم الفكرة هنا
+
+143
+00:10:55,550 --> 00:11:01,810
+هنا لدينا شيء يقول أن تحسين إيجار المجتمع الوطني
+
+144
+00:11:01,810 --> 00:11:07,630
+يتطلب أن كل مخطط مختلف يكون متواصل للطرق
+
+145
+00:11:07,630 --> 00:11:12,870
+التجارية لكلا المخططين إذا تذكر أنه عندما تحدثنا عن
+
+146
+00:11:12,870 --> 00:11:19,910
+الإيكويلبريوم الخدمة، قلنا إن أفضل أو أفضل مجموعة
+
+147
+00:11:19,910 --> 00:11:25,710
+لخدمة الخدمة تتمتع أو يحدث عندما يكون هناك تجارب
+
+148
+00:11:25,710 --> 00:11:28,470
+بين مقارنة الاختلاف والخطوط المجاورة للخطوط
+
+149
+00:11:28,470 --> 00:11:31,390
+المجاورة للخطوط المجاورة للخطوط المجاورة للخطوط
+
+150
+00:11:31,390 --> 00:11:35,990
+المجاورة للخطوط المجاورة للخطوط المجاورة للخطوط
+
+151
+00:11:35,990 --> 00:11:39,790
+المجاورة للخطوط
+
+152
+00:11:39,920 --> 00:11:47,280
+على كمية Y وعلى هذا النقطة الموجودة هنا عبارة عن
+
+153
+00:11:47,280 --> 00:11:56,020
+مراجعة تغيير الميزانية الموجودة هنا عبارة
+
+154
+00:11:56,020 --> 00:11:58,780
+عن مراجعة تغيير الميزانية X وY
+
+155
+00:12:02,860 --> 00:12:08,980
+لنحصل على مثال عملي وبعدها سوف نكمل حديثنا عن
+
+156
+00:12:08,980 --> 00:12:15,880
+الإيكويلبريوم هنا لدينا الهايبوتيزس أو الاختصارات
+
+157
+00:12:15,880 --> 00:12:24,700
+هنا تقول أن لكي تحصل على الإيكويلبريوم هنا لدينا
+
+158
+00:12:24,700 --> 00:12:29,420
+الحالة التالية اسمها الحالة الأولى أو الاختصار
+
+159
+00:12:33,010 --> 00:12:39,450
+على الآيس كريم عبر قيمة المجال للطيبين
+
+160
+00:12:39,450 --> 00:12:44,210
+هذا فوربين يجب
+
+161
+00:12:44,210 --> 00:12:53,150
+أن يكون قيمة الآيس كريم عبر قيمة الطيبين وهو قيمة
+
+162
+00:12:53,150 --> 00:12:58,730
+تغيير المجال لفوربين كيف نستطيع أن نفهم الفكرة
+
+163
+00:12:58,730 --> 00:13:06,180
+هنا؟ لفهم الفكرة أو الوضع الأول أنا سأذهب إلى مثال
+
+164
+00:13:06,180 --> 00:13:11,440
+عملي لأفهم الفكرة، حسنا؟ لذا دعنا نذهب إلى مثال
+
+165
+00:13:11,440 --> 00:13:18,840
+عملي هنا المسألة
+
+166
+00:13:18,840 --> 00:13:23,420
+هنا هي
+
+167
+00:13:23,420 --> 00:13:33,120
+أننا نتحدث عن شخص وهذا الشخص لديه قيمة X وY
+
+168
+00:13:33,120 --> 00:13:42,710
+مختلفة معاناة مختلفة دعونا هنا نتكلم عن بن المقاومة
+
+169
+00:13:42,710 --> 00:13:52,410
+هنا أو المقاومة هنا تتمثل X وY عندما يتم استخدام
+
+170
+00:13:52,410 --> 00:14:02,250
+بن نقطة X عندما يتم استخدام بن نقطة X هو يستطيع
+
+171
+00:14:02,250 --> 00:14:07,650
+الحصول على نقطة أكثر من الوضع في
+
+172
+00:14:07,650 --> 00:14:15,590
+الوضع الواضح الواضح الواضح الواضح
+
+173
+00:14:15,590 --> 00:14:16,930
+الواضح الواضح الواضح الواضح الواضح الواضح الواضح
+
+174
+00:14:16,930 --> 00:14:17,090
+الواضح الواضح الواضح الواضح الواضح الواضح الواضح
+
+175
+00:14:17,090 --> 00:14:17,590
+الواضح الواضح الواضح الواضح الواضح الواضح الواضح
+
+176
+00:14:17,590 --> 00:14:17,990
+الواضح الواضح الواضح الواضح الواضح الواضح الواضح
+
+177
+00:14:17,990 --> 00:14:19,990
+الواضح الواضح الواضح الواضح الواضح الواضح الواضح
+
+178
+00:14:19,990 --> 00:14:28,270
+الواضح الواضح الواضح الواضح ال
+
+179
+00:14:28,570 --> 00:14:32,110
+على سبيل المثال، سعر X يقل لـ 5 وسعر Y يقل لـ 10
+
+180
+00:14:32,110 --> 00:14:35,370
+ويعني 45 دولارًا.
+
+181
+00:14:38,750 --> 00:14:44,550
+إذا قمنا بالتخيل أن هذه هي كمية Y، فهذه هي كمية
+
+182
+00:14:44,550 --> 00:14:53,070
+Y. عندما يتخلص من واحدة من Y، يستطيع الحصول على 50
+
+183
+00:14:53,070 --> 00:14:54,550
+كمية Y.
+
+184
+00:15:14,120 --> 00:15:24,780
+تقريبًا تقريبًا تقريبًا تقريبًا تقريبًا تقريبًا تقريبًا
+
+185
+00:15:24,780 --> 00:15:24,900
+تقريبًا تقريبًا تقريبًا تقريبًا تقريبًا تقريبًا تقريبًا
+
+186
+00:15:24,900 --> 00:15:25,080
+تقريبًا تقريبًا تقريبًا
+
+187
+00:15:32,760 --> 00:15:41,120
+وكوكيز لتحرير الإيكويلبريوم الوصول إلى الوصول إلى الوصول
+
+188
+00:15:41,120 --> 00:15:47,660
+إلى الوصول إلى الوصول إلى الوصول إلى الوصول إلى الوصول
+
+189
+00:15:47,660 --> 00:15:53,680
+إلى الوصول إلى الوصول إلى ال
+
+190
+00:16:01,520 --> 00:16:06,280
+هنا لدينا اتفاقات أولى اتفاقات أولى اتفاقات أولى
+
+191
+00:16:06,280 --> 00:16:11,780
+اتفاقات أولى اتفاقات أولى اتفاقات أولى اتفاقات
+
+192
+00:16:11,780 --> 00:16:18,960
+أولى اتفاقات أولى اتفاقات أولى
+
+193
+00:16:18,960 --> 00:16:20,140
+اتفاقات أولى اتفاقات أولى اتفاقات أولى اتفاقات
+
+194
+00:16:20,140 --> 00:16:20,160
+اتفاقات أولى اتفاقات أولى اتفاقات أولى اتفاقات
+
+195
+00:16:20,160 --> 00:16:22,940
+أولى اتفاقات أولى اتفاقات أولى اتفاقات أولى
+
+196
+00:16:22,940 --> 00:16:27,100
+اتفاقات أولى اتف
+
+197
+00:16:30,540 --> 00:16:35,680
+In our way, when the marginal utility of X over
+
+198
+00:16:35,680 --> 00:16:39,000
+the marginal utility of Y must equals the price of
+
+199
+00:16:39,000 --> 00:16:40,560
+X over the price of Y.
+
+200
+00:16:44,660 --> 00:16:50,540
+كيف؟ اعمل دار تبادلي توصل لهدا، يعني to reach لهدا
+
+201
+00:16:50,540 --> 00:16:55,920
+هيك من هاد، بنقول هيك مارجينال يوتيليتي دار تبادلي
+
+202
+00:16:57,630 --> 00:17:04,550
+marginal utility of x times the price of y equals
+
+203
+00:17:04,550 --> 00:17:07,970
+marginal utility of y times the price of x
+
+204
+00:17:07,970 --> 00:17:17,150
+marginal utility of y times the price of x اقسم هذا
+
+205
+00:17:17,150 --> 00:17:20,150
+على هذا بسبب أن marginal utility of x over
+
+206
+00:17:20,150 --> 00:17:23,910
+marginal utility of y equals the price of x over
+
+207
+00:17:23,910 --> 00:17:27,130
+the price of y this is the first order condition
+
+208
+00:17:28,950 --> 00:17:32,290
+وهذا هو عملية تغيير عملية تغيير عملية تغيير عملية
+
+209
+00:17:32,290 --> 00:17:43,070
+تغيير عملية تغيير عملية تغيير
+
+210
+00:17:44,780 --> 00:17:49,540
+هذا هو المصطلح الأول مصطلح المصطلح الثاني مصطلح
+
+211
+00:17:49,540 --> 00:17:51,160
+مصطلح مصطلح المصطلح الثاني مصطلح مصطلح المصطلح
+
+212
+00:17:51,160 --> 00:17:54,620
+الثاني مصطلح مصطلح المصطلح الثاني مصطلح المصطلح
+
+213
+00:17:54,620 --> 00:17:56,680
+الثاني مصطلح المصطلح الثاني مصطلح المصطلح الثاني
+
+214
+00:17:56,680 --> 00:18:00,160
+مصطلح المصطلح الثاني مصطلح المصطلح الثاني مصطلح
+
+215
+00:18:00,160 --> 00:18:07,040
+المصطلح الثاني مصطلح المصطلح الثاني مصطلح المصطلح
+
+216
+00:18:07,040 --> 00:18:07,400
+الثاني مصطلح المصطلح الثاني مصطلح المصطلح الث
+
+217
+00:18:13,970 --> 00:18:22,650
+عندما يكون جميع الميزة المجاورة إلى اتجارات بين
+
+218
+00:18:22,650 --> 00:18:28,530
+اتجارات الآيس كريم والكوكيز الآيس كريم مرتفعة من X
+
+219
+00:18:28,530 --> 00:18:36,350
+مرتفعة من Y
+
+220
+00:18:36,350 --> 00:18:40,190
+مرتفعة من كوكيز مرتفعة من كوكيز
+
+221
+00:18:44,430 --> 00:18:49,330
+هذا هو مصدر البرنامج وهذا هو مصدر البرنامج وهذا هو
+
+222
+00:18:49,330 --> 00:18:51,110
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر
+
+223
+00:18:51,110 --> 00:18:51,230
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر
+
+224
+00:18:51,230 --> 00:18:51,250
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر
+
+225
+00:18:51,250 --> 00:18:51,750
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر
+
+226
+00:18:51,750 --> 00:18:52,390
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر
+
+227
+00:18:52,390 --> 00:18:59,070
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر
+
+228
+00:18:59,070 --> 00:19:07,230
+البرنامج وهذا هو مصدر البرنامج وهذا هو مصدر التحقق
+
+229
+00:19:07,230 --> 00:19:13,290
+الوضع الأول، وهو مجموع لـ X على قيمة X يقل مجموع
+
+230
+00:19:13,290 --> 00:19:25,390
+لـ Y على قيمة Y. كم هو مجموع لـ X؟ M U X يقل
+
+231
+00:19:25,390 --> 00:19:34,030
+Delta T U X أو تغيير الكميات X. سأقوم باستخدام أو
+
+232
+00:19:34,030 --> 00:19:37,690
+أتحقق الوضع الأول الذي يسمى الوضع الأساسي لـ X
+
+233
+00:19:37,690 --> 00:19:43,650
+بقيمة X يقوم باستخدام Y بقيمة Y لذلك يجب أن نتخيل
+
+234
+00:19:43,650 --> 00:19:48,190
+الوضع الأساسي لـ X الوضع الأساسي لـ X يقوم
+
+235
+00:19:48,190 --> 00:19:50,010
+باستخدام X يقوم باستخدام X يقوم باستخدام X يقوم
+
+236
+00:19:50,010 --> 00:19:50,270
+باستخدام X يقوم باستخدام X يقوم باستخدام X يقوم
+
+237
+00:19:50,270 --> 00:19:51,070
+باستخدام X يقوم باستخدام X يقوم باستخدام X يقوم
+
+238
+00:19:51,070 --> 00:19:57,110
+باستخدام X يقوم باستخدام X يقوم باستخدام X يقوم
+
+239
+00:19:57,110 --> 00:20:02,660
+باستخدام X يقوم بأو تحت هذا المثال المال هنا
+
+240
+00:20:02,660 --> 00:20:10,320
+معروف بقيمة 45 نعم
+
+241
+00:20:10,320 --> 00:20:18,480
+المال 45 وقيمة X معروفة بقيمة 5 وقيمة Y معروفة
+
+242
+00:20:18,480 --> 00:20:24,980
+بقيمة 10 دلوقتي دعونا نتكلم عن مجموعات X
+
+243
+00:20:32,100 --> 00:20:49,920
+40-0 40-0 40 40 40 40 40 40 40 40 40 40 40 40 40
+
+244
+00:20:49,920 --> 00:20:49,980
+40 40 40 40 40 40 40 40 40 40 40 40 40 40
+
+245
+00:20:54,740 --> 00:21:02,980
+هذا كم؟ ثلاثين وخمسين
+
+246
+00:21:02,980 --> 00:21:06,060
+وخمسين
+
+247
+00:21:06,060 --> 00:21:18,300
+وخمسين وخمسين وخمسين وخمسين
+
+248
+00:21:25,490 --> 00:21:32,750
+75-40 35 30
+
+249
+00:21:32,750 --> 00:21:44,910
+25 20 15 and then 10 then 5 okay let's calculate
+
+250
+00:21:44,910 --> 00:21:50,030
+the marginal utility of Y M U Y the change in 
+
+251
+00:21:50,030 --> 00:21:53,130
+total utility of Y over
+
+252
+00:21:57,630 --> 00:22:09,250
+خمسين على واحد fifty yes zero sorry fifty forty
+
+253
+00:22:09,250 --> 00:22:13,250
+one
+
+254
+00:22:13,250 --> 00:22:19,250
+hundred twenty minus ninety over three minus two
+
+255
+00:22:19,250 --> 00:22:25,690
+equals thirty yes thirty
+
+256
+00:22:27,160 --> 00:22:36,440
+ثم 20 ثم 10 ثم 15 ثم 10 ثم 5 ثم 5 ثم 0 ثم 10 ثم 5
+
+257
+00:22:36,440 --> 00:22:45,480
+ثم 0 ثم 10 ثم 5 ثم 5 ثم 0 ثم 10 ثم 10 ثم
+
+258
+00:22:45,480 --> 00:22:47,800
+5 ثم 5 ثم 5 ثم 6 ثم 6 ثم 5 ثم 5 ثم 6 ثم 5 ثم 5 ثم
+
+259
+00:22:47,800 --> 00:22:48,300
+5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم
+
+260
+00:22:48,300 --> 00:22:48,360
+5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم
+
+261
+00:22:48,360 --> 00:22:51,880
+5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم 5 ثم
+
+262
+00:22:59,530 --> 00:23:05,450
+مي و PY مي و PY مي و PY مي و PY مي و PY مي و PY مي
+
+263
+00:23:05,450 --> 00:23:12,950
+و PY مي و PY مي و PY مي و PY مي و PY مي و PY مي
+
+264
+00:23:12,950 --> 00:23:15,410
+و PY مي و PY مي و PY مي و PY مي و PY مي و PY مي و
+
+265
+00:23:15,410 --> 00:23:17,990
+PY مي و PY مي و PY مي و PY مي و PY مي و PY مي و PY
+
+266
+00:23:17,990 --> 00:23:18,470
+مي و PY مي و PY مي و PY مي و PY مي و PY مي و PY مي
+
+267
+00:23:18,470 --> 00:23:21,950
+PY مي و PY مي و PY مي و PY مي و PY مي و PY مي
+
+268
+00:23:21,950 --> 00:23:25,030
+و PY مي و P
+
+269
+00:23:34,000 --> 00:23:38,700
+خلّيني أطبّق هدوء بنرجع بنشوف التاني ماشي؟ okay
+
+270
+00:23:38,700 --> 00:23:44,360
+اوه the same the same the same result 40
+
+271
+00:23:44,360 --> 00:23:49,320
+over 587
+
+272
+00:23:49,320 --> 00:23:52,440
+30
+
+273
+00:23:52,440 --> 00:23:55,860
+over 56 yes
+
+274
+00:23:57,460 --> 00:24:03,620
+who calculated five yes نعبيهم هيك و ال excel
+
+275
+00:24:03,620 --> 00:24:08,400
+sheet أسهل لنا عطول بس بال .. أنجله ال excel sheet
+
+276
+00:24:08,400 --> 00:24:23,260
+تمام خليني أنجله كله ال excel sheet الجهاز
+
+277
+00:24:23,260 --> 00:24:31,360
+أكيد في excel sheet هذه كل البرنامج ميكروسوفت
+
+278
+00:24:31,360 --> 00:24:47,300
+اوفيس تمام
+
+279
+00:24:47,300 --> 00:24:51,900
+ميكروسوفت اوفيس ميكروسوفت اوفيس
+
+280
+00:24:56,070 --> 00:24:56,890
+مي مي مي مي مي مي مي مي مي مي مي مي مي مي مي
+
+281
+00:25:33,700 --> 00:25:41,480
+zero تمام equals mu y fifty over how much is the
+
+282
+00:25:41,480 --> 00:25:52,380
+price of y ten تمام
+
+283
+00:25:52,380 --> 00:25:54,900
+وين بيتساوى هدول
+
+284
+00:25:59,600 --> 00:26:05,380
+إن أمسك هذا هيك في هاي five يعني فيه five yes إذا
+
+285
+00:26:05,380 --> 00:26:13,940
+هذا هيك بدنا نعمله طب ليه هذا وها هيك تمام
+
+286
+00:26:13,940 --> 00:26:22,660
+something else four فيه four yes four four another
+
+287
+00:26:22,660 --> 00:26:23,400
+color
+
+288
+00:26:28,750 --> 00:26:36,590
+مش مبينة حط فاتح ثلاثة
+
+289
+00:26:36,590 --> 00:26:47,810
+هل هناك ثلاثة؟ نعم ثلاثة
+
+290
+00:27:16,870 --> 00:27:22,790
+one تمام؟ this is .. so the first order condition
+
+291
+00:27:22,790 --> 00:27:28,890
+has been met in five cases or four cases at five
+
+292
+00:27:28,890 --> 00:27:36,760
+four three two and one الآن سنقوم بتحقق موضوع
+
+293
+00:27:36,760 --> 00:27:37,200
+الاختصار الثانوي
+
+294
+00:27:46,030 --> 00:27:50,270
+طب لحظة انجرب ان ال first order condition صار بال
+
+295
+00:27:50,270 --> 00:27:55,110
+M U X over P M U Y equals price of X over price of
+
+296
+00:27:55,110 --> 00:27:58,450
+Y هل في ال five cases صار ولا لأ؟ انشوف okay so
+
+297
+00:27:58,450 --> 00:28:03,930
+the first order condition here M U X or M U X over
+
+298
+00:28:03,930 --> 00:28:08,990
+M U Y as well equals the price of X over price of
+
+299
+00:28:08,990 --> 00:28:14,460
+Y ميكس ميكس ميكس ميكس ميكس ميكس ميكس ميكس ميكس ميكس
+
+300
+00:28:14,460 --> 00:28:16,720
+ميكس ميكس ميكس ميكس ميكس ميكس ميكس ميكس ميكس ميكس
+
+301
+00:28:16,720 --> 00:28:23,080
+ميكس ميكس
+
+302
+00:28:23,080 --> 00:28:26,600
+ميكس ميكس
+
+303
+00:28:39,310 --> 00:28:48,290
+25 over 50 equals the price of eggs 5
+
+304
+00:28:48,290 --> 00:28:56,250
+over 10 it's correct half equals half at 4 here
+
+305
+00:28:56,250 --> 00:29:15,620
+round 4 M U X where is it M U X over M U Y عن طريق
+
+306
+00:29:15,620 --> 00:29:27,540
+الاختصار الاختصار الاختصار
+
+307
+00:29:27,540 --> 00:29:32,720
+الاختصار الاختصار
+
+308
+00:29:32,720 --> 00:29:33,040
+الاختصار الاختصار الاختصار الاختصار
+
+309
+00:29:37,430 --> 00:29:42,010
+أيوة إذا بتلاحظوا الـ
+
+310
+00:29:42,010 --> 00:29:59,690
+Representation هذا المحتوى بالـ Slides طلعوا ليه؟
+
+311
+00:29:59,690 --> 00:30:06,270
+الـ Condition
+
+312
+00:30:06,270 --> 00:30:14,380
+هنا MU for ice cream X for Ben over the marginal
+
+313
+00:30:14,380 --> 00:30:20,860
+utility of cookies for Ben equals the price of X
+
+314
+00:30:20,860 --> 00:30:25,820
+over the price of Y تمام؟ هذا شوهي عبارة عن شوهي
+
+315
+00:30:25,820 --> 00:30:30,480
+marginal rate of substitution of X converted to Y
+
+316
+00:30:30,480 --> 00:30:35,700
+or for Y for Ben تمام؟ the same as for Jerry here
+
+317
+00:30:37,200 --> 00:30:44,300
+مفروض استخدام آيس كريم أو X لجري على مفروض استخدام
+
+318
+00:30:44,300 --> 00:30:50,800
+كوكيز لجري يقل سعر X على سعر Y وهذا هو مفروض عدد
+
+319
+00:30:50,800 --> 00:30:59,680
+المستخدم لجري X for Y تمام؟ الواضح الثاني سأعود
+
+320
+00:30:59,680 --> 00:31:01,740
+قريبًا هنا إلى الطابق
+
+321
+00:31:05,070 --> 00:31:11,810
+الوضع الثاني عندما I إيقار 45 سنطبق الوضع الثاني
+
+322
+00:31:11,810 --> 00:31:18,310
+لتقرر أيه هو الوضع الأفضل أو الوضع الأفضل للسوق
+
+323
+00:31:18,310 --> 00:31:24,670
+الخاص هنا كما ذكرنا أن الوضع الثاني أو الوضع
+
+324
+00:31:24,670 --> 00:31:27,450
+الثاني I إيقار
+
+325
+00:31:29,850 --> 00:31:37,690
+Price of X times QX plus Price of Y times QY. This
+
+326
+00:31:37,690 --> 00:31:44,030
+side must equal this side. The income here is 45
+
+327
+00:31:44,030 --> 00:31:47,550
+must
+
+328
+00:31:47,550 --> 00:31:54,310
+equal the price of X is 5 times QX plus Price of Y
+
+329
+00:31:54,310 --> 00:31:56,470
+is 10 times QY.
+
+330
+00:31:59,010 --> 00:32:06,390
+التي كم هو الـ x و الـ y التي تحصل على أو تحصل على
+
+331
+00:32:06,390 --> 00:32:18,450
+هذا الوضع نجرب عند الخمسة at five four
+
+332
+00:32:18,450 --> 00:32:24,840
+to five must equal خمس مرات كم هي المقاومة لـ X
+
+333
+00:32:24,840 --> 00:32:30,500
+هنا؟ هنا هي المقاومة لـ X ميو X عشرة قيمة X هذا
+
+334
+00:32:30,500 --> 00:32:38,460
+يمثل QX وQX هو أكثر من 4 مرات أكثر من 10 مرات
+
+335
+00:32:38,460 --> 00:32:42,780
+مقاومة Y هنا في خمسة مرات
+
+336
+00:32:50,540 --> 00:32:55,080
+هو أكثر أولاً أو هذا الجانب يكوين هذا الجانب لا
+
+337
+00:32:55,080 --> 00:33:03,420
+أعرف 45 يجب أن يكوين 20 أكثر أكثر أكثر لا يكوين
+
+338
+00:33:03,420 --> 00:33:10,980
+لذلك يجب أن نحقق حالة أخرى يجب أن نحقق حالة أخرى
+
+339
+00:33:10,980 --> 00:33:13,100
+أكثر أكثر أكثر أكثر أكثر أكثر أكثر أكثر أكثر أكثر
+
+340
+00:33:19,470 --> 00:33:25,930
+الكوانت من X هو 5 و 4 هنا الكوانت من Y هو 2 لذلك
+
+341
+00:33:25,930 --> 00:33:32,510
+كوانت من X هو 5 و كوانت من Y هو 2 لذلك دعونا نطبق
+
+342
+00:33:32,510 --> 00:33:42,890
+هنا لذلك في 4 45 يجب أن يكون يجب أن يكون 5 مرة كم
+
+343
+00:33:42,890 --> 00:33:46,670
+هو في 4 هنا؟ 5
+
+344
+00:33:50,280 --> 00:33:57,120
+plus 10 is constant in the formula adequate of y
+
+345
+00:33:57,120 --> 00:34:04,020
+at 4 equals 2 so
+
+346
+00:34:04,020 --> 00:34:18,300
+45 must equal 25 plus 20 yes so 45 equals 25 plus
+
+347
+00:34:41,260 --> 00:34:42,820
+بس يعطي كل عافية 
diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/DjIg7T1qdyk_postprocess.srt b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/DjIg7T1qdyk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8731ee2504cdf0f24cb2aee8442c4967a7e2cbf8
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/DjIg7T1qdyk_postprocess.srt
@@ -0,0 +1,2412 @@
+1
+00:00:21,130 --> 00:00:24,390
+حسنا بسم الله الرحمن الرحيم مرحبا يا عزيزي كيف
+
+2
+00:00:24,390 --> 00:00:29,090
+حالك؟ اليوم سنبدأ في الحلقه الثالثة التي هي مفارقة
+
+3
+00:00:29,090 --> 00:00:34,350
+الإيجار والخارجية لذلك دعونا نذهب إلى مفارقة
+
+4
+00:00:34,350 --> 00:00:41,010
+الإيجار إذا تذكر في أسلوب أو التفاصيل الميكرو
+
+5
+00:00:41,010 --> 00:00:44,790
+إيقناميكس لقد قررنا أسلوب Production Possibility
+
+6
+00:00:44,790 --> 00:00:50,510
+Frontierالذي يمثل مقاومة أكتر في البلد عندما
+
+7
+00:00:50,510 --> 00:00:56,130
+تستخدم جميع مصادرها لإنتاج حركتين مختلفة عندما
+
+8
+00:00:56,130 --> 00:01:01,310
+يستخدم البلد جميع مصادرها يتمكن من إنتاج أو إذا
+
+9
+00:01:01,310 --> 00:01:06,950
+كان هناك موظف كام للمصادر أو جميع مصادرها استخدمت
+
+10
+00:01:06,950 --> 00:01:12,050
+بطريقة مفيدة أو موظف كام في هذه الحالة يتمكن من
+
+11
+00:01:12,050 --> 00:01:19,490
+إنتاجالنسبة للـPPF فكل نقطة موجهة للـPPF يعني أن
+
+12
+00:01:19,490 --> 00:01:25,310
+جميع مصادرنا مستخدمة بطريقة مفيدة أو مستخدمة
+
+13
+00:01:25,310 --> 00:01:27,010
+بطريقة مستخدمة بطريقة مستخدمة بطريقة مستخدمة
+
+14
+00:01:27,010 --> 00:01:27,690
+بطريقة مستخدمة بطريقة مستخدمة بطريقة مستخدمة
+
+15
+00:01:27,690 --> 00:01:31,030
+بطريقة مستخدمة بطريقة مستخدمة بطريقة مستخدمة
+
+16
+00:01:31,030 --> 00:01:33,510
+بطريقة مستخدمة بطريقة مستخدمة بطريقة مستخدمة
+
+17
+00:01:33,510 --> 00:01:33,710
+بطريقة مستخدمة بطريقة مستخدمة بطريقة مستخدمة
+
+18
+00:01:33,710 --> 00:01:39,290
+بطريقة مستخدمة بطريقة مستخدمة بطريقة مستخدمة
+
+19
+00:01:39,290 --> 00:01:43,390
+بطريقة مستخدمة
+
+20
+00:01:43,390 --> 00:01:56,320
+بطعلى نقطة تقريبا، حسنا، دعنا نذهب إلى شيء آخر، كل
+
+21
+00:01:56,320 --> 00:02:02,060
+نقطة هنا تتجاوز الـPPF تمثل
+
+22
+00:02:02,060 --> 00:02:09,710
+إيجابية إيجابيةكل نقطة هنا في البلد تنتج في نقطة a
+
+23
+00:02:09,710 --> 00:02:18,530
+او b او c او d هذه النقطة a,b,c,d,e,f تمثل افعالية
+
+24
+00:02:18,530 --> 00:02:26,070
+النجاح النجاحية نقطة a,b,c,d هم نقطة نجاحية
+
+25
+00:02:26,070 --> 00:02:32,770
+النجاحية ماذا عن طرق ال PPF؟
+
+26
+00:02:35,170 --> 00:02:39,570
+سلوب الPPF هنا نقاط نقاط نقاط نقاط نقاط نقاط نقاط
+
+27
+00:02:39,570 --> 00:02:41,650
+نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط
+
+28
+00:02:41,650 --> 00:02:50,050
+نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط
+
+29
+00:02:50,050 --> 00:02:52,330
+نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط
+
+30
+00:02:52,330 --> 00:02:52,370
+نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط نقاط
+
+31
+00:02:52,370 --> 00:03:03,870
+نقاط نقاط نقاط نقاط نقاط نقاط نقاط
+
+32
+00:03:03,870 --> 00:03:12,730
+نهذا الوضع يقوم بإعادة أكتر أو أكتر وهذا الوضع
+
+33
+00:03:12,730 --> 00:03:17,090
+يقوم بإعادة أكتر أو أكتر أو أكتر أو أكتر أو أكتر
+
+34
+00:03:17,090 --> 00:03:19,430
+أو أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو
+
+35
+00:03:19,430 --> 00:03:20,150
+أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو
+
+36
+00:03:20,150 --> 00:03:20,690
+أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو
+
+37
+00:03:20,690 --> 00:03:21,810
+أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو
+
+38
+00:03:21,810 --> 00:03:22,830
+أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو أكتر أو
+
+39
+00:03:22,830 --> 00:03:35,470
+أكتر أو أكتر أو
+
+40
+00:03:35,470 --> 00:03:43,950
+أبإمكاننا تغيير عقد الفرصة إلى عقد المجال أو عقد
+
+41
+00:03:43,950 --> 00:03:51,370
+المجال الاجتماعي، فعقد المجال هنا هو عقد المجال
+
+42
+00:03:51,370 --> 00:04:01,520
+الاجتماعيلأن افضل مستخدم هو أو يمثل دلتا كيو هنا
+
+43
+00:04:01,520 --> 00:04:11,000
+أو كما يزداد كوانتوم X يجب أن نخسر كميات أكتر من Y
+
+44
+00:04:11,000 --> 00:04:14,140
+دعونا
+
+45
+00:04:14,140 --> 00:04:16,300
+نذهب إلى تجارب تسريعية
+
+46
+00:04:18,570 --> 00:04:21,370
+الفرق بين الاستثمار الاستثمار الاستثمار الاستثمار
+
+47
+00:04:21,370 --> 00:04:22,230
+الاستثمار الاستثمار الاستثمار الاستثمار الاستثمار
+
+48
+00:04:22,230 --> 00:04:24,030
+الاستثمار الاستثمار الاستثمار الاستثمار الاستثمار
+
+49
+00:04:24,030 --> 00:04:27,550
+الاستثمار الاستثمار الاستثمار الاستثمار الاستثمار
+
+50
+00:04:27,550 --> 00:04:32,170
+الاستثمار الاستثمار الاستثمار الاستثمار الاستثمار
+
+51
+00:04:32,170 --> 00:04:36,550
+الاستثمار الاستثمار الاستثمار الاستثمار الاستثمار
+
+52
+00:04:36,550 --> 00:04:46,610
+الاستثمار الاستثمار الاستثمار الاستثمار الاستثم
+
+53
+00:04:48,590 --> 00:04:56,510
+أو مراجع السياسي يمكن أن يكون مراجعته بسلوك افضل
+
+54
+00:04:56,510 --> 00:05:03,450
+كما تزداد كوانتك افضل مراجع السياسي يزداد افضل او
+
+55
+00:05:03,450 --> 00:05:11,240
+مراجع السياسي يزداد كوانتك افضلعن طريق الانتقال
+
+56
+00:05:11,240 --> 00:05:14,660
+الأعلى، كما أن المجموعة التي ينتج الفيزا يتزاوز
+
+57
+00:05:14,660 --> 00:05:18,640
+المجموعة التي تنتج الفيزا يتزاوز المجموعة التي
+
+58
+00:05:18,640 --> 00:05:20,200
+تنتج الفيزا يتزاوز المجموعة التي تنتج الفيزا
+
+59
+00:05:20,200 --> 00:05:24,820
+يتزاوز المجموعة التي تنتج الفيزا يتزاوز المجموعة
+
+60
+00:05:24,820 --> 00:05:26,520
+التي تنتج الفيزا يتزاوز المجموعة التي تنتج الفيزا
+
+61
+00:05:26,520 --> 00:05:29,660
+يتزاوز المجموعة التي تنتج الفيزا يتزاوز المجموعة
+
+62
+00:05:29,660 --> 00:05:31,000
+التي تنتج الفيزا يتزاوز المجموعة التي تنتج الفيزا
+
+63
+00:05:31,000 --> 00:05:35,040
+يتزاوز المجموعة التي تنتج الفيزا
+
+64
+00:05:35,040 --> 00:05:39,020
+يتزاكما ذكرنا أن الـ Productive Efficiency يتجارب
+
+65
+00:05:39,020 --> 00:05:45,780
+تحت الـ PPF كل نقطة تتجارب تحت ال PPF تقوم بتجارب
+
+66
+00:05:45,780 --> 00:05:50,880
+الـ Productive Efficiency وهذا يعني أن هذه النقطة
+
+67
+00:05:50,880 --> 00:05:56,720
+تم تجاربها بسرعة أو المصادر تم استخدامها بسرعة
+
+68
+00:05:56,720 --> 00:06:02,740
+ماذا عن الـ Allocative Efficiency؟
+
+69
+00:06:12,330 --> 00:06:14,630
+هناك فرق بين الـ Allocative و الـ Productive
+
+70
+00:06:14,630 --> 00:06:19,050
+Efficiency قبل أن أذهب إلى الـ Allocative
+
+71
+00:06:19,050 --> 00:06:24,810
+Efficiency، لدي سؤال كما ذكرنا أن كل نقطة هنا
+
+72
+00:06:24,810 --> 00:06:29,830
+تعطينا إيه؟ إيه Productive Efficiency ولكن السؤال
+
+73
+00:06:29,830 --> 00:06:38,890
+المهم هو، أين يمكن أن يقرر البلد أن تصنع؟في A أو B
+
+74
+00:06:38,890 --> 00:06:45,590
+أو C أو D أو E أو F؟ أين هو الوضع الأفضل للمجتمع؟
+
+75
+00:06:45,590 --> 00:06:52,570
+كيف يستطيع .. كيف يستطيع البلد تقرر أن تعمل أو
+
+76
+00:06:52,570 --> 00:06:58,590
+تصنع هنا؟ هذا يعتمد على ماذا؟ عليها للمجتمع، هذا
+
+77
+00:06:58,590 --> 00:07:03,870
+يعتمد على الاختيارات للمجتمع. أحيانًا، إذا كانت
+
+78
+00:07:03,870 --> 00:07:04,630
+الحكومة تحتاج
+
+79
+00:07:07,730 --> 00:07:16,580
+هنا في هذا النقطة، في نقطة E هما مصادرهم5 CDs و 4
+
+80
+00:07:16,580 --> 00:07:21,940
+سلسلة بيزا فهي جيدة لهم و هذا يعتمد على احتاجاتهم
+
+81
+00:07:21,940 --> 00:07:26,240
+و احتياطاتهم و بعض الوقت احتياطاتهم او احتياطاتهم
+
+82
+00:07:26,240 --> 00:07:32,300
+قد يكونوا في نقطة D و يحتاجوا باعتبارهم 9 قطعة CD
+
+83
+00:07:32,300 --> 00:07:41,170
+و 3 قطعة بيزا و هذا يعتمد على احتياطاتهمإذا قرر
+
+84
+00:07:41,170 --> 00:07:53,250
+الحكومة أو البلد أن تعمل على نقطة D هنا، يمكننا أن
+
+85
+00:07:53,250 --> 00:07:58,710
+نسميها نقطة الـ Allocative
+
+86
+00:07:58,710 --> 00:07:59,470
+Efficiency
+
+87
+00:08:06,070 --> 00:08:11,010
+مثل الـ CIC الاندفع الاجتماعي أو الاندفع الاجتماعي
+
+88
+00:08:11,010 --> 00:08:17,470
+الاجتماعي الاجتماعي
+
+89
+00:08:17,470 --> 00:08:28,410
+الاجتماعي الاجتماعي الاجتماعي
+
+90
+00:08:28,410 --> 00:08:30,450
+CIC
+
+91
+00:08:32,660 --> 00:08:36,140
+ما هو أفضل بالنسبة للمجتمع؟ ممكن أن يكون الاندفع
+
+92
+00:08:36,140 --> 00:08:46,900
+الاجتماعي 1 أو 2؟ 2 أفضل من 1 لأن هنا ما هو أفضل؟
+
+93
+00:08:46,900 --> 00:08:55,840
+B أو D؟ D أفضل من B في B، حسنًا، فهو يحصل على
+
+94
+00:08:55,840 --> 00:09:00,720
+تأثير المصادرولكن نستطيع أن نحصل هنا على استخدام
+
+95
+00:09:00,720 --> 00:09:03,720
+أو بينامي تجارب التجارب التجارب التجارب التجارب
+
+96
+00:09:03,720 --> 00:09:05,320
+التجارب التجارب التجارب التجارب التجارب التجارب
+
+97
+00:09:05,320 --> 00:09:05,780
+التجارب التجارب التجارب التجارب التجارب التجارب
+
+98
+00:09:05,780 --> 00:09:07,280
+التجارب التجارب التجارب التجارب التجارب التجارب
+
+99
+00:09:07,280 --> 00:09:07,580
+التجارب التجارب التجارب التجارب التجارب التجارب
+
+100
+00:09:07,580 --> 00:09:08,760
+التجارب التجارب التجارب التجارب التجارب التجارب
+
+101
+00:09:08,760 --> 00:09:08,800
+التجارب التجارب التجارب التجارب التجارب التجارب
+
+102
+00:09:08,800 --> 00:09:24,220
+التجارب التجارب التجارب التج
+
+103
+00:09:25,730 --> 00:09:31,830
+هو النقطة الأفضل أو نسميها نسميها نسميها نسميها
+
+104
+00:09:31,830 --> 00:09:32,770
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+105
+00:09:32,770 --> 00:09:37,110
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+106
+00:09:37,110 --> 00:09:38,990
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+107
+00:09:38,990 --> 00:09:40,970
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+108
+00:09:40,970 --> 00:09:41,010
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+109
+00:09:41,010 --> 00:09:44,310
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+110
+00:09:44,310 --> 00:09:51,130
+نسميها نسميها نسميها نسميها نسميها نسميها نسميها
+
+111
+00:09:51,130 --> 00:09:55,160
+نسمهو محتاج لإيجار إيجار الـ Allocative
+
+112
+00:09:55,160 --> 00:10:01,180
+Efficiency؟ الوضع هنا A يحصل أو يقوم بإيجار الـ
+
+113
+00:10:01,180 --> 00:10:04,880
+Productive Efficiency B يحصل أو يقوم بإيجار الـ
+
+114
+00:10:04,880 --> 00:10:09,080
+Productive Efficiency ولكنه لا يعطينا أو يحصل
+
+115
+00:10:09,080 --> 00:10:12,080
+إيجار الـ Allocative Efficiency ولكن الوضع
+
+116
+00:10:12,080 --> 00:10:17,240
+Allocative Efficient يحصل
+
+117
+00:10:17,240 --> 00:10:18,500
+إيجار الـ Productive Efficiency
+
+118
+00:10:23,130 --> 00:10:26,850
+طيب، let's go to something else، what do we see
+
+119
+00:10:26,850 --> 00:10:30,170
+here؟ as we mentioned before that the indifference
+
+120
+00:10:30,170 --> 00:10:34,430
+curve،
+
+121
+00:10:34,430 --> 00:10:39,590
+this is the community indifference curveوهو
+
+122
+00:10:39,590 --> 00:10:46,390
+المجموعة التي تتمتع بـ X وY التي تعطي أو يعطي نفس
+
+123
+00:10:46,390 --> 00:10:50,010
+المفاتيح الكامة أو نفس المفاتيح الكامة. لذلك، دعنا
+
+124
+00:10:50,010 --> 00:10:53,190
+نعتمد على أن المفاتيح الكامة التي تمتع بها في
+
+125
+00:10:53,190 --> 00:10:57,950
+المجموعة الاختلافية تقريبًا 1 يقل 50. هذا يعني أن
+
+126
+00:10:57,950 --> 00:11:02,170
+هذا المجموعة التي تمتع بـ X ومجموعة يتمتع بـ Y
+
+127
+00:11:03,540 --> 00:11:07,540
+النقطة الـ H تحت مقاطع الانتجار المجتمعي تدفع أو
+
+128
+00:11:07,540 --> 00:11:12,220
+تدفع نفس ال .. ماذا؟ نفس الاختصارات الكاملة
+
+129
+00:11:12,220 --> 00:11:16,640
+للمجتمع، فهذه هي الاختصارات الكاملة للمجتمع أو
+
+130
+00:11:16,640 --> 00:11:20,360
+الاختصارات الكاملة الاجتماعية الاختصارات الكاملة
+
+131
+00:11:20,360 --> 00:11:26,580
+الاجتماعية هنا هي 50 ما رأيك؟ الاختصارات الكاملة
+
+132
+00:11:26,580 --> 00:11:30,440
+الاجتماعية هذه هي الاختصارات الكاملة الاجتماعية
+
+133
+00:11:30,440 --> 00:11:32,240
+الاختصار
+
+134
+00:11:33,710 --> 00:11:39,370
+الصحيحات الاجتماعية هنا تقريبا تقريبا
+
+135
+00:11:39,370 --> 00:11:40,550
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+136
+00:11:40,550 --> 00:11:41,170
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+137
+00:11:41,170 --> 00:11:41,230
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+138
+00:11:41,230 --> 00:11:41,250
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+139
+00:11:41,250 --> 00:11:44,890
+تقريبا تقريبا تقريبا
+
+140
+00:11:44,890 --> 00:11:49,550
+تقريبا
+
+141
+00:11:49,550 --> 00:11:53,870
+تقريبا
+
+142
+00:11:53,870 --> 00:11:57,470
+ت
+
+143
+00:12:02,810 --> 00:12:11,070
+هي تتخلص، تتخلص، هنا السلوك مرتفع، تتخلص كمان كمان
+
+144
+00:12:11,070 --> 00:12:12,350
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+145
+00:12:12,350 --> 00:12:13,110
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+146
+00:12:13,110 --> 00:12:17,070
+كمان كمان كمان كمان
+
+147
+00:12:17,070 --> 00:12:20,150
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+148
+00:12:20,150 --> 00:12:28,350
+كمان كمان كمان كمان كمان كمان
+
+149
+00:12:34,160 --> 00:12:40,080
+عن طريق عبارة عن قيمة الـ QX1 كم هو عبارة عن عبارة
+
+150
+00:12:40,080 --> 00:12:40,720
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+151
+00:12:40,720 --> 00:12:44,840
+عبارة عن عبارة عن عبارة عن عبارة
+
+152
+00:12:44,840 --> 00:12:50,680
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+153
+00:12:50,680 --> 00:12:50,880
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+154
+00:12:50,880 --> 00:12:52,380
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+155
+00:12:52,380 --> 00:12:52,500
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+156
+00:12:52,500 --> 00:12:57,040
+عبارة عن عبارة عن عبار
+
+157
+00:13:00,910 --> 00:13:04,530
+وأخيرًا يصبح صحيحًا صحيحًا صحيحًا صحيحًا صحيحًا
+
+158
+00:13:04,530 --> 00:13:06,310
+صحيحًا صحيحًا صحيحًا صحيحًا صحيحًا صحيحًا صحيحًا
+
+159
+00:13:06,310 --> 00:13:08,610
+صحيحًا صحيحًا صحيحًا صحيحًا صحيحة صحيحة صحيحة
+
+160
+00:13:08,610 --> 00:13:15,590
+صحيحة
+
+161
+00:13:15,590 --> 00:13:20,470
+صحيحة صحيحة صحيحة صحيحة صحيحة صحيحة صحيحة صحيحة
+
+162
+00:13:20,470 --> 00:13:20,710
+صحيحة صحيحة صحيحة صحيحة صحيحة صحيحة صحيحة صحيحة
+
+163
+00:13:20,710 --> 00:13:26,410
+صحيحة صحيحة صحيحة صحيح
+
+164
+00:13:30,350 --> 00:13:33,410
+هذه هي الحفرة الاجتماعية الاجتماعية الاجتماعية
+
+165
+00:13:33,410 --> 00:13:37,570
+الاجتماعية
+
+166
+00:13:37,570 --> 00:13:41,130
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+167
+00:13:41,130 --> 00:13:41,990
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+168
+00:13:41,990 --> 00:13:43,670
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+169
+00:13:43,670 --> 00:13:44,950
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+170
+00:13:44,950 --> 00:13:45,130
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+171
+00:13:45,130 --> 00:13:46,690
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+172
+00:13:46,690 --> 00:13:49,750
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+173
+00:13:49,750 --> 00:13:56,150
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية الاجفي
+
+174
+00:13:56,150 --> 00:14:01,050
+هذا النقطة اللي هي النقطة الأفضل الصحيوية الأفضل
+
+175
+00:14:01,050 --> 00:14:04,610
+النقطة اللي هي النقطة اللي هي النقطة اللي هي
+
+176
+00:14:04,610 --> 00:14:05,290
+النقطة اللي هي النقطة اللي هي النقطة اللي هي
+
+177
+00:14:05,290 --> 00:14:05,930
+النقطة اللي هي النقطة اللي هي النقطة اللي هي
+
+178
+00:14:05,930 --> 00:14:05,950
+النقطة اللي هي النقطة اللي هي النقطة اللي هي
+
+179
+00:14:05,950 --> 00:14:06,010
+النقطة اللي هي النقطة اللي هي النقطة اللي هي
+
+180
+00:14:06,010 --> 00:14:06,550
+النقطة اللي هي النقطة اللي هي النقطة اللي هي
+
+181
+00:14:06,550 --> 00:14:07,410
+النقطة اللي هي النقطة اللي هي النقطة اللي هي نقطة
+
+182
+00:14:07,410 --> 00:14:07,690
+اللي هي نقطة اللي هي نقطة اللي هي نقطة اللي هي
+
+183
+00:14:07,690 --> 00:14:12,830
+نقطة اللي هي نقطة اللي
+
+184
+00:14:12,830 --> 00:14:25,730
+هي نقطة اللي هي نقطة اللي هي نقطة اللي هي نقط
+
+185
+00:14:27,090 --> 00:14:30,610
+السلوك في الPPF وهو مجموعات الشركات الاجتماعية هي
+
+186
+00:14:30,610 --> 00:14:36,470
+مجموعات الشركات الاجتماعية وهو مجموعات الشركات
+
+187
+00:14:36,470 --> 00:14:37,550
+الاجتماعية هي مجموعات الشركات الاجتماعية هي
+
+188
+00:14:37,550 --> 00:14:42,330
+مجموعات الشركات الاجتماعية هي مجموعات الشركات
+
+189
+00:14:42,330 --> 00:14:43,750
+الاجتماعية هي مجموعات الشركات الاجتماعية هي
+
+190
+00:14:43,750 --> 00:14:45,590
+مجموعات الشركات الاجتماعية هي مجموعات الشركات
+
+191
+00:14:45,590 --> 00:14:45,750
+الاجتماعية هي مجموعات الشركات الاجتماعية هي
+
+192
+00:14:45,750 --> 00:14:45,870
+الاجتماعية هي مجموعات الشركات الاجتماعية هي
+
+193
+00:14:45,870 --> 00:14:48,730
+مجموعات الشركات الاجتماعية هي مج
+
+194
+00:14:54,660 --> 00:14:58,000
+أكيرزوين الـ Marginal Social Benefits equaled the
+
+195
+00:14:58,000 --> 00:14:59,380
+Marginal Social Cost.
+
+196
+00:15:01,960 --> 00:15:05,960
+At this point here, how much is the quantity X
+
+197
+00:15:05,960 --> 00:15:06,540
+free?
+
+198
+00:15:09,660 --> 00:15:15,880
+And the quantity of CDs may be in line. So if we
+
+199
+00:15:15,880 --> 00:15:21,670
+want to drawأو لتحرير النقطة الأفضل للاجتماعات،
+
+200
+00:15:21,670 --> 00:15:25,370
+نستطيع أن نرسم النقاط الاجتماعي الاجتماعي والنقاط
+
+201
+00:15:25,370 --> 00:15:27,490
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+202
+00:15:27,490 --> 00:15:32,810
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+203
+00:15:32,810 --> 00:15:38,070
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+204
+00:15:38,070 --> 00:15:39,530
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+205
+00:15:39,530 --> 00:15:44,950
+الاج
+
+206
+00:15:45,420 --> 00:15:51,200
+هذه المقارنة تتميز بـ Marginal Social Benefits في
+
+207
+00:15:51,200 --> 00:15:52,940
+مقارنة الـ Marginal Social Cost مقارنة الـ
+
+208
+00:15:52,940 --> 00:15:57,240
+Marginal Social Cost مقارنة
+
+209
+00:15:57,240 --> 00:15:59,600
+الـ Marginal Social Cost مقارنة الـ Marginal
+
+210
+00:15:59,600 --> 00:15:59,860
+Social Cost مقارنة الـ Marginal Social Cost مقارنة
+
+211
+00:15:59,860 --> 00:16:00,120
+الـ Marginal Social Cost مقارنة الـ Marginal
+
+212
+00:16:00,120 --> 00:16:02,480
+Social Cost مقارنة الـ Marginal Social Cost مقارنة
+
+213
+00:16:02,480 --> 00:16:03,600
+الـ Marginal Social Cost مقارنة الـ Marginal
+
+214
+00:16:03,600 --> 00:16:05,020
+الـ Marginal Social Cost مقارنة الـ Marginal
+
+215
+00:16:05,020 --> 00:16:12,840
+Social Cost مقارنة الـ Marginal
+
+216
+00:16:12,840 --> 00:16:20,620
+Socialالنقطة D هنا، حسنا، هذا هو النقطة D،
+
+217
+00:16:20,620 --> 00:16:27,000
+المقاومة للبيتزا هنا، مقاومة أفضل لبيتزا تقريبا
+
+218
+00:16:27,000 --> 00:16:31,760
+ثلاثة وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+219
+00:16:31,760 --> 00:16:31,780
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+220
+00:16:31,780 --> 00:16:32,300
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+221
+00:16:32,300 --> 00:16:33,180
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+222
+00:16:33,180 --> 00:16:33,260
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+223
+00:16:33,260 --> 00:16:41,980
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+224
+00:16:41,980 --> 00:16:53,910
+وبنشطة نشطة نشطة نشطة
+
+225
+00:16:53,910 --> 00:17:01,170
+نشطة نشطة نشطة نشطة نشطة نشطة نشطة نشطة نشطة نشطة
+
+226
+00:17:01,170 --> 00:17:09,330
+نشطة
+
+227
+00:17:09,330 --> 00:17:12,330
+نشطة
+
+228
+00:17:13,390 --> 00:17:17,930
+هي أكتر من قيمة الاجتماع الاجتماعي، لذلك في
+
+229
+00:17:17,930 --> 00:17:23,190
+المقاومة تحت اقليبريا أو المقاومة الأفضل أو
+
+230
+00:17:23,190 --> 00:17:26,030
+المقاومة الاجتماعية الأفضل المقاومة الاجتماعية
+
+231
+00:17:26,030 --> 00:17:31,850
+الاجتماعية هنا لأن المقاومة تحت مقاومة الاجتماعي
+
+232
+00:17:31,850 --> 00:17:34,930
+الاجتماعي هي أكتر من قيمة الاجتماع الاجتماعي
+
+233
+00:17:34,930 --> 00:17:38,010
+كمقاومة
+
+234
+00:17:38,010 --> 00:17:41,830
+الاجتماعي الاجتماعيوهو أكتر من مجموعاتنا
+
+235
+00:17:41,830 --> 00:17:46,630
+الاجتماعية لأننا يجب أن نزعج مصادقنا وانتاجنا من
+
+236
+00:17:46,630 --> 00:17:51,030
+الفيزا كمجموعاتنا الاجتماعية لأننا يجب أن نزعج
+
+237
+00:17:51,030 --> 00:17:56,030
+مصادقنا وانتاجنا من الفيزا كمجموعاتنا الاجتماعية
+
+238
+00:17:56,030 --> 00:18:03,610
+لأننا يجب أن نزعج مصادقنا وانتاجنا من الفيزا
+
+239
+00:18:06,130 --> 00:18:12,590
+ماذا إذا إنتجة البيتزا و الانتجة كانت أكبر من
+
+240
+00:18:12,590 --> 00:18:20,250
+ثلاثة في أربعة سنة؟ هذا
+
+241
+00:18:20,250 --> 00:18:25,250
+هو النقطة الأفضل في المجتمع و لدينا إنتجة أكبر من
+
+242
+00:18:25,250 --> 00:18:31,910
+ثلاثة بيتزا في أربعة سنة؟ ماذا نرى؟ مجموعة الانتجة
+
+243
+00:18:31,910 --> 00:18:39,370
+السياسيةهو أكتر من ميزات الاجتماعات الاجتماعية وهو
+
+244
+00:18:39,370 --> 00:18:43,230
+ميزات
+
+245
+00:18:43,230 --> 00:18:48,990
+الاجتماعات الاجتماعية ميزات الاجتماعات الاجتماعية
+
+246
+00:18:50,130 --> 00:18:53,490
+عندما يكون قيمة المجال الاجتماعي أكبر من مجال
+
+247
+00:18:53,490 --> 00:18:56,050
+المجال الاجتماعي، يجب أن نتخلص من مجال المجال
+
+248
+00:18:56,050 --> 00:18:59,410
+الاجتماعي لكي نصل إلى اقتصاد اقتصادي او اقتصاد
+
+249
+00:18:59,410 --> 00:19:04,770
+اقتصادي الاجتماعي لكي
+
+250
+00:19:04,770 --> 00:19:09,770
+نصل إلى اقتصاد اقتصادي او اقتصادي اقتصادي اقتصادي
+
+251
+00:19:09,770 --> 00:19:12,490
+اقتصادي اقتصادي اقتصادي اقتصادي اقتصادي اقتصادي
+
+252
+00:19:12,490 --> 00:19:12,570
+اقتصادي اقتصادي اقتصادي اقتصادي اقتصادي اقتصادي
+
+253
+00:19:12,570 --> 00:19:12,630
+اقتصادي اقتصادي اقتصادي اقتصادي اقتصادي اقتصادي
+
+254
+00:19:12,630 --> 00:19:15,490
+اقتصادي اقتصادي اقتصا
+
+255
+00:19:16,640 --> 00:19:22,180
+لنذهب إلى مثال عملي هنا لنقوم بتخطيط الأفعار
+
+256
+00:19:22,180 --> 00:19:24,180
+المجانية ومجانية الأسعار المجانية ونتأكد من
+
+257
+00:19:24,180 --> 00:19:28,380
+الانتقال ومن الانتقال الاجتماعي والاقتصادي للمجتمع
+
+258
+00:19:28,380 --> 00:19:32,940
+هنا لدينا
+
+259
+00:19:32,940 --> 00:19:38,660
+قائمة التابعات التالية هذه محتاجة لإنتاج وإتصال
+
+260
+00:19:38,660 --> 00:19:44,520
+بيتزا0 1 2 3 4 5 6 7 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+261
+00:19:44,520 --> 00:19:48,880
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+262
+00:19:48,880 --> 00:19:50,840
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+263
+00:19:50,840 --> 00:19:55,220
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+264
+00:19:55,220 --> 00:19:55,600
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+265
+00:19:55,600 --> 00:19:58,680
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+266
+00:19:58,680 --> 00:19:58,900
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+267
+00:19:58,900 --> 00:20:04,740
+9أو نحن سنختار النقطة الاجتماعية الاجتماعية النقطة
+
+268
+00:20:04,740 --> 00:20:10,460
+التي تقوم بإعادة الاحتياطات للمجتمع، ثم يجب أن
+
+269
+00:20:10,460 --> 00:20:12,000
+نخطط النجوم الاجتماعي الاجتماعي الاجتماعي
+
+270
+00:20:12,000 --> 00:20:16,180
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+271
+00:20:16,180 --> 00:20:20,360
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+272
+00:20:20,360 --> 00:20:21,560
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+273
+00:20:21,560 --> 00:20:22,880
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+274
+00:20:22,880 --> 00:20:29,000
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاج
+
+275
+00:20:29,680 --> 00:20:33,400
+هنا نحن لدينا أهمية المجتمع المجتمع المجتمع
+
+276
+00:20:33,400 --> 00:20:35,920
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+277
+00:20:35,920 --> 00:20:40,560
+المجتمع المجتمع
+
+278
+00:20:40,560 --> 00:20:47,740
+المجتمع المجتمع
+
+279
+00:20:47,740 --> 00:20:53,280
+المجتمع المجتمع المجتمع المجتمع
+
+280
+00:20:53,280 --> 00:20:56,440
+المجتمع
+
+281
+00:20:56,440 --> 00:20:59,080
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+282
+00:20:59,080 --> 00:20:59,160
+المجتمع المجتمع المجتمع المجتمع المجتمع المجتمع
+
+283
+00:20:59,160 --> 00:21:00,220
+المجتمع المجتمع المجتمع المجتمع المجتمع المالأموال
+
+284
+00:21:00,220 --> 00:21:02,500
+المجانية أو الأموال المجانية والمجانية الاجتماعية
+
+285
+00:21:02,500 --> 00:21:09,580
+تقريبا تقريبا تقريبا
+
+286
+00:21:09,580 --> 00:21:11,400
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+287
+00:21:11,400 --> 00:21:11,420
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+288
+00:21:11,420 --> 00:21:11,440
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+289
+00:21:11,440 --> 00:21:11,680
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+290
+00:21:11,680 --> 00:21:12,540
+تقريبا
+
+291
+00:21:24,410 --> 00:21:28,390
+لكن ليس الانتجار، فهو التغيير في الميزات الكاملة
+
+292
+00:21:28,390 --> 00:21:32,650
+عبر التغيير في الميزة المستخدمة من X أو Z أربعة،
+
+293
+00:21:32,650 --> 00:21:41,370
+وهو في الحالة الأولى 25
+
+294
+00:21:41,370 --> 00:21:51,310
+-0 عبر 1-0 كميزة مستخدمة، ف25-0 over 1 minus 0
+
+295
+00:21:51,310 --> 00:21:55,630
+equals 25 over 1 equals 25 this is the first case
+
+296
+00:21:55,630 --> 00:21:59,350
+here and
+
+297
+00:21:59,350 --> 00:22:06,910
+then 45 minus 25 over 2 minus 1 equals 20 and you
+
+298
+00:22:06,910 --> 00:22:13,460
+see the marginal benefitsتتخلص عندما تتخلص المقادة
+
+299
+00:22:13,460 --> 00:22:19,840
+من البيتزا من البيتزا من البيتزا من البيتزا من
+
+300
+00:22:19,840 --> 00:22:20,780
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+301
+00:22:20,780 --> 00:22:21,180
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+302
+00:22:21,180 --> 00:22:21,740
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+303
+00:22:21,740 --> 00:22:23,260
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+304
+00:22:23,260 --> 00:22:28,140
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+305
+00:22:28,140 --> 00:22:28,960
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+306
+00:22:28,960 --> 00:22:29,940
+البيتزا من البيتزا من البيتزا من البيتزا من
+
+307
+00:22:29,940 --> 00:22:37,520
+البيتزا من البيتزا من
+
+308
+00:22:37,520 --> 00:22:39,420
+البيت
+
+309
+00:22:40,610 --> 00:22:46,030
+مارجينال كوست اقل او مارجينال سوشيال كوست اقل
+
+310
+00:22:46,030 --> 00:22:51,810
+تغيير التواصل التواصل التواصل التواصل التواصل
+
+311
+00:22:51,810 --> 00:22:52,490
+التواصل التواصل التواصل التواصل التواصل التواصل
+
+312
+00:22:52,490 --> 00:22:52,950
+التواصل التواصل التواصل التواصل التواصل التواصل
+
+313
+00:22:52,950 --> 00:22:58,150
+التواصل التواصل التواصل التواصل التواصل التواصل
+
+314
+00:22:58,150 --> 00:22:59,290
+التواصل التواصل التواصل التواصل التواصل التواصل
+
+315
+00:22:59,290 --> 00:22:59,350
+التواصل التواصل التواصل التواصل التواصل التواصل
+
+316
+00:22:59,350 --> 00:23:09,450
+التواص
+
+317
+00:23:10,350 --> 00:23:18,170
+7-3 over 2 minus 1 equals 4 and yeah increasing as
+
+318
+00:23:18,170 --> 00:23:21,050
+you see that the marginal cost the marginal social
+
+319
+00:23:21,050 --> 00:23:25,010
+cost is increasing as much as the quantity of X
+
+320
+00:23:25,010 --> 00:23:30,730
+increases so produced X increases 0, 3, 4, 6, 10,
+
+321
+00:23:30,850 --> 00:23:36,610
+14, 20, 23 so the marginal cost we will see that
+
+322
+00:23:36,610 --> 00:23:40,710
+the marginal cost is increasing hereهذا هو قيمة
+
+323
+00:23:40,710 --> 00:23:42,970
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+324
+00:23:42,970 --> 00:23:45,450
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+325
+00:23:45,450 --> 00:23:47,690
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+326
+00:23:47,690 --> 00:23:48,050
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+327
+00:23:48,050 --> 00:23:51,070
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+328
+00:23:51,070 --> 00:23:51,510
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+329
+00:23:51,510 --> 00:23:53,370
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+330
+00:23:53,370 --> 00:23:56,450
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+331
+00:23:56,450 --> 00:23:57,930
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية الاج
+
+332
+00:24:02,590 --> 00:24:07,430
+النقطة الأفضل هي النقطة التي يعطينا هنا أو النقطة
+
+333
+00:24:07,430 --> 00:24:10,210
+التي يعطينا النجاة الاجتماعية الاجتماعية
+
+334
+00:24:10,210 --> 00:24:12,510
+الاجتماعية الاجتماعية الاجتماعية هنا نستطيع أن
+
+335
+00:24:12,510 --> 00:24:15,710
+نقول أو نستطيع أن نقول أن نستطيع أن نستطيع أن نقول
+
+336
+00:24:15,710 --> 00:24:17,390
+أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع
+
+337
+00:24:17,390 --> 00:24:17,990
+أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع
+
+338
+00:24:17,990 --> 00:24:19,610
+أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع
+
+339
+00:24:19,610 --> 00:24:19,630
+أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع
+
+340
+00:24:19,630 --> 00:24:24,370
+أن نستطيع أن
+
+341
+00:24:24,370 --> 00:24:29,100
+نستطعلى هذا النقطة، الاحتياطات المجانية تسيطر على
+
+342
+00:24:29,100 --> 00:24:32,740
+مجال الاحتياطات المجانية تسيطر على مجال الاحتياطات
+
+343
+00:24:32,740 --> 00:24:33,220
+المجانية تسيطر على مجال الاحتياطات المجانية تسيطر
+
+344
+00:24:33,220 --> 00:24:34,620
+على مجال الاحتياطات المجانية تسيطر على مجال
+
+345
+00:24:34,620 --> 00:24:36,380
+الاحتياطات المجانية تسيطر على مجال الاحتياطات
+
+346
+00:24:36,380 --> 00:24:37,860
+المجانية تسيطر على مجال الاحتياطات المجانية تسيطر
+
+347
+00:24:37,860 --> 00:24:39,620
+على مجال الاحتياطات المجانية تسيطر على مجال
+
+348
+00:24:39,620 --> 00:24:42,020
+الاحتياطات المجانية تسيطر على مجل الاحتياطات
+
+349
+00:24:42,020 --> 00:24:47,240
+المجانية تسيطر على مجل الاحتياطات المجانية تسيطر
+
+350
+00:24:47,240 --> 00:24:53,160
+على مجل ال
+
+351
+00:24:54,680 --> 00:24:57,300
+مفروض المساويات الاجتماعية مفروض المساويات
+
+352
+00:24:57,300 --> 00:24:57,720
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+353
+00:24:57,720 --> 00:25:00,420
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+354
+00:25:00,420 --> 00:25:02,960
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+355
+00:25:02,960 --> 00:25:07,860
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+356
+00:25:07,860 --> 00:25:07,880
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+357
+00:25:07,880 --> 00:25:08,940
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+358
+00:25:08,940 --> 00:25:09,080
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+359
+00:25:09,080 --> 00:25:09,920
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+360
+00:25:09,920 --> 00:25:12,280
+الاجتماعية الاج
+
+361
+00:25:18,140 --> 00:25:22,580
+how much is the marginal social cost and marginal
+
+362
+00:25:22,580 --> 00:25:26,700
+social benefits marginal benefits equals five and
+
+363
+00:25:26,700 --> 00:25:31,180
+marginal social cost equals fourteen here so at
+
+364
+00:25:31,180 --> 00:25:37,420
+five units of pizza the marginal social cost
+
+365
+00:25:37,420 --> 00:25:41,260
+equals how much fourteen and the marginal social
+
+366
+00:25:41,260 --> 00:25:49,200
+benefits equals how much fiveمعظم الهجوم هو أكتر
+
+367
+00:25:49,200 --> 00:25:53,400
+من مجموعات الاجتماعات الاجتماعية، صحيح؟ لذلك نحن
+
+368
+00:25:53,400 --> 00:25:56,940
+لدينا أكتر من مجموعات الاجتماعات الاجتماعية، 38
+
+369
+00:25:56,940 --> 00:25:57,680
+مليون مليون مليون مليون مليون مليون مليون مليون
+
+370
+00:25:57,680 --> 00:25:58,840
+مليون مليون مليون مليون مليون مليون مليون مليون
+
+371
+00:25:58,840 --> 00:25:59,960
+مليون مليون مليون مليون مليون مليون مليون مليون
+
+372
+00:25:59,960 --> 00:26:00,380
+مليون مليون مليون مليون مليون مليون مليون مليون
+
+373
+00:26:00,380 --> 00:26:00,800
+مليون مليون مليون مليون مليون مليون مليون مليون
+
+374
+00:26:00,800 --> 00:26:03,920
+مليون مليون مليون مليون مليون مليون مليون مليون
+
+375
+00:26:03,920 --> 00:26:11,340
+مليون مليون مليون مإذا تتقل
+
+376
+00:26:11,340 --> 00:26:20,040
+من 5 إلى 4، فالأموال ستزاد من 38 إلى 47 لكي تصل
+
+377
+00:26:20,040 --> 00:26:21,180
+إلى الأفضلية هنا،
+
+378
+00:26:21,180 --> 00:26:24,040
+حسنا؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟طبعا،
+
+379
+00:26:24,040 --> 00:26:28,320
+حسنا، رائع، ممتاز، ممتاز، ممتاز، ممتاز، ممتاز،
+
+380
+00:26:28,320 --> 00:26:29,380
+ممتاز، ممتاز، ممتاز، ممتاز، ممتاز، ممتاز، ممتاز،
+
+381
+00:26:29,380 --> 00:26:30,240
+ممتاز، ممتاز، ممتاز، ممتاز، ممتاز، ممتاز، ممتاز،
+
+382
+00:26:30,240 --> 00:26:32,760
+ممتاز، ممتاز، ممتاز، ممتاز، ممتاز
+
+383
+00:26:35,160 --> 00:26:37,760
+على اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+384
+00:26:37,760 --> 00:26:38,860
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+385
+00:26:38,860 --> 00:26:43,840
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+386
+00:26:43,840 --> 00:26:44,380
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+387
+00:26:44,380 --> 00:26:48,100
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+388
+00:26:48,100 --> 00:26:48,280
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+389
+00:26:48,280 --> 00:27:03,940
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال ات
+
+390
+00:27:12,100 --> 00:27:31,760
+عشان تقريبا تقريبا
+
+391
+00:27:31,760 --> 00:27:31,900
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+392
+00:27:31,900 --> 00:27:32,160
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا ت
+
+393
+00:27:47,080 --> 00:27:49,280
+هذا هو الاناليزة عندما يكون المساعدات المساعدة
+
+394
+00:27:49,280 --> 00:27:53,320
+أكبر من المساعدات المساعدة التي قد تحدثت عنها الآن
+
+395
+00:27:53,320 --> 00:27:59,970
+هنا هي مدارة المساعدات المساعدةعندما يكون عملياتنا
+
+396
+00:27:59,970 --> 00:28:03,290
+أكتر من 4، ستلاحظ أن عملياتنا أكتر من 4، ستلاحظ أن
+
+397
+00:28:03,290 --> 00:28:03,370
+عملياتنا أكتر من 4، ستلاحظ أن عملياتنا أكتر من 4،
+
+398
+00:28:03,370 --> 00:28:05,410
+ستلاحظ أن عملياتنا أكتر من 4، ستلاحظ أن عملياتنا
+
+399
+00:28:05,410 --> 00:28:08,770
+أكتر من 4، ستلاحظ أن عملياتنا أكتر من 4، ستلاحظ أن
+
+400
+00:28:08,770 --> 00:28:09,330
+عملياتنا أكتر من 4، ستلاحظ أن عملياتنا أكتر من 4،
+
+401
+00:28:09,330 --> 00:28:11,350
+ستلاحظ أن عملياتنا أكتر من 4، ستلاحظ أن عملياتنا
+
+402
+00:28:11,350 --> 00:28:18,670
+أكتر من 4، ستلاحظ أن عملياتنا أكتر من 4، ستلاحظ أن
+
+403
+00:28:18,670 --> 00:28:24,460
+عمليوهو أقل من مستخدمات مستخدمات أكبر من مستخدمات
+
+404
+00:28:24,460 --> 00:28:25,280
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+405
+00:28:25,280 --> 00:28:27,960
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+406
+00:28:27,960 --> 00:28:28,000
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+407
+00:28:28,000 --> 00:28:30,120
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+408
+00:28:30,120 --> 00:28:30,800
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+409
+00:28:30,800 --> 00:28:31,320
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+410
+00:28:31,320 --> 00:28:32,960
+مستخدمات مستخدمات مستخدمات مستخدمات مستخدمات
+
+411
+00:28:32,960 --> 00:28:38,000
+مستخدمات
+
+412
+00:28:38,000 --> 00:28:46,480
+مستخدمات مستخدمات مستخدمات
+
+413
+00:28:46,990 --> 00:28:54,530
+ما هي الاختصارات؟ الاختصارات تحدث عندما تنتج أو
+
+414
+00:28:54,530 --> 00:28:58,750
+تصميم جودة أو عملية عملية عملية عملية عملية عملية
+
+415
+00:28:58,750 --> 00:28:59,270
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+416
+00:28:59,270 --> 00:29:00,530
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+417
+00:29:00,530 --> 00:29:01,150
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+418
+00:29:01,150 --> 00:29:04,970
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+419
+00:29:04,970 --> 00:29:04,990
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+420
+00:29:04,990 --> 00:29:05,970
+عملية عملية
+
+421
+00:29:12,570 --> 00:29:18,890
+أو مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع
+
+422
+00:29:18,890 --> 00:29:21,490
+مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع
+
+423
+00:29:21,490 --> 00:29:22,730
+مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع مصنع
+
+424
+00:29:22,730 --> 00:29:35,390
+مصنع مصنع مصنع مصنع
+
+425
+00:29:38,890 --> 00:29:43,030
+الحقيقة هي أنها تنتج شيء يجعله يصيب بالطموح
+
+426
+00:29:48,170 --> 00:29:49,530
+استخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+427
+00:29:49,530 --> 00:29:57,730
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+428
+00:29:57,730 --> 00:29:59,930
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+429
+00:29:59,930 --> 00:29:59,970
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+430
+00:29:59,970 --> 00:30:00,050
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+431
+00:30:00,050 --> 00:30:01,170
+الاستخدم الاستخدم الاستخدم الاستخدم الاستخدم
+
+432
+00:30:01,170 --> 00:30:16,630
+الاستخدم الاستخدم الاستخدم الاستخدم الاستخد
+
+433
+00:30:17,060 --> 00:30:25,980
+هذه الحالات قبل أن نبدأ هنا سنقوم بالدراسة على
+
+434
+00:30:25,980 --> 00:30:28,080
+أربع نوع من الأجهزة
+
+435
+00:30:31,360 --> 00:30:35,920
+نحن لدينا أربع نوع من الاختصارات هنا كما ترى إذا
+
+436
+00:30:35,920 --> 00:30:41,080
+كانت الأفعال مفيدة، فنستطيع أن نسميها اختصارات
+
+437
+00:30:41,080 --> 00:30:47,060
+مفيدة هناك اختصارات مفيدة مضافة إلى الاختصارات
+
+438
+00:30:47,060 --> 00:30:51,480
+الخاصة للمصادر أو المشترك نحن لدينا أربع نوع من
+
+439
+00:30:51,480 --> 00:30:56,900
+الاختصارات نحن لدينا أربع نوع من الاختصارات
+
+440
+00:31:09,440 --> 00:31:19,080
+أولًا، أجزاء الخارجية الخارجية الخارجية
+
+441
+00:31:19,080 --> 00:31:22,820
+الخارجية
+
+442
+00:31:22,820 --> 00:31:27,620
+الخارجية الخارجية الخارجية الخارجية الخارجية
+
+443
+00:31:41,970 --> 00:31:44,290
+استخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+444
+00:31:44,290 --> 00:31:50,770
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+445
+00:31:50,770 --> 00:31:53,130
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+446
+00:31:53,130 --> 00:31:53,550
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+447
+00:31:53,550 --> 00:31:53,610
+الاستخدم الاستخدم الاستخدم الاستخدم الاستخدم
+
+448
+00:31:53,610 --> 00:31:59,710
+الاستخدم الاستخدم الاستخدم
+
+449
+00:31:59,710 --> 00:32:04,870
+الاستخدم الاستخد
+
+450
+00:32:04,900 --> 00:32:12,080
+smoking cigarettes smoking
+
+451
+00:32:12,080 --> 00:32:20,000
+someone smoke and it has or smoking has negative
+
+452
+00:32:20,000 --> 00:32:25,280
+impacts for the third party and the community okay
+
+453
+00:32:25,280 --> 00:32:33,240
+so we can say that the person who smokes he can
+
+454
+00:32:33,240 --> 00:32:40,900
+benefitربما يستمتع بالدخول للنار، حسنًا؟ لذلك، يجب
+
+455
+00:32:40,900 --> 00:32:48,360
+أن نقرر بين الاحتياطات الخاصة والاحتياطات
+
+456
+00:32:48,360 --> 00:32:48,760
+الاجتماعية الاحتياطية الاجتماعية الاجتماعية
+
+457
+00:32:48,760 --> 00:32:49,580
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+458
+00:32:49,580 --> 00:32:55,160
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+459
+00:32:55,160 --> 00:32:56,960
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+460
+00:32:56,960 --> 00:32:57,020
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+461
+00:32:57,020 --> 00:32:57,060
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+462
+00:32:57,060 --> 00:32:57,100
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+463
+00:32:57,100 --> 00:33:03,060
+الاجتماعية الاجتما
+
+464
+00:33:04,850 --> 00:33:13,790
+ممكن نسميها افضلات اجتماعية أو نسميها افضلات
+
+465
+00:33:13,790 --> 00:33:19,350
+اجتماعية خاطئة افضلات
+
+466
+00:33:19,350 --> 00:33:27,970
+افضلات افضلات افضلات افضلات افضلات افضلاتالأموال
+
+467
+00:33:27,970 --> 00:33:32,630
+السفرية هي أكتر من الأموال السفرية .. ال .. ال ..
+
+468
+00:33:32,630 --> 00:33:33,090
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+469
+00:33:33,090 --> 00:33:33,430
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+470
+00:33:33,430 --> 00:33:34,110
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+471
+00:33:34,110 --> 00:33:34,550
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+472
+00:33:34,550 --> 00:33:36,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+473
+00:33:36,610 --> 00:33:37,250
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+474
+00:33:37,250 --> 00:33:39,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+475
+00:33:39,110 --> 00:33:42,790
+.. ال .. ال .. ال .. ال .. ال ..
+
+476
+00:33:42,790 --> 00:33:44,410
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+477
+00:33:44,410 --> 00:33:56,130
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+478
+00:33:57,380 --> 00:34:07,160
+Externality External
+
+479
+00:34:07,160 --> 00:34:14,060
+Benefits Marginal
+
+480
+00:34:14,060 --> 00:34:17,360
+social benefits equals the marginal private
+
+481
+00:34:17,360 --> 00:34:20,060
+benefits plus external cost
+
+482
+00:34:25,500 --> 00:34:30,520
+هو الهجوم الخارجي هنا نقاط
+
+483
+00:34:30,520 --> 00:34:33,380
+او نقاط؟ نقاط او نقاط؟ نقاط او نقاط؟ نقاط او نقاط؟
+
+484
+00:34:33,380 --> 00:34:34,360
+نقاط او نقاط؟ نقاط او نقاط؟ نقاط او نقاط؟ نقاط او
+
+485
+00:34:34,360 --> 00:34:34,560
+نقاط؟ نقاط او نقاط؟ نقاط او نقاط؟ نقاط او نقاط؟
+
+486
+00:34:34,560 --> 00:34:43,140
+نقاط او نقاط؟ نقاط او نقاط؟ نقاط او نقاط؟ نقاط او
+
+487
+00:34:43,140 --> 00:34:47,740
+نقاط؟ نقاط او نقاط؟
+
+488
+00:34:51,540 --> 00:34:57,580
+مانوس، because seven minus three equals four, the
+
+489
+00:34:57,580 --> 00:35:01,980
+marginal social benefits is less than the marginal
+
+490
+00:35:01,980 --> 00:35:06,680
+private benefits. So the external cost here should
+
+491
+00:35:06,680 --> 00:35:07,340
+be negative.
+
+492
+00:35:13,640 --> 00:35:16,140
+مشروع الـ Marginal Private Benefits أو الـ
+
+493
+00:35:16,140 --> 00:35:18,320
+Marginal Social Benefits أقل من الـ Marginal
+
+494
+00:35:18,320 --> 00:35:22,020
+Private Benefits لذلك يجب أن يكون مفيدًا، لذلك الـ
+
+495
+00:35:22,020 --> 00:35:27,120
+External Cost هنا يجب
+
+496
+00:35:27,120 --> 00:35:32,740
+أن يكون مفيدًا،
+
+497
+00:35:32,740 --> 00:35:39,340
+حسنًا؟ ماذا عن الـ positive externalities of
+
+498
+00:35:39,340 --> 00:35:43,920
+consumption؟it means that someone consume
+
+499
+00:35:43,920 --> 00:35:49,500
+something that has a positive impact on the
+
+500
+00:35:49,500 --> 00:35:54,540
+community like the vaccination here
+
+501
+00:35:59,290 --> 00:36:08,390
+وإذا كان شخص ما مواثيق، فهو سيكون
+
+502
+00:36:08,390 --> 00:36:13,670
+أكثر صحيح، وهو
+
+503
+00:36:13,670 --> 00:36:14,850
+سيكون أكثر صحيح، فهو سيكون أكثر صحيح، فهو سيكون
+
+504
+00:36:14,850 --> 00:36:14,950
+أكثر صحيح، فهو سيكون أكثر صحيح، فهو سيكون أكثر
+
+505
+00:36:14,950 --> 00:36:15,290
+صحيح، فهو سيكون أكثر صحيح، فهو سيكون أكثر صحيح،
+
+506
+00:36:15,290 --> 00:36:15,310
+فهو سيكون أكثر صحيح، فهو سيكون أكثر صحيح، فهو
+
+507
+00:36:15,310 --> 00:36:17,050
+سيكون أكثر صحيح، فهو سيكون أكثر صحيح، فهو سيكون
+
+508
+00:36:17,050 --> 00:36:19,710
+أكثر صحيح، فهو سيكون أكثر صحيح، فهو سيكون أكثر
+
+509
+00:36:19,710 --> 00:36:25,540
+صحيح،الفائعات الاجتماعية الاجتماعية هي أكتر من
+
+510
+00:36:25,540 --> 00:36:30,360
+الفائعات الاجتماعية الخاصة، بالتأكيد هو فائع من
+
+511
+00:36:30,360 --> 00:36:37,600
+الواجبات، لكن الفائعات في المجتمع تصبح أكتر، ففي
+
+512
+00:36:37,600 --> 00:36:41,660
+هذه الحالة، الفائعات الاجتماعية الاجتماعية هي أكتر
+
+513
+00:36:41,660 --> 00:36:42,780
+من الفائعات الاخرى الخاصة
+
+514
+00:36:45,930 --> 00:36:49,950
+لذلك إذا كانت الميزانية الاجتماعية ميزانية
+
+515
+00:36:49,950 --> 00:36:52,350
+الاجتماعي ميزانية الاجتماعي ميزانية الاجتماعي
+
+516
+00:36:52,350 --> 00:36:53,350
+ميزانية الاجتماعي ميزانية الاجتماعي ميزانية
+
+517
+00:36:53,350 --> 00:36:54,730
+الاجتماعي ميزانية الاجتماعي ميزانية الاجتماعي
+
+518
+00:36:54,730 --> 00:36:55,270
+ميزانية الاجتماعي ميزانية الاجتماعي ميزانية
+
+519
+00:36:55,270 --> 00:36:55,570
+الاجتماعي ميزانية الاجتماعي ميزانية الاجتماعي
+
+520
+00:36:55,570 --> 00:36:59,110
+ميزانية الاجتماعي ميزانية الاجتماعي ميزانية
+
+521
+00:36:59,110 --> 00:37:07,010
+الاجتماعي ميزانية الاجتماعي ميزانية
+
+522
+00:37:07,010 --> 00:37:15,600
+الاجتماعي ميزانية الاجتكوست او الاستخدام الاستخدام
+
+523
+00:37:15,600 --> 00:37:16,180
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+524
+00:37:16,180 --> 00:37:19,540
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+525
+00:37:19,540 --> 00:37:20,820
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدام
+
+526
+00:37:20,820 --> 00:37:21,340
+الاستخدام الاستخدام الاستخدام الاستخدام الاستخدم
+
+527
+00:37:21,340 --> 00:37:21,380
+الاستخدم الاستخدم الاستخدم الاستخدم الاستخدم
+
+528
+00:37:21,380 --> 00:37:25,120
+الاستخدم الاستخدم الاستخدم الاستخدم الاستخدم
+
+529
+00:37:25,120 --> 00:37:25,880
+الاستخدم الاستخدم الاستخدم الاستخدم الاستخدم
+
+530
+00:37:25,880 --> 00:37:26,000
+الاستخدم الاستخد
+
+531
+00:37:31,580 --> 00:37:36,360
+دعنا نعتمد أن هذا سبتمبر plus ثلاثة أكتر من
+
+532
+00:37:36,360 --> 00:37:39,660
+مجموعات الاجتماعات الاجتماعية الاجتماعية
+
+533
+00:37:39,660 --> 00:37:41,060
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+534
+00:37:41,060 --> 00:37:44,160
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+535
+00:37:44,160 --> 00:37:47,740
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+536
+00:37:47,740 --> 00:37:47,760
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+537
+00:37:47,760 --> 00:37:47,780
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+538
+00:37:47,780 --> 00:37:49,920
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+539
+00:37:49,920 --> 00:37:54,980
+الاجتماعية
+
+540
+00:37:54,980 --> 00:38:00,940
+الاجت
+
+541
+00:38:01,630 --> 00:38:07,430
+التي تتسبب في المعاناة وانتج مصاريه ويعني تتسبب في
+
+542
+00:38:07,430 --> 00:38:10,710
+المصاريه ويعني تتسبب في المصاريه ويعني تتسبب في
+
+543
+00:38:10,710 --> 00:38:11,570
+المصاريه ويعني تتسبب في المصاريه ويعني تتسبب في
+
+544
+00:38:11,570 --> 00:38:13,770
+المصاريه ويعني تتسبب في المصاريه ويعني تتسبب في
+
+545
+00:38:13,770 --> 00:38:14,030
+المصاريه ويعني تتسبب في المصاريه ويعني تتسبب في
+
+546
+00:38:14,030 --> 00:38:15,070
+المصاريه ويعني تتسبب في المصاريه ويعني تتسبب في
+
+547
+00:38:15,070 --> 00:38:17,210
+المصاريه ويعني تتسبب في المصاريه ويعني تتسبب في
+
+548
+00:38:17,210 --> 00:38:21,730
+المصاريه ويعني تتسبب في المصاريه
+
+549
+00:38:21,730 --> 00:38:31,440
+ويعني تتسبب في المصاريه ويعني تتسبب فيبالتأكيد نحن
+
+550
+00:38:31,440 --> 00:38:36,760
+نتكلم عن الهجوم، فالهجوم الاجتماعي و الاجتماعي هنا
+
+551
+00:38:36,760 --> 00:38:42,320
+هو أكتر من الهجوم الاجتماعي و الاجتماعي الخاصة لأن
+
+552
+00:38:42,320 --> 00:38:49,400
+المجتمع أو هناك مصادفة للمجتمع و هي مصادفة من
+
+553
+00:38:49,400 --> 00:38:53,420
+الهجوم الاجتماعي فهو
+
+554
+00:38:53,420 --> 00:38:58,770
+أكتر من الهجوم الاجتماعي الخاصةبالعامة مجموعات
+
+555
+00:38:58,770 --> 00:39:03,070
+السعر الاجتماعي هي مجموعة السعر الاجتماعي مجموعة
+
+556
+00:39:03,070 --> 00:39:03,570
+السعر الاجتماعي مجموعة السعر الاجتماعي مجموعة
+
+557
+00:39:03,570 --> 00:39:05,050
+السعر الاجتماعي مجموعة السعر الاجتماعي مجموعة
+
+558
+00:39:05,050 --> 00:39:07,330
+السعر الاجتماعي مجموعة السعر الاجتماعي مجموعة
+
+559
+00:39:07,330 --> 00:39:08,270
+السعر الاجتماعي مجموعة السعر الاجتماعي مجموعة
+
+560
+00:39:08,270 --> 00:39:10,810
+السعر الاجتماعي مجموعة السعر الاجتماعي مجموعة
+
+561
+00:39:10,810 --> 00:39:15,970
+السعر الاجتماعي مجموعة السعر الاجتماعي مجموعة
+
+562
+00:39:15,970 --> 00:39:21,610
+السعر الاجتماعي مجموعة
+
+563
+00:39:21,610 --> 00:39:27,720
+السعرمجلد الهجوم الاجتماعي هو أكتر من مجلد الهجوم
+
+564
+00:39:27,720 --> 00:39:28,960
+الاجتماعي هو اكتر من مجلد الهجوم الاجتماعي هو اكتر
+
+565
+00:39:28,960 --> 00:39:30,160
+من مجلد الهجوم الاجتماعي هو اكتر من مجلد الهجوم
+
+566
+00:39:30,160 --> 00:39:34,800
+الاجتماعي هو اكتر من مجلد
+
+567
+00:39:34,800 --> 00:39:36,820
+الهجوم الاجتماعي هو اكتر من مجلد الهجوم الاجتماعي
+
+568
+00:39:36,820 --> 00:39:40,340
+هو اكتر من مجلد الهجوم الاجتماعي هو اكتر من مجلد
+
+569
+00:39:40,340 --> 00:39:41,140
+الهجوم الاجتماعي هو اكتر من مجلد الهجوم الاجتماعي
+
+570
+00:39:41,140 --> 00:39:48,220
+هو اكتر من
+
+571
+00:39:48,220 --> 00:39:52,780
+مجلد الهجوم الاجتماعي هو اكتر من مجلدأو نسميها
+
+572
+00:39:52,780 --> 00:39:57,600
+positive externalities of production نحن لدينا
+
+573
+00:39:57,600 --> 00:40:02,260
+مثال هنا أو نستطيع أن نقول أن المفهوم لـ positive
+
+574
+00:40:02,260 --> 00:40:07,780
+externalities of production يعني أنه عندما يصنع
+
+575
+00:40:07,780 --> 00:40:14,280
+شخص شيء يميز المجتمع بشكل افضل دعونا نتكلم عن
+
+576
+00:40:14,280 --> 00:40:18,380
+كتابة كبيرة كتابة كبيرة
+
+577
+00:40:22,080 --> 00:40:27,980
+وقاموا باستخدام عملية تدريب عملية
+
+578
+00:40:27,980 --> 00:40:31,940
+تدريب عملية
+
+579
+00:40:31,940 --> 00:40:32,880
+تدريب عملية تدريب عملية تدريب عملية تدريب عملية
+
+580
+00:40:32,880 --> 00:40:33,020
+تدريب عملية تدريب عملية تدريب عملية تدريب عملية
+
+581
+00:40:33,020 --> 00:40:50,060
+تدريب عملية تدريب عملية تدريب عملية تدريب عملية
+
+582
+00:40:50,060 --> 00:40:58,860
+تالذين لا يدفعوا تجارب التدريب لعمل تجارب التدريب
+
+583
+00:40:58,860 --> 00:41:03,700
+لشركة SSAR فهنا نستطيع أن نقول أن مجال التدريب
+
+584
+00:41:03,700 --> 00:41:08,500
+الاجتماعي هو أقل من مجال التدريب الاجتماعي
+
+585
+00:41:08,500 --> 00:41:15,260
+الاجتماعي نستطيع أن نقول أن هذا مثال للصورة هنا
+
+586
+00:41:37,880 --> 00:41:41,740
+هو مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+587
+00:41:41,740 --> 00:41:43,180
+مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+588
+00:41:43,180 --> 00:41:43,220
+مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+589
+00:41:50,040 --> 00:41:54,940
+عن طريق الاستخدام المجلد الاجتماعي يجب أن يكون أقل
+
+590
+00:41:54,940 --> 00:41:57,440
+من مجلد الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+591
+00:41:57,440 --> 00:41:58,680
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+592
+00:41:58,680 --> 00:42:00,940
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+593
+00:42:00,940 --> 00:42:01,100
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+594
+00:42:01,100 --> 00:42:01,360
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+595
+00:42:01,360 --> 00:42:03,200
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+596
+00:42:03,200 --> 00:42:09,820
+الاجتماعي الاجتماعي
+
+597
+00:42:09,820 --> 00:42:13,620
+الاجتما
+
+598
+00:42:15,470 --> 00:42:20,990
+هو صغير، فهو يجب أن يكون هنا 10-3، فالجزء الخارجي
+
+599
+00:42:20,990 --> 00:42:26,230
+يجب أن يكون نغمًا هنا لأن
+
+600
+00:42:26,230 --> 00:42:32,530
+جزء المجتمع المجاني هو أقل من جزء المجتمع المجاني
+
+601
+00:42:32,530 --> 00:42:39,730
+المجاري، فالجزء الخارجي يجب أن يكون نغمًا هنا وهو
+
+602
+00:42:39,730 --> 00:42:46,370
+يجب أن يكون نغمًايعطي كلاش تمام مرة جاي ان شاء
+
+603
+00:42:46,370 --> 00:42:46,850
+الله بنكمل
+
diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/LZ5sV9SyzkI_postprocess.srt b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/LZ5sV9SyzkI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dd0d31b7abb91916ea7d49c21c8fe72a73bf0cd7
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/LZ5sV9SyzkI_postprocess.srt
@@ -0,0 +1,1528 @@
+1
+00:00:20,750 --> 00:00:23,310
+Okay بسم الله الرحمن الرحيم اليوم إن شاء الله
+
+2
+00:00:23,310 --> 00:00:27,870
+سنقوم بالدراسة عن علاقات بين نسبة الميزانيات
+
+3
+00:00:27,870 --> 00:00:31,190
+وميزانيات الميزانية وميزانيات الميزانيات وميزانيات
+
+4
+00:00:31,190 --> 00:00:32,590
+الميزانيات وميزانيات الميزانيات وميزانيات
+
+5
+00:00:32,590 --> 00:00:34,770
+الميزانيات وميزانيات الميزانيات وميزانيات
+
+6
+00:00:34,770 --> 00:00:36,150
+الميزانيات وميزانيات الميزانيات وميزانيات
+
+7
+00:00:36,150 --> 00:00:44,790
+الميزانيات وميزانيات الميزانيات وميزانيات
+
+8
+00:00:44,790 --> 00:00:53,060
+الميزانيات وميزانيات الميزانيات وميدعنا نسأل بعض
+
+9
+00:00:53,060 --> 00:00:58,540
+الأسئلة مرتبطة بـ Interest Rate وعلاقتها مع
+
+10
+00:00:58,540 --> 00:01:05,460
+الاستثمار والاستخدام كما
+
+11
+00:01:05,460 --> 00:01:10,900
+تعلمون، الاقتصاد هو اقتصاد بشكل بسيط بلا حكومة
+
+12
+00:01:10,900 --> 00:01:17,660
+اقتصاد بشكل بسيط بلا حكومة لدينا اتصالين، اتصال
+
+13
+00:01:20,900 --> 00:01:31,040
+الانفصارات او المجتمع او المجتمع او المجتمع او
+
+14
+00:01:31,040 --> 00:01:40,060
+المجتمع او المجتمع او المجتمع او المجتمع
+
+15
+00:01:40,060 --> 00:01:43,920
+او
+
+16
+00:01:43,920 --> 00:01:44,460
+المجتمع
+
+17
+00:01:53,080 --> 00:02:02,360
+للاستثمار لان اعتقد ان مؤسسات الشركة تستخدم
+
+18
+00:02:02,360 --> 00:02:13,540
+الاستثمار و هم يريدون ان يدفعوا المال هم يريدون ان
+
+19
+00:02:13,540 --> 00:02:19,300
+يدفعوا المال من جانبين مختلفة لذلك يجب ان يدفعوا
+
+20
+00:02:19,300 --> 00:02:26,240
+المال من جانبين مختلفةعلى مستوى الأسعار، من
+
+21
+00:02:26,240 --> 00:02:37,020
+البقاء، إذا كانت قيمة الـR أعلى، فماذا سيحدث لدفع
+
+22
+00:02:37,020 --> 00:02:44,510
+المال أو دماغ المال لغاية المستخدمين؟تتسلل، نعم،
+
+23
+00:02:44,510 --> 00:02:49,870
+لأن تسلل دولة الانترنت، هنا دولة الانترنت هي طريقة
+
+24
+00:02:49,870 --> 00:02:54,150
+التدفع، لذلك تسلل دولة الانترنت يعني تسلل طريقة
+
+25
+00:02:54,150 --> 00:02:59,550
+التدفع ما
+
+26
+00:02:59,550 --> 00:03:07,450
+سيحدث لإستثمار المجموعات تتسلل، لذلك يتسبب في تدفع
+
+27
+00:03:18,500 --> 00:03:28,520
+عن طريق الاستخدام الكفاية هذه
+
+28
+00:03:28,520 --> 00:03:31,640
+هي
+
+29
+00:03:31,640 --> 00:03:38,540
+عملية الاستخدام وهذا
+
+30
+00:03:38,540 --> 00:03:40,820
+هو عملية الاستخدام الاستخدام الاستخدام الاستخدام
+
+31
+00:03:40,820 --> 00:03:42,180
+الاستخدام
+
+32
+00:03:45,720 --> 00:03:54,560
+أو قيمة الانفصار وهذا هو عملية الانفصار عندما
+
+33
+00:03:54,560 --> 00:04:02,120
+يزداد عملية الانفصار عملية الانفصار يتسلق أو يتسلق
+
+34
+00:04:02,120 --> 00:04:04,960
+عملية الانفصار يتسلق أو يتسلق عملية الانفصار يتسلق
+
+35
+00:04:04,960 --> 00:04:07,960
+أو يتسلق عملية الانفصار يتسلق أو يتسلق عملية
+
+36
+00:04:07,960 --> 00:04:08,460
+الانفصار يتسلق أو يتسلق عملية الانفصار يتسلق عملية
+
+37
+00:04:08,460 --> 00:04:10,000
+الانفصار يتسلق عملية الانفصار يتسلق عملية الانفصار
+
+38
+00:04:10,000 --> 00:04:11,900
+يتسلق عملية الانفصار يتسلق عملية الانفصار يتسلق
+
+39
+00:04:11,900 --> 00:04:17,090
+عملية الانفصار يتسلقهذه المرحلة تتمثل علاقات
+
+40
+00:04:17,090 --> 00:04:22,410
+مفارقة بين قيمة الدولة والاستثمار ماذا عن العائلات
+
+41
+00:04:22,410 --> 00:04:31,250
+هنا؟ العائلات هنا هم المستخدمين هم المستخدمين هنا
+
+42
+00:04:31,250 --> 00:04:38,410
+لديهم المال للمساعدة في المنزل أو في المجتمع
+
+43
+00:04:42,660 --> 00:04:50,380
+وهنا نتحدث عن نظام بني كرامي ليس لديه حكومة او
+
+44
+00:04:50,380 --> 00:04:51,480
+حكومة او حكومة او حكومة او حكومة او حكومة او حكومة
+
+45
+00:04:51,480 --> 00:04:51,580
+او حكومة او حكومة او حكومة او حكومة او حكومة او
+
+46
+00:04:51,580 --> 00:04:51,600
+او حكومة او حكومة او حكومة او حكومة او حكومة او
+
+47
+00:04:51,600 --> 00:04:52,180
+حكومة او حكومة او حكومة او حكومة او حكومة او حكومة
+
+48
+00:04:52,180 --> 00:04:57,960
+او حكومة او حكومة او حكومة او حكومة او
+
+49
+00:04:57,960 --> 00:05:09,320
+حكومة
+
+50
+00:05:10,990 --> 00:05:18,010
+ماذا يحدث؟ كما يزال هنا و هنا لدينا علاقة افضل بين
+
+51
+00:05:18,010 --> 00:05:25,330
+الانترستايت و حفظتك في هذه الحالة انها حفظتك، انت
+
+52
+00:05:25,330 --> 00:05:34,470
+بتاعتها حفظتك للانفصار، هذا cost، بس هذا حفظتك و
+
+53
+00:05:34,470 --> 00:05:37,430
+كما تزال حفظتك تزال حفظتك
+
+54
+00:05:43,090 --> 00:05:55,810
+وهو بالنسبالي انبسنف،
+
+55
+00:05:55,810 --> 00:05:59,190
+مش انبسنف، بمعنى انبسنف، لكن هو saving
+
+56
+00:06:01,820 --> 00:06:06,400
+وهذا يعني انه يحصل على المستحيلين للعائلات، وهذا
+
+57
+00:06:06,400 --> 00:06:12,960
+ما يسمى بالنسبة للإنقاذ، ويبدو كإستثمار فائع،
+
+58
+00:06:12,960 --> 00:06:20,580
+فهناك علاقة افضل بين قيمة دولة وإنقاذ،
+
+59
+00:06:20,580 --> 00:06:26,880
+لذلك نستطيع أن نقول أن هذه المجموعة هنا هي علاقة
+
+60
+00:06:26,880 --> 00:06:28,480
+افضل بين
+
+61
+00:06:31,350 --> 00:06:38,230
+هذا هو الانتجار وهذا هو الانتجار كما نحن لدينا
+
+62
+00:06:38,230 --> 00:06:45,630
+واحد انتجار في السوق المالي فانتجار
+
+63
+00:06:45,630 --> 00:06:50,450
+الانتجار يتميز عندما انتجار المال يقوم بالانتجار
+
+64
+00:06:50,450 --> 00:06:59,430
+المالي هذا هو انتجار الانتجار الانتجاري
+
+65
+00:07:10,790 --> 00:07:15,530
+إذا كانت دولة الاستثمارات مرتفعة فإذا كانت دولة
+
+66
+00:07:15,530 --> 00:07:16,730
+الاستثمارات مرتفعة فإذا كانت دولة الاستثمارات
+
+67
+00:07:16,730 --> 00:07:21,290
+مرتفعة فإذا كانت دولة الاستثماراتبمعنى الصورة وين؟
+
+68
+00:07:21,290 --> 00:07:25,170
+زي مين هو؟ it looks like the goods market someone
+
+69
+00:07:25,170 --> 00:07:30,030
+goes to the market to buy a trouser he finds it
+
+70
+00:07:30,030 --> 00:07:32,830
+one hundred dollars .. one hundred shekel the
+
+71
+00:07:32,830 --> 00:07:38,810
+producer ask him to pay one hundred to twenty the
+
+72
+00:07:38,810 --> 00:07:43,170
+negotiations between them reach to the optimal or
+
+73
+00:07:43,170 --> 00:07:46,350
+equilibrium price it looks like this .. it's the
+
+74
+00:07:46,350 --> 00:07:50,860
+same ideaبسبب أننا لدينا اتصالين و أحدهم يطلب
+
+75
+00:07:50,860 --> 00:07:58,620
+المال و أحدهم يدفع المال و التقارير بينهم تصلنا
+
+76
+00:07:58,620 --> 00:08:03,820
+إلى مستوى الانترال المستوى الانترال كان أعلى
+
+77
+00:08:03,820 --> 00:08:04,760
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+78
+00:08:04,760 --> 00:08:07,300
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+79
+00:08:07,300 --> 00:08:10,620
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+80
+00:08:10,620 --> 00:08:10,640
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+81
+00:08:10,640 --> 00:08:15,310
+المستوى المستوى المستوى المستوإذا كانت الدولة أعلى
+
+82
+00:08:15,310 --> 00:08:19,050
+المستوى الاقتصادي، دعنا نعتمد عليه ر، هذا هو
+
+83
+00:08:19,050 --> 00:08:29,810
+أسطورة الاقتصادي، أول، أتأول، أحضر المال، أحضر
+
+84
+00:08:29,810 --> 00:08:35,050
+المال، أحضر المال، أحضر المال، أحضر المال، أحضر
+
+85
+00:08:35,050 --> 00:08:38,840
+المال، أحضر المالأعلى من ال investment demand ..
+
+86
+00:08:38,840 --> 00:08:41,080
+sorry يعني اللي هو الطلب على اللي .. مظبوطة ولا
+
+87
+00:08:41,080 --> 00:08:47,240
+لأ؟ .. so interest rate goes down .. vice versa ..
+
+88
+00:08:47,240 --> 00:08:53,500
+if interest rate was below the equilibrium .. هذا
+
+89
+00:08:53,500 --> 00:08:58,820
+مغرر لمين؟ لأن investors .. interest rate جليل لإن
+
+90
+00:08:58,820 --> 00:09:03,970
+هو عنده عامل bondsو ببيع وانترست قليل عليها بدي
+
+91
+00:09:03,970 --> 00:09:08,390
+ياخد منك ألف و يرجعلك يوم ألف و اتنين شكل .. it's
+
+92
+00:09:08,390 --> 00:09:12,970
+really good يعني for him .. so at the lower
+
+93
+00:09:12,970 --> 00:09:20,230
+interest rates, the investment demand is high، ال
+
+94
+00:09:20,230 --> 00:09:27,050
+saving رح يكون أقلصح؟ ويعني مستحيل للعائلات تستثمر
+
+95
+00:09:27,050 --> 00:09:30,910
+في المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+96
+00:09:30,910 --> 00:09:32,070
+المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+97
+00:09:32,070 --> 00:09:32,850
+المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+98
+00:09:32,850 --> 00:09:34,070
+المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+99
+00:09:34,070 --> 00:09:36,190
+المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+100
+00:09:36,190 --> 00:09:40,610
+المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+101
+00:09:40,610 --> 00:09:45,270
+المصادر هنا، تستثمر في المصادر هنا، تستثمر في
+
+102
+00:09:45,270 --> 00:09:47,450
+المصادر هنا،
+
+103
+00:09:59,530 --> 00:10:04,250
+الدولة تقوم بإزالة المال أو الاستثمار، وهذا يسبب
+
+104
+00:10:04,250 --> 00:10:10,770
+في أزالة المال وانتقاء الاستثمار. كما تزال
+
+105
+00:10:10,770 --> 00:10:14,630
+الانتجار يزال، هناك تغيير في الطريقة التي نحن
+
+106
+00:10:14,630 --> 00:10:20,010
+نتعامل معها. تغيير المستخدم، تغيير المستخدم، تغيير
+
+107
+00:10:20,010 --> 00:10:27,350
+المستخدم، تغيير المستخدم، تغيير المستخدم، تغيير
+
+108
+00:10:27,350 --> 00:10:33,660
+المستخدم.معنى ان الانترنت تتسلق ومعمومة الاستثمار
+
+109
+00:10:33,660 --> 00:10:37,120
+تتسلق ومعمومة الانترنت تتسلق ومعمومة الانترنت
+
+110
+00:10:37,120 --> 00:10:37,560
+تتسلق ومعمومة الانترنت تتسلق ومعمومة الانترنت
+
+111
+00:10:37,560 --> 00:10:39,640
+تتسلق ومعمومة الانترنت تتسلق ومعمومة الانترنت
+
+112
+00:10:39,640 --> 00:10:40,040
+تتسلق ومعمومة الانترنت تتسلق ومعمومة الانترنت
+
+113
+00:10:40,040 --> 00:10:43,580
+تتسلق ومعمومة
+
+114
+00:10:43,580 --> 00:10:46,700
+الانترنت تتسلق
+
+115
+00:10:46,700 --> 00:10:58,040
+ومعمومة الانترنت تتسلق و
+
+116
+00:10:58,710 --> 00:11:05,930
+أو كابتن اذا تتخلص من المصادر تتخلص
+
+117
+00:11:05,930 --> 00:11:11,790
+من المحافظة ماذا يحصل؟ تتخلص من المحافظة لو تتخلص
+
+118
+00:11:11,790 --> 00:11:14,710
+من المحافظة تتخلص من المحافظة هذا المصادر يمثل
+
+119
+00:11:14,710 --> 00:11:17,390
+محافظة الهالسواتز الهالسواتز الهالسواتز الهالسواتز
+
+120
+00:11:17,390 --> 00:11:18,070
+الهالسواتز الهالسواتز الهالسواتز الهالسواتز
+
+121
+00:11:18,070 --> 00:11:21,270
+الهالسواتز الهالسواتز الهالسواتز الهالسواتز
+
+122
+00:11:21,270 --> 00:11:22,030
+الهالسواتز الهالسواتز الهالسواتز الهالسواتز
+
+123
+00:11:22,030 --> 00:11:22,310
+الهالسواتز الهالسواتز الهالسواتز الهالسواتز
+
+124
+00:11:29,980 --> 00:11:36,840
+تمام؟ what else؟ let's add the government to the
+
+125
+00:11:36,840 --> 00:11:43,720
+before
+
+126
+00:11:43,720 --> 00:11:48,380
+that .. before that
+
+127
+00:11:48,380 --> 00:11:54,200
+for the households when there is no government
+
+128
+00:11:54,200 --> 00:11:56,680
+their income .. why?
+
+129
+00:11:59,730 --> 00:12:03,890
+for the households the income is divided into two
+
+130
+00:12:03,890 --> 00:12:19,230
+parts consumption and saving for the
+
+131
+00:12:19,230 --> 00:12:23,710
+investors aggregate
+
+132
+00:12:23,710 --> 00:12:24,470
+demand
+
+133
+00:12:29,560 --> 00:12:40,740
+أجهزة البرنامج مختلفة إلى اتنين جزء من البرنامج
+
+134
+00:12:40,740 --> 00:12:44,640
+يعمل
+
+135
+00:12:44,640 --> 00:12:46,300
+فيه استخدام وجزء من البرنامج يعمل فيه استخدام وجزء
+
+136
+00:12:46,300 --> 00:12:46,540
+من البرنامج يعمل فيه استخدام وجزء من البرنامج يعمل
+
+137
+00:12:46,540 --> 00:12:47,920
+فيه استخدام وجزء من البرنامج يعمل فيه استخدام وجزء
+
+138
+00:12:47,920 --> 00:12:49,080
+من البرنامج يعمل فيه استخدام وجزء من البرنامج يعمل
+
+139
+00:12:49,080 --> 00:12:50,620
+فيه استخدام وجزء من البرنامج يعمل فيه استخدام وجزء
+
+140
+00:12:50,620 --> 00:12:50,660
+من البرنامج يعمل فيه استخدام وجزء من البرنامج يعمل
+
+141
+00:12:50,660 --> 00:12:54,280
+فيه استخدام وجزء من البرنامج يعمل فيه است
+
+142
+00:12:57,020 --> 00:13:02,020
+ولم يكن هناك حكومة تقول
+
+143
+00:13:02,020 --> 00:13:08,240
+او اين حدث الايقانابرام الايقانابرام تم إعادته
+
+144
+00:13:08,240 --> 00:13:12,820
+عندما Y يقوم بالإيقاع المجموعات او مجموعة
+
+145
+00:13:12,820 --> 00:13:13,880
+المجموعات يقوم بالطلب المجموعة
+
+146
+00:13:18,320 --> 00:13:25,540
+C plus S is equal to C plus I or C subtracted with
+
+147
+00:13:25,540 --> 00:13:30,500
+C So saving equals investment at equilibrium
+
+148
+00:13:30,500 --> 00:13:36,840
+مظبوط؟ Let's add the government Or here we can say
+
+149
+00:13:36,840 --> 00:13:41,620
+injection equals leakages out of spending stream
+
+150
+00:13:41,620 --> 00:13:48,640
+Let's add the government to the economy hereالان
+
+151
+00:13:48,640 --> 00:13:59,000
+سوف نضيف الحكومة هنا ماهي
+
+152
+00:13:59,000 --> 00:14:07,920
+الحكومة؟ سوف نضيفها هنا لدينا ثلاثة
+
+153
+00:14:07,920 --> 00:14:16,760
+مجتمعات في الاقتصاد المجلس الحكومي والحكومة
+
+154
+00:14:18,580 --> 00:14:27,640
+Why؟ For the households income
+
+155
+00:14:27,640 --> 00:14:31,200
+equals
+
+156
+00:14:31,200 --> 00:14:38,260
+how much؟ C plus S plus taxes because part of
+
+157
+00:14:38,260 --> 00:14:44,860
+income goes for C plus S plus taxes
+
+158
+00:14:49,280 --> 00:14:54,340
+ماذا عن طلب المجموعات؟ او
+
+159
+00:14:54,340 --> 00:15:09,460
+مجموعات المجموعات؟ C plus I plus G تمام
+
+160
+00:15:09,460 --> 00:15:13,160
+في
+
+161
+00:15:13,160 --> 00:15:17,080
+المقارنة مجموعات المجموعات هي Y
+
+162
+00:15:23,700 --> 00:15:26,040
+Y يقوم بالإيقاع المجموعة يقوم بالإيقاع المجموعة
+
+163
+00:15:26,040 --> 00:15:31,200
+يقوم بالإيقاع المجموعة يقوم بالإيقاع المجموعة يقوم
+
+164
+00:15:31,200 --> 00:15:35,320
+بالإيقاع المجموعة يقوم
+
+165
+00:15:35,320 --> 00:15:37,720
+بالإيقاع المجموعة يقوم بالإيقاع المجموعة يقوم
+
+166
+00:15:37,720 --> 00:15:38,080
+بالإيقاع المجموعة يقوم بالإيقاع المجموعة يقوم
+
+167
+00:15:38,080 --> 00:15:38,340
+بالإيقاع المجموعة يقوم بالإيقاع المجموعة يقوم
+
+168
+00:15:38,340 --> 00:15:39,360
+بالإيقاع المجموعة يقوم بالإيقاع المجموعة يقوم
+
+169
+00:15:39,360 --> 00:15:46,260
+بالإيقاع
+
+170
+00:15:46,260 --> 00:15:53,220
+المجموعة يقوم بالإيقاع
+
+171
+00:15:53,220 --> 00:16:00,750
+المجموعة يقEquals I plus G minus taxes تمام
+
+172
+00:16:00,750 --> 00:16:04,910
+هذا is saving aggregate saving let's go to
+
+173
+00:16:04,910 --> 00:16:11,390
+something else saving is
+
+174
+00:16:11,390 --> 00:16:21,790
+divided into two types or two parts we
+
+175
+00:16:21,790 --> 00:16:27,910
+have two types of savingpersonal saving and public
+
+176
+00:16:27,910 --> 00:16:32,990
+saving
+
+177
+00:16:32,990 --> 00:16:41,430
+personal او private saving plus
+
+178
+00:16:41,430 --> 00:16:49,670
+public saving personal
+
+179
+00:16:49,670 --> 00:16:57,850
+saving هو انت دخلك as a householdالعائلات ال
+
+180
+00:16:57,850 --> 00:17:05,390
+income equals c plus s plus taxes طب
+
+181
+00:17:05,390 --> 00:17:09,810
+ال saving تبع كده شو رح يكون هذا من ال households
+
+182
+00:17:09,810 --> 00:17:13,090
+من
+
+183
+00:17:13,090 --> 00:17:17,710
+ال personal بتجيب ال personal saving saving equals
+
+184
+00:17:17,710 --> 00:17:30,750
+y minus c minus dThis is the personal saving تمام؟
+
+185
+00:17:30,750 --> 00:17:35,490
+What are the public savings؟ ال government saving
+
+186
+00:17:35,490 --> 00:17:41,190
+إذا ال government محاصرة إيارادات أعلى من المنفقة
+
+187
+00:17:41,190 --> 00:17:46,030
+معناه فيه كلام فيه جزء saving بينهم هو ال surplus
+
+188
+00:17:46,030 --> 00:17:49,910
+هو ال saving مظبوط؟
+
+189
+00:17:49,910 --> 00:17:51,930
+إذا ال public saving
+
+190
+00:18:01,890 --> 00:18:05,770
+بالفعل هو الـ surplus كل ما كان نيجاتي هو الـ
+
+191
+00:18:05,770 --> 00:18:13,630
+deficit لأنه إذا الحكومة حصلة إيراد مليون ومنفقة
+
+192
+00:18:13,630 --> 00:18:20,390
+800 ألف عندهم saving 200 هذا عبارة عن شو؟ هذا الـ
+
+193
+00:18:20,390 --> 00:18:25,550
+public saving أو الـ garbage saving هو equals
+
+194
+00:18:28,820 --> 00:18:34,760
+Taxes minus Government Spending T
+
+195
+00:18:34,760 --> 00:18:40,200
+minus J هنا
+
+196
+00:18:40,200 --> 00:18:52,420
+نستطيع أن نقول أن الاختصار الواضح هو
+
+197
+00:18:52,420 --> 00:18:57,880
+الاختصار الشخصي اضافة إلى الاختصار الشخصي
+
+198
+00:19:04,700 --> 00:19:11,440
+الشغل personal saving هي y minus c minus c and
+
+199
+00:19:11,440 --> 00:19:17,280
+public saving is t minus your spending طبعا
+
+200
+00:19:17,280 --> 00:19:23,060
+definitely إذا كانت t minus g is bigger than zero
+
+201
+00:19:23,060 --> 00:19:25,980
+معناه كلمة we have a positive saving positive
+
+202
+00:19:25,980 --> 00:19:31,070
+public savingيعني .. يعني .. يعني .. and vice
+
+203
+00:19:31,070 --> 00:19:34,270
+versa إذا كان الـ T is less than government
+
+204
+00:19:34,270 --> 00:19:38,130
+spending, we have a negative public saving. So the
+
+205
+00:19:38,130 --> 00:19:44,270
+total saving equals
+
+206
+00:19:44,270 --> 00:19:55,070
+the personal saving Y minus C minus D plus the
+
+207
+00:19:55,070 --> 00:20:01,470
+public savingT minus
+
+208
+00:20:01,470 --> 00:20:06,490
+G صح؟
+
+209
+00:20:06,490 --> 00:20:15,950
+So the total saving equals Y minus C minus T plus
+
+210
+00:20:15,950 --> 00:20:26,250
+T minus G So subtracting T with T S equals Y minus
+
+211
+00:20:26,250 --> 00:20:34,610
+C-G وهذا هو المساعدة الكامة في الاقتصاد عندما نكون
+
+212
+00:20:34,610 --> 00:20:40,930
+لدينا حكومة ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع
+
+213
+00:20:40,930 --> 00:20:41,790
+ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع
+
+214
+00:20:41,790 --> 00:20:42,510
+ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع
+
+215
+00:20:42,510 --> 00:20:43,490
+ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع
+
+216
+00:20:43,490 --> 00:20:44,510
+ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع
+
+217
+00:20:44,510 --> 00:20:54,410
+ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع ومجتمع
+
+218
+00:20:55,360 --> 00:20:59,660
+وفي الاتصال الوضعي هنا لدينا دماغ الواقع يتم
+
+219
+00:20:59,660 --> 00:21:07,360
+تدريبه من مستخدمات الاستثمارات الموجودة في الاتصال
+
+220
+00:21:07,360 --> 00:21:13,630
+الواقعي وهو ما يسمى كرسي بولنجعن طريق اتفاقات
+
+221
+00:21:13,630 --> 00:21:18,310
+اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات
+
+222
+00:21:18,310 --> 00:21:21,050
+اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات
+
+223
+00:21:21,050 --> 00:21:22,970
+اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات
+
+224
+00:21:22,970 --> 00:21:22,990
+اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات اتفاقات
+
+225
+00:21:22,990 --> 00:21:29,410
+اتفاقات اتفاقات اتفاقات اتفاقات
+
+226
+00:21:29,410 --> 00:21:35,290
+اتفاقات اتف
+
+227
+00:21:58,410 --> 00:22:05,220
+Government followingوقلنا crowd out capital in the
+
+228
+00:22:05,220 --> 00:22:09,160
+private market shifting supply inward كل واحد تعمل
+
+229
+00:22:09,160 --> 00:22:16,400
+حاجة يعني definitely صح؟ مرالك و crowding out؟
+
+230
+00:22:16,400 --> 00:22:25,780
+تزاحوا تزاحوا، ماشي لنعود قريبا لشيء أو هذا
+
+231
+00:22:25,780 --> 00:22:29,400
+المصطلح اللي هو crowd out crowd
+
+232
+00:22:40,210 --> 00:22:47,250
+دعنا نعتمد أن الحكومة قررت استخدام تنفيذ تنفيذ
+
+233
+00:22:47,250 --> 00:22:53,070
+تنفيذ تنفيذ
+
+234
+00:22:53,070 --> 00:22:53,870
+تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ
+
+235
+00:22:53,870 --> 00:22:53,950
+تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ
+
+236
+00:22:53,950 --> 00:22:57,090
+تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ
+
+237
+00:22:57,090 --> 00:22:57,510
+تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ
+
+238
+00:22:57,510 --> 00:22:57,530
+تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ
+
+239
+00:22:57,530 --> 00:23:09,370
+تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ تنفيذ
+
+240
+00:23:11,560 --> 00:23:14,220
+to stimulate the economy by increasing the
+
+241
+00:23:14,220 --> 00:23:17,620
+government spending او يعملوا increasing the
+
+242
+00:23:17,620 --> 00:23:23,160
+transfer of payments للunemployment benefits تمام؟
+
+243
+00:23:23,160 --> 00:23:27,760
+So the government increases its spending
+
+244
+00:23:27,760 --> 00:23:34,400
+Increasing G leads to increasing the aggregate
+
+245
+00:23:34,400 --> 00:23:39,720
+expenditures لأن هذا جزء من دالة 8، الانفاق الكلي
+
+246
+00:23:41,230 --> 00:23:44,650
+أو الطلب الكلي As the government increases G
+
+247
+00:23:44,650 --> 00:23:47,670
+aggregate expenditures increases, the aggregate
+
+248
+00:23:47,670 --> 00:23:54,950
+demand for goods increases
+
+249
+00:23:54,950 --> 00:23:59,550
+Demand
+
+250
+00:23:59,550 --> 00:24:02,970
+for goods increased What will happen?
+
+251
+00:24:08,890 --> 00:24:18,760
+Prices goes upالسعر يزال يزال يزال يزال يزال يزال
+
+252
+00:24:18,760 --> 00:24:33,640
+يزال يزال يزال يزال يزال يزال
+
+253
+00:24:42,420 --> 00:24:49,120
+الرقم الانتجاري يتسلل رقم الانتجار يزال يزال يزال
+
+254
+00:24:49,120 --> 00:24:53,680
+يزال يزال يزال يزال
+
+255
+00:24:53,680 --> 00:24:56,840
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+256
+00:24:56,840 --> 00:25:01,260
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+257
+00:25:01,260 --> 00:25:01,820
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+258
+00:25:01,820 --> 00:25:02,040
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+259
+00:25:02,040 --> 00:25:03,220
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+260
+00:25:03,220 --> 00:25:03,620
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+261
+00:25:12,290 --> 00:25:16,750
+I will ask about the demand for money or money
+
+262
+00:25:16,750 --> 00:25:21,730
+demand for transactions مش
+
+263
+00:25:21,730 --> 00:25:25,270
+ايه ال effect هذا تبقى ل price اسمه الأسعار طلعت
+
+264
+00:25:25,270 --> 00:25:33,730
+نعم مش ليش what yes this is the inflation yes but
+
+265
+00:25:33,730 --> 00:25:38,290
+what are the main effects for inflation all the
+
+266
+00:25:38,290 --> 00:25:42,890
+money demand for transactions busyالأسعار في الاتم
+
+267
+00:25:42,890 --> 00:25:47,830
+تحتاج مصاري أكتر لتشتري، صح؟ So money demand for
+
+268
+00:25:47,830 --> 00:25:53,330
+transactions increased؟ Something else، الأمر
+
+269
+00:25:53,330 --> 00:25:57,890
+يتعلق على ما حصل في money demand for transactions،
+
+270
+00:25:57,890 --> 00:26:01,830
+من يشتر أكتر، الفقير أو الغني؟ اللي دخله عالي أو
+
+271
+00:26:01,830 --> 00:26:06,310
+أقل؟ من يطلب مصاري أكتر للشرائه، لل transactions
+
+272
+00:26:06,310 --> 00:26:12,420
+اللي دخله أعلى؟ So, as the price goes upتنسى،
+
+273
+00:26:12,420 --> 00:26:19,040
+وعندما تنسى تجارة المستخدم المال يزال يزال يزال
+
+274
+00:26:19,040 --> 00:26:22,680
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+275
+00:26:22,680 --> 00:26:22,820
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+276
+00:26:22,820 --> 00:26:23,080
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+277
+00:26:23,080 --> 00:26:23,500
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+278
+00:26:23,500 --> 00:26:23,620
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+279
+00:26:23,620 --> 00:26:26,960
+يزال يزال يزال يزال يزال يزال يزال يزال يزال يزال
+
+280
+00:26:26,960 --> 00:26:30,920
+يزال يزال يزال يزال
+
+281
+00:26:40,340 --> 00:26:46,040
+موال ديمان for investment for speculation المضاربة
+
+282
+00:26:46,040 --> 00:26:50,660
+بيزيد اللي معاه مصاري بيضارب و اللي معاه سعار ثلاث
+
+283
+00:26:50,660 --> 00:26:54,720
+بيصير مضاربة تمام؟ او الموال ديمان for transaction
+
+284
+00:26:54,720 --> 00:26:59,100
+بيزيد تمام؟ لأن عامل ال prices بيطلع كمان على ال
+
+285
+00:26:59,100 --> 00:27:02,340
+inputs كمان ال inflation بيعمل increasing of the
+
+286
+00:27:02,340 --> 00:27:05,300
+prices of inputs اللي بديه استثمر بده مصاري أكتر
+
+287
+00:27:06,070 --> 00:27:09,090
+بدي اعمل investment بطلب مصارع اكتر شو بيحصل في ال
+
+288
+00:27:09,090 --> 00:27:17,750
+interest rates؟ goes up هقول هى عندك انت ال money
+
+289
+00:27:17,750 --> 00:27:22,830
+market هد ال money supply money
+
+290
+00:27:22,830 --> 00:27:26,450
+demand one this is the original equilibrium
+
+291
+00:27:26,450 --> 00:27:30,170
+equilibrium point interest rate quantity of money
+
+292
+00:27:30,170 --> 00:27:36,760
+demanded one one as money demand goes upعن طريق
+
+293
+00:27:36,760 --> 00:27:39,240
+الـ rightward shifting in the mild demand curve
+
+294
+00:27:39,240 --> 00:27:48,280
+الـ MD2 سنذهب إلى الـ E2 الدرجة الداخلية الداخلية
+
+295
+00:27:48,280 --> 00:27:52,620
+تنزل إلى الأعلى هنا الدرجة الداخلية تنزل إلى
+
+296
+00:27:52,620 --> 00:27:53,040
+الأعلى
+
+297
+00:28:01,780 --> 00:28:05,120
+ماذا يحدث في قيمة الانفصار؟ نحن لدينا علاقات ناجية
+
+298
+00:28:05,120 --> 00:28:17,900
+بين انفصار هذا الانفصار يتسلق انفصار
+
+299
+00:28:17,900 --> 00:28:25,680
+يتسلق انفصار يتسلق انفصار هو جزء من الـ aggregate
+
+300
+00:28:25,680 --> 00:28:32,910
+من الـ GDPإذا تذكروا الـY هو C plus I plus G plus
+
+301
+00:28:32,910 --> 00:28:36,910
+net export أو X minus M هذا نزل، ماذا يحدث في
+
+302
+00:28:36,910 --> 00:28:42,250
+الـY؟ سينزل، تمام؟ لأن هذا aggregate expenditure
+
+303
+00:28:42,250 --> 00:28:46,910
+.. sorry؟ ليس محلوش المشكلة، لأ، بحل المشكلة، لكن
+
+304
+00:28:46,910 --> 00:28:50,970
+هذا النزول اللي هنا سيعمل decreasing في aggregate
+
+305
+00:28:50,970 --> 00:28:55,990
+expenditure ويعمل decreasing في الـYبس دائما ..
+
+306
+00:28:55,990 --> 00:29:01,050
+دائما الدراسات بتقول ان ال second cycle هذا تأثيره
+
+307
+00:29:01,050 --> 00:29:06,990
+قليل هلقيت سؤال؟ ال growth funding هنا زاد .. بدأ
+
+308
+00:29:06,990 --> 00:29:11,590
+افترض ال 100 مليون تمام؟
+
+309
+00:29:11,590 --> 00:29:15,950
+بدأ افترض due to the multiplier .. ال multiplier
+
+310
+00:29:15,950 --> 00:29:21,550
+effect ال Y .. وين رايح ال Y؟ على ال income زاد ب
+
+311
+00:29:21,550 --> 00:29:24,740
+400 مليونيعني احنا زدنا ال government spending ب
+
+312
+00:29:24,740 --> 00:29:29,100
+100 مليون ال Y increased by 400 مليون تمام؟ بال
+
+313
+00:29:29,100 --> 00:29:32,940
+second stage تأثير ال interest rate ال investment
+
+314
+00:29:32,940 --> 00:29:38,040
+وتأثيره عن ال Y هنا قد ينخفض ال Y ب 20 مليون بس
+
+315
+00:29:38,040 --> 00:29:45,380
+هذا الانزول اللي صار اسمه crowding out هذا
+
+316
+00:29:45,380 --> 00:29:50,150
+الانزولالتزاهم اللي صار هنا بين ال interest rate و
+
+317
+00:29:50,150 --> 00:29:53,330
+ال investment لأن ال interest rate طلع عمل
+
+318
+00:29:53,330 --> 00:29:57,850
+decrease في ال investment و بعدين decreasing في ال
+
+319
+00:29:57,850 --> 00:30:02,170
+Y و decreasing جليل لأن التعاخد ال third stage رح
+
+320
+00:30:02,170 --> 00:30:05,490
+تكون أجل أجل أقل ما اللي صار بال zero في الآخر
+
+321
+00:30:05,490 --> 00:30:10,850
+تمام؟ هذا هيك لنزول اللي صار في ال Yالوظيفة ده
+
+322
+00:30:10,850 --> 00:30:14,250
+تزيد الـ Interest Rate اللي هو نتيجة انه .. هذا
+
+323
+00:30:14,250 --> 00:30:17,510
+sensitive ال .. البسمة sensitive لمين؟ ال Interest
+
+324
+00:30:17,510 --> 00:30:25,650
+Rate هذا اسمه Crowding Out بمعنى
+
+325
+00:30:25,650 --> 00:30:28,690
+احنا عملنا increase في ال government spending زاد
+
+326
+00:30:28,690 --> 00:30:32,690
+ال 1 GDP تمام هذا .. this is .. that's a goal يعني
+
+327
+00:30:32,690 --> 00:30:38,030
+تمام؟ هذا ال goal تبعنا بس بال longer run in the
+
+328
+00:30:38,030 --> 00:30:43,660
+second stageرجع الانزول تاني بس الانزول بسيط هذا
+
+329
+00:30:43,660 --> 00:30:46,960
+الانزول اجا نتيجة ان ال interest rate طلع اعمل
+
+330
+00:30:46,960 --> 00:30:49,800
+decrease في ال investment وغير التالي وصار عندنا
+
+331
+00:30:49,800 --> 00:30:52,000
+crowding out وقت ايش بيكون ال crowding out equal
+
+332
+00:30:52,000 --> 00:30:55,380
+to zero؟
+
+333
+00:30:55,380 --> 00:30:58,580
+لأ
+
+334
+00:30:58,580 --> 00:31:04,220
+who can give us the answer here؟ وقت ايش بيكون ال
+
+335
+00:31:04,220 --> 00:31:07,220
+crowding out بساوي صفر؟ بمعنى لو رفعنا ال interest
+
+336
+00:31:07,220 --> 00:31:08,480
+rate مايأثرش على ال Y
+
+337
+00:31:11,670 --> 00:31:16,510
+أو لو ارتفع مش رفع النهار دي exactly
+
+338
+00:31:16,510 --> 00:31:22,430
+when there is no relationship between the interest
+
+339
+00:31:22,430 --> 00:31:30,170
+rate and investment اه بسيط اذا كان شوف ال
+
+340
+00:31:30,170 --> 00:31:37,870
+investment curve radical يعني هاي ال interest rate
+
+341
+00:31:37,870 --> 00:31:41,660
+و هاي ال investmentهو احنا عارفين ان هذا negative
+
+342
+00:31:41,660 --> 00:31:50,820
+في أي شيء، إذا كان Vertical، حكي Vertical هيك،
+
+343
+00:31:50,820 --> 00:31:55,080
+خلّيني اترسليت 5%، جدش ال brands investment انه
+
+344
+00:31:55,080 --> 00:31:59,640
+100 مليون دولار، تمام؟ ايه واحد، اما ال increasing
+
+345
+00:31:59,640 --> 00:32:05,020
+of interest rate، this is I، to 7%؟ لأ، صدق الله،
+
+346
+00:32:05,020 --> 00:32:11,290
+is Verticalهو it's always there is a relationship
+
+347
+00:32:11,290 --> 00:32:14,990
+between interest rate and investment as a negative
+
+348
+00:32:14,990 --> 00:32:19,690
+relationship بس sometimes .. sometimes crowding
+
+349
+00:32:19,690 --> 00:32:25,250
+out بيكون .. if there is no .. some assumption تش
+
+350
+00:32:25,250 --> 00:32:28,110
+بيكون crowding out equal zero when there is no
+
+351
+00:32:28,110 --> 00:32:30,950
+relationship between ال interest rate و ال
+
+352
+00:32:30,950 --> 00:32:41,990
+investment أه؟ و هذا بيحاولوا ..لأ ممكن يصير شوف
+
+353
+00:32:41,990 --> 00:32:46,370
+طبعا
+
+354
+00:32:46,370 --> 00:32:53,010
+هذا rare cases حالات نادرة جدا تمام؟ بس في جزئية
+
+355
+00:32:53,010 --> 00:33:00,050
+راح نتطرقلها بال American economy ليش بتحركوش
+
+356
+00:33:00,050 --> 00:33:03,060
+دايما بال interest rate؟يعني .. يعني .. يعني
+
+357
+00:33:03,060 --> 00:33:06,120
+بيحافظ ال .. ال congress أو ال .. ال .. ال
+
+358
+00:33:06,120 --> 00:33:09,320
+minister of finance عندهم انه ال interest rate ..
+
+359
+00:33:09,320 --> 00:33:13,280
+اقولك لو واحد حكى ال interest rate .. يعني
+
+360
+00:33:13,280 --> 00:33:16,780
+بيحاولوا انه يدل ال interest rate حوالي الرقم معين
+
+361
+00:33:16,780 --> 00:33:21,800
+لأن اي تحريك لل interest rate راح تم ال effects
+
+362
+00:33:21,800 --> 00:33:25,200
+عالمي على الدولار نفس ال change rate تبقى الدولار
+
+363
+00:33:25,200 --> 00:33:29,780
+و بتاني بيحرك المعلومة العالم كلهفالتحركات دايما
+
+364
+00:33:29,780 --> 00:33:33,020
+اقول اخلي وزير الخزانة يحكي في او محافظة البنك
+
+365
+00:33:33,020 --> 00:33:36,880
+المركزي عندهم انه يحكي انه ال interest rate بدنا
+
+366
+00:33:36,880 --> 00:33:42,160
+نوفعه شو يشوف شو بيصير في الدولار طبعا goes up انه
+
+367
+00:33:42,160 --> 00:33:45,020
+ال capital investment تيجي من الدره طب ازاي تطلب ع
+
+368
+00:33:45,020 --> 00:33:48,300
+الدولار عشان يشتري investment من الدره؟ 100% 100%
+
+369
+00:33:48,300 --> 00:33:55,260
+تمام تمام طيب I will come back quickly to here and
+
+370
+00:33:55,260 --> 00:34:01,070
+the last point I think اه I finishedطيب .. if
+
+371
+00:34:01,070 --> 00:34:09,130
+supply ..
+
+372
+00:34:09,130 --> 00:34:18,510
+goes down .. or declined .. lose saving عمليا ..
+
+373
+00:34:18,510 --> 00:34:21,410
+احنا قولنا هذا saving طبعا .. households ..
+
+374
+00:34:21,410 --> 00:34:28,040
+backward .. شو بيعمل؟بيخلّي ال interest rate يطلع
+
+375
+00:34:28,040 --> 00:34:30,720
+لأن this is the original here point interest rate
+
+376
+00:34:30,720 --> 00:34:37,720
+interest rate goes up to R2 size of investment شو
+
+377
+00:34:37,720 --> 00:34:41,480
+بيصير فيه؟
+
+378
+00:34:41,480 --> 00:34:48,200
+لو هذا الجزء عملنا crowding out تمام؟
+
+379
+00:34:48,200 --> 00:34:54,330
+اه؟ طيب ال pointلما يكون فينا budget deficit
+
+380
+00:34:54,330 --> 00:34:59,750
+يقولنا خليني الجزء يعني هذا المرة اللي جاي بناخد
+
+381
+00:34:59,750 --> 00:35:04,370
+بس fifteen minutes استكمله ممكن بعدين presentation
+
+382
+00:35:04,370 --> 00:35:06,250
+ساعة يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/LZ5sV9SyzkI_raw.json b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/LZ5sV9SyzkI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b1a3e740a0b1304b8c49010a53972d41895db748
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/LZ5sV9SyzkI_raw.json
@@ -0,0 +1 @@
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فماذا سيحدث لدفع المال أو دماغ المال لغاية المستخدمين؟", "tokens": [3615, 23942, 3714, 14851, 2407, 7578, 16247, 3794, 3615, 9640, 12399, 9154, 29739, 4587, 16606, 12399, 11933, 15730, 25961, 2655, 12174, 32640, 3660, 2423, 39184, 49, 5551, 3615, 23942, 12399, 6156, 2304, 45636, 995, 8608, 1829, 24401, 12984, 5296, 3215, 5172, 3615, 9673, 6027, 34051, 11778, 2304, 5718, 118, 9673, 6027, 5296, 17082, 995, 10632, 9673, 14851, 9778, 40448, 9957, 22807], "avg_logprob": -0.8543346485783977, "compression_ratio": 1.4850746268656716, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 142.56, "end": 143.02, "word": "على", "probability": 0.159698486328125}, {"start": 143.02, "end": 143.06, "word": " مستوى", "probability": 0.537811279296875}, {"start": 143.06, "end": 145.7, "word": " الأسعار،", "probability": 0.46497802734375}, {"start": 145.7, "end": 146.24, "word": " من", "probability": 0.24365234375}, {"start": 146.24, "end": 147.5, "word": " البقاء،", "probability": 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saving equals Y minus C minus T plus T minus G So subtracting T with T S equals Y minus C", "tokens": [51, 3175, 460, 20328, 5016, 22807, 407, 264, 3217, 6816, 6915, 398, 3175, 383, 3175, 314, 1804, 314, 3175, 460, 407, 16390, 278, 314, 365, 314, 318, 6915, 398, 3175, 383], "avg_logprob": -0.3022460797801614, "compression_ratio": 1.3370786516853932, "no_speech_prob": 0.0, "words": [{"start": 1197.67, "end": 1198.09, "word": "T", "probability": 0.2142333984375}, {"start": 1198.09, "end": 1201.47, "word": " minus", "probability": 0.1236572265625}, {"start": 1201.47, "end": 1201.89, "word": " G", "probability": 0.767578125}, {"start": 1201.89, "end": 1206.49, "word": " صح؟", "probability": 0.7386067708333334}, {"start": 1206.49, "end": 1206.93, "word": " So", "probability": 0.27685546875}, {"start": 1206.93, "end": 1207.51, "word": " the", "probability": 0.64599609375}, {"start": 1207.51, "end": 1207.87, "word": " total", "probability": 0.830078125}, {"start": 1207.87, "end": 1208.35, 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واحد حكى ال interest rate .. يعني بيحاولوا انه يدل ال interest rate حوالي الرقم معين لأن اي تحريك لل interest rate راح تم ال effects عالمي على الدولار نفس ال change rate تبقى الدولار و بتاني بيحرك المعلومة العالم كله", "tokens": [40228, 22653, 4386, 37495, 22653, 4386, 37495, 22653, 4724, 1829, 5016, 31845, 19913, 2423, 4386, 2423, 17546, 34051, 2423, 4386, 2423, 4386, 2423, 10563, 295, 10719, 43242, 16095, 16472, 3224, 2423, 1179, 3314, 4386, 1975, 39648, 4117, 45164, 36764, 24401, 11331, 4117, 7578, 2423, 1179, 3314, 4386, 37495, 22653, 4724, 1829, 5016, 995, 12610, 14407, 16472, 3224, 7251, 3215, 1211, 2423, 1179, 3314, 11331, 2407, 6027, 1829, 34892, 4587, 2304, 20449, 9957, 5296, 33456, 1975, 1829, 6055, 5016, 16572, 4117, 24976, 1179, 3314, 12602, 39319, 46811, 2423, 5065, 6225, 45340, 1829, 15844, 32748, 12610, 9640, 8717, 36178, 2423, 1319, 3314, 6055, 3555, 4587, 7578, 32748, 12610, 9640, 4032, 39894, 7649, 1829, 4724, 1829, 5016, 31747, 9673, 30241, 20498, 3660, 18863, 45340, 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"end": 2181.36, "word": " عشر", "probability": 0.93212890625}, {"start": 2181.36, "end": 2182.08, "word": " دولار،", "probability": 0.9781494140625}, {"start": 2182.08, "end": 2182.08, "word": " باعت", "probability": 0.9581705729166666}, {"start": 2182.08, "end": 2182.08, "word": " ملابس", "probability": 0.98876953125}, {"start": 2182.08, "end": 2182.08, "word": " واحد", "probability": 0.96435546875}, {"start": 2182.08, "end": 2182.08, "word": " ع", "probability": 0.97216796875}], "temperature": 1.0}, {"id": 82, "seek": 221092, "start": 2183.15, "end": 2210.93, "text": "brought one hundred by one hundred dollars clothing and pays the same seven dollars هذا sales taxes تمام؟ this person number one or the income of the person or the buyer number one was let us assume it was two thousand dollars per week هذا دخله الفين دولار", "tokens": [1443, 930, 472, 3262, 538, 472, 3262, 3808, 11502, 293, 10604, 264, 912, 3407, 3808, 23758, 5763, 10041, 46811, 10943, 22807, 341, 954, 1230, 472, 420, 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"word": " and", "probability": 0.794921875}, {"start": 2188.23, "end": 2188.77, "word": " pays", "probability": 0.822265625}, {"start": 2188.77, "end": 2189.15, "word": " the", "probability": 0.8935546875}, {"start": 2189.15, "end": 2189.45, "word": " same", "probability": 0.8984375}, {"start": 2189.45, "end": 2190.93, "word": " seven", "probability": 0.6982421875}, {"start": 2190.93, "end": 2191.39, "word": " dollars", "probability": 0.93017578125}, {"start": 2191.39, "end": 2192.81, "word": " هذا", "probability": 0.6435546875}, {"start": 2192.81, "end": 2193.15, "word": " sales", "probability": 0.6572265625}, {"start": 2193.15, "end": 2193.65, "word": " taxes", "probability": 0.89892578125}, {"start": 2193.65, "end": 2196.91, "word": " تمام؟", "probability": 0.87158203125}, {"start": 2196.91, "end": 2197.43, "word": " this", "probability": 0.52001953125}, {"start": 2197.43, "end": 2198.03, "word": " person", "probability": 0.92919921875}, {"start": 2198.03, "end": 2199.11, "word": " number", "probability": 0.94140625}, {"start": 2199.11, "end": 2199.63, "word": " one", "probability": 0.95361328125}, {"start": 2199.63, "end": 2201.17, "word": " or", "probability": 0.677734375}, {"start": 2201.17, "end": 2201.35, "word": " the", "probability": 0.86962890625}, {"start": 2201.35, "end": 2201.87, "word": " income", "probability": 0.9599609375}, {"start": 2201.87, "end": 2202.27, "word": " of", "probability": 0.9755859375}, {"start": 2202.27, "end": 2202.45, "word": " the", "probability": 0.9033203125}, {"start": 2202.45, "end": 2202.85, "word": " person", "probability": 0.7783203125}, {"start": 2202.85, "end": 2203.03, "word": " or", "probability": 0.6474609375}, {"start": 2203.03, "end": 2203.11, "word": " the", "probability": 0.66015625}, {"start": 2203.11, "end": 2203.33, "word": " buyer", "probability": 0.9697265625}, {"start": 2203.33, "end": 2203.61, "word": " number", "probability": 0.96826171875}, {"start": 2203.61, "end": 2204.07, "word": " one", "probability": 0.94873046875}, {"start": 2204.07, "end": 2205.09, "word": " was", "probability": 0.92041015625}, {"start": 2205.09, "end": 2205.37, "word": " let", "probability": 0.8720703125}, {"start": 2205.37, "end": 2205.53, "word": " us", "probability": 0.79443359375}, {"start": 2205.53, "end": 2205.93, "word": " assume", "probability": 0.89013671875}, {"start": 2205.93, "end": 2206.07, "word": " it", "probability": 0.916015625}, {"start": 2206.07, "end": 2206.39, "word": " was", "probability": 0.9599609375}, {"start": 2206.39, "end": 2206.85, "word": " two", "probability": 0.9345703125}, {"start": 2206.85, "end": 2207.47, "word": " thousand", "probability": 0.86865234375}, {"start": 2207.47, "end": 2207.95, "word": " dollars", "probability": 0.92822265625}, {"start": 2207.95, "end": 2208.41, "word": " per", "probability": 0.96484375}, {"start": 2208.41, "end": 2208.73, "word": " week", "probability": 0.9609375}, {"start": 2208.73, "end": 2209.93, "word": " هذا", "probability": 0.35986328125}, {"start": 2209.93, "end": 2210.29, "word": " دخله", "probability": 0.77685546875}, {"start": 2210.29, "end": 2210.65, "word": " الفين", "probability": 0.85791015625}, {"start": 2210.65, "end": 2210.93, "word": " دولار", "probability": 0.9723307291666666}], "temperature": 1.0}, {"id": 83, "seek": 224098, "start": 2212.82, "end": 2240.98, "text": "و هذا ال income اه هذا ال income تبعه لأ هذا ماشي معناه three hundred twenty dollars هذا income و هذا task و هذا ال purchase ال value purchase هذا هي يعني ال value purchase", "tokens": [2407, 23758, 2423, 5742, 1975, 3224, 23758, 2423, 5742, 6055, 3555, 3615, 3224, 5296, 10721, 23758, 3714, 33599, 1829, 20449, 8315, 3224, 1045, 3262, 7699, 3808, 23758, 5742, 4032, 23758, 5633, 4032, 23758, 2423, 8110, 2423, 2158, 8110, 23758, 39896, 37495, 22653, 2423, 2158, 8110], "avg_logprob": -0.2657948434352875, "compression_ratio": 1.6962962962962962, "no_speech_prob": 0.0, "words": [{"start": 2212.82, "end": 2212.98, "word": "و", 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"probability": 0.6935221354166666}, {"start": 2222.8, "end": 2223.48, "word": " three", "probability": 0.44287109375}, {"start": 2223.48, "end": 2223.78, "word": " hundred", "probability": 0.94140625}, {"start": 2223.78, "end": 2224.42, "word": " twenty", "probability": 0.53271484375}, {"start": 2224.42, "end": 2224.9, "word": " dollars", "probability": 0.6513671875}, {"start": 2224.9, "end": 2228.32, "word": " هذا", "probability": 0.859375}, {"start": 2228.32, "end": 2228.74, "word": " income", "probability": 0.94189453125}, {"start": 2228.74, "end": 2231.18, "word": " و", "probability": 0.76123046875}, {"start": 2231.18, "end": 2231.36, "word": " هذا", "probability": 0.93994140625}, {"start": 2231.36, "end": 2231.84, "word": " task", "probability": 0.525390625}, {"start": 2231.84, "end": 2233.74, "word": " و", "probability": 0.94091796875}, {"start": 2233.74, "end": 2234.08, "word": " هذا", "probability": 0.94677734375}, {"start": 2234.08, "end": 2234.56, "word": " ال", "probability": 0.96728515625}, {"start": 2234.56, "end": 2235.06, "word": " purchase", "probability": 0.97509765625}, {"start": 2235.06, "end": 2236.44, "word": " ال", "probability": 0.86572265625}, {"start": 2236.44, "end": 2236.78, "word": " value", "probability": 0.99072265625}, {"start": 2236.78, "end": 2237.7, "word": " purchase", "probability": 0.94482421875}, {"start": 2237.7, "end": 2239.46, "word": " هذا", "probability": 0.869140625}, {"start": 2239.46, "end": 2239.66, "word": " هي", "probability": 0.71240234375}, {"start": 2239.66, "end": 2239.88, "word": " يعني", "probability": 0.87353515625}, {"start": 2239.88, "end": 2240.1, "word": " ال", "probability": 0.8623046875}, {"start": 2240.1, "end": 2240.42, "word": " value", "probability": 0.994140625}, {"start": 2240.42, "end": 2240.98, "word": " purchase", "probability": 0.966796875}], "temperature": 1.0}, {"id": 84, "seek": 227338, "start": 2244.44, "end": 2273.38, "text": "و هذا ال taxes tax paid or sales taxes و هذا ال income how much is the tax rate for the first consumer or for the first payer؟ كده ايش دفع taxes هذا؟ always income is high he pays how much؟", "tokens": [2407, 23758, 2423, 10041, 3366, 4835, 420, 5763, 10041, 4032, 23758, 2423, 5742, 577, 709, 307, 264, 3366, 3314, 337, 264, 700, 9711, 420, 337, 264, 700, 38230, 22807, 9122, 3215, 3224, 1975, 1829, 8592, 11778, 5172, 3615, 10041, 23758, 22807, 1009, 5742, 307, 1090, 415, 10604, 577, 709, 22807], "avg_logprob": -0.32598040267532946, "compression_ratio": 1.4594594594594594, "no_speech_prob": 0.0, "words": [{"start": 2244.44, "end": 2244.6, "word": "و", "probability": 0.5966796875}, {"start": 2244.6, "end": 2244.82, "word": " هذا", "probability": 0.22265625}, {"start": 2244.82, "end": 2245.16, "word": " ال", "probability": 0.84228515625}, {"start": 2245.16, "end": 2245.58, "word": " taxes", "probability": 0.7939453125}, {"start": 2245.58, "end": 2248.82, "word": " tax", "probability": 0.368896484375}, {"start": 2248.82, "end": 2249.28, 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"probability": 0.6265462239583334}, {"start": 2266.42, "end": 2266.64, "word": " دفع", "probability": 0.7252604166666666}, {"start": 2266.64, "end": 2267.0, "word": " taxes", "probability": 0.53173828125}, {"start": 2267.0, "end": 2268.68, "word": " هذا؟", "probability": 0.6142578125}, {"start": 2268.68, "end": 2269.2, "word": " always", "probability": 0.32080078125}, {"start": 2269.2, "end": 2269.8, "word": " income", "probability": 0.76611328125}, {"start": 2269.8, "end": 2270.08, "word": " is", "probability": 0.96875}, {"start": 2270.08, "end": 2270.46, "word": " high", "probability": 0.91162109375}, {"start": 2270.46, "end": 2272.06, "word": " he", "probability": 0.76171875}, {"start": 2272.06, "end": 2272.46, "word": " pays", "probability": 0.9521484375}, {"start": 2272.46, "end": 2272.66, "word": " how", "probability": 0.95849609375}, {"start": 2272.66, "end": 2273.38, "word": " much؟", "probability": 0.811279296875}], "temperature": 1.0}, {"id": 85, "seek": 230215, "start": 2273.97, "end": 2302.15, "text": "7$ from 2000$ so the tax rate paid here for the first buyer equals 7$ over 2000$ equals how much? 0.35% دفع هذا الجد من دخله طب التاني نشوف جد إيش دفعها", "tokens": [22, 3, 490, 8132, 3, 370, 264, 3366, 3314, 4835, 510, 337, 264, 700, 24645, 6915, 1614, 3, 670, 8132, 3, 6915, 577, 709, 30, 1958, 13, 8794, 4, 11778, 5172, 3615, 23758, 25724, 3215, 9154, 11778, 9778, 43761, 23032, 3555, 16712, 7649, 1829, 8717, 8592, 38688, 10874, 3215, 11933, 1829, 8592, 11778, 5172, 3615, 11296], "avg_logprob": -0.29029606517992523, "compression_ratio": 1.1875, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2273.97, "end": 2274.43, "word": "7", "probability": 0.400146484375}, {"start": 2274.43, "end": 2274.91, "word": "$", "probability": 0.76904296875}, {"start": 2274.91, "end": 2275.53, "word": " from", "probability": 0.256103515625}, {"start": 2275.53, "end": 2276.37, "word": " 2000", "probability": 0.88720703125}, {"start": 2276.37, "end": 2276.71, 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inflation", "probability": 0.92431640625}, {"start": 186.64, "end": 187.32, "word": " rate", "probability": 0.9794921875}, {"start": 187.32, "end": 188.4, "word": " equals", "probability": 0.8837890625}, {"start": 188.4, "end": 189.08, "word": " 2", "probability": 0.64453125}, {"start": 189.08, "end": 190.06, "word": "%", "probability": 0.92236328125}, {"start": 190.06, "end": 192.82, "word": " ال", "probability": 0.5224609375}, {"start": 192.82, "end": 193.16, "word": " vendors", "probability": 0.489013671875}, {"start": 193.16, "end": 193.58, "word": " هدول", "probability": 0.7623697916666666}, {"start": 193.58, "end": 193.76, "word": " اللي", "probability": 0.9853515625}, {"start": 193.76, "end": 193.98, "word": " هم", "probability": 0.9296875}, {"start": 193.98, "end": 194.58, "word": " يعطونا", "probability": 0.710662841796875}, {"start": 194.58, "end": 195.08, "word": " ال", "probability": 0.8623046875}, {"start": 195.08, "end": 195.36, "word": " money", "probability": 0.9755859375}, {"start": 195.36, "end": 197.0, "word": " شو", "probability": 0.879150390625}, {"start": 197.0, "end": 197.58, "word": " استفاد؟", "probability": 0.9095458984375}], "temperature": 1.0}, {"id": 7, "seek": 22368, "start": 198.82, "end": 223.68, "text": "nothing هنقل ال interest rate شو بيساوي؟ نوم ال interest rate minus inflation rate صح؟", "tokens": [49518, 8032, 1863, 4587, 1211, 2423, 1179, 3314, 13412, 2407, 4724, 1829, 3794, 995, 45865, 22807, 8717, 20498, 2423, 1179, 3314, 3175, 15860, 3314, 20328, 5016, 22807], "avg_logprob": -0.5203683014426913, "compression_ratio": 1.1978021978021978, "no_speech_prob": 0.0, "words": [{"start": 198.82, "end": 199.34, "word": "nothing", "probability": 0.06939697265625}, {"start": 199.34, "end": 200.38, "word": " هنقل", "probability": 0.357421875}, {"start": 200.38, "end": 200.58, "word": " ال", "probability": 0.63232421875}, {"start": 200.58, "end": 200.92, "word": " interest", "probability": 0.5595703125}, {"start": 200.92, "end": 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rate 2% و عنده inflation rate طالع بالسنة 2% actually هو إيش سفات؟ Zero، nothing، مظبوط؟ هذا Zero خلّي ال inflation rate يصير 10% يعني خلّيلي ال interest rate 10% inflation rate .. sorry inflation rate", "tokens": [28814, 15730, 1975, 8315, 39894, 3615, 9566, 26895, 3224, 8978, 28239, 2304, 37977, 2423, 39184, 1179, 3314, 568, 4, 4032, 43242, 3224, 15860, 3314, 23032, 6027, 3615, 20666, 3794, 1863, 3660, 568, 4, 767, 31439, 11933, 1829, 8592, 8608, 5172, 9307, 22807, 17182, 12399, 1825, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 23758, 17182, 16490, 1211, 11703, 1829, 2423, 15860, 3314, 7251, 9381, 13546, 1266, 4, 37495, 22653, 16490, 1211, 11703, 1829, 20292, 2423, 1179, 3314, 1266, 4, 15860, 3314, 4386, 2597, 15860, 3314], "avg_logprob": -0.32426470588235295, "compression_ratio": 1.5555555555555556, "no_speech_prob": 0.0, "words": [{"start": 225.68, "end": 225.92, "word": "إذا", "probability": 0.5501708984375}, {"start": 225.92, "end": 226.06, "word": " انا", "probability": 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"probability": 0.64404296875}, {"start": 271.74, "end": 272.2, "word": " اتدينت", "probability": 0.69296875}, {"start": 272.2, "end": 272.48, "word": " منك", "probability": 0.88232421875}, {"start": 272.48, "end": 272.78, "word": " خمس", "probability": 0.70068359375}, {"start": 272.78, "end": 273.08, "word": " تلاف", "probability": 0.7018229166666666}, {"start": 273.08, "end": 273.2, "word": " و", "probability": 0.38134765625}, {"start": 273.2, "end": 273.54, "word": " تستدعي", "probability": 0.5853515625}, {"start": 273.54, "end": 273.78, "word": " خمس", "probability": 0.9920247395833334}, {"start": 273.78, "end": 274.84, "word": " تلاف،", "probability": 0.784423828125}, {"start": 274.84, "end": 275.12, "word": " لو", "probability": 0.92822265625}, {"start": 275.12, "end": 275.32, "word": " بعد", "probability": 0.69580078125}, {"start": 275.32, "end": 275.58, "word": " عشر", "probability": 0.9619140625}, {"start": 275.58, "end": 276.58, "word": " سنين،", "probability": 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0.8211263020833334}], "temperature": 1.0}, {"id": 10, "seek": 30624, "start": 283.68, "end": 306.24, "text": "لأن الـ real value of money goes down لأن الـ present value تبع المصاري تنزل إذا الـ inflation rate صار 10% عنده الـ negative 8% هو اسميا ماخد 1200", "tokens": [1211, 33456, 2423, 39184, 957, 2158, 295, 1460, 1709, 760, 5296, 33456, 2423, 39184, 1974, 2158, 6055, 3555, 3615, 9673, 9381, 9640, 1829, 6055, 1863, 11622, 1211, 11933, 15730, 2423, 39184, 15860, 3314, 20328, 9640, 1266, 4, 43242, 3224, 2423, 39184, 3671, 1649, 4, 31439, 24525, 2304, 25528, 3714, 47283, 3215, 29139], "avg_logprob": -0.49056603773584906, "compression_ratio": 1.2820512820512822, "no_speech_prob": 0.0, "words": [{"start": 283.68, "end": 284.1, "word": "لأن", "probability": 0.76904296875}, {"start": 284.1, "end": 284.48, "word": " الـ", "probability": 0.4156494140625}, {"start": 284.48, "end": 284.78, "word": " real", "probability": 0.34765625}, {"start": 284.78, "end": 285.2, "word": " value", "probability": 0.978515625}, {"start": 285.2, "end": 285.32, "word": " of", "probability": 0.93017578125}, {"start": 285.32, "end": 285.6, "word": " money", "probability": 0.94482421875}, {"start": 285.6, "end": 286.08, "word": " goes", "probability": 0.4423828125}, {"start": 286.08, "end": 286.88, "word": " down", "probability": 0.84033203125}, {"start": 286.88, "end": 288.18, "word": " لأن", "probability": 0.49786376953125}, {"start": 288.18, "end": 288.24, "word": " الـ", "probability": 0.657470703125}, {"start": 288.24, "end": 288.62, "word": " present", "probability": 0.62939453125}, {"start": 288.62, "end": 291.98, "word": " value", "probability": 0.9873046875}, {"start": 291.98, "end": 292.2, "word": " تبع", "probability": 0.4910074869791667}, {"start": 292.2, "end": 292.68, "word": " المصاري", "probability": 0.6519775390625}, {"start": 292.68, "end": 293.12, "word": " تنزل", "probability": 0.77734375}, {"start": 293.12, "end": 294.28, "word": " إذا", "probability": 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المقام.", "probability": 0.7744140625}], "temperature": 1.0}, {"id": 44, "seek": 121361, "start": 1186.8, "end": 1213.62, "text": "هو بده ايش؟ هذا ال pace year of the pace year of 2006 هي ال pace year تمام؟ بده ال consumer price index وين؟ في 2007 هاي ال .. ال .. ال .. نرجع هيك let's come back بده ال consumer price index in 2007 و ال pace .. of the pace year", "tokens": [3224, 2407, 47525, 3224, 1975, 1829, 8592, 22807, 23758, 2423, 11638, 1064, 295, 264, 11638, 1064, 295, 14062, 39896, 2423, 11638, 1064, 46811, 10943, 22807, 47525, 3224, 2423, 9711, 3218, 8186, 4032, 9957, 22807, 8978, 12656, 8032, 47302, 2423, 4386, 2423, 4386, 2423, 4386, 8717, 47341, 3615, 39896, 4117, 718, 311, 808, 646, 47525, 3224, 2423, 9711, 3218, 8186, 294, 12656, 4032, 2423, 11638, 4386, 295, 264, 11638, 1064], "avg_logprob": -0.25022320236478535, "compression_ratio": 1.7289156626506024, "no_speech_prob": 0.0, "words": [{"start": 1186.8, "end": 1187.02, "word": "هو", "probability": 0.8701171875}, {"start": 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"probability": 0.90576171875}, {"start": 1203.84, "end": 1207.2, "word": " بده", "probability": 0.60870361328125}, {"start": 1207.2, "end": 1207.28, "word": " ال", "probability": 0.88232421875}, {"start": 1207.28, "end": 1207.6, "word": " consumer", "probability": 0.923828125}, {"start": 1207.6, "end": 1207.9, "word": " price", "probability": 0.94775390625}, {"start": 1207.9, "end": 1208.24, "word": " index", "probability": 0.9052734375}, {"start": 1208.24, "end": 1208.62, "word": " in", "probability": 0.5986328125}, {"start": 1208.62, "end": 1209.54, "word": " 2007", "probability": 0.962890625}, {"start": 1209.54, "end": 1212.16, "word": " و", "probability": 0.837890625}, {"start": 1212.16, "end": 1212.24, "word": " ال", "probability": 0.90576171875}, {"start": 1212.24, "end": 1212.54, "word": " pace", "probability": 0.92333984375}, {"start": 1212.54, "end": 1212.7, "word": " ..", "probability": 0.84521484375}, {"start": 1212.7, "end": 1212.9, "word": " of", "probability": 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pay year 2006 لما روحت ال 2007 ال prices طلعت بال consumer price index inflation rate صار inflation rate equals 106.1 minus 100 كسنة أساس equals 6.1 percent this is the inflation rate", "tokens": [21, 4, 37495, 22653, 9154, 14062, 2423, 7578, 12656, 1975, 8315, 3714, 47283, 3215, 2423, 1689, 1064, 14062, 5296, 15042, 12602, 2407, 33753, 2423, 12656, 2423, 7901, 23032, 1211, 34268, 20666, 9711, 3218, 8186, 15860, 3314, 20328, 9640, 15860, 3314, 6915, 1266, 21, 13, 16, 3175, 2319, 9122, 3794, 1863, 3660, 5551, 3794, 32277, 6915, 1386, 13, 16, 3043, 341, 307, 264, 15860, 3314], "avg_logprob": -0.35528846153846155, "compression_ratio": 1.451086956521739, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1293.55, "end": 1293.91, "word": "6", "probability": 0.2186279296875}, {"start": 1293.91, "end": 1294.25, "word": "%", "probability": 0.599609375}, {"start": 1294.25, "end": 1295.27, "word": " يعني", "probability": 0.850830078125}, {"start": 1295.27, "end": 1295.39, "word": " 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بالعكس، لأ مثلا ال deflation صح ال deflation يعني لو هو قالي هيك اللي هو calculate the consumer price index في ال 2005 و ال pay year 2007", "tokens": [39237, 10943, 22807, 4032, 4724, 16254, 1975, 8592, 38688, 20666, 14062, 13412, 3224, 13063, 4032, 11778, 3224, 2423, 9711, 3218, 8186, 37893, 18863, 4117, 3794, 22807, 37893, 20666, 3615, 4117, 3794, 12399, 5296, 10721, 50113, 15040, 2423, 1060, 24278, 20328, 5016, 2423, 1060, 24278, 37495, 22653, 45164, 31439, 50239, 1829, 39896, 4117, 13672, 1829, 31439, 8873, 264, 9711, 3218, 8186, 8978, 2423, 14394, 4032, 2423, 1689, 1064, 12656], "avg_logprob": -0.4087409316629603, "compression_ratio": 1.5449735449735449, "no_speech_prob": 0.0, "words": [{"start": 1378.48, "end": 1379.24, "word": "تمام؟", "probability": 0.6505940755208334}, {"start": 1379.24, "end": 1379.52, "word": " و", "probability": 0.62548828125}, {"start": 1379.52, "end": 1379.74, "word": " بدي", "probability": 0.62451171875}, {"start": 1379.74, "end": 1380.32, "word": " 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function و بعدها بعمل اتفاضل total revenue شو بيسوي ال price times Q", "tokens": [6027, 28814, 13546, 18513, 21542, 16254, 16070, 2655, 17082, 1829, 13546, 8978, 33688, 13546, 18513, 33251, 20292, 10874, 3215, 8592, 6055, 11242, 33911, 15844, 33688, 13546, 18513, 33251, 20292, 5296, 8848, 23275, 7251, 7435, 3555, 14739, 1975, 4587, 20498, 4724, 995, 14851, 9778, 3215, 10943, 2423, 39184, 3217, 9324, 2445, 9154, 23758, 2423, 39184, 3217, 9324, 2445, 4032, 39182, 11296, 4724, 25957, 1211, 1975, 2655, 5172, 46958, 1211, 3217, 9324, 13412, 2407, 4724, 1829, 3794, 45865, 2423, 3218, 1413, 1249], "avg_logprob": -0.5243055320080415, "compression_ratio": 1.7526881720430108, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1383.93, "end": 1384.31, "word": "الإيراد", "probability": 0.72967529296875}, {"start": 1384.31, "end": 1384.77, "word": " الحدي", "probability": 0.774169921875}, {"start": 1384.77, "end": 1385.39, "word": " والتغيير", "probability": 0.84775390625}, {"start": 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1414.04, "end": 1442.24, "text": "مظبوط؟ TA equals هاي ال formula تابعة ال price times Q بيصير هاي ال price اندي انا اللي هو 400 minus 8Q كله times Q اللي هي ال Q الأساسية في ال formula مظبوط؟ so total revenue equals 400Q minus 8Q square", "tokens": [2304, 19913, 3555, 2407, 9566, 22807, 20094, 6915, 8032, 47302, 2423, 8513, 6055, 16758, 27884, 2423, 3218, 1413, 1249, 4724, 1829, 9381, 13546, 8032, 47302, 2423, 3218, 16472, 16254, 1975, 8315, 13672, 1829, 31439, 8423, 3175, 1649, 48, 28242, 3224, 1413, 1249, 13672, 1829, 39896, 2423, 1249, 16247, 3794, 32277, 10632, 8978, 2423, 8513, 3714, 19913, 3555, 2407, 9566, 22807, 370, 3217, 9324, 6915, 8423, 48, 3175, 1649, 48, 3732], "avg_logprob": -0.3105193628391749, "compression_ratio": 1.5337078651685394, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1414.04, "end": 1414.76, "word": "مظبوط؟", "probability": 0.7165934244791666}, {"start": 1414.76, "end": 1415.2, "word": " TA", "probability": 0.480712890625}, {"start": 1415.2, 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"probability": 0.951416015625}, {"start": 1437.66, "end": 1440.36, "word": " minus", "probability": 0.95166015625}, {"start": 1440.36, "end": 1441.78, "word": " 8Q", "probability": 0.9599609375}, {"start": 1441.78, "end": 1442.24, "word": " square", "probability": 0.35009765625}], "temperature": 1.0}, {"id": 50, "seek": 146545, "start": 1448.65, "end": 1465.45, "text": "400Q-8Q² كيف نستخدم الـ Marginal Revenue؟ MR هي تفاضل التفاضل في الـ Q", "tokens": [13741, 48, 12, 23, 48, 27643, 9122, 33911, 8717, 14851, 9778, 40448, 2423, 39184, 2039, 1494, 304, 1300, 29307, 22807, 9808, 39896, 6055, 5172, 5718, 114, 1211, 16712, 5172, 5718, 114, 1211, 8978, 2423, 39184, 1249], "avg_logprob": -0.7664696139258307, "compression_ratio": 1.0618556701030928, "no_speech_prob": 0.0, "words": [{"start": 1448.6499999999999, "end": 1450.05, "word": "400Q", "probability": 0.2617034912109375}, {"start": 1450.05, "end": 1451.45, "word": "-8Q²", "probability": 0.589630126953125}, {"start": 1451.45, "end": 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"temperature": 1.0}, {"id": 51, "seek": 149120, "start": 1470.44, "end": 1491.2, "text": "بتصفى إن هذا الفوضى ما يبقى بالنسبالي الـ Q بيصير equal أربعمية نقص اتنين في تمانية sixteen Q أُس اتنين نقص واحد صح ليه Q؟ مالك هو؟", "tokens": [3555, 2655, 9381, 5172, 7578, 36145, 23758, 27188, 2407, 11242, 7578, 19446, 7251, 3555, 4587, 7578, 20666, 1863, 35457, 6027, 1829, 2423, 39184, 1249, 4724, 1829, 9381, 13546, 2681, 5551, 25513, 25957, 10632, 8717, 4587, 9381, 1975, 2655, 1863, 9957, 8978, 46811, 7649, 10632, 2309, 9791, 1249, 5551, 10859, 3794, 1975, 2655, 1863, 9957, 8717, 4587, 9381, 36764, 24401, 20328, 5016, 32239, 3224, 1249, 22807, 3714, 6027, 4117, 31439, 22807], "avg_logprob": -0.43177817908810895, "compression_ratio": 1.38125, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1470.44, "end": 1471.02, "word": "بتصفى", "probability": 0.72333984375}, {"start": 1471.02, "end": 1471.18, "word": " إن", "probability": 0.25927734375}, {"start": 1471.18, "end": 1472.24, "word": " هذا", "probability": 0.63671875}, {"start": 1472.24, "end": 1472.52, "word": " الفوضى", "probability": 0.798828125}, {"start": 1472.52, "end": 1472.66, "word": " ما", "probability": 0.1617431640625}, {"start": 1472.66, "end": 1472.74, "word": " يبقى", "probability": 0.58453369140625}, {"start": 1472.74, "end": 1473.1, "word": " بالنسبالي", "probability": 0.7751953125}, {"start": 1473.1, "end": 1473.2, "word": " الـ", "probability": 0.497314453125}, {"start": 1473.2, "end": 1473.42, "word": " Q", "probability": 0.394775390625}, {"start": 1473.42, "end": 1474.1, "word": " بيصير", "probability": 0.75592041015625}, {"start": 1474.1, "end": 1474.44, "word": " equal", "probability": 0.2091064453125}, {"start": 1474.44, "end": 1475.16, "word": " أربعمية", "probability": 0.77777099609375}, {"start": 1475.16, "end": 1476.42, "word": " نقص", "probability": 0.8025716145833334}, {"start": 1476.42, "end": 1477.94, "word": " اتنين", "probability": 0.81964111328125}, {"start": 1477.94, "end": 1478.06, "word": " في", "probability": 0.87451171875}, {"start": 1478.06, "end": 1478.52, "word": " تمانية", "probability": 0.9684244791666666}, {"start": 1478.52, "end": 1480.06, "word": " sixteen", "probability": 0.501190185546875}, {"start": 1480.06, "end": 1481.66, "word": " Q", "probability": 0.55419921875}, {"start": 1481.66, "end": 1482.36, "word": " أُس", "probability": 0.5630696614583334}, {"start": 1482.36, "end": 1483.14, "word": " اتنين", "probability": 0.9384765625}, {"start": 1483.14, "end": 1483.46, "word": " نقص", "probability": 0.94873046875}, {"start": 1483.46, "end": 1483.82, "word": " واحد", "probability": 0.983154296875}, {"start": 1483.82, "end": 1487.24, "word": " صح", "probability": 0.896484375}, {"start": 1487.24, "end": 1487.8, "word": " ليه", "probability": 0.794189453125}, {"start": 1487.8, "end": 1490.48, "word": " Q؟", "probability": 0.581298828125}, {"start": 1490.48, "end": 1490.86, "word": " مالك", "probability": 0.6273193359375}, {"start": 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0.736328125}, {"start": 2218.04, "end": 2218.18, "word": " هي", "probability": 0.89599609375}, {"start": 2218.18, "end": 2218.5, "word": " هاي", "probability": 0.891845703125}, {"start": 2218.5, "end": 2221.0, "word": " 90", "probability": 0.126708984375}, {"start": 2221.0, "end": 2221.58, "word": " بشيل", "probability": 0.78369140625}, {"start": 2221.58, "end": 2221.84, "word": " Q", "probability": 0.70751953125}, {"start": 2221.84, "end": 2222.04, "word": " انا", "probability": 0.778076171875}, {"start": 2222.04, "end": 2222.48, "word": " هيك", "probability": 0.867431640625}], "temperature": 1.0}, {"id": 78, "seek": 224871, "start": 2223.16, "end": 2248.72, "text": "19 minus 0.05% taxes so the price equals 400 minus ضرب ل 8 في 19 152 minus minus positive", "tokens": [3405, 3175, 1958, 13, 13328, 4, 10041, 370, 264, 3218, 6915, 8423, 3175, 48812, 25513, 5296, 1649, 8978, 1294, 2119, 17, 3175, 3175, 3353], "avg_logprob": -0.5031250190734863, "compression_ratio": 1.0674157303370786, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2223.16, "end": 2224.18, "word": "19", "probability": 0.335693359375}, {"start": 2224.18, "end": 2225.38, "word": " minus", "probability": 0.1695556640625}, {"start": 2225.38, "end": 2226.34, "word": " 0", "probability": 0.8740234375}, {"start": 2226.34, "end": 2227.26, "word": ".05", "probability": 0.968994140625}, {"start": 2227.26, "end": 2228.04, "word": "%", "probability": 0.7861328125}, {"start": 2228.04, "end": 2228.96, "word": " taxes", "probability": 0.5546875}, {"start": 2228.96, "end": 2232.64, "word": " so", "probability": 0.127685546875}, {"start": 2232.64, "end": 2233.16, "word": " the", "probability": 0.541015625}, {"start": 2233.16, "end": 2233.52, "word": " price", "probability": 0.9462890625}, {"start": 2233.52, "end": 2234.32, "word": " equals", "probability": 0.74609375}, {"start": 2234.32, "end": 2234.88, "word": " 400", "probability": 0.8427734375}, {"start": 2234.88, "end": 2236.2, "word": " minus", "probability": 0.92333984375}, {"start": 2236.2, "end": 2236.58, "word": " ضرب", "probability": 0.56005859375}, {"start": 2236.58, "end": 2236.68, "word": " ل", "probability": 0.339599609375}, {"start": 2236.68, "end": 2236.96, "word": " 8", "probability": 0.64892578125}, {"start": 2236.96, "end": 2237.2, "word": " في", "probability": 0.435302734375}, {"start": 2237.2, "end": 2237.96, "word": " 19", "probability": 0.7431640625}, {"start": 2237.96, "end": 2244.2, "word": " 152", "probability": 0.587646484375}, {"start": 2244.2, "end": 2246.94, "word": " minus", "probability": 0.9033203125}, {"start": 2246.94, "end": 2247.62, "word": " minus", "probability": 0.9150390625}, {"start": 2247.62, "end": 2248.72, "word": " positive", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 79, "seek": 227932, "start": 2250.46, "end": 2279.32, "text": "مصفوط؟ negative في negative positive تمانية في خمسة في أربعة قولنا أربعة من عشر تين صح؟ I think أنه هيك خمسة في تمانية في أربعين رجع four و لا four ضرب لخمسة في المية في تمانية point four point four okay so the price equals كدهش أربعة مية نقص مية و خمسة و مية و اتنى و خمسين", "tokens": [2304, 9381, 5172, 2407, 9566, 22807, 3671, 8978, 3671, 3353, 46811, 7649, 10632, 8978, 16490, 2304, 3794, 3660, 8978, 5551, 25513, 27884, 12174, 12610, 8315, 5551, 25513, 27884, 9154, 6225, 46309, 6055, 9957, 20328, 5016, 22807, 286, 519, 14739, 3224, 39896, 4117, 16490, 2304, 3794, 3660, 8978, 46811, 7649, 10632, 8978, 5551, 25513, 3615, 9957, 12602, 7435, 3615, 1451, 4032, 20193, 1451, 48812, 25513, 5296, 9778, 2304, 3794, 3660, 8978, 9673, 10632, 8978, 46811, 7649, 10632, 935, 1451, 935, 1451, 1392, 370, 264, 3218, 6915, 9122, 3215, 3224, 8592, 5551, 25513, 27884, 3714, 10632, 8717, 4587, 9381, 3714, 10632, 4032, 16490, 2304, 3794, 3660, 4032, 3714, 10632, 4032, 1975, 2655, 1863, 7578, 4032, 16490, 2304, 3794, 9957], "avg_logprob": -0.3114406741776709, "compression_ratio": 1.912442396313364, "no_speech_prob": 2.384185791015625e-07, 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"probability": 0.9913736979166666}, {"start": 2268.62, "end": 2269.32, "word": " point", "probability": 0.7861328125}, {"start": 2269.32, "end": 2269.66, "word": " four", "probability": 0.814453125}, {"start": 2269.66, "end": 2269.94, "word": " point", "probability": 0.3642578125}, {"start": 2269.94, "end": 2272.24, "word": " four", "probability": 0.90478515625}, {"start": 2272.24, "end": 2272.54, "word": " okay", "probability": 0.59130859375}, {"start": 2272.54, "end": 2273.9, "word": " so", "probability": 0.4775390625}, {"start": 2273.9, "end": 2274.82, "word": " the", "probability": 0.57373046875}, {"start": 2274.82, "end": 2275.22, "word": " price", "probability": 0.93798828125}, {"start": 2275.22, "end": 2276.42, "word": " equals", "probability": 0.90966796875}, {"start": 2276.42, "end": 2277.06, "word": " كدهش", "probability": 0.76953125}, {"start": 2277.06, "end": 2277.26, "word": " أربعة", "probability": 0.7381998697916666}, {"start": 2277.26, "end": 2277.42, "word": " مية", "probability": 0.65771484375}, {"start": 2277.42, "end": 2277.78, "word": " نقص", "probability": 0.8707682291666666}, {"start": 2277.78, "end": 2278.04, "word": " مية", "probability": 0.746826171875}, {"start": 2278.04, "end": 2278.16, "word": " و", "probability": 0.96923828125}, {"start": 2278.16, "end": 2278.44, "word": " خمسة", "probability": 0.8802490234375}, {"start": 2278.44, "end": 2278.54, "word": " و", "probability": 0.8330078125}, {"start": 2278.54, "end": 2278.72, "word": " مية", "probability": 0.74853515625}, {"start": 2278.72, "end": 2278.84, "word": " و", "probability": 0.88916015625}, {"start": 2278.84, "end": 2278.86, "word": " اتنى", "probability": 0.496612548828125}, {"start": 2278.86, "end": 2278.98, "word": " و", "probability": 0.93994140625}, {"start": 2278.98, "end": 2279.32, "word": " خمسين", "probability": 0.947509765625}], "temperature": 1.0}, {"id": 80, "seek": 230379, "start": 2283.19, "end": 2303.79, "text": "نفس الرقم اللي افكري اشتغلنا فيه قبل شويه هذا plus 0.14 عارفين شو معناه؟ هذا الرقم شو بدلوله؟ كل ما بتحط one unit tax مضطر ال monopolist يزيد 4 مع 10 من الشهر", "tokens": [1863, 36178, 34892, 4587, 2304, 13672, 1829, 1975, 5172, 4117, 16572, 1975, 8592, 2655, 17082, 1211, 8315, 8978, 3224, 12174, 36150, 13412, 45865, 3224, 23758, 1804, 1958, 13, 7271, 6225, 9640, 5172, 9957, 13412, 2407, 20449, 8315, 3224, 22807, 23758, 34892, 4587, 2304, 13412, 2407, 47525, 1211, 12610, 3224, 22807, 28242, 19446, 39894, 5016, 9566, 472, 4985, 3366, 3714, 11242, 9566, 2288, 2423, 47721, 468, 7251, 11622, 25708, 1017, 20449, 1266, 9154, 25124, 3224, 2288], "avg_logprob": -0.29235195956732096, "compression_ratio": 1.4375, "no_speech_prob": 0.0, "words": [{"start": 2283.19, "end": 2283.47, "word": "نفس", "probability": 0.809814453125}, {"start": 2283.47, "end": 2283.79, "word": " الرقم", "probability": 0.9763997395833334}, {"start": 2283.79, "end": 2283.89, "word": " اللي", "probability": 0.744873046875}, {"start": 2283.89, "end": 2284.11, "word": " 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"word": " هذا", "probability": 0.8193359375}, {"start": 2291.35, "end": 2291.61, "word": " الرقم", "probability": 0.9793294270833334}, {"start": 2291.61, "end": 2291.77, "word": " شو", "probability": 0.96142578125}, {"start": 2291.77, "end": 2293.85, "word": " بدلوله؟", "probability": 0.6931640625}, {"start": 2293.85, "end": 2295.09, "word": " كل", "probability": 0.8017578125}, {"start": 2295.09, "end": 2295.25, "word": " ما", "probability": 0.80322265625}, {"start": 2295.25, "end": 2295.63, "word": " بتحط", "probability": 0.8427734375}, {"start": 2295.63, "end": 2296.31, "word": " one", "probability": 0.39697265625}, {"start": 2296.31, "end": 2296.65, "word": " unit", "probability": 0.5673828125}, {"start": 2296.65, "end": 2297.13, "word": " tax", "probability": 0.93408203125}, {"start": 2297.13, "end": 2298.99, "word": " مضطر", "probability": 0.850830078125}, {"start": 2298.99, "end": 2299.15, "word": " ال", "probability": 0.1728515625}, {"start": 2299.15, "end": 2300.57, "word": " monopolist", "probability": 0.91015625}, {"start": 2300.57, "end": 2301.49, "word": " يزيد", "probability": 0.9853515625}, {"start": 2301.49, "end": 2302.19, "word": " 4", "probability": 0.5107421875}, {"start": 2302.19, "end": 2302.45, "word": " مع", "probability": 0.1461181640625}, {"start": 2302.45, "end": 2302.69, "word": " 10", "probability": 0.93896484375}, {"start": 2302.69, "end": 2303.33, "word": " من", "probability": 0.97509765625}, {"start": 2303.33, "end": 2303.79, "word": " الشهر", "probability": 0.7307942708333334}], "temperature": 1.0}, {"id": 81, "seek": 233463, "start": 2305.29, "end": 2334.63, "text": "يعني لو السعر كان one shekel one دولار حط عليه تأكسر one point four price هيك معناه هذا اللي هو هذا الاربع من عشرة change in the price over the change in taxes حط tax واحد بيزيد ال price باربع من عشرة من ال price طب سؤال كده؟ if the tax equals zero كده ال price؟ هيه حط tax one unit", "tokens": [40228, 22653, 45164, 21136, 3615, 2288, 25961, 472, 750, 7124, 472, 11778, 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0.807861328125}, {"start": 2313.91, "end": 2314.19, "word": " معناه", "probability": 0.9085286458333334}, {"start": 2314.19, "end": 2314.45, "word": " هذا", "probability": 0.65087890625}, {"start": 2314.45, "end": 2314.81, "word": " اللي", "probability": 0.7381591796875}, {"start": 2314.81, "end": 2314.89, "word": " هو", "probability": 0.9775390625}, {"start": 2314.89, "end": 2315.23, "word": " هذا", "probability": 0.54345703125}, {"start": 2315.23, "end": 2316.01, "word": " الاربع", "probability": 0.70452880859375}, {"start": 2316.01, "end": 2316.05, "word": " من", "probability": 0.9794921875}, {"start": 2316.05, "end": 2316.29, "word": " عشرة", "probability": 0.6761067708333334}, {"start": 2316.29, "end": 2317.11, "word": " change", "probability": 0.26904296875}, {"start": 2317.11, "end": 2317.25, "word": " in", "probability": 0.875}, {"start": 2317.25, "end": 2317.35, "word": " the", "probability": 0.4228515625}, {"start": 2317.35, "end": 2317.63, "word": " price", "probability": 0.93994140625}, {"start": 2317.63, "end": 2318.03, "word": " over", "probability": 0.669921875}, {"start": 2318.03, "end": 2318.27, "word": " the", "probability": 0.8173828125}, {"start": 2318.27, "end": 2318.65, "word": " change", "probability": 0.8525390625}, {"start": 2318.65, "end": 2318.85, "word": " in", "probability": 0.9404296875}, {"start": 2318.85, "end": 2319.29, "word": " taxes", "probability": 0.83251953125}, {"start": 2319.29, "end": 2320.85, "word": " حط", "probability": 0.83935546875}, {"start": 2320.85, "end": 2321.21, "word": " tax", "probability": 0.61865234375}, {"start": 2321.21, "end": 2321.71, "word": " واحد", "probability": 0.98486328125}, {"start": 2321.71, "end": 2322.35, "word": " بيزيد", "probability": 0.9814453125}, {"start": 2322.35, "end": 2322.45, "word": " ال", "probability": 0.92333984375}, {"start": 2322.45, "end": 2322.71, "word": " price", "probability": 0.9375}, {"start": 2322.71, "end": 2323.07, "word": " باربع", "probability": 0.91357421875}, {"start": 2323.07, "end": 2323.15, "word": " من", "probability": 0.99462890625}, {"start": 2323.15, "end": 2323.37, "word": " عشرة", "probability": 0.8894856770833334}, {"start": 2323.37, "end": 2323.55, "word": " من", "probability": 0.64208984375}, {"start": 2323.55, "end": 2323.87, "word": " ال", "probability": 0.916015625}, {"start": 2323.87, "end": 2324.23, "word": " price", "probability": 0.9423828125}, {"start": 2324.23, "end": 2326.47, "word": " طب", "probability": 0.78173828125}, {"start": 2326.47, "end": 2326.65, "word": " سؤال", "probability": 0.8709309895833334}, {"start": 2326.65, "end": 2327.67, "word": " كده؟", "probability": 0.785888671875}, {"start": 2327.67, "end": 2329.23, "word": " if", "probability": 0.7958984375}, {"start": 2329.23, "end": 2329.37, "word": " the", "probability": 0.90478515625}, {"start": 2329.37, "end": 2329.63, "word": " tax", "probability": 0.9462890625}, {"start": 2329.63, "end": 2329.95, "word": " equals", "probability": 0.82177734375}, {"start": 2329.95, "end": 2330.33, "word": " zero", "probability": 0.759765625}, {"start": 2330.33, "end": 2331.11, "word": " كده", "probability": 0.9521484375}, {"start": 2331.11, "end": 2331.27, "word": " ال", "probability": 0.2314453125}, {"start": 2331.27, "end": 2331.65, "word": " price؟", "probability": 0.91064453125}, {"start": 2331.65, "end": 2331.95, "word": " هيه", "probability": 0.4149169921875}, {"start": 2331.95, "end": 2333.19, "word": " حط", "probability": 0.843017578125}, {"start": 2333.19, "end": 2333.71, "word": " tax", "probability": 0.83984375}, {"start": 2333.71, "end": 2334.29, "word": " one", "probability": 0.9482421875}, {"start": 2334.29, "end": 2334.63, "word": " unit", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 82, "seek": 235200, "start": 2347.32, "end": 2352.0, "text": "واضح الأمور؟ و لا فيها مشاكل؟ 100% طيب يعطيكوا الأف", "tokens": [2407, 46958, 5016, 16247, 2304, 13063, 22807, 4032, 20193, 8978, 11296, 37893, 995, 28820, 22807, 2319, 4, 23032, 1829, 3555, 37495, 9566, 1829, 4117, 14407, 16247, 5172], "avg_logprob": -0.4564732259937695, "compression_ratio": 1.0853658536585367, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 2347.32, "end": 2347.84, "word": "واضح", "probability": 0.4165242513020833}, {"start": 2347.84, "end": 2348.36, "word": " الأمور؟", "probability": 0.73638916015625}, {"start": 2348.36, "end": 2348.38, "word": " و", "probability": 0.50048828125}, {"start": 2348.38, "end": 2348.48, "word": " لا", "probability": 0.8916015625}, {"start": 2348.48, "end": 2348.64, "word": " فيها", "probability": 0.96142578125}, {"start": 2348.64, "end": 2349.8, "word": " مشاكل؟", "probability": 0.94677734375}, {"start": 2349.8, "end": 2350.04, "word": " 100", "probability": 0.455322265625}, {"start": 2350.04, "end": 2350.28, "word": "%", "probability": 0.93994140625}, {"start": 2350.28, "end": 2350.98, "word": " طيب", "probability": 0.8688151041666666}, {"start": 2350.98, "end": 2351.74, "word": " يعطيكوا", "probability": 0.767626953125}, {"start": 2351.74, "end": 2352.0, "word": " الأف", "probability": 0.43157958984375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2352.576125, "duration_after_vad": 2156.2524999999896}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/ehg-jNLH9-s.srt b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/ehg-jNLH9-s.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b5b7092ba57dc59be660094dc13528752a3265da
--- /dev/null
+++ b/PL9fwy3NUQKwYURTet4TZyYASkQ0Fl7vJV/ehg-jNLH9-s.srt
@@ -0,0 +1,1803 @@
+1
+00:00:20,720 --> 00:00:23,140
+Okay بسم الله الرحمن الرحيم اليوم إن شاء الله
+
+2
+00:00:23,140 --> 00:00:26,260
+سنقوم بالدراسة عن المصادر المشتركة أو الواحدات 
+
+3
+00:00:26,260 --> 00:00:29,940
+المشتركة أو الواحدات المشتركة أو الواحدات المشتركة
+
+4
+00:00:29,940 --> 00:00:31,200
+أو الواحدات المشتركة أو الواحدات المشتركة أو
+
+5
+00:00:31,200 --> 00:00:31,220
+المشتركة أو الواحدات المشتركة أو الواحدات المشتركة
+
+6
+00:00:31,220 --> 00:00:33,700
+أو الواحدات المشتركة أو الواحدات المشتركة أو
+
+7
+00:00:33,700 --> 00:00:34,980
+الواحدات المشتركة أو الواحدات المشتركة أو الواحدات
+
+8
+00:00:34,980 --> 00:00:37,600
+المشتركة أو الواحدات المشتركة أو الواحدات المشتركة
+
+9
+00:00:37,600 --> 00:00:45,300
+أو الواحدات المشتركة أو
+
+10
+00:00:45,300 --> 00:00:52,040
+الواحدات المشتركة للجمهور أو للجمهور الحقيقي، يجب أن
+
+11
+00:00:52,040 --> 00:00:56,960
+يكون مستخدماً ولا مقارنة، ولكن بالنسبة للمصادر
+
+12
+00:00:56,960 --> 00:01:10,640
+العامة هنا، لدينا مثال، وهو البحث في البحرِ البحر
+
+13
+00:01:10,640 --> 00:01:18,670
+في البحرِ هنا وهي مستخدمة ومستخدمة
+
+14
+00:01:18,670 --> 00:01:21,350
+ومستخدمة ومستخدمة ومستخدمة ومستخدمة ومستخدمة
+
+15
+00:01:21,350 --> 00:01:24,850
+ومستخدمة
+
+16
+00:01:24,850 --> 00:01:25,030
+ومستخدمة ومستخدمة ومستخدمة ومستخدمة ومستخدمة
+
+17
+00:01:25,030 --> 00:01:26,010
+ومستخدمة ومستخدمة ومستخدمة ومستخدمة ومستخدمة
+
+18
+00:01:26,010 --> 00:01:28,190
+ومستخدمة ومستخدمة ومستخدمة ومستخدمة ومستخدمة
+
+19
+00:01:28,190 --> 00:01:32,150
+ومستخدمة ومستخدمة ومستخدمة
+
+20
+00:01:32,150 --> 00:01:36,750
+ومستخدمة الاستخدام من الأشياء أو المستخدم الإضافي
+
+21
+00:01:36,750 --> 00:01:43,170
+عندما يستخدم أو يستخدم الأشياء هنا سوف يؤثر على
+
+22
+00:01:43,170 --> 00:01:49,890
+الأشياء السابقة، صح؟ هنا عندما نتحدث عن المسافة في
+
+23
+00:01:49,890 --> 00:01:59,290
+البحرِ عندما يذهب أشياء إضافية للمسافة سوف تؤثر على
+
+24
+00:01:59,290 --> 00:02:04,040
+أفعال الأشياء السابقة هنا هذا البرنامج لديه تأثير
+
+25
+00:02:04,040 --> 00:02:11,540
+ناجح، يسمى هذا البرنامج رايفل، ليس إكسكلودة، يعني
+
+26
+00:02:11,540 --> 00:02:16,840
+أنه بسهولة للمسافرين أن يذهبوا للمسافرة بدون أي
+
+27
+00:02:16,840 --> 00:02:25,010
+حاجة، لا حاجة للمدخل للمسافرة هنا الشركات العامة هي
+
+28
+00:02:25,010 --> 00:02:29,110
+الشركات التي هي مقارنة ولكنها ليست مستخدمة، الفحر
+
+29
+00:02:29,110 --> 00:02:33,690
+في البحرِ هو مقارنة لأنه عندما يحصل الشخص على
+
+30
+00:02:33,690 --> 00:02:40,570
+الفحر، فهناك أقل فحر للمجهد التالي ليحصل عليه هذا
+
+31
+00:02:40,570 --> 00:02:48,450
+يعني أنه يكون هناك تأثير نقلي على السابق أو السابق
+
+32
+00:02:48,450 --> 00:02:54,570
+أو السابق الذي يريد الذهاب للسحر هنا السحر ليس
+
+33
+00:02:54,570 --> 00:03:00,330
+مستخدماً لأنه صعب أن يوقف السحر من خروج السحر من
+
+34
+00:03:00,330 --> 00:03:00,950
+السحر
+
+35
+00:03:04,680 --> 00:03:08,160
+هو أسهل لأي شخص يذهب للتحقيق بدون أي حاجة أو حاجة
+
+36
+00:03:08,160 --> 00:03:10,880
+أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+37
+00:03:10,880 --> 00:03:10,940
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+38
+00:03:10,940 --> 00:03:13,300
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+39
+00:03:13,300 --> 00:03:15,960
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+40
+00:03:15,960 --> 00:03:18,200
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+41
+00:03:18,200 --> 00:03:18,260
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+42
+00:03:18,260 --> 00:03:19,880
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو
+
+43
+00:03:19,880 --> 00:03:31,960
+حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو حاجة أو 
+
+44
+00:03:33,030 --> 00:03:36,210
+تمام؟ طيب both are closely related to
+
+45
+00:03:36,210 --> 00:03:39,850
+externalities وشوفنا موضوع ال public goods كيف
+
+46
+00:03:39,850 --> 00:03:42,510
+معالجته في موضوع ال externalities negative و
+
+47
+00:03:42,510 --> 00:03:44,550
+positive و externalities of consumption و
+
+48
+00:03:44,550 --> 00:03:49,430
+production بصبوط and for both externalities arise
+
+49
+00:03:49,430 --> 00:03:53,450
+because something of value has no price attached
+
+50
+00:03:53,450 --> 00:04:02,130
+okay no price is free of a charge let's go to هنا
+
+51
+00:04:02,130 --> 00:04:07,730
+في التحليل إذا كان شخص ما يستخدم مصطلح عام مثل
+
+52
+00:04:07,730 --> 00:04:12,730
+المسافة في المحيط هنا مثل المحيط في المحيط أشخاص
+
+53
+00:04:12,730 --> 00:04:18,870
+آخرون أسوأ منهم ولكنهم ليسوا مجانين لهذا الاختلاف
+
+54
+00:04:18,870 --> 00:04:24,630
+فيا ال negative effects على الناس الموجودة already
+
+55
+00:04:24,630 --> 00:04:28,690
+بتسيط تمام؟ نشوف what else؟
+
+56
+00:04:34,590 --> 00:04:39,710
+عنا مصطلح اسمه sustainable production شو هي
+
+57
+00:04:39,710 --> 00:04:45,010
+sustainable production؟ مستدام for a long time،
+
+58
+00:04:45,010 --> 00:04:49,550
+بصبوط؟ طيب، هي sustainable production is the rate
+
+59
+00:04:49,550 --> 00:04:53,670
+of production that can be maintained indefinitely
+
+60
+00:04:53,670 --> 00:05:04,050
+إنتاج بيظل لأجل غير مسمّى، تمام؟ السؤال هل ال
+
+61
+00:05:04,050 --> 00:05:10,570
+fishing in the ocean here مستدام for indefinitely؟
+
+62
+00:05:10,570 --> 00:05:15,150
+this is the question here no because we have a
+
+63
+00:05:15,150 --> 00:05:21,710
+stock of fish and
+
+64
+00:05:21,710 --> 00:05:28,190
+it might be decreased due to additional catching
+
+65
+00:05:28,190 --> 00:05:36,950
+of fish صح ولا لا، تمام بقولنا،
+
+66
+00:05:36,950 --> 00:05:42,890
+this production rate depends on the existing stock
+
+67
+00:05:42,890 --> 00:05:46,630
+of fish and the number of boats that go fishing،
+
+68
+00:05:46,630 --> 00:05:53,210
+أصلًا Sustainable production of fish here depends
+
+69
+00:05:53,210 --> 00:05:58,310
+on two variables هما أولاً، كده شم ال size of the
+
+70
+00:05:58,310 --> 00:05:58,870
+stocks؟
+
+71
+00:06:05,490 --> 00:06:12,530
+و ال number of boats that go fishing خلّي
+
+72
+00:06:12,530 --> 00:06:17,190
+ال number of boats that go fishing equal to zero
+
+73
+00:06:17,190 --> 00:06:24,990
+هذا بيبقى sustainable production، مظبوط ولا لأ؟
+
+74
+00:06:24,990 --> 00:06:29,950
+زود هذا هيك، هذا بينزل، بيصير أن هذا zero
+
+75
+00:06:33,810 --> 00:06:39,250
+Okay بس في شغل دراسات ال new studies بتقول أنه في
+
+76
+00:06:39,250 --> 00:06:50,030
+عندي أنا growth rate ال
+
+77
+00:06:50,030 --> 00:06:58,610
+new studies new research prepared by FAO بتقول أنه
+
+78
+00:06:58,610 --> 00:07:00,450
+صحيح أن احنا fishing
+
+79
+00:07:03,800 --> 00:07:10,200
+و فيه أنه growth rate of
+
+80
+00:07:10,200 --> 00:07:15,900
+fish ال
+
+81
+00:07:15,900 --> 00:07:22,800
+percentage of fishing or fishing or fish caught is
+
+82
+00:07:22,800 --> 00:07:30,220
+bigger than the growth rate of fish which means أن
+
+83
+00:07:30,220 --> 00:07:41,130
+ال size of normal boats تمام؟ أو ال fish code أقل
+
+84
+00:07:41,130 --> 00:07:45,910
+من ال size of the sharks راح يصير لو انترك الموضوع
+
+85
+00:07:45,910 --> 00:07:49,570
+هيك لو احنا سيبنا الموضوع هيك without control
+
+86
+00:07:49,570 --> 00:07:55,070
+without management أُتسيب أو تُترك ال boats تعدل ال
+
+87
+00:07:55,070 --> 00:08:01,250
+fishing في ال ocean راح نوصل في الآخر sharks equal
+
+88
+00:08:01,250 --> 00:08:07,660
+zero مصموم؟ So it needs management، it needs the
+
+89
+00:08:07,660 --> 00:08:10,820
+government intervention to control or to
+
+90
+00:08:10,820 --> 00:08:15,460
+internalize the externality، هذا بيعمل negative
+
+91
+00:08:15,460 --> 00:08:19,540
+externalities على ال community، لأن أنت في الآخر
+
+92
+00:08:19,540 --> 00:08:23,740
+مافي عندك sustainable production
+
+93
+00:08:27,530 --> 00:08:31,130
+Okay substitutes بس .. بس .. وين احنا .. احنا بدنا
+
+94
+00:08:31,130 --> 00:08:34,530
+الأساس .. هذا common goods .. هذا common resources
+
+95
+00:08:34,530 --> 00:08:38,170
+.. okay هذا private intervention .. بدك تعمل أنت
+
+96
+00:08:38,170 --> 00:08:41,490
+.. اه بدك تعمل encashment لل private sector .. بس
+
+97
+00:08:41,490 --> 00:08:45,010
+أنا عندي أساس .. عندي ال ocean .. عندي السيب ..
+
+98
+00:08:45,010 --> 00:08:47,470
+بدأ أعمل عليه management .. أنا يعني .. الأصل يعمل
+
+99
+00:08:47,470 --> 00:08:51,590
+عليه control .. ليش أتركه as a government .. ليش
+
+100
+00:08:51,590 --> 00:08:56,830
+أسيب .. الـ boats اتعدى اتخلص ال stocks في يومين
+
+101
+00:08:56,830 --> 00:09:05,250
+و أنا قاعد اتفرجهم صح؟ حالة الجثة تمام؟ نشوف شو ال
+
+102
+00:09:05,250 --> 00:09:14,030
+.. ال .. ال analysis ما بعد هيك for
+
+103
+00:09:14,030 --> 00:09:18,110
+a given fish stock as more boat go fishing the
+
+104
+00:09:18,110 --> 00:09:20,530
+quantity of fish caught increases
+
+105
+00:09:22,700 --> 00:09:27,040
+صح؟ و ال boats في أولها بيروح بصيد بصيد كميات
+
+106
+00:09:27,040 --> 00:09:30,980
+كبيرة طب بعد هيك ال average coat شوف شو اللي بيصير
+
+107
+00:09:30,980 --> 00:09:38,240
+فيه but with too many boats fishing quantity of
+
+108
+00:09:38,240 --> 00:09:42,280
+fish coat decreases على the way with too many
+
+109
+00:09:42,280 --> 00:09:45,860
+boats لما بيروح على ال go fishing ال quantity
+
+110
+00:09:45,860 --> 00:09:50,900
+decreases تمام here we have the following example
+
+111
+00:09:52,650 --> 00:09:59,150
+number of boats in thousand total
+
+112
+00:09:59,150 --> 00:10:06,270
+catch marginal catch of fish and average catch of
+
+113
+00:10:06,270 --> 00:10:13,630
+fish the given data shows your point a b c d e f
+
+114
+00:10:13,630 --> 00:10:19,170
+the boats in thousand zero
+
+115
+00:10:19,170 --> 00:10:25,020
+number of boats go fishing هذا يعني أن الـ total
+
+116
+00:10:25,020 --> 00:10:28,280
+catch هنا في ألعاب ألف ألعاب في أشهر أشهر أشهر في
+
+117
+00:10:28,280 --> 00:10:32,480
+أشهر في أشهر أشهر أشهر أشهر أشهر أشهر أشهر أشهر
+
+118
+00:10:32,480 --> 00:10:34,080
+أشهر أشهر أشهر أشهر أشهر أشهر أشهر أشهر أشهر أشهر
+
+119
+00:10:34,080 --> 00:10:48,840
+أشهر أشهر أشهر أشهر أشهر أشهر أشهر أشهر أشهر 
+
+120
+00:10:50,950 --> 00:10:54,810
+و أد قارب واحد يصطاد يصطاد لك ألف يصطاد تسعين ألف طن
+
+121
+00:10:54,810 --> 00:11:01,510
+بالشهر تمام؟ adding one more boat خلي اثنين
+
+122
+00:11:01,510 --> 00:11:06,690
+يروحوا يصطادوا قاربين ال total catch of fish one
+
+123
+00:11:06,690 --> 00:11:11,450
+hundred sixty thousand tons per month طب ضيف واحد
+
+124
+00:11:11,450 --> 00:11:17,110
+ثالث ال total catch صار مئتين وعشرة يصطاد ال total
+
+125
+00:11:17,110 --> 00:11:26,780
+I'm talking about total نقطة marginal 4 240 5 250 6 
+
+126
+00:11:26,780 --> 00:11:33,800
+240 بدي ينزل شايفين بالآخر هيك with too many boats
+
+127
+00:11:33,800 --> 00:11:42,920
+ال total caught أو fish caught بينزل 250 240 210
+
+128
+00:11:42,920 --> 00:11:50,160
+طب نحسب ال marginal catch and average
+
+129
+00:11:50,160 --> 00:11:54,800
+catch marginal
+
+130
+00:11:54,800 --> 00:12:06,500
+marginal catch of fish
+
+131
+00:12:06,500 --> 00:12:15,160
+of fish this equals change in total catch
+
+132
+00:12:17,120 --> 00:12:29,180
+عن طريق تغيير رقم السيارات في الأول
+
+133
+00:12:29,180 --> 00:12:42,000
+حالة هنا 90-0 1-0 90 160-90 2-1 70
+
+134
+00:12:44,390 --> 00:12:52,290
+210-180 how much is it 50 over 3-2 equals 50 and
+
+135
+00:12:52,290 --> 00:12:59,910
+etcetera هيك and etcetera هيك and etcetera هيك and
+
+136
+00:12:59,910 --> 00:13:06,390
+etcetera هيك مصبوط مادة من البداية من البداية هو في
+
+137
+00:13:06,390 --> 00:13:11,990
+النازل تمام من البداية هو في النازل 90, 70, 50,
+
+138
+00:13:12,170 --> 00:13:20,550
+30, 10, minus 10, minus 30 في النازل تمام؟ طيب
+
+139
+00:13:20,550 --> 00:13:24,070
+نشوف ال average هذا اسم marginal social benefits
+
+140
+00:13:24,070 --> 00:13:27,250
+marginal
+
+141
+00:13:27,250 --> 00:13:33,510
+social benefits لأنه كل ما بدخل حد جديد على ال ..
+
+142
+00:13:33,510 --> 00:13:37,530
+على ال .. ال fish code فعليا الموجودة ال social
+
+143
+00:13:37,530 --> 00:13:43,530
+benefits بينزل طب شو بيصير في ال per capital ..
+
+144
+00:13:43,530 --> 00:13:48,490
+نصيب ال boat اللي بيخش جديد يصيد؟ يعني في ال new
+
+145
+00:13:48,490 --> 00:13:53,630
+boats go fishing شو بيصير في ال share تبعه؟ في
+
+146
+00:13:53,630 --> 00:14:00,680
+النصيب تبعه؟ رح ينزل أكيد ان شوف أبوش catch 1000
+
+147
+00:14:00,680 --> 00:14:10,680
+tonnes per month طبعاً average catch equals
+
+148
+00:14:10,680 --> 00:14:16,820
+total catch over
+
+149
+00:14:16,820 --> 00:14:25,120
+the number of boats شوف
+
+150
+00:14:25,120 --> 00:14:34,390
+for the first case هنا الـ total catch هو 90 كل رقم
+
+151
+00:14:34,390 --> 00:14:36,810
+السيارات هو 90 عشان 90 عشان 90 عشان 90 عشان 90
+
+152
+00:14:36,810 --> 00:14:39,870
+عشان 90 عشان 90 عشان 90 عشان 90 عشان 90 عشان 90
+
+153
+00:14:39,870 --> 00:14:43,510
+عشان 90 عشان 90 عشان 90 عشان 90 عشان 90 عشان 90
+
+154
+00:14:43,510 --> 00:14:43,530
+عشان 90 عشان 90 عشان 90 عشان 90 عشان 90 عشان 90
+
+155
+00:14:43,530 --> 00:14:43,550
+عشان 90 عشان 90 عشان 90 عشان 90 عشان 90 عشان 90
+
+156
+00:14:43,550 --> 00:14:43,630
+عشان 90 عشان 90 عشان 90 عشان 90 عشان 90 عشان 90
+
+157
+00:14:43,630 --> 00:14:52,710
+عشان 90 عشان 90 عشان 90 عشان 90 عشان 90 عش
+
+158
+00:14:58,510 --> 00:15:04,690
+نصيب الـ average .. ال average per boat صح ولا
+
+159
+00:15:04,690 --> 00:15:09,130
+لأ؟ لو هذا ال average catch per boat شو قاعد
+
+160
+00:15:09,130 --> 00:15:14,270
+بيصير فيه؟ من تسعين ل ثمانين، seventy, sixty,
+
+161
+00:15:14,630 --> 00:15:20,630
+fifty, forty, thirty، decreases it's
+
+162
+00:15:20,630 --> 00:15:23,430
+another indicator for the marginal private
+
+163
+00:15:23,430 --> 00:15:26,090
+benefits
+
+164
+00:15:32,980 --> 00:15:41,500
+هو نفسه الـ Average Catch طيب،
+
+165
+00:15:41,500 --> 00:15:45,760
+لنُقارن الـ Marginal Private Benefits و Marginal
+
+166
+00:15:45,760 --> 00:15:50,560
+Social Benefits بالكيس
+
+167
+00:15:50,560 --> 00:15:56,550
+بعيدا عن الأرقام، في الـ Fishing in the Ocean لما
+
+168
+00:15:56,550 --> 00:16:01,710
+بيعدي قارب free بيعدي على البحر و بصيد هو مستفيد
+
+169
+00:16:01,710 --> 00:16:04,870
+أكثر من المجتمع ال community مظبوط ولا لأ لأنه ال
+
+170
+00:16:04,870 --> 00:16:08,950
+stock تبع ال fish بينزل فعليا صح ولا لأ فال
+
+171
+00:16:08,950 --> 00:16:12,450
+benefits تبعته ال individual benefits هنا is
+
+172
+00:16:12,450 --> 00:16:15,410
+bigger than the private benefits is bigger than
+
+173
+00:16:15,410 --> 00:16:19,110
+the social benefits عشان هيك فيه needs لل
+
+174
+00:16:19,110 --> 00:16:21,650
+government intervention to control the case here
+
+175
+00:16:22,360 --> 00:16:31,760
+دعونا نقارن خيارات الخصوصية والخيارات الاجتماعية 8
+
+176
+00:16:31,760 --> 00:16:44,100
+أكثر من 70 7 أكثر من 50 6 أكثر من 30 50 40-10 30
+
+177
+00:16:44,100 --> 00:16:52,270
+-30 في هذه الحالة المصادر العامة هي 0 الفوضى
+
+178
+00:16:52,270 --> 00:16:53,150
+المجانية المجانية المجانية المجانية المجانية
+
+179
+00:16:53,150 --> 00:16:56,210
+المجانية المجانية المجانية المجانية المجانية
+
+180
+00:16:56,210 --> 00:16:56,670
+المجانية المجانية المجانية المجانية المجانية
+
+181
+00:16:56,670 --> 00:16:56,950
+المجانية المجانية المجانية المجانية المجانية
+
+182
+00:16:56,950 --> 00:16:59,150
+المجانية المجانية المجانية المجانية المجانية
+
+183
+00:16:59,150 --> 00:16:59,370
+المجانية المجانية المجانية المجانية المجانية
+
+184
+00:16:59,370 --> 00:16:59,730
+المجانية المجانية المجانية المجانية المجانية
+
+185
+00:16:59,730 --> 00:17:03,730
+المجانية المجانية
+
+186
+00:17:03,730 --> 00:17:07,290
+المجانية المجانية المجانية المجانية المجانية
+
+187
+00:17:07,290 --> 00:17:20,010
+المجانية المجانية المجان
+
+188
+00:17:23,180 --> 00:17:33,960
+It's bigger than the marginal social benefits صح؟
+
+189
+00:17:33,960 --> 00:17:38,320
+و أخذنا four cases إذا بتذكروا Negative
+
+190
+00:17:38,320 --> 00:17:40,440
+externalities of consumption Negative
+
+191
+00:17:40,440 --> 00:17:43,540
+externalities of production Positive consumption
+
+192
+00:17:43,540 --> 00:17:49,140
+Positive production هذا classified زي مين؟ إذا
+
+193
+00:17:49,140 --> 00:17:55,100
+بتذكروا Marginal private benefits it's bigger than
+
+194
+00:17:55,100 --> 00:17:59,840
+the marginal social benefits ليه
+
+195
+00:17:59,840 --> 00:18:04,880
+إيه؟ smoking، yes it's quite similar to smoking
+
+196
+00:18:04,880 --> 00:18:10,900
+negative externality of consumption، مظبوط؟ تمام،
+
+197
+00:18:10,900 --> 00:18:13,400
+إذا نحن مارجع ال private benefits it's bigger than
+
+198
+00:18:13,400 --> 00:18:16,020
+the marginal social benefits it's quite similar to
+
+199
+00:18:16,020 --> 00:18:19,180
+the smoking case here so the government should
+
+200
+00:18:19,180 --> 00:18:23,020
+intervene to internalize the externality here by
+
+201
+00:18:23,020 --> 00:18:24,020
+using different tools
+
+202
+00:18:30,780 --> 00:18:35,900
+طبعا نعمل analysis على ال table و نقول انه ال table
+
+203
+00:18:35,900 --> 00:18:39,000
+when shows the average and marginal catch depends
+
+204
+00:18:39,000 --> 00:18:41,660
+on the number of boats that go fishing
+
+205
+00:18:44,450 --> 00:18:50,750
+as the number of fishing boats increases هيو انه
+
+206
+00:18:50,750 --> 00:18:54,250
+لما بيزيد number of boats that go fishing شو اللي
+
+207
+00:18:54,250 --> 00:19:00,830
+بيصير؟ عملنا ال analysis عليه احنا قلنا the
+
+208
+00:19:00,830 --> 00:19:06,590
+marginal catch is decreasing and becomes negative
+
+209
+00:19:06,590 --> 00:19:11,510
+بعد فترة و هذا ال average catch لو marginal
+
+210
+00:19:11,510 --> 00:19:16,640
+private benefits برضه decreases تمام؟ و هيوصل
+
+211
+00:19:16,640 --> 00:19:21,900
+لمرحلة بعد شوية هاد راح يصير Zero بمعنى أي قارب
+
+212
+00:19:21,900 --> 00:19:28,500
+بده يعدي لصيد راح يصير صفر Zero catch Zero caught
+
+213
+00:19:28,500 --> 00:19:32,340
+طبعا ال stock equal zero هذا اللي ما بيصير يعني حط
+
+214
+00:19:32,340 --> 00:19:38,960
+eight و حط additional ذاتها هي هاد ال decreases من
+
+215
+00:19:38,960 --> 00:19:48,340
+90 ل 80 ل 70 60 50 40 30 20 10 0 إذا طبعا تلاقيه
+
+216
+00:19:48,340 --> 00:19:53,780
+zero stock equals zero بيصير تمام طيب نشوف ال
+
+217
+00:19:53,780 --> 00:20:01,600
+analysis هيك تمام marginal decreases طيب let's go
+
+218
+00:20:01,600 --> 00:20:07,460
+for to the following term which is the hour
+
+219
+00:20:07,460 --> 00:20:12,290
+fishing equilibrium hour fishing معناته يعني أن
+
+220
+00:20:12,290 --> 00:20:20,710
+هناك سيادة زيادة عن اللزوم overfishing سيادة
+
+221
+00:20:20,710 --> 00:20:26,710
+زيادة عن الحد و سنرى ما هو overfishing overfishing
+
+222
+00:20:26,710 --> 00:20:33,630
+أكثر لأن مالهم الرياضيين يعتبروا مفروضاتهم
+
+223
+00:20:33,630 --> 00:20:34,270
+مفروضاتهم مفروضاتهم مفروضاتهم مفروضاتهم مفروضاتهم
+
+224
+00:20:34,270 --> 00:20:39,110
+مفروضاتهم مفروضاتهم مفروضاتهم
+
+225
+00:20:40,210 --> 00:20:43,610
+The social consequences و اللي هي الـ Negative
+
+226
+00:20:43,610 --> 00:20:49,730
+externalities بظبط؟ بهموا حاله خلاص بهموا جدش هو
+
+227
+00:20:49,730 --> 00:20:54,710
+يروح يصيد جدش بيكلف الموضوع تمام؟ هذا هيك .. هذا
+
+228
+00:20:54,710 --> 00:21:01,410
+بيخبر عندي حالة اسمها over fishing تمام؟
+
+229
+00:21:04,680 --> 00:21:09,580
+نشوف الـ figure illustrates here the sustainable
+
+230
+00:21:09,580 --> 00:21:13,480
+production of fish نشوف شو الأمور الموجودة عندنا
+
+231
+00:21:13,480 --> 00:21:17,660
+هيك in the vertical axis here we have the
+
+232
+00:21:17,660 --> 00:21:23,360
+sustainable catch in thousand of tons per month at
+
+233
+00:21:23,360 --> 00:21:26,060
+the horizontal axis here we have the number of
+
+234
+00:21:26,060 --> 00:21:27,520
+boats in thousand
+
+235
+00:21:31,750 --> 00:21:32,930
+عندما تزداد عدد العملية عملية عملية عملية عملية
+
+236
+00:21:32,930 --> 00:21:33,590
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+237
+00:21:33,590 --> 00:21:35,850
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+238
+00:21:35,850 --> 00:21:42,790
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+239
+00:21:42,790 --> 00:21:45,350
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+240
+00:21:45,350 --> 00:21:45,630
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+241
+00:22:00,770 --> 00:22:06,230
+في المرحلة الأولى هنا كما ترى رقم السيارات الذهب
+
+242
+00:22:06,230 --> 00:22:10,490
+للسيارة يزيد كما ترى رقم السيارات الذهب للسيارة
+
+243
+00:22:10,490 --> 00:22:18,950
+يزيد كما ترى رقم
+
+244
+00:22:18,950 --> 00:22:22,430
+السيارات الذهب للسيارة يزيد كما ترى رقم السيارات
+
+245
+00:22:22,430 --> 00:22:27,750
+الذهب للسيارة يزيد
+
+246
+00:22:29,290 --> 00:22:33,590
+هي number of boats and total catch as the number
+
+247
+00:22:33,590 --> 00:22:42,270
+of boats goes up the total catch goes up the peak
+
+248
+00:22:42,270 --> 00:22:50,850
+here و بال maximum أنت 250 صح؟ طب بعدين start
+
+249
+00:22:50,850 --> 00:22:56,750
+decreased مظبوط ولا لا؟ و ضلك زيد بيوصل صفر في الآخر
+
+250
+00:22:56,750 --> 00:23:00,210
+total catch equals zero و ال marginal راح يصير
+
+251
+00:23:00,210 --> 00:23:04,830
+zero و ال average راح يصير zero تمام؟ إذا هي عندي
+
+252
+00:23:04,830 --> 00:23:11,230
+هذا ال graph تبع ال overfishing at
+
+253
+00:23:11,230 --> 00:23:16,170
+this
+
+254
+00:23:16,170 --> 00:23:23,460
+point here the maximum total fish caught وين ال
+
+255
+00:23:23,460 --> 00:23:29,720
+maximum؟ هي هنا عند الخمسة هيك عند five boats
+
+256
+00:23:29,720 --> 00:23:35,260
+بنوصل ل maximum total catch أو maximum sustainable
+
+257
+00:23:35,260 --> 00:23:40,860
+catch دخل القارب الخامس والسادس هيك ال boat
+
+258
+00:23:40,860 --> 00:23:49,300
+رقم ستة بيصير ال total catch بينزل دخل
+
+259
+00:23:49,300 --> 00:23:52,480
+لعشر بيصير zero تمام؟
+
+260
+00:23:53,950 --> 00:23:59,850
+هذا هو الوضع الـ overfishing بدهان هنا overfishing
+
+261
+00:23:59,850 --> 00:24:06,150
+بمعنى بعد القارب رقم خمسة ما تدخلش
+
+262
+00:24:06,150 --> 00:24:09,750
+حد تمام؟
+
+263
+00:24:09,750 --> 00:24:13,330
+لأنه بيبدأ negative externalities على ال community
+
+264
+00:24:13,330 --> 00:24:17,950
+marginal social benefits بيبدأ فيه problems هنا
+
+265
+00:24:18,990 --> 00:24:23,430
+تمام؟ عشان تحافظ على ال stock of fish و تحافظ على
+
+266
+00:24:23,430 --> 00:24:28,450
+ال sustainable production بدك you have to keep up
+
+267
+00:24:28,450 --> 00:24:34,290
+here to stop fishing here تمام؟ نشوف analysis
+
+268
+00:24:34,290 --> 00:24:38,070
+بقولنا overfishing occurs when the maximum
+
+269
+00:24:38,070 --> 00:24:45,290
+sustainable catch decreases هان هاي overfishing
+
+270
+00:24:45,290 --> 00:24:47,350
+هاي النقطة هيد overfishing
+
+271
+00:24:51,120 --> 00:24:54,920
+نبدأ هي لهيك over fishing يبدأ اللي هو sustainable
+
+272
+00:24:54,920 --> 00:25:02,520
+catch to decrease okay نروح لل efficient use of
+
+273
+00:25:02,520 --> 00:25:08,120
+common resources efficient use of common resources
+
+274
+00:25:08,120 --> 00:25:11,880
+here
+
+275
+00:25:11,880 --> 00:25:14,320
+in the horizontal axis we have the number of boats
+
+276
+00:25:14,320 --> 00:25:17,800
+thousand and the vertical axis the sustainable
+
+277
+00:25:17,800 --> 00:25:25,730
+catch فيه ال boat بتكون بيرمان مارجينال الـ private
+
+278
+00:25:25,730 --> 00:25:29,770
+benefits مارجينال الـ private benefits مارجينال
+
+279
+00:25:29,770 --> 00:25:33,430
+الـ private benefits مارجينال الـ private benefits
+
+280
+00:25:33,430 --> 00:25:39,010
+مارجينال الـ private benefits مارجينال الـ private
+
+281
+00:25:39,010 --> 00:25:42,290
+benefits مارجينال الـ private benefits مارجينال
+
+282
+00:25:42,290 --> 00:25:42,330
+الـ private benefits مارجينال الـ private benefits
+
+283
+00:25:42,330 --> 00:25:42,670
+مارجينال الـ private benefits مارجينال الـ private
+
+284
+00:25:42,670 --> 00:25:42,690
+benefits مارجينال الـ private benefits مارجينال
+
+285
+00:25:42,690 --> 00:25:45,850
+benefits مارجينال الـ private benefits مارجينال
+
+286
+00:25:45,850 --> 00:25:48,070
+الـ private benefits مارجينال الـ private benefits
+
+287
+00:25:48,070 --> 00:25:51,660
+مارجين of private benefits من ال data اللي
+
+288
+00:25:51,660 --> 00:26:01,520
+أخدناها قبل شوي margin of social benefits جاي
+
+289
+00:26:01,520 --> 00:26:09,820
+تحت منه ارجع لل data هيك مين
+
+290
+00:26:09,820 --> 00:26:16,570
+أعلى من مين margin of private benefitsهيو راح يكون
+
+291
+00:26:16,570 --> 00:26:20,250
+أعلى من .. at each quantity حط ال data على graph
+
+292
+00:26:20,250 --> 00:26:24,130
+تطلع معاكي ال marginal private benefits it's
+
+293
+00:26:24,130 --> 00:26:26,710
+bigger .. higher .. larger or higher than the
+
+294
+00:26:26,710 --> 00:26:30,990
+marginal social benefits صح؟ اللي هو هذا average
+
+295
+00:26:30,990 --> 00:26:35,450
+catch is bigger than the marginal catch واللي مبين
+
+296
+00:26:35,450 --> 00:26:40,230
+أنت في ال graph هم بدين مع سواء عند التسعين بعدين
+
+297
+00:26:40,230 --> 00:26:44,490
+نازلين حد أعلى من حد انا بود افترض هيك
+
+298
+00:26:51,750 --> 00:26:56,770
+عند الواحد هذا قيمته مارجينال سوشيل وعند الاتنين
+
+299
+00:26:56,770 --> 00:27:03,450
+مارجينال private هتلاقيه أعلى مارجينال مارجينال
+
+300
+00:27:03,450 --> 00:27:05,430
+مارجينال مارجينال مارجينال مارجينال مارجينال
+
+301
+00:27:05,430 --> 00:27:09,570
+مارجينال مارجينال مارجينال مارجينال مارجينال
+
+302
+00:27:09,570 --> 00:27:11,350
+مارجينال مارجينال مارجينال مارجينال مارجينال
+
+303
+00:27:11,350 --> 00:27:11,490
+مارجينال مارجينال مارجينال مارجينال مارجينال
+
+304
+00:27:11,490 --> 00:27:11,830
+مارجينال مارجينال مارجينال مارجينال مارجينال
+
+305
+00:27:11,830 --> 00:27:11,930
+مارجينال مارجينال مارجينال مارجينال مارجينال
+
+306
+00:27:11,930 --> 00:27:14,140
+مارجينال مارجينال مارجينال مارجينال مارجينال تمام؟
+
+307
+00:27:14,140 --> 00:27:17,960
+هذا من ال data لو أنت روحت على ال data بتقدر تعمل
+
+308
+00:27:17,960 --> 00:27:21,100
+driving ل marginal private benefits curve و
+
+309
+00:27:21,100 --> 00:27:26,980
+marginal social benefits curve تمام as we
+
+310
+00:27:26,980 --> 00:27:30,220
+mentioned that the marginal private benefits is
+
+311
+00:27:30,220 --> 00:27:35,520
+the average fish caught or the average catch of
+
+312
+00:27:35,520 --> 00:27:41,220
+fish marginal social benefits is the marginal
+
+313
+00:27:41,220 --> 00:27:42,160
+catch of fish
+
+314
+00:27:45,360 --> 00:27:51,120
+وهو مارجينال فش كوت يعني
+
+315
+00:27:51,120 --> 00:27:57,560
+و تبعدوا مارجينال كوست peer port يعني لو في قارب
+
+316
+00:27:57,560 --> 00:28:02,880
+يعدي جديد للصيد تكلفة الرحلة لل trip تبعه في الصيد
+
+317
+00:28:02,880 --> 00:28:08,860
+راح تكون نفس تكلفة القارب اللي قبله بمعنى بده fuel
+
+318
+00:28:08,860 --> 00:28:15,420
+بده workers بده fees اذا كان بده يعدي لل .. للصيد
+
+319
+00:28:15,420 --> 00:28:20,980
+مظبوط اذا ال marginal cost في ال boat ده same for
+
+320
+00:28:20,980 --> 00:28:29,480
+all boats in the .. the ocean here مظبوط؟ so هي
+
+321
+00:28:29,480 --> 00:28:35,380
+ال marginal cost should be fixed يعني
+
+322
+00:28:35,380 --> 00:28:45,330
+لو فينا قارب واحد راح يدفع 22 بافتراض هيك انه تكلفة
+
+323
+00:28:45,330 --> 00:28:52,790
+الرحلة ال trip for fishing بتكلفني 22$ بافتراض هيك
+
+324
+00:28:52,790 --> 00:28:56,130
+لو عندي اتنين بال average هي راح يكلفوني الواحد في
+
+325
+00:28:56,130 --> 00:29:02,610
+يوم هذك تكلفة الإضافية للبوت لأي بوت بدو يعدي جديد
+
+326
+00:29:02,610 --> 00:29:07,650
+equals 22 so the marginal coast curve should be
+
+327
+00:29:07,650 --> 00:29:18,870
+a horizontal line تمام طيب السؤال where
+
+328
+00:29:18,870 --> 00:29:22,490
+is
+
+329
+00:29:22,490 --> 00:29:26,010
+the optimal point for the officials here the
+
+330
+00:29:26,010 --> 00:29:31,030
+private sector the optimum point for the fishers
+
+331
+00:29:31,030 --> 00:29:34,690
+and where is the optimum point for the social for
+
+332
+00:29:34,690 --> 00:29:38,890
+the community؟ لأ
+
+333
+00:29:38,890 --> 00:29:47,570
+الـ interception اللي cross Marginal cost لما ال
+
+334
+00:29:47,570 --> 00:29:50,070
+marginal cost it crosses the marginal private
+
+335
+00:29:50,070 --> 00:29:53,150
+benefits هذا كويس للfishers لل private sector
+
+336
+00:29:53,150 --> 00:29:59,190
+optimum point لمين؟ للصيدين لل private sector بس لل
+
+337
+00:29:59,190 --> 00:30:02,410
+community إذا .. إذا قلنا هيك هان at this point
+
+338
+00:30:02,410 --> 00:30:05,930
+here it's
+
+339
+00:30:05,930 --> 00:30:13,430
+.. or this point E achieves the equilibrium point
+
+340
+00:30:13,430 --> 00:30:16,450
+or the optimum point for the fishers for the
+
+341
+00:30:16,450 --> 00:30:21,070
+private sector صح؟ لأنه الـ Marginal Private
+
+342
+00:30:21,070 --> 00:30:24,410
+Benefits at E here Marginal Private Benefits
+
+343
+00:30:24,410 --> 00:30:31,090
+equals the Marginal Cost اللي
+
+344
+00:30:31,090 --> 00:30:35,130
+كويس بالنسبة لل .. لل .. لل private sector بيقولك
+
+345
+00:30:35,130 --> 00:30:40,390
+أن احنا ندخل تمام تلاقي قارب للصين أن
+
+346
+00:30:40,390 --> 00:30:43,290
+تمام تلاقي boat منيح لل private sector بيقولك هو
+
+347
+00:30:43,290 --> 00:30:47,720
+يعدي انت روح الصين تمام؟ حسابات الحكومة الـ
+
+348
+00:30:47,720 --> 00:30:52,720
+Government بتختلف Related مع مين؟ مع الـ Social
+
+349
+00:30:52,720 --> 00:30:58,080
+Benefits و الـ Social Cost صح؟ هذا الـ optimum
+
+350
+00:30:58,080 --> 00:31:02,140
+point لـ ال public أو لل common resources أو لل ..
+
+351
+00:31:02,140 --> 00:31:06,180
+يعني لل community لما يكون Marginal Social
+
+352
+00:31:06,180 --> 00:31:10,900
+Benefits equals Marginal Cost اللي هي أصلا هنا
+
+353
+00:31:10,900 --> 00:31:16,490
+Marginal Social Cost و لا Marginal Private Cost صح؟
+
+354
+00:31:16,490 --> 00:31:20,070
+إذا تذكروا كنا بنفترض في ال externalities إنه إذا
+
+355
+00:31:20,070 --> 00:31:24,090
+كان في عندي أنا خطين لدمان واحد supply هذا بيفترض
+
+356
+00:31:24,090 --> 00:31:28,170
+إنه هذا marginal cost هو marginal social cost and
+
+357
+00:31:28,170 --> 00:31:35,210
+marginal private cost بعمل عليه analysis تمام؟ طيب
+
+358
+00:31:35,210 --> 00:31:39,670
+إذا لل government لل social لل community which is
+
+359
+00:31:39,670 --> 00:31:46,780
+better؟ يدخل four boats for fishing or a thousand
+
+360
+00:31:46,780 --> 00:31:51,920
+boats four تمام
+
+361
+00:31:51,920 --> 00:31:58,220
+عشان الموضوع ال social optimal عشان الموضوع الحافظ
+
+362
+00:31:58,220 --> 00:32:04,940
+على ال strokes of fish in the ocean إذا لو انترك
+
+363
+00:32:04,940 --> 00:32:11,290
+الموضوع هيك واحنا ال private sector يدخل 8000 boats
+
+364
+00:32:11,290 --> 00:32:16,730
+for fishing ال government should intervene to
+
+365
+00:32:16,730 --> 00:32:19,250
+control .. to decrease the number of boats that go
+
+366
+00:32:19,250 --> 00:32:24,490
+for fishing to 4000 boats يعني which is the social
+
+367
+00:32:24,490 --> 00:32:28,170
+optimal طب كيف تعمل ال government intervention
+
+368
+00:32:28,170 --> 00:32:33,290
+إنها تخلي ال
+
+369
+00:32:33,290 --> 00:32:39,570
+boats 4000؟ this is the major question عالـ
+
+370
+00:32:39,570 --> 00:32:45,210
+Marginal Cost صح خلّي ال Marginal Cost يطلع هيك
+
+371
+00:32:45,210 --> 00:32:52,990
+خلّصنا خلّي ال Marginal Cost بدل ما هو 22 خلّي ال
+
+372
+00:32:52,990 --> 00:33:05,430
+Marginal Cost 77 هذا Marginal Cost جديد اتحرك
+
+373
+00:33:05,430 --> 00:33:10,330
+فيها marginal social بيرفع اسمه marginal social
+
+374
+00:33:10,330 --> 00:33:16,610
+cost خلّي هيك
+
+375
+00:33:16,610 --> 00:33:20,670
+اه 
+
+376
+00:33:20,670 --> 00:33:23,590
+بره منطقة نقطة جديدة بس زود ال marginal cost عليها 
+
+377
+00:33:23,590 --> 00:33:27,870
+طول بجل عدد ال boards اللي بتعدي وهذا لأ حط عليه 
+
+378
+00:33:27,870 --> 00:33:34,100
+توشيب فيه احط عليه fees تمام؟ في أما four tools و
+
+379
+00:33:34,100 --> 00:33:36,180
+four solutions that the government or tools the
+
+380
+00:33:36,180 --> 00:33:39,620
+government can control or internalize the
+
+381
+00:33:39,620 --> 00:33:42,160
+externality here هنشوف نعمل quick presentation
+
+382
+00:33:42,160 --> 00:33:49,740
+اليوم إيش اسمه individual transferable
+
+383
+00:33:49,740 --> 00:33:50,780
+بال quota؟
+
+384
+00:33:55,220 --> 00:33:58,240
+Individual Transferable Quota هي الـ Efficient Use
+
+385
+00:33:58,240 --> 00:34:04,500
+شايفين بالغراف الـ Efficient Use تمام هي ال
+
+386
+00:34:04,500 --> 00:34:13,700
+Efficient Use شباب هذا
+
+387
+00:34:13,700 --> 00:34:15,760
+الشرح اللي شرحناه اللي هو الـ Marginal Private
+
+388
+00:34:15,760 --> 00:34:19,660
+Benefits و Marginal .. طبعا هنا بقولنا اللي
+
+389
+00:34:19,660 --> 00:34:23,930
+Marginal Private Benefits marginal private benefits
+
+390
+00:34:23,930 --> 00:34:29,990
+is the average
+
+391
+00:34:29,990 --> 00:34:35,410
+catch per boat
+
+392
+00:34:52,260 --> 00:34:55,940
+شوفون ال graph هنا، here in this graph as you see
+
+393
+00:34:55,940 --> 00:34:58,980
+this is the optimal point for the private sector
+
+394
+00:34:58,980 --> 00:35:05,660
+this is the marginal cost per boat أي قارب جديد
+
+395
+00:35:05,660 --> 00:35:11,480
+على marginal cost لأنه وهذا ال catch فيه boat as
+
+396
+00:35:11,480 --> 00:35:15,860
+the number of boats increases ال catch فيه boat رح
+
+397
+00:35:15,860 --> 00:35:19,780
+يقل بيصير فيه decreasing لأنه ال share تبعه صح ولا
+
+398
+00:35:19,780 --> 00:35:26,710
+لأ؟ وهذا overfishing equilibrium overfishing
+
+399
+00:35:26,710 --> 00:35:30,670
+equilibrium marginal private benefits equals the
+
+400
+00:35:30,670 --> 00:35:37,390
+marginal private cost هان overfishing وهنا بادي
+
+401
+00:35:37,390 --> 00:35:41,450
+المشاكل أصلا عشان اتحله راح نشوف فال gate شو اللي
+
+402
+00:35:41,450 --> 00:35:41,850
+بدى يصير
+
+403
+00:35:54,330 --> 00:35:57,690
+نشوف هنا الـ efficient use of common .. or the
+
+404
+00:35:57,690 --> 00:36:02,050
+common resources it is the use of resources that
+
+405
+00:36:02,050 --> 00:36:05,910
+maximizes its sustainable value the value of
+
+406
+00:36:05,910 --> 00:36:09,310
+resources is maximized when the marginal cost
+
+407
+00:36:09,310 --> 00:36:12,390
+using it is equal the marginal social benefits هذا
+
+408
+00:36:12,390 --> 00:36:16,150
+اللي قلناه انه ال efficiency .. social efficiency
+
+409
+00:36:16,150 --> 00:36:19,630
+بيصير لما marginal social benefits equal the
+
+410
+00:36:19,630 --> 00:36:24,380
+marginal social cost بس هاي ال analysis هيك بجود
+
+411
+00:36:24,380 --> 00:36:27,720
+طبعا ال margin ال social benefits هي ما عطينيها
+
+412
+00:36:27,720 --> 00:36:33,820
+بالان efficient
+
+413
+00:36:33,820 --> 00:36:47,080
+use هاي
+
+414
+00:36:47,080 --> 00:36:50,920
+ال tools المستخدمة quota
+
+415
+00:36:54,810 --> 00:36:59,550
+في حصص كل قارب بدي يعدي في له حصة مفروض تصيد فيها
+
+416
+00:36:59,550 --> 00:37:05,730
+لجد في له time بتيجي ممكن two days a week هاي ال
+
+417
+00:37:05,730 --> 00:37:09,910
+share تبعك بتيجي two days a week معك permission
+
+418
+00:37:09,910 --> 00:37:14,790
+معك تصريح بتيجي two days a week one day a week
+
+419
+00:37:14,790 --> 00:37:20,710
+بتيجي بتعمل fishing زي ما بدك تمام في إيش اسمه
+
+420
+00:37:20,710 --> 00:37:22,270
+هطلع لها ال efficient equilibrium
+
+421
+00:37:26,940 --> 00:37:36,520
+يشتغل vertical هنا بال quota او بيشتغل
+
+422
+00:37:36,520 --> 00:37:41,500
+increasing في ال marginal cost زود
+
+423
+00:37:41,500 --> 00:37:46,500
+ال marginal cost عليه ببطل حد يروح يصيد بظبط ولا 
+
+424
+00:37:46,500 --> 00:37:53,300
+لأ sure of something else then هنا ال efficient
+
+425
+00:37:53,300 --> 00:37:59,060
+equilibrium هذا ال market او عندنا ايش اسمه
+
+426
+00:37:59,060 --> 00:38:07,940
+individual transferable quota انت معك تصريح تصيد
+
+427
+00:38:07,940 --> 00:38:13,260
+two days a week بفرض حدث ال permission بتقدر تبيعه
+
+428
+00:38:13,260 --> 00:38:18,820
+لاي حد ثاني بقدر انا ابيعه لتوفيق بقدر ابيعه لاحمد
+
+429
+00:38:18,820 --> 00:38:23,480
+و خلاص transferable يعني انا ببيعه لاي حد ثاني و
+
+430
+00:38:23,480 --> 00:38:27,040
+خلاص حصتي انا بتتنقل ما بين .. زي .. زي .. زي ..
+
+431
+00:38:27,040 --> 00:38:31,800
+زي الاسهم بالظبط تمام؟ فببطل يعني في صح فينا
+
+432
+00:38:31,800 --> 00:38:35,660
+restrictions على موضوع ال fishing in the ocean
+
+433
+00:38:35,660 --> 00:38:41,940
+طبعا هنا how to get efficient solutions privatize
+
+434
+00:38:41,940 --> 00:38:46,900
+fishery طبعا هل هذا يعني effective or ineffective,
+
+435
+00:38:47,200 --> 00:38:51,540
+often hard to do, not popular with many؟ تعمل
+
+436
+00:38:51,540 --> 00:38:55,620
+privatization لموضوع ال fishing؟ ما اعرفش حد
+
+437
+00:38:55,620 --> 00:38:58,800
+بيستوعبه، يعني هذا واحد من ال tools اللي ممكن
+
+438
+00:38:58,800 --> 00:39:03,120
+تستخدمها انت، تعمل privatization لموضوع، سلمه ل
+
+439
+00:39:03,120 --> 00:39:06,360
+company، private sector، ان يديروا، يعملوا
+
+440
+00:39:06,360 --> 00:39:13,210
+management Impose tax on efforts حط تاكسي قال هذا
+
+441
+00:39:13,210 --> 00:39:16,790
+effective or ineffective فيه low يعني high raise
+
+442
+00:39:16,790 --> 00:39:19,510
+real cost of fishing وهذا اللي قولنا increasing
+
+443
+00:39:19,510 --> 00:39:24,190
+فيه ال marginal cost طبعا هذا common but not
+
+444
+00:39:24,190 --> 00:39:31,010
+efficient برضه مجربينه بقولك inefficient حط اشي
+
+445
+00:39:31,010 --> 00:39:35,350
+تاني طبعا gear restrictions حط قيود على ال ..
+
+446
+00:39:35,350 --> 00:39:40,780
+shorten seasons خلّي الموسم تبع السيد بدل ما هو تلت
+
+447
+00:39:40,780 --> 00:39:44,540
+شهر خلّيه شهرين في السنة أو خلّيه one month هذا
+
+448
+00:39:44,540 --> 00:39:49,940
+اسمه shorten seasons or close certain fisheries
+
+449
+00:39:49,940 --> 00:39:54,920
+خلّي مناطق مغلقة للسيد وخلاص ما تتسيب الأمور على
+
+450
+00:39:54,920 --> 00:39:59,860
+ال ocean كله يعني يصعدوا فيه خلّي افتح مناطق و سكر
+
+451
+00:39:59,860 --> 00:40:02,220
+مناطق يعطيكم العافية
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1a92f380e3d2541bd6eb536cd8e39a74f37bf59e
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_raw.json
@@ -0,0 +1 @@
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104.06, "word": " عندنا", "probability": 0.950439453125}, {"start": 104.06, "end": 104.46, "word": " دلّة", "probability": 0.885986328125}, {"start": 104.46, "end": 104.96, "word": " اسمها", "probability": 0.86181640625}, {"start": 104.96, "end": 105.22, "word": " E", "probability": 0.9248046875}, {"start": 105.22, "end": 105.58, "word": " من", "probability": 0.98388671875}, {"start": 105.58, "end": 105.96, "word": " R", "probability": 0.98486328125}, {"start": 105.96, "end": 106.08, "word": " ل", "probability": 0.978515625}, {"start": 106.08, "end": 106.28, "word": " R", "probability": 0.91943359375}, {"start": 106.28, "end": 106.58, "word": " such", "probability": 0.57861328125}, {"start": 106.58, "end": 106.96, "word": " that", "probability": 0.9296875}, {"start": 106.96, "end": 108.0, "word": " الـ", "probability": 0.3525390625}, {"start": 108.0, "end": 108.8, "word": " E", "probability": 0.84716796875}, {"start": 108.8, "end": 109.2, "word": " prime", "probability": 0.449951171875}, {"start": 109.2, "end": 109.4, "word": " of", "probability": 0.93359375}, {"start": 109.4, "end": 109.68, "word": " X", "probability": 0.923828125}, {"start": 109.68, "end": 110.12, "word": " لها", "probability": 0.725341796875}, {"start": 110.12, "end": 110.74, "word": " بساول", "probability": 0.6851806640625}, {"start": 110.74, "end": 111.46, "word": " EX", "probability": 0.54541015625}, {"start": 111.46, "end": 112.08, "word": " لكل", "probability": 0.937255859375}, {"start": 112.08, "end": 112.48, "word": " X", "probability": 0.97021484375}, {"start": 112.48, "end": 112.8, "word": " element", "probability": 0.6630859375}, {"start": 112.8, "end": 113.02, "word": " in", "probability": 0.469970703125}, {"start": 113.02, "end": 113.26, "word": " R", "probability": 0.99853515625}], "temperature": 1.0}, {"id": 6, "seek": 13352, "start": 113.9, "end": 133.52, "text": "إتنين E of Zero بساوي إيش واحد يعني الآن النظرية دي بتقولي إنه يوجد عندنا دالة domainها كل ال R و rangeها بروح بصوب في ال R هذه الدالة تحقق شرطين اللي هي E prime of X بساوي E of X و E of Zero بساوي إيش واحد", "tokens": [28814, 2655, 1863, 9957, 462, 295, 17182, 4724, 3794, 995, 45865, 11933, 1829, 8592, 36764, 24401, 37495, 22653, 6024, 48506, 28239, 19913, 2288, 10632, 11778, 1829, 39894, 39648, 1829, 36145, 3224, 7251, 29245, 3215, 43242, 8315, 11778, 6027, 3660, 9274, 11296, 28242, 2423, 497, 4032, 3613, 11296, 4724, 32887, 5016, 4724, 9381, 37746, 8978, 2423, 497, 29538, 32748, 6027, 3660, 6055, 5016, 4587, 4587, 13412, 2288, 9566, 9957, 13672, 1829, 39896, 462, 5835, 295, 1783, 4724, 3794, 995, 45865, 462, 295, 1783, 4032, 462, 295, 17182, 4724, 3794, 995, 45865, 11933, 1829, 8592, 36764, 24401], "avg_logprob": -0.24527995303894082, "compression_ratio": 1.6331658291457287, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 113.9, "end": 114.5, "word": "إتنين", "probability": 0.593170166015625}, {"start": 114.5, "end": 114.74, "word": " E", "probability": 0.5458984375}, 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"probability": 0.93798828125}, {"start": 123.92, "end": 124.7, "word": " هذه", "probability": 0.34130859375}, {"start": 124.7, "end": 126.14, "word": " الدالة", "probability": 0.9814453125}, {"start": 126.14, "end": 128.7, "word": " تحقق", "probability": 0.89794921875}, {"start": 128.7, "end": 129.38, "word": " شرطين", "probability": 0.9434814453125}, {"start": 129.38, "end": 129.56, "word": " اللي", "probability": 0.7213134765625}, {"start": 129.56, "end": 129.72, "word": " هي", "probability": 0.74462890625}, {"start": 129.72, "end": 129.96, "word": " E", "probability": 0.59423828125}, {"start": 129.96, "end": 130.22, "word": " prime", "probability": 0.5693359375}, {"start": 130.22, "end": 130.36, "word": " of", "probability": 0.9443359375}, {"start": 130.36, "end": 130.56, "word": " X", "probability": 0.96337890625}, {"start": 130.56, "end": 130.84, "word": " بساوي", "probability": 0.938232421875}, {"start": 130.84, "end": 131.02, "word": " E", "probability": 0.986328125}, {"start": 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continuous functions as follows بدي الآن اعرف اللي هو sequence of functions", "tokens": [6027, 7649, 8717, 7435, 1829, 13672, 1829, 31439, 47525, 8315, 8717, 12984, 3555, 2655, 49610, 23328, 29538, 32748, 6027, 3660, 1975, 1829, 3224, 38392, 6055, 5016, 4587, 4587, 13672, 1829, 31439, 33962, 2407, 33546, 13672, 1829, 43242, 8315, 9673, 8848, 4117, 13063, 3660, 8978, 3224, 13672, 1829, 39896, 8717, 19913, 16572, 995, 2423, 7649, 16490, 1211, 9957, 995, 6225, 8592, 7649, 8717, 32887, 5016, 4724, 9307, 7435, 40294, 1975, 12984, 3555, 9307, 49610, 23328, 29538, 32748, 6027, 3660, 16490, 1211, 9957, 995, 8717, 47283, 3215, 321, 31612, 3413, 6964, 257, 8310, 295, 10957, 6828, 382, 10002, 47525, 1829, 6024, 48506, 1975, 3615, 28480, 13672, 1829, 31439, 8310, 295, 6828], "avg_logprob": -0.19133523363958704, "compression_ratio": 1.8675213675213675, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 133.88, "end": 134.5, "word": "الان", "probability": 0.6571044921875}, {"start": 134.5, 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0.9895833333333334}, {"start": 148.64, "end": 149.2, "word": " باتجاه", "probability": 0.989990234375}, {"start": 149.2, "end": 149.64, "word": " اثبات", "probability": 0.8839111328125}, {"start": 149.64, "end": 149.96, "word": " وجود", "probability": 0.982421875}, {"start": 149.96, "end": 150.14, "word": " هذه", "probability": 0.8193359375}, {"start": 150.14, "end": 150.58, "word": " الدالة", "probability": 0.9920247395833334}, {"start": 150.58, "end": 151.1, "word": " خلينا", "probability": 0.917236328125}, {"start": 151.1, "end": 151.58, "word": " ناخد", "probability": 0.9899088541666666}, {"start": 151.58, "end": 151.98, "word": " we", "probability": 0.2138671875}, {"start": 151.98, "end": 153.38, "word": " inductively", "probability": 0.88134765625}, {"start": 153.38, "end": 153.86, "word": " define", "probability": 0.9794921875}, {"start": 153.86, "end": 154.08, "word": " a", "probability": 0.96337890625}, {"start": 154.08, "end": 154.56, "word": " sequence", "probability": 0.97509765625}, {"start": 154.56, "end": 155.28, "word": " of", "probability": 0.71728515625}, {"start": 155.28, "end": 155.84, "word": " continuous", "probability": 0.81787109375}, {"start": 155.84, "end": 156.38, "word": " functions", "probability": 0.82470703125}, {"start": 156.38, "end": 156.66, "word": " as", "probability": 0.9208984375}, {"start": 156.66, "end": 157.02, "word": " follows", "probability": 0.81982421875}, {"start": 157.02, "end": 157.9, "word": " بدي", "probability": 0.38671875}, {"start": 157.9, "end": 158.28, "word": " الآن", "probability": 0.734375}, {"start": 158.28, "end": 159.66, "word": " اعرف", "probability": 0.8196614583333334}, {"start": 159.66, "end": 160.02, "word": " اللي", "probability": 0.967529296875}, {"start": 160.02, "end": 160.44, "word": " هو", "probability": 0.98095703125}, {"start": 160.44, "end": 161.28, "word": " sequence", "probability": 0.9404296875}, {"start": 161.28, "end": 161.48, "word": " of", "probability": 0.98193359375}, {"start": 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"end": 2616.94, "word": " دالتين", "probability": 0.8677978515625}, {"start": 2616.94, "end": 2617.1, "word": " وفي", "probability": 0.8330078125}, {"start": 2617.1, "end": 2617.48, "word": " الآخر", "probability": 0.86474609375}, {"start": 2617.48, "end": 2617.94, "word": " يا", "probability": 0.58935546875}, {"start": 2617.94, "end": 2618.32, "word": " بنسأل", "probability": 0.76251220703125}, {"start": 2618.32, "end": 2618.84, "word": " لتناقض", "probability": 0.776953125}, {"start": 2618.84, "end": 2618.96, "word": " أو", "probability": 0.53955078125}, {"start": 2618.96, "end": 2619.34, "word": " بنسأل", "probability": 0.953125}, {"start": 2619.34, "end": 2619.6, "word": " لإن", "probability": 0.818359375}, {"start": 2619.6, "end": 2620.14, "word": " الدالتين", "probability": 0.976806640625}, {"start": 2620.14, "end": 2620.88, "word": " إشمالهم", "probability": 0.82177734375}, {"start": 2620.88, "end": 2622.56, "word": " متساويتين", "probability": 0.8912760416666666}, {"start": 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2852.22, "end": 2852.76, "word": " بنطبقها", "probability": 0.85517578125}, {"start": 2852.76, "end": 2852.94, "word": " على", "probability": 0.6630859375}, {"start": 2852.94, "end": 2853.3, "word": " مين", "probability": 0.888671875}, {"start": 2853.3, "end": 2853.9, "word": " اللى", "probability": 0.87646484375}, {"start": 2853.9, "end": 2854.26, "word": " هى", "probability": 0.96630859375}, {"start": 2854.26, "end": 2854.58, "word": " X", "probability": 0.90185546875}, {"start": 2854.58, "end": 2854.82, "word": " X", "probability": 0.650390625}, {"start": 2854.82, "end": 2855.04, "word": " اللى", "probability": 0.890625}, {"start": 2855.04, "end": 2855.3, "word": " هى", "probability": 0.93310546875}, {"start": 2855.3, "end": 2855.64, "word": " طبعا", "probability": 0.8924560546875}, {"start": 2855.64, "end": 2855.78, "word": " انتوا", "probability": 0.5472005208333334}, {"start": 2855.78, "end": 2856.48, "word": " متذكرين", "probability": 0.9085693359375}, {"start": 2856.48, "end": 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"probability": 0.95458984375}, {"start": 3365.71, "end": 3365.93, "word": " شغل", "probability": 0.9951171875}, {"start": 3365.93, "end": 3366.31, "word": " نهاني", "probability": 0.9249267578125}, {"start": 3366.31, "end": 3366.51, "word": " يعني", "probability": 0.89111328125}, {"start": 3366.51, "end": 3366.89, "word": " بصدي", "probability": 0.8346354166666666}], "temperature": 1.0}, {"id": 152, "seek": 338615, "start": 3367.73, "end": 3386.15, "text": "إلى أن الـ use of notation E و X of E X زي ما قلنا كله تمام تمام consistent إلى أن يجي اللي هو لبعض الخواص الأخرى لهذه اللي هي الدالة إلى أن الـ exponential function satisfies the following properties", "tokens": [28814, 23942, 14739, 2423, 39184, 764, 295, 24657, 462, 4032, 1783, 295, 462, 1783, 30767, 1829, 19446, 12174, 1211, 8315, 28242, 3224, 46811, 10943, 46811, 10943, 8398, 30731, 14739, 7251, 7435, 1829, 13672, 1829, 31439, 5296, 3555, 3615, 11242, 33962, 2407, 33546, 16247, 34740, 7578, 46740, 24192, 13672, 1829, 39896, 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{"start": 3443.0, "end": 3443.48, "word": " by", "probability": 0.623046875}, {"start": 3443.48, "end": 3444.08, "word": " contradiction", "probability": 0.88818359375}], "temperature": 1.0}, {"id": 155, "seek": 346121, "start": 3444.81, "end": 3461.21, "text": "بدي افترض انه في عندي E of α for some α element in R والـ E of α ايش تساوي تساوي سفر ونوصل لcontradiction لان suppose that there exists α element in R such that E of α ايش بساوي بساوي سفر", "tokens": [3555, 16254, 1975, 5172, 2655, 43042, 16472, 3224, 8978, 43242, 1829, 462, 295, 5691, 337, 512, 5691, 4478, 294, 497, 16070, 39184, 462, 295, 5691, 1975, 1829, 8592, 6055, 3794, 995, 45865, 6055, 3794, 995, 45865, 8608, 5172, 2288, 4032, 1863, 2407, 36520, 5296, 9000, 6206, 4105, 5296, 7649, 7297, 300, 456, 8198, 5691, 4478, 294, 497, 1270, 300, 462, 295, 5691, 1975, 1829, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.3331980457553616, "compression_ratio": 1.5582822085889572, 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13672, 1829, 31439, 1958, 5551, 46538, 3660, 34051, 5551, 46538, 4032, 30767, 13546, 3224, 11331, 35457, 12174, 32640, 3660, 16247, 46538, 3714, 29245, 49401, 34051, 8608, 6027, 49401, 23032, 1829, 3555], "avg_logprob": -0.34788603642407584, "compression_ratio": 1.4046242774566473, "no_speech_prob": 2.7477741241455078e-05, "words": [{"start": 3461.65, "end": 3462.15, "word": "الآن", "probability": 0.6617431640625}, {"start": 3462.15, "end": 3462.51, "word": " and", "probability": 0.56591796875}, {"start": 3462.51, "end": 3462.77, "word": " let", "probability": 0.94873046875}, {"start": 3462.77, "end": 3463.03, "word": " G", "probability": 0.5849609375}, {"start": 3463.03, "end": 3463.37, "word": " α", "probability": 0.36669921875}, {"start": 3463.37, "end": 3464.09, "word": " be", "probability": 0.68798828125}, {"start": 3464.09, "end": 3464.35, "word": " the", "probability": 0.83837890625}, {"start": 3464.35, "end": 3464.75, "word": " closed", "probability": 0.84521484375}, {"start": 3464.75, "end": 3465.37, "word": " interval", "probability": 0.94677734375}, {"start": 3465.37, "end": 3465.65, "word": " with", "probability": 0.85205078125}, {"start": 3465.65, "end": 3466.33, "word": " endpoints", "probability": 0.70751953125}, {"start": 3466.33, "end": 3466.79, "word": " mean", "probability": 0.42626953125}, {"start": 3466.79, "end": 3467.33, "word": " α", "probability": 0.5439453125}, {"start": 3467.33, "end": 3467.99, "word": " و", "probability": 0.53173828125}, {"start": 3467.99, "end": 3468.33, "word": " 0", "probability": 0.4638671875}, {"start": 3468.33, "end": 3469.05, "word": " يعني", "probability": 0.77978515625}, {"start": 3469.05, "end": 3469.23, "word": " الـ", "probability": 0.6767578125}, {"start": 3469.23, "end": 3469.35, "word": " G", "probability": 0.64501953125}, {"start": 3469.35, "end": 3469.49, "word": " of", "probability": 0.10418701171875}, {"start": 3469.49, "end": 3469.71, "word": " α", "probability": 0.56689453125}, {"start": 3469.71, "end": 3470.01, "word": " زي", "probability": 0.953857421875}, {"start": 3470.01, "end": 3470.13, "word": " اللي", "probability": 0.903076171875}, {"start": 3470.13, "end": 3470.73, "word": " فوق", "probability": 0.96826171875}, {"start": 3470.73, "end": 3471.23, "word": " يا", "probability": 0.30517578125}, {"start": 3471.23, "end": 3471.79, "word": " بساوي", "probability": 0.822509765625}, {"start": 3471.79, "end": 3472.03, "word": " اللي", "probability": 0.922119140625}, {"start": 3472.03, "end": 3472.17, "word": " هو", "probability": 0.9814453125}, {"start": 3472.17, "end": 3472.47, "word": " 0", "probability": 0.3232421875}, {"start": 3472.47, "end": 3473.11, "word": " ألفة", "probability": 0.5483805338541666}, {"start": 3473.11, "end": 3473.51, "word": " أو", "probability": 0.9580078125}, {"start": 3473.51, "end": 3473.75, "word": " ألف", "probability": 0.884765625}, {"start": 3473.75, "end": 3473.89, "word": " و", "probability": 0.591796875}, {"start": 3473.89, "end": 3474.23, "word": " زيره", "probability": 0.5272623697916666}, {"start": 3474.23, "end": 3474.55, "word": " حسب", "probability": 0.970458984375}, {"start": 3474.55, "end": 3474.95, "word": " قيمة", "probability": 0.994140625}, {"start": 3474.95, "end": 3475.23, "word": " الألف", "probability": 0.815185546875}, {"start": 3475.23, "end": 3475.75, "word": " موجبة", "probability": 0.8274739583333334}, {"start": 3475.75, "end": 3476.03, "word": " أو", "probability": 0.96826171875}, {"start": 3476.03, "end": 3476.45, "word": " سالبة", "probability": 0.97021484375}, {"start": 3476.45, "end": 3477.41, "word": " طيب", "probability": 0.9137369791666666}], "temperature": 1.0}, {"id": 157, "seek": 349244, "start": 3478.44, "end": 3492.44, "text": "الان زي ما قلت قبل بشوية بما ان E is continuous on a closed interval Iα او Jα اللي هو مسميها then there exist case such that اللي هو ال absolute value E of D أصفر سوى K لكل T element in G", "tokens": [6027, 7649, 30767, 1829, 19446, 12174, 1211, 2655, 12174, 36150, 4724, 8592, 2407, 10632, 4724, 15042, 16472, 462, 307, 10957, 322, 257, 5395, 15035, 286, 1529, 1975, 2407, 508, 1529, 13672, 1829, 31439, 3714, 38251, 1829, 11296, 550, 456, 2514, 1389, 1270, 300, 13672, 1829, 31439, 2423, 8236, 2158, 462, 295, 413, 5551, 9381, 5172, 2288, 8608, 2407, 7578, 591, 5296, 28820, 314, 4478, 294, 460], "avg_logprob": -0.3003731414453307, "compression_ratio": 1.3172043010752688, "no_speech_prob": 0.0, "words": [{"start": 3478.44, "end": 3478.92, "word": "الان", "probability": 0.722900390625}, {"start": 3478.92, "end": 3479.14, "word": " زي", "probability": 0.6126708984375}, {"start": 3479.14, "end": 3479.2, "word": " ما", "probability": 0.93408203125}, {"start": 3479.2, "end": 3479.44, "word": " قلت", "probability": 0.8175455729166666}, {"start": 3479.44, "end": 3479.68, "word": " قبل", "probability": 0.956787109375}, {"start": 3479.68, "end": 3480.16, "word": " بشوية", "probability": 0.8553466796875}, {"start": 3480.16, "end": 3480.52, "word": " 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"temperature": 1.0}, {"id": 158, "seek": 351979, "start": 3493.99, "end": 3519.79, "text": "الأن مشابه للي قبل دي ربالكم الان بدنا نستخدم mean taylor theorem اللي هو على اللي هي ال function اللي عندي هذه اللي هو بس في مين الآن في ال end points ألف ومين ألف وصفر اذا there exist cn element in dn such that مسرع لإنه قاعد بعيد نفس البرهان اللي قبله شوية such that اللي هو E of صفر", "tokens": [6027, 33456, 37893, 16758, 3224, 5296, 20292, 12174, 36150, 11778, 1829, 12602, 3555, 6027, 24793, 2423, 7649, 47525, 8315, 8717, 14851, 9778, 40448, 914, 39224, 6746, 20904, 13672, 1829, 31439, 15844, 13672, 1829, 39896, 2423, 2445, 13672, 1829, 18871, 16254, 29538, 13672, 1829, 31439, 4724, 3794, 8978, 3714, 9957, 6024, 48506, 8978, 2423, 917, 2793, 5551, 46538, 4032, 2304, 9957, 5551, 46538, 4032, 9381, 5172, 2288, 1975, 15730, 456, 2514, 269, 77, 4478, 294, 274, 77, 1270, 300, 3714, 3794, 2288, 3615, 5296, 28814, 1863, 3224, 12174, 995, 22488, 45030, 25708, 8717, 36178, 2423, 26890, 3224, 7649, 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3512.27, "end": 3512.61, "word": " مسرع", "probability": 0.518035888671875}, {"start": 3512.61, "end": 3512.89, "word": " لإنه", "probability": 0.70623779296875}, {"start": 3512.89, "end": 3513.07, "word": " قاعد", "probability": 0.7674153645833334}, {"start": 3513.07, "end": 3513.33, "word": " بعيد", "probability": 0.854248046875}, {"start": 3513.33, "end": 3513.59, "word": " نفس", "probability": 0.95654296875}, {"start": 3513.59, "end": 3513.97, "word": " البرهان", "probability": 0.9161376953125}, {"start": 3513.97, "end": 3514.09, "word": " اللي", "probability": 0.98193359375}, {"start": 3514.09, "end": 3514.31, "word": " قبله", "probability": 0.9182942708333334}, {"start": 3514.31, "end": 3514.73, "word": " شوية", "probability": 0.9039713541666666}, {"start": 3514.73, "end": 3515.95, "word": " such", "probability": 0.78564453125}, {"start": 3515.95, "end": 3516.33, "word": " that", "probability": 0.9521484375}, {"start": 3516.33, "end": 3517.63, "word": " اللي", "probability": 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بيصير اي أس ام عالميا على ان و هذه بيكون عندي اي أس اي او ام على ان بساوي اللي هو عبارة عن اي أس ام على ان و ام على ان was our arbitral rational number اذا صار عندي اي أس ار بساوي اي أس ار", "tokens": [3224, 24192, 13412, 2288, 3615, 9307, 5296, 28814, 1829, 4032, 36764, 24401, 3660, 2423, 7649, 28242, 24525, 1975, 2304, 37037, 15730, 6225, 3215, 3215, 6225, 995, 16254, 2423, 7649, 37037, 15730, 6225, 3215, 3215, 6225, 18513, 10632, 4724, 1829, 9381, 13546, 1975, 1829, 5551, 3794, 1975, 2304, 6225, 45340, 25528, 15844, 16472, 4032, 29538, 4724, 1829, 30544, 43242, 1829, 1975, 1829, 5551, 3794, 1975, 1829, 1975, 2407, 1975, 2304, 15844, 16472, 4724, 3794, 995, 45865, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 5551, 3794, 1975, 2304, 15844, 16472, 4032, 1975, 2304, 15844, 16472, 390, 527, 14931, 2155, 15090, 1230, 1975, 15730, 20328, 9640, 43242, 1829, 1975, 1829, 5551, 3794, 1975, 2288, 4724, 3794, 995, 45865, 1975, 1829, 5551, 3794, 1975, 2288], "avg_logprob": 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واحد اكبر من Eاش من سفر اكيد،ظبط ولا لا؟ and E of X ده بيساوي سفر for X element in R صار عندى الان هاي دالة E of 0 إلها واحد،ماشي؟", "tokens": [6027, 7649, 321, 458, 300, 462, 295, 1958, 4724, 1829, 3794, 995, 45865, 462, 33599, 36764, 24401, 1975, 4117, 26890, 9154, 462, 33599, 9154, 8608, 5172, 2288, 1975, 4117, 25708, 12399, 19913, 3555, 9566, 49429, 20193, 22807, 293, 462, 295, 1783, 11778, 3224, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 337, 1783, 4478, 294, 497, 20328, 9640, 43242, 7578, 2423, 7649, 8032, 47302, 11778, 6027, 3660, 462, 295, 1958, 11933, 1211, 11296, 36764, 24401, 12399, 2304, 33599, 1829, 22807], "avg_logprob": -0.3364197413126628, "compression_ratio": 1.4318181818181819, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 4339.57, "end": 4340.21, "word": "الان", "probability": 0.750244140625}, {"start": 4340.21, "end": 4340.85, "word": " we", "probability": 0.080322265625}, {"start": 4340.85, "end": 4341.29, "word": " know", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2__gojdcGsw_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2__gojdcGsw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a5246ff263bf31e94fb99443729571a530f9be6e
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2__gojdcGsw_raw.srt
@@ -0,0 +1,1564 @@
+1
+00:00:04,940 --> 00:00:07,660
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,660 --> 00:00:10,500
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:10,500 --> 00:00:17,340
+أجمعين هذه هي المحاضرة رقم 23 في مساق تحليل حقيقة
+
+4
+00:00:17,340 --> 00:00:22,200
+نيل طلاب وطالبات الجامعة الإسلامية قسم الرياضيات
+
+5
+00:00:22,200 --> 00:00:27,900
+كلية العلومالمحاضرة اللي هي اليوم هي عبارة عن
+
+6
+00:00:27,900 --> 00:00:33,180
+تكملة ل section تمانية تلاتة الجزء الثاني من .. من
+
+7
+00:00:33,180 --> 00:00:36,580
+.. من هذا .. اللي هو ال chapter الجزء الأول من هذا
+
+8
+00:00:36,580 --> 00:00:39,320
+ال section الجزء الأول اتحدثنا عن ال exponential
+
+9
+00:00:39,320 --> 00:00:44,670
+function وكيف أثبتنا وجودهاواخدنا خواصها الآن بدنا
+
+10
+00:00:44,670 --> 00:00:47,910
+نحكي عن الجزء التاني من اللي هو ال section اللي هو
+
+11
+00:00:47,910 --> 00:00:51,050
+ال logarithmic function ال logarithmic function
+
+12
+00:00:51,050 --> 00:00:55,290
+اللي هو نشوف كيف بدنا نثبت وجودها وكيف اللي هو
+
+13
+00:00:55,290 --> 00:01:00,410
+ناخد خواصها بنفس البناء اللي أو نبنع البناء اللي
+
+14
+00:01:00,410 --> 00:01:05,820
+بنناه المحاضرة الماضيةالان لما حكينا عن ال
+
+15
+00:01:05,820 --> 00:01:10,020
+exponential function E لجينا ان ال exponential E
+
+16
+00:01:10,020 --> 00:01:12,780
+is strictly increasing differentiable function
+
+17
+00:01:12,780 --> 00:01:18,160
+with domain R and range اللي هو Y أكبر من 0 يعني
+
+18
+00:01:18,160 --> 00:01:22,480
+لما حكينا عن ال E حكينا عن ال E من R اللي هي ال
+
+19
+00:01:22,480 --> 00:01:26,600
+exponential لعند الفترة 0 و مالا نهاية هذه ال
+
+20
+00:01:26,600 --> 00:01:31,560
+function هي rangeها و هي domainها و كانت strictly
+
+21
+00:01:31,560 --> 00:01:35,700
+increasingStrictly increasing معناته اللي هو عبارة
+
+22
+00:01:35,700 --> 00:01:40,020
+عن 120 يعني بمعنى أخر في إلها ال function هذه on
+
+23
+00:01:40,020 --> 00:01:43,940
+two وكانت differentiable الآن ال function اللي هي
+
+24
+00:01:43,940 --> 00:01:46,840
+ال exponential طبعا ما أنتوا عارفين كيف رسمتها لو
+
+25
+00:01:46,840 --> 00:01:50,460
+جينا جربنا نرسمها هنلاقي الرسمة اللي هو هذه اللي
+
+26
+00:01:50,460 --> 00:01:56,180
+هي عبارة عن رسمة ال exponentialالان انا بدى اجى
+
+27
+00:01:56,180 --> 00:02:00,300
+اللى هو من خلال اللى هو ال function ال exponential
+
+28
+00:02:00,300 --> 00:02:05,980
+اعرف ال inverse لها واسميه اللى هو logarithmic
+
+29
+00:02:05,980 --> 00:02:10,860
+function او بدى اسميه ال logarithm الطبيعى اللى هى
+
+30
+00:02:10,860 --> 00:02:16,020
+ال len functionمشروع الكلام اه لإن ايه عبارة عن
+
+31
+00:02:16,020 --> 00:02:19,240
+function one to one و one to Hana إذا صار ال
+
+32
+00:02:19,240 --> 00:02:23,580
+inverse لها موجود لإنها strictly increasing إذا
+
+33
+00:02:23,580 --> 00:02:29,560
+صار ال L من عند zero و مالة نهاية لعند ال R هادي
+
+34
+00:02:29,560 --> 00:02:34,100
+اللي هيالـ function الجديدة هي اللي بدي أسميها الـ
+
+35
+00:02:34,100 --> 00:02:38,320
+logarithmic function وهي رسمتها اللي أمامنا اللي
+
+36
+00:02:38,320 --> 00:02:42,460
+هي ال inverse لهذه الدالة اللي بدي أعرفها الآن
+
+37
+00:02:42,460 --> 00:02:47,000
+وتعريف الآن صار شرعي بناء على وجود ال exponential
+
+38
+00:02:47,000 --> 00:02:50,930
+اللي بدي أعرفه اللي هو ال inverse سبعتهاالعمل
+
+39
+00:02:50,930 --> 00:02:57,030
+المعرفي للـ E هو
+
+40
+00:02:57,030 --> 00:03:02,850
+الـ Logarithm أو الـ Nature Logarithm اللي هي It
+
+41
+00:03:02,850 --> 00:03:07,870
+will be denoted by L or by Lin الأكتر شيوعا طبعا
+
+42
+00:03:07,870 --> 00:03:11,810
+اللي هو مين الـ Lin لأن بما أن الـ E و L انفرس
+
+43
+00:03:11,810 --> 00:03:17,110
+لبعض إذا أكيد الـ E composite L composite E of X
+
+44
+00:03:17,110 --> 00:03:22,920
+هيساوي الـ Xلكل الـ x و اللي موجودة في الـ R لأن
+
+45
+00:03:22,920 --> 00:03:26,540
+الـ E بتشتغل على كل الإكسات اللي في الـ R لأن
+
+46
+00:03:26,540 --> 00:03:30,740
+بينما E composite L of Y E composite L of Y الـ L
+
+47
+00:03:30,740 --> 00:03:34,660
+بتشتغل .. بتشتغل مين على مين بس على الـ positive E
+
+48
+00:03:34,660 --> 00:03:38,240
+composite L of Y بيساوي لكل Y element in R و Y
+
+49
+00:03:38,240 --> 00:03:44,900
+أشملها أكبر من 0الان connotations .. connotations
+
+50
+00:03:44,900 --> 00:03:49,860
+بناء عليه الـ N الـ E of X لأن الـ N هي الـ L والـ
+
+51
+00:03:49,860 --> 00:03:53,880
+E هي الـ E وعندي الـ E to the N اللي هو بسوء الـ Y
+
+52
+00:03:53,880 --> 00:03:57,780
+وهو بسوء الـ X بناء على أن الواحدة inverse للتانية
+
+53
+00:04:01,010 --> 00:04:04,750
+أو كل واحدة inverse للاخرى الـ logarithm is a
+
+54
+00:04:04,750 --> 00:04:08,630
+strictly increasing function L with domain اللي هو
+
+55
+00:04:08,630 --> 00:04:12,150
+مين اللي هو ال domain اللي عندي اللي هو تعرفنا هيك
+
+56
+00:04:12,150 --> 00:04:16,210
+أصلا الان ال derivative of L is given by L prime
+
+57
+00:04:16,210 --> 00:04:19,750
+of X ايش بتساوي واحدة ل X for X أكبر من سفر الان
+
+58
+00:04:19,750 --> 00:04:23,430
+ال logarithm satisfy the functional equation تحقق
+
+59
+00:04:23,430 --> 00:04:27,010
+المعادلة الدالية التالية اللي هي L of X في Y بساوي
+
+60
+00:04:27,010 --> 00:04:31,000
+L of X زائد LL of Y for X أكبر من سفر Y أكبر من
+
+61
+00:04:31,000 --> 00:04:34,560
+سفر Y أكبر
+
+62
+00:04:34,560 --> 00:04:38,260
+من سفر
+
+63
+00:04:38,260 --> 00:04:40,560
+Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر
+
+64
+00:04:40,560 --> 00:04:40,580
+من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y
+
+65
+00:04:40,580 --> 00:04:40,640
+أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من
+
+66
+00:04:40,640 --> 00:04:40,700
+سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y
+
+67
+00:04:40,700 --> 00:04:40,700
+أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من
+
+68
+00:04:40,700 --> 00:04:41,020
+سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y
+
+69
+00:04:41,020 --> 00:04:47,140
+أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبرL of
+
+70
+00:04:47,140 --> 00:04:51,420
+XR بيساوي R لL of X لإن X أكبر من 0 وR المتر كيوه
+
+71
+00:04:51,420 --> 00:04:54,840
+كلهن اللي هي خواص انتوا بتعرفوهم قبل هيك بس الآن
+
+72
+00:04:54,840 --> 00:04:58,440
+بدنا نبرهنهم و نثبت صحتهم limit L of X لما X تروح
+
+73
+00:04:58,440 --> 00:05:01,740
+لـ0 من اليمين بساوي سالب infinity and limit L of X
+
+74
+00:05:01,740 --> 00:05:07,340
+لما X تروح لمال النهاية بتساوي مال النهاية خلينا
+
+75
+00:05:07,340 --> 00:05:14,840
+احنا نشوف نبرهن اللي هي اللي مطلوبالأن الـ L is
+
+76
+00:05:14,840 --> 00:05:17,560
+strictly increasing with domain X element alone
+
+77
+00:05:17,560 --> 00:05:20,880
+and range R follows from the fact that E is
+
+78
+00:05:20,880 --> 00:05:24,840
+strictly increasing with domain R and range اللي
+
+79
+00:05:24,840 --> 00:05:33,320
+هو اللي عندي الان عندي ال L is strictly increasing
+
+80
+00:05:33,320 --> 00:05:37,560
+بناء على مين على ال E نفسها strictly increasing
+
+81
+00:05:37,560 --> 00:05:48,560
+الان EComposite L E Composite L of Y ايش بتساوي؟ Y
+
+82
+00:05:48,560 --> 00:05:55,320
+لكل Y وY الموجودة لكل Y element in سفر وملا نهاية،
+
+83
+00:05:55,320 --> 00:06:00,780
+مظبوط؟ الان فاضلول الجهتين الان طبعا احنا بنعرف
+
+84
+00:06:00,780 --> 00:06:06,360
+انه من الاصل مدامة ال E isاللي هو differentiable
+
+85
+00:06:06,360 --> 00:06:10,480
+أكيد اللي هي ال inverse إلها is differentiable by
+
+86
+00:06:10,480 --> 00:06:14,680
+theorem 6 9 كده مش عارف إيش في اللي هو chapter 6
+
+87
+00:06:14,680 --> 00:06:18,200
+قدامة ال function اللي هي is differentiable ال
+
+88
+00:06:18,200 --> 00:06:20,880
+inverse إلها برضه is differentiable في حالة وجودها
+
+89
+00:06:20,880 --> 00:06:27,480
+الآن E فاضل الجهتين بيصير عندي E prime of L of Y
+
+90
+00:06:27,480 --> 00:06:36,600
+فL prime of Y بساوي إيش واحد ماشي الحال الآنواضح
+
+91
+00:06:36,600 --> 00:06:41,900
+أن هذا حاصل الضرب صار أكبر من مين strictly من 0
+
+92
+00:06:41,900 --> 00:06:47,920
+وبما أن الـ E is strictly increasing أثبتنا E' of
+
+93
+00:06:47,920 --> 00:06:53,420
+L of Y is strictly أكبر من 0 إذا بيظلها L' of Y is
+
+94
+00:06:53,420 --> 00:06:57,180
+strictly أكبر من 0 لكل Y هنا إذا صارت الـ L is
+
+95
+00:06:57,180 --> 00:07:02,740
+strictly increasingالان طبعا ال domain مدام ان هذه
+
+96
+00:07:02,740 --> 00:07:07,000
+ال inverse ل ال E ال domain اللي هو ال inverse هو
+
+97
+00:07:07,000 --> 00:07:11,380
+range ال function الأصلية و بيصير sub wave في
+
+98
+00:07:11,380 --> 00:07:18,460
+الفئر اذا الان احنا اثبتنا ان ال is strictly
+
+99
+00:07:18,460 --> 00:07:23,530
+increasingالان و rangeها اللي هو صار domain اللي
+
+100
+00:07:23,530 --> 00:07:28,310
+هو او range اللي هو ال .. هذي اللي صار domainها
+
+101
+00:07:28,310 --> 00:07:32,990
+domain ال L و هذي صارت اللي هو range ال L زي ما
+
+102
+00:07:32,990 --> 00:07:37,330
+قلنا قبل بشوية او عندي الان بدنا نثبت اللي هو
+
+103
+00:07:37,330 --> 00:07:42,070
+الجزء الثاني من النظرية خليني نكتب هنا عشان نتذكر
+
+104
+00:07:42,070 --> 00:07:48,430
+ايش اللي بدنا نثبته الان بدنا نثبت اين أثبتنا
+
+105
+00:07:48,430 --> 00:07:54,230
+الأولىاللي فى النص بتقلّى prime of X اللى نكتبهن
+
+106
+00:07:54,230 --> 00:07:59,330
+اللى بدنا نثبتهن عشان نتذكرهن
+
+107
+00:07:59,330 --> 00:08:12,240
+قلّى prime I او VIII قلّى primeof X بسوة واحدة ل X
+
+108
+00:08:12,240 --> 00:08:19,680
+اتنين اللي هو L of XY بسوة L X زائد L Y طبعا ال Y
+
+109
+00:08:19,680 --> 00:08:25,780
+هناك ال L of واحد بسوة سفر L of E بسوة واحد كلهم
+
+110
+00:08:25,780 --> 00:08:34,440
+بسيطاتL prime L of X to the R سوى R L of X و Limit
+
+111
+00:08:34,440 --> 00:08:39,720
+L of X لما X تروح إلى Zero من اليمين سوى سالب لما
+
+112
+00:08:39,720 --> 00:08:45,140
+لنهاية و Limit لL of X لما X تروح إلى ما لنهاية
+
+113
+00:08:45,140 --> 00:08:48,520
+سوى ما لنهاية خلّيني أشوف أن دول على السريع فانوا
+
+114
+00:08:48,520 --> 00:08:53,640
+كلها شغلات يعني بأعتقد أنه سهل أنك نثبتها
+
+115
+00:08:55,730 --> 00:09:02,210
+عندي لأن زي ما عملت قبل بشوية اللي هو لما فضلت هذه
+
+116
+00:09:02,210 --> 00:09:07,290
+تفاضله E composite L of X لما عملتها قبل بشوية
+
+117
+00:09:07,290 --> 00:09:14,250
+اللي هي كانت عندي هين أعمل E composite L of X الكل
+
+118
+00:09:14,250 --> 00:09:19,370
+اللي هي بساوي ال X فاضل هذا يصير E prime
+
+119
+00:09:26,060 --> 00:09:29,100
+بنسبة لـ x أقل الـ prime of x
+
+120
+00:09:34,780 --> 00:09:40,160
+اللي هو واحد على الـ E prime of L of X إذا الـ E
+
+121
+00:09:40,160 --> 00:09:44,300
+القلي برايم of X بيساوي واحد على E prime composite
+
+122
+00:09:44,300 --> 00:09:48,340
+L of X والـ E prime هي نفس الـ E زي ما قلنا إذا
+
+123
+00:09:48,340 --> 00:09:51,140
+بيصير واحد على E composite L of X إلى ال E
+
+124
+00:09:51,140 --> 00:09:54,640
+composite L of X زي ما قلنا إيش بتساوي بساوي X
+
+125
+00:09:54,640 --> 00:09:57,660
+فبساوي واحد على X فالقلي برايم بيساوي واحد على X
+
+126
+00:09:57,660 --> 00:10:02,910
+لكل X في الموجودة في الفترة Zeroو 1 نيجي الآن نشوف
+
+127
+00:10:02,910 --> 00:10:06,710
+اللي هي اللي بعدها الخاصية اللي بعدها خلّينا نثبت
+
+128
+00:10:06,710 --> 00:10:12,690
+اللي هو L of X في Y بسوا L of X زائد مين زائد L of
+
+129
+00:10:12,690 --> 00:10:17,270
+Y برضه الإثبات سهل وانتبهوا معايا وسهلس عندى الآن
+
+130
+00:10:24,240 --> 00:10:27,240
+F X أكبر من صفر Y أكبر من صفر F X أكبر من صفر Y
+
+131
+00:10:27,240 --> 00:10:27,740
+أكبر من صفر F X أكبر من صفر Y أكبر من صفر F X أكبر
+
+132
+00:10:27,740 --> 00:10:27,900
+من صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+133
+00:10:27,900 --> 00:10:28,100
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+134
+00:10:28,100 --> 00:10:28,700
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+135
+00:10:28,700 --> 00:10:28,920
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+136
+00:10:28,920 --> 00:10:32,100
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+137
+00:10:32,100 --> 00:10:43,400
+صفر F X أكبر من صفر F X أكبر من صفر F X
+
+138
+00:10:43,400 --> 00:10:51,850
+أكبر من صفر F Xلأن الـ E والـ L انفرسة بعض الان من
+
+139
+00:10:51,850 --> 00:10:55,130
+الخاصية تبع الـ exponential بدنا نصل لمن؟ لل
+
+140
+00:10:55,130 --> 00:11:00,970
+logarithmic إذا أضرب ل X في Y بيطلع عند X في Y
+
+141
+00:11:00,970 --> 00:11:05,190
+بتساوي E of U في E of V E of U في E of V إيش
+
+142
+00:11:05,190 --> 00:11:10,010
+بتساوي؟ E of U زائد V أثبتناها إذا من هذا الكلام
+
+143
+00:11:10,970 --> 00:11:15,270
+خُد الـ L للجهتين لإنه اللي هي ال inverse لبعض
+
+144
+00:11:15,270 --> 00:11:20,450
+بيصير عندي L of X في Y بساوي L of E of U زائد V
+
+145
+00:11:20,450 --> 00:11:24,410
+اللي هي إيش بتساوي U زائد V U اللي هي عبارة عن L
+
+146
+00:11:24,410 --> 00:11:30,750
+of X و V عبارة عن L of Y إذا أثبتت L of X زائد X
+
+147
+00:11:30,750 --> 00:11:39,370
+في Y بساوي L of X زائد L of Yالان عندى اللى هى E
+
+148
+00:11:39,370 --> 00:11:47,050
+of Zero بيساوي واحد خدلى ال L الجهتين بيصير ZL of
+
+149
+00:11:47,050 --> 00:11:53,010
+E of Zero بيساوي L of واحد ال L of E of Zero هدك
+
+150
+00:11:53,010 --> 00:11:59,450
+inverse التانية بيساوي Zero نفس الاشيالـ L of E of
+
+151
+00:11:59,450 --> 00:12:07,270
+1 بيساوي L of E، مظبوط؟ الـ L of E of 1 بيساوي 1،
+
+152
+00:12:07,270 --> 00:12:12,230
+بيصير L of E بيساوي 1 بيصير أثبتنا L of E بيساوي 1
+
+153
+00:12:12,230 --> 00:12:19,730
+و L of 1 بيساوي 0 وهذا الكلام كلام سهل، طيب بيصير
+
+154
+00:12:19,730 --> 00:12:23,710
+علاقة أنه سهل اللي بنحكيه، الآن
+
+155
+00:12:27,210 --> 00:12:32,730
+نأتي نثبت اللي هو اللي هي L of X to the R بساوة
+
+156
+00:12:32,730 --> 00:12:37,010
+Zero بساوة R في L of X هذه برضه بقاش By
+
+157
+00:12:37,010 --> 00:12:41,910
+Mathematical Induction عملناها قبل هيكة باللي هو
+
+158
+00:12:41,910 --> 00:12:47,330
+ال section اللي جابله أو اللي هو ال exponential
+
+159
+00:12:47,330 --> 00:12:52,830
+على السريع نشوف التفاصيل لإنه التفاصيل معادة
+
+160
+00:13:07,050 --> 00:13:11,430
+التفاصيل هتلاجوها معادة فخليني بسرعة نمر عليها
+
+161
+00:13:11,430 --> 00:13:17,730
+عندي we show by induction L of X بسوا L L of X زي
+
+162
+00:13:17,730 --> 00:13:21,850
+ما قلنا عشان لثبتها هذه أثبتنا اللي قبل بشوية L of
+
+163
+00:13:21,850 --> 00:13:27,190
+X عارفش الرزوم أصلا أفصل ولا لأ لكن بدي أفصل لو
+
+164
+00:13:27,190 --> 00:13:32,790
+أنتوا عندى لو اتفجنا أن نفصل ولا لأ L of X في Y
+
+165
+00:13:32,790 --> 00:13:39,580
+بسوا L of X في L of Yof x was n بساوي n في L of x
+
+166
+00:13:39,580 --> 00:13:44,060
+طبعا for n بتساوي واحد اللي هي a trivial نفترض
+
+167
+00:13:44,060 --> 00:13:48,180
+أنها صحيحة ل L ل n بتساوي k بيصير L of x was k
+
+168
+00:13:48,180 --> 00:13:53,080
+بساوي k L of x الآن بدنا نحسب ل L of x was k زائد
+
+169
+00:13:53,080 --> 00:13:59,480
+واحد اللي هي بساوي L of x was k في xهذه الـ L لها
+
+170
+00:13:59,480 --> 00:14:04,760
+حسب اللي هي الخاصية هذه بسوء L الأولى X plus K في
+
+171
+00:14:04,760 --> 00:14:09,860
+L التاني L of X اللي هو مفترض إنها صحيحة على K ده
+
+172
+00:14:09,860 --> 00:14:19,600
+بسوء K في L of X آسف زائد هذه بسوء K L of Xلأنها
+
+173
+00:14:19,600 --> 00:14:26,400
+صحيحة لـ K زائد L of X ويساوي K زائد واحد في L of
+
+174
+00:14:26,400 --> 00:14:31,520
+X إذا صارت هذه صحيحة اللي هي L ل K زائد واحد إذا
+
+175
+00:14:31,520 --> 00:14:36,760
+صارت صحيحة لكل من لكل N element in N حسب اللي هو
+
+176
+00:14:36,760 --> 00:14:43,080
+ال induction اللي بنحكي فيه إذا الأن أثبتنا أن L
+
+177
+00:14:43,080 --> 00:14:49,710
+of X هو N لL of X لكل اللي هي عنديالان by VI اللي
+
+178
+00:14:49,710 --> 00:14:53,530
+هو زي .. مشابه للي حكيناها قبل بشوية بالظبط في حد
+
+179
+00:14:53,530 --> 00:14:58,890
+ال exponential بس خليني مش وشكلة بتعيده الان شوف L
+
+180
+00:14:58,890 --> 00:15:03,680
+of XM minus M أيش بتساوي؟ L of واحداللي هي لأن هذا
+
+181
+00:15:03,680 --> 00:15:05,860
+X هو السفر اللي هي L of واحد L of واحد مش قولنا
+
+182
+00:15:05,860 --> 00:15:11,040
+عنها سفر هو يسوى L of XM في XM minus واحد ال
+
+183
+00:15:11,040 --> 00:15:16,300
+logarithmic بطلح انجمع L of XM زائد L of X minus M
+
+184
+00:15:16,300 --> 00:15:21,920
+لأن هذه أثبتناها عبارة عن M L of X زائدL of X
+
+185
+00:15:21,920 --> 00:15:27,500
+minus M صار عندي الان M في L of X زائد L of X
+
+186
+00:15:27,500 --> 00:15:32,040
+minus M بسوا سفر انجلي هذا على الجهة الثانية بطلع
+
+187
+00:15:32,040 --> 00:15:35,760
+L of X minus M اللي قعدت لحالها بسوا ناقص M في L
+
+188
+00:15:35,760 --> 00:15:41,720
+of X اذا صار عندي الان لكل M سواء موجبة او سالبة
+
+189
+00:15:41,720 --> 00:15:48,940
+بطلع عندي اللي هي L of X قص Mبساوة M في L of X
+
+190
+00:15:48,940 --> 00:15:53,860
+سواء كانت وجبة أو سالبة نيجي الآن منها بدنا ناخد
+
+191
+00:15:53,860 --> 00:15:57,360
+لمين لأ اللي هي ال R لان therefore for any M
+
+192
+00:15:57,360 --> 00:16:02,800
+element in Z و N element in Nعندي احسبلي الان L of
+
+193
+00:16:02,800 --> 00:16:07,020
+X أس M على N بس ضربليها في N بعد إذنك Y ساوي اللي
+
+194
+00:16:07,020 --> 00:16:12,460
+هي L of X أس M على N لكل ما له أس N لإنه صحيحة هذه
+
+195
+00:16:12,460 --> 00:16:18,080
+لل N اللي هي في N واتفجنا عليها الان هذه بتساوي
+
+196
+00:16:18,080 --> 00:16:21,520
+هذه واضحة لإن هذه هي ال X تبعتنا وهذه ال N بتطلع
+
+197
+00:16:21,520 --> 00:16:27,410
+براالان هذه الان مع الان بيصير L of X plus M L of
+
+198
+00:16:27,410 --> 00:16:30,870
+X plus M قبل بشوية بقى قولنا عنها بيساوي M L of X
+
+199
+00:16:30,870 --> 00:16:34,270
+سواء كانت M positive أو اللي هو negative صار هذه
+
+200
+00:16:34,270 --> 00:16:40,930
+بتساوي هذه إذا انجلي الآنالان هذه ان بيصير عندي L
+
+201
+00:16:40,930 --> 00:16:44,910
+of X of M على N بيسوي M على N في L of X إذا صار
+
+202
+00:16:44,910 --> 00:16:49,490
+عندي لأي rational number صار عندي L of X R بيسوي R
+
+203
+00:16:49,490 --> 00:16:55,670
+L of X لكل R اللي بنتميين NQ نيجي الآن لأ اللي هي
+
+204
+00:16:55,670 --> 00:16:57,230
+الجزء الأخير من النظرية
+
+205
+00:17:08,180 --> 00:17:11,120
+الكلام مشابه للي حكيناها قبل بشوية في الإثبات اللي
+
+206
+00:17:11,120 --> 00:17:15,260
+هو ال limit تبع ال exponential عند 2 أصغر من E
+
+207
+00:17:15,260 --> 00:17:19,380
+وقلنا ليش الان ال E n هنا بيصير 2 أصغر من E أصغر
+
+208
+00:17:19,380 --> 00:17:19,920
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+209
+00:17:19,920 --> 00:17:21,140
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+210
+00:17:21,140 --> 00:17:22,840
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+211
+00:17:22,840 --> 00:17:23,240
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+212
+00:17:23,240 --> 00:17:26,700
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+213
+00:17:26,700 --> 00:17:30,620
+من E أصغ
+
+214
+00:17:33,960 --> 00:17:39,580
+لكن اللي هو L of E N بسوء N and اللي هي L of E
+
+215
+00:17:39,580 --> 00:17:44,020
+minus N بسوء نقص N خليني في الذاكر هذول اذا for
+
+216
+00:17:44,020 --> 00:17:47,480
+every N element in R there exists X element in R
+
+217
+00:17:47,480 --> 00:17:52,670
+بحيث ان X أكبر من مين من Nلكل N element in N في X
+
+218
+00:17:52,670 --> 00:17:56,350
+element in R أكيد X أكبر من مين من E N لأنه أخسرت
+
+219
+00:17:56,350 --> 00:18:00,590
+N بين إيديا حسبت ال E N طلع عند رقم أخدت ال X أكبر
+
+220
+00:18:00,590 --> 00:18:03,310
+منها كيد بالله طيب لأنه unbounded real numbers
+
+221
+00:18:03,310 --> 00:18:06,710
+then L في هذه أكبر أو من L في هذه لأنه ال L
+
+222
+00:18:06,710 --> 00:18:10,810
+strictly increasing إذا صار L في X أكبر من مين من
+
+223
+00:18:10,810 --> 00:18:16,130
+ال NA ألوف E أن يعني أكبر من الان لأن limit هذه as
+
+224
+00:18:16,130 --> 00:18:21,210
+x goes to infinity اللي هو بيكون أكبر أساوي اللي
+
+225
+00:18:21,210 --> 00:18:23,950
+هي limit هذه as n goes to infinity ويساوى infinity
+
+226
+00:18:23,950 --> 00:18:27,550
+لأن لكل لما الان تروح لما لنهاية أكيد ال X بتروح
+
+227
+00:18:27,550 --> 00:18:31,270
+لمين إلى ما لنهاية فصار عندي هذه بتروح إلى ما
+
+228
+00:18:31,270 --> 00:18:34,970
+لنهاية الآن صار عندي limit L of X لما X تروح لما
+
+229
+00:18:34,970 --> 00:18:41,040
+لنهاية بيساوي ما لنهاية similarlyالان لكل نقص any
+
+230
+00:18:41,040 --> 00:18:43,100
+element in z positive بلاقي x element in r
+
+231
+00:18:43,100 --> 00:18:45,740
+positive بحيث ان x أكبر من صفر و أصغر من صفر و
+
+232
+00:18:45,740 --> 00:18:46,340
+أصغر من صفر و أصغر من صفر و أصغر من صفر و أصغر من
+
+233
+00:18:46,340 --> 00:18:47,840
+صفر و أصغر من صفر و أصغر من صفر و أصغر من صفر و
+
+234
+00:18:47,840 --> 00:18:51,500
+أصغر من صفر و أصغر من صفر و أصغر من صفر و أصغر من
+
+235
+00:18:51,500 --> 00:18:57,960
+صفر و أصغر من صفر و أصغر من صفر و أصغر من صفر و
+
+236
+00:18:57,960 --> 00:19:02,520
+أصغر من صفر و أصغر من صفر و أصغر من صفر و أصغر من
+
+237
+00:19:02,520 --> 00:19:09,620
+صفر و أصغر من صفر و أصغر من صفر و أطيب then L of X
+
+238
+00:19:09,620 --> 00:19:13,660
+هيكون أصغر يساوي ال E to the minus N يعني L of X
+
+239
+00:19:13,660 --> 00:19:17,800
+اللي هي أصغر يساوي ناقص N إذا as N goes to
+
+240
+00:19:17,800 --> 00:19:22,700
+infinity as N goes to infinity اللي هو ال E to the
+
+241
+00:19:22,700 --> 00:19:26,540
+minus N بيروح لل0 من اليمين إذا ال X بتروح لل0 من
+
+242
+00:19:26,540 --> 00:19:30,820
+اليمين إذا عندي ال X بتروح لل 0 من اليميناللي هو
+
+243
+00:19:30,820 --> 00:19:34,580
+أصغر لما الـ limit L of X أصغر من limit E to the
+
+244
+00:19:34,580 --> 00:19:37,900
+minus N لما هذا يروح لـ 0 من اليمين أو بمعنى أخر
+
+245
+00:19:37,900 --> 00:19:41,680
+لما الـ N تروح لمهة لنهاية و هذا بيروح لمين؟ لـ
+
+246
+00:19:41,680 --> 00:19:44,760
+Infinity إذا limit L of X لما X تروح لمهة لنهاية
+
+247
+00:19:44,760 --> 00:19:50,920
+بساوي سالب Infinity و هو المطلوب hence limit L of
+
+248
+00:19:50,920 --> 00:19:54,460
+X لما X تروح لـ 0 من اليمين بساوي سالب Infinity
+
+249
+00:19:54,460 --> 00:19:58,500
+طيب
+
+250
+00:20:12,260 --> 00:20:16,320
+الان سارعنا الان نقدر ان اللي هو نحكي عن ال bar
+
+251
+00:20:16,320 --> 00:20:20,080
+functions بدنا نعرف ال bar functions اللي هي بناء
+
+252
+00:20:20,080 --> 00:20:25,060
+على اللي حكيناه و اللي هي موضوع ال bar functions
+
+253
+00:20:25,060 --> 00:20:28,880
+كل ما فيه تقريبا يعني بنعتبره exercises احنا لكن
+
+254
+00:20:28,880 --> 00:20:32,520
+خلينا نعرف التعريفات و النظريات بتكون اللي هي
+
+255
+00:20:32,520 --> 00:20:35,900
+معاكم exercises بسيطة بناء على التعريف اللي
+
+256
+00:20:35,900 --> 00:20:40,720
+بنعرفها اللي هناخد α يليمنتان R و X أكبر من 0The
+
+257
+00:20:40,720 --> 00:20:43,320
+number X to the Alpha is defined to be .. الآن بدي
+
+258
+00:20:43,320 --> 00:20:46,940
+أعرف حاجة اسمها X to the Alpha X to the Alpha بدي
+
+259
+00:20:46,940 --> 00:20:49,900
+أعرفها .. إيش بدي أعرفها؟ بإيشي أنا معرف عندي من
+
+260
+00:20:49,900 --> 00:20:54,440
+الأصل ال exponential معرفة .. خلصنا منها و ال len
+
+261
+00:20:54,440 --> 00:20:59,000
+معرفة .. إذا E to the Alpha في لن ال X هذه المقدار
+
+262
+00:20:59,000 --> 00:21:03,820
+لهذا معرف و هذا معرف بدي أسمي X to the Min to the
+
+263
+00:21:03,820 --> 00:21:07,400
+Alpha اللي هو في الواقع عبارة عن Min E to the
+
+264
+00:21:07,400 --> 00:21:12,040
+AlphaL of X L of X معرفة والـ E معرفة إذا كل هذه
+
+265
+00:21:12,040 --> 00:21:16,000
+معرفة بتسميها X to the main to the alpha الآن صارت
+
+266
+00:21:16,000 --> 00:21:19,540
+عندي يعني قيمة الـ X under this function اللي
+
+267
+00:21:19,540 --> 00:21:23,120
+عرفتها لجديدة يعني إذا بتسميها دي ال function الـ
+
+268
+00:21:23,120 --> 00:21:28,240
+R of X إيش عرفتها أنا بتساوي X to the alpha؟يعني
+
+269
+00:21:28,240 --> 00:21:31,680
+كل ال X بتصير يشمل X to the Alpha و X أكبر من 0
+
+270
+00:21:31,680 --> 00:21:36,780
+هذه ال X to the Alpha هي اللي بدي أسميها ال power
+
+271
+00:21:36,780 --> 00:21:42,000
+function بدي أسميها power function with exponent
+
+272
+00:21:42,000 --> 00:21:47,540
+mean Alpha و ال X هي أشمالها المتغيرة اللي أكبر من
+
+273
+00:21:47,540 --> 00:21:54,340
+0 شوف الآن نشوف بعض الخواص اللي هو هذه اللي هي
+
+274
+00:21:54,340 --> 00:21:56,460
+الدالة طيب
+
+275
+00:22:04,730 --> 00:22:08,690
+الان if x أكبر من 0 and alpha بساوة m على n where
+
+276
+00:22:08,690 --> 00:22:12,770
+m element in z و n element in n then we define x
+
+277
+00:22:12,770 --> 00:22:17,790
+to the alpha بساوة x to the m أسواحد على n in
+
+278
+00:22:17,790 --> 00:22:23,110
+section mean خمسة ستة هتعرفناها زمان انه في حالة
+
+279
+00:22:23,110 --> 00:22:26,570
+بس اللي هي ال rational number عرفنا x to the m على
+
+280
+00:22:26,570 --> 00:22:30,630
+n بساوة x to the m لكل أسواحد على nماشي الحال
+
+281
+00:22:30,630 --> 00:22:34,510
+..الان بدنا نشوف هذا التعريف مطابق لتعريفنا اليوم
+
+282
+00:22:34,510 --> 00:22:41,670
+ولا لأ hence we have لن ال X to the Alpha لن ال X
+
+283
+00:22:41,670 --> 00:22:45,370
+to the Alpha لن ال X to the Alpha بساوي Alpha لن
+
+284
+00:22:45,370 --> 00:22:51,540
+ال Xعرفناها هذه طيب where X to the Alpha بيسوا E
+
+285
+00:22:51,540 --> 00:22:56,260
+to the Lin X to the Min to the Alpha اللي هو بيسوا
+
+286
+00:22:56,260 --> 00:23:01,020
+E to the Alpha في Min في Lin ال X كلام كله سهل ال
+
+287
+00:23:01,020 --> 00:23:05,740
+X to the Alpha هو اللي عرفناها اللي عبارة عن E
+
+288
+00:23:05,740 --> 00:23:10,570
+بتصير to the Lin X to the Alphaلأنه استبدلت الـ x
+
+289
+00:23:10,570 --> 00:23:15,090
+to the alpha بقيمتها اللي هي عبارة عن اللي هي
+
+290
+00:23:15,090 --> 00:23:18,630
+alpha ln x اللي هي بالساوية e to the ln x to the
+
+291
+00:23:18,630 --> 00:23:24,510
+mean to the alpha إذا سواء احنا بالتعريف اللي هو
+
+292
+00:23:24,510 --> 00:23:28,190
+احنا هذا بال exponent أو بال ال function اللي
+
+293
+00:23:28,190 --> 00:23:33,110
+عرفناها بالشكل هذا هيطلع عندي اللي هو القيمتين نفس
+
+294
+00:23:33,110 --> 00:23:34,790
+القيمة طيب
+
+295
+00:23:37,160 --> 00:23:42,300
+نجي الآن لبعض الخواص اللي هي تبعت ال exponential
+
+296
+00:23:42,300 --> 00:23:47,180
+ال power function و الخواص هنتركه لكم إياه لأنها
+
+297
+00:23:47,180 --> 00:23:54,600
+مباشرة على التعريف تبعنا مباشرة
+
+298
+00:23:54,600 --> 00:24:01,100
+على اللي هي التعريف اللي عندنا و هيكون في عندي
+
+299
+00:24:01,100 --> 00:24:05,760
+الآن النظرية الأولىاللي هي 8 3 11 لو كانت Alpha
+
+300
+00:24:05,760 --> 00:24:11,340
+element in R و X و Y اللي هو تنتمي للفترة Zero و
+
+301
+00:24:11,340 --> 00:24:16,500
+تمانية Zero و ما لنهاية آسف then معلش عشان ده طلعت
+
+302
+00:24:16,500 --> 00:24:20,450
+الكهربا قعد نقلف الكهربا أناIf α element in R و X
+
+303
+00:24:20,450 --> 00:24:26,350
+Y belongs to 0 α then 1 to the α بسوء 1 و X to the
+
+304
+00:24:26,350 --> 00:24:30,270
+α أكبر من 0 و X Y to the α بسوء X to the α و Y to
+
+305
+00:24:30,270 --> 00:24:35,590
+the α و X على Y to the α بسوء X to the α على Y to
+
+306
+00:24:35,590 --> 00:24:39,370
+the α هذه اللي هي النظرية طبعا اللي هي مباشرة على
+
+307
+00:24:39,370 --> 00:24:45,100
+تعريفنا اللي هو X to the α بسوء Eof α لن X يعني
+
+308
+00:24:45,100 --> 00:24:49,800
+بدك تيجي تستخدم تعريفك اللي هو اللي عرفناه وعليه
+
+309
+00:24:49,800 --> 00:24:53,480
+اللي هو بتبدأ تشتغل و تبني اللي هو اللي هي
+
+310
+00:24:53,480 --> 00:24:57,680
+القوانين اللي بنحكي عنها اللي هو تعريفنا اللي هو X
+
+311
+00:24:58,570 --> 00:25:05,210
+to the alpha بتساوي E of alpha len اللي هي L of X
+
+312
+00:25:05,210 --> 00:25:10,650
+أو حسب ال notation تبعتنا E to the alpha len ال X
+
+313
+00:25:10,650 --> 00:25:15,710
+هذا الآن التعريف اللي عليه بدك اللي هو تبدأ اللي
+
+314
+00:25:15,710 --> 00:25:23,290
+هو تشتغل على اللي هي النظريةوتبرهنها اللي عندنا
+
+315
+00:25:23,290 --> 00:25:27,630
+نظرية الأولى اللي ذكرناها قبل بشوية اللي هي هذه
+
+316
+00:25:27,630 --> 00:25:32,090
+النظرية على التعريف مباشرة ونظرية تانية أيضا برضه
+
+317
+00:25:32,090 --> 00:25:35,670
+من الخواص إذا كانت Alpha و Beta element ر و X في
+
+318
+00:25:35,670 --> 00:25:40,640
+الفترة Zero ولا نهاية إذا Xتو دا ألفة زيادة بيتا
+
+319
+00:25:40,640 --> 00:25:44,040
+برضه نفس الاشياء طبعا هتلاقي اللي هو انت لما تيجي
+
+320
+00:25:44,040 --> 00:25:48,320
+تفرد هذه هتصير تستخدم خواص المعرفة اللي هي
+
+321
+00:25:48,320 --> 00:25:52,360
+بواسطتها معرفة هتستخدم خواص ال X exponential والن
+
+322
+00:25:52,360 --> 00:25:55,420
+اللي قبله بشوية هتلاقي حالك بتصل X تو دا ألفة
+
+323
+00:25:55,420 --> 00:25:58,310
+زيادة بيتا بسوء X تو دا ألفة في X تو دا بيتاو نفس
+
+324
+00:25:58,310 --> 00:26:05,170
+الشيء x²α²β بيساوي x α beta و يساوي x²β²α و هتيجي
+
+325
+00:26:05,170 --> 00:26:08,830
+.. اللي هي كلها قوانين احنا بنعرفها x²-α بيساوي 1
+
+326
+00:26:08,830 --> 00:26:12,270
+على x²α و نفس الشيء إذا كانت alpha أصغر من beta
+
+327
+00:26:12,270 --> 00:26:17,770
+هيكون x²α أصغر من x²β لما ان x تكون أكبر من 1 و
+
+328
+00:26:17,770 --> 00:26:22,130
+هذه كلها بتكون x resources معاكم اللي هي مباشرة
+
+329
+00:26:22,130 --> 00:26:31,830
+على هذه التعريفالنظرية اللي عندنا على السريع let
+
+330
+00:26:31,830 --> 00:26:35,010
+alpha element in R then the function x بالتروح للـ
+
+331
+00:26:35,010 --> 00:26:37,670
+x alpha من 0 و 1 to R is continuous and
+
+332
+00:26:37,670 --> 00:26:41,210
+differentiable and اللي هو ال derivative لل x to
+
+333
+00:26:41,210 --> 00:26:43,630
+the alpha بسوء alpha to the x to the alpha minus 1
+
+334
+00:26:43,630 --> 00:26:47,650
+for x element in 0 و 1 طبيعي أصلا هي composition
+
+335
+00:26:47,650 --> 00:26:54,490
+of two هي عندى function هذه اللي هي continuousهذا
+
+336
+00:26:54,490 --> 00:26:57,650
+كلها على بعض الـ E كمان continuous ده اللي هتطلع
+
+337
+00:26:57,650 --> 00:26:59,850
+هذا continuous و هذا continuous و نفس الاشي ال
+
+338
+00:26:59,850 --> 00:27:02,870
+differentiability إذا أكيد اللي هي ال function
+
+339
+00:27:02,870 --> 00:27:05,890
+اللي عندنا X to the X to the Alpha حسب تعريفنا is
+
+340
+00:27:05,890 --> 00:27:09,410
+continuous and differentiable و لو بدك تسمي اللي
+
+341
+00:27:09,410 --> 00:27:13,710
+هو هذه ال derivative و بدك تبدأ تفاضل دي اتفاضل DX
+
+342
+00:27:13,710 --> 00:27:17,050
+Alpha يعني بدك تتفاضل هذه كيف تتفاضل هذه ال
+
+343
+00:27:17,050 --> 00:27:20,860
+exponential اللي هي E to the Alpha لإن ال Xفى
+
+344
+00:27:20,860 --> 00:27:25,580
+التفاضل اللى هو اللى جوا اللى هو Alpha فى واحد على
+
+345
+00:27:25,580 --> 00:27:30,120
+X ماشي الحال اللى هى بمعنى آخر بصير عندى اللى هو
+
+346
+00:27:30,120 --> 00:27:35,260
+عبارة عن E to the Alpha لن ال X اللى هى عبارة عن
+
+347
+00:27:35,260 --> 00:27:38,480
+ال X to the Alpha نفسها فى التفاضل هذه اللى هى
+
+348
+00:27:38,480 --> 00:27:43,080
+Alpha على X بيساوى Alpha أس X اللى هى هذه بتطلع
+
+349
+00:27:43,080 --> 00:27:46,680
+ناقص واحد Alpha مانس واحد for X element in zero
+
+350
+00:27:46,680 --> 00:27:53,250
+وملا نهايةالان بعض الملاحظات الأخرى اللي بيقولك
+
+351
+00:27:53,250 --> 00:28:01,010
+إياها على هذه الدالة بيقولبقول لك اللي هو عندي إذا
+
+352
+00:28:01,010 --> 00:28:07,610
+كانت Alpha أكبر من 0 فبصير
+
+353
+00:28:07,610 --> 00:28:11,970
+عندي اللي هي ال function من X and X alpha is
+
+354
+00:28:11,970 --> 00:28:15,930
+strictly increasing على فترة 0 و ملا نهاية طبيعي
+
+355
+00:28:15,930 --> 00:28:19,890
+لما Alpha أكبر من 0 هيصير عندي الان المقدر هذا
+
+356
+00:28:19,890 --> 00:28:24,120
+بظله موجبو هذه ألف أكبر من سفر بيكون بيبدو أكبر من
+
+357
+00:28:24,120 --> 00:28:27,180
+سفر إذا صارت عندي اللي هي ال derivative أكبر من
+
+358
+00:28:27,180 --> 00:28:31,160
+سفر إذا صارت عند الدلة strictly increasing لو كانت
+
+359
+00:28:31,160 --> 00:28:34,520
+ألف أصغر من سفر هتصير اللي هي العكس strictly
+
+360
+00:28:34,520 --> 00:28:38,420
+decreasing لإنه هتكون هذه سالبة وهذه مدلة موجبة
+
+361
+00:28:38,420 --> 00:28:42,180
+بتظل هذه كلها موجبة إذا صارت strictly decreasing
+
+362
+00:28:42,180 --> 00:28:45,360
+عند ألف بتساوي سفر بيكون احنا ال derivative للواحد
+
+363
+00:28:45,360 --> 00:28:48,880
+اللي هو بيكون عبارة عن constant function اللي هو
+
+364
+00:28:48,880 --> 00:28:51,300
+في حالة الألف بتساوي سفر
+
+365
+00:28:53,910 --> 00:29:02,970
+الان نيجي الى اللي هي هيك بنكون اللي هو وصلنا
+
+366
+00:29:02,970 --> 00:29:09,190
+لآخر تعريف بده يعرف اللي هو ال log function للأساس
+
+367
+00:29:09,190 --> 00:29:13,090
+a احنا اللي عرفناه ال len اللي هو للأساس e بمعنى
+
+368
+00:29:13,090 --> 00:29:16,530
+آخر كيف بده اعرفه الآن احنا لسه ماعرفش الأساسات
+
+369
+00:29:16,530 --> 00:29:19,930
+هدا كصمنا ال len و ال exponential الان بدنا نعرف
+
+370
+00:29:19,930 --> 00:29:25,920
+اللي هو نسمي ال logاللغاريثم للأساس A نفترض أن A
+
+371
+00:29:25,920 --> 00:29:28,860
+أكبر من 0 و A لات سوى 1 it is sometimes useful to
+
+372
+00:29:28,860 --> 00:29:34,820
+define the function log للأساس A كمالي الان log A
+
+373
+00:29:34,820 --> 00:29:39,560
+of X كده اللي بيساوي لن ال X على لن ال A حيث ال A
+
+374
+00:29:39,560 --> 00:29:43,940
+عدد ثابت ماشي الحال هذه الآن صارت اللي هي ال log
+
+375
+00:29:43,940 --> 00:29:49,540
+العامة هي نفس ال exponential بس مضروبة في ثابتالأن
+
+376
+00:29:49,540 --> 00:29:52,920
+إذا الـ exponential الأصلية عليها هو معرف الان
+
+377
+00:29:52,920 --> 00:29:59,140
+بقولك إنه اللي هي هذه بنسميها log أو ال logarithm
+
+378
+00:29:59,140 --> 00:30:04,620
+للأساس A لو كان الأساس E هذا بصير لن ال E واحد
+
+379
+00:30:04,620 --> 00:30:09,320
+بنصير نرجع لن ال X اللي هي الدالة الأصلية إذا لو
+
+380
+00:30:09,320 --> 00:30:14,000
+كانت ال A هي ال E بنرجع للدالة الأصلية اللي هي زي
+
+381
+00:30:14,000 --> 00:30:17,060
+ما قلنا is called the logarithm of X to the base A
+
+382
+00:30:19,560 --> 00:30:23,400
+Yields دا الـ logarithm العادي الان اللي مشهور
+
+383
+00:30:23,400 --> 00:30:28,020
+عندنا للحسابات اللي هو للأساس عشرة اللي هو بنسمي
+
+384
+00:30:28,020 --> 00:30:32,220
+اللي هو log to the base عشرة أو اللي بنسمي common
+
+385
+00:30:32,220 --> 00:30:36,720
+logarithm اللي هو اللي بنستخدمه عادة في الحسابات و
+
+386
+00:30:36,720 --> 00:30:41,620
+هيك بكون عندنا احنا انهينا اللي هو ال section اللي
+
+387
+00:30:41,620 --> 00:30:46,180
+هو تمانية تلاتة و بكون خلصنا اللي هيالجزء الثاني
+
+388
+00:30:46,180 --> 00:30:52,240
+من المحاضرة اللي هو ما يتعلق بال .. اللي هو ال
+
+389
+00:30:52,240 --> 00:30:54,660
+logarithmic function وال power function وال
+
+390
+00:30:54,660 --> 00:31:00,040
+logarithmic للأساس اللي هو زي ما قلنا ايه و إلى
+
+391
+00:31:00,040 --> 00:31:00,640
+لقاء
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/5K4iv00tzI0_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/5K4iv00tzI0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..39eeb4a2bbb11fc5a63155ccebdf8103af600830
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/5K4iv00tzI0_postprocess.srt
@@ -0,0 +1,1684 @@
+1
+00:00:05,060 --> 00:00:11,580
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 28 مساق
+
+2
+00:00:11,580 --> 00:00:16,020
+تحليل الحقيقة 2 طلاب طالبات الجامعة الإسلامية كلية
+
+3
+00:00:16,020 --> 00:00:20,360
+العلوم قسم الرياضيات الآن هنبدأ في ال section 9-3
+
+4
+00:00:20,360 --> 00:00:24,990
+اللي هو tests for noneabsolute convergence tests
+
+5
+00:00:24,990 --> 00:00:29,770
+for non-absolute convergence الآن لو لاحظنا اللي
+
+6
+00:00:29,770 --> 00:00:33,570
+هو حديثنا في السابق كان على اللي هو tests for
+
+7
+00:00:33,570 --> 00:00:36,490
+absolute convergence كل اللي هي ال series اللي
+
+8
+00:00:36,490 --> 00:00:41,510
+فحصناها اللي هي بواسطة اللي هي series of positive
+
+9
+00:00:41,510 --> 00:00:45,670
+terms أو اللي هي absolute convergence للي هي ال
+
+10
+00:00:45,670 --> 00:00:49,150
+series الآن لو كانت عندي ال series مش اللي هي
+
+11
+00:00:49,860 --> 00:00:53,660
+positive terms لو كانت اللي هي series متغيرة
+
+12
+00:00:53,660 --> 00:00:57,160
+الإشارة زي عندنا لو جينا summation ناقص واحد ثم
+
+13
+00:00:57,160 --> 00:01:00,560
+نزيد واحد على n وsummation ناقص واحد ثم نزيد واحد
+
+14
+00:01:00,560 --> 00:01:04,000
+على جدر ال n الان بدنا اللي هو نعمل testing for
+
+15
+00:01:04,000 --> 00:01:08,980
+absolute convergence او for convergence test for
+
+16
+00:01:08,980 --> 00:01:12,420
+convergence لهذه ال series مش في .. بدنا نحكي الآن
+
+17
+00:01:12,420 --> 00:01:14,700
+عن test for convergence لأن absolute convergence
+
+18
+00:01:14,700 --> 00:01:19,700
+بنعرفهمن اللي هو خلال السابق الآن بلزمنا إذا
+
+19
+00:01:19,700 --> 00:01:23,320
+الحديث عن حاجة اسمها alternating series إيش ال
+
+20
+00:01:23,320 --> 00:01:26,720
+alternating series لو كانت عندي X بالساوية XN of
+
+21
+00:01:26,720 --> 00:01:29,940
+non-zero real numbers يعني هدولة عبارة عن real
+
+22
+00:01:29,940 --> 00:01:33,500
+numbers مش صفار اللي هو ممكن تاخد مودب أو سالب
+
+23
+00:01:33,500 --> 00:01:36,840
+ولكن ال set to be alternating الآن لما بنقول عنه
+
+24
+00:01:36,840 --> 00:01:41,660
+ال alternating بدنا نيجي أنه انقيدهم بمعنى أخر it
+
+25
+00:01:41,660 --> 00:01:45,780
+is set to be alternating if the termsنقص واحد
+
+26
+00:01:45,780 --> 00:01:49,760
+أسنان زائد واحد XN are all positive or all
+
+27
+00:01:49,760 --> 00:01:53,620
+negative يعني يا كلنا دولة أيش مجبات يا كلنا أيش
+
+28
+00:01:53,620 --> 00:01:59,200
+سالبات if the sequence X بيسوي XN اللي هي is
+
+29
+00:01:59,200 --> 00:02:04,400
+alternating we say that the series summation اللي
+
+30
+00:02:04,400 --> 00:02:09,180
+هي it generates is an alternating أيش ما لها
+
+31
+00:02:09,180 --> 00:02:12,400
+seriesمدام هذه كلها positive أو كلها negative صارت
+
+32
+00:02:12,400 --> 00:02:15,360
+على بعض و هذه تنساش أنه مرة بتاخد positive و مرة
+
+33
+00:02:15,360 --> 00:02:19,300
+بتاخد negative إذا ال series ال Xn أو ال Xn الأصلي
+
+34
+00:02:19,300 --> 00:02:22,720
+هذه هتكون مرة بتاخد موجب و مرة بتاخد سالب أو مرة
+
+35
+00:02:22,720 --> 00:02:26,200
+بتاخد سالب و مرة بتاخد موجب فعشان هيك بدل ما
+
+36
+00:02:26,200 --> 00:02:29,660
+نكتبها زيك و نقول هذه دايما كلها موجبة بنيجي
+
+37
+00:02:29,660 --> 00:02:33,900
+بنكتبها بصورة ثانية بنقول خلينا نكتب ال series Xn
+
+38
+00:02:33,900 --> 00:02:39,760
+تساوي ناقص واحد زائد واحد في مين في Znو بتصير الان
+
+39
+00:02:39,760 --> 00:02:44,280
+Zn هي اللي دايما positive و هذه هي اللي بتحدد
+
+40
+00:02:44,280 --> 00:02:47,920
+الإشارة عشان هيك اللي لما نحكي عن ال alternating
+
+41
+00:02:47,920 --> 00:02:52,520
+series هنصير نكتبها على الصورة هذه ناقص واحد أس أن
+
+42
+00:02:52,520 --> 00:02:58,140
+زائد واحد أو ناقص واحد أس أن في Zn و Zn دايما تكون
+
+43
+00:02:58,140 --> 00:03:02,040
+موجبة و الناقص واحد أس أن زائد واحد أو ناقص واحد
+
+44
+00:03:02,040 --> 00:03:07,650
+أس أن هتتحدد لي هياللي هو إنها مرة موجبة و مرة
+
+45
+00:03:07,650 --> 00:03:12,390
+سالبة هل هتحدد اللي هو في الأول موجب وبعدين سالب
+
+46
+00:03:12,390 --> 00:03:18,010
+حسب اللي هو الأسئن زائد واحد أو الهاشئن الان نيجي
+
+47
+00:03:18,010 --> 00:03:22,830
+اللي هو بدنا نفحص ال series اللي منها النوع هل هذه
+
+48
+00:03:22,830 --> 00:03:26,770
+ال seriesاللي هي converge ولا diverge وهذا اللي هو
+
+49
+00:03:26,770 --> 00:03:31,270
+الشيء الجديد عن اللي هو ال section السادق الآن
+
+50
+00:03:31,270 --> 00:03:35,830
+اللي بنقوله alternating series test let Z بتساوي
+
+51
+00:03:35,830 --> 00:03:40,090
+ZN be a decreasing sequence of strictly positive
+
+52
+00:03:40,090 --> 00:03:46,050
+numbers with limit ZN بساوي سفر إذا في عندي شروط
+
+53
+00:03:46,050 --> 00:03:50,020
+الآن لل series اللي أنا بده أفحصهاأول حاجة بدي
+
+54
+00:03:50,020 --> 00:03:54,520
+أكون عندي Zn عبارة عن decreasing sequence وكل
+
+55
+00:03:54,520 --> 00:03:57,500
+واحدة of strictly positive numbers وكل واحدة إيه
+
+56
+00:03:57,500 --> 00:04:01,720
+شمالها عبارة عن positive number يعني أكبر من 0
+
+57
+00:04:01,720 --> 00:04:07,400
+strictly و اللي هو لكل N فصار عندى اللي هو شرطين
+
+58
+00:04:07,400 --> 00:04:12,120
+إنها تكون decreasing و limit و الـ Zn أكبر من 0
+
+59
+00:04:12,120 --> 00:04:17,250
+strictly لكل N و الشرط الثالثاللي هو limit الـ ZN
+
+60
+00:04:17,250 --> 00:04:22,550
+يساوي سفر إذا صارت الـ sequence اللي بده أكوّن
+
+61
+00:04:22,550 --> 00:04:26,230
+منها ال alternating series تحقق ثلاث شروط ZN
+
+62
+00:04:26,230 --> 00:04:29,890
+decreasing sequence strictly positive numbers الـ
+
+63
+00:04:29,890 --> 00:04:34,030
+ZN و limit الـ ZN بساوي سفر اللي أنا بقول لذن الان
+
+64
+00:04:34,030 --> 00:04:38,790
+النتيجة ال alternating series الصممش ناقص واحد وزن
+
+65
+00:04:38,790 --> 00:04:44,630
+زاد واحد ZN إشمالها is convergentإيش مالها؟ هتكون
+
+66
+00:04:44,630 --> 00:04:49,050
+Convergent وانت مغمض يعني لو جينا على اللي هو ال
+
+67
+00:04:49,050 --> 00:04:53,790
+series اللي فوق عندي اللي هي اللي تعرضناها في
+
+68
+00:04:53,790 --> 00:04:59,270
+الأول اللي هي ال 1 على n اللي هو نص اللي هو أكبر
+
+69
+00:04:59,270 --> 00:05:02,350
+من تلت أكبر من ربع أكبر يعني decreasing و limitها
+
+70
+00:05:02,350 --> 00:05:06,990
+بساوة سفر وهي alternating وكل واحد ما هو positive
+
+71
+00:05:06,990 --> 00:05:13,130
+ده هذه ال series إيش مالها؟ Converges حسب نظرية
+
+72
+00:05:13,430 --> 00:05:16,990
+طبعا it's not absolutely convergent لأن لو في
+
+73
+00:05:16,990 --> 00:05:20,110
+absolute convergence بترجعلنا للواحد على n series
+
+74
+00:05:20,110 --> 00:05:27,890
+ماشي الحال الآن عندي نشوف اللي عندنا اللي هو برهان
+
+75
+00:05:27,890 --> 00:05:30,330
+النظرية let z بالساوية zn be decreasing of
+
+76
+00:05:30,330 --> 00:05:33,490
+strictly positive numbers with limit zn بساوية 0
+
+77
+00:05:33,490 --> 00:05:37,490
+then the series summation نقص واحد zn is
+
+78
+00:05:37,490 --> 00:05:39,410
+convergent خلينا نشوف يا جماعة
+
+79
+00:05:42,290 --> 00:05:48,990
+عندي الآن خلّينا نطلّع وين بدنا نروح احنا بدنا
+
+80
+00:05:48,990 --> 00:05:54,530
+نثبت انه ال .. اللي هو ال series ناقص واحد أس ان
+
+81
+00:05:54,530 --> 00:06:02,810
+زائد واحد زد ان ان من واحدالى ما لا نهاية converts
+
+82
+00:06:02,810 --> 00:06:06,390
+هذا اللى بدنا نثبته ماشي الحال خلّينى نشوف ايش
+
+83
+00:06:06,390 --> 00:06:09,370
+اللى عندى summation هذا الان من واحد الى ما لا
+
+84
+00:06:09,370 --> 00:06:13,590
+نهاية converts نشوف احسب الاول ايش ايه اللى هو ال
+
+85
+00:06:13,590 --> 00:06:18,390
+partial sum S اتنين ان S اتنين ان ايش هيساوي عبارة
+
+86
+00:06:18,390 --> 00:06:25,700
+عن Z واحدنقص Z2 زي Z3 نقص Z4 بفك في ال series هذه
+
+87
+00:06:25,700 --> 00:06:29,640
+من ال N بتساوي واحد عندي N بتساوي واحد بيصير ناقص
+
+88
+00:06:29,640 --> 00:06:35,220
+واحد وزي N زي واحد زي ZN ماشي الحال الان صار عندي
+
+89
+00:06:35,220 --> 00:06:41,160
+ال Sالان من هاي ال series هاي ال series عندي ماشي
+
+90
+00:06:41,160 --> 00:06:45,360
+الان عندي أس اتنين ان زد واحد ناقص زد اتنين زائد
+
+91
+00:06:45,360 --> 00:06:48,160
+زد تلاتة ناقص زد أربعة زائد زد خمسة ناقص زد ستة
+
+92
+00:06:48,160 --> 00:06:53,680
+لما أصل لآخر two two زد اتنين ان ناقص واحد ناقص زد
+
+93
+00:06:53,680 --> 00:06:58,860
+اتنين ان هد مين هي الأس اتنين ان الان ال sequence
+
+94
+00:06:58,860 --> 00:07:04,360
+الاصلية زد k decreasingما دام decreasing إذا zk
+
+95
+00:07:04,360 --> 00:07:08,320
+نقص zk زائد واحد أكبر أو يساوي سفر يعني z واحد
+
+96
+00:07:08,320 --> 00:07:13,620
+ناقص z اتنين أكبر أو يساوي سفر و z اتنين نقص z
+
+97
+00:07:13,620 --> 00:07:17,660
+تلاتة نقص z أربعة برضه أكبر أو يساوي سفر وهذه أكبر
+
+98
+00:07:17,660 --> 00:07:21,680
+أو يساوي سفر يعني وكأنه أس اتنين اللي هي is
+
+99
+00:07:21,680 --> 00:07:26,890
+increasing sequence of partial sums ليش؟الأن it
+
+100
+00:07:26,890 --> 00:07:29,730
+follows that the subsequence S2 of partial sums is
+
+101
+00:07:29,730 --> 00:07:34,510
+increasing ليش increasing؟ خلّينا نشوف عندي لاحظ
+
+102
+00:07:34,510 --> 00:07:42,250
+الآنالأن لو أخدت S2 وS4 وS6 هتلاقي كل مرة إيش مالك
+
+103
+00:07:42,250 --> 00:07:45,830
+بتضيف term هذا ال term اللي بنضاف اللي هو positive
+
+104
+00:07:45,830 --> 00:07:49,710
+إذا حيكون الـS2 as a sequence of partial sums إيش
+
+105
+00:07:49,710 --> 00:07:54,970
+مالها عبارة عن اللي هو increasing sequence ليش؟ خد
+
+106
+00:07:54,970 --> 00:08:01,110
+بشكل أوضح من اللي حكيته فوق خد S2 خد Z1 ناقص Z2
+
+107
+00:08:01,110 --> 00:08:12,870
+ناقص Z3نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+108
+00:08:12,870 --> 00:08:13,170
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+109
+00:08:13,170 --> 00:08:15,710
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+110
+00:08:15,710 --> 00:08:16,350
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+111
+00:08:16,350 --> 00:08:29,550
+نقص نقص نقص نق
+
+112
+00:08:30,430 --> 00:08:34,770
+is decreasing يعني هيكون الـ Z أس اتنين ان هذا لما
+
+113
+00:08:34,770 --> 00:08:39,090
+انضفنا له هذولة ال terms الآن هيكون أصغر أو يساوي
+
+114
+00:08:39,090 --> 00:08:43,290
+أسف هذولة negative terms بيصير ال negative الان
+
+115
+00:08:43,290 --> 00:08:47,690
+لإن هذا negative بيصير ناقص اللي هو هنا Z اتنين
+
+116
+00:08:47,690 --> 00:08:54,070
+ناقص Z تلاتة أصغر اللي هو أكبر أو يساوي سفر وهذا
+
+117
+00:08:54,070 --> 00:08:56,750
+أكبر أو يساوي سفر وهذا أكبر أو يساوي سفريعني
+
+118
+00:08:56,750 --> 00:09:03,750
+مضيوفات له صارن سوالب لما نشيلهن هيكبر الـ Z1 لأنه
+
+119
+00:09:03,750 --> 00:09:06,690
+نكون اتخلصنا من كل السوالب هدولة بيصير أس اتنين
+
+120
+00:09:06,690 --> 00:09:10,170
+أصغر و سوء اللي هي ميانة Z1 إذا صارت اللي عند ال
+
+121
+00:09:10,170 --> 00:09:12,690
+sub sequence هذا ال partial sums اللي هو
+
+122
+00:09:12,690 --> 00:09:19,090
+increasing بتتزايدومش هيك was bounded above مدام
+
+123
+00:09:19,090 --> 00:09:23,330
+increasing و bounded إذا it follows by monotone
+
+124
+00:09:23,330 --> 00:09:27,790
+convergence theorem that S اتنين N convert to some
+
+125
+00:09:27,790 --> 00:09:34,110
+number S يعني الآن S اتنين N لو حسبناها هتطلع لك
+
+126
+00:09:34,110 --> 00:09:40,510
+increasing زائد bounded اللي هنقولنا S اتنين N
+
+127
+00:09:40,510 --> 00:09:45,800
+أصغر أو يساوي زيد واحد بدون حتى absolute valueالان
+
+128
+00:09:45,800 --> 00:09:50,000
+ومش هيك كمان و لو حسبت الاس اتنين ان ناقص اس اتنين
+
+129
+00:09:50,000 --> 00:09:54,780
+في ان ناقص واحد يعني عبارة عن اس اتنين ان ناقص اس
+
+130
+00:09:54,780 --> 00:09:59,680
+اتنين ان ناقص اتنين هتلاقيها بتساوي عبارة عن اللي
+
+131
+00:09:59,680 --> 00:10:06,860
+هي ال term اللي بطلع اللي هو عبارة عن زد واحد اللي
+
+132
+00:10:06,860 --> 00:10:11,420
+هو ناقص زد اتنين زائد
+
+133
+00:10:14,090 --> 00:10:24,970
+z2n-1-z2n ناقص اللي هو s2n-2 s2n-2 هذا كله لما
+
+134
+00:10:24,970 --> 00:10:31,070
+أشيله و أشيل هذا مع هذا بيظل z2n-1-z2n و هذا أكبر
+
+135
+00:10:31,070 --> 00:10:33,950
+أو سوى 0 لأن ال sequence الأصليه decreasing إذا
+
+136
+00:10:33,950 --> 00:10:38,990
+صار s2nناقص S2 فان ناقص واحد أكبر وسوء سفر يعني
+
+137
+00:10:38,990 --> 00:10:43,270
+صار عند الـ S2 أن هذه الـ sequence of partial sums
+
+138
+00:10:43,270 --> 00:10:47,710
+عبارة عن increasing sequence وهي bounded إذا بتكون
+
+139
+00:10:47,710 --> 00:10:51,870
+monotone الـ monotone اللي هو bounded sequence إذا
+
+140
+00:10:51,870 --> 00:10:55,010
+حسب الـ monotone convergence theorem هتكون ليها
+
+141
+00:10:55,010 --> 00:11:00,350
+هذا الـ subاللي هي sequence of partial sums is
+
+142
+00:11:00,350 --> 00:11:04,350
+convergent خلّينا نقول converged to some S element
+
+143
+00:11:04,350 --> 00:11:09,070
+of R الآن من هذه الـ subsequence اللي هي بدي
+
+144
+00:11:09,070 --> 00:11:14,570
+أثبتلك إن الـ sequence الـ S and نفسها converged
+
+145
+00:11:14,570 --> 00:11:19,200
+للـ S شوف كيفخُد أي إبسلون أكبر من صفر، there
+
+146
+00:11:19,200 --> 00:11:23,500
+exists K، such that إذا كانت N أكبر وسوء K، بما أن
+
+147
+00:11:23,500 --> 00:11:27,880
+هذا الـ sequence S2 N converge، إذا سيكون S2 N
+
+148
+00:11:27,880 --> 00:11:31,500
+ناقص S أصغر من أي إبسلون في الدنيا وليكن إبسلون
+
+149
+00:11:31,500 --> 00:11:37,970
+على 2لكن أنا بعرف إنه limit zn بساوة 0 مش جالين إن
+
+150
+00:11:37,970 --> 00:11:40,310
+هو الـ zn الـ sequence الأصلية بساوة .. limitها
+
+151
+00:11:40,310 --> 00:11:45,110
+بساوة 0 إذن أكيد limit الـ z2n زائد 1 البقى اللي
+
+152
+00:11:45,110 --> 00:11:48,570
+هي ال .. ال sub sequence منها برضه بساوة 0 مزام
+
+153
+00:11:48,570 --> 00:11:52,790
+بساوة 0 إذن من عند K معينة و نازل بيكون اللي هو
+
+154
+00:11:52,790 --> 00:11:56,350
+قيمتها أصغر من أي إبسلون في الدنيا و ليكن إبسلون
+
+155
+00:11:56,350 --> 00:11:59,580
+على 2عند اللي هي هذه إلها K واحد و هذه إلها K
+
+156
+00:11:59,580 --> 00:12:02,900
+اتنين أخدت الـ K maximum للتانين و سميتها K إذا
+
+157
+00:12:02,900 --> 00:12:05,940
+صارت هذه أصغر من نص إبسلون و هذه أصغر من نص إبسلون
+
+158
+00:12:05,940 --> 00:12:10,840
+لكل N أكبر أو يساوي K لماذا؟ لإن ال limit هذه
+
+159
+00:12:10,840 --> 00:12:14,800
+بيساوي هذه و لإن ال limit هذه بيساوي سفر إذا الآن
+
+160
+00:12:14,800 --> 00:12:20,260
+بدي أصل اللي بدي أن أثبت اللي هو ال subsequence
+
+161
+00:12:20,260 --> 00:12:25,060
+التانية اللي هي ال S2 N زائد واحد ناقص S برضه
+
+162
+00:12:25,060 --> 00:12:28,410
+هتكون أصغر من إبسلون زي اللي فاتتيعني الان اس
+
+163
+00:12:28,410 --> 00:12:32,930
+اتنين ان زائد واحد ناقص اس اش حساوياللي هو عبارة
+
+164
+00:12:32,930 --> 00:12:38,250
+عن هذه عبارة عن أس 2n مضيوفة إليها من مين ال term
+
+165
+00:12:38,250 --> 00:12:43,730
+اللي هو z2n زائد 1 z2n زائد 1 إشارته موجبة لإنه
+
+166
+00:12:43,730 --> 00:12:47,870
+الأصل في ال sequence ناقص 1 و أس n زائد 1 ف2n زائد
+
+167
+00:12:47,870 --> 00:12:52,130
+1 زائد 1 بيصير 2n زائد 2 يعني موجبة يعني فعلاً
+
+168
+00:12:52,130 --> 00:12:56,470
+بتكون هذه عبارة عن ال أس 2n زائد 1 بيساوي أس 2n
+
+169
+00:12:56,470 --> 00:13:07,840
+زائد z2n زائد 1ناقص الـ S الان هذا أصغر من نص
+
+170
+00:13:07,840 --> 00:13:10,660
+إبسلون و هذا أصغر من إبسلون و هذا المقدار أصغر من
+
+171
+00:13:10,660 --> 00:13:17,080
+إبسلون إذا صار عندي لأي إبسلون أكبر من سفر there
+
+172
+00:13:17,080 --> 00:13:23,790
+exist such thatدائما بغض النظر S2 N زائد 1 ولا S2
+
+173
+00:13:23,790 --> 00:13:29,410
+سيكون الـ S N لأن الفردي والسودي إله ناقص الـ S
+
+174
+00:13:29,410 --> 00:13:33,450
+هيطلع أصغر من إبسلون وهذا يعني أنه limit الـ S N
+
+175
+00:13:33,450 --> 00:13:38,050
+اللي هو exist ويساوي S يعني بمعنى أخر ال summation
+
+176
+00:13:38,050 --> 00:13:46,270
+هذا converge وهو المطلوب طيب الـ Nبكون هيك احنا
+
+177
+00:13:46,270 --> 00:13:50,250
+اثبتنا اللي هو مين اللي هو ال ال alternating
+
+178
+00:13:50,250 --> 00:13:54,350
+series انها converts اذا حققت الشروط اللي حكيناها
+
+179
+00:13:55,010 --> 00:13:59,530
+الان it is an exercise to show that if S is the
+
+180
+00:13:59,530 --> 00:14:04,810
+sum of the alternating series and if S N is its
+
+181
+00:14:04,810 --> 00:14:09,170
+Nth partial sum اثبتلي انه ال absolute value دايما
+
+182
+00:14:09,170 --> 00:14:17,810
+S نقص S N أصغر أو ساوي مين Z N زائد واحد الان
+
+183
+00:14:17,810 --> 00:14:23,220
+بدنا ناخد اللي هواللي هي نحكي عن test اسمه
+
+184
+00:14:23,220 --> 00:14:29,100
+differential test والقبل test لكن جابل هنا بدنا
+
+185
+00:14:29,100 --> 00:14:34,100
+ناخد هاللمة اللي هي قبل اللمة نشوف كيف اللي هو
+
+186
+00:14:34,100 --> 00:14:40,600
+نحاول ان هوانبرن هذه اللمة وبعتقد برهانة سهل لان
+
+187
+00:14:40,600 --> 00:14:45,780
+شكلها بالظبط زي كما كنا نعمل ال integration by
+
+188
+00:14:45,780 --> 00:14:50,960
+parts في calculus با خلينا نشوف ايش اللي هو اللمة
+
+189
+00:14:50,960 --> 00:14:55,040
+بتقول وكيف هذه اللمة بتفيدنا في اثبات النظريات
+
+190
+00:14:55,040 --> 00:15:00,770
+المتبقية في هذا ال sectionقبل الذلمة لت X بيساوي
+
+191
+00:15:00,770 --> 00:15:06,330
+XN و Y بيساوي YN بـSequences in R ماشي؟ نفترض أن X
+
+192
+00:15:06,330 --> 00:15:11,410
+و YN عبارة .. و Y Sequences in R and let the
+
+193
+00:15:11,410 --> 00:15:17,350
+partial sums of summation YN be denoted by Snالأن
+
+194
+00:15:17,350 --> 00:15:19,990
+الـ sequence of partial sums للـ yn سميناها Sn
+
+195
+00:15:19,990 --> 00:15:24,750
+ونفترض تسموه للأس نوت بساوي صفر عشان هيلزمنا لأن
+
+196
+00:15:24,750 --> 00:15:28,750
+بيقوللي if M أكبر من N then إذا كانت M أكبر من N
+
+197
+00:15:28,750 --> 00:15:34,350
+بيساوي إذا بيساوي ال summation Xk Yk K من N زياد
+
+198
+00:15:34,350 --> 00:15:42,990
+واحد عند M بيساوي Xm Sm ناقص Xn زياد واحد Sm Xm Xm
+
+199
+00:15:43,670 --> 00:15:51,250
+ناقص xn زائد واحد sn زائد الصماشن xk ناقص xk زائد
+
+200
+00:15:51,250 --> 00:15:55,710
+واحد sk k من n زائد واحد عند m minus واحد اتخيل
+
+201
+00:15:55,710 --> 00:15:58,170
+هذا ال integration وهذا ال integration هتلاقي اللي
+
+202
+00:15:58,170 --> 00:16:02,510
+هو مشابه ل اللي هو ال integration by parts اللي
+
+203
+00:16:02,510 --> 00:16:06,620
+كنا نعمله زمانالان هذه اللمهات .. ليش هي اللمهات؟
+
+204
+00:16:06,620 --> 00:16:08,860
+اللمهات عشان تستخدمها في برهان نظرية بعد شوية بس
+
+205
+00:16:08,860 --> 00:16:14,640
+مش أكتر الان خلينا نشوف ايش البرهان ويقول لي since
+
+206
+00:16:14,640 --> 00:16:18,640
+yk بيساوي sk نقص sk minus واحد عارفينها اللي هي sk
+
+207
+00:16:18,640 --> 00:16:22,920
+نقص sk minus واحد ايش هيسويلك ال yk عارفين ليش
+
+208
+00:16:22,920 --> 00:16:26,480
+four k بيساوي واحد واثنين الاخرين الان the left
+
+209
+00:16:26,480 --> 00:16:32,440
+side of تلاتة هذا ال left side of تلاتة is seen to
+
+210
+00:16:32,440 --> 00:16:40,620
+be obtainedto be equal to summation اللي هو XK في
+
+211
+00:16:40,620 --> 00:16:51,080
+SK minus K minus واحد الان هذا هو هذا بنفكه
+
+212
+00:16:51,080 --> 00:16:54,800
+بطلع هذا بتنشوف كيف انتبهوا عليها احسباتي انا
+
+213
+00:16:54,800 --> 00:17:00,700
+متأكد انكم هتجيبوها لحالكم الان summationXK YK K
+
+214
+00:17:00,700 --> 00:17:05,920
+من عند واحد N زائد واحد لعند مين لعند M بساوي
+
+215
+00:17:05,920 --> 00:17:11,260
+انتبه عليها بساوي بدي اعوض مكان ال YK اللي هو SK
+
+216
+00:17:11,260 --> 00:17:17,720
+minus SK minus واحد بساوي ال summation XK في YK
+
+217
+00:17:17,720 --> 00:17:25,140
+اللي هي قولنا SK-SK-1 K من عند N زائد واحد لعند
+
+218
+00:17:25,140 --> 00:17:30,300
+مين لعندها Y ساوي نفرطه هذا خلّينا نفكه بيصير
+
+219
+00:17:30,300 --> 00:17:37,260
+عبارة عن KN زائد واحد يعني XN زائد واحد في SN زائد
+
+220
+00:17:37,260 --> 00:17:45,360
+واحد ناقص SN زائد اللي بعدها XN زائد اتنين في SN
+
+221
+00:17:46,180 --> 00:17:52,140
+زائد اتنين ناقص SM زائد واحد ويكون خربط زائد اللي
+
+222
+00:17:52,140 --> 00:17:59,300
+بعدها لما اصل لآخر واحد اللي هو عبارة عن XM في SM
+
+223
+00:17:59,300 --> 00:18:07,280
+ناقص SM ناقص واحد ويساوي الان بدي اخد اللي هو اضرب
+
+224
+00:18:07,280 --> 00:18:13,350
+هذا جوا بيصير XN زائد واحداللي هو في ناقص في ..
+
+225
+00:18:13,350 --> 00:18:20,690
+بيصير xn اسمحولي اكتب هادي xn زائد واحد في Sn زائد
+
+226
+00:18:20,690 --> 00:18:27,950
+واحد ماشي ناقص عندي xn زائد واحد في Sn ناقص خليني
+
+227
+00:18:27,950 --> 00:18:34,130
+اكتبها دي لإن xn زائد واحد في Sn ضربت هادي هيها
+
+228
+00:18:34,130 --> 00:18:39,130
+وضربت هادي في هادي هيها زائد خلصت من الأولىلأن هذي
+
+229
+00:18:39,130 --> 00:18:46,750
+بتضييها هنا بعد شوية زائد اللي بعدها xn زائد خلينك
+
+230
+00:18:46,750 --> 00:18:52,130
+تبقى ضربها تصبح ضناقص اضرب هذه قبلها xn زائد اتنين
+
+231
+00:18:52,130 --> 00:18:59,710
+sn زائد اتنين زائد واحد ضربت هذه في هذه زائد اللي
+
+232
+00:18:59,710 --> 00:19:06,100
+هو xn زائد اتنين sn زائد اتنينزائد خدوا الفكرة
+
+233
+00:19:06,100 --> 00:19:09,520
+أنتوا بتحسبوا لحالكم آخر إشي اللي هو عبارة عن XM
+
+234
+00:19:09,520 --> 00:19:19,720
+في SM أين أكتبها ال XM في SM هذه ناقص اللي هو XM
+
+235
+00:19:19,720 --> 00:19:27,620
+SM ناقص واحد ويساوي عبارة
+
+236
+00:19:27,620 --> 00:19:34,360
+عن هذه اللي هي اللي بدنا إياها ال XMأسأم ناقص xn
+
+237
+00:19:34,360 --> 00:19:44,820
+زائد واحد أسأن الآن زائد الآن خدولي اللي هو xn
+
+238
+00:19:44,820 --> 00:19:57,940
+زائد واحد ناقص xn هذا يعني xn زائد واحد xn زائد
+
+239
+00:19:57,940 --> 00:20:04,760
+واحدوهنا S N زائد واحد ناقص X N زائد اتنين هدول
+
+240
+00:20:04,760 --> 00:20:08,720
+التنتين مع بعض التنتين المضروبات في مين؟ في S N
+
+241
+00:20:08,720 --> 00:20:13,940
+زائد واحد اللي بعيد ده نفس الاشي هلاقي عبارة عن
+
+242
+00:20:13,940 --> 00:20:22,420
+اللي هو S N زائد اتنين مضروبة في X N زائد اتنين
+
+243
+00:20:22,420 --> 00:20:24,600
+ناقص
+
+244
+00:20:25,460 --> 00:20:30,200
+xn زائد تلاتة و أضرب لما أخر الأصل لآخر إشي
+
+245
+00:20:30,200 --> 00:20:34,220
+هلاجيها عبارة عن هذا راح بيظل اللي جابله اللي هو
+
+246
+00:20:34,220 --> 00:20:41,560
+هلاجي اللي هو xm ناقص واحد ناقص xm مضروبة في 100
+
+247
+00:20:41,560 --> 00:20:52,840
+في Sn الآن هذه هي الأولى هذه وهذا ال summation
+
+248
+00:20:54,060 --> 00:20:58,800
+Summation هذا هو الـ Summation هذا و لو فرضتلك
+
+249
+00:20:58,800 --> 00:21:02,740
+كمان اتنين تلاتة هيكون تتأكد من هذا الكلام تماماً
+
+250
+00:21:02,740 --> 00:21:06,460
+هاي عندي اللي هو في حالة K بصي و N زائد واحد بيصير
+
+251
+00:21:06,460 --> 00:21:11,400
+X N زائد واحد ناقص X N زائد اتنين هاي ها X N زائد
+
+252
+00:21:11,400 --> 00:21:14,940
+واحد ناقص X N زائد اتنين مضروبة في S N زائد واحد و
+
+253
+00:21:14,940 --> 00:21:19,800
+لما اصل عند اخر واحدإذن اللي بيكون هيك إحنا أثبتنا
+
+254
+00:21:19,800 --> 00:21:23,800
+اللي هو هذه اللي هو اللمّة و الآن بدي أستخدم هذه
+
+255
+00:21:23,800 --> 00:21:29,660
+اللمّة في إثبات اللي هو النظريات اللي بعد هيك طيب،
+
+256
+00:21:29,660 --> 00:21:38,820
+الآن مادريش ال test بيقولّي بدنا عرض علينا إنه
+
+257
+00:21:38,820 --> 00:21:43,100
+نعرف اللي هو summation لحاصل ضرب اللي هو XN في YN
+
+258
+00:21:43,100 --> 00:21:49,230
+is convergent ولا مش convergentطيب لو عرفت معلومات
+
+259
+00:21:49,230 --> 00:21:54,210
+عن هذه XN ومعلومات عن هذه YN هل بعرف اللي هو ال
+
+260
+00:21:54,210 --> 00:21:58,170
+convergence الآن هذه ال .. ال .. ال .. ال .. ال
+
+261
+00:21:58,170 --> 00:22:02,670
+theory معاه ال test ال D test هذا هذا ال D test
+
+262
+00:22:02,670 --> 00:22:08,910
+الآن هو اللي هيعمللي testing لل summation XN في YN
+
+263
+00:22:08,910 --> 00:22:14,530
+converge اللي عندنا .. نشوف كيفبقول لي let X
+
+264
+00:22:14,530 --> 00:22:18,410
+بيساوي Xn is a decreasing sequence إذا أول حاجة
+
+265
+00:22:18,410 --> 00:22:22,430
+مفترض لإن Xn decreasing و limit Xn هيش بيساوي سفر
+
+266
+00:22:22,430 --> 00:22:27,810
+and if the partial sums Sn of Yn are bounded then
+
+267
+00:22:27,810 --> 00:22:32,150
+Xn is Y of Yn is convergent يعني بتنعرض علينا ال
+
+268
+00:22:32,150 --> 00:22:36,390
+series بالشكل هذابعدي بفحص إذا نجيت ال limit لل Xn
+
+269
+00:22:36,390 --> 00:22:39,930
+بساوة سفر وهي decreasing وكانت ال sequence of
+
+270
+00:22:39,930 --> 00:22:44,470
+partial sums Yn bounded على طول بقول هذه ال series
+
+271
+00:22:44,470 --> 00:22:48,630
+إيش ما لها is convergent إذا بتفحصلي ال
+
+272
+00:22:48,630 --> 00:22:55,380
+convergence لهذه ال series ده نشوف الآنSummation
+
+273
+00:22:55,380 --> 00:23:01,180
+XN YN convergence إذا كانت اللي هي limit XN بيساوي
+
+274
+00:23:01,180 --> 00:23:04,320
+سفر و decreasing و ال sequence of partial sums
+
+275
+00:23:04,320 --> 00:23:09,320
+اللي هي لل YN هذه اللي هو عبارة عن boundedماشي إيش
+
+276
+00:23:09,320 --> 00:23:12,720
+معناه bounded؟ يعني اللي هو عند ال absolute value
+
+277
+00:23:12,720 --> 00:23:17,020
+ل S N أصغر أو سوى B for all N and for some B إذا
+
+278
+00:23:17,020 --> 00:23:21,380
+بما أن S N is bounded إذا there exist B أكبر من 0
+
+279
+00:23:21,380 --> 00:23:25,200
+such that اللي هو ال absolute value ل S N أصغر أو
+
+280
+00:23:25,200 --> 00:23:27,060
+سوى B for all N element ن
+
+281
+00:23:30,240 --> 00:23:38,820
+بما أنه .. بما أنه اللي هو عند .. ال .. ال .. ال
+
+282
+00:23:38,820 --> 00:23:39,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+283
+00:23:39,680 --> 00:23:39,720
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+284
+00:23:39,720 --> 00:23:39,820
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+285
+00:23:39,820 --> 00:23:40,260
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+286
+00:23:40,260 --> 00:23:41,380
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+287
+00:23:41,380 --> 00:23:41,560
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+288
+00:23:41,560 --> 00:23:41,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+289
+00:23:41,840 --> 00:23:42,760
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+290
+00:23:42,760 --> 00:23:42,880
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+291
+00:23:42,880 --> 00:23:43,720
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+292
+00:23:43,720 --> 00:23:50,980
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+293
+00:23:50,980 --> 00:23:57,480
+ال .. ال ..ومفترضين إنها decreasing يعني ال XK نقص
+
+294
+00:23:57,480 --> 00:24:00,920
+XK زياد واحد أكبر ويساوي سفر إذا الشروط اللي قبل
+
+295
+00:24:00,920 --> 00:24:07,420
+لمّة متحققة أنه ال absolute summation ل XK YK K من
+
+296
+00:24:07,420 --> 00:24:10,660
+N زياد واحد لعند ال M اللي هي حتساوي لما أخد ال
+
+297
+00:24:10,660 --> 00:24:14,200
+absolute value حتساوي بالظبط بتاخد ال absolute
+
+298
+00:24:14,200 --> 00:24:20,300
+value يصير أصغر أو يساوي اللي هو ال SN في ال XM
+
+299
+00:24:20,300 --> 00:24:26,100
+زياد ال XN زياد واحد ماشي؟متذكرين الابل زمة؟ هي
+
+300
+00:24:26,100 --> 00:24:27,200
+الابل زمة
+
+301
+00:24:33,240 --> 00:24:38,140
+الآن ال absolute value
+
+302
+00:24:38,140 --> 00:24:41,540
+لهادي أصغر أو ساوي ال absolute value لهدي مضروبة
+
+303
+00:24:41,540 --> 00:24:47,320
+في مين اللي هو ال absolute value لهدي اللي هي أسأم
+
+304
+00:24:47,320 --> 00:24:51,600
+وأسئن طبعا absolute value لهن زي ال absolute value
+
+305
+00:24:51,600 --> 00:24:56,510
+لهدي ال absolute value لهدياللي هي أصغر أو يساوي
+
+306
+00:24:56,510 --> 00:25:00,870
+الـ absolute هذه زايد هذه في مين في اللي هي الـB
+
+307
+00:25:00,870 --> 00:25:04,550
+الـB أش هي الـbound للـSM والـSN لأن مفترضين
+
+308
+00:25:04,550 --> 00:25:07,330
+الـsequence of partial sums is bound إذن يعني
+
+309
+00:25:07,330 --> 00:25:10,970
+بيصير عندي الكلام هذا صحيح يعني هذا أصغر أو يساوي
+
+310
+00:25:10,970 --> 00:25:15,410
+الـXM زايد الـXN زايد واحد في مين في أش في الـB
+
+311
+00:25:15,410 --> 00:25:19,030
+لإن هدولة positive terms فبصير ال absolute value
+
+312
+00:25:19,030 --> 00:25:24,610
+نفس الشيءزائد الـ summation لـ xk-xk-xk-xk-xk-xk
+
+313
+00:25:24,610 --> 00:25:37,290
+-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk
+
+314
+00:25:37,290 --> 00:25:42,010
+-xk
+
+315
+00:25:42,010 --> 00:25:47,090
+-xk-xk
+
+316
+00:25:47,090 --> 00:25:47,950
+-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk
+
+317
+00:25:47,950 --> 00:25:49,100
+-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-xk-لو
+
+318
+00:25:49,100 --> 00:25:50,780
+جينا فكّينا هذا المقدار
+
+319
+00:25:54,980 --> 00:25:59,820
+اللي عندى هذا xk نقص xk زائد واحد كله بروح بظل عند
+
+320
+00:25:59,820 --> 00:26:04,020
+ال N زائد واحد و ال M ماي .. اللي هى ال M أخر term
+
+321
+00:26:04,020 --> 00:26:07,780
+M نقص واحد زائد واحد اللى هى ال M فبصير عندى ال B
+
+322
+00:26:07,780 --> 00:26:11,400
+طبعا متاخدة عامل مشترك كلها و بظل هذا زى ما هو و
+
+323
+00:26:11,400 --> 00:26:15,220
+هذا اللى هو ال telescoping او اللى هو بما أخر as
+
+324
+00:26:15,220 --> 00:26:18,480
+if اللى هو هذا اللى هو كل شي .. كل term بضيع اللى
+
+325
+00:26:18,480 --> 00:26:22,320
+بعدهبظل أول واحد و آخر واحد Xm زائد واحد ناقص Xm
+
+326
+00:26:22,320 --> 00:26:26,300
+هذه صارت حركة معروفة عندكم الان هذه بتروح مع هذه
+
+327
+00:26:26,300 --> 00:26:30,800
+بيصير بيظل هذه و هذه تنتين بيصير اتنين Xm زائد بي
+
+328
+00:26:30,800 --> 00:26:36,100
+في مين في بي الان قلنا limit ال Xn as n goes to
+
+329
+00:26:36,100 --> 00:26:40,760
+infinity ايش معطينيها بساوة سفر بدأ بساوة سفر اذا
+
+330
+00:26:40,760 --> 00:26:46,320
+الان بقدر ازغرها لأصغر من اي ي في الدنيا من ضمنها
+
+331
+00:26:46,320 --> 00:26:50,650
+اللي هي اي شمالهااللي هي إبسلون بالساوية إبسلون
+
+332
+00:26:50,650 --> 00:26:55,930
+على اتنين بيه يعني بمعنى آخر as N goes to infinity
+
+333
+00:26:55,930 --> 00:26:59,630
+as N goes to infinity طبعاً M أكيد هتروح ل
+
+334
+00:26:59,630 --> 00:27:06,310
+infinity يعني بمعنى آخر هيكون اللي هو الـ SM لهذه
+
+335
+00:27:06,800 --> 00:27:12,820
+هذه S M ناقص لـ S N هيكون أصغر من أي Y في الدنيا
+
+336
+00:27:12,820 --> 00:27:19,120
+for very large N و M لأن الـ N و الـ M لما N تروح
+
+337
+00:27:19,120 --> 00:27:23,000
+لما النهاية دي بتروح لـ 0 و الـ M هتكبر برضه بمعنى
+
+338
+00:27:23,000 --> 00:27:26,800
+آخر for very large N هذا هزغيرها جد ما بده يعني
+
+339
+00:27:26,800 --> 00:27:30,100
+هذا المقدار أصغر ما يمكن و هذا المقدار هو عبارة عن
+
+340
+00:27:30,100 --> 00:27:34,260
+مين يا جماعة عبارة عن الـ S M لهذه الـ sequence X
+
+341
+00:27:34,260 --> 00:27:38,310
+Mهذه الأسماء هي Sequence of Partial Sums لمين؟ لأن
+
+342
+00:27:38,310 --> 00:27:42,010
+هذه كلها على بعض وهذه نفس الشيء فسأقرص Sequence of
+
+343
+00:27:42,010 --> 00:27:45,890
+Partial Sums هذه اللي هو الـ Cauchy Criterion
+
+344
+00:27:45,890 --> 00:27:50,070
+تبعتها متحققة مدام الـ Cauchy Criterion متحققة إذن
+
+345
+00:27:50,070 --> 00:27:53,650
+صارت السيريزي الأصلية Converts إذن هذه summation
+
+346
+00:27:53,650 --> 00:27:57,810
+XKYK follows from Cauchy Convergence الـ Criterion
+
+347
+00:27:57,810 --> 00:28:03,820
+اللي هو is convergent طيبالان نجي لا اللي هو ال
+
+348
+00:28:03,820 --> 00:28:08,420
+test اللي بعده اللي هو ال apples test الان اللي هو
+
+349
+00:28:08,420 --> 00:28:12,960
+ال test الأخير عندنا في هذا ال sectionبنشوف كيف
+
+350
+00:28:12,960 --> 00:28:17,900
+بدنا .. اللي هو برضه نحكم على الصممشي للـ XN YN is
+
+351
+00:28:17,900 --> 00:28:24,280
+convergent كيف؟ بقول لي لو كانت عندك الـ XN is a
+
+352
+00:28:24,280 --> 00:28:27,860
+convergent monotone sequence convergent monotone
+
+353
+00:28:27,860 --> 00:28:31,580
+بغض النظر إنه هذه الـ sequence decreasing ولا
+
+354
+00:28:31,580 --> 00:28:37,560
+increasingأو حتى Converge لـ 0 أو غير 0 المهم تكون
+
+355
+00:28:37,560 --> 00:28:42,480
+الـ Xn عبارة عن مونوتون Convergent Sequence
+
+356
+00:28:42,480 --> 00:28:49,020
+والسيريز Yn بديها بس شوية الأن مش bounded بديها
+
+357
+00:28:49,020 --> 00:28:52,980
+تكون Convergent إذا بقولي لو كانت الـ Yn
+
+358
+00:28:52,980 --> 00:28:59,410
+Convergentوالـ Xn مش convergent بس convergence to
+
+359
+00:28:59,410 --> 00:29:03,750
+monotone يعني يا increasing يا decreasing يعني
+
+360
+00:29:03,750 --> 00:29:06,110
+ماحدش يجي يقول الـ Xn هو convergent و Yn
+
+361
+00:29:06,110 --> 00:29:08,710
+convergent إذا التلتين الـ summation convergent
+
+362
+00:29:08,710 --> 00:29:12,910
+ليس شرطا الان اللي بقوله أنه لو كانت الواحدة
+
+363
+00:29:12,910 --> 00:29:17,190
+convergent والتانية convergent to نتفة يعني
+
+364
+00:29:17,190 --> 00:29:20,330
+convergent النتفة هذه اللي هي تكون increasing أو
+
+365
+00:29:20,330 --> 00:29:23,560
+decreasing يعني monotoneخلّينا نشوف كيف اللي هو
+
+366
+00:29:23,560 --> 00:29:27,560
+البرهن النظري البرهان سهل و بعتمد على اللي جابلها
+
+367
+00:29:27,560 --> 00:29:42,030
+مباشرةإذا Xn كانت تتخلص من نقطة X إذا Xn
+
+368
+00:29:42,030 --> 00:29:47,250
+كانت تتخلص من نقطة X إذا Xn كانت تتخلص من نقطة X
+
+369
+00:29:47,250 --> 00:29:52,130
+إذا Xn
+
+370
+00:29:52,130 --> 00:29:59,650
+ناقص Xصارت الأن الـ xn ناقص x مدام الـ xn
+
+371
+00:29:59,650 --> 00:30:02,630
+decreasing وده راحنا منها إيش ثابت حتظلها
+
+372
+00:30:02,630 --> 00:30:06,250
+decreasing إذا صارت الـ yn decreasing ومش
+
+373
+00:30:06,250 --> 00:30:10,270
+decreasing كمان و limit الـ yn الـ un بساوي limit
+
+374
+00:30:10,270 --> 00:30:14,170
+الـ xn ناقص الـ x هذه ما هي ثابت يعني limit xn x
+
+375
+00:30:14,170 --> 00:30:18,870
+ناقص x صفر يعني limit الـ un صفر يعني حولت ال
+
+376
+00:30:18,870 --> 00:30:23,430
+sequence اللي عند الـ xn إلى sequence yn تكون
+
+377
+00:30:23,430 --> 00:30:28,830
+decreasing و limitها بساوي صفرI saw that UN
+
+378
+00:30:28,830 --> 00:30:35,130
+decreases to zero then XN بيساوي X زائد UN ومنه
+
+379
+00:30:35,130 --> 00:30:40,310
+once ال XN في ال YN صارت عندي ال sequence XN في YN
+
+380
+00:30:40,310 --> 00:30:49,630
+بيساوي X في YN زائد UN في YN ماشي الان عندي
+
+381
+00:30:50,650 --> 00:30:55,130
+الـ Sequence اللي هي الـ y .. from Dirichlet Test
+
+382
+00:30:55,130 --> 00:30:59,990
+الدنيا اللي هي صارت منيحة، ليش؟ لأنه بما أنه اللي
+
+383
+00:30:59,990 --> 00:31:03,650
+هو الـ u .. هذه طبعا ال .. ال .. ال y unconverts
+
+384
+00:31:03,650 --> 00:31:06,810
+إذا ال .. هي ال .. ال series summation x في y
+
+385
+00:31:06,810 --> 00:31:15,380
+unconverts، مظبوط؟ و هذه ..UNYN بما أنها تتخلص أو
+
+386
+00:31:15,380 --> 00:31:21,460
+تتخلص وفي نفس الوقت ليمتها بساوة سفر وهذه ال YN
+
+387
+00:31:21,460 --> 00:31:26,200
+التي هي is convergent إذا صارت اللي هو حسب اللي هو
+
+388
+00:31:26,200 --> 00:31:32,330
+قبل اللي هي ال threshold theoremهيها حققت الشروط
+
+389
+00:31:32,330 --> 00:31:37,250
+بس على ال U N الان الان عندي Y N bounded احنا قلنا
+
+390
+00:31:37,250 --> 00:31:40,550
+Y N نفسها convergent مادام convergent اذا ال
+
+391
+00:31:40,550 --> 00:31:42,870
+sequence of partial sums اشماله is bounded لأن
+
+392
+00:31:42,870 --> 00:31:45,650
+convergence is then bounded any sequence is
+
+393
+00:31:45,650 --> 00:31:48,890
+convergent must be bounded اذا صارت هذه bounded
+
+394
+00:31:48,890 --> 00:31:52,110
+ماشي او بمعنى اخر sequence of partial sums bounded
+
+395
+00:31:52,540 --> 00:31:56,140
+وعندها دي كثرة الـ UN اللي قبل بشوية Decreasing
+
+396
+00:31:56,140 --> 00:31:59,800
+وLimited بساوية 0 إذا اللي هي دي test is
+
+397
+00:31:59,800 --> 00:32:04,400
+applicable لنشوف كيف الآن صارت عندي ال XYN
+
+398
+00:32:04,400 --> 00:32:10,950
+converts و ال UN YN اللي هو هذي convertsهذه تتقل
+
+399
+00:32:10,950 --> 00:32:16,590
+إلى 0 وهذه مجموعة إذا صار عند الـ summation X UN
+
+400
+00:32:16,590 --> 00:32:21,970
+في XN تتقل لأن الـ summation XN تتقل بسبب الـ
+
+401
+00:32:21,970 --> 00:32:24,490
+assumption of convergence of the series summation
+
+402
+00:32:24,490 --> 00:32:27,750
+YN لأن هذه السيريز مفترضة أنها تتقل وهذا ثابت
+
+403
+00:32:27,750 --> 00:32:32,010
+بالنسبالهاصارت هذا converge وهذا converge من D
+
+404
+00:32:32,010 --> 00:32:35,890
+test إذا صار مجموح على بعض اللي هو summation xn yn
+
+405
+00:32:35,890 --> 00:32:39,650
+is convergent الان في حالة ال increasing إشي مش
+
+406
+00:32:39,650 --> 00:32:44,410
+شابه الان نفترض اللي xn is increasing with limit x
+
+407
+00:32:44,410 --> 00:32:51,120
+الان خد ال vn بدل ما هي xn ناقص x خد x ناقص xnصارت
+
+408
+00:32:51,120 --> 00:32:55,120
+اللي هي الـ sequence اللي increasing اللي هي الـ
+
+409
+00:32:55,120 --> 00:32:58,900
+XN لما ضربت بناقص صارت decreasing وضفت لها limitها
+
+410
+00:32:58,900 --> 00:33:03,340
+صار عندك اللي هو limit H بساوة سفر صارت VN
+
+411
+00:33:03,340 --> 00:33:09,040
+decreases to zero ماشي؟ إذا صارت الـ XNبساوة x
+
+412
+00:33:09,040 --> 00:33:13,200
+ناقص vn وضرب زي قبل بشوية في xn في yn بساوة هذه
+
+413
+00:33:13,200 --> 00:33:18,100
+ناقص هذه هذه نفس الأسباب اللي قبل بشوية متحققة بال
+
+414
+00:33:18,100 --> 00:33:23,420
+test إذا صارت اللي هي converts وهذه converts اللي
+
+415
+00:33:23,420 --> 00:33:25,380
+هو صبعا ال summation بحكي عن ال summation series
+
+416
+00:33:25,380 --> 00:33:28,440
+إذا صار ال series converts وهذا converts إذا صار
+
+417
+00:33:28,440 --> 00:33:33,240
+ال xn yn converts وكل هيك واحنا اللي هو أنهينا
+
+418
+00:33:33,240 --> 00:33:37,650
+اللي هو الليالـ tests اللي في هذا ال .. ال section
+
+419
+00:33:37,650 --> 00:33:41,230
+بظل اللي هو exampleين هدولة انتوا بتحاولوا تطلعوا
+
+420
+00:33:41,230 --> 00:33:47,210
+لحالكم فيه و بكون هيك انه احنا بكون انهينا section
+
+421
+00:33:47,210 --> 00:33:51,910
+اللي هو تسعة تلاتة و إلى لقاء اخر والسلام عليكم
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d0fd4d1a453cd6c4219811854a5a138996be85cd
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg.srt
@@ -0,0 +1,3703 @@
+1
+00:00:04,940 --> 00:00:11,820
+بسم الله الرحمن الرحيم اليوم المحاضرة رقم 13 مساق
+
+2
+00:00:11,820 --> 00:00:17,100
+تحليل حقيقه 2 لطلاب وطالبات الجامعة الإسلامية كلية
+
+3
+00:00:17,100 --> 00:00:21,800
+العلوم قسم رياضيات إن شاء الله ستكون المحاضرة على
+
+4
+00:00:21,800 --> 00:00:28,620
+جزئين، الجزء الأول هنستمر في الحديث عن سبعة اثنين
+
+5
+00:00:28,620 --> 00:00:34,240
+وهو الحديث أو سبعة ثلاثة وهو الحديث سبعة اثنين في
+
+6
+00:00:34,240 --> 00:00:40,130
+البداية وهو الحديث عن الخواص التكامل الريماني، حكينا
+
+7
+00:00:40,130 --> 00:00:45,310
+عن اللي هو مجموع دالتين قابلتين للتكامل اللي هو
+
+8
+00:00:45,310 --> 00:00:48,510
+قابل
+
+9
+00:00:48,510 --> 00:00:52,510
+التكامل و حاصل ضرب ثابت في دالة قابلة للتكامل برضه 
+
+10
+00:00:52,510 --> 00:00:58,630
+قابلة للتكامل، واليوم هنكمل الأمر، الحديث عن
+
+11
+00:00:58,630 --> 00:01:04,550
+composition of two integrable functions هل قابلة
+
+12
+00:01:04,550 --> 00:01:08,270
+للتكامل أم لا، وإذا قابلة للتكامل بدنا نبرهن وإذا مش 
+
+13
+00:01:08,270 --> 00:01:14,750
+قابلة بدنا نجيب counter example، الآن الجزء الثاني
+
+14
+00:01:14,750 --> 00:01:18,110
+هيكون اللي هو برضه تطبيق اللي هو composition 
+
+15
+00:01:18,110 --> 00:01:25,410
+theorem اللي هي هنشوف بعد شوية إيش المتطلب إن يكون
+
+16
+00:01:25,410 --> 00:01:30,190
+composition of two functions is integrable، أيضًا
+
+17
+00:01:30,190 --> 00:01:35,230
+هنتحدث عن اللي هو نوظفها في إثبات اللي هو أن
+
+18
+00:01:35,230 --> 00:01:38,950
+الدالة الأسية والـ absolute value of the function
+
+19
+00:01:38,950 --> 00:01:43,530
+F،  و أيضًا اللي هو مقلوب الدالة 1 على F في حالة F 
+
+20
+00:01:43,530 --> 00:01:50,090
+لا تساوي 0 على الـ domain المُعطى إنها تكون قابلة
+
+21
+00:01:50,090 --> 00:01:54,830
+للتكامل، و أيضًا اللي هو هيكون في عندنا اللي هو تطبيق
+
+22
+00:01:54,830 --> 00:01:59,640
+آخر اللي هو حاصل ضرب دالتين كيف يكون integrable أو
+
+23
+00:01:59,640 --> 00:02:03,080
+كيف تكون integrable في حالة كلا الدالتين integrable
+
+24
+00:02:03,080 --> 00:02:06,200
+نبدأ الآن في اللي هو النظرية الـ composition
+
+25
+00:02:06,200 --> 00:02:09,600
+theorem واطولوا روحكم علينا شوية على اللي هو
+
+26
+00:02:09,600 --> 00:02:14,930
+البرهان، و البرهان شوية بده تركيز، والبرهان طويل 
+
+27
+00:02:14,930 --> 00:02:20,110
+شوية، خلينا إن نعمل الآن focusing على نص النظرية و
+
+28
+00:02:20,110 --> 00:02:25,410
+بعدين بنبدأ نحكي عن البرهان، نعمل outline للبرهان، و
+
+29
+00:02:25,410 --> 00:02:27,610
+من ثم ندخل لتفاصيل البرهان
+
+30
+00:02:30,230 --> 00:02:35,470
+بنأخذ I عبارة عن closed bounded interval A و B، و J
+
+31
+00:02:35,470 --> 00:02:38,550
+عبارة عن closed bounded interval سميناها C و D
+
+32
+00:02:38,550 --> 00:02:44,830
+ونفترض أن F من I لعند R، يعني F عبارة عن دالة من عند
+
+33
+00:02:44,830 --> 00:02:49,350
+الـ A والـ B لعند R، أنها تكون integrable on I and
+
+34
+00:02:49,350 --> 00:02:52,050
+Phi من J لعند R
+
+35
+00:02:55,070 --> 00:02:58,390
+النظرية بتستلزم أن نقول continuous لأن الـ integrable
+
+36
+00:02:58,390 --> 00:03:03,270
+بالحالها مش هتعطي اللي هو النتيجة زي ما هنشوف قدام
+
+37
+00:03:03,270 --> 00:03:07,610
+في اللي هو counter example، الآن فرضنا أن Phi من J 
+
+38
+00:03:07,610 --> 00:03:12,890
+لعند R is continuous، وبدنا نفترض أن F of I .. F of
+
+39
+00:03:12,890 --> 00:03:17,450
+I جزئية من مين؟ من J عشان نعرف .. نعرف الـ
+
+40
+00:03:17,450 --> 00:03:21,670
+composition بين الـ two functions، الآن في ضوء هذه
+
+41
+00:03:21,670 --> 00:03:26,050
+المعطيات، إن الـ function F is integrable والـ
+
+42
+00:03:26,050 --> 00:03:30,410
+function Phi is continuous، لازم يطلع عندي الآن Phi
+
+43
+00:03:30,410 --> 00:03:37,450
+composite F is integrable on، mean on I، إذن F من I
+
+44
+00:03:37,450 --> 00:03:43,130
+لـ R integrable، Phi من J لعند R continuous، الآن Phi
+
+45
+00:03:43,130 --> 00:03:46,170
+composite F continuous، composite integrable
+
+46
+00:03:46,170 --> 00:03:53,500
+هيعطيني integrable function on I، الآن بدنا نثبت، الآن
+
+47
+00:03:53,500 --> 00:04:00,600
+فاى composite F من I لعند R إنّها is integrable
+
+48
+00:04:00,600 --> 00:04:04,900
+الآن كيف بدي أثبتها؟ بدي أثبتها .. بدي ألاقي
+
+49
+00:04:04,900 --> 00:04:09,040
+partition ..  ده أقول لكل Epsilon أكبر من 0 بدي ألاقي
+
+50
+00:04:09,040 --> 00:04:16,060
+partition P element in P of I such that L of أو U
+
+51
+00:04:16,060 --> 00:04:24,200
+of P و F هذا اللي جبتُه ما أعرف أسأل، آسف أنا فعلاً 
+
+52
+00:04:24,200 --> 00:04:30,690
+composed of G and F، Phi composite F ناقص L of P وفاي
+
+53
+00:04:30,690 --> 00:04:35,730
+composite F إن يكون هذا المقدار أصغر من Epsilon، إذا
+
+54
+00:04:35,730 --> 00:04:40,590
+وصلت لهذه النتيجة معناته أنه أنا أثبتت أنه اللي هي 
+
+55
+00:04:40,590 --> 00:04:46,490
+الـ Phi composite F is integrable بناء على اللي هو الـ
+
+56
+00:04:46,490 --> 00:04:48,870
+criterion of integrability اللي حكينا عنها
+
+57
+00:04:48,870 --> 00:04:53,700
+المحاضرة قبل الماضية، الآن هذا الهدف اللي بدي أوصله 
+
+58
+00:04:53,700 --> 00:04:58,020
+هيك بدي أوصل، هيك الآن عشان أوصل هيك بدي اللي هو
+
+59
+00:04:58,020 --> 00:05:02,900
+أستخدم اللي هو المعطيات اللي موجودة عندي الآن
+
+60
+00:05:02,900 --> 00:05:08,380
+هستخدم أمرين، هستخدم أكيد الـ continuity للـ Phi وهي 
+
+61
+00:05:08,380 --> 00:05:14,320
+continuous على closed bounded interval إذا حسب
+
+62
+00:05:14,320 --> 00:05:18,080
+نظرية في تحليل واحد هتكون Phi is uniformly 
+
+63
+00:05:18,080 --> 00:05:23,880
+continuous وهذا هستغله في الوصول إلى هدفي، الآن هذه
+
+64
+00:05:23,880 --> 00:05:27,960
+المعلومة بعد شوية هنخزنها ونحطها في .. في مكان ما
+
+65
+00:05:27,960 --> 00:05:33,420
+لحين نستخدمها مع اللي هو إن F is integrable، مزام F 
+
+66
+00:05:33,420 --> 00:05:37,240
+is integrable، إذا نبلج partition I بحيث إن الـ
+
+67
+00:05:37,240 --> 00:05:40,500
+U للـ P والـ F نقص الـ L للـ P والـ F أصغر من مين؟ من
+
+68
+00:05:40,500 --> 00:05:44,220
+some .. من الـ Epsilon، Epsilon تخدمني، هبدأ أسميها
+
+69
+00:05:44,220 --> 00:05:47,490
+Epsilon، هبدأ أسميها Delta، أنا حوار، المهم أكيد مدام
+
+70
+00:05:47,490 --> 00:05:51,610
+الـ Phi عندي integrability للـ F هتحقق إنه لكل اللي
+
+71
+00:05:51,610 --> 00:05:56,010
+هو Epsilon there exists partition P، وحنلاقي إن الـ
+
+72
+00:05:56,010 --> 00:05:59,510
+partition هذا اللي .. اللي نفع للـ F هو اللي هينفع
+
+73
+00:05:59,510 --> 00:06:04,300
+للـ Phi composite F، هنجمج المعلومتين التنتين مع بعض
+
+74
+00:06:04,300 --> 00:06:06,680
+اللي هي ال .. ال .. ال .. ال .. الـ uniform
+
+75
+00:06:06,680 --> 00:06:10,260
+continuity للـ Phi مع الـ integrability للـ F للوصول
+
+76
+00:06:10,260 --> 00:06:14,920
+إلى نتيجتنا وهي هذه النتيجة، هذه خلينا نقول الـ
+
+77
+00:06:14,920 --> 00:06:19,660
+outline للبرهان، نبدأ الآن في تفاصيل البرهان، وطول
+
+78
+00:06:19,660 --> 00:06:25,400
+روحكم عليها في اللي هو تفاصيل البرهان للوصول
+
+79
+00:06:25,400 --> 00:06:31,780
+للنتيجة اللي حكيتها اللي كتبت على اللوح، بدي أقول
+
+80
+00:06:31,780 --> 00:06:39,240
+الآن أول حاجة given Epsilon أكبر من صفر، أنا أخدت
+
+81
+00:06:39,240 --> 00:06:44,600
+أي Epsilon أكبر من صفر، بدي أوصل الـ U بي Phi
+
+82
+00:06:44,600 --> 00:06:50,610
+composite F ناقص الـ L بي Phi composite F أصغر من Epsilon
+
+83
+00:06:50,610 --> 00:06:55,150
+for some اللي هو partition P، إذا وصلت لهيك بكون خلصت
+
+84
+00:06:55,150 --> 00:06:58,770
+اللي هو نظريتي، طيب سلموا على النبي عليه الصلاة
+
+85
+00:06:58,770 --> 00:07:03,850
+والسلام، لأن Phi عندي، Phi عندي continuous على
+
+86
+00:07:03,850 --> 00:07:08,950
+مين؟ على اللي هي الـ J، الـ J عبارة عن closed bounded
+
+87
+00:07:08,950 --> 00:07:12,650
+interval، مدام continuous عليها إذا uniformly 
+
+88
+00:07:12,650 --> 00:07:16,690
+continuous، ماشي الحال، إذا مدام uniformly
+
+89
+00:07:16,690 --> 00:07:23,170
+continuous، إذا أكيد .. أكيد حتكون اللي هو مدام ..
+
+90
+00:07:23,170 --> 00:07:26,750
+حتى في الـ continuity أكيد حتكون إيش مالها؟ bounded
+
+91
+00:07:26,750 --> 00:07:34,710
+إذا بقدر اللي هو أقول K بتساوي الـ supremum للـ Phi
+
+92
+00:07:34,710 --> 00:07:41,540
+of T such that T element  الـ C والـ D التي هي الـ J
+
+93
+00:07:41,540 --> 00:07:45,900
+هذه الآن بقدر احكي عن حاجة اسمها Supremum، اه طبعًا
+
+94
+00:07:45,900 --> 00:07:51,720
+مش هي كلكم كمان، و الـ K هذه هتكون attains for
+
+95
+00:07:51,720 --> 00:07:55,500
+some T بين C و D، ليه؟ لأنه Phi is continuous on a
+
+96
+00:07:55,500 --> 00:07:58,340
+closed bounded interval then it attains its 
+
+97
+00:07:58,340 --> 00:08:00,920
+absolute maximum and absolute minimum on this 
+
+98
+00:08:00,920 --> 00:08:05,120
+interval، إذن أكيد في عندي K بيتساوي الـ Supremum لو 
+
+99
+00:08:05,120 --> 00:08:09,200
+سلوك يدفع له 5 T، T Element in C و D، سمّيليها دي K ليش
+
+100
+00:08:09,200 --> 00:08:13,280
+اتجهت؟ بتعرف ليش؟ هتستخدمها في الوصول إلى هدفي، إذا 
+
+101
+00:08:13,280 --> 00:08:16,960
+الآن اللي عملته لحد الآن أخدت Epsilon arbitrarily
+
+102
+00:08:16,960 --> 00:08:21,860
+أخدت اللي هو الـ supremum لهذا المقدار وسميته K، هل
+
+103
+00:08:21,860 --> 00:08:24,440
+الـ supremum موجود؟ اه الـ supremum موجود و maximum
+
+104
+00:08:24,440 --> 00:08:27,480
+كمان لأن الـ Phi is continuously on a closed
+
+105
+00:08:27,480 --> 00:08:31,840
+bounded interval C و D، طيب
+
+106
+00:08:34,510 --> 00:08:39,830
+الآن بدي آخذ بعيد إذنكم حاجة اسميها let Epsilon
+
+107
+00:08:39,830 --> 00:08:45,490
+Prime بيساوي اللي هو Epsilon على B ناقص A زائد 
+
+108
+00:08:45,490 --> 00:08:49,670
+اثنين K، الـ K هذه اللي فوق زائد اثنين K، والـ B والـ
+
+109
+00:08:49,670 --> 00:08:54,010
+A اللي هي طول الفترة اللي هي I اللي أنا عمال بشتغل
+
+110
+00:08:54,010 --> 00:09:01,100
+عليها، معرف عليها F، ليش هيك؟ بغرض الحسابات بعد شوية
+
+111
+00:09:01,100 --> 00:09:06,060
+هتشوفوا ليش، و لو أصلاً احنا في النهاية الـ Epsilon
+
+112
+00:09:06,060 --> 00:09:10,140
+الـ Prime هذه ما كتبناش بالشكل هذا، وطلع عندي اللي
+
+113
+00:09:10,140 --> 00:09:19,940
+هو الـ U of P أو Phi composite F ناقص الـ L Phi
+
+114
+00:09:19,940 --> 00:09:26,070
+composite F يكون أصغر من Epsilon مضروبة في something
+
+115
+00:09:26,070 --> 00:09:32,270
+أي شيء، something ثابت، برضه هتقدي الغرض، لإنه اللي هي 
+
+116
+00:09:32,270 --> 00:09:35,310
+زي ما قلنا المرة الماضية، مدام صحيحة لكل Epsilon
+
+117
+00:09:35,310 --> 00:09:38,150
+في الدنيا إذا صحيح الواحد على N، خد الـ limit 
+
+118
+00:09:38,150 --> 00:09:41,530
+للجهتين as N goes to infinity بيصير اللي هو هذا 
+
+119
+00:09:41,530 --> 00:09:45,670
+اللي هو يؤدي الغرض، أو الـ Epsilon اللي هنا بتكون 
+
+120
+00:09:45,670 --> 00:09:50,730
+اللي هو بيصير يعني تؤدي غرض أي أصغر من Epsilon في 
+
+121
+00:09:50,730 --> 00:09:53,510
+الدنيا، لأن الـ Epsilon مدام أتمضروبة ضرب في ثابت
+
+122
+00:09:53,510 --> 00:09:57,930
+بقدر الـ Epsilon أزغرها جد ما بدي، وتؤدي الغرض 
+
+123
+00:09:58,610 --> 00:10:05,280
+المفروض فاهمين، طيب نيجي الآن، نرجع نقول إنه أخدت 
+
+124
+00:10:05,280 --> 00:10:08,980
+Epsilon Prime بيساوي Epsilon على P minus A زائد 2K على 
+
+125
+00:10:08,980 --> 00:10:12,680
+أساس أنه اللي هي تطلع عندنا الحسابات في الآخر
+
+126
+00:10:12,680 --> 00:10:16,480
+مرتبة وخالصة، اللي هي أصغر من Epsilon، طبعًا هو 
+
+127
+00:10:16,480 --> 00:10:20,720
+الأشرف أن Epsilon Prime بالشكل هذا أصلاً هو برهن
+
+128
+00:10:20,720 --> 00:10:23,680
+النظرية أو برهنا النظرية وفي الآخر طلع إن Epsilon
+
+129
+00:10:23,680 --> 00:10:28,440
+مضروبة في رقم جيت اللي هو رتبت حالي بحيث إنه حسبت
+
+130
+00:10:28,440 --> 00:10:32,320
+إنّه عشان أطلّع Epsilon لحالها، خد Epsilon Prime بالشكل
+
+131
+00:10:32,320 --> 00:10:39,070
+هذا، طيب نشوف .. نشوف الآن عندي Phi زي ما وعدناكم
+
+132
+00:10:39,070 --> 00:10:49,690
+Phi is continuous on اللي هو C و D، مدام Phi
+
+133
+00:10:49,690 --> 00:10:53,010
+continuous on C و D يا جماعة، إذا زي ما قلنا قبل
+
+134
+00:10:53,010 --> 00:11:01,660
+بشوية إذا Phi is uniformly continuous on C و D، إيش
+
+135
+00:11:01,660 --> 00:11:07,680
+معنى uniformly continuous؟ يعني اللي هو for every
+
+136
+00:11:07,680 --> 00:11:12,100
+Epsilon في الدنيا، for every Epsilon .. خليني أخد
+
+137
+00:11:12,100 --> 00:11:15,020
+Epsilon الـ Prime، for every Epsilon الـ Prime أكبر 
+
+138
+00:11:15,020 --> 00:11:21,680
+من صفر there exists Delta Prime such that
+
+139
+00:11:21,680 --> 00:11:29,560
+uniformly continuous، for every S و T element in C و D
+
+140
+00:11:29,560 --> 00:11:38,690
+تحقق S minus T أصغر من Delta Prime يؤدي إلى Phi of S 
+
+141
+00:11:38,690 --> 00:11:43,690
+S ناقص Phi of T أصغر من مين من Epsilon prime اللي
+
+142
+00:11:43,690 --> 00:11:49,450
+أخدتها عندي لأي Epsilon في الدنيا هذا الكلام
+
+143
+00:11:49,450 --> 00:11:52,210
+بيتحقق من دون أن هم Epsilon prime اللي حكيت عنها 
+
+144
+00:11:52,210 --> 00:11:58,090
+فوق طيب إذا الآن اللي استخدمته بما أن Phi
+
+145
+00:11:58,090 --> 00:12:02,010
+continuous على C وD إذا Phi is uniformly
+
+146
+00:12:02,010 --> 00:12:08,210
+continuous on مين؟ on C أو D إذن الآن حسب التعريف
+
+147
+00:12:08,210 --> 00:12:11,530
+الـ Uniformly Continuous لأي إبسلون في الدنيا من
+
+148
+00:12:11,530 --> 00:12:14,530
+ضمنهن الإبسلون الـ prime الأكبر من 0 there exists
+
+149
+00:12:14,530 --> 00:12:17,430
+delta prime خاصة بالإبسلون الـ prime بحيث أنه لما
+
+150
+00:12:17,430 --> 00:12:20,770
+S و T في الـ C و الـ D و يكون الـ S minus T أصغر
+
+151
+00:12:20,770 --> 00:12:24,950
+من delta prime يعطيني أن Phi S ناقص Phi T أصغر من مين من
+
+152
+00:12:24,950 --> 00:12:30,990
+إبسلون الـ prime الآن أنا في delta معينة بدي
+
+153
+00:12:30,990 --> 00:12:35,830
+ألاقيها أربطها بهذه واتحققلي هذا الكلام شوفوا كيف
+
+154
+00:12:35,830 --> 00:12:44,030
+اصبروا عليها الآن if عندي delta prime هذه أصغر من
+
+155
+00:12:44,030 --> 00:12:49,430
+epsilon prime then there exists Delta بتساوي Delta 
+
+156
+00:12:49,430 --> 00:12:53,130
+prime بتاخد Delta إيش بتساوي أسميه بتسمي Delta
+
+157
+00:12:53,130 --> 00:12:56,370
+prime مين يا جماعة؟ Delta و هاد ال Delta اللي
+
+158
+00:12:56,370 --> 00:12:58,790
+سميتها اللي هي Delta prime اللي سميتها Delta هاد
+
+159
+00:12:58,790 --> 00:13:03,670
+ال Delta هتحققها ليش؟ لأنها نفسها يعني بمعنى آخر
+
+160
+00:13:03,670 --> 00:13:08,150
+إذا كانت ال S minus T أصغر من Delta prime بيعطيني
+
+161
+00:13:08,150 --> 00:13:10,830
+Automatic أصغر من Delta prime اللي سميتها Delta
+
+162
+00:13:10,830 --> 00:13:15,810
+بيعطيني Phi of S ناقص Phi of T أصغر من مين؟ من
+
+163
+00:13:15,810 --> 00:13:23,530
+Epsilon prime طيب تشوفوا الآن if delta prime أكبر
+
+164
+00:13:23,530 --> 00:13:26,430
+أو يساوي epsilon prime يا أي حالتين مافيش غير هيك
+
+165
+00:13:26,430 --> 00:13:28,830
+يا delta prime أصغر من epsilon يا delta prime أكبر
+
+166
+00:13:28,830 --> 00:13:32,090
+ساوي epsilon prime الآن if delta .. أهل جاي تفهموا
+
+167
+00:13:32,090 --> 00:13:34,530
+ليش عملت هيك if delta prime أكبر ساوي epsilon
+
+168
+00:13:34,530 --> 00:13:41,100
+prime then اللي هو there exists Delta أصغر من
+
+169
+00:13:41,100 --> 00:13:45,540
+Epsilon prime بلاجي ولا بلاجيش Epsilon prime أكبر
+
+170
+00:13:45,540 --> 00:13:50,200
+من 0 أكيد between أنا ابسلون prime أكبر من 0 إذا
+
+171
+00:13:50,200 --> 00:13:52,620
+أنا أكيد بلاجي بين Epsilon prime أكبر من 0 بلاجي
+
+172
+00:13:52,620 --> 00:13:57,340
+Delta بلاجي عدد نهائي من الأعداد اللي هو Delta أكبر
+
+173
+00:13:57,340 --> 00:14:01,400
+من صفر وأصغر من إبسلون prime إذاً بلاجي Delta أصغر
+
+174
+00:14:01,400 --> 00:14:04,820
+من إبسلون prime بلاجي أه بلاجي لإن بين الـ two
+
+175
+00:14:04,820 --> 00:14:09,820
+real numbers اللي هو بين السفر وبين أي positive
+
+176
+00:14:09,820 --> 00:14:14,360
+real number في infinite number of numbers بينهم
+
+177
+00:14:14,360 --> 00:14:17,600
+سميت واحد قلت there exists Delta أصغر من إبسلون 
+
+178
+00:14:17,600 --> 00:14:21,860
+prime such that .. طيب إيش بدك فيها هذه؟ such that
+
+179
+00:14:21,860 --> 00:14:27,400
+.. أحنا الـ gate تشوفوا if S minus T أصغر من Delta
+
+180
+00:14:27,400 --> 00:14:34,000
+فهذه الـ Delta if S minus T أصغر من Delta إذا أكيد
+
+181
+00:14:34,000 --> 00:14:37,860
+هذه الـ Delta أصغر من مين؟ المختار هي أصغر من Y'
+
+182
+00:14:38,320 --> 00:14:42,480
+وY' أصغر من مين؟ أصغر أو يساوى Delta prime من هنا
+
+183
+00:14:43,910 --> 00:14:50,290
+الآن if S-C أصغر من Delta إذا .. إذا حيث الـ S-C
+
+184
+00:14:50,290 --> 00:14:54,910
+هتكون أصغر من Y' واللي بدورها SY' أصغر بساوي Delta
+
+185
+00:14:54,910 --> 00:14:59,090
+.. أصغر بساوي Delta prime إذا صارت عندي S-C أصغر
+
+186
+00:14:59,090 --> 00:15:03,010
+من Delta قطعًا S-C أصغر من مين؟ من Delta prime
+
+187
+00:15:03,010 --> 00:15:07,450
+وبناءً على اللي كتبته بالأحمر هذا كل إشي S-C أصغر
+
+188
+00:15:07,450 --> 00:15:15,270
+من Delta prime إشي بيعطيني Phi S- Phi T أصغر من إبسلون
+
+189
+00:15:15,270 --> 00:15:20,550
+prime إذا يا جماعة سواء دلتا prime أصغر من إبسلون
+
+190
+00:15:20,550 --> 00:15:25,710
+prime أو دلتا prime أصغر من إبسلون epsilon prime
+
+191
+00:15:25,710 --> 00:15:33,020
+بقدر ألاقي دلتا تتحقق فيها الخاصية لما S minus T
+
+192
+00:15:33,020 --> 00:15:36,900
+أصغر من Delta لما S minus T أصغر من Delta يعطيني
+
+193
+00:15:36,900 --> 00:15:39,900
+هذا المقدار أصغر من Epsilon prime هذا المقدار أصغر
+
+194
+00:15:39,900 --> 00:15:44,580
+من Epsilon prime إذا أنا في النهاية there exist
+
+195
+00:15:44,580 --> 00:15:50,690
+لوصلت له there exist Delta أكبر من 0 ونفس الوجد
+
+196
+00:15:50,690 --> 00:15:55,170
+أشمالها Delta أصغر من إبسلون prime لأنه في الحالة
+
+197
+00:15:55,170 --> 00:15:59,650
+ده أصغر من إبسلون prime وفي الحالة الأولى برضه الـ
+
+198
+00:15:59,650 --> 00:16:03,630
+Delta أصغر من إبسلون prime لأنه اختار الدلتة هي
+
+199
+00:16:03,630 --> 00:16:08,490
+Delta prime إذن في كل الحالات هي المربط الفلسفي
+
+200
+00:16:08,490 --> 00:16:13,950
+الآن there exists Delta أكبر من 0 وأصغر من إبسلون
+
+201
+00:16:13,950 --> 00:16:22,170
+prime such that لكل S وT element in C وD إذا حققت
+
+202
+00:16:22,170 --> 00:16:27,610
+الخاصية S minus T أصغر من Delta بيعطيني على طول Phi S
+
+203
+00:16:27,610 --> 00:16:34,130
+ناقص Phi T أصغر من مين من إبسلون prime إذن هي
+
+204
+00:16:34,130 --> 00:16:41,710
+معلومة أخرى بدي أخذنها لأنني هحتاجها هي كمان معلومة
+
+205
+00:16:41,710 --> 00:16:46,270
+الآن اسمحولي أمسح هذا ال hand عشان أخزن معلومتي
+
+206
+00:16:46,270 --> 00:16:49,770
+اللي وصلت إلها مع المعلومات اللي موجودة عندي فوق
+
+207
+00:16:49,770 --> 00:16:57,090
+طيب الآن شطبنا اللي عندنا hand خلصنا منه ووصلنا
+
+208
+00:16:57,090 --> 00:17:03,030
+إلى المعلومة التالية اللي بدأ أخزنها الآن مع اللي
+
+209
+00:17:03,030 --> 00:17:10,620
+مخزن فوق لأن there exists Delta أكبر من 0 وأصغر من
+
+210
+00:17:10,620 --> 00:17:18,140
+Y' such that for every S وT element in C وD إذا
+
+211
+00:17:18,140 --> 00:17:25,340
+حقق S minus T أصغر من Delta بيعطيني اللي هو Phi S
+
+212
+00:17:25,340 --> 00:17:34,140
+minus Phi T أصغر من Y' وهذا سمونيها 1 سمونيها 2
+
+213
+00:17:34,140 --> 00:17:38,630
+سمونيها Star اللي بدكم إياها ماشي الحال هذا الآن
+
+214
+00:17:38,630 --> 00:17:44,170
+وصلت له وأنا بدي استخدمه بعد شوية
+
+215
+00:17:49,890 --> 00:17:54,390
+اللي اللي بحب يتابع على التلخيص
+
+216
+00:17:54,390 --> 00:17:58,130
+هاي اللي وصلت إليه الآن هايها there exists delta و
+
+217
+00:17:58,130 --> 00:18:01,390
+الـ delta أصغر من epsilon prime if S و T element
+
+218
+00:18:01,390 --> 00:18:04,470
+in J and S minus T أصغر من Delta then Phi of S
+
+219
+00:18:04,470 --> 00:18:08,030
+ناقص Phi of T أصغر من إبسلون prime هذه اللي وصلنا
+
+220
+00:18:08,030 --> 00:18:15,670
+إليها اللي قدرنا أن نصلها عشان بعد شوية بتستخدمها
+
+221
+00:18:15,670 --> 00:18:20,950
+انتبه عليها الآن الآن استغلقنا معلومة الـ if I is
+
+222
+00:18:20,950 --> 00:18:24,490
+continuous وحصلنا على معلومة مهمة جداً هي هذه
+
+223
+00:18:24,490 --> 00:18:28,630
+المعلومة الآن بدي أستخدم المعلومة الموازية لها أن
+
+224
+00:18:28,630 --> 00:18:37,770
+F is integrable الآن عندي F is integrable on I إذا
+
+225
+00:18:37,770 --> 00:18:43,010
+حسب then حسب اللي هو ال .. ال .. ال integrability
+
+226
+00:18:43,010 --> 00:18:48,570
+criterion اللي حكينا عنها there exists partition P
+
+227
+00:18:48,570 --> 00:18:56,690
+element in P of I بجزء مين I such that اللي هو U
+
+228
+00:18:56,690 --> 00:19:05,920
+of P وF معقس L بيوقف أصغر من أي إبسلون في الدنيا
+
+229
+00:19:05,920 --> 00:19:08,360
+الإبسلون اللي في الدنيا الإبسلون اللي بدها
+
+230
+00:19:08,360 --> 00:19:12,040
+استخدمها اللي حتة في الدنيا اللي هي مين هي Delta
+
+231
+00:19:12,040 --> 00:19:17,000
+تربيع أصغر من مين من Delta تربيع بقدر أه بقدر طبعا
+
+232
+00:19:17,000 --> 00:19:19,960
+مش احنا بنقول لكل إبسلون أكبر من صفر مادام F is
+
+233
+00:19:19,960 --> 00:19:23,040
+integrable لذا لكل إبسلون أكبر من صفر there exist
+
+234
+00:19:23,040 --> 00:19:27,590
+ال partition P بحيث أنه هذا أصغر من إبسلون الآن
+
+235
+00:19:27,590 --> 00:19:30,330
+أبسط من اللي بحكي عنها Delta تربيع Delta تربيع
+
+236
+00:19:30,330 --> 00:19:35,650
+أكبر من صفر إذا for Delta تربيع there exists P
+
+237
+00:19:35,650 --> 00:19:40,070
+element in P of I such that U ناقص L أصغر من مين
+
+238
+00:19:40,070 --> 00:19:44,650
+من Delta تربيع هذا ال partition P بيجزئلي مين؟
+
+239
+00:19:44,650 --> 00:19:51,670
+بيجزئلي I بعد أذنكم سموليها بيه X0 و X1 لعند مين؟
+
+240
+00:19:51,670 --> 00:19:55,230
+لعند Xn سموليها ال partition بس عشان أتعامل معاها
+
+241
+00:19:55,660 --> 00:19:57,540
+اللي هو partition للـ I partition للـ I معناه
+
+242
+00:19:57,540 --> 00:20:00,880
+بجزّه I جزّه أو ل X note X واحد X انت جداش أعدادها
+
+243
+00:20:00,880 --> 00:20:07,080
+مش عارف حسب اللي هو اللي جناه بيه طيب شوف الآن بدي
+
+244
+00:20:07,080 --> 00:20:13,520
+أعمل اللي هو شغلة بحيث عن الآن أقدر أستخدمها اللي
+
+245
+00:20:13,520 --> 00:20:18,360
+هي أصل للي بدي من خلالها الآن هجيتوا تشوفوا ليش
+
+246
+00:20:18,360 --> 00:20:23,400
+جزعين خدوا A الآن يا جماعة صارت Delta بين إيديا
+
+247
+00:20:23,400 --> 00:20:28,520
+لجهتها Delta طيب الآن خدوا A هي عبارة عن كل ال
+
+248
+00:20:28,520 --> 00:20:34,160
+indices K اللي هان هذولة و 0,1,2,3 كده هذه جزء
+
+249
+00:20:34,160 --> 00:20:38,520
+اثنين ال I هي عند X0 لعند Xn هذه الفترة
+
+250
+00:20:38,520 --> 00:20:44,000
+اللي هي من A لعند B يا جماعة لعند B ماشي الحال طيب
+
+251
+00:20:44,000 --> 00:20:49,380
+خدوله A هي عبارة عن كل ال K بحيث أن Mk ناقص mk
+
+252
+00:20:49,380 --> 00:20:54,900
+small تكون أصغر من Delta وخدول ال B بيساوي كل ال K
+
+253
+00:20:54,900 --> 00:20:59,740
+such that Mk ناقص mk أكبر يساوي Delta إيش هذول
+
+254
+00:20:59,740 --> 00:21:04,700
+عاملا؟ هذول بس ال indices عند من هنا صفر و واحد و
+
+255
+00:21:04,700 --> 00:21:08,480
+اثنين عند من؟ عند ال K إذا أتجت جزءات ال indices
+
+256
+00:21:08,480 --> 00:21:15,500
+هذول إلى جزء A الجزء اللي هو عندي اللي بخاصية
+
+257
+00:21:15,500 --> 00:21:19,980
+اللي هو ال Mk ناقص mk أصغر من Delta بده يحطه في هذا ال
+
+258
+00:21:19,980 --> 00:21:24,280
+set إذا هذه عبارة عن إيش مجموعة جزئية من ال .. من
+
+259
+00:21:24,280 --> 00:21:27,680
+ال .. من ال .. من ال .. من ال .. من ال K من صفر
+
+260
+00:21:27,680 --> 00:21:36,490
+لعند مين لعند n لعند أنا .. لعند أنا الآن هذه P
+
+261
+00:21:36,490 --> 00:21:40,870
+هي عبارة عن المتبقي منهن مين المتبقي اللي الـ Mk
+
+262
+00:21:40,870 --> 00:21:44,170
+ناقص mk أصغر أكبر أو يساوي Delta يعني بمعنى آخر
+
+263
+00:21:44,170 --> 00:21:49,430
+أداة التجزئة لهذه اللي هي الخاصية أنه Mk نقص mk
+
+264
+00:21:49,430 --> 00:21:52,010
+أصغر من مين من Delta أنتم عارفين إيش الـ Mk
+
+265
+00:21:52,010 --> 00:21:55,730
+Capital و mk small؟ أكيد الـ Mk Capital هي
+
+266
+00:21:55,730 --> 00:21:59,710
+عبارة عن الـ supremum لل F of X such that X
+
+267
+00:21:59,710 --> 00:22:04,740
+element in Xk-1 لعند الـ Xk و الـ mk small
+
+268
+00:22:04,740 --> 00:22:09,560
+بيساوي الـ infimum لل F of X such that X element
+
+269
+00:22:09,560 --> 00:22:16,640
+in Xk-1 والـ Xk إذن يا جماعة اللي جزألي
+
+270
+00:22:16,640 --> 00:22:21,900
+الـ A و الـ B هو خاصيته إن الـ mk capital يعني
+
+271
+00:22:21,900 --> 00:22:25,340
+أعلى قيمة هي .. هي .. هي .. هي عندي أنا Xk-
+
+272
+00:22:25,340 --> 00:22:29,860
+1 وهي Xk فرضنا أن الدالة هي الدالة زي هيك مثلا
+
+273
+00:22:29,860 --> 00:22:35,250
+في المنطقة هذه الآن هي أعلى قيمة وهي أقل قيمة
+
+274
+00:22:35,250 --> 00:22:41,070
+ال حاصل طرح أعلى قيمة وأقل قيمة في كل فترة .. كل
+
+275
+00:22:41,070 --> 00:22:44,770
+sub interval بادي بقول هل هذا أكبر من .. أصغر من
+
+276
+00:22:44,770 --> 00:22:49,270
+Delta ولا أكبر يساوي Delta اللي خاصيتهم الفرق
+
+277
+00:22:49,270 --> 00:22:53,930
+بينهم أصغر من Delta بحط هنا الاندسيز هذا كهن واللي
+
+278
+00:22:53,930 --> 00:22:59,930
+أكبر بحطه هن و بحط تجزيتها ليش هذه؟ هذه طريقة
+
+279
+00:22:59,930 --> 00:23:07,130
+للوصول إلى اللي بديها وهتشوفه الآن طيب نيجي الآن
+
+280
+00:23:07,130 --> 00:23:20,690
+لاللي هو نشوف الـ K Fk Element A مدام K Element A 
+
+281
+00:23:22,110 --> 00:23:26,470
+إذا تحقق الخاصية هذه يعني Mk ناقص Mk أصغر من مين؟
+
+282
+00:23:26,470 --> 00:23:32,430
+من Delta خذولي الآن أي X و Y في الفترة مين اللي هي
+
+283
+00:23:32,430 --> 00:23:39,330
+XK ناقص واحد لعند XK شوفوا إيش اللي بديها الـ .. الـ
+
+284
+00:23:39,330 --> 00:23:43,130
+.. الـ .. الـ .. الـ X و الـ Y هنا هي الـ X و الـ Y وهى
+
+285
+00:23:43,130 --> 00:23:46,430
+رسمة الدالة في المنطقة هذه الـ X و الـ Y في داخل هدول
+
+286
+00:23:46,430 --> 00:23:53,930
+طيب الآن الـ X و الـ Y هنا إذا أكيد الـ F of X الـ F
+
+287
+00:23:53,930 --> 00:24:00,090
+of X ناقص F of Y نقطتين هنا نقطتين من هنا لهنا صور
+
+288
+00:24:00,090 --> 00:24:03,750
+هنا صور هنا يعني ممكن صورة واحدة هنا و صورة
+
+289
+00:24:03,750 --> 00:24:08,440
+الثانية هنا يعني ممكن صورة الثالثة هنا وصورة الأولى
+
+290
+00:24:08,440 --> 00:24:15,500
+هنا يعني بمعنى آخر لو الـ X هنا و الـ Y هنا هي صورة
+
+291
+00:24:15,500 --> 00:24:21,400
+الـ X وهي صورة مين الـ Y لو جيتوا .. أخدتوا .. هي
+
+292
+00:24:21,400 --> 00:24:26,760
+صورة الـ Y لو أخدتوا الفرق بين هذه و بين هذه الفرق
+
+293
+00:24:26,760 --> 00:24:31,020
+بين ما هو قيمة الدالة F of X هنا و قيمة الدالة F
+
+294
+00:24:31,020 --> 00:24:36,280
+of Y هنا أكيد .. أكيد .. أكيد الفرق بينهم هيكون
+
+295
+00:24:36,280 --> 00:24:42,320
+أصغر أو يساوي Mk ناقص من Mk لسبب بسيط أصلا لأن
+
+296
+00:24:42,320 --> 00:24:49,660
+أصلا F of X هذه أصغر أو يساوي ما هو Mk أكيد و F
+
+297
+00:24:49,660 --> 00:24:54,400
+of Y أصغر أو يساويها ماشي الحال نفس الـ .. يعني ..
+
+298
+00:24:54,400 --> 00:24:57,080
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+299
+00:24:57,080 --> 00:24:57,100
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+300
+00:24:57,100 --> 00:24:57,360
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+301
+00:24:57,360 --> 00:24:57,720
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+302
+00:24:57,720 --> 00:24:58,100
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+303
+00:24:58,100 --> 00:24:59,480
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+304
+00:24:59,480 --> 00:25:00,040
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+305
+00:25:00,040 --> 00:25:07,580
+و .. و .. و .. و .. و
+
+306
+00:25:07,580 --> 00:25:08,160
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+307
+00:25:08,160 --> 00:25:11,200
+.. و .. و .. و ..
+
+308
+00:25:19,040 --> 00:25:24,000
+فبيظل قيمة f of x ناقص f of y أصغر من مين؟ Mk ناقص
+
+309
+00:25:24,000 --> 00:25:28,460
+Mk اللي مش واضح له من خلال الرسمة اللي عندي هنا
+
+310
+00:25:31,440 --> 00:25:34,520
+يعني الآن خلّيني أرى أضحّ لحسن تكون مش واضحة للبعض
+
+311
+00:25:34,520 --> 00:25:41,360
+هذه الرسمة هذه XK ناقص واحد وهذه XK خلّيني أكبر
+
+312
+00:25:41,360 --> 00:25:46,180
+الرسمة عشان تكون أوضح وهذه XK لأن نفترضها أن هذه
+
+313
+00:25:46,180 --> 00:25:53,520
+رسمتنا هيك وطلع زي هيك ماشي وهذه عندي أعلى نقطة
+
+314
+00:25:53,520 --> 00:25:58,710
+خلّيني أصغّر هذه شوية وهذه أصغر نقطة هذه اللي
+
+315
+00:25:58,710 --> 00:26:03,970
+بتتمثل لـ Mk وهذه بتتمثل لـ Mk Small هذه المسافة
+
+316
+00:26:03,970 --> 00:26:09,030
+بينهم الفرق بينهم الآن الثانية لو جيت أخذت أي نقطة
+
+317
+00:26:09,030 --> 00:26:17,190
+هنا X و أي نقطة Y هنا هذه X وهذه Y المسافة بينها دي
+
+318
+00:26:17,190 --> 00:26:21,310
+و بينها دي قيمتها دي بيصير F of X أنا بصير F of X
+
+319
+00:26:22,380 --> 00:26:26,700
+وهنا بيصير F of Y الفرق بين F of X و F of Y أكيد
+
+320
+00:26:26,700 --> 00:26:31,140
+أصغر من الفرق هذا وكل النقاط اللي بين هذه و هذه
+
+321
+00:26:31,140 --> 00:26:37,340
+هيكون يا إما زي الفرق هذا أو أصغر منه إذا أكيد
+
+322
+00:26:37,340 --> 00:26:45,820
+عندي صار المفروض وضح الأمر هيكون عندي اللي هو هذا
+
+323
+00:26:45,820 --> 00:26:50,910
+المقدار أصغر من هو هذا طيب ليش ليش هذا؟ هذا من مين للـ
+
+324
+00:26:50,910 --> 00:26:53,990
+K اللي في الـ A والـ K اللي في الـ A شخصيتها Mk
+
+325
+00:26:53,990 --> 00:26:57,610
+ناقصها Mk أصغر من مين؟ إذا صارت أصغر من الـ Delta
+
+326
+00:26:57,610 --> 00:27:04,470
+إذا صارت F of X و F of Y أصغر من مين؟ من Delta طيب
+
+327
+00:27:04,470 --> 00:27:08,430
+مادام F of X إيش علاقات هنا F of X و F of Y ما هي
+
+328
+00:27:08,430 --> 00:27:13,950
+أصلا احنا مفترضين من الأول أن F of I جزئية من الـ
+
+329
+00:27:13,950 --> 00:27:18,430
+J اللي هي عبارة عن C و D مظبوط ولا لأ إذا حيصير
+
+330
+00:27:18,430 --> 00:27:23,600
+عندي F of X و F of Y موجودات في الـ C و D F of X و
+
+331
+00:27:23,600 --> 00:27:27,000
+F of Y موجودات في الـ C و الـ D و بتحقق المسافة
+
+332
+00:27:27,000 --> 00:27:32,200
+أصغر من Delta بينهم إذا حسب واحد اللي احنا أثبتنا
+
+333
+00:27:32,200 --> 00:27:35,960
+أي نقطتين في الـ S و الـ D المسافة بينهم أصغر من
+
+334
+00:27:35,960 --> 00:27:39,600
+Delta لازم صورة الـ .. صورة Phi of S و Phi of T
+
+335
+00:27:39,600 --> 00:27:42,540
+المسافة بينهم أصغر من مين؟ من Epsilon و Prime إذا
+
+336
+00:27:42,540 --> 00:27:47,640
+هذا Automatic هيعطيني Phi of النقطة الأولى اللي هي
+
+337
+00:27:47,640 --> 00:27:56,290
+F of X ناقص Phi of النقطة الثانية يكون أصغر من
+
+338
+00:27:56,290 --> 00:28:06,890
+مين من Epsilon Prime إذا صار عندي الآن لكل اللي عندي
+
+339
+00:28:06,890 --> 00:28:13,740
+الـ K اللي في الـ A والـ X و Y في هذه المنطقة F of X
+
+340
+00:28:13,740 --> 00:28:17,920
+ناقص F of Y طلع ليه أصغر من Delta حتى ملي الـ 5 F
+
+341
+00:28:17,920 --> 00:28:25,000
+of X ناقص 5 F of Y أصغر من مين؟ من Epsilon إبراهيم ماشي
+
+342
+00:28:25,000 --> 00:28:29,820
+الحال هذا الكلام لكل X و Y موجودات في الـ XK ناقص
+
+343
+00:28:29,820 --> 00:28:33,460
+واحد والـ XK لخص الآن اللي وصلنا له لأنه بدي
+
+344
+00:28:33,460 --> 00:28:36,920
+أستخدمه خليني ألخص خليني أشيل
+
+345
+00:28:41,000 --> 00:28:45,820
+خلّيني بس أساعدك أكتب لكم في مكان هنا اتحملوني أنه
+
+346
+00:28:45,820 --> 00:28:54,640
+عشان اللوح شوية A بيساوي كل الـ K مقصد Mk أصغر من
+
+347
+00:28:54,640 --> 00:29:05,600
+Delta وعند B بيساوي كل الـ K بحيث أن Mk ناقص Mk أكبر
+
+348
+00:29:05,600 --> 00:29:10,060
+أو يساوي Delta خلّيني أقولها في الذاكرة الآن خلّيني
+
+349
+00:29:10,060 --> 00:29:16,140
+أمسح حاجة وألخص معلوماتي إيش معلوماتي بتقول دي لـ K
+
+350
+00:29:16,140 --> 00:29:26,610
+اللي في الـ A ماشي الحال لكل X و Y في الفترة XK-1
+
+351
+00:29:26,610 --> 00:29:32,750
+لعند الـ xk بيطلع عندي الـ Phi f of x يعني Phi
+
+352
+00:29:32,750 --> 00:29:40,990
+composite f of x ناقص Phi composite f of y أشماله
+
+353
+00:29:40,990 --> 00:29:48,600
+أصغر من Epsilon Prime واضح؟ إذن اللي وصلنا له لـ K
+
+354
+00:29:48,600 --> 00:29:53,700
+اللي في الـ A عندي لـ K اللي في الـ A هذا الـ
+
+355
+00:29:53,700 --> 00:29:58,380
+absolute value أظهر من مين؟ من Epsilon إبراهيم لكل
+
+356
+00:29:58,380 --> 00:30:05,580
+مين؟ لكل XY في الـ XK ناقص XK ناقص 1 طيب نكمل لكم
+
+357
+00:30:05,580 --> 00:30:10,860
+عليها هذا خلصنا منه صار عندي الآن شوفوا
+
+358
+00:30:19,430 --> 00:30:24,070
+الشغل عمودي يا جماعة على الفترة هذه طيب شوف عندي
+
+359
+00:30:24,070 --> 00:30:31,590
+Phi composite F of X ناقص Phi composite F of Y
+
+360
+00:30:31,590 --> 00:30:37,770
+أكبر من Epsilon  و أكبر من مين؟ من ناقص Epsilon Prime بدأ أخد
+
+361
+00:30:37,770 --> 00:30:43,970
+هذه الجهة خلّيني أخد الجهة من الجهتين وأبدأ أشتغل
+
+362
+00:30:43,970 --> 00:30:51,300
+عليها واضحة هذه هذه أصغر من Epsilon' أكبر من ناقص Epsilon بديش
+
+363
+00:30:51,300 --> 00:30:56,980
+هذا بتشغل هذه الآن لأن هذا الكلام صحيح لمن؟ لكل X
+
+364
+00:30:56,980 --> 00:31:02,740
+و Y في الـ sub interval هذه اللي هي لكل مين الـ case؟
+
+365
+00:31:02,740 --> 00:31:06,600
+الـ case اللي من A بس طيب شوف إذا صار عندي Phi
+
+366
+00:31:06,600 --> 00:31:14,580
+composite F of X أصغر من Epsilon' بزايد Phi composite F
+
+367
+00:31:14,580 --> 00:31:21,720
+of Y ماشي يا جماعة .. ماشي هذا الكلام لكل x و y في
+
+368
+00:31:21,720 --> 00:31:26,980
+.. اللي هو xk ناقص .. من xk ناقص 1 عند xk اللي
+
+369
+00:31:26,980 --> 00:31:31,600
+هنا .. هذا لكل x و y ثبت لي y .. ثبت لي y .. خلينا
+
+370
+00:31:31,600 --> 00:31:34,380
+نحكي عن y محدد .. arbitrary y لكن خلينا .. ثبتها
+
+371
+00:31:34,380 --> 00:31:40,180
+.. خلينا نحكي عن arbitrary fixed y بظل Epsilon' زي الـ
+
+372
+00:31:40,180 --> 00:31:47,140
+phi composite f of y is true أكبر من هذه لكل x
+
+373
+00:31:47,140 --> 00:31:52,500
+element in xk ناقص 1 لعند مين؟ لعند الـ xk أكيد
+
+374
+00:31:52,500 --> 00:32:00,060
+أكيد هذا أكبر من هذا لكل x well موجودة في xk ناقص
+
+375
+00:32:00,060 --> 00:32:04,540
+1 لعند مين؟ لعند الـ xk إذا صار هذا عبارة عن إيش
+
+376
+00:32:04,540 --> 00:32:08,880
+يا جماعة عبارة عن upper bound لهذا الـ set مدام
+
+377
+00:32:08,880 --> 00:32:13,900
+upper bound إلها إذا هيكون أكبر أو يساوي الـ least
+
+378
+00:32:13,900 --> 00:32:19,340
+upper bound يعني بمعنى آخر الـ supremum لـ Phi
+
+379
+00:32:19,340 --> 00:32:25,280
+composite F of X such that X element in XK ناقص 1
+
+380
+00:32:25,280 --> 00:32:31,240
+لعند الـ XK اللي هو أصغر أو يساوي Epsilon Prime زي Phi
+
+381
+00:32:31,240 --> 00:32:38,520
+composite F of mean of Y for any fixed Y طيب، هذا
+
+382
+00:32:38,520 --> 00:32:45,140
+مين هو؟ هذا عبارة عن الـ Mk وسميها Delta أساس أو
+
+383
+00:32:45,140 --> 00:32:48,080
+تلدا أساس اللي هي خاصة بمين الآن في الـ Phi
+
+384
+00:32:48,080 --> 00:32:53,100
+Composite F عشان نميزها بالـ Mk اسمه بالـ Mk
+
+385
+00:32:53,100 --> 00:32:59,400
+اللي خاصة بالـ F اللي عندي، ماشي الحال، طيب صار
+
+386
+00:32:59,400 --> 00:33:02,800
+عندي Mk تلدا بيساوي الـ Supremum لهذا أصغر يساوي
+
+387
+00:33:02,800 --> 00:33:07,680
+هذا هذا صار عدد صار العدد هذا أصغر من Epsilon Prime
+
+388
+00:33:07,680 --> 00:33:11,640
+في Composite F of Y for any fixed Y يعني صحيح على
+
+389
+00:33:11,640 --> 00:33:16,320
+كل Y وين موجودة في الفترة هذه إذا صار عندي الآن
+
+390
+00:33:16,320 --> 00:33:21,680
+جيب لي هذه على الجهة هذه وهذه على الجهة هذه بيصير
+
+391
+00:33:21,680 --> 00:33:28,050
+عندي اللي هو ناقص Phi Composite F of Y أصغر أو يساوي
+
+392
+00:33:28,050 --> 00:33:34,770
+Epsilon و Prime ناقص مين؟ Mk تلدا وإذا بدك ممكن نجيب
+
+393
+00:33:34,770 --> 00:33:40,050
+اللي هو الـ Epsilon و الـ Prime على الجهة الثانية مش
+
+394
+00:33:40,050 --> 00:33:50,310
+مشكلة صار عندي الآن هذا يا جماعة صار
+
+395
+00:33:50,310 --> 00:33:58,380
+عندي هذا اللي هو عبارة عن upper bound لهذا المقدار
+
+396
+00:33:58,380 --> 00:34:07,020
+أكيد ولا لا؟ عارفين ليش؟ لأن هذا الآن أكبر أو 
+
+397
+00:34:07,020 --> 00:34:11,000
+يساوي هذا المقدار لكل Y لأن كل الـ Y
+
+398
+00:34:11,000 --> 00:34:14,600
+arbitrarily fixed لكن arbitrarily، إذا صحيح على
+
+399
+00:34:14,600 --> 00:34:19,640
+كله، إذا بيصير عندي الآن اللي هو هذا أكبر أو يساوي
+
+400
+00:34:19,640 --> 00:34:24,260
+الـ supremum لهذا، يعني بمعنى آخر الـ supremum، لا
+
+401
+00:34:24,860 --> 00:34:32,200
+الناقص Phi composite F of Y such that Y element in
+
+402
+00:34:32,200 --> 00:34:39,360
+YK as if XK ناقص 1 عند XK هذا الـ Supremum له
+
+403
+00:34:39,360 --> 00:34:48,670
+أظهر أو يساوي Epsilon' ناقص Mk تلدا طيب هات إيش بتساوي
+
+404
+00:34:48,670 --> 00:34:56,670
+طلعوا الناقص برا بيساوي ناقص الـ infimum معايا لأ
+
+405
+00:34:56,670 --> 00:34:59,790
+لأنه مدام ناقص واحد طلع إذا بيقلب الـ supremum لـ
+
+406
+00:34:59,790 --> 00:35:05,530
+infimum Phi composite F of Y such that Y element
+
+407
+00:35:05,530 --> 00:35:09,610
+in XK ناقص واحد لعند الـ XK عرفتوا إيش اللي بده
+
+408
+00:35:09,610 --> 00:35:16,060
+أقوله هذا مين هي يا شباب هذه عبارة عن الـ Mk تلدا
+
+409
+00:35:16,060 --> 00:35:19,680
+اللي هي الـ infimum للـ Phi Composite F كتبت
+
+410
+00:35:19,680 --> 00:35:22,800
+التلدة عشان ترمز لمين؟ للـ Phi Composite F وفي عندي
+
+411
+00:35:22,800 --> 00:35:28,460
+ناقص قبلها إذا صارت عندي ناقص الـ Mk تلدا أصغر
+
+412
+00:35:28,460 --> 00:35:33,400
+يساوي Epsilon ناقص الـ Mk تلدا بدي أجيب هذه هنا
+
+413
+00:35:33,400 --> 00:35:42,400
+بيصير عندي إذا Mk تلدا أصغر ناقص Epsilon ناقص Mk تلدا
+
+414
+00:35:42,400 --> 00:35:51,080
+small أصغر أو يساوي مين؟ Epsilon إذا اللي وصلت له ما
+
+415
+00:35:51,080 --> 00:35:59,440
+يلي وهذه بده أصله أنه لكل K في الـ A طلع عندي Mk تلدا
+
+416
+00:35:59,440 --> 00:36:05,300
+ناقص Mk prime أصغر من إيش هو إيش؟ Epsilon خلينا نسجلها
+
+417
+00:36:05,300 --> 00:36:11,830
+عشان نبني عليها صار عندي الآن يا جماعة طولوا روحكم
+
+418
+00:36:11,830 --> 00:36:18,670
+عليا إن شاء الله مش هم طوالين نخلص Mk تلدا ناقص M
+
+419
+00:36:18,670 --> 00:36:22,890
+k تلدا small أصغر من إيش هو؟ Epsilon هذا لكل K وين
+
+420
+00:36:22,890 --> 00:36:30,330
+موجودة في الـ A لكل K في الـ A طيب هذا اللي احنا إيش 
+
+421
+00:36:30,330 --> 00:36:38,150
+مالِه أوصلنا إلى هصار عندي الآن الـ MK تلدى ناقص MK
+
+422
+00:36:38,150 --> 00:36:52,190
+تلدِى أصغر من الـ E' لكل K فيه اللى هي NA الآن
+
+423
+00:36:52,190 --> 00:36:58,330
+خد الـ summation، الـ summation للـ MK تلدى ناقص MK
+
+424
+00:36:58,330 --> 00:37:05,490
+تلدِى small K element in A اللي هو هذا اللي هو أصغر
+
+425
+00:37:05,490 --> 00:37:09,310
+أو يساوي في .. أصغر أو يساوي .. الآن قَدّوا .. قَدّوا
+
+426
+00:37:09,310 --> 00:37:11,470
+.. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا ..
+
+427
+00:37:11,470 --> 00:37:12,010
+قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا ..
+
+428
+00:37:12,010 --> 00:37:13,570
+قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا ..
+
+429
+00:37:13,570 --> 00:37:15,170
+قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا ..
+
+430
+00:37:15,170 --> 00:37:17,810
+قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا ..
+
+431
+00:37:17,810 --> 00:37:31,850
+قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا .. قَدّوا
+
+432
+00:37:31,850 --> 00:37:39,180
+..K element in A العداد هذا بعيد بعدد الـ K's اللي
+
+433
+00:37:39,180 --> 00:37:43,180
+في الـ A يعني إبسيلون مضروب في عدد الـ K's اللي 
+
+434
+00:37:43,180 --> 00:37:48,060
+موجودة في مين؟ في A هذا أكيد أكيد هذا أصغر أو
+
+435
+00:37:48,060 --> 00:37:55,320
+يساوي الـ summation للإبسيلون على كل الـ K من عند
+
+436
+00:37:55,320 --> 00:38:00,980
+صفر لعند مين؟ لعند اللي هو HN
+
+437
+00:38:03,340 --> 00:38:09,620
+بس أنا الآن بدي آجي أودي الـ summation  وأضربه في
+
+438
+00:38:09,620 --> 00:38:13,460
+مين؟ في طول الفترة؛ لأنه هي لازم لطول الفترة بعد
+
+439
+00:38:13,460 --> 00:38:20,660
+اسمهم هذا، أضربه ليه؟ في XK بدي أضربه بس أوّسع عقله
+
+440
+00:38:20,660 --> 00:38:23,700
+معلش، بدي أضربه يعني هذا الـ summation اللي حصلت
+
+441
+00:38:23,700 --> 00:38:29,320
+عليه، بدي آخذ الـ summation MK تلده ناقص mk تلدِى
+
+442
+00:38:29,320 --> 00:38:34,540
+وأضربه يا شباب في XK ناقص XK ناقص واحد K element 
+
+443
+00:38:34,540 --> 00:38:39,000
+in A هيصير أصغر أو يساوي الـ summation للإبسيلون في
+
+444
+00:38:39,000 --> 00:38:48,620
+XK ناقص XK ناقص واحد على الآن K element in A أكيد
+
+445
+00:38:48,620 --> 00:38:52,120
+أصغر زي ما قلنا من الـ summation اللي فوق إبسيلون
+
+446
+00:38:52,120 --> 00:38:59,980
+في XK ناقص XK ناقص 1 K من 0 لعند N ليش؟ هذا الـ
+
+447
+00:38:59,980 --> 00:39:02,420
+summation بس على العناصر اللي في الـ A هذا الـ
+
+448
+00:39:02,420 --> 00:39:05,260
+summation على كله على اللي في الـ A وعلى اللي في الـ
+
+449
+00:39:05,260 --> 00:39:08,760
+B على كل بقى العناصر اللي هي الـ partition اللي
+
+450
+00:39:08,760 --> 00:39:15,420
+عنده من 0 لـ 1، 2، عند مين؟ لعند الـ N طيب الـ N هذا
+
+451
+00:39:15,420 --> 00:39:20,200
+المقدار هي اللي بدي إياها الآن هذا bridge كان أو جسر
+
+452
+00:39:20,200 --> 00:39:23,860
+للوصول للي بدي إياها وحتى ممكن نُهان مباشرة لهذه هذه
+
+453
+00:39:23,860 --> 00:39:27,760
+أصغر أو يساوي هذا هذا مش هو اللي بتطلع عليه بتطلع
+
+454
+00:39:27,760 --> 00:39:32,640
+عليه هذا وبتطلع عليه هذا هذا خليه لأن أصغر يساوي
+
+455
+00:39:32,640 --> 00:39:36,460
+مين؟ هذا المقدار هذا المقدار إيش بيساوي؟ إبسيلون في
+
+456
+00:39:36,460 --> 00:39:43,790
+مين؟ X note ناقص X واحد زائد X واحد ناقص X اتنين زائد
+
+457
+00:39:43,790 --> 00:39:47,810
+X اتنين ناقص X ثلاثة لما أصل لآخر واحد يضل اللي
+
+458
+00:39:47,810 --> 00:39:53,330
+عبارة عن Y في Xn ناقص X note عملناها كثير ويساوي
+
+459
+00:39:53,330 --> 00:39:58,710
+Y prime ويساوي Y prime في مين؟ في B ناقص A لأن الـ
+
+460
+00:39:58,710 --> 00:40:03,950
+Xn هي عبارة عن B والـ X note هي مين؟ كانت هي الـ A
+
+461
+00:40:03,950 --> 00:40:10,110
+إذا اللي وصلت له يا جماعة الآن وصلت إلى ما يلي أنه
+
+462
+00:40:10,110 --> 00:40:19,170
+الـ summation للـ MK تلدى ناقص MK تلدى small لكي
+
+463
+00:40:19,170 --> 00:40:25,790
+element A في XK ناقص XK ناقص واحد أصغر أو
+
+464
+00:40:25,790 --> 00:40:34,550
+يساوي إبسيلون prime في B ناقص إيش؟ ناقص A واضح
+
+465
+00:40:34,550 --> 00:40:42,680
+أنه هذه خزّنها؛ لأنه بدي إياها بعد شوية اتحملونا
+
+466
+00:40:42,680 --> 00:40:46,880
+البرهان طويل شوية هي وصلنا إليها summation أزرع
+
+467
+00:40:46,880 --> 00:40:50,980
+شوية إبسيلون رابع في B ناقص A؛ لأن بدنا نيجي لمين؟
+
+468
+00:40:50,980 --> 00:40:59,140
+يا جماعة، بدنا نيجي للي هو انتبهوا عليها، بدنا
+
+469
+00:40:59,140 --> 00:41:03,280
+نيجي للـ M للـ K اللي موجودة في مين؟ هذا الـ K في
+
+470
+00:41:03,280 --> 00:41:06,820
+الـ A، ضال عند مين؟ احنا جزأتها إلى جزئين اللي هي
+
+471
+00:41:06,820 --> 00:41:11,340
+الـ indices اللي عنده، K اللي هي في الـ A و K اللي
+
+472
+00:41:11,340 --> 00:41:18,060
+هي في مين؟ في الـ B خذ الآن K element in B، شوف
+
+473
+00:41:18,060 --> 00:41:26,980
+إيش؟ الـ MK تلدِى ناقص mk تلدِى إيش بتساوي؟
+
+474
+00:41:26,980 --> 00:41:32,380
+بتساوي حسب التعريف Supremum للـ Phi Composite F of
+
+475
+00:41:32,380 --> 00:41:38,240
+X للـ K اللي وين؟ في الـ B اللي هي MK تلدها ناقص MK
+
+476
+00:41:38,240 --> 00:41:42,540
+تلدها اللي هي small Supremum للـ Phi F of X اللي
+
+477
+00:41:42,540 --> 00:41:47,980
+هي الأولى هذه Such that X element in XK ناقص واحد
+
+478
+00:41:47,980 --> 00:41:54,860
+وXK اللي هي زائد أو ناقص اللي هي مين؟ هذه الـ 
+
+479
+00:41:54,860 --> 00:42:01,200
+infimum لـ فاي composite F of X such that X
+
+480
+00:42:01,200 --> 00:42:10,220
+والموجودة في الـ XK ناقص واحد والـ XK مظبوط ولا
+
+481
+00:42:10,220 --> 00:42:18,690
+لأ، احنا قلنا الـ Supremum لكل الـ Phi of T T على كل
+
+482
+00:42:18,690 --> 00:42:24,130
+الـ C والـ D بيساوي إيش اسمه؟ بيساوي K هذه عبارة
+
+483
+00:42:24,130 --> 00:42:29,790
+عن مين؟ شايفين، ما بديش أعيدك، بقى أكتب مرتين خليني
+
+484
+00:42:29,790 --> 00:42:33,890
+أكتبها على شورة بتصير Phi of F of X يعني بتصير
+
+485
+00:42:33,890 --> 00:42:42,250
+عبارة عن مين؟ Phi of F of X معايا؟
+
+486
+00:42:43,040 --> 00:42:48,280
+وهاد إيش اسمها؟ بدي أدخل السالب جوا يا جماعة أو
+
+487
+00:42:48,280 --> 00:42:56,440
+قبل ما أدخله، هد بيصير فاي فاي of F of X بعد
+
+488
+00:42:56,440 --> 00:43:01,560
+أذنكم، بدي أدخل السالب جوا الـ infimum هتصير إيش ما
+
+489
+00:43:01,560 --> 00:43:06,240
+لها؟ Supremum إذا بيصير هذا زائد وهد بتصير
+
+490
+00:43:06,240 --> 00:43:14,100
+Supremum والسالب بدخل جوا طيب .. عندي الـ Phi F of
+
+491
+00:43:14,100 --> 00:43:19,800
+X والـ Phi F of X للـ X اللي موجودة هنا الـ F of X
+
+492
+00:43:19,800 --> 00:43:25,460
+هدولة من مين جايت؟ من الفترة C و D لأن زي ما قلنا F
+
+493
+00:43:25,460 --> 00:43:30,680
+of A و F of I subset من الجهة اللي هي C و D لذا كل
+
+494
+00:43:30,680 --> 00:43:35,040
+الـ element هنا موجود هنا يعني بمعنى آخر ال .. الـ
+
+495
+00:43:35,040 --> 00:43:38,720
+supreme من اللي هنا اللي هي الـ K عندي الـ absolute
+
+496
+00:43:38,720 --> 00:43:45,400
+value للـ Phi of T أكيد أكبر أو يساوي الـ Phi سالب
+
+497
+00:43:45,400 --> 00:43:51,080
+Phi of T وأصغر أو يساوي الـ Phi of T أو بالسوية
+
+498
+00:43:51,080 --> 00:43:55,280
+حتى أكيد
+
+499
+00:43:55,280 --> 00:43:57,900
+خليني آخذها على خطوتين بتسويها دي؛ لأن الـ
+
+500
+00:43:57,900 --> 00:44:06,260
+absolute value Phi of T أكبر سواء مين؟ سالب الـ Phi
+
+501
+00:44:06,260 --> 00:44:11,300
+of T فبيصير عندي الـ supremum اللي عندي اللي هالة
+
+502
+00:44:11,300 --> 00:44:18,410
+هذا Supremom لهذه أكيد أصغر أو يساوي اللي هو الـ
+
+503
+00:44:18,410 --> 00:44:22,170
+Supremum هذا اللي هو K؛ لأن الـ Supremum هذا عالمين
+
+504
+00:44:22,170 --> 00:44:26,370
+على كل الفترة C و D هنا اللي هي عالمين على X
+
+505
+00:44:26,370 --> 00:44:30,890
+element in XK ناقص واحد وXK؛ لأن هذا Similarly
+
+506
+00:44:30,890 --> 00:44:35,910
+أكيد الـ Supremum للـ Absolute Value هيكون أكبر أو
+
+507
+00:44:35,910 --> 00:44:39,070
+يساوي الـ Supremum لهذه من جهتين أنه Absolute
+
+508
+00:44:39,070 --> 00:44:42,790
+Value وفي نفس الوقت اللي هو المجموع هذه جزئية من
+
+509
+00:44:42,790 --> 00:44:48,380
+اللي فوق إذن ده برضه بيكون أصغر أو يساوي K إذا صار
+
+510
+00:44:48,380 --> 00:44:53,800
+automatic اللي هو هذه زائد هذه أصغر أو يساوي مين؟
+
+511
+00:44:53,800 --> 00:45:01,440
+اتنين K من أي حاجة أصغر أو يساوي اتنين K الآن هذه
+
+512
+00:45:01,440 --> 00:45:06,160
+الـ supremum زائد الـ supremum هذه بس لا يا ش لسانك
+
+513
+00:45:06,160 --> 00:45:11,900
+يا شباب، وهذه K أصغر يساوي K زائد K عشان التلخيص
+
+514
+00:45:11,900 --> 00:45:19,460
+بيصير أشملها اتنين K واضح إذا نخزن التانية اللي هي K
+
+515
+00:45:19,460 --> 00:45:24,480
+element in B بعد إذنكم بيصير عندي الـ MK ناقص بلاش
+
+516
+00:45:24,480 --> 00:45:30,200
+التفاصيل هذه خلصنا منها بيصير عندي الـ MK ناقص MK
+
+517
+00:45:30,200 --> 00:45:37,180
+small أصغر من تلد تلد طبعًا أصغر من مين؟ من اتنين K
+
+518
+00:45:37,180 --> 00:45:43,280
+طبعًا الـ K هنا index الـ K هذه capital هذه الـ K مين؟
+
+519
+00:45:43,280 --> 00:45:48,590
+الـ K اللي فوق هذه هذا الـ K هو الـ index للـ B وهذا
+
+520
+00:45:48,590 --> 00:45:50,690
+الـ K هو الـ index للـ B يعني الـ K هذه ليست إيادة
+
+521
+00:45:50,690 --> 00:45:57,370
+هذه K هي الـ Supremum اللي فوق طيب نجمح
+
+522
+00:45:57,370 --> 00:46:03,190
+معلوماتنا ونبدأ نجمحها الآن ونكون حصلنا على اللي
+
+523
+00:46:03,190 --> 00:46:08,410
+بدهد اتنين K آه لب تلخيص 2K يا شباب لما تشوفوها لب
+
+524
+00:46:08,410 --> 00:46:13,770
+تلخيص 2K الآن وجدت الـ summation على مين؟ على A؟
+
+525
+00:46:13,770 --> 00:46:16,710
+بدي أوجد الـ summation على الـ P باقي الـ indices؛ لأن
+
+526
+00:46:16,710 --> 00:46:21,650
+هالجات بدي أقول لكم ليش بالضيقة الآن إذا صار عندي الـ
+
+527
+00:46:21,650 --> 00:46:29,930
+summation للـ Mk ناقص Mk تلدِى تلدِى في Xk ناقص Xk
+
+528
+00:46:29,930 --> 00:46:40,680
+ناقص واحد K element in B الآن مظبوط أصغر أو يساوي
+
+529
+00:46:40,680 --> 00:46:45,120
+اللي هو 2K برضه على الـ summation هذا الـ summation
+
+530
+00:46:45,120 --> 00:46:53,040
+اللي هو 2K كابيتال كابيتال هذه ما لهاش علاقة بالـ K
+
+531
+00:46:53,040 --> 00:47:00,840
+الـ element in B هنا في XK ناقص XK ناقص 1 أخذت الـ
+
+532
+00:47:00,840 --> 00:47:03,700
+summation على الجهتين على كل الـ K الـ element in B
+
+533
+00:47:06,360 --> 00:47:20,220
+ماشي طيب وين أكتب؟ طيب اتحملوني هلجيت عندي خليني
+
+534
+00:47:20,220 --> 00:47:25,300
+أكتب هنا أشرح أنا شوية بهمش خليني أشرح على ال ..
+
+535
+00:47:25,300 --> 00:47:33,740
+الكلف الـ B، الكلف الـ B احنا من تعريف الكلف الـ B بدي
+
+536
+00:47:33,740 --> 00:47:39,160
+يكون الـ MK ناقص MK أكبر شو مين؟ دلتا صح؟
+
+537
+00:47:39,160 --> 00:47:41,980
+بيصير عندي الآن دلتا يعني أصغر شو؟ MK ناقص M
+
+538
+00:47:41,980 --> 00:47:47,000
+K الـ small A بيسمعوا على الـ دلتا هنا؟ هو أنا
+
+539
+00:47:47,000 --> 00:47:50,920
+على الـ دلتا بيصير هذا إيه شبال، هو واحد، معايا؟
+
+540
+00:47:50,920 --> 00:48:02,180
+فبيصير عندي الآن الـ summation على الواحد XK-XK- XK
+
+541
+00:48:02,180 --> 00:48:07,650
+- XK- XK- XK- XK- XK- XK- XK أصغر أو يساوي MK نقص
+
+542
+00:48:07,650 --> 00:48:13,130
+mk على دلتا ماشي خذ الـ summation للجهتين الـ
+
+543
+00:48:13,130 --> 00:48:19,030
+summation للجهتين XK ناقص XK ناقص واحد وأنا الـ
+
+544
+00:48:19,030 --> 00:48:24,310
+summation XK ناقص XK ناقص واحد K element in b
+
+545
+00:48:24,310 --> 00:48:28,850
+لأن هذا صح للـ B بس لـ K element in B مظبوط ممكن
+
+546
+00:48:28,850 --> 00:48:33,880
+حصلنا على هذا هي اللي موصول وهذا واحد على دلتا
+
+547
+00:48:33,880 --> 00:48:38,720
+طلعها برا في الـ summation اللي عندي هذا ماشي وصلنا
+
+548
+00:48:38,720 --> 00:48:45,620
+لـ هيك إذا الآن صار عندي هذا أصغر أو يساوي واحد على
+
+549
+00:48:45,620 --> 00:48:56,360
+دلتا في مين؟ في الآن هذا اللي هو الـ UPUF طب أنا دي
+
+550
+00:48:56,360 --> 00:49:00,500
+MK وMK آه مش MK تلدِى هذه آه
+
+551
+00:49:03,350 --> 00:49:07,230
+ليش؟ لأنه .. شكروا أن أنا كاتبين هنا MK وMK تلتة
+
+552
+00:49:07,230 --> 00:49:15,130
+لأن هذه الـ A، الـ B، الـ B، الـ K اللي فيها مصنفة
+
+553
+00:49:15,130 --> 00:49:19,530
+على أساس MK اسمه ناقص MK أكبر زي دلتة فبيصير عندي
+
+554
+00:49:19,530 --> 00:49:25,800
+الآن الـ MK ناقص MK اللي هو أكبر أو يساوي دلتا مش
+
+555
+00:49:25,800 --> 00:49:31,520
+دلتا هذه هذه لمين؟ اللي مصنف عليها الـ B اللي هي
+
+556
+00:49:31,520 --> 00:49:35,860
+بالنسبة للـ F هذه مش لـ Alpha Composite F إذا هذا
+
+557
+00:49:35,860 --> 00:49:38,560
+أكبر أو يساوي دلتا على دلتا بيصير أكبر أو يساوي
+
+558
+00:49:38,560 --> 00:49:41,740
+واحد على الـ summation اللي عملناها قبل بشوية أصغر
+
+559
+00:49:41,740 --> 00:49:44,720
+أو يساوي واحد على دلتا في الـ summation هذا الآن
+
+560
+00:49:44,720 --> 00:49:55,810
+.. الآن هذا مين هو؟ هو عبارة عن الـ UP وF مش كله 
+
+561
+00:49:55,810 --> 00:50:01,210
+حتى جزء منه لأن الـ U P و F أيش مال الـ M كده تبعته
+
+562
+00:50:01,210 --> 00:50:08,310
+الـ U P و F أيش هو يا شباب؟ هو عبارة عن الـ summation
+
+563
+00:50:08,310 --> 00:50:14,090
+كي من عند واحد لعند N أو من Zero لعند N من واحد
+
+564
+00:50:14,090 --> 00:50:25,770
+لعند N مظبوط لمين؟ لـ الـ Mك في xk minus xk minus
+
+565
+00:50:25,770 --> 00:50:30,070
+واحد هذا الـ summation على مين؟ على كل الـ case من
+
+566
+00:50:30,070 --> 00:50:35,290
+واحد لعند n بينما هذا الـ summation لمين؟ بس للجزء
+
+567
+00:50:35,290 --> 00:50:39,130
+اللي هو في مين؟ في الـ B فأكيد الـ summation على هذه
+
+568
+00:50:39,130 --> 00:50:44,410
+أظهر أوي ساوي الـ summation على هذه بشيء لأن الـ
+
+569
+00:50:44,410 --> 00:50:48,430
+summation على هذه ناقص هذه برضه بظهر أوي ساوي هذا
+
+570
+00:50:48,430 --> 00:50:55,190
+ناقص هذاليش؟ لأن الـ M K ناقص M نعمل كمية على جهة
+
+571
+00:50:55,190 --> 00:50:59,290
+نعملها
+
+572
+00:50:59,290 --> 00:51:03,690
+.. نعملها
+
+573
+00:51:03,690 --> 00:51:04,770
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+574
+00:51:04,770 --> 00:51:09,950
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+575
+00:51:09,950 --> 00:51:10,210
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+576
+00:51:10,210 --> 00:51:10,270
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+577
+00:51:10,270 --> 00:51:10,410
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+578
+00:51:10,410 --> 00:51:18,420
+.. نعملها .. نعملها .. نعملها ..أيش هيساوي الـ
+
+579
+00:51:18,420 --> 00:51:24,940
+summation للـ mk ناقص mk small في xk minus xk
+
+580
+00:51:24,940 --> 00:51:30,880
+minus واحد هذا k من عند واحد لعند n مظبوط ولا لأ؟
+
+581
+00:51:30,880 --> 00:51:35,360
+الآن أكيد أكيد هذا لأن هذا موجبة وهذا موجبة لأن
+
+582
+00:51:35,360 --> 00:51:42,060
+هذا أكيد أكبر أو يساوي الـ summation لل mk ناقص mk
+
+583
+00:51:43,610 --> 00:51:51,390
+xk-xk-1 k element in B لأن هذوله جزء من هذوله يعني
+
+584
+00:51:51,390 --> 00:51:56,150
+نقصت من الـ summation هذا بعض الـ terms اللي أكبر أو
+
+585
+00:51:56,150 --> 00:51:57,810
+يساوي 0 إذا نقص الـ summation
+
+586
+00:52:12,960 --> 00:52:19,320
+طيب المفروض أن هذا واضح خلينا الآن نتطلع عليه
+
+587
+00:52:19,320 --> 00:52:25,060
+عندي إذا الـ summation لل XK minus XK minus واحد K
+
+588
+00:52:25,060 --> 00:52:30,860
+element بيطلع لي أصغر أو يساوي واحد على دلتا في الـ
+
+589
+00:52:30,860 --> 00:52:39,040
+U ناقص L بس هذا أنا مخزنه لسه عندي الـ U ناقص L اللي
+
+590
+00:52:39,040 --> 00:52:40,940
+هو هذا كله على الـ partition اللي بنشتغل عليه اللي
+
+591
+00:52:40,940 --> 00:52:45,860
+لاجنناه في الأول الـU-L هذه أصغر من مين طلعت أصلاً
+
+592
+00:52:45,860 --> 00:52:48,880
+من دلتة تربيع لأن هذا اعتمدنا عليه على
+
+593
+00:52:48,880 --> 00:52:53,660
+الـ integrability للـ F الأول إذا لازمتني هنا اللي
+
+594
+00:52:53,660 --> 00:52:57,800
+هو هذا أصغر من دلتة تربيع في واحد على دلتة بيصير
+
+595
+00:52:57,800 --> 00:53:04,160
+أصغر من مين؟ من دلتة وهذا كله في ضوء الـ Delta اللي
+
+596
+00:53:04,160 --> 00:53:08,060
+أنا بدأت فيها أصغر من مين أو أثبتتها أصغر من
+
+597
+00:53:08,060 --> 00:53:11,860
+Epsilon إبراهيم اللي وجهتها أصغر من Epsilon
+
+598
+00:53:11,860 --> 00:53:16,340
+إبراهيم إذا صار عندي الـ summation هذا أصغر من Ash
+
+599
+00:53:16,340 --> 00:53:22,280
+من Epsilon إبراهيم لمين؟ لل K اللي Ash في B إذا
+
+600
+00:53:22,280 --> 00:53:25,340
+اللي وصلت إليه الآن الـ summation
+
+601
+00:53:28,540 --> 00:53:32,980
+الـ summation اللي وصلت إليه الـ summation للـ xk
+
+602
+00:53:32,980 --> 00:53:41,600
+ناقص xk minus 1 k element in B أصغر من إبسلون
+
+603
+00:53:41,600 --> 00:53:46,920
+إبراهيم الآن
+
+604
+00:53:46,920 --> 00:53:53,760
+بس إحنا أثبتنا إن الـ summation هذا أيه أصغر أو
+
+605
+00:53:53,760 --> 00:54:00,430
+يساوي 2k اتنين كيف الـ summation هذا مظبوط بدي أعوض
+
+606
+00:54:00,430 --> 00:54:06,850
+الآن أشيل هذا بيصير عندي هاي شايفين يا شباب هاي
+
+607
+00:54:06,850 --> 00:54:14,070
+عند الـ summation هذا أثبته أنه أصغر أو يساوي اللي
+
+608
+00:54:14,070 --> 00:54:24,580
+هو epsilon prime واضح ومن أربعة بيصير عندي بعوض الـ
+
+609
+00:54:24,580 --> 00:54:28,980
+summation أصغر من 2 كيف الـ summation اللي أثبتناه
+
+610
+00:54:28,980 --> 00:54:34,840
+بحيته بس قبل شوية الـ summation أصغر من 2 كيف الـ
+
+611
+00:54:34,840 --> 00:54:40,140
+summation بشيل هذا اللي هو هذا وأقول أصغر من مين
+
+612
+00:54:40,140 --> 00:54:43,760
+من epsilon prime بيصير هذا المقدار اللي هو هذا الـ
+
+613
+00:54:43,760 --> 00:54:45,680
+summation هيه
+
+614
+00:54:47,550 --> 00:54:54,290
+هيو هذا هيو أصغر من من 2k في ash في الـ epsilon
+
+615
+00:54:54,290 --> 00:55:00,110
+prime إذا طلع عندي الجزء الثاني summation خلصنا من
+
+616
+00:55:00,110 --> 00:55:07,610
+هذا صار عندي الجزء الثاني اللي أثبته summation للـ
+
+617
+00:55:07,610 --> 00:55:19,240
+mk تلدى ناقص mk تلدى في xk-xk-1 k element in B أصغر
+
+618
+00:55:19,240 --> 00:55:26,980
+من مين طلع من epsilon prime في 2k ابسلون برايم في
+
+619
+00:55:26,980 --> 00:55:36,650
+2k الآن خلصنا احسبولي إذا احنا لقينا الـ partition B
+
+620
+00:55:36,650 --> 00:55:44,330
+لكل option أكبر من 0 لقينا B بحيث أنه U B of I
+
+621
+00:55:44,330 --> 00:55:54,210
+composite F ناقص الـ B of I composite F هذا أيش ماله
+
+622
+00:55:54,210 --> 00:55:59,310
+بيساوي اللي هو الـ summation اللي هيضع على كل الـ K
+
+623
+00:55:59,310 --> 00:56:02,390
+و الـ summation اللي هيضع على كل الـ K و الـ K
+
+624
+00:56:02,390 --> 00:56:05,910
+جزّانها لجزين أيش في الـ A وايش في الـ B إذا
+
+625
+00:56:05,910 --> 00:56:14,110
+بيساوي اللي هو الـ summation لـ الـ A الـ MK ناقص
+
+626
+00:56:14,110 --> 00:56:23,140
+MK تلدة تلدة في xk-xk-1 k من واحد لعند n صح ولا لأ
+
+627
+00:56:23,140 --> 00:56:28,220
+اه طبعاً هو التعريف هذا اللي هو بيثاوي الآن الـ K
+
+628
+00:56:28,220 --> 00:56:32,460
+اللي عندك جزّالت لجزين واحد في الـ A واحد في مين؟
+
+629
+00:56:32,460 --> 00:56:37,080
+في الـ B، إذن هذا الـ summation الكل بيساوي الـ
+
+630
+00:56:37,080 --> 00:56:41,340
+summation على K في الـ A زائد الـ summation نفسه
+
+631
+00:56:41,340 --> 00:56:45,720
+على K وين ماله؟ في الـ B الـ summation لمين؟ لهذه
+
+632
+00:56:45,720 --> 00:56:53,280
+اللي هي MK تلد ناقص MK تلد small في XK minus XK
+
+633
+00:56:53,280 --> 00:57:01,450
+minus واحد زائد MKتلدة ناقص mk small في xk minus
+
+634
+00:57:01,450 --> 00:57:08,990
+xk minus واحد اه طيب يعني الآن هذا الـ U وهذا الـ L
+
+635
+00:57:08,990 --> 00:57:12,030
+صار بيساوي هذا الجزء وهذا الجزء وهذا السبب أصلاً
+
+636
+00:57:12,030 --> 00:57:17,590
+اللي خلّانه أجزء هذا طلع لي الآن مين هو؟ طلع لي أصغر
+
+637
+00:57:17,590 --> 00:57:22,970
+من epsilon prime أصغر من epsilon prime في b minus
+
+638
+00:57:22,970 --> 00:57:32,330
+a والتاني طلع أصغر من E' في 2K E' في 2K يعني هدول
+
+639
+00:57:32,330 --> 00:57:40,140
+الاثنين مع بعض أيش بيساون؟ بيساون E' فيه 2k بيزاق
+
+640
+00:57:40,140 --> 00:57:56,220
+بيزاق بيزاق بيزاق بيزاق بيزاق بيزاق
+
+641
+00:57:56,310 --> 00:58:04,950
+على b minus a زي اتنين k في اتنين k زي b minus a
+
+642
+00:58:04,950 --> 00:58:10,030
+وهذه بتروح مع حد بيساوي أيش؟ ابسلون إذا اللي وصلت له
+
+643
+00:58:11,120 --> 00:58:17,600
+لكل إبسلون أكبر من صفر لكل
+
+644
+00:58:17,600 --> 00:58:22,480
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+645
+00:58:22,480 --> 00:58:25,660
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+646
+00:58:25,660 --> 00:58:27,320
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+647
+00:58:27,320 --> 00:58:28,360
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+648
+00:58:28,360 --> 00:58:32,200
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+649
+00:58:32,200 --> 00:58:34,180
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+650
+00:58:34,180 --> 00:58:36,880
+إبسلون أكبر من صفر لكل إبسلون أكبر من صفر لكل
+
+651
+00:58:36,880 --> 00:58:47,340
+إبسلون أكبر من صفر طيب الآن نيجي بدنا اللي هو نأخذ
+
+652
+00:58:47,340 --> 00:58:55,660
+اللي هو تطبيقات على هذه النظرية ونشوف
+
+653
+00:58:55,660 --> 00:59:02,600
+كيف بدنا نطبق هذه النظرية للوصول إلى نتاج أخرى
+
+654
+00:59:02,600 --> 00:59:09,280
+تتعلق بخواص التكامل أو بخواص تكامل لريمان لأن
+
+655
+00:59:09,280 --> 00:59:15,300
+عرفنا وجاوبنا على اللي هو المجموع وعلى حسب ضرب K
+
+656
+00:59:15,300 --> 00:59:20,100
+في الـ .. في الـ F ولقينا على الـ composition وتحت أي
+
+657
+00:59:20,100 --> 00:59:24,360
+ضارف كان F I composite F is integrable الآن نكمل
+
+658
+00:59:24,360 --> 00:59:30,120
+اللي هو نأخذ اللي هو الـ corollary اللي عندي اللي
+
+659
+00:59:30,120 --> 00:59:39,150
+هي بتقولي اللي هي من تلت فروع لو كانت I عبارة عن
+
+660
+00:59:39,150 --> 00:59:43,990
+الـ closed interval A و B و F من I لعند R is
+
+661
+00:59:43,990 --> 00:59:47,370
+integrable on I then the absolute value of a
+
+662
+00:59:47,370 --> 00:59:50,630
+function F obtained by the absolute value is
+
+663
+00:59:50,630 --> 00:59:54,410
+integrable on I والـ absolute value of integration
+
+664
+00:59:54,410 --> 00:59:56,470
+أصغر يساوي الـ integration للـ absolute value للـ
+
+665
+00:59:56,470 --> 01:00:02,810
+F اللي هي أصغر يساوي K K في الـ B minus A حيث الـ K
+
+666
+01:00:02,810 --> 01:00:06,750
+هذه من أين جاية؟ هي الـ bound لل F of X لأن F is
+
+667
+01:00:06,750 --> 01:00:12,260
+integrable إذا أكيد bounded فن element in F يعني
+
+668
+01:00:12,260 --> 01:00:15,280
+اللي بتقولي هذا باختصار ده كانت F is integrable الـ
+
+669
+01:00:15,280 --> 01:00:18,100
+absolute value لل F أيش ما لها؟ integrable والـ
+
+670
+01:00:18,100 --> 01:00:20,160
+absolute value لل integration أصغر سوى الـ
+
+671
+01:00:20,160 --> 01:00:22,860
+integration لل absolute value أصغر سوى K اللي هي
+
+672
+01:00:22,860 --> 01:00:26,580
+ال maximum لل أو خليني أقول الـ bound لل F of X
+
+673
+01:00:26,580 --> 01:00:31,080
+absolute value ل F of X في B minus A الجزء الثاني
+
+674
+01:00:31,080 --> 01:00:35,460
+اللي هو هتطلع لي برضه الـ Fn is integrable لأن Fn
+
+675
+01:00:35,460 --> 01:00:41,560
+هو إنتجر
+
+676
+01:00:42,100 --> 01:00:46,780
+الآن إذا كان الشغل الثاني إذا كان فيه Delta بحيث
+
+677
+01:00:46,780 --> 01:00:50,400
+أن F of X أكبر يساوي Delta يعني F of X أكبر أو
+
+678
+01:00:50,400 --> 01:00:53,900
+يساوي Delta أكبر يساوي Delta ليش؟ على أساس إنه
+
+679
+01:00:53,900 --> 01:00:58,140
+يضمن مقلوب هيكون bounded بيصير 1 على F of X أصغر
+
+680
+01:00:58,140 --> 01:01:00,680
+أو يساوي 1 على Delta يعني بمعنى أكثر F is bounded
+
+681
+01:01:00,680 --> 01:01:04,720
+إذن بحقله يحكي عن ال Integrability لـ 1 على F ويقول
+
+682
+01:01:04,720 --> 01:01:07,780
+لي تحت الظرف هذا لو كانت F of X أكبر يساوي Delta
+
+683
+01:01:08,470 --> 01:01:12,210
+و Delta أكبر من 0 هيكون 1 على الـ F أيش ماله؟ is
+
+684
+01:01:12,210 --> 01:01:15,830
+integrable on I خليني أترجح واحدة واحدة اللي
+
+685
+01:01:15,830 --> 01:01:24,690
+عنها الـ gate F عندي من I لعين بR is integrable إذا
+
+686
+01:01:24,690 --> 01:01:29,350
+there exists K اللي هو أكبر من 0 such that
+
+687
+01:01:29,350 --> 01:01:33,330
+absolute value of F of X أصغر أو يساوي أيش؟ K مدام
+
+688
+01:01:33,330 --> 01:01:36,430
+أن تقرأ بالـ F إذا أكيد is bounded إذا الـ absolute
+
+689
+01:01:36,430 --> 01:01:43,030
+value of X أصغر أو يساوي الـ K طيب الآن يا جماعة
+
+690
+01:01:43,030 --> 01:01:47,230
+عندي هاد الـ corollary أصلاً اللي جابله بدي أظبط لي
+
+691
+01:01:47,230 --> 01:01:54,070
+two functions بدي أعرف الآن صارت عند الـ F of I الـ
+
+692
+01:01:54,070 --> 01:02:00,230
+F of I صارت الـ F of I أكيد subset بين نقص K ومين؟
+
+693
+01:02:00,230 --> 01:02:01,210
+أو K
+
+694
+01:02:07,180 --> 01:02:19,960
+طيب يعني الآن لو جيت عرفت Phi من اللي هو عنده ناقص
+
+695
+01:02:19,960 --> 01:02:27,990
+K لعند الـ K لعند الـ R عرفتها على أساس فاي ما هو
+
+696
+01:02:27,990 --> 01:02:30,950
+absolute value إذا مضحكت تجيب الـ absolute value
+
+697
+01:02:30,950 --> 01:02:38,250
+فاي of T بيساوي absolute value لمين؟ لل T ماشي الحال
+
+698
+01:02:38,250 --> 01:02:42,430
+هي الدلال عندي أكيد الـ absolute value أيش ما لها؟
+
+699
+01:02:42,430 --> 01:02:47,370
+is continuous مدام الـ absolute value الفاي is
+
+700
+01:02:47,370 --> 01:02:52,870
+continuous و الـ F معطيله إيها integrable أيضا by 
+
+701
+01:02:52,870 --> 01:03:00,670
+the above theorem, Φ composite F is integrable, Φ
+
+702
+01:03:00,670 --> 01:03:07,610
+composite F of T يساوي Φ of F of T اللي هي 
+
+703
+01:03:07,610 --> 01:03:12,330
+بتساوي إيش؟ 1 absolute value Φ of T بتساوي
+
+704
+01:03:12,330 --> 01:03:17,490
+absolute value لمين؟ للـ F of T إذاً عندي
+
+705
+01:03:17,490 --> 01:03:23,460
+absolute value للـ F is integrable, إذاً مدامة Φ
+
+706
+01:03:23,460 --> 01:03:27,460
+is continuous و F integrable لأن حسب النظرية Φ 
+
+707
+01:03:27,460 --> 01:03:30,640
+composite F is integrable و Φ composite F هي
+
+708
+01:03:30,640 --> 01:03:33,400
+طلعت من الـ absolute value للـ F طبعاً Φ
+
+709
+01:03:33,400 --> 01:03:36,880
+composite F من وين هتشتغل؟ من عند اللي هي ال
+
+710
+01:03:36,880 --> 01:03:42,920
+interval I لعند مين؟ لعند R لأن Φ اللي هو F of T 
+
+711
+01:03:42,920 --> 01:03:49,980
+هيجي يقعد في الفترة هذه و Φ هترسل اللي بيجي لوين؟
+
+712
+01:03:49,980 --> 01:03:55,250
+لعند I. ما ضحك ها طيب الآن عندي بدي أثبت أن ال
+
+713
+01:03:55,250 --> 01:03:58,590
+integration ال absolute value لل integration أصغر
+
+714
+01:03:58,590 --> 01:04:01,350
+ساوي ال integration لـ absolute value هذه صارت
+
+715
+01:04:01,350 --> 01:04:07,670
+بعضها معلومات صادقة اللي هو عندي ال F أكبر أو يساوي
+
+716
+01:04:07,670 --> 01:04:11,610
+اللي هي absolute value لل F بالسالب و أصغر أو يساوي
+
+717
+01:04:11,610 --> 01:04:14,790
+ال absolute value للـ F. صارت الآن احنا أتبعت
+
+718
+01:04:14,790 --> 01:04:17,990
+أن ال absolute value is integrable. إذاً الآن بما أن
+
+719
+01:04:17,990 --> 01:04:21,270
+F بين هذولة الدالتين حسب نظرية أخدناها المرة
+
+720
+01:04:21,270 --> 01:04:24,910
+الماضية أو remark, إذا بيصير ال integration لل
+
+721
+01:04:24,910 --> 01:04:28,590
+absolute value لل F من A ل B أصغر أو يساوي ال
+
+722
+01:04:28,590 --> 01:04:32,330
+integration لل F من A ل B أصغر أو يساوي ال
+
+723
+01:04:32,330 --> 01:04:38,190
+integration لل F من A ل B. وهذا إيش معناته؟ هذا
+
+724
+01:04:38,190 --> 01:04:43,610
+معناته إذا ال absolute value لل integration لل F 
+
+725
+01:04:43,610 --> 01:04:49,150
+من A ل B أصغر أو يساوي اللي هو ال integration لأبسل
+
+726
+01:04:49,150 --> 01:04:57,690
+و لأ للـ F من A ل B. ماشي الحال و طبيعي عندي هذه
+
+727
+01:04:57,690 --> 01:05:02,270
+أثبتناها بهذه و طبيعي مدام عندنا لسه ما 
+
+728
+01:05:07,890 --> 01:05:12,470
+أو ملاحظة سابقة، لبس ال integration من a ل b، لبس ال
+
+729
+01:05:12,470 --> 01:05:18,070
+value of F of x أصغر أو يساوي اللي هو من K في طول 
+
+730
+01:05:18,070 --> 01:05:27,050
+الفترة بـ-a. مع هذه together بنحصل على اللي هو
+
+731
+01:05:27,050 --> 01:05:30,750
+المطلوب، ال absolute value لل integration أصغر أو يساوي
+
+732
+01:05:30,750 --> 01:05:34,690
+ال integration لل absolute value أصغر أو يساوي K في ال
+
+733
+01:05:34,690 --> 01:05:39,510
+B minus A. هذه اللي هو الجزء الأول من ال corollary.
+
+734
+01:05:39,510 --> 01:05:44,310
+خلينا نشوف الجزء الثاني من ال corollary برضه اللي
+
+735
+01:05:44,310 --> 01:05:51,270
+هو برهانه سهل و برهانه اللي هو مشابه للمنطق اللي 
+
+736
+01:05:51,270 --> 01:05:57,070
+حكيناها عندنا قبل بشوية. طيب صلى الله علينا يا عزيزي
+
+737
+01:05:57,070 --> 01:06:01,410
+عليه الصلاة والسلام. الآن يا شباب عندي اللي هو
+
+738
+01:06:01,410 --> 01:06:05,110
+الجزء الثاني، بدنا نثبت أن الـ F أس N is integrable
+
+739
+01:06:05,110 --> 01:06:09,110
+في حالة الـ F integrable لأن أكيد شكلنا بدنا نيجي 
+
+740
+01:06:09,110 --> 01:06:16,950
+عند الـ F من I لعند R is integrable. الآن عندي اللي
+
+741
+01:06:16,950 --> 01:06:21,470
+هو .. بدي أسأل أن أثبت أنها Integrable. فلو جيت أنا
+
+742
+01:06:21,470 --> 01:06:30,170
+عرفت F, F أو اللي هو Φ function من اللي هو domain 
+
+743
+01:06:30,170 --> 01:06:35,150
+اللي هو F of I من اللي هو range لل F, range لل F
+
+744
+01:06:35,150 --> 01:06:45,640
+range لل F لعند ال R بحيث أن أقول Φ of T يساوي T
+
+745
+01:06:45,640 --> 01:06:51,120
+أس N. five of T إيش بيساوي؟ بيساوي T أس N أو 
+
+746
+01:06:51,120 --> 01:06:54,180
+إذا كان بدك اللي هو بدك إيش تكون ال range ل F خلاص
+
+747
+01:06:54,180 --> 01:06:57,460
+من عارفها من وين؟ من اللي من اللي قبل بشوية من ناقص 
+
+748
+01:06:57,460 --> 01:07:01,980
+K لعند K. عارفين ليه؟ لأن ال absolute value لل F of
+
+749
+01:07:01,980 --> 01:07:06,840
+X أصغر مش هو ال K؟ إذاً أكيد لما ترمي ال F of X 
+
+750
+01:07:06,840 --> 01:07:11,410
+هتكون ترمي في الفترة من ناقص K لعند K أو subset
+
+751
+01:07:11,410 --> 01:07:15,970
+بيصير الـ F of I subset من ناقص K و K. إذاً صارت
+
+752
+01:07:15,970 --> 01:07:22,510
+الـ Φ composite F, Φ composite F is defined من
+
+753
+01:07:22,510 --> 01:07:31,140
+I لعند ال R وعندي Φ composite F of T يساوي Φ
+
+754
+01:07:31,140 --> 01:07:37,200
+of F of T ويساوي F of T اللي هو Φ of T يساوي T
+
+755
+01:07:37,200 --> 01:07:41,560
+أس N. بيصير Φ of F of T اللي هي عبارة عن F of T
+
+756
+01:07:41,560 --> 01:07:48,540
+يا جماعة أس N. الآن كل الأمور طيبة ومنيحة. ليش؟
+
+757
+01:07:48,540 --> 01:07:53,260
+ووصلنا كمان عندي F integrable و F continuous
+
+758
+01:07:53,260 --> 01:07:57,420
+هتتدللوا الـ C شمالها اللي هو الـ T أس N is
+
+759
+01:07:57,420 --> 01:08:03,540
+continuous اللي جزء من البلونوميال. بيصير عندي F I
+
+760
+01:08:03,540 --> 01:08:06,660
+is continuous و F integrable. لذلك حسب النظرية اللي 
+
+761
+01:08:06,660 --> 01:08:10,680
+قبل بشوية، إيش هيطلع عندي؟ F I composite F is 
+
+762
+01:08:10,680 --> 01:08:16,440
+integrable بمعنى أن F أس N is integrable. فكرة معادلة
+
+763
+01:08:16,440 --> 01:08:22,570
+أصلها أنه سنة يعني اللي هو الأمور واضحة الآن. ضال
+
+764
+01:08:22,570 --> 01:08:30,190
+عند مين؟ اللي هو الـ .. الـ .. الـ .. الـ .. نثبت الجزء 
+
+765
+01:08:30,190 --> 01:08:36,010
+الثالث من ال corollary اللي هي بدنا نثبت أنه لو 
+
+766
+01:08:36,010 --> 01:08:43,490
+كانت ال F of X أكبر أو يساوي واحد على دلتا اللي هي 
+
+767
+01:08:43,490 --> 01:08:47,530
+for every x element in I وعندي there exists دلتا 
+
+768
+01:08:47,530 --> 01:08:52,390
+كمان وصفر ساشرات. إذا كان هذا متحقق إذن هتطلع عندي
+
+769
+01:08:52,390 --> 01:08:55,970
+اللي هي الواحد على ال F, بيدثبت أن الواحد على ال F
+
+770
+01:08:55,970 --> 01:08:58,950
+إيش is integrable. بدنا نعمل .. نجيب continuous 
+
+771
+01:08:58,950 --> 01:09:02,890
+function. أكيد كل جمجال نجيب مقلوبة دالة يعني في حوض 
+
+772
+01:09:02,890 --> 01:09:09,800
+five من ناقص K لعند K لعند R وخد Φ, عارفين ما هو
+
+773
+01:09:09,800 --> 01:09:13,000
+ال scale كده. سبب اللي قلت قبل شوية Φ دي إيش
+
+774
+01:09:13,000 --> 01:09:17,600
+متساوي؟ أكيد كلكم حيقول واحد على T. ماشي الحال، واحد 
+
+775
+01:09:17,600 --> 01:09:26,180
+على T بس اه لأ، عدم ديش أقدر أعمل hand أفععل عشان
+
+776
+01:09:26,180 --> 01:09:31,250
+مانبدعش في السفرة يا شباب. خدوها من عند Delta لعند 
+
+777
+01:09:31,250 --> 01:09:36,470
+مين؟ لعند K. ليش .. ليش .. ليش اللي هو عكيفك؟ أه F
+
+778
+01:09:36,470 --> 01:09:40,670
+of X اللي هو absolute value أصغر أو تساوي K يعني F 
+
+779
+01:09:40,670 --> 01:09:46,160
+of X أصغر أو تساوي K وأكبر أو تساوي ناقص K. و أثناء هذه
+
+780
+01:09:46,160 --> 01:10:12,580
+أكيد ما عطينيها أكبر شو مين Delta 
+
+781
+01:10:14,710 --> 01:10:21,230
+اللي هو .. إيه الكلام هذا؟ مشروع هو بيصير عنده ..
+
+782
+01:10:21,230 --> 01:10:24,170
+اللي هو Φ of T يساوي واحدة على T ما فيش أي مشكلة،
+
+783
+01:10:24,170 --> 01:10:27,470
+ما فيش مشاكل أسفار، ما فيش مشاكل كده، إذا صارت ده
+
+784
+01:10:27,470 --> 01:10:31,490
+اللي إيش مالها؟ continuous. continuous. هفهم إن فهمت
+
+785
+01:10:31,490 --> 01:10:34,810
+القصة، Φ composite of F continuous و integrable
+
+786
+01:10:34,810 --> 01:10:38,310
+إذا كلها على بعضها integrable. يعني Φ of T بتصير
+
+787
+01:10:38,310 --> 01:10:44,750
+Φ of F of T يعني بتساوي واحد على F of T. يعني صارت 
+
+788
+01:10:44,750 --> 01:10:51,650
+الدالة واحد على F is integrable. وهك
+
+789
+01:10:51,650 --> 01:10:55,670
+مكون، احنا خلصنا اللي هو ال corollary. ضال عندي الآن 
+
+790
+01:10:55,670 --> 01:11:01,570
+نجاوب على السؤال الثاني، هل حاصل ضرب ضرب دالتين 
+
+791
+01:11:01,570 --> 01:11:06,650
+integrable is integrable؟ بنقول اه integrable يعني
+
+792
+01:11:06,650 --> 01:11:11,380
+بمعنى آخر بقول ليه النظرية اللي هي اللي بعدها 7,2,7
+
+793
+01:11:11,380 --> 01:11:18,020
+بتقول ما يلي، بتقول لو كانت F و G integrable يعني
+
+794
+01:11:18,020 --> 01:11:25,480
+لو كان عندي خليني أكتب بالأصفر أفضل F و G من I
+
+795
+01:11:25,480 --> 01:11:33,700
+لعند R كانت integrable functions بيعطيني هذا أن FG
+
+796
+01:11:33,700 --> 01:11:42,500
+من I لعند R برضه إيش ماله؟ Integrable Function. الـ 
+
+797
+01:11:42,500 --> 01:11:46,740
+L صار إن حصيلة من المعلومات بتسهل علي الوصول
+
+798
+01:11:46,740 --> 01:11:53,820
+للنتيجة و Proof. و Proof بما أن F is Integrable إذن
+
+799
+01:11:53,820 --> 01:11:57,700
+فال Corollary اللي قبل بشوية أكيد F تربيع اللي هي
+
+800
+01:11:57,700 --> 01:12:01,040
+Integrable و G Integrable من النظرية اللي قبل
+
+801
+01:12:01,040 --> 01:12:04,940
+بشوية و Corollary برضه شمالها G تربيع برضه
+
+802
+01:12:04,940 --> 01:12:10,060
+Integrable صح ولا لا يا جماعة؟ صح. طيب F تربيع 
+
+803
+01:12:10,060 --> 01:12:14,260
+Integrable و G تربيع Integrable و برضه من نظرية
+
+804
+01:12:14,260 --> 01:12:18,580
+سابقة مدام F و G Integrable إذا F زائد G برضه إيش؟
+
+805
+01:12:18,580 --> 01:12:24,980
+Integrable. لأ F زائد G تربيع Integrable كمان لأن F
+
+806
+01:12:24,980 --> 01:12:27,800
+و G Integrable أدت ل F زائد G Integrable و F زائد 
+
+807
+01:12:27,800 --> 01:12:31,640
+G Integrable أدت من القرول اللي قبل شوية أنه تربيعه
+
+808
+01:12:31,640 --> 01:12:40,520
+يكون إيش؟ Integrable. طيب خلصنا إذا إذا F تربيع زائد 
+
+809
+01:12:40,520 --> 01:12:49,780
+G تربيع is integrable صح؟ مظبوط وناقص F تربيع 
+
+810
+01:12:49,780 --> 01:12:54,220
+وناقص G تربيع برضه integrable مظبوط برضه لأن اللي
+
+811
+01:12:54,220 --> 01:13:00,060
+هو عندي اللي هو ثابت في هذه integrable و ثابت في
+
+812
+01:13:00,060 --> 01:13:03,560
+ال integrable integrable ومجموع انصار انتجرابل إذاً
+
+813
+01:13:03,560 --> 01:13:09,020
+انصار هذا integrable زائد F زائد G لكل تربيع هذه 
+
+814
+01:13:09,020 --> 01:13:12,980
+integrable وهذه integrable وهذه integrable مجموحين
+
+815
+01:13:12,980 --> 01:13:17,520
+هذا إيش بيساويهذا .. هذا integrable و هذا
+
+816
+01:13:17,520 --> 01:13:19,860
+integrable و هذا integrable إذاً المجموع integrable
+
+817
+01:13:19,860 --> 01:13:23,220
+إذاً هذا كله على بعض integrable. طب هذا مين هو؟ هذا
+
+818
+01:13:23,220 --> 01:13:29,160
+عبارة عن F تربيع زائد G تربيع ناقص اللي هو إيش؟ زائد
+
+819
+01:13:29,160 --> 01:13:35,760
+2FG بيصير عبارة عن 2F main G. صارت 2FG integrable.
+
+820
+01:13:35,760 --> 01:13:40,840
+طب لو جينا قولنا خل نص هنا يعني ضربنا ثابت في 
+
+821
+01:13:40,840 --> 01:13:43,960
+integrable إذاً هيطلع اللي هو كله integrable إذاً FG 
+
+822
+01:13:43,960 --> 01:13:48,520
+إيش مالها؟ is integrable. صار عندي الآن FG
+
+823
+01:13:48,520 --> 01:13:54,040
+integrable تابعا لأن F تربيع و G تربيع و F زائد G
+
+824
+01:13:54,040 --> 01:13:59,860
+كل تربيع حاصل جمعهم و ضرب النص في هنا ثابت و بيطلع 
+
+825
+01:13:59,860 --> 01:14:04,720
+عبارة عن integrable function. نيجي لآخر اللي هو
+
+826
+01:14:04,720 --> 01:14:11,850
+نقطة في الفي الـ .. في الـ .. في الـ section 7-2 اللي
+
+827
+01:14:11,850 --> 01:14:14,790
+هو السؤال اللي سألناه في الأول، قولنا لو كانت F is
+
+828
+01:14:14,790 --> 01:14:19,570
+integrable function و Φ is integrable هل Φ
+
+829
+01:14:19,570 --> 01:14:24,310
+composite F is integrable؟ قولنا أكيد هو لو .. في
+
+830
+01:14:24,310 --> 01:14:28,430
+البداية قولنا أن Φ composite F need not to be 
+
+831
+01:14:28,430 --> 01:14:32,280
+integrable. إذاً the composition of two integrable 
+
+832
+01:14:32,280 --> 01:14:35,720
+functions need not to be integrable يعني هذا إعلان
+
+833
+01:14:35,720 --> 01:14:38,340
+the composition of two integrable functions need
+
+834
+01:14:38,340 --> 01:14:42,420
+not to be integrable but if phi the first one is
+
+835
+01:14:42,420 --> 01:14:46,340
+continuous then phi composite of f is integrable
+
+836
+01:14:46,340 --> 01:14:50,620
+كما شفنا في العقل اللي هو النظرية الأولى. طيب نيجي
+
+837
+01:14:50,620 --> 01:14:53,000
+الآن المثال الأخير بيقولنا يا جماعة the 
+
+838
+01:14:53,000 --> 01:14:55,760
+composition of integrable functions need not to be
+
+839
+01:14:55,760 --> 01:14:59,540
+integrable. في عندي سؤالين أصلاً معاكم homework
+
+840
+01:14:59,540 --> 01:15:03,860
+السؤال الأول بيقول لنا لو كانت F of x بتساوي واحد 
+
+841
+01:15:03,860 --> 01:15:07,540
+ده كانت x بتساوي صفر و zero ده كانت x is 
+
+842
+01:15:07,540 --> 01:15:11,760
+irrational و كانت f of x بتساوي واحد لما x بيساوي 
+
+843
+01:15:11,760 --> 01:15:16,160
+m على n حيث الـ m و الـ n عبارة عن integers و العامل
+
+844
+01:15:16,160 --> 01:15:19,740
+المشترك الأعلى بينهم  بيساوي واحد
+
+845
+01:15:19,740 --> 01:15:23,540
+يعني شيلنا كل العامل المشترك اللي بينهم و كتبنا x
+
+846
+01:15:23,540 --> 01:15:28,900
+بتساوي m على n طيب، هذه عبارة عن دالة معرفة من الـ 0
+
+847
+01:15:28,900 --> 01:15:32,460
+والـ 1 لعند الـ R يعني هذي X is rational well في
+
+848
+01:15:32,460 --> 01:15:36,320
+الفترة 0 و1 و X بيبقى بيساوي M على N يعني rational
+
+849
+01:15:36,320 --> 01:15:41,260
+في الفترة 0 و1 وفرضنا للـ X بتساوي صفر قيمته إيش
+
+850
+01:15:41,260 --> 01:15:48,070
+بتساوي؟ بتساوي 1 هذي الآن by exercise 7.1.11 مطلوب
+
+851
+01:15:48,070 --> 01:15:51,790
+منك أنك تثبت أن F is integrable on I
+
+852
+01:15:51,790 --> 01:15:55,070
+ويوم ما تعرفوش تحلوه إن شاء الله بنحلوه و بنصوره 
+
+853
+01:15:55,070 --> 01:16:00,030
+بإذن الله الآن السؤال الثاني اللي هعتمد عليه برضه 
+
+854
+01:16:00,030 --> 01:16:03,170
+أنه الـ function الثاني اللي هي G من I لعند R هذه
+
+855
+01:16:03,170 --> 01:16:07,790
+سهلة أصلا لإثباتها be defined by G of X step
+
+856
+01:16:07,790 --> 01:16:12,090
+function بسيطة يعني أو خلّيني أقول فيها jump و بس 
+
+857
+01:16:12,090 --> 01:16:17,030
+jump على نقطة بس جيوب x بتساوي 0 إذا كانت x بتساوي 
+
+858
+01:16:17,030 --> 01:16:21,410
+0 و بتساوي 1 إذا كانت x في الفترة من 0 لعند 1 اللي
+
+859
+01:16:21,410 --> 01:16:25,410
+هو a closed عند الواحد يعني الآن هذا الـ function
+
+860
+01:16:25,410 --> 01:16:29,110
+بيقول لي برضه في الـ exercise مطلوب برضه في exercise
+
+861
+01:16:29,110 --> 01:16:33,090
+717 برضه اللي هو homework معكم في الـ exercise
+
+862
+01:16:33,090 --> 01:16:36,270
+بيقول لك اثبت أن g إيش معناها is integrable function
+
+863
+01:16:36,920 --> 01:16:40,960
+إذا الـ F والـ G عبارة عن two integrable functions
+
+864
+01:16:40,960 --> 01:16:46,780
+two integrable functions هاي الـ F من I لعند R والـ 
+
+865
+01:16:46,780 --> 01:16:55,200
+G اللي هو من عند I لعند R لاحظ أن الـ G فيه لغة
+
+866
+01:16:55,200 --> 01:17:00,600
+ثانية zero لمين يا واحد عندي هذه فئلها الـ 1 و 0 و
+
+867
+01:17:00,600 --> 01:17:06,800
+في عندنا قيم أخرى اللي هو كثيرة طيب، الآن عندي ..
+
+868
+01:17:06,800 --> 01:17:09,660
+لو جيت حسبت الـ G composed of F مش غريبة عليكم
+
+869
+01:17:09,660 --> 01:17:14,480
+الدالة هذه G composed of F of X خلينا نحسبها مع 
+
+870
+01:17:14,480 --> 01:17:20,860
+بعض و بنقول خلصنا اللي هو S section أو قولنا أن
+
+871
+01:17:20,860 --> 01:17:24,320
+الـ G composed of F هذه اللي أنتم بتعرفوها أن هي 
+
+872
+01:17:24,320 --> 01:17:36,430
+is not integrable جي كومبوزيت F of اللي هو عندي
+
+873
+01:17:36,430 --> 01:17:46,900
+الـ جي الـ F of X هيها لأخد جي of اللي هو Zero بتساوي
+
+874
+01:17:46,900 --> 01:17:55,920
+g of f of 0 بتساوي g of f of 0 بتساوي 
+
+875
+01:17:55,920 --> 01:17:57,880
+g of f of 0 بتساوي g of f of 0 بتساوي g of f of 0
+
+876
+01:17:57,880 --> 01:18:06,220
+بتساوي g of f of 0 بتساوي g of f of 0 بتساوي g of f 
+
+877
+01:18:06,220 --> 01:18:07,060
+of 0 بتساوي g of f of 0 بتساوي g of f of 0 بتساوي g
+
+878
+01:18:07,060 --> 01:18:07,140
+of f of 0 بتساوي g of f of 0 بتساوي g of f of 0
+
+879
+01:18:07,140 --> 01:18:08,100
+بتساوي g of f of 0 بتساوي g of f of 0 بتساوي g of f
+
+880
+01:18:08,100 --> 01:18:09,880
+of 0 بتساوي g of f of 0 بتساوي g of f of 0 بتساوي g
+
+881
+01:18:09,880 --> 01:18:14,160
+of f of 0 بتساوي g of f of 0 بتساوي g of f of 0
+
+882
+01:18:14,160 --> 01:18:17,110
+of 0 بتساوي g of f of X اللي هو irrational يعني
+
+883
+01:18:17,110 --> 01:18:22,230
+irrational G of irrational اللي هو اللي هو الموجود
+
+884
+01:18:22,230 --> 01:18:25,910
+في الفترة Zero و واحد G of irrational إيش هيساوي
+
+885
+01:18:25,910 --> 01:18:31,290
+حسب التعريف .. التعريف هنا بيساوي G of F of
+
+886
+01:18:31,290 --> 01:18:38,750
+irrational irrational هاي بيساوي اللي هو G of F of 
+
+887
+01:18:38,750 --> 01:18:44,240
+irrational إيش بيساوي صفر G of 0 إيش بيساوي هنا G 
+
+888
+01:18:44,240 --> 01:18:52,420
+of 0 بيساوي Zero معرف ليها بيساوي إيش صفر؟ الثالثة 
+
+889
+01:18:54,350 --> 01:18:58,630
+Composite F of مين ضال؟ Of اللي هي irrational 
+
+890
+01:18:58,630 --> 01:19:02,530
+البوجيات غير الـ Zero هذا أصلا هو جسمها irrational
+
+891
+01:19:02,530 --> 01:19:08,410
+و rational جهتين واحدة واحدة واحدة Zero لحالها و
+
+892
+01:19:08,410 --> 01:19:11,650
+واحدة كل الـ rational اللي بين Zero و واحد ما عدا
+
+893
+01:19:11,650 --> 01:19:18,870
+الـ Zero اللي هو G of X اللي هي عبارة عن M على N 
+
+894
+01:19:19,590 --> 01:19:23,630
+اللي هي rational في الواقع رياشونال كلهم معدّن اللي 
+
+895
+01:19:23,630 --> 01:19:28,790
+فوق اللي فوق حسبناها طلعت واحد وبتساوي G of F of M 
+
+896
+01:19:28,790 --> 01:19:34,350
+على N وبتساوي G of F of M على N إيش بتساوي واحد على
+
+897
+01:19:34,350 --> 01:19:38,910
+N وبتساوي G of واحد على N إيش بتحسبها هذه هذا أصلا
+
+898
+01:19:38,910 --> 01:19:42,070
+الدالة دايما بتساوي واحد معدّن عند سفر حتى سفر عشان
+
+899
+01:19:42,070 --> 01:19:46,750
+عملنا المشكلة G of واحد على N إيش بتساوي واحد هو 
+
+900
+01:19:46,750 --> 01:19:53,580
+بيساوي واحد من هذا كله صار عندي g composite f of x
+
+901
+01:19:53,580 --> 01:20:06,710
+بتساوي 0 if x is irrational وبتساوي 1 1 إذا 
+
+902
+01:20:06,710 --> 01:20:11,790
+كانت X is هاي الـ rational كله ما عدا السفر وهي
+
+903
+01:20:11,790 --> 01:20:16,670
+السفر برضه طلع واحد if X is rational وهدّدت دالة
+
+904
+01:20:16,670 --> 01:20:20,610
+تبعتنا اللي اعتمدناها المرة الماضية أن هي is not 
+
+905
+01:20:20,610 --> 01:20:24,590
+integrable function لاحظوا أنتم بس خليني نقول شوف 
+
+906
+01:20:24,590 --> 01:20:32,660
+هالغرابة مش غرابة لأ هو مهم بالكلام أنه اللي خلف 
+
+907
+01:20:32,660 --> 01:20:37,380
+الموضوع لو كانت G continuous على كل الـ domain على
+
+908
+01:20:37,380 --> 01:20:40,820
+طول الـ G continuous ده هتطلع أن انتجر بالغصب عنها
+
+909
+01:20:40,820 --> 01:20:44,560
+من النظرية اللي قبل شوية لكن اللي خلف الموضوع شغلة
+
+910
+01:20:44,560 --> 01:20:49,440
+واحدة شايفين هالدالة هاد الـ G of X الـ G of X G of
+
+911
+01:20:49,440 --> 01:20:55,000
+X بتساوي اللي هو صفر عند السفر ومن عند الـ zero
+
+912
+01:20:55,000 --> 01:21:01,130
+لعند الواحد هنا الدالة قيمتها إيش بتساوي؟ واحد، هاي
+
+913
+01:21:01,130 --> 01:21:04,270
+قيمتها واحد، بين Zero والواحد قيمتها واحد، هذا
+
+914
+01:21:04,270 --> 01:21:09,540
+الـ G of X اللي عندي يعني هذا كل حال عالي العالي ما 
+
+915
+01:21:09,540 --> 01:21:14,120
+عدا عند من عند السفر فيه jump point هذه النقطة
+
+916
+01:21:14,120 --> 01:21:20,200
+الوحيدة اللي فيها discontinuity هي اللي .. اللي 
+
+917
+01:21:20,200 --> 01:21:25,340
+أنا بنشرت لي أن تصير decomposed F is continuous و
+
+918
+01:21:25,340 --> 01:21:29,200
+هذا عشان نعرف جداش الرياضيات أو جداش التحليل الدقيق
+
+919
+01:21:29,780 --> 01:21:35,960
+الدقيق أن إن احنا نقطة واحدة .. نقطة واحدة اللي كانت 
+
+920
+01:21:35,960 --> 01:21:40,360
+عندها point of discontinuity قالت لي أن الـ
+
+921
+01:21:40,360 --> 01:21:44,680
+decomposed F need not to be integrable وهي المثال 
+
+922
+01:21:44,680 --> 01:21:50,720
+أمامكم و .. و هيك بيكون احنا خلصنا الـ section
+
+923
+01:21:50,720 --> 01:21:56,730
+الثاني من اللي هو chapter 7 و هاي الـ homework عندكم 
+
+924
+01:21:56,730 --> 01:22:02,630
+مطلوبة 1,2,4,7,10,17,18,19 وإن شاء الله المرة
+
+925
+01:22:02,630 --> 01:22:08,950
+القادمة بنكمل وبنشرح 7.3 اللي هو الـ fundamental 
+
+926
+01:22:08,950 --> 01:22:10,550
+theorem of calculus
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..81f586541a8319406e778228554b452ad626c747
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg_postprocess.srt
@@ -0,0 +1,3704 @@
+1
+00:00:04,940 --> 00:00:11,820
+بسم الله الرحمن الرحيم اليوم المحاضرة رقم 13 مساق
+
+2
+00:00:11,820 --> 00:00:17,100
+تحليل حقيقه 2 لطلاب طالبات الجامعة الإسلامية كلية
+
+3
+00:00:17,100 --> 00:00:21,800
+العلوم قسم رياضيات ان شاء الله ستكون المحاضرة على
+
+4
+00:00:21,800 --> 00:00:28,620
+جزئينالجزء الأول هنستمر في الحديث عن سبعة اتنين
+
+5
+00:00:28,620 --> 00:00:34,240
+وهو الحديث أو سبعة تلاتة وهو الحديث سبعة اتنين في
+
+6
+00:00:34,240 --> 00:00:40,130
+البداية وهو الحديث عن الخواص التكامل الريمانحكينا
+
+7
+00:00:40,130 --> 00:00:45,310
+عن اللي هو مجموع دالتين قابلات التكامل اللي هو
+
+8
+00:00:45,310 --> 00:00:48,510
+قابل
+
+9
+00:00:48,510 --> 00:00:52,510
+التكامل وعاصل ضرب ثابت في دالة قابل التكامل برضه
+
+10
+00:00:52,510 --> 00:00:58,630
+قابل التكاملواليوم هنكمل الأمر الحديث عن
+
+11
+00:00:58,630 --> 00:01:04,550
+composition of two integrable functions هل قابل
+
+12
+00:01:04,550 --> 00:01:08,270
+التكامل أم لا وإذا قابل التكامل بدنا نبرهن وإذا مش
+
+13
+00:01:08,270 --> 00:01:14,750
+قابل بدنا نجيه counter exampleالان الجزء الثاني
+
+14
+00:01:14,750 --> 00:01:18,110
+هيكون اللي هو برضه تطبيق اللي هو composition
+
+15
+00:01:18,110 --> 00:01:25,410
+theorem اللي هي هنشوف بعد شوية ايش المتطلب ان يكون
+
+16
+00:01:25,410 --> 00:01:30,190
+composition of two functions is integrableأيضًا
+
+17
+00:01:30,190 --> 00:01:35,230
+هنتحدث عن اللي هو نوظفها في إثبات اللي هو أن
+
+18
+00:01:35,230 --> 00:01:38,950
+الدالة الأسية والـ absolute value of the function
+
+19
+00:01:38,950 --> 00:01:43,530
+F و أيضًا اللي هو مقلوب الدالة 1 على F في حالة F
+
+20
+00:01:43,530 --> 00:01:50,090
+لا تساوي 0 على ال domain المُعطَع إنها تكون قابلة
+
+21
+00:01:50,090 --> 00:01:54,830
+للتكامل و أيضًا اللي هو هيكون في عنا اللي هو تطبيق
+
+22
+00:01:54,830 --> 00:01:59,640
+أخر اللي هوحاصل ضرب دالتين كيف يكون انتجرابل أو
+
+23
+00:01:59,640 --> 00:02:03,080
+كيف تكون انتجرابل في حالة كلا الدالتين انتجرابل
+
+24
+00:02:03,080 --> 00:02:06,200
+نبدأ الآن في اللي هو النظرية الـ composition
+
+25
+00:02:06,200 --> 00:02:09,600
+theorem واطولوا روحكم علينا شوية على اللي هو
+
+26
+00:02:09,600 --> 00:02:14,930
+البرهان و البرهان شوية بده تركيز و البرهانطويل
+
+27
+00:02:14,930 --> 00:02:20,110
+شوية خلّينا ان نعمل الان focusing على نص النظرية و
+
+28
+00:02:20,110 --> 00:02:25,410
+بعدين بنبدأ نحكي عن البرهان نعمل outline للبرهان و
+
+29
+00:02:25,410 --> 00:02:27,610
+من ثم ندخل لتفاصيل البرهان
+
+30
+00:02:30,230 --> 00:02:35,470
+بنأخد I عبارة عن close bounded interval A وB وJ
+
+31
+00:02:35,470 --> 00:02:38,550
+عبارة عن close bounded interval سميناها C وD
+
+32
+00:02:38,550 --> 00:02:44,830
+ونفترض أن F من I لعند R يعني F عبارة عن دلة من عند
+
+33
+00:02:44,830 --> 00:02:49,350
+ال A و ال B لعند R أنها تكون integrable on I and
+
+34
+00:02:49,350 --> 00:02:52,050
+Phi من J لعند R
+
+35
+00:02:55,070 --> 00:02:58,390
+النظرية بتستلزم أن نقول continuous لأن ال Integra
+
+36
+00:02:58,390 --> 00:03:03,270
+بالحالها مش هتعطي اللي هو النتيجة زي ما هنشوف قدام
+
+37
+00:03:03,270 --> 00:03:07,610
+في اللي هو counter example الآن فرضنا أن فايل من J
+
+38
+00:03:07,610 --> 00:03:12,890
+لعند R is continuous وبدنا نفترض أن F of I .. F of
+
+39
+00:03:12,890 --> 00:03:17,450
+I جزئية من مين؟ من J عشان نعرف .. نعرف ال
+
+40
+00:03:17,450 --> 00:03:21,670
+composition بين ال two functions الآن في ضوء هذه
+
+41
+00:03:21,670 --> 00:03:26,050
+المعطياتإن الـ function F is integrable و الـ
+
+42
+00:03:26,050 --> 00:03:30,410
+function Phi is continuous لازم يطلع عندي الآن Phi
+
+43
+00:03:30,410 --> 00:03:37,450
+composite F is integrable on mean on I إذن F من I
+
+44
+00:03:37,450 --> 00:03:43,130
+لR انتجرابل Phi من J لعند R continuous الآن Phi
+
+45
+00:03:43,130 --> 00:03:46,170
+composite J continuous composite integrable
+
+46
+00:03:46,170 --> 00:03:53,500
+هيعطيني انتجرابل function on I الآن بدنا نثبتالأن
+
+47
+00:03:53,500 --> 00:04:00,600
+فاي composite F من I لعند R انها is integrable
+
+48
+00:04:00,600 --> 00:04:04,900
+الان كيف بدى أثبتها؟ بدى أثبتها .. بدى ألاقي
+
+49
+00:04:04,900 --> 00:04:09,040
+partition .. ده أقول لكل يبسن أكبر من 0 بدلاقي
+
+50
+00:04:09,040 --> 00:04:16,060
+partition B element in B of I such that L of أو U
+
+51
+00:04:16,060 --> 00:04:24,200
+ofB و F هذا اللي لجيته ماعرف أسأل أسف انا فعلا
+
+52
+00:04:24,200 --> 00:04:30,690
+composed of G and Fفاي كومبوزيت F ناقص L of B وفاي
+
+53
+00:04:30,690 --> 00:04:35,730
+كومبوزيت F أن يكون هذا المقدار أصغر من إبسلون إذا
+
+54
+00:04:35,730 --> 00:04:40,590
+وصلت لهذه النتيجة معناته أنه أنا أثبتت أنه اللي هي
+
+55
+00:04:40,590 --> 00:04:46,490
+الفاي كومبوزيت F is integrable بناء على اللي هو ال
+
+56
+00:04:46,490 --> 00:04:48,870
+criterion of integrability اللي حكينا عنها
+
+57
+00:04:48,870 --> 00:04:53,700
+المحاضرة قبل الباضيةالان هذا الهدف اللي بده أصله
+
+58
+00:04:53,700 --> 00:04:58,020
+هيك بده أصل هيك الان عشان أصل هيك بدي اللي هو
+
+59
+00:04:58,020 --> 00:05:02,900
+أستخدم اللي هو المعطيات اللي موجودة عندى الان
+
+60
+00:05:02,900 --> 00:05:08,380
+هستخدم أمرين هستخدم اكيد ال continuity للـ Phiوهي
+
+61
+00:05:08,380 --> 00:05:14,320
+continuous على closed bounded interval إذا حسب
+
+62
+00:05:14,320 --> 00:05:18,080
+نظرية في تحليل واحد هتكون Phi is uniformly
+
+63
+00:05:18,080 --> 00:05:23,880
+continuous وهذا هستغلها في الوصول إلى هدفيالان هذه
+
+64
+00:05:23,880 --> 00:05:27,960
+المعلومة بعد شوية هنخزنها ونحطها في .. في مكان ما
+
+65
+00:05:27,960 --> 00:05:33,420
+لحين نستخدمها مع اللي هو ان F is integrable مزام F
+
+66
+00:05:33,420 --> 00:05:37,240
+is integrable اذا نبلج Partitional I بحيث انه الـ
+
+67
+00:05:37,240 --> 00:05:40,500
+U للـ B والـ F نقص الـ B والـ F أصغر من مين؟ من
+
+68
+00:05:40,500 --> 00:05:44,220
+some .. من الـ Epsilon Epsilon تخدمني، هبدأ أسميها
+
+69
+00:05:44,220 --> 00:05:47,490
+Epsilon، هبدأ أسميها Delta، أنا حورالمهم أكيد مدام
+
+70
+00:05:47,490 --> 00:05:51,610
+الفيه عندي integrability للـ F هتحقق أنه لكل اللي
+
+71
+00:05:51,610 --> 00:05:56,010
+هو Epsilon there exists partition B وحنلاقي أنه ال
+
+72
+00:05:56,010 --> 00:05:59,510
+partition هذا اللي .. اللي نفع للـ F هو اللي هينفع
+
+73
+00:05:59,510 --> 00:06:04,300
+للـ Phi composite Fهنجمج المعلومتين التنتين مع بعض
+
+74
+00:06:04,300 --> 00:06:06,680
+اللي هي ال .. ال .. ال .. ال .. الـ uniform
+
+75
+00:06:06,680 --> 00:06:10,260
+continuity للفعل مع الintegrability للأف للوصول
+
+76
+00:06:10,260 --> 00:06:14,920
+إلى نتيجتنا وهي هذه النتيجة هذه خلينا نقول ال
+
+77
+00:06:14,920 --> 00:06:19,660
+outline للبرهان نبدأ الآن في تفاصيل البرهان وطول
+
+78
+00:06:19,660 --> 00:06:25,400
+روحكم عليها في اللي هو تفاصيل البرهانللوصول
+
+79
+00:06:25,400 --> 00:06:31,780
+للنتيجة اللى حكيتها اللى كتبت على اللوح بدي اقول
+
+80
+00:06:31,780 --> 00:06:39,240
+الان اول حاجة given epsilon أكبر من سفر انا اخدت
+
+81
+00:06:39,240 --> 00:06:44,600
+اي epsilon أكبر من سفر بدي اصل ال U بي فاي
+
+82
+00:06:44,600 --> 00:06:50,610
+composite F ناقص ال بيفاي كومبوزيت F أزر من إبسلون
+
+83
+00:06:50,610 --> 00:06:55,150
+for some اللي هو بارتي شنبي إذا وصلت لهك بكون خلصت
+
+84
+00:06:55,150 --> 00:06:58,770
+اللي هو نظريتي طيب سلموا على النبي عليه الصلاة
+
+85
+00:06:58,770 --> 00:07:03,850
+والسلام اللي لأن فاي عندى فاي عندى continuous على
+
+86
+00:07:03,850 --> 00:07:08,950
+مين على اللي هي ال J ال J عبارة عن closed bounded
+
+87
+00:07:08,950 --> 00:07:12,650
+intervalمدام continuous عليها إذا uniformly
+
+88
+00:07:12,650 --> 00:07:16,690
+continuous ماشي الحال إذا مدام uniformly
+
+89
+00:07:16,690 --> 00:07:23,170
+continuous إذا أكيد .. أكيد حتكون اللي هو مدام ..
+
+90
+00:07:23,170 --> 00:07:26,750
+حتى في ال continuity أكيد حتكون إيش ما لها bounded
+
+91
+00:07:26,750 --> 00:07:34,710
+إذا بقدر اللي هو أقول K بتساوي ال supremum لل Phi
+
+92
+00:07:34,710 --> 00:07:41,540
+of T such that T elementالـ C و D التي هي الـ J
+
+93
+00:07:41,540 --> 00:07:45,900
+هذه الآن بقدر احكي عن حاجة اسمها Supremum اه طبعا
+
+94
+00:07:45,900 --> 00:07:51,720
+مش هي ككلكم كمان و الـ K هذه هتكون attains for
+
+95
+00:07:51,720 --> 00:07:55,500
+some T بين C و D ليه؟ لأنه فايز continuous on a
+
+96
+00:07:55,500 --> 00:07:58,340
+closed bounded interval then it attains its
+
+97
+00:07:58,340 --> 00:08:00,920
+absolute maximum and absolute minimum on this
+
+98
+00:08:00,920 --> 00:08:05,120
+interval إذن أكيد في عنديK بيتساوى الـ Supremum لو
+
+99
+00:08:05,120 --> 00:08:09,200
+سلوك يدفع له 5T T Element in C وD سميليها دي K ليش
+
+100
+00:08:09,200 --> 00:08:13,280
+هتجهت بتعرف ليش هتستخدمها في الوصول إلى هدفي إذا
+
+101
+00:08:13,280 --> 00:08:16,960
+الأن اللي عملته لحد الآن أخدت epsilon arbitrarily
+
+102
+00:08:16,960 --> 00:08:21,860
+أخدت اللي هو ال supremum لهذا المقدار وسميته K هل
+
+103
+00:08:21,860 --> 00:08:24,440
+ال supremum موجود؟ أه ال supremum موجود و maximum
+
+104
+00:08:24,440 --> 00:08:27,480
+كمان لإن ال Phi is continuously on a closed
+
+105
+00:08:27,480 --> 00:08:31,840
+bounded interval COD طيب
+
+106
+00:08:34,510 --> 00:08:39,830
+الان بدي اخد بعيد اذنكم حاجة اسميها let epsilon
+
+107
+00:08:39,830 --> 00:08:45,490
+برايم بالساوي اللي هو epsilon على b ناقص a زائد
+
+108
+00:08:45,490 --> 00:08:49,670
+اتنين k ال k هذه اللي فوق زائد اتنين k وال b و ال
+
+109
+00:08:49,670 --> 00:08:54,010
+a اللي هي طول الفترة اللي هي I اللي انا عمال بشتغل
+
+110
+00:08:54,010 --> 00:09:01,100
+عليها معرف عليها Fليش هيك؟ بغرض الحسابات بعد شوية
+
+111
+00:09:01,100 --> 00:09:06,060
+هتشوفوا ليش و لو أصلا احنا في النهاية الـ Epsilon
+
+112
+00:09:06,060 --> 00:09:10,140
+الـ Prime هذه ما كتبناش بالشكل هذا و طلع عندي اللي
+
+113
+00:09:10,140 --> 00:09:19,940
+هو الـ U of B أو Phi Composite F ناقص الـ B Phi
+
+114
+00:09:19,940 --> 00:09:26,070
+Composite Fيكون أصغر من إبسلون مضروبة في something
+
+115
+00:09:26,070 --> 00:09:32,270
+أي إشي something ثابتبرضه هتقدي الغرض لإنه اللي هي
+
+116
+00:09:32,270 --> 00:09:35,310
+زي ما قلنا المرة الماضية المدام صحيحة لكل epsilon
+
+117
+00:09:35,310 --> 00:09:38,150
+في الدنيا إذا صحيح الواحد على n خد ال limit
+
+118
+00:09:38,150 --> 00:09:41,530
+للجهتين as n goes to infinity بيصير اللي هو هذا
+
+119
+00:09:41,530 --> 00:09:45,670
+اللي هو يؤد الغرض أو ال epsilon اللي هنا بتكون
+
+120
+00:09:45,670 --> 00:09:50,730
+اللي هو بيصير يعني تؤدي غرض أي أصغر من epsilon في
+
+121
+00:09:50,730 --> 00:09:53,510
+الدنيا لإن ال epsilon مدام اتمضروبة ضرب في التابط
+
+122
+00:09:53,510 --> 00:09:57,930
+بقدر ال epsilon أزغرها جد ما بدي و تؤدي الغرض
+
+123
+00:09:58,610 --> 00:10:05,280
+المفروض فاهمين طيب نيجي الآننرجع نقول أنه أخدت
+
+124
+00:10:05,280 --> 00:10:08,980
+إبسلون مراي بيساوي إبسلون على P minus A زاد 2K على
+
+125
+00:10:08,980 --> 00:10:12,680
+أساس أنه اللي هي تطلع عندنا الحسابات في الآخر
+
+126
+00:10:12,680 --> 00:10:16,480
+مرتبة وخالصة اللي هي أصغر من إبسلون طبعا هو
+
+127
+00:10:16,480 --> 00:10:20,720
+الاشعرف أن إبسلون مراي بالشكل هذا أصلا هو برهن
+
+128
+00:10:20,720 --> 00:10:23,680
+النظرية أو برهننا النظرية وفي الآخر طلع أن إبسلون
+
+129
+00:10:23,680 --> 00:10:28,440
+مضروبة في رقم جيت اللي هو رتبت حالي بحيث أنه حسبت
+
+130
+00:10:28,440 --> 00:10:32,320
+أنه عشان أطلح إبسلون لحالها خد إبسلون مبران بالشكل
+
+131
+00:10:32,320 --> 00:10:39,070
+هذاطيب نشوف .. نشوف الآن عندي فاي زي ما وعدناكم
+
+132
+00:10:39,070 --> 00:10:49,690
+فاي is continuous on اللي هو cod مدام فاي
+
+133
+00:10:49,690 --> 00:10:53,010
+continuous on cod يا جماعة إذا زي ما قلنا قبل
+
+134
+00:10:53,010 --> 00:11:01,660
+بشوية إذا5 is uniformly continuous on COD أيش
+
+135
+00:11:01,660 --> 00:11:07,680
+معناة uniformly continuous يعني اللي هو for every
+
+136
+00:11:07,680 --> 00:11:12,100
+إبسلون في الدنيا for every إبسلون .. خلّيني أخد
+
+137
+00:11:12,100 --> 00:11:15,020
+إبسلون الـ prime for every إبسلون الـ prime أكبر
+
+138
+00:11:15,020 --> 00:11:21,680
+من سفر there exists delta prime such that
+
+139
+00:11:21,680 --> 00:11:29,560
+uniformly continuousFor every S وT element in C وD
+
+140
+00:11:29,560 --> 00:11:38,690
+تحقق S minus T أصغر من Delta Prime يؤدي إلى Phiof
+
+141
+00:11:38,690 --> 00:11:43,690
+S ناقص Phi of T أصغر من مين من Epsilon برايم اللي
+
+142
+00:11:43,690 --> 00:11:49,450
+أخدتها عندي لأي Epsilon في الدنيا هذا الكلام
+
+143
+00:11:49,450 --> 00:11:52,210
+بيتحقق من دون أن هم Epsilon برايم اللي حكيت عنها
+
+144
+00:11:52,210 --> 00:11:58,090
+فوق طيب إذا الأن اللي استخدمته بما أن Phi
+
+145
+00:11:58,090 --> 00:12:02,010
+continuous على C وD إذا Phi is uniformly
+
+146
+00:12:02,010 --> 00:12:08,210
+continuous on مين؟ on C أو Dإذن الآن حسب التعريف
+
+147
+00:12:08,210 --> 00:12:11,530
+الـ Uniformly Continuous لأي إبسلون في الدنيا من
+
+148
+00:12:11,530 --> 00:12:14,530
+ضمنهن الإبسلون الـ prime الأكبر من 0 there exists
+
+149
+00:12:14,530 --> 00:12:17,430
+delta prime خاصة بالإبسلون الـ prime بحيث أنه لما
+
+150
+00:12:17,430 --> 00:12:20,770
+S و T في الـ C و الـ D و يكون الـ S minus T أصغر
+
+151
+00:12:20,770 --> 00:12:24,950
+من delta prime يعطيني أن 5S ناقص 5T أصغر من مين من
+
+152
+00:12:24,950 --> 00:12:30,990
+إبسلون الـ primeالان انا في delta معينة بدي
+
+153
+00:12:30,990 --> 00:12:35,830
+ألاقيها أربطها بهذه واتحققلي هذا الكلام شوفوا كيف
+
+154
+00:12:35,830 --> 00:12:44,030
+اصبروا عليها الان if عندي delta prime هذه أصغر من
+
+155
+00:12:44,030 --> 00:12:49,430
+epsilon prime thenThere exists Delta بتساوي Delta
+
+156
+00:12:49,430 --> 00:12:53,130
+Prime بتاخد Delta إيش بتساوي أسميه بتسمي Delta
+
+157
+00:12:53,130 --> 00:12:56,370
+Prime مين يا جماعة؟ Delta و هاد ال Delta اللي
+
+158
+00:12:56,370 --> 00:12:58,790
+سميتها اللي هي Delta Prime اللي سميتها Delta هاد
+
+159
+00:12:58,790 --> 00:13:03,670
+ال Delta هتحققها ليش؟ لأنها نفسها يعني بمعنى آخر
+
+160
+00:13:03,670 --> 00:13:08,150
+إذا كانت ال S minus T أصغر من Delta Prime بيعطيني
+
+161
+00:13:08,150 --> 00:13:10,830
+Automatic أصغر من Delta Prime اللي سميتها Delta
+
+162
+00:13:10,830 --> 00:13:15,810
+بيعطيني Phi of S ناقص Phi of T أصغر من مين؟ من
+
+163
+00:13:15,810 --> 00:13:23,530
+Epsilon Primeطيب تشوفوا الان if delta prime أكبر
+
+164
+00:13:23,530 --> 00:13:26,430
+أو يساوي epsilon prime يا أي حالتين مافيش غير هيك
+
+165
+00:13:26,430 --> 00:13:28,830
+يا delta prime أصغر من epsilon يا delta prime أكبر
+
+166
+00:13:28,830 --> 00:13:32,090
+ساوي epsilon prime الان if delta .. أهل جاي تفهموا
+
+167
+00:13:32,090 --> 00:13:34,530
+ليش عملت هيك if delta prime أكبر ساوي epsilon
+
+168
+00:13:34,530 --> 00:13:41,100
+prime thenاللي هو there exists Delta أصغر من
+
+169
+00:13:41,100 --> 00:13:45,540
+Epsilon برايم بلاجي ولا بلاجيش Epsilon برايم أكبر
+
+170
+00:13:45,540 --> 00:13:50,200
+من 0 أكيد between انا ابسلون برايم أكبر من 0 إذا
+
+171
+00:13:50,200 --> 00:13:52,620
+أنا أكيد بلاجي بين Epsilon برايم أكبر من 0 بلاجي
+
+172
+00:13:52,620 --> 00:13:57,340
+Deltaبلاجي عدد نهائي من الأعداد اللي هو Delta أكبر
+
+173
+00:13:57,340 --> 00:14:01,400
+من سفر وأصغر من إبسل و براين إذاً بلاجي Delta أصغر
+
+174
+00:14:01,400 --> 00:14:04,820
+من إبسل و براين بلاجي أه بلاجي لإن بين الـ two
+
+175
+00:14:04,820 --> 00:14:09,820
+real numbers اللي هو بين السفر وبين أي positive
+
+176
+00:14:09,820 --> 00:14:14,360
+real number في infinite number of numbers بينهم
+
+177
+00:14:14,360 --> 00:14:17,600
+سميت واحد قلت there exists Delta أصغر من إبسل و
+
+178
+00:14:17,600 --> 00:14:21,860
+براين such that .. طيب إيش بدك فيها هذه؟ such that
+
+179
+00:14:21,860 --> 00:14:27,400
+.. أحنا الـ gate تشوفواIf S minus T أصغر من Delta
+
+180
+00:14:27,400 --> 00:14:34,000
+فهذه الـ Delta If S minus T أصغر من Delta إذا أكيد
+
+181
+00:14:34,000 --> 00:14:37,860
+هذه الـ Delta أصغر من مين؟ المختار هي أصغر من Y'
+
+182
+00:14:38,320 --> 00:14:42,480
+وY' أصغر من مين؟ أصغر أو يسوى Delta Prime من هنا
+
+183
+00:14:43,910 --> 00:14:50,290
+الان if S-C أصغر من Delta إذا .. إذا حيث الـ S-C
+
+184
+00:14:50,290 --> 00:14:54,910
+هتكون أصغر من Y' واللي بدورها SY' أصغر بساوي Delta
+
+185
+00:14:54,910 --> 00:14:59,090
+.. أصغر بساوي Delta Prime إذا صارت عندي S-C أصغر
+
+186
+00:14:59,090 --> 00:15:03,010
+من Delta قطعًا S-C أصغر من مين؟ من Delta Prime
+
+187
+00:15:03,010 --> 00:15:07,450
+وبناءً على اللي كتبته بالأحمر هذا كل إشي S-C أصغر
+
+188
+00:15:07,450 --> 00:15:15,270
+من Delta Prime إشي بيعطيني5s-5t أصغر من إبسلون
+
+189
+00:15:15,270 --> 00:15:20,550
+برايم إذا يا جماعة سواء دلتا برايم أصغر من إبسلون
+
+190
+00:15:20,550 --> 00:15:25,710
+برايم أو دلتا برايم أصغر من إبسلون إبسلون برايم
+
+191
+00:15:25,710 --> 00:15:33,020
+بقدر ألاقي دلتاتتحقق فيها الخاصية لما S minus T
+
+192
+00:15:33,020 --> 00:15:36,900
+أصغر من Delta لما S minus T أصغر من Delta يعطيني
+
+193
+00:15:36,900 --> 00:15:39,900
+هذا المقدار أصغر من Epsilon Prime هذا المقدار أصغر
+
+194
+00:15:39,900 --> 00:15:44,580
+من Epsilon Prime إذا أنا في النهاية there exist
+
+195
+00:15:44,580 --> 00:15:50,690
+لوصلت له there exist Deltaأكبر من 0 ونفس الوجد
+
+196
+00:15:50,690 --> 00:15:55,170
+أشمالها Delta أصغر من يبسلون برايم لأنه في الحالة
+
+197
+00:15:55,170 --> 00:15:59,650
+ده أصغر من يبسلون برايم وفي الحالة الأولى برضه الـ
+
+198
+00:15:59,650 --> 00:16:03,630
+Delta أصغر من يبسلون برايم لأنه اختار الدلتة هي
+
+199
+00:16:03,630 --> 00:16:08,490
+Delta إبرايم إذن في كل الحالات هي المربط الفلسفي
+
+200
+00:16:08,490 --> 00:16:13,950
+الآن there exists Delta أكبر من 0 وأصغر من يبسلون
+
+201
+00:16:13,950 --> 00:16:22,170
+برايم such thatلكل S وT element in C وD إذا حققت
+
+202
+00:16:22,170 --> 00:16:27,610
+الخاصية S minus T أصغر من Delta بيعطيني على طول 5S
+
+203
+00:16:27,610 --> 00:16:34,130
+ناقص 5T أصغر من مين من إبسلون إبراهيم إذن هي
+
+204
+00:16:34,130 --> 00:16:41,710
+معلومة أخرى بدي أخذنها لأنني هحتاجهاهي كمان معلومة
+
+205
+00:16:41,710 --> 00:16:46,270
+الان اسمحولي أمسح هذا ال hand عشان أخزن معلومتي
+
+206
+00:16:46,270 --> 00:16:49,770
+اللي وصلت إلها مع المعلومات اللي موجودة عندى فوق
+
+207
+00:16:49,770 --> 00:16:57,090
+طيب الان شطبنا اللي عندنا hand خلصنا منه ووصلنا
+
+208
+00:16:57,090 --> 00:17:03,030
+إلى المعلومة التالية اللي بدأ أخزنها الآن مع اللي
+
+209
+00:17:03,030 --> 00:17:10,620
+مخزن فوق لأن there existDelta أكبر من 0 وأصغر من
+
+210
+00:17:10,620 --> 00:17:18,140
+Y' Such that for every S وT element in C وD إذا
+
+211
+00:17:18,140 --> 00:17:25,340
+حقق S minus T أصغر من Delta بيعطيني اللي هو 5S
+
+212
+00:17:25,340 --> 00:17:34,140
+minus 5T أصغر من Y' وهذا سمونيها 1 سمونيها 2
+
+213
+00:17:34,140 --> 00:17:38,630
+سمونيها Star اللي بدكم إياها ماشي الحالهذا الان
+
+214
+00:17:38,630 --> 00:17:44,170
+وصلت له وانا بدي استخدمه بعد شوية
+
+215
+00:17:49,890 --> 00:17:54,390
+اللي اللي بحب يتابع على التلخيص
+
+216
+00:17:54,390 --> 00:17:58,130
+هاي اللي وصلت إليه الآن هايها there exists delta و
+
+217
+00:17:58,130 --> 00:18:01,390
+الـ delta أصغر من epsilon prime if S و T element
+
+218
+00:18:01,390 --> 00:18:04,470
+in J and S minus T أصغر من Delta then Phi of S
+
+219
+00:18:04,470 --> 00:18:08,030
+ناقص Phi of T أصغر من إبسلون برايم هذه اللي وصلنا
+
+220
+00:18:08,030 --> 00:18:15,670
+إليها اللي قدرنا أن نصلها عشان بعد شوية بتستخدمها
+
+221
+00:18:15,670 --> 00:18:20,950
+انتبه عليها الآنالآن استغلقنا معلومة الـ if I is
+
+222
+00:18:20,950 --> 00:18:24,490
+continuous وحصلنا على معلومة مهمة جداً هي هذه
+
+223
+00:18:24,490 --> 00:18:28,630
+المعلومة الآن بدي أستخدم المعلومة الموازية لها أن
+
+224
+00:18:28,630 --> 00:18:37,770
+F is integrable الان عندي F is integrable on I إذا
+
+225
+00:18:37,770 --> 00:18:43,010
+حسب then حسب اللي هو ال .. ال .. ال integrability
+
+226
+00:18:43,010 --> 00:18:48,570
+criterionاللي حكينا عنها there exists partition B
+
+227
+00:18:48,570 --> 00:18:56,690
+element in B of I بجزء مين I such that اللي هو U
+
+228
+00:18:56,690 --> 00:19:05,920
+of B وFمعقس L بيوقف أصغر من أي إبسلون في الدنيا
+
+229
+00:19:05,920 --> 00:19:08,360
+الإبسلون اللي في الدنيا الإبسلون اللي بدها
+
+230
+00:19:08,360 --> 00:19:12,040
+استخدمها اللي حتة في الدنيا اللي هي مين هي Delta
+
+231
+00:19:12,040 --> 00:19:17,000
+تربيع أصغر من مين من Delta تربيع بقدر أه بقدر طبعا
+
+232
+00:19:17,000 --> 00:19:19,960
+مش احنا بنقول لكل إبسلون أكبر من سفر مادام F is
+
+233
+00:19:19,960 --> 00:19:23,040
+integrable لذا لكل إبسلون أكبر من سفر there exist
+
+234
+00:19:23,040 --> 00:19:27,590
+ال partition B بحيث أنه هذا أصغر من إبسلونالأن
+
+235
+00:19:27,590 --> 00:19:30,330
+أبسط من اللي بحكي عنها دلتة تربيع دلفة التربيع
+
+236
+00:19:30,330 --> 00:19:35,650
+أكبر من صفر إذا for delta تربيع there exists B
+
+237
+00:19:35,650 --> 00:19:40,070
+element in B of I such that U ناقص L أصغر من مين
+
+238
+00:19:40,070 --> 00:19:44,650
+من Delta تربيع هذا ال partition B بيجزئلي مين؟
+
+239
+00:19:44,650 --> 00:19:51,670
+بيجزئلي I بعد أذنكم سموليها بيه X0 و X1 لعند مين؟
+
+240
+00:19:51,670 --> 00:19:55,230
+لعند X سموليها ال partition بس عشان أتعامل معاها
+
+241
+00:19:55,660 --> 00:19:57,540
+اللي هو partition للـ I partition للـ I معناه
+
+242
+00:19:57,540 --> 00:20:00,880
+بجزّه I جزّه او ل X note X واحد X انت جداش أعدادها
+
+243
+00:20:00,880 --> 00:20:07,080
+مش عارف حسب اللي هو اللي جناه بيه طيب شوف الآن بدي
+
+244
+00:20:07,080 --> 00:20:13,520
+أعمل اللي هو شغلة بحيث عن الان أقدر أستخدمها اللي
+
+245
+00:20:13,520 --> 00:20:18,360
+هي أصل للي بدي من خلالها الآن هجيتوا تشوفوا ليش
+
+246
+00:20:18,360 --> 00:20:23,400
+جزعين خدوا Aالان يا جماعة صارت دلتة بين إيديا
+
+247
+00:20:23,400 --> 00:20:28,520
+لجهتها دلتة طيب الان خدوا ايه 6 هي عبارة عن كل ال
+
+248
+00:20:28,520 --> 00:20:34,160
+indices K اللي هان هذولة و 0,1,2,3 كده هذه جزء
+
+249
+00:20:34,160 --> 00:20:38,520
+اثنين ال I هي عند X note لعند X end هذه الفترة
+
+250
+00:20:38,520 --> 00:20:44,000
+اللي هي من A لعند B يا جماعة لعند Bماشي الحال طيب
+
+251
+00:20:44,000 --> 00:20:49,380
+خدوله A هي عبارة عن كل ال K بحيث ان M K ناقص M K
+
+252
+00:20:49,380 --> 00:20:54,900
+small تكون أصغر من Delta وخدول ال B بيساوي كل ال K
+
+253
+00:20:54,900 --> 00:20:59,740
+such that M K ناقص M K أكبر يساوي Delta إيش هذول
+
+254
+00:20:59,740 --> 00:21:04,700
+عاملا؟ هذول بس ال indices عند من هنا صفر و واحد و
+
+255
+00:21:04,700 --> 00:21:08,480
+اتنين عند من؟ عند ال K إذا اتجت جزءات ال indices
+
+256
+00:21:08,480 --> 00:21:15,500
+هذول إلى جزء ايه؟الجزء اللى هو عندى اللى بخاصية
+
+257
+00:21:15,500 --> 00:21:19,980
+اللى هو ال mk ناقص mk أصغر من دلتا بده حطه فهذا ال
+
+258
+00:21:19,980 --> 00:21:24,280
+set إذا هذه عبارة عن إيش مجموعة جزئية من ال .. من
+
+259
+00:21:24,280 --> 00:21:27,680
+ال .. من ال .. من ال .. من ال .. من ال ك من سفر
+
+260
+00:21:27,680 --> 00:21:36,490
+لعند مين لعند واحد لعند أنا .. لعند أناالأن هذه P
+
+261
+00:21:36,490 --> 00:21:40,870
+هي عبارة عن المتبقى منهن، مين المتبقى اللي الـ M K
+
+262
+00:21:40,870 --> 00:21:44,170
+نقص M K أصغر أكبر أو شويه دلتا، يعني بمعنى أخر
+
+263
+00:21:44,170 --> 00:21:49,430
+أداة التجزئة لهذه اللي هي الخاصية أنه M K نقص M K
+
+264
+00:21:49,430 --> 00:21:52,010
+أصغر مين مين دلتا، أنتوا عارفين إيش الـ M K
+
+265
+00:21:52,010 --> 00:21:55,730
+Capital و M K Small؟ أكيد، الـ M K Capital هي
+
+266
+00:21:55,730 --> 00:21:59,710
+عبارة عن الـ supremum لل F of X such that X
+
+267
+00:21:59,710 --> 00:22:04,740
+element in X K minus 1 لعند الـ X Kو الـ mk small
+
+268
+00:22:04,740 --> 00:22:09,560
+بيساوي الـ infimum لل F of X such that X element
+
+269
+00:22:09,560 --> 00:22:16,640
+in XK minus واحد والـ XK إذن يا جماعة اللي جزألي
+
+270
+00:22:16,640 --> 00:22:21,900
+الـ A و الـ B هو خاصيته إن الـ mk capital يعني
+
+271
+00:22:21,900 --> 00:22:25,340
+أعلى قيمة هي .. هي .. هي .. هي عندي أنا XK minus
+
+272
+00:22:25,340 --> 00:22:29,860
+واحد وهي XK فرضنا أن الدالة هي الدالة زي هيك مثلا
+
+273
+00:22:29,860 --> 00:22:35,250
+في المنطقة هذهالان هي أعلى قيمة وهي أقل قيمة
+
+274
+00:22:35,250 --> 00:22:41,070
+الحاصل طرح أعلى قيمة و أقل قيمة في كل فترة .. كل
+
+275
+00:22:41,070 --> 00:22:44,770
+sub interval بادي بقول هل هذا أكبر من .. أصغر من
+
+276
+00:22:44,770 --> 00:22:49,270
+delta ولا أكبر يساوي delta اللي خاصيتهم الفرق
+
+277
+00:22:49,270 --> 00:22:53,930
+بينهم أصغر من delta بحط هناالاندسيز هذا كهن واللي
+
+278
+00:22:53,930 --> 00:22:59,930
+أكبر بحطه نهن و بحط تجزيتها ليش هذه؟ هذه طريقة
+
+279
+00:22:59,930 --> 00:23:07,130
+للوصول إلى اللي بديها و هتشوفه الآن طيب نيجي الآن
+
+280
+00:23:07,130 --> 00:23:20,690
+لاللي هو نشوف الـ K F K Element A مدام K Element A
+
+281
+00:23:22,110 --> 00:23:26,470
+إذا تتحقق الخاصية هذه يعني Mk نقص Mk أصغر من مين؟
+
+282
+00:23:26,470 --> 00:23:32,430
+من Delta خدولي الآن أي X و Y في الفترة مين اللي هي
+
+283
+00:23:32,430 --> 00:23:39,330
+XK minus واحد لعند XK شوفوا إيش اللي بديهاال .. ال
+
+284
+00:23:39,330 --> 00:23:43,130
+.. ال .. ال .. ال X و ال Y هنا هى ال X و ال Y وهى
+
+285
+00:23:43,130 --> 00:23:46,430
+رسمة الدلة فى المنطقة هذه ال X و ال Y فى داخل هدول
+
+286
+00:23:46,430 --> 00:23:53,930
+طيب الان ال X و ال Y هنا إذا أكيد ال F of X ال F
+
+287
+00:23:53,930 --> 00:24:00,090
+of X ناقص F of Y نقطتين هنا نقطتين من هنا لهنا صور
+
+288
+00:24:00,090 --> 00:24:03,750
+هنا صور هنا يعني ممكن صورة واحدة هنا و صورة
+
+289
+00:24:03,750 --> 00:24:08,440
+التانية هنايعني ممكن صورة التالتة هنا وصورة الأولى
+
+290
+00:24:08,440 --> 00:24:15,500
+هنا يعني بمعنى آخر لو ال X هنا و ال Y هنا هي صورة
+
+291
+00:24:15,500 --> 00:24:21,400
+ال X وهي صورة مين ال Y لو جيتوا .. أخدتوا .. هي
+
+292
+00:24:21,400 --> 00:24:26,760
+صورة ال Y لو أخدتوا الفرق بين هذه و بين هذهالفرق
+
+293
+00:24:26,760 --> 00:24:31,020
+بين ما هو قيمة الدالة F of X هنا و قيمة الدالة F
+
+294
+00:24:31,020 --> 00:24:36,280
+of Y هنا أكيد .. أكيد .. أكيد الفرق بينهم هيكون
+
+295
+00:24:36,280 --> 00:24:42,320
+أصغر أو يساوي M K ناقص من M K لسبب بسيط أصلا لأن
+
+296
+00:24:42,320 --> 00:24:49,660
+أصلا F of X هذه أصغر أو يساوي ما هو M K أكيد و F
+
+297
+00:24:49,660 --> 00:24:54,400
+of Y أصغر أو يساويها ماشي الحالو نفس ال .. يعني ..
+
+298
+00:24:54,400 --> 00:24:57,080
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+299
+00:24:57,080 --> 00:24:57,100
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+300
+00:24:57,100 --> 00:24:57,360
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+301
+00:24:57,360 --> 00:24:57,720
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+302
+00:24:57,720 --> 00:24:58,100
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+303
+00:24:58,100 --> 00:24:59,480
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+304
+00:24:59,480 --> 00:25:00,040
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+305
+00:25:00,040 --> 00:25:07,580
+و .. و .. و .. و .. و
+
+306
+00:25:07,580 --> 00:25:08,160
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+307
+00:25:08,160 --> 00:25:11,200
+.. و .. و .. و ..
+
+308
+00:25:19,040 --> 00:25:24,000
+فبيظل قيمة f of x ناقص f of y أصغر شاومين مك ناقص
+
+309
+00:25:24,000 --> 00:25:28,460
+مك اللي مش واضح له من خلال الرسمة اللي عندي هنا
+
+310
+00:25:31,440 --> 00:25:34,520
+يعني الآن خلّيني أرى أضحى لحسن تكون مش واضحة للبعض
+
+311
+00:25:34,520 --> 00:25:41,360
+هاي الرسمة هاي XK minus واحد وهي XK خلّيني أكبر
+
+312
+00:25:41,360 --> 00:25:46,180
+الرسمة عشان تكون أوضح وهي XK لأن نفترضها أن هاي
+
+313
+00:25:46,180 --> 00:25:53,520
+رسمتنا هيك وطلعت زي هيك ماشي وهي عندي أعلى نقطة
+
+314
+00:25:53,520 --> 00:25:58,710
+خلّيني أزغر هذه شويةوهي أصغر النقطة هذي اللي
+
+315
+00:25:58,710 --> 00:26:03,970
+بتتمثل لـ M K وهذه بتتمثل لـ M K Small هاي المسافة
+
+316
+00:26:03,970 --> 00:26:09,030
+بينهم الفرق بينهم الآن الثانية لو جيت أخدت أي نقطة
+
+317
+00:26:09,030 --> 00:26:17,190
+هنا X و أي نقطة Y هنا هاي X وهي Y المسافة بينها دي
+
+318
+00:26:17,190 --> 00:26:21,310
+و بينها دي قيمتها دي بيصير F of X أنا بصير F of X
+
+319
+00:26:22,380 --> 00:26:26,700
+وهنا بيصير F of Y الفرق بين F of X و F of Y أكيد
+
+320
+00:26:26,700 --> 00:26:31,140
+أصغر من الفرق هذا وكل النقاط اللي بين هذه و هذه
+
+321
+00:26:31,140 --> 00:26:37,340
+هيكون يا إما زي الفرق هذا أو أصغر منه إذا أكيد
+
+322
+00:26:37,340 --> 00:26:45,820
+عندي صار المفروض وضح الأمر هيكون عندي اللي هو هذا
+
+323
+00:26:45,820 --> 00:26:50,910
+المقدار أصغر شهو هذا طب ليه ليش هذا؟هذا من مين للـ
+
+324
+00:26:50,910 --> 00:26:53,990
+K اللي في الـ A والـ K اللي في الـ A شخصيتها Mk
+
+325
+00:26:53,990 --> 00:26:57,610
+نقصها Mk أصغر من مين؟ إذا صارت أصغر من الـ Delta
+
+326
+00:26:57,610 --> 00:27:04,470
+إذا صارت F of X و F of Y أصغر من مين؟من Delta طيب
+
+327
+00:27:04,470 --> 00:27:08,430
+مادام F of X ايش علاقات هنا F of X و F of Y ما هي
+
+328
+00:27:08,430 --> 00:27:13,950
+اصلا احنا مفترضين من الاول ان F of I جزئية من الـ
+
+329
+00:27:13,950 --> 00:27:18,430
+J اللي هي عبارة عن C و D مظبوط ولا لأ اذا حيصير
+
+330
+00:27:18,430 --> 00:27:23,600
+عندي F of X و F of Y موجودات في الـ C و DF of X و
+
+331
+00:27:23,600 --> 00:27:27,000
+F of Y موجودات في الـ C و الـ D و بتحقق المسافة
+
+332
+00:27:27,000 --> 00:27:32,200
+أصغر من Delta بينهم إذا حسب واحد اللي احنا أثبتنا
+
+333
+00:27:32,200 --> 00:27:35,960
+أي نقطتين في الـ S و الـ D المسافة بينهم أصغر من
+
+334
+00:27:35,960 --> 00:27:39,600
+Delta لازم صورة ال .. صورة Phi of S و Phi of T
+
+335
+00:27:39,600 --> 00:27:42,540
+المسافة بينهم أصغر من مين؟ من Epsilon و Prime إذا
+
+336
+00:27:42,540 --> 00:27:47,640
+هذا Automatic هيعطيني Phi of النقطة الأولى اللي هي
+
+337
+00:27:47,640 --> 00:27:56,290
+F of X ناقصفاي أفضل النقطة الثانية يكون أصغر من
+
+338
+00:27:56,290 --> 00:28:06,890
+مين من إبسلون براي إذا صار عندي الآن لكل اللي عندي
+
+339
+00:28:06,890 --> 00:28:13,740
+ال K اللي في ال A وال X و Y في هذه المنطقةF of X
+
+340
+00:28:13,740 --> 00:28:17,920
+minus F of Y طلع ليه أصغر من Delta حتى ملي الـ 5 F
+
+341
+00:28:17,920 --> 00:28:25,000
+of X ناقص 5 F of Y أصغر من مين؟ من Y إبراهيم ماشي
+
+342
+00:28:25,000 --> 00:28:29,820
+الحال هذا الكلام لكل X و Y موجودات في الـ XK minus
+
+343
+00:28:29,820 --> 00:28:33,460
+واحد والـ XK لخص الآن اللي وصلنا له لأنه بدي
+
+344
+00:28:33,460 --> 00:28:36,920
+أستخدمه خليني ألخص خليني أشيل
+
+345
+00:28:41,000 --> 00:28:45,820
+خلّيني بس ساعدك اكتبلكم في مكان هنا اتحملوني انه
+
+346
+00:28:45,820 --> 00:28:54,640
+عشان اللوح شوية A بساوي كل ال K مقصد MK اصغر من
+
+347
+00:28:54,640 --> 00:29:05,600
+دلتا وعند B بساوي كلالـ K بحيث أن M K نقص M K أكبر
+
+348
+00:29:05,600 --> 00:29:10,060
+أو يساوي دلتة خلّيني أقولها في الذاكرة الآن خلّيني
+
+349
+00:29:10,060 --> 00:29:16,140
+أمسح حاجة و ألخص معلومتي إيش معلومتي بتقول دي لـ K
+
+350
+00:29:16,140 --> 00:29:26,610
+اللي في الـ A ماشي الحال لكل X و Y في الفترة X K-1
+
+351
+00:29:26,610 --> 00:29:32,750
+لعندي الـ xk بيطلع عندى الـ Phi f of x يعني Phi
+
+352
+00:29:32,750 --> 00:29:40,990
+composite f of x نقص Phi composite f of y أشماله
+
+353
+00:29:40,990 --> 00:29:48,600
+أصغر من إبسلون براي واضح؟إذن اللي وصلناله لـ K
+
+354
+00:29:48,600 --> 00:29:53,700
+اللي في الـ A عندي لـ K اللي في الـ A هذا الـ
+
+355
+00:29:53,700 --> 00:29:58,380
+absolute value أظهر من مين؟ من إبسلون إبراهيم لكل
+
+356
+00:29:58,380 --> 00:30:05,580
+مين لكل XY في ال XK minus XK minus 1 طيب نكمل لكم
+
+357
+00:30:05,580 --> 00:30:10,860
+عليها هذا خلصنا منه صار عندي الآن شوفوا
+
+358
+00:30:19,430 --> 00:30:24,070
+الشغل عميدي يا جماعة على الفترة هذه طيب شوف عندي
+
+359
+00:30:24,070 --> 00:30:31,590
+Phi composite F of X ناقص Phi composite F of Y
+
+360
+00:30:31,590 --> 00:30:37,770
+أكبر من Y و أكبر من مين من ناقص Y برايم بدأ أخد
+
+361
+00:30:37,770 --> 00:30:43,970
+هذه الجهة خليني أخد الجهة من الجهتين و أبدأ أشتغل
+
+362
+00:30:43,970 --> 00:30:51,300
+عليها واضحة هذههذه أصغر من Y' أكبر من ناقص Y بديش
+
+363
+00:30:51,300 --> 00:30:56,980
+هذا بتشغل هذه الان لان هذا الكلام صحيح لمن؟ لكل X
+
+364
+00:30:56,980 --> 00:31:02,740
+وY في ال sub interval هذه اللي هي لكل مين ال case؟
+
+365
+00:31:02,740 --> 00:31:06,600
+ال case اللي من A بس طيب شوف إذا صار عندي Phi
+
+366
+00:31:06,600 --> 00:31:14,580
+composite F of X أصغر من Y' بزايد Phi composite F
+
+367
+00:31:14,580 --> 00:31:21,720
+of Yماشي يا جماعة .. ماشي هذا الكلام لكل x و y في
+
+368
+00:31:21,720 --> 00:31:26,980
+.. اللي هو xk minus .. من xk minus 1 عند xk اللي
+
+369
+00:31:26,980 --> 00:31:31,600
+هنا .. هذا لكل x و y ثبتلي y .. ثبتلي y .. خلينا
+
+370
+00:31:31,600 --> 00:31:34,380
+نحكي عن y محدد .. arbitrary y لكن خلينا .. ثبتها
+
+371
+00:31:34,380 --> 00:31:40,180
+.. خلينا نحكي عن arbitrary fixed yبظل y' زي الـ
+
+372
+00:31:40,180 --> 00:31:47,140
+phi composite f of y is true أكبر من هذه لكل x
+
+373
+00:31:47,140 --> 00:31:52,500
+element in xk minus 1 لعند مين؟ لعند الـ xk أكيد
+
+374
+00:31:52,500 --> 00:32:00,060
+أكيد هذا أكبر من هذا لكل x well موجودة في xk minus
+
+375
+00:32:00,060 --> 00:32:04,540
+1 لعند مين؟ لعند الـ xk إذا صار هذا عبارة عن إيش
+
+376
+00:32:04,540 --> 00:32:08,880
+يا جماعة عبارة عن upper bound لهذا ال setمدام
+
+377
+00:32:08,880 --> 00:32:13,900
+upper bound إلها إذا هيكون أكبر أو يساوي ال least
+
+378
+00:32:13,900 --> 00:32:19,340
+upper bound يعني بمعنى آخر ال supremum لفاي
+
+379
+00:32:19,340 --> 00:32:25,280
+composite F of X such that X element in XK minus 1
+
+380
+00:32:25,280 --> 00:32:31,240
+لعند ال XK اللي هو أصغر أو يساوي Y prime زي فاي
+
+381
+00:32:31,240 --> 00:32:38,520
+composite F of mean of Y for any fixed Yطيب، هذا
+
+382
+00:32:38,520 --> 00:32:45,140
+مين هو؟ هذا عبارة عن الـ M K وسميها Delta أساس أو
+
+383
+00:32:45,140 --> 00:32:48,080
+تلدا أساس اللي هي خاصة بمين الآن في الـ Phi
+
+384
+00:32:48,080 --> 00:32:53,100
+Composite F عشان نميزها بالـ M K اسمه بالـ M K
+
+385
+00:32:53,100 --> 00:32:59,400
+اللي خاصة بالـ F اللي عندي، ماشي الحال، طيبصار
+
+386
+00:32:59,400 --> 00:33:02,800
+عندى MKتل ده بساوي الـ Supremum لهذا أصغر يساوي
+
+387
+00:33:02,800 --> 00:33:07,680
+هذا هذا صار عدد صار العدد هذا أصغر من يبسلون برايم
+
+388
+00:33:07,680 --> 00:33:11,640
+في كومبوزيت F of Y for any fixed Y يعني صحيح على
+
+389
+00:33:11,640 --> 00:33:16,320
+كل Y وين موجودة في الفترة هذه إذا صار عندى الآن
+
+390
+00:33:16,320 --> 00:33:21,680
+جيبولي هذه على الجهة هذه وهذه على الجهة هذه بيصير
+
+391
+00:33:21,680 --> 00:33:28,050
+عندى اللي هو ناقص في كومبوزيت F of Yأصغر أو ساوي
+
+392
+00:33:28,050 --> 00:33:34,770
+أبسلون و براين ناقص مين مك تلدة وإذا بدك ممكن نجيب
+
+393
+00:33:34,770 --> 00:33:40,050
+اللي هو الابسلون و البراين على الجهة الثانية مش
+
+394
+00:33:40,050 --> 00:33:50,310
+مشكلة صار عندي الآن هذا يا جماعة صار
+
+395
+00:33:50,310 --> 00:33:58,380
+عندي هذا اللي هو عبارة عن upper boundلهذا المقدار
+
+396
+00:33:58,380 --> 00:34:07,020
+أكيد ولا لا؟ عارفين ليش؟ لأن هذا الأن أكبر أو
+
+397
+00:34:07,020 --> 00:34:11,000
+يساوي هذا المقدار لكل Y لأن كل المخدين Y
+
+398
+00:34:11,000 --> 00:34:14,600
+arbitrarily fixed لكن arbitrarily، إذا صحيح على
+
+399
+00:34:14,600 --> 00:34:19,640
+كله، إذا بيصير عندي الآن اللي هو هذا أكبر أو يساوي
+
+400
+00:34:19,640 --> 00:34:24,260
+ال supremum لهذا، يعني بمعنى أخر ال supremum، لا
+
+401
+00:34:24,860 --> 00:34:32,200
+الناقص Phi composite F of Y such that Y element in
+
+402
+00:34:32,200 --> 00:34:39,360
+YK as if XK minus 1 عند XK هذا الـ Supremum له
+
+403
+00:34:39,360 --> 00:34:48,670
+أظهر أو يسوى Y' ناقص M K تلدةطيب هات ايش بتساوي
+
+404
+00:34:48,670 --> 00:34:56,670
+طلعون الناقص برا بيساوي ناقص الانف مام معايا لأ
+
+405
+00:34:56,670 --> 00:34:59,790
+لأنه مدام ناقص واحد طلع اذا بيقلب ال super mum ل
+
+406
+00:34:59,790 --> 00:35:05,530
+انف مام فاي composite F of Y such that Y element
+
+407
+00:35:05,530 --> 00:35:09,610
+in XK minus واحد لعند ال XK عرفتوا ايش اللي بده
+
+408
+00:35:09,610 --> 00:35:16,060
+اقوله هاد مين هي يا شبابهذه عبارة عن الـ M K تلدة
+
+409
+00:35:16,060 --> 00:35:19,680
+اللي هي الـ infimum للـ Phi Composite F كتبت
+
+410
+00:35:19,680 --> 00:35:22,800
+التلدة عشان ترمز لمين للـ Phi Composite F وفي عندي
+
+411
+00:35:22,800 --> 00:35:28,460
+ناقص قبلها إذا صارت عندي ناقص الـ M K تلدة أصغر
+
+412
+00:35:28,460 --> 00:35:33,400
+يساوي إبسلون ناقص الـ M K تلدة بدي أجيب هذه هنا
+
+413
+00:35:33,400 --> 00:35:42,400
+بيصير عندي إذا M K تلدةأصغر نقص اف ناقص مك تلد ا
+
+414
+00:35:42,400 --> 00:35:51,080
+small اصغر او يساوي مين ابسلون اذا اللي وصلتله ما
+
+415
+00:35:51,080 --> 00:35:59,440
+يلي وهذه بده اصلها انه لكلف ال a طلع عندي مك تلد
+
+416
+00:35:59,440 --> 00:36:05,300
+ناقص مك prime اصغر اش هو ايش ابسلون خلينا نسجلها
+
+417
+00:36:05,300 --> 00:36:11,830
+عشان نبني عليهاصار عندى الآن يا جماعة طولوا روحكم
+
+418
+00:36:11,830 --> 00:36:18,670
+عليا ان شاء الله مش هم طوالين نخلص M K تلدى ناقص M
+
+419
+00:36:18,670 --> 00:36:22,890
+K تلدى small أصغر يمشي هو إبسلون هذا لكل K وين
+
+420
+00:36:22,890 --> 00:36:30,330
+موجودة في ال A لكل K في ال A طيب هذا اللى احنا إيش
+
+421
+00:36:30,330 --> 00:36:38,150
+ماله أوصلنا إلهصار عندى الان الـ M K تلدى ناقص M K
+
+422
+00:36:38,150 --> 00:36:52,190
+تلدى أصغر من الـ E' لكل K فيه اللى هى N A الان
+
+423
+00:36:52,190 --> 00:36:58,330
+خد ال summation ال summation لل M K تلدى ناقص M K
+
+424
+00:36:58,330 --> 00:37:05,490
+تلدى small K element in A اللى هوهذا اللي هو أصغر
+
+425
+00:37:05,490 --> 00:37:09,310
+أو يساوي في .. أصغر أو يساوي .. الآن قدوا .. قدوا
+
+426
+00:37:09,310 --> 00:37:11,470
+.. قدوا .. قدوا .. قدوا .. قدوا .. قدوا .. قدوا ..
+
+427
+00:37:11,470 --> 00:37:12,010
+قدوا .. قدوا .. قدوا .. قدوا .. قدوا .. قدوا ..
+
+428
+00:37:12,010 --> 00:37:13,570
+قدوا .. قدوا .. قدوا .. قدوا .. قدوا .. قدوا ..
+
+429
+00:37:13,570 --> 00:37:15,170
+قدوا .. قدوا .. قدوا .. قدوا .. قدوا .. قدوا ..
+
+430
+00:37:15,170 --> 00:37:17,810
+قدوا .. قدوا .. قدوا .. قدوا .. قدوا .. قدوا ..
+
+431
+00:37:17,810 --> 00:37:31,850
+قدوا .. قدوا .. قدوا .. قدوا .. قدوا
+
+432
+00:37:31,850 --> 00:37:39,180
+..K element in A العداد هذا بعيد بعدد الـ K's اللي
+
+433
+00:37:39,180 --> 00:37:43,180
+في الـ A يعني إبسلون مضروب في عدد الـ K's اللي
+
+434
+00:37:43,180 --> 00:37:48,060
+موجودة في مين في إيه هذا أكيد أكيد هذا أصغر أو
+
+435
+00:37:48,060 --> 00:37:55,320
+يساوي ال summation للإبسلون على كل الـ K من عند
+
+436
+00:37:55,320 --> 00:38:00,980
+صفر لعند مين لعند اللي هو H N
+
+437
+00:38:03,340 --> 00:38:09,620
+بس انا الان بدي اجي اودي ال summation و اضربه فى
+
+438
+00:38:09,620 --> 00:38:13,460
+مين فى طول الفترة لإنه هي لازم لطول الفترة بعد
+
+439
+00:38:13,460 --> 00:38:20,660
+اسمهم هذا اضربه ليه فى XK بدي اضربه بس اوسع عقله
+
+440
+00:38:20,660 --> 00:38:23,700
+معلش بدي اضربه يعني هذا ال summation اللى حصلت
+
+441
+00:38:23,700 --> 00:38:29,320
+عليه بدي اخد ال summation MK تلدهنقص mk تلدى
+
+442
+00:38:29,320 --> 00:38:34,540
+وادربه يا شباب في xk minus xk minus واحد k element
+
+443
+00:38:34,540 --> 00:38:39,000
+in a هيصير اصغر او يساوي ال summation للإيبسلون في
+
+444
+00:38:39,000 --> 00:38:48,620
+xk minus xk minus واحد على الان k element in aأكيد
+
+445
+00:38:48,620 --> 00:38:52,120
+أصغر زي ما قلنا من ال summation اللي فوق epsilon
+
+446
+00:38:52,120 --> 00:38:59,980
+في xk minus xk minus 1k من 0 لعند n ليش؟ هذا ال
+
+447
+00:38:59,980 --> 00:39:02,420
+summation بس على العراصر اللي في ال A هذا ال
+
+448
+00:39:02,420 --> 00:39:05,260
+summation على كله على اللي في ال A وعلى اللي في ال
+
+449
+00:39:05,260 --> 00:39:08,760
+B على كل بقى العراصر اللي هي ال partition اللي
+
+450
+00:39:08,760 --> 00:39:15,420
+عنده من 0 ل1 اتنين عند مين لعند ال N طيب ال N هذا
+
+451
+00:39:15,420 --> 00:39:20,200
+المقدر هي اللي بديهالأن هذا bridge كان أو جسر
+
+452
+00:39:20,200 --> 00:39:23,860
+للوصول للي بديها و حتى ممكن نهان مباشرة لهذه هذه
+
+453
+00:39:23,860 --> 00:39:27,760
+أصغر أو يساوي هذا هذا مش هو اللي بتطلع عليه بتطلع
+
+454
+00:39:27,760 --> 00:39:32,640
+عليه هذا و بتطلع عليه هذا هذا خلّيه لأن أصغر يساوي
+
+455
+00:39:32,640 --> 00:39:36,460
+مين هذا المقدار هذا المقدار ايش بساوي epsilon في
+
+456
+00:39:36,460 --> 00:39:43,790
+مينx note ناقص x واحد زاد x واحد ناقص x اتنين زاد
+
+457
+00:39:43,790 --> 00:39:47,810
+x اتنين ناقص x ثلاثة لما أصل لآخر واحد يضل اللي
+
+458
+00:39:47,810 --> 00:39:53,330
+عبارة عن y في x n ناقص x note عملناها كتير ويساوي
+
+459
+00:39:53,330 --> 00:39:58,710
+y prime ويساوي y prime في مين في b minus a لأن ال
+
+460
+00:39:58,710 --> 00:40:03,950
+xn هي عبارة عن b و ال x note هي مين كانت هي ال a
+
+461
+00:40:03,950 --> 00:40:10,110
+إذا اللي وصلتله يا جماعةالان وصلت الى ما يلي انه
+
+462
+00:40:10,110 --> 00:40:19,170
+ال summation لل mk تلدى ناقص mk تلدى small لكي
+
+463
+00:40:19,170 --> 00:40:25,790
+element ايه في xk minus xk minus واحد اصغر او
+
+464
+00:40:25,790 --> 00:40:34,550
+يساوي epsilon prime في b minus ايش minus a واضح
+
+465
+00:40:34,550 --> 00:40:42,680
+الانهذه خزينها لإنه بدّيها بعد شوية اتحملونا
+
+466
+00:40:42,680 --> 00:40:46,880
+البرهان طويل شوية هي وصلنا إليها summation أزرع
+
+467
+00:40:46,880 --> 00:40:50,980
+شويه أبسلون رابع في b minus a لإن بدنا نيجي لمين
+
+468
+00:40:50,980 --> 00:40:59,140
+يا جماعة بدنا نيجي لاللي هوانتبهوا عليها، بدنا
+
+469
+00:40:59,140 --> 00:41:03,280
+نيجي للـ M للـ K اللي موجودة في مين؟ هذا الـ K في
+
+470
+00:41:03,280 --> 00:41:06,820
+الـ A، ضال عند مين؟ احنا جزأتها إلى جزئين اللي هي
+
+471
+00:41:06,820 --> 00:41:11,340
+الـ indices اللي عنده، K اللي هي في الـ A و K اللي
+
+472
+00:41:11,340 --> 00:41:18,060
+هي في مين؟ في الـ B خد الآن K element in B، شوف
+
+473
+00:41:18,060 --> 00:41:26,980
+إيش؟ الـ MK تلد إلهانقص mk تلد إلها أيش بتساوي؟
+
+474
+00:41:26,980 --> 00:41:32,380
+بتساوي حسب التعريف Supremum للـ Phi Composite F of
+
+475
+00:41:32,380 --> 00:41:38,240
+X للـ K اللي وين في الـ B اللي هي mk تلدها نقص mk
+
+476
+00:41:38,240 --> 00:41:42,540
+تلدها اللي هي small Supremum للـ Phi F of X اللي
+
+477
+00:41:42,540 --> 00:41:47,980
+هي الأولى هذه Such that X element in XK minus واحد
+
+478
+00:41:47,980 --> 00:41:54,860
+و XK اللي هي زائدأو ناقص اللي هي مين هذه الـ
+
+479
+00:41:54,860 --> 00:42:01,200
+infimum لأ فاي composite F of X such that X
+
+480
+00:42:01,200 --> 00:42:10,220
+والموجودة في ال X K minus واحد وال X K مظبوط ولا
+
+481
+00:42:10,220 --> 00:42:18,690
+لأ احنا قلناالـ Supremum لكل الـ Phi of T T على كل
+
+482
+00:42:18,690 --> 00:42:24,130
+الـ C والـ D بيساوي ايش اسمه؟ بيساوي K هذه عبارة
+
+483
+00:42:24,130 --> 00:42:29,790
+عن مين؟ شايفين، مابديش أعيدك، بقى أكتب مرتين خليني
+
+484
+00:42:29,790 --> 00:42:33,890
+أكتبها على شورة بتصير Phi of F of X يعني بتصير
+
+485
+00:42:33,890 --> 00:42:42,250
+عبارة عن مين؟ Phi of F of X معايا؟
+
+486
+00:42:43,040 --> 00:42:48,280
+وهاد ايش اسمها؟ بدي أدخل السالب جوا يا جماعة أو
+
+487
+00:42:48,280 --> 00:42:56,440
+قبل ما أدخله، هد بيصير فاي فاي of F of X بعد
+
+488
+00:42:56,440 --> 00:43:01,560
+أذنكم، بدي أدخل السالب جوا ال infimum هتصير إيش ما
+
+489
+00:43:01,560 --> 00:43:06,240
+لها؟ supremum إذا بيصير هذا زائد وهد بتصير
+
+490
+00:43:06,240 --> 00:43:14,100
+supremum والسالب بدخل جواطيب .. عندي الـ Phi F of
+
+491
+00:43:14,100 --> 00:43:19,800
+Xوالـ Phi F of X للـ X اللي موجودة هنا الـ F of X
+
+492
+00:43:19,800 --> 00:43:25,460
+هدولة من مين جايت من الفترة C و D لأن زي ما قلنا F
+
+493
+00:43:25,460 --> 00:43:30,680
+of A و F of I subset من الجهة اللي هي C و D لذا كل
+
+494
+00:43:30,680 --> 00:43:35,040
+ال element هنا موجود هنا يعني بمعنى أخر ال .. ال
+
+495
+00:43:35,040 --> 00:43:38,720
+supreme من اللي هنا اللي هي ال K عندي ال absolute
+
+496
+00:43:38,720 --> 00:43:45,400
+value للـ Phi of T أكيد أكبر أو يساويالـ Phi سالب
+
+497
+00:43:45,400 --> 00:43:51,080
+Phi of T و أصغر أو يساوي الـ Phi of T أو بالسوية
+
+498
+00:43:51,080 --> 00:43:55,280
+حتى أكيد
+
+499
+00:43:55,280 --> 00:43:57,900
+خلّيني أخدها على خطواتين بتسويها دي لأن ال
+
+500
+00:43:57,900 --> 00:44:06,260
+absolute value Phi of T أكبر سوى مين؟ سالب ال Phi
+
+501
+00:44:06,260 --> 00:44:11,300
+of T فبصير عندي ال supremum اللي عندي اللي هالة
+
+502
+00:44:11,300 --> 00:44:18,410
+هذاSupermom لهذه اكيد اصغر او يساوياللي هو الـ
+
+503
+00:44:18,410 --> 00:44:22,170
+Supremum هذا اللي هو K لأن الـ Supremum هذا عالمين
+
+504
+00:44:22,170 --> 00:44:26,370
+على كل الفترة C وD هنا اللي هي عالمين على X
+
+505
+00:44:26,370 --> 00:44:30,890
+element in XK مانس واحد و XK لأن هذا Similarly
+
+506
+00:44:30,890 --> 00:44:35,910
+أكيد الـ Supremum للـ Absolute Value هيكون أكبر أو
+
+507
+00:44:35,910 --> 00:44:39,070
+يساوي الـ Supremum لهذه من جهتين أنه Absolute
+
+508
+00:44:39,070 --> 00:44:42,790
+Value وفي نفس الوقت اللي هو المجموع هذه جزئية من
+
+509
+00:44:42,790 --> 00:44:48,380
+اللي فوق إذن ده برضه بيكون أصغر أو يساويK اذا صار
+
+510
+00:44:48,380 --> 00:44:53,800
+automatic اللي هو هذه زائد هذه اصغر او يساوي مين
+
+511
+00:44:53,800 --> 00:45:01,440
+اتنين K من اي حاجة اصغر او يساوي اتنين K الان هذه
+
+512
+00:45:01,440 --> 00:45:06,160
+ال supremum زائد ال supremum هذه بس لا ياش لسانك
+
+513
+00:45:06,160 --> 00:45:11,900
+يا شباب و هذه K اصغر يساوي K زائد K عشان التلخيص
+
+514
+00:45:11,900 --> 00:45:19,460
+بيصير اشمله اتنين Kواضح إذا نخزن التانية اللي هي K
+
+515
+00:45:19,460 --> 00:45:24,480
+element in B بعد إذنكم بيصير عندي ال M K نقص بلاش
+
+516
+00:45:24,480 --> 00:45:30,200
+التفاصيل هذه خلصنا منها بيصير عندي ال M K نقص M K
+
+517
+00:45:30,200 --> 00:45:37,180
+small أصغر من تلد تلد طبعا أصغر من مين؟ من اتنين K
+
+518
+00:45:37,180 --> 00:45:43,280
+طبعا ال K هنا index ال K هذه capital هذه ال K مين؟
+
+519
+00:45:43,280 --> 00:45:48,590
+ال K اللي فوق هذههذا الـ K هو الاندكس للـ B وهذا
+
+520
+00:45:48,590 --> 00:45:50,690
+الـ K هو الاندكس للـ B يعني الـ K هذه ليست إيادة
+
+521
+00:45:50,690 --> 00:45:57,370
+هذه K هي الـ Supremum اللي فوق طيب نجمح
+
+522
+00:45:57,370 --> 00:46:03,190
+معلوماتنا ونبدأ نجمحها الآن ونكون حصلنا على اللي
+
+523
+00:46:03,190 --> 00:46:08,410
+بدهد اتنين Kأه لب تلخيص 2K يا شباب لما تشوفوها لب
+
+524
+00:46:08,410 --> 00:46:13,770
+تلخيص 2K الان اوجدت ال summation على مين؟ على ايه؟
+
+525
+00:46:13,770 --> 00:46:16,710
+بدي اوجد ال summation على ال P باقي ال indices لإن
+
+526
+00:46:16,710 --> 00:46:21,650
+هالجات بدي أقولكم ليش بالضيقة الان اذا صار عندي ال
+
+527
+00:46:21,650 --> 00:46:29,930
+summation لل Mk ناقص Mk تلدة تلدة في Xk minus Xk
+
+528
+00:46:29,930 --> 00:46:40,680
+minus واحد K element in B الآنمظبوط أصغر أو يساوي
+
+529
+00:46:40,680 --> 00:46:45,120
+اللي هو 2K برضه على ال summation هذا ال summation
+
+530
+00:46:45,120 --> 00:46:53,040
+اللي هو 2K كابيتال كابيتال هذه مالهاش علاقة بال K
+
+531
+00:46:53,040 --> 00:47:00,840
+ال element in B هنا في XK minus XK minus 1 أخدت ال
+
+532
+00:47:00,840 --> 00:47:03,700
+summation على الجهتين على كل ال K ال element in B
+
+533
+00:47:06,360 --> 00:47:20,220
+ماشي طيب وين أكتب طيب اتحملوني هلجيت عندي خليني
+
+534
+00:47:20,220 --> 00:47:25,300
+أكتب هنا أشرح أنا شوية بهمش خليني أشرح على ال ..
+
+535
+00:47:25,300 --> 00:47:33,740
+الكلف ال B الكلف ال B احنا من تعريف الكلف ال Bبدي
+
+536
+00:47:33,740 --> 00:47:39,160
+يكون الام كي ناقص ام كي أكبر شو مين؟ Delta صح؟
+
+537
+00:47:39,160 --> 00:47:41,980
+بيصير عندى الآن Delta يعني أصغر شو ام كي ناقص ام
+
+538
+00:47:41,980 --> 00:47:47,000
+كي اله small ايه بيسمعوا على ال Delta هنا؟ هو انا
+
+539
+00:47:47,000 --> 00:47:50,920
+على ال Delta بيصير هذا إيه شبال، هو واحد، معايا؟
+
+540
+00:47:50,920 --> 00:48:02,180
+فبيصير عندى الآن ال summation على الواحدXK-XK- XK
+
+541
+00:48:02,180 --> 00:48:07,650
+- XK- XK- XK- XK- XK- XK- XKأصغر أو يساوي mk نقص
+
+542
+00:48:07,650 --> 00:48:13,130
+mk على delta ماشي خد ال summation للجهتين ال
+
+543
+00:48:13,130 --> 00:48:19,030
+summation للجهتين xk minus xk minus واحد وانا ال
+
+544
+00:48:19,030 --> 00:48:24,310
+summation xk minus xk minus واحد k element in b
+
+545
+00:48:24,310 --> 00:48:28,850
+لأن هذا صح لل b بس لكي element in b مظبوط ممكن
+
+546
+00:48:28,850 --> 00:48:33,880
+حصلنا على هذا هيهاللي موصول وهذا واحد على دلتا
+
+547
+00:48:33,880 --> 00:48:38,720
+طلعها برا في ال summation اللي عندي هذا ماشي وصلنا
+
+548
+00:48:38,720 --> 00:48:45,620
+ل هيك إذا الآن صار عندي هذا أصغر أوي ساوي واحد على
+
+549
+00:48:45,620 --> 00:48:56,360
+دلتا في مين؟ في الان هذا اللي هو ال UPUF طب أنا دي
+
+550
+00:48:56,360 --> 00:49:00,500
+MK وMK اه مش MK تلد هذه اه
+
+551
+00:49:03,350 --> 00:49:07,230
+ليش؟ لأنه .. اشكروا ان انا كتبين هنا Mk و Mk تلتة
+
+552
+00:49:07,230 --> 00:49:15,130
+لأن هذه الـ A الـ B الـ B الـ K اللي فيها مصنفة
+
+553
+00:49:15,130 --> 00:49:19,530
+على أساس Mk اسمه نقص Mk أكبر زي دلتة فبصير عندى
+
+554
+00:49:19,530 --> 00:49:25,800
+الآنالـ Mk نقص Mk اللي هو أكبر أو يساوي Delta مش
+
+555
+00:49:25,800 --> 00:49:31,520
+Delta هذه هذه لمين؟ اللي مصنف عليها الـ B اللي هي
+
+556
+00:49:31,520 --> 00:49:35,860
+بالنسبة للـ F هذه مش لـ Alpha Composite F إذا هذا
+
+557
+00:49:35,860 --> 00:49:38,560
+أكبر أو يساوي Delta على Delta بيصير أكبر أو يساوي
+
+558
+00:49:38,560 --> 00:49:41,740
+واحد على ال summation اللي عملناها قبل بشوية أصغر
+
+559
+00:49:41,740 --> 00:49:44,720
+أو يساوي واحد على Delta في ال summation هذا الآن
+
+560
+00:49:44,720 --> 00:49:55,810
+.. الآن هذا مين هو؟ هو عبارة عن الـ UP و F مش كله
+
+561
+00:49:55,810 --> 00:50:01,210
+حتى جزء منه لأن ال U P و F ايش ماله ال M كده تبعته
+
+562
+00:50:01,210 --> 00:50:08,310
+ال U P و F ايش هو يا شباب هو عبارة عن ال summation
+
+563
+00:50:08,310 --> 00:50:14,090
+كي من عند واحد لعند N او من Zero لعند N من واحد
+
+564
+00:50:14,090 --> 00:50:25,770
+لعند N مظبوط لمين لأ ال Mك في xk minus xk minus
+
+565
+00:50:25,770 --> 00:50:30,070
+واحد هذا ال summation على مين؟ على كل ال case من
+
+566
+00:50:30,070 --> 00:50:35,290
+واحد لعند n بينما هذا ال summation لمين؟ بس للجزء
+
+567
+00:50:35,290 --> 00:50:39,130
+اللي هو في مين؟ في ال B فأكيد ال summation على هذه
+
+568
+00:50:39,130 --> 00:50:44,410
+أظهر أوي ساوي ال summation على هذه باشي لأن ال
+
+569
+00:50:44,410 --> 00:50:48,430
+summation على هذه ناقص هذه برضه بظهر أوي ساوي هذا
+
+570
+00:50:48,430 --> 00:50:55,190
+ناقص هذاليش؟ لأن الـ M K ناقص M نعمل كمية على جهة
+
+571
+00:50:55,190 --> 00:50:59,290
+نعملها
+
+572
+00:50:59,290 --> 00:51:03,690
+.. نعملها
+
+573
+00:51:03,690 --> 00:51:04,770
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+574
+00:51:04,770 --> 00:51:09,950
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+575
+00:51:09,950 --> 00:51:10,210
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+576
+00:51:10,210 --> 00:51:10,270
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+577
+00:51:10,270 --> 00:51:10,410
+.. نعملها .. نعملها .. نعملها .. نعملها .. نعملها
+
+578
+00:51:10,410 --> 00:51:18,420
+.. نعملها .. نعملها .. نعملها ..أيش هيساوي الـ
+
+579
+00:51:18,420 --> 00:51:24,940
+summation للـ mk ناقص mk small في xk minus xk
+
+580
+00:51:24,940 --> 00:51:30,880
+minus واحد هذا k من عند واحد لعند n مظبوط ولا لأ؟
+
+581
+00:51:30,880 --> 00:51:35,360
+الان أكيد أكيد هذا لأن هذا موجبة وهذا موجبة لأن
+
+582
+00:51:35,360 --> 00:51:42,060
+هذا أكيد أكبر أو يساوي ال summation لل mk ناقص mk
+
+583
+00:51:43,610 --> 00:51:51,390
+xk-xk-1 k element in B لأن هذوله جزء من هذوله يعني
+
+584
+00:51:51,390 --> 00:51:56,150
+نقصت من ال summation هذا بعض ال terms اللي أكبر أو
+
+585
+00:51:56,150 --> 00:51:57,810
+يساوي 0 إذا نقص ال summation
+
+586
+00:52:12,960 --> 00:52:19,320
+طيب المفروض ان هذا واضح خلّينا الان نتطلع عليه
+
+587
+00:52:19,320 --> 00:52:25,060
+عندى اذا ال summation لل XK minus XK minus واحد K
+
+588
+00:52:25,060 --> 00:52:30,860
+element بيطلعلي اصغر او يساوي واحد على دلتا في ال
+
+589
+00:52:30,860 --> 00:52:39,040
+U ناقص L بس هذا انا مخزنه لسه عندى ال U ناقص Lاللي
+
+590
+00:52:39,040 --> 00:52:40,940
+هو هذا كله على الـ partition اللي بنشتغل عليه اللي
+
+591
+00:52:40,940 --> 00:52:45,860
+لاجيناه في الأول الـU-L هذه أصغر من مين طلعت أصلا
+
+592
+00:52:45,860 --> 00:52:48,880
+من دلتة تربيع لأن هذا اعتمدنا عليه على
+
+593
+00:52:48,880 --> 00:52:53,660
+الـintegrability للـF الأول إذا لازمتني هنا اللي
+
+594
+00:52:53,660 --> 00:52:57,800
+هو هذا أصغر من دلتة تربيع في واحد على دلتة بيصير
+
+595
+00:52:57,800 --> 00:53:04,160
+أصغر من مين؟ من دلتة وهذا كلهفى ضوء الـ Delta اللى
+
+596
+00:53:04,160 --> 00:53:08,060
+أنا بدأت فيها أصغر من مين أو أثبتتها أصغر من
+
+597
+00:53:08,060 --> 00:53:11,860
+Epsilon إبراهيم اللى وجهتها أصغر من Epsilon
+
+598
+00:53:11,860 --> 00:53:16,340
+إبراهيم إذا صار عندى ال summation هذا أصغر من Ash
+
+599
+00:53:16,340 --> 00:53:22,280
+من Epsilon إبراهيم لمين؟ لل K اللى Ash في B إذا
+
+600
+00:53:22,280 --> 00:53:25,340
+اللى وصلت إليه الآن ال summation
+
+601
+00:53:28,540 --> 00:53:32,980
+الـ summation اللي وصلت إليه الـ summation للـ xk
+
+602
+00:53:32,980 --> 00:53:41,600
+ناقص xk minus 1 k element in B أصغر من إبسلون
+
+603
+00:53:41,600 --> 00:53:46,920
+إبراهيم الآن
+
+604
+00:53:46,920 --> 00:53:53,760
+بس إحنا أثبتنا إن الـ summation هذا أيه أصغر أو
+
+605
+00:53:53,760 --> 00:54:00,430
+يساوي 2kاتنين كيف ال summation هذا مظبوط بدي اعوض
+
+606
+00:54:00,430 --> 00:54:06,850
+الان اشيل هذا بيصير عندي هاي شايفين يا شباب هاي
+
+607
+00:54:06,850 --> 00:54:14,070
+عند ال summation هذا اثبته انه اصغر او يساوي اللي
+
+608
+00:54:14,070 --> 00:54:24,580
+هو epsilon prime واضح ومن اربعةبصير عندى بعوض ال
+
+609
+00:54:24,580 --> 00:54:28,980
+summation أصغر من 2 كيف ال summation اللى أثبتناه
+
+610
+00:54:28,980 --> 00:54:34,840
+بحيته بس قبل شوية ال summation أصغر من 2 كيف ال
+
+611
+00:54:34,840 --> 00:54:40,140
+summation بشيل هذا اللى هو هذا و أقول أصغر من مين
+
+612
+00:54:40,140 --> 00:54:43,760
+من epsilon prime بصير هذا المقدار اللى هو هذا ال
+
+613
+00:54:43,760 --> 00:54:45,680
+summation هيه
+
+614
+00:54:47,550 --> 00:54:54,290
+هيو هذا هيو أصغر من من 2k في ash في ال epsilon
+
+615
+00:54:54,290 --> 00:55:00,110
+prime إذا طلع عندي الجزء الثاني summation خلصنا من
+
+616
+00:55:00,110 --> 00:55:07,610
+هذا صار عندي الجزء الثاني اللي أثبته summation لل
+
+617
+00:55:07,610 --> 00:55:19,240
+mk تلدى ناقص mk تلدىفي xk-xk-1 k element in B أصغر
+
+618
+00:55:19,240 --> 00:55:26,980
+من مين طلع من epsilon prime في 2k ابسلون برايم في
+
+619
+00:55:26,980 --> 00:55:36,650
+2k الآن خلصنااحسبولي إذا احنا لقينا ال partition B
+
+620
+00:55:36,650 --> 00:55:44,330
+لكل option أكبر من 0 لقينا B بحيث أنه U B of I
+
+621
+00:55:44,330 --> 00:55:54,210
+composite F ناقص ال B of I composite F هذا أشماله
+
+622
+00:55:54,210 --> 00:55:59,310
+بساوياللي هو الـ summation اللي هيضع على كل الـ K
+
+623
+00:55:59,310 --> 00:56:02,390
+و الـ summation اللي هيضع على كل الـ K و الـ K
+
+624
+00:56:02,390 --> 00:56:05,910
+جزّانها لجزين إيش في الـ A و إيش في الـ B إذا
+
+625
+00:56:05,910 --> 00:56:14,110
+بيساوي اللي هو الـ summation ل الـ A الـ MK ناقص
+
+626
+00:56:14,110 --> 00:56:23,140
+MK تلدة تلدةفي xk-xk-1 k من واحد ل عند n صح ولا لأ
+
+627
+00:56:23,140 --> 00:56:28,220
+اه طبعا هو التعريف هذا اللي هو بيثاويالان الـ K
+
+628
+00:56:28,220 --> 00:56:32,460
+اللي عندك جزّالت لجزين واحد في الـ A واحد في مين؟
+
+629
+00:56:32,460 --> 00:56:37,080
+في الـ B، إذاً هذا الـ summation الكل بيساوي ال
+
+630
+00:56:37,080 --> 00:56:41,340
+summation على K في الـ A زائد ال summation نفسه
+
+631
+00:56:41,340 --> 00:56:45,720
+على K وين ماله؟ في الـ B ال summation لمين؟ لهذه
+
+632
+00:56:45,720 --> 00:56:53,280
+اللي هي MK تلد ناقص MK تلد small في XK minus XK
+
+633
+00:56:53,280 --> 00:57:01,450
+minus واحد زائد MKتلدة ناقص mk small في xk minus
+
+634
+00:57:01,450 --> 00:57:08,990
+xk minus واحد اه طيب يعني الان هذا ال U و هذا ال L
+
+635
+00:57:08,990 --> 00:57:12,030
+صار بساوي هذا الجزء و هذا الجزء و هذا السبب أصلا
+
+636
+00:57:12,030 --> 00:57:17,590
+اللي خلانه أجزء هذا طلع لي الان مين هو طلع لي أصغر
+
+637
+00:57:17,590 --> 00:57:22,970
+من epsilon prime أصغر من epsilon prime في b minus
+
+638
+00:57:22,970 --> 00:57:32,330
+aوالتاني طلع أصغر من E' في 2K E' في 2K يعني هدول
+
+639
+00:57:32,330 --> 00:57:40,140
+الاتنين مع بعض إيش بيساون؟ بيساون E' فيه2k بيزاق
+
+640
+00:57:40,140 --> 00:57:56,220
+بيزاق بيزاق بيزاق بيزاق بيزاق بيزاق
+
+641
+00:57:56,310 --> 00:58:04,950
+على b minus a زي اتنين k في اتنين k زي b minus a
+
+642
+00:58:04,950 --> 00:58:10,030
+وهذه بتروح مع حد بيساوي ايش ابسلون اذا اللي وصلتله
+
+643
+00:58:11,120 --> 00:58:17,600
+لكل إبسلون أكبر من سفر لكل
+
+644
+00:58:17,600 --> 00:58:22,480
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+645
+00:58:22,480 --> 00:58:25,660
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+646
+00:58:25,660 --> 00:58:27,320
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+647
+00:58:27,320 --> 00:58:28,360
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+648
+00:58:28,360 --> 00:58:32,200
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+649
+00:58:32,200 --> 00:58:34,180
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+650
+00:58:34,180 --> 00:58:36,880
+إبسلون أكبر من سفر لكل إبسلون أكبر من سفر لكل
+
+651
+00:58:36,880 --> 00:58:47,340
+إبسلون أكبر من سفرطيب الآن نيجي بدنا اللي هو ناخد
+
+652
+00:58:47,340 --> 00:58:55,660
+اللي هو تطبيقات على هذه النظرية ونشوف
+
+653
+00:58:55,660 --> 00:59:02,600
+كيف بدنا نطبق هذه النظرية للوصول إلى نتاج أخرى
+
+654
+00:59:02,600 --> 00:59:09,280
+تتعلق بخواص التكامل أو بخواص تكامل لريمان لأن
+
+655
+00:59:09,280 --> 00:59:15,300
+عرفناو جوابنا على اللي هو المجموع وعلى حسب ضرب K
+
+656
+00:59:15,300 --> 00:59:20,100
+في ال .. في ال F ولقنا على ال composition و تحت اي
+
+657
+00:59:20,100 --> 00:59:24,360
+ضارف كان ف I composite F is integrable الان نكمل
+
+658
+00:59:24,360 --> 00:59:30,120
+اللي هو ناخد اللي هو ال corollary اللي عندي اللي
+
+659
+00:59:30,120 --> 00:59:39,150
+هي بتقولي اللي هي من تلت فروع لو كانتI عبارة عن
+
+660
+00:59:39,150 --> 00:59:43,990
+الـ closed interval A و B و F من I لعند R is
+
+661
+00:59:43,990 --> 00:59:47,370
+integrable on I then the absolute value of a
+
+662
+00:59:47,370 --> 00:59:50,630
+function F obtained by the absolute value is
+
+663
+00:59:50,630 --> 00:59:54,410
+integrable on Iوالـ absolute value of integration
+
+664
+00:59:54,410 --> 00:59:56,470
+أصغر يساوي الـ integration للـ absolute value للـ
+
+665
+00:59:56,470 --> 01:00:02,810
+F اللي هي أصغر يساوي K K في ال B minus A حيث ال K
+
+666
+01:00:02,810 --> 01:00:06,750
+هذه من أين جاية هي ال bound لل F of X لأن F is
+
+667
+01:00:06,750 --> 01:00:12,260
+integrable إذا أكيد boundedفن element in F يعني
+
+668
+01:00:12,260 --> 01:00:15,280
+اللي بتقولي هذا باختصار ده كانت F is integrable ال
+
+669
+01:00:15,280 --> 01:00:18,100
+absolute value لل F إيش ما لها integrable وال
+
+670
+01:00:18,100 --> 01:00:20,160
+absolute value لل integration أصغر سوى ال
+
+671
+01:00:20,160 --> 01:00:22,860
+integration لل absolute value أصغر سوى K اللي هي
+
+672
+01:00:22,860 --> 01:00:26,580
+ال maximum لل أو خلّيني أقول ال bound لل F of X
+
+673
+01:00:26,580 --> 01:00:31,080
+absolute value ل F of X في B minus Aالجزء الثاني
+
+674
+01:00:31,080 --> 01:00:35,460
+اللي هو هتطلع لي برضه الـ Fn is integrable لأن Fn
+
+675
+01:00:35,460 --> 01:00:41,560
+هو إنتجر
+
+676
+01:00:42,100 --> 01:00:46,780
+الآن إذا كان الشغل الثاني إذا كان فيه Delta بحيث
+
+677
+01:00:46,780 --> 01:00:50,400
+أن F of X أكبر يساوي Delta يعني F of X أكبر أو
+
+678
+01:00:50,400 --> 01:00:53,900
+يساوي Delta أكبر يساوي Delta ليش؟ على أساس إنه
+
+679
+01:00:53,900 --> 01:00:58,140
+يضمن مقلوب هيكون bounded بيصير 1 على F of X أصغر
+
+680
+01:00:58,140 --> 01:01:00,680
+أو يساوي 1 على Delta يعني بمعنى أكتر F is bounded
+
+681
+01:01:00,680 --> 01:01:04,720
+إذن بحقله يحكي عن ال Integrability ل1 على F ويقول
+
+682
+01:01:04,720 --> 01:01:07,780
+لي تحت الظرف هذا لو كانت F of X أكبر يساوي Delta
+
+683
+01:01:08,470 --> 01:01:12,210
+وDelta أكبر من 0 هيكون 1 على الـ F إيه اشمالها is
+
+684
+01:01:12,210 --> 01:01:15,830
+integrable on I خلّيني أتبرجح واحدة واحدة اللي
+
+685
+01:01:15,830 --> 01:01:24,690
+عنها ال gate F عندي من I لعين بR is integrable إذا
+
+686
+01:01:24,690 --> 01:01:29,350
+there exists K اللي هو أكبر من 0 such that
+
+687
+01:01:29,350 --> 01:01:33,330
+absolute value of F of Xأصغر أو يساوي إياش K مدام
+
+688
+01:01:33,330 --> 01:01:36,430
+ان تقرأ بالـ F إذا أكيد is bounded إذا ال absolute
+
+689
+01:01:36,430 --> 01:01:43,030
+value of X أصغر أو يساوي ال K طيب الآن يا جماعة
+
+690
+01:01:43,030 --> 01:01:47,230
+عندي هاد ال corollary أصلا اللي جابلها بدي أظبطلي
+
+691
+01:01:47,230 --> 01:01:54,070
+two functions بدي أعرف الآن صارت عند ال F of I ال
+
+692
+01:01:54,070 --> 01:02:00,230
+F of I صارت ال F of I أكيد subset بين نقص K ومين
+
+693
+01:02:00,230 --> 01:02:01,210
+أو K
+
+694
+01:02:07,180 --> 01:02:19,960
+طيب يعني الآن لو جيت عرفت Phi من اللي هو عنده ناقص
+
+695
+01:02:19,960 --> 01:02:27,990
+K لعند ال K لعند ال R عرفتها على أساسفاي ما هو
+
+696
+01:02:27,990 --> 01:02:30,950
+absolute value إذا مضحكت تجيب ال absolute value
+
+697
+01:02:30,950 --> 01:02:38,250
+فاي of T بساوة absolute value لمن؟ لل T ماشي الحال
+
+698
+01:02:38,250 --> 01:02:42,430
+هي الدلال عندى أكيد ال absolute value إيش ما لها
+
+699
+01:02:42,430 --> 01:02:47,370
+is continuous مدام ال absolute value الفاي is
+
+700
+01:02:47,370 --> 01:02:52,870
+continuous و ال F معطيله إيها integrable أيضا by
+
+701
+01:02:52,870 --> 01:03:00,670
+the above theoremفاي كومبوزيت F is integrable فاي
+
+702
+01:03:00,670 --> 01:03:07,610
+كومبوزيت F of T بيساوي فاي of F of T اللي هي
+
+703
+01:03:07,610 --> 01:03:12,330
+بتساوي ايش؟ واحدة absolute value فاي of T بتساوي
+
+704
+01:03:12,330 --> 01:03:17,490
+absolute value لمين؟ للـ F of T إذا شار عندي
+
+705
+01:03:17,490 --> 01:03:23,460
+absolute value للـ F is integrableإذاً مدامة Phi
+
+706
+01:03:23,460 --> 01:03:27,460
+is continuous و F integrable لأن حسب النظرية Phi
+
+707
+01:03:27,460 --> 01:03:30,640
+composite F is integrable و Phi composite F هي
+
+708
+01:03:30,640 --> 01:03:33,400
+طلعت من الـ absolute value للـ F طبعا Phi
+
+709
+01:03:33,400 --> 01:03:36,880
+composite F من وين هتشتغل من عند اللي هي ال
+
+710
+01:03:36,880 --> 01:03:42,920
+interval I لعند مين لعند R لأن Phi اللي هو F of T
+
+711
+01:03:42,920 --> 01:03:49,980
+هيجي يقعد في الفترة هذه و Phi هترسل اللي بيجي لوين
+
+712
+01:03:49,980 --> 01:03:55,250
+لعند Iماضح ها طيب الان عندي بدي أثبت أن ال
+
+713
+01:03:55,250 --> 01:03:58,590
+integration ال absolute value ال integration أصغر
+
+714
+01:03:58,590 --> 01:04:01,350
+ساوي ال integration ل absolute value هذه صارت
+
+715
+01:04:01,350 --> 01:04:07,670
+بعضها معلومات صادقة اللي هو عندي ال F أكبر أو ساوي
+
+716
+01:04:07,670 --> 01:04:11,610
+اللي هي absolute value لل F بالسالب و أصغر أو ساوي
+
+717
+01:04:11,610 --> 01:04:14,790
+ال absolute value ل 100 لل F صارت الان احنا أتبعت
+
+718
+01:04:14,790 --> 01:04:17,990
+أن ال absolute value is integrableإذا الان بما أن
+
+719
+01:04:17,990 --> 01:04:21,270
+F بين هذولة الدالتين حسب نظريها أخدناها المرة
+
+720
+01:04:21,270 --> 01:04:24,910
+الماضية أو remark إذا بيصير ال integration لل
+
+721
+01:04:24,910 --> 01:04:28,590
+absolute value لل F من A ل B أصغر أساوي ال
+
+722
+01:04:28,590 --> 01:04:32,330
+integration لل F من A ل B أصغر أساوي ال
+
+723
+01:04:32,330 --> 01:04:38,190
+integration لل F من A ل B وهذا إيش معناته؟ هذا
+
+724
+01:04:38,190 --> 01:04:43,610
+معناته إذا ال absolute value لل integration لل F
+
+725
+01:04:43,610 --> 01:04:49,150
+من A ل B أصغر أساوياللي هو ال integration لأ لأبسل
+
+726
+01:04:49,150 --> 01:04:57,690
+و لأ لأف من A لB ماشي الحالة و طبيعي عندي هذه
+
+727
+01:04:57,690 --> 01:05:02,270
+أثبتناها بهذه و طبيعي مدام عنا لسه ما
+
+728
+01:05:07,890 --> 01:05:12,470
+أو ملاحظة سابقة لبس الـ integration من a لb لبس ال
+
+729
+01:05:12,470 --> 01:05:18,070
+value of f of x أصغر أو شاوي اللي هو من k في طول
+
+730
+01:05:18,070 --> 01:05:27,050
+الفترة بـ-aمع هذه together بنحصل على اللي هو
+
+731
+01:05:27,050 --> 01:05:30,750
+المطلوب ال absolute value ال integration أصغر سوا
+
+732
+01:05:30,750 --> 01:05:34,690
+ال integration لل absolute value أصغر سوا K في ال
+
+733
+01:05:34,690 --> 01:05:39,510
+B minus A هذه اللي هو الجزء الأول من ال corollary
+
+734
+01:05:39,510 --> 01:05:44,310
+خلينا نشوف الجزء الثاني من ال corollary برضه اللي
+
+735
+01:05:44,310 --> 01:05:51,270
+هو برهانه سهل و برهانه اللي هو مشابهللمنطق اللي
+
+736
+01:05:51,270 --> 01:05:57,070
+حكيناها عندنا قبل بشوية طيب صلى الله عننا يا عزيزي
+
+737
+01:05:57,070 --> 01:06:01,410
+عليه الصلاة والسلام الآن يا شباب عندي اللي هو
+
+738
+01:06:01,410 --> 01:06:05,110
+الجزء الثاني بدنا نثبت أن الـ F أسئن is integrable
+
+739
+01:06:05,110 --> 01:06:09,110
+في حالة الـ F integrable لأن أكيد شكلنا بدنا نيجي
+
+740
+01:06:09,110 --> 01:06:16,950
+عند الـ F من I لعند R is integrableالان عندي اللي
+
+741
+01:06:16,950 --> 01:06:21,470
+هو .. بدي أسأل أن أثبت انها Integrable فلو جيت أنا
+
+742
+01:06:21,470 --> 01:06:30,170
+عرفت F F أو اللي هو Phi function من اللي هو domain
+
+743
+01:06:30,170 --> 01:06:35,150
+اللي هو F of I من اللي هو range ال F range ال F
+
+744
+01:06:35,150 --> 01:06:45,640
+range ال F لعند ال R بحيث ان اقول Phi of Tبساوي T
+
+745
+01:06:45,640 --> 01:06:51,120
+أُس أنت five of T أيش بيساوي بيساوي T أُس أنت أو
+
+746
+01:06:51,120 --> 01:06:54,180
+إذا كان بدك اللي هو بدكاش تكون ال range ل F خلاص
+
+747
+01:06:54,180 --> 01:06:57,460
+من عارفها من وين من اللي من اللي قبل بشوية من ناقص
+
+748
+01:06:57,460 --> 01:07:01,980
+K لعند K عارفين ليه؟ لأن ال absolute value لل F of
+
+749
+01:07:01,980 --> 01:07:06,840
+X أصغر مش هو ال K إذا أكيد لما ترمي ال F of X
+
+750
+01:07:06,840 --> 01:07:11,410
+هتكون ترمي في الفترة من ناقص K لعندكأو subset
+
+751
+01:07:11,410 --> 01:07:15,970
+بيصير الـ F of I subset من ناقص K و K إذاً صارت
+
+752
+01:07:15,970 --> 01:07:22,510
+الـ Phi composite F Phi composite F is defined من
+
+753
+01:07:22,510 --> 01:07:31,140
+I لعند ال R وعندي Phi composite F ofT بيساوي Phi
+
+754
+01:07:31,140 --> 01:07:37,200
+of F of T ويساوي F of T اللي هو Phi of T بيساوي T
+
+755
+01:07:37,200 --> 01:07:41,560
+أُس N بيصير Phi of F of T اللي هي عبارة عن F of T
+
+756
+01:07:41,560 --> 01:07:48,540
+يا جماعة أُس N الآن كل الأمور طيبة ومنيحة ليش
+
+757
+01:07:48,540 --> 01:07:53,260
+ووصلنا كمانعندي F-integrable و F-continuous
+
+758
+01:07:53,260 --> 01:07:57,420
+هتتدللوا الـ C أشمالها اللي هو الـ T أسان is
+
+759
+01:07:57,420 --> 01:08:03,540
+continuous اللي جزء من البلونوميال بيصير عندي FI
+
+760
+01:08:03,540 --> 01:08:06,660
+is continuous و F-integrable لذلك حسب النظرية اللي
+
+761
+01:08:06,660 --> 01:08:10,680
+قبل و شوية إيش هيطلع عندي FI composite F is
+
+762
+01:08:10,680 --> 01:08:16,440
+integrable بمعنى أن ف FN is integrable فكرة معادة
+
+763
+01:08:16,440 --> 01:08:22,570
+أصلالأنه سنة يعني اللي هو الأمور واضحة الآن ضال
+
+764
+01:08:22,570 --> 01:08:30,190
+عند مين اللي هو ال .. ال .. ال .. ال .. نثبت الجزء
+
+765
+01:08:30,190 --> 01:08:36,010
+الثالث من ال corollary اللي هي بدنا نثبت أنه لو
+
+766
+01:08:36,010 --> 01:08:43,490
+كانت ال F of X أكبر أو شويه واحد على دلتااللي هي
+
+767
+01:08:43,490 --> 01:08:47,530
+for every x element in I وعندي there exists دلتا
+
+768
+01:08:47,530 --> 01:08:52,390
+كمان وصفر ساشرات إذا كان هذا متحقق إذن هتطلع عندى
+
+769
+01:08:52,390 --> 01:08:55,970
+اللي هي الواحد على ال F بيدثبت أن الواحد على ال F
+
+770
+01:08:55,970 --> 01:08:58,950
+إيش is integrable بدنا نعمل .. نجيب continuous
+
+771
+01:08:58,950 --> 01:09:02,890
+function أكيد كل جمجال نجيب مقلوبة دلة يعني في حوض
+
+772
+01:09:02,890 --> 01:09:09,800
+five من ناقص K لعند Kلعند R وخد فاي عارفين ما هو
+
+773
+01:09:09,800 --> 01:09:13,000
+ال scale كده سبب اللي قلت قبل شوية فايف دي ايش
+
+774
+01:09:13,000 --> 01:09:17,600
+متساوي اكيد كلكم حيقول واحد على تي ماشي الحال واحد
+
+775
+01:09:17,600 --> 01:09:26,180
+على تي بس اه لأ عدم ديش اقدر اعمل hand افعل عشان
+
+776
+01:09:26,180 --> 01:09:31,250
+مانبدعش في السفرة يا شباب خدوها من عند Deltaلعند
+
+777
+01:09:31,250 --> 01:09:36,470
+مين؟ لعند K ليش .. ليش .. ليش اللي هو عكيفك؟ أه F
+
+778
+01:09:36,470 --> 01:09:40,670
+of X اللي هو absolute value أصغر أو تسوى K يعني F
+
+779
+01:09:40,670 --> 01:09:46,160
+of X أصغر أو تسوى K وأكبر أو تسوى نقص Kو أثناء هذه
+
+780
+01:09:46,160 --> 01:10:12,580
+أكيد ماعطينيها أكبر شو مين دلتا
+
+781
+01:10:14,710 --> 01:10:21,230
+اللي هو .. إيه الكلام هذا؟ مشروع هو بيصير عنده ..
+
+782
+01:10:21,230 --> 01:10:24,170
+اللي هو Phi of T بسواحدة على T مافيش أي مشكلة،
+
+783
+01:10:24,170 --> 01:10:27,470
+مافيش مشاكل أسفار، مافيش مشاكل كده، إذا صارت ده
+
+784
+01:10:27,470 --> 01:10:31,490
+اللي إيش مالها؟ continuous continuous هفهم إن فهمت
+
+785
+01:10:31,490 --> 01:10:34,810
+القصة Phi composite of F continuous و integrable
+
+786
+01:10:34,810 --> 01:10:38,310
+إذا كلها على بعضها integrable يعني Phi of T بتصير
+
+787
+01:10:38,310 --> 01:10:44,750
+Phiof F of T يعني بتساوي واحد على F of T يعني صارت
+
+788
+01:10:44,750 --> 01:10:51,650
+الدالة واحد على F is integrable وهك
+
+789
+01:10:51,650 --> 01:10:55,670
+مكون احنا خلصنا اللي هو ال corollary ضال عندى الآن
+
+790
+01:10:55,670 --> 01:11:01,570
+نجاوب على السؤال الثاني هل حاصل ضرب ضرب دالتين
+
+791
+01:11:01,570 --> 01:11:06,650
+integrable is integrable بنقول اه integrable يعني
+
+792
+01:11:06,650 --> 01:11:11,380
+بمعنى اخر بقول ليهالنظرية اللي هي اللي بعدها 7,2,7
+
+793
+01:11:11,380 --> 01:11:18,020
+بتقول ما يلي بتقول لو كانت F و G integrable يعني
+
+794
+01:11:18,020 --> 01:11:25,480
+لو كان عندي خليني اكتب بالأصمر أفضل F و G من I
+
+795
+01:11:25,480 --> 01:11:33,700
+لعند R كانت integrable functions بيعطيني هذا ان FG
+
+796
+01:11:33,700 --> 01:11:42,500
+من I لعند R برضه ايش ماله؟Integrable Function الـ
+
+797
+01:11:42,500 --> 01:11:46,740
+L صار إن حصيلة من المعلومات بتسهل علي الوصول
+
+798
+01:11:46,740 --> 01:11:53,820
+للنتيجة و Proof و Proof بما أن F is Integrable إذن
+
+799
+01:11:53,820 --> 01:11:57,700
+فال Corollary اللي قبل بشوية أكيد F تربيع اللي هي
+
+800
+01:11:57,700 --> 01:12:01,040
+Integrable و G Integrable من النظرية اللي قبل
+
+801
+01:12:01,040 --> 01:12:04,940
+بشوية و Corollary برضه إشمالها G تربيع برضه
+
+802
+01:12:04,940 --> 01:12:10,060
+Integrable صح ولا لا يا جماعة صحطيب F تربيع
+
+803
+01:12:10,060 --> 01:12:14,260
+Integrable و G تربيع Integrable و برضه من نظرية
+
+804
+01:12:14,260 --> 01:12:18,580
+سابقة مدام F و G Integrable إذا F زائد G برضه إيش
+
+805
+01:12:18,580 --> 01:12:24,980
+Integrable لأ F زائد G تربيع Integrable كمان لأن F
+
+806
+01:12:24,980 --> 01:12:27,800
+و G Integrable أدت ل F زائد G Integrable و F زائد
+
+807
+01:12:27,800 --> 01:12:31,640
+G Integrable أدت من القرول اللي قبل شوية أنه تربيح
+
+808
+01:12:31,640 --> 01:12:40,520
+يكون إيش Integrable طيب خلصنا إذا إذاF تربيع زائد
+
+809
+01:12:40,520 --> 01:12:49,780
+D تربيع is integrable صح؟ مظبوط وناقص F تربيع
+
+810
+01:12:49,780 --> 01:12:54,220
+وناقص D تربيع برضه integrable مظبوط برضهلأنه اللي
+
+811
+01:12:54,220 --> 01:13:00,060
+هو عندي اللي هو ثابت في هذه integrable و ثابت في
+
+812
+01:13:00,060 --> 01:13:03,560
+ال integrable integrable ومجموح انصار انتجرابل إذا
+
+813
+01:13:03,560 --> 01:13:09,020
+انصار هذا integrable زائد F زائد G لكل تربيع هذه
+
+814
+01:13:09,020 --> 01:13:12,980
+integrable وهذه integrable وهذه integrable مجموحين
+
+815
+01:13:12,980 --> 01:13:17,520
+هذا إيش بيساويهذا .. هذا integrable و هذا
+
+816
+01:13:17,520 --> 01:13:19,860
+integrable و هذا integrable إذا المجموع integrable
+
+817
+01:13:19,860 --> 01:13:23,220
+إذا هذا كله على بعض integrable طب هذا مين هو؟ هذا
+
+818
+01:13:23,220 --> 01:13:29,160
+عبارة عن F تربيع زاد G تربيع ناقص اللي هو إيش زاد
+
+819
+01:13:29,160 --> 01:13:35,760
+2FG بيصير عبارة عن 2F main G صارت 2FG integrable
+
+820
+01:13:35,760 --> 01:13:40,840
+طب لو جينا قولنا خل نص هنا يعني ضربنا ثابت في
+
+821
+01:13:40,840 --> 01:13:43,960
+integrable إذا هيطلع اللي هو كله integrable إذا FG
+
+822
+01:13:43,960 --> 01:13:48,520
+إيش ما لهاis integrable صار عندي الان fg
+
+823
+01:13:48,520 --> 01:13:54,040
+integrable تابعا لأن f تربيع و g تربيع و f زائد g
+
+824
+01:13:54,040 --> 01:13:59,860
+كل تربيع حاصل جمحين و ضرب النصفي هنا ثابت و بيطلع
+
+825
+01:13:59,860 --> 01:14:04,720
+عبارة عن integrable function نيجي لآخر اللي هو
+
+826
+01:14:04,720 --> 01:14:11,850
+نقطة في الفي ال .. في ال .. في ال section 7-2 اللي
+
+827
+01:14:11,850 --> 01:14:14,790
+هو السؤال اللي سألناه في الأول قولنا لو كانت F is
+
+828
+01:14:14,790 --> 01:14:19,570
+integrable function و Phi is integrable هل Phi
+
+829
+01:14:19,570 --> 01:14:24,310
+composite F is integrable قولنا أكيد هو لو .. في
+
+830
+01:14:24,310 --> 01:14:28,430
+البداية قولنا أن Phi composite F need not to be
+
+831
+01:14:28,430 --> 01:14:32,280
+integrableإذا the composition of two integrable
+
+832
+01:14:32,280 --> 01:14:35,720
+functions need not to be integrable يعني هذا إعلان
+
+833
+01:14:35,720 --> 01:14:38,340
+the composition of two integrable functions need
+
+834
+01:14:38,340 --> 01:14:42,420
+not to be integrable but if phi the first one is
+
+835
+01:14:42,420 --> 01:14:46,340
+continuous then phi composite of f is integrable
+
+836
+01:14:46,340 --> 01:14:50,620
+كما شفنا في العقل اللي هو النظرية الأولى طيب نيجي
+
+837
+01:14:50,620 --> 01:14:53,000
+الآن المثال الأخير بيقولنا يا جماعة the
+
+838
+01:14:53,000 --> 01:14:55,760
+composition of integrable functions need not to be
+
+839
+01:14:55,760 --> 01:14:59,540
+integrableفي عندى سؤالين اصلا معاكم homework
+
+840
+01:14:59,540 --> 01:15:03,860
+السؤال الاول بيقوللنا لو كانت f of x بتساوي واحد
+
+841
+01:15:03,860 --> 01:15:07,540
+ده كانت x بتساوي سفر و zero ده كانت x is
+
+842
+01:15:07,540 --> 01:15:11,760
+irrational و كانت f of x بتساوي واحد لما x بيساوي
+
+843
+01:15:11,760 --> 01:15:16,160
+m على n حيث ال m و ال n عبارة عن integers و العامل
+
+844
+01:15:16,160 --> 01:15:19,740
+المشترك الاعلى بينهم ايه اشمله بادر بيساوي واحد
+
+845
+01:15:19,740 --> 01:15:23,540
+يعني شولنا كل العامل المشترك اللى بينهم و كتبنا x
+
+846
+01:15:23,540 --> 01:15:28,900
+بتساوي m على nطيب، هذه عبارة عن دالة معرفة من الـ0
+
+847
+01:15:28,900 --> 01:15:32,460
+والـ1 لعند الـR يعني هذي X is rational well في
+
+848
+01:15:32,460 --> 01:15:36,320
+الفترة 0 و1 و X بيبقى بيساوي M على N يعني rational
+
+849
+01:15:36,320 --> 01:15:41,260
+في الفترة 0 و1 وفرضنا لل X بتساوي صفر قيمته إيش
+
+850
+01:15:41,260 --> 01:15:48,070
+بتساوي؟ بتساوي 1 هذي الآن by exercise 7.1.11مطلوب
+
+851
+01:15:48,070 --> 01:15:51,790
+منك أنك تثبت أن F is يشملها is integrable on I
+
+852
+01:15:51,790 --> 01:15:55,070
+ويوم ما تعرفوش تحلوه ان شاء الله بنحلوه و بنصوره
+
+853
+01:15:55,070 --> 01:16:00,030
+بإذن الله الآن السؤال التاني اللي هعتمد عليه برضه
+
+854
+01:16:00,030 --> 01:16:03,170
+أنه ال function التاني اللي هي G من I لعند R هذه
+
+855
+01:16:03,170 --> 01:16:07,790
+سهلة أصلا لإثباتها be defined by G of X step
+
+856
+01:16:07,790 --> 01:16:12,090
+function بسيطة يعنيأو خلّيني أقول فيها jump و بس
+
+857
+01:16:12,090 --> 01:16:17,030
+jump على نقطة بس جيوب x بيساوي 0 إذا كانت x بيساوي
+
+858
+01:16:17,030 --> 01:16:21,410
+0 و بيساوي 1 إذا كانت x في الفترة من 0 لعند 1 اللي
+
+859
+01:16:21,410 --> 01:16:25,410
+هو a closed عند الواحد يعني الآن هذا ال function
+
+860
+01:16:25,410 --> 01:16:29,110
+بيقوللي برضه في ال exercise مطلوب برضه في exercise
+
+861
+01:16:29,110 --> 01:16:33,090
+717 برضه اللي هو homework معكم في ال exercise
+
+862
+01:16:33,090 --> 01:16:36,270
+بيقولك اثبت ان g ايش معناها is integrable function
+
+863
+01:16:36,920 --> 01:16:40,960
+إذا الـ F والـ G عبارة عن two integrable functions
+
+864
+01:16:40,960 --> 01:16:46,780
+two integrable functions هاي ال F من I لعند R والـ
+
+865
+01:16:46,780 --> 01:16:55,200
+G اللي هو من عند I لعند R لاحظ ان الـ G فيه لغة
+
+866
+01:16:55,200 --> 01:17:00,600
+تانية zero لمين يا واحدعندي هذه فئلها الـ 1 و 0 و
+
+867
+01:17:00,600 --> 01:17:06,800
+في عندنا قيم أخرى اللي هو كثيرة طيب، الآن عندي ..
+
+868
+01:17:06,800 --> 01:17:09,660
+لو جيت حسب الـ G composed of F مش غريبة عليكم
+
+869
+01:17:09,660 --> 01:17:14,480
+الدالة هذه G composed of F of X خلينا نحسبها مع
+
+870
+01:17:14,480 --> 01:17:20,860
+بعض و بنقول خلصنا اللي هو S section أو قولنا ان
+
+871
+01:17:20,860 --> 01:17:24,320
+الـ G composed of F هذه اللي انتوا بتعرفوها انها
+
+872
+01:17:24,320 --> 01:17:36,430
+is not integrableجي كومبوزيت F of اللي هو عندي
+
+873
+01:17:36,430 --> 01:17:46,900
+الجي الـ F of X هيها لاخد جي of اللي هو Zeroبساوي
+
+874
+01:17:46,900 --> 01:17:55,920
+g of f of 0 بساوي g of f of 0 بساوي
+
+875
+01:17:55,920 --> 01:17:57,880
+g of f of 0 بساوي g of f of 0 بساوي g of f of 0
+
+876
+01:17:57,880 --> 01:18:06,220
+بساوي g of f of 0 بساوي g of f of 0 بساوي g of f
+
+877
+01:18:06,220 --> 01:18:07,060
+of 0 بساوي g of f of 0 بساوي g of f of 0 بساوي g
+
+878
+01:18:07,060 --> 01:18:07,140
+of f of 0 بساوي g of f of 0 بساوي g of f of 0
+
+879
+01:18:07,140 --> 01:18:08,100
+بساوي g of f of 0 بساوي g of f of 0 بساوي g of f
+
+880
+01:18:08,100 --> 01:18:09,880
+of 0 بساوي g of f of 0 بساوي g of f of 0 بساوي g
+
+881
+01:18:09,880 --> 01:18:14,160
+of f of 0 بساوي g of f of 0 بساوي g of f of 0
+
+882
+01:18:14,160 --> 01:18:17,110
+of 0 بساوي g of f ofX اللي هو irrational يعني
+
+883
+01:18:17,110 --> 01:18:22,230
+irrational G of irrational اللي هو اللي هو الموجود
+
+884
+01:18:22,230 --> 01:18:25,910
+في الفترة Zero و واحد G of irrational إيش هيساوي
+
+885
+01:18:25,910 --> 01:18:31,290
+حسب التعريف .. التعريف هنا بيساوي G of F of
+
+886
+01:18:31,290 --> 01:18:38,750
+irrational irrational هاي بيساوي اللي هو G of F of
+
+887
+01:18:38,750 --> 01:18:44,240
+irrational إيش بيساوي سفرو G of 0 ايش بيسوي هنا G
+
+888
+01:18:44,240 --> 01:18:52,420
+of 0 بيسوي Zero معرفليها بيسوي ايش صفر ا الثالثة
+
+889
+01:18:54,350 --> 01:18:58,630
+Composite F of مين ضال؟ Of اللي هي irrational
+
+890
+01:18:58,630 --> 01:19:02,530
+البجيات غير الـ Zero هذا أصلا هو جسمها irrational
+
+891
+01:19:02,530 --> 01:19:08,410
+و rational جهتين واحدة واحدة واحدة Zero لحالها و
+
+892
+01:19:08,410 --> 01:19:11,650
+واحدة كل ال rational اللي بين Zero و واحد ما عدا
+
+893
+01:19:11,650 --> 01:19:18,870
+ال Zero اللي هو G of X اللي هي عبارة عن M على N
+
+894
+01:19:19,590 --> 01:19:23,630
+اللي هي rational في الواقع رياشونال كلهم معدن اللي
+
+895
+01:19:23,630 --> 01:19:28,790
+فوق اللي فوق حسبناها طلعت واحد ويساوي G of F of M
+
+896
+01:19:28,790 --> 01:19:34,350
+على N ويساوي G of F of M على N أيش بتساوي واحد على
+
+897
+01:19:34,350 --> 01:19:38,910
+N ويساوي G of واحد على N أيش بتحسبها هذه هذا اصلا
+
+898
+01:19:38,910 --> 01:19:42,070
+الدالة دايما بتساوي واحد معدن عند سفر حتى سفر عشان
+
+899
+01:19:42,070 --> 01:19:46,750
+تعملنا المشكلة G of واحد على N أيش بتساوي واحد هو
+
+900
+01:19:46,750 --> 01:19:53,580
+يساوي واحدمن هذا كله صار عندي g composite f of x
+
+901
+01:19:53,580 --> 01:20:06,710
+بتساوي 0 if x أشمالها is irrational ويساوي 1 1إذا
+
+902
+01:20:06,710 --> 01:20:11,790
+كانت X is هاي ال rational كله ما عدا السفر وهي
+
+903
+01:20:11,790 --> 01:20:16,670
+السفر برضه طلع واحد if X is rational وهدد دالة
+
+904
+01:20:16,670 --> 01:20:20,610
+تبعتنا اللي اعتبتناها المرة الماضية انها is not
+
+905
+01:20:20,610 --> 01:20:24,590
+integrable function لحظوا انتوا بس خليني نقول شوف
+
+906
+01:20:24,590 --> 01:20:32,660
+هالغرابة مش غرابة لأ هو مهم بالكلامإنه اللي خلف
+
+907
+01:20:32,660 --> 01:20:37,380
+الموضوع لو كانت G continuous على كل ال domain على
+
+908
+01:20:37,380 --> 01:20:40,820
+طول الـ G continuous ده هتطلع ان انتجر بالغصب عنها
+
+909
+01:20:40,820 --> 01:20:44,560
+من النظرية اللي قبل شوية لكن اللي خلف الموضوع شغلة
+
+910
+01:20:44,560 --> 01:20:49,440
+واحدة شايفين هالدالة هاد ال G of X الـ G of X G of
+
+911
+01:20:49,440 --> 01:20:55,000
+X بتساوي اللي هو سفر عند السفر ومن عند ال zero
+
+912
+01:20:55,000 --> 01:21:01,130
+لعند الواحد هناالدالة قيمتها إيش بتساوي؟ واحد، هاي
+
+913
+01:21:01,130 --> 01:21:04,270
+قيمتها واحد، بين Zero والواحد قيمتها واحد، هذا
+
+914
+01:21:04,270 --> 01:21:09,540
+الـG of X اللي عندييعني هذا كل حال عالي العالي ما
+
+915
+01:21:09,540 --> 01:21:14,120
+عدا عند من عند السفر فيه jump point هذه النقطة
+
+916
+01:21:14,120 --> 01:21:20,200
+الوحيدة اللي فيها discontinuity هي اللي .. اللي
+
+917
+01:21:20,200 --> 01:21:25,340
+انا بنشرتلي انها تصير decomposed F is continuous و
+
+918
+01:21:25,340 --> 01:21:29,200
+هذا عشان نعرف جداش الرياضيات او جداش التحليل دقيق
+
+919
+01:21:29,780 --> 01:21:35,960
+دقيق ان ان احنا نقطة واحدة .. نقطة واحدة اللي كانت
+
+920
+01:21:35,960 --> 01:21:40,360
+عندها point of discontinuity جالتلي ان الـ
+
+921
+01:21:40,360 --> 01:21:44,680
+decomposite F need not to be integrable وهي المثال
+
+922
+01:21:44,680 --> 01:21:50,720
+أمامكم و .. و هيك بيكون احنا خلصنا ال section
+
+923
+01:21:50,720 --> 01:21:56,730
+التاني من اللي هو chapter 7و هاي ال homework عندكم
+
+924
+01:21:56,730 --> 01:22:02,630
+مطلوبة 1,2,4,7,10,17,18,19 و ان شاء الله المرة
+
+925
+01:22:02,630 --> 01:22:08,950
+القادمة بنكمل و بنشرح 7.3 اللي هو ال fundamental
+
+926
+01:22:08,950 --> 01:22:10,550
+theorem of calculus
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b609f3122ddfb7a483eeaf3ded4c818f3c698bac
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/64kJ1lF4GJg_raw.json
@@ -0,0 +1 @@
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أصل هيك بدي اللي هو أستخدم اللي هو المعطيات اللي موجودة عندى الان هستخدم أمرين هستخدم اكيد ال continuity للـ Phi", "tokens": [6027, 7649, 23758, 2423, 3224, 3215, 5172, 13672, 1829, 47525, 3224, 5551, 36520, 3224, 39896, 4117, 47525, 3224, 5551, 36520, 39896, 4117, 2423, 7649, 6225, 8592, 7649, 5551, 36520, 39896, 4117, 4724, 16254, 13672, 1829, 31439, 5551, 14851, 9778, 40448, 13672, 1829, 31439, 9673, 3615, 9566, 1829, 9307, 13672, 1829, 3714, 29245, 23328, 3660, 43242, 7578, 2423, 7649, 8032, 14851, 9778, 40448, 5551, 29973, 9957, 8032, 14851, 9778, 40448, 1975, 4117, 25708, 2423, 23807, 24976, 39184, 41435], "avg_logprob": -0.20322515662664023, "compression_ratio": 1.8525641025641026, "no_speech_prob": 2.086162567138672e-06, "words": [{"start": 291.26, "end": 291.86, "word": "الان", "probability": 0.769775390625}, {"start": 291.86, "end": 292.52, "word": " هذا", "probability": 0.82861328125}, {"start": 292.52, "end": 292.88, "word": " الهدف", "probability": 0.9697265625}, {"start": 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"ليش هيك؟ بغرض الحسابات بعد شوية هتشوفوا ليش و لو أصلا احنا في النهاية الـ Epsilon الـ Prime هذه ما كتبناش بالشكل هذا و طلع عندي اللي هو الـ U of B أو Phi Composite F ناقص الـ B Phi Composite F", "tokens": [20292, 8592, 39896, 4117, 22807, 4724, 17082, 43042, 21542, 3794, 16758, 9307, 39182, 13412, 2407, 10632, 8032, 2655, 8592, 38688, 14407, 32239, 8592, 4032, 45164, 5551, 9381, 15040, 1975, 5016, 8315, 8978, 28239, 11296, 10632, 2423, 39184, 462, 16592, 2423, 39184, 9655, 29538, 19446, 9122, 2655, 3555, 1863, 33599, 20666, 8592, 28820, 23758, 4032, 23032, 1211, 3615, 18871, 16254, 13672, 1829, 31439, 2423, 39184, 624, 295, 363, 34051, 41435, 6620, 329, 642, 479, 8717, 995, 4587, 9381, 2423, 39184, 363, 41435, 6620, 329, 642, 479], "avg_logprob": -0.2407340055634809, "compression_ratio": 1.530612244897959, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 536.94, "end": 537.56, "word": "ليش", "probability": 0.56781005859375}, {"start": 537.56, "end": 538.84, "word": " 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" B", "probability": 0.85009765625}, {"start": 558.54, "end": 559.94, "word": " Phi", "probability": 0.90673828125}, {"start": 559.94, "end": 560.98, "word": " Composite", "probability": 0.9588216145833334}, {"start": 560.98, "end": 561.38, "word": " F", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 27, "seek": 56827, "start": 561.65, "end": 568.27, "text": "يكون أصغر من إبسلون مضروبة في something أي إشي something ثابت", "tokens": [1829, 30544, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 3714, 11242, 32887, 49401, 8978, 746, 36632, 11933, 8592, 1829, 746, 38637, 16758, 2655], "avg_logprob": -0.20124421296296297, "compression_ratio": 1.1325301204819278, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 561.65, "end": 562.21, "word": "يكون", "probability": 0.916259765625}, {"start": 562.21, "end": 563.17, "word": " أصغر", "probability": 0.952880859375}, {"start": 563.17, "end": 563.49, "word": " من", "probability": 0.97802734375}, {"start": 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is uniformly continuous on مين؟ on C أو D", "tokens": [2670, 318, 8717, 995, 4587, 9381, 41435, 295, 314, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 462, 16592, 4724, 23557, 32640, 13672, 1829, 5551, 9778, 3215, 2655, 11296, 18871, 16254, 5296, 10721, 1829, 462, 16592, 8978, 32748, 22653, 995, 23758, 2423, 28820, 10943, 4724, 36081, 5016, 4587, 4587, 9154, 11778, 11536, 14739, 8032, 2304, 462, 16592, 4724, 23557, 32640, 13672, 1829, 11331, 4117, 36081, 18871, 11296, 6156, 30543, 23032, 1829, 3555, 11933, 15730, 16247, 1863, 13672, 1829, 44713, 9778, 40448, 47395, 4724, 15042, 14739, 41435, 10957, 15844, 383, 4032, 35, 11933, 15730, 41435, 307, 48806, 10957, 322, 3714, 9957, 22807, 322, 383, 34051, 413], "avg_logprob": -0.22155070079947417, "compression_ratio": 1.6398305084745763, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 698.35, "end": 698.69, "word": "of", "probability": 0.345947265625}, {"start": 698.69, "end": 699.19, "word": " S", "probability": 0.515625}, 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"end": 959.93, "word": " Delta", "probability": 0.65673828125}, {"start": 959.93, "end": 960.37, "word": " أصغر", "probability": 0.9901123046875}, {"start": 960.37, "end": 960.47, "word": " من", "probability": 0.99462890625}, {"start": 960.47, "end": 960.79, "word": " يبسلون", "probability": 0.99541015625}, {"start": 960.79, "end": 961.11, "word": " برايم", "probability": 0.98291015625}, {"start": 961.11, "end": 961.43, "word": " لأنه", "probability": 0.8776041666666666}, {"start": 961.43, "end": 962.95, "word": " اختار", "probability": 0.8216145833333334}, {"start": 962.95, "end": 963.39, "word": " الدلتة", "probability": 0.7186279296875}, {"start": 963.39, "end": 963.63, "word": " هي", "probability": 0.876953125}, {"start": 963.63, "end": 964.07, "word": " Delta", "probability": 0.63525390625}, {"start": 964.07, "end": 964.83, "word": " إبرايم", "probability": 0.645721435546875}, {"start": 964.83, "end": 965.09, "word": " إذن", "probability": 0.6666666666666666}, {"start": 965.09, "end": 965.25, "word": " في", "probability": 0.83447265625}, {"start": 965.25, "end": 965.55, "word": " كل", "probability": 0.99609375}, {"start": 965.55, "end": 966.33, "word": " الحالات", "probability": 0.9405924479166666}, {"start": 966.33, "end": 967.09, "word": " هي", "probability": 0.306396484375}, {"start": 967.09, "end": 967.97, "word": " المربط", "probability": 0.8091634114583334}, {"start": 967.97, "end": 968.49, "word": " الفلسفي", "probability": 0.8607421875}, {"start": 968.49, "end": 968.73, "word": " الآن", "probability": 0.696044921875}, {"start": 968.73, "end": 968.93, "word": " there", "probability": 0.276611328125}, {"start": 968.93, "end": 969.39, "word": " exists", "probability": 0.638671875}, {"start": 969.39, "end": 970.05, "word": " Delta", "probability": 0.59326171875}, {"start": 970.05, "end": 971.97, "word": " أكبر", "probability": 0.98095703125}, {"start": 971.97, "end": 972.17, "word": " من", "probability": 0.99853515625}, {"start": 972.17, "end": 972.45, 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Phi", "probability": 0.87353515625}, {"start": 1084.93, "end": 1085.03, "word": " of", "probability": 0.91552734375}, {"start": 1085.03, "end": 1085.15, "word": " T", "probability": 0.99267578125}, {"start": 1085.15, "end": 1085.47, "word": " أصغر", "probability": 0.9949951171875}, {"start": 1085.47, "end": 1085.65, "word": " من", "probability": 0.99462890625}, {"start": 1085.65, "end": 1086.89, "word": " إبسلون", "probability": 0.813037109375}, {"start": 1086.89, "end": 1087.21, "word": " برايم", "probability": 0.6479899088541666}, {"start": 1087.21, "end": 1087.43, "word": " هذه", "probability": 0.2183837890625}, {"start": 1087.43, "end": 1087.59, "word": " اللي", "probability": 0.97412109375}, {"start": 1087.59, "end": 1088.03, "word": " وصلنا", "probability": 0.9845377604166666}, {"start": 1088.03, "end": 1088.45, "word": " إليها", "probability": 0.9371744791666666}, {"start": 1088.45, "end": 1089.37, "word": " اللي", "probability": 0.935302734375}, {"start": 1089.37, "end": 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المعلومة الآن بدي أستخدم المعلومة الموازية لها أن F is integrable الان عندي F is integrable on I إذا حسب then حسب اللي هو ال .. ال .. ال integrability criterion", "tokens": [6027, 148, 48506, 44713, 17082, 1211, 4587, 8315, 20449, 1211, 20498, 3660, 2423, 39184, 498, 286, 307, 10957, 4032, 5016, 36520, 8315, 15844, 20449, 1211, 20498, 3660, 3714, 16095, 3660, 10874, 28259, 14111, 39896, 29538, 9673, 30241, 20498, 3660, 6024, 48506, 4724, 16254, 5551, 14851, 9778, 40448, 9673, 30241, 20498, 3660, 9673, 2407, 31377, 10632, 5296, 11296, 14739, 479, 307, 16200, 424, 638, 2423, 7649, 18871, 16254, 479, 307, 16200, 424, 638, 322, 286, 11933, 15730, 11331, 35457, 550, 11331, 35457, 13672, 1829, 31439, 2423, 4386, 2423, 4386, 2423, 3572, 2310, 46691], "avg_logprob": -0.23303091461940478, "compression_ratio": 1.7095238095238094, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1097.45, "end": 1097.95, "word": "الآن", "probability": 0.6885579427083334}, {"start": 1097.95, "end": 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1104.03, "end": 1104.23, "word": " هي", "probability": 0.6201171875}, {"start": 1104.23, "end": 1104.49, "word": " هذه", "probability": 0.90869140625}, {"start": 1104.49, "end": 1105.01, "word": " المعلومة", "probability": 0.9892578125}, {"start": 1105.01, "end": 1105.29, "word": " الآن", "probability": 0.6812744140625}, {"start": 1105.29, "end": 1105.51, "word": " بدي", "probability": 0.43359375}, {"start": 1105.51, "end": 1106.01, "word": " أستخدم", "probability": 0.85601806640625}, {"start": 1106.01, "end": 1106.57, "word": " المعلومة", "probability": 0.948486328125}, {"start": 1106.57, "end": 1108.09, "word": " الموازية", "probability": 0.9447021484375}, {"start": 1108.09, "end": 1108.43, "word": " لها", "probability": 0.667236328125}, {"start": 1108.43, "end": 1108.63, "word": " أن", "probability": 0.5390625}, {"start": 1108.63, "end": 1108.93, "word": " F", "probability": 0.496337890625}, {"start": 1108.93, "end": 1109.19, "word": " is", "probability": 0.96533203125}, {"start": 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"probability": 0.8466796875}, {"start": 1130.11, "end": 1130.33, "word": " B", "probability": 0.82421875}, {"start": 1130.33, "end": 1130.57, "word": " of", "probability": 0.87060546875}, {"start": 1130.57, "end": 1131.09, "word": " I", "probability": 0.97802734375}, {"start": 1131.09, "end": 1131.93, "word": " بجزء", "probability": 0.9259033203125}, {"start": 1131.93, "end": 1132.47, "word": " مين", "probability": 0.657958984375}, {"start": 1132.47, "end": 1133.17, "word": " I", "probability": 0.873046875}, {"start": 1133.17, "end": 1133.99, "word": " such", "probability": 0.8662109375}, {"start": 1133.99, "end": 1134.97, "word": " that", "probability": 0.9541015625}, {"start": 1134.97, "end": 1135.41, "word": " اللي", "probability": 0.603515625}, {"start": 1135.41, "end": 1135.81, "word": " هو", "probability": 0.970703125}, {"start": 1135.81, "end": 1136.69, "word": " U", "probability": 0.837890625}, {"start": 1136.69, "end": 1137.89, "word": " of", "probability": 0.88330078125}, {"start": 1137.89, "end": 1139.07, "word": " B", "probability": 0.953125}, {"start": 1139.07, "end": 1140.49, "word": " وF", "probability": 0.622314453125}], "temperature": 1.0}, {"id": 53, "seek": 116668, "start": 1140.98, "end": 1166.68, "text": "معقس L بيوقف أصغر من أي إبسلون في الدنيا الإبسلون اللي في الدنيا الإبسلون اللي بدها استخدمها اللي حتة في الدنيا اللي هي مين هي Delta تربيع أصغر من مين من Delta تربيع بقدر أه بقدر طبعا مش احنا بنقول لكل إبسلون أكبر من سفر مادام F is integrable لذا لكل إبسلون أكبر من سفر there exist ال partition B بحيث أنه هذا أصغر من إبسلون", "tokens": [2304, 3615, 4587, 3794, 441, 4724, 1829, 30543, 5172, 5551, 9381, 17082, 2288, 9154, 36632, 11933, 3555, 3794, 1211, 11536, 8978, 32748, 22653, 995, 33688, 3555, 3794, 1211, 11536, 13672, 1829, 8978, 32748, 22653, 995, 33688, 3555, 3794, 1211, 11536, 13672, 1829, 47525, 11296, 44713, 9778, 40448, 11296, 13672, 1829, 11331, 2655, 3660, 8978, 32748, 22653, 995, 13672, 1829, 39896, 3714, 9957, 39896, 18183, 6055, 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"word": " أصغر", "probability": 0.95361328125}, {"start": 1144.28, "end": 1144.4, "word": " من", "probability": 0.98876953125}, {"start": 1144.4, "end": 1144.6, "word": " أي", "probability": 0.94091796875}, {"start": 1144.6, "end": 1145.12, "word": " إبسلون", "probability": 0.77197265625}, {"start": 1145.12, "end": 1145.28, "word": " في", "probability": 0.9453125}, {"start": 1145.28, "end": 1145.92, "word": " الدنيا", "probability": 0.9905598958333334}, {"start": 1145.92, "end": 1147.0, "word": " الإبسلون", "probability": 0.91650390625}, {"start": 1147.0, "end": 1147.14, "word": " اللي", "probability": 0.910888671875}, {"start": 1147.14, "end": 1147.26, "word": " في", "probability": 0.85302734375}, {"start": 1147.26, "end": 1147.58, "word": " الدنيا", "probability": 0.99072265625}, {"start": 1147.58, "end": 1148.1, "word": " الإبسلون", "probability": 0.83017578125}, {"start": 1148.1, "end": 1148.2, "word": " اللي", "probability": 0.96044921875}, {"start": 1148.2, "end": 1148.36, "word": " بدها", "probability": 0.341796875}, {"start": 1148.36, "end": 1148.86, "word": " استخدمها", "probability": 0.8592529296875}, {"start": 1148.86, "end": 1149.0, "word": " اللي", "probability": 0.810546875}, {"start": 1149.0, "end": 1149.24, "word": " حتة", "probability": 0.709716796875}, {"start": 1149.24, "end": 1149.36, "word": " في", "probability": 0.93115234375}, {"start": 1149.36, "end": 1149.82, "word": " الدنيا", "probability": 0.9900716145833334}, {"start": 1149.82, "end": 1150.22, "word": " اللي", "probability": 0.950439453125}, {"start": 1150.22, "end": 1150.36, "word": " هي", "probability": 0.75244140625}, {"start": 1150.36, "end": 1150.62, "word": " مين", "probability": 0.886474609375}, {"start": 1150.62, "end": 1150.98, "word": " هي", "probability": 0.71337890625}, {"start": 1150.98, "end": 1152.04, "word": " Delta", "probability": 0.4404296875}, {"start": 1152.04, "end": 1152.6, "word": " تربيع", "probability": 0.76434326171875}, {"start": 1152.6, "end": 1152.98, "word": " أصغر", "probability": 0.980224609375}, {"start": 1152.98, "end": 1153.14, "word": " من", "probability": 0.98876953125}, {"start": 1153.14, "end": 1153.44, "word": " مين", "probability": 0.8642578125}, {"start": 1153.44, "end": 1153.94, "word": " من", "probability": 0.8017578125}, {"start": 1153.94, "end": 1154.32, "word": " Delta", "probability": 0.8876953125}, {"start": 1154.32, "end": 1155.22, "word": " تربيع", "probability": 0.927001953125}, {"start": 1155.22, "end": 1156.06, "word": " بقدر", "probability": 0.9225260416666666}, {"start": 1156.06, "end": 1156.26, "word": " أه", "probability": 0.7261962890625}, {"start": 1156.26, "end": 1156.6, "word": " بقدر", "probability": 0.95556640625}, {"start": 1156.6, "end": 1157.0, "word": " طبعا", "probability": 0.981201171875}, {"start": 1157.0, "end": 1157.22, "word": " مش", "probability": 0.79443359375}, {"start": 1157.22, "end": 1157.38, "word": " احنا", "probability": 0.8572591145833334}, {"start": 1157.38, "end": 1157.68, "word": " بنقول", "probability": 0.9033203125}, {"start": 1157.68, "end": 1157.94, "word": " لكل", "probability": 0.93310546875}, {"start": 1157.94, "end": 1158.2, "word": " إبسلون", "probability": 0.9771484375}, {"start": 1158.2, "end": 1158.4, "word": " أكبر", "probability": 0.9718424479166666}, {"start": 1158.4, "end": 1158.56, "word": " من", "probability": 0.9970703125}, {"start": 1158.56, "end": 1158.94, "word": " سفر", "probability": 0.7564290364583334}, {"start": 1158.94, "end": 1159.66, "word": " مادام", "probability": 0.5830891927083334}, {"start": 1159.66, "end": 1159.8, "word": " F", "probability": 0.386962890625}, {"start": 1159.8, "end": 1159.96, "word": " is", "probability": 0.9296875}, {"start": 1159.96, "end": 1160.4, "word": " integrable", "probability": 0.747802734375}, {"start": 1160.4, "end": 1160.62, "word": " لذا", "probability": 0.7216796875}, {"start": 1160.62, "end": 1160.9, "word": " لكل", "probability": 0.97705078125}, {"start": 1160.9, "end": 1161.16, "word": " إبسلون", "probability": 0.98505859375}, {"start": 1161.16, "end": 1161.38, "word": " أكبر", "probability": 0.9806315104166666}, {"start": 1161.38, "end": 1161.54, "word": " من", "probability": 0.9970703125}, {"start": 1161.54, "end": 1161.98, "word": " سفر", "probability": 0.9939778645833334}, {"start": 1161.98, "end": 1162.46, "word": " there", "probability": 0.73828125}, {"start": 1162.46, "end": 1163.04, "word": " exist", "probability": 0.623046875}, {"start": 1163.04, "end": 1163.34, "word": " ال", "probability": 0.327880859375}, {"start": 1163.34, "end": 1163.72, "word": " partition", "probability": 0.66015625}, {"start": 1163.72, "end": 1164.12, "word": " B", "probability": 0.408203125}, {"start": 1164.12, "end": 1164.56, "word": " بحيث", "probability": 0.9481201171875}, {"start": 1164.56, "end": 1164.86, "word": " أنه", "probability": 0.72705078125}, {"start": 1164.86, "end": 1165.26, "word": " هذا", "probability": 0.9150390625}, {"start": 1165.26, "end": 1165.56, "word": " أصغر", "probability": 0.9871826171875}, {"start": 1165.56, "end": 1165.72, "word": " من", "probability": 0.99365234375}, {"start": 1165.72, "end": 1166.68, "word": " إبسلون", "probability": 0.914453125}], "temperature": 1.0}, {"id": 54, "seek": 119523, "start": 1167.19, "end": 1195.23, "text": "الأن أبسط من اللي بحكي عنها دلتة تربيع دلفة التربيع أكبر من صفر إذا for delta تربيع there exists B element in B of I such that U ناقص L أصغر من مين من Delta تربيع هذا ال partition B بيجزئلي مين؟ بيجزئلي I بعد أذنكم سموليها بيه X0 و X1 لعند مين؟ لعند X سموليها ال partition بس عشان أتعامل معاها", "tokens": [6027, 33456, 5551, 3555, 3794, 9566, 9154, 13672, 1829, 4724, 5016, 4117, 1829, 18871, 11296, 11778, 1211, 2655, 3660, 6055, 2288, 21292, 3615, 11778, 46538, 3660, 16712, 2288, 21292, 3615, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 11933, 15730, 337, 8289, 6055, 2288, 21292, 3615, 456, 8198, 363, 4478, 294, 363, 295, 286, 1270, 300, 624, 8717, 995, 4587, 9381, 441, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 18183, 6055, 2288, 21292, 3615, 23758, 2423, 24808, 363, 4724, 1829, 7435, 11622, 19986, 20292, 3714, 9957, 22807, 4724, 1829, 7435, 11622, 19986, 20292, 286, 39182, 5551, 8848, 1863, 24793, 8608, 2304, 2407, 20292, 11296, 4724, 1829, 3224, 1783, 15, 4032, 1783, 16, 5296, 3615, 41260, 3714, 9957, 22807, 5296, 3615, 41260, 1783, 8608, 2304, 2407, 20292, 11296, 2423, 24808, 4724, 3794, 6225, 8592, 7649, 5551, 2655, 3615, 10943, 1211, 20449, 995, 11296], "avg_logprob": -0.2891171266148974, "compression_ratio": 1.699248120300752, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1167.19, "end": 1167.59, "word": "الأن", "probability": 0.6541748046875}, {"start": 1167.59, "end": 1167.91, "word": " أبسط", "probability": 0.704193115234375}, {"start": 1167.91, "end": 1168.03, "word": " من", "probability": 0.86376953125}, {"start": 1168.03, "end": 1168.09, "word": " اللي", "probability": 0.7130126953125}, {"start": 1168.09, "end": 1168.35, "word": " بحكي", "probability": 0.9547119140625}, {"start": 1168.35, "end": 1168.69, "word": " عنها", "probability": 0.9931640625}, {"start": 1168.69, "end": 1169.31, "word": " دلتة", "probability": 0.646484375}, {"start": 1169.31, "end": 1169.65, "word": " تربيع", "probability": 0.83544921875}, {"start": 1169.65, "end": 1170.11, "word": " دلفة", "probability": 0.4496256510416667}, {"start": 1170.11, "end": 1170.33, "word": " التربيع", "probability": 0.8265380859375}, {"start": 1170.33, "end": 1170.49, "word": " أكبر", "probability": 0.93212890625}, {"start": 1170.49, "end": 1170.63, "word": " من", "probability": 0.99609375}, {"start": 1170.63, "end": 1170.93, "word": " صفر", "probability": 0.74072265625}, {"start": 1170.93, "end": 1171.51, "word": " إذا", "probability": 0.51068115234375}, {"start": 1171.51, "end": 1172.53, "word": " for", "probability": 0.69580078125}, {"start": 1172.53, "end": 1173.49, "word": " delta", "probability": 0.4169921875}, {"start": 1173.49, "end": 1174.29, "word": " تربيع", "probability": 0.940185546875}, {"start": 1174.29, "end": 1174.65, "word": " there", "probability": 0.83056640625}, {"start": 1174.65, "end": 1175.21, "word": " exists", "probability": 0.487548828125}, {"start": 1175.21, "end": 1175.65, "word": " B", "probability": 0.50390625}, {"start": 1175.65, "end": 1176.37, "word": " element", "probability": 0.2257080078125}, {"start": 1176.37, "end": 1176.65, "word": " in", "probability": 0.89697265625}, {"start": 1176.65, "end": 1176.77, "word": " B", "probability": 0.8095703125}, {"start": 1176.77, "end": 1176.95, "word": " of", "probability": 0.80517578125}, {"start": 1176.95, "end": 1177.23, "word": " I", "probability": 0.97412109375}, {"start": 1177.23, "end": 1177.83, "word": " such", "probability": 0.8876953125}, {"start": 1177.83, "end": 1178.21, "word": " that", "probability": 0.95654296875}, {"start": 1178.21, "end": 1178.47, "word": " U", "probability": 0.83740234375}, {"start": 1178.47, "end": 1178.95, "word": " ناقص", "probability": 0.9449462890625}, {"start": 1178.95, "end": 1179.13, "word": " L", "probability": 0.5009765625}, {"start": 1179.13, "end": 1179.47, "word": " أصغر", "probability": 0.9837646484375}, {"start": 1179.47, "end": 1179.67, "word": " من", "probability": 0.99365234375}, {"start": 1179.67, "end": 1180.07, "word": " مين", "probability": 0.853515625}, {"start": 1180.07, "end": 1180.73, "word": " من", "probability": 0.94873046875}, {"start": 1180.73, "end": 1181.19, "word": " Delta", "probability": 0.31005859375}, {"start": 1181.19, "end": 1181.85, "word": " تربيع", "probability": 0.90283203125}, {"start": 1181.85, "end": 1182.57, "word": " هذا", "probability": 0.9072265625}, {"start": 1182.57, "end": 1182.73, "word": " ال", "probability": 0.943359375}, {"start": 1182.73, "end": 1183.07, "word": " partition", "probability": 0.75244140625}, {"start": 1183.07, "end": 1183.37, "word": " B", "probability": 0.79150390625}, {"start": 1183.37, "end": 1183.97, "word": " بيجزئلي", "probability": 0.7069498697916666}, {"start": 1183.97, "end": 1184.65, "word": " مين؟", "probability": 0.9060872395833334}, {"start": 1184.65, "end": 1185.23, "word": " بيجزئلي", "probability": 0.983642578125}, {"start": 1185.23, "end": 1185.45, "word": " I", "probability": 0.986328125}, {"start": 1185.45, "end": 1186.15, "word": " بعد", "probability": 0.92236328125}, {"start": 1186.15, "end": 1186.67, "word": " أذنكم", "probability": 0.7896728515625}, {"start": 1186.67, "end": 1187.59, "word": " سموليها", "probability": 0.6234375}, {"start": 1187.59, "end": 1188.49, "word": " بيه", "probability": 0.5330403645833334}, {"start": 1188.49, "end": 1189.43, "word": " X0", "probability": 0.2291259765625}, {"start": 1189.43, "end": 1189.59, "word": " و", "probability": 0.73193359375}, {"start": 1189.59, "end": 1190.37, "word": " X1", "probability": 0.861328125}, {"start": 1190.37, "end": 1190.85, "word": " لعند", "probability": 0.9148763020833334}, {"start": 1190.85, "end": 1191.67, "word": " مين؟", "probability": 0.8243815104166666}, {"start": 1191.67, "end": 1192.05, "word": " لعند", "probability": 0.9617513020833334}, {"start": 1192.05, "end": 1192.33, "word": " X", "probability": 0.9755859375}, {"start": 1192.33, "end": 1193.47, "word": " سموليها", "probability": 0.7446533203125}, {"start": 1193.47, "end": 1193.55, "word": " ال", "probability": 0.75830078125}, {"start": 1193.55, "end": 1193.81, "word": " partition", "probability": 0.87890625}, {"start": 1193.81, "end": 1194.03, "word": " بس", "probability": 0.910888671875}, {"start": 1194.03, "end": 1194.21, "word": " عشان", "probability": 0.9308268229166666}, {"start": 1194.21, "end": 1194.81, "word": " أتعامل", "probability": 0.87919921875}, {"start": 1194.81, "end": 1195.23, "word": " معاها", "probability": 0.803955078125}], "temperature": 1.0}, {"id": 55, "seek": 121964, "start": 1195.66, "end": 1219.64, "text": "اللي هو partition للـ I partition للـ I معناه بجزّه I جزّه او ل X note X واحد X انت جداش أعدادها مش عارف حسب اللي هو اللي جناه بيه طيب شوف الآن بدي أعمل اللي هو شغلة بحيث عن الان أقدر أستخدمها اللي هي أصل للي بدي من خلالها الآن هجيتوا تشوفوا ليش جزعين خدوا A", "tokens": [6027, 20292, 31439, 24808, 24976, 39184, 286, 24808, 24976, 39184, 286, 20449, 8315, 3224, 4724, 7435, 11622, 11703, 3224, 286, 10874, 11622, 11703, 3224, 1975, 2407, 5296, 1783, 3637, 1783, 36764, 24401, 1783, 16472, 2655, 10874, 3215, 33599, 5551, 22488, 18513, 11296, 37893, 6225, 9640, 5172, 11331, 35457, 13672, 1829, 31439, 13672, 1829, 10874, 8315, 3224, 4724, 1829, 3224, 23032, 1829, 3555, 13412, 38688, 6024, 48506, 4724, 16254, 5551, 25957, 1211, 13672, 1829, 31439, 13412, 17082, 37977, 4724, 5016, 1829, 12984, 18871, 2423, 7649, 5551, 28543, 2288, 5551, 14851, 9778, 40448, 11296, 13672, 1829, 39896, 5551, 36520, 5296, 20292, 4724, 16254, 9154, 16490, 1211, 6027, 11296, 6024, 48506, 8032, 7435, 36081, 14407, 6055, 8592, 38688, 14407, 32239, 8592, 10874, 11622, 3615, 9957, 16490, 3215, 14407, 316], "avg_logprob": 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أكبر", "probability": 0.9443359375}, {"start": 2642.4, "end": 2642.74, "word": " سوى", "probability": 0.7159830729166666}, {"start": 2642.74, "end": 2643.88, "word": " مين؟", "probability": 0.7667643229166666}, {"start": 2643.88, "end": 2644.32, "word": " سالب", "probability": 0.96826171875}, {"start": 2644.32, "end": 2644.46, "word": " ال", "probability": 0.8447265625}, {"start": 2644.46, "end": 2646.26, "word": " Phi", "probability": 0.437255859375}, {"start": 2646.26, "end": 2646.64, "word": " of", "probability": 0.9765625}, {"start": 2646.64, "end": 2646.84, "word": " T", "probability": 0.99072265625}, {"start": 2646.84, "end": 2648.1, "word": " فبصير", "probability": 0.9405517578125}, {"start": 2648.1, "end": 2648.5, "word": " عندي", "probability": 0.68212890625}, {"start": 2648.5, "end": 2648.82, "word": " ال", "probability": 0.7939453125}, {"start": 2648.82, "end": 2649.6, "word": " supremum", "probability": 0.7047119140625}, {"start": 2649.6, "end": 2650.38, "word": " اللي", "probability": 0.956787109375}, {"start": 2650.38, "end": 2650.7, "word": " عندي", "probability": 0.79541015625}, {"start": 2650.7, "end": 2650.92, "word": " اللي", "probability": 0.869873046875}, {"start": 2650.92, "end": 2651.3, "word": " هالة", "probability": 0.5541178385416666}, {"start": 2651.3, "end": 2651.6, "word": " هذا", "probability": 0.8779296875}], "temperature": 1.0}, {"id": 113, "seek": 265696, "start": 2652.36, "end": 2656.96, "text": "Supermom لهذه اكيد اصغر او يساوي", "tokens": [30152, 42544, 46740, 24192, 1975, 4117, 25708, 1975, 9381, 17082, 2288, 1975, 2407, 7251, 3794, 995, 45865], "avg_logprob": -0.2914496527777778, "compression_ratio": 0.9444444444444444, "no_speech_prob": 3.4570693969726562e-06, "words": [{"start": 2652.36, "end": 2653.08, "word": "Supermom", "probability": 0.504638671875}, {"start": 2653.08, "end": 2653.6, "word": " لهذه", "probability": 0.84716796875}, {"start": 2653.6, "end": 2655.42, "word": " اكيد", "probability": 0.61126708984375}, {"start": 2655.42, "end": 2656.04, "word": " اصغر", "probability": 0.9544677734375}, {"start": 2656.04, "end": 2656.22, "word": " او", "probability": 0.911865234375}, {"start": 2656.22, "end": 2656.96, "word": " يساوي", "probability": 0.9791259765625}], "temperature": 1.0}, {"id": 114, "seek": 268591, "start": 2657.71, "end": 2685.91, "text": "اللي هو الـ Supremum هذا اللي هو K لأن الـ Supremum هذا عالمين على كل الفترة C وD هنا اللي هي عالمين على X element in XK مانس واحد و XK لأن هذا Similarly أكيد الـ Supremum للـ Absolute Value هيكون أكبر أو يساوي الـ Supremum لهذه من جهتين أنه Absolute Value وفي نفس الوقت اللي هو المجموع هذه جزئية من اللي فوق إذن ده برضه بيكون أصغر أو يساوي", "tokens": [6027, 20292, 31439, 2423, 39184, 9141, 2579, 449, 23758, 13672, 1829, 31439, 591, 5296, 33456, 2423, 39184, 9141, 2579, 449, 23758, 6225, 45340, 9957, 15844, 28242, 27188, 2655, 25720, 383, 4032, 35, 34105, 13672, 1829, 39896, 6225, 45340, 9957, 15844, 1783, 4478, 294, 1783, 42, 3714, 7649, 3794, 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بحيته بس قبل شوية ال summation أصغر من 2 كيف ال summation بشيل هذا اللى هو هذا و أقول أصغر من مين من epsilon prime بصير هذا المقدار اللى هو هذا ال summation هيه", "tokens": [3555, 9381, 13546, 43242, 7578, 45030, 2407, 11242, 2423, 28811, 5551, 9381, 17082, 2288, 9154, 568, 9122, 33911, 2423, 28811, 13672, 7578, 5551, 12984, 3555, 2655, 8315, 3224, 4724, 5016, 36081, 3224, 4724, 3794, 12174, 36150, 13412, 2407, 10632, 2423, 28811, 5551, 9381, 17082, 2288, 9154, 568, 9122, 33911, 2423, 28811, 4724, 8592, 26895, 23758, 13672, 7578, 31439, 23758, 4032, 5551, 39648, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 17889, 5835, 4724, 9381, 13546, 23758, 9673, 28543, 9640, 13672, 7578, 31439, 23758, 2423, 28811, 39896, 3224], "avg_logprob": -0.17169744352048094, "compression_ratio": 1.9830508474576272, "no_speech_prob": 1.9073486328125e-06, "words": [{"start": 3261.82, "end": 3262.34, "word": "بصير", "probability": 0.8507486979166666}, {"start": 3262.34, "end": 3263.26, "word": " عندى", 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summation لل mk تلدى ناقص mk تلدى", "tokens": [3224, 1829, 2407, 23758, 39896, 2407, 5551, 9381, 17082, 2288, 9154, 9154, 568, 74, 8978, 12588, 8978, 2423, 17889, 5835, 11933, 15730, 23032, 1211, 3615, 18871, 16254, 25724, 11622, 38207, 6024, 104, 7649, 1829, 28811, 16490, 1211, 9381, 8315, 9154, 23758, 20328, 9640, 18871, 16254, 25724, 11622, 38207, 6024, 104, 7649, 1829, 13672, 1829, 5551, 12984, 3555, 47395, 28811, 24976, 275, 74, 6055, 1211, 3215, 7578, 8717, 995, 4587, 9381, 275, 74, 6055, 1211, 3215, 7578], "avg_logprob": -0.27435066173603007, "compression_ratio": 1.623456790123457, "no_speech_prob": 8.404254913330078e-06, "words": [{"start": 3287.55, "end": 3288.03, "word": "هيو", "probability": 0.3990885416666667}, {"start": 3288.03, "end": 3288.29, "word": " هذا", "probability": 0.171142578125}, {"start": 3288.29, "end": 3288.77, "word": " هيو", "probability": 0.900390625}, {"start": 3288.77, "end": 3289.73, "word": " أصغر", "probability": 0.8912353515625}, {"start": 3289.73, 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0.96630859375}, {"start": 3761.23, "end": 3761.61, "word": " value", "probability": 0.98828125}, {"start": 3761.61, "end": 3761.93, "word": " إيش", "probability": 0.7372233072916666}, {"start": 3761.93, "end": 3762.11, "word": " ما", "probability": 0.63623046875}, {"start": 3762.11, "end": 3762.43, "word": " لها", "probability": 0.76025390625}, {"start": 3762.43, "end": 3762.87, "word": " is", "probability": 0.54736328125}, {"start": 3762.87, "end": 3763.89, "word": " continuous", "probability": 0.904296875}, {"start": 3763.89, "end": 3765.27, "word": " مدام", "probability": 0.700439453125}, {"start": 3765.27, "end": 3765.41, "word": " ال", "probability": 0.9658203125}, {"start": 3765.41, "end": 3765.77, "word": " absolute", "probability": 0.97509765625}, {"start": 3765.77, "end": 3766.45, "word": " value", "probability": 0.9921875}, {"start": 3766.45, "end": 3767.17, "word": " الفاي", "probability": 0.656982421875}, {"start": 3767.17, "end": 3767.37, "word": " is", "probability": 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theorem", "probability": 0.8720703125}], "temperature": 1.0}, {"id": 160, "seek": 380099, "start": 3775.05, "end": 3800.99, "text": "فاي كومبوزيت F is integrable فاي كومبوزيت F of T بيساوي فاي of F of T اللي هي بتساوي ايش؟ واحدة absolute value فاي of T بتساوي absolute value لمين؟ للـ F of T إذا شار عندي absolute value للـ F is integrable", "tokens": [5172, 47302, 9122, 20498, 3555, 2407, 11622, 36081, 479, 307, 16200, 424, 638, 6156, 47302, 9122, 20498, 3555, 2407, 11622, 36081, 479, 295, 314, 4724, 1829, 3794, 995, 45865, 6156, 47302, 295, 479, 295, 314, 13672, 1829, 39896, 39894, 3794, 995, 45865, 1975, 1829, 8592, 22807, 36764, 24401, 3660, 8236, 2158, 6156, 47302, 295, 314, 39894, 3794, 995, 45865, 8236, 2158, 32767, 9957, 22807, 24976, 39184, 479, 295, 314, 11933, 15730, 13412, 9640, 43242, 1829, 8236, 2158, 24976, 39184, 479, 307, 16200, 424, 638], "avg_logprob": -0.35386028430041144, "compression_ratio": 1.8, "no_speech_prob": 0.0, "words": [{"start": 3775.05, "end": 3776.09, "word": "فاي", "probability": 0.1856689453125}, {"start": 3776.09, "end": 3776.67, "word": " كومبوزيت", "probability": 0.8126220703125}, {"start": 3776.67, "end": 3777.11, "word": " F", "probability": 0.7216796875}, {"start": 3777.11, "end": 3778.19, "word": " is", "probability": 0.19140625}, {"start": 3778.19, "end": 3779.27, "word": " integrable", "probability": 0.8115234375}, {"start": 3779.27, "end": 3780.67, "word": " فاي", "probability": 0.603759765625}, {"start": 3780.67, "end": 3781.13, "word": " كومبوزيت", "probability": 0.970703125}, {"start": 3781.13, "end": 3781.57, "word": " F", "probability": 0.9765625}, {"start": 3781.57, "end": 3783.05, "word": " of", "probability": 0.492919921875}, {"start": 3783.05, "end": 3783.95, "word": " T", "probability": 0.9130859375}, {"start": 3783.95, "end": 3784.55, "word": " بيساوي", "probability": 0.618994140625}, {"start": 3784.55, "end": 3785.17, "word": " فاي", "probability": 0.81640625}, {"start": 3785.17, "end": 3785.55, "word": " of", "probability": 0.46630859375}, {"start": 3785.55, "end": 3785.99, "word": " F", "probability": 0.96630859375}, {"start": 3785.99, "end": 3786.41, "word": " of", "probability": 0.9677734375}, {"start": 3786.41, "end": 3786.77, "word": " T", "probability": 0.990234375}, {"start": 3786.77, "end": 3787.45, "word": " اللي", "probability": 0.800048828125}, {"start": 3787.45, "end": 3787.61, "word": " هي", "probability": 0.64306640625}, {"start": 3787.61, "end": 3788.15, "word": " بتساوي", "probability": 0.9422607421875}, {"start": 3788.15, "end": 3789.07, "word": " ايش؟", "probability": 0.53265380859375}, {"start": 3789.07, "end": 3789.75, "word": " واحدة", "probability": 0.7861328125}, {"start": 3789.75, "end": 3790.15, "word": " absolute", "probability": 0.47802734375}, {"start": 3790.15, "end": 3791.05, "word": " value", "probability": 0.99365234375}, {"start": 3791.05, "end": 3791.79, "word": " فاي", "probability": 0.717041015625}, {"start": 3791.79, "end": 3791.91, "word": " of", "probability": 0.71875}, {"start": 3791.91, "end": 3792.03, "word": " T", "probability": 0.93212890625}, {"start": 3792.03, "end": 3792.33, "word": " بتساوي", "probability": 0.943359375}, {"start": 3792.33, "end": 3792.65, "word": " absolute", "probability": 0.52490234375}, {"start": 3792.65, "end": 3793.01, "word": " value", "probability": 0.9912109375}, {"start": 3793.01, "end": 3793.93, "word": " لمين؟", "probability": 0.5583089192708334}, {"start": 3793.93, "end": 3794.37, "word": " للـ", "probability": 0.660400390625}, {"start": 3794.37, "end": 3794.67, "word": " F", "probability": 0.6513671875}, {"start": 3794.67, "end": 3795.11, "word": " of", "probability": 0.9794921875}, {"start": 3795.11, "end": 3795.41, "word": " T", "probability": 0.9951171875}, {"start": 3795.41, "end": 3796.45, "word": " إذا", "probability": 0.5390625}, {"start": 3796.45, "end": 3797.21, "word": " شار", "probability": 0.23638916015625}, {"start": 3797.21, "end": 3797.49, "word": " عندي", "probability": 0.616455078125}, {"start": 3797.49, "end": 3797.87, "word": " absolute", "probability": 0.65283203125}, {"start": 3797.87, "end": 3798.35, "word": " value", "probability": 0.9892578125}, {"start": 3798.35, "end": 3798.63, "word": " للـ", "probability": 0.876708984375}, {"start": 3798.63, "end": 3798.93, "word": " F", "probability": 0.97265625}, {"start": 3798.93, "end": 3799.87, "word": " is", "probability": 0.9287109375}, {"start": 3799.87, "end": 3800.99, "word": " integrable", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 161, "seek": 383078, "start": 3801.94, "end": 3830.78, "text": "إذاً مدامة Phi is continuous و F integrable لأن حسب النظرية Phi composite F is integrable و Phi composite F هي طلعت من الـ absolute value للـ F طبعا Phi composite F من وين هتشتغل من عند اللي هي ال interval I لعند مين لعند R لأن Phi اللي هو F of T هيجي يقعد في الفترة هذه و Phi هترسل اللي بيجي لوين لعند I", "tokens": [28814, 15730, 14111, 3714, 3215, 10943, 3660, 41435, 307, 10957, 4032, 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ال integration لل absolute value لل F من A ل B أصغر أساوي ال integration لل F من A ل B أصغر أساوي ال integration لل F من A ل B وهذا إيش معناته؟ هذا معناته إذا ال absolute value لل integration لل F من A ل B أصغر أساوي", "tokens": [28814, 15730, 2423, 7649, 4724, 15042, 14739, 479, 49374, 8032, 8848, 12610, 3660, 32748, 6027, 2655, 9957, 11331, 35457, 8717, 19913, 16572, 11296, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 34051, 7942, 11933, 15730, 4724, 1829, 9381, 13546, 2423, 10980, 24976, 8236, 2158, 24976, 479, 9154, 316, 5296, 363, 5551, 9381, 17082, 2288, 5551, 3794, 995, 45865, 2423, 10980, 24976, 479, 9154, 316, 5296, 363, 5551, 9381, 17082, 2288, 5551, 3794, 995, 45865, 2423, 10980, 24976, 479, 9154, 316, 5296, 363, 37037, 15730, 11933, 1829, 8592, 20449, 8315, 47395, 22807, 23758, 20449, 8315, 47395, 11933, 15730, 2423, 8236, 2158, 24976, 10980, 24976, 479, 9154, 316, 5296, 363, 5551, 9381, 17082, 2288, 5551, 3794, 995, 45865], "avg_logprob": 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"probability": 0.912841796875}, {"start": 4444.2, "end": 4444.72, "word": " هو", "probability": 0.99267578125}, {"start": 4444.72, "end": 4446.88, "word": " نقطة", "probability": 0.9661458333333334}, {"start": 4446.88, "end": 4447.0, "word": " في", "probability": 0.9345703125}, {"start": 4447.0, "end": 4447.22, "word": " ال", "probability": 0.80322265625}], "temperature": 1.0}, {"id": 187, "seek": 446957, "start": 4448.55, "end": 4469.57, "text": "في ال .. في ال .. في ال section 7-2 اللي هو السؤال اللي سألناه في الأول قولنا لو كانت F is integrable function و Phi is integrable هل Phi composite F is integrable قولنا أكيد هو لو .. في البداية قولنا أن Phi composite F need not to be integrable", "tokens": [41185, 2423, 4386, 8978, 2423, 4386, 8978, 2423, 3541, 1614, 12, 17, 13672, 1829, 31439, 21136, 33604, 6027, 13672, 1829, 8608, 10721, 1211, 8315, 3224, 8978, 16247, 12610, 12174, 12610, 8315, 45164, 25961, 2655, 479, 307, 16200, 424, 638, 2445, 4032, 41435, 307, 16200, 424, 638, 8032, 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4460.01, "end": 4460.25, "word": " F", "probability": 0.90185546875}, {"start": 4460.25, "end": 4460.45, "word": " is", "probability": 0.93017578125}, {"start": 4460.45, "end": 4461.19, "word": " integrable", "probability": 0.8924153645833334}, {"start": 4461.19, "end": 4462.33, "word": " قولنا", "probability": 0.78125}, {"start": 4462.33, "end": 4462.75, "word": " أكيد", "probability": 0.84765625}, {"start": 4462.75, "end": 4462.89, "word": " هو", "probability": 0.8857421875}, {"start": 4462.89, "end": 4463.11, "word": " لو", "probability": 0.55712890625}, {"start": 4463.11, "end": 4463.41, "word": " ..", "probability": 0.40283203125}, {"start": 4463.41, "end": 4464.31, "word": " في", "probability": 0.8974609375}, {"start": 4464.31, "end": 4464.69, "word": " البداية", "probability": 0.9806315104166666}, {"start": 4464.69, "end": 4465.05, "word": " قولنا", "probability": 0.9801432291666666}, {"start": 4465.05, "end": 4465.27, "word": " أن", "probability": 0.56201171875}, {"start": 4465.27, "end": 4465.95, "word": " Phi", "probability": 0.84716796875}, {"start": 4465.95, "end": 4466.43, "word": " composite", "probability": 0.943359375}, {"start": 4466.43, "end": 4466.85, "word": " F", "probability": 0.98095703125}, {"start": 4466.85, "end": 4467.21, "word": " need", "probability": 0.6865234375}, {"start": 4467.21, "end": 4467.57, "word": " not", "probability": 0.958984375}, {"start": 4467.57, "end": 4467.75, "word": " to", "probability": 0.89794921875}, {"start": 4467.75, "end": 4468.43, "word": " be", "probability": 0.96826171875}, {"start": 4468.43, "end": 4469.57, "word": " integrable", "probability": 0.9072265625}], "temperature": 1.0}, {"id": 188, "seek": 449643, "start": 4469.98, "end": 4496.44, "text": "إذا the composition of two integrable functions need not to be integrable يعني هذا إعلان the composition of two integrable functions need not to be integrable but if phi the first one is continuous then phi composite of f is integrable كما شفنا في العقل اللي هو النظرية الأولى طيب نيجي الآن المثال الأخير بيقولنا يا جماعة the composition of integrable functions need not to be integrable", "tokens": [28814, 15730, 264, 12686, 295, 732, 16200, 424, 638, 6828, 643, 406, 281, 312, 16200, 424, 638, 37495, 22653, 23758, 11933, 30241, 7649, 264, 12686, 295, 732, 16200, 424, 638, 6828, 643, 406, 281, 312, 16200, 424, 638, 457, 498, 13107, 264, 700, 472, 307, 10957, 550, 13107, 25557, 295, 283, 307, 16200, 424, 638, 9122, 15042, 13412, 5172, 8315, 8978, 18863, 4587, 1211, 13672, 1829, 31439, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 23032, 1829, 3555, 8717, 1829, 7435, 1829, 6024, 48506, 9673, 12984, 6027, 16247, 9778, 13546, 4724, 1829, 39648, 8315, 35186, 10874, 15042, 27884, 264, 12686, 295, 16200, 424, 638, 6828, 643, 406, 281, 312, 16200, 424, 638], "avg_logprob": -0.1975446432562811, "compression_ratio": 2.0432900432900434, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 4469.98, "end": 4470.32, "word": "إذا", 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الأولى", "probability": 0.9871419270833334}, {"start": 4489.26, "end": 4489.72, "word": " طيب", "probability": 0.91552734375}, {"start": 4489.72, "end": 4490.62, "word": " نيجي", "probability": 0.88671875}, {"start": 4490.62, "end": 4490.96, "word": " الآن", "probability": 0.546630859375}, {"start": 4490.96, "end": 4491.36, "word": " المثال", "probability": 0.9606119791666666}, {"start": 4491.36, "end": 4491.84, "word": " الأخير", "probability": 0.87890625}, {"start": 4491.84, "end": 4492.3, "word": " بيقولنا", "probability": 0.83544921875}, {"start": 4492.3, "end": 4492.42, "word": " يا", "probability": 0.9833984375}, {"start": 4492.42, "end": 4492.8, "word": " جماعة", "probability": 0.99365234375}, {"start": 4492.8, "end": 4493.0, "word": " the", "probability": 0.7587890625}, {"start": 4493.0, "end": 4493.54, "word": " composition", "probability": 0.912109375}, {"start": 4493.54, "end": 4493.84, "word": " of", "probability": 0.97314453125}, {"start": 4493.84, "end": 4494.38, "word": " integrable", "probability": 0.8644205729166666}, {"start": 4494.38, "end": 4494.76, "word": " functions", "probability": 0.87939453125}, {"start": 4494.76, "end": 4495.18, "word": " need", "probability": 0.9248046875}, {"start": 4495.18, "end": 4495.44, "word": " not", "probability": 0.9541015625}, {"start": 4495.44, "end": 4495.58, "word": " to", "probability": 0.96728515625}, {"start": 4495.58, "end": 4495.76, "word": " be", "probability": 0.97314453125}, {"start": 4495.76, "end": 4496.44, "word": " integrable", "probability": 0.9217122395833334}], "temperature": 1.0}, {"id": 189, "seek": 452484, "start": 4497.2, "end": 4524.84, "text": "في عندى سؤالين اصلا معاكم homework السؤال الاول بيقوللنا لو كانت f of x بتساوي واحد ده كانت x بتساوي سفر و zero ده كانت x is irrational و كانت f of x بتساوي واحد لما x بيساوي m على n حيث ال m و ال n عبارة عن integers و العامل المشترك الاعلى بينهم ايه اشمله بادر بيساوي واحد يعني شولنا كل العامل المشترك اللى بينهم و كتبنا x بتساوي m على n", "tokens": 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G", "probability": 0.556640625}, {"start": 4566.17, "end": 4566.31, "word": " of", "probability": 0.580078125}, {"start": 4566.31, "end": 4566.65, "word": " X", "probability": 0.96923828125}, {"start": 4566.65, "end": 4567.79, "word": " step", "probability": 0.56591796875}, {"start": 4567.79, "end": 4568.13, "word": " function", "probability": 0.9462890625}, {"start": 4568.13, "end": 4568.57, "word": " بسيطة", "probability": 0.993359375}, {"start": 4568.57, "end": 4568.77, "word": " يعني", "probability": 0.896484375}], "temperature": 1.0}, {"id": 192, "seek": 459627, "start": 4569.97, "end": 4596.27, "text": "أو خلّيني أقول فيها jump و بس jump على نقطة بس جيوب x بيساوي 0 إذا كانت x بيساوي 0 و بيساوي 1 إذا كانت x في الفترة من 0 لعند 1 اللي هو a closed عند الواحد يعني الآن هذا ال function بيقوللي برضه في ال exercise مطلوب برضه في exercise 717 برضه اللي هو homework معكم في ال exercise بيقولك اثبت ان g ايش معناها is integrable function", "tokens": [10721, 2407, 16490, 1211, 11703, 9957, 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4900.22, "word": " ان", "probability": 0.73876953125}, {"start": 4900.22, "end": 4900.36, "word": " الـ", "probability": 0.3072509765625}, {"start": 4900.36, "end": 4901.02, "word": " decomposite", "probability": 0.55712890625}, {"start": 4901.02, "end": 4901.26, "word": " F", "probability": 0.509765625}, {"start": 4901.26, "end": 4901.6, "word": " need", "probability": 0.475341796875}, {"start": 4901.6, "end": 4902.0, "word": " not", "probability": 0.92822265625}, {"start": 4902.0, "end": 4902.16, "word": " to", "probability": 0.87548828125}, {"start": 4902.16, "end": 4902.28, "word": " be", "probability": 0.9619140625}, {"start": 4902.28, "end": 4903.06, "word": " integrable", "probability": 0.8777669270833334}, {"start": 4903.06, "end": 4903.82, "word": " وهي", "probability": 0.840576171875}, {"start": 4903.82, "end": 4904.68, "word": " المثال", "probability": 0.9806315104166666}, {"start": 4904.68, "end": 4906.24, "word": " أمامكم", "probability": 0.8720703125}, {"start": 4906.24, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c3b8ca422000498a22af01c69129a0112813e5bb
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM_postprocess.srt
@@ -0,0 +1,2592 @@
+1
+00:00:10,580 --> 00:00:15,760
+إيش يا أبو حسين؟ بسم الله الرحمن الرحيم الحمد لله
+
+2
+00:00:15,760 --> 00:00:18,980
+رب العالمين والصلاة والسلام على سيد المرسلين سيدنا
+
+3
+00:00:18,980 --> 00:00:24,540
+محمد وعلى آله وصحبه أجمعين هذه هي المحاضرة رقم 17
+
+4
+00:00:24,540 --> 00:00:29,900
+في مساق تحليل حقيقة 2 لطلاب وطالبات الجامعة
+
+5
+00:00:29,900 --> 00:00:37,170
+الإسلامية كلية العلود قسم الرياضيةبدأنا اليوم
+
+6
+00:00:37,170 --> 00:00:41,490
+استكمال للي بدأنا المرة الماضية حكينا المرة
+
+7
+00:00:41,490 --> 00:00:48,070
+الماضية عن الـ integration as a limit قلنا احنا
+
+8
+00:00:48,070 --> 00:00:51,970
+قبل كنا معرفين ال integration انه موجود على أساس
+
+9
+00:00:51,970 --> 00:00:56,950
+ان ال upper integral U of F يساوي ال lower
+
+10
+00:00:56,950 --> 00:01:01,710
+integral L of F قلنا المرة الماضية ان احنا بدنا
+
+11
+00:01:01,710 --> 00:01:07,300
+نروح باتجاهإنه نصل في النهاية إنه هذا الكلام اللي
+
+12
+00:01:07,300 --> 00:01:11,440
+هو الـ Integrability يكافئ إن نصل إنه ال limit
+
+13
+00:01:11,440 --> 00:01:14,760
+طبعا وفي حالة وجوده هنسميه بساوة ال integration من
+
+14
+00:01:14,760 --> 00:01:19,940
+a ل b of x dx قلنا المرة الماضية إنه هنصل في
+
+15
+00:01:19,940 --> 00:01:25,600
+النهاية في نهاية ال section 7-4 إنه هذا اللي هو ال
+
+16
+00:01:25,600 --> 00:01:28,840
+condition أو هذا ال definition يكافئ إنه نقول
+
+17
+00:01:28,840 --> 00:01:35,640
+limit اللي هو SB و F as normal B أو المش تبع الـ B
+
+18
+00:01:35,640 --> 00:01:41,100
+بيروح لـ 0 و في هذه الحالة إذا كان هذا exist بيصير
+
+19
+00:01:41,100 --> 00:01:45,380
+.. هيساوي ال integration من A ل B F of X DX يعني
+
+20
+00:01:45,380 --> 00:01:49,500
+بمعنى آخر .. بمعنى آخر أنه اللي هو هذا طبعا الـ
+
+21
+00:01:49,500 --> 00:01:55,460
+Riemann Sum أنه الـ limitلرمان sum as الـ
+
+22
+00:01:55,460 --> 00:02:00,020
+partition B بيروح للـ 0 لو كان exist حسير اللي هي
+
+23
+00:02:00,020 --> 00:02:04,220
+F is integrable والـ integration لها هو عبارة عن
+
+24
+00:02:04,220 --> 00:02:09,520
+قيمة هذا الـ limitولو كان ال integration exist
+
+25
+00:02:09,520 --> 00:02:14,040
+طبعا بالمفهوم اللي هو هذا هيكون عنده ال limit هذا
+
+26
+00:02:14,040 --> 00:02:18,300
+exist و هيساوي قيمة مين ال integration هذا اللي
+
+27
+00:02:18,300 --> 00:02:22,260
+حنصل إليه في النهاية اللي حكيناه المرة الماضية
+
+28
+00:02:22,260 --> 00:02:27,380
+بشكل سريع اللي هو عرفنا إيش هو معنات اللي هو ال
+
+29
+00:02:27,380 --> 00:02:32,080
+remand صم اللي أمامنا هذابعد هيكة اللي هو إيجينا
+
+30
+00:02:32,080 --> 00:02:36,600
+أخدنا اللي هي الخاصية الأولى قلنا دايما الريمان
+
+31
+00:02:36,600 --> 00:02:41,140
+sum بين اللي هو ال lower sum و بين ال upper sum و
+
+32
+00:02:41,140 --> 00:02:46,080
+بعدين اللي هو إيجينا قلنا اللي هو النظرية ال .. ال
+
+33
+00:02:46,080 --> 00:02:47,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+34
+00:02:47,220 --> 00:02:47,280
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+35
+00:02:47,280 --> 00:02:48,000
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+36
+00:02:48,000 --> 00:02:48,120
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+37
+00:02:48,120 --> 00:02:49,580
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+38
+00:02:49,580 --> 00:02:49,700
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+39
+00:02:49,700 --> 00:02:50,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+40
+00:02:50,220 --> 00:02:59,260
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..إذا
+
+41
+00:02:59,260 --> 00:03:03,200
+كانت F Integrable إذا لكل Y أكبر من 0 نجدر نلاقي
+
+42
+00:03:03,200 --> 00:03:07,220
+partition بي إبسلون و by such that إذا كانت بي أي
+
+43
+00:03:07,220 --> 00:03:10,600
+اللي هو refinement partition refinement للبي
+
+44
+00:03:10,600 --> 00:03:14,260
+إبسلون يعني يحتوي البي إبسلون هيكون و كان عند ال
+
+45
+00:03:14,260 --> 00:03:18,540
+SPUF عبارة عن اللي هو الريمان sumبكون الـ absolute
+
+46
+00:03:18,540 --> 00:03:21,300
+value ال integration بين S بي و F مقصد ال
+
+47
+00:03:21,300 --> 00:03:24,840
+integration أش ماله أصغر من مين من إبسلون يعني لو
+
+48
+00:03:24,840 --> 00:03:28,460
+F is integrable هنلاقي بي إبسلون بحيث كل ال B
+
+49
+00:03:28,460 --> 00:03:31,540
+بتحتوي بي إبسلون هيكون ال absolute value بين
+
+50
+00:03:31,540 --> 00:03:36,400
+الرمان صموا هذا أصغر من مين من اللي هي إيش إبسلون
+
+51
+00:03:36,820 --> 00:03:41,900
+طيب بعد هي كتب عن البرهناها هذه وصار في عندي الآن
+
+52
+00:03:41,900 --> 00:03:46,240
+اللي هو النظرية الثانية أيضا برهناها و النظرية
+
+53
+00:03:46,240 --> 00:03:52,110
+الثانية كانت تقول أنه لو كانت F is boundedالان ..
+
+54
+00:03:52,110 --> 00:03:57,250
+وقدرنا .. وبدنا الان نفترض انه لجينا اللي هو
+
+55
+00:03:57,250 --> 00:04:01,830
+number a يحقق مالي ايش هذا number a يحقق انه لكل
+
+56
+00:04:01,830 --> 00:04:04,890
+epsilon أكبر من 0 ونلاقي بي ابسلون بحيث انه أي بي
+
+57
+00:04:04,890 --> 00:04:11,040
+يحتوي بي ابسلون و S اللي هي أي رمان sumوthen اللي
+
+58
+00:04:11,040 --> 00:04:16,060
+هي s,b وf ناقص a أصغر من إبسلون إذا كان هذا الكلام
+
+59
+00:04:16,060 --> 00:04:19,480
+كله على بعض اتحقق لما نلاقي a بحيث يقول كل إبسلون
+
+60
+00:04:19,480 --> 00:04:24,180
+أكبر من سفر اللي هو نلاقي بي إبسلون لو كان بي
+
+61
+00:04:24,180 --> 00:04:27,740
+إبسلون بحيث أن بي بتحتوي بي إبسلون وهذا ال remand
+
+62
+00:04:27,740 --> 00:04:32,030
+sum هيعطيني هذههذا كله على بعض ال conditions زي ما
+
+63
+00:04:32,030 --> 00:04:35,410
+قلنا المرة الماضية بيعطينا ان F اي شمالها
+
+64
+00:04:35,410 --> 00:04:39,270
+integrable وهذا الـ A اللي حقق هذه الشروط هنا هو
+
+65
+00:04:39,270 --> 00:04:44,050
+قيمة ال integration هذا اللي حكيناه المرة الماضية
+
+66
+00:04:44,050 --> 00:04:51,120
+و بعدين اللي هوأحنا إجينا وعرفنا شو معنات ال مش أو
+
+67
+00:04:51,120 --> 00:04:54,800
+ال norm إذا بذكركم ال مش أو ال norm هو عبارة عن ال
+
+68
+00:04:54,800 --> 00:05:00,140
+supremum لاللي هي أطوال ال subintervals تبعات ال
+
+69
+00:05:00,140 --> 00:05:03,060
+partition قلنا ال norm للبيبس أو ال supremum لهذه
+
+70
+00:05:03,060 --> 00:05:07,280
+اللي هي الأطوال تبعات ال subintervals اللي ناتجة
+
+71
+00:05:07,280 --> 00:05:11,550
+من ال partition Bهذا اسمنا المش أو ال norm أخدنا
+
+72
+00:05:11,550 --> 00:05:17,230
+بعض اللي هي الخواص وصُجفنا عند مين؟ عند Darabox's
+
+73
+00:05:17,230 --> 00:05:20,690
+theorem اليوم بدنا نبدأ نشرح في مين في Darabox's
+
+74
+00:05:20,690 --> 00:05:24,230
+theorem نشوف أيش Darabox's theorem بتقول الآن بقول
+
+75
+00:05:24,230 --> 00:05:28,990
+لي let i بتساوي a و bاللي هي bounded interval و F
+
+76
+00:05:28,990 --> 00:05:32,910
+من I لعنب R Integrable on I in the sense of
+
+77
+00:05:32,910 --> 00:05:38,050
+definition mean 716 يعني بقول لي نفترض أن F is an
+
+78
+00:05:38,050 --> 00:05:42,830
+integrable function حسب تعريف mean 716 يعني ال
+
+79
+00:05:42,830 --> 00:05:46,470
+upper integral بسوء ال lower integral بسوء ال
+
+80
+00:05:46,470 --> 00:05:50,350
+integration هذا اللي هو ال definition 716 الآن
+
+81
+00:05:50,350 --> 00:05:56,710
+بقول لي then for every epsilon أكبر من 0then for
+
+82
+00:05:56,710 --> 00:06:02,450
+every epsilon أكبر من صفر there exists delta such
+
+83
+00:06:02,450 --> 00:06:07,150
+thatالان لو كان P is any partition of I و ال
+
+84
+00:06:07,150 --> 00:06:11,710
+normal P أصغر من Delta و كان عند ال S P و F اللي
+
+85
+00:06:11,710 --> 00:06:15,810
+هو is any corresponding Riemann sum then ال
+
+86
+00:06:15,810 --> 00:06:19,450
+integration بين ال S P .. البعد بين ال integration
+
+87
+00:06:19,450 --> 00:06:23,670
+بين ال S P و ال integration أصغر من مين أصغر من
+
+88
+00:06:23,670 --> 00:06:28,990
+Epsilon بس
+
+89
+00:06:28,990 --> 00:06:29,910
+بقى في دقيقة يا أبو حسن
+
+90
+00:06:59,460 --> 00:07:03,900
+أيوة أنا في محاضرة .. أنا في محاضرة وبسجل .. أيوة
+
+91
+00:07:03,900 --> 00:07:08,400
+أه في
+
+92
+00:07:08,400 --> 00:07:16,360
+كلية العلوم؟ من قالك في كلية العلوم؟
+
+93
+00:07:16,360 --> 00:07:18,500
+لأ يا عم أنا روحت على دراسات العلوم اللي قالولي
+
+94
+00:07:18,500 --> 00:07:27,580
+طلعن أه .. بعرفش .. بعرفش كلام هو صحيح ولا لأ لأ
+
+95
+00:07:27,580 --> 00:07:33,080
+لأبقى طيب يا راجل أنا في المحاضرة ماشي مع السلام
+
+96
+00:07:33,080 --> 00:07:40,800
+.. ماشي بقى كله مروح مع السلام ليش؟
+
+97
+00:07:40,800 --> 00:07:44,040
+مع السلام .. بس شوف كيف مع السلام
+
+98
+00:08:32,780 --> 00:08:36,900
+اعطيني بس تليفون هذا في العلوم 1600 انا عارف الله
+
+99
+00:08:36,900 --> 00:08:41,780
+ده
+
+100
+00:08:41,780 --> 00:08:45,660
+الدس
+
+101
+00:08:45,660 --> 00:08:50,040
+اه هو كيد روح اذا ابو بلال الموجود روح
+
+102
+00:09:15,660 --> 00:09:18,500
+عليكم السلام عليك يا أبو ساما كيف حالك؟ كيف صحتك؟
+
+103
+00:09:18,500 --> 00:09:21,980
+الله بعرفيك الحمد لله الله عزيزي عنك هل في إلي
+
+104
+00:09:21,980 --> 00:09:28,260
+عندكم رسالة تابعة السناق؟ و تابعة ياسر؟ طب .. طب
+
+105
+00:09:28,260 --> 00:09:33,820
+.. مين عندك؟ قاعد بتسأل عليه لو .. لو أبو أكرم
+
+106
+00:09:33,820 --> 00:09:36,880
+أخدن بس و حطن في غرفتي لأنه أنا قاعد بصور والله
+
+107
+00:09:36,880 --> 00:09:42,060
+يبقى اه .. اه .. اه .. الله يبارك فيا يا عزيزي انا
+
+108
+00:09:42,060 --> 00:09:50,370
+بجيبها المفتاح هوأه أه ماشي
+
+109
+00:09:50,370 --> 00:09:54,770
+لو حتى أنا يعني أنا موجود بس بنتأخر يعني التصوير
+
+110
+00:09:54,770 --> 00:09:59,950
+ممكن أظل التلاتة ماشي ماشي الله أبقى أرفع حاجة
+
+111
+00:09:59,950 --> 00:10:03,290
+لإنه بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+112
+00:10:03,290 --> 00:10:03,490
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+113
+00:10:03,490 --> 00:10:06,830
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+114
+00:10:06,830 --> 00:10:08,250
+ب
+
+115
+00:10:27,230 --> 00:10:30,330
+أدن درابكس الـ theorem زي ما قلنا إن لو كانت F
+
+116
+00:10:30,330 --> 00:10:34,600
+انتجرة بالـ functionبقول إذا لكل إبسلون أكبر من 0
+
+117
+00:10:34,600 --> 00:10:38,780
+بقدر ألاقي Delta أكبر من 0 بحيث أنه لو كان بي أي
+
+118
+00:10:38,780 --> 00:10:41,620
+partition بحيث أنه ال .. اللي هو ال .. ال .. ال
+
+119
+00:10:41,620 --> 00:10:44,980
+norm للـ B أصغر من Delta و S, B و F أي
+
+120
+00:10:44,980 --> 00:10:49,420
+corresponding remand sum بالنسبة للـ B هيعطيني أنه
+
+121
+00:10:49,420 --> 00:10:52,860
+ال absolute value بين اللي هو أو البعد بين S, B و
+
+122
+00:10:52,860 --> 00:10:57,780
+F ناقص ال integration أصغر من إبسلون يعني و كأنه
+
+123
+00:10:57,780 --> 00:11:02,190
+بقول من تحت بطنانه ال integration ال integration
+
+124
+00:11:02,190 --> 00:11:08,710
+لل F لو F is integrable بيعطينا انه بمفهوم اللي هو
+
+125
+00:11:08,710 --> 00:11:18,140
+سبعة واحد ستة بكون عنده limit ال SB وF as normal B
+
+126
+00:11:18,140 --> 00:11:24,320
+بروح للسفر بسوا بالظبط integration من A لB F of X
+
+127
+00:11:24,320 --> 00:11:29,260
+DX لأن ايش معناته هذا؟ معناته هذا اللي هو حسب الـ
+
+128
+00:11:29,260 --> 00:11:32,160
+Epsilon Delta Definition for every Epsilon أكبر من
+
+129
+00:11:32,160 --> 00:11:36,740
+سفر there exists Delta أكبر من سفر such that if
+
+130
+00:11:36,740 --> 00:11:43,170
+normal B أصغر، ناقص السفر أصغر من دلتاthen هيعطيني
+
+131
+00:11:43,170 --> 00:11:46,810
+الـ absolute value للـ S, P و F ناقص ال
+
+132
+00:11:46,810 --> 00:11:52,650
+integration من A ل B F of X DX كله أصغر من مين من
+
+133
+00:11:52,650 --> 00:11:56,790
+إبسلون إذا اللي بدنا نتبته بدنا لكل إبسلون نلاقي
+
+134
+00:11:56,790 --> 00:12:01,870
+Deltaبحيث أنه لما أي partition نورمه أصغر من Delta
+
+135
+00:12:01,870 --> 00:12:05,510
+يعطيني الفرق بين الـ Riemann Sum و بين الـ
+
+136
+00:12:05,510 --> 00:12:08,910
+Integration يكون أصغر من مين؟ من Epsilon هذه اللي
+
+137
+00:12:08,910 --> 00:12:11,990
+هي اللي بتقولنا درابوكس Theorem أنه لو F is
+
+138
+00:12:11,990 --> 00:12:15,610
+integrable إذا اللي هو الـ limit لاللي هو الـ
+
+139
+00:12:15,610 --> 00:12:18,730
+Riemann Sum هو حيساوي هذا ال integration اللي
+
+140
+00:12:18,730 --> 00:12:23,330
+فرضنا إحنا إشماله أنه موجود خلينا نشوف كيف بدنا
+
+141
+00:12:23,330 --> 00:12:29,380
+انبرهن النظرية و ركزوا معاياوتبعوا إيش اللي بدنا
+
+142
+00:12:29,380 --> 00:12:35,200
+نحكيه عشان نصل للي هو المطلوب طيب صلى الله عليه
+
+143
+00:12:35,200 --> 00:12:41,370
+الصلاة والسلام أول إشي بما أن F is integrableالـ
+
+144
+00:12:41,370 --> 00:12:42,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+145
+00:12:42,290 --> 00:12:42,330
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+146
+00:12:42,330 --> 00:12:43,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+147
+00:12:43,190 --> 00:12:43,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+148
+00:12:43,510 --> 00:12:44,470
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+149
+00:12:44,470 --> 00:12:50,750
+ال .. ال .. ال .. ال .. ال ..
+
+150
+00:12:50,750 --> 00:12:52,070
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+151
+00:12:52,070 --> 00:12:53,590
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+152
+00:12:53,590 --> 00:12:53,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+153
+00:12:53,750 --> 00:12:54,490
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+154
+00:12:54,490 --> 00:12:54,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+155
+00:12:54,910 --> 00:13:02,270
+.. ال .. ال .. ال .. الإذن الآن أخفرضت epsilon
+
+156
+00:13:02,270 --> 00:13:06,870
+arbitrary بدي أدور على الـ delta اللي لما ال
+
+157
+00:13:06,870 --> 00:13:10,630
+normal بيه أصغر من delta يعطيني الفرق بين هذه و
+
+158
+00:13:10,630 --> 00:13:14,710
+هذه أصغر من مين من epsilon لذا هيك رايح أنا لأن
+
+159
+00:13:14,710 --> 00:13:19,400
+إذن بما أن أفنتي جربت لكل epsilon أكبر من 0بقدر
+
+160
+00:13:19,400 --> 00:13:23,980
+ألاقي partition الآن سميته بي إبسلون اللي هو x0 و
+
+161
+00:13:23,980 --> 00:13:29,400
+x1 لعندي xn such that ال U ال upper sum لل بي
+
+162
+00:13:29,400 --> 00:13:32,340
+إبسلون و F ناقص ال lower sum لل بي إبسلون و F أصغر
+
+163
+00:13:32,340 --> 00:13:35,780
+من مين من إبسلون سميتهاش أنا إبسلون على تلاتة
+
+164
+00:13:35,780 --> 00:13:38,700
+للحسابات طبعا أصغر من إبسلون في الدنيا من ضمنها
+
+165
+00:13:38,700 --> 00:13:45,040
+الإبسلون على تلاتة هذا حسب الريمان criterion أو ال
+
+166
+00:13:45,040 --> 00:13:51,190
+integrable criterionطيب moreover لأن لو كانت عندي
+
+167
+00:13:51,190 --> 00:13:55,650
+ال B أي B partition بحتوى ال بي إبسلون أكيد هيكون
+
+168
+00:13:55,650 --> 00:13:59,550
+اللي هو ال .. ال .. ال .. هذا بيصير refinement
+
+169
+00:13:59,550 --> 00:14:04,410
+مدام refinement ال refinement التحسين ال lower
+
+170
+00:14:04,410 --> 00:14:09,670
+بعله و ال upper بقاشه بينزل يعني بمعنى أخر هيكون
+
+171
+00:14:09,670 --> 00:14:13,030
+ال lower لل refine .. لل refinement أو التحسين
+
+172
+00:14:13,030 --> 00:14:17,240
+أكبر أوي سوى مين ال lower للأصل ال بي إبسلونوأكيد
+
+173
+00:14:17,240 --> 00:14:20,840
+الـ lower لل B و ال F أكيد أصغر أو سوء القبر لل B
+
+174
+00:14:20,840 --> 00:14:24,780
+و ال F in general و القبر لل B و F قلنا مدامه
+
+175
+00:14:24,780 --> 00:14:29,600
+تحسين إذا أكيد بنزل بصغر عن مين عن اللي صار له
+
+176
+00:14:29,600 --> 00:14:34,960
+تحسين اللي هو مين U, B, Y و F إذا صار عندي الآن ..
+
+177
+00:14:34,960 --> 00:14:45,230
+هي عندي ال L .. ال L, B, Y و F وهذا L, B و Fوهذا
+
+178
+00:14:45,230 --> 00:14:51,650
+الـ U, B و F وهذا الـ U, B, E, F واضح إن المسافة
+
+179
+00:14:51,650 --> 00:14:58,430
+بين الـ U, B, E, F و الـ L, B, E, F أكيد أكبر أو
+
+180
+00:14:58,430 --> 00:15:02,550
+تساوي المسافة بين الـ U و الـ L للـ B و الـ F يعني
+
+181
+00:15:02,550 --> 00:15:05,710
+هذه المسافة واضح إنها أكبر أو تساوي هذه المسافة
+
+182
+00:15:05,710 --> 00:15:12,000
+يعني بمعنى آخر هيكون الـ U, B, Fنقص lbf أصغر أو
+
+183
+00:15:12,000 --> 00:15:15,240
+يساوي لـ U بي إبسلون نقص ل L بي إبسلون و F هذا
+
+184
+00:15:15,240 --> 00:15:21,260
+لمين؟ عدي ال .. ال .. ال بي إبسلون من فوق حصلنا
+
+185
+00:15:21,260 --> 00:15:24,940
+عنها أصغر من إبسلون ع تلاتة إذا صار عند ال U بي إف
+
+186
+00:15:24,940 --> 00:15:29,500
+و ال L بي إف المسافة بينهم برضه أصغر من مين؟ من
+
+187
+00:15:29,500 --> 00:15:35,360
+إبسلون ع تلاتة إذا الآن صار عند أيب لجأت الـ
+
+188
+00:15:35,360 --> 00:15:39,840
+بإبسلون و أي بي بيحتوى الـ بإبسلون لجئنا المسافة
+
+189
+00:15:39,840 --> 00:15:47,880
+بين الـ U بي و F ناقص الـ L بي و F أصغر من مين من
+
+190
+00:15:47,880 --> 00:15:53,710
+إبسلون على 3ماشي الحال هذا اللي حصلناه في الأول
+
+191
+00:15:53,710 --> 00:15:57,170
+الآن احنا زي ما قلنا ادورتنا ع مين يا جماعة
+
+192
+00:15:57,170 --> 00:16:01,210
+ادورتنا على الـ Delta اللي لما ال Normal بيه أصغر
+
+193
+00:16:01,210 --> 00:16:04,330
+من Delta يعطينا المسافة بين الريمان صموا ال
+
+194
+00:16:04,330 --> 00:16:08,670
+integration أصغر من إيش من أبسلون الآن أنا بتدعي
+
+195
+00:16:08,670 --> 00:16:15,060
+أو الكاتب بتدعي أنههناخد Delta بقيمة معينة و هتشوف
+
+196
+00:16:15,060 --> 00:16:17,960
+إنها فعلاً هذه الـ Delta بتحقق طبعاً الـ Delta هذه
+
+197
+00:16:17,960 --> 00:16:22,160
+نتيجة إحسابات اللي هو بيبقى مشة على برهان كامل و
+
+198
+00:16:22,160 --> 00:16:26,400
+في الآخر لجأ الإحساب اللي بيخلي اللي هو قيمة هنا
+
+199
+00:16:26,400 --> 00:16:30,540
+Epsilon الدلتة اللي بياخدها الآن طيب، قبل ما نقول
+
+200
+00:16:30,540 --> 00:16:34,560
+إيش الـ Delta بدنا نعطي الرمز الـ F is bounded,
+
+201
+00:16:34,740 --> 00:16:37,220
+integrable لإنها مدام bounded أو integrable
+
+202
+00:16:37,220 --> 00:16:41,460
+السبريمم إلها على كل الفترة موجودخُد الـ Supremum
+
+203
+00:16:41,460 --> 00:16:45,200
+لقيمة الدالة F of X للـ X element in the interval
+
+204
+00:16:45,200 --> 00:16:49,940
+I سميها إيش بتساوي؟ سميها بتساوي M Capital، ماشي
+
+205
+00:16:49,940 --> 00:16:54,360
+الحال، الان بادعي الان إن دلتا اللي هتظبط معنى و
+
+206
+00:16:54,360 --> 00:16:57,320
+تجيبلنا اللي هو القيمة اللي بدنا إياها اللي هي
+
+207
+00:16:57,320 --> 00:17:00,180
+أصغر من إبسلون، اللي هي دلتا بتساوي إبسلون على
+
+208
+00:17:00,180 --> 00:17:05,140
+اتناشر N في مين في M N مين هذه، N اللي ظهرت في ال
+
+209
+00:17:05,140 --> 00:17:09,750
+partition هنا اللي هو عدد عناصر ال partitionاللي
+
+210
+00:17:09,750 --> 00:17:14,490
+جزأني الفترة هي N زائد 1 هذا مين ال partition اللي
+
+211
+00:17:14,490 --> 00:17:19,790
+لجيته في الريمان من خلال الintegrability للأفإذاً
+
+212
+00:17:19,790 --> 00:17:24,370
+where الـ N زائد واحد is the number of parts in B
+
+213
+00:17:24,370 --> 00:17:29,190
+إبسلون يعني الـ Delta بتساوي إبسلون على 12 في N
+
+214
+00:17:29,190 --> 00:17:33,370
+الـ N ارتبطت بال partition اللي لجيته والـ M هي
+
+215
+00:17:33,370 --> 00:17:39,250
+عبارة عن ال supremum لكل الدالة على كل الفترة
+
+216
+00:17:39,250 --> 00:17:41,410
+المذكورة نيجي الآن
+
+217
+00:17:46,350 --> 00:17:53,750
+Now let Q بيساوي Y not Y واحد و Y اتنين لعند Y M
+
+218
+00:17:53,750 --> 00:17:59,890
+مش N، Y M ماشي بـany partition of I with ال
+
+219
+00:17:59,890 --> 00:18:03,550
+absolute value للـQ أو ال norm للـQ أصغر من Delta
+
+220
+00:18:04,420 --> 00:18:08,500
+أيش يا جماعة قاعد أنا أحاول أصل للي بديها؟ أيش
+
+221
+00:18:08,500 --> 00:18:12,080
+غرضي؟ إن لكل epsilon أكبر من 0 بدي ألاقي delta
+
+222
+00:18:12,080 --> 00:18:16,600
+بحيث أنه أي partition أصغر من delta norm يعطيني
+
+223
+00:18:16,600 --> 00:18:21,320
+الفرق بين رمان صمه وال integration أصغر من epsilon
+
+224
+00:18:21,320 --> 00:18:27,660
+وكأنه الآن بدأت أحط أيدي على الجرح وأصل أقول let Q
+
+225
+00:18:27,660 --> 00:18:34,780
+بيساوي Y0 Y1 YM بأي partitionNormal أصغر من مين؟
+
+226
+00:18:34,780 --> 00:18:40,260
+من Delta متوقع أنا أنه في النهاية عشان أخلص
+
+227
+00:18:40,260 --> 00:18:47,200
+النظرية أثبتلك أنه ال absolute value لأ اللي هو ال
+
+228
+00:18:47,200 --> 00:18:55,230
+S ال UFناقص ال integration من قلبي f of x dx يطلع
+
+229
+00:18:55,230 --> 00:19:00,290
+لي أصغر من مين من إبسلون إذا أثبتت هذا بناء على
+
+230
+00:19:00,290 --> 00:19:05,830
+إختياري للـ Delta اللي عندي وبناء على كل ال cues
+
+231
+00:19:05,830 --> 00:19:10,490
+اللي نورهم أصغر من Delta يعطيني هذا ناقص هذا أصغر
+
+232
+00:19:10,490 --> 00:19:14,210
+من إبسلون وبقول خلصت وبرهنت اللي هي نظريتي
+
+233
+00:19:14,210 --> 00:19:19,350
+درابوكسيز theoremخلّينا نشوف كيف بدنا نروح لهذه
+
+234
+00:19:19,350 --> 00:19:24,810
+اللي هي نثبتها إنها أصغر من إبسلون تعالي شوية الآن
+
+235
+00:19:24,810 --> 00:19:31,630
+لأن let Q*) بسوى Q اتحادين بإبسلون هذه بي إبسلون
+
+236
+00:19:31,630 --> 00:19:37,210
+مين اللي لجيتها فوق اللي هي عبارة عن بي إبسلون
+
+237
+00:19:38,430 --> 00:19:43,870
+بإبسلون هي الفترة من a لعند b بإبسلون اللي هي أش
+
+238
+00:19:43,870 --> 00:19:50,850
+جزأة للفترة هذه هذي x note هذي x1 هذي x2 هذي x3
+
+239
+00:19:50,850 --> 00:19:56,430
+لما أصل xn ناقص واحد لما أصل هنا عند مين xn اللي
+
+240
+00:19:56,430 --> 00:20:01,390
+هي مين ال b هذي مين جزأها جزء الفترة هذه واحدة
+
+241
+00:20:01,390 --> 00:20:08,190
+اسمها بإبسلوننيجي الآن اتجزأت الفترة بمين بالـ Q
+
+242
+00:20:08,190 --> 00:20:17,270
+الـ Q مين هي بدأت ب Y note طبعا هي ايه Y1 و Y2 و
+
+243
+00:20:17,270 --> 00:20:24,950
+Y3 لعند مؤصل لعند Y M ناقص واحدوهنا اللي هي YM
+
+244
+00:20:24,950 --> 00:20:29,730
+اللي هي طبعاً مين هي اللي هي الـB هذه الـQ جزقتها
+
+245
+00:20:29,730 --> 00:20:33,430
+بشكلها اللي أمامي مع العلم إن الـQ هي تبعتنا
+
+246
+00:20:33,430 --> 00:20:38,950
+لنورمها أصغر من مين من Delta الآن بيقوللي خد Q*)
+
+247
+00:20:38,950 --> 00:20:46,150
+إيش بتساوي؟ الـQ اتحاد من الـBإبسلون صارت الآن
+
+248
+00:20:46,150 --> 00:20:54,880
+الـQ هذهبساوة بي بي ستار اتحاد لـ Q هذه مين هي الـ
+
+249
+00:20:54,880 --> 00:21:01,100
+Q star طبعا النقطة الأولى X not هي نفسها Y not
+
+250
+00:21:01,100 --> 00:21:06,840
+والـ Xn هي مين الـ Yn اللي يعني ممكن يكون
+
+251
+00:21:06,840 --> 00:21:11,380
+المختلفات اللي هي من X واحد لعند Xn نقص واحد يكون
+
+252
+00:21:11,380 --> 00:21:16,890
+المختلفات عن هدول الاتحادأقصى حدودهم يعني إذا بدهم
+
+253
+00:21:16,890 --> 00:21:21,430
+يعملنّي sub intervals زيادات هيكون أقصى حدودهم
+
+254
+00:21:21,430 --> 00:21:27,290
+اللي لنا اللي هي X1 و X2 و X3 و X-1 ماتنطبقش ولا
+
+255
+00:21:27,290 --> 00:21:33,810
+على أي Y1 ولا Y2 ولا Y3 ولا Y أم minus 1 متى ما
+
+256
+00:21:33,810 --> 00:21:38,410
+انطبقلنش معناته أنه هيكونين وين موجودات في داخل ال
+
+257
+00:21:38,410 --> 00:21:42,630
+intervals معناته كل واحدة عملتلها إلا عن فترة تاني
+
+258
+00:21:42,630 --> 00:21:46,550
+جداداللي هو في الفترة تانية الإجداد يعني لو إجت
+
+259
+00:21:46,550 --> 00:21:51,390
+هنا الـ X1 هنا مثلا بيكون هذه عملة فترة تانية لو
+
+260
+00:21:51,390 --> 00:21:58,930
+إجينا سمينا هذه المنطقة اللي هو M1 star اللي هو M1
+
+261
+00:21:58,930 --> 00:22:02,470
+مين اللي هو ال maximum أو ال supreme على مين على
+
+262
+00:22:02,470 --> 00:22:09,510
+ال partition الجديد Q starوهذه سمناها هتكون M2*)
+
+263
+00:22:09,510 --> 00:22:15,670
+هيصير الـ M1*) بتختلف لأن هذه عبارة عن الـ
+
+264
+00:22:15,670 --> 00:22:20,490
+Supremum على المنطقة هذه بينما بالنسبة للـ Q لو
+
+265
+00:22:20,490 --> 00:22:27,030
+أجينا لـ Maximum تبعها أو Supremum تبعها هنسميه M1
+
+266
+00:22:27,030 --> 00:22:32,970
+هذا الـ M1قد يختلف عن الـ M1 Star وعن مين الـ M2
+
+267
+00:22:32,970 --> 00:22:37,610
+Star لأن الـ M1 على هذه كلها بينما الـ M1 Star على
+
+268
+00:22:37,610 --> 00:22:41,070
+هذه والـ M2 Star على هذه اللي هو الـ Supremum
+
+269
+00:22:41,070 --> 00:22:44,670
+للدالة على الجزء من هذا أو الجزء من هذا قد يختلف
+
+270
+00:22:44,670 --> 00:22:49,860
+عن الـ Supremum عن الجزء هذا يعني الآنالـ الـ الـ
+
+271
+00:22:49,860 --> 00:22:55,060
+الـ الـ subintervals جديدة هتولدلي M1 maximum
+
+272
+00:22:55,060 --> 00:23:00,700
+لعناصر للـ function على اللي هي الكلي بختلف عن مين
+
+273
+00:23:00,700 --> 00:23:07,240
+عن الجزء قد يختلفالـ N لكن اللي .. اللي .. لو كانت
+
+274
+00:23:07,240 --> 00:23:12,420
+اللي هي عدد هنا دولة اللي هي الـ N أكبر من الـ N
+
+275
+00:23:12,420 --> 00:23:19,420
+هتتوزع .. هتتوزع اللي هو الـ X1 والـ X2 لإذا
+
+276
+00:23:19,420 --> 00:23:23,280
+اختلفن كمان واتوزعن مختلفات هيتوزعن وين؟ في
+
+277
+00:23:23,280 --> 00:23:28,870
+المناطق اللي هيجبل ما نخلص الـ YM يعني هتلاقيها كل
+
+278
+00:23:28,870 --> 00:23:33,970
+واحدة مكان لأن الـ M أكبر من الـ N اللي بتضال بدون
+
+279
+00:23:33,970 --> 00:23:39,870
+ما تدخلها واحدة من الـ X1 أو X2 أو X3 هتسير في ال
+
+280
+00:23:39,870 --> 00:23:43,810
+partition الجديد Q هي نفسها في الاصل في ال
+
+281
+00:23:43,810 --> 00:23:50,140
+partition main الـ Q يعني هيكون الـ M هناstar و ال
+
+282
+00:23:50,140 --> 00:23:56,440
+M نفسها هيكون زي بعر يعني هيكون التنتين بنفس
+
+283
+00:23:56,440 --> 00:24:02,600
+القيمة عشان هيك لو أجينا طرحنا اللي هو .. اللي هي
+
+284
+00:24:02,600 --> 00:24:09,860
+قيمة ال lower sum ال upper sum على ال Q star مع ال
+
+285
+00:24:09,860 --> 00:24:16,340
+upper sum على ال Q هيصير عندي اللي هنا يظهر اللي
+
+286
+00:24:16,340 --> 00:24:22,810
+هو Mمن العادية أو M من الـ Star ناقص الـ M من الـ
+
+287
+00:24:22,810 --> 00:24:27,350
+Star لأنه بيكون قد يكون المختلفات لكن اللي هان مش
+
+288
+00:24:27,350 --> 00:24:31,050
+هيظهر لأنه هيصير الـ M ناقص M من الـ Star سفر إذن
+
+289
+00:24:31,050 --> 00:24:36,110
+هيصير عندي ظهور هذولة في أكام فترة عن أكثر هاي
+
+290
+00:24:36,110 --> 00:24:41,710
+واحدة تنتينبضل أمشي ل N ناقص واحد لإن عددنا دولة
+
+291
+00:24:41,710 --> 00:24:45,330
+من X1 عند XN ناقص واحدة كم واحدة N ناقص واحد يعني
+
+292
+00:24:45,330 --> 00:24:49,130
+على الأكثر هيكون عدد ال sub intervals اللي اجداد
+
+293
+00:24:49,130 --> 00:24:54,390
+عملاً اللي هو 2 في N ناقص واحد اللي اتجسمت تنتين
+
+294
+00:24:54,390 --> 00:25:00,590
+تنتين الآن فبصير عندي ال summation هذا لو جينا لو
+
+295
+00:25:00,590 --> 00:25:08,230
+أخدنا لك ال U ال U star معاللي الـ F ناقص الـ U
+
+296
+00:25:08,230 --> 00:25:14,910
+الـ QF هيكون عبارة عن إيش يا جماعة اللي هنا هيتصفر
+
+297
+00:25:14,910 --> 00:25:19,070
+حيساوي الصميه أكم واحدة من هذولة هيكون على الأكثر
+
+298
+00:25:19,070 --> 00:25:23,790
+الشكل هذا واحدة اسمها مثلا MK MJ زي ما هو مسميها
+
+299
+00:25:23,790 --> 00:25:28,870
+والتاني M star K هذولة على الأكثر على الأكثر على
+
+300
+00:25:28,870 --> 00:25:34,900
+الأكثر هيكون عددهم جداشعددهم عبارة عن اتنين فئة
+
+301
+00:25:34,900 --> 00:25:40,240
+ناقص واحد مضروبات في طول الفترة هذه الفترة الصغيرة
+
+302
+00:25:40,240 --> 00:25:43,680
+اللي هي .. اللي هي الفترة تبعت .. اللي هي مين
+
+303
+00:25:43,680 --> 00:25:48,720
+الـQ*) اللي هي .. واسميها مثلا ZK ناقص ZK مايس
+
+304
+00:25:48,720 --> 00:25:53,700
+واحد يعني عددهم هذولة اللي بظهر الـU ناقص الـU
+
+305
+00:25:53,700 --> 00:25:59,270
+بظهر عبارة عن أكم واحدة من هذولة سماشن لهمعبارة عن
+
+306
+00:25:59,270 --> 00:26:04,390
+الـ two فئة ناقص واحد من الـ terms نجي الآن إيش
+
+307
+00:26:04,390 --> 00:26:12,830
+اللي كاتبوا شوف قلنا لت Q star بيساوي Q اتحاد من
+
+308
+00:26:12,830 --> 00:26:17,930
+الـ B إبسلون الـ Q star صار refinement لمين؟ للـ B
+
+309
+00:26:17,930 --> 00:26:23,620
+إبسلونإذا الـ Q*) حسب اللي حكيته هناك has at most
+
+310
+00:26:23,620 --> 00:26:28,540
+N ناقص واحد more than points than main Q على
+
+311
+00:26:28,540 --> 00:26:32,660
+الأكتر هيكون عدد اللي في الـ Q*) العناقص اللي في
+
+312
+00:26:32,660 --> 00:26:38,040
+Q*) عند Canon اللي في الـ Q اللي في ال .. أمسح
+
+313
+00:26:38,040 --> 00:26:45,900
+اللي فوق بس زي ما قلت اللي في الـ By اللي في الـ
+
+314
+00:26:45,900 --> 00:26:54,870
+By هي عبارة عن X0X1 Xm-1 لعند Xm اللي في ال Q هي
+
+315
+00:26:54,870 --> 00:27:04,190
+عبارة عن Y0 Y1 Ym-1 لعند Ym اللي في ال Q*) إيش
+
+316
+00:27:04,190 --> 00:27:10,910
+هيصير انه أكيد هذي و هذي هم نفسهم فأكيد لو بدأنا ب
+
+317
+00:27:10,910 --> 00:27:17,650
+Z0 و انتهينا بأخر واحدة Z مين ZB مثلا هيكون اللي
+
+318
+00:27:17,650 --> 00:27:23,390
+هوعال أكتر، عال أكتر، عال أكتر الـQ*) بتزيد عن
+
+319
+00:27:23,390 --> 00:27:30,170
+الـP بجداش بالنقاط هذولة اللي لو كانت مش مكررات من
+
+320
+00:27:30,170 --> 00:27:35,430
+هنا خالص اللي هي بيصير عندى في داخل هذه عدد عناصر
+
+321
+00:27:35,430 --> 00:27:41,890
+الـQ*) أكتر من عدد عناصر الـQ بعال أكتر أناقص واحد
+
+322
+00:27:42,200 --> 00:27:50,720
+وكل هذا تبع اللي هو النقاط اتكرر المعها دولة او ما
+
+323
+00:27:50,720 --> 00:27:57,000
+اتكررنش ما اتكررنش بالمرة بيكون بالظبط عددهم اللي
+
+324
+00:27:57,000 --> 00:28:03,000
+هو ال YM زائد ال N ناقص واحد لو ما اتكررنش ولا
+
+325
+00:28:03,000 --> 00:28:07,700
+واحدة يعني بمعنى اخر ال Q start زيد عن ال Q ب N
+
+326
+00:28:07,700 --> 00:28:10,740
+ناقص واحد من النقاط
+
+327
+00:28:12,960 --> 00:28:17,560
+طيب زي ما قال إذن So Q star تحتوي بي إبسلون and Q
+
+328
+00:28:17,560 --> 00:28:21,780
+star has at most N نقص واحد more points than Q
+
+329
+00:28:21,780 --> 00:28:26,220
+namely those points among اللي هي النقاط اللي من
+
+330
+00:28:26,220 --> 00:28:30,080
+مين اللي بيكون الزيادات من ال X واحد لعندي ال X N
+
+331
+00:28:30,080 --> 00:28:35,200
+ال X N نقص واحد that is belongs to B star but not
+
+332
+00:28:35,200 --> 00:28:40,560
+to مين to Q اللي هدول اللي بتكون الزيادات طيب نطلع
+
+333
+00:28:40,560 --> 00:28:48,130
+لفوقالآن بما أن الـ Q صار تحتوى لـ Q إذا أكيد الـ
+
+334
+00:28:48,130 --> 00:28:53,850
+UQ ناقص الـ UQ صار أكبر سوى 0 طبعا عارفين ليش لأن
+
+335
+00:28:53,850 --> 00:28:58,890
+الـ refinement دائما لل upper sum بيجلله ماشي عشان
+
+336
+00:28:58,890 --> 00:29:02,670
+يصير refinement عشان يبطل يطلع فوق ينزل إشي بسيط
+
+337
+00:29:02,670 --> 00:29:07,730
+فهذا في الـ refinement معناته بيصير الـ UQأصغر من
+
+338
+00:29:07,730 --> 00:29:11,790
+مين؟ أكبر من مين؟ من الـUQ UQ star لأنه في
+
+339
+00:29:11,790 --> 00:29:15,630
+الـrefinement الأعلى بجلد مدام بجلد إذا هذا UQ
+
+340
+00:29:15,630 --> 00:29:20,610
+ناقص UQ star أكبر أو يساوي سفر الآن زي ما سمنا if
+
+341
+00:29:20,610 --> 00:29:25,170
+we write UQ star بيساوي Z node Z واحد عند مين؟ عند
+
+342
+00:29:25,170 --> 00:29:34,610
+ZB then لو أجينا بدنا نحسب الآن UQ F ناقص UQ star
+
+343
+00:29:34,610 --> 00:29:42,230
+وFخلّيني اوضّح لك
+
+344
+00:29:42,230 --> 00:29:53,010
+خلّيني اكتبها ماعليش عندي U Q و
+
+345
+00:29:53,010 --> 00:29:59,290
+F ناقص U Q Star و F
+
+346
+00:30:02,130 --> 00:30:07,370
+الـ summation الأولى العبارة عن الـ summation له
+
+347
+00:30:07,370 --> 00:30:19,310
+اللي هي M J في 100 في الـ Q اللي هو Y J minus Y J
+
+348
+00:30:19,310 --> 00:30:25,130
+minus 1 J من عند 1 لعند الـ M ناقص ال summation
+
+349
+00:30:25,130 --> 00:30:37,430
+للتانية اللي هي MK Star في مين؟ في Z K-Z K-1 K من
+
+350
+00:30:37,430 --> 00:30:42,750
+عند 1 لعند مين؟ لعند الـ B اللي فرضناها إيش اسمها
+
+351
+00:30:42,750 --> 00:30:49,190
+اللي هي الـ B زي ما قولت قبل بشويةلو كان هذولة
+
+352
+00:30:49,190 --> 00:30:53,870
+اللي صارن زيادات هنا اللي صارن زيادات هنا ال X
+
+353
+00:30:53,870 --> 00:30:59,410
+نقطة من X واحد لعند X اناقس واحد لو توزع بين هذولة
+
+354
+00:31:00,990 --> 00:31:04,390
+يعني بمعنى أخر كل هدف في حالة الـ M أكبر من N
+
+355
+00:31:04,390 --> 00:31:10,430
+اتوزع بينهين هيعمل اللي هو ال intervals زي ما قلنا
+
+356
+00:31:10,430 --> 00:31:15,850
+2 في N ناقص 1 في هذه ال intervals هيكون اللي هو
+
+357
+00:31:15,850 --> 00:31:22,460
+الـ Mj و الـ Mk قد يكون المختلفاتلكن في الباقي
+
+358
+00:31:22,460 --> 00:31:28,400
+اللي أصلا مادخلهنش إش جديد وضلت الـQ زي الـQ*)
+
+359
+00:31:28,400 --> 00:31:35,680
+فبتكون M تبعت الـQ و M*) تبعت الـQ*) زي بعض فبصير
+
+360
+00:31:35,680 --> 00:31:40,360
+هذه ناقص هذه بساوي 0 اللي هي الـMj والمك بساوي 0
+
+361
+00:31:40,360 --> 00:31:47,070
+يعني بمعنى آخرالـ terms اللي هتكون ع صورة MJ ناقص
+
+362
+00:31:47,070 --> 00:31:52,110
+MK star ع الأكثر ع الأكثر اللي ممكن يكون المختلفات
+
+363
+00:31:52,110 --> 00:31:57,550
+عبارة عن جداش جماعة اتنين في N ناقص واحد يعني هذول
+
+364
+00:31:57,550 --> 00:32:01,950
+عدد هنا ع الأكتر طبعا في ZK minus ZK minus واحد
+
+365
+00:32:01,950 --> 00:32:04,770
+تبعي اللي هو التجزئة الجديدة لإنه هذه التجزئة اللي
+
+366
+00:32:04,770 --> 00:32:08,950
+بتجسمها ل sub intervals يعني ع الأكتر هذول عدد هنا
+
+367
+00:32:08,950 --> 00:32:13,180
+جداش اتنين في N ناقص واحدهذا أنا قلته لما في حالتي
+
+368
+00:32:13,180 --> 00:32:18,610
+الأم أكبر من أنافي حالة الـ M أصغر أو يساوي N
+
+369
+00:32:18,610 --> 00:32:23,890
+بيصير اللي هو في الشيء .. بيصير اللي هو غصبًا عنها
+
+370
+00:32:23,890 --> 00:32:30,270
+مدام الـ N أكبر وبدها تدخل الـ X1 عليهم غصبًا عنها
+
+371
+00:32:30,270 --> 00:32:35,210
+هيكون في الداخل انطبج على مين؟ على إيش من هان يعني
+
+372
+00:32:35,210 --> 00:32:39,630
+مش هيعمل إن 2 في N ناقص 1 هيعمل إن أجل من هيك إلا
+
+373
+00:32:39,630 --> 00:32:42,150
+في حالة اللي هي M بتساوي N بتطلع اللي هو على
+
+374
+00:32:42,150 --> 00:32:47,560
+الأكثر ممكن يطلع 2 في N-1 لأنه ما بيظلش فيه عنده
+
+375
+00:32:47,560 --> 00:32:53,580
+اللي هو مكان بين هذوله يدخلن فبضطر ان اللي هو اكيد
+
+376
+00:32:53,580 --> 00:32:58,140
+هيكون من منين من جواك اللي هي هذه او بكون اللي جوا
+
+377
+00:32:58,140 --> 00:33:03,760
+برضه مش هيزيدن عن اتنين في الـ-1 اذا اللي هي دخلن
+
+378
+00:33:04,020 --> 00:33:09,620
+على أماكن غير مين حتى في حالة ال M ال M أصغر من N
+
+379
+00:33:09,620 --> 00:33:14,000
+لأ هيدخلن هيدخلن يعملن sub intervals هيختلفن برضه
+
+380
+00:33:14,000 --> 00:33:18,640
+نفس الشيء يعني لو دخلت X1 هنا و X2 هنا فبصير برضه
+
+381
+00:33:18,640 --> 00:33:22,550
+يعملن sub intervals في مجموحينلن يتجاوز ان اتنين
+
+382
+00:33:22,550 --> 00:33:29,230
+في ان ناقص واحد لأن عدد ان ناقص واحد من النقاط
+
+383
+00:33:29,230 --> 00:33:33,550
+الجديدة ال X1 X2 عند Xn ناقص واحد ان شاء الله تكون
+
+384
+00:33:33,550 --> 00:33:39,490
+واضحة هذه الصورة يعني مختصرها انههن اللي ممكن ما
+
+385
+00:33:39,490 --> 00:33:47,270
+يحفظلش على اللي هو الـ الـ الـ الـ الـ الـ الـ الـ
+
+386
+00:33:47,270 --> 00:33:48,310
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+387
+00:33:48,310 --> 00:33:48,670
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+388
+00:33:48,670 --> 00:33:48,690
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+389
+00:33:48,690 --> 00:33:48,810
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+390
+00:33:48,810 --> 00:33:49,030
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+391
+00:33:49,030 --> 00:33:52,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الاللي
+
+392
+00:33:52,480 --> 00:33:57,120
+هي بس اللي هي N ناقص واحد من النقاط اللي هتصنعني
+
+393
+00:33:57,120 --> 00:34:02,180
+بس اتنين في N ناقص واحد على الأكثر من ال .. اللي
+
+394
+00:34:02,180 --> 00:34:10,840
+هي ال M واحد أو ال Mj تختلف عن ال M كستار طيب،
+
+395
+00:34:10,840 --> 00:34:13,940
+ماشي الحالة ان شاء الله تكون المضحكة هذه لأن هي بس
+
+396
+00:34:13,940 --> 00:34:17,840
+هذه النقطة اللي بدها توضيح في الباقي هيكون بإذن
+
+397
+00:34:17,840 --> 00:34:23,040
+الله سعيد إذا صار زي ما قلنانرجع لهذا then U Q F
+
+398
+00:34:23,040 --> 00:34:27,200
+نقص U Q Star و F can be written as the sum of at
+
+399
+00:34:27,200 --> 00:34:31,920
+most اتنين في M نقص واحد terms of the form M J نقص
+
+400
+00:34:31,920 --> 00:34:37,460
+M K Star في Z K minus Z K minus واحد لأن عدد هذه
+
+401
+00:34:37,460 --> 00:34:41,680
+الدولة على الأكثر اللي هو بالشكل هذا إذا الآن لو
+
+402
+00:34:41,680 --> 00:34:51,060
+أجينا بدي أحسبلك اللي هو الـ M J نقص M K Starهذه
+
+403
+00:34:51,060 --> 00:35:00,000
+هيكون أصغر أو يساوي مج زائد مك
+
+404
+00:35:01,360 --> 00:35:05,180
+وكل واحدة طبعاً هذا supremum على فترتها وهذا
+
+405
+00:35:05,180 --> 00:35:09,240
+supremum لل F على فترتها أكيد أصغر أو يساوي ال M
+
+406
+00:35:09,240 --> 00:35:13,160
+زائد ال M لأن هذا ال M عبارة عن ال supremum على كل
+
+407
+00:35:13,160 --> 00:35:16,360
+ال interval A وB هذا على جزءه هذا على كل ال
+
+408
+00:35:16,360 --> 00:35:19,240
+interval A وB هذا على جزءه يعني في النهاية هذا
+
+409
+00:35:19,240 --> 00:35:25,460
+أصغر أو يساوي قداش 2 في M يعني هيصير عندي الآن ال
+
+410
+00:35:25,460 --> 00:35:32,980
+absolute value لل M J ناقص M K Starفي ZK-ZK-1
+
+411
+00:35:32,980 --> 00:35:39,970
+هيكون أصغر أو ساوى 2Mفي مين؟ في اللي هي طول الـ
+
+412
+00:35:39,970 --> 00:35:43,550
+interval هذه طول الـ interval هذه طب هذه الـ
+
+413
+00:35:43,550 --> 00:35:50,170
+interval zk minus zk minus 1 أكيد أصغر أو يساوي
+
+414
+00:35:50,170 --> 00:35:56,410
+مين؟ norm لـ Q star مين norm لـ Q star؟ اللي هو ال
+
+415
+00:35:56,410 --> 00:36:01,510
+supremum على مين؟ على أطوال ال subintervals ال
+
+416
+00:36:01,510 --> 00:36:05,750
+supremum أكيد أكبر أو يساوي واحدة منهم طول واحدة
+
+417
+00:36:05,750 --> 00:36:13,190
+منهملكلهم وهذه دائماً لما نزيد العدد قلنا لما نكون
+
+418
+00:36:13,190 --> 00:36:19,630
+Q يحتوي Q*) automatic norm لـ Q*) زي ما قلنا المرة
+
+419
+00:36:19,630 --> 00:36:24,710
+الفاتة هيكون أصغر أو يشوي .. آسف لما يكون Q
+
+420
+00:36:24,710 --> 00:36:28,370
+substantive لـ Q*) يكون norm لـ Q*) عكسه أصغر أو
+
+421
+00:36:28,370 --> 00:36:34,420
+يشوي norm من لـ Qإذا الـ N هذا أصغر أو يساوي هذا و
+
+422
+00:36:34,420 --> 00:36:38,940
+هذا نفسه أصغر أو يساوي مين؟ الـ Q و الـ Normal Q
+
+423
+00:36:38,940 --> 00:36:42,720
+أصغر من مين؟ من دلتا ما احنا على أساسه اللي هي
+
+424
+00:36:42,720 --> 00:36:48,120
+اشتغلنا إذا صار عندي هذا Normal أصغر من دلتا يعني
+
+425
+00:36:48,120 --> 00:36:53,380
+نرجع لهذا هذا المقدار كل واحد لحاله أصغر من اتنين
+
+426
+00:36:53,380 --> 00:36:58,350
+أم في مين بيصير؟ في دلتاالأن عدد هذول اللي ممكن
+
+427
+00:36:58,350 --> 00:37:07,870
+يظهر في UQ ناقص UQ star عبارة عن 2M ناقص 1 يعني في
+
+428
+00:37:07,870 --> 00:37:14,330
+النهاية هذا أصغر أو يساوي اللي هو عدد الـ 2M ناقص
+
+429
+00:37:14,330 --> 00:37:22,940
+1 مضروب في مين؟ في اللي هي 2M2M في Delta لأن هذا
+
+430
+00:37:22,940 --> 00:37:28,390
+نفسه أصغر يساوي 2M و هذا نفسه أصغر يساوي Deltaالان
+
+431
+00:37:28,390 --> 00:37:33,030
+هدولة بتكرر على الأكتر اتنين فئة ناقص واحد هذا ..
+
+432
+00:37:33,030 --> 00:37:36,750
+هذا بتكرر في هذا المقدار على الأكتر في هذا و
+
+433
+00:37:36,750 --> 00:37:40,370
+الباقية هيتصفر زي ما قلنا إذا صار هيكون هذا أصغر
+
+434
+00:37:40,370 --> 00:37:44,750
+أو يساوي عدد تكرار من اتنين فئة ناقص واحد في اتنين
+
+435
+00:37:44,750 --> 00:37:51,010
+M في مين في Delta فإذا صار عندي الآن ال UQF ناقص
+
+436
+00:37:51,010 --> 00:37:55,050
+ال UQ star و F أصغر أو ساوي اتنين فئة ناقص واحد في
+
+437
+00:37:55,050 --> 00:38:01,350
+اتنين M في مينفى delta نصبوت اللى هو هذا عبارة عن
+
+438
+00:38:01,350 --> 00:38:13,090
+قداشة جماعة نيجى نحسبها عشان نصل للي بدنايا صار
+
+439
+00:38:13,090 --> 00:38:26,230
+عندى اللى هو ال U Q F U star و F Q F ناقص U
+
+440
+00:38:32,930 --> 00:38:38,230
+UQF-UQF UQF
+
+441
+00:38:38,230 --> 00:38:44,130
+-UQF UQF
+
+442
+00:38:44,130 --> 00:38:45,750
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+443
+00:38:45,750 --> 00:38:45,850
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+444
+00:38:45,850 --> 00:38:54,050
+-UQF UQF-UQF UQF-UQF UQFفى اللى هو M فى Delta اللى
+
+445
+00:38:54,050 --> 00:38:59,870
+هو أكيد هذا أصغر من أربعة فى N فى M فى Deltaمظهورة
+
+446
+00:38:59,870 --> 00:39:03,790
+ولا لأ؟ لأن الـ N أكبر من مين؟ من الـ N نقص واحد
+
+447
+00:39:03,790 --> 00:39:06,370
+الـ Delta إيش اخترناها؟ ما هي الحسابات من الأول
+
+448
+00:39:06,370 --> 00:39:12,010
+حاسبينها احنا اخترنا الـ Delta فوق عبارة عن جداش
+
+449
+00:39:12,010 --> 00:39:15,710
+لإن احنا كنا عارفين حالنا أصلا بنصل لها المرحلة
+
+450
+00:39:15,710 --> 00:39:19,730
+فبدنا نخلي هذه ي على تلاتة ليش ي على تلاتة؟ بعد
+
+451
+00:39:19,730 --> 00:39:26,470
+شوية تشوف اللي هي عبارة عن ي هذه ي على 12N في مين
+
+452
+00:39:26,470 --> 00:39:31,170
+في Nهذه الآن لما أشيل هذه و أضرب هذه فيها بيصير
+
+453
+00:39:31,170 --> 00:39:34,770
+أربعة في واحد و الان مع الان و الام مع الام و هذي
+
+454
+00:39:34,770 --> 00:39:41,750
+بيصير جداش تلاتة إذا صار عندي الان U Q و F ناقص U
+
+455
+00:39:41,750 --> 00:39:48,000
+Q Star و F أصغر من epsilon ع تلاتةيعني بمعنى آخر
+
+456
+00:39:48,000 --> 00:39:55,380
+صار عند الـ U Q و F أصغر من إبسل من ع تلاتة زائد U
+
+457
+00:39:55,380 --> 00:40:01,420
+Q star من و F ماشي الحال إذا هذه ال in quality
+
+458
+00:40:01,420 --> 00:40:06,160
+التانية اللي وصلناها اللي هتوصلني في النهاية للي
+
+459
+00:40:06,160 --> 00:40:11,490
+بديه ونشوف كيف هتوصلنيطيب يا جماعة صلوا على النبي
+
+460
+00:40:11,490 --> 00:40:17,670
+عليه الصلاة والسلام تنسوش أنه احنا في الأول حصلنا
+
+461
+00:40:17,670 --> 00:40:21,730
+على U بي و أف ماطس أل بي و أف أصغر من مين من
+
+462
+00:40:21,730 --> 00:40:24,930
+إبسلون على تلاتة وحصلنا على U بي و إبسلون هذا أصغر
+
+463
+00:40:24,930 --> 00:40:27,910
+من إبسلون على تلاتة هنحتاجها بعد شوية خليني اكتبها
+
+464
+00:40:27,910 --> 00:40:35,630
+التانية عند حصلنا قبل هيك على ال U بي و أف ماطس أل
+
+465
+00:40:35,630 --> 00:40:42,970
+بي و أف أصغرمن epsilon ع تلاتة وطبعا اكيد اللي هي
+
+466
+00:40:42,970 --> 00:40:46,870
+اصغر من u بي ابسلون و اف عشان لا نرجع الهاشمون
+
+467
+00:40:46,870 --> 00:40:51,970
+اقصال بي ابسلون و اف كله اصغر من ابسلون ع تلاتة
+
+468
+00:40:51,970 --> 00:41:00,930
+هاي كمان هدول التنتين حصلناها ماشي طيب الان
+
+469
+00:41:00,930 --> 00:41:09,000
+اللي عملنا هذا اللي هو مع ال upper sumبنعمل نفسه
+
+470
+00:41:09,000 --> 00:41:14,680
+مع مين مع اللي هو our sum هنلاقي اللي هو LQ يعني
+
+471
+00:41:14,680 --> 00:41:19,060
+LQ star و F ناقص LQ F هنلاقيه هنا على الأكتر
+
+472
+00:41:19,060 --> 00:41:23,020
+باختلاف أنه هو التو فئة ناقص واحد من التلزمه و و و
+
+473
+00:41:23,020 --> 00:41:26,640
+الاخر و بنكمل نفس الاشي بطل عند LQ star و F ناقص
+
+474
+00:41:26,640 --> 00:41:30,600
+إبشر على تلاتة أصغر من مين من LQ F إذا similarly
+
+475
+00:41:30,600 --> 00:41:35,120
+for هذه اللي عملناها هذه ما حد بنعمله مع اللي هو
+
+476
+00:41:35,730 --> 00:41:47,930
+الـ L L of Q star و F ماقص اللي هو إبسلون ع تلاتة
+
+477
+00:41:47,930 --> 00:41:55,890
+أصغر من L Q O mean O F ماشي الحال، طيب and exactly
+
+478
+00:41:55,890 --> 00:42:00,310
+زي ما بنقول similar argument symbolize that اللي
+
+479
+00:42:00,310 --> 00:42:07,870
+كتبناهلنبدأ نجمع معلوماتنا عشان نصل لإنه الـ
+
+480
+00:42:07,870 --> 00:42:11,530
+Riemann Sum نقص الـ integration يكون إيه شماله
+
+481
+00:42:11,530 --> 00:42:15,890
+اللي هو أصغر من إبسلون، انتبهوا كيف عشان يمكن هيك
+
+482
+00:42:15,890 --> 00:42:23,210
+تكون أسهل لنا نرسم خط الأعداد وهنا هخلينا اللي هو
+
+483
+00:42:23,210 --> 00:42:43,920
+نحط الـ U أكي و FU Q F هي أصغر من
+
+484
+00:42:43,920 --> 00:42:55,420
+أبسلون على تلاتة زي U U أستار U F عندي
+
+485
+00:42:55,420 --> 00:42:57,860
+U Q F
+
+486
+00:43:00,380 --> 00:43:07,380
+بس خليني عشان أحط ال L قبل ل L قبل هه عشان مفيش
+
+487
+00:43:07,380 --> 00:43:14,800
+وسح أنا جماعة بعد أذنكم خليني بس هكتب الأول أشنب
+
+488
+00:43:14,800 --> 00:43:27,870
+ده بمين ب L L Q و Fالـ Refinement طبعاً لـ L, Q,
+
+489
+00:43:27,970 --> 00:43:36,450
+Star و F قبلها زي ما انتوا عارفين L, Q و F خليني
+
+490
+00:43:36,450 --> 00:43:41,090
+أعمل هذه قبلها عشان تظبط أحسن L, Q, Star و F ناقص
+
+491
+00:43:41,090 --> 00:43:50,640
+بصناعة تلاتة وهذه LUQF معايا هى هذه بتكون قبل هذه
+
+492
+00:43:50,640 --> 00:43:59,300
+طيب ال QF أكيد بعدها مين UQF صح ولا لأ أكيد طيب
+
+493
+00:43:59,300 --> 00:44:07,420
+بعد ال UQF إيش بتيجي بتيجي هنا إبسلون ع تلاتة زائد
+
+494
+00:44:07,420 --> 00:44:15,340
+UQ star و F مظبوطمظبوط اكيد؟ طيب اذا انا اجيت لخصت
+
+495
+00:44:15,340 --> 00:44:21,120
+المعلومة هذه و لخصت المعلومة هذه اللي هي أصغر من
+
+496
+00:44:21,120 --> 00:44:28,460
+epsilon ع تلاتة UQF UQF ولا ال PUF هذه المسافة
+
+497
+00:44:28,460 --> 00:44:32,910
+بينهم ايه اشمل يا جماعة؟أصغر من إبسلون ع تلاتة
+
+498
+00:44:32,910 --> 00:44:37,130
+واضح أه؟ ومن هنا قال لك U square of F نقص هذه وهذه
+
+499
+00:44:37,130 --> 00:44:43,050
+إبسلون وهذه بالترتيب اللي احنا حصلنا عليه طيب الان
+
+500
+00:44:43,050 --> 00:44:48,230
+طبيعي اللي هو ال remansum و ال integration هيكون
+
+501
+00:44:48,230 --> 00:44:52,030
+بين ال lower و بين main اللي هو إياش الأبر إذن
+
+502
+00:44:52,030 --> 00:44:57,110
+أكيد أكيد أكيد ال remansum تبعنا هي بدينا نصل للي
+
+503
+00:44:57,110 --> 00:45:04,400
+جدنا إياها ال CQFواللي هو ال integration من a إلى
+
+504
+00:45:04,400 --> 00:45:08,720
+b إلى ال F هيكون بين ال lower و بين ال upper ال
+
+505
+00:45:08,720 --> 00:45:11,720
+integration موجود لأن مراس الدور جللنا إذا هذوله
+
+506
+00:45:11,720 --> 00:45:17,800
+صار اللي هو بين هذه و بين هذه إذا صار هذه و هذه
+
+507
+00:45:17,800 --> 00:45:26,120
+بين هذه الدنتينوهذه طبعا ال U Q F و اللي قاله Q F
+
+508
+00:45:26,120 --> 00:45:31,780
+واضح .. واضح انه اللي هو وين في داخل الفترة اللي
+
+509
+00:45:31,780 --> 00:45:36,660
+هي L Q Star و F ناقص أبسل على ثلاثة و U Q Star و F
+
+510
+00:45:36,660 --> 00:45:42,500
+أبسل على تلاتة يعني بين .. هذه طبعا .. بين هذه و
+
+511
+00:45:42,500 --> 00:45:47,200
+بين مين و بين ال interval هذه يعني subset من مين
+
+512
+00:45:47,200 --> 00:45:53,460
+جايل من I أبسلوناللي هي I Epsilon بتساوي اللي هو
+
+513
+00:45:53,460 --> 00:45:59,440
+الفترة هذه من هنا لعند الـ hand هو اللي مسمينها
+
+514
+00:45:59,440 --> 00:46:05,740
+احنا اشمالها I Epsilon بين L Q Star و F نقص
+
+515
+00:46:05,740 --> 00:46:11,860
+Epsilon ع تلاتة و U Q Star F و Epsilon ع تلاتة
+
+516
+00:46:11,860 --> 00:46:20,060
+الآنU Q Star و F ناقص قالك U Star و F ما مسحتاش
+
+517
+00:46:20,060 --> 00:46:28,200
+لسه أنا U Q Star F و قالك U Star F أصغر من مين من
+
+518
+00:46:28,200 --> 00:46:36,520
+إبسلون ع تلاتة لأ اللي هي U
+
+519
+00:46:36,520 --> 00:46:42,670
+Q Star Fوقال الـ Q star F حصلنا عليها قبل هيك أنها
+
+520
+00:46:42,670 --> 00:46:46,650
+أصغر من مين من إبسل ع تلاتة طبعا من وين بنحصلها؟
+
+521
+00:46:46,650 --> 00:46:49,650
+ممكن نحصلها مبقى من هنا ده كما حصلناش أن الـ Q
+
+522
+00:46:49,650 --> 00:46:54,430
+star و F و الـ By بتحتوي الـ By فهيكون الـ U اللي
+
+523
+00:46:54,430 --> 00:47:00,090
+حصلنا أولا بالنسبة لمن؟ لاللي هي الـ By حصلنا قبل
+
+524
+00:47:00,090 --> 00:47:06,400
+هيك أن الـ Uبإبسلون و ال ال بإبسلون الفرق بين همين
+
+525
+00:47:06,400 --> 00:47:10,840
+إبسلون على تلاتة و ال Q star refinement إذا أكيد
+
+526
+00:47:10,840 --> 00:47:14,920
+المسافة بين ال other طبعا في ال refinement المسافة
+
+527
+00:47:14,920 --> 00:47:20,440
+بين ال other و ال other هتصغر لكل refinement ال U
+
+528
+00:47:20,440 --> 00:47:28,340
+بما أن هذه refinement إذا ال Uلأ الـ Q star و F
+
+529
+00:47:28,340 --> 00:47:34,960
+ناقص L Q star و F أصغر أو يساوي لأنها صارت تحسين
+
+530
+00:47:34,960 --> 00:47:38,400
+عليها مازالت صارت تحسين يعني بتجلل مسافة بين ال
+
+531
+00:47:38,400 --> 00:47:40,780
+Upper و الLower عشان نروح في الآخر لل integration
+
+532
+00:47:40,780 --> 00:47:51,520
+ناقص أصغر أو يساوي لL B epsilon و F U ناقص L B
+
+533
+00:47:51,520 --> 00:47:56,980
+epsilon و F اللي هي هذه أصغر من 100من إبسلون وينها
+
+534
+00:47:56,980 --> 00:48:03,400
+أصغر من إبسلون ع تلاتة أصغر من إبسلون ع تلاتة إذا
+
+535
+00:48:03,400 --> 00:48:10,320
+فعلا عرفنا من وين إجت هذه أصغر من مين من إبسلون ع
+
+536
+00:48:10,320 --> 00:48:18,460
+تلاتة إذا صار عندي ال length لهذهالـ length لهذه
+
+537
+00:48:18,460 --> 00:48:23,240
+سهل نوجده بعليش خلّيني أكتب فوق عشان لو جبتلكم ال
+
+538
+00:48:23,240 --> 00:48:29,780
+length إلها عشان أقولكم إنه هذه و هذه هيكون اللي
+
+539
+00:48:29,780 --> 00:48:38,900
+هو بالبعد المطلوب تحسبلي الآن هذه ناقص هذه بصير
+
+540
+00:48:38,900 --> 00:48:48,940
+عبارة عن طول ال interval mean Iy بساوي ال UQ star
+
+541
+00:48:48,940 --> 00:48:55,780
+و F زائد إبسلون على تلاتة ناقص تبعين معيار ال Q
+
+542
+00:48:55,780 --> 00:49:01,720
+star و F ناقص ناقص بيصير زائد إبسلون على تلاتة و
+
+543
+00:49:01,720 --> 00:49:04,900
+يساوي اللي هو إبسلون على تلاتة و إبسلون على تلاتة
+
+544
+00:49:04,900 --> 00:49:12,180
+اتنين إبسلون على تلاتة زائد U Q star و F ناقص ال Q
+
+545
+00:49:12,180 --> 00:49:18,800
+star و F اللي هم هذولةهذه اللي كتبتها لسه ماحتنش
+
+546
+00:49:18,800 --> 00:49:23,400
+أصغر من مين من يبسلون على تلاتة فبتصير هذه طولها
+
+547
+00:49:23,400 --> 00:49:26,700
+أصغر من اتنين يبسلون على تلاتة زائد يبسلون على
+
+548
+00:49:26,700 --> 00:49:31,620
+تلاتة ويساوي يبسلون إذا صار عندي طول الـ interval
+
+549
+00:49:31,620 --> 00:49:40,520
+اللي أسي Qf والـ integration A وBموجودة في كل
+
+550
+00:49:40,520 --> 00:49:46,660
+الفترة هذه اللي هي المسافة بينهم عبارة عن أصغر من
+
+551
+00:49:46,660 --> 00:49:53,460
+مين من Epsilon إذا صار عندي الآن ال integration
+
+552
+00:49:53,460 --> 00:50:05,480
+أين أكتب ال integration إذا صار عندي إذا صار عندي
+
+553
+00:50:05,480 --> 00:50:12,380
+المسافة بين هذه و هذهSQF نقص ال integration من A B
+
+554
+00:50:12,380 --> 00:50:16,900
+ل F أصغر من مين يا جماعة من يبسط من مين هذا تحت
+
+555
+00:50:16,900 --> 00:50:23,360
+شرط مين إنه normally Q هذا أصغر من A H من دلتا
+
+556
+00:50:23,360 --> 00:50:29,200
+أصغر من دلتا بقول إيه أحنا خلصنا اللي بدنا إياه
+
+557
+00:50:29,200 --> 00:50:32,280
+نوقف
+
+558
+00:50:32,280 --> 00:50:33,020
+الجيجا بحثها
+
+559
+00:51:39,830 --> 00:51:44,830
+أه يا أبو حسن بقول هيك أحنا خلصنا برهان نظرية أول
+
+560
+00:51:44,830 --> 00:51:48,490
+حد يقول لي أنه اللي هو المسافة بين U وQ قال الـ Q
+
+561
+00:51:48,490 --> 00:51:50,950
+أصغر من يبسلون على تلاتة لأ احنا ماقلناش هيك
+
+562
+00:51:50,950 --> 00:51:53,950
+البسافة بين الأصغر من يبسلون على تلاتة اللي هو الـ
+
+563
+00:51:53,950 --> 00:51:58,190
+P يبسلون الـ U P يبسلون والـ L P يبسلون وأي
+
+564
+00:51:58,190 --> 00:52:01,010
+refinement له بس الـ Q هنا مش refinement هذا بس
+
+565
+00:52:01,010 --> 00:52:04,830
+اللي بنعرف أنه norm لـ Q أصغر من مين من دلتا أصلا
+
+566
+00:52:04,830 --> 00:52:08,960
+احنا بدنا نصل لإنهالمسافة بين هذولة اللي هو أصغر
+
+567
+00:52:08,960 --> 00:52:13,300
+من إبسلون وعلى طول منها بنستنتج هذه فكيف وصلنا
+
+568
+00:52:13,300 --> 00:52:16,160
+بإننا قلنا اللي هو ال integration هذه في هذه
+
+569
+00:52:16,160 --> 00:52:19,780
+الفترة والفترة هذه جزء من هذه وهذه قلنا هذه طولها
+
+570
+00:52:19,780 --> 00:52:22,960
+على الأكثر بساوي إبسلون عشان هيك صارت المسافة بين
+
+571
+00:52:22,960 --> 00:52:28,000
+هذه وهذا أصغر من إبسلون وهو المطلوب طيب نيجي الآن
+
+572
+00:52:28,000 --> 00:52:34,060
+ده اللي هي النظرية اللي بعدها theorem
+
+573
+00:52:35,670 --> 00:52:45,070
+لت I بتساوي A وB و لت F من I لعند R بيكون فنكشف
+
+574
+00:52:46,090 --> 00:52:49,330
+suppose there exists a number B such that لكل Y
+
+575
+00:52:49,330 --> 00:52:54,110
+أكبر من 0 if B is any partition of I with normal B
+
+576
+00:52:54,110 --> 00:52:58,030
+أصغر من Delta and S of Bi is any corresponding
+
+577
+00:52:58,030 --> 00:53:01,950
+Riemann sum اللي هو then لهذا أصغر من إبسلون then
+
+578
+00:53:01,950 --> 00:53:06,310
+F is integrable on I in the sense of definition
+
+579
+00:53:06,310 --> 00:53:12,590
+716 يعني وكأننا جاعدين بنقول conversely إيش بنقول؟
+
+580
+00:53:12,590 --> 00:53:13,610
+بنقول
+
+581
+00:53:16,710 --> 00:53:24,890
+إنه لو كان عندي اللي هو limit لو كان عندي limit
+
+582
+00:53:24,890 --> 00:53:32,330
+اللي هو الـ S أو B و F as normal B بروح للسفر
+
+583
+00:53:32,330 --> 00:53:38,190
+exist و بسوء some number B إذن هذا الـ B بسوء ال
+
+584
+00:53:38,190 --> 00:53:43,410
+integration من A لB F of X DX يعني بقوللي لو كان
+
+585
+00:53:43,410 --> 00:53:50,850
+هذا متحققلو كان هذا متحقق بيعطيني إنه هذا هو هيطلع
+
+586
+00:53:50,850 --> 00:53:55,110
+اللي هي هتطلع F-integrable وهيكون بيه هذا اللي هو
+
+587
+00:53:55,110 --> 00:53:59,030
+ال limit هذا هو قيمة مين ال integration ليش؟ لأن
+
+588
+00:53:59,030 --> 00:54:02,490
+هذا اصلا شو معناته؟هذا معناته for every epsilon
+
+589
+00:54:02,490 --> 00:54:07,490
+أكبر من صفر there exist اللي هو delta أكبر من صفر
+
+590
+00:54:07,490 --> 00:54:14,370
+such that b أصغر من delta بيؤدي إلى S B و F ناقص
+
+591
+00:54:14,370 --> 00:54:17,630
+ال B اللي مفترضين أصغر من مين ال epsilon هذا هو
+
+592
+00:54:17,630 --> 00:54:23,290
+معناته هذا يعني أن اللي هو المعطىطبعا f bounded من
+
+593
+00:54:23,290 --> 00:54:30,590
+رأس الدور لجهنا number b بحيث ان لكل epsilon او fb
+
+594
+00:54:30,590 --> 00:54:33,270
+is any partition بحيث ان normal b أعلى من delta
+
+595
+00:54:34,000 --> 00:54:39,600
+وكانت اللي هي المسافة بين الـ B أصغر من Epsilon
+
+596
+00:54:39,600 --> 00:54:44,440
+هذا .. ده متحقق اللي هو هذا كله عبارة هو عبارة عن
+
+597
+00:54:44,440 --> 00:54:47,940
+limit S بي و F as and non-invalid اللي هو سفر
+
+598
+00:54:47,940 --> 00:54:52,160
+بساول B إذا .. إذا اتحقق هذا بتكون اللي هي F
+
+599
+00:54:52,160 --> 00:54:55,440
+integrable وقيمة الـ B هذه اللي هي قيمة ال limit
+
+600
+00:54:55,440 --> 00:54:59,420
+بساول integration هذه اللي هي عبارة عن .. النظرية
+
+601
+00:54:59,420 --> 00:55:04,470
+عبارة عن اللي هو بن ..اللي هي دمج بين اللي هي
+
+602
+00:55:04,470 --> 00:55:08,190
+نظريات السابقة المرة الماضية نشوف كيف اللي هو
+
+603
+00:55:08,190 --> 00:55:14,100
+البرهن برهن بسيط لإنه بعتمد عليه بشكل سريعلت y
+
+604
+00:55:14,100 --> 00:55:17,440
+أكبر من 0 و delta أكبر من 0 as in the theorem اللي
+
+605
+00:55:17,440 --> 00:55:20,180
+هو اللي في الـ theorem اللي فوق المقصود فيها النص
+
+606
+00:55:20,180 --> 00:55:25,820
+هذه قدت بي إبسلون بي partition of I with نفترض أنه
+
+607
+00:55:25,820 --> 00:55:30,080
+norm بي إبسلون أصغر من 200 من دلتا هذا المعطى ماشي
+
+608
+00:55:30,080 --> 00:55:36,240
+الحال نفترض أنه إبسلون أكبر من 0 arbitrarily و
+
+609
+00:55:36,240 --> 00:55:41,190
+delta أكبر من 0أو نفترض أن بي إبسلون أي partition
+
+610
+00:55:41,190 --> 00:55:45,310
+بحيث أنه نورمه إيه شماله أصغر من دلتا لكن لو جينا
+
+611
+00:55:45,310 --> 00:55:48,930
+أخدنا بيه أي partition آخر و بيه محتوى بيه إبسلون
+
+612
+00:55:48,930 --> 00:55:53,770
+هيكون نورم ال partition بيه هذا اللي هو ال
+
+613
+00:55:53,770 --> 00:55:57,470
+refinement أكيد أصغر أو سوى نورم مين الأصلي اللي
+
+614
+00:55:57,470 --> 00:56:01,030
+هو أصغر من دلتا صار عنده الآن لكل إبسلون أكبر من
+
+615
+00:56:01,030 --> 00:56:06,470
+سفر there exists دلتا بحيث أنه نورم البي إبسلون
+
+616
+00:56:06,470 --> 00:56:11,740
+أصغر من دلتاولأي partition بي refinement لبيبسلون
+
+617
+00:56:11,740 --> 00:56:17,260
+صار norm أصغر من delta إذا من اللي هو ال .. بواسط
+
+618
+00:56:17,260 --> 00:56:21,740
+اللي هو النظرية السابقة حيكون عند ال S minus البي
+
+619
+00:56:21,740 --> 00:56:27,580
+أصغر من ابسلون يؤدي إلى هذا بيبساو ال integration
+
+620
+00:56:27,580 --> 00:56:32,020
+لإن إيش كانت نظرية سبعة أربعة تلاتة بتشترط تشترط
+
+621
+00:56:32,020 --> 00:56:33,840
+إنه نلاقي لكل ابسلون
+
+622
+00:56:36,480 --> 00:56:42,920
+أي بارتشن بي ابسلون بحيث أن أي بي بتحتول بي ابسلون
+
+623
+00:56:43,910 --> 00:56:48,530
+يؤدي إلى هذا أصغر من إبسلون كله على بعض بيؤدي F
+
+624
+00:56:48,530 --> 00:56:53,790
+أشمالها is integrable إذا بيواصل 7 4 3 مدام حصلنا
+
+625
+00:56:53,790 --> 00:56:57,910
+على ال S بي و F نقص ال V أصغر من إبسلون بيكون هذا
+
+626
+00:56:57,910 --> 00:57:01,190
+اللي حصلنا عليه اللي هو P بساوة ال integration لل
+
+627
+00:57:01,190 --> 00:57:06,630
+F على الفترة من A لB يعني بمعنى أخر احنا اللي
+
+628
+00:57:06,630 --> 00:57:13,530
+حصلنا الآن من النظريتين أن F is integrableF is
+
+629
+00:57:13,530 --> 00:57:19,050
+integrable if and only if limit الـ S,B وF من
+
+630
+00:57:19,050 --> 00:57:23,890
+normal B بيروح للسفر exist وبساوي قيمة ال
+
+631
+00:57:23,890 --> 00:57:28,550
+integration يعني الآن ال integration أوصلنا له عبر
+
+632
+00:57:28,550 --> 00:57:34,330
+طريقين إما عبر طريق اللي هو limit للرمان sumيكون
+
+633
+00:57:34,330 --> 00:57:38,690
+exist أو عبر الطريق الآخر لأن ال upper .. ال upper
+
+634
+00:57:38,690 --> 00:57:42,930
+integral والlower integral يكون جد بعض ومتساويين
+
+635
+00:57:42,930 --> 00:57:52,690
+وحيكون في هذه الحالة هم ال integration وقف
+
+636
+00:57:52,690 --> 00:57:59,570
+هنا يا أبو حسن كم ساعة .. كم
+
+637
+00:57:59,570 --> 00:58:00,810
+عندك الوقت؟
+
+638
+00:58:03,290 --> 00:58:10,650
+نخلصها هيك و نبدأ تانية؟ لأن الجزء الثاني هذا اللي
+
+639
+00:58:10,650 --> 00:58:17,070
+هو الimprover integral بس بطولش بياخد نص ساعة انت
+
+640
+00:58:17,070 --> 00:58:22,090
+قاعد معايا للجد إيش؟ أكيد؟ مديش أضغط عليك يا أبو
+
+641
+00:58:22,090 --> 00:58:30,390
+حسن طيب لأ خلينا نخلص هذه ما هو درس 17 ها؟ هلجيت
+
+642
+00:58:30,390 --> 00:58:31,270
+18؟
+
+643
+00:58:41,590 --> 00:58:48,290
+هي الان بتبدأ في المحاضرة 18 خلصنا 17 كيف؟
+
+644
+00:58:54,810 --> 00:58:59,850
+هك مكون احنا خلصنا المحاضر رقم 17 اللي هو ال
+
+645
+00:58:59,850 --> 00:59:03,610
+integration as a limit بعد شوية هنكمل ال section
+
+646
+00:59:03,610 --> 00:59:08,490
+هذا مظبوط بس هنكمله بموضوع جديد اللي هو عبارة عن
+
+647
+00:59:08,490 --> 00:59:12,510
+الimprover integral وإلى لقاء آخر والسلام عليكم
+
+648
+00:59:12,510 --> 00:59:13,670
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8adbb2bf14facdd870dbb8e38ff1dbe111ee4abb
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM_raw.srt
@@ -0,0 +1,2628 @@
+1
+00:00:10,580 --> 00:00:15,760
+إيش يا أبو حسين؟ بسم الله الرحمن الرحيم الحمد لله
+
+2
+00:00:15,760 --> 00:00:18,980
+رب العالمين والصلاة والسلام على سيد المرسلين سيدنا
+
+3
+00:00:18,980 --> 00:00:24,540
+محمد وعلى آله وصحبه أجمعين هذه هي المحاضرة رقم 17
+
+4
+00:00:24,540 --> 00:00:29,900
+في مساق تحليل حقيقة 2 لطلاب وطالبات الجامعة
+
+5
+00:00:29,900 --> 00:00:37,170
+الإسلامية كلية العلود قسم الرياضيةبدأنا اليوم
+
+6
+00:00:37,170 --> 00:00:41,490
+استكمال للي بدأنا المرة الماضية حكينا المرة
+
+7
+00:00:41,490 --> 00:00:48,070
+الماضية عن الـ integration as a limit قلنا احنا
+
+8
+00:00:48,070 --> 00:00:51,970
+قبل كنا معرفين ال integration انه موجود على أساس
+
+9
+00:00:51,970 --> 00:00:56,950
+ان ال upper integral U of F يساوي ال lower
+
+10
+00:00:56,950 --> 00:01:01,710
+integral L of F قلنا المرة الماضية ان احنا بدنا
+
+11
+00:01:01,710 --> 00:01:07,300
+نروح باتجاهإنه نصل في النهاية إنه هذا الكلام اللي
+
+12
+00:01:07,300 --> 00:01:11,440
+هو الـ Integrability يكافئ إن نصل إنه ال limit
+
+13
+00:01:11,440 --> 00:01:14,760
+طبعا وفي حالة وجوده هنسميه بساوة ال integration من
+
+14
+00:01:14,760 --> 00:01:19,940
+a ل b of x dx قلنا المرة الماضية إنه هنصل في
+
+15
+00:01:19,940 --> 00:01:25,600
+النهاية في نهاية ال section 7-4 إنه هذا اللي هو ال
+
+16
+00:01:25,600 --> 00:01:28,840
+condition أو هذا ال definition يكافئ إنه نقول
+
+17
+00:01:28,840 --> 00:01:35,640
+limit اللي هو SB و F as normal B أو المش تبع الـ B
+
+18
+00:01:35,640 --> 00:01:41,100
+بيروح لـ 0 و في هذه الحالة إذا كان هذا exist بيصير
+
+19
+00:01:41,100 --> 00:01:45,380
+.. هيساوي ال integration من A ل B F of X DX يعني
+
+20
+00:01:45,380 --> 00:01:49,500
+بمعنى آخر .. بمعنى آخر أنه اللي هو هذا طبعا الـ
+
+21
+00:01:49,500 --> 00:01:55,460
+Riemann Sum أنه الـ limitلرمان sum as الـ
+
+22
+00:01:55,460 --> 00:02:00,020
+partition B بيروح للـ 0 لو كان exist حسير اللي هي
+
+23
+00:02:00,020 --> 00:02:04,220
+F is integrable والـ integration لها هو عبارة عن
+
+24
+00:02:04,220 --> 00:02:09,520
+قيمة هذا الـ limitولو كان ال integration exist
+
+25
+00:02:09,520 --> 00:02:14,040
+طبعا بالمفهوم اللي هو هذا هيكون عنده ال limit هذا
+
+26
+00:02:14,040 --> 00:02:18,300
+exist و هيساوي قيمة مين ال integration هذا اللي
+
+27
+00:02:18,300 --> 00:02:22,260
+حنصل إليه في النهاية اللي حكيناه المرة الماضية
+
+28
+00:02:22,260 --> 00:02:27,380
+بشكل سريع اللي هو عرفنا إيش هو معنات اللي هو ال
+
+29
+00:02:27,380 --> 00:02:32,080
+remand صم اللي أمامنا هذابعد هيكة اللي هو إيجينا
+
+30
+00:02:32,080 --> 00:02:36,600
+أخدنا اللي هي الخاصية الأولى قلنا دايما الريمان
+
+31
+00:02:36,600 --> 00:02:41,140
+sum بين اللي هو ال lower sum و بين ال upper sum و
+
+32
+00:02:41,140 --> 00:02:46,080
+بعدين اللي هو إيجينا قلنا اللي هو النظرية ال .. ال
+
+33
+00:02:46,080 --> 00:02:47,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+34
+00:02:47,220 --> 00:02:47,280
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+35
+00:02:47,280 --> 00:02:47,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+36
+00:02:47,280 --> 00:02:48,000
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+37
+00:02:48,000 --> 00:02:48,120
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+38
+00:02:48,120 --> 00:02:49,580
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+39
+00:02:49,580 --> 00:02:49,700
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+40
+00:02:49,700 --> 00:02:50,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+41
+00:02:50,220 --> 00:02:59,260
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..إذا
+
+42
+00:02:59,260 --> 00:03:03,200
+كانت F Integrable إذا لكل Y أكبر من 0 نجدر نلاقي
+
+43
+00:03:03,200 --> 00:03:07,220
+partition بي إبسلون و by such that إذا كانت بي أي
+
+44
+00:03:07,220 --> 00:03:10,600
+اللي هو refinement partition refinement للبي
+
+45
+00:03:10,600 --> 00:03:14,260
+إبسلون يعني يحتوي البي إبسلون هيكون و كان عند ال
+
+46
+00:03:14,260 --> 00:03:18,540
+SPUF عبارة عن اللي هو الريمان sumبكون الـ absolute
+
+47
+00:03:18,540 --> 00:03:21,300
+value ال integration بين S بي و F مقصد ال
+
+48
+00:03:21,300 --> 00:03:24,840
+integration أش ماله أصغر من مين من إبسلون يعني لو
+
+49
+00:03:24,840 --> 00:03:28,460
+F is integrable هنلاقي بي إبسلون بحيث كل ال B
+
+50
+00:03:28,460 --> 00:03:31,540
+بتحتوي بي إبسلون هيكون ال absolute value بين
+
+51
+00:03:31,540 --> 00:03:36,400
+الرمان صموا هذا أصغر من مين من اللي هي إيش إبسلون
+
+52
+00:03:36,820 --> 00:03:41,900
+طيب بعد هي كتب عن البرهناها هذه وصار في عندي الآن
+
+53
+00:03:41,900 --> 00:03:46,240
+اللي هو النظرية الثانية أيضا برهناها و النظرية
+
+54
+00:03:46,240 --> 00:03:52,110
+الثانية كانت تقول أنه لو كانت F is boundedالان ..
+
+55
+00:03:52,110 --> 00:03:57,250
+وقدرنا .. وبدنا الان نفترض انه لجينا اللي هو
+
+56
+00:03:57,250 --> 00:04:01,830
+number a يحقق مالي ايش هذا number a يحقق انه لكل
+
+57
+00:04:01,830 --> 00:04:04,890
+epsilon أكبر من 0 ونلاقي بي ابسلون بحيث انه أي بي
+
+58
+00:04:04,890 --> 00:04:11,040
+يحتوي بي ابسلون و S اللي هي أي رمان sumوthen اللي
+
+59
+00:04:11,040 --> 00:04:16,060
+هي s,b وf ناقص a أصغر من إبسلون إذا كان هذا الكلام
+
+60
+00:04:16,060 --> 00:04:19,480
+كله على بعض اتحقق لما نلاقي a بحيث يقول كل إبسلون
+
+61
+00:04:19,480 --> 00:04:24,180
+أكبر من سفر اللي هو نلاقي بي إبسلون لو كان بي
+
+62
+00:04:24,180 --> 00:04:27,740
+إبسلون بحيث أن بي بتحتوي بي إبسلون وهذا ال remand
+
+63
+00:04:27,740 --> 00:04:32,030
+sum هيعطيني هذههذا كله على بعض ال conditions زي ما
+
+64
+00:04:32,030 --> 00:04:35,410
+قلنا المرة الماضية بيعطينا ان F اي شمالها
+
+65
+00:04:35,410 --> 00:04:39,270
+integrable وهذا الـ A اللي حقق هذه الشروط هنا هو
+
+66
+00:04:39,270 --> 00:04:44,050
+قيمة ال integration هذا اللي حكيناه المرة الماضية
+
+67
+00:04:44,050 --> 00:04:51,120
+و بعدين اللي هوأحنا إجينا وعرفنا شو معنات ال مش أو
+
+68
+00:04:51,120 --> 00:04:54,800
+ال norm إذا بذكركم ال مش أو ال norm هو عبارة عن ال
+
+69
+00:04:54,800 --> 00:05:00,140
+supremum لاللي هي أطوال ال subintervals تبعات ال
+
+70
+00:05:00,140 --> 00:05:03,060
+partition قلنا ال norm للبيبس أو ال supremum لهذه
+
+71
+00:05:03,060 --> 00:05:07,280
+اللي هي الأطوال تبعات ال subintervals اللي ناتجة
+
+72
+00:05:07,280 --> 00:05:11,550
+من ال partition Bهذا اسمنا المش أو ال norm أخدنا
+
+73
+00:05:11,550 --> 00:05:17,230
+بعض اللي هي الخواص وصُجفنا عند مين؟ عند Darabox's
+
+74
+00:05:17,230 --> 00:05:20,690
+theorem اليوم بدنا نبدأ نشرح في مين في Darabox's
+
+75
+00:05:20,690 --> 00:05:24,230
+theorem نشوف أيش Darabox's theorem بتقول الآن بقول
+
+76
+00:05:24,230 --> 00:05:28,990
+لي let i بتساوي a و bاللي هي bounded interval و F
+
+77
+00:05:28,990 --> 00:05:32,910
+من I لعنب R Integrable on I in the sense of
+
+78
+00:05:32,910 --> 00:05:38,050
+definition mean 716 يعني بقول لي نفترض أن F is an
+
+79
+00:05:38,050 --> 00:05:42,830
+integrable function حسب تعريف mean 716 يعني ال
+
+80
+00:05:42,830 --> 00:05:46,470
+upper integral بسوء ال lower integral بسوء ال
+
+81
+00:05:46,470 --> 00:05:50,350
+integration هذا اللي هو ال definition 716 الآن
+
+82
+00:05:50,350 --> 00:05:56,710
+بقول لي then for every epsilon أكبر من 0then for
+
+83
+00:05:56,710 --> 00:06:02,450
+every epsilon أكبر من صفر there exists delta such
+
+84
+00:06:02,450 --> 00:06:07,150
+thatالان لو كان P is any partition of I و ال
+
+85
+00:06:07,150 --> 00:06:11,710
+normal P أصغر من Delta و كان عند ال S P و F اللي
+
+86
+00:06:11,710 --> 00:06:15,810
+هو is any corresponding Riemann sum then ال
+
+87
+00:06:15,810 --> 00:06:19,450
+integration بين ال S P .. البعد بين ال integration
+
+88
+00:06:19,450 --> 00:06:23,670
+بين ال S P و ال integration أصغر من مين أصغر من
+
+89
+00:06:23,670 --> 00:06:28,990
+Epsilon بس
+
+90
+00:06:28,990 --> 00:06:29,910
+بقى في دقيقة يا أبو حسن
+
+91
+00:06:59,460 --> 00:07:03,900
+أيوة أنا في محاضرة .. أنا في محاضرة وبسجل .. أيوة
+
+92
+00:07:03,900 --> 00:07:08,400
+أه في
+
+93
+00:07:08,400 --> 00:07:16,360
+كلية العلوم؟ من قالك في كلية العلوم؟
+
+94
+00:07:16,360 --> 00:07:18,500
+لأ يا عم أنا روحت على دراسات العلوم اللي قالولي
+
+95
+00:07:18,500 --> 00:07:27,580
+طلعن أه .. بعرفش .. بعرفش كلام هو صحيح ولا لأ لأ
+
+96
+00:07:27,580 --> 00:07:33,080
+لأبقى طيب يا راجل أنا في المحاضرة ماشي مع السلام
+
+97
+00:07:33,080 --> 00:07:40,800
+.. ماشي بقى كله مروح مع السلام ليش؟
+
+98
+00:07:40,800 --> 00:07:44,040
+مع السلام .. بس شوف كيف مع السلام
+
+99
+00:08:32,780 --> 00:08:36,900
+اعطيني بس تليفون هذا في العلوم 1600 انا عارف الله
+
+100
+00:08:36,900 --> 00:08:41,780
+ده
+
+101
+00:08:41,780 --> 00:08:45,660
+الدس
+
+102
+00:08:45,660 --> 00:08:50,040
+اه هو كيد روح اذا ابو بلال الموجود روح
+
+103
+00:09:15,660 --> 00:09:18,500
+عليكم السلام عليك يا أبو ساما كيف حالك؟ كيف صحتك؟
+
+104
+00:09:18,500 --> 00:09:21,980
+الله بعرفيك الحمد لله الله عزيزي عنك هل في إلي
+
+105
+00:09:21,980 --> 00:09:28,260
+عندكم رسالة تابعة السناق؟ و تابعة ياسر؟ طب .. طب
+
+106
+00:09:28,260 --> 00:09:33,820
+.. مين عندك؟ قاعد بتسأل عليه لو .. لو أبو أكرم
+
+107
+00:09:33,820 --> 00:09:36,880
+أخدن بس و حطن في غرفتي لأنه أنا قاعد بصور والله
+
+108
+00:09:36,880 --> 00:09:42,060
+يبقى اه .. اه .. اه .. الله يبارك فيا يا عزيزي انا
+
+109
+00:09:42,060 --> 00:09:50,370
+بجيبها المفتاح هوأه أه ماشي
+
+110
+00:09:50,370 --> 00:09:54,770
+لو حتى أنا يعني أنا موجود بس بنتأخر يعني التصوير
+
+111
+00:09:54,770 --> 00:09:59,950
+ممكن أظل التلاتة ماشي ماشي الله أبقى أرفع حاجة
+
+112
+00:09:59,950 --> 00:10:03,290
+لإنه بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+113
+00:10:03,290 --> 00:10:03,490
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+114
+00:10:03,490 --> 00:10:03,490
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+115
+00:10:03,490 --> 00:10:03,490
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+116
+00:10:03,490 --> 00:10:06,830
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+117
+00:10:06,830 --> 00:10:08,250
+ب
+
+118
+00:10:27,230 --> 00:10:30,330
+أدن درابكس الـ theorem زي ما قلنا إن لو كانت F
+
+119
+00:10:30,330 --> 00:10:34,600
+انتجرة بالـ functionبقول إذا لكل إبسلون أكبر من 0
+
+120
+00:10:34,600 --> 00:10:38,780
+بقدر ألاقي Delta أكبر من 0 بحيث أنه لو كان بي أي
+
+121
+00:10:38,780 --> 00:10:41,620
+partition بحيث أنه ال .. اللي هو ال .. ال .. ال
+
+122
+00:10:41,620 --> 00:10:44,980
+norm للـ B أصغر من Delta و S, B و F أي
+
+123
+00:10:44,980 --> 00:10:49,420
+corresponding remand sum بالنسبة للـ B هيعطيني أنه
+
+124
+00:10:49,420 --> 00:10:52,860
+ال absolute value بين اللي هو أو البعد بين S, B و
+
+125
+00:10:52,860 --> 00:10:57,780
+F ناقص ال integration أصغر من إبسلون يعني و كأنه
+
+126
+00:10:57,780 --> 00:11:02,190
+بقول من تحت بطنانه ال integration ال integration
+
+127
+00:11:02,190 --> 00:11:08,710
+لل F لو F is integrable بيعطينا انه بمفهوم اللي هو
+
+128
+00:11:08,710 --> 00:11:18,140
+سبعة واحد ستة بكون عنده limit ال SB وF as normal B
+
+129
+00:11:18,140 --> 00:11:24,320
+بروح للسفر بسوا بالظبط integration من A لB F of X
+
+130
+00:11:24,320 --> 00:11:29,260
+DX لأن ايش معناته هذا؟ معناته هذا اللي هو حسب الـ
+
+131
+00:11:29,260 --> 00:11:32,160
+Epsilon Delta Definition for every Epsilon أكبر من
+
+132
+00:11:32,160 --> 00:11:36,740
+سفر there exists Delta أكبر من سفر such that if
+
+133
+00:11:36,740 --> 00:11:43,170
+normal B أصغر، ناقص السفر أصغر من دلتاthen هيعطيني
+
+134
+00:11:43,170 --> 00:11:46,810
+الـ absolute value للـ S, P و F ناقص ال
+
+135
+00:11:46,810 --> 00:11:52,650
+integration من A ل B F of X DX كله أصغر من مين من
+
+136
+00:11:52,650 --> 00:11:56,790
+إبسلون إذا اللي بدنا نتبته بدنا لكل إبسلون نلاقي
+
+137
+00:11:56,790 --> 00:12:01,870
+Deltaبحيث أنه لما أي partition نورمه أصغر من Delta
+
+138
+00:12:01,870 --> 00:12:05,510
+يعطيني الفرق بين الـ Riemann Sum و بين الـ
+
+139
+00:12:05,510 --> 00:12:08,910
+Integration يكون أصغر من مين؟ من Epsilon هذه اللي
+
+140
+00:12:08,910 --> 00:12:11,990
+هي اللي بتقولنا درابوكس Theorem أنه لو F is
+
+141
+00:12:11,990 --> 00:12:15,610
+integrable إذا اللي هو الـ limit لاللي هو الـ
+
+142
+00:12:15,610 --> 00:12:18,730
+Riemann Sum هو حيساوي هذا ال integration اللي
+
+143
+00:12:18,730 --> 00:12:23,330
+فرضنا إحنا إشماله أنه موجود خلينا نشوف كيف بدنا
+
+144
+00:12:23,330 --> 00:12:29,380
+انبرهن النظرية و ركزوا معاياوتبعوا إيش اللي بدنا
+
+145
+00:12:29,380 --> 00:12:35,200
+نحكيه عشان نصل للي هو المطلوب طيب صلى الله عليه
+
+146
+00:12:35,200 --> 00:12:41,370
+الصلاة والسلام أول إشي بما أن F is integrableالـ
+
+147
+00:12:41,370 --> 00:12:42,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+148
+00:12:42,290 --> 00:12:42,330
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+149
+00:12:42,330 --> 00:12:43,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+150
+00:12:43,190 --> 00:12:43,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+151
+00:12:43,510 --> 00:12:44,470
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+152
+00:12:44,470 --> 00:12:50,750
+ال .. ال .. ال .. ال .. ال ..
+
+153
+00:12:50,750 --> 00:12:52,070
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+154
+00:12:52,070 --> 00:12:53,590
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+155
+00:12:53,590 --> 00:12:53,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+156
+00:12:53,750 --> 00:12:54,490
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+157
+00:12:54,490 --> 00:12:54,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+158
+00:12:54,910 --> 00:12:54,910
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+159
+00:12:54,910 --> 00:12:54,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+160
+00:12:54,910 --> 00:13:02,270
+.. ال .. ال .. ال .. الإذن الآن أخفرضت epsilon
+
+161
+00:13:02,270 --> 00:13:06,870
+arbitrary بدي أدور على الـ delta اللي لما ال
+
+162
+00:13:06,870 --> 00:13:10,630
+normal بيه أصغر من delta يعطيني الفرق بين هذه و
+
+163
+00:13:10,630 --> 00:13:14,710
+هذه أصغر من مين من epsilon لذا هيك رايح أنا لأن
+
+164
+00:13:14,710 --> 00:13:19,400
+إذن بما أن أفنتي جربت لكل epsilon أكبر من 0بقدر
+
+165
+00:13:19,400 --> 00:13:23,980
+ألاقي partition الآن سميته بي إبسلون اللي هو x0 و
+
+166
+00:13:23,980 --> 00:13:29,400
+x1 لعندي xn such that ال U ال upper sum لل بي
+
+167
+00:13:29,400 --> 00:13:32,340
+إبسلون و F ناقص ال lower sum لل بي إبسلون و F أصغر
+
+168
+00:13:32,340 --> 00:13:35,780
+من مين من إبسلون سميتهاش أنا إبسلون على تلاتة
+
+169
+00:13:35,780 --> 00:13:38,700
+للحسابات طبعا أصغر من إبسلون في الدنيا من ضمنها
+
+170
+00:13:38,700 --> 00:13:45,040
+الإبسلون على تلاتة هذا حسب الريمان criterion أو ال
+
+171
+00:13:45,040 --> 00:13:51,190
+integrable criterionطيب moreover لأن لو كانت عندي
+
+172
+00:13:51,190 --> 00:13:55,650
+ال B أي B partition بحتوى ال بي إبسلون أكيد هيكون
+
+173
+00:13:55,650 --> 00:13:59,550
+اللي هو ال .. ال .. ال .. هذا بيصير refinement
+
+174
+00:13:59,550 --> 00:14:04,410
+مدام refinement ال refinement التحسين ال lower
+
+175
+00:14:04,410 --> 00:14:09,670
+بعله و ال upper بقاشه بينزل يعني بمعنى أخر هيكون
+
+176
+00:14:09,670 --> 00:14:13,030
+ال lower لل refine .. لل refinement أو التحسين
+
+177
+00:14:13,030 --> 00:14:17,240
+أكبر أوي سوى مين ال lower للأصل ال بي إبسلونوأكيد
+
+178
+00:14:17,240 --> 00:14:20,840
+الـ lower لل B و ال F أكيد أصغر أو سوء القبر لل B
+
+179
+00:14:20,840 --> 00:14:24,780
+و ال F in general و القبر لل B و F قلنا مدامه
+
+180
+00:14:24,780 --> 00:14:29,600
+تحسين إذا أكيد بنزل بصغر عن مين عن اللي صار له
+
+181
+00:14:29,600 --> 00:14:34,960
+تحسين اللي هو مين U, B, Y و F إذا صار عندي الآن ..
+
+182
+00:14:34,960 --> 00:14:45,230
+هي عندي ال L .. ال L, B, Y و F وهذا L, B و Fوهذا
+
+183
+00:14:45,230 --> 00:14:51,650
+الـ U, B و F وهذا الـ U, B, E, F واضح إن المسافة
+
+184
+00:14:51,650 --> 00:14:58,430
+بين الـ U, B, E, F و الـ L, B, E, F أكيد أكبر أو
+
+185
+00:14:58,430 --> 00:15:02,550
+تساوي المسافة بين الـ U و الـ L للـ B و الـ F يعني
+
+186
+00:15:02,550 --> 00:15:05,710
+هذه المسافة واضح إنها أكبر أو تساوي هذه المسافة
+
+187
+00:15:05,710 --> 00:15:12,000
+يعني بمعنى آخر هيكون الـ U, B, Fنقص lbf أصغر أو
+
+188
+00:15:12,000 --> 00:15:15,240
+يساوي لـ U بي إبسلون نقص ل L بي إبسلون و F هذا
+
+189
+00:15:15,240 --> 00:15:21,260
+لمين؟ عدي ال .. ال .. ال بي إبسلون من فوق حصلنا
+
+190
+00:15:21,260 --> 00:15:24,940
+عنها أصغر من إبسلون ع تلاتة إذا صار عند ال U بي إف
+
+191
+00:15:24,940 --> 00:15:29,500
+و ال L بي إف المسافة بينهم برضه أصغر من مين؟ من
+
+192
+00:15:29,500 --> 00:15:35,360
+إبسلون ع تلاتة إذا الآن صار عند أيب لجأت الـ
+
+193
+00:15:35,360 --> 00:15:39,840
+بإبسلون و أي بي بيحتوى الـ بإبسلون لجئنا المسافة
+
+194
+00:15:39,840 --> 00:15:47,880
+بين الـ U بي و F ناقص الـ L بي و F أصغر من مين من
+
+195
+00:15:47,880 --> 00:15:53,710
+إبسلون على 3ماشي الحال هذا اللي حصلناه في الأول
+
+196
+00:15:53,710 --> 00:15:57,170
+الآن احنا زي ما قلنا ادورتنا ع مين يا جماعة
+
+197
+00:15:57,170 --> 00:16:01,210
+ادورتنا على الـ Delta اللي لما ال Normal بيه أصغر
+
+198
+00:16:01,210 --> 00:16:04,330
+من Delta يعطينا المسافة بين الريمان صموا ال
+
+199
+00:16:04,330 --> 00:16:08,670
+integration أصغر من إيش من أبسلون الآن أنا بتدعي
+
+200
+00:16:08,670 --> 00:16:15,060
+أو الكاتب بتدعي أنههناخد Delta بقيمة معينة و هتشوف
+
+201
+00:16:15,060 --> 00:16:17,960
+إنها فعلاً هذه الـ Delta بتحقق طبعاً الـ Delta هذه
+
+202
+00:16:17,960 --> 00:16:22,160
+نتيجة إحسابات اللي هو بيبقى مشة على برهان كامل و
+
+203
+00:16:22,160 --> 00:16:26,400
+في الآخر لجأ الإحساب اللي بيخلي اللي هو قيمة هنا
+
+204
+00:16:26,400 --> 00:16:30,540
+Epsilon الدلتة اللي بياخدها الآن طيب، قبل ما نقول
+
+205
+00:16:30,540 --> 00:16:34,560
+إيش الـ Delta بدنا نعطي الرمز الـ F is bounded,
+
+206
+00:16:34,740 --> 00:16:37,220
+integrable لإنها مدام bounded أو integrable
+
+207
+00:16:37,220 --> 00:16:41,460
+السبريمم إلها على كل الفترة موجودخُد الـ Supremum
+
+208
+00:16:41,460 --> 00:16:45,200
+لقيمة الدالة F of X للـ X element in the interval
+
+209
+00:16:45,200 --> 00:16:49,940
+I سميها إيش بتساوي؟ سميها بتساوي M Capital، ماشي
+
+210
+00:16:49,940 --> 00:16:54,360
+الحال، الان بادعي الان إن دلتا اللي هتظبط معنى و
+
+211
+00:16:54,360 --> 00:16:57,320
+تجيبلنا اللي هو القيمة اللي بدنا إياها اللي هي
+
+212
+00:16:57,320 --> 00:17:00,180
+أصغر من إبسلون، اللي هي دلتا بتساوي إبسلون على
+
+213
+00:17:00,180 --> 00:17:05,140
+اتناشر N في مين في M N مين هذه، N اللي ظهرت في ال
+
+214
+00:17:05,140 --> 00:17:09,750
+partition هنا اللي هو عدد عناصر ال partitionاللي
+
+215
+00:17:09,750 --> 00:17:14,490
+جزأني الفترة هي N زائد 1 هذا مين ال partition اللي
+
+216
+00:17:14,490 --> 00:17:19,790
+لجيته في الريمان من خلال الintegrability للأفإذاً
+
+217
+00:17:19,790 --> 00:17:24,370
+where الـ N زائد واحد is the number of parts in B
+
+218
+00:17:24,370 --> 00:17:29,190
+إبسلون يعني الـ Delta بتساوي إبسلون على 12 في N
+
+219
+00:17:29,190 --> 00:17:33,370
+الـ N ارتبطت بال partition اللي لجيته والـ M هي
+
+220
+00:17:33,370 --> 00:17:39,250
+عبارة عن ال supremum لكل الدالة على كل الفترة
+
+221
+00:17:39,250 --> 00:17:41,410
+المذكورة نيجي الآن
+
+222
+00:17:46,350 --> 00:17:53,750
+Now let Q بيساوي Y not Y واحد و Y اتنين لعند Y M
+
+223
+00:17:53,750 --> 00:17:59,890
+مش N، Y M ماشي بـany partition of I with ال
+
+224
+00:17:59,890 --> 00:18:03,550
+absolute value للـQ أو ال norm للـQ أصغر من Delta
+
+225
+00:18:04,420 --> 00:18:08,500
+أيش يا جماعة قاعد أنا أحاول أصل للي بديها؟ أيش
+
+226
+00:18:08,500 --> 00:18:12,080
+غرضي؟ إن لكل epsilon أكبر من 0 بدي ألاقي delta
+
+227
+00:18:12,080 --> 00:18:16,600
+بحيث أنه أي partition أصغر من delta norm يعطيني
+
+228
+00:18:16,600 --> 00:18:21,320
+الفرق بين رمان صمه وال integration أصغر من epsilon
+
+229
+00:18:21,320 --> 00:18:27,660
+وكأنه الآن بدأت أحط أيدي على الجرح وأصل أقول let Q
+
+230
+00:18:27,660 --> 00:18:34,780
+بيساوي Y0 Y1 YM بأي partitionNormal أصغر من مين؟
+
+231
+00:18:34,780 --> 00:18:40,260
+من Delta متوقع أنا أنه في النهاية عشان أخلص
+
+232
+00:18:40,260 --> 00:18:47,200
+النظرية أثبتلك أنه ال absolute value لأ اللي هو ال
+
+233
+00:18:47,200 --> 00:18:55,230
+S ال UFناقص ال integration من قلبي f of x dx يطلع
+
+234
+00:18:55,230 --> 00:19:00,290
+لي أصغر من مين من إبسلون إذا أثبتت هذا بناء على
+
+235
+00:19:00,290 --> 00:19:05,830
+إختياري للـ Delta اللي عندي وبناء على كل ال cues
+
+236
+00:19:05,830 --> 00:19:10,490
+اللي نورهم أصغر من Delta يعطيني هذا ناقص هذا أصغر
+
+237
+00:19:10,490 --> 00:19:14,210
+من إبسلون وبقول خلصت وبرهنت اللي هي نظريتي
+
+238
+00:19:14,210 --> 00:19:19,350
+درابوكسيز theoremخلّينا نشوف كيف بدنا نروح لهذه
+
+239
+00:19:19,350 --> 00:19:24,810
+اللي هي نثبتها إنها أصغر من إبسلون تعالي شوية الآن
+
+240
+00:19:24,810 --> 00:19:31,630
+لأن let Q*) بسوى Q اتحادين بإبسلون هذه بي إبسلون
+
+241
+00:19:31,630 --> 00:19:37,210
+مين اللي لجيتها فوق اللي هي عبارة عن بي إبسلون
+
+242
+00:19:38,430 --> 00:19:43,870
+بإبسلون هي الفترة من a لعند b بإبسلون اللي هي أش
+
+243
+00:19:43,870 --> 00:19:50,850
+جزأة للفترة هذه هذي x note هذي x1 هذي x2 هذي x3
+
+244
+00:19:50,850 --> 00:19:56,430
+لما أصل xn ناقص واحد لما أصل هنا عند مين xn اللي
+
+245
+00:19:56,430 --> 00:20:01,390
+هي مين ال b هذي مين جزأها جزء الفترة هذه واحدة
+
+246
+00:20:01,390 --> 00:20:08,190
+اسمها بإبسلوننيجي الآن اتجزأت الفترة بمين بالـ Q
+
+247
+00:20:08,190 --> 00:20:17,270
+الـ Q مين هي بدأت ب Y note طبعا هي ايه Y1 و Y2 و
+
+248
+00:20:17,270 --> 00:20:24,950
+Y3 لعند مؤصل لعند Y M ناقص واحدوهنا اللي هي YM
+
+249
+00:20:24,950 --> 00:20:29,730
+اللي هي طبعاً مين هي اللي هي الـB هذه الـQ جزقتها
+
+250
+00:20:29,730 --> 00:20:33,430
+بشكلها اللي أمامي مع العلم إن الـQ هي تبعتنا
+
+251
+00:20:33,430 --> 00:20:38,950
+لنورمها أصغر من مين من Delta الآن بيقوللي خد Q*)
+
+252
+00:20:38,950 --> 00:20:46,150
+إيش بتساوي؟ الـQ اتحاد من الـBإبسلون صارت الآن
+
+253
+00:20:46,150 --> 00:20:54,880
+الـQ هذهبساوة بي بي ستار اتحاد لـ Q هذه مين هي الـ
+
+254
+00:20:54,880 --> 00:21:01,100
+Q star طبعا النقطة الأولى X not هي نفسها Y not
+
+255
+00:21:01,100 --> 00:21:06,840
+والـ Xn هي مين الـ Yn اللي يعني ممكن يكون
+
+256
+00:21:06,840 --> 00:21:11,380
+المختلفات اللي هي من X واحد لعند Xn نقص واحد يكون
+
+257
+00:21:11,380 --> 00:21:16,890
+المختلفات عن هدول الاتحادأقصى حدودهم يعني إذا بدهم
+
+258
+00:21:16,890 --> 00:21:21,430
+يعملنّي sub intervals زيادات هيكون أقصى حدودهم
+
+259
+00:21:21,430 --> 00:21:27,290
+اللي لنا اللي هي X1 و X2 و X3 و X-1 ماتنطبقش ولا
+
+260
+00:21:27,290 --> 00:21:33,810
+على أي Y1 ولا Y2 ولا Y3 ولا Y أم minus 1 متى ما
+
+261
+00:21:33,810 --> 00:21:38,410
+انطبقلنش معناته أنه هيكونين وين موجودات في داخل ال
+
+262
+00:21:38,410 --> 00:21:42,630
+intervals معناته كل واحدة عملتلها إلا عن فترة تاني
+
+263
+00:21:42,630 --> 00:21:46,550
+جداداللي هو في الفترة تانية الإجداد يعني لو إجت
+
+264
+00:21:46,550 --> 00:21:51,390
+هنا الـ X1 هنا مثلا بيكون هذه عملة فترة تانية لو
+
+265
+00:21:51,390 --> 00:21:58,930
+إجينا سمينا هذه المنطقة اللي هو M1 star اللي هو M1
+
+266
+00:21:58,930 --> 00:22:02,470
+مين اللي هو ال maximum أو ال supreme على مين على
+
+267
+00:22:02,470 --> 00:22:09,510
+ال partition الجديد Q starوهذه سمناها هتكون M2*)
+
+268
+00:22:09,510 --> 00:22:15,670
+هيصير الـ M1*) بتختلف لأن هذه عبارة عن الـ
+
+269
+00:22:15,670 --> 00:22:20,490
+Supremum على المنطقة هذه بينما بالنسبة للـ Q لو
+
+270
+00:22:20,490 --> 00:22:27,030
+أجينا لـ Maximum تبعها أو Supremum تبعها هنسميه M1
+
+271
+00:22:27,030 --> 00:22:32,970
+هذا الـ M1قد يختلف عن الـ M1 Star وعن مين الـ M2
+
+272
+00:22:32,970 --> 00:22:37,610
+Star لأن الـ M1 على هذه كلها بينما الـ M1 Star على
+
+273
+00:22:37,610 --> 00:22:41,070
+هذه والـ M2 Star على هذه اللي هو الـ Supremum
+
+274
+00:22:41,070 --> 00:22:44,670
+للدالة على الجزء من هذا أو الجزء من هذا قد يختلف
+
+275
+00:22:44,670 --> 00:22:49,860
+عن الـ Supremum عن الجزء هذا يعني الآنالـ الـ الـ
+
+276
+00:22:49,860 --> 00:22:55,060
+الـ الـ subintervals جديدة هتولدلي M1 maximum
+
+277
+00:22:55,060 --> 00:23:00,700
+لعناصر للـ function على اللي هي الكلي بختلف عن مين
+
+278
+00:23:00,700 --> 00:23:07,240
+عن الجزء قد يختلفالـ N لكن اللي .. اللي .. لو كانت
+
+279
+00:23:07,240 --> 00:23:12,420
+اللي هي عدد هنا دولة اللي هي الـ N أكبر من الـ N
+
+280
+00:23:12,420 --> 00:23:19,420
+هتتوزع .. هتتوزع اللي هو الـ X1 والـ X2 لإذا
+
+281
+00:23:19,420 --> 00:23:23,280
+اختلفن كمان واتوزعن مختلفات هيتوزعن وين؟ في
+
+282
+00:23:23,280 --> 00:23:28,870
+المناطق اللي هيجبل ما نخلص الـ YM يعني هتلاقيها كل
+
+283
+00:23:28,870 --> 00:23:33,970
+واحدة مكان لأن الـ M أكبر من الـ N اللي بتضال بدون
+
+284
+00:23:33,970 --> 00:23:39,870
+ما تدخلها واحدة من الـ X1 أو X2 أو X3 هتسير في ال
+
+285
+00:23:39,870 --> 00:23:43,810
+partition الجديد Q هي نفسها في الاصل في ال
+
+286
+00:23:43,810 --> 00:23:50,140
+partition main الـ Q يعني هيكون الـ M هناstar و ال
+
+287
+00:23:50,140 --> 00:23:56,440
+M نفسها هيكون زي بعر يعني هيكون التنتين بنفس
+
+288
+00:23:56,440 --> 00:24:02,600
+القيمة عشان هيك لو أجينا طرحنا اللي هو .. اللي هي
+
+289
+00:24:02,600 --> 00:24:09,860
+قيمة ال lower sum ال upper sum على ال Q star مع ال
+
+290
+00:24:09,860 --> 00:24:16,340
+upper sum على ال Q هيصير عندي اللي هنا يظهر اللي
+
+291
+00:24:16,340 --> 00:24:22,810
+هو Mمن العادية أو M من الـ Star ناقص الـ M من الـ
+
+292
+00:24:22,810 --> 00:24:27,350
+Star لأنه بيكون قد يكون المختلفات لكن اللي هان مش
+
+293
+00:24:27,350 --> 00:24:31,050
+هيظهر لأنه هيصير الـ M ناقص M من الـ Star سفر إذن
+
+294
+00:24:31,050 --> 00:24:36,110
+هيصير عندي ظهور هذولة في أكام فترة عن أكثر هاي
+
+295
+00:24:36,110 --> 00:24:41,710
+واحدة تنتينبضل أمشي ل N ناقص واحد لإن عددنا دولة
+
+296
+00:24:41,710 --> 00:24:45,330
+من X1 عند XN ناقص واحدة كم واحدة N ناقص واحد يعني
+
+297
+00:24:45,330 --> 00:24:49,130
+على الأكثر هيكون عدد ال sub intervals اللي اجداد
+
+298
+00:24:49,130 --> 00:24:54,390
+عملاً اللي هو 2 في N ناقص واحد اللي اتجسمت تنتين
+
+299
+00:24:54,390 --> 00:25:00,590
+تنتين الآن فبصير عندي ال summation هذا لو جينا لو
+
+300
+00:25:00,590 --> 00:25:08,230
+أخدنا لك ال U ال U star معاللي الـ F ناقص الـ U
+
+301
+00:25:08,230 --> 00:25:14,910
+الـ QF هيكون عبارة عن إيش يا جماعة اللي هنا هيتصفر
+
+302
+00:25:14,910 --> 00:25:19,070
+حيساوي الصميه أكم واحدة من هذولة هيكون على الأكثر
+
+303
+00:25:19,070 --> 00:25:23,790
+الشكل هذا واحدة اسمها مثلا MK MJ زي ما هو مسميها
+
+304
+00:25:23,790 --> 00:25:28,870
+والتاني M star K هذولة على الأكثر على الأكثر على
+
+305
+00:25:28,870 --> 00:25:34,900
+الأكثر هيكون عددهم جداشعددهم عبارة عن اتنين فئة
+
+306
+00:25:34,900 --> 00:25:40,240
+ناقص واحد مضروبات في طول الفترة هذه الفترة الصغيرة
+
+307
+00:25:40,240 --> 00:25:43,680
+اللي هي .. اللي هي الفترة تبعت .. اللي هي مين
+
+308
+00:25:43,680 --> 00:25:48,720
+الـQ*) اللي هي .. واسميها مثلا ZK ناقص ZK مايس
+
+309
+00:25:48,720 --> 00:25:53,700
+واحد يعني عددهم هذولة اللي بظهر الـU ناقص الـU
+
+310
+00:25:53,700 --> 00:25:59,270
+بظهر عبارة عن أكم واحدة من هذولة سماشن لهمعبارة عن
+
+311
+00:25:59,270 --> 00:26:04,390
+الـ two فئة ناقص واحد من الـ terms نجي الآن إيش
+
+312
+00:26:04,390 --> 00:26:12,830
+اللي كاتبوا شوف قلنا لت Q star بيساوي Q اتحاد من
+
+313
+00:26:12,830 --> 00:26:17,930
+الـ B إبسلون الـ Q star صار refinement لمين؟ للـ B
+
+314
+00:26:17,930 --> 00:26:23,620
+إبسلونإذا الـ Q*) حسب اللي حكيته هناك has at most
+
+315
+00:26:23,620 --> 00:26:28,540
+N ناقص واحد more than points than main Q على
+
+316
+00:26:28,540 --> 00:26:32,660
+الأكتر هيكون عدد اللي في الـ Q*) العناقص اللي في
+
+317
+00:26:32,660 --> 00:26:38,040
+Q*) عند Canon اللي في الـ Q اللي في ال .. أمسح
+
+318
+00:26:38,040 --> 00:26:45,900
+اللي فوق بس زي ما قلت اللي في الـ By اللي في الـ
+
+319
+00:26:45,900 --> 00:26:54,870
+By هي عبارة عن X0X1 Xm-1 لعند Xm اللي في ال Q هي
+
+320
+00:26:54,870 --> 00:27:04,190
+عبارة عن Y0 Y1 Ym-1 لعند Ym اللي في ال Q*) إيش
+
+321
+00:27:04,190 --> 00:27:10,910
+هيصير انه أكيد هذي و هذي هم نفسهم فأكيد لو بدأنا ب
+
+322
+00:27:10,910 --> 00:27:17,650
+Z0 و انتهينا بأخر واحدة Z مين ZB مثلا هيكون اللي
+
+323
+00:27:17,650 --> 00:27:23,390
+هوعال أكتر، عال أكتر، عال أكتر الـQ*) بتزيد عن
+
+324
+00:27:23,390 --> 00:27:30,170
+الـP بجداش بالنقاط هذولة اللي لو كانت مش مكررات من
+
+325
+00:27:30,170 --> 00:27:35,430
+هنا خالص اللي هي بيصير عندى في داخل هذه عدد عناصر
+
+326
+00:27:35,430 --> 00:27:41,890
+الـQ*) أكتر من عدد عناصر الـQ بعال أكتر أناقص واحد
+
+327
+00:27:42,200 --> 00:27:50,720
+وكل هذا تبع اللي هو النقاط اتكرر المعها دولة او ما
+
+328
+00:27:50,720 --> 00:27:57,000
+اتكررنش ما اتكررنش بالمرة بيكون بالظبط عددهم اللي
+
+329
+00:27:57,000 --> 00:28:03,000
+هو ال YM زائد ال N ناقص واحد لو ما اتكررنش ولا
+
+330
+00:28:03,000 --> 00:28:07,700
+واحدة يعني بمعنى اخر ال Q start زيد عن ال Q ب N
+
+331
+00:28:07,700 --> 00:28:10,740
+ناقص واحد من النقاط
+
+332
+00:28:12,960 --> 00:28:17,560
+طيب زي ما قال إذن So Q star تحتوي بي إبسلون and Q
+
+333
+00:28:17,560 --> 00:28:21,780
+star has at most N نقص واحد more points than Q
+
+334
+00:28:21,780 --> 00:28:26,220
+namely those points among اللي هي النقاط اللي من
+
+335
+00:28:26,220 --> 00:28:30,080
+مين اللي بيكون الزيادات من ال X واحد لعندي ال X N
+
+336
+00:28:30,080 --> 00:28:35,200
+ال X N نقص واحد that is belongs to B star but not
+
+337
+00:28:35,200 --> 00:28:40,560
+to مين to Q اللي هدول اللي بتكون الزيادات طيب نطلع
+
+338
+00:28:40,560 --> 00:28:48,130
+لفوقالآن بما أن الـ Q صار تحتوى لـ Q إذا أكيد الـ
+
+339
+00:28:48,130 --> 00:28:53,850
+UQ ناقص الـ UQ صار أكبر سوى 0 طبعا عارفين ليش لأن
+
+340
+00:28:53,850 --> 00:28:58,890
+الـ refinement دائما لل upper sum بيجلله ماشي عشان
+
+341
+00:28:58,890 --> 00:29:02,670
+يصير refinement عشان يبطل يطلع فوق ينزل إشي بسيط
+
+342
+00:29:02,670 --> 00:29:07,730
+فهذا في الـ refinement معناته بيصير الـ UQأصغر من
+
+343
+00:29:07,730 --> 00:29:11,790
+مين؟ أكبر من مين؟ من الـUQ UQ star لأنه في
+
+344
+00:29:11,790 --> 00:29:15,630
+الـrefinement الأعلى بجلد مدام بجلد إذا هذا UQ
+
+345
+00:29:15,630 --> 00:29:20,610
+ناقص UQ star أكبر أو يساوي سفر الآن زي ما سمنا if
+
+346
+00:29:20,610 --> 00:29:25,170
+we write UQ star بيساوي Z node Z واحد عند مين؟ عند
+
+347
+00:29:25,170 --> 00:29:34,610
+ZB then لو أجينا بدنا نحسب الآن UQ F ناقص UQ star
+
+348
+00:29:34,610 --> 00:29:42,230
+وFخلّيني اوضّح لك
+
+349
+00:29:42,230 --> 00:29:53,010
+خلّيني اكتبها ماعليش عندي U Q و
+
+350
+00:29:53,010 --> 00:29:59,290
+F ناقص U Q Star و F
+
+351
+00:30:02,130 --> 00:30:07,370
+الـ summation الأولى العبارة عن الـ summation له
+
+352
+00:30:07,370 --> 00:30:19,310
+اللي هي M J في 100 في الـ Q اللي هو Y J minus Y J
+
+353
+00:30:19,310 --> 00:30:25,130
+minus 1 J من عند 1 لعند الـ M ناقص ال summation
+
+354
+00:30:25,130 --> 00:30:37,430
+للتانية اللي هي MK Star في مين؟ في Z K-Z K-1 K من
+
+355
+00:30:37,430 --> 00:30:42,750
+عند 1 لعند مين؟ لعند الـ B اللي فرضناها إيش اسمها
+
+356
+00:30:42,750 --> 00:30:49,190
+اللي هي الـ B زي ما قولت قبل بشويةلو كان هذولة
+
+357
+00:30:49,190 --> 00:30:53,870
+اللي صارن زيادات هنا اللي صارن زيادات هنا ال X
+
+358
+00:30:53,870 --> 00:30:59,410
+نقطة من X واحد لعند X اناقس واحد لو توزع بين هذولة
+
+359
+00:31:00,990 --> 00:31:04,390
+يعني بمعنى أخر كل هدف في حالة الـ M أكبر من N
+
+360
+00:31:04,390 --> 00:31:10,430
+اتوزع بينهين هيعمل اللي هو ال intervals زي ما قلنا
+
+361
+00:31:10,430 --> 00:31:15,850
+2 في N ناقص 1 في هذه ال intervals هيكون اللي هو
+
+362
+00:31:15,850 --> 00:31:22,460
+الـ Mj و الـ Mk قد يكون المختلفاتلكن في الباقي
+
+363
+00:31:22,460 --> 00:31:28,400
+اللي أصلا مادخلهنش إش جديد وضلت الـQ زي الـQ*)
+
+364
+00:31:28,400 --> 00:31:35,680
+فبتكون M تبعت الـQ و M*) تبعت الـQ*) زي بعض فبصير
+
+365
+00:31:35,680 --> 00:31:40,360
+هذه ناقص هذه بساوي 0 اللي هي الـMj والمك بساوي 0
+
+366
+00:31:40,360 --> 00:31:47,070
+يعني بمعنى آخرالـ terms اللي هتكون ع صورة MJ ناقص
+
+367
+00:31:47,070 --> 00:31:52,110
+MK star ع الأكثر ع الأكثر اللي ممكن يكون المختلفات
+
+368
+00:31:52,110 --> 00:31:57,550
+عبارة عن جداش جماعة اتنين في N ناقص واحد يعني هذول
+
+369
+00:31:57,550 --> 00:32:01,950
+عدد هنا ع الأكتر طبعا في ZK minus ZK minus واحد
+
+370
+00:32:01,950 --> 00:32:04,770
+تبعي اللي هو التجزئة الجديدة لإنه هذه التجزئة اللي
+
+371
+00:32:04,770 --> 00:32:08,950
+بتجسمها ل sub intervals يعني ع الأكتر هذول عدد هنا
+
+372
+00:32:08,950 --> 00:32:13,180
+جداش اتنين في N ناقص واحدهذا أنا قلته لما في حالتي
+
+373
+00:32:13,180 --> 00:32:18,610
+الأم أكبر من أنافي حالة الـ M أصغر أو يساوي N
+
+374
+00:32:18,610 --> 00:32:23,890
+بيصير اللي هو في الشيء .. بيصير اللي هو غصبًا عنها
+
+375
+00:32:23,890 --> 00:32:30,270
+مدام الـ N أكبر وبدها تدخل الـ X1 عليهم غصبًا عنها
+
+376
+00:32:30,270 --> 00:32:35,210
+هيكون في الداخل انطبج على مين؟ على إيش من هان يعني
+
+377
+00:32:35,210 --> 00:32:39,630
+مش هيعمل إن 2 في N ناقص 1 هيعمل إن أجل من هيك إلا
+
+378
+00:32:39,630 --> 00:32:42,150
+في حالة اللي هي M بتساوي N بتطلع اللي هو على
+
+379
+00:32:42,150 --> 00:32:47,560
+الأكثر ممكن يطلع 2 في N-1 لأنه ما بيظلش فيه عنده
+
+380
+00:32:47,560 --> 00:32:53,580
+اللي هو مكان بين هذوله يدخلن فبضطر ان اللي هو اكيد
+
+381
+00:32:53,580 --> 00:32:58,140
+هيكون من منين من جواك اللي هي هذه او بكون اللي جوا
+
+382
+00:32:58,140 --> 00:33:03,760
+برضه مش هيزيدن عن اتنين في الـ-1 اذا اللي هي دخلن
+
+383
+00:33:04,020 --> 00:33:09,620
+على أماكن غير مين حتى في حالة ال M ال M أصغر من N
+
+384
+00:33:09,620 --> 00:33:14,000
+لأ هيدخلن هيدخلن يعملن sub intervals هيختلفن برضه
+
+385
+00:33:14,000 --> 00:33:18,640
+نفس الشيء يعني لو دخلت X1 هنا و X2 هنا فبصير برضه
+
+386
+00:33:18,640 --> 00:33:22,550
+يعملن sub intervals في مجموحينلن يتجاوز ان اتنين
+
+387
+00:33:22,550 --> 00:33:29,230
+في ان ناقص واحد لأن عدد ان ناقص واحد من النقاط
+
+388
+00:33:29,230 --> 00:33:33,550
+الجديدة ال X1 X2 عند Xn ناقص واحد ان شاء الله تكون
+
+389
+00:33:33,550 --> 00:33:39,490
+واضحة هذه الصورة يعني مختصرها انههن اللي ممكن ما
+
+390
+00:33:39,490 --> 00:33:47,270
+يحفظلش على اللي هو الـ الـ الـ الـ الـ الـ الـ الـ
+
+391
+00:33:47,270 --> 00:33:48,310
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+392
+00:33:48,310 --> 00:33:48,310
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+393
+00:33:48,310 --> 00:33:48,670
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+394
+00:33:48,670 --> 00:33:48,690
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+395
+00:33:48,690 --> 00:33:48,810
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+396
+00:33:48,810 --> 00:33:49,030
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+397
+00:33:49,030 --> 00:33:49,030
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+398
+00:33:49,030 --> 00:33:52,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الاللي
+
+399
+00:33:52,480 --> 00:33:57,120
+هي بس اللي هي N ناقص واحد من النقاط اللي هتصنعني
+
+400
+00:33:57,120 --> 00:34:02,180
+بس اتنين في N ناقص واحد على الأكثر من ال .. اللي
+
+401
+00:34:02,180 --> 00:34:10,840
+هي ال M واحد أو ال Mj تختلف عن ال M كستار طيب،
+
+402
+00:34:10,840 --> 00:34:13,940
+ماشي الحالة ان شاء الله تكون المضحكة هذه لأن هي بس
+
+403
+00:34:13,940 --> 00:34:17,840
+هذه النقطة اللي بدها توضيح في الباقي هيكون بإذن
+
+404
+00:34:17,840 --> 00:34:23,040
+الله سعيد إذا صار زي ما قلنانرجع لهذا then U Q F
+
+405
+00:34:23,040 --> 00:34:27,200
+نقص U Q Star و F can be written as the sum of at
+
+406
+00:34:27,200 --> 00:34:31,920
+most اتنين في M نقص واحد terms of the form M J نقص
+
+407
+00:34:31,920 --> 00:34:37,460
+M K Star في Z K minus Z K minus واحد لأن عدد هذه
+
+408
+00:34:37,460 --> 00:34:41,680
+الدولة على الأكثر اللي هو بالشكل هذا إذا الآن لو
+
+409
+00:34:41,680 --> 00:34:51,060
+أجينا بدي أحسبلك اللي هو الـ M J نقص M K Starهذه
+
+410
+00:34:51,060 --> 00:35:00,000
+هيكون أصغر أو يساوي مج زائد مك
+
+411
+00:35:01,360 --> 00:35:05,180
+وكل واحدة طبعاً هذا supremum على فترتها وهذا
+
+412
+00:35:05,180 --> 00:35:09,240
+supremum لل F على فترتها أكيد أصغر أو يساوي ال M
+
+413
+00:35:09,240 --> 00:35:13,160
+زائد ال M لأن هذا ال M عبارة عن ال supremum على كل
+
+414
+00:35:13,160 --> 00:35:16,360
+ال interval A وB هذا على جزءه هذا على كل ال
+
+415
+00:35:16,360 --> 00:35:19,240
+interval A وB هذا على جزءه يعني في النهاية هذا
+
+416
+00:35:19,240 --> 00:35:25,460
+أصغر أو يساوي قداش 2 في M يعني هيصير عندي الآن ال
+
+417
+00:35:25,460 --> 00:35:32,980
+absolute value لل M J ناقص M K Starفي ZK-ZK-1
+
+418
+00:35:32,980 --> 00:35:39,970
+هيكون أصغر أو ساوى 2Mفي مين؟ في اللي هي طول الـ
+
+419
+00:35:39,970 --> 00:35:43,550
+interval هذه طول الـ interval هذه طب هذه الـ
+
+420
+00:35:43,550 --> 00:35:50,170
+interval zk minus zk minus 1 أكيد أصغر أو يساوي
+
+421
+00:35:50,170 --> 00:35:56,410
+مين؟ norm لـ Q star مين norm لـ Q star؟ اللي هو ال
+
+422
+00:35:56,410 --> 00:36:01,510
+supremum على مين؟ على أطوال ال subintervals ال
+
+423
+00:36:01,510 --> 00:36:05,750
+supremum أكيد أكبر أو يساوي واحدة منهم طول واحدة
+
+424
+00:36:05,750 --> 00:36:13,190
+منهملكلهم وهذه دائماً لما نزيد العدد قلنا لما نكون
+
+425
+00:36:13,190 --> 00:36:19,630
+Q يحتوي Q*) automatic norm لـ Q*) زي ما قلنا المرة
+
+426
+00:36:19,630 --> 00:36:24,710
+الفاتة هيكون أصغر أو يشوي .. آسف لما يكون Q
+
+427
+00:36:24,710 --> 00:36:28,370
+substantive لـ Q*) يكون norm لـ Q*) عكسه أصغر أو
+
+428
+00:36:28,370 --> 00:36:34,420
+يشوي norm من لـ Qإذا الـ N هذا أصغر أو يساوي هذا و
+
+429
+00:36:34,420 --> 00:36:38,940
+هذا نفسه أصغر أو يساوي مين؟ الـ Q و الـ Normal Q
+
+430
+00:36:38,940 --> 00:36:42,720
+أصغر من مين؟ من دلتا ما احنا على أساسه اللي هي
+
+431
+00:36:42,720 --> 00:36:48,120
+اشتغلنا إذا صار عندي هذا Normal أصغر من دلتا يعني
+
+432
+00:36:48,120 --> 00:36:53,380
+نرجع لهذا هذا المقدار كل واحد لحاله أصغر من اتنين
+
+433
+00:36:53,380 --> 00:36:58,350
+أم في مين بيصير؟ في دلتاالأن عدد هذول اللي ممكن
+
+434
+00:36:58,350 --> 00:37:07,870
+يظهر في UQ ناقص UQ star عبارة عن 2M ناقص 1 يعني في
+
+435
+00:37:07,870 --> 00:37:14,330
+النهاية هذا أصغر أو يساوي اللي هو عدد الـ 2M ناقص
+
+436
+00:37:14,330 --> 00:37:22,940
+1 مضروب في مين؟ في اللي هي 2M2M في Delta لأن هذا
+
+437
+00:37:22,940 --> 00:37:28,390
+نفسه أصغر يساوي 2M و هذا نفسه أصغر يساوي Deltaالان
+
+438
+00:37:28,390 --> 00:37:33,030
+هدولة بتكرر على الأكتر اتنين فئة ناقص واحد هذا ..
+
+439
+00:37:33,030 --> 00:37:36,750
+هذا بتكرر في هذا المقدار على الأكتر في هذا و
+
+440
+00:37:36,750 --> 00:37:40,370
+الباقية هيتصفر زي ما قلنا إذا صار هيكون هذا أصغر
+
+441
+00:37:40,370 --> 00:37:44,750
+أو يساوي عدد تكرار من اتنين فئة ناقص واحد في اتنين
+
+442
+00:37:44,750 --> 00:37:51,010
+M في مين في Delta فإذا صار عندي الآن ال UQF ناقص
+
+443
+00:37:51,010 --> 00:37:55,050
+ال UQ star و F أصغر أو ساوي اتنين فئة ناقص واحد في
+
+444
+00:37:55,050 --> 00:38:01,350
+اتنين M في مينفى delta نصبوت اللى هو هذا عبارة عن
+
+445
+00:38:01,350 --> 00:38:13,090
+قداشة جماعة نيجى نحسبها عشان نصل للي بدنايا صار
+
+446
+00:38:13,090 --> 00:38:26,230
+عندى اللى هو ال U Q F U star و F Q F ناقص U
+
+447
+00:38:32,930 --> 00:38:38,230
+UQF-UQF UQF
+
+448
+00:38:38,230 --> 00:38:44,130
+-UQF UQF
+
+449
+00:38:44,130 --> 00:38:45,750
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+450
+00:38:45,750 --> 00:38:45,850
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+451
+00:38:45,850 --> 00:38:45,850
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+452
+00:38:45,850 --> 00:38:45,850
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+453
+00:38:45,850 --> 00:38:54,050
+-UQF UQF-UQF UQF-UQF UQFفى اللى هو M فى Delta اللى
+
+454
+00:38:54,050 --> 00:38:59,870
+هو أكيد هذا أصغر من أربعة فى N فى M فى Deltaمظهورة
+
+455
+00:38:59,870 --> 00:39:03,790
+ولا لأ؟ لأن الـ N أكبر من مين؟ من الـ N نقص واحد
+
+456
+00:39:03,790 --> 00:39:06,370
+الـ Delta إيش اخترناها؟ ما هي الحسابات من الأول
+
+457
+00:39:06,370 --> 00:39:12,010
+حاسبينها احنا اخترنا الـ Delta فوق عبارة عن جداش
+
+458
+00:39:12,010 --> 00:39:15,710
+لإن احنا كنا عارفين حالنا أصلا بنصل لها المرحلة
+
+459
+00:39:15,710 --> 00:39:19,730
+فبدنا نخلي هذه ي على تلاتة ليش ي على تلاتة؟ بعد
+
+460
+00:39:19,730 --> 00:39:26,470
+شوية تشوف اللي هي عبارة عن ي هذه ي على 12N في مين
+
+461
+00:39:26,470 --> 00:39:31,170
+في Nهذه الآن لما أشيل هذه و أضرب هذه فيها بيصير
+
+462
+00:39:31,170 --> 00:39:34,770
+أربعة في واحد و الان مع الان و الام مع الام و هذي
+
+463
+00:39:34,770 --> 00:39:41,750
+بيصير جداش تلاتة إذا صار عندي الان U Q و F ناقص U
+
+464
+00:39:41,750 --> 00:39:48,000
+Q Star و F أصغر من epsilon ع تلاتةيعني بمعنى آخر
+
+465
+00:39:48,000 --> 00:39:55,380
+صار عند الـ U Q و F أصغر من إبسل من ع تلاتة زائد U
+
+466
+00:39:55,380 --> 00:40:01,420
+Q star من و F ماشي الحال إذا هذه ال in quality
+
+467
+00:40:01,420 --> 00:40:06,160
+التانية اللي وصلناها اللي هتوصلني في النهاية للي
+
+468
+00:40:06,160 --> 00:40:11,490
+بديه ونشوف كيف هتوصلنيطيب يا جماعة صلوا على النبي
+
+469
+00:40:11,490 --> 00:40:17,670
+عليه الصلاة والسلام تنسوش أنه احنا في الأول حصلنا
+
+470
+00:40:17,670 --> 00:40:21,730
+على U بي و أف ماطس أل بي و أف أصغر من مين من
+
+471
+00:40:21,730 --> 00:40:24,930
+إبسلون على تلاتة وحصلنا على U بي و إبسلون هذا أصغر
+
+472
+00:40:24,930 --> 00:40:27,910
+من إبسلون على تلاتة هنحتاجها بعد شوية خليني اكتبها
+
+473
+00:40:27,910 --> 00:40:35,630
+التانية عند حصلنا قبل هيك على ال U بي و أف ماطس أل
+
+474
+00:40:35,630 --> 00:40:42,970
+بي و أف أصغرمن epsilon ع تلاتة وطبعا اكيد اللي هي
+
+475
+00:40:42,970 --> 00:40:46,870
+اصغر من u بي ابسلون و اف عشان لا نرجع الهاشمون
+
+476
+00:40:46,870 --> 00:40:51,970
+اقصال بي ابسلون و اف كله اصغر من ابسلون ع تلاتة
+
+477
+00:40:51,970 --> 00:41:00,930
+هاي كمان هدول التنتين حصلناها ماشي طيب الان
+
+478
+00:41:00,930 --> 00:41:09,000
+اللي عملنا هذا اللي هو مع ال upper sumبنعمل نفسه
+
+479
+00:41:09,000 --> 00:41:14,680
+مع مين مع اللي هو our sum هنلاقي اللي هو LQ يعني
+
+480
+00:41:14,680 --> 00:41:19,060
+LQ star و F ناقص LQ F هنلاقيه هنا على الأكتر
+
+481
+00:41:19,060 --> 00:41:23,020
+باختلاف أنه هو التو فئة ناقص واحد من التلزمه و و و
+
+482
+00:41:23,020 --> 00:41:26,640
+الاخر و بنكمل نفس الاشي بطل عند LQ star و F ناقص
+
+483
+00:41:26,640 --> 00:41:30,600
+إبشر على تلاتة أصغر من مين من LQ F إذا similarly
+
+484
+00:41:30,600 --> 00:41:35,120
+for هذه اللي عملناها هذه ما حد بنعمله مع اللي هو
+
+485
+00:41:35,730 --> 00:41:47,930
+الـ L L of Q star و F ماقص اللي هو إبسلون ع تلاتة
+
+486
+00:41:47,930 --> 00:41:55,890
+أصغر من L Q O mean O F ماشي الحال، طيب and exactly
+
+487
+00:41:55,890 --> 00:42:00,310
+زي ما بنقول similar argument symbolize that اللي
+
+488
+00:42:00,310 --> 00:42:07,870
+كتبناهلنبدأ نجمع معلوماتنا عشان نصل لإنه الـ
+
+489
+00:42:07,870 --> 00:42:11,530
+Riemann Sum نقص الـ integration يكون إيه شماله
+
+490
+00:42:11,530 --> 00:42:15,890
+اللي هو أصغر من إبسلون، انتبهوا كيف عشان يمكن هيك
+
+491
+00:42:15,890 --> 00:42:23,210
+تكون أسهل لنا نرسم خط الأعداد وهنا هخلينا اللي هو
+
+492
+00:42:23,210 --> 00:42:43,920
+نحط الـ U أكي و FU Q F هي أصغر من
+
+493
+00:42:43,920 --> 00:42:55,420
+أبسلون على تلاتة زي U U أستار U F عندي
+
+494
+00:42:55,420 --> 00:42:57,860
+U Q F
+
+495
+00:43:00,380 --> 00:43:07,380
+بس خليني عشان أحط ال L قبل ل L قبل هه عشان مفيش
+
+496
+00:43:07,380 --> 00:43:14,800
+وسح أنا جماعة بعد أذنكم خليني بس هكتب الأول أشنب
+
+497
+00:43:14,800 --> 00:43:27,870
+ده بمين ب L L Q و Fالـ Refinement طبعاً لـ L, Q,
+
+498
+00:43:27,970 --> 00:43:36,450
+Star و F قبلها زي ما انتوا عارفين L, Q و F خليني
+
+499
+00:43:36,450 --> 00:43:41,090
+أعمل هذه قبلها عشان تظبط أحسن L, Q, Star و F ناقص
+
+500
+00:43:41,090 --> 00:43:50,640
+بصناعة تلاتة وهذه LUQF معايا هى هذه بتكون قبل هذه
+
+501
+00:43:50,640 --> 00:43:59,300
+طيب ال QF أكيد بعدها مين UQF صح ولا لأ أكيد طيب
+
+502
+00:43:59,300 --> 00:44:07,420
+بعد ال UQF إيش بتيجي بتيجي هنا إبسلون ع تلاتة زائد
+
+503
+00:44:07,420 --> 00:44:15,340
+UQ star و F مظبوطمظبوط اكيد؟ طيب اذا انا اجيت لخصت
+
+504
+00:44:15,340 --> 00:44:21,120
+المعلومة هذه و لخصت المعلومة هذه اللي هي أصغر من
+
+505
+00:44:21,120 --> 00:44:28,460
+epsilon ع تلاتة UQF UQF ولا ال PUF هذه المسافة
+
+506
+00:44:28,460 --> 00:44:32,910
+بينهم ايه اشمل يا جماعة؟أصغر من إبسلون ع تلاتة
+
+507
+00:44:32,910 --> 00:44:37,130
+واضح أه؟ ومن هنا قال لك U square of F نقص هذه وهذه
+
+508
+00:44:37,130 --> 00:44:43,050
+إبسلون وهذه بالترتيب اللي احنا حصلنا عليه طيب الان
+
+509
+00:44:43,050 --> 00:44:48,230
+طبيعي اللي هو ال remansum و ال integration هيكون
+
+510
+00:44:48,230 --> 00:44:52,030
+بين ال lower و بين main اللي هو إياش الأبر إذن
+
+511
+00:44:52,030 --> 00:44:57,110
+أكيد أكيد أكيد ال remansum تبعنا هي بدينا نصل للي
+
+512
+00:44:57,110 --> 00:45:04,400
+جدنا إياها ال CQFواللي هو ال integration من a إلى
+
+513
+00:45:04,400 --> 00:45:08,720
+b إلى ال F هيكون بين ال lower و بين ال upper ال
+
+514
+00:45:08,720 --> 00:45:11,720
+integration موجود لأن مراس الدور جللنا إذا هذوله
+
+515
+00:45:11,720 --> 00:45:17,800
+صار اللي هو بين هذه و بين هذه إذا صار هذه و هذه
+
+516
+00:45:17,800 --> 00:45:26,120
+بين هذه الدنتينوهذه طبعا ال U Q F و اللي قاله Q F
+
+517
+00:45:26,120 --> 00:45:31,780
+واضح .. واضح انه اللي هو وين في داخل الفترة اللي
+
+518
+00:45:31,780 --> 00:45:36,660
+هي L Q Star و F ناقص أبسل على ثلاثة و U Q Star و F
+
+519
+00:45:36,660 --> 00:45:42,500
+أبسل على تلاتة يعني بين .. هذه طبعا .. بين هذه و
+
+520
+00:45:42,500 --> 00:45:47,200
+بين مين و بين ال interval هذه يعني subset من مين
+
+521
+00:45:47,200 --> 00:45:53,460
+جايل من I أبسلوناللي هي I Epsilon بتساوي اللي هو
+
+522
+00:45:53,460 --> 00:45:59,440
+الفترة هذه من هنا لعند الـ hand هو اللي مسمينها
+
+523
+00:45:59,440 --> 00:46:05,740
+احنا اشمالها I Epsilon بين L Q Star و F نقص
+
+524
+00:46:05,740 --> 00:46:11,860
+Epsilon ع تلاتة و U Q Star F و Epsilon ع تلاتة
+
+525
+00:46:11,860 --> 00:46:20,060
+الآنU Q Star و F ناقص قالك U Star و F ما مسحتاش
+
+526
+00:46:20,060 --> 00:46:28,200
+لسه أنا U Q Star F و قالك U Star F أصغر من مين من
+
+527
+00:46:28,200 --> 00:46:36,520
+إبسلون ع تلاتة لأ اللي هي U
+
+528
+00:46:36,520 --> 00:46:42,670
+Q Star Fوقال الـ Q star F حصلنا عليها قبل هيك أنها
+
+529
+00:46:42,670 --> 00:46:46,650
+أصغر من مين من إبسل ع تلاتة طبعا من وين بنحصلها؟
+
+530
+00:46:46,650 --> 00:46:49,650
+ممكن نحصلها مبقى من هنا ده كما حصلناش أن الـ Q
+
+531
+00:46:49,650 --> 00:46:54,430
+star و F و الـ By بتحتوي الـ By فهيكون الـ U اللي
+
+532
+00:46:54,430 --> 00:47:00,090
+حصلنا أولا بالنسبة لمن؟ لاللي هي الـ By حصلنا قبل
+
+533
+00:47:00,090 --> 00:47:06,400
+هيك أن الـ Uبإبسلون و ال ال بإبسلون الفرق بين همين
+
+534
+00:47:06,400 --> 00:47:10,840
+إبسلون على تلاتة و ال Q star refinement إذا أكيد
+
+535
+00:47:10,840 --> 00:47:14,920
+المسافة بين ال other طبعا في ال refinement المسافة
+
+536
+00:47:14,920 --> 00:47:20,440
+بين ال other و ال other هتصغر لكل refinement ال U
+
+537
+00:47:20,440 --> 00:47:28,340
+بما أن هذه refinement إذا ال Uلأ الـ Q star و F
+
+538
+00:47:28,340 --> 00:47:34,960
+ناقص L Q star و F أصغر أو يساوي لأنها صارت تحسين
+
+539
+00:47:34,960 --> 00:47:38,400
+عليها مازالت صارت تحسين يعني بتجلل مسافة بين ال
+
+540
+00:47:38,400 --> 00:47:40,780
+Upper و الLower عشان نروح في الآخر لل integration
+
+541
+00:47:40,780 --> 00:47:51,520
+ناقص أصغر أو يساوي لL B epsilon و F U ناقص L B
+
+542
+00:47:51,520 --> 00:47:56,980
+epsilon و F اللي هي هذه أصغر من 100من إبسلون وينها
+
+543
+00:47:56,980 --> 00:48:03,400
+أصغر من إبسلون ع تلاتة أصغر من إبسلون ع تلاتة إذا
+
+544
+00:48:03,400 --> 00:48:10,320
+فعلا عرفنا من وين إجت هذه أصغر من مين من إبسلون ع
+
+545
+00:48:10,320 --> 00:48:18,460
+تلاتة إذا صار عندي ال length لهذهالـ length لهذه
+
+546
+00:48:18,460 --> 00:48:23,240
+سهل نوجده بعليش خلّيني أكتب فوق عشان لو جبتلكم ال
+
+547
+00:48:23,240 --> 00:48:29,780
+length إلها عشان أقولكم إنه هذه و هذه هيكون اللي
+
+548
+00:48:29,780 --> 00:48:38,900
+هو بالبعد المطلوب تحسبلي الآن هذه ناقص هذه بصير
+
+549
+00:48:38,900 --> 00:48:48,940
+عبارة عن طول ال interval mean Iy بساوي ال UQ star
+
+550
+00:48:48,940 --> 00:48:55,780
+و F زائد إبسلون على تلاتة ناقص تبعين معيار ال Q
+
+551
+00:48:55,780 --> 00:49:01,720
+star و F ناقص ناقص بيصير زائد إبسلون على تلاتة و
+
+552
+00:49:01,720 --> 00:49:04,900
+يساوي اللي هو إبسلون على تلاتة و إبسلون على تلاتة
+
+553
+00:49:04,900 --> 00:49:12,180
+اتنين إبسلون على تلاتة زائد U Q star و F ناقص ال Q
+
+554
+00:49:12,180 --> 00:49:18,800
+star و F اللي هم هذولةهذه اللي كتبتها لسه ماحتنش
+
+555
+00:49:18,800 --> 00:49:23,400
+أصغر من مين من يبسلون على تلاتة فبتصير هذه طولها
+
+556
+00:49:23,400 --> 00:49:26,700
+أصغر من اتنين يبسلون على تلاتة زائد يبسلون على
+
+557
+00:49:26,700 --> 00:49:31,620
+تلاتة ويساوي يبسلون إذا صار عندي طول الـ interval
+
+558
+00:49:31,620 --> 00:49:40,520
+اللي أسي Qf والـ integration A وBموجودة في كل
+
+559
+00:49:40,520 --> 00:49:46,660
+الفترة هذه اللي هي المسافة بينهم عبارة عن أصغر من
+
+560
+00:49:46,660 --> 00:49:53,460
+مين من Epsilon إذا صار عندي الآن ال integration
+
+561
+00:49:53,460 --> 00:50:05,480
+أين أكتب ال integration إذا صار عندي إذا صار عندي
+
+562
+00:50:05,480 --> 00:50:12,380
+المسافة بين هذه و هذهSQF نقص ال integration من A B
+
+563
+00:50:12,380 --> 00:50:16,900
+ل F أصغر من مين يا جماعة من يبسط من مين هذا تحت
+
+564
+00:50:16,900 --> 00:50:23,360
+شرط مين إنه normally Q هذا أصغر من A H من دلتا
+
+565
+00:50:23,360 --> 00:50:29,200
+أصغر من دلتا بقول إيه أحنا خلصنا اللي بدنا إياه
+
+566
+00:50:29,200 --> 00:50:32,280
+نوقف
+
+567
+00:50:32,280 --> 00:50:33,020
+الجيجا بحثها
+
+568
+00:51:39,830 --> 00:51:44,830
+أه يا أبو حسن بقول هيك أحنا خلصنا برهان نظرية أول
+
+569
+00:51:44,830 --> 00:51:48,490
+حد يقول لي أنه اللي هو المسافة بين U وQ قال الـ Q
+
+570
+00:51:48,490 --> 00:51:50,950
+أصغر من يبسلون على تلاتة لأ احنا ماقلناش هيك
+
+571
+00:51:50,950 --> 00:51:53,950
+البسافة بين الأصغر من يبسلون على تلاتة اللي هو الـ
+
+572
+00:51:53,950 --> 00:51:58,190
+P يبسلون الـ U P يبسلون والـ L P يبسلون وأي
+
+573
+00:51:58,190 --> 00:52:01,010
+refinement له بس الـ Q هنا مش refinement هذا بس
+
+574
+00:52:01,010 --> 00:52:04,830
+اللي بنعرف أنه norm لـ Q أصغر من مين من دلتا أصلا
+
+575
+00:52:04,830 --> 00:52:08,960
+احنا بدنا نصل لإنهالمسافة بين هذولة اللي هو أصغر
+
+576
+00:52:08,960 --> 00:52:13,300
+من إبسلون وعلى طول منها بنستنتج هذه فكيف وصلنا
+
+577
+00:52:13,300 --> 00:52:16,160
+بإننا قلنا اللي هو ال integration هذه في هذه
+
+578
+00:52:16,160 --> 00:52:19,780
+الفترة والفترة هذه جزء من هذه وهذه قلنا هذه طولها
+
+579
+00:52:19,780 --> 00:52:22,960
+على الأكثر بساوي إبسلون عشان هيك صارت المسافة بين
+
+580
+00:52:22,960 --> 00:52:28,000
+هذه وهذا أصغر من إبسلون وهو المطلوب طيب نيجي الآن
+
+581
+00:52:28,000 --> 00:52:34,060
+ده اللي هي النظرية اللي بعدها theorem
+
+582
+00:52:35,670 --> 00:52:45,070
+لت I بتساوي A وB و لت F من I لعند R بيكون فنكشف
+
+583
+00:52:46,090 --> 00:52:49,330
+suppose there exists a number B such that لكل Y
+
+584
+00:52:49,330 --> 00:52:54,110
+أكبر من 0 if B is any partition of I with normal B
+
+585
+00:52:54,110 --> 00:52:58,030
+أصغر من Delta and S of Bi is any corresponding
+
+586
+00:52:58,030 --> 00:53:01,950
+Riemann sum اللي هو then لهذا أصغر من إبسلون then
+
+587
+00:53:01,950 --> 00:53:06,310
+F is integrable on I in the sense of definition
+
+588
+00:53:06,310 --> 00:53:12,590
+716 يعني وكأننا جاعدين بنقول conversely إيش بنقول؟
+
+589
+00:53:12,590 --> 00:53:13,610
+بنقول
+
+590
+00:53:16,710 --> 00:53:24,890
+إنه لو كان عندي اللي هو limit لو كان عندي limit
+
+591
+00:53:24,890 --> 00:53:32,330
+اللي هو الـ S أو B و F as normal B بروح للسفر
+
+592
+00:53:32,330 --> 00:53:38,190
+exist و بسوء some number B إذن هذا الـ B بسوء ال
+
+593
+00:53:38,190 --> 00:53:43,410
+integration من A لB F of X DX يعني بقوللي لو كان
+
+594
+00:53:43,410 --> 00:53:50,850
+هذا متحققلو كان هذا متحقق بيعطيني إنه هذا هو هيطلع
+
+595
+00:53:50,850 --> 00:53:55,110
+اللي هي هتطلع F-integrable وهيكون بيه هذا اللي هو
+
+596
+00:53:55,110 --> 00:53:59,030
+ال limit هذا هو قيمة مين ال integration ليش؟ لأن
+
+597
+00:53:59,030 --> 00:54:02,490
+هذا اصلا شو معناته؟هذا معناته for every epsilon
+
+598
+00:54:02,490 --> 00:54:07,490
+أكبر من صفر there exist اللي هو delta أكبر من صفر
+
+599
+00:54:07,490 --> 00:54:14,370
+such that b أصغر من delta بيؤدي إلى S B و F ناقص
+
+600
+00:54:14,370 --> 00:54:17,630
+ال B اللي مفترضين أصغر من مين ال epsilon هذا هو
+
+601
+00:54:17,630 --> 00:54:23,290
+معناته هذا يعني أن اللي هو المعطىطبعا f bounded من
+
+602
+00:54:23,290 --> 00:54:30,590
+رأس الدور لجهنا number b بحيث ان لكل epsilon او fb
+
+603
+00:54:30,590 --> 00:54:33,270
+is any partition بحيث ان normal b أعلى من delta
+
+604
+00:54:34,000 --> 00:54:39,600
+وكانت اللي هي المسافة بين الـ B أصغر من Epsilon
+
+605
+00:54:39,600 --> 00:54:44,440
+هذا .. ده متحقق اللي هو هذا كله عبارة هو عبارة عن
+
+606
+00:54:44,440 --> 00:54:47,940
+limit S بي و F as and non-invalid اللي هو سفر
+
+607
+00:54:47,940 --> 00:54:52,160
+بساول B إذا .. إذا اتحقق هذا بتكون اللي هي F
+
+608
+00:54:52,160 --> 00:54:55,440
+integrable وقيمة الـ B هذه اللي هي قيمة ال limit
+
+609
+00:54:55,440 --> 00:54:59,420
+بساول integration هذه اللي هي عبارة عن .. النظرية
+
+610
+00:54:59,420 --> 00:55:04,470
+عبارة عن اللي هو بن ..اللي هي دمج بين اللي هي
+
+611
+00:55:04,470 --> 00:55:08,190
+نظريات السابقة المرة الماضية نشوف كيف اللي هو
+
+612
+00:55:08,190 --> 00:55:14,100
+البرهن برهن بسيط لإنه بعتمد عليه بشكل سريعلت y
+
+613
+00:55:14,100 --> 00:55:17,440
+أكبر من 0 و delta أكبر من 0 as in the theorem اللي
+
+614
+00:55:17,440 --> 00:55:20,180
+هو اللي في الـ theorem اللي فوق المقصود فيها النص
+
+615
+00:55:20,180 --> 00:55:25,820
+هذه قدت بي إبسلون بي partition of I with نفترض أنه
+
+616
+00:55:25,820 --> 00:55:30,080
+norm بي إبسلون أصغر من 200 من دلتا هذا المعطى ماشي
+
+617
+00:55:30,080 --> 00:55:36,240
+الحال نفترض أنه إبسلون أكبر من 0 arbitrarily و
+
+618
+00:55:36,240 --> 00:55:41,190
+delta أكبر من 0أو نفترض أن بي إبسلون أي partition
+
+619
+00:55:41,190 --> 00:55:45,310
+بحيث أنه نورمه إيه شماله أصغر من دلتا لكن لو جينا
+
+620
+00:55:45,310 --> 00:55:48,930
+أخدنا بيه أي partition آخر و بيه محتوى بيه إبسلون
+
+621
+00:55:48,930 --> 00:55:53,770
+هيكون نورم ال partition بيه هذا اللي هو ال
+
+622
+00:55:53,770 --> 00:55:57,470
+refinement أكيد أصغر أو سوى نورم مين الأصلي اللي
+
+623
+00:55:57,470 --> 00:56:01,030
+هو أصغر من دلتا صار عنده الآن لكل إبسلون أكبر من
+
+624
+00:56:01,030 --> 00:56:06,470
+سفر there exists دلتا بحيث أنه نورم البي إبسلون
+
+625
+00:56:06,470 --> 00:56:11,740
+أصغر من دلتاولأي partition بي refinement لبيبسلون
+
+626
+00:56:11,740 --> 00:56:17,260
+صار norm أصغر من delta إذا من اللي هو ال .. بواسط
+
+627
+00:56:17,260 --> 00:56:21,740
+اللي هو النظرية السابقة حيكون عند ال S minus البي
+
+628
+00:56:21,740 --> 00:56:27,580
+أصغر من ابسلون يؤدي إلى هذا بيبساو ال integration
+
+629
+00:56:27,580 --> 00:56:32,020
+لإن إيش كانت نظرية سبعة أربعة تلاتة بتشترط تشترط
+
+630
+00:56:32,020 --> 00:56:33,840
+إنه نلاقي لكل ابسلون
+
+631
+00:56:36,480 --> 00:56:42,920
+أي بارتشن بي ابسلون بحيث أن أي بي بتحتول بي ابسلون
+
+632
+00:56:43,910 --> 00:56:48,530
+يؤدي إلى هذا أصغر من إبسلون كله على بعض بيؤدي F
+
+633
+00:56:48,530 --> 00:56:53,790
+أشمالها is integrable إذا بيواصل 7 4 3 مدام حصلنا
+
+634
+00:56:53,790 --> 00:56:57,910
+على ال S بي و F نقص ال V أصغر من إبسلون بيكون هذا
+
+635
+00:56:57,910 --> 00:57:01,190
+اللي حصلنا عليه اللي هو P بساوة ال integration لل
+
+636
+00:57:01,190 --> 00:57:06,630
+F على الفترة من A لB يعني بمعنى أخر احنا اللي
+
+637
+00:57:06,630 --> 00:57:13,530
+حصلنا الآن من النظريتين أن F is integrableF is
+
+638
+00:57:13,530 --> 00:57:19,050
+integrable if and only if limit الـ S,B وF من
+
+639
+00:57:19,050 --> 00:57:23,890
+normal B بيروح للسفر exist وبساوي قيمة ال
+
+640
+00:57:23,890 --> 00:57:28,550
+integration يعني الآن ال integration أوصلنا له عبر
+
+641
+00:57:28,550 --> 00:57:34,330
+طريقين إما عبر طريق اللي هو limit للرمان sumيكون
+
+642
+00:57:34,330 --> 00:57:38,690
+exist أو عبر الطريق الآخر لأن ال upper .. ال upper
+
+643
+00:57:38,690 --> 00:57:42,930
+integral والlower integral يكون جد بعض ومتساويين
+
+644
+00:57:42,930 --> 00:57:52,690
+وحيكون في هذه الحالة هم ال integration وقف
+
+645
+00:57:52,690 --> 00:57:59,570
+هنا يا أبو حسن كم ساعة .. كم
+
+646
+00:57:59,570 --> 00:58:00,810
+عندك الوقت؟
+
+647
+00:58:03,290 --> 00:58:10,650
+نخلصها هيك و نبدأ تانية؟ لأن الجزء الثاني هذا اللي
+
+648
+00:58:10,650 --> 00:58:17,070
+هو الimprover integral بس بطولش بياخد نص ساعة انت
+
+649
+00:58:17,070 --> 00:58:22,090
+قاعد معايا للجد إيش؟ أكيد؟ مديش أضغط عليك يا أبو
+
+650
+00:58:22,090 --> 00:58:30,390
+حسن طيب لأ خلينا نخلص هذه ما هو درس 17 ها؟ هلجيت
+
+651
+00:58:30,390 --> 00:58:31,270
+18؟
+
+652
+00:58:41,590 --> 00:58:48,290
+هي الان بتبدأ في المحاضرة 18 خلصنا 17 كيف؟
+
+653
+00:58:54,810 --> 00:58:59,850
+هك مكون احنا خلصنا المحاضر رقم 17 اللي هو ال
+
+654
+00:58:59,850 --> 00:59:03,610
+integration as a limit بعد شوية هنكمل ال section
+
+655
+00:59:03,610 --> 00:59:08,490
+هذا مظبوط بس هنكمله بموضوع جديد اللي هو عبارة عن
+
+656
+00:59:08,490 --> 00:59:12,510
+الimprover integral وإلى لقاء آخر والسلام عليكم
+
+657
+00:59:12,510 --> 00:59:13,670
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/A0riuruZYaI.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/A0riuruZYaI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..35d046dbb570f3038acba1a70ae73f1a1befbe92
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/A0riuruZYaI.srt
@@ -0,0 +1,1999 @@
+1
+00:00:05,740 --> 00:00:08,920
+بسم الله الرحمن الرحيم الجزء الثاني من المحاضرة
+
+2
+00:00:08,920 --> 00:00:14,780
+التاسعة هيكون اللي هو عبارة عن discussion أو مناقشة
+
+3
+00:00:14,780 --> 00:00:22,060
+لـ Section 6.2 و 6.3 اللي هو مناقشة لـ Main Value 
+
+4
+00:00:22,060 --> 00:00:25,220
+Theorem and its Applications ومناقشة أيضًا لـ
+
+5
+00:00:25,220 --> 00:00:30,560
+L'Hopital's Rule نيجي الآن لـ 6.2 الأسئلة المطلوبة
+
+6
+00:00:30,560 --> 00:00:35,720
+هي كما يلي نبدأ في سؤال 6.2  ادخلنا على الكتاب 
+
+7
+00:00:35,720 --> 00:00:39,160
+خلينا نشوف الـ الـ الـ المثال الـ السؤال من
+
+8
+00:00:39,160 --> 00:00:45,790
+الكتاب نبدأ الآن بسؤال 5 السؤال الخامس هو كما يلي
+
+9
+00:00:45,790 --> 00:00:49,550
+Let a أكبر من صفر و b أكبر من صفر و a strictly
+
+10
+00:00:49,550 --> 00:00:55,570
+أكبر من b طبعًا كل العلاقة strictly وبنفترض أن n
+
+11
+00:00:55,570 --> 00:01:00,290
+أكبر أو يساوي 2 prove that a أس واحد على n ناقص b
+
+12
+00:01:00,290 --> 00:01:05,290
+أس واحد على n أصغر من a - b أس واحد على n 
+
+13
+00:01:05,290 --> 00:01:10,490
+لو جينا لاحظنا على اللي هو المطلوب عند خمسة بيقول لي
+
+14
+00:01:10,490 --> 00:01:16,710
+أن a أكبر من b أكبر من 0 أو n أكبر أو يساوي 2
+
+15
+00:01:16,710 --> 00:01:23,070
+بيقول لي prove that أن a أس واحد على n ناقص b أس واحد
+
+16
+00:01:23,070 --> 00:01:30,710
+على n أصغر من a - b الكل أس واحد على n نيجي
+
+17
+00:01:30,710 --> 00:01:36,890
+للبرهان لو جينا لاحظنا إنه عندي الـ نيجي للسؤال 
+
+18
+00:01:36,890 --> 00:01:40,770
+بس كيف نفكر في السؤال هو ما أعطيني hint في الكتاب 
+
+19
+00:01:40,770 --> 00:01:45,190
+لكن خلينا نشوف كيف كيف حصل على الـ hint لو أدينا
+
+20
+00:01:45,190 --> 00:01:50,490
+جسمنا الجهتين هذا مش من ضمن الحل طبعًا عندي a / b
+
+21
+00:01:51,290 --> 00:01:55,270
+الكل أس واحد على n ناقص جسمة على اللي هو b أس
+
+22
+00:01:55,270 --> 00:01:59,510
+واحد على n للجهتين طبعًا والـ b طبعًا موجبة ففيش شيء
+
+23
+00:01:59,510 --> 00:02:05,290
+بتغير بيصير a / b - 1 الكل أس واحد على n
+
+24
+00:02:05,290 --> 00:02:10,710
+لو نجلنا هذه a / b أس واحد على n ناقص الـ a /
+
+25
+00:02:10,710 --> 00:02:16,150
+b - 1 أس واحد على n أصغر من مين؟ من 1 الآن
+
+26
+00:02:16,700 --> 00:02:21,940
+عندي هذا الآن كله على بعضه هو نفسه الـ F ممكن
+
+27
+00:02:21,940 --> 00:02:27,680
+نستقل الدالة من خلاله أنه ناخد الـ F of X لـ F of X
+
+28
+00:02:27,680 --> 00:02:35,690
+وهتوصلنا بيساوي x أس واحد على n - x - 1 
+
+29
+00:02:35,690 --> 00:02:42,810
+أس واحد على n وطبعًا هو الآن معطيني في السؤال a
+
+30
+00:02:42,810 --> 00:02:47,790
+أكبر من b أكبر من 0 لو طلعنا نلاقي الدالة هذه
+
+31
+00:02:47,790 --> 00:02:56,610
+ولاحظنا أوجدنا الـ f prime لها f prime of x خلينا 
+
+32
+00:02:56,610 --> 00:03:02,130
+ناخد الـ x عنده الـ x أكبر أو يساوي 1 وهنشوف
+
+33
+00:03:02,130 --> 00:03:05,730
+اللي هو ليش عنده الـ x أكبر أو يساوي 1 برضه
+
+34
+00:03:05,730 --> 00:03:09,070
+بتظبط في حالتنا لأن اللي بنينا على أساسها اللي هي
+
+35
+00:03:09,070 --> 00:03:13,290
+الـ a / b نفسها أكبر strictly من مين؟ من 1
+
+36
+00:03:13,290 --> 00:03:17,150
+فالأمور متناسقة مع بعض ولو بدنا نطبق حللها جي جي
+
+37
+00:03:17,150 --> 00:03:20,670
+اللي هو تطبيق معقول اللي هنقف الـ prime of x بيساوي
+
+38
+00:03:20,670 --> 00:03:26,200
+1 / n في x أس 1 / n - 1 ناقص اللي
+
+39
+00:03:26,200 --> 00:03:30,720
+هو 1 / n في x - 1 أس 1 / n -
+
+40
+00:03:30,720 --> 00:03:36,520
+1 ويساوي 1 / n في x أس 1 / n - 1
+
+41
+00:03:36,520 --> 00:03:44,840
+ناقص اللي هو x - 1 اللي هو على 1 / n
+
+42
+00:03:44,840 --> 00:03:50,460
+ناقص 1 الآن لو طلعنا للي عندي هذا
+
+43
+00:03:53,450 --> 00:03:56,930
+لو طلعنا للمقدار اللي عندي الـ x أكبر أو يساوي إيش؟
+
+44
+00:03:56,930 --> 00:04:02,450
+1 يعني الآن الـ x أكبر يساوي 1 لذا لما عندي
+
+45
+00:04:02,450 --> 00:04:06,950
+الأس اللي هنا أس إيش؟ ماله بالسالب أو صفر على سوء
+
+46
+00:04:06,950 --> 00:04:10,130
+الظروف اللي هو بالسالب معناته اللي هو بده يصير
+
+47
+00:04:10,130 --> 00:04:16,070
+1 / x الـ 1 / x عبارة عن كسر، مظبوط؟ الآن
+
+48
+00:04:16,070 --> 00:04:20,430
+بيصير عندي المقدار اللي عندي العلاقة بين هذا وهذا
+
+49
+00:04:20,940 --> 00:04:26,360
+x أكيد أكبر من x - 1 صح ولا لأ؟ لكن لأن
+
+50
+00:04:26,360 --> 00:04:31,240
+مقلوبها هيصير إيش ماله؟ هيصير أصغر فهيصير المقدار
+
+51
+00:04:31,240 --> 00:04:35,440
+هذا أصغر من هذا المقدار ماشي فبيصير عندي المقدار
+
+52
+00:04:35,440 --> 00:04:40,180
+هذا كله على بعضه أصغر من مين؟ من صفر فالآن صارت عندي
+
+53
+00:04:40,180 --> 00:04:45,720
+f' أصغر strictly من مين؟ من صفر إذا صار عندي إذا f
+
+54
+00:04:45,720 --> 00:04:47,160
+is strictly
+
+55
+00:04:50,230 --> 00:04:54,310
+decreasing بدي استخدم الخاصية هذه مدام strictly
+
+56
+00:04:54,310 --> 00:04:59,390
+decreasing وأنا عندي a أكبر من b هسينا عندي a على
+
+57
+00:04:59,390 --> 00:05:06,110
+b أكبر من 1 والـ b طبعًا لا تساوي صفر إذا بما أن
+
+58
+00:05:06,110 --> 00:05:11,930
+f is strictly decreasing إذا f of a / b أكبر من
+
+59
+00:05:11,930 --> 00:05:18,440
+f of 1 f of a / b دلتنا بيجيب العوض فوق بيصير
+
+60
+00:05:18,440 --> 00:05:26,380
+عندي اللي هو آسف أصغر عندي f of a / b إيش
+
+61
+00:05:26,380 --> 00:05:30,920
+هتساويك؟ قولوا معايا اللي هو a / b أس 1 / n
+
+62
+00:05:30,920 --> 00:05:40,360
+ناقص a / b - 1 كل أس 1 / n هذا إيش
+
+63
+00:05:40,360 --> 00:05:45,310
+ماله؟ أصغر من مين؟ من f of 1 f of 1 حسب لي f
+
+64
+00:05:45,310 --> 00:05:50,290
+of 1 هذه 1 وهذه 0 فبيصير عبارة عن أصغر من
+
+65
+00:05:50,290 --> 00:05:53,350
+1 طبعًا هذه اللي هو بنعمل عملية عكسية للي
+
+66
+00:05:53,350 --> 00:05:57,530
+عملناها فوق فبيصير عندي اضرب الجهتين في b أس 1
+
+67
+00:05:57,530 --> 00:06:04,260
+على n فبيصير a أس 1 على n ناقص a - b أس 1 على
+
+68
+00:06:04,260 --> 00:06:10,940
+n أصغر من مين؟ من b أس 1 على n ضربت كله في مين؟
+
+69
+00:06:10,940 --> 00:06:14,980
+في b أس 1 على n إن جلّي الآن بيصير عندي a أس
+
+70
+00:06:14,980 --> 00:06:20,320
+1 على n ناقص b أس 1 على n أصغر من a - b
+
+71
+00:06:20,320 --> 00:06:26,530
+الكل أس 1 على n وهو المطلوب وهذا اللي هو بده إياه
+
+72
+00:06:26,530 --> 00:06:32,150
+يلا إيه بعده؟ خلينا نيجي للسؤال اللي المطلوب الآخر
+
+73
+00:06:32,150 --> 00:06:38,570
+اللي هو use the mean value theorem سؤال 6 use the
+
+74
+00:06:38,570 --> 00:06:42,830
+mean value theorem to prove that sin x - sin y
+
+75
+00:06:42,830 --> 00:06:47,070
+أصغر أو يساوي x - y for all x, y in R هذا
+
+76
+00:06:47,070 --> 00:06:50,610
+السؤال حلينا زيه بالظبط اللي هو mean اللي هو الـ
+
+77
+00:06:50,610 --> 00:06:52,070
+cosine مظبوط؟
+
+78
+00:06:57,300 --> 00:07:03,320
+الآن ما أعرفش فيه داعي نحله ولا إن هو نفسه أو مصور
+
+79
+00:07:03,320 --> 00:07:06,740
+عملناه
+
+80
+00:07:06,740 --> 00:07:12,000
+ولا لأ؟ اللي هي الـ cosine عملناها بنفس الأسلوب ومش
+
+81
+00:07:12,000 --> 00:07:14,340
+هيختلف اللي هو الحل
+
+82
+00:07:22,460 --> 00:07:27,840
+أحله ولا خلصت؟ الآن عندي اللي هو سبعة use the mean
+
+83
+00:07:27,840 --> 00:07:32,580
+value theorem to prove that x - 1 / x أصغر من x
+
+84
+00:07:32,580 --> 00:07:39,160
+أصغر من x - 1 for x أكبر من 1 اللي هو عند 
+
+85
+00:07:39,160 --> 00:07:45,440
+احنا حلينا واحد زائد x هذه الآن اللي هي عبارة عن
+
+86
+00:07:45,440 --> 00:07:51,040
+مين؟ عن اللي هو ln lx الدالة اللي هي f of x بيساوي ln
+
+87
+00:07:51,040 --> 00:07:56,440
+lx وبنستخدم الـ mean value theorem وبنفس الأسلوب فيه
+
+88
+00:07:56,440 --> 00:08:00,540
+داعي نحله؟ خلينا نحله خلينا نحله عشان بنصور
+
+89
+00:08:00,540 --> 00:08:12,360
+الآن سؤال سبعة الآن عندي بدأ أثبت أن ln lx أصغر من 
+
+90
+00:08:12,360 --> 00:08:20,000
+x - 1 وأكبر من x - 1 عالميًا على x 
+
+91
+00:08:20,000 --> 00:08:26,400
+solution العالمين value theorem العالمين value
+
+92
+00:08:26,400 --> 00:08:29,960
+theorem نحله العالمين value theorem لأنه لسه ما
+
+93
+00:08:29,960 --> 00:08:35,980
+خدناش اللي هو Taylor's theorem مش 
+
+94
+00:08:35,980 --> 00:08:39,340
+فاهم
+
+95
+00:08:39,340 --> 00:08:42,110
+عليك بينفع نحلها باستخدام Taylor and x not
+
+96
+00:08:42,110 --> 00:08:44,690
+بيساويها يعني الـ mainly طيب آه احنا احنا عشان
+
+97
+00:08:44,690 --> 00:08:48,850
+لسه ما خدناش Taylor's theorem بدنا نحلها على مين؟
+
+98
+00:08:48,850 --> 00:08:51,970
+على الـ mean value theorem ليش؟ لأنه احنا لسه
+
+99
+00:08:51,970 --> 00:09:00,070
+ما خدناش Taylor's theorem طيب الآن let f of x
+
+100
+00:09:00,070 --> 00:09:07,330
+بتساوي ln الـ x وعندي الـ x أكبر من مين؟ أكبر أو
+
+101
+00:09:07,330 --> 00:09:11,800
+تساوي الـ 1 ولا لأ؟ عندي الـ x أكبر من 100 من 0
+
+102
+00:09:11,800 --> 00:09:14,940
+for
+
+103
+00:09:14,940 --> 00:09:23,100
+x أكبر من 0 مش عايز إنّي ماشي الحين نيجي اللي هو أن
+
+104
+00:09:23,100 --> 00:09:26,540
+نستخدم الـ mean value theorem continuous و closed و
+
+105
+00:09:26,540 --> 00:09:31,300
+differentiable وكل الأمور هذه شاملة متحققة إذا
+
+106
+00:09:31,300 --> 00:09:38,150
+there exist c element in a و b c عندي اللي هو
+
+107
+00:09:38,150 --> 00:09:42,290
+element معايا؟
+
+108
+00:09:42,290 --> 00:09:52,610
+طيب لأن let f of x بيساوي ln x و x أكبر من 0 وعندي
+
+109
+00:09:52,610 --> 00:09:57,430
+المطلوب في الـ inequality اللي هي x أكبر من 1 يعني
+
+110
+00:09:57,430 --> 00:10:02,870
+x سنتمي إلى الـ 1 وما لا نهاية معايا؟ إذا there
+
+111
+00:10:02,870 --> 00:10:11,590
+exists c لذًا بدي أطبق الآن we apply mean value
+
+112
+00:10:11,590 --> 00:10:18,570
+theorem on وين قول معايا on 1 و x there exists
+
+113
+00:10:18,570 --> 00:10:25,090
+c element 1 و x such that معايا such that اللي
+
+114
+00:10:25,090 --> 00:10:36,890
+هو f prime of c يساوي f of x ناقص f 1 على x ناقص
+
+115
+00:10:36,890 --> 00:10:48,110
+إيش ناقص 1 آه فالآن عندي f of x قد إيش؟ ويساوي ln
+
+116
+00:10:48,110 --> 00:10:56,450
+الـ x ناقص ln الـ 1 قد إيش؟ 0 على x - 1 وهذا
+
+117
+00:10:56,450 --> 00:11:02,050
+مين؟ هو f prime of c عبارة عن ln الـ 1 على c مظبوط
+
+118
+00:11:02,870 --> 00:11:06,570
+إذا صار عندي الآن بدأ أجيب لإن الـ x أصغر من مين؟ من
+
+119
+00:11:06,570 --> 00:11:12,270
+x - 1 صار عندي إذا ln الـ x بيساوي 1 على
+
+120
+00:11:12,270 --> 00:11:18,390
+c في x - 1 واللي عند c إيش ماله؟ بأخذه أنا
+
+121
+00:11:18,390 --> 00:11:23,050
+أكبر من 1 مدام أكبر من 1 إذا 1 / c اللي
+
+122
+00:11:23,050 --> 00:11:28,390
+هو أصغر من 1 مظبوط إذا هذا أكيد هذا أصغر من x
+
+123
+00:11:28,390 --> 00:11:35,440
+- 1 مظبوط؟ لأن الـ 1 / c إيش ماله؟ عبارة
+
+124
+00:11:35,440 --> 00:11:43,990
+عن كسر الآن من جهة أخرى عندي اللي هو ln الـ x بيساوي
+
+125
+00:11:43,990 --> 00:11:49,410
+1 / c في x - 1 لكن الـ x أنا c إيش
+
+126
+00:11:49,410 --> 00:11:54,190
+معناها بين الـ 1 والـ x يعني c أصغر من مين؟ c أصغر
+
+127
+00:11:54,190 --> 00:11:59,430
+من x يعني الـ 1 / x اللي هو أصغر من مين الآن؟ c
+
+128
+00:11:59,430 --> 00:12:05,890
+أصغر من x إذا 1 / c أكبر من 1 / x فبيصير
+
+129
+00:12:05,890 --> 00:12:13,190
+عند هذا أكبر من 1 / x في x - 1 يعني بمعنى آخر
+
+130
+00:12:13,190 --> 00:12:18,230
+صار عند ln الـ x اللي هو أكبر من x - 1 على الـ x
+
+131
+00:12:18,230 --> 00:12:21,550
+هي عند الـ inequality الثانية وهي عند الـ
+
+132
+00:12:21,550 --> 00:12:26,690
+inequality الأولى من التنتين إذا ln الـ x إيش ماله؟
+
+133
+00:12:26,690 --> 00:12:32,790
+أصغر من x - 1 مظبوط اللي بعمله وأكبر من x
+
+134
+00:12:32,790 --> 00:12:41,190
+- 1 عالميًا على x وهو المطلوب إيش السؤال اللي
+
+135
+00:12:41,190 --> 00:12:49,550
+بعده؟ الآن سؤال ثمانية let f من a لعند b
+
+136
+00:13:11,390 --> 00:13:17,630
+سؤال ثمانية let
+
+137
+00:13:17,630 --> 00:13:30,470
+f من a و b لعند r إيش ماله؟ continuous أو 
+
+138
+00:13:30,470 --> 00:13:37,190
+differentiable on
+
+139
+00:13:37,190 --> 00:13:45,370
+mean on open interval a و b show
+
+140
+00:13:45,370 --> 00:13:51,730
+that if limit f prime of x عندي limit f prime of x
+
+141
+00:13:51,730 --> 00:14:01,630
+لما x تروح للـ a بساوي a capital then اللي هي f
+
+142
+00:14:01,630 --> 00:14:11,990
+prime of a  F prime of A exists and equals A
+
+143
+00:14:11,990 --> 00:14:21,750
+solution أو proof ما أعطيني
+
+144
+00:14:21,750 --> 00:14:28,650
+F is differentiable على اللي هي الفترة من A وB أو
+
+145
+00:14:28,650 --> 00:14:33,350
+continuous طبعًا open أو continuous على closed من A
+
+146
+00:14:34,120 --> 00:14:39,860
+و عندي limit f prime of x معطينيها لما x تروح إلى
+
+147
+00:14:39,860 --> 00:14:50,180
+الـ a إيش بساوي؟ بساوي اللي هو a capital اطلع 
+
+148
+00:14:50,180 --> 00:14:58,560
+لفوق الآن عندي الآن الـ f prime of a تعريفها اللي هي
+
+149
+00:14:58,560 --> 00:15:04,600
+limit F of X ناقص F of A على X minus A لما X تروح
+
+150
+00:15:04,600 --> 00:15:09,940
+للـA ماشي الحال هذا اللي هو إذا كان الـ limit هذا
+
+151
+00:15:09,940 --> 00:15:13,500
+exist إذا أثبتنا إن الـ limit هذا exist بتكون الـ F 
+
+152
+00:15:13,500 --> 00:15:18,440
+prime of A أشمالها اللي هي exist ماشي الحال الآن
+
+153
+00:15:18,440 --> 00:15:21,200
+هو ما أعطيني limit F prime of X لما X تروح لـA
+
+154
+00:15:21,200 --> 00:15:28,290
+أشمالها هي الـ exist واضح أه؟ لأن بدي أطبق الـ Mean
+
+155
+00:15:28,290 --> 00:15:33,290
+Value Theorem لأن في البداية على أي X وين في
+
+156
+00:15:33,290 --> 00:15:39,170
+الفترة A وB في الفترة A وB لو أخدنا X في الـ A وB
+
+157
+00:15:39,170 --> 00:15:44,380
+بالـ Mean Value Theorem بين على الـ A والـ X على 
+
+158
+00:15:44,380 --> 00:15:47,920
+الفترة الـ A والـ X there exists CX ما لها
+
+159
+00:15:47,920 --> 00:15:52,340
+between X and A such that F of X ناقص F of A بساوي
+
+160
+00:15:52,340 --> 00:15:57,240
+F prime C of X في X minus A هذه اللي هي تطبيق الـ
+
+161
+00:15:57,240 --> 00:16:02,860
+Mean Value Theorem على الفترة A و B and so و منه
+
+162
+00:16:02,860 --> 00:16:07,700
+اللي هي بنقول F prime C of X بساوي اللي هو F of X
+
+163
+00:16:07,700 --> 00:16:15,920
+ناقص F of A على X minus A الآن عندي
+
+164
+00:16:15,920 --> 00:16:22,520
+.. خلّينا نيجي ناخد هذه المنطقة أه عشان لسه بدأت
+
+165
+00:16:22,520 --> 00:16:26,600
+بين F prime of A أشمالها موجودة بساوي limit الـ F
+
+166
+00:16:26,600 --> 00:16:31,180
+prime CX لما X تروح لمين؟ للـ A، ماشي الحال، هذه
+
+167
+00:16:31,180 --> 00:16:36,610
+الآن لو exist بتكون F prime of A أشمالها exist الآن
+
+168
+00:16:36,610 --> 00:16:40,510
+لاحظ احنا طبقنا اللي هي الـ mean value theorem على
+
+169
+00:16:40,510 --> 00:16:46,910
+مين؟ على الفترة من a لعند مين؟ لعند x لجينا الـ cx
+
+170
+00:16:46,910 --> 00:16:53,290
+وين موجودة؟ بين الـ a والـ x الآن لما cx تروح للـ a
+
+171
+00:16:53,290 --> 00:17:00,050
+أكيد الـ x هتروح لمين؟ للـ a ماشي الحال طيب الآن
+
+172
+00:17:00,050 --> 00:17:05,700
+بيصير عندي هو ما أعطيني أصلا limit f prime of x لما x 
+
+173
+00:17:05,700 --> 00:17:10,600
+تروح للـ a exist ماشي فبيصير عندي لأن limit f prime
+
+174
+00:17:11,520 --> 00:17:17,760
+of CX لما الـ X تروح للـ A هي نفسها as X goes to A
+
+175
+00:17:17,760 --> 00:17:21,700
+CX وين هتروح لما X تروح للـ A أتوماتيك CX هتروح للـ
+
+176
+00:17:21,700 --> 00:17:26,480
+A فبيصير عندي لقى limit F prime of CX لما X تروح للـ
+
+177
+00:17:26,480 --> 00:17:29,880
+A هو نفس limit F prime of CX لما A CX تروح للـ A
+
+178
+00:17:29,880 --> 00:17:34,580
+وهذا هو ما أعطيني إيش اسمه إن existence هو إيه، إذا
+
+179
+00:17:34,580 --> 00:17:39,500
+صار هذا الـ limit exist يعني هذا اللي هو اللي مساوي
+
+180
+00:17:39,500 --> 00:17:42,620
+للـ limit هذا اللي بنين عليه إذا حيكون الـ F prime
+
+181
+00:17:42,620 --> 00:17:46,920
+of A exist وبرضه حيساوي مين؟ حيساوي إيه؟ اطلع على
+
+182
+00:17:46,920 --> 00:17:53,100
+لدك اللي بالك نخلص نعم لا اطلع على اللي بعده أيوة
+
+183
+00:17:53,100 --> 00:17:55,420
+السؤال اللي بعده
+
+184
+00:18:06,430 --> 00:18:13,030
+كبر هذا السؤال اللي سألتني عنه يا محمد
+
+185
+00:18:13,030 --> 00:18:18,450
+قبل هيك اطلع لي .. خليه بس اطلع لي على الكتاب على
+
+186
+00:18:18,450 --> 00:18:28,770
+628 النظرية 628 انزل انزل 628 اطلع لي عليها النظرية
+
+187
+00:18:28,770 --> 00:18:36,630
+عشان نقول لك إيش هو السؤال عليه لأنه مهم نعرف عن إيش،
+
+188
+00:18:36,630 --> 00:18:40,410
+الآن إذا بتتذكروا أخذنا اللي هو الـ first
+
+189
+00:18:40,410 --> 00:18:45,390
+derivative test for extrema بتقول إذا كان لجينا
+
+190
+00:18:45,390 --> 00:18:47,870
+neighborhood Hannah subset من I such that F double
+
+191
+00:18:47,870 --> 00:18:51,950
+prime أكبر ساعة وسفر وX ال .. ال .. ال .. لو F 
+
+192
+00:18:51,950 --> 00:18:54,350
+double prime أكبر ساعة وسفر مرة ع اليمين ومرة ع
+
+193
+00:18:54,350 --> 00:18:59,350
+اليسار إذا F has إيش مالها relative إيش مالها
+
+194
+00:18:59,350 --> 00:19:05,280
+maximum اللي هو اللي بتغير شرطها من موجب إلى سالب
+
+195
+00:19:05,280 --> 00:19:09,260
+فبتكون عندي relative maximum، الآن هل العكس صحيح؟
+
+196
+00:19:09,260 --> 00:19:12,440
+يعني لو كان في عندنا relative maximum، هل شرط إنها
+
+197
+00:19:12,440 --> 00:19:17,950
+تغير إشارتها في اللي دا؟ اطلع لفوق شوية عشان أورجيك
+
+198
+00:19:17,950 --> 00:19:21,170
+السؤال وين كان موجود هان remark the converse of
+
+199
+00:19:21,170 --> 00:19:25,410
+the first derivative test is not true مهم الكلام
+
+200
+00:19:25,410 --> 00:19:28,610
+هذا for example there exists a differentiable
+
+201
+00:19:28,610 --> 00:19:31,610
+function f من R لـR with absolute minimum at x
+
+202
+00:19:31,610 --> 00:19:35,210
+بالساوية صفر but such that f prime takes on both
+
+203
+00:19:35,210 --> 00:19:39,110
+positive and negative values on both sides of اللي
+
+204
+00:19:39,110 --> 00:19:45,000
+هي x بتساوي عياش بساوي صفر ماشي الحال إذا هذا الآن
+
+205
+00:19:45,000 --> 00:19:49,920
+هذا الحديث هو سؤالنا اللي عندنا اللي بدنا نحكي فيه
+
+206
+00:19:49,920 --> 00:19:52,880
+اللي هو exercise قداش؟ تسعة ارجع لي على exercise
+
+207
+00:19:52,880 --> 00:19:56,560
+تسعة إذا الـ exercise تسعة هو عبارة عن إيش؟ بيقول ليه
+
+208
+00:19:56,560 --> 00:20:00,280
+إن الـ converts of this theorem need not to be true
+
+209
+00:20:00,280 --> 00:20:04,930
+in general بالظبط إيش بيقول؟ بيقول لـ F من R لـ R بي
+
+210
+00:20:04,930 --> 00:20:08,910
+define by F of X بيساوي 2 X plus 4 زائد X plus 4
+
+211
+00:20:08,910 --> 00:20:12,770
+Sine 1 على X For X لا تساوي صفر عند F of 0 إيش
+
+212
+00:20:12,770 --> 00:20:16,450
+بيساوي Zero إذا أنا معرفت دالة الـ F بهذه الطريقة
+
+213
+00:20:16,450 --> 00:20:20,450
+بهذه لما X لا تساوي صفر وعند X بيساوي صفر عرفها F 
+
+214
+00:20:20,450 --> 00:20:25,120
+of 0 بيساوي أيش؟ Zero بيقول لشهدات أول شيء F has an
+
+215
+00:20:25,120 --> 00:20:30,440
+absolute minimum when عند الـ 0 but that its
+
+216
+00:20:30,440 --> 00:20:34,820
+derivative has both positive and negative values
+
+217
+00:20:34,820 --> 00:20:40,280
+everywhere اللي هو إيش؟ في neighborhood حوالين مين؟
+
+218
+00:20:40,280 --> 00:20:49,380
+حوالين الصفر واضح طيب، نشوف الآن، عملية فيه
+
+219
+00:20:49,380 --> 00:20:54,280
+absolute minimum مش صعبة، اللي هي بس خلينا نتطلع
+
+220
+00:20:54,280 --> 00:20:58,140
+على الحسابات، لأن الحسابات بتاخد وجه، فخلينا نتطلع
+
+221
+00:20:58,140 --> 00:21:02,900
+على اللي عندنا محسوبة وخلاص لأن لأي x الـ ينتن ار
+
+222
+00:21:02,900 --> 00:21:07,360
+أكيد الـ x الاربعة إيه أشمالها أكبر أو يساوي صفر والـ
+
+223
+00:21:07,360 --> 00:21:11,900
+sign الواحد على x أكبر اكيد أكبر أو يساوي مين؟ ناقص
+
+224
+00:21:11,900 --> 00:21:16,300
+واحد اضرب الجهتين في x الاربعة فبيصير x الاربعة في
+
+225
+00:21:16,300 --> 00:21:20,680
+هذا أكبر أو يساوي ناقص إيش؟ x الاربعة أضيف للجهتين
+
+226
+00:21:20,680 --> 00:21:26,110
+اتنين x الاربعة فبيصير 2x أس 4 زائد هذا أكبر أو
+
+227
+00:21:26,110 --> 00:21:30,470
+يساوي اللي ضفت 2x أس 4 زائد اللي هو يا عاش ناقص اللي
+
+228
+00:21:30,470 --> 00:21:34,930
+هي x أس 4 اللي هو بيطلع قداش x أس 4 اللي هو أكيد
+
+229
+00:21:34,930 --> 00:21:39,270
+أكبر أو يساوي 0 صارت عند قيمة الـ function f of x
+
+230
+00:21:39,270 --> 00:21:44,770
+اللي احنا بنحكي عنها دائما أكبر أو يساوي 0 اللي هو
+
+231
+00:21:44,770 --> 00:21:49,650
+مين؟ بيساوي اللي عرفناه F0 إذا صار في عندي F has
+
+232
+00:21:49,650 --> 00:21:58,450
+absolute minimum at mean at zero لكن عندي لطبيعة
+
+233
+00:21:58,450 --> 00:22:02,590
+الـ sine وطبيعة الـ cosine لو جيت الآن أخدت أي
+
+234
+00:22:02,590 --> 00:22:06,990
+neighborhood حوالين ناقص delta وdelta بدي أثبت لك
+
+235
+00:22:06,990 --> 00:22:12,410
+إن F prime مرة ممكن تسوي لي أصغر من صفر ومرة تكون
+
+236
+00:22:12,410 --> 00:22:21,190
+أشمالها أكبر من صفر واضح؟ إذا تعال شوف عندي خد لأي
+
+237
+00:22:21,190 --> 00:22:25,370
+neighborhood حوالين اللي هو الـ Zero خده من ناقص
+
+238
+00:22:25,370 --> 00:22:29,850
+Delta وDelta لأي Delta في الدنيا أو لأي مثلون في
+
+239
+00:22:29,850 --> 00:22:34,450
+الدنيا عندي هي الـ neighborhood اللي بحكي فيه
+
+240
+00:22:40,490 --> 00:22:45,390
+النقطة الداخلية اللي احنا مستهدفين فيها اللي هي الصفر
+
+241
+00:22:45,390 --> 00:22:51,500
+خد أي neighbor حواليه ناقص دلتا أو دلتا تقدر تلاقي
+
+242
+00:22:51,500 --> 00:22:58,220
+n أكبر أو يساوي اتنين very large اللي
+
+243
+00:22:58,220 --> 00:23:04,540
+بيكون n أشمالها very close to zero ماشي يعني مهما
+
+244
+00:23:04,540 --> 00:23:09,300
+زغرت لي الـ delta براجيلك n كبيرة كفاية إنها تضلها
+
+245
+00:23:09,300 --> 00:23:18,320
+في هذا الجوار وتحقق ما يلي إيش أخذتها؟ أخدت النقطة
+
+246
+00:23:18,320 --> 00:23:22,460
+واحد على اتنين and by طبعا الآن هذا بزغرها جدًا ما
+
+247
+00:23:22,460 --> 00:23:28,120
+بده بتكبير الآن ونفس الشيء 2 على 4 n زائد واحد في
+
+248
+00:23:28,120 --> 00:23:30,780
+باقي طبعا ليش أخدت هيك؟ عشان واحدة تخلي لي الـ sign
+
+249
+00:23:30,780 --> 00:23:34,620
+صفر وواحدة تخلي لي الـ cosine إيه؟ عشان صفر واضح وفي
+
+250
+00:23:34,620 --> 00:23:37,580
+نفس الوجه بتخلي لي الـ sign واحد والـ cosine واحد
+
+251
+00:23:37,580 --> 00:23:44,380
+بشكل معاكس ده فنشوف الشيء اللي بقوله الآن هذه الآن وهذه
+
+252
+00:23:44,380 --> 00:23:47,380
+الآن اخترت الآن اللي تخليني إياها موجودة في
+
+253
+00:23:47,380 --> 00:23:51,060
+ناقص delta وdelta هذول النقطتين في وين؟ في الجوار
+
+254
+00:23:51,060 --> 00:23:56,880
+اللي أعطيتني إياه أي جوار بتعطيني يا بدأ جيلك الآن
+
+255
+00:23:56,880 --> 00:24:01,300
+المناسبة إليه احسب لي الآن F prime F prime of X
+
+256
+00:24:01,300 --> 00:24:04,040
+بتعرف .. نعرف نحسبها خلينا نحسب F prime of X على
+
+257
+00:24:04,040 --> 00:24:08,580
+جهتها لأنه مش هحسبها عشان تكون قدامكم F prime of X
+
+258
+00:24:10,740 --> 00:24:18,560
+أف برايم of x إيش بتساوي؟ تمانية x تكعيب زائد أربعة 
+
+259
+00:24:18,560 --> 00:24:28,300
+x تكعيب sign واحد على x ناقص اللي هو ليش
+
+260
+00:24:28,300 --> 00:24:34,800
+زائد ناقص x أصبح أربعة بيصير x تربيع sign واحد على
+
+261
+00:24:34,800 --> 00:24:41,650
+x صحيح؟ هذه اليومين f prime of x بدي الآن نعوض على 
+
+262
+00:24:41,650 --> 00:24:47,310
+f عند النقطة أول شيء النقطة الأولى عبارة عن واحد
+
+263
+00:24:47,310 --> 00:24:52,450
+على اتنين and by عوضنا عنها في تمانية x سكعيب هي 
+
+264
+00:24:52,450 --> 00:24:57,210
+ثمانية في x سكعيب زائد أربعة هي x سكعيب وهي sin
+
+265
+00:24:57,210 --> 00:25:01,820
+واحد على x بيصير sin اتنين and by عشان هيك الاختيار
+
+266
+00:25:01,820 --> 00:25:05,020
+زائد واحد على اتنين and by أس أربعة اللي هي ..
+
+267
+00:25:05,020 --> 00:25:11,580
+اللي هي .. بحها دي بيصير أس اتنين أه وهاي الناقص
+
+268
+00:25:11,580 --> 00:25:16,900
+فاهمين؟ x تربيع ها دي محادي اللي هي بيصير x تربيع
+
+269
+00:25:16,900 --> 00:25:23,800
+بالسالب واضح هه في cosine من اللي هو 2 unbi الآن
+
+270
+00:25:23,800 --> 00:25:27,580
+هذا المقدار اللي في النص كله إيش حباله؟ هيصير صفر
+
+271
+00:25:27,580 --> 00:25:32,160
+لأنه sin 2 unbi صفر هذا المقدار عبارة عن اللي هو
+
+272
+00:25:32,160 --> 00:25:34,860
+ثمانية بتروح مع ثمانية اللي هم يصير واحد على unbi
+
+273
+00:25:34,860 --> 00:25:39,880
+كل تكعيب هذا الـ cosine إيش بيساوي؟ واحد إذا بيظل من
+
+274
+00:25:39,880 --> 00:25:47,480
+عنده اللي هو هذا سالب تربيع إيه الآن ناخد 1 على
+
+275
+00:25:47,480 --> 00:25:52,120
+unbi عام المشترك تربيع بيظل عندي اللي هنا عبارة عن
+
+276
+00:25:52,120 --> 00:25:59,560
+اللي هي 4 unbi لأنه ماخد هنا اللي هي 1 على 2 unbi
+
+277
+00:25:59,560 --> 00:26:03,720
+لكل تربيع اللي هو عام المشترك بيظل 4 على unbi ناقص
+
+278
+00:26:03,720 --> 00:26:08,840
+إيه؟ اش واحد واضح الـ 4 على n by للـ n أكبر أو يساوي
+
+279
+00:26:08,840 --> 00:26:14,660
+2 إن هذا المقدار بيصير يصغر لدرجة أنه أصغر من
+
+280
+00:26:14,660 --> 00:26:18,320
+الواحد للـ n أكبر يساوي 2 إذا صار هذا المقدار عبارة 
+
+281
+00:26:18,320 --> 00:26:22,460
+عن سالب في موجة بيطلع أصغر من 0 إذا F برايم طلعت
+
+282
+00:26:22,460 --> 00:26:29,390
+أصغر من 0 في نفس الوقت أف برايم ل 2 على كذا على 4n 
+
+283
+00:26:29,390 --> 00:26:34,130
+زائد 1 في π  أضربها أحسبها بيصير تمانية وعوض وعوض
+
+284
+00:26:34,130 --> 00:26:38,150
+وعوض الآن مش ال sign اللي هتت cancel هتت cancel
+
+285
+00:26:38,150 --> 00:26:43,110
+مين ال cosine فهيطلع عندي هذا المقدار هي وهيه هذا
+
+286
+00:26:43,110 --> 00:26:48,390
+المقدارين، المقدارين موجبات، إذا هيكون أكبر من
+
+287
+00:26:48,390 --> 00:26:53,510
+مين؟ من صفر، إذا في كل المنطقة، في كل المنطقة،
+
+288
+00:26:53,510 --> 00:26:58,050
+هتلاقي اللي هو جانب بعض، جانب بعض، مرة أكبر من
+
+289
+00:26:58,050 --> 00:27:00,530
+صفر، مرة أصغر من صفر، مرة أكبر من صفر، مرة أصغر من
+
+290
+00:27:00,530 --> 00:27:05,070
+صفر، ففيش عندك اللي هو تغير إشارتها من موجب إلى 
+
+291
+00:27:05,070 --> 00:27:09,750
+سالب، لا، هم جانب بعض، هذول تنفج يا واحدة تنساش في
+
+292
+00:27:09,750 --> 00:27:14,570
+جهة واحدة من الـ neighborhood مش على الجهتين هو ال
+
+293
+00:27:14,570 --> 00:27:18,270
+test اللي بنعرفه أشمل بيقول لك لو اتغير من قبل ال ..
+
+294
+00:27:18,270 --> 00:27:21,690
+قبل .. في ال neighborhood قبل النقطة ال X note من
+
+295
+00:27:21,690 --> 00:27:26,990
+موجب إلى سالب بيصير maximum من سالب إلى موجب بيصير
+
+296
+00:27:26,990 --> 00:27:34,400
+موجب بيصير minimum الآن نحن لجينا relative minimum
+
+297
+00:27:34,400 --> 00:27:38,800
+أو absolute minimum لكن في النقاط من ناقص ذلت
+
+298
+00:27:38,800 --> 00:27:44,180
+العين دلت هاين اختارت لك هنا وهنا جان بعض وجرب
+
+299
+00:27:44,180 --> 00:27:48,650
+كمان بلا جيلك كمان اللي هو بحيث أن تكون موجبة و
+
+300
+00:27:48,650 --> 00:27:53,050
+سالبة وموجبة وسالبة يعني فش derivative هنا تكون
+
+301
+00:27:53,050 --> 00:27:57,690
+موجبة كلها وهنا سالبة كلها عشان تحكم max .. تقول
+
+302
+00:27:57,690 --> 00:28:01,190
+اللي هو .. اللي هي ال .. و .. و .. و فقط اللي هي
+
+303
+00:28:01,190 --> 00:28:04,750
+the converse in and the converse need not to 
+
+304
+00:28:04,750 --> 00:28:09,990
+be true in general واضح؟ في الجوارين
+
+305
+00:28:09,990 --> 00:28:14,830
+.. هذا .. هذا من هنا .. من هنا لعين دلها فش إشارة
+
+306
+00:28:14,830 --> 00:28:19,040
+واحدة ومن هنا لعين دلها فش إشارة واحدة إذا the
+
+307
+00:28:19,040 --> 00:28:22,320
+converse need not to be true in general واضح و
+
+308
+00:28:22,320 --> 00:28:30,400
+الله واضح وأعيد واضح يا محمد اه طيب اللي بعده
+
+309
+00:28:30,400 --> 00:28:34,120
+برضه في ال .. في ال .. في ال .. في المثال ارجع لي
+
+310
+00:28:34,120 --> 00:28:38,700
+للكتاب عشان أقول لك هذا برضه بخدمين السؤال قبلها
+
+311
+00:28:38,700 --> 00:28:42,160
+انزل اطلع قبل النظرية قبل النظرية قبل النظرية في
+
+312
+00:28:42,160 --> 00:28:45,520
+عندي مثال هيو أو لا .. ايوه ال remark ال remark
+
+313
+00:28:45,520 --> 00:28:52,760
+أيوه اطلع ال remark هذه الآن إذا بتتذكروا سؤال عشر
+
+314
+00:28:52,760 --> 00:28:55,260
+اللي بناحكيها الجد حكيها أن احنا قولنا it is
+
+315
+00:28:55,260 --> 00:28:59,420
+reasonable to define a function to be increasing
+
+316
+00:28:59,420 --> 00:29:04,170
+at a point إذا كانت هناك مقارنة للمقارنة في
+
+317
+00:29:04,170 --> 00:29:13,750
+المقارنة اللي حوالها، إذا 
+
+318
+00:29:13,750 --> 00:29:18,810
+كانت هناك مقارنة في المقارنة اللي حوالها، إذا كانت
+
+319
+00:29:18,810 --> 00:29:19,510
+هناك مقارنة في المقارنة اللي حوالها،
+
+320
+00:29:22,640 --> 00:29:27,460
+من الممكن أن يكون الـ derivative صحيح بشكل صحيح في
+
+321
+00:29:27,460 --> 00:29:35,840
+نقطة فالعمل يزيد في هذه النقطة ولكن هذا الوضع غير 
+
+322
+00:29:35,840 --> 00:29:40,960
+صحيح يعني هذا الكلام إيش ماله ليس شرط أن يكون صحيح أن
+
+323
+00:29:40,960 --> 00:29:44,500
+عندي اللي هنلاقي اللي هو الـ derivative صحيح بشكل
+
+324
+00:29:44,500 --> 00:29:49,220
+صحيح لكن مافيش .. ما نقدرش نقول عنها إيش مالها is
+
+325
+00:29:49,220 --> 00:29:53,460
+increasing at this point هذا في الـ Interval صحيح
+
+326
+00:29:53,460 --> 00:29:57,020
+لكن في الـ Point إيش ماله need not to be true in
+
+327
+00:29:57,020 --> 00:30:01,860
+general وهي مثال G of X هي اللي هو بحيث أن G'
+
+328
+00:30:02,240 --> 00:30:07,940
+للـ 0 بساوي 1 لكن الـ G is not increasing in any
+
+329
+00:30:07,940 --> 00:30:14,260
+neighbourhood حوالين مين الصفر، هذا مثال على G' of
+
+330
+00:30:14,260 --> 00:30:20,200
+0 بساوي 1 اللي هو strictly أكبر من 0 but اللي هو في
+
+331
+00:30:20,200 --> 00:30:24,940
+هذا ال .. عند هذه النقطة اللي هو في الجوار تبعها
+
+332
+00:30:24,940 --> 00:30:30,260
+لا يمكن أن تكون اللي هي increasing في أي جوار
+
+333
+00:30:30,260 --> 00:30:35,610
+حواليها هذا مثلنا يلّا خلّيني نحل السؤال الآن هاي
+
+334
+00:30:35,610 --> 00:30:40,090
+سؤالنا let g من R لR be defined by g of X بيساوي X
+
+335
+00:30:40,090 --> 00:30:44,410
+زي 2 X ثانوية صين واحدة ل X for X تتساوي صفر and g
+
+336
+00:30:44,410 --> 00:30:47,550
+of 0 بيساوي 0 show that g prime of 0 إيش بيساوي
+
+337
+00:30:47,550 --> 00:30:53,030
+واحد but in every neighborhood of zero, the
+
+338
+00:30:53,030 --> 00:30:57,430
+derivative g prime takes on both positive and
+
+339
+00:30:57,430 --> 00:31:01,710
+negative values. Thus, g is not monotonic in any
+
+340
+00:31:01,710 --> 00:31:05,830
+neighborhood. هنلاقي في المنطقة هذه، وين ما كان،
+
+341
+00:31:05,830 --> 00:31:13,210
+هنلاقي الـ g prime اللي هي أكبر من صفر وأصغر من صفر
+
+342
+00:31:13,210 --> 00:31:18,410
+يعني مش هنلاقي في أي neighborhood أن الـ G' أكبر
+
+343
+00:31:18,410 --> 00:31:25,410
+من صفر لحالها أو الـ G' للـ X هي أكبر من حالها أو
+
+344
+00:31:25,410 --> 00:31:33,910
+أصغر من حالها في كل .. من صفر في كل الجوار G' مش
+
+345
+00:31:33,910 --> 00:31:38,930
+هتكون أصغر من صفر في كل الجوار ولا أكبر من صفر في
+
+346
+00:31:38,930 --> 00:31:46,630
+كل الجوار هنلاقي إلها متذبذبة في الإشارة كيف؟
+
+347
+00:31:48,510 --> 00:31:54,930
+الحل شبهه صحيح الحل شبهه بس هذا الآن موظف لمين؟ لا
+
+348
+00:31:54,930 --> 00:31:58,990
+اللي هي اللي هو counter example على اللي هي ال
+
+349
+00:31:58,990 --> 00:32:02,630
+remark اللي عندنا وده counter example على اللي هي
+
+350
+00:32:02,630 --> 00:32:08,010
+النظرية هذك بوضح أن ال theorem need not to be true
+
+351
+00:32:08,010 --> 00:32:12,170
+in general وهنا اللي هو بوضح أنه اللي هو ال
+
+352
+00:32:12,170 --> 00:32:18,000
+strictly increasing عند نقطة لا .. لا .. لا .. لا
+
+353
+00:32:18,000 --> 00:32:18,380
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+354
+00:32:18,380 --> 00:32:18,540
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+355
+00:32:18,540 --> 00:32:19,120
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+356
+00:32:19,120 --> 00:32:19,800
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+357
+00:32:19,800 --> 00:32:26,540
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+358
+00:32:26,540 --> 00:32:29,660
+..
+
+359
+00:32:29,660 --> 00:32:31,300
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+360
+00:32:31,300 --> 00:32:32,100
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+361
+00:32:32,100 --> 00:32:39,020
+.. لا .. لا
+
+362
+00:32:39,020 --> 00:32:46,020
+.. لا إيش بعمل قاعد بدي أحاول أثبت أن g prime of 0
+
+363
+00:32:46,020 --> 00:32:51,600
+اللي هو بيساوي واحد هاي التعريف هاي عنده y ساوي
+
+364
+00:32:51,600 --> 00:32:55,180
+جسمنا عليه بيصير واحد زائد اثنين limit x sin واحد
+
+365
+00:32:55,180 --> 00:33:00,380
+على x اللي هو هذا ايه شماله؟ بساوي صفر لأن الـ
+
+366
+00:33:00,380 --> 00:33:03,720
+absolute value للـ X sin واحد على X أكبر بساوي صفر
+
+367
+00:33:03,720 --> 00:33:07,740
+وأصغر أو يساوي الـ absolute value للـ X اللي هو
+
+368
+00:33:07,740 --> 00:33:11,020
+by Sandwich theorem اللي هو ال limit هذا إيش بساوي
+
+369
+00:33:11,020 --> 00:33:15,040
+صفر إذا ال limit على بعض وكله إيش بساوي واحد إذا
+
+370
+00:33:15,040 --> 00:33:17,740
+D prime of zero بساوي واحد اطلع لفوق
+
+371
+00:33:20,460 --> 00:33:26,260
+عندي for x تتساوي 0 الـ g prime سهل أن أنا أجدها
+
+372
+00:33:26,260 --> 00:33:30,300
+عبارة عن واحد زائد تفاضل قاعد أربع x sin واحد على
+
+373
+00:33:30,300 --> 00:33:34,080
+x ناقص اثنين cosine واحد على x لأن بالظبط as above
+
+374
+00:33:34,080 --> 00:33:37,520
+for any neighborhood زي اللي حكينا قبل شوية for
+
+375
+00:33:37,520 --> 00:33:43,340
+any neighborhood ناقص دلتا ودلتا حول الصفر بقدر
+
+376
+00:33:43,340 --> 00:33:49,200
+ألاقي اد أكبر سواء واحد بحيث أن هذا وهذا يكون في
+
+377
+00:33:49,200 --> 00:33:54,160
+الجوار لكن جي برايم عند الأولى أصغر من صفر وجي
+
+378
+00:33:54,160 --> 00:33:58,480
+برايم عند الثانية شماله أكبر من صفر بحسابات
+
+379
+00:33:58,480 --> 00:34:01,580
+مشابهة أي سؤال؟
+
+380
+00:34:05,050 --> 00:34:09,570
+طيب نيجي لسؤال 12 سؤال 12 بيقول إذا كانت h of x
+
+381
+00:34:09,570 --> 00:34:13,590
+بيساوي 0 إذا كانت x أصغر من 0 و1 إذا كانت x أكبر
+
+382
+00:34:13,590 --> 00:34:16,650
+بيساوي 0 prove that there does not exist a
+
+383
+00:34:16,650 --> 00:34:21,310
+function f من R لR such that f prime of x شماله
+
+384
+00:34:21,310 --> 00:34:26,190
+بيساوي h of x هذا حلنا زيه برضه اللي هو درابوكس
+
+385
+00:34:26,190 --> 00:34:29,270
+theorem using إيش درابوكس theorem إيش بنقول
+
+386
+00:34:29,270 --> 00:34:37,360
+suppose not مظبوط طبق الآن هي عند H of X هيابقول
+
+387
+00:34:37,360 --> 00:34:42,920
+لأثبت أنه فيش ولا function F لو فضلناها بتطلع مين؟
+
+388
+00:34:42,920 --> 00:34:46,540
+H of X بدنا نفترض العكس، نفترض أنه في function
+
+389
+00:34:46,540 --> 00:34:51,260
+اسمها F بحيث أن F' إيش بتساوي H صارت H نفسها
+
+390
+00:34:51,260 --> 00:34:54,400
+differentiable، ماشي آسف، F إيش ما لا؟
+
+391
+00:34:54,400 --> 00:34:57,880
+differentiable، مظبوط؟ مدام F differentiable، إذا
+
+392
+00:34:57,880 --> 00:35:03,120
+by مين؟ By Daraboux's theorem اللي هو there exist و
+
+393
+00:35:03,120 --> 00:35:07,640
+طبعا وإحنا عارفين النص بين مين؟ بين الـ 0 والـ 1
+
+394
+00:35:07,640 --> 00:35:12,880
+إذا by Daraboux's theorem there exist اللي هو ..
+
+395
+00:35:12,880 --> 00:35:19,840
+اللي هي C بين الـ X1 و X2 بحيث أن G of C بسوء أفه
+
+396
+00:35:19,840 --> 00:35:24,940
+prime of C ويساوي نص which is impossible أسرعت
+
+397
+00:35:24,940 --> 00:35:32,940
+عليكم، مظبوط؟ الآن يا جماعة بدي أفترض أن العكس صحيح
+
+398
+00:35:32,940 --> 00:35:37,880
+يعني بدي أفترض أن F من R ل R بحيث أن F prime of X
+
+399
+00:35:37,880 --> 00:35:42,740
+إيش بتساوي؟ X لكل X element in R ماشي الحال اتفجن
+
+400
+00:35:42,740 --> 00:35:47,840
+الهن إذا F نفسها بناء على هذا الحديث F is
+
+401
+00:35:47,840 --> 00:35:52,340
+differentiable على R من جهة أخرى أخرى لاحظ إن النص
+
+402
+00:35:52,340 --> 00:35:55,160
+بين الـ 0 والـ 1، مين هو الـ 0 والـ 1؟ الـ 0 والـ
+
+403
+00:35:55,160 --> 00:35:58,060
+1 هي قيم الـ function هذه اللي بحكي عنها، يعني الـ
+
+404
+00:35:58,060 --> 00:36:03,840
+0 والـ 1 هتكون الـ 0 عبارة عن أشوف X1 والـ A1
+
+405
+00:36:03,840 --> 00:36:09,390
+أشوف X2، مين X1 و X2؟ اخترت الـ X1 أصغر من 0؟ و X2
+
+406
+00:36:09,390 --> 00:36:13,690
+أكبر من 0 صار عند نقطتين X1 و X2 واحد أصغر من 0
+
+407
+00:36:13,690 --> 00:36:18,030
+واحد أكبر من 0 يعني التمتين عاملين لفترة إذا صار
+
+408
+00:36:18,030 --> 00:36:24,870
+عند نص في الفترة بين 0 و 1 اللي هو عبارة عن بين H
+
+409
+00:36:24,870 --> 00:36:31,520
+of X1 و H of X2 لكن H of X1 و H of X2 من هم؟ F' of
+
+410
+00:36:31,520 --> 00:36:36,900
+X1 و F' of X2 إذا صارت اللي هي درابوكس theorem
+
+411
+00:36:36,900 --> 00:36:41,260
+محققة F is differentiable ونص تنتمي للفترة بيه
+
+412
+00:36:41,260 --> 00:36:47,340
+اللي هي F' of X1 و F' of X2 of X2 إذا حسب اللي هي
+
+413
+00:36:47,340 --> 00:36:51,340
+درابوكس theorem أي حاجة بينهم لازم يكون لها أصل
+
+414
+00:36:51,340 --> 00:36:57,190
+إذا there exists C بين الـ x1 والـ x2 بحيث أنه
+
+415
+00:36:57,190 --> 00:37:02,450
+اللي هو f prime للـ c هذه اللي اللي جاتها بين x1 و
+
+416
+00:37:02,450 --> 00:37:08,770
+x2 هي مين النص يعني زي بمسح كل القيم اللي بين f of
+
+417
+00:37:08,770 --> 00:37:13,080
+x1 و f of x2 مش هيك تدربت في تستيرون بتقول إذا صارت
+
+418
+00:37:13,080 --> 00:37:17,460
+عندي في c بين هذه وهذه بحيث أن f prime of c بساوي
+
+419
+00:37:17,460 --> 00:37:21,480
+نص يعني g of c بساوي نص طب هذا مستحيل لأن أصلا g
+
+420
+00:37:21,480 --> 00:37:25,100
+.. h طبعا هذا مش g .. h of c .. هذا مستحيل ليش 
+
+421
+00:37:25,100 --> 00:37:28,760
+مستحيل؟ لأن h أصلا ما تأخذ رقم ثاني، يا صفر يا
+
+422
+00:37:28,760 --> 00:37:32,020
+واحد إذا contradiction، مدام contradiction إذا 
+
+423
+00:37:32,020 --> 00:37:37,940
+there is no function f من R لR بحيث أن f prime of 
+
+424
+00:37:37,940 --> 00:37:41,080
+x يساوي f of x for every x
+
+425
+00:37:45,230 --> 00:38:01,830
+في ضياع سؤالين خلنا نمر عليهم هذا
+
+426
+00:38:01,830 --> 00:38:06,130
+حلنا زيها اللي هو let I be an interval and let F
+
+427
+00:38:06,130 --> 00:38:11,110
+من I لR be differentiable on I مفترضين أن F عبارة 
+
+428
+00:38:11,110 --> 00:38:16,000
+عن اللي هو differentiable function على an interval
+
+429
+00:38:16,000 --> 00:38:19,820
+I وقول لي show that إذا كانت F prime is positive
+
+430
+00:38:19,820 --> 00:38:25,000
+on I لو F prime أكبر من 0 على I هتكون الـ F  أشمالها
+
+431
+00:38:25,000 --> 00:38:29,800
+strictly increasing on I طبعا اللي هو على السريع
+
+432
+00:38:29,800 --> 00:38:34,940
+لنفترض F prime أكبر من 0 لكل X element on I ماشي
+
+433
+00:38:34,940 --> 00:38:41,240
+هو نفسه؟ خلاص اللي بده السؤال موجود في الشريحة اللي
+
+434
+00:38:41,240 --> 00:38:44,300
+هو الـ main value theorem  اتكل الله خليني أقوله
+
+435
+00:38:44,300 --> 00:38:50,490
+عنه الآن let I be an interval and let F من I لعند R
+
+436
+00:38:50,490 --> 00:38:55,050
+سواء الـ 14 بيه differentiable on I show that if
+
+437
+00:38:55,050 --> 00:38:59,210
+the derivative F' is never zero on I يعني إذا كانت
+
+438
+00:38:59,210 --> 00:39:04,230
+F' أكبر من صفر اللي هي تساوي صفر on I then either
+
+439
+00:39:04,230 --> 00:39:08,430
+F' أكبر من صفر for all X limited on I أو F' أصغر 
+
+440
+00:39:08,430 --> 00:39:13,480
+من صفر لكل X جمالهايعني بيقول لي إذا كانت الـ F
+
+441
+00:39:13,480 --> 00:39:17,760
+differentiable على ال interval I وكانت الـ F'
+
+442
+00:39:18,160 --> 00:39:23,240
+بتساويش 0 في هذه الحالة الـ F' يا هتكون كلها موجبة
+
+443
+00:39:23,240 --> 00:39:28,940
+على ال I يا كلها سالبة عالميا على ال I مدامت ما غيرتش
+
+444
+00:39:28,940 --> 00:39:32,760
+شرطها بالمرة يعني بمعنى آخر يعني مش هتغير شرطها
+
+445
+00:39:32,760 --> 00:39:38,260
+بالمرة مدامت الـ F' مش 0 على الفترة إذا إشارتها
+
+446
+00:39:38,260 --> 00:39:43,650
+واحدة يا F أكبر من 0، يا F أكبر من .. أصغر من 0،
+
+447
+00:39:43,650 --> 00:39:47,070
+هذا في ضوء أن F is differentiable، بدنا نفترض
+
+448
+00:39:47,070 --> 00:39:51,170
+العكس ونصل لـ contradiction، suppose on the contrary
+
+449
+00:39:51,170 --> 00:39:56,290
+نفترض أن F prime of X أكبر من 0 لنقاط ... لبعض
+
+450
+00:39:56,290 --> 00:40:00,390
+النقط في I، و F prime of X أكبر من .. أصغر من 0
+
+451
+00:40:00,390 --> 00:40:04,660
+لبعض النقاط في I، يعني مخلوطة و بدنا نصلّ لمين لـ
+
+452
+00:40:04,660 --> 00:40:08,640
+contradiction طيب then there exist a و b element
+
+453
+00:40:08,640 --> 00:40:12,220
+in I such that أف برايم of a أشمالها أكبر من صفر و
+
+454
+00:40:12,220 --> 00:40:15,520
+أف برايم b أصغر من صفر لإن أنا مفترض الآن افترضت
+
+455
+00:40:15,520 --> 00:40:18,200
+أنه في نقاط اللي هي أكبر من صفر عندها ال
+
+456
+00:40:18,200 --> 00:40:20,940
+derivative وفي نقاط أصغر من صفر عندها ال
+
+457
+00:40:20,940 --> 00:40:25,040
+derivative ماشي الحال إذا بنلاقي a و b بالحقق هذه
+
+458
+00:40:25,490 --> 00:40:28,710
+الآن أكيد مدام هذا أكبر من صفر وهذا أصغر من صفر،
+
+459
+00:40:28,710 --> 00:40:32,910
+إذا الصفر بين الـ F'A و الـ F'B لأنها واحدة موجبة
+
+460
+00:40:32,910 --> 00:40:36,850
+بواحدة مين، مدام الصفر بينهم، إذا حسب Darabowski's
+
+461
+00:40:36,850 --> 00:40:40,990
+theorem، هي بتمسح كل المنطقة اللي بين الصور، لازم 
+
+462
+00:40:40,990 --> 00:40:45,570
+كلها يكون اللي هي أصولها إذن by Daraboux's theorem
+
+463
+00:40:45,570 --> 00:40:49,430
+there exists c element in I such that f prime of c
+
+464
+00:40:49,430 --> 00:40:52,970
+يساوي صفر وهذا اللي هو بناقض الفرضية اللي احنا
+
+465
+00:40:52,970 --> 00:40:57,570
+فرضناها أن f prime لا تساوي صفر على كل ال I إذن f
+
+466
+00:40:57,570 --> 00:41:01,730
+prime لا تساوي صفر على كل ال I معناته و
+
+467
+00:41:01,730 --> 00:41:05,670
+differentiable طبعا معناته يا إما كلهن ال f prime 
+
+468
+00:41:05,670 --> 00:41:11,950
+موجبات يا إما كلهن إيه أشمالها سالبة يعني يا 
+
+469
+00:41:11,950 --> 00:41:15,710
+increasing strictly increasing يا strictly يا
+
+470
+00:41:15,710 --> 00:41:23,230
+أشمالها decreasing مافيش أي تغيير للرسم والشكل طيب
+
+471
+00:41:23,230 --> 00:41:28,820
+نيجي لآخر السؤال let I Be An Interval Prove That If
+
+472
+00:41:28,820 --> 00:41:32,980
+F Is Differentiable On I And The Derivative Of F'
+
+473
+00:41:33,300 --> 00:41:37,820
+Is Bounded On I، Then F Satisfies Lipschitz
+
+474
+00:41:37,820 --> 00:41:43,920
+Condition On I، ماشي الحل، بتقول لي، بتقول لي
+
+475
+00:41:43,920 --> 00:41:48,460
+السؤال ما يعني، Lipschitz Condition
+
+476
+00:41:53,580 --> 00:41:58,020
+خلينا نشوف إيش اللي بنقوله إذا كانت F
+
+477
+00:41:58,020 --> 00:42:10,320
+differentiable on I و F' bounded on I اثبت إن F 
+
+478
+00:42:10,320 --> 00:42:15,680
+satisfies Lipschitz conditions ماشي؟ إيش Lipschitz
+
+479
+00:42:15,680 --> 00:42:23,450
+condition؟ إنه there exists K أكبر من 0 such that F
+
+480
+00:42:23,450 --> 00:42:30,130
+of X ناقص F of Y أصغر أو يساوي لبس اليود فيها ل X 
+
+481
+00:42:30,130 --> 00:42:34,330
+minus Y في مين؟ في K اللي كنا نقول عنها على طول
+
+482
+00:42:34,330 --> 00:42:40,630
+هذي بتعطي إيش ما لها uniformly continuous لكل X و 
+
+483
+00:42:40,630 --> 00:42:44,190
+Y لكل X و Y في الفترة اللي بنحكي عنها اللي بشت
+
+484
+00:42:44,190 --> 00:42:48,790
+غل condition إيش ما لها متحققة إذا الـ Absolute هذا 
+
+485
+00:42:48,790 --> 00:42:54,670
+معناه اللي بش تسكندشه نيجي نحققها هذه نيجي نحقق
+
+486
+00:42:54,670 --> 00:42:55,710
+اللي هو 
+
+487
+00:42:58,230 --> 00:43:02,930
+الـ Lipschitz condition لت x و y element in I بيه 
+
+488
+00:43:02,930 --> 00:43:06,130
+such that x strictly أصغر من 100 من y
+
+489
+00:43:27,180 --> 00:43:30,960
+إذا منها ناخذ الـ absolute value للجهتين بتطلع عندي
+
+490
+00:43:30,960 --> 00:43:36,260
+اللي أماني واضح لكن F' is bounded مدام bounded F'
+
+491
+00:43:36,740 --> 00:43:41,940
+إذا there exist K بحيث أن F' of C أصغر يساوي K لكل C
+
+492
+00:43:41,940 --> 00:43:47,550
+إيه أشمالها من ضمن الـ C اللي فوقها لأن أف برايم is
+
+493
+00:43:47,550 --> 00:43:51,870
+bounded على كل ال I و هذه الـ K بتنفع لكل مين لكل
+
+494
+00:43:51,870 --> 00:43:54,570
+الـ C's اللي في ال I إذا صارت أف برايم في C أصغر أو
+
+495
+00:43:54,570 --> 00:43:58,270
+شويه K بنعود فوق بيصير أف of X ناقص أف of Y أصغر
+
+496
+00:43:58,270 --> 00:44:02,150
+أو شويه K في X minus Y و ال X و ال Y كانت نقش
+
+497
+00:44:02,150 --> 00:44:06,870
+مالهين arbitrary إذا صار هذه أصغر أو شويه K في X
+
+498
+00:44:06,870 --> 00:44:11,790
+minus Y ودخلت المتساوية لأن في حالة ال X بتساوي Y 
+
+499
+00:44:11,790 --> 00:44:21,600
+اللي هو it is trivial therefore I satisfy اللي هو
+
+500
+00:44:21,600 --> 00:44:25,820
+Lipschitz condition و الله يعطيكوا العافية 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cdc946744eeb59593d67eaa67d45147be4364383
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ.srt
@@ -0,0 +1,1499 @@
+1
+00:00:04,910 --> 00:00:09,510
+بسم الله الرحمن الرحيم هذه المحاضرة الخامسة في
+
+2
+00:00:09,510 --> 00:00:15,630
+مساق تحليل حقيقي 2 لطلبة كلية العلوم تخصص 
+
+3
+00:00:15,630 --> 00:00:22,110
+رياضيات في الجامعة الإسلامية بغزة المحاضرة
+
+4
+00:00:22,110 --> 00:00:26,550
+اليوم هي جزئين، الجزء الأول اللي هو عبارة عن 
+
+5
+00:00:26,550 --> 00:00:31,350
+Discussion لـ 6.1 اللي هو مناقشة لموضوع اللي هو
+
+6
+00:00:31,350 --> 00:00:37,410
+Derivative أو الاشتقاق. الجزء الثاني هنكمل اللي هو
+
+7
+00:00:37,410 --> 00:00:43,210
+الحديث عن 6.2 اللي هو الـ Mean Value Theorem أو
+
+8
+00:00:43,210 --> 00:00:47,730
+نظرية القيمة المتوسطة. هناخذ بعض التطبيقات لنبدأ 
+
+9
+00:00:47,730 --> 00:00:51,750
+الآن اللي هي بالأسئلة اللي احنا طلبناها منكم
+
+10
+00:00:51,750 --> 00:00:57,230
+تحلوها كواجب المرة الماضية أو التي قبلها وكانت 
+
+11
+00:00:57,230 --> 00:01:01,210
+الأسئلة هي عبارة عن السؤال الرابع والسؤال السابع
+
+12
+00:01:02,000 --> 00:01:07,420
+والسؤال التاسع والسؤال الثالث عشر. بالنسبة للسؤال
+
+13
+00:01:07,420 --> 00:01:13,600
+الثالث اللي هو عبارة عن اللي هي برهان نظرية 6.1.3 A
+
+14
+00:01:13,600 --> 00:01:19,200
+و B. وهذه البراهين براهين سهلة اللي كانت الـ F 
+
+15
+00:01:19,200 --> 00:01:22,960
+Differentiable، الـ F Differentiable والـ Alpha
+
+16
+00:01:22,960 --> 00:01:26,560
+عبارة عن Constant بيعطينا الـ Alpha F برضه is
+
+17
+00:01:26,560 --> 00:01:30,200
+Differentiable. ولو كانت الـ F والـ G
+
+18
+00:01:30,200 --> 00:01:32,700
+Differentiable بيعطينا الـ F زائد G is
+
+19
+00:01:32,700 --> 00:01:35,660
+Differentiable. واحنا برهننا حالة الضرب وحالة
+
+20
+00:01:35,660 --> 00:01:41,500
+القسمة، وهدول حالات تعتبر سهلة مباشرة على التعريف
+
+21
+00:01:41,500 --> 00:01:45,900
+لذلك هنبدأ إن شاء الله في الحديث أو في حل الأسئلة 
+
+22
+00:01:45,900 --> 00:01:52,540
+على السؤال الرابع اللي هو بقول لي عندي معطيني F
+
+23
+00:01:52,540 --> 00:02:01,760
+من R لـ R بي defined by F of X بساوي اللي هو X
+
+24
+00:02:01,760 --> 00:02:06,420
+تربيع إذا كانت X Rational وبساوي صفر إذا كانت X 
+
+25
+00:02:06,420 --> 00:02:09,700
+Irrational. اثبت إن الـ F الـ Differential بالقدر X
+
+26
+00:02:09,700 --> 00:02:15,550
+بتساوي صفر أو جد اللي هي F prime of 0. لاحظ أن الـ
+
+27
+00:02:15,550 --> 00:02:16,610
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+28
+00:02:16,610 --> 00:02:17,090
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+29
+00:02:17,090 --> 00:02:17,910
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+30
+00:02:17,910 --> 00:02:20,450
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+31
+00:02:20,450 --> 00:02:27,990
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+32
+00:02:27,990 --> 00:02:28,350
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+33
+00:02:28,350 --> 00:02:29,630
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+34
+00:02:29,630 --> 00:02:29,690
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+35
+00:02:29,690 --> 00:02:41,470
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+36
+00:02:41,470 --> 00:02:52,150
+Find this value. a proof الآن عشان نوجد
+
+37
+00:02:52,150 --> 00:02:56,730
+اللي هي نثبت أن F prime of 0 موجودة. خلّيني ألاحظ 
+
+38
+00:02:56,730 --> 00:03:00,950
+مالي عند الـ function اللي هي X تربيع لما X
+
+39
+00:03:00,950 --> 00:03:07,150
+Rational و Zero لما X is Irrational. الآن بدنا
+
+40
+00:03:07,150 --> 00:03:11,770
+نتوقع أول شيء اللي هو لأنه هتلزمني جاي اللي بعدين
+
+41
+00:03:11,770 --> 00:03:15,890
+Find this value. بدنا نتوقع ايش قيمة اللي هو الـ
+
+42
+00:03:15,890 --> 00:03:20,950
+Derivative عند الصفر. لاحظ أنه اللي هو .. اللي ..
+
+43
+00:03:20,950 --> 00:03:25,630
+اللي لو بدنا نقول إنه الـ Derivative ممكن تكون Zero
+
+44
+00:03:25,630 --> 00:03:30,510
+كون إن F of X صفر. أو لو بدها تكون والـ 
+
+45
+00:03:30,510 --> 00:03:36,560
+Derivative هنا لو قلنا رفلا 2X بدو يكون اللي هو لو
+
+46
+00:03:36,560 --> 00:03:40,820
+بدو يكون اللي عند الـ Zero اللي هي F prime بدو في
+
+47
+00:03:40,820 --> 00:03:47,220
+النهاية تروح لـ اللي هيكون برضه قريبة من إنه نقول
+
+48
+00:03:47,220 --> 00:03:52,580
+أو نأكد إنها صفر عشان هي كالظن الغالب إن F prime
+
+49
+00:03:52,580 --> 00:03:58,660
+هتكون ايش؟ صفر. هذه مجرد تفكيرات. الآن بدي أثبت لك إنه
+
+50
+00:03:58,660 --> 00:04:03,080
+فعلًا هي الـ Derivative بتساوي 0. كيف بدي أثبتها؟
+
+51
+00:04:03,080 --> 00:04:11,280
+بدي أثبت لك إنه الـ Limit لـ F of X نقص F of 0 على
+
+52
+00:04:11,280 --> 00:04:17,600
+X minus 0 لما X تروح لـ 0 بتساوي 0. بدي أثبت لك 
+
+53
+00:04:17,600 --> 00:04:24,240
+هيها. الآن واضح إن X تقول إلى الصفر. X تقول إلى الصفر
+
+54
+00:04:24,240 --> 00:04:29,200
+هتمر بالـ Rational والـ Irrational عشان هيك صعب إن أنا
+
+55
+00:04:29,200 --> 00:04:32,600
+أتحدث عن اللي هو إيجاد الـ Derivative مباشرة من 
+
+56
+00:04:32,600 --> 00:04:36,130
+الآن أو من الـ Two Branches اللي عندي. لا بقدر أخد من
+
+57
+00:04:36,130 --> 00:04:40,030
+اليمين ولا أخد من اليسار لإنه عندي من اليمين أو من 
+
+58
+00:04:40,030 --> 00:04:44,130
+اليسار هيكون عندي اللي هو قابلنا اللي هي الأعداد الـ
+
+59
+00:04:44,130 --> 00:04:48,110
+Rational للـ Rational. فعشانك أسلم شيء إنه نستخدم
+
+60
+00:04:48,110 --> 00:04:52,650
+التعريف في إثبات هذا. يعني الآن بدي أثبت هذا الكلام
+
+61
+00:04:53,270 --> 00:04:58,090
+كيف بدي أثبته؟ بدي أثبت ما يعني بدي أصل لكل إبسلون 
+
+62
+00:04:58,090 --> 00:05:03,190
+أكبر من 0 بدلاج دلتا أكبر من 0. بدلاجية حاجيلك دلتا
+
+63
+00:05:03,190 --> 00:05:08,350
+بحيث أنه لما يكون الـ Absolute Value لـ F of X ناقص
+
+64
+00:05:08,350 --> 00:05:14,630
+F of Zero على X minus Zero يكون ناقص Zero طبعا
+
+65
+00:05:14,630 --> 00:05:19,790
+Zero هذي أصغر من إبسلون. هذا متى؟ Whenever
+
+66
+00:05:22,670 --> 00:05:28,470
+x-0 أكبر من 0 وأصغر من مين؟ من دلتا. هذا اللي بده 
+
+67
+00:05:28,470 --> 00:05:33,150
+أثبته أو هذا اللي بده أثبته. خلّينا نشوف إذا خلّينا
+
+68
+00:05:33,150 --> 00:05:36,530
+نشوف كيف بدنا نوجده عشان أثبت إن الـ Limit هذا
+
+69
+00:05:36,530 --> 00:05:43,110
+بساوي 0. لاحظ القيمة اللي عندي أول شيء الـ Absolute
+
+70
+00:05:43,110 --> 00:05:50,530
+Value of F of X ناقص F of 0 على X-0 ايش هتساوي؟
+
+71
+00:05:51,590 --> 00:05:57,390
+هتساوي اللي هو الـ Absolute Value of F of X عندي يا X
+
+72
+00:05:57,390 --> 00:06:01,070
+تربيع يمين يا صفر. خلّينها زي ما هي أول شيء. F of X
+
+73
+00:06:01,070 --> 00:06:06,010
+ناقص F of Zero اللي هو جداش بيساوي Zero لإنه F 
+
+74
+00:06:06,010 --> 00:06:10,130
+of Zero بيساوي Zero لإنه Zero Rational. على إذن هذا
+
+75
+00:06:10,130 --> 00:06:16,230
+صفر على X ناقص صفر اللي هو X. Absolute Value هذا 
+
+76
+00:06:16,230 --> 00:06:22,790
+القيمة الآن لاحظ بتساوي يا إما اللي هو X تربيع على
+
+77
+00:06:22,790 --> 00:06:30,750
+X Absolute Value في حالة X is Rational أو بتساوي
+
+78
+00:06:30,750 --> 00:06:37,450
+اللي هو صفر في حالة X شمالها is Irrational. لأن 
+
+79
+00:06:37,450 --> 00:06:42,030
+قيم F of X يا X تربيع يا صفر حسب اللي هو كتبناه
+
+80
+00:06:42,030 --> 00:06:46,790
+حاليًا. الآن هذا بالظبط هو عبارة عن الـ Absolute 
+
+81
+00:06:46,790 --> 00:06:57,590
+Value لل X if X is Rational Zero if X is
+
+82
+00:06:57,590 --> 00:07:03,950
+Irrational. الآن الصورة وضحت. خلّينا نسمي هذا اللي
+
+83
+00:07:03,950 --> 00:07:09,900
+هو واحد. الآن حضرت عشان أصل للنهاية اللي أنا كاتبها
+
+84
+00:07:09,900 --> 00:07:13,800
+هنا واشوف ايش الـ Delta اللي بتطلع عندي. الآن بتدعي
+
+85
+00:07:13,800 --> 00:07:17,380
+مالي For every Epsilon أكبر من صفر أنا بقول There
+
+86
+00:07:17,380 --> 00:07:21,800
+exists Delta هتساوي من الـ Epsilon. هتجد تشوفوا ليش 
+
+87
+00:07:21,800 --> 00:07:26,980
+There exists Delta بساوي Epsilon Such that if X
+
+88
+00:07:26,980 --> 00:07:35,210
+minus 0 أكبر من صفر وأصغر من Delta Then هذا معناته
+
+89
+00:07:35,210 --> 00:07:37,870
+ايش؟ إن إبسل يوت فيها الـ X أكبر من صفر وأصغر من 
+
+90
+00:07:37,870 --> 00:07:41,870
+مين؟ من دلتا. إذا اخترت دلتا ايش بتساوي وهي اللي 
+
+91
+00:07:41,870 --> 00:07:47,850
+هتخلص من الموضوع Then اللي هو F of X نقص F of Zero
+
+92
+00:07:47,850 --> 00:07:50,970
+على 
+
+93
+00:07:50,970 --> 00:07:57,790
+X minus Zero هو طبعًا نقص الصفر اللي قلنا عنها الـ
+
+94
+00:07:57,790 --> 00:08:01,520
+Derivative المتوقع عليا هذه بالظبط اللي فوق هذا هو
+
+95
+00:08:01,520 --> 00:08:05,920
+اللي فوق طلع ايش عندي؟ هذا بساوي هذا المقدار إذا 
+
+96
+00:08:05,920 --> 00:08:09,760
+كانت X Rational و 0 إذا كانت X Irrational يعني
+
+97
+00:08:09,760 --> 00:08:15,400
+بمعنى آخر بساوي Absolute Value لـ X if X is
+
+98
+00:08:15,400 --> 00:08:23,530
+Rational و 0 if X is Irrational. In both cases اللي 
+
+99
+00:08:23,530 --> 00:08:27,590
+هي إذا كان بساوي Absolute Value للـ X هيكون أصغر 
+
+100
+00:08:27,590 --> 00:08:31,250
+من Delta اللي أنا اخترتها شمالها Epsilon هيكون 
+
+101
+00:08:31,250 --> 00:08:34,570
+أصغر من Epsilon. وأيضا هذه متحققة لإن الـ Epsilon 
+
+102
+00:08:34,570 --> 00:08:38,850
+دائما شمالها أكبر من 0. إذا اللي حصلته إنه لكل
+
+103
+00:08:38,850 --> 00:08:42,490
+Epsilon أكبر من 0 اللي جيت Delta لما يكون هذا أصغر
+
+104
+00:08:42,490 --> 00:08:47,130
+من Delta بيعطيني هذا أصغر من Epsilon. وهذا يعني 
+
+105
+00:08:47,130 --> 00:08:54,370
+Hence Limit هذا المقدار اللي هو F of X ناقص F of 0 
+
+106
+00:08:54,370 --> 00:09:01,690
+على X minus 0 لما X تروح للصفر بساوية اللي هو
+
+107
+00:09:01,690 --> 00:09:12,870
+الصفر. وهذا هو تعريف من الـ F prime عند 0 That is F
+
+108
+00:09:12,870 --> 00:09:18,740
+prime at 0 بساوية 0. وفي نفس الواجب طبعًا أثبتنا الـ
+
+109
+00:09:18,740 --> 00:09:25,960
+Existence للـ F prime عند الـ Zero. أي سؤال؟ طيب
+
+110
+00:09:25,960 --> 00:09:30,840
+نيجي الآن نشوف السؤال الثاني. خلينا نقول السؤال الرابع
+
+111
+00:09:30,840 --> 00:09:44,220
+نيجي لسؤال 7 الآن.
+
+112
+00:09:44,220 --> 00:09:48,100
+سؤال 7 ايش اللي بيقوله؟ سؤال 7 اللي بيقوله سؤال 
+
+113
+00:09:48,100 --> 00:09:52,420
+7 مالي عندي
+
+114
+00:09:52,420 --> 00:09:55,740
+Suppose
+
+115
+00:09:55,740 --> 00:09:59,320
+that F من R لـ R is Differentiable at C. يعني نفترض
+
+116
+00:09:59,320 --> 00:10:04,520
+أنه F قابل للاشتقاق عند C. ونفترض إن F of C قيمة الـ
+
+117
+00:10:04,520 --> 00:10:07,920
+Function عند C بساوية 0. لأن بقول لشهدات الـ Absolute 
+
+118
+00:10:07,920 --> 00:10:10,960
+Value لل F of X اللي هي نسميها G of X is 
+
+119
+00:10:10,960 --> 00:10:14,080
+Differentiable at C If and only if F
+
+120
+00:10:14,080 --> 00:10:21,740
+prime of C بتساوي 0. إذا ناخد لك F من R لعند R و
+
+121
+00:10:21,740 --> 00:10:30,810
+جايلك إن F prime عند C Exist معطيك إياها أو ومعطيك
+
+122
+00:10:30,810 --> 00:10:37,390
+اللي هو F of C بتساوي صفر وبقول لي Prove that أنه
+
+123
+00:10:37,390 --> 00:10:42,370
+G of X بساوي الـ Absolute Value للـ F of X is 
+
+124
+00:10:42,370 --> 00:10:49,810
+Differentiable at C If and only if F prime عند الـ 
+
+125
+00:10:49,810 --> 00:10:57,880
+C ايش بتساوي؟ بتساوي صفر، مظبوط؟ طيب شوف. الآن خلينا
+
+126
+00:10:57,880 --> 00:11:03,380
+افترض أول شيء إن F prime عند C ايش بتساوي؟ صفر. نقول
+
+127
+00:11:03,380 --> 00:11:09,320
+Suppose proof. Suppose
+
+128
+00:11:09,320 --> 00:11:15,580
+Suppose 
+
+129
+00:11:15,580 --> 00:11:23,120
+that F prime at C بتساوي صفر. ايش هذا بيعني؟ إن Then
+
+130
+00:11:23,120 --> 00:11:25,940
+Limit
+
+131
+00:11:27,220 --> 00:11:36,680
+F of X ناقص F of C على X minus C لما X تروح للـ C
+
+132
+00:11:36,680 --> 00:11:40,240
+اللي هو بيساوي صفر لأن هذا تعريف مين؟ F براين
+
+133
+00:11:40,240 --> 00:11:46,000
+بيساوى صفر. و F of C ايش معطيني إياه؟ بيساوي صفر لأن
+
+134
+00:11:46,000 --> 00:11:53,260
+بيساوى Limit F of X على X minus C لما X تروح لمين؟ 
+
+135
+00:11:53,260 --> 00:11:58,730
+للـ C. مدامة الـ Limit هذه موجودة إذا الـ Limit من 
+
+136
+00:11:58,730 --> 00:12:02,270
+اليمين والـ Limit من اليسار أيش برضه مالها؟ موجودة
+
+137
+00:12:02,270 --> 00:12:06,710
+ماشي الحال. أنا الآن غرضي إن أو أثبت إن G of X بسبب
+
+138
+00:12:06,710 --> 00:12:09,190
+Absolute Value of F of X أيش مالها؟ Is
+
+139
+00:12:09,190 --> 00:12:14,110
+Differentiable at C. ماشي. الآن ايش اللي بدي أثبته
+
+140
+00:12:14,110 --> 00:12:22,370
+بمعنى آخر بدي أثبت لك إنه Limit الـ G of X ناقص G of C 
+
+141
+00:12:22,370 --> 00:12:29,430
+C على الـ X ناقص C لما الـ X تروح للـ C exist بشيء إذا
+
+142
+00:12:29,430 --> 00:12:31,930
+أثبتوا معناته أثبتتوا إن الـ G is differentiable
+
+143
+00:12:31,930 --> 00:12:36,970
+at C أو بمعنى آخر بالدثبت limit للـ absolute value 
+
+144
+00:12:36,970 --> 00:12:42,660
+للـ F of X ناقص الـ g of x ناقص الـ absolute value of f
+
+145
+00:12:42,660 --> 00:12:48,960
+of c على الـ X ناقص C لما الـ X بتروح للـ C exist بدي أشوف
+
+146
+00:12:48,960 --> 00:12:53,240
+هدا لسه exist ولا لأ يعني بدي أثبت اللي هو limit
+
+147
+00:12:53,240 --> 00:12:58,900
+absolute value of f of x على الـ X ناقص C as X بتروح
+
+148
+00:12:58,900 --> 00:13:07,520
+للـ C أشماله exist ماشي الحال طيب الآن واضح
+
+149
+00:13:08,360 --> 00:13:13,000
+عندي من اللي فوق الـ limit للـ F of X على الـ X ناقص C
+
+150
+00:13:13,000 --> 00:13:19,160
+as X بتروح للـ C إنه إيش بيساوي بيساوي صفر، مظبوط؟
+
+151
+00:13:19,160 --> 00:13:27,160
+إذا هيكون عندي limit اللي هو limit absolute value
+
+152
+00:13:27,160 --> 00:13:33,400
+للـ limit خليني أكتبها بس في طريقة أخرى الصفر هذا
+
+153
+00:13:33,400 --> 00:13:43,200
+اللي بدأتبته اه إنه exist عندي الـ absolute value ل
+
+154
+00:13:43,200 --> 00:13:52,020
+limit f of x على الـ X ناقص C لما الـ X تروح للـ C اللي هو
+
+155
+00:13:52,020 --> 00:13:58,020
+من اليمين ومن اليسار exist، مظبوط؟ واضحة ويساوي
+
+156
+00:13:58,020 --> 00:14:05,160
+اللي هو limit absolute value للـ F of X على الـ X ناقص
+
+157
+00:14:05,160 --> 00:14:12,420
+C as X بتروح لمين؟ للـ C بشيء
+
+158
+00:14:12,420 --> 00:14:16,820
+الحال الآن من اليمين ومن اليسار كله هيكون موجود
+
+159
+00:14:16,820 --> 00:14:20,480
+بناء على هذا إنه موجود خلّيني أخد من اليمين وهنا
+
+160
+00:14:20,480 --> 00:14:25,860
+من اليمين فبصير هذا عبارة عن limit absolute value
+
+161
+00:14:25,860 --> 00:14:32,140
+لـ F of X على الـ X ناقص C لما الـ X بتروح لـ C من وين؟ من
+
+162
+00:14:32,140 --> 00:14:38,330
+اليمين يعني هذا المقدارصار موجود وإيش بيساوي بيساوي
+
+163
+00:14:38,330 --> 00:14:42,350
+صفر هذا خلّيه لإنه هذا اللي بدنا نصلّه لأن limit
+
+164
+00:14:42,350 --> 00:14:47,310
+صار عندي معنى آخر limit absolute value of f of x
+
+165
+00:14:47,310 --> 00:14:53,850
+على الـ X ناقص C لما الـ X تروح للـ C من اليمين بيساوي صفر
+
+166
+00:14:53,850 --> 00:14:58,360
+existلاحظوا قاعد رايح لأثبت أن هذا exist ده خد الآن
+
+167
+00:14:58,360 --> 00:15:03,520
+من وين؟ من اليسار خد لأن أحسب similarly عندي صفر
+
+168
+00:15:03,520 --> 00:15:08,840
+بيساوي absolute value of limit f of x على الـ X ناقص C
+
+169
+00:15:08,840 --> 00:15:15,100
+لما الـ X تروح لـ C من وين؟ من اليسار ويساوي عبارة عن
+
+170
+00:15:15,100 --> 00:15:19,960
+limit absolute value of f of x على absolute value
+
+171
+00:15:19,960 --> 00:15:25,900
+of X ناقص C لما الـ X تروح لـ C من وين؟ من اليسار هذه
+
+172
+00:15:25,900 --> 00:15:34,580
+نفسها بيساوي limit أو بيساوي سالب limit f of x
+
+173
+00:15:34,580 --> 00:15:42,270
+absolute value على الـ X ناقص C لما الـ X تروح للـ C من
+
+174
+00:15:42,270 --> 00:15:47,030
+اليسار، ليش؟ لأن X أصغر من C، إذا X ناقص C سالبة
+
+175
+00:15:47,030 --> 00:15:50,230
+إذا الـ absolute value سالب إليها واخدت السالب برا
+
+176
+00:15:50,230 --> 00:15:54,990
+هذا الآن المخضر بيساوي صفر، إذا هذا لحاله برضه إيش
+
+177
+00:15:54,990 --> 00:16:01,270
+ماله؟ صفر، إذا limit absolute value للـ F of X على
+
+178
+00:16:01,270 --> 00:16:04,870
+X ناقص C، لما X تروح للـ C من اليسار، برضه إيش
+
+179
+00:16:04,870 --> 00:16:10,450
+بيساوي؟ بيساوي صفر، لاحظ إن الـ limit من اليمين والـ
+
+180
+00:16:10,450 --> 00:16:15,890
+limit من اليسار موجود وبساوي 0 متساويين يعني الآن
+
+181
+00:16:15,890 --> 00:16:23,130
+الـ limit هذا صار إيش بيساوي بيساوي 0 إذا الآن هذا
+
+182
+00:16:23,130 --> 00:16:29,870
+الآن بنقوله كله تحت هذا وبقول hence اللي هو الـ G
+
+183
+00:16:29,870 --> 00:16:38,310
+prime of C بيساوي limit of g of x نقص g of c على الـ X
+
+184
+00:16:38,310 --> 00:16:46,870
+ناقص C as X → C بيساوي حسب اللي عندي من هنا ومن
+
+185
+00:16:46,870 --> 00:16:55,310
+هنا ومن هنا هيساوي صفر الآن conversely بتفترض
+
+186
+00:16:55,310 --> 00:16:58,090
+طبعاً إن الـ conversely هيكون الخطوات كثير مشابهة
+
+187
+00:16:58,090 --> 00:17:03,350
+للي هنا يعني كثير اللي استخدمته هنا هستخدمه في
+
+188
+00:17:03,350 --> 00:17:03,930
+اللي بعدها
+
+189
+00:17:12,670 --> 00:17:17,790
+Conversely suppose that
+
+190
+00:17:17,790 --> 00:17:25,890
+g of x سواء absolute value أو f of x اللي
+
+191
+00:17:25,890 --> 00:17:33,550
+هو is differentiable at C بدا وجدلك الآن أثبتلك إن
+
+192
+00:17:33,550 --> 00:17:39,650
+f prime of C إيش ما لها بتساوي صفر يعني بدا أثبت
+
+193
+00:17:39,650 --> 00:17:46,880
+limit f of x ناقص f of C اللي هي صفر على الـ X ناقص C
+
+194
+00:17:46,880 --> 00:17:51,160
+لما الـ X تروح للـ C إيش بيساوي بيساوي صفر بكون خلصت
+
+195
+00:17:51,160 --> 00:17:58,500
+الآن issue مشابه عند الآن limit
+
+196
+00:17:58,500 --> 00:18:05,180
+هذا exist عند الـ C إذا عندي صار الـ g prime of C exist
+
+197
+00:18:05,180 --> 00:18:10,430
+ويساوي حسب الحديث اللي هنا limit absolute value of
+
+198
+00:18:10,430 --> 00:18:18,570
+f of x ناقص الـ absolute value of f of C صفر على الـ X
+
+199
+00:18:18,570 --> 00:18:26,310
+ناقص C لما الـ X تروح لـ C أشماله exist معيّ؟ طيب شوف
+
+200
+00:18:26,310 --> 00:18:34,960
+الآن عندي إذا احسب لي limit f of x اللي حسبناها قبل
+
+201
+00:18:34,960 --> 00:18:39,660
+بشوية بنفس الأسلوب على الـ X ناقص C لما الـ X تروح لـ C من
+
+202
+00:18:39,660 --> 00:18:47,020
+وين؟ من اليمين بيساوي limit للـ absolute value لـ f
+
+203
+00:18:47,020 --> 00:18:53,780
+of x على الـ X ناقص C لما الـ X تروح لـ C من اليمين لأن الـ
+
+204
+00:18:53,780 --> 00:19:01,840
+X أكبر من الـ C واضحة الآن من جهة أخرى احسب لي الـ
+
+205
+00:19:01,840 --> 00:19:08,060
+absolute value للـ limit للـ F of X طبعاً هذا إيش
+
+206
+00:19:08,060 --> 00:19:15,620
+هيساوي بيساوي g prime of C، مظبوط؟ بيساوي g prime of
+
+207
+00:19:15,620 --> 00:19:23,290
+C، موجود، limit f of x على الـ X ناقص C لما الـ X تروح لـ C
+
+208
+00:19:23,290 --> 00:19:28,570
+من وين؟ من اليسار بيساوي زي ما عملنا قبل شوية سالب
+
+209
+00:19:28,570 --> 00:19:33,530
+limit absolute value of f of x على الـ X ناقص C لما الـ X
+
+210
+00:19:33,530 --> 00:19:41,050
+تروح لـ C من وين؟ من اليسار الآن واضح بما أن هذه
+
+211
+00:19:41,050 --> 00:19:51,470
+exist إذا هذا المقدار وهذا المقدار زي بعض الآن هذا
+
+212
+00:19:51,470 --> 00:19:56,590
+بيساوي ناقص هذا أو بمعنى آخر نشيل الناقص من هنا ون
+
+213
+00:19:56,590 --> 00:20:03,390
+ضربه هنا صار عندي المقدرين هدولة بما إنه متساويين
+
+214
+00:20:03,390 --> 00:20:10,310
+لإن الاتنين إيش بيساوين الـ g prime of C مظبوط إذا
+
+215
+00:20:10,310 --> 00:20:13,390
+صار عندي هذا المقدار بيساوي هذا المقدار إذا صار
+
+216
+00:20:13,390 --> 00:20:20,940
+عندي الـ limit f of x على الـ X ناقص C لما الـ X تروح للـ C
+
+217
+00:20:20,940 --> 00:20:29,560
+من اليمين absolute value بيساوي ناقص limit f of x
+
+218
+00:20:29,560 --> 00:20:34,600
+على الـ X ناقص C لما الـ X تروح للـ C من وين؟ من اليسار
+
+219
+00:20:34,600 --> 00:20:41,500
+واضحة؟ لكن أصلاً عندي هذا
+
+220
+00:20:43,370 --> 00:20:49,010
+بيساوي اللي هو الاتنين بيساوي نفس القيمة ماشي الحال
+
+221
+00:20:49,010 --> 00:20:55,850
+إذا لازم عندي من هنا g prime و g prime اللي هو
+
+222
+00:20:55,850 --> 00:21:00,210
+صار بيساوي نفس القيمة إذا هيطلع الـ g prime إيش
+
+223
+00:21:00,210 --> 00:21:05,530
+ماله بيساوي صفر إذا صار المقدار هذا كله إيش بده يساوي
+
+224
+00:21:05,530 --> 00:21:08,650
+صفر وهذا بيساوي صفر يعني الـ limit من اليمين والـ
+
+225
+00:21:08,650 --> 00:21:12,070
+limit من اليسار متساويين إذا صارت limit f of x على
+
+226
+00:21:12,070 --> 00:21:23,310
+X ناقص C لما الـ X تروح للـ C بدها تساوي صفر أي سؤال؟
+
+227
+00:21:23,310 --> 00:21:31,130
+زي ما حكينا، الآن إحنا قلنا إنه لو كانت الـ D بدينا D
+
+228
+00:21:31,130 --> 00:21:34,600
+بيساوي f of x الـ differential بالأد C جبنا g prime
+
+229
+00:21:34,600 --> 00:21:37,500
+وكتبناها بالصورة اللي أمامنا بعدين أخدنا الـ
+
+230
+00:21:37,500 --> 00:21:40,120
+absolute value لـ limit f of x على الـ X ناقص C لم X
+
+231
+00:21:40,120 --> 00:21:45,200
+تروح لـ C positive طلعت عندي بيساوي g prime of C و
+
+232
+00:21:45,200 --> 00:21:48,680
+أخدنا اللي هي ناقص هذه طلعت عندي برضه g prime
+
+233
+00:21:48,680 --> 00:21:53,920
+الاتنين الـ C إذا صار هذا بيساوي هذا المقدار واحنا
+
+234
+00:21:53,920 --> 00:21:57,640
+بنعرف في الأصل إن f prime of C exist يعني
+
+235
+00:21:57,640 --> 00:22:01,900
+differentiable يعني الـ limit هذا اللي هو موجود ومن
+
+236
+00:22:01,900 --> 00:22:05,100
+اليمين ومن اليسار زي بعض يعني يعني هذا بده يساوي
+
+237
+00:22:05,100 --> 00:22:07,500
+هذا من اليمين وهذا من اليسار يعني في الواقع هذا
+
+238
+00:22:07,500 --> 00:22:10,960
+اللي جوا هو نفسه اللي جوا بيساوي limit of f of x يعني
+
+239
+00:22:10,960 --> 00:22:15,780
+بمعنى آخر absolute value لـ limit of f of x على الـ X
+
+240
+00:22:15,780 --> 00:22:22,100
+ناقص C لما الـ X تروح للـ C هو نفسه سالب limit للـ f of
+
+241
+00:22:22,100 --> 00:22:27,400
+x على الـ X ناقص C لما الـ X تروح للـ C من وين من
+
+242
+00:22:27,400 --> 00:22:31,540
+اليسار هو نفسه للـ C من وين تبت هذه لأن احنا بنقول
+
+243
+00:22:31,540 --> 00:22:34,560
+f prime of C exist يعني الـ limit هذا موجود ومن
+
+244
+00:22:34,560 --> 00:22:37,360
+اليمين ومن اليسار زي بعض إذا صار هذا المقدار نفس
+
+245
+00:22:37,360 --> 00:22:41,200
+هذا المقدار زي ما قلنا إذا صار عند هذا المقدار بيساوي
+
+246
+00:22:41,200 --> 00:22:46,800
+صفر لأن الاتنين بيساويا بيساوي صفر إذا صار عندي limit f
+
+247
+00:22:46,800 --> 00:22:50,880
+of x على الـ X ناقص C اللي هو الـ absolute value as X
+
+248
+00:22:50,880 --> 00:22:56,100
+بتروح للـ C بيساوي صفر ومن ثم اللي جوا بيساوي صفر هو
+
+249
+00:22:56,100 --> 00:22:58,740
+مين هو اللي جوا هذا اللي كنا بدنا نصله من الأول
+
+250
+00:22:58,740 --> 00:23:04,260
+اللي هو f prime of C بتساوي صفر وهو المطلوب هذا
+
+251
+00:23:04,260 --> 00:23:10,300
+توضيح بشكل كامل للي صار في اللي هو الاتجاه
+
+252
+00:23:10,300 --> 00:23:16,200
+الثاني نيجي لسؤال بعد ما خلصنا السؤال سبعة نيجي
+
+253
+00:23:16,200 --> 00:23:23,420
+لسؤال تسعة تسعة إيش اللي بقوله تسعة نشوف إيش سؤال
+
+254
+00:23:23,420 --> 00:23:31,360
+تسعة بقول ونحل سؤال تسعة سؤال تسعة بقول ليه
+
+255
+00:23:31,360 --> 00:23:39,110
+باختصار إنه لو كان عنده الـ function of عبارة عن من
+
+256
+00:23:39,110 --> 00:23:43,130
+R لـ R even function طبعاً عارفين إيش الـ even اللي
+
+257
+00:23:43,130 --> 00:23:49,130
+هو f ناقص x بيساوي f x لكل x موجودة في الـ R and
+
+258
+00:23:49,130 --> 00:23:54,310
+has a derivative at every point then f prime is an
+
+259
+00:23:54,310 --> 00:23:58,190
+odd function يعني بيقول لي لو كانت باختصار يعني لو
+
+260
+00:23:58,190 --> 00:24:01,730
+كانت الـ f even والـ derivative موجودة بتكون الـ
+
+261
+00:24:01,730 --> 00:24:07,010
+derivative odd ولو كانت الـ derivative odd بتكون
+
+262
+00:24:07,010 --> 00:24:11,350
+الـ function الـ f prime إيه شمالها is even انحل
+
+263
+00:24:11,350 --> 00:24:16,970
+واحدة من هنا والتانية similarly زيها الآن لنفترض f
+
+264
+00:24:16,970 --> 00:24:29,890
+من عند R لعند R be an odd differentiable function
+
+265
+00:24:29,890 --> 00:24:34,970
+ماشي الحال show that
+
+266
+00:24:36,040 --> 00:24:44,360
+f' is even a proof بدنا نثبت إنه لو كانت الـ f
+
+267
+00:24:44,360 --> 00:24:49,940
+اللي هي odd function بدو يكون عنده و
+
+268
+00:24:49,940 --> 00:24:52,320
+differentiable بدو يكون عنده derivative إلها إيه
+
+269
+00:24:52,320 --> 00:25:03,000
+إيش even لأن let C element in R be arbitrary and
+
+270
+00:25:03,000 --> 00:25:04,180
+fixed
+
+271
+00:25:06,310 --> 00:25:15,930
+ناخد الـ R ناخد الـ C أي اللي هو real number in
+
+272
+00:25:15,930 --> 00:25:23,360
+R لكن نحكي عن أي شيء محدد الآن f prime of C بدأ
+
+273
+00:25:23,360 --> 00:25:29,060
+أثبت لك إنه هو بيساوي f prime of ناقص C يعني f prime
+
+274
+00:25:29,060 --> 00:25:34,920
+is even إذا خد f prime ناقص C وابدأ حسب وواصلك في
+
+275
+00:25:34,920 --> 00:25:39,140
+النهاية بيساوي f prime of C إذا f prime is even بيساوي
+
+276
+00:25:39,140 --> 00:25:49,380
+limit اللي هي f of x ناقص f of ناقص C على x ناقص
+
+277
+00:25:50,570 --> 00:25:57,070
+اللي هو ناقص C لما الـ x تروح لمين لـ ناقص C مظبوط
+
+278
+00:25:57,070 --> 00:26:05,550
+طيب وبيساوي limit الـ f إيش معطينا إياها عبارة عن odd
+
+279
+00:26:05,550 --> 00:26:12,250
+إيش يعني odd يعني f of ناقص x بيساوي ناقص f of x
+
+280
+00:26:12,250 --> 00:26:16,590
+مظبوط هذه اللي هي إيش ما لها odd function اللي هو 
+
+281
+00:26:16,590 --> 00:26:28,550
+بيساوي limit F of x اللي هي ناقص f of ناقص x
+
+282
+00:26:28,550 --> 00:26:34,150
+واضح أه؟
+
+283
+00:26:34,150 --> 00:26:37,150
+f of ناقص x بيساوي ناقص f of x يعني f of x بيساوي
+
+284
+00:26:37,150 --> 00:26:41,230
+ناقص f of ناقص x فالجد تعرفوا ليش عملت هيك لأن
+
+285
+00:26:41,230 --> 00:26:48,570
+ناقص f of ناقص c الآن f is odd مظبوط بيصير زائد f 
+
+286
+00:26:48,570 --> 00:26:49,330
+of c
+
+287
+00:26:52,220 --> 00:26:58,060
+على خد الآن ناقص من هنا عامل مشترك بيصير عبارة عن
+
+288
+00:26:58,060 --> 00:27:08,220
+ناقص x الآن ناقص ال c لما x تروح لمين لسالب ال c
+
+289
+00:27:08,220 --> 00:27:14,040
+ال x بتروح لسالب ال c إذا و فقط إذا سالب ال x
+
+290
+00:27:14,040 --> 00:27:22,160
+بتروح لمين إلى ال c الآن خد لي y بيساوي سالب ال x
+
+291
+00:27:22,160 --> 00:27:29,240
+واستبدل عشان نوضح لك إياه بيساوي limit الآن خد الآن
+
+292
+00:27:29,240 --> 00:27:38,320
+عندي f  حكما كان نقص  x  سمّينا ال y limit ناقص F of y
+
+293
+00:27:38,320 --> 00:27:49,390
+زائد f of c على اللي هو y بتروح إلى ال c وهنا y
+
+294
+00:27:49,390 --> 00:27:57,430
+ناقص ال c وهنا في عندي ايش برضه ناقص برا لأن خد من
+
+295
+00:27:57,430 --> 00:28:01,670
+هنا ناقص عامل مشترك أو ضيعه مع الناقص اللي هنا
+
+296
+00:28:01,670 --> 00:28:11,160
+ما واضح أه بيصير عندي y بيساوي limit f of y ناقص f of c 
+
+297
+00:28:11,160 --> 00:28:16,800
+على y ناقص c لما y تروح لل c وهذا عبارة عن f
+
+298
+00:28:16,800 --> 00:28:22,440
+prime لمين لل c بدأنا ب f prime ناقص c وانتهينا ب f
+
+299
+00:28:22,440 --> 00:28:31,520
+prime لل c لذا therefore f prime is even whenever
+
+300
+00:28:31,520 --> 00:28:37,160
+f is odd and f is differentiable
+
+301
+00:28:40,710 --> 00:28:56,810
+السؤال الأخير السؤال 13 السؤال
+
+302
+00:28:56,810 --> 00:29:03,990
+13 هو كما يلي  ايش
+
+303
+00:29:03,990 --> 00:29:09,200
+اللي بقول السؤال 13 سؤال 13 بيقول إذا كانت f من R
+
+304
+00:29:09,200 --> 00:29:12,380
+لـ R is differentiable at c element in R show that
+
+305
+00:29:12,380 --> 00:29:16,840
+f prime of c يساوي limit N في f of c زائد 1 على N ناقص
+
+306
+00:29:16,840 --> 00:29:20,620
+f of c as N goes to infinity يعني لو كانت f
+
+307
+00:29:20,620 --> 00:29:24,900
+differentiable عند الـ c element in R بنقدر نكتب
+
+308
+00:29:24,900 --> 00:29:27,920
+ال derivative اللي هي f prime of c على صورة limit
+
+309
+00:29:27,920 --> 00:29:32,320
+N f of c زائد 1 على N ناقص f of c as N goes to
+
+310
+00:29:32,320 --> 00:29:38,120
+infinity لكن بيقول لي by example show that the
+
+311
+00:29:38,120 --> 00:29:44,000
+existence of this limit this limit need not اللي
+
+312
+00:29:44,000 --> 00:29:52,300
+هو imply the existence of the derivative نيجي
+
+313
+00:29:52,300 --> 00:30:03,960
+الآن للجزء الأول عندي f من R لـ R و f prime of c
+
+314
+00:30:03,960 --> 00:30:12,120
+exist لأنه يقول لي prove that f prime of c can be
+
+315
+00:30:12,120 --> 00:30:20,760
+written as limit N في f of c زائد 1 على N ناقص f
+
+316
+00:30:20,760 --> 00:30:26,180
+of c as N goes to infinity هذا الجزء الأول الجزء
+
+317
+00:30:26,180 --> 00:30:32,400
+الثاني حنجي الآن نقول prove للجزء الأول قبل ما نقول
+
+318
+00:30:32,400 --> 00:30:37,700
+الـ proof نذكركم بس بنظرية سابقة في الـ real واحد
+
+319
+00:30:37,700 --> 00:30:43,840
+إنه لو عندي limit f of x لما x تروح لل c لو كانت
+
+320
+00:30:43,840 --> 00:30:52,780
+بتساوي l بكون عندي أي sequence xₙ بتروح للـ c لازم
+
+321
+00:30:52,780 --> 00:30:59,020
+يتحقق لها limit f of xₙ as n goes to infinity
+
+322
+00:30:59,020 --> 00:31:05,530
+بيساوي برضه الـ كنا نتحدث بالحديث، باستبداء الحديث
+
+323
+00:31:05,530 --> 00:31:08,670
+عن الـ limit العادية للـ function S x بتروح للـ c
+
+324
+00:31:08,670 --> 00:31:13,470
+إلى limit لمين للـ sequence أو limit للـ sequences
+
+325
+00:31:13,470 --> 00:31:17,290
+الآن بنستخلص هذه اللي هو المعلومة في إثبات اللي
+
+326
+00:31:17,290 --> 00:31:22,630
+بدنا إياه عند الآن since f prime of c exist بما أنه
+
+327
+00:31:22,630 --> 00:31:29,250
+ال derivative عند c موجودة إذا أكيد عندي صار f 
+
+328
+00:31:29,250 --> 00:31:37,010
+prime of c بسهولة f of x أو اللي هي الـ x عند c
+
+329
+00:31:38,080 --> 00:31:46,140
+زائد h ناقص f of c على h as h goes to mean to zero
+
+330
+00:31:46,140 --> 00:31:49,860
+اللي هو التعريف التعريف ال derivative أو الشكل
+
+331
+00:31:49,860 --> 00:31:52,980
+الآخر للتعريف ال derivative f of c زائد ال
+
+332
+00:31:52,980 --> 00:31:55,560
+increment ناقص f of c على ال increment as ال
+
+333
+00:31:55,560 --> 00:32:01,600
+increment goes to mean to zero ماشي الحل ال l بما
+
+334
+00:32:01,600 --> 00:32:07,480
+أنه اللي هو ال 1 على N sequence بتروح للصفر وهذا
+
+335
+00:32:07,480 --> 00:32:11,440
+الـ limit exist لأن حسب النظرية اللي حكيتها قبل
+
+336
+00:32:11,440 --> 00:32:21,100
+بشوية بكون عندي لأن butكذا then f prime of c can
+
+337
+00:32:21,100 --> 00:32:26,580
+be اللي هو إعادة اللي هي rewritten as a limit of a
+
+338
+00:32:26,580 --> 00:32:36,800
+sequence f of اللي هو limit limit f of c زائد but
+
+339
+00:32:36,800 --> 00:32:40,000
+الـ h اللي هي تروح للصفر صارت mean ال sequence
+
+340
+00:32:40,000 --> 00:32:46,380
+واحدة على N تروح للصفر واحدة على N ناقص f of c على
+
+341
+00:32:46,380 --> 00:32:52,640
+واحدة على N as N goes to infinity مدامت ال sequence
+
+342
+00:32:52,640 --> 00:32:57,100
+واحدة على N بتروح للصفر صارت ال f of واحدة على N اللي
+
+343
+00:32:57,100 --> 00:33:00,900
+هي عبارة عن f of c زائد واحدة على N لأن الـ c عبارة
+
+344
+00:33:00,900 --> 00:33:07,740
+عن إياش فالتة واضح أه؟ الآن هذا بيساوي اللي هو
+
+345
+00:33:07,740 --> 00:33:14,600
+limit الآن as n goes to infinity اللي هو أكيد اللي
+
+346
+00:33:14,600 --> 00:33:21,920
+هو بيصير عندي f n في الجوس f of c زائد 1 على n
+
+347
+00:33:21,920 --> 00:33:28,260
+ناقص f of c اللي هو as n goes to infinity هو هذا
+
+348
+00:33:28,260 --> 00:33:35,150
+صار f prime of c وهو المطلوب الآن conversely the
+
+349
+00:33:35,150 --> 00:33:37,890
+converse need not to be true in general هيك بيقول
+
+350
+00:33:37,890 --> 00:33:45,390
+ليه يعني بيقول لي if if بيقول لي أو اللي بيقول if f
+
+351
+00:33:45,390 --> 00:33:53,670
+برا اللي هو limit f of c زائد 1 على n ناقص f of c
+
+352
+00:33:53,670 --> 00:34:01,610
+الكل مضروب في n as n goes to infinity exist if كده
+
+353
+00:34:02,500 --> 00:34:12,640
+then f prime at c need not be exist أصلا مش أنه
+
+354
+00:34:12,640 --> 00:34:16,180
+يكون بيساوي هذا أو لا need not to be  اشمل  exist
+
+355
+00:34:16,180 --> 00:34:19,640
+لأن لو كان exist على طول بيساوي اما need not to be
+
+356
+00:34:19,640 --> 00:34:28,200
+exist وما أخذ مثال جالي consider consider consider
+
+357
+00:34:28,200 --> 00:34:37,000
+f of x بيساوي ال absolute value لل x وخد عند ال c ايش
+
+358
+00:34:37,000 --> 00:34:46,440
+بتساوي صفر واضح f prime of 0 does not exist لأنها
+
+359
+00:34:46,440 --> 00:34:48,780
+عبارة عن corner point، أنتو عارفين احنا اللي هو
+
+360
+00:34:48,780 --> 00:34:52,480
+ال f prime عند ال zero لل absolute value does not
+
+361
+00:34:52,480 --> 00:34:59,740
+exist لكن هذه متحققة، ليش؟ but limit
+
+362
+00:35:01,280 --> 00:35:10,900
+N في f of 0 زائد 1 على N ناقص f of 0 as N goes to
+
+363
+00:35:10,900 --> 00:35:18,840
+infinity بيساوي limit N f of 0 زائد 1 على N يعني f
+
+364
+00:35:18,840 --> 00:35:23,560
+of 1 على N f of x بيساوي absolute value x ف 1 على N
+
+365
+00:35:23,560 --> 00:35:28,960
+مظبوط أه as N goes to infinity طبعا الـ N بتروح
+
+366
+00:35:29,220 --> 00:35:35,100
+يصير عبارة عن ash واحد إذا فعلا جبنا مثال أن ال
+
+367
+00:35:35,100 --> 00:35:39,720
+limit هذه تكون exist و يساوي واحد but ال f prime عند
+
+368
+00:35:39,720 --> 00:35:42,640
+هذا النقطة c اللي هي 00 في هذه الحالة does not
+
+369
+00:35:42,640 --> 00:35:47,320
+exist بيكون هيك احنا انتهينا من الجزء الأول من
+
+370
+00:35:47,320 --> 00:35:54,870
+المحاضرة الخامسة اللي هو discussion لأو مناقشة ل
+
+371
+00:35:54,870 --> 00:35:59,910
+section 6-1 اللي هو the derivative والآن سنكمل
+
+372
+00:35:59,910 --> 00:36:05,690
+الحديث في الجزء الثاني من المحاضرة اللي هو عن اللي
+
+373
+00:36:05,690 --> 00:36:09,250
+هو the mean value theorem أو اللي هي نكمل
+
+374
+00:36:09,250 --> 00:36:11,910
+applications على mean value theorem وناخد اللي هو
+
+375
+00:36:11,910 --> 00:36:12,030
+ال
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EIprZTnXBQc.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EIprZTnXBQc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..295e313baaec3dc497d460466a52a1ae3214be5f
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EIprZTnXBQc.srt
@@ -0,0 +1,3435 @@
+1
+00:00:05,090 --> 00:00:08,030
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,030 --> 00:00:11,070
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:11,070 --> 00:00:18,250
+أجمعين هذه المحاضرة رقم 24 مساق تحليل حقيقي 2 طلاب
+
+4
+00:00:18,250 --> 00:00:22,650
+وطالبات الجامعة الإسلامية قسم رياضيات كلية العلوم
+
+5
+00:00:23,470 --> 00:00:26,630
+اليوم هنكمل إن شاء الله الـ section الأخير في
+
+6
+00:00:26,630 --> 00:00:29,870
+chapter 8 اللي هو 8.4 تحت عنوان the
+
+7
+00:00:29,870 --> 00:00:35,170
+trigonometric functions وهو أيضا اللي هو الـ section
+
+8
+00:00:35,170 --> 00:00:42,210
+أو موضوع تطبيق على اللي هو الـ pointwise and
+
+9
+00:00:42,210 --> 00:00:46,030
+uniform convergence للـ sequence of functions وكيف
+
+10
+00:00:46,030 --> 00:00:50,510
+بدنا نعرف بطريقة مشابهة جدا لمعرفناها المرة
+
+11
+00:00:50,510 --> 00:00:53,330
+الماضية أو اللي قبلها بخصوص الـ exponential
+
+12
+00:00:53,330 --> 00:00:58,710
+function هنعرف اليوم اللي هو بنفس الطريقة كيف نعرف 
+
+13
+00:00:58,710 --> 00:01:03,510
+اللي هو الـ sine والـ cosine as a limit اللي هو
+
+14
+00:01:03,510 --> 00:01:07,390
+of a uniformly convergent sequence of functions
+
+15
+00:01:07,950 --> 00:01:11,230
+العنوان is in the trigonometric functions اللي هو
+
+16
+00:01:11,230 --> 00:01:15,450
+section 8.4 النظرية
+
+17
+00:01:15,450 --> 00:01:21,950
+الأولى اللي عندنا اللي مشابهة لنظرية سابقة اللي هي
+
+18
+00:01:21,950 --> 00:01:25,870
+الـ exponential اللي من خلالها بدنا نصل للي هو
+
+19
+00:01:25,870 --> 00:01:31,370
+تعريف اللي هي الـ cosine والـ sineالنظرية بتقول
+
+20
+00:01:31,370 --> 00:01:35,190
+مالها there exist functions يوجد دوال  الامنّان في 
+
+21
+00:01:35,190 --> 00:01:40,570
+بتوجد دوال C من R لـ R وS من R لـ R such that
+
+22
+00:01:40,570 --> 00:01:44,690
+اللي هي طبعا مستقبلا هنتسمي الـ C اللي هي الـ cosine
+
+23
+00:01:44,690 --> 00:01:48,910
+ومستقبلا هنتسمي الـ S اللي هي الـ sine اللي احنا 
+
+24
+00:01:48,910 --> 00:01:54,090
+بنعرفها الآن بنقول في ده اللي ثاني واحدة اسمها c
+
+25
+00:01:54,090 --> 00:01:59,950
+واحدة s تحقق ما يلي اللي هي c' of x بيساوي
+
+26
+00:01:59,950 --> 00:02:04,870
+ناقص c of x s' of x بيساوي ناقص s of x ولو
+
+27
+00:02:04,870 --> 00:02:08,730
+استذكرت أنت الـ sine والـ cosine دي ما سيحدث لاحقا
+
+28
+00:02:08,730 --> 00:02:12,270
+طبعا لو استذكرت الـ cosine لما ان.. ان.. ان.. ان
+
+29
+00:02:12,270 --> 00:02:16,130
+فاضلها مرتين هتصير اللي هي ناقص اللي هي نفسها ولو
+
+30
+00:02:16,130 --> 00:02:19,570
+فاضلت الـ sine برضه فاضلها مرتين هتلاقيها إيش هي
+
+31
+00:02:19,960 --> 00:02:23,840
+بتطلع سالب S الخاصية الثانية اللي هي C of Zero
+
+32
+00:02:23,840 --> 00:02:27,780
+بساوة واحد ولو استذكرت الكوسين كوسين الـ Zero بساوة
+
+33
+00:02:27,780 --> 00:02:31,240
+واحد ولو استذكرت الكوسين لما تاخدها الـ derivative
+
+34
+00:02:31,240 --> 00:02:35,160
+هتصير عبارة عن سالب Sin عند Zero هتطلع 0 بساوة
+
+35
+00:02:35,160 --> 00:02:38,960
+Zero and S of Zero بساوة Zero وS' of Zero
+
+36
+00:02:38,960 --> 00:02:45,330
+بساوة واحد يعني بمعنى آخر يوجد دالتين الـ دالتين
+
+37
+00:02:45,330 --> 00:02:49,770
+واحدة من C لـ R اسمها S واحدة اسمها C من R لـ R
+
+38
+00:02:49,770 --> 00:02:56,690
+تحقق الشرطين التاليين C' بساوة ناقص C وS' بساوة
+
+39
+00:02:56,690 --> 00:03:01,330
+ناقص S على كل R وC عند الـ 0 هي 1 وC' عند الـ 0
+
+40
+00:03:01,330 --> 00:03:05,650
+بساوة 0 وS عند الـ 0 بساوة 0 وS' عند الـ 0 بساوة 1
+
+41
+00:03:05,650 --> 00:03:11,250
+وبعد شوية هقولك لا يوجد في الدنيا دالتين بحقق أنّ 
+
+42
+00:03:11,250 --> 00:03:17,300
+الشروط هذولة إلا هي واحدة اسمها C واحدة اسمها S
+
+43
+00:03:17,300 --> 00:03:22,640
+يعني التنتين واحدات وهذا يجعلنا نسميهم التسمية بعد
+
+44
+00:03:22,640 --> 00:03:26,380
+ذلك واحدة اسمها cosine واحدة اسمها sine ومن ثم
+
+45
+00:03:26,380 --> 00:03:29,320
+بنجيب كل الخواص اللي احنا بنعرفها عن الـ sine والـ 
+
+46
+00:03:29,320 --> 00:03:34,020
+cosine من هذا البناء إذن الآن أنا ببني ببني ببني
+
+47
+00:03:34,020 --> 00:03:36,980
+وجود الـ sine والـ cosine وبعد شوية ببني اللي هو
+
+48
+00:03:36,980 --> 00:03:40,960
+الـ uniqueness طبقا لهذه الشروط اللي موجودة عندي
+
+49
+00:03:42,380 --> 00:03:45,860
+الآن كيف بدنا نعمل زي ما عملنا المرة الماضية في
+
+50
+00:03:45,860 --> 00:03:48,340
+الـ.. في الـ.. اللي هو الـ Exponential عشانك
+
+51
+00:03:48,340 --> 00:03:52,060
+هتلاقوني شوية مسرع لأن اللي بيحضر اللي هي محاضرة
+
+52
+00:03:52,060 --> 00:03:56,620
+الـ Exponential هيلاقي أنّ هذا في كثير من الحديث في
+
+53
+00:03:56,620 --> 00:04:00,640
+إعادة We define the sequence cn as n of continuous
+
+54
+00:04:00,640 --> 00:04:05,240
+functions inductively as بدنا نعرف اللي هي.. اللي
+
+55
+00:04:05,240 --> 00:04:09,640
+هو two sequences واحدة نسميها cn وواحدة نسميها sn
+
+56
+00:04:10,270 --> 00:04:13,890
+كيف بدنا نعرفها؟ زي ما عرفنا الـ exponential بنعرف
+
+57
+00:04:13,890 --> 00:04:19,250
+C1 of X إيش بتساوي واحد وS1 of X إيش بدنا نسميها
+
+58
+00:04:19,250 --> 00:04:26,490
+بساوة X الآن S2 of X S2 of X هيساوي الـ integration
+
+59
+00:04:26,490 --> 00:04:31,990
+من صفر لعند X C2 of T DT طب C2 من وين أجيبها؟ C2
+
+60
+00:04:31,990 --> 00:04:36,050
+بتجيبها من هنا C اللي هي واحد زائد واحد يعني C2
+
+61
+00:04:36,050 --> 00:04:41,470
+بساوة واحد ناقص الـ integration من صفر لـ X لـ S1 of
+
+62
+00:04:41,470 --> 00:04:48,870
+T اللي هذا DT فبكون جيبت الـ C2 وبتجيب الـ S2 من
+
+63
+00:04:48,870 --> 00:04:55,530
+الـ C2 لأن S3 وC3 بنفس الطريقة in general اللي أنا
+
+64
+00:04:55,530 --> 00:04:59,170
+عملت sequence of functions اللي هو بدأت اللي هي الـ
+
+65
+00:04:59,170 --> 00:05:05,120
+C1 بـ 1 S1 بـ X ومن ثم S N بتساوي من صفر لـ X
+
+66
+00:05:05,120 --> 00:05:10,760
+integration C N of T DT يعني كمالة C N of T DT وC
+
+67
+00:05:10,760 --> 00:05:13,460
+N زائد واحد of X بتساوي واحد نقص integration من
+
+68
+00:05:13,460 --> 00:05:18,700
+صفر لـ X S N of T DT الآن هو بيقول اللي هو هذه
+
+69
+00:05:18,700 --> 00:05:21,820
+sequence of continuous functions طب sequence of
+
+70
+00:05:21,820 --> 00:05:25,840
+continuous functions هذا الكلام بده إثبات طيب، الآن
+
+71
+00:05:25,840 --> 00:05:29,500
+عندي اللي هو by induction زي ما أنتم عارفين الآن
+
+72
+00:05:29,500 --> 00:05:33,600
+عندي الـC1 continuous لأن الثابتة S1 continuous
+
+73
+00:05:33,600 --> 00:05:38,880
+لأن هي شمالها بتساوي X بناء عليه هتطلع عندي اللي
+
+74
+00:05:38,880 --> 00:05:44,920
+هي C2 continuous ومن ثم C3 وC4 الآخرين الآن لو
+
+75
+00:05:44,920 --> 00:05:49,000
+بدنا نثبتها by induction بدنا نفترض أنّ هذولة
+
+76
+00:05:49,000 --> 00:05:52,560
+الـSn والـCn
+
+77
+00:05:53,920 --> 00:06:00,700
+continuous سنثبت هنا continuous لأن S1 إيش بتساوي
+
+78
+00:06:00,700 --> 00:06:06,860
+X؟ C1 إيش بتساوي 1؟ continuous إذا صارت هذه اللي
+
+79
+00:06:06,860 --> 00:06:12,340
+هي الجملة is true for N بتساوي 1 نفترض الآن
+
+80
+00:06:12,340 --> 00:06:19,900
+suppose by induction بتأدي suppose that اللي هو star
+
+81
+00:06:19,900 --> 00:06:25,960
+هذه is true for n إيش بتساوي n بتساوي k معناته
+
+82
+00:06:25,960 --> 00:06:33,820
+صارت الـ S K والـ CK are continuous بتثبت الآن من 
+
+83
+00:06:33,820 --> 00:06:38,520
+الصحيحة لـ K زائد واحد يعني بتثبت اللي هو CK زائد
+
+84
+00:06:38,520 --> 00:06:42,700
+واحد وSK زائد واحد أنّ هنا شمال هنا continuous طيب
+
+85
+00:06:42,700 --> 00:06:48,000
+الآن شوف CK زائد واحد بتساوي حسب اللي هي عندي هان
+
+86
+00:06:48,000 --> 00:06:51,740
+إيش بتساوي اللي هو عبارة عن CK واحد of X بتساوي الـ
+
+87
+00:06:51,740 --> 00:06:58,020
+integration واحد نقص الـ integration من صفر X Sk..
+
+88
+00:06:58,020 --> 00:07:03,020
+هذا Kz واحد.. هذا ك.. of DT طيب أنا مفترض أنّ Sk
+
+89
+00:07:03,020 --> 00:07:06,600
+من الـ hypothesis induction أنّها continuous إذا
+
+90
+00:07:06,600 --> 00:07:11,040
+صارت هذه كلها إيش مالها؟ اللي هي Sk integrable
+
+91
+00:07:11,040 --> 00:07:15,600
+وصارت هذه كلها على بعض by fundamental theorem of
+
+92
+00:07:15,600 --> 00:07:20,980
+calculus اللي هي الـ derivative إلها موجودة إذا
+
+93
+00:07:20,980 --> 00:07:23,440
+صارت هذه كلها الـ derivative إلها وموجودة بالنسبة
+
+94
+00:07:23,440 --> 00:07:27,680
+للـ X إذا صارت مدام هيك هاذ is differentiable إذا
+
+95
+00:07:27,680 --> 00:07:30,940
+continuous إذا صارت اللي هي Ck زائد واحد
+
+96
+00:07:30,940 --> 00:07:35,200
+continuous اللي ثبت الآن is Sk زائد واحد Sk زائد
+
+97
+00:07:35,200 --> 00:07:39,280
+واحد of x إيش بتساوي حسب اللي التعريف بتساوي الـ
+
+98
+00:07:39,280 --> 00:07:47,660
+integration من صفر لعند x Ck of t زائد واحد هذا N
+
+99
+00:07:47,660 --> 00:07:52,620
+هذا N K زائد واحد K زائد واحد DT وأنا مثبت فوق أنّ
+
+100
+00:07:52,620 --> 00:07:56,160
+Ck زائد واحد is continuous إذا صارت هذه كلها على
+
+101
+00:07:56,160 --> 00:07:59,500
+بعض integrable اللي هي Ck زائد واحد صار هذا الـ
+
+102
+00:07:59,500 --> 00:08:02,000
+integration exist ومش هيك by fundamental theorem
+
+103
+00:08:02,000 --> 00:08:04,720
+of calculus برضه الـ derivative له إيه شمالها
+
+104
+00:08:04,720 --> 00:08:07,700
+موجودة إذا صارت هذه الـ differentiable إذا
+
+105
+00:08:07,700 --> 00:08:11,060
+continuous إذا صارت Ck زائد واحد وSk زائد واحد are
+
+106
+00:08:11,060 --> 00:08:16,160
+continuous إذا صارت الجملة هذه صحيحة لـ K زائد واحد
+
+107
+00:08:16,160 --> 00:08:21,000
+إذا صارت صحيحة دائما إذا صارت عندي الآن مفرغ منه
+
+108
+00:08:21,000 --> 00:08:26,360
+الـ CN والـ SN are continuous functions وبناء عليه
+
+109
+00:08:26,360 --> 00:08:29,860
+مدام continuous functions by fundamental theorem
+
+110
+00:08:29,860 --> 00:08:35,460
+of calculus هتكون هذه الـ SN differentiable والـ CN
+
+111
+00:08:35,460 --> 00:08:39,800
+زائد واحد differentiable ومش هيك كمان وهيعطيني الـ
+
+112
+00:08:39,800 --> 00:08:43,440
+SN prime of X حسب الـ fundamental theorem of
+
+113
+00:08:43,440 --> 00:08:46,820
+calculus الـ differentiation بتضايق الـ integration
+
+114
+00:08:46,820 --> 00:08:54,580
+بتضال بساوة Cn of x الآن والـ derivative لهذه برضه
+
+115
+00:08:54,580 --> 00:08:59,900
+exist Cn زائد واحد prime of x اللي هو هي ساوي اللي
+
+116
+00:08:59,900 --> 00:09:10,170
+هو مين هتطلع ناقص Sn of X إذا صار عندي الآن اللي هي
+
+117
+00:09:10,170 --> 00:09:15,610
+الـ sequence اللي عندي صارت well defined كلها و
+
+118
+00:09:15,610 --> 00:09:20,270
+continuous كلها ولأ وdifferentiable كمان الـ SN
+
+119
+00:09:20,270 --> 00:09:25,150
+prime of X بيساوي CN of X وCN زائد واحد prime of
+
+120
+00:09:25,150 --> 00:09:31,730
+X بيساوي ناقص SN of X زي ما أنا أثبتها وأوضحت لكم
+
+121
+00:09:31,730 --> 00:09:38,710
+إياها هنا الآن induction arguments برضه induction
+
+122
+00:09:38,710 --> 00:09:42,970
+arguments بقول لي we leave this argument for you
+
+123
+00:09:42,970 --> 00:09:46,890
+خلينا نشوفها مع بعض ما هي اللي بنقصده زي ما عملت
+
+124
+00:09:46,890 --> 00:09:49,870
+بالضبط لو طلعت على الخطوات هتلاقيها مشابه لخطوات
+
+125
+00:09:49,870 --> 00:09:54,970
+تبعات الـ exponential عند الـ Sn of X زي ما قلنا
+
+126
+00:09:54,970 --> 00:10:02,060
+بساوة الـ integration من 0 لـ X Cn of T dt C N زائد
+
+127
+00:10:02,060 --> 00:10:06,140
+واحد of X بساوة واحد مقص الـ integration من C لـ X S
+
+128
+00:10:06,140 --> 00:10:15,360
+N of T DT ومعطينا طبعا احنا اخذنا الـ C واحد of X
+
+129
+00:10:15,360 --> 00:10:22,530
+بساوة واحد والـ c وS1 of x بساوة x هذه اللي هي الـ
+
+130
+00:10:22,530 --> 00:10:25,370
+sequence of functions اللي أثبتناها هذه الـ
+
+131
+00:10:25,370 --> 00:10:27,990
+sequence of functions الـ sn والـ cn زائد واحد
+
+132
+00:10:27,990 --> 00:10:32,230
+التنتين are continuous for every n وهمش هي
+
+133
+00:10:32,230 --> 00:10:34,850
+codifferentiable والـ derivative إلها زي ما قلنا
+
+134
+00:10:34,850 --> 00:10:39,430
+Sn prime of x بساوة Cn of x والـ Cn زائد واحد prime
+
+135
+00:10:39,430 --> 00:10:44,190
+of x بساوة ناقص Sn of x وخلّينا نسجلها هذه لأنّ
+
+136
+00:10:44,190 --> 00:10:52,370
+هنحتاجها بعد شوية اللي هي S N prime of X بساوي
+
+137
+00:10:52,370 --> 00:11:00,310
+C N of X and C N زائد واحد prime of X بساوي ناقص S
+
+138
+00:11:00,310 --> 00:11:09,070
+N of X طيب الآن بدنا اللي هو by induction نثبت
+
+139
+00:11:09,070 --> 00:11:12,570
+اللي هو CN زائد واحد of X بساوي اللي هو اللي 
+
+140
+00:11:12,570 --> 00:11:18,460
+أمامي هذا طبعا أكيد اللي هو بعضكم قال ما هي by
+
+141
+00:11:18,460 --> 00:11:24,960
+induction نتطلع على C2 of X C1 في القرآن بتساوي
+
+142
+00:11:24,960 --> 00:11:31,720
+واحد نثبتها يعني الآن C2 of X ايش بتساوي حسب
+
+143
+00:11:31,720 --> 00:11:35,960
+القانون بتساوي واحد ناقص ال integration من صفر ل X
+
+144
+00:11:35,960 --> 00:11:41,020
+أس واحد لأنه بواحد هنا أس واحد اللي هي جداء أس واحد
+
+145
+00:11:41,020 --> 00:11:46,060
+الـ X integration اللي هي T DT ويساوي التفاضل اللي
+
+146
+00:11:46,060 --> 00:11:49,820
+هذه بيصير واحد ناقص X تربيع على مين على اثنين إذا 
+
+147
+00:11:49,820 --> 00:11:54,410
+فعلا اللي هي C اللي هي هذه اثنين is true for any
+
+148
+00:11:54,410 --> 00:11:58,870
+ايش بتساوي n بتساوي واحد بدنا نثبت الثانية معها
+
+149
+00:11:58,870 --> 00:12:01,730
+اللي هي true for any بتساوي واحد لأنها دي جملة
+
+150
+00:12:01,730 --> 00:12:05,690
+واحدة بدأ أثبتها أن true for every any الآن for
+
+151
+00:12:05,690 --> 00:12:10,590
+any بتساوي واحد بيصير عندي أس اثنين of x بدأ أتأكد
+
+152
+00:12:10,590 --> 00:12:15,990
+أنه اللي هي بتحقق اللي هي الـ .. اللي .. ايه هذه الـ
+
+153
+00:12:15,990 --> 00:12:19,960
+equation S2 of X بيساوي من وين بده أجيبها من
+
+154
+00:12:19,960 --> 00:12:23,480
+التعريف اللي فوق بيساوي ال integration من صفر ل X
+
+155
+00:12:23,480 --> 00:12:29,180
+C2 of X ايش C2 of X هايه اللي هو واحد ناقص T تربيع
+
+156
+00:12:29,180 --> 00:12:34,800
+على اثنين لكل ما له DT ويساوي الكملة هذا بيصير
+
+157
+00:12:34,800 --> 00:12:40,200
+عبارة عن X ناقص X تكعيب على ثلاثة وفي اثنين بيصير
+
+158
+00:12:40,200 --> 00:12:44,980
+X تكعيب على مين على ثلاثة factorial اللي هي جداء
+
+159
+00:12:44,980 --> 00:12:50,380
+اللي هي ستة إذا فعلا فعلا طلع عندي اللي هو C أس
+
+160
+00:12:50,380 --> 00:12:55,400
+اثنين هي عبارة عن أنا بواحد يعني أس اثنين بيساوي X
+
+161
+00:12:55,400 --> 00:12:59,380
+ناقص X تكعيب على ثلاثة factorial يعني صارت الجملة
+
+162
+00:12:59,380 --> 00:13:02,900
+هذه برضه صحيحة for n بتساوي واحد إذا كلها على بعض
+
+163
+00:13:02,900 --> 00:13:09,650
+هذه صارت صحيحة for n بتساوي جداء الآن بدنا نفترض
+
+164
+00:13:09,650 --> 00:13:13,430
+أنها
+
+165
+00:13:13,430 --> 00:13:19,490
+true for n بتساوي k ونجيب منها مين اللي هو k زائد
+
+166
+00:13:19,490 --> 00:13:25,950
+واحد نفترض suppose that this is true for n بتساوي
+
+167
+00:13:25,950 --> 00:13:30,690
+k يعني بمعنى آخر صار عندي ck زائد واحد بتساوي هذا
+
+168
+00:13:30,690 --> 00:13:37,260
+وهنا اثنين k وهنا k وهنا اثنين K وهنا نفس الشيء
+
+169
+00:13:37,260 --> 00:13:41,640
+اللي هو نفترض أن صحيحة for N بتساوي K صارت عبارة
+
+170
+00:13:41,640 --> 00:13:48,460
+عن اثنين K و اثنين K أو أس K ماشي الحال نثبت أن
+
+171
+00:13:48,460 --> 00:13:53,480
+هذه صحيحة for من؟ for K بتساوي .. for N بتساوي
+
+172
+00:13:53,480 --> 00:14:02,020
+كدهش؟ K زائد واحد يعني بدي أديب Cك زائد جداء اثنين
+
+173
+00:14:02,020 --> 00:14:07,480
+لأن في الأصل هي K زائد واحد في الأصل سن زائد واحد
+
+174
+00:14:07,480 --> 00:14:11,620
+فرضتها صحيحة في القرآن بتساوي k لأن بتثبتها صحيحة
+
+175
+00:14:11,620 --> 00:14:15,520
+لأن بتساوي K زائد واحد يعني K زائد واحد واحد بيصير
+
+176
+00:14:15,520 --> 00:14:22,820
+K زائد اثنين of X ماذا يعني حساب تعريفها؟ تعريفها واحد
+
+177
+00:14:22,820 --> 00:14:29,300
+ناقص ال integration من 0 إلى X هذا K زائد اثنين إذا هذا K
+
+178
+00:14:29,300 --> 00:14:34,420
+N زائد 1 وهذا N K زائد 2 ماذا؟ هذا سيصبح SK زائد 1
+
+179
+00:14:34,420 --> 00:14:36,340
+of DT
+
+180
+00:14:38,530 --> 00:14:42,870
+و يساوي واحد ناقص الفكرة أنت فاهم من صفر لمين
+
+181
+00:14:42,870 --> 00:14:47,910
+لـ X مين هكامل هكامل S K زائد واحد أنا فرضت أن أنا
+
+182
+00:14:47,910 --> 00:14:52,750
+أتروه في القرآن بتساوي K اللي هي عبارة عن T ناقص
+
+183
+00:14:52,750 --> 00:15:00,450
+T تكعيب على ثلاثة factorial لما أصل لآخر واحد زائد
+
+184
+00:15:00,450 --> 00:15:12,390
+ناقص واحد أس K فيه T 2K 1 2 T 1 كل ايه ايش مالها
+
+185
+00:15:12,390 --> 00:15:16,110
+factorial الكل دي تي حسابات والله يا جماعة اللي
+
+186
+00:15:16,110 --> 00:15:22,660
+حالكم بتعملوها دي تي و يساوي واحد ناقص نفتح قوس هذه
+
+187
+00:15:22,660 --> 00:15:26,700
+T بيصير T تربيع على اثنين factorial هذه ايش بيصير
+
+188
+00:15:26,700 --> 00:15:32,820
+ناقص T أس أربعة على أربعة في ثلاثة factorial عن
+
+189
+00:15:32,820 --> 00:15:36,980
+أربعة factorial زائد لما أصل الأخر واحد ناقص واحد
+
+190
+00:15:36,980 --> 00:15:43,580
+أس K زي ما هي لأن إشارة هذه T بيصير اثنين K زائد
+
+191
+00:15:43,580 --> 00:15:49,130
+واحد زائد واحد يعني زائد اثنين على اللي هو اثنين K
+
+192
+00:15:49,130 --> 00:15:54,490
+زائد اثنين في هذا بتطلع اثنين K زائد اثنين الكل
+
+193
+00:15:54,490 --> 00:15:59,550
+ايه شمالها؟ factorial ماشي الحال هذا طبعا كله من
+
+194
+00:15:59,550 --> 00:16:04,630
+صفر ل X إذا بتصير هذا عبارة عن X وهذا X وهذا
+
+195
+00:16:04,630 --> 00:16:09,010
+الأخير برضه ايه؟ X اللي هي هذا عبارة عن ايه؟ هو
+
+196
+00:16:09,010 --> 00:16:16,350
+يساوي واحد ناقص x تربيع على اثنين factorial زائد x أس 4
+
+197
+00:16:16,350 --> 00:16:20,310
+على أربعة factorial ضربت الناقص جوا لأن أنا لما أصل
+
+198
+00:16:20,310 --> 00:16:24,910
+ناقص لما أصل الأخر واحد زائد ناقص واحد K وناقص أنا
+
+199
+00:16:24,910 --> 00:16:31,050
+بيصير K زائد 1 في X أس 2K
+
+200
+00:16:31,910 --> 00:16:37,130
+زائد اثنين على اثنين K زائد اثنين لكل vector يعني
+
+201
+00:16:37,130 --> 00:16:41,890
+صارت هذه CK زائد واحد زائد اثنين of X بتساوي هذا
+
+202
+00:16:41,890 --> 00:16:49,290
+المقدار هذا المقدار صحيح صار بالظبط هو هذا اللي هو
+
+203
+00:16:49,290 --> 00:16:53,830
+المقدار اللي عندي أثبتت و كإلمي يعني الآن أن هذا
+
+204
+00:16:54,470 --> 00:16:59,490
+اللي عندي is true for mean for k زائد لواحد لأن
+
+205
+00:16:59,490 --> 00:17:03,950
+لما أحط مكان n بتساوي K زائد واحد بيصير هذه K زائد
+
+206
+00:17:03,950 --> 00:17:09,030
+اثنين أشوف اللي طلعته صح ولا لأ بيساوي تبحانة واحد
+
+207
+00:17:09,030 --> 00:17:12,990
+ناقص x تربيع على اثنين فيكتوريا لما أثر الأخر واحد
+
+208
+00:17:12,990 --> 00:17:17,790
+اللي هي ناقص واحد نقص مين K زائد واحد في x نقص اثنين
+
+209
+00:17:17,790 --> 00:17:20,970
+في K زائد واحد يعني اثنين K زائد اثنين وها اثنين K
+
+210
+00:17:20,970 --> 00:17:25,760
+زائد اثنين كل فيكتوريا الآن صارت هذه صحيحة for n
+
+211
+00:17:25,760 --> 00:17:30,600
+ايش بتساوي K زائد واحد الثاني بنفس الأسلوب بثبتها
+
+212
+00:17:30,600 --> 00:17:35,260
+صحيحة for ايش for K زائد واحد يعني بدي أحسب مين يا
+
+213
+00:17:35,260 --> 00:17:42,300
+جماعة بدي أحسب SK زائد اثنين ايش حسب اللي فوق
+
+214
+00:17:42,300 --> 00:17:47,180
+بتساوي بتساوي ال integration من صفر ل X ل CK زائد
+
+215
+00:17:47,180 --> 00:17:54,020
+اثنين of T DT و باجي بعوضها هنا و بكملها و بتطلع
+
+216
+00:17:54,020 --> 00:17:57,800
+عندي بالظبط ال formula هذه يعني صح بيصير عندي
+
+217
+00:17:57,800 --> 00:18:01,620
+بتعملها لحالك لأن حسابات نفس الأسلوب بتطلع عندي
+
+218
+00:18:01,620 --> 00:18:06,310
+اللي هي هذه صحيحة for mean برضه for n بتساوي k
+
+219
+00:18:06,310 --> 00:18:11,050
+زائد واحد إذا هذا صار المقدار صحيح دائما for mean
+
+220
+00:18:11,050 --> 00:18:20,430
+for any k for any n element in n الآن واضح أن
+
+221
+00:18:20,430 --> 00:18:26,310
+الخطوات مشابهة لخطوات ال exponential نيجي الآن
+
+222
+00:18:26,310 --> 00:18:28,970
+قصّل n prime
+
+223
+00:18:38,770 --> 00:18:45,020
+نيجي الآن وين رايح؟ زي اللي بكونت رايحي الأيام الـ
+
+224
+00:18:45,020 --> 00:18:49,060
+exponential هثبتلك أن الـ sequence هذه converged
+
+225
+00:18:49,060 --> 00:18:52,220
+uniformly وهذه طبعا هتصبح converged uniformly
+
+226
+00:18:52,220 --> 00:18:55,000
+automatically فهتصبح اللي هي differentiable لأن بيصير
+
+227
+00:18:55,000 --> 00:18:57,860
+طبقة النظرية اللي هي تبعها الـ differentiability
+
+228
+00:18:57,860 --> 00:19:01,200
+بيصير عند مادام differentiable اللي هي الـ
+
+229
+00:19:01,200 --> 00:19:04,580
+derivative اللي لها exist و هتكون الـ derivative
+
+230
+00:19:04,580 --> 00:19:07,960
+متحقق الشروط و بيكون خلاص نعم نشوف ايش بقول طيب
+
+231
+00:19:07,960 --> 00:19:12,530
+الآن بعد ما طلعنا هدولة let a أكبر من صفر b given
+
+232
+00:19:12,530 --> 00:19:15,790
+نفس الخطوات تبعت ال exponential then if الـ absolute
+
+233
+00:19:15,790 --> 00:19:19,970
+value of x أصغر من a and m أكبر من n أكبر من 2a
+
+234
+00:19:19,970 --> 00:19:25,510
+يعني بتداخد اللي هي الامات لأكبر من n و أكبر من 2a
+
+235
+00:19:25,510 --> 00:19:29,650
+يعني الآن أنا بشتغل على n يا جماعة الفترة من ناقص
+
+236
+00:19:29,650 --> 00:19:34,570
+a لعند a وأخدت ال a arbitrarily أكبر من صفر لكن
+
+237
+00:19:34,570 --> 00:19:41,850
+fixed الآن we have عندي اللي هو .. عندي اللي هي الـ
+
+238
+00:19:41,850 --> 00:19:50,630
+A الـ A على اللي هي 2N بما أنه N أكبر من 2A اقسم
+
+239
+00:19:50,630 --> 00:19:56,790
+الجهتين على 2N هنا على 2N و هنا على 2N بيصير عند الـ
+
+240
+00:19:56,790 --> 00:20:07,710
+A على N .. A على N أصغر من النص، صح؟ هي a تروح
+
+241
+00:20:07,710 --> 00:20:11,090
+الاثنين مع الاثنين وهذه n مع ال n بيصير a أعليها أصغر
+
+242
+00:20:11,090 --> 00:20:16,050
+من نص يعني A على 2n أصغر من 1 على 4 قسمت الاثنين
+
+243
+00:20:16,050 --> 00:20:22,400
+عالميا على اثنين إذا لما تكون ال n أكبر من 2a هتطلع
+
+244
+00:20:22,400 --> 00:20:24,640
+عندها get بتعرف ليش هذه لأن بتلزمنا في الحسابات
+
+245
+00:20:24,640 --> 00:20:28,580
+بعد شوية هتكون اللي هي لما الاثنين a أصغر من n
+
+246
+00:20:28,580 --> 00:20:31,960
+بتكون عند A على اثنين n أصغر من مين من ربع المرة
+
+247
+00:20:31,960 --> 00:20:35,460
+اللي فاتت كان لازمنا A على n أصغر من نص وكملنا الـ
+
+248
+00:20:35,460 --> 00:20:40,650
+series اللي متذكر اللي عملنا في اللي هي الـ
+
+249
+00:20:40,650 --> 00:20:43,330
+Exponential أنا بحكيش تفاصيله و مفترض أن أنتم 
+
+250
+00:20:43,330 --> 00:20:47,570
+فاهمين حسب حكينا اللي هو في الـ Exponential الآن
+
+251
+00:20:47,570 --> 00:20:52,290
+للامات اللي أكبر من M أكبر من 2A بدي أحسب الـ CM
+
+252
+00:20:52,290 --> 00:20:59,870
+ناقص اثنين الـ SN عشان تظلها قدامكم اللي فوق هذه عندي
+
+253
+00:20:59,870 --> 00:21:06,960
+الآن الـ CM الـ C M الـ C M شايفينها؟ بتظلها ماشية
+
+254
+00:21:06,960 --> 00:21:10,940
+واحد لو ف .. الآن هذه M بدأ الـ N زاد واحد ايش
+
+255
+00:21:10,940 --> 00:21:14,880
+اسمها؟ M بتظلها ماشية واحد ناقص X أربعة على اثنين
+
+256
+00:21:14,880 --> 00:21:18,820
+فيكتوريال X أربعة على أربعة فيكتوريال والـ M أكبر من
+
+257
+00:21:18,820 --> 00:21:23,160
+الـ N هتجيه يقبل في طريقها من الـ N الـ N بيصير
+
+258
+00:21:23,160 --> 00:21:27,540
+الـ N طبعا ايه شمالها؟ الـ N عبارة عن في جبل الـ
+
+259
+00:21:27,540 --> 00:21:33,590
+term هذا اللي هو الـ N ناقص واحد اه فبيصير زائد اللي
+
+260
+00:21:33,590 --> 00:21:39,350
+هو ناقص واحد أس N ناقص واحد في X أس اثنين M ناقص
+
+261
+00:21:39,350 --> 00:21:44,050
+اثنين على اثنين M ناقص اثنين الكل factorial و
+
+262
+00:21:44,050 --> 00:21:48,390
+بتكمل هذا و بتبقى مكمل ايه أنت لما اتصل لعند X أس
+
+263
+00:21:48,390 --> 00:21:54,670
+اثنين M ناقص اثنين لأن هذا لـ M مش لـ N زائد
+
+264
+00:21:54,670 --> 00:21:59,730
+واحد على اثنين M ناقص اثنين الكل شمالها factorial
+
+265
+00:22:00,420 --> 00:22:08,320
+لما تطرح ال CM نقص ال CN اللي هو لها بيصير المتبقي
+
+266
+00:22:08,320 --> 00:22:12,600
+هيه زي ما عملنا بالظبط قبل هيك فبيصير ال CM نقص الـ
+
+267
+00:22:12,600 --> 00:22:18,080
+CN بتساوي الناقص واحد طبعا في absolute value عند X 2N
+
+268
+00:22:18,080 --> 00:22:21,200
+عشان هيك طيرنا مش فارقة كتير نقص و سالب أخذنا له
+
+269
+00:22:21,200 --> 00:22:25,900
+absolute value مش هتفرج معنا ال X 2N على 2N
+
+270
+00:22:25,900 --> 00:22:32,490
+vectorial ناقص X أس 2 M زائد 2 اللي بعيدها على 2 M
+
+271
+00:22:32,490 --> 00:22:35,990
+زائد 2 كله factorial لما أصل لآخر term اللي هو X
+
+272
+00:22:35,990 --> 00:22:41,170
+أس 2 M ناقص 2 على 2 M ناقص 2 كله factorial هذا
+
+273
+00:22:41,170 --> 00:22:46,670
+الآن هذا نفسه أخذنا احنا ال absolute value لـ X
+
+274
+00:22:46,670 --> 00:22:50,350
+أصغر من A في هذه الفترة احنا شغالين في الفترة الـ
+
+275
+00:22:50,350 --> 00:22:54,430
+absolute value X أصغر من A الآن بيصير عند الـ X
+
+276
+00:22:54,430 --> 00:23:05,180
+نفسها أس 2n أصغر أو يساوي هذه اللي هي a أس 2n على
+
+277
+00:23:05,180 --> 00:23:09,240
+2n الكل factorial الأولى زائد استخدمت triangle
+
+278
+00:23:09,240 --> 00:23:13,440
+inequality هذه زائد هذه زائد هذه زائد هذه الآن
+
+279
+00:23:13,440 --> 00:23:18,240
+زائد اللي بعيدها لما أصل لآخر واحدة x أو اللي جاب
+
+280
+00:23:18,240 --> 00:23:23,420
+اللي خليني أكتبها عشان x اللي هي بيصير a أس اثنين n 
+
+281
+00:23:23,420 --> 00:23:28,060
+زائد اثنين على اثنين إن زائد اثنين لكل factorial
+
+282
+00:23:28,060 --> 00:23:37,020
+زائد لما أصل لآخر term عندي هنا لما أصل لآخر term
+
+283
+00:23:37,020 --> 00:23:43,160
+اللي هو زائد
+
+284
+00:23:43,160 --> 00:23:57,230
+هذا ال term اللي هو زائد A 2M-2 2M-2 كل A شماله
+
+285
+00:23:57,230 --> 00:24:03,930
+فكتوريا خلّيني أخد هذا A 2N 2N كل فكتوريا العام
+
+286
+00:24:03,930 --> 00:24:11,460
+المشترك، بظل عندي 1 زائد a تربيع لأنه بيصير a يساوي 2
+
+287
+00:24:11,460 --> 00:24:17,960
+a تربيع على مين؟ على 2n زائد 2، أكيد ال 1 على 2n
+
+288
+00:24:17,960 --> 00:24:23,280
+زائد 2 أصغر من 1 على 2n لأنه 2n أصغر من هذه
+
+289
+00:24:23,280 --> 00:24:27,240
+فمقلوبها بيصير أكبر، ماشي، وبضل زي ما عملته المرة
+
+290
+00:24:27,240 --> 00:24:32,700
+اللي فاتت، أسحب منه A أس 2 على N، وفي الآخر أستبدل
+
+291
+00:24:32,700 --> 00:24:37,680
+اللي هو 2N هذه عن الرقم اللي أكبر منه N، فبيصير هي
+
+292
+00:24:37,680 --> 00:24:41,400
+مقلوبها أكبر، فبتضلها اللي هي ال inequality زي هيك
+
+293
+00:24:41,400 --> 00:24:45,840
+وبكون سحبت 2 من هذه، بيصير 2 ام نقص 2، ام نقص ايش؟
+
+294
+00:24:45,840 --> 00:24:53,350
+نقص 2، وصلنا لعند ال inequality هذه الآن، احنا قلنا a
+
+295
+00:24:53,350 --> 00:24:58,950
+على 2n أصغر من مين؟ من ربعه، يعني بيصير هذا المقدار
+
+296
+00:24:58,950 --> 00:25:05,310
+كله أصغر أو يساوي a أس 2n على 2n لكل factorial
+
+297
+00:25:05,310 --> 00:25:09,550
+مضروب في مين؟ أصغر أو يساوي، لأن الربع أكبر منهم بس
+
+298
+00:25:09,550 --> 00:25:14,930
+تبدأ كل واحد وقت ما كانوا إياه ربع، واحد زاد واحد
+
+299
+00:25:14,930 --> 00:25:23,510
+على أربعة تربيع، زائد لما أصل لآخر واحد a اللي هو
+
+300
+00:25:23,510 --> 00:25:31,370
+عبارة عن واحد على أربعة الكل أس اثنين ام ناقص
+
+301
+00:25:31,370 --> 00:25:36,590
+اثنين ام ناقص ايش؟ اثنين، هذه الآن الـ الـ الـ الـ
+
+302
+00:25:36,590 --> 00:25:39,710
+finite geometric series أصغر أو يساوي ال infinite
+
+303
+00:25:39,710 --> 00:25:45,770
+اللي هي a أس اثنين ان على اثنين ان لكل factorial
+
+304
+00:25:45,770 --> 00:25:53,570
+في اللي هو الـ summation ده، واحد زائد ربع تربيع
+
+305
+00:25:53,570 --> 00:26:00,310
+زائد ربع تكعيب، زائد لما أصل ربع أس أربعة، زائد إلى
+
+306
+00:26:00,310 --> 00:26:05,070
+ما لا نهاية، هذه الآن أساسها جداش وكأنه أساسها كل
+
+307
+00:26:05,070 --> 00:26:11,750
+مرة بتمّد واحد على ستة عشر، فبتصير هذه المجموحة اللي
+
+308
+00:26:11,750 --> 00:26:16,470
+هي واحد، مجموحة بتعرفوها، واحد ناقص واحد على ستة عشر
+
+309
+00:26:17,250 --> 00:26:21,750
+Passive واحد على واحد ناقص واحد على ستة عشر، ويساوي
+
+310
+00:26:21,750 --> 00:26:27,810
+جداش خمسة عشر أو ستة عشر على خمسة عشر، لأن هذه واحد
+
+311
+00:26:27,810 --> 00:26:29,870
+ناقص واحد على ستة عشر، تطلع خمسة عشر على ستة عشر
+
+312
+00:26:29,870 --> 00:26:34,830
+مقلوبة، بيصير ستة عشر على خمسة عشر، المفهوم المقصود هو
+
+313
+00:26:34,830 --> 00:26:38,670
+باسمها Geometric Series، بضل بقول هذه أصغر أو يساوي
+
+314
+00:26:38,670 --> 00:26:41,930
+الصمّاشن إلى ما له نهاية، وبزبدل هذا باللي أكبر
+
+315
+00:26:41,930 --> 00:26:46,070
+منها، فبتظل هذه أكبر، الآن مجموحها بيصير عبارة عن 16
+
+316
+00:26:46,070 --> 00:26:51,010
+في المقدار هذا اللي بدّله موخود عام المشترك، فبيصير
+
+317
+00:26:51,010 --> 00:26:58,940
+عندي الآن يا جماعة اللي هو ال CM نقص الـCN زي ما
+
+318
+00:26:58,940 --> 00:27:04,460
+حكينا قبل ذلك بالظبط، أصغر من هذا المقدار اللي هذا
+
+319
+00:27:04,460 --> 00:27:09,000
+limit، و اين بيروح as N goes to infinity بيروح لـ 0
+
+320
+00:27:09,000 --> 00:27:13,760
+إذا بيصير هذا المقدار زي ما قلنا المرة الماضية، CM
+
+321
+00:27:13,760 --> 00:27:20,800
+of X نقص CN of X، اللي هو أصغر أو يساوي Y for very
+
+322
+00:27:20,800 --> 00:27:28,700
+large M and N، M and N، لأنه لما تكبر M كثير، N كثير
+
+323
+00:27:28,700 --> 00:27:33,100
+تروح لنا لنهاية، لأنه limit بروح لها صفر as N goes
+
+324
+00:27:33,100 --> 00:27:37,080
+to infinity، ال M برضه بتكبر، إذا for very large M
+
+325
+00:27:37,080 --> 00:27:40,800
+هيكون هذا أصغر أو يساوي إبسلون لأي إبسلون في
+
+326
+00:27:40,800 --> 00:27:44,480
+الدنيا، لأنه هذا بيقدي للصفر فبيصير صغير صغير صغير
+
+327
+00:27:44,480 --> 00:27:48,720
+صغير لدرجة إنه مضروب في هذا يكون أصغر من إبسلون
+
+328
+00:27:48,720 --> 00:27:53,360
+وهذه اللي قلنا عنها اللي هي الـ Cauchy criterion
+
+329
+00:27:53,360 --> 00:28:00,040
+for uniform continuity، هذا الكلام كله لمين؟ صحيح
+
+330
+00:28:00,040 --> 00:28:06,880
+لأي X، وين؟ على الفترة اللي هو absolute value X أصغر
+
+331
+00:28:06,880 --> 00:28:11,220
+أو يساوي A، يعني على الفترة المولّقة من ناقص A لعند
+
+332
+00:28:11,220 --> 00:28:19,110
+A، وهذا بيعطيني أن الـ is uniformly continuous على
+
+333
+00:28:19,110 --> 00:28:24,150
+الفترة من ناقص A لعند A، is as if is uniformly is
+
+334
+00:28:24,150 --> 00:28:28,330
+uniformly convergence على الفترة من ناقص A لـ A، يعني
+
+335
+00:28:28,330 --> 00:28:35,790
+بمعنى آخر، صارت عندي ال sequence هذه اللي هي CNN
+
+336
+00:28:35,790 --> 00:28:43,150
+converges uniformly to some function عالمياً على
+
+337
+00:28:43,150 --> 00:28:50,730
+الفترة من ناقص a لعند مين؟ لعند a، الآن، طب ما هو اللي
+
+338
+00:28:50,730 --> 00:28:53,930
+عملناه أنا على الفترة هذه نقدر نعمله على أي شيء
+
+339
+00:28:53,930 --> 00:28:58,310
+ثاني، يعني بمعنى آخر لو جيت أخدت x element in R
+
+340
+00:28:58,310 --> 00:29:04,400
+هلاقي number a بحيث أن هذا ال number a هي ال x في
+
+341
+00:29:04,400 --> 00:29:10,180
+ال R، بقدر ألاقي a بحيث أن ناقص a و a تكون ال x في
+
+342
+00:29:10,180 --> 00:29:15,340
+الفترة بين ناقص a و a، يعني بمعنى آخر هعمل نفس اللي
+
+343
+00:29:15,340 --> 00:29:18,100
+عملته في الأول وهحصر على c أن uniformly
+
+344
+00:29:18,100 --> 00:29:23,030
+convergence على هذه الفترة، يعني بمعنى آخر الآن صار
+
+345
+00:29:23,030 --> 00:29:29,450
+عندي limit cn of x for any x exist، بدي أسميها هذه
+
+346
+00:29:29,450 --> 00:29:35,190
+limit c of x، وبناء عليه بدي أعرف الآن in
+
+347
+00:29:35,190 --> 00:29:38,710
+particular، this means that cn of x converge for
+
+348
+00:29:38,710 --> 00:29:42,710
+each x element in R، we define c من R لـR by c of x
+
+349
+00:29:42,710 --> 00:29:45,650
+بساواية limit cn of x for x element in R
+
+350
+00:29:53,570 --> 00:29:59,630
+الآن، بما أنه الآن الـCn مرتبط بشكل مرتبط لـC زي ما
+
+351
+00:29:59,630 --> 00:30:04,690
+قلنا أو الـCn of X كلهم مرتبط حسب اللي هو
+
+352
+00:30:04,690 --> 00:30:08,030
+النظرية في الـpointwise، الـuniform convergence
+
+353
+00:30:08,030 --> 00:30:12,360
+اللي هو the limit، the uniform، limit أو الـ
+
+354
+00:30:12,360 --> 00:30:15,220
+uniform convergence of a sequence of continuous
+
+355
+00:30:15,220 --> 00:30:18,480
+functions، مصمّد كونتنوياس، الـ limit تبعتها يعني
+
+356
+00:30:18,480 --> 00:30:21,160
+هتطلع عندي C of X continuous، مثلًا C of X
+
+357
+00:30:21,160 --> 00:30:25,000
+continuous، إذا عندي اللي هو صار عندي الـ
+
+358
+00:30:25,000 --> 00:30:28,160
+function هذه continuous اللي هي الـ C اللي احنا
+
+359
+00:30:28,160 --> 00:30:33,730
+بدنا إياها، ومش هيك، و limitCn of 0 as n goes to
+
+360
+00:30:33,730 --> 00:30:37,270
+infinity بساوي limit اللي هي Cn of 0 ايش بتساوي؟
+
+361
+00:30:37,270 --> 00:30:41,910
+واحد، وهي ساوية واحد اللي هي عبارة عن مين؟ الـC of
+
+362
+00:30:41,910 --> 00:30:47,370
+ايش؟ of 0، لأن احنا متّفقين الـC of X بساوي limit Cn
+
+363
+00:30:47,370 --> 00:30:51,310
+of X، و in particular for X بتساوي صفر، بساوي limit
+
+364
+00:30:51,310 --> 00:30:55,430
+Cn of 0 بساوي C of 0، وCn of 0 كلها واحد أيضاً،
+
+365
+00:30:55,430 --> 00:30:57,730
+limit الواحد اللي هو بساوي واحد، يعني الـC of 0
+
+366
+00:30:57,730 --> 00:31:05,970
+ايش هتساوي؟ هتساوي واحد، خصّلت كمان شغلة، إنه حصلت
+
+367
+00:31:05,970 --> 00:31:10,070
+عندي أن الـ c of zero بيساوي واحد
+
+368
+00:31:13,750 --> 00:31:19,670
+لأ اللي هو الـS، الـCN بعمل شيء مشابه له لمين؟ للـSN
+
+369
+00:31:19,670 --> 00:31:25,250
+عشان نثبت الآن اللي أثبتناه إنه صار في عندي ده
+
+370
+00:31:25,250 --> 00:31:31,730
+اللي عرفناها اسمها الـC of X اللي عبارة عن limit
+
+371
+00:31:31,730 --> 00:31:38,970
+CN of X، حيث الـC من R إلى R، طيب
+
+372
+00:31:41,560 --> 00:31:45,380
+الآن نأخذ أيضاً ال absolute value X أصغر من مين؟ من
+
+373
+00:31:45,380 --> 00:31:49,960
+أيه، وال M أكبر أو يساوي N، وأصغر من مين؟ من اثنين
+
+374
+00:31:49,960 --> 00:32:00,360
+أيه، الآن نحسب ل SM ناقص SN، SM أيه قيمتها؟ DT من صفر
+
+375
+00:32:00,360 --> 00:32:05,400
+الاندكس، SN، وهي SM
+
+376
+00:32:05,400 --> 00:32:11,240
+ناقص هذه، هي قيمتها، إذا صار هذه ناقص هذه هي قيمتها
+
+377
+00:32:11,240 --> 00:32:19,680
+الآن هذه سهل إثباتها أنها تتعامل ال absolute value
+
+378
+00:32:19,680 --> 00:32:24,200
+لهذه أصغر أو يساوي الـ absolute value لهذه أصغر أو
+
+379
+00:32:24,200 --> 00:32:27,700
+يساوي ال integration من 0 ل X ل absolute value CM
+
+380
+00:32:27,700 --> 00:32:35,600
+of T نقص CN of T شماله DT، ماشي الحال، أو بنكمل
+
+381
+00:32:35,600 --> 00:32:39,580
+اللي هو بنستخدم هذه الخاصية اللي هو بيكون أصغر أو
+
+382
+00:32:39,580 --> 00:32:42,820
+يساوي من الحسابات اللي حسبناها قبل شوية هذا
+
+383
+00:32:42,820 --> 00:32:45,380
+حسبناها أصغر من مين؟ الحسابات اللي قبل شوية، أصغر أو
+
+384
+00:32:45,380 --> 00:32:52,510
+يساوي A أس 2N على 2N الكل factorial، مضروبة في اللي
+
+385
+00:32:52,510 --> 00:32:58,130
+هو ستة عشر على مين؟ على خمسة، في ال integration من
+
+386
+00:32:58,130 --> 00:33:02,750
+صفر لل X ل DT، هذا ال integration ايش بيساوي؟ بيساوي
+
+387
+00:33:02,750 --> 00:33:08,230
+X، ماشي، وال X عندي احنا ماخدينها أصغر أو يساوي مين؟
+
+388
+00:33:08,230 --> 00:33:13,010
+أيه، أصغر أو يساوي أيه، فبيصير عندي هذا المقدار بيكون
+
+389
+00:33:13,680 --> 00:33:18,020
+لما نبعد مكانه بيطلع X قيمته أصغر أو يساوي A
+
+390
+00:33:18,020 --> 00:33:22,040
+فبيصير هذا مضروب في مين؟ في أيه اللي هو هاي المقدار
+
+391
+00:33:22,040 --> 00:33:26,680
+وهي 16 على 5، وهي ايش؟ ال A، صار هذا أصغر أو يساوي
+
+392
+00:33:26,680 --> 00:33:31,600
+هذا المقدار نفس ما عملنا قبل بشوية، الآن as N goes
+
+393
+00:33:31,600 --> 00:33:36,690
+to infinity هذه قيمتها بيساوي 0، إذا هذا المقدار for
+
+394
+00:33:36,690 --> 00:33:41,470
+very large M و N هيكون أصغر أو يساوي Y، وبالكوشي
+
+395
+00:33:41,470 --> 00:33:45,350
+criterion بيصير عندي اللي هي ال S N converges
+
+396
+00:33:45,350 --> 00:33:49,470
+uniformly، والآن على الفترة ناقص A و A، وال A كانت
+
+397
+00:33:49,470 --> 00:33:53,730
+arbitrary، إذا S من R لـ R بنقدر نعرفها بحيث إنه
+
+398
+00:33:53,730 --> 00:33:57,880
+limit S N of X اللي صارت موجودة على هذه، وبناء على
+
+399
+00:33:57,880 --> 00:34:00,460
+الـ A-arbitrary صارت موجودة على كل الـ R زي ما
+
+400
+00:34:00,460 --> 00:34:04,340
+قلنا، كيف هذا الكلام؟ بسمّي limit S N of X اليمين S
+
+401
+00:34:04,340 --> 00:34:08,980
+of X، وهذه اللي هي ال function الثانية، بنفس الأسلوب
+
+402
+00:34:08,980 --> 00:34:13,380
+وبنفس اللي هو المنطق، وبنفس الأسباب، بما أن ال S N
+
+403
+00:34:13,380 --> 00:34:16,860
+converges uniformly to S، وS N continuous، إذا حدّ
+
+404
+00:34:16,860 --> 00:34:22,340
+طلع ال S برضه نفس شماله continuous، وأيضًا limit
+
+405
+00:34:22,340 --> 00:34:28,540
+of S of 0 هو عبارة عن S of 0، وبما أن S of 0 دائمًا
+
+406
+00:34:28,540 --> 00:34:31,640
+0، إذًا limitها سيكون as N goes to infinity 0، يعني
+
+407
+00:34:31,640 --> 00:34:35,300
+ستظهر لدي S of 0 ايش؟ بساوي 0، إذًا الآن طلعنا
+
+408
+00:34:35,300 --> 00:34:45,840
+كمان شغلة أثبتناها، أن S of 0 بساوي 0، و C of 0 بساوي
+
+409
+00:34:45,840 --> 00:34:54,400
+1، وعرفنا هذولة الدالتين اسمها S و اسمها C اللي هي من R لعند
+
+410
+00:34:54,400 --> 00:34:59,680
+مين؟ لعند R، إذن الآن احنا الدالتين اللي أثبتنا لوجودهما الآن، اللي بحكي عنهم هذولة الدالتين، اللي هي
+
+411
+00:35:05,430 --> 00:35:10,190
+الدالة الأولى سمّيتها S، الثانية C، ولاقيت إنه C of
+
+412
+00:35:10,190 --> 00:35:15,790
+0 بساوي واحد، و S of 0 بساوي 0، وظلّ أثبت هذه وأثبت
+
+413
+00:35:15,790 --> 00:35:22,910
+هذه وأثبت هذولة اللي أستبعتنا بتحققهم، فخلينا نشوف
+
+414
+00:35:22,910 --> 00:35:29,670
+كيف نثبتها، طيب الآن أوصلنا لعند اللي هو المنطقة
+
+415
+00:35:29,670 --> 00:35:39,670
+هذه، لأن احنا اتّفقنا على ما يلي، اتّفقنا أن الـ S N
+
+416
+00:35:39,670 --> 00:35:47,170
+تتعامل بشكل عام لتعمل S، والـ C N تتعامل بشكل عام
+
+417
+00:35:47,170 --> 00:35:54,280
+لتعمل C، لكن الآن احنا أثبتنا في الأول هي إن ما
+
+418
+00:35:54,280 --> 00:36:00,880
+محتاجش ال S N برايم بساوي ال C N، مظبوط؟ يعني وكأنه
+
+419
+00:36:00,880 --> 00:36:04,860
+بناء على هذا مزام ال S N برايم بساوي ال C N، فبيصير 
+
+421
+00:36:04,860 --> 00:36:09,520
+الـ S N برايم، هذه، مكانها دي S N برايم بصير الـ S N
+
+422
+00:36:09,520 --> 00:36:15,340
+برايم converges uniformly to some function mean C
+
+423
+00:36:15,340 --> 00:36:22,060
+الآن بما أن الـ S N برايم converges uniformly to C الآن
+
+424
+00:36:22,060 --> 00:36:28,900
+والـ S N converged to S uniformly برضه حسب نظرية
+
+425
+00:36:28,900 --> 00:36:32,360
+بتطلع عندي بما أن الـ s n prime differentiable هتكون
+
+426
+00:36:32,360 --> 00:36:37,140
+الـ limit هـ differentiable والـ c prime اللي هي الـ
+
+427
+00:36:37,140 --> 00:36:42,340
+s prime هذه هي مين الـ c اللي طلعت هنا يعني الـ s n 
+
+428
+00:36:42,340 --> 00:36:45,960
+prime differentiable أو الـ s n differentiable و
+
+429
+00:36:45,960 --> 00:36:48,560
+converges to some function إذا بتتذكر كنا نسميها g
+
+430
+00:36:48,560 --> 00:36:52,520
+وهذه كنا نسميها f فكنا نقول بما أن الـ s n بتروح للـ f
+
+431
+00:36:52,520 --> 00:36:56,740
+والـ s n prime بتروح للـ g إذا نتيجة النظرية هتكون
+
+432
+00:36:56,740 --> 00:37:00,000
+اللي هي الـ F هي الـ Differentiable والـ Derivative
+
+433
+00:37:00,000 --> 00:37:04,940
+لها إيش بتطلع؟ D يعني الـ Derivative للـ S' إيش
+
+434
+00:37:04,940 --> 00:37:12,260
+هتطلع عبارة عن مين؟ C' آسف C هتطلع مين؟ اللي هي الـ
+
+435
+00:37:12,260 --> 00:37:21,000
+C إذا أثبتت أنا الآن الـ S' of X بتساوي الـ C of X هذه
+
+436
+00:37:21,000 --> 00:37:28,190
+اللي أثبتته هنا الآن من جهة أخرى من جهة أخرى إحنا
+
+437
+00:37:28,190 --> 00:37:35,850
+أثبتنا اللي هي قبل هيك أن الـ C N برايم بسوء ناقص الـ S N
+
+438
+00:37:35,850 --> 00:37:42,450
+ناقص واحد الـ C N برايم بسوء ناقص الـ S N of واحد يعني
+
+439
+00:37:42,450 --> 00:37:47,790
+بمعنى آخر الـ C N برايم of X أثبتنا بسوء ناقص الـ S N
+
+440
+00:37:47,790 --> 00:37:54,640
+ناقص واحد of X الآن بما أن الـ S N converted زي الـ S
+
+441
+00:37:54,640 --> 00:38:00,260
+خلصنا هذه اه خلصنا هذه المنطقة خليني أشرح بلغة
+
+442
+00:38:00,260 --> 00:38:05,060
+ثانية عشان أميز بين الكلامين عندي الآن انتبهوا
+
+443
+00:38:05,060 --> 00:38:08,860
+بتعمل نفسي إشي بس بالنسبة لمن الآن بالنسبة عشان
+
+444
+00:38:08,860 --> 00:38:13,780
+أجيب الـ derivative للـ S للـ C prime عندي الآن الـ C N
+
+445
+00:38:13,780 --> 00:38:19,740
+prime of X بسوء نقص الـ S N نقص واحد of X بما أن الـ S N
+
+446
+00:38:19,740 --> 00:38:23,500
+راحت للـ S إذا اللي هي الـ derivative هي اللي
+
+447
+00:38:23,500 --> 00:38:30,280
+بتساويها اللي هي الـ C N زائد واحد prime of X هتروح
+
+448
+00:38:30,280 --> 00:38:36,770
+لمين؟ اللي هي مش هي ناقصها لأن الـ S N ناقص واحد اللي
+
+449
+00:38:36,770 --> 00:38:40,730
+هي بتساوي ناقص هذه أنجل ناقصها بعد إذنكم يعني بدي
+
+450
+00:38:40,730 --> 00:38:44,810
+أستبدل الـ S N بمين؟ بقيمتها هذه صارت ناقص الـ C N
+
+451
+00:38:44,810 --> 00:38:50,330
+prime of X إيش بتساوي؟ بتروح للـ S أو بمعنى آخر صار
+
+452
+00:38:50,330 --> 00:38:56,620
+عندي من هنا من هنا اللي بتطلع عندي هنا صار عندي
+
+453
+00:38:56,620 --> 00:39:03,640
+الآن من هنا اللي هو الـ c n زائد واحد prime of x بتروح
+
+454
+00:39:03,640 --> 00:39:08,080
+لناقص طبعا uniformly بتروح لمين؟ ناقص الـ s لأنه ناقصها
+
+455
+00:39:08,080 --> 00:39:13,040
+بتروح للـ s إذا هي بتروح لناقص الـ s وفي نفس الوقت
+
+456
+00:39:13,040 --> 00:39:19,840
+أنا بقول الـ C N نفسها بتروح uniform لمين؟ للـ C بنفس
+
+457
+00:39:19,840 --> 00:39:24,740
+الإسلوب اللي قبل بشوية اللي هي بما أنه هذه اللي هي
+
+458
+00:39:24,740 --> 00:39:27,580
+differentiable sequence of functions و converge
+
+459
+00:39:27,580 --> 00:39:31,260
+uniform to some function إذا هذه هتكون اللي هي
+
+460
+00:39:31,260 --> 00:39:35,600
+عبارة عن اللي هي الـ C الأصلية differentiable والـ
+
+461
+00:39:35,600 --> 00:39:40,070
+derivative فيها لها مين؟ ناقص الـ S فبصير عندي الـ C'
+
+462
+00:39:40,530 --> 00:39:45,970
+of X بسوء ناقص S of X بكون هذه اللي هي النتيجة
+
+463
+00:39:45,970 --> 00:39:50,330
+الثانية اللي طبقنا عليها طلعت عندي اللي هو هذه
+
+464
+00:39:50,330 --> 00:39:54,050
+الخاصية وهذه الخاصية متحققة يعني الآن صار عندي
+
+465
+00:39:54,050 --> 00:40:02,590
+اللي هو تحقق ما يليه أنه تبعتنا هذه الـ C' of X
+
+466
+00:40:02,590 --> 00:40:08,530
+بيساوي ناقص S of X وطلع عندي اللي هي S prime of X
+
+467
+00:40:08,530 --> 00:40:16,290
+بيساوي C of X ماشي الحال بيكون هيك إحنا ضال علينا
+
+468
+00:40:16,290 --> 00:40:21,230
+شغل أخرى لحاول نثبتها بيكون أثبتنا اللي هو كل
+
+469
+00:40:21,230 --> 00:40:27,630
+الصفات المطلوبة اللي تتحقق في الـ S وحددت هوية الـ S
+
+470
+00:40:27,630 --> 00:40:28,050
+والـ C
+
+471
+00:40:38,700 --> 00:40:48,060
+الجزء الثاني سهل فضل الـ c w prime of x
+
+472
+00:41:00,590 --> 00:41:05,470
+بتصير c double prime هيها وهذه فضلها بنفعلها
+
+473
+00:41:05,470 --> 00:41:09,550
+لأنها قبل التفاضل اللي فضلناها وبتصير ناقص اللي هي
+
+474
+00:41:09,550 --> 00:41:15,030
+s prime of x اللي هي s prime of x إيش بتساوي؟ c of 
+
+475
+00:41:15,030 --> 00:41:20,350
+x فبصير ناقص مين؟ c of x والآن S W' of X من أين بدي
+
+476
+00:41:20,350 --> 00:41:23,650
+أجيبها؟ من هنا S W' بيساوي اللي هو هذه الـ
+
+477
+00:41:23,650 --> 00:41:26,050
+derivative اللي هي الـ derivative اللي هي عبارة عن
+
+478
+00:41:26,050 --> 00:41:31,530
+ناقص S of X فبصير عبارة عن ناقص S of X فبصير عندي
+
+479
+00:41:31,530 --> 00:41:38,910
+هذا برضه إيش تحقق؟ آخر إشي اللي هي C' of Zero C' of
+
+480
+00:41:38,910 --> 00:41:42,410
+Zero بيساوي ناقص S of Zero و S of Zero بيساوي صفر
+
+481
+00:41:42,410 --> 00:41:47,030
+إذا C' of Zero بيساوي Zero الـ S' of Zero
+
+482
+00:41:52,540 --> 00:41:56,800
+وهكذا أثبتنا وجود دالة
+
+483
+00:41:59,570 --> 00:42:04,970
+اللي هي حققت لي اللي هي الشرط الأول هذا والدالتين
+
+484
+00:42:04,970 --> 00:42:09,710
+آسف والشرط الثاني اه اللي بعده هذه بتكون أثبتنا
+
+485
+00:42:09,710 --> 00:42:15,290
+وجود الـ C والـ S لأن بعض النتائج الأخرى على اللي هي
+
+486
+00:42:15,290 --> 00:42:18,830
+الدالتين
+
+487
+00:42:18,830 --> 00:42:19,790
+اللي أوجدناهم
+
+488
+00:42:24,500 --> 00:42:28,960
+نشوف إيش الـ Corollary الأولى بقول لي if C and S
+
+489
+00:42:28,960 --> 00:42:33,680
+are the functions in 3x, 8x, 4x, 1 then C' of X
+
+490
+00:42:33,680 --> 00:42:39,560
+بيساوي نقص S of X أثبتناها هيها and طبعا في طريقنا
+
+491
+00:42:39,560 --> 00:42:44,020
+في البرهان S' of X بيساوي C of X هيها اللي هي خواص
+
+492
+00:42:44,020 --> 00:42:50,340
+اللي هي أثبتناها طيب الآن بقول لي moreover these
+
+493
+00:42:50,340 --> 00:42:54,630
+functions have derivatives of all order يعني بأي
+
+494
+00:42:54,630 --> 00:42:57,710
+order الـ derivative موجودة طبعا هذا by induction
+
+495
+00:42:57,710 --> 00:43:01,550
+by induction اللي هو بدك تثبت إنه اللي هو اللي هو
+
+496
+00:43:01,550 --> 00:43:06,670
+C N هتكون موجودة وبيساوي ناقص a of x أو زائد a of x
+
+497
+00:43:06,670 --> 00:43:11,450
+حسب اللي هي جداش درجة الـ n وممكن تساوي C of x أو
+
+498
+00:43:11,450 --> 00:43:16,930
+اللي هي ناقص C of x حسب درجة الـ n اللي موجودة إذا
+
+499
+00:43:16,930 --> 00:43:19,990
+الآن هذه by induction بنقدر نثبت إن الـ derivative
+
+500
+00:43:19,990 --> 00:43:26,390
+اللي هو موجودة for any order بناء على اللي حكيناه
+
+501
+00:43:26,390 --> 00:43:32,300
+نيجي الآن لـ Corollary اللي بعدها بقول الآن الـ
+
+502
+00:43:32,300 --> 00:43:38,280
+function C and S بحقق اللي هي الـ Pythagorean
+
+503
+00:43:38,280 --> 00:43:42,280
+Identity اللي كنا نعرفها كـ جيب تربيع زائد جتا تربيع
+
+504
+00:43:42,280 --> 00:43:47,660
+إيش بتساوي؟ بتساوي واحد فكرة البرهان سهلة بسمي هذه
+
+505
+00:43:47,660 --> 00:43:51,520
+كلها بسميها function اسمها F of X بقول سمي هذه
+
+506
+00:43:51,520 --> 00:43:56,080
+اللي هي F of X بتساوي هذه فضليها بلا بتفضليها F
+
+507
+00:43:56,080 --> 00:44:01,200
+prime of X بتساوي اثنين في C of X في تفاضل اللي جوا
+
+508
+00:44:01,200 --> 00:44:06,300
+اللي هو ناقص S of X والتانية زائد اثنين في S of X
+
+509
+00:44:06,300 --> 00:44:11,880
+فتفاضلها هي C of X هذه هي هذه بس بالسالب إذا حصل
+
+510
+00:44:11,880 --> 00:44:15,100
+طرح حلو اسم يساوي صفر إذا صارت عند الـ derivative للـ
+
+511
+00:44:15,100 --> 00:44:18,320
+function هذه إسمها بتساوي صفر يعني بمعنى آخر
+
+512
+00:44:18,320 --> 00:44:22,490
+الدالة هي دالة ثابتة يعني F is a constant function
+
+513
+00:44:22,490 --> 00:44:27,210
+يعني قيمة الـ F عند أي قيمة إيش بتساوي؟ مقدار ثابت
+
+514
+00:44:27,210 --> 00:44:31,310
+إذا اتفاجأ أنها ثابتة أسهل إشي أسهل إشي أوجد لي F of
+
+515
+00:44:31,310 --> 00:44:34,670
+Zero عشان أتعرف إيش هذه اللي بتساوي بالضبط C of
+
+516
+00:44:34,670 --> 00:44:38,730
+Zero واحد S of Zero صفر إذا صار عندي F of Zero
+
+517
+00:44:38,730 --> 00:44:42,170
+بتساوي واحد وهي ثابتة إذا صارت F of X دائما
+
+518
+00:44:42,170 --> 00:44:46,270
+بتساوي واحد يعني هذا المقدار بتساوي واحد دائما
+
+519
+00:44:46,270 --> 00:44:48,690
+طيب نيجي الآن
+
+520
+00:44:51,700 --> 00:44:57,820
+لأ الـ theorem اللي بعدها الـ functions C and S
+
+521
+00:44:57,820 --> 00:45:02,820
+satisfy the properties I and II of theorem 8-4-1
+
+522
+00:45:02,820 --> 00:45:07,020
+are unique لما بقول لي برضه هتلاقي الـ uniqueness
+
+523
+00:45:07,020 --> 00:45:13,020
+بشبه الـ uniqueness لمن؟ لأ اللي هو الـ .. الـ ..
+
+524
+00:45:13,020 --> 00:45:18,030
+قولوا معايا الـ uniqueness للـ exponential وسمناها
+
+525
+00:45:18,030 --> 00:45:21,170
+اللي هو let E واحد .. نفترض أنه في E واحد و E
+
+526
+00:45:21,170 --> 00:45:24,070
+اثنين وسمها فرق بيساوي D وفي الآخر روحنا لفرق
+
+527
+00:45:24,070 --> 00:45:28,390
+بيساوي إيش؟ بيساوي صفر هنا نفس الإشي هنشتغل وبرضه
+
+528
+00:45:28,390 --> 00:45:31,590
+هنستخدم اللي هو الـ Taylor's theorem زي ما استخدمنا
+
+529
+00:45:31,590 --> 00:45:34,470
+هناك الـ Taylor's theorem يعني هتلاقيه الـ sketch
+
+530
+00:45:34,470 --> 00:45:37,470
+للبرهان هو نفس الـ sketch الأولاني عشان هيك
+
+531
+00:45:37,470 --> 00:45:43,110
+هتلاقوني سريع فيه بدنا نثبت أن الـ C والـ S are
+
+532
+00:45:43,110 --> 00:45:47,930
+unique functions طبعا الطريقة let c1 and c2 be two
+
+533
+00:45:47,930 --> 00:45:52,290
+functions on R that satisfy it satisfies مين الـ
+
+534
+00:45:52,290 --> 00:45:55,850
+conditions اللي إحنا بنقول عنهم اللي هي الـ I و II
+
+535
+00:45:55,850 --> 00:46:00,930
+اللي هو بحيث إنه c1 double prime of x بساوي c1 of
+
+536
+00:46:00,930 --> 00:46:01,150
+x
+
+537
+00:46:16,750 --> 00:46:18,150
+2
+
+538
+00:46:18,550 --> 00:46:24,010
+لأن نفترض أن دي بتساوي C1-C2 وبدنا نصل في النهاية
+
+539
+00:46:24,010 --> 00:46:27,410
+أن دي هذه لازم تطلع إيش بتساوي؟ بتساوي 0 مدام دي
+
+540
+00:46:27,410 --> 00:46:32,710
+بتساوي 0 مدام C1 بتساوي إيش؟ C2 لاحظ الآن D W' of
+
+541
+00:46:32,710 --> 00:46:38,190
+X فاضل هذا مرتين تصير C1W'-C2W'
+
+542
+00:46:39,860 --> 00:46:47,500
+الآن بتساوي هتطلع إيش بتساوي؟ ناقص اللي هي مين؟ D of
+
+543
+00:46:47,500 --> 00:46:59,700
+X نعملها اللي هي حسابات D of X بتساوي D of X بتساوي
+
+544
+00:46:59,700 --> 00:47:08,540
+C1 ناقص C2 D prime of X إيش هيساوي؟ اللي هو عبارة
+
+545
+00:47:08,540 --> 00:47:16,670
+عن S واحد ناقص S واحد ناقص بيصير اللي هو مين؟ الـ S
+
+546
+00:47:16,670 --> 00:47:19,810
+واحد اللي هي بالنسبة لهذه اللي أوجدناها ناقص S
+
+547
+00:47:19,810 --> 00:47:25,350
+اثنين بيصير زائد لأن دي double prime بتساوي بتفاضل
+
+548
+00:47:25,350 --> 00:47:30,030
+هذا كمان مرة اللي هي بترجع مين؟ نفسها C واحد وهذه
+
+549
+00:47:30,030 --> 00:47:38,390
+ترجع نفسها C2 التي هي ناقص D التي هي ناقص D طيب
+
+550
+00:47:38,390 --> 00:47:43,410
+إذا الـ D لأنه مفترضين الـ C1 و C2 اسمها بتحقق
+
+551
+00:47:43,410 --> 00:47:52,470
+الشروط اللي فوق اللي قلنا عنها Double prime بتساوي D
+
+552
+00:47:52,470 --> 00:48:02,390
+of X أو D double prime بتساوي D double prime بتساوي
+
+553
+00:48:06,030 --> 00:48:11,870
+بتساوي D W' ناقص D W' D W' ناقص C1 و D W' اللي
+
+554
+00:48:11,870 --> 00:48:15,870
+هي ناقص ناقص C زائدة سارة D W' بتساوي ناقص D و X
+
+555
+00:48:15,870 --> 00:48:21,890
+هيك اللي هو دعنا نقول أسلم طيب الآن بستعجل لأن
+
+556
+00:48:21,890 --> 00:48:29,470
+الكلام معاد يعني أو الأفكار معادة الآن احط لي D of 0
+
+557
+00:48:29,470 --> 00:48:34,530
+إيش هيساوي؟ Zero لأن D of 0 بيساوي هذه ناقص هذه و
+
+558
+00:48:34,530 --> 00:48:37,630
+هذه عند الـ zero واحد وهذه عند الـ zero واحد
+
+559
+00:48:37,630 --> 00:48:40,010
+الاثنتين عند الـ zero واحد انحصل طرحي إن إيش هيساوي
+
+560
+00:48:40,010 --> 00:48:47,160
+صفر الآن D prime عند الـ zero و D W' عند الـ zero و و 
+
+561
+00:48:47,160 --> 00:48:48,760
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+562
+00:48:48,760 --> 00:48:50,140
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+563
+00:48:50,140 --> 00:48:52,320
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+564
+00:48:52,320 --> 00:48:52,380
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+565
+00:48:52,380 --> 00:48:55,440
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+566
+00:48:55,440 --> 00:48:59,220
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+567
+00:48:59,220 --> 00:48:59,240
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+568
+00:48:59,240 --> 00:49:00,380
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+569
+00:49:00,380 --> 00:49:01,520
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+570
+00:49:01,520 --> 00:49:05,260
+.. و
+
+571
+00:49:05,260 --> 00:49:15,970
+.. و .. و .. و .. و .. و .. وبحكي عن الـ 
+
+572
+00:49:15,970 --> 00:49:25,410
+derivative الـ dw prime عبارة عن اللي هي ناقص d of 
+
+573
+00:49:25,410 --> 00:49:30,410
+0 عند الـ 0 و الـ d عند الـ 00 إذن هذه الـ 0 هذه
+
+574
+00:49:30,410 --> 00:49:34,330
+لمن؟ لـ k اللي هي إتنين و أربعة و ستة و تمانية
+
+575
+00:49:34,330 --> 00:49:37,870
+بنفس السبب هتطلع صفر الفرديات بيجي من مين؟ من هذه
+
+576
+00:49:38,330 --> 00:49:44,430
+فردية الـ Derivative لإيش؟ لأن D' of 0 هتساوي C1'
+
+577
+00:49:44,890 --> 00:49:51,110
+ناقص C2' C1' عند الصفر صفر و C2' عند ال 0 0 إذا هذه
+
+578
+00:49:51,110 --> 00:49:56,730
+دي K عند ال 0 بالساوية 0 لكل K سواء زوجية أو إيش
+
+579
+00:49:56,730 --> 00:50:01,230
+أو فردية إذا جهزنا هذا اللي جهزناه قبل هيك يعمل 
+
+580
+00:50:01,230 --> 00:50:05,940
+Exponential وبتنا نطبّق اللي هو مين الـ Taylor's 
+
+581
+00:50:05,940 --> 00:50:09,000
+theorem نطبّق الـ Now let x element in R be
+
+582
+00:50:09,000 --> 00:50:12,760
+arbitrary element in R and let I x be the interval
+
+583
+00:50:12,760 --> 00:50:18,940
+within point 0x طبّقنا عليها إذا since D بتساوي C1
+
+584
+00:50:18,940 --> 00:50:25,220
+ناقص C2 وT بتساوي S1 ناقص S2 اللي هي مفترضين S1
+
+585
+00:50:25,220 --> 00:50:28,400
+وS2 اللي هو two functions such that اللي بيحققوا 
+
+586
+00:50:28,400 --> 00:50:34,170
+تبعات الـ sine اللي هي بالساوية S1 ايش هي مسميها
+
+587
+00:50:34,170 --> 00:50:39,950
+أنا اللي هي بدل C2 prime أو هي C2 prime والـ S2
+
+588
+00:50:39,950 --> 00:50:46,510
+اللي هي C2 A prime العكسية
+
+589
+00:50:46,510 --> 00:50:50,530
+ال derivative بيصيح بالنقص are continuous on mean
+
+590
+00:50:50,530 --> 00:50:55,930
+on Ix عارفين continuous انه احنا مفترضين ان نحقق
+
+591
+00:50:55,930 --> 00:51:00,160
+نفس اللي هو اللي قبله مدام continuous الـ D والـ T
+
+592
+00:51:00,160 --> 00:51:07,440
+continuous على closed bounded interval I X إذا في
+
+593
+00:51:07,440 --> 00:51:12,810
+اللي هو K واحد للأولى و K2 للتانية خدوا ال maximum
+
+594
+00:51:12,810 --> 00:51:18,470
+إليها واسموها K إذا في K للجهتين بحيث ان ال D of T
+
+595
+00:51:18,470 --> 00:51:22,930
+bounded علي هذه أصغر شيء T كي على كل الفترة اللي 
+
+596
+00:51:22,930 --> 00:51:27,390
+بنحكي عنها IX وT of T أصغر شيء K for all T
+
+597
+00:51:27,390 --> 00:51:30,290
+elements of IX لأنه زي ما أقول continuous function
+
+598
+00:51:30,290 --> 00:51:33,930
+in a closed bounded interval must be bounded الآن
+
+599
+00:51:33,930 --> 00:51:39,170
+جاهزين نطبق مين؟ الـ Taylor's theorem to d من Ix
+
+600
+00:51:39,170 --> 00:51:44,970
+and use the fact دي اللي أثبتناه دي 0 سواء 0 دي K0
+
+601
+00:51:44,970 --> 00:51:50,030
+سواء 0 الآن بنقول for each n unlimited n عملناها 
+
+602
+00:51:50,030 --> 00:51:56,510
+عشان هيك بس ماشي عنه بسرعة عملناها قبل هيك there
+
+603
+00:51:56,510 --> 00:51:59,630
+exist a point Cn unlimited Ix such that هذا
+
+604
+00:51:59,630 --> 00:52:03,890
+remainder بتعملي remainderD ب X بيساوي D of 0 زي
+
+605
+00:52:03,890 --> 00:52:06,850
+دي prime of 0 زائد زائد زائد زائد X ان نقص واحد 
+
+606
+00:52:06,850 --> 00:52:12,630
+لما أصل لمين لل remainder كل هذول أصفار بسبب مين
+
+607
+00:52:12,630 --> 00:52:16,430
+انه D0 وD prime of 0 وD ان نقص واحد وزير وكلهم إيه
+
+608
+00:52:16,430 --> 00:52:20,090
+شمالهم بيساوي أصفار عند الصفر بيظل هذا المقدار
+
+609
+00:52:20,090 --> 00:52:24,010
+يساوي اللي هو المقدار اللي عندي اللي تحت هذا هذا
+
+610
+00:52:24,010 --> 00:52:27,490
+ال derivative هذا ال derivative أنا بعرفش إيش هي
+
+611
+00:52:27,490 --> 00:52:31,230
+ما أنتوا عارفين ال derivative لل .. لل .. لل C
+
+612
+00:52:34,160 --> 00:52:41,940
+أو ال derivative للـC إذا فضلت مرة واحدة بتطلع
+
+613
+00:52:41,940 --> 00:52:47,120
+الـS أو سلبها فظلت تلت مرات بترجع ليها S بس
+
+614
+00:52:47,120 --> 00:52:53,180
+بالموجة فظلت خمسة بترجع ناقص S فظلت زوجي بتطلع هي
+
+615
+00:52:53,180 --> 00:52:58,920
+نفسها أو سلبها عشان هي كادل أنا بعرفش طبعا هنا
+
+616
+00:52:58,920 --> 00:53:02,400
+عندك اللي هي بتتوزع على مرة derivative تنتين
+
+617
+00:53:02,400 --> 00:53:04,620
+derivative تلاتة derivative أربعة derivative و
+
+618
+00:53:04,620 --> 00:53:08,180
+بترجع الدورة زي ما هي لإنه في الأول بيكون اللي هي
+
+619
+00:53:08,180 --> 00:53:15,520
+تفاضل الـC ناقص S بعدها بتتفاضل بترجع اللي هي ناقص
+
+620
+00:53:15,520 --> 00:53:18,770
+حالتها بعدها بترجع اللي هي
+
+621
+00:53:18,770 --> 00:53:36,410
+ببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببب
+
+622
+00:53:36,660 --> 00:53:40,180
+اللي هي الـC ويصير ناقص C كمان مرة بترجع اللي هي 
+
+623
+00:53:40,180 --> 00:53:45,740
+الـS وكمان مرة بترجع اللي هي الـC بعد هيك بتصير
+
+624
+00:53:45,740 --> 00:53:51,920
+اللي هي تكرر نفسها يعني بمعنى آخر جربوها أنتم 
+
+625
+00:53:51,920 --> 00:53:59,920
+هتلاقوا أنه حسب الأُس هنا بتطلع اللي هي عبارة عن
+
+626
+00:53:59,920 --> 00:54:11,180
+هي أو سلبها أو الـS أو سلبها بكل الأحوال بغض النظر
+
+627
+00:54:11,180 --> 00:54:15,600
+اللي هي DN of CN هي حاصل طرح التنتين اللي هي سمنها
+
+628
+00:54:15,600 --> 00:54:23,280
+يا D يا T الـ D تبعت الـ C الفرق طبعا والـ T اللي 
+
+629
+00:54:23,280 --> 00:54:29,010
+هي الفرق بين الأسات يعني في الآخر زائد أو ناقص و زاد
+
+630
+00:54:29,010 --> 00:54:33,810
+أو ناقص سواء هذه أو سواء هذه حضرنا من الأصل انها
+
+631
+00:54:33,810 --> 00:54:38,870
+bounded و كله أصغر أو يساوي من K أصغر أو يساوي إيش
+
+632
+00:54:38,870 --> 00:54:45,860
+K بناء عليه هتطلع هذه هيك absolute value أصغر أو 
+
+633
+00:54:45,860 --> 00:54:51,780
+يساوي هذه أي إن كانت K في X أُس N absolute value 
+
+634
+00:54:51,780 --> 00:54:56,880
+على N factorial  باشي الحال إذا صلعت عندي هذا
+
+635
+00:54:56,880 --> 00:55:00,860
+المقدار أصغر أو يساوي هذا as N goes to infinity
+
+636
+00:55:00,860 --> 00:55:05,540
+هذا بروح لمن؟ للصفر وهذا independent of N بيصير
+
+637
+00:55:05,540 --> 00:55:08,100
+أكبر أو يساوي الصفر يعني هذا اللي جوا بده يصير صفر
+
+638
+00:55:08,100 --> 00:55:12,930
+إذا ال D of X هاشي بدها تساوي بتساوي صفر وبكون
+
+639
+00:55:12,930 --> 00:55:21,090
+أثبتنا ان الـ C1 والـ C2 are equivalent الآن 
+
+640
+00:55:21,090 --> 00:55:27,700
+similar arguments بنفس الأسلوب وخليها إليكم إنه 
+
+641
+00:55:27,700 --> 00:55:32,120
+اللي هي بنثبت إنه S إذا كان S1 وS2 are two
+
+642
+00:55:32,120 --> 00:55:36,320
+functions such that بيحققوا اللي هما الخواص اللي
+
+643
+00:55:36,320 --> 00:55:41,700
+بنقولها عنها في النظرية اللي هي S1 double prime
+
+644
+00:55:41,700 --> 00:55:46,400
+بيساوي نفس S1 ونفس ال S2 وهذا عند Zero بيساوي Zero
+
+645
+00:55:46,400 --> 00:55:50,160
+وهذا ال prime عند Zero بيساوي Zero هيتلعلك غصب 
+
+646
+00:55:50,160 --> 00:55:52,240
+عنها في الأخر S1 بيساوي S2
+
+647
+00:55:55,620 --> 00:55:59,960
+بس بدل ما تعملوا على ال D يعني سموا اللي هو T
+
+648
+00:55:59,960 --> 00:56:04,040
+بتساوي S1 نقص S2 وطبقوا الشروط وامشوا نفس اللي 
+
+649
+00:56:04,040 --> 00:56:07,580
+امشيناها هتلاقوا حالكم انه لازم تطلع ال S1 بيساوي
+
+650
+00:56:07,580 --> 00:56:11,800
+S2 وبناء عليه صار ال ال two functions ال C والS
+
+651
+00:56:11,800 --> 00:56:17,820
+are unique functions طيب 
+
+652
+00:56:17,820 --> 00:56:24,720
+ال answer المؤهلين نذهب بالاتجاه نثبت أن افترض أن
+
+653
+00:56:24,720 --> 00:56:27,880
+الـ Definition of the unique function C من R لR و
+
+654
+00:56:27,880 --> 00:56:32,400
+اسم الـ R لR اللي يتحقق CW prime of X بيساوية نقطة
+
+655
+00:56:32,400 --> 00:56:36,650
+C of X هو الاصل الـ differential equation الثاني S 
+
+656
+00:56:36,650 --> 00:56:40,990
+w برامج و X ناقص بيساوي ناقص S X لكل X element in R
+
+657
+00:56:40,990 --> 00:56:43,470
+و ال C of Zero اللي هو ال condition ال condition 
+
+658
+00:56:43,470 --> 00:56:46,350
+بيساوي واحد و C برامج و Zero بيساوي Zero و ال S of
+
+659
+00:56:46,350 --> 00:56:49,710
+Zero بيساوي Zero و ال S برامج و Zero بيساوي Zero
+
+660
+00:56:49,710 --> 00:56:57,150
+الدالتين اللي بحقق إن الكلام هذا اللي أثبتنا إنه 
+
+661
+00:56:57,150 --> 00:57:02,740
+unique بنسميهم respectively the cosine function and 
+
+662
+00:57:02,740 --> 00:57:07,600
+the sine function اللي أنتم بتعرفوها وهي cosine X
+
+663
+00:57:07,600 --> 00:57:12,620
+اللي بتعرفوها وهي sin X اللي أنتم بتعرفوها نيجي 
+
+664
+00:57:12,620 --> 00:57:17,930
+الآن نأخذ بعض الخواص خلينا نأخذ اللي هو الخاصية 
+
+665
+00:57:17,930 --> 00:57:23,430
+اللي هي نظرية 4.6 بتقول لي إذا كانت f من R ل R is
+
+666
+00:57:23,430 --> 00:57:27,890
+such that f double prime of x بيساوي ناقص f of x for 
+
+667
+00:57:27,890 --> 00:57:30,370
+x element in R يعني هذه ال differential equation
+
+668
+00:57:30,370 --> 00:57:32,810
+بتقول لي هذه ال differential equation هي حلولها
+
+669
+00:57:32,810 --> 00:57:37,690
+مالي then there exist Alpha و Beta Such that F of X
+
+670
+00:57:37,690 --> 00:57:41,390
+بيساوي Alpha CX زائد Beta S of X بيقول لي هذه ال
+
+671
+00:57:41,390 --> 00:57:45,110
+differential equation حالة انها عبارة عن linear أو
+
+672
+00:57:45,110 --> 00:57:47,870
+خليني أقول combination أو linear combination
+
+673
+00:57:47,870 --> 00:57:55,890
+between F C of X S of X خليني آخذ نسمي g of x إيش
+
+674
+00:57:55,890 --> 00:57:59,590
+بتساوي اللي هي عبارة عن اللي هي ال c of x و ال a
+
+675
+00:57:59,590 --> 00:58:03,770
+sub x نسمي هذه f of zero و f prime of zero for x 
+
+676
+00:58:03,770 --> 00:58:10,330
+element in R الآن لو حسبت ال gw prime of x احسبها
+
+677
+00:58:10,330 --> 00:58:15,270
+فاضل هذه 
+
+678
+00:58:15,270 --> 00:58:18,550
+مرتين هدول ثوابت طبعا و هدول اللي بتنزلك
+
+679
+00:58:18,550 --> 00:58:23,970
+هتلاقيهم اللي هو بيساوي ناقص g of x أه .. و لو حسبت 
+
+680
+00:58:23,970 --> 00:58:26,730
+الـ g of zero .. g of zero هتلاقيها بيساوي of zero
+
+681
+00:58:26,730 --> 00:58:30,110
+لإن هذا صفر وهذا .. هذا واحد وهذا صفر الآن صار
+
+682
+00:58:30,110 --> 00:58:33,850
+عندي gw prime of x بيساوي ناقص g of x و g of zero
+
+683
+00:58:33,850 --> 00:58:40,410
+بيساوي f of zero الآن احسب الـ g prime of x صار عندي
+
+684
+00:58:40,410 --> 00:58:43,450
+ثلاث معلومات معلمين جي دابل برايم of X بيساوي ناقص
+
+685
+00:58:43,450 --> 00:58:45,990
+جي of X و جي of Zero بيساوي أف of Zero خلينا نجيب
+
+686
+00:58:45,990 --> 00:58:50,330
+جي برايم of X جي برايم of X مش بتساوي فاضل اللي هي 
+
+687
+00:58:50,330 --> 00:58:55,430
+عبارة عن ناقص أس of X و هذا تفضلها اللي هي C of X
+
+688
+00:58:55,430 --> 00:58:58,830
+صار عندي اللي هي جي برايم of X بيساوي هذا الكلام
+
+689
+00:58:58,830 --> 00:59:04,720
+زائد هذا الكلام الآن احسب لي g prime of 0 هيصير
+
+690
+00:59:04,720 --> 00:59:08,420
+عبارة عن هذا طبعا صفر وهذا هتصير واحد فبصير F
+
+691
+00:59:08,420 --> 00:59:13,750
+prime of 0 صار عندي الآن g prime of 0 إيش بيساوي يا
+
+692
+00:59:13,750 --> 00:59:18,090
+جماعة؟ جي برايم اف زيرو خليني أطلعلك إياها لفوق
+
+693
+00:59:18,090 --> 00:59:21,750
+صارت جي برايم اف زيرو بيساوي أف برايم اف زيرو و جي 
+
+694
+00:59:21,750 --> 00:59:26,730
+اف زيرو بيساوي أف اف زيرو الآن بديش ناشر نعيد اللي
+
+695
+00:59:26,730 --> 00:59:30,950
+هو therefore الآن the functions h بتساوي f ناقص g
+
+696
+00:59:30,950 --> 00:59:35,990
+is such that يعني عرف لي function h أيش بيساوي؟ f
+
+697
+00:59:35,990 --> 00:59:43,220
+ناقص مين ناقص g الآن الـ H double prime لها لو جيت 
+
+698
+00:59:43,220 --> 00:59:46,840
+حسبت الـ H double prime اللي هي هتلاقيها بتساوي 
+
+699
+00:59:46,840 --> 00:59:50,260
+ناقص H of X بتحسبوها لحالكم H double prime of X
+
+700
+00:59:50,260 --> 00:59:55,140
+عشان بتساوي ناقص H of X لكل X element in R لو حسبت 
+
+701
+00:59:55,140 --> 00:59:59,670
+اللي هي H of Zero هتساوي اللي هي zero لأنه احنا
+
+702
+00:59:59,670 --> 01:00:03,010
+أثبتنا أن g of zero ساوي f of zero و h prime of
+
+703
+01:00:03,010 --> 01:00:07,110
+zero h prime of zero اللي هي عبارة عن f prime ناقص
+
+704
+01:00:07,110 --> 01:00:09,210
+g prime عند ال zero الثانية و التساويات إذا إيه مش 
+
+705
+01:00:09,210 --> 01:00:15,170
+ساوي صفر الآن it then thus it follows as in the
+
+706
+01:00:15,170 --> 01:00:19,430
+proof of the preceding theorem النظرية الماضية إن
+
+707
+01:00:19,430 --> 01:00:22,170
+h of x إيه مش ساوي صفر يعني بدك تعمل نفس اللي
+
+708
+01:00:22,170 --> 01:00:25,180
+عملناها قبل هيك على ال Taylor's theorem والآخرين 
+
+709
+01:00:25,180 --> 01:00:29,300
+تصل ال H of X بساوية 0 لكل X ومنه هتقول F of X
+
+710
+01:00:29,300 --> 01:00:33,320
+بساوية G of X مدام F of X بساوية G of X إذن هذه
+
+711
+01:00:33,320 --> 01:00:38,580
+اللي هي F of X بتطلع F of X بتساوي اللي هي هذا
+
+712
+01:00:38,580 --> 01:00:42,780
+اسمها Alpha وهذا اسمها Beta وبكون عندي هي اللي هو
+
+713
+01:00:42,780 --> 01:00:46,280
+solution لـ اللي هي ال differential equation اللي
+
+714
+01:00:46,280 --> 01:00:50,260
+احنا حكينا عنها بديش أعيد نفس الكلام عشان هي كأنا
+
+715
+01:00:50,260 --> 01:00:52,780
+اختصرت لأن الحسابات كلها مشابهة
+
+716
+01:01:00,220 --> 01:01:03,430
+الآن بدنا اللي هي 8 4 7 the function C is even and 
+
+717
+01:01:03,430 --> 01:01:07,570
+S is odd in the sense that هو بتكون الصحيحة دي 
+
+718
+01:01:07,570 --> 01:01:10,610
+الأصل كلها تكون أو معظمها اللي هي عبارة عن
+
+719
+01:01:10,610 --> 01:01:14,430
+exercises لإنها تطبيقات على النظرية اللي قلتها في
+
+720
+01:01:14,430 --> 01:01:19,630
+الأول ال C ناقص X هيساوي C of X يعني عبارة عن even
+
+721
+01:01:19,630 --> 01:01:23,230
+function S ناقص X بيساوي ناقص S of X لكل X element
+
+722
+01:01:23,230 --> 01:01:28,590
+in R الآن if x,y المتنار then we have the addition
+
+723
+01:01:28,590 --> 01:01:32,230
+formula c of x زي اد y بيسبب c of x في c of y ناقص
+
+724
+01:01:32,230 --> 01:01:35,950
+s of x وs of y اللي هي اللي بتعرفوها انتوا sign ال
+
+725
+01:01:35,950 --> 01:01:38,350
+x زي اد y بيسبب sign ال x بكسان ال y زي اد كسان ال
+
+726
+01:01:38,350 --> 01:01:42,090
+y في sign ال x وهكذا هي هذه الخواص اللي احنا
+
+727
+01:01:42,090 --> 01:01:47,570
+عارفينها قبل هيك وبدنا نشوف كيف اللي هي نبرهن 
+
+728
+01:01:47,570 --> 01:01:53,660
+النظرية نشوف البرهان تبع النظرية الآن سمي لي Phi of 
+
+729
+01:01:53,660 --> 01:01:59,370
+X بيساوي C of ناقص X لكل X element in R احسب لي الـ
+
+730
+01:01:59,370 --> 01:02:05,010
+phi w prime of x لو اتيت فضلت هذه مرتين هتلاقيها 
+
+731
+01:02:05,010 --> 01:02:09,950
+ناقص phi of x وهذا الكلام تفضله سهل وبتجيبه لحالك 
+
+732
+01:02:09,950 --> 01:02:15,050
+الآن احسب لي ال phi of 0 phi of 0 هتساوي إيش؟
+
+733
+01:02:15,050 --> 01:02:19,350
+بتساوي واحد phi prime of 0 هتطلع اللي هي عبارة عن
+
+734
+01:02:19,350 --> 01:02:24,430
+اللي هي ال sign ال sign إيش معناها؟ بتساوي 0 عند 
+
+735
+01:02:24,430 --> 01:02:30,730
+ال zero الآن صار عندي الآن الفاى هي مين؟ هي الـC
+
+736
+01:02:30,730 --> 01:02:35,710
+ليش الفاى هي الـC؟ لأن حققت الفاى اللي فرضتها
+
+737
+01:02:35,710 --> 01:02:40,790
+بساوية C-X شروط الـC والـC is unique إذا الفاى هـ
+
+738
+01:02:40,790 --> 01:02:47,200
+بتساوي C إذا صار عندي الآن C-X بيساوي C of X الفكرة 
+
+739
+01:02:47,200 --> 01:02:52,060
+واضحة أنه أنا جبت سميت الـC-X هي الفاية واتبتت أن
+
+740
+01:02:52,060 --> 01:02:57,060
+هذه الفاية بتحقق الشرطين اللي احنا حكينا عنهم في
+
+741
+01:02:57,060 --> 01:03:01,300
+الأول الدالة اللي بتخلي الـC is unique فصارت 
+
+742
+01:03:01,300 --> 01:03:07,080
+الفاية إيش بتساوي الـC الآن بمعنى آخر صارت C of X
+
+743
+01:03:07,080 --> 01:03:10,720
+هي C من ناقص X اللي فرضناها الـ Phi in a similar
+
+744
+01:03:10,720 --> 01:03:16,040
+way برضه بدك تعملاش S of ناقص X اللي هو بتسمي اللي
+
+745
+01:03:16,040 --> 01:03:20,480
+هي ال .. الفا .. بتسميها بـ Psi مثلا Psi بتساوي
+
+746
+01:03:20,480 --> 01:03:25,020
+مين؟ بتساوي اللي هو ناقص هتجيبها سامي بصي بيساوي
+
+747
+01:03:25,020 --> 01:03:29,540
+ناقص S ناقص X و تجيب الشروط اللي هي تبعها ال sign
+
+748
+01:03:29,540 --> 01:03:33,500
+هتلاقيها متطابق متحققة وبما أن ال S is unique أو 
+
+749
+01:03:33,500 --> 01:03:37,240
+ال sign is unique إذا اللي هي اللي حققتها اللي
+
+750
+01:03:37,240 --> 01:03:41,500
+كتبتها بتساوي ال S وصارتين إيه جهتين متساويات بنفس
+
+751
+01:03:41,500 --> 01:03:47,980
+الأسلوب طيب الآن نيجي نثبت اللي هو مين VI شوفوا
+
+752
+01:03:47,980 --> 01:03:52,850
+صلوا على النبي عليه الصلاة والسلام هنثبت الآن إن VI
+
+753
+01:03:52,850 --> 01:03:55,830
+let y المتن عار بيجيبنا let f of x بيساوي c of x
+
+754
+01:03:55,830 --> 01:04:00,070
+زي dash زي y for x المتن عار الآن a calculation 
+
+755
+01:04:00,070 --> 01:04:04,230
+shows that يعني فضلي هذا مرتين التفاضل سهل والله
+
+756
+01:04:04,230 --> 01:04:08,010
+يا جماعة عشانك أنا يعني ما بديش نضيع وقتنا في 
+
+757
+01:04:08,010 --> 01:04:12,190
+التفاضل أو في الحسابات f w prime of x طبعا فاضل 
+
+758
+01:04:12,190 --> 01:04:15,430
+بالنسبة لي x y إيش ما على f x ثابت أسيبك منها لأن
+
+759
+01:04:15,430 --> 01:04:18,590
+لو فضلت مرتين هتلاقي ناقص f of x for x element in
+
+760
+01:04:18,590 --> 01:04:22,550
+R مدام f w prime بيساوي ناقص f of x بالحصارة اللي
+
+761
+01:04:22,550 --> 01:04:26,850
+هي حل المعادلة التفاضلية هذه اللي هي بالنظرية اللي
+
+762
+01:04:26,850 --> 01:04:32,880
+قبل شوية هي 8 4 6 هتكون اللي هي ال f of x عبارة عن
+
+763
+01:04:32,880 --> 01:04:36,300
+linear combination هذه اللي هو α C of X زي Beta S
+
+764
+01:04:36,300 --> 01:04:39,840
+of X والـ F of X مين هي احنا فرضينا C of XY صارت 
+
+765
+01:04:39,840 --> 01:04:43,180
+هذه عبارة عن هذه يعني هذه بتساوي هذه من حال
+
+766
+01:04:43,180 --> 01:04:47,260
+المعادلة التفاضلية هذه بواسطة النظرية هذه وهذه
+
+767
+01:04:47,260 --> 01:04:51,330
+أصلًا أنا نسميها هيك صارت هذه بتساوي هذا المقطع الآن 
+
+768
+01:04:51,330 --> 01:04:55,350
+جيب له F prime F prime of X اللي هي هذه التفضيلة
+
+769
+01:04:55,350 --> 01:04:59,070
+بـ C ناقص S of X زائد Y وفاضل هذه بيطلع اللي هو
+
+770
+01:04:59,070 --> 01:05:02,910
+عبارة عن ناقص Alpha S of X زائد Beta C of X ثم 
+
+771
+01:05:02,910 --> 01:05:09,710
+فضلت ماشي الآن خد X بيساوي 0 X بيساوي 0 لما X
+
+772
+01:05:09,710 --> 01:05:18,250
+بتساوي 0 بنحصل الآن عندي .. بيصير عندي عوض X بتساوي
+
+773
+01:05:18,250 --> 01:05:25,190
+صفر في اللي هي المعادلة اللي عندي هنا بيصير عندي S
+
+774
+01:05:25,190 --> 01:05:31,360
+of Zero و C of Zero بيساوي مين؟ F of Zero F of Zero
+
+775
+01:05:31,360 --> 01:05:40,100
+اللي هي عبارة عن F of Zero هي C of Y هذه فاهمين 
+
+776
+01:05:40,100 --> 01:05:44,560
+عليها؟ خليني أقولها واضحة أحسن الآن بدنا ناخد F
+
+777
+01:05:44,560 --> 01:05:52,600
+مين؟ F عند Zero فاشر؟ بيصير هذا C of Y بيساوي مين؟
+
+778
+01:05:52,600 --> 01:05:58,190
+Alpha في c of zero واحد وهذه beta s of zero زيرو
+
+779
+01:05:58,190 --> 01:06:03,890
+إذا صارت عندي ال alpha بتساوي c of y هاي واحدة لأن
+
+780
+01:06:03,890 --> 01:06:09,990
+similarly اللي هو ناقص خد عند ال zero عند ال zero 
+
+781
+01:06:09,990 --> 01:06:15,570
+بيصير ناقص s of y بيساوي هذي بيصير صفر وهذه بيصير 
+
+782
+01:06:15,570 --> 01:06:20,070
+beta بيساوي beta الآن بنعوض وين؟ في ال formula
+
+783
+01:06:20,070 --> 01:06:26,370
+الأولى بيصير عندي الآن ال formula اللي عندي اللي هي 
+
+784
+01:06:26,370 --> 01:06:30,010
+بتحط مكان C of Y بيساوي Alpha والفورمولة الأولى
+
+785
+01:06:30,010 --> 01:06:35,770
+اللي احنا عملناها بيصير عندي اللي هي C
+
+786
+01:06:38,530 --> 01:06:43,570
+Half X زائد Y بيساوي Alpha اللي هي اسمها قلنا طلعت
+
+787
+01:06:43,570 --> 01:06:48,310
+عندنا C of Y بيصير C of Y في C of X هيها مظبوطة 
+
+788
+01:06:48,310 --> 01:06:53,130
+وهذه ناقص S مكان ال Beta بيصير ناقص S of Y في S of
+
+789
+01:06:53,130 --> 01:07:01,740
+X صحيحة إذا بكون إحنا خلصنا اللي بدنا إياه وهذه بتعوض 
+
+790
+01:07:01,740 --> 01:07:08,240
+عن اللي هي Alpha C of Y بـ C ناقص C of Y وهذه بتعوضها
+
+791
+01:07:08,240 --> 01:07:13,440
+هنا بتطلع هذه بتساوي ناقص هذه اعمل الحساب الأخير
+
+792
+01:07:13,440 --> 01:07:17,400
+وضروف الدقيقتين بنقص بتطلع عندك هذا المخضر يعني
+
+793
+01:07:17,400 --> 01:07:23,840
+هذه التعويض فيها عن قيمة Alpha و Beta بهذه هنا 
+
+794
+01:07:23,840 --> 01:07:30,860
+بتطلع هذه وهذه التعويض هذه عن alpha و beta هنا اللي
+
+795
+01:07:30,860 --> 01:07:35,420
+بتطلع الأولى بكون إحنا خلصنا اللي هو اثبات هذه 
+
+796
+01:07:35,420 --> 01:07:42,800
+اللي هي النظرية وضال عندي اللي هو النظرية هذه
+
+797
+01:07:42,800 --> 01:07:47,350
+الأخيرة والباقي اللي هو لو اتطلعتوا على اللي هي 
+
+798
+01:07:47,350 --> 01:07:52,450
+باقي النظريات اللي هي بس اتطلع لعند الها بيكون
+
+799
+01:07:52,450 --> 01:07:55,990
+إحنا بيكون خلصنا chapter اللي هو المطلوب في
+
+800
+01:07:55,990 --> 01:08:00,350
+chapter في ثمانية أربعة هذه اللي هي ال theorem
+
+801
+01:08:00,350 --> 01:08:03,530
+خليني أطلع لك عليها على السريع لإن حسابات كلها
+
+802
+01:08:03,530 --> 01:08:07,840
+بتعملها لحالك أكيد بتعرف إذا كان الـ x أكبر أو أقل
+
+803
+01:08:07,840 --> 01:08:12,880
+من 0، فهناك Sx بنقص الـ x والـ x والـ c of x بين
+
+804
+01:08:12,880 --> 01:08:16,780
+الواحد ناقص x أربع عذر تو واحد والـ c of x بقدر 
+
+805
+01:08:16,780 --> 01:08:18,820
+أكمل الـ polynomial
+
+806
+01:08:21,810 --> 01:08:25,650
+باللي عملناها اللي هي الـ CN of X اللي جابله شوية و
+
+807
+01:08:25,650 --> 01:08:28,430
+الـ SN of X لأنه في النهاية limitها ال series
+
+808
+01:08:28,430 --> 01:08:30,790
+الأولى as N goes to infinity ما أنتو عارفين اللي
+
+809
+01:08:30,790 --> 01:08:34,990
+هي نقدر نكتب الـ C of X على صورة ال series اللي في 
+
+810
+01:08:34,990 --> 01:08:38,130
+الأول و الـ S of X عبارة عن limit ال series الثانية
+
+811
+01:08:38,130 --> 01:08:43,390
+ال terms إضافة term و طرح term و وجوف عند حدود بال
+
+812
+01:08:43,390 --> 01:08:47,090
+term بتعمل ال inequality اللي عندنا اللي هو كل هذه 
+
+813
+01:08:47,090 --> 01:08:49,810
+شغلات اللي أخذناها في ال calculus مافيش داعي 
+
+814
+01:08:49,810 --> 01:08:55,650
+للتفصيل فيها الآن الأولى عندي ال .. ال .. احنا قلنا 
+
+815
+01:08:55,650 --> 01:08:59,990
+sign تربيع زائد plus sign تربيع بيساوي واحد يعني في 
+
+816
+01:08:59,990 --> 01:09:02,670
+النهاية ال C of T بين ناقص واحد و واحد ده ممكن 
+
+817
+01:09:02,670 --> 01:09:06,710
+هتتجاوزها لأنه بتختل اللي هي ال C .. لو كانت أكبر 
+
+818
+01:09:06,710 --> 01:09:10,750
+من واحد معناته بـ C .. C of T تربيع زائد S of T
+
+819
+01:09:10,750 --> 01:09:14,550
+تربيع يتجاوز من واحد لكن مجموعها بيساوي واحد إذا هدي
+
+820
+01:09:14,550 --> 01:09:18,630
+بين .. يعني هدي اللي وين جاية من C تربيع زائد S
+
+821
+01:09:18,630 --> 01:09:23,030
+تربيع بيساوي واحد طيب اللي هنعمل integration لجهتين 
+
+822
+01:09:23,030 --> 01:09:26,990
+من صفر لعين DX هذه اللي هي بتطلع اللي هي main ال S
+
+823
+01:09:26,990 --> 01:09:30,750
+of X وهذه بتطلع ناقص X وهذه بتطلع X فالمعمل ال
+
+824
+01:09:30,750 --> 01:09:35,990
+integration هدول الآن بدي
+
+825
+01:09:35,990 --> 01:09:43,300
+أجيب التانية فضلي ال S of T هذه وهذه فاضليها هذه
+
+826
+01:09:43,300 --> 01:09:48,460
+فاضليها بنقل صفر عند X بتطلع اللي هي بين هذه وهذه 
+
+827
+01:09:48,460 --> 01:09:53,660
+هيتفاضوا لهذه وهذه الآن بدنا اللي هو نجيب الواحد
+
+828
+01:09:53,660 --> 01:09:58,280
+ناقص X التربيع اللي هو هذا قيمته اللي هو عبارة عن 
+
+829
+01:09:58,280 --> 01:10:02,600
+C في X بيساوي واحد ناقص هذه بنضرب الناقص و بنجمع
+
+830
+01:10:02,600 --> 01:10:08,280
+الجهتين واحد بيطلع عندي اللي هي ال inequality اللي
+
+831
+01:10:08,280 --> 01:10:13,190
+عندي هذه زي ما قلنا ضربنا في ناقص و جمعنا واحد طلعت
+
+832
+01:10:13,190 --> 01:10:16,590
+هذه أو عوضنا هذه مكان هذه تعويض عادي وبعدين ضربنا 
+
+833
+01:10:16,590 --> 01:10:20,690
+في ناقص فبيصير عندي هذه المقدار اللي عندي c of x
+
+834
+01:10:20,690 --> 01:10:24,310
+أكبر سواء هذه و ناقص هذه واللي بتستخدم الثانية 
+
+835
+01:10:24,310 --> 01:10:27,670
+بتطلع نفس الشيء الموضوع موضوع حسابات بحت عشان هيك 
+
+836
+01:10:27,670 --> 01:10:31,510
+بحت عشان هيك ما في داعي للتكميل وانتو بتكملوا 
+
+837
+01:10:31,510 --> 01:10:35,150
+باقي الحسابات اللي هي المطلوبة في هذا اللي هي 
+
+838
+01:10:35,150 --> 01:10:42,700
+النظرية الآن الجزء المتبقي هذا حبيته تطلعوا عليه
+
+839
+01:10:42,700 --> 01:10:46,880
+لكن اللي هو مش مطلوب من ضمن حديثنا وهيك ممكن 
+
+840
+01:10:46,880 --> 01:10:52,700
+نخلصنا اللي هو section ثمانية أربعة متسمة سبتر 
+
+841
+01:10:52,700 --> 01:10:58,420
+ثمانية هذا اللي هو الجزء الثالث من المادة الجزء
+
+842
+01:10:58,420 --> 01:11:00,160
+الأول كان الـ differentiation والثاني الـ
+
+843
+01:11:00,160 --> 01:11:01,960
+integration والثالث اللي هو pointwise 
+
+844
+01:11:01,960 --> 01:11:05,700
+convergence المرة الجاية إن شاء الله اللي هو بنبدأ 
+
+845
+01:11:05,700 --> 01:11:09,880
+في الجزء الرابع من المادة اللي هو الـ series وأن
+
+846
+01:11:09,880 --> 01:11:16,590
+شاء الله بقدر الإمكان هأحكي الجزء الخامس في .. من
+
+847
+01:11:16,590 --> 01:11:20,510
+المادة اللي هو عبارة عن اللي هو Topology in ℝ أو
+
+848
+01:11:20,510 --> 01:11:23,570
+اللي هو اللي هي العلاقة بين اللي هي Topological
+
+849
+01:11:23,570 --> 01:11:27,410
+Spaces والـ Normed Spaces والـ Hilbert Spaces إلى آخره
+
+850
+01:11:27,410 --> 01:11:33,530
+ويمكن بتكون هي اتجاوزت خلينا نقول حد الـ .. الـ .. الـ
+
+851
+01:11:33,530 --> 01:11:37,150
+.. المطلوب في المادة لكن على أساس إنه لو يكون
+
+852
+01:11:37,150 --> 01:11:42,210
+الوصف كامل للـ .. للوصف اللي أنا اقترحته أو اللي
+
+853
+01:11:42,210 --> 01:11:47,230
+هو الوصف اللي مقترح في الجسم اللي هو لعين نهاية الـ
+
+854
+01:11:47,230 --> 01:11:49,990
+series وطبعًا هذا الكلام قلنا احنا فيه له سبب لما
+
+855
+01:11:49,990 --> 01:11:53,450
+بدأنا في الأول إنه الـ series بتأخذوها في advanced
+
+856
+01:11:53,450 --> 01:11:56,990
+calculus واحد فعشان هيك يمكن اللي هو
+
+857
+01:12:00,350 --> 01:12:03,810
+هيكون منطقي إنه ما نأخذش الـ series ونأخذ بدلًا منها
+
+858
+01:12:03,810 --> 01:12:07,110
+اللي هو الـ topology in ℝ أو اللي هو العلاقة بين الـ
+
+859
+01:12:07,110 --> 01:12:10,550
+topological spaces والـ metric spaces وإلى لقاءٍ و
+
+860
+01:12:10,550 --> 01:12:12,650
+السلام آخر والسلام عليكم ورحمة الله وبركاته 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..17e64cf90d15c073c0b7d1633714a3fd208112f5
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_raw.json
@@ -0,0 +1 @@
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10.31, "end": 11.03, "word": " حالة", "probability": 0.9930013020833334}, {"start": 11.03, "end": 11.63, "word": " الطوارئ", "probability": 0.838623046875}], "temperature": 1.0}, {"id": 2, "seek": 3779, "start": 12.37, "end": 37.79, "text": "في مادة او مساق تحليل لرياضي 2 او تحليل حقيقي 2 لطلبة و طالبات الجامعة الإسلامية كلية العلوم قسم الرياضيات وهي المحاضرة رقم 14 في المادة او في المساق عنوان المحاضرة اليوم اللي هو fundamental theorem of", "tokens": [41185, 3714, 18513, 3660, 1975, 2407, 47524, 995, 4587, 6055, 5016, 20292, 1211, 5296, 16572, 46958, 1829, 568, 1975, 2407, 6055, 5016, 20292, 1211, 11331, 38436, 38436, 568, 5296, 9566, 46152, 3660, 4032, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 9122, 20292, 3660, 18863, 1211, 20498, 12174, 38251, 2423, 16572, 46958, 1829, 9307, 37037, 1829, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 3499, 8978, 9673, 18513, 3660, 1975, 2407, 8978, 9673, 3794, 995, 4587, 18871, 2407, 7649, 9673, 5016, 46958, 25720, 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" بتتحقق", "probability": 0.9037109375}, {"start": 466.29, "end": 466.65, "word": " نفس", "probability": 0.994873046875}, {"start": 466.65, "end": 467.31, "word": " الشروط", "probability": 0.892578125}, {"start": 467.31, "end": 468.17, "word": " بناء", "probability": 0.9765625}, {"start": 468.17, "end": 468.65, "word": " عليه", "probability": 0.955078125}, {"start": 468.65, "end": 469.69, "word": " احنا", "probability": 0.8771158854166666}, {"start": 469.69, "end": 470.27, "word": " بنعرف", "probability": 0.9441731770833334}, {"start": 470.27, "end": 471.11, "word": " قبل", "probability": 0.8662109375}, {"start": 471.11, "end": 471.49, "word": " هيك", "probability": 0.913818359375}, {"start": 471.49, "end": 471.73, "word": " خليني", "probability": 0.70941162109375}, {"start": 471.73, "end": 471.89, "word": " أبدأ", "probability": 0.62451171875}, {"start": 471.89, "end": 474.11, "word": " أشتغلها", "probability": 0.9169108072916666}, {"start": 474.11, "end": 474.83, "word": " عند", 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عارفينوا هذا الكلام احنا بنتعرف شو معناته Integrable الـ U of F هي عبارة عن مين؟ عن الـ infimum لمين؟ للكبار اللي هي U L أو U P و F", "tokens": [10721, 8848, 1863, 2423, 39184, 624, 295, 479, 4032, 2423, 39184, 441, 295, 479, 13672, 1829, 31439, 2423, 39184, 36926, 23894, 304, 4032, 2423, 39184, 25523, 23894, 304, 13672, 1829, 31439, 39896, 3794, 995, 45865, 12174, 32640, 3660, 2423, 39184, 47713, 6225, 9640, 5172, 9957, 14407, 23758, 2423, 28820, 10943, 1975, 5016, 8315, 4724, 29399, 3615, 28480, 13412, 2407, 20449, 8315, 47395, 5681, 1146, 424, 638, 2423, 39184, 624, 295, 479, 39896, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 18871, 2423, 39184, 1536, 332, 449, 5296, 2304, 9957, 22807, 5296, 23275, 3555, 9640, 13672, 1829, 39896, 624, 441, 34051, 624, 430, 4032, 479], "avg_logprob": -0.2470238072531564, "compression_ratio": 1.7609756097560976, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 891.72, "end": 892.32, "word": "أذن", "probability": 0.535888671875}, 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1086.96, "end": 1087.82, "word": " اللي", "probability": 0.923828125}, {"start": 1087.82, "end": 1088.56, "word": " لجيته", "probability": 0.82568359375}, {"start": 1088.56, "end": 1089.28, "word": " أعلى", "probability": 0.8304036458333334}, {"start": 1089.28, "end": 1090.26, "word": " إذا", "probability": 0.857666015625}, {"start": 1090.26, "end": 1090.56, "word": " صار", "probability": 0.816650390625}, {"start": 1090.56, "end": 1090.9, "word": " عندى", "probability": 0.6483154296875}, {"start": 1090.9, "end": 1091.32, "word": " الآن", "probability": 0.787353515625}, {"start": 1091.32, "end": 1092.46, "word": " اللي", "probability": 0.802490234375}, {"start": 1092.46, "end": 1093.14, "word": " وصلتله", "probability": 0.904296875}], "temperature": 1.0}, {"id": 50, "seek": 111377, "start": 1093.97, "end": 1113.77, "text": "عبارة عن اللي هو ال absolute value هذا أصغر من إبسلون وطبعا أكبر أوي ساوي سفر والإبسلون واز إيه شمالها arbitrary يعني المقدار هذا لأي إبسلون في الدنيا لأي إبسلون في الدنيا هذا أصغر من مين من الإبسلون هو أكبر أوي سفر", "tokens": [3615, 3555, 9640, 3660, 18871, 13672, 1829, 31439, 2423, 8236, 2158, 23758, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 4032, 9566, 3555, 3615, 995, 5551, 4117, 26890, 34051, 1829, 8608, 995, 45865, 8608, 5172, 2288, 4032, 6027, 28814, 3555, 3794, 1211, 11536, 4032, 31377, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 23211, 37495, 22653, 9673, 28543, 9640, 23758, 5296, 10721, 1829, 11933, 3555, 3794, 1211, 11536, 8978, 32748, 22653, 995, 5296, 10721, 1829, 11933, 3555, 3794, 1211, 11536, 8978, 32748, 22653, 995, 23758, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 33688, 3555, 3794, 1211, 11536, 31439, 5551, 4117, 26890, 34051, 1829, 8608, 5172, 2288], "avg_logprob": -0.15381307722231663, "compression_ratio": 1.9837837837837837, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 1093.97, "end": 1094.61, "word": "عبارة", "probability": 0.96826171875}, {"start": 1094.61, "end": 1094.83, 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2075.09, "word": " C", "probability": 0.98876953125}, {"start": 2075.09, "end": 2075.25, "word": " أو", "probability": 0.78173828125}, {"start": 2075.25, "end": 2075.65, "word": " C", "probability": 0.92431640625}, {"start": 2075.65, "end": 2076.49, "word": " زائد", "probability": 0.94970703125}, {"start": 2076.49, "end": 2076.73, "word": " H", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 94, "seek": 210375, "start": 2077.67, "end": 2103.75, "text": "لأن x بتروح للـ c تكافئ أنه .. اللي هو x minus c تروح للصفر، يعني بتكافئ H تروح لمين للصفر، إيش حيث هو هذا؟ F of C، إذا هذه هي تعبير آخر عن ال continuity لل F لما اللي هو اللي هي ال F عند مين، عند ال C، يعني هذه تعبير آخر، ال continuity لل function لما عند النقطة اللي هي C", "tokens": [1211, 33456, 2031, 39894, 32887, 5016, 24976, 39184, 269, 6055, 4117, 31845, 19986, 14739, 3224, 4386, 13672, 1829, 31439, 2031, 3175, 269, 6055, 32887, 5016, 24976, 9381, 5172, 2288, 12399, 37495, 22653, 39894, 4117, 31845, 19986, 389, 6055, 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2104.34, "end": 2126.4, "text": "هذه الآن شو بدي استخدمها للوصول اللي بديها لأن مادام F is continuous ده هذي متحققة هيها مادام F is continuous عن C ده هذي متحققة فمادام هذي متحققة اذا by epsilon delta definition for every epsilon أكبر من 0 there exists delta أكبر من 0 such that لما يكون ال absolute value لل H أصغر من Delta", "tokens": [3224, 24192, 6024, 48506, 13412, 2407, 4724, 16254, 44713, 9778, 40448, 11296, 24976, 2407, 9381, 12610, 13672, 1829, 4724, 16254, 11296, 5296, 33456, 3714, 18513, 10943, 479, 307, 10957, 11778, 3224, 8032, 8848, 1829, 44650, 5016, 4587, 28671, 39896, 11296, 3714, 18513, 10943, 479, 307, 10957, 18871, 383, 11778, 3224, 8032, 8848, 1829, 44650, 5016, 4587, 28671, 6156, 2304, 18513, 10943, 8032, 8848, 1829, 44650, 5016, 4587, 28671, 1975, 15730, 538, 17889, 8289, 7123, 337, 633, 17889, 5551, 4117, 26890, 9154, 1958, 456, 8198, 8289, 5551, 4117, 26890, 9154, 1958, 1270, 300, 5296, 15042, 7251, 30544, 2423, 8236, 2158, 24976, 389, 5551, 9381, 17082, 2288, 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يعني هذه صحيحة؟ يعني ال integration من ال AX لل F of التي هي T DT، هذه DT يا جماعة، بس .. بس نخلف عن هذه، F of T DT، هذا هيساوي مين؟ هيساوي F of X، ناشي؟", "tokens": [28814, 15730, 14111, 29538, 20328, 5016, 1829, 5016, 3660, 12399, 11933, 1829, 8592, 37495, 22653, 29538, 20328, 5016, 1829, 5016, 3660, 22807, 37495, 22653, 2423, 10980, 9154, 2423, 316, 55, 24976, 479, 295, 38392, 39896, 314, 413, 51, 12399, 29538, 413, 51, 35186, 10874, 15042, 27884, 12399, 4724, 3794, 4386, 4724, 3794, 8717, 9778, 46538, 18871, 29538, 12399, 479, 295, 314, 413, 51, 12399, 23758, 39896, 3794, 995, 45865, 3714, 9957, 22807, 39896, 3794, 995, 45865, 479, 295, 1783, 12399, 8717, 33599, 1829, 22807], "avg_logprob": -0.27941175909603344, "compression_ratio": 1.5722543352601157, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 2856.72, "end": 2857.56, "word": "إذاً", "probability": 0.4446614583333333}, {"start": 2857.56, "end": 2857.72, "word": " هذه", "probability": 0.62646484375}, {"start": 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" not", "probability": 0.9638671875}, {"start": 3252.28, "end": 3252.62, "word": " have", "probability": 0.96630859375}, {"start": 3252.62, "end": 3252.88, "word": " an", "probability": 0.88037109375}, {"start": 3252.88, "end": 3253.54, "word": " antiderivative", "probability": 0.95263671875}, {"start": 3253.54, "end": 3253.98, "word": " يعني", "probability": 0.83984375}, {"start": 3253.98, "end": 3255.04, "word": " هنلاقي", "probability": 0.8270263671875}, {"start": 3255.04, "end": 3255.22, "word": " في", "probability": 0.92333984375}, {"start": 3255.22, "end": 3255.64, "word": " السؤال", "probability": 0.99609375}, {"start": 3255.64, "end": 3255.92, "word": " هذا", "probability": 0.859375}, {"start": 3255.92, "end": 3256.6, "word": " integrable", "probability": 0.7609049479166666}, {"start": 3256.6, "end": 3257.22, "word": " function", "probability": 0.9677734375}, {"start": 3257.22, "end": 3259.82, "word": " ومالهاش", "probability": 0.772119140625}, {"start": 3259.82, "end": 3260.3, "word": " ..", "probability": 0.377685546875}, {"start": 3260.3, "end": 3261.82, "word": " ومالهاش", "probability": 0.923046875}, {"start": 3261.82, "end": 3262.82, "word": " antiderivative", "probability": 0.9461669921875}, {"start": 3262.82, "end": 3263.56, "word": " يعني", "probability": 0.942626953125}, {"start": 3263.56, "end": 3264.08, "word": " هنلاقي", "probability": 0.954833984375}, {"start": 3264.08, "end": 3264.6, "word": " function", "probability": 0.92138671875}, {"start": 3264.6, "end": 3265.1, "word": " F", "probability": 0.56787109375}], "temperature": 1.0}, {"id": 144, "seek": 328468, "start": 3265.94, "end": 3284.68, "text": "إنها تكون integrable لكن مالناجيش function F اللي ال derivative تبعي تاش بتساوي بتساوي F هذا اللي هو بتشوفوه في الـ 7 3 2 و 7 3 5 الأمثلة أو ال counter examples اللي وجودة هنا طيب الملاحظة التانية", "tokens": [28814, 1863, 11296, 6055, 30544, 16200, 424, 638, 44381, 19446, 1211, 1863, 26108, 1829, 8592, 2445, 479, 13672, 1829, 2423, 13760, 6055, 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not exist لكن but not integrable وهذا بتجاوب عليه برضه سبعة تلاتة خمسة يعني في function F", "tokens": [6027, 39184, 2445, 815, 362, 364, 2511, 1438, 592, 1166, 37495, 22653, 18871, 16254, 479, 4032, 39894, 5016, 4587, 4587, 479, 4032, 8978, 18871, 16254, 479, 9122, 16758, 2655, 6027, 9122, 2304, 7649, 4032, 479, 4724, 23557, 32640, 11933, 1829, 8592, 39894, 3794, 995, 45865, 4724, 3794, 2407, 38207, 479, 457, 13672, 1829, 39896, 2423, 10980, 24976, 479, 11933, 1829, 8592, 3714, 6027, 3224, 775, 406, 2514, 44381, 457, 406, 16200, 424, 638, 37037, 15730, 39894, 7435, 995, 37746, 47356, 4724, 43042, 3224, 8608, 3555, 27884, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 37495, 22653, 8978, 2445, 479], "avg_logprob": -0.22468749716877937, "compression_ratio": 1.5474137931034482, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 3285.95, "end": 3286.25, "word": "الـ", "probability": 0.5687255859375}, {"start": 3286.25, "end": 3286.63, "word": " function", "probability": 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{"start": 3296.91, "end": 3297.31, "word": " اللي", "probability": 0.923828125}, {"start": 3297.31, "end": 3297.55, "word": " هي", "probability": 0.8251953125}, {"start": 3297.55, "end": 3297.69, "word": " ال", "probability": 0.96630859375}, {"start": 3297.69, "end": 3298.21, "word": " integration", "probability": 0.94677734375}, {"start": 3298.21, "end": 3298.51, "word": " لل", "probability": 0.82470703125}, {"start": 3298.51, "end": 3298.75, "word": " F", "probability": 0.432373046875}, {"start": 3298.75, "end": 3299.01, "word": " إيش", "probability": 0.8439127604166666}, {"start": 3299.01, "end": 3299.53, "word": " ماله", "probability": 0.80322265625}, {"start": 3299.53, "end": 3300.35, "word": " does", "probability": 0.80029296875}, {"start": 3300.35, "end": 3300.95, "word": " not", "probability": 0.9677734375}, {"start": 3300.95, "end": 3301.81, "word": " exist", "probability": 0.9658203125}, {"start": 3301.81, "end": 3302.21, "word": " لكن", "probability": 0.90771484375}, {"start": 3302.21, "end": 3302.81, "word": " but", "probability": 0.84619140625}, {"start": 3302.81, "end": 3303.23, "word": " not", "probability": 0.9541015625}, {"start": 3303.23, "end": 3304.21, "word": " integrable", "probability": 0.8916015625}, {"start": 3304.21, "end": 3305.11, "word": " وهذا", "probability": 0.810546875}, {"start": 3305.11, "end": 3305.79, "word": " بتجاوب", "probability": 0.8226318359375}, {"start": 3305.79, "end": 3306.25, "word": " عليه", "probability": 0.990234375}, {"start": 3306.25, "end": 3306.91, "word": " برضه", "probability": 0.9710286458333334}, {"start": 3306.91, "end": 3307.37, "word": " سبعة", "probability": 0.8396809895833334}, {"start": 3307.37, "end": 3307.83, "word": " تلاتة", "probability": 0.8619384765625}, {"start": 3307.83, "end": 3308.45, "word": " خمسة", "probability": 0.9718017578125}, {"start": 3308.45, "end": 3308.93, "word": " يعني", "probability": 0.946044921875}, {"start": 3308.93, "end": 3309.07, "word": " في", "probability": 0.8994140625}, {"start": 3309.07, "end": 3309.49, "word": " function", "probability": 0.76171875}, {"start": 3309.49, "end": 3309.93, "word": " F", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 146, "seek": 333228, "start": 3310.64, "end": 3332.28, "text": "في إلها F' بساوة F لكن ال integration للـ F إشماله does not exist تلاتة عندي الملاحظة الثالثة a continuous function always have antiderivative طبعا ال continuous function أصلا من القوة بمكان إنها", "tokens": [41185, 11933, 1211, 11296, 479, 6, 4724, 3794, 995, 2407, 3660, 479, 44381, 2423, 10980, 24976, 39184, 479, 11933, 8592, 2304, 6027, 3224, 775, 406, 2514, 6055, 1211, 9307, 3660, 18871, 16254, 9673, 15040, 5016, 19913, 3660, 6024, 104, 6027, 12984, 3660, 257, 10957, 2445, 1009, 362, 2511, 1438, 592, 1166, 23032, 3555, 3615, 995, 2423, 10957, 2445, 5551, 9381, 15040, 9154, 25062, 2407, 3660, 4724, 2304, 41361, 36145, 11296], "avg_logprob": -0.24097711897232163, "compression_ratio": 1.3989637305699483, 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antiderivative وهذا اللي هو مباشرة من ال corollary 7 3 4 اللي كانت F continuous مدام F continuous إذا ال integration من ال X من A لعند ال X", "tokens": [2655, 9778, 1211, 11703, 1829, 43242, 11296, 7251, 30544, 5296, 11296, 2423, 39184, 914, 2511, 1438, 592, 1166, 2423, 7649, 257, 10957, 2445, 1009, 362, 2511, 1438, 592, 1166, 37037, 15730, 13672, 1829, 31439, 3714, 3555, 33599, 25720, 9154, 2423, 1181, 1833, 822, 1614, 805, 1017, 13672, 1829, 25961, 2655, 479, 10957, 3714, 3215, 10943, 479, 10957, 11933, 15730, 2423, 10980, 9154, 2423, 1783, 9154, 316, 5296, 3615, 41260, 2423, 1783], "avg_logprob": -0.3717447904249032, "compression_ratio": 1.5179487179487179, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 3333.03, "end": 3334.09, "word": "تخلّي", "probability": 0.5982421875}, {"start": 3334.09, "end": 3334.89, "word": " عندها", "probability": 0.9248046875}, {"start": 3334.89, "end": 3335.29, "word": " يكون", "probability": 0.55267333984375}, {"start": 3335.29, "end": 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{"start": 4096.03, "end": 4096.49, "word": " of", "probability": 0.9794921875}, {"start": 4096.49, "end": 4097.09, "word": " capital", "probability": 0.90087890625}, {"start": 4097.09, "end": 4098.05, "word": " في", "probability": 0.330078125}, {"start": 4098.05, "end": 4098.29, "word": " G", "probability": 0.1846923828125}, {"start": 4098.29, "end": 4099.41, "word": " من", "probability": 0.88623046875}, {"start": 4099.41, "end": 4099.75, "word": " A", "probability": 0.796875}, {"start": 4099.75, "end": 4101.51, "word": " لـ", "probability": 0.731201171875}, {"start": 4101.51, "end": 4101.79, "word": " B", "probability": 0.74169921875}, {"start": 4101.79, "end": 4103.57, "word": " وهو", "probability": 0.765625}, {"start": 4103.57, "end": 4105.35, "word": " المطلوب", "probability": 0.9730224609375}, {"start": 4105.35, "end": 4106.51, "word": " و", "probability": 0.43798828125}, {"start": 4106.51, "end": 4106.85, "word": " هيك", "probability": 0.619140625}, {"start": 4106.85, "end": 4107.23, "word": " احنا", "probability": 0.91845703125}], "temperature": 1.0}, {"id": 181, "seek": 412933, "start": 4108.05, "end": 4129.33, "text": "بنكون اليوم ان شاء الله وصلنا لعند ال first substitution theorem المرة القادمة ان شاء الله بنكمل المحاضرة او بنكمل المادة و بنكمل هذا ال section في محاضرة قادمة ان شاء الله و إلى لقائنا", "tokens": [3555, 1863, 30544, 45595, 20498, 16472, 13412, 16606, 21984, 4032, 36520, 8315, 5296, 3615, 41260, 2423, 700, 35827, 20904, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 9673, 5016, 46958, 25720, 1975, 2407, 44945, 24793, 1211, 9673, 18513, 3660, 4032, 44945, 24793, 1211, 23758, 2423, 3541, 8978, 3714, 5016, 46958, 25720, 12174, 18513, 46007, 16472, 13412, 16606, 21984, 4032, 30731, 5296, 4587, 16373, 8315], "avg_logprob": -0.1216032630291538, "compression_ratio": 1.882716049382716, "no_speech_prob": 5.3882598876953125e-05, "words": [{"start": 4108.05, "end": 4108.77, "word": "بنكون", "probability": 0.8968098958333334}, {"start": 4108.77, "end": 4109.53, "word": " اليوم", "probability": 0.962890625}, {"start": 4109.53, "end": 4109.83, "word": " ان", "probability": 0.654296875}, {"start": 4109.83, "end": 4110.07, "word": " شاء", "probability": 0.989990234375}, {"start": 4110.07, "end": 4110.49, "word": " الله", "probability": 0.94775390625}, {"start": 4110.49, "end": 4111.77, "word": " وصلنا", "probability": 0.9064127604166666}, {"start": 4111.77, "end": 4112.13, "word": " لعند", "probability": 0.86083984375}, {"start": 4112.13, "end": 4112.29, "word": " ال", "probability": 0.890625}, {"start": 4112.29, "end": 4112.49, "word": " first", "probability": 0.75146484375}, {"start": 4112.49, "end": 4113.25, "word": " substitution", "probability": 0.95361328125}, {"start": 4113.25, "end": 4113.91, "word": " theorem", "probability": 0.904296875}, {"start": 4113.91, "end": 4115.05, "word": " المرة", "probability": 0.93994140625}, {"start": 4115.05, "end": 4115.53, "word": " القادمة", "probability": 0.9930013020833334}, {"start": 4115.53, "end": 4115.71, "word": " ان", "probability": 0.79052734375}, {"start": 4115.71, "end": 4115.89, "word": " شاء", "probability": 0.99169921875}, {"start": 4115.89, "end": 4116.25, "word": " الله", "probability": 0.95654296875}, {"start": 4116.25, "end": 4117.53, "word": " بنكمل", "probability": 0.9347330729166666}, {"start": 4117.53, "end": 4119.13, "word": " المحاضرة", "probability": 0.9805908203125}, {"start": 4119.13, "end": 4120.27, "word": " او", "probability": 0.80517578125}, {"start": 4120.27, "end": 4121.87, "word": " بنكمل", "probability": 0.9168294270833334}, {"start": 4121.87, "end": 4122.63, "word": " المادة", "probability": 0.9851888020833334}, {"start": 4122.63, "end": 4124.05, "word": " و", "probability": 0.390869140625}, {"start": 4124.05, "end": 4124.59, "word": " بنكمل", "probability": 0.9166666666666666}, {"start": 4124.59, "end": 4124.87, "word": " هذا", "probability": 0.9013671875}, {"start": 4124.87, "end": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8cf74504e7a08f953b4fc9de0fb1fa38ac2a30c2
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_raw.srt
@@ -0,0 +1,3332 @@
+1
+00:00:04,910 --> 00:00:11,030
+بسم الله الرحمن الرحيم المحاضرة الرابعة بعد حالة
+
+2
+00:00:11,030 --> 00:00:19,410
+الطوارئفي مادة او مساق تحليل لرياضي 2 او تحليل
+
+3
+00:00:19,410 --> 00:00:23,970
+حقيقي 2 لطلبة و طالبات الجامعة الإسلامية كلية
+
+4
+00:00:23,970 --> 00:00:30,110
+العلوم قسم الرياضيات وهي المحاضرة رقم 14 في المادة
+
+5
+00:00:30,110 --> 00:00:35,970
+او في المساق عنوان المحاضرة اليوم اللي هو
+
+6
+00:00:35,970 --> 00:00:43,260
+fundamental theorem ofof calculus بشقيها شق تفاضل
+
+7
+00:00:43,260 --> 00:00:50,640
+التكامل وشق تكامل التفاضل roughly نبدأ اللي هو في
+
+8
+00:00:50,640 --> 00:00:54,960
+النظرية الأولة أو الجزء الأول من النظرية اللي هي
+
+9
+00:00:54,960 --> 00:00:58,760
+ال first form ال fundamental theorem of calculus
+
+10
+00:00:58,760 --> 00:01:04,870
+اللي هي الجزء الأول بتقول ما يليlet f from a و b
+
+11
+00:01:04,870 --> 00:01:08,430
+لعند R be an integrable function on a و b يعني
+
+12
+00:01:08,430 --> 00:01:12,070
+فرضنا أن الـ function f عبارة عن دالة قابلة
+
+13
+00:01:12,070 --> 00:01:17,190
+للتكامل على الفترة المغلقة a و b and let f capital
+
+14
+00:01:17,190 --> 00:01:22,190
+من a و b لعند R تحقق الشروط التاليةتحقق أول شيء
+
+15
+00:01:22,190 --> 00:01:25,110
+أنها تكون الاف كابتنال هادي continuous على الفترة
+
+16
+00:01:25,110 --> 00:01:30,530
+a و b الشرط الثاني f prime exists and f prime of x
+
+17
+00:01:30,530 --> 00:01:34,130
+بساوي الاف small اللي بدأنا فيها دي الفرض منها
+
+18
+00:01:34,130 --> 00:01:39,880
+integrable لكل x element in a و bبنقول الـ
+
+19
+00:01:39,880 --> 00:01:44,900
+integration من A لB للـ F بساوي F of B ناقص F of A
+
+20
+00:01:44,900 --> 00:01:50,400
+إذا الآن و كإني بقول نفترض أنه الـ F small
+
+21
+00:01:50,400 --> 00:01:56,100
+integrable و نفترض F continuous على closed bounded
+
+22
+00:01:56,100 --> 00:02:01,160
+interval A و B و F نفسها differentiable على الـ
+
+23
+00:02:01,160 --> 00:02:05,260
+open اللي هو interval A و B بشرط أنه الـ F prime
+
+24
+00:02:05,260 --> 00:02:07,940
+ال derivative لها الـ F capital طبعا بساوي الـ F
+
+25
+00:02:07,940 --> 00:02:13,240
+small of Xوبناء على كل المعطيات اللي حكيناها بيكون
+
+26
+00:02:13,240 --> 00:02:17,120
+ال integration من a لb لل f small هو عبارة عن fb
+
+27
+00:02:17,120 --> 00:02:21,760
+ناقص f of a او اختصارا واسهلك للحفظ ال integration
+
+28
+00:02:21,760 --> 00:02:29,670
+من a لb لل f prime of x dx هي عبارة عنوكأنه
+
+29
+00:02:29,670 --> 00:02:36,250
+التكامل بلغ التفاضل بيصير اللي هي f of b ناقص f of
+
+30
+00:02:36,250 --> 00:02:40,610
+a هذا فضوء mean يعني هاي هادة باختصار هيك فضوء
+
+31
+00:02:40,610 --> 00:02:44,710
+mean أن f prime of x تكون موجودة على الفترة من a و
+
+32
+00:02:44,710 --> 00:02:51,370
+b و أيضا بتكون انهاش integrable نفسها integrable و
+
+33
+00:02:51,370 --> 00:02:56,110
+تكون ال f نفسها continuous على close من a ل عند b
+
+34
+00:02:56,390 --> 00:03:00,270
+هذه هي النظرية إذا اللي بدنا نثبته الآن أنه قيمة
+
+35
+00:03:00,270 --> 00:03:04,470
+ال integration هذا بساوي اللي هو اللي أمامنا اللي
+
+36
+00:03:04,470 --> 00:03:09,590
+هي f of b ناقص من ناقص f of a خلينا نشوف إيش
+
+37
+00:03:09,590 --> 00:03:15,030
+البكاء في البحران يا جماعةالان اللي واضح انه انا
+
+38
+00:03:15,030 --> 00:03:18,530
+بده اثبت انه ال integration هو عبارة عن f of b
+
+39
+00:03:18,530 --> 00:03:24,990
+ناقص f of a شوف انا كيف بده اوصلك اللي هو ال
+
+40
+00:03:24,990 --> 00:03:28,670
+integration لمنقلة ال b لل f بساوي f of b ناقص f
+
+41
+00:03:28,670 --> 00:03:32,010
+of a انا بعرف اول حاجة هو معطيلي ال f small هذه
+
+42
+00:03:32,010 --> 00:03:35,290
+اللي هي ال f prime اللي هي ال f small سميتها هذه
+
+43
+00:03:35,290 --> 00:03:39,240
+معطينيها integrallyMadame Integrable إذن بواسطة
+
+44
+00:03:39,240 --> 00:03:44,160
+اللي هي .. إذا بتتذكروا Integrable criterion وهي
+
+45
+00:03:44,160 --> 00:03:46,900
+اللي بنستخدمها كثير احنا لإنها .. يعني خلّيني أقول
+
+46
+00:03:46,900 --> 00:03:51,400
+صيغة مهمة في إثبات النظريات اللي هي بما إنه أف
+
+47
+00:03:51,400 --> 00:03:56,380
+Integrable إذن لكل Y أكبر من 0 يوجد there exists a
+
+48
+00:03:56,380 --> 00:04:00,600
+partition B اللي هو X0 X1 عند X ل .. عند ..
+
+49
+00:04:00,600 --> 00:04:03,280
+partition لمين طبعاً للفترة اللي أنتوا عارفينها
+
+50
+00:04:03,280 --> 00:04:06,800
+اللي احنا بنشتغل عليها الفترة من A لعند مين لعند B
+
+51
+00:04:06,960 --> 00:04:12,920
+There exists a partition B X0 X1 XN of A و B such
+
+52
+00:04:12,920 --> 00:04:20,280
+that ال other sum B F'-LB F' أصغر من إبسلون F' من
+
+53
+00:04:20,280 --> 00:04:24,000
+هنا من هي يا جماعة؟ هي ال F لأننا مفترضين ال F
+
+54
+00:04:24,000 --> 00:04:29,940
+small أو ال F' is integrable إذا بواسطة الرماء ال
+
+55
+00:04:29,940 --> 00:04:34,760
+integrable criterion حصلنا على واحد اللي عنده
+
+56
+00:04:34,760 --> 00:04:40,880
+إلحاةأحكي عنها الآن أو أستخدمها للوصول لهدفي طيب
+
+57
+00:04:40,880 --> 00:04:44,040
+because طبعا F prime اللي هي meme زي ما قلنا F of
+
+58
+00:04:44,040 --> 00:04:48,820
+X is integrable on A أو B الآن في شغلة تانية احنا
+
+59
+00:04:48,820 --> 00:04:55,880
+بدأ الآن أستخدم اللي هو أمر آخر خلينا نكتب الآن
+
+60
+00:04:55,880 --> 00:05:00,920
+أول شغلة حصلناها عشان تعرف أين أنا رايح اللي هي
+
+61
+00:05:00,920 --> 00:05:06,550
+قلنا F is integrableF التي بيسمى F' Integrable أيش
+
+62
+00:05:06,550 --> 00:05:12,270
+أعطتنا يا جماعة؟ أعطتنا أن هناك بارتيشن B هناك B
+
+63
+00:05:12,270 --> 00:05:15,830
+طبعا for every epsilon أكبر من سفر هناك بارتيشن B
+
+64
+00:05:15,830 --> 00:05:23,390
+such that U, B و F اللي هي الـ F' طبعا الـ F يمين
+
+65
+00:05:23,390 --> 00:05:29,530
+الـ F' ناقص الـ B و F هي أصغر من Y وهذا سمناها
+
+66
+00:05:29,530 --> 00:05:34,710
+إيش؟ سمناها 1لأن من جهة أخرى يا جماعة بدي أستغل
+
+67
+00:05:34,710 --> 00:05:37,810
+اللي هو اللي معطينيه أن الأفكار بتلقوا continuous
+
+68
+00:05:37,810 --> 00:05:41,490
+أنا الآن زي ما قلنا جزاقنا اللي هي الفترة A و B
+
+69
+00:05:41,490 --> 00:05:52,230
+إلىاللي هي X0 X1 X2 فترة نموذجية Xk-1 لعند Xk لعند
+
+70
+00:05:52,230 --> 00:05:56,010
+مين لعند Xn اللي هي مين الـ B هذا ال partition
+
+71
+00:05:56,010 --> 00:05:59,930
+اللي لجيته أنا الآن أنا بعرف أن ال F capital
+
+72
+00:05:59,930 --> 00:06:03,330
+continuous على ال closed interval كلها من A لعند B
+
+73
+00:06:03,330 --> 00:06:06,870
+إذا الأكيد continuous على كل sub interval موجودة
+
+74
+00:06:06,870 --> 00:06:12,540
+يعني صارت اللي عندي ال F capital continuouson a
+
+75
+00:06:12,540 --> 00:06:18,560
+التي هي xk-1 وعند xk هذه هي ال sub interval اللي
+
+76
+00:06:18,560 --> 00:06:24,080
+ال function f continuous عليها وإحنا مفترضين أيضا
+
+77
+00:06:24,080 --> 00:06:29,220
+أن ال f prime exist على ال open interval كلها إذا
+
+78
+00:06:29,220 --> 00:06:33,860
+أكيد ال fis differentiable لأن f' exist على ال
+
+79
+00:06:33,860 --> 00:06:37,360
+open interval من a لعند b إذا أكيد f is
+
+80
+00:06:37,360 --> 00:06:41,980
+differentiable على الفترة xk minus واحد لعند مين
+
+81
+00:06:41,980 --> 00:06:45,140
+لعند ال xk يعني يا جماعة شروط ال mean value
+
+82
+00:06:45,140 --> 00:06:50,020
+theorem محققة إذا أكيد there existthere exist بما
+
+83
+00:06:50,020 --> 00:06:54,540
+انه اللي هي شروط ال mean value محققة اذا there
+
+84
+00:06:54,540 --> 00:06:59,620
+exist بسميها اللي هو bk او tk there exist tk في
+
+85
+00:06:59,620 --> 00:07:06,440
+الفترة xk minus واحد عند ال xk such that اللي هو F
+
+86
+00:07:06,440 --> 00:07:11,520
+هي الدلل اللي بطبق عليها ال mean value theorem يا
+
+87
+00:07:11,520 --> 00:07:19,320
+جماعة F of xk ناقص F of xk minus واحداللي هو
+
+88
+00:07:19,320 --> 00:07:24,560
+بتساوي اللي هو xk ناقص xk مايلوس واحد طبعا احنا
+
+89
+00:07:24,560 --> 00:07:29,280
+بنكسب عليها اللي هي ايش بتساوي اللي هي ال F prime
+
+90
+00:07:30,370 --> 00:07:35,630
+of الهي main TK هذه اللي هي الـ Main Value Theorem
+
+91
+00:07:35,630 --> 00:07:39,710
+نتجتها مطبق على مين يا جماعة على الفترة اللي هي XK
+
+92
+00:07:39,710 --> 00:07:43,770
+minus واحد لعند XK طبعا هذا الكلام لكل K لأنه لكل
+
+93
+00:07:43,770 --> 00:07:48,170
+مين لكل ال sub intervals بتتحقق نفس الشروط بناء
+
+94
+00:07:48,170 --> 00:07:55,010
+عليه احنا بنعرف قبل هيك خليني أبدأ أشتغلها عند ال
+
+95
+00:07:55,010 --> 00:08:04,450
+MK إبراهيماللي هي أكيد أصغر أو يساوي الـ Fاللي هي
+
+96
+00:08:04,450 --> 00:08:11,370
+ال F عندك ال mk' ايش نذاكركم فيها ايش هي ال mk' ال
+
+97
+00:08:11,370 --> 00:08:15,190
+mk' هي مكتوبة لنكتبها كمان مرة ال mk' هي مين ال
+
+98
+00:08:15,190 --> 00:08:19,610
+infimum لل F' F of X X element of X K minus واحد X
+
+99
+00:08:19,610 --> 00:08:24,950
+K ال F' مين هذه ال F small ماشي الحال طيب ال F او
+
+100
+00:08:24,950 --> 00:08:30,590
+ال mk' هي عبارة عن ال infimum لمين لل F' على ال
+
+101
+00:08:30,590 --> 00:08:37,110
+sub interval هذه اذا اكيدأصغر أو يساوي الـ F of أي
+
+102
+00:08:37,110 --> 00:08:41,630
+مقطوين موجودة في الـ sub-interval والـ TK هدوين
+
+103
+00:08:41,630 --> 00:08:46,410
+موجودة في هذا الـ sub-interval إذن أكيد F of TK
+
+104
+00:08:46,410 --> 00:08:50,670
+أصغر من الـ MK' لأن الـ MK' هي عبارة عن الـ
+
+105
+00:08:50,670 --> 00:08:57,290
+infimum لقيمة الدالة F' of TK عالمياً على الفترة
+
+106
+00:08:57,290 --> 00:09:01,440
+اللي هي ال sub-interval اللي بنحكي عنها ككلوهذه
+
+107
+00:09:01,440 --> 00:09:06,040
+أكيد أصغر أو يساوي من الـ MK Ibrahim مين الـ MK
+
+108
+00:09:06,040 --> 00:09:11,060
+Ibrahim هذه؟ هي عبارة عن الـ Supremum لمين؟ لقيمة
+
+109
+00:09:11,060 --> 00:09:16,990
+اللي هي الدالة هذه على الفترة اللي عندهماشي الحال
+
+110
+00:09:16,990 --> 00:09:23,110
+إذا هذه دائما صحيحة طب لو ضربت جهتي كل الأطراف في
+
+111
+00:09:23,110 --> 00:09:27,650
+طول الفترة اللي هي xk minus xk minus واحد طبعا
+
+112
+00:09:27,650 --> 00:09:31,510
+أكيد هذه xk ناقص xk minus واحد كمية موجبة إذا لما
+
+113
+00:09:31,510 --> 00:09:35,010
+أضربها في الأطراف كلها بتظلها ال inequality صحيحة
+
+114
+00:09:35,010 --> 00:09:40,610
+وزي ما هي في xk ناقص xk minus واحد وهنا في xk ناقص
+
+115
+00:09:40,610 --> 00:09:46,280
+xk minus واحد مظبوط هذا الكلام أكيد صحطيب لكن هذا
+
+116
+00:09:46,280 --> 00:09:52,220
+المقدار هو هذا إذا باجي بحط هذه هان معايا جماعة
+
+117
+00:09:52,220 --> 00:09:57,000
+بحط هذه في المنطقة هذه المكان القيمة هذه اللي هي
+
+118
+00:09:57,000 --> 00:10:05,190
+هذه إذا صار عندي الأن Fof xk ناقص f of xk minus 1
+
+119
+00:10:05,190 --> 00:10:12,070
+أكبر أو يساوي ال Mk' في ال xk minus xk minus 1
+
+120
+00:10:12,070 --> 00:10:18,490
+وهذا أصغر أو يساوي ال Mk' في ال xk minus xk minus
+
+121
+00:10:18,490 --> 00:10:24,290
+1إذا واضح إن أنا حصلت على هذه وهذه صحيحة لكل مين
+
+122
+00:10:24,290 --> 00:10:28,150
+لكل كيه لإنه أخدت أنا هذه فترة عشوائية يعني لكي
+
+123
+00:10:28,150 --> 00:10:33,790
+بتساوي اللي هو واحد واتنين لعند مين لعند الان بناء
+
+124
+00:10:33,790 --> 00:10:38,250
+عليه أنا وصلت الآن إلى ما يليه وصلت إلى هذه
+
+125
+00:10:38,250 --> 00:10:43,670
+النتيجة شايفين يا جماعة وصلت إلى هذه النتيجة اللي
+
+126
+00:10:43,670 --> 00:10:48,860
+أنا وضحتلكم إياها كيف إجتالان و ال mk prime زي ما
+
+127
+00:10:48,860 --> 00:10:55,280
+قلنا ايش هي و ال mk capital prime هيها امامكم نيجي
+
+128
+00:10:55,280 --> 00:10:59,720
+الان ايش اللي بده حصله شوف ال K ايش بده حصل انا
+
+129
+00:10:59,720 --> 00:11:03,020
+عمال بقول انه صحيح على كل K اذا لو أخدت ال
+
+130
+00:11:03,020 --> 00:11:05,900
+summation هنا و أخدت ال summation هنا و أخدت ال
+
+131
+00:11:05,900 --> 00:11:10,440
+summation هنا بظل اللي هي ال inequality صحيحة خد
+
+132
+00:11:10,440 --> 00:11:16,050
+الآن ال summationعلى الفترة الـ summation على
+
+133
+00:11:16,050 --> 00:11:19,530
+الinquality اللي حكينا عنها هيها بيصير ال
+
+134
+00:11:19,530 --> 00:11:23,630
+summation لل M K برايم في X K X K minus واحد K من
+
+135
+00:11:23,630 --> 00:11:26,630
+عند واحد لعند M وهنا هيكون أصغر أو ساوى ال
+
+136
+00:11:26,630 --> 00:11:31,090
+summation لل F of X K ناقص F of X K minus واحد
+
+137
+00:11:31,090 --> 00:11:36,190
+اللي هي احنا هنا حصلناها هان وهذه ال summation
+
+138
+00:11:36,190 --> 00:11:39,490
+عليها وهذه ال summation عليها هي ال summation هذا
+
+139
+00:11:39,850 --> 00:11:43,210
+طيب يا جماعة أكيد أنتم اذكرين هذا ال summation هو
+
+140
+00:11:43,210 --> 00:11:47,770
+عبارة عن مين يا جماعة هو عبارة عن ال lower sum لل
+
+141
+00:11:47,770 --> 00:11:52,370
+partition بي على مين على الدالة اللي بنعمل عليها
+
+142
+00:11:52,370 --> 00:11:56,330
+اللي هي ال F' اللي اشتغلنا عليها اللي أخدنا ال F'
+
+143
+00:11:57,150 --> 00:12:01,270
+ال MK' هي ال infimum لل F' على ال sub interval
+
+144
+00:12:02,160 --> 00:12:07,220
+والان هذه يشبه يا جماعة هي ال upper sum يعني بمعنى
+
+145
+00:12:07,220 --> 00:12:12,960
+آخر صار عندى الآن المقدار هذا هي المقدار هذا اللى
+
+146
+00:12:12,960 --> 00:12:17,680
+محاط بالأزرق هذا المقدار و بالأحمر صار بين اللى هو
+
+147
+00:12:17,680 --> 00:12:22,120
+ال lower sum و بين ال upper sum لكن هذا المقدار
+
+148
+00:12:22,120 --> 00:12:25,860
+الصمشي اللى احنا عملناه قبل ذلك كتير لو فرضناه
+
+149
+00:12:25,860 --> 00:12:33,860
+هيكون عبارة عن F of X واحدناقص F of X Note زائد F
+
+150
+00:12:33,860 --> 00:12:40,360
+of X 2 ناقص F of X 1 زائد F of X 3 ناقص F of X 2
+
+151
+00:12:40,360 --> 00:12:45,460
+زائد لما أصل لآخر إشي F of X N ناقص F of X N ناقص
+
+152
+00:12:45,460 --> 00:12:50,520
+1 حلاجي كله بروح و بظل عندك كل هذا بروح و بظل عندك
+
+153
+00:12:50,520 --> 00:12:54,860
+بس F of X ناقص F of X N ناقص مين F of X Note كل
+
+154
+00:12:54,860 --> 00:13:00,340
+term ب cancel اللي قبله و يساويF of Xn اللي هي
+
+155
+00:13:00,340 --> 00:13:07,420
+مين؟ F of B F of Xnot اللي هي مين؟ F of A إذا صار
+
+156
+00:13:07,420 --> 00:13:10,920
+عندي الآن الـSummation هذا اللي هو بيسوي F of B
+
+157
+00:13:10,920 --> 00:13:16,440
+نقص مين؟ نقص F of A يعني بمعنى آخر بنشيل هذا و
+
+158
+00:13:16,440 --> 00:13:20,580
+بنحط مكانه قيمته اللي هو F of B نقص F of A بيصير F
+
+159
+00:13:20,580 --> 00:13:25,320
+of B minus F of A بين اللي هو L of B و F' و بين
+
+160
+00:13:25,320 --> 00:13:34,230
+الأبقى الـU of B و F'طيب اطلع على فوق شوية خليني
+
+161
+00:13:34,230 --> 00:13:39,830
+اوضحلك هذه النقطة اللي هتوصلي للي بديها انا ايش
+
+162
+00:13:39,830 --> 00:13:44,170
+بدي اثبت انا بدي اثبت ان ال integration خليني بس
+
+163
+00:13:44,170 --> 00:13:51,710
+اشيل هذا بعد اذنكم انا
+
+164
+00:13:51,710 --> 00:13:58,260
+بدي اثبت ان ال integration لل F prime of x dxأو
+
+165
+00:13:58,260 --> 00:14:06,320
+الـ F of X DX بساوي F of B ناقص F of A من A لعند
+
+166
+00:14:06,320 --> 00:14:12,870
+مين؟ لعند B، هيا، بدي أسهلشوف الان كيف انا في
+
+167
+00:14:12,870 --> 00:14:17,590
+الواقع بتوصلكم هذا نقص هذا يكون اكبر او يساوي سفر
+
+168
+00:14:17,590 --> 00:14:20,990
+و اصغر من epsilon لأي اصغر يساوي epsilon لكل
+
+169
+00:14:20,990 --> 00:14:24,110
+epsilon في الدنيا و من ثم هيساوي سفر يعني هتحدث
+
+170
+00:14:24,110 --> 00:14:29,090
+مين المساواة اللي مافهمش عليها هي الان نجلة تفصيل
+
+171
+00:14:29,090 --> 00:14:39,060
+اتفجنا احنا انه احنا حصلنا على اللي هوالـ F of D –
+
+172
+00:14:39,060 --> 00:14:44,520
+F of A بين الـ U و بين الـ L لكن احنا بنقول الـ F
+
+173
+00:14:44,520 --> 00:14:49,420
+نفسها يا جماعة الـ F' هذه is integrable مزام
+
+174
+00:14:49,420 --> 00:14:55,380
+Integrable من A لعند Bأذن الـ U of F و الـ L of F
+
+175
+00:14:55,380 --> 00:14:58,560
+اللي هو الـ Upper Integral و الـ Lower Integral
+
+176
+00:14:58,560 --> 00:15:01,960
+اللي هو هيساوي قيمة الـ Integration عارفينوا هذا
+
+177
+00:15:01,960 --> 00:15:05,760
+الكلام احنا بنتعرف شو معناته Integrable الـ U of F
+
+178
+00:15:05,760 --> 00:15:11,640
+هي عبارة عن مين؟ عن الـ infimum لمين؟ للكبار اللي
+
+179
+00:15:11,640 --> 00:15:19,640
+هي U L أو U P و Fوهذا عبارة عن الـ Supremum لنية
+
+180
+00:15:19,640 --> 00:15:28,200
+للـ L, B و F يعني بيصير عندي اللي هو هذا عبارة عن
+
+181
+00:15:28,200 --> 00:15:32,420
+ال U of F من جهة وهذا عبارة عن ال L of F من جهة
+
+182
+00:15:32,420 --> 00:15:35,900
+أخرى هذا ال integration نقلة بيه ال F' ليش؟ لأن ال
+
+183
+00:15:35,900 --> 00:15:40,630
+F' is integrable زي ما قلناهطيب، إيش علاقة الـ L و
+
+184
+00:15:40,630 --> 00:15:44,130
+F بهذه؟ L و F عبارة عن الـ Supremum لكل هذول، إذا
+
+185
+00:15:44,130 --> 00:15:47,450
+أكيد الـ L و F أكبر أو يساوي هذه، إذا صار ال
+
+186
+00:15:47,450 --> 00:15:51,610
+integration هذا اللي عندى أكبر أو يساوي الـ L و F،
+
+187
+00:15:51,610 --> 00:15:56,070
+خلصنا من هذه، لأن من جهة ثانية ال integration لل F
+
+188
+00:15:56,070 --> 00:15:58,510
+براين هو الـ U of F، لأن الـ F is integrable زي ما
+
+189
+00:15:58,510 --> 00:16:04,770
+قلنا، و الـ U of F مين هو؟هو عبارة عن الـ infimum
+
+190
+00:16:04,770 --> 00:16:08,810
+لها دول إذا الـ U of F أصغر أو يشويها مزام أصغر أو
+
+191
+00:16:08,810 --> 00:16:12,210
+يشويها يعني صار ال integration أصغر أو يشويها يعني
+
+192
+00:16:12,210 --> 00:16:18,050
+بمعنى آخر احنا وصلنا ان ال integration تبعناالـ
+
+193
+00:16:18,050 --> 00:16:23,450
+integration اللي هو من A لعند A بي لل F برايم بين
+
+194
+00:16:23,450 --> 00:16:29,530
+ال L و بين مين و بين ال U ماشي الحالة الآن و هذا
+
+195
+00:16:29,530 --> 00:16:35,390
+برضه بين ال L و بين مين ال U اضربلي الآن اللي تحت
+
+196
+00:16:35,390 --> 00:16:41,820
+اللي هو بسالببتنعكس ال inequality وبعدين اجمعل
+
+197
+00:16:41,820 --> 00:16:46,320
+الجهتين ماشي الحال هذي بيصير سالب وهذي بيصير أكبر
+
+198
+00:16:46,320 --> 00:16:51,220
+أو يساوي سالب وهذي بيصير أكبر أو يساوي سالب اجمعل
+
+199
+00:16:51,220 --> 00:16:56,980
+الجهتين بيصير عند ال integrationأو العكس اضرب اللي
+
+200
+00:16:56,980 --> 00:16:59,720
+فوق بالسالب عساس ان اعمل زي ما عامل هو هان اضرب
+
+201
+00:16:59,720 --> 00:17:02,000
+اسف اللي هو اضرب مين اللي فوق بالسالب يصير هذا
+
+202
+00:17:02,000 --> 00:17:07,640
+ناقص وهذا كله ناقص وهذا عبارة عن ناقص وهذا اكبر او
+
+203
+00:17:07,640 --> 00:17:12,760
+يساوي وهذا اكبر او يساوي واجمح لبعض او بلغة اخرى
+
+204
+00:17:13,150 --> 00:17:16,790
+قول اللي .. اللي .. اللي .. اللي تحت ناقص اللي فوق
+
+205
+00:17:16,790 --> 00:17:20,130
+بطلع عندى ال integration لل F prime من A ل عند B
+
+206
+00:17:20,130 --> 00:17:24,730
+ناقص اللي هي F of B minus F of A أصغر يساوي ال U
+
+207
+00:17:24,730 --> 00:17:30,770
+ناقص ال L و أكبر أوي يساوي ال L ناقص ال U واضح أنه
+
+208
+00:17:30,770 --> 00:17:36,480
+هذهعبارة عن ناقص هذه وهذه كمية موجبة إذا صار عند
+
+209
+00:17:36,480 --> 00:17:41,000
+ال absolute value للقيمة هذه أصغر أو يساوي ال U
+
+210
+00:17:41,000 --> 00:17:49,300
+ناقص مين ال L كمان مرة هذه سالب هذهوهذه موجبة إذاً
+
+211
+00:17:49,300 --> 00:17:53,540
+هذه الـ Inquality صارت هي عبارة عن مفكوك الـ
+
+212
+00:17:53,540 --> 00:17:57,440
+absolute value للـ F prime ال integration ناقص
+
+213
+00:17:57,440 --> 00:18:01,840
+المقدار هذا أصغر أو يساوي هذا القيمة وهذا القيمة
+
+214
+00:18:01,840 --> 00:18:05,700
+لسه ما سحنهاش احنا إيش قلنا عنها أصغر من من إبسلان
+
+215
+00:18:05,700 --> 00:18:09,280
+وانا قاعد باشتغل على ال partition اللي لجيته أعلى
+
+216
+00:18:09,280 --> 00:18:15,390
+إذا صار عندى الآن اللي وصلتلهعبارة عن اللي هو ال
+
+217
+00:18:15,390 --> 00:18:20,150
+absolute value هذا أصغر من إبسلون وطبعا أكبر أوي
+
+218
+00:18:20,150 --> 00:18:24,790
+ساوي سفر والإبسلون واز إيه شمالها arbitrary يعني
+
+219
+00:18:24,790 --> 00:18:29,430
+المقدار هذا لأي إبسلون في الدنيا لأي إبسلون في
+
+220
+00:18:29,430 --> 00:18:33,770
+الدنيا هذا أصغر من مين من الإبسلون هو أكبر أوي سفر
+
+221
+00:18:33,970 --> 00:18:38,510
+إذاً لازم يكون هذا المقدار اللي هو عبارة عن سفر
+
+222
+00:18:38,510 --> 00:18:42,530
+يعني بمعنى آخر ال integration بساوي اللي هو F of B
+
+223
+00:18:42,530 --> 00:18:47,050
+نقص F of A و هيك و نكون حصلنا على المطلوب و أثبتنا
+
+224
+00:18:47,050 --> 00:18:51,470
+النظرية طيب
+
+225
+00:18:51,470 --> 00:18:57,850
+الجماعة الان هذا اللي هو الجزء الأولالجزء الأول من
+
+226
+00:18:57,850 --> 00:19:00,890
+اللي هو الـ Fundamental Theorem of Calculus اللي
+
+227
+00:19:00,890 --> 00:19:05,750
+هو عبارة عن تكامل التفاضل اللي هي عملية التكامل
+
+228
+00:19:05,750 --> 00:19:10,470
+هتلغى عملية التفاضل زي ما شفنا اللي هو قبل بشوية
+
+229
+00:19:10,470 --> 00:19:15,130
+وشفنا إيه اللي جالته الـ Fundamental Theorem طبعا
+
+230
+00:19:15,130 --> 00:19:20,270
+هذا الكلام تحت الشروط المذكورةالآن بقول لي .. يمكن
+
+231
+00:19:20,270 --> 00:19:24,810
+حكيت هادى حتى بقول لي corollary بقول انا أحيانا
+
+232
+00:19:24,810 --> 00:19:29,530
+بحب أريح حالي و نقول خلينا ناخد .. عشان نستذكر ال
+
+233
+00:19:29,530 --> 00:19:32,790
+.. ال .. ال .. ال fundamental theorem الجزء الأول
+
+234
+00:19:32,790 --> 00:19:37,950
+بشكل سريع بس شويه عندنا نعمل .. في الشروط ان هو قف
+
+235
+00:19:37,950 --> 00:19:41,630
+من a ل b لعند R satisfy the conditionsاللي هو F'
+
+236
+00:19:42,150 --> 00:19:45,790
+exists on A وB، مابتدش أجيب سيرة مين الـ F Small؟
+
+237
+00:19:45,790 --> 00:19:49,250
+مابتدش أشغل مين؟ على الـ F Capital لو فرضنا إن الـ
+
+238
+00:19:49,250 --> 00:19:54,010
+F هذه من A وB لعند R إنها الـ F' اللي هي الشمالها
+
+239
+00:19:54,010 --> 00:19:57,890
+exist على الـ A وB يعني فرض إنها، بس هنا زاد شوية
+
+240
+00:19:57,890 --> 00:20:01,130
+على الشروط اللي جابل بشوية إن F is differentiable
+
+241
+00:20:01,130 --> 00:20:03,790
+على الـ closed interval كنا فرضينها إنها F
+
+242
+00:20:03,790 --> 00:20:06,740
+differentiable على الـ Openوفرضين إنها continuous
+
+243
+00:20:06,740 --> 00:20:10,760
+على اللي هي الـ Closed مدام الآن إذا فيها دي سنة
+
+244
+00:20:10,760 --> 00:20:16,680
+زيادة من ال .. من اللي هي الشروط F' exists على الـ
+
+245
+00:20:16,680 --> 00:20:19,820
+A و الـ B يعني continuous و differentiable على الـ
+
+246
+00:20:19,820 --> 00:20:24,350
+closed open .. على ال closed interval A و Bالان هي
+
+247
+00:20:24,350 --> 00:20:29,550
+الشرط والشرط الثاني فرض ان ال F' مش موجودة و بس ال
+
+248
+00:20:29,550 --> 00:20:33,030
+F' انتجر بالعلى ال A و ال B إذا انتجقت شروط ال
+
+249
+00:20:33,030 --> 00:20:36,210
+fundamental theorem إذا حسب ال fundamental theorem
+
+250
+00:20:36,210 --> 00:20:39,410
+اللي قبله شوية بكون عنده ال integration من A لB
+
+251
+00:20:39,410 --> 00:20:44,190
+لمين الآنللـ f prime اللي كنا نسميه في الجبل f
+
+252
+00:20:44,190 --> 00:20:49,310
+small بتساوي f of b ناقص f of a إذا فعلا هي
+
+253
+00:20:49,310 --> 00:20:53,130
+automatic حققت شروط ال fundamental theorem وزيادة
+
+254
+00:20:53,130 --> 00:20:59,850
+سنة إذا أكيد النتيجة بتكون صحيحة يعنيتكامل الدالة
+
+255
+00:20:59,850 --> 00:21:05,210
+المتفاضلة بساوء أصل الدالة اللي هو أصل الدالة عنده
+
+256
+00:21:05,210 --> 00:21:09,070
+النقطة الأولى نقص النقطة مين بنحكي النقطة الثانية
+
+257
+00:21:09,070 --> 00:21:13,950
+اللي هو عبارة عن integration F of B نقص مين F of A
+
+258
+00:21:13,950 --> 00:21:19,210
+طب لو كانت X متغير يعني لو أخذنا أي X بين الفترتين
+
+259
+00:21:19,210 --> 00:21:23,550
+وطبّجنا نظرية على الـA اللي عند الـXفبصير ال
+
+260
+00:21:23,550 --> 00:21:27,130
+integration من إلي إلى عند ال X أف براين بساوي أف
+
+261
+00:21:27,130 --> 00:21:32,490
+of X ناقص أف of A X هذه هتصبح متغيرة والأف of A
+
+262
+00:21:32,490 --> 00:21:39,190
+ثابتة وهذا بيذكرنا انه احنا قيمة التكامل لدالة
+
+263
+00:21:39,190 --> 00:21:43,790
+بساوي اللي هو عبارة عن اللي هي الإجابة اللي هي
+
+264
+00:21:43,790 --> 00:21:47,630
+الدالة اللي بتطلع زائد some constant C اللي هو ال
+
+265
+00:21:47,630 --> 00:21:53,660
+constant طبعا لاللي هيطبيعة الديالي لقداش بيطلعلنا
+
+266
+00:21:53,660 --> 00:21:56,420
+اللي هو ال initial conditions بيسفرلنا إياه ال
+
+267
+00:21:56,420 --> 00:21:59,620
+constant أو بيعطينا إياه خمسة أربعة ستة أو بيظلوا
+
+268
+00:21:59,620 --> 00:22:03,720
+بصورة عامة Constancy طيب شوفوا صلوا على النبي عليه
+
+269
+00:22:03,720 --> 00:22:08,090
+الصلاة والسلامالآن بدنا نيجي للجزء الثاني من الـ
+
+270
+00:22:08,090 --> 00:22:11,470
+Fundamental theorem خلصنا جزء اللي هو تكامل
+
+271
+00:22:11,470 --> 00:22:16,870
+التفاضل، الآن بنتوقع إنه انفاضل التكامل، انفاضل
+
+272
+00:22:16,870 --> 00:22:20,530
+التكامل، تحت شروط، بنشوف اللي هي ال Fundamental
+
+273
+00:22:20,530 --> 00:22:24,650
+theorem of calculus second form أو اللي هو الجزء
+
+274
+00:22:24,650 --> 00:22:27,850
+الثاني من ال Fundamental theorem، إيش اللي بيقوله؟
+
+275
+00:22:27,850 --> 00:22:33,540
+اللي بيقول معايا ليه، نفترض إن F smallمن a و b
+
+276
+00:22:33,540 --> 00:22:38,060
+لعند r اللي هو is integrable in a و b إذا انفرضناه
+
+277
+00:22:38,060 --> 00:22:41,460
+انه integrable ونفرض أن f of x هو بيساوي ال
+
+278
+00:22:41,460 --> 00:22:46,160
+integration من a ل x f for all x element in a و b
+
+279
+00:22:46,160 --> 00:22:52,200
+بس لان نيجي للنتيجة thenهيطلع هذا عبارة عن
+
+280
+00:22:52,200 --> 00:22:55,360
+continuous function في ال .. في ال .. اللي هي main
+
+281
+00:22:55,360 --> 00:23:02,700
+في اللي هي على الفترة a أو b ومش هي كمان ولو كان
+
+282
+00:23:02,700 --> 00:23:09,830
+ال Fsmall continuous عند نقطة C في الفترة من A
+
+283
+00:23:09,830 --> 00:23:14,050
+لعند B أو من A لعند X هتكون ال F هذه نفسها
+
+284
+00:23:14,050 --> 00:23:16,950
+differentiable و ال derivative اللي هي إيش بساوي
+
+285
+00:23:16,950 --> 00:23:22,590
+بساوي قيمة اللي هو ال F اللي جوا يعني باختصار يا
+
+286
+00:23:22,590 --> 00:23:29,450
+جماعة بتتكررها سهل بقولك مفترض FIntegrable ماشي
+
+287
+00:23:29,450 --> 00:23:34,690
+الحال هاي بس الان بقول لو جيت اخدت من A ل X on
+
+288
+00:23:34,690 --> 00:23:44,670
+طبعا A و B لو اخدت الان A و X F small of T DT هاي
+
+289
+00:23:44,670 --> 00:23:51,510
+ده طبعا الان صارت كلها تعتمد على مين على X بقولك
+
+290
+00:23:51,510 --> 00:23:55,370
+هذههذه اللي طلع اللي هو الـ integration للـ
+
+291
+00:23:55,370 --> 00:24:01,130
+integrable function من A ل X F of T DT هتطلع لي
+
+292
+00:24:01,130 --> 00:24:05,210
+continuous function لو سميتها F capital زي ما هو
+
+293
+00:24:05,210 --> 00:24:08,730
+مسميها F of X بتكون الـ F عندها شمالها is
+
+294
+00:24:08,730 --> 00:24:16,430
+continuous الآن بقولك لو اجيت و قلت ان Fis
+
+295
+00:24:16,430 --> 00:24:21,390
+continuous الـ F اللي جوا هذه at C element in A وB
+
+296
+00:24:21,390 --> 00:24:25,650
+لو كانت F is continuous at C element in A وB
+
+297
+00:24:25,650 --> 00:24:31,730
+هيطلعلك بقولك إذا الـ F capital هذه F prime of C
+
+298
+00:24:31,730 --> 00:24:39,870
+existsو مش exist بس و ال F prime of C هتساوي ال F
+
+299
+00:24:39,870 --> 00:24:46,030
+small of إيش؟ of C يعني و كأنه بقولك لما نتفاضل
+
+300
+00:24:46,030 --> 00:24:50,210
+هذه F prime of C اللي هي من إيه اللي عند C يعني
+
+301
+00:24:50,210 --> 00:24:57,370
+تقول F prime of C بساوي تفاضل رفلة by DXعنده
+
+302
+00:24:57,370 --> 00:25:02,630
+النقطة C لل integration من A ل X F of T DT
+
+303
+00:25:27,580 --> 00:25:33,180
+C مثلاً بتساوي F of C اللي هي F small of C هو كون
+
+304
+00:25:33,180 --> 00:25:36,540
+ال F اللي جوا continuous عنده النقطة اللي بنحكي
+
+305
+00:25:36,540 --> 00:25:39,940
+عنها طب لو كانت F اللي جوا هادى continuous وين
+
+306
+00:25:39,940 --> 00:25:43,620
+ماكان على الفترة هادى بصير خلاص وانت مغمض عناك
+
+307
+00:25:43,620 --> 00:25:47,980
+بتيجي بتقول تفاضل هادي بتشيل التكامل و بتحطه اللي
+
+308
+00:25:47,980 --> 00:25:53,540
+جوا بدلالة اللي هي ال X المتغيرواضح المفروض طيب
+
+309
+00:25:53,540 --> 00:25:59,660
+نيجي الآن نثبت اللي هي النظرية نثبت شغلتين أن ال F
+
+310
+00:25:59,660 --> 00:26:02,580
+كابتنال continuous عشان أثبتلك continuous هثبتلك
+
+311
+00:26:02,580 --> 00:26:05,940
+أكثر من continuous هثبتلك uniform ل continuous لأ
+
+312
+00:26:05,940 --> 00:26:09,780
+أقولك هثبتلك أكثر من uniform ل continuous هثبتلك
+
+313
+00:26:09,780 --> 00:26:12,920
+أن ال F is Lipschitz function مثلا من Lipschitz
+
+314
+00:26:12,920 --> 00:26:15,400
+function إذا على طول uniform ل continuous ومن ثم
+
+315
+00:26:15,400 --> 00:26:18,460
+على طول إيش ما لها continuous إيش Lipschitz
+
+316
+00:26:18,460 --> 00:26:25,240
+function يعني هثبتلك أن Fof x-f of y absolute
+
+317
+00:26:25,240 --> 00:26:30,720
+value أصغر أو ساوي k في x-y had there exist k بحيث
+
+318
+00:26:30,720 --> 00:26:35,260
+أن f of x-f of y أصغر من k في xy لكل x و y element
+
+319
+00:26:35,260 --> 00:26:40,020
+in a و b هثبت لك f بتحقق هذا الشرط هثبتها ما ده
+
+320
+00:26:40,020 --> 00:26:42,540
+هثبتها ما ده هتحقق هذا الشرط إذا ما على طول اللي
+
+321
+00:26:42,540 --> 00:26:45,680
+هي هتكون lipschitz يعني بمعنى آخر هتكون is
+
+322
+00:26:45,680 --> 00:26:49,480
+continuous هذا الجزء الأول الجزء الثاني يا شباب و
+
+323
+00:26:49,480 --> 00:26:55,760
+يا بناتلأن if F is continuous at C هنثبت أن F is
+
+324
+00:26:55,760 --> 00:26:59,320
+differentiable عند C يعني بدأ أثبتلك F is
+
+325
+00:26:59,320 --> 00:27:03,460
+differentiable عند C يعني ايش F is differentiable
+
+326
+00:27:03,460 --> 00:27:14,660
+يعني بدأ أثبتلك أن limit F of X زي داتش مثلا او F
+
+327
+00:27:14,660 --> 00:27:21,440
+of C زي داتش ناقص F of Cعلى H اذا H بتروح للصفر
+
+328
+00:27:21,440 --> 00:27:27,380
+بتثبت لك ايه ايش بيساوي F capital طبعا بيساوي F
+
+329
+00:27:27,380 --> 00:27:33,660
+small of Cبدي أثبتلك يعني أو بمعنى آخر هأثبتلك لكل
+
+330
+00:27:33,660 --> 00:27:37,000
+Y أكبر من 0 داريكزيز ديلتا بحيث أنه absolute value
+
+331
+00:27:37,000 --> 00:27:41,320
+أصغر من Delta L على H أصغر من Delta يؤدي إلى F of
+
+332
+00:27:41,320 --> 00:27:48,260
+C زائد H ناقص F of C على H ناقص F of C بدي أثبتلك
+
+333
+00:27:48,260 --> 00:27:53,180
+يه أصغر من 200 من Epsilonبكون اثبتت فعلا انه هذه
+
+334
+00:27:53,180 --> 00:27:56,540
+ال limit بالساوية هذه معناته هذه ال limit طبعا ايش
+
+335
+00:27:56,540 --> 00:28:01,000
+بتعني ان F prime F capital prime of C exist و
+
+336
+00:28:01,000 --> 00:28:06,480
+بتساوية F of C اللي هو اللي هو طالبه انه لما تكون
+
+337
+00:28:06,480 --> 00:28:09,280
+F continuous عند ال C بتكون F capital
+
+338
+00:28:09,280 --> 00:28:12,040
+differentiable عند ال C و ال derivative لل F
+
+339
+00:28:12,040 --> 00:28:15,700
+capital بتساوية ال F اسمه فنشوف
+
+340
+00:28:17,960 --> 00:28:21,380
+Media نثبت الـ Continuity أو نثبت الـ Lipschitz
+
+341
+00:28:21,380 --> 00:28:27,450
+function يعني الأمر سهلأحنا مفترضين يا جماعة أن
+
+342
+00:28:27,450 --> 00:28:31,490
+الـF small هذي is integrable مزام is integrable
+
+343
+00:28:31,490 --> 00:28:37,650
+إذا is bounded S يعني أنه لكل .. نقدر نلاقي K أكبر
+
+344
+00:28:37,650 --> 00:28:41,830
+من 0 بحيث أن ال absolute value ل F of X small أصغر
+
+345
+00:28:41,830 --> 00:28:48,070
+سوى K لكل X موجودة ال A و ال B سبب هذه أن F نفسها
+
+346
+00:28:48,070 --> 00:28:52,350
+is integrable طيب، بدأ اعتمد على هذه للوصول إنها
+
+347
+00:28:52,350 --> 00:28:58,620
+لبشتالان خد اي x و y في ال a و ال b واسمحولي اخد x
+
+348
+00:28:58,620 --> 00:29:01,760
+اقل من y without loss of generality مش عاد باخد y
+
+349
+00:29:01,760 --> 00:29:06,100
+اكبر من .. اصغر من x الان حالة ال x بتساوي
+
+350
+00:29:06,100 --> 00:29:09,660
+هتلاقوها automatic بتتحقق للي بديها نشوف ايش اللي
+
+351
+00:29:09,660 --> 00:29:13,790
+بديهاالان خد x و y في ال a و ال b و نفترض ان x
+
+352
+00:29:13,790 --> 00:29:16,610
+أزرار من y without most of generality زي ما قلنا
+
+353
+00:29:16,610 --> 00:29:22,890
+الان احسبلي f of x f of y نقص مين f of x الكبيرة y
+
+354
+00:29:22,890 --> 00:29:26,630
+و الكبيرة x احسب f of y نقص f of x ايش هيساوي ال
+
+355
+00:29:26,630 --> 00:29:29,470
+integration حسب التعريف f of x بتساوي ال
+
+356
+00:29:29,470 --> 00:29:33,390
+integration من ال x ل ال f smallالأن f of y هي
+
+357
+00:29:33,390 --> 00:29:36,930
+عبارة عن ال integration من a ل y، f small، ناقص، f
+
+358
+00:29:36,930 --> 00:29:40,210
+of x إيش بتساوي؟ ال integration من a ل x ل مين؟ لل
+
+359
+00:29:40,210 --> 00:29:47,290
+F، إذا هذا ناقص هذا، الآن بدي أحول هذه، أجلبها،
+
+360
+00:29:47,290 --> 00:29:52,670
+بيصير زائد ال integration من x لعند مين، لعند ال
+
+361
+00:29:52,670 --> 00:29:57,640
+a، لل Fصار عندى الآن ال integration من X لعند ال A
+
+362
+00:29:57,640 --> 00:30:00,520
+و من A لعند ال Y إذا حيصير هذا عبارة عن ال
+
+363
+00:30:00,520 --> 00:30:05,940
+integration من X لمين من X لعند ال Y عارفين هذه
+
+364
+00:30:05,940 --> 00:30:09,960
+الخاصية إذا صار عند ال F of X F of Y ناقص F of X
+
+365
+00:30:09,960 --> 00:30:15,760
+بسوء ال integration من X ل Y لمين لل F شوف الآن
+
+366
+00:30:15,760 --> 00:30:20,100
+إيش بده أصل؟ بده أصل إنه absolute value F of Y
+
+367
+00:30:20,100 --> 00:30:24,830
+ناقص F of Xأصغر أو سوى K في الـ absolute value X
+
+368
+00:30:24,830 --> 00:30:31,450
+مانس Y يعني صارت لبشت لنشوف كيف نصلها وأكيد بعضكم
+
+369
+00:30:31,450 --> 00:30:36,450
+فهم او اتوقع كيف بتسوي لأن صار ال absolute value
+
+370
+00:30:36,450 --> 00:30:40,250
+لهذه بسوى ال absolute value لهذه هيها لأن ال
+
+371
+00:30:40,250 --> 00:30:43,010
+absolute value ال integration بخاصية احنا عارفينها
+
+372
+00:30:43,010 --> 00:30:46,770
+أصغر أو سوى ال integration لل absolute valueوالـ
+
+373
+00:30:46,770 --> 00:30:50,990
+absolute value للـ F في الفترة X وY أشملها .. هي
+
+374
+00:30:50,990 --> 00:30:53,570
+مش في الفترة X وY بس الـ absolute value للـ F الـ
+
+375
+00:30:53,570 --> 00:30:56,170
+absolute value للـ F أصغر أو سوى K على كل الفترة
+
+376
+00:30:56,170 --> 00:31:01,030
+الكبيرة اللي هي A وB فأكيد برضه هتكون أصغر أو سوى
+
+377
+00:31:01,030 --> 00:31:05,670
+K على الفترة الصغيرة فصار عندي أصغر أو سوى K في
+
+378
+00:31:05,670 --> 00:31:07,890
+مين؟ في ال integration من X لعند Y ال integration
+
+379
+00:31:07,890 --> 00:31:13,080
+من X لعند Y هو إيش بساوي؟ اللي هو Y minus Xالـ
+
+380
+00:31:13,080 --> 00:31:19,400
+integration يعني ال integration لـ DT من X لـ DT
+
+381
+00:31:19,400 --> 00:31:28,660
+ال integration لـ DT من X عند Y ايش بيساوي Y minus
+
+382
+00:31:28,660 --> 00:31:36,240
+X Y minus X فهذا صار Y minus X و اللي جوا أصغر
+
+383
+00:31:36,240 --> 00:31:40,790
+بيساوي Kالان هذا على خطوتين سهلات بتصور ان انتوا
+
+384
+00:31:40,790 --> 00:31:44,370
+فاهمينش بحكي من X لعند Y ال integration لل F فده
+
+385
+00:31:44,370 --> 00:31:47,850
+أصغر أو ساوي اللي هو ال integration من X لعند Y
+
+386
+00:31:47,850 --> 00:31:55,370
+هذه بدلة K لكل DT وهذا بساوي K برة في Y minus X
+
+387
+00:31:55,370 --> 00:31:59,230
+اللي هو أكيد حيصير عند ال absolute value هذه أصغر
+
+388
+00:31:59,230 --> 00:32:03,770
+أو ساوي K في ال absolute value Y minus Xالان هذه
+
+389
+00:32:03,770 --> 00:32:07,570
+ال Xات الأصغر من مين؟ من Y لكن زي ما انتوا عارفين
+
+390
+00:32:07,570 --> 00:32:11,150
+حالة ال X بتساوي Y is trivial لأن لما تكون X
+
+391
+00:32:11,150 --> 00:32:14,450
+بتساوي Y هذا سفر و لما تكون X بتساوي Y هذا سفر إذا
+
+392
+00:32:14,450 --> 00:32:18,610
+ال inequality هذه صحيحة دائما إذا الأن صار عندى
+
+393
+00:32:18,610 --> 00:32:25,590
+هذه ال inequality staris true for all x و y
+
+394
+00:32:25,590 --> 00:32:30,390
+limiting a و b لأنه قلنا ال x أصغر من y ال y أصغر
+
+395
+00:32:30,390 --> 00:32:33,990
+من x أكيد similarly و بنفس الأسلوب أو حتى without
+
+396
+00:32:33,990 --> 00:32:38,170
+loss of generality يعني بدون ما نفقد أي إشي من
+
+397
+00:32:38,170 --> 00:32:44,530
+التعميم بنفترض أن x أصغر من y صار
+
+398
+00:32:44,530 --> 00:32:53,230
+عندي يا جماعةالان F مستمر على A وB لأن F بيصبح
+
+399
+00:32:53,230 --> 00:33:02,750
+عملية Lipschitz اللي هي الآن ضال علي أثبت أن الـ F
+
+400
+00:33:02,750 --> 00:33:11,100
+مستخدم وزي ما قلت بدأ أثبت أن الـ Limitللـ F of C
+
+401
+00:33:11,100 --> 00:33:17,800
+زائد H نقص F of C على H لما H تروح للصفر بساوة F
+
+402
+00:33:17,800 --> 00:33:23,480
+small of C أو أثبت لكم الفرق بين هذولتين أصغر من
+
+403
+00:33:23,480 --> 00:33:28,880
+إبسلون وهذا زي ما قلنا هو اللي هيمثل F' of C ده
+
+404
+00:33:28,880 --> 00:33:34,160
+نشوف كيف طيب الصلاة على النبي صلاة والسلام عليك
+
+405
+00:33:37,390 --> 00:33:42,130
+خلّينا نجف عند .. أيوة نيجي الآن البرهان هتلاقوه
+
+406
+00:33:42,130 --> 00:33:49,730
+برضه سهل وفكرته سهلة شوفوا كيف عندي نفترض الآن
+
+407
+00:33:49,730 --> 00:33:53,550
+suppose that f is continuous at c limiting a وb
+
+408
+00:33:53,550 --> 00:33:58,790
+مدام continuous إذن limit
+
+409
+00:34:01,700 --> 00:34:08,460
+F of X as X بتروح للـ C بساوي F of C مظبوط ولا لأ؟
+
+410
+00:34:08,460 --> 00:34:12,300
+أكيد مظبوط فبقى من جهة أخرى خلينا نكتبها بصورة
+
+411
+00:34:12,300 --> 00:34:18,660
+ثانية X ناقص C بتروح للسفر if and only if اللي هو
+
+412
+00:34:18,660 --> 00:34:23,960
+X بتروح لمين للـ C سمولي هذه X minus C إيش اسمها H
+
+413
+00:34:23,960 --> 00:34:31,410
+بصير هذه اللي فوق مين هي limitF of الـ X minus C
+
+414
+00:34:31,410 --> 00:34:36,490
+بتساوي الـ H يعني الـ X بتساوي H زائد C أو C زائد
+
+415
+00:34:36,490 --> 00:34:41,190
+Hلأن x بتروح للـ c تكافئ أنه .. اللي هو x minus c
+
+416
+00:34:41,190 --> 00:34:44,610
+تروح للصفر، يعني بتكافئ H تروح لمين للصفر، إيش حيث
+
+417
+00:34:44,610 --> 00:34:49,650
+هو هذا؟ F of C، إذا هذه هي تعبير آخر عن ال
+
+418
+00:34:49,650 --> 00:34:56,250
+continuity لل F لما اللي هو اللي هي ال F عند مين،
+
+419
+00:34:56,250 --> 00:34:59,210
+عند ال C، يعني هذه تعبير آخر، ال continuity لل
+
+420
+00:34:59,210 --> 00:35:05,900
+function لما عند النقطة اللي هي Cهذه الآن شو بدي
+
+421
+00:35:05,900 --> 00:35:09,520
+استخدمها للوصول اللي بديها لأن مادام F is
+
+422
+00:35:09,520 --> 00:35:12,600
+continuous ده هذي متحققة هيها مادام F is
+
+423
+00:35:12,600 --> 00:35:15,480
+continuous عن C ده هذي متحققة فمادام هذي متحققة
+
+424
+00:35:15,480 --> 00:35:18,720
+اذا by epsilon delta definition for every epsilon
+
+425
+00:35:18,720 --> 00:35:22,880
+أكبر من 0 there exists delta أكبر من 0 such that
+
+426
+00:35:22,880 --> 00:35:28,950
+لما يكون ال absolute value لل H أصغر من Deltaو
+
+427
+00:35:28,950 --> 00:35:32,230
+طبعا انا وين بشتغل في المنطقة انها تكون C زائد H
+
+428
+00:35:32,230 --> 00:35:36,370
+وين ما لأ في الفترة تبعت من A لعند مين لعند B يعني
+
+429
+00:35:36,370 --> 00:35:41,230
+اخترت ال H صغيرة كفاية بحيث انه C زائد H اضلي وين
+
+430
+00:35:41,230 --> 00:35:45,090
+جاعد في الفترة من A و B لعنده لإن هاي الفترة A وهي
+
+431
+00:35:45,090 --> 00:35:49,330
+Bوالفترة هذه اللي هي I C عندي مثلا في داخلها اللي
+
+432
+00:35:49,330 --> 00:35:55,690
+هي بتختار H دلتتها صغيرة كفاية أنه ضال C زائد H
+
+433
+00:35:55,690 --> 00:36:01,050
+موجودة في الفترة من A لعند B عشان تصير معرفة لإن
+
+434
+00:36:01,050 --> 00:36:05,330
+دالتي أنا عشان تكون معرفة عند C زائد H لازم تكون C
+
+435
+00:36:05,330 --> 00:36:08,490
+زائد H في داخل المنطقة هذه لإن دالتي معرفة على
+
+436
+00:36:08,490 --> 00:36:11,770
+الفترة من A لعند B عشان هيك أقولنا C زائد H لازم
+
+437
+00:36:11,770 --> 00:36:16,630
+تكون في الفترة زائد Bإذن اختيار الـ Delta يعتمد
+
+438
+00:36:16,630 --> 00:36:20,210
+على ال limit ويعتمد على انه أضمن ال C زي داشر ضال
+
+439
+00:36:20,210 --> 00:36:24,510
+هوين في الفترة A وB إذا تعريف ال continuity بيقول
+
+440
+00:36:25,950 --> 00:36:27,530
+لكل y أقوم باستخدام صفر يوجد دلتا لكل y أقوم
+
+441
+00:36:27,530 --> 00:36:28,970
+باستخدام صفر يوجد دلتا لكل y أقوم باستخدام صفر
+
+442
+00:36:28,970 --> 00:36:29,950
+يوجد دلتا لكل y أقوم باستخدام صفر يوجد دلتا لكل y
+
+443
+00:36:29,950 --> 00:36:30,650
+أقوم باستخدام صفر يوجد دلتا لكل y أقوم باستخدام
+
+444
+00:36:30,650 --> 00:36:32,710
+صفر يوجد دلتا لكل y أقوم باستخدام صفر يوجد دلتا
+
+445
+00:36:32,710 --> 00:36:35,050
+لكل y أقوم باستخدام صفر يوجد دلتا لكل y أقوم
+
+446
+00:36:35,050 --> 00:36:41,110
+باستخدام صفر يوجد دلتا
+
+447
+00:36:41,110 --> 00:36:49,400
+لكل y أقوم باستخدام صفر يوجد دلتا لكل y أطيب، الآن
+
+448
+00:36:49,400 --> 00:36:54,020
+وين أنا بدأ أروح؟ بدأ أثبت لكم إنه هذا ناقص هذا
+
+449
+00:36:54,020 --> 00:36:58,240
+أصغر من epsilon عشان ذلك دعنا نحسب F of C زاد H
+
+450
+00:36:58,240 --> 00:37:03,060
+ناقص F of C على H ناقص مين يا جماعة؟ F of C ويساوي
+
+451
+00:37:03,060 --> 00:37:13,170
+الآن F of C زاد H ناقص F of Cخد الآن اللي هي الـ H
+
+452
+00:37:13,170 --> 00:37:16,850
+هدعم المشترك بالـ C الواحدة للـ H ماشي F of C زي
+
+453
+00:37:16,850 --> 00:37:21,910
+دتش تعريفها من A لعند C زي دتش لل F of X DX قلناها
+
+454
+00:37:21,910 --> 00:37:26,090
+هذه اللي ماعطيناها من رأس الدور ناقص ماشي تعريف F
+
+455
+00:37:26,090 --> 00:37:30,230
+of C Capital of C هو ال integration من A لعند C زي
+
+456
+00:37:30,230 --> 00:37:35,630
+دتش الآن دي مش C زي دتش من A لعند مين لعند الـ C
+
+457
+00:37:35,630 --> 00:37:40,110
+واحدة للـ H من A لعند الـ C اللي هي F of C زي دتش
+
+458
+00:37:40,110 --> 00:37:46,360
+هيهاوهي الواحدة الـ H اللي برا ال F of C هيها من A
+
+459
+00:37:46,360 --> 00:37:51,780
+ل C واحدة الـ H ناقص مين F of C هذا من التعريف
+
+460
+00:37:51,780 --> 00:37:55,460
+مباشرة لإنه احنا عرفنا ال F capital of X هي عبارة
+
+461
+00:37:55,460 --> 00:38:01,820
+عن integration من A لعند X F of T DT لأن لما نكون
+
+462
+00:38:01,820 --> 00:38:06,120
+F of C زي دتش بنحطها دي C زي دتش C بنحطها دي عياش
+
+463
+00:38:06,120 --> 00:38:13,460
+C وهي C زي دتش وهي الـ C وهي ساويةالان هذه من ..
+
+464
+00:38:13,460 --> 00:38:18,780
+من .. من عند A لـ C زي ده اتش وهذه من A لعند B
+
+465
+00:38:18,780 --> 00:38:23,980
+لعند C هدولة مع بعض هاي هدولة التنتين بده احسبها
+
+466
+00:38:23,980 --> 00:38:28,120
+مع بعض حسبنا زيين قبل و شوية هو عبارة عن واحد على
+
+467
+00:38:28,120 --> 00:38:32,400
+اتش خدوا عامل مشترك خدوا واحد على اتش عامل مشترك
+
+468
+00:38:32,400 --> 00:38:37,340
+بين الجهتين تصبح واحد على اتش افتح جوس ال
+
+469
+00:38:37,340 --> 00:38:41,660
+integration من A لعند C زي ده اتشلأن بدل الناقص
+
+470
+00:38:41,660 --> 00:38:46,020
+بيصير H اكتب زائد بدل هذا الناقص بيكتب زائد لأن
+
+471
+00:38:46,020 --> 00:38:52,460
+هتنقلب مين الآن من C لعند ال A نظبط اللي هو لنفسها
+
+472
+00:38:52,460 --> 00:38:58,020
+F F هذه الآن من C لعند ال A ومن A لعند ال C زاد H
+
+473
+00:38:58,020 --> 00:39:02,000
+إذا أكيد هذه كلها على بعض يصير ال integration من C
+
+474
+00:39:02,000 --> 00:39:08,930
+ل C زاد H لل F في واحد على H إذا هذه كلهابس
+
+475
+00:39:08,930 --> 00:39:11,350
+ابدلتها بقيمتها اللي قلنا عنها اللي هو ال
+
+476
+00:39:11,350 --> 00:39:15,810
+integration من C ل C زي H اللي اوجدته بدل هذا كله
+
+477
+00:39:15,810 --> 00:39:23,190
+من واحد ال H ل F of X DX ناقص الان هذا هذا اللي هي
+
+478
+00:39:23,190 --> 00:39:28,090
+F of C شوف كيف بده اعملها على جهة تعالي احسب ال
+
+479
+00:39:28,090 --> 00:39:33,660
+integrationالـ integration من C لـ C زائد H للـ
+
+480
+00:39:33,660 --> 00:39:38,180
+constant واحد بعد أذنكم DX إيش هيساوي ال
+
+481
+00:39:38,180 --> 00:39:44,140
+integration هدا عبارة عن C زائد H ناقص C وهيساوي
+
+482
+00:39:44,140 --> 00:39:48,760
+قداش H يعني بمعنى آخر لو جيتها الجد تعرفوا ليش
+
+483
+00:39:48,760 --> 00:39:52,640
+بعمل هيك واحد على H في ال integration من C لـ C
+
+484
+00:39:52,640 --> 00:39:58,720
+زايد H اللي هو الواحد هيساوي إيش؟ واحد، مظبوط ولا
+
+485
+00:39:58,720 --> 00:40:03,450
+لأ؟أكيد مظبوط ماشي هايمل هادي كسمت الديوا تاني
+
+486
+00:40:03,450 --> 00:40:10,570
+علشان تطلع حد واحد الان صار عندى لو ضربت هادي
+
+487
+00:40:11,920 --> 00:40:18,320
+الجهتين في F of C هي F of C بيساوي ايش؟ F of C صار
+
+488
+00:40:18,320 --> 00:40:21,260
+الان F of C بيساوي هذه بدي أشيل F of C تبعتي و أحط
+
+489
+00:40:21,260 --> 00:40:25,360
+مكانها هذه الصورة ليش حطيتها؟ عشان هذه أقدر أتحمل
+
+490
+00:40:25,360 --> 00:40:30,380
+محا محا دي اللي موجودة من الأصل شوف كيف الان شيلت
+
+491
+00:40:30,380 --> 00:40:33,320
+ال F of C و حطيت قيمتها اللي أوجدناها اللي هي
+
+492
+00:40:33,320 --> 00:40:37,660
+عبارة عن F of C على H في ال integration من C لC زي
+
+493
+00:40:37,660 --> 00:40:42,480
+H لمن؟ للواحدماشي لان صار هذا ال integration و هذا
+
+494
+00:40:42,480 --> 00:40:45,920
+ال integration نفس الاشي واحد ل F of X و واحد ل
+
+495
+00:40:45,920 --> 00:40:50,380
+واحد يعني بقدر اشتغل فيهم بيصير عندى خد ال واحد ال
+
+496
+00:40:50,380 --> 00:40:53,960
+H برا عن المشترك خالص بيظل عندى ال integration من
+
+497
+00:40:53,960 --> 00:40:58,720
+C ل C زاد H هذا مين ايش اسمه F of X و هذا F of C
+
+498
+00:40:58,720 --> 00:41:01,580
+دخلتها جوا و مضربتها بالواحد صارت مين بقدر اعلن و
+
+499
+00:41:01,580 --> 00:41:06,520
+ثابت اللي هي ناقص F of C لكل اش ماله DX هذا الكلام
+
+500
+00:41:06,520 --> 00:41:14,340
+كله من C ل C زاد Hصار عندى الآن الصورة هذه هيها اه
+
+501
+00:41:14,340 --> 00:41:20,840
+و هذه الصورة اصلا انا بدياها الان واحد على H أزرع
+
+502
+00:41:20,840 --> 00:41:23,760
+أو ساوي قولنا absolute value of integration أزرع
+
+503
+00:41:23,760 --> 00:41:28,740
+أو ساوي ال integration لل absolute value DX الان
+
+504
+00:41:28,740 --> 00:41:35,320
+هذا المقدار F of X ناقص F of Cقلنا عنها من راس
+
+505
+00:41:35,320 --> 00:41:40,420
+الدور أن F of X ناقص F of C اللي هو أصغر من
+
+506
+00:41:40,420 --> 00:41:44,420
+Epsilon لأن limit F of X لما X تروح للـC أشهر
+
+507
+00:41:44,420 --> 00:41:50,240
+مساوي F of C لأن X الـN هذه في الفترة من C لـC
+
+508
+00:41:50,240 --> 00:41:56,100
+زائداتش يعني بتسمح لي أن أقول limit F of X as X
+
+509
+00:41:56,100 --> 00:42:01,220
+بتروح للـC بتساوي F of C لما X بتروح للـC اللي هي
+
+510
+00:42:01,220 --> 00:42:05,980
+أدش بتروح لمينللسفر مضل في نفس المنطقة لأن قلنا
+
+511
+00:42:05,980 --> 00:42:10,300
+قبل شوية x minus c بتروح للسفر إذا وفقط إذا اللي
+
+512
+00:42:10,300 --> 00:42:13,880
+هي ال H اللي بتروح للسفر اللي هي عبارة عن x minus
+
+513
+00:42:13,880 --> 00:42:18,260
+c يعني هذا المقدار بال continuity لل F عند ال C
+
+514
+00:42:18,260 --> 00:42:21,980
+برضه بكون أصغر من إبسلون على ال absolute value
+
+515
+00:42:21,980 --> 00:42:25,160
+لمين لل H في ال integration من C لC زاد H
+
+516
+00:42:27,990 --> 00:42:33,050
+واضحة اه؟ اكيد هذا الان ايش قيمته؟ C زي داش ناقص C
+
+517
+00:42:33,050 --> 00:42:36,050
+اللي هي عبارة عن H فبصير Y عبارة عن absolute value
+
+518
+00:42:36,050 --> 00:42:42,430
+of H في mean فيه اللي هو الـH الـH اللي هو الـH
+
+519
+00:42:42,430 --> 00:42:42,470
+اللي هو الـH اللي هو الـH الـH اللي هو الـH اللي
+
+520
+00:42:42,470 --> 00:42:42,490
+هو الـH اللي هو الـH اللي هو الـH اللي هو الـH
+
+521
+00:42:42,490 --> 00:42:42,490
+اللي هو الـH اللي هو الـH اللي هو الـH اللي هو
+
+522
+00:42:42,490 --> 00:42:42,570
+الـH اللي هو الـH اللي هو الـH اللي هو الـH اللي
+
+523
+00:42:42,570 --> 00:42:42,710
+هو الـH اللي هو الـH اللي هو الـH اللي هو الـH
+
+524
+00:42:42,710 --> 00:42:42,710
+اللي هو الـH اللي هو الـH اللي هو الـH اللي هو
+
+525
+00:42:42,710 --> 00:42:46,490
+الـH اللي هو الـH اللي هو الـH
+
+526
+00:42:46,490 --> 00:42:52,450
+اللي هو الـطيب .. بيصير عندها .. بيصير أكبر من 0
+
+527
+00:42:52,450 --> 00:42:55,790
+أسف هذه بحاجة دي بتطلع أيش بتساوي .. بيساوي بساوي
+
+528
+00:42:55,790 --> 00:42:58,150
+.. بقدر أختار H positive؟ أه بقدر أختار H positive
+
+529
+00:42:58,150 --> 00:43:03,130
+طيب و لو حتى ال H negative بتكون similarly بس
+
+530
+00:43:03,130 --> 00:43:06,950
+بتكون .. كل البرهام بيصير .. بترتب على أنه اللي هي
+
+531
+00:43:06,950 --> 00:43:12,890
+ال .. ال C زائد H أصغر من مين من ال C without loss
+
+532
+00:43:12,890 --> 00:43:17,250
+of generality ال H أكبر من 0بصير عندى لان هذا
+
+533
+00:43:17,250 --> 00:43:24,750
+المقدار أصغر من مين من إبسلون إيش يعني اللى عملنا
+
+534
+00:43:24,750 --> 00:43:28,290
+اللى عملنا لكل إبسلون أكبر من Zero لاجئنا Delta
+
+535
+00:43:28,290 --> 00:43:33,350
+بحيث أنه لما H absolute value أصغر من Deltaيعطيني
+
+536
+00:43:33,350 --> 00:43:39,330
+أن هذا المقدار أصغر من مين؟ من إبسلون يعني صار
+
+537
+00:43:39,330 --> 00:43:43,450
+عندي limit هذا المقدار بسوء f of c و هذا المقدار
+
+538
+00:43:43,450 --> 00:43:46,290
+اللي هو f prime of c يعني اعتبتنا f prime of c
+
+539
+00:43:46,290 --> 00:43:56,410
+بسوء f small of c وهو المطلوب طيب نيجي الآن لاللي
+
+540
+00:43:56,410 --> 00:44:02,210
+هي ال corollaryبرضه الى النظرية اللى جاملة بشوية
+
+541
+00:44:02,210 --> 00:44:10,790
+او خلّيني نقول تلخيصها سريع واستذكرها سريعها اللى
+
+542
+00:44:10,790 --> 00:44:17,830
+هو الأولى كانت تكامل والتفاضل هذه تفاضل التكامل
+
+543
+00:44:17,830 --> 00:44:23,470
+طبعا كل واحدة تحت شروطها المذكورة في نظريتها
+
+544
+00:44:25,860 --> 00:44:30,340
+نجي نشوف يا جماعة ال corollary let f من a و b لعند
+
+545
+00:44:30,340 --> 00:44:34,940
+r بي continuous on a و b and let f of x بي سوى ال
+
+546
+00:44:34,940 --> 00:44:37,720
+integration من ال a ل ال x ل ال f إذا فرض f
+
+547
+00:44:37,720 --> 00:44:40,160
+continuous ال f اسمه ال continuous على كل الفترة
+
+548
+00:44:40,160 --> 00:44:44,980
+ريح حاله طبعا أعطى إشي أكبر من النظرية اللي فاتت
+
+549
+00:44:44,980 --> 00:44:47,640
+يعني فرض ال continuity على ال a و ال b ما زم
+
+550
+00:44:47,640 --> 00:44:49,840
+continuous إذا ما بتزمش تقول integrable لإن و أنا
+
+551
+00:44:49,840 --> 00:44:52,340
+continuous function زي ما قلنا إيش ما لها is
+
+552
+00:44:52,340 --> 00:44:58,190
+integrable إذا مدامة f continuousالان بيصير هذه ال
+
+553
+00:44:58,190 --> 00:45:01,810
+integration اللي هي من a لعند ال x نفسها
+
+554
+00:45:01,810 --> 00:45:06,030
+continuous لأ مش continuous بس is differentiable
+
+555
+00:45:06,030 --> 00:45:09,270
+يعني أجم ال continuous يعني هتكون عندي ال f is
+
+556
+00:45:09,270 --> 00:45:13,670
+differentiable و ال f برامي يمين هي ال f then f is
+
+557
+00:45:13,670 --> 00:45:17,730
+differentiable من a و b عند f برامي بيساوي كده إذن
+
+558
+00:45:17,730 --> 00:45:25,000
+باختصار من a ل x اللي هو fof t dt لو فرضنا هذه
+
+559
+00:45:25,000 --> 00:45:33,060
+continuous على ال a و ال b إذا لكل x element in a
+
+560
+00:45:33,060 --> 00:45:38,080
+و ال b بيصير f of x بالساوي هذا is differentiable
+
+561
+00:45:38,080 --> 00:45:45,500
+و ال f prime of x هتساوي f of اللي هي x يعني بمعنى
+
+562
+00:45:45,500 --> 00:45:52,590
+آخر اللي هوانفضل هذا التكامل و نزيل التفاضل و نحط
+
+563
+00:45:52,590 --> 00:46:00,830
+الـ L جوا يعني بمعنى آخر D by DX للـ integration
+
+564
+00:46:00,830 --> 00:46:08,530
+من A لعند X F of D DT لما تكون F continuous هذا
+
+565
+00:46:08,530 --> 00:46:14,610
+بكون ب cancel هذا أو عملية عكسية لهوبتظللنا F of X
+
+566
+00:46:14,610 --> 00:46:19,070
+يعدى الأحقالها أو F of T والـ T هي المتغير أو الـ
+
+567
+00:46:19,070 --> 00:46:23,370
+X هي المتغير هذه اللي هي الكلرية الآن بدوا يلمّوا
+
+568
+00:46:23,370 --> 00:46:26,610
+النظريتين اللي قبل بشوية في نظرية واحدة يلخصن في
+
+569
+00:46:26,610 --> 00:46:30,910
+نظرية واحدة نشوف كيف بدوا يلخصن في نظرية واحدة
+
+570
+00:46:30,910 --> 00:46:40,630
+يعني بدوا يعيد بس اللي هو صياغة النظريتين صلوا
+
+571
+00:46:40,630 --> 00:46:44,540
+على النبي عليه الصلاة والسلامالان fundamental
+
+572
+00:46:44,540 --> 00:46:48,580
+theorem of calculus combined form يعني التنتين
+
+573
+00:46:48,580 --> 00:46:53,790
+الان موجودات في نفس النظرية شوف ايش بقولكlet
+
+574
+00:46:53,790 --> 00:46:57,610
+Fcapital and Fsmall be continuous on a and b فرض
+
+575
+00:46:57,610 --> 00:47:00,710
+أن Fcapital و Fsmall أشمالهم إتن تان continuous
+
+576
+00:47:00,710 --> 00:47:04,670
+على الفترة a و b و فرضك أن F of a بساوة سفر يعني
+
+577
+00:47:04,670 --> 00:47:07,610
+بدي أحط ال initial condition F of a بساوة سفر عسى
+
+578
+00:47:07,610 --> 00:47:11,070
+أن يجمّل الصورة ماحطه عشان سفر بتطلع F of a في
+
+579
+00:47:11,070 --> 00:47:14,290
+الجواب then the following statements are
+
+580
+00:47:14,290 --> 00:47:18,380
+equivalentيعني لما تكون هذا صحيحة هذا صحيحة و لما
+
+581
+00:47:18,380 --> 00:47:22,640
+تكون هذا صحيحة هذا صحيحة نيجي للجزء الأول لو فرضنا
+
+582
+00:47:22,640 --> 00:47:29,160
+أن F prime of X بيساوي F of X إذا حيصير عندي ال F
+
+583
+00:47:29,160 --> 00:47:33,460
+هذه is differential الماشي هيك مفترض أن F prime of
+
+584
+00:47:33,460 --> 00:47:38,620
+X بيساوي F of X بقول إذاإذاً هذه صحيحة، إيش يعني
+
+585
+00:47:38,620 --> 00:47:43,260
+هذه صحيحة؟ يعني ال integration من ال AX لل F of
+
+586
+00:47:43,260 --> 00:47:48,400
+التي هي T DT، هذه DT يا جماعة، بس .. بس نخلف عن
+
+587
+00:47:48,400 --> 00:47:58,200
+هذه، F of T DT، هذا هيساوي مين؟ هيساوي F of X،
+
+588
+00:47:58,200 --> 00:48:03,070
+ناشي؟الان then the following statements are
+
+589
+00:48:03,070 --> 00:48:06,950
+equivalent يعني لما تكون هذه صحيحة بتعطيها دي اه
+
+590
+00:48:06,950 --> 00:48:11,350
+فرضنا ان f prime of x بيساوي f of x اذا حيكون عند
+
+591
+00:48:11,350 --> 00:48:14,290
+ال integration من a ل x f of t dt بيساوي ايش
+
+592
+00:48:14,290 --> 00:48:20,630
+بالظبط؟ f of x كيف ده تبتها؟ الان فرضنا هذا صحيح
+
+593
+00:48:20,630 --> 00:48:24,710
+اذا ال integration من a ل عند ال x f of t اللي هي
+
+594
+00:48:24,710 --> 00:48:33,010
+مين هتصير؟ f prime of tDT هذه قبل بشوية من نظرية
+
+595
+00:48:33,010 --> 00:48:36,470
+الأولى قلنا كامل التفاوض و ليش بتطلع عندك جواب F
+
+596
+00:48:36,470 --> 00:48:42,210
+of X ناقص مين F of A لإن كل الشروط متحققة ماشي
+
+597
+00:48:42,210 --> 00:48:48,110
+الآن هاي كمان مرة يا جماعة فرضنا إن هذا متحقق بدي
+
+598
+00:48:48,110 --> 00:48:51,250
+أحسب هذه أتبتها بالساوية هذه خد ال integration من
+
+599
+00:48:51,250 --> 00:48:55,510
+X F of T DTهو ماعطيني الـ F small هد مين هي الـ F
+
+600
+00:48:55,510 --> 00:48:58,830
+براهن شفت .. شيلت الـ F small إيش حطيت مكانها؟ F
+
+601
+00:48:58,830 --> 00:49:03,510
+براهن الآن هذه قبل بشوية في الـ Corollary فظلنا ..
+
+602
+00:49:03,510 --> 00:49:07,490
+كملنا التفاضل كيف كملنا التفاضل؟ إنه قولنا شيل
+
+603
+00:49:07,490 --> 00:49:11,230
+التفاضل .. شيل التكامل .. شيل التفاضل بتصير عبارة
+
+604
+00:49:11,230 --> 00:49:15,270
+عن F اللي فوق اللي كانت B ناقص F اللي تحت اللي هي
+
+605
+00:49:15,270 --> 00:49:19,390
+A ويساويأف of X نقص أف of A أف of A ماعطينيها من
+
+606
+00:49:19,390 --> 00:49:24,350
+رأس الدوار صفر إذا إيش هتساوي أف of X إذا هذه اللي
+
+607
+00:49:24,350 --> 00:49:28,290
+بدّينا حساباتها بتساوي هذه طلعت إيش بتساوي أف of X
+
+608
+00:49:28,290 --> 00:49:32,830
+يعني أف of X بتساوي هذا المقدار وهو المطلوب طيب
+
+609
+00:49:32,830 --> 00:49:36,730
+هذا الجزء الأول من النظرية اللي هو نيجي للجزء
+
+610
+00:49:36,730 --> 00:49:42,240
+الثاني نفترض الآن إن هذه صحيحة وده تعطيهاالان برضه
+
+611
+00:49:42,240 --> 00:49:44,760
+الشروط كلها متحققة لأن الـ F في اسمه ليش مالها
+
+612
+00:49:44,760 --> 00:49:47,340
+continuous لسه ان انا ما .. ما .. ما ملاحتوش انا
+
+613
+00:49:47,340 --> 00:49:52,080
+هذا ايه عندي F continuous مدام F continuous ال
+
+614
+00:49:52,080 --> 00:49:57,720
+integration من اعلى عند ال X هذا كلهاللي هو اسمه F
+
+615
+00:49:57,720 --> 00:50:01,320
+of X هيكون differentiable حسب النظرية مزام
+
+616
+00:50:01,320 --> 00:50:04,780
+differentiable حسب هذه النظرية إذا F prime of X
+
+617
+00:50:04,780 --> 00:50:11,100
+إيش هتساوي؟ F of X يعني حققنا مين؟ اللي هي I يعني
+
+618
+00:50:11,100 --> 00:50:20,070
+هذا يؤدي إلى هذانجي الآن بعض التعريفات اللي
+
+619
+00:50:20,070 --> 00:50:26,890
+هنتكرها لكم وانتوا هتكونوا اللي هو اتابعوا الأمثلة
+
+620
+00:50:26,890 --> 00:50:32,130
+من خلال ال homework اللي معاكم هنعطي اللي هي تعريف
+
+621
+00:50:32,130 --> 00:50:36,830
+ممكن انتوا حتى مر عليكم في ال calculus ومن ثم اللي
+
+622
+00:50:36,830 --> 00:50:41,710
+هونعطي بعض ال counter examples اللي هي هنرجعكم
+
+623
+00:50:41,710 --> 00:50:47,370
+فيها للي هي الأسئلة اللي في الكتاب تشوفوا نصوصها
+
+624
+00:50:47,370 --> 00:50:53,530
+على الأقل و اللي مطلوب تحلوها ايه تحلوها و اللي ما
+
+625
+00:50:53,530 --> 00:50:56,910
+بتحلوه يعرفش تحلوهافي عندنا اللي هو في ال homework
+
+626
+00:50:56,910 --> 00:51:01,230
+الحلول الموجودة بتدرسوها لحالكم مادرستوها برضه
+
+627
+00:51:01,230 --> 00:51:04,310
+مافهمتوهاش احنا بنعمل فيها discussion ولو عملناها
+
+628
+00:51:04,310 --> 00:51:07,930
+حتى بشكل صوتي على أساس اللي هو احنا يمكن مانقدرش
+
+629
+00:51:07,930 --> 00:51:12,110
+نصور بشكل كامل اللي هي ال discussions عبر اللي هو
+
+630
+00:51:12,110 --> 00:51:16,270
+التصوير اللي احنا الحالي بنصوره عبر ال power point
+
+631
+00:51:16,270 --> 00:51:22,710
+من البيت ان شاء الله طيب definitionlet I بتساوي A
+
+632
+00:51:22,710 --> 00:51:27,630
+وB subset من مين؟ من R إذا كانت F small من I لR
+
+633
+00:51:30,720 --> 00:51:35,400
+then فرضنا أنه في دالة اسم F من I لعند R then the
+
+634
+00:51:35,400 --> 00:51:42,280
+antiderivative of F يعني وكأنها عكس عملية عكس
+
+635
+00:51:42,280 --> 00:51:45,920
+الدالة اللي بنفضلها roughly antiderivative of F on
+
+636
+00:51:45,920 --> 00:51:50,620
+I is a function F من I لعند R such that F prime of
+
+637
+00:51:50,620 --> 00:51:59,830
+X سوى F of X يعني عندنا دالة Fمن عند I لعند R لو
+
+638
+00:51:59,830 --> 00:52:05,310
+جينا لجينا F تانية من عند I لعند R و لجينا F prime
+
+639
+00:52:05,310 --> 00:52:10,450
+of X للي اللي في الـ I بتساوي mean لـ F small of X
+
+640
+00:52:11,290 --> 00:52:15,490
+في هذه الحالة بنسمي ال F capital هذه عبارة عن
+
+641
+00:52:15,490 --> 00:52:19,850
+antiderivative لل F يعني بمعنى أخر لو فضلناها هذه
+
+642
+00:52:19,850 --> 00:52:25,130
+ال antiderivative هتطلع مين؟ ال F الأصلية يعني
+
+643
+00:52:25,130 --> 00:52:30,890
+بتكون عندي اللي هي ال F capital هي ال
+
+644
+00:52:30,890 --> 00:52:35,210
+antiderivative لل F وال F small هي ال derivative
+
+645
+00:52:35,210 --> 00:52:41,910
+لل F واضح أخدته في ال calculus حتى نيجي الآنلأ
+
+646
+00:52:41,910 --> 00:52:45,650
+اللي هو برضه مفهوم اخدته في الكاركولاس if f من I
+
+647
+00:52:45,650 --> 00:52:49,750
+لعند R small is integrable لو فرضنا هذي integrable
+
+648
+00:52:49,750 --> 00:52:53,950
+و جينا عرفنا
+
+649
+00:52:53,950 --> 00:52:56,910
+ادالة من A لعند X F of X DX قبل شوية قولنا هذا
+
+650
+00:52:56,910 --> 00:53:00,290
+أكيد معرفة مثلا في integrable ومش معرفة ال
+
+651
+00:53:00,290 --> 00:53:04,110
+function F of X هتطلع continuous هذه اللي هي ال
+
+652
+00:53:04,110 --> 00:53:09,930
+function أو هذا هو اللي بنسميه التكامل المحدودهذه
+
+653
+00:53:09,930 --> 00:53:15,110
+بنسميها الـ Indefinite Integral of F يعني هذا
+
+654
+00:53:15,110 --> 00:53:17,790
+بنسميه Indefinite Integral of F أو هذه الدلة
+
+655
+00:53:17,790 --> 00:53:23,030
+بنسميها اللي هي The Indefinite Integral of F on I
+
+656
+00:53:23,030 --> 00:53:28,230
+برضه هذا برضه شغلات اللي هو أخدتوها سابقا في اللي
+
+657
+00:53:28,230 --> 00:53:33,780
+هو ال calculus نيجي بعض الملاحظات بسعلى اللي هو
+
+658
+00:53:33,780 --> 00:53:42,820
+اللي بتعلق بهذه اللي هي المفاهيم نشوفها وهي طبعا
+
+659
+00:53:42,820 --> 00:53:48,760
+هذه المفاهيم في عليها counter examples التمييز
+
+660
+00:53:48,760 --> 00:53:56,400
+بينها نشوف المحبة هذه يا شباب طيب أصلي على النبي
+
+661
+00:53:56,400 --> 00:54:03,640
+عليه الصلاة والسلامالان عندي سؤال سبعة تلاتة اتنين
+
+662
+00:54:03,640 --> 00:54:06,400
+يعني في سبعة تلاتة سؤال اتنين او سبعة تلاتة سؤال
+
+663
+00:54:06,400 --> 00:54:10,660
+خمسة طبعا كله في الطبع التاني هذا اللي هو عندي an
+
+664
+00:54:10,660 --> 00:54:13,540
+integrable function may not have an antiderivative
+
+665
+00:54:13,540 --> 00:54:17,220
+يعني هنلاقي في السؤال هذا integrable function
+
+666
+00:54:17,220 --> 00:54:24,080
+ومالهاش .. ومالهاش antiderivative يعني هنلاقي
+
+667
+00:54:24,080 --> 00:54:30,660
+function Fإنها تكون integrable لكن مالناجيش
+
+668
+00:54:30,660 --> 00:54:34,540
+function F اللي ال derivative تبعي تاش بتساوي
+
+669
+00:54:34,540 --> 00:54:39,860
+بتساوي F هذا اللي هو بتشوفوه في الـ 7 3 2 و 7 3 5
+
+670
+00:54:39,860 --> 00:54:43,340
+الأمثلة أو ال counter examples اللي وجودة هنا طيب
+
+671
+00:54:43,340 --> 00:54:47,710
+الملاحظة التانيةالـ function may have an
+
+672
+00:54:47,710 --> 00:54:52,830
+antiderivative يعني عندي F و بتحقق F و في عندي F
+
+673
+00:54:52,830 --> 00:54:57,310
+كابتال كمان و F برايم إيش بتساوي بسوء F but اللي
+
+674
+00:54:57,310 --> 00:55:02,210
+هي ال integration لل F إيش ماله does not exist لكن
+
+675
+00:55:02,210 --> 00:55:07,370
+but not integrable وهذا بتجاوب عليه برضه سبعة
+
+676
+00:55:07,370 --> 00:55:12,580
+تلاتة خمسة يعني في function Fفي إلها F' بساوة F
+
+677
+00:55:12,580 --> 00:55:17,640
+لكن ال integration للـ F إشماله does not exist
+
+678
+00:55:17,640 --> 00:55:24,900
+تلاتة عندي الملاحظة الثالثة a continuous function
+
+679
+00:55:24,900 --> 00:55:27,800
+always have antiderivative طبعا ال continuous
+
+680
+00:55:27,800 --> 00:55:35,290
+function أصلا من القوة بمكان إنهاتخلّي عندها يكون
+
+681
+00:55:35,290 --> 00:55:39,490
+لها الـ mean antiderivative الان a continuous
+
+682
+00:55:39,490 --> 00:55:44,190
+function always have antiderivative وهذا اللي هو
+
+683
+00:55:44,190 --> 00:55:51,910
+مباشرة من ال corollary 7 3 4 اللي كانت F
+
+684
+00:55:51,910 --> 00:55:56,770
+continuous مدام F continuous إذا ال integration من
+
+685
+00:55:56,770 --> 00:56:07,120
+ال X من A لعند ال XA of T DT بساوة F of X اللي هي
+
+686
+00:56:07,120 --> 00:56:10,900
+is differentiable ومش differentiable كمان و F
+
+687
+00:56:10,900 --> 00:56:14,860
+prime of X بتساوي F small of X يعني مدام أف
+
+688
+00:56:14,860 --> 00:56:17,880
+continuous إذا صار لها antiderivative صارت ال F
+
+689
+00:56:17,880 --> 00:56:20,580
+اللي هي ال derivative لها بساوة F of X إذا صارت
+
+690
+00:56:20,580 --> 00:56:24,620
+إيش antiderivativeهد مين هذا اللي هو عبارة عن الـ
+
+691
+00:56:24,620 --> 00:56:28,980
+Corollary 7 3 4 مدام أن F continuous إذا هذه
+
+692
+00:56:28,980 --> 00:56:33,360
+الدالة اللي سميتها F of X is differentiable ومش هي
+
+693
+00:56:33,360 --> 00:56:35,540
+كمان هذا الجزء الثاني من ال fundamental theorem of
+
+694
+00:56:35,540 --> 00:56:39,200
+calculus و ال F prime of X إيش بيساوي F of X يعني
+
+695
+00:56:39,200 --> 00:56:44,280
+ال F capital is an antiderivative of the F small
+
+696
+00:56:44,280 --> 00:56:50,760
+اللي هو النقطة الرابعة the indefinite integralmay
+
+697
+00:56:50,760 --> 00:56:57,520
+not be an antiderivative of mean of F الآن الـ
+
+698
+00:56:57,520 --> 00:57:02,400
+indefinite integral اللي
+
+699
+00:57:02,400 --> 00:57:12,000
+هو من A لعند X F of T DT لو سميناه F of X هذاهذا
+
+700
+00:57:12,000 --> 00:57:15,480
+the indefinite integral هذا ممكن يكون هذا يعني إيش
+
+701
+00:57:15,480 --> 00:57:18,480
+بمعنى آخر؟ يعني بدنا نفترض إن ال integration من A
+
+702
+00:57:18,480 --> 00:57:22,580
+ل X F of T DT موجود طبعا اللي بقول عنه موجود بس
+
+703
+00:57:22,580 --> 00:57:25,040
+تكون F of T is integrable ماحاجيناش على control U
+
+704
+00:57:25,040 --> 00:57:29,000
+of T ال F of T is integrable إذا ال A لعندي ال X F
+
+705
+00:57:29,000 --> 00:57:35,100
+of T DT لو ممكن يكون هذا موجود و بنسمي F of X
+
+706
+00:57:35,100 --> 00:57:39,830
+بقوللي the indefinite integral هذاmay not have
+
+707
+00:57:39,830 --> 00:57:44,490
+antiderivative of F يعني ممكن مايكونش هذا بالرغم
+
+708
+00:57:44,490 --> 00:57:48,610
+انه هذا موجود مايكونش ال F capital اللي هو هذا
+
+709
+00:57:48,610 --> 00:57:53,530
+مايكونش antiderivative لمين لل F small يعني رغم
+
+710
+00:57:53,530 --> 00:57:58,670
+انه هذا موجود ليس شرطا انه يكون يتفاضل ولمّا
+
+711
+00:57:58,670 --> 00:58:03,290
+يتفاضل يطلع اللي جوا يعني مش شرط انها تكون ال F
+
+712
+00:58:03,890 --> 00:58:07,170
+اللي هي antiderivative اللي هي مين هو الـ
+
+713
+00:58:07,170 --> 00:58:10,110
+indefinite integral هيك بتقول المواحدة طب إيش
+
+714
+00:58:10,110 --> 00:58:14,150
+دليلكم دليلنا هاي في counter examples هاي سبعة
+
+715
+00:58:14,150 --> 00:58:19,390
+تلاتة أربعة وهذا ناتب ناجم ناجم عدم تحقق هذه أو
+
+716
+00:58:19,390 --> 00:58:23,910
+عدم تحقق ال antiderivative أنه it may fail to be
+
+717
+00:58:23,910 --> 00:58:28,050
+differentiable at points at the interval ممكن أصلا
+
+718
+00:58:28,050 --> 00:58:35,440
+أن ال F prime تكونش موجودة بالمرةعند نقطة اللي هو
+
+719
+00:58:35,440 --> 00:58:39,620
+في داخل الـ interval من a إلى x مزام هذي is not
+
+720
+00:58:39,620 --> 00:58:42,720
+differentiable كيف بدنا نلاقي f prime بتساوي f
+
+721
+00:58:42,720 --> 00:58:48,640
+small إذا قد ينشأ عدم وجود الـ antiderivative منه
+
+722
+00:58:48,640 --> 00:58:52,640
+إنه هذي ما تكونش differentiable عند نقطة بين ال a
+
+723
+00:58:52,640 --> 00:58:59,090
+و ال x هاي أولاللي هو سبب ممكن يؤدي إلى عدم تحقق
+
+724
+00:58:59,090 --> 00:59:03,150
+إنه يكون الـ Indefinite Integral ليس Anti
+
+725
+00:59:03,150 --> 00:59:09,650
+-derivative للدالة اللي إحنا بنكملها Or الـ
+
+726
+00:59:09,650 --> 00:59:12,850
+Derivative of Indefinite Integral ممكن يكون موجود
+
+727
+00:59:13,450 --> 00:59:18,310
+لكن يختلف عن مين but different from the value of F
+
+728
+00:59:18,310 --> 00:59:22,410
+at any point of the interval وهذا بيجيبوا سبعة
+
+729
+00:59:22,410 --> 00:59:26,990
+تلاتة تمانية يعني بقولك ممكن تكون يا محلاها و تجيب
+
+730
+00:59:26,990 --> 00:59:32,990
+اللي هو ال F prime of X لكن ما تطلع شاشة تساوي F
+
+731
+00:59:32,990 --> 00:59:38,780
+of Xففي هذه الحالة بيكون الـ Indefinite Integral
+
+732
+00:59:38,780 --> 00:59:46,320
+ليس اللي هو إيه شماله له Antiderivative عارفش
+
+733
+00:59:46,320 --> 00:59:55,080
+لحاله و هاي في مثال طبعا نأتي
+
+734
+00:59:55,080 --> 01:00:01,300
+الآن و نبدأ حديثعن الهو evaluation of integrals
+
+735
+01:00:01,300 --> 01:00:07,780
+evaluation of integrals هناخد اللي هو اللي هي اللي
+
+736
+01:00:07,780 --> 01:00:12,660
+كنا نقول عنها اللي هو integration by parts اللي
+
+737
+01:00:12,660 --> 01:00:17,380
+كنا نقول عنه integration by parts نشوف كيف اللي هو
+
+738
+01:00:17,380 --> 01:00:21,360
+البرهن الأول واحدة يعني هناخد اللي هو النظرية
+
+739
+01:00:21,360 --> 01:00:28,430
+الأولى اللي هي في من ضمن اللي هيكيف يمكن أن نجد
+
+740
+01:00:28,430 --> 01:00:33,770
+طرق لإيجاد التكامل؟ evaluation of integrals أول
+
+741
+01:00:33,770 --> 01:00:39,730
+شيء نحكي عنه هو integral by parts التكامل بالتجزيم
+
+742
+01:00:41,640 --> 01:00:48,040
+نضع الأسس النظرية للتكامل بالتجزئة أو نشرع التكامل
+
+743
+01:00:48,040 --> 01:00:50,920
+بالتجزئة من خلال النظرية اللي أمامنا، أيش بتقول
+
+744
+01:00:50,920 --> 01:00:54,720
+ليه؟ إذا كانت f و g من a و b، f small و g small
+
+745
+01:00:54,720 --> 01:00:58,520
+طبعا، لعند R، R integrable on a و b، نفترض إن
+
+746
+01:00:58,520 --> 01:01:02,040
+التنتين إما اللي هين integrable وبدنا نفترض إنه
+
+747
+01:01:02,040 --> 01:01:06,510
+لهين antiderivativesالان بدأ افرض ان F لها
+
+748
+01:01:06,510 --> 01:01:09,430
+antiderivative اسمها F capital و G لها
+
+749
+01:01:09,430 --> 01:01:13,910
+antiderivative اسمها G capital on A و B اذا الان
+
+750
+01:01:13,910 --> 01:01:22,050
+نظريتنا ترتكز في معطياتها على ان ال F small ل F و
+
+751
+01:01:22,050 --> 01:01:24,210
+G integrable هي واحد
+
+752
+01:01:36,840 --> 01:01:45,420
+ثم عرض علينا الآن نعمل integration ثم بنيجي بقول
+
+753
+01:01:45,420 --> 01:01:52,610
+ليهالـ Integration لحاصل ضرب دالتين F of X في G of
+
+754
+01:01:52,610 --> 01:01:58,890
+X DX من A لعين Bلأن طيب هذه Integrable عارفين طب F
+
+755
+01:01:58,890 --> 01:02:01,090
+capital Integrable اه Integrable لإنها
+
+756
+01:02:01,090 --> 01:02:03,930
+differentiable لإنها differentiable يعني
+
+757
+01:02:03,930 --> 01:02:07,370
+continuous أكتر من continuous يعني يعني أكيد إيش
+
+758
+01:02:07,370 --> 01:02:11,250
+ما لها Integrable إذا معقول كلامه من A لعند B F of
+
+759
+01:02:11,250 --> 01:02:15,590
+X G of X DX إيش بتساوي؟ بقولي عبارة عن F capital
+
+760
+01:02:15,590 --> 01:02:21,750
+of B G capital of B نقص F capital of A G capital
+
+761
+01:02:21,750 --> 01:02:31,040
+of A هذاناقص الـ integration F small of X G
+
+762
+01:02:31,040 --> 01:02:37,520
+capital of X dx من A لعندي هذي اللي هي ال
+
+763
+01:02:37,520 --> 01:02:41,240
+integration by parts اللي عامة اللي بتدخلته أو
+
+764
+01:02:41,240 --> 01:02:45,960
+اللي هي اللي بتقول عنه النظريةإذا if f و g من a
+
+765
+01:02:45,960 --> 01:02:49,260
+لعن بي are integrable on a و b and have
+
+766
+01:02:49,260 --> 01:02:52,140
+antiderivatives f capital and g capital on a و b
+
+767
+01:02:52,140 --> 01:02:56,580
+then ال integration من a لعن بي f of x g x dx
+
+768
+01:02:56,580 --> 01:03:00,080
+بيسوّل f of b g of b نقص f of a g of a طبعاً
+
+769
+01:03:00,080 --> 01:03:06,360
+للcapitals نقص ال integration من a لb f small g
+
+770
+01:03:06,360 --> 01:03:12,200
+capital dx ماشي الحال بدنا الآن اللي هو البرهن
+
+771
+01:03:12,200 --> 01:03:17,750
+النظري البرهن أسهل يا جماعةهو برهانة يعتمد على
+
+772
+01:03:17,750 --> 01:03:22,970
+تفاضل اللي هو حاصل ضرب دلتين ويمكن احنا كنا اصلا
+
+773
+01:03:22,970 --> 01:03:27,110
+في اتناء اول ما بنبدأ في ال integration by bars
+
+774
+01:03:27,110 --> 01:03:31,870
+سنة عارفه للطلاب في ال calculus في الواقع في كل
+
+775
+01:03:31,870 --> 01:03:36,490
+سؤال في الأول يعني و كأننا بنبرهن النظرية و بعد
+
+776
+01:03:36,490 --> 01:03:40,170
+ذلك بنسير اللي هو حافظنا الطريقة و نعملها بشكل
+
+777
+01:03:40,170 --> 01:03:48,220
+سريع طيب نشوف كيفسمّيلي اللي هو F capital of X G
+
+778
+01:03:48,220 --> 01:03:52,060
+of capital of X ايش بتساوي H of X طبعاً F is
+
+779
+01:03:52,060 --> 01:03:53,840
+differentiable و G is differentiable زي ما كنا
+
+780
+01:03:53,840 --> 01:03:56,600
+كاتبين هذه لإنه F antiderivative و G
+
+781
+01:03:56,600 --> 01:03:59,860
+antiderivative يعني F prime لها F small و G prime
+
+782
+01:03:59,860 --> 01:04:03,700
+لها G small يعني إذا صارت الـH عبارة عن
+
+783
+01:04:03,700 --> 01:04:07,160
+differentiable و مدام differentiable إذا أكيد الـH
+
+784
+01:04:07,160 --> 01:04:12,340
+شمالها continuous على الفترة A و B ماشي الحال و مش
+
+785
+01:04:12,340 --> 01:04:18,630
+هيك كمانوبنقدر نفضلها شوفوا كيف
+
+786
+01:04:22,920 --> 01:04:26,280
+واضحة كلها .. اه واضحة كلها .. ماشي زي ما قلنا يا
+
+787
+01:04:26,280 --> 01:04:29,440
+جماعة سمينا F capital of X في G capital of X
+
+788
+01:04:29,440 --> 01:04:32,240
+بالساوية H of X F differentiable و G
+
+789
+01:04:32,240 --> 01:04:35,440
+differentiable ثم H differentiable ومن ثم اكيد
+
+790
+01:04:35,440 --> 01:04:39,780
+continuous فضولي H prime of X لو حاصل ضرب دالتين
+
+791
+01:04:39,780 --> 01:04:44,740
+التفاضل الأول في التاني زي اللي هو التاني الأول في
+
+792
+01:04:44,740 --> 01:04:49,840
+التفاضل التاني ويساويتفاضل الـ F' اللي هي F small
+
+793
+01:04:49,840 --> 01:04:54,440
+وهذه تنزل زي ما هي وتفاضل هذه اللي هي G small لذا
+
+794
+01:04:54,440 --> 01:04:59,020
+صارت الـ H' بالساوية هنا يعني وكأنه صار عنده اللي
+
+795
+01:04:59,020 --> 01:05:04,360
+هي الـH هذه بدون الـPrime antiderivative لمن؟ لهذه
+
+796
+01:05:04,360 --> 01:05:09,520
+صارت يعني الـH capital is an antiderivative of FG
+
+797
+01:05:09,520 --> 01:05:17,320
+زي مين زي FGالان كل شيء نيح F وG Integrable و F
+
+798
+01:05:17,320 --> 01:05:21,560
+capital وG continuous اذا اللي هي اكيد F capital
+
+799
+01:05:21,560 --> 01:05:25,520
+وG capital Integrable ومن ثم هيطلع كل هذا اشماله
+
+800
+01:05:25,520 --> 01:05:31,920
+is integrable ماشي كمان مرة F
+
+801
+01:05:33,190 --> 01:05:36,910
+Integrable و G-Integrable و G-Capital و F-Capital
+
+802
+01:05:36,910 --> 01:05:40,450
+continuous إذا صار الـ Integrable إذا هذا كله على
+
+803
+01:05:40,450 --> 01:05:44,830
+بعض إيش ماله صار Integrable إذا صار عندي الآن اللي
+
+804
+01:05:44,830 --> 01:05:49,550
+هي كل الشروط متحققة إذا من سبعة تلاتة مدامة ال H
+
+805
+01:05:50,390 --> 01:05:53,570
+الـ H وينها الـ H ؟ هي الـ Antiderivative لهذه
+
+806
+01:05:53,570 --> 01:05:57,470
+وهذه Integrable فبصير عندى الان ال integration من
+
+807
+01:05:57,470 --> 01:06:01,770
+هنا ب F في G زايد F capital في G DX بتساوي H of B
+
+808
+01:06:01,770 --> 01:06:11,650
+ناقص مين ناقص H of A طيب صار عندى الان الأمور وضحت
+
+809
+01:06:11,650 --> 01:06:20,490
+وطلعت النتيجة H of B اتطلع عليها وين H of B؟ هيهاH
+
+810
+01:06:20,490 --> 01:06:26,610
+of B بيساوي F capital of B في G
+
+811
+01:06:26,610 --> 01:06:30,930
+of B هايها ماشي F of B في G of B عادلة لو انتوا
+
+812
+01:06:30,930 --> 01:06:36,070
+موجودين لأ على طول قلتولي هايها الان H of A بيساوي
+
+813
+01:06:36,070 --> 01:06:41,980
+F of A في G of A هايها G of A ماشي إذا إيديناهذا
+
+814
+01:06:41,980 --> 01:06:46,060
+المقدار أعوضنا عن H of B هيها وعوضنا عن H دي ها
+
+815
+01:06:46,060 --> 01:06:49,960
+ويها وإيش جينا وهذه فصلناها لإنه Integrable إذا
+
+816
+01:06:49,960 --> 01:06:52,940
+فصلناها بنجيب واحدة على الجهة دي وواحدة على الجهة
+
+817
+01:06:52,940 --> 01:06:57,940
+دي وهو المطلوب اعملكم إياها طيب ال integration من
+
+818
+01:06:57,940 --> 01:07:01,780
+A ل B integration
+
+819
+01:07:01,780 --> 01:07:10,680
+من A ل B FG capital زائد F capital في G بساوي
+
+820
+01:07:11,790 --> 01:07:24,730
+H of B هي H of B H of B سوى F of B G of B نقص H of
+
+821
+01:07:24,730 --> 01:07:31,770
+A هي F of AG of A من الجهة الثانية بيسوي ال
+
+822
+01:07:31,770 --> 01:07:35,890
+integration F في G capital زاد ال integration F
+
+823
+01:07:35,890 --> 01:07:41,070
+capital في G small من A لعند B من A لعند B لأن إن
+
+824
+01:07:41,070 --> 01:07:44,490
+قلولي هذا على الجهة هذه بيصير عند ال integration
+
+825
+01:07:44,490 --> 01:07:51,350
+المطلوب هذاأكيد فهمتم الأصل من a لعن بيه بساوي ال
+
+826
+01:07:51,350 --> 01:07:55,570
+integration f في g capital زي f capital في g small
+
+827
+01:07:55,570 --> 01:08:06,170
+لأ خلصنا منه بساوي f of b في f of a في g of a في b
+
+828
+01:08:06,170 --> 01:08:16,030
+نقص f of a في g of a كل هذاهذا المقدار integration
+
+829
+01:08:16,030 --> 01:08:27,230
+of capital في G من A لـ B وهو المطلوب و هيك احنا
+
+830
+01:08:28,050 --> 01:08:32,490
+بنكون اليوم ان شاء الله وصلنا لعند ال first
+
+831
+01:08:32,490 --> 01:08:36,250
+substitution theorem المرة القادمة ان شاء الله
+
+832
+01:08:36,250 --> 01:08:45,010
+بنكمل المحاضرة او بنكمل المادة و بنكمل هذا ال
+
+833
+01:08:45,010 --> 01:08:49,330
+section في محاضرة قادمة ان شاء الله و إلى لقائنا
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1942f319d791b966afabcd0932d9e6c7034a51af
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_postprocess.srt
@@ -0,0 +1,2252 @@
+1
+00:00:05,040 --> 00:00:12,800
+بسم الله الرحمن الرحيم المحاضرة السابعة مساق تحليل
+
+2
+00:00:12,800 --> 00:00:18,640
+حقيقي 2 اللي طلبت كلية العلوم بالجامعة الإسلامية
+
+3
+00:00:18,640 --> 00:00:23,800
+قسم الرياضيات اليوم
+
+4
+00:00:23,800 --> 00:00:29,720
+هيكون عندنا استكمال ل .. اللي هي قواعد أو قاعدة
+
+5
+00:00:29,720 --> 00:00:36,330
+Lobitalاتحدثنا المرة الماضية عن الحالة اللى بتحدث
+
+6
+00:00:36,330 --> 00:00:41,170
+سفر على سفر وكيف انعلجها وتم اللى هو برهان
+
+7
+00:00:41,170 --> 00:00:47,910
+النظريات المعنية في ذلكالآن بدنا نتحدث على الحالة
+
+8
+00:00:47,910 --> 00:00:57,110
+اللي بتحدث عندنا أيضًا 0 على 0 ولكن ال limit ال X
+
+9
+00:00:57,110 --> 00:01:00,830
+بتروح إلى مالة نهاية أو سالب مالة نهاية وقلنا عنها
+
+10
+00:01:00,830 --> 00:01:05,790
+صحيحة برضه وبعد ذلك هنتحدث عن الحالة infinity على
+
+11
+00:01:05,790 --> 00:01:10,510
+infinity نيجي الآن لنظريتنا اللي وصلنا عندها
+
+12
+00:01:10,510 --> 00:01:11,990
+suppose that
+
+13
+00:01:16,220 --> 00:01:20,260
+F and D are continuous and differentiable على
+
+14
+00:01:20,260 --> 00:01:24,600
+الفترة من A إلى ما لا نهاية ونفترض أنه limit لل F
+
+15
+00:01:24,600 --> 00:01:27,540
+of X لما X تروح إلى ما لا نهاية هي نفس limit D of
+
+16
+00:01:27,540 --> 00:01:31,200
+X لما X تروح إلى ما لا نهاية تساوي إيهاش صفر يعني
+
+17
+00:01:31,200 --> 00:01:36,080
+هذه هتخلقلي حالة اللي هو صفر على صفر ومن ثم نشوف
+
+18
+00:01:36,080 --> 00:01:40,230
+كيف انعليجهاالعنوان D of X ذاته ساوة سفر نفترض وD
+
+19
+00:01:40,230 --> 00:01:44,830
+prime of X ذاته ساوة سفر لكل X أكبر من مين من اللي
+
+20
+00:01:44,830 --> 00:01:48,290
+هو المقصود هنا بيه اللي هي أيش A يعني هذه اللي هي
+
+21
+00:01:48,290 --> 00:01:52,970
+مين اللي هي المقصود أنه A، يا ما نخلي هذه A، يا ما
+
+22
+00:01:52,970 --> 00:01:58,330
+هذه Athen limit f of x على g of x لما x تروح لما
+
+23
+00:01:58,330 --> 00:02:01,930
+النهاية هتكون بالظبط ايش بتساوي limit f prime على
+
+24
+00:02:01,930 --> 00:02:06,050
+g prime of x as x goes to infinity provided that
+
+25
+00:02:06,050 --> 00:02:09,590
+هذا ال limit بتساوي قيمة معينة أو تساوي infinity
+
+26
+00:02:09,590 --> 00:02:15,730
+او سالم infinity الان احنا في الواقع اللي هنسوي
+
+27
+00:02:16,910 --> 00:02:21,910
+وكأنه يعني عملية تحويل اللي نخلّي بدل X تروح إلى
+
+28
+00:02:21,910 --> 00:02:26,950
+ملأ نهاية نخلّي اللي هو متغير وروح لسفر يعني بدنا
+
+29
+00:02:26,950 --> 00:02:31,490
+نعيد تعريف الدالة بحيث أنه يروح هذا المتغير يعني
+
+30
+00:02:31,490 --> 00:02:34,610
+وكأنه نقول واحد على T ويروح على .. اه واحد على X
+
+31
+00:02:34,610 --> 00:02:37,950
+يروح لسفر لما X تروح إلى ملأ نهاية ومن ثم نطبق
+
+32
+00:02:37,950 --> 00:02:41,030
+النظريات اللي أخدناها المرة الماضية دعونا نشوف إيش
+
+33
+00:02:41,030 --> 00:02:47,050
+اللي بنحكيه الآن عند ..الـ الـ function F و G F و
+
+34
+00:02:47,050 --> 00:02:54,430
+G معرفات من A و ماله نهاية لعند اللي هو R الآن
+
+35
+00:02:54,430 --> 00:02:57,970
+عندي اللي هو بده أعرف اللي هو عشان أقدر أستخدم
+
+36
+00:02:57,970 --> 00:03:01,610
+نظرية المرة اللي فاتت المرة الماضية بده أعرف
+
+37
+00:03:01,610 --> 00:03:08,030
+دالتين F capital و G capital من اللي هو عندي من
+
+38
+00:03:08,030 --> 00:03:15,560
+Zero لعند اللي هو واحد على Aلعند الهو asr واضحة
+
+39
+00:03:15,560 --> 00:03:28,640
+الصورة تقريبا اكيد هنقول define f o g as f of اللي
+
+40
+00:03:28,640 --> 00:03:36,960
+نسميها اللي هو T بتساوي اللي هو Gأو F of 1 على T
+
+41
+00:03:36,960 --> 00:03:42,460
+لما T اللي هي لا تساوي سفر و طبعا T أنا معرفها
+
+42
+00:03:42,460 --> 00:03:47,140
+اللي هي في الفترة من Zero لعند واحد على A و ده
+
+43
+00:03:47,140 --> 00:03:51,560
+بيدعرف عند Zero بقول Zero إذا كان T إيش بدها تساوي
+
+44
+00:03:51,560 --> 00:03:59,760
+بتساوي سفر الآن ال .. ال G of Tبتساوي نفس الأسلوب
+
+45
+00:03:59,760 --> 00:04:06,240
+G of 1 على T لما T لا تساوي 0 و 0 إذا كانت T
+
+46
+00:04:06,240 --> 00:04:13,350
+أشمالها بتساوي 0الآن واضح العلاقة بين الدلتين اللي
+
+47
+00:04:13,350 --> 00:04:19,510
+هو F و F اللي هو على أساس أني أحول ال limit
+
+48
+00:04:19,510 --> 00:04:25,650
+المعطاع عندي limit F of X لما X تروح إلى ملا نهاية
+
+49
+00:04:25,650 --> 00:04:30,450
+تصير عندي ال limit بالنسبة لهذه اللي هي ال 1 على X
+
+50
+00:04:30,450 --> 00:04:35,320
+تبعتنا هتروح لمين في هذا الحالة للزفروبستخدم ومن
+
+51
+00:04:35,320 --> 00:04:40,600
+ثم بنكون حصلنا على المتغير لإن أنا T بروح للصفر as
+
+52
+00:04:40,600 --> 00:04:44,740
+X بتروح إلينا لنهاية ومن ثم بنستخدم النظريات اللي
+
+53
+00:04:44,740 --> 00:04:49,940
+أثبتنا صحتها في حالة T بتروح إلى A من اليمين لإن
+
+54
+00:04:49,940 --> 00:04:53,060
+احنا هنروح ل Zero من اليمين هذه اللي هي الخطة اللي
+
+55
+00:04:53,060 --> 00:04:58,480
+هنمشي عليها بنشوف أول إشي واضح أن ال F و ال G ال F
+
+56
+00:04:59,090 --> 00:05:03,930
+والـ G are differentiable على مين على الفترة من
+
+57
+00:05:03,930 --> 00:05:10,550
+سفر لعند واحد عليه هاي واحد اتنين ومدام
+
+58
+00:05:10,550 --> 00:05:13,810
+differentiable ده ن continuous عليها ومش هيك كمان
+
+59
+00:05:13,810 --> 00:05:19,230
+لو جيت أخدت انت هذه بتحسبها لحالك limit F of T as
+
+60
+00:05:19,230 --> 00:05:27,640
+T بتروح للسفر اللي هي بتساوي limitf of 1 على t as
+
+61
+00:05:27,640 --> 00:05:32,340
+t بتروح للصفر و هتلاقيها إيش هتساوي، هتساوي صفر
+
+62
+00:05:32,340 --> 00:05:36,760
+فصارت اللي هي ال F ال capital is continuous على
+
+63
+00:05:36,760 --> 00:05:43,490
+الفترة من 0 لعند 1 على a similarly limit g of tلما
+
+64
+00:05:43,490 --> 00:05:47,650
+T تروح للـ Zero طبعا كل الـ Zero من وين طبيعي من
+
+65
+00:05:47,650 --> 00:05:50,950
+اليمين لأنه أحنا عالمنا اللي بنشتغل عليه اللي هي
+
+66
+00:05:50,950 --> 00:05:53,730
+من عند Zero لعند واحد على أي من المنطقة المودة بقى
+
+67
+00:05:53,730 --> 00:05:58,750
+إذن هروح للـ Zero من جهات اليمين هيساوي نفس الأشي
+
+68
+00:05:58,750 --> 00:06:03,290
+limit F of واحد على T لما T تروح للـ Zero من
+
+69
+00:06:03,290 --> 00:06:07,590
+اليمين ويساوي اللي جيها برضه أشمالها بتساوي صفر
+
+70
+00:06:08,590 --> 00:06:12,970
+الان صارت الان الاف و الجي اشمالين are continuous
+
+71
+00:06:12,970 --> 00:06:17,390
+على الفترة اللي عندنا و differentiable على الفترة
+
+72
+00:06:17,390 --> 00:06:20,510
+ال open و .. و .. و .. و .. و .. و .. و .. و .. و
+
+73
+00:06:20,510 --> 00:06:20,590
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+74
+00:06:20,590 --> 00:06:20,790
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+75
+00:06:20,790 --> 00:06:21,070
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+76
+00:06:21,070 --> 00:06:21,290
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+77
+00:06:21,290 --> 00:06:23,330
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+78
+00:06:23,330 --> 00:06:23,350
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+79
+00:06:23,350 --> 00:06:23,650
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+80
+00:06:23,650 --> 00:06:29,210
+.. و .. و .. و .. و .. و ..
+
+81
+00:06:37,480 --> 00:06:43,680
+بنجي بنحصل على ما يلي خليني بس اسمحولي أمسح هذه
+
+82
+00:06:43,680 --> 00:06:49,760
+دلت في الذاكرة عندي بدي أحسب أنا غاية أن أوجد مين
+
+83
+00:06:49,760 --> 00:06:53,380
+يا جماعة limit اللي هو f of x على g of x لما x
+
+84
+00:06:53,380 --> 00:07:00,780
+تروح إلى وين إلى ما لنهاية لأن limit f of x على g
+
+85
+00:07:00,780 --> 00:07:07,720
+of x لما x تروح إلى ما لنهاية بتساويعبارة عن الان
+
+86
+00:07:07,720 --> 00:07:12,180
+ال X بتروح إلى ما لنهاية F and وال F الواحد على X
+
+87
+00:07:12,180 --> 00:07:20,660
+وين بتروح اللي هو السفر بتساوي limit F of واحد على
+
+88
+00:07:20,660 --> 00:07:26,040
+T خلينا نسميها على G of واحد على T لما T تروح إلى
+
+89
+00:07:26,040 --> 00:07:32,420
+مين إلى السفر من اليمينأو إذا كان عندك اتصار
+
+90
+00:07:32,420 --> 00:07:38,640
+confusion إشي والتكن X مافي مشكلة X لما X تروح ل 0
+
+91
+00:07:38,640 --> 00:07:43,660
+من اليمين اللي هي بتسير عند أسف الواحد على X بتروح
+
+92
+00:07:43,660 --> 00:07:47,860
+ل 0 من اليمين if and only if ال X بتروح لمين إلى
+
+93
+00:07:47,860 --> 00:07:51,520
+ما لنهاية ومن ثم بفخطوة تانية بترجحها للي كتبته
+
+94
+00:07:51,520 --> 00:07:57,980
+قبل بشوية limit اللي هو عبارة عن F of Tعلى اللي هو
+
+95
+00:07:57,980 --> 00:08:04,420
+G of T لما T تروح لـ 0 من وين؟ من اليمين باشي
+
+96
+00:08:04,420 --> 00:08:08,120
+الحال أنا الأن بدي أفضل في الواقع بالنسبة لمن؟
+
+97
+00:08:08,120 --> 00:08:14,040
+بالنسبة له اللي هو الـ X عندي اللي هو وديت واحدة
+
+98
+00:08:14,040 --> 00:08:19,880
+الـ X من اليمين وصارت عندي اللي هي مكان لأ لأ يا
+
+99
+00:08:19,880 --> 00:08:26,200
+جماعة هاد نزام هي بتضلها آسف أه؟X X وهنا بتصير
+
+100
+00:08:26,200 --> 00:08:30,900
+أننا مين واحد على T وهنا واحد على T واضح ليش
+
+101
+00:08:30,900 --> 00:08:36,540
+استبدلنا هنا احنا الواحد على X كله ب T فصارت هذه
+
+102
+00:08:36,540 --> 00:08:41,320
+اللي هي واحد على T وهذه واحد على T الآن صارت
+
+103
+00:08:41,320 --> 00:08:44,780
+النظرية السابقة مطبقة لأن ال T بتروح لمين ل Zero
+
+104
+00:08:44,780 --> 00:08:49,780
+من لمين لأن هدف الواقع مين هي اللي قلنا عنها أشي
+
+105
+00:08:49,780 --> 00:08:57,850
+هذه بتساوي limit ofof T على G of T لما T تروح إلى
+
+106
+00:08:57,850 --> 00:09:01,310
+Zero من وين؟ من اليمين وهذا متطبق لأن هذا Zero
+
+107
+00:09:01,310 --> 00:09:05,490
+وهذا Zero زي ما عملنا قبل بشوية إذا صار إيش بيساوي
+
+108
+00:09:05,490 --> 00:09:10,990
+تفاضل الأول على تفاضل التاني في 100 بالنسبة لعن
+
+109
+00:09:10,990 --> 00:09:17,220
+نظرية السابقة إذا بيصير limitالتي هي التفاضل هادي
+
+110
+00:09:17,220 --> 00:09:21,060
+من هنا F prime of T أيش بيساوي يا شباب؟ تفاضل
+
+111
+00:09:21,060 --> 00:09:24,960
+هادي، عن T بتروح للـ0، إذن هي عبارة عن ناقص 1 على
+
+112
+00:09:24,960 --> 00:09:34,000
+T تربيع في F prime of 1 على T تفاضل F of T، F of T
+
+113
+00:09:34,000 --> 00:09:38,930
+هيهايعني T لا تساوي سفر تفاضلها F prime بساوي ناقص
+
+114
+00:09:38,930 --> 00:09:42,710
+اللي هو F prime الواحد على T فتفاضل اللي جوا اللي
+
+115
+00:09:42,710 --> 00:09:47,450
+هو عبارة عن إيش ناقص واحد على T تربيع واضح على
+
+116
+00:09:47,450 --> 00:09:53,430
+similarly ناقص واحد على T تربيع في G prime of واحد
+
+117
+00:09:53,430 --> 00:10:00,200
+على T لما الـT تروح لمين إلى الـ0 من اليمينالنقص 1
+
+118
+00:10:00,200 --> 00:10:03,160
+دلت ال T تربيع ال نقص 1 دلت T تربيع بروحن مع بعض
+
+119
+00:10:03,160 --> 00:10:09,780
+نرجع لأصلنا بيصير limit F prime بده استبدل الآن ال
+
+120
+00:10:09,780 --> 00:10:17,800
+1 على T بال X على G prime برضه نفس الشي على X و ال
+
+121
+00:10:17,800 --> 00:10:22,540
+T تستبدل بمين اللي هو عبارة عن 1 على X بده تروح لل
+
+122
+00:10:22,540 --> 00:10:29,270
+0 من اليمين يعني ال X بده تروح لمين إلى مالكبصير
+
+123
+00:10:29,270 --> 00:10:35,510
+عندى اللى هو limit f of x على g of x بساوى limit f
+
+124
+00:10:35,510 --> 00:10:40,350
+prime of x على g prime y على x وهو المطلوب نيجى
+
+125
+00:10:40,350 --> 00:10:44,690
+للنظرية البعدها النظرية اللى بدها شغل خلينا نشوف
+
+126
+00:10:44,690 --> 00:10:53,110
+النظرية اطلع لفوق ونركز نشوف ايش هو النظرية بتحكي
+
+127
+00:10:53,110 --> 00:10:57,270
+ومن ثم نذهب الى برهان النظرية
+
+128
+00:11:04,010 --> 00:11:11,750
+عشان مساحة اللوحة شوية خلّينا نتبع على التلخيص ومن
+
+129
+00:11:11,750 --> 00:11:19,110
+ثم بنبرهن theorem 636 اللي هي باختصار هي حالة مالة
+
+130
+00:11:19,110 --> 00:11:22,570
+نهاية على مالة نهاية نفترض أن الـF و الـG are
+
+131
+00:11:22,570 --> 00:11:26,470
+differentiable على الفترة من A و B يعني إحنا شغلنا
+
+132
+00:11:26,470 --> 00:11:34,230
+الآن على الفترة أي إن كانت هذه الفترة من عند Aلعند
+
+133
+00:11:34,230 --> 00:11:41,250
+مي ان لعند بي لأننا مفترضين أن ال F و ال G اللي هو
+
+134
+00:11:41,250 --> 00:11:46,250
+قابل للاشتقاق على الفترة A و B و limit F of X لما
+
+135
+00:11:46,250 --> 00:11:48,890
+X تروح إلى مالة نهائية .. إلى Zero من اليمين ..
+
+136
+00:11:48,890 --> 00:11:53,230
+إلى A من اليمين إيش بيساوي Infinity و limit G of X
+
+137
+00:11:53,230 --> 00:11:56,090
+لما X تروح إلى ال A من اليمين برضه إيش مالها
+
+138
+00:11:56,090 --> 00:12:01,370
+Infinity يعني بمعنى آخر صار لما عرضت علينا limit F
+
+139
+00:12:01,370 --> 00:12:06,980
+of Xعلى G of X لما X راحت إلى الـ A من اليمين
+
+140
+00:12:06,980 --> 00:12:10,660
+وجدنا limit اللي فوق ملا نهاية و limit اللي تحت
+
+141
+00:12:10,660 --> 00:12:14,260
+ملا نهاية يعني حصلنا على الكمية الغير معينة
+
+142
+00:12:14,260 --> 00:12:18,220
+Infinity على Infinity إذا هذه النظرية ستعالج هذه
+
+143
+00:12:18,220 --> 00:12:23,060
+الحالة طبعا الان اللي هي بطريقة مشابهة للسابقة
+
+144
+00:12:23,060 --> 00:12:29,080
+والان احنا طبعا هنقوم ببرهان هذه النظرية نكمل النص
+
+145
+00:12:29,820 --> 00:12:35,900
+الآن فرضنا أيضًا أنه اللي هو الـ g of x لا تساوي
+
+146
+00:12:35,900 --> 00:12:40,160
+سفر والـ g prime of x لا تساوي سفر لكل x و إما لها
+
+147
+00:12:40,160 --> 00:12:44,920
+في الفترة a و b يعني مفترض أن الـ g of x لا تساوي
+
+148
+00:12:44,920 --> 00:12:52,860
+سفر على كل الفترة a و bنأتي إلى الجزئية الأولى من
+
+149
+00:12:52,860 --> 00:12:57,380
+النظرية if limit f' على g' بساوي L element in R
+
+150
+00:12:57,380 --> 00:13:02,040
+إذا فlimit f على g برضه أيضا أيش هتساوي L اللي هي
+
+151
+00:13:02,040 --> 00:13:05,280
+نظريات اللي قبل بشوية بنفس .. بنفس .. خلّيني أقول
+
+152
+00:13:05,280 --> 00:13:10,160
+بنفس المنطق ونفس النصوص بس مبدل 0 على 0 عمالة
+
+153
+00:13:10,160 --> 00:13:13,560
+نهايةفلان limit f prime على g prime صارت مالة
+
+154
+00:13:13,560 --> 00:13:17,700
+نهاية أو سالب مالة نهاية، برضه النظرية بتظبط، سير
+
+155
+00:13:17,700 --> 00:13:23,310
+limit اللي عندنا هذاهو بالظبط limit الـ F على G as
+
+156
+00:13:23,310 --> 00:13:26,170
+X وتروحنا الـ M من اليمين بساوي Infinity وسالب
+
+157
+00:13:26,170 --> 00:13:30,550
+Infinity يعني في النهاية اللي ببحث عنه هذا هو في
+
+158
+00:13:30,550 --> 00:13:34,650
+الحالة هذه أو في الحالة اللي فوق بساوي limit مين
+
+159
+00:13:34,650 --> 00:13:37,750
+الـ F prime على G prime اللي هي الطريقة المحودة
+
+160
+00:13:37,750 --> 00:13:40,330
+بنفضل اللي فوق و بنفضل اللي تحت و بنوجد limit هين
+
+161
+00:13:40,330 --> 00:13:44,670
+بيكونين هين limit اللي هي الأصل اللي احنا بدنايا
+
+162
+00:13:45,410 --> 00:13:49,590
+الان نيجي اللي هو in Berlin اللي هو a و b طبعا
+
+163
+00:13:49,590 --> 00:13:54,410
+بنفس الأسلوب الان
+
+164
+00:13:54,410 --> 00:14:02,790
+قبل ما نبدأ احنا لو اجينا و قولنا limit f of x لما
+
+165
+00:14:02,790 --> 00:14:06,610
+x تروح لأي اشي مثلا a من اليمين بساوة L
+
+166
+00:14:11,700 --> 00:14:14,480
+وقلنا اللي هو for every epsilon تعريفها for every
+
+167
+00:14:14,480 --> 00:14:16,660
+epsilon أكبر من سفر there exists a delta أكبر من
+
+168
+00:14:16,660 --> 00:14:21,300
+سفر such that if x element in A طبعا من اليمين
+
+169
+00:14:21,300 --> 00:14:27,780
+معناته A و A زائد دلتا then اللي هو هيكون عندي f
+
+170
+00:14:27,780 --> 00:14:35,230
+of x ناقص الأصغر من مين من إبسمنالان لو كانت عندي
+
+171
+00:14:35,230 --> 00:14:39,330
+ال epsilon أثبتت انا هذا الكلام ل epsilon ل
+
+172
+00:14:39,330 --> 00:14:45,410
+epsilon لو أثبتت لكل epsilon element in مثلا in
+
+173
+00:14:45,410 --> 00:14:51,970
+zero و نصأو نزيره ربع أو نزيره تلت لو أثبتت أنه
+
+174
+00:14:51,970 --> 00:14:54,950
+لكل إبسلون لجهة دلتة بحيث أن هذا الكلام أصغر من
+
+175
+00:14:54,950 --> 00:15:01,650
+مين من إبسلون برضه بيكون يجزئ عن ال limit ليش؟ لأن
+
+176
+00:15:01,650 --> 00:15:04,950
+المقدار اللي بيكون أصغر من إبسلون اللي هي أصغر من
+
+177
+00:15:04,950 --> 00:15:09,830
+النص أكيد بنفع لمين الدلتة بنفع للمقدار اللي ال
+
+178
+00:15:09,830 --> 00:15:15,450
+إبسلون أكبر من مين من النص لأنه أصلا اللي هي مشكلة
+
+179
+00:15:15,450 --> 00:15:19,620
+أو خلينا نقول ال limit في حد ذاتهاإنه لما الـ A
+
+180
+00:15:19,620 --> 00:15:24,880
+تروحالـ X تروح إلى الـ A من اليمين، بدنا نجمع أن
+
+181
+00:15:24,880 --> 00:15:27,720
+الـ F of X تقترب من مين من الأعلى، يعني التعجيز و
+
+182
+00:15:27,720 --> 00:15:31,100
+كأنه بعجزني أنه يقول لي إنك اتلاقى الـ Delta في
+
+183
+00:15:31,100 --> 00:15:34,600
+حالة الـ Epsilon أكاش اللي بيكون صغيرة فالـ Close
+
+184
+00:15:34,600 --> 00:15:38,960
+اللي هو تمين to Zero، لإنه أصلا المفهوم اللي
+
+185
+00:15:38,960 --> 00:15:43,160
+بتقيله هذا المسافة تضيق، تضيق، تضيق، بحيث أن F of
+
+186
+00:15:43,160 --> 00:15:46,760
+X تقول إلى الـ مين اللي بتعبر عنها؟ الـ Epsilon،
+
+187
+00:15:46,760 --> 00:15:51,190
+لأن بعطيك Epsilon صغيرة جدا جدابدك تلاقي لي Delta
+
+188
+00:15:51,190 --> 00:15:54,870
+أنا الآن الـ Epsilon بين Zero و نص لقيتلك الـ
+
+189
+00:15:54,870 --> 00:15:59,070
+Delta اللي طلعت هنا معناته اللي نفع للـ Epsilon
+
+190
+00:15:59,070 --> 00:16:03,510
+الصغيرة أكيد بيكون أصغر من مين من الأكبيرة إذا هذا
+
+191
+00:16:03,510 --> 00:16:09,250
+يجزء بس هذا قبل ما نبدأ لأنه هسأخدم شغلة اللي هو
+
+192
+00:16:09,250 --> 00:16:14,930
+في هذا الاتجاه نيجي الآن عندي أول إشي المعطى
+
+193
+00:16:14,930 --> 00:16:23,550
+ماتيني LimitF prime of X على G prime of X as X
+
+194
+00:16:23,550 --> 00:16:29,190
+بتروح للـ A من اليمين أيش بساوي؟ بساوي أقل تعريف
+
+195
+00:16:29,190 --> 00:16:32,850
+الـ Limit for every Y أكبر من 0 اللي هتاخد for
+
+196
+00:16:32,850 --> 00:16:39,190
+every Y element in 0 ونص اللي هي لزوم حسابات، بعد
+
+197
+00:16:39,190 --> 00:16:44,650
+شوية هنشوفهاالآن لكل y تنتمي إلى 0.5 وهذا مشروع
+
+198
+00:16:44,650 --> 00:16:49,270
+حسب ما حكيت قبل بشوية there exist delta أكبر من 0
+
+199
+00:16:49,270 --> 00:16:57,650
+such that اللي هو if x element in a و a زيادة دلتا
+
+200
+00:16:57,650 --> 00:17:04,230
+لإن رايح لل a من وين من اليمين لجيت اللي هو دلتا
+
+201
+00:17:04,230 --> 00:17:11,420
+بحيث أنه لكل x في الفترة من a لعيد a زائد دلتابصير
+
+202
+00:17:11,420 --> 00:17:16,780
+عندى لكل x المتنية زائد دلتا بتطلع عندى then f
+
+203
+00:17:16,780 --> 00:17:23,420
+prime of x على g prime of x ناقص ال L أصغر من مين
+
+204
+00:17:23,420 --> 00:17:32,060
+من ال epsilon إذا الآن من هذه ال limitحصلت على أنه
+
+205
+00:17:32,060 --> 00:17:36,540
+لأي إبسلون بين الـ 0 و نص بقدر ألاقي Delta بحيث
+
+206
+00:17:36,540 --> 00:17:40,540
+لكل الإكسات في المنطقة هذه هذه الـ Inquality إيش
+
+207
+00:17:40,540 --> 00:17:44,880
+ما لها تتحقق الآن بس خلّيني أكملها دي شويه عشان
+
+208
+00:17:44,880 --> 00:17:52,040
+بستخدمها لشغلات أخرى عند A زائد Delta هذا بس مجرد
+
+209
+00:17:52,040 --> 00:17:56,340
+تعريف الـ Limit F' على الـ G' لما X تروح للـ A من
+
+210
+00:17:56,340 --> 00:17:59,120
+اليمين الآن
+
+211
+00:18:01,110 --> 00:18:04,910
+بدي أختار .. بدي أسهل على حالي بدل من كل مرة أقول
+
+212
+00:18:04,910 --> 00:18:08,130
+a زي الـ delta و بعد شوية ألاقي delta prime و أخد
+
+213
+00:18:08,130 --> 00:18:12,010
+ال minimum بينهم الاخرى أجدفم عليه عشان اللي بحكيه
+
+214
+00:18:12,010 --> 00:18:17,910
+بدي أخد اللي هو أقول choose c1 element in a و a زي
+
+215
+00:18:17,910 --> 00:18:24,630
+الـ delta الآن اختارلي c1 من ال a لعند مين لعند ال
+
+216
+00:18:24,630 --> 00:18:30,340
+a زي ال delta سميه c1 يعنيمجرد اختيار انا اخترته
+
+217
+00:18:30,340 --> 00:18:38,260
+الان choose .. choose C1 element in A و A زائد
+
+218
+00:18:38,260 --> 00:18:44,140
+دلتا يعني C1 وين موجود؟ موجود في المنطقة التي
+
+219
+00:18:44,140 --> 00:18:50,140
+تتحقق فيها F' ع G' نقص أصغر من ميل من إبسل عشان
+
+220
+00:18:50,140 --> 00:18:56,080
+تستخدمها بعد شويةواضح طيب هذه من جهة الأن من الجهة
+
+221
+00:18:56,080 --> 00:19:03,100
+الثانية عند limit f of x لما x تروح إلى مالة نهاية
+
+222
+00:19:03,100 --> 00:19:09,880
+أسف لل a من اليمين بسوء أيش هو معطينية هي النظرية
+
+223
+00:19:09,880 --> 00:19:13,540
+هي limit f of x لما x تروح إلى ال a من اليمين بسوء
+
+224
+00:19:13,540 --> 00:19:15,760
+limit g of x لما x تروح إلى ال a من اليمين بسوء
+
+225
+00:19:15,760 --> 00:19:23,170
+أيش ماله مالة نهاية من تعريفها هذا إيش يعنيلكل K
+
+226
+00:19:23,170 --> 00:19:29,270
+اللي هو element in R there exists Delta A' أكبر من
+
+227
+00:19:29,270 --> 00:19:36,590
+0 such that اللي هو F of X أكبر من اللي هو الـ K
+
+228
+00:19:36,590 --> 00:19:42,210
+لكل X و N موجودة في الـ A و A زائد مين Delta
+
+229
+00:19:42,210 --> 00:19:49,300
+Prime، مظبوط ولا لا؟ ماشي الحلالآن لكل x element
+
+230
+00:19:49,300 --> 00:19:52,200
+in A و A زي الـ delta prime هذه ال F of X أكبر من
+
+231
+00:19:52,200 --> 00:20:02,420
+مين؟ من K الآن لو كانت ال A و ال A .. الآن عندي
+
+232
+00:20:02,420 --> 00:20:07,540
+لكل subset من هذه .. لكل subset .. لو كان عندي A و
+
+233
+00:20:07,540 --> 00:20:10,940
+C2 مثلا subset من ال A و ال A زي ال delta prime
+
+234
+00:20:12,470 --> 00:20:17,070
+برضه ال F of X أكبر من كده تحققها تحقق إيش لكل X
+
+235
+00:20:17,070 --> 00:20:24,610
+وين موجودة في الفترة من A لعند مين لعند C2 الآن لو
+
+236
+00:20:24,610 --> 00:20:30,410
+كانت ال Delta اللي لجيتها برا ولا جوا بقدر أختار
+
+237
+00:20:30,410 --> 00:20:36,990
+جوا اللي هو C2بحيث أنه لو الـ C2 هذي هو اللي
+
+238
+00:20:36,990 --> 00:20:42,450
+اخترتها جوات من الـ A والـ A زائد دلتا بتظل الـ F
+
+239
+00:20:42,450 --> 00:20:47,470
+of X A شمالها أكبر من مين؟ من الـ K، واضح؟ إذا من
+
+240
+00:20:47,470 --> 00:20:52,330
+هذه بدي أستفيد شغلتين بدي أطبق التعريف هذا لـ K
+
+241
+00:20:52,330 --> 00:20:56,730
+محددة مين الـ K اللي بدي أطبقها؟ اللي عبارة عن F
+
+242
+00:20:56,730 --> 00:21:02,560
+عند مين؟ عند C1واضح؟ إذا الأن بما أنه limit f of X
+
+243
+00:21:02,560 --> 00:21:05,680
+ثم X تروح إلى الـA باليمين يستوى Infinity إذا for
+
+244
+00:21:05,680 --> 00:21:13,720
+K .. إذا for f of C1 there exists Delta Prime أي
+
+245
+00:21:13,720 --> 00:21:19,840
+Delta Prime معينة بحيث أن f of X أكبر من 100 من f
+
+246
+00:21:19,840 --> 00:21:27,060
+of C1 لكل X موجودة بين الـA والـA زائد Delta Prime
+
+247
+00:21:27,680 --> 00:21:31,860
+أنا بدي أختار في مين لكل X الموجودة بين الـ A و
+
+248
+00:21:31,860 --> 00:21:37,940
+الـ C2 حيث الـ C2 موجودة في الفترة هذه و بديها من
+
+249
+00:21:37,940 --> 00:21:44,120
+C1 و لجاي اذا عشان هيك بقدر اقول then we can
+
+250
+00:21:44,120 --> 00:21:50,280
+choose C2 بين A و C1الـ C2 بقدر اختارها فعلا
+
+251
+00:21:50,280 --> 00:21:55,640
+بختارها بس طبعا وين تشتري تشريع اللي اختيارها انها
+
+252
+00:21:55,640 --> 00:22:01,420
+تكون بين الفترة A و A زائد Delta Prime و بدياها
+
+253
+00:22:01,420 --> 00:22:06,900
+تيجي في داخل الـ A و الـ C1 اذا then we can choose
+
+254
+00:22:06,900 --> 00:22:13,200
+C2 element A of C1 بحيث ان ال F of X أكبر من مين
+
+255
+00:22:13,200 --> 00:22:22,810
+من F of C1 لكل X وينفي الفترة بين A وC اتنين طيب
+
+256
+00:22:22,810 --> 00:22:28,050
+هذه معناته ان ال F of X هذه لكل ال Xات اللي هان ال
+
+257
+00:22:28,050 --> 00:22:34,290
+F of X أكيد اي شمالها لها تساوي ايش F of C واحد هل
+
+258
+00:22:34,290 --> 00:22:38,930
+جد تعرف ليش بديها هذه عشان لزوم تعريف شغل معينة
+
+259
+00:22:38,930 --> 00:22:44,770
+بنفعش تكون ال F of X ايش بتساوي F of C واحد الآن
+
+260
+00:22:44,770 --> 00:22:55,550
+similarlySimilarly اللي هو بما انه limit G of X
+
+261
+00:22:55,550 --> 00:23:00,690
+بساوي مالة نهاية as X بتروح للـ A من اليمين إذا
+
+262
+00:23:00,690 --> 00:23:13,160
+بقدر ألاقي اللي هو C1 برايم بحيث انه G of X أكبرأو
+
+263
+00:23:13,160 --> 00:23:17,240
+لا تساوي طبعا أكبر الـ thrifty يعني لا تساوي G of
+
+264
+00:23:17,240 --> 00:23:27,860
+C1 لكل X موجودة في الـ A و C1 إيش إبراهيم اه G C1
+
+265
+00:23:27,860 --> 00:23:34,680
+إبراهيم اه G C1 إبراهيم الآن
+
+266
+00:23:34,680 --> 00:23:40,760
+ال .. ال .. ال .. الباخدالـ Minimum عشان طبعا هذا
+
+267
+00:23:40,760 --> 00:23:46,120
+اللي لجهة N C1' ممكن اللي هي لكل X في الـ A و C1'
+
+268
+00:23:46,620 --> 00:23:52,840
+و لكل X element in A و C2' بط مانش .. مش عارف مين
+
+269
+00:23:52,840 --> 00:23:58,670
+الأكبر من هذول فباخد الـ Minimum من الجهتينو
+
+270
+00:23:58,670 --> 00:24:03,090
+بسميها C1 مثلا او C2 ال minimum من التنتين C2
+
+271
+00:24:03,090 --> 00:24:09,550
+فبتصير عندى لان لكل X في ال A و ال minimum بينهن
+
+272
+00:24:09,550 --> 00:24:14,630
+هدى بتظبط و هدى بتظبط يعنى ال G of X لا تساوي F of
+
+273
+00:24:14,630 --> 00:24:20,670
+C1 و ال F of X لا تساوي مين؟ F of C1 إبرايم و منه
+
+274
+00:24:20,670 --> 00:24:25,870
+بعرف اللى بديه او بعمل زى ما هو عامل في الكتاب إيش
+
+275
+00:24:25,870 --> 00:24:29,280
+اللى بقوله؟ نشوف اللى بعدهاإذا الأن اللي اتفجنا
+
+276
+00:24:29,280 --> 00:24:38,540
+عليه أنه في الفترة من A لعند A زائد Delta هذه
+
+277
+00:24:38,540 --> 00:24:45,480
+متحققة هاي واحد واللي اتفجنا عليه أن F of X لا
+
+278
+00:24:45,480 --> 00:24:50,140
+تساوي F of C واحد في الفترة من A لعند C تنين
+
+279
+00:24:50,140 --> 00:24:55,580
+أشمالها متحققةيعني بمعنى آخر الـ Inquality هذه
+
+280
+00:24:55,580 --> 00:25:03,800
+وهذه التنتين محققات من أين؟ من A لعين C الاتنين
+
+281
+00:25:03,800 --> 00:25:05,360
+واضح؟
+
+282
+00:25:11,650 --> 00:25:17,590
+الان اصلنا لمرحلة انه نقدر نعرف الدالة اللي بتديها
+
+283
+00:25:17,590 --> 00:25:23,890
+اللي هي F of X بتساوي واحد ناقص F of C واحد على F
+
+284
+00:25:23,890 --> 00:25:30,470
+of X وواحد ناقص G of C واحد على G of X لكل X وين
+
+285
+00:25:30,470 --> 00:25:37,330
+موجودة بين A وC تنين و F of C واحد لا تساوي F of X
+
+286
+00:25:37,330 --> 00:25:43,340
+مظبوط؟ هيا اعملهاأه لإن وين بدي أعرف هذه الدالة F
+
+287
+00:25:43,340 --> 00:25:50,480
+من A لعند مين اللي هي بتتحقق عليها خاصية F of X ده
+
+288
+00:25:50,480 --> 00:25:55,080
+تسوى مين F of C واحد و بتتحقق عليها مين اللي هي
+
+289
+00:25:55,080 --> 00:26:00,480
+الخاصية اللي عندي هذه لإن كله هيلزمني هذا إذا الأن
+
+290
+00:26:05,340 --> 00:26:09,980
+اتفجنا عليها دي اه عشان بدي امسح انه عندي f prime
+
+291
+00:26:09,980 --> 00:26:13,800
+ع الجي برايم نقصها الأصغر من يابسولون لكل ال Xات
+
+292
+00:26:13,800 --> 00:26:18,700
+من A لعند A زائد ديلتا لكل ال Xات اللي هانا
+
+293
+00:26:18,700 --> 00:26:22,040
+واتفجنا ان F of X لا تساوي F of C one برضه في
+
+294
+00:26:22,040 --> 00:26:27,350
+الفرق في المنطقة من ايش من A لC2 اتفجنا عليهالان
+
+295
+00:26:27,350 --> 00:26:33,510
+نيجي نعرف الدالة اللي هتوصلني لهدفي خد الان f of x
+
+296
+00:26:33,510 --> 00:26:42,670
+بتساوي اللي هو واحد ناقص f of c واحد على f of x
+
+297
+00:26:42,670 --> 00:26:52,450
+على واحد ناقص g of c واحد على g of xالآن g of c
+
+298
+00:26:52,450 --> 00:26:55,810
+واحد مستحيل تساوي g of x من أي أسباب اللي حكيناها
+
+299
+00:26:55,810 --> 00:27:01,710
+وليس سبب آخر أيضا اللي هو ليش أنه عندي الـ g prime
+
+300
+00:27:01,710 --> 00:27:07,570
+الـ g prime of x ده يساوي سفر إذا حسب Rolle's
+
+301
+00:27:07,570 --> 00:27:13,570
+theorem مستحيل الـ g of c واحد اللي هو تساوي g of
+
+302
+00:27:13,570 --> 00:27:20,530
+x ليش عندي g continuous
+
+303
+00:27:21,550 --> 00:27:29,350
+on a .. طبعا الـ x والي موجودة جوها منها الان من x
+
+304
+00:27:29,350 --> 00:27:37,110
+لعند c واحد صح؟ و g is differentiable on x لعند
+
+305
+00:27:37,110 --> 00:27:44,090
+اللي هي c واحد open واضحة؟
+
+306
+00:27:44,090 --> 00:27:48,670
+لأنه أثر هذا continuous و differentiable من a لعند
+
+307
+00:27:48,670 --> 00:27:52,550
+bالعلمي إذا في الجزية هذه إذا أكيد اللي هم تتحقق
+
+308
+00:27:52,550 --> 00:28:01,270
+هذه الآن لو زي ما بنقول ان جي برا لو لو عندي بدي
+
+309
+00:28:01,270 --> 00:28:09,250
+يكون g of x بسوء g of c واحد معناته حسب role
+
+310
+00:28:09,250 --> 00:28:16,360
+theorem هيعطيني there existcx element in x و c1
+
+311
+00:28:16,360 --> 00:28:22,800
+such that g prime of cx هي ساوى سفر وهذا مستحيل
+
+312
+00:28:22,800 --> 00:28:27,320
+لإن هو معطيني الـ g prime of x لاتساوى سفر لكل x
+
+313
+00:28:27,320 --> 00:28:34,630
+element من a وb معناته معناه الحديثإنه الـ G of C
+
+314
+00:28:34,630 --> 00:28:41,510
+واحد والـ G of X مستحيل يكون متساويات لكل الإكسات
+
+315
+00:28:41,510 --> 00:28:47,230
+اللي في الفترة من A لعند مين لعند C اتنين واضح إذا
+
+316
+00:28:47,230 --> 00:28:50,730
+المقام لا يساوي سفر إذا اللي هو هذي is well
+
+317
+00:28:50,730 --> 00:29:00,950
+defined على مين على الفترة Aمظبوط و C2 خلّيها في
+
+318
+00:29:00,950 --> 00:29:05,070
+الذاكرة طيب اطلع لفوق و حسب لل limit الآن هذا
+
+319
+00:29:05,070 --> 00:29:12,070
+عرفناها احفظناها بنضطر ان امسح الان احسب لل limit
+
+320
+00:29:12,070 --> 00:29:20,230
+للي فوق limit F of X لما X تروح الي وين الي ايه من
+
+321
+00:29:20,230 --> 00:29:23,390
+اليمين بساوى واحد
+
+322
+00:29:24,530 --> 00:29:32,650
+نقص limit F of C1 عدد على F of X لما X تروح للـ A
+
+323
+00:29:32,650 --> 00:29:36,950
+من اليمين على اتجرأت لأنه عارف ان ال limit موجودة
+
+324
+00:29:36,950 --> 00:29:42,290
+على التوزيع اتجرأت عليه لأنه عارف limit G of C1
+
+325
+00:29:42,290 --> 00:29:49,530
+على G of X لما X تروح لوين للـ A من اليمين واضحة
+
+326
+00:29:49,530 --> 00:29:56,130
+جدش هذه ال limit0 لأن ال F of X وين بتروح الى مالة
+
+327
+00:29:56,130 --> 00:30:00,010
+نهاية هي بداية الموضوع مش بداية الموضوع كان عندنا
+
+328
+00:30:00,010 --> 00:30:05,010
+ان ال limit F of X على G of X لما X تروح الى A من
+
+329
+00:30:05,010 --> 00:30:08,670
+اليامين اللي هو سببت لكل القصة ان هذه ال limit
+
+330
+00:30:08,670 --> 00:30:11,230
+مالة نهاية وهذه مالة نهاية صارت مالة نهاية مالة
+
+331
+00:30:11,230 --> 00:30:15,710
+نهاية وهي اللي خلتني اروح بهذا الاتجاه اذا هذه
+
+332
+00:30:16,610 --> 00:30:19,750
+بتروح إلى ملأ نهاية إذا هذه بتروح إلى سفر وهذه
+
+333
+00:30:19,750 --> 00:30:22,330
+الملأ نهاية بتروح إلى سفر إذا هذا كله على بعض إيش
+
+334
+00:30:22,330 --> 00:30:30,170
+بيساوي؟ بيساوي واحد واضح طيب الآن for every
+
+335
+00:30:30,170 --> 00:30:34,570
+epsilon أكبر من سفر اللي هي اللي فوق خلاص بدنا
+
+336
+00:30:34,570 --> 00:30:39,270
+فيها الآن بيبقى إن ال limit بيساوي واحد إذا there
+
+337
+00:30:39,270 --> 00:30:44,890
+existsDelta أكبر من سفر أي إن كانت الـ Delta أكبر
+
+338
+00:30:44,890 --> 00:30:53,790
+من سفر Such that F of X ناقص واحد أصغر من مين من
+
+339
+00:30:53,790 --> 00:30:59,190
+الـ Epsilon Epsilon اللي بدنا فيها من الأول هذا لو
+
+340
+00:30:59,190 --> 00:31:04,830
+يعني لكل الـ Xاللي في الفترة من a ل a زي الـ delta
+
+341
+00:31:04,830 --> 00:31:07,910
+هذه الـ delta الجديدة مش صارت تكون الأولى فأنا
+
+342
+00:31:07,910 --> 00:31:13,330
+عشان أريح حالي بدي أخد اللي هو أصغر delta بلاجيها
+
+343
+00:31:13,330 --> 00:31:17,910
+و أقول حطها كمان جواها هادي حر أنا مدام بتنفع لالي
+
+344
+00:31:17,910 --> 00:31:21,690
+كبيرة ايضا كده بتنفع لمن؟ للصغيرة فاهمين أنا ايش
+
+345
+00:31:21,690 --> 00:31:28,270
+بقول؟ هذه اللي هي نسميها C3 معايا؟ فبصير عندى الآن
+
+346
+00:31:28,270 --> 00:31:39,200
+F of Xلكل X element in A لعند مين؟ C3 أي
+
+347
+00:31:39,200 --> 00:31:46,120
+سؤال؟ F of X ناقص واحد أصغر من Y أكبر من سالب Y
+
+348
+00:31:46,120 --> 00:31:49,960
+تلزمني هذه المنطقة اللي اللي جاي لأن F of X هذه
+
+349
+00:31:49,960 --> 00:31:56,720
+يعني F of X يعطينا F of X أكبر من واحد ناقص Y
+
+350
+00:31:59,390 --> 00:32:03,370
+باضحة؟ لأن هذه جلبها .. اللي هذه طبعا واحد ناقص
+
+351
+00:32:03,370 --> 00:32:07,850
+إبسلون اللي هي بيصير عنده ال .. ال .. ال إبسلون
+
+352
+00:32:07,850 --> 00:32:12,650
+أصغر من مين؟ من نص الواحد ناقص إبسلون أكبر من مين؟
+
+353
+00:32:12,650 --> 00:32:20,670
+اللي هي بيصير أكبر من نص باضحة؟ اللي هي بيصير واحد
+
+354
+00:32:20,670 --> 00:32:28,400
+على f of x اللي هو أصغر من مين؟هذا لمين؟ لكل
+
+355
+00:32:28,400 --> 00:32:32,760
+الاكسات اللي من A لعند مين C3 وطبيعي ال
+
+356
+00:32:32,760 --> 00:32:36,880
+inequalities كلها اللي قبل تتحقق هنا لإنها بتتحقق
+
+357
+00:32:36,880 --> 00:32:41,360
+من هنا لهنا بعضها وبعضها بتتحقق من هنا لهنا فأكيد
+
+358
+00:32:41,360 --> 00:32:47,040
+كلها هتتحقق للإكسات اللي مين في ال A وC3 أصلا أنا
+
+359
+00:32:47,040 --> 00:32:52,620
+رايح باتجاه مين؟ رايح باتجاه أثبت لكم أنه limit of
+
+360
+00:32:53,680 --> 00:32:59,060
+of x على g of x لما x تروح لل a من اليمين بساوي
+
+361
+00:32:59,060 --> 00:33:04,880
+limit f prime of x على g prime of x as x تروح لل a
+
+362
+00:33:04,880 --> 00:33:10,080
+من اليمين اللي هو ايش نسميه احنا قال اذا انا بهمن
+
+363
+00:33:10,080 --> 00:33:14,920
+مين الاكسات اللي جنب ال a لإن انا رايح لل a من وين
+
+364
+00:33:14,920 --> 00:33:18,800
+من اليمين فانا بهمن الجوار القريب جدا من ال a لإن
+
+365
+00:33:18,800 --> 00:33:21,960
+انا رايحله اصلا من هنافالإكسات اللي فيها هي اللي
+
+366
+00:33:21,960 --> 00:33:27,760
+بتلزمني عشان أصل للي بديها خلّي هذه في الذاكرة
+
+367
+00:33:27,760 --> 00:33:34,560
+فصار عندي الآن صار
+
+368
+00:33:34,560 --> 00:33:38,800
+عندي هذا كله حكيناه وخلصنا منه الان نيجي بدنا نصل
+
+369
+00:33:38,800 --> 00:33:44,620
+للي بدنايا بتتذكروا المرة الماضية أنا أصلا جيبت
+
+370
+00:33:44,620 --> 00:33:56,350
+هذهجبت هذه اتطلع فيها و قارنليها مع ال F of X على
+
+371
+00:33:56,350 --> 00:34:01,310
+ال G of X اللي انا بديهاها ال F of X على ال G of X
+
+372
+00:34:01,310 --> 00:34:08,170
+لو جيت قارنتها F of X على ال G of X ايش هتلاقيها؟
+
+373
+00:34:08,170 --> 00:34:14,810
+لو جيت ضربت هذه في F of X وهذه في G of X
+
+374
+00:34:17,460 --> 00:34:22,500
+بنرجع ل F of X ناقص F of C واحد و G of X ناقص G of
+
+375
+00:34:22,500 --> 00:34:26,680
+C واحد طب ايش دخلنا فيه هذه F of X ناقص F of C
+
+376
+00:34:26,680 --> 00:34:30,500
+واحد و G of X ناقص G of C واحد هذه اللي بالكوشي
+
+377
+00:34:30,500 --> 00:34:33,920
+mean value theorem اللي هتجيب لل F prime و G prime
+
+378
+00:34:33,920 --> 00:34:38,340
+اللي انا اصلا موجودات limited فبحصل ع اللي بديا
+
+379
+00:34:40,230 --> 00:34:44,470
+بالظبط الشي اللي بقوله انت يعني ليش هو فكر في هذه
+
+380
+00:34:44,470 --> 00:34:50,470
+بالسبب اللي حكيته F of X على D of X بالساوي F of X
+
+381
+00:34:50,470 --> 00:34:59,890
+على D of X في F of X على D of X على F of X مظبوط؟
+
+382
+00:34:59,890 --> 00:35:09,170
+ماعملش شيء الآن اسحبلي هذه خليهاوحط ليها هذه 1 على
+
+383
+00:35:09,170 --> 00:35:15,210
+f of x ماهي الحالة هذه مين هي في الواقع هي اللي
+
+384
+00:35:15,210 --> 00:35:20,410
+فوق اللي هي عبارة عن اضرب f of x هذه في هذه بصير
+
+385
+00:35:20,410 --> 00:35:32,250
+واحد ويساوي واحد اللي هي ناقص f of c صح؟ f of x
+
+386
+00:35:32,250 --> 00:35:42,660
+ناقص f of cعلى g of x نقص g of c هذا مين هي اللي
+
+387
+00:35:42,660 --> 00:35:46,700
+هي f of x على g of x في f of x عوضت هذه و حطيتها و
+
+388
+00:35:46,700 --> 00:35:51,760
+طلع عندي هذا مضروب في كله في مين في واحدة ال f of
+
+389
+00:35:51,760 --> 00:36:01,080
+x الآن عندي خليني أطبق اللي هو مين الـ Cauchy mean
+
+390
+00:36:01,080 --> 00:36:06,390
+value theorem على الفترة من a لمين ل c تلاتةماشي
+
+391
+00:36:06,390 --> 00:36:11,130
+اللي هو there exist طبعا كله متحقق اللي هو ال F و
+
+392
+00:36:11,130 --> 00:36:15,230
+ال G continuous و differentiable على ال A و ال C 3
+
+393
+00:36:15,230 --> 00:36:21,430
+اذا there exist اللي هو ايه اللي بدكي اسميها اللي
+
+394
+00:36:21,430 --> 00:36:25,690
+هي مثلا there exist gamma او زي ما هو مسميها في
+
+395
+00:36:25,690 --> 00:36:32,230
+الكتاب there exist exi element in A و C تلاتة such
+
+396
+00:36:32,230 --> 00:36:41,500
+thatf prime of xi على g prime of xi بساوي بس ان
+
+397
+00:36:41,500 --> 00:36:44,780
+انا عشان بتطبقها على مين على الفترة f of x لعند
+
+398
+00:36:44,780 --> 00:36:48,800
+مين عشان تطلع عندي f of x of مين و f of c واحد
+
+399
+00:36:48,800 --> 00:36:53,120
+معايا للي اكسات اللي وين اللي موجودة من a لعند c
+
+400
+00:36:53,120 --> 00:36:58,060
+تلاتة بعد اذنكم بتطبقها الكوشي mean value theorem
+
+401
+00:36:58,760 --> 00:37:01,840
+ما هي اصلا continuous و differentiable على الفترة
+
+402
+00:37:01,840 --> 00:37:06,500
+دي كلها من ضمنها مين الفترة A وC ثلاثة ومن ضمنها
+
+403
+00:37:06,500 --> 00:37:11,040
+الفترة A وC واحد اللي انا بده اطبق عليها بال end
+
+404
+00:37:11,040 --> 00:37:15,900
+point مين ال end point C واحد هيها و ال end point
+
+405
+00:37:15,900 --> 00:37:21,890
+ال X اللي موجودة بين A و B مينو C3 واضح واضح اللي
+
+406
+00:37:21,890 --> 00:37:26,350
+بدي .. اذا الان الان there exists x i الان بالظبط
+
+407
+00:37:26,350 --> 00:37:30,630
+بدي اطبق الميكوشي main value term ع الفترة اللي هي
+
+408
+00:37:30,630 --> 00:37:37,790
+X و C1 اللي ال F و ال G differentiable عليها من
+
+409
+00:37:37,790 --> 00:37:40,530
+وين ال X هذه ال X اللي فوق هذه اللي بشتغل فيها
+
+410
+00:37:40,530 --> 00:37:45,890
+اللي هي من A لعن مين لعن C3إذن there exists xi
+
+411
+00:37:45,890 --> 00:37:50,750
+element in x و c واحد such that f prime of xi على
+
+412
+00:37:50,750 --> 00:37:58,770
+g prime of xi في إيش بتساوي f of c واحد أو f of x
+
+413
+00:37:58,770 --> 00:38:05,390
+ناقص f of c واحد فاهمين طبعا على g of x ناقص g of
+
+414
+00:38:05,390 --> 00:38:10,990
+c واحد بس ضربت في ناقص فوق و ناقص صحيح تتعدى زي ما
+
+415
+00:38:10,990 --> 00:38:20,080
+هي لأن هذههي هذه إذا صارت عندي F of X على G of X
+
+416
+00:38:20,080 --> 00:38:26,000
+بسوء F prime على G prime في واحد على مين على F of
+
+417
+00:38:26,000 --> 00:38:32,060
+X وهو اللي بده يوصلنا للي بدنا هي ماعليش أمسح اللي
+
+418
+00:38:32,060 --> 00:38:35,280
+هان بيصير عندى
+
+419
+00:38:38,180 --> 00:38:45,160
+بصير عندى ال F of X على مين F of X على G of X
+
+420
+00:38:45,160 --> 00:38:48,540
+بساوى
+
+421
+00:38:48,540 --> 00:38:54,120
+اللى هو هدى شلناه و حطينا مكانها مين بساوى F prime
+
+422
+00:38:54,120 --> 00:39:02,140
+of X I على G prime of X I فى مين فى واحد على ايه
+
+423
+00:39:02,140 --> 00:39:03,500
+ايش على F
+
+424
+00:39:09,880 --> 00:39:18,360
+واضح أه؟ الآن نمحى هنا هدولة ال Xات اللي هنا هما
+
+425
+00:39:18,360 --> 00:39:23,380
+ال Xات اللي وين موجودة بين A وC3 ماشي الحال بدي
+
+426
+00:39:23,380 --> 00:39:29,120
+الآن غايتي أني أوجد F of X على G of X ناقص مين؟
+
+427
+00:39:29,120 --> 00:39:34,600
+ناقص Lواضحة إذا نلخص كل اللي خدناه for every
+
+428
+00:39:34,600 --> 00:39:38,800
+epsilon element in zero نص there exists delta أكبر
+
+429
+00:39:38,800 --> 00:39:48,980
+من سفر such that if اللي هو x أكبر من a أصغر من c3
+
+430
+00:39:48,980 --> 00:39:53,260
+أصغر من c2 أصغر من c1 أصغر من a زي ال delta اللي
+
+431
+00:39:53,260 --> 00:40:02,070
+لجناها فاهمين عليها وكون عندي اللي هو قيلةالعوّض f
+
+432
+00:40:02,070 --> 00:40:08,110
+of x على g of x ناقص ال .. بدي أقبل لك يميها هذا
+
+433
+00:40:08,110 --> 00:40:12,510
+اللي هو أصغر من epsilon في something مش مشكلة و
+
+434
+00:40:12,510 --> 00:40:15,810
+epsilon is arbitral أيضا بيصير limit زي ما بدنايا
+
+435
+00:40:15,810 --> 00:40:24,170
+واضح هذا الآن بالظبط بيساوي اللي هو العوض اللي هو
+
+436
+00:40:24,170 --> 00:40:28,590
+f of x اللي هي عبارة عن واحد
+
+437
+00:40:32,680 --> 00:40:41,680
+أف برايم of x i على جي برايم of x i في واحد على أف
+
+438
+00:40:41,680 --> 00:40:48,180
+of x ناقص اللى
+
+439
+00:40:48,180 --> 00:40:54,460
+واضح لحتى الان ناخد هذه عامل مشترك برا يصبح واحد
+
+440
+00:40:54,460 --> 00:41:02,140
+على أف of x في أف برايم of x iعلى g prime of xi
+
+441
+00:41:02,140 --> 00:41:13,560
+ناقص L في F of X صح؟ أخدت
+
+442
+00:41:13,560 --> 00:41:17,300
+الواحد على F of X عام المشترك positive أه positive
+
+443
+00:41:17,300 --> 00:41:21,080
+اللي هو F of X هي أكبر من 2 طلعت اللي هو إيش ماله
+
+444
+00:41:21,080 --> 00:41:27,260
+هذا؟هنا ده بدي أضيف term و أطرح term عشان أحصل على
+
+445
+00:41:27,260 --> 00:41:31,780
+هذه اللي بدياها أصلا اللي هي الجد تفهموه مش مقصودة
+
+446
+00:41:31,780 --> 00:41:38,900
+1 على f of x في f prime of xi على g prime of xi
+
+447
+00:41:38,900 --> 00:41:50,130
+ناقص L زائد اللي هوL نقص L F of X ايش سويت استخدمت
+
+448
+00:41:50,130 --> 00:41:56,170
+ال triangle inequality باضافة L وطرحة L هذا كله
+
+449
+00:41:56,170 --> 00:42:04,130
+مضروف 100 في 1 على F of X هذا الآن ال F of X أكبر
+
+450
+00:42:04,130 --> 00:42:12,690
+من 2 حصلناها مظبوط بصير أصغر من نص واضحة
+
+451
+00:42:13,760 --> 00:42:18,920
+الآن F' على G' لـ XI الـ XI وين لاجيناها؟ في
+
+452
+00:42:18,920 --> 00:42:24,940
+الفترة بين A وC1 ينطبق عليها اللي هو من رأس الدور
+
+453
+00:42:24,940 --> 00:42:34,580
+اللي هي F' على G' of X ناقص
+
+454
+00:42:34,580 --> 00:42:41,200
+L أصغر من الـ Y من أول ما بدينايعني إنه هذا أصغر
+
+455
+00:42:41,200 --> 00:42:44,460
+من إبسلون لكل الإكسات اللي موجودة من A لعند مين؟
+
+456
+00:42:44,460 --> 00:42:48,080
+لعند الـA زاد دلتها من ضمنهم مين؟ لك فيبراين كلام
+
+457
+00:42:48,080 --> 00:42:55,940
+دقيق هذه في إبسلون زاد الآن هذا ال بطلحها برا عن
+
+458
+00:42:55,940 --> 00:43:01,760
+المشترك ال اللي هي في مين؟ في واحد ناقص F of X
+
+459
+00:43:01,760 --> 00:43:10,240
+واحد ناقص F of Xالان وهذا أصغر من نص في إبسلون
+
+460
+00:43:10,240 --> 00:43:15,440
+زائد absolute value لأل واحد ماقص F of X هذه ال
+
+461
+00:43:15,440 --> 00:43:20,260
+Xات اللي موجودة بين A وC تلاتة وهذه اللي هي قبل
+
+462
+00:43:20,260 --> 00:43:26,150
+بشوية أصغر من مين من اللي هو إبسلونأصغر من إبسلون
+
+463
+00:43:26,150 --> 00:43:30,030
+واحد ناقص F of X أصغر من مين؟ من إبسلون مش هثبتنا
+
+464
+00:43:30,030 --> 00:43:33,910
+limit F of X بيساوي واحد قبل بشوية اللي هو واحد
+
+465
+00:43:33,910 --> 00:43:37,050
+ناقص F of X اللي هي أصغر من إياش من إبسلون في
+
+466
+00:43:37,050 --> 00:43:42,850
+إبسلونصار عندي الان هذا المقدار اللي هو بساوي
+
+467
+00:43:42,850 --> 00:43:47,030
+epsilon على اتنين في واحد زايد absolute value
+
+468
+00:43:47,030 --> 00:43:52,810
+للالف لان ال epsilon مضروبة فيه اذا as لان هذا ال
+
+469
+00:43:52,810 --> 00:43:55,430
+epsilon arbitrary وهذا الكلام صحيح for every
+
+470
+00:43:55,430 --> 00:43:59,710
+epsilon epsilon بين zero و نص اذا هذا المقدار بقدر
+
+471
+00:43:59,710 --> 00:44:04,350
+ازغره جد ما بدي بتصغير epsilon لانه مضروب فيه ضرب
+
+472
+00:44:04,350 --> 00:44:08,630
+اذا صار عندي لكل epsilon أكبر من zero و نصلـ G الـ
+
+473
+00:44:08,630 --> 00:44:12,650
+Delta بحيث أنه الإكسات اللي هنا بيقدّي لي أن هذا
+
+474
+00:44:12,650 --> 00:44:20,810
+المقدار أصغر من أي قيمة بديّها إذا هذا مفهوم limit
+
+475
+00:44:20,810 --> 00:44:31,530
+F of X على G of X as X بتروح لنين؟ للـ A من اليمين
+
+476
+00:44:31,530 --> 00:44:38,920
+بساوي الـ L وهو المطلوبالثيورم اللي حكينا عنها
+
+477
+00:44:38,920 --> 00:44:45,060
+برضه صحيحة في حالة اللي هو the same .. under the
+
+478
+00:44:45,060 --> 00:44:50,160
+same conditions for the calculation of limits as x
+
+479
+00:44:50,160 --> 00:44:55,540
+goes to infinity or x as goes mean to سالبinfinity
+
+480
+00:44:55,540 --> 00:44:59,140
+بس بورهان يعني بدون modification عن اللي موجود
+
+481
+00:44:59,140 --> 00:45:03,140
+بتصلى اللي بدكيها نيجي ناخد أمثلة الأمثلة هذه طبعا
+
+482
+00:45:03,140 --> 00:45:09,500
+أمثلة سهلة ومثلة calculus نمر عليها اللي هو ونشوف
+
+483
+00:45:09,500 --> 00:45:16,480
+كيف نطبق نظريتنا أو نظرياتنا كيف نوظفها الحساب هذه
+
+484
+00:45:16,480 --> 00:45:23,260
+النهايات عندى شوفوا صلى النبي عليه الصلاة والسلام
+
+485
+00:45:24,800 --> 00:45:30,720
+Find Limitlog sin x على log x as x بتروح للـ 0 من
+
+486
+00:45:30,720 --> 00:45:35,480
+وين؟ من اليمين و احنا عارفين .. مشتغلين على الفترة
+
+487
+00:45:35,480 --> 00:45:40,460
+0 or by يعني فترة بجوار مين؟ الصفر من اليمين و
+
+488
+00:45:40,460 --> 00:45:43,540
+بدنا نروح للـ 0 من اليمين هذا طبعا لو جينا عوضنا
+
+489
+00:45:43,540 --> 00:45:48,080
+هتطلع اللي هو sin 0 0 و أنا 0 فبصير مالة نهاية على
+
+490
+00:45:48,080 --> 00:45:53,580
+مين؟ على مالة نهاية ك limits الآن صارت عندي مالة
+
+491
+00:45:53,580 --> 00:45:57,880
+نهاية على مالة نهاية إذا إيش بتنسوه؟إيش نسوي؟
+
+492
+00:45:57,880 --> 00:46:06,400
+راحين لـ 0 من اليمين بيصير عنده اللي هو بالفاضل
+
+493
+00:46:06,400 --> 00:46:11,400
+هذه و بالفاضل هذه بيصير تفاضلها هذه واضحة و هذه
+
+494
+00:46:11,400 --> 00:46:14,060
+تفاضلها هيك مافيش داعي لنا ندخل في التفاصيل لإن كل
+
+495
+00:46:14,060 --> 00:46:20,320
+بعرفها الآن بنبسط الأمر بيصير X Cos X على Sine X
+
+496
+00:46:20,930 --> 00:46:26,550
+الان لو جيت اتطلعت لهذه ال limit و لهذه ال limit
+
+497
+00:46:26,550 --> 00:46:29,530
+هذه موجودة و هذه موجودة هذه موجودة لإنه تعويض
+
+498
+00:46:29,530 --> 00:46:33,410
+مباشر واحد هذه موجودة لإنه بيصير سفر ع سفر بتعملها
+
+499
+00:46:33,410 --> 00:46:36,570
+global rule بيصير واحد على cosine بتطلع واحد برضه
+
+500
+00:46:36,570 --> 00:46:40,590
+إذا اقدرت اوزع لإنه عارف الليمتين الموجودة فبيصير
+
+501
+00:46:40,590 --> 00:46:46,220
+عبارة عن واحد في واحد بيساوي ايه؟ واحدالان خد على
+
+502
+00:46:46,220 --> 00:46:49,900
+الفترة من Zero لعند مين لعند باي على اتنين limit
+
+503
+00:46:49,900 --> 00:46:53,300
+واحد على X نقص واحد على sign ال X ثم X تروح ل Zero
+
+504
+00:46:53,300 --> 00:46:57,140
+من وين؟ من اليمين وهذه طبعا شغلات اللي هو درجنا
+
+505
+00:46:57,140 --> 00:47:01,120
+عليها في ال calculus بنوحد المقامات وبصير مكتوبة
+
+506
+00:47:01,120 --> 00:47:05,030
+على صورة sign ال X نقص X على X في sign ال Xماشي
+
+507
+00:47:05,030 --> 00:47:10,650
+الحل برضه 0 على 0 بنفضلها بيصير cos X ناقص 1 على
+
+508
+00:47:10,650 --> 00:47:15,470
+اللي هو sin X زاد X فcos X لو جينا عوضنا هتطلع
+
+509
+00:47:15,470 --> 00:47:21,250
+برضه 0 على 0 بنشتق كمان مرة بتطلع ناقص sin X على
+
+510
+00:47:21,250 --> 00:47:26,150
+هذا المقدار هذا المقدار هنا بتصفر وهنا بيصير 2
+
+511
+00:47:26,150 --> 00:47:32,680
+وهنا 0 0 على 2 مش بيساوي بيساوي 0نأتي لهذا مثال
+
+512
+00:47:32,680 --> 00:47:36,440
+معهود الـ let I بيساوين 1 إلى ما لنهاية الـ
+
+513
+00:47:36,440 --> 00:47:39,760
+interval اللي عليها بدنا نشتغل و بدنا ناخد ال
+
+514
+00:47:39,760 --> 00:47:43,600
+limit لما X تروح إلى وين إلى ما لنهاية المقدار 1
+
+515
+00:47:43,600 --> 00:47:48,960
+زائد 1 على X و الكل أُس Xهذا المقدار الان بدي
+
+516
+00:47:48,960 --> 00:47:53,460
+استخدم اللي هو يحوله ل exponential to the len ما
+
+517
+00:47:53,460 --> 00:47:55,660
+احنا عارفين ال exponential و ال len اللي هو n
+
+518
+00:47:55,660 --> 00:47:59,860
+versus لبعض فبصير عندي E to the X لن ال 1 زائد 1
+
+519
+00:47:59,860 --> 00:48:05,120
+على X هذا المقدار بدي اشغل على هذاكخطوة أولى بقول
+
+520
+00:48:05,120 --> 00:48:09,260
+limit ال X لما واحد زائد واحد على X لما X تروح إلى
+
+521
+00:48:09,260 --> 00:48:14,140
+مال نهاية بيصير هذا المقدار limit لما واحد زائد X
+
+522
+00:48:14,140 --> 00:48:18,160
+على واحد على X ليش عملت هيك لأن لما X تروح إلى مال
+
+523
+00:48:18,160 --> 00:48:21,360
+نهاية هذا سفر و لما X تروح إلى مال نهاية هذا سفر و
+
+524
+00:48:21,360 --> 00:48:25,340
+هذا لما واحد فبصير سفر على سفر بقدر استخدم ال loop
+
+525
+00:48:25,340 --> 00:48:30,730
+تالذرول اللي انا برهنتهابقى فاضل اللي فوق و فاضل
+
+526
+00:48:30,730 --> 00:48:33,850
+اللي تحت .. فضلنا اللي فوق هيه و فضلنا اللي تحت
+
+527
+00:48:33,850 --> 00:48:37,590
+هيه .. بروح هذا المقدار مع هذا المقدار .. بظل
+
+528
+00:48:37,590 --> 00:48:42,800
+limit1 زي 1 على X مقص 1 لما X تروح لمدة نهاية ده
+
+529
+00:48:42,800 --> 00:48:47,940
+بروح لصفر بطلع جداش 1 لأن 1 بنرد بنعوض وينها لأن
+
+530
+00:48:47,940 --> 00:48:50,940
+ال exponential is a continuous function لذا نصحي
+
+531
+00:48:50,940 --> 00:48:54,180
+عن عند limit ال 1 زي 1 على X لما X تروح لمدة نهاية
+
+532
+00:48:54,180 --> 00:48:57,920
+to the X وعبارة عن E to the limit لأن ال
+
+533
+00:48:57,920 --> 00:49:01,760
+exponential عبارة عن continuous function فبصير E
+
+534
+00:49:01,760 --> 00:49:08,300
+to the 1 ويساوي Eهذا اللي هو بيكون هيك احنا انهينا
+
+535
+00:49:08,300 --> 00:49:16,240
+اللي هي lobitals rules أو قواعد lobital أو صرنا
+
+536
+00:49:16,240 --> 00:49:20,360
+الآن ندخل
+
+537
+00:49:20,360 --> 00:49:28,120
+على اللي هو ال chapter ال section الأخير اللي هو
+
+538
+00:49:28,120 --> 00:49:32,120
+ال section عبارة عن ستة أربعة اللي هو taylor's
+
+539
+00:49:32,120 --> 00:49:38,540
+theoremأو tailors اللي هي .. هنحكي عن tailors
+
+540
+00:49:38,540 --> 00:49:43,640
+polynomial أو tailors أيضا اللي هو approximation
+
+541
+00:49:43,640 --> 00:49:49,820
+كيف اللي هو .. ان مرة جاية ان شاء الله كيف بنقرب
+
+542
+00:49:49,820 --> 00:49:54,840
+بعض الدوالاللي هو المحترمة اللي بتكون
+
+543
+00:49:54,840 --> 00:49:58,220
+differentiable first derivative و second
+
+544
+00:49:58,220 --> 00:50:00,400
+derivative و third derivative لأ عند ال derivative
+
+545
+00:50:00,400 --> 00:50:05,700
+اللي بدنا .. اللي .. اللي هي ما قبل اشتقاق عندها
+
+546
+00:50:05,700 --> 00:50:11,760
+بنقربها ب polynomial و طبعا انتوا عارفين جدش ال
+
+547
+00:50:11,760 --> 00:50:17,380
+polynomial من الدوال السهلةسهلة التعامل سواء في
+
+548
+00:50:17,380 --> 00:50:21,500
+تفاضل أو في تكامل أو حتى لو بدنا نحلها و نجيب
+
+549
+00:50:21,500 --> 00:50:26,340
+جذورها و نجيب كذا في شغل عليها كثير فالناس ترغب في
+
+550
+00:50:26,340 --> 00:50:30,540
+إنها تجيب بعض الدوال اللي بتكون أحيانا معقدة و
+
+551
+00:50:30,540 --> 00:50:35,380
+صعبة التكامل أو خلنا نقول بتغلب شوية في التفاضل أو
+
+552
+00:50:35,380 --> 00:50:40,040
+في وجود الجذور أو كده و نحولها إلىاللي هي
+
+553
+00:50:40,040 --> 00:50:44,020
+polynomial صبعا في مقدار خطأ الخطأ هن .. ان شاء
+
+554
+00:50:44,020 --> 00:50:47,520
+الله ال Taylor's theorem بتقولنا كيف ان هو نوجد
+
+555
+00:50:47,520 --> 00:50:51,320
+هذا الخطأ او ايش هو الخطأ و ايضا Taylor's theorem
+
+556
+00:50:51,320 --> 00:50:55,780
+زي ما انتوا عارفين هنوضح كيف هي عبارة عن تعميم لل
+
+557
+00:50:55,780 --> 00:51:00,340
+main value theorem هي تعميم لل main value theorem
+
+558
+00:51:00,340 --> 00:51:05,140
+في حالة اللي هي n بتساوي سفر بتطلع هي بالظبط ال
+
+559
+00:51:05,140 --> 00:51:09,100
+main value theorem كيف؟
+
+560
+00:51:10,860 --> 00:51:15,100
+الـ Main Value Theorem عبارة الـ Taylor's Theorem
+
+561
+00:51:15,100 --> 00:51:19,900
+عبارة عن تعميم للـ Main Value Theorem خد الآن
+
+562
+00:51:19,900 --> 00:51:25,020
+بتساوي سفر بتطلعلك الـ Main Value Theorem بيشحمها
+
+563
+00:51:25,020 --> 00:51:27,740
+و لحمها و إلى لقاء
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24e720eeb67567513db3fd873f3c88af50e167f0
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_raw.srt
@@ -0,0 +1,2256 @@
+1
+00:00:05,040 --> 00:00:12,800
+بسم الله الرحمن الرحيم المحاضرة السابعة مساق تحليل
+
+2
+00:00:12,800 --> 00:00:18,640
+حقيقي 2 اللي طلبت كلية العلوم بالجامعة الإسلامية
+
+3
+00:00:18,640 --> 00:00:23,800
+قسم الرياضيات اليوم
+
+4
+00:00:23,800 --> 00:00:29,720
+هيكون عندنا استكمال ل .. اللي هي قواعد أو قاعدة
+
+5
+00:00:29,720 --> 00:00:36,330
+Lobitalاتحدثنا المرة الماضية عن الحالة اللى بتحدث
+
+6
+00:00:36,330 --> 00:00:41,170
+سفر على سفر وكيف انعلجها وتم اللى هو برهان
+
+7
+00:00:41,170 --> 00:00:47,910
+النظريات المعنية في ذلكالآن بدنا نتحدث على الحالة
+
+8
+00:00:47,910 --> 00:00:57,110
+اللي بتحدث عندنا أيضًا 0 على 0 ولكن ال limit ال X
+
+9
+00:00:57,110 --> 00:01:00,830
+بتروح إلى مالة نهاية أو سالب مالة نهاية وقلنا عنها
+
+10
+00:01:00,830 --> 00:01:05,790
+صحيحة برضه وبعد ذلك هنتحدث عن الحالة infinity على
+
+11
+00:01:05,790 --> 00:01:10,510
+infinity نيجي الآن لنظريتنا اللي وصلنا عندها
+
+12
+00:01:10,510 --> 00:01:11,990
+suppose that
+
+13
+00:01:16,220 --> 00:01:20,260
+F and D are continuous and differentiable على
+
+14
+00:01:20,260 --> 00:01:24,600
+الفترة من A إلى ما لا نهاية ونفترض أنه limit لل F
+
+15
+00:01:24,600 --> 00:01:27,540
+of X لما X تروح إلى ما لا نهاية هي نفس limit D of
+
+16
+00:01:27,540 --> 00:01:31,200
+X لما X تروح إلى ما لا نهاية تساوي إيهاش صفر يعني
+
+17
+00:01:31,200 --> 00:01:36,080
+هذه هتخلقلي حالة اللي هو صفر على صفر ومن ثم نشوف
+
+18
+00:01:36,080 --> 00:01:40,230
+كيف انعليجهاالعنوان D of X ذاته ساوة سفر نفترض وD
+
+19
+00:01:40,230 --> 00:01:44,830
+prime of X ذاته ساوة سفر لكل X أكبر من مين من اللي
+
+20
+00:01:44,830 --> 00:01:48,290
+هو المقصود هنا بيه اللي هي أيش A يعني هذه اللي هي
+
+21
+00:01:48,290 --> 00:01:52,970
+مين اللي هي المقصود أنه A، يا ما نخلي هذه A، يا ما
+
+22
+00:01:52,970 --> 00:01:58,330
+هذه Athen limit f of x على g of x لما x تروح لما
+
+23
+00:01:58,330 --> 00:02:01,930
+النهاية هتكون بالظبط ايش بتساوي limit f prime على
+
+24
+00:02:01,930 --> 00:02:06,050
+g prime of x as x goes to infinity provided that
+
+25
+00:02:06,050 --> 00:02:09,590
+هذا ال limit بتساوي قيمة معينة أو تساوي infinity
+
+26
+00:02:09,590 --> 00:02:15,730
+او سالم infinity الان احنا في الواقع اللي هنسوي
+
+27
+00:02:16,910 --> 00:02:21,910
+وكأنه يعني عملية تحويل اللي نخلّي بدل X تروح إلى
+
+28
+00:02:21,910 --> 00:02:26,950
+ملأ نهاية نخلّي اللي هو متغير وروح لسفر يعني بدنا
+
+29
+00:02:26,950 --> 00:02:31,490
+نعيد تعريف الدالة بحيث أنه يروح هذا المتغير يعني
+
+30
+00:02:31,490 --> 00:02:34,610
+وكأنه نقول واحد على T ويروح على .. اه واحد على X
+
+31
+00:02:34,610 --> 00:02:37,950
+يروح لسفر لما X تروح إلى ملأ نهاية ومن ثم نطبق
+
+32
+00:02:37,950 --> 00:02:41,030
+النظريات اللي أخدناها المرة الماضية دعونا نشوف إيش
+
+33
+00:02:41,030 --> 00:02:47,050
+اللي بنحكيه الآن عند ..الـ الـ function F و G F و
+
+34
+00:02:47,050 --> 00:02:54,430
+G معرفات من A و ماله نهاية لعند اللي هو R الآن
+
+35
+00:02:54,430 --> 00:02:57,970
+عندي اللي هو بده أعرف اللي هو عشان أقدر أستخدم
+
+36
+00:02:57,970 --> 00:03:01,610
+نظرية المرة اللي فاتت المرة الماضية بده أعرف
+
+37
+00:03:01,610 --> 00:03:08,030
+دالتين F capital و G capital من اللي هو عندي من
+
+38
+00:03:08,030 --> 00:03:15,560
+Zero لعند اللي هو واحد على Aلعند الهو asr واضحة
+
+39
+00:03:15,560 --> 00:03:28,640
+الصورة تقريبا اكيد هنقول define f o g as f of اللي
+
+40
+00:03:28,640 --> 00:03:36,960
+نسميها اللي هو T بتساوي اللي هو Gأو F of 1 على T
+
+41
+00:03:36,960 --> 00:03:42,460
+لما T اللي هي لا تساوي سفر و طبعا T أنا معرفها
+
+42
+00:03:42,460 --> 00:03:47,140
+اللي هي في الفترة من Zero لعند واحد على A و ده
+
+43
+00:03:47,140 --> 00:03:51,560
+بيدعرف عند Zero بقول Zero إذا كان T إيش بدها تساوي
+
+44
+00:03:51,560 --> 00:03:59,760
+بتساوي سفر الآن ال .. ال G of Tبتساوي نفس الأسلوب
+
+45
+00:03:59,760 --> 00:04:06,240
+G of 1 على T لما T لا تساوي 0 و 0 إذا كانت T
+
+46
+00:04:06,240 --> 00:04:13,350
+أشمالها بتساوي 0الآن واضح العلاقة بين الدلتين اللي
+
+47
+00:04:13,350 --> 00:04:19,510
+هو F و F اللي هو على أساس أني أحول ال limit
+
+48
+00:04:19,510 --> 00:04:25,650
+المعطاع عندي limit F of X لما X تروح إلى ملا نهاية
+
+49
+00:04:25,650 --> 00:04:30,450
+تصير عندي ال limit بالنسبة لهذه اللي هي ال 1 على X
+
+50
+00:04:30,450 --> 00:04:35,320
+تبعتنا هتروح لمين في هذا الحالة للزفروبستخدم ومن
+
+51
+00:04:35,320 --> 00:04:40,600
+ثم بنكون حصلنا على المتغير لإن أنا T بروح للصفر as
+
+52
+00:04:40,600 --> 00:04:44,740
+X بتروح إلينا لنهاية ومن ثم بنستخدم النظريات اللي
+
+53
+00:04:44,740 --> 00:04:49,940
+أثبتنا صحتها في حالة T بتروح إلى A من اليمين لإن
+
+54
+00:04:49,940 --> 00:04:53,060
+احنا هنروح ل Zero من اليمين هذه اللي هي الخطة اللي
+
+55
+00:04:53,060 --> 00:04:58,480
+هنمشي عليها بنشوف أول إشي واضح أن ال F و ال G ال F
+
+56
+00:04:59,090 --> 00:05:03,930
+والـ G are differentiable على مين على الفترة من
+
+57
+00:05:03,930 --> 00:05:10,550
+سفر لعند واحد عليه هاي واحد اتنين ومدام
+
+58
+00:05:10,550 --> 00:05:13,810
+differentiable ده ن continuous عليها ومش هيك كمان
+
+59
+00:05:13,810 --> 00:05:19,230
+لو جيت أخدت انت هذه بتحسبها لحالك limit F of T as
+
+60
+00:05:19,230 --> 00:05:27,640
+T بتروح للسفر اللي هي بتساوي limitf of 1 على t as
+
+61
+00:05:27,640 --> 00:05:32,340
+t بتروح للصفر و هتلاقيها إيش هتساوي، هتساوي صفر
+
+62
+00:05:32,340 --> 00:05:36,760
+فصارت اللي هي ال F ال capital is continuous على
+
+63
+00:05:36,760 --> 00:05:43,490
+الفترة من 0 لعند 1 على a similarly limit g of tلما
+
+64
+00:05:43,490 --> 00:05:47,650
+T تروح للـ Zero طبعا كل الـ Zero من وين طبيعي من
+
+65
+00:05:47,650 --> 00:05:50,950
+اليمين لأنه أحنا عالمنا اللي بنشتغل عليه اللي هي
+
+66
+00:05:50,950 --> 00:05:53,730
+من عند Zero لعند واحد على أي من المنطقة المودة بقى
+
+67
+00:05:53,730 --> 00:05:58,750
+إذن هروح للـ Zero من جهات اليمين هيساوي نفس الأشي
+
+68
+00:05:58,750 --> 00:06:03,290
+limit F of واحد على T لما T تروح للـ Zero من
+
+69
+00:06:03,290 --> 00:06:07,590
+اليمين ويساوي اللي جيها برضه أشمالها بتساوي صفر
+
+70
+00:06:08,590 --> 00:06:12,970
+الان صارت الان الاف و الجي اشمالين are continuous
+
+71
+00:06:12,970 --> 00:06:17,390
+على الفترة اللي عندنا و differentiable على الفترة
+
+72
+00:06:17,390 --> 00:06:20,510
+ال open و .. و .. و .. و .. و .. و .. و .. و .. و
+
+73
+00:06:20,510 --> 00:06:20,590
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+74
+00:06:20,590 --> 00:06:20,790
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+75
+00:06:20,790 --> 00:06:21,070
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+76
+00:06:21,070 --> 00:06:21,290
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+77
+00:06:21,290 --> 00:06:23,330
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+78
+00:06:23,330 --> 00:06:23,350
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+79
+00:06:23,350 --> 00:06:23,650
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+80
+00:06:23,650 --> 00:06:23,650
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+81
+00:06:23,650 --> 00:06:29,210
+.. و .. و .. و .. و .. و ..
+
+82
+00:06:37,480 --> 00:06:43,680
+بنجي بنحصل على ما يلي خليني بس اسمحولي أمسح هذه
+
+83
+00:06:43,680 --> 00:06:49,760
+دلت في الذاكرة عندي بدي أحسب أنا غاية أن أوجد مين
+
+84
+00:06:49,760 --> 00:06:53,380
+يا جماعة limit اللي هو f of x على g of x لما x
+
+85
+00:06:53,380 --> 00:07:00,780
+تروح إلى وين إلى ما لنهاية لأن limit f of x على g
+
+86
+00:07:00,780 --> 00:07:07,720
+of x لما x تروح إلى ما لنهاية بتساويعبارة عن الان
+
+87
+00:07:07,720 --> 00:07:12,180
+ال X بتروح إلى ما لنهاية F and وال F الواحد على X
+
+88
+00:07:12,180 --> 00:07:20,660
+وين بتروح اللي هو السفر بتساوي limit F of واحد على
+
+89
+00:07:20,660 --> 00:07:26,040
+T خلينا نسميها على G of واحد على T لما T تروح إلى
+
+90
+00:07:26,040 --> 00:07:32,420
+مين إلى السفر من اليمينأو إذا كان عندك اتصار
+
+91
+00:07:32,420 --> 00:07:38,640
+confusion إشي والتكن X مافي مشكلة X لما X تروح ل 0
+
+92
+00:07:38,640 --> 00:07:43,660
+من اليمين اللي هي بتسير عند أسف الواحد على X بتروح
+
+93
+00:07:43,660 --> 00:07:47,860
+ل 0 من اليمين if and only if ال X بتروح لمين إلى
+
+94
+00:07:47,860 --> 00:07:51,520
+ما لنهاية ومن ثم بفخطوة تانية بترجحها للي كتبته
+
+95
+00:07:51,520 --> 00:07:57,980
+قبل بشوية limit اللي هو عبارة عن F of Tعلى اللي هو
+
+96
+00:07:57,980 --> 00:08:04,420
+G of T لما T تروح لـ 0 من وين؟ من اليمين باشي
+
+97
+00:08:04,420 --> 00:08:08,120
+الحال أنا الأن بدي أفضل في الواقع بالنسبة لمن؟
+
+98
+00:08:08,120 --> 00:08:14,040
+بالنسبة له اللي هو الـ X عندي اللي هو وديت واحدة
+
+99
+00:08:14,040 --> 00:08:19,880
+الـ X من اليمين وصارت عندي اللي هي مكان لأ لأ يا
+
+100
+00:08:19,880 --> 00:08:26,200
+جماعة هاد نزام هي بتضلها آسف أه؟X X وهنا بتصير
+
+101
+00:08:26,200 --> 00:08:30,900
+أننا مين واحد على T وهنا واحد على T واضح ليش
+
+102
+00:08:30,900 --> 00:08:36,540
+استبدلنا هنا احنا الواحد على X كله ب T فصارت هذه
+
+103
+00:08:36,540 --> 00:08:41,320
+اللي هي واحد على T وهذه واحد على T الآن صارت
+
+104
+00:08:41,320 --> 00:08:44,780
+النظرية السابقة مطبقة لأن ال T بتروح لمين ل Zero
+
+105
+00:08:44,780 --> 00:08:49,780
+من لمين لأن هدف الواقع مين هي اللي قلنا عنها أشي
+
+106
+00:08:49,780 --> 00:08:57,850
+هذه بتساوي limit ofof T على G of T لما T تروح إلى
+
+107
+00:08:57,850 --> 00:09:01,310
+Zero من وين؟ من اليمين وهذا متطبق لأن هذا Zero
+
+108
+00:09:01,310 --> 00:09:05,490
+وهذا Zero زي ما عملنا قبل بشوية إذا صار إيش بيساوي
+
+109
+00:09:05,490 --> 00:09:10,990
+تفاضل الأول على تفاضل التاني في 100 بالنسبة لعن
+
+110
+00:09:10,990 --> 00:09:17,220
+نظرية السابقة إذا بيصير limitالتي هي التفاضل هادي
+
+111
+00:09:17,220 --> 00:09:21,060
+من هنا F prime of T أيش بيساوي يا شباب؟ تفاضل
+
+112
+00:09:21,060 --> 00:09:24,960
+هادي، عن T بتروح للـ0، إذن هي عبارة عن ناقص 1 على
+
+113
+00:09:24,960 --> 00:09:34,000
+T تربيع في F prime of 1 على T تفاضل F of T، F of T
+
+114
+00:09:34,000 --> 00:09:38,930
+هيهايعني T لا تساوي سفر تفاضلها F prime بساوي ناقص
+
+115
+00:09:38,930 --> 00:09:42,710
+اللي هو F prime الواحد على T فتفاضل اللي جوا اللي
+
+116
+00:09:42,710 --> 00:09:47,450
+هو عبارة عن إيش ناقص واحد على T تربيع واضح على
+
+117
+00:09:47,450 --> 00:09:53,430
+similarly ناقص واحد على T تربيع في G prime of واحد
+
+118
+00:09:53,430 --> 00:10:00,200
+على T لما الـT تروح لمين إلى الـ0 من اليمينالنقص 1
+
+119
+00:10:00,200 --> 00:10:03,160
+دلت ال T تربيع ال نقص 1 دلت T تربيع بروحن مع بعض
+
+120
+00:10:03,160 --> 00:10:09,780
+نرجع لأصلنا بيصير limit F prime بده استبدل الآن ال
+
+121
+00:10:09,780 --> 00:10:17,800
+1 على T بال X على G prime برضه نفس الشي على X و ال
+
+122
+00:10:17,800 --> 00:10:22,540
+T تستبدل بمين اللي هو عبارة عن 1 على X بده تروح لل
+
+123
+00:10:22,540 --> 00:10:29,270
+0 من اليمين يعني ال X بده تروح لمين إلى مالكبصير
+
+124
+00:10:29,270 --> 00:10:35,510
+عندى اللى هو limit f of x على g of x بساوى limit f
+
+125
+00:10:35,510 --> 00:10:40,350
+prime of x على g prime y على x وهو المطلوب نيجى
+
+126
+00:10:40,350 --> 00:10:44,690
+للنظرية البعدها النظرية اللى بدها شغل خلينا نشوف
+
+127
+00:10:44,690 --> 00:10:53,110
+النظرية اطلع لفوق ونركز نشوف ايش هو النظرية بتحكي
+
+128
+00:10:53,110 --> 00:10:57,270
+ومن ثم نذهب الى برهان النظرية
+
+129
+00:11:04,010 --> 00:11:11,750
+عشان مساحة اللوحة شوية خلّينا نتبع على التلخيص ومن
+
+130
+00:11:11,750 --> 00:11:19,110
+ثم بنبرهن theorem 636 اللي هي باختصار هي حالة مالة
+
+131
+00:11:19,110 --> 00:11:22,570
+نهاية على مالة نهاية نفترض أن الـF و الـG are
+
+132
+00:11:22,570 --> 00:11:26,470
+differentiable على الفترة من A و B يعني إحنا شغلنا
+
+133
+00:11:26,470 --> 00:11:34,230
+الآن على الفترة أي إن كانت هذه الفترة من عند Aلعند
+
+134
+00:11:34,230 --> 00:11:41,250
+مي ان لعند بي لأننا مفترضين أن ال F و ال G اللي هو
+
+135
+00:11:41,250 --> 00:11:46,250
+قابل للاشتقاق على الفترة A و B و limit F of X لما
+
+136
+00:11:46,250 --> 00:11:48,890
+X تروح إلى مالة نهائية .. إلى Zero من اليمين ..
+
+137
+00:11:48,890 --> 00:11:53,230
+إلى A من اليمين إيش بيساوي Infinity و limit G of X
+
+138
+00:11:53,230 --> 00:11:56,090
+لما X تروح إلى ال A من اليمين برضه إيش مالها
+
+139
+00:11:56,090 --> 00:12:01,370
+Infinity يعني بمعنى آخر صار لما عرضت علينا limit F
+
+140
+00:12:01,370 --> 00:12:06,980
+of Xعلى G of X لما X راحت إلى الـ A من اليمين
+
+141
+00:12:06,980 --> 00:12:10,660
+وجدنا limit اللي فوق ملا نهاية و limit اللي تحت
+
+142
+00:12:10,660 --> 00:12:14,260
+ملا نهاية يعني حصلنا على الكمية الغير معينة
+
+143
+00:12:14,260 --> 00:12:18,220
+Infinity على Infinity إذا هذه النظرية ستعالج هذه
+
+144
+00:12:18,220 --> 00:12:23,060
+الحالة طبعا الان اللي هي بطريقة مشابهة للسابقة
+
+145
+00:12:23,060 --> 00:12:29,080
+والان احنا طبعا هنقوم ببرهان هذه النظرية نكمل النص
+
+146
+00:12:29,820 --> 00:12:35,900
+الآن فرضنا أيضًا أنه اللي هو الـ g of x لا تساوي
+
+147
+00:12:35,900 --> 00:12:40,160
+سفر والـ g prime of x لا تساوي سفر لكل x و إما لها
+
+148
+00:12:40,160 --> 00:12:44,920
+في الفترة a و b يعني مفترض أن الـ g of x لا تساوي
+
+149
+00:12:44,920 --> 00:12:52,860
+سفر على كل الفترة a و bنأتي إلى الجزئية الأولى من
+
+150
+00:12:52,860 --> 00:12:57,380
+النظرية if limit f' على g' بساوي L element in R
+
+151
+00:12:57,380 --> 00:13:02,040
+إذا فlimit f على g برضه أيضا أيش هتساوي L اللي هي
+
+152
+00:13:02,040 --> 00:13:05,280
+نظريات اللي قبل بشوية بنفس .. بنفس .. خلّيني أقول
+
+153
+00:13:05,280 --> 00:13:10,160
+بنفس المنطق ونفس النصوص بس مبدل 0 على 0 عمالة
+
+154
+00:13:10,160 --> 00:13:13,560
+نهايةفلان limit f prime على g prime صارت مالة
+
+155
+00:13:13,560 --> 00:13:17,700
+نهاية أو سالب مالة نهاية، برضه النظرية بتظبط، سير
+
+156
+00:13:17,700 --> 00:13:23,310
+limit اللي عندنا هذاهو بالظبط limit الـ F على G as
+
+157
+00:13:23,310 --> 00:13:26,170
+X وتروحنا الـ M من اليمين بساوي Infinity وسالب
+
+158
+00:13:26,170 --> 00:13:30,550
+Infinity يعني في النهاية اللي ببحث عنه هذا هو في
+
+159
+00:13:30,550 --> 00:13:34,650
+الحالة هذه أو في الحالة اللي فوق بساوي limit مين
+
+160
+00:13:34,650 --> 00:13:37,750
+الـ F prime على G prime اللي هي الطريقة المحودة
+
+161
+00:13:37,750 --> 00:13:40,330
+بنفضل اللي فوق و بنفضل اللي تحت و بنوجد limit هين
+
+162
+00:13:40,330 --> 00:13:44,670
+بيكونين هين limit اللي هي الأصل اللي احنا بدنايا
+
+163
+00:13:45,410 --> 00:13:49,590
+الان نيجي اللي هو in Berlin اللي هو a و b طبعا
+
+164
+00:13:49,590 --> 00:13:54,410
+بنفس الأسلوب الان
+
+165
+00:13:54,410 --> 00:14:02,790
+قبل ما نبدأ احنا لو اجينا و قولنا limit f of x لما
+
+166
+00:14:02,790 --> 00:14:06,610
+x تروح لأي اشي مثلا a من اليمين بساوة L
+
+167
+00:14:11,700 --> 00:14:14,480
+وقلنا اللي هو for every epsilon تعريفها for every
+
+168
+00:14:14,480 --> 00:14:16,660
+epsilon أكبر من سفر there exists a delta أكبر من
+
+169
+00:14:16,660 --> 00:14:21,300
+سفر such that if x element in A طبعا من اليمين
+
+170
+00:14:21,300 --> 00:14:27,780
+معناته A و A زائد دلتا then اللي هو هيكون عندي f
+
+171
+00:14:27,780 --> 00:14:35,230
+of x ناقص الأصغر من مين من إبسمنالان لو كانت عندي
+
+172
+00:14:35,230 --> 00:14:39,330
+ال epsilon أثبتت انا هذا الكلام ل epsilon ل
+
+173
+00:14:39,330 --> 00:14:45,410
+epsilon لو أثبتت لكل epsilon element in مثلا in
+
+174
+00:14:45,410 --> 00:14:51,970
+zero و نصأو نزيره ربع أو نزيره تلت لو أثبتت أنه
+
+175
+00:14:51,970 --> 00:14:54,950
+لكل إبسلون لجهة دلتة بحيث أن هذا الكلام أصغر من
+
+176
+00:14:54,950 --> 00:15:01,650
+مين من إبسلون برضه بيكون يجزئ عن ال limit ليش؟ لأن
+
+177
+00:15:01,650 --> 00:15:04,950
+المقدار اللي بيكون أصغر من إبسلون اللي هي أصغر من
+
+178
+00:15:04,950 --> 00:15:09,830
+النص أكيد بنفع لمين الدلتة بنفع للمقدار اللي ال
+
+179
+00:15:09,830 --> 00:15:15,450
+إبسلون أكبر من مين من النص لأنه أصلا اللي هي مشكلة
+
+180
+00:15:15,450 --> 00:15:19,620
+أو خلينا نقول ال limit في حد ذاتهاإنه لما الـ A
+
+181
+00:15:19,620 --> 00:15:24,880
+تروحالـ X تروح إلى الـ A من اليمين، بدنا نجمع أن
+
+182
+00:15:24,880 --> 00:15:27,720
+الـ F of X تقترب من مين من الأعلى، يعني التعجيز و
+
+183
+00:15:27,720 --> 00:15:31,100
+كأنه بعجزني أنه يقول لي إنك اتلاقى الـ Delta في
+
+184
+00:15:31,100 --> 00:15:34,600
+حالة الـ Epsilon أكاش اللي بيكون صغيرة فالـ Close
+
+185
+00:15:34,600 --> 00:15:38,960
+اللي هو تمين to Zero، لإنه أصلا المفهوم اللي
+
+186
+00:15:38,960 --> 00:15:43,160
+بتقيله هذا المسافة تضيق، تضيق، تضيق، بحيث أن F of
+
+187
+00:15:43,160 --> 00:15:46,760
+X تقول إلى الـ مين اللي بتعبر عنها؟ الـ Epsilon،
+
+188
+00:15:46,760 --> 00:15:51,190
+لأن بعطيك Epsilon صغيرة جدا جدابدك تلاقي لي Delta
+
+189
+00:15:51,190 --> 00:15:54,870
+أنا الآن الـ Epsilon بين Zero و نص لقيتلك الـ
+
+190
+00:15:54,870 --> 00:15:59,070
+Delta اللي طلعت هنا معناته اللي نفع للـ Epsilon
+
+191
+00:15:59,070 --> 00:16:03,510
+الصغيرة أكيد بيكون أصغر من مين من الأكبيرة إذا هذا
+
+192
+00:16:03,510 --> 00:16:09,250
+يجزء بس هذا قبل ما نبدأ لأنه هسأخدم شغلة اللي هو
+
+193
+00:16:09,250 --> 00:16:14,930
+في هذا الاتجاه نيجي الآن عندي أول إشي المعطى
+
+194
+00:16:14,930 --> 00:16:23,550
+ماتيني LimitF prime of X على G prime of X as X
+
+195
+00:16:23,550 --> 00:16:29,190
+بتروح للـ A من اليمين أيش بساوي؟ بساوي أقل تعريف
+
+196
+00:16:29,190 --> 00:16:32,850
+الـ Limit for every Y أكبر من 0 اللي هتاخد for
+
+197
+00:16:32,850 --> 00:16:39,190
+every Y element in 0 ونص اللي هي لزوم حسابات، بعد
+
+198
+00:16:39,190 --> 00:16:44,650
+شوية هنشوفهاالآن لكل y تنتمي إلى 0.5 وهذا مشروع
+
+199
+00:16:44,650 --> 00:16:49,270
+حسب ما حكيت قبل بشوية there exist delta أكبر من 0
+
+200
+00:16:49,270 --> 00:16:57,650
+such that اللي هو if x element in a و a زيادة دلتا
+
+201
+00:16:57,650 --> 00:17:04,230
+لإن رايح لل a من وين من اليمين لجيت اللي هو دلتا
+
+202
+00:17:04,230 --> 00:17:11,420
+بحيث أنه لكل x في الفترة من a لعيد a زائد دلتابصير
+
+203
+00:17:11,420 --> 00:17:16,780
+عندى لكل x المتنية زائد دلتا بتطلع عندى then f
+
+204
+00:17:16,780 --> 00:17:23,420
+prime of x على g prime of x ناقص ال L أصغر من مين
+
+205
+00:17:23,420 --> 00:17:32,060
+من ال epsilon إذا الآن من هذه ال limitحصلت على أنه
+
+206
+00:17:32,060 --> 00:17:36,540
+لأي إبسلون بين الـ 0 و نص بقدر ألاقي Delta بحيث
+
+207
+00:17:36,540 --> 00:17:40,540
+لكل الإكسات في المنطقة هذه هذه الـ Inquality إيش
+
+208
+00:17:40,540 --> 00:17:44,880
+ما لها تتحقق الآن بس خلّيني أكملها دي شويه عشان
+
+209
+00:17:44,880 --> 00:17:52,040
+بستخدمها لشغلات أخرى عند A زائد Delta هذا بس مجرد
+
+210
+00:17:52,040 --> 00:17:56,340
+تعريف الـ Limit F' على الـ G' لما X تروح للـ A من
+
+211
+00:17:56,340 --> 00:17:59,120
+اليمين الآن
+
+212
+00:18:01,110 --> 00:18:04,910
+بدي أختار .. بدي أسهل على حالي بدل من كل مرة أقول
+
+213
+00:18:04,910 --> 00:18:08,130
+a زي الـ delta و بعد شوية ألاقي delta prime و أخد
+
+214
+00:18:08,130 --> 00:18:12,010
+ال minimum بينهم الاخرى أجدفم عليه عشان اللي بحكيه
+
+215
+00:18:12,010 --> 00:18:17,910
+بدي أخد اللي هو أقول choose c1 element in a و a زي
+
+216
+00:18:17,910 --> 00:18:24,630
+الـ delta الآن اختارلي c1 من ال a لعند مين لعند ال
+
+217
+00:18:24,630 --> 00:18:30,340
+a زي ال delta سميه c1 يعنيمجرد اختيار انا اخترته
+
+218
+00:18:30,340 --> 00:18:38,260
+الان choose .. choose C1 element in A و A زائد
+
+219
+00:18:38,260 --> 00:18:44,140
+دلتا يعني C1 وين موجود؟ موجود في المنطقة التي
+
+220
+00:18:44,140 --> 00:18:50,140
+تتحقق فيها F' ع G' نقص أصغر من ميل من إبسل عشان
+
+221
+00:18:50,140 --> 00:18:56,080
+تستخدمها بعد شويةواضح طيب هذه من جهة الأن من الجهة
+
+222
+00:18:56,080 --> 00:19:03,100
+الثانية عند limit f of x لما x تروح إلى مالة نهاية
+
+223
+00:19:03,100 --> 00:19:09,880
+أسف لل a من اليمين بسوء أيش هو معطينية هي النظرية
+
+224
+00:19:09,880 --> 00:19:13,540
+هي limit f of x لما x تروح إلى ال a من اليمين بسوء
+
+225
+00:19:13,540 --> 00:19:15,760
+limit g of x لما x تروح إلى ال a من اليمين بسوء
+
+226
+00:19:15,760 --> 00:19:23,170
+أيش ماله مالة نهاية من تعريفها هذا إيش يعنيلكل K
+
+227
+00:19:23,170 --> 00:19:29,270
+اللي هو element in R there exists Delta A' أكبر من
+
+228
+00:19:29,270 --> 00:19:36,590
+0 such that اللي هو F of X أكبر من اللي هو الـ K
+
+229
+00:19:36,590 --> 00:19:42,210
+لكل X و N موجودة في الـ A و A زائد مين Delta
+
+230
+00:19:42,210 --> 00:19:49,300
+Prime، مظبوط ولا لا؟ ماشي الحلالآن لكل x element
+
+231
+00:19:49,300 --> 00:19:52,200
+in A و A زي الـ delta prime هذه ال F of X أكبر من
+
+232
+00:19:52,200 --> 00:20:02,420
+مين؟ من K الآن لو كانت ال A و ال A .. الآن عندي
+
+233
+00:20:02,420 --> 00:20:07,540
+لكل subset من هذه .. لكل subset .. لو كان عندي A و
+
+234
+00:20:07,540 --> 00:20:10,940
+C2 مثلا subset من ال A و ال A زي ال delta prime
+
+235
+00:20:12,470 --> 00:20:17,070
+برضه ال F of X أكبر من كده تحققها تحقق إيش لكل X
+
+236
+00:20:17,070 --> 00:20:24,610
+وين موجودة في الفترة من A لعند مين لعند C2 الآن لو
+
+237
+00:20:24,610 --> 00:20:30,410
+كانت ال Delta اللي لجيتها برا ولا جوا بقدر أختار
+
+238
+00:20:30,410 --> 00:20:36,990
+جوا اللي هو C2بحيث أنه لو الـ C2 هذي هو اللي
+
+239
+00:20:36,990 --> 00:20:42,450
+اخترتها جوات من الـ A والـ A زائد دلتا بتظل الـ F
+
+240
+00:20:42,450 --> 00:20:47,470
+of X A شمالها أكبر من مين؟ من الـ K، واضح؟ إذا من
+
+241
+00:20:47,470 --> 00:20:52,330
+هذه بدي أستفيد شغلتين بدي أطبق التعريف هذا لـ K
+
+242
+00:20:52,330 --> 00:20:56,730
+محددة مين الـ K اللي بدي أطبقها؟ اللي عبارة عن F
+
+243
+00:20:56,730 --> 00:21:02,560
+عند مين؟ عند C1واضح؟ إذا الأن بما أنه limit f of X
+
+244
+00:21:02,560 --> 00:21:05,680
+ثم X تروح إلى الـA باليمين يستوى Infinity إذا for
+
+245
+00:21:05,680 --> 00:21:13,720
+K .. إذا for f of C1 there exists Delta Prime أي
+
+246
+00:21:13,720 --> 00:21:19,840
+Delta Prime معينة بحيث أن f of X أكبر من 100 من f
+
+247
+00:21:19,840 --> 00:21:27,060
+of C1 لكل X موجودة بين الـA والـA زائد Delta Prime
+
+248
+00:21:27,680 --> 00:21:31,860
+أنا بدي أختار في مين لكل X الموجودة بين الـ A و
+
+249
+00:21:31,860 --> 00:21:37,940
+الـ C2 حيث الـ C2 موجودة في الفترة هذه و بديها من
+
+250
+00:21:37,940 --> 00:21:44,120
+C1 و لجاي اذا عشان هيك بقدر اقول then we can
+
+251
+00:21:44,120 --> 00:21:50,280
+choose C2 بين A و C1الـ C2 بقدر اختارها فعلا
+
+252
+00:21:50,280 --> 00:21:55,640
+بختارها بس طبعا وين تشتري تشريع اللي اختيارها انها
+
+253
+00:21:55,640 --> 00:22:01,420
+تكون بين الفترة A و A زائد Delta Prime و بدياها
+
+254
+00:22:01,420 --> 00:22:06,900
+تيجي في داخل الـ A و الـ C1 اذا then we can choose
+
+255
+00:22:06,900 --> 00:22:13,200
+C2 element A of C1 بحيث ان ال F of X أكبر من مين
+
+256
+00:22:13,200 --> 00:22:22,810
+من F of C1 لكل X وينفي الفترة بين A وC اتنين طيب
+
+257
+00:22:22,810 --> 00:22:28,050
+هذه معناته ان ال F of X هذه لكل ال Xات اللي هان ال
+
+258
+00:22:28,050 --> 00:22:34,290
+F of X أكيد اي شمالها لها تساوي ايش F of C واحد هل
+
+259
+00:22:34,290 --> 00:22:38,930
+جد تعرف ليش بديها هذه عشان لزوم تعريف شغل معينة
+
+260
+00:22:38,930 --> 00:22:44,770
+بنفعش تكون ال F of X ايش بتساوي F of C واحد الآن
+
+261
+00:22:44,770 --> 00:22:55,550
+similarlySimilarly اللي هو بما انه limit G of X
+
+262
+00:22:55,550 --> 00:23:00,690
+بساوي مالة نهاية as X بتروح للـ A من اليمين إذا
+
+263
+00:23:00,690 --> 00:23:13,160
+بقدر ألاقي اللي هو C1 برايم بحيث انه G of X أكبرأو
+
+264
+00:23:13,160 --> 00:23:17,240
+لا تساوي طبعا أكبر الـ thrifty يعني لا تساوي G of
+
+265
+00:23:17,240 --> 00:23:27,860
+C1 لكل X موجودة في الـ A و C1 إيش إبراهيم اه G C1
+
+266
+00:23:27,860 --> 00:23:34,680
+إبراهيم اه G C1 إبراهيم الآن
+
+267
+00:23:34,680 --> 00:23:40,760
+ال .. ال .. ال .. الباخدالـ Minimum عشان طبعا هذا
+
+268
+00:23:40,760 --> 00:23:46,120
+اللي لجهة N C1' ممكن اللي هي لكل X في الـ A و C1'
+
+269
+00:23:46,620 --> 00:23:52,840
+و لكل X element in A و C2' بط مانش .. مش عارف مين
+
+270
+00:23:52,840 --> 00:23:58,670
+الأكبر من هذول فباخد الـ Minimum من الجهتينو
+
+271
+00:23:58,670 --> 00:24:03,090
+بسميها C1 مثلا او C2 ال minimum من التنتين C2
+
+272
+00:24:03,090 --> 00:24:09,550
+فبتصير عندى لان لكل X في ال A و ال minimum بينهن
+
+273
+00:24:09,550 --> 00:24:14,630
+هدى بتظبط و هدى بتظبط يعنى ال G of X لا تساوي F of
+
+274
+00:24:14,630 --> 00:24:20,670
+C1 و ال F of X لا تساوي مين؟ F of C1 إبرايم و منه
+
+275
+00:24:20,670 --> 00:24:25,870
+بعرف اللى بديه او بعمل زى ما هو عامل في الكتاب إيش
+
+276
+00:24:25,870 --> 00:24:29,280
+اللى بقوله؟ نشوف اللى بعدهاإذا الأن اللي اتفجنا
+
+277
+00:24:29,280 --> 00:24:38,540
+عليه أنه في الفترة من A لعند A زائد Delta هذه
+
+278
+00:24:38,540 --> 00:24:45,480
+متحققة هاي واحد واللي اتفجنا عليه أن F of X لا
+
+279
+00:24:45,480 --> 00:24:50,140
+تساوي F of C واحد في الفترة من A لعند C تنين
+
+280
+00:24:50,140 --> 00:24:55,580
+أشمالها متحققةيعني بمعنى آخر الـ Inquality هذه
+
+281
+00:24:55,580 --> 00:25:03,800
+وهذه التنتين محققات من أين؟ من A لعين C الاتنين
+
+282
+00:25:03,800 --> 00:25:05,360
+واضح؟
+
+283
+00:25:11,650 --> 00:25:17,590
+الان اصلنا لمرحلة انه نقدر نعرف الدالة اللي بتديها
+
+284
+00:25:17,590 --> 00:25:23,890
+اللي هي F of X بتساوي واحد ناقص F of C واحد على F
+
+285
+00:25:23,890 --> 00:25:30,470
+of X وواحد ناقص G of C واحد على G of X لكل X وين
+
+286
+00:25:30,470 --> 00:25:37,330
+موجودة بين A وC تنين و F of C واحد لا تساوي F of X
+
+287
+00:25:37,330 --> 00:25:43,340
+مظبوط؟ هيا اعملهاأه لإن وين بدي أعرف هذه الدالة F
+
+288
+00:25:43,340 --> 00:25:50,480
+من A لعند مين اللي هي بتتحقق عليها خاصية F of X ده
+
+289
+00:25:50,480 --> 00:25:55,080
+تسوى مين F of C واحد و بتتحقق عليها مين اللي هي
+
+290
+00:25:55,080 --> 00:26:00,480
+الخاصية اللي عندي هذه لإن كله هيلزمني هذا إذا الأن
+
+291
+00:26:05,340 --> 00:26:09,980
+اتفجنا عليها دي اه عشان بدي امسح انه عندي f prime
+
+292
+00:26:09,980 --> 00:26:13,800
+ع الجي برايم نقصها الأصغر من يابسولون لكل ال Xات
+
+293
+00:26:13,800 --> 00:26:18,700
+من A لعند A زائد ديلتا لكل ال Xات اللي هانا
+
+294
+00:26:18,700 --> 00:26:22,040
+واتفجنا ان F of X لا تساوي F of C one برضه في
+
+295
+00:26:22,040 --> 00:26:27,350
+الفرق في المنطقة من ايش من A لC2 اتفجنا عليهالان
+
+296
+00:26:27,350 --> 00:26:33,510
+نيجي نعرف الدالة اللي هتوصلني لهدفي خد الان f of x
+
+297
+00:26:33,510 --> 00:26:42,670
+بتساوي اللي هو واحد ناقص f of c واحد على f of x
+
+298
+00:26:42,670 --> 00:26:52,450
+على واحد ناقص g of c واحد على g of xالآن g of c
+
+299
+00:26:52,450 --> 00:26:55,810
+واحد مستحيل تساوي g of x من أي أسباب اللي حكيناها
+
+300
+00:26:55,810 --> 00:27:01,710
+وليس سبب آخر أيضا اللي هو ليش أنه عندي الـ g prime
+
+301
+00:27:01,710 --> 00:27:07,570
+الـ g prime of x ده يساوي سفر إذا حسب Rolle's
+
+302
+00:27:07,570 --> 00:27:13,570
+theorem مستحيل الـ g of c واحد اللي هو تساوي g of
+
+303
+00:27:13,570 --> 00:27:20,530
+x ليش عندي g continuous
+
+304
+00:27:21,550 --> 00:27:29,350
+on a .. طبعا الـ x والي موجودة جوها منها الان من x
+
+305
+00:27:29,350 --> 00:27:37,110
+لعند c واحد صح؟ و g is differentiable on x لعند
+
+306
+00:27:37,110 --> 00:27:44,090
+اللي هي c واحد open واضحة؟
+
+307
+00:27:44,090 --> 00:27:48,670
+لأنه أثر هذا continuous و differentiable من a لعند
+
+308
+00:27:48,670 --> 00:27:52,550
+bالعلمي إذا في الجزية هذه إذا أكيد اللي هم تتحقق
+
+309
+00:27:52,550 --> 00:28:01,270
+هذه الآن لو زي ما بنقول ان جي برا لو لو عندي بدي
+
+310
+00:28:01,270 --> 00:28:09,250
+يكون g of x بسوء g of c واحد معناته حسب role
+
+311
+00:28:09,250 --> 00:28:16,360
+theorem هيعطيني there existcx element in x و c1
+
+312
+00:28:16,360 --> 00:28:22,800
+such that g prime of cx هي ساوى سفر وهذا مستحيل
+
+313
+00:28:22,800 --> 00:28:27,320
+لإن هو معطيني الـ g prime of x لاتساوى سفر لكل x
+
+314
+00:28:27,320 --> 00:28:34,630
+element من a وb معناته معناه الحديثإنه الـ G of C
+
+315
+00:28:34,630 --> 00:28:41,510
+واحد والـ G of X مستحيل يكون متساويات لكل الإكسات
+
+316
+00:28:41,510 --> 00:28:47,230
+اللي في الفترة من A لعند مين لعند C اتنين واضح إذا
+
+317
+00:28:47,230 --> 00:28:50,730
+المقام لا يساوي سفر إذا اللي هو هذي is well
+
+318
+00:28:50,730 --> 00:29:00,950
+defined على مين على الفترة Aمظبوط و C2 خلّيها في
+
+319
+00:29:00,950 --> 00:29:05,070
+الذاكرة طيب اطلع لفوق و حسب لل limit الآن هذا
+
+320
+00:29:05,070 --> 00:29:12,070
+عرفناها احفظناها بنضطر ان امسح الان احسب لل limit
+
+321
+00:29:12,070 --> 00:29:20,230
+للي فوق limit F of X لما X تروح الي وين الي ايه من
+
+322
+00:29:20,230 --> 00:29:23,390
+اليمين بساوى واحد
+
+323
+00:29:24,530 --> 00:29:32,650
+نقص limit F of C1 عدد على F of X لما X تروح للـ A
+
+324
+00:29:32,650 --> 00:29:36,950
+من اليمين على اتجرأت لأنه عارف ان ال limit موجودة
+
+325
+00:29:36,950 --> 00:29:42,290
+على التوزيع اتجرأت عليه لأنه عارف limit G of C1
+
+326
+00:29:42,290 --> 00:29:49,530
+على G of X لما X تروح لوين للـ A من اليمين واضحة
+
+327
+00:29:49,530 --> 00:29:56,130
+جدش هذه ال limit0 لأن ال F of X وين بتروح الى مالة
+
+328
+00:29:56,130 --> 00:30:00,010
+نهاية هي بداية الموضوع مش بداية الموضوع كان عندنا
+
+329
+00:30:00,010 --> 00:30:05,010
+ان ال limit F of X على G of X لما X تروح الى A من
+
+330
+00:30:05,010 --> 00:30:08,670
+اليامين اللي هو سببت لكل القصة ان هذه ال limit
+
+331
+00:30:08,670 --> 00:30:11,230
+مالة نهاية وهذه مالة نهاية صارت مالة نهاية مالة
+
+332
+00:30:11,230 --> 00:30:15,710
+نهاية وهي اللي خلتني اروح بهذا الاتجاه اذا هذه
+
+333
+00:30:16,610 --> 00:30:19,750
+بتروح إلى ملأ نهاية إذا هذه بتروح إلى سفر وهذه
+
+334
+00:30:19,750 --> 00:30:22,330
+الملأ نهاية بتروح إلى سفر إذا هذا كله على بعض إيش
+
+335
+00:30:22,330 --> 00:30:30,170
+بيساوي؟ بيساوي واحد واضح طيب الآن for every
+
+336
+00:30:30,170 --> 00:30:34,570
+epsilon أكبر من سفر اللي هي اللي فوق خلاص بدنا
+
+337
+00:30:34,570 --> 00:30:39,270
+فيها الآن بيبقى إن ال limit بيساوي واحد إذا there
+
+338
+00:30:39,270 --> 00:30:44,890
+existsDelta أكبر من سفر أي إن كانت الـ Delta أكبر
+
+339
+00:30:44,890 --> 00:30:53,790
+من سفر Such that F of X ناقص واحد أصغر من مين من
+
+340
+00:30:53,790 --> 00:30:59,190
+الـ Epsilon Epsilon اللي بدنا فيها من الأول هذا لو
+
+341
+00:30:59,190 --> 00:31:04,830
+يعني لكل الـ Xاللي في الفترة من a ل a زي الـ delta
+
+342
+00:31:04,830 --> 00:31:07,910
+هذه الـ delta الجديدة مش صارت تكون الأولى فأنا
+
+343
+00:31:07,910 --> 00:31:13,330
+عشان أريح حالي بدي أخد اللي هو أصغر delta بلاجيها
+
+344
+00:31:13,330 --> 00:31:17,910
+و أقول حطها كمان جواها هادي حر أنا مدام بتنفع لالي
+
+345
+00:31:17,910 --> 00:31:21,690
+كبيرة ايضا كده بتنفع لمن؟ للصغيرة فاهمين أنا ايش
+
+346
+00:31:21,690 --> 00:31:28,270
+بقول؟ هذه اللي هي نسميها C3 معايا؟ فبصير عندى الآن
+
+347
+00:31:28,270 --> 00:31:39,200
+F of Xلكل X element in A لعند مين؟ C3 أي
+
+348
+00:31:39,200 --> 00:31:46,120
+سؤال؟ F of X ناقص واحد أصغر من Y أكبر من سالب Y
+
+349
+00:31:46,120 --> 00:31:49,960
+تلزمني هذه المنطقة اللي اللي جاي لأن F of X هذه
+
+350
+00:31:49,960 --> 00:31:56,720
+يعني F of X يعطينا F of X أكبر من واحد ناقص Y
+
+351
+00:31:59,390 --> 00:32:03,370
+باضحة؟ لأن هذه جلبها .. اللي هذه طبعا واحد ناقص
+
+352
+00:32:03,370 --> 00:32:07,850
+إبسلون اللي هي بيصير عنده ال .. ال .. ال إبسلون
+
+353
+00:32:07,850 --> 00:32:12,650
+أصغر من مين؟ من نص الواحد ناقص إبسلون أكبر من مين؟
+
+354
+00:32:12,650 --> 00:32:20,670
+اللي هي بيصير أكبر من نص باضحة؟ اللي هي بيصير واحد
+
+355
+00:32:20,670 --> 00:32:28,400
+على f of x اللي هو أصغر من مين؟هذا لمين؟ لكل
+
+356
+00:32:28,400 --> 00:32:32,760
+الاكسات اللي من A لعند مين C3 وطبيعي ال
+
+357
+00:32:32,760 --> 00:32:36,880
+inequalities كلها اللي قبل تتحقق هنا لإنها بتتحقق
+
+358
+00:32:36,880 --> 00:32:41,360
+من هنا لهنا بعضها وبعضها بتتحقق من هنا لهنا فأكيد
+
+359
+00:32:41,360 --> 00:32:47,040
+كلها هتتحقق للإكسات اللي مين في ال A وC3 أصلا أنا
+
+360
+00:32:47,040 --> 00:32:52,620
+رايح باتجاه مين؟ رايح باتجاه أثبت لكم أنه limit of
+
+361
+00:32:53,680 --> 00:32:59,060
+of x على g of x لما x تروح لل a من اليمين بساوي
+
+362
+00:32:59,060 --> 00:33:04,880
+limit f prime of x على g prime of x as x تروح لل a
+
+363
+00:33:04,880 --> 00:33:10,080
+من اليمين اللي هو ايش نسميه احنا قال اذا انا بهمن
+
+364
+00:33:10,080 --> 00:33:14,920
+مين الاكسات اللي جنب ال a لإن انا رايح لل a من وين
+
+365
+00:33:14,920 --> 00:33:18,800
+من اليمين فانا بهمن الجوار القريب جدا من ال a لإن
+
+366
+00:33:18,800 --> 00:33:21,960
+انا رايحله اصلا من هنافالإكسات اللي فيها هي اللي
+
+367
+00:33:21,960 --> 00:33:27,760
+بتلزمني عشان أصل للي بديها خلّي هذه في الذاكرة
+
+368
+00:33:27,760 --> 00:33:34,560
+فصار عندي الآن صار
+
+369
+00:33:34,560 --> 00:33:38,800
+عندي هذا كله حكيناه وخلصنا منه الان نيجي بدنا نصل
+
+370
+00:33:38,800 --> 00:33:44,620
+للي بدنايا بتتذكروا المرة الماضية أنا أصلا جيبت
+
+371
+00:33:44,620 --> 00:33:56,350
+هذهجبت هذه اتطلع فيها و قارنليها مع ال F of X على
+
+372
+00:33:56,350 --> 00:34:01,310
+ال G of X اللي انا بديهاها ال F of X على ال G of X
+
+373
+00:34:01,310 --> 00:34:08,170
+لو جيت قارنتها F of X على ال G of X ايش هتلاقيها؟
+
+374
+00:34:08,170 --> 00:34:14,810
+لو جيت ضربت هذه في F of X وهذه في G of X
+
+375
+00:34:17,460 --> 00:34:22,500
+بنرجع ل F of X ناقص F of C واحد و G of X ناقص G of
+
+376
+00:34:22,500 --> 00:34:26,680
+C واحد طب ايش دخلنا فيه هذه F of X ناقص F of C
+
+377
+00:34:26,680 --> 00:34:30,500
+واحد و G of X ناقص G of C واحد هذه اللي بالكوشي
+
+378
+00:34:30,500 --> 00:34:33,920
+mean value theorem اللي هتجيب لل F prime و G prime
+
+379
+00:34:33,920 --> 00:34:38,340
+اللي انا اصلا موجودات limited فبحصل ع اللي بديا
+
+380
+00:34:40,230 --> 00:34:44,470
+بالظبط الشي اللي بقوله انت يعني ليش هو فكر في هذه
+
+381
+00:34:44,470 --> 00:34:50,470
+بالسبب اللي حكيته F of X على D of X بالساوي F of X
+
+382
+00:34:50,470 --> 00:34:59,890
+على D of X في F of X على D of X على F of X مظبوط؟
+
+383
+00:34:59,890 --> 00:35:09,170
+ماعملش شيء الآن اسحبلي هذه خليهاوحط ليها هذه 1 على
+
+384
+00:35:09,170 --> 00:35:15,210
+f of x ماهي الحالة هذه مين هي في الواقع هي اللي
+
+385
+00:35:15,210 --> 00:35:20,410
+فوق اللي هي عبارة عن اضرب f of x هذه في هذه بصير
+
+386
+00:35:20,410 --> 00:35:32,250
+واحد ويساوي واحد اللي هي ناقص f of c صح؟ f of x
+
+387
+00:35:32,250 --> 00:35:42,660
+ناقص f of cعلى g of x نقص g of c هذا مين هي اللي
+
+388
+00:35:42,660 --> 00:35:46,700
+هي f of x على g of x في f of x عوضت هذه و حطيتها و
+
+389
+00:35:46,700 --> 00:35:51,760
+طلع عندي هذا مضروب في كله في مين في واحدة ال f of
+
+390
+00:35:51,760 --> 00:36:01,080
+x الآن عندي خليني أطبق اللي هو مين الـ Cauchy mean
+
+391
+00:36:01,080 --> 00:36:06,390
+value theorem على الفترة من a لمين ل c تلاتةماشي
+
+392
+00:36:06,390 --> 00:36:11,130
+اللي هو there exist طبعا كله متحقق اللي هو ال F و
+
+393
+00:36:11,130 --> 00:36:15,230
+ال G continuous و differentiable على ال A و ال C 3
+
+394
+00:36:15,230 --> 00:36:21,430
+اذا there exist اللي هو ايه اللي بدكي اسميها اللي
+
+395
+00:36:21,430 --> 00:36:25,690
+هي مثلا there exist gamma او زي ما هو مسميها في
+
+396
+00:36:25,690 --> 00:36:32,230
+الكتاب there exist exi element in A و C تلاتة such
+
+397
+00:36:32,230 --> 00:36:41,500
+thatf prime of xi على g prime of xi بساوي بس ان
+
+398
+00:36:41,500 --> 00:36:44,780
+انا عشان بتطبقها على مين على الفترة f of x لعند
+
+399
+00:36:44,780 --> 00:36:48,800
+مين عشان تطلع عندي f of x of مين و f of c واحد
+
+400
+00:36:48,800 --> 00:36:53,120
+معايا للي اكسات اللي وين اللي موجودة من a لعند c
+
+401
+00:36:53,120 --> 00:36:58,060
+تلاتة بعد اذنكم بتطبقها الكوشي mean value theorem
+
+402
+00:36:58,760 --> 00:37:01,840
+ما هي اصلا continuous و differentiable على الفترة
+
+403
+00:37:01,840 --> 00:37:06,500
+دي كلها من ضمنها مين الفترة A وC ثلاثة ومن ضمنها
+
+404
+00:37:06,500 --> 00:37:11,040
+الفترة A وC واحد اللي انا بده اطبق عليها بال end
+
+405
+00:37:11,040 --> 00:37:15,900
+point مين ال end point C واحد هيها و ال end point
+
+406
+00:37:15,900 --> 00:37:21,890
+ال X اللي موجودة بين A و B مينو C3 واضح واضح اللي
+
+407
+00:37:21,890 --> 00:37:26,350
+بدي .. اذا الان الان there exists x i الان بالظبط
+
+408
+00:37:26,350 --> 00:37:30,630
+بدي اطبق الميكوشي main value term ع الفترة اللي هي
+
+409
+00:37:30,630 --> 00:37:37,790
+X و C1 اللي ال F و ال G differentiable عليها من
+
+410
+00:37:37,790 --> 00:37:40,530
+وين ال X هذه ال X اللي فوق هذه اللي بشتغل فيها
+
+411
+00:37:40,530 --> 00:37:45,890
+اللي هي من A لعن مين لعن C3إذن there exists xi
+
+412
+00:37:45,890 --> 00:37:50,750
+element in x و c واحد such that f prime of xi على
+
+413
+00:37:50,750 --> 00:37:58,770
+g prime of xi في إيش بتساوي f of c واحد أو f of x
+
+414
+00:37:58,770 --> 00:38:05,390
+ناقص f of c واحد فاهمين طبعا على g of x ناقص g of
+
+415
+00:38:05,390 --> 00:38:10,990
+c واحد بس ضربت في ناقص فوق و ناقص صحيح تتعدى زي ما
+
+416
+00:38:10,990 --> 00:38:20,080
+هي لأن هذههي هذه إذا صارت عندي F of X على G of X
+
+417
+00:38:20,080 --> 00:38:26,000
+بسوء F prime على G prime في واحد على مين على F of
+
+418
+00:38:26,000 --> 00:38:32,060
+X وهو اللي بده يوصلنا للي بدنا هي ماعليش أمسح اللي
+
+419
+00:38:32,060 --> 00:38:35,280
+هان بيصير عندى
+
+420
+00:38:38,180 --> 00:38:45,160
+بصير عندى ال F of X على مين F of X على G of X
+
+421
+00:38:45,160 --> 00:38:48,540
+بساوى
+
+422
+00:38:48,540 --> 00:38:54,120
+اللى هو هدى شلناه و حطينا مكانها مين بساوى F prime
+
+423
+00:38:54,120 --> 00:39:02,140
+of X I على G prime of X I فى مين فى واحد على ايه
+
+424
+00:39:02,140 --> 00:39:03,500
+ايش على F
+
+425
+00:39:09,880 --> 00:39:18,360
+واضح أه؟ الآن نمحى هنا هدولة ال Xات اللي هنا هما
+
+426
+00:39:18,360 --> 00:39:23,380
+ال Xات اللي وين موجودة بين A وC3 ماشي الحال بدي
+
+427
+00:39:23,380 --> 00:39:29,120
+الآن غايتي أني أوجد F of X على G of X ناقص مين؟
+
+428
+00:39:29,120 --> 00:39:34,600
+ناقص Lواضحة إذا نلخص كل اللي خدناه for every
+
+429
+00:39:34,600 --> 00:39:38,800
+epsilon element in zero نص there exists delta أكبر
+
+430
+00:39:38,800 --> 00:39:48,980
+من سفر such that if اللي هو x أكبر من a أصغر من c3
+
+431
+00:39:48,980 --> 00:39:53,260
+أصغر من c2 أصغر من c1 أصغر من a زي ال delta اللي
+
+432
+00:39:53,260 --> 00:40:02,070
+لجناها فاهمين عليها وكون عندي اللي هو قيلةالعوّض f
+
+433
+00:40:02,070 --> 00:40:08,110
+of x على g of x ناقص ال .. بدي أقبل لك يميها هذا
+
+434
+00:40:08,110 --> 00:40:12,510
+اللي هو أصغر من epsilon في something مش مشكلة و
+
+435
+00:40:12,510 --> 00:40:15,810
+epsilon is arbitral أيضا بيصير limit زي ما بدنايا
+
+436
+00:40:15,810 --> 00:40:24,170
+واضح هذا الآن بالظبط بيساوي اللي هو العوض اللي هو
+
+437
+00:40:24,170 --> 00:40:28,590
+f of x اللي هي عبارة عن واحد
+
+438
+00:40:32,680 --> 00:40:41,680
+أف برايم of x i على جي برايم of x i في واحد على أف
+
+439
+00:40:41,680 --> 00:40:48,180
+of x ناقص اللى
+
+440
+00:40:48,180 --> 00:40:54,460
+واضح لحتى الان ناخد هذه عامل مشترك برا يصبح واحد
+
+441
+00:40:54,460 --> 00:41:02,140
+على أف of x في أف برايم of x iعلى g prime of xi
+
+442
+00:41:02,140 --> 00:41:13,560
+ناقص L في F of X صح؟ أخدت
+
+443
+00:41:13,560 --> 00:41:17,300
+الواحد على F of X عام المشترك positive أه positive
+
+444
+00:41:17,300 --> 00:41:21,080
+اللي هو F of X هي أكبر من 2 طلعت اللي هو إيش ماله
+
+445
+00:41:21,080 --> 00:41:27,260
+هذا؟هنا ده بدي أضيف term و أطرح term عشان أحصل على
+
+446
+00:41:27,260 --> 00:41:31,780
+هذه اللي بدياها أصلا اللي هي الجد تفهموه مش مقصودة
+
+447
+00:41:31,780 --> 00:41:38,900
+1 على f of x في f prime of xi على g prime of xi
+
+448
+00:41:38,900 --> 00:41:50,130
+ناقص L زائد اللي هوL نقص L F of X ايش سويت استخدمت
+
+449
+00:41:50,130 --> 00:41:56,170
+ال triangle inequality باضافة L وطرحة L هذا كله
+
+450
+00:41:56,170 --> 00:42:04,130
+مضروف 100 في 1 على F of X هذا الآن ال F of X أكبر
+
+451
+00:42:04,130 --> 00:42:12,690
+من 2 حصلناها مظبوط بصير أصغر من نص واضحة
+
+452
+00:42:13,760 --> 00:42:18,920
+الآن F' على G' لـ XI الـ XI وين لاجيناها؟ في
+
+453
+00:42:18,920 --> 00:42:24,940
+الفترة بين A وC1 ينطبق عليها اللي هو من رأس الدور
+
+454
+00:42:24,940 --> 00:42:34,580
+اللي هي F' على G' of X ناقص
+
+455
+00:42:34,580 --> 00:42:41,200
+L أصغر من الـ Y من أول ما بدينايعني إنه هذا أصغر
+
+456
+00:42:41,200 --> 00:42:44,460
+من إبسلون لكل الإكسات اللي موجودة من A لعند مين؟
+
+457
+00:42:44,460 --> 00:42:48,080
+لعند الـA زاد دلتها من ضمنهم مين؟ لك فيبراين كلام
+
+458
+00:42:48,080 --> 00:42:55,940
+دقيق هذه في إبسلون زاد الآن هذا ال بطلحها برا عن
+
+459
+00:42:55,940 --> 00:43:01,760
+المشترك ال اللي هي في مين؟ في واحد ناقص F of X
+
+460
+00:43:01,760 --> 00:43:10,240
+واحد ناقص F of Xالان وهذا أصغر من نص في إبسلون
+
+461
+00:43:10,240 --> 00:43:15,440
+زائد absolute value لأل واحد ماقص F of X هذه ال
+
+462
+00:43:15,440 --> 00:43:20,260
+Xات اللي موجودة بين A وC تلاتة وهذه اللي هي قبل
+
+463
+00:43:20,260 --> 00:43:26,150
+بشوية أصغر من مين من اللي هو إبسلونأصغر من إبسلون
+
+464
+00:43:26,150 --> 00:43:30,030
+واحد ناقص F of X أصغر من مين؟ من إبسلون مش هثبتنا
+
+465
+00:43:30,030 --> 00:43:33,910
+limit F of X بيساوي واحد قبل بشوية اللي هو واحد
+
+466
+00:43:33,910 --> 00:43:37,050
+ناقص F of X اللي هي أصغر من إياش من إبسلون في
+
+467
+00:43:37,050 --> 00:43:42,850
+إبسلونصار عندي الان هذا المقدار اللي هو بساوي
+
+468
+00:43:42,850 --> 00:43:47,030
+epsilon على اتنين في واحد زايد absolute value
+
+469
+00:43:47,030 --> 00:43:52,810
+للالف لان ال epsilon مضروبة فيه اذا as لان هذا ال
+
+470
+00:43:52,810 --> 00:43:55,430
+epsilon arbitrary وهذا الكلام صحيح for every
+
+471
+00:43:55,430 --> 00:43:59,710
+epsilon epsilon بين zero و نص اذا هذا المقدار بقدر
+
+472
+00:43:59,710 --> 00:44:04,350
+ازغره جد ما بدي بتصغير epsilon لانه مضروب فيه ضرب
+
+473
+00:44:04,350 --> 00:44:08,630
+اذا صار عندي لكل epsilon أكبر من zero و نصلـ G الـ
+
+474
+00:44:08,630 --> 00:44:12,650
+Delta بحيث أنه الإكسات اللي هنا بيقدّي لي أن هذا
+
+475
+00:44:12,650 --> 00:44:20,810
+المقدار أصغر من أي قيمة بديّها إذا هذا مفهوم limit
+
+476
+00:44:20,810 --> 00:44:31,530
+F of X على G of X as X بتروح لنين؟ للـ A من اليمين
+
+477
+00:44:31,530 --> 00:44:38,920
+بساوي الـ L وهو المطلوبالثيورم اللي حكينا عنها
+
+478
+00:44:38,920 --> 00:44:45,060
+برضه صحيحة في حالة اللي هو the same .. under the
+
+479
+00:44:45,060 --> 00:44:50,160
+same conditions for the calculation of limits as x
+
+480
+00:44:50,160 --> 00:44:55,540
+goes to infinity or x as goes mean to سالبinfinity
+
+481
+00:44:55,540 --> 00:44:59,140
+بس بورهان يعني بدون modification عن اللي موجود
+
+482
+00:44:59,140 --> 00:45:03,140
+بتصلى اللي بدكيها نيجي ناخد أمثلة الأمثلة هذه طبعا
+
+483
+00:45:03,140 --> 00:45:09,500
+أمثلة سهلة ومثلة calculus نمر عليها اللي هو ونشوف
+
+484
+00:45:09,500 --> 00:45:16,480
+كيف نطبق نظريتنا أو نظرياتنا كيف نوظفها الحساب هذه
+
+485
+00:45:16,480 --> 00:45:23,260
+النهايات عندى شوفوا صلى النبي عليه الصلاة والسلام
+
+486
+00:45:24,800 --> 00:45:30,720
+Find Limitlog sin x على log x as x بتروح للـ 0 من
+
+487
+00:45:30,720 --> 00:45:35,480
+وين؟ من اليمين و احنا عارفين .. مشتغلين على الفترة
+
+488
+00:45:35,480 --> 00:45:40,460
+0 or by يعني فترة بجوار مين؟ الصفر من اليمين و
+
+489
+00:45:40,460 --> 00:45:43,540
+بدنا نروح للـ 0 من اليمين هذا طبعا لو جينا عوضنا
+
+490
+00:45:43,540 --> 00:45:48,080
+هتطلع اللي هو sin 0 0 و أنا 0 فبصير مالة نهاية على
+
+491
+00:45:48,080 --> 00:45:53,580
+مين؟ على مالة نهاية ك limits الآن صارت عندي مالة
+
+492
+00:45:53,580 --> 00:45:57,880
+نهاية على مالة نهاية إذا إيش بتنسوه؟إيش نسوي؟
+
+493
+00:45:57,880 --> 00:46:06,400
+راحين لـ 0 من اليمين بيصير عنده اللي هو بالفاضل
+
+494
+00:46:06,400 --> 00:46:11,400
+هذه و بالفاضل هذه بيصير تفاضلها هذه واضحة و هذه
+
+495
+00:46:11,400 --> 00:46:14,060
+تفاضلها هيك مافيش داعي لنا ندخل في التفاصيل لإن كل
+
+496
+00:46:14,060 --> 00:46:20,320
+بعرفها الآن بنبسط الأمر بيصير X Cos X على Sine X
+
+497
+00:46:20,930 --> 00:46:26,550
+الان لو جيت اتطلعت لهذه ال limit و لهذه ال limit
+
+498
+00:46:26,550 --> 00:46:29,530
+هذه موجودة و هذه موجودة هذه موجودة لإنه تعويض
+
+499
+00:46:29,530 --> 00:46:33,410
+مباشر واحد هذه موجودة لإنه بيصير سفر ع سفر بتعملها
+
+500
+00:46:33,410 --> 00:46:36,570
+global rule بيصير واحد على cosine بتطلع واحد برضه
+
+501
+00:46:36,570 --> 00:46:40,590
+إذا اقدرت اوزع لإنه عارف الليمتين الموجودة فبيصير
+
+502
+00:46:40,590 --> 00:46:46,220
+عبارة عن واحد في واحد بيساوي ايه؟ واحدالان خد على
+
+503
+00:46:46,220 --> 00:46:49,900
+الفترة من Zero لعند مين لعند باي على اتنين limit
+
+504
+00:46:49,900 --> 00:46:53,300
+واحد على X نقص واحد على sign ال X ثم X تروح ل Zero
+
+505
+00:46:53,300 --> 00:46:57,140
+من وين؟ من اليمين وهذه طبعا شغلات اللي هو درجنا
+
+506
+00:46:57,140 --> 00:47:01,120
+عليها في ال calculus بنوحد المقامات وبصير مكتوبة
+
+507
+00:47:01,120 --> 00:47:05,030
+على صورة sign ال X نقص X على X في sign ال Xماشي
+
+508
+00:47:05,030 --> 00:47:10,650
+الحل برضه 0 على 0 بنفضلها بيصير cos X ناقص 1 على
+
+509
+00:47:10,650 --> 00:47:15,470
+اللي هو sin X زاد X فcos X لو جينا عوضنا هتطلع
+
+510
+00:47:15,470 --> 00:47:21,250
+برضه 0 على 0 بنشتق كمان مرة بتطلع ناقص sin X على
+
+511
+00:47:21,250 --> 00:47:26,150
+هذا المقدار هذا المقدار هنا بتصفر وهنا بيصير 2
+
+512
+00:47:26,150 --> 00:47:32,680
+وهنا 0 0 على 2 مش بيساوي بيساوي 0نأتي لهذا مثال
+
+513
+00:47:32,680 --> 00:47:36,440
+معهود الـ let I بيساوين 1 إلى ما لنهاية الـ
+
+514
+00:47:36,440 --> 00:47:39,760
+interval اللي عليها بدنا نشتغل و بدنا ناخد ال
+
+515
+00:47:39,760 --> 00:47:43,600
+limit لما X تروح إلى وين إلى ما لنهاية المقدار 1
+
+516
+00:47:43,600 --> 00:47:48,960
+زائد 1 على X و الكل أُس Xهذا المقدار الان بدي
+
+517
+00:47:48,960 --> 00:47:53,460
+استخدم اللي هو يحوله ل exponential to the len ما
+
+518
+00:47:53,460 --> 00:47:55,660
+احنا عارفين ال exponential و ال len اللي هو n
+
+519
+00:47:55,660 --> 00:47:59,860
+versus لبعض فبصير عندي E to the X لن ال 1 زائد 1
+
+520
+00:47:59,860 --> 00:48:05,120
+على X هذا المقدار بدي اشغل على هذاكخطوة أولى بقول
+
+521
+00:48:05,120 --> 00:48:09,260
+limit ال X لما واحد زائد واحد على X لما X تروح إلى
+
+522
+00:48:09,260 --> 00:48:14,140
+مال نهاية بيصير هذا المقدار limit لما واحد زائد X
+
+523
+00:48:14,140 --> 00:48:18,160
+على واحد على X ليش عملت هيك لأن لما X تروح إلى مال
+
+524
+00:48:18,160 --> 00:48:21,360
+نهاية هذا سفر و لما X تروح إلى مال نهاية هذا سفر و
+
+525
+00:48:21,360 --> 00:48:25,340
+هذا لما واحد فبصير سفر على سفر بقدر استخدم ال loop
+
+526
+00:48:25,340 --> 00:48:30,730
+تالذرول اللي انا برهنتهابقى فاضل اللي فوق و فاضل
+
+527
+00:48:30,730 --> 00:48:33,850
+اللي تحت .. فضلنا اللي فوق هيه و فضلنا اللي تحت
+
+528
+00:48:33,850 --> 00:48:37,590
+هيه .. بروح هذا المقدار مع هذا المقدار .. بظل
+
+529
+00:48:37,590 --> 00:48:42,800
+limit1 زي 1 على X مقص 1 لما X تروح لمدة نهاية ده
+
+530
+00:48:42,800 --> 00:48:47,940
+بروح لصفر بطلع جداش 1 لأن 1 بنرد بنعوض وينها لأن
+
+531
+00:48:47,940 --> 00:48:50,940
+ال exponential is a continuous function لذا نصحي
+
+532
+00:48:50,940 --> 00:48:54,180
+عن عند limit ال 1 زي 1 على X لما X تروح لمدة نهاية
+
+533
+00:48:54,180 --> 00:48:57,920
+to the X وعبارة عن E to the limit لأن ال
+
+534
+00:48:57,920 --> 00:49:01,760
+exponential عبارة عن continuous function فبصير E
+
+535
+00:49:01,760 --> 00:49:08,300
+to the 1 ويساوي Eهذا اللي هو بيكون هيك احنا انهينا
+
+536
+00:49:08,300 --> 00:49:16,240
+اللي هي lobitals rules أو قواعد lobital أو صرنا
+
+537
+00:49:16,240 --> 00:49:20,360
+الآن ندخل
+
+538
+00:49:20,360 --> 00:49:28,120
+على اللي هو ال chapter ال section الأخير اللي هو
+
+539
+00:49:28,120 --> 00:49:32,120
+ال section عبارة عن ستة أربعة اللي هو taylor's
+
+540
+00:49:32,120 --> 00:49:38,540
+theoremأو tailors اللي هي .. هنحكي عن tailors
+
+541
+00:49:38,540 --> 00:49:43,640
+polynomial أو tailors أيضا اللي هو approximation
+
+542
+00:49:43,640 --> 00:49:49,820
+كيف اللي هو .. ان مرة جاية ان شاء الله كيف بنقرب
+
+543
+00:49:49,820 --> 00:49:54,840
+بعض الدوالاللي هو المحترمة اللي بتكون
+
+544
+00:49:54,840 --> 00:49:58,220
+differentiable first derivative و second
+
+545
+00:49:58,220 --> 00:50:00,400
+derivative و third derivative لأ عند ال derivative
+
+546
+00:50:00,400 --> 00:50:05,700
+اللي بدنا .. اللي .. اللي هي ما قبل اشتقاق عندها
+
+547
+00:50:05,700 --> 00:50:11,760
+بنقربها ب polynomial و طبعا انتوا عارفين جدش ال
+
+548
+00:50:11,760 --> 00:50:17,380
+polynomial من الدوال السهلةسهلة التعامل سواء في
+
+549
+00:50:17,380 --> 00:50:21,500
+تفاضل أو في تكامل أو حتى لو بدنا نحلها و نجيب
+
+550
+00:50:21,500 --> 00:50:26,340
+جذورها و نجيب كذا في شغل عليها كثير فالناس ترغب في
+
+551
+00:50:26,340 --> 00:50:30,540
+إنها تجيب بعض الدوال اللي بتكون أحيانا معقدة و
+
+552
+00:50:30,540 --> 00:50:35,380
+صعبة التكامل أو خلنا نقول بتغلب شوية في التفاضل أو
+
+553
+00:50:35,380 --> 00:50:40,040
+في وجود الجذور أو كده و نحولها إلىاللي هي
+
+554
+00:50:40,040 --> 00:50:44,020
+polynomial صبعا في مقدار خطأ الخطأ هن .. ان شاء
+
+555
+00:50:44,020 --> 00:50:47,520
+الله ال Taylor's theorem بتقولنا كيف ان هو نوجد
+
+556
+00:50:47,520 --> 00:50:51,320
+هذا الخطأ او ايش هو الخطأ و ايضا Taylor's theorem
+
+557
+00:50:51,320 --> 00:50:55,780
+زي ما انتوا عارفين هنوضح كيف هي عبارة عن تعميم لل
+
+558
+00:50:55,780 --> 00:51:00,340
+main value theorem هي تعميم لل main value theorem
+
+559
+00:51:00,340 --> 00:51:05,140
+في حالة اللي هي n بتساوي سفر بتطلع هي بالظبط ال
+
+560
+00:51:05,140 --> 00:51:09,100
+main value theorem كيف؟
+
+561
+00:51:10,860 --> 00:51:15,100
+الـ Main Value Theorem عبارة الـ Taylor's Theorem
+
+562
+00:51:15,100 --> 00:51:19,900
+عبارة عن تعميم للـ Main Value Theorem خد الآن
+
+563
+00:51:19,900 --> 00:51:25,020
+بتساوي سفر بتطلعلك الـ Main Value Theorem بيشحمها
+
+564
+00:51:25,020 --> 00:51:27,740
+و لحمها و إلى لقاء
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/H5lXnSx9bxw_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/H5lXnSx9bxw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0dc60ffa41b03998f7d39c345a7878953c30dd39
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/H5lXnSx9bxw_raw.srt
@@ -0,0 +1,4104 @@
+1
+00:00:04,890 --> 00:00:10,370
+بسم الله الرحمن الرحيم المحاضرة رقم 12 في مساق
+
+2
+00:00:10,370 --> 00:00:14,870
+تحليل حقيقه 2 لطلاب و طالبات الجامعة الإسلامية
+
+3
+00:00:14,870 --> 00:00:20,710
+كلية العلوم قسم رياضيات وهي المحاضرة الثانية بعد
+
+4
+00:00:20,710 --> 00:00:25,150
+الطوارئ لمواجهة فيروس كورونا
+
+5
+00:00:27,610 --> 00:00:31,150
+السيكشن اليوم ان شاء الله اللي هنبدأ فيه اللي هو
+
+6
+00:00:31,150 --> 00:00:35,050
+سيكشن سبعة اتنين اللي هو عبارة عن البروبارتيز of
+
+7
+00:00:35,050 --> 00:00:38,290
+the Riemann Integral او اللي هو خواص اللي هو
+
+8
+00:00:38,290 --> 00:00:43,310
+الريمان انتيجرالبندب على عدد من الأسئلة اليوم أنه
+
+9
+00:00:43,310 --> 00:00:47,190
+لو كانت عندي في عندي اللي هو two functions f و g
+
+10
+00:00:47,190 --> 00:00:51,650
+اللي هو عبارة عن integrable functions على some
+
+11
+00:00:51,650 --> 00:00:56,070
+bounded closed interval I هل مجموحين هيكون
+
+12
+00:00:56,070 --> 00:01:01,440
+integrable ولا لأ؟ هل حاصل ضرب ثابت؟في اللي هو الـ
+
+13
+00:01:01,440 --> 00:01:03,620
+F اللي هي الـ integrable function هيطلع اللي هو
+
+14
+00:01:03,620 --> 00:01:09,340
+الـ K F is integrable؟ هل حاصل ضرب دالتين F و G is
+
+15
+00:01:09,340 --> 00:01:13,700
+integrable؟ هل لو أجينا كان في عندي two functions
+
+16
+00:01:13,700 --> 00:01:17,720
+F و G integrable؟ وكان اللي هو معرفات على أساس ال
+
+17
+00:01:17,720 --> 00:01:20,900
+composition بينهين يكون معرف؟ وكان التنتين
+
+18
+00:01:20,900 --> 00:01:24,560
+integrable؟ هل اللي هو F composite G integrable
+
+19
+00:01:24,560 --> 00:01:29,020
+ولا لأ؟أيضًا لو مش Integrable طب إيش نحط condition
+
+20
+00:01:29,020 --> 00:01:32,640
+على واحدة منه عشان يصير Integrable؟ هتجاوب عليه
+
+21
+00:01:32,640 --> 00:01:37,280
+نظرية اللي هو هنحكي عنها أنه لو كانت إحداهما اللي
+
+22
+00:01:37,280 --> 00:01:41,600
+هي continuous فهيكون عندي اللي هو أو إذا كانت ال F
+
+23
+00:01:41,600 --> 00:01:45,200
+is continuous يكون F composite G is Integrable
+
+24
+00:01:45,200 --> 00:01:49,800
+وحنشوف هذا الكلام إن شاء الله خلال اللي هو هذا ال
+
+25
+00:01:49,800 --> 00:01:54,180
+section وحنوظف اللي هو نظرية ال composition هذه في
+
+26
+00:01:54,180 --> 00:01:58,210
+إثباتاللي هو بعض الدول كيف هتكون اللي هو
+
+27
+00:01:58,210 --> 00:02:02,410
+integrable نبدأ الآن في اللي هو النظرية الأولى
+
+28
+00:02:02,410 --> 00:02:06,650
+اللي هتجاوبلنا على اللي سألناه السؤال الأول انه لو
+
+29
+00:02:06,650 --> 00:02:11,090
+كانت عندي الية theorem 711 لو كانت I عبارة عن
+
+30
+00:02:11,090 --> 00:02:14,960
+closed bounded interval A وBهو الـ F و الـ G عبارة
+
+31
+00:02:14,960 --> 00:02:18,760
+عن two functions من I لعند R وفرضنا إن هنا دولة ال
+
+32
+00:02:18,760 --> 00:02:21,600
+two functions أيه شمال هنا؟ Are integrable يعني
+
+33
+00:02:21,600 --> 00:02:25,740
+نفترض let F and G be two integrable functions on I
+
+34
+00:02:25,740 --> 00:02:29,960
+الآن if K element in R عبارة عن .. عبارة عن ثابت
+
+35
+00:02:29,960 --> 00:02:35,380
+then the functions اللي هو الإجابة الآن K في F و K
+
+36
+00:02:35,380 --> 00:02:39,220
+في G يعني حاصل ضرب الثابت في الـ F هيطلع عند عبارة
+
+37
+00:02:39,220 --> 00:02:43,300
+عن integrable functionوهيطلع f زائد g integrable
+
+38
+00:02:43,300 --> 00:02:47,700
+function يعني هيكون اللي هو اللي هي بدر دول f زائد
+
+39
+00:02:47,700 --> 00:02:50,860
+g is integrable وطبعا لو أثبتنا هذا integrable
+
+40
+00:02:50,860 --> 00:02:54,000
+وهذا integrable على طول ال f ناقص g is integrable
+
+41
+00:02:54,000 --> 00:02:59,640
+ليش؟ لأن f is integrable و g is integrable هيعطيني
+
+42
+00:02:59,640 --> 00:03:05,720
+اللي هو f زائد f و k في g برضه integrable حسب اللي
+
+43
+00:03:05,720 --> 00:03:12,610
+هو مين اللي حاكيناها هذا في حالة إثباتهمدام اتكافى
+
+44
+00:03:12,610 --> 00:03:16,070
+g is integrable لكل k طبعا element are من ضمنها
+
+45
+00:03:16,070 --> 00:03:19,790
+ناقص واحد يعني هيصير عند اف وناقص g integrable
+
+46
+00:03:19,790 --> 00:03:24,890
+يعني هيصير عند حسب اللي هو ال F زائد g بصير F زائد
+
+47
+00:03:24,890 --> 00:03:29,210
+ناقص g is integrable يعني F ناقص g برضه هيطلع ايه
+
+48
+00:03:29,210 --> 00:03:33,790
+شماله is integrable هذه ملاحظات سريعة ايضا هيطلع
+
+49
+00:03:33,790 --> 00:03:39,890
+عند حسب اللي هو النظرية هذه انه in general Fزائد k
+
+50
+00:03:39,890 --> 00:03:43,330
+في g هيكون integrable و لو كان في عندي constant
+
+51
+00:03:43,330 --> 00:03:47,130
+تاني k prime هيطلع ال linear combination بينهم k
+
+52
+00:03:47,130 --> 00:03:52,630
+prime f زائد g برضه is integrable هذا كله في حال
+
+53
+00:03:52,630 --> 00:03:56,810
+أثبتنا ان ال kf و ال f زائد g is integrable عندما
+
+54
+00:03:56,810 --> 00:04:00,330
+تكون f و d is integrable خلينا نبدأ الآن اللي هو
+
+55
+00:04:00,330 --> 00:04:05,330
+نثبت ال kf is integrable قبل ما نثبت خليني أذكركم
+
+56
+00:04:05,330 --> 00:04:10,700
+ببعض اللي هي ال ..القوانين أو اللي هو ال
+
+57
+00:04:10,700 --> 00:04:14,180
+definitions اللي احنا حكيناها سابقا عشان هستخدمها
+
+58
+00:04:14,180 --> 00:04:20,420
+اليوم اللي هو lower sum لل partition B وG ال
+
+59
+00:04:20,420 --> 00:04:22,880
+partition B هو عبارة عن ال partition لل interval I
+
+60
+00:04:22,880 --> 00:04:26,700
+اللي معرف عليها G هو عبارة عن summation MK في XK
+
+61
+00:04:26,700 --> 00:04:30,440
+minus XK minus 1 والMK زي ما انتوا عارفين هي عبارة
+
+62
+00:04:30,440 --> 00:04:34,050
+عن ال infimumلقيمة الدالة على اللي هي الـ
+
+63
+00:04:34,050 --> 00:04:39,430
+Subinterval اللي بنحكي عنها XK-1 و XK والـ L of G
+
+64
+00:04:39,430 --> 00:04:43,890
+اللي هو الـ Lower Integral اللي هو عبارة عن الـ
+
+65
+00:04:43,890 --> 00:04:49,330
+Supremum لكل الـ P و G لكل P element in the set of
+
+66
+00:04:49,330 --> 00:04:54,720
+all partition P of I و أيضًا الـ UPGهي عبارة عن
+
+67
+00:04:54,720 --> 00:04:57,380
+summation نفس اللي فوق بس بدل اللي هي ال infimum
+
+68
+00:04:57,380 --> 00:05:01,340
+بنحط M كابيتال K اللي هي عبارة عن اللي هي ال
+
+69
+00:05:01,340 --> 00:05:04,180
+supremum لقيمة ال functions زي ما انتوا عارفين أو
+
+70
+00:05:04,180 --> 00:05:07,320
+زي ما شرحناها سابقاً و ال U of G في هذه الحالة
+
+71
+00:05:07,320 --> 00:05:11,740
+اللي هو عبارة عن ال other integral هو عبارة عن ال
+
+72
+00:05:11,740 --> 00:05:17,180
+infimum لاللي هي كل ال other sumsلع ال partitions
+
+73
+00:05:17,180 --> 00:05:20,160
+بيه element in B of I هذا خلّيه على أساس أنه بدأ
+
+74
+00:05:20,160 --> 00:05:26,510
+استخدمه بعد شوية في هذه البرهان للنظريةالان بدأ
+
+75
+00:05:26,510 --> 00:05:30,510
+ابرهن اللي هو KF is Integra بالواحد و بعد هيك بدأ
+
+76
+00:05:30,510 --> 00:05:33,530
+اثبت لكم ان ال integration ل KFF بيساوي كيف ال
+
+77
+00:05:33,530 --> 00:05:38,750
+integration لمين لLF الان بدأ اخد تلات حالات بدأ
+
+78
+00:05:38,750 --> 00:05:42,290
+اخد طبعا هذا كل K ألمت نهار بدأ اخد حالة K بتساوي
+
+79
+00:05:42,290 --> 00:05:47,050
+سفر و حالة K أصغر من سفر و حالة K أكبر من إياش من
+
+80
+00:05:47,050 --> 00:05:51,740
+سفروكل حالة فيها بروحانها الحالة الأولى k بساوة
+
+81
+00:05:51,740 --> 00:05:56,240
+سفر حالة سهلة وحالة trivial لماذا؟ لأن إذا كانت kf
+
+82
+00:05:56,240 --> 00:06:01,340
+بساوة سفر هيصير الـ kf عبارة عن الـ zero function
+
+83
+00:06:01,340 --> 00:06:04,720
+و ال zero function is continuous يعني constantما
+
+84
+00:06:04,720 --> 00:06:08,220
+دام continuous حسب النظرية المرة الماضية هتكون
+
+85
+00:06:08,220 --> 00:06:11,900
+اللي هو إيه شمالها is integrable إذا في حالة الـ K
+
+86
+00:06:11,900 --> 00:06:15,700
+بيساوي صفر trivial K F is integrable ومش هيك كمان
+
+87
+00:06:15,700 --> 00:06:19,540
+و K في ال integration لل F هذا عبارة عن integrable
+
+88
+00:06:19,540 --> 00:06:23,760
+يعني قيمة عددية وهذا Zero بيصير بيساوي Zero و ال
+
+89
+00:06:23,760 --> 00:06:26,860
+integration لل Zero function على الفترة A B اللي
+
+90
+00:06:26,860 --> 00:06:29,900
+هو عبارة عن ال K في ال F في هذه الحالة هيساوي صفر
+
+91
+00:06:29,900 --> 00:06:33,880
+إذا صار عندي من اللي هو الجهتين هذه ل Kفي ال
+
+92
+00:06:33,880 --> 00:06:38,220
+integration لل F بيساوي ال integration لل K F من A
+
+93
+00:06:38,220 --> 00:06:42,780
+ل B من A ل B بيساوي 0 in the case of ك بتساوي أياش
+
+94
+00:06:42,780 --> 00:06:47,380
+0 إذا زي ما قلنا فعلا لحالة ك بتساوي سفر حالة سهلة
+
+95
+00:06:47,380 --> 00:06:52,120
+و trivial case نيجي الآن بدنا نحكي عن مين يا جماعة
+
+96
+00:06:52,120 --> 00:06:58,000
+عن الحالة التانية اللي هو إذا كانت ك أصغر من 0 في
+
+97
+00:06:58,000 --> 00:07:02,620
+حالة ال K أصغر من 0 إذا نشغلنا الآن على ال K أصغر
+
+98
+00:07:02,620 --> 00:07:07,760
+من 0طيب لحظة
+
+99
+00:07:07,760 --> 00:07:13,480
+ما هي ليه؟ خلّينا نركز على الحالة اللي هو K أصغر
+
+100
+00:07:13,480 --> 00:07:21,380
+من 0 عندي K أصغر من 0 عندي
+
+101
+00:07:21,380 --> 00:07:32,980
+بدي أوجد ال L بي و K فئةالـ LBQF الـ B أشماله Any
+
+102
+00:07:32,980 --> 00:07:36,820
+Partition أخدت الـ B أشماله Any Partition بسوء X
+
+103
+00:07:36,820 --> 00:07:41,400
+نوت X1 لعند XN Any Partition of مين؟ Of the
+
+104
+00:07:41,400 --> 00:07:46,000
+interval I اللي بنحكي عنهاإذا الـ BKF حسب التعريف
+
+105
+00:07:46,000 --> 00:07:51,000
+اللي كاتبه فوق إيش بيساوي الـ summation للـ M
+
+106
+00:07:51,000 --> 00:07:54,700
+لمين؟ الـ M للـ function الجديدة اللي هي اسمها
+
+107
+00:07:54,700 --> 00:08:00,520
+إيش؟ KF اللي هي عبارة عن مين؟ عن الـ infimum هذه
+
+108
+00:08:00,520 --> 00:08:04,280
+الـ K اللي هي إيش؟ الـ MK small اللي هي الـ
+
+109
+00:08:04,280 --> 00:08:11,850
+infimumلأ اللي هي الدالة تبعتنا K F of X لكل X وين
+
+110
+00:08:11,850 --> 00:08:16,350
+موجودة في ال sub interval هذه بس بلاش عشان مايصيرش
+
+111
+00:08:16,350 --> 00:08:19,090
+conflict بين ال K اللي هنا و ال K اللي هنا خليني
+
+112
+00:08:19,090 --> 00:08:23,990
+أسميها بعد إذنكم اسمهااللي هي I I اللي هي ال sub
+
+113
+00:08:23,990 --> 00:08:28,410
+interval اللي هو X I minus واحد لعند مين لعند X I
+
+114
+00:08:28,410 --> 00:08:33,350
+هذه I من عند واحد لعند N مضروبة في مين في طول
+
+115
+00:08:33,350 --> 00:08:38,810
+الفترة هذه اللي هي X I minus X I minus واحد هذه
+
+116
+00:08:38,810 --> 00:08:45,710
+اللي هي ال B K و F Y ساوينك ايش يا جماعة احنا
+
+117
+00:08:45,710 --> 00:08:50,850
+بنشتغل ك أصغر من سفر بنشتغل على الحالة ك أشملها
+
+118
+00:08:50,850 --> 00:08:55,470
+أصغر من سفر إذا حيساو ال summation الـ K لما تطلع
+
+119
+00:08:55,470 --> 00:08:59,650
+برا ال infimum و هي سالبة على طول بتجلب ال infimum
+
+120
+00:08:59,650 --> 00:09:04,650
+إلى إيش إلى supremum إذا بيصير ك في ال supremum لل
+
+121
+00:09:04,650 --> 00:09:11,490
+F of X such that X element in II من عند 1 لعند N
+
+122
+00:09:11,490 --> 00:09:18,530
+ومضروب هذا في XI minus XI minus 1 ويساوي الآن
+
+123
+00:09:18,530 --> 00:09:22,030
+خلّينا نطلع ال K هذه برا ال summation بالمرة لأن
+
+124
+00:09:22,030 --> 00:09:25,530
+ال K عبارة عن إيش يا شباب عبارة عن K عبارة عن ثابت
+
+125
+00:09:25,530 --> 00:09:28,510
+وبيطلع برا ال summation عادي وكأنه عامل مشترك
+
+126
+00:09:28,510 --> 00:09:33,690
+بيصير K في ال summation الآن لمين لل supremum لل F
+
+127
+00:09:33,690 --> 00:09:39,590
+of Xوالـ x element in I I في مضروب في مين؟ في الـ
+
+128
+00:09:39,590 --> 00:09:43,070
+x I minus x I minus واحد اللي هو طول الـ interval
+
+129
+00:09:43,070 --> 00:09:47,190
+و هذا الكلام I من عند واحد لعند N إلى أن هذا يا
+
+130
+00:09:47,190 --> 00:09:55,220
+شباب كلهعبارة عن ايش عبارة عن بالظبط تعريف ال U بي
+
+131
+00:09:55,220 --> 00:09:58,580
+و مين و ال function اللي عندي هنا ايش هي اللي
+
+132
+00:09:58,580 --> 00:10:06,360
+بشتغل عليها هنا F اذا حيساوي K في ال U ل بي و مين
+
+133
+00:10:06,360 --> 00:10:13,360
+و F اذا اللي وصلتله يا جماعة ان عندي اللي هو ال L
+
+134
+00:10:14,150 --> 00:10:21,110
+of K و P و F بيساوي K في الـ U P و F Similarly
+
+135
+00:10:21,110 --> 00:10:29,990
+وبنفس الطريقة بقدر أحصل على ال U بنفس الطريقة ال U
+
+136
+00:10:29,990 --> 00:10:44,090
+لأ ال P و K F اللي هو هتساوي K في ال L P و Fهتساوي
+
+137
+00:10:44,090 --> 00:10:53,090
+بنفس الطريقة كفي ال L, P و F خلّي
+
+138
+00:10:53,090 --> 00:10:58,450
+هذا في الذاكرة أنه اللي حصلنا عليه اللي قلته هاي
+
+139
+00:10:58,450 --> 00:11:03,030
+هذا الكلام خلّيني أسجلها اللي حصلت عليها لإني بدي
+
+140
+00:11:03,030 --> 00:11:07,510
+أستخدمها بعد شوية اللي هو بساوي K
+
+141
+00:11:08,960 --> 00:11:15,580
+في الـ U,B وF وزي ما قلنا similarly الـ U الـ U,B
+
+142
+00:11:15,580 --> 00:11:24,670
+,K وF بساوي K في الـ L,B وFماشي الحال طبعا هذه لو
+
+143
+00:11:24,670 --> 00:11:29,250
+لو حد حاب يعرف التفاصيل التفاصيل سهلة خليني بس على
+
+144
+00:11:29,250 --> 00:11:35,050
+السريع أحكيها شفوي ال U P Q F إيش هيصير هنا بصير
+
+145
+00:11:35,050 --> 00:11:39,190
+ال summation لأن ال supremum بدل ال M K capital
+
+146
+00:11:39,190 --> 00:11:44,090
+هذي بصير اللي هي supremum لمين بدل ال G K F فلمّا
+
+147
+00:11:44,090 --> 00:11:48,730
+.. لما أطلع ال K برا عام المشترك بصير ال supremum
+
+148
+00:11:48,730 --> 00:11:54,160
+infimumفبصير اللي هو الـ K برا وهنا الـ infimum مع
+
+149
+00:11:54,160 --> 00:11:59,480
+هذه اللي هي بالظبط تعريف مين ال L of B أو F باشي
+
+150
+00:11:59,480 --> 00:12:05,060
+الحال؟ طيب، الآن بكون احنا أثبتنا الجهتين أنا وين
+
+151
+00:12:05,060 --> 00:12:09,930
+رايح؟ أنا بدي أثبت إن الـ K في الـ Fis integrable
+
+152
+00:12:09,930 --> 00:12:13,410
+in the case K أصغر من 100 من 0 طيب احسبولي يا
+
+153
+00:12:13,410 --> 00:12:19,030
+جماعة احسبولي ال L of K F ايش بتساوي حسب تعريفنا
+
+154
+00:12:19,030 --> 00:12:27,730
+اللي فوق عبارة عن ال supremum لمين لل L of B و K F
+
+155
+00:12:27,730 --> 00:12:34,210
+حيث B element in the set of partitions B of I ماشي
+
+156
+00:12:34,210 --> 00:12:37,090
+الحل يا جماعة ويساوي الآن
+
+157
+00:12:39,190 --> 00:12:45,190
+الـ LBKF أنا حضرتله أصلا بيساوي K في الـ U ويساوي
+
+158
+00:12:45,190 --> 00:12:50,790
+بطلع ال K برا هذه بيصير ال supremum لـ K الـ U, B
+
+159
+00:12:50,790 --> 00:12:59,930
+و F such that B element in B of Iو يساوي بطلع ال K
+
+160
+00:12:59,930 --> 00:13:05,370
+برا بيصير K لأن K سالب يا شباب بيصير K في مين؟ في
+
+161
+00:13:05,370 --> 00:13:12,730
+ال infimum لل U بي و F واضح أه؟ such that B
+
+162
+00:13:12,730 --> 00:13:22,080
+element in B of I الآن ال infimum لل Uللـ B و F
+
+163
+00:13:22,080 --> 00:13:25,960
+على الشغل عمين الآن عن الـ function F ديروا بالكم
+
+164
+00:13:25,960 --> 00:13:31,800
+إذاً هيساوي ك .. في مين هذه تعريف؟ تعريف بالظبط
+
+165
+00:13:31,800 --> 00:13:39,240
+الـ infimum لهذه اللي هو عبارة عن الـ U of F الـ U
+
+166
+00:13:39,240 --> 00:13:46,800
+of F هاي واحد اتنين من جهة أخرى نعتبد على هذه اللي
+
+167
+00:13:46,800 --> 00:13:57,360
+هو الـ U ofب .. آسف ال U of K F بدوجتها ال U of K
+
+168
+00:13:57,360 --> 00:14:05,400
+و F إيش حيساوي؟ حيساوي ال infimum له اللي هي ال L
+
+169
+00:14:05,400 --> 00:14:14,160
+ال U of B و K F such that B element in B of I
+
+170
+00:14:14,730 --> 00:14:19,750
+هتلاقوها بتشبه اللي فوق و يساوي هذه أثبتناها إيش
+
+171
+00:14:19,750 --> 00:14:26,610
+بتساوي كفي ال L و يساوي ال infimum لأ بدل ال U إيش
+
+172
+00:14:26,610 --> 00:14:34,510
+بده يصير عنده ك ال B و F الان such that B element
+
+173
+00:14:34,510 --> 00:14:40,810
+in B of I و يساويالان ال K بضطلحها برا ال M في
+
+174
+00:14:40,810 --> 00:14:44,430
+مامي الجماعة ال K سالبة إذا إيش هتصير عبارة عن
+
+175
+00:14:44,430 --> 00:14:49,470
+إيش؟ عن K في ال supremum إذا و يساوي K في ال
+
+176
+00:14:49,470 --> 00:14:56,430
+supremum لل L بي و F such that B element in B of I
+
+177
+00:14:56,940 --> 00:15:03,060
+الان هذه الـ supremum هذه هي بالظبط تعريف من ال L
+
+178
+00:15:03,060 --> 00:15:13,180
+of F إذا بيصير و يساوي K في L of F K في L of F إذا
+
+179
+00:15:13,180 --> 00:15:19,980
+صارت الآن بتصور الصورة جربت توضح هاي عندي L of K
+
+180
+00:15:19,980 --> 00:15:28,570
+of F أثبتناها بتساوي K of U of Fو ال U K of F
+
+181
+00:15:28,570 --> 00:15:34,990
+بتساوي K L of F خلّيني ألخصها يا شباب فوق و نقارن
+
+182
+00:15:34,990 --> 00:15:40,950
+بينها و نصل لنتجتنا اللي بدنا إياها طيب صار عندي
+
+183
+00:15:40,950 --> 00:15:51,130
+يا جماعة اللي هي L of K F بتساوي K U of F و في نفس
+
+184
+00:15:51,130 --> 00:16:01,230
+الوجهة U of K F بتساوياللي هو K L of F طيب ما احنا
+
+185
+00:16:01,230 --> 00:16:07,430
+بنقول ايش احنا مفترضين ما احنا مفترضين ان F is
+
+186
+00:16:07,430 --> 00:16:12,130
+integrable ما زم F is integrable اذا ايش هيكون
+
+187
+00:16:12,130 --> 00:16:19,770
+عندي L of F هي نفس ال U of F اذا الان من هذه و من
+
+188
+00:16:19,770 --> 00:16:26,710
+اللي فوق بيصير عندي Lof K F التي بتساوي K في U of
+
+189
+00:16:26,710 --> 00:16:31,910
+F التي بتساوي K
+
+190
+00:16:31,910 --> 00:16:38,470
+في U
+
+191
+00:16:38,470 --> 00:16:46,360
+of Fإذن بين الجهتين طلع عندي L of K of F بيساوي U
+
+192
+00:16:46,360 --> 00:16:58,180
+K F وهذا يعني إذن K F is integrable إذن صار عندي
+
+193
+00:16:58,180 --> 00:17:05,040
+ال K F is integrable طيب الآن اللي بعده سهل نشوف
+
+194
+00:17:05,040 --> 00:17:11,870
+إيش اللي بعده ضل إيش أثبت إنه ال integrationالـ
+
+195
+00:17:11,870 --> 00:17:16,350
+integration للـ KF بيساوي KF ال integration لل F
+
+196
+00:17:16,350 --> 00:17:19,550
+اللي في الأول اللي هو اللي حكيناه في الأول يا شباب
+
+197
+00:17:19,550 --> 00:17:28,970
+تشوفوه حاضر أيوة
+
+198
+00:17:28,970 --> 00:17:33,930
+يا جماعة بدنا نثبت انه ال جيت أثبتنا ان KF is
+
+199
+00:17:33,930 --> 00:17:38,060
+integrable دلقا تبت هذه بتساوي هذهسهل الأمر طيب
+
+200
+00:17:38,060 --> 00:17:42,920
+احنا الآن مادام اللي هو KF is integrable إذا ال
+
+201
+00:17:42,920 --> 00:17:47,140
+integration من A ل B لل KF اللي هي صارت integrable
+
+202
+00:17:47,140 --> 00:17:52,080
+بساوي اللي هو ال L of K of F و ال U of K of F
+
+203
+00:17:52,080 --> 00:17:56,680
+بساوي U of K F مثلاو يساوي ال U K of F أيش هتساوي
+
+204
+00:17:56,680 --> 00:18:01,900
+من هنا اللي هتبتنعها ده K في ال L of F أو ال U of
+
+205
+00:18:01,900 --> 00:18:05,600
+F مش مشكلة كتير و يساوي ما هي ال F is integrable
+
+206
+00:18:05,600 --> 00:18:09,660
+إذا ال L of F هو عبارة عن إيش؟ ع ال integration من
+
+207
+00:18:09,660 --> 00:18:15,330
+A ل B لل F و ال K براتهلأن الـ F هو من ال
+
+208
+00:18:15,330 --> 00:18:19,150
+integration من A ل B ل F لأن الـ F is integrable
+
+209
+00:18:19,150 --> 00:18:22,610
+إذا صار عند الآن ال integration من A ل B ك F سواء
+
+210
+00:18:22,610 --> 00:18:27,070
+كيف ال integration من A ل B ل F الآن ظلت الحالة
+
+211
+00:18:27,070 --> 00:18:32,990
+الأخيرة يا شباب اللي هي حالة أن Kاللي هو أكبر من
+
+212
+00:18:32,990 --> 00:18:38,170
+سفر K أكبر من سفر Similarly تماما زي الحالة اللي
+
+213
+00:18:38,170 --> 00:18:42,690
+هي مين هي اللي قبل بشوية K أصغر من سفر بس لما نطلع
+
+214
+00:18:42,690 --> 00:18:46,250
+ال K برا ال supremum بتظل ال supremum supremum و
+
+215
+00:18:46,250 --> 00:18:49,690
+لما نطلع ال K برا ال infimum بتظل ال infimum
+
+216
+00:18:49,690 --> 00:18:54,950
+infimum مدام كله بظل زي بعضه بناء عليه اللي توه
+
+217
+00:18:54,950 --> 00:19:04,090
+قبل بشوية احنا أثبتنا بصير عندي ال L ال Lالـ L of
+
+218
+00:19:04,090 --> 00:19:11,270
+F أو الـ L of B و KF هيصير عبارة عن K في الـ L، B
+
+219
+00:19:11,270 --> 00:19:15,170
+و F لأن كل الدنيا هتظلها ماشية طبيعية لإن الـ K
+
+220
+00:19:15,170 --> 00:19:17,910
+أكبر من 0 لما تطلع من ال Infant Mom بتظلها زي ما
+
+221
+00:19:17,910 --> 00:19:21,090
+هي Infant Mom و لما تطلع من ال Supremum بتظلها زي
+
+222
+00:19:21,090 --> 00:19:27,980
+ما هي Supremumو ال U of K,B و K,F هتطلع بساوي K في
+
+223
+00:19:27,980 --> 00:19:35,060
+ال U,B و F و بناء عليه حيصير عندي ال U of K,F
+
+224
+00:19:35,060 --> 00:19:43,680
+هيساوي K في U of F و Lof K F هي ساوي K في ال L of
+
+225
+00:19:43,680 --> 00:19:49,860
+F ومن الجهتين بنحصل بما انه زي اللي فوق بالظبط انه
+
+226
+00:19:49,860 --> 00:19:53,740
+ال F is integrable بيصيه U of F بساوي L of F وعلى
+
+227
+00:19:53,740 --> 00:19:57,080
+طول بتطلع هذه بتساوي هذه وبنكمل زي ما كملنا هنا
+
+228
+00:19:57,080 --> 00:20:01,420
+بالظبطإذا اللي تركينه إحنا exercise K أكبر من 0 هي
+
+229
+00:20:01,420 --> 00:20:05,420
+الحالة الأسهل وهي نشرحت اللي هو الـ hint على كيف
+
+230
+00:20:05,420 --> 00:20:10,000
+تكون اللي هو نثبت ال integration للـ K F بساوي كيف
+
+231
+00:20:10,000 --> 00:20:14,620
+ال integration لل F وبذلك بكون أن هنا هذا الجزء من
+
+232
+00:20:14,620 --> 00:20:22,760
+النظرية لكل K element in R طيب نيجي الآن يا شباب
+
+233
+00:20:25,560 --> 00:20:29,360
+نثبت اللي هو الجزء الثاني من النظرية اللي هو الـ
+
+234
+00:20:29,360 --> 00:20:34,300
+integration أنه لو كانت F و G are integrable هيطلع
+
+235
+00:20:34,300 --> 00:20:40,660
+عندي برضه F زائد G is integrable خلّينا نشوف يا
+
+236
+00:20:40,660 --> 00:20:49,460
+جماعة مع بعض نفترض أنه F و G F و G من I لعند R are
+
+237
+00:20:49,460 --> 00:20:54,820
+integrable functionsبدنا نثبت أنه اللي هو الـ F
+
+238
+00:20:54,820 --> 00:20:58,960
+زائد G is integrable وكأني بد أثبت أن الـ L of F
+
+239
+00:20:58,960 --> 00:21:05,860
+زائد G بساوي الـ U لمين للـ F زائد G ماشي يا جماعة
+
+240
+00:21:05,860 --> 00:21:13,300
+طيب بد أثبت الآن زي ما قلنا أنه F زائد G is
+
+241
+00:21:13,300 --> 00:21:14,540
+integrable
+
+242
+00:21:17,640 --> 00:21:22,580
+بس في شغلتين هيك يعني ب .. ب .. بذكركم فيه إن اللي
+
+243
+00:21:22,580 --> 00:21:27,840
+هو من .. من الـ real واحد هنستخدمهم بعد شوية عندي
+
+244
+00:21:27,840 --> 00:21:34,320
+الآن لو
+
+245
+00:21:34,320 --> 00:21:38,160
+كان عندي two functions و بده أشوف اللي هو ال
+
+246
+00:21:38,160 --> 00:21:44,080
+supremumلل F of X زائد G of X such that X element
+
+247
+00:21:44,080 --> 00:21:47,200
+in some interval اللي بدكم إياها اسمها I I زي ما
+
+248
+00:21:47,200 --> 00:21:53,740
+هم سميها هيكون أصغر أو يساوي ال supremum لل F of X
+
+249
+00:21:53,740 --> 00:21:59,870
+such that X element in I I زائد ال supremumلـ g of
+
+250
+00:21:59,870 --> 00:22:04,690
+x such that x element in I I هذه معلومة سابقة من
+
+251
+00:22:04,690 --> 00:22:10,090
+اللي هو تحليل واحد نذكركوا فيها الـ infimum برضه
+
+252
+00:22:10,090 --> 00:22:14,310
+إشي مشابه بس بعكس اللي موجود زائد g of x طبعا كله
+
+253
+00:22:14,310 --> 00:22:17,570
+.. كله .. هذا إيه الإثبات وكله أسباب واخدناها في
+
+254
+00:22:17,570 --> 00:22:23,010
+تحليل واحد x element in I I أكبر أوي ساوي اللي هو
+
+255
+00:22:23,010 --> 00:22:29,660
+الـ infimum ل اللي هو f of xsuch that x element in
+
+256
+00:22:29,660 --> 00:22:35,700
+I I زائد ال infimum ل g of x such that x element
+
+257
+00:22:35,700 --> 00:22:40,880
+in I I هدولة الآن بدي اللي هي استخدمهم عشان اللي
+
+258
+00:22:40,880 --> 00:22:48,140
+هو أصل اللي بدي إياه الآن لو أجينا حسبنا اللي هو
+
+259
+00:22:48,140 --> 00:22:59,910
+ال U لL of B of F زائد Gعشان نصل لـ L F زي الـ G
+
+260
+00:22:59,910 --> 00:23:03,590
+بسوء الـ U F زي الـ G اعتمادا على ان الـ F و الـ G
+
+261
+00:23:03,590 --> 00:23:07,030
+انتجربل يعني اعتماده على ان القلة الـ F هي الـ U
+
+262
+00:23:07,030 --> 00:23:11,050
+الـ F و القلة الـ G هي الـ U G شوفوا معايا تبقوا
+
+263
+00:23:11,050 --> 00:23:14,470
+معايا هذا حسب التعريف أشهر سبب هو يسوي الـ
+
+264
+00:23:14,470 --> 00:23:18,850
+summation الان ال .. ال .. ال .. ال .. ال .. M
+
+265
+00:23:18,850 --> 00:23:27,350
+small K بس لمين هذه لمين للـ Fزائد G هذي لمين يا
+
+266
+00:23:27,350 --> 00:23:32,770
+جماعة لل F زائد G مضروبة في XI minus XI minus 1 أو
+
+267
+00:23:32,770 --> 00:23:36,470
+XK زي ما هو نسميها زي ما بدكم نسميها سميناها فوق I
+
+268
+00:23:36,470 --> 00:23:44,020
+خلينا نسميها I I minus 1 I من عند 1 لعند Nالـ M I
+
+269
+00:23:44,020 --> 00:23:46,980
+هذه إيه يا شباب؟ الـ F زائد G هي عبارة على جهة
+
+270
+00:23:46,980 --> 00:23:54,040
+عشان منها هننطلق الـ M I F زائد G يعني الـ M I هذه
+
+271
+00:23:54,040 --> 00:23:56,740
+لمين؟ للـ function الجديدة اللي اسمها F زائد G
+
+272
+00:23:56,740 --> 00:24:05,270
+بساوي الـ infimumللـ F زائد G of X such that X
+
+273
+00:24:05,270 --> 00:24:10,310
+element in I, I وهذه من اللي كتبته الآن هنا اللي
+
+274
+00:24:10,310 --> 00:24:14,510
+قدمتله يا جماعة الانفمام اللي هنا أكبر يساوي
+
+275
+00:24:14,510 --> 00:24:18,990
+الانفمام لهذه زائد الانفمام لهذهالـ infimum لهذه
+
+276
+00:24:18,990 --> 00:24:24,350
+اللي هو اللي احنا بنسميها M K Small للـ function F
+
+277
+00:24:24,350 --> 00:24:29,530
+وهذه اللي بنسميها مين الـ M K Small للـ function
+
+278
+00:24:29,530 --> 00:24:34,230
+مين؟ للـ function G ماعليش الرموز لكن واضح انه
+
+279
+00:24:34,230 --> 00:24:38,030
+اللي هو احنا بنحكي عن إيش عساس ان نميز بين الـ M K
+
+280
+00:24:38,030 --> 00:24:43,830
+أو الـ M I سنة مسمينها I الـ M I هنا و الـ M I للـ
+
+281
+00:24:43,830 --> 00:24:49,310
+F و للـ J و للـ F زائد Jللـ F زائد J هيها وهي من
+
+282
+00:24:49,310 --> 00:24:53,850
+اللي فوق هذه أكبر أو يساوي الـ infimum على الأولى
+
+283
+00:24:53,850 --> 00:24:57,830
+للـ F زايد الـ infimum على الـ M على الـ J يعني
+
+284
+00:24:57,830 --> 00:25:02,590
+هذا بمعنى آخر لأن هذا قيمة موجة بقى صار أكبر أو
+
+285
+00:25:02,590 --> 00:25:10,260
+يساوي الـ summation اللي هو لمين للـ MI F زائد M I
+
+286
+00:25:10,260 --> 00:25:15,760
+J هذا أكبر أو يساوي من ال equality اللي فوق في X I
+
+287
+00:25:15,760 --> 00:25:21,660
+ناقص X I minus واحد I من عند واحد لعند N نوزع ال N
+
+288
+00:25:21,660 --> 00:25:30,680
+هذا بالظبط بساوي summation لل M I Fفي xi-xi-1 i من
+
+289
+00:25:30,680 --> 00:25:34,980
+عند 1 لعند n زائد ال summation نفسه على مين الآن
+
+290
+00:25:34,980 --> 00:25:44,080
+mij في xi-xi-1 i من 1 لعند n واضح يا شباب اه
+
+291
+00:25:44,080 --> 00:25:48,980
+المفروض ان الكلام واضحصيرنا عيدين الفكرة عدة مرات
+
+292
+00:25:48,980 --> 00:25:52,940
+وكلنا .. كله بندور حول اللي هو فعلا التعريف لل
+
+293
+00:25:52,940 --> 00:25:55,580
+upper thumb والlower thumb وال upper integral
+
+294
+00:25:55,580 --> 00:25:58,960
+والlower integral بس الواحد يستذكر التعريف هيلاقي
+
+295
+00:25:58,960 --> 00:26:04,020
+الأمور سهلة بإذن الله هذه بتساوي .. هذه مين هي
+
+296
+00:26:04,020 --> 00:26:10,060
+بالظبط يا شباب؟ هي عبارة عن الللـ Partition B اللي
+
+297
+00:26:10,060 --> 00:26:13,820
+بدأنا فيه الـ Arbitrary بالنسبة لمين الآن؟ للـ
+
+298
+00:26:13,820 --> 00:26:20,340
+Function F زائد هذا بين هذا الـ L of B و بالنسبة
+
+299
+00:26:20,340 --> 00:26:28,510
+لمين؟ لـ G صار عند الـ LB و F زائد G أصغر أو يساوي
+
+300
+00:26:28,510 --> 00:26:33,630
+آسف أكبر يساوي ال B و F زائد مين ال B of G خلّينا
+
+301
+00:26:33,630 --> 00:26:37,090
+نخزّن هذه المعلومة يا شباب و خلّيني أكتبها بعد
+
+302
+00:26:37,090 --> 00:26:42,930
+إذنكم هان أخزّن المعلومة لإن بعد بشوية هاجي
+
+303
+00:26:42,930 --> 00:26:49,890
+أستعملها أنا وصلت لل L B F زائد G هيكون أكبر أو
+
+304
+00:26:49,890 --> 00:26:59,790
+يساوي ال LP و F زائد ال L D و G هذه المعلومة
+
+305
+00:26:59,790 --> 00:27:06,750
+حصلناها هحصلك على إيش مشابه جدا لل U هتصير ال U P
+
+306
+00:27:06,750 --> 00:27:11,430
+و F زائد G أصغر أو يساوي تبعا للخاصية هذه اللي
+
+307
+00:27:11,430 --> 00:27:15,550
+اعتمدنا على البرهان فيها هنعتمد عليه الآن برهان في
+
+308
+00:27:15,550 --> 00:27:21,070
+ال U إيش اللي بقوله بقول ما يليه عارفين؟بدي اشتغل
+
+309
+00:27:21,070 --> 00:27:25,750
+على هذه او ارجوكم جدش الامور سهلة شيل هذه و احكي
+
+310
+00:27:25,750 --> 00:27:30,170
+عن مين عن ال U لان مدام حكيت عن ال U اذا بدي يصير
+
+311
+00:27:30,170 --> 00:27:33,630
+بدل ما هي M small مين بحكي بدل ال infinite بدي
+
+312
+00:27:33,630 --> 00:27:37,390
+يصير مين M I اللي هي ال supremum اللي هي ال
+
+313
+00:27:37,390 --> 00:27:40,930
+supremum اذا M I هذه لل F زائد G هي عبارة عن ال
+
+314
+00:27:40,930 --> 00:27:45,110
+supremum لل F of X زائد G of XX element in I لان
+
+315
+00:27:45,110 --> 00:27:50,000
+ال supremum للمجموع اللي هو هذهللـ F زائد G بدل ما
+
+316
+00:27:50,000 --> 00:27:54,220
+هيكون أكبر إيش هيساوي يا شباب أصغر أو يساوي ال
+
+317
+00:27:54,220 --> 00:28:00,140
+supremum هذا اللي هو عبارة عن M I F وهذا مين هو يا
+
+318
+00:28:00,140 --> 00:28:06,900
+شباب ال M I G إذا صار الموضوع واضح هيصير أصغر أو
+
+319
+00:28:06,900 --> 00:28:15,770
+يساوي اللي هو MI F و M I J و نفسه بظله زي ما هو و
+
+320
+00:28:15,770 --> 00:28:22,590
+هنا مسواة حقيقية M I بغير M I وزعت زي ما وزعت قبل
+
+321
+00:28:22,590 --> 00:28:27,090
+هذا عبارة عن مين صار يا شباب مدام ال M I capital
+
+322
+00:28:27,090 --> 00:28:33,490
+إذا صار U B F و هذا صار مين عبارة عن U B J إذا
+
+323
+00:28:33,490 --> 00:28:42,790
+اللي حصلنا الآن ال U B F زائد Gأصغر أو يساوي UBF
+
+324
+00:28:42,790 --> 00:28:48,110
+زاد UBJ وهي كما نكون حصلنا أو بدنا نخزن المعلومة
+
+325
+00:28:48,110 --> 00:29:00,980
+الثانيةUBF زائد G أصغر أو يساوي UBF زائد UBG هذا
+
+326
+00:29:00,980 --> 00:29:05,760
+الآن بيكون احنا حصلنا اللي هي ال ال two
+
+327
+00:29:05,760 --> 00:29:09,120
+inequalities هدولة اللي هم هم هم هم هم هم هم هم هم
+
+328
+00:29:09,120 --> 00:29:10,140
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+329
+00:29:10,140 --> 00:29:10,980
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+330
+00:29:10,980 --> 00:29:10,980
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+331
+00:29:10,980 --> 00:29:10,980
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+332
+00:29:10,980 --> 00:29:11,100
+هم هم هم هم هم هم هم هم هم هم
+
+333
+00:29:19,180 --> 00:29:23,620
+عبارة عن على كل partition بيه لكل partition بيه في
+
+334
+00:29:23,620 --> 00:29:28,960
+الدنيا الآن أنا عشان أصل لل Integrability ياما
+
+335
+00:29:28,960 --> 00:29:35,700
+بأثبت ال U ofأف زائد جي بيساوي الال بيقل أف زائد
+
+336
+00:29:35,700 --> 00:29:41,640
+جي وهذه يمكن شوية سنة بتغلب أو أن أستخدم اللي هو
+
+337
+00:29:41,640 --> 00:29:49,020
+انتجراميتي كريتيريا ان اوصل انه لكل أبسلون أكبر من
+
+338
+00:29:49,020 --> 00:29:53,510
+سفر there exist a partitionبإبسلون بحيث أن U
+
+339
+00:29:53,510 --> 00:29:57,670
+بيبسلون و F زائد G ناطس ال بيبسلون و F زائد G يكون
+
+340
+00:29:57,670 --> 00:30:01,610
+أصغر من إبسلون إذا حصلت هيك بكون على طول أثبتت أن
+
+341
+00:30:01,610 --> 00:30:07,010
+ال F زائد G is integrable واضح؟ طيب، وحروح بهذا
+
+342
+00:30:07,010 --> 00:30:14,350
+الاتجاه طيب، شوفوا معايا الآن إحنا فرضين أن F is
+
+343
+00:30:14,350 --> 00:30:19,150
+integrable إذن، مدام F is integrable إذن، by
+
+344
+00:30:19,760 --> 00:30:25,000
+Integrability criterion there exist لكل إبسلون
+
+345
+00:30:25,000 --> 00:30:31,120
+طبعا أخدت الآن إبسلون أكبر من سفر given أنا إبسلون
+
+346
+00:30:31,120 --> 00:30:34,680
+ماشي مدام F is integrable فانحارس بال
+
+347
+00:30:34,680 --> 00:30:39,860
+Integrability criterion there exist B F و إبسلون
+
+348
+00:30:39,860 --> 00:30:47,500
+partition B F و إبسلون such that U B F و إبسلون
+
+349
+00:30:48,590 --> 00:30:54,970
+والـ Function F ناقص .. ناقص ال .. معايا شباب
+
+350
+00:30:54,970 --> 00:31:00,890
+تذكرتوا هالنظرية؟ F و Epsilon و F أصغر من مين؟
+
+351
+00:31:00,890 --> 00:31:03,550
+أصغر من Epsilon على 2 للحسابات الـ Epsilon على 2
+
+352
+00:31:03,550 --> 00:31:08,270
+ماشي .. الآن خليني بس عشان أسهل عملية الحسابات
+
+353
+00:31:08,270 --> 00:31:12,070
+إليه بتدنقل هذه هنا بعد إذنكم و أقول هذا الكلام
+
+354
+00:31:12,070 --> 00:31:17,130
+أصغر من اللي هو هذا زائد هذاواضح ايش اللي بعمله؟
+
+355
+00:31:17,130 --> 00:31:20,590
+اللي صار عندي الان بما انه F is integrable إذا
+
+356
+00:31:20,590 --> 00:31:24,230
+بلاقي partition F إبسلون بحيث أنه هذا أصغر من هذا
+
+357
+00:31:24,230 --> 00:31:33,030
+زائد هذا واضح Similarly for G G is integrable
+
+358
+00:31:33,030 --> 00:31:41,770
+Similarly for G G is integrable بيعطيني
+
+359
+00:31:42,670 --> 00:31:47,530
+for every ε أكبر من 0 there exists بي ابسلون خاص
+
+360
+00:31:47,530 --> 00:31:51,610
+بال G خلّيني أسميه بعد ذلك بي جي ابسلون such that
+
+361
+00:31:51,610 --> 00:31:54,290
+طبعا partition of نفس ال interval اللي بنشتر عليها
+
+362
+00:31:54,290 --> 00:31:56,350
+لإن ال F و ال G دير بالكم معرفة على نفس ال
+
+363
+00:31:56,350 --> 00:32:05,530
+interval such that اللي هو ال U بي G و ابسلون و G
+
+364
+00:32:05,530 --> 00:32:12,270
+الآن ال function اللي بحكي عنها أصغر من Lبجي
+
+365
+00:32:12,270 --> 00:32:17,250
+وإبسلون أو الـ function ash جي زائد برضه مين
+
+366
+00:32:17,250 --> 00:32:21,690
+إبسلون على اتنين واضح يا جماعة؟ إذا من الـ
+
+367
+00:32:21,690 --> 00:32:25,430
+integrability للـ F لجي تلها partition و من ال
+
+368
+00:32:25,430 --> 00:32:29,190
+integrability للـ G لجي تلها partition الآن زي ما
+
+369
+00:32:29,190 --> 00:32:33,030
+عملنا المرة الفاتة بدي أخد partition عشان أستخدم
+
+370
+00:32:33,030 --> 00:32:38,370
+هذه و أستخدم هذه فبقول letبأبسلون وهذا بقول اللي
+
+371
+00:32:38,370 --> 00:32:42,570
+بتدعي ان اللي حلقيه اللي يثبت الـ Integrability أو
+
+372
+00:32:42,570 --> 00:32:45,970
+اللي هي criterion Integrability خدوا مين هو أكيد
+
+373
+00:32:45,970 --> 00:32:53,150
+كلكم حتقوله خد F و E اتحاد B G و E عساس ان يصير
+
+374
+00:32:53,150 --> 00:32:57,710
+بيبسلون refinement لهذهللأولى و refinement للثانية
+
+375
+00:32:57,710 --> 00:33:03,150
+و تظبط معانا ان ال refinement تحسين بيصير ال lower
+
+376
+00:33:03,150 --> 00:33:09,830
+للتحسين يكبر عشان يروح للاش .. لنساحة تحت المنحنى
+
+377
+00:33:09,830 --> 00:33:15,430
+بالظبط في حالة الموجة بقى و التحسين اللي يصير ال U
+
+378
+00:33:15,430 --> 00:33:20,390
+يصغر فبلتجن مع بعض فبعملنا بعملنا ال ال
+
+379
+00:33:20,390 --> 00:33:23,990
+integrability ماشي الحال سيانا عادينا كتير هذا
+
+380
+00:33:23,990 --> 00:33:27,920
+الكلامطيب صلى على النبي عليه الصلاة والسلام صلى
+
+381
+00:33:27,920 --> 00:33:32,720
+عليه الصلاة والسلام الآن عندي صار هذا عندي موجود
+
+382
+00:33:32,720 --> 00:33:38,280
+وهذا عندي ايش موجود انا غرض مين غرض هيه لهذه اه
+
+383
+00:33:38,280 --> 00:33:44,520
+عندي U الان بدأ ابدا احضر ان اصل U بإبسلول وافذائت
+
+384
+00:33:44,520 --> 00:33:50,860
+Gاللي هو ناقص الـ P Y و F زائد G أصغر من إبسلون
+
+385
+00:33:50,860 --> 00:33:54,440
+بيكون خلصت بيصير عندي ال F زائد G is integrable
+
+386
+00:33:54,440 --> 00:34:02,640
+إذا خلّينا نقول U بي إبسلون و F زائد G ماشي شباب
+
+387
+00:34:02,640 --> 00:34:10,050
+طيب هذه الآن أكيدأصغر أو يساوي من اللي أثبت هذا
+
+388
+00:34:10,050 --> 00:34:12,650
+أثبتنا لمين يا جماعة في الأول اللي حضرناه وقلنا
+
+389
+00:34:12,650 --> 00:34:16,690
+اتعبنا عليه هذا قلنا صحيح لكل partition في الدنيا
+
+390
+00:34:16,690 --> 00:34:21,570
+من ضمنه مين الـ BY اللي جاته إذن هذا بيصير أصغر أو
+
+391
+00:34:21,570 --> 00:34:30,620
+يساوي U BY و F زائد U BY و Gماشي يا أبو حسن؟ منيح
+
+392
+00:34:30,620 --> 00:34:34,600
+هيك بيكون أصغر أو يساوي هذه زي أن أصغر أو يساوي
+
+393
+00:34:34,600 --> 00:34:41,060
+اللي هي الثانية طيب الآن ال .. ال U P Y الان ال P
+
+394
+00:34:41,060 --> 00:34:47,060
+Y refinement لمين؟ لل P F Y و refinement لمين برضه
+
+395
+00:34:47,060 --> 00:34:52,740
+يا جماعة؟ ل P G Y مدام refinement إذن اللي هو
+
+396
+00:34:54,270 --> 00:34:59,450
+التحسين .. التحسين للـ U بصغر إذا هيصير عندي هذا
+
+397
+00:34:59,450 --> 00:35:05,270
+التحسين أكيد أصغر أو يساوي من الـ U بـ F وإبسلون
+
+398
+00:35:05,270 --> 00:35:11,310
+اللي هو هذا تحسين لهذا و F زائد برضه التحسين هذا
+
+399
+00:35:11,310 --> 00:35:17,250
+هيكون أصغر من اللي اتحسنله اللي هو الـ U بـ G
+
+400
+00:35:17,250 --> 00:35:26,010
+وإبسلون أو G ماشي الحال طيبنفس الأشياء عند احنا
+
+401
+00:35:26,010 --> 00:35:36,130
+بنعرف ان هذا المقدار U بإبسلون و F F و إبسلون
+
+402
+00:35:36,130 --> 00:35:39,830
+طلعوا على هنا هيو أصغر يساوي هذه زائد إبسلون ع
+
+403
+00:35:39,830 --> 00:35:43,730
+اتنين وهذه هيها اصلا بالعمد ان احنا عملنا الأسرع
+
+404
+00:35:43,730 --> 00:35:52,370
+عشان نعوض بيصير من هذه و من هذه بيصير أصغر من الof
+
+405
+00:35:52,370 --> 00:35:59,850
+B F و Epsilon مع ال F زائد Epsilon ع 2 زائد بدل
+
+406
+00:35:59,850 --> 00:36:08,170
+هذه اللي هي هيها منها نقل L B G و Epsilon و G زائد
+
+407
+00:36:08,170 --> 00:36:12,510
+Epsilon ع 2 ان شاء الله ما خرب 12 لأ ما خرب 12الان
+
+408
+00:36:12,510 --> 00:36:19,590
+صار عندى هذى y على اتنين و y على اتنين و اتنين
+
+409
+00:36:19,590 --> 00:36:20,810
+و اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+410
+00:36:20,810 --> 00:36:21,390
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+411
+00:36:21,390 --> 00:36:24,390
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+412
+00:36:24,390 --> 00:36:24,410
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+413
+00:36:24,410 --> 00:36:25,230
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+414
+00:36:25,230 --> 00:36:33,730
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين
+
+415
+00:36:33,730 --> 00:36:44,290
+و اتنين و اتنين و اتنين و امن أو يساوي الـ
+
+416
+00:36:44,290 --> 00:36:55,010
+refinement للـ L of B ε و F زائد اللي هو L أو B ε
+
+417
+00:36:55,010 --> 00:36:59,910
+OG سبحان الله كل الأمور متناسقة عشان في الآخر برضه
+
+418
+00:36:59,910 --> 00:37:06,150
+هذه الخاصية نستخدم اللي فوق و هذا تناسق في الخلق
+
+419
+00:37:06,150 --> 00:37:10,690
+ما بين ما ينتجه العقل و ما تنتجه الطبيعةاللي هو
+
+420
+00:37:10,690 --> 00:37:16,190
+هذا الان المقدار ال بيبسولون ال بيبسولون هي هذا
+
+421
+00:37:16,190 --> 00:37:21,890
+المقدار تطلع عليه من هنا أصغر أو يساوي ال بي أف
+
+422
+00:37:21,890 --> 00:37:26,990
+زائد إيش جي فبصير هذا أصغر أو يساوي عوضت من هنا يا
+
+423
+00:37:26,990 --> 00:37:35,150
+شباب الof B و F زائد G يعني إبسلون طبعاً لأن هذا
+
+424
+00:37:35,150 --> 00:37:38,550
+الكلام صحيح لكل partition زي ما قلنا من ضمن إن الـ
+
+425
+00:37:38,550 --> 00:37:45,880
+B إبسلون زائد إيش إبسلونصار عندى الان اللى بديها
+
+426
+00:37:45,880 --> 00:37:50,540
+الـ U بيبسلون F زائد G أصغر أو سوى L بيبسلون F
+
+427
+00:37:50,540 --> 00:37:54,260
+زائد G زايد Y يعني عشان اللى وصلت له أخدت Y
+
+428
+00:37:54,260 --> 00:37:59,320
+arbitrary لجهة partition بيبسلون بحيث ان الـ U
+
+429
+00:37:59,320 --> 00:38:06,210
+بيبسلون F زائد Gناقص القلبي Y F زائد G أصغر من Y
+
+430
+00:38:06,210 --> 00:38:10,950
+وهذا يعني انه احنا حققنا الـ Integrable criterion
+
+431
+00:38:10,950 --> 00:38:18,070
+بمعنى انه صارت الـ F زائد G is integrable إذن الآن
+
+432
+00:38:18,070 --> 00:38:26,510
+أثبتنا ان الـ F زائد G is integrable نيجي الآن
+
+433
+00:38:26,510 --> 00:38:31,450
+نحاول تخلينا بس هدولة اللي هستخدمن بعد شويةهنخلّيه
+
+434
+00:38:31,450 --> 00:38:35,610
+الموجودات و ده يعني مسحناها نضطرنا مسحناها نرجع
+
+435
+00:38:35,610 --> 00:38:39,770
+للتلخيص ركزوا معايا إيش اللي بقوله إيش اللي بحكيه
+
+436
+00:38:39,770 --> 00:38:41,150
+عندي
+
+437
+00:38:47,360 --> 00:38:49,720
+الان بدي اثبت ان ال integration لل F زي ال G يا
+
+438
+00:38:49,720 --> 00:38:52,460
+شباب سواء ال integration لل F زي ال integration لل
+
+439
+00:38:52,460 --> 00:38:54,280
+G يعني الخطوة الأولى احنا اثبتنا ان F زي ال G
+
+440
+00:38:54,280 --> 00:38:56,820
+integrable الان بدي اثبت ان ال integration لل F زي
+
+441
+00:38:56,820 --> 00:39:00,280
+ال G سواء ال integration لل F زي ال integration لل
+
+442
+00:39:00,280 --> 00:39:06,320
+G شوفوا عليها نيجي الآن ال integration من A ل B لل
+
+443
+00:39:06,320 --> 00:39:11,600
+F زي ال G ماهي الحالة ال integration لل F زي ال G
+
+444
+00:39:12,860 --> 00:39:16,920
+بتساوي الـ U of F زائد G صح ولا لأ؟ أه لأن الـ
+
+445
+00:39:16,920 --> 00:39:20,760
+Sort of زائد G is integrable إذا بتساوي الـ U of F
+
+446
+00:39:20,760 --> 00:39:25,060
+زائد G الـ U of F زائد G هي عبارة عن إيش يا جماعة؟
+
+447
+00:39:25,060 --> 00:39:30,620
+هي عبارة عن الـ infimum لكل الـ U of زائد G مع
+
+448
+00:39:30,620 --> 00:39:35,570
+الpartition Bإذن أي واحدة من اللي بموجود عليهم الـ
+
+449
+00:39:35,570 --> 00:39:40,490
+infimum هتكون هذا أصغر منها، هيصير عندي هذه أصغر
+
+450
+00:39:40,490 --> 00:39:47,990
+أو يساوي الـ U بيبسلون الـ F زائد D، أه أكيد،
+
+451
+00:39:47,990 --> 00:39:52,790
+عارفين ليش؟ لأن هذه الـ infimum لكل الـ U زلة زي
+
+452
+00:39:52,790 --> 00:39:57,850
+هيكحيث الـ PY عبارة عن الـ partition وين موجودة في
+
+453
+00:39:57,850 --> 00:40:02,410
+P of I هذه الـ U عبارة عن الـ infimum إلهم إذا
+
+454
+00:40:02,410 --> 00:40:05,890
+الواحد منهم أكبر أو يساوي اللي هو هذا الـ infimum
+
+455
+00:40:05,890 --> 00:40:10,790
+اللي هو الرابع .. ال grades اللي هو الرابع طيب هذا
+
+456
+00:40:10,790 --> 00:40:17,650
+U PY F زائد G U PY F زائد G لجناه أصغر أو يساوي
+
+457
+00:40:18,450 --> 00:40:23,430
+اللي هو ال بي أبسلون و F و بي أبسلون جي زائد
+
+458
+00:40:23,430 --> 00:40:26,010
+إبسلون شايفين هو من هنا يا شباب هاي اللي بدأ
+
+459
+00:40:26,010 --> 00:40:30,390
+استخدمه الآن هاي اللي بدأ تلزمني هنا هاي هذه هاي
+
+460
+00:40:30,390 --> 00:40:37,570
+هذه أثبتناها أصغر أو يساوي هذه خليني الآن أستخدمها
+
+461
+00:40:37,570 --> 00:40:41,570
+فوق فده ننجلها فوق هذه أصغر أو يساوي اللي بالأزرق
+
+462
+00:40:41,570 --> 00:40:46,510
+هذه أصغر أو يساوي الجيت بتعرفي أشي بتسوي ال بي
+
+463
+00:40:46,510 --> 00:40:47,650
+أبسلون و F
+
+464
+00:40:55,470 --> 00:41:02,070
+معايا شباب طيب ما هو ال F is integrable إذا ال
+
+465
+00:41:02,070 --> 00:41:10,870
+integration لل F بسوء L و F أكيد بسوء U و Fلأن هذه
+
+466
+00:41:10,870 --> 00:41:15,650
+الـ L of F هي عبارة عن الـ Supremum لهذه كلها إذاً
+
+467
+00:41:15,650 --> 00:41:23,090
+أكيد هذا أصغر أوي يساوي الـ L of F زائد و L of G
+
+468
+00:41:23,090 --> 00:41:26,350
+برضه أكبر أوي يساوي هذه لأن هذه عبارة عن الـ
+
+469
+00:41:26,350 --> 00:41:29,610
+Supremum لكل الأشكال اللي زي هذه و L of F هي عبارة
+
+470
+00:41:29,610 --> 00:41:34,230
+عن الـ Supremum لكل الـ B's و F لكل اللي هو ال
+
+471
+00:41:34,230 --> 00:41:36,190
+partitions اللي في set of all partitions
+
+472
+00:41:36,190 --> 00:41:42,590
+partitions B of Iزائد مين زائد أبسلون ولأن F is
+
+473
+00:41:42,590 --> 00:41:45,490
+integrable إذا هذا بيساوي بالظبط ال integration من
+
+474
+00:41:45,490 --> 00:41:49,330
+A ل B لل F زائد ال integration لأن G is integrable
+
+475
+00:41:49,330 --> 00:41:55,810
+ماعطينايها أصلاً G من A ل B زائد H زائد أبسلون صار
+
+476
+00:41:55,810 --> 00:42:00,250
+عندي الآن ال integration اللي حصلته يا شباب اللي
+
+477
+00:42:00,250 --> 00:42:06,510
+حصلته مالي اللي حصلته أنه صار عندي ال integration
+
+478
+00:42:06,510 --> 00:42:14,970
+لل F زائد Gمن a ل b ا اشماله اصغر او يساوي ال
+
+479
+00:42:14,970 --> 00:42:18,250
+integration لل F من a ل عند b زاد ال integration
+
+480
+00:42:18,250 --> 00:42:23,710
+لل g من a ل b زاد ابسلون هذا لكل ابسلون في الدنيا
+
+481
+00:42:23,710 --> 00:42:28,920
+لكل ابسلون في الدنيا هذا صحيحإذا المدام صحيح لكل
+
+482
+00:42:28,920 --> 00:42:33,380
+إبسلون إذا أكيد هيطلع لل integration لل F زائد G
+
+483
+00:42:33,380 --> 00:42:37,200
+من A ل B أصغر أو ساوي ال integration لل F زايد ال
+
+484
+00:42:37,200 --> 00:42:41,580
+integration لل G من A ل B من A ل B لأن اللي فوق
+
+485
+00:42:41,580 --> 00:42:46,880
+صحيح لمين لأي إبسلون في الدنيا اللي بتستشكل عليه
+
+486
+00:42:46,880 --> 00:42:51,060
+الاب أنه يفهمها عن طريق انه since إبسلون was
+
+487
+00:42:51,060 --> 00:42:55,540
+arbitrary then هذا أصغر أو ساوي هذايأخذ الحالة
+
+488
+00:42:55,540 --> 00:42:59,540
+الخاصة للإبسلونات لأن لكل إبسلون هذا صحيح من ضمنها
+
+489
+00:42:59,540 --> 00:43:04,280
+الإبسلونات اللي بيساوي 1 على N لكل N بيظل هذا ال
+
+490
+00:43:04,280 --> 00:43:07,940
+integration لل F زائد G أصغر اذا كان ال
+
+491
+00:43:07,940 --> 00:43:11,380
+integration لل F زاد ال integration لل G زائد 1
+
+492
+00:43:11,380 --> 00:43:14,720
+على N لكل N في الدنيا لأن هذا صحيح على كل إبسلون
+
+493
+00:43:14,720 --> 00:43:19,600
+من ضمنها ال 1 على أنمات ال N every Nيعني الآن مدام
+
+494
+00:43:19,600 --> 00:43:23,640
+هذه صحيحة بناء على هذه صحيحة خد ال limit للجهتين
+
+495
+00:43:23,640 --> 00:43:28,240
+as n goes to infinity ال limit للجهتين as n goes
+
+496
+00:43:28,240 --> 00:43:31,280
+to infinity هذا independent of n وهذا independent
+
+497
+00:43:31,280 --> 00:43:34,920
+of n وهذا as n goes to infinity بتروح للصفر بيصير
+
+498
+00:43:34,920 --> 00:43:39,220
+عنده اللي هو ال integration لل F زائد G هيكون أصغر
+
+499
+00:43:39,220 --> 00:43:42,420
+السهولة integration لل F زائد integration لمن؟ لل
+
+500
+00:43:42,420 --> 00:43:46,740
+G هذا فهم آخر اللي بشوية بتغلب من قصة since Y هو
+
+501
+00:43:46,740 --> 00:43:52,090
+الواضع الاربتردن كذا كدهطيب اذا صار عندى الآن
+
+502
+00:43:52,090 --> 00:43:57,250
+اثباتة ال integration ل F زي ال G اظهر سواء ال
+
+503
+00:43:57,250 --> 00:44:03,230
+integration ل F زي ال integration ل Gاللي هان بده
+
+504
+00:44:03,230 --> 00:44:05,970
+أثبت المساواة بده أثبت العكس بده أخد الـ
+
+505
+00:44:05,970 --> 00:44:09,390
+integration للـ F زي الـ integration للـ G و أصل
+
+506
+00:44:09,390 --> 00:44:14,350
+للي بديه شوف كيف اتفجنا الآن ايش أثبتنا يا شباب
+
+507
+00:44:14,350 --> 00:44:19,210
+خليني أسجلها هان أخزنها ال integration للـ F زي
+
+508
+00:44:19,210 --> 00:44:24,490
+الـ G من A ل B أصغر أصول ال integration للـ F من A
+
+509
+00:44:24,490 --> 00:44:29,570
+ل B زي ال integration للـ G من A ل Bوهذا أثبتناه
+
+510
+00:44:29,570 --> 00:44:32,970
+بالدفت بت اللي هو conversely برضه اعتمادا على
+
+511
+00:44:32,970 --> 00:44:44,310
+الحديث الأولاني خليني
+
+512
+00:44:44,310 --> 00:44:48,850
+اكتب بالأسود هنا عشان اتميز بين الجهتين عند الان
+
+513
+00:44:48,850 --> 00:44:53,330
+ال integration لل F من A ل B زاد ال integration لل
+
+514
+00:44:53,330 --> 00:45:02,420
+G من A ل Bماشي الحال هذا اللي هو أصغر أو يساوي
+
+515
+00:45:02,420 --> 00:45:07,360
+اللي هو نفس المنطق الأولاني هذا اللي هو عبارة عن
+
+516
+00:45:07,360 --> 00:45:13,760
+اللي بالظبط بيساوي ال U of F زائد ال U of G و ال U
+
+517
+00:45:13,760 --> 00:45:17,380
+of F هذه عبارة عن ال infimum على كل ال U's اللي هي
+
+518
+00:45:17,380 --> 00:45:20,000
+ال lower ال upper sums اللي هي أصغر أو يساوي ال U
+
+519
+00:45:20,000 --> 00:45:27,620
+لل بي إبسلون و F زائد ال U لل بي إبسلونوجي مظبوط
+
+520
+00:45:27,620 --> 00:45:31,540
+ولا لأ اكيد مظبوط لان هذا عبارة عن الام في مملكة
+
+521
+00:45:31,540 --> 00:45:35,060
+كل هذول وهذه عبارة عن ال supreme مملكة لكل هذول
+
+522
+00:45:35,060 --> 00:45:46,120
+ماشي الان عندي هذا نفسه ال U بي إبسلن و أف و ال U
+
+523
+00:45:46,120 --> 00:45:51,880
+بي أل إبسلن و أفأثبتناها نتطلع عليها نستخدم حاجة
+
+524
+00:45:51,880 --> 00:45:56,220
+هنا يو بي إبسل و أف و يو بي إبسل و أف أصغر يساوي
+
+525
+00:45:56,220 --> 00:46:05,420
+مين هايها ال بي إبسلون و أف زائد جي صحيح؟ مواضح
+
+526
+00:46:05,420 --> 00:46:11,180
+عشان بابا يعني بدت استخدم الآن هاي هذي يو بي
+
+527
+00:46:11,180 --> 00:46:16,550
+إبسلونشايفينها؟ هي اللي بحكي بشويش عشان تتركزوا
+
+528
+00:46:16,550 --> 00:46:19,890
+معايا اللي بالأزرق هذا اللي بالأصمر آسف معها دي
+
+529
+00:46:19,890 --> 00:46:23,970
+هذا كله أثبتناه إذا مين ده استخدمه؟ إذا هذا أصمر
+
+530
+00:46:23,970 --> 00:46:31,650
+او يساوي اللي هي L بي أبسلون و F زائد G زائد 100
+
+531
+00:46:31,650 --> 00:46:38,270
+زائد أبسلون معايا يا شباب أكيد اللي هو وضحت إيش
+
+532
+00:46:38,270 --> 00:46:44,690
+بدي أسوي هذا نفسهاللي هو أصغر أو ساوي L of F زي
+
+533
+00:46:44,690 --> 00:46:48,430
+الـ G زي الـ Epsilon لأن L of F مين زي الـ G
+
+534
+00:46:48,430 --> 00:46:51,070
+يقولونها كتير إيش هي دي؟ عبارة عن الـ Supremum لكل
+
+535
+00:46:51,070 --> 00:46:56,860
+دولةأه على كل ال partitions إذا أكيد ال L of F هو
+
+536
+00:46:56,860 --> 00:47:00,580
+أكبر أو يساوي هذا المقدر ال L of F زائد G عبارة عن
+
+537
+00:47:00,580 --> 00:47:05,680
+ال sobremom لكل اللي هي lower sums اللي انصار عندي
+
+538
+00:47:05,680 --> 00:47:09,940
+و هذا لأن F زائد G أثبتناها inintegrable بساوة ال
+
+539
+00:47:09,940 --> 00:47:15,860
+integration من A ل B لل F زائد G لكل أشماله زائد Y
+
+540
+00:47:16,670 --> 00:47:20,990
+إذا حصلنا الـ F زائد الـ integration للـ A للـ F
+
+541
+00:47:20,990 --> 00:47:23,470
+من A إلى B زائد الـ integration للـ G من A إلى B
+
+542
+00:47:23,470 --> 00:47:26,930
+أصغر أو يساوي ال integration من A إلى B للـ F زائد
+
+543
+00:47:26,930 --> 00:47:32,510
+G زائد مين زائد إبسنون مظبوط يا شباب الآن نفس
+
+544
+00:47:32,510 --> 00:47:38,580
+القصة الأولىبما أن إبسلون كان مخصصًا وبنفس المنطق
+
+545
+00:47:38,580 --> 00:47:43,320
+اللي حكيته قبل بشوية إذا ال integration لل F من A
+
+546
+00:47:43,320 --> 00:47:47,800
+لعند B زائد ال integration لل G من A لعند B هيكون
+
+547
+00:47:47,800 --> 00:47:53,720
+أصغر أو يساوي ال integration لل F زائد G هذه الآن
+
+548
+00:47:53,720 --> 00:47:58,520
+اللي بالأصمر مع هذه اللي بالأحمربيعطينا ان ال
+
+549
+00:47:58,520 --> 00:48:06,520
+integration للـ F زائد G من A لعند B يساوي بالظبط
+
+550
+00:48:06,520 --> 00:48:10,340
+integration من A لB للF زائد integration من A لB
+
+551
+00:48:10,340 --> 00:48:13,360
+للG وهو المطلوب
+
+552
+00:48:15,210 --> 00:48:20,010
+و بكون احنا هي كأثبتنا الجزء الثاني من النظرية
+
+553
+00:48:20,010 --> 00:48:23,770
+اللي هي الأولى اللي هو ال integration لل F زي ال G
+
+554
+00:48:23,770 --> 00:48:28,990
+بسبب ال integration لل F زائد ال integration لمين؟
+
+555
+00:48:28,990 --> 00:48:34,370
+لل G فيكم تصلوا علنا بيه؟ عليه الصلاة والسلام وصلى
+
+556
+00:48:34,370 --> 00:48:38,310
+الله عليه وسلم يا حمد طيب يا شباب شوفوا النظرية
+
+557
+00:48:38,310 --> 00:48:44,610
+اللي عندى كما يالي نظريتنا بقول لو كانت Fمن الـ
+
+558
+00:48:44,610 --> 00:48:48,270
+closed bounded interval A وB لعند الـ R بـ
+
+559
+00:48:48,270 --> 00:48:52,310
+Integrable function On I اللي هي دالة قابلة
+
+560
+00:48:52,310 --> 00:48:57,210
+للتكامل بالنسبة للرمان وكانت الدالة F of X أكبر أو
+
+561
+00:48:57,210 --> 00:49:01,530
+يساوي سفر يعني المنحنى وين فوق اللي هو محور
+
+562
+00:49:01,530 --> 00:49:06,090
+السينات إذا حيكون ال integration للـ F نفسه برضه
+
+563
+00:49:06,090 --> 00:49:12,370
+أشماله أكبر أو يساوي سفر يعني الآن بقولي F of X
+
+564
+00:49:13,950 --> 00:49:17,850
+أكبر أو يساوي سفر on I اللي بيعطيني ال integration
+
+565
+00:49:17,850 --> 00:49:23,490
+على ال I من A ل B لل F أكبر أو يساوي أيش برضه سفر
+
+566
+00:49:23,490 --> 00:49:29,250
+و proof سهل الأمر و ماعطيك F integrable كمان
+
+567
+00:49:29,250 --> 00:49:34,990
+ماعطيك F أشمالة is integrable معايا مدام ال F is
+
+568
+00:49:34,990 --> 00:49:40,690
+integrable إذا أكيد ال integrationللأف من عند A ل
+
+569
+00:49:40,690 --> 00:49:45,750
+B بساوي L of F مثلا أو بساوي U of F زي ما بدك
+
+570
+00:49:45,750 --> 00:49:53,410
+بساوي L of F ال L of F أكيد أكبر أوي لإنه ال L of
+
+571
+00:49:53,410 --> 00:49:57,270
+F عبارة عن إيش يا شباب عبارة عن طبعا ال L of F هنا
+
+572
+00:49:57,270 --> 00:50:02,670
+بتظبط معنا ال L of F عبارة عن إيش عبارة عن ال
+
+573
+00:50:02,670 --> 00:50:09,210
+Supermanلمين؟ لكل ال partitions اذا اكيد هي اكبر
+
+574
+00:50:09,210 --> 00:50:18,650
+او يساوي ال of بي او بي او اف ايش ال بي او بي اف؟
+
+575
+00:50:18,650 --> 00:50:23,790
+some partition انا بديهاPartition مين؟ للفترة A وB
+
+576
+00:50:23,790 --> 00:50:28,590
+اللي هي الفترة مين؟ I اللي هي A وB هذا فترة نهار
+
+577
+00:50:28,590 --> 00:50:33,090
+الآن أنا بقول ال L of F اللي هو ال supremum على كل
+
+578
+00:50:33,090 --> 00:50:37,650
+ال partitions دولة لل L على كل ال partitions دولة
+
+579
+00:50:37,650 --> 00:50:41,350
+أكيد هيكون أكبر أو يساوي طيب هذا ايش معنى هذا
+
+580
+00:50:41,350 --> 00:50:44,590
+اخترته هل جيت بتشوفوا ايش معنى اخترته؟ ايش ال
+
+581
+00:50:44,590 --> 00:50:48,290
+partition هذا B A وB؟ هذا ال partition هو B A وB
+
+582
+00:50:48,290 --> 00:50:52,310
+هو بس ال partition اللي في نقطتينأول نقطة و أخر
+
+583
+00:50:52,310 --> 00:50:55,670
+نقطة يعني ما .. ماجزقتش ال interval إلا لحالها هي
+
+584
+00:50:55,670 --> 00:50:58,510
+.. هي التجزئة هي ال interval a و b بصحيح اللي هو
+
+585
+00:50:58,510 --> 00:51:02,930
+طبعا I partition لل a و ال b طيب إيش تعريفه هذا ..
+
+586
+00:51:02,930 --> 00:51:07,550
+هذا .. هذا .. إيش تعريفه هذا بساوي اللي هو ال
+
+587
+00:51:07,550 --> 00:51:11,910
+summation مش هنحتاج ال summation لأنه بس إيش مالها
+
+588
+00:51:11,910 --> 00:51:15,750
+مافيش تغير صفر ال interval واحدة إذا بساوي اللي هو
+
+589
+00:51:15,750 --> 00:51:25,230
+ال M summation لل M Kأه في ايش في xk-xk-1 لكن اصلا
+
+590
+00:51:25,230 --> 00:51:28,690
+انا ناخد بس اللي هو فيش غير sub interval واحدة
+
+591
+00:51:28,690 --> 00:51:33,530
+اللي هي ال a و ال b يعني هذه بمعنى اخر b minus
+
+592
+00:51:33,530 --> 00:51:37,910
+mean minus a و ال mk هنا واحدة بس مين هي ال
+
+593
+00:51:37,910 --> 00:51:43,790
+maximum اللي هي خلينا نسميها m a و bهذه MAP ماذا
+
+594
+00:51:43,790 --> 00:51:49,290
+بتساوي حسب التعريف الـ infimum لل F of X حيث الـ X
+
+595
+00:51:49,290 --> 00:51:54,220
+موجودة في ال sub interval هذه اللي هي I نفسهالأن
+
+596
+00:51:54,220 --> 00:51:57,680
+هيك باخد ال .. ال .. ال .. ال partition صار عندي
+
+597
+00:51:57,680 --> 00:52:01,900
+الآن هذا أكبر يساوي ام او بي في مين؟ فانا هذه
+
+598
+00:52:01,900 --> 00:52:05,460
+infimum من ال F of X واحنا فرضين إن ال F of X أكبر
+
+599
+00:52:05,460 --> 00:52:09,040
+يساوي سفر يعني ال infimum غصب بين عنا هيطلع F أكبر
+
+600
+00:52:09,040 --> 00:52:13,060
+يساوي سفر إذا هذه أكبر أو يساوي سفر وهذه أكبر أو
+
+601
+00:52:13,060 --> 00:52:16,760
+يساوي سفر إذا مع بعض التنتين إيه شماله؟ أكبر أو
+
+602
+00:52:16,760 --> 00:52:20,460
+يساوي سفر إذا ال integration من A ل B لل F أكبر أو
+
+603
+00:52:20,460 --> 00:52:21,720
+يساوي سفر
+
+604
+00:52:24,180 --> 00:52:31,620
+هذه هي النظرية 722 نجي الآن لل remark اللي بعدها و
+
+605
+00:52:31,620 --> 00:52:36,860
+ال remark اللي بعدها يعني على اللي هي النظرية
+
+606
+00:52:36,860 --> 00:52:42,800
+الفهم النظرية هذه على طول بنستوعبها ان شاء الله و
+
+607
+00:52:42,800 --> 00:52:43,360
+بنفهمها
+
+608
+00:52:48,870 --> 00:52:52,690
+ما هي النظرية اللي تريد أن تقولها؟ إذا كانت f من I
+
+609
+00:52:52,690 --> 00:52:56,850
+a و b لعند R is integrable لكل x element in I
+
+610
+00:52:56,850 --> 00:53:00,590
+لجينا أن f of x بين مين؟ بين قيمتين بين M و بين
+
+611
+00:53:00,590 --> 00:53:04,330
+مين؟ بين M capital دائما الـ f of x يعني كأنه
+
+612
+00:53:04,330 --> 00:53:10,190
+دلتنا دلتنا هي ها هي عنا ال function أي إن كانت
+
+613
+00:53:10,190 --> 00:53:16,380
+وهي الفترة a و b عندنا من هنا a و bو B و هاي اللي
+
+614
+00:53:16,380 --> 00:53:20,720
+هو M small و هاي M capital يعني الدالة بين ..
+
+615
+00:53:20,720 --> 00:53:25,340
+دايما واجع بين هدول النغطين اللي هو بين M small و
+
+616
+00:53:25,340 --> 00:53:30,260
+بين M capital إذا ال integration تبعها من A ل B لل
+
+617
+00:53:30,260 --> 00:53:35,260
+F أكبر يساوي M في B minus A و أصغر من M في B minus
+
+618
+00:53:35,260 --> 00:53:42,380
+A capital واضح؟ طيب شوف
+
+619
+00:53:42,380 --> 00:53:50,950
+الآنأول حاجة مدام F is integrable إذا بدك تلاحظ أن
+
+620
+00:53:50,950 --> 00:53:56,830
+ال L of F بساوي ال U of F بساوي قيمة ال
+
+621
+00:53:56,830 --> 00:54:02,430
+integration من A ل B لل F of X DX، مظبوط؟ هذا من
+
+622
+00:54:02,430 --> 00:54:07,770
+تعريف أن ال F أشمالها F is integrable تعالي ال L
+
+623
+00:54:07,770 --> 00:54:12,180
+of F زي ما عملنا قبل بشوية L of Fاللي هي أشمالها
+
+624
+00:54:12,180 --> 00:54:16,560
+أكبر أو يساوي لإن السبرمام على كل مين على ال
+
+625
+00:54:16,560 --> 00:54:21,160
+partitions اللي لها إذا أكبر أو يساوي اللي هو ال
+
+626
+00:54:21,160 --> 00:54:28,960
+ال L of P أو P و F اللي قبل شوية عملته ماشي اللي
+
+627
+00:54:28,960 --> 00:54:34,780
+هو L أو P و F بساوي اللي هو ال infimum لل F of X
+
+628
+00:54:34,780 --> 00:54:41,000
+such that X element in the interval A و Bهذا الـ
+
+629
+00:54:41,000 --> 00:54:44,220
+sub interval في الشغل هي واحدة اللي هو مضروب في
+
+630
+00:54:44,220 --> 00:54:46,380
+مين؟ في طول ال interval اللي هي مين طول ال
+
+631
+00:54:46,380 --> 00:54:49,700
+interval في هذه الحالة؟ أو ال sub interval B minus
+
+632
+00:54:49,700 --> 00:54:52,940
+A هي سماشي لكن أنا أصلا ماعنديش غير sub interval
+
+633
+00:54:52,940 --> 00:54:57,780
+واحدة هيك مجزقة أنا الفترة إلى جزء واحد بس الآن ال
+
+634
+00:54:57,780 --> 00:55:01,240
+infimum هذا عمالي بقول أنا ال F of X أكبر يساوي
+
+635
+00:55:01,240 --> 00:55:07,050
+مين؟ Mإذاً، حيكون عند الـ infimum له أكيد هيكون
+
+636
+00:55:07,050 --> 00:55:12,830
+أكبر أو يساوي الـ M هذه في مين؟ في الـ B minus A
+
+637
+00:55:12,830 --> 00:55:18,090
+كمان مرة الـ F of X أكبر أو يساوي M إذاً، الـ
+
+638
+00:55:18,090 --> 00:55:22,390
+infimum تبعه أكيد هيظل أكبر أو يساوي مين؟ أكبر أو
+
+639
+00:55:22,390 --> 00:55:30,080
+يساوي M هذه من جهةه الآن، صار عندي الآناللي عملته
+
+640
+00:55:30,080 --> 00:55:36,600
+L of F هذا أتبعته أكبر أو يساوي M في B minus A
+
+641
+00:55:36,600 --> 00:55:40,520
+Similarly الآن بدي أشتغل على مين يا شباب بدي أشتغل
+
+642
+00:55:40,520 --> 00:55:44,460
+على ال U عشان أسيب أجيب اللي هي أصغر أو يساوي شوف
+
+643
+00:55:44,460 --> 00:55:50,730
+كيف بدي أعملها ال U of Fأيش بيساوي؟ طبعا الـ U في
+
+644
+00:55:50,730 --> 00:55:54,250
+F أيش ماله؟ هو الـ infimum على كل ال other sums
+
+645
+00:55:54,250 --> 00:56:01,890
+إذن هيكون أصغر أو يساوي الـ U على ال B .. ال B A و
+
+646
+00:56:01,890 --> 00:56:06,970
+B نفس ال partition بتاخده ومين و ال Fالـ U of F هو
+
+647
+00:56:06,970 --> 00:56:12,890
+عبارة عن الـ infimum على كل ال other sums هذا الأن
+
+648
+00:56:12,890 --> 00:56:16,610
+إيش بيساوي؟ بيساوي اللي هو بس ال sub interval
+
+649
+00:56:16,610 --> 00:56:19,290
+واحدة مين هي؟ أنا ماخدها اللي بردش إن أنا بس
+
+650
+00:56:19,290 --> 00:56:22,570
+نوجدتين إذا ال sub interval واحدة اللي هي B minus
+
+651
+00:56:22,570 --> 00:56:29,250
+A بيصير عند ال supremum لم K Capital لأ ال F of X
+
+652
+00:56:29,250 --> 00:56:35,080
+such that X element in A وBهو مضروب في مين في طول
+
+653
+00:56:35,080 --> 00:56:38,780
+الفترة اللي هي ال sub interval عند بي minus ايه
+
+654
+00:56:38,780 --> 00:56:44,150
+الان و يساوي هذا السبري ما معلقها يا شبابأكيد
+
+655
+00:56:44,150 --> 00:56:49,290
+مدامة الـ F of X أصغر أو يساوي M إذاً هيكون الـ
+
+656
+00:56:49,290 --> 00:56:53,070
+Supremum لأن هذا الـ Supremum إيه شماله؟ الـ Least
+
+657
+00:56:53,070 --> 00:56:58,550
+Upper Bound مدامة الـ M عبارة عن Upper Bound للـ F
+
+658
+00:56:58,550 --> 00:57:01,810
+of X لأنها أكبر يساوي F of X إذاً هيكون عند الـ
+
+659
+00:57:01,810 --> 00:57:05,090
+Least Upper Bound اللي هو الـ Supremum أصغر أو
+
+660
+00:57:05,090 --> 00:57:10,310
+يساوي الـ Upper Bound M في الـ B minus A إذاً صار
+
+661
+00:57:10,310 --> 00:57:15,540
+Luv F أصغر أو يساوي B M في B minus Aهذا صار عندى
+
+662
+00:57:15,540 --> 00:57:19,400
+اللى هو اصغر او يساوي ال M في B minus A اللى هو
+
+663
+00:57:19,400 --> 00:57:23,860
+بيساوي هذا طبعا معطى بيصير اصغر او يساوي M في B
+
+664
+00:57:23,860 --> 00:57:29,340
+minus A فبصير فعلا ال integration تبعى بين M في B
+
+665
+00:57:29,340 --> 00:57:35,120
+minus A و بين M في B minus A capital Mاللي
+
+666
+00:57:35,120 --> 00:57:39,320
+ماوضحتلهوش هذه بنفس الطريقة اللي هنا عند ال M صارت
+
+667
+00:57:39,320 --> 00:57:42,780
+lower bound لهذه و ال infimum هذه عبارة عن
+
+668
+00:57:42,780 --> 00:57:45,480
+greatest lower bound مدام greatest lower bound ده
+
+669
+00:57:45,480 --> 00:57:48,180
+الأكبر أوي سوى واحد من ال lower bound اللي هو مين
+
+670
+00:57:48,180 --> 00:57:52,720
+اللي هو ال M ماشي الحالة والباقي زي ما هو هيك
+
+671
+00:57:52,720 --> 00:57:56,040
+بيكون أثبتنا اللي هي ال remark اللي عندي
+
+672
+00:58:06,640 --> 00:58:12,280
+إن ييجي إلى الـ Corollary للنظرية اللي قبل بشوية
+
+673
+00:58:12,280 --> 00:58:19,460
+برضه
+
+674
+00:58:19,460 --> 00:58:33,220
+الإثبات ان شاء الله سهل شوفوا
+
+675
+00:58:33,220 --> 00:58:38,690
+يا شباب عندي الآنالـ Corollary بتقول ما يالي F F و
+
+676
+00:58:38,690 --> 00:58:43,730
+G من I لعند R ر انتيجرابل on I فعندي F و G
+
+677
+00:58:43,730 --> 00:58:47,870
+انتيجرابل و F of X أصغر يساوي G of X لكل X element
+
+678
+00:58:47,870 --> 00:58:51,050
+on I ده ال integration من A لB للF أصغر ال
+
+679
+00:58:51,050 --> 00:58:56,890
+integration من A لB لمن لل G ماشي الحال فبصير عندى
+
+680
+00:58:56,890 --> 00:59:03,230
+الآن ال integration أنه لو كانت ال F of X أصغر
+
+681
+00:59:03,230 --> 00:59:08,820
+يساوي G of Xon I بيعطيني ال integration لل F على
+
+682
+00:59:08,820 --> 00:59:11,380
+ال I اللي هو من A و لا B نظرها لتعرف ال
+
+683
+00:59:11,380 --> 00:59:21,080
+integration من A لB لمن لجي طيب عندي F و G
+
+684
+00:59:21,080 --> 00:59:25,860
+integrable صح ولا لأ اذا اكيد زي ما حكيت في اول
+
+685
+00:59:25,860 --> 00:59:30,900
+المحاضرة حسب اللي هو انه F integrable و G
+
+686
+00:59:30,900 --> 00:59:35,230
+integrable اذا مجموح انتجرابلأو حصل طرح الـ
+
+687
+00:59:35,230 --> 00:59:38,910
+Integrable بناء على انه K في F انتجرابل أو K في G
+
+688
+00:59:38,910 --> 00:59:41,910
+انتجرابل أو بناء على انه بيصير ناقص G is
+
+689
+00:59:41,910 --> 00:59:46,970
+integrable بيطلع عندي ال F ناقص G أشماله is
+
+690
+00:59:46,970 --> 00:59:55,830
+integrable مش الحال طيب ومش هيك كمان وقلنا ال
+
+691
+00:59:55,830 --> 01:00:02,270
+integrationللـ F ناقص G أو الـ G-F تلزمني أنا الـ
+
+692
+01:00:02,270 --> 01:00:08,830
+G-F فهن الـ G-F is integrable مدام G-F is
+
+693
+01:00:08,830 --> 01:00:14,150
+integrable إذا الـ G-Fحسب اللي .. النظرية قبل
+
+694
+01:00:14,150 --> 01:00:20,770
+بشوية الـ G minus F من هنا بصير G ناقص F of X أكبر
+
+695
+01:00:20,770 --> 01:00:24,670
+أو يساوي سفر من I إذا حيكون الـ G minus F على من A
+
+696
+01:00:24,670 --> 01:00:27,390
+لB أكبر أو يساوي سفر حسب النظرية اللي هاد
+
+697
+01:00:27,390 --> 01:00:32,170
+الكورولار إلها طيب ومن جهة أخرى بالنظرية اللي
+
+698
+01:00:32,170 --> 01:00:35,870
+حكيناها في الأول اللي هو مجموع دلتين أو حصل طرحين
+
+699
+01:00:35,870 --> 01:00:42,110
+بساوة ال integration إن الـ G من A لB زائدالـ
+
+700
+01:00:42,110 --> 01:00:51,410
+integration من A إلى B للـ
+
+701
+01:00:51,410 --> 01:00:58,230
+G ناقص الـ integration من A إلى B للـ Fاعتمدت هانا
+
+702
+01:00:58,230 --> 01:01:02,430
+في التوزيع و في إخراج النقص على الـ K F Integrable
+
+703
+01:01:02,430 --> 01:01:04,710
+و الـ K في ال integration بيساوي ال integration
+
+704
+01:01:04,710 --> 01:01:09,190
+للـ K و اللي هو اعتمادا على ال integration لل F زي
+
+705
+01:01:09,190 --> 01:01:11,190
+ال G بيساوي ال integration لل F زي ال integration
+
+706
+01:01:11,190 --> 01:01:15,250
+لل G من هنا صار عندي أنقل هذا بس على الجهة الثانية
+
+707
+01:01:15,250 --> 01:01:18,930
+بيصير ال integration لل G من A ل B لما انقل هذا
+
+708
+01:01:18,930 --> 01:01:23,130
+على الجهة الثانية أكبر أو يساوي ال integration لل
+
+709
+01:01:23,130 --> 01:01:30,850
+F من A ل B وهو المطلوبطيب يا شباب نيجينا النظرية
+
+710
+01:01:30,850 --> 01:01:36,970
+اللي بعدها اخلونا نركز شوية لأنه البرهان يعني طويل
+
+711
+01:01:36,970 --> 01:01:45,850
+شوية لكن ان شاء الله ابتستوعبوه نشوف ايش النظرية
+
+712
+01:01:45,850 --> 01:01:54,690
+بتقول النظرية
+
+713
+01:01:54,690 --> 01:02:02,260
+تقول ما يليlet I عبارة عن فترة من A لعند B هاي
+
+714
+01:02:02,260 --> 01:02:09,460
+الفترة اللي عندي هاي الفترة من A لعند B وعندي ماخد
+
+715
+01:02:09,460 --> 01:02:15,220
+أنا C نقطة في داخل الفترة A وB طبعا النظرية
+
+716
+01:02:15,220 --> 01:02:17,900
+هتلاقوها مش غريبة عليكم مرة تلاقوكم الكلكولات ولكن
+
+717
+01:02:17,900 --> 01:02:22,330
+البرمان اللي بده شغلlet I بيساوي من A لعند B and
+
+718
+01:02:22,330 --> 01:02:25,830
+let C be an element in A و B and let F من كل I
+
+719
+01:02:25,830 --> 01:02:29,210
+لعند R be a bounded function يعني ال function اللي
+
+720
+01:02:29,210 --> 01:02:32,830
+بنشتغل عليها bounded جاهزة يعني and then النتيجة
+
+721
+01:02:32,830 --> 01:02:36,970
+بقولي F is integrable on I هتكون ال F integrable
+
+722
+01:02:36,970 --> 01:02:42,990
+على كل الفترة اللي هي I من A و B إذا و فقط إذا F
+
+723
+01:02:42,990 --> 01:02:51,480
+is integrable على مين على on both I واحد من A لCو
+
+724
+01:02:51,480 --> 01:03:00,520
+I2 من C لعند B ومش هيك بقولك وكمان هيكون عند ال
+
+725
+01:03:00,520 --> 01:03:03,080
+integration من A ل B ل F سوى ال integration من A ل
+
+726
+01:03:03,080 --> 01:03:05,820
+C ل F زاد ال integration من C ل عند B ل F اللي هي
+
+727
+01:03:05,820 --> 01:03:09,460
+الاشي المعود عندنا إذا الأن بقولي الإعلان اللي
+
+728
+01:03:09,460 --> 01:03:12,560
+بقوله مالي إذا كانت F is a bounded function on the
+
+729
+01:03:12,560 --> 01:03:18,080
+interval كلها I اللي سمينها من A ل عند B Iأه إذا
+
+730
+01:03:18,080 --> 01:03:22,800
+كانت F is bounded function عليها إذا F is
+
+731
+01:03:22,800 --> 01:03:32,220
+integrable on I if and only if F is integrableon
+
+732
+01:03:32,220 --> 01:03:42,140
+I1 and F is integrable on I2 وفي هذه الحالة سيكون
+
+733
+01:03:42,140 --> 01:03:46,500
+عنده ال integration من A لعند B سوى ال integration
+
+734
+01:03:46,500 --> 01:03:52,470
+من A ل C زي ال integration من C لعند Bبدنا نفترض
+
+735
+01:03:52,470 --> 01:03:58,550
+في الأول أن F is integrable على I1 وI2 ونصل أنه
+
+736
+01:03:58,550 --> 01:04:01,450
+اللي هو إيه شماله اللي هو ال function is
+
+737
+01:04:01,450 --> 01:04:07,430
+integrable عالميا على كل الفترة اللي هي I إذا الأن
+
+738
+01:04:07,430 --> 01:04:15,030
+أول حاجة بدنا نفترضها انتبهوا عندي إيش بنسوي صبوز
+
+739
+01:04:17,840 --> 01:04:32,080
+that F is integrable on I1 and I2 ستجدون أننا
+
+740
+01:04:32,080 --> 01:04:37,580
+نعتمد كثير على الـ Integrable criterion ستجدون كم
+
+741
+01:04:37,580 --> 01:04:42,820
+هي مهمة في إثبات هذه النظريات مادام F is
+
+742
+01:04:42,820 --> 01:04:48,300
+integrableعلى I1 خلّينا ناخد Y أكبر من سفر
+
+743
+01:04:48,300 --> 01:04:52,260
+arbitrary for every Y أكبر من سفر بما أن F is
+
+744
+01:04:52,260 --> 01:05:00,440
+integrable on I1 then there exists B1Y هذا
+
+745
+01:05:00,440 --> 01:05:06,260
+partition عالميا على I1 such that لأن F is
+
+746
+01:05:06,260 --> 01:05:14,210
+integrable على I1 such that الـ UB1 و Epsilon و
+
+747
+01:05:14,210 --> 01:05:20,490
+الـ function F ناقص الـ B1 و Epsilon و الـ
+
+748
+01:05:20,490 --> 01:05:25,250
+function F أصغر من مين من Epsilon على 2 للحسابات
+
+749
+01:05:25,250 --> 01:05:30,770
+ماشي الحال هذا
+
+750
+01:05:30,770 --> 01:05:36,590
+استخداما للـ integrability للـ function F عالمين
+
+751
+01:05:36,590 --> 01:05:44,720
+على الـ I1 SimilarlyThere exist B2
+
+752
+01:05:44,720 --> 01:05:48,920
+و Epsilon بما أن F Integra بالعالم I2 إذاً there
+
+753
+01:05:48,920 --> 01:05:58,140
+exist B2 و Epsilon Such that U B2 و Epsilon هذا
+
+754
+01:05:58,140 --> 01:06:02,160
+partition لمين؟ للفترة التانية I2 اللي هي من C
+
+755
+01:06:02,160 --> 01:06:10,740
+لعند Bو F ناقص ال B إتنين و إبسلون و F أصغر من مين
+
+756
+01:06:10,740 --> 01:06:15,180
+يا جماعة أصغر برضه من إبسلون على اتنين ماشي الحال
+
+757
+01:06:15,180 --> 01:06:21,100
+الآن أنا غرضي أن أثبت أن F is Integra بالعالمين
+
+758
+01:06:21,100 --> 01:06:30,050
+على كل الفترة I من A لعند مين لعند B الان letما
+
+759
+01:06:30,050 --> 01:06:34,130
+دام بده .. بده اللي هو أثبت الـ Integrability للـ
+
+760
+01:06:34,130 --> 01:06:38,270
+F يا شباب على كل الـ I إذا بدي partition على كل
+
+761
+01:06:38,270 --> 01:06:43,070
+الـ I ال partition المؤهل ليكون الـ I الـ B1 و Y
+
+762
+01:06:43,070 --> 01:06:48,530
+جزء هذه و الـ B2 و Y جزء هذه إذا حاكيد عند let B
+
+763
+01:06:48,530 --> 01:06:55,170
+اللي هو بساوي أو بي اللي هو .. امسميه بي ابسلون
+
+764
+01:06:55,170 --> 01:07:04,240
+بساوي بي واحد و ابسلون اتحادبتنين او ابسلون واضحة؟
+
+765
+01:07:04,240 --> 01:07:10,000
+وهذا هيكون اشمال و partition partition لمين؟ لكل
+
+766
+01:07:10,000 --> 01:07:17,140
+ال I معايا يا شباب اه؟ اذا صار عندي الآن اخترت انا
+
+767
+01:07:17,140 --> 01:07:22,900
+ال ال بي ابسلون عبارة عن ب واحد ابسلون اتحاد بتنين
+
+768
+01:07:22,900 --> 01:07:26,760
+ابسلون وبدأ اصل لل U بي ابسلون نال أقل ال بي
+
+769
+01:07:26,760 --> 01:07:32,300
+ابسلون اصغر من ابسلونواضح أه؟ عشان أثبت أنه الـ
+
+770
+01:07:32,300 --> 01:07:36,180
+function F is integrable على كل الـ I هذا إيش ماله
+
+771
+01:07:36,180 --> 01:07:44,020
+صار let BY بسوا كده which هذا المهم is a partition
+
+772
+01:07:44,020 --> 01:07:50,640
+of I كلها لأن الأولان جزء هذا العندلهان والتاني
+
+773
+01:07:50,640 --> 01:07:54,960
+جزء هذا العندلهان إذا إتحادا هيجزء كل المنطقة
+
+774
+01:07:54,960 --> 01:08:06,000
+المطلوبة طيب شوف الآن احسبلي الآنU,B,Y,F-L,B,Y,F
+
+775
+01:08:06,000 --> 01:08:10,360
+ويساوي ال
+
+776
+01:08:10,360 --> 01:08:15,700
+U,B,Y,F عبارة عن إيش يا جماعة ال U,B,Y,F خلينا
+
+777
+01:08:15,700 --> 01:08:20,320
+نقول U,B,Y,F اللي هو عبارة عن some U بتحت عشان
+
+778
+01:08:20,320 --> 01:08:27,020
+تشوفوا إيش اللي بعمله U,B,Y,F عبارة
+
+779
+01:08:27,020 --> 01:08:38,620
+عن summationلأ ال M K ال N و X K minus X K minus
+
+780
+01:08:38,620 --> 01:08:43,580
+واحد K مثلا من واحد لعند مين لعند N هذه اللي
+
+781
+01:08:43,580 --> 01:08:52,700
+بتجزئلي من عند A لعند مين لعند B و أكيد هتمر في C
+
+782
+01:08:52,700 --> 01:08:58,570
+ليش؟أكيد C هتكون نقطة من النقاط، ليش هتكون نقطة من
+
+783
+01:08:58,570 --> 01:09:03,230
+النقاط؟ لأنه أنا أخدت بي إبسلون هي اتحاد هذه مع
+
+784
+01:09:03,230 --> 01:09:08,210
+هذه و آخر نقطة في هذه هي الـ C و أول نقطة في هذه
+
+785
+01:09:08,210 --> 01:09:11,210
+هي الـ C كيف هذه partition لهذه و هذه partition
+
+786
+01:09:11,210 --> 01:09:14,470
+لهذه؟ مش لما نعمل partition لكل الفترة بيكون أول
+
+787
+01:09:14,470 --> 01:09:18,390
+نقطة و أخر نقطة من ضمن ال partition؟ أكيدوالذن ال
+
+788
+01:09:18,390 --> 01:09:22,230
+partition للفترة الصغيرة هتكون اللي هي من عند A
+
+789
+01:09:22,230 --> 01:09:26,430
+لعند C إذا ال C هنا و ال C هنا إذا مضمون ال C
+
+790
+01:09:26,430 --> 01:09:32,570
+واحدة من هدول ماشي الحال إذا هذا الآن باجي ال MK
+
+791
+01:09:32,570 --> 01:09:37,600
+هي عبارة عن نفترض أنه من عند X Note لعند XNوهنا
+
+792
+01:09:37,600 --> 01:09:42,040
+الـ XL اللي هي الـ C واحدة من عناصر اللي هي ال ..
+
+793
+01:09:42,040 --> 01:09:46,020
+ال .. ال .. ال partition إذن الآن بقدر أجزء هذا
+
+794
+01:09:46,020 --> 01:09:55,690
+لجزئين MK في XK minus XK minus 1 من كامن عند 1لعند
+
+795
+01:09:55,690 --> 01:10:00,710
+اللي هي النقطة الـ K اللي خلّيني أسميها M حيث الـ
+
+796
+01:10:00,710 --> 01:10:08,330
+XM هي الـ C زائد الـ summation للـ MK الـ XK minus
+
+797
+01:10:08,330 --> 01:10:13,110
+XK minus 1 كامن
+
+798
+01:10:13,110 --> 01:10:19,210
+عند واحد آسف كامن عند مين اللي بعدها اللي هي الـ M
+
+799
+01:10:19,210 --> 01:10:26,820
+اللي عند الـ Mالعند الـ N هذه اللي هي مين XM بساوي
+
+800
+01:10:26,820 --> 01:10:32,720
+الـ C إذا في الحالتين هنا عند هذا زائد هذا ال
+
+801
+01:10:32,720 --> 01:10:36,520
+summation هو ال summation هذا على ال intervals
+
+802
+01:10:36,520 --> 01:10:41,000
+بضلي أجزء أجزء لمن أصل العند هذه بكون اللي هو
+
+803
+01:10:41,000 --> 01:10:45,980
+التجزئة الأولى و بعدين التجزئة الثانية بكمل من هنا
+
+804
+01:10:45,980 --> 01:10:51,810
+و بضلي طالعة و بوجد ال MKللنهانة و ال MK للنهانة
+
+805
+01:10:51,810 --> 01:11:00,010
+المجموع النهانة هو عبارة عن هيعمله اللي هو ال U بي
+
+806
+01:11:00,010 --> 01:11:04,910
+ابسلون طبعا MK capital آسف هذه و هذا MK capital
+
+807
+01:11:04,910 --> 01:11:09,190
+لأنه بحكي عن ال other اللي مهم الفكرة ال U بي
+
+808
+01:11:09,190 --> 01:11:16,730
+ابسلون واحد F اللي هي ال partition الأول اللي بنيت
+
+809
+01:11:16,730 --> 01:11:21,140
+عليه ميناللي هو partition بي إبسلون سميته واحد و
+
+810
+01:11:21,140 --> 01:11:28,180
+إبسلون زائد اللي هو mean المتبقى اللي هو U بي نين
+
+811
+01:11:28,180 --> 01:11:33,400
+و إبسلون و F هذا كله mean الـ U بي إبسلون و F
+
+812
+01:11:33,400 --> 01:11:37,140
+similarly mean الآن
+
+813
+01:11:40,410 --> 01:11:45,370
+Similarly mean ال L of B, Epsilon و F برضه هذا
+
+814
+01:11:45,370 --> 01:11:49,970
+بجزء المنطقة ككل و هو مبني على أساس تجزئة اللي هو
+
+815
+01:11:49,970 --> 01:11:54,450
+B 1 و Epsilon اتحاد B 2 و Epsilon إذا بالظبط هذا
+
+816
+01:11:54,450 --> 01:12:04,030
+برضه بساوي ناقص اللي هو ال L B 1 و Epsilon و F
+
+817
+01:12:04,030 --> 01:12:16,290
+زائد L الجزء التانيB2 Epsilon و F و يساوي الان
+
+818
+01:12:16,290 --> 01:12:26,530
+هذا ناقص هذا U B1 Epsilon و F ناقص ال B1 Epsilon و
+
+819
+01:12:26,530 --> 01:12:34,990
+F أخدت هذا يا جماعة مع هذا خلصنا منه زائد اللي هو
+
+820
+01:12:34,990 --> 01:12:43,780
+اللي متبقياللي هو هذا ناقص هذا اللي هو U بي تنين و
+
+821
+01:12:43,780 --> 01:12:51,520
+إبسلون و F ناقص L بي تنين و إبسلون و F هذا الآن
+
+822
+01:12:51,520 --> 01:12:59,880
+هيه من فوق اللي حضرناله أصغر من إبسلون على اتنين و
+
+823
+01:12:59,880 --> 01:13:04,320
+هذا حضرناله برضه أصغر من إبسلون على اتنينإذا صار
+
+824
+01:13:04,320 --> 01:13:10,240
+هذا الطرح بينهم أصغر من مين من إبسلون صرنا مثل تين
+
+825
+01:13:10,240 --> 01:13:13,980
+لكل إبسلون أكبر من سفر there exist B2 there exist
+
+826
+01:13:13,980 --> 01:13:18,180
+بإبسلون such that U بإبسلون و F ناقصها بيبسلون و F
+
+827
+01:13:18,180 --> 01:13:23,180
+أصغر من مين من إبسلون إذا صارت عندي F is
+
+828
+01:13:23,180 --> 01:13:30,890
+integrable on I اللي لجينا ال partition لهاهذا
+
+829
+01:13:30,890 --> 01:13:34,470
+الجزء الأول من النظرية الآن بدنا نثبت اللي هو
+
+830
+01:13:34,470 --> 01:13:40,710
+conversely بدنا نفترض أنه F is integrable على كل
+
+831
+01:13:40,710 --> 01:13:46,810
+الفترة ومن ثم نثبت أنه integrable على كل
+
+832
+01:13:46,810 --> 01:13:54,570
+subinterval من التنتين اللي موجودة إذا الآن الجزء
+
+833
+01:13:54,570 --> 01:13:57,550
+الثاني بنقول suppose
+
+834
+01:14:00,050 --> 01:14:14,710
+that F is integrable on I لها بتساوي A و B و بدنا
+
+835
+01:14:14,710 --> 01:14:20,470
+نثبت أنها integrable عالميا على الفترة الأولى A و
+
+836
+01:14:20,470 --> 01:14:26,560
+C و الفترة الثانية Cطيب خلّينا نكمل اللي هو نقول
+
+837
+01:14:26,560 --> 01:14:27,600
+conversely
+
+838
+01:14:34,910 --> 01:14:37,530
+مدام اللي هي F is integrable إذا بالـ Cauchy
+
+839
+01:14:37,530 --> 01:14:41,810
+criterion لكل ي أكبر من صفر there exists B اللي هو
+
+840
+01:14:41,810 --> 01:14:44,950
+partition اللي هو مسميه B ممكن نسميه احنا بي
+
+841
+01:14:44,950 --> 01:14:48,170
+أبسلون element in B of I هذا طبعا ال partition
+
+842
+01:14:48,170 --> 01:14:52,570
+بيعتمد على مين؟ على إبسلون such that U, B و F ناقص
+
+843
+01:14:52,570 --> 01:14:56,370
+ال U of F أصغر من مين من إبسلون هذا لإن F is
+
+844
+01:14:56,370 --> 01:15:00,630
+integrable اللي هي by Cauchy .. by .. by
+
+845
+01:15:00,630 --> 01:15:06,140
+integrability criterion حصلنا على هذهالان انا لمين
+
+846
+01:15:06,140 --> 01:15:11,400
+رايح بدي اثبت الـ Integrability لعالفترة A وC و
+
+847
+01:15:11,400 --> 01:15:15,040
+Integrability لفترة B وC فانا بدي في الـ partition
+
+848
+01:15:15,040 --> 01:15:22,140
+اللي أصلله بدي أصل للـ U لل partition B مثلا معينة
+
+849
+01:15:22,140 --> 01:15:30,020
+B' وF- L B' و F بديه أصغر من مين أصل أصغر من
+
+850
+01:15:30,020 --> 01:15:34,080
+إبسلون وهذه تكون الـ B' partition لمين للفترة
+
+851
+01:15:34,080 --> 01:15:38,000
+الأولى فعشان تكون للفترة الأولى لازم تكون ال C
+
+852
+01:15:38,000 --> 01:15:42,620
+موجودة فيها فبناء عليه أنا مش عارف ال B' ال B اللي
+
+853
+01:15:42,620 --> 01:15:46,560
+لجيته فيه ال C ولا لأ إذا بتاخدوا بعين الاعتبار
+
+854
+01:15:46,560 --> 01:15:51,760
+عشان أصل لمين لل B' اللي تكون فيها ال C عشان هيك
+
+855
+01:15:51,760 --> 01:15:58,130
+أنا إيش جيتقلنا لما لجينا الـ B هذه وفقا للـ F is
+
+856
+01:15:58,130 --> 01:16:02,690
+integrable و بتحقق هذه جيت خليني و قولت خليني ناخد
+
+857
+01:16:02,690 --> 01:16:07,730
+B' أيش بتساوي يا شباب بتساوي B اتحاد الـ C يعني
+
+858
+01:16:07,730 --> 01:16:13,390
+ضفت لل partition اللي لجيته من الـ C و هو هذا الـ
+
+859
+01:16:13,390 --> 01:16:19,070
+B' برضه هيحقق للي بدياه اللي هو A شماله صار B'
+
+860
+01:16:19,510 --> 01:16:24,420
+refinement للـ Bما دام الـ Refinement للـ B إذا
+
+861
+01:16:24,420 --> 01:16:29,960
+UB' و F أكيد الـ Refinement هذا هيصغر عن الأصل
+
+862
+01:16:29,960 --> 01:16:36,960
+اللي هو الـ UBFبينما ال B' of F هيكبر عن مين؟ عن
+
+863
+01:16:36,960 --> 01:16:41,980
+الأصل فلمّا أضربه في سالب هيصغر إذا حيصير عند U B'
+
+864
+01:16:42,300 --> 01:16:48,080
+F ناقص ال B' F أصغر يساوي U B و F ناقص ال B و F
+
+865
+01:16:48,080 --> 01:16:52,900
+وهذا أصلا أصغر من مين؟ من Epsilon إذا طلع عند ال
+
+866
+01:16:52,900 --> 01:16:58,390
+B' اللي أنا احتجتهاللي في الأصل هو الـ B الأصلية
+
+867
+01:16:58,390 --> 01:17:03,550
+اللي لجيتها اتحاد الـ C طلع برضه الـ U B' F ناقص
+
+868
+01:17:03,550 --> 01:17:08,590
+الـ B' F أصغر من إبسلون اللي أنا بعد شوية هحتاجه
+
+869
+01:17:08,590 --> 01:17:13,850
+في عملية إثبات أنه اللي هو الـ F is integrable على
+
+870
+01:17:13,850 --> 01:17:17,710
+الجزء الأول اللي هو I1 و F is integrable على الجزء
+
+871
+01:17:17,710 --> 01:17:22,410
+الثاني اللي هو I2 طب كيف بده أحصل هنا؟ شوف كيف بده
+
+872
+01:17:22,410 --> 01:17:28,890
+أحصل الـ Partition الأولانيب1 براين مثلا ب1 براين
+
+873
+01:17:28,890 --> 01:17:33,070
+اللي بيخللي هذا أصغر من إبسلون وهذا partition
+
+874
+01:17:33,070 --> 01:17:38,670
+للجزء الأول مما يؤدي لو وجدته هذا أن ال F is
+
+875
+01:17:38,670 --> 01:17:42,150
+integrable على الفترة الأولى و similarly حلاجة على
+
+876
+01:17:42,150 --> 01:17:47,180
+الفترة التانية وبكون خلصت النظرية هيك نشوف كيفالآن
+
+877
+01:17:47,180 --> 01:17:52,660
+وجدنا الـ B' أو اللي هو B اتحاد الـ C يحقق هذه
+
+878
+01:17:52,660 --> 01:17:57,800
+اللي هي المعادلة أو هذه المتباينة أصغر من مين من
+
+879
+01:17:57,800 --> 01:18:02,160
+Epsilon شوف الآن كيف دي بارتشني للجزء الأول من A
+
+880
+01:18:02,160 --> 01:18:07,760
+لعين C بكل بساطة قطع للـ B' هذا مع مين؟ مع A و C
+
+881
+01:18:07,760 --> 01:18:12,580
+أكيد هذا في C أكيدوفي A إذا النقطة الأولى موجودة
+
+882
+01:18:12,580 --> 01:18:16,680
+والنقطة C موجودة إذا هو فعلا partition لمين؟ هيكون
+
+883
+01:18:16,680 --> 01:18:21,200
+B' partition للـ A والـ C وبنفس الطريقة and let B
+
+884
+01:18:21,200 --> 01:18:27,880
+T2' بيساوي B'تقاطع الـC والـB إذا الـC موجودة هنا
+
+885
+01:18:27,880 --> 01:18:32,280
+والـB موجودة هنا إذا صار هذا بحتوى ال partition
+
+886
+01:18:32,280 --> 01:18:36,080
+على الـC وعلى الـB إذا فعلا هو partition المين
+
+887
+01:18:36,080 --> 01:18:42,640
+للفترة الثانية is a partition of C وB so that إذا
+
+888
+01:18:42,640 --> 01:18:49,380
+الآن بحضر إن لجيتاللي هو B1' وB2' واحد partition
+
+889
+01:18:49,380 --> 01:18:54,540
+للـA والـC والتاني للـC والـB وبدّعي إن هما ال
+
+890
+01:18:54,540 --> 01:18:59,540
+partitions اللي هوصلني على هذه وsimilarly زيها
+
+891
+01:18:59,540 --> 01:19:03,020
+للتانية اللي بتعطيني الintegrability للـF على
+
+892
+01:19:03,020 --> 01:19:08,780
+الأولى وintegrability للـF على الثانية نشوف إيش
+
+893
+01:19:08,780 --> 01:19:14,720
+اللي بقوله يلا صلوا عنا يا شباب صلاة والسلام عندي
+
+894
+01:19:15,170 --> 01:19:20,550
+أحسبني الآن بس خليني بس عشان تكون واضحة قدامك اللي
+
+895
+01:19:20,550 --> 01:19:26,010
+هي واحد اللي بدي استخدمها بعد شوية طيب شوفوا يا
+
+896
+01:19:26,010 --> 01:19:38,970
+جماعة أحسبني الآن U بي برايم و F اللي هو بتساوي U
+
+897
+01:19:38,970 --> 01:19:44,740
+بي برايم واحد و F زي U بي اتنين برايم و Fاللي قبل
+
+898
+01:19:44,740 --> 01:19:48,660
+بشوية عملناها هو ال partition هذا بي برايم هو
+
+899
+01:19:48,660 --> 01:19:55,790
+عبارة عن اتحاد هذا اتحاد هذا ماشي الحالماشي الان و
+
+900
+01:19:55,790 --> 01:19:59,610
+نفس الاشي عملتها قبل هيك ال b prime of f سواء ال b
+
+901
+01:19:59,610 --> 01:20:03,470
+prime واحد او ال b2 prime حيث بي اتنين برايم بي
+
+902
+01:20:03,470 --> 01:20:08,050
+واحد برايم يبوسأ اتحاد هنا شماله هو بي برايم اذا
+
+903
+01:20:08,050 --> 01:20:12,370
+زي ما عملنا قبل بشوية هذه اللي هي ال equality
+
+904
+01:20:12,370 --> 01:20:17,190
+التانيةالان من واحد و من اتنين بدي اصل اللي بديه
+
+905
+01:20:17,190 --> 01:20:25,950
+ايش اللي بديه احسبلي الان UB1' F زي UB2' F ناقص ال
+
+906
+01:20:25,950 --> 01:20:34,350
+B1' F زي ال B2' of F اللي هو من وين هذا جبت اللي
+
+907
+01:20:34,350 --> 01:20:41,050
+هو عند هي من واحد هي هذه اتقوط عنها بالقيمة هذه من
+
+908
+01:20:41,050 --> 01:20:47,720
+وين هذه من الان من هناشيلت اللي هو .. هاي من هذولة
+
+909
+01:20:47,720 --> 01:20:50,780
+يا جماعة من اللي حاطط عليهم أحمر أنات ثلاثة ..
+
+910
+01:20:50,780 --> 01:20:56,140
+التنتين هذولة عنده شيلت هذولة .. هذه و حطيت هذه
+
+911
+01:20:56,140 --> 01:21:04,180
+مكانها طلعت هذه .. هيها .. فارحة؟ و شيلت هذه و
+
+912
+01:21:04,180 --> 01:21:05,500
+حطيت هذه مكانها
+
+913
+01:21:08,330 --> 01:21:13,550
+صارت هذه مكانها إذا هذه ناقص هذه اللي هي هذه ناقص
+
+914
+01:21:13,550 --> 01:21:17,290
+هذه اللي كانت أصغر من إبسلون هتصير أصغر من إبسلون
+
+915
+01:21:17,290 --> 01:21:24,150
+إذا صار عندي هذا اللي هو ال U أوضح لكي أنا U بواحد
+
+916
+01:21:24,150 --> 01:21:36,350
+برايم و F زائد U بيتنين برايم و F ناقص ال of بواحد
+
+917
+01:21:36,350 --> 01:21:46,170
+برايم و Fزائد ال B2 prime و F هذا كله أصغر من
+
+918
+01:21:46,170 --> 01:21:50,810
+إبسلون لأن هذا أصلا كله .. ليش هذا صح؟ لأن هذا
+
+919
+01:21:50,810 --> 01:22:00,330
+أصلا هو عبارة عن U B prime و F و هذا ال B prime و
+
+920
+01:22:00,330 --> 01:22:06,440
+F اللي هو في الأصل هذامن عندي من هنا أصغر من إيش
+
+921
+01:22:06,440 --> 01:22:09,860
+من إبسلون إذاً هذا صار أصغر من إبسلون خلّي هذا
+
+922
+01:22:09,860 --> 01:22:13,160
+الكلام في الذاكر أصغر من إبسلون لأنه هيفيدني بعد
+
+923
+01:22:13,160 --> 01:22:19,900
+بشوية شوفلان فوزع خلّيني بس أمسح اللي على اللوح
+
+924
+01:22:19,900 --> 01:22:29,960
+ووزع الآن عندي هذا بيصير إيش هو هذا بيصير U ب U
+
+925
+01:22:31,310 --> 01:22:36,370
+ب1 برايم و F ناقص
+
+926
+01:22:36,370 --> 01:22:47,190
+ال ب واحد برايم و F كل هذا مع بعضه زائد U ب اتنين
+
+927
+01:22:47,190 --> 01:22:55,930
+برايم و F ناقص ال ب اتنين برايم و F هذا كله أصغر
+
+928
+01:22:55,930 --> 01:23:01,160
+من مين يا جماعة من إبسلون هذول الكميتين هذهزائد
+
+929
+01:23:01,160 --> 01:23:06,080
+هذه أصغر من إبسلون وهذه موجبة وهذه موجبة إذا
+
+930
+01:23:06,080 --> 01:23:12,140
+الكمية هذه أكيد لحالها أصغر من إبسلون والكمية هذه
+
+931
+01:23:12,140 --> 01:23:17,900
+لحالها إيش أصغر من إبسلون هذه أصغر من إبسلونتعني
+
+932
+01:23:17,900 --> 01:23:22,520
+أن لكل إبسلون لجينا partition بي واحد برايم بحيث
+
+933
+01:23:22,520 --> 01:23:26,620
+أن هذا ناقص هذا أصغر من إبسلون يعني F is
+
+934
+01:23:26,620 --> 01:23:38,540
+integrable on I واحد اللي هي من A ل Cلجينا
+
+935
+01:23:38,540 --> 01:23:45,180
+partition B2' بحيث أنه هذا نقص B2' لمين ل I2 هيكون
+
+936
+01:23:45,180 --> 01:23:49,500
+هذا نقص هذا أصغر من إبسلون وهذا يعني أن F is
+
+937
+01:23:49,500 --> 01:24:00,780
+integrable on I2 كده نكون هي كاحنا وصلنالا اللي
+
+938
+01:24:00,780 --> 01:24:08,840
+بدني من ناحية اثبات ان F is integrable on I if and
+
+939
+01:24:08,840 --> 01:24:15,760
+only if F is integrable on I واحد and on I اتنين
+
+940
+01:24:15,760 --> 01:24:23,380
+دل علي الجزء الأخير اللي اثبته ان عندي اللي هوالـ
+
+941
+01:24:23,380 --> 01:24:28,900
+integration من A إلى B أصغر أو يساوي بالبساوي ال
+
+942
+01:24:28,900 --> 01:24:32,780
+integration من A إلى C زائد ال integration من C
+
+943
+01:24:32,780 --> 01:24:39,840
+لعند B ركزوا معايا عشان نختصر الوقتشبيه باللي
+
+944
+01:24:39,840 --> 01:24:42,780
+شرحته قبل بشوية في النظرية اللي قبلها ال
+
+945
+01:24:42,780 --> 01:24:45,860
+integration من A ل B لل F مدام ان F is Integra
+
+946
+01:24:45,860 --> 01:24:50,400
+بالفرضينا احنا اذا هذا بيساوي عبارة عن ال U of F و
+
+947
+01:24:50,400 --> 01:24:53,600
+ال U of F اكيد اللي هي M في مملة كل هذوله اذا اظهر
+
+948
+01:24:53,600 --> 01:24:58,320
+يساوي U B prime و F B prime بارتشن من A لعند مين
+
+949
+01:24:58,320 --> 01:25:03,280
+لعند B و هذا قبل بشوية ايش قلنا عنه بساوي UB1 of F
+
+950
+01:25:03,280 --> 01:25:10,760
+زاد UB2 of Fهذا أكيد أصغر يساوي الأل تبعه و هذا
+
+951
+01:25:10,760 --> 01:25:16,420
+أكيد أصغر يساوي الأل اللي إله زائد 2 إبسلون من وين
+
+952
+01:25:16,420 --> 01:25:22,960
+جبته هذا قلنا بما أن F is integrable إذا U ناقص
+
+953
+01:25:22,960 --> 01:25:29,840
+هذا أصغر من إبسلون و U ناقص هذا أصغر من إبسلونإذا
+
+954
+01:25:29,840 --> 01:25:34,220
+صار عندى U زائد هذا أصغر من هذا زائد هذا زائد مين
+
+955
+01:25:34,220 --> 01:25:38,620
+اتنين إبسلون من وين جبت هذا يا جماعة من اللي هي
+
+956
+01:25:38,620 --> 01:25:45,660
+الـ integrability criterion for مين for F on the
+
+957
+01:25:45,660 --> 01:25:50,520
+interval I واحد حيكون ال U بواحد برايم و F ماقص ال
+
+958
+01:25:50,520 --> 01:25:54,400
+بواحد برايم و F أصغر من إبسلون أو بمعنى آخر ال U
+
+959
+01:25:54,400 --> 01:25:55,580
+بواحد
+
+960
+01:25:57,750 --> 01:26:03,830
+أصغر من L بي واحد إبراهيم و F زائد إبسلون هذا جبته
+
+961
+01:26:03,830 --> 01:26:09,610
+من سببه أن ال F is integrable on I واحد كلها
+
+962
+01:26:09,610 --> 01:26:15,580
+Similarly since F is integrable on I واحد كلهاI2
+
+963
+01:26:15,580 --> 01:26:19,360
+كلها إذا بيلاقي بي اتنين برايم بحيث ان U بي اتنين
+
+964
+01:26:19,360 --> 01:26:23,940
+برايم و F أصغر من L بي اتنين برايم و F زاد إبسلون
+
+965
+01:26:23,940 --> 01:26:30,900
+مع بعض صار هذا زاد هذا زادياش اتنين إبسلونبنفس
+
+966
+01:26:30,900 --> 01:26:34,380
+الطريقة اللي حكيتها قبل بشوية F is Integrable وهذا
+
+967
+01:26:34,380 --> 01:26:36,960
+أقله في F فالأقل في F هو ال supremum لها دول إذا
+
+968
+01:26:36,960 --> 01:26:40,500
+هذا أكبر وشوية هذا و هذا أكبر وشوية هذا إذا صار
+
+969
+01:26:40,500 --> 01:26:45,060
+عندي هذا المقدار أكبر أصغر وشوية هذا زائد هذا زائد
+
+970
+01:26:45,060 --> 01:26:49,270
+إيه شمالهاتنين إبسلون وزي ما حكينا قبل بشوية since
+
+971
+01:26:49,270 --> 01:26:53,290
+إبسلون was arbitrary وبنفس التوضيح الأولاني بطلع
+
+972
+01:26:53,290 --> 01:26:55,470
+عند ال integration من LB لLF أخر شهر ال
+
+973
+01:26:55,470 --> 01:26:59,110
+integration للأول زاد ال integration للتاني بدون
+
+974
+01:26:59,110 --> 01:27:03,250
+الإبسلون وقلنا ليش هذا الكلام صحيح الآن الاتجاه
+
+975
+01:27:03,250 --> 01:27:06,230
+الثاني similarly برضه هتلاقي اللي هو البرهين
+
+976
+01:27:06,230 --> 01:27:12,370
+متشابهة الآن بنفس المنطق وبنفس الطريقة وsimilarly
+
+977
+01:27:19,820 --> 01:27:22,620
+طبعا عارفين ايه رايح انا؟ انا راح اثبت ان هذا
+
+978
+01:27:22,620 --> 01:27:25,540
+المقدار اصغر أو ساوى هذا المقدار عند ال
+
+979
+01:27:25,540 --> 01:27:28,700
+integration هذا زائد ال integration هذا F is
+
+980
+01:27:28,700 --> 01:27:33,240
+integrable اذا هي بساوة ال U ال U of F ال U of F
+
+981
+01:27:33,240 --> 01:27:36,860
+هي ال infimum اذا اكيد اصغر او ساوية ال U واحدة
+
+982
+01:27:36,860 --> 01:27:40,580
+منهم وهذه برضه ال U of F على الفترة هذه برضه اصغر
+
+983
+01:27:40,580 --> 01:27:43,280
+او ساوية واحدة منهم اذا اصغر او ساوية ال U هذه
+
+984
+01:27:43,280 --> 01:27:47,820
+زائد ال U هذهفي مقابله قبل قليل أثبتنا أنه .. قلنا
+
+985
+01:27:47,820 --> 01:27:51,440
+أنه مدام تفز integrable إذا بال .. integrability
+
+986
+01:27:51,440 --> 01:27:55,980
+criterion الفرق بين هذه وهذه أصغر من إبسلون إذا
+
+987
+01:27:55,980 --> 01:28:00,260
+صار هذه أصغر من هذه زائد إبسلون وهذه نفس الشيء
+
+988
+01:28:00,260 --> 01:28:03,740
+للأفز integrable على الفترة التانية نفس اللي قلته
+
+989
+01:28:03,740 --> 01:28:07,760
+أصغر من هذه زائد إبسلون إذا صار المقدار هذا كله
+
+990
+01:28:07,760 --> 01:28:10,560
+على بعضه أصغر من هذه زائد هذه زائد اتنين إبسلون
+
+991
+01:28:10,560 --> 01:28:17,430
+لكن هذولا الثنتين اللي هنابساوين اللي هو LB'F في
+
+992
+01:28:17,430 --> 01:28:22,530
+هنا إيش مالها مساواة بساوين هذا المقدار لأن ال LB
+
+993
+01:28:22,530 --> 01:28:26,450
+'F إيش مالها عبارة عن هذه اتحاد هذه عملناها قبل
+
+994
+01:28:26,450 --> 01:28:31,150
+شوية و هذا المقدار عندى اللي هو أصغر أو ساوي هذا
+
+995
+01:28:31,150 --> 01:28:36,290
+لأن هذا عبارة عن LF و LF على هذه الفترة اللي هو
+
+996
+01:28:36,290 --> 01:28:39,210
+عبارة عن ال supreme أو أكبر أو ساوي هذه إذا صار
+
+997
+01:28:39,210 --> 01:28:43,120
+فيه عندى هذا المقدارأصغر أو يساوي ال integration
+
+998
+01:28:43,120 --> 01:28:47,360
+زي اتنين إبسلون إذا حصلنا على هذا المقدار أكبر أو
+
+999
+01:28:47,360 --> 01:28:50,800
+يساوي هذا for every إبسلون بنفس المنطق since
+
+1000
+01:28:50,800 --> 01:28:54,160
+إبسلون was arbitrary إذا ال integration هذا زائد
+
+1001
+01:28:54,160 --> 01:28:58,460
+ال integration هذا أصغر أو يساوي من هذه ومن اللي
+
+1002
+01:28:58,460 --> 01:29:03,660
+جابلها هذه بطلع عندي المساواة و هو المطلوب و هيك
+
+1003
+01:29:03,660 --> 01:29:09,860
+بنكون احنا برهن هذه النظرية أيضا بشكل كامل في
+
+1004
+01:29:09,860 --> 01:29:17,330
+ملاحظة أخيرةعلى النظرية النظرية بتقول انه عندي لو
+
+1005
+01:29:17,330 --> 01:29:21,990
+كانت c1 أصغر من c2 أصغر من cn حيث و c1 و c2 و cn
+
+1006
+01:29:21,990 --> 01:29:26,050
+في الفترة a و b اللي هو هيكون اللي هو بنقدر اللي
+
+1007
+01:29:26,050 --> 01:29:32,470
+هي نطبق النظرية هذه عدة مرات فعندي هي a و هي b و
+
+1008
+01:29:32,470 --> 01:29:38,320
+هي c1هذه C2 وهذه C3 لعند Cn مثلا بيصير أو خلّيني
+
+1009
+01:29:38,320 --> 01:29:41,720
+أقول C1 من هنا وهنا Cn من هنا بيصير ال integration
+
+1010
+01:29:41,720 --> 01:29:46,500
+من A ل B بيساوي ال integration من A ل C1 زياد ال
+
+1011
+01:29:46,500 --> 01:29:49,520
+integration من C1 ل C2 زياد المقصر اللي عند أخر
+
+1012
+01:29:49,520 --> 01:29:55,980
+واحدة ال integration من Cn لعند B لل function وهذه
+
+1013
+01:29:55,980 --> 01:30:04,230
+اللي هو الملاحظة معهودةالان في عندى اللى هي
+
+1014
+01:30:04,230 --> 01:30:08,930
+النظرية اللى .. ال .. ال .. ال .. المشهورة اللى هي
+
+1015
+01:30:08,930 --> 01:30:16,510
+composition theorem ان لو كان عندى F is a function
+
+1016
+01:30:16,510 --> 01:30:24,630
+من I لعند R وفى function من اللى هو domain ال I من
+
+1017
+01:30:24,630 --> 01:30:28,690
+range ال I .. ال F كاسف لعند ال .. لعند ال R
+
+1018
+01:30:32,310 --> 01:30:36,870
+و كانت had integrable و كانت had integrable هل ال
+
+1019
+01:30:36,870 --> 01:30:40,430
+composition بينهم integrable طبعا هذا الكلام need
+
+1020
+01:30:40,430 --> 01:30:44,570
+not to be true in general هنشوف مثال بعد شوية لكن
+
+1021
+01:30:44,570 --> 01:30:48,790
+لو كانت الـ Phi continuous يعني قوّينا الشرط الآن
+
+1022
+01:30:48,790 --> 01:30:54,290
+شوية هيصير عنده ال Phi composite ف F is integrable
+
+1023
+01:30:54,290 --> 01:30:58,410
+يعني بمعنى أخر لو كانت F is integrableالـ Phi is
+
+1024
+01:30:58,410 --> 01:31:01,510
+continuous حيكون الـ Phi composition أفضل لما يكون
+
+1025
+01:31:01,510 --> 01:31:05,730
+ال composition معرف عبارة عن integrable function
+
+1026
+01:31:05,730 --> 01:31:13,350
+وإحنا إن شاء الله المرة القادمة بنكمل وإلى لقاء
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bf2f12091855ae5e8606ce26b0abffb37d0cc0db
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0.srt
@@ -0,0 +1,1571 @@
+1
+00:00:04,890 --> 00:00:08,570
+بسم الله الرحمن الرحيم الآن نتحدث عن الجزء الثاني
+
+2
+00:00:08,570 --> 00:00:14,690
+من المحاضرة الخامسة لطلبة قسم رياضيات في كلية 
+
+3
+00:00:14,690 --> 00:00:18,850
+العلوم بالجامعة الإسلامية بغزة الجزء الثاني طبعا
+
+4
+00:00:18,850 --> 00:00:22,050
+زي ما وعدناكم في البداية قلنا اللي هو هنكمل فيه
+
+5
+00:00:22,050 --> 00:00:25,970
+اللي هو 6.2 اللي هي تطبيقات على الـ mean value
+
+6
+00:00:25,970 --> 00:00:28,490
+theorem أو applications on mean value theorem
+
+7
+00:00:28,490 --> 00:00:32,390
+هيكون في عندنا two applications اللي هو الـ
+
+8
+00:00:32,390 --> 00:00:34,790
+application الأول على الـ Mean Value Theorem هو
+
+9
+00:00:34,790 --> 00:00:38,290
+عبارة عن اللي هو Bernoulli's Inequality، هنبرهن
+
+10
+00:00:38,290 --> 00:00:42,150
+Bernoulli's Inequality، وبعدين هنتحدث عن اللي هو
+
+11
+00:00:42,150 --> 00:00:47,370
+Darboux's Theorem، تشوف كيف اللي هو بيصير الأمور،
+
+12
+00:00:47,370 --> 00:00:51,960
+نبدأ الآن في الجزء الأول، اللي هو عبارة عن
+
+13
+00:00:51,960 --> 00:00:55,840
+Bernoulli Inequality Bernoulli's Inequality اللي هي
+
+14
+00:00:55,840 --> 00:00:58,700
+بتقولنا لو كانت عندي Alpha عبارة عن real number
+
+15
+00:00:58,700 --> 00:01:02,500
+أكبر من واحد هيكون عندي الواحد زائد X to the Alpha 
+
+16
+00:01:02,500 --> 00:01:06,900
+أكبر أو يساوي واحد زائد Alpha X لكل X أكبر من من
+
+17
+00:01:06,900 --> 00:01:10,780
+ناقص واحد with equality if and only if عند X مين
+
+18
+00:01:10,780 --> 00:01:15,140
+عند X بيساوي صفر عندنا الـ equality عند X أيش
+
+19
+00:01:15,140 --> 00:01:20,390
+بتساوي بتساوي صفر شوف زي ما عملنا المرة الماضية
+
+20
+00:01:20,390 --> 00:01:26,070
+اللي هو E to the X اللي هي لما أخذناها وثبتنا إنها
+
+21
+00:01:26,070 --> 00:01:29,550
+أكبر أو يساوي اللي هي الواحد زائد Alpha X
+
+22
+00:01:29,550 --> 00:01:33,990
+والمساواة if and only if  الـ  يساوي اللي هو واحد الآن see
+
+23
+00:01:33,990 --> 00:01:42,510
+Bernoulli's inequality Bernoulli's inequality اللي
+
+24
+00:01:42,510 --> 00:01:50,040
+هي كما يعني عندي خذ Alpha أكبر من واحد فـ Alpha أكبر 
+
+25
+00:01:50,040 --> 00:01:55,740
+من واحد then لو واحد زائد X to the Alpha أكبر أو يساوي
+
+26
+00:01:55,740 --> 00:02:01,460
+واحد زائد Alpha X لكل X أكبر من ناقص واحد والشغل
+
+27
+00:02:01,460 --> 00:02:05,980
+الثاني إن الـ equality الـ equality بتحدث if and 
+
+28
+00:02:05,980 --> 00:02:13,300
+only if X بتساوي صفر طبعا الآن لو X بتساوي صفر
+
+29
+00:02:13,300 --> 00:02:19,180
+automatically automatically بيصير عندي واحد بيساوي واحد لو
+
+30
+00:02:19,180 --> 00:02:22,920
+X بتساوي صفر Conversely هيطلع من خلال البرهان
+
+31
+00:02:22,920 --> 00:02:27,520
+باقي البرهان نشوف كيف plan approved صلوا على
+
+32
+00:02:27,520 --> 00:02:32,280
+النبي عليه الصلاة والسلام نسجلها الأولى if X
+
+33
+00:02:32,280 --> 00:02:38,780
+بتساوي صفر it is clear that واحد زائد X تقريبا
+
+34
+00:02:38,780 --> 00:02:43,760
+Alpha اللي هي بتساوي واحد بتساوي واحد زائد Alpha X
+
+35
+00:02:43,760 --> 00:02:50,320
+هذه ده case X أيش بتساوي بتساوي صفر طيب الآن بدأ
+
+36
+00:02:50,320 --> 00:02:55,230
+أثبت الـ inequality هذه هأثبت لك في الواقع اللي هو
+
+37
+00:02:55,230 --> 00:02:58,470
+strict inequality أكبر strictly من واحد زائد Alpha
+
+38
+00:02:58,470 --> 00:03:03,190
+X لكل X أكبر من ناقص واحد ولا تساوي صفر في هذه
+
+39
+00:03:03,190 --> 00:03:06,930
+الحالة بيكون أمامنا أثبتنا الاتجاه الثاني طيب،
+
+40
+00:03:06,930 --> 00:03:14,900
+نشوف كيف، الآن خذ X for X أكبر من صفر الآن احنا
+
+41
+00:03:14,900 --> 00:03:17,460
+بنحكي عن تطبيقات للـ Mean Value Theorem إذا أنا 
+
+42
+00:03:17,460 --> 00:03:20,260
+متوقع إن أنا أطبقها الـ Mean Value Theorem طبعا
+
+43
+00:03:20,260 --> 00:03:24,480
+لاحظ إن الـ 1 زائد X to the Alpha هذه اللي هي
+
+44
+00:03:24,480 --> 00:03:27,640
+الدالة اللي بدي استخدمها اللي بتطبق عليها الـ Mean
+
+45
+00:03:27,640 --> 00:03:31,060
+Value Theorem وهذه أصلا is differentiable
+
+46
+00:03:31,060 --> 00:03:36,360
+everywhere it is defined قابلة الاشتقاق لكل X أكبر
+
+47
+00:03:36,360 --> 00:03:41,560
+من ناقص واحد ولكل Alpha أكبر من 100 من 1 ماشي الحال
+
+48
+00:03:41,560 --> 00:03:50,160
+إذا الآن for x أكبر من صفر we apply the mean value
+
+49
+00:03:50,160 --> 00:03:57,400
+theorem on .. مين هو؟ on f of x بيساوي 1 زائد x to
+
+50
+00:03:57,400 --> 00:04:03,340
+the alpha على الـ interval .. on the interval مين هي
+
+51
+00:04:03,340 --> 00:04:07,920
+نتوقع؟ اللي هي صفر و X زي ما عملنا المرة الماضية
+
+52
+00:04:07,920 --> 00:04:12,380
+لأننا مهتمين بمين بالمنطقة 0 و X على أساس إن نحصل
+
+53
+00:04:12,380 --> 00:04:18,260
+على هذه الـ inequality زي ما هنشوف كيف واضح اه؟ إيش
+
+54
+00:04:18,260 --> 00:04:20,400
+الـ mean value theorem بتقول إذا كانت F
+
+55
+00:04:20,400 --> 00:04:23,820
+continuous على هذه و differentiable على الـ open و
+
+56
+00:04:23,820 --> 00:04:30,940
+هذا كله متحقق إذا then there exists C element in 0
+
+57
+00:04:30,940 --> 00:04:41,560
+X such that اللي هو F prime of C بيساوي اللي هو F of
+
+58
+00:04:41,560 --> 00:04:47,840
+X ناقص F of Zero على X minus Zero اللي مضروبة وين
+
+59
+00:04:47,840 --> 00:04:53,820
+وكأنه في X على X minus Zero يعني وكأنه هذه مضروبة
+
+60
+00:04:53,820 --> 00:05:00,260
+في X واضح اه؟ الآن الـ F prime للدالة هذه اللي
+
+61
+00:05:00,260 --> 00:05:03,680
+أخدتها الـ F prime إلها أكيد كلكم بتعرفوا كام إلها
+
+62
+00:05:03,680 --> 00:05:08,800
+على جهة الـ F prime بتحسبها عند مين عند C فبيصير X
+
+63
+00:05:08,800 --> 00:05:15,780
+في الـ F prime إلها Alpha في واحد زائد X أس Alpha
+
+64
+00:05:15,780 --> 00:05:20,440
+ناقص واحد لكن بتحسبها عند مين عند C إذا هذه بتكون
+
+65
+00:05:20,440 --> 00:05:27,340
+C بيساوي اللي هو f of x قد إيش اللي هي واحد زائد x to
+
+66
+00:05:27,340 --> 00:05:30,700
+the alpha وهي اللي بدي إياها أنا f of zero أيش بتساوي
+
+67
+00:05:30,700 --> 00:05:36,400
+f of zero بتساوي واحد ناقص واحد اللي صار عندي إذا
+
+68
+00:05:36,400 --> 00:05:44,260
+اللي هو واحد زائد x to the alpha بيساوي واحد زائد
+
+69
+00:05:44,260 --> 00:05:51,850
+x في Alpha في واحد زائد c أس Alpha ناقص واحد معايا
+
+70
+00:05:51,850 --> 00:06:00,130
+يا شباب هذه سميها واحد واضح
+
+71
+00:06:00,130 --> 00:06:06,770
+اه؟ الآن عندي الـ Alpha أكبر من مين؟ من واحد لأن
+
+72
+00:06:06,770 --> 00:06:12,590
+but Alpha ناقص واحد أكبر من مين؟ من صفر لأن الـ
+
+73
+00:06:12,590 --> 00:06:19,130
+Alpha أكبر من واحد وعندي هذه الـ C أمامها بين الـ
+
+74
+00:06:19,130 --> 00:06:26,650
+0 والـ X يعني أكبر من 0 and C أكبر من 0 إذا صار
+
+75
+00:06:26,650 --> 00:06:37,420
+عندي المقدار هذا 1 زائد C نفسه أكبر من 1 ولما ترفعه
+
+76
+00:06:37,420 --> 00:06:43,080
+لأس موجب، هيظل أكبر من مين؟ و strictly أكبر من
+
+77
+00:06:43,080 --> 00:06:47,660
+واحد، والمساواة بس عند مين، عند الـ C بيساوي صفر،
+
+78
+00:06:47,660 --> 00:06:53,730
+واضح اه؟ طيب الآن صار هذا المقدار أكبر من واحد إذا
+
+79
+00:06:53,730 --> 00:07:00,250
+عندي X موجبة و Alpha موجبة مظبوط ولا لأ لأن X هي
+
+80
+00:07:00,250 --> 00:07:05,790
+أكبر من 0 و Alpha أكبر من 1 إذا أضرب الجهتين في
+
+81
+00:07:05,790 --> 00:07:13,510
+Alpha في X بيصير عندي Alpha في X and so Alpha في X
+
+82
+00:07:13,510 --> 00:07:22,710
+بالضرورة أكبر من مين Alpha X في الـ 1 زي الـ C plus
+
+83
+00:07:22,710 --> 00:07:27,110
+Alpha minus 1 بيبقى أكبر من 100 من Alpha في x
+
+84
+00:07:27,110 --> 00:07:30,670
+واضح اللي سويناه ضربنا Alpha x في الجهتين والـ 
+
+85
+00:07:30,670 --> 00:07:33,890
+Alpha x موجبة ضلت الـ inequality زي ما هي طبعا لا
+
+86
+00:07:33,890 --> 00:07:39,370
+تساوي الصفة بالألف ولا الـ X إذا من 1 ومن 2 we
+
+87
+00:07:39,370 --> 00:07:44,530
+have done from 1
+
+88
+00:07:44,530 --> 00:07:51,270
+and 2 من واحد واثنين بيطلع عندي اللي هو واحد
+
+89
+00:07:51,270 --> 00:07:57,130
+زائد X طول Alpha اللي هو بيساوي المقدار هذا اللي
+
+90
+00:07:57,130 --> 00:08:02,070
+هذا الجزء منه أثبتنا إنه أكبر من مين من Alpha في X
+
+91
+00:08:02,070 --> 00:08:13,800
+لذا صار هذا أكبر من واحد زائد Alpha X أي سؤال؟ إذا
+
+92
+00:08:13,800 --> 00:08:18,120
+في حالة الـ X أكبر من 0 وجدنا الـ 1 زائد X أو أكبر من
+
+93
+00:08:18,120 --> 00:08:25,580
+1 زائد Alpha X لأن هنعمل نفس الشيء بس في الحالة مين؟
+
+94
+00:08:25,580 --> 00:08:32,400
+في حالة الـ X أصغر من 0 وطبعا أكبر من مين؟ من سالب
+
+95
+00:08:32,400 --> 00:08:37,860
+1 إذا بدي اخذ الـ X أكبر من 0 وأكبر من ناقص 1 وأصغر
+
+96
+00:08:37,860 --> 00:08:42,250
+من مين؟ من 0 لاحظ لما تكون X أكبر من ناقص واحد أصغر
+
+97
+00:08:42,250 --> 00:08:46,110
+من صفر برضه نطبق الـ mean value theorem على هذه
+
+98
+00:08:46,110 --> 00:08:53,450
+نفس الدالة الآن on the interval الآن X وصفر
+
+99
+00:08:53,450 --> 00:08:57,850
+لأن X هي مالها الصغيرة على الـ interval X وصفر لأن
+
+100
+00:08:57,850 --> 00:09:03,110
+X سالبة طيب إذا برضه there exists C element الـ
+
+101
+00:09:03,110 --> 00:09:11,000
+mean in X وصفر is نفس البرهان such that X فـ F 
+
+102
+00:09:11,000 --> 00:09:15,000
+prime of C بيساوي F of X ناقص F of Zero نفس الحاجة
+
+103
+00:09:15,000 --> 00:09:19,140
+بيصير الـ X في Alpha في هذا المقدار وهذا المقدار
+
+104
+00:09:19,140 --> 00:09:23,160
+ما تغيرش ولا شيء بيصير واحد زائد X وده Alpha بيساوي
+
+105
+00:09:23,160 --> 00:09:26,360
+واحد زائد X في Alpha في واحد زائد C أس Alpha ناقص
+
+106
+00:09:26,360 --> 00:09:31,560
+واحد الآن بيجي الأسباب هنا الـ Alpha ناقص واحد
+
+107
+00:09:31,560 --> 00:09:36,840
+أمامها أكبر من صفر زي ما هو لكن الـ C الآن اللي
+
+108
+00:09:36,840 --> 00:09:41,110
+لجيناها وين موجودة في المنطقة السالبة ده الـ C أيش
+
+109
+00:09:41,110 --> 00:09:47,830
+هتصير معاينتوش يا بابا هتصير الـ C أصغر من مين من
+
+110
+00:09:47,830 --> 00:09:53,990
+صفر سالبة مدام الـ C سالبة إذا واحد زائد C هتصير
+
+111
+00:09:53,990 --> 00:10:01,310
+أصغر من مين من واحد واحد زائد C أصغر من واحد واضح
+
+112
+00:10:01,310 --> 00:10:09,690
+طيب مدام واحد زائد C أصغر من واحد هيكون عندي and so
+
+113
+00:10:09,690 --> 00:10:19,130
+أضرب الجهتين الآن في اللي هي Alpha Alpha Alpha
+
+114
+00:10:19,130 --> 00:10:22,410
+بتظل زي ما هي لما نضرب في Alpha لأن Alpha إيه
+
+115
+00:10:22,410 --> 00:10:26,370
+معناها موجبة ده لو ضربت في Alpha هنا و Alpha هنا
+
+116
+00:10:26,370 --> 00:10:31,600
+بتظل زي ما هي لأن بدنا نضرب في مين؟ في X و X
+
+117
+00:10:31,600 --> 00:10:37,740
+أمامها سالبة فهتنجلي بالإشارة كمان مرة بيصير and
+
+118
+00:10:37,740 --> 00:10:44,220
+so X في Alpha في واحد زائد C أس Alpha ناقص واحد
+
+119
+00:10:44,220 --> 00:10:51,150
+هتصير أكبر من Alpha في X لأن X سالبة إذا صار عندي
+
+120
+00:10:51,150 --> 00:10:56,590
+هذا المقدار أكبر من هذا لأن من واحد ومن اثنين زي
+
+121
+00:10:56,590 --> 00:11:00,650
+ما عملنا قبل بشوية بتصير المقدار هذا اللي هو أكبر
+
+122
+00:11:00,650 --> 00:11:04,750
+من واحد زائد Alpha X strictly لاحظوا إنه في
+
+123
+00:11:04,750 --> 00:11:11,630
+الجهتين سواء X أكبر من صفر أو أصغر من صفر لجينا إن
+
+124
+00:11:11,630 --> 00:11:16,350
+الـ inequality هذه متحققة أو strictly متحققة
+
+125
+00:11:19,030 --> 00:11:25,190
+الآن المساواة وين صارت؟ عند الصفر فالآن عشان ناخذ
+
+126
+00:11:25,190 --> 00:11:29,090
+بعين الاعتبار الحالة اللي هي x أكبر من ناقص واحد و
+
+127
+00:11:29,090 --> 00:11:33,430
+أصغر من صفر وحالة x أكبر من صفر وحالة x بتساوي
+
+128
+00:11:33,430 --> 00:11:38,870
+صفر بيصير هذا المقدار أكبر أو يساوي لكل x لكل x
+
+129
+00:11:38,870 --> 00:11:43,760
+ماله أكبر من ناقص واحد لأن الاتجاه الثاني من هذا
+
+130
+00:11:43,760 --> 00:11:48,880
+أثبتناه في الواقع إيش هو إنه لو كان فيه equality X
+
+131
+00:11:48,880 --> 00:11:54,280
+بتساوي 0 أو بمعنى آخر X لا تساوي 0 بيعطي إيش
+
+132
+00:11:54,280 --> 00:12:01,720
+أمامها non equality is not equal وهذا حدث كيف حدث
+
+133
+00:12:01,720 --> 00:12:06,240
+أثبتنا إنه لما X أكبر من ناقص واحد وأصغر من 0 أو X
+
+134
+00:12:06,240 --> 00:12:10,720
+أكبر من 0 لجينا إنه هذه strictly أكبر يعني بتساوي
+
+135
+00:12:10,720 --> 00:12:15,260
+hash إذا صار عند الـ equality تحدث if and only if X
+
+136
+00:12:15,260 --> 00:12:22,580
+بساوي صفر أي سؤال؟
+
+137
+00:12:22,580 --> 00:12:30,240
+طيب نيجي الآن نيجي الآن للـ intermediate value of
+
+138
+00:12:30,240 --> 00:12:35,960
+property of derivative خلّيني ألقى في عينتها إذا
+
+139
+00:12:35,960 --> 00:12:42,760
+بتتذكروا في الـ intermediate value of property اللي
+
+140
+00:12:42,760 --> 00:12:46,660
+هو for a continuous function إذا بتذكروا فيه اللي
+
+141
+00:12:46,660 --> 00:12:53,540
+هو real واحد اللي كانت تقول إذا كانت تقول إنه لو 
+
+142
+00:12:53,540 --> 00:13:01,880
+كانت الـ F function continuous على a closed open على
+
+143
+00:13:01,880 --> 00:13:07,020
+closed interval من A لعند B continuous على الفترة
+
+144
+00:13:07,020 --> 00:13:16,060
+هذهو إجيت أخدت أي نقطة K بين الـ F of A و بين الـ F
+
+145
+00:13:16,060 --> 00:13:22,900
+of B إجيت أخدت أي نقطة .. خد مثلا نقطة K بين F of
+
+146
+00:13:22,900 --> 00:13:31,240
+A .. هي F of A و هي F of B .. هي F of A و هي F of 
+
+147
+00:13:31,240 --> 00:13:36,540
+B لو إجيت أخدت أي K بينهم هتلاقي .. هو خلي ناخد K
+
+148
+00:13:36,540 --> 00:13:43,830
+هنا مثلاهتلاقي على الأقل نقطة في الفترة A وB بتكون
+
+149
+00:13:43,830 --> 00:13:49,890
+اللي هو صورتها عبارة عن مين؟ عن الـ K يعني بمعنى
+
+150
+00:13:49,890 --> 00:13:55,970
+آخر there exists C element in A و B such that F of
+
+151
+00:13:55,970 --> 00:14:01,050
+C هي مين الـ K و لا أصلا مش هتلاقيها continuous لو
+
+152
+00:14:01,050 --> 00:14:05,530
+مافشلها فئلة و جينا مدينا خطنا هلجيت و مالجيناش
+
+153
+00:14:05,530 --> 00:14:09,290
+ولا واحدة من هذه النقاط اللي هو تقطع الخط معناته
+
+154
+00:14:09,290 --> 00:14:14,410
+أنه صار فيه jump مش هيكون في continuity الان هنا مش
+
+155
+00:14:14,410 --> 00:14:19,890
+في نقطة هي نقطة هي نقطتين هي تلاتة كلهم صورتين هي
+
+156
+00:14:19,890 --> 00:14:27,610
+C1 هي C2 هي C3 كلهم F of C1 K F of C2 K F of C3 K
+
+157
+00:14:27,610 --> 00:14:33,150
+المهم على الأقل في C element in A وB اللي هي بحيث
+
+158
+00:14:33,150 --> 00:14:36,210
+F of C بالساوة K هذا لو كان اتقفز continuous على
+
+159
+00:14:36,210 --> 00:14:40,650
+closed اللي هي bounded interval اللي عندك الآن
+
+160
+00:14:43,230 --> 00:14:47,090
+الحديث بيقول لي في شيء مشابه في حالة أن الـ F' is
+
+161
+00:14:47,090 --> 00:14:53,950
+differentiable الآن بيقولك لو كانت K بين الـ F' لل
+
+162
+00:14:53,950 --> 00:14:58,970
+A و الـ F' لل B برضه هنلاقيها بتتحقق اللي هو there
+
+163
+00:14:58,970 --> 00:15:03,810
+exists C بحيث أن F prime of C بتساوي اللي هو الـ K
+
+164
+00:15:03,810 --> 00:15:10,530
+نحكي عنها بالرغم أنه مش مفترضين احنا في النظرية
+
+165
+00:15:10,530 --> 00:15:14,190
+اللي هو الـ continuity الـ continuity للـ F prime
+
+166
+00:15:16,020 --> 00:15:19,360
+فضبجنا على الـ F' لكن مش .. لأنهم افترضينا على طول
+
+167
+00:15:19,360 --> 00:15:22,300
+تتطبق الـ Intermediate Value Theorem بس على الدالة
+
+168
+00:15:22,300 --> 00:15:26,980
+الـ F' لكن لأ ما هو مخزون في دالة .. خلال الـ F'
+
+169
+00:15:27,380 --> 00:15:33,140
+من معلومات أهلها أنه في حالة F is differentiable
+
+170
+00:15:33,140 --> 00:15:37,940
+على الـ interval I و الـ F ب .. و لجينا .. وفي عندي
+
+171
+00:15:37,940 --> 00:15:43,120
+أخدت أي K بين الـ F' of A و الـ F' of B هتلاقي C
+
+172
+00:15:43,120 --> 00:15:48,380
+في الـ A و الـ B بحيث انه اللي هي F' of C هي هذه
+
+173
+00:15:48,380 --> 00:15:51,920
+الـ K هنشوفها هذه اللي بنسميها Daraboxes theorem
+
+174
+00:15:51,920 --> 00:15:55,980
+قبل ما نروح للـ Daraboxes theorem خلينا نيجي لللمة
+
+175
+00:15:55,980 --> 00:16:00,680
+اللي جابلة اللي هنستخدمها في إثبات الـ Daraboxes
+
+176
+00:16:00,680 --> 00:16:07,340
+theorem الآن النظرية هذه أو اللمّة هذه اللي هو
+
+177
+00:16:07,340 --> 00:16:10,880
+خلّينا نستذكرها من خلال الرسم ممكن يكون أسهل لكم
+
+178
+00:16:10,880 --> 00:16:16,680
+من خلال الرسم بتقولّي إنه لو كانت عندنا function F
+
+179
+00:16:16,680 --> 00:16:22,300
+is differentiable على اللي هو interval معينة
+
+180
+00:16:22,300 --> 00:16:29,120
+و لجينا عند C معينة هي F prime عند C موجبة F prime
+
+181
+00:16:29,120 --> 00:16:33,940
+عند C موجبة يعني F prime at some C أكبر من 0 يعني
+
+182
+00:16:33,940 --> 00:16:37,160
+مين المماس إيه اللي شماله اللي هو زاوية حادة عامل
+
+183
+00:16:37,160 --> 00:16:43,660
+زاوية حادة ماشي الآن بقولي هتلاقي الآن بده يبحث عن
+
+184
+00:16:43,660 --> 00:16:49,260
+نقاط تكون أكبر من مين من F of C الآن هتلاقي اللي
+
+185
+00:16:49,260 --> 00:16:56,370
+هو هذا C اللي بتحكي عنها وهنا اللي هو في جوار حوالي
+
+186
+00:16:56,370 --> 00:16:59,410
+هذين there exist إذا كان f of rank of c أكبر من
+
+187
+00:16:59,410 --> 00:17:03,630
+صفر there exists delta أكبر من صفر such that f of
+
+188
+00:17:03,630 --> 00:17:11,960
+x هنلاقيها أكبر من F of C لكل X وين متوقع أنا هان
+
+189
+00:17:11,960 --> 00:17:17,300
+لإنها الميل هيه إذا في الوين عشان C ل C زائد Delta
+
+190
+00:17:17,300 --> 00:17:19,620
+مش في الفترة اللي جابلة، في الفترة اللي جابلة
+
+191
+00:17:19,620 --> 00:17:23,960
+هتلاقي اللي هي النقطات أشملها أجل لأنا الآن ببحث
+
+192
+00:17:23,960 --> 00:17:29,420
+.. ببحث لم تبعت هيك بدها اللي هو there exist دلتا
+
+193
+00:17:29,420 --> 00:17:32,120
+أكبر من صفر ساشداد F of X أكبر من F of C لكل X
+
+194
+00:17:32,120 --> 00:17:40,200
+و اللي موجود من الـ C للـ C زائد دلتا معايا؟ الآن
+
+195
+00:17:40,200 --> 00:17:47,320
+بقولك لو لجينا F prime للـ C عند نقطة ما F prime
+
+196
+00:17:47,320 --> 00:17:54,130
+للـ C هي الـ C التانية لو لجينا F prime للـ C أصغر
+
+197
+00:17:54,130 --> 00:17:57,210
+من صفر عشان .. عشان ما تحفظهاش حفظ عشان لو انسيتها
+
+198
+00:17:57,210 --> 00:18:00,890
+تستنتجها لحالك لو كان F' للـ C أصغر من صفر يعني ميل
+
+199
+00:18:00,890 --> 00:18:06,710
+المماس سلب يعني زاوية منفرجة الآن هتلاقي Delta
+
+200
+00:18:06,710 --> 00:18:13,360
+أكبر من صفر يعني تمثل جوار بحيث أن F of X برضه أكبر
+
+201
+00:18:13,360 --> 00:18:19,000
+من F of C لكل X وين موجودة هي وارحة منها لكل X
+
+202
+00:18:19,000 --> 00:18:24,340
+موجودة وين جابلها من C نقص دلتة لعند مين؟ لعند C
+
+203
+00:18:24,340 --> 00:18:29,800
+من C نقص دلتة لعند C هذه بس اللممة للاستذكار، إيش
+
+204
+00:18:29,800 --> 00:18:32,780
+بتقول اللممة؟ تعالى نشوف بالظبط اللي بتقوله اللي
+
+205
+00:18:32,780 --> 00:18:36,220
+حكيته أنا بقول اللممة let I subset من R be an
+
+206
+00:18:36,220 --> 00:18:40,260
+interval and let F من I ل R و let C element in I
+
+207
+00:18:40,260 --> 00:18:44,700
+and assume that F has a derivative at C نفترض أن
+
+208
+00:18:44,700 --> 00:18:50,120
+الـ F الهياشق مشتقة عند النقطة C مقولي إذا F prime
+
+209
+00:18:50,120 --> 00:18:54,200
+أكبر من 0 عند الـ C هاي اللي قلته هان إذا يوجد
+
+210
+00:18:54,200 --> 00:18:58,500
+دلتة أكبر من 0 بحيث أن F of X أكبر من F of C لكل
+
+211
+00:18:58,500 --> 00:19:02,560
+الـ X وين موجودة بين الـ C و C زائد دلتة اللي هي
+
+212
+00:19:02,560 --> 00:19:03,280
+الجبل هنا
+
+213
+00:19:06,510 --> 00:19:10,590
+الثانية، إذا كانت F' أصغر من 0، حلاقي Delta بحيث
+
+214
+00:19:10,590 --> 00:19:15,430
+أن F of C أصغر واحدة في الجوار، يعني F of C أو في
+
+215
+00:19:15,430 --> 00:19:19,010
+الجزء من الجوار، هذا الجزء اللي لجاي، F of C أصغر
+
+216
+00:19:19,010 --> 00:19:24,370
+من F of X، وين هاي الـ F of X هنا؟ أكبر من F of C،
+
+217
+00:19:24,370 --> 00:19:29,870
+واضح؟ لكل X وين موجودة في الـ C minus Delta و الـ C
+
+218
+00:19:31,220 --> 00:19:36,360
+أي سؤال البرهن هو A خلّينا نبرهن به نحنا به
+
+219
+00:19:36,360 --> 00:19:40,980
+خلّينا نبرهن مع بعض به
+
+220
+00:19:40,980 --> 00:19:46,840
+الآن
+
+221
+00:19:46,840 --> 00:19:53,820
+بدنا نقول نفترض أن F برايم به
+
+222
+00:19:53,820 --> 00:20:02,190
+approved الآن ماعطينا F برايم of C أصغر من صفر،
+
+223
+00:20:02,190 --> 00:20:11,750
+مظبوط؟ لأن بتقول since f prime of c أصغر من صفر
+
+224
+00:20:11,750 --> 00:20:21,070
+then limit f of x ناقص f of c على x minus c لما x
+
+225
+00:20:21,070 --> 00:20:27,540
+تروح لل c إشماله أصغر من صفر ماشي، مدام أصغر من صفر
+
+226
+00:20:27,540 --> 00:20:31,080
+عند .. قلنا قبل هيك في نظرية إذا كان اللي هو
+
+227
+00:20:31,080 --> 00:20:35,600
+المقدار هذا أصغر من صفر إذا بقدر ألاقي جوار
+
+228
+00:20:35,600 --> 00:20:41,240
+حواليها بتكون القيم كلها إشمالها أصغر من صفر إذا
+
+229
+00:20:41,240 --> 00:20:48,560
+then there exist V Delta of C اللي هو جوار جوار من
+
+230
+00:20:48,560 --> 00:20:55,260
+عند C minus Delta لعند C زائد Delta ماشي؟ اللي هو
+
+231
+00:20:55,260 --> 00:20:58,980
+احنا أخدناها من هذا المنطقة من C نقص دلتا ل C زائد
+
+232
+00:20:58,980 --> 00:21:06,700
+دلتا such that اللي هو F of X نقص F of C على X
+
+233
+00:21:06,700 --> 00:21:16,220
+minus C أصغر من صفر لكل X وين في V دلتا of C أنا
+
+234
+00:21:16,220 --> 00:21:22,300
+غرضي أني أخلي اللي هو أوجد mean أن F of X أكبر من
+
+235
+00:21:22,300 --> 00:21:25,900
+F of C بدا وجد المنطقة اللي بتكون فيها F of
+
+236
+00:21:25,900 --> 00:21:31,880
+X أكبر من مين من F of C لاحظ انه هذا بديها وكأن F
+
+237
+00:21:31,880 --> 00:21:36,480
+of X ناقص F of C بديها أكبر من 0 صح عشان أحصل F of
+
+238
+00:21:36,480 --> 00:21:40,420
+X أكبر من مين من F of C لذن عشان أحصل على هذا
+
+239
+00:21:40,420 --> 00:21:45,000
+المقدار أكبر من 0 و أنا بعرف ان هذا كله أصغر من 0
+
+240
+00:21:45,000 --> 00:21:48,880
+بدي المنطقة هذه تكون أصغر من 0 وين هتكون أصغر من
+
+241
+00:21:48,880 --> 00:21:57,510
+0؟ في المنطقة هذه، ماشي الحال؟ الآن but for every x
+
+242
+00:21:57,510 --> 00:22:05,650
+element in c نقص delta و c ال x minus c أصغر من
+
+243
+00:22:05,650 --> 00:22:15,800
+صفر واضحة؟ إذن الآن من هذه و من هذه hence F of X
+
+244
+00:22:15,800 --> 00:22:23,300
+ناقص F of C اللي هي بتساوي X minus C في F of X
+
+245
+00:22:23,300 --> 00:22:30,300
+ناقص F of C على X minus C هذا سالب وهذا سالب لذا
+
+246
+00:22:30,300 --> 00:22:35,260
+حصل ضرب بين أشماله هكون أكبر من صفر سالب في سالب
+
+247
+00:22:35,260 --> 00:22:42,720
+موجه مظبوط لهذا الكلام لكل X وين موجودة في الـ C
+
+248
+00:22:43,730 --> 00:22:52,150
+- Delta OC وهذا معنى أن F of X أكبر من F of C لنقطة
+
+249
+00:22:52,150 --> 00:22:59,950
+المذكورة لنقات المذكورة واضح؟ أي سؤال؟ نيجي الآن
+
+250
+00:22:59,950 --> 00:23:04,930
+اللي هو انبرهن الـ Drabowski's theorem اللي حكينا
+
+251
+00:23:04,930 --> 00:23:08,350
+عنها وقدمنا لها قبل بشوية إيش الـ Drabowski's
+
+252
+00:23:08,350 --> 00:23:15,010
+theorem بتقول أنه عندي الـ F هو مستخدم للتحدي في بعض
+
+253
+00:23:15,010 --> 00:23:19,250
+الانترالين
+
+254
+00:23:19,250 --> 00:23:19,950
+A و B
+
+255
+00:23:23,800 --> 00:23:29,540
+اللي هي أي K بين F' و F'
+
+256
+00:23:32,040 --> 00:23:36,580
+of A و F' of B إذا نحن نلاقي الـ C بقيت أن F' of C
+
+257
+00:23:36,580 --> 00:23:42,020
+هي الـ K كمان مرة Drabowski's theorem بتقول if F
+
+258
+00:23:42,020 --> 00:23:47,520
+is differentiable on A و B و if K is any number
+
+259
+00:23:47,520 --> 00:23:53,610
+between F' of A و F' of B then there exists at
+
+260
+00:23:53,610 --> 00:23:56,350
+least one point C في الـ A و الـ B بحيث أن الـ Alpha
+
+261
+00:23:56,350 --> 00:24:02,650
+Prime of C أيش بتساوي؟ بتساوي K ماشي يا شباب طيب
+
+262
+00:24:02,650 --> 00:24:06,890
+اللي زي ما علقنا قبل بشوية بالرغم إنه إحنا ماحدش
+
+263
+00:24:06,890 --> 00:24:11,810
+جاب سيرة إن الـ Alpha Prime هتكون continuous لأ،
+
+264
+00:24:11,810 --> 00:24:16,310
+قلنا ما في الـ F' من مخزون، derivative من مخزون في
+
+265
+00:24:16,310 --> 00:24:21,530
+داخلنا المعلومات أهلها إنها تقدر تصل أنه لأي K بين
+
+266
+00:24:21,530 --> 00:24:27,190
+الـ F A و الـ F' A و الـ F' B بالـ Legacy، بحيث أن
+
+267
+00:24:27,190 --> 00:24:31,170
+F' اللي عند الـ C هي الـ K. إيه المرحلة دلوقتي؟
+
+268
+00:24:31,170 --> 00:24:41,150
+شوف، نفترض أنه Proof نفترض أن G of A أصغر من K أصغر
+
+269
+00:24:41,150 --> 00:24:52,230
+من مين من G أو F prime of A أصغر من F prime of B
+
+270
+00:24:52,230 --> 00:24:56,450
+ماشي الحال واضح
+
+271
+00:24:56,450 --> 00:25:02,430
+هذا فرضناه الآن بدنا نلاقي C بحيث انه F' للـ C هو
+
+272
+00:25:02,430 --> 00:25:06,530
+الـ K الآن define هالجيه تعرف ليش اعرفت defining
+
+273
+00:25:06,530 --> 00:25:15,590
+function G of X بساوي K في الـ X ناقص F of X عندي
+
+274
+00:25:15,590 --> 00:25:18,790
+اللي هي هذه الدالة هي الدالة اللي هتوصلني للي
+
+275
+00:25:18,790 --> 00:25:23,800
+بديها الآن واضح أن الـ g of x بيساوي kx ناقص f of x
+
+276
+00:25:23,800 --> 00:25:29,660
+أنها differentiable اللي هو هذه وين ما كان و هذه
+
+277
+00:25:29,660 --> 00:25:32,080
+differentiable على ال I إذا صار أن التنتين
+
+278
+00:25:32,080 --> 00:25:35,960
+differentiable على مين؟ على ال A و ال B و طبيعي
+
+279
+00:25:35,960 --> 00:25:40,440
+continuous على ال A و ال B إذا بما أن هذا الدالة
+
+280
+00:25:40,440 --> 00:25:44,440
+is continuous على closed bounded interval then it
+
+281
+00:25:44,440 --> 00:25:47,580
+attains its maximum and its minimum on this
+
+282
+00:25:47,580 --> 00:25:51,870
+interval بتشتغل عليه ال maximum و لو حد بده
+
+283
+00:25:51,870 --> 00:25:58,670
+يشتغل عليه المنهج ما بنفع برضه الآن then g of x
+
+284
+00:25:58,670 --> 00:26:09,810
+attains its maximum on mean on a و b لأن إيش اللي
+
+285
+00:26:09,810 --> 00:26:15,370
+بيثبت لك هي بيثبت لك إن الـ G هيكون ال maximum
+
+286
+00:26:15,370 --> 00:26:21,150
+إلها لا عند ال A ولا عند ال B إذا هتكون وين؟ في
+
+287
+00:26:21,150 --> 00:26:25,870
+نقطة داخلية مدام في نقطة داخلية وإحنا عارفين إن
+
+288
+00:26:25,870 --> 00:26:29,490
+الـ G differentiable على كل المنطقة هذه إذا صارت
+
+289
+00:26:29,490 --> 00:26:33,050
+غصب عني إنه لازم مدام عندها maximum و interior
+
+290
+00:26:33,050 --> 00:26:38,390
+point إذا الـ G prime إيش هتساوي؟ هتساوي 0 واضح؟
+
+291
+00:26:38,390 --> 00:26:42,590
+مدام جي برايم ما هتساوي صفر هتصير ال F prime of X
+
+292
+00:26:42,590 --> 00:26:46,550
+ال F of some C بتساوي ال K و بيكون خلصنا البرهان
+
+293
+00:26:46,550 --> 00:26:49,950
+تشوفوا اللي بقوله طيب صلوا على النبي عليه الصلاة
+
+294
+00:26:49,950 --> 00:27:05,390
+والسلام الآن عندي ال G prime of X هتساوي K ناقص F
+
+295
+00:27:05,390 --> 00:27:11,520
+prime of مين؟ of X صح ولا لأ؟ طيب الآن لو جينا
+
+296
+00:27:11,520 --> 00:27:21,540
+حسبنا الـ G' عند ال A إيش هتلاقيها؟ K ناقص F' عند
+
+297
+00:27:21,540 --> 00:27:28,740
+مين؟ عند ال A صح ولا لأ؟ K ناقص F' عند ال A هتكون
+
+298
+00:27:28,740 --> 00:27:35,260
+أكبر من مين؟ من 0 واضح مدام ال G' على ال A أكبر من
+
+299
+00:27:35,260 --> 00:27:35,520
+0
+
+300
+00:27:39,110 --> 00:27:49,430
+K-F' أكبر من صفر بما أن J' بسوء K-F' أكبر من صفر
+
+301
+00:27:49,430 --> 00:27:53,450
+يعني هذا أكبر من صفر حسب اللي قبل قليل حكينا عنها
+
+302
+00:27:53,450 --> 00:28:06,330
+ثم هناك دلتا أكبر من صفر such that G' of X أكبر من
+
+303
+00:28:06,330 --> 00:28:13,400
+G of A اللي كنا بسمينا C فاهمين عليها الـ G of X
+
+304
+00:28:13,400 --> 00:28:22,800
+أكبر من G of A for every X element in متذكرين اللي
+
+305
+00:28:22,800 --> 00:28:27,480
+قبل بشوية لما كانت جي برايم لما كانت الجي برايم
+
+306
+00:28:27,480 --> 00:28:32,860
+أكبر من صفر كانت اللي هي وين لجاي X element لغاية
+
+307
+00:28:32,860 --> 00:28:40,920
+أسف X element in C اللي هي A هنا و A زائد دلتا اللي 
+
+308
+00:28:40,920 --> 00:28:45,240
+ما اللي قبل بشوية إذا صارت عند جي of X أكبر من 
+
+309
+00:28:46,010 --> 00:28:50,890
+من الـ G of A واضح لمين؟ لكل الإكسات اللي هي في نص
+
+310
+00:28:50,890 --> 00:28:57,290
+الجوار هذا صارت عندي اللي هي الـ G of A مش maximum
+
+311
+00:28:57,290 --> 00:29:08,650
+لأن في قيم أكبر منها واضح؟ إذا أكيد then G does
+
+312
+00:29:08,650 --> 00:29:18,150
+not have a maximum at A إذا الفش مش maximum عند
+
+313
+00:29:18,150 --> 00:29:23,990
+مين؟ عند الـ A أي
+
+314
+00:29:23,990 --> 00:29:27,750
+سؤال؟
+
+315
+00:29:27,750 --> 00:29:36,990
+Similarly .. Similarly G' عند ال B معايا يا شباب
+
+316
+00:29:36,990 --> 00:29:44,340
+G' عند ال B بيساوي K نقص F' عند ال B و K ناقص F
+
+317
+00:29:44,340 --> 00:29:49,840
+prime عند الـ B أصغر من مين؟ أصغر من 0 إذا بنفس
+
+318
+00:29:49,840 --> 00:29:54,600
+اللّمة بس على الجهة الثانية then there exists
+
+319
+00:29:54,600 --> 00:30:01,000
+Delta أكبر من 0 such that G of X أكبر من G of B
+
+320
+00:30:01,000 --> 00:30:11,520
+لكل X وان الآن من عند B ناقص Delta لعند الـ B صح؟
+
+321
+00:30:12,880 --> 00:30:19,600
+وهنا end points هذول فمش هتكون برضه مين ال b مش
+
+322
+00:30:19,600 --> 00:30:24,940
+هتكون عندها maximum لأنه منها ولا جوا ال b end
+
+323
+00:30:24,940 --> 00:30:28,920
+point منها ولا جوا ال g of x أكبر من ال g of b إذن
+
+324
+00:30:28,920 --> 00:30:38,160
+مش maximum إذن hence g does not have a maximum at
+
+325
+00:30:38,160 --> 00:30:45,380
+b from هنا و from هنا from here and here we have g
+
+326
+00:30:45,380 --> 00:30:48,700
+has
+
+327
+00:30:48,700 --> 00:31:00,180
+the maximum inside a و b، مظبوط؟ يعني بمعنى آخر،
+
+328
+00:31:00,180 --> 00:31:06,100
+مدام احنا أكيد attained its maximum there exists c
+
+329
+00:31:06,100 --> 00:31:13,970
+element in a و b such that جي هز ا maximum مدام جي
+
+330
+00:31:13,970 --> 00:31:18,770
+هز ا maximum و interior point إذا جي برايم عند ال
+
+331
+00:31:18,770 --> 00:31:23,390
+C إيش بتساوي؟ بتساوي صفر مدام جي برايم عند ال C
+
+332
+00:31:23,390 --> 00:31:28,090
+بتساوي صفر إذا صار عندي hence
+
+333
+00:31:30,200 --> 00:31:33,960
+وهنا اكتب جي برايم عند الـ C إيش بيساوي؟ بيساوي
+
+334
+00:31:33,960 --> 00:31:39,120
+صفر إيش جي برايم بيساوي؟ K ناقص F برايم إذا that
+
+335
+00:31:39,120 --> 00:31:43,020
+is K
+
+336
+00:31:43,020 --> 00:31:50,510
+إن هي بدل جي برايم ناقص F' عند C بيساوي صفر أو بمعنى
+
+337
+00:31:50,510 --> 00:31:57,090
+آخر F' عند C إيش بيساوي؟ بيساوي K فعلا لقينا C في ال
+
+338
+00:31:57,090 --> 00:32:02,770
+A و ال B بحيث أن F' عند C إيش بتساوي؟ بيساوي K كما
+
+339
+00:32:02,770 --> 00:32:13,170
+هو مطلوب هيها أي سؤال الآن
+
+340
+00:32:14,940 --> 00:32:21,600
+عندي المثال الأخير بقول لي use Darboux's theorem
+
+341
+00:32:21,600 --> 00:32:25,120
+هو في الواقع مثال على Darboux's theorem بقول لي
+
+342
+00:32:25,120 --> 00:32:32,060
+the function g من
+
+343
+00:32:32,060 --> 00:32:36,080
+ناقص واحد و واحد لعند ال R defined by معرفة g of x
+
+344
+00:32:36,080 --> 00:32:39,320
+إيش بيساوي واحد إذا كانت x أكبر من صفر وأصغر
+
+345
+00:32:39,320 --> 00:32:43,680
+بساوى واحد 0 إذا كانت X بيساوي واحد و ناقص واحد إذا
+
+346
+00:32:43,680 --> 00:32:46,180
+كانت X أكبر من ناقص و أكبر بيساوي ناقص واحد و
+
+347
+00:32:46,180 --> 00:32:52,360
+بيساوي صفر بقول لي أثبت أن هذه الدالة is not the
+
+348
+00:32:52,360 --> 00:32:57,160
+derivative is not a derivative of any function
+
+349
+00:32:57,160 --> 00:33:01,580
+يعني مافيش function في الدنيا بتكون مشتقتها هي هذه
+
+350
+00:33:01,580 --> 00:33:06,420
+الـ G هذه الـ G is not a derivative of any function
+
+351
+00:33:07,400 --> 00:33:10,800
+نبدا نقول suppose not ونصل لـ contradiction ماشي
+
+352
+00:33:10,800 --> 00:33:15,440
+الحال إذا الآن ال
+
+353
+00:33:15,440 --> 00:33:27,280
+... النظرية ... ال ... المثال بقول mainly المثال
+
+354
+00:33:27,280 --> 00:33:35,540
+بقول example example show that
+
+355
+00:33:38,010 --> 00:33:47,490
+G من ناقص واحد لعند الواحد لعند ال R Defined by G
+
+356
+00:33:47,490 --> 00:33:53,610
+of X بيساوي واحد إذا كانت X أكبر من صفر وأصغر يساوى
+
+357
+00:33:53,610 --> 00:33:59,290
+واحد صفر X بتساوي صفر ناقص واحد X أكبر يساوى ناقص
+
+358
+00:33:59,290 --> 00:34:08,330
+واحد وأصغر من صفر is not a derivative of any
+
+359
+00:34:08,330 --> 00:34:20,610
+function on ناقص واحد واحد solution أو proof اللي
+
+360
+00:34:20,610 --> 00:34:25,930
+قاعد تقول suppose that
+
+361
+00:34:25,930 --> 00:34:36,550
+there exist f من ناقص واحد واحد لعند ال R such that
+
+362
+00:34:36,550 --> 00:34:46,630
+f prime of x بيساوي g of x لكل x element ناقص واحد
+
+363
+00:34:46,630 --> 00:34:51,870
+و واحد ماشي الحال إيش هذه الدالة هي في الواقع
+
+364
+00:34:51,870 --> 00:34:59,310
+الدالة هي ال g of x هذه عندي صفر و أنا عند الواحد
+
+365
+00:34:59,310 --> 00:35:04,550
+عند الواحد و أنا سالب واحد
+
+366
+00:35:07,910 --> 00:35:16,170
+لعند اللي هو سنة واحد هيدّه ده اه لأن افترض انه F
+
+367
+00:35:16,170 --> 00:35:19,130
+بين ناقص واحد واحد such that F prime of X بيساوي G
+
+368
+00:35:19,130 --> 00:35:22,650
+of X واضح انه F is differentiable مدةن اذا قلت F prime
+
+369
+00:35:22,650 --> 00:35:25,390
+of X بيساوي G of X لكل X اللي من ناقص واحد واحد
+
+370
+00:35:25,390 --> 00:35:30,070
+صارت ال F إيش مالها is differentiable مظبوط ولا لأ
+
+371
+00:35:30,070 --> 00:35:39,050
+is differentiable و اثنين لأن but النص ينتبه إلى
+
+372
+00:35:39,050 --> 00:35:43,850
+الفترة ناقص واحد و واحد اللي هي إيش بتساوي؟ اللي هي
+
+373
+00:35:43,850 --> 00:35:50,590
+عبارة عن الفترة هذه عبارة عن اللي هي F prime of
+
+374
+00:35:50,590 --> 00:36:03,650
+ناقص واحد و F prime of واحد واضح
+
+375
+00:36:03,650 --> 00:36:13,290
+اه؟ هذه F' هي مين؟ G صح ولا لا؟ فمين؟ وهذه إيه؟ F'
+
+376
+00:36:13,550 --> 00:36:21,810
+G لأن G of واحد واحد، G of ناقص واحد ونص في الفترة
+
+377
+00:36:21,810 --> 00:36:22,170
+هذه
+
+378
+00:36:25,820 --> 00:36:30,060
+أصلًا كل قيم الـ F' أو الـ G هي واحد صفر و ناقص واحد
+
+379
+00:36:30,060 --> 00:36:34,360
+هذا هيسبب لك الخلل مش نص بس تقدر تختار ربع تلت خمس
+
+380
+00:36:34,360 --> 00:36:38,680
+أي حاجة غير الـ Zero و الواحد و السالب واحد إيش ال
+
+381
+00:36:38,680 --> 00:36:49,400
+... إيش الشد في الأمر but نص element كده and D
+
+382
+00:36:49,400 --> 00:37:00,740
+F is differentiable on ناقص واحد واحد صح؟ then by
+
+383
+00:37:00,740 --> 00:37:09,800
+Darboux's theorem there exist c element ناقص واحد
+
+384
+00:37:09,800 --> 00:37:19,200
+و واحد such that اللي هو g of c أو f prime of c
+
+385
+00:37:19,200 --> 00:37:28,990
+بيساوي إيش؟ نص صح؟ i.e بمعنى آخر F prime of C اللي هو
+
+386
+00:37:28,990 --> 00:37:39,590
+G of C بيساوى نص Which is impossible Therefore
+
+387
+00:37:39,590 --> 00:37:46,480
+our first assumption is not true that is there is
+
+388
+00:37:46,480 --> 00:37:50,740
+no F من ناقص واحد لعند واحد ... من واحد ناقص واحد
+
+389
+00:37:50,740 --> 00:37:54,960
+لواحد لعند ال R بحيث أن F' بيساوي G أو بمعنى آخر G
+
+390
+00:37:54,960 --> 00:38:03,680
+is not a derivative of any function وهكذا
+
+391
+00:38:03,680 --> 00:38:07,780
+نكون خلصنا ستة اثنين والمرة اللي جاي إن شاء الله
+
+392
+00:38:07,780 --> 00:38:13,980
+بنكمل في ستة ثلاثة ويوم الأحد القادم بنناقش ستة
+
+393
+00:38:13,980 --> 00:38:16,010
+اثنين أسئلة 6
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..833cd04edb2a161577d50c1e051c277c45fc138b
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3065, "start": 4.89, "end": 30.65, "text": "بسم الله الرحمن الرحيم الان نتحدث عن الجزء الثاني من المحاضرة الخامسة لطلبة قسم رياضيات في كلية العلوم بالجامعة الإسلامية بغزا الجزء الثاني طبعا زي ما وعدناكم في البداية قلنا اللي هو هنكمل فيه اللي هو 6 اتنين اللي هي تطبيقات على ال mean value theorem او applications on mean value theorem هيكون في عندنا two applications", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 2423, 7649, 8717, 2655, 24401, 12984, 18871, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 9673, 5016, 46958, 25720, 33962, 10943, 3794, 3660, 5296, 9566, 46152, 3660, 12174, 38251, 12602, 1829, 46958, 1829, 9307, 8978, 28242, 10632, 18863, 1211, 20498, 20666, 7435, 10943, 27884, 33688, 3794, 37440, 10632, 4724, 17082, 11622, 995, 25724, 11622, 38207, 6024, 104, 7649, 1829, 23032, 3555, 3615, 995, 30767, 1829, 19446, 4032, 22488, 8315, 24793, 8978, 29739, 28259, 10632, 12174, 1211, 8315, 13672, 1829, 31439, 8032, 1863, 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50.45, "text": "اللي هو الـ Application الأول على الـ Mean Value Theorem هو عبارة عن اللي هو Bernoulli's Inquality، هنبرهن Bernoulli's Inquality، و بعدين هنتحدث عن اللي هو Daraboux's Theorem، تشوف كيف اللي هو بيصير الأمور، نبدأ الآن في الجزء الأول، اللي هو", "tokens": [6027, 20292, 31439, 2423, 39184, 39512, 16247, 12610, 15844, 2423, 39184, 12302, 39352, 440, 37956, 31439, 6225, 3555, 9640, 3660, 18871, 13672, 1829, 31439, 10781, 263, 16320, 311, 682, 11286, 12399, 8032, 1863, 26890, 3224, 1863, 10781, 263, 16320, 311, 682, 11286, 12399, 4032, 39182, 9957, 8032, 29399, 24401, 12984, 18871, 13672, 1829, 31439, 7803, 455, 30209, 311, 440, 37956, 12399, 6055, 8592, 38688, 9122, 33911, 13672, 1829, 31439, 4724, 1829, 9381, 13546, 16247, 2304, 13063, 12399, 8717, 44510, 10721, 6024, 48506, 8978, 25724, 11622, 38207, 16247, 12610, 12399, 13672, 1829, 31439], "avg_logprob": -0.24462365655488866, "compression_ratio": 1.6713615023474178, "no_speech_prob": 5.543231964111328e-06, "words": 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0.984375}, {"start": 42.01, "end": 42.15, "word": " هو", "probability": 0.98681640625}, {"start": 42.15, "end": 42.79, "word": " Daraboux's", "probability": 0.550323486328125}, {"start": 42.79, "end": 43.69, "word": " Theorem،", "probability": 0.7911783854166666}, {"start": 43.69, "end": 44.21, "word": " تشوف", "probability": 0.7232259114583334}, {"start": 44.21, "end": 44.67, "word": " كيف", "probability": 0.95703125}, {"start": 44.67, "end": 44.95, "word": " اللي", "probability": 0.927490234375}, {"start": 44.95, "end": 45.31, "word": " هو", "probability": 0.98583984375}, {"start": 45.31, "end": 46.77, "word": " بيصير", "probability": 0.888427734375}, {"start": 46.77, "end": 47.37, "word": " الأمور،", "probability": 0.9283447265625}, {"start": 47.37, "end": 47.69, "word": " نبدأ", "probability": 0.8331705729166666}, {"start": 47.69, "end": 48.05, "word": " الآن", "probability": 0.783203125}, {"start": 48.05, "end": 48.57, "word": " في", "probability": 0.91064453125}, {"start": 48.57, "end": 48.95, "word": " الجزء", "probability": 0.9573567708333334}, {"start": 48.95, "end": 49.85, "word": " الأول،", "probability": 0.9361979166666666}, {"start": 49.85, "end": 50.19, "word": " اللي", "probability": 0.82080078125}, {"start": 50.19, "end": 50.45, "word": " هو", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 3, "seek": 7730, "start": 50.84, "end": 77.3, "text": "عبارة عن Bernoulli Inquality Bernoulli's Inquality اللي هي بتقولنا لو كانت عندي Alpha عبارة عن real number أكبر من واحد هيكون عندي الواحد زايد X to the Alpha أكبر يساوي واحد زايد Alpha X لكل X أكبر من مين من ناقص واحد with equality if and only if عند X مين عند X بالساوية سفر عندنا ال equality عند X أيش بتساوي بتساوي سفر شوف", "tokens": [3615, 3555, 9640, 3660, 18871, 10781, 263, 16320, 682, 11286, 10781, 263, 16320, 311, 682, 11286, 13672, 1829, 39896, 39894, 39648, 8315, 45164, 25961, 2655, 43242, 1829, 20588, 6225, 3555, 9640, 3660, 18871, 957, 1230, 5551, 4117, 26890, 9154, 36764, 24401, 39896, 30544, 43242, 1829, 2423, 14407, 24401, 30767, 995, 25708, 1783, 281, 264, 20588, 5551, 4117, 26890, 7251, 3794, 995, 45865, 36764, 24401, 30767, 995, 25708, 20588, 1783, 5296, 28820, 1783, 5551, 4117, 26890, 9154, 3714, 9957, 9154, 8717, 995, 4587, 9381, 36764, 24401, 365, 14949, 498, 293, 787, 498, 43242, 1783, 3714, 9957, 43242, 1783, 20666, 3794, 995, 2407, 10632, 8608, 5172, 2288, 43242, 8315, 2423, 14949, 43242, 1783, 36632, 8592, 39894, 3794, 995, 45865, 39894, 3794, 995, 45865, 8608, 5172, 2288, 13412, 38688], "avg_logprob": -0.19832676907223978, "compression_ratio": 1.901185770750988, "no_speech_prob": 1.7583370208740234e-05, "words": [{"start": 50.84, "end": 51.68, "word": "عبارة", "probability": 0.8779296875}, {"start": 51.68, "end": 51.96, "word": " عن", "probability": 0.9931640625}, {"start": 51.96, "end": 52.62, "word": " Bernoulli", "probability": 0.8961588541666666}, {"start": 52.62, "end": 53.18, "word": " Inquality", "probability": 0.60595703125}, {"start": 53.18, 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"end": 68.52, "word": " with", "probability": 0.716796875}, {"start": 68.52, "end": 69.08, "word": " equality", "probability": 0.88525390625}, {"start": 69.08, "end": 69.28, "word": " if", "probability": 0.90087890625}, {"start": 69.28, "end": 69.5, "word": " and", "probability": 0.95263671875}, {"start": 69.5, "end": 69.68, "word": " only", "probability": 0.6064453125}, {"start": 69.68, "end": 69.94, "word": " if", "probability": 0.97265625}, {"start": 69.94, "end": 70.2, "word": " عند", "probability": 0.96826171875}, {"start": 70.2, "end": 70.42, "word": " X", "probability": 0.97802734375}, {"start": 70.42, "end": 70.78, "word": " مين", "probability": 0.87841796875}, {"start": 70.78, "end": 71.2, "word": " عند", "probability": 0.88916015625}, {"start": 71.2, "end": 71.42, "word": " X", "probability": 0.9892578125}, {"start": 71.42, "end": 71.84, "word": " بالساوية", "probability": 0.761669921875}, {"start": 71.84, "end": 72.18, "word": " سفر", "probability": 0.8248697916666666}, {"start": 72.18, "end": 72.52, "word": " عندنا", "probability": 0.86962890625}, {"start": 72.52, "end": 72.62, "word": " ال", "probability": 0.90966796875}, {"start": 72.62, "end": 73.58, "word": " equality", "probability": 0.65576171875}, {"start": 73.58, "end": 74.58, "word": " عند", "probability": 0.97412109375}, {"start": 74.58, "end": 74.92, "word": " X", "probability": 0.99267578125}, {"start": 74.92, "end": 75.14, "word": " أيش", "probability": 0.628173828125}, {"start": 75.14, "end": 75.76, "word": " بتساوي", "probability": 0.9569091796875}, {"start": 75.76, "end": 76.52, "word": " بتساوي", "probability": 0.7769775390625}, {"start": 76.52, "end": 76.88, "word": " سفر", "probability": 0.97998046875}, {"start": 76.88, "end": 77.3, "word": " شوف", "probability": 0.861572265625}], "temperature": 1.0}, {"id": 4, "seek": 10731, "start": 78.01, "end": 107.31, "text": "زي ما عملنا المرة الماضية اللي هو E to the X اللي هي لما أخدناها وثبتنا إنها أكبر أو يساوي اللي هي الواحد زائد Alpha X والمساوية F and W الساوية اللي هو واحد الان see Bernoulli's inequality Bernoulli's inequality اللي هي كما يعني عندى خد Alpha أكبر من واحد", "tokens": [11622, 1829, 19446, 6225, 42213, 8315, 9673, 25720, 9673, 46958, 10632, 13672, 1829, 31439, 462, 281, 264, 1783, 13672, 1829, 39896, 5296, 15042, 5551, 9778, 3215, 8315, 11296, 4032, 12984, 3555, 2655, 8315, 36145, 11296, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 13672, 1829, 39896, 2423, 14407, 24401, 30767, 16373, 3215, 20588, 1783, 16070, 2304, 3794, 995, 2407, 10632, 479, 293, 343, 21136, 995, 2407, 10632, 13672, 1829, 31439, 36764, 24401, 2423, 7649, 536, 10781, 263, 16320, 311, 16970, 10781, 263, 16320, 311, 16970, 13672, 1829, 39896, 9122, 15042, 37495, 22653, 43242, 7578, 16490, 3215, 20588, 5551, 4117, 26890, 9154, 36764, 24401], "avg_logprob": -0.26712741215641683, "compression_ratio": 1.811926605504587, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 78.01, "end": 78.39, "word": "زي", "probability": 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{"start": 89.55, "end": 90.15, "word": " والمساوية", "probability": 0.796875}, {"start": 90.15, "end": 90.43, "word": " F", "probability": 0.7626953125}, {"start": 90.43, "end": 90.61, "word": " and", "probability": 0.44091796875}, {"start": 90.61, "end": 90.85, "word": " W", "probability": 0.3046875}, {"start": 90.85, "end": 91.57, "word": " الساوية", "probability": 0.6816787719726562}, {"start": 91.57, "end": 92.05, "word": " اللي", "probability": 0.971923828125}, {"start": 92.05, "end": 92.23, "word": " هو", "probability": 0.947265625}, {"start": 92.23, "end": 92.69, "word": " واحد", "probability": 0.947021484375}, {"start": 92.69, "end": 93.59, "word": " الان", "probability": 0.650390625}, {"start": 93.59, "end": 93.99, "word": " see", "probability": 0.2454833984375}, {"start": 93.99, "end": 94.63, "word": " Bernoulli's", "probability": 0.881591796875}, {"start": 94.63, "end": 95.21, "word": " inequality", "probability": 0.92236328125}, {"start": 95.21, "end": 98.03, "word": " 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{"start": 1109.8, "end": 1110.1, "word": " بتقول", "probability": 0.9794921875}, {"start": 1110.1, "end": 1110.54, "word": " اللممة؟", "probability": 0.9395751953125}, {"start": 1110.54, "end": 1110.74, "word": " تعالى", "probability": 0.692626953125}, {"start": 1110.74, "end": 1111.18, "word": " نشوف", "probability": 0.9890950520833334}, {"start": 1111.18, "end": 1112.04, "word": " بالظبط", "probability": 0.9644775390625}, {"start": 1112.04, "end": 1112.18, "word": " اللي", "probability": 0.9599609375}, {"start": 1112.18, "end": 1112.66, "word": " بتقوله", "probability": 0.9695638020833334}, {"start": 1112.66, "end": 1112.78, "word": " اللي", "probability": 0.7093505859375}, {"start": 1112.78, "end": 1113.22, "word": " حكيته", "probability": 0.9918212890625}, {"start": 1113.22, "end": 1113.46, "word": " أنا", "probability": 0.80712890625}, {"start": 1113.46, "end": 1114.26, "word": " بقول", "probability": 0.9521484375}, {"start": 1114.26, "end": 1114.66, "word": " اللممة", 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continuous", "tokens": [19096, 456, 8198, 412, 1935, 472, 935, 383, 8978, 2423, 39184, 32, 16070, 39184, 33, 4724, 5016, 1829, 12984, 14739, 2423, 39184, 9171, 7211, 9655, 295, 383, 36632, 8592, 39894, 3794, 995, 45865, 22807, 39894, 3794, 995, 45865, 591, 3714, 33599, 1829, 35186, 13412, 3555, 16758, 23032, 1829, 3555, 13672, 1829, 30767, 1829, 19446, 11203, 4587, 8315, 12174, 36150, 4724, 8592, 2407, 10632, 20666, 2288, 17082, 2304, 36145, 3224, 11933, 5016, 8315, 19446, 24401, 8592, 10874, 16758, 8608, 48923, 36145, 2423, 39184, 9171, 7211, 9655, 8032, 2655, 30544, 10957], "avg_logprob": -0.2758680671453476, "compression_ratio": 1.4537037037037037, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1432.33, "end": 1432.67, "word": "then", "probability": 0.16845703125}, {"start": 1432.67, "end": 1432.91, "word": " there", "probability": 0.8671875}, {"start": 1432.91, "end": 1433.33, "word": " exists", "probability": 0.51025390625}, {"start": 1433.33, "end": 1433.61, 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ما", "probability": 0.78564453125}, {"start": 1444.51, "end": 1444.85, "word": " علقنا", "probability": 0.775390625}, {"start": 1444.85, "end": 1445.09, "word": " قبل", "probability": 0.937744140625}, {"start": 1445.09, "end": 1445.45, "word": " بشوية", "probability": 0.9322509765625}, {"start": 1445.45, "end": 1445.85, "word": " بالرغم", "probability": 0.888671875}, {"start": 1445.85, "end": 1446.09, "word": " إنه", "probability": 0.61328125}, {"start": 1446.09, "end": 1446.29, "word": " إحنا", "probability": 0.775634765625}, {"start": 1446.29, "end": 1446.89, "word": " ماحدش", "probability": 0.8839518229166666}, {"start": 1446.89, "end": 1447.21, "word": " جاب", "probability": 0.9580078125}, {"start": 1447.21, "end": 1447.59, "word": " سيرة", "probability": 0.96142578125}, {"start": 1447.59, "end": 1447.81, "word": " إن", "probability": 0.65576171875}, {"start": 1447.81, "end": 1448.21, "word": " الـAlpha", "probability": 0.7698974609375}, {"start": 1448.21, "end": 1448.71, "word": " Prime", "probability": 0.83544921875}, {"start": 1448.71, "end": 1449.53, "word": " هتكون", "probability": 0.7421061197916666}, {"start": 1449.53, "end": 1450.09, "word": " continuous", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 60, "seek": 147477, "start": 1451.17, "end": 1474.77, "text": "لأ، قلنا ما في الـ F' من مخزون، derivative من مخزون في داخلنا المعلومات أهلها إنها تقدر تصل أنه لأي K بين الـ F A و الـ F' A و الـ F' B بالـ Legacy، بحيث أن F' اللي عند الـ C هي الـ K. إيه المرحلة دلوقتي؟ شوف، نفترض أنه Proof", "tokens": [1211, 10721, 12399, 12174, 1211, 8315, 19446, 8978, 2423, 39184, 479, 6, 9154, 3714, 9778, 11622, 11536, 12399, 13760, 9154, 3714, 9778, 11622, 11536, 8978, 11778, 47283, 1211, 8315, 9673, 30241, 20498, 9307, 5551, 3224, 1211, 11296, 36145, 11296, 6055, 28543, 2288, 6055, 36520, 14739, 3224, 5296, 10721, 1829, 591, 49374, 2423, 39184, 479, 316, 4032, 2423, 39184, 479, 6, 316, 4032, 2423, 39184, 479, 6, 363, 20666, 39184, 42838, 12399, 4724, 5016, 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" F'", "probability": 0.9013671875}, {"start": 1464.73, "end": 1465.01, "word": " B", "probability": 0.94189453125}, {"start": 1465.01, "end": 1465.79, "word": " بالـ", "probability": 0.630859375}, {"start": 1465.79, "end": 1466.79, "word": " Legacy،", "probability": 0.5489501953125}, {"start": 1466.79, "end": 1467.07, "word": " بحيث", "probability": 0.838134765625}, {"start": 1467.07, "end": 1467.19, "word": " أن", "probability": 0.56689453125}, {"start": 1467.19, "end": 1467.51, "word": " F'", "probability": 0.6748046875}, {"start": 1467.89, "end": 1468.03, "word": " اللي", "probability": 0.873046875}, {"start": 1468.03, "end": 1468.23, "word": " عند", "probability": 0.9892578125}, {"start": 1468.23, "end": 1468.43, "word": " الـ", "probability": 0.908935546875}, {"start": 1468.43, "end": 1468.65, "word": " C", "probability": 0.84814453125}, {"start": 1468.65, "end": 1469.15, "word": " هي", "probability": 0.8544921875}, {"start": 1469.15, "end": 1469.35, "word": " الـ", "probability": 0.760986328125}, {"start": 1469.35, "end": 1469.69, "word": " K.", "probability": 0.90478515625}, {"start": 1470.15, "end": 1470.27, "word": " إيه", "probability": 0.6963704427083334}, {"start": 1470.27, "end": 1470.51, "word": " المرحلة", "probability": 0.712890625}, {"start": 1470.51, "end": 1471.17, "word": " دلوقتي؟", "probability": 0.81123046875}, {"start": 1471.17, "end": 1472.95, "word": " شوف،", "probability": 0.7511393229166666}, {"start": 1472.95, "end": 1473.75, "word": " نفترض", "probability": 0.9813232421875}, {"start": 1473.75, "end": 1474.19, "word": " أنه", "probability": 0.69384765625}, {"start": 1474.19, "end": 1474.77, "word": " Proof", "probability": 0.546234130859375}], "temperature": 1.0}, {"id": 61, "seek": 149737, "start": 1475.85, "end": 1497.37, "text": "نفترض أن G of A أصغر من K أصغر من مين من G أو F prime of A أصغر من F prime of B ماشي الحال واضح هذا فرضناه", "tokens": [1863, 5172, 2655, 43042, 14739, 460, 295, 316, 5551, 9381, 17082, 2288, 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0.7861328125}, {"start": 1480.29, "end": 1481.15, "word": " أصغر", "probability": 0.966796875}, {"start": 1481.15, "end": 1481.31, "word": " من", "probability": 0.99560546875}, {"start": 1481.31, "end": 1481.71, "word": " مين", "probability": 0.52606201171875}, {"start": 1481.71, "end": 1482.71, "word": " من", "probability": 0.78076171875}, {"start": 1482.71, "end": 1483.43, "word": " G", "probability": 0.833984375}, {"start": 1483.43, "end": 1484.13, "word": " أو", "probability": 0.79931640625}, {"start": 1484.13, "end": 1484.31, "word": " F", "probability": 0.72412109375}, {"start": 1484.31, "end": 1486.83, "word": " prime", "probability": 0.209228515625}, {"start": 1486.83, "end": 1488.05, "word": " of", "probability": 0.6787109375}, {"start": 1488.05, "end": 1488.37, "word": " A", "probability": 0.96875}, {"start": 1488.37, "end": 1488.83, "word": " أصغر", "probability": 0.9896240234375}, {"start": 1488.83, "end": 1489.07, "word": " من", "probability": 0.99267578125}, {"start": 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"end": 1808.64, "word": " لعند", "probability": 0.9404296875}, {"start": 1808.64, "end": 1808.82, "word": " الـ", "probability": 0.78271484375}, {"start": 1808.82, "end": 1808.96, "word": " B", "probability": 0.8642578125}, {"start": 1808.96, "end": 1811.52, "word": " صح؟", "probability": 0.9337565104166666}], "temperature": 1.0}, {"id": 74, "seek": 183974, "start": 1812.88, "end": 1839.74, "text": "وهنا end points هذول فمش هتكون برضه مين ال b مش هتكون عندها maximum لأنه منها ولا جوا ال b end point منها ولا جوا ال g of x أكبر من ال g of b إذن مش maximum إذن hence g does not have a maximum at b from هنا", "tokens": [2407, 3224, 8315, 917, 2793, 8032, 8848, 12610, 6156, 2304, 8592, 8032, 2655, 30544, 4724, 43042, 3224, 3714, 9957, 2423, 272, 37893, 8032, 2655, 30544, 43242, 11296, 6674, 5296, 33456, 3224, 9154, 11296, 49429, 10874, 14407, 2423, 272, 917, 935, 9154, 11296, 49429, 10874, 14407, 2423, 290, 295, 2031, 5551, 4117, 26890, 9154, 2423, 290, 295, 272, 11933, 8848, 1863, 37893, 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"probability": 0.7097981770833334}, {"start": 2191.34, "end": 2191.9, "word": " مش", "probability": 0.79150390625}, {"start": 2191.9, "end": 2192.24, "word": " نص", "probability": 0.981201171875}, {"start": 2192.24, "end": 2192.62, "word": " بس", "probability": 0.982177734375}, {"start": 2192.62, "end": 2193.0, "word": " تقدر", "probability": 0.7637532552083334}, {"start": 2193.0, "end": 2193.3, "word": " تختار", "probability": 0.9939778645833334}, {"start": 2193.3, "end": 2193.64, "word": " ربع", "probability": 0.8972981770833334}, {"start": 2193.64, "end": 2194.02, "word": " تلت", "probability": 0.8523763020833334}, {"start": 2194.02, "end": 2194.36, "word": " خمس", "probability": 0.9845377604166666}, {"start": 2194.36, "end": 2194.64, "word": " أي", "probability": 0.5302734375}, {"start": 2194.64, "end": 2195.04, "word": " حاجة", "probability": 0.990234375}, {"start": 2195.04, "end": 2195.32, "word": " غير", "probability": 0.99169921875}, {"start": 2195.32, "end": 2195.58, "word": " الـ", "probability": 0.718017578125}, {"start": 2195.58, "end": 2195.86, "word": " Zero", "probability": 0.33544921875}, {"start": 2195.86, "end": 2196.5, "word": " و", "probability": 0.55615234375}, {"start": 2196.5, "end": 2196.84, "word": " الواحد", "probability": 0.8111979166666666}, {"start": 2196.84, "end": 2197.24, "word": " والسلب", "probability": 0.6337076822916666}, {"start": 2197.24, "end": 2197.74, "word": " واحد", "probability": 0.985107421875}, {"start": 2197.74, "end": 2198.52, "word": " ايش", "probability": 0.7596028645833334}, {"start": 2198.52, "end": 2198.68, "word": " ال", "probability": 0.3212890625}, {"start": 2198.68, "end": 2198.68, "word": " ..", "probability": 0.67431640625}, {"start": 2198.68, "end": 2198.92, "word": " ايش", "probability": 0.9365234375}, {"start": 2198.92, "end": 2199.46, "word": " الشد", "probability": 0.589111328125}, {"start": 2199.46, "end": 2199.58, "word": " في", "probability": 0.861328125}, {"start": 2199.58, "end": 2200.06, "word": " الأمر", "probability": 0.855224609375}, {"start": 2200.06, "end": 2200.92, "word": " but", "probability": 0.351806640625}, {"start": 2200.92, "end": 2201.38, "word": " نص", "probability": 0.923583984375}, {"start": 2201.38, "end": 2201.76, "word": " element", "probability": 0.87158203125}, {"start": 2201.76, "end": 2203.06, "word": " كده", "probability": 0.8527018229166666}, {"start": 2203.06, "end": 2203.94, "word": " and", "probability": 0.8837890625}, {"start": 2203.94, "end": 2209.4, "word": " D", "probability": 0.3115234375}, {"start": 2209.4, "end": 2210.06, "word": " F", "probability": 0.44580078125}, {"start": 2210.06, "end": 2210.64, "word": " is", "probability": 0.92236328125}, {"start": 2210.64, "end": 2211.74, "word": " differentiable", "probability": 0.96875}, {"start": 2211.74, "end": 2213.34, "word": " on", "probability": 0.90673828125}, {"start": 2213.34, "end": 2214.1, "word": " ناقص", "probability": 0.9786376953125}, {"start": 2214.1, "end": 2214.5, "word": " واحد", "probability": 0.988525390625}, {"start": 2214.5, "end": 2215.0, "word": " واحد", "probability": 0.759033203125}], "temperature": 1.0}, {"id": 89, "seek": 224444, "start": 2215.96, "end": 2244.44, "text": "صح؟ then by Darabaux's theorem there exist c element ناقص واحد وواحد such that اللي هو g of c او f prime of c بيساوي ايش نص صح؟", "tokens": [9381, 5016, 22807, 550, 538, 7803, 455, 7511, 311, 20904, 456, 2514, 269, 4478, 8717, 995, 4587, 9381, 36764, 24401, 4032, 14407, 24401, 1270, 300, 13672, 1829, 31439, 290, 295, 269, 1975, 2407, 283, 5835, 295, 269, 4724, 1829, 3794, 995, 45865, 1975, 1829, 8592, 8717, 9381, 20328, 5016, 22807], "avg_logprob": -0.3002451038828083, "compression_ratio": 1.1956521739130435, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2215.96, "end": 2217.12, "word": "صح؟", "probability": 0.8004557291666666}, {"start": 2217.12, "end": 2218.18, "word": " then", "probability": 0.47021484375}, {"start": 2218.18, "end": 2220.74, "word": " by", "probability": 0.81689453125}, {"start": 2220.74, "end": 2222.32, "word": " Darabaux's", "probability": 0.50592041015625}, {"start": 2222.32, "end": 2223.08, "word": " theorem", "probability": 0.896484375}, {"start": 2223.08, "end": 2225.44, "word": " there", "probability": 0.828125}, {"start": 2225.44, "end": 2226.22, "word": " exist", "probability": 0.615234375}, {"start": 2226.22, "end": 2227.84, "word": " c", "probability": 0.568359375}, {"start": 2227.84, "end": 2228.42, "word": " element", "probability": 0.5888671875}, {"start": 2228.42, "end": 2229.1, "word": " ناقص", "probability": 0.8922119140625}, {"start": 2229.1, "end": 2229.8, "word": " واحد", "probability": 0.96875}, {"start": 2229.8, "end": 2232.3, "word": " وواحد", "probability": 0.8196614583333334}, {"start": 2232.3, "end": 2233.14, "word": " such", "probability": 0.96435546875}, {"start": 2233.14, "end": 2234.0, "word": " that", "probability": 0.95947265625}, {"start": 2234.0, "end": 2235.5, "word": " اللي", "probability": 0.6708984375}, {"start": 2235.5, "end": 2235.78, "word": " هو", "probability": 0.97021484375}, {"start": 2235.78, "end": 2236.64, "word": " g", "probability": 0.7109375}, {"start": 2236.64, "end": 2236.9, "word": " of", "probability": 0.6748046875}, {"start": 2236.9, "end": 2237.14, "word": " c", "probability": 0.92529296875}, {"start": 2237.14, "end": 2237.38, "word": " او", "probability": 0.6824951171875}, {"start": 2237.38, "end": 2237.6, "word": " f", "probability": 0.86279296875}, {"start": 2237.6, "end": 2238.2, "word": " prime", "probability": 0.63720703125}, {"start": 2238.2, "end": 2238.52, "word": " of", "probability": 0.98388671875}, {"start": 2238.52, "end": 2239.2, "word": " c", "probability": 0.966796875}, {"start": 2239.2, "end": 2240.74, "word": " بيساوي", "probability": 0.76103515625}, {"start": 2240.74, "end": 2241.38, "word": " ايش", "probability": 0.6034342447916666}, {"start": 2241.38, "end": 2242.74, "word": " نص", "probability": 0.78955078125}, {"start": 2242.74, "end": 2244.44, "word": " صح؟", "probability": 0.9422200520833334}], "temperature": 1.0}, {"id": 90, "seek": 226371, "start": 2244.83, "end": 2263.71, "text": "Ie بمعنى آخر F prime of C اللي هو G of C بساوة نص Which is impossible Therefore our first assumption is not true", "tokens": [40, 68, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 479, 5835, 295, 383, 13672, 1829, 31439, 460, 295, 383, 4724, 3794, 995, 2407, 3660, 8717, 9381, 3013, 307, 6243, 7504, 527, 700, 15302, 307, 406, 2074], "avg_logprob": -0.3435388384638606, "compression_ratio": 1.0555555555555556, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2244.83, "end": 2245.97, "word": "Ie", "probability": 0.3343505859375}, {"start": 2245.97, "end": 2246.61, "word": " بمعنى", "probability": 0.90205078125}, {"start": 2246.61, "end": 2247.23, "word": " آخر", "probability": 0.900634765625}, {"start": 2247.23, "end": 2248.11, "word": " F", "probability": 0.432861328125}, {"start": 2248.11, "end": 2248.41, "word": " prime", "probability": 0.2003173828125}, {"start": 2248.41, "end": 2248.59, "word": " of", "probability": 0.95166015625}, {"start": 2248.59, "end": 2248.73, "word": " C", "probability": 0.7802734375}, {"start": 2248.73, "end": 2248.87, "word": " اللي", "probability": 0.52294921875}, {"start": 2248.87, "end": 2248.99, "word": " هو", "probability": 0.9814453125}, {"start": 2248.99, "end": 2249.29, "word": " G", "probability": 0.81689453125}, {"start": 2249.29, "end": 2249.71, "word": " of", "probability": 0.92626953125}, {"start": 2249.71, "end": 2250.25, "word": " C", "probability": 0.98828125}, {"start": 2250.25, "end": 2251.15, "word": " بساوة", "probability": 0.71796875}, {"start": 2251.15, "end": 2251.53, "word": " نص", "probability": 0.961181640625}, {"start": 2251.53, "end": 2252.37, "word": " Which", "probability": 0.23291015625}, {"start": 2252.37, "end": 2254.43, "word": " is", "probability": 0.939453125}, {"start": 2254.43, "end": 2256.49, "word": " impossible", "probability": 0.7734375}, {"start": 2256.49, "end": 2259.59, "word": " Therefore", "probability": 0.72509765625}, {"start": 2259.59, "end": 2261.27, "word": " our", "probability": 0.6123046875}, {"start": 2261.27, "end": 2261.81, "word": " first", "probability": 0.90478515625}, {"start": 2261.81, "end": 2262.39, "word": " assumption", "probability": 0.97314453125}, {"start": 2262.39, "end": 2262.89, "word": " is", "probability": 0.955078125}, {"start": 2262.89, "end": 2263.19, "word": " not", "probability": 0.95166015625}, {"start": 2263.19, "end": 2263.71, "word": " true", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 91, "seek": 229436, "start": 2264.54, "end": 2294.36, "text": "that is there is no F من ناقص واحد لعند واحد .. من واحد ناقص واحد لواحد لعند ال R بحيث أن F' بيساوي G أو بمعنى أخر G is not a derivative of any function وهكذا نكون خلصنا ستة اتنين والمرة اللي جاي ان شاء الله بنكمل في ستة تلاتة ويوم الأحد القادم بنناقش ستة اتنين", "tokens": [6780, 307, 456, 307, 572, 479, 9154, 8717, 995, 4587, 9381, 36764, 24401, 5296, 3615, 41260, 36764, 24401, 4386, 9154, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 5296, 14407, 24401, 5296, 3615, 41260, 2423, 497, 4724, 5016, 1829, 12984, 14739, 479, 6, 4724, 1829, 3794, 995, 45865, 460, 34051, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 460, 307, 406, 257, 13760, 295, 604, 2445, 4032, 3224, 4117, 15730, 8717, 30544, 16490, 1211, 9381, 8315, 8608, 2655, 3660, 1975, 2655, 1863, 9957, 4032, 45340, 25720, 13672, 1829, 10874, 47302, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 8978, 8608, 2655, 3660, 6055, 1211, 9307, 3660, 4032, 1829, 20498, 16247, 24401, 25062, 18513, 2304, 44945, 8315, 4587, 8592, 8608, 2655, 3660, 1975, 2655, 1863, 9957], "avg_logprob": -0.24911795724784175, "compression_ratio": 1.6967213114754098, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 2264.54, "end": 2264.98, "word": "that", "probability": 0.28564453125}, {"start": 2264.98, "end": 2265.52, "word": " is", "probability": 0.95703125}, {"start": 2265.52, "end": 2266.2, "word": " there", "probability": 0.6484375}, {"start": 2266.2, "end": 2266.48, "word": " is", "probability": 0.958984375}, {"start": 2266.48, "end": 2267.04, "word": " no", "probability": 0.90234375}, {"start": 2267.04, "end": 2267.72, "word": " F", "probability": 0.37841796875}, {"start": 2267.72, "end": 2268.46, "word": " من", "probability": 0.88671875}, {"start": 2268.46, "end": 2268.92, "word": " ناقص", "probability": 0.763519287109375}, {"start": 2268.92, "end": 2269.26, "word": " واحد", "probability": 0.85546875}, {"start": 2269.26, "end": 2269.52, "word": " لعند", "probability": 0.7555338541666666}, {"start": 2269.52, "end": 2269.92, "word": " واحد", "probability": 0.6693115234375}, {"start": 2269.92, "end": 2270.0, "word": " ..", "probability": 0.2568359375}, {"start": 2270.0, "end": 2270.16, "word": " من", "probability": 0.74609375}, {"start": 2270.16, "end": 2270.34, "word": " واحد", "probability": 0.915283203125}, {"start": 2270.34, "end": 2270.54, "word": " ناقص", "probability": 0.773681640625}, {"start": 2270.54, "end": 2270.74, "word": " واحد", "probability": 0.989013671875}, {"start": 2270.74, "end": 2270.88, "word": " لواحد", "probability": 0.6378580729166666}, {"start": 2270.88, "end": 2271.14, "word": " لعند", "probability": 0.8995768229166666}, {"start": 2271.14, "end": 2271.32, "word": " ال", "probability": 0.90771484375}, {"start": 2271.32, "end": 2271.54, "word": " R", "probability": 0.560546875}, {"start": 2271.54, "end": 2272.18, "word": " بحيث", "probability": 0.770660400390625}, {"start": 2272.18, "end": 2272.3, "word": " أن", "probability": 0.54443359375}, {"start": 2272.3, "end": 2272.64, "word": " F'", "probability": 0.39306640625}, {"start": 2272.94, "end": 2273.38, "word": " بيساوي", "probability": 0.5843017578125}, {"start": 2273.38, "end": 2273.58, "word": " G", "probability": 0.79150390625}, {"start": 2273.58, "end": 2273.82, "word": " أو", "probability": 0.8115234375}, {"start": 2273.82, "end": 2274.16, "word": " بمعنى", "probability": 0.98837890625}, {"start": 2274.16, "end": 2274.52, "word": " أخر", "probability": 0.696533203125}, {"start": 2274.52, "end": 2274.96, "word": " G", "probability": 0.52294921875}, {"start": 2274.96, "end": 2275.76, "word": " is", "probability": 0.91552734375}, {"start": 2275.76, "end": 2276.28, "word": " not", "probability": 0.9580078125}, {"start": 2276.28, "end": 2276.76, "word": " a", "probability": 0.95654296875}, {"start": 2276.76, "end": 2277.28, "word": " derivative", "probability": 0.93212890625}, {"start": 2277.28, "end": 2277.64, "word": " of", "probability": 0.9736328125}, {"start": 2277.64, "end": 2278.04, "word": " any", "probability": 0.896484375}, {"start": 2278.04, "end": 2279.34, "word": " function", "probability": 0.96923828125}, {"start": 2279.34, "end": 2283.68, "word": " وهكذا", "probability": 0.69842529296875}, {"start": 2283.68, "end": 2283.94, "word": " نكون", "probability": 0.4031982421875}, {"start": 2283.94, "end": 2284.44, "word": " خلصنا", "probability": 0.96533203125}, {"start": 2284.44, "end": 2284.78, "word": " ستة", "probability": 0.7737630208333334}, {"start": 2284.78, "end": 2285.14, "word": " اتنين", "probability": 0.9022216796875}, {"start": 2285.14, "end": 2287.04, "word": " والمرة", "probability": 0.765380859375}, {"start": 2287.04, "end": 2287.18, "word": " اللي", "probability": 0.786865234375}, {"start": 2287.18, "end": 2287.3, "word": " جاي", "probability": 0.70947265625}, {"start": 2287.3, "end": 2287.42, "word": " ان", "probability": 0.66015625}, {"start": 2287.42, "end": 2287.6, "word": " شاء", "probability": 0.98046875}, {"start": 2287.6, "end": 2287.78, "word": " الله", "probability": 0.96142578125}, {"start": 2287.78, "end": 2288.4, "word": " بنكمل", "probability": 0.9212239583333334}, {"start": 2288.4, "end": 2288.48, "word": " في", "probability": 0.81494140625}, {"start": 2288.48, "end": 2288.76, "word": " ستة", "probability": 0.9685872395833334}, {"start": 2288.76, "end": 2289.34, "word": " تلاتة", "probability": 0.9222412109375}, {"start": 2289.34, "end": 2290.66, "word": " ويوم", "probability": 0.9615885416666666}, {"start": 2290.66, "end": 2291.86, "word": " الأحد", "probability": 0.96240234375}, {"start": 2291.86, "end": 2292.46, "word": " القادم", "probability": 0.994140625}, {"start": 2292.46, "end": 2293.46, "word": " بنناقش", "probability": 0.9775390625}, {"start": 2293.46, "end": 2293.98, "word": " ستة", "probability": 0.9694010416666666}, {"start": 2293.98, "end": 2294.36, "word": " اتنين", "probability": 0.9578857421875}], "temperature": 1.0}, {"id": 92, "seek": 229601, "start": 2295.13, "end": 2296.01, "text": "أسئلة 6", "tokens": [10721, 3794, 19986, 37977, 1386], "avg_logprob": -0.15462239583333334, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.0, "words": [{"start": 2295.13, "end": 2295.71, "word": "أسئلة", "probability": 0.9119873046875}, {"start": 2295.71, "end": 2296.01, "word": " 6", "probability": 0.70458984375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2296.9875625, "duration_after_vad": 2230.5493749999923}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/PVuSVTtYhJQ_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/PVuSVTtYhJQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ca525981e7f39494eba28daaf4173739677c0df1
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/PVuSVTtYhJQ_raw.srt
@@ -0,0 +1,4028 @@
+1
+00:00:04,910 --> 00:00:07,650
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,650 --> 00:00:10,710
+والصلاة والسلام على سيد المسالين سيدنا محمد على
+
+3
+00:00:10,710 --> 00:00:15,510
+آله وصحبه أجمعين هذه هي المحاضرة رقم واحد وعشرين
+
+4
+00:00:15,510 --> 00:00:19,630
+في مساق تحليل حقيقة نين لطلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:26,460
+الإسلامية قسم الرياضيات في كلية العلمهنكمل الحديث
+
+6
+00:00:26,460 --> 00:00:32,660
+عن اللي هو الـ Sequence of Functions خلصنا من
+
+7
+00:00:32,660 --> 00:00:36,180
+سيكشن الـ Pointwise أو الـ Uniform Convergence
+
+8
+00:00:36,180 --> 00:00:40,340
+الآن بدنا نشوف تأثير الـ Pointwise و الـ Uniform
+
+9
+00:00:40,340 --> 00:00:44,700
+Convergence على اللي هو بعض الـ Sequence of
+
+10
+00:00:44,700 --> 00:00:49,040
+Functions إيش بتسوي فيهاالان تحت عنوان 82
+
+11
+00:00:49,040 --> 00:00:53,900
+interchange of limits هنجي نشوف اللي هو الـ
+
+12
+00:00:53,900 --> 00:00:57,160
+sequence of continuous functions لو كانت اللي هي
+
+13
+00:00:57,160 --> 00:01:01,620
+pointwise convergence هل صح شرط انه لو لمين بتروح
+
+14
+00:01:01,620 --> 00:01:04,680
+في ال pointwise convergence ان يكون continuous ولا
+
+15
+00:01:04,680 --> 00:01:09,780
+بلزمها دعم شوية نخلي اللي هو بدل ال pointwise
+
+16
+00:01:09,780 --> 00:01:13,220
+convergence نخليه uniform و ال uniform يوديالـ
+
+17
+00:01:13,220 --> 00:01:16,040
+function اللي بتطلع تطلع continuous ولا لأ؟ هنشوف
+
+18
+00:01:16,040 --> 00:01:19,680
+الكلام هذا الشغل الثاني هنشوف أنه لو كانت ال
+
+19
+00:01:19,680 --> 00:01:23,360
+function is integrable هل ال sequence of functions
+
+20
+00:01:23,360 --> 00:01:27,640
+is integrable؟ هل ال limit اللي لما يكون اللي هو
+
+21
+00:01:27,640 --> 00:01:32,080
+ال Fn بتروح لل F point twice أو ال Fn بتروح لل F
+
+22
+00:01:32,080 --> 00:01:37,850
+uniform convergence؟هل هذا واحد منهم بيقدّي انه ال
+
+23
+00:01:37,850 --> 00:01:39,850
+integration لل limit بيساوي ال limit لل
+
+24
+00:01:39,850 --> 00:01:42,730
+integration يعني ال limit بتدخل جوا ال integration
+
+25
+00:01:42,730 --> 00:01:46,990
+ولا لأ؟ هل دخولها يعني بال point wise بحافظ على
+
+26
+00:01:46,990 --> 00:01:50,170
+المساواة ولا لأ بال زمن اللي هو ال uniform
+
+27
+00:01:50,170 --> 00:01:54,730
+convergence؟ هنشوفه والشغل التالثة هل انه لو كان
+
+28
+00:01:54,730 --> 00:01:59,150
+في عندي sequence of differentiable functions هتطلع
+
+29
+00:01:59,150 --> 00:02:04,040
+ان هو لو كان عندي F unconverged زي ال Fهيطلع عندي
+
+30
+00:02:04,040 --> 00:02:06,460
+اللي هو ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+31
+00:02:06,460 --> 00:02:07,500
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+32
+00:02:07,500 --> 00:02:07,620
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+33
+00:02:07,620 --> 00:02:08,200
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+34
+00:02:08,200 --> 00:02:08,300
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+35
+00:02:08,300 --> 00:02:08,340
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+36
+00:02:08,340 --> 00:02:09,020
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+37
+00:02:09,020 --> 00:02:10,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+38
+00:02:10,060 --> 00:02:11,000
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+39
+00:02:11,000 --> 00:02:13,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+40
+00:02:13,560 --> 00:02:13,560
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+41
+00:02:13,560 --> 00:02:13,720
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+42
+00:02:13,720 --> 00:02:23,020
+.. ال .. ال .. ال .. ال .. ال .. ال ..
+
+43
+00:02:28,280 --> 00:02:34,340
+المثال الأول اللي أمامنا هاي في عندى example 821 g
+
+44
+00:02:34,340 --> 00:02:38,900
+n of x بساوية x أُس n هذا شفناها يا جماعة على
+
+45
+00:02:38,900 --> 00:02:43,640
+الفترة x 01 is continuous أكيد اللي هي ال function
+
+46
+00:02:43,640 --> 00:02:47,540
+هذه g 1 of x بساوية x g 2 of x بساوية x تربيع g 3
+
+47
+00:02:47,540 --> 00:02:52,110
+of x بساوية x تكعيب كله عبارة عن دوال متصلةالان
+
+48
+00:02:52,110 --> 00:02:55,950
+and even continuously differentiable بيقولك أصلا
+
+49
+00:02:55,950 --> 00:03:00,430
+هيطلع مش ده continuous لأ و ال derivative L هتطلع
+
+50
+00:03:00,430 --> 00:03:03,190
+موجودة و ال derivative continuous يعني
+
+51
+00:03:03,190 --> 00:03:06,510
+continuously differentiable بالرغم من أنها القوة
+
+52
+00:03:06,510 --> 00:03:09,650
+اللي موجودة في ال sequence g of n of x من ناحية
+
+53
+00:03:09,650 --> 00:03:14,220
+انها continuously differentiableإلا إنه لما جينا
+
+54
+00:03:14,220 --> 00:03:17,880
+ناخد limit GN of X as N goes to infinity طلعت
+
+55
+00:03:17,880 --> 00:03:21,280
+بتساوي G of X اللي هي 0 X في الفترة 01 و 1 في
+
+56
+00:03:21,280 --> 00:03:25,180
+الفترة X اللي هو بتساوي 1 يعني اللي طلعتلنا ال
+
+57
+00:03:25,180 --> 00:03:31,040
+limit إلها طلعتلنا إياها is not continuousيعني
+
+58
+00:03:31,040 --> 00:03:35,080
+بالرغم إن ال limit موجودة طبعا هذا pointwise
+
+59
+00:03:35,080 --> 00:03:38,520
+convergence اللي هو ال pointwise convergence هنا
+
+60
+00:03:38,520 --> 00:03:44,660
+طلعلي اللي هو ال sequence of functions GN limitها
+
+61
+00:03:44,660 --> 00:03:48,820
+مش continuous ماقدرش يطلع اللي هو continuous
+
+62
+00:03:48,820 --> 00:03:52,560
+function هذا ال pointwise convergence بالرغم إنه
+
+63
+00:03:52,560 --> 00:03:56,740
+GN of X is اللي هو continuously differentiable
+
+64
+00:03:56,740 --> 00:04:03,550
+الآن ناخد مثال آخر إذاإذا كانت GN هي عملية عملية
+
+65
+00:04:03,550 --> 00:04:04,930
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+66
+00:04:04,930 --> 00:04:15,930
+عملية عملية عملية عملية عملية عملية عملية
+
+67
+00:04:15,960 --> 00:04:19,840
+طيب نشوف ال example اللي بعده الان ال example اللي
+
+68
+00:04:19,840 --> 00:04:25,400
+بعده بقول لي اللي هو let FN be هذه let FN من 0
+
+69
+00:04:25,400 --> 00:04:30,460
+لعند 1 من 01 لعند R be defined for N أكبر سواء 2
+
+70
+00:04:30,460 --> 00:04:37,150
+by مراكبين دالة تشوف هذه الدالةعندي Fn of X بساوي
+
+71
+00:04:37,150 --> 00:04:42,490
+N تربيع X الـ N هذا دالة المتغير X هذه الـ Fn و
+
+72
+00:04:42,490 --> 00:04:45,030
+الـ N تربيحة دولة اللي هنا اللي بدلن على اللي هو
+
+73
+00:04:45,030 --> 00:04:49,810
+الـ sequence F1, F2, F3, F4 أما الدالة هي F منين
+
+74
+00:04:49,810 --> 00:04:55,280
+بدلالة X الـ Fn بدلالة Xإذاً هذا عدد يعني هذه
+
+75
+00:04:55,280 --> 00:04:59,280
+Linear الدلة N تربيع X في الفترة من Zero لعند مين
+
+76
+00:04:59,280 --> 00:05:03,140
+واحدة على N لو جينا رسمناها اللي هي N تربيع عند
+
+77
+00:05:03,140 --> 00:05:07,620
+طبعا دي خطية بكفي نقطين نرسم عشان نحط خط بينهم عند
+
+78
+00:05:07,620 --> 00:05:12,900
+X بصفر بتطلع اللي هي الأولى اللي هي N تربيع X صفر
+
+79
+00:05:12,900 --> 00:05:16,540
+ال X واحدة على N بيصير واحدة على N في N تربيع
+
+80
+00:05:16,540 --> 00:05:19,640
+بتطلع اللي هي واحدة على N هي واحدة على N بتطلع
+
+81
+00:05:19,640 --> 00:05:23,760
+واحدة على Nبتطلع قيمة as an أسف an تربيع في واحدة
+
+82
+00:05:23,760 --> 00:05:30,260
+الان بتطلع an إذا هذه اللي هي الخط هيه للجزء اللي
+
+83
+00:05:30,260 --> 00:05:33,760
+هو الأولاني الجزء الثاني اللي هو بيبدأ من عند
+
+84
+00:05:33,760 --> 00:05:36,520
+واحدة الان عند مين واحدة الان عند اتنين ان خلينا
+
+85
+00:05:36,520 --> 00:05:41,150
+نرسمههذا برضه ايش معله ده اللي خطية لإنه ايش ماخده
+
+86
+00:05:41,150 --> 00:05:46,190
+عبارة عن ناقص N تربيع في X ناقص 2 على N هذي ثابت و
+
+87
+00:05:46,190 --> 00:05:50,190
+هذي ثابت بالنسبالي X الان X لحقها إذا ده اللي خطية
+
+88
+00:05:50,190 --> 00:05:53,890
+برضه و ده الخط خليني ناخد اللي هي X بتساوي 1 على N
+
+89
+00:05:53,890 --> 00:05:58,010
+خد 1 على N ناقص 2 على N بيطلع ناقص 1 على N في ناقص
+
+90
+00:05:58,010 --> 00:06:01,790
+N تربيع بيطلع 1 على N فعلا 1 على N بيطلع 1 على N و
+
+91
+00:06:01,790 --> 00:06:06,150
+N فبيطلع مين؟لأن هذا بيطلع واحدة الان في ناقص ان
+
+92
+00:06:06,150 --> 00:06:09,850
+تربيع بتطلع اللي هي ناقص واحدة الان في ناقص ان
+
+93
+00:06:09,850 --> 00:06:13,990
+تربيع بتطلع اللي هي ان ان إذا هذه واحدة الان بتطلع
+
+94
+00:06:13,990 --> 00:06:17,590
+أيهاش بالساوء اللي بعيدها النقطة الأخيرة اتنين على
+
+95
+00:06:17,590 --> 00:06:20,370
+ان اتنين على الناقص اتنين على الان سفر هذي بيصير
+
+96
+00:06:20,370 --> 00:06:24,480
+أيهاش سفر ترجع وين على سفر فبتنزل في الشكل هذاباجي
+
+97
+00:06:24,480 --> 00:06:27,540
+الدالة من عند اللي هو طبعا معرف عالميا على الفترة
+
+98
+00:06:27,540 --> 00:06:31,720
+Zero و واحد هي من Zero لعندي اتنين على N الان N
+
+99
+00:06:31,720 --> 00:06:34,340
+بتساوي واحد او اتنين او تلاتة او اربع او خمس او
+
+100
+00:06:34,340 --> 00:06:37,580
+ستة لبدكية كل دالة من هنا بتختلف عن التانية يعني
+
+101
+00:06:37,580 --> 00:06:43,220
+هذه FN in general F واحد F اتنين F تلاتة بتيجي
+
+102
+00:06:43,220 --> 00:06:46,360
+لهيك او بتروح لهيك بس بنفس اللي هي الشكل الأمامي
+
+103
+00:06:46,700 --> 00:06:49,900
+إيش عندي في فترة ماتنين على ألا واحد، ماتنين على
+
+104
+00:06:49,900 --> 00:06:53,340
+ألا واحد، الفترة ها دي ماخدين الدالة إيش بتساوي؟
+
+105
+00:06:53,340 --> 00:06:57,440
+بتساوي إيش؟ سفر واضح إن الدالة هي الدالة محترمة
+
+106
+00:06:57,440 --> 00:07:02,880
+دالة is continuousMadame Continuous أكيد اشمالها
+
+107
+00:07:02,880 --> 00:07:08,060
+is integrable إذا الدوال هذول أف واحد و أف اتنين و
+
+108
+00:07:08,060 --> 00:07:11,480
+أف تلاتة و أف أربعة و أف خمسة و أف ستة إلى ما لا
+
+109
+00:07:11,480 --> 00:07:17,380
+نهاية من الأفانز بتكون عبارة عن .. عبارة عن
+
+110
+00:07:17,380 --> 00:07:21,600
+integrable أو أف اتنين و طالعIntegrable Functions
+
+111
+00:07:21,600 --> 00:07:25,760
+من أن و طالع .. من أن واحد بيصير في المشكلة طيب
+
+112
+00:07:25,760 --> 00:07:29,520
+Note that Fn of X is continuous لكل أن أكبر ساوية
+
+113
+00:07:29,520 --> 00:07:34,180
+اتنين ناخد الفكرة احنا Hence, Integrable and ال
+
+114
+00:07:34,180 --> 00:07:38,520
+integration من صفر لأن واحد Fn of X DX ايش بيساوي؟
+
+115
+00:07:38,520 --> 00:07:42,060
+بيساوي اللي هو واحد بتعرفوا تحسبوها هي مساحة ..
+
+116
+00:07:42,060 --> 00:07:48,500
+مساحة المتلت هذا اللي هو اتنين على أناللي هو مضروب
+
+117
+00:07:48,500 --> 00:07:54,360
+في مين فان بطلع جداش اتنين في نص بطلع واحد عارف ان
+
+118
+00:07:54,360 --> 00:07:56,880
+النص القاعدة في الارتفاع إذا الجداش بطلع عندى اللي
+
+119
+00:07:56,880 --> 00:08:00,100
+هو قيمة ال integration هذا بساوي واحد لأن هذا
+
+120
+00:08:00,100 --> 00:08:04,060
+المنطقة إيه شمالها سفر إذا اللي هي قيمة ال
+
+121
+00:08:04,060 --> 00:08:08,480
+integration هذا بساوي واحد يعني ال function of
+
+122
+00:08:08,480 --> 00:08:12,980
+ands integrable وقيمة اللي هي ال integration بساوي
+
+123
+00:08:12,980 --> 00:08:18,850
+واحد لكل and أكبر أو يساوي اتنينان بيساوي واحد
+
+124
+00:08:18,850 --> 00:08:21,490
+اعوضها لحالك وشوف ايش اللي بيصير Note that as n
+
+125
+00:08:21,490 --> 00:08:25,490
+goes to infinity اللي
+
+126
+00:08:25,490 --> 00:08:31,310
+هو الفترات اللي عليها عشان نورجيكم إياهاطيب هذه
+
+127
+00:08:31,310 --> 00:08:35,230
+الدالة معرفها as n goes to infinity هذه الفترة
+
+128
+00:08:35,230 --> 00:08:39,050
+بتصير عبارة عن اللي هو النقطة zero و هذه الفترة
+
+129
+00:08:39,050 --> 00:08:43,130
+بتصير النقطة zero و الفترة 2 على n بتصير اللي هي
+
+130
+00:08:43,130 --> 00:08:48,430
+mean zero ل عند واحد and so الدالة إيش هتصير limit
+
+131
+00:08:48,430 --> 00:08:54,410
+fn of x بتساوي f of x إيش هتساوي هتساوي zeroيعني
+
+132
+00:08:54,410 --> 00:08:59,450
+الان لما ان تروح لما لنهاية هذه كلها ايش مالها
+
+133
+00:08:59,450 --> 00:09:03,870
+بتنطبق عالمين لإن كل ما كبرت ان بتفرد هذه بتفرد
+
+134
+00:09:03,870 --> 00:09:07,170
+هذه بتفرد هذه لإن as n goes to infinity هذا الكلام
+
+135
+00:09:07,170 --> 00:09:12,210
+ده اللي هتفرد و تمشي عالمين على اللي هي من سفر
+
+136
+00:09:12,210 --> 00:09:16,250
+لعند واحد هتظلها ايش قيمتها قيمتها سفر فاهمين عليش
+
+137
+00:09:16,250 --> 00:09:21,600
+بقول الان as n goes to infinityهذه الآن بتبدأ اللي
+
+138
+00:09:21,600 --> 00:09:26,000
+هي .. هذي بيصير الان نص .. هذي المنطقة كلها .. آسف
+
+139
+00:09:26,000 --> 00:09:28,040
+.. هذي المنطقة كلها هذا اللي بيتمد .. مش هدوله ..
+
+140
+00:09:28,040 --> 00:09:31,440
+هذي اللي بيتمد اللي هي اتنين على ان بتجربها ان ..
+
+141
+00:09:31,440 --> 00:09:34,220
+بتصغر as and goes to infinity واحدة على ان بتجربها
+
+142
+00:09:34,220 --> 00:09:37,850
+انلأن as n goes to infinity بيهدفك بروح لمين في دا
+
+143
+00:09:37,850 --> 00:09:42,750
+السفر يعني بيصير ده لكلها من معرفة ك zero function
+
+144
+00:09:42,750 --> 00:09:46,370
+يعني limit of n of x as n goes to infinity بيساوي
+
+145
+00:09:46,370 --> 00:09:54,030
+اللي هي سفر لكل x limit الفترة 01 مدام سفرأه إذا
+
+146
+00:09:54,030 --> 00:09:57,530
+صار عنده اللي هو لاحظوا ال convergence point wise
+
+147
+00:09:57,530 --> 00:10:01,350
+convergence بعتمد عالميا على x في كل حاجة اللي هو
+
+148
+00:10:01,350 --> 00:10:05,010
+ال integration من سفر اللي عنده واحد f of x dx إيش
+
+149
+00:10:05,010 --> 00:10:09,630
+هيساوي؟ هيساوي zero لأن قيمة ال function كله وين
+
+150
+00:10:09,630 --> 00:10:14,510
+هتيجي على اللي هي السفر فبكون ال integration اللي
+
+151
+00:10:14,510 --> 00:10:19,770
+بيساوي zero اللي بدي أنا .. اللي بدي أفله نلاحظ
+
+152
+00:10:20,580 --> 00:10:27,480
+اللي وصلتله ان ال integration من 0 و 1 لل F of X
+
+153
+00:10:27,480 --> 00:10:33,040
+DX بيساوي 0 أكيد بيسويش 1 اللي هو بيساوي اللي هو
+
+154
+00:10:33,040 --> 00:10:39,510
+مين هذا الواحد limit لل integrationمن zero and
+
+155
+00:10:39,510 --> 00:10:46,170
+واحد F N of X DX as N goes to infinity مظبوط؟ لأن
+
+156
+00:10:46,170 --> 00:10:49,530
+ال integration هذا طلع دايما إيش حيساوي؟ حيساوي
+
+157
+00:10:49,530 --> 00:10:54,130
+واحد بغض النظر عن قيمة ال N إذا هذا ال limit لل
+
+158
+00:10:54,130 --> 00:10:59,270
+integration هاي اللي بتوصله وليس شرط يساوي إيش ال
+
+159
+00:10:59,270 --> 00:11:03,250
+integration لل limit رغم إن ال F طلعت مالها
+
+160
+00:11:03,250 --> 00:11:09,070
+Integrable ال limit يعني ال N limitأف ان of X لما
+
+161
+00:11:09,070 --> 00:11:14,810
+ان تروح لنهاية اللي عندي ايش بيساوي F of X بالرغم
+
+162
+00:11:14,810 --> 00:11:19,810
+من هيك اللي هو هذا الكلام لكل X وين موجودة لكل X
+
+163
+00:11:19,810 --> 00:11:25,990
+موجودة في الفترة 01 بالرغم من هيكالان الـ
+
+164
+00:11:25,990 --> 00:11:31,790
+integration limit للـ integration من C1 لـ F of X,
+
+165
+00:11:32,290 --> 00:11:39,570
+N of X, DX ما سواش لل integration من 0 ل1 limit لـ
+
+166
+00:11:39,570 --> 00:11:45,070
+F, N of Xيعني ايش اللي بقصده اللي هو ماقدرتش ال
+
+167
+00:11:45,070 --> 00:11:49,710
+limit تدخل لجوه ال integration في ضوء ال pointwise
+
+168
+00:11:49,710 --> 00:11:53,470
+convergence وفي ضوء ان ال limit نفسها طلعت
+
+169
+00:11:53,470 --> 00:11:58,050
+integrable اذا الان هنا ال pointwise convergence
+
+170
+00:11:58,050 --> 00:12:02,570
+قد يعطي انه اللي هو ال function تكون اللي هو
+
+171
+00:12:02,570 --> 00:12:07,560
+integrable لكن لا يمكنإنه .. أو .. أيه .. أو ..
+
+172
+00:12:07,560 --> 00:12:11,280
+آسف ليس شرطا أن يكون limit لل integration بساوي ال
+
+173
+00:12:11,280 --> 00:12:14,600
+integration لل limit إذا بدنا دفعة أكبر من ال
+
+174
+00:12:14,600 --> 00:12:17,820
+pointwise convergence و الحالتين ال continuity و
+
+175
+00:12:17,820 --> 00:12:21,600
+ال integrability هانفتنتين الدفعة هذه هي ال
+
+176
+00:12:21,600 --> 00:12:25,970
+uniform convergence و هنشوف هذا الكلاممن خلال
+
+177
+00:12:25,970 --> 00:12:31,770
+النظريات القادمة أول نظرية عندنا هذه النظرية اللي
+
+178
+00:12:31,770 --> 00:12:35,750
+هي هتتعلق بالـ sequence of continuous functions
+
+179
+00:12:35,750 --> 00:12:40,090
+كيف أنه لو كانت اللي هي sequence of continuous
+
+180
+00:12:40,090 --> 00:12:43,570
+functions converts uniformly to some function F
+
+181
+00:12:43,570 --> 00:12:46,690
+then F must be continuous
+
+182
+00:12:49,500 --> 00:12:54,300
+طيب يا جماعة الان نيجي theorem 8.2.2 بتقول ما يلي
+
+183
+00:12:54,300 --> 00:12:57,520
+الان نتقف ان بيه a sequence of continuous
+
+184
+00:12:57,520 --> 00:13:02,860
+functionson a set A subset من R، إذاً Fn عبارة عن
+
+185
+00:13:02,860 --> 00:13:07,300
+متتابعة من الدوالي المتصلة على الفترة A subset من
+
+186
+00:13:07,300 --> 00:13:12,360
+R and suppose that اللي هي الـ Fn converges
+
+187
+00:13:12,360 --> 00:13:15,640
+uniformly on A to a function F من A لعند R، بقول
+
+188
+00:13:15,640 --> 00:13:21,200
+إذا ولا يهمك مضمون إن الـ F نفسها تكون إيش ما لها
+
+189
+00:13:21,200 --> 00:13:24,400
+is a continuous function، إذاً
+
+190
+00:13:30,480 --> 00:13:36,500
+المقاومة للمعاملات المستمرة هي مستمرة باستخدام
+
+191
+00:13:36,500 --> 00:13:41,880
+المعاملة المستمرة المستمرة المستمرة المستمرة
+
+192
+00:13:41,880 --> 00:13:43,080
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+193
+00:13:43,080 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+194
+00:13:43,760 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+195
+00:13:43,760 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+196
+00:13:43,760 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+197
+00:13:43,760 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+198
+00:13:43,760 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+199
+00:13:43,760 --> 00:13:43,760
+المستمرة المستمرة المستمرة المستمرة المستمرة
+
+200
+00:13:43,760 --> 00:13:50,400
+المستمرة المستمرة المستمرة المستمرة المستأو نصل
+
+201
+00:13:50,400 --> 00:13:54,440
+إلى أن الـ F نفسها continuous عالميا على الـ A
+
+202
+00:13:54,440 --> 00:13:59,280
+element الـ R خلّينا بس نرتب حاجة ده بما أن F
+
+203
+00:13:59,280 --> 00:14:03,180
+unconverts uniform للـ F on A إذا حسب التعريف الـ
+
+204
+00:14:03,180 --> 00:14:05,820
+uniform convergence لكل يسون أكبر من سفر there
+
+205
+00:14:05,820 --> 00:14:10,690
+exists actuallyof epsilon اللي هو such that أو
+
+206
+00:14:10,690 --> 00:14:13,530
+there exists H such that الـH هتتمد على مين؟ على
+
+207
+00:14:13,530 --> 00:14:16,630
+الـEpsilon if N أكبر يسوى H لأنه for convergence
+
+208
+00:14:16,630 --> 00:14:20,470
+زي ما انتوا عارفين such that if N أكبر يسوى H then
+
+209
+00:14:20,470 --> 00:14:24,610
+F N of X ناقص F of X أصغر من Epsilon ع تلاتة حرن
+
+210
+00:14:24,610 --> 00:14:27,230
+أصغر من Epsilon في الدنيا من ضمنها مين؟ Epsilon
+
+211
+00:14:27,230 --> 00:14:32,010
+على تلاتة for all X element in مين؟ in A إذا الأن
+
+212
+00:14:32,010 --> 00:14:41,540
+أول حاجة لكل Epsilonأكبر من 0 لجينا H such that
+
+213
+00:14:41,540 --> 00:14:46,780
+element of N طبعاً such that for every N أكبر أو
+
+214
+00:14:46,780 --> 00:14:55,100
+يساوي H عندي F N of X نقص F of X أصغر من Y ع تلاتة
+
+215
+00:14:55,100 --> 00:15:04,390
+لكل X element من A هذه أول واحدةلأن let C element
+
+216
+00:15:04,390 --> 00:15:09,870
+in A be arbitrary but fixed ليش؟ بدي أثبتلك أن F
+
+217
+00:15:09,870 --> 00:15:16,050
+continuous on A، F تبعتنا، هي المطلوبكيف بدى
+
+218
+00:15:16,050 --> 00:15:20,150
+أثبتها؟ بدى أخد أي C Fixed لكن Arbitrary إن إيه
+
+219
+00:15:20,150 --> 00:15:23,230
+بما إنه C Arbitrary لو أثبتنا F Continuous and
+
+220
+00:15:23,230 --> 00:15:26,190
+الـC بتكون F Continuous على كل الـMain الـA كيف
+
+221
+00:15:26,190 --> 00:15:31,530
+بدى أثبتها؟ بدى أثبتلك Limit F of X لما X بتروح
+
+222
+00:15:31,530 --> 00:15:36,430
+للـC أش بتساوي F of C إيش معناته هذا؟ معناته لكل ي
+
+223
+00:15:36,430 --> 00:15:40,910
+أكبر من صفر بدى لاجي K element none such that as
+
+224
+00:15:40,910 --> 00:15:49,500
+تلاقي Deltaاللي هو أكبر من سفر such that X minus C
+
+225
+00:15:49,500 --> 00:15:55,280
+أصغر من Delta يعطيني F of X ناقص F of C أصغر من
+
+226
+00:15:55,280 --> 00:16:00,260
+مين من Y هذا اللي بدأ أثبته عشان أصل لمين لل F
+
+227
+00:16:00,260 --> 00:16:04,440
+continuous عند ال C اللي هي كانت arbitrary في ال A
+
+228
+00:16:04,440 --> 00:16:08,620
+إذا F continuous على كل ال A ده هنشوفه الآن طيب
+
+229
+00:16:10,260 --> 00:16:13,740
+استخدمها معناه الـ for convergence هيه وأخدت C
+
+230
+00:16:13,740 --> 00:16:18,800
+arbitrary point but fixed in A then الآن احسب مالي
+
+231
+00:16:18,800 --> 00:16:24,420
+اف .. طبعا هذا الكلام بس جاب المبدأ هنا هذا صحيح
+
+232
+00:16:24,420 --> 00:16:31,800
+لكل N أكبر أو يساوي H من ضمنها صحيح للـH يعني
+
+233
+00:16:31,800 --> 00:16:36,260
+هلاجي ان FH of X ناقص F of X أصغر من مين؟ من
+
+234
+00:16:36,260 --> 00:16:41,540
+إبسلون ع تلاتة لكل X element in Aبرضه صحيح لل F H
+
+235
+00:16:41,540 --> 00:16:48,840
+of C ناقص F of C أصغر من F3 لكل X element A صحيح
+
+236
+00:16:48,840 --> 00:16:52,340
+من ضمن ال X والC وغير و الاخر هي كل العناصر اللي
+
+237
+00:16:52,340 --> 00:16:57,520
+في ال Aأحسبلي الآن F of X ناقص F of C أصغر أو
+
+238
+00:16:57,520 --> 00:17:03,120
+أساوي F of X ناقص F H of X زاد F H of X ناقص F H
+
+239
+00:17:03,120 --> 00:17:06,980
+of C زاد F H of C ناقص F of C يعني إيش اللي سويته
+
+240
+00:17:06,980 --> 00:17:11,680
+اللي هو ضفت قمتين و طرحتين ضفت ال H of X F H of X
+
+241
+00:17:11,680 --> 00:17:16,320
+وضفت ال F H of C عشان بدي أستخدم اللي فوق عشان أصل
+
+242
+00:17:16,320 --> 00:17:24,660
+للي بديها شوف كيف اللي عنديالـ Fx ناقص Fh of X من
+
+243
+00:17:24,660 --> 00:17:29,320
+اللي فوق أصغر من ي على تلاتة هذه نزلوها زي ما هي
+
+244
+00:17:29,320 --> 00:17:33,240
+تسيبوكوا منها هذه Fh of C ناقص F of C أصغر من ي
+
+245
+00:17:33,240 --> 00:17:38,760
+برضه من ي على تلاتة إذا الآن اللي حصلته لكل ي أكبر
+
+246
+00:17:38,760 --> 00:17:45,620
+من 0 لجيت H أبحث
+
+247
+00:17:46,530 --> 00:17:54,690
+إنه لكل N أكبر أو سوء H طلع عندي F X ناقص F of C
+
+248
+00:17:54,690 --> 00:18:00,470
+أصغر من Epsilon ع تلاتة وزائد Epsilon ع تلاتة يعني
+
+249
+00:18:00,470 --> 00:18:04,910
+اتنين Epsilon ع تلاتة زائد ال absolute value ل F H
+
+250
+00:18:04,910 --> 00:18:14,170
+of X ناقص F H of C هذه الآناللي هيسعفني ان هو
+
+251
+00:18:14,170 --> 00:18:18,610
+مفترض لي ان ال FN اللي هي ال sequence كلها
+
+252
+00:18:18,610 --> 00:18:24,010
+continuous عند ال A كلها، اذا اكيد ال FH اللي هي
+
+253
+00:18:24,010 --> 00:18:27,810
+واحدة من ال sequence is continuous عند مين، عند كل
+
+254
+00:18:27,810 --> 00:18:31,930
+العناصر اللي في ال A، من ضمن هنا ال C اللي أخدت
+
+255
+00:18:31,930 --> 00:18:37,490
+fixed but arbitrary و هيك، هبتكون أنا بديت أنهي
+
+256
+00:18:37,490 --> 00:18:42,700
+البرهان، شوف كيفهذه حصلناها طيب الأن أكيد هيقولنا
+
+257
+00:18:42,700 --> 00:18:47,860
+since FH is continuous at C مدام continuous at C
+
+258
+00:18:47,860 --> 00:18:53,800
+إذا لكل ي أكبر من سفر بقدر ألاقي Delta الـ Delta
+
+259
+00:18:53,800 --> 00:18:57,700
+هذه طبعا بدي نوّهلك ويقولك الـ Delta أكيد هتعتمد
+
+260
+00:18:57,700 --> 00:19:01,920
+عالميا على الـ Y وهتعتمد على الـ C لأنه أنا باخد
+
+261
+00:19:01,920 --> 00:19:06,790
+ال continuity لعند مين عند النقطة Cوهتعتمد على ال
+
+262
+00:19:06,790 --> 00:19:11,470
+FH لأنه مااخد ال continuity لمن أنا لل FH إذا
+
+263
+00:19:11,470 --> 00:19:17,610
+الدلتا هذه هي بتعتمد على ال FH و C لل Y على 3 لإنه
+
+264
+00:19:17,610 --> 00:19:24,650
+أنا بدأ استخدم limit FH of X لما X تروح للـC بسوء
+
+265
+00:19:24,650 --> 00:19:30,590
+FH of C يعني لكل Y أكبر من 0 there exists Delta
+
+266
+00:19:30,590 --> 00:19:35,630
+الـDelta هذه لمين تعتمد على الـC وتعتمد على الـFH
+
+267
+00:19:35,630 --> 00:19:40,470
+وتعتمد على مين على اللي هي الـY اللي بتاخدها
+
+268
+00:19:40,470 --> 00:19:45,340
+arbitrarily ماشي الحال طيبإذا التعريف هذا بدي
+
+269
+00:19:45,340 --> 00:19:48,860
+أترجمه لكل إبسلون أكبر من صفر there exist اللي هي
+
+270
+00:19:48,860 --> 00:19:53,300
+Delta أكبر من صفر such that لما X minus C كان أصغر
+
+271
+00:19:53,300 --> 00:19:57,420
+من Delta والـ X في الـ A يعطيني الفرق بين التنتين
+
+272
+00:19:57,420 --> 00:20:00,620
+هدولة أصغر من مين من أي إبسلون في الدنيا من ضمن
+
+273
+00:20:00,620 --> 00:20:04,820
+إبسلون ع تلاتة واضحة الصورة الآن هذه الآن بدي
+
+274
+00:20:04,820 --> 00:20:09,090
+أدمجها مع حد بيصير عندي لكل إبسلونأكبر من سفر
+
+275
+00:20:09,090 --> 00:20:13,330
+there exist Delta أكبر من سفر such that for every
+
+276
+00:20:13,330 --> 00:20:18,610
+X element in A بتحقق X minus C أصغر من Delta اللي
+
+277
+00:20:18,610 --> 00:20:26,230
+هو بيعطيني then F of X ناقص F of C أصغر من 2 Y ع 3
+
+278
+00:20:27,010 --> 00:20:31,930
+ومن هذه أصغر من ي على تلاتة يعني بمعنى أخر أصغر من
+
+279
+00:20:31,930 --> 00:20:37,270
+ي وهذا بالظبط معناته أنه limit f of x لما x تروح ل
+
+280
+00:20:37,270 --> 00:20:40,570
+c بيساوي f of c وهذا كانت c element in a
+
+281
+00:20:40,570 --> 00:20:46,170
+arbitrarily إذا f is continuous on a إذا خلصنا
+
+282
+00:20:46,170 --> 00:20:51,690
+النظرية الأولى اللي هي اللي بتتعلق بال sequence of
+
+283
+00:20:51,690 --> 00:20:52,430
+continuous functions
+
+284
+00:20:58,670 --> 00:21:05,130
+طيب نشوف ال .. ال remark يا جماعة ال
+
+285
+00:21:05,130 --> 00:21:07,430
+remark بيقول لي the limit of a sequence of
+
+286
+00:21:07,430 --> 00:21:10,370
+continuous functions may be continuous but the
+
+287
+00:21:10,370 --> 00:21:13,590
+convergence is pointwise يعني بيقولك يعني ممكن أنت
+
+288
+00:21:13,590 --> 00:21:17,250
+تلاقيلك اللي هو sequence of functions continuous
+
+289
+00:21:17,250 --> 00:21:20,870
+ويكون ال pointwise convergence ويروح لمين ل
+
+290
+00:21:20,870 --> 00:21:25,660
+continuous functions طبعا ممكن أكيدو جبلنا دوال ..
+
+291
+00:21:25,660 --> 00:21:30,920
+دوال من هالنوع اللي هو كان عندى اللي هى ال .. اذا
+
+292
+00:21:30,920 --> 00:21:37,480
+بتتذكروا اظن انتبهتنا قبل شوية انه
+
+293
+00:21:37,480 --> 00:21:48,100
+fn of x بساوى x على n هذه continuous طبعا on Rو F
+
+294
+00:21:48,100 --> 00:21:53,840
+of X اللي هي limitها limit F N of X لما N تروح لما
+
+295
+00:21:53,840 --> 00:21:57,940
+نهاية بساوي اللي هو عبارة عن سفر هذه برضه اي
+
+296
+00:21:57,940 --> 00:22:02,000
+شمالها continuous function بالرغم من ان ال F N
+
+297
+00:22:02,000 --> 00:22:06,780
+بتروح لل F point twice but ال F N does not
+
+298
+00:22:06,780 --> 00:22:10,660
+converge لل F uniformly زي ما أثبتنا يعني ممكن
+
+299
+00:22:10,660 --> 00:22:14,280
+اللي هو ال point twice convergence يكون limitه
+
+300
+00:22:14,280 --> 00:22:16,420
+continuous function لما تكون sequence of
+
+301
+00:22:16,420 --> 00:22:20,810
+continuous functionsطبيعي لكن احنا بنقول الضمان
+
+302
+00:22:20,810 --> 00:22:25,010
+انه يطلع continuous انها تكون uniform convergence
+
+303
+00:22:25,010 --> 00:22:30,830
+وجبنا مثال على انه اللي هو اللي هي sequence of
+
+304
+00:22:30,830 --> 00:22:34,130
+continuous functions converge pointwise to some
+
+305
+00:22:34,130 --> 00:22:36,730
+function that is not continuous زي ما شوفنا في
+
+306
+00:22:36,730 --> 00:22:41,610
+المثال الأول نيجي الآن نحكي عن موضوع او الجزء
+
+307
+00:22:41,610 --> 00:22:47,770
+المتعلق بمينالجزء المتعلق بالـ Integrable
+
+308
+00:22:47,770 --> 00:22:54,370
+Functions الآن نشوف أيش العلاج لإنه نضمن الـ Limit
+
+309
+00:22:54,370 --> 00:22:56,730
+للـ Integration بساوي الـ Integration للـ Limit أو
+
+310
+00:22:56,730 --> 00:22:59,850
+اللي هو لما ندخل الـ Limit للـ Integration متى
+
+311
+00:22:59,850 --> 00:23:04,590
+بنقدر ندخله ويظل المحافظة على المساوية Let FN be a
+
+312
+00:23:04,590 --> 00:23:07,750
+sequence of functions that are integrable on A وB
+
+313
+00:23:08,610 --> 00:23:13,110
+and suppose that FN converges uniformly من A و B
+
+314
+00:23:13,110 --> 00:23:19,150
+to F then إذا لما تكون ال convergence uniform then
+
+315
+00:23:19,150 --> 00:23:23,850
+ال F is integrable من A و B هاي واحد اتنين ال
+
+316
+00:23:23,850 --> 00:23:27,210
+integration لل F of X DX من A لعين B بسوء ال limit
+
+317
+00:23:27,210 --> 00:23:29,870
+لل integration يعني بمعنى أخر ال limit لل
+
+318
+00:23:29,870 --> 00:23:33,910
+integration بسوء ال integration لل limitلما نكون
+
+319
+00:23:33,910 --> 00:23:38,490
+هذا ماله uniform convergence خلّينا نشوف اللي هو
+
+320
+00:23:38,490 --> 00:23:43,270
+البرهان الان خلّينا نسمي الفترة تبعتنا let J
+
+321
+00:23:43,270 --> 00:23:47,950
+بتساوي A وB الان بما أن FN بتروح لل F uniform اللي
+
+322
+00:23:47,950 --> 00:23:53,540
+في صناعة الكلام هذاالان تنسوش ان الـ Fn is
+
+323
+00:23:53,540 --> 00:23:56,320
+integrable يعني ايش ما لها bounded يعني ال
+
+324
+00:23:56,320 --> 00:23:58,200
+sequence of bounded functions و زي ما صارت ال
+
+325
+00:23:58,200 --> 00:24:01,980
+sequence of bounded functions اذا automatic بتتحقق
+
+326
+00:24:01,980 --> 00:24:05,900
+ان اللي هي اللي ما اللي هي تبعت ال norm لل F ناقص
+
+327
+00:24:05,900 --> 00:24:13,130
+Fm اللي هو بتروح للسفر يعني Fn يعني Fnبتروح للـ F
+
+328
+00:24:13,130 --> 00:24:18,850
+uniformly معناته Fn ناقص F اللي هو ايه شماله over
+
+329
+00:24:18,850 --> 00:24:22,650
+some .. over ايه او اللي مسميها J goes to mean to
+
+330
+00:24:22,650 --> 00:24:26,890
+zero يعني normal Fn ناقص الـ F أصغر من يبسطه يعني
+
+331
+00:24:26,890 --> 00:24:29,190
+forever يبسطه نقوم نسيف it there exists كي لم
+
+332
+00:24:29,190 --> 00:24:31,710
+تنساش that forever أن أكبر شهو K أفقن ناقص أفقر
+
+333
+00:24:31,710 --> 00:24:36,150
+أصغر من مين من الـ Y عارفين هالقصة طيب .. طيب نيجي
+
+334
+00:24:36,150 --> 00:24:40,630
+الأنلت جيب سواء a و b since fn converts uniformly
+
+335
+00:24:40,630 --> 00:24:44,650
+to f و since fn is integrable then fn is bounded
+
+336
+00:24:44,650 --> 00:24:48,830
+then we can use our lemma then for every epsilon
+
+337
+00:24:48,830 --> 00:24:52,510
+there exists k of epsilon such that if n أكبر سواء
+
+338
+00:24:52,510 --> 00:24:58,940
+k of epsilon هذه we have f ناقص fnأصغر من Epsilon
+
+339
+00:24:58,940 --> 00:25:01,540
+على أربعة في B minus A أصغر من Epsilon في الدنيا
+
+340
+00:25:01,540 --> 00:25:04,280
+من ضمنها Epsilon على أربعة في B minus A هذه
+
+341
+00:25:04,280 --> 00:25:08,760
+للحسابات زي العادة ما بنحكي فيها بحكي عنها و طبعا
+
+342
+00:25:08,760 --> 00:25:14,400
+في لها تفسير و فسرنا كتير في أوقات
+
+343
+00:25:14,400 --> 00:25:19,580
+سابقة هذه سميها واحد الآن اللي سمينا ال K of
+
+344
+00:25:19,580 --> 00:25:23,520
+Epsilon هذه سمينا هي إيش K للتسهيل بس الان FK is
+
+345
+00:25:23,520 --> 00:25:28,590
+integrableأه then مدام integrable اذا there exist
+
+346
+00:25:28,590 --> 00:25:33,730
+a partition بي ابسلون لل FK هذه X not X واحد X and
+
+347
+00:25:33,730 --> 00:25:37,470
+such that ال U بي ابسلون و FK نقص ال ابسلون بي
+
+348
+00:25:37,470 --> 00:25:40,190
+ابسلون و FK أصغر من مين من أي ابسلون في الدنيا
+
+349
+00:25:40,190 --> 00:25:43,370
+نضيب انها ابسلون على اتنين عارفين هذي ايش هذي هذي
+
+350
+00:25:43,370 --> 00:25:45,950
+اللي هي ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+351
+00:25:45,950 --> 00:25:46,930
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+352
+00:25:46,930 --> 00:25:46,950
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+353
+00:25:46,950 --> 00:25:47,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+354
+00:25:47,750 --> 00:25:49,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+355
+00:25:49,330 --> 00:25:49,930
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+356
+00:25:49,930 --> 00:25:53,420
+.. ال .. ال .. ال .. ال .. ال .. الإذا صار عندى
+
+357
+00:25:53,420 --> 00:25:57,640
+الآن من الـ Integrability للـ FK حصلنا ع بارتيشين
+
+358
+00:25:57,640 --> 00:26:01,100
+بي إبسلون بحيث أن ال Upper نقص ال Lower أصغر من
+
+359
+00:26:01,100 --> 00:26:07,800
+الـ Y على 2 لهذا ال بارتيشين الآن عندى فوق F of X
+
+360
+00:26:07,800 --> 00:26:11,520
+نقص FK of X أصغر من Y على 2 على 4 B minus A for
+
+361
+00:26:11,520 --> 00:26:16,410
+every X element in A by 2 by 1 thenخلّينا اللي هو
+
+362
+00:26:16,410 --> 00:26:20,850
+نكمل ال .. ال .. ال .. البرهان هي هذه اللي هي
+
+363
+00:26:20,850 --> 00:26:29,290
+خلّينا اكتبها عشان اللي هو نتذكر اللي هي نلم
+
+364
+00:26:29,290 --> 00:26:37,950
+الخطوات تبعتنا اللي عندي FMF ناقص FM أو FN أصغر من
+
+365
+00:26:37,950 --> 00:26:40,910
+إبسلون على أربعة في B minus A هذه B minus A طول
+
+366
+00:26:40,910 --> 00:26:44,970
+الفترة تبعت AJ الـ J الآن الـ partition عندي اللي
+
+367
+00:26:44,970 --> 00:26:52,410
+هو U بإبسلون أو F ناقص FH أو FK ناقص منها ناقص L
+
+368
+00:26:52,410 --> 00:26:59,370
+بإبسلون و FK أصغر من إبسلون على كده؟ على اتنين
+
+369
+00:26:59,370 --> 00:27:07,470
+للحسابات طيب الآنبقول لي من هذه من هذه أكيد أكبر
+
+370
+00:27:07,470 --> 00:27:12,650
+أو يساوي F ناقص FN of X يعني من هذه بنقدر نحصل هذا
+
+371
+00:27:12,650 --> 00:27:17,850
+صحيح لكل N أكبر أو يساوي K من ضمنها اللي هي N إيش
+
+372
+00:27:17,850 --> 00:27:21,890
+بتساوي زي ما احنا متعودين بنستخدم اللي بلزمنا اللي
+
+373
+00:27:21,890 --> 00:27:28,910
+هي FK يعني بيصير هذا أكبر أو يساوياللي هو f of x
+
+374
+00:27:28,910 --> 00:27:35,250
+ناقص fn of x لكل x element in J لأن من ضمن الأنات
+
+375
+00:27:35,250 --> 00:27:40,010
+هذه اللي هي main الـ K يعني بيصير عنده fn أو زي ما
+
+376
+00:27:40,010 --> 00:27:47,110
+هو مسميها f of x ناقص fk of x absolute value صار
+
+377
+00:27:47,110 --> 00:27:53,430
+أصغر من ي على أربعةبـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ-
+
+378
+00:27:53,430 --> 00:27:53,490
+بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ
+
+379
+00:27:53,490 --> 00:27:54,170
+- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ-
+
+380
+00:27:54,170 --> 00:27:59,490
+بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ
+
+381
+00:27:59,490 --> 00:27:59,490
+- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ-
+
+382
+00:27:59,490 --> 00:27:59,490
+بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ- بـ
+
+383
+00:27:59,490 --> 00:28:06,630
+- بـ- بـ- بـ- بـفكنا هذه بيصير عندي الان F of X
+
+384
+00:28:06,630 --> 00:28:12,090
+ناقص Y على 4 في B minus A أذر أو يساوي FK of X
+
+385
+00:28:12,090 --> 00:28:16,450
+عارفين طبعا كيف اللي هو أكبر أذر يساوي و أكبر ساوي
+
+386
+00:28:16,450 --> 00:28:21,350
+ناقصها اللي FK نجلت هنا بيصير F of X وجبتها دي هنا
+
+387
+00:28:21,350 --> 00:28:24,310
+بيصير F of X ناقص Y على 4 في B minus A أذر يساوي
+
+388
+00:28:24,310 --> 00:28:30,250
+FK of Xوهذه نفسها fk of x أكيد أصغر أو يساوي ال
+
+389
+00:28:30,250 --> 00:28:34,410
+absolute value لل fk of x زي ما انتوا عارفين وال
+
+390
+00:28:34,410 --> 00:28:36,550
+absolute value لل fk of x أصغر أو يساوي ال
+
+391
+00:28:36,550 --> 00:28:42,230
+supremum لل absolute value له المصورة عامة اللي هو
+
+392
+00:28:42,230 --> 00:28:45,550
+على الفترة xj minus واحد لل xj اللي هو إيش اللي
+
+393
+00:28:45,550 --> 00:28:50,760
+بنسميه اللي هو ال mj اللي هو تبع ال upper sumالان
+
+394
+00:28:50,760 --> 00:28:58,040
+صار عندي ال F of X ال F of X نسجلها هذه F of X أثر
+
+395
+00:28:58,040 --> 00:29:08,440
+أو ساوي Y على 4 في B minus A زائد MJ of FK لكل X
+
+396
+00:29:08,440 --> 00:29:17,970
+لكل إيش؟ اللي هي X X وين في الفترة؟ اللي هو XJأو
+
+397
+00:29:17,970 --> 00:29:23,890
+ناقص واحد و XJ وهذا وين يا جماعة نفسه اللي هو لكل
+
+398
+00:29:23,890 --> 00:29:31,510
+J من واحد و اتنين لعند مين الان طيب لأ
+
+399
+00:29:31,510 --> 00:29:36,450
+هذه حتى لكل X لأن هذه ال X هذه أخدناها arbitrarily
+
+400
+00:29:36,450 --> 00:29:47,720
+في ال J هذه لكل X في ال J نعم خلينا نسجل صح طيبإذا
+
+401
+00:29:47,720 --> 00:29:49,960
+استخدمنا اللي هو معناته ال uniform convergence
+
+402
+00:29:49,960 --> 00:29:54,640
+حصلنا على هذه استخدمنا ال integrability لل FK اللي
+
+403
+00:29:54,640 --> 00:29:57,820
+لاجيناها هذه المرتبطة بال K اللي لاجيناها عشانها
+
+404
+00:29:57,820 --> 00:30:02,340
+اللي هي N أكوا سوا K ومنها استخدمنا اللي هو
+
+405
+00:30:05,130 --> 00:30:10,310
+اللي فوق لل FK بالذات هذه أصغر من هذه وهذه حصلنا
+
+406
+00:30:10,310 --> 00:30:13,730
+على ال inequality هذه عشان بضروح أثبت ال
+
+407
+00:30:13,730 --> 00:30:17,430
+integrability لمين لل F نفسها شوفوا كيفنا نثبت
+
+408
+00:30:17,430 --> 00:30:23,690
+الآن صار عندي الآنF of X أصغر سواء هذا في هذا
+
+409
+00:30:23,690 --> 00:30:28,770
+وعارفين إيش معنات اللي هو M J of F K الان M J of F
+
+410
+00:30:28,770 --> 00:30:31,090
+زي ما انتوا عارفين إيش بتساوي ال supermom ل F of X
+
+411
+00:30:31,090 --> 00:30:35,370
+اللي على فترة مين X اللي هي في J minus واحد وJ
+
+412
+00:30:35,370 --> 00:30:40,670
+أكيد اللي هي ال ها دي هتكون أصغر من Y على 4 في B
+
+413
+00:30:40,670 --> 00:30:48,220
+minus A زائد M J عليها عارفين ليش لأن ال F of XF
+
+414
+00:30:48,220 --> 00:30:52,440
+of X أصغر أو ساوي هذا القيمة، مظبوط؟ إذا صارت هذه
+
+415
+00:30:52,440 --> 00:30:56,940
+القيمة عبارة عن اللي هو upper bound of the mean
+
+416
+00:30:56,940 --> 00:31:01,580
+للـ F of X، ماشي الحال صارت هذه upper bound، إذا
+
+417
+00:31:01,580 --> 00:31:04,820
+ال least upper bound، ال supremum، هيظل أصغر أو
+
+418
+00:31:04,820 --> 00:31:09,140
+ساوي هذه القيمة، لأن هذه القيمة عبارة عن عدد، صار
+
+419
+00:31:09,140 --> 00:31:13,420
+الآن M J of F أصغر أو ساوي هذا المقدر، وضحكة هذه
+
+420
+00:31:13,420 --> 00:31:19,780
+أعملناها كتير، إذا صار عندي MJ of Fأصغر أو يساوي
+
+421
+00:31:19,780 --> 00:31:28,060
+MJ of FK زايد إبسلون على أربعة في B minus A هذا
+
+422
+00:31:28,060 --> 00:31:33,240
+الكلام اللي هو لكل اللي هي من J واحد واتنين عند
+
+423
+00:31:33,240 --> 00:31:36,760
+الناقص واحد الباقي انتوا عارفينه دايما بنعمله اضرب
+
+424
+00:31:36,760 --> 00:31:43,520
+لهنا في XJ ناقص XJ minus واحد واضرب هنا في XJ ناقص
+
+425
+00:31:43,520 --> 00:31:49,300
+XJ minus واحد وهنا في XJ minus XJ minus واحدضربنا
+
+426
+00:31:49,300 --> 00:31:54,200
+اللي هو الترفيه المتباينة في XJ minus XJ minus
+
+427
+00:31:54,200 --> 00:31:58,780
+واحد و بعدين أخدنا ال summation J من عند واحد لعند
+
+428
+00:31:58,780 --> 00:32:02,700
+N و أخدنا ال summation J من عند واحد لعند N و
+
+429
+00:32:02,700 --> 00:32:06,880
+أخدنا ال summation J من عند واحد لعند N هذا كله
+
+430
+00:32:06,880 --> 00:32:11,020
+على بعضه طبعا كل شغلنا على ال BY اللي لاجناها ال
+
+431
+00:32:11,020 --> 00:32:15,180
+partition اللي لاجناها فوق اللي هو عندي هذا عبارة
+
+432
+00:32:15,180 --> 00:32:23,430
+عن اللي هي ال Uof اللي هو الـ partition بي ابسلون
+
+433
+00:32:23,430 --> 00:32:28,290
+اللي بدي اشتغل عليه هدولة الهن و mean و A اللي هي
+
+434
+00:32:28,290 --> 00:32:34,250
+ال function F أصغر أو يساوي هذا mean هو ال U اللي
+
+435
+00:32:34,250 --> 00:32:40,010
+هو ال بي ابسلون و ال FK و هد ايش هتكون عبارة عن
+
+436
+00:32:40,010 --> 00:32:44,320
+ايش عشان هيك أخدنا بي مايلوس ايه هتشوفوهاالآن هذه
+
+437
+00:32:44,320 --> 00:32:50,400
+y زائد y على أربعة في b minus a ال summation هذا
+
+438
+00:32:50,400 --> 00:32:54,160
+لل sub intervals اللي هو زي ما انتوا عارفين x واحد
+
+439
+00:32:54,160 --> 00:32:57,780
+نقص x not زائد x اتنين نقص x واحد لما أصل ل xn نقص
+
+440
+00:32:57,780 --> 00:33:01,600
+xn نقص واحد يعني هيضل في الآخر xn نقص x not يعني b
+
+441
+00:33:01,600 --> 00:33:06,980
+minus a في b minus a هذه بتروح مع هذه فبصير عندي
+
+442
+00:33:06,980 --> 00:33:13,610
+ال uأصغر من الـ U هذا زي إبسلون على أربعة اللي
+
+443
+00:33:13,610 --> 00:33:17,450
+عنده اللي هو الـ U بإبسلون F أصغر يسوي U بإبسلون
+
+444
+00:33:17,450 --> 00:33:21,570
+FK زي إبسلون على أربعة Similarly وفعلا Similarly
+
+445
+00:33:21,570 --> 00:33:25,690
+بعد بدل ما نشتغل على الأبراللي فوق بدل ما نشتغل
+
+446
+00:33:25,690 --> 00:33:30,870
+على الأبر هنا بنشتغل عالميا على اللاور اللي بيطلع
+
+447
+00:33:30,870 --> 00:33:34,350
+عند ال ال ب إبسلون و أف هذا بيبقى لكم ال ب إبسلون
+
+448
+00:33:34,350 --> 00:33:38,030
+و أف كيه ناقص إبسلون على أربع أصغر من ال ب إبسلون
+
+449
+00:33:38,030 --> 00:33:44,490
+و أف إذا اللي وصلنا له ما هي ليه يا جماعة اللي
+
+450
+00:33:44,490 --> 00:33:55,110
+وصلنا له انه لكل إبسلون أكبر من 0هناك بي إبسلون
+
+451
+00:33:55,110 --> 00:34:05,870
+مثلًا U بي إبسلون و F أصغر أو يساوي U بي إبسلون و
+
+452
+00:34:05,870 --> 00:34:09,990
+FK زائد إبسلون على أربعة
+
+453
+00:34:13,830 --> 00:34:20,130
+بإبسلون و FK ناقص إبسلون على أربعة أصغره يساوي L
+
+454
+00:34:20,130 --> 00:34:25,830
+بيبسلون و F هذه اللي وصلنا له لحد الآن نيجي الان
+
+455
+00:34:25,830 --> 00:34:32,230
+نرتبهم مع بعض و نصل للي بدناه اشي معهود خدوا الان
+
+456
+00:34:32,230 --> 00:34:38,530
+U بيبسلون و Fناقص الـ P,Y,F هذه ناقص هذه لما ضروف
+
+457
+00:34:38,530 --> 00:34:43,510
+هذه في ناقص بيصير هذه ناقص هذه معهودة وهذه بيصير
+
+458
+00:34:43,510 --> 00:34:46,690
+ناقص وهذه بيصير زائد وهذه بيصير أكبر أو يساوي
+
+459
+00:34:46,690 --> 00:34:52,570
+بتجمع هذه لهذه يعني بيصير عدى هذه ناقص هذه أصغر من
+
+460
+00:34:52,570 --> 00:34:59,130
+الـ U,P,Y,F هيهازائد هادي ناقص هادي زائد هادي يعني
+
+461
+00:34:59,130 --> 00:35:03,010
+بيصير عنده هادي يو بي إبسل و أف كيه ناقص البي إبسل
+
+462
+00:35:03,010 --> 00:35:06,190
+و أف كيه زائد إبسل على أربعة وإبسل على أربعة اللي
+
+463
+00:35:06,190 --> 00:35:10,690
+هو إبسل على مين؟ على اتنين وهذه من الأول لما
+
+464
+00:35:10,690 --> 00:35:15,630
+نستخدمها اللي هو الـRiemann criterion for
+
+465
+00:35:15,630 --> 00:35:19,640
+integrability للأف كيهاللي هو أوجدتنا الـ Py هو
+
+466
+00:35:19,640 --> 00:35:23,220
+أوجدتنا أن هذه ناقصة أصغر من Y على 2 يعني صار عندي
+
+467
+00:35:23,220 --> 00:35:26,820
+Y على 2 وY على 2 إبسلون معناته هذه صارت أصغر من
+
+468
+00:35:26,820 --> 00:35:30,080
+إبسلون و بالرماني criterion for integrability
+
+469
+00:35:30,080 --> 00:35:36,560
+بتطلع الـ F is إيش is integrable وهذا اللي هو
+
+470
+00:35:36,560 --> 00:35:41,200
+الإثبات لإن ال function F is integrable دل نثبت
+
+471
+00:35:41,200 --> 00:35:43,500
+اللي هو limit لل integration بساوي integration لل
+
+472
+00:35:43,500 --> 00:35:46,630
+limitوهذا من خلال الخطوات اللي طلعت عندنا حلّجي
+
+473
+00:35:46,630 --> 00:35:55,030
+يطلع بشكل سهل وبشكل سلس وخلّينا نشوفه الان since
+
+474
+00:35:55,030 --> 00:35:58,130
+epsilon was arbitrary then f is integrable on j زي
+
+475
+00:35:58,130 --> 00:36:02,750
+ما قلنا خد ال integration من a لb f of x dx نقص ال
+
+476
+00:36:02,750 --> 00:36:07,950
+integration من a لb fn of x dx بساوي اللي هوالـ
+
+477
+00:36:07,950 --> 00:36:10,830
+absolute value طبعاً صارت هذه integrable وهذه
+
+478
+00:36:10,830 --> 00:36:14,470
+integrable ماشي الحال إذا ال integration هذا نقص
+
+479
+00:36:14,470 --> 00:36:17,010
+ال integration هذا بساوي ال integration لهذا نقص
+
+480
+00:36:17,010 --> 00:36:20,210
+هذا الكل إيش ماله DX من خواص التكامل اللي أخدناها
+
+481
+00:36:20,210 --> 00:36:25,370
+سابقاً وهذا نفسه أصغر أو يساويأصغر يساوي ال
+
+482
+00:36:25,370 --> 00:36:28,750
+integration من a لb واخدناها سابقاً absolute value
+
+483
+00:36:28,750 --> 00:36:34,370
+of f of x ماقص fn of x لكل ايش ماله dx ال absolute
+
+484
+00:36:34,370 --> 00:36:36,490
+value integration أصغر يساوي ال integration لل
+
+485
+00:36:36,490 --> 00:36:42,340
+absolute value وهذا نفسهاللي هو أصغر أو يساوي norm
+
+486
+00:36:42,340 --> 00:36:47,060
+الـ F ناقص الـ Fn over اللي هي الـ interval J
+
+487
+00:36:47,060 --> 00:36:51,320
+ماشي، الآن بيصير عندى هذا أصغر أو يساوي ال
+
+488
+00:36:51,320 --> 00:36:56,840
+integration من A ل B norm الـ F ناقص الـ Fn over J
+
+489
+00:36:56,840 --> 00:37:03,720
+الكل إيش ماله؟ DX الآن هذا يا جماعة ثابت بيطلع
+
+490
+00:37:03,720 --> 00:37:09,520
+براته بيصير عبارة عن يساوي ال absolute valueالـ
+
+491
+00:37:09,520 --> 00:37:13,700
+norm للـ f ناقص الـ fn over j في ال integration من
+
+492
+00:37:13,700 --> 00:37:20,600
+a إلى b dx هذا هيهان وهذا ال integration من a إلى
+
+493
+00:37:20,600 --> 00:37:25,840
+b إلى dx هو عبارة عن b minus a صار هذا ناقص هذا
+
+494
+00:37:25,840 --> 00:37:31,200
+أصغر من هذا في b minus a الآن as n goes to
+
+495
+00:37:31,200 --> 00:37:34,920
+infinity as n goes to infinity صار هذا أكبر أو
+
+496
+00:37:34,920 --> 00:37:42,930
+يساوي سفروهذا هيوطلع لهذه المنطقة هيها هذه بس خد
+
+497
+00:37:42,930 --> 00:37:46,170
+ال limit للجهتين as n goes to infinity هذا بيصير
+
+498
+00:37:46,170 --> 00:37:51,590
+ال limit هناas n goes to infinity وهنا ال limit as
+
+499
+00:37:51,590 --> 00:37:54,170
+n goes to infinity طبعا هذا one هيروح لإنه أفن
+
+500
+00:37:54,170 --> 00:37:57,910
+بتروح للأف uniformly هذا بتروح كله لمين للصفر إذا
+
+501
+00:37:57,910 --> 00:38:01,330
+as n goes to infinity ال limit هذا إيش بيساوي صفر
+
+502
+00:38:01,330 --> 00:38:04,990
+مدام ال limit هذا صار بيساوي صفر هذا independent
+
+503
+00:38:04,990 --> 00:38:09,170
+of the limit هذا عبارة عن فيش فيه n صار عندي اللي
+
+504
+00:38:09,170 --> 00:38:12,990
+هو مضحكة
+
+505
+00:38:12,990 --> 00:38:19,770
+بتصور الصورة صار عندي الأن limitهذا بيساوي ايش صار
+
+506
+00:38:19,770 --> 00:38:24,770
+بيساوي سفر limit لال absolute value من a لعند b f
+
+507
+00:38:24,770 --> 00:38:32,170
+of x dx نقص integration fn of x dx من a لعند b
+
+508
+00:38:32,170 --> 00:38:35,710
+limit as angles to infinity limit ال absolute
+
+509
+00:38:35,710 --> 00:38:38,810
+value صار سفر إذا أكيد ال limit بدون absolute
+
+510
+00:38:38,810 --> 00:38:42,690
+value بيساوي سفر هذا independent of the limit إذا
+
+511
+00:38:42,690 --> 00:38:48,210
+بيصير بساوي ال integration من a لb f of x dxبتدخل
+
+512
+00:38:48,210 --> 00:38:54,370
+ال limit ناقص limit ال integration fn of x dx من a
+
+513
+00:38:54,370 --> 00:38:59,310
+ل عند بيه ماشي الحل و لا نضحك الصورة هذا صار عليه؟
+
+514
+00:38:59,310 --> 00:39:05,780
+هذا كله على بعض صار بساوي سفرإذا الـ limit ننجل
+
+515
+00:39:05,780 --> 00:39:08,620
+هذا على الجهة الثانية بيصير limit ال integration
+
+516
+00:39:08,620 --> 00:39:15,080
+من a ل b fn of x dx as n goes to infinity بساوي
+
+517
+00:39:15,080 --> 00:39:20,900
+اللي بيظل هنا من a ل b f of x dx وهذا معناته إنه
+
+518
+00:39:20,900 --> 00:39:24,310
+في حالة ال uniform convergenceالـ FN sequence of
+
+519
+00:39:24,310 --> 00:39:27,030
+integrable functions هتروح لـ integrable function
+
+520
+00:39:27,030 --> 00:39:29,450
+و هيطلع عنده limit لل integration بيساوي ال
+
+521
+00:39:29,450 --> 00:39:32,150
+integration ل limit و بهي .. و هيكون كون احنا
+
+522
+00:39:32,150 --> 00:39:37,110
+علجنا اللي هو النقطة الثانية في اللي هو المحاضرة
+
+523
+00:39:37,110 --> 00:39:42,270
+ضال عندي نقطة أخيرة بس قبلها خليني نذكر هال نظرية
+
+524
+00:39:42,270 --> 00:39:47,470
+اللي هي برهانة خارج نطاق اللي هو الكتاب و نشوف
+
+525
+00:39:47,470 --> 00:39:49,110
+اللي هو
+
+526
+00:39:53,380 --> 00:39:58,540
+إيش بتقول هذه اللي هي النظرية؟ إيش بتقول bounded
+
+527
+00:39:58,540 --> 00:40:02,310
+convergence theorem؟النظرية بتقول let FN be a
+
+528
+00:40:02,310 --> 00:40:07,150
+sequence of functions that are integrable in A وB
+
+529
+00:40:07,150 --> 00:40:12,530
+مفترضين إنها integrable and suppose that بدي يبعد
+
+530
+00:40:12,530 --> 00:40:14,850
+عن ال uniform convergence بتقول لو شيلنا ال
+
+531
+00:40:14,850 --> 00:40:18,550
+uniform convergence ممكن نبدله بإيش إيه؟ ويظل
+
+532
+00:40:18,550 --> 00:40:20,850
+محافظنا على ال limit لل integration بساوي ال
+
+533
+00:40:20,850 --> 00:40:24,920
+integration لل limit؟ آه، بنفع، نشوف كيفلت أفأن بـ
+
+534
+00:40:24,920 --> 00:40:27,340
+sequence of functions that are integrable in A وB
+
+535
+00:40:27,340 --> 00:40:30,380
+بس بده يدفع ثمن برضه integrable in A وB and
+
+536
+00:40:30,380 --> 00:40:34,400
+suppose that أفأن converts in A وB to an
+
+537
+00:40:34,400 --> 00:40:37,780
+integrable function F يعني أفأن بتروح للـ F على
+
+538
+00:40:37,780 --> 00:40:44,700
+الفترة هذه اللي هو point twice ماجالش uniformly بس
+
+539
+00:40:44,700 --> 00:40:50,770
+الآن بده يفترض شغلة بده يقيد الأفأنبشغلة معينة
+
+540
+00:40:50,770 --> 00:40:54,950
+شغلة كبيرة برضه التقييد مش جليل طبعا لكن بيضل اشي
+
+541
+00:40:54,950 --> 00:40:59,830
+يعني منفذ تاني suppose also that there exist B
+
+542
+00:40:59,830 --> 00:41:05,870
+أكبر من سفر بحيث انه FN of X أصغر شهر بيه لكل X
+
+543
+00:41:05,870 --> 00:41:09,750
+element in A و B و لكل N element in B هذا في
+
+544
+00:41:09,750 --> 00:41:14,690
+الواقع اللي هو uniform boundedness ليش؟ لأن هو
+
+545
+00:41:14,690 --> 00:41:21,200
+مفترض ان ال sequence FN of Xأصغر أو يساوي اللي هو
+
+546
+00:41:21,200 --> 00:41:28,140
+B لكل X element in A وB ولكل N element in N هو مش
+
+547
+00:41:28,140 --> 00:41:32,360
+مفترض إن الـ Fn نفسها تكون bounded يعني F1 اللي
+
+548
+00:41:32,360 --> 00:41:35,580
+حالها bounded، F2 bounded، F3 bounded كل إن هيكون
+
+549
+00:41:35,580 --> 00:41:39,940
+bounded صح، بس اللي طالبه أكثر اللي طبعا في حالة
+
+550
+00:41:39,940 --> 00:41:47,640
+الـ F1 bounded، F2 bounded، هيكون عندي Fnof X أصغر
+
+551
+00:41:47,640 --> 00:41:52,480
+أو ساوى BN F4
+
+552
+00:41:53,890 --> 00:41:58,290
+أني اللي هو الآن بنقول عن FN نفسها bounded أنه
+
+553
+00:41:58,290 --> 00:42:02,750
+there exists B لها، B لمن؟ لل FN لو فرضنا أن FN
+
+554
+00:42:02,750 --> 00:42:05,950
+الحالها bounded، there exists B للـN سميتها BN
+
+555
+00:42:05,950 --> 00:42:11,850
+صشدتها، دي أصغر يساوي BN لكل X element in A وB هذا
+
+556
+00:42:11,850 --> 00:42:16,650
+لو فرضنا أنه كل واحدة على حدة A bounded هو طالب
+
+557
+00:42:16,650 --> 00:42:24,260
+أكثر جاي الـ bound هذابنفع لكل الـ mean للـ F1 و
+
+558
+00:42:24,260 --> 00:42:30,980
+للـ F2 و للـ F3 و للـ F4 يعني فارض أن FN of X أصغر
+
+559
+00:42:30,980 --> 00:42:35,920
+أو يشوي يعني درج ZEF بأكبر من صفر such that FN of
+
+560
+00:42:35,920 --> 00:42:42,040
+X أصغر شهر و B لكل N element N و لكل X element مين
+
+561
+00:42:42,040 --> 00:42:48,760
+in ال interval اللي هي A أو B طبعا هذا الكلام أكيد
+
+562
+00:42:48,760 --> 00:42:52,940
+بيعطي هذا لكن هذا مش شرط يعطي هذا لأن هذا ال BN لل
+
+563
+00:42:52,940 --> 00:42:57,540
+F1 فيه B1 ال F2 بيه F2 F3 بيه F3 F4 بيه F4 هل فيه
+
+564
+00:42:57,540 --> 00:43:01,770
+الherosoprimam هدولة ليس شرطاماقدرش نقول أه عشان
+
+565
+00:43:01,770 --> 00:43:06,070
+هيك طلبه كبير طبعا البرنامج خارج عن نطاق ال course
+
+566
+00:43:06,070 --> 00:43:10,250
+سبعنا الان تحت هذا ال condition اللي قلنا عنه
+
+567
+00:43:10,250 --> 00:43:14,190
+condition ماقدرنا نقول وازن then ال integration من
+
+568
+00:43:14,190 --> 00:43:17,450
+a ل b of x dx بسوء limit لل integration من a b ل f
+
+569
+00:43:17,450 --> 00:43:20,610
+n of x dx يعني بمعنى أخر limit لل integration بسوء
+
+570
+00:43:20,610 --> 00:43:24,950
+ال integration لل limitالان نيجي لجزيه الثالث من
+
+571
+00:43:24,950 --> 00:43:29,350
+المحاضرة اللي بتعلق بالـ sequence of
+
+572
+00:43:29,350 --> 00:43:32,550
+differentiable functions خلينا نشوف المثال أول اشي
+
+573
+00:43:32,550 --> 00:43:37,570
+و بعدين نيجي لنظريتنا let fn of x بساوي summation
+
+574
+00:43:37,570 --> 00:43:42,270
+2 to the minus k cosine 3k x k من 1 لعين ده يعني
+
+575
+00:43:42,270 --> 00:43:47,950
+الانF1 of X بيساوي اللي هو 2 تره ماينس واحد كساين
+
+576
+00:43:47,950 --> 00:43:52,810
+تلاتة X F2 of X بيساوي اللي هو 2 تره ماينس واحد
+
+577
+00:43:52,810 --> 00:43:56,930
+كساين تلاتة X زائد 2 تره ماينس اتنين كساين تلاتة
+
+578
+00:43:56,930 --> 00:44:01,070
+تربيع X و هكذاFn of X هي عبارة عن الـSummation هذا
+
+579
+00:44:01,070 --> 00:44:04,690
+من واحد لـ&N وهذه عبارة عن Sequence of Functions
+
+580
+00:44:04,690 --> 00:44:09,070
+واضح أن هذه Sequence of Functions هي عبارة عن
+
+581
+00:44:09,070 --> 00:44:12,570
+Sequence of Differentiable Functions، لماذا؟ لأن
+
+582
+00:44:12,570 --> 00:44:16,450
+كل واحدة منهم عبارة عن Summation، Finite Summation
+
+583
+00:44:16,450 --> 00:44:20,570
+لـCos Function والـCos Function مستمر في كل مكان
+
+584
+00:44:20,570 --> 00:44:25,510
+وDifferentiable في كل مكانإذا صارت عندي الـ F1 و
+
+585
+00:44:25,510 --> 00:44:29,330
+الـ F2 و الـ F3 و الـ Fn عامة R الـ differential
+
+586
+00:44:29,330 --> 00:44:33,930
+of the function on R لكن شوفت على الـ limit احنا
+
+587
+00:44:33,930 --> 00:44:37,890
+خدنا المثال هذا but limit Fn of X as N plus
+
+588
+00:44:37,890 --> 00:44:41,970
+infinity بساوة summation كمن عند واحد إلى ما لا
+
+589
+00:44:41,970 --> 00:44:47,150
+نهاية بتصير ماشي الحالة2 to the minus k cosine 3kx
+
+590
+00:44:47,150 --> 00:44:51,150
+هذه أخدنا مثال على function is continuous
+
+591
+00:44:51,150 --> 00:44:54,590
+everywhere و is not differentiable anywhere و قلنا
+
+592
+00:44:54,590 --> 00:44:59,930
+برهانة خارج نطاق اللي هو اكتبنا فهذه الدالة عبارة
+
+593
+00:44:59,930 --> 00:45:04,790
+عن ال limit هذه اللي هي طلعت هذه الدالة يعني limit
+
+594
+00:45:04,790 --> 00:45:08,590
+ال function هذه دالة هذا ال limit is not
+
+595
+00:45:08,590 --> 00:45:12,710
+differentiable at any x element in R يعني هذا
+
+596
+00:45:12,710 --> 00:45:16,620
+عبارة عن مثالعلى sequence of functions FN
+
+597
+00:45:16,620 --> 00:45:25,100
+differentiable on R but its limit FN هنشوف
+
+598
+00:45:25,100 --> 00:45:32,970
+converts كمان uniformly ل F والـ F andF can
+
+599
+00:45:32,970 --> 00:45:36,950
+converge uniformly to F but الـ F زي ما قلنا is
+
+600
+00:45:36,950 --> 00:45:44,430
+not differentiable at any X element in R وكأنه الـ
+
+601
+00:45:44,430 --> 00:45:50,980
+uniform convergence هنا برضه وصفة ما نفعتشإن نجيب
+
+602
+00:45:50,980 --> 00:45:54,340
+الـ sequence of differentiable functions تطلع
+
+603
+00:45:54,340 --> 00:45:57,220
+differentiable function يعني ال uniform
+
+604
+00:45:57,220 --> 00:46:01,220
+convergence كمان نفسه بده دعمة أو بدنا condition
+
+605
+00:46:01,220 --> 00:46:05,280
+غير هيك يوصلنا للي بدنايا انه اللي هو ال sequence
+
+606
+00:46:05,280 --> 00:46:08,060
+of differentiable functions تقول إلى
+
+607
+00:46:08,060 --> 00:46:13,940
+differentiable function ده نشوف نكمل .. نكملالان
+
+608
+00:46:13,940 --> 00:46:18,300
+هنشوف كيف ينفرج .. ينفرج .. ينفرج ينفرج ينفرج
+
+609
+00:46:18,300 --> 00:46:19,940
+ينفرج ينفرج عامة عامة عامة عامة عامة عامة عامة
+
+610
+00:46:19,940 --> 00:46:20,360
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+611
+00:46:20,360 --> 00:46:21,560
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+612
+00:46:21,560 --> 00:46:21,960
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+613
+00:46:21,960 --> 00:46:23,120
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+614
+00:46:23,120 --> 00:46:24,740
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+615
+00:46:24,740 --> 00:46:28,440
+عامة عامة عامة عامة عامة
+
+616
+00:46:29,930 --> 00:46:34,590
+هذا أكيد أصغر أو ساوي اللي هو ال absolute value of
+
+617
+00:46:34,590 --> 00:46:36,130
+summation أصغر أو ساوي ال summation لل absolute
+
+618
+00:46:36,130 --> 00:46:39,650
+value وال cosine أصغر أو ساوية حدث ان صار عبارة عن
+
+619
+00:46:39,650 --> 00:46:41,890
+ال summation ال absolute value of summation هذا
+
+620
+00:46:41,890 --> 00:46:44,910
+أصغر أو ساوي two to the minus k كمن عند n زائد
+
+621
+00:46:44,910 --> 00:46:49,430
+واحد إلى مين إلى ما لا نهايةوهذا as n goes to
+
+622
+00:46:49,430 --> 00:46:53,210
+infinity هذا بروح لل zero ماشي الحال خليها في
+
+623
+00:46:53,210 --> 00:46:59,350
+الذاكره الآن صار عندي f of x نقص fn of x أصغر أو
+
+624
+00:46:59,350 --> 00:47:04,450
+يساوي هذا الرقم ماشي مش معتمد على x صار هذا أصغر
+
+625
+00:47:04,450 --> 00:47:08,050
+أو ساوي هذا صار هذا upper bound لهذهمدام upper
+
+626
+00:47:08,050 --> 00:47:10,210
+bound إذا ال upper bound أكبر أو ساوي ال least
+
+627
+00:47:10,210 --> 00:47:14,170
+upper bound اللي هو نوم لل F ناقص FN over R أصغر
+
+628
+00:47:14,170 --> 00:47:17,310
+أو ساوي هذا as N goes to infinity هذا بيروح لل
+
+629
+00:47:17,310 --> 00:47:21,250
+zero إذا ال F ناقص FN over R بتروح لل zero وهذا
+
+630
+00:47:21,250 --> 00:47:27,570
+معناته أن FN بتروح لل F اللي هو on mean on R يعني
+
+631
+00:47:27,570 --> 00:47:31,250
+ال convergence إيش ماله uniform convergence بالرغم
+
+632
+00:47:31,250 --> 00:47:35,880
+إن ال uniform convergence حادثوالـ Fn sequence of
+
+633
+00:47:35,880 --> 00:47:40,200
+differentiable functions الـ F إيش ما لها طلعتش
+
+634
+00:47:40,200 --> 00:47:44,840
+differentiable إذا بالزمن اللي هو condition أو
+
+635
+00:47:44,840 --> 00:47:49,900
+conditions تضمنلي أنه لما Fn تروح للـ F و Fn
+
+636
+00:47:49,900 --> 00:47:52,580
+sequence of differentiable functions تطلعلي الـ F
+
+637
+00:47:52,580 --> 00:47:56,930
+differentiable خلّينا نشوف نظريتنا اللي هيأخر جزء
+
+638
+00:47:56,930 --> 00:48:00,990
+في ال section و في ال chapter اللي بدنا ناخده منه
+
+639
+00:48:00,990 --> 00:48:07,070
+اللي هي بتجاوبنا على هذا الأمر و نشوف أيش النظرية
+
+640
+00:48:07,070 --> 00:48:12,630
+بتقوله و من ثم بعد أنفة من نص نبرهن النظرية نشوف
+
+641
+00:48:12,630 --> 00:48:17,400
+let J subset من R be a bounded intervalbounded
+
+642
+00:48:17,400 --> 00:48:21,340
+interval open مش open مش فارقة معاه a closed مش
+
+643
+00:48:21,340 --> 00:48:24,560
+closed مش فارقة الان and let fn be a sequence of
+
+644
+00:48:24,560 --> 00:48:29,360
+functions on j يعني عبقى عندي عندي fn sequence of
+
+645
+00:48:29,360 --> 00:48:33,940
+functions fn sequence of functions على مين؟ على
+
+646
+00:48:33,940 --> 00:48:38,180
+الـ j اللي هي ال interval اللي عندي لعند ارف واحدة
+
+647
+00:48:38,180 --> 00:48:43,700
+اتنين ارف تلاتة الاخرين وبدنا نفترضاللي هو suppose
+
+648
+00:48:43,700 --> 00:48:49,880
+that there exist x0 element in j بحيث أن fn of x0
+
+649
+00:48:49,880 --> 00:48:56,440
+converges اللي هو to some limit الان ايش مفترض ان
+
+650
+00:48:56,440 --> 00:49:03,520
+في عندي x0في الـ J بحيث أن FN of X0 هذه صارت
+
+651
+00:49:03,520 --> 00:49:07,840
+sequence of numbers هذه converges to some number
+
+652
+00:49:07,840 --> 00:49:12,560
+ايش هو مش عارفينه الان and that ومعطيك كمان شغلة
+
+653
+00:49:12,560 --> 00:49:18,800
+هذه معطيكياها اللي هي and converges عند مقطة محددة
+
+654
+00:49:18,800 --> 00:49:24,320
+اسمها X0 في الـ J and the sequence FN prime of
+
+655
+00:49:24,320 --> 00:49:29,510
+derivatives exist on Jيعني مفترض إن الـ F N'
+
+656
+00:49:29,830 --> 00:49:32,910
+exists يعني F N sequence of differentiable
+
+657
+00:49:32,910 --> 00:49:36,390
+functions مفترض إن F N sequence of differentiable
+
+658
+00:49:36,390 --> 00:49:40,210
+functions ومش هيك، وبيقولك إن هذه الـ F N'
+
+659
+00:49:40,750 --> 00:49:45,230
+converts uniformly on J to some function F يعني
+
+660
+00:49:45,230 --> 00:49:50,950
+بيقولك F N' existsFN برايم exist لكل N وهذا الـ
+
+661
+00:49:50,950 --> 00:49:55,430
+sequence بيقول لك converges uniformly to some
+
+662
+00:49:55,430 --> 00:50:00,130
+function اسمها مين؟ اسمها J إذن sequence of
+
+663
+00:50:00,130 --> 00:50:05,510
+functions لأن في X0 في الـ J بحيث أن FN of X0
+
+664
+00:50:05,510 --> 00:50:10,830
+نفسها تكون converges FN برايم converges uniformly
+
+665
+00:50:10,830 --> 00:50:17,150
+to some Gto some G بكل الأنظم مع وجود هذه الشروط
+
+666
+00:50:17,150 --> 00:50:23,210
+اللي حكينا عليها then the sequence FN converges
+
+667
+00:50:23,210 --> 00:50:32,330
+uniformly to a function F بعد هذا بعد هذا بنلاقي
+
+668
+00:50:32,330 --> 00:50:37,370
+أن FN غصب إن عنا لازم تكون converges uniformly to
+
+669
+00:50:37,370 --> 00:50:44,660
+some function mean F ومش هيكوالـ function F هذه
+
+670
+00:50:44,660 --> 00:50:51,260
+تطلع الـ derivative تبعتها هي مين؟ هي الـ G يعني
+
+671
+00:50:51,260 --> 00:51:01,310
+وكأنه أن الـ F N converges uniformly to Fاللي هي
+
+672
+00:51:01,310 --> 00:51:07,270
+الـ derivative لها مين الاش الـ G يعني F N برايم
+
+673
+00:51:07,270 --> 00:51:10,510
+بتكون uniformly convergence to some function G
+
+674
+00:51:10,510 --> 00:51:17,890
+هتطلع الـ F N converge uniformly لل function اللي
+
+675
+00:51:17,890 --> 00:51:24,570
+تفضلها هو مين هو عبارة عن الـ Gطيب إذا في عندي
+
+676
+00:51:24,570 --> 00:51:28,210
+شغلتين بدنا نثبت ان FN can form convergence to F
+
+677
+00:51:28,210 --> 00:51:35,690
+والـ F' إيش بتساوي؟ بتساوي مين؟ اللي هي الـ G يعني
+
+678
+00:51:35,690 --> 00:51:42,830
+هتصير إنه الـ FN' اللي هو sequence of
+
+679
+00:51:42,830 --> 00:51:45,770
+differentiable functions بتطلع عندي هذه sequence
+
+680
+00:51:45,770 --> 00:51:49,210
+of differentiable functions converge to function
+
+681
+00:51:49,210 --> 00:51:54,110
+بتكون differentiableليش؟ لأن F' ايش بتتساوي G؟
+
+682
+00:51:54,110 --> 00:51:57,590
+يعني F is differentiable يعني هذه بتقول إنه لو
+
+683
+00:51:57,590 --> 00:52:00,950
+الشرطة ده و الشرطة ده تتحققوا إذن ال sequence of
+
+684
+00:52:00,950 --> 00:52:06,290
+differentiable functions FN هتكون converges to ..
+
+685
+00:52:06,290 --> 00:52:09,110
+uniform converges طبعا to a differentiable
+
+686
+00:52:09,110 --> 00:52:13,310
+function F إذن الشغلتين هدولة إحنا بدنا نثبتهم
+
+687
+00:52:13,310 --> 00:52:18,330
+خلينا نشوف كيف نثبت هدولة الشغلتين بدنا نثبت إنه
+
+688
+00:52:18,330 --> 00:52:23,460
+FNConverse Uniform للـ F وبدنا نثبت أن F' بيسوا G
+
+689
+00:52:23,460 --> 00:52:29,760
+يعني بدنا نثبت لك في النهاية أنه limit F
+
+690
+00:52:31,240 --> 00:52:37,940
+of X زائد اللي هو F of X زائد Delta X مثلا أو F of
+
+691
+00:52:37,940 --> 00:52:45,520
+X ناقص F of C على X minus C as X بتروح للـ C بدنا
+
+692
+00:52:45,520 --> 00:52:51,980
+نثبت أنه exist ويساوي G of meanof C يعني بمعنى هذا
+
+693
+00:52:51,980 --> 00:52:56,460
+for arbitrary C element in main NG يعني كأنه في
+
+694
+00:52:56,460 --> 00:53:01,300
+النهاية بدنا نثبت لك انه هذا exist يعني F prime of
+
+695
+00:53:01,300 --> 00:53:05,840
+C exist ويساوي main G of C او بمعنى اخر بدنا نثبت
+
+696
+00:53:05,840 --> 00:53:08,320
+لك انه for every Y colon of Z there exists delta
+
+697
+00:53:08,320 --> 00:53:14,490
+such that X minus Cأصغر من Delta يؤدي إلى F of X
+
+698
+00:53:14,490 --> 00:53:20,270
+ناقص F of C على X minus C ناقص G of C يكون أصغر من
+
+699
+00:53:20,270 --> 00:53:24,530
+مين من Y إذا أثبتنا هذا معناته و أثبتنا إن هذا
+
+700
+00:53:24,530 --> 00:53:28,460
+اللي هو limit existيعني الـ F' exist ويساوى مين
+
+701
+00:53:28,460 --> 00:53:31,920
+الـ G of C والـ C كون بتكون أخديها Arbitrary في
+
+702
+00:53:31,920 --> 00:53:36,680
+الـ G فبكون خلصنا أن الـ F' بيساوى الـ G وهذا كله
+
+703
+00:53:36,680 --> 00:53:40,920
+بعد ما نثبت أن الـ F أنه conversion form للمين للـ
+
+704
+00:53:40,920 --> 00:53:48,280
+F و تعالوا لتفاصيل البرهان طيب نيجي نشوف برهاننا
+
+705
+00:53:48,280 --> 00:53:51,020
+شوفوا طاولوا روحكم علينا
+
+706
+00:53:55,700 --> 00:53:58,860
+عشان نعرف بس نشتغل لبنى حيكة خلّينا نسمي ال end
+
+707
+00:53:58,860 --> 00:54:02,960
+points جيه واحدة اسمها A واحدة اسمها B يعني let A
+
+708
+00:54:02,960 --> 00:54:06,440
+أزرع من بي بي the end points of J جيه مفتوح مفتوح
+
+709
+00:54:06,440 --> 00:54:08,020
+مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح
+
+710
+00:54:08,020 --> 00:54:08,080
+مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح
+
+711
+00:54:08,080 --> 00:54:08,580
+مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح مفتوح
+
+712
+00:54:08,580 --> 00:54:13,580
+مفتوح مفتوح مفتوح مفتوح مفتووخلّيني أخد X بـ
+
+713
+00:54:13,580 --> 00:54:17,700
+Arbitrary Point في الـ J أحنا بنحكي عن أي X وين ما
+
+714
+00:54:17,700 --> 00:54:26,420
+لا في الـ J اللي هي .. if M and N element in N
+
+715
+00:54:26,420 --> 00:54:29,320
+then F minus N is differentiable on the closed
+
+716
+00:54:29,320 --> 00:54:34,550
+interval within points X0 and X أكيدمفترضين احنا
+
+717
+00:54:34,550 --> 00:54:41,010
+ان الـ F M' exist مظبوط مدام exist اذا F M
+
+718
+00:54:41,010 --> 00:54:44,850
+differentiable و F N differentiable اذا F M نقص F
+
+719
+00:54:44,850 --> 00:54:48,910
+N differentiable على كل مين؟ على كل الـ J اللي انا
+
+720
+00:54:48,910 --> 00:54:52,950
+بدي اشتغل على فترة محددة انا اخدت X element in J
+
+721
+00:54:52,950 --> 00:54:57,490
+arbitraryوهو معطيل في النظرية X0 اللي عندها اللي
+
+722
+00:54:57,490 --> 00:55:02,110
+هي Fn of X0 converts بحكي عن X0 هذه المقصودة في
+
+723
+00:55:02,110 --> 00:55:08,170
+النظرية بدي أطبّج عليها عندي بما أن Fm ناقص Fn is
+
+724
+00:55:08,170 --> 00:55:11,730
+differentiable على closed interval within points
+
+725
+00:55:11,730 --> 00:55:18,090
+X0 و X يعني يا X0 و X يا X و X0 حسب موقع كل من X و
+
+726
+00:55:18,090 --> 00:55:23,440
+X0إذا صارت Fm ناقص Fn عبارة عن الـ differential
+
+727
+00:55:23,440 --> 00:55:26,120
+بالـ function على هذه الـ closed bounded interval
+
+728
+00:55:26,120 --> 00:55:30,320
+إذا أكيد continuous عليها كمان إذا بالـ mean value
+
+729
+00:55:30,320 --> 00:55:33,940
+theorem مطبقة الـ mean value theorem ده طبقها على
+
+730
+00:55:33,940 --> 00:55:39,300
+مين يا جماعة؟ على الـ Fm ناقص Fn يعني هذه دالتنا
+
+731
+00:55:39,300 --> 00:55:43,660
+اللي بدنا نطبق عليها الـ mean value theorem إذا by
+
+732
+00:55:43,660 --> 00:55:47,760
+mean value theorem there exists Y بين الـ X0 والـ
+
+733
+00:55:47,760 --> 00:55:53,380
+X بحيثإن الـ Derivative لهذه بيساوي F M ناقص F N
+
+734
+00:55:53,380 --> 00:55:59,440
+عند اللي هي X ناقص F M ناقص F Note عند الـ X Note
+
+735
+00:55:59,440 --> 00:56:05,640
+بيساوي F M ناقص F N Prime عند مين؟ عند الـ Yby
+
+736
+00:56:05,640 --> 00:56:09,840
+mean value theorem there exists y between x0 and x
+
+737
+00:56:09,840 --> 00:56:13,700
+such that هذا الدلة كلها على بعض عند ال x fm of x
+
+738
+00:56:13,700 --> 00:56:19,300
+نقص fn of x هذا الدلة ناقص fm of x0 نقص fn of x0
+
+739
+00:56:19,300 --> 00:56:25,060
+هذا الدلة عند النقطة x0 بساوي اللي هي x minus x0فى
+
+740
+00:56:25,060 --> 00:56:30,520
+اللى هو ال derivative لهذه عند مين عنده النقطة Y
+
+741
+00:56:30,520 --> 00:56:34,700
+اللى هى F M prime of Y نقص F M prime of Y إذا
+
+742
+00:56:34,700 --> 00:56:47,340
+حصلنا على هذه النقطة طيب الآن لو أجيت بس
+
+743
+00:56:47,340 --> 00:56:50,140
+عشان بدي ألاقي مكان لما فيه كلام كتير بدي أكتبه
+
+744
+00:56:50,140 --> 00:56:57,540
+هذا عندي المفروضخلّيني أكتب إن هذولة عندي المعطيات
+
+745
+00:56:57,540 --> 00:57:07,950
+اللي هي FN of X0 Converges ومعايا اللي هو FNprime
+
+746
+00:57:07,950 --> 00:57:14,250
+converging formally to the G هذا المطلوب أن FN
+
+747
+00:57:14,250 --> 00:57:20,290
+converging formally to F و F' هي مين الـ G هذه
+
+748
+00:57:20,290 --> 00:57:24,450
+المعطيات وهي المطلوب هذا اللي هو ملخصها خلينا نشوف
+
+749
+00:57:24,450 --> 00:57:31,590
+عشان أنه احنا نبدأ اللي هو أفسلكم كل خطوة اللي هو
+
+750
+00:57:31,590 --> 00:57:35,270
+ما كانت مش مفسرة في التلخيص نفسلكم إياها بالتفصيل
+
+751
+00:57:36,790 --> 00:57:43,750
+الان وجدنا هذه يا جماعة ماشي الحال الان عندي هذا
+
+752
+00:57:43,750 --> 00:57:47,830
+الكلام صحيح لكل x عندي طبعا x note نحكي عن x note
+
+753
+00:57:47,830 --> 00:57:56,530
+محددة صار عندي الان fm of x ناقص fn of x هذه صارت
+
+754
+00:57:56,530 --> 00:58:01,600
+absolute valueأصغر أو يساوي بدي أنجل هذه على النطق
+
+755
+00:58:01,600 --> 00:58:04,420
+هذه وأقول absolute value هذه بساوي ال absolute
+
+756
+00:58:04,420 --> 00:58:07,720
+value هذه وأخد triangle inequality بيصير أصغر أو
+
+757
+00:58:07,720 --> 00:58:17,260
+يساوي ال absolute value لهذه Fn of X0 ناقص Fn of
+
+758
+00:58:17,260 --> 00:58:26,650
+X0 زائد ال absolute value لل X minus X0في الـ F M
+
+759
+00:58:26,650 --> 00:58:34,930
+prime of Y ناقص F M F N prime of mean of Y ماشي
+
+760
+00:58:34,930 --> 00:58:39,650
+الحال هذا mean ماله هذا بال mean value بال
+
+761
+00:58:39,650 --> 00:58:42,550
+triangle inequality بعد ما نجلتها على الجهة
+
+762
+00:58:42,550 --> 00:58:50,310
+الثانية الآن هذا المقدار هذا المقداراللي هو أكيد
+
+763
+00:58:50,310 --> 00:58:54,790
+هذا بيصير هذا المقدار أصغر يساوي هذا وهذا أصغر
+
+764
+00:58:54,790 --> 00:59:05,090
+يساوي FM of X not FM of X not ناقص FM of X not
+
+765
+00:59:05,090 --> 00:59:12,730
+زائد هذه اللي هي اللي هي موجودة في الفترة من عند A
+
+766
+00:59:12,730 --> 00:59:17,890
+لعند BX و X0 بغض النظر الموقع هنادي أو هنادي في
+
+767
+00:59:17,890 --> 00:59:22,470
+الآخر اللي هي B minus A أكيد أكبر من X minus X0
+
+768
+00:59:22,470 --> 00:59:29,670
+أكيد إذا زائد B minus A فيه هذا هذا أكيد أصغر أو
+
+769
+00:59:29,670 --> 00:59:36,890
+يساوي مين ال norm ل F M prime ناقص F N prime over
+
+770
+00:59:36,890 --> 00:59:40,550
+مين الجيل اللي عندي ليش لأن هذا supremum للي فوق
+
+771
+00:59:40,550 --> 00:59:45,630
+صار هذا كله عبارة عن رقمهذا كله عبارة عن رقم هذا
+
+772
+00:59:45,630 --> 00:59:51,650
+الرقم الآن أكبر أو ساوي هذه لكل X وين موجودة في
+
+773
+00:59:51,650 --> 00:59:55,350
+الجيل لأنه أخدت X مالها من رأس الدور أخدت X is
+
+774
+00:59:55,350 --> 01:00:00,290
+arbitrary point ماشي الحال صار عندي الآن هذا صار
+
+775
+01:00:00,290 --> 01:00:04,650
+upper bound لهذه عدناها مائة مرة إذا صار عند هذا
+
+776
+01:00:04,650 --> 01:00:07,250
+ال upper bound أكبر أو ساوي ال least upper bound
+
+777
+01:00:07,250 --> 01:00:10,010
+اللي هو ال supremum إذا صار عند ال supremum اللي
+
+778
+01:00:10,010 --> 01:00:15,810
+هو norm ال FMناقص FN over J أصغر أو ساوي المقدار
+
+779
+01:00:15,810 --> 01:00:20,570
+هذا وهي اللي هو حصلنا عليه هنا وتفسيره هي اللي
+
+780
+01:00:20,570 --> 01:00:26,130
+فسرتلكم إياه فوق إذا صار عندي FM ناقص FN over J
+
+781
+01:00:26,130 --> 01:00:29,490
+أصغر أو ساوي FN of X node ناقص FN of X node زاد B
+
+782
+01:00:29,490 --> 01:00:36,990
+minus A في النور اللي أمامي الآن اللاحظ أن FN of X
+
+783
+01:00:36,990 --> 01:00:41,760
+node convergeاللي هو and FN' is uniformly
+
+784
+01:00:41,760 --> 01:00:46,480
+convergent in J then by the inequality above and
+
+785
+01:00:46,480 --> 01:00:50,520
+theorem 8.11 we have FN is uniformly convergent
+
+786
+01:00:50,520 --> 01:00:55,300
+رماها على طول خلّيني أفسرلكم أيها هذه خلّيني
+
+787
+01:00:55,300 --> 01:01:01,260
+أفسرلكم اللي حكاه هنا وكيف وصل أن FN converges
+
+788
+01:01:01,260 --> 01:01:07,570
+uniformly من مين لل FNنفسرها والتفسير يمكن مرة قبل
+
+789
+01:01:07,570 --> 01:01:17,510
+هيك الان شوفوا معايا بما انه عندي ال FN of X0
+
+790
+01:01:17,510 --> 01:01:25,950
+converges اذا it is Cauchy مظبوط is it is a Cauchy
+
+791
+01:01:25,950 --> 01:01:32,270
+sequence معايا مدام Cauchy sequenceأيضا المعروف
+
+792
+01:01:32,270 --> 01:01:35,790
+ايش معناه الـ Cauchy Sequence ان لكل أبسلون أكبر
+
+793
+01:01:35,790 --> 01:01:43,440
+من سفر there exist اللي هو مثلا نسميها H1اللي هو
+
+794
+01:01:43,440 --> 01:01:49,220
+element in N such that for every N و M أكبر أو
+
+795
+01:01:49,220 --> 01:01:57,500
+يساوي H1 بكون عندي FN of X0 ناقص FN of X0 أصغر من
+
+796
+01:01:57,500 --> 01:02:02,740
+مين؟ من يبسلون على اتنين مثلا يبسلون على اتنين
+
+797
+01:02:02,740 --> 01:02:07,220
+ماشي؟ هذا من وين جبته؟ من أن FN of X0 converges
+
+798
+01:02:07,220 --> 01:02:12,910
+هذه الأولى خليها هذه اسمها واحد الانعندي معطينة
+
+799
+01:02:12,910 --> 01:02:19,030
+برضه اللي هو FN الـ Prime Uniform Convergence
+
+800
+01:02:22,150 --> 01:02:28,730
+Converges uniformly Converges uniformly Converges
+
+801
+01:02:28,730 --> 01:02:32,450
+uniformly Converges
+
+802
+01:02:32,450 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+803
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+804
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+805
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+806
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+807
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+808
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+809
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+810
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+811
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+812
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+813
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+814
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+815
+01:02:34,190 --> 01:02:34,190
+Converges uniformly Converges uniformly Converges
+
+816
+01:02:34,190 --> 01:02:34,190
+uniformly Converges uniformly Converges uniformly
+
+817
+01:02:34,190 --> 01:02:34,190
+Converges usually Converges usually Converges
+
+818
+01:02:34,190 --> 01:02:34,290
+usually Converges usually Converges usually
+
+819
+01:02:34,290 --> 01:02:34,530
+Converges usually Converges usually Converges
+
+820
+01:02:34,530 --> 01:02:38,430
+usually Converges usually Converges usually
+
+821
+01:02:38,430 --> 01:02:44,130
+Converges usually Converges usually Converges
+
+822
+01:02:44,130 --> 01:02:51,420
+usually Converges usually Converges usuallyاللي هو
+
+823
+01:02:51,420 --> 01:03:00,120
+Normal Fn-Fm أصغر من Epsilon على B-A في 2 حرّا أي
+
+824
+01:03:00,120 --> 01:03:02,860
+Epsilon في الدنيا نضب لها Epsilon على B-A في 2
+
+825
+01:03:02,860 --> 01:03:07,640
+الان بدي استخدم هذه واستخدم هذه بدي استخدم ان الان
+
+826
+01:03:07,640 --> 01:03:11,020
+و الام بتكون أكبر من H2 و الان و الام أكبر من مين
+
+827
+01:03:11,020 --> 01:03:15,420
+من H1 إذا for every Epsilonأكبر من الصفر there
+
+828
+01:03:15,420 --> 01:03:18,700
+exist H بتساوي الماكسما عشان انا اقدر استخدم
+
+829
+01:03:18,700 --> 01:03:24,360
+التنتين ال maximum بين H1 وH2 such that for every
+
+830
+01:03:24,360 --> 01:03:29,180
+N و M أكبر أو يساوي H أكبر أو يساوي H هيكون عندى
+
+831
+01:03:29,180 --> 01:03:36,260
+norm norm هذه صحيحة لكل M و N في الدنيا ال FM ناقص
+
+832
+01:03:36,260 --> 01:03:42,800
+FN over J أصغر أو يساوي الأولى زائد التانية الأولى
+
+833
+01:03:42,800 --> 01:03:47,930
+هذهالأولى أصغر أو يساوي منها نائب سن على اتنين
+
+834
+01:03:49,210 --> 01:03:52,890
+مظبوط لأن هذه أصغر من 100 على 2 لكل الـ N و الـ M
+
+835
+01:03:52,890 --> 01:03:56,670
+الأكبر يساوي H اللي هي أكيد الـ H أكبر يساوي مين؟
+
+836
+01:03:56,670 --> 01:04:00,330
+اللي هي H1 يعني N و M اللي بيكون أكبر يساوي H أكيد
+
+837
+01:04:00,330 --> 01:04:04,690
+بيكون الـ H1 اللي أنا بالفعل أستخدمها زائد التانية
+
+838
+01:04:04,690 --> 01:04:10,090
+برضه الـ F M' ناقص F M' أصغر من مين هنا؟ M' هذا
+
+839
+01:04:10,090 --> 01:04:13,050
+طبعا، هذي Prime و هذي Prime لأن F M' الـPrime الـ
+
+840
+01:04:13,050 --> 01:04:19,730
+Convergent لمن؟ لل Gإبسلون في اتنين في B minus A
+
+841
+01:04:19,730 --> 01:04:24,890
+اللي كان مضروبة في مين في B minus A فبصير هذا
+
+842
+01:04:24,890 --> 01:04:27,250
+إبسلون على اتنين و إبسلون على هذي بيصير روح مح هذي
+
+843
+01:04:27,250 --> 01:04:30,450
+و هي سوى إبسلون إذا اللي حصلته لكل إبسلون أكبر من
+
+844
+01:04:30,450 --> 01:04:34,830
+zero there exists H such that لكل N أكبر سوى H طلع
+
+845
+01:04:34,830 --> 01:04:39,590
+عندي FN نقص FN أصغر من مين من إبسلون إذا by Cauchy
+
+846
+01:04:39,590 --> 01:04:46,420
+criterion يكون عند ال FNconverges uniformly to
+
+847
+01:04:46,420 --> 01:04:52,180
+some function mean F مش عارفين لسه عنها حاجة إذا
+
+848
+01:04:52,180 --> 01:04:57,600
+اللي أثبتناه الأن أن F is uniformly convergent to
+
+849
+01:04:57,600 --> 01:05:02,880
+some function F مين هي مش عارفينها لسه أما أثبتنا
+
+850
+01:05:02,880 --> 01:05:07,280
+وجودها أثبتنا أن F converges uniformly ل F إذا
+
+851
+01:05:07,280 --> 01:05:16,630
+بقدر أجرّأ وأقولLimit الـ Fm أو الـ Fn as n goes
+
+852
+01:05:16,630 --> 01:05:21,430
+to infinity تساوي F ماقدر أتجرأ لإن أثبتت وجودها
+
+853
+01:05:21,430 --> 01:05:27,570
+الان لاحظوا بس شغلة Fn is differentiable is a
+
+854
+01:05:27,570 --> 01:05:31,360
+continuousمدام continuous و أثبتت FM بتروح
+
+855
+01:05:31,360 --> 01:05:35,080
+converts uniformly لها إذا ال limit هذه هتطلع برضه
+
+856
+01:05:35,080 --> 01:05:40,260
+إيش ماله is continuous و هذه خلوها في الذاكرة مكون
+
+857
+01:05:40,260 --> 01:05:47,340
+احنا أوصلنا أو أثبتنا الجزء الأول من النظرية أن FM
+
+858
+01:05:47,340 --> 01:05:53,820
+converts uniformly to F و ال limit لها سمناها F و
+
+859
+01:05:53,820 --> 01:05:57,720
+هيطلع لنا عبارة عن continuous function شوفوا يا
+
+860
+01:05:57,720 --> 01:05:58,420
+جماعة الآن
+
+861
+01:06:02,600 --> 01:06:09,330
+صار عندي الآنأثبتنا أن Fn تتعامل بشكل مرتبط سمينا
+
+862
+01:06:09,330 --> 01:06:13,050
+limit Fn بسوء F which is continuous because Fn زي
+
+863
+01:06:13,050 --> 01:06:14,670
+ما قلنا is continuous لأنه في الأصل هي
+
+864
+01:06:14,670 --> 01:06:18,610
+differentiable و Fn بتروح لل F إذن صارت ال F اللي
+
+865
+01:06:18,610 --> 01:06:23,330
+هي نفسها continuous الآن بدي أستخدم ال continuity
+
+866
+01:06:23,330 --> 01:06:29,090
+عند ال F بدي أصل اللي بديه طيب خد C الآن ب any
+
+867
+01:06:29,090 --> 01:06:35,950
+fixed point in J الآن بدي أروح إلى إثبات أنهالـ
+
+868
+01:06:35,950 --> 01:06:43,810
+Limit للـ F of X ناقص F of C على X minus C as X
+
+869
+01:06:43,810 --> 01:06:46,970
+بتروح للـ C هذه الـ C وينها؟ الـ C أخذناها
+
+870
+01:06:46,970 --> 01:06:51,470
+arbitrary في X in J إذا أثبتت لهذا الـ C اللي هو
+
+871
+01:06:51,470 --> 01:06:56,870
+بساوي اللي هي G of Cمعناته إذا أثبتت هذا معناته
+
+872
+01:06:56,870 --> 01:07:02,150
+أثبتت أن F' of C exist وهي ساوي G of C ومعناته
+
+873
+01:07:02,150 --> 01:07:08,310
+أثبتت أن F بتساوي G على كل J لأن C ماخدها
+
+874
+01:07:08,310 --> 01:07:12,610
+arbitrary but fixed يعني إيش بده أثبت في هذا؟يعني
+
+875
+01:07:12,610 --> 01:07:16,910
+زي ما قلنا في الأول زي ما قلنا في الأول بدنا نثبت
+
+876
+01:07:16,910 --> 01:07:21,970
+لكم الآن لكل إبسلون أكبر من سفر there exists Delta
+
+877
+01:07:21,970 --> 01:07:27,350
+أكبر من سفر such that X minus C أصغر من Delta يؤدي
+
+878
+01:07:27,350 --> 01:07:34,990
+إلى اللي هو F of X ناقص F of C على X minus C ناقص
+
+879
+01:07:34,990 --> 01:07:39,630
+G of C أصغر من إبسلون ده أثبتت بكون خلصت إذا أثبتت
+
+880
+01:07:39,630 --> 01:07:44,780
+هذا بكون خلصت اللي هوالإثبات تنشوف طيب صلوا على
+
+881
+01:07:44,780 --> 01:07:50,120
+النبي عليه الصلاة والسلام نيجي الآن قولنا C N of X
+
+882
+01:07:50,120 --> 01:07:54,020
+point in J F M ناقص F N is differentiable on the
+
+883
+01:07:54,020 --> 01:07:58,020
+closed interval with endpoints C and X الان F N
+
+884
+01:07:58,020 --> 01:08:00,840
+ناقص F N differentiable على ال closed interval
+
+885
+01:08:00,840 --> 01:08:06,120
+اللي هي C ومين وال X ال XR اللي خدناها اللي هي
+
+886
+01:08:06,120 --> 01:08:10,770
+arbitraryماشي، الآن بدأ استخدم الـ Mean Value
+
+887
+01:08:10,770 --> 01:08:14,010
+Theorem، then by mean value theorem كمان مرة there
+
+888
+01:08:14,010 --> 01:08:19,250
+exists z between c and x such that fm of x ناقص fn
+
+889
+01:08:19,250 --> 01:08:22,130
+of x النقطة الأولى، ناقص fm of c ناقص fn of c
+
+890
+01:08:22,130 --> 01:08:26,270
+النقطة التانية بساوي x minus c مضروبة في fn prime
+
+891
+01:08:26,270 --> 01:08:32,390
+of z ناقص fn prime اللي هو fm prime of zماشي الحال
+
+892
+01:08:32,390 --> 01:08:35,350
+طبقت الـ Mean Value Theorem على الدالة ال .. اللي
+
+893
+01:08:35,350 --> 01:08:41,770
+هي Fm ناقص Fn لكل M O N الان خدوا الحسبة الان خد X
+
+894
+01:08:41,770 --> 01:08:44,690
+لا تساوى C لإنه .. X لا تساوى C لإن انا بدأو أدي X
+
+895
+01:08:44,690 --> 01:08:48,430
+عالميا على C يعني X minus C اللي هو أصغر من Delta
+
+896
+01:08:48,430 --> 01:08:52,760
+يعني X بدأو أديها على Cالان اجسموا كل الأطراف على
+
+897
+01:08:52,760 --> 01:09:00,820
+x-c بيصير اللي هي fm ناقص fm of c على x-c ناقص
+
+898
+01:09:00,820 --> 01:09:08,500
+الان fn of x هي هاناقص اللي هي هذه اللي هي FN of C
+
+899
+01:09:08,500 --> 01:09:13,300
+هي ناقص وهي ناقص إذا بيطلع صحيح على X minus C
+
+900
+01:09:13,300 --> 01:09:18,400
+بساوي اللي هو F M prime of Z ناقص FN prime of Z
+
+901
+01:09:18,400 --> 01:09:24,340
+لإنه جسمت على X minus C الآن أكيد هذه .. هذه أصغر
+
+902
+01:09:24,340 --> 01:09:27,460
+أو يساوي نورمها لأن نورم هو ال supermom إلها صار
+
+903
+01:09:27,460 --> 01:09:31,320
+عندي الآن هذا المقدار أصغر أو يساوي هذا المقدار
+
+904
+01:09:31,950 --> 01:09:37,770
+الان الان اف ام ابراهيم converged uniformly اذا
+
+905
+01:09:37,770 --> 01:09:40,110
+لكل ابسلون اكبر من سفر there exists delta such
+
+906
+01:09:40,110 --> 01:09:42,390
+there exists such و في ابسلون و such ذات هذا اصغر
+
+907
+01:09:42,390 --> 01:09:44,990
+من مين some ابسلون او ابسلون على اتنين او اللي
+
+908
+01:09:44,990 --> 01:09:52,710
+بدكميا الان اذا نكمل اللي بنقوله شوفSince Fn'
+
+909
+01:09:53,010 --> 01:09:57,510
+converges uniformly on J إذا لكل ي أكبر من 0 there
+
+910
+01:09:57,510 --> 01:10:03,770
+exists H of ي H of ي such that if M و N أكبر سواء
+
+911
+01:10:03,770 --> 01:10:10,230
+H of ي then هذا المقدار اللي هو أصغر من مين من ي
+
+912
+01:10:10,230 --> 01:10:16,590
+يعني صار كل هذا المقدار أصغر من ي لمين؟ لأ ال M و
+
+913
+01:10:16,590 --> 01:10:25,840
+ال N لأأكبر من مين من H of Epsilon لان صار عندي
+
+914
+01:10:25,840 --> 01:10:31,280
+لان لكل M و N أكبر سوى H of Epsilon صار المقدار
+
+915
+01:10:31,280 --> 01:10:35,140
+هذا اللي هو أصغر أو سوى هذا اللي هو أصغر من
+
+916
+01:10:35,140 --> 01:10:37,860
+Epsilon خليها في الذاكرة هذه أصغر من مين من
+
+917
+01:10:37,860 --> 01:10:42,740
+Epsilonالان take the limit of both sides as M goes
+
+918
+01:10:42,740 --> 01:10:46,160
+to infinity بس هان عشان بياخد M رايحة لما لنهاية
+
+919
+01:10:46,160 --> 01:10:50,000
+بدنا ناخد لل M أكبر أو يساوي H N عشان لما ال M
+
+920
+01:10:50,000 --> 01:10:53,340
+تروح لما لنهاية M تبقى مرتاحة زي 100 و M لا تتحركش
+
+921
+01:10:53,340 --> 01:11:01,520
+بدنا إياها تتحرك بيصير عندى as M goes to infinity
+
+922
+01:11:01,520 --> 01:11:08,350
+ال limit لل F M of X هيساوي F of Xلأنه صارت
+
+923
+01:11:08,350 --> 01:11:14,670
+uniformly الـ Fm أثبتناها بتروح للـ F uniformly
+
+924
+01:11:14,670 --> 01:11:19,830
+إذن limit Fm of X هي F of X و limit Fm of C هي F
+
+925
+01:11:19,830 --> 01:11:25,490
+of C على X minus C معايا هذا Fn of X ناقص Fn of C
+
+926
+01:11:25,490 --> 01:11:29,370
+على X minus C زي ما هي لإن أنا إبسلتها زي ما هي
+
+927
+01:11:29,370 --> 01:11:32,890
+مين اللي طيرتها الكبيرة اللي هي M إذا صار هذا
+
+928
+01:11:32,890 --> 01:11:38,130
+المقدار أصغر أو يساوي مين؟ إبسلونفي حال مين؟ في
+
+929
+01:11:38,130 --> 01:11:43,930
+حال X لا تساوي C و للأنات اللي أكبر من مين من H of
+
+930
+01:11:43,930 --> 01:11:49,710
+Y أنا تحت هذه الشروط ماشي طيب عمالي قاعد بجرب على
+
+931
+01:11:49,710 --> 01:11:58,400
+اللي هو الهدف تبعي شوف صار عندي الآنهذه الـ
+
+932
+01:11:58,400 --> 01:12:03,740
+Inquality واحد اللي هو متحققها لكن أنا بعرف أنه
+
+933
+01:12:03,740 --> 01:12:07,780
+limit of F N prime of C أشهر بساوي G of C لأنه
+
+934
+01:12:07,780 --> 01:12:12,440
+احنا مفترضين من رأس الدور أنه F N prime converges
+
+935
+01:12:12,440 --> 01:12:18,470
+uniformly to مين؟للـ G .. طيب لأن sense limit F N
+
+936
+01:12:18,470 --> 01:12:22,330
+prime of C بيسوي G of C إذا there exists N of
+
+937
+01:12:22,330 --> 01:12:25,590
+إبسلون such that for every N أكبر بيسوي N of
+
+938
+01:12:25,590 --> 01:12:29,910
+إبسلون حيكون F N prime of C ناقص G of C اللي هو
+
+939
+01:12:29,910 --> 01:12:38,310
+أصغر من إيش من إبسلونالان صار عندى هذه متحققة للان
+
+940
+01:12:38,310 --> 01:12:43,430
+أكبر سواء H و هذه متحققة للان الأكبر سواء N عشان
+
+941
+01:12:43,430 --> 01:12:47,750
+استخدم التنتين بتاخد ال maximum بين هذه و هذه و
+
+942
+01:12:47,750 --> 01:12:52,630
+اقول let K بسوء ال maximum بين H of epsilon و N
+
+943
+01:12:52,630 --> 01:12:59,130
+epsilon اذا الان صار عندى التنتين متحققات لكل N
+
+944
+01:12:59,130 --> 01:13:04,530
+أكبر او يساوي K ومشروع استخدامهالآن من جهة ثانية
+
+945
+01:13:04,530 --> 01:13:07,750
+بدي استخدم الـ FK' of C إنها exist
+
+946
+01:13:11,040 --> 01:13:14,540
+إذا صارت عندي هذه زي ما قلنا وهذه هاتين تان بحجله
+
+947
+01:13:14,540 --> 01:13:18,620
+استخدمهم لكل ان أكبر أو ساو كي بدي استخدم هذه كمان
+
+948
+01:13:18,620 --> 01:13:22,900
+و أربط هذه مع هذه و أخلص اللي بديها since fk prime
+
+949
+01:13:22,900 --> 01:13:26,860
+of c exist مين ال K هذه ال K هذه اللي خدتها ال
+
+950
+01:13:26,860 --> 01:13:31,660
+superman بين هذه و هذه عشان ينفع استخدم هذه و هذه
+
+951
+01:13:31,660 --> 01:13:37,760
+و هذه بعد شويةthen مدام fk prime of c exist then
+
+952
+01:13:37,760 --> 01:13:42,080
+if x minus c أكبر من صفر أصغر من دلتا دلتا k طبعا
+
+953
+01:13:42,080 --> 01:13:46,480
+الدلتا هتعتمد على اللي هو ال epsilon نسميها دلتا k
+
+954
+01:13:46,480 --> 01:13:49,360
+لإنها اعتمدت على مين؟ على الكل يعنى then there
+
+955
+01:13:49,360 --> 01:13:53,380
+exists دلتا k بحيث x minus c أصغر من دلتا يعطيني
+
+956
+01:13:53,380 --> 01:13:57,540
+fk of x ناقص fk of c على x minus c اللي هي ناقص fk
+
+957
+01:13:57,540 --> 01:14:04,140
+prime of c أصغر من إبسلون فاهمين هذا؟ مدام fkprime
+
+958
+01:14:04,140 --> 01:14:09,260
+of c بيساو limit exist إذا حساو limit f of x ناقص
+
+959
+01:14:09,260 --> 01:14:14,280
+f of c بprime على x minus c طبعا كك كله as x بتروح
+
+960
+01:14:14,280 --> 01:14:17,620
+لل c صار exist يعني forever epsilon أكبر من 0
+
+961
+01:14:17,620 --> 01:14:21,740
+exist دلتا بحيث أنه لما تكون x minus c أصغر من
+
+962
+01:14:21,740 --> 01:14:24,360
+دلتا يعطيني هذا ناقص هذا أصغر من epsilon وهذا هو
+
+963
+01:14:24,360 --> 01:14:28,400
+المكتوبلذن صار عندى هذا موجود وهي اتنين وهي تلاتة
+
+964
+01:14:28,400 --> 01:14:33,020
+لأن واحد و اتنين و تلاتة بدي اصل اللي بديه خلينا
+
+965
+01:14:33,020 --> 01:14:35,720
+نكتب هنا عشان ما نجلبش الصفحة عشان يظلوا كله
+
+966
+01:14:35,720 --> 01:14:43,880
+قدامكم الان اللي وصلت اليه مالي for every epsilon
+
+967
+01:14:43,880 --> 01:14:46,660
+أكبر من سفر بقول there exists delta أكبر من سفر
+
+968
+01:14:46,660 --> 01:14:49,740
+such that if
+
+969
+01:14:51,280 --> 01:14:57,660
+x-c أصغر أكبر من صفر وأصغر من دلتا then شوف الآن
+
+970
+01:14:57,660 --> 01:15:02,400
+then إيش اللي هو بدي مين أنا هي هي اللي بديها f of
+
+971
+01:15:02,400 --> 01:15:12,880
+x minus f of c على x minus c ناقص g of c أصغر
+
+972
+01:15:12,880 --> 01:15:18,120
+أو يساوي ماشي الحال أصغر أو يساوي بدي أبدأ الآن
+
+973
+01:15:18,120 --> 01:15:24,240
+اللي هو هي هذهبدي أدخلها دي، عشان؟ أصغر أو ساوي
+
+974
+01:15:24,240 --> 01:15:32,300
+اللي هو F of X ناقص F of C على X minus C ناقص FN
+
+975
+01:15:32,300 --> 01:15:39,840
+of X ناقص FN of C على X minus C زائد اللي دخلتها
+
+976
+01:15:39,840 --> 01:15:51,830
+دي FN of X ناقص FN of C على X minus C ناقصاللي هو
+
+977
+01:15:51,830 --> 01:15:56,850
+ايش
+
+978
+01:15:56,850 --> 01:16:03,170
+التانية فك
+
+979
+01:16:03,170 --> 01:16:13,890
+prime of c a زائد فك
+
+980
+01:16:13,890 --> 01:16:21,820
+prime of c ناقص فنقص من اللي ضال G of C بظبط هيك ا
+
+981
+01:16:21,820 --> 01:16:26,460
+اظن تشوف عليها الان انا بتلزمنيش كل الانات بتلزمني
+
+982
+01:16:26,460 --> 01:16:31,480
+بس ال مين ال K لأنه الان انا بحكي على استخدام ال K
+
+983
+01:16:31,480 --> 01:16:39,280
+K K و هاد ايهاش K طيب الان نيجي نتطلعالـ K تبعتنا
+
+984
+01:16:39,280 --> 01:16:42,040
+هذه بنحكي عن K محددة الـ K اللي هي superman بين H
+
+985
+01:16:42,040 --> 01:16:46,320
+و بين N يعني الـ K أكبر أو يساوي H و الـ K أكبر أو
+
+986
+01:16:46,320 --> 01:16:51,600
+يساوي مين الـ N يعني بحججلي أستخدم F K of C F K
+
+987
+01:16:51,600 --> 01:16:55,020
+prime of C ناقص G of C أصغر من إبسلون و بحججلي
+
+988
+01:16:55,020 --> 01:16:58,320
+أستخدم هذه ناقص F K of K في K أصغر من مين من
+
+989
+01:16:58,320 --> 01:17:04,540
+إبسلون الآن هذه هذه هي هان الأولى إذا أصغر أو
+
+990
+01:17:04,540 --> 01:17:13,170
+يساوي هذه من واحدepsilon زائد هذه التانية من مين
+
+991
+01:17:13,170 --> 01:17:19,250
+من اللي هي تلاتة هي fk of x نقص fk of c عليك x
+
+992
+01:17:19,250 --> 01:17:23,490
+minus c نقص fk prime أصغر برضه من مين من epsilon
+
+993
+01:17:23,490 --> 01:17:29,290
+هذه من تلاتة وهذه من واحد هذه أكيد من مين هستخدمها
+
+994
+01:17:29,290 --> 01:17:35,610
+من اتنين اللي هي n هذه لكل n أكبر سوى nوعندي الـ K
+
+995
+01:17:35,610 --> 01:17:38,190
+أصلا أكبر أوي سواء لإنها ال maximum بين ال team
+
+996
+01:17:38,190 --> 01:17:42,910
+تان إذا هذه برضه بحق الله أستخدمها أمن اتنين أصغر
+
+997
+01:17:42,910 --> 01:17:47,470
+من إبسلون إذا صار عندي هذا المقدار اللي فوق أصغر
+
+998
+01:17:47,470 --> 01:17:52,290
+من تلاتة إبسلون وإبسلون was arbitrarily إذا صار
+
+999
+01:17:52,290 --> 01:17:57,210
+عندي limit هذا المقدار بساوي G of C إيش معناه
+
+1000
+01:17:57,210 --> 01:18:01,430
+limit هذا المقدار بساوي G of C معناته أنه اللي هو
+
+1001
+01:18:01,430 --> 01:18:08,730
+ال F primeof C هو الـ G of C وزي ما قلنا في الأول
+
+1002
+01:18:08,730 --> 01:18:12,530
+since C was arbitrary in G then صارت اللي هي F
+
+1003
+01:18:12,530 --> 01:18:18,990
+بتساوي G على كل مين على كل الـ G وهيك بنكون خلصنا
+
+1004
+01:18:18,990 --> 01:18:23,330
+النظرية وانهينا ال section اللي هو تمانية اتنين
+
+1005
+01:18:23,330 --> 01:18:26,370
+وهيك بنكون خلصنا الحديث اللي بنتحدثه في chapter
+
+1006
+01:18:26,370 --> 01:18:30,370
+تمانية وعندنا طبعا الأسئلة المطلوبة هيها في نهاية
+
+1007
+01:18:30,370 --> 01:18:33,430
+كل section تمانية واحد وتمانية اتنين وإلى لقاء
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/QjdD_6J2asI.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/QjdD_6J2asI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..16678c4e6fc6236b511954fc26f3ab977212a0d4
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/QjdD_6J2asI.srt
@@ -0,0 +1,1943 @@
+1
+00:00:04,960 --> 00:00:12,580
+بسم الله الرحمن الرحيم هذه المحاضرة رقم 16 في مساق
+
+2
+00:00:12,580 --> 00:00:18,080
+تحليل حقيقي 2 أو تحليل رياضي 2 لطلبة وطالبات كلية
+
+3
+00:00:18,080 --> 00:00:22,820
+العلوم بالجامعة الإسلامية بغزة كنا سميينها في
+
+4
+00:00:22,820 --> 00:00:29,160
+المحاضرة 15 إنها جزئين المحاضرة الجزء الأول ذكرناه 
+
+5
+00:00:29,160 --> 00:00:31,820
+في المحاضرة 15 وقلنا الجزء الثاني هنذكره في
+
+6
+00:00:31,820 --> 00:00:35,780
+المحاضرة اللي بعدها كجزء ثاني من 15 بس الآن لطول
+
+7
+00:00:35,780 --> 00:00:40,440
+فترة اللي هي المحاضرة السابقة هنسمي هذا الجزء الآن
+
+8
+00:00:40,440 --> 00:00:43,060
+اللي هو كان اسمه الجزء الثاني المحاضرة 15 لأ بدي 
+
+9
+00:00:43,060 --> 00:00:48,300
+أسميه هو المحاضرة رقم 16 وهو اللي هو بداية سيكشن 
+
+10
+00:00:48,300 --> 00:00:52,020
+جديد اللي هو سبعة أربعة اللي هو the integration as 
+
+11
+00:00:52,020 --> 00:00:56,260
+a limit اللي هو بدنا نصل ال integration عن طريق
+
+12
+00:00:56,260 --> 00:01:01,880
+اللي هو the limit of Riemann sum بس شغلة سريعة عشان
+
+13
+00:01:01,880 --> 00:01:05,820
+نربط بالسابق باللاحق بالحاضر عشان نفهم إيش اللي
+
+14
+00:01:05,820 --> 00:01:10,780
+بنحكي فيه إحنا إذا بتتذكرتتذكر واخدنا على الفترة A
+
+15
+00:01:10,780 --> 00:01:17,200
+وB وعملنا لها تجزئة P بساوي X Note X واحد لعند ال
+
+16
+00:01:17,200 --> 00:01:25,000
+XN وعرفنا اللي هو ال Upper sum اللي هو Upper اللي
+
+17
+00:01:25,000 --> 00:01:31,900
+هي L وP L لو function عندي F فعندي F of X على
+
+18
+00:01:31,900 --> 00:01:39,160
+الفترة من A لعند B اللي هو ال UpperF of B وقلنا هو
+
+19
+00:01:39,160 --> 00:01:44,780
+عبارة عن summation لل M K في X K minus X K minus
+
+20
+00:01:44,780 --> 00:01:51,060
+واحد زي ما أنتم الذاكرين K من عند واحد لعند N هذا
+
+21
+00:01:51,060 --> 00:01:54,900
+اللي هو اللي سمناه ال other sum ال M K طبعا هي ال
+
+22
+00:01:54,900 --> 00:01:57,600
+supremum على الفترة .. ال
+
+23
+00:01:57,600 --> 00:02:01,040
+supremum لدال ال F ال supremum لدال ال F على
+
+24
+00:02:01,040 --> 00:02:06,340
+الفترة اللي أمامي وعندي ال L F of P أو P و F زي ما
+
+25
+00:02:06,340 --> 00:02:10,300
+احنا بنكتبها عبارة عن summation ال M K في X K
+
+26
+00:02:10,300 --> 00:02:14,680
+minus X K minus واحد K من عند واحد لعندنا وقلنا لو
+
+27
+00:02:14,680 --> 00:02:19,380
+اتينا ال other sum أخدناله اللي هو ال infimum ال
+
+28
+00:02:19,380 --> 00:02:24,370
+other sum وقلنا أخدناله ال infimum بنسميه U of F
+
+29
+00:02:24,370 --> 00:02:29,070
+اللي هو عبارة عن الـ infimum لـ U of F و B such
+
+30
+00:02:29,070 --> 00:02:32,370
+that B element in the set of all partition B of I
+
+31
+00:02:32,370 --> 00:02:36,630
+و أخدنا ال L of F و قلنا هو عبارة عن ال supremum
+
+32
+00:02:36,630 --> 00:02:41,300
+لـ L of F و B highest B element in the set of all
+
+33
+00:02:41,300 --> 00:02:46,780
+partitions B of I قلنا إن F هتكون integrable إذا
+
+34
+00:02:46,780 --> 00:02:50,460
+اللي هو ال lower integral بساومين ال upper
+
+35
+00:02:50,460 --> 00:02:55,580
+integral هذا المدخل اللي دخلنا فيه لإثبات أو
+
+36
+00:02:55,580 --> 00:03:00,220
+لتعريف إن F is integrable مدخل اللي هو ال upper
+
+37
+00:03:00,220 --> 00:03:03,650
+sum والlower sum أو الـ Upper Integral والـ Lower
+
+38
+00:03:03,650 --> 00:03:07,470
+Integral يوم ما يتساون بنسميه الـ Integral اللي هو
+
+39
+00:03:07,470 --> 00:03:10,670
+عبارة عن قيمة الـ Integration للـ F على الفترة A
+
+40
+00:03:10,670 --> 00:03:17,640
+وB الآن ايش اللي هنسويه اللي هو الجزء الثاني من
+
+41
+00:03:17,640 --> 00:03:21,300
+المحاضرة 
+
+42
+00:03:21,300 --> 00:03:24,300
+أو اللي احنا سمينا المحاضرة 16 اللي هو في ال
+
+43
+00:03:24,300 --> 00:03:29,840
+section 7-4 هندخل لل integration بداخلة أخرى عن
+
+44
+00:03:29,840 --> 00:03:35,280
+طريق حاجة اسمها ال remansum ومن ثم نقول نثبت في
+
+45
+00:03:35,280 --> 00:03:40,000
+النهاية انه limit ال remansum لما يكون موجود بكون
+
+46
+00:03:40,000 --> 00:03:45,480
+هو الـ Integration وهذا مكافئ أو يحدث if and only
+
+47
+00:03:45,480 --> 00:03:50,580
+if إذا حدثت اللي هو معنى التكامل بصيغة ال Upper
+
+48
+00:03:50,580 --> 00:03:54,420
+Sum والLower Sum يعني الآن .. الآن في عندنا مدخلين
+
+49
+00:03:54,420 --> 00:03:57,660
+للدخول للتكامل إما عن طريق ال Upper Sum والLower
+
+50
+00:03:57,660 --> 00:04:00,560
+Sum أو ال Upper Integral والLower Integral أو عن
+
+51
+00:04:00,560 --> 00:04:04,200
+طريق اللي هو ال Remain Sum أو اللي هو ال limit
+
+52
+00:04:04,200 --> 00:04:09,000
+للRemain Sum والتنين لما نكون كل واحد ذاك ال ..
+
+53
+00:04:09,000 --> 00:04:12,740
+الملهمته موجود و هذا ال upper بساوي ال lower بكون
+
+54
+00:04:12,740 --> 00:04:19,500
+ال R equivalent إيه الآن؟ إيش ال .. ال roman sum؟
+
+55
+00:04:19,500 --> 00:04:24,200
+احنا برضه التجزية جاءت تجزية هاي P بساوي X note و
+
+56
+00:04:24,200 --> 00:04:29,280
+X واحد لعند ال XN هاي التجزية هاي X note و هاي X
+
+57
+00:04:29,280 --> 00:04:32,700
+واحد وهي الفترة الموضاجية XK minus واحد لعند ال XK
+
+58
+00:04:33,370 --> 00:04:40,570
+الآن الـ Riemann Sum بنختار في الـ Intervals نقطة
+
+59
+00:04:40,570 --> 00:04:45,830
+عشوائية لا تقول لي لا أكبر واحدة ولا أصغر واحدة
+
+60
+00:04:45,830 --> 00:04:49,150
+ولا كذا لأ نقطة عشوائية وبنسميها مثلا لو قلت لك
+
+61
+00:04:49,150 --> 00:04:54,970
+الهن بسميها XIK الآن XIK هذه صارت element في الـ
+
+62
+00:04:54,970 --> 00:05:02,000
+XK-1 والـ xk الآن بدي بضرب ال x اللي اللي هي طول
+
+63
+00:05:02,000 --> 00:05:05,140
+الفترة زي ما ضربتها زي ما وجدت ال sum اللي هو ال
+
+64
+00:05:05,140 --> 00:05:09,020
+upper sum هنا بوجد هنا بس بستبدل ال mk و ال mk
+
+65
+00:05:09,020 --> 00:05:13,380
+small و upper بستبدلها بقيمة ال function عند هذه
+
+66
+00:05:13,380 --> 00:05:18,270
+النقطة العشوائية اللي اخترتها اللي هي بيسميها xik
+
+67
+00:05:18,270 --> 00:05:24,190
+فبصير xk minus xk minus 1 في ال F عند xik و باخده
+
+68
+00:05:24,190 --> 00:05:28,290
+ال summation k من عند 1 لعند n و هذا اللي بيسميه
+
+69
+00:05:28,290 --> 00:05:36,030
+الرمان صم S of B أو مين و F S of B أو F و هذا اللي
+
+70
+00:05:36,030 --> 00:05:43,470
+بيسميه الرمان صم في النهاية هنصلكم أنه لو كان ال
+
+71
+00:05:43,470 --> 00:05:49,710
+limit للـ S, P و F as الـ N goes to infinity يعني
+
+72
+00:05:49,710 --> 00:05:53,630
+الـ N اللي هي زغرنا الفترة صارتها الجدّة و زغرنا
+
+73
+00:05:53,630 --> 00:05:57,090
+صارتها الفترة .. لما تكون N تروح إلى نهاية معناته
+
+74
+00:05:57,090 --> 00:05:59,590
+أن صارت اللي .. اللي هي و كأنه الفترات عبارة عن
+
+75
+00:05:59,590 --> 00:06:05,130
+خطوط جنب بعض هذه الخطوط بتنطبق الـ XK و XK-1 و XIK
+
+76
+00:06:05,130 --> 00:06:10,950
+على بعض و كأنه بتسير كل خط جنب خط جنب خط إلى قيمة
+
+77
+00:06:10,950 --> 00:06:14,640
+اللي هو مجموع هذه الخطوط زي ما حكينا قبل هيك اللي
+
+78
+00:06:14,640 --> 00:06:18,820
+بتعمل المساحة تحت المنحنى في حالة الموجب ومن ثم هي
+
+79
+00:06:18,820 --> 00:06:21,740
+هتعمل لي قيمة ال integration يعني لما يكون ال
+
+80
+00:06:21,740 --> 00:06:24,420
+limit لـRiemann sum as N goes to infinity exist
+
+81
+00:06:24,420 --> 00:06:29,380
+وسوّت لي رقم اسمه إيه هذا الرقم هو عبارة عن ال
+
+82
+00:06:29,380 --> 00:06:33,900
+integration إيه لـ BF of X DX على هذه الفترة هذا
+
+83
+00:06:33,900 --> 00:06:38,400
+اللي في النهاية بدنا نصل إليه أو نوصلكم إنه في
+
+84
+00:06:38,400 --> 00:06:42,680
+حالة وجود هذا ال limit هيكون هو ال integration
+
+85
+00:06:42,680 --> 00:06:47,040
+اللي بمفهوم ال upper sum والlower sum يعني
+
+86
+00:06:47,040 --> 00:06:53,160
+الدخلتين بقد إلى نفس القيمة أو إلى نفس النتيجة
+
+87
+00:06:54,950 --> 00:06:59,130
+يعني في بعض الكتب بتعرفلك أصلا اللي هو ال
+
+88
+00:06:59,130 --> 00:07:04,430
+integration as a limit of remansum في كتب و هذا
+
+89
+00:07:04,430 --> 00:07:09,650
+غالبا في ال calculus بيشتغلوه و في كتب بتعرفه عن
+
+90
+00:07:09,650 --> 00:07:12,230
+طريق ال other sum و لا other sum في ال calculus
+
+91
+00:07:12,230 --> 00:07:15,930
+لأنه ملزمش ل Supremum و ل Infimum لإن الطالب مفهم
+
+92
+00:07:15,930 --> 00:07:20,370
+ال Supremum ومفهم ال Infimum عنده اللي هو ناضج
+
+93
+00:07:24,160 --> 00:07:29,980
+بعد هذه المقدمة عن الموضوع خلّينا ندخل إلىه بشكل
+
+94
+00:07:29,980 --> 00:07:34,700
+تفصيلي The integration as a limit لت I اللي هي ال
+
+95
+00:07:34,700 --> 00:07:36,820
+interval اللي انا بده اشتغل عليها و ال function
+
+96
+00:07:36,820 --> 00:07:40,260
+أفنان I لR عبارة عن bounded function و خدنا ال B
+
+97
+00:07:40,260 --> 00:07:44,440
+هو ال partition اللي أخدناه و زي ما قلنا إذا أخدنا
+
+98
+00:07:44,440 --> 00:07:50,470
+XI 1 و XI 2 و XI N عبارة عن arbitrary numbers اللي
+
+99
+00:07:50,470 --> 00:07:53,330
+هو الـ x i 1 في ال .. في ال .. في ال interval x
+
+100
+00:07:53,330 --> 00:07:57,270
+not x 1 x i 2 في ال interval اللي .. اللي بعدها
+
+101
+00:07:57,270 --> 00:08:00,810
+ايه اخره يعني ال x i k هي في ال .. الفترة النموذج
+
+102
+00:08:00,810 --> 00:08:06,130
+الذادية x k minus 1 x k ل k من 1 لعند مين لعند ان
+
+103
+00:08:06,130 --> 00:08:08,570
+ال sum اللي قولنا عنه اللي هو عبارة عن ال
+
+104
+00:08:08,570 --> 00:08:12,530
+summation لل F of x i k مضروب في x k ناقص x k
+
+105
+00:08:12,530 --> 00:08:17,110
+minus 1 هذا ال summation من 1 لعند ان هم هو برمزه
+
+106
+00:08:17,110 --> 00:08:21,030
+للرمز SPUF اللي هو بسميه اللي هو عبارة عن the
+
+107
+00:08:21,030 --> 00:08:25,810
+remand sum الريمان صم الريمان صم الريمان صم
+
+108
+00:08:25,810 --> 00:08:30,150
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+109
+00:08:30,150 --> 00:08:31,170
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+110
+00:08:31,170 --> 00:08:32,670
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+111
+00:08:32,670 --> 00:08:33,050
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+112
+00:08:33,050 --> 00:08:33,610
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+113
+00:08:33,610 --> 00:08:34,330
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+114
+00:08:34,330 --> 00:08:36,290
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+115
+00:08:36,290 --> 00:08:43,690
+الريمان صم الريمان صم الريمان صم الريمان صم الري
+
+116
+00:08:43,710 --> 00:08:48,550
+مان صم لأن الـ F of XI K اللي هي النقطة العشوائية هذه
+
+117
+00:08:48,550 --> 00:08:53,190
+أكيد أصغر أو يساوي الـ inf mum على كل النقاط اللي
+
+118
+00:08:53,190 --> 00:08:57,710
+في ال sub interval هذه و أكبر أو يساوي و أصغر أو
+
+119
+00:08:57,710 --> 00:09:01,730
+يساوي من ال super mum يعني F of XI K هذه نقطة
+
+120
+00:09:01,730 --> 00:09:05,490
+عشوائية أكبر أو يساوي أصغر واحدة أو أصغر اللي هو
+
+121
+00:09:05,490 --> 00:09:10,070
+ال inf mum و أصغر أو يساوي اللي هي من ال super mum
+
+122
+00:09:10,610 --> 00:09:13,890
+هذا لكل مين لكل sub interval يعني هي sub interval
+
+123
+00:09:13,890 --> 00:09:20,810
+xk minus واحد وهي xk وهي xik أكيد اللي هو f of xik
+
+124
+00:09:20,810 --> 00:09:29,210
+هنا أصغر أو يساوي أكبر واحدة وأصغر أو يساوي أكبر
+
+125
+00:09:29,210 --> 00:09:34,020
+واحدة وأكبر أو يساوي أصغر واحدة اللي هي الـ MK
+
+126
+00:09:34,020 --> 00:09:38,580
+فبكون 
+
+127
+00:09:38,580 --> 00:09:43,360
+دايما هي هذه دي و هذه دي و هذه دي خدوا الآن ضربولي
+
+128
+00:09:43,360 --> 00:09:47,680
+هنا وهنا وهنا ضربولي في XK-XK-Y حط طول الفترة
+
+129
+00:09:48,770 --> 00:09:52,070
+واخدوا الـ summation من عند واحد لعند أن بيصير هذا
+
+130
+00:09:52,070 --> 00:09:55,670
+بيمثل لي اللي هو الأبر صم وهذا بيمثل لي الأور صم
+
+131
+00:09:55,670 --> 00:10:00,070
+وهذا بيمثل لي مين؟ الريمان صم إذن الريمان صم دائما
+
+132
+00:10:00,070 --> 00:10:05,250
+بين الأبر وبين الأور لأوله أصلا نحن ليش بيسميهم
+
+133
+00:10:05,250 --> 00:10:10,210
+أبر و لاور عسى إن كل اللي غيرهم الأبر كل اللي
+
+134
+00:10:10,210 --> 00:10:14,350
+غيرهم أصغر يسويهم وكل اللي غيرهم الأور أكبر منهم
+
+135
+00:10:14,350 --> 00:10:21,060
+أو يسويهم التسمية جزء من المفهوم أو تستقر من
+
+136
+00:10:21,060 --> 00:10:27,020
+المفهوم يعني بنسميها مش معقول هي أبر ونسميها لابر
+
+137
+00:10:27,020 --> 00:10:32,520
+أو أبر ونسميها اسم يخالف الأبر فأكيد اخترنا اسم
+
+138
+00:10:32,520 --> 00:10:37,660
+الأبر عشان هي فعلا أبر طيب نجي الى النظرية الأولى
+
+139
+00:10:37,660 --> 00:10:43,520
+let a و b عبارة عن فترة مغلقة و bounded و let f من
+
+140
+00:10:43,520 --> 00:10:46,960
+I ل R be integrable on I نفترض ان اف اذا احنا لما
+
+141
+00:10:46,960 --> 00:10:49,880
+نحكي integrable معناته integrable in the sense of
+
+142
+00:10:49,880 --> 00:10:53,340
+التعريف 716 اللي هو اللي بعتمد على الـ U of F
+
+143
+00:10:53,340 --> 00:10:58,080
+بتساوي الـ O of F الآن let F من I لـ R بيكون Integrable
+
+144
+00:10:58,080 --> 00:11:01,940
+I زي ما بأكد in the sense of التعريف 716 اللي
+
+145
+00:11:01,940 --> 00:11:09,070
+حكيته إذا لكل ε أكبر من صفر is given There exists a
+
+146
+00:11:09,070 --> 00:11:11,470
+partition بـ ε such that if P is any
+
+147
+00:11:11,470 --> 00:11:15,610
+partition that is a refinement of P ε and if
+
+148
+00:11:15,610 --> 00:11:19,930
+S P و F is any Riemann sum for F then هيكون
+
+149
+00:11:19,930 --> 00:11:24,110
+عنده اللي هو S P و F ناقص الـ integration لـ F 
+
+150
+00:11:24,110 --> 00:11:29,210
+أصغر من مين؟ من ε بقول باختصار يعني لو فرضنا
+
+151
+00:11:29,210 --> 00:11:34,490
+F integrable اللي هنخده لأي ε في الدنيا بقدر
+
+152
+00:11:34,490 --> 00:11:40,550
+أجيلك partition بـ ε بحيث إنه أي P partition
+
+153
+00:11:40,550 --> 00:11:45,390
+refinement لـ P ε refinement معناته الـ P بحتوي
+
+154
+00:11:45,390 --> 00:11:50,910
+مين؟ الـ P ε تحسين له هيكون عندي الـ Riemann sum S
+
+155
+00:11:50,910 --> 00:11:55,150
+P و F هذا ناقص الـ integration لـ F أصغر من مين؟ من
+
+156
+00:11:55,150 --> 00:12:04,090
+ε يعني الآن F is integrable يا جماعة الآن for
+
+157
+00:12:04,090 --> 00:12:08,070
+every ε أكبر من 0 there exist P ε such
+
+158
+00:12:08,070 --> 00:12:12,490
+that for every P يحتوي P ε اللي هو هذا اللي
+
+159
+00:12:12,490 --> 00:12:20,110
+جيته and for every Riemann sum S للـ P ولـ F هيكون
+
+160
+00:12:20,110 --> 00:12:25,410
+عندي الـ absolute value بين الـ S P و F ناقص اللي
+
+161
+00:12:25,410 --> 00:12:31,890
+هو الـ integration من A لـ B للـ F أصغر من ε منافسة
+
+162
+00:12:31,890 --> 00:12:35,790
+يعني جاعت بقول أخي يعني أصلاً يعني إني هذا في الآخر
+
+163
+00:12:35,790 --> 00:12:39,910
+في الآخر في الآخر في الآخر هتلاقي الـ Riemann sum اللي
+
+164
+00:12:39,910 --> 00:12:43,890
+هو بيكون بينه وبين الـ F إيش ما له؟ أصغر من ε
+
+165
+00:12:43,890 --> 00:12:47,870
+لما تكون الـ إيش الـ F اللي هي Integral يعني بلاقي
+
+166
+00:12:47,870 --> 00:12:52,890
+P ε بضمن لك هذا الكلام بضمن لك مش الـ P ε 
+
+167
+00:12:52,890 --> 00:12:58,550
+بس وكل الـ refinement يعني كل الـ refinement يعني
+
+168
+00:12:58,550 --> 00:13:05,310
+كل ما نزيد عدد عناصر الـ partition يعني كل ما نكبر
+
+169
+00:13:05,310 --> 00:13:09,810
+الآن يعني وكأنه بقودنا لللي بدنا نحكيه قدام إنه
+
+170
+00:13:09,810 --> 00:13:15,770
+لما الآن تروح لمحصلة النهاية limit الـ Riemann sum إذا
+
+171
+00:13:15,770 --> 00:13:18,950
+كانت موجودة integrable هيساوي الـ integration
+
+172
+00:13:18,950 --> 00:13:23,870
+والعكس هنلاقيه صحيح برضه هيسيه التعريف طيب في
+
+173
+00:13:23,870 --> 00:13:26,870
+بعض الكتب زي ما قلنا أو لو بدنا نسميه التعريف
+
+174
+00:13:26,870 --> 00:13:29,950
+بنقول equivalent لـ التعريف الأولاني وطبعاً
+
+175
+00:13:29,950 --> 00:13:37,040
+هنلاقيه حالة بتتواصل نرجع لنظريتنا نثبته الآن if F
+
+176
+00:13:37,040 --> 00:13:40,820
+is integrable and Y أكبر من 0 then by Riemann
+
+177
+00:13:40,820 --> 00:13:45,200
+criterion there exists P ε of I such that U
+
+178
+00:13:45,200 --> 00:13:48,980
+ناقص L أصغر من مين؟ من Y هذا حفظناه زي اسمنا مدام
+
+179
+00:13:48,980 --> 00:13:53,000
+F is integrable and then by Riemann criterion طبعاً
+
+180
+00:13:53,000 --> 00:13:55,620
+أكيد هتيجي على بالكم لأنه مدام قال there exists P
+
+181
+00:13:55,620 --> 00:13:59,120
+ε هيكيد أقول أكيد احنا هنستخدم مين؟ اللي بتجيب
+
+182
+00:13:59,120 --> 00:14:01,720
+الـ P ε مين اللي كانت بتجيب الـ P ε اللي
+
+183
+00:14:01,720 --> 00:14:04,870
+هي الـ Riemann criterion إذا كان الـ F مستعمل والـ
+
+184
+00:14:04,870 --> 00:14:07,790
+F أكبر من 0 فبالتالي باستخدام الـ Riemann's
+
+185
+00:14:07,790 --> 00:14:11,850
+criterion يوجد مجموعة P ε of I مثلًا الـ U
+
+186
+00:14:11,850 --> 00:14:14,950
+P ε والـ F ناقص الـ P ε والـ F أشماله
+
+187
+00:14:14,950 --> 00:14:23,290
+أصغر من مين؟ من ε الآن خدوا أي refinement بـ P
+
+188
+00:14:23,290 --> 00:14:28,590
+بحتوي مين؟ الـ P ε الـ refinement التحسين
+
+189
+00:14:28,590 --> 00:14:37,240
+الـ lower بيزيد والـ upper بيقل أكيد عارفين إن هذا الكلام
+
+190
+00:14:37,240 --> 00:14:41,220
+إذا صار عند مدام اللي هو الـ refinement الـ lower
+
+191
+00:14:41,220 --> 00:14:46,940
+بيزيد أكيد الـ L P F أصغر أو يساوي L P F اللي هو التحسين
+
+192
+00:14:46,940 --> 00:14:54,760
+والـ L P F دائماً أصغر أو يساوي U P F والـ U P F التحسين بيقل
+
+193
+00:14:54,760 --> 00:14:59,800
+عن الـ U P F إذا هذه الـ inequality محفوظة عندنا ماشي
+
+194
+00:14:59,800 --> 00:15:08,270
+الحال الآن من هنا ذولة صارت عندي high الـ L P
+
+195
+00:15:08,270 --> 00:15:15,090
+ε و F high الـ L P و F لأنه أكبر high الـ U
+
+196
+00:15:15,090 --> 00:15:22,630
+P و F high الـ U P ε و F أكيد أكيد أكيد
+
+197
+00:15:22,630 --> 00:15:27,570
+المسافة بين هذه وهذه أصغر المسافة بين هذه وهذه
+
+198
+00:15:27,570 --> 00:15:33,170
+يعني بمعنى آخر الـ U P F ناقص الـ L P F المسافة بينهم
+
+199
+00:15:33,170 --> 00:15:39,130
+أصغر أو يساوي الـ U P Y والـ L P Y من هذه وهذه من اللي
+
+200
+00:15:39,130 --> 00:15:43,990
+فوق أشماله أصغر من Y إذا صارت عندي الـ U صار عندي
+
+201
+00:15:43,990 --> 00:15:50,210
+الـ U P F ناقص الـ P F أصغر من مين؟ من Y صار عندي الـ U
+
+202
+00:15:51,040 --> 00:16:01,320
+P F ناقص الـ P F أصغر من ε لكل P يحتوي من الـ
+
+203
+00:16:01,320 --> 00:16:04,120
+P ε لكل refinement لمين؟ للـ P ε اللي
+
+204
+00:16:04,120 --> 00:16:08,280
+لجناه بوسط الـ Riemann الـ criterion خلّينا نكمل يا
+
+205
+00:16:08,280 --> 00:16:19,320
+جماعة الآن لكن احنا بنعرف إن أي Riemann sum لـ P معينة
+
+206
+00:16:19,510 --> 00:16:24,830
+هيكون بين الـ L وبين الـ U أكيد صح ولا لأ؟ طبعاً
+
+207
+00:16:24,830 --> 00:16:28,910
+الـ S بين الـ U و F اللي قلناها قبل شوية بين
+
+208
+00:16:28,910 --> 00:16:34,570
+الـ L P و F والـ U P و F طيب خد الـ integration الـ
+
+209
+00:16:34,570 --> 00:16:36,970
+integration ما هو الـ F is integrable مزبوط
+
+210
+00:16:36,970 --> 00:16:41,330
+Integrable إذا هي بتساوي زي ما عملناها كثير بتساوي
+
+211
+00:16:41,330 --> 00:16:45,430
+الـ U في F وبتساوي الـ L في F الـ L في F هي الـ
+
+212
+00:16:45,430 --> 00:16:48,070
+supremum لهذه الأشياء إذا أكيد هذا أكبر أو يساوي الـ
+
+213
+00:16:48,070 --> 00:16:52,410
+lower اللي هي sum هذا والـ Integration بيساوي الـ U
+
+214
+00:16:52,410 --> 00:16:56,370
+و F والـ U و F هو عبارة عن الـ infimum للـ U و P
+
+215
+00:16:56,370 --> 00:16:59,230
+و F إذا نحن نكون أصغر أو يساوي إذا فعلاً الـ
+
+216
+00:16:59,230 --> 00:17:04,610
+integration بين الـ lower sum وبين الـ upper sum و
+
+217
+00:17:04,610 --> 00:17:09,560
+هذه الفكرة عملناها كثير قبل هات إذا L هو أطرح هذه
+
+218
+00:17:09,560 --> 00:17:15,560
+من هذه تنتهي من بعض بيصير عندي الـ S ناقص هذه بين الـ
+
+219
+00:17:15,560 --> 00:17:20,600
+L ناقص الـ U وبين الـ U ناقص الـ L عملناها كثير طرح
+
+220
+00:17:20,600 --> 00:17:24,440
+معادلتين من بعض الآن هي الـ U وهي الـ U وهي الـ L وهي
+
+221
+00:17:24,440 --> 00:17:26,660
+الـ L وضرب واحدة في ناقص اللي بدنا نطرح هذه في
+
+222
+00:17:26,660 --> 00:17:31,220
+ناقص تنعكس الإشارات تجمح لبعض وتطلع هذه أصغر أو
+
+223
+00:17:31,220 --> 00:17:36,920
+يساوي هذه وأصغر أو يساوي هذه الآن هذه يعني هذه اللي
+
+224
+00:17:36,920 --> 00:17:41,040
+هو بتساوي سالب هذه يعني صارت الـ absolute value
+
+225
+00:17:41,040 --> 00:17:44,260
+أصغر أو يساوي اللي هو المقدار الموجود في هذا
+
+226
+00:17:44,260 --> 00:17:48,220
+والمقدار الموجود في هذا أصغر من وين؟ هنا لقينا أصغر
+
+227
+00:17:48,220 --> 00:17:51,800
+من إيش؟ من ε يعني صار عندي الـ S P و F ناقص من
+
+228
+00:17:51,800 --> 00:17:58,860
+الـ F أصغر من مين؟ من ε وهو المطلوب نجي للنظرية
+
+229
+00:17:58,860 --> 00:17:59,300
+اللي بعدها
+
+230
+00:18:09,320 --> 00:18:15,260
+النظرية 3 4 .. 7 4 3 نشوف ..
+
+231
+00:18:15,260 --> 00:18:21,920
+نتبه لنص النظرية ومن ثم نيجي إلى اللي هو البرهان
+
+232
+00:18:21,920 --> 00:18:27,380
+إذا من الـ .. من النظرية اللي قبلها شوية لكل ε
+
+233
+00:18:27,380 --> 00:18:32,760
+أكبر من صفر لجينا بـ P ε such that for every P
+
+234
+00:18:32,760 --> 00:18:38,220
+يحتوي الـ P ε أو .. وكل اللي هو S P و F
+
+235
+00:18:38,980 --> 00:18:43,700
+اللي هو corresponding to this partition بيكون S P
+
+236
+00:18:43,700 --> 00:18:49,000
+و F ناقص الـ integration من هنا لـ P للـ F أصغر من Y
+
+237
+00:18:49,000 --> 00:18:53,480
+وهذا في حال إن F is integrable هذا عنوان اللي
+
+238
+00:18:53,480 --> 00:18:57,220
+هو اللي هي النظرية اللي قبلها بشوية لإنه بتحتاجها
+
+239
+00:18:57,220 --> 00:19:03,130
+بعد شوية طيب شوف الآن إيش النظرية هذي بتقول خلّيت
+
+240
+00:19:03,130 --> 00:19:05,870
+أفضل about the closed interval A و B اللي هي I اللي
+
+241
+00:19:05,870 --> 00:19:09,110
+عند الـ R بـ A bounded function Suppose that there
+
+242
+00:19:09,110 --> 00:19:19,130
+exists a number A يحقق الخاصية التالية يحقق
+
+243
+00:19:19,130 --> 00:19:21,390
+الخاصية التالية
+
+244
+00:19:30,260 --> 00:19:34,660
+نفترض أن يوجد A بحيث إنه لكل ε أكبر من 0
+
+245
+00:19:34,660 --> 00:19:40,140
+بنلاقي partition بـ ε و F B يحتوي P ε 
+
+246
+00:19:40,140 --> 00:19:45,100
+and F S B is any Riemann sum for F corresponding to
+
+247
+00:19:45,100 --> 00:19:52,100
+P تئذن الـ S P و F ناقص A أصغر من مين؟ من ε
+
+248
+00:19:54,770 --> 00:20:02,070
+لو لجينا .. أنا افترض إن احنا بنلاقي الـ Number A
+
+249
+00:20:02,070 --> 00:20:07,190
+هذا معطى إن Number A إيش بيمتلك هذا Number A؟ إنه
+
+250
+00:20:07,190 --> 00:20:12,190
+لما يكون عندك لكل ε أكبر من صفر لجهة partition بـ ε
+
+251
+00:20:12,190 --> 00:20:15,290
+بحيث إنه لكل refinement بـ P يحتوي P ε
+
+252
+00:20:15,290 --> 00:20:19,870
+و S, P و F is any Riemann sum
+
+253
+00:20:22,380 --> 00:20:24,760
+يجب أن يكون الـ A أصغر من ε لـ S و P و F
+
+254
+00:20:24,760 --> 00:20:31,980
+ناقص من ε لـ S و P و F ناقص من ε لـ S
+
+255
+00:20:31,980 --> 00:20:32,420
+و P و F ناقص من ε لـ S و P و F ناقص
+
+256
+00:20:32,420 --> 00:20:32,460
+من ε لـ S و P و F ناقص من ε لـ S و P
+
+257
+00:20:32,460 --> 00:20:34,200
+و F ناقص من ε لـ S و P و F ناقص من
+
+258
+00:20:34,200 --> 00:20:37,640
+ε لـ S و P و F ناقص من ε لـ S و P
+
+259
+00:20:37,640 --> 00:20:42,860
+ولكل ε أكبر من 0 بلاقي P ε بحيث إنه لما الـ
+
+260
+00:20:42,860 --> 00:20:46,780
+P يحتوي الـ P ε ويكون اللي هو الـ S P والـ
+
+261
+00:20:46,780 --> 00:20:50,800
+F ناقص A أصغر من ε بقول then F أي شماله
+
+262
+00:20:50,800 --> 00:20:56,020
+must be integrable in I in the sense طبعاً في 716
+
+263
+00:20:56,020 --> 00:21:00,500
+والـ A هو من هذا الـ integration يعني بقول لنا لو
+
+264
+00:21:00,500 --> 00:21:05,360
+لجينا A بتحقق هذا الكلام هتطلع لكم الـ A يا جماعة
+
+265
+00:21:05,360 --> 00:21:10,070
+هذا هي الـ integration هي قيمة الـ integration الـ
+
+266
+00:21:10,070 --> 00:21:12,630
+integration in the sense of الـ definition اللي
+
+267
+00:21:12,630 --> 00:21:17,730
+حكينا عليه طيب شوف الآن الآن
+
+268
+00:21:17,730 --> 00:21:22,410
+بدي أعطيك شغل عامة وبعدها نخصصها على اللي بدنا إياه
+
+269
+00:21:22,410 --> 00:21:26,370
+الآن give an ε أكبر من صفر and P be any fixed
+
+270
+00:21:26,370 --> 00:21:31,250
+partition of I ماشي الحال الآن خد أي ε وخد P
+
+271
+00:21:31,250 --> 00:21:37,020
+أي شمله أي fixed partition then There exist S1
+
+272
+00:21:37,020 --> 00:21:41,800
+P و F و S2 P و F بحيث إن S U P و F ناقص S P و F
+
+273
+00:21:41,800 --> 00:21:46,800
+أصغر من مين؟ من ε و S2 ناقص الـ  أصغر من مين؟ من
+
+274
+00:21:46,800 --> 00:21:57,260
+ε شوف هذه خلينا نشوف كيف عملها هيّا أخذنا
+
+275
+00:21:57,260 --> 00:22:02,580
+أي ε في الدنيا وبأي partition الآن بقول لي
+
+276
+00:22:04,500 --> 00:22:11,460
+صار عندي S P و F صار عندي آسف الـ partition اللي هو P
+
+277
+00:22:11,460 --> 00:22:17,260
+موجود والإبسلون موجود بـ fixed partition مش partition
+
+278
+00:22:17,260 --> 00:22:21,320
+معين لأ بـ fixed partition الكلام ده بظبط عليه بقول
+
+279
+00:22:21,320 --> 00:22:32,410
+بقدر ألاقي Riemann sum S واحد مسمى P و F بحيث إنه S U
+
+280
+00:22:32,410 --> 00:22:44,070
+P و F ناقص S1 P و F يكون أصغر من مين؟ من Y المنطقي 
+
+281
+00:22:44,070 --> 00:22:49,980
+الكلام هذا الأستاذ أعطاني الـ Epsilon قالي اثبت
+
+282
+00:22:49,980 --> 00:22:54,980
+أنه بتلاقي S1 Remains sum بحيث أن الفرق بينه وبين 
+
+283
+00:22:54,980 --> 00:22:57,340
+الـ A  بر للـ B والـ F  الـ partition هذا partition معين
+
+284
+00:22:57,340 --> 00:23:01,680
+بحكي الـ partition بس fixed أنه أخدت أي
+
+285
+00:23:01,680 --> 00:23:07,900
+Epsilonأقدرت ألاقي S1 remains sum بحيث أن هذا نقص
+
+286
+00:23:07,900 --> 00:23:10,980
+هذا يكون أصغر من Epsilon طبعًا هذا الطبيعي هو أكبر
+
+287
+00:23:10,980 --> 00:23:13,760
+من هذا لكن الفرق بدي أخليه أصغر من Epsilon وأنا
+
+288
+00:23:13,760 --> 00:23:20,440
+بقدر أخليه الآن عندي الـ Mk بساوي اللي هو عبارة عن
+
+289
+00:23:20,440 --> 00:23:27,580
+الـ supremum للـ F of X such that X element XK ناقص
+
+290
+00:23:27,580 --> 00:23:33,490
+واحد و XK مظبوط؟ الآن هذا اللي هو الـ infimum ال
+
+291
+00:23:33,490 --> 00:23:37,010
+least upper bound الآن الـ least upper bound لو
+
+292
+00:23:37,010 --> 00:23:43,890
+شيلنا منه نقصنا منه أي عدد صغير كثير كثير وليكن
+
+293
+00:23:43,890 --> 00:23:49,850
+الـ y على مين على b ناقص a ببطل upper bound مدام
+
+294
+00:23:49,850 --> 00:23:55,510
+بطل upper bound إذا بقدر أناجي xik element الـ xk
+
+295
+00:23:55,510 --> 00:23:57,230
+ناقص واحد و xk
+
+296
+00:24:00,970 --> 00:24:08,050
+تكون مالها أكبر من مين من اللي هو اللي بطل upper bound
+
+297
+00:24:08,050 --> 00:24:13,600
+الآن هذا اللي سوّيته مع الـ Mk بقدر أسويه مع 
+
+298
+00:24:13,600 --> 00:24:16,280
+الـ M1 والـ M2 والـ M3 أي منهم كلهم
+
+299
+00:24:16,280 --> 00:24:21,500
+إذا صار الـ summation ك من عند واحد لعند n واضربه 
+
+300
+00:24:21,500 --> 00:24:25,940
+كمان في مين xk ناقص xk ناقص واحد ما فيش مانع لأن
+
+301
+00:24:25,940 --> 00:24:29,740
+أنا دموجة وأنا دموجة بتظهر زي ما هي xk ناقص xk
+
+302
+00:24:29,740 --> 00:24:32,720
+ناقص واحد وآخذ الـ summation هذا ك من عند واحد
+
+303
+00:24:32,720 --> 00:24:38,120
+لعند مين لعند n لجيتها الـ xik تبعت الـ S1 هذه
+
+304
+00:24:39,040 --> 00:24:47,580
+الآن هذا remain sum بسميه S1 بيعتمد على مين بيعتمد
+
+305
+00:24:47,580 --> 00:24:52,620
+على الـ exiled case اللي أنا لجيتها هذا أيش بيساوي
+
+306
+00:24:52,620 --> 00:24:59,480
+اللي هو summation Mk في Xk ناقص Xk ناقص واحد
+
+307
+00:24:59,480 --> 00:25:08,840
+ناقص الـ summationXY-XK
+
+308
+00:25:08,840 --> 00:25:10,840
+-1
+
+309
+00:25:17,430 --> 00:25:22,310
+هذا summation سامحوني على الضيق اللوح هذا بيصير الـ
+
+310
+00:25:22,310 --> 00:25:24,350
+summation على الأول زاد الـ summation على الثاني هي
+
+311
+00:25:24,350 --> 00:25:27,630
+الـ summation على الأول كم من عند واحد لعند n ناقص 
+
+312
+00:25:27,630 --> 00:25:29,910
+الـ summation على الثاني كم من عند واحد لعند n
+
+313
+00:25:29,910 --> 00:25:34,810
+آخذت الـ y ب وناقص a عن المشترك برا الـ
+
+314
+00:25:34,810 --> 00:25:37,830
+summation دلت الـ summation لهذا أصغر أو يساوي
+
+315
+00:25:37,830 --> 00:25:44,330
+بيقول لهذا مين هو أو أصغر من Remain sum أس بي و F و
+
+316
+00:25:44,330 --> 00:25:53,580
+سمّيناها أس واحدة هذا مين هو أكيد كلكم عارفينه U P و F و
+
+317
+00:25:53,580 --> 00:26:00,000
+هذا أيش هو ناقص أيش هذا؟ هذا أكيد y على b ناقص a في
+
+318
+00:26:00,000 --> 00:26:03,680
+هذا المقدار هذا المقدار عبارة عن x naught x واحد 
+
+319
+00:26:03,680 --> 00:26:08,440
+ناقص x naught زائد x اتنين ناقص x واحد زائد عرفته
+
+320
+00:26:08,440 --> 00:26:12,240
+إذا آخر واحد xn ناقص xn ناقص واحد يعني بيظل xn
+
+321
+00:26:12,240 --> 00:26:16,280
+ناقص x naught كله بكانسل بعض xn اللي هي الـ a الـ
+
+322
+00:26:16,280 --> 00:26:20,180
+b والـ x naught هي الـ a يعني هذا عبارة عن b ناقص 
+
+323
+00:26:20,180 --> 00:26:27,450
+a أصلاً من S1 بيقفيعني صار عندي الـ U ب و F و
+
+324
+00:26:27,450 --> 00:26:35,710
+جيب لي هذا هنا نقص S1 ب و Fأشماله أصغر من Epsilon
+
+325
+00:26:35,710 --> 00:26:43,150
+فعلًا أنا أجدت S1 من
+
+326
+00:26:43,150 --> 00:27:00,870
+Epsilon
+
+327
+00:27:00,980 --> 00:27:08,700
+إذا لجيت S1 و S2 بحيث تحقق هذه الخاصية انتبهوا 
+
+328
+00:27:08,700 --> 00:27:14,340
+الآن هذا الآن كل اللي حكيته هنا برهان للجزئية اللي
+
+329
+00:27:14,340 --> 00:27:20,770
+كاتبها أنا في البرهان ومش مضحك بشكلها الكامل طيب
+
+330
+00:27:20,770 --> 00:27:23,930
+فيكم تصلي على النبي اللهم صلي على سيدنا محمد نرجع 
+
+331
+00:27:23,930 --> 00:27:28,450
+نقول لكم أنه لجينا اللي هو الـ S1 والـ S2 
+
+332
+00:27:28,450 --> 00:27:31,870
+اللي بيحققن هذا طبعًا الـ P كان أيش ماله any fixed
+
+333
+00:27:31,870 --> 00:27:37,410
+partition الآن معطينا
+
+334
+00:27:37,410 --> 00:27:43,050
+هنا أنه هذا معطى هذا معطى ديروا بالكم أنه there
+
+335
+00:27:43,050 --> 00:27:46,970
+exists P Epsilon بحيث أن P بتحتوي P Epsilon هذا
+
+336
+00:27:46,970 --> 00:27:52,630
+يتحقق الآن اللي بيتحقق على الـ P اللي هام هيتحقق 
+
+337
+00:27:52,630 --> 00:27:57,010
+على الـ P Epsilon اللي هام ماشي الحال إذا الآن
+
+338
+00:27:57,010 --> 00:28:01,930
+الـ U P Epsilon والـ F ناقص الـ L P والـ F اللي هو
+
+339
+00:28:01,930 --> 00:28:10,460
+بيساو U U P والـ F ناقص L P والـ F ماشي أيش هذا؟ أخذت الـ
+
+340
+00:28:10,460 --> 00:28:13,740
+P Epsilon الـ P اللي هنا هي الـ P Epsilon عشان أقول 
+
+341
+00:28:13,740 --> 00:28:17,440
+أنه أنا اللي حققته على اللي هي الـ P فده حققته على 
+
+342
+00:28:17,440 --> 00:28:20,460
+الـ P Epsilon أنه هذا كان unfixed partition أصغر أو
+
+343
+00:28:20,460 --> 00:28:25,700
+يساوي بالـ Triangle inequality UBF ناقص SBF زي S1BF
+
+344
+00:28:25,700 --> 00:28:33,440
+ناقص A زي A ناقص S2BF ماذا فعلت؟ بالـ Triangle
+
+345
+00:28:33,440 --> 00:28:37,380
+Inequality أضفت الـ S1 وطرحت الـ S1 وضفت
+
+346
+00:28:37,380 --> 00:28:41,260
+الـ A وطرحت الـ A وضفت الـ S2 وطرحت الـ S 
+
+347
+00:28:41,260 --> 00:28:44,480
+2 وعملت الـ Triangle Inequality وطبقت هذه واحدة
+
+348
+00:28:44,480 --> 00:28:48,260
+كامتين تلاتة أربعة صار عندي أزرع يساوي هذا زائد 
+
+349
+00:28:48,260 --> 00:28:57,300
+هذا زائد هذا زائد هذا ماشي الحل صار
+
+350
+00:28:57,300 --> 00:28:58,480
+عندي يا جماعة الآن
+
+351
+00:29:12,650 --> 00:29:17,970
+صار عندي اللي هو الآن طبعًا الـ a أيش هي الـ a اللي
+
+352
+00:29:17,970 --> 00:29:20,310
+في النظرية دي بقلكم a is the number in the 
+
+353
+00:29:20,310 --> 00:29:24,270
+hypothesis of theorem then by the hypothesis of
+
+354
+00:29:24,270 --> 00:29:31,650
+theorem and star الآن من اللي هو المعطى بيعطينا أن 
+
+355
+00:29:31,650 --> 00:29:35,630
+الـ S1 نقص الـ a أصغر من Epsilon والـ S2 
+
+356
+00:29:35,630 --> 00:29:39,430
+نقص الـ a أصغر من Epsilon لأن هذا صحيح اللي فوق 
+
+357
+00:29:39,430 --> 00:29:39,850
+لأن
+
+358
+00:29:47,480 --> 00:29:53,200
+أذكركم كمان مرة بالمعطى
+
+359
+00:29:53,200 --> 00:30:00,540
+أن هناك مجموعة P Epsilon هي اللي بتشتغل في S 
+
+360
+00:30:00,540 --> 00:30:05,040
+ب و F is any remansum corresponding لأف هيكون
+
+361
+00:30:05,040 --> 00:30:07,860
+الفرق بين هذا وهذا أصغر من Epsilon من ضمن الـ S
+
+362
+00:30:07,860 --> 00:30:11,740
+1 والـ S2 اللي جاتني قبل شوية إذا صار عندي 
+
+363
+00:30:11,740 --> 00:30:20,530
+الكل اللي بيشتغلوا مشروع بيصير اللي هو الـ UB نقص
+
+364
+00:30:20,530 --> 00:30:25,730
+الـ S1 أصغر من Epsilon وهذا أصغر من الـ Epsilon معطى
+
+365
+00:30:25,730 --> 00:30:29,230
+وهذا أصغر من الـ Epsilon معطى وهذا وهذا أصغر كل
+
+366
+00:30:29,230 --> 00:30:33,370
+واحد من Epsilon من اللي أتبته هنا قبل بشوية إذا صرت 
+
+367
+00:30:33,370 --> 00:30:41,070
+اللي هي كلها أصغر من 4 Epsilon ماشي الحال Epsilon was
+
+368
+00:30:41,070 --> 00:30:48,930
+arbitrary then by 7 1 8 F is integrable F is
+
+369
+00:30:48,930 --> 00:30:53,690
+integrable لأنه وجدت بـ Epsilon لأن U نقص لأخر من
+
+370
+00:30:53,690 --> 00:30:57,430
+4 Epsilon بـ Epsilon وبعض arbitrarily إذا بيصير
+
+371
+00:30:57,430 --> 00:31:01,910
+عندي صحيح واحد متضايق من الـ 4 Epsilon في اللي
+
+372
+00:31:01,910 --> 00:31:04,430
+فوق خد Epsilon على 4 Epsilon على 4 والنظرية 
+
+373
+00:31:04,430 --> 00:31:08,730
+الأولى والمعطى برضه بتاخذوا Epsilon على 4 
+
+374
+00:31:08,730 --> 00:31:19,300
+بطريقة حسابية معه طيب إذا صار عندي لجينا الآن then 
+
+375
+00:31:19,300 --> 00:31:22,480
+by theorem 7 1 8 F is integrable and for every
+
+376
+00:31:22,480 --> 00:31:25,360
+Epsilon أكبر من 0 there exists B Epsilon of I such
+
+377
+00:31:25,360 --> 00:31:28,800
+that FB بتحتوي B Epsilon and B is a partition of I
+
+378
+00:31:28,800 --> 00:31:36,380
+then S of B و F مقصودها أصغر من 100 من Epsilon أيش
+
+379
+00:31:36,380 --> 00:31:39,840
+هذا؟ حنا أثبتنا أنه integrable مدام Integrable باللي
+
+380
+00:31:39,840 --> 00:31:44,100
+كاتبينه هنا واللي كاتبينه هيكون الفرق بين for every 
+
+381
+00:31:44,100 --> 00:31:47,320
+ε there exists B Epsilon والـ B بتحتوي B
+
+382
+00:31:47,320 --> 00:31:50,040
+Epsilon واحد يقول طب ما هو خايفين الـ B Epsilon
+
+383
+00:31:50,040 --> 00:31:53,260
+اللي لاجيناها في الأول المعطف في النظرية غير الـ
+
+384
+00:31:53,260 --> 00:31:57,260
+B Epsilon هذه مش مشكلة الـ B Epsilon فرطنة تبعة
+
+385
+00:31:57,260 --> 00:32:01,560
+النظرية B برايم of Epsilonوهذه اللي وجدناها من الـ
+
+386
+00:32:01,560 --> 00:32:05,660
+Integrability للـ F اللي أثبتناها نسميها B 
+
+387
+00:32:05,660 --> 00:32:09,480
+Epsilon دابل برايم خد الـ B Epsilon اللي بتحكي
+
+388
+00:32:09,480 --> 00:32:14,520
+عليها الآن عشان تنفع للجهتين خدها بساوي B Epsilon
+
+389
+00:32:14,520 --> 00:32:20,060
+برايم اتحاد B Epsilon دابل برايم بيصير الآن هذه اللي 
+
+390
+00:32:20,060 --> 00:32:26,280
+هي تنفع تنفع للمعطيات الأولى والمعطيات الثانية
+
+391
+00:32:26,280 --> 00:32:29,320
+لأنها بيصير refinement للأول و refinement لمن؟
+
+392
+00:32:29,320 --> 00:32:35,980
+للثاني إذا فش فيه مشكلة إذا الآن then by hypothesis 
+
+393
+00:32:35,980 --> 00:32:40,360
+of theorem أخذنا هذا أصغر من 4 Epsilon إذا سبب
+
+394
+00:32:40,360 --> 00:32:43,840
+له هذا أن هو F is integrable مدام F is integrable 
+
+395
+00:32:43,840 --> 00:32:48,620
+إذا بالنظرية بنلاقي B Epsilon بحيث أنه لكل B 
+
+396
+00:32:48,620 --> 00:32:53,000
+بيحتوي B Epsilon بيكون هذا ناقص هذا أصغر من مين من 
+
+397
+00:32:53,000 --> 00:32:58,890
+Epsilon هذا أصبح أصغر من Epsilon بس الآن أثبتنا عند
+
+398
+00:32:58,890 --> 00:33:02,990
+الـ F ب و F ناقص اللي أصغر من Epsilon من النظرية و
+
+399
+00:33:02,990 --> 00:33:06,570
+واحد يقول لي تبعت الـ B هادي بتختلف عن الـ B هادي
+
+400
+00:33:06,570 --> 00:33:10,450
+قلت لك علّجتها الـ B هادي والـ B هادي بأخذ الـ B 
+
+401
+00:33:10,450 --> 00:33:13,730
+Epsilon لتبعت النظرية والـ B Epsilon تبعت اللي هو
+
+402
+00:33:13,730 --> 00:33:17,690
+الـ integrability وبأخدهن اتحادهن بيكون اللي هو الـ
+
+403
+00:33:17,690 --> 00:33:20,990
+B Epsilon اللي لجيتها هنا اللي بدي أستخدم إيه لها
+
+404
+00:33:20,990 --> 00:33:24,770
+الجهتين وأي refinement لها بيه لـ B Epsilon و
+
+405
+00:33:24,770 --> 00:33:29,270
+لجديدة بيطلع هذا صح وهذا صح اتنين مع بعض دلوقتي
+
+406
+00:33:29,270 --> 00:33:35,030
+بأحجل اللي استخدمهم وأقول إذا الـ integration للـ F
+
+407
+00:33:35,030 --> 00:33:37,830
+من A لـ B نقص A أصغر ويساوي الـ integration للـ F
+
+408
+00:33:37,830 --> 00:33:41,990
+نقص S زاد S نقص A اللي هو ضيف الـ term و
+
+409
+00:33:41,990 --> 00:33:46,750
+طرحت الـ term هذا هي أصغر من Epsilon وهذا أصغر من
+
+410
+00:33:46,750 --> 00:33:50,210
+Epsilon إذا صار هذا أصغر من 2 Epsilon صار عندي 
+
+411
+00:33:50,210 --> 00:33:53,910
+فيه العدد هذا بين اللي هو 2 Epsilon وأكبر أو
+
+412
+00:33:53,910 --> 00:33:56,870
+ساوي صفر وEpsilon arbitrary إذا هذا المقدار لازم
+
+413
+00:33:56,870 --> 00:34:00,750
+يساوي صفر إذا الـ integration بساوي مين بساوي ليه 
+
+414
+00:34:00,750 --> 00:34:03,510
+وهو المطلوب طيب
+
+415
+00:34:10,110 --> 00:34:17,630
+نجي للي هو الـ definition 7 4 4 الـ
+
+416
+00:34:17,630 --> 00:34:23,270
+definition بسيط بده يعرف حاجة اسمها مش أو Norm هو
+
+417
+00:34:23,270 --> 00:34:27,330
+أنا بسميها مش عادة الناس بتسميها Norm أيش الـ .. الـ
+
+418
+00:34:27,330 --> 00:34:31,550
+.. الـ مش اللي بده يعرفه؟ بقول لو كان عندك 
+
+419
+00:34:31,550 --> 00:34:38,910
+partition B بساوي X0 و X1 لعندي XN الآن كل sub
+
+420
+00:34:38,910 --> 00:34:46,970
+interval لها طول الـ Norm لـ B أو مش لـ B هو 
+
+421
+00:34:46,970 --> 00:34:51,920
+عبارة عن الـ maximum أو الـ Supremum. Maximum لأن الـ
+
+422
+00:34:51,920 --> 00:34:53,860
+Supremum حاسب Maximum لإنه الـ finite دول
+
+423
+00:34:53,860 --> 00:34:59,480
+الماكسيمم لـ X1 ناقص X0 و X2 ناقص X1 لأطوال
+
+424
+00:34:59,480 --> 00:35:03,140
+الفترات يعني sub interval لعند الـ XN ناقص XN ناقص 
+
+425
+00:35:03,140 --> 00:35:07,880
+1 الماكسيمم لهن هدول أطوال الفترات هو اللي بنسميه
+
+426
+00:35:07,880 --> 00:35:14,000
+مين النورم للـ B هو النورم للـ B الآن يعني يعني لو
+
+427
+00:35:14,000 --> 00:35:20,670
+كان عندك لو كان عندك هي عند الفترة من صفر لعين
+
+428
+00:35:20,670 --> 00:35:31,410
+ثلاثة مثلا هاي عند B بتساوي صفر، نص، واحد، اثنين
+
+429
+00:35:31,410 --> 00:35:37,970
+ثلاثة مثلا، بكون الـ normal B إيش هيساوي؟ إيش الـ
+
+430
+00:35:37,970 --> 00:35:41,510
+normal B أكيد هتقولوا كلكم ثلاثة ناقص اثنين واحد
+
+431
+00:35:41,510 --> 00:35:44,710
+اثنين ناقص واحد واحد، واحد ناقص نص نص، واحد. إذا إيش
+
+432
+00:35:44,710 --> 00:35:49,110
+هيساوي واحد، أكبر، أكبر طول sub interval واحد. لو جينا 
+
+433
+00:35:49,110 --> 00:36:00,350
+أخدنا الـ Q مثلا بيساوي اللي هو صفر، نص، واحد، واحد و
+
+434
+00:36:00,350 --> 00:36:08,890
+ثلث، اثنين، اثنين ونص، وثلاثة وقلنا لكم اوجد الـ Q
+
+435
+00:36:09,620 --> 00:36:13,420
+أكيد كلكم حد هيقول الـ Q شمالها اللي هي بين الواحد و
+
+436
+00:36:13,420 --> 00:36:17,420
+ثلث والاثنين هي أكبر، أكبر مسافة اللي هي عبارة عن
+
+437
+00:36:17,420 --> 00:36:23,060
+إيه؟ ثلثين. لاحظوا أن الـ B مجموعة جزئية من مين؟ من
+
+438
+00:36:23,060 --> 00:36:33,810
+الـ Q لما ... لما الآن الـ Q كبرت، normها هيكون أصغر
+
+439
+00:36:33,810 --> 00:36:37,590
+أو يساوي norm من الـ B طبيعي لأنه دخلت نقطة جديدة
+
+440
+00:36:37,590 --> 00:36:43,690
+ممكن تزغر المسافة لكن مش ممكن تزيدها طيب وهذه اللي
+
+441
+00:36:43,690 --> 00:36:47,810
+هي بعض الملاحظات اللي هنا على اللي هي الـ norm أو
+
+442
+00:36:47,810 --> 00:36:55,800
+الـ mesh اللي الآن، بعض اللي هو الملاحظات اللي هو
+
+443
+00:36:55,800 --> 00:37:00,780
+different partition of I can have the same مش بقول
+
+444
+00:37:00,780 --> 00:37:03,280
+يعني ممكن different partition للـ ... للـ ... للـ ...
+
+445
+00:37:03,280 --> 00:37:06,140
+للـ interval اللي ده same مش آه بقدر هاد أنا أجيبلك
+
+446
+00:37:06,140 --> 00:37:12,200
+كمان واحد زي هدول، خد كمان B' بيساوي صفر، و نص
+
+447
+00:37:12,200 --> 00:37:20,030
+و واحد و اثنين و اثنين و نص و ثلاثة، هذا الـ B'
+
+448
+00:37:20,270 --> 00:37:25,170
+يختلف عن الـ B لكن نورمه التاني إيش بيساوي واحد
+
+449
+00:37:25,170 --> 00:37:30,530
+يعني الـ different partitions ممكن يكون لها نفس
+
+450
+00:37:30,530 --> 00:37:34,730
+نورم وهاي مثال وكتير فيه زي ذلك، لأن لو كانت B
+
+451
+00:37:34,730 --> 00:37:39,730
+subset من Q، norm لـ Q أظهر يساوي norm لمين؟ لـ B و
+
+452
+00:37:39,730 --> 00:37:43,720
+اتبعت السهل هذا، خد الـ B subset إذا هيكون عنده اللي
+
+453
+00:37:43,720 --> 00:37:47,080
+هو عدد النقاط اللي في Q أكتر من عدد النقاط اللي في
+
+454
+00:37:47,080 --> 00:37:53,780
+B هيكون الـ maximum على الأولى اللي هو أكبر أو يساوي
+
+455
+00:37:53,780 --> 00:37:56,720
+الـ maximum على مين؟ على الثاني لإنه اللي صار فيها
+
+456
+00:37:56,720 --> 00:38:02,070
+زيادات، صار فيه إمكانية إنها تقصر الفترات طيب لكن لو 
+
+457
+00:38:02,070 --> 00:38:05,330
+كان الـ normal الـ Q أصغر شوي، الـ normal الـ B مش شرط
+
+458
+00:38:05,330 --> 00:38:10,110
+أن يكون B subset من مين؟ من الـ Q أو كتير بتلاقي
+
+459
+00:38:10,110 --> 00:38:16,910
+أمثلة زي هي الـ normal
+
+460
+00:38:16,910 --> 00:38:25,160
+B هذا إيش بيساوي؟ normal B بيساوي واحد. الآن عندي ...
+
+461
+00:38:25,160 --> 00:38:32,320
+مش شرط ... يعني هديلك اللي هو Normal Q أصغر أو يساوي
+
+462
+00:38:32,320 --> 00:38:40,040
+Normal B، لكن الـ B اللي هو ليس شرطا أنها تكون
+
+463
+00:38:40,040 --> 00:38:47,500
+subset من مين؟ من إيش؟ من الـ Q، Normal B واحد خد
+
+464
+00:38:47,500 --> 00:38:48,060
+الـ Q 
+
+465
+00:38:53,000 --> 00:39:03,100
+بيساو اللي هو صفر، واحد، اثنين، اثنين ونص، و
+
+466
+00:39:03,100 --> 00:39:07,180
+ثلاثة، نورمال
+
+467
+00:39:07,180 --> 00:39:12,100
+Q بديه ال
+
+468
+00:39:12,100 --> 00:39:19,920
+gate
+
+469
+00:39:19,920 --> 00:39:22,280
+واحد، و واحد ونص
+
+470
+00:39:25,990 --> 00:39:34,190
+وهي نص كمان، صفر، ونص، Normal Q بيساوي نص مظبوط
+
+471
+00:39:34,190 --> 00:39:45,650
+Normal Q بيساوي نص لكن الـ B، الـ B خلي هذا ثلث ماشي
+
+472
+00:39:45,650 --> 00:39:51,220
+خلي هذا ثلث، صارت الـ B مش subset من مين؟ من الـ Q
+
+473
+00:39:51,220 --> 00:39:54,420
+ممكن تلاقي أفضل كتير هذه الـ B أكيد مش subset من
+
+474
+00:39:54,420 --> 00:40:00,460
+الـ Q، Normal B بيبقى واحد صح؟ Normal B واحد و
+
+475
+00:40:00,460 --> 00:40:06,160
+Normal Q إيش بيساوي نص؟ لأن الفرق بينهم أنصاف هذه
+
+476
+00:40:06,160 --> 00:40:12,340
+عندك Normal Q أصغر أو يساوي Normal B لأن هذا نص
+
+477
+00:40:12,340 --> 00:40:14,420
+وهذا واحد، but
+
+478
+00:40:17,620 --> 00:40:22,380
+واضح الـ B هي صفر، و ثلث، و واحد، و اثنين، و ثلاثة، ليس 
+
+479
+00:40:22,380 --> 00:40:26,100
+subset من الـ Q، صفر، ونص، و واحد، ونص، و ... و ... و
+
+480
+00:40:26,100 --> 00:40:27,400
+... و ... و ... و ... و ... و ... و ... و ... و ... و ... و
+
+481
+00:40:27,400 --> 00:40:28,940
+... و ... و ... و ... و ... و ... و ... و ... و ... و ... و
+
+482
+00:40:28,940 --> 00:40:29,640
+... و ... و ... و ... و ... و ... و ... و ... و ... و ... و
+
+483
+00:40:29,640 --> 00:40:30,360
+... و ... و ... و ... و ... و ... و ... و ... و ... و ... و
+
+484
+00:40:30,360 --> 00:40:30,380
+... و ... و ... و ... و ... و ... و ... و ... و ... و ... و
+
+485
+00:40:30,380 --> 00:40:34,960
+... و ... و ... و ... و ... و ... و ... و ... و ... و ... و
+
+486
+00:40:34,960 --> 00:40:36,340
+... و ... و ... و ... و ... و ... و ... 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/QjdD_6J2asI_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/QjdD_6J2asI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..47ba7f5e52432c24d8660d33bdf26e00029c3344
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/QjdD_6J2asI_raw.srt
@@ -0,0 +1,1960 @@
+1
+00:00:04,960 --> 00:00:12,580
+بسم الله الرحمن الرحيم هذه المحاضرة رقم 16 في مساق
+
+2
+00:00:12,580 --> 00:00:18,080
+تحليل حقيقي 2 أو تحليل رياضي 2 لطلبة وطالبات كلية
+
+3
+00:00:18,080 --> 00:00:22,820
+العلوم بالجامعة الإسلامية بغزةكنا سميينها في
+
+4
+00:00:22,820 --> 00:00:29,160
+المحاضرة 15 إنها جزئين المحاضرة الجزء الأول ذكرناه
+
+5
+00:00:29,160 --> 00:00:31,820
+في المحاضرة 15 وقلنا الجزء الثاني هنذكره في
+
+6
+00:00:31,820 --> 00:00:35,780
+المحاضرة اللي بعدها كجزء ثاني من 15 بس الآن لطول
+
+7
+00:00:35,780 --> 00:00:40,440
+فترة اللي هي المحاضرة السابقةهنسمي هذا الجزء الآن
+
+8
+00:00:40,440 --> 00:00:43,060
+اللي هو كان اسمه الجزء الثاني المحاضرة 15 لأ بدي
+
+9
+00:00:43,060 --> 00:00:48,300
+أسميه هو المحاضرة رقم 16 وهو اللي هو بداية سيكشن
+
+10
+00:00:48,300 --> 00:00:52,020
+جديد اللي هو سبعة أربعة اللي هو the integration as
+
+11
+00:00:52,020 --> 00:00:56,260
+a limit اللي هو بدنا نصل ال integration عن طريق
+
+12
+00:00:56,260 --> 00:01:01,880
+اللي هو the limit of Riemann sumبس شغلة سريعة عشان
+
+13
+00:01:01,880 --> 00:01:05,820
+نربط بالسابق باللاحق بالحاضر عشان نفهم إيش اللي
+
+14
+00:01:05,820 --> 00:01:10,780
+بنحكي فيه إحنا إذا بتتظهرتتذكر واخدنا على الفترة A
+
+15
+00:01:10,780 --> 00:01:17,200
+وB وعملنا لها تجزئة P بساوية X Note X واحد لعند ال
+
+16
+00:01:17,200 --> 00:01:25,000
+XN وعرفنا اللي هو ال Upper sum اللي هو Upper اللي
+
+17
+00:01:25,000 --> 00:01:31,900
+هي L وP L لو function عندي F فعندي F of X على
+
+18
+00:01:31,900 --> 00:01:39,160
+الفترة من A لعند B اللي هو ال UpperF of B وقلنا هو
+
+19
+00:01:39,160 --> 00:01:44,780
+عبارة عن summation لل M K في X K minus X K minus
+
+20
+00:01:44,780 --> 00:01:51,060
+واحد زي ما انتم الذاكرين K من عند واحد لعند N هذا
+
+21
+00:01:51,060 --> 00:01:54,900
+اللي هو اللي سمناه ال other sum ال M K طبعا هي ال
+
+22
+00:01:54,900 --> 00:01:57,600
+.. زي ما انتم عارفين ال supremum على الفترة .. ال
+
+23
+00:01:57,600 --> 00:02:01,040
+supremum لدال ال F ال supremum لدال ال F على
+
+24
+00:02:01,040 --> 00:02:06,340
+الفترة اللي أماميوعندي ال L F of P أو P و F زي ما
+
+25
+00:02:06,340 --> 00:02:10,300
+احنا بنكتبها عبارة عن summation ال M K في X K
+
+26
+00:02:10,300 --> 00:02:14,680
+minus X K minus واحد K من عند واحد لعندنا وقلنا لو
+
+27
+00:02:14,680 --> 00:02:19,380
+اتينا ال other sum أخدناله اللي هو ال infimum ال
+
+28
+00:02:19,380 --> 00:02:24,370
+other sum وقلنا أخدناله ال infimumبنسميه U of F
+
+29
+00:02:24,370 --> 00:02:29,070
+اللي هو عبارة عن الـ infimum لـ U of F و B such
+
+30
+00:02:29,070 --> 00:02:32,370
+that B element in the set of all partition B of I
+
+31
+00:02:32,370 --> 00:02:36,630
+و أخدنا ال L of F و قلنا هو عبارة عن ال supremum
+
+32
+00:02:36,630 --> 00:02:41,300
+لـ L of F و Bhighest B element in the set of all
+
+33
+00:02:41,300 --> 00:02:46,780
+partitions B of I قلنا إن F هتكون integrable إذا
+
+34
+00:02:46,780 --> 00:02:50,460
+اللي هو ال lower integral بساومين ال upper
+
+35
+00:02:50,460 --> 00:02:55,580
+integral هذا المدخل اللي دخلنا فيه لإثبات أو
+
+36
+00:02:55,580 --> 00:03:00,220
+لتعريف إن F is integrable مدخل اللي هو ال upper
+
+37
+00:03:00,220 --> 00:03:03,650
+sum والlower sumأو الـ Upper Integral والـ Lower
+
+38
+00:03:03,650 --> 00:03:07,470
+Integral يوم ما يتساون بنسميه الـ Integral اللي هو
+
+39
+00:03:07,470 --> 00:03:10,670
+عبارة عن قيمة الـ Integration للـ F على الفترة A
+
+40
+00:03:10,670 --> 00:03:17,640
+وBالان ايش اللي هنسويه اللي هو الجزء الثاني من
+
+41
+00:03:17,640 --> 00:03:21,300
+المحاضرة
+
+42
+00:03:21,300 --> 00:03:24,300
+او اللي احنا سمينا المحاضرة 16 اللي هو في ال
+
+43
+00:03:24,300 --> 00:03:29,840
+section 7-4 هندخل لل integration بداخلة أخرى عن
+
+44
+00:03:29,840 --> 00:03:35,280
+طريق حاجة اسمها ال remansum ومن ثم نقول نثبت في
+
+45
+00:03:35,280 --> 00:03:40,000
+النهاية انه limit ال remansum لما يكون موجودبكون
+
+46
+00:03:40,000 --> 00:03:45,480
+هو الـ Integration وهذا مكافئ أو يحدث if and only
+
+47
+00:03:45,480 --> 00:03:50,580
+if إذا حدثت اللي هو معنى التكامل بصيغة ال Upper
+
+48
+00:03:50,580 --> 00:03:54,420
+Sum والLower Sum يعني الآن .. الآن في عندنا مدخلين
+
+49
+00:03:54,420 --> 00:03:57,660
+للدخول للتكامل إما عن طريق ال Upper Sum والLower
+
+50
+00:03:57,660 --> 00:04:00,560
+Sum أو ال Upper Integral والLower Integral أو عن
+
+51
+00:04:00,560 --> 00:04:04,200
+طريق اللي هو ال Remain Sum أو اللي هو ال limit
+
+52
+00:04:04,200 --> 00:04:09,000
+للRemain Sumوالتنين لما نكون كل واحد ذاك ال ..
+
+53
+00:04:09,000 --> 00:04:12,740
+الملهمته موجود و هذا ال upper بساوي ال lower بكون
+
+54
+00:04:12,740 --> 00:04:19,500
+ال R equivalent إيه الآن؟ إيش ال .. ال roman sum؟
+
+55
+00:04:19,500 --> 00:04:24,200
+احنا برضه التجزية جاءت تجزية هاي P بساوي X note و
+
+56
+00:04:24,200 --> 00:04:29,280
+X واحد لعند ال XN هاي التجزية هاي X note و هاي X
+
+57
+00:04:29,280 --> 00:04:32,700
+واحد وهي الفترة الموضاجية XK minus واحد لعند ال XK
+
+58
+00:04:33,370 --> 00:04:40,570
+الان الـ Riemann Sum بنختار في الـ Intervals نقطة
+
+59
+00:04:40,570 --> 00:04:45,830
+عشوائية لا تقول لي لا أكبر واحدة ولا أصغر واحدة
+
+60
+00:04:45,830 --> 00:04:49,150
+ولا كذا لأ نقطة عشوائية وبنسميها مثلا لو قلت لك
+
+61
+00:04:49,150 --> 00:04:54,970
+الهن بسميها XIK الان XIK هذه صارت element في الـ
+
+62
+00:04:54,970 --> 00:05:02,000
+XK-1 والـ xk الآن بدي بضرب ال x اللي اللي هي طول
+
+63
+00:05:02,000 --> 00:05:05,140
+الفترة زي ما ضربتها زي ما وجدت ال sum اللي هو ال
+
+64
+00:05:05,140 --> 00:05:09,020
+upper sum هنا بوجد هنا بس بستبدل ال mk و ال mk
+
+65
+00:05:09,020 --> 00:05:13,380
+small و upper بستبدلها بقيمة ال function عند هذه
+
+66
+00:05:13,380 --> 00:05:18,270
+النقطة العشوائية اللي اخترتهااللي هي بيسميها xik
+
+67
+00:05:18,270 --> 00:05:24,190
+فبصير xk minus xk minus 1 في ال F عند xik و باخده
+
+68
+00:05:24,190 --> 00:05:28,290
+ال summation k من عند 1 لعند n و هذا اللي بيسميه
+
+69
+00:05:28,290 --> 00:05:36,030
+الرمان صم S of B أو مين و F S of B أو F و هذا اللي
+
+70
+00:05:36,030 --> 00:05:43,470
+بيسميه الرمان صم في النهاية هنصلكم أنه لو كان ال
+
+71
+00:05:43,470 --> 00:05:49,710
+limitللـ S, P و F as الـ N goes to infinity يعني
+
+72
+00:05:49,710 --> 00:05:53,630
+الـ N اللي هي زغرنا الفترة صارتها الجدّة و زغرنا
+
+73
+00:05:53,630 --> 00:05:57,090
+صارتها الفترة .. لما تكون N تروح إلى نهاية معناته
+
+74
+00:05:57,090 --> 00:05:59,590
+أن صارت اللي .. اللي هي و كأنه الفترات عبارة عن
+
+75
+00:05:59,590 --> 00:06:05,130
+خطوط جنب بعض هذه الخطوط بتنطبق الـ XK و XK-1 و XIK
+
+76
+00:06:05,130 --> 00:06:10,950
+على بعض و كأنه بتسير كل خط جنب خط جنب خط إلى قيمة
+
+77
+00:06:10,950 --> 00:06:14,640
+اللي هو مجموع هذه الخطوط زي ما حكينا قبل هيكاللي
+
+78
+00:06:14,640 --> 00:06:18,820
+بتعمل المساحة تحت المنحنى في حالة الموجب ومن ثم هي
+
+79
+00:06:18,820 --> 00:06:21,740
+هتعمل لي قيمة ال integration يعني لما يكون ال
+
+80
+00:06:21,740 --> 00:06:24,420
+limit لـRiemann sum as N goes to infinity exist
+
+81
+00:06:24,420 --> 00:06:29,380
+وسوّت لي رقم اسمه إيه هذا الرقم هو عبارة عن ال
+
+82
+00:06:29,380 --> 00:06:33,900
+integration إيه لـ BF of X DX على هذه الفترة هذا
+
+83
+00:06:33,900 --> 00:06:38,400
+اللي في النهاية بدنا نصل إليه أو نوصلكم إنه في
+
+84
+00:06:38,400 --> 00:06:42,680
+حالة وجود هذا ال limit هيكون هو ال integration
+
+85
+00:06:42,680 --> 00:06:47,040
+اللي بمفهوم ال upper sum والlower sum يعني
+
+86
+00:06:47,040 --> 00:06:53,160
+الدخلتين بقد إلى نفس القيمة أو إلى نفس النتيجة
+
+87
+00:06:54,950 --> 00:06:59,130
+يعني في بعض الكتب بتعرفلك أصلا اللي هو ال
+
+88
+00:06:59,130 --> 00:07:04,430
+integration as a limit of remansum في كتب و هذا
+
+89
+00:07:04,430 --> 00:07:09,650
+غالبا في ال calculus بيشتغلوه و في كتب بتعرفه عن
+
+90
+00:07:09,650 --> 00:07:12,230
+طريق ال other sum و لا other sum في ال calculus
+
+91
+00:07:12,230 --> 00:07:15,930
+لأنه ملزمش ل Supremum و ل Infimum لإن الطالب مفهم
+
+92
+00:07:15,930 --> 00:07:20,370
+ال Supremum ومفهم ال Infimum عنده اللي هو ناضج
+
+93
+00:07:24,160 --> 00:07:29,980
+بعد هذه المقدمة عن الموضوع خلّينا ندخل إلىه بشكل
+
+94
+00:07:29,980 --> 00:07:34,700
+تفصيلي The integration as a limit لت I اللي هي ال
+
+95
+00:07:34,700 --> 00:07:36,820
+interval اللي انا بده اشتغل عليها و ال function
+
+96
+00:07:36,820 --> 00:07:40,260
+أفنان I لR عبارة عن bounded function و خدنا ال B
+
+97
+00:07:40,260 --> 00:07:44,440
+هو ال partition اللي أخدناه و زي ما قلنا إذا أخدنا
+
+98
+00:07:44,440 --> 00:07:50,470
+XI 1 و XI 2 و XI N عبارة عن arbitrary numbersاللي
+
+99
+00:07:50,470 --> 00:07:53,330
+هو الـ x i 1 في ال .. في ال .. في ال interval x
+
+100
+00:07:53,330 --> 00:07:57,270
+not x 1 x i 2 في ال interval اللي .. اللي بعدها
+
+101
+00:07:57,270 --> 00:08:00,810
+ايه اخره يعني ال x i k هي في ال .. الفترة النموذج
+
+102
+00:08:00,810 --> 00:08:06,130
+الذادية x k minus 1 x k ل k من 1 لعند مين لعند ان
+
+103
+00:08:06,130 --> 00:08:08,570
+ال sum اللي قولنا عنه اللي هو عبارة عن ال
+
+104
+00:08:08,570 --> 00:08:12,530
+summation لل F of x i k مضروب في x k ناقص x k
+
+105
+00:08:12,530 --> 00:08:17,110
+minus 1 هذا ال summation من 1 لعند ان هم هو برمزه
+
+106
+00:08:17,110 --> 00:08:21,030
+للرمز SPUF اللي هو بسميهاللي هو عبارة عن the
+
+107
+00:08:21,030 --> 00:08:25,810
+remand sum الريمان صم الريمان صم الريمان صم
+
+108
+00:08:25,810 --> 00:08:30,150
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+109
+00:08:30,150 --> 00:08:31,170
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+110
+00:08:31,170 --> 00:08:32,670
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+111
+00:08:32,670 --> 00:08:33,050
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+112
+00:08:33,050 --> 00:08:33,610
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+113
+00:08:33,610 --> 00:08:34,330
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+114
+00:08:34,330 --> 00:08:36,290
+الريمان صم الريمان صم الريمان صم الريمان صم
+
+115
+00:08:36,290 --> 00:08:43,690
+الريمان صم الريمان صم الريمان صم الريمان صم الري
+
+116
+00:08:43,710 --> 00:08:48,550
+لأن الـ F of XI K اللي هي النقطة العشوائية هذه
+
+117
+00:08:48,550 --> 00:08:53,190
+أكيد أصغر أو يساوي الـ inf mum على كل النقاط اللي
+
+118
+00:08:53,190 --> 00:08:57,710
+في ال sub interval هذه و أكبر أو يساوي و أصغر أو
+
+119
+00:08:57,710 --> 00:09:01,730
+يساوي من ال super mum يعني F of XI K هذه نقطة
+
+120
+00:09:01,730 --> 00:09:05,490
+عشوائية أكبر أو يساوي أصغر واحدة أو أصغر اللي هو
+
+121
+00:09:05,490 --> 00:09:10,070
+ال inf mum و أصغر أو يساوي اللي هي من ال super mum
+
+122
+00:09:10,610 --> 00:09:13,890
+هذا لكل مين لكل sub interval يعني هي sub interval
+
+123
+00:09:13,890 --> 00:09:20,810
+xk minus واحد وهي xk وهي xik أكيد اللي هو f of xik
+
+124
+00:09:20,810 --> 00:09:29,210
+هنا أصغر أو يساوي أكبر واحدة وأصغر أو يساوي أكبر
+
+125
+00:09:29,210 --> 00:09:34,020
+واحدة وأكبر أو يساوي أصغر واحدةاللي هي الـ MK
+
+126
+00:09:34,020 --> 00:09:38,580
+فبكون
+
+127
+00:09:38,580 --> 00:09:43,360
+دايما هي هذه دي و هذه دي و هذه دي خدوا الآن ضربولي
+
+128
+00:09:43,360 --> 00:09:47,680
+هنا وهنا وهنا ضربولي في XK-XK-Y حط طول الفترة
+
+129
+00:09:48,770 --> 00:09:52,070
+واخدوا الـ summation من عند واحد لعند أن بيصير هذا
+
+130
+00:09:52,070 --> 00:09:55,670
+بيمثل لي اللي هو الأبر صم وهذا بيمثل لي الأور صم
+
+131
+00:09:55,670 --> 00:10:00,070
+وهذا بيمثل لي مين؟ الريمان صم إذن الريمان صم دائما
+
+132
+00:10:00,070 --> 00:10:05,250
+بين الأبر وبين الأور لأوله أصلا نحن ليش بيسميهم
+
+133
+00:10:05,250 --> 00:10:10,210
+أبر و لاور عسى إن كل اللي غيرهم الأبر كل اللي
+
+134
+00:10:10,210 --> 00:10:14,350
+غيرهم أصغر يسويهم وكل اللي غيرهم الأور أكبر منهم
+
+135
+00:10:14,350 --> 00:10:21,060
+أو يسويهم التسمية جزء من المفهومأو تستقر من
+
+136
+00:10:21,060 --> 00:10:27,020
+المفهوم يعني بنسميها مش معقول هي أبر ونسميها لابر
+
+137
+00:10:27,020 --> 00:10:32,520
+أو أبر ونسميها اسم يخالف الأبر فأكيد اخترنا اسم
+
+138
+00:10:32,520 --> 00:10:37,660
+الأبر عشان هي فعلا أبرطيب نجي الى النظرية الأولى
+
+139
+00:10:37,660 --> 00:10:43,520
+let a و b عبارة عن فترة مغلقة و bounded و let f من
+
+140
+00:10:43,520 --> 00:10:46,960
+I ل R be integrable on I نفترض ان اف اذا احنا لما
+
+141
+00:10:46,960 --> 00:10:49,880
+نحكي integrable معناته integrable in the sense of
+
+142
+00:10:49,880 --> 00:10:53,340
+definition 716 اللي هو اللي بعتمد على ال U of F
+
+143
+00:10:53,340 --> 00:10:58,080
+بتساوي ال O of Fالان let F من I ل R بيه Integrable
+
+144
+00:10:58,080 --> 00:11:01,940
+I زي ما بأكد in the sense of definition 716 اللي
+
+145
+00:11:01,940 --> 00:11:09,070
+حكيته إذا لكل ي أكبر من سفر is givenThere exists a
+
+146
+00:11:09,070 --> 00:11:11,470
+partition by بي إبسلون such that if بي is any
+
+147
+00:11:11,470 --> 00:11:15,610
+partition that is a refinement of بي إبسلون and if
+
+148
+00:11:15,610 --> 00:11:19,930
+أس بي و أف is any remaining sum for أف then هيكون
+
+149
+00:11:19,930 --> 00:11:24,110
+عنده اللي هو أس بي و أف ناقص ال integration لأف
+
+150
+00:11:24,110 --> 00:11:29,210
+أصغر من مين من إبسلون بقول باختصار يعني لو فرضنا
+
+151
+00:11:29,210 --> 00:11:34,490
+أف integrable اللي هنخد لأي إبسلون في الدنيا بقدر
+
+152
+00:11:34,490 --> 00:11:40,550
+أجيلك partition بي إبسلونبحيث انه اي بي بارتيشن
+
+153
+00:11:40,550 --> 00:11:45,390
+refinement لبيبسلون refinement معناته البي بحتوى
+
+154
+00:11:45,390 --> 00:11:50,910
+مين البيبسلون تحسينله هيكون عندي ال remain sum S
+
+155
+00:11:50,910 --> 00:11:55,150
+بي و F هذا ناقص integration للف أصغر من مين؟ من
+
+156
+00:11:55,150 --> 00:12:04,090
+ابسلون يعني الآن F is integrable يا جماعةالأن for
+
+157
+00:12:04,090 --> 00:12:08,070
+every epsilon أكبر من 0 there exist بي ابسلون such
+
+158
+00:12:08,070 --> 00:12:12,490
+that for every بي تحتوي بي ابسلون اللي هو هذا اللي
+
+159
+00:12:12,490 --> 00:12:20,110
+جيته and for every man some أس للبي والأفهيكون
+
+160
+00:12:20,110 --> 00:12:25,410
+عندي الـ absolute value بين الـ S بي و F ناقص اللي
+
+161
+00:12:25,410 --> 00:12:31,890
+هو ال integration من A ل B لل F أصغر من 100 منافسة
+
+162
+00:12:31,890 --> 00:12:35,790
+يعني جاعت بقول أخي يعني أصلا يعنيأني هذا في الآخر
+
+163
+00:12:35,790 --> 00:12:39,910
+في الآخر في الآخر في الآخر هتلاقي الريمان صم اللي
+
+164
+00:12:39,910 --> 00:12:43,890
+هو يكون بينه و بين ال F إيش ما له أصغر من إبسلون
+
+165
+00:12:43,890 --> 00:12:47,870
+لما تكون ال إيش ال F اللي هي Integral يعني بلاقي
+
+166
+00:12:47,870 --> 00:12:52,890
+بي إبسلون بضمنك هذا الكلام بضمنك مش ال بي إبسلون
+
+167
+00:12:52,890 --> 00:12:58,550
+بس و كل ال refinement يعني كل ال refinement يعني
+
+168
+00:12:58,550 --> 00:13:05,310
+كل ما نزيد عدد عناصر ال partitionيعني كل ما نكبر
+
+169
+00:13:05,310 --> 00:13:09,810
+الان يعني و كأنه بقودنا لللي بدنا نحكيه قدام انه
+
+170
+00:13:09,810 --> 00:13:15,770
+لما الان تروح لمالة نهاية limit ال remand sum إذا
+
+171
+00:13:15,770 --> 00:13:18,950
+كانت موجودة integrable هيساوي ال integration
+
+172
+00:13:18,950 --> 00:13:23,870
+والعكس هنلاقيه صحيح برضه هيسيه definition طيب في
+
+173
+00:13:23,870 --> 00:13:26,870
+بعض الكتب زي ما قلنا او لو بدنا نسميه definition
+
+174
+00:13:26,870 --> 00:13:29,950
+بنقول equivalent ل definition الأولاني و طبعا
+
+175
+00:13:29,950 --> 00:13:37,040
+هنلاقينا حالة بتتواصلنرجع لنظريتنا نثبتهالأن if F
+
+176
+00:13:37,040 --> 00:13:40,820
+is integrable and Y أكبر من 0 then by Riemann
+
+177
+00:13:40,820 --> 00:13:45,200
+criterion there exists B Epsilon of I such that U
+
+178
+00:13:45,200 --> 00:13:48,980
+ناقص L أصغر من مين من Y هذا أحفظناها زي اسمنا مدام
+
+179
+00:13:48,980 --> 00:13:53,000
+F is integrable and then by Riemann criterion طبعا
+
+180
+00:13:53,000 --> 00:13:55,620
+أكيد هتيجي ع بالكم لأنه مدام قال there exists B
+
+181
+00:13:55,620 --> 00:13:59,120
+Epsilon هكيد أقول أكيد احنا هنستخدم مين اللي بتجيب
+
+182
+00:13:59,120 --> 00:14:01,720
+ال B Epsilon مين اللي كانت تجيب ال B Epsilon اللي
+
+183
+00:14:01,720 --> 00:14:04,870
+هي ال Riemann criterionإذا كان الـ F مستعمل و الـ
+
+184
+00:14:04,870 --> 00:14:07,790
+F أكبر من 0 فبالتالي باستخدام الـ Riemann's
+
+185
+00:14:07,790 --> 00:14:11,850
+criterion يوجد مجموعة بي أبسلون of I مثلًا الـ U
+
+186
+00:14:11,850 --> 00:14:14,950
+بي أبسلون و الـ F نقص الـ بي أبسلون و الـ F أشماله
+
+187
+00:14:14,950 --> 00:14:23,290
+أصغر من مين من أبسلون الآن اخدوا أي refinement بيه
+
+188
+00:14:23,290 --> 00:14:28,590
+بحتوى مين الـ بي أبسلون الـ refinement التحسين
+
+189
+00:14:28,590 --> 00:14:37,240
+اللاور بزيدوال أبر بجل اكيد عارفين ان هذا الكلام
+
+190
+00:14:37,240 --> 00:14:41,220
+اذا صار عند مدام اللي هو ال refinement ال lower
+
+191
+00:14:41,220 --> 00:14:46,940
+بزيد اكيد ال LBUF أصغر بيساوي LBUF اللي هو التحسين
+
+192
+00:14:46,940 --> 00:14:54,760
+و LBUF دايما اصغر بيساوي UBF و ال UBF التحسين بجل
+
+193
+00:14:54,760 --> 00:14:59,800
+عن ال UBEF اذا هذه ال inequality محفوظة عندنا ماشي
+
+194
+00:14:59,800 --> 00:15:08,270
+الحال الآنمن هنا ذولة صارت عندي high ال L بي
+
+195
+00:15:08,270 --> 00:15:15,090
+إبسلون و أف high ال L بي و أف لأنه أكبر high ال U
+
+196
+00:15:15,090 --> 00:15:22,630
+بي و أف high ال U بي إبسلون و أف أكيد أكيد أكيد
+
+197
+00:15:22,630 --> 00:15:27,570
+المسافة بين هذه و هذهأصغر المسافة بين هذه و هذه
+
+198
+00:15:27,570 --> 00:15:33,170
+يعني بمعنى آخر ال UBF ناقص ال LBF المسافة بينهم
+
+199
+00:15:33,170 --> 00:15:39,130
+أصغر أو يساوي ال UBY و ال LBY من هذه و هذه من اللي
+
+200
+00:15:39,130 --> 00:15:43,990
+فوق أشمالها أصغر من Y إذا صارت عندي ال U صار عندي
+
+201
+00:15:43,990 --> 00:15:50,210
+ال UBF ناقص ال BF أصغر من مين؟ من Y صار عندي ال U
+
+202
+00:15:51,040 --> 00:16:01,320
+بأف ناقص ال بأف أصغر من إبسلون لكل بي يحتوي من ال
+
+203
+00:16:01,320 --> 00:16:04,120
+بي إبسلون لكل refinement لمين للبي إبسلون اللي
+
+204
+00:16:04,120 --> 00:16:08,280
+لجناه بوسط الريمان ال criterion خلّينا نكمل يا
+
+205
+00:16:08,280 --> 00:16:19,320
+جماعة الآن لكن احنا بنعرف ان اي ريمان صم لبي معينة
+
+206
+00:16:19,510 --> 00:16:24,830
+هيكون بين الـ L و بين الـ P أكيد صح ولا لأ؟ طبعا
+
+207
+00:16:24,830 --> 00:16:28,910
+الـ S بين الـ P و الـ F اللي قلناها قبل شوية بين
+
+208
+00:16:28,910 --> 00:16:34,570
+الـ L P و F و الـ U P و Fطيب خد ال integration ال
+
+209
+00:16:34,570 --> 00:16:36,970
+integration ما هو ال F is integrable مزام
+
+210
+00:16:36,970 --> 00:16:41,330
+Integrable إذا هي بتساوي زي ما عملناها كتير بساوي
+
+211
+00:16:41,330 --> 00:16:45,430
+ال U في F و بتساوي ال L في F ال L في F هي ال
+
+212
+00:16:45,430 --> 00:16:48,070
+supremum لهذه الأشياء إذا أكيد هذا أكبر يساوي ال
+
+213
+00:16:48,070 --> 00:16:52,410
+lower اللي هي sum هذاوالـ Integration بيساوي الـ U
+
+214
+00:16:52,410 --> 00:16:56,370
+و F و الـ U و F هو عبارة عن الـ M في مهم للـ U و B
+
+215
+00:16:56,370 --> 00:16:59,230
+و F إذا نحن نكون أصغر أو يساوي إذا فعلا ال
+
+216
+00:16:59,230 --> 00:17:04,610
+integration بين ال lower sum و بين ال upper sum و
+
+217
+00:17:04,610 --> 00:17:09,560
+هذه الفكرة عملناها كتير قبل هاتإذا L هو أطرح هذه
+
+218
+00:17:09,560 --> 00:17:15,560
+من هذه تنتهي من بعض بيصير عند ال S ناقص هذه بين ال
+
+219
+00:17:15,560 --> 00:17:20,600
+L ناقص ال U و بين ال U ناقص ال L عملناها كتير طرح
+
+220
+00:17:20,600 --> 00:17:24,440
+معادلتين من بعض الآن هي ال U و ال U و هي ال L و هي
+
+221
+00:17:24,440 --> 00:17:26,660
+ال L و ضرب واحدة في ناقص اللي بدنا نطرح هذه في
+
+222
+00:17:26,660 --> 00:17:31,220
+ناقص تنعكس الأشارات تجمح لبعض و تطلع هذه أصغر أو
+
+223
+00:17:31,220 --> 00:17:36,920
+ساوي هذه و أصغر أو ساوي هذهالأن هذه يعني هذه اللي
+
+224
+00:17:36,920 --> 00:17:41,040
+هو بتساوي سالب هذه يعني صارت ال absolute value
+
+225
+00:17:41,040 --> 00:17:44,260
+أصغر أو يساوي اللي هو المقدار الموجود في هذا
+
+226
+00:17:44,260 --> 00:17:48,220
+والمقدار الموجود في هذا أصغر من وين؟ هنا لقنا أصغر
+
+227
+00:17:48,220 --> 00:17:51,800
+من إياش من إبسلون يعني صار عند ال S بي و F ناقص من
+
+228
+00:17:51,800 --> 00:17:58,860
+ال F أصغر من مين من إبسلون وهو المطلوب نجي للنظرية
+
+229
+00:17:58,860 --> 00:17:59,300
+الباعتها
+
+230
+00:18:09,320 --> 00:18:15,260
+النظرية تلاتة أربعة .. سبعة أربعة تلاتة نشوف ..
+
+231
+00:18:15,260 --> 00:18:21,920
+نتبه لنص النظرية و من ثم نيجي إلى اللي هو البرهان
+
+232
+00:18:21,920 --> 00:18:27,380
+إذا من ال .. من النظرية اللي قبله شوية لكل إبسلون
+
+233
+00:18:27,380 --> 00:18:32,760
+أكبر من سفر لجينا بي إبسلون such that for every بي
+
+234
+00:18:32,760 --> 00:18:38,220
+يحتوي البي إبسلون أو .. و لكل اللي هو أس بي و أف
+
+235
+00:18:38,980 --> 00:18:43,700
+اللي هو corresponding to this partition بديكون S P
+
+236
+00:18:43,700 --> 00:18:49,000
+و F ناقص ال integration من هنا ل P لل F أصغر من P
+
+237
+00:18:49,000 --> 00:18:53,480
+ل Y وهذا في حال أن F is integrable هذا عنوان اللي
+
+238
+00:18:53,480 --> 00:18:57,220
+هو اللي هي النظرية اللي قبل بشوية لإنه بتحتاجها
+
+239
+00:18:57,220 --> 00:19:03,130
+بعد شوية طيب شوف الآن إيش النظرية هذي بتقولخلّيت
+
+240
+00:19:03,130 --> 00:19:05,870
+أفضل about the closed interval A وB اللي هي I اللي
+
+241
+00:19:05,870 --> 00:19:09,110
+عند ال R بـA bounded function Suppose that there
+
+242
+00:19:09,110 --> 00:19:19,130
+exists a number A يحقق الخاصية التالية يحقق
+
+243
+00:19:19,130 --> 00:19:21,390
+الخاصية التالية
+
+244
+00:19:30,260 --> 00:19:34,660
+نفترض أن يوجد A بحيث أنه لايه إبسلون أكبر من 0
+
+245
+00:19:34,660 --> 00:19:40,140
+بنلاقي partition بي إبسلون و FB يحتوى بي إبسلون
+
+246
+00:19:40,140 --> 00:19:45,100
+and F SB is any remand sum for F corresponding to
+
+247
+00:19:45,100 --> 00:19:52,100
+B تئذن ال S بي و F ناقص A أصغر من مين من إبسلون
+
+248
+00:19:54,770 --> 00:20:02,070
+لو لاجينا .. انا افترض ان احنا بنلاقي الـ Number A
+
+249
+00:20:02,070 --> 00:20:07,190
+هذا معطى انه Number A، ايش بتمتح هذا Number A؟ انه
+
+250
+00:20:07,190 --> 00:20:12,190
+لما يكون عندك لكل ي أكبر من سفر لجهة partition بيه
+
+251
+00:20:12,190 --> 00:20:15,290
+يبسلون بحيث انه لكل refinement بيه تحتوى بيه
+
+252
+00:20:15,290 --> 00:20:19,870
+يبسلون و ال S, B و F is any remand sum
+
+253
+00:20:22,380 --> 00:20:24,760
+يجب أن يكون الـ a أصغر من إبسلون لأس و ال b و ال f
+
+254
+00:20:24,760 --> 00:20:31,980
+نقص من إبسلون لأس و ال b و ال f نقص من إبسلون لأس
+
+255
+00:20:31,980 --> 00:20:32,420
+و ال b و ال f نقص من إبسلون لأس و ال b و ال f نقص
+
+256
+00:20:32,420 --> 00:20:32,460
+من إبسلون لأس و ال b و ال f نقص من إبسلون لأس و ال
+
+257
+00:20:32,460 --> 00:20:32,460
+b و ال f نقص من إبسلون لأس و ال b و ال f نقص من
+
+258
+00:20:32,460 --> 00:20:32,460
+إبسلون لأس و ال b و ال f نقص من إبسلون لأس و ال b
+
+259
+00:20:32,460 --> 00:20:34,200
+و ال f نقص من إبسلون لأس و ال b و ال f نقص من
+
+260
+00:20:34,200 --> 00:20:37,640
+إبسلون لأس و ال b و ال f نقص من إبسلون لأس و ال b
+
+261
+00:20:37,640 --> 00:20:42,860
+ولكل ي أكبر من 0 بلاقي بي إبسلون بحيث أنه لما ال
+
+262
+00:20:42,860 --> 00:20:46,780
+بي يحتوي ال بي إبسلون ويكون اللي هو ال أس بي و ال
+
+263
+00:20:46,780 --> 00:20:50,800
+أف ناقص ا أصغر من إبسلون بقول then أف اي شمالها
+
+264
+00:20:50,800 --> 00:20:56,020
+must be integrable in I in the sense طبعاً في 716
+
+265
+00:20:56,020 --> 00:21:00,500
+و ال a هو من هذا ال integration يعني بقولنا لو
+
+266
+00:21:00,500 --> 00:21:05,360
+لجينا a بتحقق هذا الكلام هتطلعلكم ال a يا جماعة
+
+267
+00:21:05,360 --> 00:21:10,070
+هذا هي ال integrationهي قيمة الـ integration الـ
+
+268
+00:21:10,070 --> 00:21:12,630
+integration in the sense of الـ definition اللي
+
+269
+00:21:12,630 --> 00:21:17,730
+حكينا عليه طيب شوف الآن الان
+
+270
+00:21:17,730 --> 00:21:22,410
+بدي أعطيك شغل عامة وبعدها نخصصها على اللي بدناياه
+
+271
+00:21:22,410 --> 00:21:26,370
+الان give an epsilon أكبر من سفر and be any fixed
+
+272
+00:21:26,370 --> 00:21:31,250
+partition of I ماشي الحال الان خد أي إبسلون وخد بي
+
+273
+00:21:31,250 --> 00:21:37,020
+أي شمله أي fixed partition thenThere exist S1
+
+274
+00:21:37,020 --> 00:21:41,800
+بيوقف و S2 بيوقف بحيث أن S U بيوقف نقص S بيوقف
+
+275
+00:21:41,800 --> 00:21:46,800
+أصغر من مين من إبسلون و S2 نقص ال أصغر من مين من
+
+276
+00:21:46,800 --> 00:21:57,260
+إبسلون شوف هذه خلّينا نشوف كيف عملها هيا أخدنا
+
+277
+00:21:57,260 --> 00:22:02,580
+أي إبسلون في الدنيا و بأي partition الآن بقول لي
+
+278
+00:22:04,500 --> 00:22:11,460
+صار عندى S P و F صار عندى اسف البارتيشن اللى هو P
+
+279
+00:22:11,460 --> 00:22:17,260
+موجود والإبسلون موجود بانفكس بارتيشن مش بارتيشن
+
+280
+00:22:17,260 --> 00:22:21,320
+معين لأ انفكس بارتيشن الكلام ده بظبط عليه بقول
+
+281
+00:22:21,320 --> 00:22:32,410
+بقدر ألاقي remansum S واحد مسمى P و F بحيث أنه SU
+
+282
+00:22:32,410 --> 00:22:44,070
+B و F ناقص S1 B و F يكون أصغر من مين من Y المنطقي
+
+283
+00:22:44,070 --> 00:22:49,980
+الكلام هذا الأبرهو اعطاني الـ Epsilon جالي اثبت
+
+284
+00:22:49,980 --> 00:22:54,980
+انه بتلاقي S1 Remains sum بحيث ان الفرق بينه وبين
+
+285
+00:22:54,980 --> 00:22:57,340
+ال A بر لل B والF ال partition هذا partition معين
+
+286
+00:22:57,340 --> 00:23:01,680
+بحكي الاربيوتر ال partition بس fixed انه اخدت اي
+
+287
+00:23:01,680 --> 00:23:07,900
+Epsilonأجدرت ألاقي S1 remains sum بحيث أن هذا نقص
+
+288
+00:23:07,900 --> 00:23:10,980
+هذا يكون أصغر من يبسلون طبعا هذا الطبيعي هو أكبر
+
+289
+00:23:10,980 --> 00:23:13,760
+من هذا لكن الفرق بدي أخليه أصغر من يبسلون وأنا
+
+290
+00:23:13,760 --> 00:23:20,440
+بقدر أخليه الآن عندي ال Mk بساوي اللي هو عبارة عن
+
+291
+00:23:20,440 --> 00:23:27,580
+ال supremum لل F of X such that X element XK minus
+
+292
+00:23:27,580 --> 00:23:33,490
+واحد و XK مظبوط؟الان هذا اللي هو ال infimum ال
+
+293
+00:23:33,490 --> 00:23:37,010
+least upper bound الان ال least upper bound لو
+
+294
+00:23:37,010 --> 00:23:43,890
+شيلنا منه نجفنا منه اي عدد صغير كتير كتير و ليكن
+
+295
+00:23:43,890 --> 00:23:49,850
+ال y على مين على b minus a ببطل upper bound مدام
+
+296
+00:23:49,850 --> 00:23:55,510
+بطل upper bound اذا بقدر اناجي xik element ال xk
+
+297
+00:23:55,510 --> 00:23:57,230
+minus واحد و xk
+
+298
+00:24:00,970 --> 00:24:08,050
+تكون مالها أكبر من مين من اللي هو اللي بطل other
+
+299
+00:24:08,050 --> 00:24:13,600
+boundالان هذا اللي سويته مع الام كيه بقدر اسويه مع
+
+300
+00:24:13,600 --> 00:24:16,280
+الام واحد و الام اتنين و الام تلتة ايه منهم كلهم
+
+301
+00:24:16,280 --> 00:24:21,500
+إذا صار ال summation ك من عند واحد لعند ان و اضربه
+
+302
+00:24:21,500 --> 00:24:25,940
+كمان في مين xk minus xk minus واحد مافيش مانع لإن
+
+303
+00:24:25,940 --> 00:24:29,740
+أنا دموجة و أنا دموجة بتظهر زي ما هي xk ناقص xk
+
+304
+00:24:29,740 --> 00:24:32,720
+minus واحد واخده ال summation هذا ك من عند واحد
+
+305
+00:24:32,720 --> 00:24:38,120
+لعند مين لعند ان لجيتها ال xi k تبعت ال S واحد هذه
+
+306
+00:24:39,040 --> 00:24:47,580
+الان هذا remain sum بسميه S1 بيوف على مين اعتمد
+
+307
+00:24:47,580 --> 00:24:52,620
+على ال exiled case اللي انا لجيتها هذا ايش بيساوي
+
+308
+00:24:52,620 --> 00:24:59,480
+اللي هو summation Mk في Xk minus Xk minus واحد
+
+309
+00:24:59,480 --> 00:25:08,840
+ناقص ال summationXY-XK
+
+310
+00:25:08,840 --> 00:25:10,840
+-1
+
+311
+00:25:17,430 --> 00:25:22,310
+هذا summation سامحوني على الضيق اللوح هذا بيصير ال
+
+312
+00:25:22,310 --> 00:25:24,350
+summation على الأول زاد ال summation على الثانى هي
+
+313
+00:25:24,350 --> 00:25:27,630
+ال summation على الأول كم من عند واحد لعند أن ناقص
+
+314
+00:25:27,630 --> 00:25:29,910
+ال summation على التاني كم من عند واحد لعند أن
+
+315
+00:25:29,910 --> 00:25:34,810
+واخدت ال y بي و ماينوس أيه عن المشترك برا ال
+
+316
+00:25:34,810 --> 00:25:37,830
+summation دلت ال summation لهذا أصغر أو يساوي
+
+317
+00:25:37,830 --> 00:25:44,330
+بيقول لهذا مين هو أو أصغر من رمان صم أس بي و أف و
+
+318
+00:25:44,330 --> 00:25:53,580
+سمنها أس واحدهذا مين هو اكيد كلكم عارفه U P و F و
+
+319
+00:25:53,580 --> 00:26:00,000
+هذا ايش هو ناقص ايش هذاهذا اكيد y على b minus a في
+
+320
+00:26:00,000 --> 00:26:03,680
+هذا المقدار هذا المقدار عبارة عن x naught x واحد
+
+321
+00:26:03,680 --> 00:26:08,440
+ناقص x naught زائد x اتنين ناقص x واحد زائد عرفته
+
+322
+00:26:08,440 --> 00:26:12,240
+اذا اخر واحد xn ناقص xn ناقص واحد يعني بيظل xn
+
+323
+00:26:12,240 --> 00:26:16,280
+ناقص x naught كله ب cancel بعض xn اللي هي ال a ال
+
+324
+00:26:16,280 --> 00:26:20,180
+b و ال x naught هي ال a يعني هذا عبارة عن b minus
+
+325
+00:26:20,180 --> 00:26:27,450
+a اصلا من s واحد بيقفيعني صار عندي الـ U بي و F و
+
+326
+00:26:27,450 --> 00:26:35,710
+جيب لي هذا هنا نقص S1 بي و Fأشماله أصغر من أبسلون
+
+327
+00:26:35,710 --> 00:26:43,150
+فعلا انا اجدت اس واحد من
+
+328
+00:26:43,150 --> 00:27:00,870
+أبسلون
+
+329
+00:27:00,980 --> 00:27:08,700
+إذا لجيت S1 و S2 بحيث تحقق هذه الخاصية انتبهوا
+
+330
+00:27:08,700 --> 00:27:14,340
+الان هذا الان كل اللي حكيته هنا برهان للجزئية اللي
+
+331
+00:27:14,340 --> 00:27:20,770
+كاتبها انا في البرهان و مش مضحك بشكلها الكاملطيب
+
+332
+00:27:20,770 --> 00:27:23,930
+فيكم أصلي على النبي الله مصلي على سيدنا محمد نرجع
+
+333
+00:27:23,930 --> 00:27:28,450
+نقولكم انه لجينا اللي هو الاس واحد والاس اتنين
+
+334
+00:27:28,450 --> 00:27:31,870
+اللي بيحققن هذا طبعا ال بي كان ايش ماله any fixed
+
+335
+00:27:31,870 --> 00:27:37,410
+partition الان معطينا
+
+336
+00:27:37,410 --> 00:27:43,050
+هنا انه هذا معطى هذا معطى ديروا بالكم انه there
+
+337
+00:27:43,050 --> 00:27:46,970
+exists بي ابسلون بحيث ان بي بتحتوي بي ابسلون هذا
+
+338
+00:27:46,970 --> 00:27:52,630
+يتحقق الاناللي اتحقق على الـ P اللي هام، هيتحقق
+
+339
+00:27:52,630 --> 00:27:57,010
+على الـ P الإبسلون اللي هام ماشي الحال، إذا الأن
+
+340
+00:27:57,010 --> 00:28:01,930
+الـ U P إبسلون و الـ F ناقص الـ L P و F اللي هو
+
+341
+00:28:01,930 --> 00:28:10,460
+بساوي U U P و F ناقص L P و Fماشي ايش هذا اخدت ال
+
+342
+00:28:10,460 --> 00:28:13,740
+بي إبسلون ال بي اللي هنا هي ال بي إبسلون عشان اقول
+
+343
+00:28:13,740 --> 00:28:17,440
+انه انا اللي حققته على اللي هي ال بي فده حققته على
+
+344
+00:28:17,440 --> 00:28:20,460
+ال بي إبسلون انه هذا كان unfixed partition اصغر او
+
+345
+00:28:20,460 --> 00:28:25,700
+يساوي بال triangle inequality UBF ناقص SBF زي S1BF
+
+346
+00:28:25,700 --> 00:28:33,440
+ناقص A زي A ناقص S2BFماذا فعلت؟ بالـ Triangle
+
+347
+00:28:33,440 --> 00:28:37,380
+Inquality أضفت الـ S واحد وطرحت الـ S واحد وضفت
+
+348
+00:28:37,380 --> 00:28:41,260
+الـ A وطرحت الـ A وضفت الـ S اتنين وطرحت الـ S
+
+349
+00:28:41,260 --> 00:28:44,480
+اتنين وعملت الـ Triangle Inquality وطبقت هذه واحدة
+
+350
+00:28:44,480 --> 00:28:48,260
+كامتين، تلاتة، أربعة صار عندي أزرع يساوي هذا، زائد
+
+351
+00:28:48,260 --> 00:28:57,300
+هذا، زائد هذا، زائد هذا، ماشي الحل صار
+
+352
+00:28:57,300 --> 00:28:58,480
+عندي يا جماعة الآن
+
+353
+00:29:12,650 --> 00:29:17,970
+صار عندى اللى هو الان طبعا ال a ايش هي ال a اللى
+
+354
+00:29:17,970 --> 00:29:20,310
+في النظرية دى بقالكم a is the number in the
+
+355
+00:29:20,310 --> 00:29:24,270
+hypothesis of theorem then by the hypothesis of
+
+356
+00:29:24,270 --> 00:29:31,650
+theorem and star الان من اللى هو المعطى بيعطينا ان
+
+357
+00:29:31,650 --> 00:29:35,630
+ال s واحد نقص اللى a أصغر من يبسلون و ال s اتنين
+
+358
+00:29:35,630 --> 00:29:39,430
+نقص اللى a أصغر من يبسلون لأن هذا صحيح اللى فوق
+
+359
+00:29:39,430 --> 00:29:39,850
+لان
+
+360
+00:29:47,480 --> 00:29:53,200
+أذكركم كمان مرة بالمعطى
+
+361
+00:29:53,200 --> 00:30:00,540
+ان هناك مجموعة بي اس ايبسلون هي اللي بتشتغل في اس
+
+362
+00:30:00,540 --> 00:30:05,040
+بي و اف is any remansum corresponding لأف هيكون
+
+363
+00:30:05,040 --> 00:30:07,860
+الفرق بين هذا و هذا أصغر من ايبسلون من ضمن الاس
+
+364
+00:30:07,860 --> 00:30:11,740
+واحد والاس اتنين اللي جاتني قبل شوية اذا صار عندي
+
+365
+00:30:11,740 --> 00:30:20,530
+الكل اللي بشتغلوا مشروع بيصير اللي هوالـ UB نقص
+
+366
+00:30:20,530 --> 00:30:25,730
+الـ S1 أصغر من إبسلون و هذا أصغر من الإبسلون مُعطى
+
+367
+00:30:25,730 --> 00:30:29,230
+وهذا أصغر من الإبسلون مُعطى وهذا و هذا أصغر كل
+
+368
+00:30:29,230 --> 00:30:33,370
+واحد من إبسلون من اللي أتبته هنا قبل بشوية إذا صرت
+
+369
+00:30:33,370 --> 00:30:41,070
+اللي هي كلها أصغر من 4 إبسلون ماشي الحالأبسلون was
+
+370
+00:30:41,070 --> 00:30:48,930
+arbitrary then by 4718 F is integrableF is
+
+371
+00:30:48,930 --> 00:30:53,690
+integrable لأنه وجدت بإبسلون لأن U نقص لأخر من
+
+372
+00:30:53,690 --> 00:30:57,430
+أربعة إبسلون بإبسلون وبعض arbitrarily إذا بصير
+
+373
+00:30:57,430 --> 00:31:01,910
+عندي صحيح واحد متضايق من الأربعة إبسلون في اللي
+
+374
+00:31:01,910 --> 00:31:04,430
+فوق خد إبسلون على أربعة إبسلون على أربعة و النظرية
+
+375
+00:31:04,430 --> 00:31:08,730
+الأولى و المعطى برضه بتاخدوا إبسلون على أربعة
+
+376
+00:31:08,730 --> 00:31:19,300
+بطريقة حسابية معاه طيب إذا صار عنديلجينا الان then
+
+377
+00:31:19,300 --> 00:31:22,480
+by theorem 7 1 8 F is integrable and for every
+
+378
+00:31:22,480 --> 00:31:25,360
+epsilon أكبر من 0 there exists B epsilon of I such
+
+379
+00:31:25,360 --> 00:31:28,800
+that FB بتحتول بي ابسلون and B is a partition of I
+
+380
+00:31:28,800 --> 00:31:36,380
+then S of B و F مقصدها أصغر من 100 من إبسلون إيش
+
+381
+00:31:36,380 --> 00:31:39,840
+هذا؟ حنا أثبتنا انه integrable مدام انتجرابل باللي
+
+382
+00:31:39,840 --> 00:31:44,100
+كاتبوا هناواللي كاتبوها هيكون الفرق بين for every
+
+383
+00:31:44,100 --> 00:31:47,320
+ε there exists بي إبسلون و الـ B تحتوى 100 بي
+
+384
+00:31:47,320 --> 00:31:50,040
+إبسلون واحد يقول طب ما هو خايفين الـ بي إبسلون
+
+385
+00:31:50,040 --> 00:31:53,260
+اللي لاجيناها في الأول المعطف في النظرية غير الـ
+
+386
+00:31:53,260 --> 00:31:57,260
+بي إبسلون هذه مش مشكلة الـ بي إبسلون فرطنة تبعة
+
+387
+00:31:57,260 --> 00:32:01,560
+النظرية بي برايم of إبسلونوهذه اللي وجدناها من الـ
+
+388
+00:32:01,560 --> 00:32:05,660
+Integrability للـ P للـ F اللي أثبتناها نسميها بي
+
+389
+00:32:05,660 --> 00:32:09,480
+إبسلون دابل براين خد الـ بي إبسلون اللي بتحكي
+
+390
+00:32:09,480 --> 00:32:14,520
+عليها الآن عشان تنفع للجهتين خدها بساوي بي إبسلون
+
+391
+00:32:14,520 --> 00:32:20,060
+براين اتحاد بي إبسلون دابل براينبصير الآن هذه اللي
+
+392
+00:32:20,060 --> 00:32:26,280
+هي تنفع تنفع للمعطيات الأولى والمعطيات التانية
+
+393
+00:32:26,280 --> 00:32:29,320
+لأنها بيصير refinement للأول و refinement لمن؟
+
+394
+00:32:29,320 --> 00:32:35,980
+للثاني إذا فش فيه مشكلة إذا الآنthen by hypothesis
+
+395
+00:32:35,980 --> 00:32:40,360
+of theorem أخدنا هذا أصغر من أربع إبسلون إذا سبب
+
+396
+00:32:40,360 --> 00:32:43,840
+له هذا أن هو F is integrable مدام F is integrable
+
+397
+00:32:43,840 --> 00:32:48,620
+إذا بالنظرية بنلاقي بي إبسلون بحيث أنه لكل بي
+
+398
+00:32:48,620 --> 00:32:53,000
+بيحتوي بي إبسلون بيكون هذا ناقص هذا أصغر من مين من
+
+399
+00:32:53,000 --> 00:32:58,890
+إبسلون هذا أصبح أصغر من إبسلونبس الآن اثبتنا عند
+
+400
+00:32:58,890 --> 00:33:02,990
+الـ F بي و F ناقص اللي أصغر من إبسلون من النظرية و
+
+401
+00:33:02,990 --> 00:33:06,570
+واحد يقول لي تبعت ال بي هادي بتختلف عن ال بي هادي
+
+402
+00:33:06,570 --> 00:33:10,450
+قلتلك علجتها ال بي هادي و ال بي هادي باخد ال بي
+
+403
+00:33:10,450 --> 00:33:13,730
+إبسلون لتبعت النظرية و ال بي إبسلون تبعت اللي هو
+
+404
+00:33:13,730 --> 00:33:17,690
+ال integrability و باخدهن اتحادهن بيكون اللي هو ال
+
+405
+00:33:17,690 --> 00:33:20,990
+بي إبسلون اللي لجيتها هنااللي بدى أستخدم إيه لها
+
+406
+00:33:20,990 --> 00:33:24,770
+الجهتين و أي refinement لها بيه لـ بي أبسلون و
+
+407
+00:33:24,770 --> 00:33:29,270
+لجديدة بيطلع هذا صح وهذا صح اتتين مع بعض دلوقتي
+
+408
+00:33:29,270 --> 00:33:35,030
+بحجل اللي استخدمهم و أقول إذا ال integration لل F
+
+409
+00:33:35,030 --> 00:33:37,830
+من A ل B نقص A أصغر و أساوي ال integration لل F
+
+410
+00:33:37,830 --> 00:33:41,990
+نقص ال S زاد ال S نقص ال Aاللي هو ضيف ال term و
+
+411
+00:33:41,990 --> 00:33:46,750
+طرحت ال term هذا هي أصغر من إبسلون وهذا أصغر من
+
+412
+00:33:46,750 --> 00:33:50,210
+إبسلون إذا صار هذا أصغر من اتنين إبسلون صار عندي
+
+413
+00:33:50,210 --> 00:33:53,910
+فيه العدد هذا بين اللي هو اتنين إبسلون وأكبر أو
+
+414
+00:33:53,910 --> 00:33:56,870
+ساوي سفر وإبسلون arbitrary إذا هذا المقدر لازم
+
+415
+00:33:56,870 --> 00:34:00,750
+ساوي سفر إذا ال integration بساوي مين بساوي ليه
+
+416
+00:34:00,750 --> 00:34:03,510
+وهو المطلوب طيب
+
+417
+00:34:10,110 --> 00:34:17,630
+نجي لأ اللي هو ال definition سبعة أربعة أربعة ال
+
+418
+00:34:17,630 --> 00:34:23,270
+definition بسيط بده يعرف حاجة اسمها مش أو norm هو
+
+419
+00:34:23,270 --> 00:34:27,330
+انا بسميها مش عادة الناس بتسميها norm ايش ال .. ال
+
+420
+00:34:27,330 --> 00:34:31,550
+.. ال مش اللي بده يعرفه؟ بقول لو كان عندك
+
+421
+00:34:31,550 --> 00:34:38,910
+partition B بساوي X0 و X1 لعندي XNالان كل sub
+
+422
+00:34:38,910 --> 00:34:46,970
+interval لها طول ال norm ل ال B او مش ل ال B هو
+
+423
+00:34:46,970 --> 00:34:51,920
+عبارة عن ال maximumأو الـ Supremum Maximum لأن الـ
+
+424
+00:34:51,920 --> 00:34:53,860
+Supremum حاسب Maximum لإنه الـ finite دول
+
+425
+00:34:53,860 --> 00:34:59,480
+الماكسيمم لا X1 ناقص X0 و X2 ناقص X1 لأطوال
+
+426
+00:34:59,480 --> 00:35:03,140
+الفترات يعني sub interval لعند ال XN ناقص XN ناقص
+
+427
+00:35:03,140 --> 00:35:07,880
+1 الماكسيمم الهن هدول أطوال الفترات هو اللي بنسميه
+
+428
+00:35:07,880 --> 00:35:14,000
+مين النورم للـ B هو النورم للـ B الآن يعني يعني لو
+
+429
+00:35:14,000 --> 00:35:20,670
+كان عندك لو كان عندك هي عند الفترةمن صفر لعين
+
+430
+00:35:20,670 --> 00:35:31,410
+تلاتة مثلا هاي عند بي بتساوي صفر نص واحد اتنين
+
+431
+00:35:31,410 --> 00:35:37,970
+تلاتة مثلا بكون ال normal بي ايش هيساوي ايش ال
+
+432
+00:35:37,970 --> 00:35:41,510
+normal بي اكيد هتقولوا كلكم تلاتة ناقص اتنين واحد
+
+433
+00:35:41,510 --> 00:35:44,710
+اتنين ناقص واحد واحد واحد ناقص نص نص واحد اذا ايش
+
+434
+00:35:44,710 --> 00:35:49,110
+هيساوي واحد اكبر اكبر طول sub interval واحدلو جينا
+
+435
+00:35:49,110 --> 00:36:00,350
+أخدنا الـ Q مثلا بساوي اللي هو Zero نص واحد واحد و
+
+436
+00:36:00,350 --> 00:36:08,890
+تلت اتنين اتنين و نص و تلاتة وقلنا لكم اوجد الـ Q
+
+437
+00:36:09,620 --> 00:36:13,420
+أكيد كلكم حدقول الـ Q أشمالها اللي هي بين الواحد و
+
+438
+00:36:13,420 --> 00:36:17,420
+تلت والتانين هي أكبر أكبر مسافة اللي هي عبارة عن
+
+439
+00:36:17,420 --> 00:36:23,060
+إيه؟ تلتين لاحظوا أن الـ B مجموعة جزئية من مين؟ من
+
+440
+00:36:23,060 --> 00:36:33,810
+الـ Q لما .. لما الآن الـ Q كبرت نورمهاهيكون أصغر
+
+441
+00:36:33,810 --> 00:36:37,590
+أو يساوي norm من الـ B طبيعي لأنه دخلت نقطة جديدة
+
+442
+00:36:37,590 --> 00:36:43,690
+ممكن تزخر المسافة لكن مش ممكن تزيدها طيب وهذه اللي
+
+443
+00:36:43,690 --> 00:36:47,810
+هي بعض الملاحظات اللي هنا على اللي هي ال norm أو
+
+444
+00:36:47,810 --> 00:36:55,800
+ال mesh اللي الآن بعض اللي هوالملاحظات اللي هو
+
+445
+00:36:55,800 --> 00:37:00,780
+different partition of I can have the same مش بقول
+
+446
+00:37:00,780 --> 00:37:03,280
+يعني ممكن different partition لل .. لل .. لل ..
+
+447
+00:37:03,280 --> 00:37:06,140
+للinterval اللي ده same مش اه بقدر هاد انا اجيبلك
+
+448
+00:37:06,140 --> 00:37:12,200
+كمان واحد زي هدول خد كمان بي برايم بساوي سفر و نص
+
+449
+00:37:12,200 --> 00:37:20,030
+و واحد و اتنين و اتنين و نص و تلاتةهذا الـ B'
+
+450
+00:37:20,270 --> 00:37:25,170
+يختلف عن الـ B لكن نورمه التاني الواش بيساوي واحد
+
+451
+00:37:25,170 --> 00:37:30,530
+يعني ال different partitions ممكن يكون لها نفس
+
+452
+00:37:30,530 --> 00:37:34,730
+نورم و هاي مثال و كتير فيه زي ذلك لأن لو كانت B
+
+453
+00:37:34,730 --> 00:37:39,730
+subset من Q نورم لـ Q أظهر يساوي نورم لمن؟ لـ B و
+
+454
+00:37:39,730 --> 00:37:43,720
+اتبعت السهل هذاخد الـ B subset إذا هيكون عنده اللي
+
+455
+00:37:43,720 --> 00:37:47,080
+هو عدد النقاط اللي في Q أكتر من عدد النقاط اللي في
+
+456
+00:37:47,080 --> 00:37:53,780
+B هكون ال maximum على الأولى اللي هو أكبر أو شاوي
+
+457
+00:37:53,780 --> 00:37:56,720
+ال maximum على مين على التاني لإنه اللي صار فيها
+
+458
+00:37:56,720 --> 00:38:02,070
+زيادات صار فيه إمكانية إنها تقصر الفتراتطيب لكن لو
+
+459
+00:38:02,070 --> 00:38:05,330
+كان ال normal ال Q أصغر شويه ال normal ال B مش شرط
+
+460
+00:38:05,330 --> 00:38:10,110
+أن يكون B subset من مين؟ من ال Q أو كتير بتلاقي
+
+461
+00:38:10,110 --> 00:38:16,910
+أمثلة زي هي ال normal
+
+462
+00:38:16,910 --> 00:38:25,160
+B هذا إيش بيساوي؟ normal B بيساوي واحدالان عندي ..
+
+463
+00:38:25,160 --> 00:38:32,320
+مش شرط .. يعني هديلك اللي هو Normal Q أصغر أوي
+
+464
+00:38:32,320 --> 00:38:40,040
+ساوي Normal B لكن الـ B اللي هو ليس شرطا أنها تكون
+
+465
+00:38:40,040 --> 00:38:47,500
+subset من مين؟ من إيش؟ من الـ Q Normal B واحد خد
+
+466
+00:38:47,500 --> 00:38:48,060
+الـ Q
+
+467
+00:38:53,000 --> 00:39:03,100
+بساوي اللي هو سفر و واحد و اتنين و اتنين و نص و
+
+468
+00:39:03,100 --> 00:39:07,180
+تلاتة نورمال
+
+469
+00:39:07,180 --> 00:39:12,100
+كيوه بديه ال
+
+470
+00:39:12,100 --> 00:39:19,920
+gate
+
+471
+00:39:19,920 --> 00:39:22,280
+واحد و واحد و نص
+
+472
+00:39:25,990 --> 00:39:34,190
+وهي نص كمان سفر و نص Normal Q بساوة نص مظبوط
+
+473
+00:39:34,190 --> 00:39:45,650
+Normal Q بساوة نص لكن ال B ال B خلي هذا تلت ماشي
+
+474
+00:39:45,650 --> 00:39:51,220
+خلي هذا تلت صارت ال B مش subset من مينمن الـ Q
+
+475
+00:39:51,220 --> 00:39:54,420
+ممكن تلاقي افضل اكتير هذه الـ B أكيد مش subset من
+
+476
+00:39:54,420 --> 00:40:00,460
+الـ Q Normal B بيبقى واحد صح؟ Normal B واحد و
+
+477
+00:40:00,460 --> 00:40:06,160
+Normal Q ايش بيساوي نص لأن الفرق بينهم انصاص هذه
+
+478
+00:40:06,160 --> 00:40:12,340
+عندك Normal Q أصغر او يساوي Normal B لأن هذا نص
+
+479
+00:40:12,340 --> 00:40:14,420
+وهذا واحد but
+
+480
+00:40:17,620 --> 00:40:22,380
+واضح الـ B هي سفر و تلت و واحد و اتنين و تلاتة ليس
+
+481
+00:40:22,380 --> 00:40:26,100
+subset من الـ Q صفر و نص و واحد و نص و .. و .. و
+
+482
+00:40:26,100 --> 00:40:27,400
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+483
+00:40:27,400 --> 00:40:28,940
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+484
+00:40:28,940 --> 00:40:29,640
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+485
+00:40:29,640 --> 00:40:30,360
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+486
+00:40:30,360 --> 00:40:30,360
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+487
+00:40:30,360 --> 00:40:30,380
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+488
+00:40:30,380 --> 00:40:30,380
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+489
+00:40:30,380 --> 00:40:34,960
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+490
+00:40:34,960 --> 00:40:36,340
+.. و .. و .. و .. و .. و .. و ..
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/SeyE20uTyhg.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/SeyE20uTyhg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c328f8f4f55e48e38c460d0ef203be7e5ff82cdf
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/SeyE20uTyhg.srt
@@ -0,0 +1,2439 @@
+1
+00:00:05,300 --> 00:00:13,060
+بسم الله الرحمن الرحيم المحاضرة السادسة مساق تحليل
+
+2
+00:00:13,060 --> 00:00:18,680
+حقيقة 2 لطلبة قسم رياضيات بكلية العلوم بالجامعة
+
+3
+00:00:18,680 --> 00:00:23,220
+الإسلامية بغزة. الحديث اليوم إن شاء الله هيكون حول
+
+4
+00:00:23,220 --> 00:00:30,200
+قواعد لوبيتال (L'Hôpital's Rules) 
+
+5
+00:00:30,200 --> 00:00:38,320
+بتمر في التفاضل والتكامل (calculus) بتمر من ناحية
+
+6
+00:00:38,320 --> 00:00:45,100
+عملية استخدامها وتوظيفها لحل اللي هي بعض النهايات
+
+7
+00:00:45,100 --> 00:00:50,400
+اللي بيكون .. اللي هو عجزنا عن حلها بطرق عادية
+
+8
+00:00:51,750 --> 00:00:57,550
+هنشوف الآن في الحديث عن قواعد لوبيتال حول اللي
+
+9
+00:00:57,550 --> 00:01:01,570
+هو كيف اللي هو أن نبرهن هذه اللي هي القواعد كيف نشتق
+
+10
+00:01:01,570 --> 00:01:06,310
+هذه القواعد كيف اللي هو أيضًا بشكل سريع حول اللي
+
+11
+00:01:06,310 --> 00:01:12,490
+هي استخدام هذه القواعد طبعًا 
+
+12
+00:01:12,490 --> 00:01:16,430
+في الأول هنتحدث عن الكميات الغير معينة
+
+13
+00:01:17,020 --> 00:01:23,580
+(indeterminate forms) اللي هي اللي بتعالجها اللي هي
+
+14
+00:01:23,580 --> 00:01:28,840
+قواعد لوبيتال (L'Hôpital's Rules) عندي على سبيل المثال لو جينا أخدنا
+
+15
+00:01:28,840 --> 00:01:37,090
+الـ limit اللي هو x على x<sup>3</sup> على x<sup>2</sup> مثلًا as x
+
+16
+00:01:37,090 --> 00:01:44,730
+goes to zero  الـ limit αx على x لما x تروح للزيرو
+
+17
+00:01:44,730 --> 00:01:50,670
+الـ limit اللي هو x<sup>2</sup> على x لما x تروح للزيرو
+
+18
+00:01:50,670 --> 00:01:59,900
+الـ limit x على x<sup>3</sup> لما x تروح للزيرو الـ limit مثلًا
+
+19
+00:01:59,900 --> 00:02:07,100
+-x على x<sup>3</sup> لما x تروح لـ 0 لو طلعنا على
+
+20
+00:02:07,100 --> 00:02:11,440
+اللي هي الـ limits اللي موجودة هنا كلها على صورة
+
+21
+00:02:11,440 --> 00:02:16,260
+اللي هي لو تعويض مباشر هنلاقيها على صورة 0 على 0
+
+22
+00:02:16,960 --> 00:02:21,420
+الآن كمية 0 على 0 بالطرق السابقة كان اللي هو أنه
+
+23
+00:02:21,420 --> 00:02:27,620
+احنا صعب اللي هو نتعامل معها لكن في بعض الأحيان زي
+
+24
+00:02:27,620 --> 00:02:30,520
+الحالة هذه هنلاقي أنه احنا بنعرف نتعامل معها و
+
+25
+00:02:30,520 --> 00:02:36,140
+بنعرف نحكم عليها اللي هلاحظ أنه كل رغم أن كلها 0
+
+26
+00:02:36,140 --> 00:02:41,100
+على 0 إلا أنها بتعطي في كل حالة شيء مختلف عن
+
+27
+00:02:41,100 --> 00:02:47,350
+الحالة الثانية الآن هذه مثلًا عبارة عن الـ limit 1 على x
+
+28
+00:02:47,350 --> 00:02:51,030
+لما x تروح للـ 0 طبعًا 1 على x لما x تروح للـ 0 إيش
+
+29
+00:02:51,030 --> 00:02:53,710
+مالها؟ does not exist لأنه من اليمين بتعطي ما لا نهاية
+
+30
+00:02:53,710 --> 00:02:56,790
+ومن اليسار بتعطي سالب ما لا نهاية عشان هيك
+
+31
+00:02:56,790 --> 00:03:02,510
+كده يبقى نقول عنها does not exist لأن الـ limit αx
+
+32
+00:03:02,510 --> 00:03:06,210
+على x لما x تروح للـ 0 هو يساوي عبارة عن α
+
+33
+00:03:06,960 --> 00:03:09,720
+اللي هو عبارة عن عدد حقيقي (real number) لو فرضنا أنه α
+
+34
+00:03:09,720 --> 00:03:13,480
+ماخدينها احنا عدد حقيقي (real number) إذا أنا أعطتني عدد
+
+35
+00:03:13,480 --> 00:03:16,320
+أول ما أعطتني اللي هي أنا أعطتني does not exist
+
+36
+00:03:16,320 --> 00:03:20,620
+الحالة الثانية اللي هي بتطلع الـ limit x لما x تروح ل
+
+37
+00:03:20,620 --> 00:03:24,330
+0 برضه أعطتنا إيه؟ أعطتنا عدد حقيقي (real number) في الحالة اللي
+
+38
+00:03:24,330 --> 00:03:28,670
+بعدها أعطتنا اللي هو عبارة عن الـ limit 1 على x<sup>2</sup>
+
+39
+00:03:28,670 --> 00:03:32,790
+لما x تروح للصفر يعني أعطتنا إيش؟ مالها؟ زائد ما لا نهاية
+
+40
+00:03:32,790 --> 00:03:37,070
+في الحالة الثالث الأخيرة هتعطينا اللي هو
+
+41
+00:03:37,070 --> 00:03:42,770
+ناقص الـ limit 1 على x<sup>2</sup> لما x تروح للزيرو بمعنى
+
+42
+00:03:42,770 --> 00:03:46,700
+آخر سالب ما لا نهاية يعني الـ Indeterminate Form Zero
+
+43
+00:03:46,700 --> 00:03:51,880
+على Zero أعطتنا اللي هو أجوبة أو قيم مختلفة تابعًا
+
+44
+00:03:51,880 --> 00:03:56,280
+لطبيعة كل حالة من الحالات اللي موجودة مرة أعطتنا
+
+45
+00:03:56,280 --> 00:03:59,700
+doesn't exist مرة أعطتنا ما لا نهاية ومرة أعطتنا ما لا 
+
+46
+00:03:59,700 --> 00:04:03,640
+نهاية و1 5 6 ناقص 1 اللي بدناها اللي هو
+
+47
+00:04:03,640 --> 00:04:09,020
+ناقص ما لا نهاية وما لا نهاية الآن الـ  الـ الـ الـ
+
+48
+00:04:09,020 --> 00:04:13,780
+الـ Indeterminate form هذه اللي الآن يعني بدنا
+
+49
+00:04:13,780 --> 00:04:19,780
+نحاول نعالجها بـ 
+
+50
+00:04:19,780 --> 00:04:25,400
+نحاول نعالجها بـ الـ الـ بقواعد لوبيتال (L'Hôpital's Rules) الـ
+
+51
+00:04:25,400 --> 00:04:28,640
+Indeterminate Form اللي عندنا اللي هو 0 على 0 طبعًا
+
+52
+00:04:28,640 --> 00:04:33,240
+في Indeterminate Form أخرى برضه هتعالجها اللي هي الـ L
+
+53
+00:04:33,240 --> 00:04:38,620
+'Hôpital's Rule أو Rules اللي هي زي ما لا نهاية على
+
+54
+00:04:39,400 --> 00:04:43,280
+ما لا نهاية أيضًا هذول الشغلتين الأساسيات اللي
+
+55
+00:04:43,280 --> 00:04:47,480
+هتعالجها اللي بقواعد لوبيتال (L'Hôpital's Rule) مباشرة بنظريات مباشرة
+
+56
+00:04:47,480 --> 00:04:51,240
+عليها أيضًا هتظهر لو ظهرت عندنا مثلًا ما لا نهاية ناقص
+
+57
+00:04:51,240 --> 00:04:55,640
+ما لا نهاية اللي هو Zero to Infinity Infinity to Zero
+
+58
+00:04:55,640 --> 00:05:01,160
+إلى آخره هذوله حالات أخرى اللي هو بنقدر نحولهم عن
+
+59
+00:05:01,160 --> 00:05:04,800
+طريق الـ ln أو عن طريق الـ exponential أو بطرق
+
+60
+00:05:04,800 --> 00:05:08,820
+معينة للّي هي الـ formula هذه ومن ثم استخدام اللي
+
+61
+00:05:08,820 --> 00:05:12,240
+هو قواعد لوبيتال (L'Hôpital's Rules) هذه عادة الشغلات اللي كانت
+
+62
+00:05:12,240 --> 00:05:16,460
+تعالجها اليمين اللي هو الـ calculus أو التفاضل اللي
+
+63
+00:05:16,460 --> 00:05:20,500
+أخدناه في سنة أولى أو سنة أولى أو سنة ثانية نطلع
+
+64
+00:05:20,500 --> 00:05:26,260
+لفوق نيجي الآن نأخذ النظرية الأولى اللي هي لقواعد 
+
+65
+00:05:26,260 --> 00:05:30,540
+لوبيتال الأولى الـ formula الأولى أو الصورة الأولى
+
+66
+00:05:30,540 --> 00:05:35,660
+نظرية بسيطة ونظرية مرت عليكم وإثباتها أيضًا
+
+67
+00:05:35,660 --> 00:05:41,200
+هتلاحظوا أنه اللي هو بسيط إيش النظرية بتقول؟ بتقول
+
+68
+00:05:41,200 --> 00:05:43,680
+ما يلي عندي
+
+69
+00:05:45,330 --> 00:05:51,250
+Let F be defined على الفترة المغلقة A وB ونفترض أن
+
+70
+00:05:51,250 --> 00:05:55,630
+F of A وG of A ما يساوي؟ صفر ونفترض أن G of X لا
+
+71
+00:05:55,630 --> 00:06:00,470
+تساوي صفر في الفترة اللي هي بين A وB ونفترض لو
+
+72
+00:06:00,470 --> 00:06:04,420
+كانت F وG differentiable عند الـ A وG' عند الـ A
+
+73
+00:06:04,420 --> 00:06:07,880
+لا يساوي صفر مفترضين G' لا يساوي صفر then the
+
+74
+00:06:07,880 --> 00:06:14,240
+limit of F على G at A exist وتساوي F' على G' و
+
+75
+00:06:14,240 --> 00:06:19,580
+إذا كان تحت كل هذا الشروط بيطلع عندي اللي هو ال
+
+76
+00:06:19,580 --> 00:06:24,320
+limit had exist وبالضبط هذا الـ limit بيساوي F' على
+
+77
+00:06:24,320 --> 00:06:29,780
+G' of A على F' of A نشوف النظرية ونشوف برهان النظرية
+
+78
+00:06:29,780 --> 00:06:38,960
+(theorem) عندي ماخد الـ F والـ G عبارة عن دوال من A
+
+79
+00:06:38,960 --> 00:06:47,280
+وB لعند R مفترض أن الـ F of A بيساوي الـ G of A
+
+80
+00:06:47,280 --> 00:06:53,680
+بيساوي إيش؟ بيساوي صفر ومفترض أن الـ G of X
+
+81
+00:06:58,040 --> 00:07:09,500
+لا تساوي 0 لكل X وموجودة في الفترة A وB فرضنا
+
+82
+00:07:09,500 --> 00:07:16,260
+كمان F وG differentiable عند الـ A F prime
+
+83
+00:07:16,260 --> 00:07:22,740
+of A وG prime of A exists 60 2 وهذه لا تساوي
+
+84
+00:07:22,740 --> 00:07:29,900
+إيش؟ لا تساوي صفر تحت هذه الظروف كلها بيكون عندي الـ limit
+
+85
+00:07:29,900 --> 00:07:38,410
+f of x على g of x as x بتروح لل a طبعًا ال a الفترة
+
+86
+00:07:38,410 --> 00:07:43,390
+اللي عندنا هي فترة من وين؟ من عند a لعند b إذا
+
+87
+00:07:43,390 --> 00:07:46,270
+أكيد ال x إذا تروح لل a ما فيش مجال لها ال x اللي
+
+88
+00:07:46,270 --> 00:07:49,210
+بتروح لل a اللي من وين؟ من جهة اليمين لأنه هي
+
+89
+00:07:49,210 --> 00:07:52,450
+المنطقة اللي أنا عمال قاعد بشتغل فيها الفترة من a ل
+
+90
+00:07:52,450 --> 00:07:57,870
+b إذا ال x بتروح لل a من وين؟ من اليمين هيساوي اللي
+
+91
+00:07:57,870 --> 00:08:06,930
+هو f prime عند ال a على g prime عند الـ A يعني
+
+92
+00:08:06,930 --> 00:08:09,910
+بمعنى آخر إيش اللي .. إيش .. إيش .. إيش .. كيف هم
+
+93
+00:08:09,910 --> 00:08:13,650
+نطبق هذه النظرية؟ كانت تعرض علينا الـ limit نيجي
+
+94
+00:08:13,650 --> 00:08:19,650
+يقول لنا أوجد الـ limit للـ F of X على G of X لما X
+
+95
+00:08:19,650 --> 00:08:25,090
+تروح لمين؟ لل A من اليمين نيجي الآن الـ F of A نعوض
+
+96
+00:08:25,090 --> 00:08:29,500
+تعويض مباشر ده طلعت عند 0 على 0 وكانت عندي الشروط
+
+97
+00:08:29,500 --> 00:08:32,520
+هذه مكتملة اللي هي الـ F والـ G differentiable و
+
+98
+00:08:32,520 --> 00:08:36,080
+الـ F prime والـ G prime موجودات عند الـ A على طول
+
+99
+00:08:36,080 --> 00:08:42,420
+نحط هذه إيش؟ بتساوي F prime of A على G prime of A
+
+100
+00:08:42,420 --> 00:08:48,880
+معايا فهذه اللي هي .. اللي هي .. كيفية تطبيق
+
+101
+00:08:48,880 --> 00:08:53,500
+النظرية نيجي لإثبات برهان النظرية البرهان بسيط
+
+102
+00:08:53,500 --> 00:08:54,680
+عندي
+
+103
+00:08:59,270 --> 00:09:11,330
+خذ عندي for x بين a وبين b لو جيت حسبت الهدف
+
+104
+00:09:11,330 --> 00:09:18,970
+الهدف الموجودة هذه الـ f of x على g of x إيش هتساوي؟
+
+105
+00:09:18,970 --> 00:09:28,250
+هتساوي f of x ناقص f of a على g of x ناقص g of a ليش؟
+
+106
+00:09:28,250 --> 00:09:31,110
+لأن الـ f of a والـ d of a ليش؟ ما أعطينا إياهم بيساوي
+
+107
+00:09:31,110 --> 00:09:34,170
+صفر ليش عملت هيك؟ لأ بدأت أعمل أكثر من هي بدأت أعمل
+
+108
+00:09:34,170 --> 00:09:39,110
+أقسم هذا على x minus a وهذا على x ما لها minus a
+
+109
+00:09:40,060 --> 00:09:43,580
+طبيعي ال x لا تساوي ال a الآن أنا باخد الـ limit
+
+110
+00:09:43,580 --> 00:09:47,620
+للجهتين وبتجرأ وبأخد موزع لأن أنا ضامن من الـ F
+
+111
+00:09:47,620 --> 00:09:51,260
+prime of A موجودة والـ G prime of A موجودة ومش هيك
+
+112
+00:09:51,260 --> 00:09:54,160
+وكمان الـ G prime of A لا تساوي 0 إذا كل أموري تمام
+
+113
+00:09:54,160 --> 00:09:58,220
+التمام إذا بأخذ الـ limit للجهتين لما X تروح لل A
+
+114
+00:09:58,220 --> 00:10:04,040
+من اليمين بيساوي الـ limit لما X تروح لل A من اليمين
+
+115
+00:10:05,480 --> 00:10:09,560
+والشيء اللي تحت وزعت ليش وزعت؟ ضامن أن الـ limit
+
+116
+00:10:09,560 --> 00:10:14,520
+exist والـ limit اللي تحت كمان لا تساوي صفر هذه
+
+117
+00:10:14,520 --> 00:10:20,400
+اللي هي عبارة عن مين؟ هذه تعريف F prime of A وهذه
+
+118
+00:10:20,400 --> 00:10:26,660
+تعريف G prime of A بكون أنا حصلت على اللي هو اللي
+
+119
+00:10:26,660 --> 00:10:33,300
+بدي إياه هذه اللي هي النظرية الأولى في اللي هو هذا ال
+
+120
+00:10:33,300 --> 00:10:37,890
+section اللي يعني بتحذير بقول لك أنه أنت يعني تعرضت
+
+121
+00:10:37,890 --> 00:10:46,230
+عليك الـ limit 17x ولا .. قداش؟ مش مشكلة x زائد 17 أين
+
+122
+00:10:46,230 --> 00:10:51,750
+كانت بنفع x زائد 17 على 2x زائد 3 مثلًا لما x تروح
+
+123
+00:10:51,750 --> 00:10:55,500
+لمين؟ للصفر هو مش ميقوم لما نشوف على طول ونروح
+
+124
+00:10:55,500 --> 00:11:00,960
+نفاضل بنفعش أنت يعني بتلتبس بيصير نفاضل الجهتين
+
+125
+00:11:00,960 --> 00:11:06,340
+بيطلع 1 على 2 لأ هو أنا بقول بتساوي الـ f
+
+126
+00:11:06,340 --> 00:11:10,720
+prime على g prime عند ال zero لما نكون هدي zero و
+
+127
+00:11:10,720 --> 00:11:16,080
+هدي zero لكن لا هدي zero ولا هدي zero إذا بنفعش
+
+128
+00:11:16,260 --> 00:11:21,280
+تحديد هذا نقول بتساوي اللي هو الـ limit من فعش نقول
+
+129
+00:11:21,280 --> 00:11:24,540
+بتساوي الـ limit 1 على 2 على اعتبار فاضلنا
+
+130
+00:11:24,540 --> 00:11:28,800
+ويساوي نصف وهذا الكلام غير صحيح لأن الـ limit زي ما
+
+131
+00:11:28,800 --> 00:11:32,800
+أنتم عارفين لهذا المقدار بالتعويض المباشر هو
+
+132
+00:11:32,800 --> 00:11:42,780
+عبارة عن 17 على 3 هذا كلام سهل نأخذ مثال تطبيقي
+
+133
+00:11:42,780 --> 00:11:48,310
+على النظرية اللي عندنا المثال التطبيقي برضه مثال
+
+134
+00:11:48,310 --> 00:11:56,530
+مباشر عرض علينا الآن example عرض
+
+135
+00:11:56,530 --> 00:12:04,830
+علينا بقول أو جد الـ limit x<sup>2</sup> زائد x على sin 2x
+
+136
+00:12:04,830 --> 00:12:09,530
+لما x تروح لمين؟ للزيرو بالمناسبة، النظرية اللي قبل
+
+137
+00:12:09,530 --> 00:12:13,070
+بشوية حكينا عنها سواء كانت الـ A اللي بتروح لها end
+
+138
+00:12:13,070 --> 00:12:17,150
+point أو نقطة داخلية أو حتى left end point بتظبط
+
+139
+00:12:17,150 --> 00:12:22,150
+عليها النظرية والبرهان similarly ماشي الحال؟ واضح
+
+140
+00:12:22,150 --> 00:12:28,430
+هاه؟ طيب، وإيه السبب؟
+
+141
+00:12:28,430 --> 00:12:34,390
+لأن الاختبار صفر على صفر هذه differentiable وهذه
+
+142
+00:12:34,390 --> 00:12:38,970
+differentiable كل أمورها مية وكويسة ومش هي كمان
+
+143
+00:12:38,970 --> 00:12:43,730
+ولو فضلت هتلاقي اللي هنا لا يساوي صفر إذا على طول
+
+144
+00:12:43,730 --> 00:12:50,410
+بقول 2x عند الـ zero بفاضل جاعد وبعوض يعني هذه
+
+145
+00:12:50,410 --> 00:12:56,950
+سميتها وكأنها F وهذه g f of x وهذه g of x بعوض f
+
+146
+00:12:56,950 --> 00:13:02,190
+prime of zero بعوض هنا g prime of zero الآن f
+
+147
+00:13:02,190 --> 00:13:06,490
+prime of zero 2x زائد 1 في صفر بيصير 2
+
+148
+00:13:06,490 --> 00:13:11,850
+في صفر زائد 1 وتحت اللي هو تفاضلها 2 cosine
+
+149
+00:13:11,850 --> 00:13:16,970
+2x بيصير 2 cosine 2x وعوض بصفر بيصير
+
+150
+00:13:16,970 --> 00:13:25,500
+2 cosine 2 في صفر وهذا يعني بيساوي اللي هو
+
+151
+00:13:25,500 --> 00:13:30,140
+1 على 2 على اعتبار كوصالة Zero بيساوي 1
+
+152
+00:13:30,140 --> 00:13:36,760
+هذه اللي هي تطبيق النظرية اللي عندي نيجي الآن للـ
+
+153
+00:13:36,760 --> 00:13:40,480
+Cauchy Mean Value Theorem الـ Cauchy Mean Value
+
+154
+00:13:40,480 --> 00:13:46,140
+Theorem تعميم للـ Mean Value Theorem اللي احنا 
+
+155
+00:13:46,140 --> 00:13:52,050
+عارفينها بدل ما هو على دالة نحكي عن إيش عن دالتين
+
+156
+00:13:52,050 --> 00:14:00,930
+نشوف إيش اللي بيقوله النظرية بتقول ما يلي لأن
+
+157
+00:14:00,930 --> 00:14:11,690
+theorem عند F و G دالتين من A و B ماخدهم من A و B
+
+158
+00:14:11,690 --> 00:14:17,390
+لعند R جاي لي نفس شروط الـ mean value theorem
+
+159
+00:14:17,390 --> 00:14:22,150
+العادية بدل ما هي على دالة دالتين جاي لي F و G
+
+160
+00:14:22,150 --> 00:14:35,270
+continuous on A و B and differentiable on O B ماشي
+
+161
+00:14:35,270 --> 00:14:42,230
+الحال ومعطيني أيضاً بيقولي الـ G prime لل X لا تساوي
+
+162
+00:14:42,230 --> 00:14:49,110
+صفر لكل X وين موجودة في الـA والـB اللي أنا
+
+163
+00:14:49,110 --> 00:14:59,190
+بيقول له النتيجة then there exist لنتيجة then then
+
+164
+00:14:59,190 --> 00:15:09,250
+هذا كله معطى if this hold then then
+
+165
+00:15:09,250 --> 00:15:18,160
+there exist C Element in A و B such that G أو F 
+
+166
+00:15:18,160 --> 00:15:25,820
+prime of C على G prime of C بيساوي F of B ناقص F of
+
+167
+00:15:25,820 --> 00:15:35,360
+A على G of B ناقص G of A الـ proof ده كلام سهل
+
+168
+00:15:35,360 --> 00:15:38,140
+كمان الـ proof نشوف كده
+
+169
+00:15:41,590 --> 00:15:46,050
+عندي يا جماعة أول إشي هو معطيني إيش مالها g prime
+
+170
+00:15:46,050 --> 00:15:51,650
+of x إيش مالها لا تساوي صفر إذا by rules theorem
+
+171
+00:15:51,650 --> 00:15:58,490
+هيكون g of b لا تساوي مين g of a كيف أذكركم أذكركم
+
+172
+00:15:58,490 --> 00:16:03,950
+كيف الآن إيش rules theorem كانت بتقول g من a و b
+
+173
+00:16:03,950 --> 00:16:14,130
+لعند r continuous on a و b و differentiable on a و
+
+174
+00:16:14,130 --> 00:16:21,270
+b هذا ما أعطينا إياه هو ماشي الحال بيقول لي if g of
+
+175
+00:16:21,270 --> 00:16:28,350
+a بيساوي g of b بيساوي صفر then هو في الواقع زي ما
+
+176
+00:16:28,350 --> 00:16:31,510
+قلنا أن ال role theorem تنفع لو قلنا g of a بيساوي
+
+177
+00:16:31,510 --> 00:16:37,710
+g of b وسكتنا لأنه الشاهد في الموضوع أنه المماس
+
+178
+00:16:37,710 --> 00:16:41,920
+يكون معاه موازي لمحور الصينات أه ولما تكون الـ G of
+
+179
+00:16:41,920 --> 00:16:45,440
+A بيساوي الـ G of B وسكتنا أي قاطع بينهم هيكون
+
+180
+00:16:45,440 --> 00:16:48,520
+عبارة عن موازي لمحور السينات يعني معناته اللي
+
+181
+00:16:48,520 --> 00:16:52,220
+مماثل اللي بيجي هيكون موازي لهذا يعني موازي لمحور
+
+182
+00:16:52,220 --> 00:16:57,740
+السينات طيب then .. then there exists C element in
+
+183
+00:16:57,740 --> 00:17:03,520
+A و B such that G prime of C بيساوي إيش بيساوي صفر
+
+184
+00:17:03,520 --> 00:17:10,560
+الآن هذا معطى مفرغ منه اللي فوق معطى عندي الآن عندي
+
+185
+00:17:10,560 --> 00:17:14,640
+لو كان g of a بيساوي g of b بيعطينا أنه يوجد صفر بين
+
+186
+00:17:14,640 --> 00:17:18,000
+الـ a والـ b بحيث أن g prime of c إشماله لا تساوي
+
+187
+00:17:18,000 --> 00:17:23,260
+صفر لكن هو مفترض لي أن g prime of x لا تساوي صفر لكل
+
+188
+00:17:23,260 --> 00:17:26,540
+x في الـ a والـ b يعني الآن الـ Contraposition هو
+
+189
+00:17:26,540 --> 00:17:30,800
+اللي hold hand يعني بمعنى آخر أنه بما أنه G prime
+
+190
+00:17:30,800 --> 00:17:36,160
+of X لا تساوي 0 لكل X element in A و B هيعطينا هذا
+
+191
+00:17:36,160 --> 00:17:40,940
+نفيه B implies Q تكافئ not Q implies not B وهذا
+
+192
+00:17:40,940 --> 00:17:46,240
+لسه عمله أنا بما أن g prime of x لا يساوي صفر لكل
+
+193
+00:17:46,240 --> 00:17:51,840
+x طبعاً في اللي هو b إذا g of a لا يساوي مين؟ g of
+
+194
+00:17:51,840 --> 00:17:59,900
+b واضح؟ طيب إذا صار عندي الأول حاجة by Rolle's
+
+195
+00:17:59,900 --> 00:18:09,850
+theorem g of a لا يساوي g of b because G prime of X
+
+196
+00:18:09,850 --> 00:18:15,670
+لا يساوي صفر لكل X واللي موجودة في الـA والـB هذه
+
+197
+00:18:15,670 --> 00:18:22,850
+أول نقطة خلصنا هذه بررناها نيجي الآن زي ما عملنا
+
+198
+00:18:22,850 --> 00:18:26,270
+في إثبات الـMean Value Theorem إذا بتتذكروا بدي
+
+199
+00:18:26,270 --> 00:18:29,630
+أعرف دالة أطبق عليها برضه خلي رولز الـTheorem
+
+200
+00:18:29,630 --> 00:18:32,890
+مطبقة أو الـMean Value Theorem مطبقة وأحصل عن
+
+201
+00:18:32,890 --> 00:18:38,260
+نتيجة اللي أنا بديها الآن هي الشكل اللي بديها بدي
+
+202
+00:18:38,260 --> 00:18:45,680
+أخد H of X let أو define H of X بيساوي اللي هو
+
+203
+00:18:45,680 --> 00:18:52,740
+المقدار هذا اللي بديه F of B ناقص F of A على G of
+
+204
+00:18:52,740 --> 00:18:57,910
+B minus G of A بتخلي المقدار هذا اللي هو يتصفر في
+
+205
+00:18:57,910 --> 00:19:00,650
+حالة ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+206
+00:19:00,650 --> 00:19:00,870
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+207
+00:19:00,870 --> 00:19:00,910
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+208
+00:19:00,910 --> 00:19:00,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+209
+00:19:00,970 --> 00:19:01,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+210
+00:19:01,090 --> 00:19:01,850
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+211
+00:19:01,850 --> 00:19:01,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+212
+00:19:01,890 --> 00:19:02,850
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+213
+00:19:02,850 --> 00:19:07,410
+.. ال .. ال .. ال .. ال .. ال .. ال ..
+
+214
+00:19:07,410 --> 00:19:12,650
+ال ..
+
+215
+00:19:12,650 --> 00:19:16,510
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+216
+00:19:16,510 --> 00:19:24,170
+ال .. ال ..
+
+217
+00:19:25,340 --> 00:19:30,660
+H of A بيطلع صفر لأن بدي اللي هو الجزء الثاني اللي
+
+218
+00:19:30,660 --> 00:19:39,320
+هييجيب لي قيمة مين قيمة الـ F ناقص G G of B ناقص G of
+
+219
+00:19:39,320 --> 00:19:44,060
+A أو G of X ناقص H of A عشان نروحهم مع بعض ناقص F
+
+220
+00:19:44,060 --> 00:19:50,880
+of X ناقص F of A الآن ليش عملت هيك عشان أحصل H of
+
+221
+00:19:50,880 --> 00:19:53,180
+A H of A هذه صفر
+
+222
+00:19:55,780 --> 00:20:02,140
+وهدي إيه إيه بيصير صفر H of B إذا صارت عندي H of A
+
+223
+00:20:02,140 --> 00:20:09,360
+بيساوي صفر و H of B حط H of B بيصير هدي بيه هدي
+
+224
+00:20:09,360 --> 00:20:13,780
+بتروح مع هدي بيصير F of B ناقص F of A ناقص F of B
+
+225
+00:20:13,780 --> 00:20:16,800
+ناقص F of A بيروحن مع بعض بيصير H برضه بيساوي صفر
+
+226
+00:20:16,800 --> 00:20:22,300
+إذا هدي أكيد برضه بتساوي H of B الآن
+
+227
+00:20:24,650 --> 00:20:28,050
+عندي هذا الـ differentiable و continuous وهذا الـ
+
+228
+00:20:28,050 --> 00:20:31,210
+differentiable و continuous على ما يناسبها من a و
+
+229
+00:20:31,210 --> 00:20:35,750
+b أو على ال a و b ال a و b اللي هو open
+
+230
+00:20:35,750 --> 00:20:38,770
+differentiable وعلى ال a و b closed continuous
+
+231
+00:20:38,770 --> 00:20:43,350
+تبعاً لها هتطلع أنه ثابت هذا وهدوله ثوابت حيث أن
+
+232
+00:20:43,350 --> 00:20:50,330
+عندي هذا كله على بعض continuous صار عندي H is
+
+233
+00:20:50,330 --> 00:20:59,130
+continuous on A و B و differentiable on A و B open
+
+234
+00:20:59,130 --> 00:21:03,930
+لأنه أنا من رأس الدورة الـ H of X معرفها اللي هي
+
+235
+00:21:03,930 --> 00:21:10,740
+الـ H for every X element in A و B H of X بيساوي كده
+
+236
+00:21:10,740 --> 00:21:15,360
+ماعيش يا بابا صارت الآن أنا حققت كل شروط الـ roles
+
+237
+00:21:15,360 --> 00:21:19,780
+theorem اللي هي الـ H continuous على الـ A و B والـ
+
+238
+00:21:19,780 --> 00:21:23,360
+differential على الـ A و B open أو H of A بيساوي و
+
+239
+00:21:23,360 --> 00:21:27,260
+H of B بيساوي اللي هي صفر إذا حسب roles theorem
+
+240
+00:21:27,260 --> 00:21:31,720
+إذا by roles theorem by أو حتى by main value
+
+241
+00:21:31,720 --> 00:21:38,180
+theorem by roles theorem there exists C element ال
+
+242
+00:21:38,180 --> 00:21:46,290
+A و B such that اتش prime of c إيش هيساوي صفر هذا
+
+243
+00:21:46,290 --> 00:21:52,190
+حسب الـ mean value theorem معايا يا جماعة الآن
+
+244
+00:21:52,190 --> 00:21:57,130
+بتفاضل هذه دلنا أوجد تفاضل هذه تفاضل هذه معليش
+
+245
+00:21:57,130 --> 00:22:04,760
+خلينا نكتبها لإنه ندخل على العالـ slide بدي أفاضل
+
+246
+00:22:04,760 --> 00:22:09,740
+هذه فاضلة H prime of X اللي هي عند الـ C بتساوي
+
+247
+00:22:09,740 --> 00:22:15,580
+صفر صفر بيساوي H prime of C تساوي فاضل هذه وأعوض
+
+248
+00:22:15,580 --> 00:22:20,420
+عن الـ X بصفر لأن هذا ثابت وهذا ثابت ده بيصير صفر
+
+249
+00:22:20,420 --> 00:22:23,420
+تفاضل هذا مع هذا لأن مع هذا بيصير G prime of X
+
+250
+00:22:23,420 --> 00:22:29,220
+مضروب في هذا إذا صار عندي بيساوي F of B ناقص F of A
+
+251
+00:22:30,080 --> 00:22:36,100
+على g of b ناقص g of a مضروب في مين؟ فضلت في g
+
+252
+00:22:36,100 --> 00:22:40,920
+prime of x وأنا بدي أحسبها عند مين؟ عند c، إذا g
+
+253
+00:22:40,920 --> 00:22:45,320
+prime of c ناقص تفاضل هذه، هذا ثابت صفر لأن هذا
+
+254
+00:22:45,320 --> 00:22:50,620
+قداش تفاضلها ناقص f prime عند الـ x وأنا باخدها عند
+
+255
+00:22:50,620 --> 00:22:56,280
+الـ c اللي هي h of c, فـ h prime of c فبيصير ناقص f
+
+256
+00:22:56,280 --> 00:23:02,200
+prime of c الآن بتدنجل هذه على جهة هذه بيصير عندي
+
+257
+00:23:02,200 --> 00:23:10,720
+الآن f prime of c نجلته هان وأجسمها جي برايم of c
+
+258
+00:23:10,720 --> 00:23:15,840
+لأن جي برايم of c لا تساوي صفر بيساوي f of b ناقص f
+
+259
+00:23:15,840 --> 00:23:25,710
+of a على g of b ناقص g of a وهيك بيكون حصلنا على C
+
+260
+00:23:25,710 --> 00:23:31,630
+في الـA وB بحيث أنه هذه تتحقق وهو المطلوب هذه اللي
+
+261
+00:23:31,630 --> 00:23:37,190
+بيسميها Cauchy Mean Value Theorem هذه تعميم لمين؟
+
+262
+00:23:37,190 --> 00:23:41,590
+تعميم اللي هو الـMean Value Theorem بس خد اللي هو
+
+263
+00:23:41,590 --> 00:23:47,230
+G of X بتساوي X G of X بيساوي X و G of X بيساوي X
+
+264
+00:23:47,230 --> 00:23:49,190
+اللي هي تحقق كل الشروط ال differential
+
+265
+00:23:49,190 --> 00:23:53,470
+بالـ continuous والاخره ماشي الحال بيصير عندي
+
+266
+00:23:53,470 --> 00:23:58,110
+اللي هي في حالة G of X بتساوي X معايا يا شباب
+
+267
+00:23:58,110 --> 00:24:02,450
+بيصير G of BB و G of AA وهذه اللي هي G prime اللي
+
+268
+00:24:02,450 --> 00:24:05,510
+هي 1 فبيصير F prime of C بيساوي F of B ناقص F of
+
+269
+00:24:05,510 --> 00:24:10,470
+A على B minus A إذا F
+
+270
+00:24:15,650 --> 00:24:21,210
+أمسح البرهان بس الآن
+
+271
+00:24:21,210 --> 00:24:31,930
+الـ note اللي عندي الـ note كما يلي note if
+
+272
+00:24:31,930 --> 00:24:42,820
+g of x بيساوي x then we get from الـ theorem هذه
+
+273
+00:24:42,820 --> 00:24:51,140
+اللي بقول عليها كوشي mean value theorem we get the
+
+274
+00:24:51,140 --> 00:24:59,500
+mean value theorem كيف الـ g of x بيساوي x معناه
+
+275
+00:24:59,500 --> 00:25:04,160
+انتصار الـ g of b بيساوي b و g of a بيصير a يعني
+
+276
+00:25:04,160 --> 00:25:10,530
+هذا بيصير a, b وهذه بيصير A و G prime of C اللي هي
+
+277
+00:25:10,530 --> 00:25:14,070
+بيصير 1 فبيصير F prime of C بيساوي F of B ناقص F
+
+278
+00:25:14,070 --> 00:25:20,590
+of A على B minus A وهذه هي الـ main value theorem
+
+279
+00:25:21,280 --> 00:25:24,720
+واضح .. اه .. طيب اطلع للي بعده لأن احنا اللي
+
+280
+00:25:24,720 --> 00:25:26,820
+بيهمنا هذا الكوشي بين الـ value theorem احنا 
+
+281
+00:25:26,820 --> 00:25:31,980
+حكيناها أصلاً عشان خاطر أنه احنا نحكي عن اللي هو
+
+282
+00:25:31,980 --> 00:25:37,960
+L'Hôpital's rule  ال form اللي عنده اللي أمامي دكتور
+
+283
+00:25:37,960 --> 00:25:41,860
+جديد في السؤال في غيرك مفهوم إن أنا جسمت على X
+
+284
+00:25:41,860 --> 00:25:46,640
+minus A على E minus A الطرفين أصلاً أنت بتصير F أو
+
+285
+00:25:46,640 --> 00:25:48,580
+P نقص F أو A على B minus A
+
+286
+00:26:01,110 --> 00:26:06,630
+البرهان مش صعب اللي قلناه، كتير سهل، ما هو الـ C
+
+287
+00:26:06,630 --> 00:26:09,970
+اللي لاجيناها في الحالة الأولى، هل هي الثانية؟ إذا
+
+288
+00:26:09,970 --> 00:26:13,390
+كنت تتعامل بـ Mean Value Theorem أنت؟ مش بدك تطبّق
+
+289
+00:26:13,390 --> 00:26:16,170
+الـ Mean Value Theorem بدك تطبّق الـ Mean Value Theorem لأن
+
+290
+00:26:16,170 --> 00:26:21,090
+there exists c1 such that f prime of c1 بيساوي f of
+
+291
+00:26:21,090 --> 00:26:24,030
+b minus f of a على b minus a ما فيش فيها مشكلة
+
+292
+00:26:24,030 --> 00:26:27,950
+there exists c2 such that g prime of c2 بيساوي g of
+
+293
+00:26:27,950 --> 00:26:32,550
+b نقص g of a على b minus a الـ c1 هذه مش شرط يكون
+
+294
+00:26:32,550 --> 00:26:39,630
+هي نفسها الـ c2 أو احنا لازم نثبتها هي نفسها اه ف .. و
+
+295
+00:26:39,630 --> 00:26:44,780
+بعدين البرهان سهل ماشي .. نحن الواحد يفكر 100% ..
+
+296
+00:26:44,780 --> 00:26:50,780
+جميل لكن .. يعني .. بس أنه احنا .. الـ C هذه مش
+
+297
+00:26:50,780 --> 00:26:53,700
+ضمنياً تساوي الـ C2 و بدنا نثبت أنها تساويها .. إذا
+
+298
+00:26:53,700 --> 00:26:59,920
+كانت بتساويها طيب .. نيجي لها اللي هي النظرية اللي
+
+299
+00:26:59,920 --> 00:27:05,840
+بعيدها النظرية اللي بعيدها .. أنا مرضيتش أمسح اللوح
+
+300
+00:27:05,840 --> 00:27:08,800
+أساسي منقررها من الـ theory من الأولى
+
+301
+00:27:11,650 --> 00:27:30,050
+نشوف نطلع إيش اللي بتقوله هذه النظرية نفس
+
+302
+00:27:30,050 --> 00:27:35,710
+اللي هنا F و G differentiable on A و B معايا أه؟
+
+303
+00:27:35,710 --> 00:27:42,150
+الآن such that G prime of X ده يساوي صفر G prime of
+
+304
+00:27:42,150 --> 00:27:47,970
+X لا يساوي صفر أنا مش موجودة For all X elements in
+
+305
+00:27:47,970 --> 00:27:55,070
+A و B ونفترض أن limit F of X limit F of X لما X
+
+306
+00:27:55,070 --> 00:27:59,570
+تروح إلى الـ A من اليمين موجودة و بتساوي إيش؟ صفر
+
+307
+00:27:59,570 --> 00:28:02,490
+و limit G of X لما X تروح إلى الـ A من اليمين
+
+308
+00:28:02,490 --> 00:28:09,580
+بتساوي صفر إذا صار limit الحاصل القسمة لأن بيساوي f
+
+309
+00:28:09,580 --> 00:28:14,300
+prime of a على g prime of a بيساوي limit f of x
+
+310
+00:28:14,300 --> 00:28:19,580
+على g of x لما x تروح لل a باليمين يعني وكأنه هنا
+
+311
+00:28:19,580 --> 00:28:25,460
+حول الحديث كله من افتراض أنه عند النقطة اللي هي F'
+
+312
+00:28:25,780 --> 00:28:31,240
+و G' موجودة ولا تساوي صفر وحول الحديث من إن التعويض
+
+313
+00:28:31,240 --> 00:28:35,280
+المباشر أن F of A و G of A بتساوي صفر لـ limit لـ ..
+
+314
+00:28:35,280 --> 00:28:39,220
+limit لل Function لما X تروح لـ A صفر و limit لل
+
+315
+00:28:39,220 --> 00:28:42,040
+Function لما .. اللي .. اللي هو ال X .. ال X بتروح
+
+316
+00:28:42,040 --> 00:28:48,920
+لسفر .. لل A بتساوي صفر وحول أيضاً طلب جي برايم نفسه
+
+317
+00:28:48,920 --> 00:28:54,680
+على كل الفترة اللي تكون لا تساوي صفر مش عند النقطة
+
+318
+00:28:54,680 --> 00:29:03,060
+بس وقال لك إنه حتى اللي هو النتيجة هتطلع بـ limit
+
+319
+00:29:03,060 --> 00:29:07,940
+مش هتطلع بـ F prime of A على G prime of A يعني اللي
+
+320
+00:29:07,940 --> 00:29:14,980
+بقصده إنه الآن طور هذه الحديث هنا إنه لما تُعرض
+
+321
+00:29:14,980 --> 00:29:21,580
+علينا limit F of X على G of X لما X تروح للـ A من
+
+322
+00:29:21,580 --> 00:29:24,360
+اليمين أو إن كانت حتى لو في الـ interior point الـ X
+
+323
+00:29:24,360 --> 00:29:31,300
+بتروح للـ A برضه صحيحة الآن بعدي عندي إذا لجيت limit
+
+324
+00:29:31,300 --> 00:29:34,480
+الأولى، اللي أنا بحكي عن limit سيرة مش عن تعويض
+
+325
+00:29:34,480 --> 00:29:38,340
+مباشر زي اللي جابله، الآن limit f of x لما x تروح
+
+326
+00:29:38,340 --> 00:29:41,780
+لـ a من اليمين و limit f of x لما x تروح لـ a من
+
+327
+00:29:41,780 --> 00:29:46,700
+اليمين، إذا هذه موجودة و هذه موجودة و طلع عندي 0
+
+328
+00:29:46,700 --> 00:29:51,060
+على 0، يعني طلع ال limit عبارة عن 0 على 0، هنا بدو
+
+329
+00:29:51,060 --> 00:29:57,200
+يحدث العلاج، إذا كانت الآن الـ limit اللي طلعت عندي
+
+330
+00:29:57,200 --> 00:30:02,000
+F prime of X على G prime of X لما X تروح للـ A من
+
+331
+00:30:02,000 --> 00:30:06,780
+اليمين إذا طلعت عبارة عن قيمة خلاص ارتاح هذه اللي
+
+332
+00:30:06,780 --> 00:30:12,450
+طلعت هي مين فهمت الـ limit ماشي الحال لو طلعت كمان
+
+333
+00:30:12,450 --> 00:30:18,230
+مرة zero على zero اللي هو و بتحقق كل الشروط اللي
+
+334
+00:30:18,230 --> 00:30:21,950
+.. اللي في الأول برضه بأعمل كمان مرة بفاضل لما
+
+335
+00:30:21,950 --> 00:30:26,430
+بتطلع لكن لو طلعت ال limit هذه does not exist بسكت
+
+336
+00:30:26,430 --> 00:30:31,130
+و بجاوبي عمش .. بدنا ندور على طريقة أخرى واضح؟ الآن
+
+337
+00:30:31,130 --> 00:30:34,990
+لو طلعت هذه infinity أو سالب infinity هذه آسف
+
+338
+00:30:34,990 --> 00:30:38,900
+infinity أو سالب infinity برضه إن النظرية صحيحة اللي
+
+339
+00:30:38,900 --> 00:30:45,290
+هو هدمين الجزء الثاني من النظرية if limit f prime
+
+340
+00:30:45,290 --> 00:30:48,450
+على g prime بيساوي L بيساوي infinity أو سالب
+
+341
+00:30:48,450 --> 00:30:52,190
+infinity هتطلع ال limit على طول لل F على G اللي
+
+342
+00:30:52,190 --> 00:30:56,350
+ببحث عنها إيش هتساوي برضه ال infinity أو سالب
+
+343
+00:30:56,350 --> 00:31:00,670
+infinity حسب القيمة هذه إذا أي إن كانت اللي هي ال
+
+344
+00:31:00,670 --> 00:31:05,190
+limit مادامَ exist سواء ال existence عبارة عن
+
+345
+00:31:05,190 --> 00:31:09,210
+element in R أو اللي هو عبارة عن ناقص infinity أو
+
+346
+00:31:09,210 --> 00:31:18,100
+سالب infinity فإن النظرية صحيحة واضح؟ أي سؤال؟ طيب
+
+347
+00:31:18,100 --> 00:31:27,200
+صلّى على النبي عليه الصلاة والسلام خلينا
+
+348
+00:31:27,200 --> 00:31:31,360
+نيجي للنظرية ونبرهنها
+
+349
+00:31:45,860 --> 00:31:50,880
+Theorem كده ش؟ نزلي بس النص يا محمد اللي هي theorem
+
+350
+00:31:50,880 --> 00:31:59,580
+6 3 3 إيش النظرية بتقول؟ بتقول ما يعني عندي طبعاً
+
+351
+00:31:59,580 --> 00:32:04,540
+ماخد الـ a أصغر من الـ b strictly و a ممكن حتى تأخد سالب
+
+352
+00:32:04,540 --> 00:32:07,580
+infinity والـ b تأخد infinity يعني ممكن تكون
+
+353
+00:32:07,580 --> 00:32:11,040
+الفترة من a .. الفترة كلها a ممكن تكون أي فترة sub
+
+354
+00:32:11,040 --> 00:32:16,710
+interval من اللي هو 100 من الـ real numbers فرضنا f
+
+355
+00:32:16,710 --> 00:32:26,190
+و g من a و b لعند اللي هو r وإذا كانت a infinity
+
+356
+00:32:26,190 --> 00:32:30,130
+أو سالب infinity آسف إذا كانت a سالب infinity أو b
+
+357
+00:32:30,130 --> 00:32:33,610
+infinity بتكون o من زمن بعرفي لأن عشان اللي هو
+
+358
+00:32:33,610 --> 00:32:36,890
+ناخدها من real number لـ real number لذا نفترض f و
+
+359
+00:32:36,890 --> 00:32:46,080
+g من a و b لعند الـ R ونفترض إن f و g differentiable
+
+360
+00:32:46,080 --> 00:32:54,620
+on a و b ماشي الحال و differentiable on a و b الآن
+
+361
+00:32:54,620 --> 00:32:57,900
+مش لازم يكونوا continue و تعندى و كده لأنه أنا هدخل
+
+362
+00:32:57,900 --> 00:33:02,240
+لجوه شغل هيكون لجوه هل جيت بتشوف إيش معنى لجوه
+
+363
+00:33:02,240 --> 00:33:08,620
+such that g prime of x g prime of x لا تساوي صفر
+
+364
+00:33:08,620 --> 00:33:17,430
+لكل x وين موجودة في الفترة a و b الآن بقول لي إذا
+
+365
+00:33:17,430 --> 00:33:27,170
+كانت limit limit اللي هي f of x لما x تروح للـ a من
+
+366
+00:33:27,170 --> 00:33:32,190
+اليمين بيساوي limit g of x لما x تروح للـ a من
+
+367
+00:33:32,190 --> 00:33:40,980
+اليمين بيساوي صفر هذا كله موضوع الآن بدو يوصل بدي
+
+368
+00:33:40,980 --> 00:33:46,200
+أقولك كيف أنا بدي أحصل على نتيجة limit f of x على
+
+369
+00:33:46,200 --> 00:33:51,060
+g of x لما x تروح للـ a من اليمين بقولك إذا كان أنت
+
+370
+00:33:51,060 --> 00:33:59,180
+if لأن إيه if limit f prime of x على g prime of x
+
+371
+00:33:59,180 --> 00:34:06,520
+لما x تروح للـ a من اليمين بيساوي L then أتجرا أقول
+
+372
+00:34:06,520 --> 00:34:12,020
+فاش عندي مشكلة limit f of x اللي ببحث عنها على g
+
+373
+00:34:12,020 --> 00:34:17,360
+of x لما x تروح للإيه من اليمين برضه إيش هيساوي؟
+
+374
+00:34:17,360 --> 00:34:29,740
+هيساوي ال .. من يحياتي هذه هيكون صحيحة طيب خلينا
+
+375
+00:34:29,740 --> 00:34:38,330
+الآن اللي هو البرهان شوف عليها واضح النظرية شرحناها
+
+376
+00:34:38,330 --> 00:34:45,050
+يعني نص النظرية شرحناها بشكل كامل الآن since limit
+
+377
+00:34:45,050 --> 00:34:51,730
+F prime of X على G prime of X لما X تروح لـ A من
+
+378
+00:34:51,730 --> 00:35:00,690
+وين؟ من اليمين هيعندي الفترة A و B حتى لو كانت
+
+379
+00:35:00,690 --> 00:35:05,580
+منتهية وين ما بدها، هي حاضرة الآن عندي X تذهب إلى
+
+380
+00:35:05,580 --> 00:35:09,760
+اليمين اليمين فبدي من الجهة دي طبيعي من اليمين بيساوي
+
+381
+00:35:09,760 --> 00:35:15,800
+الـ then for every epsilon أكبر من صفر لأي epsilon
+
+382
+00:35:15,800 --> 00:35:20,440
+أكبر من صفر أي epsilon there exists delta أكبر من
+
+383
+00:35:20,440 --> 00:35:24,660
+صفر such that لأن X تذهب إلى الامن وين من اليمين
+
+384
+00:35:24,660 --> 00:35:27,460
+إذن الجوار اللي حوالها هو عبارة عن جوار من A لعند
+
+385
+00:35:27,460 --> 00:35:32,340
+مين الـ A زي الـ Delta لعند الـ A زي الـ Delta صح ولا لأ
+
+386
+00:35:32,340 --> 00:35:36,260
+إذن لكل ما دامت الـ limit هي دي بيساوي L، ده لكل
+
+387
+00:35:36,260 --> 00:35:41,480
+إبسلون بقدر ألاقي Delta بحيث أن X element في A و
+
+388
+00:35:41,480 --> 00:35:46,400
+A زائد Delta ف X element في A و A زائد Delta، then
+
+389
+00:35:46,400 --> 00:35:52,180
+قطعاً .. then قطعاً هيكون عندي F prime of X على G
+
+390
+00:35:52,180 --> 00:35:58,030
+prime of X نقص L، ذويكون أصغر من 100 من إبسلون هذا
+
+391
+00:35:58,030 --> 00:36:02,370
+تعريف الـ limit للـ F prime of X على G prime of X
+
+392
+00:36:02,370 --> 00:36:06,510
+بسهولة لما X تروح لمن؟ للـ A من اليمين هو كاتبها
+
+393
+00:36:06,510 --> 00:36:11,110
+هذه A زائد Delta C في الكتاب يعني مسميها C يعني
+
+394
+00:36:11,110 --> 00:36:16,090
+مسمي إنه لكل X there exists C بحيث إنه لكل X في ال
+
+395
+00:36:16,090 --> 00:36:20,650
+A اللي عند الـ A للـ C بكون هذا الكلام متحقق أنا
+
+396
+00:36:20,650 --> 00:36:23,510
+حبيت أكتب لك اللي هو التعريف الدارجي اللي أنت ده
+
+397
+00:36:23,510 --> 00:36:27,700
+كسله كمان في ال .. في الحل واضح لحد تلاتة
+
+398
+00:36:38,080 --> 00:36:42,520
+ماشي الحال بس هي ك .. هذه .. و هذه ك صح و هذه ك صح
+
+399
+00:36:42,520 --> 00:36:47,040
+و هذه ك صح اللي كاتبها صح بس هذه للطالب أسهله في
+
+400
+00:36:47,040 --> 00:36:49,960
+ال .. في ال .. لإنه .. خلّيني أقول هذا اللي دارج
+
+401
+00:36:49,960 --> 00:36:54,640
+عليه في ال .. في .. اللي هو التعبير عن ال .. لكل x
+
+402
+00:36:54,640 --> 00:36:58,940
+في الجوار الجوار هذا سهل و .. و .. و .. وعبّرنا
+
+403
+00:36:58,940 --> 00:36:59,200
+عنه
+
+404
+00:37:02,810 --> 00:37:07,630
+-A هو أكبر من صفر وأصغر من دلتة برضه هيك صح صحيح
+
+405
+00:37:07,630 --> 00:37:11,910
+نفس الشيء طيب
+
+406
+00:37:11,910 --> 00:37:15,050
+الآن
+
+407
+00:37:15,050 --> 00:37:23,590
+هذا الكلام i.e. أو بمعنى آخر that is هيكون هذا اللي
+
+408
+00:37:23,590 --> 00:37:31,230
+هو F prime of X ناقص G prime of X أصغر ناقص L
+
+409
+00:37:31,230 --> 00:37:37,150
+بتغيرها عشان أصغر من Y وأكبر من 200 من سالب Y شيل
+
+410
+00:37:37,150 --> 00:37:43,470
+الـ L هذه بصير اللي هو أصغر من L زائد Y وأكبر من L
+
+411
+00:37:43,470 --> 00:37:49,430
+ناقص Y هذا متحقق لمين؟ لكل X و N موجودة في الفترة
+
+412
+00:37:49,430 --> 00:37:53,550
+من A لعند A زائد Delta و اكتب لي هذا سميلي
+
+413
+00:37:56,530 --> 00:38:03,990
+واحد ماشي الحال سميليه واحد الآن عندي اللي هو شروط
+
+414
+00:38:03,990 --> 00:38:06,850
+الـ Mean Value Theorem الكوشي Mean Value Theorem
+
+415
+00:38:06,850 --> 00:38:10,130
+اللي قبل بشوية الـ F والـ G differentiable على الـ A
+
+416
+00:38:10,130 --> 00:38:16,170
+و الـ B اه و الـ G prime of X لا تساوي صفر و ال ..
+
+417
+00:38:16,170 --> 00:38:22,490
+أو .. إيش كمان كلّه متحقق بس خلينا نقول
+
+418
+00:38:26,140 --> 00:38:31,240
+بدي الآن وين أطبّق الـ Mean Value Theorem بدي
+
+419
+00:38:31,240 --> 00:38:37,720
+أطبّقها على اللي هو اللي جوا عندي لداخل الـ Mean
+
+420
+00:38:37,720 --> 00:38:44,560
+لداخل الفترة هذه عشان أشتغل وين اللي بتطلع عندي 
+
+421
+00:38:44,560 --> 00:38:48,490
+أضمن تكون هنا عشان القيمة اللي هتطلع عندي اللي
+
+422
+00:38:48,490 --> 00:38:53,170
+بتحققها تكون بتحقق اللي بتطلع عندي و بتحققها دي
+
+423
+00:38:53,170 --> 00:38:57,730
+عشان هي كصح اللي أعوض مكان بعض ماشي الحال خد الآن
+
+424
+00:38:57,730 --> 00:39:07,030
+لجد تفهموا إيش اللي بقصدهم خد الآن four alpha أكبر
+
+425
+00:39:07,030 --> 00:39:16,040
+من a و أصغر من beta و أصغر من a زائد delta يعني أنا
+
+426
+00:39:16,040 --> 00:39:20,060
+غرضي أن أنا أشتغل .. أن أنا رايح .. بدي أنا limit
+
+427
+00:39:20,060 --> 00:39:24,580
+أصلًا و ال limit بديها لما أروح لمين؟ لل A يعني بدي
+
+428
+00:39:24,580 --> 00:39:29,760
+في الجوار اللي حوالين ال A و جاي ناحيتها هذا اللي
+
+429
+00:39:29,760 --> 00:39:31,740
+بهم، اللي ما أناش سغاداش، بيكون التصرف مافيش ..
+
+430
+00:39:31,740 --> 00:39:36,980
+مافيش عنده مشكلة الآن هي ال alpha أخدتها هنا و هي
+
+431
+00:39:36,980 --> 00:39:37,420
+ال beta
+
+432
+00:39:41,900 --> 00:39:44,540
+أصغر من Alpha أصغر من Beta أصغر من a زي الـ
+
+433
+00:39:44,540 --> 00:39:54,060
+Delta؟ By Cauchy Mean Value Theorem there exists
+
+434
+00:39:54,060 --> 00:40:03,220
+سموها هو نسميها U Element in mean in Alpha و Beta
+
+435
+00:40:03,220 --> 00:40:10,110
+و ال Alpha و Beta جزء من هذول، إذا اللي بنطبق
+
+436
+00:40:10,110 --> 00:40:14,750
+على هذه اللي بنطبق على .. اللي بنطبق على هذه بنطبق
+
+437
+00:40:14,750 --> 00:40:19,790
+على هذه، مظبوط؟ يعني هذه ال U اللي لجيتها بنطبق
+
+438
+00:40:19,790 --> 00:40:22,210
+عليها الكلام هذا اللي هو F prime of U على D prime
+
+439
+00:40:22,210 --> 00:40:27,510
+of U بين هذه و بين هذه واضح، و هذا الكلام مهم طيب،
+
+440
+00:40:27,510 --> 00:40:34,640
+there exists U such that F prime of U على g prime
+
+441
+00:40:34,640 --> 00:40:39,240
+of u بيساوي إيش يا جماعة بيساوي f of b أو beta
+
+442
+00:40:39,240 --> 00:40:50,260
+ناقص f of alpha على g of beta ناقص g of alpha واضح
+
+443
+00:40:50,260 --> 00:41:00,020
+آه؟ هذا سمولي يمين هو اتنين الآن عند هذه اللي
+
+444
+00:41:00,020 --> 00:41:05,260
+لجيتها هنا اللي بتحقق هذه هي وين موجودة من ضمن
+
+445
+00:41:05,260 --> 00:41:12,980
+النقاط اللي بتحقق هذه لكل X هنا وهذه جزء منها إذا
+
+446
+00:41:12,980 --> 00:41:18,100
+F prime of X of U على G prime of U بين ال L ناقص
+
+447
+00:41:18,100 --> 00:41:22,020
+إبسلون و ال L زائد مين؟ إبسلون وفي نفس الوقت F
+
+448
+00:41:22,020 --> 00:41:25,860
+prime of U هذه اللي لقيتها G prime of U بيساوي هذا
+
+449
+00:41:25,860 --> 00:41:29,840
+إذا from واحد
+
+450
+00:41:30,390 --> 00:41:40,070
+و اتنين we get اللي هو F prime of U على G prime of
+
+451
+00:41:40,070 --> 00:41:47,610
+U بستبدلها و بيصير F of Beta ناقص F of Alpha على G
+
+452
+00:41:47,610 --> 00:41:54,070
+of Beta ناقص G of Alpha بحيث أنه هذا يكون أكبر من
+
+453
+00:41:54,070 --> 00:42:03,630
+L ناقص Y و أصغر من 100 من L زائد Y لأن هذا صحيح لأي
+
+454
+00:42:03,630 --> 00:42:09,750
+Alpha و Beta بشكلهم اللي موجود Alpha أصغر من Beta
+
+455
+00:42:09,750 --> 00:42:15,570
+و Alpha بين ال A و بين مين؟ ال A زائد دلتا إذا
+
+456
+00:42:15,570 --> 00:42:22,150
+الألفة هذه حرة في كل المنطقة هذه بنفع يعني الألفة
+
+457
+00:42:22,150 --> 00:42:26,530
+هذه لو بدها تروح لل A حد مش بمنعها الألفة تروح لها
+
+458
+00:42:26,530 --> 00:42:31,060
+لأنه صحيح على كل هذه الألفات اللي لجيتها هذه الآن
+
+459
+00:42:31,060 --> 00:42:40,340
+let alpha goes to mean to a من وين؟ من اليمين
+
+460
+00:42:40,340 --> 00:42:45,720
+ماشي؟ مقدر و لن تؤثر لأ على ال beta ولا عليها زي
+
+461
+00:42:45,720 --> 00:42:50,980
+الدلتية الحرة بتروح لهذه وهذه زي ما هي يعني تصرف
+
+462
+00:42:50,980 --> 00:42:58,540
+alpha يروح لأي a beta بالنسبة لها ثابت ولا تتأثر هذا
+
+463
+00:42:58,540 --> 00:43:03,500
+الكلام مهم إذا صار عندي الآن لما Alpha تروح لأ من
+
+464
+00:43:03,500 --> 00:43:10,700
+اليمين ال up of Alpha بيصير عندي limit ال up of
+
+465
+00:43:10,700 --> 00:43:17,780
+Alpha لما ال Alpha تروح لأ من اليمين بيساوي هو في
+
+466
+00:43:17,780 --> 00:43:21,980
+الواقع limitها limitها هذه Alpha اللي كنا نسميها X
+
+467
+00:43:21,980 --> 00:43:23,980
+مثلًا ال up of X سمى X تروح لأ من اليمين لأ من
+
+468
+00:43:23,980 --> 00:43:29,480
+اليمين الآن ال Alpha راحت لليمين اليمين limitها
+
+469
+00:43:29,480 --> 00:43:35,020
+أنا ما عطيني إيش بيساوي؟ بيساوي صفر، ما عطيني
+
+470
+00:43:35,020 --> 00:43:37,080
+limit f of x عندما x تروح لليمين اليمين إيش
+
+471
+00:43:37,080 --> 00:43:40,540
+بيساوي؟ صفر، أنا سميتها إيش أنا؟ Alpha هذه اللي
+
+472
+00:43:40,540 --> 00:43:46,660
+بتتحرك، إذا هذا ال limit إيش هيساوي؟ بنفس السبب أو
+
+473
+00:43:46,660 --> 00:43:52,940
+لنفس السبب limitG of Alpha لما Alpha تروح لل A من
+
+474
+00:43:52,940 --> 00:43:59,680
+اليمين برضه مش هيساوي صفر إذا الآن برجع لهذه برجع
+
+475
+00:43:59,680 --> 00:44:09,060
+لهذه بيصير عندي الآن اللي حصلته كله على بعضه لكل ي
+
+476
+00:44:09,060 --> 00:44:17,130
+أكبر من صفر ماشي الحال ل gate Delta بحيث أنه ال Alpha
+
+477
+00:44:17,130 --> 00:44:20,050
+و beta بشكل هذا أكبر من a و أقل زي ال Delta
+
+478
+00:44:20,050 --> 00:44:24,570
+سيبك من ال L Alpha خلاص رديتها أنا beta أكبر من a و
+
+479
+00:44:24,570 --> 00:44:29,170
+أصغر من a زي ال Delta طلع عندي هذا المقدار أصغر
+
+480
+00:44:29,170 --> 00:44:33,170
+من L زي ال إبسلون و أكبر من L ناقص إبسلون ماشي؟
+
+481
+00:44:33,170 --> 00:44:37,300
+الآن رديت و أخدته من ال limit الآن بدي أخد ال
+
+482
+00:44:37,300 --> 00:44:40,940
+limit لهذا المقدار كله لما ال alpha تروح لمين؟ لل
+
+483
+00:44:40,940 --> 00:44:45,240
+a من اليمين الآن لما أخد ال limit لهذا زي ما قلت
+
+484
+00:44:45,240 --> 00:44:48,500
+ال beta مالهاش علاقة بال alpha ال beta ثابتة
+
+485
+00:44:48,500 --> 00:44:50,920
+بالنسبة لل alpha فال alpha تروح لل a من اليمين زي
+
+486
+00:44:50,920 --> 00:44:55,100
+ما بدها لن تتأثر beta فبيصير limit اللي فوق على
+
+487
+00:44:55,100 --> 00:44:59,520
+limit اللي تحت هذا ثابت و هذا ثابت و هذا limit هو
+
+488
+00:44:59,520 --> 00:45:04,300
+اللي هو صفر و هذا limit هو صفر و هذول أعداد إذا
+
+489
+00:45:04,300 --> 00:45:11,220
+أصار عندي الآن عندي take the limit بيصير عندي L
+
+490
+00:45:11,220 --> 00:45:18,100
+ناقص Epsilon أصغر أو يساوي اللي هو F of Beta على G
+
+491
+00:45:18,100 --> 00:45:23,660
+of Beta أصغر من L زائد Epsilon من وين حصلته هذا؟
+
+492
+00:45:23,660 --> 00:45:29,160
+when I take the limit of this inequality as Alpha
+
+493
+00:45:29,160 --> 00:45:37,460
+goes to A from right واضح؟ هذا حصلت عليه هذا عرفت
+
+494
+00:45:37,460 --> 00:45:40,600
+ثانوية هذا حصلت عليه من وين أن أخدت ال limit
+
+495
+00:45:40,600 --> 00:45:44,660
+للجهات التلاتة as Alpha تروح لل A من اليمين
+
+496
+00:45:44,660 --> 00:45:48,780
+واستخدمت هذه الحقيقة أن هذا صفر و هذا صفر صار هذا
+
+497
+00:45:48,780 --> 00:45:53,360
+المقدار و هذا المقدار بين هذا و هذا إذن اللي حصلت
+
+498
+00:45:53,360 --> 00:46:02,380
+عليه الآن هو ما يليه لكل epsilon أكبر من صفر لجهة
+
+499
+00:46:02,380 --> 00:46:07,610
+Delta أكبر من الصفر such that هذه beta كانت
+
+500
+00:46:07,610 --> 00:46:14,650
+arbitrary بين a و بين مين اللي هو such that if
+
+501
+00:46:14,650 --> 00:46:26,150
+beta بين ال a و ال a زائد delta we have then إيش
+
+502
+00:46:26,150 --> 00:46:31,990
+اللي حصلنا عليه اللي هو f of beta على f of alpha
+
+503
+00:46:33,100 --> 00:46:38,720
+صارت أصغر أو يساوي L زايد إبسلون و أكبر أو يساوي
+
+504
+00:46:38,720 --> 00:46:47,620
+إبسلون ناقص L أو بمعنى آخر IE F of Beta على F of
+
+505
+00:46:47,620 --> 00:46:53,340
+Alpha ناقص L absolute value أصغر أو يساوي إبسلون
+
+506
+00:46:53,340 --> 00:47:02,280
+و هذا هذا this means that hence limit
+
+507
+00:47:03,350 --> 00:47:13,590
+f of beta على f of alpha as اللي هو limit of فدي g
+
+508
+00:47:13,590 --> 00:47:23,970
+مالكم فدي g بساكتين g of beta فدي g of beta limit
+
+509
+00:47:23,970 --> 00:47:28,270
+of beta على g of beta مظبوط؟
+
+510
+00:47:29,140 --> 00:47:33,140
+as اللي هو طبعًا الآن بيت إيه شمالها لكل بيتها
+
+511
+00:47:33,140 --> 00:47:37,620
+يعني بيتها وين راحت؟ على اليمين اليمين هان لكل بيتها
+
+512
+00:47:37,620 --> 00:47:49,320
+وين؟ في الجوار هذا الآن بيساوي ال هو المطلوب مش
+
+513
+00:47:49,320 --> 00:47:53,440
+عاجبك بيتك تبقى تكسر أي سؤال
+
+514
+00:47:56,950 --> 00:48:01,030
+بتصور هيك المظهرية واضحة تمامًا هي تلت خطوات في
+
+515
+00:48:01,030 --> 00:48:05,530
+الواقع تلت خطوات مين هما؟ هو طبعًا في الكتاب يعني لو
+
+516
+00:48:05,530 --> 00:48:12,190
+لاحظت هتلاقي يعني أنه بدها بس ترتيب الآن لأ بدها
+
+517
+00:48:12,190 --> 00:48:19,150
+ترتيب طلع عليها الآن عندك هذا الآن استخدمت أنا هذا
+
+518
+00:48:19,150 --> 00:48:23,370
+في الأول بالعمدان واستخدم هذا استخدمت هذا عشان
+
+519
+00:48:23,370 --> 00:48:27,150
+أقول لك هذه ال inequality صحيح على كل المنطقة هذه لأن
+
+520
+00:48:27,150 --> 00:48:33,170
+لجيت U لأن اللي لجيتها U أنا لجيتها لجيت ال U و
+
+521
+00:48:33,170 --> 00:48:36,070
+أخدت الفترة هنا عشان أقول لك ال U اللي لجيتها في
+
+522
+00:48:36,070 --> 00:48:41,570
+داخل الفترة هذه الحديث هذه جايب عن هذه بعمل
+
+523
+00:48:41,570 --> 00:48:45,750
+confusion عند الطالب لأن اللي لجيتها من قال إنه
+
+524
+00:48:45,750 --> 00:48:49,970
+هنا موجودة ما هي اللي لجيتها هنا وين لجيتها؟ بين A
+
+525
+00:48:49,970 --> 00:48:56,050
+و B بين A و B أو بين Alpha و Beta يعني بدها يصير
+
+526
+00:48:56,050 --> 00:49:05,880
+عندي اللي هي ال F prime ال F prime عندي ال limit
+
+527
+00:49:05,880 --> 00:49:11,140
+.. ال limit لل .. خليني أكتبها يا شيخ ليش؟ ها ..
+
+528
+00:49:11,140 --> 00:49:16,120
+هذا بيساوي ال .. اللي هي إيش؟ ما لأ بأخذ ال
+
+529
+00:49:16,120 --> 00:49:20,740
+infinity بطلع حد برضه إيش؟ infinity يعني الحالة
+
+530
+00:49:20,740 --> 00:49:26,250
+التانية اللي هي F بساوة infinity هيكون ال limit لل
+
+531
+00:49:26,250 --> 00:49:33,570
+F على G شمالها بيساوي infinity الآن بدها يصير عنده
+
+532
+00:49:33,570 --> 00:49:38,750
+بدل ما أقول limit F prime على G prime بيساوي L بدها
+
+533
+00:49:38,750 --> 00:49:43,310
+يصير أشهر بيساوي infinity كيف بنعبر على إنه الرقم
+
+534
+00:49:43,310 --> 00:49:47,190
+يروح لما لنهاية ال limit أنه ناخد اللي هو صرنا
+
+535
+00:49:47,190 --> 00:49:50,250
+متعارفين for every إبسط إنه كانت عبارة عن إيش؟ صغير
+
+536
+00:49:50,250 --> 00:49:55,190
+for every K Element in R طبعًا لو أخدت K positive
+
+537
+00:49:55,190 --> 00:49:58,050
+برضه بنفعله لإذا .. إذا بيكون أكبر من ال positive
+
+538
+00:49:58,050 --> 00:50:01,170
+أكيد هيكون أكبر من مين؟ من ال negative for every K
+
+539
+00:50:01,170 --> 00:50:05,450
+element in R there exists delta such that لكل X في
+
+540
+00:50:05,450 --> 00:50:12,970
+هذه المنطقة بيطلع اللي هو F prime of X اللي هو هذا
+
+541
+00:50:12,970 --> 00:50:16,630
+.. بقى اللي بمسحه هذا بمسح من التعريف ذاك للتعريف
+
+542
+00:50:16,630 --> 00:50:20,920
+limit F prime على G prime إيش بيساوي؟ ما للهاي بما
+
+543
+00:50:20,920 --> 00:50:23,800
+أن هذا بيساوي ما لنهاية أيضًا لأ كل K المتنارة بين X
+
+544
+00:50:23,800 --> 00:50:28,200
+زي الزلتة such that لما تكون X يعني بين ال A و بين
+
+545
+00:50:28,200 --> 00:50:31,060
+Z زي الدلتة يعني روحت في ال A من اليمين then F
+
+546
+00:50:31,060 --> 00:50:35,800
+برايم على D برايم أكبر من مين؟ من K ماشي الحالة و
+
+547
+00:50:35,800 --> 00:50:39,540
+هذا اللي هو الواحد عندي و هذا كله اللي هو كلام
+
+548
+00:50:39,540 --> 00:50:46,340
+شماله نفس الشيء متحقق فبيصير عندي بأستبدل هذا هذا
+
+549
+00:50:46,340 --> 00:50:50,270
+مافيش داعي له بيصير التفاصيل هنا و بيصير عندي هذا
+
+550
+00:50:50,270 --> 00:50:55,110
+لجيته إذا from واحد عند اتنين we have اللي هو
+
+551
+00:50:55,110 --> 00:51:01,370
+نعملها مع بعض بأستبدل هذا بأحطه هان بيصير عندي f
+
+552
+00:51:01,370 --> 00:51:11,330
+prime f of beta ناقص f of alpha على g of beta ناقص
+
+553
+00:51:11,330 --> 00:51:17,220
+g of alpha أكبر من مين؟ من K ماشي الحال ونفس السبب
+
+554
+00:51:17,220 --> 00:51:21,260
+الأولاني ال alpha اللي هو limit هذه صفر و limit
+
+555
+00:51:21,260 --> 00:51:26,260
+هذه صفر المعطيلة هي هو بيصير هذه عبارة عن لما ال
+
+556
+00:51:26,260 --> 00:51:28,700
+alpha تروح لل beta فبيصير عند f في beta و d في
+
+557
+00:51:28,700 --> 00:51:33,060
+beta أكبر من مين؟ من K صار عندي الآن لكل K element
+
+558
+00:51:33,060 --> 00:51:38,360
+in R لجهة Delta بحيث أنه لما تكون Beta بين ال A و
+
+559
+00:51:38,360 --> 00:51:43,660
+A زائد Delta حصلت على هذه أكبر من مين؟ من K وهذا
+
+560
+00:51:43,660 --> 00:51:50,080
+اللي هو إيه شماله؟ هو تعريف limit F of Beta على G 
+
+561
+00:51:50,080 --> 00:51:58,480
+of Beta as Beta روح للـ A من اليمين سوى ملا نهاية
+
+562
+00:51:58,480 --> 00:52:01,440
+ولو بدنا سالب ملا نهاية بنفس الأسلوب ده بتقول for
+
+563
+00:52:01,440 --> 00:52:07,660
+every K K سالمة بيصير أصغر ونفس الكلام
+
+564
+00:52:07,660 --> 00:52:13,110
+examples .. نشوف الـ examples اللي عندنا
+
+565
+00:52:13,110 --> 00:52:20,890
+نيجي للـ examples اللي عندي الأولى يعني limit
+
+566
+00:52:22,440 --> 00:52:28,260
+Sin X على جدر X لما X تروح لـ 0 من وين؟ من اليمين،
+
+567
+00:52:28,260 --> 00:52:33,740
+ليس بسهل، دعونا نشرح عن الـ الوحش وبالكالكولس هذه لأن
+
+568
+00:52:33,740 --> 00:52:36,820
+limit Sin X على جدر X لما X تروح لـ 0 من وين؟ من
+
+569
+00:52:36,820 --> 00:52:40,620
+اليمين، الآن الـ limit اللي فوق لما X تروح لـ 0 من
+
+570
+00:52:40,620 --> 00:52:43,920
+اليمين، صفر و اللي تحت صفر، إذا صار عبارة عن 0 على
+
+571
+00:52:43,920 --> 00:52:48,020
+0 وكل أمورها إيش ما لها متحققة الـ differential
+
+572
+00:52:48,020 --> 00:52:51,190
+الـ continuous و هو و هو و الأخرى و الأخرى إذا بنفضل
+
+573
+00:52:51,190 --> 00:52:53,330
+اللي فوق و بنفضل اللي تحت فضلنا اللي فوق و طلعني
+
+574
+00:52:53,330 --> 00:52:58,430
+cos X و اللي تحت 1 على 2 في جدر الـ X الآن اللي ..
+
+575
+00:52:58,430 --> 00:53:00,150
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+576
+00:53:00,150 --> 00:53:00,750
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+577
+00:53:00,750 --> 00:53:01,710
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+578
+00:53:01,710 --> 00:53:01,750
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+579
+00:53:01,750 --> 00:53:01,830
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+580
+00:53:01,830 --> 00:53:01,850
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+581
+00:53:01,850 --> 00:53:02,510
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+582
+00:53:02,510 --> 00:53:09,470
+اللي .. اللي ..
+
+583
+00:53:09,470 --> 00:53:10,410
+اللي ..
+
+584
+00:53:15,260 --> 00:53:20,220
+الآن اللي بعدها 1-sin x على x تربيع لما x تروح
+
+585
+00:53:20,220 --> 00:53:23,520
+لمين لسه في رجولنا النظرية صحيحة برضه لو كانت اللي
+
+586
+00:53:23,520 --> 00:53:27,900
+.. اللي .. اللي بدنا نروحلها جوا نقطة interior أو
+
+587
+00:53:27,900 --> 00:53:30,700
+على الـ end points كلها صحيحة وبنفس الأسلوب البرهان
+
+588
+00:53:30,700 --> 00:53:34,700
+زي ما برهننا عن اليمين بنبرهن في الوسط فبناخد بدل
+
+589
+00:53:34,700 --> 00:53:37,700
+ما هو الجوار من a لعند a زائد delta إذا كانت جوا
+
+590
+00:53:37,700 --> 00:53:40,640
+من a ناقص delta لعند a زائد delta وده كان على
+
+591
+00:53:40,640 --> 00:53:47,360
+الجهة الثانية من a ناقص delta لعند الـ a فاهمين
+
+592
+00:53:47,360 --> 00:53:51,060
+عليها هذه اللي هي برضه عبارة عن لو أخدنا limit للي
+
+593
+00:53:51,060 --> 00:53:54,780
+فوق صفر و limit للي تحت صفر إلى أن فضلنا اللي فوق
+
+594
+00:53:54,780 --> 00:53:58,940
+و فضلنا اللي تحت طالع عندي sin x على 2x إلى أن طلع
+
+595
+00:53:58,940 --> 00:54:04,360
+عندي 0 على 0 كمان مرة و متحقق كل أمورها إذا بنشتقل
+
+596
+00:54:04,360 --> 00:54:07,520
+كمان مرة بيصير cosine x على 2 و يساوي نص و هكذا
+
+597
+00:54:07,520 --> 00:54:09,180
+اللي بعدها
+
+598
+00:54:11,950 --> 00:54:16,150
+limit e to the x نقص واحد على x لما x تروح لمين
+
+599
+00:54:16,150 --> 00:54:20,730
+للصفر برضه نفس الاشي هذي بيصير صفر على صفر لـ limit
+
+600
+00:54:20,730 --> 00:54:24,750
+الأولى بنشتق أن تطلع عندي واحد
+
+601
+00:54:28,600 --> 00:54:33,500
+الآن الأخيرة نفس الشيء لإن الـ X على X minus واحد
+
+602
+00:54:33,500 --> 00:54:36,560
+برضه نفس الشيء Zero ع Zero بيطلع عندي اللي هو
+
+603
+00:54:36,560 --> 00:54:39,240
+بالفاضل هذي بتطلع واحد على X بالفاضل هذي واحد
+
+604
+00:54:39,240 --> 00:54:44,220
+بيصير الآن لما الـ X تروح للواحد بيساوي الواحد أطلع
+
+605
+00:54:44,220 --> 00:54:48,920
+لفوق بيكون وصلنا احنا عند مين عند آخر نظرية اللي
+
+606
+00:54:48,920 --> 00:54:56,000
+هي Lobitals Rule اللي هي في حالة اللي هي إنّها تطلع
+
+607
+00:54:56,000 --> 00:54:59,960
+عندي infinity او ناقص infinity الـ limit يعني الـ
+
+608
+00:54:59,960 --> 00:55:03,280
+indeterminate form اللي هو infinity على infinity
+
+609
+00:55:03,280 --> 00:55:07,080
+او ناقص infinity على infinity برضه المرة الجاية إن
+
+610
+00:55:07,080 --> 00:55:07,620
+شاء الله 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/SeyE20uTyhg_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/SeyE20uTyhg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0246a46ab922bed556b883519bf52736e28310f5
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/SeyE20uTyhg_raw.srt
@@ -0,0 +1,2456 @@
+1
+00:00:05,300 --> 00:00:13,060
+بسم الله الرحمن الرحيم المحاضرة السادسة مساق تحليل
+
+2
+00:00:13,060 --> 00:00:18,680
+حقيقة 2 لطلبة قسم رياضيات بكلية العلوم بالجامعة
+
+3
+00:00:18,680 --> 00:00:23,220
+الإسلامية بغزةالحديث اليوم إن شاء الله هيكون حول
+
+4
+00:00:23,220 --> 00:00:30,200
+ال Lobitals Rules أو قواعد Lobitals Lobitals Rules
+
+5
+00:00:30,200 --> 00:00:38,320
+بتمر في calculus في تفاضل وتكامل بتمر من ناحية
+
+6
+00:00:38,320 --> 00:00:45,100
+عملية استخدامها وتوظيفها لحل اللي هي بعض النهايات
+
+7
+00:00:45,100 --> 00:00:50,400
+اللي بيكون .. اللي هو عجزنا عن حلها بطرق عادية
+
+8
+00:00:51,750 --> 00:00:57,550
+هنشوف الآن في الحديث عن الـ Lobital Zerol حول اللي
+
+9
+00:00:57,550 --> 00:01:01,570
+هو كيف اللي هو انبرهن هذه اللي هي القواعد كيف نشتق
+
+10
+00:01:01,570 --> 00:01:06,310
+هذه القواعد كيف اللي هو أيضًا بشكل سريع حول اللي
+
+11
+00:01:06,310 --> 00:01:12,490
+هي استخدام هذه القواعد طبعًا
+
+12
+00:01:12,490 --> 00:01:16,430
+في الأول هنتحدث عن الكميات الغير معينة
+
+13
+00:01:17,020 --> 00:01:23,580
+indeterminate forms اللي هي اللي بتعالجها اللي هي
+
+14
+00:01:23,580 --> 00:01:28,840
+lobitals rules عندي على سبيل المثال لو جينا أخدنا
+
+15
+00:01:28,840 --> 00:01:37,090
+limitاللي هو x على x تكعيب على x تربيع مثلا as x
+
+16
+00:01:37,090 --> 00:01:44,730
+goes to zero limit alpha x على x لما x تروح للزيرو
+
+17
+00:01:44,730 --> 00:01:50,670
+limit اللي هو x تربيع على x لما x تروح للزيرو
+
+18
+00:01:50,670 --> 00:01:59,900
+limit x على x تكعيب لما x تروح للزيرو limitمثلًا
+
+19
+00:01:59,900 --> 00:02:07,100
+سلب X على X تكعيب لما X تروح لـ 0 لو طلعنا على
+
+20
+00:02:07,100 --> 00:02:11,440
+اللي هي ال limits اللي موجودة هنا كلها على صورة
+
+21
+00:02:11,440 --> 00:02:16,260
+اللي هي لو تعويض مباشر هنلاقيها على صورة 0 على 0
+
+22
+00:02:16,960 --> 00:02:21,420
+الان كمية 0 على 0 بالطرق السابقة كان اللي هو انه
+
+23
+00:02:21,420 --> 00:02:27,620
+احنا صعب اللي هو نتعامل معها لكن في بعض الأحيان زي
+
+24
+00:02:27,620 --> 00:02:30,520
+الحالة هذه حلاقي انه احنا بنعرف نتعامل معها و
+
+25
+00:02:30,520 --> 00:02:36,140
+بنعرف نحكم عليها اللي هلاحظ انه كل الرغم ان كلها 0
+
+26
+00:02:36,140 --> 00:02:41,100
+على 0 الا انها بتعطي في كل حالة اشي مختلف عن
+
+27
+00:02:41,100 --> 00:02:47,350
+الحالة الثانية الان هذه مثلا عبارة عن limit1 على X
+
+28
+00:02:47,350 --> 00:02:51,030
+لما X تروح للـ 0 طبعا 1 على X لما X تروح للـ 0 إيش
+
+29
+00:02:51,030 --> 00:02:53,710
+مالها؟ does not exist لأنه من اليمين بتعطي مالة
+
+30
+00:02:53,710 --> 00:02:56,790
+نهاية ومن اليسار بتعطي سالب مالة نهاية عشان هيك
+
+31
+00:02:56,790 --> 00:03:02,510
+كده يبقى نقول عنها does not exist لأن limit Alpha
+
+32
+00:03:02,510 --> 00:03:06,210
+X على X لما X تروح للـ 0 هو يساوي عبارة عن Alpha
+
+33
+00:03:06,960 --> 00:03:09,720
+اللي هو عبارة عن real number لو فرضنا أنه Alpha
+
+34
+00:03:09,720 --> 00:03:13,480
+ماخدينها احنا real number اذا انا اعطت number عادل
+
+35
+00:03:13,480 --> 00:03:16,320
+اول ما اعطتش اللي هي انا اعطت does not exist
+
+36
+00:03:16,320 --> 00:03:20,620
+الحالة الثانية اللي هي بتطلع limit X لما X تروح ل
+
+37
+00:03:20,620 --> 00:03:24,330
+0 برضه اعطتنا أيه شمالها real numberفي الحالة اللي
+
+38
+00:03:24,330 --> 00:03:28,670
+بعدها أعطتنا اللي هو عبارة عن limit 1 على X تربيع
+
+39
+00:03:28,670 --> 00:03:32,790
+لما X تروح للصفر يعني أعطتنا إيش مالها زائد ملا
+
+40
+00:03:32,790 --> 00:03:37,070
+نهاية في الحالة الثالث الأخيرة هتعطينا اللي هو
+
+41
+00:03:37,070 --> 00:03:42,770
+ناقص limit 1 على X تربيع لما X تروح للزيرو بمعنى
+
+42
+00:03:42,770 --> 00:03:46,700
+أخر سالب ملا نهايةيعني الـ Indeterminate Form Zero
+
+43
+00:03:46,700 --> 00:03:51,880
+على Zero أعطتنا اللي هو أجوبة أو قيم مختلفة تابعًا
+
+44
+00:03:51,880 --> 00:03:56,280
+لطبيعة كل حالة من الحالات اللي موجودة مرة أعطتنا
+
+45
+00:03:56,280 --> 00:03:59,700
+doesn't exist مرة أعطتنا بسوء سفر ومرة أعطتنا بسوء
+
+46
+00:03:59,700 --> 00:04:03,640
+ألف وواحد خمسة ستة ناقص واحد اللي بدناها اللي هو
+
+47
+00:04:03,640 --> 00:04:09,020
+ناقص Infinity و Infinityالان ال .. ال .. ال .. ال
+
+48
+00:04:09,020 --> 00:04:13,780
+.. الـ Indeterminate form هذه اللي الآن يعني بدنا
+
+49
+00:04:13,780 --> 00:04:19,780
+نحاول نعليجها ب ..
+
+50
+00:04:19,780 --> 00:04:25,400
+نحاول نعليجها بال .. بال .. بالـ Lobitals rulesالـ
+
+51
+00:04:25,400 --> 00:04:28,640
+Indeterminate Form اللي عندنا اللي هو 0 على 0 طبعا
+
+52
+00:04:28,640 --> 00:04:33,240
+في Indeterminate Form أخرى برضه هتعالجها اللي هي L
+
+53
+00:04:33,240 --> 00:04:38,620
+'Hôpital's Rule أو Rules اللي هي زي Infinity على
+
+54
+00:04:39,400 --> 00:04:43,280
+Infinity أيضًا هذول الشغلتين الأساسيات اللي
+
+55
+00:04:43,280 --> 00:04:47,480
+هتعالجه اللي بطل الزرول مباشرة بنظريات مباشرة
+
+56
+00:04:47,480 --> 00:04:51,240
+عليها أيضًا هتظهر لو ظهرت عندنا مثلًا Infinity نقص
+
+57
+00:04:51,240 --> 00:04:55,640
+Infinity اللي هو Zero to Infinity Infinity to Zero
+
+58
+00:04:55,640 --> 00:05:01,160
+إلى آخره هذوله حالات أخرىاللي هو بنقدر نحولهم عن
+
+59
+00:05:01,160 --> 00:05:04,800
+طريق الـ ln أو عن طريق ال exponential أو بطرق
+
+60
+00:05:04,800 --> 00:05:08,820
+معينة لاللي هي ال formula هذه ومن ثم استخدام اللي
+
+61
+00:05:08,820 --> 00:05:12,240
+هو ال lobitals rules هذه عادة الشغلات اللي كانت
+
+62
+00:05:12,240 --> 00:05:16,460
+تعالجها اليمين اللي هو ال calculus أو التفاضل اللي
+
+63
+00:05:16,460 --> 00:05:20,500
+أخدناه في سنة أولى أو سنة أولى أو سنة تانية اطلع
+
+64
+00:05:20,500 --> 00:05:26,260
+لفوق نيجي الآن ناخد النظرية الأولىاللي هي لبتة
+
+65
+00:05:26,260 --> 00:05:30,540
+الزرولي الأولى ال formula الأولى أو الصورة الأولى
+
+66
+00:05:30,540 --> 00:05:35,660
+نظرية بسيطة و نظرية مرت عليكم و اثباتها أيضا
+
+67
+00:05:35,660 --> 00:05:41,200
+هتلاحظوا انه اللي هو بسيط ايش النظرية بتقول؟ بتقول
+
+68
+00:05:41,200 --> 00:05:43,680
+مايالي عندي
+
+69
+00:05:45,330 --> 00:05:51,250
+لت F be defined على الفترة المغلقة A وB ونفترض أن
+
+70
+00:05:51,250 --> 00:05:55,630
+F of A وG of A مايساوي؟ سفر ونفترض أن G of X لا
+
+71
+00:05:55,630 --> 00:06:00,470
+تساوي سفر في الفترة اللي هي بين A وB ونفترض لو
+
+72
+00:06:00,470 --> 00:06:04,420
+كانت F وG differentiable عند الـ Aو G' عند الـ A
+
+73
+00:06:04,420 --> 00:06:07,880
+لا يساوي سفر مفترضين G' لا يساوي سفر then the
+
+74
+00:06:07,880 --> 00:06:14,240
+limit of F على G at A exist و تساوي F' على G' و
+
+75
+00:06:14,240 --> 00:06:19,580
+إذا كان تحت كل هذا الشروط بطلع عنده اللي هو ال
+
+76
+00:06:19,580 --> 00:06:24,320
+limit had exist و بالظبط هذا ال limit بساوي F' على
+
+77
+00:06:24,320 --> 00:06:29,780
+F A على G' of A نشوف النظرية و نشوف برهان النظرية
+
+78
+00:06:29,780 --> 00:06:38,960
+theoremعندي ماخد الـ F و الـ G عبارة عن دوال من A
+
+79
+00:06:38,960 --> 00:06:47,280
+و B لعند R مفترض أن الـ F of A بيساوي الـ G of A
+
+80
+00:06:47,280 --> 00:06:53,680
+بيساوي إيش؟ بيساوي سفر و مفترض أن الـ G of X
+
+81
+00:06:58,040 --> 00:07:09,500
+لاتساوى 0 لكل X و M موجودة في الفترة A و B فرضنا
+
+82
+00:07:09,500 --> 00:07:16,260
+كمان F و G differentiable عند الـ A F prime
+
+83
+00:07:16,260 --> 00:07:22,740
+of A و G prime of A exists ستين تين وهذه لاتساوى
+
+84
+00:07:22,740 --> 00:07:29,900
+إيش لاتساوى سفرتحت هذه الظروف كلها بكون عندى limit
+
+85
+00:07:29,900 --> 00:07:38,410
+f of xعلى g of x as x بتروح لل a طبعا ال a الفترة
+
+86
+00:07:38,410 --> 00:07:43,390
+اللي عندنا هي فترة من وين من عند a ل عند b إذا
+
+87
+00:07:43,390 --> 00:07:46,270
+أكيد ال x إذا تروح لل a مافيش مجال لها ال x اللي
+
+88
+00:07:46,270 --> 00:07:49,210
+بتروح لل a اللي من وين من جهة اليمين لأنه هي
+
+89
+00:07:49,210 --> 00:07:52,450
+العالم اللي أنا عمال قاعد بشتغل فيه الفترة من a ل
+
+90
+00:07:52,450 --> 00:07:57,870
+b إذا ال x بتروح لل a من وين من اليمين هيساوي اللي
+
+91
+00:07:57,870 --> 00:08:06,930
+هو f prime عند ال a على g primeعند الـ A يعني
+
+92
+00:08:06,930 --> 00:08:09,910
+بمعنى أخر إيش اللي .. إيش .. إيش .. إيش .. كيف هم
+
+93
+00:08:09,910 --> 00:08:13,650
+نطبّك هذه النظرية؟ كانت تعرض علينا limit نيجي
+
+94
+00:08:13,650 --> 00:08:19,650
+يقولنا أوجد ال limit لل F of X على G of X لما X
+
+95
+00:08:19,650 --> 00:08:25,090
+تروح لمين؟ لل A من الأمين نيجي الآن ال F of A نعود
+
+96
+00:08:25,090 --> 00:08:29,500
+تعويض مباشر ده طلعت عند 0 على 0وكانت عندى الشروط
+
+97
+00:08:29,500 --> 00:08:32,520
+هذه مكتملة اللى هى الـF و الـG differentiable و
+
+98
+00:08:32,520 --> 00:08:36,080
+الـF prime و الـG prime موجودات عند الـA على طول
+
+99
+00:08:36,080 --> 00:08:42,420
+نحط هذه إيش بتساوي F prime of A على G prime of A
+
+100
+00:08:42,420 --> 00:08:48,880
+معايا فهذه اللى هي .. اللى هي .. كيفية تطبيق
+
+101
+00:08:48,880 --> 00:08:53,500
+النظرية نيجي لأهلنا برهان النظرية البرهان بسيط
+
+102
+00:08:53,500 --> 00:08:54,680
+عندى
+
+103
+00:08:59,270 --> 00:09:11,330
+خد عندي four x بين a و بين b لو جيت حسبت الغرض
+
+104
+00:09:11,330 --> 00:09:18,970
+الأوجود هذه ال f of x على g of x إيش هتساوي؟
+
+105
+00:09:18,970 --> 00:09:28,250
+هتساوي f of x ناقص f of aعلى g of x نقص g of a ليش
+
+106
+00:09:28,250 --> 00:09:31,110
+لأن ال f of a و ال d of a ليش ماعطينا إيها بساوة
+
+107
+00:09:31,110 --> 00:09:34,170
+سفر ليش عملت هيك لأ بدت أعمل أكتر من هي بدت أعمل
+
+108
+00:09:34,170 --> 00:09:39,110
+أقسم هذا على x minus a و هذا على x ما لها minus a
+
+109
+00:09:40,060 --> 00:09:43,580
+طبيعي ال X لا تسوى ال A الآن أنا باخد ال limit
+
+110
+00:09:43,580 --> 00:09:47,620
+للجهتين وبتجرأ و باخد موزع لإن أنا ضائع من ال F
+
+111
+00:09:47,620 --> 00:09:51,260
+prime of A موجودة و ال G prime of A شمالها ومش هيك
+
+112
+00:09:51,260 --> 00:09:54,160
+و كمان ال G prime of A لا تسوى 0 إذا كل أموري تمام
+
+113
+00:09:54,160 --> 00:09:58,220
+التمام إذا باخد ال limit للجهتين لما X تروح لل A
+
+114
+00:09:58,220 --> 00:10:04,040
+من اليمين بسوى ال limit لما X تروح لل A من اليمين
+
+115
+00:10:05,480 --> 00:10:09,560
+والاشي اللي تحت وزعت ليش وزعت ضامن أن ال limit
+
+116
+00:10:09,560 --> 00:10:14,520
+exist و ال limit اللي تحت كمان لا تساوي سفر هذه
+
+117
+00:10:14,520 --> 00:10:20,400
+اللي هي عبارة عن مين هذه تعريف F prime of A وهذه
+
+118
+00:10:20,400 --> 00:10:26,660
+تعريف G prime of A بكون أنا حصلت على اللي هو اللي
+
+119
+00:10:26,660 --> 00:10:33,300
+بديها هذه اللي هي النظرية الأولى في اللي هو هذا ال
+
+120
+00:10:33,300 --> 00:10:37,890
+sectionاللي يعني بتحذير بقولك أنه انت يعني انعرضت
+
+121
+00:10:37,890 --> 00:10:46,230
+عليك limit 17x ولا .. قداش؟ مش مشكلة x زياد 17 أين
+
+122
+00:10:46,230 --> 00:10:51,750
+كانت بنفع x زياد 17 على 2x زياد 3 مثلا لما x تروح
+
+123
+00:10:51,750 --> 00:10:55,500
+لمين للزفرهو مش ميقوم لما نشوف على طول و نروح
+
+124
+00:10:55,500 --> 00:11:00,960
+نفاضل بنفعش انت يعني فتالت بيصير فاضل الجهتين
+
+125
+00:11:00,960 --> 00:11:06,340
+بيطلع واحد على اتنين لأ هو انا بقول بتسوي الو أف
+
+126
+00:11:06,340 --> 00:11:10,720
+برايم على جي برايم عند ال zero لما نكون هدي zero و
+
+127
+00:11:10,720 --> 00:11:16,080
+هدي zero لكن لا هدي zero ولا هدي zero إذا بنفعش
+
+128
+00:11:16,260 --> 00:11:21,280
+تحديد هذا نقول بتساوي اللي هو limit من فعش نقول
+
+129
+00:11:21,280 --> 00:11:24,540
+بتساوي limit واحد على اتنين على اعتبار فضلنا
+
+130
+00:11:24,540 --> 00:11:28,800
+ويساوي نص وهذا الكلام غير صحيح لأن ال limit زي ما
+
+131
+00:11:28,800 --> 00:11:32,800
+انتوا عارفين لهذا المقدار بالتعويض المباشر هو
+
+132
+00:11:32,800 --> 00:11:42,780
+عبارة عن 0017 ع 3 هذا كلام سهل ناخد مثال تطبيقي
+
+133
+00:11:42,780 --> 00:11:48,310
+على النظرية اللي عندناالمثال التطبيقي برضه مثال
+
+134
+00:11:48,310 --> 00:11:56,530
+مباشر عرض علينا الآن example عرض
+
+135
+00:11:56,530 --> 00:12:04,830
+علينا بقول او جد limit x تربيع زاد x على sign 2x
+
+136
+00:12:04,830 --> 00:12:09,530
+لما x تروح لمين لزي روبالمناسبة، النظرية اللي قبل
+
+137
+00:12:09,530 --> 00:12:13,070
+بشوية حكينا عنها سواء كانت الـA اللي بتروحلها end
+
+138
+00:12:13,070 --> 00:12:17,150
+point أو نقطة داخلية أو حتى left end point بتظبط
+
+139
+00:12:17,150 --> 00:12:22,150
+عليها النظرية والبرهان similarly ماشي الحال؟ واضح
+
+140
+00:12:22,150 --> 00:12:28,430
+هاه؟ طيب، وإيه السبب؟
+
+141
+00:12:28,430 --> 00:12:34,390
+لأن الإختبار صفر على صفرو هذه differentiable و هذه
+
+142
+00:12:34,390 --> 00:12:38,970
+differentiable كل أمورها ميحة و كويسة و مش هي كمان
+
+143
+00:12:38,970 --> 00:12:43,730
+و لو فضلت هتلاقي اللي هنا لا يساوي سفر اذا على طول
+
+144
+00:12:43,730 --> 00:12:50,410
+بقول 2x عند ال zero بفاضل جاعد و بعوض يعني هذه
+
+145
+00:12:50,410 --> 00:12:56,950
+سميتها و كأنها Fوهذه g f of x وهذه g of x بعوض f
+
+146
+00:12:56,950 --> 00:13:02,190
+prime of zero بعوض هنا g prime of zero الان f
+
+147
+00:13:02,190 --> 00:13:06,490
+prime of zero اتنين x زائد واحد في سفر بيصير اتنين
+
+148
+00:13:06,490 --> 00:13:11,850
+في سفر زائد واحد وتحت اللي هو تفاضلها اتنين cosine
+
+149
+00:13:11,850 --> 00:13:16,970
+اتنين x بيصير اتنين cosine اتنين x وعوض بسفر بيصير
+
+150
+00:13:16,970 --> 00:13:25,500
+اتنين cosine اتنين في zero وهذا يعنيبساوي اللي هو
+
+151
+00:13:25,500 --> 00:13:30,140
+واحد على اتنين على اعتبار كوصالة Zero بساوي واحد
+
+152
+00:13:30,140 --> 00:13:36,760
+هذه اللي هي تطبيق النظرية اللي عندي نيجي الآن للـ
+
+153
+00:13:36,760 --> 00:13:40,480
+Cauchy Mean Value Theorem الـ Cauchy Mean Value
+
+154
+00:13:40,480 --> 00:13:46,140
+Theorem تعميم للـ Mean Value Theorem اللي احنا
+
+155
+00:13:46,140 --> 00:13:52,050
+عارفينهابدل ما هو على دالب نحكي عن إيش عن دالتين
+
+156
+00:13:52,050 --> 00:14:00,930
+نشوف إيش اللي بقوله النظرية بتقول ما يلي لأن
+
+157
+00:14:00,930 --> 00:14:11,690
+theorem عند F و G دالتين من A و B مخدهم من A و B
+
+158
+00:14:11,690 --> 00:14:17,390
+لعند Rجاي لي نفس شروط الـ mean value theorem
+
+159
+00:14:17,390 --> 00:14:22,150
+العادية بدل ما هي على دالها دالتين جاي لي F و G
+
+160
+00:14:22,150 --> 00:14:35,270
+continuous on A و B and differentiable on O B ماشي
+
+161
+00:14:35,270 --> 00:14:42,230
+الحال ومعطيني أيضا بقولي الـ G prime لل X لا تساوي
+
+162
+00:14:42,230 --> 00:14:49,110
+سفرلكل X وين موجودة في الـA و الـB اللي أنا
+
+163
+00:14:49,110 --> 00:14:59,190
+بقولليه النتيجة then there exist لنتيجة then then
+
+164
+00:14:59,190 --> 00:15:09,250
+هذا كله معطى if this hold then then
+
+165
+00:15:09,250 --> 00:15:18,160
+there exist CElement in A و B such that G أو F
+
+166
+00:15:18,160 --> 00:15:25,820
+prime of C على G prime of C بساوي F of B ناقص F of
+
+167
+00:15:25,820 --> 00:15:35,360
+A على G of B ناقص مياً G of A ال proof ده كلام سهل
+
+168
+00:15:35,360 --> 00:15:38,140
+كمان ال proof نشوف كده
+
+169
+00:15:41,590 --> 00:15:46,050
+عندي يا جماعة أول إشي هو معطيني إيش مالها g prime
+
+170
+00:15:46,050 --> 00:15:51,650
+of x إيش مالها لا تساوي سفر إذا by rules theorem
+
+171
+00:15:51,650 --> 00:15:58,490
+هيكون g of b لا تساوي مين g of a كيف أذكركم أذكركم
+
+172
+00:15:58,490 --> 00:16:03,950
+كيف الآن إيش rules theorem كانت بتقول g من a و b
+
+173
+00:16:03,950 --> 00:16:14,130
+لعند r continuous on a و bو differentiable on a و
+
+174
+00:16:14,130 --> 00:16:21,270
+b هذا ما أعطينا إياه هو ماشي الحال بقول لي if g of
+
+175
+00:16:21,270 --> 00:16:28,350
+a بساوي g of b بساوي سفر then هو في الواقع زي ما
+
+176
+00:16:28,350 --> 00:16:31,510
+قلنا أن ال role theorem تنفع لو قلنا g of a بساوي
+
+177
+00:16:31,510 --> 00:16:37,710
+g of b و سكتنا لأنه الشهد في الموضوع أنه المماس
+
+178
+00:16:37,710 --> 00:16:41,920
+يكون معله موازي لمحور الصينةأه و لما تكون الـ G of
+
+179
+00:16:41,920 --> 00:16:45,440
+A بيساوي الـ G of B وسكتنا أي قاطع بينهم هيكون
+
+180
+00:16:45,440 --> 00:16:48,520
+عبارة عن موازي لمحور السينات يعني معناته اللي
+
+181
+00:16:48,520 --> 00:16:52,220
+مماثل اللي باجيه هيكون موازي لهذا يعني موازي لمحور
+
+182
+00:16:52,220 --> 00:16:57,740
+السينات طيب then .. then there exists C element in
+
+183
+00:16:57,740 --> 00:17:03,520
+A و B such that G prime of C بيساوي إيش بيساوي سفر
+
+184
+00:17:03,520 --> 00:17:10,560
+الآن هذا معطى مفرغ منه اللي فوق معطى عنديالان عندى
+
+185
+00:17:10,560 --> 00:17:14,640
+لو كان g of a بسوى g of b بيعطينا انه يوجد صفر بين
+
+186
+00:17:14,640 --> 00:17:18,000
+ال a و ال b بحيث ان g prime of c اشماله لا تسوى
+
+187
+00:17:18,000 --> 00:17:23,260
+صفر لكن هو مفترضلى ان g prime of x لا تسوى صفر لكل
+
+188
+00:17:23,260 --> 00:17:26,540
+x في ال a و ال bيعني الآن الـ Contraposition هو
+
+189
+00:17:26,540 --> 00:17:30,800
+اللي hold hand يعني بمعنى آخر أنه بما أنه G prime
+
+190
+00:17:30,800 --> 00:17:36,160
+of X لا تساوي 0 لكل X element in A و B هيعطينا هذا
+
+191
+00:17:36,160 --> 00:17:40,940
+نفيه B implies Q تكافئ not Q implies not B وهذا
+
+192
+00:17:40,940 --> 00:17:46,240
+لسه عملته أنابما أن g prime of x لا يساوي سفر لكل
+
+193
+00:17:46,240 --> 00:17:51,840
+x طبعا في اللي هو b اذا g of a لا يساوي مين؟ g of
+
+194
+00:17:51,840 --> 00:17:59,900
+b واضح؟ طيب اذا صار عندي الأول حاجة by Rolle's
+
+195
+00:17:59,900 --> 00:18:09,850
+theorem g of a لا يساوي g of b becauseG prime of X
+
+196
+00:18:09,850 --> 00:18:15,670
+لا يساوي سفر لكل X والي موجودة في الـA والـB هذه
+
+197
+00:18:15,670 --> 00:18:22,850
+أول نقطة خلصنا هذه بررناها نيجي الآن زي ما عملنا
+
+198
+00:18:22,850 --> 00:18:26,270
+في إثبات الـMean Value Theorem إذا بتتذكروا بدي
+
+199
+00:18:26,270 --> 00:18:29,630
+أعرف دالة أطبق عليها برضه خلّي رولز الـTheorem
+
+200
+00:18:29,630 --> 00:18:32,890
+مطبقة أو الـMean Value Theorem مطبقة و أحصل عن
+
+201
+00:18:32,890 --> 00:18:38,260
+نتيجة اللي أنا بديهاالأن هي الشكل اللي بديها بدي
+
+202
+00:18:38,260 --> 00:18:45,680
+أخد H of X let أو define H of X بساوة اللي هو
+
+203
+00:18:45,680 --> 00:18:52,740
+المقدار هذا اللي بديه F of B ناقص F of A على G of
+
+204
+00:18:52,740 --> 00:18:57,910
+B minus G of Aبتخلي المقدار هذا اللي هو يتصفر في
+
+205
+00:18:57,910 --> 00:19:00,650
+حالة ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+206
+00:19:00,650 --> 00:19:00,870
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+207
+00:19:00,870 --> 00:19:00,870
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+208
+00:19:00,870 --> 00:19:00,910
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+209
+00:19:00,910 --> 00:19:00,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+210
+00:19:00,970 --> 00:19:01,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+211
+00:19:01,090 --> 00:19:01,850
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+212
+00:19:01,850 --> 00:19:01,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+213
+00:19:01,890 --> 00:19:02,850
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+214
+00:19:02,850 --> 00:19:07,410
+.. ال .. ال .. ال .. ال .. ال .. ال ..
+
+215
+00:19:07,410 --> 00:19:12,650
+ال ..
+
+216
+00:19:12,650 --> 00:19:12,650
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+217
+00:19:12,650 --> 00:19:16,510
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+218
+00:19:16,510 --> 00:19:24,170
+ال .. ال ..
+
+219
+00:19:25,340 --> 00:19:30,660
+H of A بيطلع سفر لإن بدي اللي هو الجزء الثاني اللي
+
+220
+00:19:30,660 --> 00:19:39,320
+هيجيبلي قيمة مين قيمة ال F نقص G G of B ناقص G of
+
+221
+00:19:39,320 --> 00:19:44,060
+A أو G of X ناقص H of A عشان نروحهم مع بعض ناقص F
+
+222
+00:19:44,060 --> 00:19:50,880
+of X ناقص F of A الآن ليش عملت هيك عشان أحصل H of
+
+223
+00:19:50,880 --> 00:19:53,180
+A H of A هذه سفر
+
+224
+00:19:55,780 --> 00:20:02,140
+و هد ايه ايه بيصير سفر H of B إذا صارت عندي H of A
+
+225
+00:20:02,140 --> 00:20:09,360
+بساوي سفر و H of B حط H of B بيصير هدي بيه هدي
+
+226
+00:20:09,360 --> 00:20:13,780
+بتروح مع هدي بيصير F of B ناقص F of A ناقص F of B
+
+227
+00:20:13,780 --> 00:20:16,800
+ناقص F of A بروحن مع بعض بيصير H برضه بيساوي سفر
+
+228
+00:20:16,800 --> 00:20:22,300
+إذا هدي أكيد برضه بتساوي H of B الآن
+
+229
+00:20:24,650 --> 00:20:28,050
+عندي هذا الـ differentiable و continuous و هذا الـ
+
+230
+00:20:28,050 --> 00:20:31,210
+differentiable و continuous على ما يناسبها من a و
+
+231
+00:20:31,210 --> 00:20:35,750
+b أو على ال a و b ال a و b اللي هو open
+
+232
+00:20:35,750 --> 00:20:38,770
+differentiable و على ال a و b closed continuous
+
+233
+00:20:38,770 --> 00:20:43,350
+تبعاً لها هتطلع انه ثابت هذا و هدوله ثوابت حيث ان
+
+234
+00:20:43,350 --> 00:20:50,330
+عندي هذا كله ع بعض continuous صار عنديH is
+
+235
+00:20:50,330 --> 00:20:59,130
+continuous on A وB وdifferentiable on A وB open
+
+236
+00:20:59,130 --> 00:21:03,930
+لأنه أنا من رأس الدورة الـ H of X معرفها اللي هي
+
+237
+00:21:03,930 --> 00:21:10,740
+الـ H for every X element in A وBH of X بيساوي كده
+
+238
+00:21:10,740 --> 00:21:15,360
+ماعيش يا بابا صارت الآن أنا حققت كل شروط ال roles
+
+239
+00:21:15,360 --> 00:21:19,780
+theorem اللي هي ال H continuous على ال A و B و ال
+
+240
+00:21:19,780 --> 00:21:23,360
+differential على ال A و B open أو H of A بيساوي و
+
+241
+00:21:23,360 --> 00:21:27,260
+H of B بيساوي اللي هي سفر إذا حسب roles theorem
+
+242
+00:21:27,260 --> 00:21:31,720
+إذا by roles theorem by أو حتى by main value
+
+243
+00:21:31,720 --> 00:21:38,180
+theorem by roles theorem there exists C element ال
+
+244
+00:21:38,180 --> 00:21:46,290
+A و Bsuch that اتش prime of c ايش هيساوي سفر هذا
+
+245
+00:21:46,290 --> 00:21:52,190
+حسب ال mean value theorem معايا يا جماعة الآن
+
+246
+00:21:52,190 --> 00:21:57,130
+بتفاضل هذه دلنا اوجد تفاضل هذه تفاضل هذه ماعليش
+
+247
+00:21:57,130 --> 00:22:04,760
+خلينا نكتبها لإنه ندخل على العالـ slide بدي أفاضل
+
+248
+00:22:04,760 --> 00:22:09,740
+هذه فاضله H prime of X اللي هي عند الـ C بتساوي
+
+249
+00:22:09,740 --> 00:22:15,580
+سفر سفر بساوي H prime of C تساوي فاضل هذه و أعوض
+
+250
+00:22:15,580 --> 00:22:20,420
+عن الـ X بسفر لأن هذا ثابت و هذا ثابت ده بيصير سفر
+
+251
+00:22:20,420 --> 00:22:23,420
+تفاضل هذا مع هذا لأن مع هذا بيصير G prime of X
+
+252
+00:22:23,420 --> 00:22:29,220
+مضروب في هذا إذا صار عندي بساوي F of B ناقص F of A
+
+253
+00:22:30,080 --> 00:22:36,100
+على g of b ناقص g of a مضروب في مين؟ فضلت في g
+
+254
+00:22:36,100 --> 00:22:40,920
+prime of x وانا بدي أحسبها عند مين؟ عند c، اذا g
+
+255
+00:22:40,920 --> 00:22:45,320
+prime of c ناقص تفاضل هذه، هذا ثابت سفر لأن هذا
+
+256
+00:22:45,320 --> 00:22:50,620
+قداش تفاضلها ناقص f prime عند ال x وانا باخدها عند
+
+257
+00:22:50,620 --> 00:22:56,280
+ال c اللي هي h of c, فh prime of c فبصير ناقص f
+
+258
+00:22:56,280 --> 00:23:02,200
+prime of cالان بتدنجل هذه على جهة هذه بصير عندى
+
+259
+00:23:02,200 --> 00:23:10,720
+الان f prime of c نجلته هان و اجسمها جي برايم of c
+
+260
+00:23:10,720 --> 00:23:15,840
+لأن جي برايم of c لاتساوى سفر بساوة f of b ناقص f
+
+261
+00:23:15,840 --> 00:23:25,710
+of a على g of b ناقص g of a و هيكبكون حصلنا على C
+
+262
+00:23:25,710 --> 00:23:31,630
+في الـA وB بحيث أنه هذه تتحقق وهو المطلوب هذه اللي
+
+263
+00:23:31,630 --> 00:23:37,190
+بيسميها Cauchy Mean Value Theorem هذه تعميم لمين؟
+
+264
+00:23:37,190 --> 00:23:41,590
+تعميم اللي هو الـMean Value Theorem بس خد اللي هو
+
+265
+00:23:41,590 --> 00:23:47,230
+G of X بتساوي XG of X بيساوي X و G of X بيساوي X
+
+266
+00:23:47,230 --> 00:23:49,190
+اللي هي تحقق كل الشروط ال differential
+
+267
+00:23:49,190 --> 00:23:53,470
+بالcontinuous و و الاخره ماشي الحال بيصير عندي
+
+268
+00:23:53,470 --> 00:23:58,110
+اللي هي في حالة G of X بتساوي X معايا يا شباب
+
+269
+00:23:58,110 --> 00:24:02,450
+بيصير G of BB و G of AA و هذه اللي هي G prime اللي
+
+270
+00:24:02,450 --> 00:24:05,510
+هي واحد فبيصير F prime of C بيساوي F of B نقص F of
+
+271
+00:24:05,510 --> 00:24:10,470
+A على B minus A إذا F
+
+272
+00:24:15,650 --> 00:24:21,210
+أمسح البرهان بس الان
+
+273
+00:24:21,210 --> 00:24:31,930
+ال note اللي عندي ال note كما يالي note if
+
+274
+00:24:31,930 --> 00:24:42,820
+g of x بيساوي x then we get fromالـ theorem هذه
+
+275
+00:24:42,820 --> 00:24:51,140
+اللي بقول عليها كوشي mean value theorem we get the
+
+276
+00:24:51,140 --> 00:24:59,500
+mean value theorem كيف الـ g of x بيساوي x معناه
+
+277
+00:24:59,500 --> 00:25:04,160
+انتصار الـ g of b بيساوي b و g of a بيصير a يعني
+
+278
+00:25:04,160 --> 00:25:10,530
+هذا بيصير a, bوهذه بيصير A و G prime of C اللي هي
+
+279
+00:25:10,530 --> 00:25:14,070
+بيصير واحد فبصير F prime of C بيسوي F of B نقص F
+
+280
+00:25:14,070 --> 00:25:20,590
+of A على B minus A وهذه هي ال main value theorem
+
+281
+00:25:21,280 --> 00:25:24,720
+واضح .. اه .. طيب اطلع للي بعده لإن احنا اللي
+
+282
+00:25:24,720 --> 00:25:26,820
+بيهمنا هذا الكوشي بين ال value theorem احنا
+
+283
+00:25:26,820 --> 00:25:31,980
+حكيناها أصلا عشان خاطر انه احنا نحكي عن اللي هو
+
+284
+00:25:31,980 --> 00:25:37,960
+Lobital's rule ال form اللي عنده اللي أمامي دكتور
+
+285
+00:25:37,960 --> 00:25:41,860
+جديد في السؤال في غيرك مفهوم ان انا جسمت على X
+
+286
+00:25:41,860 --> 00:25:46,640
+minus A على E minus A الطرفين اصلا انت بتصير F أو
+
+287
+00:25:46,640 --> 00:25:48,580
+P نقص F أو A على B minus A
+
+288
+00:26:01,110 --> 00:26:06,630
+البرهام مش صعب اللي قلناه، كتير سهل، ما هو الـ C
+
+289
+00:26:06,630 --> 00:26:09,970
+اللي لاجيناها في الحالة الأولى، هل هي التانية؟ إذا
+
+290
+00:26:09,970 --> 00:26:13,390
+كنت تتعامل بجلمين Value Theorem أنت؟مش بدك تطبّق
+
+291
+00:26:13,390 --> 00:26:16,170
+الـ Value Theory بدك تطبّق الـ Value Theory لأن
+
+292
+00:26:16,170 --> 00:26:21,090
+there exists c1 such that f prime of c1 بيسوء f of
+
+293
+00:26:21,090 --> 00:26:24,030
+b minus f of a على b minus a مافيش فيها مشكلة
+
+294
+00:26:24,030 --> 00:26:27,950
+there exists c2 such that g prime of c2 بيسوء g of
+
+295
+00:26:27,950 --> 00:26:32,550
+b نقص g of a على b minus a الـ c1 هذه مش شرط هيكون
+
+296
+00:26:32,550 --> 00:26:39,630
+main الـ c2 او احنا لازم نثبتها هي نفسها اه ف .. و
+
+297
+00:26:39,630 --> 00:26:44,780
+بعدين البرمجان سهلماشي .. نحن الواحد يفكر 100% ..
+
+298
+00:26:44,780 --> 00:26:50,780
+جميل لكن .. يعني .. بس أنه احنا .. الـC هذه مش
+
+299
+00:26:50,780 --> 00:26:53,700
+ضمنية تساوي الـC2 و بدنا نثبت أنها تساويها .. إذا
+
+300
+00:26:53,700 --> 00:26:59,920
+كانت بتساويها طيب .. نيجي لها اللي هي النظرية اللي
+
+301
+00:26:59,920 --> 00:27:05,840
+بعيدها النظرية اللي بعيدها .. أنا مرضيش أمسح اللوح
+
+302
+00:27:05,840 --> 00:27:08,800
+أساسي منقررها من الـtheory من الأولى
+
+303
+00:27:11,650 --> 00:27:30,050
+نشوف نطلع إيش اللي بتقوله هذه النظرية نفس
+
+304
+00:27:30,050 --> 00:27:35,710
+اللي هنا F و G differentiable on A و B معايا أه؟
+
+305
+00:27:35,710 --> 00:27:42,150
+الان such that G prime of X ده تساوي سفرG prime of
+
+306
+00:27:42,150 --> 00:27:47,970
+X لا تساوي سفر أنا مش موجودة For all X elements in
+
+307
+00:27:47,970 --> 00:27:55,070
+A وB ونفترض أنه limit F of X limit F of X لما X
+
+308
+00:27:55,070 --> 00:27:59,570
+تروح إلى الـ A من اليمين موجودة و بتساوي أياش؟ سفر
+
+309
+00:27:59,570 --> 00:28:02,490
+و limit G of X لما X تروح إلى الـ A من اليمين
+
+310
+00:28:02,490 --> 00:28:09,580
+بتساوي سفر اذا صار limit الحاصل القسمةلأن بيسويش f
+
+311
+00:28:09,580 --> 00:28:14,300
+prime of a على g prime of a بيساوياش limit f of x
+
+312
+00:28:14,300 --> 00:28:19,580
+على g of x لما x تروح لل a باليمينيعني وكأنه هنا
+
+313
+00:28:19,580 --> 00:28:25,460
+حول الحديث كله من افتراض أنه عند النقطة اللي هي F'
+
+314
+00:28:25,780 --> 00:28:31,240
+وG' موجودة ولا تساوي سفر وحول الحديث من إن التعويض
+
+315
+00:28:31,240 --> 00:28:35,280
+المباشر أن F of A وG of A بتساوي سفر ل limit لـ ..
+
+316
+00:28:35,280 --> 00:28:39,220
+limit لل function لما X تروح لـ A سفر و limit لل
+
+317
+00:28:39,220 --> 00:28:42,040
+function لما .. اللي .. اللي هو ال X .. ال X بتروح
+
+318
+00:28:42,040 --> 00:28:48,920
+لسفر .. لل A بتساوي سفروحول أيضا طلب جي برايم نفسه
+
+319
+00:28:48,920 --> 00:28:54,680
+على كل الفترة اللي تكون لا تساوي سفر مش عند النقطة
+
+320
+00:28:54,680 --> 00:29:03,060
+بس وقال لك انه حتى اللي هو النتيجة هتطلع ب limit
+
+321
+00:29:03,060 --> 00:29:07,940
+مش هتطلع ب F prime of A على G prime of A يعني اللي
+
+322
+00:29:07,940 --> 00:29:14,980
+بقصده انه الآن طور هذه الحديث هناإنه لما تُعرض
+
+323
+00:29:14,980 --> 00:29:21,580
+علينا limit F of X على G of X لما X تروح للـA من
+
+324
+00:29:21,580 --> 00:29:24,360
+لمين أو إن كانت حتى لو في الـinterior point الـX
+
+325
+00:29:24,360 --> 00:29:31,300
+بتروح للـA برضه صحيحة الآن بعدي عنديإذا لجيت limit
+
+326
+00:29:31,300 --> 00:29:34,480
+الأولى، اللي أنا بحكي عن limit سيرة مش عن تعويض
+
+327
+00:29:34,480 --> 00:29:38,340
+مباشر زي اللي جابله، الآن limit f of x لما x تروح
+
+328
+00:29:38,340 --> 00:29:41,780
+ل a من اليمين و limit f of x لما x تروح ل a من
+
+329
+00:29:41,780 --> 00:29:46,700
+اليمين، إذا هذه موجودة و هذه موجودة و طلع عندي 0
+
+330
+00:29:46,700 --> 00:29:51,060
+على 0، يعني طلع ال limit عبارة عن 0 على 0، هنا بدو
+
+331
+00:29:51,060 --> 00:29:57,200
+يحدث العلاج، إذا كانت الآنالـ limit اللي طلعت عندي
+
+332
+00:29:57,200 --> 00:30:02,000
+F prime of X على G prime of X لما X تروح للـ A من
+
+333
+00:30:02,000 --> 00:30:06,780
+اليمين إذا طلعت عبارة عن قيمة خلاص ارتاح هذه اللي
+
+334
+00:30:06,780 --> 00:30:12,450
+طلعت هي مين فهمت ال limitماشي الحال لو طلعت كمان
+
+335
+00:30:12,450 --> 00:30:18,230
+مرة zero على zero اللي هو و بتحقق كل الشروط اللي
+
+336
+00:30:18,230 --> 00:30:21,950
+.. اللي في الأول برضه بأعمل كمان مرة بفاضل لما
+
+337
+00:30:21,950 --> 00:30:26,430
+بتطلع لكن لو طلعت ال limit هذه does not exist بسكت
+
+338
+00:30:26,430 --> 00:30:31,130
+و بجوبي عمش .. بدنا ندور على طريقة أخرى واضح؟ الآن
+
+339
+00:30:31,130 --> 00:30:34,990
+لو طلعت هذه infinity أو سالب infinity هذه آسف
+
+340
+00:30:34,990 --> 00:30:38,900
+infinity أو سالب infinity برضه أن نظرية صحيحةاللي
+
+341
+00:30:38,900 --> 00:30:45,290
+هو هدمين الجزء الثاني من النظريةif limit f prime
+
+342
+00:30:45,290 --> 00:30:48,450
+على g prime بساوة L بساوة infinity أو سالب
+
+343
+00:30:48,450 --> 00:30:52,190
+infinity هتطلع ال limit على طول لل F على G اللي
+
+344
+00:30:52,190 --> 00:30:56,350
+ببحث عنها إيش هتساوي برضه ال infinity أو سالب
+
+345
+00:30:56,350 --> 00:31:00,670
+infinity حسب القيمة هذه إذا أي إن كانت اللي هي ال
+
+346
+00:31:00,670 --> 00:31:05,190
+limit مادامة exist سواء ال existence عبارة عن
+
+347
+00:31:05,190 --> 00:31:09,210
+element in R أو اللي هو عبارة عن ناقص infinity أو
+
+348
+00:31:09,210 --> 00:31:18,100
+سالب infinity فإن النظرية صحيحةواضح؟ أي سؤال؟ طيب
+
+349
+00:31:18,100 --> 00:31:27,200
+صلى على النبي عليه الصلاة والسلام خلينا
+
+350
+00:31:27,200 --> 00:31:31,360
+نيجي للنظرية ونبرنها
+
+351
+00:31:45,860 --> 00:31:50,880
+Theorem كدهش؟ نزلي بس النص يا محمد اللي هي theorem
+
+352
+00:31:50,880 --> 00:31:59,580
+6 3 3 إيش النظرية بتقول؟ بتقول ما يعني عندي طبعا
+
+353
+00:31:59,580 --> 00:32:04,540
+ماخد ال a أصغر من b strictly و a ممكن حتى تاخد سلب
+
+354
+00:32:04,540 --> 00:32:07,580
+infinity و ال b تاخد infinity يعني ممكن تكون
+
+355
+00:32:07,580 --> 00:32:11,040
+الفترة من a .. الفترة كلها a ممكن تكون أي فترة sub
+
+356
+00:32:11,040 --> 00:32:16,710
+interval من اللي هو 100 من ال real numbersفرضنا f
+
+357
+00:32:16,710 --> 00:32:26,190
+و g من a و b لعند اللي هو r وإذا كانت a infinity
+
+358
+00:32:26,190 --> 00:32:30,130
+أو سلب infinity أسف إذا كانت a سلب infinity أو b
+
+359
+00:32:30,130 --> 00:32:33,610
+infinity بتكون o من زمن بعرفي لأن عشان اللي هو
+
+360
+00:32:33,610 --> 00:32:36,890
+ناخدها من real number ل real number لذا نفترض f و
+
+361
+00:32:36,890 --> 00:32:46,080
+g من a و b لعند ال R ونفترض إن f و gdifferentiable
+
+362
+00:32:46,080 --> 00:32:54,620
+on a و b ماشي الحال و differentiable on a و b الان
+
+363
+00:32:54,620 --> 00:32:57,900
+مش لازم ي continue و تعندى و كده لأنه انا هدخل
+
+364
+00:32:57,900 --> 00:33:02,240
+لجوه شغل هيكون لجوه هل جيت بتشوف واش معنى لجوه
+
+365
+00:33:02,240 --> 00:33:08,620
+such that g prime of x g prime of x لا تسوى سفر
+
+366
+00:33:08,620 --> 00:33:17,430
+لكل x وين موجودة في الفترة a و bالان بقول لي إذا
+
+367
+00:33:17,430 --> 00:33:27,170
+كانت limit limit اللي هي f of x لما x تروح لل a من
+
+368
+00:33:27,170 --> 00:33:32,190
+اليمين بساوي limit g of x لما x تروح لل a من
+
+369
+00:33:32,190 --> 00:33:40,980
+اليمين بساوي سفر هذا كله موضوع الان بدو يوصلبدي
+
+370
+00:33:40,980 --> 00:33:46,200
+أقولك كيف أنا بدي أحصل على نتيجة limit f of x على
+
+371
+00:33:46,200 --> 00:33:51,060
+g of x لما x تروح لل a من اليمين بقولك إذا كان انت
+
+372
+00:33:51,060 --> 00:33:59,180
+if لان ايه if limit f prime of x على g prime of x
+
+373
+00:33:59,180 --> 00:34:06,520
+لما x تروح لل a من اليمين بساوي L thenأتجرأ أقول
+
+374
+00:34:06,520 --> 00:34:12,020
+فاش عندى مشكلة limit f of x اللى ببحث عنها على g
+
+375
+00:34:12,020 --> 00:34:17,360
+of x لما x تروح للإيه من اليمين برضه ايش هيساوي؟
+
+376
+00:34:17,360 --> 00:34:29,740
+هيساوي ال .. من يحياتي هذه هيكون صحيحة طيب خلينا
+
+377
+00:34:29,740 --> 00:34:38,330
+الآن اللى هو البرهن شوف عليهاواضح النظرية شرحناها
+
+378
+00:34:38,330 --> 00:34:45,050
+يعني نص النظرية شرحناها بشكل كامل الان since limit
+
+379
+00:34:45,050 --> 00:34:51,730
+F prime of X على G prime of X لما X تروح ل A من
+
+380
+00:34:51,730 --> 00:35:00,690
+وين؟ من اليمين هيعندي الفترة A وB حتى لو كانت
+
+381
+00:35:00,690 --> 00:35:05,580
+منتده وين ما بدها، هي حاضرة الان عنديX تذهب إلى
+
+382
+00:35:05,580 --> 00:35:09,760
+اليمن اليمين فبدي من الجهة دي طبيعي من اليمين بسوء
+
+383
+00:35:09,760 --> 00:35:15,800
+ال then for every epsilon أكبر من سفر لأي epsilon
+
+384
+00:35:15,800 --> 00:35:20,440
+أكبر من سفر أي epsilon there exists delta أكبر من
+
+385
+00:35:20,440 --> 00:35:24,660
+سفر such that لأن X تذهب إلى الامن وين من اليمين
+
+386
+00:35:24,660 --> 00:35:27,460
+إذن الجوار اللي حوالها هو عبارة عن جوار من A لعند
+
+387
+00:35:27,460 --> 00:35:32,340
+مين ال A زي ال Delta لعند A زي ال Delta صح ولا لأ
+
+388
+00:35:32,340 --> 00:35:36,260
+إذن لكلما دامت ال limit هي دي بساوي L، ده لكل
+
+389
+00:35:36,260 --> 00:35:41,480
+إبسلون بقدر ألاقي Delta بحيث أنه X element في A و
+
+390
+00:35:41,480 --> 00:35:46,400
+A زائد Delta ف X element في A و A زائد Delta، then
+
+391
+00:35:46,400 --> 00:35:52,180
+قطعا .. then قطعا هيكون عندي F prime of X على G
+
+392
+00:35:52,180 --> 00:35:58,030
+prime of X نقص L، ذوكون أصغر من 100 من إبسلونهذا
+
+393
+00:35:58,030 --> 00:36:02,370
+تعريف ال limit لل F prime of X على G prime of X
+
+394
+00:36:02,370 --> 00:36:06,510
+بسهولة لما X تروح لمن؟ لل A من اليمين هو كاتبها
+
+395
+00:36:06,510 --> 00:36:11,110
+هذه A زائد Delta C في الكتاب يعني مسميها C يعني
+
+396
+00:36:11,110 --> 00:36:16,090
+مسمي انه لكل X there exists C بحيث انه لكل X في ال
+
+397
+00:36:16,090 --> 00:36:20,650
+A اللي عند ال A لل C بكون هذا الكلام متحقق أنا
+
+398
+00:36:20,650 --> 00:36:23,510
+حبيت اكتبلك اللي هو التعريف الدارجي اللي انت ده
+
+399
+00:36:23,510 --> 00:36:27,700
+كسله كمان في ال .. في الحلواضح لحد تلاتة
+
+400
+00:36:38,080 --> 00:36:42,520
+ماشي الحال بس هي ك .. هذه .. و هذه ك صح و هذه ك صح
+
+401
+00:36:42,520 --> 00:36:47,040
+و هذه ك صح اللي كاتبها صح بس هذه للطالب أسهله في
+
+402
+00:36:47,040 --> 00:36:49,960
+ال .. في ال .. لإنه .. خلّيني أقول هذا اللي درج
+
+403
+00:36:49,960 --> 00:36:54,640
+عليه في ال .. في .. اللي هو التعبير عن ال .. لكل x
+
+404
+00:36:54,640 --> 00:36:58,940
+في الجوار الجوار هذا سهل و .. و .. و .. وعبّرنا
+
+405
+00:36:58,940 --> 00:36:59,200
+عنه
+
+406
+00:37:02,810 --> 00:37:07,630
+-A هو أكبر من سفر وأصغر من دلتة برضه هيك صح صحيح
+
+407
+00:37:07,630 --> 00:37:11,910
+نفس الاشي طيب
+
+408
+00:37:11,910 --> 00:37:15,050
+الان
+
+409
+00:37:15,050 --> 00:37:23,590
+هذا الكلام IA او بمعنى اخر that is هيكون هذا اللي
+
+410
+00:37:23,590 --> 00:37:31,230
+هو F prime of X ناقص G prime of Xأصغر ناقص L
+
+411
+00:37:31,230 --> 00:37:37,150
+بتغيرها عشان أصغر من Y وأكبر من 200 من سالب Y شيل
+
+412
+00:37:37,150 --> 00:37:43,470
+ال L هذه بصير اللي هو أصغر من L زائد Y وأكبر من L
+
+413
+00:37:43,470 --> 00:37:49,430
+ناقص Y هذا متحقق لمين لكل X و N موجودة في الفترة
+
+414
+00:37:49,430 --> 00:37:53,550
+من A لعند A زائد Delta و اكتب لي هذا سميلي
+
+415
+00:37:56,530 --> 00:38:03,990
+واحد ماشي الحال سميليه واحد الآن عندي اللي هو شروط
+
+416
+00:38:03,990 --> 00:38:06,850
+ال mean value theorem الكوشي mean value theorem
+
+417
+00:38:06,850 --> 00:38:10,130
+اللي قبل بشوية ال F و ال G differentiable على ال A
+
+418
+00:38:10,130 --> 00:38:16,170
+و ال B اه و ال G prime of X لها تساوي سفر و ال ..
+
+419
+00:38:16,170 --> 00:38:22,490
+او .. ايش كمان كله متحقق بس خلينا نقول
+
+420
+00:38:26,140 --> 00:38:31,240
+بدي الآن اوين اطبق الـ mean value theorem بدي
+
+421
+00:38:31,240 --> 00:38:37,720
+اطبقها على اللي هو اللي جوا عندى لداخل الـ mean
+
+422
+00:38:37,720 --> 00:38:44,560
+لداخل الفترة هذه عشان اشتغل وين اللي بتطلع عندى
+
+423
+00:38:44,560 --> 00:38:48,490
+اضمن تكون هناعشان القيمة اللى هتطلع عندى اللى
+
+424
+00:38:48,490 --> 00:38:53,170
+بتحققها تكون بتحقق اللى بتطلع عندى و بتحققها دى
+
+425
+00:38:53,170 --> 00:38:57,730
+عشان هي كصح اللى أعوض مكان بعض ماشي الحال خد الآن
+
+426
+00:38:57,730 --> 00:39:07,030
+لجد تفهموا إيش اللى بقصدهم خد الآن four alpha أكبر
+
+427
+00:39:07,030 --> 00:39:16,040
+من a و أصغر من beta و أصغر من a زائد deltaيعني أنا
+
+428
+00:39:16,040 --> 00:39:20,060
+غرضي ان انا اشتغل .. ان انا رايح .. بدي انا limit
+
+429
+00:39:20,060 --> 00:39:24,580
+اصلا و ال limit بديها لما اروح لمين؟ لل A يعني بدي
+
+430
+00:39:24,580 --> 00:39:29,760
+في الجوار اللي عيمين ال A و جاي ناحيتها هذا اللي
+
+431
+00:39:29,760 --> 00:39:31,740
+بهم، اللي مانيش سغاداش، بيكون التصرف مافيش ..
+
+432
+00:39:31,740 --> 00:39:36,980
+مافيش عنده مشكلة الآن هي ال alpha أخدتها هنا و هي
+
+433
+00:39:36,980 --> 00:39:37,420
+ال beta
+
+434
+00:39:41,900 --> 00:39:44,540
+أصغر من Alpha أصغر من Beta أصغر من ايه زي الـ
+
+435
+00:39:44,540 --> 00:39:54,060
+Delta؟ By Cauchy Mean Value Theorem there exists
+
+436
+00:39:54,060 --> 00:40:03,220
+سموها هو نسميها U Element in mean in Alpha و Beta
+
+437
+00:40:03,220 --> 00:40:10,110
+والـ Alpha و Beta جزء من هذهدُول، إذا اللي بنطبق
+
+438
+00:40:10,110 --> 00:40:14,750
+على هذه اللي بنطبق على .. اللي بنطبق على هذه بنطبق
+
+439
+00:40:14,750 --> 00:40:19,790
+على هذه، مظبوط؟ يعني هذه الـU اللي لجيتها بنطبق
+
+440
+00:40:19,790 --> 00:40:22,210
+عليها الكلام هذا اللي هو F prime of U على D prime
+
+441
+00:40:22,210 --> 00:40:27,510
+of U بين هذه و بين هذه واضح، و هذا الكلام مهم طيب،
+
+442
+00:40:27,510 --> 00:40:34,640
+there exists U such that F prime of Uعلى g prime
+
+443
+00:40:34,640 --> 00:40:39,240
+of u بيساوي ايش يا جماعة بيساوي f of b أو beta
+
+444
+00:40:39,240 --> 00:40:50,260
+ناقص f of alpha على g of beta ناقص g of alpha واضح
+
+445
+00:40:50,260 --> 00:41:00,020
+اه؟ هذا سمولي يمين هو اتنين الآن عند هذه اللي
+
+446
+00:41:00,020 --> 00:41:05,260
+لجيتها هنا اللي بتحقق هذههي وين موجودة من ضمن
+
+447
+00:41:05,260 --> 00:41:12,980
+النقاط اللي بتحقق هذه لكل X هنا وهذه جزء منها إذا
+
+448
+00:41:12,980 --> 00:41:18,100
+F prime of X of U على G prime of U بين الـ L ناقص
+
+449
+00:41:18,100 --> 00:41:22,020
+إبسلون والـ L زائد مين إبسلون وفي نفس الوقت F
+
+450
+00:41:22,020 --> 00:41:25,860
+prime of U هذه اللي لقيتها G prime of U بساوي هذا
+
+451
+00:41:25,860 --> 00:41:29,840
+إذا from واحد
+
+452
+00:41:30,390 --> 00:41:40,070
+واتنين we get اللي هو F prime of U على G prime of
+
+453
+00:41:40,070 --> 00:41:47,610
+U بستبدلها و بيصير F of Beta ناقص F of Alpha على G
+
+454
+00:41:47,610 --> 00:41:54,070
+of Beta ناقص G of Alpha بحيث أنه هذا يكون أكبر من
+
+455
+00:41:54,070 --> 00:42:03,630
+L ناقص Y و أصغر من 100 من L زائد Yلأن هذا صحيح لأي
+
+456
+00:42:03,630 --> 00:42:09,750
+Alpha و Beta بشكلهم اللي موجود Alpha أصغر من Beta
+
+457
+00:42:09,750 --> 00:42:15,570
+و Alpha بين الـA و بين مين الـA زائد دلتا إذا
+
+458
+00:42:15,570 --> 00:42:22,150
+الألفة هذه حرة في كل المنطقة هذه بنفع يعني الألفة
+
+459
+00:42:22,150 --> 00:42:26,530
+هذه لو بدها تروح للـA حد مش بمنحها الألفة تروح لها
+
+460
+00:42:26,530 --> 00:42:31,060
+لأنه صحيح على كل هذه الألفات اللي لجيتها هذهالان
+
+461
+00:42:31,060 --> 00:42:40,340
+let alpha goes to mean to a من وين؟ من اليمين
+
+462
+00:42:40,340 --> 00:42:45,720
+ماشي؟ مقدر و لن تؤثر لأ على ال beta ولا عليها زي
+
+463
+00:42:45,720 --> 00:42:50,980
+الدلتية الحرة بتروح لهذه وهذه زي ما هي يعني تصرف
+
+464
+00:42:50,980 --> 00:42:58,540
+alpha يروح لأي a beta بالنسبالها ثابت ولا تتأثرهذا
+
+465
+00:42:58,540 --> 00:43:03,500
+الكلام مهم إذا صار عندي الآن لما Alpha تروح لأ من
+
+466
+00:43:03,500 --> 00:43:10,700
+اليمين ال up of Alpha بيصير عندي limit ال up of
+
+467
+00:43:10,700 --> 00:43:17,780
+Alpha لما ال Alpha تروح لأ من اليمين بساوي هو في
+
+468
+00:43:17,780 --> 00:43:21,980
+الواقع limitها limitها هذه Alpha اللي كنا نسميها X
+
+469
+00:43:21,980 --> 00:43:23,980
+مثلا ال up of X سمى X تروح لأ من اليمين لأ من
+
+470
+00:43:23,980 --> 00:43:29,480
+اليمينالآن الـ Alpha راحت للإيمن اليمين limitها
+
+471
+00:43:29,480 --> 00:43:35,020
+أنا ماعطينيها إيش بيساوي؟ بيساوي صفر، ماعطيني
+
+472
+00:43:35,020 --> 00:43:37,080
+limit f of x عندما x تروح للإيمن اليمين إيش
+
+473
+00:43:37,080 --> 00:43:40,540
+بيساوي؟ صفر، أنا سميتها إيش أنا؟ Alpha هذه اللي
+
+474
+00:43:40,540 --> 00:43:46,660
+بتتحرك، إذا هذا ال limit إيش هيساوي؟ بنفس السبب أو
+
+475
+00:43:46,660 --> 00:43:52,940
+لنفس السبب limitG of Alpha لما Alpha تروح للـ A من
+
+476
+00:43:52,940 --> 00:43:59,680
+اليمين برضه مش هيساوي سفر إذا الآن برجع لهذه برجع
+
+477
+00:43:59,680 --> 00:44:09,060
+لهذه بصير عندى الآن اللي حصلته كله على بعضه لكل ي
+
+478
+00:44:09,060 --> 00:44:17,130
+أكبر من سفر ماشي الحال ل gate Deltaبحيث أنه الـ α
+
+479
+00:44:17,130 --> 00:44:20,050
+و beta بشكل هذا أكبر من إيه و أقل زي الـ delta
+
+480
+00:44:20,050 --> 00:44:24,570
+سيبك من الـ L α خلاص رديتها أنا beta أكبر من إيه و
+
+481
+00:44:24,570 --> 00:44:29,170
+أصغر من إيه زي الـ delta طلع عندي هذا المقدار أصغر
+
+482
+00:44:29,170 --> 00:44:33,170
+من L زي الـ يبسلون وأكبر من L ناقص يبسلون ماشي؟
+
+483
+00:44:33,170 --> 00:44:37,300
+الآن رديت و أخدتله من ال limitالان بدي أخد ال
+
+484
+00:44:37,300 --> 00:44:40,940
+limit لهذا المقدار كله لما ال alpha تروح لمين؟ لل
+
+485
+00:44:40,940 --> 00:44:45,240
+a من اليمين الان لما أخد ال limit لهذا زي ما قولت
+
+486
+00:44:45,240 --> 00:44:48,500
+ال beta مالهاش علاقة بال alpha ال beta ثابتة
+
+487
+00:44:48,500 --> 00:44:50,920
+بالنسبة لل alpha فال alpha تروح لل a من اليمين زي
+
+488
+00:44:50,920 --> 00:44:55,100
+ما بدها لن تتأثر beta فبصير limit اللي فوق على
+
+489
+00:44:55,100 --> 00:44:59,520
+limit اللي اتحد هذا ثابت و هذا ثابت و هذا limit هو
+
+490
+00:44:59,520 --> 00:45:04,300
+اللي هو صفر و هذا limit هو صفر و هذول أعداد إذا
+
+491
+00:45:04,300 --> 00:45:11,220
+أصار عندي الآنعندي take the limit بيصير عندي L
+
+492
+00:45:11,220 --> 00:45:18,100
+ناقص Epsilon أصغر أو يساوي اللي هو F of Beta على G
+
+493
+00:45:18,100 --> 00:45:23,660
+of Beta أصغر من L زائد Epsilon من وين حصلته هذا؟
+
+494
+00:45:23,660 --> 00:45:29,160
+when I take the limit of this inequality as Alpha
+
+495
+00:45:29,160 --> 00:45:37,460
+goes to A from right واضح؟هذا حصلت عليه هذا عرفت
+
+496
+00:45:37,460 --> 00:45:40,600
+ثانوية هذا حصلت عليه من وين أن أخدت ال limit
+
+497
+00:45:40,600 --> 00:45:44,660
+للجهات التلاتة as Alpha تروح لل A من اليمين
+
+498
+00:45:44,660 --> 00:45:48,780
+واستخدمت هذه الحقيقة أن هذا سفر و هذا سفر صار هذا
+
+499
+00:45:48,780 --> 00:45:53,360
+المقدار و هذا المقدار بين هذا و هذا إذن اللي حصلت
+
+500
+00:45:53,360 --> 00:46:02,380
+عليه الآن هو ما يليه لكل epsilon أكبر من سفر لجهة
+
+501
+00:46:02,380 --> 00:46:07,610
+Deltaأكبر من السفر such that هذه beta كانت
+
+502
+00:46:07,610 --> 00:46:14,650
+arbitrary بين a و بين مين اللي هو such that if
+
+503
+00:46:14,650 --> 00:46:26,150
+beta بين ال a و ال a زائد delta we have then ايش
+
+504
+00:46:26,150 --> 00:46:31,990
+اللي حصلنا عليه اللي هو f of beta على f of alpha
+
+505
+00:46:33,100 --> 00:46:38,720
+صارت أصغر أو يساوي L زايد إبسلون وأكبر أو يساوي
+
+506
+00:46:38,720 --> 00:46:47,620
+إبسلون ناقص L أو بمعنى آخر IE F of Beta على F of
+
+507
+00:46:47,620 --> 00:46:53,340
+Alpha ناقص L absolute value أصغر أو يساوي إبسلون
+
+508
+00:46:53,340 --> 00:47:02,280
+وهذا هذا this means that hence limit
+
+509
+00:47:03,350 --> 00:47:13,590
+f of beta على f of alpha as اللي هو limit of فدي g
+
+510
+00:47:13,590 --> 00:47:23,970
+مالكم فدي g بساكتين g of beta فدي g of beta limit
+
+511
+00:47:23,970 --> 00:47:28,270
+of beta على g of beta مظبوط؟
+
+512
+00:47:29,140 --> 00:47:33,140
+as اللي هو طبعا الان بيت ايه اشمالها لكل بيتها
+
+513
+00:47:33,140 --> 00:47:37,620
+يعني بيتها وين راحت على الايم اليمين هان لكل بيتها
+
+514
+00:47:37,620 --> 00:47:49,320
+وين في الجوار هذا الان بيساوي ال هو المطلوب مش
+
+515
+00:47:49,320 --> 00:47:53,440
+عاجبك بيتك تبقى اكسر اي سؤال
+
+516
+00:47:56,950 --> 00:48:01,030
+بتصور هيك المظهرية واضحة تماما هي تلت خطوات في
+
+517
+00:48:01,030 --> 00:48:05,530
+الواقع تلت خطوات مين هما هو طبعا في الكتاب يعني لو
+
+518
+00:48:05,530 --> 00:48:12,190
+راحظت هتلاقي يعني أنه بدها بس ترتيب الان لأ بدها
+
+519
+00:48:12,190 --> 00:48:19,150
+ترتيب طلع عليها الان عندك هذا الان استخدمت أنا هذا
+
+520
+00:48:19,150 --> 00:48:23,370
+في الأول بالعمدان و استخدم هذا استخدمت هذا عشان
+
+521
+00:48:23,370 --> 00:48:27,150
+أقولك هذه ال inequality صحيح على كل المنطقة هذهلأن
+
+522
+00:48:27,150 --> 00:48:33,170
+لجي U لأن اللي لجيتها U أنا لجيتها لجيت ال U و
+
+523
+00:48:33,170 --> 00:48:36,070
+أخدت الفترة هنا عشان أقول لك ال U اللي لجيتها في
+
+524
+00:48:36,070 --> 00:48:41,570
+داخل الفترة هذه الحديث هذه جابل عن هذه بعمل
+
+525
+00:48:41,570 --> 00:48:45,750
+confusion عند الطالب لأن اللي لجيتها من قال إنه
+
+526
+00:48:45,750 --> 00:48:49,970
+هنا موجودة ما هي اللي لجيتها هنا وين لجيتها بين A
+
+527
+00:48:49,970 --> 00:48:56,050
+و B بين A و B أو بين Alpha و Beta يعني بده يصير
+
+528
+00:48:56,050 --> 00:49:05,880
+عندىاللي هي الـ F prime الـ F prime عندي ال limit
+
+529
+00:49:05,880 --> 00:49:11,140
+.. ال limit لل .. خليني أكتبها يا شيخ ليش؟ ها ..
+
+530
+00:49:11,140 --> 00:49:16,120
+هذا بالساوي ال .. اللي هي إيش ما لأ باخد ال
+
+531
+00:49:16,120 --> 00:49:20,740
+infinity بطلع حد برضه إيش infinity يعني الحالة
+
+532
+00:49:20,740 --> 00:49:26,250
+التانية اللي هي Fبساوة infinity هيكون ال limit لل
+
+533
+00:49:26,250 --> 00:49:33,570
+F على G أشماله بساوة infinity الان بده يصير عنده
+
+534
+00:49:33,570 --> 00:49:38,750
+بدل ما قول limit F prime على G prime بساوة L بده
+
+535
+00:49:38,750 --> 00:49:43,310
+يصير أشهر بساوة infinity كيف بنعبر على إنه الرقم
+
+536
+00:49:43,310 --> 00:49:47,190
+يروح لما لنهاية ال limit أنه ناخد اللي هو صرنا
+
+537
+00:49:47,190 --> 00:49:50,250
+متعارفين for every إبسط إنه كانت عبارة عن إيش صغير
+
+538
+00:49:50,250 --> 00:49:55,190
+for every KElement in R طبعا لو أخدت K positive
+
+539
+00:49:55,190 --> 00:49:58,050
+برضه بنفعله لإذا .. إذا بيكون أكبر من ال positive
+
+540
+00:49:58,050 --> 00:50:01,170
+أكيد هيكون أكبر من مين؟ من ال negative for every K
+
+541
+00:50:01,170 --> 00:50:05,450
+element in R there exists delta such that لكل X في
+
+542
+00:50:05,450 --> 00:50:12,970
+هذه المنطقة بيطلع اللي هو F prime of X اللي هو هذا
+
+543
+00:50:12,970 --> 00:50:16,630
+.. بقى اللي بمسحه هذا بمسح من التعريف ذاك للتعريف
+
+544
+00:50:16,630 --> 00:50:20,920
+limit F prime على G prime إيش بيساوي؟ما للهاي بما
+
+545
+00:50:20,920 --> 00:50:23,800
+أن هذا بيساوي ما لنهاي ايضا لأ كل K المتنارة بين X
+
+546
+00:50:23,800 --> 00:50:28,200
+زي الزلتة such that لما تكون X يعني بين ال A و بين
+
+547
+00:50:28,200 --> 00:50:31,060
+Z زي الدلتة يعني روحت في ال A من اليمين then F
+
+548
+00:50:31,060 --> 00:50:35,800
+برايم على D برايم أكبر من مين من K ماشي الحالة و
+
+549
+00:50:35,800 --> 00:50:39,540
+هذا اللي هو الواحد عندى و هذا كله اللي هو كلام
+
+550
+00:50:39,540 --> 00:50:46,340
+أشمله نفس الاشي متحقق فبصير عندى بستبدل هذا هذا
+
+551
+00:50:46,340 --> 00:50:50,270
+مافيش داعي له بيصير التفاصيل هناو بيصير عندى هذا
+
+552
+00:50:50,270 --> 00:50:55,110
+لجيتو اذا from واحد عند اتنين we have اللى هو
+
+553
+00:50:55,110 --> 00:51:01,370
+نعملها مع بعض بستبدل هذا بحطه هان بيصير عندى f
+
+554
+00:51:01,370 --> 00:51:11,330
+prime f of beta ناقص f of alpha على g of beta ناقص
+
+555
+00:51:11,330 --> 00:51:17,220
+g of alphaأكبر من مين من K ماشي الحال و نفس السبب
+
+556
+00:51:17,220 --> 00:51:21,260
+الأولاني الـ alpha اللي هو limit هذه سفر و limit
+
+557
+00:51:21,260 --> 00:51:26,260
+هذه سفر المعطيلة هي هو بيصير هذه عبارة عن لما ال
+
+558
+00:51:26,260 --> 00:51:28,700
+alpha تروح لل beta فبيصير عند أف في beta و دي في
+
+559
+00:51:28,700 --> 00:51:33,060
+beta أكبر من مين من K صار عندي الآن لكل K element
+
+560
+00:51:33,060 --> 00:51:38,360
+in R لجهة Delta بحيث أنه لما تكون Beta بين ال A و
+
+561
+00:51:38,360 --> 00:51:43,660
+A زائد Deltaحصلت على هذه أكبر من مين؟ من K وهذا
+
+562
+00:51:43,660 --> 00:51:50,080
+اللي هو إيه شماله؟ هو تعريف limit F of Beta على G
+
+563
+00:51:50,080 --> 00:51:58,480
+of Beta as Beta روح لل A من اليمين سوى ملا نهاية
+
+564
+00:51:58,480 --> 00:52:01,440
+ولو بدنا سالب ملا نهاية بنفس الأسلوب ده بتقول for
+
+565
+00:52:01,440 --> 00:52:07,660
+every K K سالمة بيصير أصغر ونفس الكلام
+
+566
+00:52:07,660 --> 00:52:13,110
+exampleexamples .. نشوف ال examples اللي عندنا
+
+567
+00:52:13,110 --> 00:52:20,890
+نيجي لل examples اللي عندى الأولى يعني limit
+
+568
+00:52:22,440 --> 00:52:28,260
+Sin X على جدر X لما X تروح لـ 0 من وين؟ من اليمين،
+
+569
+00:52:28,260 --> 00:52:33,740
+ليس بسهل، دعونا نشرح عن الوحش وبالكالكولس هذه لأن
+
+570
+00:52:33,740 --> 00:52:36,820
+limit Sin X على جدر X لما X تروح لـ 0 من وين؟ من
+
+571
+00:52:36,820 --> 00:52:40,620
+اليمين، الآن الـ limit اللي فوق لما X تروح لـ 0 من
+
+572
+00:52:40,620 --> 00:52:43,920
+اليمين، سفر و اللي تحت سفر، إذا صار عبارة عن 0 على
+
+573
+00:52:43,920 --> 00:52:48,020
+0 وكل أمورها إيش ما لها متحققة ال differential
+
+574
+00:52:48,020 --> 00:52:51,190
+الcontinuous و هو و هو و الاخري و الاخريإذا بنفضل
+
+575
+00:52:51,190 --> 00:52:53,330
+اللي فوق و بنفضل اللي تحت فضلنا اللي فوق و طلعني
+
+576
+00:52:53,330 --> 00:52:58,430
+cos X و اللي تحت 1 على 2 في جدر ال X الآن اللي ..
+
+577
+00:52:58,430 --> 00:53:00,150
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+578
+00:53:00,150 --> 00:53:00,750
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+579
+00:53:00,750 --> 00:53:01,710
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+580
+00:53:01,710 --> 00:53:01,750
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+581
+00:53:01,750 --> 00:53:01,750
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+582
+00:53:01,750 --> 00:53:01,830
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+583
+00:53:01,830 --> 00:53:01,850
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+584
+00:53:01,850 --> 00:53:02,510
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+585
+00:53:02,510 --> 00:53:02,510
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+586
+00:53:02,510 --> 00:53:09,470
+اللي .. اللي ..
+
+587
+00:53:09,470 --> 00:53:10,410
+اللي ..
+
+588
+00:53:15,260 --> 00:53:20,220
+الان اللي بعدها 1-sin x على x تربيه لما x تروح
+
+589
+00:53:20,220 --> 00:53:23,520
+لمين لسه في رجولنا النظرية صحيحة برضه لو كانت اللي
+
+590
+00:53:23,520 --> 00:53:27,900
+.. اللي .. اللي بدنا نروحلها جوا نقطة interior أو
+
+591
+00:53:27,900 --> 00:53:30,700
+على ال end points كلها صحيحة وبنفس الأسلوب البرهان
+
+592
+00:53:30,700 --> 00:53:34,700
+زي ما برهننا عن اليمين بنبرهن في الوسط فبناخد بدل
+
+593
+00:53:34,700 --> 00:53:37,700
+ما هو الجوار من a لعند a زائد delta إذا كانت جوا
+
+594
+00:53:37,700 --> 00:53:40,640
+من a ناقص delta لعند a زائد delta وده كان على
+
+595
+00:53:40,640 --> 00:53:47,360
+الجهة الثانية من a ناقص delta لعند ال aفاهمين
+
+596
+00:53:47,360 --> 00:53:51,060
+عليها هذه اللي هي برضه عبارة عن لو أخدنا limit للي
+
+597
+00:53:51,060 --> 00:53:54,780
+فوق سفر و limit للي تحت سفر إلى أن فضلنا اللي فوق
+
+598
+00:53:54,780 --> 00:53:58,940
+و فضلنا اللي تحت طالع عندي sin x على 2x إلى أن طلع
+
+599
+00:53:58,940 --> 00:54:04,360
+عندي 0 على 0 كمان مرة و متحقق كل أمورها إذا بنشتقل
+
+600
+00:54:04,360 --> 00:54:07,520
+كمان مرة بيصير cosine x على 2 و يساوي نص و هكذا
+
+601
+00:54:07,520 --> 00:54:09,180
+اللي بعدها
+
+602
+00:54:11,950 --> 00:54:16,150
+limit e to the x نقص واحد على x لما x تروح لمين
+
+603
+00:54:16,150 --> 00:54:20,730
+للصفر برضه نفس الاشي هذي بيصير صفر على صفر لlimit
+
+604
+00:54:20,730 --> 00:54:24,750
+الأولى بنشتق أن تطلع عنده واحد
+
+605
+00:54:28,600 --> 00:54:33,500
+الان الأخيرة نفس الشيء لإن ال X على X minus واحد
+
+606
+00:54:33,500 --> 00:54:36,560
+برضه نفس الشيء Zero ع Zero بطلع عندى اللى هو
+
+607
+00:54:36,560 --> 00:54:39,240
+بالفاضل هدى بتطلع واحد على X بالفاضل هدى واحد
+
+608
+00:54:39,240 --> 00:54:44,220
+بيصير الان لما ال X تروح للواحد بساوي الواحد اطلع
+
+609
+00:54:44,220 --> 00:54:48,920
+لفوق بيكون وصلنا احنا عند مين عند اخر نظرية اللى
+
+610
+00:54:48,920 --> 00:54:56,000
+هى Lobitals Ruleاللي هي في حالة اللي هي انها تطلع
+
+611
+00:54:56,000 --> 00:54:59,960
+عندى infinity او ناقص infinity ال limit يعني ال
+
+612
+00:54:59,960 --> 00:55:03,280
+indeterminate form اللي هو infinity على infinity
+
+613
+00:55:03,280 --> 00:55:07,080
+او ناقص infinity على infinity برضه المرة الجاية ان
+
+614
+00:55:07,080 --> 00:55:07,620
+شاء الله
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..185164b6fe32956d1de9886d1344ec6eacb39c18
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE.srt
@@ -0,0 +1,2863 @@
+1
+00:00:11,170 --> 00:00:17,190
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم خمسة عشر
+
+2
+00:00:17,190 --> 00:00:25,090
+لمساق تحليل حقيقي 2 لطلبة وطالبات الجامعة
+
+3
+00:00:25,090 --> 00:00:31,380
+الإسلامية كلية العلوم قسم الرياضيات المحاضرة اليوم
+
+4
+00:00:31,380 --> 00:00:35,940
+إن شاء الله التي ستكون على جزئين الجزء الأول
+
+5
+00:00:35,940 --> 00:00:40,940
+سنكمل ما بدأنا المرة الماضية الذي هو سنكمل
+
+6
+00:00:40,940 --> 00:00:45,100
+الذي هو تطبيقات على الـ Fundamental Theorem of
+
+7
+00:00:45,100 --> 00:00:50,540
+Calculus الجزء الأول هذا التطبيق طبعًا هو سيكون عن
+
+8
+00:00:50,540 --> 00:00:53,880
+evaluation of integrals برضه كنا فيه المرة
+
+9
+00:00:53,880 --> 00:00:58,220
+الماضية وسنكمله اليوم إن شاء الله الجزء الثاني من
+
+10
+00:00:58,220 --> 00:01:04,180
+المحاضرة سنتحدث عن الذي هو التكامل أن ندخل 
+
+11
+00:01:04,180 --> 00:01:08,620
+للتعاملية التكامل بطريقة غير ال upper sum وال lower
+
+12
+00:01:08,620 --> 00:01:15,060
+sum عن طريق شيء اسمه Riemann sum هذا الآن هو الجزء 
+
+13
+00:01:15,060 --> 00:01:19,080
+الثاني الآن بدنا نبدأ في الجزء الأول بس على السريع
+
+14
+00:01:19,080 --> 00:01:22,540
+نطلع على ما تحدثنا عنه المرة الماضية كنا تحدثنا عن
+
+15
+00:01:22,540 --> 00:01:26,120
+الـ Fundamental Theorem of Calculus وتحدثنا عن الذي 
+
+16
+00:01:26,120 --> 00:01:30,800
+هو الـ Two Forms إيها أو التفاضل والتكامل كما
+
+17
+00:01:30,800 --> 00:01:35,240
+تحدثنا وتكامل التفاضل Roughly الكلام وبعدين أتينا
+
+18
+00:01:35,240 --> 00:01:38,980
+لبعض الملاحظات وبعض التعريفات وتحدثنا عن الـ
+
+19
+00:01:38,980 --> 00:01:42,780
+evaluation of integralsبدأنا في evaluation of
+
+20
+00:01:42,780 --> 00:01:46,600
+integrals الذي هو الذي يمثل الجزء الأول من هذه
+
+21
+00:01:46,600 --> 00:01:51,320
+المحاضرة اليوم تحدثنا عن الذي هو ال integration by
+
+22
+00:01:51,320 --> 00:01:55,480
+parts ال integration by parts تحدثنا عنه المرة
+
+23
+00:01:55,480 --> 00:02:02,130
+الماضية وشرحناه ووقفنا عند الذي هو الـ ال .. ال ..
+
+24
+00:02:02,130 --> 00:02:06,230
+ال .. ال .. ال first substitution form الذي سنبدأ
+
+25
+00:02:06,230 --> 00:02:10,650
+فيه اليوم إن شاء الله الآن ال first substitution
+
+26
+00:02:10,650 --> 00:02:15,310
+form أو الذي هو التكامل بالتعويض عن طريق الذي هي 
+
+27
+00:02:15,310 --> 00:02:18,870
+التعويض وهذه طبعًا طريقة كنا نستخدمها كما
+
+28
+00:02:18,870 --> 00:02:22,670
+استخدمنا الذي هي طريقة ال integration by parts في
+
+29
+00:02:22,670 --> 00:02:27,910
+calculus B أيضًا استخدمنا الذي هو التكامل بالتعويض
+
+30
+00:02:27,910 --> 00:02:36,840
+للإيجاد أو لعملية إيجاد الذي هي التكامل الآن بدنا
+
+31
+00:02:36,840 --> 00:02:41,720
+نعطي النظرية التي تشرح لنا أو نثبت النظرية التي
+
+32
+00:02:41,720 --> 00:02:46,840
+تسمح لنا بالتكامل بالتعويض نجي نطلع لنظريتنا
+
+33
+00:02:46,840 --> 00:02:51,120
+التي هي ال first substitution theorem نيجي ناخذ
+
+34
+00:02:51,120 --> 00:02:55,300
+الذي هو ال J فترة عبارة عن ال closed interval Alpha
+
+35
+00:02:55,300 --> 00:03:01,120
+و Beta  إن نأخذ Φ function من J لعند R have a
+
+36
+00:03:01,120 --> 00:03:04,620
+continuous derivative on J يعني أخذنا الآن يا
+
+37
+00:03:04,620 --> 00:03:09,660
+جماعة Φ عبارة عن function من التي هي الفترة 
+
+38
+00:03:09,660 --> 00:03:17,090
+Alpha و Beta لعند R وفرضنا إن هذه الدالة التي هي 
+
+39
+00:03:17,090 --> 00:03:22,050
+Φ ال derivative لها موجودة ونفسها مشتقتها
+
+40
+00:03:22,050 --> 00:03:26,690
+continuous إذا فرضنا إن الذي هو الـ Φ have a
+
+41
+00:03:26,690 --> 00:03:31,230
+continuous derivative on the interval J التي
+
+42
+00:03:31,230 --> 00:03:35,080
+سميناها ليه Alpha و Beta لأن لو كان في عندي function
+
+43
+00:03:35,080 --> 00:03:39,300
+F is continuous on any interval I containing Φ
+
+44
+00:03:39,300 --> 00:03:46,160
+of J لأن فرضنا أن F دالة على I تحتوي Φ of J عشان
+
+45
+00:03:46,160 --> 00:03:51,180
+إن بعد شوية هعرّف .. هيلزمني الذي هو composition
+
+46
+00:03:51,180 --> 00:03:55,160
+of two functions عشان هيك أنا باخد ال F عبارة عن
+
+47
+00:03:55,160 --> 00:04:00,840
+function من I لعند من؟ لعند ال R إيش ال I هذه؟
+
+48
+00:04:00,840 --> 00:04:08,290
+هذه I interval بتحتوي التي هي من الـ Φ of J التي
+
+49
+00:04:08,290 --> 00:04:13,790
+عندي، يعني هيصير عندي بناء عليها هيصير عندي F of
+
+50
+00:04:13,790 --> 00:04:20,270
+Φ of I T فيه التي هي الـ J عبارة عن قيمة معرفة
+
+51
+00:04:20,270 --> 00:04:24,790
+عشان تكون ال composition معرفة، إذا الآن باختصار
+
+52
+00:04:24,790 --> 00:04:28,010
+Φ التي هي ال derivative التي موجودة والـ
+
+53
+00:04:28,010 --> 00:04:31,670
+derivative continuous وال function F الصغيرة هذي is
+
+54
+00:04:31,670 --> 00:04:35,510
+continuous وهنا ال interval I، then الآن نجي
+
+55
+00:04:35,510 --> 00:04:40,050
+للنتيجة التي نحن نمارسها عمليًا دائمًا التي هو
+
+56
+00:04:40,050 --> 00:04:46,790
+بكون عندي ال integration من Alpha ل Beta لF of Φ
+
+57
+00:04:46,790 --> 00:04:53,960
+of T Φ prime of T DT نحن ندعي بتساوي كنا نجي
+
+58
+00:04:53,960 --> 00:04:58,100
+ماذا نفعل نأخذ هذه التي هي نعوض عن Φ of T ب X
+
+59
+00:04:58,100 --> 00:05:03,360
+بناء عليه بيصير عبارة عن هذا ال integration F of
+
+60
+00:05:03,360 --> 00:05:09,920
+X و Φ prime of T نعوض عن Φ of T ب X فبيصير
+
+61
+00:05:09,920 --> 00:05:14,200
+عند Φ prime of T DT هو عبارة عن من DX كنا هيك
+
+62
+00:05:14,200 --> 00:05:17,890
+نفعل في ال calculus الآن نجي نقول DX بِسُوء Φ
+
+63
+00:05:17,890 --> 00:05:22,670
+prime T DT أو DX على DT بِسُوء Φ prime of T ونشيل
+
+64
+00:05:22,670 --> 00:05:26,630
+Φ prime of T DT ونحط مكانها شمالها DX حدود ال
+
+65
+00:05:26,630 --> 00:05:30,110
+integration كانت من Alpha ل Beta يعني لما كانت T
+
+66
+00:05:30,110 --> 00:05:33,350
+ب Alpha بصير X التي هي Φ of T التي هي Φ of
+
+67
+00:05:33,350 --> 00:05:39,190
+Alpha بتروح لمن؟ ل الذي هي Φ of من؟ Φ of
+
+68
+00:05:39,190 --> 00:05:45,180
+Beta لماذا؟ لأنه لما كانت T بساوي Beta أكيد الـ X
+
+69
+00:05:45,180 --> 00:05:48,760
+التي هي Φ of T بتساوي الـ X بتساوي Φ of T، الـ
+
+70
+00:05:48,760 --> 00:05:53,640
+X بتساوي Φ of Beta إذن نظريتنا هذه التي أمامنا
+
+71
+00:05:53,640 --> 00:05:59,160
+هي نظرية إحنا يعني استعملناها أو بنستعملها عادة في
+
+72
+00:05:59,160 --> 00:06:02,600
+الذي هو إيجاد الـ integration وإحدى الطرق لإيجاد
+
+73
+00:06:02,600 --> 00:06:07,860
+الـ integration فعندي
+
+74
+00:06:07,860 --> 00:06:14,140
+الآن هذه الآن نظريتنا، بدنا نبرهن هذه النظرية ونشوف
+
+75
+00:06:14,140 --> 00:06:18,840
+كيف نبرهنها، برهانها بسيط، الآن هي التي بدنا
+
+76
+00:06:18,840 --> 00:06:23,280
+نبرهنه، خلينا نشوف كيف البرهانة وكيف نبرهن
+
+77
+00:06:23,280 --> 00:06:26,380
+الكتاب،
+
+78
+00:06:26,380 --> 00:06:32,520
+عنده يجينا عرفنا، بدنا نعرف function F، لأن عرش
+
+79
+00:06:32,520 --> 00:06:35,990
+function F  لا تنسوا هذا الـ Function ماذا مالها يا
+
+80
+00:06:35,990 --> 00:06:40,070
+جماعة؟ Continuous وهذا يعني كثير بالنسبة للـ 
+
+81
+00:06:40,070 --> 00:06:43,210
+Fundamental Theorem أعرف الـ Function F من الـ
+
+82
+00:06:43,210 --> 00:06:50,310
+Interval I لعند من R F Capital أعرف الـ F Capital
+
+83
+00:06:50,310 --> 00:06:59,070
+F of U بساوي الـ Integration من الذي هو عند الـ I
+
+84
+00:06:59,070 --> 00:07:04,870
+بتحتوي من الـ Φ of J يعني هي الـ Interval I هي
+
+85
+00:07:04,870 --> 00:07:08,870
+الـ interval I وفي داخلها Φ of J Φ of J طبعًا
+
+86
+00:07:08,870 --> 00:07:12,330
+في عند Φ of Alpha لعند Φ of Beta لو كانت التي
+
+87
+00:07:12,330 --> 00:07:15,590
+هي Alpha أكبر من Beta الأخرى Φ of J التي هم
+
+88
+00:07:15,590 --> 00:07:19,990
+مفترضينها نحن أين في داخل الفترة التي أمامي الآن
+
+89
+00:07:19,990 --> 00:07:24,050
+بتأخذ ال integration تعرفه من عند Φ of Alpha
+
+90
+00:07:24,050 --> 00:07:29,980
+لعند من U الـ U المتغيرة التي ستكون أين موجودة في
+
+91
+00:07:29,980 --> 00:07:35,240
+داخل الـ I التي تحتوي الـ Φ of G إذا عرفنا
+
+92
+00:07:35,240 --> 00:07:37,440
+function f of u بيستوي ال integration من Φ of
+
+93
+00:07:37,440 --> 00:07:42,780
+Alpha ثابت Φ of Alpha يا جماعة لعند U لمن؟ لل f
+
+94
+00:07:42,780 --> 00:07:49,410
+of x dx لاحظ هذه الدالة التي عندي التي عرفتها من
+
+95
+00:07:49,410 --> 00:07:53,830
+الـ Fundamental theorem بما أن F is continuous إذا
+
+96
+00:07:53,830 --> 00:07:58,810
+هذا كله الآن الذي هو صار function في U عبارة عن
+
+97
+00:07:58,810 --> 00:08:03,990
+differentiable ومش هيك كمان و F prime of U ستساوي
+
+98
+00:08:03,990 --> 00:08:11,090
+من؟ التي هي الدالة F of U إذا من الـ Fundamental
+
+99
+00:08:11,090 --> 00:08:15,350
+theorem بما أن F is continuous إذا F prime of U
+
+100
+00:08:15,350 --> 00:08:20,210
+بتساوي F of U التي هي by Fundamental theorem of
+
+101
+00:08:20,210 --> 00:08:23,370
+calculus إذا by Fundamental theorem of calculus ف F
+
+102
+00:08:23,370 --> 00:08:27,710
+of X .. F of U طبعًا هذه ننطقها بسوء ال integration
+
+103
+00:08:27,710 --> 00:08:32,200
+من C .. C الذي هو نحن نسميه هنا هي التي هي Φ of
+
+104
+00:08:32,200 --> 00:08:35,820
+Alpha ما أريد أن أخبركم في التسميات على طول من Φ of
+
+105
+00:08:35,820 --> 00:08:40,140
+Alpha لعند من لعنده إذا الذي فعلته أنا بس لحتى
+
+106
+00:08:40,140 --> 00:08:46,340
+الآن إن عرفنا دالة التي هي ال func ال F Capital هذه
+
+107
+00:08:46,340 --> 00:08:53,760
+ال F Capital عرفناها من I من I لعند R by F of U
+
+108
+00:08:53,760 --> 00:08:58,060
+بسؤ ال integration من C ل U F of X DX for U
+
+109
+00:08:58,060 --> 00:09:03,310
+element من in ال interval I الآن قاعد أحضر للي 
+
+110
+00:09:03,310 --> 00:09:08,630
+أريدها and now consider the function H من J لعند R
+
+111
+00:09:08,630 --> 00:09:12,690
+بعد ما عرفنا ال function F هذه التي أمامي بدي 
+
+112
+00:09:12,690 --> 00:09:18,330
+أعرف لكم دالة ثانية الدالة التي أريد أن أعرفها يا جماعة 
+
+113
+00:09:18,330 --> 00:09:26,530
+هي عبارة عن HH هذه أريد أن أعرفها من J لعند R شوف كيف
+
+114
+00:09:26,530 --> 00:09:30,510
+أريد أن أعرفها بطريقة التي هي تخدمني بعد شوية للوصول
+
+115
+00:09:30,510 --> 00:09:36,730
+للنتيجة التي أريدها التي هي H of T أريد أن أعرفها H of
+
+116
+00:09:36,730 --> 00:09:46,170
+T بساوي F Capital هذه التي عرفناها of Φ of T Φ
+
+117
+00:09:46,170 --> 00:09:52,220
+of T الآن جهة دي اليمين هي الفترة Alpha و Beta Φ
+
+118
+00:09:52,220 --> 00:09:57,740
+of T التي هي إذا T من في J Φ of T معرّفة على الـJ
+
+119
+00:09:57,740 --> 00:10:03,440
+الـJ Φ of T مشتقتها معرّفة على الـJ الـF لها
+
+120
+00:10:03,440 --> 00:10:07,640
+معرّفة لأن الـF domainها I الذي هو الذي يحتوي Φ
+
+121
+00:10:07,640 --> 00:10:11,360
+of J يعني فعلًا Φ of T موجودة في Φ of J التي هي 
+
+122
+00:10:11,360 --> 00:10:14,600
+موجودة في من في I إذا المعرفة التي دالها H of T
+
+123
+00:10:14,600 --> 00:10:23,370
+بيساوي Φ of I of T طيب الآن الـ F تفاجأنا للـ F
+
+124
+00:10:23,370 --> 00:10:27,030
+هذه إنها differentiable الـ F كابيتال والـ Φ
+
+125
+00:10:27,030 --> 00:10:29,470
+differentiable لماذا differentiable؟ لأن Φ prime
+
+126
+00:10:29,470 --> 00:10:32,390
+موجودة و continuous إذا أقدر .. هي أفاضل هذه 
+
+127
+00:10:32,390 --> 00:10:38,340
+الدالة إذا أقدر أن أقول إنه عند الـ H prime of T
+
+128
+00:10:38,340 --> 00:10:44,340
+بيساوي F' Φ of T تشيرن رول طبعًا يا جماعة في Φ
+
+129
+00:10:44,340 --> 00:10:51,460
+prime of T فإذا تفاضل ال H' هو F' في Φ prime of 
+
+130
+00:10:51,460 --> 00:10:59,000
+T كما نحن ذكرنا في برهان النظرية هنا الآن عندي
+
+131
+00:10:59,000 --> 00:11:03,540
+أيضًا نحن قلنا ال F prime of U ماذا تساوي F of U
+
+132
+00:11:03,540 --> 00:11:08,920
+وقلنا لماذا السبب الآن لو أتينا كل هذا تحضير للي 
+
+133
+00:11:08,920 --> 00:11:13,980
+أريدها بعد شوية المعلومات هذه الآن عندي احسب لي H of
+
+134
+00:11:13,980 --> 00:11:22,380
+Alpha H of Alpha من هذه H of Alpha أكيد كلكم شاهد
+
+135
+00:11:22,380 --> 00:11:29,960
+أن H of Alpha بتساوي عوض بتساوي F of Φ of Alpha
+
+136
+00:11:29,960 --> 00:11:33,560
+صحيحة يا جماعة ويساوي F of Φ of Alpha طب ماذا
+
+137
+00:11:33,560 --> 00:11:37,980
+تعريف F of U؟ هي عبارة عن ال integration من Φ of
+
+138
+00:11:37,980 --> 00:11:43,520
+Alpha لعند U U أنا الآن ماذا هي؟ اسمها U التي هي 5
+
+139
+00:11:43,520 --> 00:11:46,420
+Alpha إذا من 5 Alpha ل 5 Alpha يعني ال integration
+
+140
+00:11:46,420 --> 00:11:51,100
+ماذا سيُساوي هذا؟ يساوي صفر إذا نرى Alpha فعلاً ماذا 
+
+141
+00:11:51,100 --> 00:11:55,200
+بتساوي .. بتساوي إيش .. بتساوي صفر إذا تلت حاجات
+
+142
+00:11:55,200 --> 00:11:59,860
+الآن عرفت الـ F من I لـ عند R بالطريقة اللي أمامي
+
+143
+00:12:00,190 --> 00:12:05,030
+وجدت أن F' بيساوي F of U الشغل الثاني عرفت H of T
+
+144
+00:12:05,030 --> 00:12:08,530
+بيساوي F of Phi of T اللي هو F is differentiable,
+
+145
+00:12:08,590 --> 00:12:11,950
+Phi is differentiable إذاً نفسي H is differentiable
+
+146
+00:12:11,950 --> 00:12:14,850
+و الـ derivative إليها إيه؟ الشمال هذه بيساوي اللي
+
+147
+00:12:14,850 --> 00:12:19,670
+أمامي و الشغل الثاني اللي حصلنا عليه أن H of
+
+148
+00:12:19,670 --> 00:12:25,010
+Alpha إيش هيساوي يا شباب؟ هو يساوي 0 نيجي الآن
+
+149
+00:12:25,010 --> 00:12:31,250
+بدنا نوصل لمين إحنا؟ إحنا هدفنا يا جماعة اللي هو
+
+150
+00:12:31,250 --> 00:12:38,310
+هدفنا سامحونا على اللوح الصغير اللوح هدفنا هو الـ
+
+151
+00:12:38,310 --> 00:12:47,210
+integration من Alpha لعند Beta F of Phi of T Phi
+
+152
+00:12:47,210 --> 00:12:54,670
+prime of T dt بساوي الـ integration للـ F of X DX من
+
+153
+00:12:54,670 --> 00:12:59,290
+Phi of Alpha لعند Phi of Beta هذا اللي بدنا نثبته
+
+154
+00:12:59,290 --> 00:13:09,190
+شوف كيف بدنا نصل لهذا اللي هو المطلوب نيجي
+
+155
+00:13:09,190 --> 00:13:16,090
+لهذا الـ integration اللي قبلنا هذا اللي هو الطرف
+
+156
+00:13:16,090 --> 00:13:20,580
+اللي إحنا بدنا نثبته بساوي هذا الطرف هذا الطرف اللي
+
+157
+00:13:20,580 --> 00:13:23,340
+أنا ساويه هذا، نبدأ بهذا الطرف اللي هنا ونبني
+
+158
+00:13:23,340 --> 00:13:26,920
+المعلومات ونحصل على اللي بدنا إياه بكل سهولة الآن الـ
+
+159
+00:13:26,920 --> 00:13:29,920
+integration من Alpha لعند الـ Beta F of five T five
+
+160
+00:13:29,920 --> 00:13:35,620
+prime of T DT بتساوي الآن الـ F هذه في الواقع مين
+
+161
+00:13:35,620 --> 00:13:41,850
+هي؟ هذه هي عبارة عن F prime إذا صار عندي الآن هذا
+
+162
+00:13:41,850 --> 00:13:45,790
+المقدار هو عبارة عن f prime of five a t five prime
+
+163
+00:13:45,790 --> 00:13:51,350
+a شماله of t يعني وكأنني مين بفاضل؟ أنا بفاضل كل
+
+164
+00:13:51,350 --> 00:13:58,890
+هذا المقدار طلع مين هو؟ h prime of t وكل أموره حلوة
+
+165
+00:13:58,890 --> 00:14:05,170
+ومحترمة الـ f اللي هي continuous والـ Phi prime
+
+166
+00:14:05,170 --> 00:14:09,090
+continuous معطيني إياها إذاً هذه صارت الـ H' كلها مالها
+
+167
+00:14:09,090 --> 00:14:11,970
+continuous إذا الـ integration من Alpha لـ Beta
+
+168
+00:14:11,970 --> 00:14:17,390
+لـ H' of T اللي هو الـ integration بـ cancel الـ
+
+169
+00:14:17,390 --> 00:14:19,990
+differentiation اللي هي الجزء الأول من الـ
+
+170
+00:14:19,990 --> 00:14:22,790
+fundamental theorem of calculus يا جماعة فبيصير
+
+171
+00:14:22,790 --> 00:14:29,910
+إيش بيساوي الجواب؟ H of Beta ناقص H of mean of
+
+172
+00:14:29,910 --> 00:14:33,960
+Alpha إذن صار عندي الآن h of alpha قبل شوية شهية
+
+173
+00:14:33,960 --> 00:14:36,720
+نذكّر و كده لسه كاتب إنها إيش بتساوي صفر إذا صار
+
+174
+00:14:36,720 --> 00:14:41,860
+المقدار هذا كله اللي أنا بدي إياه إيش صار بيساوي؟ h of
+
+175
+00:14:41,860 --> 00:14:47,720
+Beta إذا اللي أثبتته تقريباً عندي خلصت أثبتت إن الـ
+
+176
+00:14:47,720 --> 00:14:54,080
+integration اللي أمامي هذا كله بيساوي مين؟ H of Beta
+
+177
+00:14:54,080 --> 00:15:01,480
+خلّينا نحسب H of Beta H of T إحنا F of Phi of T إذا H
+
+178
+00:15:01,480 --> 00:15:08,220
+of Beta بيساوي F of Phi of Beta H of Beta بيساوي F of
+
+179
+00:15:08,220 --> 00:15:14,040
+Phi of Beta الآن ما يساوي؟ الـ integration .. الـ
+
+180
+00:15:14,040 --> 00:15:17,260
+integration سبوكوا من الـ D لأن أنا ما أستخدمش الرموز
+
+181
+00:15:17,260 --> 00:15:23,040
+هذه إيش هذا بيساوي؟ بيصير عندي F .. F اللي هو of
+
+182
+00:15:23,040 --> 00:15:28,260
+Phi of Beta حسب التعريف F of U هاي و أماني بيساوي الـ
+
+183
+00:15:28,260 --> 00:15:37,600
+integration من Phi of Alpha لعند Phi of Beta F of X
+
+184
+00:15:37,600 --> 00:15:45,960
+DX وهو هذا المطلوب صار عندي الـ integration لـ .. اللي
+
+185
+00:15:45,960 --> 00:15:49,600
+هي F of X DX من five of alpha لعند five of beta
+
+186
+00:15:49,600 --> 00:15:54,460
+اللي هو H of Beta بساوي اللي هو الـ integration اللي
+
+187
+00:15:54,460 --> 00:16:02,040
+أمامي وهو المطلوب طيب نيجي الآن للنظرية الثانية
+
+188
+00:16:02,040 --> 00:16:08,740
+النظرية الثانية اللي هي second substitution
+
+189
+00:16:08,740 --> 00:16:20,020
+theorem اللي هي .. أيضًا بنستخدمها وحنشوف إيش اللي
+
+190
+00:16:20,020 --> 00:16:26,260
+هي هذه النظرية وكيف نبرهن النظرية والبرهان برضه
+
+191
+00:16:26,260 --> 00:16:33,080
+مش صعب أو البرهان اللي هو سهل هنشوف الـ second
+
+192
+00:16:33,080 --> 00:16:36,960
+substitution theorem بتقول ما يلي عند في function
+
+193
+00:16:38,340 --> 00:16:42,180
+فاي من J لعند بار J هي نفس الفترة اللي .. الفترة
+
+194
+00:16:42,180 --> 00:16:45,700
+اللي إحنا حكينا عنها اللي هي عبارة عن Alpha و Beta
+
+195
+00:16:45,700 --> 00:16:49,980
+بدنا نفترض أن الـ فاي هذه have a continuous
+
+196
+00:16:49,980 --> 00:16:57,700
+derivative برضه نفس اللي هي المعتاد أولاني ونفترض I
+
+197
+00:16:57,700 --> 00:17:02,700
+عبارة عن interval بتحتوي Phi of J نفس المعتاد في
+
+198
+00:17:02,700 --> 00:17:07,220
+النظرية السابقة الآن المعتاد جديد بدنا نفترض أنه
+
+199
+00:17:07,220 --> 00:17:12,160
+فيه function ψ من I لعند R بـ a function اللي هو
+
+200
+00:17:12,160 --> 00:17:16,740
+inverse لـ مين اللي هي الـ Phi يعني عندي Phi
+
+201
+00:17:16,740 --> 00:17:24,140
+بشروط النظرية اللي فاتت من J لعند مين؟ لعند R وعندي
+
+202
+00:17:24,140 --> 00:17:29,800
+بـ Psi من عند I لعند R ومفترضين أنه بـ Psi هي الـ
+
+203
+00:17:29,800 --> 00:17:33,940
+inverse لـ مين للـ Phi يعني Phi composite بـ Psi
+
+204
+00:17:35,340 --> 00:17:39,940
+بساوي مين؟ الـ identity function أو Psi composite الـ
+
+205
+00:17:39,940 --> 00:17:45,960
+Phi عبارة عن الـ identity function وكل اللي هو عندي
+
+206
+00:17:45,960 --> 00:17:53,460
+مفترضين أن Phi of J subset من مين؟ من الـ I عشان
+
+207
+00:17:53,460 --> 00:18:00,680
+يكون اللي هو الـ composition معرف إحنا 
+
+208
+00:18:08,270 --> 00:18:15,850
+صارت بـ Psi هي الـ inverse لـ Phi و F برضه نفس
+
+209
+00:18:15,850 --> 00:18:20,230
+المعطيات الفاترة continuous on I إذا ما يعني، إذا
+
+210
+00:18:20,230 --> 00:18:25,190
+يعني اللي بحكيه وكأنه نفس شروط النظرية السابقة بس
+
+211
+00:18:25,190 --> 00:18:30,190
+اللي أضفنا إن الـ Phi اللي عندنا في هذه الحالة
+
+212
+00:18:30,190 --> 00:18:35,220
+فيه إلها inverse فيه لها inverse فبتعطيني مجال
+
+213
+00:18:35,220 --> 00:18:39,900
+للتحرك أكثر من الأولى إلها دي بتفترضش أنه في
+
+214
+00:18:39,900 --> 00:18:42,900
+لها inverse وبنبدأ بنعوّض زي ما عوضنا قبل إيش
+
+215
+00:18:42,900 --> 00:18:48,580
+النتيجة طيب النتيجة هي ما يلي اللي هو إذا الـ
+
+216
+00:18:48,580 --> 00:18:56,560
+integration أبو حسين ازيحه بس نجاعي شوية
+
+217
+00:19:03,530 --> 00:19:21,050
+النص اللي لدك على الحيط أصلا السلام
+
+218
+00:19:21,050 --> 00:19:22,150
+عليكم السلام عليكم
+
+219
+00:19:41,080 --> 00:19:43,960
+خلاص ساعة سبعة يا عزيزي خلاص خلاص
+
+220
+00:19:46,210 --> 00:19:50,670
+إذا الآن الـ .. الـ .. الـ .. الـ .. second
+
+221
+00:19:50,670 --> 00:19:54,290
+substitution theorem نفس شروط اللي هو الـ fair
+
+222
+00:19:54,290 --> 00:19:58,590
+substitution theorem بس الآن اللي هيضيفنا عليها أنه
+
+223
+00:19:58,590 --> 00:20:02,150
+بـ Psi عندي فرضنا أنه في عندي Psi function من I
+
+224
+00:20:02,150 --> 00:20:07,270
+لعند R هي عبارة عن الـ inverse لمين؟ لفاي بناء ..
+
+225
+00:20:07,270 --> 00:20:12,990
+بناء عليه هيصير الـ integration من Alpha لعند Beta F
+
+226
+00:20:12,990 --> 00:20:19,230
+of Phi of T DT لأن مش ظاهرة عندنا هنا مين الـ
+
+227
+00:20:19,230 --> 00:20:23,650
+derivative لمين؟ لإي اللي هي الـ Phi بالرغم من هيك
+
+228
+00:20:23,650 --> 00:20:27,470
+هيطلع عندي بساوي الـ integration F of X بـ Phi prime
+
+229
+00:20:27,470 --> 00:20:31,810
+of X DX اللي هو عندي من Phi of Alpha لعند مين؟
+
+230
+00:20:31,810 --> 00:20:33,770
+لعند Phi of Beta
+
+231
+00:20:36,860 --> 00:20:42,520
+الآن نشوف اللي هو كيف نبرهن نظريتنا خلينا نكتب
+
+232
+00:20:42,520 --> 00:20:46,800
+هذه على جهة عشان نعرف إحنا لوين رايحين الـ
+
+233
+00:20:46,800 --> 00:20:55,880
+integration من Alpha لعند Beta F of Phi of T dt
+
+234
+00:20:55,880 --> 00:21:08,520
+بساوي الـ integration لـ Psi of Alpha F of أو F of X
+
+235
+00:21:08,520 --> 00:21:21,440
+Phi prime of .. Psi prime of X DX Phi prime of X
+
+236
+00:21:21,440 --> 00:21:27,600
+DX من Phi of Alpha لعند
+
+237
+00:21:27,600 --> 00:21:36,060
+Phi of Beta دعونا نشوف كيف .. نيجي نشوف البرهان جرب
+
+238
+00:21:36,060 --> 00:21:42,560
+انت لحالك عوض اللي هو عشان تشوف منطقية النظرية زي
+
+239
+00:21:42,560 --> 00:21:49,880
+ما كنا نعوض في الـ calculus عوض عن X بـ Phi of T ها
+
+240
+00:21:49,880 --> 00:21:55,540
+هيطلع عندك اللي هو في النهاية DT هو عبارة عن كل
+
+241
+00:21:55,540 --> 00:21:59,890
+هذه لو عوضت طبعاً باستخدام اللي هو العلاقة بين الـ
+
+242
+00:21:59,890 --> 00:22:03,170
+.. ال .. الـ inverse اللي هي الـ Psi إنها inverse
+
+243
+00:22:03,170 --> 00:22:07,210
+على Phi هتحصل على اللي هو .. اللي هو كل هذا
+
+244
+00:22:07,210 --> 00:22:12,750
+المقدار هو هيطلع مين هو؟ دي T و هتصير بدل Alpha Phi
+
+245
+00:22:12,750 --> 00:22:15,550
+of Alpha و Beta Phi of Beta زي ما أنتم عارفين
+
+246
+00:22:15,550 --> 00:22:19,490
+لأنه لما كانت T بتساوي Alpha طلعت اللي هي Phi of
+
+247
+00:22:19,490 --> 00:22:21,970
+T لعوضة مكانها اللي هي Phi of Alpha و الثانية
+
+248
+00:22:21,970 --> 00:22:29,420
+هتطلع Phi of Beta طب نيجي الآن لبرهان النظرية الآن
+
+249
+00:22:29,420 --> 00:22:34,860
+عندي أول حاجة five prime of T بعطينا إياها شماله
+
+250
+00:22:34,860 --> 00:22:39,660
+لا تساوي صفر طبعاً هذا لزوم لزوم أن تكون الـ inverse
+
+251
+00:22:39,660 --> 00:22:44,900
+موجودة five prime of T لا تساوي صفر يعني الآن five
+
+252
+00:22:44,900 --> 00:22:49,180
+prime of T يا أكبر من صفر يا أصغر من صفر عندي
+
+253
+00:22:49,180 --> 00:22:52,680
+المنطق اللي هيكون عندي اللي هي strictly increasing
+
+254
+00:22:52,680 --> 00:22:55,860
+أو strictly decreasing على المنطقة اللي هي فيها
+
+255
+00:22:55,860 --> 00:23:00,060
+إذا في عندي بمعنى آخر strictly monotone مدام
+
+256
+00:23:00,060 --> 00:23:04,940
+strictly monotone إذا الـ inverse إلها موجود و في
+
+257
+00:23:04,940 --> 00:23:08,900
+بتساوي الـ inverse زي ما هو معطينا إياها طبعاً إحنا
+
+258
+00:23:08,900 --> 00:23:14,410
+معطينا الـ فيالـ Phi مش differentiable بس Phi مش
+
+259
+00:23:14,410 --> 00:23:17,990
+differentiable اللي هو الـ derivative موجودة و
+
+260
+00:23:17,990 --> 00:23:22,310
+شماله continuous طيب لأن بما أنه اللي هي Phi
+
+261
+00:23:22,310 --> 00:23:27,850
+prime exist إذا بنظرية أخذناها اللي هي 6 1 9 هتكون
+
+262
+00:23:27,850 --> 00:23:32,170
+الـ Phi prime exist وبتساوي واحد على في برايم في
+
+263
+00:23:32,170 --> 00:23:36,350
+مين؟ في بساي كمان مرة يا جماعة أذكركم في النظرية
+
+264
+00:23:36,350 --> 00:23:41,410
+الآن عندي مدامة بساي بساوي في انفرس والفي نفسها
+
+265
+00:23:41,410 --> 00:23:45,450
+عبارة عن differentiable هتكون الـ inverse اللي هي
+
+266
+00:23:45,450 --> 00:23:48,910
+بساي is differentiable والـ derivative اللي هي بساي
+
+267
+00:23:48,910 --> 00:23:53,490
+برايم هي عبارة عن واحد على في برايم ماله؟ composite
+
+268
+00:23:53,490 --> 00:23:58,400
+بساي اللي هي .. أو مش هيك هتطلع .. هتطلع continuous
+
+269
+00:23:58,400 --> 00:24:01,500
+ليش continuous؟ لأنه أصلاً ما فيش أسفار في المقام
+
+270
+00:24:01,500 --> 00:24:05,100
+أكيد وعند Phi prime نفسها Phi prime نفسها
+
+271
+00:24:05,100 --> 00:24:08,520
+continuous معطيني إياها و بـ Psi is continuous لأنها
+
+272
+00:24:08,520 --> 00:24:11,800
+أصلًا differentiable فهتطلع عندي اللي هي بـ Psi prime
+
+273
+00:24:11,800 --> 00:24:17,180
+برضه مالها؟ is continuous إذن اللي استنتجناه الآن
+
+274
+00:24:17,180 --> 00:24:22,590
+أن الـ inverse function is continuous وقيمتها الـ
+
+275
+00:24:22,590 --> 00:24:26,310
+Derivative إليها هي عبارة عن واحد على Psi Prime في
+
+276
+00:24:26,310 --> 00:24:31,890
+Phi Prime في مين؟ في Psi نشوف الآن بدنا نعرف اللي
+
+277
+00:24:31,890 --> 00:24:36,850
+هو بأسلوب مشابه قبل بشوية أنه نعرف دوال بحيث أنه
+
+278
+00:24:36,850 --> 00:24:41,810
+لما نيجي اللي هو ناخده تبقى derivative لشيء سهل
+
+279
+00:24:41,810 --> 00:24:45,210
+إيجاده ولما ناخده له الـ integration يطلع اللي هو
+
+280
+00:24:45,210 --> 00:24:48,350
+نفس الدالة عند نقطة الأولى ناقص النقطة الثانية 
+
+281
+00:24:48,350 --> 00:24:50,950
+اللي هو باستعماله في أنظمة التلفيرموفكالكلاس أيش
+
+282
+00:24:50,950 --> 00:24:55,480
+اللي بقوله؟ خلّيني نشوفه اللي هنعرّف ليها جمعة جي
+
+283
+00:24:55,480 --> 00:24:59,360
+من جي لعند R اللي هي عبارة عن ف ليها أنها تكون
+
+284
+00:24:59,360 --> 00:25:02,960
+إيه شمالها Anti-derivative للـ continuous function
+
+285
+00:25:02,960 --> 00:25:06,500
+of composite phiF composite Phi continuous؟ أه
+
+286
+00:25:06,500 --> 00:25:09,440
+continuous لأن الـ Phi is continuous قلنا ال
+
+287
+00:25:09,440 --> 00:25:12,160
+derivative إليها continuous كمان مش كايكوا بس و ال
+
+288
+00:25:12,160 --> 00:25:16,340
+F معطينا إياها continuous فلمّا أقول إن عرف G
+
+289
+00:25:16,340 --> 00:25:19,180
+هتكون antiderivative لمين هذه؟ طب هدي إياها
+
+290
+00:25:19,180 --> 00:25:21,320
+antiderivative؟ أه مدام continuous و المرة اللي
+
+291
+00:25:21,320 --> 00:25:23,260
+فاتت قولنا ده كانت الدالة continuous على طول فيه
+
+292
+00:25:23,260 --> 00:25:26,640
+إليها antiderivative إيش يعني؟ يعني الـ G prime
+
+293
+00:25:26,640 --> 00:25:33,270
+هتكون مين؟ الـ F composite Phi طيب الآن دي إذا مدام
+
+294
+00:25:33,270 --> 00:25:37,130
+اللي هي الـ G Antiderivative للـ F Composite Phi
+
+295
+00:25:37,130 --> 00:25:40,530
+إذا الـ G' Exists إذا الـ G Differentiable و لو
+
+296
+00:25:40,530 --> 00:25:42,690
+بصي Differentiable إذا الـ Composition اللي هو إيش
+
+297
+00:25:42,690 --> 00:25:47,870
+برضه هيطلع Differentiable إيش يعني؟ طيب .. طب وإيش
+
+298
+00:25:47,870 --> 00:25:50,950
+يعني الـ differentiable؟ ها .. هالـ gate هيوصّلني
+
+299
+00:25:50,950 --> 00:25:54,290
+لإن Decomposite Phi Prime of X ده وجود الـ
+
+300
+00:25:54,290 --> 00:25:56,970
+derivative بنعرف أنه وجود الـ derivative هي عبارة
+
+301
+00:25:56,970 --> 00:26:01,610
+عن D Prime of Psi of X Psi Prime of X اللي هي
+
+302
+00:26:01,610 --> 00:26:07,600
+Chain Rule استخدام الـ Chain Rule ويساوي لأنقلنا
+
+303
+00:26:07,600 --> 00:26:11,480
+جي برايم هي مين؟ الـ F composite في إذا بشيل الجي
+
+304
+00:26:11,480 --> 00:26:15,320
+برايم و بحط مكانها F composite إيش يا جماعة في في
+
+305
+00:26:15,320 --> 00:26:19,840
+بساي of X اللي هو هيها F composite .. هي دي بدلها
+
+306
+00:26:19,840 --> 00:26:24,720
+F composite في of بساي of X في بساي برايم من of X
+
+307
+00:26:24,720 --> 00:26:32,120
+و يساوي F of اللي هو في composite بساي of X في
+
+308
+00:26:32,120 --> 00:26:37,570
+بساي برايم من of X كتبتها بس على صورة هو اللي هي
+
+309
+00:26:37,570 --> 00:26:41,510
+فكّت ال composition إيه الآن؟ ليش عملت هيك؟ عشان
+
+310
+00:26:41,510 --> 00:26:44,530
+أسهل عليكم وأقولكم أحنا بيقولوا Psi أشملن ال
+
+311
+00:26:44,530 --> 00:26:47,310
+inverse للـ Phi مزام الـ inverse مع بعض ده هو ال
+
+312
+00:26:47,310 --> 00:26:49,850
+identity ده هو الـ identity of X ده هو الـ X يعني
+
+313
+00:26:49,850 --> 00:26:54,850
+كلها هتصير F of X Psi prime إذا صار عندي هذا
+
+314
+00:26:54,850 --> 00:27:02,220
+شايفينه؟ هو عبارة عن F small of X في Psi prime of X
+
+315
+00:27:02,220 --> 00:27:07,800
+طيب سهلة الموضوع الآن إذا ناخد ال integration من
+
+316
+00:27:07,800 --> 00:27:11,100
+Phi of Alpha لـ Phi of Beta لـ F of X بـ Psi prime of
+
+317
+00:27:11,100 --> 00:27:15,540
+X DX إيش هذه؟ أه هذه اللي بدنا إياها هيها Psi
+
+318
+00:27:15,540 --> 00:27:20,130
+prime of X DX إذا نوصلنا إذا الـ integration هذا
+
+319
+00:27:20,130 --> 00:27:23,290
+بيساوي الـ integration لهذا الـ integration لهذا
+
+320
+00:27:23,290 --> 00:27:30,570
+عندي هذه اللي هان جي كوميزيت في بسايد الكل برايم
+
+321
+00:27:30,570 --> 00:27:37,870
+of x dx الان الان هنا الـ domain هذه اللي هيكون من
+
+322
+00:27:37,870 --> 00:27:42,600
+عندي اللي هي الـ I يعني لما ال .. ال .. ال .. ال ..
+
+323
+00:27:42,600 --> 00:27:43,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+324
+00:27:43,320 --> 00:27:43,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+325
+00:27:43,440 --> 00:27:44,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+326
+00:27:44,420 --> 00:27:45,660
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+327
+00:27:45,660 --> 00:27:50,280
+..
+
+328
+00:27:50,280 --> 00:27:54,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+329
+00:27:54,440 --> 00:27:55,100
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+330
+00:27:55,100 --> 00:27:57,300
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+331
+00:27:57,300 --> 00:28:06,760
+.. ال .. ال .. ال ..الآن صارت الـ derivative إلها
+
+332
+00:28:06,760 --> 00:28:09,620
+الـ integration هيلغي الـ derivative اللي هي by
+
+333
+00:28:09,620 --> 00:28:12,300
+fundamental theorem of calculus وكل الشروط زي ما
+
+334
+00:28:12,300 --> 00:28:17,420
+قلنا و انتحققها هيصير هذه اللي جوا عند هذه و هذه
+
+335
+00:28:17,420 --> 00:28:24,060
+اللي جوا عند هذه حاصل طرحين اللي هي G Phi
+
+336
+00:28:24,060 --> 00:28:29,140
+Composite Psi الكل of a G composed of Psi الكل of
+
+337
+00:28:29,140 --> 00:28:33,540
+Phi of X اللي هي الـ X في هذه الحالة إيش اسمها اللي
+
+338
+00:28:33,540 --> 00:28:39,600
+هي Alpha معلش و هذه الثانية الـ Beta آسف اللي قولها
+
+339
+00:28:39,600 --> 00:28:44,660
+Beta حد الأول و هذه الحد اللي تحت Alpha ماشي
+
+340
+00:28:44,660 --> 00:28:49,430
+الحالة هذه يعني كلها على بعض زي ما عملنا قبل هيك
+
+341
+00:28:49,430 --> 00:28:53,370
+الـ Psi و الـ Phi اللي هو عبارة عن inverse لبعض، إذا 
+
+342
+00:28:53,370 --> 00:28:58,530
+الـ Identity يعني هتصير الـ G of Beta و هذا هتصير
+
+343
+00:28:58,530 --> 00:29:04,270
+الـ G of Alpha، إذا صار عندي المقدار اللي أمامي هذا
+
+344
+00:29:04,270 --> 00:29:11,130
+اللي هو اللي أنا ببحث عنه، هذا المقدار، شايفينه؟
+
+345
+00:29:11,130 --> 00:29:15,790
+هذا المقدار طلع عبارة عن عشان استخدمه بعد شوية
+
+346
+00:29:15,790 --> 00:29:22,650
+خلينا يمكن أوضح يكون هيصير عبارة عن g of beta ناقص
+
+347
+00:29:22,650 --> 00:29:26,910
+g of alpha بتثبت لكم الثاني برضه هيكون g of beta
+
+348
+00:29:26,910 --> 00:29:31,850
+ناقص g of alpha و بكون خلصنا اللي هو برهان النظرية
+
+349
+00:29:31,850 --> 00:29:36,990
+خلصنا هذا الجزء نيجي ل اللي هو الجزء الثاني اللي
+
+350
+00:29:36,990 --> 00:29:38,410
+أسهل كمان
+
+351
+00:29:41,370 --> 00:29:44,990
+شوف يا جماعة صلى الله عليه وسلم بالسلامة احنا قلنا
+
+352
+00:29:44,990 --> 00:29:47,790
+الـ G هي الـ antiderivative لهذه يعني الـ G' بساوية
+
+353
+00:29:47,790 --> 00:29:51,850
+هذا المقدار إذا الآن بنقدر نستخدم اللي هو ال
+
+354
+00:29:51,850 --> 00:29:53,930
+fundamental theorem of calculus أو اللي هو ال
+
+355
+00:29:53,930 --> 00:29:58,090
+corollary لها بكون عند ال integration هيه للمقدار
+
+356
+00:29:58,090 --> 00:30:02,790
+هذا هيطلع ليه اللي هو مباشرة بساوية يعني ممكن
+
+357
+00:30:02,790 --> 00:30:07,230
+بعضكم لاحظ الاشي اللي بتسويه من قبل ما اشرح الآن ال
+
+358
+00:30:07,230 --> 00:30:09,670
+integration f of I of T من Alpha لـ Beta إيش
+
+359
+00:30:09,670 --> 00:30:14,370
+بيساوي؟ هذا كله بدك تشيل مكانه منين؟ تحطه G' ال
+
+360
+00:30:14,370 --> 00:30:19,390
+integration لـ G' of T dt من Alpha لعند Beta نفس
+
+361
+00:30:19,390 --> 00:30:22,690
+الحدود لأنه ما غيرناش اللي هو الـ variability اللي
+
+362
+00:30:22,690 --> 00:30:26,170
+بدنا نكامل بالنسبة له، ما يساوي على طول هذه اللي هي
+
+363
+00:30:26,170 --> 00:30:30,330
+تفاضل بـ cancel اللي هي أو التكامل بـ cancel التفاضل
+
+364
+00:30:30,330 --> 00:30:32,730
+اللي هي الـ corollary اللي حكينا عنها اللي هي
+
+365
+00:30:32,730 --> 00:30:36,090
+corollary of fundamental theorem of calculus بساوية
+
+366
+00:30:36,090 --> 00:30:41,480
+G of beta ناقص g of alpha الآن هذه صارت g of beta
+
+367
+00:30:41,480 --> 00:30:44,620
+ناقص g of alpha و هذه صارت g of beta ناقص g of
+
+368
+00:30:44,620 --> 00:30:48,320
+alpha إذا صار عندي هذا المقدار بساوي هذا المقدار
+
+369
+00:30:48,320 --> 00:30:51,400
+أو الـ integration بساوي الـ integration و بكون هيك
+
+370
+00:30:51,400 --> 00:30:55,160
+أثبتنا اللي هي النظرية الثانية أو اللي هو second
+
+371
+00:30:55,160 --> 00:31:00,200
+substitution theorem الآن تطبيقات هذه النظريات ما
+
+372
+00:31:00,200 --> 00:31:04,500
+هو هدولة تطبيقاتهم اللي هو إشبعنا فيها من Calculus
+
+373
+00:31:04,500 --> 00:31:04,780
+B
+
+374
+00:31:08,400 --> 00:31:14,420
+فبصير بس انه انت لحالك في البيت لو قعدت و عملتلك
+
+375
+00:31:14,420 --> 00:31:18,380
+سؤال سؤالين على ال substitution في الحالتين بتكون
+
+376
+00:31:18,380 --> 00:31:23,680
+اللي هو خليني نقول عمقت المفهوم عندك بشكل أكبر
+
+377
+00:31:23,680 --> 00:31:30,370
+نيجي الآن نحكي عن اللي هو احنا طبعا حكينا عن الـ
+
+378
+00:31:30,370 --> 00:31:32,690
+mean value theorem أو نظرية القيمة المتوسطة في
+
+379
+00:31:32,690 --> 00:31:36,730
+حالة ال differentiation الآن هنحكي عن القيمة
+
+380
+00:31:36,730 --> 00:31:44,470
+المتوسطة في حالة ال integration اللي
+
+381
+00:31:44,470 --> 00:31:48,190
+هو نوجينا
+
+382
+00:31:49,730 --> 00:31:53,670
+أخذنا مثلا خلّيني أخد المنطقة الموجب عشان أسهل في
+
+383
+00:31:53,670 --> 00:31:57,850
+الحديث هي عندي اللي هو function f على الفترة من a
+
+384
+00:31:57,850 --> 00:32:02,790
+لعند b الآن بتقول لي اللي هو بتقول لي هذا طبعا نظري
+
+385
+00:32:02,790 --> 00:32:06,010
+أكثر من هيك أبعد من هيك بس خلّيني أقول خلّيني أخد
+
+386
+00:32:06,010 --> 00:32:11,370
+الحالة السهلة أو خلّيني أخد الحالة اللي بتوضح
+
+387
+00:32:11,370 --> 00:32:17,210
+معانا القيمة المتوسطة الآن قيمة ال integration من
+
+388
+00:32:17,210 --> 00:32:23,660
+a لعند b هو عبارة عن المنطقة هذه ككل مساحتها لو
+
+389
+00:32:23,660 --> 00:32:31,070
+جسمناها على الـ B minus A وكأننا بناخد متوسط قيمة
+
+390
+00:32:31,070 --> 00:32:34,850
+الدالة لإنه لو اتخيلنا إنه هي قيمة الدالة و
+
+391
+00:32:34,850 --> 00:32:38,810
+بنضربها يعني تخيل إنها دي مساحة خط جنب خط جنب خط
+
+392
+00:32:38,810 --> 00:32:42,070
+جنب خط جنب خط لما اتخلص أدولها إلى أن حصل ضرب
+
+393
+00:32:42,070 --> 00:32:45,530
+الفترة هذه كلها P minus A في قيمة ال .. الها دي
+
+394
+00:32:45,530 --> 00:32:48,530
+اللي هي اللي عنده لو فرضنا إنهم يعني ال .. ال ..
+
+395
+00:32:48,530 --> 00:32:52,550
+ال .. هذه القيمة المتوسطة لهم يعني متوسطهم فبصير
+
+396
+00:32:52,550 --> 00:32:57,080
+عند كلّه على بعض المساحة بساوي اللي هو حصل ضرب P
+
+397
+00:32:57,080 --> 00:33:02,700
+minus A في متوسط قيمة التكامل اللي هو عند نقطة
+
+398
+00:33:02,700 --> 00:33:07,370
+معاه وهذا اللي بتقوله هي بتقول إذا كانت F اللي هي
+
+399
+00:33:07,370 --> 00:33:11,370
+في شروط معينة بكون عند F of X DX على B minus A
+
+400
+00:33:11,370 --> 00:33:18,210
+بساوة F of C for some C وين موجودة بين الـ A و الـ
+
+401
+00:33:18,210 --> 00:33:23,230
+B و هذه اللي هي القيمة المتوسطة للمساحة أو قيمة ال
+
+402
+00:33:23,230 --> 00:33:27,930
+integration على طول اللي هي الفترة إذن هذه اللي هي
+
+403
+00:33:27,930 --> 00:33:34,290
+خلّيني أقول حالة خاصة من نظرية القيمة المتوسطة
+
+404
+00:33:34,290 --> 00:33:38,300
+اللي بصورة عامة اللي هي .. اللي هي .. اللي نسميها
+
+405
+00:33:38,300 --> 00:33:41,960
+الـ Mean Value Theorem for Integrals نشوف الكلام،
+
+406
+00:33:41,960 --> 00:33:45,800
+يمكن الآن الكلام يكون أوضح في المن .. بشكل أوضح
+
+407
+00:33:45,800 --> 00:33:48,920
+لما نبرهن النظرية و ناخد نصها و ناخد الـ Corollary
+
+408
+00:33:48,920 --> 00:33:54,070
+اللي عليها اللي هي الحالة اللي ذكرته الآن ما بحكيه
+
+409
+00:33:54,070 --> 00:33:57,170
+عبارة عن الـ Mean Value Theorem for اللي هي أياش
+
+410
+00:33:57,170 --> 00:34:01,910
+integrals نظرية القيمة المتوسطة على التكامل طبعا
+
+411
+00:34:01,910 --> 00:34:05,470
+أنتم متذكرين القيمة المتوسطة العادية أنه لو كانت F
+
+412
+00:34:05,470 --> 00:34:08,410
+is continuous على closed interval differentiable
+
+413
+00:34:08,410 --> 00:34:11,710
+على الـ open إذاً there exists C element in A و B
+
+414
+00:34:11,710 --> 00:34:17,310
+such that اللي هي F prime of C سوى F of B ناقص F
+
+415
+00:34:17,310 --> 00:34:22,940
+of A على B minus A هنا الآن بقول لك اللي في الجزئية
+
+416
+00:34:22,940 --> 00:34:28,020
+هذه أن F is continuous على الـ A و الـ B إذن there
+
+417
+00:34:28,020 --> 00:34:32,220
+exists C في الـ A و الـ B such that ال integration من
+
+418
+00:34:32,220 --> 00:34:38,160
+A لعند B F of X DX بساوي F of C على B minus A
+
+419
+00:34:38,160 --> 00:34:44,180
+بساوة مين؟ بساوي اللي هي الـ F of C roughly ..
+
+420
+00:34:44,180 --> 00:34:47,940
+roughly .. roughly .. roughly اتخيل أنه الآن هذه 
+
+421
+00:34:47,940 --> 00:34:51,880
+عبارة عن الـderivative F هذا ثابت طبعا ال
+
+422
+00:34:51,880 --> 00:34:54,920
+derivative F prime of C وهذه اللي خدنا derivative
+
+423
+00:34:54,920 --> 00:34:58,580
+لأن integration كان اللي هو اللي هي متغيرات فبيصير
+
+424
+00:34:58,580 --> 00:35:00,580
+عند F of B بيروح ال integration مع ال
+
+425
+00:35:00,580 --> 00:35:04,040
+differentiation بيصير F of B ناقص F of A اللي فوق
+
+426
+00:35:04,040 --> 00:35:07,300
+هذا الكلام رفلي بس على أساس أن هو أن أنت اللي هو
+
+427
+00:35:07,300 --> 00:35:11,260
+تستذكر العلاقة اللي هو بين هذه وبين اللي هي
+
+428
+00:35:11,260 --> 00:35:16,550
+الأصلية، أما القيمة المتوسطة المفهوم بالمتوسط اللي
+
+429
+00:35:16,550 --> 00:35:20,510
+هو مساحة اللي هو قيمة ال integration على طول فترته
+
+430
+00:35:20,510 --> 00:35:24,370
+اللي هو بتطلع قيمة متوسطة، هذه القيمة اللي هو عبارة
+
+431
+00:35:24,370 --> 00:35:29,050
+عن متوسط قيمة وكأنه كل اللي هي قيمة ال integration
+
+432
+00:35:29,050 --> 00:35:33,630
+عنده اللي هو تحت اللي هي النقطة اللي عنده في F of
+
+433
+00:35:33,630 --> 00:35:37,150
+C بتساوي قيمة هذا ال integration على B minus A أو
+
+434
+00:35:37,150 --> 00:35:41,590
+متوسط المساحة على طول الفترة اللي هي بتساوي قيمة
+
+435
+00:35:41,590 --> 00:35:47,800
+الدالة F of C، وفعلا الـ C موجودة هي المهم أن الـ C
+
+436
+00:35:47,800 --> 00:35:51,000
+هي دي فعلا هنلاقيها موجودة وبتمثل قيمة ال
+
+437
+00:35:51,000 --> 00:35:54,620
+integration على طول الفترة، وهذا معناه اللي هو
+
+438
+00:35:54,620 --> 00:35:58,340
+المتوسط قيمة ال integration على طول الفترة هنلاقيه
+
+439
+00:35:58,340 --> 00:36:02,620
+فعلا بيمثله مقطع بين ال A و ال B وهذا بسميها
+
+440
+00:36:02,620 --> 00:36:08,510
+القيمة المتوسطة mean value theorem for integrals
+
+441
+00:36:08,510 --> 00:36:12,930
+let F be continuous on I and let B be integrable
+
+442
+00:36:12,930 --> 00:36:16,920
+function on I الـ B هذه أنا ما أخدها بتقبل بشوية في
+
+443
+00:36:16,920 --> 00:36:22,680
+مثال على أنها بتساوي واحد طيب let F be continuous
+
+444
+00:36:22,680 --> 00:36:25,560
+on I of A و B and let B be an integrable function
+
+445
+00:36:25,560 --> 00:36:29,740
+on I and نفترض أن B of X أكبر يساوي صفر for every
+
+446
+00:36:29,740 --> 00:36:32,900
+X element in I then there exists C element in I
+
+447
+00:36:32,900 --> 00:36:37,880
+such that الآن هاي الـ C اللي هي بدها تمثل اللي هي
+
+448
+00:36:37,880 --> 00:36:40,980
+النقطة اللي بنلاقيها في الـ I بحيث أن ال
+
+449
+00:36:40,980 --> 00:36:46,230
+integration من A لB F of X DX DX على اللي هي ال
+
+450
+00:36:46,230 --> 00:36:48,170
+integration من a إلى b بيقوم باقوم باقوم باقوم
+
+451
+00:36:48,170 --> 00:36:49,190
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+452
+00:36:49,190 --> 00:36:50,170
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+453
+00:36:50,170 --> 00:36:55,050
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+454
+00:36:55,050 --> 00:36:55,210
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+455
+00:36:55,210 --> 00:36:56,930
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+456
+00:36:56,930 --> 00:37:02,790
+باقوم باقوم
+
+457
+00:37:02,790 --> 00:37:04,290
+ب
+
+458
+00:37:11,900 --> 00:37:19,760
+الـ integration من a ل b f of x b of x dx على ال
+
+459
+00:37:19,760 --> 00:37:23,820
+integration نفترض أنه ليس فارق بيه بيه بيه بيه بيه
+
+460
+00:37:23,820 --> 00:37:25,260
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+461
+00:37:25,260 --> 00:37:26,640
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+462
+00:37:26,640 --> 00:37:29,220
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+463
+00:37:29,220 --> 00:37:38,400
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+464
+00:37:38,400 --> 00:37:43,710
+بي بيصير هذه واحد اللي هي بيصير هذه B minus A اللي
+
+465
+00:37:43,710 --> 00:37:48,390
+قلت قبل شوية اللي هو قيمة المساحة أو قيمة ال
+
+466
+00:37:48,390 --> 00:37:52,670
+integration على طول الفترة بيساوي فعلا مقطع فعلي
+
+467
+00:37:52,670 --> 00:38:00,790
+في الفترة I، نيجي نبرهن أن هذه هي بصورة عامة عند F
+
+468
+00:38:00,790 --> 00:38:08,600
+continuous إذا F is integrable and so F اللي هو A
+
+469
+00:38:08,600 --> 00:38:12,760
+of X في B of X is Integrable لأن B Integrable و F
+
+470
+00:38:12,760 --> 00:38:15,300
+Integrable صار الـ composition اللي هنا Integrable
+
+471
+00:38:15,300 --> 00:38:19,280
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+472
+00:38:19,280 --> 00:38:19,580
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+473
+00:38:19,580 --> 00:38:20,220
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+474
+00:38:20,220 --> 00:38:20,300
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+475
+00:38:20,300 --> 00:38:20,360
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+476
+00:38:20,360 --> 00:38:20,380
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+477
+00:38:20,380 --> 00:38:21,740
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+478
+00:38:21,740 --> 00:38:23,080
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+479
+00:38:23,080 --> 00:38:25,040
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+480
+00:38:25,040 --> 00:38:27,280
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+481
+00:38:27,280 --> 00:38:34,460
+اللي هنا Integrable اللي هنا Integ
+
+482
+00:38:42,230 --> 00:38:46,930
+عندي F continuous إذا انتيجرابل و B-integrable إذا 
+
+483
+00:38:46,930 --> 00:38:52,610
+FB-integrable سمّيلي الـ M small هي الـ infimum للـ
+
+484
+00:38:52,610 --> 00:38:55,830
+F of I موجودة أه طبعا و هي F is integrable is
+
+485
+00:38:55,830 --> 00:39:00,610
+unbounded M capital بيساوي ال supremum لمين؟ لل F of
+
+486
+00:39:00,610 --> 00:39:05,210
+I، إذن الآن الدروب صارت عندي ال F of X بين ال M
+
+487
+00:39:05,210 --> 00:39:09,030
+small و بين ال M capital الدروب لكل انفمين في B of
+
+488
+00:39:09,030 --> 00:39:14,190
+X، وبنقدر أه بنقدر لإن بي بيضالها زي ما هي أه لإن
+
+489
+00:39:14,190 --> 00:39:20,450
+بي موجبة، إذا صار عندي الآن هذه ال inequality صحيحة
+
+490
+00:39:20,450 --> 00:39:23,830
+و كلها integrable إذا ال integration على الأولى
+
+491
+00:39:23,830 --> 00:39:26,350
+أصغر أو يساوي ال integration على الثانية أصغر أو يساوي
+
+492
+00:39:26,350 --> 00:39:29,850
+ال integration على الثالثة و ال M بتطلع برا لإنه
+
+493
+00:39:29,850 --> 00:39:38,110
+ال M يشملها ثابتة الآن لو ال integration لل .. لل
+
+494
+00:39:38,110 --> 00:39:44,710
+.. لل .. لل B بيساوي 0 إذا ال integration هيكون اللي
+
+495
+00:39:44,710 --> 00:39:49,730
+هو اللي فوق ال .. ال .. ال .. ال .. النظرية بتصلح
+
+496
+00:39:49,730 --> 00:39:55,930
+لأي قيمة اللي هو للـ C لأن هيكون إيش بيساوي ..
+
+497
+00:39:55,930 --> 00:40:00,310
+أنا أطلعلكم فوق لأن لو فرضنا ال integration للـ B
+
+498
+00:40:00,310 --> 00:40:05,930
+بيساوي صفر integration للـ B بيساوي صفر بيصير اللي
+
+499
+00:40:05,930 --> 00:40:10,990
+هو هذه برضه ال integration هذا هيساوي إيش؟ هيساوي
+
+500
+00:40:10,990 --> 00:40:14,810
+صفر عارفين ليش؟ لأن مادام ال integration هذا صفر
+
+501
+00:40:14,810 --> 00:40:16,710
+و ال integration هذا صفر إذا ال integration اللي
+
+502
+00:40:16,710 --> 00:40:22,170
+في النص إيش هيساوي؟ صفر إذا صارت هذا المقدار صفر
+
+503
+00:40:22,170 --> 00:40:28,430
+وهذا صفر إيش ما تختار C هتتحقق اللي هي مين؟ طرفي
+
+504
+00:40:28,430 --> 00:40:33,790
+المعادلة، إذن الآن حالة الصفر is a trivial case يعني
+
+505
+00:40:33,790 --> 00:40:36,890
+حالة أن تكون هذه صفر is a trivial case لأن
+
+506
+00:40:36,890 --> 00:40:39,890
+automatic زي ما قلنا مدامة هذه صفر وهذه صفر مدامنا
+
+507
+00:40:39,890 --> 00:40:43,310
+في النص صفر إذن اللي هو أي اختيار للـC هيكون طرف
+
+508
+00:40:43,310 --> 00:40:47,410
+أي معادلة صحيحة يعني اللي هو ال equality تبعتنا
+
+509
+00:40:47,410 --> 00:40:51,470
+صحيحة، الآن بدنا نيجي لمين يا جماعة؟ إيش غرضنا؟
+
+510
+00:40:51,470 --> 00:40:56,460
+غرضنا نلاقي C بحيث أن هذا بيساوي هذا خلصنا حالة اللي
+
+511
+00:40:56,460 --> 00:40:59,240
+هي ال integration بيساوي صفر، نفترض أن ال
+
+512
+00:40:59,240 --> 00:41:02,480
+integration مش صفر، ليش؟ أنه بدي أكسب عنه إذا صار
+
+513
+00:41:02,480 --> 00:41:05,860
+عندي ال integration أكسب الجهتين عن ال integration
+
+514
+00:41:05,860 --> 00:41:09,360
+لل B ال integration لل B اللي فرضنا أنه مش صفر إذا
+
+515
+00:41:09,360 --> 00:41:11,580
+صار ال integration هذا على ال integration هذا بين
+
+516
+00:41:11,580 --> 00:41:16,840
+ال M small و ال M أشمالها capital ماشي، الحالة الآن
+
+517
+00:41:16,840 --> 00:41:25,420
+احنا بنقول أن هذا صار رقم بين الـ M small والـ M
+
+518
+00:41:25,420 --> 00:41:35,540
+capital، وبنقول أن F continuous on الفترة A وB then
+
+519
+00:41:35,540 --> 00:41:46,560
+أي رقم .. أي رقم الآن للدالة اللي هو .. هوضح لكم
+
+520
+00:41:46,560 --> 00:41:48,900
+هي .. أذكركم الـ intermediate value theorem اللي
+
+521
+00:41:48,900 --> 00:41:53,720
+نسيها هي عندي مثلا هي أعلى قيمة أقل قيمة وهي أعلى
+
+522
+00:41:53,720 --> 00:42:02,140
+قيمة، هذه الآن الـ function f of x اللي هي بين اللي
+
+523
+00:42:02,140 --> 00:42:12,640
+هو M capital M small أو بين مين؟ M capital، الآن
+
+524
+00:42:12,640 --> 00:42:20,220
+لو إجينا أخدنا أي قيمة أي قيمة عدد أي عدد A بين الـ
+
+525
+00:42:20,220 --> 00:42:23,980
+M small والـ M capital، متامة الـ F continuously عن
+
+526
+00:42:23,980 --> 00:42:28,200
+أي قيمة هنا أخدناها قيمة هنلاقي اللي هو there
+
+527
+00:42:28,200 --> 00:42:32,040
+exists C element في الفترة A وB المعرف عليها
+
+528
+00:42:32,040 --> 00:42:38,040
+الدائرة هتسميها C مثلا أو D هنلاقي الـ C في الفترة
+
+529
+00:42:38,040 --> 00:42:45,030
+بين A وB بحيث أن F of C هي مين؟ القيمة F of D اللي
+
+530
+00:42:45,030 --> 00:42:47,050
+هي الـ Intermediate Value Theorem اللي أنتو
+
+531
+00:42:47,050 --> 00:42:50,790
+عارفينها اللي هي For Continuous Function، إذا بما
+
+532
+00:42:50,790 --> 00:42:55,790
+أن الـ function F is continuous و هذه القيمة بين
+
+533
+00:42:55,790 --> 00:43:00,490
+أعلى قيمة .. بين أعلى قيمة و أقل قيمة للدالة إذا
+
+534
+00:43:00,490 --> 00:43:05,950
+أكيد هقدر ألاقي C element in I بحيث أن F of C
+
+535
+00:43:05,950 --> 00:43:10,830
+بيساوى هذا الرقم اللي هو هذه القيمة اللي هو ال
+
+536
+00:43:10,830 --> 00:43:16,520
+integration بيساوي اللي هو F of C في القيمة هذه وهو
+
+537
+00:43:16,520 --> 00:43:22,000
+المطلوب يعني النظرية برهانة بسيطة يا جماعة بس مدام
+
+538
+00:43:22,000 --> 00:43:27,740
+حصرنا قيمة للقيمة هذه اللي هي بين اللي هي ال M و
+
+539
+00:43:27,740 --> 00:43:30,840
+ال M إذا بال intermediate value theorem في C
+
+540
+00:43:30,840 --> 00:43:37,500
+وخلصنا طيب اللي بعده ال corollary حكيتها هذه إن
+
+541
+00:43:37,500 --> 00:43:38,360
+لو كانت F 
+
+542
+00:43:43,100 --> 00:43:47,820
+الـ Corollary حكيتها لو كانت F continuous على اللي
+
+543
+00:43:47,820 --> 00:43:50,940
+هي الـ closed interval A و B هنلاقي الـC في الـI
+
+544
+00:43:50,940 --> 00:43:53,720
+بحيث أن ال integration من A لB للF سواء F of C في
+
+545
+00:43:53,720 --> 00:44:00,900
+B minus A، قلنا هذه اللي هي حالة خاصة من النظرية بس
+
+546
+00:44:00,900 --> 00:44:08,160
+حط لي الـF الـB of X بيساوي 1، حالة خاصة من النظرية
+
+547
+00:44:08,160 --> 00:44:10,480
+النظريتنا
+
+548
+00:44:11,580 --> 00:44:17,340
+أن الـ integration للـ F في B بيساوي F of C في الـ
+
+549
+00:44:17,340 --> 00:44:21,320
+integration للـ B من Alpha لعند Beta و لا من A
+
+550
+00:44:21,320 --> 00:44:29,620
+لعند B من A لعند B for some C element in I، مظبوط؟
+
+551
+00:44:29,620 --> 00:44:33,180
+الآن بقول لي اللي هو ال integration للـ F بيساوي F
+
+552
+00:44:33,180 --> 00:44:36,720
+of C في B minus A for some C، حط الـ B بيساوي،
+
+553
+00:44:36,720 --> 00:44:41,420
+هتجسي ال integration للـ F بس بي بي بي بي بي بي بي
+
+554
+00:44:41,420 --> 00:44:48,320
+بي بي بي بي بي بي بي
+
+555
+00:44:51,410 --> 00:44:58,470
+اللي هو dx y بيساوي اللي هو f of c هدف b minus a وهو
+
+556
+00:44:58,470 --> 00:45:02,690
+المطلوب هنلحقه كمان مرة، إذا الـ Corollary اللي
+
+557
+00:45:02,690 --> 00:45:09,030
+هي اللي أمامنا تم برهانها مرة أخرى، نيجي الآن للي
+
+558
+00:45:09,030 --> 00:45:13,310
+هي Taylor's theorem أخدناها Taylor's theorem كان
+
+559
+00:45:13,310 --> 00:45:20,900
+ال remainder اللي هو اللي هو شيء مفضل أو الـ
+
+560
+00:45:20,900 --> 00:45:26,560
+Taylor's theorem إذا صح التعبير for integration و 
+
+561
+00:45:26,560 --> 00:45:29,500
+Taylor's theorem for differentiations الآن الجزء 
+
+562
+00:45:29,500 --> 00:45:33,060
+اللي هو الـ for integration نشوف شيء اللي بقوله
+
+563
+00:45:35,050 --> 00:45:38,890
+suppose that the function f and its derivatives f 
+
+564
+00:45:38,890 --> 00:45:43,030
+prime up to f n and f n زائد واحد are كلهم
+
+565
+00:45:43,030 --> 00:45:46,330
+أيّ  شمالهم continuous يعني نفترض أن الـ 
+
+566
+00:45:46,330 --> 00:45:49,710
+derivative الـ n زائد واحد derivative is
+
+567
+00:45:49,710 --> 00:45:53,890
+continuous exist  وcontinuous نفترض أن الدالة f
+
+568
+00:45:53,890 --> 00:45:59,610
+عبارة عن دالة قابلة للاشتقاق n زائد واحد من المرات
+
+569
+00:45:59,610 --> 00:46:05,310
+وتكون الـ n زائد واحد كمان نفسها continuous ماشية على
+
+570
+00:46:05,310 --> 00:46:10,290
+الفترة a و b then بقول لي اللي هو f of b بيساوي f
+
+571
+00:46:10,290 --> 00:46:14,170
+of a زائد f prime of a على 1 factorial في b minus a
+
+572
+00:46:14,170 --> 00:46:18,990
+زائد f double prime of a على 2 factorial في b minus
+
+573
+00:46:18,990 --> 00:46:22,410
+a تربيع زائد لما أصل عند f n of a على n factorial
+
+574
+00:46:22,410 --> 00:46:26,530
+في b minus a الكلّ أُسّ n هذا كله إيش معناه؟ عارفينه قبل
+
+575
+00:46:26,530 --> 00:46:30,050
+كده وعملنا زائد مين؟ الـ remainder are n الـ
+
+576
+00:46:30,050 --> 00:46:34,730
+remainder are n كتبوا على صورة integration بس الـ
+
+577
+00:46:34,730 --> 00:46:37,550
+remainder are n كتب على صورة واحدة الـ N factorial
+
+578
+00:46:37,550 --> 00:46:41,150
+في الـ integration من a لـ b بـ ماينس تي أُسّ n  f n زائد
+
+579
+00:46:41,150 --> 00:46:50,010
+واحد of T دي تي إذن الآن بقول لك f of b f of
+
+580
+00:46:50,010 --> 00:47:02,410
+b بيساوي الـ summation f .. f N هو f k of a على 
+
+581
+00:47:02,410 --> 00:47:10,470
+k factorial في b minus a أُسّ k  k من عند 0 .. من صفر
+
+582
+00:47:10,470 --> 00:47:19,390
+k من عند صفر لعند مين؟ لعند n زائد الـ remainder مين؟
+
+583
+00:47:19,390 --> 00:47:27,090
+r n الـ remainder are n مين هو؟ بيساوي اللي هو 1 على n
+
+584
+00:47:27,090 --> 00:47:35,390
+factorial في الـ integration من a لعند b b minus t 
+
+585
+00:47:35,390 --> 00:47:45,690
+أُسّ n في f n زائد 1 of T دي تي نثبت لكم إن الـ f of b
+
+586
+00:47:45,690 --> 00:47:52,520
+can be written as this حيث الـ r n هو هذا الآن
+
+587
+00:47:52,520 --> 00:47:59,500
+الفكرة في الحل أو الفكرة في البرهان أنه أنا بدي 
+
+588
+00:47:59,500 --> 00:48:05,260
+أجي أوجد قيمة الـ remainder r n اللي هو هذا المقدار
+
+589
+00:48:05,260 --> 00:48:10,700
+و بدي أثبت لكم أن هذا المقدار اللي هو منه بقدر أكتب
+
+590
+00:48:10,700 --> 00:48:14,040
+اللي هو يعني الـ r n أثبت لكم هي عبارة عن f of b
+
+591
+00:48:14,040 --> 00:48:19,720
+ناقص هذا الـ summation يعني بدي أثبت لكم أن الـ r n
+
+592
+00:48:19,720 --> 00:48:23,560
+بتساوي f of b ناقص المجموع هذا يعني بدي أبدأ 
+
+593
+00:48:23,560 --> 00:48:30,700
+بهذا الآن يعني بدي أبدأ بالـ r n بيساوي هذا المقدار 
+
+594
+00:48:30,700 --> 00:48:34,740
+شايفينه هذا المقدار من a لعند b واحد على n factorial
+
+595
+00:48:34,740 --> 00:48:42,380
+بدي أكامله أكامله by parts آه بدّه كامل وشوفوا كيف
+
+596
+00:48:42,380 --> 00:48:47,280
+بتطلع الأمور إن شاء الله سلسة ومنيحة by parts خدوا
+
+597
+00:48:47,280 --> 00:48:53,160
+الـ u عبارة هنسّميها عبارة عن u وهذه سنّسميها إيش يا 
+
+598
+00:48:53,160 --> 00:48:59,970
+جماعة dv ماشي الحال بيصير القانون هو عبارة عن اللي
+
+599
+00:48:59,970 --> 00:49:07,490
+هو u dv يعني بيساوي uv ناقص v du تحت مين؟ تحت الـ
+
+600
+00:49:07,490 --> 00:49:11,310
+integration هذا كلام تعرفوه أنتم الآن برضه من وين
+
+601
+00:49:11,310 --> 00:49:16,150
+لوين؟ من a لعند b على السريع عشان اللي هو تأخذوا 
+
+602
+00:49:16,150 --> 00:49:20,100
+الفكرة اللي هي الحسابات أنت بتعرف تعملوها الكلّ
+
+603
+00:49:20,100 --> 00:49:24,620
+بيعرف يعملها هي أخذنا الـ u زي ما أخذناها هنا
+
+604
+00:49:24,620 --> 00:49:30,200
+كتبتها على اللوح وهي الـ dv هيها لـ f n زائد واحد of T
+
+605
+00:49:30,200 --> 00:49:36,300
+dt الآن الـ du أكيد اللي هو تفاضل هذا n في b minus
+
+606
+00:49:36,300 --> 00:49:41,100
+t أُسّ n ناقص واحد في تفاضل اللي هو اللي جوا ناقص
+
+607
+00:49:41,100 --> 00:49:45,900
+واحد بيصير عندي ناقص n في b minus t أُسّ n ناقص واحد 
+
+608
+00:49:45,900 --> 00:49:51,040
+dt هذه مين هي؟ الـ du اللي بدي أحطها هان الآن الـ v
+
+609
+00:49:51,040 --> 00:49:57,380
+الـ dv هيها الـ v هتطلع الـ integration هذه بيخفّ
+
+610
+00:49:57,380 --> 00:50:01,340
+واحد من الـ derivatives بيصير عندي f n of T طبعاً
+
+611
+00:50:01,340 --> 00:50:05,620
+فاهمين إيش بقول؟ الـ v بيساوي f n of T الآن بيجي
+
+612
+00:50:05,620 --> 00:50:09,260
+بنعوّض بيصير عندي عبارة عن الـ integration اللي هو
+
+613
+00:50:09,260 --> 00:50:15,160
+بيساوي الـ r n بيساوي u في v u اللي هو عبارة عن b
+
+614
+00:50:15,160 --> 00:50:24,580
+minus t أُسّ n في u هذه u في v v اللي هو عبارة عن f n 
+
+615
+00:50:24,580 --> 00:50:37,200
+of T، مظبوط؟ هذا اللي هو u طبعاً الـ r n احنا مضروب
+
+616
+00:50:37,200 --> 00:50:41,730
+كله في 1 على n factorial لأنّها هي اللي فضلنا
+
+617
+00:50:41,730 --> 00:50:47,110
+هي الجزء اللي حسبناه هذا 1 على n factorial موجودة
+
+618
+00:50:47,110 --> 00:50:50,490
+فيها 1 على n factorial بيصير هنا برضه على n
+
+619
+00:50:50,490 --> 00:51:00,050
+factorial بدأت أمورنا تظهر ناقص 1 على n factorial
+
+620
+00:51:00,050 --> 00:51:06,310
+في الـ integration من a لعند b v ، v هي f
+
+621
+00:51:08,970 --> 00:51:18,530
+of T مظبوط dt في du du إيش du؟ du اللي هو
+
+622
+00:51:18,530 --> 00:51:30,650
+ناقص n ناقص n في b minus t أُسّ
+
+623
+00:51:30,650 --> 00:51:32,330
+n ناقص واحد 
+
+624
+00:51:35,190 --> 00:51:43,550
+واضحة الصورة نجي نخلي الصورة منيحة b-t أُسّ n على n
+
+625
+00:51:43,550 --> 00:51:51,210
+factorial f n of T خلصنا منه هذا ناقص وهذا ناقص
+
+626
+00:51:51,210 --> 00:51:56,250
+يصبح زاد يصبح هذا أشمل هو واحد على n واحد factorial
+
+627
+00:51:56,250 --> 00:52:04,450
+في الـ integration من a لعند b b-t أُسّ n ناقص واحد 
+
+628
+00:52:04,450 --> 00:52:12,530
+f n of T dt مظبوط؟ مظبوط هذا أوجدنا مين؟ الـ r n
+
+629
+00:52:12,530 --> 00:52:18,350
+بيساوي هذا زائد هذا طيب اللي عملناه مين هو هذا أصلاً
+
+630
+00:52:18,350 --> 00:52:23,570
+الـ r n اللي أوجدناه هي اللي هو b-1 t أُسّ n f n زائد 
+
+631
+00:52:23,570 --> 00:52:29,370
+واحد of T dt طلع عبارة عن اللي هو اللي جوا هذا بأسّ
+
+632
+00:52:29,370 --> 00:52:38,770
+n وهذا زي ما هو أُسّ n ناقص بيصير هو هذا زائد واحد صار
+
+633
+00:52:38,770 --> 00:52:42,670
+زائد طبعاً ما عرفتم كيف صارت زائد واحد على n
+
+634
+00:52:42,670 --> 00:52:46,130
+ناقص واحد factorial واحد على n ناقص واحد
+
+635
+00:52:46,130 --> 00:52:49,850
+factorial في هذا المقدار لاحظوا أن هذا المقدار 
+
+636
+00:52:49,850 --> 00:52:56,610
+شبيه بالـ remainder يعني بالضبط اللي عملناه على الـ
+
+637
+00:52:56,610 --> 00:53:01,750
+remainder بنعمله هان بنعمله على هذا اللي هنعمله هان 
+
+638
+00:53:01,750 --> 00:53:05,810
+هييطلع مقدار زي هذا ومقدار زي هذا بس هينقص كمان
+
+639
+00:53:05,810 --> 00:53:09,770
+واحد اللي n هيصير هذا n ناقص اثنين كان n .. كان
+
+640
+00:53:09,770 --> 00:53:13,210
+n صار هيصير n ناقص اثنين والخطوة اللي بعدها 
+
+641
+00:53:13,210 --> 00:53:15,850
+بنعمل كمان مرة بنوجد بيصير n ناقص ثلاثة وn ناقص
+
+642
+00:53:15,850 --> 00:53:20,070
+أربعة في الآخر الـ and finite إذا هنصل للنهاية إذا
+
+643
+00:53:20,070 --> 00:53:29,950
+هذا هيصير بيساوي b-t أُسّ n على n factorial f n of t
+
+644
+00:53:29,950 --> 00:53:35,250
+زائد هذا بتعمله بالضبط زي ما عملت مين؟ زي ما عملت
+
+645
+00:53:35,250 --> 00:53:42,150
+الـ r n يعني وكأنه اسم هذا r n-1 بيصير بنفس الأسلوب b
+
+646
+00:53:42,150 --> 00:53:49,410
+minus t أُسّ n ناقص واحد على n ناقص واحد factorial f
+
+647
+00:53:49,410 --> 00:54:00,270
+n ناقص واحد of t زائد بعتقد
+
+648
+00:54:00,270 --> 00:54:08,770
+بس في ناقص هنا في الـ u في v u في v
+
+649
+00:54:17,570 --> 00:54:22,590
+آه ما حسبناش عند a و b آه بس هذا نسينا نحسب هذا عند
+
+650
+00:54:22,590 --> 00:54:27,990
+b، من عند a لعند b، معلش سامحونا، من عند a لعند b
+
+651
+00:54:27,990 --> 00:54:33,230
+هذا الكلام صحيح، بس بدي أحسبه من a لعند b، عند b
+
+652
+00:54:33,230 --> 00:54:38,250
+صفر، صح؟ عند b صفر، مش احنا حسبنا قيمة الـ
+
+653
+00:54:38,250 --> 00:54:40,830
+remainder، قيمة الـ integration، هذا الـ integration
+
+654
+00:54:40,830 --> 00:54:47,820
+اللي هو من وين لوين؟ من a لعند b الآن هذا من a لعند
+
+655
+00:54:47,820 --> 00:54:56,920
+b بيصير عند b ناقص b بيصير صفر الآن ناقص من b ناقص 
+
+656
+00:54:56,920 --> 00:55:01,680
+a فبيصير هذه شمالها b ناقص a وهنا ناقص وهنا a 
+
+657
+00:55:01,680 --> 00:55:06,760
+شمالها f of a لأنّ عوضنا عن مين؟ عن a فبيصير عند b
+
+658
+00:55:06,760 --> 00:55:11,220
+ناقص a أُسّ n بالسالب على n factor of n of a زائد 
+
+659
+00:55:11,220 --> 00:55:15,190
+هذا المقدار لأنّ هذا المقدار زي هذا المقدار هذا 
+
+660
+00:55:15,190 --> 00:55:19,010
+المقدار بنفس الأسلوب زي ما قلنا بيصير عبارة عن زي
+
+661
+00:55:19,010 --> 00:55:24,650
+هذا ماشي بس برضه هيطلع لي إيش؟ برضه هيطلع لي نقص لما
+
+662
+00:55:24,650 --> 00:55:27,730
+نعوض بيصير b minus a أسئلة ناقص واحدة الآن ناقص 
+
+663
+00:55:27,730 --> 00:55:33,830
+واحدة factorial f n ناقص واحد of 2 of a زائد اللي
+
+664
+00:55:33,830 --> 00:55:38,630
+بيطلع هنا n ناقص 2 factorial في الـ integration من
+
+665
+00:55:38,630 --> 00:55:47,770
+a لـ b b minus t أسئلة ناقص 2 الآن وهذه f n ناقص
+
+666
+00:55:47,770 --> 00:55:55,740
+واحدة of t dt نفس
+
+667
+00:55:55,740 --> 00:55:59,960
+اللي عملته على هذا بدي أعمله على هذا هأظلّ مستمرّ
+
+668
+00:55:59,960 --> 00:56:10,880
+لما يوصل عندي اللي هو .. وين بدي أكتب؟ 
+
+669
+00:56:10,880 --> 00:56:12,360
+خليني أكتب فوق
+
+670
+00:56:16,010 --> 00:56:22,150
+الآن تفجّأنا يا جماعة إنّ الـ r n هي هو هذا اللي هو r n 
+
+671
+00:56:22,150 --> 00:56:28,690
+بيساوي هذا المقدار ناقص هذا المقدار ناقص ناقص زائد
+
+672
+00:56:28,690 --> 00:56:34,370
+هذا إذا صار عند الـ r n بيساوي
+
+673
+00:56:34,370 --> 00:56:49,900
+ناقص b minus a أُسّ n على n factorial f n of a ناقص b
+
+674
+00:56:49,900 --> 00:56:54,740
+minus a زائد n ناقص واحد على n ناقص واحد factorial 
+
+675
+00:56:54,740 --> 00:57:04,840
+f n ناقص واحد of a زائد المقدار هذا الآن بتعملوا
+
+676
+00:57:04,840 --> 00:57:09,500
+هذا اللي عملته مع جابلو هيظلّوا بنفس الأسلوب ماشي
+
+677
+00:57:10,430 --> 00:57:17,990
+لما أصل لعند اللي هو آخر term اللي هو هيكون عندي
+
+678
+00:57:17,990 --> 00:57:28,270
+هييطلع عندي اللي هو b minus a في f يعني n اللي هي
+
+679
+00:57:28,270 --> 00:57:41,300
+بيصير باتنين b minus a في f prime of a على اللي هو
+
+680
+00:57:41,300 --> 00:57:46,360
+1 factorial زي ما هي زائد اللي بعدها الـ 
+
+681
+00:57:46,360 --> 00:57:51,200
+integration تبعها اللي هي هذه عند n بجدّاشها أنا بـ 2
+
+682
+00:57:51,200 --> 00:57:56,060
+n بـ 2 اللي هي بيصير 1 إلى 0 factorial يعني بيصير
+
+683
+00:57:56,060 --> 00:58:00,060
+اللي هو 1 بمعنى آخر فالـ integration من a لعند b
+
+684
+00:58:00,060 --> 00:58:06,660
+وهذا بيصير b minus t أُسّ 0 يعني 1 في f prime of dt
+
+685
+00:58:08,080 --> 00:58:12,180
+لما أكرّر العملية أظلّ أكرّرها لما أصل لهذه الخطوة 
+
+686
+00:58:12,180 --> 00:58:17,620
+وحنّتي لأنّ الـ n is finite ويساوي اللي هو المقدار
+
+687
+00:58:17,620 --> 00:58:20,220
+هذا كله اللي هو عبارة عن الـ summation طبعاً كله
+
+688
+00:58:20,220 --> 00:58:23,060
+بالسالب هذا مع هذا الأخير بالموجب بيصير ناقص الـ
+
+689
+00:58:23,060 --> 00:58:32,660
+summation لـ b minus a أُسّ k على k factorial في f k of 
+
+690
+00:58:32,660 --> 00:58:43,520
+a k الآن من عند اللي هو واحد عند واحد هيها لعند مين
+
+691
+00:58:43,520 --> 00:58:51,280
+لعند n هذا مجموع من هنا من هنا لهنا هذا كله في
+
+692
+00:58:51,280 --> 00:58:56,640
+قيب واحد بتطلع هذه kيب 2 بتطلع اللي هان kيب 3 لما 
+
+693
+00:58:56,640 --> 00:58:59,580
+نقصها لكيب n بتطلع اللي عندها هان زائد الـ 
+
+694
+00:58:59,580 --> 00:59:02,580
+integration هذا الـ integration هذا اللي هي f 
+
+695
+00:59:02,580 --> 00:59:05,660
+continuous اللي عند الـ integration للـ f طبعاً الـ f
+
+696
+00:59:05,660 --> 00:59:08,820
+نفسها كانت continuous فالـ integration هذا بفرض ضمن 
+
+697
+00:59:08,820 --> 00:59:11,140
+الـ fundamental of calculus على طول بيطلع عبارة عن f
+
+698
+00:59:11,140 --> 00:59:20,780
+of b ناقص من f of a ماشي الحال فبيصير الآن اللي هو
+
+699
+00:59:20,780 --> 00:59:28,010
+وصلنا للي بدّنا إياه كيف؟ شوف كيف وصلنا للنتيجة الآن
+
+700
+00:59:28,010 --> 00:59:37,210
+طلعت عندي خلّي اللي هو الـ remainder احنا الـ f of
+
+701
+00:59:37,210 --> 00:59:42,430
+P خليها في الجهة هذه وانقل كله هنا فبيصير F of P
+
+702
+00:59:42,430 --> 00:59:48,760
+بساوي هذه بتنضف لهذه ما هي ناقص الثانية بيصير ..
+
+703
+00:59:48,760 --> 00:59:51,380
+لما تيجي الجهتين علي الجهتين بيصير موجة بس
+
+704
+00:59:51,380 --> 00:59:57,440
+summation لـ B minus A أُس K FK  the derivative هذه
+
+705
+00:59:57,440 --> 01:00:04,160
+of A على K factorial K الـ N من واحد لعند N وهذه
+
+706
+01:00:04,160 --> 01:00:09,340
+حالة السفر K من صفر لعند N زائد مين الـ remainder
+
+707
+01:00:09,340 --> 01:00:13,900
+are n ليش حالة السفر هذه لأن في حالة K بصفر بيصير
+
+708
+01:00:13,900 --> 01:00:17,500
+هذا واحد وهذا واحد وهذا مافيش derivative يعني
+
+709
+01:00:17,500 --> 01:00:22,320
+بيصير F of A فبيصير عندي اللي هو F of B بساوي ال
+
+710
+01:00:22,320 --> 01:00:25,160
+summation زائد ال remainder are n the remainder
+
+711
+01:00:25,160 --> 01:00:30,500
+اللي هو اللي احنا بدأنا فيه وهو المطلوب فعلا أنا 
+
+712
+01:00:30,500 --> 01:00:36,940
+قدرت أكتب اللي هي ال F of B على الصورة اللي أمامي
+
+713
+01:00:36,940 --> 01:00:42,600
+هيك بنكون احنا برهنا Taylor's theorem وهي آخر 
+
+714
+01:00:42,600 --> 01:00:48,860
+جزء في هذا ال section والآن إن شاء الله بكون
+
+715
+01:00:48,860 --> 01:00:54,800
+خلصنا الجزء الأول من المحاضرة ونبدأ إن شاء الله 
+
+716
+01:00:54,800 --> 01:00:58,740
+بعد شوية في الجزء الثاني بارك الله فيكم 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7b772cdd3272c0bf2e592f8ad764d3c201e7ab07
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2591, "start": 11.17, "end": 25.91, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة رقم خمستاشر لمساق تحليل حقيقي اتنين لطلبات وطالبات الجامعة الإسلامية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 16490, 2304, 14851, 33599, 2288, 32767, 3794, 995, 4587, 6055, 5016, 20292, 1211, 11331, 38436, 38436, 1975, 2655, 1863, 9957, 5296, 9566, 46152, 9307, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632], "avg_logprob": -0.10575283982537009, "compression_ratio": 1.584, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 11.17, "end": 12.57, "word": "بسم", "probability": 0.72900390625}, {"start": 12.57, "end": 12.81, "word": " الله", "probability": 0.95166015625}, {"start": 12.81, "end": 13.27, "word": " الرحمن", "probability": 0.9713541666666666}, {"start": 13.27, "end": 13.83, "word": " الرحيم", "probability": 0.994140625}, {"start": 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171.76, "end": 172.08, "word": " ال", "probability": 0.763671875}, {"start": 172.08, "end": 172.86, "word": " J", "probability": 0.423583984375}, {"start": 172.86, "end": 173.38, "word": " فترة", "probability": 0.9768880208333334}, {"start": 173.38, "end": 173.72, "word": " عبارة", "probability": 0.994873046875}, {"start": 173.72, "end": 173.9, "word": " عن", "probability": 0.99658203125}, {"start": 173.9, "end": 174.26, "word": " ال", "probability": 0.8125}, {"start": 174.26, "end": 174.52, "word": " close", "probability": 0.455322265625}, {"start": 174.52, "end": 175.02, "word": " interval", "probability": 0.9775390625}, {"start": 175.02, "end": 175.3, "word": " Alpha", "probability": 0.501953125}, {"start": 175.3, "end": 176.14, "word": " و", "probability": 0.88427734375}, {"start": 176.14, "end": 176.46, "word": " Beta", "probability": 0.8271484375}], "temperature": 1.0}, {"id": 8, "seek": 19046, "start": 177.2, "end": 190.46, "text": "إن ناخد فاي function من J لعند R have a continuous derivative on J يعني أخدنا الآن يا جماعة فاي عبارة عن function من اللي هي الفترة Alpha و Beta", "tokens": [28814, 1863, 8717, 47283, 3215, 6156, 47302, 2445, 9154, 508, 5296, 3615, 41260, 497, 362, 257, 10957, 13760, 322, 508, 37495, 22653, 5551, 9778, 3215, 8315, 6024, 48506, 35186, 10874, 15042, 27884, 6156, 47302, 6225, 3555, 9640, 3660, 18871, 2445, 9154, 13672, 1829, 39896, 27188, 2655, 25720, 20588, 4032, 33286], "avg_logprob": -0.25428922152986716, "compression_ratio": 1.3161290322580645, "no_speech_prob": 7.68899917602539e-06, "words": [{"start": 177.2, "end": 177.6, "word": "إن", "probability": 0.6680908203125}, {"start": 177.6, "end": 178.04, "word": " ناخد", "probability": 0.8284505208333334}, {"start": 178.04, "end": 178.32, "word": " فاي", "probability": 0.3641357421875}, {"start": 178.32, "end": 178.76, "word": " function", "probability": 0.654296875}, {"start": 178.76, "end": 179.04, "word": " من", "probability": 0.95751953125}, {"start": 179.04, "end": 179.3, 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24208, "start": 213.52, "end": 242.08, "text": "لأن لو كان في عندي function F is continuous on any interval I containing Phi of J لأن فرضنا أن F دالة على I تحتوي Phi of J عساس إن بعد شوية هعرّق .. هيلزمني اللي هو composition of two functions عشان هيك أنا باخد ال F عبارة عن function من I لعند مين؟ لعند ال R إيش ال I هذه؟ هذه I interval", "tokens": [1211, 33456, 45164, 25961, 8978, 18871, 16254, 2445, 479, 307, 10957, 322, 604, 15035, 286, 19273, 41435, 295, 508, 5296, 33456, 6156, 43042, 8315, 14739, 479, 11778, 6027, 3660, 15844, 286, 6055, 33753, 45865, 41435, 295, 508, 6225, 3794, 32277, 36145, 39182, 13412, 2407, 10632, 8032, 3615, 2288, 11703, 4587, 4386, 39896, 1211, 11622, 2304, 22653, 13672, 1829, 31439, 12686, 295, 732, 6828, 6225, 8592, 7649, 39896, 4117, 41850, 4724, 47283, 3215, 2423, 479, 6225, 3555, 9640, 3660, 18871, 2445, 9154, 286, 5296, 3615, 41260, 3714, 9957, 22807, 5296, 3615, 41260, 2423, 497, 11933, 1829, 8592, 2423, 286, 29538, 22807, 29538, 286, 15035], 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ونشيل Phi prime of T DT ونحط مكان هي شمالها DX حدود ال integration كانت من Alpha ل Beta يعني لما كانت T بAlpha بصير X اللي هي Phi of T اللي هي Phi of Alpha بتروح لمين؟ لأ اللي هي Phi of مين؟ Phi of Beta", "tokens": [6027, 148, 48506, 8717, 1829, 7435, 1829, 8717, 39648, 48817, 4724, 3794, 2407, 38207, 41435, 5835, 314, 413, 51, 34051, 48817, 15844, 413, 51, 4724, 3794, 2407, 38207, 41435, 5835, 295, 314, 4032, 1863, 8592, 26895, 41435, 5835, 295, 314, 413, 51, 4032, 1863, 5016, 9566, 3714, 41361, 39896, 13412, 2304, 6027, 11296, 48817, 11331, 3215, 23328, 2423, 10980, 25961, 2655, 9154, 20588, 5296, 33286, 37495, 22653, 5296, 15042, 25961, 2655, 314, 4724, 9171, 7211, 4724, 9381, 13546, 1783, 13672, 1829, 39896, 41435, 295, 314, 13672, 1829, 39896, 41435, 295, 20588, 39894, 32887, 5016, 32767, 9957, 22807, 5296, 10721, 13672, 1829, 39896, 41435, 295, 3714, 9957, 22807, 41435, 295, 33286], "avg_logprob": -0.21044481847737287, "compression_ratio": 1.7850467289719627, "no_speech_prob": 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F of U طبعا هذه صيحوها بسوء ال integration من C .. 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1045.74, "end": 1046.18, "word": " عند", "probability": 0.92041015625}, {"start": 1046.18, "end": 1046.56, "word": " I", "probability": 0.9873046875}, {"start": 1046.56, "end": 1047.04, "word": " لعند", "probability": 0.9679361979166666}, {"start": 1047.04, "end": 1047.46, "word": " R", "probability": 0.9921875}, {"start": 1047.46, "end": 1048.92, "word": " ومفترضين", "probability": 0.9532877604166666}, {"start": 1048.92, "end": 1049.14, "word": " أنه", "probability": 0.6763916015625}, {"start": 1049.14, "end": 1049.42, "word": " بPsi", "probability": 0.8533528645833334}, {"start": 1049.42, "end": 1049.62, "word": " هي", "probability": 0.8984375}, {"start": 1049.62, "end": 1049.8, "word": " ال", "probability": 0.51904296875}, {"start": 1049.8, "end": 1050.12, "word": " inverse", "probability": 0.87451171875}, {"start": 1050.12, "end": 1050.32, "word": " ل", "probability": 0.7744140625}, {"start": 1050.32, "end": 1050.58, "word": " mean", "probability": 0.43359375}, {"start": 1050.58, "end": 1050.96, "word": " للـ", "probability": 0.546142578125}, {"start": 1050.96, "end": 1051.26, "word": " Phi", "probability": 0.80322265625}, {"start": 1051.26, "end": 1052.0, "word": " يعني", "probability": 0.969970703125}, {"start": 1052.0, "end": 1052.52, "word": " Phi", "probability": 0.94873046875}, {"start": 1052.52, "end": 1053.18, "word": " composite", "probability": 0.81982421875}, {"start": 1053.18, "end": 1053.94, "word": " بPsi", "probability": 0.9222005208333334}], "temperature": 1.0}, {"id": 47, "seek": 108068, "start": 1055.34, "end": 1080.68, "text": "بساومين الـ identity function أو Psi composite الـ Phi عبارة عن ال identity function وكل اللي هو عندى مفترضين ان Phi of J subset من مين من الـ I عشان يكون اللي هو ال composition معرف احنا", "tokens": [3555, 3794, 995, 20498, 9957, 2423, 39184, 6575, 2445, 34051, 430, 7691, 25557, 2423, 39184, 41435, 6225, 3555, 9640, 3660, 18871, 2423, 6575, 2445, 4032, 28820, 13672, 1829, 31439, 43242, 7578, 3714, 5172, 2655, 43042, 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1503.96, "text": "اللي هنعرّف ليها جمعة جيه من جيه لعند R اللي هي عبارة علّف ليها أنها تكون إيه شمالها Anti-derivative لل continuous function of composite phi", "tokens": [6027, 20292, 8032, 1863, 3615, 2288, 11703, 5172, 32239, 11296, 10874, 2304, 27884, 10874, 1829, 3224, 9154, 10874, 1829, 3224, 5296, 3615, 41260, 497, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 11203, 11703, 5172, 32239, 11296, 14739, 11296, 6055, 30544, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 27757, 12, 1068, 592, 1166, 24976, 10957, 2445, 295, 25557, 13107], "avg_logprob": -0.36228812852148284, "compression_ratio": 1.3506493506493507, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 1493.14, "end": 1493.9, "word": "اللي", "probability": 0.810302734375}, {"start": 1493.9, "end": 1494.32, "word": " هنعرّف", "probability": 0.80322265625}, {"start": 1494.32, "end": 1494.52, "word": " ليها", "probability": 0.487060546875}, {"start": 1494.52, "end": 1494.9, "word": " جمعة", "probability": 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"end": 2719.43, "text": "اللي هو dx y ساوي اللي هو f of c هدف b minus a وهو المطلوب هيلحقناه كمان مرة إذا الـ Corollary اللي هي اللي أمامنا تم برهانها مرة أخرى نيجي الآن للي هي Taylor's theorem أخدناها Taylor's theorem كان ال remainder اللي هو اللي هو إشي مفاضل", "tokens": [6027, 20292, 31439, 30017, 288, 8608, 995, 45865, 13672, 1829, 31439, 283, 295, 269, 8032, 3215, 5172, 272, 3175, 257, 37037, 2407, 9673, 9566, 1211, 37746, 8032, 26895, 5016, 4587, 8315, 3224, 9122, 2304, 7649, 3714, 25720, 11933, 15730, 2423, 39184, 3925, 1833, 822, 13672, 1829, 39896, 13672, 1829, 5551, 2304, 10943, 8315, 46811, 4724, 2288, 3224, 7649, 11296, 3714, 25720, 5551, 34740, 7578, 8717, 1829, 7435, 1829, 6024, 48506, 5296, 20292, 39896, 12060, 311, 20904, 5551, 9778, 3215, 8315, 11296, 12060, 311, 20904, 25961, 2423, 29837, 13672, 1829, 31439, 13672, 1829, 31439, 11933, 8592, 1829, 3714, 5172, 46958, 1211], "avg_logprob": -0.23499380538959314, "compression_ratio": 1.6883720930232557, "no_speech_prob": 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شمالهم continuous يعني نفترض أن الانث derivative الانث زائد واحد derivative is continuous exist وcontinuous نفترض أن الدالة f عبارة عن دالة قابلة للاشتقاق n زائد واحد من المرات وتكون الان زائد واحد كمان نفسها continuous", "tokens": [36622, 541, 300, 264, 2445, 283, 293, 1080, 33733, 283, 5835, 295, 261, 5835, 43242, 283, 77, 293, 283, 77, 30767, 16373, 3215, 36764, 24401, 366, 28242, 16095, 11933, 1829, 3224, 13412, 2304, 6027, 16095, 10957, 37495, 22653, 8717, 5172, 2655, 43042, 14739, 2423, 7649, 12984, 13760, 2423, 7649, 12984, 30767, 16373, 3215, 36764, 24401, 13760, 307, 10957, 2514, 4032, 9000, 259, 12549, 8717, 5172, 2655, 43042, 14739, 32748, 6027, 3660, 283, 6225, 3555, 9640, 3660, 18871, 11778, 6027, 3660, 12174, 16758, 37977, 24976, 33599, 2655, 4587, 995, 4587, 297, 30767, 16373, 3215, 36764, 24401, 9154, 9673, 2288, 9307, 34683, 30544, 2423, 7649, 30767, 16373, 3215, 36764, 24401, 9122, 2304, 7649, 8717, 36178, 11296, 10957], "avg_logprob": -0.2050107698245295, 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"end": 3609.68, "word": " are", "probability": 0.2061767578125}, {"start": 3609.68, "end": 3609.84, "word": " n", "probability": 0.2005615234375}, {"start": 3609.84, "end": 3610.28, "word": " ليش", "probability": 0.76806640625}, {"start": 3610.28, "end": 3610.6, "word": " حالة", "probability": 0.9563802083333334}, {"start": 3610.6, "end": 3611.0, "word": " السفر", "probability": 0.8723958333333334}, {"start": 3611.0, "end": 3611.34, "word": " هذه", "probability": 0.81103515625}, {"start": 3611.34, "end": 3611.98, "word": " لأن", "probability": 0.74951171875}, {"start": 3611.98, "end": 3612.1, "word": " في", "probability": 0.76708984375}, {"start": 3612.1, "end": 3612.54, "word": " حالة", "probability": 0.9957682291666666}, {"start": 3612.54, "end": 3612.72, "word": " K", "probability": 0.37109375}, {"start": 3612.72, "end": 3613.28, "word": " بسفر", "probability": 0.82049560546875}, {"start": 3613.28, "end": 3613.9, "word": " بيصير", "probability": 0.8209228515625}, {"start": 3613.9, "end": 3614.1, "word": " هذا", "probability": 0.80908203125}, {"start": 3614.1, "end": 3614.56, "word": " واحد", "probability": 0.967041015625}, {"start": 3614.56, "end": 3614.96, "word": " وهذا", "probability": 0.7142333984375}, {"start": 3614.96, "end": 3615.5, "word": " واحد", "probability": 0.970947265625}, {"start": 3615.5, "end": 3616.24, "word": " وهذا", "probability": 0.6573486328125}, {"start": 3616.24, "end": 3616.56, "word": " مافيش", "probability": 0.52734375}, {"start": 3616.56, "end": 3617.08, "word": " derivative", "probability": 0.83154296875}, {"start": 3617.08, "end": 3617.5, "word": " يعني", "probability": 0.937744140625}, {"start": 3617.5, "end": 3617.9, "word": " بيصير", "probability": 0.9603271484375}, {"start": 3617.9, "end": 3618.26, "word": " F", "probability": 0.78857421875}, {"start": 3618.26, "end": 3618.86, "word": " of", "probability": 0.82568359375}, {"start": 3618.86, "end": 3619.1, "word": " A", "probability": 0.90966796875}, {"start": 3619.1, "end": 3619.88, "word": " فبيصير", "probability": 0.83876953125}, {"start": 3619.88, "end": 3620.32, "word": " عندي", "probability": 0.69873046875}, {"start": 3620.32, "end": 3620.6, "word": " اللي", "probability": 0.9169921875}, {"start": 3620.6, "end": 3620.84, "word": " هو", "probability": 0.95947265625}, {"start": 3620.84, "end": 3621.12, "word": " F", "probability": 0.88818359375}, {"start": 3621.12, "end": 3621.34, "word": " of", "probability": 0.6376953125}, {"start": 3621.34, "end": 3621.64, "word": " B", "probability": 0.7939453125}, {"start": 3621.64, "end": 3622.2, "word": " بساوي", "probability": 0.49591064453125}, {"start": 3622.2, "end": 3622.32, "word": " ال", "probability": 0.693359375}, {"start": 3622.32, "end": 3622.74, "word": " summation", "probability": 0.62353515625}, {"start": 3622.74, "end": 3623.12, "word": " زائد", "probability": 0.8502604166666666}, {"start": 3623.12, "end": 3623.26, "word": " ال", "probability": 0.8896484375}, {"start": 3623.26, "end": 3623.52, "word": " remainder", "probability": 0.9052734375}, {"start": 3623.52, "end": 3623.9, "word": " are", "probability": 0.90087890625}, {"start": 3623.9, "end": 3624.18, "word": " n", "probability": 0.63232421875}, {"start": 3624.18, "end": 3624.72, "word": " ال", "probability": 0.87109375}, {"start": 3624.72, "end": 3625.16, "word": " remainder", "probability": 0.78564453125}, {"start": 3625.16, "end": 3625.76, "word": " اللي", "probability": 0.984375}, {"start": 3625.76, "end": 3626.08, "word": " هو", "probability": 0.78466796875}, {"start": 3626.08, "end": 3626.42, "word": " اللي", "probability": 0.98095703125}, {"start": 3626.42, "end": 3626.6, "word": " احنا", "probability": 0.7420654296875}, {"start": 3626.6, "end": 3626.98, "word": " بدأنا", "probability": 0.7887369791666666}, {"start": 3626.98, "end": 3627.64, "word": " فيه", "probability": 0.929931640625}, {"start": 3627.64, "end": 3628.24, "word": " وهو", "probability": 0.805908203125}, {"start": 3628.24, "end": 3629.66, "word": " المطلوب", "probability": 0.9761962890625}, {"start": 3629.66, "end": 3630.28, "word": " فعلا", "probability": 0.9503580729166666}, {"start": 3630.28, "end": 3630.5, "word": " انا", "probability": 0.7191162109375}, {"start": 3630.5, "end": 3630.76, "word": " قدرت", "probability": 0.769775390625}, {"start": 3630.76, "end": 3631.08, "word": " اكتب", "probability": 0.968017578125}, {"start": 3631.08, "end": 3631.22, "word": " اللي", "probability": 0.9677734375}, {"start": 3631.22, "end": 3631.5, "word": " هي", "probability": 0.7021484375}, {"start": 3631.5, "end": 3632.04, "word": " ال", "probability": 0.89599609375}, {"start": 3632.04, "end": 3632.2, "word": " F", "probability": 0.830078125}, {"start": 3632.2, "end": 3632.38, "word": " of", "probability": 0.927734375}, {"start": 3632.38, "end": 3632.52, "word": " B", "probability": 0.90283203125}, {"start": 3632.52, "end": 3632.76, "word": " على", "probability": 0.83544921875}, {"start": 3632.76, "end": 3633.34, "word": " الصورة", "probability": 0.98388671875}, {"start": 3633.34, "end": 3633.94, "word": " اللي", "probability": 0.9775390625}, {"start": 3633.94, "end": 3634.7, "word": " أمامي", "probability": 0.870361328125}], "temperature": 1.0}, {"id": 153, "seek": 365874, "start": 3636.7, "end": 3658.74, "text": "و هيك بنكون احنا برهننا Taylor's theorem و هي اخر جزء في هذا ال section و الان ان شاء الله بكون خلصنا الجزء الاول من المحاضرة و نبدأ ان شاء الله بعد شوية في الجزء الثاني برك الله فيكم", "tokens": [2407, 39896, 4117, 44945, 30544, 1975, 5016, 8315, 4724, 2288, 3224, 1863, 8315, 12060, 311, 20904, 4032, 39896, 1975, 34740, 10874, 11622, 38207, 8978, 23758, 2423, 3541, 4032, 2423, 7649, 16472, 13412, 16606, 21984, 4724, 30544, 16490, 1211, 9381, 8315, 25724, 11622, 38207, 42963, 12610, 9154, 9673, 5016, 46958, 25720, 4032, 8717, 44510, 10721, 16472, 13412, 16606, 21984, 39182, 13412, 2407, 10632, 8978, 25724, 11622, 38207, 6024, 104, 7649, 1829, 4724, 31747, 21984, 8978, 24793], "avg_logprob": -0.17290295738922923, "compression_ratio": 1.654054054054054, "no_speech_prob": 1.7285346984863281e-06, "words": [{"start": 3636.7, "end": 3636.94, "word": "و", "probability": 0.9580078125}, {"start": 3636.94, "end": 3637.18, "word": " هيك", "probability": 0.6787109375}, {"start": 3637.18, "end": 3637.7, "word": " بنكون", "probability": 0.9638671875}, {"start": 3637.7, "end": 3639.32, "word": " احنا", "probability": 0.9264322916666666}, {"start": 3639.32, "end": 3641.08, "word": " برهننا", "probability": 0.757421875}, {"start": 3641.08, "end": 3641.56, "word": " Taylor's", "probability": 0.4576416015625}, {"start": 3641.56, "end": 3641.86, "word": " theorem", "probability": 0.8203125}, {"start": 3641.86, "end": 3642.04, "word": " و", "probability": 0.474365234375}, {"start": 3642.04, "end": 3642.22, "word": " هي", "probability": 0.92236328125}, {"start": 3642.22, "end": 3642.6, "word": " اخر", "probability": 0.816650390625}, {"start": 3642.6, "end": 3643.02, "word": " جزء", "probability": 0.9923502604166666}, {"start": 3643.02, "end": 3643.68, "word": " في", "probability": 0.841796875}, {"start": 3643.68, "end": 3644.06, "word": " هذا", "probability": 0.94677734375}, {"start": 3644.06, "end": 3644.32, "word": " ال", "probability": 0.52294921875}, {"start": 3644.32, "end": 3644.78, "word": " section", "probability": 0.8798828125}, {"start": 3644.78, "end": 3647.08, "word": " و", "probability": 0.78759765625}, {"start": 3647.08, "end": 3647.58, "word": " الان", "probability": 0.6407470703125}, {"start": 3647.58, "end": 3648.14, "word": " ان", "probability": 0.88232421875}, {"start": 3648.14, "end": 3648.34, "word": " شاء", "probability": 0.9853515625}, {"start": 3648.34, "end": 3648.54, "word": " الله", "probability": 0.935546875}, {"start": 3648.54, "end": 3648.86, "word": " بكون", "probability": 0.894287109375}, {"start": 3648.86, "end": 3649.32, "word": " خلصنا", "probability": 0.974365234375}, {"start": 3649.32, "end": 3649.56, "word": " الجزء", "probability": 0.83154296875}, {"start": 3649.56, "end": 3649.92, "word": " الاول", "probability": 0.8974609375}, {"start": 3649.92, "end": 3650.16, "word": " من", "probability": 0.9912109375}, {"start": 3650.16, "end": 3651.94, "word": " المحاضرة", "probability": 0.9801025390625}, {"start": 3651.94, "end": 3653.62, "word": " و", "probability": 0.9326171875}, {"start": 3653.62, "end": 3654.16, "word": " نبدأ", "probability": 0.93212890625}, {"start": 3654.16, "end": 3654.3, "word": " ان", "probability": 0.7763671875}, {"start": 3654.3, "end": 3654.44, "word": " شاء", "probability": 0.99609375}, {"start": 3654.44, "end": 3654.8, "word": " الله", "probability": 0.94921875}, {"start": 3654.8, "end": 3655.42, "word": " بعد", "probability": 0.908203125}, {"start": 3655.42, "end": 3655.76, "word": " شوية", "probability": 0.8841145833333334}, {"start": 3655.76, "end": 3655.92, "word": " في", "probability": 0.9404296875}, {"start": 3655.92, "end": 3656.2, "word": " الجزء", "probability": 0.990234375}, {"start": 3656.2, "end": 3656.7, "word": " الثاني", "probability": 0.90673828125}, {"start": 3656.7, "end": 3658.28, "word": " برك", "probability": 0.627685546875}, {"start": 3658.28, "end": 3658.42, "word": " الله", "probability": 0.95263671875}, {"start": 3658.42, "end": 3658.74, "word": " فيكم", "probability": 0.856201171875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3660.6955, "duration_after_vad": 3532.949999999985}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5ddd00fc2bab58add9508ed0b9b15d66b5b51c2c
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_raw.srt
@@ -0,0 +1,2892 @@
+1
+00:00:11,170 --> 00:00:17,190
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم خمستاشر
+
+2
+00:00:17,190 --> 00:00:25,090
+لمساق تحليل حقيقي اتنين لطلبات وطالبات الجامعة
+
+3
+00:00:25,090 --> 00:00:31,380
+الإسلاميةكلية العلوم قسم الرياضيات المحاضرة اليوم
+
+4
+00:00:31,380 --> 00:00:35,940
+إن شاء الله اللي هي ستكون على جزئين الجزء الأول
+
+5
+00:00:35,940 --> 00:00:40,940
+هنكمل اللي بدناه المرة الماضية اللي هو اللي نكمل
+
+6
+00:00:40,940 --> 00:00:45,100
+اللي هي تطبيقات على الـ Fundamental Theorem of
+
+7
+00:00:45,100 --> 00:00:50,540
+Calculus الجزء الأول هذا التطبيق طبعاً هو هيكون عن
+
+8
+00:00:50,540 --> 00:00:53,880
+evaluation of integrals برضه بدنا فيه المرة
+
+9
+00:00:53,880 --> 00:00:58,220
+الماضية و هنكمله اليوم إن شاء اللهالجزء الثاني من
+
+10
+00:00:58,220 --> 00:01:04,180
+المحاضرة هنتحدث عن اللي هو التكامل أن ندخل
+
+11
+00:01:04,180 --> 00:01:08,620
+لتعاملية التكامل بطريقة غير ال upper sum والlower
+
+12
+00:01:08,620 --> 00:01:15,060
+sum عن طريق حاجة اسمها الرمان sumهذا الآن هو الجزء
+
+13
+00:01:15,060 --> 00:01:19,080
+الثاني الآن بدنا نبدأ في الجزء الأول بس على السريع
+
+14
+00:01:19,080 --> 00:01:22,540
+نطلع على اللي حكيناه المرة الماضية بدنا حكينا عن
+
+15
+00:01:22,540 --> 00:01:26,120
+الـ Fundamental Theorem of Calculus وحكينا عن اللي
+
+16
+00:01:26,120 --> 00:01:30,800
+هو الـ Two Forms إيها أو التفاضل والتكامل زي ما
+
+17
+00:01:30,800 --> 00:01:35,240
+حكينا وتكامل التفاضل Roughly الكلام و بعدين أتينا
+
+18
+00:01:35,240 --> 00:01:38,980
+لبعض الملاحظات وبعض التعريفات وحكينا عن ال
+
+19
+00:01:38,980 --> 00:01:42,780
+evaluation of integralsبدأنا في evaluation of
+
+20
+00:01:42,780 --> 00:01:46,600
+integrals اللي هو اللي بيمثل الجزء الأول من هذه
+
+21
+00:01:46,600 --> 00:01:51,320
+المحاضرة اليوم حكينا عن اللي هو ال integration by
+
+22
+00:01:51,320 --> 00:01:55,480
+parts ال integration by parts حكينا عنه المرة
+
+23
+00:01:55,480 --> 00:02:02,130
+الماضية وشرحناها وقفنا عند اللي هوالـ ال .. ال ..
+
+24
+00:02:02,130 --> 00:02:06,230
+ال .. ال .. ال first substitution form اللي هنبدأ
+
+25
+00:02:06,230 --> 00:02:10,650
+فيها اليوم إن شاء الله الآن ال first substitution
+
+26
+00:02:10,650 --> 00:02:15,310
+form أو اللي هو التكامل بالتعويض عن طريق اللي هي
+
+27
+00:02:15,310 --> 00:02:18,870
+التعويض وهذه طبعا طريقة كنا نستخدمها زي ما
+
+28
+00:02:18,870 --> 00:02:22,670
+استخدمنا اللي هي طريقة ال integration by parts في
+
+29
+00:02:22,670 --> 00:02:27,910
+calculus B أيضا استخدمنا اللي هو التكامل بالتعويض
+
+30
+00:02:27,910 --> 00:02:36,840
+للإيجادأو لعملية إيجاد اللي هي التكامل الآن بدنا
+
+31
+00:02:36,840 --> 00:02:41,720
+نعطي النظرية اللي بتشرع لنا أو نثبت النظرية اللي
+
+32
+00:02:41,720 --> 00:02:46,840
+بتسمح لنا بالتكامل بالتعويض نيجي نطلع لنظريتنا
+
+33
+00:02:46,840 --> 00:02:51,120
+اللي هي ال first substitution theorem نيجي ناخد
+
+34
+00:02:51,120 --> 00:02:55,300
+اللي هو ال J فترة عبارة عن ال close interval Alpha
+
+35
+00:02:55,300 --> 00:03:01,120
+و Betaإن ناخد فاي function من J لعند R have a
+
+36
+00:03:01,120 --> 00:03:04,620
+continuous derivative on J يعني أخدنا الآن يا
+
+37
+00:03:04,620 --> 00:03:09,660
+جماعة فاي عبارة عن function من اللي هي الفترة
+
+38
+00:03:09,660 --> 00:03:17,090
+Alpha و Betaلعين بـ R وفرضنا إن هذه الدالة اللي هي
+
+39
+00:03:17,090 --> 00:03:22,050
+Phi ال derivative إلها موجودة ونفسها إشمالها
+
+40
+00:03:22,050 --> 00:03:26,690
+continuous إذا فرضنا إن اللي هو الـ Phi have a
+
+41
+00:03:26,690 --> 00:03:31,230
+continuous derivative on the interval J اللي
+
+42
+00:03:31,230 --> 00:03:35,080
+سمناها ليه Alpha و Betaلأن لو كان في عندي function
+
+43
+00:03:35,080 --> 00:03:39,300
+F is continuous on any interval I containing Phi
+
+44
+00:03:39,300 --> 00:03:46,160
+of J لأن فرضنا أن F دالة على I تحتوي Phi of J عساس
+
+45
+00:03:46,160 --> 00:03:51,180
+إن بعد شوية هعرّق .. هيلزمني اللي هو composition
+
+46
+00:03:51,180 --> 00:03:55,160
+of two functions عشان هيك أنا باخد ال F عبارة عن
+
+47
+00:03:55,160 --> 00:04:00,840
+function من I لعند مين؟ لعند ال R إيش ال I هذه؟
+
+48
+00:04:00,840 --> 00:04:08,290
+هذه I intervalبتحتوي اللي هي مين الـ Phi of Jاللي
+
+49
+00:04:08,290 --> 00:04:13,790
+عندى، يعني هيصير عندى بناء عليها هيصير عندى F of
+
+50
+00:04:13,790 --> 00:04:20,270
+Phi of I T فيه اللي هي الـ J عبارة عن قيمة معرفة
+
+51
+00:04:20,270 --> 00:04:24,790
+عشان تكون ال composition معرفة، إذا الآن باختصار
+
+52
+00:04:24,790 --> 00:04:28,010
+Phi اللي هي ال derivative اللي موجودة و ال
+
+53
+00:04:28,010 --> 00:04:31,670
+derivative continuous و ال function F small هذي is
+
+54
+00:04:31,670 --> 00:04:35,510
+continuous و هنا ال interval I، thenالان نجي
+
+55
+00:04:35,510 --> 00:04:40,050
+للنتيجة اللى احنا بنمارسها عمليا دائما اللى هو
+
+56
+00:04:40,050 --> 00:04:46,790
+بكون عندى ال integration من Alpha ل Beta لF of Phi
+
+57
+00:04:46,790 --> 00:04:53,960
+of T Phi prime of TDT احنا بندعي بتساوي كنا نيجي
+
+58
+00:04:53,960 --> 00:04:58,100
+ايش نسوي ناخد هذه اللي هي نعوض عن Phi of T ب X
+
+59
+00:04:58,100 --> 00:05:03,360
+بناء عليها بيصير عبارة عن هذا ال integration F of
+
+60
+00:05:03,360 --> 00:05:09,920
+X و Phi prime of T بنعوض عن Phi of T ب X فبيصير
+
+61
+00:05:09,920 --> 00:05:14,200
+عند Phi prime of T DT هو عبارة عن مين DX كنا هيك
+
+62
+00:05:14,200 --> 00:05:17,890
+نسوي في ال calculusالآن نيجي نقول DX بسوء Phi
+
+63
+00:05:17,890 --> 00:05:22,670
+prime T DT أو DX على DT بسوء Phi prime of T ونشيل
+
+64
+00:05:22,670 --> 00:05:26,630
+Phi prime of T DT ونحط مكان هي شمالها DX حدود ال
+
+65
+00:05:26,630 --> 00:05:30,110
+integration كانت من Alpha ل Beta يعني لما كانت T
+
+66
+00:05:30,110 --> 00:05:33,350
+بAlpha بصير X اللي هي Phi of T اللي هي Phi of
+
+67
+00:05:33,350 --> 00:05:39,190
+Alpha بتروح لمين؟ لأ اللي هي Phi of مين؟ Phi of
+
+68
+00:05:39,190 --> 00:05:45,180
+Betaليش؟ لأنه لما كانت T بساوي Beta أكيد الـ X
+
+69
+00:05:45,180 --> 00:05:48,760
+اللي هي Phi of T بتساوي الـ X بتساوي Phi of T، الـ
+
+70
+00:05:48,760 --> 00:05:53,640
+X بتساوي Phi of Beta إذن نظريتنا هذه اللي أمامنا
+
+71
+00:05:53,640 --> 00:05:59,160
+هي نظرية إحنا يعني استعملناها أو بنستعملها عادة في
+
+72
+00:05:59,160 --> 00:06:02,600
+اللي هو إيجاد الـ integration وإحدى الطرق لإيجاد
+
+73
+00:06:02,600 --> 00:06:07,860
+الـ integration فعندي
+
+74
+00:06:07,860 --> 00:06:14,140
+الآنهذه الآن نظريتنا، بدنا نبرهن هذه النظرية ونشوف
+
+75
+00:06:14,140 --> 00:06:18,840
+كيف نبرهنها، برهانها بسيط، الآن هي اللي بدنا
+
+76
+00:06:18,840 --> 00:06:23,280
+نبرهنه، خلّينا نشوف كيف البرهانة وكيف نبرهن
+
+77
+00:06:23,280 --> 00:06:26,380
+الكتاب،
+
+78
+00:06:26,380 --> 00:06:32,520
+عنده يجينا عرفنا، بدنا نعرف function F، لأن عرش
+
+79
+00:06:32,520 --> 00:06:35,990
+function Fتنسوش هذا الـ Function ايش مالها يا
+
+80
+00:06:35,990 --> 00:06:40,070
+جماعة؟ Continuous وهذا بتعني كتير بالنسبة للـ
+
+81
+00:06:40,070 --> 00:06:43,210
+Fundamental Theorem أعرف الـ Function F من الـ
+
+82
+00:06:43,210 --> 00:06:50,310
+Interval I لعند مين R F Capital أعرف الـ F Capital
+
+83
+00:06:50,310 --> 00:06:59,070
+F of U بساوة الـ Integration من اللي هو عند الـ I
+
+84
+00:06:59,070 --> 00:07:04,870
+بتحتوي مين الـ Phi of J يعني هي الـ Interval Iهي
+
+85
+00:07:04,870 --> 00:07:08,870
+الـ interval I وفي داخلها Phi of J Phi of J طبعاً
+
+86
+00:07:08,870 --> 00:07:12,330
+في عند Phi of Alpha لعند Phi of Beta لو كانت اللي
+
+87
+00:07:12,330 --> 00:07:15,590
+هي Alpha أكبر من Beta الاخرى Phi of J اللي هم
+
+88
+00:07:15,590 --> 00:07:19,990
+مفترضينها احنا وين في داخل الفترة اللي أمامي الآن
+
+89
+00:07:19,990 --> 00:07:24,050
+بتاخد ال integration تعرفه من عند Phi of Alpha
+
+90
+00:07:24,050 --> 00:07:29,980
+لعند main U الـ U المتغيرةاللي هتكون وين موجودة في
+
+91
+00:07:29,980 --> 00:07:35,240
+داخل الـ I اللي بتحتوي الـ Phi of G إذا عرفت
+
+92
+00:07:35,240 --> 00:07:37,440
+function f of u بيستوي ال integration من Phi of
+
+93
+00:07:37,440 --> 00:07:42,780
+Alpha ثابت Phi of Alpha يا جماعة لعند U لمين؟ للf
+
+94
+00:07:42,780 --> 00:07:49,410
+of x dxلاحظ هذه الدالة اللي عندي اللي عرفتها من
+
+95
+00:07:49,410 --> 00:07:53,830
+الـ Fundamental theorem بما أن F is continuous إذا
+
+96
+00:07:53,830 --> 00:07:58,810
+هذا كله الآن اللي هو صار function في U عبارة عن
+
+97
+00:07:58,810 --> 00:08:03,990
+differentiable ومش هيك كمان و F prime of U هتساوي
+
+98
+00:08:03,990 --> 00:08:11,090
+مين؟ اللي هي الدالة F of Uإذا من الـ Fundamental
+
+99
+00:08:11,090 --> 00:08:15,350
+theorem بما أن F is continuous إذا F prime of U
+
+100
+00:08:15,350 --> 00:08:20,210
+بتساوي F of U اللي هي by Fundamental theorem of
+
+101
+00:08:20,210 --> 00:08:23,370
+calculus إذا by Fundamental theorem of calculus فF
+
+102
+00:08:23,370 --> 00:08:27,710
+of X .. F of U طبعا هذه صيحوها بسوء ال integration
+
+103
+00:08:27,710 --> 00:08:32,200
+من C .. C اللي هو احنا بسميه همين هياللي هي Phi of
+
+104
+00:08:32,200 --> 00:08:35,820
+Alpha مابديش أخبركم في التسميات على طول من Phi of
+
+105
+00:08:35,820 --> 00:08:40,140
+Alpha لعند مين لعنديه إذا اللي سويته أنا بس لحتى
+
+106
+00:08:40,140 --> 00:08:46,340
+الآن إن عرفت دالة اللي هي ال func ال F capital هذه
+
+107
+00:08:46,340 --> 00:08:53,760
+ال F capital عرفتها من I من I لعند R by F of U
+
+108
+00:08:53,760 --> 00:08:58,060
+بسوء ال integration من C ل U F of X DX for U
+
+109
+00:08:58,060 --> 00:09:03,310
+element من in ال interval Iالان قاعد بحضر للي
+
+110
+00:09:03,310 --> 00:09:08,630
+بديها and now consider the function H من J لعند R
+
+111
+00:09:08,630 --> 00:09:12,690
+بعد ما عرفت ال function F هذه اللي أمامي بدي
+
+112
+00:09:12,690 --> 00:09:18,330
+أعرفلكم دالة تانية الدالة اللي بدي أعرفها يا جماعة
+
+113
+00:09:18,330 --> 00:09:26,530
+هي عبارة عن HH هذه بدي أعرفها من J لعند R شوف كيف
+
+114
+00:09:26,530 --> 00:09:30,510
+بدي أعرفها بطريقة اللي هي تخدمني بعد شوية للوصول
+
+115
+00:09:30,510 --> 00:09:36,730
+للنتيجة اللي بديها اللي هي H of T بدي أعرفها H of
+
+116
+00:09:36,730 --> 00:09:46,170
+T بساوية F capital هذه اللي عرفتها of Phi of T Phi
+
+117
+00:09:46,170 --> 00:09:52,220
+of Tالان جهة دي اليمين هي الفترة Alpha و Beta Phi
+
+118
+00:09:52,220 --> 00:09:57,740
+of Tاللي هي إذا T من في J Phi of T معرّفة على الـJ
+
+119
+00:09:57,740 --> 00:10:03,440
+الـJ Phi of T إشمالها معرّفة على الـJ الـF إلها
+
+120
+00:10:03,440 --> 00:10:07,640
+معرّفة لإن الـF domainها I اللي هو اللي بيحتوى Phi
+
+121
+00:10:07,640 --> 00:10:11,360
+of J يعني فعلا Phi of T موجودة في Phi of J اللي هي
+
+122
+00:10:11,360 --> 00:10:14,600
+موجودة في مين في I إذا المعرّفة اللي دالها H of T
+
+123
+00:10:14,600 --> 00:10:23,370
+بيساوي Phi of I of T طيبالأن الـ F اتفاجنا للـ F
+
+124
+00:10:23,370 --> 00:10:27,030
+هذه إنها differentiable الـ F كابيتال والـ Phi
+
+125
+00:10:27,030 --> 00:10:29,470
+differentiable ليش differentiable؟ لأن Phi prime
+
+126
+00:10:29,470 --> 00:10:32,390
+موجودة و continuous إذا بقدر .. هي أفاضل هذه
+
+127
+00:10:32,390 --> 00:10:38,340
+الدالة إذا بقدر أقول إنه عند الـ H primeof T
+
+128
+00:10:38,340 --> 00:10:44,340
+بيساوي F' Phi of T بتشيرن رول طبعا يا جماعة في Phi
+
+129
+00:10:44,340 --> 00:10:51,460
+prime of T فإذا تفاضل ال H' هو F' في Phi prime of
+
+130
+00:10:51,460 --> 00:10:59,000
+T زي ما احنا ذكرين في برهان النظرية هان الآن عندي
+
+131
+00:10:59,000 --> 00:11:03,540
+ايضا احنا قلنا ال F prime of U ايش بتساوي F of U
+
+132
+00:11:03,540 --> 00:11:08,920
+وقلنا ليش السببالان لو اجينا كل هذا تحضير للي
+
+133
+00:11:08,920 --> 00:11:13,980
+بديها بعد شوية المعلومات هذه الان عندي احسبلي H of
+
+134
+00:11:13,980 --> 00:11:22,380
+Alpha H of Alpha من هذه H of Alpha اكيد كلكم شاف
+
+135
+00:11:22,380 --> 00:11:29,960
+ان H of Alpha بتساوي عوض بتساوي Fof Phi of Alpha
+
+136
+00:11:29,960 --> 00:11:33,560
+صحيه يا جماعة ويساوي F of Phi of Alpha طب إيش
+
+137
+00:11:33,560 --> 00:11:37,980
+تعريف F of U؟ هي عبارة عن ال integration من Phi of
+
+138
+00:11:37,980 --> 00:11:43,520
+Alpha لعند U U أنا الآن إيش هي؟ اسمها Uاللي هو 5
+
+139
+00:11:43,520 --> 00:11:46,420
+Alpha إذا من 5 Alpha ل 5 Alpha يعني ال integration
+
+140
+00:11:46,420 --> 00:11:51,100
+إيش هيساوي هذا بساوي سفر إذا أتشوف Alpha فعلا إيش
+
+141
+00:11:51,100 --> 00:11:55,200
+بتساوي .. بتساوي إيش .. بتساوي سفر إذا تلت حاجات
+
+142
+00:11:55,200 --> 00:11:59,860
+الآن عرفت ال F من I ل عند R بالطريقة اللي أمامي
+
+143
+00:12:00,190 --> 00:12:05,030
+وجدت أن F' بيساوي F of U الشغل الثاني عرفت H of T
+
+144
+00:12:05,030 --> 00:12:08,530
+بيساوي F of Phi of T اللي هو F is differentiable,
+
+145
+00:12:08,590 --> 00:12:11,950
+Phi is differentiable إذا نفسي H is differentiable
+
+146
+00:12:11,950 --> 00:12:14,850
+و ال derivative إليها إيه الشمال هذه بيساوي اللي
+
+147
+00:12:14,850 --> 00:12:19,670
+أمامي و الشغل الثاني اللي حصلنا عليها أن H of
+
+148
+00:12:19,670 --> 00:12:25,010
+Alpha إيش هيساوي يا شباب؟ هو يساوي 0 نيجي الآن
+
+149
+00:12:25,010 --> 00:12:31,250
+بدنا نوصل لمين إحنا؟أحنا هدفنا يا جماعة اللي هو
+
+150
+00:12:31,250 --> 00:12:38,310
+هدفنا سامحونا على اللوح الصغير اللوح هدفنا هو ال
+
+151
+00:12:38,310 --> 00:12:47,210
+integration من Alpha لعند Beta F of Phi of T Phi
+
+152
+00:12:47,210 --> 00:12:54,670
+prime of T dt بساوة ال integration لل F of XDX من
+
+153
+00:12:54,670 --> 00:12:59,290
+Phi of Alpha لعين Phi of Beta هذا اللي بدنا نثبته
+
+154
+00:12:59,290 --> 00:13:09,190
+شوف كيف بدنا نصل لهذا اللي هو المطلوب نيجي
+
+155
+00:13:09,190 --> 00:13:16,090
+لهو ال integration اللي قبلنا هذا اللي هو الطرف
+
+156
+00:13:16,090 --> 00:13:20,580
+اللي احنا بدنا نثبته بساوى هذا الطرفهذا الطرف اللي
+
+157
+00:13:20,580 --> 00:13:23,340
+أنا ساويه هذا، نبدأ بهذا الطرف اللي هنا ونبنع
+
+158
+00:13:23,340 --> 00:13:26,920
+المعلومات ونحصل على اللي بدناه بكل سهولة الآن ال
+
+159
+00:13:26,920 --> 00:13:29,920
+integration من Alpha لعين ال Beta F of five T five
+
+160
+00:13:29,920 --> 00:13:35,620
+prime of T DT بتساوي الان ال F هذه في الواقع مين
+
+161
+00:13:35,620 --> 00:13:41,850
+هي؟ هذه هي عبارة عن F primeإذا صار عندي الآن هذا
+
+162
+00:13:41,850 --> 00:13:45,790
+المقدار هو عبارة عن f prime of five a t five prime
+
+163
+00:13:45,790 --> 00:13:51,350
+a شماله of t يعني وكأنني مين بفاضل أنا بفاضل كل
+
+164
+00:13:51,350 --> 00:13:58,890
+هذا المقدار طلع مين هو h prime of t وكل أموره حلوة
+
+165
+00:13:58,890 --> 00:14:05,170
+ومحترمة ال fاللي هي continuous والـ Phi prime
+
+166
+00:14:05,170 --> 00:14:09,090
+continuous معطينيها إذاً هذه صارت الـ H' كلها يشمع
+
+167
+00:14:09,090 --> 00:14:11,970
+لها continuous إذا ال integration من Alpha ل Beta
+
+168
+00:14:11,970 --> 00:14:17,390
+لH' of T اللي هو ال integration بـ cancel ال
+
+169
+00:14:17,390 --> 00:14:19,990
+differentiation اللي هي الجزء الأول من ال
+
+170
+00:14:19,990 --> 00:14:22,790
+fundamental theorem of calculus يا جماعة فبيصير
+
+171
+00:14:22,790 --> 00:14:29,910
+إيش بيساوي الجواب H of Beta ناقص H of mean of
+
+172
+00:14:29,910 --> 00:14:33,960
+Alphaإذن صار عندى الان h of alpha قبل شوية شهية
+
+173
+00:14:33,960 --> 00:14:36,720
+نفكرة و كده لسه كتبه إنها إيش بتساوي سفر إذا صار
+
+174
+00:14:36,720 --> 00:14:41,860
+المقدار هذا كله اللي أنا بديه إيش صار بيساوي h of
+
+175
+00:14:41,860 --> 00:14:47,720
+b إذا اللي أثبتته تقريبا عندي خلصت أثبتت إن ال
+
+176
+00:14:47,720 --> 00:14:54,080
+integration ال layأمامي هذا كله بيساوي مين؟ H of B
+
+177
+00:14:54,080 --> 00:15:01,480
+خلّينا نحسب H of B H of T احنا F of Phi of T إذا H
+
+178
+00:15:01,480 --> 00:15:08,220
+of B بيساوي F of Phi of Beta H of Beta بيساوي F of
+
+179
+00:15:08,220 --> 00:15:14,040
+Phi of Beta الآن ما يساوي؟الـ integration .. ال
+
+180
+00:15:14,040 --> 00:15:17,260
+integration سبوكوا من ال D لأن أنا ماستخدمش الرموز
+
+181
+00:15:17,260 --> 00:15:23,040
+هذه إيش هذا بيساوي؟ بيصير عند F .. F اللي هو of
+
+182
+00:15:23,040 --> 00:15:28,260
+Phi of B حسب التعريف F of U هاي و أماني بيساوي ال
+
+183
+00:15:28,260 --> 00:15:37,600
+integration من Phi of Alpha لعن Phi of Beta F of X
+
+184
+00:15:37,600 --> 00:15:45,960
+DXوهو هذا المطلوب صار عند ال integration ل .. اللي
+
+185
+00:15:45,960 --> 00:15:49,600
+هي f of x dx من five of alpha لعند five of beta
+
+186
+00:15:49,600 --> 00:15:54,460
+اللي هو h of b بساوي اللي هو ال integration اللي
+
+187
+00:15:54,460 --> 00:16:02,040
+أمامي وهو المطلوب طيب نيجي الآن للنظرية الثانية
+
+188
+00:16:02,040 --> 00:16:08,740
+النظرية الثانية اللي هي second substitution
+
+189
+00:16:08,740 --> 00:16:20,020
+theoremاللي هي .. أيضًا بنستخدمها وحنشوف إيش اللي
+
+190
+00:16:20,020 --> 00:16:26,260
+هي هذا النظرية وكيف انبرهن النظرية والبرهان برضه
+
+191
+00:16:26,260 --> 00:16:33,080
+مش صعب أو البرهان اللي هو سهل هنشوف ال second
+
+192
+00:16:33,080 --> 00:16:36,960
+substitution theorem بتقول ما يلي عند في function
+
+193
+00:16:38,340 --> 00:16:42,180
+فاي من جي لعين بار جي هي نفس الفترة اللي .. الفترة
+
+194
+00:16:42,180 --> 00:16:45,700
+اللي احنا حكينا عنها اللي هي عبارة عن Alpha و Beta
+
+195
+00:16:45,700 --> 00:16:49,980
+بدنا نفترض ان الفاي هذه have a continuous
+
+196
+00:16:49,980 --> 00:16:57,700
+derivativeبرضه نفس اللي هي المعتل أولاني ونفترض I
+
+197
+00:16:57,700 --> 00:17:02,700
+عبارة عن interval بتحتوي Phi of J نفس المعتل في
+
+198
+00:17:02,700 --> 00:17:07,220
+النظرية السابقة الآن المعتل جديد بدنا نفترض أنه
+
+199
+00:17:07,220 --> 00:17:12,160
+فيه function ψ من I لعند Rبـ a function اللي هو
+
+200
+00:17:12,160 --> 00:17:16,740
+inverse لـ mean اللي هي الـ Phi يعني عندي Phi
+
+201
+00:17:16,740 --> 00:17:24,140
+بشروط النظرية اللي فاتت من J لعند مين لعند R وعندي
+
+202
+00:17:24,140 --> 00:17:29,800
+ب Psi من عند I لعند R ومفترضين أنه بPsi هي ال
+
+203
+00:17:29,800 --> 00:17:33,940
+inverse ل mean للـ Phi يعني Phi composite بPsi
+
+204
+00:17:35,340 --> 00:17:39,940
+بساومين الـ identity function أو Psi composite الـ
+
+205
+00:17:39,940 --> 00:17:45,960
+Phi عبارة عن ال identity function وكل اللي هو عندى
+
+206
+00:17:45,960 --> 00:17:53,460
+مفترضين ان Phi of J subset من مين من الـ I عشان
+
+207
+00:17:53,460 --> 00:18:00,680
+يكون اللي هو ال composition معرف احنا
+
+208
+00:18:08,270 --> 00:18:15,850
+صارت بـ Psi هي ال inverse لـ Phi و F برضه نفس
+
+209
+00:18:15,850 --> 00:18:20,230
+المعطيات الفاترة continuous on I إذا ما يعني، إذا
+
+210
+00:18:20,230 --> 00:18:25,190
+يعني اللي بحكيه و كأنه نفس شروط النظرية السابقة بس
+
+211
+00:18:25,190 --> 00:18:30,190
+اللي أنضفنا إن الـ Phi اللي عندنا في هذه الحالة
+
+212
+00:18:30,190 --> 00:18:35,220
+فيه إلها inverseفي الها inverse فبتعطيني مجال
+
+213
+00:18:35,220 --> 00:18:39,900
+للتحرك أكثر من الأولى الألهة دي بتفترضش أنه في
+
+214
+00:18:39,900 --> 00:18:42,900
+الها inverse وبنبدأ بنعوض زي ما عوضنا قبل ايش
+
+215
+00:18:42,900 --> 00:18:48,580
+النتيجة طيب النتيجة هي ما يلي اللي هو إذا ال
+
+216
+00:18:48,580 --> 00:18:56,560
+integration أبو حسين ازيحه بس نجاعي شوية
+
+217
+00:19:03,530 --> 00:19:21,050
+النص اللي لدك على الحيط أصلا السلام
+
+218
+00:19:21,050 --> 00:19:22,150
+عليكم السلام عليكم
+
+219
+00:19:41,080 --> 00:19:43,960
+خلاص ساعة سبعة يا عزيزي خلاص خلاص
+
+220
+00:19:46,210 --> 00:19:50,670
+إذا الآن ال .. ال .. ال .. ال .. second
+
+221
+00:19:50,670 --> 00:19:54,290
+substitution theorem نفس شروط اللي هو ال fair
+
+222
+00:19:54,290 --> 00:19:58,590
+substitution theorem بس الآن اللي هيضفنا عليها أنه
+
+223
+00:19:58,590 --> 00:20:02,150
+بـ Psi عندي فرضنا أنه في عندي Psi function من I
+
+224
+00:20:02,150 --> 00:20:07,270
+لعند R هي عبارة عن ال inverse لمين لفاي بناء ..
+
+225
+00:20:07,270 --> 00:20:12,990
+بناء عليه هيصير ال integration من Alpha لعند BetaF
+
+226
+00:20:12,990 --> 00:20:19,230
+of Phi of T DT لأن مش ظاهرة عندنا هنا مين الـ
+
+227
+00:20:19,230 --> 00:20:23,650
+derivative لمين لإي اللي هي الـ Phi بالرغم من هيك
+
+228
+00:20:23,650 --> 00:20:27,470
+هيطلع عندى بساوة ال integration F of X ب Phi prime
+
+229
+00:20:27,470 --> 00:20:31,810
+of X DX اللي هو عندى من Phi of Alpha لعند مين؟
+
+230
+00:20:31,810 --> 00:20:33,770
+لعند Phi of Beta
+
+231
+00:20:36,860 --> 00:20:42,520
+الان نشوف اللي هو كيف انبرهن نظريتنا خلينا نكتب
+
+232
+00:20:42,520 --> 00:20:46,800
+هذه على جهة عشان نعرف احنا لوين رايحين ال
+
+233
+00:20:46,800 --> 00:20:55,880
+integration من Alpha لعين Beta F of Phi of T dt
+
+234
+00:20:55,880 --> 00:21:08,520
+بساوة ال integration لPsi of Alpha F ofأو F of X
+
+235
+00:21:08,520 --> 00:21:21,440
+Phi prime of .. Psi prime of X DX Phi prime of X
+
+236
+00:21:21,440 --> 00:21:27,600
+DX من Phi of Alpha عن
+
+237
+00:21:27,600 --> 00:21:36,060
+Phi of Beta دعونا نشوف كيف .. نيجي نشوف البرهانجرب
+
+238
+00:21:36,060 --> 00:21:42,560
+انت لحالك عوض اللي هو عشان تشوف منطقية النظرية زي
+
+239
+00:21:42,560 --> 00:21:49,880
+ما كنا نعوض في ال calculus عوض عن X ب Phi of T ها
+
+240
+00:21:49,880 --> 00:21:55,540
+هيطلع عندك اللي هو في النهاية DT هو عبارة عن كل
+
+241
+00:21:55,540 --> 00:21:59,890
+هذهلو عوضت طبعاً باستخدام اللي هو العلاقة بين ال
+
+242
+00:21:59,890 --> 00:22:03,170
+.. ال .. ال inverse اللي هي الـ Psi إنها inverse
+
+243
+00:22:03,170 --> 00:22:07,210
+على Phi هتحصل على اللي هو .. اللي هو كل هذا
+
+244
+00:22:07,210 --> 00:22:12,750
+المقدار هو هيطلع مين هو دي T و هتسير بدل Alpha Phi
+
+245
+00:22:12,750 --> 00:22:15,550
+of Alpha و Beta Phi of Beta زي ما أنتوا عارفين
+
+246
+00:22:15,550 --> 00:22:19,490
+لأنه لما كانت T بتساوية Alpha طلعت اللي هي Phi of
+
+247
+00:22:19,490 --> 00:22:21,970
+T لعوضة مكانها اللي هي Phi of Alpha و التانية
+
+248
+00:22:21,970 --> 00:22:29,420
+هتطلع Phi of Beta طب نيجي الآن لبرهان النظريةالان
+
+249
+00:22:29,420 --> 00:22:34,860
+عندى اول حاجة five prime of T بعطينا اياها اشمالها
+
+250
+00:22:34,860 --> 00:22:39,660
+لا تساوى سفر طبعا هذا لزوم لزوم ان تكون ال inverse
+
+251
+00:22:39,660 --> 00:22:44,900
+موجودة five prime of T لا تساوى سفر يعنى الان five
+
+252
+00:22:44,900 --> 00:22:49,180
+prime of T يا اكبر من سفر يا اصغر من سفرعندي
+
+253
+00:22:49,180 --> 00:22:52,680
+المنطق اللي هيكون عندي اللي هي strictly increasing
+
+254
+00:22:52,680 --> 00:22:55,860
+أو strictly decreasing على المنطقة اللي هي فيها
+
+255
+00:22:55,860 --> 00:23:00,060
+إذا في عندى بمعنى آخر strictly monotone مدام
+
+256
+00:23:00,060 --> 00:23:04,940
+strictly monotone إذا ال inverse إلها موجود و في
+
+257
+00:23:04,940 --> 00:23:08,900
+بتساوي في inverse زي ما هو معطينا إياها طبعا إحنا
+
+258
+00:23:08,900 --> 00:23:14,410
+معطينا ال فيالـ Phi مش differentiable بس Phi مش
+
+259
+00:23:14,410 --> 00:23:17,990
+differentiable اللي هو ال derivative موجودة و
+
+260
+00:23:17,990 --> 00:23:22,310
+الاشمالها continuous طيب لان بما انه اللي هي Phi
+
+261
+00:23:22,310 --> 00:23:27,850
+prime exist إذا بنظرية أخدناها اللي هي 6 1 9 هتكون
+
+262
+00:23:27,850 --> 00:23:32,170
+ال Phi prime existوبتساوي واحد على في برايم في
+
+263
+00:23:32,170 --> 00:23:36,350
+مين؟ في بساي كمان مرة يا جماعة أذكركم في النظرية
+
+264
+00:23:36,350 --> 00:23:41,410
+الآن عندى مدامة بساي بساوي في انفرس والفي نفسها
+
+265
+00:23:41,410 --> 00:23:45,450
+عبارة عن differentiable هتكون ال inverse اللي هي
+
+266
+00:23:45,450 --> 00:23:48,910
+بساي is differentiable وال derivative اللي هي بساي
+
+267
+00:23:48,910 --> 00:23:53,490
+برايم هي عبارة عن واحد على في برايم ماله composite
+
+268
+00:23:53,490 --> 00:23:58,400
+بساياللي هي .. أو مش هيك هتطلع .. هتطلع continuous
+
+269
+00:23:58,400 --> 00:24:01,500
+ليش continuous؟ لأنه أصلا مافيش أسفار في المقام
+
+270
+00:24:01,500 --> 00:24:05,100
+أكيد وعند Phi prime نفسها Phi prime نفسها
+
+271
+00:24:05,100 --> 00:24:08,520
+continuous ماتينياها و ب Psi is continuous لأنها
+
+272
+00:24:08,520 --> 00:24:11,800
+أصلا differentiable فهتطلع عند اللي ب Psi prime
+
+273
+00:24:11,800 --> 00:24:17,180
+برضه مالها is continuous إذن اللي استنتجناه الآن
+
+274
+00:24:17,180 --> 00:24:22,590
+أن ال inverse function is continuous وقيمتهاالـ
+
+275
+00:24:22,590 --> 00:24:26,310
+Derivative إليها هي عبارة عن واحد على Psi Prime في
+
+276
+00:24:26,310 --> 00:24:31,890
+Phi Prime في مين؟ في Psi نشوف الآن بدنا نعرف اللي
+
+277
+00:24:31,890 --> 00:24:36,850
+هو بأسلوب مشابه قبل بشوية أنه نعرف دوال بحيث أنه
+
+278
+00:24:36,850 --> 00:24:41,810
+لما نيجي اللي هو ناخده تبقى derivative لشيء سهل
+
+279
+00:24:41,810 --> 00:24:45,210
+إيجاده ولمّا ناخده له ال integration يطلع اللي هو
+
+280
+00:24:45,210 --> 00:24:48,350
+نفس الدالة عند نقطة الأولى نقصه النقطة الثانية
+
+281
+00:24:48,350 --> 00:24:50,950
+اللي هو باستعماله في أنظم التلفيرموفكالكلاس أيش
+
+282
+00:24:50,950 --> 00:24:55,480
+اللي بقوله؟ خلّيني نشوفهاللي هنعرّف ليها جمعة جيه
+
+283
+00:24:55,480 --> 00:24:59,360
+من جيه لعند R اللي هي عبارة علّف ليها أنها تكون
+
+284
+00:24:59,360 --> 00:25:02,960
+إيه شمالها Anti-derivative لل continuous function
+
+285
+00:25:02,960 --> 00:25:06,500
+of composite phiF composite Phi continuous؟ أه
+
+286
+00:25:06,500 --> 00:25:09,440
+continuous لأن الـ Phi is continuous قلنا ال
+
+287
+00:25:09,440 --> 00:25:12,160
+derivative إليها continuous كمان مش كايكوا بس و ال
+
+288
+00:25:12,160 --> 00:25:16,340
+F معطينا إليها continuous فلمّا أقول إن عرف G
+
+289
+00:25:16,340 --> 00:25:19,180
+هتكون antiderivative لمين هذه طب هدي إليها
+
+290
+00:25:19,180 --> 00:25:21,320
+antiderivative؟ أه مدام continuous و المرة اللي
+
+291
+00:25:21,320 --> 00:25:23,260
+فاتت قولنا ده كانت الدالة continuous على طول فيه
+
+292
+00:25:23,260 --> 00:25:26,640
+إليها antiderivative إيش يعني؟ يعني ال G prime
+
+293
+00:25:26,640 --> 00:25:33,270
+هتكون مين؟ ال F composite Phi طيبالآن دي إذا مدام
+
+294
+00:25:33,270 --> 00:25:37,130
+اللي هي الـ G Antiderivative للـ F Composite Phi
+
+295
+00:25:37,130 --> 00:25:40,530
+إذا الـ G' Exists إذا الـ G Differentiable و لو
+
+296
+00:25:40,530 --> 00:25:42,690
+بصي Differentiable إذا الـ Composition اللي هو إيش
+
+297
+00:25:42,690 --> 00:25:47,870
+برضه هيطلع Differentiableأيش يعني طيب .. طب و إيش
+
+298
+00:25:47,870 --> 00:25:50,950
+يعني الـ differentiable؟ ها .. هالـ gate هيوصّلني
+
+299
+00:25:50,950 --> 00:25:54,290
+لإن Decomposite Phi Prime of X ده وجود الـ
+
+300
+00:25:54,290 --> 00:25:56,970
+derivative بنعرف أنه وجود الـ derivative هي عبارة
+
+301
+00:25:56,970 --> 00:26:01,610
+عن D Prime of Psi of X Psi Prime of X اللي هي
+
+302
+00:26:01,610 --> 00:26:07,600
+Chain Rule استخدام الـ Chain Rule ويساوي لأنقلنا
+
+303
+00:26:07,600 --> 00:26:11,480
+جي برايم هي مين الـ F composite في إذا بشيل الجي
+
+304
+00:26:11,480 --> 00:26:15,320
+برايم و بحط مكانها F composite إيش يا جماعة في في
+
+305
+00:26:15,320 --> 00:26:19,840
+بساي of X اللي هو هيها F composite .. هي دي بدلها
+
+306
+00:26:19,840 --> 00:26:24,720
+F composite في of بساي of X في بساي برايم من of X
+
+307
+00:26:24,720 --> 00:26:32,120
+و يساوي F of اللي هو في composite بساي of X في
+
+308
+00:26:32,120 --> 00:26:37,570
+بساي برايم من of Xكتبتها بس على صورة هو اللي هي
+
+309
+00:26:37,570 --> 00:26:41,510
+فكّت ال composition إيه الآن؟ ليش عملت هيك؟ عشان
+
+310
+00:26:41,510 --> 00:26:44,530
+أسهل عليكم و أقولكم أحنا بيقولوا Psi أشملن ال
+
+311
+00:26:44,530 --> 00:26:47,310
+inverse لل Phi مزام ال inverse مع بعض ده هو ال
+
+312
+00:26:47,310 --> 00:26:49,850
+identity ده هو ال identity of X ده هو ال X يعني
+
+313
+00:26:49,850 --> 00:26:54,850
+كلها هتصير F of X Psi prime إذا صار عندي هذا
+
+314
+00:26:54,850 --> 00:27:02,220
+شايفينه؟هو عبارة عن F small of X في Psi prime of X
+
+315
+00:27:02,220 --> 00:27:07,800
+طيب سهلة الموضوع الآن إذا نخد ال integration من
+
+316
+00:27:07,800 --> 00:27:11,100
+Phi of Alpha ل Phi of Beta ل F of X بPsi prime of
+
+317
+00:27:11,100 --> 00:27:15,540
+X DX إيش هذه؟ أه هذه اللي بدنا إياها هيها Psi
+
+318
+00:27:15,540 --> 00:27:20,130
+prime of X DX إذا نوصلناإذا الـ integration هذا
+
+319
+00:27:20,130 --> 00:27:23,290
+بيساوي ال integration لهذا ال integration لهذا
+
+320
+00:27:23,290 --> 00:27:30,570
+عندي هذه اللي هان جي كوميزيت في بسايد الكل برايم
+
+321
+00:27:30,570 --> 00:27:37,870
+of x dx الان الان هنا ال domain هذه اللي هيكون من
+
+322
+00:27:37,870 --> 00:27:42,600
+عندي اللي هي ال Iيعني لما ال .. ال .. ال .. ال ..
+
+323
+00:27:42,600 --> 00:27:43,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+324
+00:27:43,320 --> 00:27:43,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+325
+00:27:43,440 --> 00:27:43,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+326
+00:27:43,440 --> 00:27:44,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+327
+00:27:44,420 --> 00:27:45,660
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+328
+00:27:45,660 --> 00:27:50,280
+..
+
+329
+00:27:50,280 --> 00:27:54,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+330
+00:27:54,440 --> 00:27:54,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+331
+00:27:54,440 --> 00:27:54,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+332
+00:27:54,440 --> 00:27:54,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+333
+00:27:54,440 --> 00:27:55,100
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+334
+00:27:55,100 --> 00:27:57,300
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+335
+00:27:57,300 --> 00:27:57,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+336
+00:27:57,300 --> 00:28:06,760
+.. ال .. ال .. ال ..الآن صارت الـ derivative إلها
+
+337
+00:28:06,760 --> 00:28:09,620
+الـ integration هيلغى الـ derivative اللي هي by
+
+338
+00:28:09,620 --> 00:28:12,300
+fundamental theorem of calculus وكل الشروط زي ما
+
+339
+00:28:12,300 --> 00:28:17,420
+قلنا وانتحققها هيصير هذه اللي جوا عند هذه وهذه
+
+340
+00:28:17,420 --> 00:28:24,060
+اللي جوا عند هذه حاصل طرحين اللي هي G Phi
+
+341
+00:28:24,060 --> 00:28:29,140
+Composite Psiالكل of a G composed of Psi الكل of
+
+342
+00:28:29,140 --> 00:28:33,540
+Phi of X اللي هي ال X في هذه الحالة إيش اسمها اللي
+
+343
+00:28:33,540 --> 00:28:39,600
+هي Alpha معلش و هذه التانية ال Beta آسف اللي قولها
+
+344
+00:28:39,600 --> 00:28:44,660
+Beta حد الأول و هذه الحد اللي تحت Alpha ماشي
+
+345
+00:28:44,660 --> 00:28:49,430
+الحالة هذه يعني كلها على بعضزي ما عملنا قبل هيك
+
+346
+00:28:49,430 --> 00:28:53,370
+الـPsi و الـPhi اللي هو عبارة عن inverse لبعض، إذا
+
+347
+00:28:53,370 --> 00:28:58,530
+الـIdentity يعني هتصير الـG of Beta وهذا هتصير
+
+348
+00:28:58,530 --> 00:29:04,270
+الـG of Alpha، إذا صار عند المقدار اللي أمامي هذا
+
+349
+00:29:04,270 --> 00:29:11,130
+اللي هو اللي أنا ببحث عنه، هذا المقدار، شايفينه؟
+
+350
+00:29:11,130 --> 00:29:15,790
+هذا المقدارطلع عبارة عن عشان استخدمه بعد شوية
+
+351
+00:29:15,790 --> 00:29:22,650
+خلينا يمكن أوضح يكون هيصير عبارة عن g of beta ناقص
+
+352
+00:29:22,650 --> 00:29:26,910
+g of alpha بتثبت لكم الثاني برضه هيكون g of beta
+
+353
+00:29:26,910 --> 00:29:31,850
+ناقص g of alpha وبكون خلصنا اللي هو برهان النظرية
+
+354
+00:29:31,850 --> 00:29:36,990
+خلصنا هذا الجزء نيجي لا اللي هو الجزء الثاني اللي
+
+355
+00:29:36,990 --> 00:29:38,410
+أسهل كمان
+
+356
+00:29:41,370 --> 00:29:44,990
+شوف يا جماعة صلى الله عليه وسلم بالسلامة احنا قلنا
+
+357
+00:29:44,990 --> 00:29:47,790
+الـ G هي الـ antiderivative لهذه يعني الـ G' بساوة
+
+358
+00:29:47,790 --> 00:29:51,850
+هذا المقدار اذا الان بنقدر نستخدم اللي هو ال
+
+359
+00:29:51,850 --> 00:29:53,930
+fundamental theorem of calculus او اللي هو ال
+
+360
+00:29:53,930 --> 00:29:58,090
+corollary لها بكون عند ال integration هيه للمقدار
+
+361
+00:29:58,090 --> 00:30:02,790
+هذا هيطلع ليه اللي هو مباشرة بساوية يعني ممكن
+
+362
+00:30:02,790 --> 00:30:07,230
+بعضكم لاحظ الاشي اللي بتسويه من قبل ما اشرحالان ال
+
+363
+00:30:07,230 --> 00:30:09,670
+integration f of I of T من Alpha ل Beta ايش
+
+364
+00:30:09,670 --> 00:30:14,370
+بيساوي؟ هذا كله بدك تشيل مكانه منين؟ تحطه G' ال
+
+365
+00:30:14,370 --> 00:30:19,390
+integration ل G' of T dt من Alpha ل عند Beta نفس
+
+366
+00:30:19,390 --> 00:30:22,690
+الحدود لأنه ماغيرناش اللي هو ال variability اللي
+
+367
+00:30:22,690 --> 00:30:26,170
+بدنا نكامل بالنسبة له، مايساويعلى طول هذه اللي هي
+
+368
+00:30:26,170 --> 00:30:30,330
+تفاضل ب cancel اللي هي أو التكامل ب cancel التفاضل
+
+369
+00:30:30,330 --> 00:30:32,730
+اللي هي ال corollary اللي حكينا عنها اللي هي
+
+370
+00:30:32,730 --> 00:30:36,090
+corollary of fundamental theorem of calculus بساوة
+
+371
+00:30:36,090 --> 00:30:41,480
+Gof beta ناقص g of alpha الآن هذه صارت g of beta
+
+372
+00:30:41,480 --> 00:30:44,620
+ناقص g of alpha وهذه صارت g of beta ناقص g of
+
+373
+00:30:44,620 --> 00:30:48,320
+alpha إذا صار عندي هذا المقدار بساوي هذا المقدار
+
+374
+00:30:48,320 --> 00:30:51,400
+أو ال integration بساوي ال integration وبكون هيك
+
+375
+00:30:51,400 --> 00:30:55,160
+أثبتنا اللي هي النظرية الثانية أو اللي هو second
+
+376
+00:30:55,160 --> 00:31:00,200
+substitution theorem الآن تطبيقات هذه النظريات ما
+
+377
+00:31:00,200 --> 00:31:04,500
+هو هدولة تطبيقاتهم اللي هو إشبعنا فيها من Calculus
+
+378
+00:31:04,500 --> 00:31:04,780
+B
+
+379
+00:31:08,400 --> 00:31:14,420
+فبصير بس انه انت لحالك في البيت لو قعدت وعملتلك
+
+380
+00:31:14,420 --> 00:31:18,380
+سؤال سؤالين على ال substitution في الحالتين بتكون
+
+381
+00:31:18,380 --> 00:31:23,680
+اللي هو خليني نقول عمقت المفهوم عندك بشكل أكبر
+
+382
+00:31:23,680 --> 00:31:30,370
+نيجي الآننحكي عن اللي هو احنا طبعا حكينا عن الـ
+
+383
+00:31:30,370 --> 00:31:32,690
+mean value theorem أو نظرية القيمة المتوسطة في
+
+384
+00:31:32,690 --> 00:31:36,730
+حالة ال differentiation الآن هنحكي عن القيمة
+
+385
+00:31:36,730 --> 00:31:44,470
+المتوسطة في حالة ال integration اللي
+
+386
+00:31:44,470 --> 00:31:48,190
+هو نوجينا
+
+387
+00:31:49,730 --> 00:31:53,670
+أخدنا مثلا خلّيني أخد المنطقة الموجب عشان أسهل في
+
+388
+00:31:53,670 --> 00:31:57,850
+الحديث هي عندي اللي هو function f على الفترة من a
+
+389
+00:31:57,850 --> 00:32:02,790
+ل عند b الآن بتقوللي اللي هو بتقوللي هذا طبعا نظري
+
+390
+00:32:02,790 --> 00:32:06,010
+أكثر من هيك أبعد من هيك بس خلّيني أقول خلّيني أخد
+
+391
+00:32:06,010 --> 00:32:11,370
+الحالة السهلة أو خلّيني أخد الحالة اللي بتوضح
+
+392
+00:32:11,370 --> 00:32:17,210
+معانا القيمة المتوسطة الآن قيمة ال integration من
+
+393
+00:32:17,210 --> 00:32:23,660
+a ل عند bهو عبارة عن المنطقة هذه ككل مسحتها لو
+
+394
+00:32:23,660 --> 00:32:31,070
+جسمناها على الـ B minus Aوكأننا بناخد متوسط قيمة
+
+395
+00:32:31,070 --> 00:32:34,850
+الدالة لإنه لو اتخيلنا إنه هي قيمة الدالة و
+
+396
+00:32:34,850 --> 00:32:38,810
+بنضربها يعني تخيل إنها دي مساحة خط جنب خط جنب خط
+
+397
+00:32:38,810 --> 00:32:42,070
+جنب خط جنب خط لما اتخلص أدولها إلى أن حصل ضرب
+
+398
+00:32:42,070 --> 00:32:45,530
+الفترة هذه كلها P minus A في قيمة ال .. الها دي
+
+399
+00:32:45,530 --> 00:32:48,530
+اللي هي اللي عنده لو فرضنا إنهم يعني ال .. ال ..
+
+400
+00:32:48,530 --> 00:32:52,550
+ال .. هذه القيمة المتوسطة لهم يعني متوسطهم فبصير
+
+401
+00:32:52,550 --> 00:32:57,080
+عند كله على بعض المساحة بساوياللي هو حصل ضرب P
+
+402
+00:32:57,080 --> 00:33:02,700
+minus A في متوسط قيمة التكامل اللي هو عند نقطة
+
+403
+00:33:02,700 --> 00:33:07,370
+معاه وهذا اللي بتقوله هي بتقول إذا كانت Fاللي هي
+
+404
+00:33:07,370 --> 00:33:11,370
+في شروط معينة بكون عند F of X DX على B minus A
+
+405
+00:33:11,370 --> 00:33:18,210
+بساوي F of C for some C وين موجودة بين الـ A و الـ
+
+406
+00:33:18,210 --> 00:33:23,230
+B وهذه اللي هي القيمة المتوسطة للمساحة أو قيمة ال
+
+407
+00:33:23,230 --> 00:33:27,930
+integration على طول اللي هي الفترة إذن هذه اللي هي
+
+408
+00:33:27,930 --> 00:33:34,290
+خلّيني أقول حالة خاصة من نظرية القيمة المتوسطة
+
+409
+00:33:34,290 --> 00:33:38,300
+اللي بصورة عامةاللي هي .. اللي هي .. اللي نسميها
+
+410
+00:33:38,300 --> 00:33:41,960
+الـ Mean Value Theorem for Integrals نشوف الكلام،
+
+411
+00:33:41,960 --> 00:33:45,800
+يمكن الآن الكلام يكون أوضح في المن .. بشكل أوضح
+
+412
+00:33:45,800 --> 00:33:48,920
+لما نبرهن النظرية وناخد نصها وناخد الـ Corollary
+
+413
+00:33:48,920 --> 00:33:54,070
+اللي عليها اللي هي الحالة اللي ذكرتهالأن ما بحكيه
+
+414
+00:33:54,070 --> 00:33:57,170
+عبارة عن الـ Mean Value Theorem for اللي هي أياش
+
+415
+00:33:57,170 --> 00:34:01,910
+integrals نظرية القيمة المتوسطة على التكامل طبعا
+
+416
+00:34:01,910 --> 00:34:05,470
+أنتم متذكرين القيمة المتوسطة العادية أنه لو كانت F
+
+417
+00:34:05,470 --> 00:34:08,410
+is continuous على closed interval differentiable
+
+418
+00:34:08,410 --> 00:34:11,710
+على ال open إذاً there exists C element in A وB
+
+419
+00:34:11,710 --> 00:34:17,310
+such that اللي هي F prime of C سوى F of B ناقص F
+
+420
+00:34:17,310 --> 00:34:22,940
+of A على B minus Aهنا الأن بقولك اللي في الجزئية
+
+421
+00:34:22,940 --> 00:34:28,020
+هذه أن F is continuous على الـA والـB إذن there
+
+422
+00:34:28,020 --> 00:34:32,220
+exists C في الـA والـB such that ال integration من
+
+423
+00:34:32,220 --> 00:34:38,160
+A لعند B F of X DX بساوي F of C على B minus A
+
+424
+00:34:38,160 --> 00:34:44,180
+بساوي مين؟ بساوي اللي هي الـF of C roughly ..
+
+425
+00:34:44,180 --> 00:34:47,940
+roughly .. roughly .. roughly اتخيل أنه الآن هذه
+
+426
+00:34:47,940 --> 00:34:51,880
+عبارة عن الـderivativeF هذا ثابت طبعا ال
+
+427
+00:34:51,880 --> 00:34:54,920
+derivative F prime of C وهذه اللي خدنا derivative
+
+428
+00:34:54,920 --> 00:34:58,580
+لان integration كان اللي هو اللي هي متغيرات فبصير
+
+429
+00:34:58,580 --> 00:35:00,580
+عند F of B بروح ال integration مع ال
+
+430
+00:35:00,580 --> 00:35:04,040
+differentiation بصير F of B ناقص F of A اللي فوق
+
+431
+00:35:04,040 --> 00:35:07,300
+هذا الكلام رفلي بس على أساس ان هو ان انت اللي هو
+
+432
+00:35:07,300 --> 00:35:11,260
+تستذكر العلاقة اللي هو بين هذه وبين اللي هي
+
+433
+00:35:11,260 --> 00:35:16,550
+الأصليةأما القيمة المتوسطة المفهوم بالمتوسط اللي
+
+434
+00:35:16,550 --> 00:35:20,510
+هو مساحة اللي هو قيمة ال integration على طول فترته
+
+435
+00:35:20,510 --> 00:35:24,370
+اللي هو بتطلع قيمة متوسطة هذه القيمة اللي هو عبارة
+
+436
+00:35:24,370 --> 00:35:29,050
+عن متوسط قيمة وكأنه كل اللي هي قيمة ال integration
+
+437
+00:35:29,050 --> 00:35:33,630
+عنده اللي هو تحت اللي هي النقطة اللي عنده في F of
+
+438
+00:35:33,630 --> 00:35:37,150
+C بتساوي قيمة هذا ال integration على B minus A أو
+
+439
+00:35:37,150 --> 00:35:41,590
+متوسط المساحة على طول الفترة اللي هي بتساوي قيمة
+
+440
+00:35:41,590 --> 00:35:47,800
+الدالةF of C وفعلا الـ C موجودة هي المهم ان الـ C
+
+441
+00:35:47,800 --> 00:35:51,000
+هي دي فعلا حنلاجيها موجودة وبتمثل قيمة ال
+
+442
+00:35:51,000 --> 00:35:54,620
+integration على طول الفترة وهذا معناته اللي هو
+
+443
+00:35:54,620 --> 00:35:58,340
+المتوسط قيمة ال integration على طول الفترة حنلاجيه
+
+444
+00:35:58,340 --> 00:36:02,620
+فعلا بمثله مقبسي بين ال A و ال B وهذا بسميها
+
+445
+00:36:02,620 --> 00:36:08,510
+القيمة المتوسطةmean value theorem for integrals
+
+446
+00:36:08,510 --> 00:36:12,930
+let F be continuous on I and let B be integrable
+
+447
+00:36:12,930 --> 00:36:16,920
+function on Iالـ B هذه أنا مااخدها تقبل بشوية في
+
+448
+00:36:16,920 --> 00:36:22,680
+مثالي على أنها بتساوي واحد طيب let F be continuous
+
+449
+00:36:22,680 --> 00:36:25,560
+on I of A و B and let B be an integrable function
+
+450
+00:36:25,560 --> 00:36:29,740
+on I and نفترض أنه B of X أكبر يساوي سفر for every
+
+451
+00:36:29,740 --> 00:36:32,900
+X element in I then there exists C element in I
+
+452
+00:36:32,900 --> 00:36:37,880
+such that الآن هاي الـ C اللي هي بدها تمثل اللي هي
+
+453
+00:36:37,880 --> 00:36:40,980
+النقطة اللي بنلاقيها في الـ I بحيث أنه ال
+
+454
+00:36:40,980 --> 00:36:46,230
+integration من A لB F of X DX DXعلى اللي هي ال
+
+455
+00:36:46,230 --> 00:36:48,170
+integration من a إلى b بيقوم باقوم باقوم باقوم
+
+456
+00:36:48,170 --> 00:36:49,190
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+457
+00:36:49,190 --> 00:36:50,170
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+458
+00:36:50,170 --> 00:36:55,050
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+459
+00:36:55,050 --> 00:36:55,210
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+460
+00:36:55,210 --> 00:36:55,210
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+461
+00:36:55,210 --> 00:36:56,930
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+462
+00:36:56,930 --> 00:37:02,790
+باقوم باقوم
+
+463
+00:37:02,790 --> 00:37:04,290
+ب
+
+464
+00:37:11,900 --> 00:37:19,760
+الـ integration من a ل b f of x b of x dx على ال
+
+465
+00:37:19,760 --> 00:37:23,820
+integration نفترض أنه ليس فارق بيه بيه بيه بيه بيه
+
+466
+00:37:23,820 --> 00:37:25,260
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+467
+00:37:25,260 --> 00:37:26,640
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+468
+00:37:26,640 --> 00:37:29,220
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+469
+00:37:29,220 --> 00:37:29,220
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+470
+00:37:29,220 --> 00:37:38,400
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+471
+00:37:38,400 --> 00:37:43,710
+بو بيصير هذه واحد اللي هي بيصير هذه P minus A اللي
+
+472
+00:37:43,710 --> 00:37:48,390
+قلت قبل شوية اللي هو قيمة المساحة أو قيمة ال
+
+473
+00:37:48,390 --> 00:37:52,670
+integration على طول الفترة بساوي فعلا مقطة فعلية
+
+474
+00:37:52,670 --> 00:38:00,790
+في الفترة I نيجي نبره ان هذه هي بصورة عامة عند F
+
+475
+00:38:00,790 --> 00:38:08,600
+continuous إذا F is integrable and so F اللي هوA
+
+476
+00:38:08,600 --> 00:38:12,760
+of X في B of X is Integrable لأن B Integrable و F
+
+477
+00:38:12,760 --> 00:38:15,300
+Integrable صار الـ composition اللي هنا Integrable
+
+478
+00:38:15,300 --> 00:38:19,280
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+479
+00:38:19,280 --> 00:38:19,580
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+480
+00:38:19,580 --> 00:38:20,220
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+481
+00:38:20,220 --> 00:38:20,300
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+482
+00:38:20,300 --> 00:38:20,360
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+483
+00:38:20,360 --> 00:38:20,380
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+484
+00:38:20,380 --> 00:38:21,740
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+485
+00:38:21,740 --> 00:38:23,080
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+486
+00:38:23,080 --> 00:38:25,040
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+487
+00:38:25,040 --> 00:38:27,280
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+488
+00:38:27,280 --> 00:38:34,460
+اللي هنا Integrable اللي هنا Integ
+
+489
+00:38:42,230 --> 00:38:46,930
+عندي F continuous إذا انتيجرابل و B-integrable إذا
+
+490
+00:38:46,930 --> 00:38:52,610
+FB-integrableسمّيلي الـ M small هي الـ infimum للـ
+
+491
+00:38:52,610 --> 00:38:55,830
+F of I موجودة أه طبعا و هي F is integrable is
+
+492
+00:38:55,830 --> 00:39:00,610
+unbounded M capital بسوى ال supremum لمين لل F of
+
+493
+00:39:00,610 --> 00:39:05,210
+I إذن الآن الدروب صارت عندي ال F of X بين ال M
+
+494
+00:39:05,210 --> 00:39:09,030
+small و بين ال M capital الدروب لكل انفمين في B of
+
+495
+00:39:09,030 --> 00:39:14,190
+X وبنقدر أه بنقدر لإن بي بيضالها زي ما هي أه لإن
+
+496
+00:39:14,190 --> 00:39:20,450
+بي موجبةإذا صار عندى الآن هذه ال inequality صحيحة
+
+497
+00:39:20,450 --> 00:39:23,830
+و كلها integrable إذا ال integration على الأولى
+
+498
+00:39:23,830 --> 00:39:26,350
+أصغر أو سوى ال integration على الثانية أصغر أو سوى
+
+499
+00:39:26,350 --> 00:39:29,850
+ال integration على الثالثة و ال M بتطلع برا لإنه
+
+500
+00:39:29,850 --> 00:39:38,110
+ال M يشملها ثابتة الآن لو ال integration لل .. لل
+
+501
+00:39:38,110 --> 00:39:44,710
+.. لل .. لل B بساوى 0 إذا ال integration هيكوناللي
+
+502
+00:39:44,710 --> 00:39:49,730
+هو اللي فوق ال .. ال .. ال .. ال .. النظرية بتصلح
+
+503
+00:39:49,730 --> 00:39:55,930
+لأي قيمة اللي هو للـ C لأنه هيكون إيش بيساوي ..
+
+504
+00:39:55,930 --> 00:40:00,310
+أنا أطلعلكم فوق لأن لو فرضنا ال integration للـ B
+
+505
+00:40:00,310 --> 00:40:05,930
+بيساوي سفر integration للـ B بيساوي سفربصير اللي
+
+506
+00:40:05,930 --> 00:40:10,990
+هو هذه برضه ال integration هذا هيساوي أيش؟ هيساوي
+
+507
+00:40:10,990 --> 00:40:14,810
+سفر عارفين ليش؟ لأنه مادام ال integration هذا سفر
+
+508
+00:40:14,810 --> 00:40:16,710
+و ال integration هذا سفر إذا ال integration اللي
+
+509
+00:40:16,710 --> 00:40:22,170
+في النص أيش هيساوي؟ سفر إذا صارت هذا المقدار سفر
+
+510
+00:40:22,170 --> 00:40:28,430
+وهذا سفر إيش ما تختار C هتتحقق اللي هي مين طرفي
+
+511
+00:40:28,430 --> 00:40:33,790
+المعادلةإذن الآن حالة الصفر is a trivial case يعني
+
+512
+00:40:33,790 --> 00:40:36,890
+حالة أن تكون هذه صفر is a trivial case لأن
+
+513
+00:40:36,890 --> 00:40:39,890
+automatic زي ما قلنا مدامة هذه صفر وهذه صفر دمنا
+
+514
+00:40:39,890 --> 00:40:43,310
+في النص صفر إذن اللي هو أي اختيار للـC هيكون طرف
+
+515
+00:40:43,310 --> 00:40:47,410
+أي معادلة صحيحة يعني اللي هو ال equality تبعتنا
+
+516
+00:40:47,410 --> 00:40:51,470
+صحيحة الآن بدنا نيجي لمين يا جماعة؟ إيش غرضنا؟
+
+517
+00:40:51,470 --> 00:40:56,460
+غرضنا نلاقي C بحيث أن هذا بساوي هذاخلصنا حالة اللي
+
+518
+00:40:56,460 --> 00:40:59,240
+هي ال integration بساوة سفر نفترض ان ال
+
+519
+00:40:59,240 --> 00:41:02,480
+integration مش سفر ليش انه بدي أكسب عنه إذا صار
+
+520
+00:41:02,480 --> 00:41:05,860
+عندي ال integration أكسب الجهتين عن ال integration
+
+521
+00:41:05,860 --> 00:41:09,360
+لل B ال integration لل B اللي فرضنا انه مش سفر إذا
+
+522
+00:41:09,360 --> 00:41:11,580
+صار ال integration هذا على ال integration هذا بين
+
+523
+00:41:11,580 --> 00:41:16,840
+ال M small و ال M أشمالها capital ماشي الحالة الآن
+
+524
+00:41:16,840 --> 00:41:25,420
+احنا بنقول ان هذا صار رقمبين الـ M small والـ M
+
+525
+00:41:25,420 --> 00:41:35,540
+capital وبنقول أن F continuous on الفترة A وB then
+
+526
+00:41:35,540 --> 00:41:46,560
+أي رقم .. أي رقم الآن للدالة اللي هو .. هوضح لكم
+
+527
+00:41:46,560 --> 00:41:48,900
+هي .. اذكركم الـ intermediate value theorem اللي
+
+528
+00:41:48,900 --> 00:41:53,720
+نسيها هي عندى مثلا هي أعلى قيمةأقل قيمة وهي أعلى
+
+529
+00:41:53,720 --> 00:42:02,140
+قيمة هذه الآن الـ function f of x اللي هي بين اللي
+
+530
+00:42:02,140 --> 00:42:12,640
+هو ام capital ام small او بين مين ام capital الان
+
+531
+00:42:12,640 --> 00:42:20,220
+لو اجينا اخدنا اي قيمةأي قيمة عدد أي عدد A بين الـ
+
+532
+00:42:20,220 --> 00:42:23,980
+M small والـ M capital متامة الـ F continuously عن
+
+533
+00:42:23,980 --> 00:42:28,200
+أي قيمة هنا أخدناها قيمة هنلاقي اللي هو there
+
+534
+00:42:28,200 --> 00:42:32,040
+exists C element في الفترة A وB المعرف عليها
+
+535
+00:42:32,040 --> 00:42:38,040
+الدائرة هتسميها C مثلا أو D هنلاقي الـ C في الفترة
+
+536
+00:42:38,040 --> 00:42:45,030
+بين A وB بحيث أن F of C هي مين القيمة F of Dاللي
+
+537
+00:42:45,030 --> 00:42:47,050
+هي الـ Intermediate Value Theorem اللي انتوا
+
+538
+00:42:47,050 --> 00:42:50,790
+عارفينها اللي هي Four Continuous Function اذا بما
+
+539
+00:42:50,790 --> 00:42:55,790
+انه الـ function F is continuous و هذه القيمة بين
+
+540
+00:42:55,790 --> 00:43:00,490
+أعلى قيمة .. بين أعلى قيمة و أقل قيمة للدالة إذا
+
+541
+00:43:00,490 --> 00:43:05,950
+أكيد هقدر ألاقي C element in I بحيث ان F of C
+
+542
+00:43:05,950 --> 00:43:10,830
+بساوي هذا الرقم اللي هو هذه القيمة اللي هو ال
+
+543
+00:43:10,830 --> 00:43:16,520
+integrationبساوى اللي هو F of C في القيمة هذه وهو
+
+544
+00:43:16,520 --> 00:43:22,000
+المطلوب يعني النظرية برهانة بسيطة يا جماعة بس مدام
+
+545
+00:43:22,000 --> 00:43:27,740
+حصرنا قيمة للقيمة هذه اللي هي بين اللي هي ال M و
+
+546
+00:43:27,740 --> 00:43:30,840
+ال M إذا بال intermediate value theorem في C
+
+547
+00:43:30,840 --> 00:43:37,500
+وخلصنا طيب اللي بعده ال quaternary حكيتها هذه إن
+
+548
+00:43:37,500 --> 00:43:38,360
+لو كانت F
+
+549
+00:43:43,100 --> 00:43:47,820
+الـ Corollary حكيتها لو كانت F continuous على اللي
+
+550
+00:43:47,820 --> 00:43:50,940
+هي الـ closed interval A و B هلاجي الـC في الـI
+
+551
+00:43:50,940 --> 00:43:53,720
+بحيث ان ال integration من A لB للF سواء F of C في
+
+552
+00:43:53,720 --> 00:44:00,900
+B minus A قلنا هذه اللي هي حالة خاصة من النظرية بس
+
+553
+00:44:00,900 --> 00:44:08,160
+حطلي الـF الـP of X بساوية 1 حالة خاصة من النظرية
+
+554
+00:44:08,160 --> 00:44:10,480
+النظريتنا
+
+555
+00:44:11,580 --> 00:44:17,340
+إن الـ integration للـ F في B بساوي F of C في الـ
+
+556
+00:44:17,340 --> 00:44:21,320
+integration للـ B من Alpha لعند Beta و لا من A
+
+557
+00:44:21,320 --> 00:44:29,620
+لعند B من A لعند B for some C element in I، مظبوط؟
+
+558
+00:44:29,620 --> 00:44:33,180
+الآن بقول لي اللي هو ال integration للـ F بساوية F
+
+559
+00:44:33,180 --> 00:44:36,720
+of C في B minus A for some C حط الـ B بساوية،
+
+560
+00:44:36,720 --> 00:44:41,420
+هتجسي ال integration للـ Fبس بي بي بي بي بي بي بي
+
+561
+00:44:41,420 --> 00:44:48,320
+بي بي بي بي بي بي بي
+
+562
+00:44:51,410 --> 00:44:58,470
+اللي هو dx y ساوي اللي هو f of c هدف b minus a وهو
+
+563
+00:44:58,470 --> 00:45:02,690
+المطلوب هيلحقناه كمان مرة إذا الـ Corollary اللي
+
+564
+00:45:02,690 --> 00:45:09,030
+هي اللي أمامنا تم برهانها مرة أخرى نيجي الآن للي
+
+565
+00:45:09,030 --> 00:45:13,310
+هي Taylor's theorem أخدناها Taylor's theorem كان
+
+566
+00:45:13,310 --> 00:45:20,900
+ال remainder اللي هو اللي هو إشي مفاضلأو الـ
+
+567
+00:45:20,900 --> 00:45:26,560
+Taylor's theorem إذا صح التعبير for integration و
+
+568
+00:45:26,560 --> 00:45:29,500
+Taylor's theorem for differentiations الآن الجزء
+
+569
+00:45:29,500 --> 00:45:33,060
+اللي هو الـ for integration نشوف أشي اللي بقوله
+
+570
+00:45:35,050 --> 00:45:38,890
+suppose that the function f and its derivatives f
+
+571
+00:45:38,890 --> 00:45:43,030
+prime of w prime عند fn and fn زائد واحد are كلهم
+
+572
+00:45:43,030 --> 00:45:46,330
+إيه شمالهم continuous يعني نفترض أن الانث
+
+573
+00:45:46,330 --> 00:45:49,710
+derivative الانث زائد واحد derivative is
+
+574
+00:45:49,710 --> 00:45:53,890
+continuous exist وcontinuous نفترض أن الدالة f
+
+575
+00:45:53,890 --> 00:45:59,610
+عبارة عن دالة قابلة للاشتقاق n زائد واحد من المرات
+
+576
+00:45:59,610 --> 00:46:05,310
+وتكون الان زائد واحد كمان نفسها continuousماشي على
+
+577
+00:46:05,310 --> 00:46:10,290
+الفترة a و b then بقوللي اللي هو f of b بيساوي f
+
+578
+00:46:10,290 --> 00:46:14,170
+of a زي f prime of v على 1 factorial في b minus a
+
+579
+00:46:14,170 --> 00:46:18,990
+زي f double prime of a على 2 factorial في b minus
+
+580
+00:46:18,990 --> 00:46:22,410
+a تربيع زائد لما أصل عند f n of a على n factorial
+
+581
+00:46:22,410 --> 00:46:26,530
+في b minus a الكولوسن هذا كله إيش معلهعارفينه قبل
+
+582
+00:46:26,530 --> 00:46:30,050
+ليك وعملنا زائد مين ال remainder are n ال
+
+583
+00:46:30,050 --> 00:46:34,730
+remainder are n كتبوا على صورة integration بس ال
+
+584
+00:46:34,730 --> 00:46:37,550
+remainder are n كتب على صورة واحدة ال N factorial
+
+585
+00:46:37,550 --> 00:46:41,150
+في ال integration من a ل b بي ماينس تي وصة ن ففن
+
+586
+00:46:41,150 --> 00:46:50,010
+زي واحد of T دي تي إذن الآن بقولك أف of بي أف of
+
+587
+00:46:50,010 --> 00:47:02,410
+بي بساوي ال summation أف .. أف Nهو FK of A على
+
+588
+00:47:02,410 --> 00:47:10,470
+K factorial في B minus A أس K K من عند و .. من صفر
+
+589
+00:47:10,470 --> 00:47:19,390
+K من عند صفر لعند مين لعند N زائد ال remainder مين
+
+590
+00:47:19,390 --> 00:47:27,090
+RNالـ remainder are N مين هو بساوي اللي هو 1 على N
+
+591
+00:47:27,090 --> 00:47:35,390
+factorial في ال integration من A لعند B بي minus T
+
+592
+00:47:35,390 --> 00:47:45,690
+أس N في F N زائد 1 of T دي T نثبت لكم إن ال F of B
+
+593
+00:47:45,690 --> 00:47:52,520
+can be written as thisحيث الـ Rn هو هذا الآن
+
+594
+00:47:52,520 --> 00:47:59,500
+الفكرة في الحل أو الفكرة في البرهان أنه أنا بدي
+
+595
+00:47:59,500 --> 00:48:05,260
+أجي أوجد قيمة الـ remainder Rn اللي هو هذا المقدار
+
+596
+00:48:05,260 --> 00:48:10,700
+و بدي أثبتلكم أن هذا المقدار اللي هو منه بقدر أكتب
+
+597
+00:48:10,700 --> 00:48:14,040
+اللي هو يعني الـ Rn أثبتلكي هي عبارة عن F of B
+
+598
+00:48:14,040 --> 00:48:19,720
+ناقص هذا الـ summationيعني بدي أثبتلكم أن الـ RN
+
+599
+00:48:19,720 --> 00:48:23,560
+بتساوي F of B نقص ال machine هذا يعني بدي أبدأ
+
+600
+00:48:23,560 --> 00:48:30,700
+بهذا الآن يعني بدي أبدأ بالـ RN بساوي هذا المقدار
+
+601
+00:48:30,700 --> 00:48:34,740
+شايفينه هذا المقدار من A لعند B وحدة لـN factorial
+
+602
+00:48:34,740 --> 00:48:42,380
+بدي أكامله أكامله by partsأه بده كامل وشوفوا كيف
+
+603
+00:48:42,380 --> 00:48:47,280
+بتطلع الأمور ان شاء الله سلسة ومنيحة by parts خدوا
+
+604
+00:48:47,280 --> 00:48:53,160
+ال U عبارة هسموها عبارة عن U وهذه سموها ايش يا
+
+605
+00:48:53,160 --> 00:48:59,970
+جماعة DV ماشي الحال بيصير القرأن هو عبارة عناللي
+
+606
+00:48:59,970 --> 00:49:07,490
+هو UDV يعني بيساوي UV ناقص V DU تحت مين تحت ال
+
+607
+00:49:07,490 --> 00:49:11,310
+integration هذا كلام تعرفوه انتوا الآن برضه من وين
+
+608
+00:49:11,310 --> 00:49:16,150
+لوين من A لعند B على السريع عساسي اللي هو تاخدوا
+
+609
+00:49:16,150 --> 00:49:20,100
+الفكرةاللي هي الحسابات انت بتعرف تعملوها الكل
+
+610
+00:49:20,100 --> 00:49:24,620
+بيعرف يعملها هي أخدنا ال U زي ما أخدناها هنا
+
+611
+00:49:24,620 --> 00:49:30,200
+كتبتها على اللوح وهي ال DV هيها لأفن زي واحد of T
+
+612
+00:49:30,200 --> 00:49:36,300
+DT الان ال DU أكيد اللي هو تفاضل هذا N في B minus
+
+613
+00:49:36,300 --> 00:49:41,100
+Tأس N ناقص واحد في تفاضل اللي هو اللي جوا ناقص
+
+614
+00:49:41,100 --> 00:49:45,900
+واحد بيصير عندي ناقص N في B minus T أس N ناقص واحد
+
+615
+00:49:45,900 --> 00:49:51,040
+DT هذه مين هي الـ DU اللي بدي أحطها هانالان ال V
+
+616
+00:49:51,040 --> 00:49:57,380
+ال D V هيها ال V هتطلع ال integration هذه بيخف
+
+617
+00:49:57,380 --> 00:50:01,340
+واحد من ال derivatives بيصير عندي F N of T طبعا
+
+618
+00:50:01,340 --> 00:50:05,620
+فاهمين اش بقول ال V بيساوي F N of T الان بيجي
+
+619
+00:50:05,620 --> 00:50:09,260
+بنعوض بيصير عندي عبارة عن ال integration اللي هو
+
+620
+00:50:09,260 --> 00:50:15,160
+بيساوي ال R N بيساوي U في V U اللي هو عبارة عن B
+
+621
+00:50:15,160 --> 00:50:24,580
+minus T أس Nفي U هذه U في V V اللي هو عبارة عن FN
+
+622
+00:50:24,580 --> 00:50:37,200
+of T، مظبوط؟ هذا اللي هو U طبعا الـ RN احنا مضروب
+
+623
+00:50:37,200 --> 00:50:41,730
+كله في meanفى 1 على n factorial لأن هى اللى فضلنا
+
+624
+00:50:41,730 --> 00:50:47,110
+هى الجزء اللى حسبناه هذا 1 على n factorial موجودة
+
+625
+00:50:47,110 --> 00:50:50,490
+فيها 1 على n factorial بيصير هنا برضه على n
+
+626
+00:50:50,490 --> 00:51:00,050
+factorial بدت أمورنا تظهر ناقص 1 على n factorial
+
+627
+00:51:00,050 --> 00:51:06,310
+فى ال integration من a لعند b mean v , v هي ف
+
+628
+00:51:08,970 --> 00:51:18,530
+of T مظبوط دي T في D U D U ايش D U D U اللي هو
+
+629
+00:51:18,530 --> 00:51:30,650
+ناقص N ناقص N في B minus T أس
+
+630
+00:51:30,650 --> 00:51:32,330
+N ناقص واحد
+
+631
+00:51:35,190 --> 00:51:43,550
+واضحة الصورة نجي نخلي صورة منيحة B-T أُس N على N
+
+632
+00:51:43,550 --> 00:51:51,210
+factorial F N of T خلصنا منه هذا ناقص وهذا ناقص
+
+633
+00:51:51,210 --> 00:51:56,250
+يصبح زاد يصبح هذا أشمل هواحد على N واحد factorial
+
+634
+00:51:56,250 --> 00:52:04,450
+في ال integration من A لعند BB-T أُس N ناقص واحد
+
+635
+00:52:04,450 --> 00:52:12,530
+FN of T DT مظبوط؟ مظبوط هذا أوجدنا مين الـ RN
+
+636
+00:52:12,530 --> 00:52:18,350
+بساوي هذا زائد هذا طيب اللي عملناه مين هو هذا أصلا
+
+637
+00:52:18,350 --> 00:52:23,570
+الـ RN اللي أوجدناه هيه اللي هو B-1 T أس N FN زائد
+
+638
+00:52:23,570 --> 00:52:29,370
+واحد of T DT طلع عبارة عن اللي هو اللي جوا هذا بأس
+
+639
+00:52:29,370 --> 00:52:38,770
+Nوهذا زي ما هو أسن ناقص بيصير هو هذا زائد واحد صار
+
+640
+00:52:38,770 --> 00:52:42,670
+زائد طبعا ما عرفتوا كيفي صارت زائد واحد على أن
+
+641
+00:52:42,670 --> 00:52:46,130
+ناقص واحد factorial واحد على أن ناقص واحد
+
+642
+00:52:46,130 --> 00:52:49,850
+factorial في هذا المقدار لاحظوا أن هذا المقدار
+
+643
+00:52:49,850 --> 00:52:56,610
+شبيه بال remainderيعني بالظبط اللي عملناه على الـ
+
+644
+00:52:56,610 --> 00:53:01,750
+remainder بنعملهان بنعمله على هذا اللي هنعملهان
+
+645
+00:53:01,750 --> 00:53:05,810
+هيطلع مقدار زي هذا و مقدار زي هذا بس هينجس كمان
+
+646
+00:53:05,810 --> 00:53:09,770
+واحد اللي أن هيصير هذا أن نقص اتنين كان أن .. كان
+
+647
+00:53:09,770 --> 00:53:13,210
+أن صار هيصير أن نقص اتنين و الخطوة اللي بعدها
+
+648
+00:53:13,210 --> 00:53:15,850
+بنعمل كمان مرة بنوجد بيصير أن نقص ثلاثة و أن نقص
+
+649
+00:53:15,850 --> 00:53:20,070
+أربعة في الآخر الـ and finite إذا هنصل للنهاية إذا
+
+650
+00:53:20,070 --> 00:53:29,950
+هذا هيصير بساويB-T أُس N على N factorial FN of T
+
+651
+00:53:29,950 --> 00:53:35,250
+زائد هذا بتعمله بالظبط زي ما عملت مين زي ما عملت
+
+652
+00:53:35,250 --> 00:53:42,150
+ال RN يعني و كأنه اسم هذا RN-1بصير بنفس الأسلوب B
+
+653
+00:53:42,150 --> 00:53:49,410
+minus T أس N ناقص واحد على N ناقص واحد factorial F
+
+654
+00:53:49,410 --> 00:54:00,270
+N ناقص واحد of T زائد بعتقد
+
+655
+00:54:00,270 --> 00:54:08,770
+بس في ناقص هنا في ال U في V U في V
+
+656
+00:54:17,570 --> 00:54:22,590
+أه ماحسبناش عند A و B أه بس هذا نسينا نحسب هذا عند
+
+657
+00:54:22,590 --> 00:54:27,990
+B، من عند A لعند B، معلش سامحونا، من عند A لعند B
+
+658
+00:54:27,990 --> 00:54:33,230
+هذا الكلام صحيح، بس بدي أحسبه من A لعند B، عند B
+
+659
+00:54:33,230 --> 00:54:38,250
+صفر، صح؟ عند B صفر، مش احنا حسبنا قيمة الـ
+
+660
+00:54:38,250 --> 00:54:40,830
+remainder، قيمة ال integration، هذا ال integration
+
+661
+00:54:40,830 --> 00:54:47,820
+اللي هو من وين لوين، من A لعند Bالآن هذا من a لعند
+
+662
+00:54:47,820 --> 00:54:56,920
+b بيصير عند بي ناقص b بصير سفر الان ناقص من b ناقص
+
+663
+00:54:56,920 --> 00:55:01,680
+a فبصير هذه اشمالها b ناقص a وهنا ناقص وهنا a
+
+664
+00:55:01,680 --> 00:55:06,760
+شمالها f of a لان عوضنا عن مين عن ايه فبصير عند بي
+
+665
+00:55:06,760 --> 00:55:11,220
+ناقص a أس n بالسالب على n factor of n of a زائد
+
+666
+00:55:11,220 --> 00:55:15,190
+هذا المقدرلأن هذا المقدار زي هذا المقدار هذا
+
+667
+00:55:15,190 --> 00:55:19,010
+المقدار بنفس الأسلوب زي ما قلنا بيصير عبارة عن زي
+
+668
+00:55:19,010 --> 00:55:24,650
+هذاماشي بس برضه هيطلع لي إيش برضه هيطلع لي نقص لما
+
+669
+00:55:24,650 --> 00:55:27,730
+نعوض بيصير b minus a أسئلة ناقص واحدة الان ناقص
+
+670
+00:55:27,730 --> 00:55:33,830
+واحدة factorial f n ناقص واحد of 2 of a زائد اللي
+
+671
+00:55:33,830 --> 00:55:38,630
+بيطلع هنا n ناقص 2 factorial في ال integration من
+
+672
+00:55:38,630 --> 00:55:47,770
+a لb b minus t أسئلة ناقص 2 الان وهذه f n ناقص
+
+673
+00:55:47,770 --> 00:55:55,740
+واحدةof T D T نفس
+
+674
+00:55:55,740 --> 00:55:59,960
+اللي عملته على هذا بدي أعمله على هذا هضلي مستمر
+
+675
+00:55:59,960 --> 00:56:10,880
+لما يصلي عندي اللي هو .. وين بدي أكتب؟
+
+676
+00:56:10,880 --> 00:56:12,360
+خليني أكتب فوق
+
+677
+00:56:16,010 --> 00:56:22,150
+الان اتفجنا يا جماعة ان الـ RN هيوا هذا اللي هو RN
+
+678
+00:56:22,150 --> 00:56:28,690
+بساوي هذا المقدار ناقص هذا المقدار ناقص ناقص زائد
+
+679
+00:56:28,690 --> 00:56:34,370
+هذا إذا صار عند الـ RN بساوي
+
+680
+00:56:34,370 --> 00:56:49,900
+ناقص B minus A أس N على N factorialf n of a ناقص b
+
+681
+00:56:49,900 --> 00:56:54,740
+minus a plus n ناقص واحد على n ناقص واحد factorial
+
+682
+00:56:54,740 --> 00:57:04,840
+f n ناقص واحد of a زائد المقدار هذا الآن بتعملوا
+
+683
+00:57:04,840 --> 00:57:09,500
+هذا اللي عملته مع جابلو هيظلوا بنفس الأسلوب ماشي
+
+684
+00:57:10,430 --> 00:57:17,990
+لما أصل لعند اللي هو آخر term اللي هو هيكون عندي
+
+685
+00:57:17,990 --> 00:57:28,270
+هيطلع عندي اللي هو B minus A في F يعني N اللي هي
+
+686
+00:57:28,270 --> 00:57:41,300
+بيصير باتنين B minus A في F prime of A علىاللي هو
+
+687
+00:57:41,300 --> 00:57:46,360
+1 factorial زي ما هي زائد اللي بعدها ال
+
+688
+00:57:46,360 --> 00:57:51,200
+integration تبعها اللي هي هذه عند N بجداشها أنا ب2
+
+689
+00:57:51,200 --> 00:57:56,060
+N ب2 اللي هي بيصير 1 إلى 0 factorial يعني بيصير
+
+690
+00:57:56,060 --> 00:58:00,060
+اللي هو 1 بمعنى آخر فال integration من A لعند B
+
+691
+00:58:00,060 --> 00:58:06,660
+وهذا بيصير B minus T أُس 0 يعني 1 في F prime of DT
+
+692
+00:58:08,080 --> 00:58:12,180
+لما اكرر العملية اظل اكررها لما اصل لهذه الخطوة
+
+693
+00:58:12,180 --> 00:58:17,620
+وحنتي لأن الان is finite ويساوي اللي هو المقدار
+
+694
+00:58:17,620 --> 00:58:20,220
+هذا كله اللي هو عبارة عن ال summation طبعا كله
+
+695
+00:58:20,220 --> 00:58:23,060
+بالسالب هذا مع هذا الأخير بالموجة بيصير نقص ال
+
+696
+00:58:23,060 --> 00:58:32,660
+summation ل B minus A أس K على K factorial ف FK of
+
+697
+00:58:32,660 --> 00:58:43,520
+A K الان من عنداللي هو واحد عند واحد هيها لعند مين
+
+698
+00:58:43,520 --> 00:58:51,280
+لعند الأن هذا مجموع من هنا من هنا لهنا هذا كله في
+
+699
+00:58:51,280 --> 00:58:56,640
+قيب واحد بتطلع هذهكيب 2 بتطلع اللي هان كيب 3 لما
+
+700
+00:58:56,640 --> 00:58:59,580
+قصها لكيب n بتطلع اللي عنده هان زائد ال
+
+701
+00:58:59,580 --> 00:59:02,580
+integration هذا ال integration هذا اللي هي f
+
+702
+00:59:02,580 --> 00:59:05,660
+continuous اللي عند ال integration للـ f طبعا ال f
+
+703
+00:59:05,660 --> 00:59:08,820
+نفسها كانت continuous فال integration هذا بفرن ضمن
+
+704
+00:59:08,820 --> 00:59:11,140
+ال interferon of calculus على طول بطلع عبارة عن f
+
+705
+00:59:11,140 --> 00:59:20,780
+of b ناقص من f of a ماشي الحال فبصير الآن اللي هو
+
+706
+00:59:20,780 --> 00:59:28,010
+أوصلنا للي بدناهكيف؟ شوف كيف وصلنا للبيتمية الآن
+
+707
+00:59:28,010 --> 00:59:37,210
+طلعت عندي خلّي اللي هو الـ remainder احنا ال F of
+
+708
+00:59:37,210 --> 00:59:42,430
+P خليها في الجهة هذه و انقل كله هنا فبصير F of P
+
+709
+00:59:42,430 --> 00:59:48,760
+بساوي هذه بتنضف لهذه ما هي ناقص التانيةبيصير ..
+
+710
+00:59:48,760 --> 00:59:51,380
+لما تيجي الجهتين علي الجهتين بيصير موجة بس
+
+711
+00:59:51,380 --> 00:59:57,440
+summation لـ B minus A أُس K FK ال derivative هذه
+
+712
+00:59:57,440 --> 01:00:04,160
+of A على K factorial K الـ N من واحد لعند N وهذه
+
+713
+01:00:04,160 --> 01:00:09,340
+حالة السفر K من سفر لعند Nزائد مين الـ remainder
+
+714
+01:00:09,340 --> 01:00:13,900
+are n ليش حالة السفر هذه لأن في حالة K بسفر بيصير
+
+715
+01:00:13,900 --> 01:00:17,500
+هذا واحد وهذا واحد وهذا مافيش derivative يعني
+
+716
+01:00:17,500 --> 01:00:22,320
+بيصير F of A فبيصير عندي اللي هو F of B بساوي ال
+
+717
+01:00:22,320 --> 01:00:25,160
+summation زائد ال remainder are n ال remainder
+
+718
+01:00:25,160 --> 01:00:30,500
+اللي هو اللي احنا بدأنا فيه وهو المطلوب فعلا انا
+
+719
+01:00:30,500 --> 01:00:36,940
+قدرت اكتب اللي هي ال F of B على الصورة اللي أماميو
+
+720
+01:00:36,940 --> 01:00:42,600
+هيك بنكون احنا برهننا Taylor's theorem و هي اخر
+
+721
+01:00:42,600 --> 01:00:48,860
+جزء في هذا ال section و الان ان شاء الله بكون
+
+722
+01:00:48,860 --> 01:00:54,800
+خلصنا الجزء الاول من المحاضرة و نبدأ ان شاء الله
+
+723
+01:00:54,800 --> 01:00:58,740
+بعد شوية في الجزء الثاني برك الله فيكم
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/UEye6Xfb9c0.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/UEye6Xfb9c0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fc41e9f5ce9ed8878dc8bd9ee7cc1df091eb3959
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/UEye6Xfb9c0.srt
@@ -0,0 +1,4003 @@
+1
+00:00:05,180 --> 00:00:07,960
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,960 --> 00:00:10,980
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,980 --> 00:00:16,800
+آله وصحبه أجمعين هذه المحاضرة رقم 25 مساق تحليل 
+
+4
+00:00:16,800 --> 00:00:21,880
+حقيقي 2 طلاب وطالبات الجامعة الإسلامية قسم الرياضيات
+
+5
+00:00:21,880 --> 00:00:27,060
+كلية العلوم اليوم هنبدأ إن شاء الله بال chapter
+
+6
+00:00:27,060 --> 00:00:32,290
+الرابع في المادة اللي هو الـ chapter 9 أو الجزء
+
+7
+00:00:32,290 --> 00:00:35,410
+الرابع من المادة اللي هو chapter 9 تحت عنوان
+
+8
+00:00:35,410 --> 00:00:39,670
+infinite series هنحكي اليوم في هذه المحاضرة على
+
+9
+00:00:39,670 --> 00:00:47,900
+اللي هو convergence of infinite series الـ infinite
+
+10
+00:00:47,900 --> 00:00:54,380
+series طبعًا هو موضوع معهود للطلاب أو لطلبة العلوم 
+
+11
+00:00:54,380 --> 00:00:58,440
+والهندسة بصورة عامة لإنه تم الحديث عنه في اللي هو
+
+12
+00:00:58,440 --> 00:01:03,340
+calculus باه الآن بنحكي عن اللي هو النظرة
+
+13
+00:01:03,340 --> 00:01:08,300
+التحليلية لـ اللي هو الـ infinite series طبعًا كنا
+
+14
+00:01:08,300 --> 00:01:14,180
+حكينا في في chapter ثلاثة في تحليل حقيقي واحد على
+
+15
+00:01:14,180 --> 00:01:18,540
+اللي هي الـ sequences الآن هذا مبني على اللي هو مين
+
+16
+00:01:18,540 --> 00:01:22,750
+الـ sequences خلّينا نشوف التعريف الأول 911
+
+17
+00:01:22,750 --> 00:01:27,130
+definition fx بساوي xn is a sequence in R يعني 
+
+18
+00:01:27,130 --> 00:01:32,330
+فرضنا أن xn عبارة عن متتابع في R then the infinite
+
+19
+00:01:32,330 --> 00:01:37,990
+series اللي هي simply the series بنا نحكي عن ..
+
+20
+00:01:37,990 --> 00:01:42,330
+نعرف الأن الـ infinite series أو الـ series بناء على
+
+21
+00:01:42,330 --> 00:01:46,850
+اللي هي الـ sequence x بساوي xn اللي هي the
+
+22
+00:01:46,850 --> 00:01:51,390
+infinite series generated by this sequence x is
+
+23
+00:01:51,390 --> 00:01:54,610
+the sequence S إذن الـ infinite series هي عبارة عن 
+
+24
+00:01:54,610 --> 00:02:00,170
+إيش؟ بتعرفها عبارة عن sequence S بساوي SK بس إيش
+
+25
+00:02:00,170 --> 00:02:05,230
+الـ SK اللي هي اللي بنسميها اللي هي sequence of
+
+26
+00:02:05,230 --> 00:02:11,510
+partial sums يعني الـ S K defined by S1 إيش بتساوي؟
+
+27
+00:02:11,510 --> 00:02:17,270
+X1 S2 إيش بتساوي؟ X1 زائد X2 لاحظوا بقى اجمع
+
+28
+00:02:17,270 --> 00:02:19,430
+العناصر اللي وين موجودة اللي في الـ sequence
+
+29
+00:02:19,430 --> 00:02:24,490
+الأصلية اللي هي بتعمل generation لـ اللي هي إيش؟ الـ
+
+30
+00:02:24,490 --> 00:02:28,710
+sequence of partial sums الـ S K S 3 إيش هتكون X 1
+
+31
+00:02:28,710 --> 00:02:34,290
+زائد X 2 زائد X 3 S K in general هي عبارة عن X 1 زائد
+
+32
+00:02:34,290 --> 00:02:39,820
+X 2 عند من؟ اللي عند X K أو بمعنى آخر Sk
+
+33
+00:02:39,820 --> 00:02:56,100
+= X1 + X2 + ... + XK
+
+34
+00:02:56,560 --> 00:03:02,220
+لأن if S converges, we refer to limit S as the sum
+
+35
+00:03:02,220 --> 00:03:06,160
+of infinite series يعني لو كانت الـSK عندي هذه 
+
+36
+00:03:06,160 --> 00:03:10,880
+converges to some limit S، بنقول احنا اللي هو
+
+37
+00:03:10,880 --> 00:03:16,260
+limit الـ S K اللي هو بيساوي S اللي هو اللي بنسمي S
+
+38
+00:03:16,260 --> 00:03:19,500
+K طبعًا goes to infinity أو N اللي بدكيها اللي هي
+
+39
+00:03:19,500 --> 00:03:24,120
+بيساوي الـ summation اللي هي X K كي من عند واحد إلى
+
+40
+00:03:24,120 --> 00:03:29,780
+وين إلى ما لا نهاية سمي هذه S N وهذه S N وهذه S N كل
+
+41
+00:03:29,780 --> 00:03:34,440
+برج للاسهذه اللي بنسميها الـ infinite series اللي
+
+42
+00:03:34,440 --> 00:03:37,300
+هي في حالة الـ convergence أو الـ limit هذه exist
+
+43
+00:03:37,300 --> 00:03:40,520
+تبع الـ sequence of partial sums بنسميها اللي هي 
+
+44
+00:03:40,520 --> 00:03:45,880
+limit exist بنسميها S لأن الـ elements XN are
+
+45
+00:03:45,880 --> 00:03:50,550
+called the terms and S and are called the partial
+
+46
+00:03:50,550 --> 00:03:54,450
+sums of this infinite series يعني هدولة اللي هي الـ
+
+47
+00:03:54,450 --> 00:03:58,390
+.. الـ xk's بنسميها اللي هي الـ terms تبعة الـ
+
+48
+00:03:58,390 --> 00:04:02,170
+infinite series و الـ S and أو الـ Sk بنسميها اللي
+
+49
+00:04:02,170 --> 00:04:06,310
+هي عبارة عن إيش الـ sequence of partial sums أو
+
+50
+00:04:06,310 --> 00:04:10,330
+بنسميهم are partial sums of this infinite series
+
+51
+00:04:10,330 --> 00:04:14,650
+نيجي الآن بما أنه اللي هو في النهاية الـ series
+
+52
+00:04:14,650 --> 00:04:17,960
+اللي عندنا هذه عبارة عن limit في حالة الـ
+
+53
+00:04:17,960 --> 00:04:22,080
+convergence هو عبارة عن limit of a sequence إذا
+
+54
+00:04:22,080 --> 00:04:25,520
+تنطبق عليها قوانين الـ sequences اللي أخدناها في
+
+55
+00:04:25,520 --> 00:04:30,960
+chapter 3 إذا متوقع إنه احنا نستخدم ما تحدثنا فيه
+
+56
+00:04:30,960 --> 00:04:36,420
+في chapter 3 أو نتائجها للحصول على النظريات اللي 
+
+57
+00:04:36,420 --> 00:04:37,520
+احنا بدنا نبرهنها
+
+58
+00:04:40,050 --> 00:04:44,350
+النظرية الأولى تسعة واحد اثنين theorem a if the
+
+59
+00:04:44,350 --> 00:04:48,610
+series summation xn and summation yn converge يعني
+
+60
+00:04:48,610 --> 00:04:52,490
+السيريز هذه من n من واحد إلى ما لا نهاية لو فرضنا 
+
+61
+00:04:52,490 --> 00:04:55,670
+أن هذا الـ sum موجود و هذا الـ sum موجود يعني
+
+62
+00:04:55,670 --> 00:05:00,010
+السيريز هذه اللي هي sequence of partial sums
+
+63
+00:05:00,010 --> 00:05:03,850
+سبعتها الـ limit لها موجودة و الـ summation yn
+
+64
+00:05:03,850 --> 00:05:07,310
+converge يعني السيريز sequence الـ partial sums 
+
+65
+00:05:07,310 --> 00:05:10,790
+السبعية ده برضه موجودة limit لها then the series
+
+66
+00:05:10,790 --> 00:05:16,190
+summation xn زائد yn برضه converges ومش هيك كمان
+
+67
+00:05:16,190 --> 00:05:20,510
+وقيمة السيكوه السيريز الجديدة summation xn زائد yn
+
+68
+00:05:20,510 --> 00:05:26,380
+بساوي السيريز الأولى زائد السيريز الثانية الآن إشي
+
+69
+00:05:26,380 --> 00:05:32,100
+مُشابه لـ 4 Xn ناقص Yn بيساوي summation Xn ناقص
+
+70
+00:05:32,100 --> 00:05:36,940
+summation Min Yn الآن بي if the series summation
+
+71
+00:05:36,940 --> 00:05:41,560
+Xn is convergent is convergent and C is any real
+
+72
+00:05:41,560 --> 00:05:46,120
+number then the series summation C في Xn برضه 
+
+73
+00:05:46,120 --> 00:05:50,960
+هيخليها تظلها convergent و بيطلع عند الـ summation
+
+74
+00:05:50,960 --> 00:05:55,930
+لـ C Xn بيساوي C في الـ summation ل Min للـ XL الآن 
+
+75
+00:05:55,930 --> 00:06:00,990
+مدام نحكي عن series بده ترجم اللي هو الـ series إلى
+
+76
+00:06:00,990 --> 00:06:04,450
+sequences إلى sequence of partial sums واستخدم
+
+77
+00:06:04,450 --> 00:06:07,730
+اللي هي قوانين الـ limits القديمة يعني الموضوع
+
+78
+00:06:07,730 --> 00:06:13,160
+البرهان أمر سهل إن شاء الله الآن نفترض إنه السميق
+
+79
+00:06:13,160 --> 00:06:16,580
+.. مدام هذا converts و هذا converts بدي افترض انه
+
+80
+00:06:16,580 --> 00:06:21,580
+هذه قيمتها بساوي S وهذا قيمتها مثلًا بساوي S' يعني
+
+81
+00:06:21,580 --> 00:06:25,300
+جاي let S بتساوي summation xi I من واحد إلى وين
+
+82
+00:06:25,300 --> 00:06:27,140
+إلى اللي هي 
+
+83
+00:06:52,810 --> 00:06:54,210
+كيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكي
+
+84
+00:06:54,500 --> 00:07:01,180
+الـ XI لأن هو جالني ان الـ limit لأن الـ series هذه 
+
+85
+00:07:01,180 --> 00:07:05,160
+لما ما حطش إشي معناته من واحد إلى ما لا نهاية لما
+
+86
+00:07:05,160 --> 00:07:09,090
+لا حطش إشي معناته بقصد الـ finite sum الآن هو جاهز
+
+87
+00:07:09,090 --> 00:07:11,790
+لأن هذا الـ series الـ summation هو موجود وهذا 
+
+88
+00:07:11,790 --> 00:07:16,350
+موجود يعني بمعنى آخر الـ limit للـ S اللي هي هذه
+
+89
+00:07:16,350 --> 00:07:20,690
+limit للـ S بساوي الـ series هذه و limit للـ S برايم
+
+90
+00:07:20,690 --> 00:07:24,650
+بساوي الـ series هذه من واحد إلى ما لا نهاية الآن
+
+91
+00:07:24,650 --> 00:07:28,990
+صارت عندي هذا عبارة عن limit of what؟ of sequence
+
+92
+00:07:29,460 --> 00:07:33,960
+هذا عبارة عن limit of what؟ of sequence إذا حسب
+
+93
+00:07:33,960 --> 00:07:39,280
+اللي هو اللي هي النظريات اللي هي في chapter ثلاثة
+
+94
+00:07:39,280 --> 00:07:43,140
+الـ limit إذا كانت الـ limit للـ sequence exist و
+
+95
+00:07:43,140 --> 00:07:45,560
+limit للـ sequence الثانية exist فبكون limit
+
+96
+00:07:45,560 --> 00:07:49,560
+المجموع بتوزع يعني limit S زائد S prime إيش
+
+97
+00:07:49,560 --> 00:07:53,720
+هيساوي؟ limit للـ sequence الأولى زائد limit للـ
+
+98
+00:07:53,720 --> 00:07:56,760
+sequence الثانية هذا من وين جبته؟ هذا جبته من 
+
+99
+00:07:56,760 --> 00:08:03,000
+chapter ثلاثة طيب الآن لكن S زي S برايم كـ sequence
+
+100
+00:08:03,000 --> 00:08:06,540
+هذا S زي S برايم مجموعة و sequences يعني الـ
+
+101
+00:08:06,540 --> 00:08:09,300
+sequence of partial sums الأولى زي الـ sequence of 
+
+102
+00:08:09,300 --> 00:08:12,880
+partial sums الثانية إيش هتساوي؟ اللي هي عبارة عن 
+
+103
+00:08:12,880 --> 00:08:16,760
+الـ sequence اللي الصمشي XI I من عند واحد لعند K
+
+104
+00:08:16,760 --> 00:08:21,460
+هذا اللي صميتها أنا S K زي مين S K برايم هدولة
+
+105
+00:08:21,460 --> 00:08:25,410
+finite هدولة terms الآن هدولة finite و هدولة finite
+
+106
+00:08:25,410 --> 00:08:31,090
+إذا المجموع من إيش بيساوي summation xi زائد yi من 
+
+107
+00:08:31,090 --> 00:08:36,490
+عند واحد لعند مين لعند k هذه هي عبارة عن sk زائد
+
+108
+00:08:36,490 --> 00:08:42,250
+sk برايم صارت عندي sequence جديدة اللي هي s زائد s 
+
+109
+00:08:42,250 --> 00:08:47,840
+برايم هذه S زي ده S برايم إيش هتساوي يا جماعة اللي
+
+110
+00:08:47,840 --> 00:08:52,660
+هو الـ sequence اللي عندي اللي الـ .. الـ .. الـ K
+
+111
+00:08:52,660 --> 00:08:56,440
+ثيرم إلها أو اللي هو الـ sequence of partial sums
+
+112
+00:08:56,440 --> 00:09:02,680
+إلها هو عبارة عن XI زي ده YI I من واحد لعند K هذا
+
+113
+00:09:02,680 --> 00:09:09,500
+الآن صار بساوي هذا طيب الآن بده نبدأ ناخد الـ limit 
+
+114
+00:09:09,500 --> 00:09:17,310
+and then الـ summation بناء عليه الـ summation الـ S
+
+115
+00:09:17,310 --> 00:09:22,210
+زي الـ S' اللي هو حسب اللي هنا بيصير limit الـ S
+
+116
+00:09:22,210 --> 00:09:26,710
+زي الـ S' هذه اللي هو limit لهذه الـ sequence إيش 
+
+117
+00:09:26,710 --> 00:09:29,790
+هيصير عند هذا الـ limit لهذه الـ sequence؟ هيعندي
+
+118
+00:09:29,790 --> 00:09:36,150
+هذا بساوي اللي هو هذا المقدار طيب limit S زي الـ 
+
+119
+00:09:36,150 --> 00:09:42,010
+S' اللي هو limit هذا المقدار اللي هو limit S زائد S
+
+120
+00:09:42,010 --> 00:09:49,710
+برايم بساوي limit الـ summation XI زائد YI I من عند
+
+121
+00:09:49,710 --> 00:09:54,070
+واحد لعند N أو لعند K زي ما بدي as N goes to
+
+122
+00:09:54,070 --> 00:09:57,390
+infinity هذا notation عبارة عن notation لمين للـ
+
+123
+00:09:57,390 --> 00:10:02,630
+summation لأنه صار هذا exist من أين؟ لأن هذا زائد
+
+124
+00:10:02,630 --> 00:10:06,170
+هذا exist لأن هذا exist بما أن هذا exist نحسس إنه 
+
+125
+00:10:06,170 --> 00:10:11,250
+summation xi زائد yi I من عند واحد إلى ما لا نهاية
+
+126
+00:10:11,250 --> 00:10:14,850
+من جهة أخرى هذا أخبرني إيش بيساوي limit S زائد مين
+
+127
+00:10:14,850 --> 00:10:19,630
+S prime limit S اللي هو limit هذه limit هذه إيش 
+
+128
+00:10:19,630 --> 00:10:27,710
+هيكون limit S بساوي summation xi I من واحد لمن الآن
+
+129
+00:10:27,710 --> 00:10:33,010
+لأن K راحت الى وين إلى ما لا نهاية هذه limitها إذا
+
+130
+00:10:33,010 --> 00:10:36,730
+بتساوي اللي هو I من واحد لعند ما لا نهاية و limit S 
+
+131
+00:10:36,730 --> 00:10:41,110
+prime زيها SK بتروح لما لا نهاية أو N بتروح لما لا
+
+132
+00:10:41,110 --> 00:10:44,370
+نهاية بتساوي summation YI I من واحد إلى ما لا
+
+133
+00:10:44,370 --> 00:10:49,050
+نهاية بناء على أن هذه بتساوي هذه إذا صار المقدار 
+
+134
+00:10:49,050 --> 00:10:54,070
+هذا بساوي المقدار هذا زائد المقدار هذا أو بمعنى
+
+135
+00:10:54,070 --> 00:10:57,130
+آخر summation XN زائد YN بساوي summation XN زائد
+
+136
+00:10:57,130 --> 00:11:00,930
+YN وهو المطلوب
+
+137
+00:11:02,570 --> 00:11:05,930
+Similarly, summation XN ناقص YN بساوي summation XN 
+
+138
+00:11:05,930 --> 00:11:09,410
+ناقص YN بساوي summation XN ناقص YN بساوي summation XN
+
+139
+00:11:09,410 --> 00:11:09,610
+ناقص YN بساوي summation XN ناقص YN بساوي summation XN
+
+140
+00:11:09,610 --> 00:11:09,790
+ناقص YN بساوي summation XN ناقص YN بساوي summation XN
+
+141
+00:11:09,790 --> 00:11:09,830
+نقص YN بسوء summation XN نقص YN بسوء summation XN
+
+142
+00:11:09,830 --> 00:11:12,850
+نقص YN بسوء summation XN نقص YN بسوء summation XN
+
+143
+00:11:12,850 --> 00:11:15,170
+نقص YN بسوء summation XN ن
+
+144
+00:11:19,400 --> 00:11:25,440
+الـ S ناقص S برايم بساوي limit S ناقص limit S
+
+145
+00:11:25,440 --> 00:11:29,240
+برايم و بنجري نفس اللي جريناها قبل بشوية واللي 
+
+146
+00:11:29,240 --> 00:11:34,020
+الثانية لأنه بنحول وكأن حديثنا من series ل
+
+147
+00:11:34,020 --> 00:11:38,560
+sequence وكل قوانين ال sequence تم إثباتها سابقا
+
+148
+00:11:38,560 --> 00:11:43,100
+بـ mean بواسطة اللي هو شعب طر تلاتة أو في تحليل
+
+149
+00:11:43,100 --> 00:11:50,570
+حقيقي واحد الآن الأخيرة ال summationلـCn بيساوي
+
+150
+00:11:50,570 --> 00:11:56,250
+الـC في الصممشي للـXn برضه اعتمادا على limit الـC
+
+151
+00:11:56,250 --> 00:12:00,990
+في الـS بيساوي الـC في limit الـS وبنجري نفس اللي
+
+152
+00:12:00,990 --> 00:12:04,950
+أجرناها قبل بشوية اللي هو تحويلها من .. اللي هو
+
+153
+00:12:04,950 --> 00:12:09,330
+sequence .. من .. من series إلى sequences ومن ثم
+
+154
+00:12:09,330 --> 00:12:15,690
+استخدام اللي هي قوانين الـsequences طيب الآن نجي ل
+
+155
+00:12:15,690 --> 00:12:25,090
+اللي هي اللمّةاللي هي اللمّة
+
+156
+00:12:25,090 --> 00:12:28,970
+اللي بعدها اللي هي المشهورة 
+
+157
+00:12:30,530 --> 00:12:34,010
+وهذه test for divergence في الواقع كنا نقول عنها
+
+158
+00:12:34,010 --> 00:12:39,130
+في calculus باه ايش ال sequence هذه أو اللي هي
+
+159
+00:12:39,130 --> 00:12:42,330
+sequence of partial sums أو ال series بقول إذا
+
+160
+00:12:42,330 --> 00:12:46,490
+كانت ال series summation xn converges in R إذا كان
+
+161
+00:12:46,490 --> 00:12:50,650
+اللي هي ال summation لل xn converges in R لازم
+
+162
+00:12:50,650 --> 00:12:54,810
+يكون limit اللي هي ال sequence الأصلي اللي بنكون
+
+163
+00:12:54,810 --> 00:12:58,310
+منها sequence of partial sums لازم limit هيش يساوي
+
+164
+00:12:59,640 --> 00:13:04,000
+يساوي صفر وبناء عليه لو كانت ال limit لها تساوي
+
+165
+00:13:04,000 --> 00:13:07,640
+صفر على طول بنحكم على summation لل Xn إيش ماله
+
+166
+00:13:07,640 --> 00:13:12,580
+diverse وكنا نقول هذا test of divergence مش test
+
+167
+00:13:12,580 --> 00:13:16,360
+of convergence لأن ممكن ال limit تساوي صفر لكن ال
+
+168
+00:13:16,360 --> 00:13:19,960
+summation لل Xn يكون diverse والمثال اللي أنتو
+
+169
+00:13:19,960 --> 00:13:24,160
+مشهور اللي هو summation 1 على n هذا اللي هو limit
+
+170
+00:13:24,680 --> 00:13:29,900
+الواحد على ان بيساوي صفر but this series diverges
+
+171
+00:13:29,900 --> 00:13:33,860
+زي ما هنشوف بعد شوية وزي ما احنا اصلا عارفين ولكن 
+
+172
+00:13:33,860 --> 00:13:38,780
+احنا هنثبته اثبات الآن كنا اللي هو اخدناها معلومة 
+
+173
+00:13:38,780 --> 00:13:44,890
+في تفاضل بام طيب صلى الله عليه وسلم الآن
+
+174
+00:13:44,890 --> 00:13:49,650
+by definition the convergence of summation xn
+
+175
+00:13:49,650 --> 00:13:54,430
+means that limit ال sk شماله exist ايش ال sk
+
+176
+00:13:54,430 --> 00:13:59,570
+عارفين ايش ال sk ال sk هو عبارة عن x واحد زائد x
+
+177
+00:13:59,570 --> 00:14:06,190
+اتنين لما اصل عند xk الآن بما أنه اللي هو limit sk
+
+178
+00:14:06,190 --> 00:14:11,280
+بساوي اللي هو ال summation لل xnلأن نحن مفترضين أن
+
+179
+00:14:11,280 --> 00:14:14,900
+نصمش ال Xn إيش ما له exist مثلا م exist ونقول صمش
+
+180
+00:14:14,900 --> 00:14:20,120
+لل Xn اللي هو بساوي limit ال S K الآن من جهة أخرى
+
+181
+00:14:20,120 --> 00:14:24,640
+لو جيت حسبت انت ال S K ناقص S K minus واحد ال S K
+
+182
+00:14:24,640 --> 00:14:28,760
+ناقص S K minus واحد ايش هيساوي؟ هذي من عند واحد
+
+183
+00:14:28,760 --> 00:14:33,020
+لعند K وهذه من عند واحد لعند K minus واحد حصل ترحل
+
+184
+00:14:33,020 --> 00:14:38,230
+هيظلمين ال X Kالآن خد ال limit للجهتين S k goes to
+
+185
+00:14:38,230 --> 00:14:42,930
+infinity بصير limit S k as k goes to infinity ناقص
+
+186
+00:14:42,930 --> 00:14:46,450
+limit S k minus واحد لما k تروح لما لا نهاية
+
+187
+00:14:46,450 --> 00:14:52,210
+بيساوي limit X k as k goes to infinity الآن اتجرأت
+
+188
+00:14:52,210 --> 00:14:54,590
+ووزعت ال limit لأنه يعرف هذه ال sequence of
+
+189
+00:14:54,590 --> 00:14:58,350
+partial sums اللي بتبدأ من عند واحد وبضالها طالعة
+
+190
+00:14:58,350 --> 00:15:02,310
+limit هل هو summation لل X n exists ما احنا نقوله
+
+191
+00:15:02,310 --> 00:15:06,170
+لأ وهذه اصلا الـ tail تبعتها من عند الواحد وطالع
+
+192
+00:15:06,170 --> 00:15:10,490
+limitها برضه ايش ما ساوي اللي هو صماش ال اكسان لان
+
+193
+00:15:10,490 --> 00:15:13,130
+احنا بنعرف limit ال sequence و ال tail لها زي بعض
+
+194
+00:15:13,130 --> 00:15:16,890
+ما دامت ال limit exist لذن هدولة هذه ناقصت ايش
+
+195
+00:15:16,890 --> 00:15:21,010
+هيطلع صفر لذن صار limit ال اكسان ايش بساوي بساوي
+
+196
+00:15:21,010 --> 00:15:27,480
+صفر بكون عندنا الي هو وصلنا ل theorem 914 اللي هي
+
+197
+00:15:27,480 --> 00:15:39,680
+خلينا نشوف ايش هذه ال theorem بتقول ركزوا معانا بس
+
+198
+00:15:39,680 --> 00:15:46,160
+اذكركم بشغلة إنه إحنا في الـ monotone convergence
+
+199
+00:15:46,160 --> 00:15:52,500
+theorem في تحليل حقيقي واحد كنا نقول إنه إذا كانت
+
+200
+00:15:52,500 --> 00:15:55,140
+ال sequence increasing أو decreasing يعني لو كانت
+
+201
+00:15:55,140 --> 00:15:59,780
+monotone then the sequence converge if and only if
+
+202
+00:15:59,780 --> 00:16:04,180
+it is bounded هذه اللي هو في حالة مين الـ monotone
+
+203
+00:16:04,180 --> 00:16:07,620
+functions لكن in general كنا نقول إن الـ sequence
+
+204
+00:16:07,620 --> 00:16:10,360
+is convergent على طول اللي بيعطينا then it is
+
+205
+00:16:10,360 --> 00:16:15,820
+bounded but it may be bounded بط إي شمالها is not
+
+206
+00:16:15,820 --> 00:16:21,140
+convergent وكنا نقول ناخد مثال ناقص واحد على أن ال
+
+207
+00:16:21,140 --> 00:16:26,200
+sequence هذه أو ناقص واحد أس أن ناقص واحد أس أن نقص
+
+208
+00:16:26,200 --> 00:16:29,520
+واحد وثاني هذه الـ sequence bounded لأن قيمتها الـ
+
+209
+00:16:29,520 --> 00:16:32,940
+absolute value لها واحد but اللي هو ال limit اللي
+
+210
+00:16:32,940 --> 00:16:35,500
+لها does not exist لكن في حالة الـ monotone
+
+211
+00:16:35,500 --> 00:16:39,240
+function لأ ال boundedness يكافئ ال convergence
+
+212
+00:16:39,240 --> 00:16:43,880
+لأن هذا بدنا اللي هو الآن نطبق على ال monotone
+
+213
+00:16:43,880 --> 00:16:48,760
+convergence theorem أو نستخدمها في إثبات نظريتنا
+
+214
+00:16:48,760 --> 00:16:52,980
+اللي هي 914 theorem لت XN be a sequence of non
+
+215
+00:16:52,980 --> 00:16:57,500
+-negative real numbersإذا حكينا عن مين عن sequence
+
+216
+00:16:57,500 --> 00:17:01,900
+xn عنصرها إيش ما لها non negative real numbers
+
+217
+00:17:01,900 --> 00:17:08,630
+يعني أكبر أو تساوي صفر ثم الـ summation لـ xn من
+
+218
+00:17:08,630 --> 00:17:12,050
+السيريز تبعتها converts if and only if the
+
+219
+00:17:12,050 --> 00:17:15,750
+sequence S بتسوى Sk of partial sums is bounded
+
+220
+00:17:15,750 --> 00:17:21,110
+يعني الآن السيريز ال summation xn اللي هي هتكون
+
+221
+00:17:21,110 --> 00:17:26,470
+converts إذا و فقط إذا ال Sk إشمالها is bounded in
+
+222
+00:17:26,470 --> 00:17:30,970
+this case ال summation لـ xn بسوى limit لSk بسوى
+
+223
+00:17:30,970 --> 00:17:36,990
+صفر يمان لSk يعني الآن و كأنه بيقوللي إنه limitالـ
+
+224
+00:17:36,990 --> 00:17:45,130
+SK exists if and only if SK is bounded هذه الـ SK
+
+225
+00:17:45,130 --> 00:17:48,410
+هي الـ sequence of partial sums تبع السيريز limit
+
+226
+00:17:48,410 --> 00:17:52,090
+الـ SK هي السيريز نفسها الـ x and n من واحد إلى
+
+227
+00:17:52,090 --> 00:17:58,110
+ما لا نهاية الآن باختصار اللي هو هنقوله أنه أصلا هذه
+
+228
+00:17:58,110 --> 00:18:01,810
+ال SQL sequence of partial sums is an increasing
+
+229
+00:18:01,810 --> 00:18:05,950
+sequence مدام increasing يعني بمعنى آخر monotone
+
+230
+00:18:05,950 --> 00:18:10,090
+أو بالظبط اللي هو خلّيني أقول واحدة من ال monotone
+
+231
+00:18:10,090 --> 00:18:12,530
+هي increasing ت increasing هي increasing علنا الآن
+
+232
+00:18:12,530 --> 00:18:17,490
+مدام increasingهيكون عنده الـ Existence limit
+
+233
+00:18:17,490 --> 00:18:21,330
+يكافي الـ Boundedness ويكون خلصنا برهان النظرية
+
+234
+00:18:21,330 --> 00:18:24,310
+حسب الـ Newton convergence theorem ومش هيك وهيكون
+
+235
+00:18:24,310 --> 00:18:30,770
+limit هاش ما لمدام increasing السبريمام لعنصرها
+
+236
+00:18:30,770 --> 00:18:34,410
+هذه الـ Newton convergence theorem خليني نشوف هذا
+
+237
+00:18:34,410 --> 00:18:39,680
+الكلام بالتفصيل اللي حكيته بما أن xn أكبر يساوي 0
+
+238
+00:18:39,680 --> 00:18:43,300
+الـ xn أكبر يساوي 0 then the sequence of partial
+
+239
+00:18:43,300 --> 00:18:48,540
+sums is monotone increasing function ليش؟ لأن S1
+
+240
+00:18:48,540 --> 00:18:55,720
+عبارة عن x1 S1 عبارة عن x1 أكيد أصغر من x1 زائد x2
+
+241
+00:18:55,720 --> 00:19:00,670
+التي هي مين؟ S2لأن هذا الـ X2 اللي ضفته أكبر أو
+
+242
+00:19:00,670 --> 00:19:06,090
+يساوي 0 وهذا أصغر من S3 اللي هو X1 زائد X2 زائد X3 in
+
+243
+00:19:06,090 --> 00:19:12,890
+general سيكون ال S K أصغر من S K زائد 1 أو أصغر أو
+
+244
+00:19:12,890 --> 00:19:16,830
+يساوي حسب اللي هو الإضافة 0 أو كمية موجبة ماشي
+
+245
+00:19:16,830 --> 00:19:21,340
+الحال إذا صارت عندي ال sequence of partial sumاللي
+
+246
+00:19:21,340 --> 00:19:24,560
+هو صارت عبارة عن increasing إذا according to the
+
+247
+00:19:24,560 --> 00:19:27,240
+monotone convergence theorem اللي قلت قبل بشوية
+
+248
+00:19:27,240 --> 00:19:30,480
+اللي هي بالظبط رقمها 3.2 the
+
+249
+00:19:30,480 --> 00:19:37,580
+sequence S of partial sums converts if and only if
+
+250
+00:19:37,580 --> 00:19:41,640
+it is bounded يعني مدام الـ sequence of partial
+
+251
+00:19:41,640 --> 00:19:44,640
+sums as converges يعني الصممش للـ xn يعني السريز
+
+252
+00:19:44,640 --> 00:19:50,000
+هذه اللي هي is convergent if and only if it is
+
+253
+00:19:50,000 --> 00:19:52,260
+bounded اللي هي ال sequence of partial sums طبعاً
+
+254
+00:19:52,670 --> 00:19:57,030
+عند الـ summation لـ xn مش مساوي limit الـsk و الـ
+
+255
+00:19:57,030 --> 00:20:00,430
+sk increasing limit همين حيكون ال sub .. طبعا
+
+256
+00:20:00,430 --> 00:20:02,790
+increasing وصارك bounded مادام bounded then فيه
+
+257
+00:20:02,790 --> 00:20:06,470
+لها bound إذا صار عند ال supremum ل ال x .. ل ال
+
+258
+00:20:06,470 --> 00:20:09,190
+sk هو عبارة عن limit ال sk حسب ال molten
+
+259
+00:20:09,190 --> 00:20:12,410
+convergence theorem و سوى ال summation ل xn و هو
+
+260
+00:20:12,410 --> 00:20:18,270
+المطلوب طيب هذا لما يكون ال terms سبعات ال
+
+261
+00:20:18,270 --> 00:20:23,510
+sequence يشملها موجبات أو non negativeالآن كوشي
+
+262
+00:20:23,510 --> 00:20:29,610
+criterion for اللي هو series احنا زي ما كنا نقول
+
+263
+00:20:29,610 --> 00:20:33,130
+في التحليل الحقيقي واحد احيانا ما بنقدرش نعرف ايش
+
+264
+00:20:33,130 --> 00:20:37,990
+ال limit لكن بنكون عارفين ان ال sequence نفسها
+
+265
+00:20:37,990 --> 00:20:42,190
+converts فبدنا نعبر عن ال convergence لل sequence
+
+266
+00:20:42,190 --> 00:20:45,770
+بطريقة اللي هي ال terms تبعتها مش عن طريقة اللي هي
+
+267
+00:20:45,770 --> 00:20:50,450
+معرفة ال limit فكنا نقول إن الـ xn مثلاً is a
+
+268
+00:20:50,450 --> 00:20:52,850
+Cauchy sequence if and only if for every y أكبر من
+
+269
+00:20:52,850 --> 00:20:56,190
+0 there exists k element in N such that for every
+
+270
+00:20:56,190 --> 00:21:00,290
+n و m أكبر من k يكون الـ absolute value للـ xn
+
+271
+00:21:00,290 --> 00:21:03,990
+ناقص xm أصغر من إبسلول نحن نجيب اللي هو Cauchy
+
+272
+00:21:03,990 --> 00:21:07,750
+criterion مشابه إليها بس لمين لحالة السيريز ما هي
+
+273
+00:21:07,750 --> 00:21:11,170
+هذه السيريز زي ما قلنا هي عبارة عن في النهاية
+
+274
+00:21:11,170 --> 00:21:17,950
+sequence of partial sums طيب يا جماعة نيجي لكوشيك
+
+275
+00:21:17,950 --> 00:21:21,250
+ال 915 اللي هي quotient criterion for series the
+
+276
+00:21:21,250 --> 00:21:25,370
+series summation xn in R converts if and only if
+
+277
+00:21:25,370 --> 00:21:29,690
+for every ي أكبر من سفر there is a natural number
+
+278
+00:21:29,690 --> 00:21:35,010
+M such that if M و N أكبر أو سوى M of Y هكون
+
+279
+00:21:35,010 --> 00:21:40,020
+الأسئلة ماقصة أسئلة M اللي هو بسوى xn زائد 1 الـ M
+
+280
+00:21:40,020 --> 00:21:45,060
+أشملها أكبر أو يساوي N فبصير الـ SM عبارة عن X1 زائد
+
+281
+00:21:45,060 --> 00:21:49,660
+X2 و بياخد في طريقه الـ XN وبعدين بكمل XN زي X1
+
+282
+00:21:49,660 --> 00:21:54,000
+لما أصل عند XM لما نطرح منه الـ SM اللي هي X1 عند
+
+283
+00:21:54,000 --> 00:21:58,920
+الـ XN بروح كلهم بضال مين اللي هي XN زي X1 و XN زي 
+
+284
+00:21:58,920 --> 00:22:03,040
+X2 لما أصل عند مين عند XM هذا حيكون أصغر من مين من
+
+285
+00:22:03,040 --> 00:22:07,560
+إبسلون هذا اللي بنلثبته إنه الـ series summation xn
+
+286
+00:22:07,560 --> 00:22:12,300
+converges if and only if اللي هي الـ Cauchy 
+
+287
+00:22:12,300 --> 00:22:15,760
+criterion يعني مين هو لكل ي أكبر من 0 there exists
+
+288
+00:22:15,760 --> 00:22:19,420
+M such that for every M أكبر من M أكبر أو يساوي
+
+289
+00:22:19,420 --> 00:22:22,900
+الـ M اللي راجناها هيكون Absolute value أسمها M
+
+290
+00:22:22,900 --> 00:22:26,980
+نقص أس N اللي هو بساوية هذا المقدار أصغر من أيش من
+
+291
+00:22:26,980 --> 00:22:31,670
+يالان في الواقع احنا قلنا في نظرية سابقة .. نظرية
+
+292
+00:22:31,670 --> 00:22:36,090
+في السابقة في التحليل الحقيقي واحد ان الـ sequence
+
+293
+00:22:36,090 --> 00:22:40,610
+converges if and only if it is cauchy وهذه اللي
+
+294
+00:22:40,610 --> 00:22:46,950
+هنستخدمها، شوفوا صلى الله عليه وسلم الصممش للـ xn
+
+295
+00:22:46,950 --> 00:22:51,090
+converts in R if and only if the sequence of
+
+296
+00:22:51,090 --> 00:22:55,990
+partial sums الـ Sn converts in R هذا التعريف الـ
+
+297
+00:22:55,990 --> 00:23:00,150
+sequence Sn converts in R if and only if اللي قلت
+
+298
+00:23:00,150 --> 00:23:04,250
+عنها نظرية 3.5.4 اللي هي the convergent if and only
+
+299
+00:23:04,250 --> 00:23:08,490
+if Sn is a Cauchy sequence ماشي ايش تعريفه اس ام
+
+300
+00:23:08,490 --> 00:23:11,850
+كوشي سيكوانس لكل يبسلون أكبر من صفر there exist M
+
+301
+00:23:11,850 --> 00:23:16,090
+such that if M أكبر من N أكبر أو يساوي ال M اللي ده
+
+302
+00:23:16,090 --> 00:23:19,850
+جيتها اللي هو هيكون عبارة عن اس ام نقص اس ن أصغر
+
+303
+00:23:19,850 --> 00:23:24,330
+من يبسلون هاي اللي عند الهان اللي هي نظرية أصغر من
+
+304
+00:23:24,330 --> 00:23:27,830
+يبسلون اللي هي الكوشي بساوي مين أو بكافي ال
+
+305
+00:23:27,830 --> 00:23:31,330
+convergence هذه حساباتها زي ما قلنا الاس ام عبارة
+
+306
+00:23:31,330 --> 00:23:39,840
+عن مين X واحد x1 زائد لما أصل عند xn زائد xn زائد 1
+
+307
+00:23:39,840 --> 00:23:44,040
+لما أصل عند آخر واحد ال xm لأن ال M أكبر من N
+
+308
+00:23:44,040 --> 00:23:47,780
+فهلاجي في طريق اللي هو مين ال x ال x واحد عند ال
+
+309
+00:23:47,780 --> 00:23:55,300
+xn ناقص ال sn ناقص ال x1 ناقص ال x2 ناقص ال xn هذا
+
+310
+00:23:55,300 --> 00:24:00,750
+ال absolute value اللي هو هذولة بروح لهنامع هذولة
+
+311
+00:24:00,750 --> 00:24:06,590
+بضل عندى xn زائد واحد زائد xn زائد اتنين زائد xm
+
+312
+00:24:06,590 --> 00:24:10,070
+اللى هى هذه اصغر من مين من ابسلون اذا هذا صار اصغر
+
+313
+00:24:10,070 --> 00:24:13,150
+من ابسلون وهو المطلوب طيب
+
+314
+00:24:17,320 --> 00:24:22,820
+طيب، الان نعرف حاجة اسمها absolutely convergent
+
+315
+00:24:22,820 --> 00:24:27,380
+absolutely convergent برضه اللي مرت علينا في تفاضل
+
+316
+00:24:27,380 --> 00:24:31,620
+بها خلينا نذكركم فيها اللي هو let x بالـ
+
+317
+00:24:31,620 --> 00:24:36,760
+definition 916 let x بسوء xn be a sequence in R we
+
+318
+00:24:36,760 --> 00:24:41,020
+say that the series سماشي xn is absolutely
+
+319
+00:24:41,020 --> 00:24:42,180
+convergent
+
+320
+00:24:44,650 --> 00:24:52,470
+إذا كانت سلسلة أبسط قيم XN مرتبطة بالـ R
+
+321
+00:24:57,860 --> 00:25:01,700
+if it is convergent but not إيش ما لها absolutely
+
+322
+00:25:01,700 --> 00:25:05,620
+convergent يعني في series في الدنيا أكيد بتكون
+
+323
+00:25:05,620 --> 00:25:11,100
+convergent لكن مش absolutely convergent هذه ال
+
+324
+00:25:11,100 --> 00:25:13,620
+series اللي من هالنوع اللي بتكون convergent لكن مش
+
+325
+00:25:13,620 --> 00:25:16,220
+absolutely convergent بنسميه إيش ما لها
+
+326
+00:25:16,220 --> 00:25:18,820
+conditionally convergent
+
+327
+00:25:20,920 --> 00:25:24,240
+لكن بعد شوية هنقول ان any absolutely convergent
+
+328
+00:25:24,240 --> 00:25:33,240
+هتكون إيش ما لها is convergent طيب الان نيجي طبعا
+
+329
+00:25:33,240 --> 00:25:37,040
+هذا في R كل الشغل في ال real numbers تسعة واحد
+
+330
+00:25:37,040 --> 00:25:42,650
+سبعة theorem إذا كانت سلسلة مرتبطة بالكامل فهي
+
+331
+00:25:42,650 --> 00:25:45,530
+مرتبطة بالكامل أيضًا، فهي مرتبطة بالكامل أيضًا،
+
+332
+00:25:45,530 --> 00:25:54,310
+فهي مرتبطة بالكامل أيضًا، فهي مرتبطة
+
+333
+00:25:54,310 --> 00:25:56,430
+بالكامل أيضًا
+
+334
+00:25:57,710 --> 00:26:00,150
+ماذا يعني أبسليوت يكون convergent؟ يعني معناته
+
+335
+00:26:00,150 --> 00:26:03,270
+الصمشي اللي هي أبسليوت value أيش ماله is
+
+336
+00:26:03,270 --> 00:26:07,830
+convergent ماشي then by Cauchy criterion بنطبقها
+
+337
+00:26:07,830 --> 00:26:11,590
+على هذه ال series اللي هو لكل أبسلون أكبر من صفر
+
+338
+00:26:11,590 --> 00:26:14,970
+there exists m of epsilon element and such that if
+
+339
+00:26:14,970 --> 00:26:18,190
+m أكبر من n أكبر يسوى m epsilon اللي حكيناها قبل
+
+340
+00:26:18,190 --> 00:26:23,100
+شوية then اللي هو اللي عندي الأولى اللي هي n زائد
+
+341
+00:26:23,100 --> 00:26:26,560
+واحد n زائد اتنين لما أصل عند ال M بس كيف شكل ال
+
+342
+00:26:26,560 --> 00:26:28,920
+term هنا اللي هو ال absolute value اذا absolute
+
+343
+00:26:28,920 --> 00:26:33,180
+value ل Xn زائد واحد زائد .. مين ماخد ال M أكبر ان
+
+344
+00:26:33,180 --> 00:26:36,720
+اه زائد absolute value Xn زائد اتنين لما أصل عند
+
+345
+00:26:36,720 --> 00:26:40,380
+زائد absolute value ل ال مين ل Xm أصغر من إيه يا
+
+346
+00:26:40,380 --> 00:26:47,510
+عياش؟ من Y هذه اللي هي عبارة عن الاسم لهذه نقص الـ
+
+347
+00:26:47,510 --> 00:26:51,610
+SM لها الـ SM فرضا نسميها prime الـ SM اللي هي
+
+348
+00:26:51,610 --> 00:26:54,610
+عبارة عن absolute value X1 زائد absolute value X2
+
+349
+00:26:54,610 --> 00:26:58,290
+لما أصل عند ال absolute value Xm وهذه تزيلها منها
+
+350
+00:26:58,290 --> 00:27:02,250
+بيظل ال absolute value عند Xm N زائد 1 لعند ال
+
+351
+00:27:02,250 --> 00:27:05,990
+absolute value ل Xm اللي هي هتكون أصغر من Y حسب ال
+
+352
+00:27:05,990 --> 00:27:09,330
+Cauchy criterion ها وهذه سهلة بال Cauchy criterion
+
+353
+00:27:09,330 --> 00:27:10,010
+مباشرة
+
+354
+00:27:18,700 --> 00:27:23,480
+لو سمنا الـ sequence of partial sums للـ XN اللي
+
+355
+00:27:23,480 --> 00:27:28,090
+عبارة عن SSN وهذه سمنها mean للـ absolute values و
+
+356
+00:27:28,090 --> 00:27:32,430
+SM prime طيب شوفي لان احسبلي لهذه عشان اثبت هذه ال
+
+357
+00:27:32,430 --> 00:27:37,590
+conversion تلان احسبلي SM ماقص SM لمين الامات للام
+
+358
+00:27:37,590 --> 00:27:42,190
+الأكبر من انه أكبر يساوي مين M of Y بساوي اللي
+
+359
+00:27:42,190 --> 00:27:45,350
+هذولة حسبناها قبل و شوية طلعت XN زاد واحد XN زاد
+
+360
+00:27:45,350 --> 00:27:49,000
+اتنين عند X mean XM هذا الـ Absolute Value بالـ
+
+361
+00:27:49,000 --> 00:27:51,340
+Triangling Quality أصغر من الأولى زاد التانية لما
+
+362
+00:27:51,340 --> 00:27:55,780
+أصل للأخيرة هذا من فوق أصغر من مين؟ من إبسلون إذا
+
+363
+00:27:55,780 --> 00:27:59,220
+لجينا لكل إبسلون أكبر من صفر there exists M such
+
+364
+00:27:59,220 --> 00:28:01,480
+that F M أكبر من M أكبر من M أكبر من M أكبر من M
+
+365
+00:28:01,480 --> 00:28:05,740
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+366
+00:28:05,740 --> 00:28:08,560
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+367
+00:28:08,560 --> 00:28:14,340
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+368
+00:28:17,760 --> 00:28:21,960
+is الهى عبارة عن convergence اللي هي طبعا ال
+
+369
+00:28:21,960 --> 00:28:24,960
+sequence of partial sums تبع ال xn then by Cauchy
+
+370
+00:28:24,960 --> 00:28:30,140
+criterion ال summation لل xn is convergent طيب
+
+371
+00:28:30,140 --> 00:28:33,800
+نيجي
+
+372
+00:28:33,800 --> 00:28:42,360
+الان ناخد example 918 نشوف هذا ال example نشوف كيف
+
+373
+00:28:42,360 --> 00:28:47,970
+بدنا اللي هو انحل أو اللي هو نشرح هذا الـ Example
+
+374
+00:28:47,970 --> 00:28:49,410
+918
+
+375
+00:28:51,320 --> 00:28:55,460
+لت اكس بسوء a n then the geometric series ال
+
+376
+00:28:55,460 --> 00:28:59,820
+summation ل a n من واحد اللي مالنها هي converts if
+
+377
+00:28:59,820 --> 00:29:04,200
+ال absolute value لل a أشمالها أصغر من واحد إذا ال
+
+378
+00:29:04,200 --> 00:29:07,080
+geometric series هذا هتكون converts معلومة طبعا
+
+379
+00:29:07,080 --> 00:29:10,300
+عارفينها إذا كان ال absolute value لل a أصغر من
+
+380
+00:29:10,300 --> 00:29:15,680
+واحد فبتكون هذه a أشمالها converts الآن الجزء
+
+381
+00:29:15,680 --> 00:29:27,690
+الثاني b اللي هو بنشوفه لاحقًا الآن ونفترض
+
+382
+00:29:27,690 --> 00:29:31,390
+أن الـ summation لـ a أُسن من نقص واحد إلى ملا
+
+383
+00:29:31,390 --> 00:29:34,930
+نهاية is convergent مادام الـ convergent هذا حسب
+
+384
+00:29:34,930 --> 00:29:40,490
+الحكيمات التي قبل قليل اللي هي على طول limit الـ a
+
+385
+00:29:40,490 --> 00:29:44,480
+n النظرية as n goes to infinity إيش بساوي؟ صفر مدام
+
+386
+00:29:44,480 --> 00:29:47,760
+limit الـ A N بيساوي 0 إذا نكيد الـ absolute value
+
+387
+00:29:47,760 --> 00:29:51,180
+للـ A أصغر من 1، ليش؟ لأن لو كانت ال absolute
+
+388
+00:29:51,180 --> 00:29:54,960
+value للـ A بتساوي 1 مثلا، بيصير ال limit بيساوي
+
+389
+00:29:54,960 --> 00:29:58,520
+1، يعني مش 0، ولو كان هذا ال absolute value للـ A
+
+390
+00:29:58,520 --> 00:30:03,020
+أكبر من 1، بيصير limit الـ A N، بالذات، بيروح إلى
+
+391
+00:30:03,020 --> 00:30:05,560
+.. بيروح إلى وين؟ إلى مالة نهاية أو سلبة مالة
+
+392
+00:30:05,560 --> 00:30:09,000
+نهاية أو دصدات exist حسب اللي هي .. اللي هي الـ A
+
+393
+00:30:09,000 --> 00:30:13,420
+مدبا أو سلبة، بيكون limit A الـ N لو كانت أكبر من
+
+394
+00:30:13,420 --> 00:30:20,340
+1، اللي هي بتكون .. اللي هي diverse الآن في النهاية
+
+395
+00:30:20,340 --> 00:30:23,780
+مدامة ال limit لل a n as n goes to infinity بساوي
+
+396
+00:30:23,780 --> 00:30:27,240
+صفر فال absolute value أصبعناها هتكون أصغر من واحد
+
+397
+00:30:27,240 --> 00:30:32,760
+conversely suppose ذات ال absolute value لل a أصغر
+
+398
+00:30:32,760 --> 00:30:39,100
+من واحد بيثبتلك أن ال summation لل a n converts
+
+399
+00:30:39,100 --> 00:30:44,720
+بيثبتلك ال summation لل a n converts فبتنشوف الملاحظ
+
+400
+00:30:44,720 --> 00:30:49,260
+ة هذه المشهورة عندى لو جيت a n زائد واحد
+
+401
+00:30:49,260 --> 00:30:53,640
+زائد a n زائد اتنين لما اصل عند ال a m هذا طبعا
+
+402
+00:30:53,640 --> 00:30:59,550
+انا باخده في حالة ال m اكبر من مين من n وضربت في 1
+
+403
+00:30:59,550 --> 00:31:07,930
+-a لما أضرب و أجمع ال terms لبعض كله هي cancel كله
+
+404
+00:31:07,930 --> 00:31:12,590
+هيظل بس أول term اللي هو am زائد واحد و آخر term
+
+405
+00:31:12,590 --> 00:31:17,510
+اللي هو am زائد واحد فالان هذا ضرب هذا هيطلع am
+
+406
+00:31:17,510 --> 00:31:22,180
+زائد واحد ناقص a os m زائد واحدهذا بيساوي المقدار
+
+407
+00:31:22,180 --> 00:31:27,500
+هذا لكل الأمات اللي أكبر بالمئة من N لأن بدي
+
+408
+00:31:27,500 --> 00:31:29,860
+أستخدم شكل بدي أستخدم الـ Cauchy criterion في
+
+409
+00:31:29,860 --> 00:31:34,960
+إثبات ال convergence احسب ل S M نقص S N صرنا
+
+410
+00:31:34,960 --> 00:31:38,080
+حاسبينها وعارفين كيف بتنحسب ل الأم الأكبر من N
+
+411
+00:31:38,080 --> 00:31:41,700
+هيطلع عند A N زائد واحد لعند A M absolute value
+
+412
+00:31:41,700 --> 00:31:48,100
+هذا بيساوي اللي هو حسب اللي هنا عبارة عن ال
+
+413
+00:31:48,100 --> 00:31:55,100
+absolute value لهذاهي ساوي هذا absolute value على
+
+414
+00:31:55,100 --> 00:32:00,200
+المقدار هذا واحد ناقص a absolute value إذا استبدلت
+
+415
+00:32:00,200 --> 00:32:06,100
+هذا اللي هو هذا على هذا من هذه اللي هي اللي فوق مش
+
+416
+00:32:06,100 --> 00:32:09,920
+الحال إذا صار عند الآن استخدمت اللي فوق هذه أخدت
+
+417
+00:32:09,920 --> 00:32:13,040
+ال absolute value للجهتين وأخدت اللي هو قيمة هذا
+
+418
+00:32:13,040 --> 00:32:16,400
+صار عبارة عن absolute value للإيهان على ال
+
+419
+00:32:16,400 --> 00:32:21,230
+absolute value اللي هو واحد minus a طيب هذا أصغر أو
+
+420
+00:32:21,230 --> 00:32:24,310
+يساوي بال triangle inequality اللي هو ال absolute 
+
+421
+00:32:24,310 --> 00:32:27,810
+value للي فوق زاد ال absolute value للي جنبه على 
+
+422
+00:32:27,810 --> 00:32:33,050
+المقدار هذا نفس اللي هي نفس القيمة ما غيرتهاش لأن
+
+423
+00:32:33,050 --> 00:32:37,610
+ال absolute value لأصغر من واحد implies that أن ال
+
+424
+00:32:37,610 --> 00:32:42,090
+limit اللي فوق هذا بيروح لصفر يعني الآن as n goes
+
+425
+00:32:42,090 --> 00:32:46,730
+to infinity as n goes to infinity طبعاً أكيد ال M
+
+426
+00:32:46,730 --> 00:32:50,330
+هتروح برضه لوين؟ لملان هي اللي أكبر منها يعني ال N
+
+427
+00:32:50,330 --> 00:32:53,970
+as n goes to infinity هذا المقدار هيصغر كتير كتير
+
+428
+00:32:53,970 --> 00:32:57,490
+كتير وهذا هيصغر كتير كتير لدرجة أن هذا كله على 
+
+429
+00:32:57,490 --> 00:33:03,030
+بعضه as n goes to infinity هيكون اللي هو أصغر من
+
+430
+00:33:03,030 --> 00:33:07,130
+أي رقم في الدنيا هيصير أصغر من أبسلون معناته سارة
+
+431
+00:33:07,130 --> 00:33:12,390
+أن دي اللي هو الـ S M نقص S N أصغر من إبسلون هيكون
+
+432
+00:33:12,390 --> 00:33:16,410
+اللي هو في هذه الحالة أثبتت أنه اللي هو الـ S N by
+
+433
+00:33:16,410 --> 00:33:20,970
+Cauchy criterion is convergent اللي هو صار عندي
+
+434
+00:33:20,970 --> 00:33:26,170
+الخلاصة إلى الآن convergence طيب المثال اللي هو
+
+435
+00:33:26,170 --> 00:33:30,200
+المثال اللي بعده المثال المشهور اللي هو بـ little
+
+436
+00:33:30,200 --> 00:33:38,500
+bit show that summation للواحد and diverse هذه الـ
+
+437
+00:33:38,500 --> 00:33:42,800
+sequence، هذه الـ series اللي هي series مشهورة 
+
+438
+00:33:42,800 --> 00:33:46,380
+اللي كنا نسميها الـ B series الـ B بيساوي واحد في 
+
+439
+00:33:46,380 --> 00:33:49,440
+هذه الحالة هذه الـ summation يليها واحد and إيش
+
+440
+00:33:49,440 --> 00:33:54,400
+ماله؟ diverge نشوف to show that summation وحدة ل N
+
+441
+00:33:54,400 --> 00:33:58,480
+divergent, we construct unbounded subsequence SKN
+
+442
+00:33:58,480 --> 00:34:04,860
+of SK قلنا قبل هيك أن إذا كانت ال sequence
+
+443
+00:34:04,860 --> 00:34:09,800
+converges أكيد هتكون bounded إذا لو كانت ال 
+
+444
+00:34:09,800 --> 00:34:16,060
+sequence unbounded أكيد diverges ماشي الحال طيب I
+
+445
+00:34:16,060 --> 00:34:19,250
+was not convergent بناءً عليه لو احنا جبنا
+
+446
+00:34:19,250 --> 00:34:24,830
+subsequence من ال sequence تكون unbounded فمن باب
+
+447
+00:34:24,830 --> 00:34:28,530
+الأولى هتصير ال sequence الأصلية نفسها unbounded
+
+448
+00:34:28,530 --> 00:34:31,450
+مدام أن صارت ال sequence الأصلية unbounded إذا ال
+
+449
+00:34:31,450 --> 00:34:36,030
+sequence صارت diverge بناءً عليه عشان أثبت اللي هو 
+
+450
+00:34:36,030 --> 00:34:41,030
+ال sequence of partial sums هذه ال sequence of
+
+451
+00:34:41,030 --> 00:34:44,430
+partial sums لها اللي هي الـ sk مثلاً أو ال sum
+
+452
+00:34:44,430 --> 00:34:48,530
+عشان أثبتها أن هي diverge ال sequence of partial
+
+453
+00:34:48,530 --> 00:34:52,370
+sums يعني بمعنى آخر عشان أسميها الـ diverge ال
+
+454
+00:34:52,370 --> 00:34:58,120
+series بدي اجيب Unbounded subsequence بدنا نعمل
+
+455
+00:34:58,120 --> 00:35:00,940
+construction Unbounded وده اللي هو ال construction
+
+456
+00:35:00,940 --> 00:35:05,200
+المشهور إذا الآن بدأ أعمل we construct Unbounded
+
+457
+00:35:05,200 --> 00:35:08,520
+subsequence as K زائد واحد of the sequence of 
+
+458
+00:35:08,520 --> 00:35:14,660
+partial sums SL of this series طيب شوف الآن كيف
+
+459
+00:35:14,660 --> 00:35:20,780
+بدنا نشتغل اللي هو اللي هي ال subsequence هذه خدلي
+
+460
+00:35:20,780 --> 00:35:27,830
+الآن بدأ أعمل subsequence as KR of mean of this 
+
+461
+00:35:27,830 --> 00:35:34,210
+sequence خدلي أول اشي K واحد بساوي اللي هو عبارة 
+
+462
+00:35:34,210 --> 00:35:39,750
+عن اتنين أس واحد فبصير SK واحد بساوي اللي هو 
+
+463
+00:35:39,750 --> 00:35:45,480
+عبارة عن اللي هيتنين أقصد واحد يعني اتنين ال
+
+464
+00:35:45,480 --> 00:35:50,820
+sequence of partial sums ال summation واحدة لان ان
+
+465
+00:35:50,820 --> 00:35:55,500
+من واحد لعند كي ماشي لان عندي اش ماخدها اتنين كي
+
+466
+00:35:55,500 --> 00:36:01,840
+لان بيصير عندي اللي هي عبارة عن واحد زائد نص مظبوط 
+
+467
+00:36:01,840 --> 00:36:07,720
+واحد زائد نص اكيد اكبر من مين؟ اللي هي اكبر من إيش
+
+468
+00:36:07,720 --> 00:36:14,780
+من الواحد طيب خد الآن K تنين بيساوي اتنين قس اتنين
+
+469
+00:36:14,780 --> 00:36:22,300
+فبيصير أس كتنين بيساوي اللي هو عبارة عن واحد زائد
+
+470
+00:36:22,300 --> 00:36:29,480
+نص زائد تلت زائد ربع مظبوط اللي هي هذه عبارة عن 
+
+471
+00:36:29,480 --> 00:36:38,020
+تساوي أس كواحد أي أس كواحد زائد اللي هو مين
+
+472
+00:36:40,830 --> 00:36:47,350
+تلت زائد إيش زائد ربع أكيد هتكون هذه خلّيني أكتب 
+
+473
+00:36:47,350 --> 00:36:53,410
+أربعة أكبر وأقول هذه زائد ربع زائد إيش ربع لأن
+
+474
+00:36:53,410 --> 00:36:57,430
+التلت أكبر من ربع حطيت بدل هذا فبصير عند هذا
+
+475
+00:36:57,430 --> 00:37:02,890
+المقدار SK2 أكبر من SK1 زائد ربع زائد ربع يعني 
+
+476
+00:37:02,890 --> 00:37:10,820
+بمعنى آخر سيكون أكبر من SK1 زائد واحد اللي هو اتنين 
+
+477
+00:37:10,820 --> 00:37:16,820
+في مين؟ في الربع اللي هو بيساوي SK واحد زاد اتنين في
+
+478
+00:37:16,820 --> 00:37:23,440
+واحد على اتنين تربيع بأشي اللي هو هذا اكيد اكبر من
+
+479
+00:37:23,440 --> 00:37:27,740
+واحد زائد لأن SK واحد اكبر من مين؟ من واحد اكبر من
+
+480
+00:37:27,740 --> 00:37:33,900
+واحد زائد اتنين اتنين في واحد على اتنين تربيع
+
+481
+00:37:44,670 --> 00:37:51,130
+خلّينا نحسب أس كي تلاتة ماذا يساوي؟ از كي تلاتة خد
+
+482
+00:37:51,130 --> 00:37:54,070
+كي تلاتة طبعاً واضحة إيش كي تلاتة؟ بدأ أخدها اتنين أقصى
+
+483
+00:37:54,070 --> 00:37:57,770
+اتنين هاخد اتنين أقصى تلاتة اللي هي تمانية اللي
+
+484
+00:37:57,770 --> 00:38:04,870
+عبارة عن واحد زائد نص زائد تلت زائد ربع زائد خمس
+
+485
+00:38:04,870 --> 00:38:14,050
+زائد سدس زائد سبع زائد تمن ماشي الحال طيب شوف عندي
+
+486
+00:38:14,050 --> 00:38:24,890
+الآن من واحد لعند اللي هو جذاش ربع هذا اللي هي SK2
+
+487
+00:38:27,420 --> 00:38:31,960
+الباقية الـ SK تلاتة إذاً هذا بيصير عبارة عن SK
+
+488
+00:38:31,960 --> 00:38:38,340
+تنين اللي هو يعني أكبر من SK تنين زائد آخر واحد زي
+
+489
+00:38:38,340 --> 00:38:44,320
+ما أخدت هنا آخر واحد هنا اللي هو تمن زائد تمن زائد
+
+490
+00:38:44,320 --> 00:38:50,100
+تمن زائد تمن زائد تمن أربعة، واحد، تنين، واحد،
+
+491
+00:38:50,100 --> 00:38:54,880
+تنين، تلاتة، أربعة، عين أربعة ماشي الحال هدول الآن
+
+492
+00:38:56,220 --> 00:38:58,780
+من هنا إلى هنا أصغر من هنا إلى هنا عشان هيك بيصير
+
+493
+00:38:58,780 --> 00:39:02,120
+هذا المقدار أكبر من SK2 زائد هدوله هدوله إيش
+
+494
+00:39:02,120 --> 00:39:08,400
+بيساووا؟ هو يساوي SK2 زائد اللي هو أكمتهم؟ أربعة
+
+495
+00:39:08,400 --> 00:39:14,940
+أتمان يعني أربعة في تمن أربعة
+
+496
+00:39:14,940 --> 00:39:19,880
+في تمن هو يساوي الآن أربعة في تمن يعني عبارة عن 
+
+497
+00:39:19,880 --> 00:39:28,720
+نص مظبوط يعني بيساوي اللي هو SK2 زائد نص نشوف من
+
+498
+00:39:28,720 --> 00:39:33,360
+اللي فوق هنا SK2 أكبر من واحد زائد اتنين على اتنين
+
+499
+00:39:33,360 --> 00:39:38,800
+إذا حيصير هذا أكبر من واحد زائد اتنين على اتنين
+
+500
+00:39:38,800 --> 00:39:43,500
+تربيع اتنين على اتنين تربيع هذه واحدة ممكن نخليها 
+
+501
+00:39:43,500 --> 00:39:50,800
+زي ما هي واحد اتنين تلاتة أربعة مش مشكلة نص اللي
+
+502
+00:39:50,800 --> 00:39:57,500
+هو إيش بيساوي؟ هذا زائد اللي هو نص هذا اس كي اتنين
+
+503
+00:39:57,500 --> 00:40:02,720
+أكبر من هذا وهي نص بيصير زائد نص وهي ساوي واحد
+
+504
+00:40:02,720 --> 00:40:06,560
+زائد تلاتة
+
+505
+00:40:06,560 --> 00:40:13,820
+على مين؟ أكم نص؟ أنا بس هاد الخلبطة هنا اتنين في نص
+
+506
+00:40:13,820 --> 00:40:21,540
+تربيع يعني اتنين على اتنين تربيع اللي 
+
+507
+00:40:21,540 --> 00:40:22,580
+هي بتساوي
+
+508
+00:40:26,450 --> 00:40:32,410
+و SK3 بيساوي واحد زائد اتنين على اتنين تربيع زائد نص
+
+509
+00:40:32,410 --> 00:40:38,030
+هذه 
+
+510
+00:40:38,030 --> 00:40:46,650
+خلّينا نقول واحد زائد نص أكبر من بس هيأدي احنا بس
+
+511
+00:40:46,650 --> 00:40:55,560
+اللي هي SK1 SK1 اللي عبارة عن واحد زائد نص أكبر من
+
+512
+00:40:55,560 --> 00:41:01,700
+S K واحد هذه واحد زائد نص قيمة ال S خليها S K واحد
+
+513
+00:41:01,700 --> 00:41:04,860
+مش مشكلة S K واحد لما أنا عوضتها أنا عوضت بواحد ده
+
+514
+00:41:04,860 --> 00:41:10,120
+هي واحد زائد نص هي واحد زائد نص زائد هذه ماشي
+
+515
+00:41:10,120 --> 00:41:14,220
+الحال ويساوي صار عندها نص وهنا كمان اتنين مع 
+
+516
+00:41:14,220 --> 00:41:18,910
+اتنين بطلع كمان نص بصير اتنين على اتنين صح بيصير 2
+
+517
+00:41:18,910 --> 00:41:23,330
+على 2 وهذا نص وكمان نص هنا الآن لما نعوض عليها دي 
+
+518
+00:41:23,330 --> 00:41:28,830
+برضه بنفس الطريقة اللي صار عندي SK2 اللي هو عبارة 
+
+519
+00:41:28,830 --> 00:41:36,930
+عن واحد زاد اتنين على اتنين واحد نعود تحت SK2 بصير
+
+520
+00:41:36,930 --> 00:41:42,010
+واحد زاد اتنين على اتنين بصير عند واحد زاد اتنين
+
+521
+00:41:42,010 --> 00:41:44,890
+على اتنين يعني واحد زائد تلاتة على من؟ على اتنين
+
+522
+00:41:44,890 --> 00:41:53,410
+اللي وصلتله يعني الآن الـ اس كي واحد أكبر من واحد زائد
+
+523
+00:41:53,410 --> 00:42:00,370
+اتنين اصفر على أو خلّيني أقول بيساوي اسد بيساوي
+
+524
+00:42:00,370 --> 00:42:08,680
+واحد زائد واحد على اتنين اصفر SK3 SK2 عبارة عن أكبر 
+
+525
+00:42:08,680 --> 00:42:13,440
+من وصلنا أخر أشي أكبر من واحد زائد اتنين على اتنين
+
+526
+00:42:13,440 --> 00:42:21,400
+SK3 أكبر يعني هان اتنين هاي اتنين SK3 اللي هو 
+
+527
+00:42:21,400 --> 00:42:28,420
+عبارة عن أكبر من واحد واحد زائد تلاتة على اتنين
+
+528
+00:42:28,420 --> 00:42:38,580
+لاحظ هنا تلاتة هنا على اتنين هنا في حالة هذه اللي
+
+529
+00:42:38,580 --> 00:42:43,920
+هي اتنين تربيع يعني اتنين على اتنين وفي حالة 
+
+530
+00:42:43,920 --> 00:42:49,980
+الأخيرة أكبر من واحد اللي هو أكبر من واحد زائد نص 
+
+531
+00:42:49,980 --> 00:42:54,260
+اللي هو عبارة عن اللي هو اتنين أو سفر أو بيساوي
+
+532
+00:42:54,260 --> 00:42:58,940
+أنا اتنين أو سفر اللي هو على اتنين يعني الآن و
+
+533
+00:42:58,940 --> 00:43:07,250
+كأنه in general in general هناك تلاتة وهنا K2 وهنا
+
+534
+00:43:07,250 --> 00:43:13,230
+K1 in general بيصير عندي SK3 أكبر من 1 زائد 3 على 
+
+535
+00:43:13,230 --> 00:43:20,550
+2 يعني صار عندي الآن بصورة عامة ال SKR اللي هو 
+
+536
+00:43:20,550 --> 00:43:25,590
+أكبر من 1 زائد R على 2 ومرّينا في الخطوات في
+
+537
+00:43:25,590 --> 00:43:32,870
+أثناءها اللي هي على ما يلي مرّينا على أنها أكبر من 
+
+538
+00:43:32,870 --> 00:43:42,290
+SKR-1 زاد 2 أس R-1 في 1 على 2R اللي سميناها SKR-1 
+
+539
+00:43:42,290 --> 00:43:52,460
+زاد إيش نص الآن هذه بدي أثبتها by induction أنا
+
+540
+00:43:52,460 --> 00:43:56,520
+لأن عملتلها لتلاتتين لكن هذا طبعاً تلاتتين بس 
+
+541
+00:43:56,520 --> 00:44:02,280
+استقرار لأن in general بدأ أثبتها كما يلي عندي هي 
+
+542
+00:44:02,280 --> 00:44:05,860
+SK اتنين
+
+543
+00:44:05,860 --> 00:44:12,700
+اللي هي R ناقص واحد زائد اللي هو اتنين أس ار ماينس
+
+544
+00:44:12,700 --> 00:44:16,060
+واحد لأن اتنين أس اتنين هذه اللي هي R إيش بيساوي
+
+545
+00:44:16,060 --> 00:44:18,800
+تلاتة بيصير اتنين أس تلاتة ناقص واحد على اتنين أس
+
+546
+00:44:18,800 --> 00:44:22,880
+اتنين في واحد على اتنين تكعيب اللي هي واحد على
+
+547
+00:44:22,880 --> 00:44:27,600
+اتنين تكعيب اللي هي واحد على اتنين أس ار إذا هذه هي
+
+548
+00:44:27,600 --> 00:44:33,920
+هيها هذه اللي هي بتساوي اللي هي SK اللي هي R ناقص 
+
+549
+00:44:33,920 --> 00:44:39,600
+واحد يعني اتنين زائد إيش؟ زائد نص أكبر من مين؟ من
+
+550
+00:44:39,600 --> 00:44:42,960
+واحد زائد تلاتة على اتنين اللي هي واحد زائد R على 
+
+551
+00:44:42,960 --> 00:44:47,480
+اتنين حيث ال R هنا إيش بتساوي؟ بتساوي تلاتة إذا هذا 
+
+552
+00:44:47,480 --> 00:44:53,130
+الاستقراء الآن بطلّع لي هذه بس هذا مش إثبات بدنا 
+
+553
+00:44:53,130 --> 00:44:57,970
+نثبتها for r بتساوي واحد على طول for r بتساوي واحد
+
+554
+00:44:57,970 --> 00:45:05,140
+اس كي واحد اس كي واحد بيساوي اللي هو R بتساوي اللي هي 
+
+555
+00:45:05,140 --> 00:45:10,960
+واحد SK واحد بيساوي اللي هو واحد زائد نص واحد زائد 
+
+556
+00:45:10,960 --> 00:45:14,180
+نص طب علشان ما فيش إجابة لك خلّيني أخد أن ال R إيش
+
+557
+00:45:14,180 --> 00:45:18,120
+بتساوي ال R بيساوي اتنين لأن ال R زيرو مش معرفة 
+
+558
+00:45:18,120 --> 00:45:21,220
+فاهمين عليها إذا أن ال R بيساوي اتنين R بيساوي
+
+559
+00:45:21,220 --> 00:45:25,720
+اتنين SK اتنين هي SK اتنين عشان مديش أعيدها SK
+
+560
+00:45:25,720 --> 00:45:34,820
+اتنين أكبر من اللي هو اللي هي SK1 هيها SK2 أكبر من 
+
+561
+00:45:34,820 --> 00:45:42,460
+SK1 زائد 2 أُس 2 ناقص 1 يعني أُس واحد في مين في
+
+562
+00:45:42,460 --> 00:45:45,980
+رُبع اللي هو 1 على 2 تربيع إذن هذا صح لأن
+
+563
+00:45:45,980 --> 00:45:52,740
+اللي بعدها اللي هي SK1 زائد اللي هي نصاللي هو هذا
+
+564
+00:45:52,740 --> 00:45:56,200
+ما حد بروح بصيله نص اللي هي أكبر من 1 زائد
+
+565
+00:45:56,200 --> 00:45:59,500
+2 على 2 اللي هي 1 زائد R على 2 اللي
+
+566
+00:45:59,500 --> 00:46:03,940
+هي R بساوي 2 إذا هذه true for mean for R
+
+567
+00:46:03,940 --> 00:46:08,160
+بتساوي 2 لإنه بتبدأ من عند مين من عند R بساوي
+
+568
+00:46:08,160 --> 00:46:15,700
+2 الآن بدنا نفترض إنها صحيحة صحيحة for
+
+569
+00:46:17,620 --> 00:46:24,820
+R و نثبت صحيتها في مين لـ R زائد 1 بيكون خلصنا
+
+570
+00:46:24,820 --> 00:46:34,060
+إذا هي اللي بدنا نفترض صحتها لعند مين عند R بتساوي
+
+571
+00:46:34,060 --> 00:46:43,980
+R ماشي و بدنا نثبت صحتها لـ SKR زائد 1 SKR زائد 
+
+572
+00:46:43,980 --> 00:46:51,130
+واحد إيش بتساوي؟ بتساوي 1 طبعاً كر زائد 1 زي ما
+
+573
+00:46:51,130 --> 00:46:55,310
+اتفرجنا عبارة عن 2 أثار زائد 1 بيصير 1
+
+574
+00:46:55,310 --> 00:47:02,990
+زائد نص زائد تلت زائد لما أصل عند 1 على 2
+
+575
+00:47:02,990 --> 00:47:10,210
+أثار ماشي عند أثار هذه اللي هتمثل الـ mean اللي هي
+
+576
+00:47:10,210 --> 00:47:22,240
+skr زائد زائد زائد
+
+577
+00:47:22,240 --> 00:47:33,660
+زائد زائد زائد
+
+578
+00:47:34,490 --> 00:47:40,870
+زائد 1 زائد 1 على 2 أثار زائد 2 بضل
+
+579
+00:47:40,870 --> 00:47:46,110
+أضيف 1 لما أصل عند آخر واحدة اللي هي 1 على
+
+580
+00:47:46,110 --> 00:47:51,050
+2 أثار زائد 1 هذول المضافات على مين؟ على ال
+
+581
+00:47:51,050 --> 00:47:57,930
+SKR ويساوي SKR زائد المضافات هي دي .. ده شوف في
+
+582
+00:47:57,930 --> 00:48:01,230
+الجليد ماجدش عددين 1 على 2 أسقار زائد 1
+
+583
+00:48:01,230 --> 00:48:05,190
+زائد 1 على 2 أسقار زائد 2 زائد .. لما
+
+584
+00:48:05,190 --> 00:48:10,650
+أصل لآخر واحد .. 1 على 2 أسقار في 1 زائد
+
+585
+00:48:10,650 --> 00:48:16,820
+1، مظبوط؟ يعني 2 أسقار في 2 هدولة 2
+
+586
+00:48:16,820 --> 00:48:19,940
+مضروبات يعني 2 أثار زائد 1 اللي هي هدى لما
+
+587
+00:48:19,940 --> 00:48:24,680
+اضربها جوا بيصير عبارة عن 2 أثار زائد 2
+
+588
+00:48:24,680 --> 00:48:30,760
+أثار مظبوط طيب يعني وكأن عدد الـ terms اللي ضفته
+
+589
+00:48:30,760 --> 00:48:36,020
+هدى هدول عددهن جزء عددهن هدول إيش بيساوي 2
+
+590
+00:48:36,020 --> 00:48:44,280
+أصاريعني هيساوي هذا هيكون أكبر من SKR زائد 1
+
+591
+00:48:44,280 --> 00:48:50,380
+على 2 أثار زائد 1 أكيد لأن هذا الـ term أصغر
+
+592
+00:48:50,380 --> 00:48:54,660
+من هذا الـ term زائد 1 على 2 أثار زائد 1
+
+593
+00:48:54,660 --> 00:48:57,740
+زي ما عملت قبل زائد لما أصل الاخر واحد 1 على
+
+594
+00:48:57,740 --> 00:49:02,720
+2 أثار زائد 1 أكم واحد هدولة عدد هنا عدد
+
+595
+00:49:02,720 --> 00:49:06,960
+الـ 2 أُس R زي ما عدنا إنها ينهار إذا هذا بيصير
+
+596
+00:49:06,960 --> 00:49:16,980
+عبارة عن أكبر من الـ SKR زائد 2 أُس R في 1 على 2
+
+597
+00:49:16,980 --> 00:49:24,700
+أُس R زائد 1 يعني صارت هذه صحيحة لهنا صحيحة for R
+
+598
+00:49:24,700 --> 00:49:29,580
+بتساوي R زائد 1 لـ R زائد 1 صحيحة لهنا اللي بعدها
+
+599
+00:49:29,580 --> 00:49:35,680
+طبيعي هذه automatic بتطلع SKR زائد نص لأن هذه
+
+600
+00:49:35,680 --> 00:49:38,220
+بيساوي اللي هو بضال بس 2 و اللي فوق بتروح محق اللي
+
+601
+00:49:38,220 --> 00:49:46,730
+تحت الآن هذه ما احنا مفترضينها الـ SKR اللي هي أكبر
+
+602
+00:49:46,730 --> 00:49:54,160
+من 1 زائد اللي هي R على 2 هم مفترضين أن هذه
+
+603
+00:49:54,160 --> 00:49:58,880
+صحيحة إذا الـ SKR أكبر من 1 زائد R على 2 إذا
+
+604
+00:49:58,880 --> 00:50:03,240
+by induction الـ hypothesis بيصير هذا أكبر مكان هذه
+
+605
+00:50:03,240 --> 00:50:07,760
+اللي هو 1 زائد R على 2 زائد النص الأصلي
+
+606
+00:50:07,760 --> 00:50:12,460
+ويساوي 1 زائد R زائد 1 على مين؟ على 2
+
+607
+00:50:12,460 --> 00:50:18,330
+إذا صارت عند الـ SKR زائد 1 أكبر من 1 زائد R زائد
+
+608
+00:50:18,330 --> 00:50:23,110
+1 على 2 يعني صارت هذه الجملة صحيحة for R زائد 1
+
+609
+00:50:23,110 --> 00:50:27,270
+إذا صحيحة دائماً إذا هيك بيكون أثبتنا by
+
+610
+00:50:27,270 --> 00:50:32,770
+mathematical induction كل اللي بدنا إياه بخصوص هذا ال
+
+611
+00:50:32,770 --> 00:50:38,060
+subsequence SKR هذه الـ subsequence وضحنا انها أكبر
+
+612
+00:50:38,060 --> 00:50:41,720
+أو يساوي 1 على أرضها أو 2 يعني as R goes to
+
+613
+00:50:41,720 --> 00:50:44,540
+infinity هذا المقدار بروح لما لنهاية يعني هذه ال
+
+614
+00:50:44,540 --> 00:50:51,240
+sequence is unbounded إذا صار عندي اللي هو SKR is
+
+615
+00:50:51,240 --> 00:50:57,440
+unbounded subsequence of the sequence of partial
+
+616
+00:50:57,440 --> 00:51:04,240
+sums SN of summation 1 على N then it must diverge
+
+617
+00:51:04,240 --> 00:51:08,960
+وهو المطلوب بكون هي أثبتنا أن summation 1 على N is
+
+618
+00:51:08,960 --> 00:51:12,820
+a divergent series
+
+619
+00:51:17,210 --> 00:51:22,830
+بنكمل قصة الـ B-Series الـ B-Series المشهورة عندي
+
+620
+00:51:22,830 --> 00:51:28,750
+summation للواحد N أس بي N من 1 إلى مالنهاية
+
+621
+00:51:28,750 --> 00:51:33,050
+هذه الـ Series بدنا نفحص اللي هو متى converge و
+
+622
+00:51:33,050 --> 00:51:37,310
+متى diverge يعني converge for what بي and diverge
+
+623
+00:51:37,310 --> 00:51:41,850
+for what بي لجينا عند الـ B بساوي 1 it converge
+
+624
+00:51:41,850 --> 00:51:49,090
+بدنا نشوف الآن for مين بـ مين؟ for b بين الـ 0 و بين
+
+625
+00:51:49,090 --> 00:51:52,730
+الـ 1 show that the b series summation 1 على n b
+
+626
+00:51:52,730 --> 00:51:57,830
+diverges for b اللي أصغر أو يساوي 1 و أكبر من مين
+
+627
+00:51:57,830 --> 00:52:01,850
+من 0 طبعاً حد يقول لي لو كانت b سالبة لو كانت b
+
+628
+00:52:01,850 --> 00:52:07,690
+سالبة بتطلع أس فوق مثلاً معناه تطارد طيب
+
+629
+00:52:12,030 --> 00:52:17,770
+عندي for n element in n, b element in 0, 1 أنقص b
+
+630
+00:52:17,770 --> 00:52:21,330
+أصغر أو أصغر من 1 أصغر أو أصغر من 1 طبعاً المقصود
+
+631
+00:52:21,330 --> 00:52:24,530
+بي أكبر من .. بي أصغر من سالب 1 ده اللي بقول
+
+632
+00:52:24,530 --> 00:52:29,370
+عنها اللي بتكبر الـ b السالب اللي أصغر من 1 طيب
+
+633
+00:52:29,370 --> 00:52:32,750
+لأن احنا بنحكي عن بي أكبر من 0 أصغر أو أصغر من 1
+
+634
+00:52:32,750 --> 00:52:36,490
+شوفوا
+
+635
+00:52:36,490 --> 00:52:42,780
+صلى عنا بيه كلام سهلبنزيل 1 بي أصغر أو يساوي
+
+636
+00:52:42,780 --> 00:52:46,680
+مين أو أصغر أو يساوي n لأن الـ بي هنا عبارة عن إيش
+
+637
+00:52:46,680 --> 00:52:49,940
+عن كسر وكأنه بأخد يدوري ده هتكون أصغر أو يساوي n
+
+638
+00:52:49,940 --> 00:52:54,100
+سو 1 على n أصغر أو يساوي مين؟ 1 على n بي
+
+639
+00:52:54,100 --> 00:52:57,780
+لأنها بتنقل لأن however the sequence of partial
+
+640
+00:52:57,780 --> 00:53:01,080
+sums is unbounded، الـ sequence of partial sums
+
+641
+00:53:01,080 --> 00:53:05,200
+لهذه unbounded فما بالك الأكبر منها، إذن أكيد it
+
+642
+00:53:05,200 --> 00:53:09,140
+has a subsequence of un، اللي هي sequence of
+
+643
+00:53:09,140 --> 00:53:12,000
+partial sums which is unbounded، إذن هيكون ال
+
+644
+00:53:12,000 --> 00:53:17,120
+summation واحدة لأن بي divergence هذه السيريزة هي
+
+645
+00:53:17,120 --> 00:53:20,220
+بـ Unbounded subsequence of partial sums أكيد اللي
+
+646
+00:53:20,220 --> 00:53:22,940
+عاجبال هذه الـ subsequence of partial sums is
+
+647
+00:53:22,940 --> 00:53:30,700
+unbounded إذا السيريزة هذه is divergent حلاني
+
+648
+00:53:30,700 --> 00:53:37,160
+جي لمينة اللي هي السيريز اللي هي الـ B سيريز التانية
+
+649
+00:53:37,160 --> 00:53:40,780
+اللي هي for B أكبر من 1 الـ power series واحدة
+
+650
+00:53:40,780 --> 00:53:45,860
+لأن بي اشملها converts هذه الآن في خطواتها كثير
+
+651
+00:53:45,860 --> 00:53:48,840
+بتشابه اللي هو الخطوات اللي حكينا عليها قبل شوية
+
+652
+00:53:48,840 --> 00:53:52,660
+بس باتجاه الـ convergence عشان هيك مش هعيد الخطوات
+
+653
+00:53:52,660 --> 00:53:57,680
+اللي عيدتها في الـ B سيريز أو الـ 1 سيريز اه اللي
+
+654
+00:53:57,680 --> 00:54:02,560
+هي summation 1 على n الآن for B أكبر من 1 the
+
+655
+00:54:02,560 --> 00:54:07,480
+power series هذي converts ركزوا الآن معايا first
+
+656
+00:54:07,480 --> 00:54:13,080
+note that Sn أصغر أو يساوي Sm for every M أكبر أو
+
+657
+00:54:13,080 --> 00:54:18,690
+يساوي N يعني بمعنى آخر طب ما هي أصلاً مبينة 1 على n
+
+658
+00:54:18,690 --> 00:54:23,870
+أس بي دائماً موجبة إذا أكيد مدام موجبة أصغر من أس
+
+659
+00:54:23,870 --> 00:54:28,170
+1 أصغر من أس 3 أصغر من أس 4 إذا ال
+
+660
+00:54:28,170 --> 00:54:33,430
+sequence of partial sums أي شمالها is increasing
+
+661
+00:54:33,430 --> 00:54:39,190
+sequence طيب مدام increasing يعني بمعنى أو هتكون
+
+662
+00:54:39,190 --> 00:54:45,840
+أي شمالها monotone Madame Monotone بيكفيني أثبت أنه
+
+663
+00:54:45,840 --> 00:54:52,420
+SK is bounded ماشي بدي أثبت اللي هو الـ sequence
+
+664
+00:54:52,420 --> 00:54:58,120
+of partial sums is bounded SK عشان أثبت أنها
+
+665
+00:54:58,120 --> 00:55:02,140
+bounded، شوفوا هالاشي الغريب، بس الغرابة بتروح من
+
+666
+00:55:02,140 --> 00:55:08,160
+تصرف الـ increasing تبعته الآن SK is bounded عشان
+
+667
+00:55:08,160 --> 00:55:12,460
+أثبتها bounded يكفيني أني أثبت subsequence منها
+
+668
+00:55:12,460 --> 00:55:21,320
+bounded يعني أثبت لك إنه SK1 SK2 SK3 SKN in general
+
+669
+00:55:21,320 --> 00:55:25,860
+هذه الـ subsequence يكفي أني أثبت إنها bounded عشان
+
+670
+00:55:25,860 --> 00:55:29,960
+تكون اللي فوق bounded طب ما بلاقي subsequence
+
+671
+00:55:29,960 --> 00:55:33,580
+تانية بتكون اللي هي unbounded ما هو لو لجيت
+
+672
+00:55:33,580 --> 00:55:36,640
+subsequence تانية زي ما بتقول إنها unbounded أو لو
+
+673
+00:55:36,640 --> 00:55:40,660
+كانت هذه unbounded في حالة هذه bounded معناته ما
+
+674
+00:55:40,660 --> 00:55:45,640
+هي increasing هذه هتلاقي اللي هو term من هذه بعد
+
+675
+00:55:45,640 --> 00:55:49,080
+الـ .. بعد الـ term اللي أنت حكيت عنه من هذه مادام
+
+676
+00:55:49,080 --> 00:55:53,930
+هتلاقيه بعده إذاً معناته بخلي الـ bounded نصف مين
+
+677
+00:55:53,930 --> 00:55:56,970
+في هذه الـ sequence إذاً في حالة الـ increasing
+
+678
+00:55:56,970 --> 00:56:00,750
+sequence لإنها increasing يكفي أن ألاقي واحدة منهم
+
+679
+00:56:00,750 --> 00:56:04,610
+الـ subsequences إنها bounded عشان أقول كل ال
+
+680
+00:56:04,610 --> 00:56:08,210
+sequence bounded لأنه لو كانت اللي هو فيه عندك
+
+681
+00:56:08,210 --> 00:56:14,470
+اللي هو الـ sequence أصلاً مش bounded معناته في عنصر
+
+682
+00:56:14,470 --> 00:56:17,550
+من عناصر الـ subsequence اللي قولنا عنها bounded
+
+683
+00:56:17,550 --> 00:56:21,370
+تخططت اللي هو اللي بنحكي فيه لأنه دي روحي لما
+
+684
+00:56:21,370 --> 00:56:26,890
+لنهاية فعشان هيك غصب عنها مادام لجينا واحدة من ال
+
+685
+00:56:26,890 --> 00:56:31,250
+subsequences للـ increasing sequence is bounded
+
+686
+00:56:31,250 --> 00:56:37,810
+هتكون كل الـ sequence is bounded طيب، شوفوا عليها،
+
+687
+00:56:37,810 --> 00:56:40,870
+إذا اللي ضال علينا بس نعمل construction لـ
+
+688
+00:56:40,870 --> 00:56:46,310
+subsequence skr تكون bounded طبعاً لمن؟ لسريزة
+
+689
+00:56:46,310 --> 00:56:51,510
+summation 1 على n أس بي اللي ماياخدوا إشي مشابه للي
+
+690
+00:56:51,510 --> 00:56:55,730
+قبل بشوية عشان هيك مش هعيد الـ induction اللي قبل
+
+691
+00:56:55,730 --> 00:57:01,030
+بشوية طريقة الـ induction بتعملوها باسلوب مشابه،
+
+692
+00:57:01,030 --> 00:57:05,190
+إيش بقولت؟ انتبهوا عليه الـ K1 بيساوي 2 أس 1
+
+693
+00:57:05,190 --> 00:57:09,930
+ناقص 1، ماشي؟ هناك يقول لنا خد K1 اتنين، K2
+
+694
+00:57:09,930 --> 00:57:13,950
+2 تربيع، لأ هاد يقول لنا خدها KR بيساوي 2 أس R
+
+695
+00:57:13,950 --> 00:57:18,550
+ناقص 1، ماشي الحال؟ اللي كان غلط حسابات ويساوي
+
+696
+00:57:18,550 --> 00:57:23,790
+1، أس K1 1، K2 2 أس 2 ناقص 1
+
+697
+00:57:23,790 --> 00:57:29,690
+ويساوي 3 لو جيت حسبة SK2 احسبها لحالك هيصير
+
+698
+00:57:29,690 --> 00:57:35,590
+عبارة عن 1 على 1 على اللي هي زائد لأنه عند P
+
+699
+00:57:35,590 --> 00:57:40,790
+من وين بتبدأ؟ من عند اللي هو عند N من 1 إلى كده
+
+700
+00:57:40,790 --> 00:57:45,430
+بيصير 1 على 1 و P على 1 زاد 1 على 2 أس بي 
+
+701
+00:57:45,430 --> 00:57:51,510
+زاد 1 على 3 أس بي هذا أصغر من 1 زاد اللي هو 1 على
+
+702
+00:57:51,510 --> 00:57:55,690
+2 أس بي زاد 1 على 2 أس بي يعني بأخذ الأولى مش 
+
+703
+00:57:55,690 --> 00:57:59,510
+الأخيرة زي ما كنت آخذ قبل صار عندي 1 زائد 2 على 2
+
+704
+00:57:59,510 --> 00:58:05,200
+أس بي ويساوي 1 زائد 1 على 2 أس بي minus 1 الآن اللي
+
+705
+00:58:05,200 --> 00:58:09,460
+عملته للـ S K 2 بدي أعمله للـ S K 3 الـ S K 3 اللي هي 2
+
+706
+00:58:09,460 --> 00:58:13,340
+أقصى 3 ناقص 1 اللي هي S بتطلع 7 اللي هي 8 ناقص 1
+
+707
+00:58:13,340 --> 00:58:18,760
+الأولى S K 3 اللي هي عبارة عن S K 2 زائد زي ما
+
+708
+00:58:18,760 --> 00:58:22,040
+عملت قبل شوي ربع أس بي خمس أس بي ست أس بي زائد
+
+709
+00:58:22,040 --> 00:58:25,940
+سبع أس بي الآن بأخذ مش آخر واحدة بأخذ الأولى 
+
+710
+00:58:25,940 --> 00:58:30,580
+عشان يظل هذا المقدار لهان أكبر من لهان بيصير S K 2 زي
+
+711
+00:58:30,580 --> 00:58:37,580
+4 على 4 أس بي اللي هو عبارة عن 1 زي 1 على 2 أس 
+
+712
+00:58:37,580 --> 00:58:42,580
+بي minus 1 زي 1 على 4 أس بي minus 1 ماشي الحال
+
+713
+00:58:42,580 --> 00:58:48,320
+الآن سمّي لي بقول لي سمّي اللي هو 1 على 2 بي minus
+
+714
+00:58:48,320 --> 00:58:53,840
+1 هذه اللي هي سمّي ليها اسمها إيه ككتلة واحدة عشان
+
+715
+00:58:53,840 --> 00:58:59,680
+ما نضلش نكتبها طيب الآن since ب أكبر من واحد إذا
+
+716
+00:58:59,680 --> 00:59:04,100
+بدأ ب أكبر من واحد هذه لأن هي مفترضينها صارت الـ a
+
+717
+00:59:04,100 --> 00:59:07,520
+اللي عندي هنا بين الصفر وبين الواحد لأن ده صارت
+
+718
+00:59:07,520 --> 00:59:12,120
+اللي عدد أكبر من اثنين أو أكبر إذا صارت هذه عبارة
+
+719
+00:59:12,120 --> 00:59:18,140
+عن كسر يعني كسر بين الصفر وبين الواحد الآن by
+
+720
+00:59:18,140 --> 00:59:21,260
+mathematical induction زي اللي عملته قبل شوي we
+
+721
+00:59:21,260 --> 00:59:29,180
+find if اللي هو K R بيساوي 2R-1 هلاجي دائماً S K R
+
+722
+00:59:29,180 --> 00:59:36,400
+أكبر من 0 وأصغر من 1 زائد A زائد A تربيع لما أصل
+
+723
+00:59:36,400 --> 00:59:41,440
+عند A R-1 مين الـ A الـ A الـ A اللي هي 1 على 2 أس B
+
+724
+00:59:41,440 --> 00:59:46,480
+-1 وحالها هذه الـ induction بتاعتها سهلة بنفس
+
+725
+00:59:46,480 --> 00:59:50,500
+الطريقة اللي عملتها أنا قبل شوي بتفترضها صحيحة لـ
+
+726
+00:59:50,500 --> 00:59:57,810
+R بتثبتها صحيحة عند R بساوي 2 هنا أثبتناها للـ S K 2
+
+727
+00:59:57,810 --> 01:00:02,570
+هنا أثبتناها فوق وبعدين بتثبتها صحيحة لمين بتفرض 
+
+728
+01:00:02,570 --> 01:00:08,150
+صحيتها لـ R وبتثبت صحيتها منها لـ R زائد 1 بيكون 
+
+729
+01:00:08,150 --> 01:00:11,850
+صحيحة دائماً زي ما عملت قبل شوي بالظبط في الحساب
+
+730
+01:00:13,320 --> 01:00:17,100
+الآن as r goes to infinity هذه مجهزينها اللي هي a
+
+731
+01:00:17,100 --> 01:00:21,140
+أصغر من واحد as r goes to infinity هذا المقدار 
+
+732
+01:00:21,140 --> 01:00:26,020
+هيروح لواحد على واحد ناقص a ماشي لإن هذه بيصير 
+
+733
+01:00:26,020 --> 01:00:30,360
+اللي هي عبارة عن geometric series مجموعها infinite
+
+734
+01:00:30,360 --> 01:00:35,260
+geometric series بيصير عبارة عن summation a r, r
+
+735
+01:00:35,260 --> 01:00:42,170
+من صفر من واحد لعند ما لا نهاية مظبوط؟ هو يساوي الـ
+
+736
+01:00:42,170 --> 01:00:47,170
+summation واحد على واحد ناقص اللي هي a حرفينها a
+
+737
+01:00:47,170 --> 01:00:54,070
+اللي هي واحد على واحد ناقص a r من العين صفر هيها 
+
+738
+01:00:54,070 --> 01:00:57,450
+من العين صفر واحد زائد اثنين تربيع إلى ما لا نهاية
+
+739
+01:00:57,450 --> 01:00:59,530
+دي geometric series واحد على واحد ناقص a
+
+740
+01:00:59,530 --> 01:01:06,890
+therefore اللي هي واحد ناقص a هيكون عبارة عن إيش؟ 
+
+741
+01:01:06,890 --> 01:01:12,970
+bound for the partial sums of bar series ليش؟ لأن
+
+742
+01:01:12,970 --> 01:01:19,670
+صارت الـ S K R limit الـ S K R as R goes to infinity
+
+743
+01:01:19,670 --> 01:01:25,530
+أكبر أو يساوي أكبر من 0 أكبر يساوي 0 وأصغر أو 
+
+744
+01:01:25,530 --> 01:01:29,790
+يساوي 100 الـ limit اللي طلعت عندي 1 على 1 ناقص 
+
+745
+01:01:29,790 --> 01:01:35,880
+1 ناقص A صارت مدام الـ sequence of partial sums
+
+746
+01:01:35,880 --> 01:01:43,940
+هذه is bounded هيها by واحد على ناقص a اه then by
+
+747
+01:01:43,940 --> 01:01:48,180
+ثانو تسعة واحد اربعة مدامت هذه عبارة عن كل ان
+
+748
+01:01:48,180 --> 01:01:52,780
+عناصر موجبة يكفي عشان نثبت انها اللي هي converge
+
+749
+01:01:52,780 --> 01:01:58,220
+انها تكون bounded اللي صارت اللي هي الـ series هذه
+
+750
+01:01:58,220 --> 01:02:03,530
+converge زي ما قلت ماذا قلت؟ هذه صارت الـ
+
+751
+01:02:03,530 --> 01:02:09,230
+subsequence of partial sums إيش ما لها صارت عبارة 
+
+752
+01:02:09,230 --> 01:02:13,930
+عن bounded ماشي، مدام bounded إذا أثبتنا إن هناك
+
+753
+01:02:13,930 --> 01:02:17,570
+sub-sequence bounded من an increasing sequence إذا 
+
+754
+01:02:17,570 --> 01:02:19,770
+اتفجنا إن هذا الـ increasing sequence سيكون
+
+755
+01:02:19,770 --> 01:02:23,450
+bounded وهي increasing إذا convergence حسب الـ
+
+756
+01:02:23,450 --> 01:02:26,730
+monotone convergence theorem ومن ثم بيكون خلصنا
+
+757
+01:02:26,730 --> 01:02:32,880
+أثبتنا هذا is a convergent series for B أكبر من
+
+758
+01:02:32,880 --> 01:02:33,720
+واحد
+
+759
+01:02:36,760 --> 01:02:41,140
+Show that 1 على N تربيع زائد N من 1 إلى ما لا نهاية
+
+760
+01:02:41,140 --> 01:02:45,700
+إيش بتساوي؟ بتساوي 1 هذا بتاع مشهور وسؤال مشهور في
+
+761
+01:02:45,700 --> 01:02:50,480
+الـ .. في الـ calculus أو سهل إثباته لو جينا طلعنا
+
+762
+01:02:50,480 --> 01:02:53,900
+على اللي قولنا بنعمله partial fraction كنا نقول الـ
+
+763
+01:02:53,900 --> 01:02:57,860
+1 على K تربيع زائد K بيساوي 1 على K في K زائد 1
+
+764
+01:02:57,860 --> 01:03:02,440
+نار اللي هي عبارة عن 1 على K ناقص 1 على K زائد 1
+
+765
+01:03:03,050 --> 01:03:07,550
+ماشي الحال الآن صارت الـ sequence هذا الـ series هذه 
+
+766
+01:03:07,550 --> 01:03:10,970
+عبارة عن هذا ناقص هذا يعني الـ partial sums صارت 
+
+767
+01:03:10,970 --> 01:03:16,150
+عبارة عن واحد على N ناقص واحد على N زائد واحد ويساوي
+
+768
+01:03:16,150 --> 01:03:17,150
+كمية
+
+769
+01:03:20,550 --> 01:03:26,150
+كيب واحد بيصير واحد على واحد ناقص نصف اللي بعده
+
+770
+01:03:26,150 --> 01:03:29,830
+بإثنين اللي هو نصف ناقص ثلث اللي بعده ثلث ناقص ربع
+
+771
+01:03:29,830 --> 01:03:33,070
+لما أصل الآخر واحد واحد على N ناقص واحد على
+
+772
+01:03:33,070 --> 01:03:36,450
+N زائد واحد كلهم بيروحوا مع بعض وضل أول term وآخر
+
+773
+01:03:36,450 --> 01:03:40,470
+term الواحد ناقص واحد على N زائد واحد لأن هذا صار
+
+774
+01:03:40,470 --> 01:03:44,770
+اللي هو اللي هو الـ partial sum أو الـ sequence of 
+
+775
+01:03:44,770 --> 01:03:50,810
+الـ term of the partial sums of this series خذوله
+
+776
+01:03:50,810 --> 01:03:54,630
+limit الـ S N as n goes to infinity بيساوي واحد ناقص
+
+777
+01:03:54,630 --> 01:03:58,090
+limit الواحد الآن زائد واحد هذا بيروح للصفر ويساوي
+
+778
+01:03:58,090 --> 01:04:01,110
+واحد لأن صارت الـ series اللي عندي هذه الأصلية
+
+779
+01:04:01,110 --> 01:04:04,630
+converged ويساوي الـ convergent إيش بيساوي بيساوي
+
+780
+01:04:04,630 --> 01:04:10,470
+واحد الآن آخر موضوع في اللي هو الـ section الأول
+
+781
+01:04:12,460 --> 01:04:16,700
+حاجة اسمها rearrangement of series يعني إعادة 
+
+782
+01:04:16,700 --> 01:04:21,220
+ترتيب العناصر اللي هو اللي هي الـ series أو الـ term
+
+783
+01:04:21,220 --> 01:04:25,160
+سبعة الـ series الـ rearrangement of a series is
+
+784
+01:04:25,160 --> 01:04:29,140
+another series هي في ريز أخرى هتكون which is
+
+785
+01:04:29,140 --> 01:04:32,540
+obtained from the given one يعني بأخذها من من من
+
+786
+01:04:32,540 --> 01:04:38,660
+الأصلية by using all of the terms exactly one once
+
+787
+01:04:38,660 --> 01:04:44,020
+يعني بإننا نستخدم عناصر الـ series مرة واحدة فقط
+
+788
+01:04:44,020 --> 01:04:49,900
+لازم نستخدمها وبنستخدمها بمرة واحدة but scrambling
+
+789
+01:04:49,900 --> 01:04:55,720
+the order in which the terms are taken يعني بس إيش
+
+790
+01:04:55,720 --> 01:05:00,820
+بنسوي، بنعيد ترتيب اللي هي أماكن اللي هي S series
+
+791
+01:05:00,820 --> 01:05:06,540
+الآن يعني الـ summation XN summation XN هي series
+
+792
+01:05:06,540 --> 01:05:12,950
+قعدنا ترتيبها اللي هي summation YN الآن الـ XL و
+
+793
+01:05:12,950 --> 01:05:18,770
+الـ YN لو جينا حاطناها في مجموعتين هنقول أكيد أكيد
+
+794
+01:05:18,770 --> 01:05:24,890
+الـ X1 لعند الـ XN لعند ما لا نهاية هي نفسها
+
+795
+01:05:24,890 --> 01:05:31,940
+Y1 لعند Y2 لعند الـ YN إلى ما لا نهاية لكن الـ X1
+
+796
+01:05:31,940 --> 01:05:35,400
+مش شرط الـ Y1 الـ X2 مش شرط الـ Y2 أما هذه كمجموعة
+
+797
+01:05:35,400 --> 01:05:41,900
+هي نفس المجموعة وبنستخدمش الـ term الجديد إلا ..
+
+798
+01:05:41,900 --> 01:05:45,840
+بنستخدمش اللي هنا إلا غير مرة واحدة في اللي هي هنا
+
+799
+01:05:45,840 --> 01:05:51,380
+يعني كل اللي هنا موجودة هنا ولكن بترتيب آخر فبتكون 
+
+800
+01:05:51,380 --> 01:05:56,020
+هذه rearrangement of the original series الـ
+
+801
+01:05:56,020 --> 01:06:04,620
+summation لـ X طيب نأخذ مثال أو أكثر من مثال بقول 
+
+802
+01:06:04,620 --> 01:06:07,800
+the harmonic series اللي جابله بشوية هذه إلى
+
+803
+01:06:07,800 --> 01:06:12,940
+summation 1 على n 1 زائد نصف زائد ثلث زائد ربع زائد 
+
+804
+01:06:12,940 --> 01:06:17,560
+1 على n has rearrangements like فيه rearrangements
+
+805
+01:06:17,560 --> 01:06:22,040
+واحد إيش قال قال أنا اسمعوا خلوني أحط لكم اللي هي
+
+806
+01:06:22,040 --> 01:06:27,920
+أجسمها جسمين الزوجيات والفرديات كيف؟ بأبدأ أولاً بالزوج
+
+807
+01:06:27,920 --> 01:06:31,540
+نصف وربع، سُدُس، ثُمن، واحدة على اثنين، N وضلّ
+
+808
+01:06:31,540 --> 01:06:36,020
+ماشي لما لا نهاية وبين هن بأبدأ أحضر الفرديات واحدة 
+
+809
+01:06:36,020 --> 01:06:38,760
+على واحد، واحدة على ثلاث، واحدة على خمسة، واحدة على
+
+810
+01:06:38,760 --> 01:06:42,040
+اثنين، N ناقص واحد، إلى ما لا نهاية، ماشي الحال
+
+811
+01:06:42,040 --> 01:06:48,080
+هذه الـ series عنصرها N بالظبط اللي هنا بس معمول 
+
+812
+01:06:48,080 --> 01:06:51,890
+اللي هن إعادة الترتيب واحد ثاني جال اسمعه بِيرتبها
+
+813
+01:06:51,890 --> 01:06:55,450
+بترتيب ثاني إيش اللي طبعاً بِيرتبها حسب ما يخدمه أو
+
+814
+01:06:55,450 --> 01:06:58,170
+حسب ما يطلع معه في الـ .. في الـ .. في الـ شيء العملي
+
+815
+01:06:58,170 --> 01:07:02,310
+مثلاً الآن أول واحد بيقولك بتأخذ اللي هو الـ .. الـ
+
+816
+01:07:02,310 --> 01:07:04,030
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. 
+
+817
+01:07:04,030 --> 01:07:04,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+818
+01:07:04,050 --> 01:07:04,310
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+819
+01:07:04,310 --> 01:07:04,350
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+820
+01:07:04,350 --> 01:07:04,430
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+821
+01:07:04,430 --> 01:07:05,110
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+822
+01:07:05,110 --> 01:07:06,250
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+823
+01:07:07,640 --> 01:07:12,480
+الثاني بتاخده اثنين even نصف وربع بأخذ صوت على
+
+824
+01:07:12,480 --> 01:07:16,560
+المقام even الآن الثالث بتاخده الثلاثة اللي بعده 
+
+825
+01:07:16,560 --> 01:07:21,740
+الـ odd اللي هو ثلث خمس سبع اللي بعده الأربعة اللي
+
+826
+01:07:21,740 --> 01:07:27,340
+بعده الـ even 6 8 10 12 اللي بعده الـ 5 اللي
+
+827
+01:07:27,340 --> 01:07:31,440
+بعده الـ odd 9 11 11 11 13 11 15 11 16 17 اللي
+
+828
+01:07:31,440 --> 01:07:34,300
+بعده الـ 6 الـ even اللي بعده الـ 7 الـ odd وهكذا و
+
+829
+01:07:34,300 --> 01:07:37,840
+نظل ماشيين إلى ما لا نهاية هذه برضه rearrangement 
+
+830
+01:07:37,840 --> 01:07:43,860
+لمين؟ لـ اللي هي الـ series اللي هي summation 1 على
+
+831
+01:07:53,010 --> 01:07:57,590
+التعريف الرياضي يسمى الـ Series يسمى التعريف 
+
+832
+01:07:57,590 --> 01:08:00,790
+الرياضي الرياضي الرياضي الرياضي الرياضي الرياضي
+
+833
+01:08:00,790 --> 01:08:06,170
+الرياضي الرياضي الرياضي الرياضي يعني هذا الـ 
+
+834
+01:08:06,170 --> 01:08:10,510
+bijection عبارة عن إعادة الترتيب من السيريز
+
+835
+01:08:10,510 --> 01:08:16,090
+الأصلية إلى السيريز الجديدة لأن هذه ترتيبها I وهذه
+
+836
+01:08:16,090 --> 01:08:19,770
+ترتيبها F of I صارت بس مدام أن الـ function one to
+
+837
+01:08:19,770 --> 01:08:24,710
+one و onto معناته أن كله هيستخدم الـ terms وكله لا
+
+838
+01:08:24,710 --> 01:08:28,510
+يستخدم إلا مرة واحدة لأن الـ function one to one
+
+839
+01:08:28,510 --> 01:08:30,750
+و onto فصار عند الـ Yم
+
+840
+01:08:36,050 --> 01:08:43,730
+Y1 XF1 Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2 
+
+841
+01:08:43,730 --> 01:08:46,350
+Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2 Y2 XF2
+
+842
+01:08:46,350 --> 01:08:52,210
+Y2 XF2 Y2 XF2 Y2 XF2 ما تأثير الـ Rearrangements على
+
+843
+01:08:52,210 --> 01:08:56,890
+السيريز الأصلية بقولك لو كانت السيريز absolutely 
+
+844
+01:08:56,890 --> 01:09:00,350
+convergent وده اللي هنتطرقله بس لو كانت السيريز
+
+845
+01:09:00,350 --> 01:09:04,250
+absolutely convergent ترتب زي ما بدك مش هتفرق 
+
+846
+01:09:04,250 --> 01:09:08,090
+معانا اللي هو إيه ال convergence يعني let
+
+847
+01:09:08,090 --> 01:09:11,690
+summation xn be an absolutely convergent series in
+
+848
+01:09:11,690 --> 01:09:18,610
+R then any rearrangement of summation xn converge
+
+849
+01:09:18,610 --> 01:09:21,770
+to the same value يعني لو كانت ال series
+
+850
+01:09:21,770 --> 01:09:27,150
+absolutely convergent أي ترتيب لها آخر وفق تعريف
+
+851
+01:09:27,150 --> 01:09:31,390
+الترتيب اللي احنا حكينا عنه اللي هو هيعطي نفس ال
+
+852
+01:09:31,390 --> 01:09:34,510
+limit هتكون converge  وله نفس ال limit خلّينا
+
+853
+01:09:34,510 --> 01:09:38,910
+نشوف البرهان ونمر عليه let summation xn converge
+
+854
+01:09:38,910 --> 01:09:44,410
+to x and let yn be a rearrangement of summation xn
+
+855
+01:09:44,410 --> 01:09:46,590
+and let yn be a rearrangement of summation xn and
+
+856
+01:09:46,590 --> 01:09:46,870
+let yn be a rearrangement of summation xn and 
+
+857
+01:09:46,870 --> 01:09:46,950
+rearrangement of summation xn and let yn be a
+
+858
+01:09:46,950 --> 01:09:47,870
+rearrangement of summation xn and let yn be a
+
+859
+01:09:47,870 --> 01:09:49,130
+rearrangement of summation xn and let yn be a
+
+860
+01:09:49,130 --> 01:09:51,570
+rearrangement of summation xn and let εn be a
+
+861
+01:09:51,570 --> 01:09:51,590
+rearrangement of summation xn and let εn be a
+
+862
+01:09:51,590 --> 01:09:51,690
+rearrangement of summation xn and let εn be a
+
+863
+01:09:51,690 --> 01:09:52,390
+rearrangement of summation xn and let εn be a
+
+864
+01:09:52,390 --> 01:09:55,870
+rearrangement of summation xn and let εn be a
+
+865
+01:09:55,870 --> 01:09:59,130
+rearrangement of summation xn and let εn be a
+
+866
+01:09:59,130 --> 01:10:02,130
+rearrangement of summation xn and let εn be
+
+867
+01:10:07,510 --> 01:10:10,290
+ماذا يعني xn xn xn xn xn xn
+
+868
+01:10:10,290 --> 01:10:10,790
+xn xn xn xn xn xn xn xn
+
+869
+01:10:10,790 --> 01:10:10,850
+xn xn xn xn xn xn xn xn
+
+870
+01:10:10,850 --> 01:10:11,450
+xn xn xn xn xn xn xn xn
+
+871
+01:10:11,450 --> 01:10:12,530
+xn xn xn xn xn xn xn xn
+
+872
+01:10:12,530 --> 01:10:15,790
+xn xn xn xn xn xn xn xn
+
+873
+01:10:15,790 --> 01:10:23,530
+xn xn xn xn xn xn xn xn
+
+874
+01:10:23,530 --> 01:10:30,260
+اكسهو هيعيده كمان مرة الحديث كمان بقول إن ده ما
+
+875
+01:10:30,260 --> 01:10:34,040
+يضمنش إن الـ xn converts إذا لكل y أكبر من 0 there
+
+876
+01:10:34,040 --> 01:10:41,900
+exists n such that fq أكبر من n واللي هي sn x1
+
+877
+01:10:41,900 --> 01:10:50,260
+x2 اللي عند xn then هيكون عندي الـ X K K من عند R
+
+878
+01:10:50,260 --> 01:10:54,540
+زي الواحد عند Q أصغر من مين من إبسلون كانت بطريقة
+
+879
+01:10:54,540 --> 01:10:59,000
+ثانية نتحمل و مهم مش الان الان إيش اللي هي
+
+880
+01:10:59,000 --> 01:11:04,760
+summation X N بساوة مين بساوة X خلاص نعتبرنا اللي
+
+881
+01:11:04,760 --> 01:11:08,320
+هو absolute convergence يعني ونعتبرنا ال terms
+
+882
+01:11:08,320 --> 01:11:12,000
+positive  وخلاص ونشتغل عليها summation X N بساوة
+
+883
+01:11:12,000 --> 01:11:19,230
+مين بساوة X الان for every epsilon أكبر من سفر
+
+884
+01:11:19,230 --> 01:11:25,350
+there exists N such that for every N أو Q سميها
+
+885
+01:11:25,940 --> 01:11:30,460
+أكبر من N أكبر يساوي N عندي اللي هو ال summation
+
+886
+01:11:30,460 --> 01:11:35,240
+هذا اللي هو خلّيني أسميه اللي هو ال sequence of
+
+887
+01:11:35,240 --> 01:11:40,580
+partial sums ل S N اللي هي S N ناقص X أصغر من مين
+
+888
+01:11:40,580 --> 01:11:46,400
+من إبسلون for every N أكبر أو يساوي H N هذا اللي
+
+889
+01:11:46,400 --> 01:11:49,780
+هو ال limit العادية الكوشي criterion لها أنه هيكون
+
+890
+01:11:49,780 --> 01:11:56,890
+عندي ال summation اللي هي S N باخد الـ S N و S Q هو
+
+891
+01:11:56,890 --> 01:12:03,490
+ما ياخد الـ S N ناقص
+
+892
+01:12:03,490 --> 01:12:09,510
+S P لأكبر الـ Q S Q ناقص S N مش مش ممكن أتكلم عن
+
+893
+01:12:09,510 --> 01:12:14,370
+داخل absolute value ناقص S N فبنفع S N اه ما هي
+
+894
+01:12:14,370 --> 01:12:18,480
+صحيحة على كل N أكبر سواء من ضمنها مين؟ N أصغر من
+
+895
+01:12:18,480 --> 01:12:21,940
+مين من إبسلون هذا هذا إيش .. إيش هذا قيمته يساوي
+
+896
+01:12:21,940 --> 01:12:25,700
+summation اللي هو حاطة ال absolute value ماخد ال
+
+897
+01:12:25,700 --> 01:12:30,240
+absolute convergence K من عند N زائد واحد إلى مالة
+
+898
+01:12:30,240 --> 01:12:35,800
+نهائية لعند Q اللي هو أصغر من مين من إبسلون عارفين
+
+899
+01:12:35,800 --> 01:12:39,640
+هذا اه؟ اللي هي أسة Q نقص أسن لأن ماخد ال series
+
+900
+01:12:39,640 --> 01:12:41,620
+إيش صمت absolute value مش مشكلة
+
+901
+01:12:44,600 --> 01:12:48,740
+SN هي الـ sequence of partial sums لهذه للـ
+
+902
+01:12:48,740 --> 01:12:52,140
+absolute values مش للـ XN للـ absolute values فصار
+
+903
+01:12:52,140 --> 01:12:57,620
+عندي الآن استخدام اللي هو limit as a limit و as a
+
+904
+01:12:57,620 --> 01:13:02,760
+convergence to X و استخدامها as a Cauchy criterion
+
+905
+01:13:02,760 --> 01:13:06,840
+ماشي؟ قول ما هي هذه بالنسبة ليها N و هذه بالنسبة
+
+906
+01:13:06,840 --> 01:13:10,880
+ليها N تانية مليش استعملت نفس الـ N؟ take N
+
+907
+01:13:10,880 --> 01:13:17,610
+maximum بين الجهتين بين فعلامين للجهتين طبيعي طيب
+
+908
+01:13:17,610 --> 01:13:21,350
+.. لا
+
+909
+01:13:21,350 --> 01:13:24,510
+والله نستخدم الأسئلة لمين؟ لهذه
+
+910
+01:13:27,810 --> 01:13:30,230
+بطبيعي، ما هو مدانة Absolutely Convergent دا
+
+911
+01:13:30,230 --> 01:13:33,030
+Convergent مدانة Convergent دا مطبقة هذه على مين
+
+912
+01:13:33,030 --> 01:13:35,930
+على الـ Convergence وهذه مطبقة على مين على الـ
+
+913
+01:13:35,930 --> 01:13:38,430
+Absolutely Convergent برضه بنفع .. آه بنفع بناخد
+
+914
+01:13:38,430 --> 01:13:41,570
+اللي هو بطلعله أن واحد هذه وهذا أن اتنين وبناخده
+
+915
+01:13:41,570 --> 01:13:44,010
+من ال maximum للتان تان بيصير لي هذه ال inequality
+
+916
+01:13:44,010 --> 01:13:47,230
+و هذه ال inequality صحيحة .. صحيحات لمين للان اللي
+
+917
+01:13:47,230 --> 01:13:50,720
+هي ال maximum اللي عنده طيب الآن إذا صار عندي هذه
+
+918
+01:13:50,720 --> 01:13:54,120
+الـ Sn بقصود فيها فعلًا اللي هي ال sequence of 
+
+919
+01:13:54,120 --> 01:14:01,060
+partial sums لسيريز الأصلية Xn والـ Sn' هي مين ال
+
+920
+01:14:01,060 --> 01:14:05,400
+sequence اللي هو تبعت ال absolute values هذه طبعا
+
+921
+01:14:05,400 --> 01:14:09,700
+حسبناها as q prime نقص as n prime بساوي هذه نقص
+
+922
+01:14:09,700 --> 01:14:13,060
+هذه من واحد عند q ومن واحد عند n اللي هي بساوي هذه
+
+923
+01:14:13,060 --> 01:14:16,940
+اللي هي هذه حسبناها عارفينها طيب مش هذا الموضوع
+
+924
+01:14:16,940 --> 01:14:23,500
+هذا الأمر سهل يعني إذا صار عندي الآن هي هذه أو هي
+
+925
+01:14:23,500 --> 01:14:32,260
+هذه أو هذه كلها بدي أشوف كيف أستعملها احنا ليش بدنا
+
+926
+01:14:32,260 --> 01:14:36,580
+.. بدنا الـ Series الجديدة Summation Yn اللي هي
+
+927
+01:14:36,580 --> 01:14:40,980
+الـ Rearrangement شوف كده لأن Now let M limited M
+
+928
+01:14:40,980 --> 01:14:45,260
+be such that all of the terms X1 لعند الـ Xm are
+
+929
+01:14:45,260 --> 01:14:52,680
+contained as a sum and in T M Y1 لعند ال Ym إيش
+
+930
+01:14:52,680 --> 01:14:55,820
+اللي بيقولوا هذا؟ وهذا الكلام اللي هو اللي احنا
+
+931
+01:14:55,820 --> 01:14:59,760
+بدنا نتهيئله وهو اللي بيفتحنا الطريق أمام البرهان
+
+932
+01:15:01,400 --> 01:15:09,360
+جالي بيحكيلي انه خلّينا نختار M في الـ N ابحث الـ TM
+
+933
+01:15:09,360 --> 01:15:14,740
+هذه اللي هي الـ Sequence of partial sums لمين للـ YN
+
+934
+01:15:14,740 --> 01:15:20,960
+اللي هي Y1 زائد Y2 زائد YM بقوللي أنا بدأ اختار
+
+935
+01:15:20,960 --> 01:15:29,370
+الـ M هذه على أساس إنه كل ال terms اللي لجيتها من ال
+
+936
+01:15:29,370 --> 01:15:34,310
+N اللي فوق من X1 لعند XN تكون موجودة من بين هدول
+
+937
+01:15:34,310 --> 01:15:37,970
+ال terms بقدر اه بقدر لأن هدول عشمها ال hand
+
+938
+01:15:37,970 --> 01:15:44,210
+finite وفي النهاية مدام finite إذا هيكون من ضمن
+
+939
+01:15:44,210 --> 01:15:49,890
+ال Y1 Y2 إلى 100 ألف ألف مليون سميته ال 100 ألف
+
+940
+01:15:49,890 --> 01:15:54,480
+ألف مليون اللي هو 100 YN إذا الأم اخترتها بناءً
+
+941
+01:15:54,480 --> 01:16:02,060
+على إني أضمن الـ X1 والـ X2 لعند الـ XN تين لعند
+
+942
+01:16:02,060 --> 01:16:06,080
+الـ XN كابيتال تين هدولة من هدول يعني بس إعادة
+
+943
+01:16:06,080 --> 01:16:10,890
+تسميتهم إذا الآن اللي .. اللي .. اللي اخترته انه
+
+944
+01:16:10,890 --> 01:16:15,570
+قلتله let M element in N مهما كانت كبيرة be such
+
+945
+01:16:15,570 --> 01:16:21,510
+that all of the terms X1, X2, XN are contained as
+
+946
+01:16:21,510 --> 01:16:26,610
+a sum and يعني مجموعات من ضمن المجموع هذا Y1 زي Y2
+
+947
+01:16:26,610 --> 01:16:35,330
+عند مين؟ YM it follows الآن if M أكبر أو يساوي M
+
+948
+01:16:36,630 --> 01:16:42,970
+then T M ناقص S M ناقص
+
+949
+01:16:42,970 --> 01:16:48,770
+S M ناقص S M ناقص S M ناقص S M ناقص S M ناقص S M
+
+950
+01:16:48,770 --> 01:16:48,910
+S M ناقص S M ناقص S M ناقص S M ناقص S M ناقص S M
+
+951
+01:16:48,910 --> 01:16:48,970
+ناقص S M ناقص S M ناقص S M ناقص S M ناقص S M ناقص
+
+952
+01:16:48,970 --> 01:16:49,030
+S M ناقص S M ناقص S M ناقص S M ناقص S M ناقص S M
+
+953
+01:16:49,030 --> 01:16:49,850
+ناقص S M ناقص S M ناقص S M ناقص S M ناقص S M ناقص
+
+954
+01:16:49,850 --> 01:16:54,450
+S M ناقص S M ناقص S
+
+955
+01:16:56,000 --> 01:16:58,900
+ممكن اللي عندها وممكن يظل معاها عندها نور على نور
+
+956
+01:16:58,900 --> 01:17:04,620
+يعني بدنا نشيل منه مين ال S N ال S N ال N هذه
+
+957
+01:17:04,620 --> 01:17:11,220
+شمالها أكبر من مين أكبر أو تساوي ال N طيب إذا هذه
+
+958
+01:17:11,220 --> 01:17:21,340
+هيكون consist of finite sum of terms X K with K
+
+959
+01:17:21,340 --> 01:17:24,600
+أكبر من مين من ال N
+
+960
+01:17:29,340 --> 01:17:37,280
+الان من عند الواحد لعند الان انا شيلتهم من ال T M
+
+961
+01:17:37,280 --> 01:17:47,000
+باشي اه ال S N هذه واحد اتنين لعند اللي هي ال N و
+
+962
+01:17:47,000 --> 01:17:53,840
+جلطتها لأن ال N ايه شمالها اكبر او يساوي M N اكبر
+
+963
+01:17:53,840 --> 01:17:58,980
+او يساوي M ماشي طيب صار عندي ال N ال TM انشال منها
+
+964
+01:17:58,980 --> 01:18:05,180
+ال X1 وال X2 وال XN اه اذا اللي ضلن من ال terms
+
+965
+01:18:05,180 --> 01:18:10,940
+هذه او ماينة اللي هنا موجودة ال TM اللي موجودة هنا
+
+966
+01:18:10,940 --> 01:18:20,090
+اللي فيها اكيد هيكون بعد ال N اللي ضلنا ماشي؟ لأنه
+
+967
+01:18:20,090 --> 01:18:24,770
+شيلت منه لإن عندك S1 لإن عندك S2 و هذه S N ضال
+
+968
+01:18:24,770 --> 01:18:31,090
+منها من اللي بعد ال N برضه إذا في النهاية ال terms
+
+969
+01:18:31,090 --> 01:18:36,790
+اللي هنا هيكون اللي بيحتوي على sums of terms ل X K
+
+970
+01:18:36,790 --> 01:18:42,250
+و ال K هيكون أكبر من 100 من ال N لإن اللي ترتيبه
+
+971
+01:18:42,250 --> 01:18:45,770
+من ال N و اتنازل كله راح من عملية الطرح هذه
+
+972
+01:18:49,100 --> 01:18:55,660
+اذا for some q أكبر من n we have Tm ناقص Tn هذا
+
+973
+01:18:55,660 --> 01:19:00,820
+absolute value بساوى ال summation لل X K كي من
+
+974
+01:19:00,820 --> 01:19:06,420
+وين؟ من n زائد واحد لعند مين؟ لعند Q ليش؟ لأنه انا
+
+975
+01:19:06,420 --> 01:19:10,320
+شيلت كل العناصر اللي هي انها من عند X1 لعند Xn
+
+976
+01:19:10,320 --> 01:19:14,600
+اللي هي من هنا ماضلش فيها ولا إشي إذا إذا بده يضل
+
+977
+01:19:14,600 --> 01:19:17,940
+مجموح هذا هيكونه تضل المجموع اللي هو من N زائد
+
+978
+01:19:17,940 --> 01:19:21,520
+واحد وطالع لوين مش عارف ماتفرجش معايا ان شاء الله
+
+979
+01:19:21,520 --> 01:19:25,480
+يضلوا لـ 100 ألف ألف ألف مليون بعدها المهم من بعد
+
+980
+01:19:25,480 --> 01:19:33,930
+ال N زائد واحد لعند Q XK أصغر من مين من Y ماشيلش 
+
+981
+01:19:33,930 --> 01:19:39,150
+أصغر من إبسلون؟ لأن هذا دائماً أصغر من إبسلون لكل
+
+982
+01:19:39,150 --> 01:19:45,630
+QH أكبر من H من N سواء الـQ هذه أو الـQ الأكبر 
+
+983
+01:19:45,630 --> 01:19:53,010
+منها إيش ضمنك أن هذا Q أكبر من هذا؟ أنا لما اخترت
+
+984
+01:19:53,010 --> 01:19:56,030
+شيلت كل الـ terms، ضلت الـ terms اللي بعد الـ N
+
+985
+01:19:56,030 --> 01:19:59,210
+capital لما شيلتها منها طيب، إذن أكيد الـQ هذه
+
+986
+01:19:59,210 --> 01:20:04,780
+أكبر من الـ N الآن نُلخّص المعلومات اللي هنستخدمها
+
+987
+01:20:04,780 --> 01:20:08,180
+Therefore if M أكبر أو يساوي N, if M أكبر أو يساوي N,
+
+988
+01:20:08,500 --> 01:20:12,440
+we have الـTM ناقص الـ X أصغر من الـ triangle
+
+989
+01:20:12,440 --> 01:20:16,840
+equality TM ناقص SN زي SN ناقص EH ناقص X هذا يقول
+
+990
+01:20:16,840 --> 01:20:20,560
+إنه أصغر من مين؟ من هنا من إبسلون طيب الـ SN ناقص X
+
+991
+01:20:21,200 --> 01:20:24,260
+اللي هو برضه هتكون إيه؟ شمالها أصغر من إبسلون لإنه
+
+992
+01:20:24,260 --> 01:20:28,180
+هذا أثبتناها صحيحة لكل N أكبر أو يساوي N وهذه الـN
+
+993
+01:20:28,180 --> 01:20:32,040
+هي أكبر أو يساوي N إذا صار عندنا أكبر أو يساوي N إذا 
+
+994
+01:20:32,040 --> 01:20:34,580
+الـN أكبر أو يساوي N capital إذا صار هذا أصغر من
+
+995
+01:20:34,580 --> 01:20:36,960
+إبسلون زي إبسلون أصغر من اثنين إبسلون إذا صار عندنا
+
+996
+01:20:36,960 --> 01:20:41,620
+الـTM ناقص X أصغر من اثنين إبسلون لكل M أكبر أو
+
+997
+01:20:41,620 --> 01:20:50,260
+يساوي N وهذا يعني أنه اللي هي الـ summation هذي طبعاً
+
+998
+01:20:50,260 --> 01:20:53,600
+هي عبارة عن sequence of partial sums للـ YM صحيح الـ
+
+999
+01:20:53,600 --> 01:20:57,380
+summation للـ YM converge  و converge to X
+
+1000
+01:20:57,380 --> 01:21:00,940
+وبهيك بيكون احنا انهينا هنا اللي هو الـ section
+
+1001
+01:21:00,940 --> 01:21:03,680
+الأول في شبط التسعة وإلى لقاكم
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..795cdcf678e4076c1067f0c838ae8a827c695fb0
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM.srt
@@ -0,0 +1,2419 @@
+1
+00:00:05,280 --> 00:00:12,080
+بسم الله الرحمن الرحيم المحاضرة الرابعة مساق تحليل
+
+2
+00:00:12,080 --> 00:00:18,780
+حقيقة 2 لطلبة الجامعة الإسلامية كلية العلوم قسم
+
+3
+00:00:18,780 --> 00:00:26,480
+الرياضيات نستكمل الحديث عن نظرية القيمة المتوسطة
+
+4
+00:00:26,480 --> 00:00:33,380
+أو the mean value theorem وما يتعلق بذلك تحدثنا
+
+5
+00:00:33,380 --> 00:00:40,130
+المرة الماضية عن معنى relative extrema سواء relative
+
+6
+00:00:40,130 --> 00:00:43,290
+maximum أو relative minimum أو بمعنى آخر ال
+
+7
+00:00:43,290 --> 00:00:47,450
+local maximum و ال local minimum
+
+8
+00:00:47,450 --> 00:00:53,910
+وعرفناها المرة الماضية وتحدثنا أيضًا عن اللي هو
+
+9
+00:00:53,910 --> 00:00:58,650
+ال interior extreme theorem ال interior extreme
+
+10
+00:00:58,650 --> 00:01:03,430
+theorem اللي هي جاوبتنا على السؤال اللي بنحكي فيه
+
+11
+00:01:03,770 --> 00:01:09,170
+أين يمكن إيجاد القيم العظمى أو القيم الصغرى
+
+12
+00:01:09,170 --> 00:01:14,730
+النظرية اللي بتحكي كانت إن لو كانت C عبارة عن
+
+13
+00:01:14,730 --> 00:01:20,610
+interior point اللي هي في ال interval I اللي عندها
+
+14
+00:01:20,610 --> 00:01:27,220
+اللي هي ال function F ال derivative موجودة بقول لو
+
+15
+00:01:27,220 --> 00:01:32,140
+كان عند النقطة هذه في relative extremum سواء
+
+16
+00:01:32,140 --> 00:01:36,740
+minimum أو maximum للـ F عنده نقطة C  قطعا الـ F 
+
+17
+00:01:36,740 --> 00:01:42,900
+prime of C هتساوي 0 ومن هنا استقينا أن أين يمكن
+
+18
+00:01:42,900 --> 00:01:48,060
+إيجاد النقطة العظمى والنقطة الصغرى المحلية وقلنا
+
+19
+00:01:48,060 --> 00:01:52,480
+هي في أحد ثلاث مناطق اللي هو أما الـ F prime بتساوي 0
+
+20
+00:01:53,060 --> 00:01:58,080
+أو الـ F prime does not exist للنقاط الداخلية طبعا أو
+
+21
+00:01:58,080 --> 00:02:02,120
+اللي هو ال end points فثلاث مناطق اللي هي بنفحص
+
+22
+00:02:02,120 --> 00:02:07,360
+فيها اللي هي ال relative maximum أو ال relative
+
+23
+00:02:07,360 --> 00:02:11,400
+minimum والـ Corollary اللي بعدها اللي حكيته عنه
+
+24
+00:02:11,400 --> 00:02:16,400
+قبل بشوية الآن وبعدين تحدثنا .. بدنا نتحدث على
+
+25
+00:02:16,400 --> 00:02:21,180
+الـ Rolle's theorem وقولنا الـ Rolle's theorem اللي هي
+
+26
+00:02:21,180 --> 00:02:25,840
+كانت بتعالج أنه لو كانت عندي function F من عند A و
+
+27
+00:02:25,840 --> 00:02:31,880
+B لعند R وكانت هذه ال function is continuous على
+
+28
+00:02:31,880 --> 00:02:37,830
+closed interval اللي هي من a لعند b و
+
+29
+00:02:37,830 --> 00:02:42,030
+differentiable على ال open interval من a ل b  و أيضا
+
+30
+00:02:42,030 --> 00:02:47,230
+وضعنا شرط أن f of a بيساوي f of b بيساوي صفر
+
+31
+00:02:47,230 --> 00:02:54,210
+بقولنا الـ f differentiable on a وb والـ F
+
+32
+00:02:54,210 --> 00:03:00,110
+continuous on A وB كله مع بعض هذا أعطانا أنه there
+
+33
+00:03:00,110 --> 00:03:05,130
+exists C element in A وB بنلاقي النقطة C بين A وB
+
+34
+00:03:05,130 --> 00:03:10,530
+بحيث أن يكون ميل المماس عندها يساوي صفر أو الـ F prime
+
+35
+00:03:10,530 --> 00:03:16,370
+of C بساوي صفر أو بمعنى آخر يوجد مماس عند هذه
+
+36
+00:03:16,370 --> 00:03:22,030
+النقطة يوازي محور الـ x بعد ذلك طبعا تحدثنا عن
+
+37
+00:03:22,030 --> 00:03:27,650
+الـ Mean Value Theorem الـ Mean Value Theorem اللي
+
+38
+00:03:27,650 --> 00:03:31,710
+كانت أيضا على الرسم خلينا نشوف الـ Mean Value
+
+39
+00:03:31,710 --> 00:03:35,590
+Theorem قالت إن لو كانت الـ function is continuous
+
+40
+00:03:35,590 --> 00:03:40,750
+على closed interval من A لB وكانت اللي هي
+
+41
+00:03:40,750 --> 00:03:43,470
+differentiable على الـ open interval A وB
+
+42
+00:03:49,160 --> 00:03:57,260
+الآن الاستنتاج اللي بيكون تعميم لـ Rolle's theorem
+
+43
+00:03:57,260 --> 00:04:03,350
+إيش هو الاستنتاج إن بنلاقي نقطة في المنطقة بين A و
+
+44
+00:04:03,350 --> 00:04:10,890
+B بكون المماس عندها موازيا للقاطع اللي بين مين الـ
+
+45
+00:04:10,890 --> 00:04:14,850
+A والـ B أو بمعنى آخر بكون عند النقطة C اللي
+
+46
+00:04:14,850 --> 00:04:21,890
+لايجناها اللي هي الـ F prime of C بساوي F of B minus F
+
+47
+00:04:21,890 --> 00:04:29,310
+of A على B minus A وهذا هو الذي يمثل ميل القاطع بين
+
+48
+00:04:29,310 --> 00:04:34,170
+النقطة A أو بين النقطة B أو بين النقطة A و F of A
+
+49
+00:04:34,170 --> 00:04:38,430
+ونقطة B و F of B فبتكون هذه عبارة عن نظرية القيمة
+
+50
+00:04:38,430 --> 00:04:44,030
+المتوسطة اللي هي تعميم لـ Rolle's theorem بعدها
+
+51
+00:04:44,030 --> 00:04:51,790
+تحدثنا عن اللي هو بعض النتائج قلنا إن لو كانت الـ
+
+52
+00:04:51,790 --> 00:04:56,930
+function F continuous على closed interval I وكانت
+
+53
+00:04:56,930 --> 00:05:00,410
+F differentiable على ال open interval وكانت اللي
+
+54
+00:05:00,410 --> 00:05:05,090
+هي الـ F prime بتساوي 0 على كل الفترة A وB قلنا هذه
+
+55
+00:05:05,090 --> 00:05:09,430
+الدالة هي الدالة الثابتة هتكون The F is constant
+
+56
+00:05:09,430 --> 00:05:16,400
+على الفترة المغلقة A أو B أيضا Corollary لهذه
+
+57
+00:05:16,400 --> 00:05:20,840
+النظرية برضه اللي هي معلومات معهودة من ال calculus
+
+58
+00:05:20,840 --> 00:05:26,340
+اللي هي أنه لو كان في عندنا دالتين F و G وهذولة
+
+59
+00:05:26,340 --> 00:05:30,600
+الدالتين اللي عندنا اللي هن .. اللي هن نفس المشتقة
+
+60
+00:05:30,600 --> 00:05:36,380
+على الفترة A و B open بكون عندي الفرق بين اللي هي
+
+61
+00:05:36,380 --> 00:05:39,460
+الـ F والـ G هو عبارة عن ثابت أو بمعنى آخر F
+
+62
+00:05:39,460 --> 00:05:44,880
+بتساوي G زائد C for some constant C على الفترة I
+
+63
+00:05:44,880 --> 00:05:51,160
+بعد هيك اللي دخلنا وعرفنا شو معنى F من I لعند R
+
+64
+00:05:51,160 --> 00:05:55,780
+is increasing على ال interval قلنا أن F is
+
+65
+00:05:55,780 --> 00:06:03,570
+increasing إذا كانت اللي هي أخذنا أي نقطتين في الـ
+
+66
+00:06:03,570 --> 00:06:09,870
+I X1 وX2  بتحقق إن X1 أصغر من X2 إذا قدنا هذا أن
+
+67
+00:06:09,870 --> 00:06:13,430
+f of X1 أصغر أو يساوي f of X2 من جهة عن ال function
+
+68
+00:06:13,430 --> 00:06:19,430
+اللي شمالها is increasing الآن اللي هو similar لتعريف
+
+69
+00:06:19,430 --> 00:06:24,190
+الـ decreasing إن X1 أصغر من X2 تؤدي إلى F of X1
+
+70
+00:06:24,190 --> 00:06:29,230
+أكبر أو يساوي F of X2 بتكون اليد اللي شمالها
+
+71
+00:06:29,230 --> 00:06:33,970
+is decreasing على هذه الفترة في المقابل أيضًا في
+
+72
+00:06:33,970 --> 00:06:36,810
+تعريف حاجة اسمها برضه ذكرناه هو strictly
+
+73
+00:06:36,810 --> 00:06:40,230
+increasing أو strictly decreasing strictly
+
+74
+00:06:40,230 --> 00:06:44,070
+increasing أو strictly decreasing نحكي عن ال
+
+75
+00:06:44,070 --> 00:06:48,610
+strictly increasing بتكون اللي هي بتحقق مالي لو x1
+
+76
+00:06:48,610 --> 00:06:54,590
+وx2 في ال I وx1 أصغر من x2 هذا بيقودني إلى f of
+
+77
+00:06:54,590 --> 00:07:00,530
+x1 strictly أصغر من f of x2 مع عدم إمكانية
+
+78
+00:07:00,530 --> 00:07:06,340
+المساو الان similarly for الـ F is اللي هو
+
+79
+00:07:06,340 --> 00:07:10,820
+strictly decreasing هذا تحدثنا فيه المرة الماضية
+
+80
+00:07:10,820 --> 00:07:14,240
+النظرية
+
+81
+00:07:14,240 --> 00:07:17,860
+اللي هي let F من I لعند R be differentiable اللي
+
+82
+00:07:17,860 --> 00:07:23,100
+هي أوصلنا عند هذه النظرية خلينا نشوف هذه النظرية و
+
+83
+00:07:23,100 --> 00:07:30,900
+نتفحص إيش هي النظرية بتقول ومن ثم نشوف لماذا اللي هو
+
+84
+00:07:30,900 --> 00:07:38,960
+هي صحيحة عندي
+
+85
+00:07:38,960 --> 00:07:46,440
+النظرية بتقول لي theorem 6.2.7 اللي بتحكي النظرية
+
+86
+00:07:46,440 --> 00:07:54,580
+بتقول لي لو كان عندي F let F من I لعند R be
+
+87
+00:07:54,580 --> 00:08:05,490
+differentiable on the interval .. the interval I
+
+88
+00:08:05,490 --> 00:08:11,910
+فرضنا إن F is differentiable على ال interval I الآن
+
+89
+00:08:11,910 --> 00:08:17,690
+اللي بدأ أقوله عبارة عن test بنستعمل ال test في
+
+90
+00:08:17,690 --> 00:08:22,030
+معرفة إن F is increasing أو لا و F is decreasing
+
+91
+00:08:22,030 --> 00:08:27,530
+أو لا بنقول F is increasing
+
+92
+00:08:29,130 --> 00:08:36,650
+on I إيش الفحص؟ if and only if F prime of X أكبر
+
+93
+00:08:36,650 --> 00:08:44,130
+أو يساوي صفر لكل X موجودة في الـ I والآن F is
+
+94
+00:08:44,130 --> 00:08:52,450
+decreasing on I if and only if F prime of X أصغر
+
+95
+00:08:52,450 --> 00:08:57,750
+أو يساوي صفر لكل X element in I هذه هي النظرية
+
+96
+00:08:57,750 --> 00:09:04,430
+اللي عندنا وهنبرهن اللي هو A أو B في الكتاب نبرهن
+
+97
+00:09:04,430 --> 00:09:09,370
+A خلّينا نبرهن مين نبرهن B وهتكون A similarly for
+
+98
+00:09:09,370 --> 00:09:17,550
+B الآن بي .. بدنا نفترض suppose that
+
+99
+00:09:17,550 --> 00:09:30,710
+F is decreasing on I F is decreasing on I بدنا ..
+
+100
+00:09:30,710 --> 00:09:36,650
+بدنا نثبت الآن أن الـ F prime of X اللي هي أصغر أو
+
+101
+00:09:36,650 --> 00:09:43,190
+يساوي مين صفر طبعاً F prime of X في النهاية إيش
+
+102
+00:09:43,190 --> 00:09:47,930
+هي؟ عشان نشوف كيف بنفكر أول شيء F prime of X بساوي
+
+103
+00:09:47,930 --> 00:09:55,080
+limit F of X أو f prime of c مثلا for arbitrary c f
+
+104
+00:09:55,080 --> 00:10:00,820
+of x نقص f of c على x minus c لما x تروح لل c إذا
+
+105
+00:10:00,820 --> 00:10:05,520
+ال limit هذا أثبتناه أصغر أو يساوي صفر معناته صارت
+
+106
+00:10:05,520 --> 00:10:12,030
+اللي هي ال f prime أصغر أو يساوي صفر الآن عندي أنا
+
+107
+00:10:12,030 --> 00:10:16,990
+لو أثبتت هذا المقدار أصغر أو يساوي صفر في المنطقة
+
+108
+00:10:16,990 --> 00:10:20,870
+حول الـ C بقدر أقول إن ال limit على طول إيه شماله
+
+109
+00:10:20,870 --> 00:10:27,550
+أصغر أو يساوي إيه صفر ده نشوف كيف عندي الآن بدي
+
+110
+00:10:27,550 --> 00:10:32,170
+أثبت إنها هذه F prime أصغر أو يساوي صفر على كل X
+
+111
+00:10:32,170 --> 00:10:39,450
+element in I بدي أقول let C be an arbitrary
+
+112
+00:10:41,100 --> 00:10:47,160
+and fixed in I يعني بتحكي عنها عن C لكن هي
+
+113
+00:10:47,160 --> 00:10:54,780
+arbitrary لكن بحكي عن C معينة الآن عندي يا X أكبر
+
+114
+00:10:54,780 --> 00:11:01,800
+من C يا X شمالها أصغر من C ماشي الحال ليش أخذت
+
+115
+00:11:01,800 --> 00:11:04,160
+أكبر أو أصغر؟ لأن عمّالي بآخد limit فالـ X ده
+
+116
+00:11:04,160 --> 00:11:09,060
+بتساوي C في حالة الـ C اللي هو الأمر اللي هيكون
+
+117
+00:11:09,060 --> 00:11:13,180
+اللي هي عبارة
+
+118
+00:11:13,180 --> 00:11:17,520
+عن الـ trivial case نشوف كيف، إيش اللي بنحكيه؟
+
+119
+00:11:17,520 --> 00:11:23,440
+الآن X أكبر من C عندي إيش مفترضين إحنا؟ F is
+
+120
+00:11:23,440 --> 00:11:30,920
+decreasing لذا then F of X أصغر أو يساوي F of C
+
+121
+00:11:30,920 --> 00:11:38,100
+مظبوط أه بيصير عندي الحسب اللي كتبته قبل وشوية F
+
+122
+00:11:38,100 --> 00:11:47,680
+of X نقص F of C اللي هو بساوي على X minus C اللي
+
+123
+00:11:47,680 --> 00:11:52,290
+هو هذا سالب f of x نقص f of z أصغر أو أكبر من صفر و
+
+124
+00:11:52,290 --> 00:11:57,110
+ال x minus z شماله أكبر من صفر هذا الآن أكبر
+
+125
+00:11:57,110 --> 00:12:02,650
+أو سالب أو صفر وهذا موجب إذا حيكون أصغر أو يساوي إيش
+
+126
+00:12:02,650 --> 00:12:08,760
+صفر واضح أه Similarly الحالة الثانية من X هذا لكل
+
+127
+00:12:08,760 --> 00:12:12,800
+الـ Xات اللي مين اللي أكبر من C طبعا والـ Xات أنا من
+
+128
+00:12:12,800 --> 00:12:16,740
+وين باخدها من I على كل شغلي في داخل من ال interval
+
+129
+00:12:16,740 --> 00:12:21,320
+I يعني Xات اللي بشتغل فيها داخل I الآن X أصغر من C
+
+130
+00:12:21,320 --> 00:12:24,900
+أكيد similarly بنفس الطريقة مدام ال decreasing
+
+131
+00:12:24,900 --> 00:12:31,580
+بيصير F of X أكبر أو يساوي F of C بيصير عندي الآن
+
+132
+00:12:31,580 --> 00:12:40,060
+إذا F of X نقص F of C وهو موجب وهذه X minus C
+
+133
+00:12:40,060 --> 00:12:44,880
+سالب إذا هذولة على X minus C برضه هتطلع إيه
+
+134
+00:12:44,880 --> 00:12:49,720
+شمالها أصغر أو يساوي صفر إذا صار عندي من الجهتين
+
+135
+00:12:49,720 --> 00:12:55,660
+هنا for any X
+
+136
+00:12:55,660 --> 00:13:03,040
+element in I وX لا تساوي C أنا أصلا ملزمني حوالين
+
+137
+00:13:03,040 --> 00:13:09,810
+الـ C لكن هذا كله كلام صحيح لـ X ∈ I X ≤ C طالع
+
+138
+00:13:09,810 --> 00:13:17,350
+عندي اللي هو F of X نقص F of C على X minus C أصغر
+
+139
+00:13:17,350 --> 00:13:23,610
+أو يساوي 0 الآن مدام هذا صحيح لكل X إذا ال limit هذا
+
+140
+00:13:23,610 --> 00:13:27,530
+المقدار لما X تروح للـ C برضه هيظل أصغر أو يساوي 
+
+141
+00:13:27,530 --> 00:13:33,950
+سفر وهذا هو إيش اسمه F prime of C يعني أثبتنا F 
+
+142
+00:13:33,950 --> 00:13:38,530
+prime of C أصغر أو يساوي السفر وعند C كانت
+
+143
+00:13:38,530 --> 00:13:42,550
+arbitrary and fixed in I إذا صار بناء على هذا
+
+144
+00:13:42,550 --> 00:13:49,050
+الحديث صار F prime of X أصغر أو يساوي سفر لكل X 
+
+145
+00:13:49,050 --> 00:13:54,760
+element in I لأنه كانت C is arbitrary هذا اللي هو
+
+146
+00:13:54,760 --> 00:14:00,440
+الجزء الأول من النظرية من اللي هو B أنه بدنا الأن
+
+147
+00:14:00,440 --> 00:14:03,180
+نيجي ل conversely بدنا نفترض هذا أصحى و أصحى و صفر
+
+148
+00:14:03,180 --> 00:14:09,040
+و نوصل لمين لل F is decreasing نيجي الأن
+
+149
+00:14:09,040 --> 00:14:19,240
+conversely و نشوف كيف نبرهن conversely الأن
+
+150
+00:14:19,240 --> 00:14:25,030
+conversely طبعاً ببرهن في AVP برضه أنا conversely
+
+151
+00:14:25,030 --> 00:14:30,810
+suppose that
+
+152
+00:14:32,170 --> 00:14:39,270
+F prime of X أصغر أو يساوي سفر لكل X موجودة في الآية
+
+153
+00:14:39,270 --> 00:14:43,790
+ماشي الحال شوفوا صلى الله عليه الصلاة والسلام أنا
+
+154
+00:14:43,790 --> 00:14:47,810
+بدأ أثبت أن F is decreasing يعني بدأ أفترض أن X 
+
+155
+00:14:47,810 --> 00:14:53,650
+أصغر أو أخد أي قيمتين X واحد و X اتنين element
+
+156
+00:14:53,650 --> 00:14:59,250
+اتنينأخدت أي two elements element x1 وx2 element
+
+157
+00:14:59,250 --> 00:15:06,850
+in I تحقق such that x1 أصغر من مين من x2 أصغر أو
+
+158
+00:15:06,850 --> 00:15:10,570
+يساوي x .. x1 أصغر أو يساوي x2 بس في حالة ال x1 
+
+159
+00:15:10,570 --> 00:15:14,490
+بيساوي x2 ما هي automatic F of x1 بيساوي F of x2
+
+160
+00:15:14,490 --> 00:15:19,920
+يعني متحققةإذن الان x1 أصغر من x2 عملتها strictly 
+
+161
+00:15:19,920 --> 00:15:23,720
+عشان بتعمل منها interval وحالتي ال x1 بيساوي x2 is
+
+162
+00:15:23,720 --> 00:15:28,000
+a trivial case تتحقق مدامة x1 أصغر تساوي x2 إذن 
+
+163
+00:15:28,000 --> 00:15:32,100
+عشان a function f of x1 بيساوي f of x2 إذا التحقق
+
+164
+00:15:32,100 --> 00:15:39,340
+اللي هي مين ال decreasing واضحة الان x1 أصغر من x2
+
+165
+00:15:39,340 --> 00:15:41,620
+الآن we apply
+
+166
+00:15:45,100 --> 00:15:48,880
+الـ Mean Value Theorem لأن احنا هذه نبارع كورولرز
+
+167
+00:15:48,880 --> 00:15:52,380
+أو نظريات على الـ Mean Value Theorem فالمتوقع أن
+
+168
+00:15:52,380 --> 00:15:55,240
+نستخدم الـ Mean Value Theorem في أثباتها فهنا
+
+169
+00:15:55,240 --> 00:15:59,000
+سنستخدم الـ Mean Value Theorem نطبق الـ Mean Value
+
+170
+00:15:59,000 --> 00:16:05,470
+Theorem على الانترفل الموجود بين X1 و X2 طبعاً عندي 
+
+171
+00:16:05,470 --> 00:16:10,330
+F هذه X1 و X2 عبارة عن جزئية من مين؟ من الـ I إذا 
+
+172
+00:16:10,330 --> 00:16:12,790
+الـ F is differentiable عليها مادام differentiable
+
+173
+00:16:12,790 --> 00:16:16,050
+إذا continuous علي close و differentiable علي open
+
+174
+00:16:16,050 --> 00:16:19,240
+لإنها differentiable علي كلها إذا شروط الـ Mean
+
+175
+00:16:19,240 --> 00:16:24,580
+Value Theorem مالها متحققة إذا there exist then
+
+176
+00:16:24,580 --> 00:16:31,060
+there exist C تنتمي إلى الفترة X1 و X2 يعني موجودة
+
+177
+00:16:31,060 --> 00:16:35,220
+في الـ I اللي هي لإن هذي جزئية من مين من I there
+
+178
+00:16:35,220 --> 00:16:43,480
+exist C such that F prime of C بساوي F of X1 أو F 
+
+179
+00:16:43,480 --> 00:16:55,670
+of X2 ناقصF of X1 على X2 ناقص X1 واضح أه؟ أضرب
+
+180
+00:16:55,670 --> 00:17:00,510
+طرفين في وسطين أضرب هذه في هذه بيصير عندي F of X2 
+
+181
+00:17:00,510 --> 00:17:08,170
+ناقص F of X1 اللي هو بيساوي X2 ناقص X1 في F prime
+
+182
+00:17:08,170 --> 00:17:16,190
+of C الآن عندي X2 ناقص X1 موجبة مظبوط؟ و F prime of 
+
+183
+00:17:16,190 --> 00:17:20,290
+C اللي هي سالبة لإنه C واحدة من نقاط ال I و F
+
+184
+00:17:20,290 --> 00:17:24,890
+prime أصغر من سفر فيها كلها إذا صار عندي هذه سالبة
+
+185
+00:17:24,890 --> 00:17:30,150
+و هذه موجبة إذا حاصل ضربهم إيه شماله أصغر أو يساوي 
+
+186
+00:17:30,150 --> 00:17:40,640
+سفر إذا صار عندي F of X2 أصغر أو يساوي Fof X1 الان
+
+187
+00:17:40,640 --> 00:17:45,900
+بدنا ب X1 أصغر من X2 وانتهينا ب F of X2 أصغر من F 
+
+188
+00:17:45,900 --> 00:17:51,260
+of X1 but .. but .. but .. احنا بنعرف خلينا نكملها
+
+189
+00:17:51,260 --> 00:17:56,300
+كدا من اللي حكيناه في الأول X2 بيساوي X1 implies F
+
+190
+00:17:56,300 --> 00:18:04,100
+of X2 بتساوي F of X1 مظبوط؟ الان من هذه اللي عندي
+
+191
+00:18:04,100 --> 00:18:10,460
+الحقيقة هذه ومن اللي أثبتته من هنا لعند هنا التنتين
+
+192
+00:18:10,460 --> 00:18:20,280
+together بنستنتج أنه if x1 أصغر أو يساوي x2 then f
+
+193
+00:18:20,280 --> 00:18:23,660
+of x2 
+
+194
+00:18:23,660 --> 00:18:32,800
+أصغر أو يساوي fof x واحد هذا فيضوء أن f prime of x 
+
+195
+00:18:32,800 --> 00:18:37,220
+أصغر أو أشهر أو شفر لكل x element in I وهذا يعني
+
+196
+00:18:37,220 --> 00:18:50,740
+أن hence f is decreasing on mean on I واضح طيب
+
+197
+00:18:50,740 --> 00:18:58,280
+الآن بدنا نعرف حاجة اسمها Strictly increasing 
+
+198
+00:18:58,280 --> 00:19:04,300
+Strictly increasing قبل شوية قلتها أنه بنقول أن F 
+
+199
+00:19:04,300 --> 00:19:09,140
+is strictly increasing إذا كانت اللي هي strictly 
+
+200
+00:19:09,140 --> 00:19:14,600
+increasing بديش أمسح حد لإن أنا اللي بديه بعد شوية
+
+201
+00:19:14,600 --> 00:19:23,720
+خليني أمسح النظرية برهنة بيه أنا هو ماشي بدي بس من
+
+202
+00:19:23,720 --> 00:19:30,890
+الآن X بنقول Fis strictly increasing إيش معناته
+
+203
+00:19:30,890 --> 00:19:38,470
+إنه X هنا يكافئ إن X1 أصغر من X2 لل X1 وال X2 اللي 
+
+204
+00:19:38,470 --> 00:19:46,790
+في I such that يؤدي F of X1 strictly أصغر من F of 
+
+205
+00:19:46,790 --> 00:19:53,580
+X2 هذا يعني على بعضه إن F is strictly increasing
+
+206
+00:19:53,580 --> 00:19:58,440
+similarly for decreasing for strictly decreasing f 
+
+207
+00:19:58,440 --> 00:20:04,360
+is strictly decreasing لما x1 أصغر من x2 تؤدي إلى 
+
+208
+00:20:04,360 --> 00:20:10,160
+f of x1 أكبر strictly من مين من f of x2 هذا معناته
+
+209
+00:20:10,160 --> 00:20:16,640
+strictly أيش decreasing الآن السؤال اللي بطرحه 
+
+210
+00:20:16,640 --> 00:20:23,380
+الآن هو بقولني إن انت حكيت في حالة الـ increasing F
+
+211
+00:20:23,380 --> 00:20:27,980
+is increasing in I if and only if F' أصغر أوي
+
+212
+00:20:27,980 --> 00:20:31,960
+يساوي 0 لكل X element in I بقول لي هل هذا الكلام 
+
+213
+00:20:31,960 --> 00:20:37,020
+بضل صحيح في حالة ال strictly increasing يعني لو
+
+214
+00:20:37,020 --> 00:20:43,480
+كانت بسأل السؤال لو كانت F is strictly 
+
+215
+00:20:45,290 --> 00:20:49,790
+increasing او decreasing اللي بدك هي increasing او
+
+216
+00:20:49,790 --> 00:20:57,630
+decreasing هل هذا بيكون if and only if F prime of
+
+217
+00:20:57,630 --> 00:21:04,270
+X أصغر strictly من 0 لكل X element in I ولا لأ؟ 
+
+218
+00:21:04,270 --> 00:21:12,010
+الآن لو كان F prime أصغر strictly من 0 ل X element 
+
+219
+00:21:12,010 --> 00:21:17,620
+in I اللي هو الـ conversely هذا اللي هو بيعطينا F's 
+
+220
+00:21:17,620 --> 00:21:22,620
+strictly decreasing يعني الاتجاه هذا متوقعين أنه 
+
+221
+00:21:22,620 --> 00:21:27,500
+إحنا إيه شماله يكون صحيح يعني متوقعين أنه لو F 
+
+222
+00:21:27,500 --> 00:21:31,520
+prime أصغر strictly من Zero لكل X element of I
+
+223
+00:21:31,520 --> 00:21:36,260
+يعطينا F's strictly أشماله decreasing و زيه برضه الـ 
+
+224
+00:21:36,260 --> 00:21:41,580
+increasing لو كانت F' أكبر strictly من 0 بيعطينا F 
+
+225
+00:21:41,580 --> 00:21:46,380
+is strictly increasing هذا متوقع أن يكون صحيح
+
+226
+00:21:46,380 --> 00:21:53,440
+و البرهان هيه موجود علّه لسه ما شطبطوش لسه الآن بدأ
+
+227
+00:21:53,440 --> 00:21:56,780
+افترض أنه بدل ما هي أكبر أصغر أو أسعار بدأ افترضها
+
+228
+00:21:56,780 --> 00:22:02,500
+أشمالها Strictly أصغر ماشي الحال الان بفترض ان X1 
+
+229
+00:22:02,500 --> 00:22:07,120
+أصغر من X2 و بطبق كل اللي عملته و لعند ال hand
+
+230
+00:22:07,120 --> 00:22:14,860
+بشطب هذا بالديشيا و بقف ال hand و بقول بما أنه هذا
+
+231
+00:22:14,860 --> 00:22:18,480
+المقدار f prime of c اللي هي f prime of x strictly
+
+232
+00:22:18,480 --> 00:22:22,840
+أصغر من 0 يعني مافي إمكانية أن تساوي 0 وهذا x2 
+
+233
+00:22:22,840 --> 00:22:28,320
+ناقص x1 من هذا برضه strictly أكبر من 0 إذا صار هذا
+
+234
+00:22:28,320 --> 00:22:32,520
+عبارة عن strictly أصغر من 0 ولا يوجد إمكانية
+
+235
+00:22:32,520 --> 00:22:36,620
+للمساوية إذا بمعنى آخر صار هذا المقدار strictly 
+
+236
+00:22:36,620 --> 00:22:40,680
+أصغر من هذا يعني لما كانت f prime أصغر strictly من 
+
+237
+00:22:40,680 --> 00:22:45,770
+0 لكل x element in RI وجدنا إن X1 أصغر strictly من 
+
+238
+00:22:45,770 --> 00:22:51,010
+X2 تؤدي F of X2 أصغر strictly من F of X1 وهذا يعني
+
+239
+00:22:51,010 --> 00:22:59,690
+strictly stick raising واضح، أه؟ الآن السؤال هل
+
+240
+00:22:59,690 --> 00:23:07,830
+the converse is true؟ هل the converse is true؟
+
+241
+00:23:07,830 --> 00:23:10,650
+الآن يعني
+
+242
+00:23:13,960 --> 00:23:21,020
+الاتجاه هذا صحيح لما يقول الاتجاه الثاني هذا need
+
+243
+00:23:21,020 --> 00:23:26,500
+not to be true in general بدنا نجيب مثال ان تكون F 
+
+244
+00:23:26,500 --> 00:23:30,780
+strictly decreasing لكن ال F براي مش أصغر strictly 
+
+245
+00:23:30,780 --> 00:23:37,120
+من مين؟ من 0 على I خد الآن F of X بساو سالب X تكعيب
+
+246
+00:23:37,120 --> 00:23:42,220
+هذا الدالة هذا الدالة بنعمل reference مثل F of X 
+
+247
+00:23:42,220 --> 00:23:47,120
+ساو سالب X تكعيب بالشكل هذا هذا الان strictly ايه
+
+248
+00:23:47,120 --> 00:23:54,800
+شمالها decreasing هذه F is strictly decreasing
+
+249
+00:23:55,740 --> 00:24:03,860
+لأن لو كانت X1 أصغر من X2 أكيد X1 تكعيب strictly 
+
+250
+00:24:03,860 --> 00:24:13,420
+أكبر من X2 إيه شمالها تكعيب آسف ناقص مظبوط الانصار
+
+251
+00:24:13,420 --> 00:24:18,320
+عندي الآن يعني اللي هي ال F عندي أنا strictly 
+
+252
+00:24:18,320 --> 00:24:23,770
+decreasing but طبعاً على كل مين على كل ال I اللي
+
+253
+00:24:23,770 --> 00:24:27,090
+أخدت منها لها خد أي I من A لعند B من ناقص خمسة 
+
+254
+00:24:27,090 --> 00:24:31,410
+مثلا لعند خمسة على الفترة اللي بدك إياها but F
+
+255
+00:24:31,410 --> 00:24:40,250
+prime عند اللي هو نقطة ال zero إيش بساوي بساوي سفر
+
+256
+00:24:40,250 --> 00:24:45,150
+إذا اللي هو ماعطنيش الشرط إن F prime أصغر من سفر
+
+257
+00:24:45,150 --> 00:24:51,290
+على كل النقاط ال X اللي وين في ال I واضح أه الان
+
+258
+00:24:51,290 --> 00:24:58,210
+معطيني معرفلي
+
+259
+00:24:58,210 --> 00:25:04,150
+اللي هو شو معناته طبعا احنا عرفنا ال increasing و 
+
+260
+00:25:04,150 --> 00:25:09,670
+ال decreasing على ال interval لأنها مقارنة بالنقاط
+
+261
+00:25:09,670 --> 00:25:14,510
+فالان بقولي طب كيف؟ ايش رايكم؟ بدنا نحكي عن ال
+
+262
+00:25:14,510 --> 00:25:18,860
+increasing او ال decreasing عند نقطة ال increasing
+
+263
+00:25:18,860 --> 00:25:21,640
+أو ال decreasing وعنده ضغطة عموماً هذه الفلسفة
+
+264
+00:25:21,640 --> 00:25:26,360
+موجودة يعني في أكثر من مجال للتعريف في الرياضيات
+
+265
+00:25:26,360 --> 00:25:31,380
+في المناطق اللي ممكن اللي هو تحتاج أو في المفاهيم
+
+266
+00:25:31,380 --> 00:25:37,020
+اللي ممكن تحتاج لمنطقة لتعريف اللي هو المفهوم
+
+267
+00:25:37,020 --> 00:25:41,400
+المقصود بمنطقة زي الـ interval اللي قبل بشوية يعني
+
+268
+00:25:41,400 --> 00:25:48,200
+مش عند نقطة لأ عند منطقة فبصير التعريف اللي هو أن
+
+269
+00:25:48,200 --> 00:25:53,920
+يتحقق المفهوم في الجوار ده النقطة اللي مذكورة يعني
+
+270
+00:25:53,920 --> 00:25:59,120
+بنقول أنه النقطة C تتمتع بهذه الخاصية إذا تمتع
+
+271
+00:25:59,120 --> 00:26:03,940
+الجوار بهذه الخاصية هذا فلسفة التعريف فالآن بدنا
+
+272
+00:26:03,940 --> 00:26:04,260
+نقول
+
+273
+00:26:09,560 --> 00:26:14,260
+F من I لعند R اللي عبارة عن function أي إن كانت 
+
+274
+00:26:14,260 --> 00:26:18,260
+الـ function هذه واخدنا
+
+275
+00:26:18,260 --> 00:26:28,780
+C element in I بدنا نعرف شو معنات عند النقطة C عند
+
+276
+00:26:28,780 --> 00:26:33,240
+النقطة C شو معنات F is increasing at this point
+
+277
+00:26:33,240 --> 00:26:40,880
+بدنا نشوف شو معنات F is increasing at C element in
+
+278
+00:26:40,880 --> 00:26:48,420
+I معناته انه there exist هذا يكافئ there exist V 
+
+279
+00:26:48,420 --> 00:26:53,440
+Delta of C يعني U ده الجوار حوالين من الـ C هذا
+
+280
+00:26:53,440 --> 00:27:03,210
+الجوار C ناقص دلتا و C زائد دلتا ابحث ان تكون Fis
+
+281
+00:27:03,210 --> 00:27:08,770
+increasing on this جوار أو on this neighbourhood
+
+282
+00:27:08,770 --> 00:27:14,770
+إذا تحقق الشرط هذا معناته أنه بنقول عن الـ
+
+283
+00:27:14,770 --> 00:27:18,450
+function F أنّها increasing at the point
+
+284
+00:27:18,450 --> 00:27:23,090
+mean C يعني بمعنى آخر إذا تحقق اللي هو there
+
+285
+00:27:23,090 --> 00:27:29,870
+exists a V Delta of C such that if X1 و X2 element
+
+286
+00:27:29,870 --> 00:27:42,110
+in V Delta of C with X1 أصغر من X2 أصغر
+
+287
+00:27:42,110 --> 00:27:49,350
+من X2 أصغر 
+
+288
+00:27:49,350 --> 00:27:54,840
+من X2 يعني اتحققت الخاصية أو الـ increasing في جوار
+
+289
+00:27:54,840 --> 00:27:58,120
+حول الـ C هذا معناته اللي هو مين؟ اللي هو
+
+290
+00:27:58,120 --> 00:28:01,820
+increasing similarly for strictly increasing ..
+
+291
+00:28:01,820 --> 00:28:07,000
+strictly increasing .. strictly increasing X1 أصغر
+
+292
+00:28:07,000 --> 00:28:11,160
+من X2 يؤدي إلى F of X1 strictly أصغر من F of X2 في هذا
+
+293
+00:28:11,160 --> 00:28:15,480
+الجوار similarly for اللي هو مين؟ decreasing و
+
+294
+00:28:15,480 --> 00:28:20,150
+strictly decreasing بما يتلقى أمهم التلازم معناته
+
+295
+00:28:20,150 --> 00:28:25,490
+X1 أصغر من X2 بيعطينا F of X1 أكبر أو يساوي F
+
+296
+00:28:25,490 --> 00:28:31,890
+of X2 لـ Decreasing للي بيكون Strictly أكبر منها
+
+297
+00:28:31,890 --> 00:28:39,410
+طيب .. الآن السؤال .. السؤال اللي بيقول ليه .. طيب
+
+298
+00:28:39,410 --> 00:28:49,320
+.. الآن أنت قلت أنه لو كانت F prime أكبر من 0f
+
+299
+00:28:49,320 --> 00:28:57,040
+prime of x أكبر من 0 لكل x element in I اللي
+
+300
+00:28:57,040 --> 00:29:05,200
+بيعطيني اللي هو f is strictly increasing صح ولا
+
+301
+00:29:05,200 --> 00:29:10,560
+لأ؟ قلنا هيك معايا لكن قلنا ال .. ال .. ال
+
+302
+00:29:10,560 --> 00:29:13,600
+converse need not to be true in general جبنا مثال
+
+303
+00:29:15,110 --> 00:29:18,590
+أf of X بسوء X تكعيب للـ increasing أو ناقص X
+
+304
+00:29:18,590 --> 00:29:23,690
+تكعيب لل decreasing ماشي الحال .. الآن هو بقول طيب
+
+305
+00:29:23,690 --> 00:29:26,330
+لأ أنا بديش أسأله عن الاتجاه الثاني لإنه خلاص احنا
+
+306
+00:29:26,330 --> 00:29:29,990
+شفنا الاتجاه الثاني عند اللي هو ال interval مش
+
+307
+00:29:29,990 --> 00:29:35,450
+متحقق فالآن بقوللي أنا بدأ أسأل السؤال على اللي هي
+
+308
+00:29:35,450 --> 00:29:39,750
+.. اللي هو هذا السؤال اللي اتحقق في ال interval هل
+
+309
+00:29:39,750 --> 00:29:44,790
+بتحقق عنده النقطة؟ يعني بمعنى أخر لو كانت عندي a
+
+310
+00:29:44,790 --> 00:29:53,390
+February at c أكبر من 0 هل هذا يؤدي أن f is
+
+311
+00:29:53,390 --> 00:30:03,070
+strictly increasing on c أو at c؟ هل هذا يؤدي أن
+
+312
+00:30:03,070 --> 00:30:06,090
+لو كانت f' of c أكبر من 0 هل يؤدي إلى أن f is
+
+313
+00:30:06,090 --> 00:30:09,910
+strictly increasing at c؟ بقول لك، this need not
+
+314
+00:30:09,910 --> 00:30:14,430
+to be true in general وهذا هو exercise عشرة اللي
+
+315
+00:30:14,430 --> 00:30:18,660
+معاكم homework اللي هو أعطاني function g of x بيساوي
+
+316
+00:30:18,660 --> 00:30:23,120
+x زي 2x تربيع sin 1 علي x إذا كانت x بتساوي صفر و
+
+317
+00:30:23,120 --> 00:30:27,780
+0 إذا كانت x بتساوي صفر و بقول لي لو جيت فحصة ال G
+
+318
+00:30:27,780 --> 00:30:32,960
+prime عند ال zero هتلاقيها أنّها بتساوي 1 ماشي
+
+319
+00:30:32,960 --> 00:30:37,320
+الحال يعني بتساوي واحد يعني strictly أكبر منين من
+
+320
+00:30:37,320 --> 00:30:44,050
+صفر but ولا جوار، there is no neighbourhood around
+
+321
+00:30:44,050 --> 00:30:52,850
+zero in which F is increasing أه فشي دير جي is not
+
+322
+00:30:52,850 --> 00:30:56,850
+increasing in any neighborhood of x بتساوي صفر
+
+323
+00:30:56,850 --> 00:31:02,770
+والتفاصيل إن شاء الله لما في ال discussion لما
+
+324
+00:31:02,770 --> 00:31:06,550
+نعمل discussion اللي هو ال section اللي هو 6 2
+
+325
+00:31:06,550 --> 00:31:11,210
+وتجربوا تحلوه في البيت في حال أنتم ما عرفتو تحلوه 
+
+326
+00:31:11,210 --> 00:31:15,670
+بنحكي فيه بتفاصيله في ال discussion إن شاء الله
+
+327
+00:31:22,930 --> 00:31:27,050
+لأ الجوار هتلاقي اللي هو .. اللي هو .. اللي هو
+
+328
+00:31:27,050 --> 00:31:32,830
+مستحيل يعني تلاقي اللي هو جوار تكون X1 أصغر من X2
+
+329
+00:31:32,830 --> 00:31:37,150
+و تضمن أن F of X1 أصغر من F of X2 لكل واحدة بتحقق
+
+330
+00:31:37,150 --> 00:31:43,010
+ال X1 أصغر من X2 يعني هتلاقي نقاط هتلاقي هل جت V
+
+331
+00:31:43,010 --> 00:31:48,510
+Delta of C مثلا لأ كانت Delta بساوة C نقص Delta و
+
+332
+00:31:48,510 --> 00:31:53,690
+C زائد Delta ماشي الحال .. الآن هتلاقي أنه .. أنه
+
+333
+00:31:53,690 --> 00:31:59,090
+مستحيل يعني أنه في أي .. لو مهما زغرت المسافة
+
+334
+00:31:59,090 --> 00:32:05,110
+بينهم يتلاقي X1 أصغر من X2 تضمن يتلاقي أف of X1
+
+335
+00:32:05,110 --> 00:32:10,050
+أكبر أو يساوي أف of X2 في حالة ال decreasing أو
+
+336
+00:32:10,050 --> 00:32:13,690
+أصغر أو يساوي في حالة ال increasing أو اللي بنحكي
+
+337
+00:32:13,690 --> 00:32:16,770
+عنه أنّها strictly increasing يعني هتلاقي نقاط
+
+338
+00:32:16,770 --> 00:32:21,030
+جانب بعض واحدة أكبر من الثانية و very close .. very
+
+339
+00:32:21,030 --> 00:32:25,870
+close اللي هو .. و تكون .. اللي هو واحدة اللي هو
+
+340
+00:32:25,870 --> 00:32:30,970
+اتلاقيها أكبر و التانية اتلاقيها نقطش أخر اه .. اه
+
+341
+00:32:30,970 --> 00:32:34,230
+.. اه .. في .. اه .. في .. اتلاقيهم يعني ال .. ال
+
+342
+00:32:34,230 --> 00:32:37,630
+.. ال .. ال .. ال طبعا هو يمكن السبب بالذبذبة لو
+
+343
+00:32:37,630 --> 00:32:43,710
+لاحظت هدي sign واحد على X فال X اللي هو بتساوي
+
+344
+00:32:43,710 --> 00:32:48,720
+اتنين .. واحد على اتنين on by أو 2 and by هتلاقي
+
+345
+00:32:48,720 --> 00:32:52,740
+اللي هي إيش بيعملك صفر و إيش بيعملك واحد في حالة
+
+346
+00:32:52,740 --> 00:32:55,920
+ال F of prime و في حالة ال F العادية فهيسببلك اللي
+
+347
+00:32:55,920 --> 00:33:01,180
+هو مش هتظلها اللي هي ال .. اللي هي ال .. ال .. ال
+
+348
+00:33:01,180 --> 00:33:08,300
+.. القيم .. قيم هتلاقيها مستحيل إن X1 أصغر من X2 و
+
+349
+00:33:08,300 --> 00:33:12,580
+تظلها على نفس المنوال F of X1 أصغر من F of X2 يعني
+
+350
+00:33:12,580 --> 00:33:18,070
+ممكن تلاقيه لك إنه جدتين closed لجوه هتلاقي بتحققش
+
+351
+00:33:18,070 --> 00:33:26,150
+هذه يا بتحقق مساوية يا بتحقق الأصغر ولو لجيتلك
+
+352
+00:33:26,150 --> 00:33:30,510
+تنتين بحقق الأكبر هتلاقي برضه very closed إيش بحقق
+
+353
+00:33:30,510 --> 00:33:36,810
+الأصغر ان
+
+354
+00:33:36,810 --> 00:33:45,360
+شاء الله لما نحل السؤال بتتضح الأمور تماما هذا اللي
+
+355
+00:33:45,360 --> 00:33:54,900
+هو من ضمن الأسئلة اللي معاكم homework سألنا
+
+356
+00:33:54,900 --> 00:34:08,980
+سؤال اللي هو وين يمكن إيجاد ال relative maximum و
+
+357
+00:34:08,980 --> 00:34:13,430
+relative minimum و جاوبنا عليه في النظرية اللي
+
+358
+00:34:13,430 --> 00:34:17,230
+حكيناها في البداية أنّها توجد عند أحد ثلاث مناطق F'
+
+359
+00:34:17,450 --> 00:34:21,370
+بيساوي صفر F' لا تساوي صفر لإنها في حالة ال
+
+360
+00:34:21,370 --> 00:34:26,410
+interior points أو اللي هو المكان الثالث اللي هو
+
+361
+00:34:26,410 --> 00:34:32,210
+ال end points الآن عشان نكمل الحديث عن ال maximum
+
+362
+00:34:32,210 --> 00:34:39,370
+و ال minimum بدنا نفحص نفحص هل النقاط هذه مين فيها
+
+363
+00:34:39,370 --> 00:34:43,910
+عندها maximum و في مين فيها عندها minimum و مين لا
+
+364
+00:34:43,910 --> 00:34:48,530
+عندها maximum ولا عندها minimum و هو ال test اللي
+
+365
+00:34:48,530 --> 00:34:54,410
+أنتم اخذتوها في اللي هو سواء في الثانوية أو حتى
+
+366
+00:34:54,410 --> 00:34:59,330
+في calculus ألف و عشان نساعدكم على أنكم تتذكروا
+
+367
+00:34:59,330 --> 00:35:05,620
+أنا بفضل أنّنا نتذكروا من خلال الرسم الفحص ساعتها
+
+368
+00:35:05,620 --> 00:35:12,780
+بيكون سهل و بيكون أنت بتعرف اللي هو تحدد أن هذا
+
+369
+00:35:12,780 --> 00:35:17,020
+النقطة في عندها maximum أو عندها minimum خلينا
+
+370
+00:35:17,020 --> 00:35:22,420
+نستذكر نستذكر من خلال الرسم النظرية اللي بدنا
+
+371
+00:35:22,420 --> 00:35:26,160
+نحكيها الآن اللي اخذناها في الثانوية أو اخذناها
+
+372
+00:35:26,160 --> 00:35:30,850
+اللي هي تغيير إشارة F prime اللي هو من موجب إلى
+
+373
+00:35:30,850 --> 00:35:35,450
+سالب أو من سالب إلى موجب الان نرسم واحدة Maximum
+
+374
+00:35:35,450 --> 00:35:39,210
+وواحدة Minimum هذه النقطة هذه طبعا Maximum بس تذكر
+
+375
+00:35:39,210 --> 00:35:43,190
+في النظرية قاعدة الان هذه النقطة C الجوار اللي
+
+376
+00:35:43,190 --> 00:35:51,710
+حوالها C زائد Delta و C ناقص Delta مظبوط؟ طيب الان
+
+377
+00:35:51,710 --> 00:35:57,430
+عند النقاط المنطقة هذه كلها لاحظ مين المماس إيه
+
+378
+00:35:57,430 --> 00:36:01,710
+شماله بس ما بعمل المماس زاوية حادة إذا مين إيه
+
+379
+00:36:01,710 --> 00:36:10,970
+شماله موجب يعني F prime of X أكبر أو يساوي صفر لكل
+
+380
+00:36:10,970 --> 00:36:16,950
+X وين موجودة في الجوار V Delta of C من الجهة هذه
+
+381
+00:36:16,950 --> 00:36:23,710
+بالتحديد في المنطقة C minus Delta OC واضح، مفهوم
+
+382
+00:36:24,520 --> 00:36:31,040
+الآن الـ F' هنا أو ميل المماس هنا بيعمل .. أو
+
+383
+00:36:31,040 --> 00:36:36,080
+المماس بيعمل زاوية منفرجة إذا الـ F' عند النقاط
+
+384
+00:36:36,080 --> 00:36:40,480
+هذه اللي هي اللي في المنطقة هذه اللي هي بيكون أصغر
+
+385
+00:36:40,480 --> 00:36:45,660
+أو يساوي صفر لكل X وهي الموجودة C C زائد Delta وهذا
+
+386
+00:36:45,660 --> 00:36:49,660
+اللي كنا نقول عنه إذا بتتغير إشارة ال derivative
+
+387
+00:36:49,660 --> 00:36:55,940
+حول النقطة C من موجب إلى سالب هذا على بعضه بيعطيني
+
+388
+00:36:55,940 --> 00:37:05,700
+أنّ F has a local أو relative maximum at mean الـ C
+
+389
+00:37:05,700 --> 00:37:11,420
+Similarly for the other هذه النقطة هان C اللي هي
+
+390
+00:37:11,420 --> 00:37:16,980
+المنطقة ماضح عند ميل المماس جابلها سالب لإنه زاوية
+
+391
+00:37:16,980 --> 00:37:22,420
+منفرجة وراح لمين لموجبة لإنها زاوية حادة يعني بمعنى
+
+392
+00:37:22,420 --> 00:37:29,680
+آخر F prime of X أصغر أو يساوي 0 لكل X في الـ V أو
+
+393
+00:37:29,680 --> 00:37:36,160
+الجزء من C ما نزلت لعند C فاهمين عليها؟ هي C نقص
+
+394
+00:37:36,160 --> 00:37:43,880
+Delta C و C لعند C زائد Delta و F prime of X أكبر أو
+
+395
+00:37:43,880 --> 00:37:49,620
+يساوي 0 لكل X والي موجودة من C لعند C زائد Delta
+
+396
+00:37:49,620 --> 00:37:59,200
+هذولتين مع بعض بيعطينا أنّ F has local minimum أو
+
+397
+00:37:59,200 --> 00:38:05,850
+relative minimum at C فصار عندي الآن يا جماعة اللي
+
+398
+00:38:05,850 --> 00:38:11,730
+هو ال test التحول شرط الدال ال derivative من موجب
+
+399
+00:38:11,730 --> 00:38:18,410
+إلى سالب local maximum هذه النقاط اللي احنا اخذناه
+
+400
+00:38:18,410 --> 00:38:22,790
+من النظرية السابقة طبعا بنحكي عن ال interior
+
+401
+00:38:22,790 --> 00:38:28,850
+points و F اللي هي اتحولت F prime من سالب إلى موجب
+
+402
+00:38:28,850 --> 00:38:33,870
+local maximum هذه اللي هي معلومة توجيهي أو معلومة
+
+403
+00:38:33,870 --> 00:38:40,730
+اللي هو calculus ألف الآن احنا بدنا نثبت صحة هذا
+
+404
+00:38:40,730 --> 00:38:41,770
+الحديث
+
+405
+00:38:49,440 --> 00:38:53,520
+نجرها بس من عندنا هنا هي اللي قلته بس نجرها من
+
+406
+00:38:53,520 --> 00:38:57,520
+النظرية let f be continuous on the interval a و b
+
+407
+00:38:57,520 --> 00:39:01,080
+إذا إيش مخصر دين أنّ ال function is continuous على
+
+408
+00:39:01,080 --> 00:39:04,780
+فترة a و b و ناخد c عبارة عن interior point لمين
+
+409
+00:39:05,450 --> 00:39:10,090
+للـ I Assume that F is differentiable إيه على الفترة
+
+410
+00:39:10,090 --> 00:39:13,430
+A و C و C و B يعني مش لازم أنّها تكون differentiable
+
+411
+00:39:13,430 --> 00:39:16,170
+عند الـ C أصلا ممكن تكون مش differentiable و هي
+
+412
+00:39:16,170 --> 00:39:21,290
+نقطة بدنا نبحث عندها بس بالزمن هذه اللي هي من A ل
+
+413
+00:39:21,290 --> 00:39:25,490
+C و من C ل B then الآن
+
+414
+00:39:26,890 --> 00:39:31,430
+إذا كان هناك مقارنة V Delta of C Subset من I بحيث
+
+415
+00:39:31,430 --> 00:39:35,110
+أنّ F' بتكون أكبر أو سوى 0 قبلها في الفترة اللي
+
+416
+00:39:35,110 --> 00:39:39,830
+قبل اللي هو و F' اتحولت إلى أصغر أو سوى 0 يعني
+
+417
+00:39:39,830 --> 00:39:44,750
+اتحولت الإشارة من موجب إلى سالب في الفترة الأولى
+
+418
+00:39:44,750 --> 00:39:48,210
+للفترة الثانية هيكون عند relative maximum زي ما
+
+419
+00:39:48,210 --> 00:39:54,260
+حكيناها الآن في الثانية نفس الشي بس بالعكس if
+
+420
+00:39:54,260 --> 00:39:57,480
+there is a neighborhood اللي هو كذا such that F' 
+
+421
+00:39:57,940 --> 00:40:02,160
+أصغر من صفر هي اللي هو زاوية منفرجة تحولت إلى F'
+
+422
+00:40:02,540 --> 00:40:06,820
+أكبر من صفر هي بيعطينا عندي ايش ماله relative
+
+423
+00:40:06,820 --> 00:40:14,040
+minimum طيب ده عندي A وعندي BM مبرهنة خليني نبرهن
+
+424
+00:40:14,040 --> 00:40:18,440
+مين؟ B خليني نشوف المبرهنة مع بعض اللي هو B
+
+425
+00:40:29,950 --> 00:40:33,710
+شوفوا صلوا على النبي عليه الصلاة والسلام الآن بيه
+
+426
+00:40:33,710 --> 00:40:39,410
+اللي هو عندي F prime معطيني F prime of X أصغر أو 
+
+427
+00:40:39,410 --> 00:40:47,170
+يساوي صفر صح لكل X في الفترة C minus Delta وC
+
+428
+00:40:47,170 --> 00:40:49,710
+ومعطيني أيضاً
+
+429
+00:40:52,140 --> 00:40:57,040
+اللي تحت أنا بحكي عن اللي تحت بيه ال .. البعدها F
+
+430
+00:40:57,040 --> 00:41:02,980
+prime of X أكبر أو يساوي صفر لكل X وين موجودة في 
+
+431
+00:41:02,980 --> 00:41:09,740
+الفترة من C إلى C زائد ايش؟ إلى C زائد دلتا الآن ايش
+
+432
+00:41:09,740 --> 00:41:14,560
+غايتي أثبت أن F has a relative minimum؟ يعني بدي
+
+433
+00:41:14,560 --> 00:41:21,340
+أثبت أن F of X أكبر أو Minimum أصغر أو أكبر أو يساوي 
+
+434
+00:41:21,340 --> 00:41:28,380
+F of C لكل X وين موجودة في V Delta of C إذا أثبتت
+
+435
+00:41:28,380 --> 00:41:32,200
+هذا الكلام معناته صار عندي في Neighborhood حوالي ال
+
+436
+00:41:32,200 --> 00:41:37,140
+F عند ال C أصغر واحدة فيهم يعني في عندها relative
+
+437
+00:41:37,140 --> 00:41:42,560
+minimum اللي هو في المنطقة هذه هأقول لك إنها بتتحقق
+
+438
+00:41:42,560 --> 00:41:45,700
+هذه وفي المنطقة هذه بتتحقق هذه معناها تقول لكل 
+
+439
+00:41:45,700 --> 00:41:49,100
+النقاط اللي هنا لكل النقاط اللي هنا هذه بتتحقق 
+
+440
+00:41:49,100 --> 00:41:54,740
+معايا؟ والكلام إن شاء الله سهل الآن طبيعي إحنا 
+
+441
+00:41:54,740 --> 00:41:58,920
+قاعدين في جوه ال mean value theorem فأكيد هذا
+
+442
+00:41:58,920 --> 00:42:02,440
+جايبينه في نفس ال section عشان إنه إحنا نطبق ال
+
+443
+00:42:02,440 --> 00:42:07,220
+mean value theorem عشان اللي هو إن نصل لنتائجنا
+
+444
+00:42:07,770 --> 00:42:14,790
+الآن x element in c minus delta of c، مظبوط؟ إذا
+
+445
+00:42:14,790 --> 00:42:18,590
+صار عندي الآن طبعاً أنا غايتي أن أجيب اللي هو علاقة
+
+446
+00:42:18,590 --> 00:42:23,610
+بين f of c و f of x فالآن ال x في الفترة هذه
+
+447
+00:42:23,610 --> 00:42:28,410
+معناته إنه أنا بدي أطبق ال mean value theorem على
+
+448
+00:42:28,410 --> 00:42:32,790
+ال x وعلى ال c الفترة اللي فيهم يعني بدي أقول لكم
+
+449
+00:42:32,790 --> 00:42:40,940
+consider the interval x و meanOc XOC
+
+450
+00:42:41,980 --> 00:42:47,220
+الـ file الـ data continuous على X وC، ليش؟ لأن
+
+451
+00:42:47,220 --> 00:42:51,120
+continuous على كل ال interval A وB اللي من ضمنها C
+
+452
+00:42:51,120 --> 00:42:55,680
+إذن، هذا أول شرط متحقق لـ mean value theorem
+
+453
+00:42:55,680 --> 00:42:59,900
+وأيضاً F is differentiable على ال open اللي هي
+
+454
+00:42:59,900 --> 00:43:02,940
+مستثنية الـ C بس واللي بالضمن في ال mean value
+
+455
+00:43:02,940 --> 00:43:08,060
+theorem بس ال open إذن الشرطين متحققتين على هذه
+
+456
+00:43:08,060 --> 00:43:14,470
+الفترة لمين؟ للـ Mean Value Theorem إذا نطبق الـ
+
+457
+00:43:14,470 --> 00:43:18,730
+Mean Value Theorem على هذا الانترفال لكي نحصل على 
+
+458
+00:43:18,730 --> 00:43:27,890
+ذلك اللي هو F there exist CX element in X وC such
+
+459
+00:43:27,890 --> 00:43:38,850
+that F of CX فبرايم of CX يساوي F of C ناقص F of X
+
+460
+00:43:38,850 --> 00:43:48,870
+على X C ناقص X اللي هو اللي بالضمن هذا أمور جهزة
+
+461
+00:43:48,870 --> 00:43:57,090
+ليش جهزة؟ من هنا إذا F of C ناقص F of X يساوي C
+
+462
+00:43:57,090 --> 00:44:04,760
+ناقص X في F prime of CX الـ CX هي دي وين موجودة في
+
+463
+00:44:04,760 --> 00:44:10,760
+الـ X و C يعني هنا مدام هنا حسب المعطى الـ F prime
+
+464
+00:44:10,760 --> 00:44:15,380
+اللي هيش ماله سالبة إذا هذا أصغر أو يساوي صفر هذا
+
+465
+00:44:15,380 --> 00:44:20,260
+أكبر أو يساوي صفر مع بعض ايش ماله؟ أصغر أو يساوي
+
+466
+00:44:20,260 --> 00:44:24,240
+صفر إذا صار عندي هذا أصغر أو يساوي صفر أو بمعنى
+
+467
+00:44:24,240 --> 00:44:31,560
+آخر F of C أصغر أو يساوي F of X لمين؟ لكل X في هذه
+
+468
+00:44:31,560 --> 00:44:36,440
+الفترة لأن X كانت arbitrary فيها Similarly for
+
+469
+00:44:36,440 --> 00:44:43,700
+اللي هو الجزء الثاني بتأخذ الآن X وين موجودة؟ في 
+
+470
+00:44:43,700 --> 00:44:48,520
+الـ C إلى C زائد دلتا وبرضه اللي عملته فوق حطب
+
+471
+00:44:48,520 --> 00:44:54,400
+جهانة بس عالميا على الفترة C O X ونفس الحديث
+
+472
+00:44:54,400 --> 00:44:57,580
+الأولاني F is continuous هلأ و differentiable على
+
+473
+00:44:57,580 --> 00:45:01,480
+ال open then there exist اللي هو by mean value
+
+474
+00:45:01,480 --> 00:45:06,780
+theorem there exist C X C prime X element in C O X
+
+475
+00:45:06,780 --> 00:45:20,440
+such that F prime of Cx' يساوي f of x ناقص f of c
+
+476
+00:45:20,440 --> 00:45:27,800
+على x minus c يساوي هذا وزي ما عملنا بالضبط اللي
+
+477
+00:45:27,800 --> 00:45:31,040
+هو بيصير عندي أضرب طرفين في وسطين بيصير هنا x
+
+478
+00:45:31,040 --> 00:45:37,060
+ناقص c وهذه بتطلع فوق فبيصير عندي هذه x ناقص c
+
+479
+00:45:37,060 --> 00:45:44,680
+موجبة وهذه f prime cx اللي هو موجبة X ناقص C
+
+480
+00:45:44,680 --> 00:45:49,780
+موجبة مظبوط و F prime اللي هي أكبر أو يساوي صفر
+
+481
+00:45:49,780 --> 00:45:53,780
+فبيصير هذا المقدار كله على بعض ايش ماله؟ أكبر أو يساوي
+
+482
+00:45:53,780 --> 00:45:58,400
+صفر يعني هذا المقدار أكبر أو يساوي ايش؟ صفر يعني من
+
+483
+00:45:58,400 --> 00:46:05,820
+هنا بيصير عند F of X أكبر أو يساوي F of ايش؟ of C هذا
+
+484
+00:46:05,820 --> 00:46:11,760
+الكلام صحيح برضه لمين؟ لكل X هنا الآن في الجهتين أي 
+
+485
+00:46:11,760 --> 00:46:16,040
+إن كان طلعت ال F of C أصغر أو يساوي F of X أصغر أو
+
+486
+00:46:16,040 --> 00:46:21,640
+يساوي F of X لكل X وين موجودة؟ هنا وهنا يعني بمعنى
+
+487
+00:46:21,640 --> 00:46:25,980
+آخر لكل X وين موجودة في ال neighborhood يعني صارت 
+
+488
+00:46:25,980 --> 00:46:33,020
+F of X أكبر أو يساوي F of C لكل X في ال V Delta of
+
+489
+00:46:33,020 --> 00:46:41,440
+C وهذا يعني أن F has a local minimum at mean الـ C
+
+490
+00:46:41,440 --> 00:46:44,640
+أي سؤال؟
+
+491
+00:47:03,950 --> 00:47:07,150
+عندي the converse of the theorem اللي فوقني not to
+
+492
+00:47:07,150 --> 00:47:10,690
+be true in general وهذا اللي هو عبارة عن مين؟ عن
+
+493
+00:47:10,690 --> 00:47:15,090
+exercise 9 برضه exercise 9 من ضمن ال homework اللي 
+
+494
+00:47:15,090 --> 00:47:18,090
+معاكم اللي هنتحدث فيه إن شاء الله في ال discussion
+
+495
+00:47:18,090 --> 00:47:22,590
+الآن بعض التطبيقات الأخرى على ال mean value
+
+496
+00:47:22,590 --> 00:47:29,600
+theorem وهذا التطبيق بعض التطبيقات اللي هي علمين
+
+497
+00:47:29,600 --> 00:47:34,120
+value theory ممكن شيء اخذنا مشابه له في ال
+
+498
+00:47:34,120 --> 00:47:40,300
+calculus لكن خلينا نشوف هنا يعني ايش اللي بيقوله
+
+499
+00:47:40,300 --> 00:47:47,700
+عندنا التطبيق الأول اللي
+
+500
+00:47:47,700 --> 00:47:54,080
+بيقوله ما هي ليه example example اللي هو
+
+501
+00:48:00,540 --> 00:48:12,120
+show that أكبر
+
+502
+00:48:12,120 --> 00:48:18,080
+أو يساوي واحد زائد X لكل X element in R هذا واحد
+
+503
+00:48:18,080 --> 00:48:24,500
+اثنين اللي هو نفس ال W أو A اللي هو E to the X
+
+504
+00:48:25,160 --> 00:48:33,500
+يساوي واحد زائد X F أندولي F X بتساوي صفر و proof
+
+505
+00:48:33,500 --> 00:48:42,480
+خلينا نشوف نبرهن هذا الأمر أو هذا الجزء طيب
+
+506
+00:48:42,480 --> 00:48:45,920
+بناء على أن E to the X أكبر أو يساوي واحد زائد X لكل
+
+507
+00:48:45,920 --> 00:48:47,880
+X وين موجودة في ال R
+
+508
+00:48:51,200 --> 00:48:55,040
+الآن عندنا طبيعي حالة الـ X بتساوي صفر الـ Z بأخذ
+
+509
+00:48:55,040 --> 00:48:57,860
+الـ function مين أنا؟ عشان الرأس الدولة يعرف عن مين؟
+
+510
+00:48:57,860 --> 00:49:03,740
+بنحكي let F of X ايش هتساوي؟ طبعاً E to the X طبعاً E
+
+511
+00:49:03,740 --> 00:49:09,120
+to the X معرف هو المكان الانفي حالة ال .. ال ..
+
+512
+00:49:09,120 --> 00:49:12,280
+الأول حاجة لو جينا طلعنا لحالة ال X بتساوي صفر 
+
+513
+00:49:12,280 --> 00:49:18,000
+المساواة حادثة ولا لا it was a zero ليه واحد يساوي
+
+514
+00:49:18,000 --> 00:49:21,520
+واحد زائد زيرو اللي هو واحد يعني المساواة حادثة في
+
+515
+00:49:21,520 --> 00:49:25,120
+حالة ال .. ال X بتساوي زيرو الآن خليني اخذ ال X 
+
+516
+00:49:25,120 --> 00:49:31,970
+ايش ماله؟ لا تساوي ايش؟ صفر الـ X لا تساوي صفر هأثبت لك 
+
+517
+00:49:31,970 --> 00:49:36,950
+إن E to the X strictly أكبر من واحد زائد X بكون 
+
+518
+00:49:36,950 --> 00:49:42,410
+خلصت هذه وخلصت هذه مع بعض افتمتين بنشوف كيف لأن X 
+
+519
+00:49:42,410 --> 00:49:46,930
+لا تساوي Zero عندي حالتين X أكبر من صفر و X أصغر
+
+520
+00:49:46,930 --> 00:49:52,130
+من صفر الآن f of x ده اللي هي من الدوال الحلوة اللي
+
+521
+00:49:52,130 --> 00:49:54,230
+differentiable everywhere إذا continuous
+
+522
+00:49:54,230 --> 00:49:56,830
+everywhere إذا ال mean value theorem على أي
+
+523
+00:49:56,830 --> 00:50:01,610
+interval أو sub interval منها من الار متحققة إذا x 
+
+524
+00:50:01,610 --> 00:50:04,930
+أكبر من 0 معناته بتأخذ أطبق ال mean value theorem
+
+525
+00:50:04,930 --> 00:50:10,910
+من عند ال zero لعند الـ x معايا إذا by mean 
+
+526
+00:50:10,910 --> 00:50:16,490
+value theorem there exists element in zero x such
+
+527
+00:50:16,490 --> 00:50:25,720
+that F prime of C يساوي F of X ناقص F of Zero على X
+
+528
+00:50:25,720 --> 00:50:30,400
+ناقص Zero، مظبوط ولا لا؟ هذه اللي هي F prime of C 
+
+529
+00:50:30,400 --> 00:50:34,120
+طبعاً ال derivative للـ E to the X هي نفسها عند الـ C 
+
+530
+00:50:34,120 --> 00:50:38,560
+في الـ C E to the C وهذه اللي هي عبارة عن E to the 
+
+531
+00:50:38,560 --> 00:50:41,900
+X F of Zero اللي هي E to the Zero اللي هي واحد
+
+532
+00:50:41,900 --> 00:50:46,860
+ناقص واحد على مين؟ على X اضربوا طرفين في وسطين 
+
+533
+00:50:46,860 --> 00:50:52,340
+فبيصير E to the X ناقص واحد يساوي X في مين؟ في E
+
+534
+00:50:52,340 --> 00:50:59,020
+أس C ماشي الحالة الآن هذه الآن ال E to the C C 
+
+535
+00:50:59,020 --> 00:51:05,100
+موجبة صح ال E to the C هتكون أكبر أو تساوي واحد إن
+
+536
+00:51:05,100 --> 00:51:09,120
+هي أكبر strictly من واحد في الواقع مظبوط E to the 
+
+537
+00:51:09,120 --> 00:51:13,960
+C أكبر strictly من مين؟ من الواحد الآن X في ال E to
+
+538
+00:51:13,960 --> 00:51:20,920
+the C هتكون أكبر strictly من مين؟ من اللي هي ال X مع
+
+539
+00:51:20,920 --> 00:51:24,880
+بعض الثنتين بيصير عندي E to the X أكبر من واحد
+
+540
+00:51:24,880 --> 00:51:31,860
+زائد مين؟ زائد ال X الآن في حالة ال X أصغر من صفر
+
+541
+00:51:31,860 --> 00:51:36,600
+في حالة ال X أصغر من صفر بدنا نطبق على مين؟ على
+
+542
+00:51:36,600 --> 00:51:43,380
+الفترة اللي هي X و Zero مظبوط؟ على الفترة X و Zero 
+
+543
+00:51:47,630 --> 00:51:53,510
+ب .. كله كله ماشي there exists c element in x و
+
+544
+00:51:53,510 --> 00:52:00,930
+zero such that أقول معايا f prime of c يساوي f of 
+
+545
+00:52:00,930 --> 00:52:10,010
+zero ناقص f of x على zero ناقص x هو يساوي واحد
+
+546
+00:52:10,010 --> 00:52:19,700
+ناقص x ناقص e to the x على سالم X هذا ايش بيساوي E
+
+547
+00:52:19,700 --> 00:52:25,820
+to the C أضرب الطرفين في وسطين بيصير واحد ناقص E
+
+548
+00:52:25,820 --> 00:52:34,760
+to the X يساوي ناقص X E to the C أضرب اللي هو في 
+
+549
+00:52:34,760 --> 00:52:41,840
+ناقص واحد بيصير E to the X ناقص واحد يساوي X في E
+
+550
+00:52:41,840 --> 00:52:50,110
+to the C الآن ال C سالبة مظبوط فبيصير كسر فبيصير عند 
+
+551
+00:52:50,110 --> 00:52:56,150
+ال E to the C اللي هو ايش ماله؟ أصغر من واحد فالآن 
+
+552
+00:52:56,150 --> 00:53:01,210
+لما نضرب ال X السالبة فيه ال X سالبة هنا فبيصير 
+
+553
+00:53:01,210 --> 00:53:08,110
+أكبر من مين؟ من X فبيصير
+
+554
+00:53:08,110 --> 00:53:12,350
+عند E to the X أكبر
+
+555
+00:53:13,170 --> 00:53:21,630
+من واحد زائد مين؟ زائد X الآن صار عندي من الجهتين
+
+556
+00:53:21,630 --> 00:53:26,590
+لما X لا تساوي صفر E to the X strictly أكبر من 
+
+557
+00:53:26,590 --> 00:53:32,590
+واحد زائد X إذا X لا تساوي صفر بتعني
+
+558
+00:53:43,580 --> 00:53:50,840
+E to the X أكبر strictly من واحد زائد X هذه واحد 
+
+559
+00:53:50,840 --> 00:53:58,260
+الآن اثنين في حالة X بتساوي صفر هذا بيعطينا إن E
+
+560
+00:53:58,260 --> 00:54:03,480
+to the X يساوي واحد زائد X والجهتين هيساوين واحد 
+
+561
+00:54:03,480 --> 00:54:09,600
+واحد في e to the zero واحد الآن الجهتين مع بعض هذول
+
+562
+00:54:11,120 --> 00:54:15,880
+بتدي لمّا الـ x لا تساوي 0 و الـ x بتساوي 0 يعني e 
+
+563
+00:54:15,880 --> 00:54:19,740
+to the x بتاخد بعين الاعتبار المساواة هنا بيصير e 
+
+564
+00:54:19,740 --> 00:54:24,740
+to the x أكبر و بيساوي 1 زيادة x لكل x عنصر 
+
+565
+00:54:24,740 --> 00:54:29,120
+in R بالظبط في حالة x بتساوي صفر e to the x بتساوي
+
+566
+00:54:29,120 --> 00:54:33,520
+في حالة x لا تساوي صفر e to the x strictly أكبر 
+
+567
+00:54:33,520 --> 00:54:40,750
+الآن هذا x بتساوي صفر يؤدي إلى هذا الـ Trivia زي ما
+
+568
+00:54:40,750 --> 00:54:45,510
+قلنا الآن conversely بدنا نثبت هذا هذا أثبتناه في 
+
+569
+00:54:45,510 --> 00:54:52,290
+الواقع كيف أثبتناه بدنا نقول بدّنا نثبت الآن الاتجاه 
+
+570
+00:54:52,290 --> 00:54:57,370
+هذا هذا الاتجاه اللي محيته اتجاه الـ Trivia اللي
+
+571
+00:54:57,370 --> 00:55:02,050
+سهل  دلّ هذا هذا عشان أثبته بقول Contraposition لو
+
+572
+00:55:02,050 --> 00:55:07,480
+كانت X لا تساوي صفر يعطينا الـ E to the X لا يساوي
+
+573
+00:55:07,480 --> 00:55:12,080
+واحد زيادة X ليش؟ لأنه أثبتته أنه strictly أكبر من 
+
+574
+00:55:12,080 --> 00:55:15,920
+strictly أكبر إذا إيه شماله؟ لا يساوي إذا صار
+
+575
+00:55:15,920 --> 00:55:23,420
+عندي اللي هو هذا وهذا متحققين الإثنين طيب نيجي
+
+576
+00:55:23,420 --> 00:55:30,920
+نيجي الآن لل example الثاني example معهود ومعروف 
+
+577
+00:55:30,920 --> 00:55:36,860
+أو ننهي فيه المرة الجاية إن شاء الله بنكمل باقي 
+
+578
+00:55:36,860 --> 00:55:41,360
+اللي هي ال applications المرة دي إن شاء الله هنعمل 
+
+579
+00:55:41,360 --> 00:55:46,780
+discussion في 6-1 يعني أصل 6-1 هنيجي ونحلهم و
+
+580
+00:55:46,780 --> 00:55:52,340
+بالإضافة ل .. اللي هو نكمل 6-2 هنكمل 6-2 و نعمل 
+
+581
+00:55:52,340 --> 00:55:57,560
+discussion ل 6-1 طيب اللي مصلّي على سيدنا محمد 
+
+582
+00:55:57,560 --> 00:56:05,210
+example الثاني example اللي هو show that show that
+
+583
+00:56:05,210 --> 00:56:15,930
+show that show that sign ال X أكبر أو يساوي سالب X و
+
+584
+00:56:15,930 --> 00:56:24,410
+أصغر أو يساوي X for every X أكبر من 0 الغروف الآن 
+
+585
+00:56:24,410 --> 00:56:28,990
+الدالة اللي بناحكيها عنها مين هي sign ال X هذه
+
+586
+00:56:28,990 --> 00:56:35,260
+letf of x بتساوي sign الـ x وهذه continuous
+
+587
+00:56:35,260 --> 00:56:41,320
+everywhere و differentiable everywhere عند اللي هي
+
+588
+00:56:41,320 --> 00:56:47,160
+عند ال zero عند x بتساوي zero ال trivial هذه بتتحقق
+
+589
+00:56:47,160 --> 00:56:50,900
+كـ trivial لأن ده صفر و ده صفر و ده صفر، مظبوط؟ اللي
+
+590
+00:56:50,900 --> 00:56:57,660
+هنخد الآن for x أكبر من 0 بدنا نعمل
+
+591
+00:56:57,660 --> 00:57:01,560
+application أو we apply the mean value theorem on
+
+592
+00:57:01,560 --> 00:57:08,120
+the interval 0,x  نظرا نتحقق الشروط بيكون
+
+593
+00:57:08,120 --> 00:57:14,500
+عند there exist c element in 0,x such that f prime 
+
+594
+00:57:14,500 --> 00:57:24,510
+of c بيساوي f of x ناقص f of 0 على x ناقص 0 
+
+595
+00:57:24,510 --> 00:57:29,410
+F prime of C هي عبارة عن Cos C لأن انتفاضه للـSin
+
+596
+00:57:29,410 --> 00:57:38,890
+Cos ويساوي F of X هي Sin X Sin 0 0 على X أضرب طرفين 
+
+597
+00:57:38,890 --> 00:57:45,870
+في وسطين بيصير عندي Sin X بيساوي X في Cos C لكن
+
+598
+00:57:45,870 --> 00:57:54,420
+الآن أنا عندي Cos C محصورة but cos c محصورة بين
+
+599
+00:57:54,420 --> 00:58:01,660
+ناقص واحد وبين واحد قل عند x أكبر من 0 اضرب
+
+600
+00:58:01,660 --> 00:58:08,600
+الجهتين في x بيصير هان x و هان x و هان x صح؟ الآن
+
+601
+00:58:08,600 --> 00:58:16,550
+x cos c هي sin x إذا صار عندي sin x أظهر يساوي X 
+
+602
+00:58:16,550 --> 00:58:22,050
+وأكبر أو يساوي سالب X هذا الآن لكل X لاتش أكبر من 
+
+603
+00:58:22,050 --> 00:58:26,490
+صفر but for X بتساوي zero this is trivial إذا صار 
+
+604
+00:58:26,490 --> 00:58:33,250
+sin ال X بين نقص X و X لكل X أكبر أو يساوي صفر و
+
+605
+00:58:33,250 --> 00:58:34,970
+المرة القادمة إن شاء الله 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..967f837f77160ac49c7b07ea07fcee4ce25c4efa
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM_postprocess.srt
@@ -0,0 +1,2420 @@
+1
+00:00:05,280 --> 00:00:12,080
+بسم الله الرحمن الرحيم المحاضرة الرابعة مساق تحليل
+
+2
+00:00:12,080 --> 00:00:18,780
+حقيقة 2 لطلبة الجامعة الإسلامية كلية العلوم قسم
+
+3
+00:00:18,780 --> 00:00:26,480
+الرياضيات نستكمل الحديث عن نظرية القيمة المتوسطة
+
+4
+00:00:26,480 --> 00:00:33,380
+أو the mean value theorem وما يتعلق بذلك تحدثنا
+
+5
+00:00:33,380 --> 00:00:40,130
+المرة الماضيةمعنى relative extrema سواء relative
+
+6
+00:00:40,130 --> 00:00:43,290
+maximum أو relative minimum أو بمعنى أخر ال
+
+7
+00:00:43,290 --> 00:00:47,450
+absolute ال local maximum و ال local minimum
+
+8
+00:00:47,450 --> 00:00:53,910
+معرفناها المرة الماضية و أتحدثنا أيضًا عن اللي هو
+
+9
+00:00:53,910 --> 00:00:58,650
+ال interior extreme theorem ال interior extreme
+
+10
+00:00:58,650 --> 00:01:03,430
+theorem اللي هي جوابتنا على السؤال اللي بنحكي فيه
+
+11
+00:01:03,770 --> 00:01:09,170
+أين يمكن إيجاد القيم العظمى أو القيم الصغرى
+
+12
+00:01:09,170 --> 00:01:14,730
+النظرية اللي بتحكي كانت ان لو كانت C عبارة عن
+
+13
+00:01:14,730 --> 00:01:20,610
+interior point اللي هي ال interval I اللي عندها
+
+14
+00:01:20,610 --> 00:01:27,220
+اللي هي ال function F ال derivative موجودةبقول لو
+
+15
+00:01:27,220 --> 00:01:32,140
+كان عند النقطة هذه في relative extremum سواء
+
+16
+00:01:32,140 --> 00:01:36,740
+minimum أو maximum لل F عنده نقطة C قطعا ال F
+
+17
+00:01:36,740 --> 00:01:42,900
+prime of C هتساوي 0 ومن هنا استقينا أن أين يمكن
+
+18
+00:01:42,900 --> 00:01:48,060
+إيجاد النقطة العظمى والنقطة الصغيرة المحلية وقلنا
+
+19
+00:01:48,060 --> 00:01:52,480
+هي في أحد ثلاث مناطق اللي هو أما F prime بتساوي 0
+
+20
+00:01:53,060 --> 00:01:58,080
+أو F prime does not exist للنقاط الداخلية طبعا أو
+
+21
+00:01:58,080 --> 00:02:02,120
+اللي هو ال end points فتلت مناطق اللي هي بنفحص
+
+22
+00:02:02,120 --> 00:02:07,360
+فيها اللي هي ال relative maximum أو ال relative
+
+23
+00:02:07,360 --> 00:02:11,400
+minimumوالـ Corollary اللي بعد هي اللي حكيته عنه
+
+24
+00:02:11,400 --> 00:02:16,400
+قبل بشوية الآن و بعدين اتحدثنا .. بدنا نتحدث على
+
+25
+00:02:16,400 --> 00:02:21,180
+ال roles theorem و قولنا ال roles theorem اللي هي
+
+26
+00:02:21,180 --> 00:02:25,840
+كانت بتعالج أنه لو كانت عندي function F من عند A و
+
+27
+00:02:25,840 --> 00:02:31,880
+B لعند R و كانت هذه ال function is continuous على
+
+28
+00:02:31,880 --> 00:02:37,830
+closed intervalاللي هي من a لعند b و
+
+29
+00:02:37,830 --> 00:02:42,030
+differentiable على ال open interval من a لb و أيضا
+
+30
+00:02:42,030 --> 00:02:47,230
+وضعنا شرط أن f of a بيساوي f of b بيساوي سفر
+
+31
+00:02:47,230 --> 00:02:54,210
+بقولنا ال f differentiable on a و bوالـ F
+
+32
+00:02:54,210 --> 00:03:00,110
+continuous on A وB كله مع بعض هذا أعطانا أنه there
+
+33
+00:03:00,110 --> 00:03:05,130
+exists C element in A وB بنلاقي النقطة C بين A وB
+
+34
+00:03:05,130 --> 00:03:10,530
+بحيث أن يكون ميل المماس عندها يساوي سفر أو F prime
+
+35
+00:03:10,530 --> 00:03:16,370
+of C بساوي سفر أو بمعنى آخر يوجد مماس عند هذه
+
+36
+00:03:16,370 --> 00:03:22,030
+النقطة يوازي محور الـ CNETبعد ذلك طبعا تحدثنا عن
+
+37
+00:03:22,030 --> 00:03:27,650
+الـ Mean Value Theorem الـ Mean Value Theorem اللي
+
+38
+00:03:27,650 --> 00:03:31,710
+كانت أيضا على الرسم خلينا نشوف الـ Mean Value
+
+39
+00:03:31,710 --> 00:03:35,590
+Theorem قالت إن لو كانت الـ function is continuous
+
+40
+00:03:35,590 --> 00:03:40,750
+على closed interval من A لB وكانت اللي هي
+
+41
+00:03:40,750 --> 00:03:43,470
+differentiable على الـ open interval A وB
+
+42
+00:03:49,160 --> 00:03:57,260
+الان الاستنتاج اللى بيكون تعميم للهو Rawls theorem
+
+43
+00:03:57,260 --> 00:04:03,350
+ايش هو الاستنتاج انهبنلاقي نقطة في المنطقة بين A و
+
+44
+00:04:03,350 --> 00:04:10,890
+B بكون المماس عندها موازلة القاطع اللي بين مين الـ
+
+45
+00:04:10,890 --> 00:04:14,850
+A و الـ B أو بمعنى آخر بكون عنده النقطة C اللي
+
+46
+00:04:14,850 --> 00:04:21,890
+لاجناها اللي هي F prime of C بساوي F of B minus F
+
+47
+00:04:21,890 --> 00:04:29,310
+of A على B minus A وهذا هو الذي يمثلميل القاطع بين
+
+48
+00:04:29,310 --> 00:04:34,170
+النقطة A أو بين النقطة B أو بين النقطة A و F of A
+
+49
+00:04:34,170 --> 00:04:38,430
+ونقطة B و F of B فبتكون هذه عبارة عن نظرية القيمة
+
+50
+00:04:38,430 --> 00:04:44,030
+المتوسطة اللي هي تعميم لـ Lowell's theorem بعدها
+
+51
+00:04:44,030 --> 00:04:51,790
+تحدثناعن اللي هو البعض النتائج قلنا إن لو كانت الـ
+
+52
+00:04:51,790 --> 00:04:56,930
+function F continuous على closed interval I وكانت
+
+53
+00:04:56,930 --> 00:05:00,410
+F differentiable على ال open interval وكانت اللي
+
+54
+00:05:00,410 --> 00:05:05,090
+هي F prime بتساوي 0 على كل الفترة A وB قلنا هذه
+
+55
+00:05:05,090 --> 00:05:09,430
+الدالة هي الدالة الثابتة هتكون The F is constant
+
+56
+00:05:09,430 --> 00:05:16,400
+على الفترة المغلقة A O Bأيضًا Corollary لهذه
+
+57
+00:05:16,400 --> 00:05:20,840
+النظرية برضه اللي هي معلومات معهودة من ال calculus
+
+58
+00:05:20,840 --> 00:05:26,340
+اللي هي أنه لو كان في عندنا دالتين F و G و هذولة
+
+59
+00:05:26,340 --> 00:05:30,600
+الدالتين اللي عندنا اللي هن .. اللي هن نفس المشتقة
+
+60
+00:05:30,600 --> 00:05:36,380
+على الفترة A و B Openبكون عندى الفرق بين اللى هى
+
+61
+00:05:36,380 --> 00:05:39,460
+الـ F و الـ G هو عبارة عن ثابت أو بمعنى آخر F
+
+62
+00:05:39,460 --> 00:05:44,880
+بتساوي G زائد C for some constant C على الفترة I
+
+63
+00:05:44,880 --> 00:05:51,160
+بعد هيك اللى دخلنا و أعرفنا شو معنات F من I لعند R
+
+64
+00:05:51,160 --> 00:05:55,780
+is increasing على ال interval قلنا أن F is
+
+65
+00:05:55,780 --> 00:06:03,570
+increasing إذا كانت اللى هىأخدنا أي نقطتين في الـ
+
+66
+00:06:03,570 --> 00:06:09,870
+I X1 و X2 بحقق ان X1 أصغر من X2 إذا قدلنا هذا أن
+
+67
+00:06:09,870 --> 00:06:13,430
+أف X1 أصغر أو أسوأ من أف X2 من جول عن الـ function
+
+68
+00:06:13,430 --> 00:06:19,430
+A شمالها is increasingالان اللي هو similar لتعريف
+
+69
+00:06:19,430 --> 00:06:24,190
+الـ decreasing إن X1 أصغر من X2 تؤدي إلى F of X1
+
+70
+00:06:24,190 --> 00:06:29,230
+أكبر أو يساوي F of X2 بتكون اليد ده اللي أشمالها
+
+71
+00:06:29,230 --> 00:06:33,970
+is decreasing على هذه الفترةفي المقابل أيضًا في
+
+72
+00:06:33,970 --> 00:06:36,810
+تعريف حاجة اسمها برضه ذكرناه هو strictly
+
+73
+00:06:36,810 --> 00:06:40,230
+increasing أو strictly decreasing strictly
+
+74
+00:06:40,230 --> 00:06:44,070
+increasing أو strictly decreasing نحكي عن ال
+
+75
+00:06:44,070 --> 00:06:48,610
+strictly increasing بتكون اللي هي تحقق مالي لو x1
+
+76
+00:06:48,610 --> 00:06:54,590
+و x2 في ال I و x1 أصغر من x2 هذا بيقديلي إلى f of
+
+77
+00:06:54,590 --> 00:07:00,530
+x1 strictly أصغر من f of x2 مع عدم إمكانية
+
+78
+00:07:00,530 --> 00:07:06,340
+المساويةالان similarly for الـ F is اللي هو
+
+79
+00:07:06,340 --> 00:07:10,820
+strictly decreasing هذا اتحدثنا فيه المرة الماضية
+
+80
+00:07:10,820 --> 00:07:14,240
+النظرية
+
+81
+00:07:14,240 --> 00:07:17,860
+اللي هي let F من I لعند R be differentiable اللي
+
+82
+00:07:17,860 --> 00:07:23,100
+هي أوصلنا عند هذه النظرية خلينا نشوف هذه النظرية و
+
+83
+00:07:23,100 --> 00:07:30,900
+نتفحص إيش هي نظرية بتقول و من ثم نشوف لماذااللي هو
+
+84
+00:07:30,900 --> 00:07:38,960
+هي صحيحة عندي
+
+85
+00:07:38,960 --> 00:07:46,440
+نظرية بتقوللي theorem 6.2.7 اللي بتحكي النظرية
+
+86
+00:07:46,440 --> 00:07:54,580
+بتقوللي لو كان عندي F let F من I لعنب R be
+
+87
+00:07:54,580 --> 00:08:05,490
+differentiable onthe interval .. the interval I
+
+88
+00:08:05,490 --> 00:08:11,910
+فرضنا إن F is differentiable على الinterval I الآن
+
+89
+00:08:11,910 --> 00:08:17,690
+اللي بدأ أقوله عبارة عن test بنستعمل ال test في
+
+90
+00:08:17,690 --> 00:08:22,030
+معرفة إن F is increasing أو لأ و F is decreasing
+
+91
+00:08:22,030 --> 00:08:27,530
+أو لأ بنقول F is increasing
+
+92
+00:08:29,130 --> 00:08:36,650
+on I إيش الفحص؟ if and only if F prime of X أكبر
+
+93
+00:08:36,650 --> 00:08:44,130
+أو يساوي سفر لكل X موجودة في الـ I والآن F is
+
+94
+00:08:44,130 --> 00:08:52,450
+decreasing on I if and only if F prime of X أصغر
+
+95
+00:08:52,450 --> 00:08:57,750
+أو يساوي سفر لكل X element in I هذه هي النظرية
+
+96
+00:08:57,750 --> 00:09:04,430
+اللي عندناو هنبرهن اللي هو A أو B في الكتاب نبرهن
+
+97
+00:09:04,430 --> 00:09:09,370
+A خلّينا نبرهن مين نبرهن B و هتكون A similarly for
+
+98
+00:09:09,370 --> 00:09:17,550
+B الان بي .. بدنا نفترض suppose that
+
+99
+00:09:17,550 --> 00:09:30,710
+F is decreasing on IF is decreasing on I بدنا ..
+
+100
+00:09:30,710 --> 00:09:36,650
+بدنا نثبت الآن أن الـ F prime of X اللي هي أصغر أو
+
+101
+00:09:36,650 --> 00:09:43,190
+يساوي مين سفر طبعاً F prime of X في النهاية إيش
+
+102
+00:09:43,190 --> 00:09:47,930
+هي؟ عشان نشوف كيف بنفكر أول إشي F prime of X بساوي
+
+103
+00:09:47,930 --> 00:09:55,080
+limit F of Xأو f prime of c مثلا for arbitrary c f
+
+104
+00:09:55,080 --> 00:10:00,820
+of x نقص f of c على x minus c لما x تروح لل c إذا
+
+105
+00:10:00,820 --> 00:10:05,520
+ال limit هذا أثبتناه أصغر أو يساوي سفر معناته صارت
+
+106
+00:10:05,520 --> 00:10:12,030
+اللي هي ال f prime أصغر أو يساوي سفرالان عندى انا
+
+107
+00:10:12,030 --> 00:10:16,990
+لو اثبتت هذا المقدار اصغر او يساوي سفر في المنطقة
+
+108
+00:10:16,990 --> 00:10:20,870
+حول الـC بقدر اقول ان ال limit على طول ايه اشماله
+
+109
+00:10:20,870 --> 00:10:27,550
+اصغر او يساوي ايه سفر ده نشوف كيف عندى الان بدي
+
+110
+00:10:27,550 --> 00:10:32,170
+اثبت انها هذه F prime اصغر او يساوي سفر على كل X
+
+111
+00:10:32,170 --> 00:10:39,450
+element in I بدي اقول let C be an arbitrary
+
+112
+00:10:41,100 --> 00:10:47,160
+and fixed in I يعني بتحكي عنها عن C لكن هي
+
+113
+00:10:47,160 --> 00:10:54,780
+arbitrary لكن بحكي عن C معينة الآن عندي يا X أكبر
+
+114
+00:10:54,780 --> 00:11:01,800
+من C يا X أشمالها أصغر من Cماشي الحال ليش أخدت
+
+115
+00:11:01,800 --> 00:11:04,160
+أكبر أو أصغر؟ لأن عمّالي بيداخد limit فالـ X ده
+
+116
+00:11:04,160 --> 00:11:09,060
+تساوي C في حالة الـ C اللي هو الأمر اللي هيكون
+
+117
+00:11:09,060 --> 00:11:13,180
+اللي هي عبارة
+
+118
+00:11:13,180 --> 00:11:17,520
+عن الـ trivial case نشوف كيف، إيش اللي بنحكيه؟
+
+119
+00:11:17,520 --> 00:11:23,440
+الآن X أكبر من C عندي إيش مفترضين إحنا؟ F is
+
+120
+00:11:23,440 --> 00:11:30,920
+decreasing لذا then F of Xأصغر أو يساوي F of C
+
+121
+00:11:30,920 --> 00:11:38,100
+مظبوط أه بصير عندي الحسب اللي كتبته قبل و شوية F
+
+122
+00:11:38,100 --> 00:11:47,680
+of X نقص F of C اللي هو بساوي على X minus C اللي
+
+123
+00:11:47,680 --> 00:11:52,290
+هو هذا سالبf of x نقص f of z أصغر أو أكبر من صفر و
+
+124
+00:11:52,290 --> 00:11:57,110
+ال x minus z أشماله أكبر من صفر هذا الأن أكبر
+
+125
+00:11:57,110 --> 00:12:02,650
+أسالب أو صفر وهذا موجب إذا حيكون أصغر أو يساوي أيش
+
+126
+00:12:02,650 --> 00:12:08,760
+صفرواضح اه Similarly الحالة التانية من X هذا لكل
+
+127
+00:12:08,760 --> 00:12:12,800
+ال Xات اللي مين اللي أكبر من C طبعا وال Xات أنا من
+
+128
+00:12:12,800 --> 00:12:16,740
+وين باخدها من I على كل شغلي في داخل من ال interval
+
+129
+00:12:16,740 --> 00:12:21,320
+I يعني Xات اللي بشتغل فيها داخل I الان X أصغر من C
+
+130
+00:12:21,320 --> 00:12:24,900
+أكيد similarly بنفس الطريقة مدام ال decreasing
+
+131
+00:12:24,900 --> 00:12:31,580
+بيصير F of X أكبر أو يساوي F of C بيصير عندي الآن
+
+132
+00:12:31,580 --> 00:12:40,060
+اذا F of Xنقص F of C وهو موجبة وهذه X minus C
+
+133
+00:12:40,060 --> 00:12:44,880
+سالبة إذا هذولة على X minus C برضه هتطلع إيه
+
+134
+00:12:44,880 --> 00:12:49,720
+شمالها أصغر أو يساوي سفر إذا صار عندي من الجهتين
+
+135
+00:12:49,720 --> 00:12:55,660
+هنا for any X
+
+136
+00:12:55,660 --> 00:13:03,040
+element in I و X لا تساوي C أنا أصلا ملزمني حوالين
+
+137
+00:13:03,040 --> 00:13:09,810
+الـ Cلكن هذا كله كلام صحيح لـ X ∈ I X ≤ C طالع
+
+138
+00:13:09,810 --> 00:13:17,350
+عندي اللي هو F of X نعقص F of C على X minus C أصغر
+
+139
+00:13:17,350 --> 00:13:23,610
+و سوى 0 الآن مدام هذا صحيح لكل X إذا ال limitهذا
+
+140
+00:13:23,610 --> 00:13:27,530
+المقدار لما X تروح للـ C برضه هيظل أصغر أو يساوي
+
+141
+00:13:27,530 --> 00:13:33,950
+سفر وهذا هو إيش اسمه F prime of C يعني أثبتنا F
+
+142
+00:13:33,950 --> 00:13:38,530
+prime of C أصغر أو يساوي السفر وعند C كانت
+
+143
+00:13:38,530 --> 00:13:42,550
+arbitrary and fixed in I إذا صار بناء على هذا
+
+144
+00:13:42,550 --> 00:13:49,050
+الحديث صار F prime of X أصغر أو يساوي سفر لكل X
+
+145
+00:13:49,050 --> 00:13:54,760
+element in I لأنه كانت C is arbitraryهذا اللي هو
+
+146
+00:13:54,760 --> 00:14:00,440
+الجزء الأول من النظرية من اللي هو B أنه بدنا الأن
+
+147
+00:14:00,440 --> 00:14:03,180
+نيجي ل conversely بدنا نفترض هذا أصحى و أصحى و صفر
+
+148
+00:14:03,180 --> 00:14:09,040
+و نوصل لمين لل F is decreasing نيجي الأن
+
+149
+00:14:09,040 --> 00:14:19,240
+conversely و نشوف كيف نبرهن conversely الأن
+
+150
+00:14:19,240 --> 00:14:25,030
+converselyطبعاً ببرهم في AVP برضه انا conversely
+
+151
+00:14:25,030 --> 00:14:30,810
+suppose that
+
+152
+00:14:32,170 --> 00:14:39,270
+F prime of X أصغر أو سوى سفر لكل X موجودة في الآية
+
+153
+00:14:39,270 --> 00:14:43,790
+ماشي الحال شوفوا صلى الله عليه الصلاة والسلام أنا
+
+154
+00:14:43,790 --> 00:14:47,810
+بدأ أثبت أن F is decreasing يعني بدأ أفترض أن X
+
+155
+00:14:47,810 --> 00:14:53,650
+أصغر أو أخد أي قيمتين X واحد و X اتنين element
+
+156
+00:14:53,650 --> 00:14:59,250
+اتنينأخدت أي two elements element x1 وx2 element
+
+157
+00:14:59,250 --> 00:15:06,850
+in I تحقق such that x1 أصغر من مين من x2 أصغر أو
+
+158
+00:15:06,850 --> 00:15:10,570
+يساوي x .. x1 أصغر أو يساوي x2 بس في حالة ال x1
+
+159
+00:15:10,570 --> 00:15:14,490
+بيساوي x2 ما هي automatic F of x1 بيساوي F of x2
+
+160
+00:15:14,490 --> 00:15:19,920
+يعني متحققةإذن الان x1 أصغر من x2 عملتها strictly
+
+161
+00:15:19,920 --> 00:15:23,720
+عشان بتعمل منها interval وحالتي ال x1 بيساوي x2 is
+
+162
+00:15:23,720 --> 00:15:28,000
+a trivial case تتحقق مدامة x1 أصغر تساوي x2 إذن
+
+163
+00:15:28,000 --> 00:15:32,100
+عشان a function f of x1 بيساوي f of x2 إذا التحقق
+
+164
+00:15:32,100 --> 00:15:39,340
+اللي هي مين ال decreasing واضحة الان x1 أصغر من x2
+
+165
+00:15:39,340 --> 00:15:41,620
+الآن we apply
+
+166
+00:15:45,100 --> 00:15:48,880
+الـ Mean Value Theorem لأن احنا هذه نبارع كورولرز
+
+167
+00:15:48,880 --> 00:15:52,380
+أو نظريات على الـ Mean Value Theorem فالمتوقع أن
+
+168
+00:15:52,380 --> 00:15:55,240
+نستخدم الـ Mean Value Theorem في أثباتها فهنا
+
+169
+00:15:55,240 --> 00:15:59,000
+سنستخدم الـ Mean Value Theorem نطبق الـ Mean Value
+
+170
+00:15:59,000 --> 00:16:05,470
+Theorem على الانترفل الموجود بين X1 و X2طبعاً عندي
+
+171
+00:16:05,470 --> 00:16:10,330
+F هذه X1 و X2 عبارة عن جزئية من مين؟ من الـ I إذا
+
+172
+00:16:10,330 --> 00:16:12,790
+الـ F is differentiable عليها مادام differentiable
+
+173
+00:16:12,790 --> 00:16:16,050
+إذا continuous علي close و differentiable علي open
+
+174
+00:16:16,050 --> 00:16:19,240
+لإنها differentiable علي كلهاإذا شروط الـ Mean
+
+175
+00:16:19,240 --> 00:16:24,580
+Value Theorem مالها متحققة إذا there exist then
+
+176
+00:16:24,580 --> 00:16:31,060
+there exist C تنتمي إلى الفترة X1 و X2 يعني موجودة
+
+177
+00:16:31,060 --> 00:16:35,220
+في الـ I اللي هي لإن هذي جزئية من مين من I there
+
+178
+00:16:35,220 --> 00:16:43,480
+exist C such that F prime of C بساوي F of X1 أو F
+
+179
+00:16:43,480 --> 00:16:55,670
+of X2 ناقصF of X1 على X2 ناقص X1 واضح أه؟ أضرب
+
+180
+00:16:55,670 --> 00:17:00,510
+طرفين في وسطين أضرب هذه في هذه بيصير عندي F of X2
+
+181
+00:17:00,510 --> 00:17:08,170
+ناقص F of X1 اللي هو بيساوي X2 ناقص X1 في F prime
+
+182
+00:17:08,170 --> 00:17:16,190
+of C الآن عندي X2 ناقص X1 موجبةمظبوط؟ و F prime of
+
+183
+00:17:16,190 --> 00:17:20,290
+C اللي هي سالبة لإنه C واحدة من نقاط ال I و F
+
+184
+00:17:20,290 --> 00:17:24,890
+prime أصغر من سفر فيها كلها إذا صار عندي هذه سالبة
+
+185
+00:17:24,890 --> 00:17:30,150
+و هذه موجبة إذا حاصل ضربهم إيه شماله أصغر أو يساوي
+
+186
+00:17:30,150 --> 00:17:40,640
+سفر إذا صار عندي F of X2 أصغر أو يساوي Fof X1 الان
+
+187
+00:17:40,640 --> 00:17:45,900
+بدنا ب X1 أصغر من X2 وانتهينا ب F of X2 أصغر من F
+
+188
+00:17:45,900 --> 00:17:51,260
+of X1 but .. but .. but .. احنا بنعرف خلينا نكملها
+
+189
+00:17:51,260 --> 00:17:56,300
+كدا من اللي حكيناه في الأول X2 بيساوي X1 implies F
+
+190
+00:17:56,300 --> 00:18:04,100
+of X2 بتساوي F of X1 مظبوط؟ الان من هذه اللي عندي
+
+191
+00:18:04,100 --> 00:18:10,460
+الحقيقة هذهومن اللي أثبتته من هنا لعند هنا التنتين
+
+192
+00:18:10,460 --> 00:18:20,280
+together بنستنتج أنه if x1 أصغر أو يساوي x2 then f
+
+193
+00:18:20,280 --> 00:18:23,660
+of x2
+
+194
+00:18:23,660 --> 00:18:32,800
+أصغر أو يساوي fof x واحد هذا فيضوء أن f prime of x
+
+195
+00:18:32,800 --> 00:18:37,220
+أصغر أو أشهر أو شفر لكل x element in I وهذا يعني
+
+196
+00:18:37,220 --> 00:18:50,740
+أن hence f is decreasing on mean on I واضح طيب
+
+197
+00:18:50,740 --> 00:18:58,280
+الآن بدنا نعرف حاجة اسمهاStrictly increasing
+
+198
+00:18:58,280 --> 00:19:04,300
+Strictly increasing قبل شوية قلتها أنه بنقول أن F
+
+199
+00:19:04,300 --> 00:19:09,140
+is strictly increasing إذا كانت اللي هي strictly
+
+200
+00:19:09,140 --> 00:19:14,600
+increasing بديش أمسح حد لإن أنا اللي بديه بعد شوية
+
+201
+00:19:14,600 --> 00:19:23,720
+خليني أمسح النظرية برهنة بيه أنا هو ماشي بدي بس من
+
+202
+00:19:23,720 --> 00:19:30,890
+الآن X بنقول Fis strictly increasing إيش معناته
+
+203
+00:19:30,890 --> 00:19:38,470
+إنه X هنا يكافئ إن X1 أصغر من X2 لل X1 وال X2 اللي
+
+204
+00:19:38,470 --> 00:19:46,790
+في I such that يؤدي F of X1 strictly أصغر من F of
+
+205
+00:19:46,790 --> 00:19:53,580
+X2 هذا يعني على بعضه إن F is strictlyincreasing
+
+206
+00:19:53,580 --> 00:19:58,440
+similarly for decreasing for strictly decreasing f
+
+207
+00:19:58,440 --> 00:20:04,360
+is strictly decreasing لما x1 أصغر من x2 تؤدي إلى
+
+208
+00:20:04,360 --> 00:20:10,160
+f of x1 أكبر strictly من مين من f of x2 هذا معناته
+
+209
+00:20:10,160 --> 00:20:16,640
+strictly أيش decreasing الآن السؤال اللي بطرحه
+
+210
+00:20:16,640 --> 00:20:23,380
+الآن هو بقولنيإن انت حكيت في حالة الـ increasing F
+
+211
+00:20:23,380 --> 00:20:27,980
+is increasing in I if and only if F' أصغر أوي
+
+212
+00:20:27,980 --> 00:20:31,960
+يساوي 0 لكل X element in I بقول لي هل هذا الكلام
+
+213
+00:20:31,960 --> 00:20:37,020
+بضل صحيح في حالة ال strictly increasing يعني لو
+
+214
+00:20:37,020 --> 00:20:43,480
+كانت بسأل السؤال لو كانت F is strictly
+
+215
+00:20:45,290 --> 00:20:49,790
+increasing او decreasing اللي بدك هي increasing او
+
+216
+00:20:49,790 --> 00:20:57,630
+decreasing هل هذا بيكون if and only if F prime of
+
+217
+00:20:57,630 --> 00:21:04,270
+X أصغر strictly من 0 لكل X element in I ولا لأ؟
+
+218
+00:21:04,270 --> 00:21:12,010
+الآن لو كان F prime أصغر strictly من 0 ل X element
+
+219
+00:21:12,010 --> 00:21:17,620
+in Iاللي هو الـ conversely هذا اللي هو بيعطينا F's
+
+220
+00:21:17,620 --> 00:21:22,620
+strictly decreasing يعني الاتجاه هذا متوقعين أنه
+
+221
+00:21:22,620 --> 00:21:27,500
+إحنا إيه شماله يكون صحيح يعني متوقعين أنه لو F
+
+222
+00:21:27,500 --> 00:21:31,520
+prime أصغر strictly من Zero لكل X element of I
+
+223
+00:21:31,520 --> 00:21:36,260
+يعطينا F's strictly أشماله decreasingوزيه برضه الـ
+
+224
+00:21:36,260 --> 00:21:41,580
+increasing لو كانت F' أكبر strictly من 0 بيعطينا F
+
+225
+00:21:41,580 --> 00:21:46,380
+is strictly increasing هذا متوقع أن يكون صحيح
+
+226
+00:21:46,380 --> 00:21:53,440
+والبرهان هيه موجود علّه لسه ما شطبطوش لسه الآن بدأ
+
+227
+00:21:53,440 --> 00:21:56,780
+افترض أنه بدل ما هي أكبر أصغر أو أسعار بدأ افترضها
+
+228
+00:21:56,780 --> 00:22:02,500
+أشمالهاStrictly أصغر ماشي الحال الان بفترض ان X1
+
+229
+00:22:02,500 --> 00:22:07,120
+أصغر من X2 و بطبق كل اللي عملته و لعند ال hand
+
+230
+00:22:07,120 --> 00:22:14,860
+بشطب هذا بالديشيا و بقف ال hand و بقولبما أنه هذا
+
+231
+00:22:14,860 --> 00:22:18,480
+المقدار f prime of c اللي هي f prime of x strictly
+
+232
+00:22:18,480 --> 00:22:22,840
+أصغر من 0 يعني مافي إمكانية أن تساوي 0 وهذا x2
+
+233
+00:22:22,840 --> 00:22:28,320
+ناقص x1 من هذا برضه strictly أكبر من 0 إذا صار هذا
+
+234
+00:22:28,320 --> 00:22:32,520
+عبارة عن strictly أصغر من 0 ولا يوجد إمكانية
+
+235
+00:22:32,520 --> 00:22:36,620
+للمساوية إذا بمعنى آخر صار هذا المقدار strictly
+
+236
+00:22:36,620 --> 00:22:40,680
+أصغر من هذا يعني لما كانت f prime أصغر strictly من
+
+237
+00:22:40,680 --> 00:22:45,770
+0 لكل x element in RI وجدنا إن X1 أصغر strictly من
+
+238
+00:22:45,770 --> 00:22:51,010
+X2 تؤدي F of X2 أصغر strictly من F of X1 وهذا يعني
+
+239
+00:22:51,010 --> 00:22:59,690
+strictly stick raising واضح، أه؟ الآن السؤال هل
+
+240
+00:22:59,690 --> 00:23:07,830
+the converse is true؟ هل the converse is true؟
+
+241
+00:23:07,830 --> 00:23:10,650
+الآن يعني
+
+242
+00:23:13,960 --> 00:23:21,020
+الاتجاه هذا صحيح لما يقول الاتجاه الثاني هذا need
+
+243
+00:23:21,020 --> 00:23:26,500
+not to be true in general بدنا نجيب مثال ان تكون F
+
+244
+00:23:26,500 --> 00:23:30,780
+strictly decreasing لكن ال F براي مش أصغر strictly
+
+245
+00:23:30,780 --> 00:23:37,120
+من مين؟ من 0 على I خد الآن F of Xبساو سالب X تكعيب
+
+246
+00:23:37,120 --> 00:23:42,220
+هذا الدالة هذا الدالة بنعمل reference مثل F of X
+
+247
+00:23:42,220 --> 00:23:47,120
+ساو سالب X تكعيب بالشكل هذا هذا الان strictly ايه
+
+248
+00:23:47,120 --> 00:23:54,800
+شمالها decreasing هذه F is strictly decreasing
+
+249
+00:23:55,740 --> 00:24:03,860
+لأن لو كانت X1 أصغر من X2 أكيد X1 تكعيب strictly
+
+250
+00:24:03,860 --> 00:24:13,420
+أكبر من X2 إيه شمالها تكعيب آسف ناقص مظبوط الانصار
+
+251
+00:24:13,420 --> 00:24:18,320
+عندي الآن يعني اللي هي ال F عندي أنا strictly
+
+252
+00:24:18,320 --> 00:24:23,770
+decreasingbut طبعاً على كل مين على كل ال I اللي
+
+253
+00:24:23,770 --> 00:24:27,090
+أخدت منها لها خد أي I من A لعند B من ناقص خمسة
+
+254
+00:24:27,090 --> 00:24:31,410
+مثلا لعند خمسة على الفترة اللي بدك إياها but F
+
+255
+00:24:31,410 --> 00:24:40,250
+prime عند اللي هو نقطة ال zero إيش بساوي بساوي سفر
+
+256
+00:24:40,250 --> 00:24:45,150
+إذا اللي هو ماعطنيش الشرط إن F prime أصغر من سفر
+
+257
+00:24:45,150 --> 00:24:51,290
+على كل النقاط ال X اللي وين في ال I واضح أهالان
+
+258
+00:24:51,290 --> 00:24:58,210
+معطيني معرفلي
+
+259
+00:24:58,210 --> 00:25:04,150
+اللي هو شو معناته طبعا احنا عرفنا ال increasing و
+
+260
+00:25:04,150 --> 00:25:09,670
+ال decreasing على ال interval لأنها مقارنة بالنقاط
+
+261
+00:25:09,670 --> 00:25:14,510
+فالان بقولي طب كيف؟ ايش رايكم؟ بدنا نحكي عن ال
+
+262
+00:25:14,510 --> 00:25:18,860
+increasing او ال decreasing عند نقطةالـ increasing
+
+263
+00:25:18,860 --> 00:25:21,640
+أو الـ decreasing و عنده ضغطة عموماً هذه الفلسفة
+
+264
+00:25:21,640 --> 00:25:26,360
+موجودة يعني في أكثر من مجال للتعريف في الرياضيات
+
+265
+00:25:26,360 --> 00:25:31,380
+في المناطق اللي ممكن اللي هو تحتاج أو في المفاهيم
+
+266
+00:25:31,380 --> 00:25:37,020
+اللي ممكن تحتاج لمنطقة لتعريفاللي هو المفهوم
+
+267
+00:25:37,020 --> 00:25:41,400
+المقصود بمنطقة زي الـ interval اللي قبل بشوية يعني
+
+268
+00:25:41,400 --> 00:25:48,200
+مش عند نقطة لأ عند منطقة فبصير التعريف اللي هو أن
+
+269
+00:25:48,200 --> 00:25:53,920
+يتحقق المفهوم في الجوار ده النقطة اللي مذكورة يعني
+
+270
+00:25:53,920 --> 00:25:59,120
+بنقول أنه النقطة C تتمتع بهذه الخاصية إذا تمتع
+
+271
+00:25:59,120 --> 00:26:03,940
+الجوار بهذه الخاصية هذا فلسفة التعريف فالآن بدنا
+
+272
+00:26:03,940 --> 00:26:04,260
+نقول
+
+273
+00:26:09,560 --> 00:26:14,260
+F من I لعند R اللي عبارة عن function أي إن كانت
+
+274
+00:26:14,260 --> 00:26:18,260
+الـ function هذه واخدنا
+
+275
+00:26:18,260 --> 00:26:28,780
+C element in I بدنا نعرف شو معنات عند النقطة C عند
+
+276
+00:26:28,780 --> 00:26:33,240
+النقطة C شو معنات F is increasing at this point
+
+277
+00:26:33,240 --> 00:26:40,880
+بدنا نشوف شو معنات F is increasingat C element in
+
+278
+00:26:40,880 --> 00:26:48,420
+I معناته انه there exist هذا يكافئ there exist V
+
+279
+00:26:48,420 --> 00:26:53,440
+Delta of C يعني U ده الجوار حوالين من الـ C هذا
+
+280
+00:26:53,440 --> 00:27:03,210
+الجوار C ناقص دلتا و C زائد دلتا ابحث ان تكون Fis
+
+281
+00:27:03,210 --> 00:27:08,770
+increasing on this جوار أو on this neighbourhood
+
+282
+00:27:08,770 --> 00:27:14,770
+إذا تحقق الشرط هذا معناته أنه بنقول عن الـ
+
+283
+00:27:14,770 --> 00:27:18,450
+function F أشمالها إنها increasing at the point
+
+284
+00:27:18,450 --> 00:27:23,090
+mean C يعني بمعنى آخر إذا تحقق اللي هو there
+
+285
+00:27:23,090 --> 00:27:29,870
+exists V Delta of C such that if X1 و X2 element
+
+286
+00:27:29,870 --> 00:27:42,110
+in V Delta of C withX1 أصغر من X2 أصغر
+
+287
+00:27:42,110 --> 00:27:49,350
+من X2 أصغر
+
+288
+00:27:49,350 --> 00:27:54,840
+من X2يعني اتحققت الخاصية أو الـ increasing في جوار
+
+289
+00:27:54,840 --> 00:27:58,120
+حول الـ C هذا معناته اللي هو مين؟ اللي هو
+
+290
+00:27:58,120 --> 00:28:01,820
+increasing similarly for strictly increasing ..
+
+291
+00:28:01,820 --> 00:28:07,000
+strictly increasing .. strictly increasing X1 أصغر
+
+292
+00:28:07,000 --> 00:28:11,160
+من X2 يؤد F of X1 strictly أصغر من F of X2 في هذا
+
+293
+00:28:11,160 --> 00:28:15,480
+الجوار similarly for اللي هو مين؟ decreasing و
+
+294
+00:28:15,480 --> 00:28:20,150
+strictly decreasing بما يتلقى أمهمالتلاقم معناته
+
+295
+00:28:20,150 --> 00:28:25,490
+X1 أصغر من X2 بيعطينا F of X1 أصغر أكبر أو يساوي F
+
+296
+00:28:25,490 --> 00:28:31,890
+of X2 لـ Decreasing للي بيكون Strictly أكبر منها
+
+297
+00:28:31,890 --> 00:28:39,410
+طيب .. الآن السؤال .. السؤال اللي بيقول ليه .. طيب
+
+298
+00:28:39,410 --> 00:28:49,320
+.. الآن أنت قلت أنه لو كانت F prime أكبر من 0f
+
+299
+00:28:49,320 --> 00:28:57,040
+prime of x أكبر من 0 لكل x element in I اللي
+
+300
+00:28:57,040 --> 00:29:05,200
+بيعطيني اللي هو f is strictly increasing صح ولا
+
+301
+00:29:05,200 --> 00:29:10,560
+لأ؟ قلنا هيك معايا لكن قلنا ال .. ال .. ال
+
+302
+00:29:10,560 --> 00:29:13,600
+converse need not to be true in general جبنا مثال
+
+303
+00:29:15,110 --> 00:29:18,590
+أف of X بسوء X تكعيب للـ increasing أو ناقص X
+
+304
+00:29:18,590 --> 00:29:23,690
+تكعيب لل decreasingماشي الحال .. الآن هو بقول طيب
+
+305
+00:29:23,690 --> 00:29:26,330
+لأ أنا بديش أسأله عن الاتجاه الثاني لإنه خلاص احنا
+
+306
+00:29:26,330 --> 00:29:29,990
+شفنا الاتجاه الثاني عند اللي هو ال interval مش
+
+307
+00:29:29,990 --> 00:29:35,450
+متحقق فالآن بقوللي أنا بدأ أسأل السؤال على اللي هي
+
+308
+00:29:35,450 --> 00:29:39,750
+.. اللي هو هذا السؤال اللي اتحقق في ال interval هل
+
+309
+00:29:39,750 --> 00:29:44,790
+بتحقق عنده النقطة؟ يعني بمعنى أخر لو كانت عندي a
+
+310
+00:29:44,790 --> 00:29:53,390
+February at c أكبر من 0هل هذا يؤدي أن f is
+
+311
+00:29:53,390 --> 00:30:03,070
+strictly increasing on c أو at c؟ هل هذا يؤدي أن
+
+312
+00:30:03,070 --> 00:30:06,090
+لو كانت f' of c أكبر من 0 هل يؤدي إلى أن f is
+
+313
+00:30:06,090 --> 00:30:09,910
+strictly increasing at c؟ بقول لك، this need not
+
+314
+00:30:09,910 --> 00:30:14,430
+to be true in general وهذا هو exercise عشرة اللي
+
+315
+00:30:14,430 --> 00:30:18,660
+معاكم homework اللي هو أعطاني function g of xبساوي
+
+316
+00:30:18,660 --> 00:30:23,120
+x زي 2x تربيع sin 1 علي x إذا كانت x بتساوي سفر و
+
+317
+00:30:23,120 --> 00:30:27,780
+0 إذا كانت x بتساوي سفر و بقول لي لو جيت فحصة ال G
+
+318
+00:30:27,780 --> 00:30:32,960
+prime عند ال zero هتلاقيها أشمالها بتساوي 1 ماشي
+
+319
+00:30:32,960 --> 00:30:37,320
+الحال يعني بتساوي واحد يعني strictly أكبر منين من
+
+320
+00:30:37,320 --> 00:30:44,050
+سفر butولا جوار، there is no neighbourhood around
+
+321
+00:30:44,050 --> 00:30:52,850
+zero in which F is increasingأه فشي دير جي is not
+
+322
+00:30:52,850 --> 00:30:56,850
+increasing in any neighborhood of x بتساوي سفر
+
+323
+00:30:56,850 --> 00:31:02,770
+والتفاصيل ان شاء الله لما في ال discussion لما
+
+324
+00:31:02,770 --> 00:31:06,550
+نعمل discussion اللي هو ال section اللي هو 6 2
+
+325
+00:31:06,550 --> 00:31:11,210
+وتجربوا تحلوه في البيت في حال انتوا ماعرفتوش تحلوه
+
+326
+00:31:11,210 --> 00:31:15,670
+بنحكي فيه بتفاصيله في ال discussion ان شاء الله
+
+327
+00:31:22,930 --> 00:31:27,050
+لأ الجوار هتلاقي اللي هو .. اللي هو .. اللي هو
+
+328
+00:31:27,050 --> 00:31:32,830
+مستحيل يعني تلاقي اللي هو جوار تكون X1 أصغر من X2
+
+329
+00:31:32,830 --> 00:31:37,150
+و تضمن أن F of X1 أصغر من F of X2 لكل واحدة بتحقق
+
+330
+00:31:37,150 --> 00:31:43,010
+ال X1 أصغر من X2 يعني هتلاقي نقاط هتلاقي هل جت V
+
+331
+00:31:43,010 --> 00:31:48,510
+Delta of C مثلا لأ كانت Delta بساوة C نقص Delta و
+
+332
+00:31:48,510 --> 00:31:53,690
+C زائد Deltaماشي الحال .. الآن هتلاقي أنه .. أنه
+
+333
+00:31:53,690 --> 00:31:59,090
+مستحيل يعني أنه في أي .. لو مهما زغرت المسافة
+
+334
+00:31:59,090 --> 00:32:05,110
+بينهم يتلاقي X1 أصغر من X2 تضمن يتلاقي أف of X1
+
+335
+00:32:05,110 --> 00:32:10,050
+أكبر أو يساوي أف of X2 في حالة ال decreasing أو
+
+336
+00:32:10,050 --> 00:32:13,690
+أصغر أو يساوي في حالة ال increasing أو اللي بنحكي
+
+337
+00:32:13,690 --> 00:32:16,770
+عنه أش ماله strictly increasing يعني هتلاقي نقاط
+
+338
+00:32:16,770 --> 00:32:21,030
+جانب بعضوحدة أكبر من التانية و very close .. very
+
+339
+00:32:21,030 --> 00:32:25,870
+close اللي هو .. و تكون .. اللي هو واحدة اللي هو
+
+340
+00:32:25,870 --> 00:32:30,970
+اتلاقيها أكبر و التانية اتلاقيها نقطش أخر اه .. اه
+
+341
+00:32:30,970 --> 00:32:34,230
+.. اه .. في .. اه .. في .. اتلاقيهم يعني ال .. ال
+
+342
+00:32:34,230 --> 00:32:37,630
+.. ال .. ال .. طبعا هو يمكن السبب بالذبذبحان لو
+
+343
+00:32:37,630 --> 00:32:43,710
+لاحظت هدي sign واحد على X فال X اللي هو بتساوي
+
+344
+00:32:43,710 --> 00:32:48,720
+اتنين .. واحد على اتنين on byأو 2 and by هتلاقي
+
+345
+00:32:48,720 --> 00:32:52,740
+اللي هي إيش بيعملك سفر و إيش بيعملك واحد في حالة
+
+346
+00:32:52,740 --> 00:32:55,920
+ال F of prime و في حالة ال F العادية فهيسببلك اللي
+
+347
+00:32:55,920 --> 00:33:01,180
+هو مش هتظلها اللي هي ال .. اللي هي ال .. ال .. ال
+
+348
+00:33:01,180 --> 00:33:08,300
+.. القيم .. قيم هتلاقيها مستحيل إن X1 أصغر من X2 و
+
+349
+00:33:08,300 --> 00:33:12,580
+تظلها على نفس المنوال F of X1 أصغر من F of X2 يعني
+
+350
+00:33:12,580 --> 00:33:18,070
+ممكن تلاقيه لك إنه جدتينclosed لجوه هتلاقي بتحققش
+
+351
+00:33:18,070 --> 00:33:26,150
+هذه يا بتحقق مسواء يا بتحقق الأصغر ولو لجيتلك
+
+352
+00:33:26,150 --> 00:33:30,510
+تنتين بحقق الأكبر هتلاقي برضه very closed إيش بحقق
+
+353
+00:33:30,510 --> 00:33:36,810
+الأصغر ان
+
+354
+00:33:36,810 --> 00:33:45,360
+شاء الله لما نحل السؤال بتتضح الأمور تماماهذا اللي
+
+355
+00:33:45,360 --> 00:33:54,900
+هو من ضمن الأسئلة اللي معاكم homework سألنا
+
+356
+00:33:54,900 --> 00:34:08,980
+سؤال اللي هو وين يمكن إيجاد ال relative maximum و
+
+357
+00:34:08,980 --> 00:34:13,430
+relative minimumو جاوبنا عليه في النظرية اللي
+
+358
+00:34:13,430 --> 00:34:17,230
+حكيناها في البداية أنه توجد عند أحد ثلاث مناطق F'
+
+359
+00:34:17,450 --> 00:34:21,370
+بيساوي سفر F' لاتساوي سفر لإنها في حالة ال
+
+360
+00:34:21,370 --> 00:34:26,410
+interior points أو اللي هو المكان الثالث اللي هو
+
+361
+00:34:26,410 --> 00:34:32,210
+ال end points الآن عشان نكمل الحديث عن ال maximum
+
+362
+00:34:32,210 --> 00:34:39,370
+و ال minimum بدنا نفحصنفحص هل النقاط هذه مين فيها
+
+363
+00:34:39,370 --> 00:34:43,910
+عندها maximum و في مين فيها عندها minimum و مين لا
+
+364
+00:34:43,910 --> 00:34:48,530
+عندها maximum ولا عندها minimum و هو ال test اللي
+
+365
+00:34:48,530 --> 00:34:54,410
+انتوا أخدتهوا في اللي هو سواء في الثانوية أو حتى
+
+366
+00:34:54,410 --> 00:34:59,330
+في calculus ألف و عشان نساعدكم على انكم تتذكروا
+
+367
+00:34:59,330 --> 00:35:05,620
+انا بفضل انه نتذكروا من خلال الرسم الفحصساعتها
+
+368
+00:35:05,620 --> 00:35:12,780
+بيكون سهل وبكون انت بتعرف اللي هو تحدد ان هذا
+
+369
+00:35:12,780 --> 00:35:17,020
+النقطة في عندها maximum أو عندها minimum خلينا
+
+370
+00:35:17,020 --> 00:35:22,420
+نستذكر نستذكر من خلال الرسم النظرية اللي بدنا
+
+371
+00:35:22,420 --> 00:35:26,160
+نحكيها الآن اللي أخدناها في الثانوية أو أخدناها
+
+372
+00:35:26,160 --> 00:35:30,850
+اللي هي تغيير إشارة أفر براياللي هو من موجب إلى
+
+373
+00:35:30,850 --> 00:35:35,450
+سالب أو من سالب إلى موجب الان نرسم واحدة Maximum
+
+374
+00:35:35,450 --> 00:35:39,210
+وواحدة Minimum هذه النقطة هذه طبعا Maximum بس تذكر
+
+375
+00:35:39,210 --> 00:35:43,190
+في النظرية قاعدة الان هذه النقطة C الجوار اللي
+
+376
+00:35:43,190 --> 00:35:51,710
+حوالها C زائد Delta وC ناقص Delta مظبوط؟ طيب الان
+
+377
+00:35:51,710 --> 00:35:57,430
+عند النقاط المنطقة هذه كلهالاحظ مين المماس إيه
+
+378
+00:35:57,430 --> 00:36:01,710
+شماله بس ما بعمل المماس زاوية حادة إذا مينه إيه
+
+379
+00:36:01,710 --> 00:36:10,970
+شماله موجب يعني F prime of X أكبر أو يساوي سفر لكل
+
+380
+00:36:10,970 --> 00:36:16,950
+X وين موجودة في الجوار V Delta of C من الجهة هذه
+
+381
+00:36:16,950 --> 00:36:23,710
+بالتحديد في المنطقة C minus Delta OC واضح، مفهوم
+
+382
+00:36:24,520 --> 00:36:31,040
+الآن الـ F' هنا أو ميل المماس هنا بيعمل .. أو
+
+383
+00:36:31,040 --> 00:36:36,080
+المماس بيعمل زاوية منفرجة إذا الـ F' عند النقاط
+
+384
+00:36:36,080 --> 00:36:40,480
+هذه اللي هي اللي في المنطقة هذه اللي هي بيكون أصغر
+
+385
+00:36:40,480 --> 00:36:45,660
+أو يساوي سفر لكل X وهي الموجودةC C زائد دلتا وهذا
+
+386
+00:36:45,660 --> 00:36:49,660
+اللي كنا نقول عنه إذا بتتغير إشارة ال derivative
+
+387
+00:36:49,660 --> 00:36:55,940
+حول النقطة C من موجب إلى سالب هذا على بعضه بيعطيني
+
+388
+00:36:55,940 --> 00:37:05,700
+أن F has a local أو relative maximum at meanالـ C
+
+389
+00:37:05,700 --> 00:37:11,420
+Similarly for the other هذه النقطة هان C اللي هي
+
+390
+00:37:11,420 --> 00:37:16,980
+المنمة ماضح عند ميل المناس جابلها سالب لإنه زاوية
+
+391
+00:37:16,980 --> 00:37:22,420
+منفرجة وراح لمين لموجة لإنها زاوية حادة يعني بمعنى
+
+392
+00:37:22,420 --> 00:37:29,680
+آخر F prime of X أصغر أو يساوي 0 لكل X في الـ V أو
+
+393
+00:37:29,680 --> 00:37:36,160
+الجزء من C ما نزلت لعين C فاهمين عليها؟هي C نقص
+
+394
+00:37:36,160 --> 00:37:43,880
+دلتة C وC لعن C زائد دلتة و F prime of X أكبر أو
+
+395
+00:37:43,880 --> 00:37:49,620
+سوى 0 لكل X والي موجودة من C لعن C زائد دلتة
+
+396
+00:37:49,620 --> 00:37:59,200
+هذولتين مع بعض بيعطينا أن F has local minimum أو
+
+397
+00:37:59,200 --> 00:38:05,850
+relative minimum at Cفصار عندى الآن يا جماعة اللى
+
+398
+00:38:05,850 --> 00:38:11,730
+هو ال test التحول شرط الدال ال derivative من موجب
+
+399
+00:38:11,730 --> 00:38:18,410
+إلى سلب local maximum هذه النقاط اللى احنا اخدناه
+
+400
+00:38:18,410 --> 00:38:22,790
+من النظرية السابقة طبعا بنحكي عن ال interior
+
+401
+00:38:22,790 --> 00:38:28,850
+points و Fاللي هي اتحولت F prime من سالب إلى موجب
+
+402
+00:38:28,850 --> 00:38:33,870
+local maximum هذه اللي هي معلومة توجيهي أو معلومة
+
+403
+00:38:33,870 --> 00:38:40,730
+اللي هو calculus ألف الآن احنا بدنا نثبت صحة هذا
+
+404
+00:38:40,730 --> 00:38:41,770
+الحديث
+
+405
+00:38:49,440 --> 00:38:53,520
+نجرها بس من عندنا هنا هي اللي قلته بس نجرها من
+
+406
+00:38:53,520 --> 00:38:57,520
+النظرية let f be continuous on the interval a و b
+
+407
+00:38:57,520 --> 00:39:01,080
+إذا إيش مخصر دين إن ال function is continuous على
+
+408
+00:39:01,080 --> 00:39:04,780
+فترة a و b و ناخد c عبارة عن interior point لمين
+
+409
+00:39:05,450 --> 00:39:10,090
+للـ I Assume that F is differentiable إيه ع الفترة
+
+410
+00:39:10,090 --> 00:39:13,430
+A وC وC وB يعني مش لزمني إنها تكون differentiable
+
+411
+00:39:13,430 --> 00:39:16,170
+عند الـ C أصلا ممكن تكون مش differentiable و هي
+
+412
+00:39:16,170 --> 00:39:21,290
+نقطة بدنا نبحث عندها بس بالزمن هذه اللي هي من A ل
+
+413
+00:39:21,290 --> 00:39:25,490
+C و من C ل B then الآن
+
+414
+00:39:26,890 --> 00:39:31,430
+إذا كان هناك مقارنة V Delta of C Subset من I بحيث
+
+415
+00:39:31,430 --> 00:39:35,110
+أن F' بتكون أكبر أو سوى 0 قبلها في الفترة اللي
+
+416
+00:39:35,110 --> 00:39:39,830
+قبل، اللي هو و F' اتحولت إلى أصغر أو سوى 0، يعني
+
+417
+00:39:39,830 --> 00:39:44,750
+اتحولت الإشارة من موجب إلى سالب في الفترة الأولى
+
+418
+00:39:44,750 --> 00:39:48,210
+للفترة الثانية، هيكون عند relative maximum زي ما
+
+419
+00:39:48,210 --> 00:39:54,260
+حكيناهاالان في الثانية نفس الاشي بس بالعكس if
+
+420
+00:39:54,260 --> 00:39:57,480
+there is a neighborhood اللي هو كذا such that F'
+
+421
+00:39:57,940 --> 00:40:02,160
+أصغر من سفر هيه اللي هو زاوية منفرجة اتحول لF'
+
+422
+00:40:02,540 --> 00:40:06,820
+أكبر من سفر هيه بيعطينا عندي ايش ماله relative
+
+423
+00:40:06,820 --> 00:40:14,040
+minimum طيب ده عندي A و عندي BM مبرهنة خليني نبرهن
+
+424
+00:40:14,040 --> 00:40:18,440
+مين؟ B خليني نشوف مبرهن مع بعض اللي هو B
+
+425
+00:40:29,950 --> 00:40:33,710
+شوفوا صلوا ع النادي عليه الصلاة والسلام الان بيه
+
+426
+00:40:33,710 --> 00:40:39,410
+اللي هو عندي F prime معطيني F prime of X أصغر أو
+
+427
+00:40:39,410 --> 00:40:47,170
+سوى سفر صح لكل X في الفترة C minus Delta وC
+
+428
+00:40:47,170 --> 00:40:49,710
+ومعطيني أيضا
+
+429
+00:40:52,140 --> 00:40:57,040
+اللي تحت أنا بحكي عن اللي تحت بيه ال .. البعدها F
+
+430
+00:40:57,040 --> 00:41:02,980
+prime of X أكبر أشهر و سفر لكل X وين موجودة في
+
+431
+00:41:02,980 --> 00:41:09,740
+الفترة من C لـC زائد إيش؟ لـC زائد دلتا الآن إيش
+
+432
+00:41:09,740 --> 00:41:14,560
+غاية أثبت أن F has a relative minimum؟ يعني بدي
+
+433
+00:41:14,560 --> 00:41:21,340
+أثبت أن F of Xأكبر الـ Minimum أصغر أكبر أو يساوي
+
+434
+00:41:21,340 --> 00:41:28,380
+F of C لكل X وين موجودة في V Delta of C إذا أثبتت
+
+435
+00:41:28,380 --> 00:41:32,200
+هذا الكلام معناته صار عند في Neighborhood حوالي ال
+
+436
+00:41:32,200 --> 00:41:37,140
+F عند ال C أصغر واحدة فيهم يعني في عندها relative
+
+437
+00:41:37,140 --> 00:41:42,560
+minimumاللي هو في المنطقة هذه هقولك إنها بتتحقق
+
+438
+00:41:42,560 --> 00:41:45,700
+هذه وفي المنطقة هذه بتتحقق هذه معناها تقول لكل
+
+439
+00:41:45,700 --> 00:41:49,100
+النقاط اللي هان لكل النقاط اللي هان هذه بتتحقق
+
+440
+00:41:49,100 --> 00:41:54,740
+معايا؟ والكلام إن شاء الله سهل الآن طبيعي إحنا
+
+441
+00:41:54,740 --> 00:41:58,920
+قاعدين في جوه ال mean value theorem فأكيد هذا
+
+442
+00:41:58,920 --> 00:42:02,440
+جايبينه في نفس ال section عساس إنه إحنا نطبق ال
+
+443
+00:42:02,440 --> 00:42:07,220
+mean value theorem عشان اللي هو إن نصل لنتائجنا
+
+444
+00:42:07,770 --> 00:42:14,790
+الان x element in c minus delta of c، مظبوط؟ اذا
+
+445
+00:42:14,790 --> 00:42:18,590
+صار عندى الان طبعا انا غاية ان اجيب اللى هو علاقة
+
+446
+00:42:18,590 --> 00:42:23,610
+بين f of c و f of x فالان ال x في الفترة هذه
+
+447
+00:42:23,610 --> 00:42:28,410
+معناته انه انا بدي اطبق ال mean value theorem على
+
+448
+00:42:28,410 --> 00:42:32,790
+ال x وعلى ال c الفترة اللى فيهم يعني بدي اقولكن
+
+449
+00:42:32,790 --> 00:42:40,940
+consider the interval x و meanOc XOC
+
+450
+00:42:41,980 --> 00:42:47,220
+الـ file الـ data continuous على X وC، ليش؟ لأن
+
+451
+00:42:47,220 --> 00:42:51,120
+continuous على كل ال interval A وB اللي من ضمنها C
+
+452
+00:42:51,120 --> 00:42:55,680
+إذن، هاي أول شرط متحقق لـ mean value theorem
+
+453
+00:42:55,680 --> 00:42:59,900
+وأيضاً F is differentiable على ال open اللي هي
+
+454
+00:42:59,900 --> 00:43:02,940
+مستثنية الـ C بس و اللي بالزمن في ال mean value
+
+455
+00:43:02,940 --> 00:43:08,060
+theorem بس ال open إذن الشرطين المتحققات على هذه
+
+456
+00:43:08,060 --> 00:43:14,470
+الفترة لمين؟للـ Mean Value Theorem إذا نطبق الـ
+
+457
+00:43:14,470 --> 00:43:18,730
+Mean Value Theorem على هذا الانترال لكي نحصل على
+
+458
+00:43:18,730 --> 00:43:27,890
+ذلك اللي هو F there exist CX element in X وC such
+
+459
+00:43:27,890 --> 00:43:38,850
+that F of CX فبرايم of CX بساوي F of C ناقصF of X
+
+460
+00:43:38,850 --> 00:43:48,870
+على X C نقص X اللي هو اللي بالذنب هذا أمور جهزة
+
+461
+00:43:48,870 --> 00:43:57,090
+ليش جهزة من هنا إذا F of C نقص F of X بساوي C
+
+462
+00:43:57,090 --> 00:44:04,760
+minus Xفى F prime of CX الـ CX هى دى وين موجودة فى
+
+463
+00:44:04,760 --> 00:44:10,760
+الـ X و C يعنى هنا مدام هنا حسب المعطى الـ F prime
+
+464
+00:44:10,760 --> 00:44:15,380
+اللى هيش ماله سالبة إذا هذا أصغر أو يساوي سفروهذا
+
+465
+00:44:15,380 --> 00:44:20,260
+أكبر أو يساوي صفر مع بعض إيه شماله؟ أصغر أو يساوي
+
+466
+00:44:20,260 --> 00:44:24,240
+صفر إذا صار عندي هذا أصغر أو يساوي صفر أو بمعنى
+
+467
+00:44:24,240 --> 00:44:31,560
+آخر F of C أصغر أو يساوي F of X لمين؟ لكل X في هذه
+
+468
+00:44:31,560 --> 00:44:36,440
+الفترة لأن X كانت arbitrary فيها Similarly for
+
+469
+00:44:36,440 --> 00:44:43,700
+اللي هو الجزء الثاني بتاخد الآن X وين موجودة؟في
+
+470
+00:44:43,700 --> 00:44:48,520
+الـ C لـ C زائد دلتا و برضه اللي عملته فوق حطب
+
+471
+00:44:48,520 --> 00:44:54,400
+جهانة بس عالميا على الفترة C O X و نفس الحديث
+
+472
+00:44:54,400 --> 00:44:57,580
+الأولاني F is continuous هلأ و differentiable على
+
+473
+00:44:57,580 --> 00:45:01,480
+ال open then there exist اللي هو by mean value
+
+474
+00:45:01,480 --> 00:45:06,780
+theorem there exist C X C prime X element in C O X
+
+475
+00:45:06,780 --> 00:45:20,440
+such that F prime of Cx' بساوة f of x ناقص f of c
+
+476
+00:45:20,440 --> 00:45:27,800
+على x minus c بساوة هذا و زي ما عملنا بالظبط اللي
+
+477
+00:45:27,800 --> 00:45:31,040
+هو بيصير عندي أضرب طرفين في وسطين بيصير هنا x
+
+478
+00:45:31,040 --> 00:45:37,060
+minus c و هذه بتطلع فوق فبصير عندي هذه x minus c
+
+479
+00:45:37,060 --> 00:45:44,680
+موجبة و هذه f prime cxاللي هو موجبة X minus C
+
+480
+00:45:44,680 --> 00:45:49,780
+موجبة مظبوط و F prime اللي هي أكبر أو سواء صفر
+
+481
+00:45:49,780 --> 00:45:53,780
+فبصير هذا المقدر كله على بعض أشماله أكبر أو سواء
+
+482
+00:45:53,780 --> 00:45:58,400
+صفر يعني هذا المقدر أكبر أو سواء إيش صفر يعني من
+
+483
+00:45:58,400 --> 00:46:05,820
+هنا بصير عند F of X أكبر أو سواء F of إيش of C هذا
+
+484
+00:46:05,820 --> 00:46:11,760
+الكلام صحيح برضه لمين لكل X هناالأن في الجهتين أي
+
+485
+00:46:11,760 --> 00:46:16,040
+إن كان طلعت ال F of C أصغر أو يساوي F of X أصغر أو
+
+486
+00:46:16,040 --> 00:46:21,640
+يساوي F of X لكل X وين موجودة هنا و هنا يعني بمعنى
+
+487
+00:46:21,640 --> 00:46:25,980
+آخر لكل X وين موجودة في ال neighborhood يعني صارت
+
+488
+00:46:25,980 --> 00:46:33,020
+F of X أكبر أو يساوي F of C لكل X في ال V Delta of
+
+489
+00:46:33,020 --> 00:46:41,440
+C وهذا يعني أن F has a local minimum at meanالـ C
+
+490
+00:46:41,440 --> 00:46:44,640
+أي سؤال
+
+491
+00:47:03,950 --> 00:47:07,150
+عندي the converse of the theorem اللي فوقني not to
+
+492
+00:47:07,150 --> 00:47:10,690
+be true in general وهذا اللي هو عبارة عن مين عن
+
+493
+00:47:10,690 --> 00:47:15,090
+exercise 9 برضه exercise 9 من ضمن ال homework اللي
+
+494
+00:47:15,090 --> 00:47:18,090
+معاكم اللي هنتحدث فيه ان شاء الله في ال discussion
+
+495
+00:47:18,090 --> 00:47:22,590
+الآن بعض التطبيقات الأخرى على ال mean value
+
+496
+00:47:22,590 --> 00:47:29,600
+theorem وهذا التطبيقبعض التطبيقات اللي هي علمين
+
+497
+00:47:29,600 --> 00:47:34,120
+value theory ممكن اشي اخدنا مشابه له في ال
+
+498
+00:47:34,120 --> 00:47:40,300
+calculus لكن خلينا نشوف هنا يعني اش اللي بيقوله
+
+499
+00:47:40,300 --> 00:47:47,700
+عندنا التطبيق الأول اللي
+
+500
+00:47:47,700 --> 00:47:54,080
+بيقوله ما هي ليه example example اللي هو
+
+501
+00:48:00,540 --> 00:48:12,120
+show that اكبر
+
+502
+00:48:12,120 --> 00:48:18,080
+او ساوي واحد زائد X لكل X element in R هذا واحد
+
+503
+00:48:18,080 --> 00:48:24,500
+اتنين اللي هو نفس ال W او A اللي هو E to the X
+
+504
+00:48:25,160 --> 00:48:33,500
+بساوي واحد زائد X F أندولي F X بتساوي سفر و proof
+
+505
+00:48:33,500 --> 00:48:42,480
+خلّينا نشوف أنبرهن هذا الأمر أو هذا الجزء طيب
+
+506
+00:48:42,480 --> 00:48:45,920
+بنناسبة أن E to the X أكبر بساوية واحد زائد X لكل
+
+507
+00:48:45,920 --> 00:48:47,880
+X way الموجودة في ال R
+
+508
+00:48:51,200 --> 00:48:55,040
+الان عندنا طبيعي حالة الـ X بتساوي صفر الـ Z باخد
+
+509
+00:48:55,040 --> 00:48:57,860
+الـ function مين انا عشان الرأس الدولة يعرف عن مين
+
+510
+00:48:57,860 --> 00:49:03,740
+بنحكي let F of X ايش هتساوي طبعا E to the X طبعا E
+
+511
+00:49:03,740 --> 00:49:09,120
+to the X معرف هو المكان الانفي حالة ال .. ال ..
+
+512
+00:49:09,120 --> 00:49:12,280
+الأول حاجة لو جينا طلعنا لحالة ال X بتساوي سفر
+
+513
+00:49:12,280 --> 00:49:18,000
+المساواة حادثة ولا لا it was a zero ليه واحد بساوي
+
+514
+00:49:18,000 --> 00:49:21,520
+واحد زائد زيرو اللي هو واحد يعني المساواة حادثة في
+
+515
+00:49:21,520 --> 00:49:25,120
+حالة ال .. ال X بتساوي زيرو الان خليني أخد ال X
+
+516
+00:49:25,120 --> 00:49:31,970
+أشمالها لاتساوي أيش؟ سفرالـ X لا تساوي سفر هثبتلك
+
+517
+00:49:31,970 --> 00:49:36,950
+إنه E to the X strictly أكبر من واحد زاد X بكون
+
+518
+00:49:36,950 --> 00:49:42,410
+خلصت هذه و خلصت هذه مع بعض افتمتين بنشوف كيف لأن X
+
+519
+00:49:42,410 --> 00:49:46,930
+لا تساوي Zero عندي حالتين X أكبر من سفر و X أصغر
+
+520
+00:49:46,930 --> 00:49:52,130
+من سفرالان f of x ده اللي هي من الدوال الحلوة اللي
+
+521
+00:49:52,130 --> 00:49:54,230
+differentiable everywhere إذا continuous
+
+522
+00:49:54,230 --> 00:49:56,830
+everywhere إذا ال mean value theorem على أي
+
+523
+00:49:56,830 --> 00:50:01,610
+interval أو sub interval منها من الار متحققة إذا x
+
+524
+00:50:01,610 --> 00:50:04,930
+أكبر من 0 معناته بتتخد أطبق ال mean value theorem
+
+525
+00:50:04,930 --> 00:50:10,910
+من عند ال zero لعند main ال x معايا إذا by mean
+
+526
+00:50:10,910 --> 00:50:16,490
+value theorem there exists element in zero x such
+
+527
+00:50:16,490 --> 00:50:25,720
+thatF prime of C بساوي F of X ناقص F of Zero على X
+
+528
+00:50:25,720 --> 00:50:30,400
+minus Zero، مظبوط ولا لأ؟ هذه اللي هي F prime of C
+
+529
+00:50:30,400 --> 00:50:34,120
+طبعا ال derivative للـE to the X هي نفسها عند الـC
+
+530
+00:50:34,120 --> 00:50:38,560
+في السير E to the Cوهذه اللي هي عبارة عن E to the
+
+531
+00:50:38,560 --> 00:50:41,900
+X F of Zero اللي هي E to the Zero اللي هي واحد
+
+532
+00:50:41,900 --> 00:50:46,860
+ناقص واحد على مين على X اضربوا طرفين في وساطين
+
+533
+00:50:46,860 --> 00:50:52,340
+فبصير E to the X ناقص واحد بساوي X في مين في E
+
+534
+00:50:52,340 --> 00:50:59,020
+أُسي ماشي الحالة الآنهذه الآن ال E to the C C
+
+535
+00:50:59,020 --> 00:51:05,100
+موجبة صح ال E to the C هتكون أكبر أو تساوي واحد ان
+
+536
+00:51:05,100 --> 00:51:09,120
+هي أكبر strictly من واحد في الواقع مظبوط E to the
+
+537
+00:51:09,120 --> 00:51:13,960
+C أكبر strictly من مين من الواحد الآن X في ال E to
+
+538
+00:51:13,960 --> 00:51:20,920
+the C هتكون أكبر strictly من مين من اللي هي ال Xمع
+
+539
+00:51:20,920 --> 00:51:24,880
+بعض الثنتين بيصير عندى E to the X أكبر من واحد
+
+540
+00:51:24,880 --> 00:51:31,860
+زائد مين زائد ال X الآن في حالة ال X أصغر من سفر
+
+541
+00:51:31,860 --> 00:51:36,600
+في حالة ال X أصغر من سفر بدنا نطبق على مين؟ على
+
+542
+00:51:36,600 --> 00:51:43,380
+الفترة اللي هي X و Zero مظبوط؟ على الفترة X و Zero
+
+543
+00:51:47,630 --> 00:51:53,510
+ب .. كله كله ماشي there exists c element in x و
+
+544
+00:51:53,510 --> 00:52:00,930
+zero such that أقول معايا f prime of c بسوى f of
+
+545
+00:52:00,930 --> 00:52:10,010
+zero نقص f of x على zero minus x هو يساوي واحد
+
+546
+00:52:10,010 --> 00:52:19,700
+minus x نقص e to the xعلى سالم X هذا إيش بيساوي E
+
+547
+00:52:19,700 --> 00:52:25,820
+to the C أضرب الطرفين في وسطين بيصير واحد ناقص E
+
+548
+00:52:25,820 --> 00:52:34,760
+to the X بيساوي ناقص X E to the C أضرب اللي هو في
+
+549
+00:52:34,760 --> 00:52:41,840
+ناقص واحد بيصير E to the X ناقص واحد بيساوي X في E
+
+550
+00:52:41,840 --> 00:52:50,110
+to the Cالان ال C سالبة مظبوط فبصير كسر فبصير عند
+
+551
+00:52:50,110 --> 00:52:56,150
+ال E to the C اللي هو ايش ماله اصغر من واحد فالان
+
+552
+00:52:56,150 --> 00:53:01,210
+لما نضرب ال X السالبة فيه ال X سالبة هنا فبصير
+
+553
+00:53:01,210 --> 00:53:08,110
+اكبر من مين من X فبصير
+
+554
+00:53:08,110 --> 00:53:12,350
+عند E to the X اكبر
+
+555
+00:53:13,170 --> 00:53:21,630
+من واحد زائد مين زائد X الآن صار عندي من الجهتين
+
+556
+00:53:21,630 --> 00:53:26,590
+لما X لا تساوي سفر E to the X strictly أكبر من
+
+557
+00:53:26,590 --> 00:53:32,590
+واحد زائد X إذا X لا تساوي سفر بتعني
+
+558
+00:53:43,580 --> 00:53:50,840
+E to the X أكبر strictly من واحد زائد X هذي واحد
+
+559
+00:53:50,840 --> 00:53:58,260
+الآن اتنين في حالة X بتساوي سفر هذا بيعطينا ان E
+
+560
+00:53:58,260 --> 00:54:03,480
+to the X بيساوي واحد زائد X والجهتين هيساوين واحد
+
+561
+00:54:03,480 --> 00:54:09,600
+واحد فE to the Zero واحد الآن الجهتين مع بعض هذولة
+
+562
+00:54:11,120 --> 00:54:15,880
+بتده لمّ الـ x لا تساوي 0 و الـ x بتساوي 0 يعني e
+
+563
+00:54:15,880 --> 00:54:19,740
+to the x بتاخد بعين الاعتبار المساواة هنا بيصير e
+
+564
+00:54:19,740 --> 00:54:24,740
+to the x أكبر و بيساوي 1 زياد x لكل x نين element
+
+565
+00:54:24,740 --> 00:54:29,120
+in R بالظبط في حالة x بتساوي صفر e to the x بتساوي
+
+566
+00:54:29,120 --> 00:54:33,520
+في حالة x لا تساوي صفر e to the x strictly أكبر
+
+567
+00:54:33,520 --> 00:54:40,750
+الآن هذا x بتساوي صفر يؤدي إلى هذاالـ Trivia زي ما
+
+568
+00:54:40,750 --> 00:54:45,510
+قلنا الان conversely بدنا نثبت هذا هذا أثبتناه في
+
+569
+00:54:45,510 --> 00:54:52,290
+الواقع كيف أثبتناه بدنا نقول بد أثبت الآن الاتجاه
+
+570
+00:54:52,290 --> 00:54:57,370
+هذا هذا الاتجاه اللي محيته اتجاه الـ Trivia اللي
+
+571
+00:54:57,370 --> 00:55:02,050
+سهل دل هذا هذا عشان أثبته بقول Contraposition لو
+
+572
+00:55:02,050 --> 00:55:07,480
+كانت X لا تساوي سفربيعطينا الـ E to the X لا يساوي
+
+573
+00:55:07,480 --> 00:55:12,080
+واحد زاد X ليش؟ لأنه أثبتته أنه strictly أكبر مزام
+
+574
+00:55:12,080 --> 00:55:15,920
+strictly أكبر إذا إيه أشماله؟ لا يساوي إذا صار
+
+575
+00:55:15,920 --> 00:55:23,420
+عندي اللي هو هذا وهذا متحققين الإثنين طيب نيجي
+
+576
+00:55:23,420 --> 00:55:30,920
+نيجي الآن لل example الثاني example معهود ومعروف
+
+577
+00:55:30,920 --> 00:55:36,860
+أو ننهي فيه المرة الجاية ان شاء اللهبنكمل باقي
+
+578
+00:55:36,860 --> 00:55:41,360
+اللي هي ال applications المرة دي ان شاء الله هنعمل
+
+579
+00:55:41,360 --> 00:55:46,780
+discussion في 6-1 يعني أصل 6-1 هنيجي ونحلهم و
+
+580
+00:55:46,780 --> 00:55:52,340
+بالإضافة ل .. اللي هو نكمل 6-2 هنكمل 6-2 و نعمل
+
+581
+00:55:52,340 --> 00:55:57,560
+discussion ل 6-1 طيب اللي مصل على سيدنا محمد
+
+582
+00:55:57,560 --> 00:56:05,210
+example التاني example اللي هو show thatshow that
+
+583
+00:56:05,210 --> 00:56:15,930
+show that show that sign ال X أكبر سوى سالب X و
+
+584
+00:56:15,930 --> 00:56:24,410
+أصغر سوى X for every X أكبر سوى 0 الغروف الآن
+
+585
+00:56:24,410 --> 00:56:28,990
+الدالة اللي بناحكيها عندها مين هي sign ال X هذه
+
+586
+00:56:28,990 --> 00:56:35,260
+letf of x بساوة صين الـ x وهذه continuous
+
+587
+00:56:35,260 --> 00:56:41,320
+everywhere و differentiable everywhere عند اللي هي
+
+588
+00:56:41,320 --> 00:56:47,160
+عند ال zero عند x بساوة zero ال trivial هذه بتتحقق
+
+589
+00:56:47,160 --> 00:56:50,900
+كtrivial لإن ده سفر و ده سفر و ده سفر، مظبوط؟ اللي
+
+590
+00:56:50,900 --> 00:56:57,660
+هنخد الآن forx أكبر من 100 من 0 بدنا نعمل
+
+591
+00:56:57,660 --> 00:57:01,560
+application أو we apply the mean value theorem on
+
+592
+00:57:01,560 --> 00:57:08,120
+the interval 0,100 أو x نظرا نتحقق الشروط بيكون
+
+593
+00:57:08,120 --> 00:57:14,500
+عند there exist c element in 0,x such that f prime
+
+594
+00:57:14,500 --> 00:57:24,510
+of c بيساوي f of x ناقص f of 0 على x minus 0F
+
+595
+00:57:24,510 --> 00:57:29,410
+prime of C هي عبارة عن Cos C لأن انتفاضه للـSin
+
+596
+00:57:29,410 --> 00:57:38,890
+Cos ويساوي F of X هي Sin X Sin 00 على X أضرب طرفين
+
+597
+00:57:38,890 --> 00:57:45,870
+في وسطين بيصير عندي Sin X بيساوي X في Cos C لكن
+
+598
+00:57:45,870 --> 00:57:54,420
+الآن أنا عندي Cos C محصورة butcos c محصورة بين
+
+599
+00:57:54,420 --> 00:58:01,660
+ناقص واحد وبين ash الواحد قل عند x أكبر من 0 اضرب
+
+600
+00:58:01,660 --> 00:58:08,600
+الجهتين في x بيصير هان x و هان x و هان x صح؟ الآن
+
+601
+00:58:08,600 --> 00:58:16,550
+x cos c هي sin x إذا صار عند sin xأظهر يساوي X
+
+602
+00:58:16,550 --> 00:58:22,050
+وأكبر أو يساوي سالب X هذا الأن لكل X لاتش أكبر من
+
+603
+00:58:22,050 --> 00:58:26,490
+صفر but for X بتساوي zero this is trivial إذا صار
+
+604
+00:58:26,490 --> 00:58:33,250
+صين ال X بين نقص X و X لكل X أكبر أو يساوي صفر و
+
+605
+00:58:33,250 --> 00:58:34,970
+المرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f63a72489568d62f6deecf3052c2484bc237f0a4
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA_postprocess.srt
@@ -0,0 +1,2760 @@
+1
+00:00:04,820 --> 00:00:10,480
+بسم الله الرحمن الرحيم المحاضرة الثانية في مساق
+
+2
+00:00:10,480 --> 00:00:18,480
+تحليل رياضي 2 أو تحليل حقيقي 2 اتحدثنا
+
+3
+00:00:18,480 --> 00:00:24,100
+المرة الماضية عنالـ differentiation بدأنا بشرتر
+
+4
+00:00:24,100 --> 00:00:28,200
+ستة بدأنا في ال section الأول ستة واحد اللي هو ال
+
+5
+00:00:28,200 --> 00:00:32,600
+derivative او اللي هو الاشتقاق او المشتق الأولى
+
+6
+00:00:32,600 --> 00:00:37,840
+وعرفنا شو معناه اللي هو الاشتقاق عرفنا شو معناه ان
+
+7
+00:00:37,840 --> 00:00:44,910
+الدولة تكون differentiable عند نقطة اللي هيفي
+
+8
+00:00:44,910 --> 00:00:49,970
+interval I حيث أخدنا F عبارة عن الـ function من I
+
+9
+00:00:49,970 --> 00:00:55,230
+ل R وقلنا C element in I بتكون الدالة عندها قابلة
+
+10
+00:00:55,230 --> 00:01:01,490
+للاشتقاق يعني F prime of C exist if the following
+
+11
+00:01:01,490 --> 00:01:08,230
+limit exist اللي هو limitf of x ناقص f of c على x
+
+12
+00:01:08,230 --> 00:01:14,230
+minus c as x goes to c exist إذا كانت هذه الـ
+
+13
+00:01:14,230 --> 00:01:20,210
+limit exist بنقول عن الـ f برايب exist و بتكون هي
+
+14
+00:01:20,210 --> 00:01:26,650
+قيمة هذه ال limit الآن و بعد ذلك مرّينا على اللي
+
+15
+00:01:26,650 --> 00:01:34,600
+هو بعض الخواصوقلنا الخاصية الأولى عندنا اللى هى
+
+16
+00:01:34,600 --> 00:01:41,540
+انه لو كانت الدالة اللى هى differentiable at C
+
+17
+00:01:41,540 --> 00:01:45,520
+بتكون continuous برضه وين عند C يعني اي
+
+18
+00:01:45,520 --> 00:01:50,080
+differentiable function must be continuousقلنا إن
+
+19
+00:01:50,080 --> 00:01:53,960
+الـ converse need not to be true in general واخدنا
+
+20
+00:01:53,960 --> 00:01:58,020
+مثال قلنا f of x بتساوي ال absolute value لل x
+
+21
+00:01:58,020 --> 00:02:01,780
+اللي هي عبارة عن continuous function لكن مش
+
+22
+00:02:01,780 --> 00:02:05,460
+differentiable عند ال zero continuous everywhere
+
+23
+00:02:05,460 --> 00:02:09,340
+but it is not differentiable at zeroوبرهننا الكلام
+
+24
+00:02:09,340 --> 00:02:13,140
+هذا واخدنا مثال آخر على f of x بتساوي ال summation
+
+25
+00:02:13,140 --> 00:02:17,760
+ل x minus cii من عند واحد لعند n وقلنا إن هذا
+
+26
+00:02:17,760 --> 00:02:22,600
+الدالة برضه is continuous everywhere but it is not
+
+27
+00:02:22,600 --> 00:02:29,440
+differentiable at c1, c2, c3 لعند cn بعد ذلك سألنا
+
+28
+00:02:29,440 --> 00:02:34,100
+وقلنا هل ممكن اللي جينا دالة تكون continuous وين
+
+29
+00:02:34,100 --> 00:02:39,790
+ما كانو مش differentiable ولا في مكان قلنا اه و
+
+30
+00:02:39,790 --> 00:02:42,470
+قلنا اخد الدالة f of x بساعة ال summation واحد على
+
+31
+00:02:42,470 --> 00:02:47,350
+اتنين أس ان كسين تلاتة أس ان اكس هذه الدالة is
+
+32
+00:02:47,350 --> 00:02:51,850
+continuous everywhere but it is not differentiable
+
+33
+00:02:51,850 --> 00:02:56,310
+anywhere وبعد هيك اتينا
+
+34
+00:03:04,880 --> 00:03:11,100
+حكينا عن بعض اللي هو قوانين الاشتقاق قولنا لو كانت
+
+35
+00:03:11,100 --> 00:03:16,520
+الدالةF والدالة G التنتين من نفس الـ domain
+
+36
+00:03:16,520 --> 00:03:22,000
+والتنتين قابلات للاشتقاق عند نقطة اسمها C سمناها
+
+37
+00:03:22,000 --> 00:03:26,560
+قلنا اللي هو مجموع الدالتين هيكون مشتقتهم موجودة
+
+38
+00:03:26,560 --> 00:03:31,660
+عند هذه النقطة وحاصل ضربهم وحاصل قسمتهم أيضا
+
+39
+00:03:31,660 --> 00:03:35,860
+provided that G of C اللي في المقام لا تساوي سفر
+
+40
+00:03:35,860 --> 00:03:41,950
+وأيضا الالف في ال FA constant برضه ألف في أف قابلة
+
+41
+00:03:41,950 --> 00:03:46,290
+للاشتقاء وأثبتنا
+
+42
+00:03:46,290 --> 00:03:53,330
+هذا الكلام وبرهنناه ووصلنا لعند اللي هو التعميم
+
+43
+00:03:53,330 --> 00:04:00,030
+قلنا لو كانت FF1 وF2 وF3 عند F1 كلهم دوال قابلة
+
+44
+00:04:00,030 --> 00:04:04,710
+للاشتقاق حيكون حاصل جمحا قابل للاشتقاق وحاصل ضربا
+
+45
+00:04:04,710 --> 00:04:09,510
+أيضا قابل للاشتقاق وفق القوانين اللي ذكرناها سابقا
+
+46
+00:04:10,150 --> 00:04:14,370
+وجفنا عند اللي هو النقطة اللي هي the chain rule أو
+
+47
+00:04:14,370 --> 00:04:20,650
+قاعدة السلسلة قاعدة السلسلة طبعا ليست غريبة عنكم
+
+48
+00:04:20,650 --> 00:04:29,240
+مرت علينا في تفاضل الف ومرت علينا في ال complexأو
+
+49
+00:04:29,240 --> 00:04:32,780
+مرت علينا اللي هو استخدمناها في الـ differential
+
+50
+00:04:32,780 --> 00:04:38,220
+equations وفي مساقات أخرى الآن نظرة نظرة تحليلية
+
+51
+00:04:38,220 --> 00:04:44,060
+فهنشوف اللي هو كيف أثبتنا أو كيف بدنا نثبت اللي هو
+
+52
+00:04:44,060 --> 00:04:48,840
+قاعدة السلسلة أي سؤال بتقدر تسأله يعني اللي بدكم
+
+53
+00:04:48,840 --> 00:04:53,960
+إياه و تتفعلوا بالطريقة اللي بتلاقوها مناسبة let i
+
+54
+00:04:53,960 --> 00:04:56,200
+و j be intervals and let g
+
+55
+00:04:59,060 --> 00:05:06,800
+عبارة عن دالة دي
+
+56
+00:05:06,800 --> 00:05:14,660
+عبارة عن دالة من I لعند مين لعند R و ال F عبارة عن
+
+57
+00:05:14,660 --> 00:05:21,700
+دالة من عند J لعند R حيث I و J اللي هو أشمل عبارة
+
+58
+00:05:21,700 --> 00:05:26,440
+عن intervalsالان انا اللي هي الـ chain rule هي في
+
+59
+00:05:26,440 --> 00:05:33,380
+الواقع عملية فحص إمكانية إنها تكون ال composition
+
+60
+00:05:33,380 --> 00:05:37,780
+of two functions is differentiable ولا لأ؟ وإيش
+
+61
+00:05:37,780 --> 00:05:41,200
+الشروط اللي بتخلي اللي هو g composite of is
+
+62
+00:05:41,200 --> 00:05:45,620
+differentiable؟ إذا أنا بدي أحكي عن g composite of
+
+63
+00:05:45,620 --> 00:05:49,590
+اللي هو ال derivative إيه لها؟ما دام بدي احكي عن g
+
+64
+00:05:49,590 --> 00:05:56,690
+composite of f اذا انا الان domain ال g ال domain
+
+65
+00:05:56,690 --> 00:06:03,850
+ال f هيكون من عند g لعند مين لعند r معناته ان f of
+
+66
+00:06:03,850 --> 00:06:09,310
+g عشان تكون g معرفة لازم تكون من ضمن مين اللي هو
+
+67
+00:06:09,310 --> 00:06:16,680
+domain ال I اذا انا بدي افترض ان fof J جزئية من I
+
+68
+00:06:16,680 --> 00:06:22,020
+على أساس ان هتكون الـ G composite F is defined
+
+69
+00:06:22,020 --> 00:06:29,960
+وهتكون defined من وين؟ من عند J لعند R عشان هيك
+
+70
+00:06:29,960 --> 00:06:34,400
+احنا لما بدنا نيجياللي هو .. اللي نفترض .. هنفترض
+
+71
+00:06:34,400 --> 00:06:40,220
+G من I لعند R وF من عند G لعند R دوال ونقول F of I
+
+72
+00:06:40,220 --> 00:06:43,640
+subset او F of G subset من I عشان تصير اللي هو
+
+73
+00:06:43,640 --> 00:06:46,980
+اللي بنحكي عنه قاعدة السلسلية اللي هي بمعنى اخر
+
+74
+00:06:46,980 --> 00:06:50,040
+التفاضل ال composition of two functions is well
+
+75
+00:06:50,040 --> 00:06:54,420
+defined او is defined اللي هم let C element in مين
+
+76
+00:06:54,420 --> 00:07:00,120
+in G؟ بدنا ناخد الـ C element in G اللي هم بقولي C
+
+77
+00:07:00,120 --> 00:07:06,430
+element in Gعشان أقدر أحكي عن g composite of f
+
+78
+00:07:06,430 --> 00:07:12,530
+prime of c تكون exist بده شرطين الشرط الأول بده ال
+
+79
+00:07:12,530 --> 00:07:17,190
+g ال f تكون differentiable عند مين؟ عند ال c
+
+80
+00:07:17,190 --> 00:07:22,150
+والشرط التاني أن ال g تكون differentiable عند ال f
+
+81
+00:07:22,150 --> 00:07:30,530
+of c واضح؟ إذن الآنإذا كان الـ F مميز لـ C و الـ G
+
+82
+00:07:30,530 --> 00:07:36,710
+مميز لـ F of C فإن مفهوم الـ G مميز لـ F يجب أن
+
+83
+00:07:36,710 --> 00:07:42,410
+يكون مميز لـ C وبكون عنده الـ G مميز لـ F' of C
+
+84
+00:07:42,410 --> 00:07:48,710
+أيش حيساوي؟ حيساوي G' of F of C في F' لمن؟ للـ F
+
+85
+00:07:48,710 --> 00:07:54,350
+of C اللي كنا نقول عنه في التفاضلأنه تفاضل اللي هو
+
+86
+00:07:54,350 --> 00:08:01,320
+القوس ثم تفاضل ما فيه داخل القوس واضح؟أو تفاضل
+
+87
+00:08:01,320 --> 00:08:05,280
+الدالة في تفاضل ما بداخل الدالة هو طبعا في الواقع
+
+88
+00:08:05,280 --> 00:08:07,940
+اللي هو عبارة عن تفاضل ل composite of two
+
+89
+00:08:07,940 --> 00:08:12,200
+functions أو اللي هو ال chain rule وكنا إذا
+
+90
+00:08:12,200 --> 00:08:16,680
+بتتذكروا كانت صورة أخرى لل chain rule غير الصورة
+
+91
+00:08:16,680 --> 00:08:23,100
+هذه اللي هي g prime of f of c في f prime of c كنا
+
+92
+00:08:23,100 --> 00:08:29,900
+ناخد صورة أخرى نقول dy by dxاللي هو عبارة عن ..
+
+93
+00:08:29,900 --> 00:08:38,960
+عبارة عن dy مثلا by du في du by d إيش؟ dx اللي هو
+
+94
+00:08:38,960 --> 00:08:44,620
+ال y و كأنها بتتمثل اللي هي ال g تفاضل ال g و ال u
+
+95
+00:08:44,620 --> 00:08:48,600
+بتكون اللي هي مين؟ اللي هي ال F اللي هي F إبراى
+
+96
+00:08:48,600 --> 00:08:52,180
+فكانت اللي هي هذه الصورة أو هذه الصورة احنا الآن
+
+97
+00:08:52,180 --> 00:08:59,630
+خلينا نحكي عن هذه الصورة و نبرهن اللي هيكيف اللي
+
+98
+00:08:59,630 --> 00:09:07,290
+هو نثبت ان هذا الكلام صحيح الان بس خلّينا نحط ..
+
+99
+00:09:07,290 --> 00:09:13,730
+نشوف .. نشوف عندنا الان نشوف ايش اللي بدنا نثبته
+
+100
+00:09:13,730 --> 00:09:16,770
+احنا في الواقع اللي بدنا نثبته .. بدنا نجوه ..
+
+101
+00:09:16,770 --> 00:09:22,290
+بدنا نثبت ان G composite F a prime of C exist عشان
+
+102
+00:09:22,290 --> 00:09:29,500
+نثبت انها exist بإيش بتبلزمني؟ بدي اخد limitG of
+
+103
+00:09:29,500 --> 00:09:39,520
+F, G circle F اللي هي GF of X ناقص G of F of C على
+
+104
+00:09:39,520 --> 00:09:46,960
+X minus C لما X تروح للـ C نثبت أن هذا إش ماله
+
+105
+00:09:46,960 --> 00:09:51,920
+existواضح عشان اللي بدنا نسويه؟ بدنا نثبت انه
+
+106
+00:09:51,920 --> 00:09:55,800
+exist عشان نثبت انه هذا exist بلزمني عاملين
+
+107
+00:09:55,800 --> 00:10:01,020
+مساعدات الآن هنشوف كيف نعمل هذول العاملين طبعا
+
+108
+00:10:01,020 --> 00:10:05,200
+طبيعي طبيعي انا معطين ان هو ال F' موجودة وD'
+
+109
+00:10:05,480 --> 00:10:10,600
+موجودة اذا اكيد انا هعمل حسابي ان استخدمهم على
+
+110
+00:10:10,600 --> 00:10:14,280
+اساس ان اصل الهدف اللي بديه الان خلينا نيجي
+
+111
+00:10:14,280 --> 00:10:14,900
+للبرهان
+
+112
+00:10:20,860 --> 00:10:26,680
+الحين الـ proof بدنا
+
+113
+00:10:26,680 --> 00:10:36,080
+نثبت انه اللي هو الـ Gبنثبت إنه لو كانت G و F
+
+114
+00:10:36,080 --> 00:10:39,980
+differentiable الأول عند F of C والتاني عند C
+
+115
+00:10:39,980 --> 00:10:45,840
+بيعطينا هذا إنه G composed of F prime of C exist
+
+116
+00:10:45,840 --> 00:10:50,420
+ويساوي G prime of F of C في F prime of C هذا ما
+
+117
+00:10:50,420 --> 00:10:58,000
+بنثبته شوف كيف يعني
+
+118
+00:10:58,000 --> 00:11:06,450
+بقى بدنا نبرهن النظريةخلّيني أعرّف الآن Define G
+
+119
+00:11:06,450 --> 00:11:14,850
+Capital من I لعند ال R By شوف كيف بدي .. اللي هي
+
+120
+00:11:14,850 --> 00:11:21,050
+يعني أعرف الـ G بطريقة توصّلني لحساب D composed of
+
+121
+00:11:21,050 --> 00:11:24,890
+F prime of إيش؟ of C جبل بشوية قلنا D composed of
+
+122
+00:11:24,890 --> 00:11:30,590
+F prime of C المتوقع لهاإنه تكون عبارة عن إذا كانت
+
+123
+00:11:30,590 --> 00:11:34,850
+تكون موجودة هي عبارة عن ال limit ل G F of X نقص G
+
+124
+00:11:34,850 --> 00:11:41,270
+F of C على X minus C أو G of Y نقص G F of C ماشي
+
+125
+00:11:41,270 --> 00:11:47,250
+الحال الآن بدي أعرف G على هذا الأساس G of Y بتساوي
+
+126
+00:11:47,250 --> 00:12:01,160
+اللي هو G of F of Yالعند ناقص g f of c على y minus
+
+127
+00:12:01,160 --> 00:12:06,480
+f of c الان قسمت على y minus f of c اكيد اللي هو
+
+128
+00:12:06,480 --> 00:12:15,600
+ال y انا بديش ايها تساومين f of c الان g of y ايش
+
+129
+00:12:15,600 --> 00:12:23,980
+بديها انا بديها المتوقع ال limit لهذهالـ limit
+
+130
+00:12:23,980 --> 00:12:30,300
+لهذه لما y تروح لل F of C اللي هو و كأنه عبارة عن
+
+131
+00:12:30,300 --> 00:12:37,540
+D prime of مين of F of C فالان بتديها D prime of F
+
+132
+00:12:37,540 --> 00:12:44,180
+of C ليش هال gate بتشوف ليش اللي بنحكيهاالان عرفت
+
+133
+00:12:44,180 --> 00:12:49,140
+اللي هي الـ function طبعاً هذا الكلام مستقى من
+
+134
+00:12:49,140 --> 00:12:54,120
+اللي هو f prime of c إيش متوقع limitه تساوي هذا
+
+135
+00:12:54,120 --> 00:12:58,200
+مستقى .. مستقى منه بعد شوية هتلاقيني هذه كتبت على
+
+136
+00:12:58,200 --> 00:13:02,980
+صورة هذه في شغل تانية برضه موجودة اللي هي f prime
+
+137
+00:13:02,980 --> 00:13:07,260
+of c اه
+
+138
+00:13:07,260 --> 00:13:16,350
+أسف g of yالان نشوف هذه الدالة لو جيت للدالة اللى
+
+139
+00:13:16,350 --> 00:13:26,010
+عندى هذه خد limit g of y لما y تروح لل F of C ايش
+
+140
+00:13:26,010 --> 00:13:32,500
+هتلاقيها بتساوي؟ بتساوي limitG of Y بعوض جاعد Y
+
+141
+00:13:32,500 --> 00:13:38,080
+تروح لل F of C يعني Y أشمالها لاتساوي F of C ناقص
+
+142
+00:13:38,080 --> 00:13:45,340
+G of F of C على مين على Y minus F of C لما Y تروح
+
+143
+00:13:45,340 --> 00:13:51,560
+لمين لل F of C وهذه بالظبط هي تعريف مينتعريف الـ
+
+144
+00:13:51,560 --> 00:13:56,480
+derivative للـ G عند النقطة مين؟ النقطة اسمها F of
+
+145
+00:13:56,480 --> 00:14:01,280
+C واضح؟ لأن الـ C من الـ A .. من الـ J الـ F of C
+
+146
+00:14:01,280 --> 00:14:08,260
+وين هتكون؟ من مين؟ من الـ I واضح؟ فالان هذه عبارة
+
+147
+00:14:08,260 --> 00:14:16,920
+عن G prime للـ F of C ليش هذا؟ because ..G is
+
+148
+00:14:16,920 --> 00:14:25,200
+differentiable at mean at F of C هذا معطى طيب الآن
+
+149
+00:14:25,200 --> 00:14:30,160
+ال limit لـ G of Y طلعت لما يتروح ل F of C أش طلعت
+
+150
+00:14:30,160 --> 00:14:34,520
+G prime ل F of C أصلا هذا السبب اللي أنا عارف أنه
+
+151
+00:14:34,520 --> 00:14:37,440
+هتطلع حاجة السبب اللي خلاني أعرف الـ G of Y أش
+
+152
+00:14:37,440 --> 00:14:44,510
+متساوي G prime F of C عشان تطلعلي منه هذا بساويG
+
+153
+00:14:44,510 --> 00:14:52,510
+عند مين عند Y بتساوي F of C يعني هذا سبب لإنه الـ
+
+154
+00:14:52,510 --> 00:14:57,610
+G هذه تصير إيش ماله is continuous عند مين عند ال F
+
+155
+00:14:57,610 --> 00:15:07,490
+of C إذا hence G is continuous at F of C طب ليش
+
+156
+00:15:07,490 --> 00:15:15,570
+هذا بعد شوية هنشوف وين هنستخدمهاالآن limit g of y
+
+157
+00:15:15,570 --> 00:15:22,890
+طالع عندي بيساوي g of f of c اللي هي هذه g of f of
+
+158
+00:15:22,890 --> 00:15:29,550
+c بيساوي g برايم f of c نيجي الآن انا ايش اللي بدي
+
+159
+00:15:29,550 --> 00:15:35,910
+ا .. بدي الآن اثبتلك ان g composite f برايم of c
+
+160
+00:15:35,910 --> 00:15:48,970
+بيساوي limit gof F of X ناقص G of F of C على X
+
+161
+00:15:48,970 --> 00:15:55,410
+minus C لما X تروح لل C بدي أثبت أنه exist بظبط؟
+
+162
+00:15:55,410 --> 00:16:02,610
+واضح هاه؟ طيب بناءً عليه خليني أكتب هذه بدلالة إشي
+
+163
+00:16:02,610 --> 00:16:11,060
+بوصلني للي بديها شوف كيفالان نحسب هذه هذه لمين for
+
+164
+00:16:11,060 --> 00:16:22,260
+x element n اللي هي j أو x لا تساوي مين لا تساوي c
+
+165
+00:16:22,260 --> 00:16:30,120
+معايا اه الان احسبولي هذه هذه عبارة عن تساوي g of
+
+166
+00:16:30,120 --> 00:16:37,650
+f of x اللي هونقص g f of c بدي اكتبها بطريقة g f
+
+167
+00:16:37,650 --> 00:16:49,250
+of x نقص g of f of c على f of x نقص f of c في f of
+
+168
+00:16:49,250 --> 00:16:58,630
+x نقص f of c على x minus cدخلت هذا المقدار في الـ
+
+169
+00:16:58,630 --> 00:17:04,410
+bust و هنا في المقام اللي هو على أساس ان احصل على
+
+170
+00:17:04,410 --> 00:17:10,530
+هذه مضروبة في هذه اللي انا عندي معلومات عن هذه و
+
+171
+00:17:10,530 --> 00:17:20,290
+عن هذه واضح؟ اي سؤال؟ و يساوي؟ الان هذا كله على
+
+172
+00:17:20,290 --> 00:17:33,910
+بعضه مين هو عبارة عن جيcapital of F of X اه F
+
+173
+00:17:33,910 --> 00:17:40,510
+of X اللي هي G of Y بدل ال Y ايش اسمها F of X واضح
+
+174
+00:17:40,510 --> 00:17:46,790
+مضروبة في مين هذا المقدار طلع هذا مضروب في F of X
+
+175
+00:17:48,050 --> 00:17:54,710
+نقص f of c على x minus c خد الآن ال limit للجهتين
+
+176
+00:17:54,710 --> 00:18:01,550
+ال limit للجهتين بيصير ال limit لهذا المقدار ال
+
+177
+00:18:01,550 --> 00:18:09,430
+limit لهذا المقدار معايا يا شباب لما x تروح لل c
+
+178
+00:18:09,430 --> 00:18:18,040
+بساوي خلينا أمسح هان بهمشبعد اذنكم اثبتنا احنا
+
+179
+00:18:18,040 --> 00:18:22,940
+الـG كابيتال continuous خليني انجل هذا الكلام فوق
+
+180
+00:18:22,940 --> 00:18:32,700
+اذا صارت عندي limit الـG of F of X ناقص G of F of
+
+181
+00:18:32,700 --> 00:18:42,160
+C على X minus C لما X تروح للـC بساوي limit اللي
+
+182
+00:18:42,160 --> 00:18:54,190
+هو G of F of Xلما X تروح للـ C أه فيه limit اللي
+
+183
+00:18:54,190 --> 00:19:00,710
+هو F of X ناقص F of C على X minus C لما X تروح
+
+184
+00:19:00,710 --> 00:19:07,820
+لمين للـ Cطبعا طبيعي لما X تروح لل C ال F of X
+
+185
+00:19:07,820 --> 00:19:13,660
+نفسها هتروح لمين؟ لل F of C، مظبوط؟ لما X تروح لل
+
+186
+00:19:13,660 --> 00:19:18,960
+C، ال F of X هتروح لمين؟ لل F of C، لإن أصلا F is
+
+187
+00:19:18,960 --> 00:19:23,240
+differential، بالإذن continuous، معايا؟ طيب، إذن
+
+188
+00:19:23,240 --> 00:19:29,380
+الآن عندي بدي أستخدم ال continuity لمين؟ لل G،
+
+189
+00:19:29,380 --> 00:19:35,050
+limit G of F of Cلما .. لو سمينا هذه كلها على بعض
+
+190
+00:19:35,050 --> 00:19:39,770
+Y قلنا لما X تروح لل C ال Y اللي هي F of X بتروح
+
+191
+00:19:39,770 --> 00:19:45,430
+لمين؟ لل F of C بتصير هذه و كأنها اسمها G of Y و
+
+192
+00:19:45,430 --> 00:19:52,190
+بدل هذه بنحط Y بتروح لمين؟ لل F of C والـ G
+
+193
+00:19:52,190 --> 00:19:56,450
+capital is continuous عند ال F of C إذا على طول
+
+194
+00:19:56,450 --> 00:20:05,010
+limitها بتساوي G of F of Cمظبوط؟ مضروبة في مين؟ في
+
+195
+00:20:05,010 --> 00:20:08,010
+limit F of X نقص F of C على X minus C لما X تروح
+
+196
+00:20:08,010 --> 00:20:14,190
+لمين؟ لـC ليها دي تعريف مين المشتقة الأولى للـF
+
+197
+00:20:14,190 --> 00:20:19,310
+عند الـC نرجع الآن G of F of C إيش بتساوي حسب
+
+198
+00:20:19,310 --> 00:20:22,610
+التعريف الأولاني؟ بساوي G prime
+
+199
+00:20:26,140 --> 00:20:36,180
+للـ F of C بدل هذه في F prime of C وهو المطلوب أي
+
+200
+00:20:36,180 --> 00:20:41,000
+سؤال؟
+
+201
+00:20:41,000 --> 00:20:46,740
+لذالك الآن أثبتنا أنه لو كانت F is differentiable
+
+202
+00:20:46,740 --> 00:20:53,080
+أو G is differentiableو يكون الـ composite الهن is
+
+203
+00:20:53,080 --> 00:20:57,900
+differentiable طبعا ما أخد بعين الاعتبار انه يكون
+
+204
+00:20:57,900 --> 00:21:00,600
+جي كمبوسيت F is defined
+
+205
+00:21:16,030 --> 00:21:25,010
+في عنا اللي هو المثال الأول مثال
+
+206
+00:21:25,010 --> 00:21:30,750
+يعني بسيط كلنا بنعرف انفاضه بس بنشوف كيف احنا
+
+207
+00:21:30,750 --> 00:21:35,530
+بنستخدم ال .. ال .. ال .. ال chain rule الصورة
+
+208
+00:21:35,530 --> 00:21:39,470
+اللي احنا كتبناها في اللي هو ايجاد ال derivative
+
+209
+00:21:39,470 --> 00:21:46,520
+جاي اللي عند في example جاي اللي خدExample جاي لنت
+
+210
+00:21:46,520 --> 00:21:56,300
+F من عند I لعند R بيه a differentiable function من
+
+211
+00:21:56,300 --> 00:22:00,080
+هنا نفترض ان ال F أشبه لها يا جماعة عبارة عندها
+
+212
+00:22:00,080 --> 00:22:05,860
+لقابلة للاشتقاق عند نقطة وين على ال I أو عند ال I
+
+213
+00:22:05,860 --> 00:22:13,230
+كلها مش مشكلة ماشي الحال بقولك اثبتليبس قبل ما
+
+214
+00:22:13,230 --> 00:22:20,750
+بتخلينا نقل تقول احنا بتوجدولنا الـ Fn لان في عندي
+
+215
+00:22:20,750 --> 00:22:24,890
+دالة اسمها Fn يعني F مرفوعة للقوة انا بدي اوجدلها
+
+216
+00:22:24,890 --> 00:22:30,140
+ال derivative طبعا الـ Fn كله prime of Xمن
+
+217
+00:22:30,140 --> 00:22:36,040
+معلوماتنا في الـ Calculus كنا نقول أن تفاضل القوس
+
+218
+00:22:36,040 --> 00:22:41,560
+كله نهو N في F N ناقص واحد في تفاضل ما بداخل القوس
+
+219
+00:22:41,560 --> 00:22:47,990
+اللي هو عبارة عن F prime of Xهذا تفضل الآن بدنا
+
+220
+00:22:47,990 --> 00:22:54,650
+نبرهن هذا الكلام باستخدام نظرية الـ chain rule
+
+221
+00:22:54,650 --> 00:22:58,050
+يعني هذا شغل المكان زي ما بقوله الآن بدنا نشوف كيف
+
+222
+00:22:58,050 --> 00:23:01,670
+بتشتغل المكينة أو ايش اللي شغل المكينة طيب ال
+
+223
+00:23:01,670 --> 00:23:13,110
+proof ال proof لندن كده بدي اعرف function let g
+
+224
+00:23:13,110 --> 00:23:23,530
+fromsome interval J لعند R defined by G يعني أصلا
+
+225
+00:23:23,530 --> 00:23:30,330
+ممكن أعرفها من R حتى G of Y بيسوا Y أساش N element
+
+226
+00:23:30,330 --> 00:23:35,070
+in N يعني حتى لو أعرفتها من R مابعرفها الدالة
+
+227
+00:23:35,070 --> 00:23:46,200
+معايا الآن بناء على هيك صار عندي الآن اللي هوالـ G
+
+228
+00:23:46,200 --> 00:23:56,700
+composite F of X إيش هي هتطلع؟ G of F of X يعني
+
+229
+00:23:56,700 --> 00:24:05,340
+هتطلع FN of X صح ولا لأ؟ إذن هاي دالتنا اللي بدنا
+
+230
+00:24:05,340 --> 00:24:12,000
+نفضلها كتبتها على صورة مين؟ G composite Fوالـ F of
+
+231
+00:24:12,000 --> 00:24:17,520
+X الـ F of X اللي هي الـ F of X من وين جاي بترمي
+
+232
+00:24:17,520 --> 00:24:22,680
+في الـ R يعني بترمي في مين؟ في domain الـ G واضح
+
+233
+00:24:22,680 --> 00:24:27,840
+أهإذا كل أموري تمام وهذه الدالة الدالة الأسية is
+
+234
+00:24:27,840 --> 00:24:30,980
+differentiable وهو جاي اللي أن ال F is
+
+235
+00:24:30,980 --> 00:24:33,780
+differentiable إذا جي كومبوزيت F حسب ال channel
+
+236
+00:24:33,780 --> 00:24:38,140
+أشمالها is differentiable و ال derivative لها جي
+
+237
+00:24:38,140 --> 00:24:42,900
+كومبوزيت F prime of X حسب ال channel اللي حكيناها
+
+238
+00:24:42,900 --> 00:24:49,560
+اللي برهنناها بساوت G prime of F of Xفي f prime of
+
+239
+00:24:49,560 --> 00:24:53,580
+x وي ساون and g of y بيساوي y أس 2 ال derivative
+
+240
+00:24:53,580 --> 00:24:59,420
+الهنين هي and y أس n ناقص واحد يعني and y أس n
+
+241
+00:24:59,420 --> 00:25:04,220
+ناقص واحد في f prime of x لكن احنا بنفاضل عند مين
+
+242
+00:25:04,220 --> 00:25:08,860
+عند f of x فبنشيل ال y بنحكم مكانها قيمتها اللي هي
+
+243
+00:25:08,860 --> 00:25:14,240
+f of x فبتطلع and f of x n ناقص واحد في f prime of
+
+244
+00:25:14,240 --> 00:25:19,610
+xهذه اللي هي اللي احنا بنشتغلها وبدون ما .. طبعا
+
+245
+00:25:19,610 --> 00:25:24,930
+احنا هذا تشريع لاستخدام اللي هو Kedemstrain rule
+
+246
+00:25:24,930 --> 00:25:28,150
+it's اللي احنا بنعرفها زي ما نيجي لما كنا نقولكم
+
+247
+00:25:28,150 --> 00:25:34,810
+مثلا اوجد ال derivative y لعندك y بالساوى sin x
+
+248
+00:25:34,810 --> 00:25:39,460
+تكعيب مثلاكنتش تسوي على طول ماتيش ايش تقول والله
+
+249
+00:25:39,460 --> 00:25:44,040
+بيضاف رضاف of X بيساوي X تتعيب و G of Y تساوي Sin
+
+250
+00:25:44,040 --> 00:25:47,600
+Y و تقول اذا صارت هذه عبارة عن composite of two
+
+251
+00:25:47,600 --> 00:25:53,240
+functions خلاص بنتجاوز المرحلة هذهوعرفنا وين أصل
+
+252
+00:25:53,240 --> 00:25:58,160
+الأمر اللى بيقوللنا why prime بتساوي تفاضل اللى
+
+253
+00:25:58,160 --> 00:26:03,760
+برا اللى هو cosine x كعيب فى تفاضل اللى جوا تلاتة
+
+254
+00:26:03,760 --> 00:26:08,100
+x تربية هذا فى الواقع هو عبارة عن استخدام mean لل
+
+255
+00:26:08,100 --> 00:26:19,080
+chain rule واضح أي سؤال؟ طيب هذا عندنا فى عندنا
+
+256
+00:26:19,080 --> 00:26:31,850
+مثال آخرالمثال .. نعم المثال اللي هو .. يمكن مرشك
+
+257
+00:26:31,850 --> 00:26:36,330
+للمثال حتى معاكم في تحليل واحد لكن كان هدفه اللي
+
+258
+00:26:36,330 --> 00:26:42,910
+هو في حينه ال continuity اذا اعطيك F of X بتساوي
+
+259
+00:26:42,910 --> 00:26:52,400
+هاي B مثال B F of X بتساوي اللي هو X تربيعSin 1
+
+260
+00:26:52,400 --> 00:26:59,800
+على X لما X لا تساوي سفر أو سفر لما X ايش بتساوي
+
+261
+00:26:59,800 --> 00:27:07,140
+سفر الان بيقول لي بيعطيني طبعا هو بيسأل سؤال جابله
+
+262
+00:27:07,140 --> 00:27:10,640
+تعليق سؤال في الكتاب بيقول لي لو كانت ال F is
+
+263
+00:27:10,640 --> 00:27:14,040
+differentiable ركز معاه لو كانت ال F is
+
+264
+00:27:14,040 --> 00:27:17,800
+differentiable الشرط ان ال derivative تماما تطلع
+
+265
+00:27:17,800 --> 00:27:23,590
+continuousهذا ليس شرطًا، هذا بس وينفي الـ R لما
+
+266
+00:27:23,590 --> 00:27:26,430
+نحكي عن الهو نحكي عن الـ real valued functions
+
+267
+00:27:26,430 --> 00:27:33,210
+from R to R كمان لكن في ال complex الأمر بيختلف ال
+
+268
+00:27:33,210 --> 00:27:36,610
+complex أو ال derivative مرة لجيتها معناته اللي
+
+269
+00:27:36,610 --> 00:27:39,210
+بعيدها و اللي بعيدها و اللي بعيدها هتظلها إشمالها
+
+270
+00:27:39,210 --> 00:27:43,830
+موجودة يعني if F prime exists then F double prime
+
+271
+00:27:43,830 --> 00:27:48,630
+and F triple F كذا إذا هتطلع مجرد ما تكون الدالة
+
+272
+00:27:48,630 --> 00:27:53,230
+analytic أو differentiableهتظلها على طول
+
+273
+00:27:53,230 --> 00:27:56,750
+differentiable و continuous و و و الاخرين هذا وين
+
+274
+00:27:56,750 --> 00:28:01,890
+في ال complex أما في ال real الوضع ليس كذلك وهي
+
+275
+00:28:01,890 --> 00:28:07,970
+مثال على F is differentiable everywhere طبعا is
+
+276
+00:28:07,970 --> 00:28:11,310
+differentiable عنده نقطة zero بالذات لكن its
+
+277
+00:28:11,310 --> 00:28:15,450
+derivative is not continuous at this point باضح
+
+278
+00:28:15,450 --> 00:28:20,330
+اليوم اه طيب الآن show
+
+279
+00:28:23,010 --> 00:28:30,750
+that F prime of X exists everywhere
+
+280
+00:28:30,750 --> 00:28:41,270
+but F prime is not continuous at zero و proof
+
+281
+00:28:41,270 --> 00:28:45,470
+البرهن .. طبعا البرهن كامل موجود هنا بس خلينا
+
+282
+00:28:45,470 --> 00:28:50,670
+نبرهن لك .. نوضح إيش ال .. إيش البرهنشوفوا صلى
+
+283
+00:28:50,670 --> 00:28:56,670
+الله عليه الصلاة والسلام الان f prime exist طبيعي
+
+284
+00:28:56,670 --> 00:29:03,310
+for x لا يساوي 0 مقابر سهل مجرد تفاضل عادي f prime
+
+285
+00:29:03,310 --> 00:29:07,290
+of x لأن هذا الدلة قابلة للاشتقاء عند كل النقطة ما
+
+286
+00:29:07,290 --> 00:29:11,430
+عدا عند ال x بالساوية 0 هدى بحكي عن هدى لحالها f
+
+287
+00:29:11,430 --> 00:29:19,020
+prime of x بالساوية2x sin 1 على x لأن x تربيع في
+
+288
+00:29:19,020 --> 00:29:24,360
+sin تفاضل الـ sin cos و تفاضل اللي جوا سالب x
+
+289
+00:29:24,360 --> 00:29:30,440
+تربيع x minus 2 بتروح حد ما حد فبصير سالب cos 1
+
+290
+00:29:30,440 --> 00:29:36,480
+على xالان هذا for x لا تساوي صفر طب for x متساوي
+
+291
+00:29:36,480 --> 00:29:39,660
+صفر for x متساوي صفر الوضع اللي لان بختلف اللي هو
+
+292
+00:29:39,660 --> 00:29:43,880
+فيه عندي اللي هو الدالة أصلا مش معرفة عند ال zero
+
+293
+00:29:43,880 --> 00:29:47,620
+لكن معرفة الدالة ككل عند ال zero عند مين بتساوي
+
+294
+00:29:47,620 --> 00:29:52,060
+صفر فمضطر أنا أستخدم التعريف لإثبات أو فحص إذا
+
+295
+00:29:52,060 --> 00:29:56,680
+كانت الدالة إلها مشتقة عند الصفر ولا لأ فباجي بقول
+
+296
+00:29:56,680 --> 00:30:03,810
+الان بتدا فحص limitاللي هو F of X ناقص F of Zero
+
+297
+00:30:03,810 --> 00:30:08,910
+على X minus Zero as X بتروح للزيرو بدي أشوف هل هذه
+
+298
+00:30:08,910 --> 00:30:13,250
+ال limit موجودة ولا مش موجودة ماشي الحال Y ساوي
+
+299
+00:30:13,250 --> 00:30:16,930
+هذا
+
+300
+00:30:16,930 --> 00:30:20,370
+عشان خاطر أوجد مين أشوف ال F prime عند ال Zero
+
+301
+00:30:20,370 --> 00:30:25,630
+موجودة أو لا بساوي limitF of X مين هي عبارة عن X
+
+302
+00:30:25,630 --> 00:30:29,030
+تربيع .. لأن X بتروح للزيرو، لأن X مش سفر، اللي هي
+
+303
+00:30:29,030 --> 00:30:34,450
+عبارة عن X تربيع صين واحد على X نقص F of Zero اللي
+
+304
+00:30:34,450 --> 00:30:39,310
+هي عبارة عن سفر على X minus سفر لما X تروح لمين
+
+305
+00:30:39,310 --> 00:30:46,870
+للسفر ويساوي limitx term x sin 1 على x لما x تروح
+
+306
+00:30:46,870 --> 00:30:50,670
+لمين للصفر هذه اللي هي by sandwich theorem حلقيها
+
+307
+00:30:50,670 --> 00:30:56,650
+إيش بتساوي سفر كيف by sandwich theorem عندك x sin
+
+308
+00:30:56,650 --> 00:31:00,470
+1 على x absolute value أصغر أو ساوي ال absolute
+
+309
+00:31:00,470 --> 00:31:05,050
+value لل x وهذه الطبيعة أكبر أو ساوي مين سفر as x
+
+310
+00:31:05,050 --> 00:31:07,870
+goes to zero هذه بتروح للزيرو وهذه بتروح للزيرو
+
+311
+00:31:07,870 --> 00:31:10,570
+إذا اللي في النص هذه لازم ال limit هيروح لمين
+
+312
+00:31:10,570 --> 00:31:15,840
+للصفرومن ثم لل continuity لل .. بسبب ال continuity
+
+313
+00:31:15,840 --> 00:31:18,040
+لل .. لل absolute value بتطلع ال limit اللي جوا
+
+314
+00:31:18,040 --> 00:31:20,740
+برضه أشمالها بتساوي 0 لأن ال limit ال absolute
+
+315
+00:31:20,740 --> 00:31:23,380
+value بيساوي absolute value لل limit إذا صار عندى
+
+316
+00:31:23,380 --> 00:31:32,120
+limit اللي جوا بيساوي 0 معايا؟ طيب
+
+317
+00:31:32,120 --> 00:31:35,940
+بما أنه ال limit هذه موجودة بتساوي 0 إذا بنقول
+
+318
+00:31:35,940 --> 00:31:42,580
+بعيدها since كده بيساوي كده thenF prime of 0
+
+319
+00:31:42,580 --> 00:31:50,520
+بتساوي صفر إذا اللي أثبتنا إحنا أنه F prime exist
+
+320
+00:31:50,520 --> 00:31:55,460
+وين ما كان وإيش ال F prime اللي أثبتناها كمان
+
+321
+00:31:55,460 --> 00:32:01,160
+أثبتنا إنه الآن F prime of X أثبتناها إنها بتساوي
+
+322
+00:32:02,250 --> 00:32:08,870
+2x sin 1 على x نقص cos 1 على x لما x ايش معناه لأ
+
+323
+00:32:08,870 --> 00:32:13,070
+تساوي سفر واتبعتناها بتساوي سفر لما x بتساوي سفر
+
+324
+00:32:13,070 --> 00:32:16,990
+إذا صارت ال F is functional everywhere الآن بدنا
+
+325
+00:32:16,990 --> 00:32:23,350
+نثبت إنه is not this F prime is not continuous at
+
+326
+00:32:23,350 --> 00:32:27,150
+zero شوف
+
+327
+00:32:27,150 --> 00:32:29,410
+الآن عندي
+
+328
+00:32:31,690 --> 00:32:41,570
+بدي أشوف limit اللي هي 2x sin 1 على x ناقصه sin 1
+
+329
+00:32:41,570 --> 00:32:49,080
+على x لما x تروح للزيرو exist ولا لأالان limit ال
+
+330
+00:32:49,080 --> 00:32:53,540
+أولى 2x sin 1 على x مضمون انه exist قبل مش
+
+331
+00:32:53,540 --> 00:32:57,560
+ويعملناها نفسها باي اللي هو sandwich theorem هتطلع
+
+332
+00:32:57,560 --> 00:33:03,720
+سفر اذا الان اول حاجة اكتب لها since الان limit
+
+333
+00:33:03,720 --> 00:33:09,420
+sin 1 على x بساوي سفر exist الان
+
+334
+00:33:09,420 --> 00:33:19,480
+but butlimit cos 1 على x لما x تروح لصفر does not
+
+335
+00:33:19,480 --> 00:33:24,360
+exist وهلجت بنشوف ليش does not exist but this
+
+336
+00:33:24,360 --> 00:33:26,140
+limit اشمالها does not exist
+
+337
+00:33:28,950 --> 00:33:33,830
+ما دام هذا exist و هذا does not exist حاصل جمح أو
+
+338
+00:33:33,830 --> 00:33:38,290
+طرح أكيد ايش ماله does not exist لأنه لو exist
+
+339
+00:33:38,290 --> 00:33:42,810
+معناه تصير هذا اللي يطلع و هذا exist بيصير مجموح
+
+340
+00:33:42,810 --> 00:33:45,170
+أو طرح يساوي هذا ايضا صار هذا exist و هذا
+
+341
+00:33:45,170 --> 00:33:51,550
+contradiction فاهمين اه الان hence limit اتنين x
+
+342
+00:33:51,550 --> 00:33:56,410
+sin واحد على x نقص cosine واحد على x لما x تروح
+
+343
+00:33:56,410 --> 00:34:05,340
+للسفر اللي هو does notexist دل عليا بس اوضح اللي
+
+344
+00:34:05,340 --> 00:34:12,220
+هو ليش هذا does not exist بده اوضح ليش هذا does
+
+345
+00:34:12,220 --> 00:34:18,740
+not exist اخدتوا انتوا اخدتوا اللي هو ايش نظرية ان
+
+346
+00:34:18,740 --> 00:34:28,240
+لو كانت limitF of X لما X بتروح ل A بساوي L إذا أي
+
+347
+00:34:28,240 --> 00:34:34,560
+sequence XN بتروح لل A لازم يعطيك اللي هو F of XN
+
+348
+00:34:34,560 --> 00:34:39,780
+برضه يروح لمين لل L، بصبوط؟ هذه كcontinuity اللي
+
+349
+00:34:39,780 --> 00:34:43,530
+بتحكي عنهااللي كده كانت limit F of X لما X تروح
+
+350
+00:34:43,530 --> 00:34:48,930
+للـ A بساوي L و IG تأخدت أي sequence XN بتروح للـ
+
+351
+00:34:48,930 --> 00:34:54,670
+A هيطلع limit F of XN مش بيروح بساوي لL ماشي هذه
+
+352
+00:34:54,670 --> 00:35:00,780
+اللي هي النظريةبناء على هذه النظرية كنا نقول انه
+
+353
+00:35:00,780 --> 00:35:07,180
+لو وجيت two sequences على الأقل ايكون بروح للـA
+
+354
+00:35:07,180 --> 00:35:13,500
+لكن بروح لـLimits مختلفات او واحدة من Limits does
+
+355
+00:35:13,500 --> 00:35:18,600
+not exist بكفالك ان الـLimit هذه اشمالها does not
+
+356
+00:35:18,600 --> 00:35:25,170
+exist واضح؟ الان اذا بدي اعتمد على هذهفي إثبات إنه
+
+357
+00:35:25,170 --> 00:35:29,690
+limit cosine واحد على X does not exist أكيد كلكم
+
+358
+00:35:29,690 --> 00:35:40,730
+جال take the sequences أو the two sequences X and
+
+359
+00:35:40,730 --> 00:35:50,290
+بتساوي واحد على اتنين and by and Y and بتساوي واحد
+
+360
+00:35:50,290 --> 00:35:57,030
+على اتنين and زائد واحد في byمظبوط أكيد قلته هيك
+
+361
+00:35:57,030 --> 00:36:05,290
+where x and goes to zero and y and goes to zero
+
+362
+00:36:05,290 --> 00:36:13,130
+but cosine واحد على ايه؟ cosine واحد على x and
+
+363
+00:36:13,130 --> 00:36:23,100
+اللي هو بتساوي او goes to واحد and cosine1 على I
+
+364
+00:36:23,100 --> 00:36:30,500
+and goes to ناقص واحد اوضحها
+
+365
+00:36:30,500 --> 00:36:35,600
+اوضحها اذكركم الان
+
+366
+00:36:35,600 --> 00:36:39,980
+هذا بيصير cosine مين اتنين and by اتنين and by ايش
+
+367
+00:36:39,980 --> 00:36:45,470
+مالها واحدا اتنين ان زاد واحد لكل في باقي ايش
+
+368
+00:36:45,470 --> 00:36:49,030
+بتصير؟ اللي هو سالب واحد فبصير هاد ال cosine
+
+369
+00:36:49,030 --> 00:36:53,450
+converts واحد و هاد ال cosine converts لمين؟ لسالب
+
+370
+00:36:53,450 --> 00:36:58,490
+واحد اذا حسب اللي حكيناها قبل شوية hence hence
+
+371
+00:36:58,490 --> 00:37:05,910
+hence limit cosine واحد على x لما x تروح ل zero
+
+372
+00:37:05,910 --> 00:37:17,800
+does not existهذا توضيح .. توضيح لماذا اللي هو cos
+
+373
+00:37:17,800 --> 00:37:24,000
+1 على x does not exist لاحظ التالي على جهة لكن لو
+
+374
+00:37:24,000 --> 00:37:28,440
+كانت .. بالمناسبة لو كانت هذه does not exist
+
+375
+00:37:28,440 --> 00:37:33,640
+limitها و هذه does not exist بقدرش أؤكد على إن ال
+
+376
+00:37:33,640 --> 00:37:40,460
+limit للطرح أو الجامعه does not exist صح؟ في مثال؟
+
+377
+00:37:45,330 --> 00:37:50,850
+أه و خروجتها واحدة لأن واحدة لأن بينهين سالم بيصير
+
+378
+00:37:50,850 --> 00:37:53,450
+limit لها دي موجودة أو limit لها دي موجودة .. آسف
+
+379
+00:37:53,450 --> 00:37:55,890
+limit لها دي مش موجودة أو limit لها دي مش موجودة
+
+380
+00:37:55,890 --> 00:38:01,490
+لكن اللي هو حصل إيش طرح موجود أو لو بدك جمحن بتحط
+
+381
+00:38:01,490 --> 00:38:04,890
+اللي هو للتانية تاخد واحدة لأن ونقص واحدة لأن و
+
+382
+00:38:04,890 --> 00:38:10,490
+هكذا أي سؤال؟
+
+383
+00:38:10,490 --> 00:38:11,330
+طيب
+
+384
+00:38:15,770 --> 00:38:21,510
+اللي ييجي الأن إلى
+
+385
+00:38:21,510 --> 00:38:37,290
+النقطة اللي بعيدها أين
+
+386
+00:38:37,290 --> 00:38:38,330
+رحلت أنا؟
+
+387
+00:38:48,090 --> 00:38:53,250
+طيب انتبهونا خلينا لهذه النظرية نحكي عن نصها أو
+
+388
+00:38:53,250 --> 00:39:00,150
+الإشي بالتفصيل و بعدين نيجي نلخصلكم كل المعلومة
+
+389
+00:39:00,150 --> 00:39:05,130
+اللي .. اللي في الأول هنحس إنها بتغلب في اللي هو
+
+390
+00:39:05,130 --> 00:39:13,470
+سفر و من ثم نحاول نبرهنها أه
+
+391
+00:39:13,470 --> 00:39:18,970
+.. أه .. أه .. لأ .. أه ..لت I subsequent R be an
+
+392
+00:39:18,970 --> 00:39:19,610
+interval
+
+393
+00:39:28,670 --> 00:39:34,370
+لأنه احنا بتتذكروا في real واحد خلاص اللي هي ال ..
+
+394
+00:39:34,370 --> 00:39:37,010
+ال .. ال .. ال .. الاشي اللي بده شغل اللي هو
+
+395
+00:39:37,010 --> 00:39:39,890
+النقطة اللي بتكون في ال interval اللي بتكون
+
+396
+00:39:39,890 --> 00:39:42,250
+cluster point اللي مش cluster point automatic
+
+397
+00:39:42,250 --> 00:39:45,970
+هتكون ال limit exist فمش داعي لأصلا لدراسة الموضوع
+
+398
+00:39:45,970 --> 00:39:52,440
+لإنه بيصير كتير من الأمور trivialعشان هي احنا
+
+399
+00:39:52,440 --> 00:39:55,740
+بنشتغل على الـ Intervals let I subset من R بيكون
+
+400
+00:39:55,740 --> 00:39:59,680
+Interval and let F من I لعند R بيكون strictly
+
+401
+00:39:59,680 --> 00:40:09,720
+Monotone F من عند هذه theorem أنا مكتبش ال theorem
+
+402
+00:40:09,720 --> 00:40:19,060
+تمام لأنه موجود هنا theorem 618 عند F من Iلعند R
+
+403
+00:40:19,060 --> 00:40:25,440
+غير عنها strictly monotone
+
+404
+00:40:25,440 --> 00:40:36,900
+ماشي الحال و continuous and continuous الان لاحظ
+
+405
+00:40:36,900 --> 00:40:41,100
+على ال function هذهمدام حكالة عنها strictly
+
+406
+00:40:41,100 --> 00:40:44,540
+monotone يعني strictly increasing او strictly
+
+407
+00:40:44,540 --> 00:40:49,240
+decreasing معناته صارت automatic اتدالة اشمالها
+
+408
+00:40:49,240 --> 00:40:53,800
+one to one ليش؟ لأنه لو كانت strictly increasing
+
+409
+00:40:53,800 --> 00:40:59,060
+معناته x1 أصغر من x2 اللي بتعطيني f of x1 أصغر
+
+410
+00:40:59,060 --> 00:41:03,840
+strictly من f of x2 هذا في حالة نين strictly
+
+411
+00:41:03,840 --> 00:41:09,540
+increasing أه مش ممكنية للمساواةهاالأن في حالة
+
+412
+00:41:09,540 --> 00:41:14,520
+strictly decreasing X1 أكبر من X2 بيعطيني F of X1
+
+413
+00:41:14,520 --> 00:41:21,220
+أصغر من F of X2 هذا strictly decreasing الآن سواء
+
+414
+00:41:21,220 --> 00:41:25,060
+هنا الحالة هذه أو الحالة هذه هيكون عندي ال
+
+415
+00:41:25,060 --> 00:41:29,200
+function one to one غصب عنها، ليش؟ لأن لو كانت X1
+
+416
+00:41:29,200 --> 00:41:35,640
+لا تساوي X2 يا أصغر يا أكبر، ما زال مقت أصغرهتكون
+
+417
+00:41:35,640 --> 00:41:40,680
+strictly أصغر يعني بمعنى أخر f of x1 لا تساوي f of
+
+418
+00:41:40,680 --> 00:41:45,460
+x2 ولو كانت هذه أكبر هتكون f of x1 أكبر برضه هتكون
+
+419
+00:41:45,460 --> 00:41:49,060
+إشمالها لا تساوي و similarly في حالة ال decreasing
+
+420
+00:41:49,850 --> 00:41:56,250
+إذن واضح إن X1 ≤ X2 بيعطينا F X1 ≤ F X2 أو بمعنى
+
+421
+00:41:56,250 --> 00:42:03,730
+آخر F X1 هذه هي الcontraposition ل F X1 ≤ F X2
+
+422
+00:42:03,730 --> 00:42:10,010
+بيعطينا X1 ≤ X2 وهذا يعني ال F أشمالها is one to
+
+423
+00:42:10,010 --> 00:42:15,810
+one يعني الآن أنا بوضحليش أعطاني F strictly
+
+424
+00:42:15,810 --> 00:42:20,790
+monotone؟ عشان شكله أصلا احنا قاعد .. هذه النظرية
+
+425
+00:42:20,790 --> 00:42:25,030
+الحاكية عن ال inverse بدنا نشوف العلاقة بين ال
+
+426
+00:42:25,030 --> 00:42:27,950
+derivative لل inverse و ال derivative للدالة
+
+427
+00:42:27,950 --> 00:42:32,520
+الأصليةإذا بدأ أهل الدالة الأصلية أن يكون لها
+
+428
+00:42:32,520 --> 00:42:36,640
+inverse عشان يكون لها inverse لازم أفترض أن الدالة
+
+429
+00:42:36,640 --> 00:42:40,740
+إشمالها one to one فالآن فرضنا إنها strictly
+
+430
+00:42:40,740 --> 00:42:43,980
+monotone يعني strictly increasing أو strictly
+
+431
+00:42:43,980 --> 00:42:50,920
+decreasing الآن مدامة one to one إذا في إمكانية
+
+432
+00:42:50,920 --> 00:42:58,230
+نحكيعن inverse إلها F inverse إلها اللي هو بده
+
+433
+00:42:58,230 --> 00:43:03,290
+يسميه هو الآن بده يسميه G هو بده يسميه G هياخد ال
+
+434
+00:43:03,290 --> 00:43:10,950
+G من وين من ال range لل F يعني من ال F of I لعند
+
+435
+00:43:10,950 --> 00:43:17,150
+مين لعند ال R ماشي ال F of I هذي مسميها مين هو
+
+436
+00:43:17,150 --> 00:43:25,150
+مسميها هو J يعني ماياخد ال Gمن G لعند R الـ G هي
+
+437
+00:43:25,150 --> 00:43:30,750
+عبارة عن مين؟ عن الـ F inverse معايا؟ قولي يا محمد
+
+438
+00:43:30,750 --> 00:43:42,570
+لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ
+
+439
+00:43:42,570 --> 00:43:42,670
+R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R
+
+440
+00:43:42,670 --> 00:43:43,910
+.. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R ..
+
+441
+00:43:43,910 --> 00:43:44,630
+لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ
+
+442
+00:43:44,630 --> 00:43:47,530
+R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R
+
+443
+00:43:47,530 --> 00:43:47,590
+.. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R ..
+
+444
+00:43:47,590 --> 00:43:47,610
+لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ
+
+445
+00:43:47,610 --> 00:43:53,500
+R .. لـ R .. لـ R .. لـبس لما نكتب I R ايش برضه
+
+446
+00:43:53,500 --> 00:43:57,420
+صحيح بس على أساس انه .. خلاني أقول المعلومات بت ..
+
+447
+00:43:57,420 --> 00:44:01,780
+بت .. بتأهلني ان اكون أدق لعند مين لعند I خلان
+
+448
+00:44:01,780 --> 00:44:06,600
+صحيح طيب الآن عشان ما نبعدش عن اللي بدنايا F من I
+
+449
+00:44:06,600 --> 00:44:12,080
+ل R strictly monotone و G من F of I ل عند I أصلا
+
+450
+00:44:12,080 --> 00:44:15,140
+إذا كانت ال F من I ل عند R strictly monotone و
+
+451
+00:44:15,140 --> 00:44:19,960
+continuousهتكون الـ G اللي هي ال F inverse من F of
+
+452
+00:44:19,960 --> 00:44:24,400
+I ل I برضه strictly monotone و إيش و continuous
+
+453
+00:44:24,400 --> 00:44:27,940
+strictly monotone و continuous إذن الآن ال F عند
+
+454
+00:44:27,940 --> 00:44:30,660
+me strictly monotone و continuous و ال F inverse
+
+455
+00:44:30,660 --> 00:44:41,160
+برضه strictly monotone و إيش و continuous معايا ؟
+
+456
+00:44:41,160 --> 00:44:49,090
+طيبالان لحد الان بعتبر انه احنا بنحكي عن معطيات
+
+457
+00:44:49,090 --> 00:44:54,030
+حتى لو كنا استنتجنا جزء منها من بعض الان بقوللي
+
+458
+00:44:54,030 --> 00:44:58,970
+اللي هو موضوعنا if f is differentiable at c if
+
+459
+00:44:58,970 --> 00:45:12,350
+الان if if f is differentiable at c element in I
+
+460
+00:45:13,160 --> 00:45:17,380
+ماشي الحال يعني F differentiable عنده نقطة C
+
+461
+00:45:17,380 --> 00:45:24,600
+element وين؟ ن I بقول لك then طبعاً A و F prime of
+
+462
+00:45:24,600 --> 00:45:28,340
+C أشمالها لاتساوي سفر لأنه هيلزمنا القسم عليها
+
+463
+00:45:28,340 --> 00:45:32,420
+عشان هيك لازم اللي هو عشان نحكي عن ال inverse لال
+
+464
+00:45:32,420 --> 00:45:34,880
+derivative تكون ال F prime عند ال C أشمالها
+
+465
+00:45:34,880 --> 00:45:42,730
+لاتساوي سفر الآن thenاللي هي الـ G الـ G اللي
+
+466
+00:45:42,730 --> 00:45:47,810
+سميناها F inverse اللي سميناها F inverse الـ G is
+
+467
+00:45:47,810 --> 00:45:51,150
+differentiable
+
+468
+00:45:51,150 --> 00:46:00,490
+is differentiable at اللي هو F of C is
+
+469
+00:46:00,490 --> 00:46:04,610
+differentiable at إيش؟ at F of C اللي هو مسميها
+
+470
+00:46:04,610 --> 00:46:11,800
+إيش اسمها ديالان الإعلان الواضح أنه لو كانت F
+
+471
+00:46:11,800 --> 00:46:15,960
+differentiable عند الـC و F' للـC لاتساوي سفر
+
+472
+00:46:15,960 --> 00:46:20,400
+هتكون الـF inverse differentiable عند مين؟ عند
+
+473
+00:46:20,400 --> 00:46:34,300
+الـF of C اه and .. and F inverse prime at F of C
+
+474
+00:46:35,750 --> 00:46:46,830
+At F of C هتساوي واحد على F prime لمين؟ Let's see
+
+475
+00:46:46,830 --> 00:46:59,390
+يعني وكأنه وكأنه بمجول F inverse prime لل Yبتساوي
+
+476
+00:46:59,390 --> 00:47:07,690
+واحد على F prime of X where العلاقة بين Y و X اللي
+
+477
+00:47:07,690 --> 00:47:16,070
+هي Y بتساوي F of X واضح، اه، الكلام واضح وسهلاللي
+
+478
+00:47:16,070 --> 00:47:21,190
+هي f prime of c بدي ابتبها طريقة ثانية بيساوي واحد
+
+479
+00:47:21,190 --> 00:47:30,010
+على f prime of الان هو سم ال f of c أشمها D يعني
+
+480
+00:47:30,010 --> 00:47:37,080
+ال c بتساوي f انفر سلاميين ل Dصح؟ يعني بمعنى آخر
+
+481
+00:47:37,080 --> 00:47:45,060
+هو بقول F inverse prime عند مين؟ عند ال D بسوء
+
+482
+00:47:45,060 --> 00:47:50,580
+واحد على F prime مكان ال C إيش ودي يحط؟ F inverse
+
+483
+00:47:50,580 --> 00:48:01,420
+of D يعني واحد على F prime فلأ بكفي اللي هى ماشي
+
+484
+00:48:01,420 --> 00:48:07,720
+الحل G of D لأ لأاللي هو كاتبها يعني لإنه كاتب هو
+
+485
+00:48:07,720 --> 00:48:15,000
+بدل ال F inverse كاتب مين الـG واضح واضحة طبعا هذه
+
+486
+00:48:15,000 --> 00:48:22,200
+اللي هي اللي احنا بدنا نثبته نيجي للإثبات
+
+487
+00:48:27,580 --> 00:48:32,740
+بدنا نطبل روحنا شوية عرفناش اننا نطبط اه عشان اللي
+
+488
+00:48:32,740 --> 00:48:41,260
+خاطر امسح وبدأ ابدأ اشتغل من فوق النظرية
+
+489
+00:48:41,260 --> 00:48:45,720
+احفظناها اه او خلينا نقول هي موجودة يعني اه بس
+
+490
+00:48:45,720 --> 00:48:49,160
+بدنا نطلع عالميا على البرهان ال proof
+
+491
+00:48:56,060 --> 00:49:04,920
+بدنا نثبت احنا اللي هو g prime of
+
+492
+00:49:04,920 --> 00:49:14,460
+D بساوة واحد على F prime of C هاي اللي بدنا نثبته
+
+493
+00:49:14,460 --> 00:49:17,820
+او واحد على F prime .. الـ G prime هذا طالع من
+
+494
+00:49:17,820 --> 00:49:22,140
+اليمين الـ G عبارة عن F inverse ماشي؟ شوفي الآن
+
+495
+00:49:25,040 --> 00:49:33,140
+بدي اعرف ده اللي برضه مساعدة لان خد Y لا تساوي D و
+
+496
+00:49:33,140 --> 00:49:39,760
+Y طبعا وين موجودة؟ Y element in J في domain من ال
+
+497
+00:49:39,760 --> 00:49:43,640
+F inverse متذكرين؟
+
+498
+00:49:43,640 --> 00:49:52,360
+ال F من I لعند R و ال G اللي هي ال F inverseمن F
+
+499
+00:49:52,360 --> 00:49:59,500
+of I اللي سمناها J لعند مين؟ لعند الـ I مظبوط؟ طيب
+
+500
+00:49:59,500 --> 00:50:10,320
+الآن هعرف ال H of Y H of Y بتساوي اللي هو F F
+
+501
+00:50:10,320 --> 00:50:20,250
+inverse of Y اللي هي F of G of Y ماقص F of Gof
+
+502
+00:50:20,250 --> 00:50:25,430
+مين؟ of D نحطها على جنب ايش اللي بنعني فيه F of C
+
+503
+00:50:25,430 --> 00:50:33,110
+بتساوي D او G of D اللي هي F inverse استذكروا انه
+
+504
+00:50:33,110 --> 00:50:36,390
+انا الـ G هي مين هي F inverse عشان تسهي عليكم
+
+505
+00:50:36,390 --> 00:50:41,630
+عملية الحسابات ايش بتساوي؟ C ماشي الان F of G of Y
+
+506
+00:50:41,630 --> 00:50:48,750
+ناقص F of G of D على G of Y ناقص G of D
+
+507
+00:50:51,950 --> 00:50:56,890
+معايا؟ واضح اه؟ الان انا مفترض ان ال Y لا تساوي D
+
+508
+00:50:56,890 --> 00:51:01,290
+طبعا ال functions سبعنا سواء ال F او ال G تمتين
+
+509
+00:51:01,290 --> 00:51:05,870
+one to one مأكيد ال G of Y ايش مالها لا تساوي G of
+
+510
+00:51:05,870 --> 00:51:09,990
+D اذا ان انا مرتاح انا ماخد Y لا تساوي Z اذا ان
+
+511
+00:51:09,990 --> 00:51:13,450
+automatic هذه is well defined يعني G of Y ايش
+
+512
+00:51:13,450 --> 00:51:19,270
+مالها لا تساوي مين؟ G of D واضح اه؟ اي سؤال؟
+
+513
+00:51:22,880 --> 00:51:28,700
+الان الـ H of Y اللي هي بتساوي اللي هو F of G of Y
+
+514
+00:51:28,700 --> 00:51:33,120
+نقص F وكذا على G of Y minus G of D is اللي هي well
+
+515
+00:51:33,120 --> 00:51:38,640
+defined طبعا الان اللي فوقبناء على ما كتبناه
+
+516
+00:51:38,640 --> 00:51:45,220
+المستعملينه هنا كرموز هذه نفسها ممكن نطلع إليها
+
+517
+00:51:45,220 --> 00:51:50,520
+كصيغة أخرى أفما هي inverse تبعدها دول فبصير عبارة
+
+518
+00:51:50,520 --> 00:51:57,980
+عن Y ناقص D صح ولا لأ على G of Y ناقص مين G of D
+
+519
+00:51:57,980 --> 00:52:04,840
+هذا نظرة أخرى لمين للH of Y اللي عندناأي سؤال؟
+
+520
+00:52:04,840 --> 00:52:10,740
+طبعا الـH of Y واضح أنها مش سفر لأن الـY أشمالها
+
+521
+00:52:10,740 --> 00:52:15,500
+لاتساوي D لأن بعد شوية بدي أجسم عليها عشان هيك بدي
+
+522
+00:52:15,500 --> 00:52:22,000
+أكتد لكم أن الـY الـH of Y أشمالها لاتساوي سفر
+
+523
+00:52:22,000 --> 00:52:31,170
+واضح لحد الآن، ماشي الحال، الآن بدي أستخدماللي هو
+
+524
+00:52:31,170 --> 00:52:35,090
+التعريف في الوصول الـ Epsilon Delta Definition في
+
+525
+00:52:35,090 --> 00:52:42,570
+الوصول للي بديهاللي هو G prime of D بيساوي limit G
+
+526
+00:52:42,570 --> 00:52:48,770
+of Y نقص G of D على Y minus D الـY بتروح للـD اللي
+
+527
+00:52:48,770 --> 00:52:51,490
+هو exist .. that .. that .. that .. that مثلك انه
+
+528
+00:52:51,490 --> 00:52:54,470
+لكل يكبر من صفر يوجد Delta او Gamma او اللي هي
+
+529
+00:52:54,470 --> 00:52:58,490
+such that لما تكون مسافة بين Y و D أصغر من Delta
+
+530
+00:52:58,490 --> 00:53:01,900
+يعطينا هدف أصغر من مين؟ من يبسلونهذا كيف بده
+
+531
+00:53:01,900 --> 00:53:07,060
+أثبته؟ بالاستعانة بيه اللي هو أنا بعرف أن الـ F is
+
+532
+00:53:07,060 --> 00:53:10,320
+differentiable و بالاستعانة بتدلة اللي عندى هذه
+
+533
+00:53:10,320 --> 00:53:14,080
+السؤال أي سؤال حتى الآن حتى الآن احنا اللي أثبتنا
+
+534
+00:53:14,080 --> 00:53:17,540
+ان H و Y اللي ركّبناها دي إيش مانع لا تساوى سفر
+
+535
+00:53:17,540 --> 00:53:27,380
+الان عندى since F is differentiable at مين معطينى؟
+
+536
+00:53:27,380 --> 00:53:34,100
+at Cاذن thenfor every epsilon أكبر من صفر بتستخدم
+
+537
+00:53:34,100 --> 00:53:38,920
+على طول اللي هو limit واضح then for every epsilon
+
+538
+00:53:38,920 --> 00:53:42,660
+أكبر من صفر there exist نستخدم نفس التعبير دلتا
+
+539
+00:53:42,660 --> 00:53:47,840
+أكبر من صفر أو نفس الرموز such that X minus C أكبر
+
+540
+00:53:47,840 --> 00:53:54,020
+من صفر وأصغر من دلتا implies F of X ناقص F of C
+
+541
+00:53:54,020 --> 00:53:59,240
+على X minus C ناقص اللي هو ال derivative اللي هي F
+
+542
+00:53:59,240 --> 00:54:06,500
+prime of C صح؟أصغر من مين؟ من أبسل وسمي هذه ايش
+
+543
+00:54:06,500 --> 00:54:17,000
+مسميها هو؟ همسميها واحد هذا سمي واحد واضح
+
+544
+00:54:17,000 --> 00:54:21,360
+أه؟ في معنى و كده الان f is differentiable in c
+
+545
+00:54:21,360 --> 00:54:25,580
+than لكل y نقل المستقبل اللي يعني استخدمنا limit f
+
+546
+00:54:25,580 --> 00:54:30,470
+of x نقص f of c على x minus c سوى f prime of cطبعا
+
+547
+00:54:30,470 --> 00:54:34,630
+أنا بعيد على أساس اللي بتابعنا مش سواعب انكم مش
+
+548
+00:54:34,630 --> 00:54:42,350
+سواعبته واضح؟ ماشي الحاجة الآن بدنا نستخدم ال
+
+549
+00:54:42,350 --> 00:54:47,410
+continuity لمين؟ لجي جي is continuous طبعا جي is
+
+550
+00:54:47,410 --> 00:54:51,870
+differentiable أصلا جي is differentiable عند مين؟
+
+551
+00:54:51,870 --> 00:54:56,690
+عند اللي هو D يعني جي is differentiable عند F of C
+
+552
+00:54:56,690 --> 00:55:03,740
+إذا continuousمظبوط؟ اذا الان since .. since G is
+
+553
+00:55:03,740 --> 00:55:12,540
+continuous at D بتساوي F of C اذا يعني صار عندى
+
+554
+00:55:12,540 --> 00:55:24,060
+limit G of Y لما Y تروح ل D بساوة مين؟ G of D اه
+
+555
+00:55:25,340 --> 00:55:29,760
+واضح ها؟ واضح .. واضح ها؟ خلّيني نعمل .. على أساس
+
+556
+00:55:29,760 --> 00:55:32,980
+ما نستخدم الرموز هذه نربطها باللي بقى بالها ..
+
+557
+00:55:32,980 --> 00:55:37,900
+بنغير بعدين معايا؟ طيب .. هذه إيش معناتها by
+
+558
+00:55:37,900 --> 00:55:41,460
+epsilon delta definition؟ أنه لكل .. الآن بدي
+
+559
+00:55:41,460 --> 00:55:45,780
+أستخدم الـ delta هذه لإن بدي أستخدم الاتنين مع بعض
+
+560
+00:55:45,780 --> 00:55:49,800
+الوصول اللي بديهاواضح؟ هذه لكل إبسلون في الدنيا،
+
+561
+00:55:49,800 --> 00:55:53,140
+أي إن كانت من ضمن إنيين الـDelta اللي لاجيناها،
+
+562
+00:55:53,140 --> 00:55:57,300
+واضح اللي بحكيه؟ الآن لكل إبسلون أكبر من 0، there
+
+563
+00:55:57,300 --> 00:56:01,160
+exists Gamma اللي هي .. ابحثت إنه لما يكون Y minus
+
+564
+00:56:01,160 --> 00:56:05,100
+D أصغر من Gamma، يعطيني هذا أصغر، اللي هو من اللي
+
+565
+00:56:05,100 --> 00:56:08,180
+بديه .. من اللي بدي أن أناسك دموع، اللي هو
+
+566
+00:56:08,180 --> 00:56:16,030
+الـDelta، الآنcontinuous ات كده then for every
+
+567
+00:56:16,030 --> 00:56:18,930
+ابسلون الابسلون اللي بده استخدمها اللي من ضمن
+
+568
+00:56:18,930 --> 00:56:21,290
+الابسلون هي اللي بتنفع ايه اللي بتنفع على ال delta
+
+569
+00:56:21,290 --> 00:56:25,970
+هذه then for delta أكبر من سفر there exist gamma
+
+570
+00:56:25,970 --> 00:56:32,670
+أكبر من سفر such that لما y minus d كون أكبر من
+
+571
+00:56:32,670 --> 00:56:37,170
+سفر وأصغر من الجامعة اللي لجيتها هذا بيعطيني اللي
+
+572
+00:56:37,170 --> 00:56:46,080
+هو ال Gof Y نقص الـ G of D يكون أصغر من مين من الـ
+
+573
+00:56:46,080 --> 00:56:51,820
+Epsilon اللي هي سميتها H Delta أي سؤال هذا بده
+
+574
+00:56:51,820 --> 00:57:01,100
+سميه H اسمه بده سميه اتنين اه هساخد من ال N طيب
+
+575
+00:57:01,100 --> 00:57:07,080
+شوفوا
+
+576
+00:57:07,080 --> 00:57:17,060
+الآنأنا في الآخر بدي اللي هو أصل لإنه اللي هي ال
+
+577
+00:57:17,060 --> 00:57:21,680
+derivative لل F prime اللي هو واحد ال F inverse
+
+578
+00:57:21,680 --> 00:57:29,840
+prime واحد على ال F prime ماشي طيب لما
+
+579
+00:57:29,840 --> 00:57:37,150
+تسيري الآن ال Yطبعا ال y .. ال .. ال .. ال .. ال
+
+580
+00:57:37,150 --> 00:57:37,190
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+581
+00:57:37,190 --> 00:57:37,210
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+582
+00:57:37,210 --> 00:57:37,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+583
+00:57:37,750 --> 00:57:37,770
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+584
+00:57:37,770 --> 00:57:38,230
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+585
+00:57:38,230 --> 00:57:46,550
+.. ال ..
+
+586
+00:57:46,550 --> 00:57:47,090
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+587
+00:57:47,090 --> 00:57:47,550
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+588
+00:57:47,550 --> 00:57:48,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+589
+00:57:48,510 --> 00:57:48,870
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+590
+00:57:48,870 --> 00:57:49,850
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+591
+00:57:49,850 --> 00:57:57,250
+ال ..
+
+592
+00:57:57,250 --> 00:57:58,030
+ال
+
+593
+00:58:03,070 --> 00:58:09,070
+إذا حيطلع عند الـ GY نقص GY دي إيش معلها؟ أقل من
+
+594
+00:58:09,070 --> 00:58:14,570
+مين؟ من دلتا اللي هي by using اتنين G of Y إيش
+
+595
+00:58:14,570 --> 00:58:19,730
+اسمها؟ اللي هي G of Y اللي هي Y إيش بتسوى F of X
+
+596
+00:58:19,730 --> 00:58:25,580
+عن G of Y بتسوى Xأه اللي هي عبارة عن X minus G of
+
+597
+00:58:25,580 --> 00:58:31,900
+D الـ D اللي هي عبارة عن مين؟ اللي هي F of C و الـ
+
+598
+00:58:31,900 --> 00:58:35,820
+G inverse للـ F إذا هتطلع عبارة عن مين؟ عن C أصغر
+
+599
+00:58:35,820 --> 00:58:45,140
+من مين؟ من دلتا واضح طبيعي وأكبر أكيد أكيد أكيد
+
+600
+00:58:45,140 --> 00:58:52,230
+أكيدواضح لحد الآن الان هذا بده يخليني أستخدم مين
+
+601
+00:58:52,230 --> 00:58:59,750
+أستخدم واحد إذا صار عندي then هذا متحقق الان then
+
+602
+00:58:59,750 --> 00:59:04,830
+بدي أربط هذا الكلام بمين باللي فوق اللي هو H of Y
+
+603
+00:59:04,830 --> 00:59:12,450
+H of Y ناقص F prime of C شوف كيف بده F مثلك الان
+
+604
+00:59:12,450 --> 00:59:19,780
+اللي هو بساويH of Y مين؟ H of Y اللي هو عبارة عن Y
+
+605
+00:59:19,780 --> 00:59:27,960
+ناقص D على G of Y ناقص G of D، مظبوط؟ اللي هو بيه
+
+606
+00:59:27,960 --> 00:59:30,960
+عبارة عن مين؟ F of G of Y ناقص كده، إلى آخرين
+
+607
+00:59:30,960 --> 00:59:42,000
+بيصير بساوي اللي هو F of G of Y ناقص F of G of D
+
+608
+00:59:42,000 --> 00:59:52,730
+على Yعلى g of y ناقص g of d اللي هو ناقص f prime
+
+609
+00:59:52,730 --> 01:00:00,150
+of c أصغر من مين؟ من y عارفين ليش؟ لأن الـ g of y
+
+610
+01:00:00,150 --> 01:00:04,880
+مين هي؟ الـ xو الـ G of D اللي هي مين الـ C
+
+611
+01:00:04,880 --> 01:00:10,480
+فاهمين؟ أنا قصد أكتبها بالصورة هذه عشان أقولكم أيش
+
+612
+01:00:10,480 --> 01:00:14,580
+لو سُلتله H of I ناقص أفرو برايم of C بساوي هذا
+
+613
+01:00:14,580 --> 01:00:21,500
+المقدار ناقص هذا متحقق كمان مرة يا جماعة اللي
+
+614
+01:00:21,500 --> 01:00:26,220
+بيحقق هذا غصب عنه بيحقق هذا و اللي بيحقق هذا بيحقق
+
+615
+01:00:26,220 --> 01:00:31,240
+هذا ماشي الحال أنا الأن أخدت عندي Y element in J
+
+616
+01:00:31,920 --> 01:00:36,960
+والـ Y لا تساوي D واخدت هذا يكون أصغر من دولتا تحت
+
+617
+01:00:36,960 --> 01:00:41,320
+هذا الشرط الآن أنا بشتغل تحت هذا الشرط الآن هذا
+
+618
+01:00:41,320 --> 01:00:46,140
+أدالي حسب اللي هي اتنين ان هذا ناقص هذا أصغر من
+
+619
+01:00:46,140 --> 01:00:51,090
+دولتا هذا اللي هو X وهذا اللي هو mean الـCالان
+
+620
+01:00:51,090 --> 01:00:54,790
+مادام أصغر من دلتا إذا أعطاني واحد إذا أعطاتني هذه
+
+621
+01:00:54,790 --> 01:00:59,510
+أصغر من هذه هذه في الواقع مين هي F of X هي عبارة
+
+622
+01:00:59,510 --> 01:01:03,830
+عن F of G of Y لأن G of Y هي ال X و C ليه F of D
+
+623
+01:01:03,830 --> 01:01:08,690
+صار هذا ناقص هذا أصغر من مين من إبسلون من جهة أخرى
+
+624
+01:01:08,690 --> 01:01:13,650
+هذا المقدار مين هو عبارة عن H of Y وهذا اللي هي F
+
+625
+01:01:13,650 --> 01:01:18,550
+prime of Cإذا القالة اللي وصلت إليه أنه لكل إبسلون
+
+626
+01:01:18,550 --> 01:01:22,670
+أكبر من 0 وجدت Gamma لأن Gamma بين إيديا واجدتها
+
+627
+01:01:22,670 --> 01:01:27,050
+من الأصل إلى لكل إبسلون أكبر من 0 لجيت Gamma ابحث
+
+628
+01:01:27,050 --> 01:01:30,290
+أنه لما يكون هذه المسافة بينها أصغر من Gamma
+
+629
+01:01:30,290 --> 01:01:33,610
+يعطينا المسافة أصغر من إبسلون يعني المسافة هذه
+
+630
+01:01:33,610 --> 01:01:40,760
+أصغر من إبسلون أو بمعنى آخر limitH of Y لما الـ Y
+
+631
+01:01:40,760 --> 01:01:50,320
+تروح للـ D بساوة F prime of مين؟ of C تصيرنا
+
+632
+01:01:50,320 --> 01:01:55,660
+جريبين من اللي بدنايا عند الـ H of Y limitها بساوة
+
+633
+01:01:55,660 --> 01:02:02,980
+limit هذا بساوة F prime of C هذا عبارة عن مين؟ عن
+
+634
+01:02:02,980 --> 01:02:10,910
+G prime مقلوق G primeإذا الآن خلصنا تقريبا نمسح
+
+635
+01:02:10,910 --> 01:02:16,130
+حده و نمسك
+
+636
+01:02:16,130 --> 01:02:28,150
+بهدي مع هدي صار عندي limit h of y لما ال y تقول
+
+637
+01:02:28,150 --> 01:02:34,960
+الى d limitH of Y لما Y تقول إلى D طلع عندي عبارة
+
+638
+01:02:34,960 --> 01:02:40,960
+عن F prime of C هي تحت من جهة أخرى هذا بيساوي مين؟
+
+639
+01:02:40,960 --> 01:02:48,720
+limit Y نقص D على G of Y نقص G of D لما Y تروح
+
+640
+01:02:48,720 --> 01:02:55,980
+لمين؟ للـ D صح؟ هذا عبارة عن limit أو واحد على
+
+641
+01:02:55,980 --> 01:03:03,130
+limitG of Y نقص G of D على Y minus D لما Y تروح لـ
+
+642
+01:03:03,130 --> 01:03:10,310
+D1 على الـ limit هذا فهي
+
+643
+01:03:10,310 --> 01:03:16,390
+ساوية 1 على g prime of D إذا صارت عندي F prime of
+
+644
+01:03:16,390 --> 01:03:23,710
+C بساوية 1 على g prime of D أو بمعنى آخر F prime
+
+645
+01:03:23,710 --> 01:03:31,800
+of C بساوية 1 على F G prime اللي هي Finverse prime
+
+646
+01:03:31,800 --> 01:03:42,000
+of D أو بتعبير آخر F inverse prime of D بساوية
+
+647
+01:03:42,000 --> 01:03:55,700
+واحد على F of C وهو المطلوب طيب
+
+648
+01:04:01,020 --> 01:04:02,360
+خدّيني أجف عن نقطة
+
+649
+01:04:19,990 --> 01:04:25,110
+هي نفس اللي فوق بس كانت اللي فوق عنده نقطة هنا in
+
+650
+01:04:25,110 --> 01:04:29,510
+general الان لو كانت على كل ال domain يعني الان
+
+651
+01:04:29,510 --> 01:04:33,150
+بقولي لو كانت I subset من R بيه an interval and F
+
+652
+01:04:33,150 --> 01:04:37,510
+من I لعند R strictly monotone on I ماشي ..
+
+653
+01:04:37,510 --> 01:04:42,750
+strictly monotone و let J بيسوء F of I and let G
+
+654
+01:04:42,750 --> 01:04:47,410
+من I لعند R بيه the function inverse of F ماشي ..
+
+655
+01:04:47,980 --> 01:04:52,360
+لأن إذا كانت F as differential على الـ I كلها إذا
+
+656
+01:04:52,360 --> 01:04:55,860
+أكيد هتكون continuous على الـ I كلها مدام هتكون
+
+657
+01:04:55,860 --> 01:04:58,300
+continuous على الـ I كلها و strictly monotone
+
+658
+01:04:58,300 --> 01:05:02,180
+هتكون الـ G العجبالها برضه strictly monotone و
+
+659
+01:05:02,180 --> 01:05:06,870
+continuous إذا شروط اللي فوق اتحققتإذا الـ J ..
+
+660
+01:05:06,870 --> 01:05:10,030
+طبعا ال F' of X معطينيها إشمالها تسوى X على كل ال
+
+661
+01:05:10,030 --> 01:05:13,350
+I إذا أكيد حسب النظر اللي قبل شوية G is
+
+662
+01:05:13,350 --> 01:05:17,230
+differentiable على كل ال J و ال G' بساوية واحدة
+
+663
+01:05:17,230 --> 01:05:22,210
+على F' لإنه composite مين؟ composite G واضح؟ يعني
+
+664
+01:05:22,210 --> 01:05:28,130
+.. كمان مرة؟ إذا كانت ال F strictly monotone و
+
+665
+01:05:28,130 --> 01:05:32,890
+كانت اللي هي ال J بتساوي كل ال F of Iوكانت الـ G
+
+666
+01:05:32,890 --> 01:05:37,310
+هي عبارة عن ال inverse للـ F وكانت ال F
+
+667
+01:05:37,310 --> 01:05:39,570
+differentiable على ال I مدام F differentiable على
+
+668
+01:05:39,570 --> 01:05:42,210
+ال I إذا صارت continuous على كل ال I مدام
+
+669
+01:05:42,210 --> 01:05:44,710
+continuous على ال I و strictly monotone هتكون ال
+
+670
+01:05:44,710 --> 01:05:47,710
+inverse سبعتها اللي هي ال G برضه continuous و
+
+671
+01:05:47,710 --> 01:05:51,700
+strictly monotoneإذا انتحققت شروط النظرية السابقة
+
+672
+01:05:51,700 --> 01:05:55,680
+إذا هتكون ال F و طبعا ال F' طبعا لها تساوي صفر ع
+
+673
+01:05:55,680 --> 01:05:59,020
+كل ال I إذا صارت ال G ال differential بالع كل ال J
+
+674
+01:05:59,020 --> 01:06:02,220
+و العلاقة بين التنتين G' بسوء واحد على F'
+
+675
+01:06:02,680 --> 01:06:09,040
+composite mean composite J أو زي ما بنقول G' of Y
+
+676
+01:06:09,040 --> 01:06:16,220
+بسوء واحد على F' of mean of X تحت العلاقة X بتساوي
+
+677
+01:06:16,220 --> 01:06:25,320
+F of Yأو Y بس هوقف و فكس Y بس هوقف و فكس طبعا هذا
+
+678
+01:06:25,320 --> 01:06:32,220
+البرهان كله حكيناه ال remark اللي عندنا ال remark
+
+679
+01:06:32,220 --> 01:06:37,100
+اللي عندنا ال
+
+680
+01:06:37,100 --> 01:06:43,460
+remark
+
+681
+01:06:43,460 --> 01:06:51,180
+اللي عندنا هي اللي حكيتها الآنD'Y بسوء واحد عالميا
+
+682
+01:06:51,180 --> 01:06:53,660
+على F'X
+
+683
+01:06:57,210 --> 01:06:59,530
+التي قبل بشوية حكيناها جي برايم أو اي بيسوا واحد
+
+684
+01:06:59,530 --> 01:07:03,890
+على اف برايم كومبز الجي ماشي الحال الآن صارت عندي
+
+685
+01:07:03,890 --> 01:07:08,950
+هذه جي برايم كومبز كومبز اف of X بيسوا جي برايم اف
+
+686
+01:07:08,950 --> 01:07:12,290
+of X بيسوا واحد على اف برايم كومبز الجي أو اي
+
+687
+01:07:12,290 --> 01:07:15,470
+بياخد نظرية مرتين و يسوا واحد على اف برايم of X
+
+688
+01:07:15,470 --> 01:07:18,370
+التانيين مع بعض جي برايم بيسوا واحد على اف برايم
+
+689
+01:07:18,370 --> 01:07:24,310
+of X و المرة الجاهزة اللي بنكمل بنعيد هذا اللي إذا
+
+690
+01:07:24,310 --> 01:07:26,470
+كان حكيناها على السريع
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0cc13ed05c1eab9ef7914952d87e2c3a4d08162
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2076, "start": 4.82, "end": 20.76, "text": "بسم الله الرحمن الرحيم المحاضرة الثانية في مساق تحليل رياضي 2 أو تحليل حقيقي 2 اتحدثنا المرة الماضية عن", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 6024, 104, 7649, 10632, 8978, 47524, 995, 4587, 6055, 5016, 20292, 1211, 12602, 1829, 46958, 1829, 568, 34051, 6055, 5016, 20292, 1211, 11331, 38436, 4587, 1829, 568, 1975, 2655, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632, 18871], "avg_logprob": -0.08165565262047145, "compression_ratio": 1.6460176991150441, "no_speech_prob": 6.157159805297852e-05, "words": [{"start": 4.82, "end": 5.16, "word": "بسم", "probability": 0.88330078125}, {"start": 5.16, "end": 5.32, "word": " الله", "probability": 0.95361328125}, {"start": 5.32, "end": 5.66, "word": " الرحمن", "probability": 0.9597981770833334}, {"start": 5.66, "end": 6.22, "word": " الرحيم", "probability": 0.994140625}, {"start": 6.22, "end": 8.02, "word": " 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"end": 19.66, "word": " الماضية", "probability": 0.99462890625}, {"start": 19.66, "end": 20.76, "word": " عن", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 2, "seek": 4240, "start": 21.4, "end": 42.4, "text": "الـ differentiation بدأنا بشرتر ستة بدأنا في ال section الأول ستة واحد اللي هو ال derivative او اللي هو الاشتقاق او المشتق الأولى وعرفنا شو معناه اللي هو الاشتقاق عرفنا شو معناه ان الدولة تكون differentiable عند نقطة اللي هي", "tokens": [6027, 39184, 38902, 47525, 10721, 8315, 4724, 8592, 43500, 2288, 8608, 2655, 3660, 47525, 10721, 8315, 8978, 2423, 3541, 16247, 12610, 8608, 2655, 3660, 36764, 24401, 13672, 1829, 31439, 2423, 13760, 1975, 2407, 13672, 1829, 31439, 2423, 33599, 2655, 4587, 995, 4587, 1975, 2407, 9673, 8592, 2655, 4587, 16247, 12610, 7578, 4032, 3615, 28480, 8315, 13412, 2407, 20449, 8315, 3224, 13672, 1829, 31439, 2423, 33599, 2655, 4587, 995, 4587, 6225, 28480, 8315, 13412, 2407, 20449, 8315, 3224, 16472, 32748, 12610, 3660, 6055, 30544, 819, 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"end": 40.04, "word": " differentiable", "probability": 0.811279296875}, {"start": 40.04, "end": 40.78, "word": " عند", "probability": 0.97412109375}, {"start": 40.78, "end": 41.66, "word": " نقطة", "probability": 0.9490559895833334}, {"start": 41.66, "end": 41.92, "word": " اللي", "probability": 0.8427734375}, {"start": 41.92, "end": 42.4, "word": " هي", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 3, "seek": 6341, "start": 44.57, "end": 63.41, "text": "في interval I حيث أخدنا F عبارة عن الـ function من I ل R وقلنا C element in I بتكون الدالة عندها قابلة للاشتقاق يعني F prime of C exist if the following limit exist اللي هو limit", "tokens": [41185, 15035, 286, 11331, 1829, 12984, 5551, 9778, 3215, 8315, 479, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 2445, 9154, 286, 5296, 497, 4032, 4587, 1211, 8315, 383, 4478, 294, 286, 39894, 30544, 32748, 6027, 3660, 43242, 11296, 12174, 16758, 37977, 24976, 33599, 2655, 4587, 995, 4587, 37495, 22653, 479, 5835, 295, 383, 2514, 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{"start": 70.05, "end": 70.45, "word": " x", "probability": 0.974609375}, {"start": 70.45, "end": 70.77, "word": " goes", "probability": 0.90673828125}, {"start": 70.77, "end": 71.01, "word": " to", "probability": 0.97900390625}, {"start": 71.01, "end": 71.45, "word": " c", "probability": 0.91650390625}, {"start": 71.45, "end": 72.75, "word": " exist", "probability": 0.58837890625}, {"start": 72.75, "end": 73.53, "word": " إذا", "probability": 0.890380859375}, {"start": 73.53, "end": 73.91, "word": " كانت", "probability": 0.97216796875}, {"start": 73.91, "end": 74.11, "word": " هذه", "probability": 0.720703125}, {"start": 74.11, "end": 74.23, "word": " الـ", "probability": 0.3470458984375}, {"start": 74.23, "end": 74.45, "word": " limit", "probability": 0.9091796875}, {"start": 74.45, "end": 75.11, "word": " exist", "probability": 0.8017578125}, {"start": 75.11, "end": 76.57, "word": " بنقول", "probability": 0.6844482421875}, {"start": 76.57, "end": 76.95, "word": " عن", "probability": 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و", "probability": 0.69873046875}, {"start": 83.63, "end": 84.21, "word": " بعد", "probability": 0.953125}, {"start": 84.21, "end": 84.91, "word": " ذلك", "probability": 0.9873046875}, {"start": 84.91, "end": 85.91, "word": " مرّينا", "probability": 0.78330078125}, {"start": 85.91, "end": 86.31, "word": " على", "probability": 0.9169921875}, {"start": 86.31, "end": 86.65, "word": " اللي", "probability": 0.92724609375}, {"start": 86.65, "end": 87.11, "word": " هو", "probability": 0.994140625}, {"start": 87.11, "end": 88.73, "word": " بعض", "probability": 0.93017578125}, {"start": 88.73, "end": 89.55, "word": " الخواص", "probability": 0.8126627604166666}], "temperature": 1.0}, {"id": 5, "seek": 10838, "start": 90.36, "end": 108.38, "text": "وقلنا الخاصية الأولى عندنا اللى هى انه لو كانت الدالة اللى هى differentiable at C بتكون continuous برضه وين عند C يعني اي differentiable function must be continuous", "tokens": [2407, 4587, 1211, 8315, 33962, 33546, 10632, 16247, 12610, 7578, 43242, 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{"start": 215.46, "end": 215.86, "word": " سفر", "probability": 0.8058268229166666}, {"start": 215.86, "end": 216.72, "word": " وأيضا", "probability": 0.80523681640625}, {"start": 216.72, "end": 217.12, "word": " الالف", "probability": 0.6422119140625}, {"start": 217.12, "end": 217.28, "word": " في", "probability": 0.84765625}, {"start": 217.28, "end": 217.42, "word": " ال", "probability": 0.8623046875}, {"start": 217.42, "end": 217.6, "word": " F", "probability": 0.56640625}], "temperature": 1.0}, {"id": 11, "seek": 23495, "start": 218.93, "end": 234.95, "text": "A constant برضه ألف في أف قابلة للاشتقاء وأثبتنا هذا الكلام وبرهنناه ووصلنا لعند اللي هو التعميم قلنا لو كانت F", "tokens": [32, 5754, 4724, 43042, 3224, 5551, 46538, 8978, 5551, 5172, 12174, 16758, 37977, 24976, 33599, 2655, 4587, 16606, 36725, 12984, 3555, 2655, 8315, 23758, 2423, 28820, 10943, 4032, 26890, 3224, 1863, 8315, 3224, 4032, 2407, 36520, 8315, 5296, 3615, 41260, 13672, 1829, 31439, 16712, 25957, 32640, 12174, 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كلهم دوال قابلة للاشتقاق حيكون حاصل جمحا قابل للاشتقاق وحاصل ضربا أيضا قابل للاشتقاق وفق القوانين اللي ذكرناها سابقا", "tokens": [37, 16, 4032, 37, 17, 4032, 37, 18, 43242, 479, 16, 28242, 16095, 11778, 2407, 6027, 12174, 16758, 37977, 24976, 33599, 2655, 4587, 995, 4587, 11331, 1829, 30544, 11331, 33546, 1211, 10874, 2304, 5016, 995, 12174, 16758, 1211, 24976, 33599, 2655, 4587, 995, 4587, 4032, 5016, 33546, 1211, 48812, 25513, 995, 36632, 11242, 995, 12174, 16758, 1211, 24976, 33599, 2655, 4587, 995, 4587, 4032, 5172, 4587, 25062, 2407, 7649, 9957, 13672, 1829, 29910, 37983, 8315, 11296, 8608, 16758, 4587, 995], "avg_logprob": -0.15007716638070565, "compression_ratio": 1.7050359712230216, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 236.05, "end": 236.57, "word": "F1", "probability": 0.534576416015625}, {"start": 236.57, "end": 237.31, "word": " وF2", "probability": 0.8128255208333334}, {"start": 237.31, "end": 237.95, "word": " وF3", "probability": 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بدنا نثبت انه اللي هو الـ G", "tokens": [6027, 5016, 9957, 2423, 39184, 8177, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 3224, 13672, 1829, 31439, 2423, 39184, 460], "avg_logprob": -0.3428199461528233, "compression_ratio": 1.0923076923076922, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 620.86, "end": 621.24, "word": "الحين", "probability": 0.520263671875}, {"start": 621.24, "end": 621.34, "word": " الـ", "probability": 0.731201171875}, {"start": 621.34, "end": 621.7, "word": " proof", "probability": 0.58203125}, {"start": 621.7, "end": 626.68, "word": " بدنا", "probability": 0.6195068359375}, {"start": 626.68, "end": 627.28, "word": " نثبت", "probability": 0.995361328125}, {"start": 627.28, "end": 628.38, "word": " انه", "probability": 0.6240234375}, {"start": 628.38, "end": 628.6, "word": " اللي", "probability": 0.8896484375}, {"start": 628.6, "end": 628.92, "word": " هو", "probability": 0.98876953125}, {"start": 628.92, "end": 630.04, "word": " الـ", 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{"start": 2047.9, "end": 2048.4, "word": " not", "probability": 0.9677734375}, {"start": 2048.4, "end": 2049.38, "word": " exist", "probability": 0.978515625}, {"start": 2049.38, "end": 2050.78, "word": " بده", "probability": 0.48779296875}, {"start": 2050.78, "end": 2051.18, "word": " اوضح", "probability": 0.9599609375}, {"start": 2051.18, "end": 2051.52, "word": " ليش", "probability": 0.965576171875}, {"start": 2051.52, "end": 2051.88, "word": " هذا", "probability": 0.93603515625}, {"start": 2051.88, "end": 2052.22, "word": " does", "probability": 0.82421875}, {"start": 2052.22, "end": 2052.46, "word": " not", "probability": 0.96630859375}, {"start": 2052.46, "end": 2052.96, "word": " exist", "probability": 0.9755859375}, {"start": 2052.96, "end": 2053.84, "word": " اخدتوا", "probability": 0.7966796875}, {"start": 2053.84, "end": 2054.78, "word": " انتوا", "probability": 0.8927408854166666}, {"start": 2054.78, "end": 2055.8, "word": " اخدتوا", "probability": 0.924609375}, {"start": 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11933, 15730, 36632, 8310, 1783, 45, 39894, 32887, 5016, 24976, 316, 5296, 31377, 2304, 37495, 9566, 1829, 4117, 13672, 1829, 31439, 479, 295, 1783, 45, 4724, 43042, 3224, 7251, 32887, 5016, 32767, 9957, 24976, 441, 12399, 4724, 9381, 3555, 2407, 9566, 22807, 29538, 9122, 9000, 259, 21757, 13672, 1829, 39894, 5016, 4117, 1829, 18871, 11296], "avg_logprob": -0.239149305348595, "compression_ratio": 1.3950617283950617, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 2061.8, "end": 2062.12, "word": "F", "probability": 0.4208984375}, {"start": 2062.12, "end": 2062.32, "word": " of", "probability": 0.32470703125}, {"start": 2062.32, "end": 2062.78, "word": " X", "probability": 0.94482421875}, {"start": 2062.78, "end": 2063.82, "word": " لما", "probability": 0.7318115234375}, {"start": 2063.82, "end": 2064.12, "word": " X", "probability": 0.966796875}, {"start": 2064.12, "end": 2064.68, "word": " بتروح", "probability": 0.8080240885416666}, {"start": 2064.68, "end": 2064.88, "word": " ل", "probability": 0.890625}, {"start": 2064.88, "end": 2065.24, "word": " A", "probability": 0.40185546875}, {"start": 2065.24, "end": 2066.46, "word": " بساوي", "probability": 0.8031005859375}, {"start": 2066.46, "end": 2066.8, "word": " L", "probability": 0.9560546875}, {"start": 2066.8, "end": 2067.86, "word": " إذا", "probability": 0.65869140625}, {"start": 2067.86, "end": 2068.24, "word": " أي", "probability": 0.7529296875}, {"start": 2068.24, "end": 2069.22, "word": " sequence", "probability": 0.654296875}, {"start": 2069.22, "end": 2070.34, "word": " XN", "probability": 0.6201171875}, {"start": 2070.34, "end": 2070.9, "word": " بتروح", "probability": 0.97021484375}, {"start": 2070.9, "end": 2071.12, "word": " لل", "probability": 0.71728515625}, {"start": 2071.12, "end": 2071.5, "word": " A", "probability": 0.8154296875}, {"start": 2071.5, "end": 2072.54, "word": " لازم", "probability": 0.9860026041666666}, {"start": 2072.54, "end": 2073.12, "word": " يعطيك", "probability": 0.984130859375}, {"start": 2073.12, "end": 2073.24, "word": " اللي", "probability": 0.869140625}, {"start": 2073.24, "end": 2073.4, "word": " هو", "probability": 0.98095703125}, {"start": 2073.4, "end": 2073.68, "word": " F", "probability": 0.94189453125}, {"start": 2073.68, "end": 2073.88, "word": " of", "probability": 0.8525390625}, {"start": 2073.88, "end": 2074.56, "word": " XN", "probability": 0.91015625}, {"start": 2074.56, "end": 2075.26, "word": " برضه", "probability": 0.9773763020833334}, {"start": 2075.26, "end": 2075.56, "word": " يروح", "probability": 0.9933268229166666}, {"start": 2075.56, "end": 2076.24, "word": " لمين", "probability": 0.83935546875}, {"start": 2076.24, "end": 2076.8, "word": " لل", "probability": 0.4580078125}, {"start": 2076.8, "end": 2077.76, "word": " L،", "probability": 0.578857421875}, {"start": 2077.76, "end": 2078.78, "word": " بصبوط؟", "probability": 0.708984375}, {"start": 2078.78, "end": 2078.96, "word": " هذه", "probability": 0.266845703125}, {"start": 2078.96, "end": 2079.66, "word": " كcontinuity", "probability": 0.6693115234375}, {"start": 2079.66, "end": 2079.78, "word": " اللي", "probability": 0.91015625}, {"start": 2079.78, "end": 2080.04, "word": " بتحكي", "probability": 0.949462890625}, {"start": 2080.04, "end": 2080.26, "word": " عنها", "probability": 0.994384765625}], "temperature": 1.0}, {"id": 88, "seek": 209583, "start": 2080.89, "end": 2095.83, "text": "اللي كده كانت limit F of X لما X تروح للـ A بساوي L و IG تأخدت أي sequence XN بتروح للـ A هيطلع limit F of XN مش بيروح بساوي لL ماشي هذه اللي هي النظرية", "tokens": [6027, 20292, 9122, 3215, 3224, 25961, 2655, 4948, 479, 295, 1783, 5296, 15042, 1783, 6055, 32887, 5016, 24976, 39184, 316, 4724, 3794, 995, 45865, 441, 4032, 26367, 6055, 10721, 9778, 3215, 2655, 36632, 8310, 1783, 45, 39894, 32887, 5016, 24976, 39184, 316, 39896, 9566, 1211, 3615, 4948, 479, 295, 1783, 45, 37893, 4724, 13546, 2407, 5016, 4724, 3794, 995, 45865, 5296, 43, 3714, 33599, 1829, 29538, 13672, 1829, 39896, 28239, 19913, 2288, 10632], "avg_logprob": -0.41554054295694504, "compression_ratio": 1.4409937888198758, "no_speech_prob": 1.2874603271484375e-05, "words": [{"start": 2080.89, "end": 2081.23, "word": "اللي", "probability": 0.24969482421875}, {"start": 2081.23, "end": 2081.49, "word": " كده", "probability": 0.6397298177083334}, {"start": 2081.49, "end": 2081.87, "word": " كانت", "probability": 0.945556640625}, {"start": 2081.87, "end": 2082.13, "word": " limit", "probability": 0.82080078125}, {"start": 2082.13, "end": 2082.37, "word": " F", "probability": 0.1705322265625}, {"start": 2082.37, "end": 2082.55, "word": " of", "probability": 0.57177734375}, {"start": 2082.55, "end": 2082.81, "word": " X", "probability": 0.951171875}, {"start": 2082.81, "end": 2083.11, "word": " لما", "probability": 0.72314453125}, {"start": 2083.11, "end": 2083.29, "word": " X", "probability": 0.94091796875}, {"start": 2083.29, "end": 2083.53, "word": " تروح", "probability": 0.9065755208333334}, {"start": 2083.53, "end": 2083.73, "word": " للـ", "probability": 0.3826904296875}, {"start": 2083.73, "end": 2083.77, "word": " A", "probability": 0.458251953125}, {"start": 2083.77, "end": 2084.21, "word": " بساوي", "probability": 0.6617431640625}, {"start": 2084.21, "end": 2084.55, "word": " L", "probability": 0.89208984375}, {"start": 2084.55, "end": 2085.83, "word": " و", "probability": 0.12066650390625}, {"start": 2085.83, "end": 2086.89, "word": " IG", "probability": 0.455322265625}, {"start": 2086.89, "end": 2087.37, "word": " تأخدت", "probability": 0.69072265625}, {"start": 2087.37, "end": 2087.53, "word": " أي", "probability": 0.8681640625}, {"start": 2087.53, "end": 2088.03, "word": " sequence", "probability": 0.52685546875}, {"start": 2088.03, "end": 2088.35, "word": " XN", "probability": 0.515869140625}, {"start": 2088.35, "end": 2088.65, "word": " بتروح", "probability": 0.93798828125}, {"start": 2088.65, "end": 2088.93, "word": " للـ", "probability": 0.701171875}, {"start": 2088.93, "end": 2089.07, "word": " A", "probability": 0.85693359375}, {"start": 2089.07, "end": 2089.75, "word": " هيطلع", "probability": 0.780029296875}, {"start": 2089.75, "end": 2090.01, "word": " limit", "probability": 0.88916015625}, {"start": 2090.01, "end": 2090.21, "word": " F", "probability": 0.9013671875}, {"start": 2090.21, "end": 2090.37, "word": " of", "probability": 0.9169921875}, {"start": 2090.37, "end": 2090.73, "word": " XN", "probability": 0.89599609375}, {"start": 2090.73, "end": 2090.87, "word": " مش", "probability": 0.10577392578125}, {"start": 2090.87, "end": 2091.43, "word": " بيروح", "probability": 0.868896484375}, {"start": 2091.43, "end": 2092.23, "word": " بساوي", "probability": 0.916748046875}, {"start": 2092.23, "end": 2092.59, "word": " لL", "probability": 0.4432373046875}, {"start": 2092.59, "end": 2094.13, "word": " ماشي", "probability": 0.7257486979166666}, {"start": 2094.13, "end": 2094.67, "word": " هذه", "probability": 0.53271484375}, {"start": 2094.67, "end": 2094.81, "word": " اللي", "probability": 0.9736328125}, {"start": 2094.81, "end": 2095.05, "word": " هي", "probability": 0.8828125}, {"start": 2095.05, "end": 2095.83, "word": " النظرية", "probability": 0.962646484375}], "temperature": 1.0}, {"id": 89, "seek": 212296, "start": 2097.22, "end": 2122.96, "text": "بناء على هذه النظرية كنا نقول انه لو وجيت two sequences على الأقل ايكون بروح للـA لكن بروح لـLimits مختلفات او واحدة من Limits does not exist بكفالك ان الـLimit هذه اشمالها does not exist واضح؟ الان اذا بدي اعتمد على هذه", "tokens": [3555, 1863, 16606, 15844, 29538, 28239, 19913, 2288, 10632, 9122, 8315, 8717, 39648, 16472, 3224, 45164, 49610, 36081, 732, 22978, 15844, 16247, 4587, 1211, 1975, 1829, 30544, 4724, 32887, 5016, 24976, 39184, 32, 44381, 4724, 32887, 5016, 5296, 39184, 43, 332, 1208, 3714, 46456, 46538, 9307, 1975, 2407, 36764, 24401, 3660, 9154, 16406, 1208, 775, 406, 2514, 4724, 4117, 5172, 6027, 4117, 16472, 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2101.96, "word": " وجيت", "probability": 0.408935546875}, {"start": 2101.96, "end": 2102.96, "word": " two", "probability": 0.6396484375}, {"start": 2102.96, "end": 2104.18, "word": " sequences", "probability": 0.86669921875}, {"start": 2104.18, "end": 2104.8, "word": " على", "probability": 0.5859375}, {"start": 2104.8, "end": 2105.4, "word": " الأقل", "probability": 0.9558919270833334}, {"start": 2105.4, "end": 2106.0, "word": " ايكون", "probability": 0.66943359375}, {"start": 2106.0, "end": 2106.52, "word": " بروح", "probability": 0.9000651041666666}, {"start": 2106.52, "end": 2107.18, "word": " للـA", "probability": 0.377685546875}, {"start": 2107.18, "end": 2108.14, "word": " لكن", "probability": 0.76318359375}, {"start": 2108.14, "end": 2108.78, "word": " بروح", "probability": 0.9933268229166666}, {"start": 2108.78, "end": 2109.64, "word": " لـLimits", "probability": 0.585595703125}, {"start": 2109.64, "end": 2111.0, "word": " مختلفات", "probability": 0.837890625}, {"start": 2111.0, "end": 2112.0, "word": " او", "probability": 0.7081298828125}, {"start": 2112.0, "end": 2112.4, "word": " واحدة", "probability": 0.9772135416666666}, {"start": 2112.4, "end": 2112.58, "word": " من", "probability": 0.9912109375}, {"start": 2112.58, "end": 2113.06, "word": " Limits", "probability": 0.612548828125}, {"start": 2113.06, "end": 2113.5, "word": " does", "probability": 0.1541748046875}, {"start": 2113.5, "end": 2113.84, "word": " not", "probability": 0.96484375}, {"start": 2113.84, "end": 2114.4, "word": " exist", "probability": 0.96240234375}, {"start": 2114.4, "end": 2115.76, "word": " بكفالك", "probability": 0.744921875}, {"start": 2115.76, "end": 2116.0, "word": " ان", "probability": 0.8779296875}, {"start": 2116.0, "end": 2116.44, "word": " الـLimit", "probability": 0.6369140625}, {"start": 2116.44, "end": 2116.66, "word": " هذه", "probability": 0.392822265625}, {"start": 2116.66, "end": 2117.4, "word": " اشمالها", "probability": 0.8484375}, {"start": 2117.4, "end": 2118.08, "word": " does", "probability": 0.73583984375}, {"start": 2118.08, "end": 2118.6, "word": " not", "probability": 0.9638671875}, {"start": 2118.6, "end": 2119.42, "word": " exist", "probability": 0.9697265625}, {"start": 2119.42, "end": 2120.68, "word": " واضح؟", "probability": 0.7655029296875}, {"start": 2120.68, "end": 2121.16, "word": " الان", "probability": 0.657470703125}, {"start": 2121.16, "end": 2121.46, "word": " اذا", "probability": 0.827880859375}, {"start": 2121.46, "end": 2121.72, "word": " بدي", "probability": 0.5670166015625}, {"start": 2121.72, "end": 2122.16, "word": " اعتمد", "probability": 0.96630859375}, {"start": 2122.16, "end": 2122.4, "word": " على", "probability": 0.8388671875}, {"start": 2122.4, "end": 2122.96, "word": " هذه", "probability": 0.87890625}], "temperature": 1.0}, {"id": 90, "seek": 215296, "start": 2123.57, "end": 2152.97, "text": "في إثبات إنه limit cosine واحد على X does not exist أكيد كلكم جال take the sequences أو the two 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diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8a1bb5263051b78eaeaad5b71424d3854a4ace45
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY.srt
@@ -0,0 +1,1817 @@
+1
+00:00:05,030 --> 00:00:07,750
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,750 --> 00:00:10,710
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه 
+
+3
+00:00:10,710 --> 00:00:16,270
+أجمعين هذه هي المحاضرة رقم 26 مساق تحليل حقيقة 2
+
+4
+00:00:16,270 --> 00:00:20,290
+طلاب وطالبات الجامعة الإسلامية قسم رياضيات كلية
+
+5
+00:00:20,290 --> 00:00:24,650
+العلوم اليوم هنكمل حديثنا في شطر 9 ولكن في the section
+
+6
+00:00:24,650 --> 00:00:29,050
+الجديد the section هنبدأ فيه اللي هو tests for
+
+7
+00:00:29,050 --> 00:00:36,950
+absolute convergence اختبارات الـ Series التي تحتوي 
+
+8
+00:00:36,950 --> 00:00:40,490
+على الـ Positive Terms أو اللي هو بمفهوم الـ 
+
+9
+00:00:40,490 --> 00:00:46,010
+Absolute Convergence نأتي الآن للأولاني المشهور
+
+10
+00:00:46,010 --> 00:00:51,130
+9.21 بنسميه ال comparison test أو اللي هو اختبار
+
+11
+00:00:51,130 --> 00:00:55,490
+المقارن ال let x يعني اللي بيكون عندنا فيه the series وبنقارنها بـ Series أخرى بنعرفها عارفين
+
+12
+00:00:55,490 --> 00:00:58,910
+اللي هو converged ولا diverse وبناء عليه بنحكم على 
+
+13
+00:00:58,910 --> 00:01:02,930
+الـ Series اللي بيبقى إحنا بنقارنها اللي هي إن هي 
+
+14
+00:01:02,930 --> 00:01:07,250
+converged أو diverse Led X بيساوي XN وY بيساوي YN
+
+15
+00:01:07,250 --> 00:01:11,900
+بـ Real Sequences Suppose that for some natural 
+
+16
+00:01:11,900 --> 00:01:17,420
+numbers K اللي هو XN أكبر أو أصغر أو يساوي YN يعني 
+
+17
+00:01:17,420 --> 00:01:22,340
+بمعنى آخر أننا بنحكي عن Sequence of Positive Terms
+
+18
+00:01:22,340 --> 00:01:26,400
+ماشي إذا هذه اللي هي عبارة عن Test لـ Series مكونة
+
+19
+00:01:26,400 --> 00:01:32,160
+من الـ Terms تبعتها من Positive Terms for N أكبر و
+
+20
+00:01:32,160 --> 00:01:36,420
+ساوي و K then the convergence of summation yn
+
+21
+00:01:36,420 --> 00:01:40,320
+implies the convergence of xn and the divergence
+
+22
+00:01:40,320 --> 00:01:44,320
+of xn implies the divergence of summation yn اللي
+
+23
+00:01:44,320 --> 00:01:48,440
+أنا بقول ليه ال test بيقول بيحكي لي معايا ليه إن لو
+
+24
+00:01:48,440 --> 00:01:53,680
+كان في عندي two sequences xn و yn هم اللي بيكون
+
+25
+00:01:53,680 --> 00:01:56,820
+جسم اللي هو ال series باجي إذا كان عندي Xn أصغر
+
+26
+00:01:56,820 --> 00:02:01,920
+من أو يساوي Yn لكل n طبعا وإثنتين positive باجي بقول
+
+27
+00:02:01,920 --> 00:02:05,700
+إذا كان اللي هي الكبيرة اللي هي converts ال Yn
+
+28
+00:02:05,700 --> 00:02:10,800
+أكيد من باب أولى الصغيرة أشمالها converts يعني ال
+
+29
+00:02:10,800 --> 00:02:14,280
+convergence لل Yn بيعطي ال convergence لمن؟ لل Xn
+
+30
+00:02:14,280 --> 00:02:18,520
+إذا كانت الصغيرة diverges من باب أولاد كل كبيرة
+
+31
+00:02:19,050 --> 00:02:23,830
+إيش ما لها، diverges خلينا نبرهن الآن Suppose
+
+32
+00:02:27,750 --> 00:02:33,730
+that yn is convergent، ماشي الحال؟ suppose that 
+
+33
+00:02:33,730 --> 00:02:37,090
+summation yn converges نفترض للكبير أنها converges 
+
+34
+00:02:37,090 --> 00:02:41,050
+then for every ي أكبر من صفر there exists m of
+
+35
+00:02:41,050 --> 00:02:45,850
+epsilon element in n such that for every m أكبر من 
+
+36
+00:02:45,850 --> 00:02:50,330
+n وأكبر من م يبسلون اللي هو ال الكوشي criterion
+
+37
+00:02:50,330 --> 00:02:55,530
+اللي هو y واحد زي ym ناقص y واحد زي yn أصغر من مين
+
+38
+00:02:55,530 --> 00:03:02,870
+من إبسلون ماشي الحال الآن هذا الكلام اللي هو عندي 
+
+39
+00:03:02,870 --> 00:03:06,710
+صحيح لكل N أكبر ويساوي K يعني مش من بداية ال
+
+40
+00:03:06,710 --> 00:03:10,970
+sequence مش كتير مهم أنا عند بداية ال sequence إن
+
+41
+00:03:10,970 --> 00:03:12,950
+اللي بحكم على ال convergence وال divergence اللي 
+
+42
+00:03:12,950 --> 00:03:17,330
+هو mean اللي هو ال terms من عند حد إلى ما لا نهاية
+
+43
+00:03:17,330 --> 00:03:20,630
+اللي هو اللي هيأثر على المجموع إن اللي هو موجود
+
+44
+00:03:20,630 --> 00:03:26,630
+أو مش موجود طيب الآن هذه اللي هي صحيحة لكل N و M
+
+45
+00:03:26,630 --> 00:03:32,180
+أكبر من M اللي جبناها وعندي هذه صحيحة لكل n
+
+46
+00:03:32,180 --> 00:03:37,840
+أكبر أو يساوي K عشان أستخدم (1) وأستخدم (*) لازم 
+
+47
+00:03:37,840 --> 00:03:42,520
+أختار أقول from one and star we have for every
+
+48
+00:03:42,520 --> 00:03:46,480
+epsilon there exists N عشان أستخدم (1) و(*) بدي 
+
+49
+00:03:46,480 --> 00:03:50,500
+أخذ N هي ال maximum بين ال K وبين ال M of epsilon
+
+50
+00:03:50,500 --> 00:03:54,720
+such that لما تكون ال M أكبر من N وأكبر من ال K
+
+51
+00:03:54,720 --> 00:03:58,140
+الماكسيموم معناته أكبر من K وأكبر من هذه معناته 
+
+52
+00:03:58,140 --> 00:04:02,880
+هذه صحيحة وهذه صحيحة يعني بحق اللي الناس تخدمها 
+
+53
+00:04:02,880 --> 00:04:09,920
+we have X1 زائد X2 زائد XM اللي هي ال partial sum ل
+
+54
+00:04:09,920 --> 00:04:17,290
+X وهذه ناقص اللي هي X1 لعند XN اترحوا من بعض اللي 
+
+55
+00:04:17,290 --> 00:04:21,670
+هو حيساوي ال XM زائد 1 لعند ال XM ال XN زائد
+
+56
+00:04:21,670 --> 00:04:25,650
+1 أكيد اللي هو أصغر من أو يساوي YN زائد 1 ال XN
+
+57
+00:04:25,650 --> 00:04:28,150
+زائد 2 أصغر من YN زائد 2 لما أصل ال XM 
+
+58
+00:04:28,150 --> 00:04:33,770
+أصغر من أو يساوي ال YM الآن هذه عبارة عن مين؟ عن هذه
+
+59
+00:04:33,770 --> 00:04:38,470
+ناقص هذه اللي هي Y1 زي Ym ناقص Y1 زي Yn اللي هي 
+
+60
+00:04:38,470 --> 00:04:42,610
+أصغر من وين؟ من ي لإنه converges اللي هي ال Yn بناء
+
+61
+00:04:42,610 --> 00:04:49,190
+عليه اللي هو أثبتنا إن ال SM ناقص ال SN بالنسبة لل
+
+62
+00:04:49,190 --> 00:04:53,570
+X اللي هي satisfies كوشي criterion إن أنا أصغر من 
+
+63
+00:04:53,570 --> 00:04:58,510
+Y معناه تصميش لل XN إيش ما لها؟ converges العنوان
+
+64
+00:04:58,510 --> 00:05:03,110
+الثاني هو Contrapositive للعنوان الأول لماذا؟ لأن 
+
+65
+00:05:03,110 --> 00:05:09,870
+لو كانت ال summation Xn مختلفة وليس مرتبطة، فأكيد 
+
+66
+00:05:09,870 --> 00:05:14,390
+ستعطي ال summation Yn أشمالها التي ليست مرتبطة
+
+67
+00:05:14,650 --> 00:05:19,810
+يعني diverse يعني الجزء الثاني هذا ما هو إلا عبارة 
+
+68
+00:05:19,810 --> 00:05:23,650
+عن اللي هو الجزء الأول بس شماله موفود بال
+
+69
+00:05:23,650 --> 00:05:27,890
+contraposition يعني B implies Q يعني not Q implies
+
+70
+00:05:27,890 --> 00:05:32,730
+not B طيب الآن نيجي هذا اللي هو ال Comparison Test 
+
+71
+00:05:32,730 --> 00:05:38,070
+اللي هو المقارنة المباشرة بين ال terms تبعات مين
+
+72
+00:05:38,070 --> 00:05:41,890
+تبعات اللي هو ال sequences أحياناً عملياً هذه مش
+
+73
+00:05:41,890 --> 00:05:46,830
+كتير الناس بترغبها في test ثاني comparison test 
+
+74
+00:05:46,830 --> 00:05:50,530
+لكن هذا ال test اللي هو بنسميه limit comparison
+
+75
+00:05:50,530 --> 00:05:53,910
+test وهذا أسهل في الاستخدام وأوسع في الاستخدام
+
+76
+00:05:53,910 --> 00:05:59,310
+والناس بتميل عادة لاستخدامها ماشي الحال الآن اصبح 
+
+77
+00:05:59,310 --> 00:06:02,450
+both that X بيساوي XN وY بيساوي YN are
+
+78
+00:06:02,450 --> 00:06:07,570
+positive serial sequences if the relation limit XN
+
+79
+00:06:07,570 --> 00:06:12,730
+على YN لأن limit XN على YN لا يساوي صفر يعني عبارة
+
+80
+00:06:12,730 --> 00:06:17,400
+عن عدد هذا يعني عبارة عن عدد يعني سير ال XN وسير
+
+81
+00:06:17,400 --> 00:06:23,260
+ال YN قريب من بعض لما نقول بطلع عدد limit XN على
+
+82
+00:06:23,260 --> 00:06:29,000
+YN يعني سيرهم قريب من بعض لدرجة أنه في الآخر بطلع
+
+83
+00:06:29,000 --> 00:06:32,280
+عدد يعني لا هو طلع ما له نهاية نقول اللي فوق أسرع 
+
+84
+00:06:32,280 --> 00:06:37,180
+كتير ولا طلع صفر نقول اللي تحت أسرع كتير لأ اللي
+
+85
+00:06:37,180 --> 00:06:42,770
+هو limit XN على YN طلع لي عدد عشان هيك لما هذا يحدث 
+
+86
+00:06:42,770 --> 00:06:45,970
+if the relation limit xn على yn لا يساوي صفر hold
+
+87
+00:06:45,970 --> 00:06:51,570
+then ال summation xn is convergent if and only if
+
+88
+00:06:51,570 --> 00:06:56,650
+ال summation ال yn أشمالها is convergent لأن سيرهما
+
+89
+00:06:56,650 --> 00:07:01,770
+متقارب عشان هيك بنقول يا التنتين converges يا
+
+90
+00:07:01,770 --> 00:07:08,570
+التنتين diverse لكن if the limit in two هنا is
+
+91
+00:07:08,570 --> 00:07:13,540
+zero معناته اللي تحت star طار على ما لا نهاية يعني
+
+92
+00:07:13,540 --> 00:07:18,400
+صار كله على إيش بيساوي؟ صفر فبكون الآن ال YN إذا 
+
+93
+00:07:18,400 --> 00:07:22,840
+الكبير Convergent من باب أولى لصغير إيش ماله؟
+
+94
+00:07:22,840 --> 00:07:27,000
+Convergent لأنه هذا صار صفر معناته هذا أسرع من هذا
+
+95
+00:07:27,000 --> 00:07:32,340
+بكتير معناته لو كان اللي تحت Converged أكيد أكيد
+
+96
+00:07:32,340 --> 00:07:36,600
+أكيد سيكون اللي فوق أشماله convergence لأن اللي
+
+97
+00:07:36,600 --> 00:07:42,420
+فوق بيكون أبطأ أو أقل قيمة يعني نحو الصفر يعني
+
+98
+00:07:42,420 --> 00:07:46,040
+معناته إن اللي هو ال summation لل YN ال 
+
+99
+00:07:46,040 --> 00:07:49,120
+convergence له على طول بيعطي اللي هو ال
+
+100
+00:07:49,120 --> 00:07:52,980
+convergence لل XN هذه حول اللي هو نص النظرية نيجي 
+
+101
+00:07:52,980 --> 00:07:59,670
+الآن للبرهان نأتي لبرهان نثبت أنه نفترض إن ال
+
+102
+00:07:59,670 --> 00:08:02,810
+summation نثبت إن ال summation XN is convergent
+
+103
+00:08:02,810 --> 00:08:05,510
+فندهلي في ال summation YN اللي هو convergent الآن
+
+104
+00:08:05,510 --> 00:08:09,790
+بدنا نأتي للبرهان قلنا عندي limit ال XN على ال YN
+
+105
+00:08:09,790 --> 00:08:13,430
+إيش بيساوي؟ بيساوي L لا يساوي صفر إذاً حسب التعريف
+
+106
+00:08:13,430 --> 00:08:16,050
+الـ Epsilon Delta Definition أو الـ Epsilon K
+
+107
+00:08:16,050 --> 00:08:19,650
+Definition for Epsilon بيساوي L على 2 أخذت لأي 
+
+108
+00:08:19,650 --> 00:08:22,550
+Epsilon أخذت من ضمنها L على 2 للحسابات there
+
+109
+00:08:22,550 --> 00:08:27,210
+exists K such that اللي هو XN على YN ناقص L أصغر
+
+110
+00:08:27,210 --> 00:08:30,470
+من Epsilon اللي هي L على 2 لكل N أكبر أو يساوي K
+
+111
+00:08:30,470 --> 00:08:35,350
+خلينا نفرضها هذه بيصير عندي XN على YN أكبر من L
+
+112
+00:08:35,350 --> 00:08:40,280
+ناقص L على 2 وأصغر من L زائد L على 2 الآن صار 
+
+113
+00:08:40,280 --> 00:08:43,560
+عندي الآن اللي هي ال ... ال ... ال ... ال ... ال ... ال
+
+114
+00:08:43,560 --> 00:08:44,080
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+115
+00:08:44,080 --> 00:08:44,380
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+116
+00:08:44,380 --> 00:08:44,700
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+117
+00:08:44,700 --> 00:08:45,400
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+118
+00:08:45,400 --> 00:08:45,680
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+119
+00:08:45,680 --> 00:08:45,940
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+120
+00:08:45,940 --> 00:08:46,620
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+121
+00:08:46,620 --> 00:08:47,900
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+122
+00:08:47,900 --> 00:08:48,420
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+123
+00:08:48,420 --> 00:08:50,320
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+124
+00:08:50,320 --> 00:08:59,540
+ال ... ال ... ال ... ال ... ال ...
+
+125
+00:08:59,540 --> 00:09:01,420
+ال ... ال ...
+
+126
+00:09:06,850 --> 00:09:11,550
+بال test اللي قبل بشوية إذا ال summation yn مش هذا
+
+127
+00:09:11,550 --> 00:09:16,790
+اللي هنستخدمه هنستخدم اللي هو xn أكبر من yn في L
+
+128
+00:09:16,790 --> 00:09:19,750
+على 2 إذا كانت هذه convergent هتكون هذه إيش ما لها؟
+
+129
+00:09:19,750 --> 00:09:24,410
+convergent وبما أن yn في L على 2 convergent هتطلع 
+
+130
+00:09:24,410 --> 00:09:28,410
+عندي اللي هي ال summation yn إيش ما لها؟ is
+
+131
+00:09:28,410 --> 00:09:34,660
+convergent ماشي طيب الآن conversely بدي أفترض اللي 
+
+132
+00:09:34,660 --> 00:09:39,480
+هو ال summation ل Yn إيش ماله؟ is convergent ال 
+
+133
+00:09:39,480 --> 00:09:41,920
+summation ل Yn is convergent مدام ال summation ل
+
+134
+00:09:41,920 --> 00:09:46,680
+Yn is convergent هيكون ال summation اللي هي 
+
+135
+00:09:46,680 --> 00:09:50,500
+الثلاثة في L على 2 في Yn is convergent لأن هذا
+
+136
+00:09:50,500 --> 00:09:54,000
+عبارة عن ثابت هذا لما افترضنا ال yn is summation
+
+137
+00:09:54,000 --> 00:09:57,320
+ال yn convergent إذا هيكون ال summation الكبير 
+
+138
+00:09:57,320 --> 00:10:00,940
+هذا convergent من باب أولى ال summation لل xn
+
+139
+00:10:00,940 --> 00:10:06,200
+إيش ماله؟ is convergent يعني اتبعوا اللي حكيته هنا
+
+
+
+141
+00:10:06,200 --> 00:10:14,030
+هذه اللي هي الـconvergence للـ Xn اللي هي الكبيرة
+
+142
+00:10:14,030 --> 00:10:17,850
+بيعطي الـconvergence لهذه هو من ثم الـconvergence 
+
+143
+00:10:17,850 --> 00:10:22,710
+لهذه لأن في الجزء الثاني الـconvergence للـ Yn
+
+144
+00:10:22,710 --> 00:10:26,430
+بيعطي الـconvergence لهذه الـconvergence لهذه اللي
+
+145
+00:10:26,430 --> 00:10:31,930
+هو الكبير بيعطي الـconvergence لمن؟ للـ Xn طيب نيجي 
+
+146
+00:10:31,930 --> 00:10:35,910
+الآن طبعا
+
+147
+00:10:35,910 --> 00:10:42,080
+الـ .. الـ .. الـ .. المطلوب بي .. بدنا نفترض
+
+148
+00:10:44,730 --> 00:10:51,270
+suppose that limit xn على yn  بساوي صفر ونفترض أن 
+
+149
+00:10:51,270 --> 00:10:54,130
+الـ yn أشمالها is convergent بالذات بت الـ xn
+
+150
+00:10:54,130 --> 00:10:59,330
+أشمالها is convergent لأن شو معناه limit xn على yn 
+
+151
+00:10:59,330 --> 00:11:03,230
+بساوي صفر لكل y أكبر من صفر؟ there exists k 
+
+152
+00:11:03,230 --> 00:11:06,810
+element in n such that xn على yn أصغر من مين؟ من
+
+153
+00:11:06,810 --> 00:11:10,810
+إبسلون لكل n أكبر أو يساوي k هذا اللي هو تعريف الـ
+
+154
+00:11:10,810 --> 00:11:15,700
+limit للـ xn على yn بساوي صفر ومنه هذا دروب طرفين في
+
+155
+00:11:15,700 --> 00:11:20,680
+وسطين XN أصلا من YN في Y ن إحنا مفترضين أن الـ YN
+
+156
+00:11:20,680 --> 00:11:24,240
+is convergent يعني الـ Y في الـ YN ثابتة ما هي الـ Y
+
+157
+00:11:24,240 --> 00:11:27,620
+is convergent إذا كان الكبيرة convergent من باب
+
+158
+00:11:27,620 --> 00:11:32,680
+أولى الصماش للـ XN إيش هتكون اللي هي is convergent
+
+159
+00:11:32,680 --> 00:11:39,020
+by اللي هو comparison test الأصلي الآن إذا خلصنا من
+
+160
+00:11:39,020 --> 00:11:42,300
+الـtestين اللي هو الـ comparison test والـ limit
+
+161
+00:11:42,300 --> 00:11:45,880
+comparison test وكانت الـtestين عبارة عن على 
+
+162
+00:11:45,880 --> 00:11:50,520
+positive sequences الآن بدنا نحكي عن حاجة اسمها
+
+163
+00:11:50,520 --> 00:11:53,700
+the root and the ratio test نشوف الـ root و الـ
+
+164
+00:11:53,700 --> 00:11:57,260
+ratio test الـtest الأولان اللي هو الـ root test
+
+165
+00:11:57,260 --> 00:12:03,010
+ايه؟ fx بساوي xnis a sequence in A and R and there
+
+166
+00:12:03,010 --> 00:12:07,410
+exists a positive number R أصغر من واحد and a
+
+167
+00:12:07,410 --> 00:12:11,590
+natural number K such that يعني الخاصية هذه بدوا
+
+168
+00:12:11,590 --> 00:12:16,590
+إياها X N أس واحد على N أصغر أو يساوي R تتحقق لكل N
+
+169
+00:12:16,590 --> 00:12:20,550
+أكبر أو يساوي K من عند K وطالع مش مشكلة لأن أنا
+
+170
+00:12:20,550 --> 00:12:22,670
+اللي في الـ divergence و الـ convergence مين اللي
+
+171
+00:12:22,670 --> 00:12:26,990
+بتحكم اللي هو الـ terms اللي لما .. لإنها بتروح إلى
+
+172
+00:12:26,990 --> 00:12:29,890
+مالة نهاية يعني لو كان أول مليون term أو أول متين
+
+173
+00:12:29,890 --> 00:12:33,970
+مليون أو جد ما يكون في الأول اللي هو لا تحقق
+
+174
+00:12:33,970 --> 00:12:38,250
+الخاصية اللي بديها أنا بهم مني اللي فيما بعد يحقق
+
+175
+00:12:38,250 --> 00:12:40,550
+الخاصية اللي بديها اللي بدوا تحكم على الـ
+
+176
+00:12:40,550 --> 00:12:44,950
+convergence أو الـ divergence إذن الآن لو كان عندي
+
+177
+00:12:44,950 --> 00:12:49,520
+X أقص .. X أس واحد أنا الأصغر يستخدم Rلكل n أكبر
+
+178
+00:12:49,520 --> 00:12:51,020
+يساوي كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+179
+00:12:51,020 --> 00:12:53,220
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+180
+00:12:53,220 --> 00:13:03,200
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+181
+00:13:03,200 --> 00:13:05,720
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+182
+00:13:05,720 --> 00:13:15,340
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+183
+00:13:15,340 --> 00:13:22,200
+كتنفترض أنه تلاتة holes يعني نفترض أنه XN أس واحد
+
+184
+00:13:22,200 --> 00:13:26,500
+على N أصغر أو يساوي R لكل N أكبر أو يساوي K الآن
+
+185
+00:13:26,500 --> 00:13:29,760
+منها هيكون عند الـ absolute value XN أكبر أو يساوي
+
+186
+00:13:29,760 --> 00:13:35,680
+0 أصغر أو يساوي 100 RN لكل N أكبر أو يساوي K الآن
+
+187
+00:13:37,230 --> 00:13:42,990
+الـ summation للـ R أُس عن R نحن ناخدها أصغر من
+
+188
+00:13:42,990 --> 00:13:45,950
+واحد و positive طبعا أصغر من واحد معناته الـ
+
+189
+00:13:45,950 --> 00:13:50,250
+summation للـ R أن converge مظبوط؟ مدام الـ R أن
+
+190
+00:13:50,250 --> 00:13:55,310
+converge فالـ summation للـ XN is converge يعني
+
+191
+00:13:55,310 --> 00:13:58,150
+بمعنى آخر صارت الـ summation للـ XN is absolutely
+
+192
+00:13:58,150 --> 00:14:06,100
+convergent طيب suppose that أربعة holds اللي هي مين
+
+193
+00:14:06,100 --> 00:14:10,840
+أربعة هذا أكبر أو يساوي واحد لأن لكل N أكبر أو يساوي
+
+194
+00:14:10,840 --> 00:14:17,920
+K معناته اللي هو الـ XN اللي هي أس واحد على N لو 
+
+195
+00:14:17,920 --> 00:14:23,700
+جيت أخدته limitها limit اللي هي الـ XN هيكون عند الـ
+
+196
+00:14:23,700 --> 00:14:28,600
+absolute value للـ XN أكبر أو يساوي واحد يعني limit
+
+197
+00:14:28,600 --> 00:14:33,340
+الـ absolute value لـ Xn as n goes to infinity أكيد
+
+198
+00:14:33,340 --> 00:14:37,640
+أكبر أو يساوي واحد إذا exist يعني بتساوي صفر مدام
+
+199
+00:14:37,640 --> 00:14:41,920
+بتساوي صفر إذا نصممش للـ Xn بالـ test اللي هو
+
+200
+00:14:41,920 --> 00:14:46,780
+الأولان اللي أخدناه الآن مدام الـ summation xn الـ
+
+201
+00:14:46,780 --> 00:14:51,260
+absolute value xn does not converge to 0 إذا هتكون
+
+202
+00:14:51,260 --> 00:14:55,580
+الـ xn does not converge to 0 ومن ثم الـ summation
+
+203
+00:14:55,580 --> 00:15:00,560
+للـ xn أشمالها diverse حسب اللي هو اللي قلنا عنه الـ
+
+204
+00:15:00,560 --> 00:15:03,420
+divergence test اللي هو الـ summation للـ xn
+
+205
+00:15:03,420 --> 00:15:06,820
+converges بلاقاء الـ limit للـ xn بساوي 0 لكن عندي
+
+206
+00:15:06,820 --> 00:15:11,360
+طلعت limit للـ xn لا تساوي 0 طيب corollary لللي
+
+207
+00:15:11,360 --> 00:15:15,870
+فوقالأن الـ Corollary بتقول ما هي ليه؟ let X 
+
+208
+00:15:15,870 --> 00:15:20,230
+بساوي Xn بيبقى Sequence اند R and let R بساوي
+
+209
+00:15:20,230 --> 00:15:25,350
+Limit Xn أس واحدة لان هناك كانت اللي هي بتاخد الـ
+
+210
+00:15:25,350 --> 00:15:29,830
+and roots لمن؟ للـ terms و بتشوف اللي هنا إذا كان
+
+211
+00:15:29,830 --> 00:15:33,410
+الـ and roots للـ terms اللي هي أكبر أو يساوي R من
+
+212
+00:15:33,410 --> 00:15:43,630
+عند K و طالع الآن بتحكم ليه؟ الآن بتحكم ليه؟ الآن
+
+213
+00:15:43,630 --> 00:15:48,470
+بتحكم ليه؟ الآن بتحكم ليه؟ الآن بتحكم ليه؟ الآن
+
+214
+00:15:48,470 --> 00:15:48,530
+بتحكم ليه؟ الآن بتحكم ليه؟ الآن بتحكم ليه؟ الآن
+
+215
+00:15:48,530 --> 00:15:48,750
+بتحكم ليه؟ الآن بتحكم ليه؟ الآن بتحكم ليه؟ الآن
+
+216
+00:15:48,750 --> 00:15:49,210
+بتحكم ليه؟ الآن بتحكم ليه؟ الآن بتحكم ليه؟ الآن
+
+217
+00:15:49,210 --> 00:15:53,220
+بتحكم ليه؟ الآن بتحكم ليه؟ نفترض إن Xn بيكون
+
+218
+00:15:53,220 --> 00:15:57,500
+سيكوينس في R وR بساوي Limit Xn plus 1 لـ N نفترض
+
+219
+00:15:57,500 --> 00:16:02,840
+إن هذا الـ Limit موجود ثم الصممش للـ Xn هو
+
+220
+00:16:02,840 --> 00:16:10,360
+بالتأكيد مرتبط لما R أصغر من 1 وهو مرتبط عندما R
+
+221
+00:16:10,360 --> 00:16:13,140
+أكبر من 1 وهذا الـ test انتوا عارفينه يعني بمعنى
+
+222
+00:16:13,140 --> 00:16:18,040
+آخر باجي بقول باخد Limit Xn 
+
+223
+00:16:18,970 --> 00:16:23,270
+أس واحد لأن أس أن قصة infinity طلع عندي إيش
+
+224
+00:16:23,270 --> 00:16:28,550
+بساوي بساوي R احنا مفترضين ان الـ limit exist إذا
+
+225
+00:16:28,550 --> 00:16:34,550
+R أكبر من واحد خلاص الـ series xn divers إذا R أصغر
+
+226
+00:16:34,550 --> 00:16:39,030
+من واحد الـ series إيش مالها converge و absolutely
+
+227
+00:16:39,030 --> 00:16:44,370
+convergent لكن إذا كانت R بتساوي واحد بنقول الـ test
+
+228
+00:16:44,370 --> 00:16:47,650
+fail يعني ممكن يكون convergence وممكن تكون إيش ما
+
+229
+00:16:47,650 --> 00:16:53,650
+لها divergence وفيه أمثلة واضح؟ طيب الآن بدنا نيجي
+
+230
+00:16:53,650 --> 00:16:59,570
+للبرهان suppose that limit Xn أس واحد على N بساوي
+
+231
+00:16:59,570 --> 00:17:05,790
+R وR إيش ما لها أصغر من واحد نفترض إنه limit Xn أس
+
+232
+00:17:05,790 --> 00:17:07,670
+واحد على N بساوي R أصغر من واحد
+
+233
+00:17:10,860 --> 00:17:22,100
+طيب عندي لما اقول limit xn أس واحدة لان بساوي واحد
+
+234
+00:17:22,100 --> 00:17:29,260
+أو بساوي R اللي هي أصغر من واحد إيش معناته هذا هذا
+
+235
+00:17:29,260 --> 00:17:35,490
+معناته لكل ي أكبر من صفر There exist k element in N
+
+236
+00:17:35,490 --> 00:17:39,550
+such that for every N أكبر أو يساوي k اللي هو بيكون
+
+237
+00:17:39,550 --> 00:17:50,390
+عند X N أس واحدة ل N ناقص R ناقص R أصغر من مين؟ من
+
+238
+00:17:50,390 --> 00:17:58,340
+إبسلون أصغر من إبسلون خد الآن إبسلون إبسلون بتساوي
+
+239
+00:17:58,340 --> 00:18:02,780
+عند واحد ناقص R أكبر من صفر لغرض الحسابات بتاخد
+
+240
+00:18:02,780 --> 00:18:06,720
+إبسلون عبارة عن واحد ناقص R على اثنين واحد ناقص R
+
+241
+00:18:06,720 --> 00:18:09,640
+على اثنين أكيد أكبر من صفر إذا هتصير أصغر من واحد
+
+242
+00:18:09,640 --> 00:18:14,420
+ناقص R على اثنين على اثنين صار عندي الآن Xn أس واحد
+
+243
+00:18:14,420 --> 00:18:20,120
+على N أصغر من واحد ناقص R على اثنين زائد R وأكبر
+
+244
+00:18:20,120 --> 00:18:27,300
+من R ناقص .. اللي هو واحد ناقص R على مين؟ على اثنين
+
+245
+00:18:27,300 --> 00:18:32,080
+أنا بتهيب من المنطقة هذه ماشي الحال صار عندي اللي
+
+246
+00:18:32,080 --> 00:18:40,540
+هو الـ XL أس واحد على N أصغر من اللي هو واحد
+
+247
+00:18:42,070 --> 00:18:47,950
+1 الآن هذه اثنين R اللي هي واحد زائد R على مين؟ على
+
+248
+00:18:47,950 --> 00:18:52,210
+اثنين ماشي؟ لذا صارت الـ Xn أس واحد على N absolute
+
+249
+00:18:52,210 --> 00:18:57,790
+value أصغر من واحد زائد R على اثنين لكل N أكبر أو
+
+250
+00:18:57,790 --> 00:19:06,720
+يساوي مين؟ K لذا حصلت على هذه هذه سموليها R' R' أو
+
+251
+00:19:06,720 --> 00:19:20,880
+يسمونها R واحد هذي R واحد أكبر أو 
+
+252
+00:19:20,880 --> 00:19:30,580
+أكبر أكبر أكبر أكبر أكبر أكبر أكبر أكبر أكبر أكبر
+
+253
+00:19:30,580 --> 00:19:33,070
+أكبر أكبر أكبر أكبر أكبر R أصغر من واحد يعني عبارة
+
+254
+00:19:33,070 --> 00:19:38,010
+عن هدولة عبارة عن R يعني R واحد أصغر من مين؟ من R
+
+255
+00:19:38,010 --> 00:19:44,070
+في نفس الوقت هتكون أصغر من واحد اللي وصلتله أنا
+
+256
+00:19:44,070 --> 00:19:48,030
+suppose that اللي مش مشروح أنا شرحته هناك limit x
+
+257
+00:19:48,030 --> 00:19:51,070
+ناقص واحد على n بساوي R أصغر من واحد then there
+
+258
+00:19:51,070 --> 00:19:55,650
+exists R واحد such that R واحد أكبر من R وأصغر من
+
+259
+00:19:55,650 --> 00:20:02,090
+مين؟ من واحد R واحد أكبر من R وأكيد أصغر من واحد
+
+260
+00:20:02,090 --> 00:20:07,590
+زائد واحد على اثنين ويساوي واحد اللي هي and اللي هو
+
+261
+00:20:07,590 --> 00:20:11,270
+إيش هيكون عنده a natural number K اللي لجيته such
+
+262
+00:20:11,270 --> 00:20:15,210
+that XN plus 1 الآن أصغر أو يساوي R1 لكل N أكبر أو
+
+263
+00:20:15,210 --> 00:20:21,930
+يساوي K والها وهيني فصلتلكم إياها هان الآن صار جاهز
+
+264
+00:20:21,930 --> 00:20:25,250
+اللي هو النظرية اللي احنا هتذكرولها لها الـ
+
+265
+00:20:25,250 --> 00:20:30,990
+comparison test اللي هو عندي summation للـ R1 هذه
+
+266
+00:20:30,990 --> 00:20:37,810
+صارت الآن XN plus 1 الآن أصغر من R1 يعني بمهادر تبه
+
+267
+00:20:37,810 --> 00:20:44,030
+عليها ده خلينا نعملها برضه أفصلها صار عندي الآن يا
+
+268
+00:20:44,030 --> 00:20:53,890
+جماعة عندي اللي هو x and هيها x and absolute value
+
+269
+00:20:53,890 --> 00:21:01,550
+other أو يساوي R واحد أس ان ماشي هذي الآن الـ R1 أصغر
+
+270
+00:21:01,550 --> 00:21:07,590
+من واحد مدام أصغر واحد وهذه الـ series converts
+
+271
+00:21:07,590 --> 00:21:12,030
+الكبيرة إذا بقى بأول هذه الـ series الشمالة تكون
+
+272
+00:21:12,030 --> 00:21:16,690
+converts then by comparison test الآن اللي هي
+
+273
+00:21:16,690 --> 00:21:21,350
+summation R1Rn converges implies بواسطة هذه أن الـ
+
+274
+00:21:21,350 --> 00:21:26,350
+summation للـ Xn is absolutely convergent الآن لو
+
+275
+00:21:26,350 --> 00:21:30,530
+فرضنا أن limit Xn أس واحدة بساوي R أكبر من واحد
+
+276
+00:21:31,090 --> 00:21:34,410
+بنفس الطريقة اللي جيتها قبل بشوية بس هاخد الـY
+
+277
+00:21:34,410 --> 00:21:39,010
+اللي هو هستخدم الـY definition بس هاخد الـY R ناقص
+
+278
+00:21:39,010 --> 00:21:42,250
+واحد على اثنين و هطبّك زي ما طبّجت بالظبط قبل
+
+279
+00:21:42,250 --> 00:21:47,650
+بشوية هلاجي natural number K such that الـ X أنقص
+
+280
+00:21:47,650 --> 00:21:52,490
+واحد على N أكبر من واحد ولا لأ أنا بلزمش حتى على 
+
+281
+00:21:52,490 --> 00:21:56,150
+طول limit xn أسواه دلان اللي هو بسوء r أكبر من 
+
+282
+00:21:56,150 --> 00:21:59,010
+واحد هيطلع عندي xn أسواه دلان أكبر من واحد فهو r
+
+283
+00:21:59,010 --> 00:22:03,290
+أكبر سواء k ومنه على طول بما أن هذه اللي هو أكبر
+
+284
+00:22:03,290 --> 00:22:05,590
+من واحد حسب الـ test اللي قبل بشوية الـ summation للـ
+
+285
+00:22:05,590 --> 00:22:11,290
+xn is divergent وده ما أعرفش أعملها زي ما
+
+286
+00:22:11,290 --> 00:22:15,830
+عملتها قبل بشوية أنا no conclusion وهذا
+
+287
+00:22:15,830 --> 00:22:21,070
+حكيتها no conclusion When R بيساوي واحد either
+
+288
+00:22:21,070 --> 00:22:28,830
+convergence or divergence is possible في حالة لما
+
+289
+00:22:28,830 --> 00:22:32,730
+جينا .. أخدنا الـ limit و لجينا الـ limit لأن
+
+290
+00:22:32,730 --> 00:22:36,750
+through الـ test بيساوي واحد معناته أنه يمكن يكون
+
+291
+00:22:36,750 --> 00:22:43,190
+convergence و ممكن يكون divergence طيب نيجي الآن
+
+292
+00:22:43,190 --> 00:22:49,470
+للـ ratio test الـ ratio test مشابه أخدنا اللي هو
+
+293
+00:22:49,470 --> 00:22:53,090
+الآن comparison test بشقيه العادي و الـ limit و
+
+294
+00:22:53,090 --> 00:22:55,890
+أخدنا الآن through الـ test بشقيه العادي و الـ limit
+
+295
+00:22:55,890 --> 00:22:59,630
+العادي اللي هو اللي قصدنا فيه اللي هو X أنوس واحدة
+
+296
+00:22:59,630 --> 00:23:05,910
+أكبر من واحد اللي هو أو أصغر اللي كانت الأولى و
+
+297
+00:23:05,910 --> 00:23:08,350
+اللي بعدها limit comparison test نفس الأشياء أكبر
+
+298
+00:23:08,350 --> 00:23:13,440
+أو أصغر طيب الـ ratio test Fx بيساوي xn is a
+
+299
+00:23:13,440 --> 00:23:18,280
+sequence of non-zero terms هذه ميزتها إنها
+
+300
+00:23:18,280 --> 00:23:21,760
+بيلزمهاش طبعا زي اللي جابلها بيلزمها الأولى
+
+301
+00:23:21,760 --> 00:23:25,920
+بيلزمها الـ comparison test بيلزمها تقارن بسيريز
+
+302
+00:23:25,920 --> 00:23:30,920
+أخرى الآن الآنثرويد test والـ ratio test تقارن
+
+303
+00:23:30,920 --> 00:23:35,790
+بنفسها يعني من داخل نفسها بتقدر تعرف اللي هو ..
+
+304
+00:23:35,790 --> 00:23:38,810
+اللي هي بطريقة معينة تعرف إن هي converged ولا
+
+305
+00:23:38,810 --> 00:23:42,810
+diverse يعني الآن Fx بسوء Xn is a sequence of non
+
+306
+00:23:42,810 --> 00:23:43,910
+-zero elements
+
+307
+00:23:46,750 --> 00:23:51,010
+of R and there is a positive number R أصغر من واحد
+
+308
+00:23:51,010 --> 00:23:55,730
+and a natural number K such that Xn زائد واحد على 
+
+309
+00:23:55,730 --> 00:23:59,950
+Xn أصغر سوء R for N أكبر سوء K then the summation
+
+310
+00:23:59,950 --> 00:24:04,030
+Xn is absolutely convergent يعني الآن جيت أنت لجيت
+
+311
+00:24:04,030 --> 00:24:08,310
+Xn زائد واحد على Xn اللي جيتها دائماً أصغر أو يساوي
+
+312
+00:24:08,310 --> 00:24:12,130
+R والـ R أصغر strictly من مين؟ من واحد يعني دائماً
+
+313
+00:24:12,130 --> 00:24:15,830
+الـ ratio هذا اللي بعده على اللي جابه اللي بعد على
+
+314
+00:24:15,830 --> 00:24:19,870
+اللي جاب اللي جيته أصغر معناته أنه صارت اللي هي
+
+315
+00:24:19,870 --> 00:24:23,890
+أشمالها عمالها بتصغر الـ sequence كل ما ماشيت قدام
+
+316
+00:24:23,890 --> 00:24:27,330
+بيصير اللي ورا على اللي قدام أصغر من واحد اللي ورا على
+
+317
+00:24:27,330 --> 00:24:31,570
+اللي قدام أصغر من واحد يعني واضح أنه في اللي هو في
+
+318
+00:24:31,570 --> 00:24:36,410
+الـ submission للـ XN is absolutely convergent لأن
+
+319
+00:24:36,410 --> 00:24:39,570
+بيقول if there exists a natural number k such that
+
+320
+00:24:39,570 --> 00:24:44,650
+بعده بيصير تصرفها إن xn زي 1 على xn هيكون أكبر
+
+321
+00:24:44,650 --> 00:24:48,350
+ويساوي 1 مدام أكبر ويساوي 1 معناته صار اللي هو كل
+
+322
+00:24:48,350 --> 00:24:51,890
+ما ماشيت قدام الـ term بيكبر مثلا بيكبر الـ term نفسه
+
+323
+00:24:51,890 --> 00:24:55,170
+إذا الـ limit مش هيروح للصفر إذا معناته إنه صارت الـ
+
+324
+00:24:55,170 --> 00:25:01,530
+series divergent طيب الـ proof خلينا نبرهن إيه if 6
+
+325
+00:25:01,530 --> 00:25:06,550
+holds يعني لو هو كانت هذا متحقق then by induction
+
+326
+00:25:06,550 --> 00:25:12,590
+one can see that for M أكبر أو يساوي واحد K X K M
+
+327
+00:25:12,590 --> 00:25:18,890
+أصغر أو يساوي أرقص M X K بتصور مش صعب إثبات هذه
+
+328
+00:25:18,890 --> 00:25:24,370
+for عندي خد X الـ induction عالميا for M أكبر أو
+
+329
+00:25:24,370 --> 00:25:32,360
+يساوي واحد على M اللي هان بيصير xk زائد واحد اللي
+
+330
+00:25:32,360 --> 00:25:37,820
+هو xk زائد واحد هنا لأنها بتتحقق من k وطالع k زائد
+
+331
+00:25:37,820 --> 00:25:45,920
+واحد بيصير على الـ xk يعني أصغر يساوي R في xk درم
+
+332
+00:25:45,920 --> 00:25:52,980
+التفرق الطرفين في وسطين xk إذن هذه صحيحة R M في
+
+333
+00:25:52,980 --> 00:25:56,020
+حالة الواحد صحيحة في حالة الـ M يساوي واحد الآن
+
+334
+00:25:56,020 --> 00:26:01,420
+suppose that this true for M بدا تبت صحيتها for me
+
+335
+00:26:01,420 --> 00:26:08,360
+in M زائد واحد X K زائد M زائد واحد بدا تبت صحيتها
+
+336
+00:26:08,360 --> 00:26:12,940
+في حالة الـ M زائد واحد اللي هو حسب اللي هنا اللي
+
+337
+00:26:12,940 --> 00:26:21,080
+أصغر أو يساوي الـ R ثمين في اللي هي هنا N زائد واحد S
+
+338
+00:26:21,080 --> 00:26:28,160
+زائد واحد K M K زائد M K زائد M إذا R في absolute
+
+339
+00:26:28,160 --> 00:26:34,280
+value X K زائد M ماشي لأن و بما أن هذا true for M
+
+340
+00:26:34,280 --> 00:26:38,840
+يعني هذا متحققه إذا من هنا بـ hypothesis induction
+
+341
+00:26:38,840 --> 00:26:47,440
+بيصير R في R أس M في XK يساوي R أقصى M زائد واحد
+
+342
+00:26:47,440 --> 00:26:54,500
+في XK يعني صارت هذه صحيحة for M زائد واحد إذا صارت
+
+343
+00:26:54,500 --> 00:26:59,440
+صحيحة لكل M إذا هذه دائما صحيحة لأي M أكبر أو يساوي
+
+344
+00:26:59,440 --> 00:27:03,120
+واحد في ضوء العلاقة اللي هي 6 صحيحة
+
+345
+00:27:06,690 --> 00:27:13,130
+إذاً هذا لكل M أكبر أو يساوي واحد عندي لكل N أكبر
+
+346
+00:27:13,130 --> 00:27:17,350
+أو يساوي K الآن
+
+347
+00:27:17,350 --> 00:27:27,330
+شيلي الـ K زائد M وحط مكانها N يعني N بتساوي K زائد
+
+348
+00:27:27,330 --> 00:27:36,860
+M بصير هذه X Nأثر أو يساوي الـ M بتساوي N ناقص K و
+
+349
+00:27:36,860 --> 00:27:42,100
+X K زي ما هي X K لأنه شيلت الـ N و حطيت مكانها K
+
+350
+00:27:42,100 --> 00:27:46,100
+زائد M و الـ N طبعا اللي هي بتساوي K زائد M أكيد
+
+351
+00:27:46,100 --> 00:27:50,400
+أكبر أو يساوي K إذن هذه اللي هي صحيحة إذن صار عندي
+
+352
+00:27:50,400 --> 00:27:56,340
+الآن اللي عشان بعد شوية هتستخدمها صار عندي الآن الـ
+
+353
+00:27:56,340 --> 00:28:03,180
+absolute value للـ Xn أصغر أو يساوي R أُس N ناقص K
+
+354
+00:28:03,180 --> 00:28:10,180
+في X K ماشي الحال هذا لكل N أكبر أو يساوي إيش K
+
+355
+00:28:10,180 --> 00:28:19,740
+طيب نكمل للبرهان الـ N summation للـ R أُس N
+
+356
+00:28:19,740 --> 00:28:20,660
+converts
+
+357
+00:28:23,610 --> 00:28:29,250
+لأن الـ r مالها بين صفر و واحد مادام هذي متغيرت
+
+358
+00:28:29,250 --> 00:28:33,450
+طبعا هذا term مجرد عدد يعني term لأنه عند ك كهذا
+
+359
+00:28:33,450 --> 00:28:37,390
+هو شيء fixed يعني هو عبارة عن عدد والمتغير من الـ n
+
+360
+00:28:37,390 --> 00:28:44,510
+هذه اللي أنا الـ summation لها للـ r الناقص K يعني بس
+
+361
+00:28:44,510 --> 00:28:48,670
+بنشيل K من الـ terms مش مشكلة بتضل اللي هو converge
+
+362
+00:28:48,670 --> 00:28:52,270
+اللي هي summation R أُس N converge ثم summation
+
+363
+00:28:52,270 --> 00:28:56,430
+أُس R N ناقص K كيفيكس number عبارة عن converge ثم
+
+364
+00:28:56,430 --> 00:28:59,530
+صارت هذه الـ series converge من باب أولى للـ series
+
+365
+00:28:59,530 --> 00:29:02,670
+اللي أصغر منها اللي هتكون converge ثم صارت عندي
+
+366
+00:29:02,670 --> 00:29:05,070
+summation absolute value converge أو بمعنى آخر
+
+367
+00:29:05,070 --> 00:29:12,450
+summation XN is absolutely convergent الآن نيجي لـ
+
+368
+00:29:12,450 --> 00:29:18,050
+الجزء الثاني الآن إذا كانت اللي هي سبعة holes سبعة
+
+369
+00:29:18,050 --> 00:29:21,970
+هي سبعة شايفينها هي سبعة اللي هو الـ XN زائد واحد
+
+370
+00:29:21,970 --> 00:29:28,990
+على XN أكبر أو يساوي واحد لكل N أكبر أو يساوي مين
+
+371
+00:29:28,990 --> 00:29:36,420
+أكبر أو يساوي K كلام مشابه كلام مشابه if 7 holds
+
+372
+00:29:36,420 --> 00:29:41,900
+then by induction one can see that xkm أكبر أو
+
+373
+00:29:41,900 --> 00:29:46,880
+يساوي xk for m يساوي واحد و بعدين it is true for m
+
+374
+00:29:46,880 --> 00:29:49,480
+then it is true for m زائد واحد و زي ما عملت قبل
+
+375
+00:29:49,480 --> 00:29:54,170
+بشوية هتلاجوها بكل سهولة تطلع الآن خد الـ limit هذا
+
+376
+00:29:54,170 --> 00:29:58,690
+الآن هذا صحيح لكل M أكبر أو يساوي واحد الآن خد الـ
+
+377
+00:29:58,690 --> 00:30:01,630
+limit as M goes to infinity بيصير أكبر أو يساوي
+
+378
+00:30:01,630 --> 00:30:05,090
+اللي هو المقدار هذا والمقدار هذا strictly أكبر من
+
+379
+00:30:05,090 --> 00:30:09,970
+100 من 0 لأن الـ terms اللي عندي كلها لا تساوي 0 من
+
+380
+00:30:09,970 --> 00:30:14,930
+عند K وطالع إذا انتر عندي اللي هو limit الـ Xn اللي
+
+381
+00:30:14,930 --> 00:30:20,490
+هو أكبر من 0 and so summation للـ Xn is divergent
+
+382
+00:30:21,110 --> 00:30:26,670
+طيب، نريد الآن لإيه الـ Corollary الأخيرة في
+
+383
+00:30:26,670 --> 00:30:32,050
+محاضرة اليوم اللي هي بتقول ليت X بسوء XN بيه
+
+384
+00:30:32,050 --> 00:30:36,790
+Sequence in R and Set واضح إنه بيعطي اللي هو عادي و
+
+385
+00:30:36,790 --> 00:30:38,990
+بعدين limit عادي و بعدين limit وفي الـ ratio test
+
+386
+00:30:38,990 --> 00:30:42,410
+نفس الشيء بده ياخد limit الـ exant زائد واحد على الـ
+
+387
+00:30:42,410 --> 00:30:47,410
+exant يساوي R و الناس هتميل في الحلول في معظمها
+
+388
+00:30:47,410 --> 00:30:51,270
+اللي هي limits whenever the limit exist إذا كانت
+
+389
+00:30:51,270 --> 00:30:55,230
+الـ limit هذه exist بنيجي then the series summation
+
+390
+00:30:55,230 --> 00:30:58,630
+xn converges أو absolutely convergent إذا كان r
+
+391
+00:30:58,630 --> 00:31:02,210
+أصغر من واحد و divergent إذا كانت يشملها أكبر من
+
+392
+00:31:02,210 --> 00:31:06,110
+واحد يعني بناخد limit xn زائد واحد على xn absolute
+
+393
+00:31:06,110 --> 00:31:09,110
+value طبعا إذا كانت positive terms على طول بدون
+
+394
+00:31:09,110 --> 00:31:13,780
+absolute values طلع إن دي limit موجود ما دام طلع
+
+395
+00:31:13,780 --> 00:31:18,300
+الـ limit موجود في عندي حكم إذا كان اللي هو أكبر من
+
+396
+00:31:18,300 --> 00:31:21,780
+واحد diverse إذا كان أصغر من واحد converge إذا
+
+397
+00:31:21,780 --> 00:31:26,220
+بيساوي واحد معناته the test fails و بنبحث اللي عن
+
+398
+00:31:26,220 --> 00:31:30,440
+test آخر طيب الآن suppose that limit xn زائد واحد
+
+399
+00:31:30,440 --> 00:31:33,300
+على xn as n goes to infinity بيساوي R أصغر من مين
+
+400
+00:31:33,300 --> 00:31:38,410
+من واحد بنفس الطريقة اللي عملناها قبل بشوية في
+
+401
+00:31:38,410 --> 00:31:44,230
+الأول let R1 satisfies R1 أكبر من R أصغر من 1 then
+
+402
+00:31:44,230 --> 00:31:48,810
+اللي هو لأن طبيعي between any two real numbers فيه
+
+403
+00:31:48,810 --> 00:31:53,770
+real number سميته مين؟ R1 الآن بما أن الـ limit هذا
+
+404
+00:31:53,770 --> 00:31:57,370
+بيساوي R يدل كل إيبسلون أكبر من 0 من ضمن مين
+
+405
+00:31:57,370 --> 00:32:02,760
+الإيبسلون اللي بدأ أخدها؟ R1-R Then for epsilon
+
+406
+00:32:02,760 --> 00:32:07,280
+يساوي R واحد ناقص R أكبر من صفر there exists K
+
+407
+00:32:07,280 --> 00:32:10,260
+elements in N such that الـ absolute value لهذا
+
+408
+00:32:10,260 --> 00:32:13,160
+ناقص هذا أصغر من مين من الـ epsilon هي R واحد ناقص
+
+409
+00:32:13,160 --> 00:32:18,180
+مين ناقص R هذا صحيح لكل مين لكل N أكبر أو يساوي K
+
+410
+00:32:18,800 --> 00:32:23,600
+الآن نفردها هذه بس بتاخد الجهة اللي على اليمين هي
+
+411
+00:32:23,600 --> 00:32:27,420
+اللي بتمنى اللي هو صار عندي xn زائد واحد على xn
+
+412
+00:32:27,420 --> 00:32:31,540
+أصغر من r واحد ناقص r ولمّا تجيب هذا على الجهة
+
+413
+00:32:31,540 --> 00:32:34,240
+الثانية بعد ما فكرا absolute value بصير r يساوي
+
+414
+00:32:34,240 --> 00:32:39,400
+إيش بتساوي؟ يساوي يساوي r واحد الآن و يساوي R واحد
+
+415
+00:32:39,400 --> 00:32:44,620
+إذا اللي هي .. اللي هيكون عندي اللي بالـ ..
+
+416
+00:32:44,620 --> 00:32:47,480
+بالنظرية اللي هي تسعة اثنين خمسها هتطلع عندي
+
+417
+00:32:47,480 --> 00:32:51,280
+الاصابيش الـ absolute value اكسن اشمالها is
+
+418
+00:32:51,280 --> 00:32:56,110
+absolutely convergent هيطلع عندي summation للـ xn
+
+419
+00:32:56,110 --> 00:32:59,350
+is absolutely convergent اللي هي من نظرية تسعة
+
+420
+00:32:59,350 --> 00:33:02,450
+اثنين خمسة لإنه صار عندي الـ absolute value لـ xn
+
+421
+00:33:02,450 --> 00:33:07,750
+زائد واحد على xn أصغر من رقم أصغر من واحد لكل n
+
+422
+00:33:07,750 --> 00:33:11,710
+أكبر سواء k من عند k وطالع بمعنى آخر صار عندي اللي
+
+423
+00:33:11,710 --> 00:33:15,530
+هي the series is convergent لإنه هذا أصلا corollary
+
+424
+00:33:15,530 --> 00:33:21,830
+للي جابها الآن وناخد اللي هو الجزء الثاني من اللي
+
+425
+00:33:21,830 --> 00:33:25,470
+هي ال .. ال .. ال .. البرهان اللي هو اللي بتعلق في
+
+426
+00:33:25,470 --> 00:33:28,330
+الجزء الثاني من ال Corollary بدنا نفترض انه limit
+
+427
+00:33:28,330 --> 00:33:33,390
+لل Xn زائد واحد ع ال Xn اللي هو بيساوي R أكبر من
+
+428
+00:33:33,390 --> 00:33:37,910
+واحد وبدنا نشوف اللي هو كيف diverse يعني بدنا نفترض
+
+429
+00:33:37,910 --> 00:33:40,670
+انه limit limit
+
+430
+00:33:42,720 --> 00:33:46,740
+Xn زائد واحد على Xn as n goes to infinity اللي هو
+
+431
+00:33:46,740 --> 00:33:51,940
+إجماله عبارة عن رقم اللي هو أكبر من واحد نسميها R
+
+432
+00:33:51,940 --> 00:33:58,260
+يساوي R أكبر من واحد ونشوف كيف أن هو عندي اللي هي
+
+433
+00:33:58,260 --> 00:34:04,040
+diverse الآنخد الـ Epsilon حلو خد Epsilon for
+
+434
+00:34:04,040 --> 00:34:09,560
+Epsilon for Epsilon بيساوي R ناقص واحد أكبر من صفر
+
+435
+00:34:09,560 --> 00:34:13,220
+there exists K element in N such that for every N
+
+436
+00:34:13,220 --> 00:34:19,000
+أكبر سواء K بطلع عندي هو XN زائد واحد على XN
+
+437
+00:34:19,510 --> 00:34:25,650
+absolute value ناقص الـ R أكبر من أصغر من مين من
+
+438
+00:34:25,650 --> 00:34:30,190
+إبسلون اللي هي عبارة عن R ناقص واحد هي ال إبسلون
+
+439
+00:34:30,190 --> 00:34:33,130
+اللي أخدت R ناقص واحد أو زي ما هو عاملها هنا أصغر
+
+440
+00:34:33,130 --> 00:34:36,550
+من هيها أصغر من R minus واحد اللي هي الإبسلون اللي
+
+441
+00:34:36,550 --> 00:34:40,570
+هنا فوق فوق اللي هنا مش بيهمنيش الجهة اللي هنا
+
+442
+00:34:40,570 --> 00:34:43,850
+بيهمني الجهة الثانية عكس اللي أولاني اللي عن حيط
+
+443
+00:34:43,850 --> 00:34:47,790
+لعندي xn زائد واحد على xn أكبر من واحد اللي هي r
+
+444
+00:34:47,790 --> 00:34:50,870
+ناقص r minus واحد اللي هي ايش بتطلع واحد صار هذا
+
+445
+00:34:50,870 --> 00:34:54,030
+المقدار أكبر من واحد و بال test اللي قبل بشوية ال
+
+446
+00:34:54,030 --> 00:34:57,790
+theorem تسعة اتنين خمسة بما انه صار هذا من عند n
+
+447
+00:34:57,790 --> 00:35:01,670
+أكبر يساوي k وطالع من عند k وطالع طلع عندي هذا
+
+448
+00:35:01,670 --> 00:35:05,050
+أكبر من واحد معناته صارت ال information هذه is
+
+449
+00:35:05,050 --> 00:35:10,340
+divergent وطبعا اللي دايما بنقولها دايما اللي هي no
+
+450
+00:35:10,340 --> 00:35:14,320
+conclusion و ال R بتساوي واحد اللي هو ممكن تكون
+
+451
+00:35:14,320 --> 00:35:17,080
+convergent و ممكن تكون divergent عشان هذا الأساس
+
+452
+00:35:17,080 --> 00:35:22,160
+بنقول ال test fail في حالة ال R بتساوي واحد و نبحث
+
+453
+00:35:22,160 --> 00:35:26,900
+عن test آخر و الآن بنيجي ل اللي هو المرة الجاية ان
+
+454
+00:35:26,900 --> 00:35:30,440
+شاء الله بناخد ال integral test و إلى لقاء آخر
+
+455
+00:35:30,440 --> 00:35:31,400
+والسلام عليكم و رحمه الله 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dbebb10b4572deec11962c1ce4ce5cbf3cdc7324
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY_raw.srt
@@ -0,0 +1,1848 @@
+1
+00:00:05,030 --> 00:00:07,750
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,750 --> 00:00:10,710
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:10,710 --> 00:00:16,270
+أجمعين هذه هي المحاضرة رقم 26 مساق تحليل حقيقه 2
+
+4
+00:00:16,270 --> 00:00:20,290
+طلاب طالبات الجامعة الإسلامية قسم رياضيات كلية
+
+5
+00:00:20,290 --> 00:00:24,650
+العلوم اليوم هنكمل حديثنا في شطر 9 ولكن في section
+
+6
+00:00:24,650 --> 00:00:29,050
+جديد ال section هنبدأ فيه اللي هو tests for
+
+7
+00:00:29,050 --> 00:00:36,950
+absolute convergenceاختبارات الـ Series التي تحتوي
+
+8
+00:00:36,950 --> 00:00:40,490
+على الـ Positive Terms أو اللي هو بمفهوم الـ
+
+9
+00:00:40,490 --> 00:00:46,010
+Absolute Convergence نأتي الآن للأولاني المشهور
+
+10
+00:00:46,010 --> 00:00:51,130
+921بنسميه ال comparison test او اللي هو اختبار
+
+11
+00:00:51,130 --> 00:00:55,490
+المقارن ال let x يعني اللي بيكون عندنا فيه C ال
+
+12
+00:00:55,490 --> 00:00:58,910
+series و بنقارنها ب series أخرى بنعبجها عارفين
+
+13
+00:00:58,910 --> 00:01:02,930
+اللي هو converged ولا diverse وبناء عليه بنحكم على
+
+14
+00:01:02,930 --> 00:01:07,250
+ال series اللي بيبقى انقارنها اللي هي انها
+
+15
+00:01:07,250 --> 00:01:11,900
+converged او diverseLed X بيساوي XN وY بيساوي YN
+
+16
+00:01:11,900 --> 00:01:17,420
+بـReal Sequences Suppose that for some natural
+
+17
+00:01:17,420 --> 00:01:22,340
+numbers K اللي هو XN أكبر أو أصغر أو يساوي YN يعني
+
+18
+00:01:22,340 --> 00:01:26,400
+بمعنى آخر أننا بنحكي عن Sequence of Positive Terms
+
+19
+00:01:26,400 --> 00:01:32,160
+ماشي إذا هذه اللي هي عبارة عن Testلـ Series مكوّنة
+
+20
+00:01:32,160 --> 00:01:36,420
+الـ Terms تبعتها من Positive Terms for N أكبر و
+
+21
+00:01:36,420 --> 00:01:40,320
+ساوة و K then the convergence of summation yn
+
+22
+00:01:40,320 --> 00:01:44,320
+implies the convergence of xn and the divergence
+
+23
+00:01:44,320 --> 00:01:48,440
+of xn implies the divergence of summation yn اللي
+
+24
+00:01:48,440 --> 00:01:53,680
+أنا بقول ليه ال test بيقول بيحكيلي معايا ليه ان لو
+
+25
+00:01:53,680 --> 00:01:56,820
+كان في عندي two sequences xn و yn هم اللي بيكون
+
+26
+00:01:56,820 --> 00:02:01,920
+جسم اللي هو ال seriesباجي إذا كان عندي Xn أصغر
+
+27
+00:02:01,920 --> 00:02:05,700
+سواء و Yn لكل انه طبعا و اتنتين positive باجي بقول
+
+28
+00:02:05,700 --> 00:02:10,800
+إذا كان اللي هي الكبيرة اللي هي converts ال Yn
+
+29
+00:02:10,800 --> 00:02:14,280
+أكيد من باب أولى الصغيرة أشمالها converts يعني ال
+
+30
+00:02:14,280 --> 00:02:18,520
+convergence لل Yn بيعطي ال convergence لمن؟ لل Xn
+
+31
+00:02:19,050 --> 00:02:23,830
+إذا كانت الصغيرة diverges من باب أولاد كل كبيرة
+
+32
+00:02:23,830 --> 00:02:27,750
+إيش ما لها، diverges خلّينا نبرهن الآن Suppose
+
+33
+00:02:27,750 --> 00:02:33,730
+that yn is convergent، ماشي الحال؟suppose that
+
+34
+00:02:33,730 --> 00:02:37,090
+summation yn converges نفترض لكبير أنها converges
+
+35
+00:02:37,090 --> 00:02:41,050
+then for every ي أكبر من صفر there exists m of
+
+36
+00:02:41,050 --> 00:02:45,850
+epsilon element in n such that for every m أكبر من
+
+37
+00:02:45,850 --> 00:02:50,330
+n و أكبر من م يبسلون اللي هو ال الكوشي criterion
+
+38
+00:02:50,330 --> 00:02:55,530
+اللي هو y واحد زي ym ناقص y واحد زي yn أصغر من مين
+
+39
+00:02:55,530 --> 00:03:02,870
+من إبسلون ماشي الحال الان هذا الكلاماللي هو عندي
+
+40
+00:03:02,870 --> 00:03:06,710
+صحيح لكل N أكبر وسوء ASK يعني مش من بداية ال
+
+41
+00:03:06,710 --> 00:03:10,970
+sequence مش كتير مهم أنا عند بداية ال sequence ان
+
+42
+00:03:10,970 --> 00:03:12,950
+اللي بحكم على ال convergence و ال divergence اللي
+
+43
+00:03:12,950 --> 00:03:17,330
+هو mean اللي هو ال terms من عند حد إلى ما لنهاية
+
+44
+00:03:17,330 --> 00:03:20,630
+اللي هو اللي هيأثر على المجموع انه اللي هو موجود
+
+45
+00:03:20,630 --> 00:03:26,630
+او مش موجود طيب الآن هذه اللي هي صحيحة لكل N و M
+
+46
+00:03:26,630 --> 00:03:32,180
+أكبر من M اللي لجناهاوعندي هذه صحيحة لكل mean N
+
+47
+00:03:32,180 --> 00:03:37,840
+أكبر وساوة K عشان أستخدم واحد و أستخدم star لازم
+
+48
+00:03:37,840 --> 00:03:42,520
+أختار أقول from one and star we have for every
+
+49
+00:03:42,520 --> 00:03:46,480
+epsilon there exists N عشان أستخدم واحد و star بدي
+
+50
+00:03:46,480 --> 00:03:50,500
+أخد N هي ال maximum بين ال K و بين ال M of epsilon
+
+51
+00:03:50,500 --> 00:03:54,720
+such thatلما تكون ال M أكبر من N و أكبر من ال K
+
+52
+00:03:54,720 --> 00:03:58,140
+الماكسيموم معناته أكبر من K و أكبر من هذه معناته
+
+53
+00:03:58,140 --> 00:04:02,880
+هذه صحيحة و هذه صحيحة يعني بحج اللي الناس تخدمها
+
+54
+00:04:02,880 --> 00:04:09,920
+we have X1 زيد X2 زيد XM اللي هي ال partial sum ل
+
+55
+00:04:09,920 --> 00:04:17,290
+X و هذه ناقص اللي هي X1 لعند XNأترحى من بعض اللي
+
+56
+00:04:17,290 --> 00:04:21,670
+هو حيساوى الـ XM زائد واحد لعند الـ XM الـ XN زائد
+
+57
+00:04:21,670 --> 00:04:25,650
+واحد أكيد اللي هو أصغر أشهر من YN زائد واحد الـ XN
+
+58
+00:04:25,650 --> 00:04:28,150
+زائد اتنين أصغر من YN زائد اتنين لما أصل الـ XM
+
+59
+00:04:28,150 --> 00:04:33,770
+أصغر أشهر من الـ YMالان هذه عبارة عن مين؟ عن هذه
+
+60
+00:04:33,770 --> 00:04:38,470
+ناقص هذه اللي هي Y1 زي Ym ناقص Y1 زي Yn اللي هي
+
+61
+00:04:38,470 --> 00:04:42,610
+أصغر من وين من Y لإنه converges اللي هي ال Yn بناء
+
+62
+00:04:42,610 --> 00:04:49,190
+عليه اللي هو أثبتنا إن ال SM ناقص ال SN بالنسبة لل
+
+63
+00:04:49,190 --> 00:04:53,570
+X اللي هي satisfies كوشي كراي كتير إن أنا أصغر من
+
+64
+00:04:53,570 --> 00:04:58,510
+Y معناه تصميش لل XN إيش ما لها convergesالعنوان
+
+65
+00:04:58,510 --> 00:05:03,110
+الثاني هو Contrapositive للعنوان الأول لماذا؟ لأن
+
+66
+00:05:03,110 --> 00:05:09,870
+لو كانت الـ summation Xn مختلفة وليس مرتبطة، فأكيد
+
+67
+00:05:09,870 --> 00:05:14,390
+ستعطي الـ summation Yn أشمالها التي ليست مرتبطة
+
+68
+00:05:14,650 --> 00:05:19,810
+يعني diverse يعني الجزء الثاني هذا ما هو إلا عبارة
+
+69
+00:05:19,810 --> 00:05:23,650
+عن اللي هو الجزء الأول بس شماله موفود بال
+
+70
+00:05:23,650 --> 00:05:27,890
+contraposition يعني B implies Q يعني not Q implies
+
+71
+00:05:27,890 --> 00:05:32,730
+not B طيبالان نيجي هذا اللي هو الـ Comparison Test
+
+72
+00:05:32,730 --> 00:05:38,070
+اللي هو المقارنة المباشرة بين ال terms تبعات مين
+
+73
+00:05:38,070 --> 00:05:41,890
+تبعات اللي هو الـ sequences أحياناً عملياً هذه مش
+
+74
+00:05:41,890 --> 00:05:46,830
+كتير الناس بترغبها في test تاني comparison test
+
+75
+00:05:46,830 --> 00:05:50,530
+لكن هذا ال test اللي هو بنسميه limit comparison
+
+76
+00:05:50,530 --> 00:05:53,910
+test وهذا أسهل في الاستخدام وأوسع في الاستخدام
+
+77
+00:05:53,910 --> 00:05:59,310
+والناس بتنيل عادة لاستخدامهاماشي الحال الانصاب
+
+78
+00:05:59,310 --> 00:06:02,450
+both that X بالساوية XN وY بالساوية YN are
+
+79
+00:06:02,450 --> 00:06:07,570
+positive serial sequences if the relation limit XN
+
+80
+00:06:07,570 --> 00:06:12,730
+على YN لان limit XN على YN لا يساوي سفر يعني عبارة
+
+81
+00:06:12,730 --> 00:06:17,400
+عن عدد هذايعني عبارة عن عدد يعني سير ال XN و سير
+
+82
+00:06:17,400 --> 00:06:23,260
+ال YN جريب من بعض لما نقول بطلع عدد limit XN على
+
+83
+00:06:23,260 --> 00:06:29,000
+YN يعني سيرهم جريب من بعض لدرجة أنه في الآخر بطلع
+
+84
+00:06:29,000 --> 00:06:32,280
+عدد يعني لا هو طلع مالة نهاية نقول اللي فوق أسرع
+
+85
+00:06:32,280 --> 00:06:37,180
+كتير ولا طلع سفر نقول اللي تحت أسرع كتير لأ اللي
+
+86
+00:06:37,180 --> 00:06:42,770
+هو limit XN على YN طلعلي عدد عشان هيكلما هذا يحدث
+
+87
+00:06:42,770 --> 00:06:45,970
+if the relation limit xn على yn لا يساوي سفر hold
+
+88
+00:06:45,970 --> 00:06:51,570
+then ال summation xn is convergent if and only if
+
+89
+00:06:51,570 --> 00:06:56,650
+ال summation ال yn أشمال is convergent لأن سيرهما
+
+90
+00:06:56,650 --> 00:07:01,770
+متقارب عشان هيك بنقول يا التنتين converges يا
+
+91
+00:07:01,770 --> 00:07:08,570
+التنتين diverse لكن if the limit in two هنا is
+
+92
+00:07:08,570 --> 00:07:13,540
+zeroمعناته اللي تحت Star طير على المالة نهاية يعني
+
+93
+00:07:13,540 --> 00:07:18,400
+صار كله على إيش بساوي سفر فبكون الآن ال YN إذا
+
+94
+00:07:18,400 --> 00:07:22,840
+الكبير Convergent من باب أولى لصغير إيش ماله؟
+
+95
+00:07:22,840 --> 00:07:27,000
+Convergent لأنه هذا صار سفر معناته هذا أسرع من هذا
+
+96
+00:07:27,000 --> 00:07:32,340
+بكتير معناته لو كان اللي تحت Converged أكيد أكيد
+
+97
+00:07:32,340 --> 00:07:36,600
+أكيد أكيدهيكون اللي فوق اشمله convergence لأن اللي
+
+98
+00:07:36,600 --> 00:07:42,420
+فوق بيكون أبطأ أو أقل قيمة يعني نحو الكبر يعني
+
+99
+00:07:42,420 --> 00:07:46,040
+معناته انه اللي هو ال summation لل YN ال
+
+100
+00:07:46,040 --> 00:07:49,120
+convergence له على طول بيعطي اللي هو ال
+
+101
+00:07:49,120 --> 00:07:52,980
+convergence لل XN هذه حول اللي هو نص النظرية نيجي
+
+102
+00:07:52,980 --> 00:07:59,670
+الآنللبرهان نأتي لبرهان نثبت أنه نفترض ان ال
+
+103
+00:07:59,670 --> 00:08:02,810
+summation نثبت ان ال summation XN is convergent
+
+104
+00:08:02,810 --> 00:08:05,510
+فندهلي في ال summation YN اللي هو convergent الان
+
+105
+00:08:05,510 --> 00:08:09,790
+بدنا نأتي للبرهان قلنا عندي limit ال XN على ال YN
+
+106
+00:08:09,790 --> 00:08:13,430
+ايش بيساوي؟ بيساوي L لأ تساوي سفرإذاً حسب التعريف
+
+107
+00:08:13,430 --> 00:08:16,050
+الـ Epsilon Delta Definition أو الـ Epsilon K
+
+108
+00:08:16,050 --> 00:08:19,650
+Definition for Epsilon بساوة L على 2 أخدت لأي
+
+109
+00:08:19,650 --> 00:08:22,550
+Epsilon أخدت من ضمنها L على 2 للحسابات there
+
+110
+00:08:22,550 --> 00:08:27,210
+exists K such that اللي هو XN على YN ناقص L أصغر
+
+111
+00:08:27,210 --> 00:08:30,470
+من Epsilon اللي هي L على 2 لكل N أكبر أو يساوي K
+
+112
+00:08:30,470 --> 00:08:35,350
+خلّيني نفرضها هذه بيصير عند XN على YN أكبر من L
+
+113
+00:08:35,350 --> 00:08:40,280
+ناقص L على 2 وأصغر من L زائد من L على 2الان صار
+
+114
+00:08:40,280 --> 00:08:43,560
+عندى الان اللى هى ال .. ال .. ال .. ال .. ال .. ال
+
+115
+00:08:43,560 --> 00:08:44,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+116
+00:08:44,080 --> 00:08:44,380
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+117
+00:08:44,380 --> 00:08:44,700
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+118
+00:08:44,700 --> 00:08:45,400
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+119
+00:08:45,400 --> 00:08:45,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+120
+00:08:45,680 --> 00:08:45,940
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+121
+00:08:45,940 --> 00:08:46,620
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+122
+00:08:46,620 --> 00:08:47,900
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+123
+00:08:47,900 --> 00:08:48,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+124
+00:08:48,420 --> 00:08:48,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+125
+00:08:48,420 --> 00:08:50,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+126
+00:08:50,320 --> 00:08:59,540
+ال .. ال .. ال .. ال .. ال ..
+
+127
+00:08:59,540 --> 00:09:01,420
+ال .. ال ..
+
+128
+00:09:06,850 --> 00:09:11,550
+بال test اللي قبل بشوية إذا ال summation yn مش هذا
+
+129
+00:09:11,550 --> 00:09:16,790
+اللي هنستخدمه هنستخدم اللي هو xn أكبر من yn في L
+
+130
+00:09:16,790 --> 00:09:19,750
+على 2 إذا كانت هذي convergent هتكون هذي إيش مهلها
+
+131
+00:09:19,750 --> 00:09:24,410
+convergent وبما أن yn في L على 2 convergent هتطلع
+
+132
+00:09:24,410 --> 00:09:28,410
+عندي اللي هي ال summation yn إيش مهلها is
+
+133
+00:09:28,410 --> 00:09:34,660
+convergentماشي طيب الان conversely بدي افترض اللي
+
+134
+00:09:34,660 --> 00:09:39,480
+هو ال summation ل Yn ايش ماله is convergent ال
+
+135
+00:09:39,480 --> 00:09:41,920
+summation ل Yn is convergent مدام ال summation ل
+
+136
+00:09:41,920 --> 00:09:46,680
+Yn is convergent هيكون ال summation اللي هي
+
+137
+00:09:46,680 --> 00:09:50,500
+التلاتة في L على 2 في Yn is convergent لأن هذا
+
+138
+00:09:50,500 --> 00:09:54,000
+عبارة عن ثابتهذا لما انفرضنا الـ yn is summation
+
+139
+00:09:54,000 --> 00:09:57,320
+الـ yn convergent إذا هيكون ال summation الكبير
+
+140
+00:09:57,320 --> 00:10:00,940
+هذا convergent من باب أو لا ال summation للـ xn
+
+141
+00:10:00,940 --> 00:10:06,200
+إيش ماله is convergent يعني اتبعوا اللي حكيته هان
+
+142
+00:10:06,200 --> 00:10:14,030
+هذه اللي هي ال convergenceللـ Xn اللي هي الكبيرة
+
+143
+00:10:14,030 --> 00:10:17,850
+بيعطي ال convergence لهذه هو من ثم ال convergence
+
+144
+00:10:17,850 --> 00:10:22,710
+لهذه لأن في الجزء الثاني ال convergence لل Yn
+
+145
+00:10:22,710 --> 00:10:26,430
+بيعطي ال convergence لهذه ال convergence لهذه اللي
+
+146
+00:10:26,430 --> 00:10:31,930
+هو الكبير بيعطي ال convergence لمن؟ لل Xn طيب نيجي
+
+147
+00:10:31,930 --> 00:10:35,910
+الآن طبعا
+
+148
+00:10:35,910 --> 00:10:42,080
+ال .. ال .. ال .. المطلوب بي ..بدنا نفترض
+
+149
+00:10:44,730 --> 00:10:51,270
+suppose that limit xn على yn بساوة سفر ونفترض أن
+
+150
+00:10:51,270 --> 00:10:54,130
+الـ yn أشمالها is convergent بالذات بت الـ xn
+
+151
+00:10:54,130 --> 00:10:59,330
+أشمالها is convergent لأن شو معناه limit xn على yn
+
+152
+00:10:59,330 --> 00:11:03,230
+بساوة سفر لكل y أكبر من سفر؟ there exists k
+
+153
+00:11:03,230 --> 00:11:06,810
+element in n such that xn على yn أصغر من مين من
+
+154
+00:11:06,810 --> 00:11:10,810
+إبسلون لكل n أكبر وسوء k هذا اللي هو تعريف ال
+
+155
+00:11:10,810 --> 00:11:15,700
+limit لل xn على yn بساوة سفرومنه هذا دروب طرفين في
+
+156
+00:11:15,700 --> 00:11:20,680
+وسطين XN أصلا من YN في Y ن إحنا مفترضين أن ال YN
+
+157
+00:11:20,680 --> 00:11:24,240
+is convergent يعني ال Y في ال YN ثابتة ما هي ال Y
+
+158
+00:11:24,240 --> 00:11:27,620
+is convergent إذا كان الكبيرة convergent من باب
+
+159
+00:11:27,620 --> 00:11:32,680
+أولى الصماش لل XN إيش هتكون اللي هي is convergent
+
+160
+00:11:32,680 --> 00:11:39,020
+by اللي هو comparison test الأصليالان اذا خلصنا من
+
+161
+00:11:39,020 --> 00:11:42,300
+ال testين اللي هو ال comparison test وال limit
+
+162
+00:11:42,300 --> 00:11:45,880
+comparison test وكانت ال testين عبارة عن على
+
+163
+00:11:45,880 --> 00:11:50,520
+positive sequences الان بدنا نحكي عن حاجة اسمها
+
+164
+00:11:50,520 --> 00:11:53,700
+the root and the ratio test نشوف ال root و ال
+
+165
+00:11:53,700 --> 00:11:57,260
+ratio test ال test الأولان اللي هو ال root test
+
+166
+00:11:57,260 --> 00:12:03,010
+ايه؟ fx بسوي xnis a sequence in A and R and there
+
+167
+00:12:03,010 --> 00:12:07,410
+exists a positive number R أصغر من واحد and a
+
+168
+00:12:07,410 --> 00:12:11,590
+natural number K such that يعني الخاصية هذه بدوا
+
+169
+00:12:11,590 --> 00:12:16,590
+إياها X N أسواحد على N أصغر أو ساوي R تتحقق لكل N
+
+170
+00:12:16,590 --> 00:12:20,550
+أكبر أو يساوي K من عند K وطالع مش مشكلةلأن أنا
+
+171
+00:12:20,550 --> 00:12:22,670
+اللي في ال divergence و ال convergence مين اللي
+
+172
+00:12:22,670 --> 00:12:26,990
+بتحكم اللي هو ال terms اللي لما .. لإنها بتروح إلى
+
+173
+00:12:26,990 --> 00:12:29,890
+مالة نهاية يعني لو كان أول مليون term أو أول متين
+
+174
+00:12:29,890 --> 00:12:33,970
+مليون أو جد ما يكون في الأول اللي هو لا تحقق
+
+175
+00:12:33,970 --> 00:12:38,250
+الخاصية اللي بديها أنا بهم مني اللي فيما بعد يحقق
+
+176
+00:12:38,250 --> 00:12:40,550
+الخاصية اللي بديها اللي بدا تحكم على ال
+
+177
+00:12:40,550 --> 00:12:44,950
+convergence أو ال divergence إذن الآن لو كان عندي
+
+178
+00:12:44,950 --> 00:12:49,520
+X أقص .. X أقص واحد أنا الأصغر يستخدم Rلكل n أكبر
+
+179
+00:12:49,520 --> 00:12:51,020
+يساوي كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+180
+00:12:51,020 --> 00:12:53,220
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+181
+00:12:53,220 --> 00:13:03,200
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+182
+00:13:03,200 --> 00:13:05,720
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+183
+00:13:05,720 --> 00:13:05,720
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+184
+00:13:05,720 --> 00:13:05,720
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+185
+00:13:05,720 --> 00:13:15,340
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+186
+00:13:15,340 --> 00:13:22,200
+كتنفترض أنه تلاتة holes يعني نفترض أنه XN أسواحد
+
+187
+00:13:22,200 --> 00:13:26,500
+على N أصغر أو يساوي R لكل N أكبر أو يساوي K الان
+
+188
+00:13:26,500 --> 00:13:29,760
+منها هيكون عند ال absolute value XN أكبر أو يساوي
+
+189
+00:13:29,760 --> 00:13:35,680
+0 أصغر أو يساوي 100 RN لكل N أكبر أو يساوي K الان
+
+190
+00:13:37,230 --> 00:13:42,990
+الـ summation للـ R أُس عن R نحن ناخدها أصغر من
+
+191
+00:13:42,990 --> 00:13:45,950
+واحد و positive طبعاً أصغر من واحد معناته ال
+
+192
+00:13:45,950 --> 00:13:50,250
+summation للـ R أن converge مظبوط؟ مدام الـ R أن
+
+193
+00:13:50,250 --> 00:13:55,310
+converge فال summation لل XN is converge يعني
+
+194
+00:13:55,310 --> 00:13:58,150
+بمعنى أخر صارت ال summation لل XN is absolutely
+
+195
+00:13:58,150 --> 00:14:06,100
+convergent طيبsuppose that أربعة holds اللي هي مين
+
+196
+00:14:06,100 --> 00:14:10,840
+أربعة هذا أكبر أو ساوء واحد لأن لكل N أكبر أو ساوء
+
+197
+00:14:10,840 --> 00:14:17,920
+K معناته اللي هو ال XN اللي هي أس واحد على N لو
+
+198
+00:14:17,920 --> 00:14:23,700
+جيت أخدته limitها limit اللي هي ال XN هيكون عند ال
+
+199
+00:14:23,700 --> 00:14:28,600
+absolute value لل XNأكبر أو ساوء واحد يعني limit
+
+200
+00:14:28,600 --> 00:14:33,340
+ال absolute value ل Xn as n goes to infinity أكيد
+
+201
+00:14:33,340 --> 00:14:37,640
+أكبر أو ساوء واحد إذا exist يعني بتسويش سفر مدام
+
+202
+00:14:37,640 --> 00:14:41,920
+بتسويش سفر إذا نصممش لل Xn بال test اللي هو
+
+203
+00:14:41,920 --> 00:14:46,780
+الأولان اللي أخدناهالان مدام الـ summation xn الـ
+
+204
+00:14:46,780 --> 00:14:51,260
+absolute value xn does not converge to 0 إذا هتكون
+
+205
+00:14:51,260 --> 00:14:55,580
+الـ xn does not converge to 0 ومن ثم ال summation
+
+206
+00:14:55,580 --> 00:15:00,560
+للـ xn أشملها diverse حسب اللي هو اللي قلنا عنه ال
+
+207
+00:15:00,560 --> 00:15:03,420
+divergence test اللي هو ال summation للـ xn
+
+208
+00:15:03,420 --> 00:15:06,820
+converges بلاقاء ال limit للـ xn بساوة 0 لكن عندي
+
+209
+00:15:06,820 --> 00:15:11,360
+طلعت limit للـ xn لا تساوة 0 طيب corollary لللي
+
+210
+00:15:11,360 --> 00:15:15,870
+فوقالأن الـ Corollary بتقول ما هي ليه؟ let X
+
+211
+00:15:15,870 --> 00:15:20,230
+بيساوي Xn بيبقى Sequence اند R and let R بيساوي
+
+212
+00:15:20,230 --> 00:15:25,350
+Limit Xn أس واحدة لان هناك كانت اللي هي بتاخد ال
+
+213
+00:15:25,350 --> 00:15:29,830
+and roots لمن؟ لل terms و بتشوف اللي هنا إذا كان
+
+214
+00:15:29,830 --> 00:15:33,410
+ال and roots لل terms اللي هي أكبر أو يساوي R من
+
+215
+00:15:33,410 --> 00:15:43,630
+عند K و طالعالان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+216
+00:15:43,630 --> 00:15:48,470
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+217
+00:15:48,470 --> 00:15:48,470
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+218
+00:15:48,470 --> 00:15:48,470
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+219
+00:15:48,470 --> 00:15:48,470
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+220
+00:15:48,470 --> 00:15:48,530
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+221
+00:15:48,530 --> 00:15:48,750
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+222
+00:15:48,750 --> 00:15:49,210
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+223
+00:15:49,210 --> 00:15:49,210
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+224
+00:15:49,210 --> 00:15:53,220
+بتحكم ليه؟ الان بتحكم ليه؟نفترض إن Xn بيكون
+
+225
+00:15:53,220 --> 00:15:57,500
+سيكوينس في R وR بيسوى Limit Xn plus 1 لـ N نفترض
+
+226
+00:15:57,500 --> 00:16:02,840
+إن هذا الـ Limit موجود ثم الصممش للـ Xn هو
+
+227
+00:16:02,840 --> 00:16:10,360
+بالتأكيد مرتبط لما R أصغر من 1 وهو مرتبط عندما R
+
+228
+00:16:10,360 --> 00:16:13,140
+أكبر من 1 وهذا ال test انتوا عارفينه يعني بمعنى
+
+229
+00:16:13,140 --> 00:16:18,040
+آخر باجي بقول باخد Limit Xn
+
+230
+00:16:18,970 --> 00:16:23,270
+أُس واحدة لأن أس أن قصة infinity طلع عندي ايش
+
+231
+00:16:23,270 --> 00:16:28,550
+بيساوي بيساوي R احنا مفترضين ان ال limit exist اذا
+
+232
+00:16:28,550 --> 00:16:34,550
+R أكبر من واحد خلاص ال series xn divers اذا R أصغر
+
+233
+00:16:34,550 --> 00:16:39,030
+من واحد ال series ايش مالها converge و absolutely
+
+234
+00:16:39,030 --> 00:16:44,370
+convergentلكن إذا كانت R بتساوي واحد بنقول ال test
+
+235
+00:16:44,370 --> 00:16:47,650
+fail يعني ممكن يكون convergence وممكن تكون إيش ما
+
+236
+00:16:47,650 --> 00:16:53,650
+لها divergence وفيه أمثلة واضح؟ طيب الآن بدنا نيجي
+
+237
+00:16:53,650 --> 00:16:59,570
+للبرهان suppose that limit Xn أس واحد على N بساوي
+
+238
+00:16:59,570 --> 00:17:05,790
+R وR إيش ما لها أصغر من واحد نفترض إنه limit Xn أس
+
+239
+00:17:05,790 --> 00:17:07,670
+واحد على N بساوي R أصغر من واحد
+
+240
+00:17:10,860 --> 00:17:22,100
+طيب عندى لما اقول limit xn أس واحدة لان بساوى واحد
+
+241
+00:17:22,100 --> 00:17:29,260
+او بساوى R اللى هى أصغر من واحد ايش معناته هذا هذا
+
+242
+00:17:29,260 --> 00:17:35,490
+معناته لكل ي أكبر من سفرThere exist k element in N
+
+243
+00:17:35,490 --> 00:17:39,550
+such that for every N أكبر وسوء k اللي هو بيكون
+
+244
+00:17:39,550 --> 00:17:50,390
+عند X N أسواحدة ل N ناقص R ناقص R أصغر من مين؟ من
+
+245
+00:17:50,390 --> 00:17:58,340
+إبسلونأصغر من إبسلون خد الآن إبسلون إبسلون بتساوي
+
+246
+00:17:58,340 --> 00:18:02,780
+عند واحد ناقص R أكبر من سفر لغرض الحسابات بتاخد
+
+247
+00:18:02,780 --> 00:18:06,720
+إبسلون عبارة عن واحد ناقص R على اتنين واحد ناقص R
+
+248
+00:18:06,720 --> 00:18:09,640
+على اتنين أكيد أكبر من سفر إذا هتصير أصغر من واحد
+
+249
+00:18:09,640 --> 00:18:14,420
+ناقص R على اتنين على اتنين صار عندي الآن Xn أسواحد
+
+250
+00:18:14,420 --> 00:18:20,120
+على N أصغر من واحد ناقص R على اتنين زائد R وأكبر
+
+251
+00:18:20,120 --> 00:18:27,300
+منR ناقص .. اللي هو واحد ناقص R على مين؟ على اتنين
+
+252
+00:18:27,300 --> 00:18:32,080
+انا بتهيب من المنطقة هذه ماشي الحال صار عندى اللي
+
+253
+00:18:32,080 --> 00:18:40,540
+هو ال XL أسواحد على N أصغر من اللي هو واحد
+
+254
+00:18:42,070 --> 00:18:47,950
+1 الان هذه اتنين R اللي هي واحد زائد R على مين على
+
+255
+00:18:47,950 --> 00:18:52,210
+اتنين ماشي؟ لذا صارت ال Xn أسواحد على N absolute
+
+256
+00:18:52,210 --> 00:18:57,790
+value أصغر من واحد زائد R على اتنين لكل N أكبر أو
+
+257
+00:18:57,790 --> 00:19:06,720
+يساوي مين K لذا حصلت على هذه هذه سموليها R'R' أو
+
+258
+00:19:06,720 --> 00:19:20,880
+يسمونها R واحد هذي R واحد اكبر او
+
+259
+00:19:20,880 --> 00:19:30,580
+اكبر اكبر اكبر اكبر اكبر اكبر اكبر اكبر اكبر
+
+260
+00:19:30,580 --> 00:19:33,070
+اكبر اكبر اكبر اكبر اكبرR أصغر من واحد يعني عبارة
+
+261
+00:19:33,070 --> 00:19:38,010
+عن هدولة عبارة عن R يعني R واحد أصغر من مين من R
+
+262
+00:19:38,010 --> 00:19:44,070
+في نفس الوقت هتكون أصغر من واحداللي وصلتله انا
+
+263
+00:19:44,070 --> 00:19:48,030
+suppose that اللي مش مشروح انا شرحته هناك limit x
+
+264
+00:19:48,030 --> 00:19:51,070
+minus واحد على n بساوي R أصغر من واحد then there
+
+265
+00:19:51,070 --> 00:19:55,650
+exists R واحد such that R واحد أكبر من R وأصغر من
+
+266
+00:19:55,650 --> 00:20:02,090
+مين من واحد R واحد أكبر من R وأكيد أصغر من واحد
+
+267
+00:20:02,090 --> 00:20:07,590
+زائد واحد على اتنين ويساوي واحد اللي هي andاللي هو
+
+268
+00:20:07,590 --> 00:20:11,270
+إيش هيكون عنده a natural number K اللي لجيته such
+
+269
+00:20:11,270 --> 00:20:15,210
+that XN plus 1 الان أصغر يسوء R1 لكل N أكبر أو
+
+270
+00:20:15,210 --> 00:20:21,930
+يسوء K والها وهيني فصلتلكم إيها هان الان صار جاهز
+
+271
+00:20:21,930 --> 00:20:25,250
+اللي هو النظرية اللي احنا هتذكرولها لها ال
+
+272
+00:20:25,250 --> 00:20:30,990
+comparison test اللي هو عندي summation لل R1 هذه
+
+273
+00:20:30,990 --> 00:20:37,810
+صارت الآن XN plus 1 الان أصغر من R1 يعنيبمهادر تبه
+
+274
+00:20:37,810 --> 00:20:44,030
+عليها ده خلينا نعملها برضه أفصلها صار عندي الآن يا
+
+275
+00:20:44,030 --> 00:20:53,890
+جماعة عندي اللي هو x and هيها x and absolute value
+
+276
+00:20:53,890 --> 00:21:01,550
+other أو ساوي R واحد أس انماشي هذي الان ال R1 أصغر
+
+277
+00:21:01,550 --> 00:21:07,590
+من واحد مدام أصغر واحد وهذه ال series converts
+
+278
+00:21:07,590 --> 00:21:12,030
+الكبيرة إذا بقى بأول هذه ال series الشمالة تكون
+
+279
+00:21:12,030 --> 00:21:16,690
+converts then by comparison testالآن اللي هي
+
+280
+00:21:16,690 --> 00:21:21,350
+summation R1Rn converges implies بواسطة هذه ان ال
+
+281
+00:21:21,350 --> 00:21:26,350
+summation لل Xn is absolutely convergent الان لو
+
+282
+00:21:26,350 --> 00:21:30,530
+فرضنا ان limit Xn أس واحدة بساوي R أكبر من واحد
+
+283
+00:21:31,090 --> 00:21:34,410
+بنفس الطريقة اللى جيتها قبل بشوية بس هاخد الـY
+
+284
+00:21:34,410 --> 00:21:39,010
+اللى هو هستخدم الـY definition بس هاخد الـY R ناقص
+
+285
+00:21:39,010 --> 00:21:42,250
+واحد على اتنين و هطبّك زي ما طبّجت بالظبط قبل
+
+286
+00:21:42,250 --> 00:21:47,650
+بشوية هلاجي natural number K such that ال X أنقص
+
+287
+00:21:47,650 --> 00:21:52,490
+واحد على N أكبر من واحد ولا لأ أنا بلزمش حتىعلى
+
+288
+00:21:52,490 --> 00:21:56,150
+طول limit xn أسواه دلان اللي هو بسوء r أكبر من
+
+289
+00:21:56,150 --> 00:21:59,010
+واحد هيطلع عندي xn أسواه دلان أكبر من واحد فهو r
+
+290
+00:21:59,010 --> 00:22:03,290
+أكبر سواء k ومنه على طول بما أن هذه اللي هو أكبر
+
+291
+00:22:03,290 --> 00:22:05,590
+من واحد حسب ال test اللي قبل بشوية ال summation لل
+
+292
+00:22:05,590 --> 00:22:11,290
+xn is divergent وده ماعرفش أعمل أعملها زي ما
+
+293
+00:22:11,290 --> 00:22:15,830
+عملتها قبل بشوية أنا none no conclusion وهذا
+
+294
+00:22:15,830 --> 00:22:21,070
+حكيتها no conclusionWhen R بيساوي واحد either
+
+295
+00:22:21,070 --> 00:22:28,830
+convergence or divergence is possible في حالة لما
+
+296
+00:22:28,830 --> 00:22:32,730
+جينا .. أخدنا ال limit و لجينا ال limit لان
+
+297
+00:22:32,730 --> 00:22:36,750
+through ال test بيساوي واحد معناته انه يمكن يكون
+
+298
+00:22:36,750 --> 00:22:43,190
+convergence و ممكن يكون divergence طيب نيجي الآن
+
+299
+00:22:43,190 --> 00:22:49,470
+لل ratio test ال ratio test مشابهأخدنا اللي هو
+
+300
+00:22:49,470 --> 00:22:53,090
+الان comparison test بشقيه العادي و ال limit و
+
+301
+00:22:53,090 --> 00:22:55,890
+أخدنا الان through ال test بشقيه العادي و ال limit
+
+302
+00:22:55,890 --> 00:22:59,630
+العادي اللي هو اللي قصدنا فيه اللي هو X أنوس واحدة
+
+303
+00:22:59,630 --> 00:23:05,910
+أكبر من واحد اللي هو أو أصغر اللي كانت الأولى و
+
+304
+00:23:05,910 --> 00:23:08,350
+اللي بعدها limit comparison test نفس الأشياء أكبر
+
+305
+00:23:08,350 --> 00:23:13,440
+أو أصغر طيب ال ratio testFx بيساوي xn is a
+
+306
+00:23:13,440 --> 00:23:18,280
+sequence of non-zero terms هذه ميزتها إنها
+
+307
+00:23:18,280 --> 00:23:21,760
+بيلزمهاش طبعا زي اللي جابلها بيلزمها الأولى
+
+308
+00:23:21,760 --> 00:23:25,920
+بيلزمها ال comparison test بيلزمها تقارن بسيريز
+
+309
+00:23:25,920 --> 00:23:30,920
+أخرى الان الانثرويد test وال ratio test تقارن
+
+310
+00:23:30,920 --> 00:23:35,790
+بنفسهايعني من داخل نفسها بتقدر تعرف اللي هو ..
+
+311
+00:23:35,790 --> 00:23:38,810
+اللي هي بطريقة معينة تعرف إن هي converged ولا
+
+312
+00:23:38,810 --> 00:23:42,810
+diverse يعني الآن Fx بسوء Xn is a sequence of non
+
+313
+00:23:42,810 --> 00:23:43,910
+-zero elements
+
+314
+00:23:46,750 --> 00:23:51,010
+of R and there is a positive number R أصغر من واحد
+
+315
+00:23:51,010 --> 00:23:55,730
+and a natural number K such that Xn زائد واحد على
+
+316
+00:23:55,730 --> 00:23:59,950
+Xn أصغر سوء R for N أكبر سوء K then the summation
+
+317
+00:23:59,950 --> 00:24:04,030
+Xn is absolutely convergent يعني الآن جيت انت لجيت
+
+318
+00:24:04,030 --> 00:24:08,310
+Xn زائد واحد على Xnاللي جيتها دايماً أصغر أوي ساوي
+
+319
+00:24:08,310 --> 00:24:12,130
+R والـ R أصغر strictly من مين؟ من واحد يعني دايماً
+
+320
+00:24:12,130 --> 00:24:15,830
+ال ratio هذا اللي بعده على اللي جابله اللي بعد على
+
+321
+00:24:15,830 --> 00:24:19,870
+اللي جاب اللي جيته أصغر معناته أنه صارت اللي هي
+
+322
+00:24:19,870 --> 00:24:23,890
+أشمالها عمالها بتصغر ال sequence كل ما ماشيت قدام
+
+323
+00:24:23,890 --> 00:24:27,330
+بيصير اللي ورا ع اللي قدام أصغر من واحد اللي ورا ع
+
+324
+00:24:27,330 --> 00:24:31,570
+اللي قدام أصغر من واحد يعني واضح أنه في اللي هو في
+
+325
+00:24:31,570 --> 00:24:36,410
+ال submission للـ XN is absolutely convergentلأن
+
+326
+00:24:36,410 --> 00:24:39,570
+بيقول if there exists a natural number k such that
+
+327
+00:24:39,570 --> 00:24:44,650
+بعده بيصير تصرفها ان xn زي 1 على xn هيكون أكبر
+
+328
+00:24:44,650 --> 00:24:48,350
+ويسوء 1 مدام أكبر ويسوء 1 معناته صار اللي هو كل
+
+329
+00:24:48,350 --> 00:24:51,890
+مامشيت قدام ال term بيكبر مثلا بيكبر ال term نفسه
+
+330
+00:24:51,890 --> 00:24:55,170
+إذا ال limit مش هيروح للصفر إذا معناته انه صارت ال
+
+331
+00:24:55,170 --> 00:25:01,530
+series divergent طيب ال proof خلينا نبرهن ايهif 6
+
+332
+00:25:01,530 --> 00:25:06,550
+holds يعني لو هو كانت هذا متحقق then by induction
+
+333
+00:25:06,550 --> 00:25:12,590
+one can see that for M أكبر أوي ساوية واحد K X K M
+
+334
+00:25:12,590 --> 00:25:18,890
+أصغر أوي ساوية أرقص M X K بتصور مش صعب إثبات هذه
+
+335
+00:25:18,890 --> 00:25:24,370
+for عندي خد X ال induction عالميا for M أكبر أوي
+
+336
+00:25:24,370 --> 00:25:32,360
+ساوية واحد على Mاللي هان بيصير xk زائد واحد اللي
+
+337
+00:25:32,360 --> 00:25:37,820
+هو xk زائد واحد هنا لإنها بتتحقق من k وطالع k زائد
+
+338
+00:25:37,820 --> 00:25:45,920
+واحد بيصير على ال xk يعني أصغر ساوي R في xk درم
+
+339
+00:25:45,920 --> 00:25:52,980
+التفرق الطرفين في وسطين xk إذن هذه صحيحةR M في
+
+340
+00:25:52,980 --> 00:25:56,020
+حالة الواحد صحيحة في حالة ال M ساو واحد الان
+
+341
+00:25:56,020 --> 00:26:01,420
+suppose that this true for M بدا تبت صحيتها for me
+
+342
+00:26:01,420 --> 00:26:08,360
+in M زائد واحد X K زائد M زائد واحد بدا تبت صحيتها
+
+343
+00:26:08,360 --> 00:26:12,940
+في حالة ال M زائد واحد اللي هو حسب اللي هنا اللي
+
+344
+00:26:12,940 --> 00:26:21,080
+أصغر أو ساوي ال Rثمين في اللي هي هنا N زائد واحد S
+
+345
+00:26:21,080 --> 00:26:28,160
+زائد واحد K M K زائد M K زائد M اذا R في absolute
+
+346
+00:26:28,160 --> 00:26:34,280
+value X K زائد M ماشي لان و بما ان هذا true for M
+
+347
+00:26:34,280 --> 00:26:38,840
+يعني هذا متحققه اذا من هنا ب hypothesis induction
+
+348
+00:26:38,840 --> 00:26:47,440
+بيصير R في R أس Mفي XK Y ساوية R أقصى M زايد واحد
+
+349
+00:26:47,440 --> 00:26:54,500
+في XK يعني صارت هذه صحيحة for M زايد واحد إذا صارت
+
+350
+00:26:54,500 --> 00:26:59,440
+صحيحة لكل M إذا هذه دائما صحيحة لأي M أكبر وساوية
+
+351
+00:26:59,440 --> 00:27:03,120
+واحد في ضوء العلاقة اللي هي 6 صحيحة
+
+352
+00:27:06,690 --> 00:27:13,130
+إذاً هذا لكل M أكبر أو يساوي واحد عندي لكل N أكبر
+
+353
+00:27:13,130 --> 00:27:17,350
+أو يساوي K الان
+
+354
+00:27:17,350 --> 00:27:27,330
+شيلي ال K زائد M وحط مكانها N يعني N بتساوي K زائد
+
+355
+00:27:27,330 --> 00:27:36,860
+M بصير هذه X Nأثر أو يساوي الـ M بتساوي N ناقص K و
+
+356
+00:27:36,860 --> 00:27:42,100
+X K زي ما هي X K لأنه شيلت ال N و حطيت مكانها K
+
+357
+00:27:42,100 --> 00:27:46,100
+زائد M و ال N طبعا اللي هي بتساوي K زائد M أكيد
+
+358
+00:27:46,100 --> 00:27:50,400
+أكبر أو يساوي K إذن هذه اللي هي صحيحة إذن صار عندي
+
+359
+00:27:50,400 --> 00:27:56,340
+الآن اللي عشان بعد شوية هتستخدمها صار عندي الآن ال
+
+360
+00:27:56,340 --> 00:28:03,180
+absolute valueللـ Xn أصغر أو يساوي R أُس N ناقص K
+
+361
+00:28:03,180 --> 00:28:10,180
+في X K ماشي الحال هذا لكل N أكبر أو يساوي إيش K
+
+362
+00:28:10,180 --> 00:28:19,740
+طيب نكمل للبرهان الـ N summation لل R أُس N
+
+363
+00:28:19,740 --> 00:28:20,660
+converts
+
+364
+00:28:23,610 --> 00:28:29,250
+لأن الار مالها بين صفر و واحد مادام هذي متغيرت
+
+365
+00:28:29,250 --> 00:28:33,450
+طبعا هذا term مجرد عدد يعنى term لأنه عند ك كهذا
+
+366
+00:28:33,450 --> 00:28:37,390
+هو اشي fixed يعني هو عبارة عن عدد والمتغير من الان
+
+367
+00:28:37,390 --> 00:28:44,510
+هذه اللي أنا ال summation لها للار الناقص كيعني بس
+
+368
+00:28:44,510 --> 00:28:48,670
+بنشيل K من ال terms مش مشكلة بتضل اللي هو converge
+
+369
+00:28:48,670 --> 00:28:52,270
+اللي هي summation R أُس N converge ثم summation
+
+370
+00:28:52,270 --> 00:28:56,430
+أُس R N ناقص K كيفيكس number عبارة عن converge ثم
+
+371
+00:28:56,430 --> 00:28:59,530
+صارت هذه ال series converge من باب أولى لل series
+
+372
+00:28:59,530 --> 00:29:02,670
+اللي أصغر منها اللي هتكون converge ثم صارت عندي
+
+373
+00:29:02,670 --> 00:29:05,070
+summation absolute value converge او بمعنى اخر
+
+374
+00:29:05,070 --> 00:29:12,450
+summation XN is absolutely convergent الان نيجيلأ
+
+375
+00:29:12,450 --> 00:29:18,050
+الجزء الثاني الان إذا كانت اللي هي سبعة holes سبعة
+
+376
+00:29:18,050 --> 00:29:21,970
+هي سبعة شايفينها هي سبعة اللي هو ال XN زائد واحد
+
+377
+00:29:21,970 --> 00:29:28,990
+على XN أكبر أو ساوى واحد لكل N أكبر أو ساوى مين
+
+378
+00:29:28,990 --> 00:29:36,420
+أكبر أو ساوى K كلام مشابهكلام مشابه if 7 holds
+
+379
+00:29:36,420 --> 00:29:41,900
+then by induction one can see that xkm أكبر أو
+
+380
+00:29:41,900 --> 00:29:46,880
+يساوي xk for m بساوي واحد و بعدين it is true for m
+
+381
+00:29:46,880 --> 00:29:49,480
+then it is true for m زائد واحد و زي ما عملت قبل
+
+382
+00:29:49,480 --> 00:29:54,170
+بشوية هتلاجوها بكل سهولة تطلعالان خد ال limit هذا
+
+383
+00:29:54,170 --> 00:29:58,690
+الان هذا صحيح لكل M أكبر أو يساوي واحد الان خد ال
+
+384
+00:29:58,690 --> 00:30:01,630
+limit as M goes to infinity بيصير أكبر أو يساوي
+
+385
+00:30:01,630 --> 00:30:05,090
+اللي هو المقدار هذا والمقدار هذا strictly أكبر من
+
+386
+00:30:05,090 --> 00:30:09,970
+100 من 0 لأن ال terms اللي عندي كلها لاتساوي 0 من
+
+387
+00:30:09,970 --> 00:30:14,930
+عند K وطالع اذا انتر عندي اللي هو limit ال Xn اللي
+
+388
+00:30:14,930 --> 00:30:20,490
+هو أكبر من 0 and so summation لل Xn is divergent
+
+389
+00:30:21,110 --> 00:30:26,670
+طيب، نريد الان لإيه الـ Corollary الأخيرة في
+
+390
+00:30:26,670 --> 00:30:32,050
+محاضرة اليوم اللي هي بتقول ليت X بسوء XN بيه
+
+391
+00:30:32,050 --> 00:30:36,790
+Sequence in R and Setواضح انه بيعطي اللي هو عادي و
+
+392
+00:30:36,790 --> 00:30:38,990
+بعدين limit عادي و بعدين limit و في ال ratio test
+
+393
+00:30:38,990 --> 00:30:42,410
+نفس الاشي بده ياخد limit ال exant زائد واحد على ال
+
+394
+00:30:42,410 --> 00:30:47,410
+exant بساوي R و الناس هتميل في الحلول في معظمها
+
+395
+00:30:47,410 --> 00:30:51,270
+اللي هي limits whenever the limit exist إذا كانت
+
+396
+00:30:51,270 --> 00:30:55,230
+ال limit هذه exist بنيجيthen the series summation
+
+397
+00:30:55,230 --> 00:30:58,630
+xn converges أو absolutely convergent إذا كان آر
+
+398
+00:30:58,630 --> 00:31:02,210
+أصغر من واحد وdivergent إذا كانت يشملها أكبر من
+
+399
+00:31:02,210 --> 00:31:06,110
+واحد يعني بناخد limit xn زائد واحد على xn absolute
+
+400
+00:31:06,110 --> 00:31:09,110
+value طبعا إذا كانت positive terms على طول بدون
+
+401
+00:31:09,110 --> 00:31:13,780
+absolute values طلع أن دي limit موجودما دام اطلع
+
+402
+00:31:13,780 --> 00:31:18,300
+ال limit موجود في عندي حكم إذا كان اللي هو أكبر من
+
+403
+00:31:18,300 --> 00:31:21,780
+واحد diverse إذا كان أصغر من واحد converge إذا
+
+404
+00:31:21,780 --> 00:31:26,220
+بيساوي واحد معناته the test fails وبنبحث اللي عن
+
+405
+00:31:26,220 --> 00:31:30,440
+test آخر طيب الآن suppose that limit xn زاد واحد
+
+406
+00:31:30,440 --> 00:31:33,300
+على xn as n goes to infinity بيساوي R أصغر من مين
+
+407
+00:31:33,300 --> 00:31:38,410
+من واحدبنفس الطريقة اللي عملناها قبل بشوية في
+
+408
+00:31:38,410 --> 00:31:44,230
+الأول let R1 satisfies R1 أكبر من R أصغر من 1 then
+
+409
+00:31:44,230 --> 00:31:48,810
+اللي هو لأن طبيعي between any two real numbers فيه
+
+410
+00:31:48,810 --> 00:31:53,770
+real number سميته مين؟ R1 الآن بما أن ال limit هذا
+
+411
+00:31:53,770 --> 00:31:57,370
+بيساوي R يدل كل إيبسلون أكبر من 0 من ضمن مين
+
+412
+00:31:57,370 --> 00:32:02,760
+الإيبسلون اللي بدأ أخدها؟ R1-RThen for epsilon
+
+413
+00:32:02,760 --> 00:32:07,280
+بساوة R واحد ناقص R أكبر من سفر there exists K
+
+414
+00:32:07,280 --> 00:32:10,260
+elements in N such that ال absolute value لهذا
+
+415
+00:32:10,260 --> 00:32:13,160
+ناقص هذا أصغر من مين من ال epsilon هي R واحد ناقص
+
+416
+00:32:13,160 --> 00:32:18,180
+مين ناقص R هذا صحيح لكل مين لكل N أكبر أو ساوة K
+
+417
+00:32:18,800 --> 00:32:23,600
+الآن نفردها هذه بس بتاخد الجهة اللي على اليمين هي
+
+418
+00:32:23,600 --> 00:32:27,420
+اللي بتمنى اللي هو صار عندى xn زائد واحد على xn
+
+419
+00:32:27,420 --> 00:32:31,540
+أصغر من r واحد ناقص r ولمّا تجيب هذا على الجهة
+
+420
+00:32:31,540 --> 00:32:34,240
+الثانية بعد ما فكرا absolute value بصير r ويساوي
+
+421
+00:32:34,240 --> 00:32:39,400
+ايش بتساوي؟ ويساوي بساوي r واحدالان و تساوي R واحد
+
+422
+00:32:39,400 --> 00:32:44,620
+اذا اللي هي .. اللي هيكون عندى اللي بال ..
+
+423
+00:32:44,620 --> 00:32:47,480
+بالنظرية اللي هي تسعة اتنين خمسها هتطلع عندى
+
+424
+00:32:47,480 --> 00:32:51,280
+الاصابيش ال absolute value اكسن اشمالها is
+
+425
+00:32:51,280 --> 00:32:56,110
+absolutely convergentهيطلع عندي summation للـ xn
+
+426
+00:32:56,110 --> 00:32:59,350
+is absolutely convergent اللي هي من نظرية تسعة
+
+427
+00:32:59,350 --> 00:33:02,450
+اتنين خمسة لإنه صار عندي ال absolute value لـ xn
+
+428
+00:33:02,450 --> 00:33:07,750
+زائد واحد على xn أصغر من رقم أصغر من واحد لكل n
+
+429
+00:33:07,750 --> 00:33:11,710
+أكبر سوى k من عند k وطالع بمعنى آخر صار عندي اللي
+
+430
+00:33:11,710 --> 00:33:15,530
+هي ال series is convergent لإنه هذا أصلا corollary
+
+431
+00:33:15,530 --> 00:33:21,830
+للي جابلها الآنودناخد اللي هو الجزء الثاني من اللي
+
+432
+00:33:21,830 --> 00:33:25,470
+هي ال .. ال .. ال .. البرهان اللي هو اللي بتعلق في
+
+433
+00:33:25,470 --> 00:33:28,330
+الجزء الثاني من ال Corollary بدنا نفترض انه limit
+
+434
+00:33:28,330 --> 00:33:33,390
+لل Xn زائد واحد ع ال Xn اللي هو بساوي R أكبر من
+
+435
+00:33:33,390 --> 00:33:37,910
+واحد وبدنا نشوف اللي هو كيف diverse يعني بدأ افترض
+
+436
+00:33:37,910 --> 00:33:40,670
+انه limit limit
+
+437
+00:33:42,720 --> 00:33:46,740
+Xn زائد واحد على Xn as n جثه infinity اللي هو
+
+438
+00:33:46,740 --> 00:33:51,940
+إجماله عبارة عن رقم اللي هو أكبر من واحد نسميها R
+
+439
+00:33:51,940 --> 00:33:58,260
+يساوي R أكبر من واحد ونشوف كيف أن هو عندي اللي هي
+
+440
+00:33:58,260 --> 00:34:04,040
+diverse الآنخد الـ Epsilon حلو خد Epsilon for
+
+441
+00:34:04,040 --> 00:34:09,560
+Epsilon for Epsilon بساوي R ناقص واحد أكبر من سفر
+
+442
+00:34:09,560 --> 00:34:13,220
+there exists K element in N such that for every N
+
+443
+00:34:13,220 --> 00:34:19,000
+أكبر وسوء K بطلع عنده هو XN زائد واحد على XN
+
+444
+00:34:19,510 --> 00:34:25,650
+absolute value ناقص الـ R أكبر من أصغر من مين من
+
+445
+00:34:25,650 --> 00:34:30,190
+إبسلون اللي هي عبارة عن R ناقص واحد هي ال إبسلون
+
+446
+00:34:30,190 --> 00:34:33,130
+اللي أخدت R ناقص واحد أو زي ما هو عاملها هان أصغر
+
+447
+00:34:33,130 --> 00:34:36,550
+من هيها أصغر من R minus واحد اللي هي الإبسلون اللي
+
+448
+00:34:36,550 --> 00:34:40,570
+هان فوق فوق اللي هان مش بيهمنيش الجهة اللي هان
+
+449
+00:34:40,570 --> 00:34:43,850
+بيهمني الجهة الثانية عكس اللي أولانياللي عن حيط
+
+450
+00:34:43,850 --> 00:34:47,790
+لعندي xn زائد واحد على xn أكبر من واحد اللي هي r
+
+451
+00:34:47,790 --> 00:34:50,870
+ناقص r minus واحد اللي هي ايش بتطلع واحد صار هذا
+
+452
+00:34:50,870 --> 00:34:54,030
+المقدار أكبر من واحد و بال test اللي قبل بشوية ال
+
+453
+00:34:54,030 --> 00:34:57,790
+theorem تسعة اتنين خمسة بما أنه صار هذا من عند n
+
+454
+00:34:57,790 --> 00:35:01,670
+أكبر يساوي k وطالع من عند k وطالع طلع عندي هذا
+
+455
+00:35:01,670 --> 00:35:05,050
+أكبر من واحد معناته صارت ال information هذه is
+
+456
+00:35:05,050 --> 00:35:10,340
+divergentوطبعا اللي دايما بنقولها دايما اللي هي no
+
+457
+00:35:10,340 --> 00:35:14,320
+conclusion و ال R بتساوي واحد اللي هو ممكن تكون
+
+458
+00:35:14,320 --> 00:35:17,080
+conversion و ممكن تكون diversion عشان هذا الأساس
+
+459
+00:35:17,080 --> 00:35:22,160
+بنقول ال test fail في حالة ال R بتساوي واحد و نبحث
+
+460
+00:35:22,160 --> 00:35:26,900
+عن test آخر و الآن بنيجي ل اللي هو المرة الجاية ان
+
+461
+00:35:26,900 --> 00:35:30,440
+شاء الله بناخد ال integral test و إلى لقاء آخر
+
+462
+00:35:30,440 --> 00:35:31,400
+والسلام عليكم و رحمه الله
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/qX3DwVzbv6I.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/qX3DwVzbv6I.srt
new file mode 100644
index 0000000000000000000000000000000000000000..136586065a9e7ad3755ca510ff2009ed556fa606
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/qX3DwVzbv6I.srt
@@ -0,0 +1,2250 @@
+1
+00:00:01,920 --> 00:00:04,660
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,660 --> 00:00:07,640
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:07,640 --> 00:00:13,600
+أهله وصحبه أجمعين هذه هي المحاضرة الرقم 19 في مساق 
+
+4
+00:00:13,600 --> 00:00:18,980
+تحليل حقيقي 2 لطلاب وطالبات الجامعة الإسلامية كلية
+
+5
+00:00:18,980 --> 00:00:25,600
+العلوم قسم الرياضيات. اليوم هنتحدث عن الجزء الثالث 
+
+6
+00:00:25,600 --> 00:00:29,980
+من المادة. الجزء الأول تحدثنا عن اللي هو الـ
+
+7
+00:00:29,980 --> 00:00:33,960
+differentiation أو الـ derivative وما يتعلق بها.
+
+8
+00:00:33,960 --> 00:00:38,160
+طبعا الجزء الثاني تعرّفنا على ال integration وما 
+
+9
+00:00:38,160 --> 00:00:43,320
+يتعلق به. الآن هنحكي عن اللي هو الـ sequence of 
+
+10
+00:00:43,320 --> 00:00:48,650
+functions اللي هي المتتابعات أو المتتاليات اللي هي 
+
+11
+00:00:48,650 --> 00:00:53,010
+بيكون عنصر المتتابعة أو المتتالية هو عبارة عن دالة.
+
+12
+00:00:53,010 --> 00:00:58,350
+وحنعرف العلاقة بين اللي هو الأنواع الـ convergence
+
+13
+00:00:58,350 --> 00:01:05,630
+اللي للدوال واللي هي تأثير هذا النوع من الـ
+
+14
+00:01:05,630 --> 00:01:10,730
+convergence على إنه اللي هو يدخل هذا الـ limit لجوة
+
+15
+00:01:10,730 --> 00:01:14,650
+ال integration أو لو جوة الـ .. الناتج هيكون اللي 
+
+16
+00:01:14,650 --> 00:01:17,750
+هو الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+17
+00:01:17,750 --> 00:01:17,770
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+18
+00:01:17,770 --> 00:01:18,110
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+19
+00:01:18,110 --> 00:01:18,530
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+20
+00:01:18,530 --> 00:01:19,010
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+21
+00:01:19,010 --> 00:01:26,890
+الـ الـ الـ الـ الـ الـ الـ
+
+22
+00:01:26,890 --> 00:01:28,030
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+23
+00:01:28,030 --> 00:01:28,210
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+24
+00:01:28,210 --> 00:01:31,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ إلى continuity
+
+25
+00:01:31,480 --> 00:01:38,400
+للـ limit أو اللي هو الـ differentiability اللي هو
+
+26
+00:01:38,400 --> 00:01:41,240
+الـ sequence of functions هل تؤدي إلى 
+
+27
+00:01:41,240 --> 00:01:43,820
+differentiability و الـ integrability و الأخر و 
+
+28
+00:01:43,820 --> 00:01:46,040
+مين اللي بيقدر يحافظ على هيك؟ و هل في counter 
+
+29
+00:01:46,040 --> 00:01:51,160
+examples تضحط أو اللي هو في نظريات اتبرهن. اليوم بدنا
+
+30
+00:01:51,160 --> 00:01:55,140
+نتعرف على اللي هو أو بدنا نحكي عن شغلتين اللي هي
+
+31
+00:01:55,140 --> 00:01:59,700
+pointwise and uniform convergence نشوف شو معناه
+
+32
+00:01:59,700 --> 00:02:02,720
+pointwise convergence وشو معناه uniform
+
+33
+00:02:02,720 --> 00:02:08,660
+convergence وما الفرق بينهما. نيجي الآن لـ definition
+
+34
+00:02:08,660 --> 00:02:12,580
+let FN هذا عنوان محاضرتنا زي ما قلنا point twice 
+
+35
+00:02:12,580 --> 00:02:15,700
+and uniform convergence وعنوان الشطر كله
+
+36
+00:02:15,700 --> 00:02:20,160
+sequences of functions. الآن definition let FN be a 
+
+37
+00:02:20,160 --> 00:02:24,020
+sequence of functions on A subset من R to R ماشي
+
+38
+00:02:24,020 --> 00:02:27,840
+الحال الآن نفترض أن FN عبارة عن sequence of 
+
+39
+00:02:27,840 --> 00:02:32,000
+functions اللي هي من domain A جزء من R لأن كل 
+
+40
+00:02:32,000 --> 00:02:36,550
+شغلنا في R احنا لعند مين؟ لعند R. هذه اللي هي 
+
+41
+00:02:36,550 --> 00:02:39,710
+sequence of functions يعني في عندي F1 وفي عندي F2
+
+42
+00:02:39,710 --> 00:02:44,410
+وفي عندي F3 وفي عندي F4 إلى ما لا نهاية من الدوال
+
+43
+00:02:44,410 --> 00:02:50,790
+عالمين على الـ subset من R. الآن بنجيء ولو جينا
+
+44
+00:02:50,790 --> 00:02:57,010
+فرضنا اللي هو عندنا function F من A note لعند مين
+
+45
+00:02:57,010 --> 00:03:02,830
+لعند الـ R. الـ A note مين هي؟ A note عبارة عن مجموعة
+
+46
+00:03:02,830 --> 00:03:08,210
+جزئية من مين؟ من الـ 6A اللي فوق. الآن بنقول we 
+
+47
+00:03:08,210 --> 00:03:14,550
+say that the sequence FN converts on Anote يعني 
+
+48
+00:03:14,550 --> 00:03:20,270
+converts عالميا على a note to f إذا كان لكل x 
+
+49
+00:03:20,270 --> 00:03:24,350
+element in A the sequence fn of x converts to f of 
+
+50
+00:03:24,350 --> 00:03:29,970
+x in R. لكل sequence لكل x element in A هو a note
+
+51
+00:03:30,750 --> 00:03:37,430
+بنقول الآن أنه F نحن نقول أن Fن تتعامل على A نوت
+
+52
+00:03:37,430 --> 00:03:48,490
+يعني بنقول Fن هذه الـ sequence تتعامل على F على A
+
+53
+00:03:48,490 --> 00:03:55,240
+نوت على مين؟ على A نوت. إذا كان لكل X element in A 
+
+54
+00:03:55,240 --> 00:04:00,280
+note على كل X element in A note بتطلع للـ F N of X
+
+55
+00:04:00,280 --> 00:04:07,560
+إيه أشمالها converge to mean to F of X. إذا هذا حدث
+
+56
+00:04:07,560 --> 00:04:13,380
+بنقول أن F N converge to F on A note. في الواقع 
+
+57
+00:04:13,380 --> 00:04:18,060
+point twice يعني نقطة نقطة. كيف نقطة نقطة؟ يعني الـ
+
+58
+00:04:18,060 --> 00:04:30,670
+Nx1 بتكون fn of x1 converts to f of x1. شكّلتنا x2 fn
+
+59
+00:04:30,670 --> 00:04:35,830
+of x2 converts to mean to f of x2 لكل نقطة على حدى
+
+60
+00:04:35,830 --> 00:04:40,150
+الـ fn of x بتروح لمين؟ للـ f of x. هذه بنسميها
+
+61
+00:04:40,150 --> 00:04:44,750
+pointwise convergence. طب كيف؟ ده إيش معناه احنا
+
+62
+00:04:44,750 --> 00:04:49,590
+بالـ Epsilon Delta Definition يعني وكأنه بنقول لكل
+
+63
+00:04:49,590 --> 00:04:56,890
+x إلمتين a0 limitF N of X as N goes to infinity
+
+64
+00:04:56,890 --> 00:05:05,860
+بساوي F of X. يعني لكل إبسلون هذا نحكي عن X محددة 
+
+65
+00:05:05,860 --> 00:05:11,620
+لكل إبسلون أكبر من سفر ولكل X element in A note
+
+66
+00:05:11,620 --> 00:05:15,740
+لأن أنا بحكي عن مين؟ عن الـ X هذه. there exists
+
+67
+00:05:15,740 --> 00:05:21,840
+Delta. الآن الـ Delta اللي لجيتها بتعتمد على إبسلون
+
+68
+00:05:21,840 --> 00:05:26,460
+و بتعتمد على الـ X لأن أنا بحكي عن X point محددة.
+
+69
+00:05:26,460 --> 00:05:30,300
+there exists .. arbitrary في الـ A note لكن fixed
+
+70
+00:05:31,000 --> 00:05:34,580
+there exists Delta بتعتمد عليه. طبعا احنا بدنا ما
+
+71
+00:05:34,580 --> 00:05:39,600
+نكتب Delta هنكتب K ليش؟ لأن Delta احنا متعرفين
+
+72
+00:05:39,600 --> 00:05:44,600
+عليها تعبر عن المسافة بين two numbers لكن الشيء
+
+73
+00:05:44,600 --> 00:05:48,300
+اللي بروح إلى ما لا نهاية بدنا نعبر عنه أو متفقين
+
+74
+00:05:48,300 --> 00:05:53,700
+نعبر عنه برقم يدل على القبر. إذا بنقول there exists 
+
+75
+00:05:53,700 --> 00:06:02,110
+K نسميه K of هيعتمد على Y و XElement in N such
+
+76
+00:06:02,110 --> 00:06:10,750
+that for every N أكبر أو يساوي هذا الـ K of Y و X
+
+77
+00:06:10,750 --> 00:06:19,530
+بكون عندي المسافة F N of X ناقص F of X أصغر من مين
+
+78
+00:06:19,530 --> 00:06:28,790
+من Y. إذن الـ N هذا معناه أن Fn of X بتروح للـ F of 
+
+79
+00:06:28,790 --> 00:06:33,790
+X pointwise. ليش pointwise؟ لأن الـ K اللي لاجيناها 
+
+80
+00:06:33,790 --> 00:06:39,250
+اعتمدت على القيمة الـ X اللي احنا عارفين اللي قلنا
+
+81
+00:06:39,250 --> 00:06:44,530
+عنه limit Fn of X ايش بتساوي؟ بتساوي F of X وهذا
+
+82
+00:06:44,530 --> 00:06:47,850
+اللي بختلف أصلا عن ال uniform convergence. ال
+
+83
+00:06:47,850 --> 00:06:53,560
+uniform convergence. ال K اللي بنلاجيها بتكون الـ K
+
+84
+00:06:53,560 --> 00:06:59,120
+اللي بنلاقيها هنلاقيها أصلا بتنفع على كل الإكسات
+
+85
+00:06:59,120 --> 00:07:02,660
+عشان الـ K هيك. في ال uniform convergence الـ K 
+
+86
+00:07:02,660 --> 00:07:06,580
+اللي بنلاقيها تعتمد بس على الـ Epsilon لكن بتنفع 
+
+87
+00:07:06,580 --> 00:07:12,840
+على كل الإكسات. عشان هيك فيش عندي أي مشكلة أنه اللي
+
+88
+00:07:12,840 --> 00:07:17,520
+هو تكون الـ K اللي هو أنه ال point wise
+
+89
+00:07:17,520 --> 00:07:22,400
+convergence اللي هو عبارة الـ .. الـ .. آسف ال
+
+90
+00:07:22,400 --> 00:07:25,700
+uniform convergence يؤدي إلى ال point twice لكن ال
+
+91
+00:07:25,700 --> 00:07:29,340
+point twice ليس شرطاً وحنشوف هذا الكلام بالتفصيل
+
+92
+00:07:29,340 --> 00:07:38,860
+قدام. أيوة يا أبو حسن فجأة لأ هانا فيش شيء لسه أه
+
+93
+00:08:27,530 --> 00:08:31,330
+إذا .. إذا يا جماعة هذا هو تعريف اللي هو الـ
+
+94
+00:08:31,330 --> 00:08:35,450
+pointwise convergence. نيجي الآن للي هي الأمثلة
+
+95
+00:08:35,450 --> 00:08:40,970
+خلّينا ناخد أول مثال. عندي نيجي ناخد اللي هو المثال
+
+96
+00:08:40,970 --> 00:08:49,310
+الأول let g n of x بساوة x أس n x element in R and 
+
+97
+00:08:49,310 --> 00:08:53,230
+n element in N show that g n of x هذه الدالة
+
+98
+00:08:53,230 --> 00:08:59,050
+converge pointwise to g of x على الفترة ناقص واحد
+
+99
+00:08:59,050 --> 00:09:02,770
+وواحد طبعا اللي هو open من عند الناقص واحد لعند
+
+100
+00:09:02,770 --> 00:09:08,040
+الواحد. الآن الـ g of x اللي متوقع انه اللي هو تكون 
+
+101
+00:09:08,040 --> 00:09:11,000
+الـ g of x converts لها هي عبارة عن g of x
+
+102
+00:09:11,000 --> 00:09:14,320
+بالساوية صفر إذا كانت x في الفترة من ناقص واحد لواحد
+
+103
+00:09:14,320 --> 00:09:19,360
+و بالساوية واحد في حالة الـ x بتساوي واحد. نشوف
+
+104
+00:09:19,360 --> 00:09:23,480
+كيف اللي هو اثبات اللي هي ان الـ limit هذه سهل اللي
+
+105
+00:09:23,480 --> 00:09:26,840
+بتساوي اللي هي limit الـ g of x بساوية الـ g of
+
+106
+00:09:26,840 --> 00:09:32,280
+x على الفترة المذكورة. الكلام هلأ جاي سهل ونشوف كيف
+
+107
+00:09:32,940 --> 00:09:37,160
+اللي هو نوجد هذه اللي هي أول شيء بيت الـ convergence
+
+108
+00:09:37,160 --> 00:09:44,360
+الآن في حالة الـ X عندي هنا في حالة الـ X عندي 
+
+109
+00:09:44,360 --> 00:09:48,820
+بتساوي واحد. ال GN of X اللي هي عبارة عن X أس n
+
+110
+00:09:48,820 --> 00:09:54,340
+مظبوط. ال X أس n اللي هي واحد بتصير عبارة عن جدّاش عن 
+
+111
+00:09:54,340 --> 00:09:58,400
+واحد. خلي بس واضح لكم الـ .. الـ ..
+
+112
+00:10:00,790 --> 00:10:07,310
+المثال يظهر كله عندكم. هي عندي الـ GN of X بساوي X
+
+113
+00:10:07,310 --> 00:10:13,050
+أس N. في حالة الـ X بيساوي 1، هيكون GN of 1 بيساوي
+
+114
+00:10:13,050 --> 00:10:17,630
+1 أس N اللي هو إيش؟ واحد. هذه دالة ثابتة أكيد
+
+115
+00:10:17,630 --> 00:10:21,830
+limited GN لما N تروح إلى ما لا نهاية اللي هو limit
+
+116
+00:10:21,830 --> 00:10:25,150
+الواحد اللي هو واحد. ثابت طيب. الآن لو كانت الـ X
+
+117
+00:10:25,150 --> 00:10:27,730
+في الفترة بيه ناقص واحد واحد يعني absolute بين
+
+118
+00:10:27,730 --> 00:10:31,920
+الـ X أصغر من واحد يعني كثير ماشي. إذا limit GN of
+
+119
+00:10:31,920 --> 00:10:36,320
+X as N goes to infinity بساوي limit X أس N لما N
+
+120
+00:10:36,320 --> 00:10:39,840
+تروح إلى ما لا نهاية. هذا الـ X بين الناقص واحد 
+
+121
+00:10:39,840 --> 00:10:43,220
+والواحد يعني كسر وكسر كل ما رفعته لأس بصغر بروح لـ
+
+122
+00:10:43,220 --> 00:10:47,700
+بساوي بساوي صفر لأن في حالة الـ absolute value للـ
+
+123
+00:10:47,700 --> 00:10:53,180
+X أكبر من واحد لأنه ليش بنبحث .. ب .. ب .. ب ..
+
+124
+00:10:53,180 --> 00:10:58,500
+احنا بدنا نبحث في برة للفترة لإنه أصلا الـ GN of X
+
+125
+00:10:59,470 --> 00:11:05,550
+معرفة على كل الـ R. آه بس برا اللي هي الفترة بناقص
+
+126
+00:11:05,550 --> 00:11:09,930
+واحد وواحد مش هيكون لها limit لسبب أنتو عارفينه
+
+127
+00:11:09,930 --> 00:11:12,830
+ليش هو؟ إنّه في حالة الـ absolute value X أكبر من 
+
+128
+00:11:12,830 --> 00:11:17,990
+واحد بيكون limit GN of X بيساوي limit X أس n الـ X 
+
+129
+00:11:17,990 --> 00:11:22,710
+عبارة عن اللي هي أشمالها قيمته اللي هو الـ absolute
+
+130
+00:11:22,710 --> 00:11:27,490
+value كبير. فالآن limit الـ X أس N هيكون إيه أشماله
+
+131
+00:11:27,490 --> 00:11:33,510
+does not converge does not converge الآن لإنه
+
+132
+00:11:33,510 --> 00:11:39,430
+بيصير إيه أشماله unbounded. طيب أكيد عارفين هذه
+
+133
+00:11:39,430 --> 00:11:42,730
+المعلومة. في حالة الـ X أكبر من واحد if X بساوي
+
+134
+00:11:42,730 --> 00:11:47,750
+سالب واحد. عند الواحد قلنا بيطلع له قيمة بين الواحد
+
+135
+00:11:47,750 --> 00:11:52,480
+والسالب واحد. طلع عنده قيمة Limit يعني لأن عند الـ X
+
+136
+00:11:52,480 --> 00:11:55,860
+بساوي سالب واحد بيصير هذا عبارة عن ناقص واحد 
+
+137
+00:11:55,860 --> 00:11:59,820
+أس n. ناقص واحد أس n اللي هي limit هذه مشهورة اللي هو
+
+138
+00:11:59,820 --> 00:12:02,880
+مثال على إنّه limit على bounded function و limit
+
+139
+00:12:02,880 --> 00:12:05,520
+اللي هي أشماله does not exist أو bounded sequence
+
+140
+00:12:05,520 --> 00:12:08,500
+و limit اللي هي does not exist. ال limit لهذه does 
+
+141
+00:12:08,500 --> 00:12:12,200
+not exist وعارفين أنتو ليش إذا صار عندي limit gn
+
+142
+00:12:12,200 --> 00:12:18,220
+of x بيساوي g of x في الفترة من ناقص واحد لعند مين
+
+143
+00:12:18,220 --> 00:12:23,220
+لعند الواحد حيث الـ g of x كما هي مذكورة أعلى إذا 
+
+144
+00:12:23,220 --> 00:12:26,540
+هذه مثال عالمين عن ال point wise convergence
+
+145
+00:12:26,540 --> 00:12:31,840
+وشوفنا كيف بنوجد ال point wise convergence طيب نيجي
+
+146
+00:12:31,840 --> 00:12:38,720
+لاللي هو مثال آخر برضه مثال يعني بتصور مثال سهل و
+
+147
+00:12:38,720 --> 00:12:43,760
+بتعرفوا تعملوه حتى لو سيبناه لكم لحالكم إيش بيقول
+
+148
+00:12:45,080 --> 00:12:51,960
+وعند الدالة إيش اسمها الدالة F of X بتساوي F of X
+
+149
+00:12:51,960 --> 00:12:58,400
+بتساوي اللي هو واحدة الان sign الان X زائد ان الان
+
+150
+00:12:58,400 --> 00:13:03,200
+هذه ال function sign function ماشي الحال بقول اثبت 
+
+151
+00:13:03,200 --> 00:13:08,490
+أن ال limit لها بيساوي ايه عشان بيساوي صفر الآن لكل
+
+152
+00:13:08,490 --> 00:13:11,530
+x² موجودة في الـ R إحنا بنحكي عن pointwise
+
+153
+00:13:11,530 --> 00:13:16,130
+convergence مدينة pointwise convergence خُدلي الآن 
+
+154
+00:13:16,130 --> 00:13:20,310
+هذه الـ function اللي هي fn of x زي ما هو مسميها
+
+155
+00:13:20,310 --> 00:13:24,210
+لأنها ترتبط بـ n اللي هي f1 of x واحدة، f2 of x
+
+156
+00:13:24,210 --> 00:13:27,710
+واحدة، f3 of x واحدة، طبعا متعود عنه في كل مرة n 
+
+157
+00:13:27,710 --> 00:13:30,010
+بواحد، n باتنين، n تلاتة، بتطلعلك عبارة عن
+
+158
+00:13:30,010 --> 00:13:32,350
+sequence of functions هذه الـ sequence of
+
+159
+00:13:32,350 --> 00:13:37,220
+functions الآن متوقعين احنا limit هي ايش يساوي صفر
+
+160
+00:13:37,220 --> 00:13:40,800
+يعني ال F of X ايش بتتساوي بساوي صفر شوف الآن
+
+161
+00:13:40,800 --> 00:13:46,340
+احسبلي ال F N of X ناقص F of X اللي هي عبارة عن 1/N
+
+162
+00:13:46,340 --> 00:13:51,500
+Sin N X زيادة هذه أكيد أصغر أو أصغر من 1 لأن الـ
+
+163
+00:13:51,500 --> 00:13:55,220
+Sin دائما أصغر أو أصغر من 1 إذا صار عندي اللي هي
+
+164
+00:13:55,220 --> 00:14:00,440
+هذه القيمة بين الصفر و بين 1 لـ N بدنا ال limit as
+
+165
+00:14:00,440 --> 00:14:03,660
+N goes to infinity هذه بتروح للصفر وهذه صفر إذا 
+
+166
+00:14:03,660 --> 00:14:07,120
+limit هذه as N goes to infinity بيساوي جداش بيساوي 
+
+167
+00:14:07,120 --> 00:14:12,220
+صفر أو بمعنى آخر limit F N of X بيساوي F of x فعلاً 
+
+168
+00:14:12,220 --> 00:14:16,020
+صار طالع عندي ال limit الـ 1/n الـ n sin n x زي n 
+
+169
+00:14:16,020 --> 00:14:20,740
+بيساوى اللي هو f of x اللي هي صفر إذا هدول مثلن
+
+170
+00:14:20,740 --> 00:14:24,460
+على pointwise convergence كيف نوددهم وهذه أمثلة
+
+171
+00:14:24,460 --> 00:14:29,580
+بسيطة يعني أخدنا زيها في اللي هو تحليل واحد أو حتى
+
+172
+00:14:29,580 --> 00:14:35,960
+في الcalculus الآن لما هلان a sequence of
+
+173
+00:14:35,960 --> 00:14:41,490
+functions fn of functions on A subset from R to R
+
+174
+00:14:41,490 --> 00:14:46,090
+converge to a function F on A note if and only if
+
+175
+00:14:46,090 --> 00:14:49,970
+for every Y أكبر من 0 and for every X element in A
+
+176
+00:14:49,970 --> 00:14:54,230
+there exists K element in N such that الـ K مين
+
+177
+00:14:54,230 --> 00:14:59,390
+هي؟ KY of X قصده if N أكبر سوى K then FN of X ناقص
+
+178
+00:14:59,390 --> 00:15:02,210
+F of X أصغر من Y هذا قلته أصلا هذا من التعريف
+
+179
+00:15:02,210 --> 00:15:06,510
+مباشرة بما أنه اللي هو عندي الـ FN 
+
+180
+00:15:09,190 --> 00:15:16,670
+converges pointwise to F on اللي هو main A إيش
+
+181
+00:15:16,670 --> 00:15:21,390
+معناته هذا؟ معناته for every X element in A هذا 
+
+182
+00:15:21,390 --> 00:15:26,350
+بكافئ for every X element in A limit F on of X لما 
+
+183
+00:15:26,350 --> 00:15:31,150
+on تروح لما لنهاية بسوء F of X مظبوط؟ ده كل X وين 
+
+184
+00:15:31,150 --> 00:15:33,930
+موجودة في الـA أو وين و تحسب ما اللي بدناها هذا
+
+185
+00:15:33,930 --> 00:15:37,580
+بكافئ أن اللي هو بالـ Epsilon Delta Definition for
+
+186
+00:15:37,580 --> 00:15:41,500
+every X element in A for every Y أكبر من 0 there
+
+187
+00:15:41,500 --> 00:15:45,520
+exists K الآن الـ K هتعتمد عالمياً على الـ Epsilon
+
+188
+00:15:45,520 --> 00:15:51,120
+والـ X element in N such that for every N أكبر 
+
+189
+00:15:51,120 --> 00:15:54,740
+يساوي K اللي هي مين هذه؟ اللي هي K Epsilon و X 
+
+190
+00:15:54,740 --> 00:16:01,810
+هيكون عندي الـ F N of X ناقص f of x أصغر من مين من
+
+191
+00:16:01,810 --> 00:16:06,090
+إبسلون وهذه اللي هي مين قلنا ما هذا الأصل لو remark
+
+192
+00:16:06,090 --> 00:16:10,050
+بتنفع وخلاص أساس أنه مباشرة من التعريف الآن 
+
+193
+00:16:10,050 --> 00:16:15,370
+definition لأن a sequence fn of functions a subset
+
+194
+00:16:15,370 --> 00:16:22,450
+من R to R converts الآن إيش uniformly on a نقطة
+
+195
+00:16:22,450 --> 00:16:27,740
+subset من R to a function f من a نقطة عند R if الآن 
+
+196
+00:16:27,740 --> 00:16:31,420
+convergence uniformly قلت أنا قبل بشوية أو في 
+
+197
+00:16:31,420 --> 00:16:35,520
+بداية المحاضرة إن ال convergence uniformly معناته
+
+198
+00:16:35,520 --> 00:16:40,480
+الـ K اللي لجيناها إيش مالها بتنفع لكل ال X يعني ما
+
+199
+00:16:40,480 --> 00:16:44,020
+بنقولش لكل X element نهي أو لكل Y أكبر من 0 there
+
+200
+00:16:44,020 --> 00:16:49,740
+exists K لأ بنقول لكل إبسلون there exist K such
+
+201
+00:16:49,740 --> 00:16:56,380
+that لكل N أكبر يساوي K و لكل X هذه بتنفع يعني ال
+
+202
+00:16:56,380 --> 00:17:00,540
+K اللي جيتها بس بتعتمد على مين؟ على ال إبسلون وهذا
+
+203
+00:17:00,540 --> 00:17:04,120
+معناه ال uniform convergence وهي اللي مكتوب هنا
+
+204
+00:17:04,120 --> 00:17:09,420
+أن بنقول Fn sequence of functions من A على A 
+
+205
+00:17:09,420 --> 00:17:12,680
+subset من R converges uniformly on A node subset
+
+206
+00:17:12,680 --> 00:17:17,660
+من A من A to a function F من A نقطة عند R if for
+
+207
+00:17:17,660 --> 00:17:21,900
+every epsilon أكبر من 0 there exists K of epsilon 
+
+208
+00:17:21,900 --> 00:17:25,620
+تعتمد بس على مين على إبسلون such that if N أكبر 
+
+209
+00:17:25,620 --> 00:17:31,720
+سوء K and X element in A هذا بيكون أصغر من مين من 
+
+210
+00:17:31,720 --> 00:17:36,170
+إبسلون هذا التعبير لما أقول لكل إبسلون there exists
+
+211
+00:17:36,170 --> 00:17:41,250
+K يعني الـ K تعتمد بس على مين على إبسلون وبعدين
+
+212
+00:17:41,250 --> 00:17:46,590
+كل هذا اللي هي هنا بتنفع لكل الـ N أكبر من K و لكل 
+
+213
+00:17:46,590 --> 00:17:50,190
+الـ X elements in R لكن لو أقول لكل إبسلون أكبر من
+
+214
+00:17:50,190 --> 00:17:53,730
+صفرهم لكل X there exists K الـ K هتعتمد على
+
+215
+00:17:53,730 --> 00:17:56,790
+الإبسلون و على الـ X في الـ point twice هنا لكل
+
+216
+00:17:56,790 --> 00:18:00,050
+إبسلون بيلاجي K بس بتعتمد على مين على الإبسلون إذا 
+
+217
+00:18:00,050 --> 00:18:05,050
+if the sequence of N converge uniformly to some
+
+218
+00:18:05,050 --> 00:18:09,050
+function f على الـ A note إذا أكيد A شمالها this
+
+219
+00:18:09,050 --> 00:18:13,470
+sequence converges pointwise لأنه أنت أصلا نور على
+
+220
+00:18:13,470 --> 00:18:17,550
+نور في حالة الـ uniform لجيت K of إبسلون الآن هذا
+
+221
+00:18:17,550 --> 00:18:22,030
+الـ K of إبسلون هنا بس بيقول لي لجيلي K تعتمد في
+
+222
+00:18:22,030 --> 00:18:25,210
+ال pointwise تعتمد على الإبسلون تعتمد على ال X
+
+223
+00:18:25,210 --> 00:18:29,830
+ما تفرجش عندي أنا عشان pointwise بس لجيلي ال K بحيث
+
+224
+00:18:29,830 --> 00:18:33,750
+إنه لكل N أكبر و كده هيكون هذا متحقق طيب مانا في ال
+
+225
+00:18:33,750 --> 00:18:36,750
+uniform اللي ملاقيها وأصلا ملاقيها مجردة بتنفع 
+
+226
+00:18:36,750 --> 00:18:41,790
+على كل ال X إذا أكيد بتنفع على كل X عليها حدها إذا
+
+227
+00:18:41,790 --> 00:18:46,330
+ال uniform convergence يؤدي إلى ال point wise لكن 
+
+228
+00:18:46,330 --> 00:18:49,890
+ال converts need not to be true in general أكيد 
+
+229
+00:18:49,890 --> 00:18:54,890
+لأن وإلا ليش إحنا نحكي عن اثنين متساويين و
+
+230
+00:18:54,890 --> 00:19:02,970
+المكان طيب نيجي الآن اللي مال اللي عندي أسيقونس fn
+
+231
+00:19:02,970 --> 00:19:06,970
+of functions on A subset من R to R بدون في التعريف
+
+232
+00:19:06,970 --> 00:19:10,650
+الآن، بيقول لـ fn a sequence of functions fn on A 
+
+233
+00:19:10,650 --> 00:19:14,690
+subset من R to R does not converge uniformly in O
+
+234
+00:19:14,690 --> 00:19:19,130
+naught to a function f من A naught عند R if and
+
+235
+00:19:19,130 --> 00:19:22,650
+only if for every أكبر من سفر، there exists a
+
+236
+00:19:22,650 --> 00:19:30,220
+subsequence fnk of fn and أسيقونس xk in a نوت such
+
+237
+00:19:30,220 --> 00:19:34,720
+that fnk of xk ناقص f of xk أكبر أو يساوي y نوت
+
+238
+00:19:34,720 --> 00:19:43,220
+لكل k element ان نيجي نطلع لهذه ونشوف كيف بدنا
+
+239
+00:19:43,220 --> 00:19:51,640
+نبرهنها الآن 
+
+240
+00:19:51,640 --> 00:19:58,880
+إحنا اتفجنا قبل بشوية أن fn converges uniformly to
+
+241
+00:19:58,880 --> 00:20:03,240
+F هذه رمزها A شمالها converges uniformly سهم واحد
+
+242
+00:20:03,240 --> 00:20:08,820
+إصطلاحا هذا مع بعض سهم واحد بنقصد فيه ال bond
+
+243
+00:20:08,820 --> 00:20:14,000
+twice سهمين بنقصد فيهم uniformly convergence فان
+
+244
+00:20:14,000 --> 00:20:18,400
+convergence uniformly on A أو بسميه هو A ولا A not
+
+245
+00:20:18,400 --> 00:20:24,460
+on A not الآن الـ function f من أين؟ f من a note
+
+246
+00:20:24,460 --> 00:20:29,980
+لعند اللي هي hr و الـ fn sequence من a لعند r يعني 
+
+247
+00:20:29,980 --> 00:20:33,020
+a note جزء من مين اللي هو قد تكون اللي هي مين كل 
+
+248
+00:20:33,020 --> 00:20:35,820
+الـ a المهم أخدها a note subset من a على أساس اللي
+
+249
+00:20:35,820 --> 00:20:39,920
+هو يحكي in general إذن fn converges الـ f on a
+
+250
+00:20:39,920 --> 00:20:44,480
+note if and only if هذا معناه if and only if for
+
+251
+00:20:44,480 --> 00:20:49,060
+every epsilon أكبر من 0 there exists k تعتمد على
+
+252
+00:20:49,060 --> 00:20:55,490
+الـ epsilon element in N such that for every n أكبر
+
+253
+00:20:55,490 --> 00:21:01,510
+أو سوء k و for every x element in A0 مكون عندي fn
+
+254
+00:21:01,510 --> 00:21:08,470
+of x ناقص f of x أصغر من مين من إبسلون هذا معناة
+
+255
+00:21:08,470 --> 00:21:12,250
+الـ Uniform Convergence بدي أنفي اللي أنا بقول لـ
+
+256
+00:21:12,250 --> 00:21:17,090
+fn يعني هو كأنني بتعمله proof proof لهمين؟ لهذه مش 
+
+257
+00:21:17,090 --> 00:21:23,260
+ال proof لهذه proof لهذه يعني الـ fn Does not
+
+258
+00:21:23,260 --> 00:21:28,800
+converge uniformly لمن؟ لـ F on A node if and only
+
+259
+00:21:28,800 --> 00:21:33,480
+if بدي ن في هذا، إيش بيصير عندي؟ for every epsilon
+
+260
+00:21:33,480 --> 00:21:37,240
+أكبر من 0 بيصير there exists epsilon not أكبر من 0
+
+261
+00:21:37,240 --> 00:21:41,420
+لأن there exists .. لكل epsilon there exists K لأن 
+
+262
+00:21:41,420 --> 00:21:45,480
+there exists epsilon not such that for every K،
+
+263
+00:21:45,480 --> 00:21:50,410
+element الـ N اه اللي هال for every n أكبر من .. ان
+
+264
+00:21:50,410 --> 00:21:54,470
+هاذي بيصير there exist n الـ n هتعتمد على مين؟ على
+
+265
+00:21:54,470 --> 00:22:01,290
+k عشان هي كم سميها nk أكبر أو يساوي k ماشي there
+
+266
+00:22:01,290 --> 00:22:04,090
+exist لأن بدل من for every n أكبر سوا k بصير there
+
+267
+00:22:04,090 --> 00:22:09,090
+exist nk أكبر سوا k such that لأن for every x أيش
+
+268
+00:22:09,090 --> 00:22:14,410
+بيكون ل for every k there exist x برضه ال x هتعتمد
+
+269
+00:22:14,410 --> 00:22:18,690
+على مين على k يعني لكل k باللي جيلها nk و باللي
+
+270
+00:22:18,690 --> 00:22:23,330
+جيلها ال xk such that fn 
+
+271
+00:22:24,480 --> 00:22:31,420
+اللي سميته إيش اسمها أنا nk of x اللي هي xk ناقص f 
+
+272
+00:22:31,420 --> 00:22:39,580
+of xk أكبر أو يساوى مين إبسلون نقطة إذا صار عندي،
+
+273
+00:22:39,580 --> 00:22:45,510
+الآن نفي هذه لكل y there exist k لأن there exist y
+
+274
+00:22:45,510 --> 00:22:51,210
+note such that لكل k يعني لو k بواحد بقدر ألاقي أن 
+
+275
+00:22:51,210 --> 00:22:57,530
+واحد أكبر شو k و x واحد بحيث أن f x واحد أن واحد
+
+276
+00:22:57,530 --> 00:23:03,010
+ناقص f of x واحد أكبر شو y note لأن there exist y 
+
+277
+00:23:03,010 --> 00:23:06,110
+note for every هذا ال y note ثبتت واحدة بلقيتها
+
+278
+00:23:06,110 --> 00:23:09,510
+للكل there exist of note such that for every k إيش 
+
+279
+00:23:09,510 --> 00:23:15,840
+بتساوي اتنين there exists N2 بحيث أن X2 أو there
+
+280
+00:23:15,840 --> 00:23:23,600
+exists X2 بحيث أن F of X2 F N2 of X2 نقص F of X2 
+
+281
+00:23:23,600 --> 00:23:30,350
+أكبر سوى Y نوت كذا بسوء ثلاثة نفس الشيء كي بيساوي
+
+282
+00:23:30,350 --> 00:23:34,770
+أربعة، نفس الشيء إذا وكأن الـ gate A شمالها أفقًا
+
+283
+00:23:34,770 --> 00:23:37,810
+واحد أفقًا اثنين أفقًا ثلاثة أفقًا أربعة أفقًا خمسة،
+
+284
+00:23:37,810 --> 00:23:42,570
+من مين؟ من اللي هم الأفقان هذولة، يعني هذولة sub
+
+285
+00:23:42,570 --> 00:23:46,090
+sequence من مين هذولة، يعني هذا معناته if and only
+
+286
+00:23:46,090 --> 00:23:49,470
+if there exists epsilon not أكبر من صفر such that
+
+287
+00:23:49,470 --> 00:23:57,630
+أو such that واللي هو الآن هذا لجت منها لكل كده
+
+288
+00:23:57,630 --> 00:24:10,710
+كده لجت من a subsequence اللي هي FNK of FN and a
+
+289
+00:24:10,710 --> 00:24:17,130
+sequence XK من وين هذه الـ XK طبعًا من وين موجودة من
+
+290
+00:24:17,130 --> 00:24:25,430
+الـ A جايات من وين من الـ A XK in A such that FNK
+
+291
+00:24:25,430 --> 00:24:34,230
+of XK ناقص F of XK أكبر أو يساوي epsilon note وهذا
+
+292
+00:24:34,230 --> 00:24:40,770
+اللي هو المطلوب هذا الكلام لكل K ومالها لكل K
+
+293
+00:24:42,530 --> 00:24:48,610
+Element in N يعني بمعنى آخر عشان أقول FN does not
+
+294
+00:24:48,610 --> 00:24:52,330
+converge للـ F on A note does not converge in a
+
+295
+00:24:52,330 --> 00:24:56,970
+formula طبعًا إيش معناته أنه بلاجة epsilon note؟
+
+296
+00:24:57,540 --> 00:25:03,660
+وsub-sequence fnk من fn وsequence xak in a بحيث أن
+
+297
+00:25:03,660 --> 00:25:09,100
+الـ absolute value of fnk of xk ناقص f of xk أصغر
+
+298
+00:25:09,100 --> 00:25:13,880
+من الـ y0 لكل k element هنا إذًا a sequence of
+
+299
+00:25:13,880 --> 00:25:17,480
+functions from A subset من R to R does not
+
+300
+00:25:17,480 --> 00:25:21,420
+converge uniformly أو does not converge uniformly
+
+301
+00:25:21,420 --> 00:25:25,440
+من A نوت subset من A to a function F من A نوت لعند
+
+302
+00:25:25,440 --> 00:25:32,000
+R هذا يكافئ أن هناك ي أكبر من صفر ي نوتهندق
+
+303
+00:25:32,000 --> 00:25:36,140
+subsequence fnk of fn and a sequence xk in a node
+
+304
+00:25:36,140 --> 00:25:41,180
+such that fnk of xk نقص f of xk أكبر وساوي epsilon
+
+305
+00:25:41,180 --> 00:25:46,340
+note هذه اللي هي نفي الـ uniform convergence يعني
+
+306
+00:25:46,340 --> 00:25:51,040
+هنستخدمها في إثبات أنه اللي هو الـ C الـ function
+
+307
+00:25:52,030 --> 00:25:56,170
+الـ sequence of functions does not converge
+
+308
+00:25:56,170 --> 00:26:04,410
+uniformly to some function مثلًا F أو غيره طيب أخد
+
+309
+00:26:04,410 --> 00:26:12,730
+أمثلة إذا الآن نيجي نشوف هذه اللي هي النظرية عشان
+
+310
+00:26:12,730 --> 00:26:17,570
+دالكم متذكرينها نشوف
+
+311
+00:26:17,570 --> 00:26:27,720
+سؤالنا أو مثالنا الآن مثالين الـ Dn of X بيساوي X أس
+
+312
+00:26:27,720 --> 00:26:32,380
+أن و X element in R و N element in R يظهر أن Dn لا
+
+313
+00:26:32,380 --> 00:26:37,460
+يتعامل بشكل عام على الفترة ناقص واحد واحد إلى Dn
+
+314
+00:26:37,460 --> 00:26:43,590
+.. إلى D of X اللي هي هذه بقول هذه أثبتناها قبل
+
+315
+00:26:43,590 --> 00:26:47,910
+بشوية إنها convergence pointwise على الفترة بين
+
+316
+00:26:47,910 --> 00:26:52,330
+ناقص واحد وواحد يعني هذا مثال على sequence of
+
+317
+00:26:52,330 --> 00:26:56,890
+functions convergence pointwise على الفترة بين
+
+318
+00:26:56,890 --> 00:27:00,570
+ناقص واحد وواحد لكن does not converge uniformly
+
+319
+00:27:00,570 --> 00:27:06,150
+على الفترة ناقص واحد وواحد هذا مثال على إن ال
+
+320
+00:27:06,150 --> 00:27:12,510
+pointwise convergence need not to imply اللي هو
+
+321
+00:27:12,510 --> 00:27:19,730
+uniform convergence الآن هو طبعًا حاسب حسبته عملها
+
+322
+00:27:19,730 --> 00:27:22,150
+و كده و كده و دارسها و أعطيني على طول اللي هو الـY
+
+323
+00:27:22,150 --> 00:27:27,370
+النقطة اللي بتنفع خليني نشوف احنا الآن عندي اللي
+
+324
+00:27:27,370 --> 00:27:33,350
+هو GN of X بيساوي X أسئلة غلطي اني ألاجي اللي هو
+
+325
+00:27:33,350 --> 00:27:37,230
+subsequence fnk من الـ sequence هذه إيش الـ
+
+326
+00:27:37,230 --> 00:27:41,210
+sequence اللي عندي؟ اللي هي x أُس n ماشي الحال
+
+327
+00:27:41,210 --> 00:27:46,150
+اللي بحيث أنه fnk of xk ناقص f of xk يكون أكبر
+
+328
+00:27:46,150 --> 00:27:50,530
+يساوي y نوت اللي هو فكرته هو بيقولك أنا خليني أجيب
+
+329
+00:27:50,530 --> 00:27:56,290
+subsequence fnk اللي هو .. أو sequence xk بحيث أن
+
+330
+00:27:56,290 --> 00:28:01,510
+يكون هذه قيمته عبارة عن ثابت وهذي يصير عبارة عن
+
+331
+00:28:01,510 --> 00:28:05,290
+إيش ثابت لإنه في الأصل ثابت ما أعطيني يا واحد و صفر
+
+332
+00:28:05,290 --> 00:28:09,610
+يعني يقول لي هذا ثابت ناقص ثابت بطلع رقم فبختار ال
+
+333
+00:28:09,610 --> 00:28:12,590
+epsilon المعينة اللي بتكون هذا الرقم أكثر منها
+
+334
+00:28:12,590 --> 00:28:16,790
+يعني بسمع علي أن أعمل حسابات لهذه أنها تطلع قيمة
+
+335
+00:28:16,790 --> 00:28:21,230
+ثابتة أختار F and K sequence من هنا يطلع اللي هي F
+
+336
+00:28:21,230 --> 00:28:25,080
+and K of xk يكون ثابته بيصير هذا المقدار ثابت و
+
+337
+00:28:25,080 --> 00:28:28,560
+على طول بختار الـ Epsilon Note اللي بتأدي الغلط
+
+338
+00:28:28,560 --> 00:28:35,240
+الآن إيش أختار؟ قال لي خليني آخد اللي هي عند FGN
+
+339
+00:28:35,240 --> 00:28:39,660
+of X عشان بيساوي XSAN الآن بيقول لي خليني آخد ال
+
+340
+00:28:39,660 --> 00:28:44,580
+NK اللي هي عبارة عن من؟ عن ال K، عن ال K، ماشي؟
+
+341
+00:28:44,580 --> 00:28:49,180
+هذا الجد تعرف ليش اختار ال K و آخد الـ XK هو عارف أنه
+
+342
+00:28:49,180 --> 00:28:53,380
+الـ X الآن الـ XK بده يخلي هذا كابت لما يطلع ليه
+
+343
+00:28:53,380 --> 00:29:00,260
+الـ GN وكده آخد الـ XK بتساوي 1 على 2 أس 1 على K
+
+344
+00:29:00,260 --> 00:29:08,850
+طبعًا أضحك ليش؟ عشان الآن لما آخد الـ XK بيساوي نص
+
+345
+00:29:08,850 --> 00:29:12,090
+مثلًا مش عاجبك نص حط ثلث ربع خمس عشرة مليون اللي
+
+346
+00:29:12,090 --> 00:29:16,090
+بدك إياه بس وين في الفترة يطلع قيمته في الفترة وين
+
+347
+00:29:16,090 --> 00:29:19,630
+ناقص واحد واحد عشان ظلنا ال sequence سبعتنا
+
+348
+00:29:19,630 --> 00:29:22,550
+does not converge على الفترة ناقص واحد واحد عشان
+
+349
+00:29:22,550 --> 00:29:28,210
+هي آخد ال XA شمالها ال XK نص أس واحد على K كيف ما
+
+350
+00:29:28,210 --> 00:29:32,450
+تعمل لو ترفحها هتظل بين الفترة ناقص واحد ومين واحد
+
+351
+00:29:33,630 --> 00:29:43,770
+الآن F NK of XK بيساوي X كله نص أس واحد على K أس
+
+352
+00:29:43,770 --> 00:29:50,450
+مين أس NK عشان يخلي هذا المقدار ثابت بده يخلي الآن
+
+353
+00:29:50,450 --> 00:29:55,790
+كاش بتساوي K فبيصير واحد على K في K بتطلع واحد
+
+354
+00:29:55,790 --> 00:30:00,570
+فعشان هيك آخد الآن K بيساوي K فصارت الآن ال
+
+355
+00:30:00,570 --> 00:30:07,550
+subsequence اللي هو عبارة عن FK of XK يعني ال
+
+356
+00:30:07,550 --> 00:30:11,650
+index هنا والـ index هنا بقى صح أبنفع أبنفع لأنه
+
+357
+00:30:11,650 --> 00:30:17,540
+أشماله الآن هذا الآن الآن K ليه subsequence من
+
+358
+00:30:17,540 --> 00:30:22,680
+مين؟ من ال F N فالآن عندي ال K اللي جاته بيصير
+
+359
+00:30:22,680 --> 00:30:26,180
+عندي K بواحد باتنين بثلاثة بأربعة بجد ما بدي أو K K
+
+360
+00:30:26,180 --> 00:30:29,780
+زائد واحد K زائد اثنين من ضمن مين؟ من ضمن ال
+
+361
+00:30:29,780 --> 00:30:33,400
+sequence F N بتكون نفسها بس بدت من وين؟ من عند ال
+
+362
+00:30:33,400 --> 00:30:40,350
+K اللي آخدها الآن صار عندي الآن الـ xk اختارها
+
+363
+00:30:40,350 --> 00:30:45,510
+بالشكل هذا والآن k اختارها كيه بيصير عندي الآن gk
+
+364
+00:30:45,510 --> 00:30:50,630
+of xk أنا بسميها f معلش هي g gk of xk ناقص g of xk
+
+365
+00:30:50,630 --> 00:30:57,510
+بيساوي gk of xk زي ما حسبناها هذا g k of xk بيساوي
+
+366
+00:30:57,510 --> 00:31:04,970
+هذه ويساوي نص بيصير عبارة عن نص ناقص g of x كأي x في
+
+367
+00:31:04,970 --> 00:31:07,890
+الفترة هذه الـ g of x اللي هيش بتساوي صفر ناقص صفر
+
+368
+00:31:07,890 --> 00:31:11,850
+هو يساوي نص الآن الـ E لقطة اللي بدي أختارها عشان
+
+369
+00:31:11,850 --> 00:31:16,330
+ما يصير النص أكبر منها أختارها جدّيش عبارة عن ربع
+
+370
+00:31:16,330 --> 00:31:19,210
+يعني واحد قال لي أنا أقولك تأخذ ثلث أو تأخذ ربع
+
+371
+00:31:19,210 --> 00:31:23,820
+بيصير ال E لقطة اللي اخترتها تعتمد على إنها تكون
+
+372
+00:31:23,820 --> 00:31:27,420
+اللي هي اللي بيطلع أكبر من الـ Epsilon Note يعني
+
+373
+00:31:27,420 --> 00:31:32,000
+لو بتأخذها ربع هنا .. هنا ربع أس واحد على K اللي هي
+
+374
+00:31:32,000 --> 00:31:36,220
+الـ XK بيصير هذه Epsilon Note تأخذها مثلًا عبارة عن
+
+375
+00:31:36,220 --> 00:31:40,170
+خمس أو سُدُس أو إلى آخره إذا اللي جينا epsilon note
+
+376
+00:31:40,170 --> 00:31:44,030
+و sub sequence من ال functions اللي هي f and k اللي
+
+377
+00:31:44,030 --> 00:31:47,950
+هي fk في الواقع و sequence xk في الـ .. في الـ a
+
+378
+00:31:47,950 --> 00:31:52,990
+هيها بحيث أنه gk of xk نقص g of xk اللي هي أكبر من
+
+379
+00:31:52,990 --> 00:31:56,150
+epsilon note إذا صار عندي اللي هي g and does not
+
+380
+00:31:56,150 --> 00:32:02,030
+converge uniformly to g on this interval طيب
+
+381
+00:32:07,270 --> 00:32:10,430
+هدّ سيبكوا منها لأن هدّ بتيجي بعدين بعد شوية لما
+
+382
+00:32:10,430 --> 00:32:15,290
+بنعرف لسه ال norm خلينا اللي هو هي ال norm عرفناها
+
+383
+00:32:15,290 --> 00:32:22,110
+تحت definition
+
+384
+00:32:22,110 --> 00:32:29,270
+F هي subset من R and Phi من R لR is a function we
+
+385
+00:32:29,270 --> 00:32:36,140
+say that Phi is bounded on A if the set of phi of A
+
+386
+00:32:36,140 --> 00:32:41,600
+is bounded subset of R يعني الآن الـ function عندي
+
+387
+00:32:41,600 --> 00:32:47,140
+هذه بقول عنها bounded على الـ A إذا كان يعني phi
+
+388
+00:32:47,140 --> 00:32:52,680
+of X absolute value أصغر أو يساوي some number K أو
+
+389
+00:32:52,680 --> 00:32:57,360
+some number M for every X element in A في هذا
+
+390
+00:32:57,360 --> 00:33:00,700
+الحالة بقول إن الـ function phi A شمالها is
+
+391
+00:33:00,700 --> 00:33:06,210
+bounded on A يعني عندي function .. عندي function
+
+392
+00:33:06,210 --> 00:33:16,830
+Phi من R لعند R بقول Phi is bounded on A اللي هي
+
+393
+00:33:16,830 --> 00:33:22,470
+subset من R if there exist M أكبر من 0 such that
+
+394
+00:33:22,470 --> 00:33:27,790
+Phi of X أصغر أو يساوي الـ M لكل الـ X وين موجودة
+
+395
+00:33:27,790 --> 00:33:34,230
+في الـ A فبتكون Phi is bounded on A طيب، الآن أو
+
+396
+00:33:34,230 --> 00:33:39,090
+بمعنى آخر زي ما هو جايل أنه بدل هذا جايل أنه Phi
+
+397
+00:33:39,090 --> 00:33:44,690
+of A نفسها is bounded إيش Phi of A هي؟ Phi of A ما
+
+398
+00:33:44,690 --> 00:33:49,330
+أنتوا عارفينها هي عبارة عن كل Phi of X such that X
+
+399
+00:33:49,330 --> 00:33:52,730
+element in A إيش معناته هذه تكون bounded؟ إن there
+
+400
+00:33:52,730 --> 00:33:56,230
+exists M أكبر من 0 such that ال absolute value
+
+401
+00:33:56,230 --> 00:34:03,050
+لـ Phi of X كل اللي هنا أصغر أو يساوي M لكل X where
+
+402
+00:34:03,050 --> 00:34:09,610
+موجودة في الـ A إذا الـ boundedness للـ Phi on A هي
+
+403
+00:34:09,610 --> 00:34:13,530
+بالشكل هذا، يا أن نقول Phi of A هذي bounded، تنتهي
+
+404
+00:34:13,530 --> 00:34:20,390
+زي بعض طيب، بقول لي if A subset من R and Phi من R لR
+
+405
+00:34:20,390 --> 00:34:26,410
+is a function نقول أن فاية مرتبطة بالـ A إذا كانت
+
+406
+00:34:26,410 --> 00:34:33,190
+سلسلة فاية A مرتبطة بالمجلد R مايعني أن هناك M
+
+407
+00:34:33,190 --> 00:34:37,270
+أكبر من 0 إذا كانت سلسلة فاية X أصغر يساوي M لكل X
+
+408
+00:34:37,270 --> 00:34:40,570
+المجلد A إذا كانت فاية مرتبطة
+
+409
+00:34:43,890 --> 00:34:50,690
+norm of phi إذا الآن فرض أنه find phi bounded on a
+
+410
+00:34:50,690 --> 00:34:55,070
+عشان يعرف حاجة اسمها ال uniform norm اللي هو نفس
+
+411
+00:34:55,070 --> 00:35:00,050
+الـ مش .. نفس رمزه اللي هو إيش .. إيش .. إيش ال
+
+412
+00:35:00,050 --> 00:35:04,650
+norm ال uniform norm ال uniform norm لل phi over a
+
+413
+00:35:04,650 --> 00:35:09,790
+بيساوي ال supremum لل phi of x لكل x element الميين
+
+414
+00:35:09,790 --> 00:35:14,310
+in a إذا هذا اللي هو معناته اللي هو الـ Uniform
+
+415
+00:35:14,310 --> 00:35:20,130
+Norm إذا من الآن وطالع Phi
+
+416
+00:35:20,130 --> 00:35:27,060
+is a function Normal Phi  نورم الـ Phi على الـ A هو
+
+417
+00:35:27,060 --> 00:35:32,280
+عبارة عن الـ supremum لل absolute value لـ 5X such
+
+418
+00:35:32,280 --> 00:35:35,800
+that X element in A هل هذا الـ supremum موجود؟ آه
+
+419
+00:35:35,800 --> 00:35:40,760
+لأننا مفترضين Phi bounded على مين؟ على الـ A طيب،
+
+420
+00:35:40,760 --> 00:35:45,620
+إذا هذا معناته اللي هو ال uniform norm أو norm لـ
+
+421
+00:35:45,620 --> 00:35:53,920
+لاحظوا أن الـ norm لو عندي بقول لي ملاحظة اللي هو
+
+422
+00:35:53,920 --> 00:35:57,360
+Normal Φ A أصغر أو يساوي ε F and ولا F
+
+423
+00:35:57,360 --> 00:36:00,240
+Φ of X أصغر أو يساوي ε، ليش؟ لأن لما يكون
+
+424
+00:36:00,240 --> 00:36:03,180
+هذا أصغر أو يساوي ε لكل X element in A، إذا
+
+425
+00:36:03,180 --> 00:36:06,600
+الـ Supremum هيكون أصغر أو يساوي ε، لأن صار
+
+426
+00:36:06,600 --> 00:36:09,420
+هذا عبارة عن Upper Bound اللي هنا، الـ Supremum هو
+
+427
+00:36:09,420 --> 00:36:12,360
+الـ Least Upper Bound أصغر أو يساوي ε، يعني
+
+428
+00:36:12,360 --> 00:36:14,960
+شو الـ Supremum اللي هنا، اللي هو Normal Φ V أصغر
+
+429
+00:36:14,960 --> 00:36:18,390
+أو يساوي ε Conversely، لو هذا كان أصغر أو
+
+430
+00:36:18,390 --> 00:36:22,310
+يساوي ε وأكيد هذا الـ Supremum أكبر أو يساوي الـ
+
+431
+00:36:22,310 --> 00:36:25,710
+Absolute Value لـ Φ of X لكل X Elementين اللي هو
+
+432
+00:36:25,710 --> 00:36:28,950
+أن هذا Supremum من الهن كلهن فهيكون هذا أكبر يساوي
+
+433
+00:36:28,950 --> 00:36:32,130
+هذا، معناته هذا أصغر يساوي هذا لكل X، معناته هذا A
+
+434
+00:36:32,130 --> 00:36:36,770
+شماله متحقق، إذن If and Only If متحققة Normal Φ 
+
+435
+00:36:36,770 --> 00:36:40,490
+of A أصغر أو يساوي ε، If and Only If الـ Absolute
+
+436
+00:36:40,490 --> 00:36:44,310
+Value لـ Φ of X أصغر أو يساوي ε لكل X Element
+
+437
+00:36:44,310 --> 00:36:44,730
+منهم
+
+438
+00:36:48,470 --> 00:36:56,890
+نيجي الآن لللمّة اللي عندي نيجي
+
+439
+00:36:56,890 --> 00:37:01,650
+لللمّة اللي عندنا
+
+440
+00:37:01,650 --> 00:37:05,750
+أوقف
+
+441
+00:37:05,750 --> 00:37:09,930
+شوية دقيقة يا أبو حسن يكبر الخط الصغير لما أنا
+
+442
+00:37:09,930 --> 00:37:10,650
+شايف كويس
+
+443
+00:37:16,640 --> 00:37:23,300
+الدسعة صارت وحسن مين
+
+444
+00:37:23,300 --> 00:37:28,860
+محمد راضي؟
+
+445
+00:37:28,860 --> 00:37:32,060
+خلاص
+
+446
+00:37:32,060 --> 00:37:33,760
+يا شيخ ما نأخلوه يساعد مش شاء الله
+
+447
+00:38:18,040 --> 00:38:23,680
+لكن واضح عندك بيكون يا أبو حسين واضح بيكون عندك
+
+448
+00:38:23,680 --> 00:38:25,020
+إلا وحن يا راجل
+
+449
+00:39:40,390 --> 00:39:49,610
+جدّاش هدول صارن على بعض اللي كم ساعة؟ والله
+
+450
+00:39:49,610 --> 00:39:52,810
+هي ... هي ... يمكن بديها كمان جدّ هن ده كان بس كتير
+
+451
+00:39:52,810 --> 00:39:57,970
+جدّ هن خليني أنا أخلص اللي كمان طول الساعة وخلاص
+
+452
+00:39:57,970 --> 00:40:05,350
+على كم معادك؟ على كم معادك؟ كده الساعة اللي جيت؟
+
+453
+00:40:05,350 --> 00:40:11,970
+خلاص بنقول له إنه عشر دقائق ربع ساعة بنفع ولا خلاص؟
+
+454
+00:40:11,970 --> 00:40:17,050
+أنا لو المشكلة المواصلة بيكون صعبة وين؟ هتخليهوا
+
+455
+00:40:17,050 --> 00:40:25,090
+ناس؟ طب بناخدك معانا بس خليني أشوف طب
+
+456
+00:40:25,090 --> 00:40:32,070
+استنى أشوف أبو محمد إذا كان جاهز لأ مش مشكلة .. لأ
+
+457
+00:40:32,070 --> 00:40:36,810
+بنطلع معاه .. لأ بدي أشوف .. بنوصلك
+
+458
+00:40:36,810 --> 00:40:39,550
+على طول هتعطيني بس جوالي
+
+459
+00:40:47,550 --> 00:40:53,450
+قول له أبو يوسف اللي أخرني تخيلت
+
+460
+00:40:53,450 --> 00:40:56,830
+.. تخيلت .. تخيلت .. تخيلت .. تخيلت .. تخيلت
+
+461
+00:40:56,830 --> 00:41:03,210
+.. تخيلت .. تخيلت .. تخيلت .. تخيلت .. تخيلت
+
+462
+00:41:03,210 --> 00:41:03,490
+.. تخيلت .. تخيلت .. تخيلت .. تخيلت .. تخيلت
+
+463
+00:41:03,490 --> 00:41:04,150
+.. تخيلت .. تخيلت .. تخيلت .. تخيلت .. تخيلت
+
+464
+00:41:04,150 --> 00:41:14,810
+.. تخيلت .. تخيلت .. تخيلت .. تخيلت
+
+465
+00:41:14,810 --> 00:41:14,950
+.. ا
+
+466
+00:41:31,180 --> 00:41:36,980
+خليني أشرح الحل نظرية وبن .. وبن .. وبنخلص
+
+467
+00:42:10,200 --> 00:42:16,380
+آه محمد السلام عليكم أهلا بك الله يبارك فيك إيش؟
+
+468
+00:42:16,380 --> 00:42:22,360
+يعني .. طب لأ سنة وخمسة .. عشر دقائق بس أه عشر
+
+469
+00:42:22,360 --> 00:42:25,240
+دقائق وبنزلك كي ما .. أنت بتروح هان ولا هان ولا
+
+470
+00:42:25,240 --> 00:42:31,940
+على طول أه عشان معنا واحد .. خلاص ماشي خلاص ماشي
+
+471
+00:42:31,940 --> 00:42:37,800
+ماشي يا محمد ماشي لأ
+
+472
+00:42:37,800 --> 00:42:46,370
+خلاص بروح معاك بروح معاك بروح معاك ماشي بس ديش
+
+473
+00:42:46,370 --> 00:42:51,070
+أخرك برضه طب
+
+474
+00:42:51,070 --> 00:42:56,210
+أنت هي هتقابلك وين مرتك؟ اه اه اه اه
+
+475
+00:43:01,510 --> 00:43:07,230
+وصلنا عند اللمّة اللي أمامنا 818 a sequence fn of
+
+476
+00:43:07,230 --> 00:43:10,410
+bounded functions on A subset من R converts
+
+477
+00:43:10,410 --> 00:43:14,930
+uniformly on A to F if and only if normal fn نقص F
+
+478
+00:43:14,930 --> 00:43:21,820
+بروح لمين converts to 0 الآن يعني بده يعطينا غير
+
+479
+00:43:21,820 --> 00:43:26,260
+التعريف نعمل testing لمين؟ لأن ال sequence of
+
+480
+00:43:26,260 --> 00:43:29,480
+functions هتكون يشمالها uniform يكون convergent
+
+481
+00:43:29,480 --> 00:43:33,580
+ولا لأ الآن بقول لي بس هذا لمين ال testing ل
+
+482
+00:43:33,580 --> 00:43:37,400
+sequence of functions fn تكون bounded functions
+
+483
+00:43:37,400 --> 00:43:41,460
+يعني عناصر اللي هان كل واحدة من هدول fn is
+
+484
+00:43:41,460 --> 00:43:47,200
+bounded بقول لي لو كانت sequence of functions Fn is
+
+485
+00:43:47,200 --> 00:43:53,840
+bounded من رأس الدور، then بنقول إن Fn converges
+
+486
+00:43:53,840 --> 00:43:59,680
+uniformly to some function F if and only if norm
+
+487
+00:43:59,680 --> 00:44:05,040
+الـ Fn ناقص الـ F over A الـ A converts the mean
+
+488
+00:44:05,040 --> 00:44:11,860
+لـ 0 إذا أنت عشان اللي هو تفحص أن ال sequence of
+
+489
+00:44:11,860 --> 00:44:16,800
+bounded functions Fn أنها converts uniformly للـ F
+
+490
+00:44:16,800 --> 00:44:22,680
+يكفي أنك تيجي تأخد norm الـ Fn ناقص F اللي هو over
+
+491
+00:44:22,680 --> 00:44:27,110
+A إذا لاجيتوا اللي هو الـ Limit صار أعدادها لديروا
+
+492
+00:44:27,110 --> 00:44:31,110
+بالكم Normal لأن صار الـ Limit له إذا كان الـ
+
+493
+00:44:31,110 --> 00:44:35,050
+Limit له راح للسفر خلاص كل سنة وأنت سالن بتكون الـ
+
+494
+00:44:35,050 --> 00:44:38,310
+F un converts uniformly للـ F لو ما راحش للسفر
+
+495
+00:44:38,310 --> 00:44:41,010
+معناته الـ F un does not converge uniformly to
+
+496
+00:44:41,010 --> 00:44:46,490
+mean to F الآن بدأ أفترض الآن نفترض أن F un a
+
+497
+00:44:46,490 --> 00:44:52,240
+proof بدي أفترض أن FN converts uniformly to mean to
+
+498
+00:44:52,240 --> 00:44:57,720
+F ماشي الحال عشان اللي هو أثبت أن هذا النورم بروح
+
+499
+00:44:57,720 --> 00:45:03,100
+للـ 0 أول إشي بدي أثبت لك أن هذا الـ FN نقص F is
+
+500
+00:45:03,100 --> 00:45:07,720
+bounded أو بمعنى آخر الـ F is bounded لو كانت الـ
+
+501
+00:45:07,720 --> 00:45:11,680
+F is bounded بصير FN نقص F bounded يعني نورم الـ A
+
+502
+00:45:11,680 --> 00:45:17,330
+بكون أشماله موجود موجود لأن هذا شرط اللي هو يكون
+
+503
+00:45:17,330 --> 00:45:20,390
+موجود أنه تكون اللي جواته bounded زي ما عرفنا قبل
+
+504
+00:45:20,390 --> 00:45:25,270
+بشوية طيب Fn بتروح لل F uniformly إذا لكل Y أكبر
+
+505
+00:45:25,270 --> 00:45:29,250
+من 0 there exists K element in N such that for
+
+506
+00:45:29,250 --> 00:45:33,410
+every N أكبر يساوي K و for every X element in A
+
+507
+00:45:33,410 --> 00:45:40,180
+اللي عندي A ولا إيش نسميها A بكون عندي Fn of X نقص
+
+508
+00:45:40,180 --> 00:45:46,380
+F of X أشماله أصغر من مين؟ من Y طيب قولنا بدنا نثبت
+
+509
+00:45:46,380 --> 00:45:52,560
+أن الـ F is bounded الآن سهل خد الآن F of X أصغر أو
+
+510
+00:45:52,560 --> 00:45:58,050
+ساوي اللي هو Fn of X بالـ Triangle Inequality ناقص F
+
+511
+00:45:58,050 --> 00:46:06,190
+of X زائد اللي هي mean Fn of X، مظبوط؟ هذه بالـ
+
+512
+00:46:06,190 --> 00:46:09,530
+Triangle Inequality هذه bounded، هذه bounded ما هو
+
+513
+00:46:09,530 --> 00:46:12,250
+sequence of bounded functions هذا الكلام لكل N
+
+514
+00:46:12,250 --> 00:46:18,210
+أكبر يساوي mean K هذه متحققة لكل N أكبر يساوي K من ضمن
+
+515
+00:46:18,210 --> 00:46:26,090
+ال mean الـ K صار عندي F of X أصغر أو يساوي FK of X
+
+516
+00:46:26,090 --> 00:46:33,930
+ناقص F of X زائد FK of X، مظبوط؟ هذه من اللي فوق
+
+517
+00:46:33,930 --> 00:46:37,190
+أصغر من ε لكل أن أكبر يساوي K من ضمن إن الـK
+
+518
+00:46:37,190 --> 00:46:41,810
+إذا هذه بيصير أصغر من ε زائد هذه الآن بحكي عن
+
+519
+00:46:41,810 --> 00:46:46,270
+function محددة اللي هي اسمها fk of x هو جاين لكل
+
+520
+00:46:46,270 --> 00:46:50,550
+ال fns هدول bounded من ضمن إن ال fk bounded، مدام
+
+521
+00:46:50,550 --> 00:46:54,510
+bounded إذا في النهاية هذه أصغر أو يساوي some
+
+522
+00:46:54,510 --> 00:46:59,690
+number m أو k اللي بدك إياه أو s لكل x وين موجودة
+
+523
+00:46:59,690 --> 00:47:03,380
+في الـ A صارت F of X أصغر يساوي Y زائد M يعني عبارة
+
+524
+00:47:03,380 --> 00:47:07,060
+عن رقم لكل X element in A صارت الـ F نفسها إيش
+
+525
+00:47:07,060 --> 00:47:11,960
+مالها is bounded إذن الآن شرعت إني أحكي عن F N
+
+526
+00:47:11,960 --> 00:47:15,420
+ناقص F as a bounded function لإن F N bounded والـ
+
+527
+00:47:15,420 --> 00:47:17,900
+F bounded إذا انتمتين مع بعض إيش مالهن bounded
+
+528
+00:47:17,900 --> 00:47:23,120
+إذن صارت هذه معرفة، ماشي الحال، طيب مدام معرفة إذن
+
+529
+00:47:23,120 --> 00:47:28,480
+على طول هنامدام هذه أصغر من ε في الملاحظة
+
+530
+00:47:28,480 --> 00:47:31,560
+اللي كتبناها في الأول قبل التعريف وبعدين شرحناها
+
+531
+00:47:31,560 --> 00:47:37,020
+بعد التعريف إذا بتذكروا مدامة اللي هي هذه كلها هذه
+
+532
+00:47:37,020 --> 00:47:41,980
+كلها as Φ absolute value Φ of X أصغر أو يساوي
+
+533
+00:47:41,980 --> 00:47:46,100
+أقل من ε بيكون normها أصغر أو يساوي ε
+
+534
+00:47:46,100 --> 00:47:51,440
+معناته إحنا حصلنا على ال supremum للـ absolute
+
+535
+00:47:51,440 --> 00:47:57,980
+value للـ Fn of X ناقص F of X اللي هو أصغر من Y
+
+536
+00:47:57,980 --> 00:48:03,930
+أصغر من Y اللي هو هذا .. والـ X اللي بيبقى A هذا
+
+537
+00:48:03,930 --> 00:48:09,850
+اللي هو عبارة عن norm الـ Fn ناقص F over A إذا صار
+
+538
+00:48:09,850 --> 00:48:14,090
+هذا أصغر يساوي ε، تحت مين؟ يعني لكل Y أكبر من
+
+539
+00:48:14,090 --> 00:48:20,570
+0 لجينا K لكل N أكبر يساوي K الـ Fn ناقص الـ F أصغر
+
+540
+00:48:20,570 --> 00:48:25,790
+من ε وهذا يعني إنه limit norm الـ Fn ناقص الـ
+
+541
+00:48:25,790 --> 00:48:31,160
+F as N goes to infinity يساوي صفر إذن بيكون إحنا
+
+542
+00:48:31,160 --> 00:48:37,640
+خلصنا الاتجاه الأول وأثبتنا إنه اللي هو norm للأف
+
+543
+00:48:37,640 --> 00:48:41,660
+أن نقص أف بيروح لصفر لما اللي هو الـ Fn تكون
+
+544
+00:48:41,660 --> 00:48:47,380
+converge uniformly الآن الـ converse إن لو كان ال
+
+545
+00:48:47,380 --> 00:48:55,660
+norm للـ Fn بيروح لصفر هيكون اللي هو الـ Fn تكون
+
+546
+00:48:55,660 --> 00:49:01,380
+converge uniformly to F أنتوا هذا سهل هذا شوف كيف
+
+547
+00:49:01,380 --> 00:49:10,420
+لأن بدنا نفترض suppose that norm الـ Fn ناقص الـ F
+
+548
+00:49:10,420 --> 00:49:15,540
+over A converge لبين للصفر إيش معناته هذا؟ معناته
+
+549
+00:49:15,540 --> 00:49:22,420
+لكل ε أكبر من صفر there exists k كي اعتمدت على
+
+550
+00:49:22,420 --> 00:49:26,260
+مين بس of ε ال limit in n لأن ما فيش اصلا
+
+551
+00:49:26,260 --> 00:49:34,560
+إكسات هذه limit هذا يساوي ده such that اللي هو fn
+
+552
+00:49:34,560 --> 00:49:45,460
+ناقص f اللي هو ناقص صفر ناقص صفر أصغر من ε لكل
+
+553
+00:49:45,460 --> 00:49:51,560
+N أكبر أو يساوي K هذا مين هو؟ هذا norm ال FN ناقص F
+
+554
+00:49:51,560 --> 00:49:56,740
+over A أصغر من ε وهذا أكيد أكبر أو يساوي ال
+
+555
+00:49:56,740 --> 00:50:01,700
+supremum آسف هو ال supremum أكبر أو يساوي ال FN of
+
+556
+00:50:01,700 --> 00:50:08,460
+X ناقص F of X لكل X element in A لأن هذا أكبر يساوي
+
+557
+00:50:08,460 --> 00:50:11,380
+هذا لأن هذا supremum من إلهم إذا صار عند الأل لكل
+
+558
+00:50:11,380 --> 00:50:18,140
+Y أكبر من 0 there exists K such that Fn of X ناقص
+
+559
+00:50:18,140 --> 00:50:25,620
+F of X أصغر من Y لكل X element in A وهذا معناته مع
+
+560
+00:50:25,620 --> 00:50:35,330
+هذا إذا fn converges uniformly to f هذا ما مكتوب 
+
+561
+00:50:35,330 --> 00:50:35,670
+هنا
+
+562
+00:50:57,490 --> 00:51:03,190
+باللي هو نكمل المحاضرة اللي هي نكمل الموضوع وإلى 
+563
+00:51:03,190 --> 00:51:04,170
+لقاء آخر 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/qX3DwVzbv6I_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/qX3DwVzbv6I_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8b1a95d8e14f7b74e4b6e433a35e59572fe81b21
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/qX3DwVzbv6I_postprocess.srt
@@ -0,0 +1,2252 @@
+1
+00:00:01,920 --> 00:00:04,660
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,660 --> 00:00:07,640
+والصلاة والسلام على سيد المسلم سيدنا محمد وعلى
+
+3
+00:00:07,640 --> 00:00:13,600
+أهله وصحبه أجمعين هذه هي المحاضرة الرقم 19 في مساق
+
+4
+00:00:13,600 --> 00:00:18,980
+تحليل حقيقه 2 لطلاب وطالبات الجامعة الإسلامية كلية
+
+5
+00:00:18,980 --> 00:00:25,600
+العلوم قسم الرياضياتاليوم هنتحدث عن الجزء الثالث
+
+6
+00:00:25,600 --> 00:00:29,980
+من المادة الجزء الأول اتحدثنا عن اللي هو الـ
+
+7
+00:00:29,980 --> 00:00:33,960
+differentiation أو الـ derivative وما يتعلق بها
+
+8
+00:00:33,960 --> 00:00:38,160
+طبعا الجزء الثاني اتعرفنا على ال integration وما
+
+9
+00:00:38,160 --> 00:00:43,320
+يتعلق به الآن هنحكي عن اللي هو الـ sequence of
+
+10
+00:00:43,320 --> 00:00:48,650
+functions اللي هي المتتابعات أو المتتالياتاللي هي
+
+11
+00:00:48,650 --> 00:00:53,010
+بيكون عنصر المتتابعة أو المتتالية هو عبارة عن دالة
+
+12
+00:00:53,010 --> 00:00:58,350
+وحنعرف العلاقة بين اللي هو الأنواع ال convergence
+
+13
+00:00:58,350 --> 00:01:05,630
+اللي للدوال واللي هي تأثير هذا النوع من ال
+
+14
+00:01:05,630 --> 00:01:10,730
+convergence على إنه اللي هو يدخل هذا ال limit لجوة
+
+15
+00:01:10,730 --> 00:01:14,650
+ال integration أو لو جوة ال .. الناتج هيكون اللي
+
+16
+00:01:14,650 --> 00:01:17,750
+هوالـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+17
+00:01:17,750 --> 00:01:17,770
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+18
+00:01:17,770 --> 00:01:18,110
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+19
+00:01:18,110 --> 00:01:18,530
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+20
+00:01:18,530 --> 00:01:19,010
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+21
+00:01:19,010 --> 00:01:26,890
+الـ الـ الـ الـ الـ الـ الـ
+
+22
+00:01:26,890 --> 00:01:28,030
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+23
+00:01:28,030 --> 00:01:28,210
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+24
+00:01:28,210 --> 00:01:31,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـإلى continuity
+
+25
+00:01:31,480 --> 00:01:38,400
+للـ limit أو اللي هو الـ differentiability اللي هو
+
+26
+00:01:38,400 --> 00:01:41,240
+الـ sequence of functions هل تؤدي إلى
+
+27
+00:01:41,240 --> 00:01:43,820
+differentiability و الـ integrability و الاخره و
+
+28
+00:01:43,820 --> 00:01:46,040
+مين اللي بيقدر يحافظ على هيك و هل في counter
+
+29
+00:01:46,040 --> 00:01:51,160
+examples تضحط أو اللي هو في نظريات اتبرناليوم بدنا
+
+30
+00:01:51,160 --> 00:01:55,140
+نتعرف على اللي هو أو بدنا نحكي عن شغلتين اللي هي
+
+31
+00:01:55,140 --> 00:01:59,700
+pointwise and uniform convergence نشوف شو معناته
+
+32
+00:01:59,700 --> 00:02:02,720
+pointwise convergence وشو معناته uniform
+
+33
+00:02:02,720 --> 00:02:08,660
+convergence وما الفرق بينهما نيجي الآنdefinition
+
+34
+00:02:08,660 --> 00:02:12,580
+let FN هذا عنوان ما حضرتنا زي ما قلنا point twice
+
+35
+00:02:12,580 --> 00:02:15,700
+and uniform convergence وعنوان الشبطر كله
+
+36
+00:02:15,700 --> 00:02:20,160
+sequences of functions الان definition let FN be a
+
+37
+00:02:20,160 --> 00:02:24,020
+sequence of functions on A subset من R to R ماشي
+
+38
+00:02:24,020 --> 00:02:27,840
+الحال الان نفترض ان FN عبارة عن sequence of
+
+39
+00:02:27,840 --> 00:02:32,000
+functions اللي هي من domain A جزء من R لأن كل
+
+40
+00:02:32,000 --> 00:02:36,550
+شغلنا في R احنا لعند مين لعند Rهذه اللي هي
+
+41
+00:02:36,550 --> 00:02:39,710
+sequence of functions يعني في عندي F1 وفي عندي F2
+
+42
+00:02:39,710 --> 00:02:44,410
+وفي عندي F3 وفي عندي F4 إلى ما لا نهاية من الدوال
+
+43
+00:02:44,410 --> 00:02:50,790
+عالمين على ال subset من R الآن بنجوء و لو جينا
+
+44
+00:02:50,790 --> 00:02:57,010
+فرضنا اللي هو عندنا function F من A note لعند مين
+
+45
+00:02:57,010 --> 00:03:02,830
+لعند ال Rالـ A note مين هي؟ A note عبارة عن مجموعة
+
+46
+00:03:02,830 --> 00:03:08,210
+جزئية من مين؟ من الـ 6A اللي فوق، الآن بنقول we
+
+47
+00:03:08,210 --> 00:03:14,550
+say that the sequence FN converts on Anote يعني
+
+48
+00:03:14,550 --> 00:03:20,270
+converts عالميا على a note to f إذا كان لكل x
+
+49
+00:03:20,270 --> 00:03:24,350
+element in A the sequence fn of x converts to f of
+
+50
+00:03:24,350 --> 00:03:29,970
+x in R لكل sequence لكل x element in A هو a note
+
+51
+00:03:30,750 --> 00:03:37,430
+بنقول الآن أنه F نحن نقول أن Fن تتعامل على A نوت
+
+52
+00:03:37,430 --> 00:03:48,490
+يعني بنقول Fن هذه الـ sequence تتعامل على F على A
+
+53
+00:03:48,490 --> 00:03:55,240
+نوت على مين؟ على A نوتإذا كان لكل X element in A
+
+54
+00:03:55,240 --> 00:04:00,280
+note على كل X element in A note بتطلع للـ F N of X
+
+55
+00:04:00,280 --> 00:04:07,560
+إيه اشمالها converge to mean to F of X إذا هذا حدث
+
+56
+00:04:07,560 --> 00:04:13,380
+بنقول أن F N converge to F on A note في الواقع
+
+57
+00:04:13,380 --> 00:04:18,060
+point twice يعني نقطة نقطة كيف نقطة نقطة يعني الـ
+
+58
+00:04:18,060 --> 00:04:30,670
+Nx1 بتكون fn of x1 converts to f of x1 شكتناx2 fn
+
+59
+00:04:30,670 --> 00:04:35,830
+of x2 converts to mean to f of x2 لكل نقطة على حدى
+
+60
+00:04:35,830 --> 00:04:40,150
+الـ fn of x بتروح لمين للـ f of x هذه بنسميها
+
+61
+00:04:40,150 --> 00:04:44,750
+pointwise convergence طب كيف، ده إيش معناته إحنا
+
+62
+00:04:44,750 --> 00:04:49,590
+بالـ Epsilon Delta Definition يعني وكأنه بنقول لكل
+
+63
+00:04:49,590 --> 00:04:56,890
+x إلمتين a0 limitF N of X as N goes to infinity
+
+64
+00:04:56,890 --> 00:05:05,860
+بساوي F of X يعني لكل إبسلونهذا نحكي عن X محددة
+
+65
+00:05:05,860 --> 00:05:11,620
+لكل إبسلون أكبر من سفر و لكل X element in A note
+
+66
+00:05:11,620 --> 00:05:15,740
+لأن أنا بحكي عن مين عن الـ X هذه there exists
+
+67
+00:05:15,740 --> 00:05:21,840
+Delta الآن الـ Delta اللي لجيتها بتعتمد على إبسلون
+
+68
+00:05:21,840 --> 00:05:26,460
+و بتعتمد على الـ X لأن أنا بحكي عن X point محددة
+
+69
+00:05:26,460 --> 00:05:30,300
+there exists .. arbitrary في الـ A note لكن fixed
+
+70
+00:05:31,000 --> 00:05:34,580
+there exists Delta بتعتمد عليه طبعا احنا بدنا ما
+
+71
+00:05:34,580 --> 00:05:39,600
+نكتب Delta هنكتب K ليش؟ لأن Delta احنا متعرفين
+
+72
+00:05:39,600 --> 00:05:44,600
+عليها تعبر عن المسافة بين two numbers لكن الاشي
+
+73
+00:05:44,600 --> 00:05:48,300
+اللي بروح إلى مال نهاية بدنا نعبر عنه أو متفجين
+
+74
+00:05:48,300 --> 00:05:53,700
+نعبر عنه برقم يدل على القبر إذا بنقول there exists
+
+75
+00:05:53,700 --> 00:06:02,110
+K نسميه K of هيعتمد على Y و XElement in N such
+
+76
+00:06:02,110 --> 00:06:10,750
+that for every N أكبر أو يساوي هذا الـ K of Y و X
+
+77
+00:06:10,750 --> 00:06:19,530
+بكون عندي المسافة F N of X ناقص F of X أصغر من مين
+
+78
+00:06:19,530 --> 00:06:28,790
+من Y إذن الـ N هذامعناته أن Fn of X بتروح للـ F of
+
+79
+00:06:28,790 --> 00:06:33,790
+X pointwise ليش pointwise؟ لأن الـ K اللي لاجيناها
+
+80
+00:06:33,790 --> 00:06:39,250
+اعتمدت على القيمة الـ X اللي احنا عارفين اللي قلنا
+
+81
+00:06:39,250 --> 00:06:44,530
+عنه limit Fn of X ايش بتساوي؟ بساوي F of X وهذا
+
+82
+00:06:44,530 --> 00:06:47,850
+اللي بختلف أصلا عن ال uniform convergence ال
+
+83
+00:06:47,850 --> 00:06:53,560
+uniform convergence ال K اللي بنلاجيها بتكونالـ K
+
+84
+00:06:53,560 --> 00:06:59,120
+اللي بنلاقيها هنلاقيها أصلا بتنفع على كل الإكسات
+
+85
+00:06:59,120 --> 00:07:02,660
+عشان الـ K هيك في ال uniform convergence الـ K
+
+86
+00:07:02,660 --> 00:07:06,580
+اللي بنلاقيها تعتمد بس على الـ Epsilon لكن بتنفع
+
+87
+00:07:06,580 --> 00:07:12,840
+على كل الإكسات عشان هيك فيش عندي أي مشكلة أنه اللي
+
+88
+00:07:12,840 --> 00:07:17,520
+هو تكون الـ K اللي هو أنه ال point wise
+
+89
+00:07:17,520 --> 00:07:22,400
+convergenceاللي هو عبارة ال .. ال .. آسف ال
+
+90
+00:07:22,400 --> 00:07:25,700
+uniform convergence يؤدي إلى ال point twice لكن ال
+
+91
+00:07:25,700 --> 00:07:29,340
+point twice ليس شرطاً وحنشوف هذا الكلام بالتفصيل
+
+92
+00:07:29,340 --> 00:07:38,860
+قدام أيوة يا أبو حسن فجأة لأ هانا فيش شيء لسه أه
+
+93
+00:08:27,530 --> 00:08:31,330
+اذا .. اذا يا جماعة هذا هو تعريف اللي هو الـ
+
+94
+00:08:31,330 --> 00:08:35,450
+pointwise convergence نيجي الآن لاللي هي الأمثلة
+
+95
+00:08:35,450 --> 00:08:40,970
+خلّينا ناخد أول مثال عندي نيجي ناخد اللي هو المثال
+
+96
+00:08:40,970 --> 00:08:49,310
+الأول let g n of xبساوة x اسم n x element in R and
+
+97
+00:08:49,310 --> 00:08:53,230
+n element in N show that g n of x هذه الدالة
+
+98
+00:08:53,230 --> 00:08:59,050
+converge pointwise to g of x على الفترة ناقص واحد
+
+99
+00:08:59,050 --> 00:09:02,770
+وواحد طبعا اللي هو open من عند الناقص واحد لعند
+
+100
+00:09:02,770 --> 00:09:08,040
+الواحدالان الـ g of x اللي متوقع انه اللي هو تكون
+
+101
+00:09:08,040 --> 00:09:11,000
+الـ g of x converts لها هي عبارة عن g of x
+
+102
+00:09:11,000 --> 00:09:14,320
+بالساوية سفر إذا كانت x في الفترة من نقص واحد واحد
+
+103
+00:09:14,320 --> 00:09:19,360
+و بالساوية واحد في حالة الـ x بتساوية واحد نشوف
+
+104
+00:09:19,360 --> 00:09:23,480
+كيف اللي هو اثبات اللي هي ان ال limit هذه سهل اللي
+
+105
+00:09:23,480 --> 00:09:26,840
+بتساوي اللي هي limit الـ g of x بالساوية الـ g of
+
+106
+00:09:26,840 --> 00:09:32,280
+x على الفترة المذكورة الكلام هلأ جيه سهل ونشوف كيف
+
+107
+00:09:32,940 --> 00:09:37,160
+اللي هو نوجد هذه اللي هي أولث بيت ال convergence
+
+108
+00:09:37,160 --> 00:09:44,360
+الآن في حالة ال X عندي هنا في حالة ال X عندي
+
+109
+00:09:44,360 --> 00:09:48,820
+بتساوي واحد ال GN of X اللي هي عبارة عن X أسن
+
+110
+00:09:48,820 --> 00:09:54,340
+مظبوط ال X أسن اللي هي واحد بتصير عبارة عن جداش عن
+
+111
+00:09:54,340 --> 00:09:58,400
+واحد خلّي بس واضح لكم ال .. ال ..
+
+112
+00:10:00,790 --> 00:10:07,310
+المثال يظهر كله عندكم، هي عندى الـGN of X بساوي X
+
+113
+00:10:07,310 --> 00:10:13,050
+أُس N في حالة الـX بيساوي 1، هيكون GN of 1 بيساوي
+
+114
+00:10:13,050 --> 00:10:17,630
+1 أُس N اللي هو إيش؟ واحد، هذه دالة ثابتة أكيد
+
+115
+00:10:17,630 --> 00:10:21,830
+limited GN لما N تروح إلى مالة نهاية اللي هو limit
+
+116
+00:10:21,830 --> 00:10:25,150
+الواحد اللي هو واحد، ثابت طيب، الآن لو كانت الـX
+
+117
+00:10:25,150 --> 00:10:27,730
+في الفترة بيه ناقص واحد واحد، يعني absolute بين
+
+118
+00:10:27,730 --> 00:10:31,920
+الـX أصغر من واحد، يعني كثيرماشي، إذا limit GN of
+
+119
+00:10:31,920 --> 00:10:36,320
+X as N goes to infinity بساوة limit X أُس N لما N
+
+120
+00:10:36,320 --> 00:10:39,840
+تروح إلى ما لنهاية هذا الـ X بين الناقص واحد
+
+121
+00:10:39,840 --> 00:10:43,220
+والواحد يعني كسر وكسر كل ما رفعته لأس بصغر بروحش
+
+122
+00:10:43,220 --> 00:10:47,700
+بساوة بساوة سفر لأن في حالة ال absolute value للـ
+
+123
+00:10:47,700 --> 00:10:53,180
+X أكبر من واحد لأنه ليش بنبحث .. ب .. ب .. ب ..
+
+124
+00:10:53,180 --> 00:10:58,500
+احنا بدنا نبحث في برة للفترة لإنه أصلا الـ GN of X
+
+125
+00:10:59,470 --> 00:11:05,550
+معرفة على كل الـR آه بس برا اللي هي الفترة بناقص
+
+126
+00:11:05,550 --> 00:11:09,930
+واحد وواحد مش هيكونلها limit لسبب انتوا عارفينه
+
+127
+00:11:09,930 --> 00:11:12,830
+ليش هو انه في حالة ال absolute value X أكبر من
+
+128
+00:11:12,830 --> 00:11:17,990
+واحد بيكون limit GN of X بيساوي limit X أسن ال X
+
+129
+00:11:17,990 --> 00:11:22,710
+عبارة عن اللي هي أشمالها قيمته اللي هو ال absolute
+
+130
+00:11:22,710 --> 00:11:27,490
+value كبيرفالان limit ال X أُس N هيكون إيه أشماله
+
+131
+00:11:27,490 --> 00:11:33,510
+does not converge does not converge الآن لإنه
+
+132
+00:11:33,510 --> 00:11:39,430
+بيصير إيه أشماله unbounded طيب أكيد عارفين هذه
+
+133
+00:11:39,430 --> 00:11:42,730
+المعلومة في حالة ال X أكبر من واحد if X بالساوى
+
+134
+00:11:42,730 --> 00:11:47,750
+سالب واحد عند الواحد قلنا بيطلع له قيمة بين الواحد
+
+135
+00:11:47,750 --> 00:11:52,480
+والسالب واحد طلع عنده قيمةLimit يعني لأن عند ال X
+
+136
+00:11:52,480 --> 00:11:55,860
+بالساوية سالب واحد بيصير هذا عبارة عن ناقص واحد
+
+137
+00:11:55,860 --> 00:11:59,820
+أسن ناقص واحد أسن اللي هي limit هذه مشهورة اللي هو
+
+138
+00:11:59,820 --> 00:12:02,880
+مثال على انه limit على bounded function و limit
+
+139
+00:12:02,880 --> 00:12:05,520
+اللي هي أشماله does not exist أو bounded sequence
+
+140
+00:12:05,520 --> 00:12:08,500
+و limit اللي هي does not exist ال limit لهذه does
+
+141
+00:12:08,500 --> 00:12:12,200
+not exist وعارفين انتوا ليشإذا صار عندى limit gn
+
+142
+00:12:12,200 --> 00:12:18,220
+of x بيساوي g of x في الفترة من ناقص واحد لعند مين
+
+143
+00:12:18,220 --> 00:12:23,220
+لعند الواحد حيث الـ g of x كما هي مذكورة أعلى إذا
+
+144
+00:12:23,220 --> 00:12:26,540
+هذه مثال عالمين عن ال point wise convergence
+
+145
+00:12:26,540 --> 00:12:31,840
+وشوفنا كيف بنوجد ال point wise convergenceطيب نيجي
+
+146
+00:12:31,840 --> 00:12:38,720
+لاللي هو مثال آخر برضه مثال يعني بتصور مثال سهل و
+
+147
+00:12:38,720 --> 00:12:43,760
+بتعرفوا تعملوه حتى لو سيبناه لكم لحالكم إيش بيقول
+
+148
+00:12:45,080 --> 00:12:51,960
+وعند الدالة ايش اسمها الدالة F of X بتساوي F of X
+
+149
+00:12:51,960 --> 00:12:58,400
+بتساوي اللي هو واحدة الان sign الان X زائد ان الان
+
+150
+00:12:58,400 --> 00:13:03,200
+هذه ال function sign function ماشي الحال بقول اثبت
+
+151
+00:13:03,200 --> 00:13:08,490
+ان ال limit لها بيساوي ايه عشان بيساوي سفرالآن لكل
+
+152
+00:13:08,490 --> 00:13:11,530
+x² موجودة في الـ R إحنا بنحكي عن pointwise
+
+153
+00:13:11,530 --> 00:13:16,130
+convergence مدينة pointwise convergence خُدلي الآن
+
+154
+00:13:16,130 --> 00:13:20,310
+هذه الـ function اللي هي fn of x زي ما هو مسميها
+
+155
+00:13:20,310 --> 00:13:24,210
+لإنها ترتبط بـ n اللي هي f1 of x واحدة، f2 of x
+
+156
+00:13:24,210 --> 00:13:27,710
+واحدة، f3 of x واحدة، طبعا متعود عنه في كل مرة n
+
+157
+00:13:27,710 --> 00:13:30,010
+بواحد، n باتنين، n تلاتة، بتطلعلك عبارة عن
+
+158
+00:13:30,010 --> 00:13:32,350
+sequence of functions هذه الـ sequence of
+
+159
+00:13:32,350 --> 00:13:37,220
+functionsالان متوقعين احنا limit هي ايش يساوي سفر
+
+160
+00:13:37,220 --> 00:13:40,800
+يعني ال F of X ايش بتتساوي بساوي سفر شوف الان
+
+161
+00:13:40,800 --> 00:13:46,340
+احسبلي ال F N of X ناقص F of Xاللي هي عبارة عن 1N
+
+162
+00:13:46,340 --> 00:13:51,500
+Sin N X زيادة هذي أكيد أصغر أو أصغر من 1 لأن الـ
+
+163
+00:13:51,500 --> 00:13:55,220
+Sin دائما أصغر أو أصغر من 1 إذا صار عندي اللي هي
+
+164
+00:13:55,220 --> 00:14:00,440
+هذه القيمة بين السفر و بين 1 لـ N بدنا ال limit as
+
+165
+00:14:00,440 --> 00:14:03,660
+N goes to infinity هذه بتروح للسفر وهذه سفر إذا
+
+166
+00:14:03,660 --> 00:14:07,120
+limit هذه as N goes to infinity بيساوي جداش بيساوي
+
+167
+00:14:07,120 --> 00:14:12,220
+سفر أو بمعنى آخر limit F N of X بيساوي Fof x فعلاً
+
+168
+00:14:12,220 --> 00:14:16,020
+صار طالع عند ال limit الـ 1 الـ n sin n x زي n
+
+169
+00:14:16,020 --> 00:14:20,740
+بساوي اللي هو f of x اللي هي سفر إذا هدولا مثلين
+
+170
+00:14:20,740 --> 00:14:24,460
+على pointwise convergence كيف نوددهم وهذه أمثلة
+
+171
+00:14:24,460 --> 00:14:29,580
+بسيطة يعني أخدنا زيها في اللي هو تحليل واحد أو حتى
+
+172
+00:14:29,580 --> 00:14:35,960
+في الcalculus الآن لما هلان a sequence of
+
+173
+00:14:35,960 --> 00:14:41,490
+functions f nof functions on A subset from R to R
+
+174
+00:14:41,490 --> 00:14:46,090
+converge to a function F on A note if and only if
+
+175
+00:14:46,090 --> 00:14:49,970
+for every Y أكبر من 0 and for every X element in A
+
+176
+00:14:49,970 --> 00:14:54,230
+there exists K element in N such that الـ K مين
+
+177
+00:14:54,230 --> 00:14:59,390
+هي؟ KY of X قصده if N أكبر سوى K then FN of X ناقص
+
+178
+00:14:59,390 --> 00:15:02,210
+F of X أصغر من Y هذا قلته أصلا هذا من التعريف
+
+179
+00:15:02,210 --> 00:15:06,510
+مباشرة بما أنه اللي هو عندي الـ FN
+
+180
+00:15:09,190 --> 00:15:16,670
+converges pointwise to F on اللي هو main A إيش
+
+181
+00:15:16,670 --> 00:15:21,390
+معناته هذا؟ معناته for every X element in A هذا
+
+182
+00:15:21,390 --> 00:15:26,350
+بكافئ for every X element in A limit F on of X لما
+
+183
+00:15:26,350 --> 00:15:31,150
+on تروح لما لنهاية بسوء F of X مظبوط؟ ده كل X وين
+
+184
+00:15:31,150 --> 00:15:33,930
+موجودة في الـA أو وين و تحسب ما اللي بدناها هذا
+
+185
+00:15:33,930 --> 00:15:37,580
+بكافئ أنهاللي هو بالـ Epsilon Delta Definition for
+
+186
+00:15:37,580 --> 00:15:41,500
+every X element in A for every Y أكبر من 0 there
+
+187
+00:15:41,500 --> 00:15:45,520
+exists K الآن الـ K هتعتمد عالمياً على الـ Epsilon
+
+188
+00:15:45,520 --> 00:15:51,120
+والـ X element in N such that for every N أكبر
+
+189
+00:15:51,120 --> 00:15:54,740
+يساوي K اللي هي مين هذه؟ اللي هي K Epsilon و X
+
+190
+00:15:54,740 --> 00:16:01,810
+هيكون عند الـ F N of Xناقص f of x أصغر من مين من
+
+191
+00:16:01,810 --> 00:16:06,090
+إبسنون وهذه اللي هي مين قلن ما هذا الأصل لو remark
+
+192
+00:16:06,090 --> 00:16:10,050
+بتنفع وخلاص أساس أنه مباشرة من التعريف الان
+
+193
+00:16:10,050 --> 00:16:15,370
+definition لأن a sequence fn of functions a subset
+
+194
+00:16:15,370 --> 00:16:22,450
+من R to R converts الأن إيش uniformly on a نقطة
+
+195
+00:16:22,450 --> 00:16:27,740
+subset من R to a function f من a نقطة عند R ifالآن
+
+196
+00:16:27,740 --> 00:16:31,420
+convergence uniformly قلت أنا قبل بشوية أو في
+
+197
+00:16:31,420 --> 00:16:35,520
+بداية المحاضرة إن ال convergence uniformly معناته
+
+198
+00:16:35,520 --> 00:16:40,480
+الـ K اللي لجيناها أش مالها بتنفع لكل ال X يعني ما
+
+199
+00:16:40,480 --> 00:16:44,020
+بنقولش لكل X element نهي أو لكل Y أكبر من 0 there
+
+200
+00:16:44,020 --> 00:16:49,740
+exists K لأبنقول لكل إبسلون there exist K such
+
+201
+00:16:49,740 --> 00:16:56,380
+that لكل N أكبر يساوي K و لكل X هذه بتنفع يعني ال
+
+202
+00:16:56,380 --> 00:17:00,540
+K اللي جيتها بس بتعتمد على مين؟ على ال إبسلون وهذا
+
+203
+00:17:00,540 --> 00:17:04,120
+معناه ال uniform convergence وهي اللي مكتوب هنا
+
+204
+00:17:04,120 --> 00:17:09,420
+أنه بنقولFn sequence of functions من A على A
+
+205
+00:17:09,420 --> 00:17:12,680
+subset من R converges uniformly on A node subset
+
+206
+00:17:12,680 --> 00:17:17,660
+من A من A to a function F من A نقطة عند R if for
+
+207
+00:17:17,660 --> 00:17:21,900
+every epsilon أكبر من 0 there exists K of epsilon
+
+208
+00:17:21,900 --> 00:17:25,620
+تعتمد بس على مين على إبسلون such that if N أكبر
+
+209
+00:17:25,620 --> 00:17:31,720
+سوء K and X element in A هذا بيكون أصغر من مين من
+
+210
+00:17:31,720 --> 00:17:36,170
+إبسلون هذا التعبيرلما أقول لكل إبسلون there exists
+
+211
+00:17:36,170 --> 00:17:41,250
+K يعني الـ K تعتمد بس على مين على إبسلون و بعدين
+
+212
+00:17:41,250 --> 00:17:46,590
+كل هذا اللي هي هنا بتنفع لكل الـ N أكبر من K و لكل
+
+213
+00:17:46,590 --> 00:17:50,190
+الـ X elements in R لكن لو أقول لكل إبسلون أكبر من
+
+214
+00:17:50,190 --> 00:17:53,730
+صفرهم لكل X there exists K الـ K هتعتمد على
+
+215
+00:17:53,730 --> 00:17:56,790
+الإبسلون و على الـ X في الـ point twice هنا لكل
+
+216
+00:17:56,790 --> 00:18:00,050
+إبسلون بيلاجي K بس بتعتمد على مين على الإبسلون إذا
+
+217
+00:18:00,050 --> 00:18:05,050
+if the sequence of N converge uniformlyto some
+
+218
+00:18:05,050 --> 00:18:09,050
+function f على الـ A note إذا أكيد A شمالها this
+
+219
+00:18:09,050 --> 00:18:13,470
+sequence converges pointwise لأنه أنت أصلا نور على
+
+220
+00:18:13,470 --> 00:18:17,550
+نور في حالة الـ uniform لجيت K of إبسلون الآن هذا
+
+221
+00:18:17,550 --> 00:18:22,030
+الـ K of إبسلون هانا بس بيقول لي لجيلي K تعتمد في
+
+222
+00:18:22,030 --> 00:18:25,210
+ال pointwise تعتمد على الإبسلون تعتمد على ال X
+
+223
+00:18:25,210 --> 00:18:29,830
+ماتفرجش عندي أنا عشان pointwise بس لجيلي ال K بحيث
+
+224
+00:18:29,830 --> 00:18:33,750
+إنه لكل N أكبر و كده هيكون هذا متحققطب مانا في ال
+
+225
+00:18:33,750 --> 00:18:36,750
+uniform اللي ملاقيها و أصلا ملاقيها مجردة بتنفع
+
+226
+00:18:36,750 --> 00:18:41,790
+على كل ال X إذا أكيد بتنفع على كل X عليها حدها إذا
+
+227
+00:18:41,790 --> 00:18:46,330
+ال uniform convergence يؤدي إلى ال point wise لكن
+
+228
+00:18:46,330 --> 00:18:49,890
+ال converts need not to be true in general أكيد
+
+229
+00:18:49,890 --> 00:18:54,890
+لأن وإلا ليش احنا نحكي عن اشت اتنين متساويين و
+
+230
+00:18:54,890 --> 00:19:02,970
+المكان طيب نيجي الآن اللي مال اللي عنديأسيقونس fn
+
+231
+00:19:02,970 --> 00:19:06,970
+of functions on A subset من R to R بدون في التعريف
+
+232
+00:19:06,970 --> 00:19:10,650
+الآن، بيقول لـ fn a sequence of functions fn on A
+
+233
+00:19:10,650 --> 00:19:14,690
+subset من R to R does not converge uniformly in O
+
+234
+00:19:14,690 --> 00:19:19,130
+naught to a function f من A naught عند R if and
+
+235
+00:19:19,130 --> 00:19:22,650
+only if for every أكبر من سفر، there exists a
+
+236
+00:19:22,650 --> 00:19:30,220
+subsequence fnk of fn andأسيقونس xk in a نوت such
+
+237
+00:19:30,220 --> 00:19:34,720
+that fnk of xk ناقص f of xk أكبر أو يساوي y نوت
+
+238
+00:19:34,720 --> 00:19:43,220
+لكل k element ان نيجي نطلع لهذه ونشوف كيف بدنا
+
+239
+00:19:43,220 --> 00:19:51,640
+نبرهنها الآن
+
+240
+00:19:51,640 --> 00:19:58,880
+احنا اتفجنا قبل بشوية ان fnconverges uniformly to
+
+241
+00:19:58,880 --> 00:20:03,240
+F هذه رمزها A شمالها converges uniformly سهم واحد
+
+242
+00:20:03,240 --> 00:20:08,820
+اسطلاحا هذا مع بعض سهم واحد بنقصد فيه ال bond
+
+243
+00:20:08,820 --> 00:20:14,000
+twice سهمين بنقصد فيهم uniformly convergence فان
+
+244
+00:20:14,000 --> 00:20:18,400
+convergence uniformly on A أو بسميه هو A ولا A not
+
+245
+00:20:18,400 --> 00:20:24,460
+on A not الانلـ function f من أين؟ f من a note
+
+246
+00:20:24,460 --> 00:20:29,980
+لعند اللي هي hr و الـ fn sequence من a لعند r يعني
+
+247
+00:20:29,980 --> 00:20:33,020
+a note جزء من مين اللي هو قد تكون اللي هي مين كل
+
+248
+00:20:33,020 --> 00:20:35,820
+الـ a المهم أخدها a note subset من a على أساس اللي
+
+249
+00:20:35,820 --> 00:20:39,920
+هو يحكي in general إذن fn converges الـ f on a
+
+250
+00:20:39,920 --> 00:20:44,480
+note if and only if هذا معناه if and only if for
+
+251
+00:20:44,480 --> 00:20:49,060
+every epsilon أكبر من 0 there exists k تعتمد على
+
+252
+00:20:49,060 --> 00:20:55,490
+الـ epsilon element in Nsuch that for every n أكبر
+
+253
+00:20:55,490 --> 00:21:01,510
+أو سوء k و for every x element in A0 مكون عندي fn
+
+254
+00:21:01,510 --> 00:21:08,470
+of x ناقص f of x أصغر من مين من إبسلون هذا معناة
+
+255
+00:21:08,470 --> 00:21:12,250
+الـ Uniform Convergence بدي أنفي اللي أنا بقول لـ
+
+256
+00:21:12,250 --> 00:21:17,090
+fn يعني هو كأنني بتعمله proof proof لهمين؟ لهذه مش
+
+257
+00:21:17,090 --> 00:21:23,260
+ال proof لهذه proof لهذه يعني الـ fnDoes not
+
+258
+00:21:23,260 --> 00:21:28,800
+converge uniformly لمن؟ لـ F on A node if and only
+
+259
+00:21:28,800 --> 00:21:33,480
+if بدي ن في هذا، إيش بيصير عندي؟ for every epsilon
+
+260
+00:21:33,480 --> 00:21:37,240
+أكبر من 0 بيصير there exists epsilon not أكبر من 0
+
+261
+00:21:37,240 --> 00:21:41,420
+لأن there exists .. لكل epsilon there exists K لأن
+
+262
+00:21:41,420 --> 00:21:45,480
+there exists epsilon not such that for every K،
+
+263
+00:21:45,480 --> 00:21:50,410
+element الـ Nأه اللي هال for every n أكبر من .. ان
+
+264
+00:21:50,410 --> 00:21:54,470
+هاذي بيصير there exist n الـ n هتعتمد على مين؟ على
+
+265
+00:21:54,470 --> 00:22:01,290
+k عشان هي كم سميها nk أكبر أو يساوي k ماشيthere
+
+266
+00:22:01,290 --> 00:22:04,090
+exist لأن بدل من for every n أكبر سوا k بصير there
+
+267
+00:22:04,090 --> 00:22:09,090
+exist nk أكبر سوا k such that لأن for every x أيش
+
+268
+00:22:09,090 --> 00:22:14,410
+بيكون ل for every k there exist x برضه ال x هتعتمد
+
+269
+00:22:14,410 --> 00:22:18,690
+على مين على k يعني لكل k باللي جيلها nk و باللي
+
+270
+00:22:18,690 --> 00:22:23,330
+جيلها ال xk such that fn
+
+271
+00:22:24,480 --> 00:22:31,420
+اللي سميته إيش اسمها أنا nk of x اللي هي xk ناقص f
+
+272
+00:22:31,420 --> 00:22:39,580
+of xk أكبر أو يساوى مين إبسلون نقطة إذا صار عندي،
+
+273
+00:22:39,580 --> 00:22:45,510
+الآننفي هذه لكل y there exist k لأن there exist y
+
+274
+00:22:45,510 --> 00:22:51,210
+note such that لكل k يعني لو k بواحد بقدر ألاقي أن
+
+275
+00:22:51,210 --> 00:22:57,530
+واحد أكبر شو k و x واحد بحيث أن f x واحد أن واحد
+
+276
+00:22:57,530 --> 00:23:03,010
+ناقص f of x واحد أكبر شو y note لأن there exist y
+
+277
+00:23:03,010 --> 00:23:06,110
+note for every هذا ال y note ثبتت واحدة بلقيتها
+
+278
+00:23:06,110 --> 00:23:09,510
+للكل there exist of note such that for every k أش
+
+279
+00:23:09,510 --> 00:23:15,840
+بتساوي اتنينthere exists N2 بحيث أن X2 أو there
+
+280
+00:23:15,840 --> 00:23:23,600
+exists X2 بحيث أن F of X2 F N2 of X2 نقص F of X2
+
+281
+00:23:23,600 --> 00:23:30,350
+أكبر سوى Y نوت كذا بسوء تلاتةنفس الاشي كي بيساوي
+
+282
+00:23:30,350 --> 00:23:34,770
+أربعة، نفس الاشي إذا وكأن الـ gate A شمالها أفقًا
+
+283
+00:23:34,770 --> 00:23:37,810
+واحد أفقًا اتنين أفقًا تلت أفقًا أربع أفقًا خمسة،
+
+284
+00:23:37,810 --> 00:23:42,570
+من مين؟ من اللي هم الأفقان هذولة، يعني هذولة sub
+
+285
+00:23:42,570 --> 00:23:46,090
+sequence من مين هذولة، يعني هذا معناته if and only
+
+286
+00:23:46,090 --> 00:23:49,470
+if there exists epsilon not أكبر من سفر such that
+
+287
+00:23:49,470 --> 00:23:57,630
+أو such that andاللي هو الأن هذا لجت منها لكل كده
+
+288
+00:23:57,630 --> 00:24:10,710
+كده لجت من a subsequence اللي هي FNK of FN and a
+
+289
+00:24:10,710 --> 00:24:17,130
+sequenceXK من وين هذه الـ XK طبعا من وين موجودة من
+
+290
+00:24:17,130 --> 00:24:25,430
+الـ A جايات من وين من الـ A XK in A such that FNK
+
+291
+00:24:25,430 --> 00:24:34,230
+of XK ناقص F of XK أكبر أو يساوي epsilon note وهذا
+
+292
+00:24:34,230 --> 00:24:40,770
+اللي هو المطلوب هذا الكلام لكل K ومالها لكل K
+
+293
+00:24:42,530 --> 00:24:48,610
+Element in N يعني بمعنى أخر عشان أقول FN does not
+
+294
+00:24:48,610 --> 00:24:52,330
+converge لل F on A note does not converge in a
+
+295
+00:24:52,330 --> 00:24:56,970
+formula طبعا إيش معناته أنه بلاجة epsilon note؟
+
+296
+00:24:57,540 --> 00:25:03,660
+وsub-sequence fnk من fn وsequence xak in a بحيث أن
+
+297
+00:25:03,660 --> 00:25:09,100
+الـ absolute value of fnk of xk ناقص f of xk أصغر
+
+298
+00:25:09,100 --> 00:25:13,880
+من الـ y0 لكل k element هناإذًا a sequence of
+
+299
+00:25:13,880 --> 00:25:17,480
+functions from A subset من R to R does not
+
+300
+00:25:17,480 --> 00:25:21,420
+converge uniformly أو does not converge uniformly
+
+301
+00:25:21,420 --> 00:25:25,440
+من A نوت subset من A to a function F من A نوت لعند
+
+302
+00:25:25,440 --> 00:25:32,000
+R هذا يكافئ أن هناك ي أكبر من صفر ي نوتهندق
+
+303
+00:25:32,000 --> 00:25:36,140
+subsequence fnk of fn and a sequence xk in a node
+
+304
+00:25:36,140 --> 00:25:41,180
+such that fnk of xk نقص f of xk أكبر وساوي epsilon
+
+305
+00:25:41,180 --> 00:25:46,340
+note هذه اللي هي نفي الـ uniform convergence يعني
+
+306
+00:25:46,340 --> 00:25:51,040
+هنستخدمها في إثبات أنه اللي هو الـ C الـ function
+
+307
+00:25:52,030 --> 00:25:56,170
+الـ sequence of functions does not converge
+
+308
+00:25:56,170 --> 00:26:04,410
+uniformly to some function مثلًا F أو غيره طيب أخد
+
+309
+00:26:04,410 --> 00:26:12,730
+أمثلة إذا الآن نيجي نشوف هذه اللي هي النظرية عشان
+
+310
+00:26:12,730 --> 00:26:17,570
+دالكم متذكرينها نشوف
+
+311
+00:26:17,570 --> 00:26:27,720
+سؤالنا أو مثالناالآن مثالين الـ Dn of X بساوي X أس
+
+312
+00:26:27,720 --> 00:26:32,380
+أن و X element in R و N element in R يظهر أن Dn لا
+
+313
+00:26:32,380 --> 00:26:37,460
+يتعامل بشكل عام على الفترة ناقص واحد واحد إلى Dn
+
+314
+00:26:37,460 --> 00:26:43,590
+.. إلى D of X اللي هي هذه بقولهذه أثبتناها قبل
+
+315
+00:26:43,590 --> 00:26:47,910
+بشوية إنها convergence pointwise على الفترة بين
+
+316
+00:26:47,910 --> 00:26:52,330
+ناقص واحد وواحد يعني هذا مثال على sequence of
+
+317
+00:26:52,330 --> 00:26:56,890
+functions convergence pointwise على الفترة بين
+
+318
+00:26:56,890 --> 00:27:00,570
+ناقص واحد وواحد لكن does not converge uniformly
+
+319
+00:27:00,570 --> 00:27:06,150
+على الفترة ناقص واحد وواحد هذا مثال على إن ال
+
+320
+00:27:06,150 --> 00:27:12,510
+pointwise convergence need notto imply اللي هو
+
+321
+00:27:12,510 --> 00:27:19,730
+uniform convergence الان هو طبعا حاسب حسبته عملها
+
+322
+00:27:19,730 --> 00:27:22,150
+و كده و كده و دارسها و اعطيني على طول اللي هو الـY
+
+323
+00:27:22,150 --> 00:27:27,370
+النقطة اللي بتنفع خليني نشوف احنا الان عندي اللي
+
+324
+00:27:27,370 --> 00:27:33,350
+هو GN of X بسوء X أسئلة غلطي اني ألاجياللي هو
+
+325
+00:27:33,350 --> 00:27:37,230
+subsequence fnk من الـ sequence هذه إيش الـ
+
+326
+00:27:37,230 --> 00:27:41,210
+sequence اللي عندي؟ اللي هي x أُس n ماشي الحال
+
+327
+00:27:41,210 --> 00:27:46,150
+اللي بحيث أنه fnk of xk ناقص f of xk يكون أكبر
+
+328
+00:27:46,150 --> 00:27:50,530
+يساوي y نوت اللي هو فكرته هو بيقولك أنا خليني أجيب
+
+329
+00:27:50,530 --> 00:27:56,290
+subsequence fnkاللي هو .. او sequence xk بحيث ان
+
+330
+00:27:56,290 --> 00:28:01,510
+يكون هذه قيمته عبارة عن ثابت و هذي يصير عبارة عن
+
+331
+00:28:01,510 --> 00:28:05,290
+إيش ثابت لإنه في الأصل ثابت ماعطيني يا واحد و سفر
+
+332
+00:28:05,290 --> 00:28:09,610
+يعني يقوللي هذا ثابت ناقص ثابت بطلع رقم فبختار ال
+
+333
+00:28:09,610 --> 00:28:12,590
+epsilon المعينة اللي بتكون هذا الرقم أكتر منها
+
+334
+00:28:12,590 --> 00:28:16,790
+يعني بسمع علي أن أعمل حسابات لهذه أنها تطلع قيمة
+
+335
+00:28:16,790 --> 00:28:21,230
+ثابتة أختار F and K sequence من هنا يطلع اللي هي F
+
+336
+00:28:21,230 --> 00:28:25,080
+and K of xk يكون ثابتو بيصير هذا المقدار ثابت و
+
+337
+00:28:25,080 --> 00:28:28,560
+على طول بختار الـ Epsilon Note اللي بتأدي الغلط
+
+338
+00:28:28,560 --> 00:28:35,240
+الان ايش اختار؟ قال لي خليني اخد اللي هي عند FGN
+
+339
+00:28:35,240 --> 00:28:39,660
+of X عشان بيساوي XSAN الان بيقول لي خليني اخد ال
+
+340
+00:28:39,660 --> 00:28:44,580
+NK اللي هي عبارة عن من؟ عن ال K، عن ال K، ماشي؟
+
+341
+00:28:44,580 --> 00:28:49,180
+هالجد تعرف ليش اختار ال Kوخد الـ XK هو عارف أنه
+
+342
+00:28:49,180 --> 00:28:53,380
+الـ X الان الـ XK بده يخلي هذا كابت لما يطلع ليه
+
+343
+00:28:53,380 --> 00:29:00,260
+الـ GN وكده خد الـ XK بتساوي 1 على 2 أس 1 على K
+
+344
+00:29:00,260 --> 00:29:08,850
+طبعا أضحك ليش؟ عشان الآن لما أخد الـ XKبساوة نص
+
+345
+00:29:08,850 --> 00:29:12,090
+مثلا مش عاجبك نص حط تلت ربع خمس عشرة مليون اللي
+
+346
+00:29:12,090 --> 00:29:16,090
+بدك إياه بس وين في الفترة يطلع قيمته في الفترة وين
+
+347
+00:29:16,090 --> 00:29:19,630
+ناقص واحد واحد عساس ان ظلنا ال sequence سبعتنا
+
+348
+00:29:19,630 --> 00:29:22,550
+does not converge على الفترة ناقص واحد واحد عشان
+
+349
+00:29:22,550 --> 00:29:28,210
+هي أخد ال XA شمالها ال XK نص أس واحد على K كيف ما
+
+350
+00:29:28,210 --> 00:29:32,450
+تعمل لو ترفحها هتظل بين الفترة ناقص واحد ومين واحد
+
+351
+00:29:33,630 --> 00:29:43,770
+الان F NK of XK بساوي X كله نص أس واحد على K أس
+
+352
+00:29:43,770 --> 00:29:50,450
+مين أس NK عشان يخلي هذا المقدار ثابتبدو يخلّي الان
+
+353
+00:29:50,450 --> 00:29:55,790
+كاش بتساوي K فبصير واحد على K في K بتطلع واحد
+
+354
+00:29:55,790 --> 00:30:00,570
+فعشان هيك أخد الان K بساوي K فصارت الان ال
+
+355
+00:30:00,570 --> 00:30:07,550
+subsequence اللي هو عبارة عن FK of XK يعني ال
+
+356
+00:30:07,550 --> 00:30:11,650
+index هنا و ال index هنا بقى صح أبنفع أبنفع لأنه
+
+357
+00:30:11,650 --> 00:30:17,540
+أشماله عند الان هذا الانالان K ليه subsequence من
+
+358
+00:30:17,540 --> 00:30:22,680
+مين؟ من ال F N فالان عندي ال K اللي جاته بيصير
+
+359
+00:30:22,680 --> 00:30:26,180
+عندي K بواحد باتنين بتلتة باربعة بجد ما بدي أو K K
+
+360
+00:30:26,180 --> 00:30:29,780
+زائد واحد K زايد اتنين من ضمن مين؟ من ضمن ال
+
+361
+00:30:29,780 --> 00:30:33,400
+sequence F N بتكون نفسها بس بدت من وين؟ من عند ال
+
+362
+00:30:33,400 --> 00:30:40,350
+K اللي أخدها الآن صار عندي الآنالـ xk اختارها
+
+363
+00:30:40,350 --> 00:30:45,510
+بالشكل هذا والان k اختارها كيه بيصير عندي الان gk
+
+364
+00:30:45,510 --> 00:30:50,630
+of xk أنا بسميها f معلش هي g gk of xk ناقص g of xk
+
+365
+00:30:50,630 --> 00:30:57,510
+بساوي gk of xk زي ما حسبناها هذا g k of xk بساوي
+
+366
+00:30:57,510 --> 00:31:04,970
+هذه ويساوي نصبصير عبارة عن نص ناقص g of x كأي x في
+
+367
+00:31:04,970 --> 00:31:07,890
+الفترة هذه الـ g of x اللي هيش بتساوي سفر ناقص سفر
+
+368
+00:31:07,890 --> 00:31:11,850
+هو يساوي نص الان الـ E لقطة اللي بدي أختارها عشان
+
+369
+00:31:11,850 --> 00:31:16,330
+ما يصير النص أكبر منها أختارها جديش عبارة عن ربع
+
+370
+00:31:16,330 --> 00:31:19,210
+يعني واحد قال لي أنا أقولك تاخد تلت أو تاخد ربع
+
+371
+00:31:19,210 --> 00:31:23,820
+بصير ال E لقطة اللي اختارهاتعتمد على إنها تكون
+
+372
+00:31:23,820 --> 00:31:27,420
+اللي هي اللي بيطلع أكبر من الـ Epsilon Note يعني
+
+373
+00:31:27,420 --> 00:31:32,000
+لو بتارها ربع هنا .. هنا ربع أس واحد على K اللي هي
+
+374
+00:31:32,000 --> 00:31:36,220
+الـ XK بيصير هذه Epsilon Note تاخدها مثلا عبارة عن
+
+375
+00:31:36,220 --> 00:31:40,170
+خمس أو سدوس أو إلى آخرينإذا اللي جينا epsilon note
+
+376
+00:31:40,170 --> 00:31:44,030
+وsub sequence من ال functions اللي هي f and k اللي
+
+377
+00:31:44,030 --> 00:31:47,950
+هي fk في الواقع و sequence xk في ال .. في ال a
+
+378
+00:31:47,950 --> 00:31:52,990
+هيها بحيث أنه gk of xk نقص g of xk اللي هي أكبر من
+
+379
+00:31:52,990 --> 00:31:56,150
+epsilon note إذا صار عندي اللي هي g and does not
+
+380
+00:31:56,150 --> 00:32:02,030
+converge uniformly to g on this interval طيب
+
+381
+00:32:07,270 --> 00:32:10,430
+هد سيبكوا منها لإن هد بتيجي بعدين بعد شوية لما
+
+382
+00:32:10,430 --> 00:32:15,290
+بنعرف لسه ال norm خلينا اللي هو هي ال norm عرفناها
+
+383
+00:32:15,290 --> 00:32:22,110
+تحت definition
+
+384
+00:32:22,110 --> 00:32:29,270
+F هي subset من R and Phi من R لR is a function we
+
+385
+00:32:29,270 --> 00:32:36,140
+say that Phi is bounded on Aif the set of phi of A
+
+386
+00:32:36,140 --> 00:32:41,600
+is bounded subset of R يعني الآن الـ function عندي
+
+387
+00:32:41,600 --> 00:32:47,140
+هذه بقول عنها bounded على الـ A إذا كان يعني phi
+
+388
+00:32:47,140 --> 00:32:52,680
+of X absolute value أصغر أو سوى some number K أو
+
+389
+00:32:52,680 --> 00:32:57,360
+some number M for every X element in A فيهذا
+
+390
+00:32:57,360 --> 00:33:00,700
+الحالة بقول إن الـ function phi A شمالها is
+
+391
+00:33:00,700 --> 00:33:06,210
+bounded on Aيعني عندي function .. عندي function
+
+392
+00:33:06,210 --> 00:33:16,830
+Phi من R لعند R بقول Phi is bounded on A اللي هي
+
+393
+00:33:16,830 --> 00:33:22,470
+subset من R if there exist M أكبر من 0 such that
+
+394
+00:33:22,470 --> 00:33:27,790
+Phi of X أصغر أو يساوي الـ M لكل الـ X وين موجودة
+
+395
+00:33:27,790 --> 00:33:34,230
+في الـ A فبتكون Phi is bounded on Aطيب، الآن أو
+
+396
+00:33:34,230 --> 00:33:39,090
+بمعنى آخر زي ما هو جائل أنه بدل هذا جائل أنه Phi
+
+397
+00:33:39,090 --> 00:33:44,690
+of A نفسها is bounded إيش Phi of A هي؟ Phi of A ما
+
+398
+00:33:44,690 --> 00:33:49,330
+أنتوا عارفينها هي عبارة عن كل Phi of X such that X
+
+399
+00:33:49,330 --> 00:33:52,730
+element in A إيش معناته هذه تكون bounded؟ إن there
+
+400
+00:33:52,730 --> 00:33:56,230
+exists M أكبر من 0 such that ال absolute value
+
+401
+00:33:56,230 --> 00:34:03,050
+لPhi of Xكل اللي هنا أصغر أو ساوي M لكل X where
+
+402
+00:34:03,050 --> 00:34:09,610
+موجودة في الـA إذا الـboundedness للـPhi on A هي
+
+403
+00:34:09,610 --> 00:34:13,530
+بالشكل هذا، يا أن نقول Phi of A هذي bounded، تنتهي
+
+404
+00:34:13,530 --> 00:34:20,390
+زي بعض طيب، بقولي if A subset من R and Phi من R لR
+
+405
+00:34:20,390 --> 00:34:26,410
+is a functionنقول أن فاية مرتبطة بالـ A إذا كانت
+
+406
+00:34:26,410 --> 00:34:33,190
+سلسلة فاية A مرتبطة بالمجلد R مايعني أن هناك M
+
+407
+00:34:33,190 --> 00:34:37,270
+أكبر من 0 إذا كانت سلسلة فاية X أصغر سوى M لكل X
+
+408
+00:34:37,270 --> 00:34:40,570
+المجلد A إذا كانت فاية مرتبطة
+
+409
+00:34:43,890 --> 00:34:50,690
+norm of phi إذا الآن فرض أنه find phi bounded on a
+
+410
+00:34:50,690 --> 00:34:55,070
+عشان يعرف حاجة اسمها ال uniform norm اللي هو نفس
+
+411
+00:34:55,070 --> 00:35:00,050
+ال مش .. نفس رمزه اللي هو إيش .. إيش .. إيش ال
+
+412
+00:35:00,050 --> 00:35:04,650
+norm ال uniform norm ال uniform norm لل phi over a
+
+413
+00:35:04,650 --> 00:35:09,790
+بساوي ال supremum لل phi of x لكل x element الميين
+
+414
+00:35:09,790 --> 00:35:14,310
+in aإذا هذا اللي هو معناته اللي هو الـ Uniform
+
+415
+00:35:14,310 --> 00:35:20,130
+Norm إذا من الآن و طالع Phi
+
+416
+00:35:20,130 --> 00:35:27,060
+is a function Normal Phiنورم الـ Phi على الـ A هو
+
+417
+00:35:27,060 --> 00:35:32,280
+عبارة عن الـ supremum لل absolute value لـ 5X such
+
+418
+00:35:32,280 --> 00:35:35,800
+that X element in A هل هذا الـ supremum موجود؟ أه
+
+419
+00:35:35,800 --> 00:35:40,760
+لأننا مفترضين Phi bounded على مين؟ على الـ A طيب،
+
+420
+00:35:40,760 --> 00:35:45,620
+إذا هذا معناته اللي هو ال uniform norm أو norm لـ
+
+421
+00:35:45,620 --> 00:35:53,920
+Phi لاحظوا أن ال norm لو عندبقولّي ملاحظة اللي هو
+
+422
+00:35:53,920 --> 00:35:57,360
+Normal Phi A أصغر أو يساوي يابسولون F and ولا F
+
+423
+00:35:57,360 --> 00:36:00,240
+Phi of X أصغر أو يساوي يابسولون، ليش؟ لأن لما يكون
+
+424
+00:36:00,240 --> 00:36:03,180
+هذا أصغر أو يساوي يابسولون لكل X element in A، إذا
+
+425
+00:36:03,180 --> 00:36:06,600
+الـSupremum هيكون أصغر أو يساوي يابسولون، لأن صار
+
+426
+00:36:06,600 --> 00:36:09,420
+هذا عبارة عن Upper Bound اللي هنا، الـSupremum هو
+
+427
+00:36:09,420 --> 00:36:12,360
+الـLeast Upper Bound أصغر أو يساوي يابسولون، يعني
+
+428
+00:36:12,360 --> 00:36:14,960
+شو الـSupremum اللي هنا، اللي هو Normal Phi V أصغر
+
+429
+00:36:14,960 --> 00:36:18,390
+أو يساوي يابسولونConversely، لو هذا كان أصغر أو
+
+430
+00:36:18,390 --> 00:36:22,310
+يساوي Y وأكيد هذا الـ Supremum أكبر أو يساوي الـ
+
+431
+00:36:22,310 --> 00:36:25,710
+Absolute Value لـ Phi of X لكل X Elementين اللي هو
+
+432
+00:36:25,710 --> 00:36:28,950
+أن هذا Supremum من الهن كلهن فهيكون هذا أكبر يساوي
+
+433
+00:36:28,950 --> 00:36:32,130
+هذا، معناته هذا أصغر يساوي هذا لكل X، معناته هذا A
+
+434
+00:36:32,130 --> 00:36:36,770
+شماله متحقق، إذن If and Only If متحققة Normal Phi
+
+435
+00:36:36,770 --> 00:36:40,490
+of A أصغر أو يساوي Y، If and Only If الـ Absolute
+
+436
+00:36:40,490 --> 00:36:44,310
+Value لـ Phi of X أصغر من يساوي Y لكل X Element
+
+437
+00:36:44,310 --> 00:36:44,730
+منهم
+
+438
+00:36:48,470 --> 00:36:56,890
+نيجي الان لللمّة اللي عندى نيجي
+
+439
+00:36:56,890 --> 00:37:01,650
+لللمّة اللي عندنا
+
+440
+00:37:01,650 --> 00:37:05,750
+اوقف
+
+441
+00:37:05,750 --> 00:37:09,930
+شوية دقيقة يا أبو حسن ميدكبر الخط الصغير لما أنا
+
+442
+00:37:09,930 --> 00:37:10,650
+شايف كويس
+
+443
+00:37:16,640 --> 00:37:23,300
+الدسعة صارت وحسن مين
+
+444
+00:37:23,300 --> 00:37:28,860
+محمد راضي؟
+
+445
+00:37:28,860 --> 00:37:32,060
+خلاص
+
+446
+00:37:32,060 --> 00:37:33,760
+يا شيخ مانا أخلوه يساعد مش شاء الله
+
+447
+00:38:18,040 --> 00:38:23,680
+لكن واضح عندك بيكون يا أبو حسين واضح بيكون عندك
+
+448
+00:38:23,680 --> 00:38:25,020
+الا وحن يا راجل
+
+449
+00:39:40,390 --> 00:39:49,610
+جداش هدولة صارن على بعض اللي كام ساعة؟ و الله
+
+450
+00:39:49,610 --> 00:39:52,810
+هي .. هي .. يمكن بيديها كمان جد هن ده كان بس كتير
+
+451
+00:39:52,810 --> 00:39:57,970
+جد هن خليني أنا أخلص اللي كمان طول الساعة و خلاص
+
+452
+00:39:57,970 --> 00:40:05,350
+على كم معادك؟ على كم معادك؟ كده الساعة اللي جيت؟
+
+453
+00:40:05,350 --> 00:40:11,970
+خلاص بنقوله إنه عشر دقايق ربع ساعةبنفع ولا خلاص؟
+
+454
+00:40:11,970 --> 00:40:17,050
+انا لو المشكلة المواصلة بيكون صعبة وين؟ هتخليهوا
+
+455
+00:40:17,050 --> 00:40:25,090
+ناس؟ طب بناخدك معانا بس خليني أشوف طب
+
+456
+00:40:25,090 --> 00:40:32,070
+استنى أشوف أبو محمد إذا كان جاهز لأ مش مشكلة .. لأ
+
+457
+00:40:32,070 --> 00:40:36,810
+بنطلع معاه .. لأ بدي أشوف .. بنوصلك
+
+458
+00:40:36,810 --> 00:40:39,550
+على طول هتعطيني بس جوالي
+
+459
+00:40:47,550 --> 00:40:53,450
+قول له أبو يوسف اللي أخرني اتخيلت
+
+460
+00:40:53,450 --> 00:40:56,830
+.. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت
+
+461
+00:40:56,830 --> 00:41:03,210
+.. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت
+
+462
+00:41:03,210 --> 00:41:03,490
+.. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت
+
+463
+00:41:03,490 --> 00:41:04,150
+.. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت
+
+464
+00:41:04,150 --> 00:41:14,810
+.. اتخيلت .. اتخيلت .. اتخيلت .. اتخيلت
+
+465
+00:41:14,810 --> 00:41:14,950
+.. ا
+
+466
+00:41:31,180 --> 00:41:36,980
+خليني أشرح الحل نظرية و بن .. و بن .. و بنخلص
+
+467
+00:42:10,200 --> 00:42:16,380
+آه محمد السلام عليكم أهلا بيك الله يبارك فيك إيش؟
+
+468
+00:42:16,380 --> 00:42:22,360
+يعني .. طب لأ سنة و خمسة .. عشر دقايق بس أه عشر
+
+469
+00:42:22,360 --> 00:42:25,240
+دقايق و بنزلك كي ما .. انت بتروح هان و لا هان و لا
+
+470
+00:42:25,240 --> 00:42:31,940
+على طول أه عشان معنا واحد .. خلاص ماشي خلاص ماشي
+
+471
+00:42:31,940 --> 00:42:37,800
+ماشي يا محمد ماشي لأ
+
+472
+00:42:37,800 --> 00:42:46,370
+خلاص بروح معاك بروح معاك بروح معاكماشي بس ديش
+
+473
+00:42:46,370 --> 00:42:51,070
+أخرك برضه طب
+
+474
+00:42:51,070 --> 00:42:56,210
+انت هي هتقابلك وين مرتك؟ اه اه اه اه
+
+475
+00:43:01,510 --> 00:43:07,230
+وصلنا عند اللمّة اللي أمامنا 818 a sequence fn of
+
+476
+00:43:07,230 --> 00:43:10,410
+bounded functions on A subset من R converts
+
+477
+00:43:10,410 --> 00:43:14,930
+uniformly on A to F if and only if normal fn نقص F
+
+478
+00:43:14,930 --> 00:43:21,820
+بروح لمين converts to 0الان يعني بده يعطينا غير
+
+479
+00:43:21,820 --> 00:43:26,260
+التعريف نعمل testing لمين لأن ال sequence of
+
+480
+00:43:26,260 --> 00:43:29,480
+functions هتكون يشمالها uniform يكون convergent
+
+481
+00:43:29,480 --> 00:43:33,580
+ولا لأ الان بقوللي بس هذا لمين ال testing ل
+
+482
+00:43:33,580 --> 00:43:37,400
+sequence of functions أفن تكون bounded functions
+
+483
+00:43:37,400 --> 00:43:41,460
+يعني عناصر اللي هان كل واحدة من هدول أفن is
+
+484
+00:43:41,460 --> 00:43:47,200
+bounded بقولليلو كانت sequence of functions Fn is
+
+485
+00:43:47,200 --> 00:43:53,840
+bounded من رأس الدور، then بنقول إن Fn converges
+
+486
+00:43:53,840 --> 00:43:59,680
+uniformly to some function Fif and only if norm
+
+487
+00:43:59,680 --> 00:44:05,040
+الـ Fn ناقص الـ F over A الـ A converts the mean
+
+488
+00:44:05,040 --> 00:44:11,860
+لـ 0 إذا انت عشان اللي هو تفحص ان ال sequence of
+
+489
+00:44:11,860 --> 00:44:16,800
+bounded functions Fn انها converts uniformly للـ F
+
+490
+00:44:16,800 --> 00:44:22,680
+يكفي انك تيجي تاخد norm الـ Fn ناقص F اللي هو over
+
+491
+00:44:22,680 --> 00:44:27,110
+Aإذا لاجيتوا اللي هو الـ Limit صار أعدادها لديروا
+
+492
+00:44:27,110 --> 00:44:31,110
+بالكم Normal لأن صار الـ Limit له إذا كان الـ
+
+493
+00:44:31,110 --> 00:44:35,050
+Limit له راح للسفر خلاص كل سنة و انتسالن بتكون الـ
+
+494
+00:44:35,050 --> 00:44:38,310
+F un converts uniformly للـ F لو ماراحش للسفر
+
+495
+00:44:38,310 --> 00:44:41,010
+معناته الـ F un does not converge uniformly to
+
+496
+00:44:41,010 --> 00:44:46,490
+mean to F الآن بدأ أفترض الآن نفترض أن F un a
+
+497
+00:44:46,490 --> 00:44:52,240
+proofبدي أفترض أن FN converts uniformly to mean to
+
+498
+00:44:52,240 --> 00:44:57,720
+F ماشي الحال عشان اللي هو أثبت أن هذا النورم بروح
+
+499
+00:44:57,720 --> 00:45:03,100
+للـ 0 أول إشي بدي أثبت لك أن هذا الـ FN نقص F is
+
+500
+00:45:03,100 --> 00:45:07,720
+bounded أو بمعنى أخر الـ F is bounded لو كانت الـ
+
+501
+00:45:07,720 --> 00:45:11,680
+F is bounded بصير FN نقص F bounded يعني نورم الـ A
+
+502
+00:45:11,680 --> 00:45:17,330
+بكون أشماله موجودموجود لأن هذا شرط اللي هو يكون
+
+503
+00:45:17,330 --> 00:45:20,390
+موجود أنه تكون اللي جواته bounded زي ما عرفنا قبل
+
+504
+00:45:20,390 --> 00:45:25,270
+بشوية طيب Fn بتروح لل F uniformly إذا لكل Y أكبر
+
+505
+00:45:25,270 --> 00:45:29,250
+من 0 there exists K element in N such that for
+
+506
+00:45:29,250 --> 00:45:33,410
+every N أكبر يساوي K و for every X element in A
+
+507
+00:45:33,410 --> 00:45:40,180
+اللي عندي A ولا إيش نسميها A بكون عندي Fnof X نقص
+
+508
+00:45:40,180 --> 00:45:46,380
+F of X أشماله أصغر من مين من Y طيب قولنا بدنا نثبت
+
+509
+00:45:46,380 --> 00:45:52,560
+أن ال F is bounded الآن سهل خد الآن F of X أصغر أو
+
+510
+00:45:52,560 --> 00:45:58,050
+ساوي اللي هو FNof X بالـ Triangle Inquality ناقص F
+
+511
+00:45:58,050 --> 00:46:06,190
+of X زائد اللي هي mean F and of X، مظبوط؟ هذه بالـ
+
+512
+00:46:06,190 --> 00:46:09,530
+Triangle Inquality هذه bounded، هذه bounded ما هو
+
+513
+00:46:09,530 --> 00:46:12,250
+sequence of bounded functions هذا الكلام لكل N
+
+514
+00:46:12,250 --> 00:46:18,210
+أكبر سوى mean K هذه متحققة لكل N أكبر سوى K من ضمن
+
+515
+00:46:18,210 --> 00:46:26,090
+ال mean الـ K صار عندي F of Xأصغر أو ساوي FK of X
+
+516
+00:46:26,090 --> 00:46:33,930
+ناقص F of X زائد FK of X، مظبوط؟ هذه من اللي فوق
+
+517
+00:46:33,930 --> 00:46:37,190
+أصغر من إبسلون لكل أن أكبر ساوي K من ضمن إن الـK
+
+518
+00:46:37,190 --> 00:46:41,810
+إذا هذه بيصير أصغر من إبسلون زائد هذهالآن بحكي عن
+
+519
+00:46:41,810 --> 00:46:46,270
+function محددة اللي هي اسمها fk of x هو جاين لكل
+
+520
+00:46:46,270 --> 00:46:50,550
+ال fns هدولة bounded من ضمن إن ال fk bounded، مدام
+
+521
+00:46:50,550 --> 00:46:54,510
+bounded إذا في النهاية هذه أصغر أو يسوى some
+
+522
+00:46:54,510 --> 00:46:59,690
+number m أو k اللي بدك إياه أو s لكل x وين موجودة
+
+523
+00:46:59,690 --> 00:47:03,380
+في الـAصارت F of X أصغر سواء Y زائد M يعني عبارة
+
+524
+00:47:03,380 --> 00:47:07,060
+عن رقم لكل X element in A صارت الـ F نفسها إيش
+
+525
+00:47:07,060 --> 00:47:11,960
+مالها is bounded إذن الآن شرعت إني أحكي عن F N
+
+526
+00:47:11,960 --> 00:47:15,420
+ناقص F as a bounded function لإن F N bounded والـ
+
+527
+00:47:15,420 --> 00:47:17,900
+F bounded إذا انتمتين مع بعض إيش مالهين bounded
+
+528
+00:47:17,900 --> 00:47:23,120
+إذن صارت هذه معرفة، ماشي الحال، طيب مدام معرفة إذن
+
+529
+00:47:23,120 --> 00:47:28,480
+على طول هنامدام هذه أصغر من إبسلون في الملاحظة
+
+530
+00:47:28,480 --> 00:47:31,560
+اللي كتبناها في الأول قبل التعريف وبعدين شرحناها
+
+531
+00:47:31,560 --> 00:47:37,020
+بعد التعريف إذا بتذكروا مدامة اللي هي هذه كلها هذه
+
+532
+00:47:37,020 --> 00:47:41,980
+كلها as Phi absolute value Phi of X أصغر أو يساوي
+
+533
+00:47:41,980 --> 00:47:46,100
+أقل من إبسلون بيكون normها أصغر أو يساوي إبسلون
+
+534
+00:47:46,100 --> 00:47:51,440
+معناته إحنا حصلنا على ال supremumللـ absolute
+
+535
+00:47:51,440 --> 00:47:57,980
+value للـ Fn of X ناقص F of X اللي هو أصغر من Y
+
+536
+00:47:57,980 --> 00:48:03,930
+أصغر من Y اللي هو هذا .. و الـ X اللي بيبقى Aهذا
+
+537
+00:48:03,930 --> 00:48:09,850
+اللي هو عبارة عن norm الـ Fn ناقص F over A إذا صار
+
+538
+00:48:09,850 --> 00:48:14,090
+هذا أصغر يسوا إبسلون، تحت مين؟ يعني لكل Y أكبر من
+
+539
+00:48:14,090 --> 00:48:20,570
+0 لجينا K لكل N أكبر سوا K الـ Fn ناقص الـ F أصغر
+
+540
+00:48:20,570 --> 00:48:25,790
+من إبسلون وهذا يعني إنه limit norm الـ Fn ناقص الـ
+
+541
+00:48:25,790 --> 00:48:31,160
+F as N goes to infinity بسوا سفرإذن بيكون إحنا
+
+542
+00:48:31,160 --> 00:48:37,640
+خلصنا الاتجاه الأول و أثبتنا إنه اللي هو norm للأف
+
+543
+00:48:37,640 --> 00:48:41,660
+أن نقص أف بيروح للسفر لما اللي هو الـFn تكون
+
+544
+00:48:41,660 --> 00:48:47,380
+converse uniformly الان الـconverse إن لو كان ال
+
+545
+00:48:47,380 --> 00:48:55,660
+norm للـFn بيروح للسفر هيكون اللي هوالـ Fn تكون
+
+546
+00:48:55,660 --> 00:49:01,380
+converge uniformly to F انتوا هذا سهل هذا شوف كيف
+
+547
+00:49:01,380 --> 00:49:10,420
+لان بدنا نفترض suppose that norm الـ Fn ناقص الـ F
+
+548
+00:49:10,420 --> 00:49:15,540
+over A converge لبين للزفر إيش معناته هذا؟ معناته
+
+549
+00:49:15,540 --> 00:49:22,420
+لكل إبسلونأكبر من سفر there exists k كي اعتمدت على
+
+550
+00:49:22,420 --> 00:49:26,260
+مين بس of إبسلون ال limit in n لأن مافيش اصلا
+
+551
+00:49:26,260 --> 00:49:34,560
+إكسات هذه limit هذا بسوة ده such that اللي هو fn
+
+552
+00:49:34,560 --> 00:49:45,460
+ناقص f اللي هو ناقص سفر ناقص سفرأصغر من إبسلون لكل
+
+553
+00:49:45,460 --> 00:49:51,560
+N أكبر أو يساوي K هذا مين هو هذا norm ال FN ناقص F
+
+554
+00:49:51,560 --> 00:49:56,740
+over A أصغر من إبسلون وهذا أكيد أكبر أو يساوي ال
+
+555
+00:49:56,740 --> 00:50:01,700
+supremum أسف هو ال supremum أكبر أو يساوي ال FN of
+
+556
+00:50:01,700 --> 00:50:08,460
+X ناقص F of Xلكل X element in A لأن هذا أكبر سوى
+
+557
+00:50:08,460 --> 00:50:11,380
+هذا لأن هذا supremum من إلهم إذا صار عند الأل لكل
+
+558
+00:50:11,380 --> 00:50:18,140
+Y أكبر من 0 there exists K such that Fn of X ناقص
+
+559
+00:50:18,140 --> 00:50:25,620
+F of X أصغر من Y لكل X element in A وهذا معناته مع
+
+560
+00:50:25,620 --> 00:50:35,330
+هذاإذا fn converges uniformly to f هذا ما مكتوب
+
+561
+00:50:35,330 --> 00:50:35,670
+هنا
+
+562
+00:50:57,490 --> 00:51:03,190
+باللي هو نكمل المحاضرة اللي هي نكمل الموضوع وإلى
+
+563
+00:51:03,190 --> 00:51:04,170
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8509ba511ac95d7a3685ff861f408fe4672b2354
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ.srt
@@ -0,0 +1,1703 @@
+1
+00:00:05,480 --> 00:00:11,800
+بسم الله الرحمن الرحيم محاضرة رقم تسعة مساق تحليل
+
+2
+00:00:11,800 --> 00:00:19,160
+حقيقي اثنان طلاب الجامعة الإسلامية كلية العلوم قسم
+
+3
+00:00:19,160 --> 00:00:24,470
+الرياضيات، المحاضرة اليوم على جزئين، الجزء الأول
+
+4
+00:00:24,470 --> 00:00:29,350
+هنتحدث عن applications of Taylor's theorem والجزء
+
+5
+00:00:29,350 --> 00:00:34,250
+الثاني هنتحدث عن اللي هو discussion لـ section 6.2
+
+6
+00:00:34,250 --> 00:00:37,890
+و6.3 اللي هو discussion لـ mean value theorem وإذا
+
+7
+00:00:37,890 --> 00:00:43,270
+في وجهة بنعمل discussion لـ اللي هو L'Hôpital's rule
+
+8
+00:00:43,960 --> 00:00:48,240
+الآن خلّينا نكمل اللي اتحدثنا عنه المرة الماضية
+
+9
+00:00:48,240 --> 00:00:53,200
+ولكن على صورة تطبيقات ليه؟ اللي هو Taylor's 
+
+10
+00:00:53,200 --> 00:00:58,660
+theorem وكيف بدنا اللي هو نستغل Taylor's theorem في
+
+11
+00:00:58,660 --> 00:01:03,360
+إثبات بعض النظريات المهمة في موضوع اللي هو ال
+
+12
+00:01:03,360 --> 00:01:08,080
+maximum و ال minimum أو اللي هو الـ test لإن اللي 
+
+13
+00:01:08,080 --> 00:01:12,140
+عندنا هل هي local maximum أو local minimum ولا لا
+
+14
+00:01:12,140 --> 00:01:15,860
+هي local maximum ولا هي local minimum كنا اتحدثنا
+
+15
+00:01:15,860 --> 00:01:20,560
+سابقا على اللي هو الـ first derivative test لإن
+
+16
+00:01:20,560 --> 00:01:23,200
+النقطة اللي تكون الداخلية هل في عندها local
+
+17
+00:01:23,200 --> 00:01:27,540
+maximum أو local minimum، الآن بدنا نتحدث عن الـ
+
+18
+00:01:27,540 --> 00:01:31,140
+Higher Derivative Test، احنا يمكن نمر عنا اللي هو
+
+19
+00:01:31,140 --> 00:01:33,720
+الـ Second Derivative Test اللي هو في الـ .. في
+
+20
+00:01:33,720 --> 00:01:36,900
+الـ Calculus اللي قابل نتحدث على الـ Higher
+
+21
+00:01:36,900 --> 00:01:40,080
+Derivative Test و اللي هي .. اللي هي الـ Second
+
+22
+00:01:40,080 --> 00:01:44,090
+Derivative Test جزء من هذا اللي هو الـ test، نتطلع
+
+23
+00:01:44,090 --> 00:01:48,030
+على الـ test إيش بقول اللي هي عبارة عن theorem 6.4.4
+
+24
+00:01:48,030 --> 00:01:52,310
+Let I be an interval، نفترض أن I عبارة عن interval
+
+25
+00:01:52,310 --> 00:01:57,510
+و X0 اللي هي نقطة اللي احنا بدنا نفحص عندها هل
+
+26
+00:01:57,510 --> 00:02:02,770
+في maximum أو في minimum أو لا في maximum ولا في
+
+27
+00:02:02,770 --> 00:02:06,470
+minimum، X0 اللي هي عبارة عن interior point
+
+28
+00:02:06,470 --> 00:02:10,890
+لمن؟ للـ interval I يعني نقطة داخلية، ونفترض الـ N
+
+29
+00:02:10,890 --> 00:02:14,570
+تبعتنا أكبر أو يساوي 2 لأن الـ N أكبر أو يساوي 2
+
+30
+00:02:14,570 --> 00:02:17,690
+يعني الـ Second Derivative Test أو أعلى هو اللي
+
+31
+00:02:17,690 --> 00:02:20,910
+بده يحددنا أنه عندنا Maximum أو Minimum أو مافيش
+
+32
+00:02:20,910 --> 00:02:25,450
+لا Maximum ولا Minimum، Suppose ده الـ derivatives
+
+33
+00:02:25,450 --> 00:02:31,120
+اللي هي F' و F'' لعند FN exist and are 
+
+34
+00:02:31,120 --> 00:02:34,040
+continuous in a neighborhood of x0، نفترض إن
+
+35
+00:02:34,040 --> 00:02:39,140
+هدولة continuous وموجودة في اللي هو
+
+36
+00:02:41,860 --> 00:02:44,760
+اللي هي في neighborhood حوالي مين؟ الـ X0
+
+37
+00:02:44,760 --> 00:02:49,920
+ونفترض أن F' عند X0 لعند F N ناقص واحد prime
+
+38
+00:02:49,920 --> 00:02:54,060
+of X0 إيش بيساوي؟ صفر لكن عند FN of X0
+
+39
+00:02:54,060 --> 00:02:59,140
+إيش مالها؟ لا تساوي صفر، إذا الـ test إيش بيصير؟ أول
+
+40
+00:02:59,140 --> 00:03:06,120
+شيء بنشوف F prime نقطة X0، هذه نقطة متوقع عندها
+
+41
+00:03:06,120 --> 00:03:10,340
+maximum أو minimum أو مافيش شيء من النقاط اللي هي
+
+42
+00:03:10,340 --> 00:03:13,520
+بدنا نفحص عندها maximum أو minimum، إيش بدنا نسوي
+
+43
+00:03:13,520 --> 00:03:18,520
+في هذا الـ test بنجيب F prime عند الـ X0 إذا
+
+44
+00:03:18,520 --> 00:03:23,500
+لجيناها صفر بنيجي للـ F double prime عند الـ X0
+
+45
+00:03:23,500 --> 00:03:29,130
+إذا لجيناها صفر اللي هو بنيجي للـ F triple prime عند الـ X0
+
+46
+00:03:29,130 --> 00:03:34,830
+وين بنصل للـ F triple prime .. وين بنصل للـ FN of X0 لا
+
+47
+00:03:34,830 --> 00:03:39,210
+تساوي صفر؟ بيبدأ الخطوات تبعات الـ test، إيش الـ
+
+48
+00:03:39,210 --> 00:03:43,710
+test؟ اللي هي الأول إذا كانت N even طلعت عندنا N
+
+49
+00:03:43,710 --> 00:03:47,850
+هذه أول واحدة الـ derivative عندها عند الـ X0 مش
+
+50
+00:03:47,850 --> 00:03:53,930
+صفر وكانت الـ FN of X0 أكبر من 0 بتكون الـ F أيه
+
+51
+00:03:53,930 --> 00:03:57,470
+شمالها؟ اللي هي relative minimum، زي الـ second
+
+52
+00:03:57,470 --> 00:04:01,710
+derivative test كنا لما نقول الـ F double prime عند الـ X0 أكبر
+
+53
+00:04:01,710 --> 00:04:06,170
+من 0 على طول نحكم أنه في local minimum، هنا الآن لأ
+
+54
+00:04:06,170 --> 00:04:08,510
+احنا على الـ higher derivative وهتحللنا المشاكل
+
+55
+00:04:08,510 --> 00:04:10,290
+اللي كانت ما تتحلش باللي هي second
+
+56
+00:04:10,290 --> 00:04:16,670
+derivative test، الآن FN is even و الـ FN of X0 أصغر
+
+57
+00:04:16,670 --> 00:04:21,510
+من 0 إذا Fها زي إيه شمالها؟ relative maximum at X0
+
+58
+00:04:21,510 --> 00:04:25,670
+إذا لو طلعت عندي N is odd، إيش يعني N is odd؟ يعني
+
+59
+00:04:25,670 --> 00:04:31,130
+أول .. أول derivative الـ FN عندها لا تساوي 0، طلعت
+
+60
+00:04:31,130 --> 00:04:35,390
+عندي هذه odd طبعا أكبر إذا هو 2، 3 أو 5 أو 7 إلى
+
+61
+00:04:35,390 --> 00:04:39,490
+آخره، على طول احنا بنحكم then F has neither
+
+62
+00:04:39,490 --> 00:04:43,610
+relative minimum nor إيش ما لها؟ relative maximum
+
+63
+00:04:43,610 --> 00:04:50,790
+at X0، بتصور هيك النظرية واضحة، إيش نصها؟ بنجيب F
+
+64
+00:04:50,790 --> 00:04:56,570
+prime of X0 و F double prime of X0 إلى آخره إذا
+
+65
+00:04:56,570 --> 00:05:01,170
+هذا بيساوي صفر بهذا بيساوي صفر بضلي ماشي لعند FN
+
+66
+00:05:01,170 --> 00:05:08,550
+of X0 لا تساوي صفر و أجيب test تصل لا تساوي صفر باجي لل
+
+67
+00:05:08,550 --> 00:05:17,620
+test اللي هو uneven عند حالتين، الحالة الأولى FN of
+
+68
+00:05:17,620 --> 00:05:27,280
+X0 أكبر من 0 Local Minimum، FN of X0 أصغر من 0 Local 
+
+69
+00:05:27,280 --> 00:05:33,180
+maximum، لكن إذا طلعت n is odd يعني أول واحدة بعد
+
+70
+00:05:33,180 --> 00:05:37,720
+الاثنين اللي هو بيطلع عند F الـ derivative لها FN of 
+
+71
+00:05:37,720 --> 00:05:43,200
+X0 لا تساوي 0، طلعت عند n is odd إذا بحكم على طول F
+
+72
+00:05:43,200 --> 00:05:52,030
+has neither Local maximum nor Local minimum، تعالوا
+
+73
+00:05:52,030 --> 00:05:58,670
+اللي هو نبرهن اللي هو النظرية ونشوف إنه حجر الأساس
+
+74
+00:05:58,670 --> 00:06:02,470
+للبرهان اللي هي Taylor's theorem، هي Taylor's 
+
+75
+00:06:02,470 --> 00:06:12,430
+theorem، نشوف كيف الآن عندي بدنا نطبق Taylor's
+
+76
+00:06:12,430 --> 00:06:15,820
+theorem على .. طبعا احنا بنشتغل على الـ interval من
+
+77
+00:06:15,820 --> 00:06:21,520
+I بناخد اللي هو X element من I و بنطبقلها من الـ
+
+78
+00:06:21,520 --> 00:06:26,120
+Taylor's theorem عند النقطة اللي احنا بدنا نختبر
+
+79
+00:06:26,120 --> 00:06:29,840
+عند X0، فهي اللي بده أجيب Taylor's theorem حواليها
+
+80
+00:06:29,840 --> 00:06:36,160
+إذا حسب Taylor's theorem إن there exists C between
+
+81
+00:06:36,160 --> 00:06:45,630
+اللي هي X و X0 such that اللي هو F of X، F of X 
+
+82
+00:06:45,630 --> 00:06:52,110
+بيساوي بي n ناقص واحد، بدا أقبّقها اللي بحيث أن الـ
+
+83
+00:06:52,110 --> 00:06:56,250
+polynomial ما n ناقص واحد، ليش؟ لإنه أنا ما عطيني
+
+84
+00:06:56,250 --> 00:07:01,110
+هو عنده الـ derivative اللي هي لعند FN ناقص واحد
+
+85
+00:07:01,110 --> 00:07:05,870
+كلها صفر واللي مش صفر اللي هي مين؟ FN of X0
+
+86
+00:07:06,550 --> 00:07:11,390
+فعند اللي هي R n ناقص واحد هطبق عشان تحكم للـ FN of X
+
+87
+00:07:11,390 --> 00:07:15,310
+0 على إنه عندني local maximum أو local minimum
+
+88
+00:07:15,310 --> 00:07:19,750
+أو neither، كيف؟ خلّينا نطبق الـ Taylor's theorem
+
+89
+00:07:19,750 --> 00:07:28,350
+زائد اللي هو أشملها R N ناقص واحد of X، هذه عندي
+
+90
+00:07:28,350 --> 00:07:33,230
+Taylor's theorem، الآن الـ PN ناقص واحد اللي هي عبارة
+
+91
+00:07:33,230 --> 00:07:40,820
+عن إيش؟ F of X0 زائد F prime of X0 في X
+
+92
+00:07:40,820 --> 00:07:45,440
+minus X0 اللي هو على واحد factorial، زائد لما
+
+93
+00:07:45,440 --> 00:07:51,400
+أصل لآخر واحد FN ناقص واحد of X0 في X minus
+
+94
+00:07:51,400 --> 00:07:55,540
+X0 قس N ناقص واحد على N ناقص واحد لكل
+
+95
+00:07:55,540 --> 00:08:02,700
+factorial، زائد main الـ remainder اللي هو main اللي
+
+96
+00:08:02,700 --> 00:08:09,810
+هو عبارة عن X ناقص X0 أس N على N factorial في F
+
+97
+00:08:09,810 --> 00:08:18,850
+N of c، عندي C والـ C مالها؟ between X0
+
+98
+00:08:18,850 --> 00:08:27,170
+and C and X، واضح و يساوي، الأن كل هذول أصفار صح
+
+99
+00:08:27,170 --> 00:08:33,500
+ولا لأ؟ إذا حيصير عندي هذا بيساوي لإنه معطيلي الـ F
+
+100
+00:08:33,500 --> 00:08:41,120
+prime of X0 لعند FN ناقص واحد of X0 كله
+
+101
+00:08:41,120 --> 00:08:46,700
+صفر، إذا صلي عندي هذا بيساوي F of X0 لأن هذا
+
+102
+00:08:46,700 --> 00:08:55,740
+كله بتصفر زائد X minus X0 أس N على N factorial
+
+103
+00:08:55,740 --> 00:09:09,290
+في FN of C، واضح اه أي سؤال؟ طيب عندي أنا اللي هو
+
+104
+00:09:09,290 --> 00:09:19,230
+معطيني الـ الـ FN of X0 اللي هي لا تساوي صفر
+
+105
+00:09:19,230 --> 00:09:25,170
+إذا الـ FN of X0 يا أكبر من صفر يا أصغر من 0
+
+106
+00:09:25,170 --> 00:09:36,570
+من صفر، إذا أكيد عندي الـ FN of X0 و الـ FN of C
+
+107
+00:09:36,570 --> 00:09:43,810
+الهن أيش الهن؟ the same sign، ماشي اه الهن نفس الـ
+
+108
+00:09:43,810 --> 00:09:50,770
+نفس اللي هو الإشارة، طبعا السبب أن FN شمالها is
+
+109
+00:09:50,770 --> 00:09:55,950
+continuous، أنوضح لكم إياها تتذكروا
+
+110
+00:09:57,370 --> 00:10:02,330
+قلنا خلّينا ناخد حالة، نفترض أن هذا أكبر من مين؟ من
+
+111
+00:10:02,330 --> 00:10:12,690
+صفر، احنا كنا نقول limit أي حاجة g of X لما X تروح
+
+112
+00:10:12,690 --> 00:10:18,970
+للـ C مثلا أكبر من صفر، معناته في جوار في جوار
+
+113
+00:10:18,970 --> 00:10:23,210
+حوالين اللي هو الـ C الـ g of X نفسها إيش هتكون؟ أكبر
+
+114
+00:10:23,210 --> 00:10:28,110
+من صفر لكل X في هذا الجوار، يعني هيكون عندي إذاً g
+
+115
+00:10:28,110 --> 00:10:37,710
+of X أكبر من 0 لكل X في some جوار delta of c 
+
+116
+00:10:37,710 --> 00:10:41,690
+هذا اللي بدأ أستخدمها الآن في الوصول للي بديها
+
+117
+00:10:41,690 --> 00:10:45,590
+خلّيني نشوف كيف بدأ نستخدم هذه المعلومة، الآن أنا
+
+118
+00:10:45,590 --> 00:10:55,750
+عندي الـ FN is continuous نفسها، إذاً limit FN of X
+
+119
+00:10:55,750 --> 00:11:03,290
+أفقًا of X اللي هو لما الـ X تروح للـ X0 اللي هو
+
+120
+00:11:03,290 --> 00:11:10,070
+أيش متساوي؟ أفقًا of X0، وبرضه continuous عند مين؟
+
+121
+00:11:11,690 --> 00:11:16,810
+وبرضه continuous عند مين؟ عند الـ C معايا وعند الـ
+
+122
+00:11:16,810 --> 00:11:21,030
+C إيش مالها؟ continuous، أنا اللي هيلزمني مين؟ هنا
+
+123
+00:11:21,030 --> 00:11:26,930
+الـ X0 مظبوط ولا لأ؟ عندي هتلزمني مين؟ اللي هي
+
+124
+00:11:26,930 --> 00:11:35,950
+الـ X0، إذا صار عندي FN of X0 هي اللي هتحددلي
+
+125
+00:11:35,950 --> 00:11:45,090
+من هنا اللي هي إشارة مين؟ FN of C، واضح الآن من هذه
+
+126
+00:11:45,090 --> 00:11:54,310
+إذا كانت F of X0 مثلا أكبر من صفر هتطلع حد
+
+127
+00:11:54,310 --> 00:11:58,870
+أكبر من صفر، خلينا نشوفها، إذا الآن خليني أبدأ في
+
+128
+00:11:58,870 --> 00:12:06,270
+مين؟ في I بدي افترض مين؟ الآن FN of X0 أكبر من أيش؟
+
+129
+00:12:06,270 --> 00:12:13,010
+من صفر و افترض أن الآن عند أيش؟ معنها is even بدي 
+
+130
+00:12:13,010 --> 00:12:19,950
+أنطلق من هذه، إذا الآن FN of X0 أكبر من صفر و N
+
+131
+00:12:19,950 --> 00:12:25,730
+is even، بناء على هذه for every y أكبر من صفر there
+
+132
+00:12:25,730 --> 00:12:32,440
+exists delta such that المهم بيطلع عندي اللي هو F هذه أيش
+
+133
+00:12:32,440 --> 00:12:37,880
+مفترضين احنا أكبر من ايه؟ أيش؟ من صفر، إذا حسب اللي
+
+134
+00:12:37,880 --> 00:12:45,450
+حكيته قبل بشوية، there exists V Delta of إيش؟ of X0
+
+135
+00:12:45,450 --> 00:12:53,590
+حوالي مين؟ الـ X0 such that اللي هو FN of X زي
+
+136
+00:12:53,590 --> 00:12:59,290
+إشارة هذه اللي هي أكبر من 0 لكل X وين؟ في الـ V
+
+137
+00:12:59,290 --> 00:13:06,880
+Delta of مين؟ of X0، ماشي الحال واللي من ضمن هدولة
+
+138
+00:13:06,880 --> 00:13:15,060
+مين؟ C، إذا صارت عندي الآن FN of C برضه إيه شمالها؟
+
+139
+00:13:15,060 --> 00:13:21,860
+أكبر من صفر، الآن اتضحت الصورة، الآن صارت عندي من
+
+140
+00:13:21,860 --> 00:13:26,420
+الأصل F of X بسوء F of X0 زائد هذا المقدار، بدا 
+
+141
+00:13:26,420 --> 00:13:31,020
+أقول الآن بما أن هذه أكبر من صفر وأنّ أنا مفترضها
+
+142
+00:13:31,020 --> 00:13:36,490
+إنها even إذا صار عندي هذا أكبر من صفر وهذا أكبر 
+
+143
+00:13:36,490 --> 00:13:41,570
+من صفر إذا الـ remainder كله إيش ماله؟ أكبر من صفر
+
+144
+00:13:41,570 --> 00:13:47,710
+مدام الـ remainder أكبر من صفر واضح اللي بحكي Fn 
+
+145
+00:13:47,710 --> 00:13:53,010
+of C أكبر من صفر وهذا المقدار أكبر من صفر لأنه N is
+
+146
+00:13:53,010 --> 00:13:58,710
+even إذا صار كل هذا أكبر من صفر إذا automatic لما
+
+147
+00:13:58,710 --> 00:14:04,660
+أشيله يصغر المقدار، بظبط ولا لأ؟ فيصير عند الـ F
+
+148
+00:14:04,660 --> 00:14:12,040
+of X اللي هو أكبر من مين؟ من الـ F of X naught لأن F
+
+149
+00:14:12,040 --> 00:14:17,680
+of X بيساوي هذا زائد هذا فأكيد عند الـ F of X أكبر
+
+150
+00:14:17,680 --> 00:14:22,160
+من مين؟ من F of X naught في وين؟ لكل X وين موجودة
+
+151
+00:14:22,160 --> 00:14:30,530
+في الجوار اللي حواليها، إذا صار عند F has local
+
+152
+00:14:30,530 --> 00:14:40,870
+minimum at x0 similarly لو
+
+153
+00:14:40,870 --> 00:14:53,630
+بدنا نفترض أنّ المقدار هذا عندي Fn of x0 أصغر من 0
+
+154
+00:14:54,540 --> 00:15:00,740
+وبدأ أبدأ أحكي عن مين؟ عن I I بيصير عندي الآن حسب
+
+155
+00:15:00,740 --> 00:15:07,320
+الحديث هنا الـ FN of C اللي هي أصغر من 0 لأنّ هتكون
+
+156
+00:15:07,320 --> 00:15:13,600
+الـ FN of X لكل X في هذا الجوار the same sign as FN
+
+157
+00:15:13,600 --> 00:15:18,120
+of X note أصغر من 0 إذا صارت عندي FN of C أصغر من
+
+158
+00:15:18,120 --> 00:15:24,050
+0 هذه صارت سالبة وهذه موجبة لأنّ and is even إذا 
+
+159
+00:15:24,050 --> 00:15:28,290
+صار المقدار هذا كله على بعض إيش شماله؟ سالب في كل
+
+160
+00:15:28,290 --> 00:15:33,070
+هذا الجوار ما ده صار سالب معناته أنّ لما أنا أشيله
+
+161
+00:15:33,070 --> 00:15:39,330
+بكبر اللي بظهر يعني بيصير F of X note بناء عليه
+
+162
+00:15:39,330 --> 00:15:46,630
+أكبر من F of X مظبوط؟ وهذا يعني أنّ صار الـ F في هذه
+
+163
+00:15:46,630 --> 00:15:56,010
+الحالة عندها local maximum local maximum واضح؟ أي 
+
+164
+00:15:56,010 --> 00:16:01,510
+سؤال؟ طيب، ضال عند مين؟ الحالة الأخيرة، هذي
+
+165
+00:16:01,510 --> 00:16:09,170
+تذكرينها لأنّ برضه بدي اشتغل نفس الشيء في الحالة
+
+166
+00:16:09,170 --> 00:16:15,680
+الأخيرة أو شيء مشابه عند الآن بدي افترض mean أنّ
+
+167
+00:16:15,680 --> 00:16:25,980
+الحالة الثالثة بدي افترض أنّ ال is mean of of زي
+
+168
+00:16:25,980 --> 00:16:35,810
+ما عملنا قبل بشوية إذا كانت اللي هي F فن of x not
+
+169
+00:16:35,810 --> 00:16:40,890
+أكبر من صفر زي ما عملنا قبل شوية هيعطيني Fn of c
+
+170
+00:16:40,890 --> 00:16:49,990
+أكبر من إيش؟ من صفر معايا؟ طيب الآن هذا الكلام لو
+
+171
+00:16:49,990 --> 00:16:56,930
+جيت أخدت عندي هي عندي هذه اللي هي x not وهنا 
+
+172
+00:16:56,930 --> 00:17:01,650
+الجوار اللي حواليها الجوار اللي حواليها اللي لجئت
+
+173
+00:17:01,650 --> 00:17:09,230
+في كل الجوار زي ما عملت قبل شوية fn of x هيكون
+
+174
+00:17:09,230 --> 00:17:15,830
+اللي هو هنا اللي هو هنا وهنا موجب ماشي الحال الآن
+
+175
+00:17:15,830 --> 00:17:21,850
+مدام موجب هنا وهنا اللي هيتحكم في الموضوع اليمين
+
+176
+00:17:21,850 --> 00:17:27,770
+x minus x naught أس n لكن لسوء الحظ لو كانت x هنا 
+
+177
+00:17:28,970 --> 00:17:35,350
+بيصير عندي وهذا طبعا لكل X وين؟ على يمين الـ X node
+
+178
+00:17:35,350 --> 00:17:41,450
+هيطلع عندي الـ X minus X node أس N وهذه إيش شمالها؟
+
+179
+00:17:41,450 --> 00:17:49,110
+odd is أكبر من إيش؟ من صفر فصارت الآن هذه أكبر من
+
+180
+00:17:49,110 --> 00:17:54,330
+صفر وهذه أكبر من صفر التنتير مع بعض أكبر من صفر
+
+181
+00:17:55,160 --> 00:18:01,380
+ماشي فصارت عندي الـ F of X أكبر من مين؟ من الـ F of X
+
+182
+00:18:01,380 --> 00:18:07,600
+naught ماشي الحال في المنطقة هذه هذه المنطقة هذه 
+
+183
+00:18:07,600 --> 00:18:16,060
+صارت عندي الـ F of X أكبر من F of X naught فاهمين؟
+
+184
+00:18:16,060 --> 00:18:23,240
+لأنّ الجزء الثاني الـ X في المنطقة اللي هان أي X في
+
+185
+00:18:23,240 --> 00:18:27,880
+المنطقة اللي هان عند الـ x minus x naught أصغر من 
+
+186
+00:18:27,880 --> 00:18:32,480
+مين؟ من صفر فبيصير عند هذا المقدار أصغر من صفر وهذا
+
+187
+00:18:32,480 --> 00:18:37,020
+أكبر من صفر حاصل الضرب أصغر من صفر أصغر من صفر بقد
+
+188
+00:18:37,020 --> 00:18:42,200
+إلى أنّ أف of x في المنطقة هذه تصير أصغر من أف of x
+
+189
+00:18:42,200 --> 00:18:47,250
+naught يعني لو أتيت لأي جوار حوالي الـ X Note
+
+190
+00:18:47,250 --> 00:18:51,770
+هتلاقي اللي هو مرة الـ F of X Note أصغر من F of X
+
+191
+00:18:51,770 --> 00:18:56,810
+ومرة F of X Note أكبر من مين؟ من F of X يعني بمعنى
+
+192
+00:18:56,810 --> 00:19:02,270
+آخر لا في عندي Local Maximum ولا Local Minimum في 
+
+193
+00:19:02,270 --> 00:19:08,450
+هذه المنطقة Similarly وبنفس الأسلوب لو كانت FN of
+
+194
+00:19:08,450 --> 00:19:14,000
+X Note أصغر من مين؟ من صفر معايا بيصير هذه أصغر من
+
+195
+00:19:14,000 --> 00:19:19,020
+صفر وبيصير بس بتنقلب بيصير هذه في المنطقة هذه
+
+196
+00:19:19,020 --> 00:19:23,840
+أصغر وهذه في المنطقة هذه إيش؟ أكبر إذا in both
+
+197
+00:19:23,840 --> 00:19:30,160
+cases عندي if and is odd إذا we have neither اللي
+
+198
+00:19:30,160 --> 00:19:37,660
+هو relative maximum nor relative minimum أي سؤال
+
+199
+00:19:37,660 --> 00:19:45,760
+واضح اه؟ اللي بعده اللي بعده الآن بدنا نعرف حاجة 
+
+200
+00:19:45,760 --> 00:19:51,140
+اسمها اللي هي مين؟ ال convex function تعال على
+
+201
+00:19:51,140 --> 00:19:55,640
+الرسم يا بو محمد عندي بدنا نعرف مين ال convex
+
+202
+00:19:55,640 --> 00:19:59,860
+function الآن ال convex function إيش يكون؟ cave
+
+203
+00:19:59,860 --> 00:20:05,200
+اللي هو إيش؟ up خليني نشوف إيش هذي اللي هو بعبر شو
+
+204
+00:20:05,200 --> 00:20:07,980
+معناه الـ F is convex
+
+205
+00:20:10,750 --> 00:20:14,990
+خاصية الـ convex أو الـ convexity بنحكي فيها على 
+
+206
+00:20:14,990 --> 00:20:22,090
+interval يعني بنقول F من عند I لعند R بنقول عنها F
+
+207
+00:20:22,090 --> 00:20:28,170
+is convex on إيش؟ on I on وين؟ ع ال interval I إذا
+
+208
+00:20:28,170 --> 00:20:35,970
+كان شوف كيف خدلي الآن X1 أي نقطة في داخل الـ I و
+
+209
+00:20:35,970 --> 00:20:41,970
+X2 أي نقطة في داخل الـ I وخدلي ال parameter T بين 
+
+210
+00:20:41,970 --> 00:20:45,830
+الصفر وبين الواحد الآن النقطة ال linear
+
+211
+00:20:45,830 --> 00:20:51,230
+combination بين X1 و X2 بواسطة 1-T X1 زائد T X2
+
+212
+00:20:51,230 --> 00:20:56,530
+هتكون بين X1 وبين X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+213
+00:20:56,530 --> 00:20:56,950
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+214
+00:20:56,950 --> 00:21:06,250
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+215
+00:21:06,250 --> 00:21:14,050
+X2 X2 X2 X2 X2 X2 X2 لو إجيت ل F of X1 هيها وهذا F
+
+216
+00:21:14,050 --> 00:21:20,650
+of X2 لو ضربت ال F of X1 و 1 minus T وجمعتها ل T
+
+217
+00:21:20,650 --> 00:21:25,170
+في F of X2 هتلاقيها بين اللي هو مين؟ على اللي هو
+
+218
+00:21:25,170 --> 00:21:32,010
+الخط المستقيم القاطع بين X1 و F of X1 وبين X2 و F
+
+219
+00:21:32,010 --> 00:21:37,970
+of X2 دائما هتلاقي هذه النقطة الصورة هنا أعلى من
+
+220
+00:21:37,970 --> 00:21:42,910
+هذه وهذا معنى اللي هو ال convex وعن عرف ال convex
+
+221
+00:21:42,910 --> 00:21:50,390
+على هذا الأساس بيقول F is convex on I طلعلي على 
+
+222
+00:21:50,390 --> 00:21:54,650
+التعريف إذا كان أخدنا أي X واحد و X اتنين element
+
+223
+00:21:54,650 --> 00:22:00,690
+in I وأخدنا T اللي هو element in 01 يعني بين 01
+
+224
+00:22:00,690 --> 00:22:13,020
+بيحققلي F اللي هو for any كده f
+
+225
+00:22:13,020 --> 00:22:19,140
+is a convex in I if for any كده وكده we have
+
+226
+00:22:19,140 --> 00:22:25,940
+فاهمين عليا f of واحد minus T X واحد زائد T في X
+
+227
+00:22:25,940 --> 00:22:32,520
+اتنين إيش ماله؟ هيسير أصغر أو يساوي واحد ناقص T في
+
+228
+00:22:32,520 --> 00:22:38,000
+X واحد زائد T في F of X اتنين
+
+229
+00:22:40,410 --> 00:22:44,370
+طبعاً اللي هو ال .. ال .. ال .. ال .. ال convex
+
+230
+00:22:44,370 --> 00:22:48,330
+functions في عليها دراسات كثيرة ودراسات حديثة كمان
+
+231
+00:22:48,330 --> 00:22:55,070
+حتى يعني في اللي هو real analysis بما يتعلق بال ..
+
+232
+00:22:55,070 --> 00:22:58,950
+مش بال integration العادي كمان باللي هو .. و
+
+233
+00:22:58,950 --> 00:23:03,310
+علاقتها بال integration في اللي هو ال .. ال big
+
+234
+00:23:03,310 --> 00:23:08,760
+integra كمان وطبعاً وإليها اللي هو خلّيني أقول
+
+235
+00:23:08,760 --> 00:23:14,020
+تطبيقات أو استخدامات في اللي هو optimization اللي
+
+236
+00:23:14,020 --> 00:23:20,350
+هي theory الآن احنا هنتحك .. هنحكي فيها بما يتعلق
+
+237
+00:23:20,350 --> 00:23:24,470
+في هذا الجزء من ال chapter اللي هو اللي بتعلق ك ..
+
+238
+00:23:24,470 --> 00:23:28,350
+ك .. كمين؟ ك Taylor's theorem وكيف بدنا نطبق ال
+
+239
+00:23:28,350 --> 00:23:32,590
+Taylor's theorem في إثبات نظرية تعرف لنا ال test
+
+240
+00:23:32,590 --> 00:23:37,730
+إيش لها؟ قول يا محمد هل 
+
+241
+00:23:37,730 --> 00:23:46,670
+جيت وشفتها؟ في ال calculus في ال calculus كنا
+
+242
+00:23:46,670 --> 00:23:52,670
+ناخد اللي هو test لل increasing وال decreasing
+
+243
+00:23:52,670 --> 00:23:59,380
+باستخدام ال first derivative إذا بتتذكروا كنا ناخد
+
+244
+00:23:59,380 --> 00:24:04,220
+أيضا اللي هو عشان نعرف الدالة concave up أو
+
+245
+00:24:04,220 --> 00:24:08,340
+concave down بواسطة تمين ال second derivative test
+
+246
+00:24:08,340 --> 00:24:11,880
+ماشي الحال إذا كانت F double prime أكبر من صفر
+
+247
+00:24:11,880 --> 00:24:15,360
+كانت اللي هي concave up إذا كانت F double prime
+
+248
+00:24:15,360 --> 00:24:20,060
+أصغر من صفر كانت إيش مالها؟ concave down الآن هتشوفوا
+
+249
+00:24:20,060 --> 00:24:25,000
+النظرية اللي بتشابه اللي بنحكي وهتستنتج إيش اللي
+
+250
+00:24:25,000 --> 00:24:32,080
+بحكيه بجاوب على سؤالك شوف الآن الآن عندي واضح أنّ
+
+251
+00:24:32,080 --> 00:24:36,940
+من التعريف أنّ نفحص الدالة أنّها convex ولا مش
+
+252
+00:24:36,940 --> 00:24:41,920
+convex بالشكل اللي حكيناه بالتعريف اللي حكيناه
+
+253
+00:24:41,920 --> 00:24:46,380
+بغلب وبعض الدول مش هنقدر أو مش هنعرف اللي هو
+
+254
+00:24:46,380 --> 00:24:49,980
+لصعوبة الحسابات أنّ نثبت أنّها convex أو مش convex
+
+255
+00:24:49,980 --> 00:24:58,330
+فأكيد بدنا test يسهّل لنا عملية إيجاد أو معرفة أنّ هذه
+
+256
+00:24:58,330 --> 00:25:03,070
+الدالة is convex ولا لأ واضح اللي بحكيه؟ يلّا نشوف
+
+257
+00:25:03,070 --> 00:25:07,810
+مع بعض الآن قبلها بيعطينا بس counter example
+
+258
+00:25:07,810 --> 00:25:15,110
+بيقول لي أنّ ال convex function ممكن ما تكونش 
+
+259
+00:25:15,110 --> 00:25:18,540
+differentiable على الفترة اللي فيها convex يعني
+
+260
+00:25:18,540 --> 00:25:20,660
+ممكن اللي هي ال .. ال .. ال .. احنا اللي جابنا قبل 
+
+261
+00:25:20,660 --> 00:25:24,800
+شوية اللي جيبناها الدالة هي محلاها في انسياب وفي 
+
+262
+00:25:24,800 --> 00:25:27,860
+differentiability وال short أعلى من ال .. من
+
+263
+00:25:27,860 --> 00:25:31,260
+الدالة نفسها وكده وال function differentiable
+
+264
+00:25:31,260 --> 00:25:34,440
+لكن هذا الكلام مش دائماً حاصل أنّ ال convex
+
+265
+00:25:34,440 --> 00:25:37,100
+function تكون differentiable وأشهر منه ومثال
+
+266
+00:25:37,100 --> 00:25:41,460
+مشهور وسهل اللي هو F of X بسوء ال absolute value
+
+267
+00:25:41,460 --> 00:25:45,720
+لل X F of X بسوء ال absolute value لل X هذا اللي
+
+268
+00:25:45,720 --> 00:25:52,270
+هو is أكيد كلكم عارفين أنّها not differentiable at 0
+
+269
+00:25:52,270 --> 00:26:01,530
+but it is convex on any interval I containing إيش؟
+
+270
+00:26:01,530 --> 00:26:05,370
+إيش ال 0، بظبط؟ ال .. ال .. it is not
+
+271
+00:26:05,370 --> 00:26:08,030
+differentiable اللي عارفينها ال .. ال .. ال .. ال
+
+272
+00:26:08,030 --> 00:26:13,730
+.. نثبت أنّها convex let على interval I X1 و X2
+
+273
+00:26:13,730 --> 00:26:19,800
+element in I و T element in 0 و 1 احسب اللي لأنّ F
+
+274
+00:26:19,800 --> 00:26:29,780
+of 1 minus T في X1 زي T في X2 بيساوي عبارة عن ال
+
+275
+00:26:29,780 --> 00:26:36,240
+absolute value واحد نقص T X1 زي T في X2 وهذا من
+
+276
+00:26:36,240 --> 00:26:39,700
+خلاص ال absolute value أصغر بساوية واحد نقص T في
+
+277
+00:26:39,700 --> 00:26:46,100
+X1 زاية T في X2 وهذا طبعا مين هو؟ هو عبارة عن 1 نقص
+
+278
+00:26:46,100 --> 00:26:53,120
+T F of X1 زاية T في F of X2 إذا صار عندي ال F
+
+279
+00:26:53,120 --> 00:26:56,240
+إيش مالها؟ is convex but it is not differentiable
+
+280
+00:26:56,240 --> 00:27:00,620
+اطلع لفوق الآن يجي لي اللي هو ال test اللي معطيني إياه 
+
+281
+00:27:00,620 --> 00:27:07,060
+اللي بقوللي اللي بجاوب على سؤالك يا محمد let it be
+
+282
+00:27:08,590 --> 00:27:13,190
+And open interval and let f من I لR have a second
+
+283
+00:27:13,190 --> 00:27:18,890
+derivative on I نفترض أن الـ F''  إيش ما لها موجودة
+
+284
+00:27:18,890 --> 00:27:25,600
+على I إذا من رأس الدور مفترضين الـ F'' موجودة الـ
+
+285
+00:27:25,600 --> 00:27:30,140
+test هو كما قالي f is convex on i if and only if f 
+
+286
+00:27:30,140 --> 00:27:34,740
+double prime of  أكبر من 0 لكل x when element
+
+287
+00:27:34,740 --> 00:27:39,300
+in I بصور واضحة الأمر الآن بدي أستخدم في المرهان
+
+288
+00:27:39,300 --> 00:27:44,520
+اللي هو سؤال اللي هو 16 في ال exercises و هنحله
+
+289
+00:27:44,520 --> 00:27:48,380
+وهذا من ضمن ال exercises اللي معاكم هو Morgue و
+
+290
+00:27:48,380 --> 00:27:53,910
+هنحله في حينهالان ايش اللي هو ال .. ال .. ال .. ال
+
+291
+00:27:53,910 --> 00:27:58,390
+.. السؤال بيقول اذا كانت f double prime موجودة ثم
+
+292
+00:27:58,390 --> 00:28:02,570
+اثبت لي ان f double prime can be written as limit
+
+293
+00:28:02,570 --> 00:28:06,470
+f of a زائد h ناقص اتنين f of a زائد f of a ناقص h
+
+294
+00:28:06,470 --> 00:28:11,850
+على مين على h تربيع ماشي الحال هذا بدأ اعتمد على
+
+295
+00:28:11,850 --> 00:28:17,950
+انه اللي هو مثبت في اثبات النظرية ونشوف كيف ناخد
+
+296
+00:28:17,950 --> 00:28:23,540
+الاتجاه الاول اول اشي بده اللي هو بنفترض انه عندي
+
+297
+00:28:23,540 --> 00:28:29,080
+ال .. اللي هو ال F is convex ومنها نصل لإنه ال
+
+298
+00:28:29,080 --> 00:28:34,300
+derivative of  أكبر أو يساوي صفر ماشي الحال
+
+299
+00:28:34,300 --> 00:28:43,480
+خليني نشوف مع بعض كيف اللي هو نثبت
+
+300
+00:28:43,480 --> 00:28:55,740
+انه if F is convex then F double prime of A أكبر
+
+301
+00:28:55,740 --> 00:29:01,720
+من صفر لما نقول suppose that
+
+302
+00:29:01,720 --> 00:29:11,780
+proof فوضيح بس .. suppose that أن F is convex
+
+303
+00:29:11,780 --> 00:29:16,880
+لنثبت أن F double prime of A أكبر من صفر الان
+
+304
+00:29:16,880 --> 00:29:21,240
+انا ال F is convex وين على ال I و differentiable
+
+305
+00:29:21,240 --> 00:29:25,560
+وين second derivative لها على ال I خليني اختار
+
+306
+00:29:25,560 --> 00:29:31,280
+الان اللي هو ال H بحيث بدي اختار H بحيث انه A
+
+307
+00:29:31,280 --> 00:29:36,440
+ناقص H و A زائد H التانين يكون هنا وين موجودات في
+
+308
+00:29:36,440 --> 00:29:39,600
+ال interval I اللي عليها شغل اللي انا بدي اشتغل
+
+309
+00:29:39,600 --> 00:29:49,760
+عليها الان خدلي الان F of A واكتبها على صورة F of
+
+310
+00:29:49,760 --> 00:29:59,450
+نصف في A زائد H زائد نصف في A ناقص H لأن هذه عبارة عن
+
+311
+00:29:59,450 --> 00:30:03,330
+نصف A و نصف A هي الـ A و نصف H ناقص نصف H بروحهم مع
+
+312
+00:30:03,330 --> 00:30:06,730
+بعض ده منرجع لمين لل F و فيها كده تعرفي ليش عملتيل
+
+313
+00:30:06,730 --> 00:30:12,450
+طبعا هذه هتشتغل بمثابة واحد ناقص T و هذه T إذا T
+
+314
+00:30:12,450 --> 00:30:16,370
+بين ال Zero و الواحد صحيحة و بما أن F is convex و
+
+315
+00:30:16,370 --> 00:30:20,750
+هذولة اتتين نقطين عبارة عن نقطين في I لأن هيك
+
+316
+00:30:20,750 --> 00:30:26,520
+اختار ال H هنا هيكون هذا أصغر أو يساوي نصف F of A
+
+317
+00:30:26,520 --> 00:30:35,620
+زائد H زائد نصف F of A ناقص H واضح؟
+
+318
+00:30:35,620 --> 00:30:43,000
+أي سؤال؟ واضح أه؟ جيبلي هذا على الجهة التانية
+
+319
+00:30:43,000 --> 00:30:51,620
+بيصير عندي نصف F of A زائد H زائد نصف F of A ناقص H
+
+320
+00:30:51,620 --> 00:30:59,230
+ناقص F of A الكل of  أكبر أو يساوي إيش أكبر
+
+321
+00:30:59,230 --> 00:31:05,010
+أو يساوي صفر وضرب الجهتين في اتنين بيصير عندي
+
+322
+00:31:05,010 --> 00:31:10,550
+مضروبة في اتنين بيصير هذه اللي هو النص بيصير واحد و
+
+323
+00:31:10,550 --> 00:31:14,490
+النص هذا بيصير واحد و هذا بيصير of  ناقص
+
+324
+00:31:14,490 --> 00:31:22,650
+اتنين f of a اقسم لليه الآن على h تربيع و h
+
+325
+00:31:22,650 --> 00:31:26,370
+تربيع موجبة بقى، إذا بيضلوا هذا of  أكبر
+
+326
+00:31:26,370 --> 00:31:32,030
+أو يساوي صفر خد ال limit للجهتين limit as H goes
+
+327
+00:31:32,030 --> 00:31:40,440
+to zero بيضلوا أكبر أو يساوي صفر، مظبوط؟ و هذا by
+
+328
+00:31:40,440 --> 00:31:44,920
+ال exercise اللي بنحكي عنه هو عبارة عن مين؟ F
+
+329
+00:31:44,920 --> 00:31:48,100
+double prime of A فطلع عندي F double prime of A
+
+330
+00:31:48,100 --> 00:31:52,320
+أكبر أو يساوي الصفر طبعا ماقدرتش أستخدم هذا أنه بنكتب
+
+331
+00:31:52,320 --> 00:31:56,840
+على صورة هذا إلا في ضوء أن هو أصلا حاكي لي ال F
+
+332
+00:31:56,840 --> 00:32:03,940
+double prime exist on I واضح أه؟ أي سؤال إذا الان
+
+333
+00:32:03,940 --> 00:32:08,580
+اطلع لفوق و بنكون احنا خلصنا الجزء الأول و بنكون
+
+334
+00:32:08,580 --> 00:32:11,860
+بدنا نبدأ بالجزء الثاني اللي هو بال prime أكبر
+
+335
+00:32:11,860 --> 00:32:17,600
+من صفر و نصل لمين لل F is convex أوضحت هذه خليني
+
+336
+00:32:17,600 --> 00:32:24,100
+بس أنسحها و أقول ما يليه
+
+337
+00:32:24,100 --> 00:32:27,560
+نفترض
+
+338
+00:32:27,560 --> 00:32:30,060
+لأن صبوذ
+
+339
+00:32:32,450 --> 00:32:39,370
+that f double prime of a أكبر أو يساوي صفر
+
+340
+00:32:39,370 --> 00:32:45,330
+ماشي الحال .. بدنا نثبت لك أن f is convex كيف بدنا
+
+341
+00:32:45,330 --> 00:32:52,130
+نثبت ان f is convex؟ بدنا نقول let x1 و x2 بيه أي
+
+342
+00:32:52,130 --> 00:32:57,630
+element in مين؟ في i و t element in zero و واحد و
+
+343
+00:32:57,630 --> 00:33:06,820
+واحد وسميلي X naught هي عبارة عن واحد ناقص T في X
+
+344
+00:33:06,820 --> 00:33:13,580
+واحد زائد T في مين في X اتنين الآن بدي اطبق اللي
+
+345
+00:33:13,580 --> 00:33:16,480
+هو taylor's theorem اول اشي طبعا taylor's theorem
+
+346
+00:33:16,480 --> 00:33:21,960
+قابل للتطبيق اللي عند مين عند a بتساوي واحد بس
+
+347
+00:33:21,960 --> 00:33:25,640
+لأن المشتقة الأولى والتانية موجودة بعد هيك ماحدش
+
+348
+00:33:25,640 --> 00:33:29,480
+حكالي فإذا بيحجلي ان اطبق Taylor's theorem بس على
+
+349
+00:33:29,480 --> 00:33:34,260
+وين على اللي هو a بتساوي صفر أو a بتساوي واحد
+
+350
+00:33:34,260 --> 00:33:36,800
+a بتساوي صفر بيصير main value theorem a بتساوي
+
+351
+00:33:36,800 --> 00:33:41,000
+واحد اللي هو اللي بتطبق عليها و هتخدمني ماشي الحال
+
+352
+00:33:41,000 --> 00:33:46,470
+نشوف الان apply taylor's theorem ع الفترة على اللي
+
+353
+00:33:46,470 --> 00:33:51,970
+هو ال X واحد و ال X naught اللي عندى there exist اللي
+
+354
+00:33:51,970 --> 00:34:00,270
+هو C واحد between X واحد و X naught such that اه
+
+355
+00:34:00,270 --> 00:34:08,370
+اللي هو F of X naught مظبوط أو F of .. ده طبقه على X
+
+356
+00:34:08,370 --> 00:34:15,010
+واحد اول شي F of X واحد بيساوي اللي هو F of X naught
+
+357
+00:34:15,010 --> 00:34:22,550
+زائد F prime of X naught في X واحد ناقص X naught زائد مين
+
+358
+00:34:22,550 --> 00:34:26,950
+الان ال remainder زائد ال remainder ال remainder
+
+359
+00:34:26,950 --> 00:34:33,950
+إيش هو F double prime عند ال C واحد اللي لاجيناها
+
+360
+00:34:33,950 --> 00:34:41,390
+في X ناقص X naught الكل تربيع على 2 factorial أصغر من
+
+361
+00:34:41,390 --> 00:34:48,530
+اللي هو similarly there exist c2 بتطبقها على x1
+
+362
+00:34:48,530 --> 00:34:57,090
+على x2 و x0 there exist a c2 between x2 و x0
+
+363
+00:34:57,090 --> 00:35:07,070
+such that f of x2 بيساوي f of x0 زائد f prime of x0 في
+
+364
+00:35:07,070 --> 00:35:17,690
+x2 ناقص x0 زائد f double prime of c2 في x ناقص x0
+
+365
+00:35:17,690 --> 00:35:24,950
+الكل تربيع على 2 factorial واضح اللي بعمله
+
+366
+00:35:28,900 --> 00:35:37,440
+فهي عندي اللي هي هذه مع هذه هي اللي بدي استخدمه
+
+367
+00:35:37,440 --> 00:35:43,500
+هنا الان في الوصول لإنه F is convex يعني F of هذا
+
+368
+00:35:43,500 --> 00:35:49,180
+المقدار يكون أصغر أو يساوي اللي هو F 1 ناقص T
+
+369
+00:35:49,180 --> 00:35:56,920
+فهذه زائد T فهذه إذا بدي أحسب الان 1 ناقص T في F
+
+370
+00:35:56,920 --> 00:36:05,420
+of X 1 زائد T في F of إيش X2 بدي أحسبها و أوصلها
+
+371
+00:36:05,420 --> 00:36:09,080
+لعلاقتها مع مين مع F of X naught اللي هي F of هذه
+
+372
+00:36:09,080 --> 00:36:20,940
+بيساوي اضربلي بيصير T واحد ناقص T في F of X naught
+
+373
+00:36:20,940 --> 00:36:31,310
+معايا يا شباب زائد واحد ناقص T في F prime of X naught
+
+374
+00:36:31,310 --> 00:36:40,590
+في X واحد ناقص X naught زائد اللي هو mean ده دروفة
+
+375
+00:36:40,590 --> 00:36:47,390
+هذه اللي هو واحد ناقص T في F double prime of C
+
+376
+00:36:47,390 --> 00:36:52,970
+واحد في X ناقص X naught الكل تربيع على اتنين
+
+377
+00:36:52,970 --> 00:37:02,060
+factorial اللي هو اتنين معايا يا شباب زائد T .. T
+
+378
+00:37:02,060 --> 00:37:10,500
+.. F of X2 هيها اللي هي F of X naught زائد T في F
+
+379
+00:37:10,500 --> 00:37:15,860
+prime of X naught بضرب فادي قاعد في X2 ناقص X naught
+
+380
+00:37:15,860 --> 00:37:26,720
+زائد اللي هو T في F double prime of c2 fx-x0 الكل
+
+381
+00:37:26,720 --> 00:37:34,100
+تربيع على مين؟ على اتنين نيجي الان و يساوي اطلعلي
+
+382
+00:37:34,100 --> 00:37:41,720
+على هذه الان واحد ناقص T في F of X0 و T في F of X0
+
+383
+00:37:41,720 --> 00:37:51,520
+بيصير عبارة عن F of X0 مظبوط؟ زائد الان هذا f prime
+
+384
+00:37:51,520 --> 00:37:55,420
+of x naught مضروبة في T مضروبة في هذه إذا عبارة عن
+
+385
+00:37:55,420 --> 00:38:03,660
+واحد ناقص T زائد T اه اللي هو مية المية بيصير
+
+386
+00:38:03,660 --> 00:38:10,300
+عندي الان خد اللي هي x واحد ناقص x naught و خلينا
+
+387
+00:38:10,300 --> 00:38:19,510
+نجمحها واحد ناقص يعني خلينا نضيع ال T فيها ناقص
+
+388
+00:38:19,510 --> 00:38:24,730
+اتنين و X واحد او X او X واحد نفردها واحد ناقص T
+
+389
+00:38:24,730 --> 00:38:32,970
+في F ناخد عن المشترك يمكن أسهلنا F prime of X naught
+
+390
+00:38:32,970 --> 00:38:43,330
+في واحد ناقص T في X واحد ناقص X naught معايا شباب
+
+391
+00:38:43,330 --> 00:38:51,670
+زائد باخد بين هذه هي عمالو بين هذه أخدت ال F prime
+
+392
+00:38:51,670 --> 00:38:57,430
+of X naught عام مشترك بينهم زائد T في X2 ناقص X
+
+393
+00:38:57,430 --> 00:39:06,290
+naught زائد هذا المقدار كله بعد إذنكم هي اللي
+
+394
+00:39:06,290 --> 00:39:12,390
+بلزرج هذا اللي حطيته بلزرج سميني يا إيش R واضح
+
+395
+00:39:12,390 --> 00:39:21,890
+زائد R الان نطلع على اللي عندي هذا واحد ناقص T اول
+
+396
+00:39:21,890 --> 00:39:27,670
+اشي ناقص T في ناقص X Note بيصير اللي هو زائد T في
+
+397
+00:39:27,670 --> 00:39:31,850
+X Note مع ناقص T في X Note بروحين مظبوط؟ اذا هذا
+
+398
+00:39:31,850 --> 00:39:38,410
+الان بروح و هذا
+
+399
+00:39:38,410 --> 00:39:44,290
+برضه بروح صح ولا لأ؟ نتأكد في اللي عملناه
+
+400
+00:39:48,090 --> 00:40:00,190
+واضح اه بظل x .. x note اه بظل ناقص اللي هو زائد x
+
+401
+00:40:00,190 --> 00:40:07,950
+note ناقص x note ناقص x note عملها كمان مرة بظل
+
+402
+00:40:07,950 --> 00:40:15,160
+ناقص x note من هنا و من هنا بيظهر مين ناقص X note
+
+403
+00:40:15,160 --> 00:40:21,640
+لأنه بتظهر تبعت اللي هنا تظهر ناقص X note واضح أه؟
+
+404
+00:40:21,640 --> 00:40:28,760
+الان هذه كلها على بعض مين هي؟ هذه إيش اسمها؟ كلها
+
+405
+00:40:28,760 --> 00:40:32,900
+اسمها X note أه؟
+
+406
+00:40:32,900 --> 00:40:36,960
+فبيصير X note ناقص X note إيش بيصير؟ صفر فبيصير
+
+407
+00:40:36,960 --> 00:40:41,560
+هذا المقدار عبارة عن F of x naught زائد ال
+
+408
+00:40:41,560 --> 00:40:45,380
+remainder مين؟ R نتطلع على الـ R هذا أو هو R لما
+
+409
+00:40:45,380 --> 00:40:48,000
+نقول remainder؟ الـ R مجموع الـ remainder  دولين
+
+410
+00:40:48,000 --> 00:40:58,960
+الان ملاحظ هو ماعطيني عندي الان أفضل براءة عندي
+
+411
+00:40:58,960 --> 00:41:05,340
+هذا X ناقص X واحد الكل تربيع على اتنين موجبة و X ناقص
+
+412
+00:41:05,340 --> 00:41:10,330
+X اتنين نوت على اتنين of  موجبة و الان ال f
+
+413
+00:41:10,330 --> 00:41:15,510
+double prime عندي اللي هتطلع of  موجبة بنفس
+
+414
+00:41:15,510 --> 00:41:21,550
+الطريقة السابقة زي ما عملنا قبل شوية عندي f double
+
+415
+00:41:21,550 --> 00:41:27,310
+prime أكبر يساوي صفر هيطلع عندي في الجوار اللي
+
+416
+00:41:27,310 --> 00:41:30,610
+بطبق عليه برضه أكبر يساوي صفر فبطلع عندي هذا موجب
+
+417
+00:41:30,610 --> 00:41:35,690
+و هذا موجب فبطلع عندي هذا المقدار اللي بدأنا فيه
+
+418
+00:41:36,380 --> 00:41:41,720
+هذا المقدار اللي بدأنا فيه طلع بيساوي هذا المقدار
+
+419
+00:41:41,720 --> 00:41:49,760
+اللي هو هذا أكبر أو يساوي F of X naught اللي هي
+
+420
+00:41:49,760 --> 00:41:57,540
+يعني F of X naught اللي عبارة عن F معين واحد ناقص T 
+
+421
+00:41:57,540 --> 00:42:07,040
+في X واحد زائد T في X اثنين هذا اللي وصلنا إليه مع
+
+422
+00:42:07,040 --> 00:42:21,020
+هذا وهذا تعريف أيّه؟ F is convex F is convex أي
+
+423
+00:42:21,020 --> 00:42:21,680
+سؤال؟
+
+424
+00:42:24,290 --> 00:42:29,090
+وبهيك نكون خلصنا الـ section اللي الأخير في 
+
+425
+00:42:29,090 --> 00:42:34,250
+chapter اللي هو 6. خلصنا الجزء الأول من المحاضرة و
+
+426
+00:42:34,250 --> 00:42:37,250
+الآن بدنا نبدأ في الجزء الثاني من المحاضرة 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..260e3c008b4cbe27fb572cc0c338615c84c2a739
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_postprocess.srt
@@ -0,0 +1,1704 @@
+1
+00:00:05,480 --> 00:00:11,800
+بسم الله الرحمن الرحيم محاضرة رقم تسعة مساق تحليل
+
+2
+00:00:11,800 --> 00:00:19,160
+حقيقي اتنين طلاب الجامعة الإسلامية كلية العلوم قسم
+
+3
+00:00:19,160 --> 00:00:24,470
+الرياضياتالمحاضرة اليوم على جزئين الجزء الأول
+
+4
+00:00:24,470 --> 00:00:29,350
+هنتحدث عن applications of taylor's theorem والجزء
+
+5
+00:00:29,350 --> 00:00:34,250
+الثاني هنتحدث عن اللي هو discussion لsection 6.2
+
+6
+00:00:34,250 --> 00:00:37,890
+و6.3 اللي هو discussion لل mean value theorem وإذا
+
+7
+00:00:37,890 --> 00:00:43,270
+في وجهة بنعمل discussion ل اللي هو lobitals rules
+
+8
+00:00:43,960 --> 00:00:48,240
+الان خلّينا نكمل اللي اتحدثنا عنه المرة الماضية
+
+9
+00:00:48,240 --> 00:00:53,200
+ولكن على صورة تطبيقات ليه؟ اللي هو Taylor's
+
+10
+00:00:53,200 --> 00:00:58,660
+theorem وكيف بدنا اللي هو نستغل Taylor's theoremفي
+
+11
+00:00:58,660 --> 00:01:03,360
+إثبات بعض النظريات المهمة في موضوع اللي هو ال
+
+12
+00:01:03,360 --> 00:01:08,080
+maximum و ال minimum أو اللي هو ال test لإن اللي
+
+13
+00:01:08,080 --> 00:01:12,140
+عندنا هل هي local maximum أو local minimum ولا لا
+
+14
+00:01:12,140 --> 00:01:15,860
+هي local maximum ولا هي local minimum كنا اتحدثنا
+
+15
+00:01:15,860 --> 00:01:20,560
+سابقا على اللي هو ال first derivative test لإن
+
+16
+00:01:20,560 --> 00:01:23,200
+النقطة اللي تكون الداخلية هل في عندها local
+
+17
+00:01:23,200 --> 00:01:27,540
+maximum أو local minimumالان بدنا نتحدث عن الـ
+
+18
+00:01:27,540 --> 00:01:31,140
+Higher Derivative Test احنا يمكن نمر عنا اللي هو
+
+19
+00:01:31,140 --> 00:01:33,720
+الـ Second Derivative Test اللي هو في ال .. في
+
+20
+00:01:33,720 --> 00:01:36,900
+الCalculus اللي قابلة نتحدث على ال Higher
+
+21
+00:01:36,900 --> 00:01:40,080
+Derivative Test و اللي هي .. اللي هي ال Second
+
+22
+00:01:40,080 --> 00:01:44,090
+Derivative Test جزء من هذا اللي هو ال testنتطلع
+
+23
+00:01:44,090 --> 00:01:48,030
+على الـ test إيش بقول اللي هي عبارة عن theorem 644
+
+24
+00:01:48,030 --> 00:01:52,310
+let I be an interval نفترض أن I عبارة عن interval
+
+25
+00:01:52,310 --> 00:01:57,510
+و X note اللي هي نقطة اللي احنا بدنا نفحص عندها هل
+
+26
+00:01:57,510 --> 00:02:02,770
+في maximum أو في minimum أو لا في maximum ولا في
+
+27
+00:02:02,770 --> 00:02:06,470
+minimum X note اللي هي عبارة عن interior point
+
+28
+00:02:06,470 --> 00:02:10,890
+لمن؟ لل interval I يعني نقطة داخليةونفترض الـ N
+
+29
+00:02:10,890 --> 00:02:14,570
+تبعتنا أكبر أو ساوى 2 لأن الـ N أكبر أو ساوى 2
+
+30
+00:02:14,570 --> 00:02:17,690
+يعني الـ Second Derivative Test أو أعلى هو اللي
+
+31
+00:02:17,690 --> 00:02:20,910
+بده يحددنا أنه عندنا Maximum أو Minimum أو مافيش
+
+32
+00:02:20,910 --> 00:02:25,450
+لا Maximum ولا Minimum Suppose ده ال derivatives
+
+33
+00:02:25,450 --> 00:02:31,120
+اللي هي F' و F'' لعند FN existsexist and are
+
+34
+00:02:31,120 --> 00:02:34,040
+continuous in a neighborhood of x naught نفترض إن
+
+35
+00:02:34,040 --> 00:02:39,140
+هدولة continuous وموجودة في اللي هو
+
+36
+00:02:41,860 --> 00:02:44,760
+اللي هي في neighborhood حوالي مين الـ X Note
+
+37
+00:02:44,760 --> 00:02:49,920
+ونفترض أن F' عند X Note لعند F N ناقص واحد prime
+
+38
+00:02:49,920 --> 00:02:54,060
+of X Note إيش بيساوي؟ سفر لكن عند F N of X Note
+
+39
+00:02:54,060 --> 00:02:59,140
+إيش مالها؟ لاتساوي سفر إذا ال test إيش بيصير؟ أول
+
+40
+00:02:59,140 --> 00:03:06,120
+إشيبنشوف f prime نقطة x note هذه نقطة متوقع عندها
+
+41
+00:03:06,120 --> 00:03:10,340
+maximum أو minimum أو مافيش شيء من النقاط اللي هي
+
+42
+00:03:10,340 --> 00:03:13,520
+بدنا نفحص عندها maximum أو minimum إيش بدنا نسوي
+
+43
+00:03:13,520 --> 00:03:18,520
+في هذا ال test بنجيب f prime عند ال x note إذا
+
+44
+00:03:18,520 --> 00:03:23,500
+لجيناها سفر بنيجي لل f double prime عند ال x note
+
+45
+00:03:23,500 --> 00:03:29,130
+إذا لجيناها سفراللي هو بنيجي للـ F W' عند الـ X0
+
+46
+00:03:29,130 --> 00:03:34,830
+وين بنصل للـ F W' .. وين بنصل للـ F N of X0 لا
+
+47
+00:03:34,830 --> 00:03:39,210
+تساوي سفر؟ بيبدأ الخطوات تبعات ال test ايش ال
+
+48
+00:03:39,210 --> 00:03:43,710
+test؟ اللي هي الأول إذا كانت N even طلعت عندنا N
+
+49
+00:03:43,710 --> 00:03:47,850
+هادئية أول واحدة ال derivative عندها عند ال X0 مش
+
+50
+00:03:47,850 --> 00:03:53,930
+سفروكانت ال Fn of X0 أكبر من 0 بتكون ال F أيه
+
+51
+00:03:53,930 --> 00:03:57,470
+شمالها؟ اللي هي relative minimum زي ال second
+
+52
+00:03:57,470 --> 00:04:01,710
+derivative test كنا لما نقول ال FW' عند ال X0 أكبر
+
+53
+00:04:01,710 --> 00:04:06,170
+من 0 على طول نحكم أنه في local minimum هنا الآن لأ
+
+54
+00:04:06,170 --> 00:04:08,510
+احنا على ال higher derivative و هتحللنا المشاكل
+
+55
+00:04:08,510 --> 00:04:10,290
+اللي كانت ماتتحللاش جامعي اللي هي second
+
+56
+00:04:10,290 --> 00:04:16,670
+derivative test الان Fn is evenو ال F N of X0 أصغر
+
+57
+00:04:16,670 --> 00:04:21,510
+من 0 إذا Fها زي إيه شمالها relative maximum at X0
+
+58
+00:04:21,510 --> 00:04:25,670
+إذا لو طلعت عندي N is odd إيش يعني N is odd؟ يعني
+
+59
+00:04:25,670 --> 00:04:31,130
+أول .. أول derivative ال F N عندها لاتساوي 0 طلعت
+
+60
+00:04:31,130 --> 00:04:35,390
+عندي هذه oddطبعا أكبر إذا هو 2، 3 أو 5 أو 7 إلى
+
+61
+00:04:35,390 --> 00:04:39,490
+آخره على طول احنا بنحكم then F has neither
+
+62
+00:04:39,490 --> 00:04:43,610
+relative minimum nor إيش ما لها relative maximum
+
+63
+00:04:43,610 --> 00:04:50,790
+at X note بتصور هيك النظرية واضحة إيش نصها بنجيبF
+
+64
+00:04:50,790 --> 00:04:56,570
+prime of X0 و F double prime of X0 إلى آخره إذا
+
+65
+00:04:56,570 --> 00:05:01,170
+هذا بيساوي سفر بهذا بيساوي سفر بضلي ماشي لعند F N
+
+66
+00:05:01,170 --> 00:05:08,550
+of X0 لاتساوي سفر و اگ تست تصل لاتساوي سفر باجي لل
+
+67
+00:05:08,550 --> 00:05:17,620
+test اللي هو uneven عند حالتينالحالة الأولى FN of
+
+68
+00:05:17,620 --> 00:05:27,280
+X0 أكبر من 0 Local MinimumFn of X0 أصغر من 0 Local
+
+69
+00:05:27,280 --> 00:05:33,180
+maximum لكن إذا طلعت n is odd يعني أول واحدة بعد
+
+70
+00:05:33,180 --> 00:05:37,720
+التنين اللي هو بيطلع عند F ال derivative لها Fn of
+
+71
+00:05:37,720 --> 00:05:43,200
+X0 لا تساوي 0 طلعت عند n is odd إذا بحكم على طول F
+
+72
+00:05:43,200 --> 00:05:52,030
+has neither Local maximum nor Local minimumتعالوا
+
+73
+00:05:52,030 --> 00:05:58,670
+اللي هو نبرهم اللي هو النظرية ونشوف إنه حجر الأساس
+
+74
+00:05:58,670 --> 00:06:02,470
+للبرهان اللي هي taylor's theorem هي taylor's
+
+75
+00:06:02,470 --> 00:06:12,430
+theorem تنشوف كيف الآن عندي بدنا نطبق taylor's
+
+76
+00:06:12,430 --> 00:06:15,820
+theoremعلى .. طبعا احنا بنشتغل على الـ interval من
+
+77
+00:06:15,820 --> 00:06:21,520
+I بناخد اللي هو X element من I و بنطبقلها من الـ
+
+78
+00:06:21,520 --> 00:06:26,120
+Taylor's theorem عند النقطة اللي احنا بدنا نختبر
+
+79
+00:06:26,120 --> 00:06:29,840
+عند X0 فهي اللي بده أجيب Taylor's theorem حواليها
+
+80
+00:06:29,840 --> 00:06:36,160
+اذا حسب Taylor's theorem ان there exists C between
+
+81
+00:06:36,160 --> 00:06:45,630
+اللي هي X and X0 such thatاللي هو F of X F of X
+
+82
+00:06:45,630 --> 00:06:52,110
+بساوي بي أن ناقص واحد بدا أقبّقها اللي بحيث أن ال
+
+83
+00:06:52,110 --> 00:06:56,250
+polynomial ما أن ناقص واحد ليش؟ لإنه أنا ماعطيني
+
+84
+00:06:56,250 --> 00:07:01,110
+هو عنده ال derivative اللي هي لعند F أن ناقص واحد
+
+85
+00:07:01,110 --> 00:07:05,870
+كلها سفار واللي مش سفر اللي هي مين F n of X not
+
+86
+00:07:06,550 --> 00:07:11,390
+فعند اللي هي R نقص واحد هطبق عشان تحكم لل FN of X
+
+87
+00:07:11,390 --> 00:07:15,310
+node على إنه عندني local maximum أو local minimum
+
+88
+00:07:15,310 --> 00:07:19,750
+أو neither كيف؟ خلّينا نطبق ال Taylor's theorem
+
+89
+00:07:19,750 --> 00:07:28,350
+زائد اللي هو أشملها R N نقص واحد of X هذه عندي
+
+90
+00:07:28,350 --> 00:07:33,230
+Taylor's theorem الآن ال BN نقص واحد اللي هي عبارة
+
+91
+00:07:33,230 --> 00:07:40,820
+عن إياش Fof x naught زائد f prime of x naught في x
+
+92
+00:07:40,820 --> 00:07:45,440
+minus x naught اللي هو على واحد factorial زائد لما
+
+93
+00:07:45,440 --> 00:07:51,400
+أصل لآخر واحد f n ناقص واحد of x naught في x minus
+
+94
+00:07:51,400 --> 00:07:55,540
+x naught قس n ناقص واحد على n ناقص واحد لكل
+
+95
+00:07:55,540 --> 00:08:02,700
+factorial زائد main ال remainder اللي هو main اللي
+
+96
+00:08:02,700 --> 00:08:09,810
+هو عبارة عن xنقص x note أس n على n factorial في f
+
+97
+00:08:09,810 --> 00:08:18,850
+n of mean of عندي c و ال c مالها between x note
+
+98
+00:08:18,850 --> 00:08:27,170
+and mean and x واضح و يساوي الأن كل هذول أصفار صح
+
+99
+00:08:27,170 --> 00:08:33,500
+ولا لأ إذا حيصير عندي هذا بيساوي لإنه معطيليالـ F
+
+100
+00:08:33,500 --> 00:08:41,120
+prime of X note لعند FN نقص واحد of X note كله
+
+101
+00:08:41,120 --> 00:08:46,700
+نصفار إذا صلي عندي هذا بيساوي F of X note لأن هذا
+
+102
+00:08:46,700 --> 00:08:55,740
+كله بتصفر زاد X minus X note أس N على N factorial
+
+103
+00:08:55,740 --> 00:09:09,290
+في FNof c واضح اه اي سؤال طيب عندى انا اللى هو
+
+104
+00:09:09,290 --> 00:09:19,230
+معطينى ال ال f n of x naught اللى هى لاتساوى سفر
+
+105
+00:09:19,230 --> 00:09:25,170
+اذا ال f n of x naught يا اكبر من سفر يا اصغر من h
+
+106
+00:09:25,170 --> 00:09:36,570
+من سفرإذا أكيد عندي ال FN of X note و ال FN of C
+
+107
+00:09:36,570 --> 00:09:43,810
+الهن أيش الهن the same sign ماشي اه الهن نفس نين
+
+108
+00:09:43,810 --> 00:09:50,770
+نفس اللي هو الإشارة طبعا السبب أن FN أشمالها is
+
+109
+00:09:50,770 --> 00:09:55,950
+continuous انوضحلكم إياها تتذكروا
+
+110
+00:09:57,370 --> 00:10:02,330
+قلنا خلّينا ناخد حالة نفترض أن هذا أكبر من مين من
+
+111
+00:10:02,330 --> 00:10:12,690
+سفر احنا كنا نقول limit أي حاجة g of x لما x تروح
+
+112
+00:10:12,690 --> 00:10:18,970
+لل c مثلا أكبر من سفر معناته في جوار في جوار
+
+113
+00:10:18,970 --> 00:10:23,210
+حوالين اللي هو ال c ال g of x نفسها إيش هتكون أكبر
+
+114
+00:10:23,210 --> 00:10:28,110
+من سفر لكل x في هذا الجواريعني هيكون عندي إذاً g
+
+115
+00:10:28,110 --> 00:10:37,710
+of x أكبر من 0 لكل x في sum جوار delta of mean of
+
+116
+00:10:37,710 --> 00:10:41,690
+z هذا اللي بدأ أستخدمها الآن في الوصول للي بديها
+
+117
+00:10:41,690 --> 00:10:45,590
+خلّيني نشوف كيف بدأ نستخدم هذه المعلومة الآن أنا
+
+118
+00:10:45,590 --> 00:10:55,750
+عندي الـ Fn is continuous نفسها إذاً limit Fnof X
+
+119
+00:10:55,750 --> 00:11:03,290
+أفقًا of X اللي هو لما الـ X تروح للـ X0 اللي هو
+
+120
+00:11:03,290 --> 00:11:10,070
+أش متساوي أفقًا of X0 وبرضه continuous عند مين؟
+
+121
+00:11:11,690 --> 00:11:16,810
+وبرضه continuous عند مين؟ عند الـ C معايا وعند الـ
+
+122
+00:11:16,810 --> 00:11:21,030
+C إيش مالها؟ continuous أنا اللي هيلزمني مين؟ هنا
+
+123
+00:11:21,030 --> 00:11:26,930
+الـ X note مظبوط ولا لأ؟ عندي هتلزمني مين؟ اللي هي
+
+124
+00:11:26,930 --> 00:11:35,950
+ال X note إذا صار عنديفن of X note هي اللي هتحددلي
+
+125
+00:11:35,950 --> 00:11:45,090
+من هنا اللي هي إشارة مين فن of C واضح الآن من هذه
+
+126
+00:11:45,090 --> 00:11:54,310
+إذا كانت F of X note مثلا أكبر من سفر هتطلع حد
+
+127
+00:11:54,310 --> 00:11:58,870
+أكبر من سفر خلينا نشوفها إذا الآن خليني أبدأ في
+
+128
+00:11:58,870 --> 00:12:06,270
+مينفي I بدي افترض مين الان fn of x not أكبر من أيش
+
+129
+00:12:06,270 --> 00:12:13,010
+من سفر و افترض ان الان عند ايش معنها is even بدي
+
+130
+00:12:13,010 --> 00:12:19,950
+أنطلق من هذه اذا الان fn of x not أكبر من سفر و n
+
+131
+00:12:19,950 --> 00:12:25,730
+is even بناء على هذه for every y أكبر من سفر there
+
+132
+00:12:25,730 --> 00:12:32,440
+exists such that المهم بيطلع عندىاللي هو F هذه ايش
+
+133
+00:12:32,440 --> 00:12:37,880
+مفترضين احنا اكبر من ايه ايش من سفر اذا حسب اللي
+
+134
+00:12:37,880 --> 00:12:45,450
+حكيته قبل بشوية there existV Delta of إيش؟ Of X0
+
+135
+00:12:45,450 --> 00:12:53,590
+حوالي مين؟ الـ X0 Such that اللي هو FN of X زي
+
+136
+00:12:53,590 --> 00:12:59,290
+إشارة هذه اللي هي أكبر من 0 لكل X وين في الـ V
+
+137
+00:12:59,290 --> 00:13:06,880
+Delta of مين؟ Of X0ماشي الحال واللي من ضمن هدوله
+
+138
+00:13:06,880 --> 00:13:15,060
+مين؟ C إذا صارت عندي الان FN of C برضه إيه شمالها؟
+
+139
+00:13:15,060 --> 00:13:21,860
+أكبر من سفر الان اتضحت الصورة الان صارت عندي من
+
+140
+00:13:21,860 --> 00:13:26,420
+الأصل F of X بسوء F of X note زائد هذا المقدار بدا
+
+141
+00:13:26,420 --> 00:13:31,020
+أقول الآن بما أن هذه أكبر من سفر وان أنا مفترضها
+
+142
+00:13:31,020 --> 00:13:36,490
+إنها evenإذا حيصير عندى هذا أكبر من صفر وهذا أكبر
+
+143
+00:13:36,490 --> 00:13:41,570
+من صفر إذا الـ remainder كله إيش ماله أكبر من صفر
+
+144
+00:13:41,570 --> 00:13:47,710
+مدام الـ remainder أكبر من صفر واضح اللي بحكي FN
+
+145
+00:13:47,710 --> 00:13:53,010
+of C أكبر من صفر وهذا المقدر أكبر من صفر لأنه N is
+
+146
+00:13:53,010 --> 00:13:58,710
+even إذا صار كل هذا أكبر من صفر إذا automatic لما
+
+147
+00:13:58,710 --> 00:14:04,660
+أشيلههيصغر المقدار، بظبط ولا لأ؟ فهيصير عند ال F
+
+148
+00:14:04,660 --> 00:14:12,040
+of X اللي هو أكبر من مين من ال F of X naught لأن F
+
+149
+00:14:12,040 --> 00:14:17,680
+of X بساوي هذا زائد هذا فأكيد عند ال F of X أكبر
+
+150
+00:14:17,680 --> 00:14:22,160
+من مين من F of X naught في وين، لكل X وين موجودة
+
+151
+00:14:22,160 --> 00:14:30,530
+في الجوار اللي حواليها، إذا صار عند Fhas local
+
+152
+00:14:30,530 --> 00:14:40,870
+minimum at x0 similarly لو
+
+153
+00:14:40,870 --> 00:14:53,630
+بدنا نفترض ان المقدار هذا عندي fn of x0 أصغر من 0
+
+154
+00:14:54,540 --> 00:15:00,740
+وبدأ أبدأ أحكي عن مين؟ عن I I بيصير عندي الآن حسب
+
+155
+00:15:00,740 --> 00:15:07,320
+الحديث هنا ال FN of C اللي هي أصغر من 0 لإنه هتكون
+
+156
+00:15:07,320 --> 00:15:13,600
+ال FN of X لكل X في هذا الدوار the same sign as FN
+
+157
+00:15:13,600 --> 00:15:18,120
+of X note أصغر من 0 إذا صارت عندي FN of C أصغر من
+
+158
+00:15:18,120 --> 00:15:24,050
+0هذه صارت سالبة وهذه موجبة لإنه and is even إذا
+
+159
+00:15:24,050 --> 00:15:28,290
+صار المقدار هذا كله على بعض إيه شماله؟ سالب في كل
+
+160
+00:15:28,290 --> 00:15:33,070
+هذا الجوار ما ده صار سالب معناته إنه لما أنا أشيله
+
+161
+00:15:33,070 --> 00:15:39,330
+بكبر اللي بظهر يعني بيصير F of X note بناء عليه
+
+162
+00:15:39,330 --> 00:15:46,630
+أكبر من F of X مظبوط؟وهذا يعني انه صار ال F في هذه
+
+163
+00:15:46,630 --> 00:15:56,010
+الحالة عندها local maximum local maximum واضح ؟ اي
+
+164
+00:15:56,010 --> 00:16:01,510
+سؤال ؟ طيب، ضال عند مين الحالة الأخيرة، هذي
+
+165
+00:16:01,510 --> 00:16:09,170
+تذكرينها لأنه برضه بدي اشتغل نفس الشيء في الحالة
+
+166
+00:16:09,170 --> 00:16:15,680
+الأخيرة او اشي مشابهعند الان بدي افترض mean ان
+
+167
+00:16:15,680 --> 00:16:25,980
+الحالة الثالثة بدي افترض ان ال is mean of of زي
+
+168
+00:16:25,980 --> 00:16:35,810
+ما عملنا قبل بشوية إذا كانت اللي هي Fفن of x not
+
+169
+00:16:35,810 --> 00:16:40,890
+أكبر من سفر زي ما عملنا قبل شوية هيعطيني فن of c
+
+170
+00:16:40,890 --> 00:16:49,990
+أكبر من إيش؟ من سفر معايا؟ طيب الآن هذا الكلام لو
+
+171
+00:16:49,990 --> 00:16:56,930
+جيت أخدت عندي هي عندي هذه اللي هي x not وهنا
+
+172
+00:16:56,930 --> 00:17:01,650
+الجوار اللي حواليهاالجوار اللي حواليها اللي لاجئت
+
+173
+00:17:01,650 --> 00:17:09,230
+في كل الجوار زي ما عملت قبل شوية fn of x هيكون
+
+174
+00:17:09,230 --> 00:17:15,830
+اللي هو هنا اللي هو هنا و هنا موجب ماشي الحال الآن
+
+175
+00:17:15,830 --> 00:17:21,850
+مدام موجب هنا و هنا اللي هيتحكم في الموضوع اليمين
+
+176
+00:17:21,850 --> 00:17:27,770
+x minus x naught أسن لكن لسوء الحظ لو كانت x هنا
+
+177
+00:17:28,970 --> 00:17:35,350
+بصير عندى و هذا طبعا لكل X وين على يمين ال X node
+
+178
+00:17:35,350 --> 00:17:41,450
+هيطلع عندى ال X minus X node أس N وهذه إيه شمالها
+
+179
+00:17:41,450 --> 00:17:49,110
+odd is أكبر من أيش من سفر فصارت الآن هذه أكبر من
+
+180
+00:17:49,110 --> 00:17:54,330
+سفر وهذه أكبر من سفر التنتير مع بعض أكبر من سفر
+
+181
+00:17:55,160 --> 00:18:01,380
+ماشي فصارت عندي ال F of X أكبر من مين من ال F of X
+
+182
+00:18:01,380 --> 00:18:07,600
+naught ماشي الحال في المنطقة هذه هذه المنطقة هذه
+
+183
+00:18:07,600 --> 00:18:16,060
+صارت عندي ال F of X أكبر من F of X naught فاهمين؟
+
+184
+00:18:16,060 --> 00:18:23,240
+لأن الجزء الثاني ال Xفي المنطقة اللي هان أي x في
+
+185
+00:18:23,240 --> 00:18:27,880
+المنطقة اللي هان عند الـ x minus x naught أصغر من
+
+186
+00:18:27,880 --> 00:18:32,480
+مين من سفر فبصير عند هذا المقدار أصغر من سفر وهذا
+
+187
+00:18:32,480 --> 00:18:37,020
+أكبر من سفر حاصل الدرب أصغر من سفر أصغر من سفر بقد
+
+188
+00:18:37,020 --> 00:18:42,200
+إلى أن أف of x في المنطقة هذه تصير أصغر من أف of x
+
+189
+00:18:42,200 --> 00:18:47,250
+naught يعني لو أتيت لأي جوارحوالين الـ X Note
+
+190
+00:18:47,250 --> 00:18:51,770
+هتلاقي اللي هو مرة الـ F of X Note أصغر من F of X
+
+191
+00:18:51,770 --> 00:18:56,810
+ومرة F of X Note أكبر من مين من F of X يعني بمعنى
+
+192
+00:18:56,810 --> 00:19:02,270
+آخر لا في عندي Local Maximum ولا Local Minimum في
+
+193
+00:19:02,270 --> 00:19:08,450
+هذه المنطقة Similarly وبنفس الأسلوب لو كانت FN of
+
+194
+00:19:08,450 --> 00:19:14,000
+X Note أصغر من مينمن صفر معايا بيصير هذه أصغر من
+
+195
+00:19:14,000 --> 00:19:19,020
+صفر و بيصير بس بتنقلب بيصير هذه في المنطقة هذه
+
+196
+00:19:19,020 --> 00:19:23,840
+أصغر و هذه في المنطقة هذه ايش اكبر اذا in both
+
+197
+00:19:23,840 --> 00:19:30,160
+cases عندي if and is odd اذا we have neither اللي
+
+198
+00:19:30,160 --> 00:19:37,660
+هو relative maximum nor relative minimum اي سؤال
+
+199
+00:19:37,660 --> 00:19:45,760
+واضح اه؟اللي بعده اللي بعده الان بدنا نعرف حاجة
+
+200
+00:19:45,760 --> 00:19:51,140
+اسمها اللي هي مين ال convex function تعالي على
+
+201
+00:19:51,140 --> 00:19:55,640
+الرسم يا بو محمد عندي بدنا نعرف مين ال convex
+
+202
+00:19:55,640 --> 00:19:59,860
+function الان ال convex function إيش يكون cave
+
+203
+00:19:59,860 --> 00:20:05,200
+اللي هو إيش up خليني نشوف إيش هذي اللي هو بعبر شو
+
+204
+00:20:05,200 --> 00:20:07,980
+معناه ال F is convex
+
+205
+00:20:10,750 --> 00:20:14,990
+خاصية الـ convex أو الـ convexity بنحكي فيها على
+
+206
+00:20:14,990 --> 00:20:22,090
+interval يعني بنقول F من عند I لعند R بنقول عنها F
+
+207
+00:20:22,090 --> 00:20:28,170
+is convex on إيش؟ on I on وين؟ ع ال interval I إذا
+
+208
+00:20:28,170 --> 00:20:35,970
+كان شوف كيف خدلي الآن X1 أي نقطة في داخل الـ I و
+
+209
+00:20:35,970 --> 00:20:41,970
+X2 أي نقطة في داخل الـ Iوخدلي ال parameter T بين
+
+210
+00:20:41,970 --> 00:20:45,830
+السفر و بين الواحد الان النقطة ال linear
+
+211
+00:20:45,830 --> 00:20:51,230
+combination بين X1 و X2 بواسطة 1-T X1 زائد T X2
+
+212
+00:20:51,230 --> 00:20:56,530
+هتكون بين X1 و بين X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+213
+00:20:56,530 --> 00:20:56,950
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+214
+00:20:56,950 --> 00:21:06,250
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+215
+00:21:06,250 --> 00:21:14,050
+X2 X2 X2 X2 X2 X2 X2لو إجيت ل F of X1 هيها وهذا F
+
+216
+00:21:14,050 --> 00:21:20,650
+of X2 لو ضربت ال F of X1 و 1 minus T و جمعتها ل T
+
+217
+00:21:20,650 --> 00:21:25,170
+في F of X2 هتلاقيها بين اللي هو مين على اللي هو
+
+218
+00:21:25,170 --> 00:21:32,010
+الخط المستقيم القاطع بين X1 و F of X1 و بين X2 و F
+
+219
+00:21:32,010 --> 00:21:37,970
+of X2 دائما هتلاقي هذه النقطةالصورة هنا أعلى من
+
+220
+00:21:37,970 --> 00:21:42,910
+هذه وهذا معنى اللي هو ال convex وعن عرف ال convex
+
+221
+00:21:42,910 --> 00:21:50,390
+على هذا الأساس بيقول F is convex on I طلعلي على
+
+222
+00:21:50,390 --> 00:21:54,650
+التعريف إذا كان أخدنا أي X واحد و X اتنين element
+
+223
+00:21:54,650 --> 00:22:00,690
+in I و أخدنا T اللي هو element in 01 يعني بين 01
+
+224
+00:22:00,690 --> 00:22:13,020
+بيحققلي F اللي هوfor any كده f
+
+225
+00:22:13,020 --> 00:22:19,140
+is a convex in I if for any كده وكده we have
+
+226
+00:22:19,140 --> 00:22:25,940
+فاهمين عليا f of واحد minus T X واحد زائد T في X
+
+227
+00:22:25,940 --> 00:22:32,520
+اتنين ايش ماله هيسير؟أصغر أو يساوي واحد ناقص T في
+
+228
+00:22:32,520 --> 00:22:38,000
+X واحد زائد T في F of X اتنين
+
+229
+00:22:40,410 --> 00:22:44,370
+طبعاً اللي هو ال .. ال .. ال .. ال .. ال convex
+
+230
+00:22:44,370 --> 00:22:48,330
+functions في عليها دراسات كثيرة ودراسات حديثة كمان
+
+231
+00:22:48,330 --> 00:22:55,070
+حتى يعني في اللي هو real analysis بما يتعلق بال ..
+
+232
+00:22:55,070 --> 00:22:58,950
+مش بال integration العادي كمان باللي هو .. و
+
+233
+00:22:58,950 --> 00:23:03,310
+علاقتها بال integration في اللي هو ال .. ال big
+
+234
+00:23:03,310 --> 00:23:08,760
+integra كمانوطبعاً وإليها اللي هو خلّيني أقول
+
+235
+00:23:08,760 --> 00:23:14,020
+تطبيقات أو استخدامات في اللي هو optimization اللي
+
+236
+00:23:14,020 --> 00:23:20,350
+هي theoryالان احنا هنتحك .. هنحكي فيها بما يتعلق
+
+237
+00:23:20,350 --> 00:23:24,470
+في هذا الجزء من ال chapter اللي هو اللي بتعلق ك ..
+
+238
+00:23:24,470 --> 00:23:28,350
+ك .. كمين؟ ك Taylor's theorem وكيف بدنا نطبق ال
+
+239
+00:23:28,350 --> 00:23:32,590
+Taylor's theorem في إثبات نظرية تعرف لنا ال test
+
+240
+00:23:32,590 --> 00:23:37,730
+إيه لها؟ قول يا محمد هل
+
+241
+00:23:37,730 --> 00:23:46,670
+جيت و تشوفها؟ في ال calculus في ال calculusكنا
+
+242
+00:23:46,670 --> 00:23:52,670
+ناخد اللي هو test لل increasing وال decreasing
+
+243
+00:23:52,670 --> 00:23:59,380
+باستخدام ال first derivativeإذا بتتذكروا كنا ناخد
+
+244
+00:23:59,380 --> 00:24:04,220
+أيضا اللي هو عشان نعرف الدالة concave up أو
+
+245
+00:24:04,220 --> 00:24:08,340
+concave down بوسط تمين ال second derivative test
+
+246
+00:24:08,340 --> 00:24:11,880
+ماشي الحال إذا كانت F double prime أكبر من صفر
+
+247
+00:24:11,880 --> 00:24:15,360
+كانت اللي هي concave up إذا كانت F double prime
+
+248
+00:24:15,360 --> 00:24:20,060
+أصغر من صفر كانت أشمالها concave down الآن هتشوفوا
+
+249
+00:24:20,060 --> 00:24:25,000
+النظرية اللي بتشابه اللي بنحكي و هتستنتج أيش اللي
+
+250
+00:24:25,000 --> 00:24:32,080
+بحكيهبجاوب على سؤالك شوف الآن الان عندي واضح انه
+
+251
+00:24:32,080 --> 00:24:36,940
+من التعريف ان نفحص الدالة انها convex ولا مش
+
+252
+00:24:36,940 --> 00:24:41,920
+convex بالشكل اللي حكيناه بالتعريف اللي حكيناه
+
+253
+00:24:41,920 --> 00:24:46,380
+بغلب وبعض الدول مش هنقدر او مش هنعرف اللي هو
+
+254
+00:24:46,380 --> 00:24:49,980
+لصعوبة الحسابات ان نثبت انها convex او مش convex
+
+255
+00:24:49,980 --> 00:24:58,330
+فاكيد بدنا testيسهّلنا عملية إيجاد أو معرفة إن هذه
+
+256
+00:24:58,330 --> 00:25:03,070
+الدالة is convex ولا لأ واضح اللي بحكيه؟ يلّا نشوف
+
+257
+00:25:03,070 --> 00:25:07,810
+مع بعض الان قبلها بيعطينا بس counter example
+
+258
+00:25:07,810 --> 00:25:15,110
+بقولّي إن ال convex function ممكن ما تكونش
+
+259
+00:25:15,110 --> 00:25:18,540
+differentiable على الفترة اللي فيها convexيعني
+
+260
+00:25:18,540 --> 00:25:20,660
+ممكن اللي هي ال .. ال .. ال .. احنا اللي جابنا قبل
+
+261
+00:25:20,660 --> 00:25:24,800
+شوية اللي جيبناها الدالة هي محلاها في انسياب وفي
+
+262
+00:25:24,800 --> 00:25:27,860
+differentiability و ال short أعلى من ال .. من
+
+263
+00:25:27,860 --> 00:25:31,260
+الدالة نفسها و كده و ال function differentiable
+
+264
+00:25:31,260 --> 00:25:34,440
+لكن هذا الكلام مش دايما حاصل انه ال convex
+
+265
+00:25:34,440 --> 00:25:37,100
+function تكون differentiable و أشهر منه و مثال
+
+266
+00:25:37,100 --> 00:25:41,460
+مشهور وسهل اللي هو F of X بسوء ال absolute value
+
+267
+00:25:41,460 --> 00:25:45,720
+لل X F of X بسوء ال absolute value لل X هذا اللي
+
+268
+00:25:45,720 --> 00:25:52,270
+هوis أكيد كلكم عارف إنها not differentiable at 0
+
+269
+00:25:52,270 --> 00:26:01,530
+but it is convex on any interval I containing إيه
+
+270
+00:26:01,530 --> 00:26:05,370
+إيش الـ0، بظبط؟ ال .. ال .. it is not
+
+271
+00:26:05,370 --> 00:26:08,030
+differentiable اللي عارفينها ال .. ال .. ال .. ال
+
+272
+00:26:08,030 --> 00:26:13,730
+.. نثبت إنها convex let على interval I X1 و X2
+
+273
+00:26:13,730 --> 00:26:19,800
+element in Iو T element in 0 و 1 اخسب اللي لان F
+
+274
+00:26:19,800 --> 00:26:29,780
+of 1 minus T في X1 زي T في X2 بساوية عبارة عن ال
+
+275
+00:26:29,780 --> 00:26:36,240
+absolute value واحد نقص T X1 زي T في X2 وهذا من
+
+276
+00:26:36,240 --> 00:26:39,700
+خلاص ال absolute value اصغر بساوية واحد نقص T في
+
+277
+00:26:39,700 --> 00:26:46,100
+X1زاية T في X2 وهذا طبعا مين هو؟ هو عبارة عن 1 نقص
+
+278
+00:26:46,100 --> 00:26:53,120
+T F of X1 زاية T في F of X2 إذا صار عندي ال F
+
+279
+00:26:53,120 --> 00:26:56,240
+أشمالها is convex but it is not differentiable
+
+280
+00:26:56,240 --> 00:27:00,620
+اطلع لفوق الان يجيلا اللي هو ال test اللي معطينيا
+
+281
+00:27:00,620 --> 00:27:07,060
+اللي بقوللي اللي بجاوب على سؤالك يا محمد let I be
+
+282
+00:27:08,590 --> 00:27:13,190
+And open interval and let f من I لR have a second
+
+283
+00:27:13,190 --> 00:27:18,890
+derivative on I نفترض أن الـ F'' إيش ما لها موجودة
+
+284
+00:27:18,890 --> 00:27:25,600
+على I إذا من رأس الدور مفترضين الـ F'' موجودةالـ
+
+285
+00:27:25,600 --> 00:27:30,140
+test هو كما قالي f is convex on i if and only if f
+
+286
+00:27:30,140 --> 00:27:34,740
+double prime a شمالها أكبر من 0 لكل x when element
+
+287
+00:27:34,740 --> 00:27:39,300
+in I بصور واضحة الأمر الآن بدي أستخدم في المرهان
+
+288
+00:27:39,300 --> 00:27:44,520
+اللي هو سؤال اللي هو 16 في ال exercises و هنحله
+
+289
+00:27:44,520 --> 00:27:48,380
+وهذا من ضمن ال exercises اللي معاكم هو Morgue و
+
+290
+00:27:48,380 --> 00:27:53,910
+هنحله في حينهالان ايش اللي هو ال .. ال .. ال .. ال
+
+291
+00:27:53,910 --> 00:27:58,390
+.. السؤال بيقول اذا كانت f double prime موجودةثم
+
+292
+00:27:58,390 --> 00:28:02,570
+اثبت لي ان f double prime can be written as limit
+
+293
+00:28:02,570 --> 00:28:06,470
+f of a زاد h نقص اتنين f of a زاد f of a minus h
+
+294
+00:28:06,470 --> 00:28:11,850
+على مين على h تربية ماشي الحال هذا بدأ اعتمد على
+
+295
+00:28:11,850 --> 00:28:17,950
+انه اللي هو مثبت في اثبات النظرية ونشوف كيف ناخد
+
+296
+00:28:17,950 --> 00:28:23,540
+الاتجاه الاول اول اشي بده اللي هو بنفترض انهعندي
+
+297
+00:28:23,540 --> 00:28:29,080
+ال .. اللي هو ال F is convex ومنها نصل لإنه ال
+
+298
+00:28:29,080 --> 00:28:34,300
+derivative ايه شمالها أكبر أو يساوي سفر ماشي الحال
+
+299
+00:28:34,300 --> 00:28:43,480
+خليني نشوف مع بعض كيف اللي هو نثبت
+
+300
+00:28:43,480 --> 00:28:55,740
+انه if F is convex thenF double prime of A أكبر
+
+301
+00:28:55,740 --> 00:29:01,720
+شهر السفر لما نقول suppose that
+
+302
+00:29:01,720 --> 00:29:11,780
+proof فوضيح بس .. suppose that أن F is convex
+
+303
+00:29:11,780 --> 00:29:16,880
+لنثبت أن F double prime of A أكبر شهر السفرالان
+
+304
+00:29:16,880 --> 00:29:21,240
+انا ال F is convex وين على ال I و differentiable
+
+305
+00:29:21,240 --> 00:29:25,560
+وين second derivative لها على ال I خليني اختار
+
+306
+00:29:25,560 --> 00:29:31,280
+الان اللي هو ال H بحيث بدي اختار H بحيث انه A
+
+307
+00:29:31,280 --> 00:29:36,440
+minus H و A زائد H التانين يكون هنا وين موجودات في
+
+308
+00:29:36,440 --> 00:29:39,600
+ال interval I اللي عليها شغل اللي انا بدي اشتغل
+
+309
+00:29:39,600 --> 00:29:49,760
+عليها الان خدلي الان Fof A واكتبها على صورة F of
+
+310
+00:29:49,760 --> 00:29:59,450
+نص في A زاد H زاد نص في A minus Hلأن هذه عبارة عن
+
+311
+00:29:59,450 --> 00:30:03,330
+نص A و نص A هي الـ A و نص H ناقص نص H بروحهم مع
+
+312
+00:30:03,330 --> 00:30:06,730
+بعض ده منرجع لمين لل F و فيها كده تعرفي ليش عملتيل
+
+313
+00:30:06,730 --> 00:30:12,450
+طبعا هذه هتشتغل بمثابة واحد ناقص T و هذه T إذا T
+
+314
+00:30:12,450 --> 00:30:16,370
+بين ال Zero و الواحد صحيحة و بما أن F is convex و
+
+315
+00:30:16,370 --> 00:30:20,750
+هذولة اتتين نقطين عبارة عن نقطين في I لأن هيك
+
+316
+00:30:20,750 --> 00:30:26,520
+اختار ال H هنا هيكون هذا أصغر أو يساوينص F of A
+
+317
+00:30:26,520 --> 00:30:35,620
+زائد H زائد نص F of A minus H واضح؟
+
+318
+00:30:35,620 --> 00:30:43,000
+أي سؤال؟ واضح أه؟ جيبلي هذا على الجهة التانية
+
+319
+00:30:43,000 --> 00:30:51,620
+بيصير عندي نص F of A زائد H زائد نص F of A minus H
+
+320
+00:30:51,620 --> 00:30:59,230
+ناقص F of Aكل و إيه شماله أكبر أو يساوي إيش أكبر
+
+321
+00:30:59,230 --> 00:31:05,010
+أو يساوي سفر وضرب الجهتين في اتنين بيصير عندي
+
+322
+00:31:05,010 --> 00:31:10,550
+مضربت في اتنين بيصير هذه اللي هو النص بيصير واحد و
+
+323
+00:31:10,550 --> 00:31:14,490
+النص هذا بيصير واحد و هذا بيصير إيه شماله ناقص
+
+324
+00:31:14,490 --> 00:31:22,650
+اتنين of of ايه اقسم لليه الآن على اتش تربيعوH
+
+325
+00:31:22,650 --> 00:31:26,370
+تربيع موجة بقى، إذا بيضلوا هذا أشمال المفضل أكبر
+
+326
+00:31:26,370 --> 00:31:32,030
+أو يساوي سفر خد ال limit للجهتين limit as H goes
+
+327
+00:31:32,030 --> 00:31:40,440
+to zero بيضلوا أكبر أو يساوي سفر، مظبوط؟ و هذاBy
+
+328
+00:31:40,440 --> 00:31:44,920
+ال exercise اللي بنحكي عنه هو عبارة عن مين؟ F
+
+329
+00:31:44,920 --> 00:31:48,100
+double prime of A فطلع عندي F double prime of A
+
+330
+00:31:48,100 --> 00:31:52,320
+أكبر أساوي الصفر طبعا ماقدرتش أستخدم هذا أنه بنكتب
+
+331
+00:31:52,320 --> 00:31:56,840
+على صورة هذا إلا في ضوء أن هو أصلا حاكي لي ال F
+
+332
+00:31:56,840 --> 00:32:03,940
+double prime exist on I واضح أه؟أي سؤال إذا الان
+
+333
+00:32:03,940 --> 00:32:08,580
+اطلع لفوق و بنكون احنا خلصنا الجزء الأول و بنكون
+
+334
+00:32:08,580 --> 00:32:11,860
+بدنا نبدأ بالجزء الثاني اللي هو بال prime أكبر
+
+335
+00:32:11,860 --> 00:32:17,600
+سواء سفر و نصل لمين لل F is convex أوضحت هذه خليني
+
+336
+00:32:17,600 --> 00:32:24,100
+بس أنسحها و أقول ما يليه
+
+337
+00:32:24,100 --> 00:32:27,560
+نفترض
+
+338
+00:32:27,560 --> 00:32:30,060
+لأن صبوذ
+
+339
+00:32:32,450 --> 00:32:39,370
+that f double prime of a أشمالها أكبر أو يساوي سفر
+
+340
+00:32:39,370 --> 00:32:45,330
+ماشي الحال .. بدنا نثبت لك أن f is convex كيف بدنا
+
+341
+00:32:45,330 --> 00:32:52,130
+نثبت ان f is convex؟ بدنا نقول let x1 و x2 بيه أي
+
+342
+00:32:52,130 --> 00:32:57,630
+element in مين؟ ان i و t element in zero واش و
+
+343
+00:32:57,630 --> 00:33:06,820
+واحدوسميلي X not هي عبارة عن واحد minus T في X
+
+344
+00:33:06,820 --> 00:33:13,580
+واحد زائد T في مين في X اتنين الآن بدي اطبق اللي
+
+345
+00:33:13,580 --> 00:33:16,480
+هو taylor's theorem اول اش طبعا taylor's theorem
+
+346
+00:33:16,480 --> 00:33:21,960
+قابل للتطبيق اللي عند مينعند and بتساوي واحد بس
+
+347
+00:33:21,960 --> 00:33:25,640
+لأن المشتقة الأولى والتانية موجودة بعد هيك ماحدش
+
+348
+00:33:25,640 --> 00:33:29,480
+حكالي فإذا بيحجلي ان اطبق Taylor's theorem بس على
+
+349
+00:33:29,480 --> 00:33:34,260
+وين على اللي هو and بتساوي سفر او and بتساوي واحد
+
+350
+00:33:34,260 --> 00:33:36,800
+and بتساوي سفر بيصير main value theorem and بتساوي
+
+351
+00:33:36,800 --> 00:33:41,000
+واحد اللي هو اللي بتطبق عليها و هتخدمني ماشي الحال
+
+352
+00:33:41,000 --> 00:33:46,470
+نشوفالان apply taylor's theorem ع الفترة على اللي
+
+353
+00:33:46,470 --> 00:33:51,970
+هو ال X واحد وال X note اللي عندى there exist اللي
+
+354
+00:33:51,970 --> 00:34:00,270
+هو C واحد between X واحد and X note such that اه
+
+355
+00:34:00,270 --> 00:34:08,370
+اللي هو F of X note مظبوط او F of .. ده طبقه على X
+
+356
+00:34:08,370 --> 00:34:15,010
+واحد اول شي F of X واحد بساوياللي هو F of X not
+
+357
+00:34:15,010 --> 00:34:22,550
+زائد F prime of X not في X واحد نقص X not زائد مين
+
+358
+00:34:22,550 --> 00:34:26,950
+الآن ال remainder زائد ال remainder ال remainder
+
+359
+00:34:26,950 --> 00:34:33,950
+إيش هو F double prime عند ال C واحد اللي لاجيناها
+
+360
+00:34:33,950 --> 00:34:41,390
+في X minus X not الكل تربيع على 2 فكتورياأصغر من
+
+361
+00:34:41,390 --> 00:34:48,530
+اللي هو similarly there exist c2 بتطبقها على x1
+
+362
+00:34:48,530 --> 00:34:57,090
+على x2 و x0 there exist a c2 between x2 and x0
+
+363
+00:34:57,090 --> 00:35:07,070
+such thatof x2 بيساوي f of x0 زاد f prime of x0 في
+
+364
+00:35:07,070 --> 00:35:17,690
+x2 ناقص x0 زاد f double prime of c2 في x minus x0
+
+365
+00:35:17,690 --> 00:35:24,950
+الكل تربيع على 2 factorial واضح اللي بعمله
+
+366
+00:35:28,900 --> 00:35:37,440
+فهي عندى اللى هى هذه مع هذه هى اللى بدى استخدمه
+
+367
+00:35:37,440 --> 00:35:43,500
+هنا الآن فى الوصول لإنه F is convex يعنى F of هذا
+
+368
+00:35:43,500 --> 00:35:49,180
+المقدار يكون أصغر أو يساوي اللى هو F 1 minus T
+
+369
+00:35:49,180 --> 00:35:56,920
+فهذه زائد T فهذه إذا بدى أحسب الآن 1 minus T ف F
+
+370
+00:35:56,920 --> 00:36:05,420
+of X 1زائد T في F of إيش X2 بدي أحسبها و أوصلها
+
+371
+00:36:05,420 --> 00:36:09,080
+لعلاقتها مع مين مع F of X note اللي هي F of هذه
+
+372
+00:36:09,080 --> 00:36:20,940
+بساوي اضربلي بيصير T واحد نقص T في F of X note
+
+373
+00:36:20,940 --> 00:36:31,310
+معايا يا شباب زائد واحد minus Tف F prime of X note
+
+374
+00:36:31,310 --> 00:36:40,590
+في X واحد minus X note زائد اللي هو mean ده دروفة
+
+375
+00:36:40,590 --> 00:36:47,390
+هادة اللي هو واحد minus T في F double prime of C
+
+376
+00:36:47,390 --> 00:36:52,970
+واحد في X minus X note اللي كل تربيع على اتنين
+
+377
+00:36:52,970 --> 00:37:02,060
+factorial اللي هو اتنين معايا يا شبابزائد T .. T
+
+378
+00:37:02,060 --> 00:37:10,500
+.. F of X2 هيها اللي هي F of X note زائد T في F
+
+379
+00:37:10,500 --> 00:37:15,860
+prime of X note بضرب فادي قاعد في X2 نقص X note
+
+380
+00:37:15,860 --> 00:37:26,720
+زائد اللي هو T في F double prime of C2fx-x0 الكل
+
+381
+00:37:26,720 --> 00:37:34,100
+تربيه على مين؟ على اتنين نيجي الان و يساوي اطلعلي
+
+382
+00:37:34,100 --> 00:37:41,720
+على هذه الان واحد minus T في F of X0 وT في F of X0
+
+383
+00:37:41,720 --> 00:37:51,520
+بيصير عبارة عن F of X0 مظبوط؟ زائدالان هذا f prime
+
+384
+00:37:51,520 --> 00:37:55,420
+of x naught مضروبة في T مضروبة في هذه إذا عبارة عن
+
+385
+00:37:55,420 --> 00:38:03,660
+واحد minus T زائد T اه اللي هو مية المية بيصير
+
+386
+00:38:03,660 --> 00:38:10,300
+عندي الآن خد اللي هي x واحد ناقص x naught وخلينا
+
+387
+00:38:10,300 --> 00:38:19,510
+نجمحها واحد minus يعني خلينا نضيع ال Tفيها نقص
+
+388
+00:38:19,510 --> 00:38:24,730
+اتنين و X واحد او X او X واحد نفردها واحد minus T
+
+389
+00:38:24,730 --> 00:38:32,970
+في F ناخد عن المشترك يمكن أسهلنا F prime of X note
+
+390
+00:38:32,970 --> 00:38:43,330
+في واحد minus T في X واحد ناقص X note معايا شباب
+
+391
+00:38:43,330 --> 00:38:51,670
+زائد باخد بين هذه هي عمالو بين هذه أخدت ال F prime
+
+392
+00:38:51,670 --> 00:38:57,430
+of X naught عام نشترك بينهم زائد T في X2 ناقص X
+
+393
+00:38:57,430 --> 00:39:06,290
+naught زائد هذا المقدار كله بعد إذنكم هي اللي
+
+394
+00:39:06,290 --> 00:39:12,390
+بلزرج هذا اللي حطيته بلزرج سميني يا إيش R واضح
+
+395
+00:39:12,390 --> 00:39:21,890
+زائد Rالان نطلع على اللي عندي هدا واحد ناقص T اول
+
+396
+00:39:21,890 --> 00:39:27,670
+اشي ناقص T في ناقص X Note بيصير اللي هو زائد T في
+
+397
+00:39:27,670 --> 00:39:31,850
+X Note مع ناقص T في X Note بروحين مظبوط؟ اذا هذا
+
+398
+00:39:31,850 --> 00:39:38,410
+الان بروح وهذا
+
+399
+00:39:38,410 --> 00:39:44,290
+برضه بروح صح ولا لأ؟ نتأكد في اللي عملناه
+
+400
+00:39:48,090 --> 00:40:00,190
+واضح اه بظل x .. x note اه بظل ناقص اللي هو زائد x
+
+401
+00:40:00,190 --> 00:40:07,950
+note ناقص x note ناقص x note عملها كمان مرة بظل
+
+402
+00:40:07,950 --> 00:40:15,160
+ناقص x note من هناو من هنا بيظهر مين ناقص X note
+
+403
+00:40:15,160 --> 00:40:21,640
+لأنه بتظهر تبعت اللي هنا تظهر ناقص X note واضح أه؟
+
+404
+00:40:21,640 --> 00:40:28,760
+الان هذه كلها على بعض مين هي؟ هذه إيش اسمها؟ كلها
+
+405
+00:40:28,760 --> 00:40:32,900
+اسمها X note أه؟
+
+406
+00:40:32,900 --> 00:40:36,960
+فبيصير X note ناقص X note إيش بيصير؟ سفر فبيصير
+
+407
+00:40:36,960 --> 00:40:41,560
+هذا المقدار عبارة عن Fof x naught زائد ال
+
+408
+00:40:41,560 --> 00:40:45,380
+remainder مين؟ R نتطلع على الـ R هذا أو هو R لما
+
+409
+00:40:45,380 --> 00:40:48,000
+نقول remainder؟ الـ R مجموع الـ remainder دلين
+
+410
+00:40:48,000 --> 00:40:58,960
+الان ملاحظ هو ماعطيني عندي الان أفضل براءة عندي
+
+411
+00:40:58,960 --> 00:41:05,340
+هذا X نقص X واحد كل تربيع على اتنين موجبة و X نقص
+
+412
+00:41:05,340 --> 00:41:10,330
+X اتنين نوت على اتنين اشمالها موجبةوالان ال f
+
+413
+00:41:10,330 --> 00:41:15,510
+double prime عندى اللى هتطلع أشمالها موجبة بنفس
+
+414
+00:41:15,510 --> 00:41:21,550
+الطريقة السابقة زى ما عملنا قبل شوية عندى f double
+
+415
+00:41:21,550 --> 00:41:27,310
+prime أكبر يساوي سفر هيطلع عندى في الجوار اللى
+
+416
+00:41:27,310 --> 00:41:30,610
+بطبق عليه برضه أكبر يساوي سفر فبطلع عندى هذا موجب
+
+417
+00:41:30,610 --> 00:41:35,690
+و هذا موجب فبطلع عندى هذا المقدار اللى بدأنا فيه
+
+418
+00:41:36,380 --> 00:41:41,720
+هذا المقدار اللي بدأنا فيه طلع بساوي هذا المقدار
+
+419
+00:41:41,720 --> 00:41:49,760
+اللي هو هذا أكبر أو يساوي F of X naught اللي هي
+
+420
+00:41:49,760 --> 00:41:57,540
+mean F of X naught اللي عبارة عن F معين واحد نقص T
+
+421
+00:41:57,540 --> 00:42:07,040
+في X واحد زائد T في X اتنين هاي اللي وصلنا إليهمع
+
+422
+00:42:07,040 --> 00:42:21,020
+هذا وهذا تعريف أيه؟ F is convex F is convex أي
+
+423
+00:42:21,020 --> 00:42:21,680
+سؤال؟
+
+424
+00:42:24,290 --> 00:42:29,090
+و بهيك نكون خلصنا ال section اللي الأخير في
+
+425
+00:42:29,090 --> 00:42:34,250
+chapter اللي هو 6 خلصنا الجزء الأول من المحاضرة و
+
+426
+00:42:34,250 --> 00:42:37,250
+الآن بدنا نبدأ في الجزء الثاني من المحاضرة
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..200776e43e2b0ead4cb1f0a1eddba56a9d2016e8
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_raw.srt
@@ -0,0 +1,1712 @@
+1
+00:00:05,480 --> 00:00:11,800
+بسم الله الرحمن الرحيم محاضرة رقم تسعة مساق تحليل
+
+2
+00:00:11,800 --> 00:00:19,160
+حقيقي اتنين طلاب الجامعة الإسلامية كلية العلوم قسم
+
+3
+00:00:19,160 --> 00:00:24,470
+الرياضياتالمحاضرة اليوم على جزئين الجزء الأول
+
+4
+00:00:24,470 --> 00:00:29,350
+هنتحدث عن applications of taylor's theorem والجزء
+
+5
+00:00:29,350 --> 00:00:34,250
+الثاني هنتحدث عن اللي هو discussion لsection 6.2
+
+6
+00:00:34,250 --> 00:00:37,890
+و6.3 اللي هو discussion لل mean value theorem وإذا
+
+7
+00:00:37,890 --> 00:00:43,270
+في وجهة بنعمل discussion ل اللي هو lobitals rules
+
+8
+00:00:43,960 --> 00:00:48,240
+الان خلّينا نكمل اللي اتحدثنا عنه المرة الماضية
+
+9
+00:00:48,240 --> 00:00:53,200
+ولكن على صورة تطبيقات ليه؟ اللي هو Taylor's
+
+10
+00:00:53,200 --> 00:00:58,660
+theorem وكيف بدنا اللي هو نستغل Taylor's theoremفي
+
+11
+00:00:58,660 --> 00:01:03,360
+إثبات بعض النظريات المهمة في موضوع اللي هو ال
+
+12
+00:01:03,360 --> 00:01:08,080
+maximum و ال minimum أو اللي هو ال test لإن اللي
+
+13
+00:01:08,080 --> 00:01:12,140
+عندنا هل هي local maximum أو local minimum ولا لا
+
+14
+00:01:12,140 --> 00:01:15,860
+هي local maximum ولا هي local minimum كنا اتحدثنا
+
+15
+00:01:15,860 --> 00:01:20,560
+سابقا على اللي هو ال first derivative test لإن
+
+16
+00:01:20,560 --> 00:01:23,200
+النقطة اللي تكون الداخلية هل في عندها local
+
+17
+00:01:23,200 --> 00:01:27,540
+maximum أو local minimumالان بدنا نتحدث عن الـ
+
+18
+00:01:27,540 --> 00:01:31,140
+Higher Derivative Test احنا يمكن نمر عنا اللي هو
+
+19
+00:01:31,140 --> 00:01:33,720
+الـ Second Derivative Test اللي هو في ال .. في
+
+20
+00:01:33,720 --> 00:01:36,900
+الCalculus اللي قابلة نتحدث على ال Higher
+
+21
+00:01:36,900 --> 00:01:40,080
+Derivative Test و اللي هي .. اللي هي ال Second
+
+22
+00:01:40,080 --> 00:01:44,090
+Derivative Test جزء من هذا اللي هو ال testنتطلع
+
+23
+00:01:44,090 --> 00:01:48,030
+على الـ test إيش بقول اللي هي عبارة عن theorem 644
+
+24
+00:01:48,030 --> 00:01:52,310
+let I be an interval نفترض أن I عبارة عن interval
+
+25
+00:01:52,310 --> 00:01:57,510
+و X note اللي هي نقطة اللي احنا بدنا نفحص عندها هل
+
+26
+00:01:57,510 --> 00:02:02,770
+في maximum أو في minimum أو لا في maximum ولا في
+
+27
+00:02:02,770 --> 00:02:06,470
+minimum X note اللي هي عبارة عن interior point
+
+28
+00:02:06,470 --> 00:02:10,890
+لمن؟ لل interval I يعني نقطة داخليةونفترض الـ N
+
+29
+00:02:10,890 --> 00:02:14,570
+تبعتنا أكبر أو ساوى 2 لأن الـ N أكبر أو ساوى 2
+
+30
+00:02:14,570 --> 00:02:17,690
+يعني الـ Second Derivative Test أو أعلى هو اللي
+
+31
+00:02:17,690 --> 00:02:20,910
+بده يحددنا أنه عندنا Maximum أو Minimum أو مافيش
+
+32
+00:02:20,910 --> 00:02:25,450
+لا Maximum ولا Minimum Suppose ده ال derivatives
+
+33
+00:02:25,450 --> 00:02:31,120
+اللي هي F' و F'' لعند FN existsexist and are
+
+34
+00:02:31,120 --> 00:02:34,040
+continuous in a neighborhood of x naught نفترض إن
+
+35
+00:02:34,040 --> 00:02:39,140
+هدولة continuous وموجودة في اللي هو
+
+36
+00:02:41,860 --> 00:02:44,760
+اللي هي في neighborhood حوالي مين الـ X Note
+
+37
+00:02:44,760 --> 00:02:49,920
+ونفترض أن F' عند X Note لعند F N ناقص واحد prime
+
+38
+00:02:49,920 --> 00:02:54,060
+of X Note إيش بيساوي؟ سفر لكن عند F N of X Note
+
+39
+00:02:54,060 --> 00:02:59,140
+إيش مالها؟ لاتساوي سفر إذا ال test إيش بيصير؟ أول
+
+40
+00:02:59,140 --> 00:03:06,120
+إشيبنشوف f prime نقطة x note هذه نقطة متوقع عندها
+
+41
+00:03:06,120 --> 00:03:10,340
+maximum أو minimum أو مافيش شيء من النقاط اللي هي
+
+42
+00:03:10,340 --> 00:03:13,520
+بدنا نفحص عندها maximum أو minimum إيش بدنا نسوي
+
+43
+00:03:13,520 --> 00:03:18,520
+في هذا ال test بنجيب f prime عند ال x note إذا
+
+44
+00:03:18,520 --> 00:03:23,500
+لجيناها سفر بنيجي لل f double prime عند ال x note
+
+45
+00:03:23,500 --> 00:03:29,130
+إذا لجيناها سفراللي هو بنيجي للـ F W' عند الـ X0
+
+46
+00:03:29,130 --> 00:03:34,830
+وين بنصل للـ F W' .. وين بنصل للـ F N of X0 لا
+
+47
+00:03:34,830 --> 00:03:39,210
+تساوي سفر؟ بيبدأ الخطوات تبعات ال test ايش ال
+
+48
+00:03:39,210 --> 00:03:43,710
+test؟ اللي هي الأول إذا كانت N even طلعت عندنا N
+
+49
+00:03:43,710 --> 00:03:47,850
+هادئية أول واحدة ال derivative عندها عند ال X0 مش
+
+50
+00:03:47,850 --> 00:03:53,930
+سفروكانت ال Fn of X0 أكبر من 0 بتكون ال F أيه
+
+51
+00:03:53,930 --> 00:03:57,470
+شمالها؟ اللي هي relative minimum زي ال second
+
+52
+00:03:57,470 --> 00:04:01,710
+derivative test كنا لما نقول ال FW' عند ال X0 أكبر
+
+53
+00:04:01,710 --> 00:04:06,170
+من 0 على طول نحكم أنه في local minimum هنا الآن لأ
+
+54
+00:04:06,170 --> 00:04:08,510
+احنا على ال higher derivative و هتحللنا المشاكل
+
+55
+00:04:08,510 --> 00:04:10,290
+اللي كانت ماتتحللاش جامعي اللي هي second
+
+56
+00:04:10,290 --> 00:04:16,670
+derivative test الان Fn is evenو ال F N of X0 أصغر
+
+57
+00:04:16,670 --> 00:04:21,510
+من 0 إذا Fها زي إيه شمالها relative maximum at X0
+
+58
+00:04:21,510 --> 00:04:25,670
+إذا لو طلعت عندي N is odd إيش يعني N is odd؟ يعني
+
+59
+00:04:25,670 --> 00:04:31,130
+أول .. أول derivative ال F N عندها لاتساوي 0 طلعت
+
+60
+00:04:31,130 --> 00:04:35,390
+عندي هذه oddطبعا أكبر إذا هو 2، 3 أو 5 أو 7 إلى
+
+61
+00:04:35,390 --> 00:04:39,490
+آخره على طول احنا بنحكم then F has neither
+
+62
+00:04:39,490 --> 00:04:43,610
+relative minimum nor إيش ما لها relative maximum
+
+63
+00:04:43,610 --> 00:04:50,790
+at X note بتصور هيك النظرية واضحة إيش نصها بنجيبF
+
+64
+00:04:50,790 --> 00:04:56,570
+prime of X0 و F double prime of X0 إلى آخره إذا
+
+65
+00:04:56,570 --> 00:05:01,170
+هذا بيساوي سفر بهذا بيساوي سفر بضلي ماشي لعند F N
+
+66
+00:05:01,170 --> 00:05:08,550
+of X0 لاتساوي سفر و اگ تست تصل لاتساوي سفر باجي لل
+
+67
+00:05:08,550 --> 00:05:17,620
+test اللي هو uneven عند حالتينالحالة الأولى FN of
+
+68
+00:05:17,620 --> 00:05:27,280
+X0 أكبر من 0 Local MinimumFn of X0 أصغر من 0 Local
+
+69
+00:05:27,280 --> 00:05:33,180
+maximum لكن إذا طلعت n is odd يعني أول واحدة بعد
+
+70
+00:05:33,180 --> 00:05:37,720
+التنين اللي هو بيطلع عند F ال derivative لها Fn of
+
+71
+00:05:37,720 --> 00:05:43,200
+X0 لا تساوي 0 طلعت عند n is odd إذا بحكم على طول F
+
+72
+00:05:43,200 --> 00:05:52,030
+has neither Local maximum nor Local minimumتعالوا
+
+73
+00:05:52,030 --> 00:05:58,670
+اللي هو نبرهم اللي هو النظرية ونشوف إنه حجر الأساس
+
+74
+00:05:58,670 --> 00:06:02,470
+للبرهان اللي هي taylor's theorem هي taylor's
+
+75
+00:06:02,470 --> 00:06:12,430
+theorem تنشوف كيف الآن عندي بدنا نطبق taylor's
+
+76
+00:06:12,430 --> 00:06:15,820
+theoremعلى .. طبعا احنا بنشتغل على الـ interval من
+
+77
+00:06:15,820 --> 00:06:21,520
+I بناخد اللي هو X element من I و بنطبقلها من الـ
+
+78
+00:06:21,520 --> 00:06:26,120
+Taylor's theorem عند النقطة اللي احنا بدنا نختبر
+
+79
+00:06:26,120 --> 00:06:29,840
+عند X0 فهي اللي بده أجيب Taylor's theorem حواليها
+
+80
+00:06:29,840 --> 00:06:36,160
+اذا حسب Taylor's theorem ان there exists C between
+
+81
+00:06:36,160 --> 00:06:45,630
+اللي هي X and X0 such thatاللي هو F of X F of X
+
+82
+00:06:45,630 --> 00:06:52,110
+بساوي بي أن ناقص واحد بدا أقبّقها اللي بحيث أن ال
+
+83
+00:06:52,110 --> 00:06:56,250
+polynomial ما أن ناقص واحد ليش؟ لإنه أنا ماعطيني
+
+84
+00:06:56,250 --> 00:07:01,110
+هو عنده ال derivative اللي هي لعند F أن ناقص واحد
+
+85
+00:07:01,110 --> 00:07:05,870
+كلها سفار واللي مش سفر اللي هي مين F n of X not
+
+86
+00:07:06,550 --> 00:07:11,390
+فعند اللي هي R نقص واحد هطبق عشان تحكم لل FN of X
+
+87
+00:07:11,390 --> 00:07:15,310
+node على إنه عندني local maximum أو local minimum
+
+88
+00:07:15,310 --> 00:07:19,750
+أو neither كيف؟ خلّينا نطبق ال Taylor's theorem
+
+89
+00:07:19,750 --> 00:07:28,350
+زائد اللي هو أشملها R N نقص واحد of X هذه عندي
+
+90
+00:07:28,350 --> 00:07:33,230
+Taylor's theorem الآن ال BN نقص واحد اللي هي عبارة
+
+91
+00:07:33,230 --> 00:07:40,820
+عن إياش Fof x naught زائد f prime of x naught في x
+
+92
+00:07:40,820 --> 00:07:45,440
+minus x naught اللي هو على واحد factorial زائد لما
+
+93
+00:07:45,440 --> 00:07:51,400
+أصل لآخر واحد f n ناقص واحد of x naught في x minus
+
+94
+00:07:51,400 --> 00:07:55,540
+x naught قس n ناقص واحد على n ناقص واحد لكل
+
+95
+00:07:55,540 --> 00:08:02,700
+factorial زائد main ال remainder اللي هو main اللي
+
+96
+00:08:02,700 --> 00:08:09,810
+هو عبارة عن xنقص x note أس n على n factorial في f
+
+97
+00:08:09,810 --> 00:08:18,850
+n of mean of عندي c و ال c مالها between x note
+
+98
+00:08:18,850 --> 00:08:27,170
+and mean and x واضح و يساوي الأن كل هذول أصفار صح
+
+99
+00:08:27,170 --> 00:08:33,500
+ولا لأ إذا حيصير عندي هذا بيساوي لإنه معطيليالـ F
+
+100
+00:08:33,500 --> 00:08:41,120
+prime of X note لعند FN نقص واحد of X note كله
+
+101
+00:08:41,120 --> 00:08:46,700
+نصفار إذا صلي عندي هذا بيساوي F of X note لأن هذا
+
+102
+00:08:46,700 --> 00:08:55,740
+كله بتصفر زاد X minus X note أس N على N factorial
+
+103
+00:08:55,740 --> 00:09:09,290
+في FNof c واضح اه اي سؤال طيب عندى انا اللى هو
+
+104
+00:09:09,290 --> 00:09:19,230
+معطينى ال ال f n of x naught اللى هى لاتساوى سفر
+
+105
+00:09:19,230 --> 00:09:25,170
+اذا ال f n of x naught يا اكبر من سفر يا اصغر من h
+
+106
+00:09:25,170 --> 00:09:36,570
+من سفرإذا أكيد عندي ال FN of X note و ال FN of C
+
+107
+00:09:36,570 --> 00:09:43,810
+الهن أيش الهن the same sign ماشي اه الهن نفس نين
+
+108
+00:09:43,810 --> 00:09:50,770
+نفس اللي هو الإشارة طبعا السبب أن FN أشمالها is
+
+109
+00:09:50,770 --> 00:09:55,950
+continuous انوضحلكم إياها تتذكروا
+
+110
+00:09:57,370 --> 00:10:02,330
+قلنا خلّينا ناخد حالة نفترض أن هذا أكبر من مين من
+
+111
+00:10:02,330 --> 00:10:12,690
+سفر احنا كنا نقول limit أي حاجة g of x لما x تروح
+
+112
+00:10:12,690 --> 00:10:18,970
+لل c مثلا أكبر من سفر معناته في جوار في جوار
+
+113
+00:10:18,970 --> 00:10:23,210
+حوالين اللي هو ال c ال g of x نفسها إيش هتكون أكبر
+
+114
+00:10:23,210 --> 00:10:28,110
+من سفر لكل x في هذا الجواريعني هيكون عندي إذاً g
+
+115
+00:10:28,110 --> 00:10:37,710
+of x أكبر من 0 لكل x في sum جوار delta of mean of
+
+116
+00:10:37,710 --> 00:10:41,690
+z هذا اللي بدأ أستخدمها الآن في الوصول للي بديها
+
+117
+00:10:41,690 --> 00:10:45,590
+خلّيني نشوف كيف بدأ نستخدم هذه المعلومة الآن أنا
+
+118
+00:10:45,590 --> 00:10:55,750
+عندي الـ Fn is continuous نفسها إذاً limit Fnof X
+
+119
+00:10:55,750 --> 00:11:03,290
+أفقًا of X اللي هو لما الـ X تروح للـ X0 اللي هو
+
+120
+00:11:03,290 --> 00:11:10,070
+أش متساوي أفقًا of X0 وبرضه continuous عند مين؟
+
+121
+00:11:11,690 --> 00:11:16,810
+وبرضه continuous عند مين؟ عند الـ C معايا وعند الـ
+
+122
+00:11:16,810 --> 00:11:21,030
+C إيش مالها؟ continuous أنا اللي هيلزمني مين؟ هنا
+
+123
+00:11:21,030 --> 00:11:26,930
+الـ X note مظبوط ولا لأ؟ عندي هتلزمني مين؟ اللي هي
+
+124
+00:11:26,930 --> 00:11:35,950
+ال X note إذا صار عنديفن of X note هي اللي هتحددلي
+
+125
+00:11:35,950 --> 00:11:45,090
+من هنا اللي هي إشارة مين فن of C واضح الآن من هذه
+
+126
+00:11:45,090 --> 00:11:54,310
+إذا كانت F of X note مثلا أكبر من سفر هتطلع حد
+
+127
+00:11:54,310 --> 00:11:58,870
+أكبر من سفر خلينا نشوفها إذا الآن خليني أبدأ في
+
+128
+00:11:58,870 --> 00:12:06,270
+مينفي I بدي افترض مين الان fn of x not أكبر من أيش
+
+129
+00:12:06,270 --> 00:12:13,010
+من سفر و افترض ان الان عند ايش معنها is even بدي
+
+130
+00:12:13,010 --> 00:12:19,950
+أنطلق من هذه اذا الان fn of x not أكبر من سفر و n
+
+131
+00:12:19,950 --> 00:12:25,730
+is even بناء على هذه for every y أكبر من سفر there
+
+132
+00:12:25,730 --> 00:12:32,440
+exists such that المهم بيطلع عندىاللي هو F هذه ايش
+
+133
+00:12:32,440 --> 00:12:37,880
+مفترضين احنا اكبر من ايه ايش من سفر اذا حسب اللي
+
+134
+00:12:37,880 --> 00:12:45,450
+حكيته قبل بشوية there existV Delta of إيش؟ Of X0
+
+135
+00:12:45,450 --> 00:12:53,590
+حوالي مين؟ الـ X0 Such that اللي هو FN of X زي
+
+136
+00:12:53,590 --> 00:12:59,290
+إشارة هذه اللي هي أكبر من 0 لكل X وين في الـ V
+
+137
+00:12:59,290 --> 00:13:06,880
+Delta of مين؟ Of X0ماشي الحال واللي من ضمن هدوله
+
+138
+00:13:06,880 --> 00:13:15,060
+مين؟ C إذا صارت عندي الان FN of C برضه إيه شمالها؟
+
+139
+00:13:15,060 --> 00:13:21,860
+أكبر من سفر الان اتضحت الصورة الان صارت عندي من
+
+140
+00:13:21,860 --> 00:13:26,420
+الأصل F of X بسوء F of X note زائد هذا المقدار بدا
+
+141
+00:13:26,420 --> 00:13:31,020
+أقول الآن بما أن هذه أكبر من سفر وان أنا مفترضها
+
+142
+00:13:31,020 --> 00:13:36,490
+إنها evenإذا حيصير عندى هذا أكبر من صفر وهذا أكبر
+
+143
+00:13:36,490 --> 00:13:41,570
+من صفر إذا الـ remainder كله إيش ماله أكبر من صفر
+
+144
+00:13:41,570 --> 00:13:47,710
+مدام الـ remainder أكبر من صفر واضح اللي بحكي FN
+
+145
+00:13:47,710 --> 00:13:53,010
+of C أكبر من صفر وهذا المقدر أكبر من صفر لأنه N is
+
+146
+00:13:53,010 --> 00:13:58,710
+even إذا صار كل هذا أكبر من صفر إذا automatic لما
+
+147
+00:13:58,710 --> 00:14:04,660
+أشيلههيصغر المقدار، بظبط ولا لأ؟ فهيصير عند ال F
+
+148
+00:14:04,660 --> 00:14:12,040
+of X اللي هو أكبر من مين من ال F of X naught لأن F
+
+149
+00:14:12,040 --> 00:14:17,680
+of X بساوي هذا زائد هذا فأكيد عند ال F of X أكبر
+
+150
+00:14:17,680 --> 00:14:22,160
+من مين من F of X naught في وين، لكل X وين موجودة
+
+151
+00:14:22,160 --> 00:14:30,530
+في الجوار اللي حواليها، إذا صار عند Fhas local
+
+152
+00:14:30,530 --> 00:14:40,870
+minimum at x0 similarly لو
+
+153
+00:14:40,870 --> 00:14:53,630
+بدنا نفترض ان المقدار هذا عندي fn of x0 أصغر من 0
+
+154
+00:14:54,540 --> 00:15:00,740
+وبدأ أبدأ أحكي عن مين؟ عن I I بيصير عندي الآن حسب
+
+155
+00:15:00,740 --> 00:15:07,320
+الحديث هنا ال FN of C اللي هي أصغر من 0 لإنه هتكون
+
+156
+00:15:07,320 --> 00:15:13,600
+ال FN of X لكل X في هذا الدوار the same sign as FN
+
+157
+00:15:13,600 --> 00:15:18,120
+of X note أصغر من 0 إذا صارت عندي FN of C أصغر من
+
+158
+00:15:18,120 --> 00:15:24,050
+0هذه صارت سالبة وهذه موجبة لإنه and is even إذا
+
+159
+00:15:24,050 --> 00:15:28,290
+صار المقدار هذا كله على بعض إيه شماله؟ سالب في كل
+
+160
+00:15:28,290 --> 00:15:33,070
+هذا الجوار ما ده صار سالب معناته إنه لما أنا أشيله
+
+161
+00:15:33,070 --> 00:15:39,330
+بكبر اللي بظهر يعني بيصير F of X note بناء عليه
+
+162
+00:15:39,330 --> 00:15:46,630
+أكبر من F of X مظبوط؟وهذا يعني انه صار ال F في هذه
+
+163
+00:15:46,630 --> 00:15:56,010
+الحالة عندها local maximum local maximum واضح ؟ اي
+
+164
+00:15:56,010 --> 00:16:01,510
+سؤال ؟ طيب، ضال عند مين الحالة الأخيرة، هذي
+
+165
+00:16:01,510 --> 00:16:09,170
+تذكرينها لأنه برضه بدي اشتغل نفس الشيء في الحالة
+
+166
+00:16:09,170 --> 00:16:15,680
+الأخيرة او اشي مشابهعند الان بدي افترض mean ان
+
+167
+00:16:15,680 --> 00:16:25,980
+الحالة الثالثة بدي افترض ان ال is mean of of زي
+
+168
+00:16:25,980 --> 00:16:35,810
+ما عملنا قبل بشوية إذا كانت اللي هي Fفن of x not
+
+169
+00:16:35,810 --> 00:16:40,890
+أكبر من سفر زي ما عملنا قبل شوية هيعطيني فن of c
+
+170
+00:16:40,890 --> 00:16:49,990
+أكبر من إيش؟ من سفر معايا؟ طيب الآن هذا الكلام لو
+
+171
+00:16:49,990 --> 00:16:56,930
+جيت أخدت عندي هي عندي هذه اللي هي x not وهنا
+
+172
+00:16:56,930 --> 00:17:01,650
+الجوار اللي حواليهاالجوار اللي حواليها اللي لاجئت
+
+173
+00:17:01,650 --> 00:17:09,230
+في كل الجوار زي ما عملت قبل شوية fn of x هيكون
+
+174
+00:17:09,230 --> 00:17:15,830
+اللي هو هنا اللي هو هنا و هنا موجب ماشي الحال الآن
+
+175
+00:17:15,830 --> 00:17:21,850
+مدام موجب هنا و هنا اللي هيتحكم في الموضوع اليمين
+
+176
+00:17:21,850 --> 00:17:27,770
+x minus x naught أسن لكن لسوء الحظ لو كانت x هنا
+
+177
+00:17:28,970 --> 00:17:35,350
+بصير عندى و هذا طبعا لكل X وين على يمين ال X node
+
+178
+00:17:35,350 --> 00:17:41,450
+هيطلع عندى ال X minus X node أس N وهذه إيه شمالها
+
+179
+00:17:41,450 --> 00:17:49,110
+odd is أكبر من أيش من سفر فصارت الآن هذه أكبر من
+
+180
+00:17:49,110 --> 00:17:54,330
+سفر وهذه أكبر من سفر التنتير مع بعض أكبر من سفر
+
+181
+00:17:55,160 --> 00:18:01,380
+ماشي فصارت عندي ال F of X أكبر من مين من ال F of X
+
+182
+00:18:01,380 --> 00:18:07,600
+naught ماشي الحال في المنطقة هذه هذه المنطقة هذه
+
+183
+00:18:07,600 --> 00:18:16,060
+صارت عندي ال F of X أكبر من F of X naught فاهمين؟
+
+184
+00:18:16,060 --> 00:18:23,240
+لأن الجزء الثاني ال Xفي المنطقة اللي هان أي x في
+
+185
+00:18:23,240 --> 00:18:27,880
+المنطقة اللي هان عند الـ x minus x naught أصغر من
+
+186
+00:18:27,880 --> 00:18:32,480
+مين من سفر فبصير عند هذا المقدار أصغر من سفر وهذا
+
+187
+00:18:32,480 --> 00:18:37,020
+أكبر من سفر حاصل الدرب أصغر من سفر أصغر من سفر بقد
+
+188
+00:18:37,020 --> 00:18:42,200
+إلى أن أف of x في المنطقة هذه تصير أصغر من أف of x
+
+189
+00:18:42,200 --> 00:18:47,250
+naught يعني لو أتيت لأي جوارحوالين الـ X Note
+
+190
+00:18:47,250 --> 00:18:51,770
+هتلاقي اللي هو مرة الـ F of X Note أصغر من F of X
+
+191
+00:18:51,770 --> 00:18:56,810
+ومرة F of X Note أكبر من مين من F of X يعني بمعنى
+
+192
+00:18:56,810 --> 00:19:02,270
+آخر لا في عندي Local Maximum ولا Local Minimum في
+
+193
+00:19:02,270 --> 00:19:08,450
+هذه المنطقة Similarly وبنفس الأسلوب لو كانت FN of
+
+194
+00:19:08,450 --> 00:19:14,000
+X Note أصغر من مينمن صفر معايا بيصير هذه أصغر من
+
+195
+00:19:14,000 --> 00:19:19,020
+صفر و بيصير بس بتنقلب بيصير هذه في المنطقة هذه
+
+196
+00:19:19,020 --> 00:19:23,840
+أصغر و هذه في المنطقة هذه ايش اكبر اذا in both
+
+197
+00:19:23,840 --> 00:19:30,160
+cases عندي if and is odd اذا we have neither اللي
+
+198
+00:19:30,160 --> 00:19:37,660
+هو relative maximum nor relative minimum اي سؤال
+
+199
+00:19:37,660 --> 00:19:45,760
+واضح اه؟اللي بعده اللي بعده الان بدنا نعرف حاجة
+
+200
+00:19:45,760 --> 00:19:51,140
+اسمها اللي هي مين ال convex function تعالي على
+
+201
+00:19:51,140 --> 00:19:55,640
+الرسم يا بو محمد عندي بدنا نعرف مين ال convex
+
+202
+00:19:55,640 --> 00:19:59,860
+function الان ال convex function إيش يكون cave
+
+203
+00:19:59,860 --> 00:20:05,200
+اللي هو إيش up خليني نشوف إيش هذي اللي هو بعبر شو
+
+204
+00:20:05,200 --> 00:20:07,980
+معناه ال F is convex
+
+205
+00:20:10,750 --> 00:20:14,990
+خاصية الـ convex أو الـ convexity بنحكي فيها على
+
+206
+00:20:14,990 --> 00:20:22,090
+interval يعني بنقول F من عند I لعند R بنقول عنها F
+
+207
+00:20:22,090 --> 00:20:28,170
+is convex on إيش؟ on I on وين؟ ع ال interval I إذا
+
+208
+00:20:28,170 --> 00:20:35,970
+كان شوف كيف خدلي الآن X1 أي نقطة في داخل الـ I و
+
+209
+00:20:35,970 --> 00:20:41,970
+X2 أي نقطة في داخل الـ Iوخدلي ال parameter T بين
+
+210
+00:20:41,970 --> 00:20:45,830
+السفر و بين الواحد الان النقطة ال linear
+
+211
+00:20:45,830 --> 00:20:51,230
+combination بين X1 و X2 بواسطة 1-T X1 زائد T X2
+
+212
+00:20:51,230 --> 00:20:56,530
+هتكون بين X1 و بين X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+213
+00:20:56,530 --> 00:20:56,950
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+214
+00:20:56,950 --> 00:21:06,250
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+215
+00:21:06,250 --> 00:21:06,250
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+216
+00:21:06,250 --> 00:21:06,250
+X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2 X2
+
+217
+00:21:06,250 --> 00:21:14,050
+X2 X2 X2 X2 X2 X2 X2لو إجيت ل F of X1 هيها وهذا F
+
+218
+00:21:14,050 --> 00:21:20,650
+of X2 لو ضربت ال F of X1 و 1 minus T و جمعتها ل T
+
+219
+00:21:20,650 --> 00:21:25,170
+في F of X2 هتلاقيها بين اللي هو مين على اللي هو
+
+220
+00:21:25,170 --> 00:21:32,010
+الخط المستقيم القاطع بين X1 و F of X1 و بين X2 و F
+
+221
+00:21:32,010 --> 00:21:37,970
+of X2 دائما هتلاقي هذه النقطةالصورة هنا أعلى من
+
+222
+00:21:37,970 --> 00:21:42,910
+هذه وهذا معنى اللي هو ال convex وعن عرف ال convex
+
+223
+00:21:42,910 --> 00:21:50,390
+على هذا الأساس بيقول F is convex on I طلعلي على
+
+224
+00:21:50,390 --> 00:21:54,650
+التعريف إذا كان أخدنا أي X واحد و X اتنين element
+
+225
+00:21:54,650 --> 00:22:00,690
+in I و أخدنا T اللي هو element in 01 يعني بين 01
+
+226
+00:22:00,690 --> 00:22:13,020
+بيحققلي F اللي هوfor any كده f
+
+227
+00:22:13,020 --> 00:22:19,140
+is a convex in I if for any كده وكده we have
+
+228
+00:22:19,140 --> 00:22:25,940
+فاهمين عليا f of واحد minus T X واحد زائد T في X
+
+229
+00:22:25,940 --> 00:22:32,520
+اتنين ايش ماله هيسير؟أصغر أو يساوي واحد ناقص T في
+
+230
+00:22:32,520 --> 00:22:38,000
+X واحد زائد T في F of X اتنين
+
+231
+00:22:40,410 --> 00:22:44,370
+طبعاً اللي هو ال .. ال .. ال .. ال .. ال convex
+
+232
+00:22:44,370 --> 00:22:48,330
+functions في عليها دراسات كثيرة ودراسات حديثة كمان
+
+233
+00:22:48,330 --> 00:22:55,070
+حتى يعني في اللي هو real analysis بما يتعلق بال ..
+
+234
+00:22:55,070 --> 00:22:58,950
+مش بال integration العادي كمان باللي هو .. و
+
+235
+00:22:58,950 --> 00:23:03,310
+علاقتها بال integration في اللي هو ال .. ال big
+
+236
+00:23:03,310 --> 00:23:08,760
+integra كمانوطبعاً وإليها اللي هو خلّيني أقول
+
+237
+00:23:08,760 --> 00:23:14,020
+تطبيقات أو استخدامات في اللي هو optimization اللي
+
+238
+00:23:14,020 --> 00:23:20,350
+هي theoryالان احنا هنتحك .. هنحكي فيها بما يتعلق
+
+239
+00:23:20,350 --> 00:23:24,470
+في هذا الجزء من ال chapter اللي هو اللي بتعلق ك ..
+
+240
+00:23:24,470 --> 00:23:28,350
+ك .. كمين؟ ك Taylor's theorem وكيف بدنا نطبق ال
+
+241
+00:23:28,350 --> 00:23:32,590
+Taylor's theorem في إثبات نظرية تعرف لنا ال test
+
+242
+00:23:32,590 --> 00:23:37,730
+إيه لها؟ قول يا محمد هل
+
+243
+00:23:37,730 --> 00:23:46,670
+جيت و تشوفها؟ في ال calculus في ال calculusكنا
+
+244
+00:23:46,670 --> 00:23:52,670
+ناخد اللي هو test لل increasing وال decreasing
+
+245
+00:23:52,670 --> 00:23:59,380
+باستخدام ال first derivativeإذا بتتذكروا كنا ناخد
+
+246
+00:23:59,380 --> 00:24:04,220
+أيضا اللي هو عشان نعرف الدالة concave up أو
+
+247
+00:24:04,220 --> 00:24:08,340
+concave down بوسط تمين ال second derivative test
+
+248
+00:24:08,340 --> 00:24:11,880
+ماشي الحال إذا كانت F double prime أكبر من صفر
+
+249
+00:24:11,880 --> 00:24:15,360
+كانت اللي هي concave up إذا كانت F double prime
+
+250
+00:24:15,360 --> 00:24:20,060
+أصغر من صفر كانت أشمالها concave down الآن هتشوفوا
+
+251
+00:24:20,060 --> 00:24:25,000
+النظرية اللي بتشابه اللي بنحكي و هتستنتج أيش اللي
+
+252
+00:24:25,000 --> 00:24:32,080
+بحكيهبجاوب على سؤالك شوف الآن الان عندي واضح انه
+
+253
+00:24:32,080 --> 00:24:36,940
+من التعريف ان نفحص الدالة انها convex ولا مش
+
+254
+00:24:36,940 --> 00:24:41,920
+convex بالشكل اللي حكيناه بالتعريف اللي حكيناه
+
+255
+00:24:41,920 --> 00:24:46,380
+بغلب وبعض الدول مش هنقدر او مش هنعرف اللي هو
+
+256
+00:24:46,380 --> 00:24:49,980
+لصعوبة الحسابات ان نثبت انها convex او مش convex
+
+257
+00:24:49,980 --> 00:24:58,330
+فاكيد بدنا testيسهّلنا عملية إيجاد أو معرفة إن هذه
+
+258
+00:24:58,330 --> 00:25:03,070
+الدالة is convex ولا لأ واضح اللي بحكيه؟ يلّا نشوف
+
+259
+00:25:03,070 --> 00:25:07,810
+مع بعض الان قبلها بيعطينا بس counter example
+
+260
+00:25:07,810 --> 00:25:15,110
+بقولّي إن ال convex function ممكن ما تكونش
+
+261
+00:25:15,110 --> 00:25:18,540
+differentiable على الفترة اللي فيها convexيعني
+
+262
+00:25:18,540 --> 00:25:20,660
+ممكن اللي هي ال .. ال .. ال .. احنا اللي جابنا قبل
+
+263
+00:25:20,660 --> 00:25:24,800
+شوية اللي جيبناها الدالة هي محلاها في انسياب وفي
+
+264
+00:25:24,800 --> 00:25:27,860
+differentiability و ال short أعلى من ال .. من
+
+265
+00:25:27,860 --> 00:25:31,260
+الدالة نفسها و كده و ال function differentiable
+
+266
+00:25:31,260 --> 00:25:34,440
+لكن هذا الكلام مش دايما حاصل انه ال convex
+
+267
+00:25:34,440 --> 00:25:37,100
+function تكون differentiable و أشهر منه و مثال
+
+268
+00:25:37,100 --> 00:25:41,460
+مشهور وسهل اللي هو F of X بسوء ال absolute value
+
+269
+00:25:41,460 --> 00:25:45,720
+لل X F of X بسوء ال absolute value لل X هذا اللي
+
+270
+00:25:45,720 --> 00:25:52,270
+هوis أكيد كلكم عارف إنها not differentiable at 0
+
+271
+00:25:52,270 --> 00:26:01,530
+but it is convex on any interval I containing إيه
+
+272
+00:26:01,530 --> 00:26:05,370
+إيش الـ0، بظبط؟ ال .. ال .. it is not
+
+273
+00:26:05,370 --> 00:26:08,030
+differentiable اللي عارفينها ال .. ال .. ال .. ال
+
+274
+00:26:08,030 --> 00:26:13,730
+.. نثبت إنها convex let على interval I X1 و X2
+
+275
+00:26:13,730 --> 00:26:19,800
+element in Iو T element in 0 و 1 اخسب اللي لان F
+
+276
+00:26:19,800 --> 00:26:29,780
+of 1 minus T في X1 زي T في X2 بساوية عبارة عن ال
+
+277
+00:26:29,780 --> 00:26:36,240
+absolute value واحد نقص T X1 زي T في X2 وهذا من
+
+278
+00:26:36,240 --> 00:26:39,700
+خلاص ال absolute value اصغر بساوية واحد نقص T في
+
+279
+00:26:39,700 --> 00:26:46,100
+X1زاية T في X2 وهذا طبعا مين هو؟ هو عبارة عن 1 نقص
+
+280
+00:26:46,100 --> 00:26:53,120
+T F of X1 زاية T في F of X2 إذا صار عندي ال F
+
+281
+00:26:53,120 --> 00:26:56,240
+أشمالها is convex but it is not differentiable
+
+282
+00:26:56,240 --> 00:27:00,620
+اطلع لفوق الان يجيلا اللي هو ال test اللي معطينيا
+
+283
+00:27:00,620 --> 00:27:07,060
+اللي بقوللي اللي بجاوب على سؤالك يا محمد let I be
+
+284
+00:27:08,590 --> 00:27:13,190
+And open interval and let f من I لR have a second
+
+285
+00:27:13,190 --> 00:27:18,890
+derivative on I نفترض أن الـ F'' إيش ما لها موجودة
+
+286
+00:27:18,890 --> 00:27:25,600
+على I إذا من رأس الدور مفترضين الـ F'' موجودةالـ
+
+287
+00:27:25,600 --> 00:27:30,140
+test هو كما قالي f is convex on i if and only if f
+
+288
+00:27:30,140 --> 00:27:34,740
+double prime a شمالها أكبر من 0 لكل x when element
+
+289
+00:27:34,740 --> 00:27:39,300
+in I بصور واضحة الأمر الآن بدي أستخدم في المرهان
+
+290
+00:27:39,300 --> 00:27:44,520
+اللي هو سؤال اللي هو 16 في ال exercises و هنحله
+
+291
+00:27:44,520 --> 00:27:48,380
+وهذا من ضمن ال exercises اللي معاكم هو Morgue و
+
+292
+00:27:48,380 --> 00:27:53,910
+هنحله في حينهالان ايش اللي هو ال .. ال .. ال .. ال
+
+293
+00:27:53,910 --> 00:27:58,390
+.. السؤال بيقول اذا كانت f double prime موجودةثم
+
+294
+00:27:58,390 --> 00:28:02,570
+اثبت لي ان f double prime can be written as limit
+
+295
+00:28:02,570 --> 00:28:06,470
+f of a زاد h نقص اتنين f of a زاد f of a minus h
+
+296
+00:28:06,470 --> 00:28:11,850
+على مين على h تربية ماشي الحال هذا بدأ اعتمد على
+
+297
+00:28:11,850 --> 00:28:17,950
+انه اللي هو مثبت في اثبات النظرية ونشوف كيف ناخد
+
+298
+00:28:17,950 --> 00:28:23,540
+الاتجاه الاول اول اشي بده اللي هو بنفترض انهعندي
+
+299
+00:28:23,540 --> 00:28:29,080
+ال .. اللي هو ال F is convex ومنها نصل لإنه ال
+
+300
+00:28:29,080 --> 00:28:34,300
+derivative ايه شمالها أكبر أو يساوي سفر ماشي الحال
+
+301
+00:28:34,300 --> 00:28:43,480
+خليني نشوف مع بعض كيف اللي هو نثبت
+
+302
+00:28:43,480 --> 00:28:55,740
+انه if F is convex thenF double prime of A أكبر
+
+303
+00:28:55,740 --> 00:29:01,720
+شهر السفر لما نقول suppose that
+
+304
+00:29:01,720 --> 00:29:11,780
+proof فوضيح بس .. suppose that أن F is convex
+
+305
+00:29:11,780 --> 00:29:16,880
+لنثبت أن F double prime of A أكبر شهر السفرالان
+
+306
+00:29:16,880 --> 00:29:21,240
+انا ال F is convex وين على ال I و differentiable
+
+307
+00:29:21,240 --> 00:29:25,560
+وين second derivative لها على ال I خليني اختار
+
+308
+00:29:25,560 --> 00:29:31,280
+الان اللي هو ال H بحيث بدي اختار H بحيث انه A
+
+309
+00:29:31,280 --> 00:29:36,440
+minus H و A زائد H التانين يكون هنا وين موجودات في
+
+310
+00:29:36,440 --> 00:29:39,600
+ال interval I اللي عليها شغل اللي انا بدي اشتغل
+
+311
+00:29:39,600 --> 00:29:49,760
+عليها الان خدلي الان Fof A واكتبها على صورة F of
+
+312
+00:29:49,760 --> 00:29:59,450
+نص في A زاد H زاد نص في A minus Hلأن هذه عبارة عن
+
+313
+00:29:59,450 --> 00:30:03,330
+نص A و نص A هي الـ A و نص H ناقص نص H بروحهم مع
+
+314
+00:30:03,330 --> 00:30:06,730
+بعض ده منرجع لمين لل F و فيها كده تعرفي ليش عملتيل
+
+315
+00:30:06,730 --> 00:30:12,450
+طبعا هذه هتشتغل بمثابة واحد ناقص T و هذه T إذا T
+
+316
+00:30:12,450 --> 00:30:16,370
+بين ال Zero و الواحد صحيحة و بما أن F is convex و
+
+317
+00:30:16,370 --> 00:30:20,750
+هذولة اتتين نقطين عبارة عن نقطين في I لأن هيك
+
+318
+00:30:20,750 --> 00:30:26,520
+اختار ال H هنا هيكون هذا أصغر أو يساوينص F of A
+
+319
+00:30:26,520 --> 00:30:35,620
+زائد H زائد نص F of A minus H واضح؟
+
+320
+00:30:35,620 --> 00:30:43,000
+أي سؤال؟ واضح أه؟ جيبلي هذا على الجهة التانية
+
+321
+00:30:43,000 --> 00:30:51,620
+بيصير عندي نص F of A زائد H زائد نص F of A minus H
+
+322
+00:30:51,620 --> 00:30:59,230
+ناقص F of Aكل و إيه شماله أكبر أو يساوي إيش أكبر
+
+323
+00:30:59,230 --> 00:31:05,010
+أو يساوي سفر وضرب الجهتين في اتنين بيصير عندي
+
+324
+00:31:05,010 --> 00:31:10,550
+مضربت في اتنين بيصير هذه اللي هو النص بيصير واحد و
+
+325
+00:31:10,550 --> 00:31:14,490
+النص هذا بيصير واحد و هذا بيصير إيه شماله ناقص
+
+326
+00:31:14,490 --> 00:31:22,650
+اتنين of of ايه اقسم لليه الآن على اتش تربيعوH
+
+327
+00:31:22,650 --> 00:31:26,370
+تربيع موجة بقى، إذا بيضلوا هذا أشمال المفضل أكبر
+
+328
+00:31:26,370 --> 00:31:32,030
+أو يساوي سفر خد ال limit للجهتين limit as H goes
+
+329
+00:31:32,030 --> 00:31:40,440
+to zero بيضلوا أكبر أو يساوي سفر، مظبوط؟ و هذاBy
+
+330
+00:31:40,440 --> 00:31:44,920
+ال exercise اللي بنحكي عنه هو عبارة عن مين؟ F
+
+331
+00:31:44,920 --> 00:31:48,100
+double prime of A فطلع عندي F double prime of A
+
+332
+00:31:48,100 --> 00:31:52,320
+أكبر أساوي الصفر طبعا ماقدرتش أستخدم هذا أنه بنكتب
+
+333
+00:31:52,320 --> 00:31:56,840
+على صورة هذا إلا في ضوء أن هو أصلا حاكي لي ال F
+
+334
+00:31:56,840 --> 00:32:03,940
+double prime exist on I واضح أه؟أي سؤال إذا الان
+
+335
+00:32:03,940 --> 00:32:08,580
+اطلع لفوق و بنكون احنا خلصنا الجزء الأول و بنكون
+
+336
+00:32:08,580 --> 00:32:11,860
+بدنا نبدأ بالجزء الثاني اللي هو بال prime أكبر
+
+337
+00:32:11,860 --> 00:32:17,600
+سواء سفر و نصل لمين لل F is convex أوضحت هذه خليني
+
+338
+00:32:17,600 --> 00:32:24,100
+بس أنسحها و أقول ما يليه
+
+339
+00:32:24,100 --> 00:32:27,560
+نفترض
+
+340
+00:32:27,560 --> 00:32:30,060
+لأن صبوذ
+
+341
+00:32:32,450 --> 00:32:39,370
+that f double prime of a أشمالها أكبر أو يساوي سفر
+
+342
+00:32:39,370 --> 00:32:45,330
+ماشي الحال .. بدنا نثبت لك أن f is convex كيف بدنا
+
+343
+00:32:45,330 --> 00:32:52,130
+نثبت ان f is convex؟ بدنا نقول let x1 و x2 بيه أي
+
+344
+00:32:52,130 --> 00:32:57,630
+element in مين؟ ان i و t element in zero واش و
+
+345
+00:32:57,630 --> 00:33:06,820
+واحدوسميلي X not هي عبارة عن واحد minus T في X
+
+346
+00:33:06,820 --> 00:33:13,580
+واحد زائد T في مين في X اتنين الآن بدي اطبق اللي
+
+347
+00:33:13,580 --> 00:33:16,480
+هو taylor's theorem اول اش طبعا taylor's theorem
+
+348
+00:33:16,480 --> 00:33:21,960
+قابل للتطبيق اللي عند مينعند and بتساوي واحد بس
+
+349
+00:33:21,960 --> 00:33:25,640
+لأن المشتقة الأولى والتانية موجودة بعد هيك ماحدش
+
+350
+00:33:25,640 --> 00:33:29,480
+حكالي فإذا بيحجلي ان اطبق Taylor's theorem بس على
+
+351
+00:33:29,480 --> 00:33:34,260
+وين على اللي هو and بتساوي سفر او and بتساوي واحد
+
+352
+00:33:34,260 --> 00:33:36,800
+and بتساوي سفر بيصير main value theorem and بتساوي
+
+353
+00:33:36,800 --> 00:33:41,000
+واحد اللي هو اللي بتطبق عليها و هتخدمني ماشي الحال
+
+354
+00:33:41,000 --> 00:33:46,470
+نشوفالان apply taylor's theorem ع الفترة على اللي
+
+355
+00:33:46,470 --> 00:33:51,970
+هو ال X واحد وال X note اللي عندى there exist اللي
+
+356
+00:33:51,970 --> 00:34:00,270
+هو C واحد between X واحد and X note such that اه
+
+357
+00:34:00,270 --> 00:34:08,370
+اللي هو F of X note مظبوط او F of .. ده طبقه على X
+
+358
+00:34:08,370 --> 00:34:15,010
+واحد اول شي F of X واحد بساوياللي هو F of X not
+
+359
+00:34:15,010 --> 00:34:22,550
+زائد F prime of X not في X واحد نقص X not زائد مين
+
+360
+00:34:22,550 --> 00:34:26,950
+الآن ال remainder زائد ال remainder ال remainder
+
+361
+00:34:26,950 --> 00:34:33,950
+إيش هو F double prime عند ال C واحد اللي لاجيناها
+
+362
+00:34:33,950 --> 00:34:41,390
+في X minus X not الكل تربيع على 2 فكتورياأصغر من
+
+363
+00:34:41,390 --> 00:34:48,530
+اللي هو similarly there exist c2 بتطبقها على x1
+
+364
+00:34:48,530 --> 00:34:57,090
+على x2 و x0 there exist a c2 between x2 and x0
+
+365
+00:34:57,090 --> 00:35:07,070
+such thatof x2 بيساوي f of x0 زاد f prime of x0 في
+
+366
+00:35:07,070 --> 00:35:17,690
+x2 ناقص x0 زاد f double prime of c2 في x minus x0
+
+367
+00:35:17,690 --> 00:35:24,950
+الكل تربيع على 2 factorial واضح اللي بعمله
+
+368
+00:35:28,900 --> 00:35:37,440
+فهي عندى اللى هى هذه مع هذه هى اللى بدى استخدمه
+
+369
+00:35:37,440 --> 00:35:43,500
+هنا الآن فى الوصول لإنه F is convex يعنى F of هذا
+
+370
+00:35:43,500 --> 00:35:49,180
+المقدار يكون أصغر أو يساوي اللى هو F 1 minus T
+
+371
+00:35:49,180 --> 00:35:56,920
+فهذه زائد T فهذه إذا بدى أحسب الآن 1 minus T ف F
+
+372
+00:35:56,920 --> 00:36:05,420
+of X 1زائد T في F of إيش X2 بدي أحسبها و أوصلها
+
+373
+00:36:05,420 --> 00:36:09,080
+لعلاقتها مع مين مع F of X note اللي هي F of هذه
+
+374
+00:36:09,080 --> 00:36:20,940
+بساوي اضربلي بيصير T واحد نقص T في F of X note
+
+375
+00:36:20,940 --> 00:36:31,310
+معايا يا شباب زائد واحد minus Tف F prime of X note
+
+376
+00:36:31,310 --> 00:36:40,590
+في X واحد minus X note زائد اللي هو mean ده دروفة
+
+377
+00:36:40,590 --> 00:36:47,390
+هادة اللي هو واحد minus T في F double prime of C
+
+378
+00:36:47,390 --> 00:36:52,970
+واحد في X minus X note اللي كل تربيع على اتنين
+
+379
+00:36:52,970 --> 00:37:02,060
+factorial اللي هو اتنين معايا يا شبابزائد T .. T
+
+380
+00:37:02,060 --> 00:37:10,500
+.. F of X2 هيها اللي هي F of X note زائد T في F
+
+381
+00:37:10,500 --> 00:37:15,860
+prime of X note بضرب فادي قاعد في X2 نقص X note
+
+382
+00:37:15,860 --> 00:37:26,720
+زائد اللي هو T في F double prime of C2fx-x0 الكل
+
+383
+00:37:26,720 --> 00:37:34,100
+تربيه على مين؟ على اتنين نيجي الان و يساوي اطلعلي
+
+384
+00:37:34,100 --> 00:37:41,720
+على هذه الان واحد minus T في F of X0 وT في F of X0
+
+385
+00:37:41,720 --> 00:37:51,520
+بيصير عبارة عن F of X0 مظبوط؟ زائدالان هذا f prime
+
+386
+00:37:51,520 --> 00:37:55,420
+of x naught مضروبة في T مضروبة في هذه إذا عبارة عن
+
+387
+00:37:55,420 --> 00:38:03,660
+واحد minus T زائد T اه اللي هو مية المية بيصير
+
+388
+00:38:03,660 --> 00:38:10,300
+عندي الآن خد اللي هي x واحد ناقص x naught وخلينا
+
+389
+00:38:10,300 --> 00:38:19,510
+نجمحها واحد minus يعني خلينا نضيع ال Tفيها نقص
+
+390
+00:38:19,510 --> 00:38:24,730
+اتنين و X واحد او X او X واحد نفردها واحد minus T
+
+391
+00:38:24,730 --> 00:38:32,970
+في F ناخد عن المشترك يمكن أسهلنا F prime of X note
+
+392
+00:38:32,970 --> 00:38:43,330
+في واحد minus T في X واحد ناقص X note معايا شباب
+
+393
+00:38:43,330 --> 00:38:51,670
+زائد باخد بين هذه هي عمالو بين هذه أخدت ال F prime
+
+394
+00:38:51,670 --> 00:38:57,430
+of X naught عام نشترك بينهم زائد T في X2 ناقص X
+
+395
+00:38:57,430 --> 00:39:06,290
+naught زائد هذا المقدار كله بعد إذنكم هي اللي
+
+396
+00:39:06,290 --> 00:39:12,390
+بلزرج هذا اللي حطيته بلزرج سميني يا إيش R واضح
+
+397
+00:39:12,390 --> 00:39:21,890
+زائد Rالان نطلع على اللي عندي هدا واحد ناقص T اول
+
+398
+00:39:21,890 --> 00:39:27,670
+اشي ناقص T في ناقص X Note بيصير اللي هو زائد T في
+
+399
+00:39:27,670 --> 00:39:31,850
+X Note مع ناقص T في X Note بروحين مظبوط؟ اذا هذا
+
+400
+00:39:31,850 --> 00:39:38,410
+الان بروح وهذا
+
+401
+00:39:38,410 --> 00:39:44,290
+برضه بروح صح ولا لأ؟ نتأكد في اللي عملناه
+
+402
+00:39:48,090 --> 00:40:00,190
+واضح اه بظل x .. x note اه بظل ناقص اللي هو زائد x
+
+403
+00:40:00,190 --> 00:40:07,950
+note ناقص x note ناقص x note عملها كمان مرة بظل
+
+404
+00:40:07,950 --> 00:40:15,160
+ناقص x note من هناو من هنا بيظهر مين ناقص X note
+
+405
+00:40:15,160 --> 00:40:21,640
+لأنه بتظهر تبعت اللي هنا تظهر ناقص X note واضح أه؟
+
+406
+00:40:21,640 --> 00:40:28,760
+الان هذه كلها على بعض مين هي؟ هذه إيش اسمها؟ كلها
+
+407
+00:40:28,760 --> 00:40:32,900
+اسمها X note أه؟
+
+408
+00:40:32,900 --> 00:40:36,960
+فبيصير X note ناقص X note إيش بيصير؟ سفر فبيصير
+
+409
+00:40:36,960 --> 00:40:41,560
+هذا المقدار عبارة عن Fof x naught زائد ال
+
+410
+00:40:41,560 --> 00:40:45,380
+remainder مين؟ R نتطلع على الـ R هذا أو هو R لما
+
+411
+00:40:45,380 --> 00:40:48,000
+نقول remainder؟ الـ R مجموع الـ remainder دلين
+
+412
+00:40:48,000 --> 00:40:58,960
+الان ملاحظ هو ماعطيني عندي الان أفضل براءة عندي
+
+413
+00:40:58,960 --> 00:41:05,340
+هذا X نقص X واحد كل تربيع على اتنين موجبة و X نقص
+
+414
+00:41:05,340 --> 00:41:10,330
+X اتنين نوت على اتنين اشمالها موجبةوالان ال f
+
+415
+00:41:10,330 --> 00:41:15,510
+double prime عندى اللى هتطلع أشمالها موجبة بنفس
+
+416
+00:41:15,510 --> 00:41:21,550
+الطريقة السابقة زى ما عملنا قبل شوية عندى f double
+
+417
+00:41:21,550 --> 00:41:27,310
+prime أكبر يساوي سفر هيطلع عندى في الجوار اللى
+
+418
+00:41:27,310 --> 00:41:30,610
+بطبق عليه برضه أكبر يساوي سفر فبطلع عندى هذا موجب
+
+419
+00:41:30,610 --> 00:41:35,690
+و هذا موجب فبطلع عندى هذا المقدار اللى بدأنا فيه
+
+420
+00:41:36,380 --> 00:41:41,720
+هذا المقدار اللي بدأنا فيه طلع بساوي هذا المقدار
+
+421
+00:41:41,720 --> 00:41:49,760
+اللي هو هذا أكبر أو يساوي F of X naught اللي هي
+
+422
+00:41:49,760 --> 00:41:57,540
+mean F of X naught اللي عبارة عن F معين واحد نقص T
+
+423
+00:41:57,540 --> 00:42:07,040
+في X واحد زائد T في X اتنين هاي اللي وصلنا إليهمع
+
+424
+00:42:07,040 --> 00:42:21,020
+هذا وهذا تعريف أيه؟ F is convex F is convex أي
+
+425
+00:42:21,020 --> 00:42:21,680
+سؤال؟
+
+426
+00:42:24,290 --> 00:42:29,090
+و بهيك نكون خلصنا ال section اللي الأخير في
+
+427
+00:42:29,090 --> 00:42:34,250
+chapter اللي هو 6 خلصنا الجزء الأول من المحاضرة و
+
+428
+00:42:34,250 --> 00:42:37,250
+الآن بدنا نبدأ في الجزء الثاني من المحاضرة
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c1e85864e3b21a086ad8029934fffc2ed442d229
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_postprocess.srt
@@ -0,0 +1,2520 @@
+1
+00:00:05,620 --> 00:00:11,560
+بسم الله الرحمن الرحيم المحاضرة الثالثة في مساق
+
+2
+00:00:11,560 --> 00:00:19,660
+تحليل رياضي 2 أو تحليل حقيقي 2 كلية العلوم قسم
+
+3
+00:00:19,660 --> 00:00:28,520
+الرياضيات بالجامعة الإسلامية مراجعة سريعة لما تم
+
+4
+00:00:28,520 --> 00:00:34,380
+في المحاضرة السابقة والتي قبلهاحكينا عن شو معناته
+
+5
+00:00:34,380 --> 00:00:37,500
+اللي هو الـ derivative قلنا f prime of c عند نقطة
+
+6
+00:00:37,500 --> 00:00:41,760
+c لو كانت f function من i لعند ال r هو عبارة عن
+
+7
+00:00:41,760 --> 00:00:49,200
+limit f of x نقص f of c على x minus c لما x تروح
+
+8
+00:00:49,200 --> 00:00:53,460
+أو تقول ل c قلنا لو كانت ال limit exist هذه بنقول
+
+9
+00:00:53,460 --> 00:00:56,740
+إنه ال derivative موجودة بنرمزلها بالرمز f prime
+
+10
+00:00:56,740 --> 00:01:02,600
+of cأخدنا بعيدة اللي هو نظرية قولنا لو كانت f is
+
+11
+00:01:02,600 --> 00:01:11,860
+differentiable at c then it is continuous at c
+
+12
+00:01:11,860 --> 00:01:15,320
+قولنا the converse need not to be true in general
+
+13
+00:01:15,320 --> 00:01:20,100
+وأخدنا مثال على هيك قولنا خد ال f of x بسوء ال
+
+14
+00:01:20,100 --> 00:01:23,560
+absolute value لل x is continuous اللي هو
+
+15
+00:01:23,560 --> 00:01:26,880
+everywhere but it is not differentiable at zero
+
+16
+00:01:27,430 --> 00:01:30,590
+واخدنا مثال آخر قولنا f of x بيساوي ال summation
+
+17
+00:01:30,590 --> 00:01:36,090
+لل x ناقص ci i من عند 1 لعند n قولنا هذا ال
+
+18
+00:01:36,090 --> 00:01:39,210
+function is continuous everywhere but it is not
+
+19
+00:01:39,210 --> 00:01:43,250
+differentiable at the corner points which are c1,
+
+20
+00:01:43,350 --> 00:01:49,170
+c2 لعند ال cl و بعدين أخدنا مثال f of x بيساوي ال
+
+21
+00:01:49,170 --> 00:01:56,590
+summation 1 على 2 to the n cosinecos 3 أُس N X N
+
+22
+00:01:56,590 --> 00:02:01,690
+من واحد إلى ملا نهاية قلنا إن الـ function is
+
+23
+00:02:01,690 --> 00:02:07,750
+continuous everywhere but it is not differentiable
+
+24
+00:02:07,750 --> 00:02:16,850
+anywhere الـ function متصلة دائما لكن ليس لها أي
+
+25
+00:02:16,850 --> 00:02:22,760
+derivative عند أي نقطة من النقاط دومينابعد هيك
+
+26
+00:02:22,760 --> 00:02:28,500
+أخدنا اللي هو .. اللي هو نظرية اللي هي بنحكي فيها
+
+27
+00:02:28,500 --> 00:02:34,950
+عن خواص اللي هي التفاضل قلنا لو كانت ال Fوالـ G
+
+28
+00:02:34,950 --> 00:02:39,370
+are differentiable اللي هو كان من I لعند R
+
+29
+00:02:39,370 --> 00:02:44,730
+differentiable عند نقطة C بيكون مجموعة Alpha F حيث
+
+30
+00:02:44,730 --> 00:02:49,570
+Alpha اللي هو عبارة عن constant Alpha F' موجودة
+
+31
+00:02:49,570 --> 00:02:57,230
+وبتساوي Alpha في F' عند نقطة Cو بعدين قلنا أن f زي
+
+32
+00:02:57,230 --> 00:03:03,290
+g أو نقص prime of c برضه exist بسوء f prime of c
+
+33
+00:03:03,290 --> 00:03:09,390
+زي أو نقص g prime of c هذه من الخواصل هو ال
+
+34
+00:03:09,390 --> 00:03:15,040
+derivative و أيضا قلنااللي هو الخواص الأخرى أنه
+
+35
+00:03:15,040 --> 00:03:21,000
+الـ F في G الكل prime عنده نقطة C حاصل ضرر دلتين
+
+36
+00:03:21,000 --> 00:03:28,400
+بساوي اللي هو F primeof c في g of c زائد f of c في
+
+37
+00:03:28,400 --> 00:03:33,320
+g prime of c ومن ثم أخدنا أيضًا اللي هو
+
+38
+00:03:54,080 --> 00:03:59,480
+و من ثم أيضا حكينا عن اللي هو اخدنا اللي هو ال
+
+39
+00:03:59,480 --> 00:04:04,540
+chain rule theorem ال chain rule لو كانت F من I
+
+40
+00:04:04,540 --> 00:04:12,080
+لعند ال R و G من عند ال J لعند ال R حيث ال F of I
+
+41
+00:04:12,080 --> 00:04:15,780
+subset من ال J عشان نعرف اللي هو ال composition
+
+42
+00:04:15,780 --> 00:04:19,480
+قلنا لو كانت F is differentiable و G is
+
+43
+00:04:19,480 --> 00:04:23,890
+differentiable يعني F is differentiable عند Cis
+
+44
+00:04:23,890 --> 00:04:32,470
+differentiable at c and g is differentiable at f
+
+45
+00:04:32,470 --> 00:04:39,210
+of c then the composition اللي هو ال general يعني
+
+46
+00:04:39,210 --> 00:04:44,490
+التفاضل ال composition the composition تفاضله كما
+
+47
+00:04:44,490 --> 00:04:55,650
+يلي then fcomposite G prime of C بساوة F prime عند
+
+48
+00:04:55,650 --> 00:05:02,070
+G of C في G prime of C هذا اللي حكينا عنه المرة
+
+49
+00:05:02,070 --> 00:05:06,830
+الماضية وأيضا أخدنا طبعا أمثلة على هيك وأخدنا
+
+50
+00:05:06,830 --> 00:05:15,030
+نظرية أخرى اللي هي لو كانت عند F من عند I لعند R
+
+51
+00:05:15,030 --> 00:05:17,730
+قلنا is strictly
+
+52
+00:05:25,190 --> 00:05:31,450
+monotone and continuous
+
+53
+00:05:31,450 --> 00:05:41,770
+وكانت اللي هو G من عند J لعند I برضه strictly is
+
+54
+00:05:41,770 --> 00:05:55,620
+strictly monotone andcontinuous قلنا هنا at C وهنا
+
+55
+00:05:55,620 --> 00:06:06,340
+continuous at F of C حيث اللي هو الـ G بتساوي F of
+
+56
+00:06:06,340 --> 00:06:12,180
+mean of I عشان نقدر نعرف اللي هو تكون inverse is
+
+57
+00:06:12,180 --> 00:06:17,640
+strictly monotone and continuous where G
+
+58
+00:06:19,450 --> 00:06:28,790
+is the inverse of F، مظبوط؟ طبعاً، اللي بضماننا إن
+
+59
+00:06:28,790 --> 00:06:31,070
+ال inverse موجود إن هو strictly إيش؟ معناها
+
+60
+00:06:31,070 --> 00:06:33,490
+monotone، strictly monotone سواء increasing أو
+
+61
+00:06:33,490 --> 00:06:37,090
+decreasing، معناته one to one معناته إن هو اللي هي
+
+62
+00:06:37,090 --> 00:06:41,030
+ال inverse موجودة من اللي هو F of I اللي هي J،
+
+63
+00:06:41,030 --> 00:06:44,610
+لعند مين؟ لعند ال I، وهذه ال J في الواقع كل عنها
+
+64
+00:06:44,610 --> 00:06:52,800
+مين؟ هي ال F inverseالآن الشرط أنه if F is
+
+65
+00:06:52,800 --> 00:07:03,640
+differentiable at C at C then اللي هي G اللي هي
+
+66
+00:07:03,640 --> 00:07:07,280
+الـ F inverse دي في الواقع F inverse اللي سمناها
+
+67
+00:07:07,280 --> 00:07:14,020
+مين؟ F inverse لازم تكون differentiable at F of C
+
+68
+00:07:14,020 --> 00:07:15,660
+and
+
+69
+00:07:18,190 --> 00:07:23,390
+اللي سمناها F of C في حين وده بتتذكره D اللي هي
+
+70
+00:07:23,390 --> 00:07:35,170
+and F prime أو F inverse prime at this D بتساوي
+
+71
+00:07:35,170 --> 00:07:44,930
+واحد على F prime of C أو بمعنى آخر بتساوي واحد على
+
+72
+00:07:44,930 --> 00:07:53,880
+F primeF of C بيساوي D يعني C بيساوي G of D أو F
+
+73
+00:07:53,880 --> 00:07:59,600
+inverse of D اللي هي يعني composite G الكل أفمين
+
+74
+00:07:59,600 --> 00:08:13,970
+of C واضح هاه F of مين of Dقلنا بعدين اللي هو in
+
+75
+00:08:13,970 --> 00:08:18,530
+general لو كانت اللي هي هذه تحت الشروط هذه بس الآن
+
+76
+00:08:18,530 --> 00:08:24,430
+مش عند اللي هو نقطة لو F is differentiable على كل
+
+77
+00:08:24,430 --> 00:08:29,470
+ال I هتكون ال G is differentiable على ال J و
+
+78
+00:08:29,470 --> 00:08:36,110
+العلاقة بينهم زي ما حكينا المرة الماضية هتكون اللي
+
+79
+00:08:36,110 --> 00:08:43,620
+هوطب هالمرة F is differentiable on I then G is
+
+80
+00:08:43,620 --> 00:08:47,280
+differentiable on J اللي هي بساوة F of I طبعا تحت
+
+81
+00:08:47,280 --> 00:08:55,140
+هذا الشروط and هيكون F inverse prime of Y بساوة 1
+
+82
+00:08:55,140 --> 00:09:01,330
+على F prime of Xحيث العلاقة بين Y و X اللي هي Y
+
+83
+00:09:01,330 --> 00:09:08,050
+بتساوي F of X أو بتعبير آخر بتساوي 1 على F prime
+
+84
+00:09:08,050 --> 00:09:13,630
+of composite G اللي هي بتسميها F inverse كله of
+
+85
+00:09:13,630 --> 00:09:23,790
+mean of Y هذا اللي حكينا المرة الماضية نيجي
+
+86
+00:09:23,790 --> 00:09:26,510
+الآن نكمل
+
+87
+00:09:27,590 --> 00:09:33,710
+وصلنا عند المثال اللي هو 6 1 10 وقلنا لو كانت عند
+
+88
+00:09:33,710 --> 00:09:41,270
+g of y example وقفنا عند ال example التالي g of y
+
+89
+00:09:41,270 --> 00:09:48,710
+بتساوي y أسواحدة ل n for y element in j اللي هي
+
+90
+00:09:48,710 --> 00:09:54,970
+عبارة عن ال interval من zero ل infinity الآن بقول
+
+91
+00:09:54,970 --> 00:10:03,260
+show thatG prime of Y بتساوي 1 على N Y أس 1 على N
+
+92
+00:10:03,260 --> 00:10:12,580
+ناغس 1 حيث N is even solution نيجي الأن نحل تطبيق
+
+93
+00:10:12,580 --> 00:10:20,240
+على ال theorem الأخيرة اللي هو ناخد inverse لهذه
+
+94
+00:10:20,240 --> 00:10:25,750
+طبعا واضح أن ال inverse لو قلنا let F of Xبساوي X
+
+95
+00:10:25,750 --> 00:10:30,230
+أُس N هذا عبارة عن polynomial أو اللي هو دالة
+
+96
+00:10:30,230 --> 00:10:35,170
+أُسية أو جزء من polynomial عند X أُس N طبعاً لأي X
+
+97
+00:10:35,170 --> 00:10:39,350
+في الفترة 01 هذا is differentiable ومش هيك كمان
+
+98
+00:10:39,350 --> 00:10:42,910
+ومدامة الـ N even في الفترة هذه strictly
+
+99
+00:10:42,910 --> 00:10:46,580
+increasingده الـ Strict increase in continuous ده
+
+100
+00:10:46,580 --> 00:10:50,860
+كل .. كل أمورها متحققة اللي قبل بشوية في النظرية
+
+101
+00:10:50,860 --> 00:10:56,000
+فالآن و هذه عبارة عن ال inverse لمين؟ للـ G فبكون
+
+102
+00:10:56,000 --> 00:11:04,540
+الآن G prime of Y إيش هتساوي؟ بتساوي 1 على F prime
+
+103
+00:11:04,540 --> 00:11:11,410
+عند G of Yمظبوط ولا لا؟ Y ساوي الان ال F prime هنا
+
+104
+00:11:11,410 --> 00:11:15,930
+واضح اللي هي N X أس N نقص واحد يعني عبارة عن واحد
+
+105
+00:11:15,930 --> 00:11:22,070
+على بدل ال X إيش هحط؟ G of Y لأن هذا F prime of X
+
+106
+00:11:22,070 --> 00:11:26,290
+بساوي N X N نقص واحد طب F prime of G Y هي عبارة عن
+
+107
+00:11:26,290 --> 00:11:33,870
+G of Y أس N نقص واحد مضروبة في مين؟ في ال N Y ساوي
+
+108
+00:11:35,600 --> 00:11:43,600
+1 على N في G of Y إيش هي عبارة عن Y أس 1 على N
+
+109
+00:11:43,600 --> 00:11:49,640
+فبيصير اللي هو هذي بالمرة نرفحها بعد إذنكم G of Y
+
+110
+00:11:49,640 --> 00:11:59,620
+أس 1 ناقص N ويساوي إن عوض 1 على N في Yأس واحد على
+
+111
+00:11:59,620 --> 00:12:07,260
+N أس واحد ناقص N ويساوي واحد على N Y أس واحد على N
+
+112
+00:12:07,260 --> 00:12:12,660
+ناقص واحد وهو المطلوب هذه اللي هي تطبيق مباشرة على
+
+113
+00:12:12,660 --> 00:12:17,580
+النظرية السابقة الآن تطبيق آخر مثال آخر أيضا مثال
+
+114
+00:12:17,580 --> 00:12:20,380
+يعني شبيه بالأمثل اللي كنتوا تاخدوه في ال calculus
+
+115
+00:12:20,380 --> 00:12:29,610
+المثال دي اللي بناخده اللي هو Y بتساوي صين ال Xو
+
+116
+00:12:29,610 --> 00:12:37,590
+الـ x في ناقص πي على اتنين لعين باي على اتنين الآن
+
+117
+00:12:37,590 --> 00:12:43,470
+بقوللي اثبت انه sign inverse prove that اللي هو
+
+118
+00:12:43,470 --> 00:12:54,110
+show that sign inverse لل Y بتساوي واحد على جدر
+
+119
+00:12:54,110 --> 00:12:57,750
+التربيع لواحد ناقص مين Y تربيع
+
+120
+00:13:00,300 --> 00:13:04,160
+prime اه اه ال derivative لل sign inverse ايش
+
+121
+00:13:04,160 --> 00:13:06,840
+بتساوي واحدة الجدر تربيعه لو واحد نقص Y تربيعه
+
+122
+00:13:06,840 --> 00:13:10,940
+برضه تطبيق مباشر خلينا نشوف كيف نطبق على النظرية
+
+123
+00:13:10,940 --> 00:13:20,000
+ناخد let F of X اللي هو بيساوي sign ال X عشان عند
+
+124
+00:13:20,000 --> 00:13:24,500
+G of Y او عند F of X بيساوي sign ال X اللي بتسميها
+
+125
+00:13:24,500 --> 00:13:31,610
+Y يعني الآن بتصير عند G of Y ايش بتساويSin Inverse
+
+126
+00:13:31,610 --> 00:13:37,790
+لمن؟ لـ Y معايا يا شباب، أه؟ لأن حسب الـ F of X
+
+127
+00:13:37,790 --> 00:13:41,510
+بساعة و شوية إن الـ X الـ X في الفترة ناقص Y على 2
+
+128
+00:13:41,510 --> 00:13:47,690
+و Y على 2 الـ Y القيمة المقابلة إليها هتكون بين
+
+129
+00:13:47,690 --> 00:13:54,560
+ناقص 1 و 1لكن لاحظ الآن لما أشتق المشتقة لازم تكون
+
+130
+00:13:54,560 --> 00:13:58,380
+لا تساوي صفر في الفترة هذه ففي الفترة هذه اللي هي
+
+131
+00:13:58,380 --> 00:14:02,900
+المشتقة طبعا لهذه اللي هي عبارة عن cosine فهتكون
+
+132
+00:14:02,900 --> 00:14:06,900
+اللي هي ال X بس في ال open interval من ناقص y على
+
+133
+00:14:06,900 --> 00:14:11,540
+2 على y على 2 عساس ما نجسمش عالميا على الصفر إذا
+
+134
+00:14:11,540 --> 00:14:17,620
+الآن صار عندي G prime of Yنفسي اللي عملناه فوق،
+
+135
+00:14:17,620 --> 00:14:23,720
+إيش بتساوي؟ واحد على F prime of G of Y Y ساوي،
+
+136
+00:14:23,720 --> 00:14:28,880
+واحد F .. اللي هي مين الأن F prime؟ اللي هي cosine
+
+137
+00:14:28,880 --> 00:14:36,320
+اللي هو G of Y، مظبوط؟ وال cosine احنا إيش؟ عبارة
+
+138
+00:14:36,320 --> 00:14:39,160
+عن إيش؟ عبارة عن إيش تكون؟ عبارة عن الجدر
+
+139
+00:14:39,160 --> 00:14:44,080
+التربيعي؟ لا، طبعا ال cosine X إيش بتساوي؟ هذا
+
+140
+00:14:44,080 --> 00:14:52,100
+عبارة عن X، مظبوط؟هو الجدر التربيعي؟ لا، واحد ناقص
+
+141
+00:14:52,100 --> 00:14:57,980
+sign تربيع الـ X اللي هي G of Y، مظبوط؟ معايا يا
+
+142
+00:14:57,980 --> 00:15:03,200
+شبابY ساوي واحد على جدر التربيع إلى واحد ناقص Y
+
+143
+00:15:03,200 --> 00:15:08,940
+تربيع و Y في الفترة ناقص باي على اتنين و باي على
+
+144
+00:15:08,940 --> 00:15:13,800
+اتنين اللي هي الـ X و اللي موجودة أسفل X في ناقص
+
+145
+00:15:13,800 --> 00:15:16,560
+باي على اتنين و باي على اتنين و الـ Y في الفترة
+
+146
+00:15:16,560 --> 00:15:21,640
+ناقص واحد و واحد حتى نتجنب القسمة عالميا على اللي
+
+147
+00:15:21,640 --> 00:15:25,380
+هو الصفر هذا التطبيق على النظرية
+
+148
+00:15:27,410 --> 00:15:30,770
+ال homework عندنا تلاتة أو أربعة أو سبعة أو تسعة
+
+149
+00:15:30,770 --> 00:15:34,250
+أو تلاتاش من section 6-1 ان شاء الله المرة الجاية
+
+150
+00:15:34,250 --> 00:15:39,510
+أو اللي بعدها بنحاول نعمل discussion فيا ريت اللي
+
+151
+00:15:39,510 --> 00:15:44,410
+هو أنكم اتحلوا الأسئلة و اللي بتعرفوش اتحلوا او
+
+152
+00:15:44,410 --> 00:15:50,880
+بدكم نذاك بنحلو ان شاء اللهنيجي الآن لصفحة
+
+153
+00:15:50,880 --> 00:15:53,800
+اللي بعدي ده اللي هو ال section التاني ممكن هيكنا
+
+154
+00:15:53,800 --> 00:15:58,460
+هنا ستة واحد الآن هنبدأ في ال section التاني اللي
+
+155
+00:15:58,460 --> 00:16:02,380
+هو ال main value theorem وهو محاضرة اليوم بشكل
+
+156
+00:16:02,380 --> 00:16:06,740
+أساسي عالمي على the main value theorem ومتعلقات
+
+157
+00:16:06,740 --> 00:16:12,870
+هذه النظريةهنلاقي جدّاش مهمة هذه النظرية وجدّاش
+
+158
+00:16:12,870 --> 00:16:17,650
+فيه عندنا نتائج تتعلق إيه بها وإحنا يعني فعلا
+
+159
+00:16:17,650 --> 00:16:25,530
+بستعملها كثير وفعلا بتساعدنا اللي هو في اللي ده
+
+160
+00:16:25,530 --> 00:16:30,270
+يعني إذا رح أطلب لما حتى أخدنا ال Calculus كانت
+
+161
+00:16:30,270 --> 00:16:37,010
+اللي هي إلها تطبيقات واسعة وحنشوف الآن وين أهمية
+
+162
+00:16:37,680 --> 00:16:42,520
+هذه نظرية نظرية القيم المتوسطة من خلال الحديث أو
+
+163
+00:16:42,520 --> 00:16:47,080
+شرح حادي المادة الآن في الأول زي ما قلنا ال
+
+164
+00:16:47,080 --> 00:16:49,420
+section 6.2 the mean value theorem نيجي لل
+
+165
+00:16:49,420 --> 00:16:53,420
+definition الأول ال definition اللي هو مر علينا
+
+166
+00:16:53,420 --> 00:16:58,380
+اشي زيه أو مر علينا اللي هو تعريف ال local
+
+167
+00:16:58,380 --> 00:17:04,500
+extremum أو اللي هو relative extremumأو اللي هو
+
+168
+00:17:04,500 --> 00:17:07,460
+الـ local maximum أو الـ local minimum أو الـ
+
+169
+00:17:07,460 --> 00:17:10,840
+relative extremum أو الـ relative اللي هو الـ
+
+170
+00:17:10,840 --> 00:17:17,900
+minimum طبعاً بتعرفوا أن أنا بدي أعرف شو معناته دي
+
+171
+00:17:17,900 --> 00:17:24,480
+اللي هي النقطة عنده النقطة C في عند local .. local
+
+172
+00:17:24,480 --> 00:17:29,860
+maximum مثلا أو relative maximum بنقول في عند C
+
+173
+00:17:30,870 --> 00:17:35,370
+عندي function f من some interval I لعند R هاي الـ
+
+174
+00:17:35,370 --> 00:17:39,490
+function اللي عندي هنا من هنا لهنا بنقول C element
+
+175
+00:17:39,490 --> 00:17:48,430
+in I at C element in I we have a local أو relative
+
+176
+00:17:48,430 --> 00:18:00,820
+maximum when اللي هو there existsV Delta of C يعني
+
+177
+00:18:00,820 --> 00:18:05,800
+بنلاقي جوار حوالين الـ C بنصف قطر Delta C نقص
+
+178
+00:18:05,800 --> 00:18:12,060
+Delta of C زائد Delta في هذا الجوار such that
+
+179
+00:18:12,060 --> 00:18:20,320
+بتكون F of C هي أكبر قيمة للدالة F of C أكبر أو
+
+180
+00:18:20,320 --> 00:18:27,920
+سوى F of X لكل X في هذا الجوارإذا تحقق هذا الشرط
+
+181
+00:18:27,920 --> 00:18:35,840
+بنقول إن F has a relative maximum
+
+182
+00:18:35,840 --> 00:18:36,780
+at C
+
+183
+00:18:39,910 --> 00:18:45,290
+v delta neighborhood يعني جوار بنصف قطر دلتا بحيث
+
+184
+00:18:45,290 --> 00:18:50,590
+يتحقق أن ال f of c أكبر شو f of x لكل x في هذا
+
+185
+00:18:50,590 --> 00:19:01,850
+الجوار similarly بنقول at d element in I we have a
+
+186
+00:19:01,850 --> 00:19:11,870
+relative minimum whenthere exist أي جوار آخر بتكون
+
+187
+00:19:11,870 --> 00:19:17,390
+تسموه V Delta Prime أو V Delta of D such that يعني
+
+188
+00:19:17,390 --> 00:19:20,870
+بنلاقي .. بنقول هذه النقطة في عندها relative
+
+189
+00:19:20,870 --> 00:19:27,970
+minimum إذا كان لقينا جوار حواليهاهذه النقطة C D
+
+190
+00:19:27,970 --> 00:19:33,810
+وهذه D زائد Delta وهذه D نقص Delta في جوار حواليها
+
+191
+00:19:33,810 --> 00:19:38,670
+بتكون قيمة الدالة أصغر من كل القيم اللي حواليها
+
+192
+00:19:38,670 --> 00:19:45,210
+يعني اللي هو there exists V Delta of D such that F
+
+193
+00:19:45,990 --> 00:19:53,190
+of D أصغر أو ساوى F of X لكل X موجودة في V Delta
+
+194
+00:19:53,190 --> 00:20:01,370
+of D فهذه نسميها نقطة صغيرة محلية وهذه نسميها نقطة
+
+195
+00:20:01,370 --> 00:20:06,460
+عظمة محليةهذا معناته اللي هو الـ local maximum و
+
+196
+00:20:06,460 --> 00:20:10,340
+الـ local minimum أو زي ما هو مصطلح عليها ال
+
+197
+00:20:10,340 --> 00:20:14,580
+relative maximum و relative minimum لما بنقصد و
+
+198
+00:20:14,580 --> 00:20:20,880
+بنقول local extremum معناته يا local maximum أو
+
+199
+00:20:20,880 --> 00:20:24,520
+local minimum أو relative extremum يا relative
+
+200
+00:20:24,520 --> 00:20:30,120
+maximum يا relative minimumنجي الآن لنظريتنا
+
+201
+00:20:30,120 --> 00:20:33,720
+الأولى احنا كنا في ال calculus إذا بتتذكر و نسأل
+
+202
+00:20:33,720 --> 00:20:43,110
+سؤاللما بدنا نبحث في مسألة اللي هو الـ maximum و
+
+203
+00:20:43,110 --> 00:20:46,410
+الـ minimum سواء local maximum و local minimum أو
+
+204
+00:20:46,410 --> 00:20:50,230
+absolute maximum و absolute minimum كنا نسأل حالنا
+
+205
+00:20:50,230 --> 00:20:54,390
+سؤال طبعا مش معجول أنا بدي آجي كل نقاط ال domain
+
+206
+00:20:54,390 --> 00:20:57,990
+أفحص فيه عند maximum ولا minimum لأن نقاط ال
+
+207
+00:20:57,990 --> 00:21:01,170
+domain عدد لا نهائي uncountable number of points
+
+208
+00:21:01,170 --> 00:21:07,180
+في غالبهافإيش كنت حصرها؟ كنا نقول أين يمكن إيجاد
+
+209
+00:21:07,180 --> 00:21:12,480
+الـlocal maximum أو الـlocal minimum بعد ما نحدد
+
+210
+00:21:12,480 --> 00:21:17,100
+النقاط هذه بنقول يأتي الآن الفحص إنه هل هي local
+
+211
+00:21:17,100 --> 00:21:21,660
+maximum ولا local minimum إذن مسألة اللي هو إيجاد
+
+212
+00:21:21,660 --> 00:21:25,180
+ال maximum و ال minimum تبرع عبر خطوتين الخطوة
+
+213
+00:21:25,180 --> 00:21:31,380
+الأولى وين ممكن نلاقيهاوالخطوة الثانية اللي هي هل
+
+214
+00:21:31,380 --> 00:21:36,220
+هي فعلا local maximum ولا local minimum ولا لا
+
+215
+00:21:36,220 --> 00:21:40,500
+local maximum ولا local minimum اللي بده يشرعلنا
+
+216
+00:21:40,500 --> 00:21:45,130
+الإجابة الأولى هي النظرية هذهالنظرية هذه كنا كمان
+
+217
+00:21:45,130 --> 00:21:49,390
+نجاوب نقول الإجابة توجد الـlocal maximum أو
+
+218
+00:21:49,390 --> 00:21:53,030
+الـlocal minimum في أحد ثلاث مناطق إما F prime
+
+219
+00:21:53,030 --> 00:21:58,070
+بساوي سفر أو F prime does not exist كنقات داخلية
+
+220
+00:21:58,070 --> 00:22:03,410
+أو عند الـendpoints فكنا نحصرها في تلت أنهي مناطق
+
+221
+00:22:03,410 --> 00:22:07,530
+فبصير عدد النقاط اللي بدنا نفحص الـlocal max أو
+
+222
+00:22:07,530 --> 00:22:11,490
+الـlocal minimum عددها محدود وقليل بصير السؤال
+
+223
+00:22:11,490 --> 00:22:15,630
+مقدور عليهالان النظرية اللي بتتشرح علناها دي ايش
+
+224
+00:22:15,630 --> 00:22:23,390
+النظرية بتقول بتقول ما يليه اللي بتقوله ال theorem
+
+225
+00:22:23,390 --> 00:22:29,120
+اللي هيحتى اسمها اللي هي interior extremum theorem
+
+226
+00:22:29,120 --> 00:22:32,920
+interior extremum theorem يعني هنحكي عن ال
+
+227
+00:22:32,920 --> 00:22:38,020
+interior point بتقولي نفترض إن C عبارة عن نقطة
+
+228
+00:22:38,020 --> 00:22:43,400
+داخلية لمين ل some interval I C اللي هو إشمالة
+
+229
+00:22:43,400 --> 00:22:49,140
+نقطة داخلية ل I ال interval اللي عنديوعند الـ
+
+230
+00:22:49,140 --> 00:22:55,040
+function F من I لعند R لو فرضنا أن الـ function F
+
+231
+00:22:55,040 --> 00:23:02,000
+has a relative extremum at let's say element كده
+
+232
+00:23:02,000 --> 00:23:18,480
+if F has a relative extremum at C element in I0عند
+
+233
+00:23:18,480 --> 00:23:23,520
+C an interior point of the interval I at which F
+
+234
+00:23:23,520 --> 00:23:27,640
+has a relative extremum يعني مفترضين أنه في عندي
+
+235
+00:23:27,640 --> 00:23:33,140
+يا relative maximum يا relative minimum عند هذه
+
+236
+00:23:33,140 --> 00:23:43,660
+النقطة الداخلية ونفرض كمان أن F prime of C exist
+
+237
+00:23:43,660 --> 00:23:51,610
+تحت كل هذه الشروطلازم تطلع عند F prime of C ايش
+
+238
+00:23:51,610 --> 00:23:56,050
+بتساوي؟ بتساوي سفر يعني بمعنى اخر لو كانت النقطة
+
+239
+00:23:56,050 --> 00:24:00,690
+داخلية و النقطة هذه الـ derivative عندها موجودة
+
+240
+00:24:01,820 --> 00:24:05,280
+وكانت عندها relative maximum أو relative minimum
+
+241
+00:24:05,280 --> 00:24:09,280
+قطعاً هتكون الـ F prime إليها إيش بتساوي .. بتساوي
+
+242
+00:24:09,280 --> 00:24:12,960
+سفر يعني عند .. عند النقاط الداخلية اللي الـ F
+
+243
+00:24:12,960 --> 00:24:17,280
+prime إليها موجودة و بتشاويش سفر انساها و ماتبحثش
+
+244
+00:24:17,280 --> 00:24:20,780
+فيها قطعا فيش فيها لا relative maximum ولا
+
+245
+00:24:20,780 --> 00:24:25,750
+relative إيش .. minimumالآن هذه النظرية وكأنه
+
+246
+00:24:25,750 --> 00:24:31,810
+بتحكيلنا في داخلها أن النقاط اللي بتكون داخلية
+
+247
+00:24:31,810 --> 00:24:36,590
+واحتمال يكون عندها relative maximum و relative
+
+248
+00:24:36,590 --> 00:24:42,410
+minimum نوعين يا f prime مش موجودةأو الـ F' أيش
+
+249
+00:24:42,410 --> 00:24:48,190
+بتساوي؟ بتساوي 0 لأنه إذا كانت F' موجودة وقفقلها
+
+250
+00:24:48,190 --> 00:24:51,910
+relative maximum أو relative minimum وكانت النقطة
+
+251
+00:24:51,910 --> 00:24:56,710
+داخلية لازم الـ F' أيش ما لها تساوي 0 ولاحظ هنا إن
+
+252
+00:24:56,710 --> 00:25:02,190
+الحديث عن مين؟ عن النقاط الداخلية يعني من فحوة
+
+253
+00:25:02,190 --> 00:25:06,110
+الحديث هنا بنجاوب على سؤالنا، هذه اللي بتجاوبنا
+
+254
+00:25:06,110 --> 00:25:09,860
+على سؤالنا بتقولاللي هو الـ relative maximum أو
+
+255
+00:25:09,860 --> 00:25:13,880
+الـ relative minimum هتكون في أحد ثلاث مناطق يا F
+
+256
+00:25:13,880 --> 00:25:18,060
+prime does not exist يا F prime بالساوية سفر يا
+
+257
+00:25:18,060 --> 00:25:27,960
+end point واضح؟ أي سؤال؟ واضح أه؟ طيب، دي يجي
+
+258
+00:25:27,960 --> 00:25:36,550
+تبرهن النظريةالآن هو البروحان اللي مكتوب هنا we
+
+259
+00:25:36,550 --> 00:25:41,170
+prove for the case that F has relative maximum at
+
+260
+00:25:41,170 --> 00:25:45,150
+C هيه مكتوب أنا مابديش أبرهن ال maximum بتبرهنكم
+
+261
+00:25:45,150 --> 00:25:52,290
+مين ال minimum إذا الآن بدنا نفترض نفترض ال proof
+
+262
+00:25:52,290 --> 00:25:57,870
+خليني أكتب هنا ال proof بدي
+
+263
+00:25:57,870 --> 00:26:04,820
+أفترضC نقطة داخلية ونفترض إن F أشبهلها have a
+
+264
+00:26:04,820 --> 00:26:08,560
+relative minimum relative maximum محلولة لأن
+
+265
+00:26:08,560 --> 00:26:12,640
+suppose that
+
+266
+00:26:12,640 --> 00:26:21,020
+F has a relative maximum
+
+267
+00:26:21,020 --> 00:26:28,120
+at C element in I0 ماشي؟
+
+268
+00:26:37,000 --> 00:26:41,080
+نعم نفترض إنها minimum لأن ال case تبعت ال maximum
+
+269
+00:26:41,080 --> 00:26:47,860
+محلولةواضح؟ الان لو كان F as relative extremum
+
+270
+00:26:47,860 --> 00:26:52,160
+بدنا نصل الان extreme يابتكون maximum يابتكون
+
+271
+00:26:52,160 --> 00:26:56,440
+minimum case ال maximum هي مكتوبة بتجروها لحالكوا
+
+272
+00:26:56,440 --> 00:27:01,980
+نفس الفكرة ده أكتف بت mean F as a relative H
+
+273
+00:27:01,980 --> 00:27:08,360
+minimumالآن بدي أفترض لك أن الـ F' أي شمالها لا
+
+274
+00:27:08,360 --> 00:27:11,700
+تساوي صفر و أسألك لـ contradiction إذا الآن بدي
+
+275
+00:27:11,700 --> 00:27:18,780
+أفترض لك و بدي أقول لك suppose that F prime of C
+
+276
+00:27:18,780 --> 00:27:25,620
+لا تساوي أيش؟ صفر، ماشي الحال، إذا عندي two cases
+
+277
+00:27:25,620 --> 00:27:34,360
+ال case الأول أن F prime of C أكبر من أيش؟من صفر
+
+278
+00:27:34,360 --> 00:27:43,580
+ماشي الحال إذا الآن عندي limit f of x ناقص f of c
+
+279
+00:27:43,580 --> 00:27:50,340
+على x minus c as x بتروح ل c أشماله اللي هو هذا f
+
+280
+00:27:50,340 --> 00:27:57,040
+prime of c حسب المعطى إيش هيكون أكبر من صفر ماشي
+
+281
+00:27:57,040 --> 00:28:03,480
+الحال طيب الآن مدام ال f prime of c أكبر من صفرإذا
+
+282
+00:28:03,480 --> 00:28:07,700
+حسب نظرية قلنا قبل هيك إنه لو كانت ال limit لل
+
+283
+00:28:07,700 --> 00:28:12,800
+function أكبر من 0 هنلاقي جوار حوالين النقطة اللي
+
+284
+00:28:12,800 --> 00:28:16,660
+بدنا نروحلها يكون اللي هو قيمة اللي جوا ال limit
+
+285
+00:28:16,660 --> 00:28:21,780
+أكبر من 100 من 0 لأن كما قالي مدام ال limit هذا
+
+286
+00:28:21,780 --> 00:28:29,260
+أكبر من 0 then there exists Deltaأكبر من سفر أو V
+
+287
+00:28:29,260 --> 00:28:35,380
+Delta أكبر من سفر Such that اللي هو F of X نقص F
+
+288
+00:28:35,380 --> 00:28:43,400
+of C على X minus C أكبر من سفر لكل X وين موجودة في
+
+289
+00:28:43,400 --> 00:28:48,240
+الـ V Delta of C صح؟
+
+290
+00:28:48,240 --> 00:28:53,820
+هاي عندي احنا مفترضين إن هي أشملها relative
+
+291
+00:28:53,820 --> 00:28:57,940
+minimum خلّيني أشتغل على هذه المنطقةأساسي أن
+
+292
+00:28:57,940 --> 00:29:02,260
+تشوفوها على الرسم
+
+293
+00:29:02,260 --> 00:29:13,880
+يمكن تكون أوضح عندي هي النقطة C وهذا C ناقص Delta
+
+294
+00:29:13,880 --> 00:29:21,060
+وهذا C زائد Delta، راضح؟ الـ F of X ناقص F of Z
+
+295
+00:29:21,060 --> 00:29:24,000
+على X minus C أكبر من مين من سفر لكل X و الموجودة
+
+296
+00:29:24,000 --> 00:29:32,040
+في الـ V Delta of Cأه، الآن .. الآن عندي هو .. بدي
+
+297
+00:29:32,040 --> 00:29:37,020
+.. عندي أنا مفترض أنه اللي هو F هذا relative A
+
+298
+00:29:37,020 --> 00:29:45,580
+شماله minimum إذا في جوار .. في جوار بتكون F of C
+
+299
+00:29:45,580 --> 00:29:52,700
+أصغر أو ساوة F of X لكل X في هذا الجوار اللي هو V
+
+300
+00:29:52,700 --> 00:29:59,440
+Delta Prime of إيش؟ Of C، ماشي الحالالآن الـ Delta
+
+301
+00:29:59,440 --> 00:30:03,820
+هذه فيه Delta أكبر من 0 باخدها الـ Delta أصغر من
+
+302
+00:30:03,820 --> 00:30:08,840
+هذه بحكم فيها، فده بتنفع للـ Delta أكبر من هذه إن
+
+303
+00:30:08,840 --> 00:30:11,880
+هذا الكون المقدر لكل X في الـ V Delta يكون أكبر من
+
+304
+00:30:11,880 --> 00:30:17,100
+0، إذا بديجه، برضه بنفع، إذا بختار الـ Delta هذه
+
+305
+00:30:17,100 --> 00:30:20,420
+بناء على اختيار لهذه، فبتكون الـ Delta هذه أنا
+
+306
+00:30:20,420 --> 00:30:24,770
+بختارها أصغر أو سوء من الـ Delta primeماشي الحال
+
+307
+00:30:24,770 --> 00:30:28,770
+طيب إذا صار عندي F of X نقص F of C على X minus C
+
+308
+00:30:28,770 --> 00:30:34,970
+أكبر من 100 من 0 لكل X limited V Delta O of C
+
+309
+00:30:34,970 --> 00:30:38,090
+أذكركم مش بده أنا أنا بده أصل يكون contradiction
+
+310
+00:30:38,090 --> 00:30:45,050
+يعني بده أصل لنقاط في المكان هذا تتحققش هذه معايا؟
+
+311
+00:30:46,850 --> 00:30:48,790
+بدي أسأل ال contradiction كيف أسأل ال
+
+312
+00:30:48,790 --> 00:30:53,210
+contradiction؟ بدي أسأل ألاقي نقاط في المنطقة هذه
+
+313
+00:30:53,210 --> 00:30:59,750
+و هذه لا تتحقق شوف الآن عندي هذا المقدار إيش ماله؟
+
+314
+00:30:59,750 --> 00:31:07,730
+موجب، مظبوط ولا لأ؟ ماشي، الآن اللي بدي أخلي اللي
+
+315
+00:31:07,730 --> 00:31:13,830
+هي F of X minus F of C تظل أكبر من 0لأن لو خلّيتها
+
+316
+00:31:13,830 --> 00:31:19,210
+أكبر من صفر بيصير F أصغر من صفر بيصير F of X لما
+
+317
+00:31:19,210 --> 00:31:22,030
+صير أصغر من صفر بيصير أصغر من F of C بتبطّل أش
+
+318
+00:31:22,030 --> 00:31:28,650
+مالها عبارة عن minimum بتخلي
+
+319
+00:31:28,650 --> 00:31:35,130
+هذا المقدار أصغر من أش من صفر بدون هذا أه؟ بيصير F
+
+320
+00:31:35,130 --> 00:31:41,120
+of X أصغر من F of C بيصير F of Z مش minimumواضح؟
+
+321
+00:31:41,120 --> 00:31:45,560
+طيب إيش اللي بده يخليلي هذا أصغر من 0 هذا المقدار
+
+322
+00:31:45,560 --> 00:31:52,560
+أصغر من 0 أني أضرب أعمل choose x بحيث أنه يكون هذا
+
+323
+00:31:52,560 --> 00:31:57,380
+سالب وإن هيكون سالب x minus c بختار اللي هي x
+
+324
+00:31:57,380 --> 00:32:01,680
+minus c بختار x وإن ما أقول بقول choose x element
+
+325
+00:32:01,680 --> 00:32:07,240
+أن c نقص دلتة وc فاشي الحال then
+
+326
+00:32:09,590 --> 00:32:15,310
+اللي هو لما اخترت الـ X هنا هيكون الـ X minus C
+
+327
+00:32:15,310 --> 00:32:20,570
+أصغر من 0 مدام صار الـ X minus C أصغر من 0 وهذا
+
+328
+00:32:20,570 --> 00:32:26,630
+أكبر من 0 معطى من التنتين مع بعض بيصير عند X minus
+
+329
+00:32:26,630 --> 00:32:37,630
+C في F of X minus F of C على X minus Cأصغر من 0،
+
+330
+00:32:37,630 --> 00:32:43,370
+اللي هو هذا في الواقع مين؟ هو عبارة عن F of X ناقص
+
+331
+00:32:43,370 --> 00:32:47,210
+F of C صار الـ F of X minus F of C، لأن هذا بتروح
+
+332
+00:32:47,210 --> 00:32:50,690
+محدد، لأنه مش سفر، بصير F of X ناقص F of C أصغر من
+
+333
+00:32:50,690 --> 00:32:57,150
+0، معناته صار F of X أصغر من F of C، هذا لمين؟
+
+334
+00:32:57,150 --> 00:33:02,050
+للنقطة X اللي في هذا الجوار، يعني اللي لجأت نقطة
+
+335
+00:33:02,050 --> 00:33:04,790
+في هذا الجوار، لا تحقق هذا
+
+336
+00:33:07,600 --> 00:33:15,160
+هذا contradiction طيب اللي ما وضحتلوش هذه خلّينا
+
+337
+00:33:15,160 --> 00:33:19,780
+نوضحها في الحالة التانية هذا في حالة مين أه في
+
+338
+00:33:19,780 --> 00:33:24,440
+prime و في c أشمالها أكبر من سفر الآن بدأ أقول
+
+339
+00:33:24,440 --> 00:33:31,000
+suppose that الحالة التانية كاس اتنينيعني اللي
+
+340
+00:33:31,000 --> 00:33:37,320
+بقوله في حالة فرضت F prime لا تساوي سفر هأصل دائما
+
+341
+00:33:37,320 --> 00:33:41,200
+لتناقض F prime أكبر من سفر حصل لتناقض وصلت لتناقض
+
+342
+00:33:41,200 --> 00:33:47,060
+والآن حالة F prime of C أصغر من سفر برضه حصل لمين؟
+
+343
+00:33:47,460 --> 00:33:51,860
+لطلاقط ماشي الحال الان ايش معناه f prime of c أكبر
+
+344
+00:33:51,860 --> 00:33:58,040
+من 0 بنفس الأسلوب limit f of x ناقص f of c على x
+
+345
+00:33:58,040 --> 00:34:03,860
+minus c as x بتروح لل c برضه ايش ماله أصغر من 0
+
+346
+00:34:03,860 --> 00:34:09,820
+إذا في جوار there exist v delta of x و باخد ال
+
+347
+00:34:09,820 --> 00:34:13,500
+delta اللي هي delta prime بقدر أخدها و أصغر يساوي
+
+348
+00:34:13,500 --> 00:34:20,950
+ال delta prime by such thatاللي هو f of x ناقص f
+
+349
+00:34:20,950 --> 00:34:27,310
+of c على x minus c أصغر من مين؟ من 0 الآن اللي
+
+350
+00:34:27,310 --> 00:34:31,430
+بيوصلني لتناقض هتلاقيها مش choosing x هنا و انا
+
+351
+00:34:31,430 --> 00:34:35,450
+هاختارها في الجهة التانية في الجهة بتشوف كيف لأن
+
+352
+00:34:35,450 --> 00:34:43,570
+بيقول choose x element in c و c زائد delta then
+
+353
+00:34:47,030 --> 00:34:54,130
+هيكون عندى الآن الـ X minus C إيش ماله أكبر من 0
+
+354
+00:34:54,130 --> 00:35:00,610
+واضح أه؟لأن هذا أكبر من صفر وهذا أكبر أصغر من صفر
+
+355
+00:35:00,610 --> 00:35:07,110
+ثم اللي هي F of X ناقص F of C اللي هي بتساوي X
+
+356
+00:35:07,110 --> 00:35:10,670
+minus C اللي هي أكبر من صفر في المقدار اللي هو F
+
+357
+00:35:10,670 --> 00:35:15,390
+of X ناقص F of C على X minus C اللي هو أصغر من صفر
+
+358
+00:35:15,390 --> 00:35:19,430
+حصل أصغر من صفر وأكبر من صفر حيكون أصغر من صفر
+
+359
+00:35:19,430 --> 00:35:26,680
+ومنه henceF of X أصغر من F of C لنقطة في هذا
+
+360
+00:35:26,680 --> 00:35:30,720
+الجوار اللي هو باخدها very close to C يعني معناته
+
+361
+00:35:30,720 --> 00:35:35,040
+هتكون في داخل هذا الجوار لجهة نقطة بحيث أنه F of C
+
+362
+00:35:35,040 --> 00:35:41,540
+أكبر من F of X which is a contradiction thereforeF
+
+363
+00:35:41,540 --> 00:35:47,240
+prime of C must equal zero إذن بيكون أثبتنا إن لو
+
+364
+00:35:47,240 --> 00:35:52,000
+كان في عندي local minimum عند ال interior point C
+
+365
+00:35:52,000 --> 00:35:59,200
+إذن اللي هي بتكون ال F prime of C بالساعة سفر طبعا
+
+366
+00:35:59,200 --> 00:36:04,660
+لاحظوا أنا كل الجوارات اللي أخدت هنا ال V Delta و
+
+367
+00:36:04,660 --> 00:36:09,010
+V Delta prime كل في داخل الintervalعشان هيك هو
+
+368
+00:36:09,010 --> 00:36:12,850
+طبعا هو كاتب تقاطع ال .. بكتب تقاطع ال subset من
+
+369
+00:36:12,850 --> 00:36:17,450
+ال interval لأن كل اللي بشتغله وين بشتغله؟ جوات ال
+
+370
+00:36:17,450 --> 00:36:25,510
+interval أي سؤال؟ اللي هو؟
+
+371
+00:36:25,510 --> 00:36:33,890
+تكمّل
+
+372
+00:36:33,890 --> 00:36:38,810
+يعني f of c أقل من f of xدقيقة بس هنكتب اللي
+
+373
+00:36:38,810 --> 00:36:45,870
+بتقوله عشان اللي بشوف تصويرنا و بسمع كل معاناه
+
+374
+00:36:45,870 --> 00:36:49,050
+أيوة
+
+375
+00:36:49,050 --> 00:36:54,330
+يا محمد قول أصغر
+
+376
+00:36:54,330 --> 00:37:02,390
+يسوي F of X لكل X في V Delta of Z F
+
+377
+00:37:02,390 --> 00:37:12,690
+of C معقص F of Xأصغر من 0 مش
+
+378
+00:37:12,690 --> 00:37:22,070
+مشكلة limit
+
+379
+00:37:22,070 --> 00:37:31,690
+f of x نقص f of c على x minus c لما x تروح ل c من
+
+380
+00:37:31,690 --> 00:37:36,360
+اليسارمعناته الـ X أكبر من الـ C إذاً هذه صارت
+
+381
+00:37:36,360 --> 00:37:41,080
+موجبة هذه موجبة و هذه موجبة ده بتكون أشماله أكبر
+
+382
+00:37:41,080 --> 00:37:48,060
+من سفر أكبر أو يساوي سفر similarly limit F of X
+
+383
+00:37:48,060 --> 00:37:54,380
+ناقص F of C على X minus C لما X تروح ل C من اليسار
+
+384
+00:37:54,380 --> 00:38:00,110
+اللي هو هذه اللي هي أصغر من سفروهذه تصبح أصغر أو
+
+385
+00:38:00,110 --> 00:38:06,970
+ساوى 0 ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+386
+00:38:06,970 --> 00:38:07,570
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+387
+00:38:07,570 --> 00:38:08,030
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+388
+00:38:08,030 --> 00:38:08,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+389
+00:38:08,130 --> 00:38:08,690
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+390
+00:38:08,690 --> 00:38:10,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+391
+00:38:10,510 --> 00:38:11,170
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+392
+00:38:11,170 --> 00:38:19,550
+.. ال .. ال .. ال ..F of X ناقص F of C على X minus
+
+393
+00:38:19,550 --> 00:38:24,130
+C as X بتروح للـ C exist إذا ال limit من اليمين
+
+394
+00:38:24,130 --> 00:38:26,010
+تساوي ال limit من اليسار مش ال continuity ال
+
+395
+00:38:26,010 --> 00:38:28,850
+differentiability إذا ال limit من اليمين تساوي ال
+
+396
+00:38:28,850 --> 00:38:32,610
+limit من اليسار هذا لا يمكن أن يحدث في هذه الحالة
+
+397
+00:38:32,610 --> 00:38:38,490
+إلا غير لما تكون كلام صحيح بدك تستخدم الصحيح بنفع
+
+398
+00:38:38,490 --> 00:38:42,210
+بنفع بنفع
+
+399
+00:38:45,000 --> 00:38:51,520
+بدونها .. بدونها .. بدونها بنفع اه
+
+400
+00:38:51,520 --> 00:38:55,380
+بنفع اه .. اه ما هو by contradiction هو انت لو ..
+
+401
+00:38:55,380 --> 00:38:58,200
+لو يعني لاحظت في ال .. في ال .. طبعا احنا ما
+
+402
+00:38:58,200 --> 00:39:00,220
+ساخدمناش limit من اليمين و limit من اليسار،
+
+403
+00:39:00,220 --> 00:39:08,700
+ساخدمنا ال limit مباشرة، بصير، بصير، فهم صحيحهو
+
+404
+00:39:08,700 --> 00:39:13,640
+الحل اللي انت بتعرفه و يعني خليني أقوله مرتاح له
+
+405
+00:39:13,640 --> 00:39:17,500
+هو الأسهل اه يعني انت ممكن تشوف هذا أسهل و هذا
+
+406
+00:39:17,500 --> 00:39:24,260
+أسهل كلام صحيح يلا اللي بعده الان corollary منيحي
+
+407
+00:39:24,260 --> 00:39:26,620
+محمد اللي بعده
+
+408
+00:39:33,180 --> 00:39:36,640
+corollary اللي ممكن حكيتها الـ corollary هذه أنا
+
+409
+00:39:36,640 --> 00:39:40,380
+اللي هي من المعلومات اللي قبل بشوية لو كانت ال
+
+410
+00:39:40,380 --> 00:39:44,420
+function f اللي هو has اللي هي f من I من I اللي
+
+411
+00:39:44,420 --> 00:39:47,980
+عندها continuous و non-interval and suppose that f
+
+412
+00:39:47,980 --> 00:39:51,420
+has a relative extremum of an interior point c of
+
+413
+00:39:51,420 --> 00:39:58,540
+I then either the derivative of f exists or f بسوة
+
+414
+00:39:58,540 --> 00:40:02,780
+سفرعادت صيغة للي قبل بشوية أنه لو كانت الـ
+
+415
+00:40:02,780 --> 00:40:08,720
+function عندي من I لعند R continuous وكانت اللي هي
+
+416
+00:40:08,720 --> 00:40:13,540
+الـ C interior point عندها relative maximum أو
+
+417
+00:40:13,540 --> 00:40:17,920
+relative minimum هذا لازم يعطينا أن الـ F prime يا
+
+418
+00:40:17,920 --> 00:40:21,860
+does not exist يا إما zero طبعا و هذي مباشرة لو
+
+419
+00:40:21,860 --> 00:40:28,150
+جلنا نفترض أن F prime existبنحصل عالميين على الـ 0
+
+420
+00:40:28,150 --> 00:40:32,190
+من النظرية اللي قبله شوية وهو المطلوب واضح نجي
+
+421
+00:40:32,190 --> 00:40:35,230
+للنظرية البعيدة اللي هي إيش اسمها النظرية المشهورة
+
+422
+00:40:35,230 --> 00:40:41,090
+اللي هي اسمها Rawls theorem Rawls theorem يا جماعة
+
+423
+00:40:41,090 --> 00:40:44,370
+طبعا مرت علينا في ال calculus ويمكن كمان صارت في
+
+424
+00:40:44,370 --> 00:40:49,690
+الثانوية يدرسوها النظرية طبعا معناها الهندسي كمان
+
+425
+00:40:49,690 --> 00:40:53,910
+بمر معاكم أنه لو كانت عند ال function is
+
+426
+00:40:53,910 --> 00:41:05,950
+continuousعلى F من A و B لعند R continuous on A و
+
+427
+00:41:05,950 --> 00:41:15,830
+B و differentiable on A و B open وعندي F of A .. F
+
+428
+00:41:15,830 --> 00:41:22,960
+of A هيها و F of B هيهابصير عندي معطيني كمان f of
+
+429
+00:41:22,960 --> 00:41:26,900
+a بساوي f of b ماعطينيهاش بساوي، بساوي سفر، لو
+
+430
+00:41:26,900 --> 00:41:30,260
+كانت بتساوي ثابت برضه بتظبط، بتكون نفسها، تعميم
+
+431
+00:41:30,260 --> 00:41:35,500
+بسيط لها ال f of a بساوي f of b بساوي سفر، بقوللي
+
+432
+00:41:35,500 --> 00:41:46,320
+إذا هالاجي نقطة then هذا معطى if this holds then
+
+433
+00:41:47,250 --> 00:41:52,110
+there exists C وحدة، تنتين، تلات، او .. المهم على
+
+434
+00:41:52,110 --> 00:41:55,790
+الأقل في واحدة there exists C المتل A و B such
+
+435
+00:41:55,790 --> 00:42:01,290
+that F prime of C بيساوز فماذا يعني؟ يعني بالله
+
+436
+00:42:01,290 --> 00:42:06,230
+بمعنى اخر نقطة C او اكثر في بين ال A و ال B بحيث
+
+437
+00:42:06,230 --> 00:42:11,390
+انه ميل المماس عندها او المماس اللي عندها بوازمين
+
+438
+00:42:11,390 --> 00:42:15,570
+محور السناد طبعا هنا في واحد هاي اتنين هاي تلاتة
+
+439
+00:42:16,090 --> 00:42:21,070
+طبعا حسب .. حسب الدالة اللي هو أكيد بتلاقي إذا
+
+440
+00:42:21,070 --> 00:42:26,130
+تحققت الشروط الأقل في نقطة عندها اللي هو المماس
+
+441
+00:42:26,130 --> 00:42:35,870
+بوازي محور السينات أي سؤال؟ ال proof ال proof برضه
+
+442
+00:42:35,870 --> 00:42:39,570
+احنا كنا أحيانا نبرهنه في ال calculus خلينا
+
+443
+00:42:39,570 --> 00:42:46,150
+نبرهنوها، أكيد هندرهنوها عنديلو كانت الـ F هي
+
+444
+00:42:46,150 --> 00:42:51,550
+الدالة الصفرية يعني F بتساوي 0 it is a trivial أنه
+
+445
+00:42:51,550 --> 00:42:54,390
+مش حلها جنوبها كل نقاطها الـ F prime of C هي إيش
+
+446
+00:42:54,390 --> 00:42:59,770
+بتتساوي؟ بتساوي 0 إذا ال case F بتساوي 0 is a
+
+447
+00:42:59,770 --> 00:43:07,590
+trivial case الآن case 2 case 1 الآن F ليست الدالة
+
+448
+00:43:07,590 --> 00:43:14,870
+الصفرية في الاحتمالين أنه بدأ عملها أن Fassumes
+
+449
+00:43:14,870 --> 00:43:25,310
+positive values الاحتمال التانوي F assumes
+
+450
+00:43:25,310 --> 00:43:33,730
+negative values أنا بدعي ان هذولا بيجيبن كل الحلال
+
+451
+00:43:34,430 --> 00:43:38,270
+لو كانت F assumes positive value ممكن تاخد
+
+452
+00:43:38,270 --> 00:43:40,830
+positive وتاخد negative وممكن تاخد positive لحالها
+
+453
+00:43:40,830 --> 00:43:46,250
+بظبط ولا لأ ال F assume negative values إذا هتاخد
+
+454
+00:43:46,250 --> 00:43:49,530
+حالة F assumes negative values لحالها أو negative
+
+455
+00:43:49,530 --> 00:43:56,780
+values مع مين؟ مع positive values واضح؟طيب، الآن
+
+456
+00:43:56,780 --> 00:44:00,520
+بدي أثبتلك في الحالة الأولى على طول هتطلع F prime
+
+457
+00:44:00,520 --> 00:44:06,700
+of C == 0 وفي الحالة التانية similarly، معايا؟الآن
+
+458
+00:44:06,700 --> 00:44:10,780
+في عندنا نظرية في تحليل واحد أو في الكالكولاست حتى
+
+459
+00:44:10,780 --> 00:44:16,640
+كنا نقول if F is continuous on a closed bounded
+
+460
+00:44:16,640 --> 00:44:22,640
+interval then it must attain its maximum and its
+
+461
+00:44:22,640 --> 00:44:28,140
+minimum in this absolute كمان in its interval،
+
+462
+00:44:28,140 --> 00:44:35,130
+مظبوط؟ يعني بمعنى آخرعندي بما أن F continuous على
+
+463
+00:44:35,130 --> 00:44:39,830
+closed bounded interval then its absolute maximum
+
+464
+00:44:39,830 --> 00:44:43,650
+and absolute minimum is attained here يعني بمعنى
+
+465
+00:44:43,650 --> 00:44:50,470
+أخر there exists C element in A وB such that F of
+
+466
+00:44:50,470 --> 00:44:55,900
+C هي ال maximumإيه في ال maximum يعني؟ يعني ال
+
+467
+00:44:55,900 --> 00:45:01,040
+supremum أو ال maximum لكل F of X حيث X وين موجودة
+
+468
+00:45:01,040 --> 00:45:08,400
+في ال A و ال B، مظبوط؟ إذا صارت عندي في C في ال A
+
+469
+00:45:08,400 --> 00:45:12,180
+و ال B بحيث أن F of C بالساوى ال supremum هذا ال
+
+470
+00:45:12,180 --> 00:45:17,780
+supremum يا جماعة أكيد A شماله أكبر strictly من A
+
+471
+00:45:18,660 --> 00:45:23,920
+من صفر ليش؟ لأن احنا تحت أي عنوان بنشتغل F assumes
+
+472
+00:45:23,920 --> 00:45:27,640
+positive values إذا في على أقل قيمة واحدة positive
+
+473
+00:45:27,640 --> 00:45:33,440
+إذا F of C هيكون strictly أكبر من مين؟ من صفر طيب
+
+474
+00:45:33,440 --> 00:45:41,920
+بقول برضه F of C صارت عبارة عن maximum point الـ C
+
+475
+00:45:41,920 --> 00:45:50,520
+مظبوط؟ هذا واحد اتنين الـ Cقطعاً لا هي الـ A ولا
+
+476
+00:45:50,520 --> 00:45:58,060
+هي الـ B ليش؟ لأنه بما أن أف of A بساوي أف of B
+
+477
+00:45:58,060 --> 00:46:06,240
+بساوي 0 إذا أكيد C هتكون نقطة داخلية لا هتكون الـ
+
+478
+00:46:06,240 --> 00:46:10,120
+A ولا هتكون الـ B إذا صار في عندي شغلتين إنه C
+
+479
+00:46:10,120 --> 00:46:16,880
+نقطة داخلية وC عندها maximumإذا وكانت وعندي ال F
+
+480
+00:46:16,880 --> 00:46:19,800
+is differentiable على ال A و ال B على ال open
+
+481
+00:46:19,800 --> 00:46:24,260
+interval إذا حسب النظرية اللي قبله شوية لازم تكون
+
+482
+00:46:24,260 --> 00:46:30,800
+F prime of C عشان تساوي ساو سفر then F prime of C
+
+483
+00:46:30,800 --> 00:46:40,530
+ساو سفر واضح أه طيب الآنالحالة الثانية F assumes
+
+484
+00:46:40,530 --> 00:46:44,670
+negative values مدام F assumes negative values إذا
+
+485
+00:46:44,670 --> 00:46:53,930
+ناقص الـ F assumes positive values صح ولا لا؟ الآن
+
+486
+00:46:53,930 --> 00:46:56,870
+اللي بنتبج على الـ F اللي فوق صار ينتبج على ناقص F
+
+487
+00:46:56,870 --> 00:46:57,390
+كله
+
+488
+00:47:05,040 --> 00:47:08,060
+differentiable على الـ A و الـ B و continuous على
+
+489
+00:47:08,060 --> 00:47:12,620
+الـ closed interval و هذا هيتحقق على مين بس؟ على
+
+490
+00:47:12,620 --> 00:47:19,480
+ناقص F إذا من ال case التانية ناقص F of C prime
+
+491
+00:47:19,480 --> 00:47:26,300
+هتساوي سفر أو بمعنى آخر F prime of C هيساوي سفر
+
+492
+00:47:26,300 --> 00:47:32,380
+for some C element in A و B هذه برهان ال roles
+
+493
+00:47:32,380 --> 00:47:45,410
+theoryأي سؤال اللي بعده الآن أوصلنا لإن نقدر الآن
+
+494
+00:47:45,410 --> 00:47:50,890
+نحكي عن اللي هو نظرية القيمة المتوسطة أو الـ Mean
+
+495
+00:47:50,890 --> 00:47:54,990
+Value Theorem نظرية القيمة المتوسطة أو الـ Mean
+
+496
+00:47:54,990 --> 00:47:57,510
+Value Theorem برضه
+
+497
+00:47:59,060 --> 00:48:03,900
+اللي هو مرت عليكم في calculus ألف و بتمر أيضًا في
+
+498
+00:48:03,900 --> 00:48:09,000
+اللي هو ملهجة ثانوية إيش ال mean value theorem؟ هي
+
+499
+00:48:09,000 --> 00:48:15,840
+عبارة عن تعميم لمين لل roles theorem إيش بتقول ال
+
+500
+00:48:15,840 --> 00:48:27,580
+mean value theorem؟ mean value theorem if F من A و
+
+501
+00:48:27,580 --> 00:48:38,570
+Bالعلب R is continuous and differentiable on A وB
+
+502
+00:48:38,570 --> 00:48:47,130
+then there exists C element in A وB such that F
+
+503
+00:48:47,130 --> 00:48:54,010
+prime of C سواء F of B ناقص F of A على B minus A
+
+504
+00:48:54,010 --> 00:48:57,590
+طبعا معناها الأهندسية برضه مارة عليكم خلّيني أقول
+
+505
+00:48:57,590 --> 00:49:05,120
+كمان مرةإيش اللي بتقوله النظرية؟ بتقول كمايا ليه؟
+
+506
+00:49:05,120 --> 00:49:14,860
+لإن مش مزايد بس ماشي
+
+507
+00:49:14,860 --> 00:49:22,960
+مفترض إن هي اللي عندي الـA وهي عند مين الـBالان F
+
+508
+00:49:22,960 --> 00:49:27,180
+of B نقص F of A على B minus A اللي هو عبارة عن ميل
+
+509
+00:49:27,180 --> 00:49:34,540
+عن ميل القاطع هذا ها .. هايه هذا اللي هو عبارة عن
+
+510
+00:49:34,540 --> 00:49:43,760
+النقطة B و F of B و هذا النقطة A و F of A طبعا ميل
+
+511
+00:49:43,760 --> 00:49:50,380
+القاطع زي ما انتوا عارفين هو F of B لهناناقص F of
+
+512
+00:49:50,380 --> 00:49:57,060
+A هذه فبكون هذا على اللي هو B كلها هذه ناقص A
+
+513
+00:49:57,060 --> 00:50:02,360
+فبكون اللي هو ميل القاطع هذا اللي هو F of B ناقص F
+
+514
+00:50:02,360 --> 00:50:06,900
+of A على B minus Aوالـ F prime of C اللي هو عبارة
+
+515
+00:50:06,900 --> 00:50:10,860
+عن إيش؟ عن ميل المماس عنده النقطة C يعني وكأنه
+
+516
+00:50:10,860 --> 00:50:14,400
+نظرية بتقولنا إنه لو كانت F is continuous على
+
+517
+00:50:14,400 --> 00:50:17,840
+closed interval A وB و differentiable على ال open
+
+518
+00:50:17,840 --> 00:50:22,340
+interval A وB بلاجي اللي هو مما .. وهي عند القاطع
+
+519
+00:50:22,340 --> 00:50:29,040
+هيه بلاجي مماس لدالة مماس واحد او اتنين او تلاتة
+
+520
+00:50:29,040 --> 00:50:37,560
+موازن مينيعني عند نقطة C بلاق اللي هو مماس يوازمين
+
+521
+00:50:37,560 --> 00:50:41,260
+.. يوازم القاطع في rule theorem كانت اللي هو ال A
+
+522
+00:50:41,260 --> 00:50:45,740
+و ال B صورة .. صورة انتحار على ال X axis فطبيعي ما
+
+523
+00:50:45,740 --> 00:50:49,980
+اللي هو قطح هو ال X axis من القاطع اللي هو سفر
+
+524
+00:50:50,790 --> 00:50:56,170
+فاهمين؟ فبكون اللي هو الـ F' اللي هو طبيعي موازي
+
+525
+00:50:56,170 --> 00:51:00,890
+أو صفر أو موازي للـ X-axis يعني بمعنى أخر والـ
+
+526
+00:51:00,890 --> 00:51:05,750
+theorem هي حالة خاصة من الـ mean value theorem
+
+527
+00:51:05,750 --> 00:51:12,490
+واضح؟ طيب، الآن ال proof ال proof طبعا أكيد هنعتمد
+
+528
+00:51:13,290 --> 00:51:16,690
+على اللي هو الـ mean على الـ Rolle's theorem في
+
+529
+00:51:16,690 --> 00:51:21,950
+الإثبات بدنا اللي هو نركب اللي هو الـ function
+
+530
+00:51:21,950 --> 00:51:27,210
+تكون بتحقق الـ mean value theorem و بتجيبلنا اللي
+
+531
+00:51:27,210 --> 00:51:33,750
+هي الصورة هذه لو أخدنا 5x بساوي f of x ناقص f of a
+
+532
+00:51:33,750 --> 00:51:38,110
+ناقص اللي هو المال اللي بديه f of b ناقص f of a
+
+533
+00:51:38,110 --> 00:51:45,970
+على b minus a مضروبةفي X minus A هلجيت بتشوف ليش
+
+534
+00:51:45,970 --> 00:51:52,910
+أخدنا الدالة الدالة الأن هذه لو جيت حسبة Phi of A
+
+535
+00:51:52,910 --> 00:51:57,630
+لها يعني consider this function Phi of A هيساوي F
+
+536
+00:51:57,630 --> 00:52:02,730
+of A نقص F of A سفر وA نقص A سفر فبصير بالسفر هذا
+
+537
+00:52:02,730 --> 00:52:10,040
+إذن بيساوي سفر لو جيت حسبة Phi of B5 of B هيصير 5
+
+538
+00:52:10,040 --> 00:52:14,280
+of B بيساوي F of B نقص F of A خليني عندك و B minus
+
+539
+00:52:14,280 --> 00:52:18,260
+A بتروح هذه محادي هذه ناقص لنفسها بيطلع برضه أياش
+
+540
+00:52:18,260 --> 00:52:23,000
+سفر إذا الأن 5 of A بيساوي 5 of B بيساوي سفر هاي
+
+541
+00:52:23,000 --> 00:52:27,600
+واحد اتنين عندي هذه الدالة is continuous على
+
+542
+00:52:27,600 --> 00:52:33,120
+closed bounded intervalوهذه ثوابت و X minus A X
+
+543
+00:52:33,120 --> 00:52:36,120
+minus A ده اللي خطية continuous وين مكان و
+
+544
+00:52:36,120 --> 00:52:39,520
+differentiable وين مكان إذا صارت هذه الدالة كلها
+
+545
+00:52:39,520 --> 00:52:43,360
+على بعض اللي هي A Phi of X is continuous وين مكان
+
+546
+00:52:43,360 --> 00:52:45,900
+بما فيها اللي .. ال .. ال .. ال .. ال .. ال .. ال
+
+547
+00:52:45,900 --> 00:52:46,040
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+548
+00:52:46,040 --> 00:52:46,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+549
+00:52:46,320 --> 00:52:46,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+550
+00:52:46,420 --> 00:52:48,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+551
+00:52:48,560 --> 00:52:48,600
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+552
+00:52:48,600 --> 00:52:49,020
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+553
+00:52:49,020 --> 00:52:49,700
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+554
+00:52:49,700 --> 00:52:50,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+555
+00:52:50,180 --> 00:52:50,420
+.. ال .. ال .. ال .. ال .. ال
+
+556
+00:52:59,650 --> 00:53:05,310
+و differentiable on a و b و أيضا اللي هو five a
+
+557
+00:53:05,310 --> 00:53:10,410
+بيساوي five b بيساوي سفر اذا .. اذا by Rolle's
+
+558
+00:53:10,410 --> 00:53:16,810
+theorem there exists c element in a و b such that
+
+559
+00:53:16,810 --> 00:53:22,230
+five prime of c ايش بتساويك؟ بتساوي سفر طيب سفر
+
+560
+00:53:22,230 --> 00:53:26,490
+يعني بتساوي five prime of c ايش five prime of c؟
+
+561
+00:53:26,490 --> 00:53:31,900
+خلينا نفرض لهناهي عبارة عن F prime of C مكان الـ
+
+562
+00:53:31,900 --> 00:53:36,840
+XC وهذه سفر وهذه اللي هي تفاضل الـ X وهذه سفر
+
+563
+00:53:36,840 --> 00:53:42,640
+طبعاً ضال الـ X هي شمالها واحد بصير ناقص F of B
+
+564
+00:53:42,640 --> 00:53:49,300
+فاهمين؟ F of A على B minus A هذا بيسوء سفر وهذا
+
+565
+00:53:49,300 --> 00:53:56,140
+يعني أن F prime of C بيسوء F of B ناقص F of A على
+
+566
+00:53:56,140 --> 00:54:06,450
+B minus Aوهو المطلوب، مظبوط؟ نيجي الآن لبعض
+
+567
+00:54:06,450 --> 00:54:14,290
+النتائج اللي احنا بستعملها كتير اللي
+
+568
+00:54:14,290 --> 00:54:20,630
+هي في الواقع برهانة عن طريق الـ Mean Value Theorem
+
+569
+00:54:20,630 --> 00:54:26,120
+النظرية اللي بتقول ليهاللي هي اللي باختصار بنقول
+
+570
+00:54:26,120 --> 00:54:33,900
+أنه لو كانت المشتقة الأولى لدالة بتساوي سفر إذن هي
+
+571
+00:54:33,900 --> 00:54:41,340
+اللي هتكون مين هي المشتقة الثابتة طيب نشوف بالظبط
+
+572
+00:54:41,340 --> 00:54:46,960
+أيش اللي بقوله بقولوا .. نفترض أن F continuous F
+
+573
+00:54:46,960 --> 00:54:53,280
+عبارة عن دالة من A و Bلعيد R continuous ماشي
+
+574
+00:54:53,280 --> 00:54:57,060
+continuous على closed اللي هو open closed bounded
+
+575
+00:54:57,060 --> 00:55:02,060
+interval الان او كانت differentiable و F
+
+576
+00:55:02,060 --> 00:55:08,080
+differentiable على ال A و ال B باشي الحال بالاضافة
+
+577
+00:55:08,080 --> 00:55:15,300
+معطيك and F prime of X بساوة سفر لكل X element in
+
+578
+00:55:15,300 --> 00:55:19,600
+A و B هذا بقوللي على بعضه then
+
+579
+00:55:22,250 --> 00:55:29,470
+then اللي هو f of x بساوي c لكل x element in a و b
+
+580
+00:55:29,470 --> 00:55:39,910
+for some c constant for some constant c طيب الآن
+
+581
+00:55:39,910 --> 00:55:46,370
+ال proof البرهانة عمبرا عن exercise صغير بسيط
+
+582
+00:55:46,370 --> 00:55:56,110
+نبرهنه مع بعض الآن خد xlet x element in a و b ماشي
+
+583
+00:55:56,110 --> 00:56:00,530
+و خلّينا ناخد ال x أكبر من مين من a يعني x في أين
+
+584
+00:56:00,530 --> 00:56:04,410
+موجود في ال open .. في ال half open interval من a
+
+585
+00:56:04,410 --> 00:56:11,610
+و b let x be fixed but arbitrary ماشي الآن بدي
+
+586
+00:56:11,610 --> 00:56:17,570
+أطبّق المي .. طبعا هي ال a و ال b هي ال a و هي ال
+
+587
+00:56:17,570 --> 00:56:21,960
+bوأخدت X أي نقطة هنا هنا .. هنا .. هنا .. هنا ..
+
+588
+00:56:21,960 --> 00:56:26,160
+هنا .. هنا .. حتى لو كانت ال .. إيش ال B إذا صارت
+
+589
+00:56:26,160 --> 00:56:36,020
+ال F عندي ال F صارت ال F continuous on اللي هو X و
+
+590
+00:56:36,020 --> 00:56:43,300
+B صح؟ continuous عليها دي أكيد و لا بناخدها على
+
+591
+00:56:43,300 --> 00:56:53,420
+الفترة A و X أه عشان A و Xو differentiable on a و
+
+592
+00:56:53,420 --> 00:57:01,100
+x صح ولا لأ اذا by الهو mean value theorem there
+
+593
+00:57:01,100 --> 00:57:09,660
+exist c element in a و x such that f prime of c
+
+594
+00:57:09,660 --> 00:57:21,390
+بساوي f of x ناقص f of a على x minus aصحيح؟ حيث C
+
+595
+00:57:21,390 --> 00:57:27,630
+في A و B طب احنا مدام C في A و X بين A و X و احنا
+
+596
+00:57:27,630 --> 00:57:31,830
+مفترضين ان F prime of X بيساوي صفر لكل X في A و B
+
+597
+00:57:31,830 --> 00:57:38,930
+معايا اه؟ اه، اذا هتصير هذا اشمالها صفر، اذا صارت
+
+598
+00:57:38,930 --> 00:57:46,680
+عندي F هذا بيساوي صفر، اذا صارت F of X بتساوي Fof
+
+599
+00:57:46,680 --> 00:57:53,220
+A لكل X وين موجودة الآن for all such X وهذه كانت X
+
+600
+00:57:53,220 --> 00:57:58,000
+fixed but arbitrary إذا صار F of X بيساوي F of A
+
+601
+00:57:58,000 --> 00:58:02,800
+لكل X في الفترة A و B بما فيها ميني الـ A لأنه
+
+602
+00:58:02,800 --> 00:58:12,520
+نفسها بتساوي إذا صارت عندي hence F is constant أي
+
+603
+00:58:12,520 --> 00:58:20,890
+سؤالطيب اللي بعدها corollary
+
+604
+00:58:20,890 --> 00:58:24,470
+الـ corollary برضه من الاشي المشهور اللي احنا
+
+605
+00:58:24,470 --> 00:58:29,190
+بنستخدمه اللي هو لو كان دالتين بحاجة عن الشروط
+
+606
+00:58:29,190 --> 00:58:34,910
+طبعا لأنها تفاضلن زي بعض إذن هيكون اللي هو هن نفس
+
+607
+00:58:34,910 --> 00:58:42,990
+الاشي بس باختلف عن بعض بالأكترين ثابت طيب الآن ال
+
+608
+00:58:42,990 --> 00:58:50,450
+corollary كما يليهالـ Corollary بتقول suppose that
+
+609
+00:58:50,450 --> 00:58:56,970
+F and G are continuous on I, A وB then that they
+
+610
+00:58:56,970 --> 00:59:01,190
+are differentiable on A وB يعني نفترض أن الدالتين
+
+611
+00:59:01,190 --> 00:59:05,230
+F وG continuous على ال closed اللي هي bounded
+
+612
+00:59:05,230 --> 00:59:08,910
+interval A وB وdifferentiable على ال open interval
+
+613
+00:59:08,910 --> 00:59:12,070
+A وBوالـ derivative للأولى بساوي ال derivative
+
+614
+00:59:12,070 --> 00:59:15,690
+للثانية عند كل نقطة من النقاط الـ A و الـ B إذا
+
+615
+00:59:15,690 --> 00:59:18,910
+there exists a constant C such that F بتساوي G
+
+616
+00:59:18,910 --> 00:59:25,350
+زائد H زائد C طبعا البرهان سهل و أكيد يمكن بعضكم
+
+617
+00:59:25,350 --> 00:59:34,390
+برهنه في راسه let H بتساوي F ناقص G مظبوط؟ الآن
+
+618
+00:59:34,390 --> 00:59:43,530
+thenF و G continuous إذن H is continuous on A و B
+
+619
+00:59:43,530 --> 00:59:51,210
+و أيضًا F و G differentiable على A و B and H is
+
+620
+00:59:51,210 --> 00:59:55,210
+differentiable on A و B moreover
+
+621
+00:59:57,700 --> 01:00:02,620
+عندي H برايم اللي هو بساوي F برايم نقص G برايم
+
+622
+01:00:02,620 --> 01:00:08,340
+طبعا عند ال X عند ال X of X of X of X بساوي صفر
+
+623
+01:00:08,340 --> 01:00:16,340
+لكل X موجودة في ال A و ال B then by the above
+
+624
+01:00:16,340 --> 01:00:20,300
+theorem اللي بنحكي عنها اللي هي theorem by theorem
+
+625
+01:00:20,300 --> 01:00:31,180
+625 Hof X بتساوي C for every X element in A وB and
+
+626
+01:00:31,180 --> 01:00:35,300
+hence F
+
+627
+01:00:35,300 --> 01:00:44,040
+of X بساوي G of X زاد some constant C
+
+628
+01:00:50,890 --> 01:00:54,570
+بكونوا احنا وصلنا لعين theorem 627 ان شاء الله
+
+629
+01:00:54,570 --> 01:01:01,010
+المرة القادمة بنكمل والسلام عليكم ورحمة الله
+
+630
+01:01:01,010 --> 01:01:01,670
+وبركاته
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ed0c92337235d517407b3aacf01ba0887fa3ad67
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_raw.json
@@ -0,0 +1 @@
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{"id": 46, "seek": 116555, "start": 1148.27, "end": 1165.55, "text": "there exist أي جوار آخر بتكون تسموه V Delta Prime أو V Delta of D such that يعني بنلاقي .. بنقول هذه النقطة في عندها relative minimum إذا كان لقينا جوار حواليها", "tokens": [15456, 2514, 36632, 10874, 2407, 9640, 19753, 34740, 39894, 30544, 6055, 38251, 2407, 3224, 691, 18183, 9655, 34051, 691, 18183, 295, 413, 1270, 300, 37495, 22653, 44945, 15040, 38436, 4386, 44945, 39648, 29538, 28239, 47432, 3660, 8978, 43242, 11296, 4972, 7285, 11933, 15730, 25961, 5296, 4587, 9957, 995, 10874, 2407, 9640, 11331, 2407, 6027, 1829, 11296], "avg_logprob": -0.23985745614035087, "compression_ratio": 1.3072625698324023, "no_speech_prob": 1.8477439880371094e-06, "words": [{"start": 1148.27, "end": 1148.71, "word": "there", "probability": 0.2462158203125}, {"start": 1148.71, "end": 1149.57, "word": " exist", "probability": 0.6259765625}, {"start": 1149.57, "end": 1150.69, "word": " أي", "probability": 0.81103515625}, {"start": 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1177.19, "end": 1177.67, "word": " القيم", "probability": 0.956787109375}, {"start": 1177.67, "end": 1177.91, "word": " اللي", "probability": 0.98486328125}, {"start": 1177.91, "end": 1178.67, "word": " حواليها", "probability": 0.90859375}, {"start": 1178.67, "end": 1180.73, "word": " يعني", "probability": 0.907958984375}, {"start": 1180.73, "end": 1181.45, "word": " اللي", "probability": 0.960205078125}, {"start": 1181.45, "end": 1181.79, "word": " هو", "probability": 0.9658203125}, {"start": 1181.79, "end": 1182.31, "word": " there", "probability": 0.44189453125}, {"start": 1182.31, "end": 1182.67, "word": " exists", "probability": 0.55078125}, {"start": 1182.67, "end": 1182.85, "word": " V", "probability": 0.7255859375}, {"start": 1182.85, "end": 1183.11, "word": " Delta", "probability": 0.7158203125}, {"start": 1183.11, "end": 1183.29, "word": " of", "probability": 0.8994140625}, {"start": 1183.29, "end": 1183.43, "word": " D", "probability": 0.9814453125}, {"start": 1183.43, "end": 1183.69, "word": " such", "probability": 0.90185546875}, {"start": 1183.69, "end": 1184.65, "word": " that", "probability": 0.9521484375}, {"start": 1184.65, "end": 1185.21, "word": " F", "probability": 0.85986328125}], "temperature": 1.0}, {"id": 48, "seek": 120297, "start": 1185.99, "end": 1202.97, "text": "of D أصغر أو ساوى F of X لكل X موجودة في V Delta of D فهذه نسميها نقطة صغيرة محلية وهذه نسميها نقطة عظمة محلية", "tokens": [2670, 413, 5551, 9381, 17082, 2288, 34051, 8608, 995, 2407, 7578, 479, 295, 1783, 5296, 28820, 1783, 3714, 29245, 23328, 3660, 8978, 691, 18183, 295, 413, 6156, 3224, 24192, 8717, 38251, 1829, 11296, 8717, 47432, 3660, 20328, 17082, 48923, 3714, 5016, 1211, 10632, 37037, 24192, 8717, 38251, 1829, 11296, 8717, 47432, 3660, 6225, 19913, 46007, 3714, 5016, 1211, 10632], "avg_logprob": -0.1214192741860946, "compression_ratio": 1.4015748031496063, "no_speech_prob": 5.829334259033203e-05, "words": [{"start": 1185.99, "end": 1186.29, "word": "of", 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0.919921875}, {"start": 1327.53, "end": 1327.95, "word": " الـlocal", "probability": 0.938232421875}, {"start": 1327.95, "end": 1328.25, "word": " minimum", "probability": 0.9658203125}, {"start": 1328.25, "end": 1329.15, "word": " عددها", "probability": 0.989990234375}, {"start": 1329.15, "end": 1329.57, "word": " محدود", "probability": 0.9886067708333334}, {"start": 1329.57, "end": 1330.21, "word": " وقليل", "probability": 0.9818115234375}, {"start": 1330.21, "end": 1330.93, "word": " بصير", "probability": 0.8572591145833334}, {"start": 1330.93, "end": 1331.49, "word": " السؤال", "probability": 0.99072265625}, {"start": 1331.49, "end": 1332.07, "word": " مقدور", "probability": 0.90478515625}, {"start": 1332.07, "end": 1332.37, "word": " عليه", "probability": 0.57861328125}], "temperature": 1.0}, {"id": 55, "seek": 134431, "start": 1332.89, "end": 1344.31, "text": "الان النظرية اللي بتتشرح علناها دي ايش النظرية بتقول بتقول ما يليه اللي بتقوله ال theorem اللي هي", "tokens": [6027, 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1367.9, "text": "حتى اسمها اللي هي interior extremum theorem interior extremum theorem يعني هنحكي عن ال interior point بتقولي نفترض إن C عبارة عن نقطة داخلية لمين ل some interval I C اللي هو إشمالة نقطة داخلية ل I ال interval اللي عندي", "tokens": [33753, 7578, 24525, 2304, 11296, 13672, 1829, 39896, 10636, 4040, 449, 20904, 10636, 4040, 449, 20904, 37495, 22653, 8032, 1863, 5016, 4117, 1829, 18871, 2423, 10636, 935, 39894, 39648, 1829, 8717, 5172, 2655, 43042, 36145, 383, 6225, 3555, 9640, 3660, 18871, 8717, 47432, 3660, 11778, 47283, 1211, 10632, 32767, 9957, 5296, 512, 15035, 286, 383, 13672, 1829, 31439, 11933, 8592, 2304, 6027, 3660, 8717, 47432, 3660, 11778, 47283, 1211, 10632, 5296, 286, 2423, 15035, 13672, 1829, 18871, 16254], "avg_logprob": -0.19363132722770113, "compression_ratio": 1.7486033519553073, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1345.56, "end": 1346.12, "word": "حتى", "probability": 0.945556640625}, {"start": 1346.12, "end": 1346.58, "word": 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0.9329427083333334}, {"start": 1461.84, "end": 1462.36, "word": " ..", "probability": 0.39306640625}, {"start": 1462.36, "end": 1462.7, "word": " minimum", "probability": 0.8623046875}], "temperature": 1.0}, {"id": 61, "seek": 148011, "start": 1463.33, "end": 1480.11, "text": "الآن هذه النظرية وكأنه بتحكيلنا في داخلها أن النقاط اللي بتكون داخلية واحتمال يكون عندها relative maximum و relative minimum نوعين يا f prime مش موجودة", "tokens": [6027, 148, 48506, 29538, 28239, 19913, 2288, 10632, 4032, 4117, 33456, 3224, 39894, 5016, 4117, 26895, 8315, 8978, 11778, 47283, 1211, 11296, 14739, 28239, 4587, 41193, 13672, 1829, 39894, 30544, 11778, 47283, 1211, 10632, 36764, 33753, 2304, 6027, 7251, 30544, 43242, 11296, 4972, 6674, 4032, 4972, 7285, 8717, 45367, 9957, 35186, 283, 5835, 37893, 3714, 29245, 23328, 3660], "avg_logprob": -0.14605401885711541, "compression_ratio": 1.478527607361963, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 1463.33, "end": 1463.93, "word": "الآن", 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"word": " واحتمال", "probability": 0.9266357421875}, {"start": 1474.45, "end": 1474.79, "word": " يكون", "probability": 0.98583984375}, {"start": 1474.79, "end": 1475.23, "word": " عندها", "probability": 0.996826171875}, {"start": 1475.23, "end": 1475.57, "word": " relative", "probability": 0.9443359375}, {"start": 1475.57, "end": 1476.07, "word": " maximum", "probability": 0.8310546875}, {"start": 1476.07, "end": 1476.33, "word": " و", "probability": 0.931640625}, {"start": 1476.33, "end": 1476.59, "word": " relative", "probability": 0.8583984375}, {"start": 1476.59, "end": 1477.13, "word": " minimum", "probability": 0.9833984375}, {"start": 1477.13, "end": 1477.79, "word": " نوعين", "probability": 0.8372395833333334}, {"start": 1477.79, "end": 1478.63, "word": " يا", "probability": 0.53076171875}, {"start": 1478.63, "end": 1478.87, "word": " f", "probability": 0.275146484375}, {"start": 1478.87, "end": 1479.23, "word": " prime", "probability": 0.486572265625}, {"start": 1479.23, "end": 1479.45, "word": " مش", "probability": 0.986328125}, {"start": 1479.45, "end": 1480.11, "word": " موجودة", "probability": 0.9930419921875}], "temperature": 1.0}, {"id": 62, "seek": 150697, "start": 1481.03, "end": 1506.97, "text": "أو الـ F' أيش بتساوي؟ بتساوي 0 لأنه إذا كانت F' موجودة وقفقلها relative maximum أو relative minimum وكانت النقطة داخلية لازم الـ F' أيش ما لها تساوي 0 ولاحظ هنا إن الحديث عن مين؟ عن النقاط الداخلية يعني من فحوة الحديث هنا بنجاوب على سؤالنا، هذه اللي بتجاوبنا على سؤالنا بتقول", "tokens": [10721, 2407, 2423, 39184, 479, 6, 36632, 8592, 39894, 3794, 995, 45865, 22807, 39894, 3794, 995, 45865, 1958, 5296, 33456, 3224, 11933, 15730, 25961, 2655, 479, 6, 3714, 29245, 23328, 3660, 4032, 4587, 5172, 4587, 1211, 11296, 4972, 6674, 34051, 4972, 7285, 4032, 41361, 2655, 28239, 47432, 3660, 11778, 47283, 1211, 10632, 5296, 31377, 2304, 2423, 39184, 479, 6, 36632, 8592, 19446, 5296, 11296, 6055, 3794, 995, 45865, 1958, 4032, 15040, 5016, 19913, 34105, 36145, 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1491.57, "word": " وكانت", "probability": 0.9733072916666666}, {"start": 1491.57, "end": 1491.91, "word": " النقطة", "probability": 0.7367757161458334}, {"start": 1491.91, "end": 1492.47, "word": " داخلية", "probability": 0.96826171875}, {"start": 1492.47, "end": 1493.15, "word": " لازم", "probability": 0.9591471354166666}, {"start": 1493.15, "end": 1493.29, "word": " الـ", "probability": 0.84423828125}, {"start": 1493.29, "end": 1493.45, "word": " F'", "probability": 0.90185546875}, {"start": 1493.79, "end": 1494.05, "word": " أيش", "probability": 0.87158203125}, {"start": 1494.05, "end": 1494.21, "word": " ما", "probability": 0.619140625}, {"start": 1494.21, "end": 1494.53, "word": " لها", "probability": 0.917236328125}, {"start": 1494.53, "end": 1495.29, "word": " تساوي", "probability": 0.93212890625}, {"start": 1495.29, "end": 1495.55, "word": " 0", "probability": 0.94970703125}, {"start": 1495.55, "end": 1496.15, "word": " ولاحظ", "probability": 0.86865234375}, {"start": 1496.15, "end": 1496.49, "word": " هنا", "probability": 0.9833984375}, {"start": 1496.49, "end": 1496.71, "word": " إن", "probability": 0.30810546875}, {"start": 1496.71, "end": 1498.11, "word": " الحديث", "probability": 0.8763020833333334}, {"start": 1498.11, "end": 1498.29, "word": " عن", "probability": 0.81005859375}, {"start": 1498.29, "end": 1498.69, "word": " مين؟", "probability": 0.6761067708333334}, {"start": 1498.69, "end": 1498.85, "word": " عن", "probability": 0.97509765625}, {"start": 1498.85, "end": 1499.45, "word": " النقاط", "probability": 0.9571940104166666}, {"start": 1499.45, "end": 1500.33, "word": " الداخلية", "probability": 0.9940185546875}, {"start": 1500.33, "end": 1501.29, "word": " يعني", "probability": 0.968505859375}, {"start": 1501.29, "end": 1501.67, "word": " من", "probability": 0.9619140625}, {"start": 1501.67, "end": 1502.19, "word": " فحوة", "probability": 0.942138671875}, {"start": 1502.19, "end": 1502.85, "word": " الحديث", "probability": 0.9931640625}, {"start": 1502.85, "end": 1503.29, "word": " هنا", "probability": 0.97314453125}, {"start": 1503.29, "end": 1504.47, "word": " بنجاوب", "probability": 0.9381103515625}, {"start": 1504.47, "end": 1504.63, "word": " على", "probability": 0.76904296875}, {"start": 1504.63, "end": 1505.23, "word": " سؤالنا،", "probability": 0.8673828125}, {"start": 1505.23, "end": 1505.49, "word": " هذه", "probability": 0.431396484375}, {"start": 1505.49, "end": 1505.61, "word": " اللي", "probability": 0.988525390625}, {"start": 1505.61, "end": 1506.11, "word": " بتجاوبنا", "probability": 0.97900390625}, {"start": 1506.11, "end": 1506.23, "word": " على", "probability": 0.875}, {"start": 1506.23, "end": 1506.55, "word": " سؤالنا", "probability": 0.9429931640625}, {"start": 1506.55, "end": 1506.97, "word": " بتقول", "probability": 0.901611328125}], "temperature": 1.0}, {"id": 63, "seek": 153038, "start": 1507.24, "end": 1530.38, "text": "اللي هو الـ relative maximum أو الـ relative minimum هتكون في أحد ثلاث مناطق يا F prime does not exist يا F prime بالساوية سفر يا end point واضح؟ أي سؤال؟ واضح أه؟ طيب، دي يجي تبرهن النظرية", "tokens": [6027, 20292, 31439, 2423, 39184, 4972, 6674, 34051, 2423, 39184, 4972, 7285, 8032, 2655, 30544, 8978, 5551, 24401, 38637, 1211, 5718, 104, 9154, 41193, 4587, 35186, 479, 5835, 775, 406, 2514, 35186, 479, 5835, 20666, 3794, 995, 2407, 10632, 8608, 5172, 2288, 35186, 917, 935, 4032, 46958, 5016, 22807, 36632, 8608, 33604, 6027, 22807, 4032, 46958, 5016, 5551, 3224, 22807, 23032, 1829, 3555, 12399, 11778, 1829, 7251, 7435, 1829, 6055, 26890, 3224, 1863, 28239, 19913, 2288, 10632], "avg_logprob": -0.20773236701885858, "compression_ratio": 1.4607329842931938, "no_speech_prob": 1.9073486328125e-06, "words": [{"start": 1507.24, "end": 1507.82, "word": "اللي", "probability": 0.704833984375}, {"start": 1507.82, "end": 1508.06, "word": " هو", "probability": 0.97607421875}, {"start": 1508.06, "end": 1508.66, "word": " الـ", "probability": 0.742919921875}, {"start": 1508.66, "end": 1508.98, "word": " relative", "probability": 0.80810546875}, {"start": 1508.98, "end": 1509.58, "word": " maximum", "probability": 0.953125}, {"start": 1509.58, "end": 1509.86, "word": " أو", "probability": 0.84521484375}, {"start": 1509.86, "end": 1509.98, "word": " الـ", "probability": 0.76904296875}, {"start": 1509.98, "end": 1510.2, "word": " relative", "probability": 0.9775390625}, {"start": 1510.2, "end": 1510.56, "word": " minimum", "probability": 0.9833984375}, {"start": 1510.56, "end": 1511.1, "word": " هتكون", "probability": 0.7933756510416666}, {"start": 1511.1, "end": 1511.28, "word": " في", "probability": 0.96826171875}, {"start": 1511.28, "end": 1511.48, "word": " أحد", "probability": 0.927978515625}, {"start": 1511.48, "end": 1511.8, "word": " ثلاث", "probability": 0.9642333984375}, {"start": 1511.8, "end": 1512.34, "word": " مناطق", "probability": 0.96826171875}, {"start": 1512.34, "end": 1513.16, "word": " يا", "probability": 0.6171875}, {"start": 1513.16, "end": 1513.88, "word": " F", "probability": 0.529296875}, {"start": 1513.88, "end": 1514.28, "word": " prime", "probability": 0.2744140625}, {"start": 1514.28, "end": 1514.5, "word": " does", "probability": 0.72314453125}, {"start": 1514.5, "end": 1514.7, "word": " not", "probability": 0.966796875}, {"start": 1514.7, "end": 1515.24, "word": " exist", "probability": 0.9501953125}, {"start": 1515.24, "end": 1516.0, "word": " يا", "probability": 0.75927734375}, {"start": 1516.0, "end": 1516.24, "word": " F", "probability": 0.98876953125}, {"start": 1516.24, "end": 1516.54, "word": " prime", "probability": 0.81201171875}, {"start": 1516.54, "end": 1516.94, "word": " بالساوية", "probability": 0.7162109375}, {"start": 1516.94, "end": 1517.36, "word": " سفر", "probability": 0.8170572916666666}, {"start": 1517.36, "end": 1518.06, "word": " يا", "probability": 0.57861328125}, {"start": 1518.06, "end": 1518.56, "word": " end", "probability": 0.7275390625}, {"start": 1518.56, "end": 1519.3, "word": " point", "probability": 0.634765625}, {"start": 1519.3, "end": 1522.0, "word": " واضح؟", "probability": 0.876953125}, {"start": 1522.0, "end": 1522.72, "word": " أي", "probability": 0.80224609375}, {"start": 1522.72, "end": 1524.96, "word": " سؤال؟", "probability": 0.9730224609375}, {"start": 1524.96, "end": 1526.04, "word": " واضح", "probability": 0.9871419270833334}, {"start": 1526.04, "end": 1527.18, "word": " أه؟", "probability": 0.6534016927083334}, {"start": 1527.18, "end": 1527.64, "word": " طيب،", "probability": 0.76947021484375}, {"start": 1527.64, "end": 1527.78, "word": " دي", "probability": 0.9208984375}, {"start": 1527.78, "end": 1527.96, "word": " يجي", "probability": 0.7312825520833334}, {"start": 1527.96, "end": 1528.4, "word": " تبرهن", "probability": 0.8951416015625}, {"start": 1528.4, "end": 1530.38, "word": " النظرية", "probability": 0.9403076171875}], "temperature": 1.0}, {"id": 64, "seek": 155839, "start": 1530.93, "end": 1558.39, "text": "الآن هو البروحان اللي مكتوب هنا we prove for the case that F has relative maximum at C هيه مكتوب أنا مابديش أبرهن ال maximum بتبرهنكم مين ال minimum إذا الآن بدنا نفترض نفترض ال proof خليني أكتب هنا ال proof بدي أفترض", "tokens": [6027, 148, 48506, 31439, 2423, 26890, 2407, 5016, 7649, 13672, 1829, 3714, 4117, 2655, 37746, 34105, 321, 7081, 337, 264, 1389, 300, 479, 575, 4972, 6674, 412, 383, 39896, 3224, 3714, 4117, 2655, 37746, 41850, 3714, 16758, 16254, 8592, 5551, 26890, 3224, 1863, 2423, 6674, 39894, 26890, 3224, 1863, 24793, 3714, 9957, 2423, 7285, 11933, 15730, 6024, 48506, 47525, 8315, 8717, 5172, 2655, 43042, 8717, 5172, 2655, 43042, 2423, 8177, 16490, 1211, 9957, 1829, 5551, 4117, 2655, 3555, 34105, 2423, 8177, 4724, 16254, 5551, 5172, 2655, 43042], "avg_logprob": -0.2745028402317654, "compression_ratio": 1.6927083333333333, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1530.93, "end": 1531.55, "word": "الآن", "probability": 0.71728515625}, {"start": 1531.55, "end": 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" has", "probability": 0.90869140625}, {"start": 1539.89, "end": 1540.29, "word": " relative", "probability": 0.90185546875}, {"start": 1540.29, "end": 1540.91, "word": " maximum", "probability": 0.94677734375}, {"start": 1540.91, "end": 1541.17, "word": " at", "probability": 0.50439453125}, {"start": 1541.17, "end": 1541.37, "word": " C", "probability": 0.61083984375}, {"start": 1541.37, "end": 1541.91, "word": " هيه", "probability": 0.3560791015625}, {"start": 1541.91, "end": 1542.41, "word": " مكتوب", "probability": 0.9825439453125}, {"start": 1542.41, "end": 1543.09, "word": " أنا", "probability": 0.767578125}, {"start": 1543.09, "end": 1543.51, "word": " مابديش", "probability": 0.70440673828125}, {"start": 1543.51, "end": 1543.95, "word": " أبرهن", "probability": 0.85986328125}, {"start": 1543.95, "end": 1544.05, "word": " ال", "probability": 0.84716796875}, {"start": 1544.05, "end": 1544.37, "word": " maximum", "probability": 0.939453125}, {"start": 1544.37, "end": 1545.15, "word": " بتبرهنكم", "probability": 0.7531494140625}, {"start": 1545.15, "end": 1545.49, "word": " مين", "probability": 0.5552978515625}, {"start": 1545.49, "end": 1546.03, "word": " ال", "probability": 0.8935546875}, {"start": 1546.03, "end": 1546.39, "word": " minimum", "probability": 0.97119140625}, {"start": 1546.39, "end": 1546.85, "word": " إذا", "probability": 0.7685546875}, {"start": 1546.85, "end": 1547.41, "word": " الآن", "probability": 0.761474609375}, {"start": 1547.41, "end": 1548.43, "word": " بدنا", "probability": 0.942138671875}, {"start": 1548.43, "end": 1549.81, "word": " نفترض", "probability": 0.9906005859375}, {"start": 1549.81, "end": 1551.73, "word": " نفترض", "probability": 0.9288330078125}, {"start": 1551.73, "end": 1551.89, "word": " ال", "probability": 0.182373046875}, {"start": 1551.89, "end": 1552.29, "word": " proof", "probability": 0.8857421875}, {"start": 1552.29, "end": 1552.69, "word": " خليني", "probability": 0.7745361328125}, {"start": 1552.69, "end": 1552.93, "word": " أكتب", "probability": 0.874267578125}, {"start": 1552.93, "end": 1553.29, "word": " هنا", "probability": 0.97705078125}, {"start": 1553.29, "end": 1554.23, "word": " ال", "probability": 0.72265625}, {"start": 1554.23, "end": 1554.79, "word": " proof", "probability": 0.98828125}, {"start": 1554.79, "end": 1557.87, "word": " بدي", "probability": 0.4412841796875}, {"start": 1557.87, "end": 1558.39, "word": " أفترض", "probability": 0.8985595703125}], "temperature": 1.0}, {"id": 65, "seek": 158812, "start": 1559.3, "end": 1588.12, "text": "C نقطة داخلية ونفترض إن F أشبهلها have a relative minimum relative maximum محلولة لأن suppose that F has a relative maximum at C element in I0 ماشي؟", "tokens": [34, 8717, 47432, 3660, 11778, 47283, 1211, 10632, 4032, 1863, 5172, 2655, 43042, 36145, 479, 5551, 8592, 3555, 3224, 1211, 11296, 362, 257, 4972, 7285, 4972, 6674, 3714, 5016, 1211, 12610, 3660, 5296, 33456, 7297, 300, 479, 575, 257, 4972, 6674, 412, 383, 4478, 294, 286, 15, 3714, 33599, 1829, 22807], "avg_logprob": -0.30618990843112653, "compression_ratio": 1.230263157894737, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1559.3, "end": 1559.76, "word": "C", "probability": 0.625}, {"start": 1559.76, "end": 1560.5, "word": " نقطة", "probability": 0.89697265625}, {"start": 1560.5, "end": 1561.18, "word": " داخلية", "probability": 0.9940185546875}, {"start": 1561.18, "end": 1562.6, "word": " ونفترض", "probability": 0.95107421875}, {"start": 1562.6, "end": 1562.76, "word": " إن", "probability": 0.2734375}, {"start": 1562.76, "end": 1563.0, "word": " F", "probability": 0.6982421875}, {"start": 1563.0, "end": 1563.84, "word": " أشبهلها", "probability": 0.7257080078125}, {"start": 1563.84, "end": 1564.56, "word": " have", "probability": 0.251708984375}, {"start": 1564.56, "end": 1564.82, "word": " a", "probability": 0.8427734375}, {"start": 1564.82, "end": 1565.14, "word": " relative", "probability": 0.9736328125}, {"start": 1565.14, "end": 1565.56, "word": " minimum", "probability": 0.7353515625}, {"start": 1565.56, "end": 1566.04, "word": " relative", "probability": 0.71826171875}, {"start": 1566.04, "end": 1566.42, "word": " maximum", "probability": 0.97802734375}, {"start": 1566.42, "end": 1568.02, "word": " محلولة", "probability": 0.8470703125}, {"start": 1568.02, "end": 1568.56, "word": " لأن", "probability": 0.3917236328125}, {"start": 1568.56, "end": 1569.46, "word": " suppose", "probability": 0.79736328125}, {"start": 1569.46, "end": 1572.64, "word": " that", "probability": 0.8896484375}, {"start": 1572.64, "end": 1574.32, "word": " F", "probability": 0.8720703125}, {"start": 1574.32, "end": 1576.08, "word": " has", "probability": 0.93798828125}, {"start": 1576.08, "end": 1577.2, "word": " a", "probability": 0.8193359375}, {"start": 1577.2, "end": 1578.0, "word": " relative", "probability": 0.9599609375}, {"start": 1578.0, "end": 1581.02, "word": " maximum", "probability": 0.9677734375}, {"start": 1581.02, "end": 1582.6, "word": " at", "probability": 0.9638671875}, {"start": 1582.6, "end": 1583.38, "word": " C", "probability": 0.8583984375}, {"start": 1583.38, "end": 1584.0, "word": " element", "probability": 0.83935546875}, {"start": 1584.0, "end": 1584.4, "word": " in", "probability": 0.59814453125}, {"start": 1584.4, "end": 1586.46, "word": " I0", "probability": 0.3023681640625}, {"start": 1586.46, "end": 1588.12, "word": " ماشي؟", "probability": 0.88427734375}], "temperature": 1.0}, {"id": 66, "seek": 160188, "start": 1597.0, "end": 1601.88, "text": "نعم نفترض إنها minimum لأن ال case تبعت ال maximum محلولة", "tokens": [1863, 25957, 8717, 5172, 2655, 43042, 36145, 11296, 7285, 5296, 33456, 2423, 1389, 6055, 3555, 34268, 2423, 6674, 3714, 5016, 1211, 12610, 3660], "avg_logprob": -0.359375, "compression_ratio": 1.011764705882353, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 1596.9999999999998, "end": 1597.6799999999998, "word": "نعم", "probability": 0.78125}, {"start": 1597.6799999999998, "end": 1598.36, "word": " نفترض", "probability": 0.6769866943359375}, {"start": 1598.36, "end": 1598.62, "word": " إنها", "probability": 0.639404296875}, {"start": 1598.62, "end": 1599.02, "word": " minimum", "probability": 0.85498046875}, {"start": 1599.02, "end": 1599.84, "word": " لأن", "probability": 0.671630859375}, {"start": 1599.84, "end": 1599.98, "word": " ال", "probability": 0.306396484375}, {"start": 1599.98, "end": 1600.28, "word": " case", "probability": 0.810546875}, {"start": 1600.28, "end": 1600.62, "word": " تبعت", "probability": 0.76904296875}, {"start": 1600.62, "end": 1600.74, "word": " ال", "probability": 0.4853515625}, {"start": 1600.74, "end": 1601.08, "word": " maximum", "probability": 0.95703125}, {"start": 1601.08, "end": 1601.88, "word": " محلولة", "probability": 0.97841796875}], "temperature": 1.0}, {"id": 67, "seek": 162266, "start": 1602.38, "end": 1622.66, "text": "واضح؟ الان لو كان F as relative extremum بدنا نصل الان extreme يابتكون maximum يابتكون minimum case ال maximum هي مكتوبة بتجروها لحالكوا نفس الفكرة ده أكتف بت mean F as a relative H minimum", "tokens": [2407, 46958, 5016, 22807, 2423, 7649, 45164, 25961, 479, 382, 4972, 4040, 449, 47525, 8315, 8717, 36520, 2423, 7649, 8084, 7251, 16758, 2655, 30544, 6674, 7251, 16758, 2655, 30544, 7285, 1389, 2423, 6674, 39896, 3714, 4117, 2655, 37746, 3660, 39894, 7435, 32887, 11296, 5296, 5016, 6027, 4117, 14407, 8717, 36178, 27188, 4117, 25720, 11778, 3224, 5551, 4117, 2655, 5172, 39894, 914, 479, 382, 257, 4972, 389, 7285], "avg_logprob": -0.3384650792269146, "compression_ratio": 1.5549132947976878, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1602.38, "end": 1603.62, "word": "واضح؟", "probability": 0.926513671875}, {"start": 1603.62, "end": 1604.12, "word": " الان", "probability": 0.53082275390625}, {"start": 1604.12, "end": 1605.72, "word": " لو", "probability": 0.68505859375}, {"start": 1605.72, "end": 1606.02, "word": " كان", "probability": 0.9755859375}, {"start": 1606.02, "end": 1606.26, "word": " F", "probability": 0.39501953125}, {"start": 1606.26, "end": 1606.46, "word": " as", "probability": 0.38671875}, {"start": 1606.46, "end": 1606.8, "word": " relative", "probability": 0.9169921875}, {"start": 1606.8, "end": 1607.86, "word": " extremum", "probability": 0.844970703125}, {"start": 1607.86, "end": 1608.78, "word": " بدنا", "probability": 0.7418212890625}, {"start": 1608.78, "end": 1609.14, "word": " نصل", "probability": 0.938232421875}, {"start": 1609.14, "end": 1610.18, "word": " الان", "probability": 0.804443359375}, {"start": 1610.18, "end": 1610.64, "word": " extreme", "probability": 0.285400390625}, {"start": 1610.64, "end": 1611.26, "word": " يابتكون", "probability": 0.74853515625}, {"start": 1611.26, "end": 1611.72, "word": " maximum", "probability": 0.93798828125}, {"start": 1611.72, "end": 1612.16, "word": " يابتكون", "probability": 0.9228515625}, {"start": 1612.16, "end": 1612.48, "word": " minimum", "probability": 0.9794921875}, {"start": 1612.48, "end": 1613.16, "word": " case", "probability": 0.77734375}, {"start": 1613.16, "end": 1613.32, "word": " ال", "probability": 0.458984375}, {"start": 1613.32, "end": 1613.76, "word": " maximum", "probability": 0.9765625}, {"start": 1613.76, "end": 1614.0, "word": " هي", "probability": 0.9228515625}, {"start": 1614.0, "end": 1614.5, "word": " مكتوبة", "probability": 0.94052734375}, {"start": 1614.5, "end": 1615.92, "word": " بتجروها", "probability": 0.6373291015625}, {"start": 1615.92, "end": 1616.44, "word": " لحالكوا", "probability": 0.802734375}, {"start": 1616.44, "end": 1617.62, "word": " نفس", "probability": 0.95263671875}, {"start": 1617.62, "end": 1618.64, "word": " الفكرة", "probability": 0.9736328125}, {"start": 1618.64, "end": 1619.34, "word": " ده", "probability": 0.21820068359375}, {"start": 1619.34, "end": 1619.62, "word": " أكتف", "probability": 0.578125}, {"start": 1619.62, "end": 1619.78, "word": " بت", "probability": 0.72705078125}, {"start": 1619.78, "end": 1620.1, "word": " mean", "probability": 0.71826171875}, {"start": 1620.1, "end": 1620.76, "word": " F", "probability": 0.796875}, {"start": 1620.76, "end": 1621.02, "word": " as", "probability": 0.89697265625}, {"start": 1621.02, "end": 1621.16, "word": " a", "probability": 0.7265625}, {"start": 1621.16, "end": 1621.44, "word": " relative", "probability": 0.9384765625}, {"start": 1621.44, "end": 1621.98, "word": " H", "probability": 0.395751953125}, {"start": 1621.98, "end": 1622.66, "word": " minimum", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 68, "seek": 165318, "start": 1623.54, "end": 1653.18, "text": "الآن بدي أفترض لك أن الـ F' أي شمالها لا تساوي صفر و أسألك لـ contradiction إذا الآن بدي أفترض لك و بدي أقول لك suppose that F prime of C لا تساوي أيش؟ صفر، ماشي الحال، إذا عندي two cases ال case الأول أن F prime of C أكبر من أيش؟", "tokens": [6027, 148, 48506, 4724, 16254, 5551, 5172, 2655, 43042, 5296, 4117, 14739, 2423, 39184, 479, 6, 36632, 13412, 2304, 6027, 11296, 20193, 6055, 3794, 995, 45865, 20328, 5172, 2288, 4032, 5551, 3794, 10721, 23275, 5296, 39184, 34937, 11933, 15730, 6024, 48506, 4724, 16254, 5551, 5172, 2655, 43042, 5296, 4117, 4032, 4724, 16254, 5551, 39648, 5296, 4117, 7297, 300, 479, 5835, 295, 383, 20193, 6055, 3794, 995, 45865, 36632, 8592, 22807, 20328, 5172, 2288, 12399, 3714, 33599, 1829, 21542, 6027, 12399, 11933, 15730, 18871, 16254, 732, 3331, 2423, 1389, 16247, 12610, 14739, 479, 5835, 295, 383, 5551, 4117, 26890, 9154, 36632, 8592, 22807], "avg_logprob": -0.2850424647331238, "compression_ratio": 1.7135922330097086, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1623.54, "end": 1624.22, "word": "الآن", "probability": 0.71337890625}, {"start": 1624.22, "end": 1625.02, "word": " بدي", "probability": 0.4896240234375}, {"start": 1625.02, "end": 1625.5, "word": " أفترض", "probability": 0.8516845703125}, {"start": 1625.5, "end": 1625.82, "word": " لك", "probability": 0.6610107421875}, {"start": 1625.82, "end": 1626.0, "word": " أن", "probability": 0.63427734375}, {"start": 1626.0, "end": 1626.16, "word": " الـ", "probability": 0.5091552734375}, {"start": 1626.16, "end": 1626.36, "word": " F'", "probability": 0.45703125}, {"start": 1626.76, "end": 1626.96, "word": " أي", "probability": 0.4482421875}, {"start": 1626.96, "end": 1627.7, "word": " شمالها", "probability": 0.8634033203125}, {"start": 1627.7, "end": 1628.36, "word": " لا", "probability": 0.51708984375}, {"start": 1628.36, "end": 1628.72, "word": " تساوي", "probability": 0.94140625}, {"start": 1628.72, "end": 1629.1, "word": " صفر", "probability": 0.7587076822916666}, {"start": 1629.1, "end": 1629.34, "word": " و", "probability": 0.8203125}, {"start": 1629.34, "end": 1629.7, "word": " أسألك", "probability": 0.822998046875}, {"start": 1629.7, "end": 1629.86, "word": " لـ", "probability": 0.40618896484375}, {"start": 1629.86, "end": 1630.32, "word": " contradiction", "probability": 0.72021484375}, {"start": 1630.32, "end": 1631.2, "word": " إذا", "probability": 0.655517578125}, {"start": 1631.2, "end": 1631.54, "word": " الآن", "probability": 0.58990478515625}, {"start": 1631.54, "end": 1631.7, "word": " بدي", "probability": 0.9296875}, {"start": 1631.7, "end": 1631.96, "word": " أفترض", "probability": 0.9598388671875}, {"start": 1631.96, "end": 1632.2, "word": " لك", "probability": 0.904541015625}, {"start": 1632.2, "end": 1632.28, "word": " و", "probability": 0.397216796875}, {"start": 1632.28, "end": 1632.38, "word": " بدي", "probability": 0.79296875}, {"start": 1632.38, "end": 1632.52, "word": " أقول", "probability": 0.988525390625}, {"start": 1632.52, "end": 1632.7, "word": " لك", "probability": 0.922119140625}, {"start": 1632.7, "end": 1633.56, "word": " suppose", "probability": 0.462158203125}, {"start": 1633.56, "end": 1635.88, "word": " that", "probability": 0.861328125}, {"start": 1635.88, "end": 1637.34, "word": " F", "probability": 0.74658203125}, {"start": 1637.34, "end": 1637.94, "word": " prime", "probability": 0.41748046875}, {"start": 1637.94, "end": 1638.26, "word": " of", "probability": 0.96533203125}, {"start": 1638.26, "end": 1638.78, "word": " C", "probability": 0.869140625}, {"start": 1638.78, "end": 1639.8, "word": " لا", "probability": 0.86376953125}, {"start": 1639.8, "end": 1640.38, "word": " تساوي", "probability": 0.98193359375}, {"start": 1640.38, "end": 1641.74, "word": " أيش؟", "probability": 0.59716796875}, {"start": 1641.74, "end": 1643.52, "word": " صفر،", "probability": 0.7703857421875}, {"start": 1643.52, "end": 1643.84, "word": " ماشي", "probability": 0.8723958333333334}, {"start": 1643.84, "end": 1644.34, "word": " الحال،", "probability": 0.7368977864583334}, {"start": 1644.34, "end": 1644.56, "word": " إذا", "probability": 0.913818359375}, {"start": 1644.56, "end": 1644.92, "word": " عندي", "probability": 0.814453125}, {"start": 1644.92, "end": 1645.12, "word": " two", "probability": 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"temperature": 1.0}, {"id": 69, "seek": 168204, "start": 1653.68, "end": 1682.04, "text": "من صفر ماشي الحال إذا الآن عندي limit f of x ناقص f of c على x minus c as x بتروح ل c أشماله اللي هو هذا f prime of c حسب المعطى إيش هيكون أكبر من صفر ماشي الحال طيب الآن مدام ال f prime of c أكبر من صفر", "tokens": [27842, 20328, 5172, 2288, 3714, 33599, 1829, 21542, 6027, 11933, 15730, 6024, 48506, 18871, 16254, 4948, 283, 295, 2031, 8717, 995, 4587, 9381, 283, 295, 269, 15844, 2031, 3175, 269, 382, 2031, 39894, 32887, 5016, 5296, 269, 5551, 8592, 2304, 6027, 3224, 13672, 1829, 31439, 23758, 283, 5835, 295, 269, 11331, 35457, 9673, 3615, 9566, 7578, 11933, 1829, 8592, 39896, 30544, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 3714, 33599, 1829, 21542, 6027, 23032, 1829, 3555, 6024, 48506, 3714, 3215, 10943, 2423, 283, 5835, 295, 269, 5551, 4117, 26890, 9154, 20328, 5172, 2288], "avg_logprob": -0.1963098448641757, "compression_ratio": 1.738888888888889, "no_speech_prob": 6.324052810668945e-05, 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"word": " f", "probability": 0.71533203125}, {"start": 2060.95, "end": 2061.17, "word": " of", "probability": 0.951171875}, {"start": 2061.17, "end": 2061.51, "word": " c", "probability": 0.64013671875}, {"start": 2061.51, "end": 2062.65, "word": " على", "probability": 0.5673828125}, {"start": 2062.65, "end": 2062.91, "word": " x", "probability": 0.91259765625}, {"start": 2062.91, "end": 2063.23, "word": " minus", "probability": 0.83349609375}, {"start": 2063.23, "end": 2063.49, "word": " c", "probability": 0.95849609375}, {"start": 2063.49, "end": 2063.87, "word": " أصغر", "probability": 0.8880615234375}, {"start": 2063.87, "end": 2064.07, "word": " من", "probability": 0.98828125}, {"start": 2064.07, "end": 2065.09, "word": " مين؟", "probability": 0.5852864583333334}, {"start": 2065.09, "end": 2065.41, "word": " من", "probability": 0.98046875}, {"start": 2065.41, "end": 2065.71, "word": " 0", "probability": 0.59716796875}, {"start": 2065.71, "end": 2067.17, "word": " الآن", "probability": 0.6885986328125}, {"start": 2067.17, "end": 2067.31, "word": " اللي", "probability": 0.94287109375}, {"start": 2067.31, "end": 2067.93, "word": " بيوصلني", "probability": 0.759814453125}, {"start": 2067.93, "end": 2068.59, "word": " لتناقض", "probability": 0.9298828125}, {"start": 2068.59, "end": 2069.23, "word": " هتلاقيها", "probability": 0.87958984375}, {"start": 2069.23, "end": 2069.49, "word": " مش", "probability": 0.884765625}, {"start": 2069.49, "end": 2069.99, "word": " choosing", "probability": 0.828125}, {"start": 2069.99, "end": 2070.39, "word": " x", "probability": 0.88720703125}, {"start": 2070.39, "end": 2070.77, "word": " هنا", "probability": 0.8916015625}, {"start": 2070.77, "end": 2071.33, "word": " و", "probability": 0.94384765625}, {"start": 2071.33, "end": 2071.43, "word": " انا", "probability": 0.39508056640625}, {"start": 2071.43, "end": 2072.27, "word": " هاختارها", "probability": 0.832958984375}, {"start": 2072.27, "end": 2072.87, "word": " في", "probability": 0.9541015625}, {"start": 2072.87, "end": 2073.19, "word": " الجهة", "probability": 0.9845377604166666}, {"start": 2073.19, "end": 2073.47, "word": " التانية", "probability": 0.9500325520833334}, {"start": 2073.47, "end": 2073.59, "word": " في", "probability": 0.1221923828125}, {"start": 2073.59, "end": 2073.85, "word": " الجهة", "probability": 0.8935546875}, {"start": 2073.85, "end": 2074.47, "word": " بتشوف", "probability": 0.7584635416666666}, {"start": 2074.47, "end": 2074.79, "word": " كيف", "probability": 0.9765625}, {"start": 2074.79, "end": 2075.45, "word": " لأن", "probability": 0.6796875}, {"start": 2075.45, "end": 2075.79, "word": " بيقول", "probability": 0.8924153645833334}, {"start": 2075.79, "end": 2077.17, "word": " choose", "probability": 0.87939453125}, {"start": 2077.17, "end": 2078.69, "word": " x", "probability": 0.85302734375}, {"start": 2078.69, "end": 2079.39, "word": " element", "probability": 0.84423828125}, {"start": 2079.39, "end": 2079.77, "word": " in", "probability": 0.89208984375}, {"start": 2079.77, "end": 2080.13, "word": " c", "probability": 0.63916015625}, {"start": 2080.13, "end": 2080.37, "word": " و", "probability": 0.9326171875}, {"start": 2080.37, "end": 2080.75, "word": " c", "probability": 0.75732421875}, {"start": 2080.75, "end": 2081.41, "word": " زائد", "probability": 0.79931640625}, {"start": 2081.41, "end": 2081.83, "word": " delta", "probability": 0.3720703125}, {"start": 2081.83, "end": 2083.57, "word": " then", "probability": 0.292724609375}], "temperature": 1.0}, {"id": 85, "seek": 209719, "start": 2087.03, "end": 2097.19, "text": "هيكون عندى الآن الـ X minus C إيش ماله أكبر من 0 واضح أه؟", "tokens": [3224, 1829, 30544, 43242, 7578, 6024, 48506, 2423, 39184, 1783, 3175, 383, 11933, 1829, 8592, 3714, 6027, 3224, 5551, 4117, 26890, 9154, 1958, 4032, 46958, 5016, 5551, 3224, 22807], "avg_logprob": -0.29244790474573773, "compression_ratio": 1.0108695652173914, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2087.03, "end": 2087.53, "word": "هيكون", "probability": 0.7618001302083334}, {"start": 2087.53, "end": 2087.93, "word": " عندى", "probability": 0.8251953125}, {"start": 2087.93, "end": 2088.31, "word": " الآن", "probability": 0.6416015625}, {"start": 2088.31, "end": 2088.71, "word": " الـ", "probability": 0.89306640625}, {"start": 2088.71, "end": 2088.97, "word": " X", "probability": 0.488037109375}, {"start": 2088.97, "end": 2089.41, "word": " minus", "probability": 0.33203125}, {"start": 2089.41, "end": 2089.99, "word": " C", "probability": 0.95556640625}, {"start": 2089.99, "end": 2091.25, "word": " إيش", "probability": 0.6885579427083334}, {"start": 2091.25, "end": 2091.79, "word": " ماله", "probability": 0.8185221354166666}, {"start": 2091.79, "end": 2093.71, "word": " أكبر", "probability": 0.8929036458333334}, {"start": 2093.71, "end": 2093.87, "word": " من", "probability": 0.9970703125}, {"start": 2093.87, "end": 2094.13, "word": " 0", "probability": 0.5087890625}, {"start": 2094.13, "end": 2096.75, "word": " واضح", "probability": 0.9441731770833334}, {"start": 2096.75, "end": 2097.19, "word": " أه؟", "probability": 0.7765299479166666}], "temperature": 1.0}, {"id": 86, "seek": 212087, "start": 2097.71, "end": 2120.87, "text": "لأن هذا أكبر من صفر وهذا أكبر أصغر من صفر ثم اللي هي F of X ناقص F of C اللي هي بتساوي X minus C اللي هي أكبر من صفر في المقدار اللي هو F of X ناقص F of C على X minus C اللي هو أصغر من صفر حصل أصغر من صفر وأكبر من صفر حيكون أصغر من صفر ومنه hence", "tokens": [1211, 33456, 23758, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 37037, 15730, 5551, 4117, 26890, 5551, 9381, 17082, 2288, 9154, 20328, 5172, 2288, 38637, 2304, 13672, 1829, 39896, 479, 295, 1783, 8717, 995, 4587, 9381, 479, 295, 383, 13672, 1829, 39896, 39894, 3794, 995, 45865, 1783, 3175, 383, 13672, 1829, 39896, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 8978, 9673, 28543, 9640, 13672, 1829, 31439, 479, 295, 1783, 8717, 995, 4587, 9381, 479, 295, 383, 15844, 1783, 3175, 383, 13672, 1829, 31439, 5551, 9381, 17082, 2288, 9154, 20328, 5172, 2288, 11331, 36520, 5551, 9381, 17082, 2288, 9154, 20328, 5172, 2288, 36725, 4117, 26890, 9154, 20328, 5172, 2288, 11331, 1829, 30544, 5551, 9381, 17082, 2288, 9154, 20328, 5172, 2288, 4032, 27842, 3224, 16678], "avg_logprob": -0.1416412594357157, "compression_ratio": 2.4171779141104293, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 2097.71, "end": 2098.11, "word": "لأن", "probability": 0.47332763671875}, {"start": 2098.11, "end": 2098.35, "word": " هذا", "probability": 0.426025390625}, {"start": 2098.35, "end": 2098.69, "word": " أكبر", "probability": 0.95263671875}, {"start": 2098.69, "end": 2098.85, "word": " من", "probability": 0.9912109375}, {"start": 2098.85, "end": 2099.15, "word": " صفر", "probability": 0.7601725260416666}, {"start": 2099.15, "end": 2099.43, "word": " وهذا", "probability": 0.786865234375}, {"start": 2099.43, "end": 2099.71, "word": " أكبر", "probability": 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0.95654296875}, {"start": 2105.07, "end": 2105.35, "word": " C", "probability": 0.92822265625}, {"start": 2105.35, "end": 2105.55, "word": " اللي", "probability": 0.795654296875}, {"start": 2105.55, "end": 2105.77, "word": " هي", "probability": 0.78466796875}, {"start": 2105.77, "end": 2106.49, "word": " بتساوي", "probability": 0.9388427734375}, {"start": 2106.49, "end": 2107.11, "word": " X", "probability": 0.88232421875}, {"start": 2107.11, "end": 2107.47, "word": " minus", "probability": 0.82421875}, {"start": 2107.47, "end": 2107.75, "word": " C", "probability": 0.9287109375}, {"start": 2107.75, "end": 2107.95, "word": " اللي", "probability": 0.963623046875}, {"start": 2107.95, "end": 2108.09, "word": " هي", "probability": 0.9326171875}, {"start": 2108.09, "end": 2108.43, "word": " أكبر", "probability": 0.9752604166666666}, {"start": 2108.43, "end": 2108.63, "word": " من", "probability": 0.99853515625}, {"start": 2108.63, "end": 2109.01, "word": " صفر", "probability": 0.986328125}, {"start": 2109.01, "end": 2109.45, "word": " في", "probability": 0.8291015625}, {"start": 2109.45, "end": 2110.07, "word": " المقدار", "probability": 0.9840494791666666}, {"start": 2110.07, "end": 2110.23, "word": " اللي", "probability": 0.96484375}, {"start": 2110.23, "end": 2110.41, "word": " هو", "probability": 0.98046875}, {"start": 2110.41, "end": 2110.67, "word": " F", "probability": 0.939453125}, {"start": 2110.67, "end": 2110.91, "word": " of", "probability": 0.96337890625}, {"start": 2110.91, "end": 2111.25, "word": " X", "probability": 0.99755859375}, {"start": 2111.25, "end": 2111.79, "word": " ناقص", "probability": 0.9915771484375}, {"start": 2111.79, "end": 2112.09, "word": " F", "probability": 0.97509765625}, {"start": 2112.09, "end": 2112.31, "word": " of", "probability": 0.97412109375}, {"start": 2112.31, "end": 2112.63, "word": " C", "probability": 0.9931640625}, {"start": 2112.63, "end": 2113.29, "word": " على", "probability": 0.74755859375}, {"start": 2113.29, "end": 2113.59, "word": " X", "probability": 0.98388671875}, {"start": 2113.59, "end": 2113.97, "word": " minus", "probability": 0.9873046875}, {"start": 2113.97, "end": 2114.25, "word": " C", "probability": 0.994140625}, {"start": 2114.25, "end": 2114.37, "word": " اللي", "probability": 0.98291015625}, {"start": 2114.37, "end": 2114.53, "word": " هو", "probability": 0.98779296875}, {"start": 2114.53, "end": 2114.91, "word": " أصغر", "probability": 0.9892578125}, {"start": 2114.91, "end": 2115.09, "word": " من", "probability": 0.998046875}, {"start": 2115.09, "end": 2115.39, "word": " صفر", "probability": 0.9833984375}, {"start": 2115.39, "end": 2115.79, "word": " حصل", "probability": 0.73876953125}, {"start": 2115.79, "end": 2116.17, "word": " أصغر", "probability": 0.988037109375}, {"start": 2116.17, "end": 2116.33, "word": " من", "probability": 0.9970703125}, {"start": 2116.33, "end": 2116.55, "word": " صفر", "probability": 0.9827473958333334}, {"start": 2116.55, "end": 2116.91, "word": " وأكبر", "probability": 0.9137369791666666}, {"start": 2116.91, "end": 2117.07, "word": " من", "probability": 0.9970703125}, {"start": 2117.07, "end": 2117.35, "word": " صفر", "probability": 0.9716796875}, {"start": 2117.35, "end": 2117.65, "word": " حيكون", "probability": 0.8121744791666666}, {"start": 2117.65, "end": 2118.31, "word": " أصغر", "probability": 0.9896240234375}, {"start": 2118.31, "end": 2118.99, "word": " من", "probability": 0.99609375}, {"start": 2118.99, "end": 2119.43, "word": " صفر", "probability": 0.9895833333333334}, {"start": 2119.43, "end": 2120.39, "word": " ومنه", "probability": 0.81689453125}, {"start": 2120.39, "end": 2120.87, "word": " hence", "probability": 0.70263671875}], "temperature": 1.0}, {"id": 87, "seek": 213950, "start": 2121.84, "end": 2139.5, "text": "F of X أصغر من F of C لنقطة في هذا الجوار اللي هو باخدها very close to C يعني معناته هتكون في داخل هذا الجوار لجهة نقطة بحيث أنه F of C أكبر من F of X which is a contradiction therefore", "tokens": 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"probability": 0.983642578125}, {"start": 2628.59, "end": 2629.13, "word": " أو", "probability": 0.94384765625}, {"start": 2629.13, "end": 2629.53, "word": " negative", "probability": 0.93603515625}, {"start": 2629.53, "end": 2630.13, "word": " values", "probability": 0.96630859375}, {"start": 2630.13, "end": 2630.43, "word": " مع", "probability": 0.9912109375}, {"start": 2630.43, "end": 2631.35, "word": " مين؟", "probability": 0.7960611979166666}, {"start": 2631.35, "end": 2631.65, "word": " مع", "probability": 0.97802734375}, {"start": 2631.65, "end": 2632.73, "word": " positive", "probability": 0.89013671875}, {"start": 2632.73, "end": 2633.45, "word": " values", "probability": 0.96484375}, {"start": 2633.45, "end": 2634.49, "word": " واضح؟", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 107, "seek": 264530, "start": 2635.6, "end": 2645.3, "text": "طيب، الآن بدي أثبتلك في الحالة الأولى على طول هتطلع F prime of C == 0 وفي الحالة التانية similarly، معايا؟", "tokens": 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" الأولى", "probability": 0.9920247395833334}, {"start": 2639.32, "end": 2639.5, "word": " على", "probability": 0.64892578125}, {"start": 2639.5, "end": 2639.72, "word": " طول", "probability": 0.99609375}, {"start": 2639.72, "end": 2640.12, "word": " هتطلع", "probability": 0.91513671875}, {"start": 2640.12, "end": 2640.26, "word": " F", "probability": 0.496826171875}, {"start": 2640.26, "end": 2640.52, "word": " prime", "probability": 0.25390625}, {"start": 2640.52, "end": 2640.7, "word": " of", "probability": 0.94873046875}, {"start": 2640.7, "end": 2640.92, "word": " C", "probability": 0.8125}, {"start": 2640.92, "end": 2641.22, "word": " ==", "probability": 0.00954437255859375}, {"start": 2641.22, "end": 2641.56, "word": " 0", "probability": 0.90673828125}, {"start": 2641.56, "end": 2642.06, "word": " وفي", "probability": 0.842041015625}, {"start": 2642.06, "end": 2642.4, "word": " الحالة", "probability": 0.9910481770833334}, {"start": 2642.4, "end": 2642.86, "word": " التانية", 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"seek": 281739, "start": 2798.75, "end": 2817.39, "text": "الحالة الثانية F assumes negative values مدام F assumes negative values إذا ناقص الـ F assumes positive values صح ولا لا؟ الآن اللي بنتبج على الـ F اللي فوق صار ينتبج على ناقص F كله", "tokens": [6027, 5016, 6027, 3660, 6024, 104, 7649, 10632, 479, 37808, 3671, 4190, 3714, 3215, 10943, 479, 37808, 3671, 4190, 11933, 15730, 8717, 995, 4587, 9381, 2423, 39184, 479, 37808, 3353, 4190, 20328, 5016, 49429, 20193, 22807, 6024, 48506, 13672, 1829, 4724, 29399, 3555, 7435, 15844, 2423, 39184, 479, 13672, 1829, 6156, 30543, 20328, 9640, 7251, 29399, 3555, 7435, 15844, 8717, 995, 4587, 9381, 479, 28242, 3224], "avg_logprob": -0.17490671108018108, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 2798.75, "end": 2799.37, "word": "الحالة", "probability": 0.96875}, {"start": 2799.37, "end": 2799.75, "word": " الثانية", "probability": 0.90771484375}, {"start": 2799.75, "end": 2800.01, "word": " F", 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{"start": 3061.21, "end": 3061.39, "word": " هي", "probability": 0.8134765625}, {"start": 3061.39, "end": 3061.65, "word": " حالة", "probability": 0.9920247395833334}, {"start": 3061.65, "end": 3062.65, "word": " خاصة", "probability": 0.98046875}, {"start": 3062.65, "end": 3063.23, "word": " من", "probability": 0.94482421875}, {"start": 3063.23, "end": 3063.35, "word": " الـ", "probability": 0.604248046875}, {"start": 3063.35, "end": 3063.49, "word": " mean", "probability": 0.515625}, {"start": 3063.49, "end": 3063.99, "word": " value", "probability": 0.96337890625}, {"start": 3063.99, "end": 3065.75, "word": " theorem", "probability": 0.78515625}, {"start": 3065.75, "end": 3067.55, "word": " واضح؟", "probability": 0.82427978515625}, {"start": 3067.55, "end": 3068.51, "word": " طيب،", "probability": 0.884521484375}, {"start": 3068.51, "end": 3069.09, "word": " الآن", "probability": 0.7152099609375}, {"start": 3069.09, "end": 3069.23, "word": " ال", "probability": 0.438720703125}, 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"probability": 0.69122314453125}, {"start": 3508.75, "end": 3508.87, "word": " عن", "probability": 0.2437744140625}, {"start": 3508.87, "end": 3509.19, "word": " الشروط", "probability": 0.8562825520833334}, {"start": 3509.19, "end": 3509.47, "word": " طبعا", "probability": 0.9708251953125}, {"start": 3509.47, "end": 3510.19, "word": " لأنها", "probability": 0.6463216145833334}, {"start": 3510.19, "end": 3511.13, "word": " تفاضلن", "probability": 0.84443359375}, {"start": 3511.13, "end": 3511.35, "word": " زي", "probability": 0.982421875}, {"start": 3511.35, "end": 3511.75, "word": " بعض", "probability": 0.998046875}, {"start": 3511.75, "end": 3512.89, "word": " إذن", "probability": 0.7105305989583334}, {"start": 3512.89, "end": 3513.49, "word": " هيكون", "probability": 0.812744140625}, {"start": 3513.49, "end": 3513.69, "word": " اللي", "probability": 0.978271484375}, {"start": 3513.69, "end": 3514.07, "word": " هو", "probability": 0.98486328125}, {"start": 3514.07, "end": 3514.57, "word": " هن", "probability": 0.610107421875}, {"start": 3514.57, "end": 3514.91, "word": " نفس", "probability": 0.989013671875}, {"start": 3514.91, "end": 3515.29, "word": " الاشي", "probability": 0.96484375}, {"start": 3515.29, "end": 3515.47, "word": " بس", "probability": 0.989501953125}, {"start": 3515.47, "end": 3515.87, "word": " باختلف", "probability": 0.7579345703125}, {"start": 3515.87, "end": 3516.07, "word": " عن", "probability": 0.6435546875}, {"start": 3516.07, "end": 3516.97, "word": " بعض", "probability": 0.993896484375}, {"start": 3516.97, "end": 3517.67, "word": " بالأكترين", "probability": 0.7668050130208334}, {"start": 3517.67, "end": 3518.23, "word": " ثابت", "probability": 0.91259765625}, {"start": 3518.23, "end": 3520.67, "word": " طيب", "probability": 0.7991536458333334}, {"start": 3520.67, "end": 3521.15, "word": " الآن", "probability": 0.736083984375}, {"start": 3521.15, "end": 3522.99, "word": " ال", "probability": 0.9541015625}, {"start": 3522.99, "end": 3523.57, "word": " corollary", "probability": 0.8095703125}, {"start": 3523.57, "end": 3524.01, "word": " كما", "probability": 0.857666015625}, {"start": 3524.01, "end": 3524.49, "word": " يليه", "probability": 0.94140625}], "temperature": 1.0}, {"id": 141, "seek": 354943, "start": 3526.33, "end": 3549.43, "text": "الـ Corollary بتقول suppose that F and G are continuous on I, A وB then that they are differentiable on A وB يعني نفترض أن الدالتين F وG continuous على ال closed اللي هي bounded interval A وB وdifferentiable على ال open interval A وB", "tokens": [6027, 39184, 3925, 1833, 822, 39894, 39648, 7297, 300, 479, 293, 460, 366, 10957, 322, 286, 11, 316, 4032, 33, 550, 300, 436, 366, 819, 9364, 322, 316, 4032, 33, 37495, 22653, 8717, 5172, 2655, 43042, 14739, 32748, 6027, 2655, 9957, 479, 4032, 38, 10957, 15844, 2423, 5395, 13672, 1829, 39896, 37498, 15035, 316, 4032, 33, 4032, 67, 15790, 9364, 15844, 2423, 1269, 15035, 316, 4032, 33], "avg_logprob": -0.2022058751214953, 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و الـ B إذا there exists a constant C such that F بتساوي G زائد H زائد C طبعا البرهان سهل و أكيد يمكن بعضكم برهنه في راسه let H بتساوي F ناقص G مظبوط؟ الآن then", "tokens": [2407, 6027, 39184, 13760, 24976, 10721, 12610, 7578, 4724, 3794, 995, 45865, 2423, 13760, 24976, 12984, 7649, 10632, 43242, 28242, 8717, 47432, 3660, 9154, 28239, 4587, 41193, 2423, 39184, 316, 4032, 2423, 39184, 363, 11933, 15730, 456, 8198, 257, 5754, 383, 1270, 300, 479, 4724, 2655, 3794, 995, 45865, 460, 30767, 16373, 3215, 389, 30767, 16373, 3215, 383, 23032, 3555, 3615, 995, 2423, 26890, 3224, 7649, 8608, 3224, 1211, 4032, 5551, 4117, 25708, 7251, 43020, 45030, 11242, 24793, 4724, 2288, 3224, 1863, 3224, 8978, 12602, 32277, 3224, 718, 389, 4724, 2655, 3794, 995, 45865, 479, 8717, 995, 4587, 9381, 460, 3714, 19913, 3555, 2407, 9566, 22807, 6024, 48506, 550], "avg_logprob": -0.2410511404275894, "compression_ratio": 1.5381355932203389, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 3550.11, "end": 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G", "probability": 0.62841796875}, {"start": 3577.37, "end": 3578.11, "word": " continuous", "probability": 0.6259765625}, {"start": 3578.11, "end": 3578.57, "word": " إذن", "probability": 0.5338541666666666}, {"start": 3578.57, "end": 3578.97, "word": " H", "probability": 0.87353515625}, {"start": 3578.97, "end": 3579.53, "word": " is", "probability": 0.7978515625}, {"start": 3579.53, "end": 3581.11, "word": " continuous", "probability": 0.9150390625}, {"start": 3581.11, "end": 3582.35, "word": " on", "probability": 0.91162109375}, {"start": 3582.35, "end": 3582.89, "word": " A", "probability": 0.91357421875}, {"start": 3582.89, "end": 3583.27, "word": " و", "probability": 0.95556640625}, {"start": 3583.27, "end": 3583.53, "word": " B", "probability": 0.517578125}, {"start": 3583.53, "end": 3584.47, "word": " و", "probability": 0.69091796875}, {"start": 3584.47, "end": 3585.05, "word": " أيضًا", "probability": 0.8682861328125}, {"start": 3585.05, "end": 3585.65, "word": " F", "probability": 0.88916015625}, {"start": 3585.65, "end": 3585.83, "word": " و", "probability": 0.98095703125}, {"start": 3585.83, "end": 3585.93, "word": " G", "probability": 0.95654296875}, {"start": 3585.93, "end": 3586.83, "word": " differentiable", "probability": 0.859375}, {"start": 3586.83, "end": 3587.23, "word": " على", "probability": 0.73388671875}, {"start": 3587.23, "end": 3587.43, "word": " A", "probability": 0.8828125}, {"start": 3587.43, "end": 3587.51, "word": " و", "probability": 0.98583984375}, {"start": 3587.51, "end": 3587.83, "word": " B", "probability": 0.814453125}, {"start": 3587.83, "end": 3588.93, "word": " and", "probability": 0.57373046875}, {"start": 3588.93, "end": 3590.17, "word": " H", "probability": 0.9560546875}, {"start": 3590.17, "end": 3591.21, "word": " is", "probability": 0.96533203125}, {"start": 3591.21, "end": 3592.23, "word": " differentiable", "probability": 0.973388671875}, {"start": 3592.23, "end": 3593.41, "word": " on", "probability": 0.94873046875}, {"start": 3593.41, "end": 3593.91, "word": " A", "probability": 0.99169921875}, {"start": 3593.91, "end": 3594.07, "word": " و", "probability": 0.99072265625}, {"start": 3594.07, "end": 3594.27, "word": " B", "probability": 0.87158203125}, {"start": 3594.27, "end": 3595.21, "word": " moreover", "probability": 0.827392578125}], "temperature": 1.0}, {"id": 144, "seek": 362386, "start": 3597.7, "end": 3623.86, "text": "عندي H برايم اللي هو بساوي F برايم نقص G برايم طبعا عند ال X عند ال X of X of X of X بساوي صفر لكل X موجودة في ال A و ال B then by the above theorem اللي بنحكي عنها اللي هي theorem by theorem 625 H", "tokens": [3615, 1863, 16254, 389, 4724, 23557, 32640, 13672, 1829, 31439, 4724, 3794, 995, 45865, 479, 4724, 23557, 32640, 8717, 4587, 9381, 460, 4724, 23557, 32640, 23032, 3555, 3615, 995, 43242, 2423, 1783, 43242, 2423, 1783, 295, 1783, 295, 1783, 295, 1783, 4724, 3794, 995, 45865, 20328, 5172, 2288, 5296, 28820, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 316, 4032, 2423, 363, 550, 538, 264, 3673, 20904, 13672, 1829, 44945, 5016, 4117, 1829, 18871, 11296, 13672, 1829, 39896, 20904, 538, 20904, 1386, 6074, 389], "avg_logprob": -0.22135415957087562, "compression_ratio": 1.6783625730994152, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3597.7, "end": 3598.26, "word": "عندي", "probability": 0.89794921875}, {"start": 3598.26, "end": 3598.68, "word": " H", "probability": 0.56591796875}, {"start": 3598.68, "end": 3599.46, "word": " برايم", "probability": 0.6527913411458334}, {"start": 3599.46, "end": 3599.76, "word": " اللي", "probability": 0.50421142578125}, {"start": 3599.76, "end": 3599.86, "word": " هو", "probability": 0.8876953125}, {"start": 3599.86, "end": 3600.22, "word": " بساوي", "probability": 0.70556640625}, {"start": 3600.22, "end": 3600.48, "word": " F", "probability": 0.87255859375}, {"start": 3600.48, "end": 3601.14, "word": " برايم", "probability": 0.9599609375}, {"start": 3601.14, "end": 3601.82, "word": " نقص", "probability": 0.90673828125}, {"start": 3601.82, "end": 3602.02, "word": " G", "probability": 0.884765625}, {"start": 3602.02, "end": 3602.62, "word": " برايم", "probability": 0.9825846354166666}, {"start": 3602.62, "end": 3603.12, "word": " طبعا", "probability": 0.90869140625}, {"start": 3603.12, "end": 3603.34, "word": " عند", "probability": 0.55126953125}, {"start": 3603.34, "end": 3603.46, "word": " ال", "probability": 0.88818359375}, {"start": 3603.46, "end": 3603.6, "word": " X", "probability": 0.87744140625}, {"start": 3603.6, "end": 3603.84, "word": " عند", "probability": 0.8251953125}, {"start": 3603.84, "end": 3604.02, "word": " ال", "probability": 0.90576171875}, {"start": 3604.02, "end": 3604.4, "word": " X", "probability": 0.97216796875}, {"start": 3604.4, "end": 3605.02, "word": " of", "probability": 0.85546875}, {"start": 3605.02, "end": 3605.44, "word": " X", "probability": 0.98291015625}, {"start": 3605.44, "end": 3605.76, "word": " of", "probability": 0.86328125}, {"start": 3605.76, "end": 3606.22, "word": " X", "probability": 0.99560546875}, {"start": 3606.22, "end": 3606.52, "word": " of", "probability": 0.95556640625}, {"start": 3606.52, "end": 3606.94, "word": " X", "probability": 0.99658203125}, {"start": 3606.94, "end": 3607.8, "word": " بساوي", "probability": 0.93505859375}, {"start": 3607.8, "end": 3608.34, "word": " صفر", "probability": 0.736328125}, {"start": 3608.34, "end": 3609.4, "word": " لكل", "probability": 0.9697265625}, {"start": 3609.4, "end": 3609.7, "word": " X", "probability": 0.91259765625}, {"start": 3609.7, "end": 3610.74, "word": " موجودة", "probability": 0.838623046875}, {"start": 3610.74, "end": 3611.72, "word": " في", "probability": 0.91357421875}, {"start": 3611.72, "end": 3611.9, "word": " ال", "probability": 0.8095703125}, {"start": 3611.9, "end": 3612.06, "word": " A", "probability": 0.76220703125}, {"start": 3612.06, "end": 3612.22, "word": " و", "probability": 0.8037109375}, {"start": 3612.22, "end": 3612.34, "word": " ال", "probability": 0.7958984375}, {"start": 3612.34, "end": 3612.7, "word": " B", "probability": 0.974609375}, {"start": 3612.7, "end": 3613.78, "word": " then", "probability": 0.6455078125}, {"start": 3613.78, "end": 3615.58, "word": " by", "probability": 0.904296875}, {"start": 3615.58, "end": 3615.94, "word": " the", "probability": 0.91259765625}, {"start": 3615.94, "end": 3616.34, "word": " above", "probability": 0.892578125}, {"start": 3616.34, "end": 3616.84, "word": " theorem", "probability": 0.875}, {"start": 3616.84, "end": 3617.04, "word": " اللي", "probability": 0.97705078125}, {"start": 3617.04, "end": 3617.86, "word": " بنحكي", "probability": 0.7933349609375}, {"start": 3617.86, "end": 3618.12, "word": " عنها", "probability": 0.992919921875}, {"start": 3618.12, "end": 3618.24, "word": " اللي", "probability": 0.7110595703125}, {"start": 3618.24, "end": 3618.38, "word": " هي", "probability": 0.95654296875}, {"start": 3618.38, "end": 3618.88, "word": " theorem", "probability": 0.82470703125}, {"start": 3618.88, "end": 3619.64, "word": " by", "probability": 0.7802734375}, {"start": 3619.64, "end": 3620.3, "word": " theorem", "probability": 0.81103515625}, {"start": 3620.3, "end": 3621.84, "word": " 625", "probability": 0.626708984375}, {"start": 3621.84, "end": 3623.86, "word": " H", "probability": 0.51318359375}], "temperature": 1.0}, {"id": 145, "seek": 364404, "start": 3624.48, "end": 3644.04, "text": "of X بتساوي C for every X element in A وB and hence F of X بساوي G of X زاد some constant C", "tokens": [2670, 1783, 39894, 3794, 995, 45865, 383, 337, 633, 1783, 4478, 294, 316, 4032, 33, 293, 16678, 479, 295, 1783, 4724, 3794, 995, 45865, 460, 295, 1783, 30767, 18513, 512, 5754, 383], "avg_logprob": -0.25047348484848486, "compression_ratio": 1.0816326530612246, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3624.48, "end": 3624.86, "word": "of", "probability": 0.1802978515625}, {"start": 3624.86, "end": 3625.28, "word": " X", "probability": 0.4375}, {"start": 3625.28, "end": 3625.88, "word": " بتساوي", "probability": 0.80487060546875}, {"start": 3625.88, "end": 3626.28, "word": " C", "probability": 0.87060546875}, {"start": 3626.28, "end": 3627.02, "word": " for", "probability": 0.9091796875}, {"start": 3627.02, "end": 3627.34, "word": " every", "probability": 0.81884765625}, {"start": 3627.34, "end": 3627.76, "word": " X", "probability": 0.958984375}, {"start": 3627.76, "end": 3628.22, "word": " element", "probability": 0.90283203125}, {"start": 3628.22, "end": 3628.6, "word": " in", "probability": 0.92724609375}, {"start": 3628.6, "end": 3628.98, "word": " A", "probability": 0.951171875}, {"start": 3628.98, "end": 3630.14, "word": " وB", "probability": 0.734130859375}, {"start": 3630.14, "end": 3631.18, "word": " and", "probability": 0.80615234375}, {"start": 3631.18, "end": 3631.94, "word": " hence", "probability": 0.92333984375}, {"start": 3631.94, "end": 3635.3, "word": " F", "probability": 0.5791015625}, {"start": 3635.3, "end": 3636.62, "word": " of", "probability": 0.8662109375}, {"start": 3636.62, "end": 3637.26, "word": " X", "probability": 0.99365234375}, {"start": 3637.26, "end": 3638.26, "word": " بساوي", "probability": 0.801025390625}, {"start": 3638.26, "end": 3639.02, "word": " G", "probability": 0.83642578125}, {"start": 3639.02, "end": 3639.28, "word": " of", "probability": 0.93310546875}, {"start": 3639.28, "end": 3640.2, "word": " X", "probability": 0.9970703125}, {"start": 3640.2, "end": 3641.24, "word": " زاد", "probability": 0.5318603515625}, {"start": 3641.24, "end": 3641.5, "word": " some", "probability": 0.8583984375}, {"start": 3641.5, "end": 3642.08, "word": " constant", "probability": 0.97265625}, {"start": 3642.08, "end": 3644.04, "word": " C", "probability": 0.94921875}], "temperature": 1.0}, {"id": 146, "seek": 366167, "start": 3650.89, "end": 3661.67, "text": "بكونوا احنا وصلنا لعين theorem 627 ان شاء الله المرة القادمة بنكمل والسلام عليكم ورحمة الله وبركاته", "tokens": [3555, 30544, 14407, 1975, 5016, 8315, 4032, 36520, 8315, 5296, 3615, 9957, 20904, 1386, 10076, 16472, 13412, 16606, 21984, 9673, 25720, 25062, 18513, 46007, 44945, 24793, 1211, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.10092659953028657, "compression_ratio": 1.3333333333333333, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3650.89, "end": 3651.69, "word": "بكونوا", "probability": 0.7145182291666666}, {"start": 3651.69, "end": 3651.87, "word": " احنا", "probability": 0.9046223958333334}, {"start": 3651.87, "end": 3652.39, "word": " وصلنا", "probability": 0.9747721354166666}, {"start": 3652.39, "end": 3652.79, "word": " لعين", "probability": 0.8857421875}, {"start": 3652.79, "end": 3653.17, "word": " theorem", "probability": 0.69140625}, {"start": 3653.17, "end": 3654.05, "word": " 627", "probability": 0.7958984375}, {"start": 3654.05, "end": 3654.27, "word": " ان", "probability": 0.66455078125}, {"start": 3654.27, "end": 3654.41, "word": " شاء", "probability": 0.98095703125}, {"start": 3654.41, "end": 3654.57, "word": " الله", "probability": 0.92529296875}, {"start": 3654.57, "end": 3654.91, "word": " المرة", "probability": 0.918701171875}, {"start": 3654.91, "end": 3655.93, "word": " القادمة", "probability": 0.982421875}, {"start": 3655.93, "end": 3657.99, "word": " بنكمل", "probability": 0.8976236979166666}, {"start": 3657.99, "end": 3660.01, "word": " والسلام", "probability": 0.8955078125}, {"start": 3660.01, "end": 3660.41, "word": " عليكم", "probability": 0.939453125}, {"start": 3660.41, "end": 3660.85, "word": " ورحمة", "probability": 0.9814453125}, {"start": 3660.85, "end": 3661.01, "word": " الله", "probability": 0.9677734375}, {"start": 3661.01, "end": 3661.67, "word": " وبركاته", "probability": 0.9828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3661.972625, "duration_after_vad": 3547.896249999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..70ade4c86e177df137c65f02146613063557775b
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/xgo_ibuk2Tw_raw.srt
@@ -0,0 +1,2540 @@
+1
+00:00:05,620 --> 00:00:11,560
+بسم الله الرحمن الرحيم المحاضرة الثالثة في مساق
+
+2
+00:00:11,560 --> 00:00:19,660
+تحليل رياضي 2 أو تحليل حقيقي 2 كلية العلوم قسم
+
+3
+00:00:19,660 --> 00:00:28,520
+الرياضيات بالجامعة الإسلامية مراجعة سريعة لما تم
+
+4
+00:00:28,520 --> 00:00:34,380
+في المحاضرة السابقة والتي قبلهاحكينا عن شو معناته
+
+5
+00:00:34,380 --> 00:00:37,500
+اللي هو الـ derivative قلنا f prime of c عند نقطة
+
+6
+00:00:37,500 --> 00:00:41,760
+c لو كانت f function من i لعند ال r هو عبارة عن
+
+7
+00:00:41,760 --> 00:00:49,200
+limit f of x نقص f of c على x minus c لما x تروح
+
+8
+00:00:49,200 --> 00:00:53,460
+أو تقول ل c قلنا لو كانت ال limit exist هذه بنقول
+
+9
+00:00:53,460 --> 00:00:56,740
+إنه ال derivative موجودة بنرمزلها بالرمز f prime
+
+10
+00:00:56,740 --> 00:01:02,600
+of cأخدنا بعيدة اللي هو نظرية قولنا لو كانت f is
+
+11
+00:01:02,600 --> 00:01:11,860
+differentiable at c then it is continuous at c
+
+12
+00:01:11,860 --> 00:01:15,320
+قولنا the converse need not to be true in general
+
+13
+00:01:15,320 --> 00:01:20,100
+وأخدنا مثال على هيك قولنا خد ال f of x بسوء ال
+
+14
+00:01:20,100 --> 00:01:23,560
+absolute value لل x is continuous اللي هو
+
+15
+00:01:23,560 --> 00:01:26,880
+everywhere but it is not differentiable at zero
+
+16
+00:01:27,430 --> 00:01:30,590
+واخدنا مثال آخر قولنا f of x بيساوي ال summation
+
+17
+00:01:30,590 --> 00:01:36,090
+لل x ناقص ci i من عند 1 لعند n قولنا هذا ال
+
+18
+00:01:36,090 --> 00:01:39,210
+function is continuous everywhere but it is not
+
+19
+00:01:39,210 --> 00:01:43,250
+differentiable at the corner points which are c1,
+
+20
+00:01:43,350 --> 00:01:49,170
+c2 لعند ال cl و بعدين أخدنا مثال f of x بيساوي ال
+
+21
+00:01:49,170 --> 00:01:56,590
+summation 1 على 2 to the n cosinecos 3 أُس N X N
+
+22
+00:01:56,590 --> 00:02:01,690
+من واحد إلى ملا نهاية قلنا إن الـ function is
+
+23
+00:02:01,690 --> 00:02:07,750
+continuous everywhere but it is not differentiable
+
+24
+00:02:07,750 --> 00:02:16,850
+anywhere الـ function متصلة دائما لكن ليس لها أي
+
+25
+00:02:16,850 --> 00:02:22,760
+derivative عند أي نقطة من النقاط دومينابعد هيك
+
+26
+00:02:22,760 --> 00:02:28,500
+أخدنا اللي هو .. اللي هو نظرية اللي هي بنحكي فيها
+
+27
+00:02:28,500 --> 00:02:34,950
+عن خواص اللي هي التفاضل قلنا لو كانت ال Fوالـ G
+
+28
+00:02:34,950 --> 00:02:39,370
+are differentiable اللي هو كان من I لعند R
+
+29
+00:02:39,370 --> 00:02:44,730
+differentiable عند نقطة C بيكون مجموعة Alpha F حيث
+
+30
+00:02:44,730 --> 00:02:49,570
+Alpha اللي هو عبارة عن constant Alpha F' موجودة
+
+31
+00:02:49,570 --> 00:02:57,230
+وبتساوي Alpha في F' عند نقطة Cو بعدين قلنا أن f زي
+
+32
+00:02:57,230 --> 00:03:03,290
+g أو نقص prime of c برضه exist بسوء f prime of c
+
+33
+00:03:03,290 --> 00:03:09,390
+زي أو نقص g prime of c هذه من الخواصل هو ال
+
+34
+00:03:09,390 --> 00:03:15,040
+derivative و أيضا قلنااللي هو الخواص الأخرى أنه
+
+35
+00:03:15,040 --> 00:03:21,000
+الـ F في G الكل prime عنده نقطة C حاصل ضرر دلتين
+
+36
+00:03:21,000 --> 00:03:28,400
+بساوي اللي هو F primeof c في g of c زائد f of c في
+
+37
+00:03:28,400 --> 00:03:33,320
+g prime of c ومن ثم أخدنا أيضًا اللي هو
+
+38
+00:03:54,080 --> 00:03:59,480
+و من ثم أيضا حكينا عن اللي هو اخدنا اللي هو ال
+
+39
+00:03:59,480 --> 00:04:04,540
+chain rule theorem ال chain rule لو كانت F من I
+
+40
+00:04:04,540 --> 00:04:12,080
+لعند ال R و G من عند ال J لعند ال R حيث ال F of I
+
+41
+00:04:12,080 --> 00:04:15,780
+subset من ال J عشان نعرف اللي هو ال composition
+
+42
+00:04:15,780 --> 00:04:19,480
+قلنا لو كانت F is differentiable و G is
+
+43
+00:04:19,480 --> 00:04:23,890
+differentiable يعني F is differentiable عند Cis
+
+44
+00:04:23,890 --> 00:04:32,470
+differentiable at c and g is differentiable at f
+
+45
+00:04:32,470 --> 00:04:39,210
+of c then the composition اللي هو ال general يعني
+
+46
+00:04:39,210 --> 00:04:44,490
+التفاضل ال composition the composition تفاضله كما
+
+47
+00:04:44,490 --> 00:04:55,650
+يلي then fcomposite G prime of C بساوة F prime عند
+
+48
+00:04:55,650 --> 00:05:02,070
+G of C في G prime of C هذا اللي حكينا عنه المرة
+
+49
+00:05:02,070 --> 00:05:06,830
+الماضية وأيضا أخدنا طبعا أمثلة على هيك وأخدنا
+
+50
+00:05:06,830 --> 00:05:15,030
+نظرية أخرى اللي هي لو كانت عند F من عند I لعند R
+
+51
+00:05:15,030 --> 00:05:17,730
+قلنا is strictly
+
+52
+00:05:25,190 --> 00:05:31,450
+monotone and continuous
+
+53
+00:05:31,450 --> 00:05:41,770
+وكانت اللي هو G من عند J لعند I برضه strictly is
+
+54
+00:05:41,770 --> 00:05:55,620
+strictly monotone andcontinuous قلنا هنا at C وهنا
+
+55
+00:05:55,620 --> 00:06:06,340
+continuous at F of C حيث اللي هو الـ G بتساوي F of
+
+56
+00:06:06,340 --> 00:06:12,180
+mean of I عشان نقدر نعرف اللي هو تكون inverse is
+
+57
+00:06:12,180 --> 00:06:17,640
+strictly monotone and continuous where G
+
+58
+00:06:19,450 --> 00:06:28,790
+is the inverse of F، مظبوط؟ طبعاً، اللي بضماننا إن
+
+59
+00:06:28,790 --> 00:06:31,070
+ال inverse موجود إن هو strictly إيش؟ معناها
+
+60
+00:06:31,070 --> 00:06:33,490
+monotone، strictly monotone سواء increasing أو
+
+61
+00:06:33,490 --> 00:06:37,090
+decreasing، معناته one to one معناته إن هو اللي هي
+
+62
+00:06:37,090 --> 00:06:41,030
+ال inverse موجودة من اللي هو F of I اللي هي J،
+
+63
+00:06:41,030 --> 00:06:44,610
+لعند مين؟ لعند ال I، وهذه ال J في الواقع كل عنها
+
+64
+00:06:44,610 --> 00:06:52,800
+مين؟ هي ال F inverseالآن الشرط أنه if F is
+
+65
+00:06:52,800 --> 00:07:03,640
+differentiable at C at C then اللي هي G اللي هي
+
+66
+00:07:03,640 --> 00:07:07,280
+الـ F inverse دي في الواقع F inverse اللي سمناها
+
+67
+00:07:07,280 --> 00:07:14,020
+مين؟ F inverse لازم تكون differentiable at F of C
+
+68
+00:07:14,020 --> 00:07:15,660
+and
+
+69
+00:07:18,190 --> 00:07:23,390
+اللي سمناها F of C في حين وده بتتذكره D اللي هي
+
+70
+00:07:23,390 --> 00:07:35,170
+and F prime أو F inverse prime at this D بتساوي
+
+71
+00:07:35,170 --> 00:07:44,930
+واحد على F prime of C أو بمعنى آخر بتساوي واحد على
+
+72
+00:07:44,930 --> 00:07:53,880
+F primeF of C بيساوي D يعني C بيساوي G of D أو F
+
+73
+00:07:53,880 --> 00:07:59,600
+inverse of D اللي هي يعني composite G الكل أفمين
+
+74
+00:07:59,600 --> 00:08:13,970
+of C واضح هاه F of مين of Dقلنا بعدين اللي هو in
+
+75
+00:08:13,970 --> 00:08:18,530
+general لو كانت اللي هي هذه تحت الشروط هذه بس الآن
+
+76
+00:08:18,530 --> 00:08:24,430
+مش عند اللي هو نقطة لو F is differentiable على كل
+
+77
+00:08:24,430 --> 00:08:29,470
+ال I هتكون ال G is differentiable على ال J و
+
+78
+00:08:29,470 --> 00:08:36,110
+العلاقة بينهم زي ما حكينا المرة الماضية هتكون اللي
+
+79
+00:08:36,110 --> 00:08:43,620
+هوطب هالمرة F is differentiable on I then G is
+
+80
+00:08:43,620 --> 00:08:47,280
+differentiable on J اللي هي بساوة F of I طبعا تحت
+
+81
+00:08:47,280 --> 00:08:55,140
+هذا الشروط and هيكون F inverse prime of Y بساوة 1
+
+82
+00:08:55,140 --> 00:09:01,330
+على F prime of Xحيث العلاقة بين Y و X اللي هي Y
+
+83
+00:09:01,330 --> 00:09:08,050
+بتساوي F of X أو بتعبير آخر بتساوي 1 على F prime
+
+84
+00:09:08,050 --> 00:09:13,630
+of composite G اللي هي بتسميها F inverse كله of
+
+85
+00:09:13,630 --> 00:09:23,790
+mean of Y هذا اللي حكينا المرة الماضية نيجي
+
+86
+00:09:23,790 --> 00:09:26,510
+الآن نكمل
+
+87
+00:09:27,590 --> 00:09:33,710
+وصلنا عند المثال اللي هو 6 1 10 وقلنا لو كانت عند
+
+88
+00:09:33,710 --> 00:09:41,270
+g of y example وقفنا عند ال example التالي g of y
+
+89
+00:09:41,270 --> 00:09:48,710
+بتساوي y أسواحدة ل n for y element in j اللي هي
+
+90
+00:09:48,710 --> 00:09:54,970
+عبارة عن ال interval من zero ل infinity الآن بقول
+
+91
+00:09:54,970 --> 00:10:03,260
+show thatG prime of Y بتساوي 1 على N Y أس 1 على N
+
+92
+00:10:03,260 --> 00:10:12,580
+ناغس 1 حيث N is even solution نيجي الأن نحل تطبيق
+
+93
+00:10:12,580 --> 00:10:20,240
+على ال theorem الأخيرة اللي هو ناخد inverse لهذه
+
+94
+00:10:20,240 --> 00:10:25,750
+طبعا واضح أن ال inverse لو قلنا let F of Xبساوي X
+
+95
+00:10:25,750 --> 00:10:30,230
+أُس N هذا عبارة عن polynomial أو اللي هو دالة
+
+96
+00:10:30,230 --> 00:10:35,170
+أُسية أو جزء من polynomial عند X أُس N طبعاً لأي X
+
+97
+00:10:35,170 --> 00:10:39,350
+في الفترة 01 هذا is differentiable ومش هيك كمان
+
+98
+00:10:39,350 --> 00:10:42,910
+ومدامة الـ N even في الفترة هذه strictly
+
+99
+00:10:42,910 --> 00:10:46,580
+increasingده الـ Strict increase in continuous ده
+
+100
+00:10:46,580 --> 00:10:50,860
+كل .. كل أمورها متحققة اللي قبل بشوية في النظرية
+
+101
+00:10:50,860 --> 00:10:56,000
+فالآن و هذه عبارة عن ال inverse لمين؟ للـ G فبكون
+
+102
+00:10:56,000 --> 00:11:04,540
+الآن G prime of Y إيش هتساوي؟ بتساوي 1 على F prime
+
+103
+00:11:04,540 --> 00:11:11,410
+عند G of Yمظبوط ولا لا؟ Y ساوي الان ال F prime هنا
+
+104
+00:11:11,410 --> 00:11:15,930
+واضح اللي هي N X أس N نقص واحد يعني عبارة عن واحد
+
+105
+00:11:15,930 --> 00:11:22,070
+على بدل ال X إيش هحط؟ G of Y لأن هذا F prime of X
+
+106
+00:11:22,070 --> 00:11:26,290
+بساوي N X N نقص واحد طب F prime of G Y هي عبارة عن
+
+107
+00:11:26,290 --> 00:11:33,870
+G of Y أس N نقص واحد مضروبة في مين؟ في ال N Y ساوي
+
+108
+00:11:35,600 --> 00:11:43,600
+1 على N في G of Y إيش هي عبارة عن Y أس 1 على N
+
+109
+00:11:43,600 --> 00:11:49,640
+فبيصير اللي هو هذي بالمرة نرفحها بعد إذنكم G of Y
+
+110
+00:11:49,640 --> 00:11:59,620
+أس 1 ناقص N ويساوي إن عوض 1 على N في Yأس واحد على
+
+111
+00:11:59,620 --> 00:12:07,260
+N أس واحد ناقص N ويساوي واحد على N Y أس واحد على N
+
+112
+00:12:07,260 --> 00:12:12,660
+ناقص واحد وهو المطلوب هذه اللي هي تطبيق مباشرة على
+
+113
+00:12:12,660 --> 00:12:17,580
+النظرية السابقة الآن تطبيق آخر مثال آخر أيضا مثال
+
+114
+00:12:17,580 --> 00:12:20,380
+يعني شبيه بالأمثل اللي كنتوا تاخدوه في ال calculus
+
+115
+00:12:20,380 --> 00:12:29,610
+المثال دي اللي بناخده اللي هو Y بتساوي صين ال Xو
+
+116
+00:12:29,610 --> 00:12:37,590
+الـ x في ناقص πي على اتنين لعين باي على اتنين الآن
+
+117
+00:12:37,590 --> 00:12:43,470
+بقوللي اثبت انه sign inverse prove that اللي هو
+
+118
+00:12:43,470 --> 00:12:54,110
+show that sign inverse لل Y بتساوي واحد على جدر
+
+119
+00:12:54,110 --> 00:12:57,750
+التربيع لواحد ناقص مين Y تربيع
+
+120
+00:13:00,300 --> 00:13:04,160
+prime اه اه ال derivative لل sign inverse ايش
+
+121
+00:13:04,160 --> 00:13:06,840
+بتساوي واحدة الجدر تربيعه لو واحد نقص Y تربيعه
+
+122
+00:13:06,840 --> 00:13:10,940
+برضه تطبيق مباشر خلينا نشوف كيف نطبق على النظرية
+
+123
+00:13:10,940 --> 00:13:20,000
+ناخد let F of X اللي هو بيساوي sign ال X عشان عند
+
+124
+00:13:20,000 --> 00:13:24,500
+G of Y او عند F of X بيساوي sign ال X اللي بتسميها
+
+125
+00:13:24,500 --> 00:13:31,610
+Y يعني الآن بتصير عند G of Y ايش بتساويSin Inverse
+
+126
+00:13:31,610 --> 00:13:37,790
+لمن؟ لـ Y معايا يا شباب، أه؟ لأن حسب الـ F of X
+
+127
+00:13:37,790 --> 00:13:41,510
+بساعة و شوية إن الـ X الـ X في الفترة ناقص Y على 2
+
+128
+00:13:41,510 --> 00:13:47,690
+و Y على 2 الـ Y القيمة المقابلة إليها هتكون بين
+
+129
+00:13:47,690 --> 00:13:54,560
+ناقص 1 و 1لكن لاحظ الآن لما أشتق المشتقة لازم تكون
+
+130
+00:13:54,560 --> 00:13:58,380
+لا تساوي صفر في الفترة هذه ففي الفترة هذه اللي هي
+
+131
+00:13:58,380 --> 00:14:02,900
+المشتقة طبعا لهذه اللي هي عبارة عن cosine فهتكون
+
+132
+00:14:02,900 --> 00:14:06,900
+اللي هي ال X بس في ال open interval من ناقص y على
+
+133
+00:14:06,900 --> 00:14:11,540
+2 على y على 2 عساس ما نجسمش عالميا على الصفر إذا
+
+134
+00:14:11,540 --> 00:14:17,620
+الآن صار عندي G prime of Yنفسي اللي عملناه فوق،
+
+135
+00:14:17,620 --> 00:14:23,720
+إيش بتساوي؟ واحد على F prime of G of Y Y ساوي،
+
+136
+00:14:23,720 --> 00:14:28,880
+واحد F .. اللي هي مين الأن F prime؟ اللي هي cosine
+
+137
+00:14:28,880 --> 00:14:36,320
+اللي هو G of Y، مظبوط؟ وال cosine احنا إيش؟ عبارة
+
+138
+00:14:36,320 --> 00:14:39,160
+عن إيش؟ عبارة عن إيش تكون؟ عبارة عن الجدر
+
+139
+00:14:39,160 --> 00:14:44,080
+التربيعي؟ لا، طبعا ال cosine X إيش بتساوي؟ هذا
+
+140
+00:14:44,080 --> 00:14:52,100
+عبارة عن X، مظبوط؟هو الجدر التربيعي؟ لا، واحد ناقص
+
+141
+00:14:52,100 --> 00:14:57,980
+sign تربيع الـ X اللي هي G of Y، مظبوط؟ معايا يا
+
+142
+00:14:57,980 --> 00:15:03,200
+شبابY ساوي واحد على جدر التربيع إلى واحد ناقص Y
+
+143
+00:15:03,200 --> 00:15:08,940
+تربيع و Y في الفترة ناقص باي على اتنين و باي على
+
+144
+00:15:08,940 --> 00:15:13,800
+اتنين اللي هي الـ X و اللي موجودة أسفل X في ناقص
+
+145
+00:15:13,800 --> 00:15:16,560
+باي على اتنين و باي على اتنين و الـ Y في الفترة
+
+146
+00:15:16,560 --> 00:15:21,640
+ناقص واحد و واحد حتى نتجنب القسمة عالميا على اللي
+
+147
+00:15:21,640 --> 00:15:25,380
+هو الصفر هذا التطبيق على النظرية
+
+148
+00:15:27,410 --> 00:15:30,770
+ال homework عندنا تلاتة أو أربعة أو سبعة أو تسعة
+
+149
+00:15:30,770 --> 00:15:34,250
+أو تلاتاش من section 6-1 ان شاء الله المرة الجاية
+
+150
+00:15:34,250 --> 00:15:39,510
+أو اللي بعدها بنحاول نعمل discussion فيا ريت اللي
+
+151
+00:15:39,510 --> 00:15:44,410
+هو أنكم اتحلوا الأسئلة و اللي بتعرفوش اتحلوا او
+
+152
+00:15:44,410 --> 00:15:50,880
+بدكم نذاك بنحلو ان شاء اللهنيجي الآن لصفحة
+
+153
+00:15:50,880 --> 00:15:53,800
+اللي بعدي ده اللي هو ال section التاني ممكن هيكنا
+
+154
+00:15:53,800 --> 00:15:58,460
+هنا ستة واحد الآن هنبدأ في ال section التاني اللي
+
+155
+00:15:58,460 --> 00:16:02,380
+هو ال main value theorem وهو محاضرة اليوم بشكل
+
+156
+00:16:02,380 --> 00:16:06,740
+أساسي عالمي على the main value theorem ومتعلقات
+
+157
+00:16:06,740 --> 00:16:12,870
+هذه النظريةهنلاقي جدّاش مهمة هذه النظرية وجدّاش
+
+158
+00:16:12,870 --> 00:16:17,650
+فيه عندنا نتائج تتعلق إيه بها وإحنا يعني فعلا
+
+159
+00:16:17,650 --> 00:16:25,530
+بستعملها كثير وفعلا بتساعدنا اللي هو في اللي ده
+
+160
+00:16:25,530 --> 00:16:30,270
+يعني إذا رح أطلب لما حتى أخدنا ال Calculus كانت
+
+161
+00:16:30,270 --> 00:16:37,010
+اللي هي إلها تطبيقات واسعة وحنشوف الآن وين أهمية
+
+162
+00:16:37,680 --> 00:16:42,520
+هذه نظرية نظرية القيم المتوسطة من خلال الحديث أو
+
+163
+00:16:42,520 --> 00:16:47,080
+شرح حادي المادة الآن في الأول زي ما قلنا ال
+
+164
+00:16:47,080 --> 00:16:49,420
+section 6.2 the mean value theorem نيجي لل
+
+165
+00:16:49,420 --> 00:16:53,420
+definition الأول ال definition اللي هو مر علينا
+
+166
+00:16:53,420 --> 00:16:58,380
+اشي زيه أو مر علينا اللي هو تعريف ال local
+
+167
+00:16:58,380 --> 00:17:04,500
+extremum أو اللي هو relative extremumأو اللي هو
+
+168
+00:17:04,500 --> 00:17:07,460
+الـ local maximum أو الـ local minimum أو الـ
+
+169
+00:17:07,460 --> 00:17:10,840
+relative extremum أو الـ relative اللي هو الـ
+
+170
+00:17:10,840 --> 00:17:17,900
+minimum طبعاً بتعرفوا أن أنا بدي أعرف شو معناته دي
+
+171
+00:17:17,900 --> 00:17:24,480
+اللي هي النقطة عنده النقطة C في عند local .. local
+
+172
+00:17:24,480 --> 00:17:29,860
+maximum مثلا أو relative maximum بنقول في عند C
+
+173
+00:17:30,870 --> 00:17:35,370
+عندي function f من some interval I لعند R هاي الـ
+
+174
+00:17:35,370 --> 00:17:39,490
+function اللي عندي هنا من هنا لهنا بنقول C element
+
+175
+00:17:39,490 --> 00:17:48,430
+in I at C element in I we have a local أو relative
+
+176
+00:17:48,430 --> 00:18:00,820
+maximum when اللي هو there existsV Delta of C يعني
+
+177
+00:18:00,820 --> 00:18:05,800
+بنلاقي جوار حوالين الـ C بنصف قطر Delta C نقص
+
+178
+00:18:05,800 --> 00:18:12,060
+Delta of C زائد Delta في هذا الجوار such that
+
+179
+00:18:12,060 --> 00:18:20,320
+بتكون F of C هي أكبر قيمة للدالة F of C أكبر أو
+
+180
+00:18:20,320 --> 00:18:27,920
+سوى F of X لكل X في هذا الجوارإذا تحقق هذا الشرط
+
+181
+00:18:27,920 --> 00:18:35,840
+بنقول إن F has a relative maximum
+
+182
+00:18:35,840 --> 00:18:36,780
+at C
+
+183
+00:18:39,910 --> 00:18:45,290
+v delta neighborhood يعني جوار بنصف قطر دلتا بحيث
+
+184
+00:18:45,290 --> 00:18:50,590
+يتحقق أن ال f of c أكبر شو f of x لكل x في هذا
+
+185
+00:18:50,590 --> 00:19:01,850
+الجوار similarly بنقول at d element in I we have a
+
+186
+00:19:01,850 --> 00:19:11,870
+relative minimum whenthere exist أي جوار آخر بتكون
+
+187
+00:19:11,870 --> 00:19:17,390
+تسموه V Delta Prime أو V Delta of D such that يعني
+
+188
+00:19:17,390 --> 00:19:20,870
+بنلاقي .. بنقول هذه النقطة في عندها relative
+
+189
+00:19:20,870 --> 00:19:27,970
+minimum إذا كان لقينا جوار حواليهاهذه النقطة C D
+
+190
+00:19:27,970 --> 00:19:33,810
+وهذه D زائد Delta وهذه D نقص Delta في جوار حواليها
+
+191
+00:19:33,810 --> 00:19:38,670
+بتكون قيمة الدالة أصغر من كل القيم اللي حواليها
+
+192
+00:19:38,670 --> 00:19:45,210
+يعني اللي هو there exists V Delta of D such that F
+
+193
+00:19:45,990 --> 00:19:53,190
+of D أصغر أو ساوى F of X لكل X موجودة في V Delta
+
+194
+00:19:53,190 --> 00:20:01,370
+of D فهذه نسميها نقطة صغيرة محلية وهذه نسميها نقطة
+
+195
+00:20:01,370 --> 00:20:06,460
+عظمة محليةهذا معناته اللي هو الـ local maximum و
+
+196
+00:20:06,460 --> 00:20:10,340
+الـ local minimum أو زي ما هو مصطلح عليها ال
+
+197
+00:20:10,340 --> 00:20:14,580
+relative maximum و relative minimum لما بنقصد و
+
+198
+00:20:14,580 --> 00:20:20,880
+بنقول local extremum معناته يا local maximum أو
+
+199
+00:20:20,880 --> 00:20:24,520
+local minimum أو relative extremum يا relative
+
+200
+00:20:24,520 --> 00:20:30,120
+maximum يا relative minimumنجي الآن لنظريتنا
+
+201
+00:20:30,120 --> 00:20:33,720
+الأولى احنا كنا في ال calculus إذا بتتذكر و نسأل
+
+202
+00:20:33,720 --> 00:20:43,110
+سؤاللما بدنا نبحث في مسألة اللي هو الـ maximum و
+
+203
+00:20:43,110 --> 00:20:46,410
+الـ minimum سواء local maximum و local minimum أو
+
+204
+00:20:46,410 --> 00:20:50,230
+absolute maximum و absolute minimum كنا نسأل حالنا
+
+205
+00:20:50,230 --> 00:20:54,390
+سؤال طبعا مش معجول أنا بدي آجي كل نقاط ال domain
+
+206
+00:20:54,390 --> 00:20:57,990
+أفحص فيه عند maximum ولا minimum لأن نقاط ال
+
+207
+00:20:57,990 --> 00:21:01,170
+domain عدد لا نهائي uncountable number of points
+
+208
+00:21:01,170 --> 00:21:07,180
+في غالبهافإيش كنت حصرها؟ كنا نقول أين يمكن إيجاد
+
+209
+00:21:07,180 --> 00:21:12,480
+الـlocal maximum أو الـlocal minimum بعد ما نحدد
+
+210
+00:21:12,480 --> 00:21:17,100
+النقاط هذه بنقول يأتي الآن الفحص إنه هل هي local
+
+211
+00:21:17,100 --> 00:21:21,660
+maximum ولا local minimum إذن مسألة اللي هو إيجاد
+
+212
+00:21:21,660 --> 00:21:25,180
+ال maximum و ال minimum تبرع عبر خطوتين الخطوة
+
+213
+00:21:25,180 --> 00:21:31,380
+الأولى وين ممكن نلاقيهاوالخطوة الثانية اللي هي هل
+
+214
+00:21:31,380 --> 00:21:36,220
+هي فعلا local maximum ولا local minimum ولا لا
+
+215
+00:21:36,220 --> 00:21:40,500
+local maximum ولا local minimum اللي بده يشرعلنا
+
+216
+00:21:40,500 --> 00:21:45,130
+الإجابة الأولى هي النظرية هذهالنظرية هذه كنا كمان
+
+217
+00:21:45,130 --> 00:21:49,390
+نجاوب نقول الإجابة توجد الـlocal maximum أو
+
+218
+00:21:49,390 --> 00:21:53,030
+الـlocal minimum في أحد ثلاث مناطق إما F prime
+
+219
+00:21:53,030 --> 00:21:58,070
+بساوي سفر أو F prime does not exist كنقات داخلية
+
+220
+00:21:58,070 --> 00:22:03,410
+أو عند الـendpoints فكنا نحصرها في تلت أنهي مناطق
+
+221
+00:22:03,410 --> 00:22:07,530
+فبصير عدد النقاط اللي بدنا نفحص الـlocal max أو
+
+222
+00:22:07,530 --> 00:22:11,490
+الـlocal minimum عددها محدود وقليل بصير السؤال
+
+223
+00:22:11,490 --> 00:22:15,630
+مقدور عليهالان النظرية اللي بتتشرح علناها دي ايش
+
+224
+00:22:15,630 --> 00:22:23,390
+النظرية بتقول بتقول ما يليه اللي بتقوله ال theorem
+
+225
+00:22:23,390 --> 00:22:29,120
+اللي هيحتى اسمها اللي هي interior extremum theorem
+
+226
+00:22:29,120 --> 00:22:32,920
+interior extremum theorem يعني هنحكي عن ال
+
+227
+00:22:32,920 --> 00:22:38,020
+interior point بتقولي نفترض إن C عبارة عن نقطة
+
+228
+00:22:38,020 --> 00:22:43,400
+داخلية لمين ل some interval I C اللي هو إشمالة
+
+229
+00:22:43,400 --> 00:22:49,140
+نقطة داخلية ل I ال interval اللي عنديوعند الـ
+
+230
+00:22:49,140 --> 00:22:55,040
+function F من I لعند R لو فرضنا أن الـ function F
+
+231
+00:22:55,040 --> 00:23:02,000
+has a relative extremum at let's say element كده
+
+232
+00:23:02,000 --> 00:23:18,480
+if F has a relative extremum at C element in I0عند
+
+233
+00:23:18,480 --> 00:23:23,520
+C an interior point of the interval I at which F
+
+234
+00:23:23,520 --> 00:23:27,640
+has a relative extremum يعني مفترضين أنه في عندي
+
+235
+00:23:27,640 --> 00:23:33,140
+يا relative maximum يا relative minimum عند هذه
+
+236
+00:23:33,140 --> 00:23:43,660
+النقطة الداخلية ونفرض كمان أن F prime of C exist
+
+237
+00:23:43,660 --> 00:23:51,610
+تحت كل هذه الشروطلازم تطلع عند F prime of C ايش
+
+238
+00:23:51,610 --> 00:23:56,050
+بتساوي؟ بتساوي سفر يعني بمعنى اخر لو كانت النقطة
+
+239
+00:23:56,050 --> 00:24:00,690
+داخلية و النقطة هذه الـ derivative عندها موجودة
+
+240
+00:24:01,820 --> 00:24:05,280
+وكانت عندها relative maximum أو relative minimum
+
+241
+00:24:05,280 --> 00:24:09,280
+قطعاً هتكون الـ F prime إليها إيش بتساوي .. بتساوي
+
+242
+00:24:09,280 --> 00:24:12,960
+سفر يعني عند .. عند النقاط الداخلية اللي الـ F
+
+243
+00:24:12,960 --> 00:24:17,280
+prime إليها موجودة و بتشاويش سفر انساها و ماتبحثش
+
+244
+00:24:17,280 --> 00:24:20,780
+فيها قطعا فيش فيها لا relative maximum ولا
+
+245
+00:24:20,780 --> 00:24:25,750
+relative إيش .. minimumالآن هذه النظرية وكأنه
+
+246
+00:24:25,750 --> 00:24:31,810
+بتحكيلنا في داخلها أن النقاط اللي بتكون داخلية
+
+247
+00:24:31,810 --> 00:24:36,590
+واحتمال يكون عندها relative maximum و relative
+
+248
+00:24:36,590 --> 00:24:42,410
+minimum نوعين يا f prime مش موجودةأو الـ F' أيش
+
+249
+00:24:42,410 --> 00:24:48,190
+بتساوي؟ بتساوي 0 لأنه إذا كانت F' موجودة وقفقلها
+
+250
+00:24:48,190 --> 00:24:51,910
+relative maximum أو relative minimum وكانت النقطة
+
+251
+00:24:51,910 --> 00:24:56,710
+داخلية لازم الـ F' أيش ما لها تساوي 0 ولاحظ هنا إن
+
+252
+00:24:56,710 --> 00:25:02,190
+الحديث عن مين؟ عن النقاط الداخلية يعني من فحوة
+
+253
+00:25:02,190 --> 00:25:06,110
+الحديث هنا بنجاوب على سؤالنا، هذه اللي بتجاوبنا
+
+254
+00:25:06,110 --> 00:25:09,860
+على سؤالنا بتقولاللي هو الـ relative maximum أو
+
+255
+00:25:09,860 --> 00:25:13,880
+الـ relative minimum هتكون في أحد ثلاث مناطق يا F
+
+256
+00:25:13,880 --> 00:25:18,060
+prime does not exist يا F prime بالساوية سفر يا
+
+257
+00:25:18,060 --> 00:25:27,960
+end point واضح؟ أي سؤال؟ واضح أه؟ طيب، دي يجي
+
+258
+00:25:27,960 --> 00:25:36,550
+تبرهن النظريةالآن هو البروحان اللي مكتوب هنا we
+
+259
+00:25:36,550 --> 00:25:41,170
+prove for the case that F has relative maximum at
+
+260
+00:25:41,170 --> 00:25:45,150
+C هيه مكتوب أنا مابديش أبرهن ال maximum بتبرهنكم
+
+261
+00:25:45,150 --> 00:25:52,290
+مين ال minimum إذا الآن بدنا نفترض نفترض ال proof
+
+262
+00:25:52,290 --> 00:25:57,870
+خليني أكتب هنا ال proof بدي
+
+263
+00:25:57,870 --> 00:26:04,820
+أفترضC نقطة داخلية ونفترض إن F أشبهلها have a
+
+264
+00:26:04,820 --> 00:26:08,560
+relative minimum relative maximum محلولة لأن
+
+265
+00:26:08,560 --> 00:26:12,640
+suppose that
+
+266
+00:26:12,640 --> 00:26:21,020
+F has a relative maximum
+
+267
+00:26:21,020 --> 00:26:28,120
+at C element in I0 ماشي؟
+
+268
+00:26:37,000 --> 00:26:41,080
+نعم نفترض إنها minimum لأن ال case تبعت ال maximum
+
+269
+00:26:41,080 --> 00:26:47,860
+محلولةواضح؟ الان لو كان F as relative extremum
+
+270
+00:26:47,860 --> 00:26:52,160
+بدنا نصل الان extreme يابتكون maximum يابتكون
+
+271
+00:26:52,160 --> 00:26:56,440
+minimum case ال maximum هي مكتوبة بتجروها لحالكوا
+
+272
+00:26:56,440 --> 00:27:01,980
+نفس الفكرة ده أكتف بت mean F as a relative H
+
+273
+00:27:01,980 --> 00:27:08,360
+minimumالآن بدي أفترض لك أن الـ F' أي شمالها لا
+
+274
+00:27:08,360 --> 00:27:11,700
+تساوي صفر و أسألك لـ contradiction إذا الآن بدي
+
+275
+00:27:11,700 --> 00:27:18,780
+أفترض لك و بدي أقول لك suppose that F prime of C
+
+276
+00:27:18,780 --> 00:27:25,620
+لا تساوي أيش؟ صفر، ماشي الحال، إذا عندي two cases
+
+277
+00:27:25,620 --> 00:27:34,360
+ال case الأول أن F prime of C أكبر من أيش؟من صفر
+
+278
+00:27:34,360 --> 00:27:43,580
+ماشي الحال إذا الآن عندي limit f of x ناقص f of c
+
+279
+00:27:43,580 --> 00:27:50,340
+على x minus c as x بتروح ل c أشماله اللي هو هذا f
+
+280
+00:27:50,340 --> 00:27:57,040
+prime of c حسب المعطى إيش هيكون أكبر من صفر ماشي
+
+281
+00:27:57,040 --> 00:28:03,480
+الحال طيب الآن مدام ال f prime of c أكبر من صفرإذا
+
+282
+00:28:03,480 --> 00:28:07,700
+حسب نظرية قلنا قبل هيك إنه لو كانت ال limit لل
+
+283
+00:28:07,700 --> 00:28:12,800
+function أكبر من 0 هنلاقي جوار حوالين النقطة اللي
+
+284
+00:28:12,800 --> 00:28:16,660
+بدنا نروحلها يكون اللي هو قيمة اللي جوا ال limit
+
+285
+00:28:16,660 --> 00:28:21,780
+أكبر من 100 من 0 لأن كما قالي مدام ال limit هذا
+
+286
+00:28:21,780 --> 00:28:29,260
+أكبر من 0 then there exists Deltaأكبر من سفر أو V
+
+287
+00:28:29,260 --> 00:28:35,380
+Delta أكبر من سفر Such that اللي هو F of X نقص F
+
+288
+00:28:35,380 --> 00:28:43,400
+of C على X minus C أكبر من سفر لكل X وين موجودة في
+
+289
+00:28:43,400 --> 00:28:48,240
+الـ V Delta of C صح؟
+
+290
+00:28:48,240 --> 00:28:53,820
+هاي عندي احنا مفترضين إن هي أشملها relative
+
+291
+00:28:53,820 --> 00:28:57,940
+minimum خلّيني أشتغل على هذه المنطقةأساسي أن
+
+292
+00:28:57,940 --> 00:29:02,260
+تشوفوها على الرسم
+
+293
+00:29:02,260 --> 00:29:13,880
+يمكن تكون أوضح عندي هي النقطة C وهذا C ناقص Delta
+
+294
+00:29:13,880 --> 00:29:21,060
+وهذا C زائد Delta، راضح؟ الـ F of X ناقص F of Z
+
+295
+00:29:21,060 --> 00:29:24,000
+على X minus C أكبر من مين من سفر لكل X و الموجودة
+
+296
+00:29:24,000 --> 00:29:32,040
+في الـ V Delta of Cأه، الآن .. الآن عندي هو .. بدي
+
+297
+00:29:32,040 --> 00:29:37,020
+.. عندي أنا مفترض أنه اللي هو F هذا relative A
+
+298
+00:29:37,020 --> 00:29:45,580
+شماله minimum إذا في جوار .. في جوار بتكون F of C
+
+299
+00:29:45,580 --> 00:29:52,700
+أصغر أو ساوة F of X لكل X في هذا الجوار اللي هو V
+
+300
+00:29:52,700 --> 00:29:59,440
+Delta Prime of إيش؟ Of C، ماشي الحالالآن الـ Delta
+
+301
+00:29:59,440 --> 00:30:03,820
+هذه فيه Delta أكبر من 0 باخدها الـ Delta أصغر من
+
+302
+00:30:03,820 --> 00:30:08,840
+هذه بحكم فيها، فده بتنفع للـ Delta أكبر من هذه إن
+
+303
+00:30:08,840 --> 00:30:11,880
+هذا الكون المقدر لكل X في الـ V Delta يكون أكبر من
+
+304
+00:30:11,880 --> 00:30:17,100
+0، إذا بديجه، برضه بنفع، إذا بختار الـ Delta هذه
+
+305
+00:30:17,100 --> 00:30:20,420
+بناء على اختيار لهذه، فبتكون الـ Delta هذه أنا
+
+306
+00:30:20,420 --> 00:30:24,770
+بختارها أصغر أو سوء من الـ Delta primeماشي الحال
+
+307
+00:30:24,770 --> 00:30:28,770
+طيب إذا صار عندي F of X نقص F of C على X minus C
+
+308
+00:30:28,770 --> 00:30:34,970
+أكبر من 100 من 0 لكل X limited V Delta O of C
+
+309
+00:30:34,970 --> 00:30:38,090
+أذكركم مش بده أنا أنا بده أصل يكون contradiction
+
+310
+00:30:38,090 --> 00:30:45,050
+يعني بده أصل لنقاط في المكان هذا تتحققش هذه معايا؟
+
+311
+00:30:46,850 --> 00:30:48,790
+بدي أسأل ال contradiction كيف أسأل ال
+
+312
+00:30:48,790 --> 00:30:53,210
+contradiction؟ بدي أسأل ألاقي نقاط في المنطقة هذه
+
+313
+00:30:53,210 --> 00:30:59,750
+و هذه لا تتحقق شوف الآن عندي هذا المقدار إيش ماله؟
+
+314
+00:30:59,750 --> 00:31:07,730
+موجب، مظبوط ولا لأ؟ ماشي، الآن اللي بدي أخلي اللي
+
+315
+00:31:07,730 --> 00:31:13,830
+هي F of X minus F of C تظل أكبر من 0لأن لو خلّيتها
+
+316
+00:31:13,830 --> 00:31:19,210
+أكبر من صفر بيصير F أصغر من صفر بيصير F of X لما
+
+317
+00:31:19,210 --> 00:31:22,030
+صير أصغر من صفر بيصير أصغر من F of C بتبطّل أش
+
+318
+00:31:22,030 --> 00:31:28,650
+مالها عبارة عن minimum بتخلي
+
+319
+00:31:28,650 --> 00:31:35,130
+هذا المقدار أصغر من أش من صفر بدون هذا أه؟ بيصير F
+
+320
+00:31:35,130 --> 00:31:41,120
+of X أصغر من F of C بيصير F of Z مش minimumواضح؟
+
+321
+00:31:41,120 --> 00:31:45,560
+طيب إيش اللي بده يخليلي هذا أصغر من 0 هذا المقدار
+
+322
+00:31:45,560 --> 00:31:52,560
+أصغر من 0 أني أضرب أعمل choose x بحيث أنه يكون هذا
+
+323
+00:31:52,560 --> 00:31:57,380
+سالب وإن هيكون سالب x minus c بختار اللي هي x
+
+324
+00:31:57,380 --> 00:32:01,680
+minus c بختار x وإن ما أقول بقول choose x element
+
+325
+00:32:01,680 --> 00:32:07,240
+أن c نقص دلتة وc فاشي الحال then
+
+326
+00:32:09,590 --> 00:32:15,310
+اللي هو لما اخترت الـ X هنا هيكون الـ X minus C
+
+327
+00:32:15,310 --> 00:32:20,570
+أصغر من 0 مدام صار الـ X minus C أصغر من 0 وهذا
+
+328
+00:32:20,570 --> 00:32:26,630
+أكبر من 0 معطى من التنتين مع بعض بيصير عند X minus
+
+329
+00:32:26,630 --> 00:32:37,630
+C في F of X minus F of C على X minus Cأصغر من 0،
+
+330
+00:32:37,630 --> 00:32:43,370
+اللي هو هذا في الواقع مين؟ هو عبارة عن F of X ناقص
+
+331
+00:32:43,370 --> 00:32:47,210
+F of C صار الـ F of X minus F of C، لأن هذا بتروح
+
+332
+00:32:47,210 --> 00:32:50,690
+محدد، لأنه مش سفر، بصير F of X ناقص F of C أصغر من
+
+333
+00:32:50,690 --> 00:32:57,150
+0، معناته صار F of X أصغر من F of C، هذا لمين؟
+
+334
+00:32:57,150 --> 00:33:02,050
+للنقطة X اللي في هذا الجوار، يعني اللي لجأت نقطة
+
+335
+00:33:02,050 --> 00:33:04,790
+في هذا الجوار، لا تحقق هذا
+
+336
+00:33:07,600 --> 00:33:15,160
+هذا contradiction طيب اللي ما وضحتلوش هذه خلّينا
+
+337
+00:33:15,160 --> 00:33:19,780
+نوضحها في الحالة التانية هذا في حالة مين أه في
+
+338
+00:33:19,780 --> 00:33:24,440
+prime و في c أشمالها أكبر من سفر الآن بدأ أقول
+
+339
+00:33:24,440 --> 00:33:31,000
+suppose that الحالة التانية كاس اتنينيعني اللي
+
+340
+00:33:31,000 --> 00:33:37,320
+بقوله في حالة فرضت F prime لا تساوي سفر هأصل دائما
+
+341
+00:33:37,320 --> 00:33:41,200
+لتناقض F prime أكبر من سفر حصل لتناقض وصلت لتناقض
+
+342
+00:33:41,200 --> 00:33:47,060
+والآن حالة F prime of C أصغر من سفر برضه حصل لمين؟
+
+343
+00:33:47,460 --> 00:33:51,860
+لطلاقط ماشي الحال الان ايش معناه f prime of c أكبر
+
+344
+00:33:51,860 --> 00:33:58,040
+من 0 بنفس الأسلوب limit f of x ناقص f of c على x
+
+345
+00:33:58,040 --> 00:34:03,860
+minus c as x بتروح لل c برضه ايش ماله أصغر من 0
+
+346
+00:34:03,860 --> 00:34:09,820
+إذا في جوار there exist v delta of x و باخد ال
+
+347
+00:34:09,820 --> 00:34:13,500
+delta اللي هي delta prime بقدر أخدها و أصغر يساوي
+
+348
+00:34:13,500 --> 00:34:20,950
+ال delta prime by such thatاللي هو f of x ناقص f
+
+349
+00:34:20,950 --> 00:34:27,310
+of c على x minus c أصغر من مين؟ من 0 الآن اللي
+
+350
+00:34:27,310 --> 00:34:31,430
+بيوصلني لتناقض هتلاقيها مش choosing x هنا و انا
+
+351
+00:34:31,430 --> 00:34:35,450
+هاختارها في الجهة التانية في الجهة بتشوف كيف لأن
+
+352
+00:34:35,450 --> 00:34:43,570
+بيقول choose x element in c و c زائد delta then
+
+353
+00:34:47,030 --> 00:34:54,130
+هيكون عندى الآن الـ X minus C إيش ماله أكبر من 0
+
+354
+00:34:54,130 --> 00:35:00,610
+واضح أه؟لأن هذا أكبر من صفر وهذا أكبر أصغر من صفر
+
+355
+00:35:00,610 --> 00:35:07,110
+ثم اللي هي F of X ناقص F of C اللي هي بتساوي X
+
+356
+00:35:07,110 --> 00:35:10,670
+minus C اللي هي أكبر من صفر في المقدار اللي هو F
+
+357
+00:35:10,670 --> 00:35:15,390
+of X ناقص F of C على X minus C اللي هو أصغر من صفر
+
+358
+00:35:15,390 --> 00:35:19,430
+حصل أصغر من صفر وأكبر من صفر حيكون أصغر من صفر
+
+359
+00:35:19,430 --> 00:35:26,680
+ومنه henceF of X أصغر من F of C لنقطة في هذا
+
+360
+00:35:26,680 --> 00:35:30,720
+الجوار اللي هو باخدها very close to C يعني معناته
+
+361
+00:35:30,720 --> 00:35:35,040
+هتكون في داخل هذا الجوار لجهة نقطة بحيث أنه F of C
+
+362
+00:35:35,040 --> 00:35:41,540
+أكبر من F of X which is a contradiction thereforeF
+
+363
+00:35:41,540 --> 00:35:47,240
+prime of C must equal zero إذن بيكون أثبتنا إن لو
+
+364
+00:35:47,240 --> 00:35:52,000
+كان في عندي local minimum عند ال interior point C
+
+365
+00:35:52,000 --> 00:35:59,200
+إذن اللي هي بتكون ال F prime of C بالساعة سفر طبعا
+
+366
+00:35:59,200 --> 00:36:04,660
+لاحظوا أنا كل الجوارات اللي أخدت هنا ال V Delta و
+
+367
+00:36:04,660 --> 00:36:09,010
+V Delta prime كل في داخل الintervalعشان هيك هو
+
+368
+00:36:09,010 --> 00:36:12,850
+طبعا هو كاتب تقاطع ال .. بكتب تقاطع ال subset من
+
+369
+00:36:12,850 --> 00:36:17,450
+ال interval لأن كل اللي بشتغله وين بشتغله؟ جوات ال
+
+370
+00:36:17,450 --> 00:36:25,510
+interval أي سؤال؟ اللي هو؟
+
+371
+00:36:25,510 --> 00:36:33,890
+تكمّل
+
+372
+00:36:33,890 --> 00:36:38,810
+يعني f of c أقل من f of xدقيقة بس هنكتب اللي
+
+373
+00:36:38,810 --> 00:36:45,870
+بتقوله عشان اللي بشوف تصويرنا و بسمع كل معاناه
+
+374
+00:36:45,870 --> 00:36:49,050
+أيوة
+
+375
+00:36:49,050 --> 00:36:54,330
+يا محمد قول أصغر
+
+376
+00:36:54,330 --> 00:37:02,390
+يسوي F of X لكل X في V Delta of Z F
+
+377
+00:37:02,390 --> 00:37:12,690
+of C معقص F of Xأصغر من 0 مش
+
+378
+00:37:12,690 --> 00:37:22,070
+مشكلة limit
+
+379
+00:37:22,070 --> 00:37:31,690
+f of x نقص f of c على x minus c لما x تروح ل c من
+
+380
+00:37:31,690 --> 00:37:36,360
+اليسارمعناته الـ X أكبر من الـ C إذاً هذه صارت
+
+381
+00:37:36,360 --> 00:37:41,080
+موجبة هذه موجبة و هذه موجبة ده بتكون أشماله أكبر
+
+382
+00:37:41,080 --> 00:37:48,060
+من سفر أكبر أو يساوي سفر similarly limit F of X
+
+383
+00:37:48,060 --> 00:37:54,380
+ناقص F of C على X minus C لما X تروح ل C من اليسار
+
+384
+00:37:54,380 --> 00:38:00,110
+اللي هو هذه اللي هي أصغر من سفروهذه تصبح أصغر أو
+
+385
+00:38:00,110 --> 00:38:06,970
+ساوى 0 ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+386
+00:38:06,970 --> 00:38:07,570
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+387
+00:38:07,570 --> 00:38:07,570
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+388
+00:38:07,570 --> 00:38:08,030
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+389
+00:38:08,030 --> 00:38:08,030
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+390
+00:38:08,030 --> 00:38:08,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+391
+00:38:08,130 --> 00:38:08,690
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+392
+00:38:08,690 --> 00:38:10,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+393
+00:38:10,510 --> 00:38:10,510
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+394
+00:38:10,510 --> 00:38:10,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+395
+00:38:10,510 --> 00:38:10,510
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+396
+00:38:10,510 --> 00:38:11,170
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+397
+00:38:11,170 --> 00:38:19,550
+.. ال .. ال .. ال ..F of X ناقص F of C على X minus
+
+398
+00:38:19,550 --> 00:38:24,130
+C as X بتروح للـ C exist إذا ال limit من اليمين
+
+399
+00:38:24,130 --> 00:38:26,010
+تساوي ال limit من اليسار مش ال continuity ال
+
+400
+00:38:26,010 --> 00:38:28,850
+differentiability إذا ال limit من اليمين تساوي ال
+
+401
+00:38:28,850 --> 00:38:32,610
+limit من اليسار هذا لا يمكن أن يحدث في هذه الحالة
+
+402
+00:38:32,610 --> 00:38:38,490
+إلا غير لما تكون كلام صحيح بدك تستخدم الصحيح بنفع
+
+403
+00:38:38,490 --> 00:38:42,210
+بنفع بنفع
+
+404
+00:38:45,000 --> 00:38:51,520
+بدونها .. بدونها .. بدونها بنفع اه
+
+405
+00:38:51,520 --> 00:38:55,380
+بنفع اه .. اه ما هو by contradiction هو انت لو ..
+
+406
+00:38:55,380 --> 00:38:58,200
+لو يعني لاحظت في ال .. في ال .. طبعا احنا ما
+
+407
+00:38:58,200 --> 00:39:00,220
+ساخدمناش limit من اليمين و limit من اليسار،
+
+408
+00:39:00,220 --> 00:39:08,700
+ساخدمنا ال limit مباشرة، بصير، بصير، فهم صحيحهو
+
+409
+00:39:08,700 --> 00:39:13,640
+الحل اللي انت بتعرفه و يعني خليني أقوله مرتاح له
+
+410
+00:39:13,640 --> 00:39:17,500
+هو الأسهل اه يعني انت ممكن تشوف هذا أسهل و هذا
+
+411
+00:39:17,500 --> 00:39:24,260
+أسهل كلام صحيح يلا اللي بعده الان corollary منيحي
+
+412
+00:39:24,260 --> 00:39:26,620
+محمد اللي بعده
+
+413
+00:39:33,180 --> 00:39:36,640
+corollary اللي ممكن حكيتها الـ corollary هذه أنا
+
+414
+00:39:36,640 --> 00:39:40,380
+اللي هي من المعلومات اللي قبل بشوية لو كانت ال
+
+415
+00:39:40,380 --> 00:39:44,420
+function f اللي هو has اللي هي f من I من I اللي
+
+416
+00:39:44,420 --> 00:39:47,980
+عندها continuous و non-interval and suppose that f
+
+417
+00:39:47,980 --> 00:39:51,420
+has a relative extremum of an interior point c of
+
+418
+00:39:51,420 --> 00:39:58,540
+I then either the derivative of f exists or f بسوة
+
+419
+00:39:58,540 --> 00:40:02,780
+سفرعادت صيغة للي قبل بشوية أنه لو كانت الـ
+
+420
+00:40:02,780 --> 00:40:08,720
+function عندي من I لعند R continuous وكانت اللي هي
+
+421
+00:40:08,720 --> 00:40:13,540
+الـ C interior point عندها relative maximum أو
+
+422
+00:40:13,540 --> 00:40:17,920
+relative minimum هذا لازم يعطينا أن الـ F prime يا
+
+423
+00:40:17,920 --> 00:40:21,860
+does not exist يا إما zero طبعا و هذي مباشرة لو
+
+424
+00:40:21,860 --> 00:40:28,150
+جلنا نفترض أن F prime existبنحصل عالميين على الـ 0
+
+425
+00:40:28,150 --> 00:40:32,190
+من النظرية اللي قبله شوية وهو المطلوب واضح نجي
+
+426
+00:40:32,190 --> 00:40:35,230
+للنظرية البعيدة اللي هي إيش اسمها النظرية المشهورة
+
+427
+00:40:35,230 --> 00:40:41,090
+اللي هي اسمها Rawls theorem Rawls theorem يا جماعة
+
+428
+00:40:41,090 --> 00:40:44,370
+طبعا مرت علينا في ال calculus ويمكن كمان صارت في
+
+429
+00:40:44,370 --> 00:40:49,690
+الثانوية يدرسوها النظرية طبعا معناها الهندسي كمان
+
+430
+00:40:49,690 --> 00:40:53,910
+بمر معاكم أنه لو كانت عند ال function is
+
+431
+00:40:53,910 --> 00:41:05,950
+continuousعلى F من A و B لعند R continuous on A و
+
+432
+00:41:05,950 --> 00:41:15,830
+B و differentiable on A و B open وعندي F of A .. F
+
+433
+00:41:15,830 --> 00:41:22,960
+of A هيها و F of B هيهابصير عندي معطيني كمان f of
+
+434
+00:41:22,960 --> 00:41:26,900
+a بساوي f of b ماعطينيهاش بساوي، بساوي سفر، لو
+
+435
+00:41:26,900 --> 00:41:30,260
+كانت بتساوي ثابت برضه بتظبط، بتكون نفسها، تعميم
+
+436
+00:41:30,260 --> 00:41:35,500
+بسيط لها ال f of a بساوي f of b بساوي سفر، بقوللي
+
+437
+00:41:35,500 --> 00:41:46,320
+إذا هالاجي نقطة then هذا معطى if this holds then
+
+438
+00:41:47,250 --> 00:41:52,110
+there exists C وحدة، تنتين، تلات، او .. المهم على
+
+439
+00:41:52,110 --> 00:41:55,790
+الأقل في واحدة there exists C المتل A و B such
+
+440
+00:41:55,790 --> 00:42:01,290
+that F prime of C بيساوز فماذا يعني؟ يعني بالله
+
+441
+00:42:01,290 --> 00:42:06,230
+بمعنى اخر نقطة C او اكثر في بين ال A و ال B بحيث
+
+442
+00:42:06,230 --> 00:42:11,390
+انه ميل المماس عندها او المماس اللي عندها بوازمين
+
+443
+00:42:11,390 --> 00:42:15,570
+محور السناد طبعا هنا في واحد هاي اتنين هاي تلاتة
+
+444
+00:42:16,090 --> 00:42:21,070
+طبعا حسب .. حسب الدالة اللي هو أكيد بتلاقي إذا
+
+445
+00:42:21,070 --> 00:42:26,130
+تحققت الشروط الأقل في نقطة عندها اللي هو المماس
+
+446
+00:42:26,130 --> 00:42:35,870
+بوازي محور السينات أي سؤال؟ ال proof ال proof برضه
+
+447
+00:42:35,870 --> 00:42:39,570
+احنا كنا أحيانا نبرهنه في ال calculus خلينا
+
+448
+00:42:39,570 --> 00:42:46,150
+نبرهنوها، أكيد هندرهنوها عنديلو كانت الـ F هي
+
+449
+00:42:46,150 --> 00:42:51,550
+الدالة الصفرية يعني F بتساوي 0 it is a trivial أنه
+
+450
+00:42:51,550 --> 00:42:54,390
+مش حلها جنوبها كل نقاطها الـ F prime of C هي إيش
+
+451
+00:42:54,390 --> 00:42:59,770
+بتتساوي؟ بتساوي 0 إذا ال case F بتساوي 0 is a
+
+452
+00:42:59,770 --> 00:43:07,590
+trivial case الآن case 2 case 1 الآن F ليست الدالة
+
+453
+00:43:07,590 --> 00:43:14,870
+الصفرية في الاحتمالين أنه بدأ عملها أن Fassumes
+
+454
+00:43:14,870 --> 00:43:25,310
+positive values الاحتمال التانوي F assumes
+
+455
+00:43:25,310 --> 00:43:33,730
+negative values أنا بدعي ان هذولا بيجيبن كل الحلال
+
+456
+00:43:34,430 --> 00:43:38,270
+لو كانت F assumes positive value ممكن تاخد
+
+457
+00:43:38,270 --> 00:43:40,830
+positive وتاخد negative وممكن تاخد positive لحالها
+
+458
+00:43:40,830 --> 00:43:46,250
+بظبط ولا لأ ال F assume negative values إذا هتاخد
+
+459
+00:43:46,250 --> 00:43:49,530
+حالة F assumes negative values لحالها أو negative
+
+460
+00:43:49,530 --> 00:43:56,780
+values مع مين؟ مع positive values واضح؟طيب، الآن
+
+461
+00:43:56,780 --> 00:44:00,520
+بدي أثبتلك في الحالة الأولى على طول هتطلع F prime
+
+462
+00:44:00,520 --> 00:44:06,700
+of C == 0 وفي الحالة التانية similarly، معايا؟الآن
+
+463
+00:44:06,700 --> 00:44:10,780
+في عندنا نظرية في تحليل واحد أو في الكالكولاست حتى
+
+464
+00:44:10,780 --> 00:44:16,640
+كنا نقول if F is continuous on a closed bounded
+
+465
+00:44:16,640 --> 00:44:22,640
+interval then it must attain its maximum and its
+
+466
+00:44:22,640 --> 00:44:28,140
+minimum in this absolute كمان in its interval،
+
+467
+00:44:28,140 --> 00:44:35,130
+مظبوط؟ يعني بمعنى آخرعندي بما أن F continuous على
+
+468
+00:44:35,130 --> 00:44:39,830
+closed bounded interval then its absolute maximum
+
+469
+00:44:39,830 --> 00:44:43,650
+and absolute minimum is attained here يعني بمعنى
+
+470
+00:44:43,650 --> 00:44:50,470
+أخر there exists C element in A وB such that F of
+
+471
+00:44:50,470 --> 00:44:55,900
+C هي ال maximumإيه في ال maximum يعني؟ يعني ال
+
+472
+00:44:55,900 --> 00:45:01,040
+supremum أو ال maximum لكل F of X حيث X وين موجودة
+
+473
+00:45:01,040 --> 00:45:08,400
+في ال A و ال B، مظبوط؟ إذا صارت عندي في C في ال A
+
+474
+00:45:08,400 --> 00:45:12,180
+و ال B بحيث أن F of C بالساوى ال supremum هذا ال
+
+475
+00:45:12,180 --> 00:45:17,780
+supremum يا جماعة أكيد A شماله أكبر strictly من A
+
+476
+00:45:18,660 --> 00:45:23,920
+من صفر ليش؟ لأن احنا تحت أي عنوان بنشتغل F assumes
+
+477
+00:45:23,920 --> 00:45:27,640
+positive values إذا في على أقل قيمة واحدة positive
+
+478
+00:45:27,640 --> 00:45:33,440
+إذا F of C هيكون strictly أكبر من مين؟ من صفر طيب
+
+479
+00:45:33,440 --> 00:45:41,920
+بقول برضه F of C صارت عبارة عن maximum point الـ C
+
+480
+00:45:41,920 --> 00:45:50,520
+مظبوط؟ هذا واحد اتنين الـ Cقطعاً لا هي الـ A ولا
+
+481
+00:45:50,520 --> 00:45:58,060
+هي الـ B ليش؟ لأنه بما أن أف of A بساوي أف of B
+
+482
+00:45:58,060 --> 00:46:06,240
+بساوي 0 إذا أكيد C هتكون نقطة داخلية لا هتكون الـ
+
+483
+00:46:06,240 --> 00:46:10,120
+A ولا هتكون الـ B إذا صار في عندي شغلتين إنه C
+
+484
+00:46:10,120 --> 00:46:16,880
+نقطة داخلية وC عندها maximumإذا وكانت وعندي ال F
+
+485
+00:46:16,880 --> 00:46:19,800
+is differentiable على ال A و ال B على ال open
+
+486
+00:46:19,800 --> 00:46:24,260
+interval إذا حسب النظرية اللي قبله شوية لازم تكون
+
+487
+00:46:24,260 --> 00:46:30,800
+F prime of C عشان تساوي ساو سفر then F prime of C
+
+488
+00:46:30,800 --> 00:46:40,530
+ساو سفر واضح أه طيب الآنالحالة الثانية F assumes
+
+489
+00:46:40,530 --> 00:46:44,670
+negative values مدام F assumes negative values إذا
+
+490
+00:46:44,670 --> 00:46:53,930
+ناقص الـ F assumes positive values صح ولا لا؟ الآن
+
+491
+00:46:53,930 --> 00:46:56,870
+اللي بنتبج على الـ F اللي فوق صار ينتبج على ناقص F
+
+492
+00:46:56,870 --> 00:46:57,390
+كله
+
+493
+00:47:05,040 --> 00:47:08,060
+differentiable على الـ A و الـ B و continuous على
+
+494
+00:47:08,060 --> 00:47:12,620
+الـ closed interval و هذا هيتحقق على مين بس؟ على
+
+495
+00:47:12,620 --> 00:47:19,480
+ناقص F إذا من ال case التانية ناقص F of C prime
+
+496
+00:47:19,480 --> 00:47:26,300
+هتساوي سفر أو بمعنى آخر F prime of C هيساوي سفر
+
+497
+00:47:26,300 --> 00:47:32,380
+for some C element in A و B هذه برهان ال roles
+
+498
+00:47:32,380 --> 00:47:45,410
+theoryأي سؤال اللي بعده الآن أوصلنا لإن نقدر الآن
+
+499
+00:47:45,410 --> 00:47:50,890
+نحكي عن اللي هو نظرية القيمة المتوسطة أو الـ Mean
+
+500
+00:47:50,890 --> 00:47:54,990
+Value Theorem نظرية القيمة المتوسطة أو الـ Mean
+
+501
+00:47:54,990 --> 00:47:57,510
+Value Theorem برضه
+
+502
+00:47:59,060 --> 00:48:03,900
+اللي هو مرت عليكم في calculus ألف و بتمر أيضًا في
+
+503
+00:48:03,900 --> 00:48:09,000
+اللي هو ملهجة ثانوية إيش ال mean value theorem؟ هي
+
+504
+00:48:09,000 --> 00:48:15,840
+عبارة عن تعميم لمين لل roles theorem إيش بتقول ال
+
+505
+00:48:15,840 --> 00:48:27,580
+mean value theorem؟ mean value theorem if F من A و
+
+506
+00:48:27,580 --> 00:48:38,570
+Bالعلب R is continuous and differentiable on A وB
+
+507
+00:48:38,570 --> 00:48:47,130
+then there exists C element in A وB such that F
+
+508
+00:48:47,130 --> 00:48:54,010
+prime of C سواء F of B ناقص F of A على B minus A
+
+509
+00:48:54,010 --> 00:48:57,590
+طبعا معناها الأهندسية برضه مارة عليكم خلّيني أقول
+
+510
+00:48:57,590 --> 00:49:05,120
+كمان مرةإيش اللي بتقوله النظرية؟ بتقول كمايا ليه؟
+
+511
+00:49:05,120 --> 00:49:14,860
+لإن مش مزايد بس ماشي
+
+512
+00:49:14,860 --> 00:49:22,960
+مفترض إن هي اللي عندي الـA وهي عند مين الـBالان F
+
+513
+00:49:22,960 --> 00:49:27,180
+of B نقص F of A على B minus A اللي هو عبارة عن ميل
+
+514
+00:49:27,180 --> 00:49:34,540
+عن ميل القاطع هذا ها .. هايه هذا اللي هو عبارة عن
+
+515
+00:49:34,540 --> 00:49:43,760
+النقطة B و F of B و هذا النقطة A و F of A طبعا ميل
+
+516
+00:49:43,760 --> 00:49:50,380
+القاطع زي ما انتوا عارفين هو F of B لهناناقص F of
+
+517
+00:49:50,380 --> 00:49:57,060
+A هذه فبكون هذا على اللي هو B كلها هذه ناقص A
+
+518
+00:49:57,060 --> 00:50:02,360
+فبكون اللي هو ميل القاطع هذا اللي هو F of B ناقص F
+
+519
+00:50:02,360 --> 00:50:06,900
+of A على B minus Aوالـ F prime of C اللي هو عبارة
+
+520
+00:50:06,900 --> 00:50:10,860
+عن إيش؟ عن ميل المماس عنده النقطة C يعني وكأنه
+
+521
+00:50:10,860 --> 00:50:14,400
+نظرية بتقولنا إنه لو كانت F is continuous على
+
+522
+00:50:14,400 --> 00:50:17,840
+closed interval A وB و differentiable على ال open
+
+523
+00:50:17,840 --> 00:50:22,340
+interval A وB بلاجي اللي هو مما .. وهي عند القاطع
+
+524
+00:50:22,340 --> 00:50:29,040
+هيه بلاجي مماس لدالة مماس واحد او اتنين او تلاتة
+
+525
+00:50:29,040 --> 00:50:37,560
+موازن مينيعني عند نقطة C بلاق اللي هو مماس يوازمين
+
+526
+00:50:37,560 --> 00:50:41,260
+.. يوازم القاطع في rule theorem كانت اللي هو ال A
+
+527
+00:50:41,260 --> 00:50:45,740
+و ال B صورة .. صورة انتحار على ال X axis فطبيعي ما
+
+528
+00:50:45,740 --> 00:50:49,980
+اللي هو قطح هو ال X axis من القاطع اللي هو سفر
+
+529
+00:50:50,790 --> 00:50:56,170
+فاهمين؟ فبكون اللي هو الـ F' اللي هو طبيعي موازي
+
+530
+00:50:56,170 --> 00:51:00,890
+أو صفر أو موازي للـ X-axis يعني بمعنى أخر والـ
+
+531
+00:51:00,890 --> 00:51:05,750
+theorem هي حالة خاصة من الـ mean value theorem
+
+532
+00:51:05,750 --> 00:51:12,490
+واضح؟ طيب، الآن ال proof ال proof طبعا أكيد هنعتمد
+
+533
+00:51:13,290 --> 00:51:16,690
+على اللي هو الـ mean على الـ Rolle's theorem في
+
+534
+00:51:16,690 --> 00:51:21,950
+الإثبات بدنا اللي هو نركب اللي هو الـ function
+
+535
+00:51:21,950 --> 00:51:27,210
+تكون بتحقق الـ mean value theorem و بتجيبلنا اللي
+
+536
+00:51:27,210 --> 00:51:33,750
+هي الصورة هذه لو أخدنا 5x بساوي f of x ناقص f of a
+
+537
+00:51:33,750 --> 00:51:38,110
+ناقص اللي هو المال اللي بديه f of b ناقص f of a
+
+538
+00:51:38,110 --> 00:51:45,970
+على b minus a مضروبةفي X minus A هلجيت بتشوف ليش
+
+539
+00:51:45,970 --> 00:51:52,910
+أخدنا الدالة الدالة الأن هذه لو جيت حسبة Phi of A
+
+540
+00:51:52,910 --> 00:51:57,630
+لها يعني consider this function Phi of A هيساوي F
+
+541
+00:51:57,630 --> 00:52:02,730
+of A نقص F of A سفر وA نقص A سفر فبصير بالسفر هذا
+
+542
+00:52:02,730 --> 00:52:10,040
+إذن بيساوي سفر لو جيت حسبة Phi of B5 of B هيصير 5
+
+543
+00:52:10,040 --> 00:52:14,280
+of B بيساوي F of B نقص F of A خليني عندك و B minus
+
+544
+00:52:14,280 --> 00:52:18,260
+A بتروح هذه محادي هذه ناقص لنفسها بيطلع برضه أياش
+
+545
+00:52:18,260 --> 00:52:23,000
+سفر إذا الأن 5 of A بيساوي 5 of B بيساوي سفر هاي
+
+546
+00:52:23,000 --> 00:52:27,600
+واحد اتنين عندي هذه الدالة is continuous على
+
+547
+00:52:27,600 --> 00:52:33,120
+closed bounded intervalوهذه ثوابت و X minus A X
+
+548
+00:52:33,120 --> 00:52:36,120
+minus A ده اللي خطية continuous وين مكان و
+
+549
+00:52:36,120 --> 00:52:39,520
+differentiable وين مكان إذا صارت هذه الدالة كلها
+
+550
+00:52:39,520 --> 00:52:43,360
+على بعض اللي هي A Phi of X is continuous وين مكان
+
+551
+00:52:43,360 --> 00:52:45,900
+بما فيها اللي .. ال .. ال .. ال .. ال .. ال .. ال
+
+552
+00:52:45,900 --> 00:52:46,040
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+553
+00:52:46,040 --> 00:52:46,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+554
+00:52:46,320 --> 00:52:46,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+555
+00:52:46,420 --> 00:52:48,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+556
+00:52:48,560 --> 00:52:48,600
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+557
+00:52:48,600 --> 00:52:49,020
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+558
+00:52:49,020 --> 00:52:49,700
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+559
+00:52:49,700 --> 00:52:50,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+560
+00:52:50,180 --> 00:52:50,420
+.. ال .. ال .. ال .. ال .. ال
+
+561
+00:52:59,650 --> 00:53:05,310
+و differentiable on a و b و أيضا اللي هو five a
+
+562
+00:53:05,310 --> 00:53:10,410
+بيساوي five b بيساوي سفر اذا .. اذا by Rolle's
+
+563
+00:53:10,410 --> 00:53:16,810
+theorem there exists c element in a و b such that
+
+564
+00:53:16,810 --> 00:53:22,230
+five prime of c ايش بتساويك؟ بتساوي سفر طيب سفر
+
+565
+00:53:22,230 --> 00:53:26,490
+يعني بتساوي five prime of c ايش five prime of c؟
+
+566
+00:53:26,490 --> 00:53:31,900
+خلينا نفرض لهناهي عبارة عن F prime of C مكان الـ
+
+567
+00:53:31,900 --> 00:53:36,840
+XC وهذه سفر وهذه اللي هي تفاضل الـ X وهذه سفر
+
+568
+00:53:36,840 --> 00:53:42,640
+طبعاً ضال الـ X هي شمالها واحد بصير ناقص F of B
+
+569
+00:53:42,640 --> 00:53:49,300
+فاهمين؟ F of A على B minus A هذا بيسوء سفر وهذا
+
+570
+00:53:49,300 --> 00:53:56,140
+يعني أن F prime of C بيسوء F of B ناقص F of A على
+
+571
+00:53:56,140 --> 00:54:06,450
+B minus Aوهو المطلوب، مظبوط؟ نيجي الآن لبعض
+
+572
+00:54:06,450 --> 00:54:14,290
+النتائج اللي احنا بستعملها كتير اللي
+
+573
+00:54:14,290 --> 00:54:20,630
+هي في الواقع برهانة عن طريق الـ Mean Value Theorem
+
+574
+00:54:20,630 --> 00:54:26,120
+النظرية اللي بتقول ليهاللي هي اللي باختصار بنقول
+
+575
+00:54:26,120 --> 00:54:33,900
+أنه لو كانت المشتقة الأولى لدالة بتساوي سفر إذن هي
+
+576
+00:54:33,900 --> 00:54:41,340
+اللي هتكون مين هي المشتقة الثابتة طيب نشوف بالظبط
+
+577
+00:54:41,340 --> 00:54:46,960
+أيش اللي بقوله بقولوا .. نفترض أن F continuous F
+
+578
+00:54:46,960 --> 00:54:53,280
+عبارة عن دالة من A و Bلعيد R continuous ماشي
+
+579
+00:54:53,280 --> 00:54:57,060
+continuous على closed اللي هو open closed bounded
+
+580
+00:54:57,060 --> 00:55:02,060
+interval الان او كانت differentiable و F
+
+581
+00:55:02,060 --> 00:55:08,080
+differentiable على ال A و ال B باشي الحال بالاضافة
+
+582
+00:55:08,080 --> 00:55:15,300
+معطيك and F prime of X بساوة سفر لكل X element in
+
+583
+00:55:15,300 --> 00:55:19,600
+A و B هذا بقوللي على بعضه then
+
+584
+00:55:22,250 --> 00:55:29,470
+then اللي هو f of x بساوي c لكل x element in a و b
+
+585
+00:55:29,470 --> 00:55:39,910
+for some c constant for some constant c طيب الآن
+
+586
+00:55:39,910 --> 00:55:46,370
+ال proof البرهانة عمبرا عن exercise صغير بسيط
+
+587
+00:55:46,370 --> 00:55:56,110
+نبرهنه مع بعض الآن خد xlet x element in a و b ماشي
+
+588
+00:55:56,110 --> 00:56:00,530
+و خلّينا ناخد ال x أكبر من مين من a يعني x في أين
+
+589
+00:56:00,530 --> 00:56:04,410
+موجود في ال open .. في ال half open interval من a
+
+590
+00:56:04,410 --> 00:56:11,610
+و b let x be fixed but arbitrary ماشي الآن بدي
+
+591
+00:56:11,610 --> 00:56:17,570
+أطبّق المي .. طبعا هي ال a و ال b هي ال a و هي ال
+
+592
+00:56:17,570 --> 00:56:21,960
+bوأخدت X أي نقطة هنا هنا .. هنا .. هنا .. هنا ..
+
+593
+00:56:21,960 --> 00:56:26,160
+هنا .. هنا .. حتى لو كانت ال .. إيش ال B إذا صارت
+
+594
+00:56:26,160 --> 00:56:36,020
+ال F عندي ال F صارت ال F continuous on اللي هو X و
+
+595
+00:56:36,020 --> 00:56:43,300
+B صح؟ continuous عليها دي أكيد و لا بناخدها على
+
+596
+00:56:43,300 --> 00:56:53,420
+الفترة A و X أه عشان A و Xو differentiable on a و
+
+597
+00:56:53,420 --> 00:57:01,100
+x صح ولا لأ اذا by الهو mean value theorem there
+
+598
+00:57:01,100 --> 00:57:09,660
+exist c element in a و x such that f prime of c
+
+599
+00:57:09,660 --> 00:57:21,390
+بساوي f of x ناقص f of a على x minus aصحيح؟ حيث C
+
+600
+00:57:21,390 --> 00:57:27,630
+في A و B طب احنا مدام C في A و X بين A و X و احنا
+
+601
+00:57:27,630 --> 00:57:31,830
+مفترضين ان F prime of X بيساوي صفر لكل X في A و B
+
+602
+00:57:31,830 --> 00:57:38,930
+معايا اه؟ اه، اذا هتصير هذا اشمالها صفر، اذا صارت
+
+603
+00:57:38,930 --> 00:57:46,680
+عندي F هذا بيساوي صفر، اذا صارت F of X بتساوي Fof
+
+604
+00:57:46,680 --> 00:57:53,220
+A لكل X وين موجودة الآن for all such X وهذه كانت X
+
+605
+00:57:53,220 --> 00:57:58,000
+fixed but arbitrary إذا صار F of X بيساوي F of A
+
+606
+00:57:58,000 --> 00:58:02,800
+لكل X في الفترة A و B بما فيها ميني الـ A لأنه
+
+607
+00:58:02,800 --> 00:58:12,520
+نفسها بتساوي إذا صارت عندي hence F is constant أي
+
+608
+00:58:12,520 --> 00:58:20,890
+سؤالطيب اللي بعدها corollary
+
+609
+00:58:20,890 --> 00:58:24,470
+الـ corollary برضه من الاشي المشهور اللي احنا
+
+610
+00:58:24,470 --> 00:58:29,190
+بنستخدمه اللي هو لو كان دالتين بحاجة عن الشروط
+
+611
+00:58:29,190 --> 00:58:34,910
+طبعا لأنها تفاضلن زي بعض إذن هيكون اللي هو هن نفس
+
+612
+00:58:34,910 --> 00:58:42,990
+الاشي بس باختلف عن بعض بالأكترين ثابت طيب الآن ال
+
+613
+00:58:42,990 --> 00:58:50,450
+corollary كما يليهالـ Corollary بتقول suppose that
+
+614
+00:58:50,450 --> 00:58:56,970
+F and G are continuous on I, A وB then that they
+
+615
+00:58:56,970 --> 00:59:01,190
+are differentiable on A وB يعني نفترض أن الدالتين
+
+616
+00:59:01,190 --> 00:59:05,230
+F وG continuous على ال closed اللي هي bounded
+
+617
+00:59:05,230 --> 00:59:08,910
+interval A وB وdifferentiable على ال open interval
+
+618
+00:59:08,910 --> 00:59:12,070
+A وBوالـ derivative للأولى بساوي ال derivative
+
+619
+00:59:12,070 --> 00:59:15,690
+للثانية عند كل نقطة من النقاط الـ A و الـ B إذا
+
+620
+00:59:15,690 --> 00:59:18,910
+there exists a constant C such that F بتساوي G
+
+621
+00:59:18,910 --> 00:59:25,350
+زائد H زائد C طبعا البرهان سهل و أكيد يمكن بعضكم
+
+622
+00:59:25,350 --> 00:59:34,390
+برهنه في راسه let H بتساوي F ناقص G مظبوط؟ الآن
+
+623
+00:59:34,390 --> 00:59:43,530
+thenF و G continuous إذن H is continuous on A و B
+
+624
+00:59:43,530 --> 00:59:51,210
+و أيضًا F و G differentiable على A و B and H is
+
+625
+00:59:51,210 --> 00:59:55,210
+differentiable on A و B moreover
+
+626
+00:59:57,700 --> 01:00:02,620
+عندي H برايم اللي هو بساوي F برايم نقص G برايم
+
+627
+01:00:02,620 --> 01:00:08,340
+طبعا عند ال X عند ال X of X of X of X بساوي صفر
+
+628
+01:00:08,340 --> 01:00:16,340
+لكل X موجودة في ال A و ال B then by the above
+
+629
+01:00:16,340 --> 01:00:20,300
+theorem اللي بنحكي عنها اللي هي theorem by theorem
+
+630
+01:00:20,300 --> 01:00:31,180
+625 Hof X بتساوي C for every X element in A وB and
+
+631
+01:00:31,180 --> 01:00:35,300
+hence F
+
+632
+01:00:35,300 --> 01:00:44,040
+of X بساوي G of X زاد some constant C
+
+633
+01:00:50,890 --> 01:00:54,570
+بكونوا احنا وصلنا لعين theorem 627 ان شاء الله
+
+634
+01:00:54,570 --> 01:01:01,010
+المرة القادمة بنكمل والسلام عليكم ورحمة الله
+
+635
+01:01:01,010 --> 01:01:01,670
+وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/4uzI_79FzRE_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/4uzI_79FzRE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..06f70f9afd5ae97ceca265d6f8c26e2e97627add
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/4uzI_79FzRE_raw.srt
@@ -0,0 +1,1452 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,300 --> 00:00:13,800
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+3
+00:00:13,800 --> 00:00:18,020
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+4
+00:00:18,020 --> 00:00:22,220
+آله وصحابه وسلم موضوعنا اليوم يا أخوات عن المخارج
+
+5
+00:00:22,220 --> 00:00:25,720
+والصفات طبعا معروف أنه كل حرف من حروف اللغة
+
+6
+00:00:25,720 --> 00:00:31,660
+العربية لابد أن يكون له مخرج وله صفات فمثلا حرف ال
+
+7
+00:00:31,660 --> 00:00:36,860
+ب من أين يخرج؟ يخرج من الشفتين عند انطباق الشفتين
+
+8
+00:00:36,860 --> 00:00:43,310
+فنقول ابعند المكان الذي ينحصر عنده الصوت بيكون هو
+
+9
+00:00:43,310 --> 00:00:49,070
+مخرج الحرف و كذلك حرف ال M أيضا عند أنطباق الشفتين
+
+10
+00:00:49,070 --> 00:00:53,670
+حرف الأق بأيضا عند أقصى اللسان مع ما يحاذيه من
+
+11
+00:00:53,670 --> 00:00:58,170
+الحناك الأعلى يعني بيكون هذا هو مخرجهم فكل حرف من
+
+12
+00:00:58,170 --> 00:01:02,090
+الحروف لابد أن يكون له مخرج و لابد أن يكون له صفات
+
+13
+00:01:02,090 --> 00:01:05,670
+نحن في هذا الدرس ان شاء الله نتعرف على مخارج
+
+14
+00:01:05,670 --> 00:01:11,630
+الحروف و كذلك صفات الحروففي بعض الدول أو بعض
+
+15
+00:01:11,630 --> 00:01:16,270
+البلدان و بعض الناس يخطؤون فيخرجون الحرف من غير
+
+16
+00:01:16,270 --> 00:01:22,450
+مخرجه مثلا حرف الath يخرجونه فيقول is يقولون ذلك
+
+17
+00:01:22,450 --> 00:01:27,450
+الكتاب طبعا خطأ الأصل أن نقول ذلك الكتاب و العراية
+
+18
+00:01:27,450 --> 00:01:34,210
+فيه كذلك مثلا حرف الathيخرجونه فيقول اس فهذا خطأ
+
+19
+00:01:34,210 --> 00:01:39,430
+يقولون سيبات وأبكارة بدل من أن يقولوا ثيبات
+
+20
+00:01:39,430 --> 00:01:45,810
+وأبكارة أو مثلا حرف ال اث يقولون اس يقولون ثمة ثمة
+
+21
+00:01:45,810 --> 00:01:51,390
+وهذا طبعا خطأأو أزالك ذهب بدل من أن ذهب، إذا لابد
+
+22
+00:01:51,390 --> 00:01:56,230
+أن نتعرف على مخرج كل حرف وصفات كل حرف ومعيب على
+
+23
+00:01:56,230 --> 00:02:00,430
+طالب العلم أن يخرج الحرف من غير مخرجه، يعني إن كان
+
+24
+00:02:00,430 --> 00:02:05,370
+قد يقبل من الإنسان العام، لكن طلب العلم سواء كانوا
+
+25
+00:02:05,370 --> 00:02:09,030
+الطلاب أو الطالبات عليهم أن يتعلموا مخرج الحروف
+
+26
+00:02:09,030 --> 00:02:13,890
+ويخرجوا كل حرف من مخرجه في كلامهم العاديفكيف إذا
+
+27
+00:02:13,890 --> 00:02:18,090
+كانت الأخت تقرأ القرآن؟ إذا هذا الموضوع مهم جدا
+
+28
+00:02:18,090 --> 00:02:24,570
+لأن الذي يقرأ القرآن ويلحن لحن جليا في القرآن يقول
+
+29
+00:02:24,570 --> 00:02:30,230
+علماء عنه لا تصح قراءته ولا إمامته ويأثم فاعله مع
+
+30
+00:02:30,230 --> 00:02:34,850
+الإصرار يعني يحرم على الإنسان أن يقرأ القرآن ويلحن
+
+31
+00:02:34,850 --> 00:02:39,090
+في قراءته للقرآن والذي يقرأ القرآن ويلحن في قراءته
+
+32
+00:02:39,090 --> 00:02:44,070
+لا تصح قراءته ولا إمامتهويأثم فاعله مع الإصرار
+
+33
+00:02:44,070 --> 00:02:49,410
+لذلك نحن نتعلم مخرج الحروف والمخرج يا أخوات هو جمع
+
+34
+00:02:49,410 --> 00:02:54,090
+مخرج وهو اسم لموضع خروج الشيء يعني المكان الذي
+
+35
+00:02:54,090 --> 00:02:58,910
+يخرج منه الشيء مثلا هذه القاعة أين مخرجها؟اللي هو
+
+36
+00:02:58,910 --> 00:03:03,570
+هذا الباب، إذا مخرج القاعة هذا الباب، مخرج السيارة
+
+37
+00:03:03,570 --> 00:03:08,230
+باب الكراج مثلا وها كان مخرج الجامعة باب الجامعة،
+
+38
+00:03:08,230 --> 00:03:12,850
+إذا المخرج .. المخارج جامعة مخرج والمخرج هو اسم
+
+39
+00:03:12,850 --> 00:03:17,750
+لموضع خروج الشاي، هذا من حيث اللغة أما من حيث
+
+40
+00:03:17,750 --> 00:03:22,550
+الإصطلاح، من يعرف لنا المخرج من حيث الإصطلاح؟ تفضل
+
+41
+00:03:22,550 --> 00:03:31,250
+أختالذي ينقضع عنده الصوت فيميزه .. فيميزأحسنتي إذا
+
+42
+00:03:31,250 --> 00:03:35,650
+المخرج من حيث الإصطلاح هو محل خروج الحرف الذي
+
+43
+00:03:35,650 --> 00:03:40,510
+ينقطع عنده الصوت فيتميز الحرف عن غيره من الأحرف
+
+44
+00:03:40,510 --> 00:03:45,550
+يعني المكان الذي ينحصر عنده الصوت أو ينقطع عنده
+
+45
+00:03:45,550 --> 00:03:50,890
+الصوت بكون هو مخرج الحرف الذي نتعلمه هذا بالنسبة
+
+46
+00:03:50,890 --> 00:03:55,650
+للمخرج محل خروج الحرف الذي ينقطع عنده الصوت فيتميز
+
+47
+00:03:55,650 --> 00:04:01,040
+الحرف عن غيره من الحروفأما بالنسبة للحروف فالحروف
+
+48
+00:04:01,040 --> 00:04:07,580
+جمع حرف والحرف في أخوات هو الطرف من كل شيء ومنه
+
+49
+00:04:07,580 --> 00:04:13,880
+قوله تعالى ومن الناس من يعبد الله على حرف ما معنى
+
+50
+00:04:13,880 --> 00:04:18,740
+ومن الناس من يعبد الله على حرف يعني على طرف الدين
+
+51
+00:04:18,740 --> 00:04:24,520
+يعني إن أصابه خيرأطمأننا وإذا أصابه شر كفر وهذه
+
+52
+00:04:24,520 --> 00:04:30,000
+حياة الكفار أو المنافقين يعني يتشبهون بالمسلمين
+
+53
+00:04:30,000 --> 00:04:35,640
+إذا كان فيه خير مستمر وإذا أصابه سوء يعني انه
+
+54
+00:04:35,640 --> 00:04:39,480
+انقلب على عقباه وهذا الذي يقول عنه الله سبحانه
+
+55
+00:04:39,480 --> 00:04:44,120
+وتعالى ومن الناس من يعبد الله على حرف يعني على طرف
+
+56
+00:04:44,120 --> 00:04:49,390
+من الدينهذا في اللغة أما من حيث الإصطلاح فالحرف يا
+
+57
+00:04:49,390 --> 00:04:55,390
+أخوات هو صوت معتمد على مخرج محقق أو مقدر الحرف
+
+58
+00:04:55,390 --> 00:04:59,390
+عبارة عن صوت و الصوت هذا يعتمد على مخرج محقق أو
+
+59
+00:04:59,390 --> 00:05:03,310
+مقدر لأن الإنسان يا أخوات عندما يخرج النفس من
+
+60
+00:05:03,310 --> 00:05:08,350
+الرئتين يمر الهواء عن طريق القصبة الهوائية و يحتك
+
+61
+00:05:08,350 --> 00:05:12,470
+بالأحبال الصوتية الموجودة في الحنجرة فيخرج الصوت
+
+62
+00:05:13,540 --> 00:05:17,780
+هذا الصوت يخرج فمن نتيجة احتكاكه بالأحباد الصوتية
+
+63
+00:05:17,780 --> 00:05:22,400
+بعد ذلك يمر على الفم فالفم هو الذي يحدد الحط أو
+
+64
+00:05:22,400 --> 00:05:26,460
+هذا الصوت فيجعله حرف الإب إذا كان أخرجه من الشفتين
+
+65
+00:05:26,460 --> 00:05:30,760
+أو حرف الأق إذا كان أخرجه من أقصى اللسان أو حرف
+
+66
+00:05:30,760 --> 00:05:35,380
+الإج إذا كان أخرجه من وسط اللسان أو حرف الإأ أو
+
+67
+00:05:35,380 --> 00:05:41,490
+الإههذا أخرجه من الحلق إذا هو عبارة عن صور يعتمد
+
+68
+00:05:41,490 --> 00:05:47,030
+على مخرج محقق أو مقدر أما بالنسبة للمخرج المحقق
+
+69
+00:05:47,030 --> 00:05:52,490
+فهو الذي يعتمد على جزء معين من أيزاء الفم كالحلقي
+
+70
+00:05:52,490 --> 00:05:57,410
+واللساني والشفتين إذا في عندنا المخرج أخوات مخرج
+
+71
+00:05:57,410 --> 00:06:03,750
+محققو مخرج مقدر المخرج المحقق هو الذي يعتمد على
+
+72
+00:06:03,750 --> 00:06:09,350
+جزء معين من أيزاء الفم ما هي أيزاء الفم؟ طبعا هي
+
+73
+00:06:09,350 --> 00:06:12,930
+ثلاثة تفضلي الحلق
+
+74
+00:06:13,830 --> 00:06:19,190
+اللسان الشفتان هذه أيزاء الفم يخرج من الحلق مخارج
+
+75
+00:06:19,190 --> 00:06:22,390
+معينة ومن اللسان مخارج معينة ومن الشفتان أيضا
+
+76
+00:06:22,390 --> 00:06:26,810
+مخرجين وبالتالي هذا هي المخارج المحقق فتخرج منها
+
+77
+00:06:26,810 --> 00:06:31,530
+الحروف كل حرف يخرج من هذه المخارج الثلاثة يعد
+
+78
+00:06:31,530 --> 00:06:37,090
+مخرجه محقق ولكن هناك في مخرج مقدر يخرج من غير هذه
+
+79
+00:06:37,090 --> 00:06:40,630
+الأماكن ما هي المخرج المقدرة او ما معنى المخرج
+
+80
+00:06:40,630 --> 00:06:42,370
+المقدر افضله
+
+81
+00:06:50,300 --> 00:06:54,620
+ممتاز، إذا المخرج المقدر هو الحرف الذي لا يعتمد
+
+82
+00:06:54,620 --> 00:06:59,200
+على مخرج أو جزء معين من أيزاء الفم مثل الغنة، من
+
+83
+00:06:59,200 --> 00:07:03,040
+أين تخرج الغنة؟ من الخيشوم، هل الخيشوم جزء من
+
+84
+00:07:03,040 --> 00:07:08,060
+أيزاء الفم؟ لأ، طبعا نحن ممكن واحد يخرج الغنة و هو
+
+85
+00:07:08,060 --> 00:07:13,180
+مغلق لفمه مثلا، أريد أن أغلق فمي وأخرج الغنة
+
+86
+00:07:19,420 --> 00:07:26,580
+من أين تخرج
+
+87
+00:07:26,580 --> 00:07:29,620
+حروف
+
+88
+00:07:29,620 --> 00:07:32,960
+المادة الثلاثة؟
+
+89
+00:07:34,210 --> 00:07:38,110
+من الجوف يعني لا عمل لللسان ولا الشفتين ولا حتى
+
+90
+00:07:38,110 --> 00:07:44,910
+الحلق به يعني ممكن واحد يقول ا ا ا ا ا ا ا ا ا ا ا
+
+91
+00:07:44,910 --> 00:07:44,910
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+92
+00:07:44,910 --> 00:07:45,430
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+93
+00:07:45,430 --> 00:07:45,470
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+94
+00:07:45,470 --> 00:07:46,210
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+95
+00:07:46,210 --> 00:07:47,050
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+96
+00:07:47,050 --> 00:07:49,650
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+97
+00:07:49,650 --> 00:07:49,670
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+98
+00:07:49,670 --> 00:07:49,670
+ا ا ا ا ا ا
+
+99
+00:08:04,230 --> 00:08:09,190
+مقدرة و كذلك يا أخوات بالنسبة لأقسام الحروف يعني
+
+100
+00:08:09,190 --> 00:08:14,310
+الحروف نفسها لها أقسام في عندنا حروف أصلية و في
+
+101
+00:08:14,310 --> 00:08:19,230
+عندنا حروف فرعية الحروف الأصلية و هي الحروف التي
+
+102
+00:08:19,230 --> 00:08:23,730
+معهودة عندنا و نخرجها من مخرجها بشكل طبيعي و هي
+
+103
+00:08:23,730 --> 00:08:30,630
+عندنا كام حرف الحروف الأصلية؟28 حرف و أضاف إليها
+
+104
+00:08:30,630 --> 00:08:35,190
+العلماء التالت حروف التالت الأخرى و هي حروف المادة
+
+105
+00:08:35,190 --> 00:08:41,170
+الثلاثة يبقى هي في عند 28 حرف تبدأ بألف ب ت ثاجم
+
+106
+00:08:41,170 --> 00:08:47,550
+وتنتهي بها ويا 28 حرف و يزاد عليها حرف الألف
+
+107
+00:08:47,550 --> 00:08:53,400
+الماديةيعني بال hand زي مثلا الأدفة المادية والواو
+
+108
+00:08:53,400 --> 00:08:59,480
+المادية والياء المادية بيكون عددها واحد و تلاتين
+
+109
+00:08:59,480 --> 00:09:04,460
+حرف من الحروف الحروف اللغة العربية وهي عندنا حروف
+
+110
+00:09:04,460 --> 00:09:08,740
+أصليةأما بالنسبة يا أخوات للحروف الفرعية فهي
+
+111
+00:09:08,740 --> 00:09:13,860
+الحروف التي تخرج من مخرجين أو تتردد بين حرفين أو
+
+112
+00:09:13,860 --> 00:09:19,440
+صفتين يعني في عندنا بعض الحروف تتردد هذه الحرف ما
+
+113
+00:09:19,440 --> 00:09:25,380
+بين مخرجين أو صفتين الأمثلة على ذلك مثلا في عندنا
+
+114
+00:09:25,380 --> 00:09:30,540
+الهمزة المسهلة الهمزة المسهلة هي التي تتردد ما بين
+
+115
+00:09:30,540 --> 00:09:35,620
+الهمزة والألفالحمزة والألف يعني ما هي حمزة يعني
+
+116
+00:09:35,620 --> 00:09:43,040
+مثلا كلمة أعجمي وعربي لا نقول أعجمي ولا نقول أعجمي
+
+117
+00:09:43,040 --> 00:09:48,800
+نقول أعجمي أعجمي وعربي أعجمي يعني هي عبارة عن حمزة
+
+118
+00:09:48,800 --> 00:09:54,440
+استفهام دخلت على كلمة أعجمي فتقرأ الحمزة بالتسهيل
+
+119
+00:09:54,440 --> 00:09:59,180
+تسهيل الحمزة الأولى وتقرأ ما بين الحمزة والألف
+
+120
+00:09:59,180 --> 00:10:07,230
+أعجمي وعربيكذلك عندنا من الحروف التي تخرج بين
+
+121
+00:10:07,230 --> 00:10:13,270
+حرفين و تتردد ما بين حرفين هي الألف الممالة. الألف
+
+122
+00:10:13,270 --> 00:10:17,650
+الممالة هي التي تتردد ما بين الألث واليا. مثال ذلك
+
+123
+00:10:17,650 --> 00:10:23,680
+بسم الله مجريها ومرساهانحن نقرأها وقال اركبوا فيها
+
+124
+00:10:23,680 --> 00:10:29,200
+بسم الله مجريها ومرساها مجريها هي الكلمة الوحيدة
+
+125
+00:10:29,200 --> 00:10:33,700
+عندنا في قراءة حفظ عن عاصم التي تقرأ بالإمالة إذا
+
+126
+00:10:33,700 --> 00:10:38,080
+هذه الألف الممالة باقي الألفات عندنا تقرأ بتحقيق
+
+127
+00:10:38,080 --> 00:10:44,340
+الألف عادي يعني تعد حرف مد الألف لكن هذه عندنا بسم
+
+128
+00:10:44,340 --> 00:10:50,850
+الله مجريها ومرساها ده نقول مجراهابالألف ولا نقول
+
+129
+00:10:50,850 --> 00:10:57,350
+مجريها باليا بل نقول إيش مجريها بين الألف واليا
+
+130
+00:10:57,350 --> 00:11:02,430
+إذا الألف الممالة هي الألف التي تتردد ما بين الألف
+
+131
+00:11:02,430 --> 00:11:07,630
+واليا ونسميها الألف الممالة عندنا في قراءة حفظ عن
+
+132
+00:11:07,630 --> 00:11:12,910
+عاصم لا يوجد ألف ممالة إلا في هذه الكلمة بسم الله
+
+133
+00:11:12,910 --> 00:11:19,160
+مجريها ومرساهافي قراءات أخرى مثلا و النجم إذا هوى،
+
+134
+00:11:19,160 --> 00:11:24,000
+احنا نقرأها هوى، هي تقرأ بالإيمالة في قراءات أخرى
+
+135
+00:11:24,000 --> 00:11:29,640
+قرأت ورشع النافع هوى و الضحى، و هكذا عندهم قراءة
+
+136
+00:11:29,640 --> 00:11:35,760
+معينة، حسب القراءة التي يمتاز بها هذا الحرفكذلك في
+
+137
+00:11:35,760 --> 00:11:40,560
+عندنا أخوات مثلا من الحرف الحروف التي تتردد ما بين
+
+138
+00:11:40,560 --> 00:11:46,440
+الصاد والزاى اسمها الصاد المشمّى الصاد المشمّى
+
+139
+00:11:46,440 --> 00:11:50,860
+بصوت الزاى هذه لا نقرأها نحن ولا يوجد في أي كلمة
+
+140
+00:11:50,860 --> 00:11:56,480
+من القرآن يعني كلمة في حرف صاد مشم بصوت الزاى
+
+141
+00:11:56,480 --> 00:12:01,200
+لكنها في قراءات أخرىيعني الصاد المشمّف بصوت الزي
+
+142
+00:12:01,200 --> 00:12:05,780
+مثل اهدنا الصراطة المستقيم نحن نقول الصراطة لكنها
+
+143
+00:12:05,780 --> 00:12:11,580
+تقرأ بالزراطة ما بين الصاد وزي اهدنا الصراطة
+
+144
+00:12:11,580 --> 00:12:16,610
+المستقيمفهذه الحرفة هي ليست عندنا في قراءتنا حفص
+
+145
+00:12:16,610 --> 00:12:23,070
+عن عاصم كذلك الياء المشم بصوت الواو يعني ايضا
+
+146
+00:12:23,070 --> 00:12:28,110
+عندنا الياء اللتي تتردد ما بين الواو والياه وهذه
+
+147
+00:12:28,110 --> 00:12:31,910
+ليست قراءتنا وانما هي قراءة هشام او قراءة الكسائي
+
+148
+00:12:33,110 --> 00:12:39,210
+تقرأ الصاد أو الياء المشمّى بصوت الواو يعني تقرأ
+
+149
+00:12:39,210 --> 00:12:45,790
+الياء ما بين الواوي واليا مثال ذلك وقيلة كيف تقرأ
+
+150
+00:12:45,790 --> 00:12:51,650
+هذه الكلمة نقول قيلة بس من ضم الشفتين وقيلة وقيلة
+
+151
+00:12:51,650 --> 00:12:59,040
+من مراوقيلة أو وغيظة الماء نقول وغيظة وغيظة يعني
+
+152
+00:12:59,040 --> 00:13:05,280
+بعد نقول وغيظة لكن من ضم الشفتين فتقرأ الياء بصوت
+
+153
+00:13:05,280 --> 00:13:10,820
+الوا أو مشمة يعني فعلها ريحة الواو أو تترددنا بين
+
+154
+00:13:10,820 --> 00:13:15,040
+اليائي والواو وهذه ليست عندنا ليست في قراءتنا وهي
+
+155
+00:13:15,040 --> 00:13:19,400
+قراءة حفص عن عاصم وإنما هي قراءة هشاو والكسائر
+
+156
+00:13:20,240 --> 00:13:25,460
+عندنا كذلك من الحروف التي تتردد ما بين الصفتين هي
+
+157
+00:13:25,460 --> 00:13:31,420
+مثلا حرف اللام في لفظ الجلالة هذه عندنا تفخم اللام
+
+158
+00:13:31,420 --> 00:13:37,380
+في أحيانا و ترقق أحيانا متى تفخم اللام يا أخوات في
+
+159
+00:13:37,380 --> 00:13:38,840
+لفظ الجلالة؟ تفضلي
+
+160
+00:13:42,850 --> 00:13:48,770
+أحسنتِ إذا اللام في لفظ الجلالة أحيانا نقول الله و
+
+161
+00:13:48,770 --> 00:13:54,770
+أحيانا نقول الله متى نقول الله و متى نقول الله حسب
+
+162
+00:13:54,770 --> 00:13:58,710
+ما سبقها والله إذا كانت اللام في لفظ الجلالة
+
+163
+00:13:58,710 --> 00:14:05,090
+مسبوقة بألف بفتحة يعني إِنَّ اللَّهَ إِنَّ اللَّهَ
+
+164
+00:14:05,090 --> 00:14:10,040
+بتكون مفخمة لإن نقول الله تملأ الفملكن إذا كانت
+
+165
+00:14:10,040 --> 00:14:16,000
+مسبوقة بكسرة نقول بسم الله لا نقول بسم الله أصلا
+
+166
+00:14:16,000 --> 00:14:20,620
+بتكون ثقيلة على اللسان إنما نقول بسم الله بسم الله
+
+167
+00:14:20,620 --> 00:14:25,790
+الرحمن الرحيم لأنها مسبوقة بكسر من رسول اللهأه
+
+168
+00:14:25,790 --> 00:14:33,830
+الحمد لله .. الحمد لله مضمونة لأن الله مكسورة، لله
+
+169
+00:14:33,830 --> 00:14:38,970
+مرققة، يعني هي أصلا الكلمة الله .. يعني لما قولنا
+
+170
+00:14:38,970 --> 00:14:45,170
+لله تحدث الهمس الواصل وتقرأ ..الحمد لله فبتكون
+
+171
+00:14:45,170 --> 00:14:48,910
+اللام تحت لفظ الجلالة مسبوقة بكثرة فتقرأ بالترقير
+
+172
+00:14:48,910 --> 00:14:55,390
+ولا نقول الحمد لله إنما الحمد لله إذا لله اللام
+
+173
+00:14:55,390 --> 00:15:03,410
+مراققة بسم الله اللام إيه مراققة طيب إن الله اللام
+
+174
+00:15:03,410 --> 00:15:08,870
+مفخمة لماذا مفخمة؟ لأنها مسبوقة بحرف مفتوح مثلا
+
+175
+00:15:08,870 --> 00:15:22,140
+رسول اللهمسبوقة بضمن مثلا هنا اللها اللها
+
+176
+00:15:22,140 --> 00:15:23,680
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+177
+00:15:23,680 --> 00:15:23,680
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+178
+00:15:23,680 --> 00:15:23,680
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+179
+00:15:23,680 --> 00:15:24,380
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+180
+00:15:24,380 --> 00:15:24,820
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+181
+00:15:24,820 --> 00:15:29,560
+اللها
+
+182
+00:15:29,560 --> 00:15:31,040
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+183
+00:15:31,040 --> 00:15:31,040
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+184
+00:15:31,040 --> 00:15:31,060
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+185
+00:15:31,060 --> 00:15:31,060
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+186
+00:15:31,060 --> 00:15:31,060
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+187
+00:15:31,060 --> 00:15:31,060
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+188
+00:15:31,060 --> 00:15:31,060
+اللها اللها اللها اللها اللها اللها اللها اللها
+
+189
+00:15:31,060 --> 00:15:38,360
+اللها اللها اللها اللها اللها اللها اللها
+
+190
+00:15:38,360 --> 00:15:43,120
+اللهالأنها مسبوقة بضم، إذا حكم اللام أحيانا في لطف
+
+191
+00:15:43,120 --> 00:15:48,160
+الجلالة أحيانا تفخم و أحيانا ترقق حسب ما قبلها،
+
+192
+00:15:48,160 --> 00:15:52,440
+فإن كان ما قبلها مفتوح أو مضموم فُخمت، وإن كان ما
+
+193
+00:15:52,440 --> 00:15:58,440
+قبلها مكسور رُقِخَت كذلك في عندنا أخوات الألف،
+
+194
+00:15:58,440 --> 00:16:04,550
+الألف المفخرةالألف زي ما قلنا لام تفخم و هي عندنا
+
+195
+00:16:04,550 --> 00:16:08,610
+في قراءة حفص على عاصم تفخم في حالات وترقق في حالات
+
+196
+00:16:08,610 --> 00:16:13,950
+كذلك الألف أيضا تفخم في حالات وترقق في حالات
+
+197
+00:16:13,950 --> 00:16:19,510
+فالألف تتبع ما قبلها من حيث التفخيم والترقير فإن
+
+198
+00:16:19,510 --> 00:16:23,690
+كان ما قبلها مفخما يعني من حروف التفخيم اللي هي
+
+199
+00:16:23,690 --> 00:16:29,950
+حروف استعلاء فخما وإن كان ما قبلها مرققا رقيقا
+
+200
+00:16:29,950 --> 00:16:31,270
+مثال ذلك مثلا
+
+201
+00:16:36,170 --> 00:16:41,650
+الطامة مالها مفخمة ولا مراققة؟ مفخمة ماني أقرأ
+
+202
+00:16:41,650 --> 00:16:43,690
+ليها؟ تفضلي
+
+203
+00:16:48,200 --> 00:16:52,840
+أحسنتي إذا الطام
+
+204
+00:16:52,840 --> 00:16:58,720
+فخمنا الألف لأن ما قبلها حرف الطا و حرف الطا حرف
+
+205
+00:16:58,720 --> 00:17:01,980
+مفخم من حروف الاستعلاء المجموعة في قوله إيش
+
+206
+00:17:01,980 --> 00:17:07,800
+أخواته؟ خصة، ضغط، قض طب لو قلنا تامة
+
+207
+00:17:09,900 --> 00:17:21,700
+الألف مرقق لأن
+
+208
+00:17:21,700 --> 00:17:26,460
+حرف النون مرقق كذلك ظالمين
+
+209
+00:17:28,460 --> 00:17:34,140
+مفخمة، إذا تفخم الألف حسب ما قبلها إن كان ما قبلها
+
+210
+00:17:34,140 --> 00:17:40,340
+مفخما فخمة وإن كان ما قبلها مراققة رقيقة وهذه طبعا
+
+211
+00:17:40,340 --> 00:17:47,100
+في قرائتنا ممكن أن نعتمد عليها كذلك يا أخوات النون
+
+212
+00:17:47,100 --> 00:17:51,800
+المخفاةالنون هذا أيضا من صفاتها أو تتردد ما بين
+
+213
+00:17:51,800 --> 00:17:58,240
+الصفتين ما بين الإظهار والإضغام يعني نعطي النون
+
+214
+00:17:58,240 --> 00:18:02,260
+مثلا أو الحرف الصفة ما بين الإظهار والإضغام لأن
+
+215
+00:18:02,260 --> 00:18:07,360
+الحرف النون نفسها أو الحرف المخفى نعطيه الصفة لا
+
+216
+00:18:07,360 --> 00:18:11,750
+هو إظهار ولا هو إضغام يعني ما بين الإظهاريوالاضغاب
+
+217
+00:18:11,750 --> 00:18:16,250
+ونحن عندنا أحكام النون الساكنة والتنوين من ضمن
+
+218
+00:18:16,250 --> 00:18:20,810
+الأحكام حكم الإخفاء متى تخفى النون الساكنة يا
+
+219
+00:18:20,810 --> 00:18:25,730
+أخواتي متى تخفى النون الساكنة أو التنوين إذا جاء
+
+220
+00:18:25,730 --> 00:18:32,460
+بعدهاأي حرف من حروف صف ذاثنى كمجهد شخص قد سمدهم
+
+221
+00:18:32,460 --> 00:18:36,860
+طيبا زد في طقن بعظامه أول حرف من كل كلمة مثل
+
+222
+00:18:36,860 --> 00:18:44,640
+مياصالصال الان او ماذالذي الانسان عندما اقول انا
+
+223
+00:18:44,640 --> 00:18:51,100
+الانسانلم أقول الانسان مباشرة يعني أخرجت النون
+
+224
+00:18:51,100 --> 00:18:57,080
+الساكنة أعطيتها صفة ما بين الإظهار و الإضغام لا هي
+
+225
+00:18:57,080 --> 00:19:00,840
+إظهار ولا هي إضغام بدي أقول مع مراعاة الغنى طبعا
+
+226
+00:19:00,840 --> 00:19:07,030
+بدي أقول الانسانو هي تخفى عند الحرف اللذي يليها
+
+227
+00:19:07,030 --> 00:19:14,350
+ماذا الذي؟ مصالصال؟ وهكذا بالنسبة لأن المفاهة دي
+
+228
+00:19:14,350 --> 00:19:18,910
+احنا بنستخدمها نحن و في كذلك حكم الإخفاء الشافوي
+
+229
+00:19:18,910 --> 00:19:21,850
+مان يقول اللي .. مامعنى الإخفاء الشافوي؟ او ماهو
+
+230
+00:19:21,850 --> 00:19:25,690
+الإخفاء الشافوي؟طبعا هو من أحكام ايه؟ ال ميم
+
+231
+00:19:25,690 --> 00:19:29,150
+الساكنة، إذا جاء عند الميم الساكنة حرف واحد وهو
+
+232
+00:19:29,150 --> 00:19:33,830
+حرف ال ب بكون في عيننا إخفاء شفوي، من يأتي بمثال
+
+233
+00:19:33,830 --> 00:19:40,340
+على الإخفاء الشفوي؟وقضي بينهم بالحق كيف نقراه؟
+
+234
+00:19:40,340 --> 00:19:46,620
+وقضي بينهم بالحق نعطي الميم الساكنة صفة ما بين
+
+235
+00:19:46,620 --> 00:19:51,960
+الإظهار والإضغام وقضي بينهم بالحق يعني لا هي إظهار
+
+236
+00:19:51,960 --> 00:19:56,320
+ولا هي إضغام والمهم أن اللون تُخفى وكذلك الميم
+
+237
+00:19:56,320 --> 00:20:00,360
+تُعطى حالة إخفاء هذه يا أخوات بالنسبة للحروف
+
+238
+00:20:00,360 --> 00:20:06,170
+الفرعية التي تتردد ما بين مخرجينأو تتردد ما بين
+
+239
+00:20:06,170 --> 00:20:12,890
+الصفتين أخدناها ننتقل إلى موضوع أخر وهو المخارج
+
+240
+00:20:12,890 --> 00:20:17,350
+والصفات أو أقسام المخارج طبعا المخارج يا أخوات
+
+241
+00:20:17,350 --> 00:20:23,110
+تنقسم إلى قسمين في مخارج رئيسية عامة ومخارج خاصة
+
+242
+00:20:23,110 --> 00:20:28,530
+فرعية نسميها مخارج عامة ومخارج خاصة المخارج العامة
+
+243
+00:20:28,530 --> 00:20:30,930
+كان مخرج عام عندنا نحن
+
+244
+00:20:35,580 --> 00:20:40,180
+أحسنتى، عندنا يا أخوات خمس مخارج عامة، و هي من
+
+245
+00:20:40,180 --> 00:20:44,740
+أسفل أو من الداخل إلى الخارج، أول مخرج الجوف،
+
+246
+00:20:44,740 --> 00:20:50,200
+بعدين الحلق، بعدين اللسان، الشفتان، الخشوم، إذا
+
+247
+00:20:50,200 --> 00:20:55,440
+كام مخرج حرف على حسبالدراسة التي ندرسها نحن وهي
+
+248
+00:20:55,440 --> 00:20:59,640
+قراءة ابن الجزري أو على .. على .. حسب رواية ابن
+
+249
+00:20:59,640 --> 00:21:06,130
+الجزري، اللي هي خمس مخارج عامة، ما هي الجوفالحلق،
+
+250
+00:21:06,130 --> 00:21:13,110
+اللسان، الشفتان، الخشوم خمس مخارج ينبثق ويتفرع عن
+
+251
+00:21:13,110 --> 00:21:19,530
+هذه المخارج الخمسة سبعة عشرة مخرجان فرعيا حتى تخرج
+
+252
+00:21:19,530 --> 00:21:25,550
+جميع باقي الحروف مثلا الجوفب يخرج منه مخرج واحد
+
+253
+00:21:25,550 --> 00:21:29,910
+فرعي بتلت حروف اللي هي حروف المادة الثلاثة الحلق
+
+254
+00:21:29,910 --> 00:21:35,960
+يخرج منهتلات مخارج أقفى الحلق ووسط الحلق و أدنى
+
+255
+00:21:35,960 --> 00:21:41,920
+الحلق اللسان بيخرج منه عشر مخارج هي عشرة و كمان
+
+256
+00:21:41,920 --> 00:21:47,500
+اربعة اربعتاشر مخرجالشفتان يخرج منه مخرجان فرعيان
+
+257
+00:21:47,500 --> 00:21:53,420
+هي 16 مخرج الخشوم مخرج واحد بيخرج منه صاروا 17
+
+258
+00:21:53,420 --> 00:21:58,240
+مخرج إذا المخرج العامة خمسة و المخرج الخاصة أو
+
+259
+00:21:58,240 --> 00:22:04,220
+الفرعية نسميها خاصة أو فرعية بيخرج منها 17 مخرجان
+
+260
+00:22:04,220 --> 00:22:07,820
+فرعيا يعني سندرسهم ان شاء الله بالتفصيل بعد
+
+261
+00:22:07,820 --> 00:22:14,730
+اللاحقةاختلف العلماء في تحديد المخارج الخامسة
+
+262
+00:22:14,730 --> 00:22:19,880
+والسبعتاشرواختلفوا إلى كام قول يا أخوات؟ إلى ثلاث
+
+263
+00:22:19,880 --> 00:22:25,440
+أقوال القول الذي يعني نحن عليه وهو قول أو رأي ابن
+
+264
+00:22:25,440 --> 00:22:29,940
+الجزري قالوا إن المخارج العامة خمسة والمخارج
+
+265
+00:22:29,940 --> 00:22:33,920
+الخاصة سبعتاش وهذه التي سوف ندرسها إن شاء الله
+
+266
+00:22:33,920 --> 00:22:40,020
+كذلك القول الثاني الرأي الثاني يعني هو قالوا خمس
+
+267
+00:22:40,020 --> 00:22:45,880
+مخارج بيطلع منها سبعتاشر مخرج فرعيخمس مخرج التي
+
+268
+00:22:45,880 --> 00:22:50,260
+ذكرناها الجوف الحلق اللسان الشفتان الخشوم سبعتاشر
+
+269
+00:22:50,260 --> 00:22:56,400
+مخرج تاني مخرج من الجوف تلت مخرج من الحلق عشر مخرج
+
+270
+00:22:56,400 --> 00:23:01,740
+من اللسان مخرجان من الشفتين ومخرج واحد من الخشوم
+
+271
+00:23:01,740 --> 00:23:06,720
+هي سبعتاشر مخرج وهذا الرأي الذي سوف ندرس عليه
+
+272
+00:23:06,720 --> 00:23:11,590
+والذي نحن عليه وهو على حسب رأي ابن الجزريالقول
+
+273
+00:23:11,590 --> 00:23:14,930
+الثاني يا أخوات وهو رئيس سيبا ويه والإمام الشاطبي
+
+274
+00:23:14,930 --> 00:23:21,010
+ذهبوا إلى أن المخارج العامة ليست خمسة بل أربع
+
+275
+00:23:21,010 --> 00:23:26,710
+مخارج عامة بينبثق عنها و بتفرع منها 16 مخرجا
+
+276
+00:23:26,710 --> 00:23:31,410
+المخارج العامة احنا قلنا خمسة عندناهم بيقولوا
+
+277
+00:23:31,410 --> 00:23:35,490
+أربعة أين المخرج الذي حُذِفه اللي هو الجوف فقالوا
+
+278
+00:23:35,490 --> 00:23:41,190
+أن المخرج مافيه جوف فيه حلق لسان شفتان خشوم إذا
+
+279
+00:23:41,190 --> 00:23:48,050
+ألغوا مخرج واحد و هو مخرج الجوف و الفرعية أيضا
+
+280
+00:23:48,050 --> 00:23:51,710
+ألغوا مخرج الجوف الفرعي لأن أحنا قلنا أن مخرج
+
+281
+00:23:51,710 --> 00:23:58,310
+الجوف في مخرج فأعامعام أصلي و مخرج فرعي و برضه
+
+282
+00:23:58,310 --> 00:24:02,650
+واحد فإذا التغى من الخمسة واحد فصاروا أربعة و
+
+283
+00:24:02,650 --> 00:24:07,650
+التغى من السبعتاشر مخرج واحد اللي هو صاروا ستاشر
+
+284
+00:24:07,650 --> 00:24:14,220
+مخرج إذا الرأي الثاني وهو رأي الإمام الشاطبيقال أن
+
+285
+00:24:14,220 --> 00:24:18,580
+المخارج العامة أربعة و ليست خمسة و المخارج الخاصة
+
+286
+00:24:18,580 --> 00:24:22,600
+ستة عشر مخرجا و المخارج المحذوفة اللي هي مخرج
+
+287
+00:24:22,600 --> 00:24:28,660
+العام الجوف و كذلك مخرج الفرع اللي هو تمع الجوف و
+
+288
+00:24:28,660 --> 00:24:34,000
+هؤلاء الناس جعلوا المخرج الفرع و حروف المخرج الفرع
+
+289
+00:24:34,000 --> 00:24:37,000
+اللي هو اللتي حذفوه و هو حروف المادة الثلاثة
+
+290
+00:24:37,000 --> 00:24:41,580
+جعلوها مدمجوها في الحروف اللتي تخرج من باقي أجزاء
+
+291
+00:24:41,580 --> 00:24:48,230
+الفم فمثلاحرف الألف قالوا يخرجوا مع الهمزة احنا
+
+292
+00:24:48,230 --> 00:24:54,650
+قلنا الألف أ أ ده هيدخل مع المد فيقول أهمزة أ
+
+293
+00:24:54,650 --> 00:25:00,810
+بيصير ايه بيصير الجوف أو حرف مد أ أ مخرجه من عند
+
+294
+00:25:00,810 --> 00:25:07,170
+مخرج الحرف الحرف الثاني حرف الوا الياه الياه بيخرج
+
+295
+00:25:07,170 --> 00:25:12,470
+مع الياء المتحركةمن أين تخرج الياء المتحركة؟ الياء
+
+296
+00:25:12,470 --> 00:25:16,250
+المتحركة يعني يه يه يه يه يه يه يه يه يه يه يه يه
+
+297
+00:25:16,250 --> 00:25:19,690
+يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه
+
+298
+00:25:19,690 --> 00:25:20,050
+يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه
+
+299
+00:25:20,050 --> 00:25:22,210
+يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه
+
+300
+00:25:22,210 --> 00:25:23,310
+يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه
+
+301
+00:25:23,310 --> 00:25:23,970
+يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه يه
+
+302
+00:25:23,970 --> 00:25:31,110
+يه يه يه يكذلك الواو المادية اللي هي و بتخرج من
+
+303
+00:25:31,110 --> 00:25:35,870
+وين؟ من الشفتين أو عند ضم الشفتين مع الواو
+
+304
+00:25:35,870 --> 00:25:40,030
+المتحركة الواو المتحركة اللي بتخرج من الشفتين نقول
+
+305
+00:25:40,030 --> 00:25:48,350
+و وي يعني ضم الشفتين وانفرجهماوقالوا إن حرف المد
+
+306
+00:25:48,350 --> 00:25:54,190
+يخرج مع الواو المتحركة، أصحاب هذا الرأي قالوا 4
+
+307
+00:25:54,190 --> 00:26:02,440
+مخرج عامة و 16 مخرج فرعيأين ذهبت حروف الجوفية
+
+308
+00:26:02,440 --> 00:26:05,660
+الفرعية الثلاثة لحروف المادية الثلاثة دمجوها مع
+
+309
+00:26:05,660 --> 00:26:11,060
+الحروف التي تشبيها فالألف دمجت مع حرف الهمزة
+
+310
+00:26:11,060 --> 00:26:16,780
+والياء المدية دمجت مع الياء المتحركة فلقول E
+
+311
+00:26:20,750 --> 00:26:26,670
+والواو المادية دمجت مع الواو المتحركة اللي هي واوي
+
+312
+00:26:26,670 --> 00:26:32,610
+دمجت معها حرف ال او اللي هي من الشفتين او عند ضم
+
+313
+00:26:32,610 --> 00:26:33,310
+الشفتين
+
+314
+00:26:35,870 --> 00:26:38,930
+هذا الرأي الثاني يا اخوان اما بالنسبة للرأي الثالث
+
+315
+00:26:38,930 --> 00:26:43,670
+و هو رأي الفراء و قطربو بن كيسان قالوا ان المخارج
+
+316
+00:26:43,670 --> 00:26:49,130
+أربعة العامة أربعة لكن بيخرج منها اربعتاشر مخرج
+
+317
+00:26:49,130 --> 00:26:54,110
+فرعينإذا قالوا المخرج العام الاربعة مثل القول
+
+318
+00:26:54,110 --> 00:26:59,270
+الثاني وحذفوا المخرج اللي هو مخرج الجوف قالوا
+
+319
+00:26:59,270 --> 00:27:04,270
+اربعة طب المخرج الفرعية لم يقولوا سبعتاش مثل الرأي
+
+320
+00:27:04,270 --> 00:27:08,670
+الأول ولم يقولوا ستاشر مثل الرأي الثاني بل قالوا
+
+321
+00:27:08,670 --> 00:27:15,500
+اربعتاش يبقى في حاجة يعني دمجةما هي اللسان؟ قالوا
+
+322
+00:27:15,500 --> 00:27:21,140
+ان اللسان بيخرج منه عشر مخارج عندنا احنا عشر مخارج
+
+323
+00:27:21,140 --> 00:27:27,520
+هم .. يعني احنا بنعتمد ان في عندنا مخرج حرف اللام
+
+324
+00:27:27,520 --> 00:27:33,450
+ومخرج حرف النون ومخرج حرف الراء، تلت مخارجقالوا إن
+
+325
+00:27:33,450 --> 00:27:37,970
+التلات مخرج هذه بدل ما نسميها تلات مخرج النون
+
+326
+00:27:37,970 --> 00:27:42,290
+واللام والرا هنقول إن هذه كل هائب تخرج من طرف
+
+327
+00:27:42,290 --> 00:27:45,930
+اللسان مع لثة الثنائي العليا يعني مخرجها واحد إذا
+
+328
+00:27:45,930 --> 00:27:50,670
+التلات مخرج صاروا واحد يعني في عندنا مخرجين فرعيان
+
+329
+00:27:50,670 --> 00:27:56,030
+انحدفوا فصار عندنا 14 مخرج فرعي إذا أصحاب الرأي
+
+330
+00:27:56,030 --> 00:28:02,070
+الثالث ماذا قالوا؟أن أربع مخرج عامة بتفرع منها
+
+331
+00:28:02,070 --> 00:28:07,390
+أربع تاشر مخرج فرعي ما هي الحروف المدموجة أول شيء
+
+332
+00:28:07,390 --> 00:28:13,250
+مخرج الجوف دمجه مثل الراي الثاني و كذلك دمجه اللي
+
+333
+00:28:13,250 --> 00:28:18,860
+هي المخرج الثلاثةمخرج اللام ومخرج النون ومخرج الرا
+
+334
+00:28:18,860 --> 00:28:23,480
+جعلوها مخرجا واحدا وهو طرف اللسان مع ما يليه من
+
+335
+00:28:23,480 --> 00:28:27,140
+لثة الأسنان العليا أو الثناء العليا فتخرج منه هذه
+
+336
+00:28:27,140 --> 00:28:31,460
+الحروف وبالتالي يعني اعتبروا ان التلاتة صارت واحد
+
+337
+00:28:31,460 --> 00:28:36,880
+لذلك قالوا ان في عندنا اربع مخرج عامة ويخرج منها
+
+338
+00:28:36,880 --> 00:28:44,170
+اربع اتناشر مخرج فرعطيب طريقة معرفة المخرج يا
+
+339
+00:28:44,170 --> 00:28:49,250
+أخوات أو أي حرف من هذه أو أي مخرج بنتعرف على مخرج
+
+340
+00:28:49,250 --> 00:28:53,410
+أي حرف ماذا نفعل؟ ما هي الطريقة الميسرة والسهلة
+
+341
+00:28:53,410 --> 00:28:57,430
+التي من خلالها نتعرف على مخرج أي حرف؟ تفضل أخت
+
+342
+00:29:04,180 --> 00:29:08,840
+أحسنتى إذا حتى نتعرف على مخرج أي حرف نأتي بالحرف
+
+343
+00:29:08,840 --> 00:29:15,320
+ساكنا أو مشددا مسبوكا بهمزا فحيثما حصر الصوت فهو
+
+344
+00:29:15,320 --> 00:29:21,420
+مخرجه فنقول مثلا لأ نقول حرف البا لو أن البا والتا
+
+345
+00:29:21,420 --> 00:29:26,700
+والعين واللام بتضيع مش عارفين إنما نأتي بذات الحرف
+
+346
+00:29:26,700 --> 00:29:32,700
+ساكن أو مشددا فنقول ابفحيث ثم انحصر الصوت في
+
+347
+00:29:32,700 --> 00:29:37,720
+المكان اللي بينحصر فيه الصوت يكون هذا هو مخرجه أين
+
+348
+00:29:37,720 --> 00:29:43,420
+مخرج حرف الأب خرجه عند انطباق الشفتين طيب مخرج حرف
+
+349
+00:29:43,420 --> 00:29:50,380
+الام ماذا نقول نقول ام او ام بيخرج أيضا عند انطباق
+
+350
+00:29:50,380 --> 00:29:55,200
+الشفتين يعني أين انحصر مخرج حرف الام عند انطباق
+
+351
+00:29:55,200 --> 00:30:02,970
+الشفتين أين انحصر مخرج حرف ال اف افعند وضع أطراف
+
+352
+00:30:02,970 --> 00:30:09,270
+الثنائي العليا على بطن الشفة السفلة فنقول اف اين
+
+353
+00:30:09,270 --> 00:30:16,210
+مخرج حرف الأقصى اللسان مع ما يحاذيه من الحناك
+
+354
+00:30:16,210 --> 00:30:24,770
+الأعلى؟ اين مخرج حرف الأقصى
+
+355
+00:30:24,770 --> 00:30:33,470
+الحلو؟ اين مخرج حرف الأخ؟أو اغ .. أدنى الحلق و
+
+356
+00:30:33,470 --> 00:30:38,130
+هكذا إذا أردنا أن نتعرف على مخرج أي حرف من الحروف
+
+357
+00:30:38,130 --> 00:30:44,230
+نأتي بالحرف ساكنا أو مشددا مسبوكا بهمزا فحيثما حصل
+
+358
+00:30:44,230 --> 00:30:48,990
+الصوت فهو مخرجهنكتفي بهذا القدر ونكمل إن شاء الله
+
+359
+00:30:48,990 --> 00:30:54,170
+أيضا الموضوع المخرج وصفات بالتفصيل حسب قراءة أو
+
+360
+00:30:54,170 --> 00:30:59,150
+حسب رأي ابن الجزري وهي خمس مخرج عامة وسبعة عشر
+
+361
+00:30:59,150 --> 00:31:02,410
+مخرج رفعيا في المحاضرة القادمة إن شاء الله تعالى
+
+362
+00:31:02,410 --> 00:31:05,210
+وبرك الله فيكم جميعا والسلام عليكم ورحمة الله
+
+363
+00:31:05,210 --> 00:31:05,890
+وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ed2r3iV6WnM_raw.json b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ed2r3iV6WnM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cc7674fe0e97ad1cdbb0f588a6724a036083a0a3
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ed2r3iV6WnM_raw.json
@@ -0,0 +1 @@
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"word": " واحد", "probability": 0.984130859375}, {"start": 1870.8, "end": 1871.24, "word": " قال", "probability": 0.98876953125}, {"start": 1871.24, "end": 1872.08, "word": " لماذا", "probability": 0.9669596354166666}, {"start": 1872.08, "end": 1873.2, "word": " تخشوني", "probability": 0.98173828125}, {"start": 1873.2, "end": 1873.84, "word": " أحدف", "probability": 0.6101888020833334}, {"start": 1873.84, "end": 1874.18, "word": " اليا", "probability": 0.5458984375}, {"start": 1874.18, "end": 1874.8, "word": " زي", "probability": 0.970703125}, {"start": 1874.8, "end": 1875.5, "word": " ذعان", "probability": 0.84130859375}, {"start": 1875.5, "end": 1876.26, "word": " فأقول", "probability": 0.8722330729166666}, {"start": 1876.26, "end": 1876.64, "word": " فلا", "probability": 0.950927734375}, {"start": 1876.64, "end": 1877.54, "word": " تخشوهم", "probability": 0.985546875}, {"start": 1877.54, "end": 1878.8, "word": " واخشون", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 85, "seek": 188812, "start": 1879.52, "end": 1888.12, "text": "بدون يا .. أيضا هذا ماذا يسمى يا أخوات؟ يسمى لحنجلي وبالتالي يعني أخطأ هذا القارئ بهذا الكلام", "tokens": [44510, 11536, 35186, 4386, 36632, 11242, 995, 23758, 3714, 45636, 995, 7251, 38251, 7578, 35186, 5551, 9778, 2407, 9307, 22807, 7251, 38251, 7578, 5296, 5016, 1863, 7435, 20292, 4032, 3555, 6027, 2655, 6027, 1829, 37495, 22653, 5551, 9778, 9566, 10721, 23758, 25062, 9640, 19986, 39627, 15730, 2423, 28820, 10943], "avg_logprob": -0.1567968714237213, "compression_ratio": 1.4778761061946903, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1879.52, "end": 1880.06, "word": "بدون", "probability": 0.938232421875}, {"start": 1880.06, "end": 1880.32, "word": " يا", "probability": 0.58740234375}, {"start": 1880.32, "end": 1880.74, "word": " ..", "probability": 0.438232421875}, {"start": 1880.74, "end": 1881.2, "word": " أيضا", "probability": 0.7849934895833334}, {"start": 1881.2, "end": 1881.4, "word": " هذا", 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"word": " بهذا", "probability": 0.973876953125}, {"start": 1887.66, "end": 1888.12, "word": " الكلام", "probability": 0.9532877604166666}], "temperature": 1.0}, {"id": 86, "seek": 191378, "start": 1888.92, "end": 1913.78, "text": "هذا يا أخوات هو اللحن الجلي في الحروف عندنا كذلك لحن جلي في الكلمات وعنا لحن جلي في الحركات هذا ان شاء الله في المحاضرات القادمة سوف ناخد اللحن الجلي في الكلمات واللحن الجلي في الحركات ونكتفي بهذا القدر ونكمن ان شاء الله في المحاضرة القادمة بارك الله فيكم والسلام عليكم ورحمة الله وبركاته", "tokens": [3224, 15730, 35186, 5551, 9778, 2407, 9307, 31439, 13672, 5016, 1863, 25724, 20292, 8978, 21542, 32887, 5172, 43242, 8315, 9122, 8848, 23275, 5296, 5016, 1863, 10874, 20292, 8978, 33251, 19528, 9307, 4032, 3615, 8315, 5296, 5016, 1863, 10874, 20292, 8978, 21542, 31747, 9307, 23758, 16472, 13412, 16606, 21984, 8978, 9673, 5016, 46958, 2288, 9307, 25062, 18513, 46007, 8608, 38688, 8717, 47283, 3215, 13672, 5016, 1863, 25724, 20292, 8978, 33251, 19528, 9307, 4032, 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{"start": 1891.12, "end": 1891.7, "word": " في", "probability": 0.93310546875}, {"start": 1891.7, "end": 1892.22, "word": " الحروف", "probability": 0.9827473958333334}, {"start": 1892.22, "end": 1893.12, "word": " عندنا", "probability": 0.94091796875}, {"start": 1893.12, "end": 1893.6, "word": " كذلك", "probability": 0.9908854166666666}, {"start": 1893.6, "end": 1894.68, "word": " لحن", "probability": 0.9661458333333334}, {"start": 1894.68, "end": 1895.28, "word": " جلي", "probability": 0.984619140625}, {"start": 1895.28, "end": 1895.92, "word": " في", "probability": 0.96875}, {"start": 1895.92, "end": 1896.66, "word": " الكلمات", "probability": 0.95166015625}, {"start": 1896.66, "end": 1897.4, "word": " وعنا", "probability": 0.8522135416666666}, {"start": 1897.4, "end": 1898.04, "word": " لحن", "probability": 0.9855143229166666}, {"start": 1898.04, "end": 1898.54, "word": " جلي", "probability": 0.988525390625}, {"start": 1898.54, "end": 1899.18, "word": " في", "probability": 0.9697265625}, {"start": 1899.18, "end": 1899.84, "word": " الحركات", "probability": 0.9861653645833334}, {"start": 1899.84, "end": 1900.32, "word": " هذا", "probability": 0.78564453125}, {"start": 1900.32, "end": 1900.46, "word": " ان", "probability": 0.673828125}, {"start": 1900.46, "end": 1900.62, "word": " شاء", "probability": 0.990478515625}, {"start": 1900.62, "end": 1900.88, "word": " الله", "probability": 0.95654296875}, {"start": 1900.88, "end": 1901.18, "word": " في", "probability": 0.9306640625}, {"start": 1901.18, "end": 1901.88, "word": " المحاضرات", "probability": 0.96181640625}, {"start": 1901.88, "end": 1902.44, "word": " القادمة", "probability": 0.9957682291666666}, {"start": 1902.44, "end": 1903.12, "word": " سوف", "probability": 0.96826171875}, {"start": 1903.12, "end": 1903.66, "word": " ناخد", "probability": 0.7667643229166666}, {"start": 1903.66, "end": 1904.02, "word": " اللحن", "probability": 0.9921875}, {"start": 1904.02, "end": 1904.44, "word": " الجلي", 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وبركاته", "probability": 0.9666015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1914.27625, "duration_after_vad": 1865.3015937499977}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ie8S8rcMI0w.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ie8S8rcMI0w.srt
new file mode 100644
index 0000000000000000000000000000000000000000..18e2c22198cdc33457798ccf66bdca0f502c0d56
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ie8S8rcMI0w.srt
@@ -0,0 +1,1469 @@
+1
+00:00:11,700 --> 00:00:14,400
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,400 --> 00:00:18,500
+الرحيم الحمد لله الصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:18,500 --> 00:00:22,600
+آله وصحبه وسلم موضوعنا اليوم يا أخوات عن السكت
+
+4
+00:00:23,520 --> 00:00:28,680
+السكت من حيث اللغة هو المنع يقال سكت عن الكلام 
+
+5
+00:00:28,680 --> 00:00:33,760
+بمعنى امتنعت عنه أما في الاصطلاح فهو قطع الصوت 
+
+6
+00:00:33,760 --> 00:00:39,200
+على الكلمة القرآنية زمنا يسيرًا بدون تنفس مقدار
+
+7
+00:00:39,200 --> 00:00:43,360
+حركة أو حركتين من يعرف لنا السكت يا أخوات؟ فضلي
+
+8
+00:00:48,550 --> 00:00:53,870
+بدون تنفس يعني نقطع الصوت والسكت يختلف عن الوقف
+
+9
+00:00:53,870 --> 00:00:59,070
+الوقف يتنفس فيه القارئ عادة لكن السكت هو نقطع 
+
+10
+00:00:59,070 --> 00:01:03,010
+الصوت على الكلمة القرآنية زمنا يسيرًا نقدره حركتين 
+
+11
+00:01:03,010 --> 00:01:07,970
+بدون تنفس وهذا طبعًا في مواضع معينة عند الإمام حفص
+
+12
+00:01:07,970 --> 00:01:13,370
+فهناك أربع مواضع للسكتات اللي فيها سكتات واجبة عند 
+
+13
+00:01:13,370 --> 00:01:19,910
+الإمام حفص وموضعين للسكتات سكتات جائزة، واسكته في 
+
+14
+00:01:19,910 --> 00:01:23,690
+المواضع الأربع نشوف الموضوع الأول هو السكت على
+
+15
+00:01:23,690 --> 00:01:28,230
+الألف المبدل من التنوين في كلمة عوجاء من قوله 
+
+16
+00:01:28,230 --> 00:01:34,190
+تعالى الحمد لله الذي أنزل على عبده الكتاب ولم يجعل 
+
+17
+00:01:34,190 --> 00:01:39,930
+له عوجاء قيمًا لينذر بأسًا شديدًا بدون تنفس ولم يجعل
+
+18
+00:01:39,930 --> 00:01:47,150
+له عوجًا قيمًا لينذر بأسًا شديدًا من يقرأها ويسكت سكتة
+
+19
+00:01:47,150 --> 00:01:52,450
+لطيفة على ألف عوجاء من قول تعالى ولم يجعل له عوجًا 
+
+20
+00:01:52,450 --> 00:01:57,010
+قيمًا لينذر بأسًا شديدًا من يقرأ؟ فضلي
+
+21
+00:02:02,650 --> 00:02:08,410
+ولم يجعل له عوجاء قيمًا لينظر بأس شديدًا من لده بس
+
+22
+00:02:08,410 --> 00:02:15,530
+يكفي ولم يجعل له عوجاء قيمًا لينظر بأس شديدًا من يعيد؟ 
+
+23
+00:02:15,530 --> 00:02:21,390
+فضل أخت الحمد لله الذي أنزل على عبد الكتاب ولم
+
+24
+00:02:21,390 --> 00:02:28,980
+يجعل له عوجاء قيمًا لينظر بأس شديدًا من لده بسابدئيها
+
+25
+00:02:28,980 --> 00:02:34,760
+ولم يجعل له مش عوجة عوجة ولم يجعل له عوجاء قيمًا
+
+26
+00:02:34,760 --> 00:02:39,240
+لينذر بأسًا شديدة عساسا أن الآية .. الآية طويلة
+
+27
+00:02:39,240 --> 00:02:43,220
+قليلا فلا نريد أن نبدأها من أولها كأننا وقفا .. 
+
+28
+00:02:43,220 --> 00:02:46,860
+وقفنا وقفًا اضطراريا عند قول على عبده الكتاب ولم
+
+29
+00:02:46,860 --> 00:02:51,700
+يجعل له الكتاب ونريد أن نكمل ونصلح من يقراها قراءة 
+
+30
+00:02:51,700 --> 00:02:58,370
+سليمة ولم يجعل له عوجاء قيمًا اللي يُنذِر بأسًا شديدًا،
+
+31
+00:02:58,370 --> 00:03:04,570
+تفضّلي إيه؟ ولم يجعل له عوجاء قيمًا اللي يُنذِر بأسًا
+
+32
+00:03:04,570 --> 00:03:05,830
+شديدًا، تفضّلي إيه؟ ولم يجعل له عوجاء قيمًا اللي
+
+33
+00:03:05,830 --> 00:03:06,830
+يُنذِر بأسًا شديدًا، تفضّلي إيه؟ لذلك الأخير، إذا 
+
+34
+00:03:06,830 --> 00:03:11,790
+السكت على ألف، الألف عوجاء من قوله تعالى ولم يجعل 
+
+35
+00:03:11,790 --> 00:03:16,190
+له عوجاء قيمًا اللي يُنذِر بأسًا شديدًا، هنا الوقف يسمى 
+
+36
+00:03:16,190 --> 00:03:19,690
+أو السكت اللي هنا سكتة لطيفة وهي من السكتات
+
+37
+00:03:19,690 --> 00:03:24,860
+الواجبة عند الإمام حفص، وأصلها هنا وقف تام الأصل في 
+
+38
+00:03:24,860 --> 00:03:28,620
+عوجاء وقف تام على رأس الآية يعني الأصل أن نقف عندها 
+
+39
+00:03:28,620 --> 00:03:32,680
+لكن في حالة الواصل لو أردنا أن نوصلها عند الإمام 
+
+40
+00:03:32,680 --> 00:03:38,300
+حفص يجب أن نسكت سكتة لطيفة لو قلنا يعني ما الحكمة 
+
+41
+00:03:38,300 --> 00:03:42,900
+أو ما هو وجه السكت على ألف عوجاء؟ لماذا نسكت نحن
+
+42
+00:03:42,900 --> 00:03:46,360
+على ألف عوجاء؟ أو ما الحكمة من الوقف أو السكت على
+
+43
+00:03:46,360 --> 00:03:54,780
+ألف عوجاء؟ من يعرف؟ فضلي صحيح يعني حتى نوضح أن هناك 
+
+44
+00:03:54,780 --> 00:04:00,660
+كلمتين كلمة عوجاء وكذلك قيمًا وأن كلمة قيمًا ليست
+
+45
+00:04:00,660 --> 00:04:04,480
+صفة لعيوجاء لأنه يحصل تناقض لو قلنا عوجاء اللي هو
+
+46
+00:04:04,480 --> 00:04:08,680
+أعوج وقيمًا بمعنى مستقيمة حتى لا يظن أو يتوهم
+
+47
+00:04:08,680 --> 00:04:14,000
+المتوهم أن كلمة قيمًا قيمًا صفة لعيوجاء فيحصل تناقض
+
+48
+00:04:14,000 --> 00:04:18,740
+فلابد أن يسكت سكتة لطيفة على ألف عوجاء فنقول ولم 
+
+49
+00:04:18,740 --> 00:04:26,180
+يجعل له عوجاء قيمًا لينذر بأس شديد، وهنا تقديره أنزله 
+
+50
+00:04:26,180 --> 00:04:32,840
+قيمًا أو ليكون قيمًا يعني كلمة جديدة فالوقف على ألف 
+
+51
+00:04:32,840 --> 00:04:36,300
+عوجاء أو الوقف على آخر الآية على نفس الآية اسمه وقف 
+
+52
+00:04:36,300 --> 00:04:40,940
+تام، ولكن عندما نصل الآيتين مع بعضهما البعض لابد من 
+
+53
+00:04:40,940 --> 00:04:45,430
+السكت سكتة لطيفة وهي سكت واجب عند حفص على ألف عوجاء 
+
+54
+00:04:45,430 --> 00:04:50,250
+لنبيّن يعني وجه .. وجه السكت لنبيّن أن قيمًا ليست 
+
+55
+00:04:50,250 --> 00:04:55,470
+تابعة في إعرابها لعوجاء بل هي كلمة مستأنفة أو جملة
+
+56
+00:04:55,470 --> 00:05:01,290
+مستأنفة تقديره أنزله يعني قيمًا أو ليكون قيمًا هذا 
+
+57
+00:05:01,290 --> 00:05:04,170
+هو يعني السؤال الذي ممكن أن يأتي إليكم يا أخوات
+
+58
+00:05:04,170 --> 00:05:10,770
+يعني أبيني مثلًا جانبًا أو مثلًا مثلًا على السكت أو عرف 
+
+59
+00:05:10,770 --> 00:05:14,370
+السكت في ما ذكره مثلًا عليه مع بيان وجهه للسكت 
+
+60
+00:05:14,370 --> 00:05:18,830
+هتقولي إنه السكت هو قطع الصوت على الكلمة القرآنية
+
+61
+00:05:18,830 --> 00:05:24,410
+زمنا يسيرًا بدون تنفس مقداره حركتين والمثال وعلى
+
+62
+00:05:24,410 --> 00:05:30,210
+ذلك في عندنا سكتات واجبة أربع سكتات وسكتتين يعني 
+
+63
+00:05:30,210 --> 00:05:34,190
+الجائزتين السكت الواجب الأول اللي أخذناها الآن أن 
+
+64
+00:05:34,190 --> 00:05:39,170
+يسكت سكتة لطيفة على ألف عوجاء من قوله ولم يجعل له
+
+65
+00:05:39,170 --> 00:05:44,370
+عوجاء قيمًا لينذر بأسًا شديدًا لو سألناكم ما هو وجه
+
+66
+00:05:44,370 --> 00:05:50,490
+السكت هنقول حتى نبيّن أن قيمًا ليس تابع في إعرابها
+
+67
+00:05:50,490 --> 00:05:55,090
+لعوجاء وأن الوقف على عوجاء إنما هو وقف تام وتم 
+
+68
+00:05:55,090 --> 00:05:59,030
+المنع عنده ليس له علاقة بما بعده لا لفظًا ولا معنى
+
+69
+00:05:59,030 --> 00:06:04,070
+وأن قيمًا كلمة مستأنفة جديدة بمعنى أو بتقديره أنزله 
+
+70
+00:06:04,070 --> 00:06:08,770
+قيمًا هذا هي يا أخواتي هي السكتة الأولى عندنا
+
+71
+00:06:08,770 --> 00:06:13,600
+السكتة الثانية وهي قوله تعالى قالوا يا ويلنا ما 
+
+72
+00:06:13,600 --> 00:06:19,920
+بعثنا من مرقدنا هذا ما وعد الرحمن وصدق المرسلون أن
+
+73
+00:06:19,920 --> 00:06:26,560
+يسكت سكتة لطيفة على ألف مرقدنا حتى نبيّن أن هذا الكلام 
+
+74
+00:06:26,560 --> 00:06:30,900
+هذا ما وعد الرحمن وصدق المرسلون ليس تابعًا لما قبله
+
+75
+00:06:30,900 --> 00:06:37,870
+لأنه الأول كلام من كلام الكفار الذين كانوا ينكرون 
+
+76
+00:06:37,870 --> 00:06:43,210
+البعث فلمّا بعثهم الله سبحانه وتعالى قال للكفار يا
+
+77
+00:06:43,210 --> 00:06:47,870
+ويلنا من بعثنا من مرقدنا؟ فالكلام الذي بعده كلام 
+
+78
+00:06:47,870 --> 00:06:52,490
+جديد فيقول الملائكة أو يقول المؤمنون هذا ما وعد
+
+79
+00:06:52,490 --> 00:06:56,210
+الرحمن وصدق المرسلون، لكن لو وصلنا الكلام مع بعضه 
+
+80
+00:06:56,210 --> 00:07:00,590
+البعض، فهذا ما وعد الرحمن وصدق المرسلون هو من قول
+
+81
+00:07:00,590 --> 00:07:04,510
+الكفار، والكفار لم يقولوا هذا الكلام لأنهم أصلاً لا
+
+82
+00:07:04,510 --> 00:07:09,690
+يؤمنون بيوم القيامة. إذن نسكت سكتة لطيفة على ألف 
+
+83
+00:07:09,690 --> 00:07:15,100
+مرقدنا هنا، حتى نبيّن أن جملة هذا ما وعد الرحمن ليس 
+
+84
+00:07:15,100 --> 00:07:19,780
+تابعة لما قبلها بل هو كلام جديد من قول الملائكة أو 
+
+85
+00:07:19,780 --> 00:07:24,420
+من قول المؤمنين الذين يقررون بأن هذا ما وعد الرحمن 
+
+86
+00:07:24,420 --> 00:07:28,580
+وصدق المرسلون، أما كلام الكفار الذين كانوا ينكرون
+
+87
+00:07:28,580 --> 00:07:34,760
+البعث والجزاء والحساب قالوا يا ويلنا من بعثنا من 
+
+88
+00:07:34,760 --> 00:07:40,290
+مرقدنا؟ نسكت سكتة لطيفة ثم نقرأ بدون تنفس هذا ما 
+
+89
+00:07:40,290 --> 00:07:45,490
+وعد الرحمن وصدق المرسلون، إذا من يقف أو يسكت سكتة 
+
+90
+00:07:45,490 --> 00:07:48,810
+لطيفة على ألف مرقدنا ويقرأ قراءة سليمة بالنسبة 
+
+91
+00:07:48,810 --> 00:07:55,210
+لهذه الآية فضل أختك قالوا يا ويلنا من بعثنا من
+
+92
+00:07:55,210 --> 00:08:01,930
+مرقدنا هدل مرقدنا هذا ما وعد الرحمن وصدق المرسلون
+
+93
+00:08:03,500 --> 00:08:08,980
+بس بدون تنفس، من يقرأ بدون تنفس؟ قالوا يا ويلنا من
+
+94
+00:08:08,980 --> 00:08:14,960
+بعثنا من مرقدنا هذا ما وعد الرحمن وصدق المرسلون
+
+95
+00:08:14,960 --> 00:08:24,600
+أحسنتي، 
+
+96
+00:08:24,600 --> 00:08:30,040
+طيب ما هو وجه السكت على ألف مرقدنا؟ ما الحكمة من
+
+97
+00:08:30,040 --> 00:08:32,440
+السكت على ألف مرقدنا؟
+
+98
+00:08:35,140 --> 00:08:39,780
+أحسنتي يعني بيان أن هذا ما وعد الرحمن وصدق 
+
+99
+00:08:39,780 --> 00:08:44,180
+المرسلون ليس تابع للكلام السابق فإن الكلام السابق
+
+100
+00:08:44,180 --> 00:08:47,760
+إنما هو كلام الكفار أما الكلام اللاحق فهو كلام 
+
+101
+00:08:47,760 --> 00:08:51,380
+المؤمنين هذا المؤمنين أو الملائكة هذا يا أخوات هو 
+
+102
+00:08:51,380 --> 00:08:55,180
+المثال الثاني يعني مافيه عنا مثالين، السكت على
+
+103
+00:08:55,180 --> 00:08:59,660
+ألف عوجاء والسكت على ألف مرقدنا، وإذا أردنا السؤال
+
+104
+00:08:59,660 --> 00:09:02,840
+لابد أن نأتي بالآية كاملة يعني الذي لو سألناكم
+
+105
+00:09:02,840 --> 00:09:07,960
+سؤال فقاله أو قالت الأخت السكت على ألف عوجاء والسكت 
+
+106
+00:09:07,960 --> 00:09:11,720
+على ألف مرقدنا بدون ذكر الآية يعني لا تكون الإجابة 
+
+107
+00:09:11,720 --> 00:09:15,900
+سليمة، لابد أن نذكر الآية أقل شيء الكلمتين أقل شيء 
+
+108
+00:09:15,900 --> 00:09:20,680
+لكن لابد أن نذكر الآية كاملة بالشطرين سواء من
+
+109
+00:09:20,680 --> 00:09:25,130
+بعثنا من مرقدنا هذا ما وعد الرحمن أو لم يجعل له عوجاء
+
+110
+00:09:25,130 --> 00:09:29,470
+قيمًا لينذر بأسًا شديدًا، لكن لو ذكرت الأخت فقط قالت 
+
+111
+00:09:29,470 --> 00:09:33,630
+ألف عوجاء أو ألف مرقدنا بتكون الإجابة يعني مش سليمة
+
+112
+00:09:33,630 --> 00:09:37,290
+لأنه لابد أن تكون الإجابة كاملة ونذكر الكلمتين 
+
+113
+00:09:37,290 --> 00:09:41,650
+على أساس أنه نسكت سكتة لطيفة هذا الإجابة الكتابة
+
+114
+00:09:41,650 --> 00:09:45,790
+لكن بالنسبة للفظ لابد أن نذكر التنوين ولم يجعل له
+
+115
+00:09:45,790 --> 00:09:46,650
+عوجاء
+
+116
+00:09:56,280 --> 00:10:03,000
+طيب السكت الثالث يا أخوات الواجب أيضًا هي السكت على 
+
+117
+00:10:03,000 --> 00:10:11,710
+نون من وقيل من راق، وقيل من راق وظن أنه الفراق 
+
+118
+00:10:11,710 --> 00:10:16,310
+وتلفت الساق بالساق إلى ربك يومئذٍ المساق، هنا 
+
+119
+00:10:16,310 --> 00:10:23,890
+السكت على نون من نسكت سكتة لطيفة وقيل من راق، طيب لو 
+
+120
+00:10:23,890 --> 00:10:29,290
+سألنا سؤال ما الحكمة أو ما هو وجه السكت على نون 
+
+121
+00:10:29,290 --> 00:10:30,930
+من؟ فضل أخت
+
+122
+00:10:36,680 --> 00:10:43,800
+حتى نبيّن بأن كلمة من وراق إنما هما كلمتان لأنه في 
+
+123
+00:10:43,800 --> 00:10:49,780
+نون وراق إضغام متقارب أو إضغام بيغرقونا فعندما 
+
+124
+00:10:49,780 --> 00:10:54,220
+نقراها مع بعضها البعض يعني بتبين عند إضغام نقول
+
+125
+00:10:54,220 --> 00:10:58,980
+مراق ومراق يعني ممكن تكون سيرة مبالغة من كثرة
+
+126
+00:10:58,980 --> 00:11:05,000
+المروق أو كلمة تدل على أنه بائع مرق مراق، لكنها يعني
+
+127
+00:11:05,000 --> 00:11:10,360
+لابد أن نبيّن أن كلمة من كلمة وراق كلمة ثانية ما 
+
+128
+00:11:10,360 --> 00:11:18,040
+معنى راق؟ راق .. راق لحالها من .. راق .. راق يعني 
+
+129
+00:11:18,040 --> 00:11:23,520
+من الرقية والرقية هو الشفاء من المرض يعني يرقي لنا 
+
+130
+00:11:23,520 --> 00:11:26,580
+رقية عن طريق قراءة القرآن، قراءة الفاتحة، قراءة 
+
+131
+00:11:26,580 --> 00:11:30,320
+آية الكرسي، أي .. أي آية بيرقي لنا المريض فالآية
+
+132
+00:11:30,320 --> 00:11:34,740
+تتكلم يعني كالة إذا بلغت التراقي، ما هو الذي بلغ 
+
+133
+00:11:34,740 --> 00:11:39,540
+التراقي؟ الروح، يعني الآية تتكلم عن واحد يعني في 
+
+134
+00:11:39,540 --> 00:11:43,520
+حالة النزاع .. في حالة النزاع مريض وبلغت الروح 
+
+135
+00:11:43,520 --> 00:11:47,660
+التراقي يعني منطقة ال .. ال .. ترقوة اللي هي .. هي 
+
+136
+00:11:47,660 --> 00:11:51,300
+ترقوة هنا، هذه ترقوة، هذه ترقوة، يعني كدت أن تخرج
+
+137
+00:11:51,300 --> 00:11:56,250
+من .. من الروح .. الروح، وقيل من راق أصحابه وأهله
+
+138
+00:11:56,250 --> 00:12:01,970
+وذووه يقولون من يشفي لنا ويعالج لنا هذا المريض وقيل 
+
+139
+00:12:01,970 --> 00:12:07,990
+من راق يعني من يرقي لنا هذا المريض وظن أنه الفراق 
+
+140
+00:12:07,990 --> 00:12:12,330
+.. وظن بمعنى تيقن بأنه الفراق أنه هيموت هذا الإنسان 
+
+141
+00:12:12,330 --> 00:12:16,900
+والتفت الساق بالساق كده يعني شدة الموتى ربك
+
+142
+00:12:16,900 --> 00:12:21,340
+يومئذ المساق إذا الكلام راق بمعنى من الرقيا
+
+143
+00:12:21,340 --> 00:12:26,840
+والرقيا بمعنى الشفاء والعلاج فالمن راق لو قرأناها
+
+144
+00:12:26,840 --> 00:12:32,560
+وقيل من راق ممكن واحد يتوهم من راق من كثرة المروق
+
+145
+00:12:32,560 --> 00:12:37,340
+واحد من راق طريق أو من راق يعني بياع مرقة بمعنى
+
+146
+00:12:37,340 --> 00:12:41,200
+أنه يعمل في مطبخ مثلاً فحتى لا يتوهم هذا التوهم
+
+147
+00:12:41,200 --> 00:12:47,310
+نسكت سكتة لطيفة على نون من وهذا هو وجه السكت على
+
+148
+00:12:47,310 --> 00:12:52,110
+نون من اللي هي من رأى انظر كذلك يا أخوات إلى
+
+149
+00:12:52,110 --> 00:12:56,690
+المثال الرابع إحنا فيه عندنا أربع أمثلة ولم يجعل 
+
+150
+00:12:56,690 --> 00:13:02,660
+له عوجة قيمة يويدنا من بعثنا من مرقدنا هذا المواد
+
+151
+00:13:02,660 --> 00:13:09,580
+الرحمن وقيل من قراق المثال الرابع كلا بل ران على 
+
+152
+00:13:09,580 --> 00:13:15,020
+قلوبهم ما كانوا يكسبون كلا بل رانة النقل اللي أسكت
+
+153
+00:13:15,020 --> 00:13:21,820
+على لام بل كلا بل ران على قلوبهم ما كانوا يكسبون
+
+154
+00:13:21,820 --> 00:13:31,540
+ما معنى بل رانة؟ رانة بمعنى غطى الصدق غطى على قلب
+
+155
+00:13:31,540 --> 00:13:38,040
+قلب الإنسان يعني الإنسان عندما يعصى الله ينكته على
+
+156
+00:13:38,040 --> 00:13:42,380
+قلبه بنقطة سوداء أو الله سبحانه وتعالى يفتح له 
+
+157
+00:13:42,380 --> 00:13:47,260
+المجال فإن استغفر بعد المعصية غفر الله له وإن أصر 
+
+158
+00:13:47,260 --> 00:13:51,080
+على المعصية يعني نكطة على قلبه بنقطة سوداء
+
+159
+00:13:54,070 --> 00:13:59,990
+زادت المعاصي وكثرة الذنوب يصبح قلبه أسود لأن
+
+160
+00:13:59,990 --> 00:14:03,390
+القلوب لتصدق كما يقول النبي عليه الصلاة والسلام
+
+161
+00:14:03,390 --> 00:14:08,950
+كما يصدق الحديد أو النحاس وجلاءها الاستغفار الإنسان 
+
+162
+00:14:08,950 --> 00:14:13,850
+الذي يعصى الله يصبح قلبه مغطى بالران والران معناته 
+
+163
+00:14:13,850 --> 00:14:18,910
+الصدق لذلك هذا الإنسان الذي يكثر من المعاصي ويزداد
+
+164
+00:14:18,910 --> 00:14:23,490
+في المعاصي يصبح قلبه أسوداً فهذا الإنسان لا يرى 
+
+165
+00:14:23,490 --> 00:14:28,410
+بنور الله بل يرى الحق باطلاً والباطل حقاً بسبب 
+
+166
+00:14:28,410 --> 00:14:34,330
+ذنوبه فالذنوب والمعاصي سرب أكيد في دمار الأفراد
+
+167
+00:14:34,330 --> 00:14:39,030
+والأمم والشعوب الإنسان لما يكثر .. أو الأمة لما 
+
+168
+00:14:39,030 --> 00:14:43,490
+تكثر الذنوب وتكبر المعاصي والفواحش والمنكرات الله
+
+169
+00:14:43,490 --> 00:14:47,480
+سبحانه وتعالى يهلكهم والأنبياء الذين أرسلهم الله عز
+
+170
+00:14:47,480 --> 00:14:51,020
+وجل إلى أقوامهم يرسلهم إلى أقوامهم بعد أن يعني
+
+171
+00:14:51,020 --> 00:14:55,880
+أعصوا الله وارتكبوا المعاصي والمنكرات فأصروا على
+
+172
+00:14:55,880 --> 00:14:59,020
+الارتكاب المعاصي والمنكرات فأهلكهم الله عز وجل 
+
+173
+00:14:59,020 --> 00:15:03,840
+فالذنوب والمعاصي سرد أكيد في دمار الأمم والأفراد
+
+174
+00:15:03,840 --> 00:15:09,440
+والشعوب هنا كلا بل ران على قلوبهم يعني غطى على
+
+175
+00:15:09,440 --> 00:15:13,680
+قلوبهم ما كانوا يكسبون لكن لو قرأناها بالإظهار لأن
+
+176
+00:15:13,680 --> 00:15:18,040
+اللام مع الراء إظهار متقارب لو قرأناها كيف تقرأ
+
+177
+00:15:18,040 --> 00:15:25,830
+بالإظهار بران ما معنى بران؟ مثنى بر يعني أرض أرضان
+
+178
+00:15:25,830 --> 00:15:32,870
+بحر بحران سماء سماءان هنا بر بران فهنا لحتى لا
+
+179
+00:15:32,870 --> 00:15:38,110
+يتوهم المستمع عندما يقرأها بالإظهار كلا بران على
+
+180
+00:15:38,110 --> 00:15:41,830
+قلوبهم يعني مش بر واحد لأ هو بران على قلوبهم فحتى
+
+181
+00:15:41,830 --> 00:15:45,890
+لا يتوهم هذا التوهم لابد أن نسكت سكتة لطيفة على
+
+182
+00:15:45,890 --> 00:15:52,110
+لام بل كلا بل ران على قلوبهم ما كانوا يكسبون من
+
+183
+00:15:52,110 --> 00:16:01,330
+يقرأها مع تطبيق حكم السكت هنا تفضلي أختي أحسنتي
+
+184
+00:16:01,330 --> 00:16:07,960
+في عندنا لو واحد قال كلا بل ران على قلوبهم ما كان
+
+185
+00:16:07,960 --> 00:16:12,760
+يكسبون .. صحيح قراءتك؟ لأنه تنفس .. لابد أن نقطع 
+
+186
+00:16:12,760 --> 00:16:18,120
+الصوت بدون تنفس .. كلا بل ران على قلوبهم والغرض 
+
+187
+00:16:18,120 --> 00:16:22,640
+من قطع الصوت أو السكت بدون تنفس أن لا يتوهم
+
+188
+00:16:22,640 --> 00:16:28,620
+المتوهم بأنه كلمة واحدة بل هي كلمتين اللي هي كلا بل
+
+189
+00:16:28,620 --> 00:16:35,360
+كلمة وران كلمة وهذا ما يسمى بوجه السكت على لام
+
+190
+00:16:35,360 --> 00:16:40,640
+بل حتى لا يتوهم المتوهم بأنها كلمة واحدة ويبين 
+
+191
+00:16:40,640 --> 00:16:45,310
+بأنها كلمتين لأنه لو أضغمها بتصير برا هذه يا أخوات
+
+192
+00:16:45,310 --> 00:16:50,710
+هي السكتات الأربع الواجبة في عندنا كذلك سكتتين 
+
+193
+00:16:50,710 --> 00:16:55,930
+جائزتين لكن نريد أن نذكر السكتات الأربع التي
+
+194
+00:16:55,930 --> 00:17:03,750
+ذكرناها السكت الأولى ما هي يا بنات؟ ولم يجعل له 
+
+195
+00:17:03,750 --> 00:17:09,010
+عوجة قيمة يقرأ ليها من تقرأها يا أخوات ولم يجعل له 
+
+196
+00:17:09,010 --> 00:17:12,750
+عوجة قيمة لينظرة بأس شديدة تفضلي
+
+197
+00:17:18,920 --> 00:17:23,380
+بس يكفي إذا كان الله خير طيب قولوا يا ويلنا من
+
+198
+00:17:23,380 --> 00:17:29,420
+بعثنا من مرقدنا هذا ما وعد الرحمن وصدق المرسلون 
+
+199
+00:17:29,420 --> 00:17:32,660
+قالوا يا ويلنا من بعثنا من مرقدنا هذا ما وعد
+
+200
+00:17:32,660 --> 00:17:39,380
+الرحمن وصدق المرسلون من تقرأها؟ فضل أختي قالوا يا 
+
+201
+00:17:39,380 --> 00:17:44,260
+ويلنا من بعثنا من مرقدنا هذا ما وعد الرحمن وصدق 
+
+202
+00:17:44,260 --> 00:17:49,920
+المرسلون المثال الثالث من يقعه اللي هي قول تعالى 
+
+203
+00:17:49,920 --> 00:17:58,520
+وقيل من راق تفضلي هنا
+
+204
+00:17:58,520 --> 00:18:06,180
+كلا إذا بلغت التراقية وقيل من راق يعني سكتنا على
+
+205
+00:18:06,180 --> 00:18:11,180
+نون من في هذا المثال المثال الرابع كلا بل أرانا
+
+206
+00:18:11,180 --> 00:18:12,080
+تفضلي
+
+207
+00:18:17,280 --> 00:18:21,280
+هذه السكتات الأربع اللي هي السكتات الواجبة لكن في 
+
+208
+00:18:21,280 --> 00:18:26,360
+عندنا يا أخوات سكتتين جائزتين يجب أن نسكت عندها و
+
+209
+00:18:26,360 --> 00:18:32,720
+يجب أن نصل والواصل له حكم والوقف عليها له حكم
+
+210
+00:18:32,720 --> 00:18:38,360
+نشوف هنا السكتة الجائزة السكتة الأولى بين آخر صورة 
+
+211
+00:18:38,360 --> 00:18:43,970
+الأنفال مع التوبة يعني آخر صورة التوبة أو أي صورة 
+
+212
+00:18:43,970 --> 00:18:48,610
+سبقت صورة التوبة يعني اللي هي آخر صورة الأنفال مع
+
+213
+00:18:48,610 --> 00:18:53,430
+صورة التوبة نشوف مثلاً هنا المثال إن الله بكل شيء
+
+214
+00:18:53,430 --> 00:18:58,850
+عليم عليم هي آخر آية في صورة الأنفال أو أي صورة
+
+215
+00:18:58,850 --> 00:19:06,830
+سبقتها والتي بعدها براءة من الله ورسوله إلى الذين
+
+216
+00:19:06,830 --> 00:19:12,110
+عاهدتم من المشركين لو بدنا نوصلها .. طبعاً الأصل أن
+
+217
+00:19:12,110 --> 00:19:16,810
+نقف نهاية الصورة وبداية صورة الأنفال نوع الوقف 
+
+218
+00:19:16,810 --> 00:19:19,950
+اللي هنا يا أخوات الوقف الرسمي في نهاية الصورة
+
+219
+00:19:19,950 --> 00:19:25,450
+يسمى وقف إيش؟ وقف تام تام المانع عنده لا علاقة له مع
+
+220
+00:19:25,450 --> 00:19:30,930
+ما بعده لا لفظة ولا معنى وهذا ما يسمى بالإيش؟ الوقف
+
+221
+00:19:30,930 --> 00:19:37,700
+التام فالقطع عليه قطع يعني جائز والوقف عليه وقف لكن 
+
+222
+00:19:37,700 --> 00:19:41,500
+إحنا نتكلم في حالة الوصل يعني الحالة الأولى يجوز
+
+223
+00:19:41,500 --> 00:19:45,500
+الوقف عليها وقف تام لأنه طبيعي جداً نقف على رؤوس
+
+224
+00:19:45,500 --> 00:19:51,180
+الآيات وفي آخر الصورة لكن في حالة وصل الصورتين مع 
+
+225
+00:19:51,180 --> 00:19:55,560
+بعضهم البعض إن الله بكل شيء عليم بلاء في هذه
+
+226
+00:19:55,560 --> 00:20:01,960
+الحالة عندنا إما أن نصلها بالسكت وهو جائز وإما أن 
+
+227
+00:20:01,960 --> 00:20:07,140
+نصلها بالوصل اللي هو عن طريق الإقلاب نقلب نشوف مثلاً
+
+228
+00:20:07,140 --> 00:20:14,680
+أو الأولى إن الله بكل شيء عليم براءة من الله
+
+229
+00:20:14,680 --> 00:20:20,760
+ورسوله كويس عليم براءة سكتنا سكتة لطيفة وبعدين
+
+230
+00:20:20,760 --> 00:20:23,880
+قلنا براءة حتى يعني نبقي أنه إحنا بدأنا بصورة
+
+231
+00:20:23,880 --> 00:20:29,400
+جديدة مش عليم براءة طب لو وصلناها يجب أيضاً نصلها و
+
+232
+00:20:29,400 --> 00:20:36,750
+نقول عليم براءة من الله ورسوله يعني يمكن أن نصلها
+
+233
+00:20:36,750 --> 00:20:42,530
+بتطبيق حكم الإقلاب عليم تنوين وراها حرف الباء
+
+234
+00:20:42,530 --> 00:20:49,550
+كون في عندنا إقلاب نقرأها عليم براءة من الله ورسوله 
+
+235
+00:20:49,550 --> 00:20:53,830
+لكن إذا أردنا أن نوصلها يجب أيضاً أن نوصلها وهو
+
+236
+00:20:53,830 --> 00:21:00,370
+جائز ساكت جائز نقول عليم براءة من الله ورسوله من
+
+237
+00:21:00,370 --> 00:21:03,370
+يقرأها؟ فضلي
+
+238
+00:21:09,760 --> 00:21:15,000
+لا تتنفسوا بدون تنفس أحسنتي
+
+239
+00:21:15,000 --> 00:21:23,360
+تفضلي اقرأي أحسنتي
+
+240
+00:21:23,360 --> 00:21:27,620
+هذه يا أخوتي هي السكتة الجائزة الأولى ما بين صورة
+
+241
+00:21:27,620 --> 00:21:31,820
+الأنفال التي سبقت صورة التوبة وبعدها صورة التوبة
+
+242
+00:21:31,820 --> 00:21:38,170
+طبعاً بداية صورة التوبة أما .. أما إذا كان .. طب لو
+
+243
+00:21:38,170 --> 00:21:42,670
+قلنا صورة التوبة لماذا لم تبدأ بقوله بسم الله
+
+244
+00:21:42,670 --> 00:21:47,070
+الرحمن الرحيم مثلها كمثل أي صورة ثانية؟ فضلي لأن
+
+245
+00:21:47,070 --> 00:21:50,010
+بسم الله الرحمن الرحيم بتعني الأمام وصورة التوبة
+
+246
+00:21:50,010 --> 00:21:57,510
+نزلت بالمدينة صحيح صورة التوبة يعني بدايتها إعلان
+
+247
+00:21:57,510 --> 00:22:00,870
+الحرب على الكفار ويقول علماء أنها نزلت بالسيف
+
+248
+00:22:00,870 --> 00:22:04,770
+بمعنى أنه من أول آية فيها حرب على الكفار والتبرؤ
+
+249
+00:22:04,770 --> 00:22:10,210
+منهم واستباحة أموالهم وكذلك استباحة أرواحهم تبدأ 
+
+250
+00:22:10,210 --> 00:22:11,190
+براءة
+
+251
+00:22:16,950 --> 00:22:22,650
+وتبدأ تقريباً 28 آية في بيان الأحكام النهائية ما
+
+252
+00:22:22,650 --> 00:22:26,950
+بين المسلمين والمشركين عشان إيه كده بتبدأ باسم
+
+253
+00:22:26,950 --> 00:22:30,230
+الله الرحمن الرحيم فإذا وصلت مع أي صورة سبقتها
+
+254
+00:22:30,230 --> 00:22:38,370
+هناك سكتة لطيفة على صورة وهذه الصورة السكتة
+
+255
+00:22:38,370 --> 00:22:45,200
+الثانية أخواتي الجائزة وهي السكتة على هاء مالية من قول 
+
+256
+00:22:45,200 --> 00:22:51,500
+تعالى ما أغنى عني مالية هلك عني سلطانية
+
+257
+00:23:15,190 --> 00:23:20,650
+هلك عني سلطانية يعني وقفنا عليها لأن الوقف على 
+
+258
+00:23:20,650 --> 00:23:25,850
+رؤوس الآيات إيه سنة أما في حالة الواصل في عندنا يا 
+
+259
+00:23:25,850 --> 00:23:32,830
+إما بالسكت يا إما بالإظهار بالسكت نقول ما أغنى عني
+
+260
+00:23:32,830 --> 00:23:40,370
+مالية هلك عني سلطانية مالية هلكة نسكت سكتة لطيفة
+
+261
+00:23:40,370 --> 00:23:46,770
+أو نُظهرها مع بعضها لبعض فنقول ما أغنى عني مالية 
+
+262
+00:23:46,770 --> 00:23:51,990
+هلك عني سلطانية لأن الهاء الأولى ساكنة والهاء
+
+263
+00:23:51,990 --> 00:23:57,250
+الثانية متحركة والإظهار معناته إخراج حرف ساكن بحرف
+
+264
+00:23:57,250 --> 00:24:02,930
+متحرك بحيث يصيراني حرفا واحدا مشددة من جنس الثاني 
+
+265
+00:24:03,500 --> 00:24:08,020
+الآن يا أخوات إحنا أنهينا .. إيه؟ أنهينا السكت ..
+
+266
+00:24:08,020 --> 00:24:15,500
+حكم السكت ننتقل إلى حكم آخر وهو حكم همزة الوصل طب
+
+267
+00:24:15,500 --> 00:24:18,040
+مع المعروف همزة الوصل؟ ما اللي بتعرفونه عن همزة
+
+268
+00:24:18,040 --> 00:24:23,500
+الوصل؟ همزة
+
+269
+00:24:23,500 --> 00:24:30,100
+الوصل بتكون في أول الأسماء أو الأفعال أو الحروف
+
+270
+00:24:30,840 --> 00:24:34,920
+تثبت إذا ابتدأنا بها الكلام وتُسقط إذا وصلت بما
+
+271
+00:24:34,920 --> 00:24:41,600
+قبلها من يأتي بمثال على همزة الوصل؟ من يأتي بمثال؟
+
+272
+00:24:41,600 --> 00:24:45,700
+اذهب
+
+273
+00:24:45,700 --> 00:24:52,020
+أو اضرب اضرب لهم مثلاً كلمة اضرب لهم مثلاً هي أصلاً 
+
+274
+00:24:52,020 --> 00:24:58,130
+ضربة من الفعل ضربة لكن إذا أردنا تصريف ضربة الأمر 
+
+275
+00:24:58,130 --> 00:25:03,730
+منه يقتضي أن يكون الحرف الأول مش مفتوح ساكن اضرب
+
+276
+00:25:03,730 --> 00:25:08,490
+فحتى نتمكن من الابتداء بحرف الساكن أو نتوصل
+
+277
+00:25:08,490 --> 00:25:13,590
+الابتداء بالحرف الساكن بتصريف الفعل يوضع قبله همزة 
+
+278
+00:25:13,590 --> 00:25:19,130
+وصل تسمى وصل لأننا نتوصل للابتداء بالحرف الساكن
+
+279
+00:25:19,130 --> 00:25:25,210
+لأن العرب يا إخوان لا يبدأون الكلام بحرف ساكن ولا
+
+280
+00:25:25,210 --> 00:25:30,050
+يقفون على متحرك إذا وقف الواحد على آخر الجملة يقف
+
+281
+00:25:30,050 --> 00:25:35,510
+يسكن لذلك في عندنا مدلول للسكون أو مدلولين لكن
+
+282
+00:25:35,510 --> 00:25:39,750
+إذا كذلك ابتدأ الكلمة لا يبدأون الكلام بحرف ساكن
+
+283
+00:25:39,750 --> 00:25:43,730
+ولا يقفون على متحرك كقاعدة عند العرب، لكن بعض
+
+284
+00:25:43,730 --> 00:25:48,730
+تصريفات الكلمات تقتضي أن يكون الحرف الأول ساكن
+
+285
+00:25:48,730 --> 00:25:54,310
+فحتى نبدأ بالحرف الساكن، تصريف الكلمة يوضع قبلها
+
+286
+00:25:54,310 --> 00:25:59,070
+همزة، يتسمى همزة وصل، الغرض منها التوصل إلى
+
+287
+00:25:59,070 --> 00:26:04,880
+الابتدائي بالحرف الساكن، مثال ذلك كلمة ضربة 
+
+288
+00:26:04,880 --> 00:26:09,680
+أولها مفتوح، لكن إذا الأمر منها يقتضي أن يكون حرف
+
+289
+00:26:09,680 --> 00:26:16,140
+الأول ساكن، نقول اضرب، فعشان نبدأ بحرف أوله ساكن في
+
+290
+00:26:16,140 --> 00:26:21,160
+تصريفات اللغة، يوضع قبله همزة تسمى همزة الوصل، نقول
+
+291
+00:26:21,160 --> 00:26:27,720
+اضرب، لما ليش نلفظها؟ تظهر، فنقول اضرب، هه مكسورة، اضرب
+
+292
+00:26:27,720 --> 00:26:33,350
+لكن إذا وصلناها باللي قبلها، قلنا اضرب، قلنا ضرب...
+
+293
+00:26:33,350 --> 00:26:38,390
+وين راحت الهمزة؟ سقطت... إذا تسقط، إذا يعني وصلت 
+
+294
+00:26:38,390 --> 00:26:42,810
+مما قبلها، وتظهر وتثبت إذا بدأنا بها الكلام، إذا 
+
+295
+00:26:42,810 --> 00:26:48,230
+بدأنا بها، قولنا اضرب هـ... اضرب... استغفر... انطلق...
+
+296
+00:26:48,230 --> 00:26:52,150
+...هي نلفظ من الهمزة، لكن لو وصلناها من اللي قبلها
+
+297
+00:26:52,150 --> 00:26:57,290
+وضرب... طبعا نضع قبلها واو، بتقول أنه أنا موصولة
+
+298
+00:26:57,290 --> 00:27:02,190
+باللي قبلي، بس حرف الواو أسهل، وضرب أو نقول قلنا نضرب
+
+299
+00:27:02,190 --> 00:27:07,030
+عصاك البحر فال... هنا ال... ال... الهمزة تسقط
+
+300
+00:27:07,030 --> 00:27:11,610
+لأننا وصلنا بما قبلها، مثلا استغفر نقول واستغفر
+
+301
+00:27:11,610 --> 00:27:17,270
+أيضا تسقط الهمزة، انطلق، وانطلق بتسقط الهمزة لأننا
+
+302
+00:27:17,270 --> 00:27:23,640
+وصلنا بما قبلها، ومن هنا نشوف ما هو تعريف همزة الوصل
+
+303
+00:27:23,640 --> 00:27:28,540
+همزة الوصل هنا، كما عرفها العلماء، هي همزة زائدة عن
+
+304
+00:27:28,540 --> 00:27:35,020
+بنية الكلمة، تلحق أول الأسماء والأفعال والحروف، تثبت
+
+305
+00:27:35,020 --> 00:27:39,320
+عند الابتداء بها، وتسقط إذا وصلت بما قبلها، إذا هي
+
+306
+00:27:39,320 --> 00:27:44,980
+يا أخوات، همزة أصلية ولا همزة زائدة؟ همزة زائدة عن 
+
+307
+00:27:44,980 --> 00:27:49,860
+بنية الكلمة، همزة زائدة عن بنية الكلمة، تلحق أول
+
+308
+00:27:49,860 --> 00:27:54,240
+الأسماء أو الأفعال أو الحروف، وتثبت عند الابتداء
+
+309
+00:27:54,240 --> 00:27:58,680
+بها، إذا ابتدأنا بها الكلام نثبتها، وإذا وصلت بما
+
+310
+00:27:58,680 --> 00:28:02,900
+قبلها تسقط، وتسقط إذا وصلت بما قبلها، من يعرف لنا
+
+311
+00:28:02,900 --> 00:28:07,580
+همزة الوصل؟ فضل أختي، هي همزة زائدة عن بنية الكلمة 
+
+312
+00:28:07,580 --> 00:28:10,960
+تلحق أول الأسماء أو الأفعال أو الحروف، تثبت عند
+
+313
+00:28:10,960 --> 00:28:16,860
+الابتداء، صحيح، همزة زائدة عن بنية الكلمة، تلحق
+
+314
+00:28:16,860 --> 00:28:21,520
+الأسماء والأفعال والحروف، تثبت إذا ابتدأنا بها
+
+315
+00:28:21,520 --> 00:28:25,600
+الكلام، وتسقط إذا وصلت بما قبلها، ما هو سبب
+
+316
+00:28:25,600 --> 00:28:30,220
+سقوطها؟ سبب سقوطها يا أخوات، أن الحرف اعتمد على
+
+317
+00:28:30,220 --> 00:28:33,900
+الحرف الساكن من أول الكلمة، اللي هو حرف الضاد مثلا 
+
+318
+00:28:33,900 --> 00:28:39,860
+هذا... حرف الضاد، واضرب ساكن... لما قولنا اضرب، حتى 
+
+319
+00:28:39,860 --> 00:28:44,260
+نبدأ بحرف ساكن، اقتضت أصلي في الكلمة اللي ندعوها
+
+320
+00:28:44,260 --> 00:28:49,460
+قبل همزة وصل، أما وقد وصلت هذه الكلمة بالجملة
+
+321
+00:28:49,460 --> 00:28:54,200
+السابقة أو بحرف سابقها، فأيهم أصلي حرف الواو تحت
+
+322
+00:28:54,200 --> 00:28:58,860
+وضرب، ولا الهمزة تحت اضرب؟ أيهم الأصلي؟ حرف الواو 
+
+323
+00:28:58,860 --> 00:29:03,340
+أصلي، وحرف الهمزة زائد، فيسقط الزائد لأن الحرف
+
+324
+00:29:03,340 --> 00:29:09,000
+الساكن اعتمد على حرف أصلي وهو حرف الواو، فنقول وضرب
+
+325
+00:29:09,000 --> 00:29:13,360
+لهم مثلا، مفهوم يا أخوات؟ إذا ما هو سبب سقوط همزة
+
+326
+00:29:13,360 --> 00:29:17,710
+الوصل؟ لأن الحرف الساكن في الكلمة التي ابتدأناها
+
+327
+00:29:17,710 --> 00:29:22,790
+بهمزة وصل، يعني اعتمدت على حرف أصلي سبقها فسقطت 
+
+328
+00:29:22,790 --> 00:29:28,050
+همزة الوصل، فنقول بدل من أن نقول اضرب، وصلت لمقبلها
+
+329
+00:29:28,050 --> 00:29:34,730
+فنقول وضرب، سقطت ايه؟ سقطت الهمزة، كذلك استغفرة، طبعا
+
+330
+00:29:34,730 --> 00:29:39,610
+هذا اضرب ثلاثي، أمر الثلاثي، همزة وهمزة وصل، استغفر
+
+331
+00:29:39,610 --> 00:29:46,850
+سداسي، همزة وهمزة وصل، استغفر، استنشق، استنثر، استكبر
+
+332
+00:29:46,850 --> 00:29:52,350
+كل هذا همزة وهمزة وصل، لأنه سداسي، الحرف الأول ساكن
+
+333
+00:29:53,030 --> 00:29:57,730
+اعتمد، عشان نبدأ بحرف ساكن، جئنا بهمزة الوصل، فنقول
+
+334
+00:29:57,730 --> 00:30:04,650
+استغفر بهمزة وصل، فأما إذا وصلت بما قبلها، بيكون حرف
+
+335
+00:30:04,650 --> 00:30:09,590
+الأول تحت استغفر، اعتمد على حرف أصلي سبقها وهو
+
+336
+00:30:09,590 --> 00:30:14,670
+الواو، فتسقط همزة الوصل، وسميت همزة الوصل بهذا الاسم
+
+337
+00:30:14,670 --> 00:30:20,650
+لأنه يتوصلوا بهمزة الوصل للنطق بالحرف الساكن، يعني 
+
+338
+00:30:20,650 --> 00:30:25,070
+حتى نتوصل للنطق بحرف الساكن أو نبدأ الكلمة بحرف
+
+339
+00:30:25,070 --> 00:30:28,870
+ساكن، جئنا بهمزة الوصل وسمناها إيش يا أخوات؟ سمناها
+
+340
+00:30:28,870 --> 00:30:32,650
+همزة الوصل، لو قلنا ما هو الفرق بين همزة الوصل
+
+341
+00:30:32,650 --> 00:30:41,410
+وهمزة القطع؟ في إن همزة القطع مثلا أكرمها، أحسنة، هذا
+
+342
+00:30:41,410 --> 00:30:45,190
+أصلي، فيه... ما الفرق بين همزة الوصل وهمزة 
+
+343
+00:30:45,190 --> 00:30:48,050
+القطع؟ اتفضلي، نعم، أنتِ 
+
+344
+00:30:53,890 --> 00:30:59,190
+أحسنتِ، يكفي، همزة الوصل أولا بتكون أول هي الوصل
+
+345
+00:30:59,190 --> 00:31:03,010
+زائدة عن بنية الكلمة، وتلحق الأسماء والأفعال و
+
+346
+00:31:03,010 --> 00:31:07,230
+الحروف، أما همزة القطع فهي ايه؟ فهي أصلية، هي النقطة
+
+347
+00:31:07,230 --> 00:31:11,110
+الأولى، همزة الوصل زائدة، وهمزة القطع مايلة أصلية في
+
+348
+00:31:11,110 --> 00:31:16,680
+الكلمة، مثل أكرمه، أحسنه، طيب كلمة أكرمه أو أحسنه لو
+
+349
+00:31:16,680 --> 00:31:23,820
+وصلناها بما قبلها، يأتي بجملة، و أكرمه، و أكرمنا، هل 
+
+350
+00:31:23,820 --> 00:31:29,020
+نقول و أكرمنا، و أكرمنا؟ لأ، إنما نقول و أكرمنا، و
+
+351
+00:31:29,020 --> 00:31:35,100
+أكرمنا، كذلك و أحسنه، و أحسنه، الهمزة همزة قطع، لأن 
+
+352
+00:31:35,100 --> 00:31:40,360
+اسمها ماضي الرباعي، وماضي الرباعي، وماضي الثلاثي
+
+353
+00:31:40,360 --> 00:31:47,380
+همزة وهمزة ايه؟ همزة وهمزة قطع، أما أمر الثلاثي، و
+
+354
+00:31:47,380 --> 00:31:49,960
+أمر الخماسي، والثلاثي، كم أحسن أخذها إن شاء الله 
+
+355
+00:31:49,960 --> 00:31:55,680
+فهي همزة وهمزة وصل، إذا الأولى أن الوصل زائدة، والقطع
+
+356
+00:31:55,680 --> 00:31:59,060
+أصلية وجئنا بمثال على الوصل الزائدة اضرب، وعلى 
+
+357
+00:31:59,060 --> 00:32:04,820
+القطع الأصلية اللي هي أكرمه، وأحسنه، أكثر لك فرق 
+
+358
+00:32:04,820 --> 00:32:07,200
+آخر، اه، فضلي
+
+359
+00:32:15,880 --> 00:32:21,820
+أحسنتِ، همزة الوصل يا أخوات تثبت عند الابتداء بها، و
+
+360
+00:32:21,820 --> 00:32:25,840
+تسقط إذا وصلت بما قبلها كما أخذناها، أما همزة القطع
+
+361
+00:32:25,840 --> 00:32:31,100
+تثبت عند الابتداء بها، وعند وصلها كذلك بتثبت في
+
+362
+00:32:31,100 --> 00:32:37,120
+حالة الوصل، وفي حالة القطع أيضا بتثبت، همزة القطع
+
+363
+00:32:38,370 --> 00:32:42,370
+الآن في عندنا حالات همزة الوصل، إن شاء الله هنخلطها
+
+364
+00:32:42,370 --> 00:32:45,730
+بإذن الله عز وجل، في المحاضرة الماضية، هنعيد الكلمتين
+
+365
+00:32:45,730 --> 00:32:49,690
+اللي ذكرناهم، ثم نستنفد بعد ذلك همزة الوصل بإذن الله
+
+366
+00:32:49,690 --> 00:32:53,250
+عز وجل، نكتفي بهذا القدر، ونكمل إن شاء الله في
+
+367
+00:32:53,250 --> 00:32:55,590
+اللقاء القادم، بارك الله فيكم، والسلام عليكم
+
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ie8S8rcMI0w_postprocess.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ie8S8rcMI0w_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fdd886f7578041ba0adbf8a11f3432e0e9dfc5c5
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Ie8S8rcMI0w_postprocess.srt
@@ -0,0 +1,1468 @@
+1
+00:00:11,700 --> 00:00:14,400
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,400 --> 00:00:18,500
+الرحيم الحمد لله الصلاة والسلام على رسول الله وعلى
+
+3
+00:00:18,500 --> 00:00:22,600
+آله وصحبه وسلم موضوعنا اليوم يا أخوات عن السكت
+
+4
+00:00:23,520 --> 00:00:28,680
+السكت من حيث اللغة هو المنع يقال سكت عن الكلام
+
+5
+00:00:28,680 --> 00:00:33,760
+بمعنى امتنعت عنه أما في الاصطلاح فهو قطع الصوتي
+
+6
+00:00:33,760 --> 00:00:39,200
+على الكلمة القرأنية زملا يسيرا بدون تنفس مقدار
+
+7
+00:00:39,200 --> 00:00:43,360
+حركة أو حركتين من يعرف لنا السكت يا أخوات؟ فضلي
+
+8
+00:00:48,550 --> 00:00:53,870
+بدون تنفس يعني نقطع الصوت والسكت يختلف عن الوقف
+
+9
+00:00:53,870 --> 00:00:59,070
+الوقف يتنفس فيه القارئ عادة لكن السكت هو نقطع
+
+10
+00:00:59,070 --> 00:01:03,010
+الصوت على الكلمة القرأنية زمنا يسينا نقدره حركتين
+
+11
+00:01:03,010 --> 00:01:07,970
+بدون تنفس وهذا طبعا في مواضع معينة عند الإمام حفظ
+
+12
+00:01:07,970 --> 00:01:13,370
+فهناك أربع مواضع السكتات اللي فيها سكتات واجبة عند
+
+13
+00:01:13,370 --> 00:01:19,910
+الإمام حفظ وموضعين السكتات سكتات جائزةو أسكته في
+
+14
+00:01:19,910 --> 00:01:23,690
+المواضع الأربع نشوف الموضوع الأول هو أسكت على
+
+15
+00:01:23,690 --> 00:01:28,230
+الألف المبدل من التنوين في كلمة عيوجة من قوله
+
+16
+00:01:28,230 --> 00:01:34,190
+تعالى الحمد لله الذي أنزل على عبده الكتاب ولم يجعل
+
+17
+00:01:34,190 --> 00:01:39,930
+له عيوجةقيما لينذر بأسا شديدا بدون تنفس ولم يجعل
+
+18
+00:01:39,930 --> 00:01:47,150
+له عوجا قيما لينذر بأسا شديدا من يقرأها ويسكت سكتة
+
+19
+00:01:47,150 --> 00:01:52,450
+لطيفة على ألف عوجا من قول تعالى ولم يجعل له عوجا
+
+20
+00:01:52,450 --> 00:01:57,010
+قيما لينذر بأسا شديدا من يقرأ؟ فضلي
+
+21
+00:02:02,650 --> 00:02:08,410
+ولم يجعل له عوجة قيم لينظر بأس شديدا من لده بس
+
+22
+00:02:08,410 --> 00:02:15,530
+يكفي ولم يجعل له عوجة قيم لينظر بأس شديدا من يعيد؟
+
+23
+00:02:15,530 --> 00:02:21,390
+فضل أخت الحمد لله الذي أنزل على عبد الكتاب ولم
+
+24
+00:02:21,390 --> 00:02:28,980
+يجعل له عوجة قيم لينظر بأس شديدا من لده بسابدئيها
+
+25
+00:02:28,980 --> 00:02:34,760
+ولم يجعل له مش عوجة عوجة ولم يجعل له عوجة قيم
+
+26
+00:02:34,760 --> 00:02:39,240
+لينذر بأسا شديدة عساسا أن الآية .. الآية طويلة
+
+27
+00:02:39,240 --> 00:02:43,220
+قليلا فلا نريد أن نبدأها من أولها كأننا وقفا ..
+
+28
+00:02:43,220 --> 00:02:46,860
+وقفنا وقفا اضطراريا عند قول على عبده الكتاب ولم
+
+29
+00:02:46,860 --> 00:02:51,700
+يجعل له الكتاب ونريد أن نكمل ونصلح من يقراها قراءة
+
+30
+00:02:51,700 --> 00:02:58,370
+سليمةولم يجعل له عوجة قيم اللي يُنذِر بأسا شديدا،
+
+31
+00:02:58,370 --> 00:03:04,570
+تفضّال إيه؟ ولم يجعل له عوجة قيم اللي يُنذِر بأسا
+
+32
+00:03:04,570 --> 00:03:05,830
+شديدا، تفضّال إيه؟ ولم يجعل له عوجة قيم اللي
+
+33
+00:03:05,830 --> 00:03:06,830
+يُنذِر بأسا شديدا، تفضّال إيه؟ لذلك الأخير، إذا
+
+34
+00:03:06,830 --> 00:03:11,790
+السكت على ألف، الألف عوجة من قوله تعالى ولم يجعل
+
+35
+00:03:11,790 --> 00:03:16,190
+له عوجة قيم اللي يُنذِر بأسا شديدا، هنا الوقف يسمى
+
+36
+00:03:16,190 --> 00:03:19,690
+أو السكت اللي هنا سكتة لطيفة وهي من السكتات
+
+37
+00:03:19,690 --> 00:03:24,860
+الواجبة عند الإمام حفظو أصلها هنا وقف تام الاصل في
+
+38
+00:03:24,860 --> 00:03:28,620
+عوجة وقف تام على رأس الآية يعني الأصل أن نقف عندها
+
+39
+00:03:28,620 --> 00:03:32,680
+لكن في حالة الواصل لو أردنا أن نوصلها عند الإمام
+
+40
+00:03:32,680 --> 00:03:38,300
+حفص يجب أن نسكت سكتة لطيفة لو قلنا يعني ما الحكمة
+
+41
+00:03:38,300 --> 00:03:42,900
+أو ما هو وجه السكت على ألف عوجة؟ لماذا نسكت نحن
+
+42
+00:03:42,900 --> 00:03:46,360
+على ألف عوجة؟ أو ما الحكمة من الوقف أو السكت على
+
+43
+00:03:46,360 --> 00:03:54,780
+ألف عوجة؟ من يعرف؟ فضليصحيح يعني حتى نوضح أن هناك
+
+44
+00:03:54,780 --> 00:04:00,660
+كلمتين كلمة عيوجة و كذلك قيمة و أن كلمة قيمة ليست
+
+45
+00:04:00,660 --> 00:04:04,480
+صفة لعيوجة لأنه يحصل تناقض لو قلنا عيوجة اللي هو
+
+46
+00:04:04,480 --> 00:04:08,680
+أعوج و قيمة بمعنى مستقيمة حتى لا يظن أو يتوهم
+
+47
+00:04:08,680 --> 00:04:14,000
+المتوهم أن كلمة قيمة قيمة صفة لعيوجة فيحصل تناقض
+
+48
+00:04:14,000 --> 00:04:18,740
+فلبد أن يسكت سكتة لطيفة على ألف عيوجة فنقول و لم
+
+49
+00:04:18,740 --> 00:04:26,180
+يجعلله عيوجةقيم لينذر بأس شديده وهنا تقديره أنزله
+
+50
+00:04:26,180 --> 00:04:32,840
+قيمة أو ليكون قيمة يعني كلمة جديدة فالوقف على ألف
+
+51
+00:04:32,840 --> 00:04:36,300
+عيوج أو الوقف على آخر الآية على نفس الآية اسمه وقف
+
+52
+00:04:36,300 --> 00:04:40,940
+تام ولكن عندما نصل الآيتين مع بعضهم البعض لابد من
+
+53
+00:04:40,940 --> 00:04:45,430
+السكت سكت لطيفة وهي سكت واجب عند حفظعلى ألف عوجة
+
+54
+00:04:45,430 --> 00:04:50,250
+لنبين يعني وجه .. وجه السكت لنبين أن قيمة ليست
+
+55
+00:04:50,250 --> 00:04:55,470
+تابعة في إعرابها العوجة بل هي كلمة مستأنفة أو جملة
+
+56
+00:04:55,470 --> 00:05:01,290
+مستأنفة تقديره أنزله يعني قيمة أو ليكون قيمة هذا
+
+57
+00:05:01,290 --> 00:05:04,170
+هو يعني السؤال الذي ممكن أن يأتي إليكم يا أخوات
+
+58
+00:05:04,170 --> 00:05:10,770
+يعني أبيني مثلاجانب أو مثلا مثلا على السكت أو عرف
+
+59
+00:05:10,770 --> 00:05:14,370
+السكت في ما ذكره مثلا عليه مع بيان وجهه السكتي
+
+60
+00:05:14,370 --> 00:05:18,830
+هتقول إنه السكت هو قطع الصوت على الكلمة القرأنية
+
+61
+00:05:18,830 --> 00:05:24,410
+زمنا يسيرا بدون تنفس مقداره حركتين والمثال وعلى
+
+62
+00:05:24,410 --> 00:05:30,210
+ذلك في عندنا سكتات واجب أربع سكتاتو سكتتين يعني
+
+63
+00:05:30,210 --> 00:05:34,190
+الجائزتين السكت الواجب الأول اللي أخدناها الآن أن
+
+64
+00:05:34,190 --> 00:05:39,170
+يسكت سكت لطيفة على ألف عوجة من قوله ولم يجعلله
+
+65
+00:05:39,170 --> 00:05:44,370
+عوجة قيمة لينذر بأسا شديدة لو سألناكم ما هو وجه
+
+66
+00:05:44,370 --> 00:05:50,490
+السكت هنقول حتى نبينأن قيمًا ليس تابع في إعرابها
+
+67
+00:05:50,490 --> 00:05:55,090
+لعيوجة وأن الوقف على عيوجة إنما هو وقف تام وتم
+
+68
+00:05:55,090 --> 00:05:59,030
+المنع عنده ليس له علاقة بما بعده لا لفظة ولا معنى
+
+69
+00:05:59,030 --> 00:06:04,070
+وأن قيمًا كلمة مستنفة جديدة بمعنى أو بتقديره أنزله
+
+70
+00:06:04,070 --> 00:06:08,770
+قيمة هذا هي يا أخواتي هي السكتة الأولى عندنا
+
+71
+00:06:08,770 --> 00:06:13,600
+السكتة الثانية وهي قوله تعالىقالوا يا ويلنا ما
+
+72
+00:06:13,600 --> 00:06:19,920
+بعثنا من مرقدنا هذا ما وعد الرحمن وصدق المرسلون أن
+
+73
+00:06:19,920 --> 00:06:26,560
+يسكت لطيفة على ألف مرقدنا حتى نبين أن هذا الكلام
+
+74
+00:06:26,560 --> 00:06:30,900
+هذا ما وعد الرحمن وصدق المرسلون ليس تابعا لما قبله
+
+75
+00:06:30,900 --> 00:06:37,870
+لأنه الأول كلام منكلام الكفار الذين كانوا ينكرونا
+
+76
+00:06:37,870 --> 00:06:43,210
+البعث فلمّا بعثهم الله سبحانه وتعالى قال للكفار يا
+
+77
+00:06:43,210 --> 00:06:47,870
+ويلنا من بعثنا من مرقدنا؟ فالكلام الذي بعده كلام
+
+78
+00:06:47,870 --> 00:06:52,490
+جديد فيقول الملائكة أو يقول المؤمنون هذا ما وعد
+
+79
+00:06:52,490 --> 00:06:56,210
+الرحمن وصدق المرسلونلكن لو وصلنا الكلام مع بعضه
+
+80
+00:06:56,210 --> 00:07:00,590
+البعض، فهذا ما وعد الرحمن وصدق المرسلون هو من قول
+
+81
+00:07:00,590 --> 00:07:04,510
+الكفار، والكفار لم يقولوا هذا الكلام لأنهم أصلا لا
+
+82
+00:07:04,510 --> 00:07:09,690
+يؤمنون بيوم القيامة. إذن نسكت سكتة لطيفة على ألف
+
+83
+00:07:09,690 --> 00:07:15,100
+مر قدنا هنا،حتى نبيّن أن جملة هذا مواهد الرحمن ليس
+
+84
+00:07:15,100 --> 00:07:19,780
+تابعة لما قبلها بل هو كلام جديد من قول الملائكة أو
+
+85
+00:07:19,780 --> 00:07:24,420
+من قول المؤمنين الذين يقررون بأن هذا مواهد الرحمن
+
+86
+00:07:24,420 --> 00:07:28,580
+وصدق المرسلون أما كلام الكفار الذين كانوا ينكرون
+
+87
+00:07:28,580 --> 00:07:34,760
+البعث والجزاء والحساب قالوا يا ويلنا من بعثنا من
+
+88
+00:07:34,760 --> 00:07:40,290
+مرقدنا؟نسكت سكتة لطيفة ثم نقرأ بدون تنفس هذا ما
+
+89
+00:07:40,290 --> 00:07:45,490
+وعد الرحمن وصداق المرسلون إذا من يقف أو يسكت سكتة
+
+90
+00:07:45,490 --> 00:07:48,810
+لطيفة على ألف مرقدنا ويقرأ قراءة سليمة بالنسبة
+
+91
+00:07:48,810 --> 00:07:55,210
+لهذه الآية فضل أختك قالوا يا ويلنا من بعثنا من
+
+92
+00:07:55,210 --> 00:08:01,930
+مرقدنا هدل مرقدنا هذا ما وعد الرحمن وصداق المرسلون
+
+93
+00:08:03,500 --> 00:08:08,980
+بس بدون تنفس، من يقرأ بدون تنفس؟ قالوا يا ويلنا من
+
+94
+00:08:08,980 --> 00:08:14,960
+بعثنا من مرقدنا هذا ما وعد الرحمن وصدق المرسلون
+
+95
+00:08:14,960 --> 00:08:24,600
+أحسنتي،
+
+96
+00:08:24,600 --> 00:08:30,040
+طيب ما هو وجه السكت على ألف مرقدنا؟ ما الحكمة من
+
+97
+00:08:30,040 --> 00:08:32,440
+السكت على ألف مرقدنا؟
+
+98
+00:08:35,140 --> 00:08:39,780
+أحسنتي يعني بيان أن هذا ما وعد الرحمن وصدق
+
+99
+00:08:39,780 --> 00:08:44,180
+المرسلون ليس تابع للكلام السابق فإن الكلام السابق
+
+100
+00:08:44,180 --> 00:08:47,760
+إنما هو كلام الكفار أما الكلام اللاحق فهو كلام
+
+101
+00:08:47,760 --> 00:08:51,380
+المؤمنين هذا المؤمنين أو الملائكة هذا يا أخوات هو
+
+102
+00:08:51,380 --> 00:08:55,180
+المثال الثاني يعني مافيه عنا مثالينالواء السكت على
+
+103
+00:08:55,180 --> 00:08:59,660
+ألف عوجة والسكت على ألف مرقدنا وإذا أردنا السؤال
+
+104
+00:08:59,660 --> 00:09:02,840
+لابد أن نأتي بالآية كاملة يعني الذي لو سألناكم
+
+105
+00:09:02,840 --> 00:09:07,960
+سؤال فقالة أو قالت الأخت السكت على ألف عوجة والسكت
+
+106
+00:09:07,960 --> 00:09:11,720
+على ألف مرقدنا بدون ذكر الآية يعني لا تكون الإجابة
+
+107
+00:09:11,720 --> 00:09:15,900
+سليمة لابد أن نذكر الآية أقل شيء الكلمتين أقل شيء
+
+108
+00:09:15,900 --> 00:09:20,680
+لكن لابد أن نذكر الآية كاملة بالشطرين سواء من
+
+109
+00:09:20,680 --> 00:09:25,130
+بعثنا من مرقدنا هذا مواد الرحمنأو لم يجعل له عوجة
+
+110
+00:09:25,130 --> 00:09:29,470
+قيما لينذر بأسان شديدة لكن لو ذكرت الأخت فقط قالت
+
+111
+00:09:29,470 --> 00:09:33,630
+ألف عوجة أو ألف مرقدنة بتكون الإجابة يعني مش سليمة
+
+112
+00:09:33,630 --> 00:09:37,290
+لأنه لابد أن تكون الإجابة كاملة و نذكر الكلمتين
+
+113
+00:09:37,290 --> 00:09:41,650
+على أساس أنه نسكت سكتة لطيفة هذا الإجابة الكتابة
+
+114
+00:09:41,650 --> 00:09:45,790
+لكن بالنسبة لللفظ لابد أن نذكر التنتين ولم يجعل له
+
+115
+00:09:45,790 --> 00:09:46,650
+عوجة
+
+116
+00:09:56,280 --> 00:10:03,000
+طيب السكت التالت يا أخوات الواجب أيضا هي السكت على
+
+117
+00:10:03,000 --> 00:10:11,710
+نون من وقيل من راقوقيل من راق وظن أنه الفراق
+
+118
+00:10:11,710 --> 00:10:16,310
+والتفت الساق بالساق إلى ربك يوم إذن المساق هنا
+
+119
+00:10:16,310 --> 00:10:23,890
+السكت على نون من نسكت سكت لطيفة وقيل من راق طيب لو
+
+120
+00:10:23,890 --> 00:10:29,290
+سألنا سؤال ما الحكمة أو ما هو وجه السكت على نون
+
+121
+00:10:29,290 --> 00:10:30,930
+من؟ فضل أخت
+
+122
+00:10:36,680 --> 00:10:43,800
+حتى نبين بأن كلمة من و راق انما هما كلمتان لأنه في
+
+123
+00:10:43,800 --> 00:10:49,780
+نون و راق اضغام متقارب او اضغام بيغرقونا فعندما
+
+124
+00:10:49,780 --> 00:10:54,220
+نقراها مع بعضها لبعض يعني بتبين عند اضغام نقول
+
+125
+00:10:54,220 --> 00:10:58,980
+مراق و مراق يعني ممكن تكون سيرة مبالغة من كثرة
+
+126
+00:10:58,980 --> 00:11:05,000
+المروق أو كلمة تدل على أنه بياع مرق مراقلكنها يعني
+
+127
+00:11:05,000 --> 00:11:10,360
+لابد أن نبين أن كلمة من كلمة و راق كلمة ثانية ما
+
+128
+00:11:10,360 --> 00:11:18,040
+معنى راق؟ راق .. راق لحالها من .. راق .. راق يعني
+
+129
+00:11:18,040 --> 00:11:23,520
+من الرقية والرقية هو الشفاء من المرض يعني يرقي لنا
+
+130
+00:11:23,520 --> 00:11:26,580
+رقية عن طريق قراءة القرآن، قراءة الفاتحة، قراءة
+
+131
+00:11:26,580 --> 00:11:30,320
+آية الكرسي، أي .. أي آية بيرقي لنا المريض فالآية
+
+132
+00:11:30,320 --> 00:11:34,740
+تتكلم يعني كالة إذا بلغت التراقيةما هو الذي بلغ
+
+133
+00:11:34,740 --> 00:11:39,540
+التراقية؟ الروح، يعني الآية تتكلم عن واحد يعني في
+
+134
+00:11:39,540 --> 00:11:43,520
+حالة النزاع .. في حالة النزاع مريض وبلغت الروح
+
+135
+00:11:43,520 --> 00:11:47,660
+التراقي يعني منطقة ال .. ال .. ترقوة اللي هي .. هي
+
+136
+00:11:47,660 --> 00:11:51,300
+ترقوة هنا، هذي ترقوة، هذي ترقوة، يعني كدت أن تخرج
+
+137
+00:11:51,300 --> 00:11:56,250
+من .. من الروح .. الروحوقيل من راق أصحابه وأهله
+
+138
+00:11:56,250 --> 00:12:01,970
+وذوه يقولون من يشفي لنا ويعالج لنا هذا المريض وقيل
+
+139
+00:12:01,970 --> 00:12:07,990
+من راق يعني من يرقي لنا هذا المريض وظن أنه الفراق
+
+140
+00:12:07,990 --> 00:12:12,330
+..ظن بمعنى تيقن بأنه الفراق أنه هيموت هذا الإنسان
+
+141
+00:12:12,330 --> 00:12:16,900
+والتفت الساق بالساق كده يعني شدة الموتالى ربك
+
+142
+00:12:16,900 --> 00:12:21,340
+يومئذ المساق إذا الكلام راق بمعنى من الرقيا
+
+143
+00:12:21,340 --> 00:12:26,840
+والرقيا بمعنى الشفاء والعلاج فالمن راق لو قرأناها
+
+144
+00:12:26,840 --> 00:12:32,560
+وقيل من راق ممكن واحد يتوهم من راق من كثرة المروق
+
+145
+00:12:32,560 --> 00:12:37,340
+واحد من راق طريق او من راق يعني بياع مرقة بمعنى
+
+146
+00:12:37,340 --> 00:12:41,200
+انه يعمل في مطبخ مثلا فحتى لا يتوهم هذا التوهم
+
+147
+00:12:41,200 --> 00:12:47,310
+نسكت و سكت لطيفةعلى نون من وهذا هو وجه السكت على
+
+148
+00:12:47,310 --> 00:12:52,110
+نون من اللي هي من رأى انظر كذلك يا أخوات إلى
+
+149
+00:12:52,110 --> 00:12:56,690
+المثال الرابع احنا فيه عندنا اربع امثلة ولم يجعل
+
+150
+00:12:56,690 --> 00:13:02,660
+له عواجة قيمةيويدنا من بعثنا من مرقدنا هذا المواد
+
+151
+00:13:02,660 --> 00:13:09,580
+الرحمن وقيل من قراق المثال الرابع كلا بل ران على
+
+152
+00:13:09,580 --> 00:13:15,020
+قلوبهم ما كانوا يكسبون كلا بل رانة النقل اللي أسكت
+
+153
+00:13:15,020 --> 00:13:21,820
+على لام بل كلا بل ران على قلوبهم ما كانوا يكسبون
+
+154
+00:13:21,820 --> 00:13:31,540
+ما معنى بل رانة رانة بمعنى غطىالصدق غطى على قلبه
+
+155
+00:13:31,540 --> 00:13:38,040
+قلب الإنسان يعني الإنسان عندما يعصى الله ينكطه على
+
+156
+00:13:38,040 --> 00:13:42,380
+قلبه بنكطة سوداء أو الله سبحانه وتعالى يفتح له
+
+157
+00:13:42,380 --> 00:13:47,260
+المجال فإن استغفر بعد المعصية غفر الله له وإن أصر
+
+158
+00:13:47,260 --> 00:13:51,080
+على المعصية يعني نكطة على قلبه بنكطة سوداء
+
+159
+00:13:54,070 --> 00:13:59,990
+زادت المعاصي وكثرة الذنوب يصبح قلبه أسود لأن
+
+160
+00:13:59,990 --> 00:14:03,390
+القلوب لتصدق كما يقول النبي عليه الصلاة والسلام
+
+161
+00:14:03,390 --> 00:14:08,950
+كما يصدق الحديد أو النحاس وجلاءها الاستغفارالإنسان
+
+162
+00:14:08,950 --> 00:14:13,850
+الذي يعصى الله يصبح قلبه مغطى بالران والران معناته
+
+163
+00:14:13,850 --> 00:14:18,910
+الصدق لذلك هذا الإنسان الذي يكثر من المعاصي ويزداد
+
+164
+00:14:18,910 --> 00:14:23,490
+في المعاصي يصبح قلبه أسودا فهذا الإنسان لا يرى
+
+165
+00:14:23,490 --> 00:14:28,410
+بنور الله بل يرى الحق باطلا و الباطلة حقا بسبب
+
+166
+00:14:28,410 --> 00:14:34,330
+ذنوبهفالذنوب والمعاصي سرب أكيد في دمار الأفراد
+
+167
+00:14:34,330 --> 00:14:39,030
+والأمم والشعوب الإنسان لما يكثر .. أو الأمة لما
+
+168
+00:14:39,030 --> 00:14:43,490
+تكثر الذنوب وتكبر المعاصي والفواحش والمنكرات الله
+
+169
+00:14:43,490 --> 00:14:47,480
+سبحانه وتعالى يهلكهموالأنبياء الذين أرسلهم الله عز
+
+170
+00:14:47,480 --> 00:14:51,020
+وجل إلى أقوامهم يرسلهم إلى أقوامهم بعد أن يعني
+
+171
+00:14:51,020 --> 00:14:55,880
+اضعصوا الله وارتكبوا المعاصي والمنكرات فأصروا على
+
+172
+00:14:55,880 --> 00:14:59,020
+الارتكاب المعاصي والمنكرات فأهلكهم الله عز وجل
+
+173
+00:14:59,020 --> 00:15:03,840
+فالذنوب والمعاصي سرد أكيد في دمار الأمم والأفراد
+
+174
+00:15:03,840 --> 00:15:09,440
+والشعوب هنا كالة بل ران على قلوبهم يعني غطى على
+
+175
+00:15:09,440 --> 00:15:13,680
+قلوبهم ما كانوا يكسبون لكن لو قرأناها بالاضغام لأن
+
+176
+00:15:13,680 --> 00:15:18,040
+اللاممع الرأي اضغام متقارب لو قرأناها كيف تقرأ
+
+177
+00:15:18,040 --> 00:15:25,830
+بالاضغام بران مامعنى بران؟مثنى بر يعني أرض أرضان
+
+178
+00:15:25,830 --> 00:15:32,870
+بحر بحران سماء سماءان هنا بر بران فهنا لحتى لا
+
+179
+00:15:32,870 --> 00:15:38,110
+يتوهم المستمع عندما يقرأها بالاضغام كلا بران على
+
+180
+00:15:38,110 --> 00:15:41,830
+قلوبهم يعني مش بر واحد لأ هو بران على قلوبهم فحتى
+
+181
+00:15:41,830 --> 00:15:45,890
+لا يتوهم هذا التوهم لابد أن نسكت سكتة لطيفة على
+
+182
+00:15:45,890 --> 00:15:52,110
+لام بلكلا بل ران على قلوبهم ما كانوا يكسبون من
+
+183
+00:15:52,110 --> 00:16:01,330
+يقرأها مع تطبيق حكم السكت هنا اتفضل اختك احسنتك
+
+184
+00:16:01,330 --> 00:16:07,960
+في عندنا لو واحد قال كلا بلران على قلوبهم ما كان
+
+185
+00:16:07,960 --> 00:16:12,760
+يفسبون .. صحيح قراته؟ لأنه تنفس .. لابد أن نقطع
+
+186
+00:16:12,760 --> 00:16:18,120
+الصوت بدون تنفس .. كلا بل ران على قلوبهم و الغرض
+
+187
+00:16:18,120 --> 00:16:22,640
+من قطع الصوت أو السكت بدون تنفس أن لا يتوهم
+
+188
+00:16:22,640 --> 00:16:28,620
+المتوهم بأنه كلمة واحدةبل هي كلمتين اللي هي كان لأ
+
+189
+00:16:28,620 --> 00:16:35,360
+بل كلمة وران كلمة و هذا ما يسمى بوجه السكت على لام
+
+190
+00:16:35,360 --> 00:16:40,640
+بل حتى لا يتوحم المتوحم بأنها كلمة واحدة و يبين
+
+191
+00:16:40,640 --> 00:16:45,310
+بأنها كلمتين لأنه لو أضغمها بتصير براهذه يا أخوات
+
+192
+00:16:45,310 --> 00:16:50,710
+هي السكتات الأربعة الواجبة في عندنا كذلك سكتتين
+
+193
+00:16:50,710 --> 00:16:55,930
+جازتين لكن نريد أن نذكر السكتات الأربعة التي
+
+194
+00:16:55,930 --> 00:17:03,750
+ذكرناها السكت الأولى ما هي يا ابنات؟ ولم يجعل له
+
+195
+00:17:03,750 --> 00:17:09,010
+عواجة قيمة يقرأ ليها من تقراه يا أخوات ولم يجعل له
+
+196
+00:17:09,010 --> 00:17:12,750
+عواجة قيمة لينظرة بأس شديدة تفضلي
+
+197
+00:17:18,920 --> 00:17:23,380
+بس يكفي اذا كان الله خير طيب اقولوا يا ويلنا من
+
+198
+00:17:23,380 --> 00:17:29,420
+بعثنا من مرقدنا هذا ما وعد الرحمن وصدق المرسلون
+
+199
+00:17:29,420 --> 00:17:32,660
+قالوا يا ويلنا من بعثنا من مرقدنا هذا ما وعد
+
+200
+00:17:32,660 --> 00:17:39,380
+الرحمن وصدق المرسلون من يقرأها؟ فضل أخت قالوا يا
+
+201
+00:17:39,380 --> 00:17:44,260
+ويلنا من بعثنا من مرقدنا هذا ما وعد الرحمن وصدق
+
+202
+00:17:44,260 --> 00:17:49,920
+المرسلونالمثال الثالث من يقعه اللي هي قول تعالى
+
+203
+00:17:49,920 --> 00:17:58,520
+وقيل من راق فضليه هنا
+
+204
+00:17:58,520 --> 00:18:06,180
+كلا إذا بلغت التراقية وقيل من راق يعني سكتنا على
+
+205
+00:18:06,180 --> 00:18:11,180
+non من في هذا المثال المثال الرابع كلا بل أرانا
+
+206
+00:18:11,180 --> 00:18:12,080
+فضليه
+
+207
+00:18:17,280 --> 00:18:21,280
+هذه السكتات الأربعة اللي هي السكتات الواجبة لكن في
+
+208
+00:18:21,280 --> 00:18:26,360
+عندنا يا أخوات سكتتين جائزتين يجب أن نسكت عندها و
+
+209
+00:18:26,360 --> 00:18:32,720
+يجب أن نصل و الواصل له حكم و الوقف عليها له حكم
+
+210
+00:18:32,720 --> 00:18:38,360
+نشوف هنا السكتة الجائزة السكتة الأولى بين أخر صورة
+
+211
+00:18:38,360 --> 00:18:43,970
+الأنفال مع التوبة يعني أخر صورة التوبةأو أي صورة
+
+212
+00:18:43,970 --> 00:18:48,610
+سبقت صورة التوبة يعني اللي هي أخر صورة الأنفال مع
+
+213
+00:18:48,610 --> 00:18:53,430
+صورة التوبة نشوف مثلا هنا المثال إن الله بكل شيء
+
+214
+00:18:53,430 --> 00:18:58,850
+عليم عليم هي آخر آية في صورة الأنفال أو أي صورة
+
+215
+00:18:58,850 --> 00:19:06,830
+سبقتها والتي بعدها براءتم من الله ورسوله إلى الذين
+
+216
+00:19:06,830 --> 00:19:12,110
+عاهدتم من المشرفينلو بدنا نوصلها .. طبعا أصل أن
+
+217
+00:19:12,110 --> 00:19:16,810
+نقف نهاية الصورة و بداية صوت الأنفال نوع الوقف
+
+218
+00:19:16,810 --> 00:19:19,950
+اللي هنا يا أخوات الوقف الرسمي في نهاية الصورة
+
+219
+00:19:19,950 --> 00:19:25,450
+يسمى وقف إيش؟ وقف تم تم المانع عنده لا علاقة له مع
+
+220
+00:19:25,450 --> 00:19:30,930
+ما بعده لا لفظة ولا معنى وهذا ما يسمى بالإيش الوقف
+
+221
+00:19:30,930 --> 00:19:37,700
+التام فالقطع عليه قطع يعني جائز والوقف عليه وقفلكن
+
+222
+00:19:37,700 --> 00:19:41,500
+احنا نتكلم في حالة الوصل يعني الحالة الأولى يجوز
+
+223
+00:19:41,500 --> 00:19:45,500
+الوقف عليها وقف تام لأنه طبيعي جدا نقف على رؤوس
+
+224
+00:19:45,500 --> 00:19:51,180
+الآيات وفي آخر الصورة لكن في حالة وصل الصورتين مع
+
+225
+00:19:51,180 --> 00:19:55,560
+بعضهم البعض إن الله بكل شيء عليم بلاء في هذه
+
+226
+00:19:55,560 --> 00:20:01,960
+الحالة عنا إما أن نصلها بالسكت وهو جائز وإما أن
+
+227
+00:20:01,960 --> 00:20:07,140
+نصلها بالوصل اللي هو عن طريق الإقلاب تقلبنشوف مثلا
+
+228
+00:20:07,140 --> 00:20:14,680
+أو الأولى إن الله بكل شيء عليم براءة من الله
+
+229
+00:20:14,680 --> 00:20:20,760
+ورسوله كويس عليم براءة سكتنا سكتة لطيفة و بعدين
+
+230
+00:20:20,760 --> 00:20:23,880
+قلنا براءة حتى يعني نبقي أنه احنا بدأنا بصورة
+
+231
+00:20:23,880 --> 00:20:29,400
+جديدة مش عليم براء طب لو وصلناها يجب أيضا نصلها و
+
+232
+00:20:29,400 --> 00:20:36,750
+نقول عليم براءة من الله ورسولهيعني يمكن أن نصلها
+
+233
+00:20:36,750 --> 00:20:42,530
+بالتطبيق حكم الإقلاب عليم تنوين وراها حرف الباب
+
+234
+00:20:42,530 --> 00:20:49,550
+كون في عنا إقلاب نقرأها عليم براءة من الله ورسوله
+
+235
+00:20:49,550 --> 00:20:53,830
+لكن إذا أردنا أن نوصلها يجب أيضا أن نوصلها وهو
+
+236
+00:20:53,830 --> 00:21:00,370
+جائز ساكت جائز نقول عليم براءة من الله ورسوله من
+
+237
+00:21:00,370 --> 00:21:03,370
+يقرأها؟ فضل
+
+238
+00:21:09,760 --> 00:21:15,000
+لأ تتنفسوش بدون تنفس أحسنتي
+
+239
+00:21:15,000 --> 00:21:23,360
+تفضلي اقراي أحسنتي
+
+240
+00:21:23,360 --> 00:21:27,620
+هذه يا أخوتي هي السكتة الجائزة الأولى ما بين صورة
+
+241
+00:21:27,620 --> 00:21:31,820
+الأنفال التي سبقت صورة التوبة وبعدها صورة التوبة
+
+242
+00:21:31,820 --> 00:21:38,170
+طبعابداية صورة التوبة اما .. اما اذا كان .. طب لو
+
+243
+00:21:38,170 --> 00:21:42,670
+قولنا صورة التوبة لماذا لم تبدأ بقوله بسم الله
+
+244
+00:21:42,670 --> 00:21:47,070
+الرحمن الرحيم مثله كمثل اي صورة ثانية؟ فضليه لأن
+
+245
+00:21:47,070 --> 00:21:50,010
+بسم الله الرحمن الرحيم بتعني الأمام وصورة التوبة
+
+246
+00:21:50,010 --> 00:21:57,510
+نزلت بالصينصحيح صورة التوبة يعني بدايتها إعلان
+
+247
+00:21:57,510 --> 00:22:00,870
+الحرب على الكفار ويقول علماء أنها نزلت بالسيف
+
+248
+00:22:00,870 --> 00:22:04,770
+بمعنى أنه من أول آية فيها حرب على الكفار و التبرؤ
+
+249
+00:22:04,770 --> 00:22:10,210
+منهم و استباحة أموالهم و كذلك استباحة أرواحهم تبدأ
+
+250
+00:22:10,210 --> 00:22:11,190
+براة
+
+251
+00:22:16,950 --> 00:22:22,650
+و تبدأ تقريبا 28 آية في بيان الأحكام النهائية ما
+
+252
+00:22:22,650 --> 00:22:26,950
+بين المسلمين والمشركين عشان ايه كدا بتبدأ باسم
+
+253
+00:22:26,950 --> 00:22:30,230
+الله الرحمن الرحيم فإذا وصلت مع أي صورة سبقتها
+
+254
+00:22:30,230 --> 00:22:38,370
+هناك سكتة لطيفة على صورة و هذه الصورة السكتة
+
+255
+00:22:38,370 --> 00:22:45,200
+الثانية أخوات الجائزةوهي السكتة على ها ماليةمن قول
+
+256
+00:22:45,200 --> 00:22:51,500
+تعالى ما أغنى عنى مالية هلك عنى سلطانية
+
+257
+00:23:15,190 --> 00:23:20,650
+هلك عني سلطانية يعني وقفنا عليها لأن الوقف على
+
+258
+00:23:20,650 --> 00:23:25,850
+رؤوس الأيات إيه سنة أما في حالة الواصل في عندنا يا
+
+259
+00:23:25,850 --> 00:23:32,830
+إما بالسكت يا إما بالاضغام بالسكت نقول ما أغنى عني
+
+260
+00:23:32,830 --> 00:23:40,370
+مالية هلك عني سلطانية ماليةهلكة نسكت و سكت لطيفة
+
+261
+00:23:40,370 --> 00:23:46,770
+أو نضغيمها مع بعضها لبعض فنقول ما أغنى عني مالية
+
+262
+00:23:46,770 --> 00:23:51,990
+هلك عني سلطانية لأن الهاء الأولى ساكنة والهاء
+
+263
+00:23:51,990 --> 00:23:57,250
+الثاني متحركة والاضغام معناته ادخال حرف ساكن بحرف
+
+264
+00:23:57,250 --> 00:24:02,930
+متحرك بحيث يصيراني حرفا واحدا مشددة من جنس الثاني
+
+265
+00:24:03,500 --> 00:24:08,020
+الان يا اخوات احنا انهينا .. ايه؟ انهينا السكت ..
+
+266
+00:24:08,020 --> 00:24:15,500
+حكم السكت ننتقل الى حكم اخر و هو حكم همزة الوصل طب
+
+267
+00:24:15,500 --> 00:24:18,040
+مع المعروف همزة الوصل؟ ما اللي بتعرفون عن همزة
+
+268
+00:24:18,040 --> 00:24:23,500
+الوصل؟ همزة
+
+269
+00:24:23,500 --> 00:24:30,100
+الوصل بتكون في أول الأسماء أو الأفعال أو الحروف
+
+270
+00:24:30,840 --> 00:24:34,920
+تثبت إذا ابتدأنا بها الكلام وتصفط إذا وصلت بما
+
+271
+00:24:34,920 --> 00:24:41,600
+قبلها من ياتي بمثال على همس الوصل؟ من ياتي بمثال؟
+
+272
+00:24:41,600 --> 00:24:45,700
+اذهب
+
+273
+00:24:45,700 --> 00:24:52,020
+او اضرب اضرب لهم مثلا كلمة اضرب لهم مثلا هي أصلا
+
+274
+00:24:52,020 --> 00:24:58,130
+ضربةمن الفعل ضربة لكن إذا أردنا تصريف ضربة الأمر
+
+275
+00:24:58,130 --> 00:25:03,730
+منه يقتضي أن يكون الحرف الأول مش مفتوح ساكن اضرب
+
+276
+00:25:03,730 --> 00:25:08,490
+فحتى نتمكن من الابتداء بحرف الساكن او نتوصل
+
+277
+00:25:08,490 --> 00:25:13,590
+الابتداء بالحرف الساكن بتصريف الفعل يوضع قبله همزة
+
+278
+00:25:13,590 --> 00:25:19,130
+بصلوتسمى وصل لأننا نتوصل للابتداء بالحرف الساكن
+
+279
+00:25:19,130 --> 00:25:25,210
+لأن العرب يا أخوان لا يبدأون الكلام بحرف ساكن ولا
+
+280
+00:25:25,210 --> 00:25:30,050
+يقفون على متحرك إذا وقف الواحد على آخر الجملة بيقف
+
+281
+00:25:30,050 --> 00:25:35,510
+بيسكن يسكن لذلك في عنا مدعر للسكون أو مدلين لكن
+
+282
+00:25:35,510 --> 00:25:39,750
+إذا كذلك ابتداء الكلمة لا يبدأون الكلام بحرف ساكن
+
+283
+00:25:39,750 --> 00:25:43,730
+ولا يقفون على متحرك كقاعدة عند العربلكن بعض
+
+284
+00:25:43,730 --> 00:25:48,730
+تصريفات الكلمات تقتضي أن يكون الحرف الأول ساكن
+
+285
+00:25:48,730 --> 00:25:54,310
+فحتى نبدأ بالحرف الساكن تصريف الكلمة يوضع قبلها
+
+286
+00:25:54,310 --> 00:25:59,070
+همزة يتسمى همزة وصل الغرض منها التوصل إلى
+
+287
+00:25:59,070 --> 00:26:04,880
+الإبتدائي بالحرف الساكن مثال ذلك كلمة ضربةضربة
+
+288
+00:26:04,880 --> 00:26:09,680
+أولها مفتوح لكن إذا الأمر منها يقتضي أن يكون حرف
+
+289
+00:26:09,680 --> 00:26:16,140
+الأض ساكن نقول اضرب فعشان نبدأ بحرف أوله ساكن في
+
+290
+00:26:16,140 --> 00:26:21,160
+تصريفات اللغة يوضع قبله همزة تسمى همزة الواصل نقول
+
+291
+00:26:21,160 --> 00:26:27,720
+اضرب لما ليش نلفظها تظهر فنقول اضرب هه مكسورة اضرب
+
+292
+00:26:27,720 --> 00:26:33,350
+لكن إذا وصلناها باللي قبلها قلنا اضربقلنا ضرب ..
+
+293
+00:26:33,350 --> 00:26:38,390
+وين راحت الهمزة؟ سقطت .. اذا تسقط إذا يعني وصلت
+
+294
+00:26:38,390 --> 00:26:42,810
+مما قبلها وتظهر وتثبت إذا بدأنا بيها الكلام إذا
+
+295
+00:26:42,810 --> 00:26:48,230
+بدأنا بيها قولنا اضرب ه .. اضرب .. استغفر .. انطلق
+
+296
+00:26:48,230 --> 00:26:52,150
+.. هي نرفض من الهمزة لكن لو وصلناها من اللي قبلها
+
+297
+00:26:52,150 --> 00:26:57,290
+وضرب .. طبعا نضع قبلها wowبتقول أنه أنا موصولة
+
+298
+00:26:57,290 --> 00:27:02,190
+باللي قبلي بس حرف الواو أسهل وضرب أو نقول قل نضرب
+
+299
+00:27:02,190 --> 00:27:07,030
+عصاك البحر فال .. هنا ال .. ال .. الهمزة تسقط
+
+300
+00:27:07,030 --> 00:27:11,610
+لأننا وصلنا بما قبلها مثلا استغفر نقول واستغفر
+
+301
+00:27:11,610 --> 00:27:17,270
+أيضا تسقط الهمزة انطلق وانطلق بتسقط الهمزة لأننا
+
+302
+00:27:17,270 --> 00:27:23,640
+وصلنا بما قبلهاومن هنا نشوف ما هو تعريف همزة الوصل
+
+303
+00:27:23,640 --> 00:27:28,540
+همزة الوصل هنا كما عرفها العلماء هي همزة زائدة عن
+
+304
+00:27:28,540 --> 00:27:35,020
+بنية الكلمة تلحق أول الأسماء والأفعال والحروف تثبت
+
+305
+00:27:35,020 --> 00:27:39,320
+عند الإبتداء بيها وتسقط إذا وصلت بما قبلها إذا هي
+
+306
+00:27:39,320 --> 00:27:44,980
+يا أخوات همزة أصلية ولا همزة زائدة؟همزة زائدة عن
+
+307
+00:27:44,980 --> 00:27:49,860
+بنية الكلمة همزة زائدة عن بنية الكلمة تلحق أول
+
+308
+00:27:49,860 --> 00:27:54,240
+الأسماء أو الأفعال أو الحروف وتثبت عند الإبتداء
+
+309
+00:27:54,240 --> 00:27:58,680
+بها إذا ابتدأنا بها الكلام نثبتها وإذا وصلت بما
+
+310
+00:27:58,680 --> 00:28:02,900
+قبلها تسقط وتسقط إذا وصلت بما قبلها من يعرف لنا
+
+311
+00:28:02,900 --> 00:28:07,580
+همزة الواصل فضل أختي هي همزة زائدة عن بنية الكلمة
+
+312
+00:28:07,580 --> 00:28:10,960
+تلحق أول الأسماء أو الأفعال أو الحروف تثبت عند
+
+313
+00:28:10,960 --> 00:28:16,860
+الإبتداءصحيح، همزة زائدة عن بنية الكلمة، تلحق
+
+314
+00:28:16,860 --> 00:28:21,520
+الأسماء والأفعال والحروف، تثبت إذا ابتدأنا بها
+
+315
+00:28:21,520 --> 00:28:25,600
+الكلام، وتسقط إذا وصلت بما قبلها، ما هو سبب
+
+316
+00:28:25,600 --> 00:28:30,220
+سقوتها؟ سبب سقوتها يا أخوات، أن الحرف اعتمد على
+
+317
+00:28:30,220 --> 00:28:33,900
+الحرف الساكن من أول الكلمةاللي هو حرف الضاد مثلا
+
+318
+00:28:33,900 --> 00:28:39,860
+هذا .. حرف الضاد و اضرب ساكن .. لما قولنا اضرب حتى
+
+319
+00:28:39,860 --> 00:28:44,260
+نبدأ بحرف ساكن اقتدت أصلي في الكلمة اللي ندعوها
+
+320
+00:28:44,260 --> 00:28:49,460
+قبل همزة وصلأما وقد وصلت هذه الكلمة بالجملة
+
+321
+00:28:49,460 --> 00:28:54,200
+السابقة أو بحرف سابقها فأيهم أصلي حرف الواو تحت
+
+322
+00:28:54,200 --> 00:28:58,860
+وضرب ولا الهمزة تحت اضرب؟ أيهم الأصلي؟ حرف الواو
+
+323
+00:28:58,860 --> 00:29:03,340
+أصلي وحرف الهمزة زائد فيسقط الزائد لأن الحرف
+
+324
+00:29:03,340 --> 00:29:09,000
+الساكن اعتمد على حرف أصلي وهو حرف الواو فنقول وضرب
+
+325
+00:29:09,000 --> 00:29:13,360
+لهم مثلا، مفهوم يا أخوات؟ إذا ما هو سبب سقوط حمزة
+
+326
+00:29:13,360 --> 00:29:17,710
+الوصل؟لأن الحرف الساكن في الكلمة التي ابتدأناها
+
+327
+00:29:17,710 --> 00:29:22,790
+بهمزة وصل يعني اعتمدت على حرف أصلي سبقها فسقطت
+
+328
+00:29:22,790 --> 00:29:28,050
+همزة الوصل فنقول بدل من أن نقول اضرب وصلت لمقبلها
+
+329
+00:29:28,050 --> 00:29:34,730
+فنقول وضرب سقطت ايه؟ سقطت الهمزة كذلك استغفرةطبعا
+
+330
+00:29:34,730 --> 00:29:39,610
+هذا اضرب ثلاثي امر الثلاثي همزة و همزة وصل استغفر
+
+331
+00:29:39,610 --> 00:29:46,850
+سداسي همزة و همزة وصل استغفر استنشق استنثر استكبر
+
+332
+00:29:46,850 --> 00:29:52,350
+كل هذا همزة و همزة وصل لانه سداسي الحرف الصين ساكن
+
+333
+00:29:53,030 --> 00:29:57,730
+اعتمد عشان نبدأ بحرف ساكن جئنا بهمزة الوصل فنقول
+
+334
+00:29:57,730 --> 00:30:04,650
+استغفر بهمزة وصل فأما إذا وصلت بما قبلها بيكون حرف
+
+335
+00:30:04,650 --> 00:30:09,590
+الصين تحت استغفر اعتمد على حرف أصلي سبقها وهو
+
+336
+00:30:09,590 --> 00:30:14,670
+الواو فتسقط همزة الوصلوسميت همزة الوصل بهذا الإسم
+
+337
+00:30:14,670 --> 00:30:20,650
+لأنه يتوصلوا بهمزة الوصل للنطق بالحرف الساكن يعني
+
+338
+00:30:20,650 --> 00:30:25,070
+حتى نتوصل للنطق بحرف الساكن أو نبدأ الكلمة بحرف
+
+339
+00:30:25,070 --> 00:30:28,870
+ساكن جينا بهمزة الوصل وسمناها إيش يا أخوات؟ سمناها
+
+340
+00:30:28,870 --> 00:30:32,650
+همزة الوصل لو قلنا ما هو الفرق بين همزة الوصل
+
+341
+00:30:32,650 --> 00:30:41,410
+وهمزة القطع في إن همزة القطع مثلا أكرمهاأحسنة، هذا
+
+342
+00:30:41,410 --> 00:30:45,190
+أصلي، فيه .. ما الفرق بين همزة الواصل و همزة
+
+343
+00:30:45,190 --> 00:30:48,050
+القطع؟ اتفضلي، نعم أنتي
+
+344
+00:30:53,890 --> 00:30:59,190
+أحسنتي يكفي همس الوصل أولا بتكون أول هي الوصل
+
+345
+00:30:59,190 --> 00:31:03,010
+زائدة عن بنية الكلمة و تلحق الأسماء و الأفعال و
+
+346
+00:31:03,010 --> 00:31:07,230
+الحروف أما همس القطع فهي إيه فهي أصلية هي النقطة
+
+347
+00:31:07,230 --> 00:31:11,110
+الأولى همس الوصل زائدة و همس القطع مايلها أصلية في
+
+348
+00:31:11,110 --> 00:31:16,680
+الكلمة مثل أكرمةأحسنة طيب كلمة أكرمة أو أحسنة لو
+
+349
+00:31:16,680 --> 00:31:23,820
+وصلناها بما قبلها يأتي بجملة و أكرمة و أكرمنا هل
+
+350
+00:31:23,820 --> 00:31:29,020
+نقول و أكرمنا و أكرمنا لأ انما نقول و أكرمنا و
+
+351
+00:31:29,020 --> 00:31:35,100
+أكرمنا كذلك و أحسنة و أحسنة الهمزة همزة قطع لأن
+
+352
+00:31:35,100 --> 00:31:40,360
+اسمها ماضي الرباعي و ماضي الرباعي و ماضي الثلاثي
+
+353
+00:31:40,360 --> 00:31:47,380
+همزة و همزة ايه؟همزة و همزة قطع أما أمر الثلاثي و
+
+354
+00:31:47,380 --> 00:31:49,960
+أمر الخماسي و الثلاثي كم أحسن أخدها إن شاء الله
+
+355
+00:31:49,960 --> 00:31:55,680
+فهمزة و همزة وصل إذا الأولى أن الوصل زائدة و القطع
+
+356
+00:31:55,680 --> 00:31:59,060
+أصلية و جيبنا مثال على الوصل الزائدة اضرب و على
+
+357
+00:31:59,060 --> 00:32:04,820
+القطع الأصلية اللي هي أكرمة و أحسنة اكتر لك فرق
+
+358
+00:32:04,820 --> 00:32:07,200
+آخر اه فضلي
+
+359
+00:32:15,880 --> 00:32:21,820
+أحسنتى همزة الوصل لأخوات تثبت عند الإبتداء بيها و
+
+360
+00:32:21,820 --> 00:32:25,840
+تسقط إذا وصلت بما قبلها كما أخدناها أما همزة القطع
+
+361
+00:32:25,840 --> 00:32:31,100
+تثبت عند الإبتداء بيها و عند وصلها كذلك بتثبت في
+
+362
+00:32:31,100 --> 00:32:37,120
+حالة الوصل و في حالة القطع أيضا بتثبت همزة القطع
+
+363
+00:32:38,370 --> 00:32:42,370
+الان في عندنا حالات همزة الوصل ان شاء الله هنخلطها
+
+364
+00:32:42,370 --> 00:32:45,730
+بإذن الله عزوجل في المحاضرة الماضية هنعيد الكلمتين
+
+365
+00:32:45,730 --> 00:32:49,690
+اللي ذكرناهم ثم نستنف بعد ذلك همزة الوصل بإذن الله
+
+366
+00:32:49,690 --> 00:32:53,250
+عزوجل نكتفي بهذا القدر و نكمل ان شاء الله في
+
+367
+00:32:53,250 --> 00:32:55,590
+اللقاء القادم بارك الله فيكم والسلام عليكم
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/K9YX36Ie-xk.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/K9YX36Ie-xk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f8ca7856349df5a3b7bce8b4a33416f5b33ab812
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/K9YX36Ie-xk.srt
@@ -0,0 +1,1575 @@
+1
+00:00:11,700 --> 00:00:14,480
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,480 --> 00:00:18,480
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:18,480 --> 00:00:22,940
+آله وصحبه ونسلم اليوم إن شاء الله موضوعنا عن أحكام
+
+4
+00:00:22,940 --> 00:00:27,840
+النون الساكنة والتنوين طبعا للنون الساكنة والتنوين 
+
+5
+00:00:27,840 --> 00:00:32,550
+أربعة أحكام لكن نريد أن نتعرف على أحكام النون
+
+6
+00:00:32,550 --> 00:00:36,410
+الساكنة والتنوين ونتعرف على معنى النون الساكنة أو
+
+7
+00:00:36,410 --> 00:00:40,050
+نعرف النون الساكنة ونعرف التنوين من يعرف لنا النون 
+
+8
+00:00:40,050 --> 00:00:42,030
+الساكنة؟ ما هي النون الساكنة؟
+
+9
+00:00:47,160 --> 00:00:51,680
+صحيح يبقى النون الساكنة هي نون خالية من الحركة تثبت 
+
+10
+00:00:51,680 --> 00:00:56,880
+لفظا وخطا واصلا ووقفا وتوجد في الأسماء والأفعال
+
+11
+00:00:56,880 --> 00:01:03,380
+والحروف في الأسماء نحو منذر منذر نون وراها حرف الذال
+
+12
+00:01:03,380 --> 00:01:11,420
+وفي الأفعال مثل ينذر ينذرنون وراها حرف الذال وفي
+
+13
+00:01:11,420 --> 00:01:18,360
+الحروف مثل من فعل نون ساكنة وراها حرف الألف وبهذا
+
+14
+00:01:18,360 --> 00:01:23,940
+التعريف للنون الساكنة يخرج منها مثل كلمة يمنون
+
+15
+00:01:23,940 --> 00:01:29,980
+يمنون أول شيء النون المشددة تخرج من النون الساكنة
+
+16
+00:01:29,980 --> 00:01:35,430
+وكذلك النون المتحركة يمنون كذلك النون المتحركة 
+
+17
+00:01:35,430 --> 00:01:39,370
+تخرج فلا تعدّ من النون الساكنة لأن أحكامنا هي
+
+18
+00:01:39,370 --> 00:01:44,590
+أحكام النون الساكنة والتنوين كذلك يخرج من النون
+
+19
+00:01:44,590 --> 00:01:49,410
+الساكنة النون التي زال سكونها فتحركت تخلصا من 
+
+20
+00:01:49,410 --> 00:01:54,690
+التقاء الساكنين يعني لو في عندنا كلمة آخرها نون
+
+21
+00:01:54,690 --> 00:01:59,170
+ساكنة وبعدها الكلمة التي تليها أيضا نون ساكنة
+
+22
+00:01:59,170 --> 00:02:04,400
+نتخلص من التقاء الساكنين أما بكانة بالحدث لو كان
+
+23
+00:02:04,400 --> 00:02:10,340
+الساكن الأول حرف مد أو نتخلص منه بالتخفيف سواء كان
+
+24
+00:02:10,340 --> 00:02:15,200
+بالكسرة أو بالفتحة أو بالضم هنا مثلا في قول تعالى 
+
+25
+00:02:15,200 --> 00:02:20,540
+إن ارتبتم طبعا لا نقرأها إن ارتبتم لأنها بتكون 
+
+26
+00:02:20,540 --> 00:02:26,260
+ثقيلة على اللسان كيف نقرأها إن ارتبتم؟ كيف نقرأها؟
+
+27
+00:02:26,260 --> 00:02:31,190
+إن ارتبتم إن ارتبتم النون وراها حرف الراء
+
+28
+00:02:31,190 --> 00:02:35,950
+نقول إن ارتبتم لأنه الراء ساكنة إن ارتبتم الراء 
+
+29
+00:02:35,950 --> 00:02:40,450
+ساكنة والنون تاعت إن برضه ساكنة يعني ثقيلة على 
+
+30
+00:02:40,450 --> 00:02:44,010
+اللسان أن نقول إن ارتبتم فبنتخلص من التقاء
+
+31
+00:02:44,010 --> 00:02:49,870
+الساكنين بالتحريك بالكسر فنقول إن ارتبتم كذلك من
+
+32
+00:02:49,870 --> 00:02:55,170
+المؤمنين أصلا من المؤمنين ثقيلة على اللسان من
+
+33
+00:02:55,170 --> 00:03:01,440
+ساكنة والآن في المؤمنين برضه ساكنة نتخلص من التقاء 
+
+34
+00:03:01,440 --> 00:03:05,920
+الساكنين بالتحريك لكن هنا بنحركها بالفتحة من
+
+35
+00:03:05,920 --> 00:03:11,900
+المؤمنين لأنه إنه من الجارة لو جاء بعدها حرف ساكن
+
+36
+00:03:11,900 --> 00:03:18,180
+نتخلص من التقاء الساكنين بالفتحة هذا بالنسبة لتعريف 
+
+37
+00:03:18,180 --> 00:03:22,480
+النون الساكنة في عندنا كذلك إحنا أحكامنا النون
+
+38
+00:03:22,480 --> 00:03:26,260
+الساكنة والتعريف عرفنا النون الساكنة هي نون خالية
+
+39
+00:03:26,260 --> 00:03:30,920
+من الحركة تلعق الأسماء والأفعال والحروف ومثل
+
+40
+00:03:30,920 --> 00:03:37,640
+ينذر، منذر أو من.. من أنظر مثلا أما بالنسبة 
+
+41
+00:03:37,640 --> 00:03:40,300
+للتنوين فمن يعرف لنا التنوين؟ فضلي
+
+42
+00:03:49,850 --> 00:03:54,310
+النون ال.. التي أنا بقول عنها الت.. التنوين هي 
+
+43
+00:03:54,310 --> 00:03:58,790
+نون لكنها إيش؟ زائدة، نون ساكنة زائدة عن بنية 
+
+44
+00:03:58,790 --> 00:04:04,890
+الحركة تلحق آخر الأسماء تثبت لفظا لا خطا واصلا لا
+
+45
+00:04:04,890 --> 00:04:09,530
+وقفا يعني تثبت لفظة نقول سميعن، لكننا لا نكتبها 
+
+46
+00:04:09,530 --> 00:04:16,890
+بالنون، نقول سميعن تثبت لفظا لا خطا، وصلة لا وقفة، لأن 
+
+47
+00:04:16,890 --> 00:04:21,330
+كلمة سميعن لو وقفنا عليها، لا نقف عليها بقولنا 
+
+48
+00:04:21,330 --> 00:04:26,130
+سميعن، بل نقف عليها بقولنا إيه؟ سمية، إذا التنوين 
+
+49
+00:04:26,130 --> 00:04:31,180
+هو نون ساكنة زائدة عن بنية الحركة تلحق آخر الأسماء 
+
+50
+00:04:31,180 --> 00:04:36,280
+تثبت لفظا لا خطا واصلا لا وقفا والأمثلة على ذلك 
+
+51
+00:04:36,280 --> 00:04:41,140
+كثيرة ومتعددة من هذه الأمثلة من جدّكوا المثال تفضلي
+
+52
+00:05:03,830 --> 00:05:09,010
+النون الساكنة يا أخوات تلحق الأسماء والأفعال
+
+53
+00:05:09,010 --> 00:05:15,380
+والحروف الأسماء مثل مُنذِر والأفعال مثل يُنذِرو
+
+54
+00:05:15,380 --> 00:05:20,340
+الحروف مثل من فعله.. من فعله أو من فعله لكن 
+
+55
+00:05:20,340 --> 00:05:25,460
+بالنسبة لل.. لل.. للتنوين فهي لا تكون إلا في
+
+56
+00:05:25,460 --> 00:05:30,160
+.. في الأسماء أو آخر الأسماء فقط الفرق الثالث يا 
+
+57
+00:05:30,160 --> 00:05:36,900
+أخوات.. فضلي النون
+
+58
+00:05:36,900 --> 00:05:44,870
+الساكنة تكون متوسطة مثل منذر ومتطرفة مثل من لكن 
+
+59
+00:05:44,870 --> 00:05:49,570
+التنوين لا يقع إلا متطرفا، يعني نحن لا نجد أن هناك 
+
+60
+00:05:49,570 --> 00:05:54,630
+تنوين ضم ولا تنوين فتح ولا تنوين كسر في أول الكلمة
+
+61
+00:05:54,630 --> 00:05:58,630
+ولا في منتصفها، إذا أنه التنوين لا يكون إلا في 
+
+62
+00:05:58,630 --> 00:06:03,930
+نهاية الكلمة أو في نهاية الأسماء طبعا هناك عندنا 
+
+63
+00:06:03,930 --> 00:06:09,150
+ملاحظة أو ملاحظات متعددة الملاحظة الأولى أن النون
+
+64
+00:06:09,150 --> 00:06:14,090
+الساكنة رسمت في بعض الكلمات على صورة التنوين يعني
+
+65
+00:06:14,090 --> 00:06:18,850
+حسب الرسم العثماني الذي رسم القرآن به في عهد عثمان 
+
+66
+00:06:18,850 --> 00:06:23,370
+بن عفان يعني رسم رسما بحيث يحتمل أوجه الاختلاف في
+
+67
+00:06:23,370 --> 00:06:27,070
+الحروف الأخرى أو في القراءات الأخرى فمثلا بعض
+
+68
+00:06:27,070 --> 00:06:31,910
+الكلمات رسمت النون على صورة التنوين وبتأخذ نفس حكم 
+
+69
+00:06:31,910 --> 00:06:39,340
+التنوين مثال ذلك في قوله تعالى أو كلمة وليكون في
+
+70
+00:06:39,340 --> 00:06:48,320
+قوله تعالى ليسجنن وليكون من الصاغرين ولا يكونن أصلا 
+
+71
+00:06:48,320 --> 00:06:52,360
+هي نون التوكيد الخفيفة ولا يكونن نون التوكيد
+
+72
+00:06:52,360 --> 00:06:58,660
+الخفيفة لكنها رسمت رسما في القرآن بالتنوين فتقرأ 
+
+73
+00:06:58,660 --> 00:07:02,260
+نفس تأخذ نفس حكم التنوين يعني الله سبحانه وتعالى
+
+74
+00:07:02,260 --> 00:07:09,520
+يقول ولا يسجنن ولا يكون من الصاغرين في سورة يوسف
+
+75
+00:07:09,520 --> 00:07:16,720
+آية 32 كذلك كلمة لنسفعن من قول تعالى كلا لإن لم 
+
+76
+00:07:16,720 --> 00:07:24,280
+ينتهي لناسفعن بالناصية لناسفعن بالناصية لناسفعن 
+
+77
+00:07:24,280 --> 00:07:28,760
+هي أصلا يعني نون والنون هي نون التوكيد الخفيفة لكن 
+
+78
+00:07:30,120 --> 00:07:35,040
+رسمت في الرسم العثماني بالتنوين فودأخذ نفس حكم
+
+79
+00:07:35,040 --> 00:07:42,060
+التنوين الذي هو نون عادي لنسفعن بالناصية كذلك كلمة
+
+80
+00:07:42,060 --> 00:07:45,060
+إذن وهذه هي الكلمات الثلاث الوحيدة يعني ليست 
+
+81
+00:07:45,060 --> 00:07:51,960
+قاعدة في القرآن وإنما هي في ثلاث كلمات وليكونن لناسفعن 
+
+82
+00:07:51,960 --> 00:07:58,710
+وكذلك إذن إذن في قول تعالى وإذا لاتخذوك خليلا وإذا
+
+83
+00:07:58,710 --> 00:08:03,810
+لاتخذوك هي أصلا إذا بالنون لكنها رسمت في الرسم
+
+84
+00:08:03,810 --> 00:08:08,870
+العثماني وإذا بالتنوين وهذا يعني بعض الكلمات اللي
+
+85
+00:08:08,870 --> 00:08:13,910
+موجودة في القرآن رسمت النون ليس على أصلها وإنما
+
+86
+00:08:13,910 --> 00:08:20,500
+رسمت على صورة التنوين وبتاخد نفس حكم التنوين كما أن 
+
+87
+00:08:20,500 --> 00:08:24,520
+النون رسمت على صوت التنوين وهذا حالة شاذة ولكل
+
+88
+00:08:24,520 --> 00:08:29,940
+قاعدة شواذ، كذلك يا أخوات التنوين نفسه رسمة في وضع
+
+89
+00:08:29,940 --> 00:08:37,520
+معين على شكل النون مثلا في قوله تعالى وكأي من نبي
+
+90
+00:08:37,520 --> 00:08:45,010
+قاتل معه ربيون كثير وكأين هي أصلا وكأي وعليها 
+
+91
+00:08:45,010 --> 00:08:51,270
+شدة وتنوين كثير وكأين لكنها في المصحف ترسم وكأين 
+
+92
+00:08:51,270 --> 00:08:56,630
+بالنون وهذا طبعا خلاف القاعدة ولكن حتى نقول بأن في
+
+93
+00:08:56,630 --> 00:09:00,850
+الرسم العثماني هناك النون رسمت على صورة التنوين في
+
+94
+00:09:00,850 --> 00:09:07,660
+ثلاث كلمات وهي وليكونن لناسفعن وإذن ورسمها التنوين
+
+95
+00:09:07,660 --> 00:09:13,740
+على صورة نون في كما في قوله وكأيم من نبيين طيب هذه 
+
+96
+00:09:13,740 --> 00:09:18,020
+الأحكام تكون تعريف للنون الساكنة والتنوين لكن 
+
+97
+00:09:18,020 --> 00:09:21,780
+للنون الساكنة والتنوين أربعة أحكام ما هي هذه
+
+98
+00:09:21,780 --> 00:09:25,760
+الأحكام الأربعة يا أخوات؟ فضل أخت الإظهار الإقلاب
+
+99
+00:09:25,760 --> 00:09:29,360
+الإضغام الإخفاء أحسن عندنا يا أخوات الإظهار 
+
+100
+00:09:29,360 --> 00:09:36,210
+الإضغام الإقلاب والإخفاء أربعة أحكام هذه الأربعة 
+
+101
+00:09:36,210 --> 00:09:40,010
+أحكام تتقاسم حروف اللغة العربية يعني حروف اللغة
+
+102
+00:09:40,010 --> 00:09:45,030
+العربية 28 حرف تنتسم على الأحكام هذه حروف الإظهار
+
+103
+00:09:45,030 --> 00:09:50,290
+حروف الإضغام حروف الإقلاب وحروف الإخفاء أما بالنسبة 
+
+104
+00:09:50,290 --> 00:09:55,690
+للحكم الأول وهو الإظهار طبعا هذه الأحكام الإظهار و
+
+105
+00:09:55,690 --> 00:10:01,370
+الإضغام والإقلاب والإخفاء الحروف التي تتبع هذه
+
+106
+00:10:01,370 --> 00:10:06,450
+الأحكام هي التي تحكم على النون الساكنة بالإظهار أو 
+
+107
+00:10:06,450 --> 00:10:10,570
+تحكم عليها بالإضغام أو الإقلاب أو الإخفاء الحكم
+
+108
+00:10:10,570 --> 00:10:14,410
+الأول من هذه الأحكام يا أخوات هو الإظهار ما معنى
+
+109
+00:10:14,410 --> 00:10:19,850
+الإظهار في اللغة أظهرت الشيء بمعنى إيه؟ أظهرت 
+
+110
+00:10:19,850 --> 00:10:24,770
+الشيء بمعنى بينته وأظهرته ووضّحته، إذا الإظهار
+
+111
+00:10:24,770 --> 00:10:29,550
+لغة يأتي بمعنى البيان والوضوح والإظهار في
+
+112
+00:10:29,550 --> 00:10:35,210
+الاصطلاح هو إخراج الحرف المظهر من مخرجه من غير غنة 
+
+113
+00:10:35,210 --> 00:10:39,910
+ظاهرة عليه إذا إظهار أو إخراج الحرف المظهر من مخرجه
+
+114
+00:10:39,910 --> 00:10:45,090
+من غير غنة ظاهرة فيه يعني بمعنى إن النون الساكنة 
+
+115
+00:10:45,090 --> 00:10:50,090
+لو جاء بعدها أي حرف من حروف الإظهار المجموعة في
+
+116
+00:10:50,090 --> 00:10:56,290
+قوله إيه؟ أول حرف من هذا البيت أخي هكى علما حازه 
+
+117
+00:10:56,290 --> 00:11:02,130
+غير خاسني اللي هي نفسها همزة فهاء ثم عين حاء 
+
+118
+00:11:02,130 --> 00:11:07,740
+مهملتان ثم غين خاء يعني الهمزة والهاء والعين 
+
+119
+00:11:07,740 --> 00:11:12,480
+والحاء والغين والخاء هذه أخوات هي حروف الإظهار وهي 
+
+120
+00:11:12,480 --> 00:11:16,760
+الحروف التي تحكم على النون الساكنة بالإظهار إذا 
+
+121
+00:11:16,760 --> 00:11:19,500
+جاء بعد النون الساكنة أو التنوين يعني إذا جاء
+
+122
+00:11:19,500 --> 00:11:23,220
+النون الساكنة أو حتى التنوين وجاء بعدها أي حرف من 
+
+123
+00:11:23,220 --> 00:11:27,040
+هذه الحروف الحرف نفسه يحكم على النون الساكنة 
+
+124
+00:11:27,040 --> 00:11:35,900
+بالإظهار فنقول منه مثلا أو ين أون اسميع عليم حسب
+
+125
+00:11:35,900 --> 00:11:41,660
+الحرف اللي هي للنون هو اللي يحكم عليها بالإظهار و
+
+126
+00:11:41,660 --> 00:11:48,630
+كما قلنا أن أول حرف من هذا البيت أخي حرف الهمزة هكى
+
+127
+00:11:48,630 --> 00:11:53,790
+حرف الهاء علما حرف العين حازه غيره خاسر أول حرف من 
+
+128
+00:11:53,790 --> 00:11:57,610
+كل كلمة وهذه الحروف الستة يا أخوات حسب مخرجها من 
+
+129
+00:11:57,610 --> 00:12:01,170
+الحلق يعني لماذا أسمي الإظهار الحلقي بالإظهار
+
+130
+00:12:01,170 --> 00:12:05,310
+الحلقي؟ لأنه يخرجوا من الحلق يعني في عندنا حرفان 
+
+131
+00:12:05,310 --> 00:12:11,050
+يخرجان من أقصى الحلق اللي هي الهمزة والهاء ويليه وسط 
+
+132
+00:12:11,050 --> 00:12:18,580
+الحلق حرفان العين والحاء ثم الغين والخاء لذلك نقول ثم 
+
+133
+00:12:18,580 --> 00:12:23,960
+عين حاء مهملتان ثاني ما معناه يا أخوات مهملتان يعني
+
+134
+00:12:23,960 --> 00:12:29,960
+غير معجمات يعني ما فيش عليها نقط لأن الحاء والعين لو 
+
+135
+00:12:29,960 --> 00:12:34,320
+وضع على الحاء نقطة أسفل بصير جيم لو وضع نقطة أعلى
+
+136
+00:12:34,320 --> 00:12:40,970
+بصير خاء كذلك العين لو وضع علي فوقها نقطة تصبح غين
+
+137
+00:12:40,970 --> 00:12:45,450
+لذلك نقول همزة فهاء وقلنا همزة فهاء يعني الهمزة 
+
+138
+00:12:45,450 --> 00:12:51,270
+والهاء مباشرة وراها تأتي من مخرج أقصى الحلق ثم عين
+
+139
+00:12:51,270 --> 00:12:56,190
+حاء كلمة ثم يفيد التراخي يعني ثم بعد ذلك
+
+140
+00:12:56,190 --> 00:13:00,270
+المرتبة الثانية عين حاء وهو وسط الحلق بيخرج
+
+141
+00:13:00,270 --> 00:13:06,370
+منه العين والحاء وهم المهملتان ثم غين الخاء يعني
+
+142
+00:13:06,370 --> 00:13:10,410
+المرتبة الثالثة في عندنا الغين والخاء وكأن في 
+
+143
+00:13:10,410 --> 00:13:15,050
+الحلق في سلم أو ثلاث درجات أقصى الحلق وسط الحلق
+
+144
+00:13:15,050 --> 00:13:19,750
+أدنى الحلق لذلك إذا جاء أي حرف من هذه الحروف بعد 
+
+145
+00:13:19,750 --> 00:13:24,570
+النون الساكنة أو التنوين بنسميه إظهار حلقي وسمينا
+
+146
+00:13:24,570 --> 00:13:30,140
+إظهار عشان يظهر، يحكم على النون بالإظهار، من هو
+
+147
+00:13:30,140 --> 00:13:33,620
+الذي يظهر يا أخوك؟ هل هي النون ولا الحرف؟ الحرف
+
+148
+00:13:33,620 --> 00:13:39,950
+الإظهار؟ النون، من الذي يحكم على النون بالإظهار اللي 
+
+149
+00:13:39,950 --> 00:13:43,790
+هو حروف الإظهار، يبقى عندما نقول إظهار حلقي يعني 
+
+150
+00:13:43,790 --> 00:13:46,830
+حروف الإظهار الحلقي اللي هي الهمزة و الهاء و العين
+
+151
+00:13:46,830 --> 00:13:50,370
+والحاء والغين والخاء، أي حرف جاء بعد النون الساكنة
+
+152
+00:13:50,370 --> 00:13:53,690
+أو التنوين بيحكم على النون الساكنة أو التنوين
+
+153
+00:13:53,690 --> 00:13:58,350
+بالإظهار، والأمثلة على ذلك متعددة، مثال ذلك مثلا 
+
+154
+00:13:58,350 --> 00:14:07,600
+وانحر، أين الإظهار؟ هي عندنا النون، وانحر النون ساكنة
+
+155
+00:14:07,600 --> 00:14:13,720
+وراها في عندنا الحاء، فنقول وانحر، الحاء من حروف
+
+156
+00:14:13,720 --> 00:14:18,360
+الإظهار، بيحكم على النون الساكنة بالإظهار، كذلك ممكن 
+
+157
+00:14:18,360 --> 00:14:22,600
+يقع في كلمتين، لأن الإظهار يقع في كلمة أو في كلمتين
+
+158
+00:14:22,600 --> 00:14:28,160
+سواء كان يعني نون ساكنة أو حتى تنوين، لكن التنوين
+
+159
+00:14:28,160 --> 00:14:31,140
+لا يقع إلا في كلمتين، لأن التنوين لا يكون إلا في 
+
+160
+00:14:31,140 --> 00:14:35,580
+نهاية الأسماء، يعني كلمة وانحر، نون ساكنة وراها حرف 
+
+161
+00:14:35,580 --> 00:14:42,580
+الحاء، نضمها، لا نقول وحّر ولا نقفيها نقول وانحر 
+
+162
+00:14:42,580 --> 00:14:47,640
+ولا يعني نقلبها، نقلبها النون، لا تقلب وإنما نقول
+
+163
+00:14:47,640 --> 00:14:54,060
+وانحر، يخرج حرف النون من مخرجه بغير غنة، لأن معنى 
+
+164
+00:14:54,060 --> 00:14:59,560
+الإظهار هو إخراج الحرف المظهر من مخرجه بغير غنة
+
+165
+00:14:59,560 --> 00:15:05,400
+طيب كذلك لو كان في كلمتين مثل من عمل، من عاملة صالحا 
+
+166
+00:15:05,400 --> 00:15:10,780
+لنفسها، من عاملة، الآن نقول من لا نضمها ولا نقفيها 
+
+167
+00:15:10,780 --> 00:15:16,920
+ولا نقلبها نقول من عاملة، ما الذي يحكم على... أو ما 
+
+168
+00:15:16,920 --> 00:15:19,620
+هو الحرف الذي يحكم على النون الساكنة اللي هو 
+
+169
+00:15:19,620 --> 00:15:23,220
+الحرف الذي يليه وهو حرف العين، وممكن يا أخوات
+
+170
+00:15:23,220 --> 00:15:29,680
+يكون في التنوين أيضا، مثال ذلك سميعا عليما أو سميع
+
+171
+00:15:29,680 --> 00:15:34,800
+عليم في آية أخرى سميعا عليما هي تنوين جاء وراها 
+
+172
+00:15:34,800 --> 00:15:39,440
+حرف العين، وحرف العين من حروف الإظهار، بيحكم على 
+
+173
+00:15:39,440 --> 00:15:44,720
+التنوين بالإظهار، لو سألنا سؤال يا إخوان، ما هو سبب 
+
+174
+00:15:44,720 --> 00:15:49,420
+الإظهار؟ يعني لماذا تظهر النون فيها مع هذه الحروف 
+
+175
+00:15:49,420 --> 00:15:53,960
+بالذات؟ أه، تفضلي، بسبب فوضى مخرج النون عند مخرج 
+
+176
+00:15:53,960 --> 00:15:56,480
+حروف الإظهار ورأينا النون تخلط من طرف اللسان بتاع
+
+177
+00:15:56,480 --> 00:16:02,850
+مع.. يعني صرف الإظهار هو التباعد ما بين مخرج حرف
+
+178
+00:16:02,850 --> 00:16:07,230
+النون مع مخرج حرف الـ.. الحروف الإظهار، حروف
+
+179
+00:16:07,230 --> 00:16:10,090
+الإظهار، قولنا من أي مكان تخرج من الإظهار.. من..
+
+180
+00:16:10,090 --> 00:16:14,590
+اللي هي الفم اللي هو من الحلق، لكن حرف النون يخرجه
+
+181
+00:16:14,590 --> 00:16:18,730
+من طرف اللسان مع ما يليه من لثة الثنايا العليا ها
+
+182
+00:16:18,730 --> 00:16:23,460
+نقول ان.. ان.. اللي بيبقى طرف اللسان بينما الـ
+
+183
+00:16:23,460 --> 00:16:27,460
+من أقصى الحلق 
+
+184
+00:16:27,460 --> 00:16:31,880
+فيوجد تباعد، لأنه يوجد تباعد ما بين حروف الإظهار 
+
+185
+00:16:31,880 --> 00:16:36,020
+والنون، بيحكم حروف الإظهار، تحكم على النون الساكنة 
+
+186
+00:16:36,020 --> 00:16:41,100
+بالإظهار، وهذا هو سبب الإظهار، عندنا العديد يا أخوات
+
+187
+00:16:41,100 --> 00:16:45,560
+من الأمثلة على حرف الهمزة مثلا، من يأتي بأمثلة على 
+
+188
+00:16:45,560 --> 00:16:53,490
+حرف الهمزة فيها إظهار، مع حرف الهاء في، ما في كلمة 
+
+189
+00:16:53,490 --> 00:16:59,770
+واحدة، ينهونا، ينهونا، ينهونا مع التنوين؟ وفي كلمة 
+
+190
+00:16:59,770 --> 00:17:06,290
+مع التنوين، رسول أمين، رسول أمين، رسول أمين، طيب مع
+
+191
+00:17:06,290 --> 00:17:13,970
+حرف الهاء أو الهاء من هي تبقى مثلها؟ فضلي ينهونا، ين
+
+192
+00:17:13,970 --> 00:17:20,310
+حرف الهاء يعني النون وراها ينهونا.. ينهونا، أما
+
+193
+00:17:20,310 --> 00:17:27,210
+بالنسبة للتنوين مثلا فريقا هدا.. فريقا هدا، حرف 
+
+194
+00:17:27,210 --> 00:17:34,170
+العين.. فضلي أختك، ورا أنعمت.. أنعمت النون ساكنة
+
+195
+00:17:34,170 --> 00:17:37,090
+وراها حرف العين مع فكرة متين 
+
+196
+00:17:40,020 --> 00:17:45,860
+من عمل أو تنوين سميع عليم، لأن التنوين بياخد نفس 
+
+197
+00:17:45,860 --> 00:17:53,740
+حكم النون الساكنة، حرف الحاء ينهونا، ينهونا، بنظهر 
+
+198
+00:17:53,740 --> 00:18:01,990
+النون، من حسنة، من حسنة، أظهرنا النون وكذلك مثلا عليم
+
+199
+00:18:01,990 --> 00:18:09,230
+حكيم، عليم حكيم، أظهرنا التنوين لأنه جاء وراها حرف 
+
+200
+00:18:09,230 --> 00:18:15,190
+الحاء، وكذلك في باقي الحروف مثلا فسينغضون، فسينغضون
+
+201
+00:18:15,190 --> 00:18:23,950
+إليك أو من غل أو رب غفور، رب غفور، كذلك حرف الخاء والمن
+
+202
+00:18:23,950 --> 00:18:30,330
+خانقة والمن خانقة، النون ورا حرف الخاء أو في قوله من
+
+203
+00:18:30,330 --> 00:18:37,250
+خلاف، من خلاف، كذلك علي من خبير، إذا أي حرف من حروف
+
+204
+00:18:37,250 --> 00:18:41,450
+الإظهار جاء بعد النون الساكنة أو التنوين بيحكم على 
+
+205
+00:18:41,450 --> 00:18:46,030
+النون الساكنة أو التنوين بالإظهار، وهذا هو حكم 
+
+206
+00:18:46,030 --> 00:18:48,450
+الإظهار
+
+207
+00:18:52,220 --> 00:18:56,080
+الحكم الثاني يا أخوات من أحكام النون الساكنة هو
+
+208
+00:18:56,080 --> 00:19:01,780
+التنوين هو الإضغام، الإضغام يعني لغة من حيث اللغة 
+
+209
+00:19:01,780 --> 00:19:06,140
+إدخال الشيء بالشيء، كادخال اليد في الجيب أدخلتها 
+
+210
+00:19:06,140 --> 00:19:11,380
+الشيء في الشيء يعني دمجته فيه، أدخلتها فيه، يسهر من
+
+211
+00:19:11,380 --> 00:19:16,560
+حيث اللغة وفي الاصطلاح معنى الإضغام فضل أختك، أدخل
+
+212
+00:19:16,560 --> 00:19:18,160
+حرف ساكن بحرف متحرك
+
+213
+00:19:20,860 --> 00:19:26,020
+أحسنتي، إذا من حيث الاصطلاح معنى الإضغام إدخال حرف
+
+214
+00:19:26,020 --> 00:19:32,060
+ساكن بحرف متحرك بحيث يصيران حرفا واحدا مشددة من 
+
+215
+00:19:32,060 --> 00:19:36,380
+جنس الثاني، يعني هي أصلا في علاقة ما بين التعريف
+
+216
+00:19:36,380 --> 00:19:41,040
+اللغوي والتعريف الاصطلاحي طبعا في لأنه من حيث 
+
+217
+00:19:41,040 --> 00:19:45,400
+اللغة إدخال الشيء بالشيء، وفي الاصطلاح يعني إدخال
+
+218
+00:19:45,400 --> 00:19:50,880
+حرف ساكن بحرف متحرك بحيث يصيران حرفا واحدا مشددة 
+
+219
+00:19:50,880 --> 00:19:55,720
+من جنس الثاني، هذا الإضغام ليس بمعنى أنه أي حرفين
+
+220
+00:19:55,720 --> 00:19:58,880
+يعني سواء كان إضغام متمثلين إضغام متقاربين إضغام
+
+221
+00:19:58,880 --> 00:20:04,880
+متجانسين أي إضغام شفوي هو إدخال حرف ساكن بحرف 
+
+222
+00:20:04,880 --> 00:20:09,340
+متحرك بحيث يصيران حرفا واحدا مشددة من جنس الثاني
+
+223
+00:20:09,610 --> 00:20:14,570
+لكن المراد هنا الإضغام اللي تابع لأحكام النون
+
+224
+00:20:14,570 --> 00:20:19,770
+ال ساكنة يعني إضغام بمعنى إدخال حرف النون الساكنة
+
+225
+00:20:19,770 --> 00:20:24,410
+بالحرف الذي يليه إن كان من حروف الإضغام اللي هي
+
+226
+00:20:24,410 --> 00:20:29,890
+مجموعة في قوله يرملون بحيث الحرفين يصيران كأنهم
+
+227
+00:20:29,890 --> 00:20:35,970
+حرفا واحدا مشددة، إذا ما هي حروف الإضغام التابعة
+
+228
+00:20:35,970 --> 00:20:39,150
+لأحكام النون الساكنة والتنوين؟ من على الفضل أختك؟
+
+229
+00:20:39,800 --> 00:20:44,820
+مجموعة في قوله يرملون، الياء والراء والميم واللام 
+
+230
+00:20:44,820 --> 00:20:49,340
+والواو والنون، كم حرف هذه الكلمة؟ ستة حروف، مجموعة 
+
+231
+00:20:49,340 --> 00:20:55,300
+في قوله يرملون، لكن هذه الكلمة يرملون هي بتجمع حروف 
+
+232
+00:20:55,300 --> 00:21:00,520
+الإضغام اللي بتنقسم إلى قسمين، إضغام بغنة وإضغام 
+
+233
+00:21:00,520 --> 00:21:05,430
+بغير غنة، الإضغام اللي بقولنا يا أخوات، ماكنت جزء من
+
+234
+00:21:05,430 --> 00:21:10,790
+حروف يرملون وهو مجموعة في قوله ينمو، يأي حرف من
+
+235
+00:21:10,790 --> 00:21:16,350
+حروف ينمو ياء نون ميم واو، طبعا العلماء يعني بيجمعوا
+
+236
+00:21:16,350 --> 00:21:21,330
+الحروف في كلمة ولا في كلمتين ولا في بيت شعر على 
+
+237
+00:21:21,330 --> 00:21:25,990
+حسب أنه يسهل حفظها، لأنه لو ترك المجال للتذكر 
+
+238
+00:21:25,990 --> 00:21:31,470
+ممكن واحد يعني يخطئ فيقول حروف الإضغام شيل واو واش 
+
+239
+00:21:31,470 --> 00:21:37,440
+كمان ولام وراء وعين حتى لا يصبح يعني مترددا يقول
+
+240
+00:21:37,440 --> 00:21:42,180
+يرملون، ينموا أو مثلا أخي هكذا علمان حازة وغيره خاسر
+
+241
+00:21:42,180 --> 00:21:47,500
+يعني حاسس أنه تسهيل حفظ هذه الكلمات والعلماء بدلوا
+
+242
+00:21:47,500 --> 00:21:51,500
+مجهود يعني حتى يعني يسهلوا ويوسروا لنا أحكام
+
+243
+00:21:51,500 --> 00:21:55,540
+التجويد، إذا حروف الإضغام مجموعة في قوله يرملون
+
+244
+00:21:56,130 --> 00:22:00,610
+والإضغام ينقسم إلى قسمين إضغام بغنة وإضغام بغير
+
+245
+00:22:00,610 --> 00:22:05,170
+غنة، الإضغام اللي بغنة حروفه ينمو، والإضغام اللي 
+
+246
+00:22:05,170 --> 00:22:10,030
+بغير غنة باقي حروف يرملون وهو اللام والراء و
+
+247
+00:22:10,030 --> 00:22:15,030
+الميم، معنى الغنة ما معنى إضغام بغنة؟ ما معنى الغنة؟ آه
+
+248
+00:22:15,030 --> 00:22:15,530
+فضل أخت
+
+249
+00:22:19,320 --> 00:22:24,060
+هو صوت أغنية مركب في جسمي الميم والنون ولو
+
+250
+00:22:24,060 --> 00:22:28,480
+تنوينا يخرج من الخيشوم مقدار حركة وحركتين، عندما نقول 
+
+251
+00:22:28,480 --> 00:22:36,020
+أن من، أين يخرج الصوت هذا اللي هي الغنة يخرج من
+
+252
+00:22:36,020 --> 00:22:39,600
+الخيشوم، ما معنى الخيشوم اللي هو الأنف، أهل الأنف
+
+253
+00:22:39,600 --> 00:22:44,480
+يعني بحيث الواحد لو أغلق أنفه، لو أغلق أنفه وقال
+
+254
+00:22:44,480 --> 00:22:51,590
+أن، أن، يصبح منخنق، لا يستطيع أن يخرج حرف نون، إذا حتى لو
+
+255
+00:22:51,590 --> 00:22:57,730
+كان واحد يعني مذكر، واحد مرشح يعني لا تخرج معه 
+
+256
+00:22:57,730 --> 00:23:04,550
+الغنة بسهولة، لذلك نقول يخرج
+
+257
+00:23:04,550 --> 00:23:11,230
+الصوت من الخشوم أو برضه بيخرج الصوت من الخشوم إذا 
+
+258
+00:23:11,230 --> 00:23:16,740
+معنى الغنة يا أخوات هو صوت أغنية مركب في جسمه
+
+259
+00:23:16,740 --> 00:23:21,680
+حرفي الميم والنون ولو تنوينه، ما معنى ولو تنوينه
+
+260
+00:23:21,680 --> 00:23:27,420
+يعني النون ولو تنوينه يعني التنوين، التنوين يخرج 
+
+261
+00:23:27,420 --> 00:23:32,340
+من الخشوم مقداره حركتين، مقدار الحركتين أو الحركة
+
+262
+00:23:32,340 --> 00:23:36,800
+الواحدة قدّره العلماء بشيء موجود في جسم الإنسان
+
+263
+00:23:36,800 --> 00:23:42,280
+بمقدار قبضة الأصبع أو بصته، حركتين يعني حركة حركتين
+
+264
+00:23:42,560 --> 00:23:47,800
+أو بمقدار عندما يقول واحد مثلا رقم مكون من رقمين
+
+265
+00:23:47,800 --> 00:23:52,840
+يعني واحد وعشرين اثنين وعشرين ثلاثة وعشرين أربعة 
+
+266
+00:23:52,840 --> 00:23:58,200
+وعشرين مثلا، رقمين، خمسة وعشرين، ستة وعشرين أو
+
+267
+00:23:58,200 --> 00:24:02,320
+بمقدار قبضة الأصبع أو بصره أو مثلا الحركتين نفسها
+
+268
+00:24:02,320 --> 00:24:06,660
+تعدل ثانية وهي عبارة عن وحدة زمنية يقدرها العقل 
+
+269
+00:24:06,660 --> 00:24:12,650
+يعني مثلا الإنسان مع التعود لو واحد مثلا أعطى الغنة
+
+270
+00:24:12,650 --> 00:24:17,630
+أكثر من حركتين، أعطيها أربع حركات يعني قال مثلا من
+
+271
+00:24:17,630 --> 00:24:23,890
+نعمة، بيقول غلط مباشرة، هذا خطأ، مش من نعمة، هي اصلا 
+
+272
+00:24:23,890 --> 00:24:28,570
+من نعمة بمقدار حركتين يعني بمقدار ايه، بمقدار 
+
+273
+00:24:28,570 --> 00:24:33,730
+ثانية، طيب كثير قوي يا أخوات الإضغام اللي نحن بصدد
+
+274
+00:24:33,730 --> 00:24:37,730
+الكلام عنه له شروط يعني يشترط في الإضغام أن يكون
+
+275
+00:24:37,730 --> 00:24:42,440
+في كلمتين، فإذا حصل ووقع الإضغام يعني حرف النون و
+
+276
+00:24:42,440 --> 00:24:46,280
+وراها حرف من حروف يرملون في كلمة واحدة لا يكونوا 
+
+277
+00:24:46,280 --> 00:24:51,100
+إضغاما بل يجب أن نظهره وله اسم نسميه الإظهار 
+
+278
+00:24:51,100 --> 00:24:57,020
+المطلق، ومن هنا نقول ما هو الإظهار المطلق؟ ما هو
+
+279
+00:24:57,020 --> 00:24:59,900
+الإظهار المطلق يا أخوات؟ الإظهار المطلق.. يا
+
+280
+00:24:59,900 --> 00:25:00,400
+أخوات فضليه 
+
+281
+00:25:07,240 --> 00:25:11,580
+صحيح إذا جاء بعد النون الساكنة حرف من حروف الإضغام
+
+282
+00:25:11,580 --> 00:25:17,420
+في كلمة واحدة لا يضغم حتى لا يعني يختلف بنية 
+
+283
+00:25:17,420 --> 00:25:21,580
+الكلمة فإذا اختلفت بنية الكلمة يعني يصبح خطأ مثلا
+
+284
+00:25:21,580 --> 00:25:27,710
+صن وانهذه النون ساكنة وراها جاءت حرف الواو صنوان
+
+285
+00:25:27,710 --> 00:25:34,150
+لو قلنا مثلا صوان صوان يعني أدغمنا النون بالواو 
+
+286
+00:25:34,150 --> 00:25:39,550
+بيختلف المعنى فالصنوان يختلف عن الصوان الصوان يعني
+
+287
+00:25:39,550 --> 00:25:44,330
+حجر أملس لكن الصنوان هي عبارة عن الشتلة شتلة
+
+288
+00:25:44,330 --> 00:25:50,600
+الشجرةيعني نجد الشجرة لها نحن نسميها الخنزير خنزير
+
+289
+00:25:50,600 --> 00:25:54,460
+يعني بيخرج لها شتلة صغيرة تنبت من الأرض تسمى صنوان
+
+290
+00:25:54,460 --> 00:26:00,600
+وبالتالي يختلف المعنى كذلك كلمة دنيا هينون وراها
+
+291
+00:26:00,600 --> 00:26:06,180
+يا لو طبقنا عليها قاعة الإدغار ماذا نقول دُيّا
+
+292
+00:26:06,180 --> 00:26:10,780
+دُيّا تختلف عن الدنيا ما معنى دُيّا لا معنى لها
+
+293
+00:26:10,780 --> 00:26:17,240
+لكنها دُنيامعنى الإظهار المطلق يا خوات هو إذا جاء
+
+294
+00:26:17,240 --> 00:26:21,940
+بعد حرف النون الساكنة طبعا بنفع نقوله التنوين لأن
+
+295
+00:26:21,940 --> 00:26:25,540
+التنوين لا يكون في المنتصف إذا جاء بعد نون الساكنة
+
+296
+00:26:25,540 --> 00:26:30,140
+حرف من حروف الإضغام في كلمة واحدة نسمي إظهار مطلق
+
+297
+00:26:30,140 --> 00:26:35,540
+ويجب أن نظهره و لا يجوز أن نضغمه لأننا لو أضغمناه
+
+298
+00:26:35,540 --> 00:26:41,360
+تختل بنية الكلمة وهذا بحمد الله لم يقع في القرآن 
+
+299
+00:26:41,360 --> 00:26:46,900
+إلا في كلمات محددة ما هي الكلمات التي فيها إظهار
+
+300
+00:26:46,900 --> 00:26:52,480
+مطلق؟ فضلي دنيا و كلمة صنوان و قنوان و بنيان أحسنتِ
+
+301
+00:26:52,480 --> 00:26:59,400
+دنيا صنوان قنوان بنيان لا يصح لنا أن نقول دو ..
+
+302
+00:26:59,400 --> 00:27:05,760
+دويا أو صنوان نقول صوان أو قنوان نقول قوان أو 
+
+303
+00:27:05,760 --> 00:27:12,540
+بنيان نقول بيان هذا خطأ بل نقول صن .. دنيا صنوان
+
+304
+00:27:12,540 --> 00:27:16,500
+لأن لو قلنا صوان بيختلف المعنى الصوان هو الحجر 
+
+305
+00:27:16,500 --> 00:27:23,100
+الأملس والصوان هو الحجر الأملس والصنوان هي عبارة
+
+306
+00:27:23,100 --> 00:27:26,760
+عن الشتلة اللي تخرج مع الأرض يعني ابنت الشجرة أو 
+
+307
+00:27:26,760 --> 00:27:32,360
+بنت الشجرة الصغيرة كذلك قنوان ما معنى قنوان؟ قنوان
+
+308
+00:27:32,360 --> 00:27:37,940
+التي تخرج القنو إذا شجرة البلح تخرج قنبلح يعني 
+
+309
+00:27:37,940 --> 00:27:42,760
+ثمرة البلح يسمى قنوان لكن لو قلنا قوان ما معنى
+
+310
+00:27:42,760 --> 00:27:47,900
+قوان ليس لها معنى إذا تختلف بنية الكلمة إذا إظهار
+
+311
+00:27:47,900 --> 00:27:52,040
+المطلق يعني ممكن يقع في كلمة وهي أربع كلمات في
+
+312
+00:27:52,040 --> 00:27:58,340
+القرآن دنيا سنوان قنوان بنيان وكذلك بعض العلماء 
+
+313
+00:27:58,340 --> 00:28:04,220
+قالوا أنه ممكن أن يقع في جملة وهي في أوائل الحروف
+
+314
+00:28:04,220 --> 00:28:09,060
+الهجائية مثال ذلك ياسين
+
+315
+00:28:09,060 --> 00:28:16,580
+والقرآن الحكيم لو وصلناها يعني لو قلنا ياسين
+
+316
+00:28:16,580 --> 00:28:20,420
+والقرآن الحكيم ما نفعلش نقول ياسيو والقرآن الحكيم
+
+317
+00:28:20,420 --> 00:28:28,900
+ولا حتى نقول نو القلم وما يسترون إنما نون
+
+318
+00:28:29,810 --> 00:28:37,190
+والقلم وما يسطرون يعني نظهرها ولو وصلناها معها
+
+319
+00:28:37,190 --> 00:28:41,880
+أيضا تظهر نون والقلم ولا نقول
+
+320
+00:28:41,880 --> 00:29:05,340
+نوووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووو
+
+321
+00:29:10,660 --> 00:29:16,280
+وإظهار مطلق في جملة نشوف الأمثلة على الإظهار
+
+322
+00:29:16,280 --> 00:29:22,780
+العادي الإظهار في حرف الياء والنون والميم والواو
+
+323
+00:29:22,780 --> 00:29:28,670
+منيئة بأمثلة على الإضغام الموجود في الياء فمن يعمل 
+
+324
+00:29:28,670 --> 00:29:34,570
+مثلا فمن يعمل كيف نقرأها؟ فما يعمل فما يعمل ماذا 
+
+325
+00:29:34,570 --> 00:29:40,030
+حصل نجد بأنه النون أضغمت في الياء ولو طبقني عليها
+
+326
+00:29:40,030 --> 00:29:44,190
+التعريف يعني أدخل حرف ساكن اللي هو النون بحرف
+
+327
+00:29:44,190 --> 00:29:50,330
+متحرك وهو الياء فيصيران حرفا واحدة مشددة من جنس
+
+328
+00:29:50,330 --> 00:29:53,980
+الأول ولا الثاني من جنس الثانية وبالتالي بنجد أن
+
+329
+00:29:53,980 --> 00:29:59,400
+الياء تصبح مضغمة يعني فيها مشددة فنقرأها فنقول 
+
+330
+00:29:59,400 --> 00:30:08,000
+فما يعمل أو مثلا خيرا يرا كيف نقرأها خيرا يرا
+
+331
+00:30:08,000 --> 00:30:14,200
+التنوين بيضغن في الياء بيصير الياء مشددة خيرا يرا
+
+332
+00:30:14,200 --> 00:30:21,530
+كذلك حرف النون ومن عمرهم يعني بتضغم النون الأولى في 
+
+333
+00:30:21,530 --> 00:30:25,410
+النون الثاني بحيث يصيراني نونا واحدة مشددة أو مثلا
+
+334
+00:30:25,410 --> 00:30:32,530
+أمنة نعاسى تنوين ورا حرف النون يضغم التنوين مع حرف
+
+335
+00:30:32,530 --> 00:30:39,850
+النون فبتصير أمنة نعاسى ولابد أن نحقق الغنى يعني 
+
+336
+00:30:39,850 --> 00:30:45,130
+لو قلنا مثلا فميعمل بيكون خطأ قراءتنا خطأ لابد أن
+
+337
+00:30:45,130 --> 00:30:53,720
+نحقق الغنى فنقول فميعمل أمنة نعاسى أو مثلا من مال
+
+338
+00:30:53,720 --> 00:31:01,280
+كيف نقرأها يا أخوات؟ نقول ميمال أضغمت النون مع حرف
+
+339
+00:31:01,280 --> 00:31:05,780
+الـميم بحيث يصيراني ميما واحدة مشددة اللي هي جنس
+
+340
+00:31:05,780 --> 00:31:12,460
+الثاني نقول ميمال ونحقق الغنى لا نقول ميمال نقول
+
+341
+00:31:12,460 --> 00:31:21,290
+ميمال أو مثلا في قوله قول معروف كيف نقرأها؟ قول قول
+
+342
+00:31:21,290 --> 00:31:41,010
+معروف قول معروف قول
+
+343
+00:31:41,010 --> 00:31:46,630
+معروف قول معروف قول معروف قول معروف قول معروف قول
+
+344
+00:31:46,630 --> 00:31:47,050
+معروف قول معروف قول معروف قول معروف قول معروف قول
+
+345
+00:31:47,050 --> 00:31:47,330
+معروف قول معروف قول معروف قول معروف قول معروف قول
+
+346
+00:31:47,330 --> 00:31:51,320
+معروف قول معروف قول معووالدي وما ولده .. ووالدي
+
+347
+00:31:51,320 --> 00:31:59,140
+وما ولده .. ووالدي
+
+348
+00:31:59,140 --> 00:31:59,540
+وما ولده .. ووالدي وماولده .. ووالدي وماولده ..
+
+349
+00:31:59,540 --> 00:31:59,820
+وماولده .. ووالدي وماولده .. ووالدي وماولده ..
+
+350
+00:31:59,820 --> 00:31:59,980
+.. ووالدي وماولده .. ووالدي وماولده .. ووالدي
+
+351
+00:31:59,980 --> 00:32:00,880
+وماولده .. ووالدي وماولده .. ووالدي وماولده ..
+
+352
+00:32:00,880 --> 00:32:05,930
+ووالدي وماولده .. ووالدي حروف ينمو اضغام بغنى
+
+353
+00:32:05,930 --> 00:32:09,910
+واللام والرا اضغام بغير غنى فإذا جاء بعد النون
+
+354
+00:32:09,910 --> 00:32:15,110
+الساكنة أو التنوين أحد حرفي اللام أو الرا تضغم
+
+355
+00:32:15,110 --> 00:32:19,750
+النون الساكنة في اللام أو الرا اضغام يعني كامل
+
+356
+00:32:19,750 --> 00:32:26,550
+بذاته وصفاته فنقول مثلا مثلا من ربهم نقول من ربهم
+
+357
+00:32:26,550 --> 00:32:33,130
+طبعا يضغم اضغام كامل أو اضغام بغير غنى إلا في حالة
+
+358
+00:32:33,130 --> 00:32:39,230
+واحدة في كل القرآن وهو في قوله وقيل من راق نسكت
+
+359
+00:32:39,230 --> 00:32:45,930
+سكتة لطيفة على النون من فنقول وقيل من راق ما معنى
+
+360
+00:32:45,930 --> 00:32:52,090
+من راق لماذا نسكت هنا؟ طبعا هنا يا أخوات سكتة واجبة
+
+361
+00:32:52,090 --> 00:32:58,170
+عند الإمام حفص حتى نفرق ما بين من وراه بمعنى من
+
+362
+00:32:58,170 --> 00:33:02,710
+يرقي لنا المريض عندهم كان الآية تتكلم عن واحد مات 
+
+363
+00:33:02,710 --> 00:33:10,110
+تخرج روحه أو تكاد تخرج روحه ويقف قاربه حوله
+
+364
+00:33:10,110 --> 00:33:15,510
+يلتفون حوله فيقول بعضهم من راق يعني من يرقي لنا
+
+365
+00:33:15,510 --> 00:33:21,160
+بمعنى من يعالج لنا هذا المريض فلو أضغمت لصارت كلمة 
+
+366
+00:33:21,160 --> 00:33:27,380
+واحدة مراق يعني لو قرأناها بالاضغام وقيل مراق مراق
+
+367
+00:33:27,380 --> 00:33:31,900
+يعني ممكن أن يكون مراق طريق أو مراق من بائع المرقة
+
+368
+00:33:31,900 --> 00:33:36,800
+وهو طباخ يعني طبيخ لذلك لابد أن نسكت سكت لطيفة
+
+369
+00:33:36,800 --> 00:33:41,400
+عند حفص الإمام حفص يسكت سكت لطيفة يعني عند غيره قد
+
+370
+00:33:41,400 --> 00:33:45,240
+لا يسكت لكن عندنا في الإمام حفص يسكت في أربع مواضع
+
+371
+00:33:45,590 --> 00:33:51,730
+من القرآن من ضمنها من راق حتى لا يتوهم المستمع إذا 
+
+372
+00:33:51,730 --> 00:33:57,030
+أضغمت النون بالرا بأنهما كلمة واحدة وهي بمعنى مراق
+
+373
+00:33:57,030 --> 00:34:02,760
+يعني بائع المرقة أو واحد مراق طريق ومعنى السكت الذي 
+
+374
+00:34:02,760 --> 00:34:08,160
+نتحدث عنه هو قطع الصوت على الكلمة القرآنية زمنا 
+
+375
+00:34:08,160 --> 00:34:16,060
+يسيرا بدون تنفس مقدار حركته يعني نقول وقيل من راه
+
+376
+00:34:16,060 --> 00:34:21,210
+لا نتنفس راق بدون نفس وسبب ترك الغنة مع اللام
+
+377
+00:34:21,210 --> 00:34:25,490
+والرا هو التخفيف وعدم التثقيل عندنا أمثلة على
+
+378
+00:34:25,490 --> 00:34:31,130
+الإضغام اللي بغير غنة مثلا في قوله من لدنه كيف 
+
+379
+00:34:31,130 --> 00:34:36,970
+نقرأها يا أخوات؟ من لدنه يعني النون تضغم في اللام
+
+380
+00:34:36,970 --> 00:34:41,850
+مباشرة بدون غنة نحن نقول بدون غنة يعني لا يصح
+
+381
+00:34:41,850 --> 00:34:49,380
+لنا أن نقول من لدنه تجيش أصلا خطأ إيه نقول من لدنه
+
+382
+00:34:49,380 --> 00:34:57,500
+مباشرة أو مالا لبدا .. كيف نقرأها؟ نقول مالا اللوبة
+
+383
+00:34:57,500 --> 00:35:03,520
+دا مالا اللوبة دا الـلام التنوين يضغم بالـلام أو مثلا
+
+384
+00:35:03,520 --> 00:35:09,020
+من ربهم أصلا من ربهم النون وراها الراء نقول من ربهم
+
+385
+00:35:09,020 --> 00:35:13,640
+ما فيش فيها غنة ما بينفع أحد يقول من ربهم بتكون 
+
+386
+00:35:13,640 --> 00:35:19,100
+ثقيلة على اللسان ولا تصلح إنما من ربهم مباشرة كذلك 
+
+387
+00:35:19,100 --> 00:35:25,950
+في قوله في عيشة راضية عيشة راضية نقول في عيشة 
+
+388
+00:35:25,950 --> 00:35:31,270
+الراضية عيشة الراضية إضغام بإيه؟ إضغام بغنى طبعا
+
+389
+00:35:31,270 --> 00:35:35,050
+نكتفي بهذا القدر لأن في عندنا إضغام نفس الإضغام 
+
+390
+00:35:35,050 --> 00:35:40,910
+هذا اللي بغنى واللي بغير غنى له أيضا عنوان آخر من
+
+391
+00:35:40,910 --> 00:35:45,350
+حيث الكمال أو النقص إن شاء الله الإضغام نتحدث عنه
+
+392
+00:35:45,350 --> 00:35:48,590
+من حيث الكمال أو النقص في المحاضرة القادمة نكتفي
+
+393
+00:35:48,590 --> 00:35:51,470
+بهذا القدر وبارك الله فيكم جميعا وجزاكم الله خير
+
+394
+00:35:51,470 --> 00:35:53,570
+والسلام عليكم ورحمة الله وبركاته العربية
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..853498880d40989d726c4ec01f93302aa8b9849a
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc.srt
@@ -0,0 +1,1511 @@
+1
+00:00:11,740 --> 00:00:14,900
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,900 --> 00:00:19,400
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:19,400 --> 00:00:22,800
+آله وصحابه وسلم موضوعنا اليوم يا أخوات هو حكم
+
+4
+00:00:22,800 --> 00:00:27,980
+التقاء الساكنين طبعا المقصود بهذا العنوان أن هناك
+
+5
+00:00:27,980 --> 00:00:32,170
+كلمتين، الكلمة الأخيرة آخرها حرف ساكن والكلمة
+
+6
+00:00:32,170 --> 00:00:37,390
+الثانية  بها حرف ساكن عندما نُنْطِق اتصالاً الكلمتان مع 
+
+7
+00:00:37,390 --> 00:00:41,030
+بعضهما البعض ما هو حكم التقاء الساكنين يعني إذا
+
+8
+00:00:41,030 --> 00:00:45,240
+التقت ساكنان أو حرفان ساكنان في كلمتين ولا يكون 
+
+9
+00:00:45,240 --> 00:00:49,500
+التقائهما إلا حالة الوصلة فلابد من التخلص من التقاء
+
+10
+00:00:49,500 --> 00:00:54,320
+الساكنين إما بالحذف لو كان الساكن الأول حرف مد
+
+11
+00:00:54,320 --> 00:00:58,900
+وإما بالتحريك سواء كان بالكسرة على الأصل أو الفتح 
+
+12
+00:00:58,900 --> 00:01:03,830
+أو الضم لو لم يكن الساكن الأول حرف مد، إذا حكم 
+
+13
+00:01:03,830 --> 00:01:08,770
+التقاء الساكنين بمعنى إن إذا التقى حرفان ساكنان في 
+
+14
+00:01:08,770 --> 00:01:13,510
+كلمتين ولا يكون التقائهما إلا حالة الوصلة لابد 
+
+15
+00:01:13,510 --> 00:01:17,530
+أن نتخلص من التقاء الساكنين إما بالحذف، ما نتخلص
+
+16
+00:01:17,530 --> 00:01:21,730
+من التقاء الساكنين بالحذف لو كان الساكن الأول حرف 
+
+17
+00:01:21,730 --> 00:01:26,090
+مد، أما إذا لم يكن الساكن الأول حرف مد في كلمتين
+
+18
+00:01:26,090 --> 00:01:31,050
+نتخلص من التقاء الساكنين إما بالكسرة على الأصل و
+
+19
+00:01:31,050 --> 00:01:36,990
+إما بالتحريك بالفتحة أو بالضمة أيضًا بحالات معدودة
+
+20
+00:01:36,990 --> 00:01:40,190
+كذلك،  أما بالنسبة للتخلص من التقاء الساكنين
+
+21
+00:01:40,190 --> 00:01:45,670
+بالحذف، فهنا إذا كان الساكن الأول حرف مد والساكن
+
+22
+00:01:45,670 --> 00:01:49,810
+الثاني في الكلمة الثانية حرفًا يعني ليس مدًا نتخلص من 
+
+23
+00:01:49,810 --> 00:01:54,680
+التقاء الساكنين بإيه؟ بالحذف، إذا متى نتخلص من التقاء
+
+24
+00:01:54,680 --> 00:01:59,660
+الساكنين يا أخوات؟ نتخلص 
+
+25
+00:01:59,660 --> 00:02:03,540
+من التقاء الساكنين بالحذف إذا كان الساكن الأول حرف 
+
+26
+00:02:03,540 --> 00:02:08,960
+مد. مثال ذلك قول تعالى: فلمّا ذاق الشجرة ثقيلة
+
+27
+00:02:08,960 --> 00:02:14,700
+أن نقول فلمّا ذا قاء الشجرة بدت لهم سوئاتهم إنما 
+
+28
+00:02:14,700 --> 00:02:21,050
+نقرأها فلمّا ذاق الشجرة، فلمّا ذاق الشجرة، الألف 
+
+29
+00:02:21,050 --> 00:02:27,150
+هنا حذفت نتيجة التقاء الساكنين هنا، الألف ذاق ساكنة
+
+30
+00:02:27,150 --> 00:02:34,190
+والشجرة، حرف الشين أيضًا ساكن، بالنسبة للحمزة، هي 
+
+31
+00:02:34,190 --> 00:02:40,270
+أصلًا  الشجرة، الحمزة تنوّصل طبعًا هنا، الحمزة تُنْوَصَل تُحذف 
+
+32
+00:02:40,900 --> 00:02:46,300
+واللام في قلة التعليف تُضْغَم مع الشين، فتصير اشق
+
+33
+00:02:46,300 --> 00:02:51,340
+الشجرة فلا اللام تظهر ولا الهمزة تظهر فنقراها
+
+34
+00:02:51,340 --> 00:02:57,540
+فلمّا ذاق الشجرة، الألف حُوّلت فتُعت ذاقا، الهمزة الواصلة
+
+35
+00:02:57,540 --> 00:03:01,580
+أصلًا  مُحَدَّثة على الواصلة، حكم اللام الساكنة في قلة 
+
+36
+00:03:01,580 --> 00:03:05,880
+التعليف مع الشين لأنها من حروف الإضغام، اللي هي
+
+37
+00:03:05,880 --> 00:03:09,060
+سُمّيت اللام الشمسية، تبدأ قبل ما عشرين، فعندما 
+
+38
+00:03:09,060 --> 00:03:15,060
+نقرأها نقول: فلمّا ذاقش شجرة، ذاقش شجرة، يبقى الألف 
+
+39
+00:03:15,060 --> 00:03:21,080
+طبعًا  مُحذفة، مثال آخر كذلك في قول تعالى: وَإِذْ قَالُوا 
+
+40
+00:03:21,080 --> 00:03:28,240
+اللهم، وَإِذْ قَالُوا اللهم، أين الحرف اللي حُذف؟ طبعًا 
+
+41
+00:03:28,240 --> 00:03:37,310
+هنقول وَإِذْ قَالُوا اللهم، حرف المد ماله؟ حرف المد 
+
+42
+00:03:37,310 --> 00:03:43,630
+الواو ساكن، وهنا اللهم اللام أيضًا ساكنة نتيجة
+
+43
+00:03:43,630 --> 00:03:58,810
+التقاء الساكنين اللهم اللهم اللهم
+
+44
+00:03:58,810 --> 00:04:01,930
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+45
+00:04:01,930 --> 00:04:02,010
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+46
+00:04:02,010 --> 00:04:02,030
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+47
+00:04:02,030 --> 00:04:02,970
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+48
+00:04:02,970 --> 00:04:02,990
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+49
+00:04:02,990 --> 00:04:05,720
+اللهم اللهم اللهم، التي لُفِظَتْ هنا، قالوا يعني اللام
+
+50
+00:04:05,720 --> 00:04:11,500
+المضمومة وَإِذْ قَالُوا اللهم، فَحَقُّوا واللام طبعًا  تظهر
+
+51
+00:04:11,500 --> 00:04:16,060
+وهنا عندما ننظر إلى القراءة نقول وَإِذْ قَالُوا اللهم
+
+52
+00:04:16,060 --> 00:04:22,020
+في عندنا الواو جماعة، تقولوا وفي عندنا كذلك الألف
+
+53
+00:04:22,020 --> 00:04:27,440
+هنا ماذا نسميه هذا الألف؟ ألف الفارقة التي تُفَرِّقُ ما
+
+54
+00:04:27,440 --> 00:04:31,580
+بين الواو جماعة والواو الكلمة وَإِذْ قَالُوا، هذا تكتب ولا
+
+55
+00:04:31,580 --> 00:04:35,440
+تُلْفَظْ، تُكتَب ولا تُلْفَظ لا حالة الوصل ولا حالة الوقف
+
+56
+00:04:35,440 --> 00:04:39,460
+نقول وَإِذْ قَالُوا، لا نقول وَإِذْ قَالُوا وَ، فالمقصود
+
+57
+00:04:39,460 --> 00:04:43,820
+بِالأَلِف هنا ليس الألف اللي هي هذه الصغيرة التي تكتب 
+
+58
+00:04:43,820 --> 00:04:48,300
+ولا تُلْفَظْ، وإنما المقصود بها واو الجماعة وَإِذْ قَالُوا 
+
+59
+00:04:48,690 --> 00:04:53,530
+والهمزة اللي هنا تُعْطِي اللهم همزة الوصل واللام مع
+
+60
+00:04:53,530 --> 00:04:58,750
+اللام تُضْغَم يعني من حروف الإدغام تُلْفَظ لاما واحدة 
+
+61
+00:04:58,750 --> 00:05:04,210
+مُشَدَّدة لأن معنى الإدغام إدخال حرف ساكن بحرف متحرك 
+
+62
+00:05:04,210 --> 00:05:09,810
+بحيث يصيران حرفًا واحدة مشددة، إذا الذي يُلْفَظُ هنا وَإِذْ 
+
+63
+00:05:09,810 --> 00:05:17,530
+قَالُوا اللهم من يقرأها بحرف الواو؟ آه فضلي
+
+64
+00:05:20,200 --> 00:05:25,200
+أحسنتي وَإِذْ قَالُوا اللهم، لا نقول وَإِذْ قَالُوا اللهم 
+
+65
+00:05:25,200 --> 00:05:30,480
+لماذا؟ لنا ثقيلة على اللسان، ثقيلة أن نقول وَإِذْ قَالُوا 
+
+66
+00:05:30,480 --> 00:05:35,520
+اللهم، إنما هنا نتيجة التقاء الساكنين، فلمّا كان
+
+67
+00:05:35,520 --> 00:05:40,830
+الساكن الأول وهو الواو حرف مد، يُحذف حرف المد، 
+
+68
+00:05:40,830 --> 00:05:44,610
+نتخلص من التقاء الساكنين بحذف حرف المد، الذي
+
+69
+00:05:44,610 --> 00:05:49,470
+يُظْهِرُ اللي هي الضمة وَإِذْ قَالُوا اللهم إن كان هذا هو 
+
+70
+00:05:49,470 --> 00:05:56,780
+الحق من عندك، كذلك مثال آخر وَفِي الْأَرْضِ آيَاتٌ لِلْمُؤْمِنِينَ
+
+71
+00:05:56,780 --> 00:06:01,300
+طبعًا  ثقيل على اللسان أن نقرأها وَفِي الْأَرْضِ، كيف 
+
+72
+00:06:01,300 --> 00:06:06,740
+نقرأها؟ وَفِي الْأَرْضِ آيَاتٌ لِلْمُؤْمِنِينَ، وَفِي الْأَرْضِ آيَاتٌ 
+
+73
+00:06:06,740 --> 00:06:13,030
+لِلْمُؤْمِنِينَ، وَفِي الْأَرْضِ، وَفِي الْأَرْضِ، أين الحرف المحذوف؟ حرف
+
+74
+00:06:13,030 --> 00:06:18,950
+الياء، لا نقول وَفِي الْأَرْضِ، نقول وَفِي الْأَرْضِ، يعني عندنا 
+
+75
+00:06:18,950 --> 00:06:24,270
+حرفان ساكنان في كلمتين، حرف الياء في كلمة في آخر 
+
+76
+00:06:24,270 --> 00:06:29,090
+الكلمة وحرف الأرض، اللام هذه، اللام ساكنة، لأنها تظهر
+
+77
+00:06:29,090 --> 00:06:33,690
+مع الهمزة، فنتيجة التقاء الساكنين نتخلص من التقاء 
+
+78
+00:06:33,690 --> 00:06:37,550
+الساكنين بالحذف، لماذا تخلصنا من التقاء الساكنين
+
+79
+00:06:37,550 --> 00:06:43,590
+بالحذف؟ لأن الساكن الأول حرف مد، صحيح، إذا تخلصنا من
+
+80
+00:06:43,590 --> 00:06:47,410
+القراءة الساكنة، عندما نقرأها، لا نقول وَفِي الْأَرْضِ،
+
+81
+00:06:47,410 --> 00:06:51,790
+لأنها بتكون ثقيلة على اللسان، كيف نقرأها؟ وَفِي 
+
+82
+00:06:51,790 --> 00:06:56,890
+الْأَرْضِ آيَاتٌ، وَفِي الْأَرْضِ، لا نقول وَفِي الْأَرْضِ، يعني
+
+83
+00:06:56,890 --> 00:07:01,150
+يُحذف حرف المد هناك، في حالة الواصلة، أما إذا وقفنا
+
+84
+00:07:01,150 --> 00:07:06,050
+عليه فيثبت لثبوته في رسم المصحف، لو واحدة مثلًا  وقفت 
+
+85
+00:07:06,050 --> 00:07:11,490
+عند كلمة وَفِي، طبعًا  سواء كان اختبارًا أو اضطرارًا يعني
+
+86
+00:07:11,490 --> 00:07:16,530
+انقطع النفس فوقفت عند كلمة وَفِي، نُرَفِضُها أو من باب
+
+87
+00:07:16,530 --> 00:07:21,430
+الاختبار، يعني كيف يكون من باب الاختبار؟ يعني الأخت
+
+88
+00:07:21,430 --> 00:07:27,390
+مثلًا  قالت وَفِي الْأَرْضِ آيَاتٌ لِلْمُؤْمِنِينَ، فقلت لها لو سمحت 
+
+89
+00:07:27,390 --> 00:07:33,770
+قفِي عند كلمة الأرض، اختبارًا، إذا أرى كيف تقف على كلمة
+
+90
+00:07:33,770 --> 00:07:40,770
+وَفِي، فتقول وَفِي، طب ينفع نقرأها؟ تقرأ، تُكَمِّل الآيات، تقول
+
+91
+00:07:40,770 --> 00:07:45,210
+الْأَرْضِ آيَاتٌ لِلْمُؤْمِنِينَ، طبعًا  ليه؟ صح عليها، ترجع كلمة أو 
+
+92
+00:07:45,210 --> 00:07:48,990
+كلمتين فتقول وَفِي الْأَرْضِ آيَاتٌ لِلْمُؤْمِنِينَ 
+
+93
+00:07:51,620 --> 00:07:56,400
+طيب، هذا اللي هو التخلص من التقاء الساكنين بالحذف لو 
+
+94
+00:07:56,400 --> 00:08:02,540
+كان الساكن الأول حرف مد، أما إذا كان حرف المد غير 
+
+95
+00:08:02,540 --> 00:08:06,180
+ثابت في رسم المصحف، في الرسم المصحف، الرسم العثماني
+
+96
+00:08:06,180 --> 00:08:11,760
+نجد أنه بعض الكلمات فيها حرف مد غير ثابت، هذا حرف 
+
+97
+00:08:11,760 --> 00:08:16,240
+المد غير ثابت، أما إذا كان حرف المد غير ثابت يعني 
+
+98
+00:08:16,240 --> 00:08:20,390
+لا يُكتب في رسم المصحف، لعلة التقاء الساكنين فيكون
+
+99
+00:08:20,390 --> 00:08:25,330
+حذفه وصلًا ووقفًا، يعني يُحذف وصلًا ووقفًا، لو وقفنا
+
+100
+00:08:25,330 --> 00:08:33,290
+عليها نقول وَفِي، هنا مثلًا  أَرِنِي كَيْفَ تُحْيِي، وصلًا قرأنا كيف 
+
+101
+00:08:33,290 --> 00:08:38,790
+تُحْيِي الموتى، مُحذوف وصلًا، وكذلك وقفًا، الكلمة التي سوف
+
+102
+00:08:38,790 --> 00:08:43,750
+نراها هنا، كيف تُحْيِي الموتى هي أصلًا  تُحْيِي في رسم 
+
+103
+00:08:43,750 --> 00:08:47,390
+المصحف هذه ياء واحدة، والياء الثانية ياء تُسَمّى 
+
+104
+00:08:47,390 --> 00:08:51,210
+الياء الكوفية غير موجودة في رسم المصحف لكن هنا في
+
+105
+00:08:51,210 --> 00:08:55,490
+حسب المصحف المساعد يعني مكتوب ياء ثانية لكن في 
+
+106
+00:08:55,490 --> 00:09:02,980
+الرسم العثماني موجودة تُحْيِي، وبعدين بما يُسَمّى الياء
+
+107
+00:09:02,980 --> 00:09:10,540
+الكوفية وهي طول فضاء ولا تُكتب، فنقراها تُحْيِي الموتى
+
+108
+00:09:10,540 --> 00:09:17,660
+إذا وصلناها كيف نقراها؟ هنا وَإِذْ قَالَ إِبْرَاهِيمُ رَبِّي
+
+109
+00:09:17,660 --> 00:09:22,800
+أَرِنِي كَيْفَ تُحْيِي الْمَوْتَى، أَرِنِي كَيْفَ تُحْيِي الْمَوْتَى، ياء واحدة
+
+110
+00:09:22,800 --> 00:09:27,100
+الياء الثانية هنا ماذا يصير فيها؟ تُحذف، لماذا حُذفت؟
+
+111
+00:09:27,960 --> 00:09:32,020
+تخلصنا منها من التقاء الساكنين، لو وقفنا عليها نلفظ 
+
+112
+00:09:32,020 --> 00:09:34,520
+الياء الأولى وليس الياء الثانية لأن الياء الثانية
+
+113
+00:09:34,520 --> 00:09:41,340
+مُحذفة يعني مُحذفة في رسم المصحف نقول كَيْفَ تُحْيِي، لكن
+
+114
+00:09:41,340 --> 00:09:45,620
+لو وصلناها كَيْفَ تُحْيِي الْمَوْتَى، كذلك في قول تعالى: قَالَ 
+
+115
+00:09:45,620 --> 00:09:52,280
+مَنْ يُحْيِي الْعِظَامَ وَهِيَ رَمِيمٌ، قَالَ مَنْ يُحْيِي الْعِظَامَ يعني 
+
+116
+00:09:52,280 --> 00:09:58,170
+ياء أولى، هذا بالنسبة للتخلص من التقاء الساكنين
+
+117
+00:09:58,170 --> 00:10:02,870
+بالحذف، متى نتخلص من التقاء الساكنين بالحذف لو كان
+
+118
+00:10:02,870 --> 00:10:07,890
+الساكن الأول حرف مد، الحرف الثاني يا أخوات هو 
+
+119
+00:10:07,890 --> 00:10:11,650
+التخلص من التقاء الساكنين بالتحريك، ماذا نقصد
+
+120
+00:10:11,650 --> 00:10:19,270
+بالتحريك؟ يا تحريكها فتحة أو ضمة أو الكسرة، الأصل أن 
+
+121
+00:10:19,270 --> 00:10:23,190
+يُتَمّ التخلص من التقاء الساكنين بالتحريك بالكسر وهذا 
+
+122
+00:10:23,190 --> 00:10:27,870
+هو على الأصل دائماً، تتخلص من التقاء الساكنين بالكسر
+
+123
+00:10:27,870 --> 00:10:32,030
+ والأمثلة على ذلك كثيرة، لكن بالنسبة لغير الكسر
+
+124
+00:10:32,030 --> 00:10:36,910
+بحالات محدودة، نرى هنا مثلًا  قُلْ ادْعُوا اللَّهَ، أو ادْعُوا
+
+125
+00:10:36,910 --> 00:10:43,060
+الرَّحْمَنَ، قُلْ ادْعُوا، المثال اللي عندنا قُلْ ادْعُوا، هنا قُلْ 
+
+126
+00:10:43,060 --> 00:10:48,860
+ادْعُوا اللام ساكنة فعل أمر مُجْزَمٌ بالسكون قُلْ ادْعُوا
+
+127
+00:10:48,860 --> 00:10:53,700
+الدال ساكنة، هنا طبعًا الهمزة الوصل في حالة الوصل
+
+128
+00:10:53,700 --> 00:11:01,140
+تَسْقُطُ، فال ساكنين، اللام ساكنة قُلْ وادْعُوا الدال ساكنة
+
+129
+00:11:01,140 --> 00:11:06,480
+نتخلص من التقاء الساكنين بالتحريك بالكسر فنقول قُلْ
+
+130
+00:11:06,480 --> 00:11:12,460
+ادْعُوا الله، قُلْ ادْعُوا، قُلْ ادْعُوا الله، أو ادْعُوا الرحمن
+
+131
+00:11:12,460 --> 00:11:20,460
+فاللام هنا مكسورة، هي أصلًا  ساكنة، قُلْ، بس عندما نصلها
+
+132
+00:11:20,460 --> 00:11:26,600
+نقرأها قُلْ ادْعُوا بالكسر، كذلك قوله تعالى: وَقَالَتْ أَخْرِجْ 
+
+133
+00:11:26,600 --> 00:11:33,740
+عَلَيْهِنَّ، وَقَالَتْ طبعًا  فعل ماضي يعني ساكن، قالت ثاني
+
+134
+00:11:33,740 --> 00:11:39,200
+ساكنة، قَالَتْ أَخْرِجْ عَلَيْهِنَّ حرف الخاء ساكن، طبعًا أخرج
+
+135
+00:11:39,200 --> 00:11:45,410
+الهمزة اللي هنا تُسَمّى همزة وصل، ننْطِقُها، قالت تُخْرِجْ
+
+136
+00:11:45,410 --> 00:11:49,970
+عَلَيْهِنَّ، طبعًا الفعل الماضي خرج، الفعل الأمر من خرج أخرج
+
+137
+00:11:49,970 --> 00:11:54,930
+فَهُنا أمر الثلاثي وهمزة الأمر الثلاثي زي اضرب 
+
+138
+00:11:54,930 --> 00:12:00,530
+همزة وهمزة وصل تُسْقُطُ حالة الوصل وتُثْبَتُ حالة اللي 
+
+139
+00:12:00,530 --> 00:12:04,210
+ابتدأوا بها لو ابتدأنا بها إيه؟ تُثْبَتُ، نقول أخرج 
+
+140
+00:12:04,860 --> 00:12:09,220
+لكن لو وصلناها قَالَتْ أَخْرِجْ عَلَيْهِنَّ فالخاء هي التي تظهر
+
+141
+00:12:09,220 --> 00:12:16,120
+عندما نقول قالت أخرج أنا ساكنين أستا ساكنة والخاء 
+
+142
+00:12:16,120 --> 00:12:19,860
+ساكنة نتخلص من تقرأ الساكنين بالتحريك بالكسر
+
+143
+00:12:19,860 --> 00:12:25,300
+نقرأها قالت أخرج عليهن قالت مكسورة قالت أخرج عليهن
+
+144
+00:12:25,300 --> 00:12:32,940
+كذلك في قول تعالى و لقد استهزئ و لقد أين السكون
+
+145
+00:12:33,940 --> 00:12:39,660
+عدان قاعدين استهزئة .. إيه ال .. استهزئة حرف الصين
+
+146
+00:12:39,660 --> 00:12:44,040
+ساكن ما تخلص من التقاء الساكنين بال .. بالكسري
+
+147
+00:12:44,040 --> 00:12:49,660
+فنقول ولا قد استهزئة .. ولا قد استهزئة ما تخلص من
+
+148
+00:12:49,660 --> 00:12:53,780
+التقاء الساكنين بالكسري وهذا طبعا أخوات على الأصل
+
+149
+00:12:54,340 --> 00:12:59,100
+وممكن يكون أيضا التنوين يعني قد يكون الساكن الأول
+
+150
+00:12:59,100 --> 00:13:03,600
+تنوين سواء كان تنوين ضم أو تنوين كسر والساكن
+
+151
+00:13:03,600 --> 00:13:07,440
+الثاني متحرك يعني ساكن في الكلمة الثانية التنوين
+
+152
+00:13:07,440 --> 00:13:14,460
+هو أصلا نون ساكنة مثلا عندما نقول هنا إن زيّن سماء
+
+153
+00:13:14,460 --> 00:13:19,400
+الدنيا بزينات الكواكب هي أصلا بزيناتِنا تن
+
+154
+00:13:19,400 --> 00:13:22,700
+التنوين هذا عبارة عن نون ساكنة نقول بزيناتِنا
+
+155
+00:13:22,700 --> 00:13:29,060
+الكواكب لكنها ثقيلة أن نقول بزيناتِنا تن الكواكب نتخلص
+
+156
+00:13:29,060 --> 00:13:33,040
+من التقاء الساكنين بالكسر يعني يكسر التنوين اللي
+
+157
+00:13:33,040 --> 00:13:39,630
+هو نون أصلا بزيناتِنا هو صحيح تنوين لكنه يرفض نون
+
+158
+00:13:39,630 --> 00:13:44,030
+ساكنة لذلك في عيننا أحكام النون الساكنة والتنوين
+
+159
+00:13:44,030 --> 00:13:48,170
+لأن التنوين هو أخو النون الساكنة فنقول بزيناتِنا
+
+160
+00:13:48,170 --> 00:13:54,710
+الكواكب فتقيل أن نقول بزيناتِنا الكواكب فالتنوين
+
+161
+00:13:54,710 --> 00:14:01,500
+نفسه اللي هي النون تكسر فنقول بزيناتِنا الكواكب وإن
+
+162
+00:14:01,500 --> 00:14:08,400
+زيننا السماء الدنيا بزيناتنا الكواكب بزيناتنا
+
+163
+00:14:08,400 --> 00:14:12,080
+الكواكب من يقراها بزيناتنا الكواكب؟
+
+164
+00:14:13,670 --> 00:14:19,090
+أيوة بزيناتِنا الكواكب حركنا التنوين التنوين يُلفظ
+
+165
+00:14:19,090 --> 00:14:24,890
+نون ساكنة فلما جاءت النون ساكنة ساكنة وجاء الكواكب
+
+166
+00:14:24,890 --> 00:14:28,790
+اللام برضه في الكواكب الساكنة تخلصنا من التقاء
+
+167
+00:14:28,790 --> 00:14:34,990
+الساكنين بالكسر في هذا المثال كذلك قد يكون الساكن
+
+168
+00:14:34,990 --> 00:14:39,570
+الأول اللي هو الياء اللينة ما هي الياء اللينة يا
+
+169
+00:14:39,570 --> 00:14:46,860
+أخوات؟ ما فيه عندنا حروف اللين وهما .. ما هما؟
+
+170
+00:14:46,860 --> 00:14:52,640
+تفضّلي إيه؟ الألف والواو والياء الواو الساكنة
+
+171
+00:14:52,640 --> 00:14:55,420
+المفتوح ما قبلها والياء الساكنة المفتوح ما قبلها
+
+172
+00:14:55,420 --> 00:14:59,760
+فعندما نقول الياء اللينة يعني الياء الساكنة المفتوح
+
+173
+00:14:59,760 --> 00:15:04,280
+ما قبلها إذا القاعدة عندنا قد يكون الساكن الأول هو
+
+174
+00:15:04,280 --> 00:15:09,120
+الياء اللينة والساكن الثاني هو ساكن الكلمة نتخلص
+
+175
+00:15:09,120 --> 00:15:13,500
+من التقاء الساكنين بالكسر يعني الياء اللينة نكسرها
+
+176
+00:15:13,500 --> 00:15:19,520
+مثال ذلك هنا يا صاحبي السجن صاحبي الياء ساكنة
+
+177
+00:15:19,520 --> 00:15:24,440
+وقابلها مفتوح هي ياء مادية ولا ياء لينة؟ لماذا
+
+178
+00:15:24,440 --> 00:15:30,660
+لينة؟ لأنها ساكنة قبلها مفتوح فتقرأ يا صاحبي فهنا
+
+179
+00:15:30,660 --> 00:15:38,170
+ياء ساكنة ياء لينة والسجن السين ساكنة نتخلص من
+
+180
+00:15:38,170 --> 00:15:42,510
+التقاء الساكنين بكسر الياء اللينة فنقول يا صاحبي
+
+181
+00:15:42,510 --> 00:15:48,110
+السجن صاحبي مكسورة صاحبي السجن إذا الياء اللي هنا
+
+182
+00:15:48,110 --> 00:15:53,670
+ياء لينة كسرناها لأنها ساكنة وجاملها مفتوح نكسر
+
+183
+00:15:53,670 --> 00:15:56,910
+الياء اللينة لأنها وقعت نتخلصنا من التقاء
+
+184
+00:15:56,910 --> 00:16:00,730
+الساكنين وكان الساكن الأول الياء اللينة فكيف
+
+185
+00:16:00,730 --> 00:16:02,010
+نقرأه؟ مين يقرأ ليها؟
+
+186
+00:16:07,890 --> 00:16:12,190
+حركنا الياء اللينة بالكسر مع أنها ياء لكننا
+
+187
+00:16:12,190 --> 00:16:16,950
+حركناها بالكسر لأنها ياء لينة كذلك هنا في
+
+188
+00:16:16,950 --> 00:16:22,630
+المثال الآخر إن ربك يعلم أنك تقوم أدنى من ثلثي الليل
+
+189
+00:16:22,630 --> 00:16:29,570
+ثلثي الليل ثلثي الياء هنا ساكنة وجابلها لامفتوحة
+
+190
+00:16:29,570 --> 00:16:33,890
+يبقى الياء لينة وليس الياء المادية وجات الساكنة
+
+191
+00:16:33,890 --> 00:16:38,710
+الأول هو ياء لينة والليل اللام اللي هنا ساكنة
+
+192
+00:16:38,710 --> 00:16:43,910
+نتخلص من التقاء الساكنين بالتحريك بالكسرة فنقول من
+
+193
+00:16:43,910 --> 00:16:50,050
+ثلثي الليل ثلثي ثلثي الليلي ونصفهم طيب يعني هنا
+
+194
+00:16:50,050 --> 00:16:58,320
+حركنا الياء اللينة بالكسرة هذا يا أخوات اللي هو التخلص
+
+195
+00:16:58,320 --> 00:17:02,140
+من التقاء الساكنين بالتحريك بالكسر وهذا يا بنات
+
+196
+00:17:02,140 --> 00:17:05,940
+على الأصل على الأصل ولا ما تتخلص من التقاء
+
+197
+00:17:05,940 --> 00:17:11,410
+الساكنين بالحرف عند أي حرف عند حرف المد نشوف الحالة
+
+198
+00:17:11,410 --> 00:17:16,150
+الثالثة التخلص من التقاء الساكنين بالفتح متى نتخلص
+
+199
+00:17:16,150 --> 00:17:20,350
+من التقاء الساكنين بالفتح طبعا هذا خلاف الأصل ولكن
+
+200
+00:17:20,350 --> 00:17:23,830
+في عندنا حالتين يعني متى نتخلص من التقاء الساكنين
+
+201
+00:17:23,830 --> 00:17:28,730
+بالفتح في حالتين الحالة الأولى لو كان الساكن الأول
+
+202
+00:17:28,730 --> 00:17:35,150
+نون من تحت حرف الجر نون من الجر زي من المؤمنين
+
+203
+00:17:35,150 --> 00:17:42,240
+كيف نقرأ هذه؟ من المؤمنين طيب إذا لو واحدة قرأتها
+
+204
+00:17:42,240 --> 00:17:46,700
+مثلا من المؤمنين نشوف ثقيلة على اللسان لذلك لا
+
+205
+00:17:46,700 --> 00:17:53,080
+تقرأ من المؤمنين رجال وإنما نقرأها من المؤمنين من
+
+206
+00:17:53,080 --> 00:17:58,220
+المؤمنين رجال صدقوا ما عاهدوا الله عليه من
+
+207
+00:17:58,220 --> 00:18:04,430
+المؤمنين هي أصلا من المؤمنين عشان نون من الجارة
+
+208
+00:18:04,430 --> 00:18:09,670
+تخلصنا من التقاء الساكنين بالفتحة بس في حالتين
+
+209
+00:18:09,670 --> 00:18:16,570
+معينتين الحالة الأولى من النون من الجارة ومثلا آخر
+
+210
+00:18:16,570 --> 00:18:22,270
+أوفوا الكيلة ولا تكونوا من المخسرين من المخسرين
+
+211
+00:18:22,270 --> 00:18:27,820
+أصلا من المخسرين أصلا هي ساكنة لكن تخلصنا من التقاء
+
+212
+00:18:27,820 --> 00:18:33,680
+الساكنين بالفتحي لأن هذه نون من الجارة وهي الحالة
+
+213
+00:18:33,680 --> 00:18:38,000
+الأولى من حالات التخلص من التقاء الساكنين بالفتحة
+
+214
+00:18:38,000 --> 00:18:43,130
+يعني متى يتم التخلص من التقاء الساكنين بالفتحي؟ في
+
+215
+00:18:43,130 --> 00:18:47,430
+الحالة الأولى اللي هو نون من الجارة إذا كان الساكن
+
+216
+00:18:47,430 --> 00:18:54,210
+الأول هو نون من الجارة نقرأها من المؤمنين من
+
+217
+00:18:54,210 --> 00:19:01,360
+المخسرين وهكذا في كل حرف من ثانيا يتم التخلص من
+
+218
+00:19:01,360 --> 00:19:06,460
+التقاء الساكنين بالفتح لحالة ثانية عند التقاء
+
+219
+00:19:06,460 --> 00:19:14,260
+الساكنين ميم ألف لام ميم نقرأها ألف لام ميم الله في
+
+220
+00:19:14,260 --> 00:19:18,600
+حالة الواصل لكن لو وقفنا عليها ألف لام ميم نقف
+
+221
+00:19:18,600 --> 00:19:25,690
+عليها بالماد اللازم الحرفي المخفف ميم هي ساكنة لو
+
+222
+00:19:25,690 --> 00:19:35,150
+وصلناها نقرأها ألف لام ميم الله ميم الله نفتحها إذا
+
+223
+00:19:35,150 --> 00:19:37,910
+في عندنا حالتين بس في هذا الموضوع في كل المصحف
+
+224
+00:19:37,910 --> 00:19:42,390
+لأنه يعني ألف لام ميم وبعدها ساكن في حالة الواصل
+
+225
+00:19:42,390 --> 00:19:51,470
+ألف لام ميم الله لا إله إلا هو الحي القيوم إذا هنا
+
+226
+00:19:51,470 --> 00:19:57,690
+ألف لام ميم الله إذا في عندنا بس حالتين ما هي حالات
+
+227
+00:19:57,690 --> 00:20:02,990
+التخلص من التقاء الساكنين بالفتحة؟ فضلا أخت نون من
+
+228
+00:20:02,990 --> 00:20:09,850
+الجارة والحالة الثانية؟ إذا كان الساكن أول هي ميم
+
+229
+00:20:09,850 --> 00:20:14,870
+ألف لام ميم في صورة العمران التي بعد حرف ساكن ألف
+
+230
+00:20:14,870 --> 00:20:19,550
+لام ميم الله لا إله إلا هو الحي القيوم هذا بالنسبة
+
+231
+00:20:19,550 --> 00:20:24,230
+للتخلص من التقاء الساكنين بإيش؟ بالفتحة الحالة
+
+232
+00:20:24,230 --> 00:20:27,850
+الثالثة أخوات ثالثا التخلص من التقاء الساكنين
+
+233
+00:20:27,850 --> 00:20:32,500
+بالضم يتم التخلص من التقاء الساكنين بالضم؟ في
+
+234
+00:20:32,500 --> 00:20:38,580
+عندنا أيضا حالتين الحالة الأولى نتخلص منها إذا كان
+
+235
+00:20:38,580 --> 00:20:43,540
+الساكن الأول هو الواو واو اللين التي للجمع الواو
+
+236
+00:20:43,540 --> 00:20:49,400
+اللينة يعني واو ساكنة جامدها مفتوح هي للجمع زي ما
+
+237
+00:20:49,400 --> 00:20:52,260
+قلنا التخلص من التقاء الساكنين بالكسر لو كانت
+
+238
+00:20:52,260 --> 00:20:56,170
+الياء اللينة الساكن الأول الياء اللينة هنا نتخلص
+
+239
+00:20:56,170 --> 00:20:59,990
+من تقرأ الساكنين بالضم لو كان الساكن الأول هو
+
+240
+00:20:59,990 --> 00:21:05,010
+الواو اللينة التي هي للجمع مثال ذلك وأقاموا
+
+241
+00:21:05,010 --> 00:21:13,990
+الصلاة وآتوا الذكاء وآتوا الذكاء فالواو هنا
+
+242
+00:21:13,990 --> 00:21:19,030
+أصلها وآتوا الذكاء وآتوا الذكاء ثقيلة على اللسان
+
+243
+00:21:19,030 --> 00:21:24,670
+أن نقرأها وآتوا الذكاء كيف بنعمل؟ نتخلص من التقاء
+
+244
+00:21:24,670 --> 00:21:31,450
+الساكنين بالضم فنقول وآتوا الذكاء هنا وآتوا و
+
+245
+00:21:31,450 --> 00:21:36,650
+ساكن الأصل طبعا لا تنظر إلى الضم اللي هنا لأنه
+
+246
+00:21:36,650 --> 00:21:42,210
+بيرسمون ليها على حسب الوصل لكن هي في الأساس هي واو
+
+247
+00:21:42,210 --> 00:21:46,250
+ساكنة جامدها مفتوح وهي واو الجماعة وتسمى الواو
+
+248
+00:21:46,250 --> 00:21:52,050
+اللينة التي للجماعة فنقول وآتوا الزكاة وقاموا
+
+249
+00:21:52,050 --> 00:21:57,130
+الصلاة وآتوا الزكاة وآتوا الواو مضمومة طبعا يا
+
+250
+00:21:57,130 --> 00:22:03,860
+أخوات الألف اللي هنا تسمى ألف إيش؟ الألف الفارقة تكتب ولا
+
+251
+00:22:03,860 --> 00:22:08,160
+تلفظ لا وصلا ولا وقفا ويُوضع فوقها في رسم المصحف
+
+252
+00:22:08,160 --> 00:22:14,220
+الصفر المستدير معناته أن هذا الحرف يُكتب لكنها لا
+
+253
+00:22:14,220 --> 00:22:18,180
+تُلفظ لا في حالة الوصل ولا في حالة الوقف يعني لو
+
+254
+00:22:18,180 --> 00:22:23,700
+أقفنا على كلمة وآتوا بس
+
+255
+00:22:23,700 --> 00:22:28,140
+لا نقول وآتوا كذلك يعني هنا وآتى والذكى الألف
+
+256
+00:22:28,140 --> 00:22:31,840
+اللي هنا ألف فارقة تسقط طبيعي لا تلفظ الألف
+
+257
+00:22:31,840 --> 00:22:37,040
+الثانية بتاعة الذكاة هي أل التعريف همزة الوصل تسقط
+
+258
+00:22:37,040 --> 00:22:40,240
+في حال الوصل لو ابتدأنا بها الكلام وقولنا
+
+259
+00:22:40,240 --> 00:22:44,280
+الذكاة الذكاة لفظناها لأنه إذا ابتدأنا بهمزة
+
+260
+00:22:44,280 --> 00:22:49,820
+الوصل نبدأ بها مفتوحة فـ أل التعريف لكن هنا نقول
+
+261
+00:22:49,820 --> 00:22:56,840
+وآتى والذكى طب اللي ما عايزين اللام تضغم ما هي حروف
+
+262
+00:22:56,840 --> 00:23:03,190
+الاضغام اللام أل التعريف طب ثم صل رحمن تفوزها تفوز
+
+263
+00:23:03,190 --> 00:23:10,010
+زين ضف ذا نعم دع سوء ظن زر حزر شريفا للكرام طب ثم
+
+264
+00:23:10,010 --> 00:23:13,810
+صل رحمن تفوزها تفوزها تفوز زين ضف ذا نعم دع سوء ظن
+
+265
+00:23:13,810 --> 00:23:17,850
+زر حزر
+
+266
+00:23:17,850 --> 00:23:22,930
+شريفا للكرام طب ثم صل رحمن تفوزها تفوزها تفوزها
+
+267
+00:23:22,930 --> 00:23:23,090
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها
+
+268
+00:23:23,090 --> 00:23:25,830
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تولى ال
+
+269
+00:23:25,830 --> 00:23:30,570
+همزة الوصل ولا اللام التي يلفظ هو بس حرف الزاي
+
+270
+00:23:30,570 --> 00:23:35,290
+وكذلك حرف الواو التي هي للجامع اللي إحنا نتخلص من
+
+271
+00:23:35,290 --> 00:23:39,850
+التقاء الساكنين بالضم فنقول وآتوا الذكاء وآتوا
+
+272
+00:23:39,850 --> 00:23:44,990
+الذكاء كذلك هنا يومئذ يودوا الذين كفروا وعصوا
+
+273
+00:23:44,990 --> 00:23:51,490
+الرسول وعصوا هي أصلا وعصوا الرسول أصلها ساكن وعصوا
+
+274
+00:23:51,490 --> 00:23:56,070
+لحالها لكن نتيجة التقاء الساكنين يتم التخلص من
+
+275
+00:23:56,070 --> 00:24:00,330
+التقاء الساكنين بإيش يا أخوات؟ بالضم نقول وعصوا
+
+276
+00:24:00,330 --> 00:24:05,920
+الرسول هنا نلاحظ أن واو اللين الساكنة حركت بالضم
+
+277
+00:24:05,920 --> 00:24:09,980
+نتخلص من التقاء الساكنين فقرأها وعصى والرسول
+
+278
+00:24:09,980 --> 00:24:14,600
+هذه هي حالات التخلص من التقاء الساكنين بالضم أو
+
+279
+00:24:14,600 --> 00:24:19,360
+بالفتح أو بالكسري متى يتم التخلص من التقاء
+
+280
+00:24:19,360 --> 00:24:25,010
+الساكنين بالكسري؟ طبعا على الأصل دائما إن في حالات 
+
+281
+00:24:25,010 --> 00:24:29,150
+حالات نتخلص من التقاء الساكنين بالفتح في حالتين و
+
+282
+00:24:29,150 --> 00:24:32,890
+بالضم أيضا في حالتين متى نتخلص من التقاء الساكنين
+
+283
+00:24:32,890 --> 00:24:37,410
+بالفتح؟ إذا 
+
+284
+00:24:37,410 --> 00:24:41,010
+كان 
+
+285
+00:24:41,010 --> 00:24:46,250
+الساكن الأول نون من النونين إذا كانت الساكن
+
+286
+00:24:46,250 --> 00:24:54,410
+الأول ميم ألف لا ميم في أول صورة العمران ألف لا ميم
+
+287
+00:24:54,410 --> 00:24:58,090
+الله لا إله إلا هو الحي القيوم أما بالنسبة للتخلص 
+
+288
+00:24:58,090 --> 00:25:01,810
+من التقاء الساكنين بالضم نتخلص منها في حالتين
+
+289
+00:25:01,810 --> 00:25:05,410
+الحالة الأولى ما هي؟ في الحالة الأولى إذا كان الساكن
+
+290
+00:25:05,410 --> 00:25:08,250
+الأول الذي هو واو اللينية
+
+291
+00:25:10,990 --> 00:25:19,170
+الحالة الثانية إذا كانت ميم الجماعة مثل تجري من 
+
+292
+00:25:19,170 --> 00:25:25,400
+تحتهم الأنهار فنقيل أن نقول تجري من تحتهم الأنهار
+
+293
+00:25:25,400 --> 00:25:30,780
+كيف نقرأها؟ نتخلص من التقاء الساكنين بالضم فنقول 
+
+294
+00:25:30,780 --> 00:25:36,900
+تجري من تحتهم الأنهار إذا تجري من تحتهم الأنهار هي
+
+295
+00:25:36,900 --> 00:25:40,660
+الحالة الثانية من حالات التخلص من التقاء الساكنين
+
+296
+00:25:40,660 --> 00:25:46,740
+بالضم فنقول تجري من تحتهم الأنهار كذلك في قول
+
+297
+00:25:46,740 --> 00:25:53,630
+تعالى ثم رددنا لكم الكرة عليهم لا نقول لكم الكرة
+
+298
+00:25:53,630 --> 00:26:01,150
+عليهم بل نقول ثم رددنا لكم الكرة عليهم لكم الكرة 
+
+299
+00:26:01,150 --> 00:26:06,190
+عليهم ثم رددنا لكم الكرة عليهم الميم ما لها 
+
+300
+00:26:06,190 --> 00:26:11,430
+مضمومة هي في الأساس ما لها ساكنة لكن لأنها ميم
+
+301
+00:26:11,430 --> 00:26:17,460
+الجماعة ساكنة والحرف الذي يليه في كلمة ثانية ساكنة
+
+302
+00:26:17,460 --> 00:26:24,000
+الذي هو التاء تخلصنا من التقاء الساكنين بالضم هذه هي
+
+303
+00:26:24,000 --> 00:26:28,160
+حالات التخلص من التقاء الساكنين سواء كان بالحرف أو
+
+304
+00:26:28,160 --> 00:26:33,350
+كان حرف مد أو بالتحريك أو كان الساكن الأول يعني نون
+
+305
+00:26:33,350 --> 00:26:37,610
+من النونين بالتحريك بالكسرة وهو على الأصل أو
+
+306
+00:26:37,610 --> 00:26:43,590
+بالفتحة لو كان نون من النونين أو ميم ألف لا ميم في 
+
+307
+00:26:43,590 --> 00:26:47,550
+أول صورة العمران التي تليها ألف لا ميم الله لا إله
+
+308
+00:26:47,550 --> 00:26:51,570
+إلا هو الحي القيوم أو بالضم عندما .. إذا جاء
+
+309
+00:26:51,570 --> 00:26:56,270
+الساكن الأول الواو اللينية أو التي هي ميم التي هي
+
+310
+00:26:56,270 --> 00:26:59,490
+للجماعة هذه هي حالات التخلص من التقاء الساكنين
+
+311
+00:26:59,490 --> 00:27:05,230
+كلها لكن في أحيان يعني يجوز التقاء الحرفين ساكنين
+
+312
+00:27:05,230 --> 00:27:09,830
+في كلمة واحدة سواء كان في أولها أو في آخرها أو
+
+313
+00:27:09,830 --> 00:27:14,570
+في نصفها يعني ممكن يكون حرفين ساكنين في آخر الكلمة
+
+314
+00:27:14,570 --> 00:27:21,850
+مثال ذلك الحمد لله رب العالمين العالمين الياء هنا
+
+315
+00:27:21,850 --> 00:27:26,350
+في آخر الكلمة الياء ساكنة لأن الحرف الذي قبلها ساكن وجبل 
+
+316
+00:27:26,350 --> 00:27:32,890
+مكسور والنون ساكنة سكونا معارضا فنقول الحمد 
+
+317
+00:27:32,890 --> 00:27:39,010
+لله رب العالمين بهذا الشكل يعني التقاء ساكنين في
+
+318
+00:27:39,010 --> 00:27:43,570
+آخر كلمة في كلمة واحدة يجوز العالمين هنا مثلا 
+
+319
+00:27:43,570 --> 00:27:48,610
+فعليهم يعبدوا رب هذا البيت البيت يعني هنا البيت حرف
+
+320
+00:27:48,610 --> 00:27:53,540
+الياء اسمها لينية أم مادية؟ إذا حرف المد لو كان
+
+321
+00:27:53,540 --> 00:27:59,240
+ليني أو حرف مد سواء العالمين أو اليالي هي اللينية 
+
+322
+00:27:59,240 --> 00:28:03,800
+بنفع تكون ساكنة و وراها حرف ساكن في نهاية الكلمة
+
+323
+00:28:03,800 --> 00:28:09,290
+فهذا يجوز أو كان مثلا ليس حرف مد يعني هنا يجوز 
+
+324
+00:28:09,290 --> 00:28:13,070
+التقاء حرفين ساكنين في كلمة واحدة وقفا ويبقى
+
+325
+00:28:13,070 --> 00:28:18,010
+الحرفان ساكنان أو يبقى الحرفان ساكنين سواء كان
+
+326
+00:28:18,010 --> 00:28:23,390
+الساكن الأول حرف مد أو حرف لين أو ساكن صحيحا مثل 
+
+327
+00:28:23,390 --> 00:28:29,840
+والفجر في قوله والفجر ما هما الحرفين الساكنين؟ الجيم
+
+328
+00:28:29,840 --> 00:28:34,620
+والراء والفجر طبعا في حالة الوقف عليها .. في حالة
+
+329
+00:28:34,620 --> 00:28:39,440
+الوقف والفجر إيه؟ في حالة الوقف والفجر الجيم ساكنة 
+
+330
+00:28:39,440 --> 00:28:44,100
+والراء ساكنة يعني يجوز في آخر الكلمة أو عشر وليالي
+
+331
+00:28:44,100 --> 00:28:47,940
+عشر برضه نفس الموضوع الشين ساكنة والراء ساكنة 
+
+332
+00:28:47,940 --> 00:28:54,660
+والشفعي والوتر برضه التاء ساكنة وراء ساكنة يجوز التقاء
+
+333
+00:28:54,660 --> 00:28:59,540
+الساكنين في آخر الكلمة يجوز وفي أول الكلمة برضه
+
+334
+00:28:59,540 --> 00:29:03,880
+يجوز لو كان في عندنا ساكنين في أول الكلمة أيضا يجوز
+
+335
+00:29:03,880 --> 00:29:11,240
+مثال ذلك في أول الكلمة هنا مثلا قوله الآن
+
+336
+00:29:11,240 --> 00:29:18,920
+وقد كنتم به تستعجلون عندنا حرف مد الألف وهو ساكن
+
+337
+00:29:18,920 --> 00:29:22,680
+الذي هو مثلا يعني عندنا هذا يسمى الذي هو المادة
+
+338
+00:29:22,680 --> 00:29:28,160
+اللازمة الكلام أيه؟ مفقه أم مخفف؟ مد لازم كلمي 
+
+339
+00:29:28,160 --> 00:29:33,300
+مخفف واحنا كذلك أخذنا هو مد الفرق وأصله عندنا هو 
+
+340
+00:29:33,300 --> 00:29:39,760
+حرف مد وحرف المد حرف ساكن الآن
+
+341
+00:29:39,760 --> 00:29:45,040
+واللام حرف ساكنة يعني يجوز التقاء حرفين ساكنين في 
+
+342
+00:29:45,040 --> 00:29:51,850
+أول الكلمة عندنا الألف حرف مد ساكن واللام حرف مد
+
+343
+00:29:51,850 --> 00:29:56,270
+ساكن قد يخطئ بعض الناس عندما نأتي نقول يعني في
+
+344
+00:29:56,270 --> 00:30:00,670
+هذه الكلمة فيظنوا بأن الحرف المطلوب هنا الألف الألف
+
+345
+00:30:00,670 --> 00:30:07,630
+انتهت الآن ويجف عليها طبعا لو جلنا الآن وجفنا
+
+346
+00:30:07,630 --> 00:30:13,330
+على الآن الحرف هذا حرف إيش بيكون أو مد إيش يسمى
+
+347
+00:30:13,330 --> 00:30:17,770
+مدٌّ عارض السكون مثلا لأنه جاء حرف المد قبل آخر حرف
+
+348
+00:30:17,770 --> 00:30:21,450
+الكلمة ساكن نتيجة الوقف عليه فالذي نريد احنا
+
+349
+00:30:21,450 --> 00:30:28,070
+ليس الألف الآن في هذه الكلمة التي هي الألف الآن كان
+
+350
+00:30:28,070 --> 00:30:33,820
+حركة من مدّها تست حركات لازم و نسميه مد لازم كلمي
+
+351
+00:30:33,820 --> 00:30:38,800
+مخفف لماذا مد لازم كلمي مخفف؟ لأنه جاء حرف المد و
+
+352
+00:30:38,800 --> 00:30:45,200
+جاء بعده حرف ساكن طيب لو جاء بعدها حرف مشدد يصير مد
+
+353
+00:30:45,200 --> 00:30:49,340
+لازم كلمي مثقل ما ناتي بكلمة فيها مد لازم كلمي
+
+354
+00:30:49,340 --> 00:30:55,060
+مثقل أنت 
+
+355
+00:30:55,060 --> 00:30:58,160
+نص الكلمة هي الحقه الإغريل هي الحقه 
+
+356
+00:31:02,240 --> 00:31:08,060
+مدّنا حرف المد لأنه جاء وراها حرف مش حرف مشدد ومن 
+
+357
+00:31:08,060 --> 00:31:13,240
+سمّيه مد لازم كله مثقل وهو نفسه ألحق أو أطام أو
+
+358
+00:31:13,240 --> 00:31:18,360
+أتحاجون أيضا نفس الموضوع بمعنى ممكن يأتي حرفان
+
+359
+00:31:18,360 --> 00:31:22,800
+ساكنين برضه في نص الكلمة إذا الحرفين الساكنين لو
+
+360
+00:31:22,800 --> 00:31:27,140
+جاءوا في آخر الكلمة أو أول الكلمة أو وسط الكلمة
+
+361
+00:31:27,140 --> 00:31:32,460
+ممكن أن يقع حرفان ساكنان وننطقهم زي مثلا كما قلنا
+
+362
+00:31:32,460 --> 00:31:38,080
+مثلا المستقيم الحمد لله رب العالمين الياء والنون
+
+363
+00:31:38,080 --> 00:31:44,350
+في آخر الكلمة أو في أول كلمة مثلا الآن حرفين
+
+364
+00:31:44,350 --> 00:31:49,050
+ساكنين في أول كلمة تقع أو في وسط الكلمة مثلا
+
+365
+00:31:49,050 --> 00:31:52,110
+الطامة 
+
+366
+00:31:52,110 --> 00:31:58,170
+هي حرف مد وحرف م يعني ساكن أيضا يسمى أيضا إيه
+
+367
+00:31:58,170 --> 00:32:02,270
+يعني حرفان ساكنان إذا الحرفان الساكنان لو وقعا في 
+
+368
+00:32:02,270 --> 00:32:05,070
+كلمة واحدة سواء كان في الأول أو في الآخر أو في
+
+369
+00:32:05,070 --> 00:32:09,290
+المنتصف ما فيش إنحكان فيها أنهم نقرأهم صحيح بنسمي مد 
+
+370
+00:32:09,290 --> 00:32:13,050
+لازم كلمي مخفف أو مد لازم كلمي مثقل أو مد عارض
+
+371
+00:32:13,050 --> 00:32:17,690
+السكون أو مد لين مش مشكلة لكن بالنسبة للو وقع بين
+
+372
+00:32:17,690 --> 00:32:20,890
+كلمتين يقع ساكنين في الكلمتين هذا الذي نحن نتخلص
+
+373
+00:32:20,890 --> 00:32:25,150
+منه أما بالحرف لو كان الساكن الأول حرف مد أو
+
+374
+00:32:25,150 --> 00:32:29,970
+بالتحريك بالكسر على الأصل أو بالفتحي في حالتين أو
+
+375
+00:32:29,970 --> 00:32:35,090
+بالضم كما يعني أخذناها سابقا وبهذا احنا يعني أنهينا
+
+376
+00:32:35,090 --> 00:32:38,810
+موضوع حكم التقاء الساكنين ونكمل إن شاء الله في
+
+377
+00:32:38,810 --> 00:32:42,990
+اللقاء القادم مع موضوع جديد بارك الله فيكم والسلام
+
+378
+00:32:42,990 --> 00:32:44,270
+عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_postprocess.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bc03bb9921403e8772ebdbc44b030389b4750f83
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_postprocess.srt
@@ -0,0 +1,1512 @@
+1
+00:00:11,740 --> 00:00:14,900
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,900 --> 00:00:19,400
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+3
+00:00:19,400 --> 00:00:22,800
+آله وصحابه وسلم موضوعنا اليوم يا أخوات هو حكم
+
+4
+00:00:22,800 --> 00:00:27,980
+التقاء الساكنين طبعا المقصود بهذا العنوان أن هناك
+
+5
+00:00:27,980 --> 00:00:32,170
+كلمتينأ الكلمة الأخيرة أخرها حرف ساكن والكلمة
+
+6
+00:00:32,170 --> 00:00:37,390
+الثانية حرف ساكن عندما نطني اتصالان الكلمتان مع
+
+7
+00:00:37,390 --> 00:00:41,030
+بعضهم البعض ما هو حكم التقاء الساكنين يعني إذا
+
+8
+00:00:41,030 --> 00:00:45,240
+التقت ساكنان أو حرفان ساكنان في كلمتينولا يكونوا
+
+9
+00:00:45,240 --> 00:00:49,500
+التقائهم إلا حالة الوصلة فلابد من التخلص من التقاء
+
+10
+00:00:49,500 --> 00:00:54,320
+الساكنين إما بالحذف لو كان الساكن الأول حرف مد
+
+11
+00:00:54,320 --> 00:00:58,900
+وإما بالتحريك سواء كان بالكسرة على الأصل أو الفتح
+
+12
+00:00:58,900 --> 00:01:03,830
+أو الضم لو لم يكن الساكن الأول حرف مدإذا حكم
+
+13
+00:01:03,830 --> 00:01:08,770
+التقاء الساكنين بمعنى إن إذا التقى حرفان ساكنان في
+
+14
+00:01:08,770 --> 00:01:13,510
+كلمتين ولا يكونوا التقائهم إلا حالة الواصلة لابد
+
+15
+00:01:13,510 --> 00:01:17,530
+أن نتخلص من التقاء الساكنين إما بالحدث مات نتخلص
+
+16
+00:01:17,530 --> 00:01:21,730
+من التقاء الساكنين بالحدث لو كان الساكن الأول حرف
+
+17
+00:01:21,730 --> 00:01:26,090
+مدأما إذا لم يكن الساكن الأول حرف مد في كلمتين
+
+18
+00:01:26,090 --> 00:01:31,050
+نتخلص من اتقاء الساكنين إما بالكسري على الأصل و
+
+19
+00:01:31,050 --> 00:01:36,990
+إما بالتحريك بالفتحة أو بالضمة أيضا بحالات معدودة
+
+20
+00:01:36,990 --> 00:01:40,190
+كما ناخد أما بالنسبة للتخلص من اتقاء الساكنين
+
+21
+00:01:40,190 --> 00:01:45,670
+بالحرف فهنا إذا كان الساكن الأول حرف مد والساكن
+
+22
+00:01:45,670 --> 00:01:49,810
+الثاني في الكلمة الثانية حرف يعني ليس مدا نتخلص من
+
+23
+00:01:49,810 --> 00:01:54,680
+اتقاء الساكنين بإيه بالحرفإذا متى نتخلص من التقاء
+
+24
+00:01:54,680 --> 00:01:59,660
+الساكنين يا أخوات؟ نتخلص
+
+25
+00:01:59,660 --> 00:02:03,540
+من التقاء الساكنين بالحرف إذا كان الساكن الأول حرف
+
+26
+00:02:03,540 --> 00:02:08,960
+مد. مثال ذلك قول تعالى فلمّا ذا قاء الشجرة ثقيلة
+
+27
+00:02:08,960 --> 00:02:14,700
+أن نقول فلمّا ذا قاء الشجرة بدت لهم سوئاتهم إنما
+
+28
+00:02:14,700 --> 00:02:21,050
+نقرأها فلمّا ذا قى الشجرةفلمّا ذاق الشجرة الالف
+
+29
+00:02:21,050 --> 00:02:27,150
+هنا حذفت لنتيجة التقاء الساكن هنا الالف ذاق ساكنة
+
+30
+00:02:27,150 --> 00:02:34,190
+و الشجرة حرف الشين أيضا ساكن بالنسبة للحمزة أ هي
+
+31
+00:02:34,190 --> 00:02:40,270
+أصلا الشجرة الحمزة تتأل طبعا هنا الحمزة تنوصل تحذف
+
+32
+00:02:40,900 --> 00:02:46,300
+واللام في قلة التعليف تضغم مع الشين فبصير اشق
+
+33
+00:02:46,300 --> 00:02:51,340
+الشجرة فلا اللام تظهر ولا الهمزة بتظهر فنقراها
+
+34
+00:02:51,340 --> 00:02:57,540
+فلما ذاق الشجرة الالف حولي فتعت ذاقا الهمزة الواصل
+
+35
+00:02:57,540 --> 00:03:01,580
+أصلا محدوثة على الواصل حكم اللام الساكنة في قلة
+
+36
+00:03:01,580 --> 00:03:05,880
+التعليف مع الشين لأنها من حروف الإضغاماللي هى
+
+37
+00:03:05,880 --> 00:03:09,060
+سموها اللام الشمسية تبدأ قبل ما عشرين فعندما
+
+38
+00:03:09,060 --> 00:03:15,060
+نقرأها نقول فلمّا ذاقش شجرة ذاقش شجرة يبقى الألف
+
+39
+00:03:15,060 --> 00:03:21,080
+طبعا محلفة مثال آخر كذلك في قول تعالى واذ قالوا
+
+40
+00:03:21,080 --> 00:03:28,240
+اللهم واذ قالوا اللهم أين الحرف اللى حُذفه طبعا
+
+41
+00:03:28,240 --> 00:03:37,310
+هنقول واذ قالوا اللهم حرف المد ماله؟حرف المادة
+
+42
+00:03:37,310 --> 00:03:43,630
+الواو ساكن وهنا اللهم اللام أيضا ساكنة نتيجة
+
+43
+00:03:43,630 --> 00:03:58,810
+انتقاء الساكنين اللهم اللهم اللهم
+
+44
+00:03:58,810 --> 00:04:01,930
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+45
+00:04:01,930 --> 00:04:02,010
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+46
+00:04:02,010 --> 00:04:02,030
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+47
+00:04:02,030 --> 00:04:02,970
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+48
+00:04:02,970 --> 00:04:02,990
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+49
+00:04:02,990 --> 00:04:05,720
+اللهم اللهم اللهموالتي لفظت هنا قالوا يعني اللام
+
+50
+00:04:05,720 --> 00:04:11,500
+المضمومة وإذ قالوا اللهم فحقوا واللام طبعا تظهر
+
+51
+00:04:11,500 --> 00:04:16,060
+وهنا عندما ننظر إلى القراءة نقول وإذ قالوا اللهم
+
+52
+00:04:16,060 --> 00:04:22,020
+في عندنا و ال جماعة تقولوا وفي عندنا كذلك الألف
+
+53
+00:04:22,020 --> 00:04:27,440
+هنا ماذا نسميه هذا الألف ألف الفارقة التي تفرق ما
+
+54
+00:04:27,440 --> 00:04:31,580
+بين و الجماعة و و الكلمة وإذ قالوا هذا تكتب ولا
+
+55
+00:04:31,580 --> 00:04:35,440
+تلفظتكتب ولا تلفظ لا حالة الوصن ولا حالة الوقف
+
+56
+00:04:35,440 --> 00:04:39,460
+نقول واذ قالوا لا نقول واذ قالوا وا فالمقصود
+
+57
+00:04:39,460 --> 00:04:43,820
+بالألف هنا ليس الألف اللي هي هذه الصغيرة التي تكتب
+
+58
+00:04:43,820 --> 00:04:48,300
+ولا تلفظ وإنما المقصود بها واو الجماعة واذ قالوا
+
+59
+00:04:48,690 --> 00:04:53,530
+والهمزة اللي هنا تعطي اللهم همزة الوصل واللام مع
+
+60
+00:04:53,530 --> 00:04:58,750
+اللام تدغم يعني من حرف الإدغام فتلفظ لاما واحدة
+
+61
+00:04:58,750 --> 00:05:04,210
+مشددة لأن معنى الإدغام إدخال حرف زاكن بحرف متحرك
+
+62
+00:05:04,210 --> 00:05:09,810
+بحيث يصيران حرفا واحدة مشددة إذا الذي يرفض هنا وإذ
+
+63
+00:05:09,810 --> 00:05:17,530
+قالوا اللهم من يقرأها بحرف حرف الواو؟ اه فضلي
+
+64
+00:05:20,200 --> 00:05:25,200
+أحسنتي واذ قالوا اللهم لا نقول واذ قالوا اللهم
+
+65
+00:05:25,200 --> 00:05:30,480
+لماذا لنا ثقيلة على اللسان ثقيلة أن نقول واذ قالوا
+
+66
+00:05:30,480 --> 00:05:35,520
+اللهم إنما هنا نتيجة ارتقاء الساكنين فلمّا كان
+
+67
+00:05:35,520 --> 00:05:40,830
+الساكن الأول وهو ال wowحرف مد يُحذف حرف المد،
+
+68
+00:05:40,830 --> 00:05:44,610
+نتخلص من الإتقاء الساكنين بحذف حرف المد، اللذي
+
+69
+00:05:44,610 --> 00:05:49,470
+يظهر اللي هي الضمة وإذ قالوا اللهم إن كان هذا هو
+
+70
+00:05:49,470 --> 00:05:56,780
+الحق من عندككذلك مثال آخر وفي الأرض آيات للموقنين
+
+71
+00:05:56,780 --> 00:06:01,300
+طبعا ثقيل على اللسان أن نقرأها وفي الأرض كيف
+
+72
+00:06:01,300 --> 00:06:06,740
+نقرأها؟ وفي الأرض آيات للموقنين وفي الأرض آيات
+
+73
+00:06:06,740 --> 00:06:13,030
+للموقنين وفي الأرض وفي الأرض أين الحرف المحذوف؟حرف
+
+74
+00:06:13,030 --> 00:06:18,950
+اليا لا نقول وفي الأرض نقول وفي الأرض يعني عندنا
+
+75
+00:06:18,950 --> 00:06:24,270
+حرفان ساكنان في كلمتين حرف اليا في كلمة في آخر
+
+76
+00:06:24,270 --> 00:06:29,090
+الكلمة وحرف الأرض اللام هذه اللام ساكنة لان تظهر
+
+77
+00:06:29,090 --> 00:06:33,690
+مع الهمزة فنتيجة التقاء الساكنين نتخلص من التقاء
+
+78
+00:06:33,690 --> 00:06:37,550
+الساكنين بالحذف لماذا تخلصنا من التقاء الساكنين
+
+79
+00:06:37,550 --> 00:06:43,590
+بالحذف لأن الساكن الأولحرف مد، صحيح، إذا تخلصت من
+
+80
+00:06:43,590 --> 00:06:47,410
+التقرأة الساكنة، عندما نقرأها، لا نقول وفي الأرض،
+
+81
+00:06:47,410 --> 00:06:51,790
+لأنها بتكون ثقيلة على اللسان، كيف نقرأها؟ وفي
+
+82
+00:06:51,790 --> 00:06:56,890
+الأرض آيات، وفي الأرضي، لا نقول وفي الأرض، يعني
+
+83
+00:06:56,890 --> 00:07:01,150
+يحذف حرف المد هناك في حالة الواصلة، أما إذا وقفنا
+
+84
+00:07:01,150 --> 00:07:06,050
+عليه فيثبت لثبوته في رسم المصحفلو واحدة مثلا وقفت
+
+85
+00:07:06,050 --> 00:07:11,490
+عند كلمة وفي طبعا سواء كان اختبارا او اضطرارا يعني
+
+86
+00:07:11,490 --> 00:07:16,530
+انقطع النفس فوقفت عند كلمة وفي بنرفضها او من باب
+
+87
+00:07:16,530 --> 00:07:21,430
+الاختبار يعني كيف يكون من باب الاختبار؟ يعني الأخت
+
+88
+00:07:21,430 --> 00:07:27,390
+مثلا قالت وفي الأرض آيات للموقنين فقلت لها لو سمحت
+
+89
+00:07:27,390 --> 00:07:33,770
+قفى عند كلمة الأرضاختبارا إذا أرى كيف تقف على كلمة
+
+90
+00:07:33,770 --> 00:07:40,770
+وفي فتقول وفي طب ينفع نقرأها تقرأ تكمل الأيات تقول
+
+91
+00:07:40,770 --> 00:07:45,210
+الأرض آيات للموقنين طبعا ليه صح عليها ترجع كلمة أو
+
+92
+00:07:45,210 --> 00:07:48,990
+كلمتين فتقول وفي الأرض آيات للموقنين
+
+93
+00:07:51,620 --> 00:07:56,400
+طيب هذا اللي هو التخلص من اتقاء الساكنين بالحدث لو
+
+94
+00:07:56,400 --> 00:08:02,540
+كان الساكن الأول حرف مد اما اذا كان حرف المد غير
+
+95
+00:08:02,540 --> 00:08:06,180
+ثابت في رسم المصحف في الرسم المصحف الرسم العثماني
+
+96
+00:08:06,180 --> 00:08:11,760
+نجد انه بعض الكلمات فيها حرف مد غير ثابت هذا حرف
+
+97
+00:08:11,760 --> 00:08:16,240
+المد غير ثابت اما اذا كان حرف المد غير ثابت يعني
+
+98
+00:08:16,240 --> 00:08:20,390
+لا يكتب في رسم المصحفلعلة ابتقاء الساكنين فيكون
+
+99
+00:08:20,390 --> 00:08:25,330
+حدفه وصلا ووقفا يعني يحذف وصلا ووقفا لو وقفنا
+
+100
+00:08:25,330 --> 00:08:33,290
+عليها نقول وفي هنا مثلا ارنكي فتوحيووصلا قرنا كيف
+
+101
+00:08:33,290 --> 00:08:38,790
+تحيي الموتى محروف وصلا وكذلك وقفا الكلمة اللتي سوف
+
+102
+00:08:38,790 --> 00:08:43,750
+نراها هنا كيف تحيي الموتى هي أصلا تحيي في رسم
+
+103
+00:08:43,750 --> 00:08:47,390
+المصحف هذه ياء واحدة والياء الثانية ياء بتسموها
+
+104
+00:08:47,390 --> 00:08:51,210
+الياء الكوفية غير موجودة في رسم المصحف لكن هنا في
+
+105
+00:08:51,210 --> 00:08:55,490
+حسب المصحف المساعد يعني مكتوب دياء تاني لكن في
+
+106
+00:08:55,490 --> 00:09:02,980
+الرسم العثماني موجودة تحيي و بعدينما بيسموها اليأ
+
+107
+00:09:02,980 --> 00:09:10,540
+الكوفية وهي طول فضو ولا تكتب فنقراها تحي الموتة
+
+108
+00:09:10,540 --> 00:09:17,660
+إذا وصلناها كيف نقراها؟ هنا واذ قال إبراهيم ربي
+
+109
+00:09:17,660 --> 00:09:22,800
+أرني كيف تحي الموتة أرني كيف تحي الموتة يأ واحدة
+
+110
+00:09:22,800 --> 00:09:27,100
+اليأ الثانية هنا ماذا يصير فيها؟ تحدف لماذا حدفت؟
+
+111
+00:09:27,960 --> 00:09:32,020
+تخلصها من التقاء الساكنين لو وقفنا عليها نلفظ
+
+112
+00:09:32,020 --> 00:09:34,520
+الياء الأولى وليس الياء الثاني لأن الياء الثاني
+
+113
+00:09:34,520 --> 00:09:41,340
+محذوفة يعني محذوفة في رسم المصحف نقول كيف تحيي لكن
+
+114
+00:09:41,340 --> 00:09:45,620
+لو وصلناها كيف تحيي الموتى كذلك في قول تعالى قال
+
+115
+00:09:45,620 --> 00:09:52,280
+من يحيي العظام و هي رميم قال من يحيي العظام يعني
+
+116
+00:09:52,280 --> 00:09:58,170
+ياء أولىهذا بالنسبة للتخلص من التقاء الساكنين
+
+117
+00:09:58,170 --> 00:10:02,870
+بالحذف متى نتخلص من التقاء الساكنين بالحذف لو كان
+
+118
+00:10:02,870 --> 00:10:07,890
+الساكن الأول حرف مجد الحرف الثاني يا أخوات هو
+
+119
+00:10:07,890 --> 00:10:11,650
+التخلص من التقاء الساكنين بالتحريك ماذا نقصد
+
+120
+00:10:11,650 --> 00:10:19,270
+بالتحريك؟يا تحريكها فتحة أو ضمة أو الكسرة الأصل أن
+
+121
+00:10:19,270 --> 00:10:23,190
+يتم التخلص من التقاء الساكنين بالتحريك بالكسر وهذا
+
+122
+00:10:23,190 --> 00:10:27,870
+هو على الأصل دائما تتخلص من التقاء الساكنين بالكسر
+
+123
+00:10:27,870 --> 00:10:32,030
+والأمثلة على ذلك كثيرة لكن بالنسبة لغير الكسر
+
+124
+00:10:32,030 --> 00:10:36,910
+بحالات محدودة نرى هنا مثلا قل ادعو الله او ادعو
+
+125
+00:10:36,910 --> 00:10:43,060
+الرحمن قل ادعوالمثال اللي عندنا قل ادعو هنا قل
+
+126
+00:10:43,060 --> 00:10:48,860
+ادعو اللام ساكنة فعل أمر مجزمهم بالسكون قل ادعوا
+
+127
+00:10:48,860 --> 00:10:53,700
+الدال ساكنة هنا طبعا الهمس الوصل في حالة الوصل
+
+128
+00:10:53,700 --> 00:11:01,140
+تسقطفالساكنين اللام الساكنة قل و ادعو الدال ساكنة
+
+129
+00:11:01,140 --> 00:11:06,480
+نتخلص من التقاء الساكنين بالتحريك بالكسر فنقول قل
+
+130
+00:11:06,480 --> 00:11:12,460
+ادعو الله قل ادعو قل ادعو الله او ادعو الرحمن
+
+131
+00:11:12,460 --> 00:11:20,460
+فاللام هنا مكسورة هي أصلا ساكنة قل بس عندما نصلها
+
+132
+00:11:20,460 --> 00:11:26,600
+نقرأها قل ادعو بالكسر كذلك قوله تعالىو قالت أخرج
+
+133
+00:11:26,600 --> 00:11:33,740
+عليهن و قالت طبعا فعل ماضي يعني ساكن قالت تانيت
+
+134
+00:11:33,740 --> 00:11:39,200
+ساكنة قالت أخرج عليهن حرف الخ ساكن طبعا أخرج
+
+135
+00:11:39,200 --> 00:11:45,410
+الهمزة اللي هناتسمى همزة وصل لنقاها وقال تخرج
+
+136
+00:11:45,410 --> 00:11:49,970
+عليهم طبعا الفعل الماضي خرج الفعل الأمر من خرجه
+
+137
+00:11:49,970 --> 00:11:54,930
+أخرج فهنا أمر الثلاثي وهمزة الأمر الثلاثي زي اضرب
+
+138
+00:11:54,930 --> 00:12:00,530
+همزة وهمزة وصل تسقط حالة الوصل وتثبت حالة اللي
+
+139
+00:12:00,530 --> 00:12:04,210
+ابتدأوا بيها لو ابتدأنا بيها إيه بتثبت نقول أخرج
+
+140
+00:12:04,860 --> 00:12:09,220
+لكن لو وصلناها قالت أخرج عليهن فالخى هي التي تظهر
+
+141
+00:12:09,220 --> 00:12:16,120
+عندما نقول قالت أخرج أنا ساكنين أستا ساكنة و الخى
+
+142
+00:12:16,120 --> 00:12:19,860
+ساكنة نتخلص من تقراء الساكنين بالتحريك بالكسر
+
+143
+00:12:19,860 --> 00:12:25,300
+نقرأها قالت أخرج عليهن قالت مكسورة قالت أخرج عليهم
+
+144
+00:12:25,300 --> 00:12:32,940
+كذلك في قول تعالى و لقد استهزئ و لقد أين السكون
+
+145
+00:12:33,940 --> 00:12:39,660
+عدان قاعدين استهزئة .. إيه ال .. استهزئة حرف الصين
+
+146
+00:12:39,660 --> 00:12:44,040
+ساكن ما تخلص من التقاء الساكنين بال .. بالكسري
+
+147
+00:12:44,040 --> 00:12:49,660
+فنقول ولا قد استهزئة .. ولا قد استهزئة ما تخلص من
+
+148
+00:12:49,660 --> 00:12:53,780
+التقاء الساكنين بالكسري وهذا طبعا أخوات على الأصلي
+
+149
+00:12:54,340 --> 00:12:59,100
+و ممكن يكون أيضا التنوين يعني قد يكون الساكن الأول
+
+150
+00:12:59,100 --> 00:13:03,600
+تنوين سواء كان تنوين ضام أو تنوين كسر والساكن
+
+151
+00:13:03,600 --> 00:13:07,440
+الثاني متحرر يعني ساكن في الكلمة الثانية التنوين
+
+152
+00:13:07,440 --> 00:13:14,460
+هو أصلا نون ساكنة مثلا عندما نقول هنا إن زيّن سماء
+
+153
+00:13:14,460 --> 00:13:19,400
+الدنيا بزينات الكواكب هي أصلا بزيناتزينا تن
+
+154
+00:13:19,400 --> 00:13:22,700
+التنوين هذا عبارة عن نون ساكنة نقول بزينا تن
+
+155
+00:13:22,700 --> 00:13:29,060
+الكواكب لكنها ثقيلة أن نقول بزينا تن الكواكب نتخلص
+
+156
+00:13:29,060 --> 00:13:33,040
+من التقاء الساكنين بالكسر يعني يكسر التنوين اللي
+
+157
+00:13:33,040 --> 00:13:39,630
+هو نونأصلا بزيناتن هو صحيح تنوين لكنه يرفض نون
+
+158
+00:13:39,630 --> 00:13:44,030
+ساكنة لذلك في عيننا أحكام النون الساكنة والتنوين
+
+159
+00:13:44,030 --> 00:13:48,170
+لأن التنوين هو أخو النون الساكنة فنقول بزيناتن
+
+160
+00:13:48,170 --> 00:13:54,710
+الكواكب فتقيل أن نقول بزيناتن الكواكب فالتنوين
+
+161
+00:13:54,710 --> 00:14:01,500
+نفسه اللي هي النون تكسر فنقول بزيناتن الكواكبوإن
+
+162
+00:14:01,500 --> 00:14:08,400
+زيننا السماء الدنيا بزيناتنا الكواكم بزيناتنا
+
+163
+00:14:08,400 --> 00:14:12,080
+الكواكم من يقراها بزيناتنا الكواكم؟
+
+164
+00:14:13,670 --> 00:14:19,090
+أيوة بزيناتين الكواكب حركنا التنوين التنوين يُلفظ
+
+165
+00:14:19,090 --> 00:14:24,890
+نون ساكنة فلما جاءت النون ساكنة ساكنة وجاء الكواكب
+
+166
+00:14:24,890 --> 00:14:28,790
+اللام برضه في الكواكب الساكنة تخلصنا من التقاء
+
+167
+00:14:28,790 --> 00:14:34,990
+الساكنين بالكسر في هذا المثال كذلك قد يكون الساكن
+
+168
+00:14:34,990 --> 00:14:39,570
+الأول اللي هو الياء اللينية ما هي الياء اللينية يا
+
+169
+00:14:39,570 --> 00:14:46,860
+أخوات؟ماش فيه عندنا حرفاء اللين و هما .. ما هما؟
+
+170
+00:14:46,860 --> 00:14:52,640
+تفضّال إيه؟ الألف الواو واليا الواو الساكنة
+
+171
+00:14:52,640 --> 00:14:55,420
+المفتوح ما قبلها واليا الساكنة المفتوح ما قبلها
+
+172
+00:14:55,420 --> 00:14:59,760
+فعندما نقول اليا اللينية يعني اليا الساكنة المفتوح
+
+173
+00:14:59,760 --> 00:15:04,280
+ما قبلهاإذا القاعدة عندنا قد يكون الساكن الأول هو
+
+174
+00:15:04,280 --> 00:15:09,120
+الياء اللينية والساكن الثاني هو ساكن الكلمة نتخلص
+
+175
+00:15:09,120 --> 00:15:13,500
+من اتقاء الساكنين بالكثر يعني الياء اللينية نكسرها
+
+176
+00:15:13,500 --> 00:15:19,520
+مثال ذلك هنا يا صاحبي السجن صاحبي الياء الساكنة
+
+177
+00:15:19,520 --> 00:15:24,440
+وقابلها مفتوح هي ياء مادية ولا ياء لينية؟ لماذا
+
+178
+00:15:24,440 --> 00:15:30,660
+لينية؟لأنها ساكنة قبلها مفتوح فتقرأ يا صاحبي فهنا
+
+179
+00:15:30,660 --> 00:15:38,170
+يا ساكنة يا اللينية و السجنالسين ساكنة نتخلص من
+
+180
+00:15:38,170 --> 00:15:42,510
+التقاء الساكنين بكسر الياء اللينية فنقول يا صاحبي
+
+181
+00:15:42,510 --> 00:15:48,110
+السجن صاحبي مكسورة صاحبي السجن إذا الياء اللي هنا
+
+182
+00:15:48,110 --> 00:15:53,670
+ياء لينية كسرناها لأنها ساكنة وجاملها مفتوح نكسر
+
+183
+00:15:53,670 --> 00:15:56,910
+الياء اللينية لأنها وقعت نتخلصنا من التقاء
+
+184
+00:15:56,910 --> 00:16:00,730
+الساكنين وكان الساكن الأول الياء اللينية فكيف
+
+185
+00:16:00,730 --> 00:16:02,010
+نقرأه؟ مين يقرأ ليها؟
+
+186
+00:16:07,890 --> 00:16:12,190
+حركنا الياء اللينية بالكسر مع أنها ياء لكننا
+
+187
+00:16:12,190 --> 00:16:16,950
+حركناها بالكسر لأنها ياء اللينية كذلك هنا في
+
+188
+00:16:16,950 --> 00:16:22,630
+المثال آخر إن ربك يعلم أنك تقوم أدنى من ثلثي الليل
+
+189
+00:16:22,630 --> 00:16:29,570
+ثلثي الليل ثلثي الياء هنا ساكنة وجابلها لامفتوحة
+
+190
+00:16:29,570 --> 00:16:33,890
+يبقى الياء اللينية وليس الياء الماديةوجات الساكنة
+
+191
+00:16:33,890 --> 00:16:38,710
+الأول هو يألينية و الليل اللامن اللي هنا ساكنة
+
+192
+00:16:38,710 --> 00:16:43,910
+نتخلص من التقاء الساكنين بالتحريك بالكسرة فنقول من
+
+193
+00:16:43,910 --> 00:16:50,050
+ثلثي الليل ثلثي ثلثي الليلي و نصفهم طيب يعني هنا
+
+194
+00:16:50,050 --> 00:16:58,320
+حركنا اليألينية بالكسرةهذا يا أخوات اللي هو التخلص
+
+195
+00:16:58,320 --> 00:17:02,140
+من التقاء الساكنين بالتحريك بالكسر وهذا يا بنات
+
+196
+00:17:02,140 --> 00:17:05,940
+على الأصل على الأصل ولا ما تتخلص من التقاء
+
+197
+00:17:05,940 --> 00:17:11,410
+الساكنين بالحرف عند أي حرفعند حرف المد نشوف الحالة
+
+198
+00:17:11,410 --> 00:17:16,150
+الثالثة التخلص من التقاء الساكنين بالفتح متى نتخلص
+
+199
+00:17:16,150 --> 00:17:20,350
+من التقاء الساكنين بالفتح طبعا هذا خلاف الأصل ولكن
+
+200
+00:17:20,350 --> 00:17:23,830
+في عندنا حالتين يعني متى نتخلص من التقاء الساكنين
+
+201
+00:17:23,830 --> 00:17:28,730
+بالفتح في حالتين الحال الأولى لو كان الساكن الأول
+
+202
+00:17:28,730 --> 00:17:35,150
+none من تحت حرف الجر none من الجر زي من المؤمنين
+
+203
+00:17:35,150 --> 00:17:42,240
+كيف نقرأ هذه؟من المؤمنين طيب إذا لو واحدة قرأتها
+
+204
+00:17:42,240 --> 00:17:46,700
+مثلا من المؤمنين نشوف ثقيلة على اللسان لذلك لا
+
+205
+00:17:46,700 --> 00:17:53,080
+تقرأ من المؤمنين رجال وإنما نقرأها من المؤمنين من
+
+206
+00:17:53,080 --> 00:17:58,220
+المؤمنين رجال صدقوا ما عاهدوا الله عليه من
+
+207
+00:17:58,220 --> 00:18:04,430
+المؤمنينهي أصلا من المؤمنين عشان نون من الجارة
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+208
+00:18:04,430 --> 00:18:09,670
+تخلصنا من التقاء الساكنين بالفتحة بس في حالتين
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+209
+00:18:09,670 --> 00:18:16,570
+معينتين الحالة الأولى من النون من الجارة ومثلا آخر
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+210
+00:18:16,570 --> 00:18:22,270
+أوفوا الكيلة ولا تكونوا من المخسرين من المخسرين
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+211
+00:18:22,270 --> 00:18:27,820
+أصلا من المخسرين أصلا هي ساكنةلكن تخلصنا من التقاء
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+212
+00:18:27,820 --> 00:18:33,680
+الساكنين بالفتحي لأن هذه نون من الجارة وهي الحالة
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+213
+00:18:33,680 --> 00:18:38,000
+الأولى من حالات التخلص من التقاء الساكنين بالفتحة
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+214
+00:18:38,000 --> 00:18:43,130
+يعني متى يتم التخلص من التقاء الساكنين بالفتحي؟في
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+215
+00:18:43,130 --> 00:18:47,430
+الحالة الأولى اللى هو ن من الجارة إذا كان الساكن
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+216
+00:18:47,430 --> 00:18:54,210
+الأول هو ن من الجارة نقرأها من المؤمنين من
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+217
+00:18:54,210 --> 00:19:01,360
+المخسرين و هكذا في كل حرف منثانيا يتم التخلص من
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+218
+00:19:01,360 --> 00:19:06,460
+التقاء الساكنين بالفتح لحالة ثانية عند التقاء
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+219
+00:19:06,460 --> 00:19:14,260
+الساكنين ميم ألف لا ميم نقراها ألف لا ميم الله في
+
+220
+00:19:14,260 --> 00:19:18,600
+حالة الواصل لكن لو وقفنا عليها ألف لا ميم نقف
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+221
+00:19:18,600 --> 00:19:25,690
+عليها بالماد اللازم الحرفي المخفف ميم هي ساكنةلو
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+222
+00:19:25,690 --> 00:19:35,150
+وصلناها نقرأها ألف لا ميم الله ميم الله نفتحها إذا
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+223
+00:19:35,150 --> 00:19:37,910
+في عندنا حالتين بس في هذا الموضوع في كل المصحف
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+224
+00:19:37,910 --> 00:19:42,390
+لأنه يعني ألف لا ميم و بعدها ساكن في حالة الواصل
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+225
+00:19:42,390 --> 00:19:51,470
+ألف لا ميم الله لا إله إلا هو الحي القيوم إذا هنا
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+226
+00:19:51,470 --> 00:19:57,690
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+227
+00:19:57,690 --> 00:20:02,990
+التخلص من اتقاء الساكنين بالفتحة؟ فضلا أخت نون من
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+228
+00:20:02,990 --> 00:20:09,850
+الجارة والحالة التانية؟إذا كان الساكن أول هي ميم
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+229
+00:20:09,850 --> 00:20:14,870
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+230
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+لا ميم الله لا إله إلا هو الحي القيوم هذا بالنسبة
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+231
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+232
+00:20:24,230 --> 00:20:27,850
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+233
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+234
+00:20:32,500 --> 00:20:38,580
+عندنا أيضا حالتين الحالة الأولى بتخلص منها إذا كان
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+235
+00:20:38,580 --> 00:20:43,540
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+236
+00:20:43,540 --> 00:20:49,400
+اللينية يعني واو ساكنة جامدها مفتوح هي الجمة زي ما
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+237
+00:20:49,400 --> 00:20:52,260
+قلنا التخلص من التقاء الساكنين بالكسر لو كانت
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+238
+00:20:52,260 --> 00:20:56,170
+الياء اللينية الساكن الأول الياء اللينيةهنا نتخلص
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+239
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+240
+00:20:59,990 --> 00:21:05,010
+الواو اللينية التي هي للجمع مثال ذلك و أقاموا
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+241
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+242
+00:21:13,990 --> 00:21:19,030
+أصلها و آتوا الذكاء و آتوا الذكاء فقيلة على اللسان
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+243
+00:21:19,030 --> 00:21:24,670
+أن نقرأها و آتوا الذكاءكيف بنعمل؟ نتخلص من التقاء
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+244
+00:21:24,670 --> 00:21:31,450
+الساكنين بالضم فنقول و آتوا الذكاء هنا و آتوا و
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+245
+00:21:31,450 --> 00:21:36,650
+ساكن الأصل طبعا لا تنظر إلى الضم اللي هنا لأنه
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+246
+00:21:36,650 --> 00:21:42,210
+بيرسمون ليها على حسب الوصليلكن هي في الأساس هى wow
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+247
+00:21:42,210 --> 00:21:46,250
+ساكنة جابتها مفتوح وهى wow الجماعة وتسمى ال wow
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+248
+00:21:46,250 --> 00:21:52,050
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+249
+00:21:52,050 --> 00:21:57,130
+الصلاة و آتوا الزكاة و آتوا ال wow مضمومة طبعا يا
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+250
+00:21:57,130 --> 00:22:03,860
+أخوات الألف اللى هنا تسمى ألف إيش؟الفارقة تكتب ولا
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+251
+00:22:03,860 --> 00:22:08,160
+تلفظ لا وصلا ولا وقفا ويوضع فوقها في رسم المصحف
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+252
+00:22:08,160 --> 00:22:14,220
+الصفر المستدير معناته أن هذا الحرف يكتب لكنها لا
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+253
+00:22:14,220 --> 00:22:18,180
+يرفض لا في حالة الوصل ولا في حالة الوقف يعني لو
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+254
+00:22:18,180 --> 00:22:23,700
+أقفنا على كلمة و آتوا بس
+
+255
+00:22:23,700 --> 00:22:28,140
+لا نقول و آتواكذلك يعني هنا و قاتى و الذكى الألف
+
+256
+00:22:28,140 --> 00:22:31,840
+اللي هنا أولف الفارقة تسقط طبيعي لا تلفظ الألف
+
+257
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+الثاني بتاعة الذكى هي أل التعريف همس الوصل بتسقط
+
+258
+00:22:37,040 --> 00:22:40,240
+في حال الوصل لو ابتدأنا بيها الكلام و قولنا
+
+259
+00:22:40,240 --> 00:22:44,280
+الذكاها الذكاها لفظناها لأنه إذا ابتدأنا بهمس
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+260
+00:22:44,280 --> 00:22:49,820
+الوصل بنبدأ بيها مفتوحة فالأل التعريف لكن هنا نقول
+
+261
+00:22:49,820 --> 00:22:56,840
+و قاتى و الذكى طب اللي ماعزيناللام تضغم ما هي حروف
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+262
+00:22:56,840 --> 00:23:03,190
+الاضغام اللام قال التعريفطب ثم صل رحمن تفوزها تفوز
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+263
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+زين ضف ذا نعم دع سوء ظن زر حزر شريفا للكرام طب ثم
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+264
+00:23:10,010 --> 00:23:13,810
+صل رحمن تفوزها تفوزها تفوز زين ضف ذا نعم دع سوء ظن
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+265
+00:23:13,810 --> 00:23:17,850
+زر حزر
+
+266
+00:23:17,850 --> 00:23:22,930
+شريفا للكرام طب ثم صل رحمن تفوزها تفوزها تفوزها
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+267
+00:23:22,930 --> 00:23:23,090
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها
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+268
+00:23:23,090 --> 00:23:25,830
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تولا الف
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+269
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+الهمس الوصل ولا اللام الذي يلفظ هو بس حرف الزاي
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+270
+00:23:30,570 --> 00:23:35,290
+وكذلك حرف الواو التي هي للجامع اللي احنا نتخلص من
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+271
+00:23:35,290 --> 00:23:39,850
+اتقاء الساكنين بالضم فنقول وآتوا الذكاء وآتوا
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+272
+00:23:39,850 --> 00:23:44,990
+الذكاء كذلك هنا يومئذ يودوا الذين كفروا وعصوا
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+273
+00:23:44,990 --> 00:23:51,490
+الرسول وعصوا هي أصلا وعصوا الرسولأصلها ساكن وعصوا
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+274
+00:23:51,490 --> 00:23:56,070
+لحالها لكن نتيجة التقاء الساكنين يتم التخلص من
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+275
+00:23:56,070 --> 00:24:00,330
+التقاء الساكنين بإيش يا أخوات؟ بالضمن نقول وعصوا
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+276
+00:24:00,330 --> 00:24:05,920
+الرسولهنا نراحظ أن ووالين الساكنة حركت بالضم
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+277
+00:24:05,920 --> 00:24:09,980
+تخلصهم من إلتقاء الساكنين فلقرأها وعصى و الرسول
+
+278
+00:24:09,980 --> 00:24:14,600
+هذه هي حالات التخلص من إلتقاء الساكنين بالضم أو
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+279
+00:24:14,600 --> 00:24:19,360
+بالفتح أو بالكسري متى يتم التخلص من إلتقاء
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+280
+00:24:19,360 --> 00:24:25,010
+الساكنين بالكسري؟ طبعا على الأصلدائما إن في حالات
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+281
+00:24:25,010 --> 00:24:29,150
+حالات متخلص من اتقال الساكنين بالفتح في حالتين و
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+282
+00:24:29,150 --> 00:24:32,890
+بالضمي أيضا في حالتين متى متخلص من اتقال الساكنين
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+283
+00:24:32,890 --> 00:24:37,410
+بالفتح؟ إذا
+
+284
+00:24:37,410 --> 00:24:41,010
+كان
+
+285
+00:24:41,010 --> 00:24:46,250
+الساكن الأول نون من الجارة إتنين إذا كانت الساكن
+
+286
+00:24:46,250 --> 00:24:54,410
+الأولميم ألف لا ميم في أول صورة العمران ألف لا ميم
+
+287
+00:24:54,410 --> 00:24:58,090
+الله لا إله إلا هو الحي القيوم أما بالنسبة للتخلص
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+288
+00:24:58,090 --> 00:25:01,810
+من التقاء الساكنين بالضم نتخلص منها في حالتين
+
+289
+00:25:01,810 --> 00:25:05,410
+الحال الأولى ماها؟ في الحال الأولى إذا كان الساكن
+
+290
+00:25:05,410 --> 00:25:08,250
+الأول اللي هو wow اللينية
+
+291
+00:25:10,990 --> 00:25:19,170
+الحالة الثانية إذا كانت ميم الجماعة مثل تجري من
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+292
+00:25:19,170 --> 00:25:25,400
+تحتهم الأنهارفقيل أن نقول تجري من تحتهم الأنهار
+
+293
+00:25:25,400 --> 00:25:30,780
+كيف نقرأها؟ نتخلص من التقاء الساكنين بالضمي فنقول
+
+294
+00:25:30,780 --> 00:25:36,900
+تجري من تحتهم الأنهار إذا تجري من تحتهم الأنهار هي
+
+295
+00:25:36,900 --> 00:25:40,660
+الحالة الثانية من حالات التخلص من التقاء الساكنين
+
+296
+00:25:40,660 --> 00:25:46,740
+بالضمي فنقول تجري من تحتهم الأنهار كذلك في قول
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+297
+00:25:46,740 --> 00:25:53,630
+تعالىثم رددنا لكم الكرة عليهم لا نقول لكم الكرة
+
+298
+00:25:53,630 --> 00:26:01,150
+عليهم بل نقول ثم رددنا لكم الكرة عليهم لكم الكرة
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+299
+00:26:01,150 --> 00:26:06,190
+عليهم ثم رددنا لكم الكرة عليهم ال meme ما لها
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+300
+00:26:06,190 --> 00:26:11,430
+مضمومة هي في الأساس ما لها ساكنة لكن لأنها meme
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+301
+00:26:11,430 --> 00:26:17,460
+الجماعةساكنة والحرف اللي يليه في كلمة ثانية ساكنة
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+302
+00:26:17,460 --> 00:26:24,000
+اللي هو ال تخلصت من التقاء الساكنين بالضمن هذه هي
+
+303
+00:26:24,000 --> 00:26:28,160
+حالات التخلص من التقاء الساكنين سواء كان بالحرف لو
+
+304
+00:26:28,160 --> 00:26:33,350
+كان حرف مدأو بالتحريك لو كان الساكن الأول يعني نون
+
+305
+00:26:33,350 --> 00:26:37,610
+من ال .. بالتحريك بالكسرة و هو على الأصل أو
+
+306
+00:26:37,610 --> 00:26:43,590
+بالفتحة لو كان نون من الجارة أو ميم ألف لا ميم في
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+307
+00:26:43,590 --> 00:26:47,550
+أول صورة العمران التي تليها ألف لا ميم الله لا إله
+
+308
+00:26:47,550 --> 00:26:51,570
+إلا هو اللي حي القيوم أو بالضمي عندما .. إذا جاء
+
+309
+00:26:51,570 --> 00:26:56,270
+الساكن الأول الواو اللينيةأو اللي هي مين التي هي
+
+310
+00:26:56,270 --> 00:26:59,490
+للجماعة هذه هي حالات التخلص من ابتقاء الساكنين
+
+311
+00:26:59,490 --> 00:27:05,230
+كلها لكن في أحيانا يعني يجوز ابتقاء الحرفين ساكنين
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+312
+00:27:05,230 --> 00:27:09,830
+في كلمة الواحدة سواء كان في أولها ولا في آخرها ولا
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+313
+00:27:09,830 --> 00:27:14,570
+في نصفها يعني ممكن يكون حرفين ساكنين في آخر الكلمة
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+314
+00:27:14,570 --> 00:27:21,850
+مثال ذلكالحمد لله رب العالمين العالمين الياء هنا
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+315
+00:27:21,850 --> 00:27:26,350
+في آخر الكلمة الياء ساكنة لأن الحرف مد ساكنة وجبل
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+316
+00:27:26,350 --> 00:27:32,890
+مكسور والنون ساكنة سكونة معارضة فبنفت نقول الحمد
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+317
+00:27:32,890 --> 00:27:39,010
+لله رب العالمينبهذا الشكل يعني انتقاء ساكنين في
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+318
+00:27:39,010 --> 00:27:43,570
+آخر كلمة في كلمة واحدة يجوز العالمين هنا مثلا
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+319
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+فاليعبدوا رب هذا البيت البيت يعني هنا البيت حرف
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+320
+00:27:48,610 --> 00:27:53,540
+اليا اسمها لينية ولا مادية؟إذا حرف المد لو كان
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+321
+00:27:53,540 --> 00:27:59,240
+ليني أو حرف مد سواء العالمين أو اليالي هي اللينية
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+322
+00:27:59,240 --> 00:28:03,800
+بنفع تكون ساكنة و وراها حرف ساكن في نهاية الكلمة
+
+323
+00:28:03,800 --> 00:28:09,290
+فهذا يجوز أو كان مثلاليس حرف مد يعني هنا يجوز
+
+324
+00:28:09,290 --> 00:28:13,070
+اتقاء حرفين ساكنين في كلمة واحدة وقفا ويبقى
+
+325
+00:28:13,070 --> 00:28:18,010
+الحرفان ساكنان او يبقى الحرفان ساكنين سواء كان
+
+326
+00:28:18,010 --> 00:28:23,390
+الساكن اول حرف مد او حرف لين او ساكنا صحيحا مثل
+
+327
+00:28:23,390 --> 00:28:29,840
+والفجر في قوله والفجر ايه الحرفين الساكنين؟الجيم
+
+328
+00:28:29,840 --> 00:28:34,620
+والرا والفجر طبعا في حالة الوقف عليها .. في حالة
+
+329
+00:28:34,620 --> 00:28:39,440
+الوصف والفجر إيه؟ في حالة الوقف والفجر الجيم ساكنة
+
+330
+00:28:39,440 --> 00:28:44,100
+والرا ساكنة يعني يجوز في أخر الكلمة أو عشر وليالي
+
+331
+00:28:44,100 --> 00:28:47,940
+عشر برضه نفس الموضوع الشين ساكنة والرا ساكنة
+
+332
+00:28:47,940 --> 00:28:54,660
+والشفعي والوتر برضه تا ساكنةوراء ساكنة يجوز التقاء
+
+333
+00:28:54,660 --> 00:28:59,540
+الساكنين في آخر الكلمة يجوز وفي أول الكلمة برضه
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+334
+00:28:59,540 --> 00:29:03,880
+يجوز لو كان في عنا ساكنين في أول الكلمة أيضا يجوز
+
+335
+00:29:03,880 --> 00:29:11,240
+مثال ذلك في أول الكلمة هنا مثلا قوله الان
+
+336
+00:29:11,240 --> 00:29:18,920
+وقد كنتم به تستعجلون ا عندنا حرف مدالـ A وهو ساكن
+
+337
+00:29:18,920 --> 00:29:22,680
+اللي هو مثلا يعني عندنا هذا يسمى اللي هو المادة
+
+338
+00:29:22,680 --> 00:29:28,160
+اللازمة الكلام الأيه؟ مفقه ولا مخفف؟مد لازم كلمي
+
+339
+00:29:28,160 --> 00:29:33,300
+مخفر و احنا كذلك أخدنا هو مد الفرق و أصله عندنا هو
+
+340
+00:29:33,300 --> 00:29:39,760
+حرف مد و حرف المد حرف ساكن الان
+
+341
+00:29:39,760 --> 00:29:45,040
+و اللام حرف ساكنة يعني يجوز التقاء حرفين ساكنين في
+
+342
+00:29:45,040 --> 00:29:51,850
+أول الكلمة عندنا الألف حرف مد ساكنوالـ La حرف ماد
+
+343
+00:29:51,850 --> 00:29:56,270
+ساكن قد يخطئ بعض الناس عندما نأتي نقولك يعني في
+
+344
+00:29:56,270 --> 00:30:00,670
+هذه الكلمة فيظنوا بأن الحرف المطلوب هنا الال الالف
+
+345
+00:30:00,670 --> 00:30:07,630
+انتهت الان ويجف عليها طبعا لو جلنا الالان وجفنا
+
+346
+00:30:07,630 --> 00:30:13,330
+على الانالحرف هذا حرف ايش بيكون او مد ايش يسمى
+
+347
+00:30:13,330 --> 00:30:17,770
+مدارد السكون مثلا لأنه جاء حرف المد قبل اخر حرف
+
+348
+00:30:17,770 --> 00:30:21,450
+الكلمة ساكن نتيجة الوقف عليه فاللي بدنا اياه احنا
+
+349
+00:30:21,450 --> 00:30:28,070
+ليس ال a الآن في هذه الكلمة اللي هي a الان كان
+
+350
+00:30:28,070 --> 00:30:33,820
+حركة من مدهست حركات لزومان و بنسميه مد لازم كلمي
+
+351
+00:30:33,820 --> 00:30:38,800
+مخفف لماذا مد لازم كلمي مخفف؟ لأنه جاء حرف المد و
+
+352
+00:30:38,800 --> 00:30:45,200
+جاء بعده حرف ساكن طب لو جاء بعدها حرف مشدد بصير مد
+
+353
+00:30:45,200 --> 00:30:49,340
+لازم كلمي مثقل ماني أتي بكلمة فيها مد لازم كلمي
+
+354
+00:30:49,340 --> 00:30:55,060
+مثقل انت
+
+355
+00:30:55,060 --> 00:30:58,160
+نص الكلمة هي الحقه ال إغريل هي الحقه
+
+356
+00:31:02,240 --> 00:31:08,060
+مدنا حرف المد لأنه جاء وراها حرف مش حرف مشدد ومن
+
+357
+00:31:08,060 --> 00:31:13,240
+سميه مد لازم كله مثقل و هو نفسه ألحق أو أطام أو
+
+358
+00:31:13,240 --> 00:31:18,360
+أتحاجون أيضا نفس الموضوع بمعنى ممكن يأتي حرفان
+
+359
+00:31:18,360 --> 00:31:22,800
+ساكنين برضه في نص الكلمة إذا الحرفين الساكنين لو
+
+360
+00:31:22,800 --> 00:31:27,140
+جاءوا في آخر الكلمةأو أول الكلمة أو وسط الكلمة
+
+361
+00:31:27,140 --> 00:31:32,460
+ممكن أن يقع حرفان ساكنان وننطقهم زي مثلا كما قلنا
+
+362
+00:31:32,460 --> 00:31:38,080
+مثلا المستقيم الحمد لله رب العالمين الياه والنون
+
+363
+00:31:38,080 --> 00:31:44,350
+في أخر الكلمةأو في أول كلمة مثلًا الانا حرفين
+
+364
+00:31:44,350 --> 00:31:49,050
+ساكنين في أول كلمة تقع أو في وسط الكلمة مثلًا
+
+365
+00:31:49,050 --> 00:31:52,110
+الطامة
+
+366
+00:31:52,110 --> 00:31:58,170
+هي حرف مد وحرف م يعني ساكن أيضًا يسمى أيضًا إيه
+
+367
+00:31:58,170 --> 00:32:02,270
+يعني حرفان ساكنان إذا الحرفان الساكنين لو وقعوا في
+
+368
+00:32:02,270 --> 00:32:05,070
+كلمة واحدة سواء كان في الأول ولا في الآخر ولا في
+
+369
+00:32:05,070 --> 00:32:09,290
+المنتصف مافيش إنحكان فيها أنهم تقهمصحيح بنصمي مد
+
+370
+00:32:09,290 --> 00:32:13,050
+لازم كلمة مخفف أو مد لازم كلمة مثقل أو مد عرض
+
+371
+00:32:13,050 --> 00:32:17,690
+السكون أو مد لين مش مشكلة لكن بالنسبة للو وقع بين
+
+372
+00:32:17,690 --> 00:32:20,890
+كلمتين تقع ساكنين في الكلمتين هذا اللي احنا بنتخلص
+
+373
+00:32:20,890 --> 00:32:25,150
+منه اما بالحرف لو كان الساكن الأول حرف مد أو
+
+374
+00:32:25,150 --> 00:32:29,970
+بالتحريكي بالكسر على الأصل أو بالفتحي في حالتين أو
+
+375
+00:32:29,970 --> 00:32:35,090
+بالضم كما يعني أخذناها سابقا وبهذا احنايعني أنهينا
+
+376
+00:32:35,090 --> 00:32:38,810
+موضوع حكم التقاء الساكنين ونكمل ان شاء الله في
+
+377
+00:32:38,810 --> 00:32:42,990
+اللقاء القادم مع موضوع جديد بارك الله فيكم والسلام
+
+378
+00:32:42,990 --> 00:32:44,270
+عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_raw.json b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..dee47c81e349c229dbec714cda97dad29936ed32
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_raw.json
@@ -0,0 +1 @@
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نطني اتصالان الكلمتان مع بعضهم البعض ما هو حكم التقاء الساكنين يعني إذا التقت ساكنان أو حرفان ساكنان في كلمتين", "tokens": [10721, 33251, 19528, 3660, 16247, 9778, 48923, 5551, 34740, 11296, 11331, 28480, 8608, 995, 19452, 16070, 4117, 19528, 3660, 6024, 104, 7649, 10632, 11331, 28480, 8608, 995, 19452, 43242, 15042, 8717, 9566, 22653, 1975, 2655, 9381, 6027, 7649, 33251, 19528, 2655, 7649, 20449, 45030, 11242, 16095, 29739, 3615, 11242, 19446, 31439, 11331, 24793, 16712, 4587, 16606, 21136, 995, 19452, 9957, 37495, 22653, 11933, 15730, 16712, 4587, 2655, 8608, 995, 19452, 7649, 34051, 11331, 28480, 7649, 8608, 995, 19452, 7649, 8978, 9122, 19528, 2655, 9957], "avg_logprob": -0.11424632212694953, "compression_ratio": 2.0127388535031847, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 29.11, "end": 29.37, "word": "أ", "probability": 0.373046875}, {"start": 29.37, "end": 29.83, "word": " الكلمة", "probability": 0.7774251302083334}, {"start": 29.83, "end": 30.17, "word": " 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أخرج عليهم كذلك في قول تعالى و لقد استهزئ و لقد أين السكون", "tokens": [1211, 19452, 45164, 4032, 36520, 8315, 11296, 50239, 2655, 5551, 34740, 7435, 25894, 3224, 1863, 6156, 6027, 9778, 7578, 39896, 38392, 6055, 19913, 3224, 2288, 43242, 15042, 8717, 39648, 50239, 2655, 5551, 34740, 7435, 41850, 8608, 995, 19452, 9957, 5551, 14851, 995, 8608, 995, 19452, 3660, 4032, 33962, 7578, 8608, 995, 19452, 3660, 8717, 2655, 9778, 1211, 9381, 9154, 6055, 4587, 2288, 16606, 21136, 995, 19452, 9957, 20666, 2655, 5016, 16572, 4117, 20666, 4117, 3794, 2288, 8717, 4587, 2288, 10721, 11296, 50239, 2655, 5551, 34740, 7435, 25894, 3224, 1863, 50239, 2655, 3714, 4117, 3794, 13063, 3660, 50239, 2655, 5551, 34740, 7435, 25894, 16095, 9122, 8848, 23275, 8978, 12174, 12610, 37279, 6027, 7578, 4032, 5296, 28543, 44713, 3224, 11622, 19986, 4032, 5296, 28543, 5551, 9957, 21136, 30544], "avg_logprob": -0.17175196381065788, "compression_ratio": 2.1881188118811883, "no_speech_prob": 0.0, "words": [{"start": 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بالكسري فنقول ولا قد استهزئة .. ولا قد استهزئة ما تخلص من التقاء الساكنين بالكسري وهذا طبعا أخوات على الأصلي", "tokens": [22488, 7649, 12174, 995, 22488, 9957, 44713, 3224, 11622, 19986, 3660, 4386, 11933, 1829, 3224, 2423, 4386, 44713, 3224, 11622, 19986, 3660, 11331, 28480, 31767, 9957, 8608, 995, 19452, 19446, 6055, 9778, 1211, 9381, 9154, 16712, 4587, 16606, 21136, 995, 19452, 9957, 20666, 4386, 20666, 4117, 3794, 16572, 6156, 1863, 39648, 49429, 12174, 3215, 44713, 3224, 11622, 19986, 3660, 4386, 49429, 12174, 3215, 44713, 3224, 11622, 19986, 3660, 19446, 6055, 9778, 1211, 9381, 9154, 16712, 4587, 16606, 21136, 995, 19452, 9957, 20666, 4117, 3794, 16572, 37037, 15730, 23032, 3555, 3615, 995, 5551, 9778, 2407, 9307, 15844, 16247, 9381, 20292], "avg_logprob": -0.21843749821186065, "compression_ratio": 2.2356687898089174, "no_speech_prob": 0.0, "words": [{"start": 753.94, "end": 754.48, "word": "عدان", "probability": 0.5706787109375}, {"start": 754.48, "end": 755.74, "word": " قاعدين", "probability": 0.69000244140625}, {"start": 755.74, "end": 756.78, "word": " استهزئة", "probability": 0.8048828125}, {"start": 756.78, "end": 756.96, "word": " ..", "probability": 0.194091796875}, {"start": 756.96, "end": 757.0, "word": " إيه", "probability": 0.7967122395833334}, {"start": 757.0, "end": 757.12, "word": " ال", "probability": 0.79541015625}, {"start": 757.12, "end": 757.28, "word": " ..", "probability": 0.175537109375}, {"start": 757.28, "end": 758.9, "word": " استهزئة", "probability": 0.8066650390625}, {"start": 758.9, "end": 759.26, "word": " حرف", "probability": 0.7149658203125}, {"start": 759.26, "end": 759.66, "word": " الصين", "probability": 0.7724609375}, {"start": 759.66, "end": 760.6, "word": " ساكن", "probability": 0.9658203125}, {"start": 760.6, "end": 761.08, "word": " ما", "probability": 0.3818359375}, {"start": 761.08, "end": 761.42, "word": " تخلص", "probability": 0.854248046875}, {"start": 761.42, "end": 761.52, "word": " من", "probability": 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الساكنة حركت بالضم تخلصهم من إلتقاء الساكنين فلقرأها وعصى و الرسول هذه هي حالات التخلص من إلتقاء الساكنين بالضم أو بالفتح أو بالكسري متى يتم التخلص من إلتقاء الساكنين بالكسري؟ طبعا على الأصل", "tokens": [3224, 8315, 8717, 23557, 5016, 19913, 14739, 4032, 2407, 6027, 9957, 21136, 995, 19452, 3660, 11331, 31747, 2655, 20666, 11242, 2304, 6055, 9778, 1211, 9381, 16095, 9154, 11933, 1211, 2655, 4587, 16606, 21136, 995, 19452, 9957, 6156, 1211, 4587, 2288, 10721, 11296, 4032, 3615, 9381, 7578, 4032, 34892, 3794, 12610, 29538, 39896, 11331, 6027, 9307, 16712, 9778, 1211, 9381, 9154, 11933, 1211, 2655, 4587, 16606, 21136, 995, 19452, 9957, 20666, 11242, 2304, 34051, 20666, 5172, 2655, 5016, 34051, 20666, 4117, 3794, 16572, 44650, 7578, 7251, 39237, 16712, 9778, 1211, 9381, 9154, 11933, 1211, 2655, 4587, 16606, 21136, 995, 19452, 9957, 20666, 4117, 3794, 16572, 22807, 23032, 3555, 3615, 995, 15844, 16247, 36520], "avg_logprob": -0.1628871744712897, "compression_ratio": 2.206896551724138, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..83db5d4657b8fbe870e577029ce0c9db6e437985
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/OWQw9pUJ3rc_raw.srt
@@ -0,0 +1,1540 @@
+1
+00:00:11,740 --> 00:00:14,900
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,900 --> 00:00:19,400
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+3
+00:00:19,400 --> 00:00:22,800
+آله وصحابه وسلم موضوعنا اليوم يا أخوات هو حكم
+
+4
+00:00:22,800 --> 00:00:27,980
+التقاء الساكنين طبعا المقصود بهذا العنوان أن هناك
+
+5
+00:00:27,980 --> 00:00:32,170
+كلمتينأ الكلمة الأخيرة أخرها حرف ساكن والكلمة
+
+6
+00:00:32,170 --> 00:00:37,390
+الثانية حرف ساكن عندما نطني اتصالان الكلمتان مع
+
+7
+00:00:37,390 --> 00:00:41,030
+بعضهم البعض ما هو حكم التقاء الساكنين يعني إذا
+
+8
+00:00:41,030 --> 00:00:45,240
+التقت ساكنان أو حرفان ساكنان في كلمتينولا يكونوا
+
+9
+00:00:45,240 --> 00:00:49,500
+التقائهم إلا حالة الوصلة فلابد من التخلص من التقاء
+
+10
+00:00:49,500 --> 00:00:54,320
+الساكنين إما بالحذف لو كان الساكن الأول حرف مد
+
+11
+00:00:54,320 --> 00:00:58,900
+وإما بالتحريك سواء كان بالكسرة على الأصل أو الفتح
+
+12
+00:00:58,900 --> 00:01:03,830
+أو الضم لو لم يكن الساكن الأول حرف مدإذا حكم
+
+13
+00:01:03,830 --> 00:01:08,770
+التقاء الساكنين بمعنى إن إذا التقى حرفان ساكنان في
+
+14
+00:01:08,770 --> 00:01:13,510
+كلمتين ولا يكونوا التقائهم إلا حالة الواصلة لابد
+
+15
+00:01:13,510 --> 00:01:17,530
+أن نتخلص من التقاء الساكنين إما بالحدث مات نتخلص
+
+16
+00:01:17,530 --> 00:01:21,730
+من التقاء الساكنين بالحدث لو كان الساكن الأول حرف
+
+17
+00:01:21,730 --> 00:01:26,090
+مدأما إذا لم يكن الساكن الأول حرف مد في كلمتين
+
+18
+00:01:26,090 --> 00:01:31,050
+نتخلص من اتقاء الساكنين إما بالكسري على الأصل و
+
+19
+00:01:31,050 --> 00:01:36,990
+إما بالتحريك بالفتحة أو بالضمة أيضا بحالات معدودة
+
+20
+00:01:36,990 --> 00:01:40,190
+كما ناخد أما بالنسبة للتخلص من اتقاء الساكنين
+
+21
+00:01:40,190 --> 00:01:45,670
+بالحرف فهنا إذا كان الساكن الأول حرف مد والساكن
+
+22
+00:01:45,670 --> 00:01:49,810
+الثاني في الكلمة الثانية حرف يعني ليس مدا نتخلص من
+
+23
+00:01:49,810 --> 00:01:54,680
+اتقاء الساكنين بإيه بالحرفإذا متى نتخلص من التقاء
+
+24
+00:01:54,680 --> 00:01:59,660
+الساكنين يا أخوات؟ نتخلص
+
+25
+00:01:59,660 --> 00:02:03,540
+من التقاء الساكنين بالحرف إذا كان الساكن الأول حرف
+
+26
+00:02:03,540 --> 00:02:08,960
+مد. مثال ذلك قول تعالى فلمّا ذا قاء الشجرة ثقيلة
+
+27
+00:02:08,960 --> 00:02:14,700
+أن نقول فلمّا ذا قاء الشجرة بدت لهم سوئاتهم إنما
+
+28
+00:02:14,700 --> 00:02:21,050
+نقرأها فلمّا ذا قى الشجرةفلمّا ذاق الشجرة الالف
+
+29
+00:02:21,050 --> 00:02:27,150
+هنا حذفت لنتيجة التقاء الساكن هنا الالف ذاق ساكنة
+
+30
+00:02:27,150 --> 00:02:34,190
+و الشجرة حرف الشين أيضا ساكن بالنسبة للحمزة أ هي
+
+31
+00:02:34,190 --> 00:02:40,270
+أصلا الشجرة الحمزة تتأل طبعا هنا الحمزة تنوصل تحذف
+
+32
+00:02:40,900 --> 00:02:46,300
+واللام في قلة التعليف تضغم مع الشين فبصير اشق
+
+33
+00:02:46,300 --> 00:02:51,340
+الشجرة فلا اللام تظهر ولا الهمزة بتظهر فنقراها
+
+34
+00:02:51,340 --> 00:02:57,540
+فلما ذاق الشجرة الالف حولي فتعت ذاقا الهمزة الواصل
+
+35
+00:02:57,540 --> 00:03:01,580
+أصلا محدوثة على الواصل حكم اللام الساكنة في قلة
+
+36
+00:03:01,580 --> 00:03:05,880
+التعليف مع الشين لأنها من حروف الإضغاماللي هى
+
+37
+00:03:05,880 --> 00:03:09,060
+سموها اللام الشمسية تبدأ قبل ما عشرين فعندما
+
+38
+00:03:09,060 --> 00:03:15,060
+نقرأها نقول فلمّا ذاقش شجرة ذاقش شجرة يبقى الألف
+
+39
+00:03:15,060 --> 00:03:21,080
+طبعا محلفة مثال آخر كذلك في قول تعالى واذ قالوا
+
+40
+00:03:21,080 --> 00:03:28,240
+اللهم واذ قالوا اللهم أين الحرف اللى حُذفه طبعا
+
+41
+00:03:28,240 --> 00:03:37,310
+هنقول واذ قالوا اللهم حرف المد ماله؟حرف المادة
+
+42
+00:03:37,310 --> 00:03:43,630
+الواو ساكن وهنا اللهم اللام أيضا ساكنة نتيجة
+
+43
+00:03:43,630 --> 00:03:58,810
+انتقاء الساكنين اللهم اللهم اللهم
+
+44
+00:03:58,810 --> 00:03:58,810
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+45
+00:03:58,810 --> 00:03:58,810
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+46
+00:03:58,810 --> 00:04:01,930
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+47
+00:04:01,930 --> 00:04:02,010
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+48
+00:04:02,010 --> 00:04:02,030
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+49
+00:04:02,030 --> 00:04:02,970
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+50
+00:04:02,970 --> 00:04:02,970
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+51
+00:04:02,970 --> 00:04:02,990
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+52
+00:04:02,990 --> 00:04:02,990
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+53
+00:04:02,990 --> 00:04:02,990
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+54
+00:04:02,990 --> 00:04:02,990
+اللهم اللهم اللهم اللهم اللهم اللهم اللهم اللهم
+
+55
+00:04:02,990 --> 00:04:05,720
+اللهم اللهم اللهموالتي لفظت هنا قالوا يعني اللام
+
+56
+00:04:05,720 --> 00:04:11,500
+المضمومة وإذ قالوا اللهم فحقوا واللام طبعا تظهر
+
+57
+00:04:11,500 --> 00:04:16,060
+وهنا عندما ننظر إلى القراءة نقول وإذ قالوا اللهم
+
+58
+00:04:16,060 --> 00:04:22,020
+في عندنا و ال جماعة تقولوا وفي عندنا كذلك الألف
+
+59
+00:04:22,020 --> 00:04:27,440
+هنا ماذا نسميه هذا الألف ألف الفارقة التي تفرق ما
+
+60
+00:04:27,440 --> 00:04:31,580
+بين و الجماعة و و الكلمة وإذ قالوا هذا تكتب ولا
+
+61
+00:04:31,580 --> 00:04:35,440
+تلفظتكتب ولا تلفظ لا حالة الوصن ولا حالة الوقف
+
+62
+00:04:35,440 --> 00:04:39,460
+نقول واذ قالوا لا نقول واذ قالوا وا فالمقصود
+
+63
+00:04:39,460 --> 00:04:43,820
+بالألف هنا ليس الألف اللي هي هذه الصغيرة التي تكتب
+
+64
+00:04:43,820 --> 00:04:48,300
+ولا تلفظ وإنما المقصود بها واو الجماعة واذ قالوا
+
+65
+00:04:48,690 --> 00:04:53,530
+والهمزة اللي هنا تعطي اللهم همزة الوصل واللام مع
+
+66
+00:04:53,530 --> 00:04:58,750
+اللام تدغم يعني من حرف الإدغام فتلفظ لاما واحدة
+
+67
+00:04:58,750 --> 00:05:04,210
+مشددة لأن معنى الإدغام إدخال حرف زاكن بحرف متحرك
+
+68
+00:05:04,210 --> 00:05:09,810
+بحيث يصيران حرفا واحدة مشددة إذا الذي يرفض هنا وإذ
+
+69
+00:05:09,810 --> 00:05:17,530
+قالوا اللهم من يقرأها بحرف حرف الواو؟ اه فضلي
+
+70
+00:05:20,200 --> 00:05:25,200
+أحسنتي واذ قالوا اللهم لا نقول واذ قالوا اللهم
+
+71
+00:05:25,200 --> 00:05:30,480
+لماذا لنا ثقيلة على اللسان ثقيلة أن نقول واذ قالوا
+
+72
+00:05:30,480 --> 00:05:35,520
+اللهم إنما هنا نتيجة ارتقاء الساكنين فلمّا كان
+
+73
+00:05:35,520 --> 00:05:40,830
+الساكن الأول وهو ال wowحرف مد يُحذف حرف المد،
+
+74
+00:05:40,830 --> 00:05:44,610
+نتخلص من الإتقاء الساكنين بحذف حرف المد، اللذي
+
+75
+00:05:44,610 --> 00:05:49,470
+يظهر اللي هي الضمة وإذ قالوا اللهم إن كان هذا هو
+
+76
+00:05:49,470 --> 00:05:56,780
+الحق من عندككذلك مثال آخر وفي الأرض آيات للموقنين
+
+77
+00:05:56,780 --> 00:06:01,300
+طبعا ثقيل على اللسان أن نقرأها وفي الأرض كيف
+
+78
+00:06:01,300 --> 00:06:06,740
+نقرأها؟ وفي الأرض آيات للموقنين وفي الأرض آيات
+
+79
+00:06:06,740 --> 00:06:13,030
+للموقنين وفي الأرض وفي الأرض أين الحرف المحذوف؟حرف
+
+80
+00:06:13,030 --> 00:06:18,950
+اليا لا نقول وفي الأرض نقول وفي الأرض يعني عندنا
+
+81
+00:06:18,950 --> 00:06:24,270
+حرفان ساكنان في كلمتين حرف اليا في كلمة في آخر
+
+82
+00:06:24,270 --> 00:06:29,090
+الكلمة وحرف الأرض اللام هذه اللام ساكنة لان تظهر
+
+83
+00:06:29,090 --> 00:06:33,690
+مع الهمزة فنتيجة التقاء الساكنين نتخلص من التقاء
+
+84
+00:06:33,690 --> 00:06:37,550
+الساكنين بالحذف لماذا تخلصنا من التقاء الساكنين
+
+85
+00:06:37,550 --> 00:06:43,590
+بالحذف لأن الساكن الأولحرف مد، صحيح، إذا تخلصت من
+
+86
+00:06:43,590 --> 00:06:47,410
+التقرأة الساكنة، عندما نقرأها، لا نقول وفي الأرض،
+
+87
+00:06:47,410 --> 00:06:51,790
+لأنها بتكون ثقيلة على اللسان، كيف نقرأها؟ وفي
+
+88
+00:06:51,790 --> 00:06:56,890
+الأرض آيات، وفي الأرضي، لا نقول وفي الأرض، يعني
+
+89
+00:06:56,890 --> 00:07:01,150
+يحذف حرف المد هناك في حالة الواصلة، أما إذا وقفنا
+
+90
+00:07:01,150 --> 00:07:06,050
+عليه فيثبت لثبوته في رسم المصحفلو واحدة مثلا وقفت
+
+91
+00:07:06,050 --> 00:07:11,490
+عند كلمة وفي طبعا سواء كان اختبارا او اضطرارا يعني
+
+92
+00:07:11,490 --> 00:07:16,530
+انقطع النفس فوقفت عند كلمة وفي بنرفضها او من باب
+
+93
+00:07:16,530 --> 00:07:21,430
+الاختبار يعني كيف يكون من باب الاختبار؟ يعني الأخت
+
+94
+00:07:21,430 --> 00:07:27,390
+مثلا قالت وفي الأرض آيات للموقنين فقلت لها لو سمحت
+
+95
+00:07:27,390 --> 00:07:33,770
+قفى عند كلمة الأرضاختبارا إذا أرى كيف تقف على كلمة
+
+96
+00:07:33,770 --> 00:07:40,770
+وفي فتقول وفي طب ينفع نقرأها تقرأ تكمل الأيات تقول
+
+97
+00:07:40,770 --> 00:07:45,210
+الأرض آيات للموقنين طبعا ليه صح عليها ترجع كلمة أو
+
+98
+00:07:45,210 --> 00:07:48,990
+كلمتين فتقول وفي الأرض آيات للموقنين
+
+99
+00:07:51,620 --> 00:07:56,400
+طيب هذا اللي هو التخلص من اتقاء الساكنين بالحدث لو
+
+100
+00:07:56,400 --> 00:08:02,540
+كان الساكن الأول حرف مد اما اذا كان حرف المد غير
+
+101
+00:08:02,540 --> 00:08:06,180
+ثابت في رسم المصحف في الرسم المصحف الرسم العثماني
+
+102
+00:08:06,180 --> 00:08:11,760
+نجد انه بعض الكلمات فيها حرف مد غير ثابت هذا حرف
+
+103
+00:08:11,760 --> 00:08:16,240
+المد غير ثابت اما اذا كان حرف المد غير ثابت يعني
+
+104
+00:08:16,240 --> 00:08:20,390
+لا يكتب في رسم المصحفلعلة ابتقاء الساكنين فيكون
+
+105
+00:08:20,390 --> 00:08:25,330
+حدفه وصلا ووقفا يعني يحذف وصلا ووقفا لو وقفنا
+
+106
+00:08:25,330 --> 00:08:33,290
+عليها نقول وفي هنا مثلا ارنكي فتوحيووصلا قرنا كيف
+
+107
+00:08:33,290 --> 00:08:38,790
+تحيي الموتى محروف وصلا وكذلك وقفا الكلمة اللتي سوف
+
+108
+00:08:38,790 --> 00:08:43,750
+نراها هنا كيف تحيي الموتى هي أصلا تحيي في رسم
+
+109
+00:08:43,750 --> 00:08:47,390
+المصحف هذه ياء واحدة والياء الثانية ياء بتسموها
+
+110
+00:08:47,390 --> 00:08:51,210
+الياء الكوفية غير موجودة في رسم المصحف لكن هنا في
+
+111
+00:08:51,210 --> 00:08:55,490
+حسب المصحف المساعد يعني مكتوب دياء تاني لكن في
+
+112
+00:08:55,490 --> 00:09:02,980
+الرسم العثماني موجودة تحيي و بعدينما بيسموها اليأ
+
+113
+00:09:02,980 --> 00:09:10,540
+الكوفية وهي طول فضو ولا تكتب فنقراها تحي الموتة
+
+114
+00:09:10,540 --> 00:09:17,660
+إذا وصلناها كيف نقراها؟ هنا واذ قال إبراهيم ربي
+
+115
+00:09:17,660 --> 00:09:22,800
+أرني كيف تحي الموتة أرني كيف تحي الموتة يأ واحدة
+
+116
+00:09:22,800 --> 00:09:27,100
+اليأ الثانية هنا ماذا يصير فيها؟ تحدف لماذا حدفت؟
+
+117
+00:09:27,960 --> 00:09:32,020
+تخلصها من التقاء الساكنين لو وقفنا عليها نلفظ
+
+118
+00:09:32,020 --> 00:09:34,520
+الياء الأولى وليس الياء الثاني لأن الياء الثاني
+
+119
+00:09:34,520 --> 00:09:41,340
+محذوفة يعني محذوفة في رسم المصحف نقول كيف تحيي لكن
+
+120
+00:09:41,340 --> 00:09:45,620
+لو وصلناها كيف تحيي الموتى كذلك في قول تعالى قال
+
+121
+00:09:45,620 --> 00:09:52,280
+من يحيي العظام و هي رميم قال من يحيي العظام يعني
+
+122
+00:09:52,280 --> 00:09:58,170
+ياء أولىهذا بالنسبة للتخلص من التقاء الساكنين
+
+123
+00:09:58,170 --> 00:10:02,870
+بالحذف متى نتخلص من التقاء الساكنين بالحذف لو كان
+
+124
+00:10:02,870 --> 00:10:07,890
+الساكن الأول حرف مجد الحرف الثاني يا أخوات هو
+
+125
+00:10:07,890 --> 00:10:11,650
+التخلص من التقاء الساكنين بالتحريك ماذا نقصد
+
+126
+00:10:11,650 --> 00:10:19,270
+بالتحريك؟يا تحريكها فتحة أو ضمة أو الكسرة الأصل أن
+
+127
+00:10:19,270 --> 00:10:23,190
+يتم التخلص من التقاء الساكنين بالتحريك بالكسر وهذا
+
+128
+00:10:23,190 --> 00:10:27,870
+هو على الأصل دائما تتخلص من التقاء الساكنين بالكسر
+
+129
+00:10:27,870 --> 00:10:32,030
+والأمثلة على ذلك كثيرة لكن بالنسبة لغير الكسر
+
+130
+00:10:32,030 --> 00:10:36,910
+بحالات محدودة نرى هنا مثلا قل ادعو الله او ادعو
+
+131
+00:10:36,910 --> 00:10:43,060
+الرحمن قل ادعوالمثال اللي عندنا قل ادعو هنا قل
+
+132
+00:10:43,060 --> 00:10:48,860
+ادعو اللام ساكنة فعل أمر مجزمهم بالسكون قل ادعوا
+
+133
+00:10:48,860 --> 00:10:53,700
+الدال ساكنة هنا طبعا الهمس الوصل في حالة الوصل
+
+134
+00:10:53,700 --> 00:11:01,140
+تسقطفالساكنين اللام الساكنة قل و ادعو الدال ساكنة
+
+135
+00:11:01,140 --> 00:11:06,480
+نتخلص من التقاء الساكنين بالتحريك بالكسر فنقول قل
+
+136
+00:11:06,480 --> 00:11:12,460
+ادعو الله قل ادعو قل ادعو الله او ادعو الرحمن
+
+137
+00:11:12,460 --> 00:11:20,460
+فاللام هنا مكسورة هي أصلا ساكنة قل بس عندما نصلها
+
+138
+00:11:20,460 --> 00:11:26,600
+نقرأها قل ادعو بالكسر كذلك قوله تعالىو قالت أخرج
+
+139
+00:11:26,600 --> 00:11:33,740
+عليهن و قالت طبعا فعل ماضي يعني ساكن قالت تانيت
+
+140
+00:11:33,740 --> 00:11:39,200
+ساكنة قالت أخرج عليهن حرف الخ ساكن طبعا أخرج
+
+141
+00:11:39,200 --> 00:11:45,410
+الهمزة اللي هناتسمى همزة وصل لنقاها وقال تخرج
+
+142
+00:11:45,410 --> 00:11:49,970
+عليهم طبعا الفعل الماضي خرج الفعل الأمر من خرجه
+
+143
+00:11:49,970 --> 00:11:54,930
+أخرج فهنا أمر الثلاثي وهمزة الأمر الثلاثي زي اضرب
+
+144
+00:11:54,930 --> 00:12:00,530
+همزة وهمزة وصل تسقط حالة الوصل وتثبت حالة اللي
+
+145
+00:12:00,530 --> 00:12:04,210
+ابتدأوا بيها لو ابتدأنا بيها إيه بتثبت نقول أخرج
+
+146
+00:12:04,860 --> 00:12:09,220
+لكن لو وصلناها قالت أخرج عليهن فالخى هي التي تظهر
+
+147
+00:12:09,220 --> 00:12:16,120
+عندما نقول قالت أخرج أنا ساكنين أستا ساكنة و الخى
+
+148
+00:12:16,120 --> 00:12:19,860
+ساكنة نتخلص من تقراء الساكنين بالتحريك بالكسر
+
+149
+00:12:19,860 --> 00:12:25,300
+نقرأها قالت أخرج عليهن قالت مكسورة قالت أخرج عليهم
+
+150
+00:12:25,300 --> 00:12:32,940
+كذلك في قول تعالى و لقد استهزئ و لقد أين السكون
+
+151
+00:12:33,940 --> 00:12:39,660
+عدان قاعدين استهزئة .. إيه ال .. استهزئة حرف الصين
+
+152
+00:12:39,660 --> 00:12:44,040
+ساكن ما تخلص من التقاء الساكنين بال .. بالكسري
+
+153
+00:12:44,040 --> 00:12:49,660
+فنقول ولا قد استهزئة .. ولا قد استهزئة ما تخلص من
+
+154
+00:12:49,660 --> 00:12:53,780
+التقاء الساكنين بالكسري وهذا طبعا أخوات على الأصلي
+
+155
+00:12:54,340 --> 00:12:59,100
+و ممكن يكون أيضا التنوين يعني قد يكون الساكن الأول
+
+156
+00:12:59,100 --> 00:13:03,600
+تنوين سواء كان تنوين ضام أو تنوين كسر والساكن
+
+157
+00:13:03,600 --> 00:13:07,440
+الثاني متحرر يعني ساكن في الكلمة الثانية التنوين
+
+158
+00:13:07,440 --> 00:13:14,460
+هو أصلا نون ساكنة مثلا عندما نقول هنا إن زيّن سماء
+
+159
+00:13:14,460 --> 00:13:19,400
+الدنيا بزينات الكواكب هي أصلا بزيناتزينا تن
+
+160
+00:13:19,400 --> 00:13:22,700
+التنوين هذا عبارة عن نون ساكنة نقول بزينا تن
+
+161
+00:13:22,700 --> 00:13:29,060
+الكواكب لكنها ثقيلة أن نقول بزينا تن الكواكب نتخلص
+
+162
+00:13:29,060 --> 00:13:33,040
+من التقاء الساكنين بالكسر يعني يكسر التنوين اللي
+
+163
+00:13:33,040 --> 00:13:39,630
+هو نونأصلا بزيناتن هو صحيح تنوين لكنه يرفض نون
+
+164
+00:13:39,630 --> 00:13:44,030
+ساكنة لذلك في عيننا أحكام النون الساكنة والتنوين
+
+165
+00:13:44,030 --> 00:13:48,170
+لأن التنوين هو أخو النون الساكنة فنقول بزيناتن
+
+166
+00:13:48,170 --> 00:13:54,710
+الكواكب فتقيل أن نقول بزيناتن الكواكب فالتنوين
+
+167
+00:13:54,710 --> 00:14:01,500
+نفسه اللي هي النون تكسر فنقول بزيناتن الكواكبوإن
+
+168
+00:14:01,500 --> 00:14:08,400
+زيننا السماء الدنيا بزيناتنا الكواكم بزيناتنا
+
+169
+00:14:08,400 --> 00:14:12,080
+الكواكم من يقراها بزيناتنا الكواكم؟
+
+170
+00:14:13,670 --> 00:14:19,090
+أيوة بزيناتين الكواكب حركنا التنوين التنوين يُلفظ
+
+171
+00:14:19,090 --> 00:14:24,890
+نون ساكنة فلما جاءت النون ساكنة ساكنة وجاء الكواكب
+
+172
+00:14:24,890 --> 00:14:28,790
+اللام برضه في الكواكب الساكنة تخلصنا من التقاء
+
+173
+00:14:28,790 --> 00:14:34,990
+الساكنين بالكسر في هذا المثال كذلك قد يكون الساكن
+
+174
+00:14:34,990 --> 00:14:39,570
+الأول اللي هو الياء اللينية ما هي الياء اللينية يا
+
+175
+00:14:39,570 --> 00:14:46,860
+أخوات؟ماش فيه عندنا حرفاء اللين و هما .. ما هما؟
+
+176
+00:14:46,860 --> 00:14:52,640
+تفضّال إيه؟ الألف الواو واليا الواو الساكنة
+
+177
+00:14:52,640 --> 00:14:55,420
+المفتوح ما قبلها واليا الساكنة المفتوح ما قبلها
+
+178
+00:14:55,420 --> 00:14:59,760
+فعندما نقول اليا اللينية يعني اليا الساكنة المفتوح
+
+179
+00:14:59,760 --> 00:15:04,280
+ما قبلهاإذا القاعدة عندنا قد يكون الساكن الأول هو
+
+180
+00:15:04,280 --> 00:15:09,120
+الياء اللينية والساكن الثاني هو ساكن الكلمة نتخلص
+
+181
+00:15:09,120 --> 00:15:13,500
+من اتقاء الساكنين بالكثر يعني الياء اللينية نكسرها
+
+182
+00:15:13,500 --> 00:15:19,520
+مثال ذلك هنا يا صاحبي السجن صاحبي الياء الساكنة
+
+183
+00:15:19,520 --> 00:15:24,440
+وقابلها مفتوح هي ياء مادية ولا ياء لينية؟ لماذا
+
+184
+00:15:24,440 --> 00:15:30,660
+لينية؟لأنها ساكنة قبلها مفتوح فتقرأ يا صاحبي فهنا
+
+185
+00:15:30,660 --> 00:15:38,170
+يا ساكنة يا اللينية و السجنالسين ساكنة نتخلص من
+
+186
+00:15:38,170 --> 00:15:42,510
+التقاء الساكنين بكسر الياء اللينية فنقول يا صاحبي
+
+187
+00:15:42,510 --> 00:15:48,110
+السجن صاحبي مكسورة صاحبي السجن إذا الياء اللي هنا
+
+188
+00:15:48,110 --> 00:15:53,670
+ياء لينية كسرناها لأنها ساكنة وجاملها مفتوح نكسر
+
+189
+00:15:53,670 --> 00:15:56,910
+الياء اللينية لأنها وقعت نتخلصنا من التقاء
+
+190
+00:15:56,910 --> 00:16:00,730
+الساكنين وكان الساكن الأول الياء اللينية فكيف
+
+191
+00:16:00,730 --> 00:16:02,010
+نقرأه؟ مين يقرأ ليها؟
+
+192
+00:16:07,890 --> 00:16:12,190
+حركنا الياء اللينية بالكسر مع أنها ياء لكننا
+
+193
+00:16:12,190 --> 00:16:16,950
+حركناها بالكسر لأنها ياء اللينية كذلك هنا في
+
+194
+00:16:16,950 --> 00:16:22,630
+المثال آخر إن ربك يعلم أنك تقوم أدنى من ثلثي الليل
+
+195
+00:16:22,630 --> 00:16:29,570
+ثلثي الليل ثلثي الياء هنا ساكنة وجابلها لامفتوحة
+
+196
+00:16:29,570 --> 00:16:33,890
+يبقى الياء اللينية وليس الياء الماديةوجات الساكنة
+
+197
+00:16:33,890 --> 00:16:38,710
+الأول هو يألينية و الليل اللامن اللي هنا ساكنة
+
+198
+00:16:38,710 --> 00:16:43,910
+نتخلص من التقاء الساكنين بالتحريك بالكسرة فنقول من
+
+199
+00:16:43,910 --> 00:16:50,050
+ثلثي الليل ثلثي ثلثي الليلي و نصفهم طيب يعني هنا
+
+200
+00:16:50,050 --> 00:16:58,320
+حركنا اليألينية بالكسرةهذا يا أخوات اللي هو التخلص
+
+201
+00:16:58,320 --> 00:17:02,140
+من التقاء الساكنين بالتحريك بالكسر وهذا يا بنات
+
+202
+00:17:02,140 --> 00:17:05,940
+على الأصل على الأصل ولا ما تتخلص من التقاء
+
+203
+00:17:05,940 --> 00:17:11,410
+الساكنين بالحرف عند أي حرفعند حرف المد نشوف الحالة
+
+204
+00:17:11,410 --> 00:17:16,150
+الثالثة التخلص من التقاء الساكنين بالفتح متى نتخلص
+
+205
+00:17:16,150 --> 00:17:20,350
+من التقاء الساكنين بالفتح طبعا هذا خلاف الأصل ولكن
+
+206
+00:17:20,350 --> 00:17:23,830
+في عندنا حالتين يعني متى نتخلص من التقاء الساكنين
+
+207
+00:17:23,830 --> 00:17:28,730
+بالفتح في حالتين الحال الأولى لو كان الساكن الأول
+
+208
+00:17:28,730 --> 00:17:35,150
+none من تحت حرف الجر none من الجر زي من المؤمنين
+
+209
+00:17:35,150 --> 00:17:42,240
+كيف نقرأ هذه؟من المؤمنين طيب إذا لو واحدة قرأتها
+
+210
+00:17:42,240 --> 00:17:46,700
+مثلا من المؤمنين نشوف ثقيلة على اللسان لذلك لا
+
+211
+00:17:46,700 --> 00:17:53,080
+تقرأ من المؤمنين رجال وإنما نقرأها من المؤمنين من
+
+212
+00:17:53,080 --> 00:17:58,220
+المؤمنين رجال صدقوا ما عاهدوا الله عليه من
+
+213
+00:17:58,220 --> 00:18:04,430
+المؤمنينهي أصلا من المؤمنين عشان نون من الجارة
+
+214
+00:18:04,430 --> 00:18:09,670
+تخلصنا من التقاء الساكنين بالفتحة بس في حالتين
+
+215
+00:18:09,670 --> 00:18:16,570
+معينتين الحالة الأولى من النون من الجارة ومثلا آخر
+
+216
+00:18:16,570 --> 00:18:22,270
+أوفوا الكيلة ولا تكونوا من المخسرين من المخسرين
+
+217
+00:18:22,270 --> 00:18:27,820
+أصلا من المخسرين أصلا هي ساكنةلكن تخلصنا من التقاء
+
+218
+00:18:27,820 --> 00:18:33,680
+الساكنين بالفتحي لأن هذه نون من الجارة وهي الحالة
+
+219
+00:18:33,680 --> 00:18:38,000
+الأولى من حالات التخلص من التقاء الساكنين بالفتحة
+
+220
+00:18:38,000 --> 00:18:43,130
+يعني متى يتم التخلص من التقاء الساكنين بالفتحي؟في
+
+221
+00:18:43,130 --> 00:18:47,430
+الحالة الأولى اللى هو ن من الجارة إذا كان الساكن
+
+222
+00:18:47,430 --> 00:18:54,210
+الأول هو ن من الجارة نقرأها من المؤمنين من
+
+223
+00:18:54,210 --> 00:19:01,360
+المخسرين و هكذا في كل حرف منثانيا يتم التخلص من
+
+224
+00:19:01,360 --> 00:19:06,460
+التقاء الساكنين بالفتح لحالة ثانية عند التقاء
+
+225
+00:19:06,460 --> 00:19:14,260
+الساكنين ميم ألف لا ميم نقراها ألف لا ميم الله في
+
+226
+00:19:14,260 --> 00:19:18,600
+حالة الواصل لكن لو وقفنا عليها ألف لا ميم نقف
+
+227
+00:19:18,600 --> 00:19:25,690
+عليها بالماد اللازم الحرفي المخفف ميم هي ساكنةلو
+
+228
+00:19:25,690 --> 00:19:35,150
+وصلناها نقرأها ألف لا ميم الله ميم الله نفتحها إذا
+
+229
+00:19:35,150 --> 00:19:37,910
+في عندنا حالتين بس في هذا الموضوع في كل المصحف
+
+230
+00:19:37,910 --> 00:19:42,390
+لأنه يعني ألف لا ميم و بعدها ساكن في حالة الواصل
+
+231
+00:19:42,390 --> 00:19:51,470
+ألف لا ميم الله لا إله إلا هو الحي القيوم إذا هنا
+
+232
+00:19:51,470 --> 00:19:57,690
+ألف لا ميم اللهإذا في عندنا بس حالتين ما هي حالات
+
+233
+00:19:57,690 --> 00:20:02,990
+التخلص من اتقاء الساكنين بالفتحة؟ فضلا أخت نون من
+
+234
+00:20:02,990 --> 00:20:09,850
+الجارة والحالة التانية؟إذا كان الساكن أول هي ميم
+
+235
+00:20:09,850 --> 00:20:14,870
+ألف لا ميم في صورة العمران التي بعد حرف ساكن ألف
+
+236
+00:20:14,870 --> 00:20:19,550
+لا ميم الله لا إله إلا هو الحي القيوم هذا بالنسبة
+
+237
+00:20:19,550 --> 00:20:24,230
+للتخلص من التقاء الساكنين بإيش؟ بالفتحة الحالة
+
+238
+00:20:24,230 --> 00:20:27,850
+التالتة أخوات ثالثا التخلص من التقاء الساكنين
+
+239
+00:20:27,850 --> 00:20:32,500
+بالضممتى يتم التخلص من التقاء الساكنين بالضم؟ في
+
+240
+00:20:32,500 --> 00:20:38,580
+عندنا أيضا حالتين الحالة الأولى بتخلص منها إذا كان
+
+241
+00:20:38,580 --> 00:20:43,540
+الساكن الأول هو الواو واو اللين التي للجمة الواو
+
+242
+00:20:43,540 --> 00:20:49,400
+اللينية يعني واو ساكنة جامدها مفتوح هي الجمة زي ما
+
+243
+00:20:49,400 --> 00:20:52,260
+قلنا التخلص من التقاء الساكنين بالكسر لو كانت
+
+244
+00:20:52,260 --> 00:20:56,170
+الياء اللينية الساكن الأول الياء اللينيةهنا نتخلص
+
+245
+00:20:56,170 --> 00:20:59,990
+من التقراء الساكنين بالضم لو كان الساكن الأول هو
+
+246
+00:20:59,990 --> 00:21:05,010
+الواو اللينية التي هي للجمع مثال ذلك و أقاموا
+
+247
+00:21:05,010 --> 00:21:13,990
+الصلاة و آتوا الذكاء و آتوا الذكاء فالواو هنا
+
+248
+00:21:13,990 --> 00:21:19,030
+أصلها و آتوا الذكاء و آتوا الذكاء فقيلة على اللسان
+
+249
+00:21:19,030 --> 00:21:24,670
+أن نقرأها و آتوا الذكاءكيف بنعمل؟ نتخلص من التقاء
+
+250
+00:21:24,670 --> 00:21:31,450
+الساكنين بالضم فنقول و آتوا الذكاء هنا و آتوا و
+
+251
+00:21:31,450 --> 00:21:36,650
+ساكن الأصل طبعا لا تنظر إلى الضم اللي هنا لأنه
+
+252
+00:21:36,650 --> 00:21:42,210
+بيرسمون ليها على حسب الوصليلكن هي في الأساس هى wow
+
+253
+00:21:42,210 --> 00:21:46,250
+ساكنة جابتها مفتوح وهى wow الجماعة وتسمى ال wow
+
+254
+00:21:46,250 --> 00:21:52,050
+اللينية اللتي للجماعة فنقول و آتوا الزكاة و قاموا
+
+255
+00:21:52,050 --> 00:21:57,130
+الصلاة و آتوا الزكاة و آتوا ال wow مضمومة طبعا يا
+
+256
+00:21:57,130 --> 00:22:03,860
+أخوات الألف اللى هنا تسمى ألف إيش؟الفارقة تكتب ولا
+
+257
+00:22:03,860 --> 00:22:08,160
+تلفظ لا وصلا ولا وقفا ويوضع فوقها في رسم المصحف
+
+258
+00:22:08,160 --> 00:22:14,220
+الصفر المستدير معناته أن هذا الحرف يكتب لكنها لا
+
+259
+00:22:14,220 --> 00:22:18,180
+يرفض لا في حالة الوصل ولا في حالة الوقف يعني لو
+
+260
+00:22:18,180 --> 00:22:23,700
+أقفنا على كلمة و آتوا بس
+
+261
+00:22:23,700 --> 00:22:28,140
+لا نقول و آتواكذلك يعني هنا و قاتى و الذكى الألف
+
+262
+00:22:28,140 --> 00:22:31,840
+اللي هنا أولف الفارقة تسقط طبيعي لا تلفظ الألف
+
+263
+00:22:31,840 --> 00:22:37,040
+الثاني بتاعة الذكى هي أل التعريف همس الوصل بتسقط
+
+264
+00:22:37,040 --> 00:22:40,240
+في حال الوصل لو ابتدأنا بيها الكلام و قولنا
+
+265
+00:22:40,240 --> 00:22:44,280
+الذكاها الذكاها لفظناها لأنه إذا ابتدأنا بهمس
+
+266
+00:22:44,280 --> 00:22:49,820
+الوصل بنبدأ بيها مفتوحة فالأل التعريف لكن هنا نقول
+
+267
+00:22:49,820 --> 00:22:56,840
+و قاتى و الذكى طب اللي ماعزيناللام تضغم ما هي حروف
+
+268
+00:22:56,840 --> 00:23:03,190
+الاضغام اللام قال التعريفطب ثم صل رحمن تفوزها تفوز
+
+269
+00:23:03,190 --> 00:23:10,010
+زين ضف ذا نعم دع سوء ظن زر حزر شريفا للكرام طب ثم
+
+270
+00:23:10,010 --> 00:23:13,810
+صل رحمن تفوزها تفوزها تفوز زين ضف ذا نعم دع سوء ظن
+
+271
+00:23:13,810 --> 00:23:17,850
+زر حزر
+
+272
+00:23:17,850 --> 00:23:22,930
+شريفا للكرام طب ثم صل رحمن تفوزها تفوزها تفوزها
+
+273
+00:23:22,930 --> 00:23:23,090
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها
+
+274
+00:23:23,090 --> 00:23:23,090
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها
+
+275
+00:23:23,090 --> 00:23:25,830
+تفوزها تفوزها تفوزها تفوزها تفوزها تفوزها تولا الف
+
+276
+00:23:25,830 --> 00:23:30,570
+الهمس الوصل ولا اللام الذي يلفظ هو بس حرف الزاي
+
+277
+00:23:30,570 --> 00:23:35,290
+وكذلك حرف الواو التي هي للجامع اللي احنا نتخلص من
+
+278
+00:23:35,290 --> 00:23:39,850
+اتقاء الساكنين بالضم فنقول وآتوا الذكاء وآتوا
+
+279
+00:23:39,850 --> 00:23:44,990
+الذكاء كذلك هنا يومئذ يودوا الذين كفروا وعصوا
+
+280
+00:23:44,990 --> 00:23:51,490
+الرسول وعصوا هي أصلا وعصوا الرسولأصلها ساكن وعصوا
+
+281
+00:23:51,490 --> 00:23:56,070
+لحالها لكن نتيجة التقاء الساكنين يتم التخلص من
+
+282
+00:23:56,070 --> 00:24:00,330
+التقاء الساكنين بإيش يا أخوات؟ بالضمن نقول وعصوا
+
+283
+00:24:00,330 --> 00:24:05,920
+الرسولهنا نراحظ أن ووالين الساكنة حركت بالضم
+
+284
+00:24:05,920 --> 00:24:09,980
+تخلصهم من إلتقاء الساكنين فلقرأها وعصى و الرسول
+
+285
+00:24:09,980 --> 00:24:14,600
+هذه هي حالات التخلص من إلتقاء الساكنين بالضم أو
+
+286
+00:24:14,600 --> 00:24:19,360
+بالفتح أو بالكسري متى يتم التخلص من إلتقاء
+
+287
+00:24:19,360 --> 00:24:25,010
+الساكنين بالكسري؟ طبعا على الأصلدائما إن في حالات
+
+288
+00:24:25,010 --> 00:24:29,150
+حالات متخلص من اتقال الساكنين بالفتح في حالتين و
+
+289
+00:24:29,150 --> 00:24:32,890
+بالضمي أيضا في حالتين متى متخلص من اتقال الساكنين
+
+290
+00:24:32,890 --> 00:24:37,410
+بالفتح؟ إذا
+
+291
+00:24:37,410 --> 00:24:41,010
+كان
+
+292
+00:24:41,010 --> 00:24:46,250
+الساكن الأول نون من الجارة إتنين إذا كانت الساكن
+
+293
+00:24:46,250 --> 00:24:54,410
+الأولميم ألف لا ميم في أول صورة العمران ألف لا ميم
+
+294
+00:24:54,410 --> 00:24:58,090
+الله لا إله إلا هو الحي القيوم أما بالنسبة للتخلص
+
+295
+00:24:58,090 --> 00:25:01,810
+من التقاء الساكنين بالضم نتخلص منها في حالتين
+
+296
+00:25:01,810 --> 00:25:05,410
+الحال الأولى ماها؟ في الحال الأولى إذا كان الساكن
+
+297
+00:25:05,410 --> 00:25:08,250
+الأول اللي هو wow اللينية
+
+298
+00:25:10,990 --> 00:25:19,170
+الحالة الثانية إذا كانت ميم الجماعة مثل تجري من
+
+299
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+تحتهم الأنهارفقيل أن نقول تجري من تحتهم الأنهار
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+كيف نقرأها؟ نتخلص من التقاء الساكنين بالضمي فنقول
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+تجري من تحتهم الأنهار إذا تجري من تحتهم الأنهار هي
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+الحالة الثانية من حالات التخلص من التقاء الساكنين
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+بالضمي فنقول تجري من تحتهم الأنهار كذلك في قول
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+تعالىثم رددنا لكم الكرة عليهم لا نقول لكم الكرة
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+305
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+عليهم بل نقول ثم رددنا لكم الكرة عليهم لكم الكرة
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+عليهم ثم رددنا لكم الكرة عليهم ال meme ما لها
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+مضمومة هي في الأساس ما لها ساكنة لكن لأنها meme
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+حالات التخلص من التقاء الساكنين سواء كان بالحرف لو
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+كان حرف مدأو بالتحريك لو كان الساكن الأول يعني نون
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+312
+00:26:33,350 --> 00:26:37,610
+من ال .. بالتحريك بالكسرة و هو على الأصل أو
+
+313
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+بالفتحة لو كان نون من الجارة أو ميم ألف لا ميم في
+
+314
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+أول صورة العمران التي تليها ألف لا ميم الله لا إله
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+315
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+إلا هو اللي حي القيوم أو بالضمي عندما .. إذا جاء
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+316
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+الساكن الأول الواو اللينيةأو اللي هي مين التي هي
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+للجماعة هذه هي حالات التخلص من ابتقاء الساكنين
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+كلها لكن في أحيانا يعني يجوز ابتقاء الحرفين ساكنين
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+في كلمة الواحدة سواء كان في أولها ولا في آخرها ولا
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+في نصفها يعني ممكن يكون حرفين ساكنين في آخر الكلمة
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+مثال ذلكالحمد لله رب العالمين العالمين الياء هنا
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+مكسور والنون ساكنة سكونة معارضة فبنفت نقول الحمد
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+324
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+لله رب العالمينبهذا الشكل يعني انتقاء ساكنين في
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+325
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+آخر كلمة في كلمة واحدة يجوز العالمين هنا مثلا
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+فاليعبدوا رب هذا البيت البيت يعني هنا البيت حرف
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+اليا اسمها لينية ولا مادية؟إذا حرف المد لو كان
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+ليني أو حرف مد سواء العالمين أو اليالي هي اللينية
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+فهذا يجوز أو كان مثلاليس حرف مد يعني هنا يجوز
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+اتقاء حرفين ساكنين في كلمة واحدة وقفا ويبقى
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+الساكن اول حرف مد او حرف لين او ساكنا صحيحا مثل
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+والفجر في قوله والفجر ايه الحرفين الساكنين؟الجيم
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+335
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+والرا والفجر طبعا في حالة الوقف عليها .. في حالة
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+الوصف والفجر إيه؟ في حالة الوقف والفجر الجيم ساكنة
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+والرا ساكنة يعني يجوز في أخر الكلمة أو عشر وليالي
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+عشر برضه نفس الموضوع الشين ساكنة والرا ساكنة
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+والشفعي والوتر برضه تا ساكنةوراء ساكنة يجوز التقاء
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+الساكنين في آخر الكلمة يجوز وفي أول الكلمة برضه
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+يجوز لو كان في عنا ساكنين في أول الكلمة أيضا يجوز
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+مثال ذلك في أول الكلمة هنا مثلا قوله الان
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+وقد كنتم به تستعجلون ا عندنا حرف مدالـ A وهو ساكن
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+344
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+اللي هو مثلا يعني عندنا هذا يسمى اللي هو المادة
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+345
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+اللازمة الكلام الأيه؟ مفقه ولا مخفف؟مد لازم كلمي
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+346
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+مخفر و احنا كذلك أخدنا هو مد الفرق و أصله عندنا هو
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+حرف مد و حرف المد حرف ساكن الان
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+348
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+و اللام حرف ساكنة يعني يجوز التقاء حرفين ساكنين في
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+349
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+أول الكلمة عندنا الألف حرف مد ساكنوالـ La حرف ماد
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+350
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+ساكن قد يخطئ بعض الناس عندما نأتي نقولك يعني في
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+هذه الكلمة فيظنوا بأن الحرف المطلوب هنا الال الالف
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+انتهت الان ويجف عليها طبعا لو جلنا الالان وجفنا
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+على الانالحرف هذا حرف ايش بيكون او مد ايش يسمى
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+مدارد السكون مثلا لأنه جاء حرف المد قبل اخر حرف
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+الكلمة ساكن نتيجة الوقف عليه فاللي بدنا اياه احنا
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+ليس ال a الآن في هذه الكلمة اللي هي a الان كان
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+حركة من مدهست حركات لزومان و بنسميه مد لازم كلمي
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+مخفف لماذا مد لازم كلمي مخفف؟ لأنه جاء حرف المد و
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+جاء بعده حرف ساكن طب لو جاء بعدها حرف مشدد بصير مد
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+لازم كلمي مثقل ماني أتي بكلمة فيها مد لازم كلمي
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+مثقل انت
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+نص الكلمة هي الحقه ال إغريل هي الحقه
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+مدنا حرف المد لأنه جاء وراها حرف مش حرف مشدد ومن
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+364
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+سميه مد لازم كله مثقل و هو نفسه ألحق أو أطام أو
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+أتحاجون أيضا نفس الموضوع بمعنى ممكن يأتي حرفان
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+ساكنين برضه في نص الكلمة إذا الحرفين الساكنين لو
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+جاءوا في آخر الكلمةأو أول الكلمة أو وسط الكلمة
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+ممكن أن يقع حرفان ساكنان وننطقهم زي مثلا كما قلنا
+
+369
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+مثلا المستقيم الحمد لله رب العالمين الياه والنون
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+في أخر الكلمةأو في أول كلمة مثلًا الانا حرفين
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+ساكنين في أول كلمة تقع أو في وسط الكلمة مثلًا
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+الطامة
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+هي حرف مد وحرف م يعني ساكن أيضًا يسمى أيضًا إيه
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+يعني حرفان ساكنان إذا الحرفان الساكنين لو وقعوا في
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+كلمة واحدة سواء كان في الأول ولا في الآخر ولا في
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+المنتصف مافيش إنحكان فيها أنهم تقهمصحيح بنصمي مد
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+لازم كلمة مخفف أو مد لازم كلمة مثقل أو مد عرض
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+السكون أو مد لين مش مشكلة لكن بالنسبة للو وقع بين
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+كلمتين تقع ساكنين في الكلمتين هذا اللي احنا بنتخلص
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+منه اما بالحرف لو كان الساكن الأول حرف مد أو
+
+381
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+بالتحريكي بالكسر على الأصل أو بالفتحي في حالتين أو
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+382
+00:32:29,970 --> 00:32:35,090
+بالضم كما يعني أخذناها سابقا وبهذا احنايعني أنهينا
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+383
+00:32:35,090 --> 00:32:38,810
+موضوع حكم التقاء الساكنين ونكمل ان شاء الله في
+
+384
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+اللقاء القادم مع موضوع جديد بارك الله فيكم والسلام
+
+385
+00:32:42,990 --> 00:32:44,270
+عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/QNKTalKj7ZU_postprocess.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/QNKTalKj7ZU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..763b9414705fc1de99172dbe61fe9a2d76289f45
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/QNKTalKj7ZU_postprocess.srt
@@ -0,0 +1,20 @@
+1
+00:00:11,260 --> 00:00:14,280
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,280 --> 00:00:18,300
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+3
+00:00:18,300 --> 00:00:21,640
+آله وصحابه وسلم أخدنا يا أخوات في المحاضرة الماضية
+
+4
+00:00:21,640 --> 00:00:26,760
+التفخيم والترقيب أخدنا التفخيم هو سمن يدخل على صوت
+
+5
+00:00:26,760 --> 00:00:28,220
+الحرف عند النطق
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/QNKTalKj7ZU_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/QNKTalKj7ZU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..763b9414705fc1de99172dbe61fe9a2d76289f45
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/QNKTalKj7ZU_raw.srt
@@ -0,0 +1,20 @@
+1
+00:00:11,260 --> 00:00:14,280
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:14,280 --> 00:00:18,300
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+3
+00:00:18,300 --> 00:00:21,640
+آله وصحابه وسلم أخدنا يا أخوات في المحاضرة الماضية
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+4
+00:00:21,640 --> 00:00:26,760
+التفخيم والترقيب أخدنا التفخيم هو سمن يدخل على صوت
+
+5
+00:00:26,760 --> 00:00:28,220
+الحرف عند النطق
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Vq4dc1VnhK8_raw.json b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Vq4dc1VnhK8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cedf3040c6a7370fbda9b5f91107c573eac85d60
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Vq4dc1VnhK8_raw.json
@@ -0,0 +1 @@
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"إذا في القرآن الكريم لفظة العجوز لا ترد إلا أو لا تطلق إلا على مين؟ على المرأة العجوز و أما بالنسبة للرجل و أبونا شيخ كبير", "tokens": [28814, 15730, 8978, 25062, 2288, 148, 48506, 33251, 16572, 2304, 5296, 5172, 19913, 3660, 18863, 7435, 2407, 11622, 20193, 6055, 2288, 3215, 11933, 15040, 34051, 20193, 6055, 9566, 1211, 4587, 11933, 15040, 15844, 3714, 9957, 22807, 15844, 9673, 2288, 10721, 3660, 18863, 7435, 2407, 11622, 4032, 5551, 15042, 20666, 1863, 35457, 3660, 24976, 47341, 1211, 4032, 5551, 3555, 2407, 8315, 44049, 9778, 9122, 3555, 13546], "avg_logprob": -0.1300899594119101, "compression_ratio": 1.6717557251908397, "no_speech_prob": 0.0, "words": [{"start": 891.0, "end": 891.26, "word": "إذا", "probability": 0.5634765625}, {"start": 891.26, "end": 891.4, "word": " في", "probability": 0.833984375}, {"start": 891.4, "end": 891.86, "word": " القرآن", "probability": 0.8902587890625}, {"start": 891.86, "end": 892.38, "word": " الكريم", "probability": 0.9881184895833334}, {"start": 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إلى أمرين يعني ليش في عندنا قراءات قرأنية واختلاف بين القراءات القرأنية اللي هي بقايا الأحرف السبعة؟", "tokens": [9566, 1829, 3555, 45164, 12174, 1211, 8315, 35186, 5551, 9778, 2407, 9307, 19446, 31439, 8608, 3555, 3555, 1975, 46456, 15040, 5172, 25062, 2288, 16606, 9307, 25062, 2288, 33456, 10632, 38392, 39896, 10874, 11622, 38207, 9154, 16247, 5016, 28480, 21136, 3555, 27884, 34051, 39896, 19446, 6055, 3555, 4587, 7578, 9154, 16247, 5016, 28480, 21136, 3555, 27884, 22807, 19446, 31439, 8608, 3555, 3555, 2423, 47283, 2655, 15040, 5172, 22807, 37495, 23328, 14407, 30731, 5551, 29973, 9957, 37495, 22653, 32239, 8592, 8978, 43242, 8315, 12174, 2288, 16606, 9307, 12174, 2288, 33456, 10632, 4032, 47283, 2655, 15040, 5172, 49374, 25062, 2288, 16606, 9307, 25062, 2288, 33456, 10632, 13672, 1829, 39896, 4724, 4587, 995, 25528, 16247, 5016, 28480, 21136, 3555, 27884, 22807], "avg_logprob": -0.10043696850790816, "compression_ratio": 2.331578947368421, "no_speech_prob": 2.980232238769531e-07, 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قيل أن الأحرف السبعة من الاحتلافات ال 35 قيل أن الأحرف السبعة هي القراءات من ضمن الأكوال الخمسة و تلاتين القول لكن حقيقة الأمر أن القراءات ليست هي الأحرف السبعة بل هي بقايا الأحرف السبعة", "tokens": [9566, 3555, 3615, 995, 12174, 26895, 14739, 16247, 5016, 28480, 21136, 3555, 27884, 9154, 42963, 33753, 15040, 5172, 9307, 2423, 6976, 12174, 26895, 14739, 16247, 5016, 28480, 21136, 3555, 27884, 39896, 25062, 2288, 16606, 9307, 9154, 48812, 27842, 16247, 4117, 2407, 6027, 33962, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 25062, 12610, 44381, 11331, 38436, 28671, 16247, 29973, 14739, 25062, 2288, 16606, 9307, 32239, 14851, 39896, 16247, 5016, 28480, 21136, 3555, 27884, 4724, 1211, 39896, 4724, 4587, 995, 25528, 16247, 5016, 28480, 21136, 3555, 27884], "avg_logprob": -0.1546336244577649, "compression_ratio": 2.2549019607843137, "no_speech_prob": 0.0, "words": [{"start": 947.19, "end": 947.67, "word": "طبعا", "probability": 0.886962890625}, {"start": 947.67, "end": 948.39, "word": " 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بقايا الأحرف السبعة التي وردت متواترة نقلها الأئمة والعلماء وأصبحت قراءات يقرأ بها وهي قراءات متواترة", "tokens": [1211, 33456, 3224, 10874, 2304, 3615, 25062, 2288, 148, 48506, 15844, 11331, 28480, 36764, 24401, 34683, 31747, 2655, 4724, 995, 38436, 21542, 32887, 5172, 6156, 6027, 4587, 2288, 16606, 9307, 29739, 995, 4587, 10632, 39896, 4724, 4587, 995, 25528, 16247, 5016, 28480, 21136, 3555, 27884, 38392, 4032, 2288, 3215, 2655, 44650, 2407, 9307, 25720, 8717, 4587, 1211, 11296, 16247, 19986, 46007, 16070, 3615, 19528, 16606, 36725, 9381, 3555, 33753, 12174, 2288, 16606, 9307, 7251, 4587, 2288, 10721, 4724, 11296, 4032, 3224, 1829, 12174, 2288, 16606, 9307, 44650, 2407, 9307, 25720], "avg_logprob": -0.12148008323632754, "compression_ratio": 1.8734939759036144, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 965.45, "end": 966.05, "word": "لأنه", "probability": 0.76416015625}, {"start": 966.05, "end": 966.37, "word": " جمع", "probability": 0.9033203125}, {"start": 966.37, 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"end": 975.17, "word": " السبعة", "probability": 0.7967122395833334}, {"start": 975.17, "end": 975.51, "word": " التي", "probability": 0.8466796875}, {"start": 975.51, "end": 976.13, "word": " وردت", "probability": 0.91357421875}, {"start": 976.13, "end": 977.17, "word": " متواترة", "probability": 0.9625244140625}, {"start": 977.17, "end": 977.95, "word": " نقلها", "probability": 0.896728515625}, {"start": 977.95, "end": 978.65, "word": " الأئمة", "probability": 0.8351236979166666}, {"start": 978.65, "end": 979.47, "word": " والعلماء", "probability": 0.823486328125}, {"start": 979.47, "end": 980.27, "word": " وأصبحت", "probability": 0.8868408203125}, {"start": 980.27, "end": 980.81, "word": " قراءات", "probability": 0.94287109375}, {"start": 980.81, "end": 981.25, "word": " يقرأ", "probability": 0.89111328125}, {"start": 981.25, "end": 981.49, "word": " بها", "probability": 0.787353515625}, {"start": 981.49, "end": 981.75, "word": " وهي", "probability": 0.7298177083333334}, {"start": 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" اللغة", "probability": 0.904296875}, {"start": 990.42, "end": 991.04, "word": " اللغات", "probability": 0.7679036458333334}, {"start": 991.04, "end": 991.2, "word": " أو", "probability": 0.65625}, {"start": 991.2, "end": 991.6, "word": " اختلاف", "probability": 0.9539794921875}, {"start": 991.6, "end": 992.2, "word": " اللغات", "probability": 0.9928385416666666}, {"start": 992.2, "end": 993.2, "word": " واللهجات", "probability": 0.89111328125}, {"start": 993.2, "end": 993.94, "word": " العربية", "probability": 0.96875}, {"start": 993.94, "end": 994.68, "word": " أو", "probability": 0.671875}, {"start": 994.68, "end": 994.9, "word": " ما", "probability": 0.97607421875}, {"start": 994.9, "end": 995.16, "word": " كان", "probability": 0.97802734375}, {"start": 995.16, "end": 995.78, "word": " مرجعه", "probability": 0.9752197265625}, {"start": 995.78, "end": 996.1, "word": " إلى", "probability": 0.919921875}, {"start": 996.1, "end": 997.18, "word": " الإعجاز", "probability": 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والسلام ولا على الصحابة وهذا الذي أدى إلى اختلاف العلماء في تحديد المراد باللغات أو بالأحرف السبعة إلى عشرة أقوال يبقى في عيننا عشر أقوال كلها مختلفة بعضهم قالها لغة قريش وتميم وبني بكر وكذا وكذا", "tokens": [19528, 7251, 2288, 3215, 20193, 18871, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 49429, 15844, 31767, 5016, 16758, 3660, 37037, 15730, 43527, 5551, 3215, 7578, 30731, 1975, 46456, 15040, 5172, 18863, 19528, 16606, 8978, 6055, 5016, 16254, 3215, 9673, 2288, 18513, 20666, 1211, 17082, 9307, 34051, 20666, 10721, 5016, 28480, 21136, 3555, 27884, 30731, 6225, 8592, 25720, 5551, 4587, 2407, 6027, 7251, 3555, 4587, 7578, 8978, 6225, 9957, 8315, 6225, 46309, 5551, 4587, 2407, 6027, 28242, 11296, 3714, 46456, 46538, 3660, 45030, 11242, 16095, 50239, 11296, 5296, 17082, 3660, 12174, 16572, 8592, 34683, 2304, 32640, 46599, 22653, 4724, 37983, 4032, 4117, 15730, 4032, 4117, 15730], "avg_logprob": -0.1298466480716511, "compression_ratio": 1.9339622641509433, 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أراد", "probability": 0.8688151041666666}, {"start": 2385.78, "end": 2385.96, "word": " أن", "probability": 0.93408203125}, {"start": 2385.96, "end": 2386.5, "word": " يقرأها", "probability": 0.885205078125}, {"start": 2386.5, "end": 2387.16, "word": " الصلاة", "probability": 0.9786783854166666}, {"start": 2387.16, "end": 2387.6, "word": " قرأها", "probability": 0.93505859375}, {"start": 2387.6, "end": 2388.1, "word": " الصلاة", "probability": 0.9680989583333334}, {"start": 2388.1, "end": 2390.32, "word": " وفوقها", "probability": 0.892333984375}, {"start": 2390.32, "end": 2390.68, "word": " الألف", "probability": 0.900634765625}, {"start": 2390.68, "end": 2391.38, "word": " ومن", "probability": 0.906005859375}, {"start": 2391.38, "end": 2391.9, "word": " أراد", "probability": 0.96484375}, {"start": 2391.9, "end": 2392.06, "word": " أن", "probability": 0.951171875}, {"start": 2392.06, "end": 2392.54, "word": " يقرأها", "probability": 0.9193359375}, {"start": 2392.54, "end": 2393.26, "word": " الصلوات", "probability": 0.9532470703125}, {"start": 2393.26, "end": 2393.68, "word": " أقيم", "probability": 0.9212239583333334}, {"start": 2393.68, "end": 2394.52, "word": " الصلوات", "probability": 0.8623046875}, {"start": 2394.52, "end": 2395.2, "word": " وآتوا", "probability": 0.8333984375}, {"start": 2395.2, "end": 2396.04, "word": " الذكوات", "probability": 0.8536376953125}, {"start": 2396.04, "end": 2396.7, "word": " أيضا", "probability": 0.7882486979166666}, {"start": 2396.7, "end": 2397.08, "word": " قرأها", "probability": 0.952880859375}, {"start": 2397.08, "end": 2397.4, "word": " بهذا", "probability": 0.9482421875}, {"start": 2397.4, "end": 2397.76, "word": " الشكل", "probability": 0.99462890625}, {"start": 2397.76, "end": 2399.38, "word": " الكتابة", "probability": 0.8345947265625}, {"start": 2399.38, "end": 2400.04, "word": " تحت", "probability": 0.848388671875}], "temperature": 1.0}, {"id": 108, "seek": 242767, "start": 2400.18, "end": 2427.68, "text": "كتبات 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2406.74, "word": " القراءات", "probability": 0.9178466796875}, {"start": 2406.74, "end": 2407.9, "word": " الأخرى", "probability": 0.98388671875}, {"start": 2407.9, "end": 2408.38, "word": " وبعد", "probability": 0.780517578125}, {"start": 2408.38, "end": 2408.62, "word": " ذلك", "probability": 0.997802734375}, {"start": 2408.62, "end": 2409.0, "word": " ظهر", "probability": 0.84796142578125}, {"start": 2409.0, "end": 2409.96, "word": " القراء", "probability": 0.9265950520833334}, {"start": 2409.96, "end": 2410.86, "word": " واشتغر", "probability": 0.81689453125}, {"start": 2410.86, "end": 2411.74, "word": " مجموعة", "probability": 0.88544921875}, {"start": 2411.74, "end": 2411.86, "word": " من", "probability": 0.97509765625}, {"start": 2411.86, "end": 2412.34, "word": " القراء", "probability": 0.9822591145833334}, {"start": 2412.34, "end": 2413.56, "word": " وظهر", "probability": 0.9754638671875}, {"start": 2413.56, "end": 2414.48, "word": " مجموعة", "probability": 0.9599609375}, {"start": 2414.48, "end": 2415.06, "word": " من", "probability": 0.96484375}, {"start": 2415.06, "end": 2415.48, "word": " القراءات", "probability": 0.836669921875}, {"start": 2415.48, "end": 2416.0, "word": " السابعة", "probability": 0.8893229166666666}, {"start": 2416.0, "end": 2416.2, "word": " أو", "probability": 0.8896484375}, {"start": 2416.2, "end": 2416.56, "word": " القراءات", "probability": 0.9229736328125}, {"start": 2416.56, "end": 2416.92, "word": " العشرة", "probability": 0.8333333333333334}, {"start": 2416.92, "end": 2417.36, "word": " ان", "probability": 0.5048828125}, {"start": 2417.36, "end": 2417.56, "word": " شاء", "probability": 0.987060546875}, {"start": 2417.56, "end": 2417.8, "word": " الله", "probability": 0.94873046875}, {"start": 2417.8, "end": 2418.3, "word": " في", "probability": 0.94189453125}, {"start": 2418.3, "end": 2418.88, "word": " المحاضرة", "probability": 0.95361328125}, {"start": 2418.88, "end": 2419.32, "word": " القادمة", "probability": 0.9957682291666666}, {"start": 2419.32, "end": 2419.96, "word": " بنتكلم", "probability": 0.8826904296875}, {"start": 2419.96, "end": 2420.5, "word": " على", "probability": 0.59033203125}, {"start": 2420.5, "end": 2421.74, "word": " القراءات", "probability": 0.9315185546875}, {"start": 2421.74, "end": 2422.3, "word": " والقراء", "probability": 0.8360595703125}, {"start": 2422.3, "end": 2422.6, "word": " بإذن", "probability": 0.840576171875}, {"start": 2422.6, "end": 2422.7, "word": " الله", "probability": 0.92626953125}, {"start": 2422.7, "end": 2422.94, "word": " عز", "probability": 0.862548828125}, {"start": 2422.94, "end": 2423.22, "word": " وجل", "probability": 0.86474609375}, {"start": 2423.22, "end": 2424.1, "word": " ونكتفي", "probability": 0.9306640625}, {"start": 2424.1, "end": 2424.34, "word": " بهذا", "probability": 0.96337890625}, {"start": 2424.34, "end": 2424.6, "word": " القدر", "probability": 0.9871419270833334}, {"start": 2424.6, "end": 2424.92, "word": " وبرك", "probability": 0.8338216145833334}, {"start": 2424.92, "end": 2425.0, "word": " الله", "probability": 0.89208984375}, {"start": 2425.0, "end": 2425.4, "word": " فيكم", "probability": 0.9755859375}, {"start": 2425.4, "end": 2425.96, "word": " والسلام", "probability": 0.8504231770833334}, {"start": 2425.96, "end": 2426.24, "word": " عليكم", "probability": 0.949462890625}, {"start": 2426.24, "end": 2426.6, "word": " ورحمة", "probability": 0.978271484375}, {"start": 2426.6, "end": 2426.86, "word": " الله", "probability": 0.966796875}, {"start": 2426.86, "end": 2427.68, "word": " وبركاته", "probability": 0.9828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2428.31975, "duration_after_vad": 2397.9815937499984}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Xijp8fKVgz0_postprocess.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Xijp8fKVgz0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ec1b42c2399406af3ff9353f3b134542ff3dc577
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Xijp8fKVgz0_postprocess.srt
@@ -0,0 +1,168 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,200 --> 00:00:13,380
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+3
+00:00:13,380 --> 00:00:17,140
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+4
+00:00:17,140 --> 00:00:19,840
+آله وصحابه وسلم أخذنا يا أخوات في المحاضرة الماضية
+
+5
+00:00:19,840 --> 00:00:23,540
+التفخيم والترقيق وعرفنا أن هناك حروف تفخم دائما
+
+6
+00:00:23,540 --> 00:00:27,420
+وهي حروف الاستلاء وحروف ترقق دائما وهي حروف
+
+7
+00:00:27,420 --> 00:00:31,210
+الاستفال وحروف تفخم في حالات وترقق في حالاتوهي
+
+8
+00:00:31,210 --> 00:00:36,250
+الألف واللام والرا شرحنا حكم الألف تتبع ما قبلها
+
+9
+00:00:36,250 --> 00:00:41,190
+وحكم اللام في لفظ الجلالة تتبع ما قبلها إذا كان
+
+10
+00:00:41,190 --> 00:00:46,430
+مفتوح أو مضموم أو تفخم مثل إن الله رسول الله أو
+
+11
+00:00:46,430 --> 00:00:51,110
+كان مكسور أو ترقق مثل بسم الله الرحمن الرحيمبقى
+
+12
+00:00:51,110 --> 00:00:56,830
+علينا حكم الراء أيضا أخدنا حكم الراء وبقى عندنا
+
+13
+00:00:56,830 --> 00:01:01,910
+جواز الوجهين لأن الراء .. هناك راء تفخ .. حالات
+
+14
+00:01:01,910 --> 00:01:05,790
+الراء تفخم يعني إذا كانت مفتوحة، كانت مضمومة، كانت
+
+15
+00:01:05,790 --> 00:01:11,070
+مضمومة وقوف عليها بالراوم مثلا الراء ساكن بعد فتح،
+
+16
+00:01:11,070 --> 00:01:16,210
+ساكن بعد ضمن، ساكن بعد ألف، ساكن بعد واو، ساكن بعد
+
+17
+00:01:16,210 --> 00:01:20,450
+ساكن مسبوك بالفتح، ساكن بعد ساكن ..مسبوق بضم ساكنة
+
+18
+00:01:20,450 --> 00:01:23,890
+بعد كسر وبعد حرف من حروف الاستعلاء زي قرطاص تفخم
+
+19
+00:01:23,890 --> 00:01:27,250
+وفي عندنا حالات الترقيق وفي عندنا حالات جواز
+
+20
+00:01:27,250 --> 00:01:30,850
+الواجهين نشرح الآن بالنسبة لجواز الواجهين في عندنا
+
+21
+00:01:30,850 --> 00:01:34,330
+يا أخوات خمس كلمات في القرآن يجوزوا فيها الواجهين
+
+22
+00:01:34,330 --> 00:01:40,630
+يعني اللي هي مصر وقرطاص .. مصر أقسم .. مصر وفرق
+
+23
+00:01:40,630 --> 00:01:48,940
+والقطر يعني القطر وفسري و كذلك يسرييعني عدة كلمات
+
+24
+00:01:48,940 --> 00:01:52,860
+هذه الكلمات هي يجوز فيها الوجهان لو جاءكم أي سؤال
+
+25
+00:01:52,860 --> 00:02:05,600
+نظر نظري يسري فسري مصر القطر فرق هي ست كلمات يجوز
+
+26
+00:02:05,600 --> 00:02:09,800
+فيها الوجهان الحالة الأولى يا اخوات من جواز
+
+27
+00:02:09,800 --> 00:02:16,310
+الوجهين كلمة مصريجب فيها التفهيم ويجب فيها الترقيق
+
+28
+00:02:16,310 --> 00:02:21,870
+ولكن العلماء يقولون أنا التفهيم أولى لماذا مصر يجب
+
+29
+00:02:21,870 --> 00:02:23,350
+فيها التفهيم و الترقيق؟ تفضلي
+
+30
+00:02:28,330 --> 00:02:32,370
+التفخيم أولى صحيحة لأنها في حالة الوصل بتكون مفخمة
+
+31
+00:02:32,370 --> 00:02:38,330
+مثل وقال الذي اشتراه من مصر الرأ مفتوحة وهي مفخمة
+
+32
+00:02:38,330 --> 00:02:44,730
+في حالة الوصل كذلك وقال ادخلوا مصر ايضا مفعول بيه
+
+33
+00:02:44,730 --> 00:02:48,250
+منصب الفتحة مفتوحة الرأ مفتوحة لكن يجوز فيها
+
+34
+00:02:48,250 --> 00:02:52,110
+الوجهان اللي يجوز فيها التفخيم ويجوز فيها الترقيق
+
+35
+00:02:52,110 --> 00:02:57,150
+نشوف مثلا من قال بالتفخيممن قال بالتفهيم نظرة إلى
+
+36
+00:02:57,150 --> 00:03:04,710
+أن الرأس ساكنة يعني في حالة الوقف ساكنة بعد ساكن
+
+37
+00:03:04,710 --> 00:03:09,590
+مستعلن يعني حرف بحرف استعلاء مسبوق بكسر فقالوا أن
+
+38
+00:03:09,590 --> 00:03:16,750
+حرف الصاد مصر حرف استعلاء يحول ما بين تأثير كسرة
+
+39
+00:03:16,750 --> 00:03:22,520
+الميم على الرأس لذلك تفخمبالإضافة إلى كونها حال
+
+40
+00:03:22,520 --> 00:03:27,460
+الوصلي تفخم، ادخلوا مصر، ادخلوا مصر في حالة الكلام
+
+41
+00:03:27,460 --> 00:03:34,080
+مفخمة، لكن هنا ما قال في عندنا رأيان، الرأي الأول
+
+42
+00:03:34,080 --> 00:03:36,780
+رأي تفخم ورأي ترقق
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Xijp8fKVgz0_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Xijp8fKVgz0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ec1b42c2399406af3ff9353f3b134542ff3dc577
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Xijp8fKVgz0_raw.srt
@@ -0,0 +1,168 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,200 --> 00:00:13,380
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+3
+00:00:13,380 --> 00:00:17,140
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+4
+00:00:17,140 --> 00:00:19,840
+آله وصحابه وسلم أخذنا يا أخوات في المحاضرة الماضية
+
+5
+00:00:19,840 --> 00:00:23,540
+التفخيم والترقيق وعرفنا أن هناك حروف تفخم دائما
+
+6
+00:00:23,540 --> 00:00:27,420
+وهي حروف الاستلاء وحروف ترقق دائما وهي حروف
+
+7
+00:00:27,420 --> 00:00:31,210
+الاستفال وحروف تفخم في حالات وترقق في حالاتوهي
+
+8
+00:00:31,210 --> 00:00:36,250
+الألف واللام والرا شرحنا حكم الألف تتبع ما قبلها
+
+9
+00:00:36,250 --> 00:00:41,190
+وحكم اللام في لفظ الجلالة تتبع ما قبلها إذا كان
+
+10
+00:00:41,190 --> 00:00:46,430
+مفتوح أو مضموم أو تفخم مثل إن الله رسول الله أو
+
+11
+00:00:46,430 --> 00:00:51,110
+كان مكسور أو ترقق مثل بسم الله الرحمن الرحيمبقى
+
+12
+00:00:51,110 --> 00:00:56,830
+علينا حكم الراء أيضا أخدنا حكم الراء وبقى عندنا
+
+13
+00:00:56,830 --> 00:01:01,910
+جواز الوجهين لأن الراء .. هناك راء تفخ .. حالات
+
+14
+00:01:01,910 --> 00:01:05,790
+الراء تفخم يعني إذا كانت مفتوحة، كانت مضمومة، كانت
+
+15
+00:01:05,790 --> 00:01:11,070
+مضمومة وقوف عليها بالراوم مثلا الراء ساكن بعد فتح،
+
+16
+00:01:11,070 --> 00:01:16,210
+ساكن بعد ضمن، ساكن بعد ألف، ساكن بعد واو، ساكن بعد
+
+17
+00:01:16,210 --> 00:01:20,450
+ساكن مسبوك بالفتح، ساكن بعد ساكن ..مسبوق بضم ساكنة
+
+18
+00:01:20,450 --> 00:01:23,890
+بعد كسر وبعد حرف من حروف الاستعلاء زي قرطاص تفخم
+
+19
+00:01:23,890 --> 00:01:27,250
+وفي عندنا حالات الترقيق وفي عندنا حالات جواز
+
+20
+00:01:27,250 --> 00:01:30,850
+الواجهين نشرح الآن بالنسبة لجواز الواجهين في عندنا
+
+21
+00:01:30,850 --> 00:01:34,330
+يا أخوات خمس كلمات في القرآن يجوزوا فيها الواجهين
+
+22
+00:01:34,330 --> 00:01:40,630
+يعني اللي هي مصر وقرطاص .. مصر أقسم .. مصر وفرق
+
+23
+00:01:40,630 --> 00:01:48,940
+والقطر يعني القطر وفسري و كذلك يسرييعني عدة كلمات
+
+24
+00:01:48,940 --> 00:01:52,860
+هذه الكلمات هي يجوز فيها الوجهان لو جاءكم أي سؤال
+
+25
+00:01:52,860 --> 00:02:05,600
+نظر نظري يسري فسري مصر القطر فرق هي ست كلمات يجوز
+
+26
+00:02:05,600 --> 00:02:09,800
+فيها الوجهان الحالة الأولى يا اخوات من جواز
+
+27
+00:02:09,800 --> 00:02:16,310
+الوجهين كلمة مصريجب فيها التفهيم ويجب فيها الترقيق
+
+28
+00:02:16,310 --> 00:02:21,870
+ولكن العلماء يقولون أنا التفهيم أولى لماذا مصر يجب
+
+29
+00:02:21,870 --> 00:02:23,350
+فيها التفهيم و الترقيق؟ تفضلي
+
+30
+00:02:28,330 --> 00:02:32,370
+التفخيم أولى صحيحة لأنها في حالة الوصل بتكون مفخمة
+
+31
+00:02:32,370 --> 00:02:38,330
+مثل وقال الذي اشتراه من مصر الرأ مفتوحة وهي مفخمة
+
+32
+00:02:38,330 --> 00:02:44,730
+في حالة الوصل كذلك وقال ادخلوا مصر ايضا مفعول بيه
+
+33
+00:02:44,730 --> 00:02:48,250
+منصب الفتحة مفتوحة الرأ مفتوحة لكن يجوز فيها
+
+34
+00:02:48,250 --> 00:02:52,110
+الوجهان اللي يجوز فيها التفخيم ويجوز فيها الترقيق
+
+35
+00:02:52,110 --> 00:02:57,150
+نشوف مثلا من قال بالتفخيممن قال بالتفهيم نظرة إلى
+
+36
+00:02:57,150 --> 00:03:04,710
+أن الرأس ساكنة يعني في حالة الوقف ساكنة بعد ساكن
+
+37
+00:03:04,710 --> 00:03:09,590
+مستعلن يعني حرف بحرف استعلاء مسبوق بكسر فقالوا أن
+
+38
+00:03:09,590 --> 00:03:16,750
+حرف الصاد مصر حرف استعلاء يحول ما بين تأثير كسرة
+
+39
+00:03:16,750 --> 00:03:22,520
+الميم على الرأس لذلك تفخمبالإضافة إلى كونها حال
+
+40
+00:03:22,520 --> 00:03:27,460
+الوصلي تفخم، ادخلوا مصر، ادخلوا مصر في حالة الكلام
+
+41
+00:03:27,460 --> 00:03:34,080
+مفخمة، لكن هنا ما قال في عندنا رأيان، الرأي الأول
+
+42
+00:03:34,080 --> 00:03:36,780
+رأي تفخم ورأي ترقق
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Z1X0oo3jPmY_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Z1X0oo3jPmY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6fa3bbbc78ac38ceb3cac527c39ebf9aeba4e774
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/Z1X0oo3jPmY_raw.srt
@@ -0,0 +1,1576 @@
+1
+00:00:10,720 --> 00:00:13,580
+السلام عليكم و رحمة الله و بركاته باسم الله الرحمن
+
+2
+00:00:13,580 --> 00:00:17,020
+الرحيم الحمد لله والصلاة والسلام على رسول الله
+
+3
+00:00:17,020 --> 00:00:20,920
+وعلى آله وصحابه وسلم اليوم يا أخوات موضوعنا
+
+4
+00:00:20,920 --> 00:00:26,590
+التفخيم و الترقيمهناك حروف اللغة العربية تفخم و
+
+5
+00:00:26,590 --> 00:00:31,410
+هناك حروف ترقق يعني أصلا هناك حروف تفخموا دائما و
+
+6
+00:00:31,410 --> 00:00:35,590
+حروف ترققوا دائما و حروف تفخموا في حالات و ترققوا
+
+7
+00:00:35,590 --> 00:00:39,110
+في حالات في هذا الدرس نتعرف على الحروف التي تفخموا
+
+8
+00:00:39,110 --> 00:00:42,470
+دائما و الحروف التي ترققوا دائما و الحروف التي
+
+9
+00:00:42,470 --> 00:00:46,970
+تفخموا في حالات و ترققوا في حالات لكن نتعرف بداية
+
+10
+00:00:46,970 --> 00:00:52,210
+على معنى التفخيم ما معنى التفخيم؟ فضلي
+
+11
+00:00:54,270 --> 00:00:59,690
+التفخيم لغة هو التسمين والتغلير وفي الإصطلاح مان
+
+12
+00:00:59,690 --> 00:01:03,070
+يعرف لنا التفخيم إصطلاحا، فضل أختك التفخيم إصطلاحا
+
+13
+00:01:03,070 --> 00:01:05,730
+هو عبارة عن سمن يدخل على صوت الحرف عند النط بيه
+
+14
+00:01:05,730 --> 00:01:10,050
+فيمتلق الفم بصدار أحسنتى هو سمن يدخل على صوت الحرف
+
+15
+00:01:10,050 --> 00:01:15,690
+عند النط بيه فيمتلق الفم بصدار يعني نقول مثلا هأطط
+
+16
+00:01:15,690 --> 00:01:23,260
+عندما أقول أطط بيجد أنه في غلطة غير عنمع أن الاط و
+
+17
+00:01:23,260 --> 00:01:27,840
+ال it يخرجان من نفس المخرج لكن حرف الاط حرف مفخم
+
+18
+00:01:27,840 --> 00:01:34,380
+بيمتلق الفم بصدا هذا الحرف ولكن ال it حرف مرقق نجد
+
+19
+00:01:34,380 --> 00:01:39,100
+أنه يخرج يعني رقيقا، نحيفا، نحيلا، لذلك هو حرف
+
+20
+00:01:39,100 --> 00:01:42,740
+الطام، حرف التفخيم، إذا التفخيم في اللغة معناته
+
+21
+00:01:42,740 --> 00:01:48,240
+التسمين والتغليظوفي الاصطلاح هو سمن يدخل على صوت
+
+22
+00:01:48,240 --> 00:01:54,340
+الحرف عند النطق به فيمتلق الفم بصداع وعادة ما يسمى
+
+23
+00:01:54,340 --> 00:01:58,940
+التفهيم للحروف اللغة العربية المفخمة وهي حروف خصة
+
+24
+00:01:58,940 --> 00:02:04,460
+ضغط انقذ ولكن التغليظ يأتي لحرف اللام نقول لام
+
+25
+00:02:04,460 --> 00:02:10,490
+مغلظة يعني لام مفخمةو .. يعني التسمين والتفخيم
+
+26
+00:02:10,490 --> 00:02:14,090
+والتغليظ كلهما بمعنى واحد كل هذه الحروف أو
+
+27
+00:02:14,090 --> 00:02:18,550
+المصطلحات معناها التفخيم سواء كام تفخيم ولا تسمين
+
+28
+00:02:18,550 --> 00:02:24,270
+ولا تغليظ كله بمعنى التفخيم لكن عادة التغليظ يكون
+
+29
+00:02:24,270 --> 00:02:31,370
+لحرف اللام والتفخيم يكونوا لباقي حروف التفخيم هذا
+
+30
+00:02:31,370 --> 00:02:36,580
+بالنسبة للتفخيمالمضاد للتفهيم هو الترقيق ما معنى
+
+31
+00:02:36,580 --> 00:02:44,780
+الترقيق؟ الترقيق لغة التنحيل والتنحيث وفي الإصطلاح
+
+32
+00:02:44,780 --> 00:02:45,240
+هو
+
+33
+00:02:49,680 --> 00:02:54,120
+نحول يدخلوا على صوت الحرفي عند النطق به فلا يمتلئ
+
+34
+00:02:54,120 --> 00:03:00,120
+الفم بصداه نقول مثلا ساهر ساهر لا نقول صاهر نقول
+
+35
+00:03:00,120 --> 00:03:07,800
+ساهر أما الصاخر الصاخر حرف الصاخر مفخم فنجد فيه
+
+36
+00:03:07,800 --> 00:03:16,640
+التغليظ ونجد فيه التفخيم و القوةساهر، سامر، تامر،
+
+37
+00:03:16,640 --> 00:03:21,140
+النار، هذه كلها حروف مُرَقَقة، ففي عندنا التفخيم
+
+38
+00:03:21,140 --> 00:03:25,660
+وفي عندنا التغليظ لكن بالنسبة لكيفية التفخيم نجد
+
+39
+00:03:25,660 --> 00:03:30,240
+أن التفخيم يعني كيف .. كيفية التفخيم يكون التفخيم
+
+40
+00:03:30,240 --> 00:03:35,620
+عندما أو نرفع اللسان أو يستعلي اللسان إلى الحنك
+
+41
+00:03:35,620 --> 00:03:41,660
+الأعلى ويتوسع تجويف الفم وتضيق فتحة الشفتين يعني
+
+42
+00:03:41,660 --> 00:03:48,920
+عندما أقول أنا مثلابأجد أن اللسان يرتفع إلى الحناك
+
+43
+00:03:48,920 --> 00:03:54,320
+الأعلى ويمتلئ الفم أو يتوسع دائرة الفم من تجويف
+
+44
+00:03:54,320 --> 00:04:00,230
+الفم بيتسع وتضيق فتحة الشفاتين فنقولهاالشفتين
+
+45
+00:04:00,230 --> 00:04:05,550
+تضيق، التجويف الفم يتسع، اللسان يرتفع إلى أعلى،
+
+46
+00:04:05,550 --> 00:04:11,170
+بيرتج الصوت داخل الفم، فيخرج الحرف مفخرًا، إذا
+
+47
+00:04:11,170 --> 00:04:15,570
+كيفية تفخيم؟ يكون تفخيم باستعلاء أقصى اللسان إلى
+
+48
+00:04:15,570 --> 00:04:20,650
+الحنك الأعلى، ويتوسع تجويف الفم، وتضيق تحت
+
+49
+00:04:20,650 --> 00:04:26,630
+الشفتين، فيرتج الصوت داخل الفم، فيخرج الحرف مفخرًا
+
+50
+00:04:27,260 --> 00:04:34,040
+الترقيق عكسه، بنجد أن اللسان ينخفض إلى قاع الفم و
+
+51
+00:04:34,040 --> 00:04:43,300
+يضيق تجويف الفم و تتسع أو تنفتح فتحة الشفتين فبنجد
+
+52
+00:04:43,300 --> 00:04:48,600
+أن الحرف يكون نحيدا فنقول مثلا أنر مثلا حرف النور
+
+53
+00:04:48,600 --> 00:04:58,310
+مراققة تامر سامر سهر كل هذا حروف مراققةوتفخيم يا
+
+54
+00:04:58,310 --> 00:05:03,270
+أخوات من حيث أقسام التفخيم في عنا تلات أقسام قسم
+
+55
+00:05:03,270 --> 00:05:08,370
+يفخم دائما، يعني حروف اللغة العربية تفخم دائما،
+
+56
+00:05:08,370 --> 00:05:14,780
+دائما مفخمة وقسم يرقق دائماوالقسم الثالث ما يفخم
+
+57
+00:05:14,780 --> 00:05:19,800
+أحيانا يعني في حالات ويرقق في حالات إذا هذه أقسام
+
+58
+00:05:19,800 --> 00:05:25,000
+التفهيم و الترقيق يعني حروف تفخم دائما حروف ترقق
+
+59
+00:05:25,000 --> 00:05:29,200
+دائما حروف تفخم في حالات و ترقق في حالات أما
+
+60
+00:05:29,200 --> 00:05:33,640
+بالنسبة للنوع الأول أو القسم الأول وهي الحروف التي
+
+61
+00:05:33,640 --> 00:05:38,500
+تفخم دائما ما هي الحروف التي تفخم دائما؟ تفضلي
+
+62
+00:05:40,720 --> 00:05:46,240
+حروف الاستعلاء التي أخذناها وهي ارتفاع اللسان إلى
+
+63
+00:05:46,240 --> 00:05:49,540
+الحنك الأعلى عشان أنها بتكون حروف مفخمة حروف
+
+64
+00:05:49,540 --> 00:05:52,400
+الاستعلاء المجموعة في قوله ما هي حروف الاستعلاء يا
+
+65
+00:05:52,400 --> 00:05:59,590
+أخوات؟ مجموعة في قولهخصة ضغط قذ وهي سبعة حروف خصة
+
+66
+00:05:59,590 --> 00:06:05,170
+ضغط قذ سبعة أحرف هذه الحروف كلها تفخموا دائما يعني
+
+67
+00:06:05,170 --> 00:06:08,970
+إذا جاءت لوحدها تفخم وإذا جاءت قبلها .. بعدها ألف
+
+68
+00:06:08,970 --> 00:06:12,970
+تفخم وإذا جاءت مضمومة أو مفتوحة أو ساكنة تفخم فهي
+
+69
+00:06:12,970 --> 00:06:19,190
+حروف تفخموا دائما في جميع أحوالهاولكن حتى تفخيمها
+
+70
+00:06:19,190 --> 00:06:22,850
+يكون من حيث القوة .. في عندنا حروف أقوى من حروف ..
+
+71
+00:06:22,850 --> 00:06:26,610
+يعني أقوى حروف اللغة العربية من حيث التفخيم حرف
+
+72
+00:06:26,610 --> 00:06:33,530
+الأطط .. نقول الطارق .. الطامة .. تفخم .. يرتج
+
+73
+00:06:33,530 --> 00:06:38,760
+الصوت داخل الفم .. أقوى حرف و حرف .. الأطط ..و
+
+74
+00:06:38,760 --> 00:06:43,520
+يأتي بعده حرف الأض بعد ذلك حرف الأص بعد ذلك حرف
+
+75
+00:06:43,520 --> 00:06:48,540
+الأض ثم يأتي القاف ثم العين ثم الخى هذا الترتيب
+
+76
+00:06:48,540 --> 00:06:53,360
+الحروف الاستعلاقية خص ضغط القذر من حيث القوة
+
+77
+00:06:53,360 --> 00:07:03,020
+بالتولي حرف الأط الأض الأص الأذ الأق الأع ثم بعد
+
+78
+00:07:03,020 --> 00:07:10,220
+ذلك الخى هذه حروف التفهيم وترتيبهامقطة تانية يا
+
+79
+00:07:10,220 --> 00:07:14,480
+أخوات هو مراتب حروف اللغة العربية أو تفخيم يعني
+
+80
+00:07:14,480 --> 00:07:19,020
+للتفخيم مراتب ماهي مراتب التفخيم حددها العلماء
+
+81
+00:07:19,020 --> 00:07:24,200
+بأنها كم مرتبة؟ خمس مرتب نشوف المرتبة الأولى عندما
+
+82
+00:07:24,200 --> 00:07:29,540
+يأتي حرف الاستعلاء مفتوحا وبعده ألف إذا جاء حرف
+
+83
+00:07:29,540 --> 00:07:34,380
+الاستعلاء أي حرف من الحروف خصة ضغط انقض مفتوح عليه
+
+84
+00:07:34,380 --> 00:07:40,530
+فتحة وبعده ألف بيكون إيه؟ بيكون الحرف مفخرامثال
+
+85
+00:07:40,530 --> 00:07:44,270
+ذلك عندنا أمثلة من ياتي بيه أمثلة على الحرف
+
+86
+00:07:44,270 --> 00:07:47,510
+المفتوح .. الحرف الإستادال المفتوح الذي بعدها ألف
+
+87
+00:07:47,510 --> 00:07:48,310
+.. فضليه
+
+88
+00:07:52,310 --> 00:08:00,330
+الطامة الط او الطارق الطارق مثلا عند المثال الطامة
+
+89
+00:08:00,330 --> 00:08:05,050
+حرف الط و جاء بعده حرف الألف الط مفتوح و بعدها ألف
+
+90
+00:08:05,050 --> 00:08:08,870
+بتكون المرتبة الأولى من مراتب التفخيم كذلك
+
+91
+00:08:08,870 --> 00:08:16,730
+الصادقين الصاص الصادقين حرف الص مفتوح و ورا أيضا
+
+92
+00:08:16,730 --> 00:08:20,030
+ألف مين يأتي بمثال آخر؟
+
+93
+00:08:24,020 --> 00:08:29,420
+الضالين احنا لما نقول الضالين نجد أنه يعني تجويف
+
+94
+00:08:29,420 --> 00:08:34,020
+الفم اتسع ارتفع لسائل الحناك الأعلى دقة فتحت
+
+95
+00:08:34,020 --> 00:08:39,440
+الشفتين ارتج الصوت في داخل الفم فخرج حرف الض أو
+
+96
+00:08:39,440 --> 00:08:45,040
+الط أو ض مفخما فقولنا الضالين
+
+97
+00:08:46,930 --> 00:08:52,070
+الظالمين، القانتين، الطامة، الطارق، كل هذه حروف
+
+98
+00:08:52,070 --> 00:08:56,650
+حروف الاستعلاء لأنها جاءت الحرف مفتوح وبعد أقول
+
+99
+00:08:56,650 --> 00:09:00,570
+ألف بيكون أقوى مراتب التفخيم المرتبة الثانية يا
+
+100
+00:09:00,570 --> 00:09:05,410
+اخوات هي إذا جاء حرف الاستعلاء مفتوح وليس بعده ألف
+
+101
+00:09:05,410 --> 00:09:12,530
+من يأتي بأمثلة؟ فطرينعم طبعا إذا جاء حرف الاستعلاق
+
+102
+00:09:12,530 --> 00:09:20,710
+مفتوح فقط طبعة مثلا ضلة صبرة أو الصبر ظلمة القمر
+
+103
+00:09:20,710 --> 00:09:26,890
+أو قمر الغيب الخير كل هذه الحروف حرف الاستعلاق جاء
+
+104
+00:09:26,890 --> 00:09:31,710
+مفتوح بكون مفخم ولكنه من حيث المرتبة بكون مرتبة
+
+105
+00:09:31,710 --> 00:09:35,430
+ثانية يبقى في عنا مرتبة أولى إذا جاء حرف الاستعلاق
+
+106
+00:09:35,430 --> 00:09:39,360
+مفتوح وبعده ألفالمرتبة الثانية إذا جاء حرف
+
+107
+00:09:39,360 --> 00:09:43,940
+الاستعلاق مفتوح وليس بعده ألف المرتبة الثالثة إذا
+
+108
+00:09:43,940 --> 00:09:48,980
+جاء حرف الاستعلاق مضموم والأمثلة على ذلك مثل طبيعة
+
+109
+00:09:48,980 --> 00:09:54,580
+طبيعة نحن نجد أنه في يعني مرتبة أقليعني الطامة غير
+
+110
+00:09:54,580 --> 00:10:00,200
+عن طبيعة صحيح ان طبيعة مفخم لكن مرتبته اقل من
+
+111
+00:10:00,200 --> 00:10:06,400
+مرتبة الطامة او الظالمين او الظالمين هذا مفخم اذا
+
+112
+00:10:06,400 --> 00:10:11,160
+طبيعة هذا مرتبة تالتة مفخم لكنه من المرتبة الثالثة
+
+113
+00:10:12,800 --> 00:10:18,700
+منصورة حرف الصاد ماله؟ مضموم اذا مفخم لكنه من
+
+114
+00:10:18,700 --> 00:10:24,120
+المرتبة الثالثة منضود .. منضود .. الاض .. منضو ..
+
+115
+00:10:24,120 --> 00:10:28,980
+الضاد مضمومة بيكون من المرتبة الثالثة محظورة ..
+
+116
+00:10:28,980 --> 00:10:33,660
+محظورة حرف الضاد ايضا مضموم هو حروف استلاءه لكنه
+
+117
+00:10:33,660 --> 00:10:39,440
+مفخم من المرتبة التالتة قتلى غُلبت خُلِقوا هذا هي
+
+118
+00:10:39,440 --> 00:10:43,730
+المرتبة الثالثةالمرتبة الرابعة إذا جاء حرف
+
+119
+00:10:43,730 --> 00:10:48,310
+الاستعلاء ساكن لا مفتوح ولا مضموم ولا بعده ألف
+
+120
+00:10:48,310 --> 00:10:54,430
+إنما جاء حرف الاستعلاء ساكن مثال ذلك يطبع نجد أنها
+
+121
+00:10:54,430 --> 00:11:00,470
+بسيطة يطبع حرف الط يعني من حروف الاستعلاء لكن
+
+122
+00:11:00,470 --> 00:11:07,030
+مرتبته مرتبة رابعة يضرب حرف الضاد مرتبة رابعة لأن
+
+123
+00:11:07,030 --> 00:11:15,630
+الضاد ماله ساكن إنما أصبرأصفر الصاد ساكن يظلم يغلب
+
+124
+00:11:15,630 --> 00:11:21,350
+يخلق هذه كلها حروف الاستعلاء ساكنة بتكون من
+
+125
+00:11:21,350 --> 00:11:26,690
+المرتبة الرابعة اخر مرتبة من مراتب الاستعلاء او
+
+126
+00:11:26,690 --> 00:11:31,410
+المرتبة التفخيم هي لو كان حرف الاستعلاء مكسورمثال
+
+127
+00:11:31,410 --> 00:11:37,610
+و ذلك باطيرات باطيرات حرف يعني حرف الأط باطي طي
+
+128
+00:11:37,610 --> 00:11:42,330
+بتلاقي صحيح إنه مفخم لكنه يعني أقل مرتبة يعني
+
+129
+00:11:42,330 --> 00:11:47,770
+مرتبة خامسة باطيرات غير عن الطام الطام مفخم لكن
+
+130
+00:11:47,770 --> 00:11:52,750
+باطيراتفيه تفخيم يعني إذا قسناه بالترقيد تفخيم
+
+131
+00:11:52,750 --> 00:12:00,170
+لكنه تفخيم من المرتبة الخامسة كذلك ضعافة ضعافة حرف
+
+132
+00:12:00,170 --> 00:12:05,450
+الضاد مكسور ضعافة ضعافة بيكون من المرتبة الخامسة
+
+133
+00:12:05,880 --> 00:12:12,660
+سراط .. سراط .. سراط الصاد مكسور، ضلال .. ضلال،
+
+134
+00:12:12,660 --> 00:12:18,560
+حرف الض مكسور، غلال أو خلال، و كذلك غيظة الماء، كل
+
+135
+00:12:18,560 --> 00:12:22,480
+هذه هي المرتبة الخامسة، إذا في عندنا خمس ملاتب،
+
+136
+00:12:22,480 --> 00:12:26,020
+نعيدها بشكل سريع، ما هي المرتبة الأولى يا أخوات؟
+
+137
+00:12:26,020 --> 00:12:29,400
+أحسن
+
+138
+00:12:29,400 --> 00:12:32,500
+بس واحد واحد، الاستعلاق مفتوح و بعده ألف اتنين
+
+139
+00:12:35,370 --> 00:12:41,410
+إذا جاء حرف الاستلاء مفتوح وليس وراقه ألف إذا كان
+
+140
+00:12:41,410 --> 00:12:46,930
+حرف الاستلاء مضمون فضلي الساكن
+
+141
+00:12:46,930 --> 00:12:50,560
+بيكون مرتبة رابعة الخامس فضلي أختكإذا كان حرف
+
+142
+00:12:50,560 --> 00:12:54,800
+الاستعلاء مكسور إذا في عندنا خمس مراتب من مراتب
+
+143
+00:12:54,800 --> 00:12:58,780
+الاستعلاء لكن في عندنا ملاحظات أن حرف الاستعلاء
+
+144
+00:12:58,780 --> 00:13:05,020
+هذا لو كان مفتوح ومشدد وبراءه ألف أقوى من المفتوح
+
+145
+00:13:05,020 --> 00:13:08,720
+الغير مشدد الذي وراءه ألف يعني في عندنا مثلا
+
+146
+00:13:08,720 --> 00:13:17,210
+الطارق أو الطامة الطارق حرف الطامالهمشدد لأن اللام
+
+147
+00:13:17,210 --> 00:13:22,510
+مضغمة بحرف الطه وحرف الطه من حروف اللام الشمسية
+
+148
+00:13:22,510 --> 00:13:28,390
+الطارق مضغمة الطام حرف الطه مضغم باللام لذا كان
+
+149
+00:13:28,390 --> 00:13:35,460
+اقول الطارق طيب هذه الطارقأقوى من طارق لحالها طارق
+
+150
+00:13:35,460 --> 00:13:40,000
+بدون مضغام يعني حرف الطا إذا كان مشددا ورا ألف
+
+151
+00:13:40,000 --> 00:13:46,160
+أقوى من حرف الطا الغير مشدد المفتوح وراه ألف يعني
+
+152
+00:13:46,160 --> 00:13:55,620
+الطارقالطامة أقوى من طارق وطامة لحالها وهذه ملاحظة
+
+153
+00:13:55,620 --> 00:13:59,940
+الملاحظة الثانية وهو ما يسمى بالتفخيم النسبي
+
+154
+00:13:59,940 --> 00:14:04,240
+التفخيم النسبي إنه في عنا آخر تلت حروف من حروف
+
+155
+00:14:04,240 --> 00:14:09,860
+الاستعلاء اللي هو حرف القاف وحرف الغين وخالقاف
+
+156
+00:14:09,860 --> 00:14:16,780
+والغين والخى إذا كانت مكسورة تفخم تفخيما نسبيا إذا
+
+157
+00:14:16,780 --> 00:14:22,100
+قسناها بحروف الترقيق يعني هي أصلا بتكون مفخمة
+
+158
+00:14:22,100 --> 00:14:27,000
+بالنسبة للترقيق لكنها بتكون أدنى درجات التفخيم
+
+159
+00:14:27,000 --> 00:14:34,580
+وعشان هي أصلا هييعني حرف ضعيف نوعا ما و كمان مكسور
+
+160
+00:14:34,580 --> 00:14:40,120
+من تفخيم و تفخيم نسبي إذا التفخيم النسبي يكون مع
+
+161
+00:14:40,120 --> 00:14:44,280
+التلت حروف اللي هو حرف الغين والخ أو القاف الغين
+
+162
+00:14:44,280 --> 00:14:50,780
+والخ عندما تكون مكسورة أول شيء الحرف نفسه يعني ليس
+
+163
+00:14:50,780 --> 00:14:56,520
+قويا جداوشيء ثاني هو مكسور من أضعف مراتب التفخيم،
+
+164
+00:14:56,520 --> 00:15:02,840
+لذلك إذا كان الغين والقاف والخاء مكسور فقط نسميه
+
+165
+00:15:02,840 --> 00:15:08,400
+تفخيما نسبيا، يعني مفخم نسبة إذا قسنا بإيش؟ إذا
+
+166
+00:15:08,400 --> 00:15:14,640
+قسنا مع الحروف الترقيةطيب أو كذلك مثلا حرف الغين
+
+167
+00:15:14,640 --> 00:15:20,160
+والخ حرف الغين والخ يا أخوات لو كان مثلا هو ساكن
+
+168
+00:15:20,160 --> 00:15:26,480
+وقبله مكسور أيضا يفخم تفخيمه نسبيا حرف الغين إذا
+
+169
+00:15:26,480 --> 00:15:31,920
+كان ساكن وما قبله مكسور أيضا نسميه مفخم تفخيم نسبى
+
+170
+00:15:31,920 --> 00:15:36,080
+هذه يا أخوات هو القسم الأول وهو التفخيم أو الحروف
+
+171
+00:15:36,080 --> 00:15:39,640
+التي تفخمه دائما ما هي الحروف التي تفخمه دائما؟
+
+172
+00:15:41,390 --> 00:15:46,070
+حروف الاستعلاء المجموعة في قوله خص صداق تنقر كذلك
+
+173
+00:15:46,070 --> 00:15:50,710
+في عندنا القسم الثاني وهو حروف التي ترقق دائما وهي
+
+174
+00:15:50,710 --> 00:15:54,870
+التي نسميها حروف الاستفان حروف الاستفال وهي باقي
+
+175
+00:15:54,870 --> 00:15:58,810
+حروف اللغة العربية نحن أخدنا في المخالج الحروف في
+
+176
+00:15:58,810 --> 00:16:04,000
+عندنا الصفات حروف الاستعلاء وضده الاستفانحروف
+
+177
+00:16:04,000 --> 00:16:07,840
+الاستعلاق مجموعة في قوله خص ضغط القذر وهي الحروف
+
+178
+00:16:07,840 --> 00:16:13,580
+التي تفخم دائما وضدها الاستفال وهي يعني كل الحروف
+
+179
+00:16:13,580 --> 00:16:18,680
+ترقق دائما معدى حرف الألف واللام والرا لأن هذه
+
+180
+00:16:18,680 --> 00:16:23,060
+الحروف التلاتة اللي تندرج تحت القسم الثالث وهو
+
+181
+00:16:23,060 --> 00:16:26,740
+الذي يفخم في حالات ويرقق في حالات إذا حروف
+
+182
+00:16:26,740 --> 00:16:31,080
+الاستفال كلها ترققلو .. لو قلنا مثلا من ياتي
+
+183
+00:16:31,080 --> 00:16:35,340
+بأمثلة على الحروف الاستفال المراققة طبعا باقي حروف
+
+184
+00:16:35,340 --> 00:16:38,840
+اللغة العربية ما عدا إلا الألف وإلا موراة فهي لها
+
+185
+00:16:38,840 --> 00:16:43,380
+حالات معينة طيب، الآن من ياتي بأمثلة على حروف
+
+186
+00:16:43,380 --> 00:16:51,310
+الاستفال، فضليسائلين هل نقول ها سائلين ها سائلين
+
+187
+00:16:51,310 --> 00:16:58,190
+أو سائلين لا نقول صا انما نقول سا فنجد ان ال S
+
+188
+00:16:58,190 --> 00:17:04,290
+مرققة او مثال اخر منية بأمثلة تفضلي تامر لا نقول
+
+189
+00:17:04,290 --> 00:17:11,270
+طامر تامر حرف الت مرقق منية بأمثلة اخرىنادمين أو
+
+190
+00:17:11,270 --> 00:17:17,650
+النار لا نقول النار النار مفخمة لأ هي النار ملققة
+
+191
+00:17:17,650 --> 00:17:27,130
+النادمين تامر سامر ساهر سائد دافق كل هذه حروف ما
+
+192
+00:17:27,130 --> 00:17:31,930
+لها؟مُرَقَقَة فعندنا القسم الثاني وهي حروف
+
+193
+00:17:31,930 --> 00:17:37,410
+الاستفال تُرَقَق دائما معدى تلت حروف اللي هي الألف
+
+194
+00:17:37,410 --> 00:17:41,750
+واللام والرا وهذه الحروف التلاتة هي التي تُفخّم في
+
+195
+00:17:41,750 --> 00:17:45,730
+حالات وتُرَقَق في حالات نشوف القسم الثالث أيضا هي
+
+196
+00:17:45,730 --> 00:17:49,730
+اللتي يُفخّم في حالات ويرقق في حالات وهي الألف
+
+197
+00:17:49,730 --> 00:17:57,700
+واللام والرا ويلحق فيها الغُنّةالحال الأولى وهي
+
+198
+00:17:57,700 --> 00:18:03,180
+أحوال الألف طبعا الألف لا يوصف بتفخيم ولا ترقيم
+
+199
+00:18:03,180 --> 00:18:07,820
+لأنه يفخم في حالات ويرقق في حالات والألف يا أخوات
+
+200
+00:18:07,820 --> 00:18:13,600
+يتبع الحرف الذي قبله فإن كان ما قبله مفخما فخما
+
+201
+00:18:13,600 --> 00:18:18,920
+وإن كان ما قبله مرقق رققإذا حرف الألف لا يوصف
+
+202
+00:18:18,920 --> 00:18:23,300
+بحروف الاستعلاء ولا الاستفال يعني لا يوصف بالتفخين
+
+203
+00:18:23,300 --> 00:18:27,960
+الدائم ولا بالتقيق الدائم بل هو حرف تابع للحرف
+
+204
+00:18:27,960 --> 00:18:33,360
+الذي قبله فإن كان ما قبله حرف مفخم فخم وإن كان ما
+
+205
+00:18:33,360 --> 00:18:38,200
+قبله حرف مراقق رقم نرى أول شيء النقطة الأولى إذا
+
+206
+00:18:38,200 --> 00:18:41,980
+كان الحرف اللي قبله مفخما مثل الط
+
+207
+00:18:44,450 --> 00:18:50,870
+إما نجد هنا يا أخوات أن حرف الألف قلنا آه مفخّم
+
+208
+00:18:50,870 --> 00:18:56,510
+يعني لا نقول التامة نقول الطا فالألف آه طول الفضل
+
+209
+00:18:56,510 --> 00:19:02,650
+ليش قلنا آه لأنها مفخمة تتبع ما قبلها فلمّا كان
+
+210
+00:19:02,650 --> 00:19:08,750
+حرف الطا هذا مفخما فخمة الألف الذي تليهي كذلك
+
+211
+00:19:09,470 --> 00:19:15,690
+الصابرين لا نقول السابرين نقول الصى الصابرين
+
+212
+00:19:15,690 --> 00:19:20,010
+فاهمنا الألف لأن حرف اللذي قبل الألف هو حرف
+
+213
+00:19:20,010 --> 00:19:27,010
+الصادماله مفهما كذلك الضالين لا نقول الدالين لو
+
+214
+00:19:27,010 --> 00:19:32,540
+قلنا الدالين معناها دال دال ملققةلكن هي الضاه ..
+
+215
+00:19:32,540 --> 00:19:36,620
+الضاه .. فلمّا كانت الضاه حرف من حروف الاستعناء
+
+216
+00:19:36,620 --> 00:19:42,160
+ومفخم بيحكم على حرف الألف الذي يليه أيضا بالتفهيم
+
+217
+00:19:42,160 --> 00:19:46,440
+فنقول الضالين
+
+218
+00:19:46,440 --> 00:19:54,310
+كذا كقولةقال حرف القاف و جاء وراه حرف الألف إذا
+
+219
+00:19:54,310 --> 00:19:58,970
+بيحكم على الألف بالتفخيم هذه اللي هو حرف الألف
+
+220
+00:19:58,970 --> 00:20:05,510
+اللي يتبع ما قبله تفخيما طيب لو كان ما قبله مرققا
+
+221
+00:20:05,510 --> 00:20:12,510
+يرقق من يأتي بأمثلة على الألف المرققة التي تتبع ما
+
+222
+00:20:12,510 --> 00:20:19,830
+قبلها؟ فضليسائلين بنفع نقول سائلين ما .. لا نقول
+
+223
+00:20:19,830 --> 00:20:28,270
+سائلين نقول سائلين سائلين تفضلي ملادنة
+
+224
+00:20:28,270 --> 00:20:33,090
+تائلين
+
+225
+00:20:35,810 --> 00:20:40,870
+العالمين بنفع نقول العالمين، العالمين، ما بنفع
+
+226
+00:20:40,870 --> 00:20:44,890
+نقول العالمين صحيح أنه مثلا بعض الدول تفخم الحروف
+
+227
+00:20:44,890 --> 00:20:48,610
+كلها مثلا يعني أقولنا أهل الكويت تفخموا تفخيم
+
+228
+00:20:48,610 --> 00:20:49,490
+الحروف العالمين
+
+229
+00:21:07,410 --> 00:21:16,770
+هنا سائلينتائمين شاء جاء يعني ترقق الألف لأن ما
+
+230
+00:21:16,770 --> 00:21:21,990
+قبلها مرققا إلا في حالة الألف بعد اللام أو الرا
+
+231
+00:21:22,820 --> 00:21:28,300
+الألف اللي بعد اللام تتبع اللام في لفظ الجلالة لأن
+
+232
+00:21:28,300 --> 00:21:32,800
+اللام نفسها في لفظ الجلالة أحيانا تفخم وأحيانا
+
+233
+00:21:32,800 --> 00:21:37,560
+ترقق إذا كانت اللام مفخمة هي الألف فخمناها وإذا
+
+234
+00:21:37,560 --> 00:21:43,260
+كانت اللام مراققة تراقق الألف يعني الألف بعد اللام
+
+235
+00:21:43,260 --> 00:21:48,280
+في لفظ الجلالة الله يعني أنا أقول مثلا إحناالله
+
+236
+00:21:48,280 --> 00:21:53,440
+الان الله الالف اللي بعد الام في لفظ الجلالة قلنا
+
+237
+00:21:53,440 --> 00:22:01,340
+اه الله ان الله رسول الله لأن الله ممكن مرققة مثلا
+
+238
+00:22:01,340 --> 00:22:08,880
+قال الله مثلا يقول الله مثلا الام في لفظ الجلالة
+
+239
+00:22:08,880 --> 00:22:13,200
+مفخمة لأن الالف مفخمة لأن اللام مفخمة لكن باسم
+
+240
+00:22:13,200 --> 00:22:19,850
+اللهالألف مراققة لأن اللام مراققة لأن اللام طبعا
+
+241
+00:22:19,850 --> 00:22:24,070
+لها أحكام حكم اللام في رفض الجلالة تفخم في حالات
+
+242
+00:22:24,070 --> 00:22:28,810
+وترقق في حالات الألف بتتبع اللام إن كانت اللام
+
+243
+00:22:28,810 --> 00:22:33,950
+مفخمة فخمنها وإن كانت اللام مراققة رققناها نشوف
+
+244
+00:22:33,950 --> 00:22:39,510
+هنا مثلا قال الله قال الله الله اللام مفخم ولا
+
+245
+00:22:39,510 --> 00:22:46,580
+مراققة؟مفخمة لذلك الله الألف مفخمة إذا الألف اللي
+
+246
+00:22:46,580 --> 00:22:51,860
+في لفظ الجلالة تتبع اللام اللي في لفظ الجلالة فإن
+
+247
+00:22:51,860 --> 00:22:57,400
+كانت اللام مفخمة فقمت وإن كانت اللام مرققة رققت
+
+248
+00:22:57,400 --> 00:23:02,400
+يعني تدقيق مثلا بسم الله الرحمن الرحيم أو لله ما
+
+249
+00:23:02,400 --> 00:23:10,340
+في السماوات وما في الأرض لله بنفع نقول للهما بتفخن
+
+250
+00:23:10,340 --> 00:23:18,320
+او بسم الله الاله الالف مرققة لانه بتكون اللام
+
+251
+00:23:18,320 --> 00:23:25,060
+مرققة اذا كسر اذا كانت مسموقة بيكسركذلك يا أخوات
+
+252
+00:23:25,060 --> 00:23:30,320
+الألف اللى بعد الرا بس الألف اللى بعد الرا دائما
+
+253
+00:23:30,320 --> 00:23:36,540
+بتكون مالها مفخمة ليش طيب؟ لأنه معروفة الرا اللى
+
+254
+00:23:36,540 --> 00:23:42,380
+وراها ألف بتكون مفتوحة فاش مجال ان تكون الرا وراها
+
+255
+00:23:42,380 --> 00:23:46,640
+ألف ومقصورة يعني لو واحد قال مثلا راشد بنفع يقول
+
+256
+00:23:46,640 --> 00:23:51,100
+راشد إلا إذا كان في حالة واحدة عندنا في قرائتنا
+
+257
+00:23:51,100 --> 00:23:55,070
+اللى بسم الله مجريها ومرساهاهنا طبعا باسم الله
+
+258
+00:23:55,070 --> 00:24:01,610
+مجريها ومرساها لأن الرا مرجريه الألف كمان هي ترفض
+
+259
+00:24:01,610 --> 00:24:06,670
+بالإمالة ومعنى الإمالة يعني أن الألف يرفض ما بين
+
+260
+00:24:06,670 --> 00:24:13,110
+الألف واليا لا نقول ا ولا اي نقول ايه فعشان هيك
+
+261
+00:24:13,110 --> 00:24:20,020
+هذه مستثنيةبمعنى إن الألف بعد الرا دائما بتكون
+
+262
+00:24:20,020 --> 00:24:25,640
+مالها مفخمة، لأن الرا التي وراءها الألف لا تكون
+
+263
+00:24:25,640 --> 00:24:30,240
+إلا مفتوحة، وإذا كانت الرا مفتوحة كما سوف نأخذها
+
+264
+00:24:30,240 --> 00:24:34,930
+إن شاء الله في أحكام الرا، الرا المفتوحة تفخمفلما
+
+265
+00:24:34,930 --> 00:24:42,030
+كان حرف الرا مفخما قبل الألف، فالألف مالها؟ مفخمة،
+
+266
+00:24:42,030 --> 00:24:45,970
+إذا الألف بعد الرا مفخمة، المفهوم يا أخوات، إلا في
+
+267
+00:24:45,970 --> 00:24:50,750
+حالة واحدة، وهي في قوله تعالى بسم الله مجريها
+
+268
+00:24:50,750 --> 00:24:54,970
+ومرساهاوهذه يعني القراءة في قراءة حفظ تقرأ
+
+269
+00:24:54,970 --> 00:24:58,850
+بالإمالة وهي الكلمة الوحيدة في كل المصحف على حسب
+
+270
+00:24:58,850 --> 00:25:03,670
+قراءة حفظ طبعا في قراءات أخرى بنجد هناك إمالة لكن
+
+271
+00:25:03,670 --> 00:25:08,050
+عندنا نحن لا يوجد إمالة إلا في هذه الكلمة بسم الله
+
+272
+00:25:08,050 --> 00:25:12,990
+مجريها ومرساها فلما كانت الرا يعني وراها ألف و
+
+273
+00:25:12,990 --> 00:25:18,790
+الألف ما بين اليائي و الألف إذا بتكون الرا ممالة و
+
+274
+00:25:18,790 --> 00:25:24,510
+الألف ممالة فنقول مجريها ومرساهاإذا أخذنا حكم
+
+275
+00:25:24,510 --> 00:25:28,870
+الألف يتبع ما قبله من حيث التفخيم والترقيق نستثنى
+
+276
+00:25:28,870 --> 00:25:33,410
+منه الألف اللي بعد اللام في لفظ الجلالة الألف إذا
+
+277
+00:25:33,410 --> 00:25:38,430
+كانت اللام مفخّة مفخّة منها في لفظ الجلالة زي الله
+
+278
+00:25:38,430 --> 00:25:46,500
+أو مرققةرققناها بسم الله لانقول بسم الله كويس؟
+
+279
+00:25:46,500 --> 00:25:51,480
+وكذلك بعد الرا الألف بعد الرا بتكون دايما مفخمة
+
+280
+00:25:51,480 --> 00:25:56,720
+لأن الرا بتكون مفخمة دايما إلا في حالة واحدة في
+
+281
+00:25:56,720 --> 00:26:00,120
+المصحف عندنا في حسب قراءة حفصة عن عاصم وهي بسم
+
+282
+00:26:00,120 --> 00:26:05,690
+الله مجريها ومرساها تقرأ بالإمالةيلحقوا في هذه
+
+283
+00:26:05,690 --> 00:26:09,910
+الحروف اللي هي الغنى، الغنى في التثقيم أو في
+
+284
+00:26:09,910 --> 00:26:17,290
+الإخفاء، يعني متى تُخفى الحروف أو النون الساكنة؟
+
+285
+00:26:17,290 --> 00:26:20,870
+تُخفى النون الساكنة إذا جاء بعدها أي حرف من حروف
+
+286
+00:26:20,870 --> 00:26:25,050
+الإخفاء، ما هي حروف الإخفاء يا أخوات؟ مجموعة في
+
+287
+00:26:25,050 --> 00:26:28,890
+قوله؟ أحسنتي
+
+288
+00:26:35,240 --> 00:26:40,060
+أول حرف من كل كلمة بتكون خمساشر كلمات خمساشر حرف
+
+289
+00:26:40,060 --> 00:26:45,100
+أي حرف من هذه الحروف جاء بعد النون الساكنة أو
+
+290
+00:26:45,100 --> 00:26:48,780
+التنوين بيحكم على النون الساكنة أو التنوين
+
+291
+00:26:48,780 --> 00:26:55,080
+بالاخفاء طيب الاخفاء هذا اخفاء بغنىفالغنة اللي في
+
+292
+00:26:55,080 --> 00:27:00,420
+الإخفاء أحيانًا بتكون مفخمة و أحيانًا بتكون مرققة،
+
+293
+00:27:00,420 --> 00:27:05,500
+ما تتفخم إذا كان الحرف، حرف الإخفاء الذي جاء بعدها
+
+294
+00:27:05,500 --> 00:27:12,180
+مفخّان، و إذا ما تترقق، لو كان ما بعدها حرف مرقق،
+
+295
+00:27:12,180 --> 00:27:15,780
+وهي غنة اللي تبقى في الإخفاء فقط، يعني مثلًا، هي
+
+296
+00:27:15,780 --> 00:27:22,690
+عكس الألف نعمالألف تتبع ما قبلها الغنى تتبع ما
+
+297
+00:27:22,690 --> 00:27:29,910
+بعدها هنا يا أخوات مثلا لتركبن طبق عن طبق عن طبق
+
+298
+00:27:29,910 --> 00:27:36,630
+فنجد أن النون بعدها حرف الط هنا عن طبق حرف الط من
+
+299
+00:27:36,630 --> 00:27:43,740
+حروف الإخفاء كيف نقرأها؟عان طبق فلما كان حرف الطة
+
+300
+00:27:43,740 --> 00:27:48,680
+حرف من حروف الاستعلاء يعني مفخما بيحكم على الغنى
+
+301
+00:27:48,680 --> 00:27:55,520
+بالتفخيم فمنقرأها ونملأ الفم بها نقول عن طبقة عن
+
+302
+00:27:55,520 --> 00:28:01,590
+طبقة فالغنى بتفخم فالغنى تتبع ما قبلها كذلكمن
+
+303
+00:28:01,590 --> 00:28:08,990
+صلصال، من صلصال، الغنى بيكون مفخمة لأن حرف الصد
+
+304
+00:28:08,990 --> 00:28:14,630
+الذي جاء بعد النون الساكنة من حروف الاستعلاق، كذلك
+
+305
+00:28:14,630 --> 00:28:41,170
+من ضلةماذا الذي؟ ماذا الذي؟ ماذا
+
+306
+00:28:41,170 --> 00:28:46,970
+الذي؟لنجد أن الغنى تُرقّق إذا جاء بعدها حرف من
+
+307
+00:28:46,970 --> 00:28:52,310
+حروف الاستفال يعني مُرَقَقًا وإذا كان قد جاء بعدها
+
+308
+00:28:52,310 --> 00:28:55,650
+حرف من حروف الاستعلاء يعني مُفَخّمًا يُفَخّ
+
+309
+00:28:55,650 --> 00:29:01,090
+تُفَخّم الغنى إذا الألف تتبع ما قبلها والغنى تتبع
+
+310
+00:29:01,090 --> 00:29:07,670
+ما بعدهاالنقطة الثالثة يا أخوات هي الـ lamb اللام
+
+311
+00:29:07,670 --> 00:29:12,010
+في رفض الجلالة اللام بشكل عام دايما بتكون مرقق على
+
+312
+00:29:12,010 --> 00:29:21,880
+وحدها مثال و ذلك ولي طلطفولي ترطف واختلاف ألسنتكم
+
+313
+00:29:21,880 --> 00:29:30,740
+وألوانكم اللام ساكنة وكذلك نجدها أنها مرققة فالأصل
+
+314
+00:29:30,740 --> 00:29:36,480
+في اللام الترقيق لكن اللام في لفظ الجلالة تفخم في
+
+315
+00:29:36,480 --> 00:29:40,740
+حالات وترقق في حالات ما هو حكم اللام في لفظ
+
+316
+00:29:40,740 --> 00:29:44,820
+الجلالة من حيث التفخيم والترقيق؟يعني متى تفخم
+
+317
+00:29:44,820 --> 00:29:52,640
+اللام في لفظ الجلالة الله؟ احسنتى
+
+318
+00:29:52,640 --> 00:29:57,740
+اذا سبقها حرف مفتوح من يأتي بمثال على حرف المفتوح؟
+
+319
+00:29:59,530 --> 00:30:11,090
+قال الله إن الله شهد الله من فخم اللام إن الله من
+
+320
+00:30:11,090 --> 00:30:16,810
+فخم اللام قال الله من فخم اللام ليش؟ لأن اللام في
+
+321
+00:30:16,810 --> 00:30:23,390
+لفظ الجلالة سُبق بحرف مفتوحطب هى واحدة يعني متى
+
+322
+00:30:23,390 --> 00:30:28,910
+يفخم اللام فى لفظ الجلالة إذا سبقها حرف مفتوح هى
+
+323
+00:30:28,910 --> 00:30:33,230
+واحدة اتنين اذا
+
+324
+00:30:33,230 --> 00:30:38,110
+سبقت بحرف مضموم إذا سبقها حرف مضموم مثال ذلك عبد
+
+325
+00:30:38,110 --> 00:30:44,870
+الله عبد الله مابينفع نقول عبد الله عبد الله بتجيش
+
+326
+00:30:44,870 --> 00:30:48,610
+أصلا بتكون ثقيلة على اللسان لأن أحكام التجويد يعني
+
+327
+00:30:48,610 --> 00:30:53,670
+وجدتوحتى تكون خفيفة على اللسان و تيسر النطب
+
+328
+00:30:53,670 --> 00:30:59,270
+بالحروف فعندما نقول ناقة الله ناقة الله فخمنا
+
+329
+00:30:59,270 --> 00:31:08,450
+اللام كتاب الله رسول الله محمد الرسول الله او مثلا
+
+330
+00:31:08,450 --> 00:31:15,490
+في قوله واذ قالوا اللهم واذ قالوا اللهم اللام مفخم
+
+331
+00:31:15,490 --> 00:31:21,060
+ولا مرقق هنامفاخمة دى واذ قالوا اللهم طبعا واذ
+
+332
+00:31:21,060 --> 00:31:25,580
+قالوا اللهم ال .. ال wow طبعا هنا تخلصنا من التقاء
+
+333
+00:31:25,580 --> 00:31:29,260
+الساكنين أخذناها احنا سابقا في واذ قالوا اللهم
+
+334
+00:31:29,260 --> 00:31:32,840
+تخلصنا من التقاء الساكنين بحث ايه؟ بحث الساكن
+
+335
+00:31:32,840 --> 00:31:37,180
+الأول وهو حرف ال wow وهو الجماعةأه يعني الاصل في
+
+336
+00:31:37,180 --> 00:31:42,700
+كلمة و إذ قالوا اللهم في عيننا ال wow هنا بتحدث
+
+337
+00:31:42,700 --> 00:31:45,920
+لأنه تخلصه من الاتقاء الساكنين ال wow ساكنة و
+
+338
+00:31:45,920 --> 00:31:51,800
+اللهم ساكنة تخلص من الاتقاء الساكنين بحث ايه؟ بحث
+
+339
+00:31:51,800 --> 00:31:56,960
+الساكن الأول إذا كان حرف من حروف المدوالألف اللي
+
+340
+00:31:56,960 --> 00:32:07,120
+هنا قالوا هي الفارقة تكتب ولا تلفظ ولا وقف ولا
+
+341
+00:32:07,120 --> 00:32:12,470
+وصلةواللهم همس الوصف طبعا تسفط وتلفظ اللام فإذا
+
+342
+00:32:12,470 --> 00:32:15,550
+الساكنين اللي عندنا أو الحرفين اللي عندنا واذ
+
+343
+00:32:15,550 --> 00:32:22,510
+قالوا اللهم اللام مضمومة اللام مضموطة قالوا اللام
+
+344
+00:32:22,510 --> 00:32:25,310
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+345
+00:32:25,310 --> 00:32:27,230
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+346
+00:32:27,230 --> 00:32:27,230
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+347
+00:32:27,230 --> 00:32:27,250
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+348
+00:32:27,250 --> 00:32:33,330
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+349
+00:32:33,330 --> 00:32:33,330
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+350
+00:32:33,330 --> 00:32:33,330
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+351
+00:32:33,330 --> 00:32:33,330
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+352
+00:32:33,330 --> 00:32:33,330
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+353
+00:32:33,330 --> 00:32:37,100
+اللام اللام اللام اللام اللام اللأو مثلا في قوله
+
+354
+00:32:37,100 --> 00:32:43,440
+تعالى وما الله وما الله أيضا في قوله تعالى وما
+
+355
+00:32:43,440 --> 00:32:48,780
+الله ما طبعا هنا ما حرف مد حرف المد ساكن وقبله
+
+356
+00:32:48,780 --> 00:32:54,400
+مفتوح والله اللام ساكنه تخلص من اتقاء الساكنين
+
+357
+00:32:54,400 --> 00:33:01,100
+بحذف حرف المد الأول لماليش نقرأها نقول وما الله
+
+358
+00:33:01,100 --> 00:33:07,360
+فالميم مفتوحةواللام في لفظ الجلالة جاء بعد الميم
+
+359
+00:33:07,360 --> 00:33:12,360
+المفتوحة بتفخم اللام فنقول وما الله هذا بالنسبة
+
+360
+00:33:12,360 --> 00:33:16,640
+لللام في لفظ الجلالة من حيث التفهيم يعني متى تفخم
+
+361
+00:33:16,640 --> 00:33:21,100
+اللام في لفظ الجلالة؟ إذا
+
+362
+00:33:21,100 --> 00:33:29,560
+سبقها فتح مثل شهد الله أو سبقها ضم مثل رسول الله
+
+363
+00:33:29,560 --> 00:33:35,560
+طب متى توقق اللام في لفظ الجلالة؟إذا سُبقت بكسر
+
+364
+00:33:35,560 --> 00:33:40,540
+تُرقق اللام في لفظ الجلالة إذا سُبقت بكسر فنلفظ
+
+365
+00:33:40,540 --> 00:33:45,780
+اللام لا نقول الله نقول الله مثال ذلك هتفضل إيه
+
+366
+00:33:45,780 --> 00:33:51,960
+بسم الله الرحمن الرحيم بسم الله لا نقول باسم الله
+
+367
+00:33:51,960 --> 00:33:56,940
+لا نقول باسم الله وإنما نقول باسم الله الرحمن
+
+368
+00:33:56,940 --> 00:34:04,880
+الرحيم أو مثلا في قول تعالى لله لله الحمدلله الحمد
+
+369
+00:34:04,880 --> 00:34:07,280
+اللام هنا اللام اللي في لفظ الجلالة هي اللام
+
+370
+00:34:07,280 --> 00:34:11,920
+الثانية اللام الأولى اللام الجر هي أصلا لالله
+
+371
+00:34:11,920 --> 00:34:15,080
+الحمد و حدثت همسة الوصل و أضغمت اللام مع اللام
+
+372
+00:34:15,080 --> 00:34:20,040
+فتقرأ لله اللام الأولى هي اللام الجر المكسورة و
+
+373
+00:34:20,040 --> 00:34:24,360
+اللام الثانية هذه هي اللام بتاعة لفظ الجلالة فلما
+
+374
+00:34:24,360 --> 00:34:29,380
+سُبقت اللام في لفظ الجلالة بحرف مكسور لا نقول لله
+
+375
+00:34:29,380 --> 00:34:35,930
+الحمدماذا نقول؟ لله الحمد كذلك في قوله قُل اللهم
+
+376
+00:34:35,930 --> 00:34:42,170
+طبعا هي أصلا قُل اللهم اللام ساكنة كيف نتخلص من
+
+377
+00:34:42,170 --> 00:34:48,370
+التقاء الساكنين؟ بالكسر فنقول قُل اللهم قُل اللهم
+
+378
+00:34:48,370 --> 00:34:52,830
+تخلصنا من التقاء الساكنين بالكسر فقلنا قُل اللهم
+
+379
+00:34:52,830 --> 00:34:58,820
+بمعنى أن اللام في رفض الجلالة اللهممسبوقة بحرف كسر
+
+380
+00:34:58,820 --> 00:35:03,400
+فنقرأها قُل اللهم قُل اللهم كذلك في قول الله تعالى
+
+381
+00:35:03,400 --> 00:35:07,660
+قُلْ هُوَ اللَّهُ أَحَدٌ اللَّهُ الصَّمَدُ هنا أحد
+
+382
+00:35:07,660 --> 00:35:14,130
+الله الصمد لا أقرأها أحد الله الصمدنقرأها لوحدها
+
+383
+00:35:14,130 --> 00:35:19,930
+قل هو الله أحدون الله الصمد أحدونيه تخلصنا من
+
+384
+00:35:19,930 --> 00:35:24,930
+التقاء الساكنين بالكسر هي أصلا أحدون أنهم ساكنة
+
+385
+00:35:24,930 --> 00:35:28,930
+والله الصمد أيضا اللام ساكنة نتخلص من التقاء
+
+386
+00:35:28,930 --> 00:35:33,350
+الساكنين بالتحريك بالكسر فنقول قل هو الله أحدون
+
+387
+00:35:33,350 --> 00:35:39,420
+الله الصمد لكن لو وقفنا عن قل هو الله أحدالله
+
+388
+00:35:39,420 --> 00:35:42,980
+الصمد يجوز فاش فيه مانع لكن في حالة الواصل قل هو
+
+389
+00:35:42,980 --> 00:35:46,260
+الله أحد واني الله الصمد ان اكتفي أخوات بهذا القدر
+
+390
+00:35:46,260 --> 00:35:51,680
+لأن الحرف التالت ان شاء الله وهو الحرف الرا الذي
+
+391
+00:35:51,680 --> 00:35:55,100
+يجوز في حالات يفكر في حالات ويرقق في حالات هذا
+
+392
+00:35:55,100 --> 00:35:58,280
+يحتاج إلى يعني موضوع آخر ان شاء الله هناخده في
+
+393
+00:35:58,280 --> 00:36:00,800
+الدرس القادم بارك الله فيكم والسلام عليكم ورحمة
+
+394
+00:36:00,800 --> 00:36:01,420
+الله وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/akGe2V3J0HY_raw.json b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/akGe2V3J0HY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ddac1d6bb6700116a407c4310548e27224a7e384
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/akGe2V3J0HY_raw.json
@@ -0,0 +1 @@
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"probability": 0.90283203125}, {"start": 282.37, "end": 282.61, "word": " لا", "probability": 0.53466796875}, {"start": 282.61, "end": 282.95, "word": " بنية", "probability": 0.947998046875}, {"start": 282.95, "end": 283.37, "word": " الإعراض", "probability": 0.91357421875}, {"start": 283.37, "end": 283.91, "word": " عنها", "probability": 0.99365234375}, {"start": 283.91, "end": 284.23, "word": " يعني", "probability": 0.943115234375}, {"start": 284.23, "end": 284.41, "word": " أنا", "probability": 0.7353515625}, {"start": 284.41, "end": 284.71, "word": " عندما", "probability": 0.90185546875}, {"start": 284.71, "end": 285.05, "word": " أقول", "probability": 0.95166015625}, {"start": 285.05, "end": 285.91, "word": " الحمد", "probability": 0.9501953125}, {"start": 285.91, "end": 286.41, "word": " لله", "probability": 0.974365234375}, {"start": 286.41, "end": 286.87, "word": " ربي", "probability": 0.76220703125}, {"start": 286.87, "end": 288.25, "word": " العالمين", "probability": 0.9928385416666666}, {"start": 288.25, "end": 289.39, "word": " الآن", "probability": 0.6470947265625}, {"start": 289.39, "end": 289.73, "word": " أنا", "probability": 0.81396484375}, {"start": 289.73, "end": 290.35, "word": " وقفت", "probability": 0.8583984375}, {"start": 290.35, "end": 290.91, "word": " ولا", "probability": 0.6708984375}, {"start": 290.91, "end": 291.45, "word": " قطعت", "probability": 0.9597981770833334}], "temperature": 1.0}, {"id": 14, "seek": 31266, "start": 292.78, "end": 312.66, "text": "و أوقفت القراءة بنية التنفس تنفست بعدين قلت الرحمن الرحيم وقف برضه مالك يوم الدين أوقفت القراءة إذا هذا كله يسمى وقف أوقفتها بنية استيناف التلوة و بتنفس حتى أاخد نفس و أستمر في التلوة", "tokens": [2407, 5551, 30543, 5172, 2655, 25062, 2288, 16606, 3660, 44945, 10632, 16712, 1863, 36178, 6055, 1863, 36178, 2655, 39182, 9957, 12174, 1211, 2655, 34892, 5016, 27842, 34892, 5016, 32640, 4032, 4587, 5172, 4724, 43042, 3224, 3714, 6027, 4117, 7251, 20498, 32748, 9957, 5551, 30543, 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"probability": 0.6529541015625}, {"start": 297.56, "end": 297.96, "word": " قلت", "probability": 0.8658854166666666}, {"start": 297.96, "end": 298.58, "word": " الرحمن", "probability": 0.8076171875}, {"start": 298.58, "end": 299.56, "word": " الرحيم", "probability": 0.9775390625}, {"start": 299.56, "end": 300.94, "word": " وقف", "probability": 0.88671875}, {"start": 300.94, "end": 301.26, "word": " برضه", "probability": 0.8797200520833334}, {"start": 301.26, "end": 302.24, "word": " مالك", "probability": 0.88818359375}, {"start": 302.24, "end": 302.6, "word": " يوم", "probability": 0.964111328125}, {"start": 302.6, "end": 303.5, "word": " الدين", "probability": 0.930908203125}, {"start": 303.5, "end": 304.32, "word": " أوقفت", "probability": 0.862548828125}, {"start": 304.32, "end": 304.88, "word": " القراءة", "probability": 0.9100341796875}, {"start": 304.88, "end": 305.28, "word": " إذا", "probability": 0.656982421875}, {"start": 305.28, "end": 305.5, "word": " هذا", "probability": 0.75732421875}, {"start": 305.5, "end": 305.8, "word": " كله", "probability": 0.970458984375}, {"start": 305.8, "end": 306.2, "word": " يسمى", "probability": 0.9879557291666666}, {"start": 306.2, "end": 306.64, "word": " وقف", "probability": 0.97119140625}, {"start": 306.64, "end": 307.68, "word": " أوقفتها", "probability": 0.91630859375}, {"start": 307.68, "end": 308.4, "word": " بنية", "probability": 0.837158203125}, {"start": 308.4, "end": 309.0, "word": " استيناف", "probability": 0.735107421875}, {"start": 309.0, "end": 309.5, "word": " التلوة", "probability": 0.8106689453125}, {"start": 309.5, "end": 309.7, "word": " و", "probability": 0.50634765625}, {"start": 309.7, "end": 310.3, "word": " بتنفس", "probability": 0.8819986979166666}, {"start": 310.3, "end": 310.84, "word": " حتى", "probability": 0.89892578125}, {"start": 310.84, "end": 311.12, "word": " أاخد", "probability": 0.720458984375}, {"start": 311.12, "end": 311.38, "word": " نفس", "probability": 0.992431640625}, 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320.65, "end": 321.45, "word": " بنيئة", "probability": 0.9271240234375}, {"start": 321.45, "end": 322.07, "word": " الإعراض", "probability": 0.9141845703125}, {"start": 322.07, "end": 322.47, "word": " عنها", "probability": 0.9892578125}, {"start": 322.47, "end": 323.47, "word": " والوقف", "probability": 0.75048828125}, {"start": 323.47, "end": 323.81, "word": " دائمًا", "probability": 0.787890625}, {"start": 323.81, "end": 323.85, "word": " يا", "probability": 0.57861328125}, {"start": 323.85, "end": 324.17, "word": " أخوات", "probability": 0.7757568359375}, {"start": 324.17, "end": 324.61, "word": " يكون", "probability": 0.97021484375}, {"start": 324.61, "end": 325.25, "word": " في", "probability": 0.9814453125}, {"start": 325.25, "end": 325.87, "word": " آخر", "probability": 0.991455078125}, {"start": 325.87, "end": 326.49, "word": " الكلمة", "probability": 0.9630533854166666}, {"start": 326.49, "end": 327.07, "word": " القرأنية", "probability": 0.9869384765625}, {"start": 327.07, "end": 327.79, "word": " ولا", "probability": 0.6826171875}, {"start": 327.79, "end": 328.11, "word": " يمكن", "probability": 0.9755859375}, {"start": 328.11, "end": 328.31, "word": " أن", "probability": 0.92529296875}, {"start": 328.31, "end": 328.69, "word": " يقع", "probability": 0.9895833333333334}, {"start": 328.69, "end": 328.87, "word": " في", "probability": 0.99072265625}, {"start": 328.87, "end": 329.65, "word": " منتصف", "probability": 0.979736328125}, {"start": 329.65, "end": 330.53, "word": " الكلمة", "probability": 0.9228515625}, {"start": 330.53, "end": 331.07, "word": " يعني", "probability": 0.785400390625}, {"start": 331.07, "end": 331.21, "word": " لا", "probability": 0.2509765625}, {"start": 331.21, "end": 331.37, "word": " يمكن", "probability": 0.829833984375}, {"start": 331.37, "end": 331.57, "word": " أن", "probability": 0.7177734375}, {"start": 331.57, "end": 331.69, "word": " يقول", "probability": 0.9189453125}, {"start": 331.69, "end": 333.35, "word": " المؤمنون", "probability": 0.93359375}, {"start": 333.35, "end": 333.57, "word": " أو", "probability": 0.71142578125}, {"start": 333.57, "end": 335.59, "word": " المؤمنون", "probability": 0.86767578125}, {"start": 335.59, "end": 336.07, "word": " مثلًا", "probability": 0.8609619140625}, {"start": 336.07, "end": 336.61, "word": " أو", "probability": 0.86572265625}, {"start": 336.61, "end": 337.07, "word": " يقطع", "probability": 0.7431640625}, {"start": 337.07, "end": 337.19, "word": " الكلمة", "probability": 0.78076171875}, {"start": 337.19, "end": 337.75, "word": " المستقي", "probability": 0.7517903645833334}], "temperature": 1.0}, {"id": 16, "seek": 35156, "start": 339.24, "end": 351.56, "text": "و بعدين قيم ما بينفع يقنع الكلمة أو يقف على منتصف الكلمة فالوقف يكون في على آخر الكلمة القرأنية حتى لو كان عندنا يعني كلمتين متصلات في الرسم", "tokens": [2407, 39182, 9957, 12174, 32640, 19446, 49374, 5172, 3615, 7251, 4587, 1863, 3615, 33251, 19528, 3660, 34051, 7251, 4587, 5172, 15844, 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الله فيكم و السلام عليكم", "tokens": [1863, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 4032, 1863, 24793, 1211, 16472, 13412, 16606, 21984, 8978, 13672, 4587, 16606, 25062, 18513, 2304, 4032, 26890, 4117, 21984, 8978, 24793, 4032, 21136, 37440, 25894, 24793], "avg_logprob": -0.1529947875274552, "compression_ratio": 1.5473684210526315, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1909.76, "end": 1910.48, "word": "نكتفي", "probability": 0.8126220703125}, {"start": 1910.48, "end": 1910.74, "word": " بهذا", "probability": 0.936279296875}, {"start": 1910.74, "end": 1911.2, "word": " القدر", "probability": 0.8347981770833334}, {"start": 1911.2, "end": 1912.02, "word": " ونكمل", "probability": 0.8819580078125}, {"start": 1912.02, "end": 1912.08, "word": " ان", "probability": 0.60546875}, {"start": 1912.08, "end": 1912.26, "word": " شاء", "probability": 0.97607421875}, {"start": 1912.26, "end": 1912.34, "word": " الله", "probability": 0.95654296875}, {"start": 1912.34, "end": 1912.46, "word": " في", "probability": 0.84228515625}, {"start": 1912.46, "end": 1912.8, "word": " اللقاء", "probability": 0.994140625}, {"start": 1912.8, "end": 1913.26, "word": " القادم", "probability": 0.99560546875}, {"start": 1913.26, "end": 1913.7, "word": " وبرك", "probability": 0.6270345052083334}, {"start": 1913.7, "end": 1913.8, "word": " الله", "probability": 0.92041015625}, {"start": 1913.8, "end": 1914.22, "word": " فيكم", "probability": 0.961669921875}, {"start": 1914.22, "end": 1914.44, "word": " و", "probability": 0.71875}, {"start": 1914.44, "end": 1914.68, "word": " السلام", "probability": 0.947021484375}, {"start": 1914.68, "end": 1915.0, "word": " عليكم", "probability": 0.93115234375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1915.576625, "duration_after_vad": 1851.755968749996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/bGzmOGH00Y0_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/bGzmOGH00Y0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..140878208eb968d7a00e04200a02894cdd7f6a4c
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/bGzmOGH00Y0_raw.srt
@@ -0,0 +1,2156 @@
+1
+00:00:12,800 --> 00:00:15,640
+أعوذ بالله السلام عليك من الشيطان الرجيم بسم الله
+
+2
+00:00:15,640 --> 00:00:19,200
+الرحمن الرحيم الصلاة والسلام على أشرف المرسلين ما
+
+3
+00:00:19,200 --> 00:00:23,340
+بعد يلا نبدأ يا بنات يلا اقرأيا بس
+
+4
+00:00:26,370 --> 00:00:33,340
+أهو من الله السميع العليم من الشيطان الراجيمبسم
+
+5
+00:00:33,340 --> 00:00:40,040
+الله الرحمن الرحيم حميم
+
+6
+00:00:40,040 --> 00:00:49,260
+تنزل الكتاب من الله العزيزي الحكيم إن في السماوات
+
+7
+00:00:49,260 --> 00:00:57,820
+والأرض لآيات للمؤمنين وفي خلقكم وما يبث من
+
+8
+00:01:01,400 --> 00:01:13,500
+أيات .. أيات لقوم يوقنون واختلاف الليل والنهار وما
+
+9
+00:01:13,500 --> 00:01:26,320
+أنزل الله وما أنزل الله من السماء من رزقهمن رزق
+
+10
+00:01:26,320 --> 00:01:34,740
+فأحيا به الأرض بعد موتها وتصريف الرياح وتصريف
+
+11
+00:01:34,740 --> 00:01:44,760
+الرياح آيات لقوم يعقلون تلك آيات الله نتلوها عليك
+
+12
+00:01:44,760 --> 00:01:56,460
+بالحق فبأي حديث بعد الله وآياته يؤمنونويل لكل أفاك
+
+13
+00:01:56,460 --> 00:02:08,700
+أثيم يسمع آية الله تتلى عليه ثم يصر مستكبرا ثم يصر
+
+14
+00:02:08,700 --> 00:02:19,120
+مستكبرا كأن لم يسمعها فبشره بعذاب أليموإذا علم من
+
+15
+00:02:19,120 --> 00:02:30,600
+آياتنا شيئا اتخذها هزوا أولئك لهم عذاب مهين من
+
+16
+00:02:30,600 --> 00:02:40,860
+ورائهم جهنم ولا يغني عنهم ولا يغني عنهم ما كسبوا
+
+17
+00:02:40,860 --> 00:02:50,790
+شيئا ولا ما اتخذواولما اتخذوا من دون الله أولياء
+
+18
+00:02:50,790 --> 00:03:01,990
+ولهم عذاب عظيم هذا هدا .. هذا هدا والذين كفروا
+
+19
+00:03:01,990 --> 00:03:09,290
+بآيات ربهم لهم عذاب من رجس أليم الله يفتح عليك
+
+20
+00:03:15,210 --> 00:03:20,290
+اقرايا هادئة يالا
+
+21
+00:03:20,290 --> 00:03:29,470
+اعوذ بالله من الشيطان الرجيم بسم الله وعظمه رباطيه
+
+22
+00:03:29,470 --> 00:03:35,590
+أبوه والذي سخر لكم البحر وانشجرهم ملكه فيه بأمره
+
+23
+00:03:35,590 --> 00:03:39,730
+لأ ماتمديش حرف المادة زيها ده حركتين فيه هي بأمره
+
+24
+00:03:41,400 --> 00:03:47,440
+الله الذي سخّ لكم البحر لتجري الحق فيه الأبرز
+
+25
+00:03:47,440 --> 00:03:54,600
+ويتبذروا من حبه و لعنكم تشكرهم و سخّ لكم ما في
+
+26
+00:03:54,600 --> 00:04:01,820
+السماوات و ما في الأرض جميعا منه إن في ذلك الآية
+
+27
+00:04:01,820 --> 00:04:09,710
+اللي قاملآيات لقوم يتفكرون تنوي المعلم اتغام بدون
+
+28
+00:04:09,710 --> 00:04:16,130
+غنى، تجافيش عنده لآيات
+
+29
+00:04:16,130 --> 00:04:21,250
+لقوم لآيات لقوم يتفكرون
+
+30
+00:04:30,610 --> 00:04:37,950
+بآيات لقوم يتفكرون أحسنت، نعم كل الذين آمنوا
+
+31
+00:04:37,950 --> 00:04:44,870
+يغفروا للذين لا يردون أي رضا ليجزي قوما بما كانوا
+
+32
+00:04:44,870 --> 00:04:52,230
+يفسدون قوما بما كانوا كل الذين آمنوا يغفروا للذين
+
+33
+00:04:52,230 --> 00:05:00,380
+لا يردون أي رضا ليجزي قوما بما كانوا يفسدونمن
+
+34
+00:05:00,380 --> 00:05:08,840
+عاملة .. من عاملة اظهار .. من عاملة اظهار .. من
+
+35
+00:05:08,840 --> 00:05:17,160
+عاملة اظهارها فلنفس ال .. ومن أساء .. لأ نفس الاشي
+
+36
+00:05:17,160 --> 00:05:26,320
+اظهر ومن أساءومنها سأب عليها ثم إلى ربكم ترجعون
+
+37
+00:05:26,320 --> 00:05:34,140
+ولقد آتينا بني إسرائيل الكتاب والقرن والنبوة
+
+38
+00:05:34,140 --> 00:05:43,660
+ورزقناهم من الطيبات وفضلناهم على العالمين وآتيناهم
+
+39
+00:05:43,660 --> 00:05:53,450
+بينات من الأمرفمقتله إلا من بعد ما .. إلا من بعد
+
+40
+00:05:53,450 --> 00:06:03,350
+ما جاءه العلم بغيا بينهم إن ربك
+
+41
+00:06:03,350 --> 00:06:10,750
+يقضي بينهم يوم القيامة يقضي بينهم يوم القيامة فيما
+
+42
+00:06:10,750 --> 00:06:18,930
+كان فيهمسجد بيه كانوا ال wow حركتين كانوا فيه في
+
+43
+00:06:18,930 --> 00:06:24,030
+ما كانوا فيه اختلفوا لأ هي كان زيها ده الحركتين في
+
+44
+00:06:24,030 --> 00:06:33,510
+ما كانوا فيه في ما كانوا فيه اختلفوا ثم جعلناك على
+
+45
+00:06:33,510 --> 00:06:39,790
+شريعة النمي الأمري فاتتبعها ولا تتبع أمك اوصلي
+
+46
+00:06:39,790 --> 00:06:42,270
+فاتتبعها ولا تتبع أمك
+
+47
+00:07:01,200 --> 00:07:09,820
+إنهم ليه غنوه في
+
+48
+00:07:09,820 --> 00:07:19,490
+إضغام ليه غنوهإنهم ليه قُلوا عنك من الله شيئا، وإن
+
+49
+00:07:19,490 --> 00:07:26,230
+الظالمين بعضهم أولياء
+
+50
+00:07:26,230 --> 00:07:34,310
+بعض، وإن الظالمين بعضهم أولياء بعض، والله وليهم
+
+51
+00:07:34,310 --> 00:07:35,510
+المستقيم
+
+52
+00:07:39,840 --> 00:07:49,080
+وهده ورحمه وهده ورحمته لقوم يوقنون
+
+53
+00:07:49,080 --> 00:07:58,660
+هذا بصار من الناس وهده ورحمه وهده ورحمه لقوم
+
+54
+00:07:58,660 --> 00:08:06,350
+يوقنونأم حسب الذين اشتغلوا السيئات أن نجعلهم
+
+55
+00:08:06,350 --> 00:08:16,590
+كالذين آملوا وعملوا الصيف سواء .. سواء نحياهم ..
+
+56
+00:08:16,590 --> 00:08:28,010
+بس مده مده كويس سواء نحياهم سواء نحياهم وماراتهم
+
+57
+00:08:32,270 --> 00:08:37,770
+الله يفتح عليك يقرايا
+
+58
+00:08:37,770 --> 00:08:38,190
+و يصرا
+
+59
+00:08:57,350 --> 00:09:08,250
+ولي تجزا في wow في wow ولي تجزا ولي .. ولي تجزا
+
+60
+00:09:10,900 --> 00:09:18,360
+والتجزا كل نفس بما كسبته لا يخلقه موظف أفرأت من
+
+61
+00:09:18,360 --> 00:09:23,080
+اتخذ إله هو هواب وأضربه الله على علمه وختم على
+
+62
+00:09:23,080 --> 00:09:31,220
+سمعه وقلبه وسب على سمعه وقلبه وجعل على
+
+63
+00:09:31,220 --> 00:09:39,400
+بصره غشا وتم فملو جعل على بصيره غشاوة فما يأتي من
+
+64
+00:09:39,400 --> 00:09:45,740
+بعد الله أفلا أتذكرون؟ وقالوا ما هي إن حياتنا
+
+65
+00:09:45,740 --> 00:09:52,360
+الدنيا نموت ونحيا وما يبقنا إلا الذهب وما لهم بذلك
+
+66
+00:09:52,360 --> 00:09:58,880
+من علم .. وما لهم بذلك من
+
+67
+00:09:58,880 --> 00:10:04,240
+علم .. من علم إنهم إلا يظنون .. قولني عنه الحرب
+
+68
+00:10:04,240 --> 00:10:11,410
+تانيةوإن .. إن .. إن هم .. إن هم إلا يظنون وإذا
+
+69
+00:10:11,410 --> 00:10:18,850
+تتلى عليه آياتنا بينات .. وإذا تتلى عليهم وإذا
+
+70
+00:10:18,850 --> 00:10:24,950
+تتلى عليهم آياتنا بينات إن ما كان حجتهم إلا ما كان
+
+71
+00:10:24,950 --> 00:10:35,720
+حجتهم كمفتوحة ما كان حجتهم إلاما كان حُشتهم إلا أن
+
+72
+00:10:35,720 --> 00:10:44,160
+قالوا أتوا بأبائنا
+
+73
+00:10:44,160 --> 00:10:48,180
+ما كان
+
+74
+00:10:48,180 --> 00:10:55,420
+حُشتهم إلا أن قالوا أتوا بأبائنا قالوا أتوا إلا أن
+
+75
+00:10:55,420 --> 00:11:01,420
+قالوا أتوا بأبائنا عن التقاء ساكنين قالوا
+
+76
+00:11:01,420 --> 00:11:07,650
+أتواما كان حجاتهم إلا أن قالوا أتوا بأبانا .. جيبي
+
+77
+00:11:07,650 --> 00:11:15,150
+.. جيبي الإخفاء أول .. أن قالوا أتوا ..
+
+78
+00:11:15,150 --> 00:11:20,810
+كويس يعني ما كان حجاتهم إلا أن قالوا .. أن قالوا
+
+79
+00:11:20,810 --> 00:11:25,170
+أتوا بأبانا .. صح؟ صح، بس جيبي الحرف المدحر اتين
+
+80
+00:11:25,170 --> 00:11:32,890
+.. قالوا أتوا بأبانا ..ما كانت مجزتهم إلا أن قالوا
+
+81
+00:11:32,890 --> 00:11:37,270
+أنتوا أبا .. بأبائنا إن كنتوا صادقين .. بالمبدل
+
+82
+00:11:37,270 --> 00:11:51,200
+تاني بأبائنا إن كنتوا .. بأبائنا إن كنتوا صادقينقل
+
+83
+00:11:51,200 --> 00:11:57,580
+الله يحييكم ثم يميتكم ثم يجمعكم إلى يوم القيامة لا
+
+84
+00:11:57,580 --> 00:12:03,740
+ريب فيه ولكن أكتر الناس لا يعلمون ولله ملك
+
+85
+00:12:03,740 --> 00:12:09,340
+السماوات والأرض ويوم تقوم الساعة يوم إذ يخسروا
+
+86
+00:12:09,340 --> 00:12:25,570
+المبطلون و ترى كل أمة جاثيةكل أمة
+
+87
+00:12:25,570 --> 00:12:34,830
+تدعى
+
+88
+00:12:34,830 --> 00:12:39,950
+إلى كتابها اليوم تجزون ما كنتم تعملون
+
+89
+00:12:46,310 --> 00:12:54,410
+أقرأ يا نهار بسم
+
+90
+00:12:54,410 --> 00:12:58,730
+الله الرحمن الرحيم بسم الله الرحمن الرحيم يعني
+
+91
+00:12:58,730 --> 00:13:02,970
+اعلى صوتك يا نهار مش ثاني اعشق اعشق اعشق اعشق اعشق
+
+92
+00:13:02,970 --> 00:13:03,730
+اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق
+
+93
+00:13:03,730 --> 00:13:05,570
+اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق
+
+94
+00:13:05,570 --> 00:13:08,190
+اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق
+
+95
+00:13:08,190 --> 00:13:14,210
+اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق اعشق
+
+96
+00:13:14,210 --> 00:13:20,120
+اععليكم بالحق
+
+97
+00:13:20,120 --> 00:13:24,620
+.. ترجعي
+
+98
+00:13:24,620 --> 00:13:31,940
+و قولي على النهار .. اننا كنا نستنفيكم .. نعم ..
+
+99
+00:13:31,940 --> 00:13:36,100
+جاهز؟ بعد انها لقراك
+
+100
+00:13:44,200 --> 00:13:45,600
+ماكنطون
+
+101
+00:14:14,360 --> 00:14:23,520
+وكنتم .. دي بيقول كمقوما مجرمين .. قوما مجرمين
+
+102
+00:14:23,520 --> 00:14:29,640
+وإذا قيل لهم وعد الله حق والساعة لا ريب فيها ..
+
+103
+00:14:29,640 --> 00:14:34,900
+اوصلي .. اوصلي يعني وعد الله حقه والساعته .. وعد
+
+104
+00:14:34,900 --> 00:14:38,140
+الله حقه والساعة لا ريب فيها .. والساعته ..
+
+105
+00:14:38,140 --> 00:14:44,560
+والساعة لا ريب فيها كنتم .. كنتم ندري ما الساعة
+
+106
+00:14:44,890 --> 00:14:53,770
+فانتظنوا ان اضنوا ان اضنوا وما دخلوه مصريقون
+
+107
+00:14:53,770 --> 00:14:56,970
+وبدلوهم
+
+108
+00:14:56,970 --> 00:15:03,670
+سيئات ما عملوه سيئات ما عملوه فحقق بهم ما كانوا
+
+109
+00:15:03,670 --> 00:15:11,450
+فيهم وحقق بهم ما كانوا فيه يستزقون وقيل لهم
+
+110
+00:15:15,200 --> 00:15:22,000
+ننساكم وقيل اليوم ننساكم مش اليوم، اليومة اليومة
+
+111
+00:15:22,000 --> 00:15:27,960
+وقيل اليوم ننساكم كما نسيتم اليوم ننساكم وقيل
+
+112
+00:15:27,960 --> 00:15:37,920
+اليوم ننساكم كما نسيتم لقاء يومكم لقاء لقاء يومكم
+
+113
+00:15:37,920 --> 00:15:39,240
+هذا
+
+114
+00:15:44,460 --> 00:15:53,140
+غنى عنه الحركتان وما لكم وما لكم ناصرين وما لكم
+
+115
+00:15:53,140 --> 00:16:03,880
+ناصرين قدى وما لكم وما لكم ناصرين ذلكم بأنكم
+
+116
+00:16:03,880 --> 00:16:07,900
+اتخدتم ايه اللي .. دي باولش يرفع الشفاوي و بعدين
+
+117
+00:16:07,900 --> 00:16:13,320
+ضم الميل بأنكم ذلكم بأنكم اتخدتم
+
+118
+00:16:15,950 --> 00:16:27,150
+بأنكم .. نهار .. بأنكم تخذتم
+
+119
+00:16:27,150 --> 00:16:39,010
+.. تخذتم .. آيات الله مذوة .. مذوة ووردكم
+
+120
+00:16:40,160 --> 00:16:49,880
+فغرقوا من حياته
+
+121
+00:16:49,880 --> 00:16:59,080
+الدنيا فاللهم لا يخرجوها منها ولا هم يستعبون
+
+122
+00:16:59,590 --> 00:17:05,510
+فلله الحمد رب السماوات .. فلله .. فلله الحمد رب
+
+123
+00:17:05,510 --> 00:17:09,350
+السماوات .. مافيش بس صح بس ارجع وصلك فلله .. فلله
+
+124
+00:17:09,350 --> 00:17:13,810
+الأرض و رب السماوات و رب الأرض و رب العالمين ..
+
+125
+00:17:13,810 --> 00:17:19,290
+مافيش و رب الأرض و رب العالمين .. و له الكبرياء في
+
+126
+00:17:19,290 --> 00:17:21,550
+السماوات .. و له الكبرياء
+
+127
+00:17:26,400 --> 00:17:30,920
+و في السماوات و القرض و هو العزيز الحكيم و هو
+
+128
+00:17:30,920 --> 00:17:38,260
+العزيز الحكيم و هو العزيز الحكيم و هو العزيز
+
+129
+00:17:38,260 --> 00:17:40,480
+الحكيم و هو العزيز الحكيم و هو العزيز الحكيم و هو
+
+130
+00:17:40,480 --> 00:17:40,480
+العزيز الحكيم و هو العزيز الحكيم و هو العزيز
+
+131
+00:17:40,480 --> 00:17:40,480
+الحكيم و هو العزيز الحكيم و هو العزيز الحكيم و هو
+
+132
+00:17:40,480 --> 00:17:40,480
+العزيز الحكيم و هو العزيز الحكيم و هو العزيز
+
+133
+00:17:40,480 --> 00:17:40,480
+الحكيم و هو العزيز الحكيم و هو العزيز الحكيم و هو
+
+134
+00:17:40,480 --> 00:17:40,700
+العزيز الحكيم و هو العزيز الحكيم و هو العزيز
+
+135
+00:17:40,700 --> 00:17:45,260
+الحكيم و هو العزيز الحكيم و هو العزيز الحكيم و هو
+
+136
+00:17:45,260 --> 00:17:54,440
+العزيز الحكيم و هو العزيز الحكيم و هو العزيز الحك
+
+137
+00:18:01,230 --> 00:18:10,970
+كل أمة تدعى إلى كتابها اليوم .. كل أمة تدعى إلى
+
+138
+00:18:10,970 --> 00:18:15,150
+كتابها اليوم .. تدعى
+
+139
+00:18:15,150 --> 00:18:22,130
+إلى .. كل أمة تدعى إلى كتابها اليوم تجيزون ما كنتم
+
+140
+00:18:22,130 --> 00:18:34,030
+تعملونهذا كتابنا ينطق عليكم بالحق إننا كنا نستنتق
+
+141
+00:18:34,030 --> 00:18:41,900
+ما كنتم تعملونفأما الذين آمنوا وعملوا الصالحات
+
+142
+00:18:41,900 --> 00:18:50,320
+فيدخلهم ربهم في رحمته، ذلك هو الفوز المبين وأما
+
+143
+00:18:50,320 --> 00:18:56,300
+الذين كفروا، أفلم تكنوا الآيات كتلة عليكم،
+
+144
+00:18:56,300 --> 00:19:05,930
+فاستكبرتم، فاستكبرتم وكنتم قوما مجرمينوإذا قيل إن
+
+145
+00:19:05,930 --> 00:19:13,190
+وعد الله حقه و الساعة لا عيب فيها، قلت ماندري ما
+
+146
+00:19:13,190 --> 00:19:17,430
+الساعة إن ضنوا إلا ضنوا
+
+147
+00:19:28,960 --> 00:19:35,880
+لو وما نحن بالمصطلح استيقنين وبدالهم سيئات ما
+
+148
+00:19:35,880 --> 00:19:43,060
+عملوا وحاق بهم ما كانوا بيه يستهزمون وقيل اليوم
+
+149
+00:19:43,060 --> 00:19:52,860
+ننساكم كما نسيتم لقاء يومكم هذا كما نسيتم لقاء
+
+150
+00:19:52,860 --> 00:19:57,560
+يومكم هذا ومأواكم الدار وما لكم
+
+151
+00:20:00,190 --> 00:20:08,210
+الناصرين. ذلكم بأنكم اتخذتم اي .. اتخذتم ايات الله
+
+152
+00:20:08,210 --> 00:20:15,610
+حذفا وغرزكم الحياة الدنيا فاليوم لا يخرجون منها
+
+153
+00:20:15,610 --> 00:20:23,350
+ولا هم يستعتقونفلله الحمد ورب السماوات ورب الأرض
+
+154
+00:20:23,350 --> 00:20:31,270
+ورب العالمين وله الكبرياء في السماوات والأرض وهو
+
+155
+00:20:31,270 --> 00:20:35,390
+العزيز والحجير بظهوم لها إيه كويس؟ هو هو وهو
+
+156
+00:20:35,390 --> 00:20:40,970
+العزيز والحجير الله أكبر الله أكبر إيش هالقناة؟
+
+157
+00:20:53,150 --> 00:21:16,330
+تعاصر في الضخان اه تقراي
+
+158
+00:21:16,330 --> 00:21:20,150
+اسرائيل بسم
+
+159
+00:21:20,150 --> 00:21:33,260
+الله الرحمن الرحيمحميم والكتاب المبين إنا أنفله في
+
+160
+00:21:33,260 --> 00:21:44,800
+ليلة مباركة إنا كنا منفلين فيها يفرق كل .. فيها
+
+161
+00:21:44,800 --> 00:21:57,330
+يفرق .. فيها يفرق كل أمر حكيمأمرا من عندنا إنا كنا
+
+162
+00:21:57,330 --> 00:22:02,410
+مرسلين رحمة
+
+163
+00:22:02,410 --> 00:22:14,650
+من ربك إنه هو السميع العليم رب السماوات والأرضوما
+
+164
+00:22:14,650 --> 00:22:26,050
+بينهما إن .. إن كنتم موقنين لا إله إلا هو يحيي
+
+165
+00:22:26,050 --> 00:22:38,410
+ويميت ربكم ورب آبائكم الأولين بل هم في شك يلعبون
+
+166
+00:22:38,890 --> 00:22:53,470
+فارتق بيوم تأتي السماء بدخان مبين يغش الناس
+
+167
+00:22:53,470 --> 00:23:04,230
+هذا عذاب عليم رب نكشف عن العذاب إنا مؤمنين مؤمنون
+
+168
+00:23:04,230 --> 00:23:12,800
+أنا له مثلأن لهم الذكرا وقد جاءهم .. أن لهم الذكرا
+
+169
+00:23:12,800 --> 00:23:22,740
+وقد .. أن لهم الذكرا وقد جاءهم رسول مبين ثم تولوا
+
+170
+00:23:22,740 --> 00:23:34,610
+عنه وقالوا معلمفقالوا معلم مجنون فقالوا معلم مجنون
+
+171
+00:23:34,610 --> 00:23:44,330
+إنكاشفوا العذاب قليلا إنكاشفوا العذاب إنكاشفوا
+
+172
+00:23:44,330 --> 00:23:54,200
+العذاب قليلا إنكم عائدون يوم نفسكيوم نبقش البقشة
+
+173
+00:23:54,200 --> 00:24:03,580
+الكبرى يوم نبقش البقشة الكبرى اننا منتقمون الله
+
+174
+00:24:03,580 --> 00:24:08,280
+يفتح عليها اقرأ يا صبري
+
+175
+00:24:11,050 --> 00:24:17,450
+من الله الرحمن الرحيم ولقد فتن قبلهم قوم فرعون
+
+176
+00:24:17,450 --> 00:24:30,670
+وجاءهم رسول كريم ان أدوا الي عباد الله ان أدوا
+
+177
+00:24:30,670 --> 00:24:36,410
+الي عباد الله اني لكم رسول أمين
+
+178
+00:24:39,310 --> 00:24:45,170
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+179
+00:24:45,170 --> 00:24:47,850
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+180
+00:24:47,850 --> 00:24:48,090
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+181
+00:24:48,090 --> 00:24:48,690
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+182
+00:24:48,690 --> 00:24:54,630
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+183
+00:24:54,630 --> 00:24:56,870
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+184
+00:24:56,870 --> 00:24:56,890
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+185
+00:24:56,890 --> 00:24:56,890
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+186
+00:24:56,890 --> 00:24:56,890
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+187
+00:24:56,890 --> 00:24:56,890
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+188
+00:24:56,890 --> 00:24:56,890
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+189
+00:24:56,890 --> 00:24:57,250
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+190
+00:24:57,250 --> 00:24:59,790
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+191
+00:24:59,790 --> 00:25:07,330
+و قال لا تعالوا على الله و قال لا تعالوا على الله
+
+192
+00:25:07,630 --> 00:25:19,730
+وإني عدت بربى وربكم أترجمون وإن
+
+193
+00:25:19,730 --> 00:25:25,790
+لم تؤمنوا لي
+
+194
+00:25:25,790 --> 00:25:38,230
+فاتسلون فدعى ربه أن هؤلاء قوم مجرمونفأسرق .. فأسرق
+
+195
+00:25:38,230 --> 00:25:42,110
+يا عبادي .. فأسرق يا عبادي .. فأسرق يا عبادي .. لأ
+
+196
+00:25:42,110 --> 00:25:44,950
+مافيش يعني الرقم اكسره فقط فأسرق يا عبادي .. أسرق
+
+197
+00:25:44,950 --> 00:25:52,650
+يا عبادي ليلة قيلة إنكم متبعون و أترك البحر .. و
+
+198
+00:25:52,650 --> 00:25:56,570
+أترك البحر .. و أترك البحر رهوان .. نمزق وصل يا
+
+199
+00:25:56,570 --> 00:26:01,950
+سابريا و أترك البحر .. و أترك البحر رهوان إنهم
+
+200
+00:26:01,950 --> 00:26:12,480
+جدهم مغرقونكم تركوا من جنة وعيون وزروع ومقام كريم
+
+201
+00:26:12,480 --> 00:26:19,660
+ونعمتين كانوا .. ونعمتين كانوا .. ونعمتين كانوا ..
+
+202
+00:26:19,660 --> 00:26:27,420
+ونعمتين كانوا فيها فاتين كذلك وأورثناها قوما آخرين
+
+203
+00:26:27,420 --> 00:26:32,450
+وأورثناها .. أجيب الحرف من الدب خلاصوأورثناها قوما
+
+204
+00:26:32,450 --> 00:26:42,130
+آخرين فما بكت عليهم السماء والأرض وما كانوا مغضرين
+
+205
+00:26:42,130 --> 00:26:50,870
+ولقد رجينا بني إسرائيل من العذاب المهيم من فرعون
+
+206
+00:26:50,870 --> 00:26:57,430
+إنه كان عليا من المسرفين ولقد اختارناهم على علم
+
+207
+00:26:57,430 --> 00:27:04,510
+على العالمينو آتيناهم من الآيات ما فيه بلاء .. و
+
+208
+00:27:04,510 --> 00:27:12,050
+آتيناهم من الآيات ما فيه بلاء مبين الله يفتح حاله
+
+209
+00:27:12,050 --> 00:27:22,690
+سجلت
+
+210
+00:27:22,690 --> 00:27:26,230
+اسمك يا عزيزي؟ ايه الشعب التناشي؟
+
+211
+00:27:30,920 --> 00:27:34,300
+شايف يامان عبد الراجل؟ لأ يامان الحماية اه يامان
+
+212
+00:27:34,300 --> 00:27:41,900
+الحماية بجانبك
+
+213
+00:27:41,900 --> 00:27:52,620
+عابير عبد الراجل عابير اليوم؟ اقرأ
+
+214
+00:27:52,620 --> 00:27:53,180
+يا عابير يا
+
+215
+00:27:57,590 --> 00:28:05,330
+إن أولئك لا يقولون إن هي إلا موتتنا الأولى وما ..
+
+216
+00:28:05,330 --> 00:28:11,430
+وما نحن بمشزين وما
+
+217
+00:28:11,430 --> 00:28:21,650
+نحن بمشارين فاتوا بأبائنا إن كنتوا صادقينأهم خير
+
+218
+00:28:21,650 --> 00:28:26,490
+أم قوم تبعوا
+
+219
+00:28:26,490 --> 00:28:30,570
+الذين قبلهم؟
+
+220
+00:28:30,570 --> 00:28:43,110
+أهم خير أم قوم تبعوا
+
+221
+00:28:43,110 --> 00:28:51,820
+الذينبعيوه الذين من يوم قبلهم أخلقناهم إنهم كانوا
+
+222
+00:28:51,820 --> 00:28:59,080
+مجرمين وما خلقنا السماوات والأرض وما بينهما لاعبين
+
+223
+00:28:59,080 --> 00:29:07,100
+ما خلقناهما إلا بالحق ولكن أكثرهم لا يعرفوا ولكن
+
+224
+00:29:07,100 --> 00:29:10,040
+أكثرهم ولكن
+
+225
+00:29:14,000 --> 00:29:21,600
+إن يوم الفصل
+
+226
+00:29:21,600 --> 00:29:24,980
+نقاتهم
+
+227
+00:29:24,980 --> 00:29:32,620
+أجمعين يوم لا يغني مودة عن مودة شديد
+
+228
+00:29:34,790 --> 00:29:49,310
+يوم لا يبني مولا عن مولا
+
+229
+00:29:49,310 --> 00:29:57,410
+شيئا ولا هم ينصرون إلا من رحم الله إنه هو العزيز
+
+230
+00:29:57,410 --> 00:29:57,690
+رحمه
+
+231
+00:30:04,610 --> 00:30:14,410
+ليغضي فالبطون كغني الحميم خلوه فاكلوه
+
+232
+00:30:14,410 --> 00:30:20,870
+إلى سواء الجحيم
+
+233
+00:30:20,870 --> 00:30:24,150
+ثم
+
+234
+00:30:24,150 --> 00:30:33,950
+صبوا فوق رأسي من عذاب الحميمنلعب بالحنين ضغ انك
+
+235
+00:30:33,950 --> 00:30:42,030
+أنت
+
+236
+00:30:42,030 --> 00:30:58,270
+العزيز الكريم ان هذا ما كنتم بيتمتعون كنتم
+
+237
+00:30:58,270 --> 00:30:59,190
+بيه
+
+238
+00:31:28,970 --> 00:31:36,920
+خلوني اعنوهجناه .. نقول جنه و اجيب الاطراف في جناه
+
+239
+00:31:36,920 --> 00:31:47,340
+و عيون يلبسون من صندس
+
+240
+00:31:47,340 --> 00:31:52,740
+و استبرق متقابلين
+
+241
+00:32:01,020 --> 00:32:10,600
+واستبرق المتقابلين كذلك وزوجناهم في قرنين يدعون
+
+242
+00:32:10,600 --> 00:32:19,720
+فيها يدعون فيها بكل فاتحة آمنين لا يضغطون فيها
+
+243
+00:32:19,720 --> 00:32:27,460
+الموت إلا الموتة الأولى ووقعهم عذاب الجحيم فضل من
+
+244
+00:32:27,460 --> 00:32:28,780
+ربك كذب
+
+245
+00:32:42,700 --> 00:32:45,820
+الله يفتح حالته
+
+246
+00:33:12,290 --> 00:33:23,690
+عشان ده درسك عشان ده درسك عشان
+
+247
+00:33:23,690 --> 00:33:27,510
+ده درسك عشان ده درسك عشان ده درسك عشان ده درسك
+
+248
+00:33:27,510 --> 00:33:29,390
+عشان ده درسك عشان ده درسك عشان ده درسك
+
+249
+00:33:32,880 --> 00:33:39,900
+أعوذ بالله من الشيطان الرجيم بسم الله الرحمن
+
+250
+00:33:39,900 --> 00:33:44,840
+الرحيم حاميم
+
+251
+00:33:52,780 --> 00:34:02,360
+حاميم والكتاب المبين إنا جعلناه قرآنا عربيا لعلكم
+
+252
+00:34:02,360 --> 00:34:13,410
+تعقلون وإنه في أمناالكتاب لدينا لعلي حكيم أفنضرب
+
+253
+00:34:13,410 --> 00:34:23,350
+عنكم الذكر صفحا أن كنتم قوما مسرفين وكم أرسلنا من
+
+254
+00:34:23,350 --> 00:34:33,010
+نبي في الأولين وما يأتيهم من نبي إلا كانوا به
+
+255
+00:34:33,010 --> 00:34:35,010
+يستهزئون
+
+256
+00:34:37,000 --> 00:34:47,880
+فأهلكنا أشد منهم بطشا ومضى مثل الأولين ولئن سألتهم
+
+257
+00:34:47,880 --> 00:34:55,640
+من خلق السماوات والأرضمن خلق السماوات والأرض ليقول
+
+258
+00:34:55,640 --> 00:35:03,800
+إن خلقهن العزيز العليم الذي جعل لكم الأرض مهدا
+
+259
+00:35:03,800 --> 00:35:11,800
+وجعل لكم فيها سبولا لعلكم تهتدون والذي .. والذي
+
+260
+00:35:11,800 --> 00:35:23,400
+نزل من السماء .. والذي نزل ..والذي نزل من السماء
+
+261
+00:35:23,400 --> 00:35:30,600
+ماء بقدر و الذي نزل من السماء
+
+262
+00:35:37,500 --> 00:35:47,920
+بقدر فأنشرنا به بلدة ميتة كذلك تخرجون والذي خلق
+
+263
+00:35:47,920 --> 00:35:56,420
+الأزواج كلها وجعل لكم من الفلك والأنعام ما تركبون
+
+264
+00:35:56,420 --> 00:36:05,700
+لتستووا على ظهوره ثم تذكروا نعمة ربكمثم تذكروا
+
+265
+00:36:05,700 --> 00:36:12,520
+نعمة ربكم إذا استويتم عليه وتقولوا سبحان الذي سخر
+
+266
+00:36:12,520 --> 00:36:19,040
+لنا هذا
+
+267
+00:36:19,040 --> 00:36:30,100
+وما كنا له مقرنين وإنا إلى ربنا لمن قلبون
+
+268
+00:36:45,240 --> 00:36:51,880
+هيبقى هيبقى هيبقى .. فلمّا آسفون .. فلمّا آسفون
+
+269
+00:36:51,880 --> 00:36:56,440
+انتقمنا منهم فأغرقناهم أشمعين فقمنا اغار منهم
+
+270
+00:36:56,440 --> 00:37:04,380
+فأغرقناهم انتقمنا منهم فأغرقناهم أشمعين فجعلناهم
+
+271
+00:37:04,380 --> 00:37:13,000
+سلفه ومثلا للآخرين للآخرين .. للآخرين ولمّا ضربت
+
+272
+00:37:13,440 --> 00:37:19,440
+ولمّا ضرب ابن مريم مثلا إذا قومك منه يصدون .. إذا
+
+273
+00:37:19,440 --> 00:37:26,240
+قومك .. إذا قومك منه يصدون .. ليش بدي بيخاف نون؟
+
+274
+00:37:26,240 --> 00:37:36,360
+منه يصدون .. منه يصدون .. يصدون .. يصدون .. وقالوا
+
+275
+00:37:36,360 --> 00:37:43,210
+آيات أخيهم هو ما ضربوه لك إلا جدالة إلا جدالةإلا
+
+276
+00:37:43,210 --> 00:37:49,430
+جدلا بل هم قوم قصمهم أنه إلا عبد أنعمنا عليه
+
+277
+00:37:49,430 --> 00:37:56,630
+واجعلناه مثلا لبني إسرائيل واجعلناه مثلا لبني
+
+278
+00:37:56,630 --> 00:38:06,010
+إسرائيل و لو نشاء لجعلنا منكم ملائكة ملائكة في
+
+279
+00:38:06,010 --> 00:38:12,310
+الأرض يخلقون الله يفتح عليه يالا يا مريم
+
+280
+00:38:15,570 --> 00:38:24,770
+بسم الله الرحمن الرحيم وإنه لعلم للساعة فلا تنهرن
+
+281
+00:38:24,770 --> 00:38:38,590
+بها واتبعون هذا صراط مستقيم ولا يصدنكم الشيطان إنه
+
+282
+00:38:38,590 --> 00:38:41,690
+لكم عدو مبين
+
+283
+00:38:43,380 --> 00:38:59,900
+ولما جاء عيسى بالبينات قال قد جئتكم بالحكمة
+
+284
+00:38:59,900 --> 00:39:04,600
+ولمبين لكم بعض الذي تختلفون فيه
+
+285
+00:39:08,290 --> 00:39:16,710
+قال قد جئتكم بالحكمة ولأبين لكم بعض الذي تختلفون
+
+286
+00:39:16,710 --> 00:39:26,490
+فيه فاتقوا الله وأطيعون إن الله هو ربي وربكم
+
+287
+00:39:26,490 --> 00:39:32,670
+فاعقدوا هذا صراط مستقيم
+
+288
+00:39:34,360 --> 00:39:42,840
+فاختلف الأحزاب من بينهم فويل للذين ظلموا من عذاب
+
+289
+00:39:42,840 --> 00:39:57,040
+يوم أليم هل ينظرون إلى الساعة تأتيهم بغتة وهم لأهل
+
+290
+00:39:57,040 --> 00:40:06,160
+ينظرون إلى الساعة تأتيهم بغتته و هم لا يشعرون
+
+291
+00:40:12,040 --> 00:40:23,280
+هل ينظرون إلى الساعة أن تأتيهم بغتة و هم لا يشعرون
+
+292
+00:40:23,280 --> 00:40:26,380
+الأخلاق
+
+293
+00:40:26,380 --> 00:40:31,300
+يومئذ بعضهم لبعض عدون
+
+294
+00:40:33,570 --> 00:40:44,870
+يا عباد لا خوف عليكم اليوم ولا أنتم تحزنون الذين
+
+295
+00:40:44,870 --> 00:40:54,710
+آمنوا بآياتنا وكانوا مسلمين ادخلوا الجنة أنتم
+
+296
+00:40:54,710 --> 00:41:07,110
+وأزواجكم تحبرونيقاف عليهم
+
+297
+00:41:07,110 --> 00:41:19,230
+بصحاف من ذهب وكواب وفيها ماذا اشتهي الأنفس وتلد
+
+298
+00:41:19,230 --> 00:41:26,890
+الأعين وانتم فيها خالدون الله أكبر عليك بسم الله
+
+299
+00:41:26,890 --> 00:41:27,110
+الرحمن الرحيم
+
+300
+00:41:31,780 --> 00:41:37,500
+تقرا يا إسراء؟ بسم الله الرحمن الرحيم و تلك الجنة
+
+301
+00:41:37,500 --> 00:41:42,360
+التي أورستموها
+
+302
+00:41:42,360 --> 00:41:50,320
+بما كنتم تعملون بما كنتم تعملون لكم فيها فاكهة
+
+303
+00:41:50,320 --> 00:42:00,180
+كتيرة منها تأكلونإن المجرمين في عداد جهنم خالدون
+
+304
+00:42:00,180 --> 00:42:05,160
+لا يفتروا
+
+305
+00:42:05,160 --> 00:42:12,220
+عنهم وهم فيه مبلسون وما ظلمناهم ولكن .. ولكن كانوا
+
+306
+00:42:12,220 --> 00:42:13,380
+هم الظالمين
+
+307
+00:42:18,770 --> 00:42:23,710
+ونادوا يا مالك .. ونادوا .. ونادوا يا مالك ..
+
+308
+00:42:23,710 --> 00:42:29,190
+ونادوا يا مالك .. ونادوا يا مالك ليقضي .. يا مالك
+
+309
+00:42:29,190 --> 00:42:34,470
+.. ونادوا يا مالك ليقضي .. ليقضي علينا ربك ..
+
+310
+00:42:34,470 --> 00:42:39,970
+مافيش يعني، الظهر مكسور، ليقضي علينا ربك ليقضي ..
+
+311
+00:42:39,970 --> 00:42:45,570
+ليقضي .. ليقضي علينا ربك، مافيش يعني، ليقضي ..
+
+312
+00:42:45,570 --> 00:42:54,800
+ليقضي علينا ..ليقضي علينا .. ليقضي علينا .. ليقضي
+
+313
+00:42:54,800 --> 00:43:00,400
+علينا .. ليقضي علينا .. ليقضي علينا ربك قال .. ربك
+
+314
+00:43:00,400 --> 00:43:05,000
+.. ربك قال ان .. لأ ربك ديك تقصري .. ديك تجفي قولي
+
+315
+00:43:05,000 --> 00:43:13,080
+ربك ليقضي علينا ربك .. ربك .. ليقضي علينا .. ليقضي
+
+316
+00:43:13,080 --> 00:43:22,460
+علينا ربك ..ليقضي علينا ربك .. ليقضي علينا ربك ..
+
+317
+00:43:22,460 --> 00:43:28,360
+ليقضي علينا ربك .. ليقضي علينا ربك .. ليقضي علينا
+
+318
+00:43:28,360 --> 00:43:34,820
+ربك .. ليقضي علينا ربك .. ليقضي علينا ربك .. ليقضي
+
+319
+00:43:34,820 --> 00:43:39,620
+علينا ربك .. ليقضي علينا ربك .. ليقضي علينا ربك ..
+
+320
+00:43:39,620 --> 00:43:43,040
+ليقضي علينا ربك .. ليقضي علينا ربك .. ليقضي علينا
+
+321
+00:43:43,040 --> 00:43:43,040
+ربك .. ليقضي علينا ربك .. ليقضي علينا ربك .. ليقضي
+
+322
+00:43:43,040 --> 00:43:43,040
+علينا ربك .. ليقضي علينا ربك .. ليقضي علينا ربك ..
+
+323
+00:43:43,040 --> 00:43:43,040
+ليقضي علينا ربك .. ليقضي علينا ربك .. ليقضي علينا
+
+324
+00:43:43,040 --> 00:43:47,010
+ربك .. ليقضي علينا ربك .. ليقضيفقد جئناكم بالحق
+
+325
+00:43:47,010 --> 00:43:53,190
+ولكن أكتركم للحق كارهون أبرموا
+
+326
+00:43:56,160 --> 00:44:02,140
+أم أبرموا أمرا فإننا مبرمون .. مبرمون .. مبرم ..
+
+327
+00:44:02,140 --> 00:44:09,360
+فإننا مبرمون أم يحسبون أن .. أم يحسبون .. أم يحسب
+
+328
+00:44:09,360 --> 00:44:16,300
+.. أم يحسبون أننا لا نسمع سرهم والجواهم بل ورسلنا
+
+329
+00:44:16,300 --> 00:44:22,520
+لابلى و رسولنا لديهم يكتبون .. بلى و رسولنا لديهم
+
+330
+00:44:22,520 --> 00:44:23,800
+يكتبون .. بلى و رسولنا لديهم يكتبون .. بلى و
+
+331
+00:44:23,800 --> 00:44:24,000
+رسولنا لديهم يكتبون .. بلى و رسولنا لديهم يكتبون
+
+332
+00:44:24,000 --> 00:44:24,420
+.. بلى و رسولنا لديهم يكتبون .. بلى و رسولنا لديهم
+
+333
+00:44:24,420 --> 00:44:28,540
+يكتبون .. بلى و رسولنا لديهم يكتبون .. بلى و
+
+334
+00:44:28,540 --> 00:44:33,060
+رسولنا لديهم يكتبون .. بلى و رسولنا لديهم يكتبون
+
+335
+00:44:33,060 --> 00:44:36,680
+.. بلى و رسولنا لديهم يكتبون .. بلى و رسولنا لديهم
+
+336
+00:44:36,680 --> 00:44:40,520
+يكتبون .. بلى و رسولنا لديهم يكتبون .. بلى و
+
+337
+00:44:40,520 --> 00:44:48,690
+رسولنا لديهم يكتبون ..فأنا أول العابدين، سبحان رب
+
+338
+00:44:48,690 --> 00:44:55,230
+.. سبحان رب السماوات والأرض، رب العرش، عما يطفون،
+
+339
+00:44:55,230 --> 00:45:00,950
+فبرهم يخوضوا ويلعبوا ويلعبوا حتى .. حتى يلاقوا
+
+340
+00:45:00,950 --> 00:45:06,730
+يومهم اللي .. يومهم .. يوم .. حتى يلاقوا يومهم ..
+
+341
+00:45:06,730 --> 00:45:12,030
+مش فخمة، مش يلاقوا .. ملاقوا .. حتى يلاقوا يومهم
+
+342
+00:45:12,030 --> 00:45:23,290
+اللي .. يومهم .. يومهم ..يومه .. يومهم .. فذرهم
+
+343
+00:45:23,290 --> 00:45:29,890
+يخوضوا ويلعبوا حتى يلاقوا يومهم يومهم .. يومهم
+
+344
+00:45:29,890 --> 00:45:35,410
+اللي .. يومهم .. يومهم .. يومهم .. يومهم .. يومهم
+
+345
+00:45:35,410 --> 00:45:40,530
+.. يومهم .. يومهم .. يومهم .. يومهم .. يومهم ..
+
+346
+00:45:40,530 --> 00:45:40,850
+يومهم .. يومهم .. يومهم .. يومهم .. يومهم .. يومهم
+
+347
+00:45:40,850 --> 00:45:40,850
+.. يومهم .. يومهم .. يومهم .. يومهم .. يومهم ..
+
+348
+00:45:40,850 --> 00:45:42,610
+يومهم .. يومهم .. يومهم .. يومهم .. يومهم .. يومهم
+
+349
+00:45:42,610 --> 00:45:43,370
+.. يومهم .. يومهم .. يومهم .. يومهم .. يومهم ..
+
+350
+00:45:43,370 --> 00:45:43,370
+يومهم .. يومهم .. يومهم .. يومهم .. يومهم .. يومهم
+
+351
+00:45:43,370 --> 00:45:43,370
+.. يومهم .. يومهم .. يومهم .. يومهم .. يومهم ..
+
+352
+00:45:43,370 --> 00:45:43,430
+يومهم .. يومهم .. يومهم
+
+353
+00:45:48,090 --> 00:45:56,410
+سماء إله وفي الأرض إله وهو الحكيم العليم وستجرف
+
+354
+00:45:56,410 --> 00:46:03,290
+الذي له المُلف السماوات والأرض وما بينهما وعنده
+
+355
+00:46:03,290 --> 00:46:12,050
+علم الساعة وعنده علم الساعة وإليه ترجعون ولا يملك
+
+356
+00:46:12,050 --> 00:46:14,010
+الذين يجعون منه
+
+357
+00:46:26,430 --> 00:46:34,490
+ولئن سألتهم اظهار
+
+358
+00:46:34,490 --> 00:46:43,730
+من خلقهمولإن سألتهم ما خلقهم ليقولوا .. ليقولوا إن
+
+359
+00:46:43,730 --> 00:46:52,930
+الله فأنهم فخون و .. و قيل يا ربي .. و قيل يا ربي
+
+360
+00:46:52,930 --> 00:47:01,850
+إنها .. إن هؤلاء قوم لا يفهمون فاصبح عنهم و قل
+
+361
+00:47:01,850 --> 00:47:05,090
+سلام فسوف يعلمون
+
+362
+00:47:09,260 --> 00:47:11,920
+افتح على الصورة في الصورة اقرأ ايه تاني يعني ايه
+
+363
+00:47:11,920 --> 00:47:22,120
+تاني بسم
+
+364
+00:47:22,120 --> 00:47:30,080
+الله الرحمن الرحيم حامي لأ مش حامي حامي حركتين فقط
+
+365
+00:47:30,080 --> 00:47:33,080
+حامي حامي
+
+366
+00:47:37,610 --> 00:47:43,750
+لأ مد السين أكتر سينقاف
+
+367
+00:47:43,750 --> 00:47:55,470
+عين عين سينقاف كذلك يوحي إليك و إلى الذين من قبلك
+
+368
+00:47:55,470 --> 00:48:03,990
+الله العزيز الحكيم له ما في السماوات و ما في الأرض
+
+369
+00:48:03,990 --> 00:48:10,470
+و هو اللانيل العظيمالتكاب السماوات يتفطرن ..
+
+370
+00:48:10,470 --> 00:48:17,290
+يتفطرن من فوقهم والملائكة
+
+371
+00:48:17,290 --> 00:48:26,230
+يصفحون بحمد ربهم ويتقفلو يستغفرون لمن في الأرض لمن
+
+372
+00:48:26,230 --> 00:48:34,370
+في الأرض لمن في الأرض ألا إن الله هو الغفور الرحيم
+
+373
+00:48:34,370 --> 00:48:45,130
+والذين اتخذوا من دونه أولياء الله الله حفيظ عليهم
+
+374
+00:48:45,130 --> 00:48:56,500
+وما أنت عليهم بوتيك الله يفتح عناقرأ يالا بسم
+
+375
+00:48:56,500 --> 00:49:08,440
+الله بسم الله كمان شفايا كلنا بناخدها بسم
+
+376
+00:49:08,440 --> 00:49:15,500
+الله الرحمن الرحيم وكذلك أوحينا اليك قرآن عربي
+
+377
+00:49:15,500 --> 00:49:36,210
+لتنذرهم للقراءة لتنذرهملتنذر أم القرى ومن حولها
+
+378
+00:49:36,210 --> 00:49:44,170
+ومن حولها وتنذر يوم الجمع لا ريب فيه فريقهم في
+
+379
+00:49:44,170 --> 00:49:53,920
+الجنة وفريقهم ..فريق في الجنة وفريق في السعير ولو
+
+380
+00:49:53,920 --> 00:50:04,700
+شاء الله لجعلهم همته واحدة ولكن يدخل من يشاء في
+
+381
+00:50:04,700 --> 00:50:12,260
+رحمته والظالمون ما لهم وليهم ولا نصير ما لهم
+
+382
+00:50:14,190 --> 00:50:23,570
+والظالبون ما لهم ولي ولا نصير أن اتخذوا من دومه
+
+383
+00:50:23,570 --> 00:50:31,770
+أولياء فللقلق الله هو الولي و الله هو الولي و هو
+
+384
+00:50:31,770 --> 00:50:38,760
+يحيي الموت و هو يحيي الموتفالله هو الولي وهو يحيي
+
+385
+00:50:38,760 --> 00:50:50,180
+الموتى وهو على كل شي قدير وما اختلفتم فيه
+
+386
+00:50:50,180 --> 00:50:55,500
+فحكمه
+
+387
+00:50:55,500 --> 00:51:04,730
+إلى الله ذلكم الله ربي عليه توكلت وإليه القنينفاضر
+
+388
+00:51:04,730 --> 00:51:12,750
+السماوات والأرض جعل لكم
+
+389
+00:51:12,750 --> 00:51:16,830
+من أنفسكم
+
+390
+00:51:16,830 --> 00:51:18,010
+أزواجا
+
+391
+00:51:22,070 --> 00:51:31,310
+فاطر السماوات والأرض جعل لكم من أنفسكم أزواجا ومن
+
+392
+00:51:31,310 --> 00:51:39,170
+الأنعان أزواجا جعل
+
+393
+00:51:39,170 --> 00:51:46,070
+لكم من .. جعل لكم من أنفسكم أزواجا ومن الأنعان من
+
+394
+00:51:46,070 --> 00:51:47,430
+أنفسكم
+
+395
+00:51:51,650 --> 00:51:57,870
+جعل لكم من أنفسكم أزواجا .. من أنفسكم أزواجا زي
+
+396
+00:51:57,870 --> 00:52:07,810
+الاخفاء الأول من أنفسكم جعل لكم من أنفسكم أزواجا
+
+397
+00:52:07,810 --> 00:52:15,150
+ومن الأنعان أزواجا يدرعكم .. أزواجا يدرعكم ومن
+
+398
+00:52:15,150 --> 00:52:22,290
+الأنعان أزواجا يدرعكم .. يدرعكمو من الأنعان أزواجا
+
+399
+00:52:22,290 --> 00:52:32,950
+يدرأكم فيه
+
+400
+00:52:32,950 --> 00:52:39,990
+ليس كمثله شيء وهو السميع
+
+401
+00:52:39,990 --> 00:52:47,910
+البصير الله يفتح عليه، ترأي هنا؟له مقاليد السماوات
+
+402
+00:52:47,910 --> 00:52:52,950
+والأرض يبسط الرزقى .. الرزقى .. يبسط الرزقى ..
+
+403
+00:52:52,950 --> 00:52:58,650
+يبسط الرزقى .. يبسط الرزقى لمن يشاء .. لمن يشاء ..
+
+404
+00:52:58,650 --> 00:53:05,850
+لمن يشاء ويقدر .. ويقدر .. ويقدر .. لمن يشاء ويقدر
+
+405
+00:53:05,850 --> 00:53:15,500
+.. لمن يشاء ويقدر إنه بكل شيء ناليمشرع لكم من
+
+406
+00:53:15,500 --> 00:53:23,880
+الدين ما وصى
+
+407
+00:53:23,880 --> 00:53:37,380
+به نوحا والذي أوحىنوحى والذى
+
+408
+00:53:37,380 --> 00:53:42,940
+أوحينا
+
+409
+00:53:42,940 --> 00:53:47,220
+اليك وما وصينا به إبراهيم
+
+410
+00:53:49,690 --> 00:53:57,390
+وما وصينا به إبراهيم .. به إبراهيم وموسى وعيسى
+
+411
+00:53:57,390 --> 00:54:06,250
+إبراهيم وموسى وعيسى أن أقيم الدين ولا .. وعيسى أن
+
+412
+00:54:06,250 --> 00:54:12,330
+.. وعيسى أن أقيم الدين ولا تتفرقوا
+
+413
+00:54:16,670 --> 00:54:23,930
+لأ ماشي معاك ما تدعوهم
+
+414
+00:54:23,930 --> 00:54:35,770
+اليه
+
+415
+00:54:35,770 --> 00:54:43,530
+اللهالله يشتبئ ال .. يشتبئ ال .. الله يجتبي إليه
+
+416
+00:54:43,530 --> 00:54:47,850
+الله يشتبئ إليه من .. مد .. مد المدة من خاصة الله
+
+417
+00:54:47,850 --> 00:54:54,390
+يشتبئ إليه من يشاء .. من يشاء .. من يشاء ويهدي
+
+418
+00:54:54,390 --> 00:55:01,070
+إليه مين .. مين ينيب .. مين ينيب .. مين ينيب وما
+
+419
+00:55:01,070 --> 00:55:05,530
+تفرقوا إلا من .. مين .. مد المدة يا عزيزيوما
+
+420
+00:55:05,530 --> 00:55:13,910
+تفرقوا إلا ما .. من بعد ما جاءهم ال .. ما جاءهم
+
+421
+00:55:13,910 --> 00:55:20,390
+العلم ما جاءهم العلم بغيا .. بغيا بينهم .. بغيا
+
+422
+00:55:20,390 --> 00:55:29,370
+بينهم ولولا كلمة سبقت من ربهم ولولا كلمة سبقتولولا
+
+423
+00:55:29,370 --> 00:55:41,370
+كلمة سبقت من ربك الإله إلى أجن مسمى
+
+424
+00:55:41,370 --> 00:55:53,170
+لقضى بينهم وإن الذين أورثوا الكتاب من بعدهم لفي شك
+
+425
+00:55:53,170 --> 00:55:54,770
+منه مريم
+
+426
+00:55:59,950 --> 00:56:06,050
+اقرأ يا رواندي اقرأ من أول الصفة فاضل السماوات
+
+427
+00:56:06,050 --> 00:56:12,690
+والأرض فاضل السماوات والأرض جعل لكم من أنفسكم
+
+428
+00:56:12,690 --> 00:56:19,250
+أذواجا ومن الأنعان أذواجا ومن الأنعان أذواجا
+
+429
+00:56:19,250 --> 00:56:28,080
+يضرؤكم فيه يضرؤكم فيهليس كمثلي شيء و هو السامع و
+
+430
+00:56:28,080 --> 00:56:33,760
+البصير له مقاليد السماوات و الأرض يبسطوا الرزق
+
+431
+00:56:33,760 --> 00:56:37,060
+يبسطوا
+
+432
+00:56:37,060 --> 00:56:40,640
+الرزق لمن يشاء و يقدر
+
+433
+00:56:43,940 --> 00:56:51,420
+بكل شيء عليم شرع لكم من الدين ما وصى بيه نوحه و
+
+434
+00:56:51,420 --> 00:56:57,300
+اللى بيه نوحه و اللى بيه نوحه و اللى بيه نوحه و
+
+435
+00:56:57,300 --> 00:57:03,020
+اللى اوحينا اليك و ما وصينا بيه إبراهيم
+
+436
+00:57:04,950 --> 00:57:21,050
+به إبراهيم وموسى وعيسى أن أقيم
+
+437
+00:57:21,050 --> 00:57:27,930
+الدين ولا تتفرقوا بكفرة على المشركين ما تدعوهم
+
+438
+00:57:27,930 --> 00:57:35,570
+إليه الله يشتري إليه من يشارما يشاء .. جيبوا
+
+439
+00:57:35,570 --> 00:57:45,830
+الأبران .. ما يشاء و يهدي إليه من ينيب وما تطرقوا
+
+440
+00:57:45,830 --> 00:57:58,010
+إلا من بعد ما جاءه من العلمما جاءهم
+
+441
+00:57:58,010 --> 00:58:06,690
+العلم بغيا بينهم ولولا كلمة سبقت من ربك إلى أجر
+
+442
+00:58:06,690 --> 00:58:13,830
+مسمى لقد يبينهم
+
+443
+00:58:16,850 --> 00:58:25,830
+لأخذ يابينهم وإن الذين أورثوا الكتاب
+
+444
+00:58:25,830 --> 00:58:33,770
+من بعدهم لدي شك منهم وليه الله يفتح عليه رأيه يا
+
+445
+00:58:33,770 --> 00:58:36,990
+نور؟
+
+446
+00:58:36,990 --> 00:58:40,230
+أبدا
+
+447
+00:58:40,230 --> 00:58:46,470
+من الشيطان العظيمفلذلك فادعوا واستقموا كما أمرت
+
+448
+00:58:46,470 --> 00:58:54,650
+فلذلك فادعوا واستقموا كما أمرت فلذلك فادعوا
+
+449
+00:58:54,650 --> 00:58:57,030
+واستقموا كما أمرت فلذلك فادعوا واستقموا كما أمرت
+
+450
+00:58:57,030 --> 00:58:57,610
+فلذلك فادعوا واستقموا كما أمرت فلذلك فادعوا
+
+451
+00:58:57,610 --> 00:58:57,610
+واستقموا كما أمرت فلذلك فادعوا واستقموا كما أمرت
+
+452
+00:58:57,610 --> 00:58:57,610
+فلذلك فادعوا واستقموا كما أمرت فلذلك فادعوا
+
+453
+00:58:57,610 --> 00:58:57,910
+واستقموا كما أمرت فلذلك فادعوا واستقموا كما أمرت
+
+454
+00:58:57,910 --> 00:59:04,570
+فلذلك فادعوا واستقموا كما أمرت فلذلك فادعوا
+
+455
+00:59:04,570 --> 00:59:09,650
+واستقموا كما أمرت فلذلك فادعوا
+
+456
+00:59:12,610 --> 00:59:21,350
+لنا أعمالنا ولكم أعمالكم لا حجة بيننا وبينكم الله
+
+457
+00:59:21,350 --> 00:59:29,210
+يجمع بيننا وإلى النصير والذين يحاجون في الله من
+
+458
+00:59:29,210 --> 00:59:37,090
+بعد ما استجيب لوحج من بعد ما استجيب لوحج حجتهم
+
+459
+00:59:37,090 --> 00:59:44,750
+واحدة عند ربهمعند ربهم و عليهم غضب و لهم عذاب و
+
+460
+00:59:44,750 --> 00:59:53,970
+عليهم غضب و لهم .. غضب و لهم عذاب شديد الله الذي
+
+461
+00:59:53,970 --> 01:00:01,610
+أنزل الكتاب بالحق و الميزان و ما أدري قد علم
+
+462
+01:00:01,610 --> 01:00:10,670
+الساعة قريب يستعجل بها الذين لا يؤمنون بهاوالذين
+
+463
+01:00:10,670 --> 01:00:17,850
+آمنوا مش .. مشفقون منها ويعلمون أنها الحق ألا إن
+
+464
+01:00:17,850 --> 01:00:24,330
+الذين .. نبدأ نبدأ نبدأ ألا إن الذين يمار .. ألا
+
+465
+01:00:24,330 --> 01:00:32,410
+إن الذين يمارون في الساعة مافي غلال بعيد غلال بعيد
+
+466
+01:00:32,410 --> 01:00:42,780
+مافي غلال بعيدالله لطيف من عباده يرزق من يشاء و هو
+
+467
+01:00:42,780 --> 01:00:51,260
+القوي العزيز من كان يريد حرث ال .. من كان يريد حرث
+
+468
+01:00:51,260 --> 01:00:59,580
+الآخر فما زده في حرثه و من كان يريدومن كان يريد
+
+469
+01:00:59,580 --> 01:01:07,380
+حرطة الدنيا نبطيه منها وما له في الآخرة من نصيب
+
+470
+01:01:07,380 --> 01:01:13,620
+يقولني حركتين من نصيب؟ من نصيب ما يفتحنا من قراي
+
+471
+01:01:13,620 --> 01:01:24,220
+أسنان أم لهم شرك .. أم لهم شركاء .. أم لهم شركاء
+
+472
+01:01:24,220 --> 01:01:26,700
+شرعوا .. شرعوا .. شرعوا
+
+473
+01:01:29,080 --> 01:01:33,220
+ما لم يأذن
+
+474
+01:01:33,220 --> 01:01:40,070
+بإلهما لم يقدم به الله و لو لا كلمة .. و لو لا
+
+475
+01:01:40,070 --> 01:01:47,530
+كلمة قصد القضية بينهم وإن الظالمين لهم عذاب أليم
+
+476
+01:01:47,530 --> 01:01:52,550
+ترى الظالمين .. ترى الظالمين .. ترى الظالمين مشفق
+
+477
+01:01:52,550 --> 01:01:58,650
+.. مشفقين مما كسبوا هم يعني اللي خلقتهم مما كسبوا
+
+478
+01:01:58,650 --> 01:02:00,710
+و ترى الظالمين ..
+
+479
+01:02:07,040 --> 01:02:13,620
+وهو واقع .. وهو .. وهو واقع بهم والذين آمنوا
+
+480
+01:02:13,620 --> 01:02:19,780
+وعملوا الصالحات في روضات الجنات هم يعملون في روضات
+
+481
+01:02:19,780 --> 01:02:27,220
+الجنات .. في روضات الجنات لهم ما يشاء .. لهم ..
+
+482
+01:02:27,220 --> 01:02:36,770
+لهم ما يشاء .. لهم ما يشاءون عند ربهم .. عند ..عند
+
+483
+01:02:36,770 --> 01:02:43,210
+ربهم ذلك هو ال .. هو الفضل العظيم الكبير ذلك الذي
+
+484
+01:02:43,210 --> 01:02:49,510
+يبشر الله عباده اللذين .. يبشر الله يبشر الله
+
+485
+01:02:49,510 --> 01:02:55,630
+عباده اللذين .. يبشر الله عباده .. يبشر الله
+
+486
+01:02:59,590 --> 01:03:08,850
+عباده الذين آمنوا وعملوا الصالحان قل لا أسألكم
+
+487
+01:03:08,850 --> 01:03:15,770
+عليه أجرا .. أجرا إلا .. أجرا إلاأجراً إلا المو ..
+
+488
+01:03:15,770 --> 01:03:20,650
+إلا المودة .. إلا المودة في القربى إلا المودة ..
+
+489
+01:03:20,650 --> 01:03:27,090
+إلا المودة في القربى ومن يقترب حسنة نزد لهم حسنة
+
+490
+01:03:27,090 --> 01:03:32,610
+نزدهم ومن يقترب حسنة .. ومن .. ومن يقترب .. ومن
+
+491
+01:03:32,610 --> 01:03:38,630
+يقترب حسنة .. حسنة نزدهم فأسات ما يسمعون ومن يقترب
+
+492
+01:03:38,630 --> 01:03:45,370
+حسنة نزدهمومن .. ومن .. ومن يقترف حسنة .. ومن
+
+493
+01:03:45,370 --> 01:03:51,710
+يقترف حسنة نزده .. ومن يقترف حسنة نزده .. فا ..
+
+494
+01:03:51,710 --> 01:03:57,510
+فاكرة يقترف .. يقترف .. طيب .. ومن يقترفو من يقترف
+
+495
+01:03:57,510 --> 01:04:03,490
+حسنة نزد له فيها حسنة بس جيب القسم حسنة نزد له
+
+496
+01:04:03,490 --> 01:04:11,930
+فيها حسنة نزد له فيها حسنة إن الله غفور شكور
+
+497
+01:04:14,770 --> 01:04:24,450
+فإن يشأ الله
+
+498
+01:04:24,450 --> 01:04:31,850
+فإن يشأ الله فإن يشأ الله فإن يشأ الله فإن يشأ
+
+499
+01:04:31,850 --> 01:04:35,070
+الله فإن يشأ الله فإن يشأ الله فإن يشأ الله فإن
+
+500
+01:04:35,070 --> 01:04:41,970
+يشأ الله فإن يشأ الله فإن يشأ الله فإن يشأ الله
+
+501
+01:04:41,970 --> 01:05:08,670
+فإن يشأ الله فإن يشأ اللهيشأ الله يختم
+
+502
+01:05:08,670 --> 01:05:15,240
+على قلبه لأ مش يختمه، يختم علىيختم على .. يختم ..
+
+503
+01:05:15,240 --> 01:05:20,820
+يختم على قلبه ويمحو الله ال .. ويمحو الله الباطل
+
+504
+01:05:20,820 --> 01:05:27,520
+ويحق .. ويحقوا الحق .. ويحقوا الحق بكلماته إنه
+
+505
+01:05:27,520 --> 01:05:34,180
+عليم بذات الصدوة عليم بذات الصدوة و هو .. و هو
+
+506
+01:05:34,180 --> 01:05:38,020
+اللي يقبلته .. و هو .. يقول العظم الهائات .. و هو
+
+507
+01:05:38,020 --> 01:05:43,350
+..وهو اللذي .. وهو اللذي يقبل التوبة عن عباده
+
+508
+01:05:43,350 --> 01:05:49,230
+ويعفو عن .. ويعفو عن السيئات ويعلم ما تفعلوا ..
+
+509
+01:05:49,230 --> 01:05:54,950
+ويعلموا ما تفعلون ويستجيبوا الذين آمنوا وعملوا
+
+510
+01:05:54,950 --> 01:06:01,370
+الصالحات ويزيدهم بالفرد .. ويزيدهم .. ويزيدهم
+
+511
+01:06:12,620 --> 01:06:13,920
+الله يفتح عليه
+
+512
+01:06:17,170 --> 01:06:25,470
+اقرا يا شايمة نعم طيب دي؟ ليش؟ طيب كويس انا خبصت
+
+513
+01:06:25,470 --> 01:06:28,590
+متوتريني شوية بس بس انا كويس مش عارفة ايه خبصت؟
+
+514
+01:06:28,590 --> 01:06:37,990
+انا هراعي نعم خبصت بعدين؟ نعم مش كده يعني
+
+515
+01:06:37,990 --> 01:06:40,970
+الكوركو اغلبته اكتر من المحاضرات العادية بس انا
+
+516
+01:06:40,970 --> 01:06:44,790
+مراعيت التوتر يعني ان شاء الله باخص مشكلة يالا يا
+
+517
+01:06:44,790 --> 01:06:51,830
+شايمةعشان نعيد من عندنا بدأت اسمها أم لهم شركاء و
+
+518
+01:06:51,830 --> 01:06:57,170
+شرعون لآية 21 أعوذ بالله من الشيطان الرجيم باسم
+
+519
+01:06:57,170 --> 01:07:03,590
+الله الرحمن الرحيم أم لهم شركاء و شرعوا لهم من
+
+520
+01:07:03,590 --> 01:07:09,830
+الدين ما لم يألم بالله و لو لا كلمة الفصل لقضية
+
+521
+01:07:09,830 --> 01:07:17,840
+بينهم و إن الظالمين لهم عذاب قليلتروى الذين مشفقين
+
+522
+01:07:17,840 --> 01:07:24,680
+لما كسبوا و هو واقع .. و هو .. و هو واقع بهم و
+
+523
+01:07:24,680 --> 01:07:31,980
+الذين آملوا و عملوا الصالحات في روضات جنات لهم ما
+
+524
+01:07:31,980 --> 01:07:41,920
+يشاءون عند ربهم ذلك هو الفضل الكبيرذلك الذي يبشر
+
+525
+01:07:41,920 --> 01:07:48,980
+الله .. ذلك الذي يبشر الله عباده الذين آمنوا
+
+526
+01:07:48,980 --> 01:07:55,010
+وعملوا الصالحاتقول لا أسألكم عليه أجوا .. أسألكم
+
+527
+01:07:55,010 --> 01:08:02,390
+.. قول لا أسألكم عليه أجوا .. لا أسألكم عليه أجوا
+
+528
+01:08:02,390 --> 01:08:08,790
+إلا المودة في القربة وما يقدر يفحسنة نزد لو فيها
+
+529
+01:08:08,790 --> 01:08:12,050
+.. بتزيد الحكم حركتين اشهرها .. نزد او نزد؟ لأ
+
+530
+01:08:12,050 --> 01:08:21,510
+حسنة نزدةو من يقترب حسنة حسنة نزد له فيها حسنة و
+
+531
+01:08:21,510 --> 01:08:30,710
+من يقترب حسنة حسنة نزد له فيها حسنة إن الله غفور
+
+532
+01:08:30,710 --> 01:08:39,690
+شكوه أم يقولون افتراض على الله كذبه فإيش إلا و
+
+533
+01:08:39,690 --> 01:08:46,290
+يختم على قلبكوينفو الله الباطل ويحق الحق بكلماته،
+
+534
+01:08:46,290 --> 01:08:55,970
+ويحق الحق بكلماته، إنه عليهم وبدات صدوق، وهو الذي
+
+535
+01:08:55,970 --> 01:09:02,030
+يقبل التوبة عن عباده، ويعفو عن السيئات ويعلم ما
+
+536
+01:09:02,030 --> 01:09:08,620
+تفعلونو يستجيب الذين آمنوا و عملوا الصالحات و
+
+537
+01:09:08,620 --> 01:09:16,360
+يزيدهم يثغلهم و الكافرون لهم أعداب شديدة الله يفتح
+
+538
+01:09:16,360 --> 01:09:20,780
+عليك كل ما قرأت هنا اعطيك الله ان شاء الله افتح
+
+539
+01:09:20,780 --> 01:09:21,140
+عليك
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/cdyZjFeK51A_postprocess.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/cdyZjFeK51A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aee222acdf7a7cb6687e0747d797b5c9e722712f
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/cdyZjFeK51A_postprocess.srt
@@ -0,0 +1,3044 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,790 --> 00:00:15,830
+أعوذ بالله من الشيطان الرجيم بسم الله الرحمن
+
+3
+00:00:15,830 --> 00:00:21,030
+الرحيم والصلاة والسلام على أشرف المرسلين سيدنا
+
+4
+00:00:21,030 --> 00:00:27,450
+محمد وعلى آله وصحبه وتابعيه ومن تبعهم بإحسان إلى
+
+5
+00:00:27,450 --> 00:00:33,670
+يوم الدين أخوات الكريمات أحييكن بتحية الإسلام تحية
+
+6
+00:00:33,670 --> 00:00:38,210
+أهل الجنة فالسلام عليكم ورحمة الله تعالى وبركاته
+
+7
+00:00:40,900 --> 00:00:45,520
+اللهم أشرحلي صدري ويسرلي أمري واحلل عقدة من لساني
+
+8
+00:00:45,520 --> 00:00:50,820
+يفقه قولي اللهم أعلمنا من القرآن ما ينفعنا وانفعنا
+
+9
+00:00:50,820 --> 00:00:56,360
+بما علمتنا وزدنا اللهم علمة الحمد لله الذي جعلنا
+
+10
+00:00:56,360 --> 00:01:01,320
+من خدام كتابه الكريم وأسأل الله العظيم أن يجعلني
+
+11
+00:01:01,320 --> 00:01:06,040
+وإياكم ممن يتلون آياته ويقيمون حدودها
+
+12
+00:01:09,930 --> 00:01:16,810
+ونبدأ رحلتنا القرأنية مع صورة المؤمنون مع الأخت
+
+13
+00:01:16,810 --> 00:01:22,930
+Hiba Ibrahim يلا يا حبيبتي بس
+
+14
+00:01:22,930 --> 00:01:24,170
+ممكن نرفع صوتنا شوية
+
+15
+00:01:28,170 --> 00:01:35,850
+شوفي حبيبتي اعوذوا .. اعوذوا بالله من الشيطان
+
+16
+00:01:35,850 --> 00:01:42,050
+الرجيم تفخيم الtaa في كلمة الشيطان يلا و اعوذوا
+
+17
+00:01:42,050 --> 00:01:47,250
+ضمي تمك حبيبتي ضمي لقدام عشان تطلع العو دون غنة
+
+18
+00:01:47,250 --> 00:01:52,530
+اعوذوا يلا كمان مرة اعوذوا
+
+19
+00:01:59,640 --> 00:02:07,920
+الشيطان .. ايوة بسم الله الرحمن الرحيم قد أفلح
+
+20
+00:02:07,920 --> 00:02:13,920
+المؤمنون بدنا انقلق الأداء في قد .. قد .. قد ..
+
+21
+00:02:13,920 --> 00:02:19,200
+ايوة قد أفلح المؤمنون نعيد تاني قد أفلح المؤمنون
+
+22
+00:02:19,200 --> 00:02:22,920
+.. ايوة قد أفلح المؤمنون
+
+23
+00:02:27,940 --> 00:02:37,360
+الذين هم في صلاتهم
+
+24
+00:02:37,360 --> 00:02:43,420
+خاشعون الصاد مفخمة و الخا برضه كنا نفخمها أيوة
+
+25
+00:02:43,420 --> 00:02:47,460
+..الذين هم في صلاة .. صلاة .. صلاة
+
+26
+00:02:50,700 --> 00:03:00,680
+خاشرون .. خاشرون .. خاشرون .. خاشرون .. خاشرون ..
+
+27
+00:03:00,680 --> 00:03:11,760
+خاشرون .. خاشرون .. خاشرون .. خاشرون
+
+28
+00:03:11,760 --> 00:03:17,900
+..أيوة لأ .. لز .. أيوة هذه ال wow تكتب ولا تلفظ
+
+29
+00:03:17,900 --> 00:03:25,720
+نقول والذين هم للزكاة فاعلون للزكاة والذين هم
+
+30
+00:03:25,720 --> 00:03:34,800
+للزكاة فاعلون والذين هم لخروجهم حافظون إلا على
+
+31
+00:03:34,800 --> 00:03:40,960
+أزواجهم أو ما ملكت أيمانهم فإن .. فإنهم غير ملوكين
+
+32
+00:03:41,530 --> 00:03:47,830
+إيش بدنا نقول؟ على أزواجهم هنا مد جائز منفصل جاء
+
+33
+00:03:47,830 --> 00:03:52,970
+بعد حرف المد همزة في كلمة التي تليها في الكلمة
+
+34
+00:03:52,970 --> 00:03:58,150
+التي تليها نوعه جائز منفصل بينمده أربع أو خمس
+
+35
+00:03:58,150 --> 00:04:08,330
+حركات هتقولي كيف؟ الا على أزواجهم الا على أزواجهم
+
+36
+00:04:08,330 --> 00:04:09,110
+يالا حميد
+
+37
+00:04:19,130 --> 00:04:25,390
+بس إيش بدنا نسوي هنا؟ بدنا نفخم الغاء غيرهم، الغاء
+
+38
+00:04:25,390 --> 00:04:32,070
+هنا مفخم، ياما فإنهم غير ملومين
+
+39
+00:04:40,260 --> 00:04:46,880
+فمن ابتغى وراء ذلك فأولئك هم العادلون لأ شوف ياهي
+
+40
+00:04:46,880 --> 00:04:54,100
+بقى فمن ابتغى وراء ذلك .. أيوة هنقلقل الباق في
+
+41
+00:04:54,100 --> 00:04:59,920
+ابتغى حروف القلقلة قطر جد يبقى هنا الباق ساكنة إذا
+
+42
+00:04:59,920 --> 00:05:04,860
+هقلقلها القلقلة يعني اضطراب في المخرج اضطراب في
+
+43
+00:05:04,860 --> 00:05:11,880
+المخرج هتقولي ابي .. ابي وراءجاء بعد حرف المد همزة
+
+44
+00:05:11,880 --> 00:05:17,340
+في كلمة واحدة فايقنش بنقول هنا واجب متصل همده أربع
+
+45
+00:05:17,340 --> 00:05:21,400
+أو خمس حركات أما ذلك انت مدتيها ومافيش فيها مد
+
+46
+00:05:21,400 --> 00:05:25,400
+مافيش فيها مد يعني مافيش فيها زيادة عن حركتين هقول
+
+47
+00:05:25,400 --> 00:05:33,940
+ذلك ذلك فقط نعم فضليه فمن ابتغاه لأ مش ابتغاه ايه
+
+48
+00:05:33,940 --> 00:05:36,400
+بيه فمن ابتغاه
+
+49
+00:05:40,450 --> 00:05:47,130
+لأ إيش قلنا؟ مين هنمدها؟ الرعالين هنمدها وراء ذلك
+
+50
+00:05:47,130 --> 00:05:58,010
+.. وراء ذلك فما نبتغى .. فما نبتغى .. وراء
+
+51
+00:05:58,010 --> 00:06:04,950
+ذلك .. وراء ذلكمحنمد أولئك لأن واجب متصل صح ولا لأ
+
+52
+00:06:04,950 --> 00:06:11,110
+جاء بعض حرف المد همزة في كلمة واحدة إذا فأولئك ..
+
+53
+00:06:11,110 --> 00:06:20,350
+فأولئك .. فأولئك هم العادون بس مش هم العادون الميم
+
+54
+00:06:20,350 --> 00:06:26,290
+مضمومة من عن الاتقاء الساكنين هقول هم العادون ..
+
+55
+00:06:26,290 --> 00:06:28,690
+هم .. هم العادون
+
+56
+00:06:33,730 --> 00:06:42,150
+ممتاز جدا، انعيد الآية يا حبا .. انعيد الآية فماني
+
+57
+00:06:42,150 --> 00:06:46,410
+بتغا .. فماني
+
+58
+00:06:46,410 --> 00:06:51,390
+بتغا .. فماني بتغا .. فماني بتغا .. فماني بتغا ..
+
+59
+00:06:51,390 --> 00:06:53,570
+فماني بتغا .. فماني بتغا .. فماني بتغا .. فماني
+
+60
+00:06:53,570 --> 00:07:02,250
+بتغا .. فماني بتغا ..أحسنت حبيبتيا و الذين هم
+
+61
+00:07:02,250 --> 00:07:09,070
+لأماناتهم و عهدهم راعون عيد الآية و الذين هم
+
+62
+00:07:09,070 --> 00:07:16,870
+لأماناتهم و عهدهم راعون راعون تفهم الرا راعون
+
+63
+00:07:16,870 --> 00:07:27,350
+راعون نعم و الذين هم على صلواتهم يحافظون أولئك
+
+64
+00:07:28,960 --> 00:07:34,120
+أحسنت شفت كيف مدتي أولئك عشانها واجب متصل أولئك
+
+65
+00:07:34,120 --> 00:07:41,300
+نعم اللذين يروحون الفردوسون الفردوسون .. انشوف ..
+
+66
+00:07:41,300 --> 00:07:47,280
+انشوف الحركات إيه الرائش عليها؟ كسرة يري .. يري ..
+
+67
+00:07:47,280 --> 00:07:54,700
+ثون .. نعم اللذين يريثون الفردوسون فيها قادرون ..
+
+68
+00:07:56,040 --> 00:08:04,440
+الذين يريثون الفردوسة هم فيها خالدون نعيد الذين
+
+69
+00:08:04,440 --> 00:08:09,040
+يريثون .. مش يريثون بدناش تطلع معانا ياء بعد
+
+70
+00:08:09,040 --> 00:08:14,200
+الكسرة يريثون على طول كسرة و نخش على مين؟ على الثا
+
+71
+00:08:14,200 --> 00:08:18,640
+على إيش؟ الثا نعم الذين يريثون .. أه لأ قلتي
+
+72
+00:08:18,640 --> 00:08:24,890
+بتقولي أنتي يريثونلأ ياريثون .. ياريثون عسر يعني
+
+73
+00:08:24,890 --> 00:08:35,290
+خطف .. نعم يالا
+
+74
+00:08:35,290 --> 00:08:46,330
+يهيبقى بنظبط من ياريثون، بدلاش نقول ياريثون يبقى
+
+75
+00:08:46,330 --> 00:08:49,370
+ياريثون .. ياريثون عسرية
+
+76
+00:08:52,240 --> 00:08:59,760
+لأ لسه فيها ياريثون أيوة قولي ياريثون يالا نظبطها
+
+77
+00:08:59,760 --> 00:09:08,580
+مع الآية آخر
+
+78
+00:09:08,580 --> 00:09:12,120
+مرة لأ
+
+79
+00:09:12,120 --> 00:09:17,960
+قولت يا هنا ياريثون ياريثون
+
+80
+00:09:21,160 --> 00:09:24,480
+لأ احنا مانقدرش إياش نتمشى .. نمشي عنها لازم
+
+81
+00:09:24,480 --> 00:09:29,960
+نظبطها عشان هذا لحن جالي بنحط ياء بعد الاش بعد
+
+82
+00:09:29,960 --> 00:09:37,120
+الرا لا يجوز بنقول الذين .. الذين يريثون .. يريثون
+
+83
+00:09:37,120 --> 00:09:42,980
+الذين يريثون أيوة كمان مرة الذين يريثون أيوة
+
+84
+00:09:42,980 --> 00:09:46,860
+أحسنتي مبارك الله فيك يلا كمل الآية الذين يريثون
+
+85
+00:09:46,860 --> 00:09:55,030
+.. لأ ارجعنا تاني نقول ياءالذين يريثون .. الذين
+
+86
+00:09:55,030 --> 00:10:02,210
+يريثون .. الذين يريثون الفردوسة .. الذين يريثون
+
+87
+00:10:02,210 --> 00:10:06,710
+الفردوسة و فيها خالدون .. هنتدرب عليها في البيت يا
+
+88
+00:10:06,710 --> 00:10:12,670
+هيبة و نقول ياريثون مش ياريثون، بدناش نحط ياريثون
+
+89
+00:10:12,670 --> 00:10:22,590
+كسرة فقط، نعمولقد خلقنا الإحسان من سلسلة مهمةأه و
+
+90
+00:10:22,590 --> 00:10:27,030
+لا قد خلقنا في عند القلقلة في الدال و في عند
+
+91
+00:10:27,030 --> 00:10:31,530
+القلقلة في القاف و لا قد .. اليوم حباك القلقلة
+
+92
+00:10:31,530 --> 00:10:37,630
+يعني ف .. و لا قد خلقنا .. خلقنا .. الإنسانة هذه
+
+93
+00:10:37,630 --> 00:10:44,010
+من سلالة من طين، سلالة، في ألف .. في ألف هي تشيفها
+
+94
+00:10:44,010 --> 00:10:47,730
+الواحد الصغير، هذا عبارة عن ألف، و هذه أساء ال CH
+
+95
+00:10:47,730 --> 00:11:00,430
+مضمومة، سلالةولقد خلقنا الإنسان من سلالة من طين و
+
+96
+00:11:00,430 --> 00:11:08,870
+لقد خلقنا الإنسان من سلالة من طين و لقد خلقنا ..
+
+97
+00:11:08,870 --> 00:11:15,240
+خلقلي .. خلقلي الدالةمش اد ما تقوليش هيبقى و لا قد
+
+98
+00:11:15,240 --> 00:11:20,640
+اد هد مافيش فيها قلقلة و لا قد اد ها في اضطراب في
+
+99
+00:11:20,640 --> 00:11:22,560
+المخرج يا حبيبتي ايوة؟
+
+100
+00:11:26,960 --> 00:11:31,580
+بس بدنا نجيب الإخفاء عند من سلالة إيش بنقول؟ من
+
+101
+00:11:31,580 --> 00:11:36,080
+سلالة تمنطين
+
+102
+00:11:36,080 --> 00:11:41,080
+في عندك النون مع السيم إخفاء و التأ اللي هي النون
+
+103
+00:11:41,080 --> 00:11:46,340
+في التنوين مع الميم إيش هنا؟ اتغام بغنى و في عندك
+
+104
+00:11:46,340 --> 00:11:50,200
+النون مع التأ إذا أجت بعدين تأ ضردك إيش؟ إخفاء
+
+105
+00:11:50,200 --> 00:11:56,970
+ولكن بمع تفخيم الغنى يالا يا حبيبتي أشوفولا قد
+
+106
+00:11:56,970 --> 00:12:04,850
+..ولا قد خلقنا ليه سلالة من قيمة .. بس إيش؟ بس
+
+107
+00:12:04,850 --> 00:12:09,350
+سلالة مش هنمدها كتير، بس هنمدها حركتين .. من سلالة
+
+108
+00:12:09,350 --> 00:12:17,250
+من قيمة .. نعم .. ثم جعلنا ضموته فتن بقرار ممكن
+
+109
+00:12:17,250 --> 00:12:18,510
+..ماشي
+
+110
+00:12:22,970 --> 00:12:31,050
+ثم .. ثم خلقنا هذه مش جعلنا ..
+
+111
+00:12:31,050 --> 00:12:36,570
+ايوة برضك هنا بدلاش نحط ألف بعد الفتحة مابديش اقول
+
+112
+00:12:36,570 --> 00:12:45,330
+ثم .. لأ على طول ثم خلقنا النقفة علقا شافي كيف؟
+
+113
+00:12:45,330 --> 00:12:45,810
+يالا حبيبي
+
+114
+00:12:55,780 --> 00:12:59,840
+لأ مدال إيش لما ينقطع نفسنا بدنا نقف خلاص نقف على
+
+115
+00:12:59,840 --> 00:13:07,020
+ها ساكنة بدي أقول فخلقنا العلاقة مضغه .. مضغه ها
+
+116
+00:13:07,020 --> 00:13:12,100
+ساكنة بعدين بأوصل الكلام بأرجع كلمة و بأوصل الكلام
+
+117
+00:13:12,100 --> 00:13:17,640
+نعم فخلقنا
+
+118
+00:13:17,640 --> 00:13:18,860
+العلاقة مضغه
+
+119
+00:13:23,060 --> 00:13:27,100
+بدك توصل ايه؟ بدك تجيب حكم التنوين .. حكم التنوين
+
+120
+00:13:27,100 --> 00:13:33,780
+أجى تنوين بعدى ف .. إيش الحكم؟ اخفاء .. يلا مضغة
+
+121
+00:13:33,780 --> 00:13:44,900
+فخلقنا .. مضغة فخلقنا المضغة عظاما فكسونا العظام
+
+122
+00:13:44,900 --> 00:13:45,860
+لحما
+
+123
+00:13:49,400 --> 00:13:57,860
+فكسونا العظام لحمة ممكن تقفل فكسونا العظام لحمة
+
+124
+00:13:57,860 --> 00:14:08,260
+يلا فكسونا العظام لحمة لحمة ثم أنشأناه خلقا أخر
+
+125
+00:14:08,260 --> 00:14:11,540
+فكسونا
+
+126
+00:14:11,540 --> 00:14:12,960
+العظام لحمة
+
+127
+00:14:19,570 --> 00:14:28,030
+فتبارك الله أحسن الخالقين فتبارك
+
+128
+00:14:28,030 --> 00:14:34,030
+الله أحسن الخالقين فتبارك الله أحسن الخالقين
+
+129
+00:14:34,030 --> 00:14:35,510
+فتبارك الله أحسن الخالقين فتبارك الله أحسن
+
+130
+00:14:35,510 --> 00:14:40,670
+الخالقين فتبارك الله أحسن الخالقين
+
+131
+00:14:48,970 --> 00:14:53,590
+أحسنتي شفتي كيف جبت الغنى ع الميم في ثمة قولتي ثم
+
+132
+00:14:53,590 --> 00:14:59,190
+الميم المتشدد عليها غنى مقدار حركتين أحسنتي ثم
+
+133
+00:14:59,190 --> 00:15:07,310
+إنكم بعد إنكم بعد إيش في هنا إنكم بعد الميم
+
+134
+00:15:07,310 --> 00:15:12,310
+الساكنة أجي بعديها بقى فالحكم إخفاء شفوي بدي أخفي
+
+135
+00:15:12,310 --> 00:15:18,310
+الميم بدي أقول إنكم بعد مع الغنى نعم
+
+136
+00:15:23,450 --> 00:15:26,750
+بس بدأ أطول شوية جبت الإخفاء بس طول شوية عشان
+
+137
+00:15:26,750 --> 00:15:38,530
+الغنى ميم إنكم ميم بعد .. إنكم بعد ثم إنكم بعد ذلك
+
+138
+00:15:38,530 --> 00:15:43,070
+لما يدوم ثم
+
+139
+00:15:43,070 --> 00:15:50,810
+إنكم يوم القيامة تبعثون بدنا نقلق للباب تبعثون
+
+140
+00:15:52,250 --> 00:15:57,590
+أحسنتى بارك الله فيك يا هبا هبا انت بيعليه يبقى فى
+
+141
+00:15:57,590 --> 00:16:04,330
+البيت هنتدرب على الحركات بنشوف الحركات كويس الضمة
+
+142
+00:16:04,330 --> 00:16:07,390
+ضمة و الكسرة كسرة و الفتحة فتحة الحاجة التانية
+
+143
+00:16:07,390 --> 00:16:12,210
+حروف القلقلة حروف القلقلة قطب جد خمس أحرف إذا ..
+
+144
+00:16:12,210 --> 00:16:15,910
+إذا جاءت ساكنة بدنا نقلقلها القلقلة يعني اضطراب فى
+
+145
+00:16:15,910 --> 00:16:22,060
+المخرج يعني أبى أطى زى نىوال .. و الحاجة التانية
+
+146
+00:16:22,060 --> 00:16:26,780
+أحسنتي .. جبتي ال .. ال meme الساكنة المشددة ال
+
+147
+00:16:26,780 --> 00:16:30,840
+meme المشددة جبت عليها إيش؟ غنة ممتازة المدود ..
+
+148
+00:16:30,840 --> 00:16:34,780
+المدود بدنا إيش؟ ندق عليها أيضا المنفصل .. المتصل
+
+149
+00:16:34,780 --> 00:16:41,580
+بدنا نمده أربع أو خمس حركات ننتبه
+
+150
+00:16:41,580 --> 00:16:44,420
+للحاجات هذه و إن شاء الله المرة الجاية كل شيء تمام
+
+151
+00:16:44,420 --> 00:16:48,640
+و الآن مع الأخت عزيزة
+
+152
+00:16:54,860 --> 00:17:02,900
+أعوذ بالله من الشيطان الرجيم بسم الله الرحمن
+
+153
+00:17:02,900 --> 00:17:15,140
+الرحيم ولقد خلقنا فوقكم سبع طرائق وما كنا .. وما
+
+154
+00:17:15,140 --> 00:17:21,240
+كنا عن القلق غافلين غا .. ممكن نفخم الغا أكتر
+
+155
+00:17:21,240 --> 00:17:32,730
+غافلين .. غاوما كنا عن القلق غافلين وأنزلنا
+
+156
+00:17:32,730 --> 00:17:48,210
+من السماء ماء بقدر فأسلكناه فأسكنّاه
+
+157
+00:17:48,210 --> 00:17:59,400
+في الأرض وإنوإن على ذهب به لقدرون بس ننغن أكتر وإن
+
+158
+00:17:59,400 --> 00:18:04,340
+على ذهب به لقدرون
+
+159
+00:18:06,110 --> 00:18:15,570
+فأنشأنا لكم بجنات من نخيل جبت الإضغام بس ماجبتيش
+
+160
+00:18:15,570 --> 00:18:24,770
+الغنى طوالى جنات من نخيل .. من نخيل هتبقى الأولى
+
+161
+00:18:24,770 --> 00:18:34,920
+قد التانية يالا قد جنات من ..من نخيل و أعناب لكم
+
+162
+00:18:34,920 --> 00:18:42,900
+فيها فواكه كثيرة و منها تأكلوني ممكن من نخيل و
+
+163
+00:18:42,900 --> 00:18:48,660
+أعناب ممكن نربط الكلام مع بعض و أعناب لكم فيها ..
+
+164
+00:18:48,660 --> 00:18:58,640
+نربط الكلام مع بعضلو أعناب لكم فيها فواكو كثيرة و
+
+165
+00:18:58,640 --> 00:19:04,040
+منها تأكلون عزيزا حبيبتي بدنا الناقش بدنا نظبط زمن
+
+166
+00:19:04,040 --> 00:19:07,800
+الغنان زمن الغنان هنخليه كل ناقش تقريبا قط بعض
+
+167
+00:19:07,800 --> 00:19:14,180
+ياما فأنشأنا لكم به جنات
+
+168
+00:19:16,190 --> 00:19:23,830
+النخيل و أعناب لكم في عندك أكتر من غنى يالا
+
+169
+00:19:23,830 --> 00:19:33,470
+فأنشأنا لكم بجنات من نخيل ليش ماتطولتيش؟ جنات من
+
+170
+00:19:36,070 --> 00:19:43,530
+فأنشأنا لكم بيه جنة لكم بيه .. برضه في إخفاء لكم
+
+171
+00:19:43,530 --> 00:19:54,190
+بيه .. هنجيب الغنى أيوة فأنشأنا لكم بيه جنات من
+
+172
+00:19:54,190 --> 00:20:00,350
+نخيل و أعناب جبتهم كلهم بس نخيل و أعناب؟ جيب الغنى
+
+173
+00:20:00,350 --> 00:20:07,670
+عشان السير تمام يالا حبيبتيمن نخيل و أعناب لكم
+
+174
+00:20:07,670 --> 00:20:17,030
+فيها فواكه كثيرة و منها تأكلون لأ فواكه كثيرة و
+
+175
+00:20:17,030 --> 00:20:21,930
+منها تأكلون بدنا نوصل المعنى، نرجع كلمة أو كلمتين
+
+176
+00:20:21,930 --> 00:20:30,670
+نوصل المعنىلكم فيها فواكه كثيرة و منها تأكلون
+
+177
+00:20:30,670 --> 00:20:35,150
+عزيزة الغنان .. انت بتجيب ال .. ال .. الضغام تمام
+
+178
+00:20:35,150 --> 00:20:41,050
+بس إيش؟ زمن الغناء بتأثر فيه شوية، هتقولي إيش؟
+
+179
+00:20:41,050 --> 00:20:47,290
+كثيرة و منها .. كثيرة و منها .. الغناء مقدار
+
+180
+00:20:47,290 --> 00:20:58,930
+حركتين، نعملكم فيها فواكه كثيرة ومنها تأكلون وشجرة
+
+181
+00:20:58,930 --> 00:21:04,570
+تخرج من طور سينائة
+
+182
+00:21:06,400 --> 00:21:13,940
+تنبت بالدهن وصبغ للآكلين أحسن تشايفي إيش الآكلين
+
+183
+00:21:13,940 --> 00:21:19,280
+وين الهمزة؟ وين الهمزة مرسومة قبل الألف؟ الهمزة
+
+184
+00:21:19,280 --> 00:21:25,160
+لما تكون مرسومة قبل الألف هذه A وإن
+
+185
+00:21:25,160 --> 00:21:36,760
+لكم في الأنعام لعبرة نسقيكم مما في بطونهانصطيق من
+
+186
+00:21:36,760 --> 00:21:49,140
+ما في بطونها ولكم فيها منافع كثيرة ومنها
+
+187
+00:21:49,140 --> 00:21:57,530
+تأكلون وعليها وعلى الفلك تحملونأحسنت يا عزيزي ما
+
+188
+00:21:57,530 --> 00:22:03,090
+شاء الله قراءتك جيدة بس بدنا نركز على حكاية زمان
+
+189
+00:22:03,090 --> 00:22:08,910
+الغنان زمان الغنان بدنا نخليه تقريبا متساوي و خاصة
+
+190
+00:22:08,910 --> 00:22:12,590
+في الإضغام مع مين مع الواو انت بتجيب الإضغامات بس
+
+191
+00:22:12,590 --> 00:22:17,350
+الزمن عشان قراءتك ممتازة فاحنا بنخليها أحسن وأحسن
+
+192
+00:22:17,350 --> 00:22:24,130
+بارك الله فيك الآن مع الأخت Manal Esfahy
+
+193
+00:22:33,420 --> 00:22:47,360
+بسم الله الرحمن
+
+194
+00:22:47,360 --> 00:22:50,540
+الرحيم
+
+195
+00:22:50,540 --> 00:22:58,240
+و لقد أرسلنا نوحا إلى قومه فقال يا قوم اعبدوا الله
+
+196
+00:22:58,240 --> 00:23:10,680
+ما لكمما لكم من إناه غيره أفلا تتقون فقال الملأ
+
+197
+00:23:10,680 --> 00:23:22,300
+الذين كفروا من قومه ما هذا ما هذا إلا بشر مثلكم
+
+198
+00:23:22,300 --> 00:23:33,880
+يريد يريدوا أن يتفضل عليكميريد أن يتفضل عليكم ولو
+
+199
+00:23:33,880 --> 00:23:47,060
+شاء الله لأنزل ولو شاء الله لأنزل ملائكة ما سمعنا
+
+200
+00:23:47,060 --> 00:23:57,880
+بهذا ما سمعنا بهذا في أبائنا الأولين
+
+201
+00:23:59,490 --> 00:24:09,750
+إن هو إلا رجل به جنة فتربصوا به حتى حينه نجيب
+
+202
+00:24:09,750 --> 00:24:20,050
+الاشغنة الإخفاء إن هو إلا رجل به جنة فتربصوا به
+
+203
+00:24:20,050 --> 00:24:33,630
+حتى حينهقال رب انصرني بما كذبون فأوحينا اليه أنصنع
+
+204
+00:24:33,630 --> 00:24:43,910
+الفلك بأعيننا ووحينا فإذا جاء .. فإذا جاء أمرنا
+
+205
+00:24:43,910 --> 00:24:52,960
+وفاردت النور فاسدب فيهافاسلك فيها من كل زوجين ..
+
+206
+00:24:52,960 --> 00:25:04,440
+فاسلك
+
+207
+00:25:04,440 --> 00:25:12,340
+من .. فاسلك فيها من كل زوجين إثنين وأهلك إلا من
+
+208
+00:25:12,340 --> 00:25:22,790
+سبقسبق إلا من سبق عليه القول منهم ولا تخاطبني في
+
+209
+00:25:22,790 --> 00:25:34,850
+الذين ظلموا إنهم مغرقون فإذا استويت أنت ومن معك
+
+210
+00:25:34,850 --> 00:25:43,150
+على الفلك فقول الحمد لله الذي نجّهنا من القوملأ بس
+
+211
+00:25:43,150 --> 00:25:48,990
+من الفخم الله .. من القوم الظالمين .. الله .. نعم
+
+212
+00:25:48,990 --> 00:25:54,770
+حبيبتي .. فقول الحمد لله الذي نجّانا من القوم
+
+213
+00:25:54,770 --> 00:26:00,690
+الظالمين .. أحسنتي .. و قل ربي أنت .. لأ كتير ..
+
+214
+00:26:00,690 --> 00:26:04,910
+كتير قررنا .. مش و قل ربي .. لأ .. و قل .. و قل
+
+215
+00:26:04,910 --> 00:26:14,400
+ربي ع السرينوقول رب أنزلني منزلا مبركا وانت خير
+
+216
+00:26:14,400 --> 00:26:28,940
+المنزلين إما في ذلك لأيات وإن كنا لمقتلين ثم
+
+217
+00:26:28,940 --> 00:26:34,900
+أنشأنا من بعضهم قرن آخرين
+
+218
+00:26:36,550 --> 00:26:45,010
+فأرسلنا فيهم رسولا منهم أنعبدوا الله ما لكم من إله
+
+219
+00:26:45,010 --> 00:26:51,110
+غيره أفلا تتقوا أحسنتي رائع يا منال ما شاء الله
+
+220
+00:26:51,110 --> 00:26:58,370
+عليك يعني مخارج ممتازة وأحكام رائعة يعني ليس لنا
+
+221
+00:26:58,370 --> 00:27:01,930
+في هذه القراءة إلا المدح والثناء بس في عندي ملاحظة
+
+222
+00:27:01,930 --> 00:27:07,970
+بسيطة يا منال في مد العارض للسكوناحيانا بتقصري انت
+
+223
+00:27:07,970 --> 00:27:11,730
+تقريبا قرأتك أربعة جبتيها بس أحيانا كنت تقللي عن
+
+224
+00:27:11,730 --> 00:27:14,990
+أربعة فالعرض ده سيكون .. أيوة فالعرض ده سيكون كله
+
+225
+00:27:14,990 --> 00:27:18,970
+بيكون نفس المقدار بدأتي في اتنين اتنين بدأتي
+
+226
+00:27:18,970 --> 00:27:23,850
+باربعة كله أربعة بدأتي بستة كله ستة عشان تبقى إيش
+
+227
+00:27:23,850 --> 00:27:30,710
+اتلاوة هيك جيدةملاحظاتي بسيطة يعني كانت في .. هي
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+228
+00:27:30,710 --> 00:27:34,590
+هذه اللي كانت و حكاية التفخيم، التفخيم بده تفخيم
+
+229
+00:27:34,590 --> 00:27:39,350
+أكتر اللي هو إيش الطا، الظا، حاول إنك اتفخمي أكتر
+
+230
+00:27:39,350 --> 00:27:41,410
+بس ما شاء الله عليك يا مانال
+
+231
+00:27:44,080 --> 00:27:50,620
+ممكن مروة .. مروة المصدر اعوذ بالله من الشيطان
+
+232
+00:27:50,620 --> 00:27:57,300
+الرجيم اعوذ بالله من الشيطان الرجيم اعوذ بالله من
+
+233
+00:27:57,300 --> 00:28:03,100
+الشيطان الرجيم اعوذ بالله من الشيطان الرجيم اعوذ
+
+234
+00:28:03,100 --> 00:28:04,760
+بالله من الشيطان الرجيم اعوذ بالله من الشيطان
+
+235
+00:28:04,760 --> 00:28:07,140
+الرجيم اعوذ بالله من الشيطان الرجيم اعوذ بالله من
+
+236
+00:28:07,140 --> 00:28:09,890
+الشيطان الرجيم اعوذ بالله من الشيطان الرجيمأعوذ
+
+237
+00:28:09,890 --> 00:28:17,270
+بالله من الشيطان الرجيم الشيطان أعوذ بالله من
+
+238
+00:28:17,270 --> 00:28:23,550
+الشيطان الرجيم الشيطان الطا فاهم أكتر من الشيطان
+
+239
+00:28:23,550 --> 00:28:27,750
+الرجيم الشيطان الرجيم مش .. بعدك الطا مش مفخم عندك
+
+240
+00:28:27,750 --> 00:28:33,970
+طا فاهمين أعوذ بالله من الشيطان الرجيمده أحسن بس
+
+241
+00:28:33,970 --> 00:28:37,010
+إيش نحاول نظبطها في الدار أكتر بسم الله الرحمن
+
+242
+00:28:37,010 --> 00:28:46,130
+الرحيم وقال الملأ من قومه الذين كفروا وكذبوا بلقاء
+
+243
+00:28:46,130 --> 00:28:52,770
+الآخرة و أترفناهم
+
+244
+00:28:52,770 --> 00:28:59,500
+في الحياة الدنيا لحظة شويةمره وقال الملؤ من قومه
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+245
+00:28:59,500 --> 00:29:02,980
+الذين كفروا، بدك توقفي على كلمة كفروا، بدك تجيه
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+246
+00:29:02,980 --> 00:29:08,400
+بمقدار حركتين بس، بنقولش كفروا، بنقولش كفروا، لأ
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+247
+00:29:08,400 --> 00:29:15,620
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+248
+00:29:15,620 --> 00:29:19,460
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+249
+00:29:19,460 --> 00:29:25,040
+همسو أترفنهم .. و أترفنهم ايه بتجيب فيها همسة
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+250
+00:29:25,040 --> 00:29:29,540
+بسيطة من غير قلقلة يالا حبيبتي و قال الملء ..
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+251
+00:29:29,540 --> 00:29:37,140
+الملء .. و قال .. و قال .. و قال .. و قال الملء من
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+252
+00:29:37,140 --> 00:29:45,300
+قبل الملأ و قال الملء من قومهم الذين كفروا و كذبوا
+
+253
+00:29:45,300 --> 00:29:48,970
+.. نعيد تاني؟ لأ لأ نعيد الآيةعيد من أولها؟ اه و
+
+254
+00:29:48,970 --> 00:29:52,770
+قال .. و قال الملأ من قومهم الذين كفروا .. ايوة
+
+255
+00:29:52,770 --> 00:29:57,370
+هنا هنا .. هنا انا مش من قومهم هذه قومه الذين ..
+
+256
+00:29:57,370 --> 00:30:03,030
+قومه الذين .. اتبعي و قال الملأ من قومه الذين
+
+257
+00:30:03,030 --> 00:30:08,570
+كفروا و كسببوا بلقاء الآخرة و أترفنا .. لأ لأ
+
+258
+00:30:09,220 --> 00:30:14,360
+واترفناهم .. واترفناهم .. واترفناهم في الحياة
+
+259
+00:30:14,360 --> 00:30:23,080
+الدنيا ماذا إلا بشر مثلكم .. مثلكم ماذا إلا بشر
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+260
+00:30:23,080 --> 00:30:33,380
+مثلكم يكون .. أجي تاني ماذا إلا بشر مثلكم كمما هذا
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+261
+00:30:33,380 --> 00:30:38,760
+إلا بشر مثلكم يأكلون .. لحظة شوية يا أخوات مافيش
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+262
+00:30:38,760 --> 00:30:43,460
+حاجة اسمها come .. come هذه مش لغة عربية هي come
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+263
+00:30:43,460 --> 00:30:48,900
+نضم تمنا كويس لقدام الاش .. ال .. هنا الشفاية
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+264
+00:30:48,900 --> 00:30:54,680
+فهنضمهم من الجانبين هنضم لقدام comeكو م و ارجع
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+265
+00:30:54,680 --> 00:30:58,980
+تاني إياش على محطة السكون في حكاية إياش في الشفايف
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+266
+00:30:58,980 --> 00:31:02,600
+موضع الشفايف كم نضم و نرجع تاني لموضع السكون في
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+267
+00:31:02,600 --> 00:31:09,400
+الشفايف نقول كم كم مش كم كم هذه ليست لغة عربية كم
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+268
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+أيوة ما هذا إلا بشر مثلكم كم أحسنتي رائعة يا أكلوا
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+269
+00:31:16,540 --> 00:31:23,860
+مما تأكلون منهلأ مش من .. من .. من في اياش؟ اظهار
+
+270
+00:31:23,860 --> 00:31:28,560
+.. اظهار عندنا في النون الساكنة عديها تاني يأكلوا
+
+271
+00:31:28,560 --> 00:31:34,200
+.. يأكلوا من ..
+
+272
+00:31:34,200 --> 00:31:41,580
+من .. أيوة من يأكلوا مما تأكلون منه و يشربوا مما
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+273
+00:31:41,580 --> 00:31:47,580
+تشربوا منه بس بدنا نوضح اضم فيه يشربواو يشربوا مما
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+274
+00:31:47,580 --> 00:31:55,360
+تشربون و يشربوا مما تشربون ها بدنا نجيب الراحة وين
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+275
+00:31:55,360 --> 00:32:00,660
+في حرف الشين الشين كمان فيها إيش؟ تفششين أيوة نشوف
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+276
+00:32:00,660 --> 00:32:09,100
+و يشربوا مما تشربون و يشربوا مما تشربون خليها
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+277
+00:32:09,100 --> 00:32:12,380
+الزمن الشين الأولى نفس الزمن في الشين التانى
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+278
+00:32:36,720 --> 00:32:41,020
+لأ هنوصل الكلام هنرجع كلمة أو كلمتين عشان المعنى
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+279
+00:32:41,020 --> 00:32:50,110
+يكون كاملوكنتم ترابا وعظاما أنكم مخرجون هيهات
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+280
+00:32:50,110 --> 00:32:56,990
+هيهات لماذا تعدون لأ انتبهي هيهات هيهات لماذا
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+281
+00:32:56,990 --> 00:33:05,030
+تعدون تشوفي هيهات هيهات لماذا تعدون توعدون بدنا
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+282
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+نجيب إيش ال wow ساكنة بدناش نخطفها خطف نجيبهاهيهات
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+283
+00:33:10,100 --> 00:33:16,660
+هيهات لما توعدون إن هي إلا حياتنا الدنيا نموت و
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+284
+00:33:16,660 --> 00:33:23,200
+نحيا نموت و نحيا و ما نحن مبعوثين
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+285
+00:33:23,200 --> 00:33:26,660
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+286
+00:33:26,660 --> 00:33:31,280
+لكنها فيها قلقة لإنتي و قلتي و نحيا و نحيا .. بس
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+287
+00:33:31,280 --> 00:33:37,020
+إيش؟ فيها همس و فيها رخابة و نحيا .. و نحيا ..
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+288
+00:33:42,060 --> 00:33:47,360
+شوفتي كيف نحن قلتيها و نحن روحتي قلقلتيها و نحن
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+289
+00:33:49,520 --> 00:33:53,960
+الـha في نحيا نفس الـha في نحن نفس الزمان و نفس
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+290
+00:33:53,960 --> 00:33:57,560
+الصفات يالا يا حبيبتي إن هي إلا حياتنا الدنيا ..
+
+291
+00:33:57,560 --> 00:34:02,060
+إن هي إلا حياتنا الدنيا نموت و نحيا و ما نحن
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+292
+00:34:02,060 --> 00:34:07,520
+بمبعوثين لأ ما أظبط معاهاش و نحيا و ما نحن
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+293
+00:34:07,520 --> 00:34:14,800
+بمبعوثين نحيا و ما نحن .. اقري شوي شوي عشان تجي
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+294
+00:34:14,800 --> 00:34:17,720
+معاكي إيش الهمس و تجي الرخاوة تمشيش بسرعة فتجي
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+295
+00:34:17,720 --> 00:34:27,540
+بقلقة معاكيإن هي إلا حياتنا الدنيا نموت ونحيا وما
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+296
+00:34:27,540 --> 00:34:34,020
+نحن مبعوثين لأ انت زبطيها هيك لا قلقليها انت و
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+297
+00:34:34,020 --> 00:34:38,660
+نحيا و نحيا انت لو تريحي تريح معاكي في الصوت و
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+298
+00:34:38,660 --> 00:34:45,720
+نحيا جريان النفس معاكي و جريان الصوت كمان و نحيا
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+299
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+300
+00:34:52,690 --> 00:34:59,910
+بمبعوثين أخر مرة نموت و نحيا و ما نحن .. نموت و
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+301
+00:34:59,910 --> 00:35:05,810
+نحيا و ما نحن بمبعوثين هنظبطها في البيت و نحيا و
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+302
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+303
+00:35:11,350 --> 00:35:17,230
+نموت ونحيا وما نحن بمجعوثين برضك بتقلقلي نحيا ..
+
+304
+00:35:17,230 --> 00:35:23,310
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
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+305
+00:35:23,310 --> 00:35:28,470
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
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+306
+00:35:28,470 --> 00:35:30,270
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+307
+00:35:30,270 --> 00:35:30,810
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+308
+00:35:30,870 --> 00:35:36,110
+نظبطها في الآية نموت و نحيا و ما نحن بمبعوثين كمان
+
+309
+00:35:36,110 --> 00:35:46,850
+مرة نموت و نحيا و ما نحن بمبعوثين نحيا نحنا
+
+310
+00:35:46,850 --> 00:35:50,210
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+311
+00:35:50,210 --> 00:35:54,420
+نحنا نحنا نحنا نحنا نحنا ننحيا نحن نحنا نحنا نحنا
+
+312
+00:35:54,420 --> 00:35:58,740
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+313
+00:35:58,740 --> 00:36:00,020
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+314
+00:36:00,020 --> 00:36:00,100
+نحنا نحنا نحنا نحنا نحانا نحانا نحانا نحانا نحانا
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+315
+00:36:00,100 --> 00:36:02,340
+نحانا نحانا نحانا نحانا نحانا نحانا نحانا نحانا
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+316
+00:36:02,340 --> 00:36:08,650
+نحانا نحانا نحانا نحانا نحانا نحانا نيظهر و إيش
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+317
+00:36:08,650 --> 00:36:12,230
+كمان؟ في جيبيلي إيش زمن النون، انت بتخطفي النون، ع
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+318
+00:36:12,230 --> 00:36:16,510
+السريع بتجيب النون، مابتبينش واضحة ان هو إلا
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+319
+00:36:16,510 --> 00:36:22,570
+رجلوني افترى، رجلوني، رجلوني افترى، ليش يا أخوات
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+320
+00:36:22,570 --> 00:36:28,320
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+321
+00:36:28,320 --> 00:36:33,280
+هو إلا رجول .. رجولي في طرائف علوية كذبة بس برضه
+
+322
+00:36:33,280 --> 00:36:38,340
+إنت حياتك بدالك تقلقل .. بتقلقل كتير رجول نفس
+
+323
+00:36:38,340 --> 00:36:44,520
+طرائف .. رجول نفس طرائف .. بدناش نقلقل الفاقرجل
+
+324
+00:36:44,520 --> 00:36:50,960
+نفترع الله
+
+325
+00:36:50,960 --> 00:36:59,740
+كذبة وما نحن له بمؤمنين رجعتلك نحن وما نحن .. و ما
+
+326
+00:36:59,740 --> 00:37:03,480
+نحن له بمبعوثين
+
+327
+00:37:03,480 --> 00:37:07,580
+.. بمؤمنين عديها و ما نحن .. و ما نحن .. و ما نحن
+
+328
+00:37:07,580 --> 00:37:14,060
+له بمؤمنينهيجبتيها نحن هنا ممتازة قال ربي انصرني
+
+329
+00:37:14,060 --> 00:37:20,520
+بما كذبون قال ربي انصرني الصاد مفخمة مع الرق مفخمة
+
+330
+00:37:20,520 --> 00:37:26,860
+قال ربي انصرني بما كذبون بس أصليها مع بعض قال ربي
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+331
+00:37:26,860 --> 00:37:34,880
+انصرني بما كذبون أحسنتي قال عما قليل يصبحن نادمين
+
+332
+00:37:34,970 --> 00:37:41,130
+عيد تاني قال عم قليل ليصبح .. ليص .. ليصبح ..
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+333
+00:37:41,130 --> 00:37:54,310
+ليصبح نادمين قال عم قليل ليصبح .. ليصبح نادمين
+
+334
+00:37:54,310 --> 00:38:00,110
+عيدها تاني قال عم قليل ليصبح .. ليصبح نادمينلا
+
+335
+00:38:00,110 --> 00:38:07,210
+يصبحننا .. لا يصبحننا نادمين .. نعم فأخذتهم الصيحة
+
+336
+00:38:07,210 --> 00:38:10,470
+بالحقد .. برضه كده .. برضه .. برضه فأخذتهم ..
+
+337
+00:38:10,470 --> 00:38:16,510
+فأخذتهم .. فأخذتهم .. فأخذتهم الtaa مش فيها قلقلة
+
+338
+00:38:16,510 --> 00:38:22,110
+فيها همس فأخذتهم الصيحة بالحقد فجعلنا .. فأخذتهم
+
+339
+00:38:22,110 --> 00:38:30,050
+الصيحة بالحقد .. بالحقد فأخذتهم الصيحة بالحقدفجأة
+
+340
+00:38:30,050 --> 00:38:35,410
+.. لأ مش هيك .. بالحق .. بالحق .. بالحق .. لأ هيك
+
+341
+00:38:35,410 --> 00:38:39,130
+بتجيب الشد ده و بعدين تجيب القلقه لأ .. بالحق ..
+
+342
+00:38:39,130 --> 00:38:44,210
+بالحق .. بالحق .. لأ هيك بتجيبينها ناعم هيك ..
+
+343
+00:38:44,210 --> 00:38:51,070
+بالحق .. بالحق .. بالحق .. شد ع القاف .. بالحق ..
+
+344
+00:38:51,070 --> 00:38:58,330
+مش أقف .. مش أقف بس .. بالحق ..بالحق بعدين .. جيب
+
+345
+00:38:58,330 --> 00:39:03,950
+الشدة بعدين جيب القلقلة بالحق .. بالحق .. بالحق
+
+346
+00:39:03,950 --> 00:39:10,170
+طيب أوصليها أشوف فأخذتهم الصيحد بالحق إذا جعلناهم
+
+347
+00:39:10,170 --> 00:39:19,550
+غثاء صح غثاء هنا مد إيش يا أخواتي؟ مد متصل طيب
+
+348
+00:39:19,550 --> 00:39:27,090
+متصل و نقف على مد عواض نعمفبعدا للقوم الظالمين
+
+349
+00:39:27,090 --> 00:39:32,710
+فبعدا للقوم الظالمين تفهم الظالم فبعدا للقوم
+
+350
+00:39:32,710 --> 00:39:42,350
+الظالمين نعم ثم نشأنا من بعدهم قرون .. قرون آخرين
+
+351
+00:39:42,350 --> 00:39:50,800
+لأ هنا تنوي تنوي قرون آخرين قرون آخرين قرونعيد دي
+
+352
+00:39:50,800 --> 00:39:55,200
+.. عيد دي الآية ا
+
+353
+00:39:55,200 --> 00:40:07,260
+مش ا ا خرين ا خرين ا خرين احسنتي
+
+354
+00:40:09,040 --> 00:40:14,520
+أخر آية ما تسبق .. ما تسبق من أمة .. لأ ليش هناك
+
+355
+00:40:14,520 --> 00:40:18,720
+إخفاء؟ من أمة إظهار ما تسبق من أمة أجلها وما
+
+356
+00:40:18,720 --> 00:40:25,120
+يستأخرون ننتبه للحركات ما تسبق من .. ما تسبق من
+
+357
+00:40:25,120 --> 00:40:32,980
+أمة أجلها وما .. أجلها وما يستأخرون ما تسبق من أمة
+
+358
+00:40:32,980 --> 00:40:37,140
+أجلها .. أمة أجلها
+
+359
+00:40:38,930 --> 00:40:47,330
+ماتصبق من أمة أجالها وما يستأخرون أحسنت مارفعة
+
+360
+00:40:48,430 --> 00:40:52,070
+مروة راح ندق على إيش؟ على القلقلة، راح ندق على
+
+361
+00:40:52,070 --> 00:40:55,890
+إيش؟ بدنا نقلقل بس الحروف المقلقلة، الحروف المش
+
+362
+00:40:55,890 --> 00:40:58,710
+مقلقلة بدناش نقلقلها، الحروف القلقلة اللي هي مين؟
+
+363
+00:40:58,710 --> 00:41:02,790
+قطب جد، خمس أحرف بس، الأحرف الساكنة، أي أحر غير
+
+364
+00:41:02,790 --> 00:41:07,230
+قطب جد بدناش نقلقلها، و بدنا ننتبه على الحركات،
+
+365
+00:41:07,230 --> 00:41:10,210
+يعني كانت يعني أكتر شيء مميز في قرائتك اللي هو
+
+366
+00:41:10,210 --> 00:41:14,750
+حكاية إيش؟ القلقلة فيما لا يجب أن يقلقل، فإيش؟
+
+367
+00:41:14,750 --> 00:41:19,440
+فانتبهي لهذا الإشيما هي كله يعني في الأشياء كلها
+
+368
+00:41:19,440 --> 00:41:25,240
+يعني أغلبيتها عايش هنا و برك الله فيك يا حبيبتي ان
+
+369
+00:41:25,240 --> 00:41:27,860
+شاء الله بتتربي عليها في البيت أكتر و خاصة و ما
+
+370
+00:41:27,860 --> 00:41:33,000
+نحن و نحيا و ما نحن و نحيا اللهم صلى على سيدنا
+
+371
+00:41:33,000 --> 00:41:35,220
+محمد هلاقيت مع الأخت ان شاء الله
+
+372
+00:41:43,460 --> 00:41:52,340
+هيبا أبو جراي هيبا أبو جراي تفضلي حاجة برضك
+
+373
+00:41:52,340 --> 00:42:02,820
+نفس الحاجة بدنا نفخم الطا الشيطا الشيطا لأ
+
+374
+00:42:02,820 --> 00:42:08,060
+بس بدناش نطول يعنيأيوة أحسنتى بس حركتين أعوذ بالله
+
+375
+00:42:08,060 --> 00:42:15,460
+من الشيطان الرجيم .. نعم بسم الله الرحمن الرحيم ثم
+
+376
+00:42:15,460 --> 00:42:22,130
+أرسلنا رسولنا .. رسولنالحظة شوية ثم الميم مشددة
+
+377
+00:42:22,130 --> 00:42:30,310
+هنجيب عليها الغنى مقدار حركتين ثم .. ثم .. أرسلنا
+
+378
+00:42:30,310 --> 00:42:37,870
+أ الأ مرققة و الرا مفخمة أرسلنا رسولنا تترا مش
+
+379
+00:42:37,870 --> 00:42:43,050
+تترا مقلقة للتأ تترا همس في التأ الاش الوصطانية
+
+380
+00:42:43,050 --> 00:42:43,310
+يلا
+
+381
+00:42:50,750 --> 00:42:54,470
+شوفي .. شوفي يا هباب .. نقف عن تترا .. نقف عن تترا
+
+382
+00:42:54,470 --> 00:43:04,050
+.. أقف عن تترا ثم .. أرسلنا نسولنا تترا كلما جاء
+
+383
+00:43:04,050 --> 00:43:09,190
+أمة رسولها .. رسولها كذبوا .. بس الهباب على كله بس
+
+384
+00:43:09,190 --> 00:43:13,270
+شدهوا بس .. بدناش نغل .. بدناش نقول كل ما جاء ..
+
+385
+00:43:13,270 --> 00:43:16,890
+اه لأ .. كل .. كل ما على السريع .. كل ما ..
+
+386
+00:43:21,580 --> 00:43:27,800
+الميم مشددة في أمة هنغن عليها أمة رسولها كذبوه
+
+387
+00:43:27,800 --> 00:43:33,620
+نعيد الآية كل ما جاء كل ما .. كل ما جاء كمان مرة
+
+388
+00:43:33,620 --> 00:43:41,680
+كل ما جاء أمة رسولها كذبوه نعم فأتبعنا بعضهم بعضا
+
+389
+00:43:41,680 --> 00:43:48,980
+و جعلناهم أحادي تفضحا لقوم لا يؤمنانت في عليّ يا
+
+390
+00:43:48,980 --> 00:43:56,160
+هباب فاتبعنا التأ فيها همس فاتبعنا فاتبعنا و بعضهم
+
+391
+00:43:56,160 --> 00:44:03,760
+بعضة في عندك إخفاء شفوي هنجيب الغنى بعضهم بعضةو
+
+392
+00:44:03,760 --> 00:44:08,680
+بعدين إيش؟ بعضا و جعلناهم .. هنجيب غنّة ال إيش؟
+
+393
+00:44:08,680 --> 00:44:13,400
+الإضام، مظبوط؟ بس بدناش نقول و جعلناهم .. بدناش
+
+394
+00:44:13,400 --> 00:44:17,360
+إيش؟ نطول على اللام في جعلناهم انتبهي و ركزي
+
+395
+00:44:17,360 --> 00:44:21,120
+معايا، ما شاء الله صوتك حلو فإيش؟ هنصقله إن شاء
+
+396
+00:44:21,120 --> 00:44:26,840
+الله بالأحكام الجيدة، يلّا فأدفعنا بعضا بعضا و
+
+397
+00:44:26,840 --> 00:44:34,330
+جعلناهم أحد الحديثة فزعدني قوم لا يؤمنونثم أرسلنا
+
+398
+00:44:34,330 --> 00:44:38,190
+موسى و أخاه حرون ..لأ فيش هنا ..فيش مد ..فيش مد
+
+399
+00:44:38,190 --> 00:44:43,190
+زيادة ثم أرسلنا موسى و أخاه حرون بآياتنا و سلطان
+
+400
+00:44:43,190 --> 00:44:50,590
+مبين ..لأ غني و سلطان مبين إلى فرعون و ملئيه
+
+401
+00:44:50,590 --> 00:44:53,170
+فاستكبروا و كانوا قوما
+
+402
+00:44:55,640 --> 00:44:59,920
+شوفي عليه بقى إلى فرعونة أول إشي الراء في فرعونة
+
+403
+00:44:59,920 --> 00:45:04,260
+إيش؟ مرققة جأمة قبلها مكسور وهي ساكلة إذا فهي
+
+404
+00:45:04,260 --> 00:45:10,260
+مرققة بنقول فرعونة إلى فرعونة أما وملئه الياء يا
+
+405
+00:45:10,260 --> 00:45:17,120
+أخواتي هذه إيش عليها؟ صفر مستديرصفر مستدير أي حرف
+
+406
+00:45:17,120 --> 00:45:22,600
+عليه صفر مستدير هذا الحرف ساقط وصلا ووقفا يبقى مش
+
+407
+00:45:22,600 --> 00:45:27,700
+هتنفذيه نهائيا بتقولي وملئيه ع السريع مش وملئيه
+
+408
+00:45:27,700 --> 00:45:34,280
+يلا أشوف إلى فرعونة .. فرعونة إلى فرعونة .. فر ..
+
+409
+00:45:34,280 --> 00:45:38,980
+ايوة إلى فرعونة وملائكي فاستقبضوا وكانوا قوما
+
+410
+00:45:38,980 --> 00:45:47,400
+عالين فقالوا أقنلوا لبشرينلأ بنقولش ليه بشرين ..
+
+411
+00:45:47,400 --> 00:45:51,400
+إذا وقفتي على بشرين ممكن تمدي لكن إذا إنتي وصلتي
+
+412
+00:45:51,400 --> 00:45:56,420
+هتجيبي بس .. هتجيبي بس حرف ساكن و فقط يعني ليه
+
+413
+00:45:56,420 --> 00:46:02,500
+بشرين مثلنا .. مثلنا .. هتقولوا أنه أملوا لبشرين
+
+414
+00:46:02,500 --> 00:46:08,560
+مثلنا و قومهم .. و قوم .. و قومهما لنا عارفينعيدي
+
+415
+00:46:08,560 --> 00:46:14,080
+الآية أشوف فقالوا أنا أملون بشرين مثلنا و قولوه ما
+
+416
+00:46:14,080 --> 00:46:21,780
+لنا عابلون فكذبوهما فكانوا من المهلكين بتركزي يا
+
+417
+00:46:21,780 --> 00:46:26,220
+هبة أحيانا على النغمة إيش؟ فبيطلع ماك أحيانا
+
+418
+00:46:26,220 --> 00:46:31,980
+المدود مش .. مش موضع مده فكذبوهما فكانوا من
+
+419
+00:46:31,980 --> 00:46:37,320
+المهلكين فقط يعني إيش؟ No بس مقدار حركتين نعيد؟
+
+420
+00:46:41,690 --> 00:46:47,510
+أحسنتي قلقلي و لقد .. و لقد آتينا موسى الكتاب
+
+421
+00:46:47,510 --> 00:46:53,350
+لعلهم يهتزون وجعلنا ابن مريم و أم .. و أمه .. و
+
+422
+00:46:53,350 --> 00:46:58,770
+أمه آية .. انتبه .. انتبه .. انتبه وجعلنا ابن مريم
+
+423
+00:46:58,770 --> 00:47:06,530
+و أمه في غنة .. في غنة وجعلنا ابن مريم .. م ..
+
+424
+00:47:06,530 --> 00:47:13,930
+مريم .. م .. مش مريم .. م ..أيوة مريمة و جعلنا
+
+425
+00:47:13,930 --> 00:47:22,170
+ابنا مريمة و أمه آية و أويلهما إلى ربوة ذات قرار و
+
+426
+00:47:22,170 --> 00:47:30,190
+معين و أمه آية هنمد أربع أو خمس حركات و ذات مش
+
+427
+00:47:30,190 --> 00:47:37,230
+هنمدها إلا مقدار حركتينو جعلنا ابن مريم و أمه آيتا
+
+428
+00:47:37,230 --> 00:47:43,750
+و آوينهما إلى رفوة ذات قرار و معين و جعلنا ابن
+
+429
+00:47:43,750 --> 00:47:53,530
+مريم و أمه آيته و آوينهما عشان تفكر؟ آيته و في إيش
+
+430
+00:47:53,530 --> 00:48:01,490
+إبغام نغنى و جعلنا ابن مريم و أمهالناس يقول آية ..
+
+431
+00:48:01,490 --> 00:48:01,770
+لأ
+
+432
+00:48:08,340 --> 00:48:16,000
+لأ بنعيد الآية ونظبط وجعلنا ابن مريم وأمه آيتا
+
+433
+00:48:16,000 --> 00:48:24,280
+وأويناهما .. ممكن نقف .. وأويناهما إلى ربوة ذات
+
+434
+00:48:24,280 --> 00:48:31,920
+قرار ومعين قرار ومعين وبعدين نجيب الغنى وجعلنا ابن
+
+435
+00:48:31,920 --> 00:48:44,220
+مريم وأمه آيتا .. آيتا و ..بس قولني آيتو .. ربي
+
+436
+00:48:44,220 --> 00:48:48,080
+.. ربي
+
+437
+00:48:48,080 --> 00:48:51,460
+أحسن
+
+438
+00:48:51,460 --> 00:48:57,600
+شايف كيف؟ عندك إضغام ذات قراري و معين يا أيها
+
+439
+00:48:57,600 --> 00:49:04,110
+الرسل كله من الطيبةمينات طيبات .. مينات طيبات ..
+
+440
+00:49:04,110 --> 00:49:07,810
+مينات طيبات .. مينات طيبات .. مينات طيبات .. مينات
+
+441
+00:49:07,810 --> 00:49:07,830
+طيبات .. مينات طيبات .. مينات طيبات .. مينات طيبات
+
+442
+00:49:07,830 --> 00:49:09,170
+.. مينات طيبات .. مينات طيبات .. مينات طيبات ..
+
+443
+00:49:09,170 --> 00:49:11,190
+مينات طيبات .. مينات طيبات .. مينات طيبات .. مينات
+
+444
+00:49:11,190 --> 00:49:13,630
+طيبات .. مينات طيبات .. مينات طيبات .. مينات طيبات
+
+445
+00:49:13,630 --> 00:49:17,790
+.. مينات طيبات .. مينات طيبات .. مينات طيبات ..
+
+446
+00:49:17,790 --> 00:49:24,790
+مينات طيبات .. مينات طيبات .. مينات طيباتيا أيها
+
+447
+00:49:24,790 --> 00:49:30,150
+ال .. يا أيها الرسل قلوا من الطيبات لأ مش هيك من
+
+448
+00:49:30,150 --> 00:49:34,710
+الطيبات .. ضبطي بس حرق .. بس عادي شدوا بس من
+
+449
+00:49:34,710 --> 00:49:41,550
+الطيبات و أعملوا صالحا إني .. إني لما تعملون علي
+
+450
+00:49:41,550 --> 00:49:54,120
+وإن هذه أمتهم .. لأ أغني وإن هذه أمتهم ..أمة واحدة
+
+451
+00:49:54,120 --> 00:50:03,660
+و أنا ربكم فاتقون تبهي عليها بقى وإن هذه أمتكم أمة
+
+452
+00:50:03,660 --> 00:50:14,640
+واحدة أمة واحدة و أنا ربكم فاتقون نجيب المد موضع
+
+453
+00:50:14,640 --> 00:50:21,190
+مد ما نمدش مناشي المد في مواضع لا يوجد فيها مدمدّي
+
+454
+00:50:21,190 --> 00:50:31,890
+أكتر، أربعة أو خمس أحسنتي،
+
+455
+00:50:31,890 --> 00:50:36,870
+رائع أمرهم
+
+456
+00:50:36,870 --> 00:50:43,450
+.. أمرهم أمرهم بينهم زغرا أمرهم بينهم في إخفاء،
+
+457
+00:50:43,450 --> 00:50:51,840
+بنجيب الغنى أمرهم بينهم زغراكل حزب .. كل حزب بما
+
+458
+00:50:51,840 --> 00:50:58,920
+لديهم فرحون فضوهم في غمرتهم حتى حين فضوهم في
+
+459
+00:50:58,920 --> 00:51:03,820
+غمرتهم حتى حين برضك حتى حين ماعرفش المادة كتير حتى
+
+460
+00:51:03,820 --> 00:51:10,720
+حين بس حركتي نعم فضوهم في غمرتهم حتى حين أيحسبوا
+
+461
+00:51:10,720 --> 00:51:16,660
+.. أيحسبوا لأنما .. أنما نمدهم .. نمدهم
+
+462
+00:51:19,370 --> 00:51:24,810
+نعيد الآية، نظبط المدود احسبون أن ما .. أن ما
+
+463
+00:51:24,810 --> 00:51:35,900
+نمدهم بيه من ذلكأ يحسبون أنما نمدهم به من مال و
+
+464
+00:51:35,900 --> 00:51:42,140
+وبنين نمدهم به .. إيش في ميم ساكنة؟ أجي بعدها بقى
+
+465
+00:51:42,140 --> 00:51:46,900
+إيش الحكم؟ إخفاء شفوي بدي أخفي مع الغنى ميم مال
+
+466
+00:51:46,900 --> 00:51:51,800
+برضه هغن لإنه اضغان بغنى مالي و وبنين أيضا اضغان
+
+467
+00:51:51,800 --> 00:51:58,100
+بس ميم مال بديش أمدها كتير بس حركتين مال بسلأ
+
+468
+00:51:58,100 --> 00:52:03,880
+بنقولش أ يحسبونا أنهم .. أ يحسبونا .. أ يحسبونا
+
+469
+00:52:03,880 --> 00:52:13,320
+أنما نمدهم به .. لأ نمدهم به .. نمدهم به مال و بني
+
+470
+00:52:13,320 --> 00:52:18,920
+.. لأ نظبط .. نظبط أكتر عيد الآية أ يحسبونا أنما
+
+471
+00:52:18,920 --> 00:52:26,640
+نمدهم به مال ..بنقولش مين مالي و .. مين مالي و بني
+
+472
+00:52:26,640 --> 00:52:29,920
+.. غني .. لإن انت تركز على الغنى بتهيش معاك المد
+
+473
+00:52:29,920 --> 00:52:34,120
+اللي مش لازم .. مين مالي و بني .. هيحسبون أنما
+
+474
+00:52:34,120 --> 00:52:44,380
+نمدهم به مين مالي و بني .. هيحسبون أنما نمدهم به
+
+475
+00:52:44,380 --> 00:52:49,580
+.. نمدهم به .. غني .. نمد .. نمدهم .. نمدهم .. نمد
+
+476
+00:52:49,580 --> 00:52:57,580
+.. نمدهم به ..نمدهم، أيحسبوا لأننا نمدهم بهي
+
+477
+00:52:57,580 --> 00:53:05,800
+بالمال ومالين نسارع لهم في الخيرات بل لا يشعبون إن
+
+478
+00:53:05,800 --> 00:53:11,420
+الذين هم من خش .. هم قلني
+
+479
+00:53:11,420 --> 00:53:17,360
+إن الذين هم من خشية .. من خشية ربهم مشفقون ربهم
+
+480
+00:53:17,360 --> 00:53:26,910
+مشفقون اضغام؟ بيقول نعمإن الذين
+
+481
+00:53:26,910 --> 00:53:34,790
+هم من خشية ربهم يشرفون و الذين هم بآيات ربهم
+
+482
+00:53:34,790 --> 00:53:42,310
+يؤمنون و الذين هم بآيات ربهم يؤمنون و الذين هم
+
+483
+00:53:42,310 --> 00:53:47,150
+بربهم لا يشرفون هم بربهم انت حكاية الأخفاء الشفوي
+
+484
+00:53:47,150 --> 00:53:53,450
+أجت معاك كتيروالذين هم بربهم أرض أيضا اخفاء شفويح
+
+485
+00:53:53,450 --> 00:53:54,510
+الجيب الغنى
+
+486
+00:53:58,910 --> 00:54:03,610
+أحسنت يا هبة و بارك الله فيك ماشاء الله عليك صوتك
+
+487
+00:54:03,610 --> 00:54:07,410
+حلو كتير يا هبة صوتك حلو كتير بس إيش المشكلة أنك
+
+488
+00:54:07,410 --> 00:54:11,670
+أحيانا بتمدي في موضع لا يجيب فيه المد فإيش ..
+
+489
+00:54:11,670 --> 00:54:16,050
+فإحنا بدنا نظبط عشان نجيب .. عشان نظبط اللحن و
+
+490
+00:54:16,050 --> 00:54:19,930
+نجبط ال .. ال .. اه فعلى حساب الأحكام لأ فإحنا
+
+491
+00:54:19,930 --> 00:54:23,170
+بدنا نجيب الأحكام أولا فبيجي معنا إيش ان شاء الله
+
+492
+00:54:23,170 --> 00:54:27,240
+الصوت ال .. الحلوفركزي ع .. زي ما قلتلك أنا على
+
+493
+00:54:27,240 --> 00:54:30,800
+الأشياء اللي فيش فيها مدناش نمدها و الإخفاء الشفوي
+
+494
+00:54:30,800 --> 00:54:35,440
+الميم الساكنة بعدها بقى بدنا نغن نجيب إخفاء و
+
+495
+00:54:35,440 --> 00:54:42,300
+بعدها أياش غنة معاها غنة ميم بعد ربي يهم بيه أه ان
+
+496
+00:54:42,300 --> 00:54:49,540
+شاء الله و أحسنتي و ما شاء الله عليكي نيجي ل ..
+
+497
+00:54:49,540 --> 00:54:53,380
+موجودة ألاء حنون؟ يلا حبيت
+
+498
+00:54:59,890 --> 00:55:10,470
+يبتون ماء ماء و قلبهم ودلة أنهم إلى ربهم راجعون
+
+499
+00:55:10,470 --> 00:55:19,310
+أولئك يسارعون في الخيرات و هم لها سابحون و لا مكلف
+
+500
+00:55:19,310 --> 00:55:27,770
+نفسا إلا وسعها و لدينا كتاب إن ينطق بالحق و هم لا
+
+501
+00:55:27,770 --> 00:55:36,980
+يظلمونبل قلوبهم في غمرة من هذا ولهم أعمال من دون
+
+502
+00:55:36,980 --> 00:55:48,220
+ذلك هم لها عاملون حتى إذا أخذنا مصرفهم بالعذاب إذا
+
+503
+00:55:48,220 --> 00:55:58,580
+هم يجأرون لا تجأروا اليوم إنكم مننا لا تنصرون
+
+504
+00:55:59,170 --> 00:56:07,090
+قد كانت آياتي .. قد كانت آياتي تتلى عليكم فكنتم
+
+505
+00:56:07,090 --> 00:56:18,230
+على أعقابكم تنكسون مستكبرين به سامرا تهجرون أفلم
+
+506
+00:56:18,230 --> 00:56:28,090
+يتدبروا القول أم جاءهم ما لم يأتي آبائهم الأولينأم
+
+507
+00:56:28,090 --> 00:56:37,850
+لم يعرفوا رسولهم فهم له منكرون أم يقولون به جنة بل
+
+508
+00:56:37,850 --> 00:56:46,910
+جاءهم بالحق وأكثرهم للحق كارئون ولو اتبع الحق
+
+509
+00:56:46,910 --> 00:56:55,980
+أهواءهم لفسدت السماوات والأرض ومن فيهنبل أتيناهم
+
+510
+00:56:55,980 --> 00:57:05,100
+بذكرهم فهم عن ذكرهم معرضون أم تسألهم خرجا فخراج
+
+511
+00:57:05,100 --> 00:57:13,540
+ربك خير وهو خير الرازقين وإنك لتدعوهم إلى صراط
+
+512
+00:57:13,540 --> 00:57:22,310
+مستقيموإن الذين لا يؤمنون بالآخرة عن الصراط لنا
+
+513
+00:57:22,310 --> 00:57:27,890
+كيبوه أحسنتي ما شاء الله عليك رائعة مخارج تمام غنن
+
+514
+00:57:27,890 --> 00:57:32,570
+تمام حتى العرض المد العرض السكون برضك تمام أحسنتي
+
+515
+00:57:32,570 --> 00:57:37,370
+يعني ليس لنا إلا المدح والثناء على هذه القراءة
+
+516
+00:57:37,370 --> 00:57:40,750
+الأخت ألائي الفراه افضل حبتي
+
+517
+00:57:49,950 --> 00:57:56,890
+لأ مش هذي رحم انتبهي الحائش عليها كسرة و لو
+
+518
+00:57:56,890 --> 00:58:05,290
+راحمناهم و لو راحمناهم و كشفنا مابيهم من ضرر نلجوا
+
+519
+00:58:05,290 --> 00:58:12,050
+في عدو في طبيانهم يعمهم نعيد الآية و لو راحمناهم و
+
+520
+00:58:12,050 --> 00:58:17,930
+كشفنا مابيهم هنا و كشفنا .. مابدناش نقلق الفاء و
+
+521
+00:58:17,930 --> 00:58:19,250
+كشفنا ..
+
+522
+00:58:24,990 --> 00:58:42,230
+الغن أكتر للضرر للجو للجو
+
+523
+00:58:42,230 --> 00:58:45,610
+نجيب
+
+524
+00:58:45,610 --> 00:58:53,800
+للجو قوليأه مش ju دي ال aj تخرج من وسط اللسان مع
+
+525
+00:58:53,800 --> 00:58:57,160
+ميحذية من الحنق الأعلى مابدناش نجيب فيها إيش تفشي
+
+526
+00:58:57,160 --> 00:59:07,500
+اج اج للد جو جو ارجع سالك لورا شوية للد جو أكتر
+
+527
+00:59:07,500 --> 00:59:15,610
+شوية أصبح اج اج ايوة للد جوطيب، ضبطها في البيت
+
+528
+00:59:15,610 --> 00:59:23,110
+أكتر و لا قد أخذناهم بمعذار مش أخذناهم أخذناهم و
+
+529
+00:59:23,110 --> 00:59:32,490
+لا قد أخذناهم أخى و لذا ساكنة أخذ و لا قد أخذناهم
+
+530
+00:59:32,490 --> 00:59:40,110
+بمعذار أخى، الخى مفخمة أخذولقد أخذناهم بالعذاب ثم
+
+531
+00:59:40,110 --> 00:59:46,030
+استكانوا لربهم وما يطرعهم أخذناهم .. أخذناهم
+
+532
+00:59:46,030 --> 00:59:50,730
+بالعذاب أجت ال meme بعديها زي اللي مين أخطب أيوة
+
+533
+00:59:50,730 --> 00:59:57,950
+ال meme إخفاء شفوي هنقول ولقد أخذناهم بالعذاب هم
+
+534
+00:59:57,950 --> 01:00:05,770
+بالعذاب ولقد أخذناهم .. لأ قلت ذأ ولقد أخذناهم
+
+535
+01:00:05,770 --> 01:00:13,540
+بالعذابما فخمتيش الخطأ أخذناهم ولا قد أخذناهم
+
+536
+01:00:13,540 --> 01:00:24,100
+بالعذاب فما استكانوا لربهم وما يتضرعون حتى .. حتى
+
+537
+01:00:26,720 --> 01:00:33,500
+نفس الحياة زي اتنعت مين مانع مش فتحنا .. فتحنا حتى
+
+538
+01:00:33,500 --> 01:00:40,780
+إذا فتحنا عليهم .. فتحنا الحقيقة فيها رخاوة و فيها
+
+539
+01:00:40,780 --> 01:00:46,660
+إش و فيها همس و مش فيها قلقلق حتى إذا فتحنا .. لأ
+
+540
+01:00:46,660 --> 01:00:58,290
+حتى إذا فتحنا عليهم بابا .. بابا بعذاب شديدذا ذالع
+
+541
+01:00:58,290 --> 01:01:05,110
+شديد إذا هم فيه مبلسون بس هنا مافيش غنة هم فيه
+
+542
+01:01:05,110 --> 01:01:11,570
+إظهار هم فيه إظهار شفوي هألفظ الميم ظاهرة دون غنة
+
+543
+01:01:11,570 --> 01:01:19,470
+هقش أقول إذا هم في .. هم في .. هم في فقط إذا هم في
+
+544
+01:01:19,470 --> 01:01:31,040
+مبلسون و هو الذي أنه .. مددمدر و هو الذي .. و هو
+
+545
+01:01:31,040 --> 01:01:41,470
+الذي .. و هو الذي .. و هو الذي .. نعمبس مقولش و ..
+
+546
+01:01:41,470 --> 01:01:47,530
+و هو .. و هو .. ال و بس بجيب ال و فقط دون ألف و ..
+
+547
+01:01:47,530 --> 01:01:58,110
+و هو .. و هو الذي .. و هو الذي ..
+
+548
+01:01:58,110 --> 01:02:06,260
+نعم مش و هو .. و هو .. ضم تمك .. و هووهو الذي .. و
+
+549
+01:02:06,260 --> 01:02:12,800
+هو الذي أنشأ لكم السمعة و الابصار و الأدئة لأ عيدي
+
+550
+01:02:12,800 --> 01:02:18,640
+ثاني و هو اللذي .. و هو اللذي تخلفي أخوات صح تخلف
+
+551
+01:02:18,640 --> 01:02:27,500
+و هو عن و هو و هو الذي .. و هو الذي أنشأ لكم
+
+552
+01:02:27,500 --> 01:02:36,670
+السمعة و الأبصار و الأدئةوالأبيصار فخم الصاد و هو
+
+553
+01:02:36,670 --> 01:02:45,130
+الذي أنشأ له مستمع والأبصار والأفئده والأبيصار ..
+
+554
+01:02:45,130 --> 01:02:51,430
+صار .. نقول صار مفخمة والأبيصار والأفئده ..
+
+555
+01:02:51,430 --> 01:02:54,390
+والأبيصار والأفئده
+
+556
+01:02:56,810 --> 01:03:03,190
+لأ ممكن تفهم أكتر؟ و الأب يصار .. صا .. صا .. و
+
+557
+01:03:03,190 --> 01:03:07,670
+الأب يصار .. و الأفقلا .. لأ هيك مش تفخين و الأب
+
+558
+01:03:07,670 --> 01:03:12,290
+يصار .. صا .. صا .. و الأب يصار .. بدين .. بدين ..
+
+559
+01:03:12,290 --> 01:03:16,330
+يعني الهواء .. الفم ينتلق بالهواء صا .. و الأب
+
+560
+01:03:16,330 --> 01:03:17,310
+يصار ..
+
+561
+01:03:21,990 --> 01:03:27,530
+انسبتها في البيت تشكرون
+
+562
+01:03:27,530 --> 01:03:36,150
+مدي رول قليل ما تشكرون مش رول .. هذي إيش دي
+
+563
+01:03:36,150 --> 01:03:40,510
+الراهنة؟ الراهنة مليئة بالغنة ال wow اللي عندك
+
+564
+01:03:40,510 --> 01:03:44,210
+مليئة بالغنة كيف بدي أتخلص من الغنة يا أخوات؟
+
+565
+01:03:44,210 --> 01:03:49,670
+بأتخلص من الغنة بإني أضمهضم شفايفي أكتر، هضم
+
+566
+01:03:49,670 --> 01:03:54,950
+شفايفي، إذا أنا زميت، مانطلعش إيش، تطلع غنة،
+
+567
+01:03:54,950 --> 01:03:59,570
+القاعدة اللي بتقول إيش، ضمي ولا تزمين، ماتقوليش و
+
+568
+01:03:59,570 --> 01:04:03,050
+تروحي شفايفك اللي هنا إيش، ينزم ولا تحتها، بده من
+
+569
+01:04:03,050 --> 01:04:09,570
+هنا ينضموايشكرون روق بحيث انت لو حد اللي عملت يعني
+
+570
+01:04:09,570 --> 01:04:12,970
+هنا روق من غير بطلعش .. بطلعش فيها غنة لو .. لو
+
+571
+01:04:12,970 --> 01:04:19,350
+سكرتي أنفك روح روح روح وفتحتي روح نفس الحاجة روح
+
+572
+01:04:19,350 --> 01:04:25,050
+يشكرون رون يالا
+
+573
+01:04:25,050 --> 01:04:35,680
+ضم و لا تزم يالا فين ما تشكرونرول .. رول .. رول ..
+
+574
+01:04:35,680 --> 01:04:44,220
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+575
+01:04:44,220 --> 01:04:46,120
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+576
+01:04:46,120 --> 01:04:46,180
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+577
+01:04:46,180 --> 01:04:46,200
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+578
+01:04:46,200 --> 01:04:46,260
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+579
+01:04:46,260 --> 01:04:46,400
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+580
+01:04:46,400 --> 01:04:48,040
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+581
+01:04:48,040 --> 01:05:00,480
+رول .. رول
+
+582
+01:05:00,790 --> 01:05:07,730
+وهو الذي يحيي ويميت وله اختلاف الليل والنهار ده
+
+583
+01:05:07,730 --> 01:05:15,490
+عادي ..وهو الذي يحيي ويميت .. يحيي ويميت وله
+
+584
+01:05:15,490 --> 01:05:22,670
+اختلاف الليل والنهار أفلا تعقلون؟ دي اللي حاجته
+
+585
+01:05:22,670 --> 01:05:29,280
+..وهو الذي يحيي ويميت وله اختلاف الليل والنهاروهو
+
+586
+01:05:29,280 --> 01:05:37,840
+الذي يحي ويميد وله اختلاف الليل والنهار والنهار
+
+587
+01:05:37,840 --> 01:05:46,440
+بدك تقفى؟ بدها تكون الرق مفخّنة والنهار والنهار
+
+588
+01:05:46,440 --> 01:05:56,720
+والنهار أيوة أفلا تعقلون تعقلون أفلاأيوة العين
+
+589
+01:05:56,720 --> 01:06:01,920
+تخرج من وسط الحلقة أحسنتى بل قالوا مثل ما قال
+
+590
+01:06:01,920 --> 01:06:11,220
+الأولون قالوا .. قالوا .. قالوا .. قالوا .. قالوا
+
+591
+01:06:11,220 --> 01:06:17,270
+.. من غير مادة قالوا .. مدّي هنا اللو مدّيهاقالوا
+
+592
+01:06:17,270 --> 01:06:26,350
+أيذا ميتنا و كنا ترادا و عضادا أننا مابعدوا .. هذه
+
+593
+01:06:26,350 --> 01:06:30,850
+إيش؟ أإنا .. أيوة أإنا .. أحسنتي .. أإنا .. نعم
+
+594
+01:06:30,850 --> 01:06:34,090
+قالوا
+
+595
+01:06:34,090 --> 01:06:40,010
+أيذا .. أيذا ميتنا و كنا .. مش ميتنا .. ميتنا ..
+
+596
+01:06:40,010 --> 01:06:42,710
+ميتنا .. بس همس بسيط
+
+597
+01:06:46,660 --> 01:06:52,580
+ما .. ما تمديش قالوا أذا ميتنا .. ميتنا .. ميتنا
+
+598
+01:06:52,580 --> 01:07:02,180
+.. نعم قالوا أذا ميتنا و كنا جرادا و عظاما أإنا
+
+599
+01:07:02,180 --> 01:07:08,800
+لمبعوثون لمبعوثون لمبعوثون
+
+600
+01:07:10,310 --> 01:07:19,050
+لقد وعدنا نحن و آذاؤنا لهذا منطلق إن هذا إلا
+
+601
+01:07:19,050 --> 01:07:27,110
+أفاطير الأولين نعيد الآية لقد وعدنا نحن .. لقد
+
+602
+01:07:27,110 --> 01:07:33,070
+وعدنا نحن وعدنا و .. وعدنا من غير مدد كتير بس
+
+603
+01:07:33,070 --> 01:07:39,210
+طبيعيمش لقد .. لقد على السريع من غير ما نحط ألف
+
+604
+01:07:39,210 --> 01:07:45,550
+بعد اللام نفس
+
+605
+01:07:45,550 --> 01:07:54,900
+الحاجة مش نحن نحن نعملقد وعدنا نحن وأباقنا زانيا
+
+606
+01:07:54,900 --> 01:08:02,280
+قبل إنها بقالا أساطير الأولين أحسنت يا قلاء شكرا و
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+607
+01:08:02,280 --> 01:08:05,140
+مبارك الله فيكي هندق يا قلاء على الأشياء اللي
+
+608
+01:08:05,140 --> 01:08:09,020
+حكينا عليها اللي هي الغنة في ال wow مش هتكون ..
+
+609
+01:08:09,020 --> 01:08:13,600
+هنتخلص منها عن طريق اللي هو إيه ضم الشفتين أكتر
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+610
+01:08:13,600 --> 01:08:17,140
+لقدام فتطلع عنا من غير غنة حكاية الحروف المقلقة
+
+611
+01:08:17,140 --> 01:08:22,510
+اللي ليس ..اللي مش فيها إيش اسمه قلقلة مش هقلقلها
+
+612
+01:08:22,510 --> 01:08:28,750
+زي نحن نحن نقول نحن نحن نحن إيش كمان قلنا على
+
+613
+01:08:28,750 --> 01:08:33,330
+الأشياء اللي هي إيش التائل مهموسة التائل مهموسة
+
+614
+01:08:33,330 --> 01:08:39,590
+الساكنة فقط فيها همس وليس فيها قلقلة متنا .. متنا
+
+615
+01:08:39,590 --> 01:08:43,890
+..و النهار إيش؟ الراء .. إذا أنا وقفت على الراء
+
+616
+01:08:43,890 --> 01:08:49,410
+الساكنة ما قبلها حرف مد .. بد إيش؟ أنا أفخمها
+
+617
+01:08:49,410 --> 01:08:52,930
+النهار .. مبارك الله فيك ندوق على الأشياء الهادئ
+
+618
+01:08:52,930 --> 01:08:58,850
+وين في أرضها أخر واحدة معانا هتكون الأخت موجودة
+
+619
+01:08:58,850 --> 01:09:03,250
+فاطمة عدوان فاطمة .. فضلي فاطمة
+
+620
+01:09:12,430 --> 01:09:24,370
+قل لمن الأرض ومن فيها إن كنتم تعلمون سيقولون لله
+
+621
+01:09:24,370 --> 01:09:31,950
+قل أفلا تذكرون قل ما الرب السماوات السبعي ورب
+
+622
+01:09:31,950 --> 01:09:43,860
+العرش العظيم سيقولون لله قل أفلا تفتقونقل من بيده
+
+623
+01:09:43,860 --> 01:09:52,260
+ملكوت كل شيء و هو يجير .. و هو يجير و لا يجار عليه
+
+624
+01:09:52,260 --> 01:10:05,880
+إن كنتم تعلمون سيقولون الله قل فإنا تسحرون بل
+
+625
+01:10:05,880 --> 01:10:09,960
+آتيناهم لأ بل .. بل آتيناهم
+
+626
+01:10:16,500 --> 01:10:19,360
+نفس الحاجة يا .. يا ما شاء الله عليك يا فاطمة
+
+627
+01:10:19,360 --> 01:10:24,500
+قراءتك رائعة وجميلة فحاول تتخلص من الغنى في الأو
+
+628
+01:10:24,500 --> 01:10:32,460
+بضم التم، ضم الشفاية وإن هم لكاذبونبون أيوة ضم
+
+629
+01:10:32,460 --> 01:10:35,560
+أكتر فبتطلعش عندك القنة لأن قراءتك رائعة فهذه
+
+630
+01:10:35,560 --> 01:10:44,250
+النقطة بدنا نظبطهابل قتيناهم بالحق وإنهم لكاذبون
+
+631
+01:10:44,250 --> 01:10:49,290
+أيوة شفتي كتلة عطها دي بون رائع من غير قلنا متخذا
+
+632
+01:10:49,290 --> 01:10:58,010
+.. متخ .. متخذا الله متخذا متخذا الله من ولده وما
+
+633
+01:10:58,010 --> 01:11:08,280
+كان معهم إله إذا لذهب كلكل إله .. كل إله بما خلق
+
+634
+01:11:08,280 --> 01:11:15,740
+قال على بعضه كل إله بما خلق أشوف كيف عندك الإقلاب
+
+635
+01:11:15,740 --> 01:11:23,510
+هنا أشوف كيف إذا لذهب كل إله .. كل إلهلأ إيش ..
+
+636
+01:11:23,510 --> 01:11:27,930
+إيش هنعمل هناك؟ إلا هم هنقلب النون الساكنة إلى ميم
+
+637
+01:11:27,930 --> 01:11:32,230
+ثم نخفي الميم عند البان، هإيش؟ هنطبق على ميم
+
+638
+01:11:32,230 --> 01:11:39,080
+يسيرة، انطباقا يسيرا، هقول كيفنالذهب كل إله .. إله
+
+639
+01:11:39,080 --> 01:11:46,600
+بما .. إله بما .. أطبق على ميم بشكل يسير ثم أدخل
+
+640
+01:11:46,600 --> 01:11:51,760
+على مخرج من البار يلا .. إله بما .. طلع علي .. طلع
+
+641
+01:11:51,760 --> 01:12:00,910
+علي .. قوليها طلع عليإلهي بما إلهي
+
+642
+01:12:00,910 --> 01:12:08,370
+بما إلهي بما إلهي بما إلهي بما إلهي بما إلهي بما
+
+643
+01:12:08,370 --> 01:12:11,530
+إلهي بما إلهي بما إلهي بما إلهي بما إلهي بما إلهي
+
+644
+01:12:11,530 --> 01:12:11,950
+بما إلهي بما إلهي بما إلهي بما إلهي بما إلهي بما
+
+645
+01:12:11,950 --> 01:12:14,850
+إلهي بما إلهي بما إلهي بما إلهي بما إلهي بما إلهي
+
+646
+01:12:14,850 --> 01:12:22,030
+بما إلهي بما إلهي بما إلهي بما إلهي بما إلهي بما
+
+647
+01:12:22,030 --> 01:12:22,610
+إلهي بما إلهي بما إلهي بما إلهي بما إلهي بأديها
+
+648
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+تاني؟ أيوة أحسنت
+
+649
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+أحسن انت ما شاء الله عليك يا فاطمة قراءتك رائعة
+
+650
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+651
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+اللي هم الغنى في ال .. المادة بالواو وحكاية
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+652
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+الإقلاب أو الإخفاء الشفوي هتكون كيف هنحقق الإخفاء
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+653
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+654
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+يسيرة نطبق الشفتين انطباقا يسيرا ثم ندخل على مخرج
+
+655
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+656
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+سوزان
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+657
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+أعوذ بالله من الشيخان الرجيم أيوة سيزان جيم كيف؟
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+658
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+زبطت .. حاولت تزبطيه في الدار؟ رجيم أيوة مش جيم ..
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+659
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+مش جيم .. جيم .. جيم .. جيم من وسط اللسان مع ما
+
+660
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+يحذيه من الحنق الأعلى أجي .. قولي أج .. أجي هي ..
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+661
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+هي ممتازة هذه حاولي تطبيقهاأعوذ بالله من الشيطان
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+662
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+
+663
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+بالله من الشيطان الرجيم لأ .. اتجي .. اتجي .. راجع
+
+664
+01:13:57,580 --> 01:14:00,380
+.. راجع لسانك لورا شوية .. اتجي .. اتجي .. ايوة
+
+665
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+انت لحالة بتجي بيها صح بس إيش بده الحكاية؟ عشان
+
+666
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+تجي مع الآيات بدها ممارسة و بده تدريب بسم الله
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+667
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+الرحمن الرحيمعالم الغيب والشهادة فتعالى عما يشركون
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+668
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+اسمه كان فخم الغائب .. الغيب عالم الغيب .. الغيب
+
+669
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+عالم الغيب والشهادة فتعالى عما يشركون قل ربي إما
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+670
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+تريد تريد تريني ما يبعدون لأ انت بيقبل عليها شدة
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+671
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+النون علشان تا اما تريانني ما يوعدون تري تريانني
+
+672
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+ونغني عن النون تريانني اما تريانني ما يوعدون بس
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+673
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+ممكن الرق قرأ في تري تريانني .. تري
+
+674
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+دربتها أكتر في البيت يا ربي فلا تجعلني في القوم
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+675
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+الظالمين وإنا على النور يك .. نوري كما نعدهم
+
+676
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+لقادرون سوزان في عندك مشكلة في الراء المرققة اللي
+
+677
+01:15:24,950 --> 01:15:36,040
+هي الراء المكسورة نوري نوري نوري نوري أيوةوإن ..
+
+678
+01:15:36,040 --> 01:15:40,620
+ممكن
+
+679
+01:15:40,620 --> 01:15:46,940
+نلقيقها أكتر نوريا .. نورياك .. نورياك
+
+680
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+ادفع بالذي أحسن السيئة نعم أحسن السيئةادفع ..ادفع
+
+681
+01:15:57,300 --> 01:16:05,540
+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+682
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+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+683
+01:16:12,820 --> 01:16:14,400
+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+684
+01:16:14,400 --> 01:16:17,940
+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+685
+01:16:17,940 --> 01:16:19,320
+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+686
+01:16:19,320 --> 01:16:20,440
+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+687
+01:16:20,440 --> 01:16:22,520
+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
+
+688
+01:16:22,520 --> 01:16:27,270
+..من همزات اظهر من همزات دي ناس يقول من همزات
+
+689
+01:16:27,270 --> 01:16:51,430
+مافيش فيها أقول لأ من همزات اعيدي
+
+690
+01:16:51,430 --> 01:16:51,770
+تاني
+
+691
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+جاء في عندك إيش يا أخوات؟ مد واجب متصل لماذا أنا
+
+692
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+أمد؟ لأقوى الضعيف حتى أتوصل إلى النطق القوي وهو
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+693
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+مين؟ الهمزة عشان هيك إذا إنت مد كويس أجيب الهمزة
+
+694
+01:17:14,220 --> 01:17:17,900
+إنت أحيانا .. إنت إيش عملت يا سوزان؟ أكلتي الهمزة
+
+695
+01:17:17,900 --> 01:17:24,790
+موضحتيهاش، محققتيهاش، هنقول إيش؟حتى إذا جاء أحدهم
+
+696
+01:17:24,790 --> 01:17:36,030
+جاء أحدهم جاء أحدهم جاء أحدهم
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+697
+01:17:36,030 --> 01:17:40,370
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+698
+01:17:40,370 --> 01:17:42,050
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+699
+01:17:42,050 --> 01:17:45,410
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+700
+01:17:45,410 --> 01:17:47,670
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+701
+01:17:47,670 --> 01:17:47,730
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+702
+01:17:47,730 --> 01:17:47,850
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+703
+01:17:47,850 --> 01:17:49,430
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+704
+01:17:49,430 --> 01:17:58,520
+جاء أحدهم جاء أحدهم جلعلي أعمل صالحا فيما
+
+705
+01:17:58,520 --> 01:18:05,940
+تركت لعلي
+
+706
+01:18:05,940 --> 01:18:15,940
+أعمل صالحا فيما تركت لعلي
+
+707
+01:18:15,940 --> 01:18:18,840
+أعمل صالحا فيما تركت لعلي أعمل صالحا فيما تركت
+
+708
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+تركت لعلي أعمل صالحا فيما تركتكلا إنها كلمة هو
+
+709
+01:18:24,150 --> 01:18:31,930
+قائلها حقق الإظهار كلا إنها كلمة هو قائلها حقق
+
+710
+01:18:31,930 --> 01:18:34,510
+الإظهار كلا إنها كلمة هو قائلها حقق الإظهار كلا
+
+711
+01:18:34,510 --> 01:18:35,930
+إنها كلمة هو قائلها حقق الإظهار كلا إنها كلمة هو
+
+712
+01:18:35,930 --> 01:18:36,130
+قائلها حقق الإظهار كلا إنها كلمة هو قائلها حقق
+
+713
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+الإظهار كلا إنها كلمة هو قائلها حقق الإظهار كلا
+
+714
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+الإظهار كلا إنها كلمة هو قائلها حقق الإظهار كلا
+
+715
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+إنها كلمة هو قائلها حقق
+
+716
+01:18:48,100 --> 01:18:54,380
+أيوة أحسنت يبارك الله فيك ومن وراعيهم برزخ .. و من
+
+717
+01:18:54,380 --> 01:19:01,680
+وراعيهم برزخوا إلى يومي .. إلى يومي يبعثوا و من
+
+718
+01:19:01,680 --> 01:19:08,060
+وراعيهم برزخوا ال .. ها إيش قلنا؟ وراعيهم برزخوا
+
+719
+01:19:08,060 --> 01:19:11,560
+الميم الساكنة جاء بعدها بفهمنا حقق الإخفاء الشفوي
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+720
+01:19:11,560 --> 01:19:13,700
+مع الغنى يلا؟
+
+721
+01:19:16,980 --> 01:19:25,140
+و من وراهم درزخ .. درزخ إلى يوم يبعته شايفة؟ درزخ
+
+722
+01:19:25,140 --> 01:19:34,440
+إلى أيضا إظهار نعم فإلى كيخ في الصور ثلاث .. ثلاث
+
+723
+01:19:34,440 --> 01:19:42,810
+ساب بينهم يوم إذا و لا يتساءلبعدين فلا أنساب نفسها
+
+724
+01:19:42,810 --> 01:19:49,030
+زي جهة حقق الهمزة بعد المد يلا أشوف فإذا نودي قربي
+
+725
+01:19:49,030 --> 01:19:53,830
+الصور فلا .. لأ هي كإنت مابينتيش الهمزة صح يا
+
+726
+01:19:53,830 --> 01:19:59,710
+أخوات؟ مابيناتش الهمزة لما نقول فلا أنساب .. فلا
+
+727
+01:19:59,710 --> 01:20:01,470
+أنساب
+
+728
+01:20:10,070 --> 01:20:14,150
+مدّي أكتر وحقق الهمزة في التساءل
+
+729
+01:20:28,800 --> 01:20:32,740
+شايف كيف؟ بدي أجيب الهمزة و بعدين يوم إذ و لا في
+
+730
+01:20:32,740 --> 01:20:40,770
+إضغام بيغنى حقيقي يوم إذ و لا يتساءلونأحسنت فنفق
+
+731
+01:20:40,770 --> 01:20:46,910
+لك موازينه فأولئك هم ال .. هم المفلحون
+
+732
+01:20:49,320 --> 01:20:58,440
+نفس الحاجة في عندك اظهر ومن .. ومن خفت ومن خفت
+
+733
+01:20:58,440 --> 01:21:04,780
+موازين .. سوزان ومن خفت ومن .. حقق النون مظهر يلا
+
+734
+01:21:04,780 --> 01:21:09,720
+ومن خفت .. لأ بس من غير غنى ظاهرة فيها بس أصل
+
+735
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+الغنى، مدناش غنى ظاهرة ومن خفت موازينه ومن خفت
+
+736
+01:21:16,680 --> 01:21:17,600
+موازينه .. أيوة أحسنت
+
+737
+01:21:25,060 --> 01:21:36,540
+الذين خسروا أنفسهم في جهنم قالدون تلفح وجوههم
+
+738
+01:21:36,540 --> 01:21:45,360
+النار .. النار وهم فيها كائحون تلفح وجوههم النار
+
+739
+01:21:45,360 --> 01:21:48,640
+.. النار
+
+740
+01:21:48,640 --> 01:21:49,640
+وهم فيها كائحون
+
+741
+01:21:52,950 --> 01:22:00,930
+قولني أكتر وجوههم النار أنها .. لأ اعدي الآية تنفع
+
+742
+01:22:00,930 --> 01:22:07,620
+وجوههم النار فيها كرمأحسنت يا سيزان ماشاء الله
+
+743
+01:22:07,620 --> 01:22:10,500
+عليك يا سيزان ومبارك الله فيك يا حبيبتي بدنا بعض
+
+744
+01:22:10,500 --> 01:22:13,640
+الملاحظات اللي حكيناها الإظهار .. الإظهار في النون
+
+745
+01:22:13,640 --> 01:22:17,440
+الساكنة والتنوين إذا جاء بعدها أحد أحرف الإظهار
+
+746
+01:22:17,440 --> 01:22:21,080
+اللي هم مين؟ أخي هاكى علما، هزهوا وغيروا وخاسروا،
+
+747
+01:22:21,080 --> 01:22:24,540
+ست حروف إذا جاءت بعد النون الساكنة والتنوين، النون
+
+748
+01:22:24,540 --> 01:22:30,670
+فيها أصل الغنى فقط وهي مظهرة .. مظهرة من؟عمل .. من
+
+749
+01:22:30,670 --> 01:22:35,750
+عمل و في انها .. و من خفت .. و من خفت الحاجة
+
+750
+01:22:35,750 --> 01:22:38,690
+التانية اللي بدنا ندق عليها حكاية إيه؟ شقولنا يا
+
+751
+01:22:38,690 --> 01:22:46,030
+Suzanne اللي هوالاخفاء .. الاخفاء الشفوي .. الميم
+
+752
+01:22:46,030 --> 01:22:49,470
+الساكنة و بعدها باق .. و الباق .. بدنا نجيب اخفاء
+
+753
+01:22:49,470 --> 01:22:53,690
+شفوي .. نطبق الشفتين انتباقا يسيرا .. ثم ايش ..
+
+754
+01:22:53,690 --> 01:22:58,970
+ندخل على مخرج الباق .. فالاخفاء الشفوي .. و المدود
+
+755
+01:22:58,970 --> 01:23:02,650
+برضك .. انتبع المدود .. أخوات الكريمات انتهينا من
+
+756
+01:23:02,650 --> 01:23:05,330
+محاضرتنا الكريمة .. و الحمد لله رب العالمين ..
+
+757
+01:23:05,330 --> 01:23:08,210
+سبحانك اللهم و بحمدك أشهد أن لا إله إلا أنت
+
+758
+01:23:08,210 --> 01:23:11,210
+أستغفرك من كل ذنب و أتوب إليك .. بسم الله الرحمن
+
+759
+01:23:11,210 --> 01:23:15,600
+الرحيموالعصر إن الإنسان لا في خسر إلا الذين آمنوا
+
+760
+01:23:15,600 --> 01:23:20,200
+وعملوا الصالحات وتواصوا بالحق وتواصوا بالصبر شكرا
+
+761
+01:23:20,200 --> 01:23:22,820
+لكم والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/cdyZjFeK51A_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/cdyZjFeK51A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3513770c28cefdb0055cebe2ed22ce21b63bba6d
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/cdyZjFeK51A_raw.srt
@@ -0,0 +1,3120 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,790 --> 00:00:15,830
+أعوذ بالله من الشيطان الرجيم بسم الله الرحمن
+
+3
+00:00:15,830 --> 00:00:21,030
+الرحيم والصلاة والسلام على أشرف المرسلين سيدنا
+
+4
+00:00:21,030 --> 00:00:27,450
+محمد وعلى آله وصحبه وتابعيه ومن تبعهم بإحسان إلى
+
+5
+00:00:27,450 --> 00:00:33,670
+يوم الدين أخوات الكريمات أحييكن بتحية الإسلام تحية
+
+6
+00:00:33,670 --> 00:00:38,210
+أهل الجنة فالسلام عليكم ورحمة الله تعالى وبركاته
+
+7
+00:00:40,900 --> 00:00:45,520
+اللهم أشرحلي صدري ويسرلي أمري واحلل عقدة من لساني
+
+8
+00:00:45,520 --> 00:00:50,820
+يفقه قولي اللهم أعلمنا من القرآن ما ينفعنا وانفعنا
+
+9
+00:00:50,820 --> 00:00:56,360
+بما علمتنا وزدنا اللهم علمة الحمد لله الذي جعلنا
+
+10
+00:00:56,360 --> 00:01:01,320
+من خدام كتابه الكريم وأسأل الله العظيم أن يجعلني
+
+11
+00:01:01,320 --> 00:01:06,040
+وإياكم ممن يتلون آياته ويقيمون حدودها
+
+12
+00:01:09,930 --> 00:01:16,810
+ونبدأ رحلتنا القرأنية مع صورة المؤمنون مع الأخت
+
+13
+00:01:16,810 --> 00:01:22,930
+Hiba Ibrahim يلا يا حبيبتي بس
+
+14
+00:01:22,930 --> 00:01:24,170
+ممكن نرفع صوتنا شوية
+
+15
+00:01:28,170 --> 00:01:35,850
+شوفي حبيبتي اعوذوا .. اعوذوا بالله من الشيطان
+
+16
+00:01:35,850 --> 00:01:42,050
+الرجيم تفخيم الtaa في كلمة الشيطان يلا و اعوذوا
+
+17
+00:01:42,050 --> 00:01:47,250
+ضمي تمك حبيبتي ضمي لقدام عشان تطلع العو دون غنة
+
+18
+00:01:47,250 --> 00:01:52,530
+اعوذوا يلا كمان مرة اعوذوا
+
+19
+00:01:59,640 --> 00:02:07,920
+الشيطان .. ايوة بسم الله الرحمن الرحيم قد أفلح
+
+20
+00:02:07,920 --> 00:02:13,920
+المؤمنون بدنا انقلق الأداء في قد .. قد .. قد ..
+
+21
+00:02:13,920 --> 00:02:19,200
+ايوة قد أفلح المؤمنون نعيد تاني قد أفلح المؤمنون
+
+22
+00:02:19,200 --> 00:02:22,920
+.. ايوة قد أفلح المؤمنون
+
+23
+00:02:27,940 --> 00:02:37,360
+الذين هم في صلاتهم
+
+24
+00:02:37,360 --> 00:02:43,420
+خاشعون الصاد مفخمة و الخا برضه كنا نفخمها أيوة
+
+25
+00:02:43,420 --> 00:02:47,460
+..الذين هم في صلاة .. صلاة .. صلاة
+
+26
+00:02:50,700 --> 00:03:00,680
+خاشرون .. خاشرون .. خاشرون .. خاشرون .. خاشرون ..
+
+27
+00:03:00,680 --> 00:03:11,760
+خاشرون .. خاشرون .. خاشرون .. خاشرون
+
+28
+00:03:11,760 --> 00:03:17,900
+..أيوة لأ .. لز .. أيوة هذه ال wow تكتب ولا تلفظ
+
+29
+00:03:17,900 --> 00:03:25,720
+نقول والذين هم للزكاة فاعلون للزكاة والذين هم
+
+30
+00:03:25,720 --> 00:03:34,800
+للزكاة فاعلون والذين هم لخروجهم حافظون إلا على
+
+31
+00:03:34,800 --> 00:03:40,960
+أزواجهم أو ما ملكت أيمانهم فإن .. فإنهم غير ملوكين
+
+32
+00:03:41,530 --> 00:03:47,830
+إيش بدنا نقول؟ على أزواجهم هنا مد جائز منفصل جاء
+
+33
+00:03:47,830 --> 00:03:52,970
+بعد حرف المد همزة في كلمة التي تليها في الكلمة
+
+34
+00:03:52,970 --> 00:03:58,150
+التي تليها نوعه جائز منفصل بينمده أربع أو خمس
+
+35
+00:03:58,150 --> 00:04:08,330
+حركات هتقولي كيف؟ الا على أزواجهم الا على أزواجهم
+
+36
+00:04:08,330 --> 00:04:09,110
+يالا حميد
+
+37
+00:04:19,130 --> 00:04:25,390
+بس إيش بدنا نسوي هنا؟ بدنا نفخم الغاء غيرهم، الغاء
+
+38
+00:04:25,390 --> 00:04:32,070
+هنا مفخم، ياما فإنهم غير ملومين
+
+39
+00:04:40,260 --> 00:04:46,880
+فمن ابتغى وراء ذلك فأولئك هم العادلون لأ شوف ياهي
+
+40
+00:04:46,880 --> 00:04:54,100
+بقى فمن ابتغى وراء ذلك .. أيوة هنقلقل الباق في
+
+41
+00:04:54,100 --> 00:04:59,920
+ابتغى حروف القلقلة قطر جد يبقى هنا الباق ساكنة إذا
+
+42
+00:04:59,920 --> 00:05:04,860
+هقلقلها القلقلة يعني اضطراب في المخرج اضطراب في
+
+43
+00:05:04,860 --> 00:05:11,880
+المخرج هتقولي ابي .. ابي وراءجاء بعد حرف المد همزة
+
+44
+00:05:11,880 --> 00:05:17,340
+في كلمة واحدة فايقنش بنقول هنا واجب متصل همده أربع
+
+45
+00:05:17,340 --> 00:05:21,400
+أو خمس حركات أما ذلك انت مدتيها ومافيش فيها مد
+
+46
+00:05:21,400 --> 00:05:25,400
+مافيش فيها مد يعني مافيش فيها زيادة عن حركتين هقول
+
+47
+00:05:25,400 --> 00:05:33,940
+ذلك ذلك فقط نعم فضليه فمن ابتغاه لأ مش ابتغاه ايه
+
+48
+00:05:33,940 --> 00:05:36,400
+بيه فمن ابتغاه
+
+49
+00:05:40,450 --> 00:05:47,130
+لأ إيش قلنا؟ مين هنمدها؟ الرعالين هنمدها وراء ذلك
+
+50
+00:05:47,130 --> 00:05:58,010
+.. وراء ذلك فما نبتغى .. فما نبتغى .. وراء
+
+51
+00:05:58,010 --> 00:06:04,950
+ذلك .. وراء ذلكمحنمد أولئك لأن واجب متصل صح ولا لأ
+
+52
+00:06:04,950 --> 00:06:11,110
+جاء بعض حرف المد همزة في كلمة واحدة إذا فأولئك ..
+
+53
+00:06:11,110 --> 00:06:20,350
+فأولئك .. فأولئك هم العادون بس مش هم العادون الميم
+
+54
+00:06:20,350 --> 00:06:26,290
+مضمومة من عن الاتقاء الساكنين هقول هم العادون ..
+
+55
+00:06:26,290 --> 00:06:28,690
+هم .. هم العادون
+
+56
+00:06:33,730 --> 00:06:42,150
+ممتاز جدا، انعيد الآية يا حبا .. انعيد الآية فماني
+
+57
+00:06:42,150 --> 00:06:46,410
+بتغا .. فماني
+
+58
+00:06:46,410 --> 00:06:51,390
+بتغا .. فماني بتغا .. فماني بتغا .. فماني بتغا ..
+
+59
+00:06:51,390 --> 00:06:53,570
+فماني بتغا .. فماني بتغا .. فماني بتغا .. فماني
+
+60
+00:06:53,570 --> 00:07:02,250
+بتغا .. فماني بتغا ..أحسنت حبيبتيا و الذين هم
+
+61
+00:07:02,250 --> 00:07:09,070
+لأماناتهم و عهدهم راعون عيد الآية و الذين هم
+
+62
+00:07:09,070 --> 00:07:16,870
+لأماناتهم و عهدهم راعون راعون تفهم الرا راعون
+
+63
+00:07:16,870 --> 00:07:27,350
+راعون نعم و الذين هم على صلواتهم يحافظون أولئك
+
+64
+00:07:28,960 --> 00:07:34,120
+أحسنت شفت كيف مدتي أولئك عشانها واجب متصل أولئك
+
+65
+00:07:34,120 --> 00:07:41,300
+نعم اللذين يروحون الفردوسون الفردوسون .. انشوف ..
+
+66
+00:07:41,300 --> 00:07:47,280
+انشوف الحركات إيه الرائش عليها؟ كسرة يري .. يري ..
+
+67
+00:07:47,280 --> 00:07:54,700
+ثون .. نعم اللذين يريثون الفردوسون فيها قادرون ..
+
+68
+00:07:56,040 --> 00:08:04,440
+الذين يريثون الفردوسة هم فيها خالدون نعيد الذين
+
+69
+00:08:04,440 --> 00:08:09,040
+يريثون .. مش يريثون بدناش تطلع معانا ياء بعد
+
+70
+00:08:09,040 --> 00:08:14,200
+الكسرة يريثون على طول كسرة و نخش على مين؟ على الثا
+
+71
+00:08:14,200 --> 00:08:18,640
+على إيش؟ الثا نعم الذين يريثون .. أه لأ قلتي
+
+72
+00:08:18,640 --> 00:08:24,890
+بتقولي أنتي يريثونلأ ياريثون .. ياريثون عسر يعني
+
+73
+00:08:24,890 --> 00:08:35,290
+خطف .. نعم يالا
+
+74
+00:08:35,290 --> 00:08:46,330
+يهيبقى بنظبط من ياريثون، بدلاش نقول ياريثون يبقى
+
+75
+00:08:46,330 --> 00:08:49,370
+ياريثون .. ياريثون عسرية
+
+76
+00:08:52,240 --> 00:08:59,760
+لأ لسه فيها ياريثون أيوة قولي ياريثون يالا نظبطها
+
+77
+00:08:59,760 --> 00:09:08,580
+مع الآية آخر
+
+78
+00:09:08,580 --> 00:09:12,120
+مرة لأ
+
+79
+00:09:12,120 --> 00:09:17,960
+قولت يا هنا ياريثون ياريثون
+
+80
+00:09:21,160 --> 00:09:24,480
+لأ احنا مانقدرش إياش نتمشى .. نمشي عنها لازم
+
+81
+00:09:24,480 --> 00:09:29,960
+نظبطها عشان هذا لحن جالي بنحط ياء بعد الاش بعد
+
+82
+00:09:29,960 --> 00:09:37,120
+الرا لا يجوز بنقول الذين .. الذين يريثون .. يريثون
+
+83
+00:09:37,120 --> 00:09:42,980
+الذين يريثون أيوة كمان مرة الذين يريثون أيوة
+
+84
+00:09:42,980 --> 00:09:46,860
+أحسنتي مبارك الله فيك يلا كمل الآية الذين يريثون
+
+85
+00:09:46,860 --> 00:09:55,030
+.. لأ ارجعنا تاني نقول ياءالذين يريثون .. الذين
+
+86
+00:09:55,030 --> 00:10:02,210
+يريثون .. الذين يريثون الفردوسة .. الذين يريثون
+
+87
+00:10:02,210 --> 00:10:06,710
+الفردوسة و فيها خالدون .. هنتدرب عليها في البيت يا
+
+88
+00:10:06,710 --> 00:10:12,670
+هيبة و نقول ياريثون مش ياريثون، بدناش نحط ياريثون
+
+89
+00:10:12,670 --> 00:10:22,590
+كسرة فقط، نعمولقد خلقنا الإحسان من سلسلة مهمةأه و
+
+90
+00:10:22,590 --> 00:10:27,030
+لا قد خلقنا في عند القلقلة في الدال و في عند
+
+91
+00:10:27,030 --> 00:10:31,530
+القلقلة في القاف و لا قد .. اليوم حباك القلقلة
+
+92
+00:10:31,530 --> 00:10:37,630
+يعني ف .. و لا قد خلقنا .. خلقنا .. الإنسانة هذه
+
+93
+00:10:37,630 --> 00:10:44,010
+من سلالة من طين، سلالة، في ألف .. في ألف هي تشيفها
+
+94
+00:10:44,010 --> 00:10:47,730
+الواحد الصغير، هذا عبارة عن ألف، و هذه أساء ال CH
+
+95
+00:10:47,730 --> 00:11:00,430
+مضمومة، سلالةولقد خلقنا الإنسان من سلالة من طين و
+
+96
+00:11:00,430 --> 00:11:08,870
+لقد خلقنا الإنسان من سلالة من طين و لقد خلقنا ..
+
+97
+00:11:08,870 --> 00:11:15,240
+خلقلي .. خلقلي الدالةمش اد ما تقوليش هيبقى و لا قد
+
+98
+00:11:15,240 --> 00:11:20,640
+اد هد مافيش فيها قلقلة و لا قد اد ها في اضطراب في
+
+99
+00:11:20,640 --> 00:11:22,560
+المخرج يا حبيبتي ايوة؟
+
+100
+00:11:26,960 --> 00:11:31,580
+بس بدنا نجيب الإخفاء عند من سلالة إيش بنقول؟ من
+
+101
+00:11:31,580 --> 00:11:36,080
+سلالة تمنطين
+
+102
+00:11:36,080 --> 00:11:41,080
+في عندك النون مع السيم إخفاء و التأ اللي هي النون
+
+103
+00:11:41,080 --> 00:11:46,340
+في التنوين مع الميم إيش هنا؟ اتغام بغنى و في عندك
+
+104
+00:11:46,340 --> 00:11:50,200
+النون مع التأ إذا أجت بعدين تأ ضردك إيش؟ إخفاء
+
+105
+00:11:50,200 --> 00:11:56,970
+ولكن بمع تفخيم الغنى يالا يا حبيبتي أشوفولا قد
+
+106
+00:11:56,970 --> 00:12:04,850
+..ولا قد خلقنا ليه سلالة من قيمة .. بس إيش؟ بس
+
+107
+00:12:04,850 --> 00:12:09,350
+سلالة مش هنمدها كتير، بس هنمدها حركتين .. من سلالة
+
+108
+00:12:09,350 --> 00:12:17,250
+من قيمة .. نعم .. ثم جعلنا ضموته فتن بقرار ممكن
+
+109
+00:12:17,250 --> 00:12:18,510
+..ماشي
+
+110
+00:12:22,970 --> 00:12:31,050
+ثم .. ثم خلقنا هذه مش جعلنا ..
+
+111
+00:12:31,050 --> 00:12:36,570
+ايوة برضك هنا بدلاش نحط ألف بعد الفتحة مابديش اقول
+
+112
+00:12:36,570 --> 00:12:45,330
+ثم .. لأ على طول ثم خلقنا النقفة علقا شافي كيف؟
+
+113
+00:12:45,330 --> 00:12:45,810
+يالا حبيبي
+
+114
+00:12:55,780 --> 00:12:59,840
+لأ مدال إيش لما ينقطع نفسنا بدنا نقف خلاص نقف على
+
+115
+00:12:59,840 --> 00:13:07,020
+ها ساكنة بدي أقول فخلقنا العلاقة مضغه .. مضغه ها
+
+116
+00:13:07,020 --> 00:13:12,100
+ساكنة بعدين بأوصل الكلام بأرجع كلمة و بأوصل الكلام
+
+117
+00:13:12,100 --> 00:13:17,640
+نعم فخلقنا
+
+118
+00:13:17,640 --> 00:13:18,860
+العلاقة مضغه
+
+119
+00:13:23,060 --> 00:13:27,100
+بدك توصل ايه؟ بدك تجيب حكم التنوين .. حكم التنوين
+
+120
+00:13:27,100 --> 00:13:33,780
+أجى تنوين بعدى ف .. إيش الحكم؟ اخفاء .. يلا مضغة
+
+121
+00:13:33,780 --> 00:13:44,900
+فخلقنا .. مضغة فخلقنا المضغة عظاما فكسونا العظام
+
+122
+00:13:44,900 --> 00:13:45,860
+لحما
+
+123
+00:13:49,400 --> 00:13:57,860
+فكسونا العظام لحمة ممكن تقفل فكسونا العظام لحمة
+
+124
+00:13:57,860 --> 00:14:08,260
+يلا فكسونا العظام لحمة لحمة ثم أنشأناه خلقا أخر
+
+125
+00:14:08,260 --> 00:14:11,540
+فكسونا
+
+126
+00:14:11,540 --> 00:14:12,960
+العظام لحمة
+
+127
+00:14:19,570 --> 00:14:28,030
+فتبارك الله أحسن الخالقين فتبارك
+
+128
+00:14:28,030 --> 00:14:34,030
+الله أحسن الخالقين فتبارك الله أحسن الخالقين
+
+129
+00:14:34,030 --> 00:14:35,510
+فتبارك الله أحسن الخالقين فتبارك الله أحسن
+
+130
+00:14:35,510 --> 00:14:40,670
+الخالقين فتبارك الله أحسن الخالقين
+
+131
+00:14:48,970 --> 00:14:53,590
+أحسنتي شفتي كيف جبت الغنى ع الميم في ثمة قولتي ثم
+
+132
+00:14:53,590 --> 00:14:59,190
+الميم المتشدد عليها غنى مقدار حركتين أحسنتي ثم
+
+133
+00:14:59,190 --> 00:15:07,310
+إنكم بعد إنكم بعد إيش في هنا إنكم بعد الميم
+
+134
+00:15:07,310 --> 00:15:12,310
+الساكنة أجي بعديها بقى فالحكم إخفاء شفوي بدي أخفي
+
+135
+00:15:12,310 --> 00:15:18,310
+الميم بدي أقول إنكم بعد مع الغنى نعم
+
+136
+00:15:23,450 --> 00:15:26,750
+بس بدأ أطول شوية جبت الإخفاء بس طول شوية عشان
+
+137
+00:15:26,750 --> 00:15:38,530
+الغنى ميم إنكم ميم بعد .. إنكم بعد ثم إنكم بعد ذلك
+
+138
+00:15:38,530 --> 00:15:43,070
+لما يدوم ثم
+
+139
+00:15:43,070 --> 00:15:50,810
+إنكم يوم القيامة تبعثون بدنا نقلق للباب تبعثون
+
+140
+00:15:52,250 --> 00:15:57,590
+أحسنتى بارك الله فيك يا هبا هبا انت بيعليه يبقى فى
+
+141
+00:15:57,590 --> 00:16:04,330
+البيت هنتدرب على الحركات بنشوف الحركات كويس الضمة
+
+142
+00:16:04,330 --> 00:16:07,390
+ضمة و الكسرة كسرة و الفتحة فتحة الحاجة التانية
+
+143
+00:16:07,390 --> 00:16:12,210
+حروف القلقلة حروف القلقلة قطب جد خمس أحرف إذا ..
+
+144
+00:16:12,210 --> 00:16:15,910
+إذا جاءت ساكنة بدنا نقلقلها القلقلة يعني اضطراب فى
+
+145
+00:16:15,910 --> 00:16:22,060
+المخرج يعني أبى أطى زى نىوال .. و الحاجة التانية
+
+146
+00:16:22,060 --> 00:16:26,780
+أحسنتي .. جبتي ال .. ال meme الساكنة المشددة ال
+
+147
+00:16:26,780 --> 00:16:30,840
+meme المشددة جبت عليها إيش؟ غنة ممتازة المدود ..
+
+148
+00:16:30,840 --> 00:16:34,780
+المدود بدنا إيش؟ ندق عليها أيضا المنفصل .. المتصل
+
+149
+00:16:34,780 --> 00:16:41,580
+بدنا نمده أربع أو خمس حركات ننتبه
+
+150
+00:16:41,580 --> 00:16:44,420
+للحاجات هذه و إن شاء الله المرة الجاية كل شيء تمام
+
+151
+00:16:44,420 --> 00:16:48,640
+و الآن مع الأخت عزيزة
+
+152
+00:16:54,860 --> 00:17:02,900
+أعوذ بالله من الشيطان الرجيم بسم الله الرحمن
+
+153
+00:17:02,900 --> 00:17:15,140
+الرحيم ولقد خلقنا فوقكم سبع طرائق وما كنا .. وما
+
+154
+00:17:15,140 --> 00:17:21,240
+كنا عن القلق غافلين غا .. ممكن نفخم الغا أكتر
+
+155
+00:17:21,240 --> 00:17:32,730
+غافلين .. غاوما كنا عن القلق غافلين وأنزلنا
+
+156
+00:17:32,730 --> 00:17:48,210
+من السماء ماء بقدر فأسلكناه فأسكنّاه
+
+157
+00:17:48,210 --> 00:17:59,400
+في الأرض وإنوإن على ذهب به لقدرون بس ننغن أكتر وإن
+
+158
+00:17:59,400 --> 00:18:04,340
+على ذهب به لقدرون
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+159
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+160
+00:18:15,570 --> 00:18:24,770
+الغنى طوالى جنات من نخيل .. من نخيل هتبقى الأولى
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+161
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+قد التانية يالا قد جنات من ..من نخيل و أعناب لكم
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+163
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+أعناب ممكن نربط الكلام مع بعض و أعناب لكم فيها ..
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+164
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+نربط الكلام مع بعضلو أعناب لكم فيها فواكو كثيرة و
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+165
+00:18:58,640 --> 00:19:04,040
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+167
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+ياما فأنشأنا لكم به جنات
+
+168
+00:19:16,190 --> 00:19:23,830
+النخيل و أعناب لكم في عندك أكتر من غنى يالا
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+169
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+فأنشأنا لكم بجنات من نخيل ليش ماتطولتيش؟ جنات من
+
+170
+00:19:36,070 --> 00:19:43,530
+فأنشأنا لكم بيه جنة لكم بيه .. برضه في إخفاء لكم
+
+171
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+بيه .. هنجيب الغنى أيوة فأنشأنا لكم بيه جنات من
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+172
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+نخيل و أعناب جبتهم كلهم بس نخيل و أعناب؟ جيب الغنى
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+173
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+عشان السير تمام يالا حبيبتيمن نخيل و أعناب لكم
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+174
+00:20:07,670 --> 00:20:17,030
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+
+175
+00:20:17,030 --> 00:20:21,930
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+177
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+178
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+179
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+
+180
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+
+181
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+تخرج من طور سينائة
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+182
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+تنبت بالدهن وصبغ للآكلين أحسن تشايفي إيش الآكلين
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+183
+00:21:13,940 --> 00:21:19,280
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+
+184
+00:21:19,280 --> 00:21:25,160
+لما تكون مرسومة قبل الألف هذه A وإن
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+185
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+لكم في الأنعام لعبرة نسقيكم مما في بطونهانصطيق من
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+186
+00:21:36,760 --> 00:21:49,140
+ما في بطونها ولكم فيها منافع كثيرة ومنها
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+187
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+188
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+شاء الله قراءتك جيدة بس بدنا نركز على حكاية زمان
+
+189
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+الغنان زمان الغنان بدنا نخليه تقريبا متساوي و خاصة
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+190
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+في الإضغام مع مين مع الواو انت بتجيب الإضغامات بس
+
+191
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+الزمن عشان قراءتك ممتازة فاحنا بنخليها أحسن وأحسن
+
+192
+00:22:17,350 --> 00:22:24,130
+بارك الله فيك الآن مع الأخت Manal Esfahy
+
+193
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+بسم الله الرحمن
+
+194
+00:22:47,360 --> 00:22:50,540
+الرحيم
+
+195
+00:22:50,540 --> 00:22:58,240
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+196
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+198
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+199
+00:23:33,880 --> 00:23:47,060
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+200
+00:23:47,060 --> 00:23:57,880
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+201
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+204
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+الفلك بأعيننا ووحينا فإذا جاء .. فإذا جاء أمرنا
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+205
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+206
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+فاسلك
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+207
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+من .. فاسلك فيها من كل زوجين إثنين وأهلك إلا من
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+208
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+سبقسبق إلا من سبق عليه القول منهم ولا تخاطبني في
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+209
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+الذين ظلموا إنهم مغرقون فإذا استويت أنت ومن معك
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+210
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+على الفلك فقول الحمد لله الذي نجّهنا من القوملأ بس
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+211
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+من الفخم الله .. من القوم الظالمين .. الله .. نعم
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+212
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+حبيبتي .. فقول الحمد لله الذي نجّانا من القوم
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+213
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+الظالمين .. أحسنتي .. و قل ربي أنت .. لأ كتير ..
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+214
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+ربي ع السرينوقول رب أنزلني منزلا مبركا وانت خير
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+المنزلين إما في ذلك لأيات وإن كنا لمقتلين ثم
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+217
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+أنشأنا من بعضهم قرن آخرين
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+220
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+عليك يعني مخارج ممتازة وأحكام رائعة يعني ليس لنا
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+221
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+في هذه القراءة إلا المدح والثناء بس في عندي ملاحظة
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+222
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+بسيطة يا منال في مد العارض للسكوناحيانا بتقصري انت
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+223
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+224
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+اتلاوة هيك جيدةملاحظاتي بسيطة يعني كانت في .. هي
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+228
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+هذه اللي كانت و حكاية التفخيم، التفخيم بده تفخيم
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+أكتر اللي هو إيش الطا، الظا، حاول إنك اتفخمي أكتر
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+بس ما شاء الله عليك يا مانال
+
+231
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+ممكن مروة .. مروة المصدر اعوذ بالله من الشيطان
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+232
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+الرجيم اعوذ بالله من الشيطان الرجيم اعوذ بالله من
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+الشيطان الرجيم اعوذ بالله من الشيطان الرجيم اعوذ
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+234
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+بالله من الشيطان الرجيم اعوذ بالله من الشيطان
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+235
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+الرجيم اعوذ بالله من الشيطان الرجيم اعوذ بالله من
+
+236
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+الشيطان الرجيم اعوذ بالله من الشيطان الرجيمأعوذ
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+237
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+بالله من الشيطان الرجيم الشيطان أعوذ بالله من
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+238
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+الشيطان الرجيم الشيطان الطا فاهم أكتر من الشيطان
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+239
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+الرجيم الشيطان الرجيم مش .. بعدك الطا مش مفخم عندك
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+240
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+طا فاهمين أعوذ بالله من الشيطان الرجيمده أحسن بس
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+إيش نحاول نظبطها في الدار أكتر بسم الله الرحمن
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+243
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+الآخرة و أترفناهم
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+249
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+همسو أترفنهم .. و أترفنهم ايه بتجيب فيها همسة
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+250
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+بسيطة من غير قلقلة يالا حبيبتي و قال الملء ..
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+251
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+الملء .. و قال .. و قال .. و قال .. و قال الملء من
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+252
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+قبل الملأ و قال الملء من قومهم الذين كفروا و كذبوا
+
+253
+00:29:45,300 --> 00:29:48,970
+.. نعيد تاني؟ لأ لأ نعيد الآيةعيد من أولها؟ اه و
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+254
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+قال .. و قال الملأ من قومهم الذين كفروا .. ايوة
+
+255
+00:29:52,770 --> 00:29:57,370
+هنا هنا .. هنا انا مش من قومهم هذه قومه الذين ..
+
+256
+00:29:57,370 --> 00:30:03,030
+قومه الذين .. اتبعي و قال الملأ من قومه الذين
+
+257
+00:30:03,030 --> 00:30:08,570
+كفروا و كسببوا بلقاء الآخرة و أترفنا .. لأ لأ
+
+258
+00:30:09,220 --> 00:30:14,360
+واترفناهم .. واترفناهم .. واترفناهم في الحياة
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+259
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+الدنيا ماذا إلا بشر مثلكم .. مثلكم ماذا إلا بشر
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+260
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+إلا بشر مثلكم يأكلون .. لحظة شوية يا أخوات مافيش
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+حاجة اسمها come .. come هذه مش لغة عربية هي come
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+نضم تمنا كويس لقدام الاش .. ال .. هنا الشفاية
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+.. اظهار عندنا في النون الساكنة عديها تاني يأكلوا
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+271
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+.. يأكلوا من ..
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+272
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+في حرف الشين الشين كمان فيها إيش؟ تفششين أيوة نشوف
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+الزمن الشين الأولى نفس الزمن في الشين التانى
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+يكون كاملوكنتم ترابا وعظاما أنكم مخرجون هيهات
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+280
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+281
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+
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+287
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+إيش؟ فيها همس و فيها رخابة و نحيا .. و نحيا ..
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+288
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+شوفتي كيف نحن قلتيها و نحن روحتي قلقلتيها و نحن
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+الـha في نحيا نفس الـha في نحن نفس الزمان و نفس
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+290
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+الصفات يالا يا حبيبتي إن هي إلا حياتنا الدنيا ..
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+
+292
+00:34:02,060 --> 00:34:07,520
+بمبعوثين لأ ما أظبط معاهاش و نحيا و ما نحن
+
+293
+00:34:07,520 --> 00:34:14,800
+بمبعوثين نحيا و ما نحن .. اقري شوي شوي عشان تجي
+
+294
+00:34:14,800 --> 00:34:17,720
+معاكي إيش الهمس و تجي الرخاوة تمشيش بسرعة فتجي
+
+295
+00:34:17,720 --> 00:34:27,540
+بقلقة معاكيإن هي إلا حياتنا الدنيا نموت ونحيا وما
+
+296
+00:34:27,540 --> 00:34:34,020
+نحن مبعوثين لأ انت زبطيها هيك لا قلقليها انت و
+
+297
+00:34:34,020 --> 00:34:38,660
+نحيا و نحيا انت لو تريحي تريح معاكي في الصوت و
+
+298
+00:34:38,660 --> 00:34:45,720
+نحيا جريان النفس معاكي و جريان الصوت كمان و نحيا
+
+299
+00:34:46,930 --> 00:34:52,690
+انهي انهي إلا حياتنا الدنيا نموت و نحيا و ما نحن
+
+300
+00:34:52,690 --> 00:34:59,910
+بمبعوثين أخر مرة نموت و نحيا و ما نحن .. نموت و
+
+301
+00:34:59,910 --> 00:35:05,810
+نحيا و ما نحن بمبعوثين هنظبطها في البيت و نحيا و
+
+302
+00:35:05,810 --> 00:35:10,670
+نحيا قولي نحيا نحيا صح نحيا طب اظبطينا مع الأية
+
+303
+00:35:11,350 --> 00:35:17,230
+نموت ونحيا وما نحن بمجعوثين برضك بتقلقلي نحيا ..
+
+304
+00:35:17,230 --> 00:35:23,310
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+305
+00:35:23,310 --> 00:35:28,470
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+306
+00:35:28,470 --> 00:35:30,270
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+307
+00:35:30,270 --> 00:35:30,810
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+308
+00:35:30,810 --> 00:35:30,810
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+309
+00:35:30,810 --> 00:35:30,810
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+310
+00:35:30,810 --> 00:35:30,810
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا ..
+
+311
+00:35:30,810 --> 00:35:30,810
+نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. نحيا .. ن
+
+312
+00:35:30,870 --> 00:35:36,110
+نظبطها في الآية نموت و نحيا و ما نحن بمبعوثين كمان
+
+313
+00:35:36,110 --> 00:35:46,850
+مرة نموت و نحيا و ما نحن بمبعوثين نحيا نحنا
+
+314
+00:35:46,850 --> 00:35:50,210
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+315
+00:35:50,210 --> 00:35:50,210
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+316
+00:35:50,210 --> 00:35:50,210
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+317
+00:35:50,210 --> 00:35:50,210
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+318
+00:35:50,210 --> 00:35:50,210
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+319
+00:35:50,210 --> 00:35:54,420
+نحنا نحنا نحنا نحنا نحنا ننحيا نحن نحنا نحنا نحنا
+
+320
+00:35:54,420 --> 00:35:58,740
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+321
+00:35:58,740 --> 00:36:00,020
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+322
+00:36:00,020 --> 00:36:00,020
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+323
+00:36:00,020 --> 00:36:00,020
+نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا نحنا
+
+324
+00:36:00,020 --> 00:36:00,100
+نحنا نحنا نحنا نحنا نحانا نحانا نحانا نحانا نحانا
+
+325
+00:36:00,100 --> 00:36:02,340
+نحانا نحانا نحانا نحانا نحانا نحانا نحانا نحانا
+
+326
+00:36:02,340 --> 00:36:08,650
+نحانا نحانا نحانا نحانا نحانا نحانا نيظهر و إيش
+
+327
+00:36:08,650 --> 00:36:12,230
+كمان؟ في جيبيلي إيش زمن النون، انت بتخطفي النون، ع
+
+328
+00:36:12,230 --> 00:36:16,510
+السريع بتجيب النون، مابتبينش واضحة ان هو إلا
+
+329
+00:36:16,510 --> 00:36:22,570
+رجلوني افترى، رجلوني، رجلوني افترى، ليش يا أخوات
+
+330
+00:36:22,570 --> 00:36:28,320
+عملنا زي هيك؟ عشان التقاء الساكني، نعمإن هو .. إن
+
+331
+00:36:28,320 --> 00:36:33,280
+هو إلا رجول .. رجولي في طرائف علوية كذبة بس برضه
+
+332
+00:36:33,280 --> 00:36:38,340
+إنت حياتك بدالك تقلقل .. بتقلقل كتير رجول نفس
+
+333
+00:36:38,340 --> 00:36:44,520
+طرائف .. رجول نفس طرائف .. بدناش نقلقل الفاقرجل
+
+334
+00:36:44,520 --> 00:36:50,960
+نفترع الله
+
+335
+00:36:50,960 --> 00:36:59,740
+كذبة وما نحن له بمؤمنين رجعتلك نحن وما نحن .. و ما
+
+336
+00:36:59,740 --> 00:37:03,480
+نحن له بمبعوثين
+
+337
+00:37:03,480 --> 00:37:07,580
+.. بمؤمنين عديها و ما نحن .. و ما نحن .. و ما نحن
+
+338
+00:37:07,580 --> 00:37:14,060
+له بمؤمنينهيجبتيها نحن هنا ممتازة قال ربي انصرني
+
+339
+00:37:14,060 --> 00:37:20,520
+بما كذبون قال ربي انصرني الصاد مفخمة مع الرق مفخمة
+
+340
+00:37:20,520 --> 00:37:26,860
+قال ربي انصرني بما كذبون بس أصليها مع بعض قال ربي
+
+341
+00:37:26,860 --> 00:37:34,880
+انصرني بما كذبون أحسنتي قال عما قليل يصبحن نادمين
+
+342
+00:37:34,970 --> 00:37:41,130
+عيد تاني قال عم قليل ليصبح .. ليص .. ليصبح ..
+
+343
+00:37:41,130 --> 00:37:54,310
+ليصبح نادمين قال عم قليل ليصبح .. ليصبح نادمين
+
+344
+00:37:54,310 --> 00:38:00,110
+عيدها تاني قال عم قليل ليصبح .. ليصبح نادمينلا
+
+345
+00:38:00,110 --> 00:38:07,210
+يصبحننا .. لا يصبحننا نادمين .. نعم فأخذتهم الصيحة
+
+346
+00:38:07,210 --> 00:38:10,470
+بالحقد .. برضه كده .. برضه .. برضه فأخذتهم ..
+
+347
+00:38:10,470 --> 00:38:16,510
+فأخذتهم .. فأخذتهم .. فأخذتهم الtaa مش فيها قلقلة
+
+348
+00:38:16,510 --> 00:38:22,110
+فيها همس فأخذتهم الصيحة بالحقد فجعلنا .. فأخذتهم
+
+349
+00:38:22,110 --> 00:38:30,050
+الصيحة بالحقد .. بالحقد فأخذتهم الصيحة بالحقدفجأة
+
+350
+00:38:30,050 --> 00:38:35,410
+.. لأ مش هيك .. بالحق .. بالحق .. بالحق .. لأ هيك
+
+351
+00:38:35,410 --> 00:38:39,130
+بتجيب الشد ده و بعدين تجيب القلقه لأ .. بالحق ..
+
+352
+00:38:39,130 --> 00:38:44,210
+بالحق .. بالحق .. لأ هيك بتجيبينها ناعم هيك ..
+
+353
+00:38:44,210 --> 00:38:51,070
+بالحق .. بالحق .. بالحق .. شد ع القاف .. بالحق ..
+
+354
+00:38:51,070 --> 00:38:58,330
+مش أقف .. مش أقف بس .. بالحق ..بالحق بعدين .. جيب
+
+355
+00:38:58,330 --> 00:39:03,950
+الشدة بعدين جيب القلقلة بالحق .. بالحق .. بالحق
+
+356
+00:39:03,950 --> 00:39:10,170
+طيب أوصليها أشوف فأخذتهم الصيحد بالحق إذا جعلناهم
+
+357
+00:39:10,170 --> 00:39:19,550
+غثاء صح غثاء هنا مد إيش يا أخواتي؟ مد متصل طيب
+
+358
+00:39:19,550 --> 00:39:27,090
+متصل و نقف على مد عواض نعمفبعدا للقوم الظالمين
+
+359
+00:39:27,090 --> 00:39:32,710
+فبعدا للقوم الظالمين تفهم الظالم فبعدا للقوم
+
+360
+00:39:32,710 --> 00:39:42,350
+الظالمين نعم ثم نشأنا من بعدهم قرون .. قرون آخرين
+
+361
+00:39:42,350 --> 00:39:50,800
+لأ هنا تنوي تنوي قرون آخرين قرون آخرين قرونعيد دي
+
+362
+00:39:50,800 --> 00:39:55,200
+.. عيد دي الآية ا
+
+363
+00:39:55,200 --> 00:40:07,260
+مش ا ا خرين ا خرين ا خرين احسنتي
+
+364
+00:40:09,040 --> 00:40:14,520
+أخر آية ما تسبق .. ما تسبق من أمة .. لأ ليش هناك
+
+365
+00:40:14,520 --> 00:40:18,720
+إخفاء؟ من أمة إظهار ما تسبق من أمة أجلها وما
+
+366
+00:40:18,720 --> 00:40:25,120
+يستأخرون ننتبه للحركات ما تسبق من .. ما تسبق من
+
+367
+00:40:25,120 --> 00:40:32,980
+أمة أجلها وما .. أجلها وما يستأخرون ما تسبق من أمة
+
+368
+00:40:32,980 --> 00:40:37,140
+أجلها .. أمة أجلها
+
+369
+00:40:38,930 --> 00:40:47,330
+ماتصبق من أمة أجالها وما يستأخرون أحسنت مارفعة
+
+370
+00:40:48,430 --> 00:40:52,070
+مروة راح ندق على إيش؟ على القلقلة، راح ندق على
+
+371
+00:40:52,070 --> 00:40:55,890
+إيش؟ بدنا نقلقل بس الحروف المقلقلة، الحروف المش
+
+372
+00:40:55,890 --> 00:40:58,710
+مقلقلة بدناش نقلقلها، الحروف القلقلة اللي هي مين؟
+
+373
+00:40:58,710 --> 00:41:02,790
+قطب جد، خمس أحرف بس، الأحرف الساكنة، أي أحر غير
+
+374
+00:41:02,790 --> 00:41:07,230
+قطب جد بدناش نقلقلها، و بدنا ننتبه على الحركات،
+
+375
+00:41:07,230 --> 00:41:10,210
+يعني كانت يعني أكتر شيء مميز في قرائتك اللي هو
+
+376
+00:41:10,210 --> 00:41:14,750
+حكاية إيش؟ القلقلة فيما لا يجب أن يقلقل، فإيش؟
+
+377
+00:41:14,750 --> 00:41:19,440
+فانتبهي لهذا الإشيما هي كله يعني في الأشياء كلها
+
+378
+00:41:19,440 --> 00:41:25,240
+يعني أغلبيتها عايش هنا و برك الله فيك يا حبيبتي ان
+
+379
+00:41:25,240 --> 00:41:27,860
+شاء الله بتتربي عليها في البيت أكتر و خاصة و ما
+
+380
+00:41:27,860 --> 00:41:33,000
+نحن و نحيا و ما نحن و نحيا اللهم صلى على سيدنا
+
+381
+00:41:33,000 --> 00:41:35,220
+محمد هلاقيت مع الأخت ان شاء الله
+
+382
+00:41:43,460 --> 00:41:52,340
+هيبا أبو جراي هيبا أبو جراي تفضلي حاجة برضك
+
+383
+00:41:52,340 --> 00:42:02,820
+نفس الحاجة بدنا نفخم الطا الشيطا الشيطا لأ
+
+384
+00:42:02,820 --> 00:42:08,060
+بس بدناش نطول يعنيأيوة أحسنتى بس حركتين أعوذ بالله
+
+385
+00:42:08,060 --> 00:42:15,460
+من الشيطان الرجيم .. نعم بسم الله الرحمن الرحيم ثم
+
+386
+00:42:15,460 --> 00:42:22,130
+أرسلنا رسولنا .. رسولنالحظة شوية ثم الميم مشددة
+
+387
+00:42:22,130 --> 00:42:30,310
+هنجيب عليها الغنى مقدار حركتين ثم .. ثم .. أرسلنا
+
+388
+00:42:30,310 --> 00:42:37,870
+أ الأ مرققة و الرا مفخمة أرسلنا رسولنا تترا مش
+
+389
+00:42:37,870 --> 00:42:43,050
+تترا مقلقة للتأ تترا همس في التأ الاش الوصطانية
+
+390
+00:42:43,050 --> 00:42:43,310
+يلا
+
+391
+00:42:50,750 --> 00:42:54,470
+شوفي .. شوفي يا هباب .. نقف عن تترا .. نقف عن تترا
+
+392
+00:42:54,470 --> 00:43:04,050
+.. أقف عن تترا ثم .. أرسلنا نسولنا تترا كلما جاء
+
+393
+00:43:04,050 --> 00:43:09,190
+أمة رسولها .. رسولها كذبوا .. بس الهباب على كله بس
+
+394
+00:43:09,190 --> 00:43:13,270
+شدهوا بس .. بدناش نغل .. بدناش نقول كل ما جاء ..
+
+395
+00:43:13,270 --> 00:43:16,890
+اه لأ .. كل .. كل ما على السريع .. كل ما ..
+
+396
+00:43:21,580 --> 00:43:27,800
+الميم مشددة في أمة هنغن عليها أمة رسولها كذبوه
+
+397
+00:43:27,800 --> 00:43:33,620
+نعيد الآية كل ما جاء كل ما .. كل ما جاء كمان مرة
+
+398
+00:43:33,620 --> 00:43:41,680
+كل ما جاء أمة رسولها كذبوه نعم فأتبعنا بعضهم بعضا
+
+399
+00:43:41,680 --> 00:43:48,980
+و جعلناهم أحادي تفضحا لقوم لا يؤمنانت في عليّ يا
+
+400
+00:43:48,980 --> 00:43:56,160
+هباب فاتبعنا التأ فيها همس فاتبعنا فاتبعنا و بعضهم
+
+401
+00:43:56,160 --> 00:44:03,760
+بعضة في عندك إخفاء شفوي هنجيب الغنى بعضهم بعضةو
+
+402
+00:44:03,760 --> 00:44:08,680
+بعدين إيش؟ بعضا و جعلناهم .. هنجيب غنّة ال إيش؟
+
+403
+00:44:08,680 --> 00:44:13,400
+الإضام، مظبوط؟ بس بدناش نقول و جعلناهم .. بدناش
+
+404
+00:44:13,400 --> 00:44:17,360
+إيش؟ نطول على اللام في جعلناهم انتبهي و ركزي
+
+405
+00:44:17,360 --> 00:44:21,120
+معايا، ما شاء الله صوتك حلو فإيش؟ هنصقله إن شاء
+
+406
+00:44:21,120 --> 00:44:26,840
+الله بالأحكام الجيدة، يلّا فأدفعنا بعضا بعضا و
+
+407
+00:44:26,840 --> 00:44:34,330
+جعلناهم أحد الحديثة فزعدني قوم لا يؤمنونثم أرسلنا
+
+408
+00:44:34,330 --> 00:44:38,190
+موسى و أخاه حرون ..لأ فيش هنا ..فيش مد ..فيش مد
+
+409
+00:44:38,190 --> 00:44:43,190
+زيادة ثم أرسلنا موسى و أخاه حرون بآياتنا و سلطان
+
+410
+00:44:43,190 --> 00:44:50,590
+مبين ..لأ غني و سلطان مبين إلى فرعون و ملئيه
+
+411
+00:44:50,590 --> 00:44:53,170
+فاستكبروا و كانوا قوما
+
+412
+00:44:55,640 --> 00:44:59,920
+شوفي عليه بقى إلى فرعونة أول إشي الراء في فرعونة
+
+413
+00:44:59,920 --> 00:45:04,260
+إيش؟ مرققة جأمة قبلها مكسور وهي ساكلة إذا فهي
+
+414
+00:45:04,260 --> 00:45:10,260
+مرققة بنقول فرعونة إلى فرعونة أما وملئه الياء يا
+
+415
+00:45:10,260 --> 00:45:17,120
+أخواتي هذه إيش عليها؟ صفر مستديرصفر مستدير أي حرف
+
+416
+00:45:17,120 --> 00:45:22,600
+عليه صفر مستدير هذا الحرف ساقط وصلا ووقفا يبقى مش
+
+417
+00:45:22,600 --> 00:45:27,700
+هتنفذيه نهائيا بتقولي وملئيه ع السريع مش وملئيه
+
+418
+00:45:27,700 --> 00:45:34,280
+يلا أشوف إلى فرعونة .. فرعونة إلى فرعونة .. فر ..
+
+419
+00:45:34,280 --> 00:45:38,980
+ايوة إلى فرعونة وملائكي فاستقبضوا وكانوا قوما
+
+420
+00:45:38,980 --> 00:45:47,400
+عالين فقالوا أقنلوا لبشرينلأ بنقولش ليه بشرين ..
+
+421
+00:45:47,400 --> 00:45:51,400
+إذا وقفتي على بشرين ممكن تمدي لكن إذا إنتي وصلتي
+
+422
+00:45:51,400 --> 00:45:56,420
+هتجيبي بس .. هتجيبي بس حرف ساكن و فقط يعني ليه
+
+423
+00:45:56,420 --> 00:46:02,500
+بشرين مثلنا .. مثلنا .. هتقولوا أنه أملوا لبشرين
+
+424
+00:46:02,500 --> 00:46:08,560
+مثلنا و قومهم .. و قوم .. و قومهما لنا عارفينعيدي
+
+425
+00:46:08,560 --> 00:46:14,080
+الآية أشوف فقالوا أنا أملون بشرين مثلنا و قولوه ما
+
+426
+00:46:14,080 --> 00:46:21,780
+لنا عابلون فكذبوهما فكانوا من المهلكين بتركزي يا
+
+427
+00:46:21,780 --> 00:46:26,220
+هبة أحيانا على النغمة إيش؟ فبيطلع ماك أحيانا
+
+428
+00:46:26,220 --> 00:46:31,980
+المدود مش .. مش موضع مده فكذبوهما فكانوا من
+
+429
+00:46:31,980 --> 00:46:37,320
+المهلكين فقط يعني إيش؟ No بس مقدار حركتين نعيد؟
+
+430
+00:46:41,690 --> 00:46:47,510
+أحسنتي قلقلي و لقد .. و لقد آتينا موسى الكتاب
+
+431
+00:46:47,510 --> 00:46:53,350
+لعلهم يهتزون وجعلنا ابن مريم و أم .. و أمه .. و
+
+432
+00:46:53,350 --> 00:46:58,770
+أمه آية .. انتبه .. انتبه .. انتبه وجعلنا ابن مريم
+
+433
+00:46:58,770 --> 00:47:06,530
+و أمه في غنة .. في غنة وجعلنا ابن مريم .. م ..
+
+434
+00:47:06,530 --> 00:47:13,930
+مريم .. م .. مش مريم .. م ..أيوة مريمة و جعلنا
+
+435
+00:47:13,930 --> 00:47:22,170
+ابنا مريمة و أمه آية و أويلهما إلى ربوة ذات قرار و
+
+436
+00:47:22,170 --> 00:47:30,190
+معين و أمه آية هنمد أربع أو خمس حركات و ذات مش
+
+437
+00:47:30,190 --> 00:47:37,230
+هنمدها إلا مقدار حركتينو جعلنا ابن مريم و أمه آيتا
+
+438
+00:47:37,230 --> 00:47:43,750
+و آوينهما إلى رفوة ذات قرار و معين و جعلنا ابن
+
+439
+00:47:43,750 --> 00:47:53,530
+مريم و أمه آيته و آوينهما عشان تفكر؟ آيته و في إيش
+
+440
+00:47:53,530 --> 00:48:01,490
+إبغام نغنى و جعلنا ابن مريم و أمهالناس يقول آية ..
+
+441
+00:48:01,490 --> 00:48:01,770
+لأ
+
+442
+00:48:08,340 --> 00:48:16,000
+لأ بنعيد الآية ونظبط وجعلنا ابن مريم وأمه آيتا
+
+443
+00:48:16,000 --> 00:48:24,280
+وأويناهما .. ممكن نقف .. وأويناهما إلى ربوة ذات
+
+444
+00:48:24,280 --> 00:48:31,920
+قرار ومعين قرار ومعين وبعدين نجيب الغنى وجعلنا ابن
+
+445
+00:48:31,920 --> 00:48:44,220
+مريم وأمه آيتا .. آيتا و ..بس قولني آيتو .. ربي
+
+446
+00:48:44,220 --> 00:48:48,080
+.. ربي
+
+447
+00:48:48,080 --> 00:48:51,460
+أحسن
+
+448
+00:48:51,460 --> 00:48:57,600
+شايف كيف؟ عندك إضغام ذات قراري و معين يا أيها
+
+449
+00:48:57,600 --> 00:49:04,110
+الرسل كله من الطيبةمينات طيبات .. مينات طيبات ..
+
+450
+00:49:04,110 --> 00:49:07,810
+مينات طيبات .. مينات طيبات .. مينات طيبات .. مينات
+
+451
+00:49:07,810 --> 00:49:07,830
+طيبات .. مينات طيبات .. مينات طيبات .. مينات طيبات
+
+452
+00:49:07,830 --> 00:49:09,170
+.. مينات طيبات .. مينات طيبات .. مينات طيبات ..
+
+453
+00:49:09,170 --> 00:49:11,190
+مينات طيبات .. مينات طيبات .. مينات طيبات .. مينات
+
+454
+00:49:11,190 --> 00:49:13,630
+طيبات .. مينات طيبات .. مينات طيبات .. مينات طيبات
+
+455
+00:49:13,630 --> 00:49:17,790
+.. مينات طيبات .. مينات طيبات .. مينات طيبات ..
+
+456
+00:49:17,790 --> 00:49:24,790
+مينات طيبات .. مينات طيبات .. مينات طيباتيا أيها
+
+457
+00:49:24,790 --> 00:49:30,150
+ال .. يا أيها الرسل قلوا من الطيبات لأ مش هيك من
+
+458
+00:49:30,150 --> 00:49:34,710
+الطيبات .. ضبطي بس حرق .. بس عادي شدوا بس من
+
+459
+00:49:34,710 --> 00:49:41,550
+الطيبات و أعملوا صالحا إني .. إني لما تعملون علي
+
+460
+00:49:41,550 --> 00:49:54,120
+وإن هذه أمتهم .. لأ أغني وإن هذه أمتهم ..أمة واحدة
+
+461
+00:49:54,120 --> 00:50:03,660
+و أنا ربكم فاتقون تبهي عليها بقى وإن هذه أمتكم أمة
+
+462
+00:50:03,660 --> 00:50:14,640
+واحدة أمة واحدة و أنا ربكم فاتقون نجيب المد موضع
+
+463
+00:50:14,640 --> 00:50:21,190
+مد ما نمدش مناشي المد في مواضع لا يوجد فيها مدمدّي
+
+464
+00:50:21,190 --> 00:50:31,890
+أكتر، أربعة أو خمس أحسنتي،
+
+465
+00:50:31,890 --> 00:50:36,870
+رائع أمرهم
+
+466
+00:50:36,870 --> 00:50:43,450
+.. أمرهم أمرهم بينهم زغرا أمرهم بينهم في إخفاء،
+
+467
+00:50:43,450 --> 00:50:51,840
+بنجيب الغنى أمرهم بينهم زغراكل حزب .. كل حزب بما
+
+468
+00:50:51,840 --> 00:50:58,920
+لديهم فرحون فضوهم في غمرتهم حتى حين فضوهم في
+
+469
+00:50:58,920 --> 00:51:03,820
+غمرتهم حتى حين برضك حتى حين ماعرفش المادة كتير حتى
+
+470
+00:51:03,820 --> 00:51:10,720
+حين بس حركتي نعم فضوهم في غمرتهم حتى حين أيحسبوا
+
+471
+00:51:10,720 --> 00:51:16,660
+.. أيحسبوا لأنما .. أنما نمدهم .. نمدهم
+
+472
+00:51:19,370 --> 00:51:24,810
+نعيد الآية، نظبط المدود احسبون أن ما .. أن ما
+
+473
+00:51:24,810 --> 00:51:35,900
+نمدهم بيه من ذلكأ يحسبون أنما نمدهم به من مال و
+
+474
+00:51:35,900 --> 00:51:42,140
+وبنين نمدهم به .. إيش في ميم ساكنة؟ أجي بعدها بقى
+
+475
+00:51:42,140 --> 00:51:46,900
+إيش الحكم؟ إخفاء شفوي بدي أخفي مع الغنى ميم مال
+
+476
+00:51:46,900 --> 00:51:51,800
+برضه هغن لإنه اضغان بغنى مالي و وبنين أيضا اضغان
+
+477
+00:51:51,800 --> 00:51:58,100
+بس ميم مال بديش أمدها كتير بس حركتين مال بسلأ
+
+478
+00:51:58,100 --> 00:52:03,880
+بنقولش أ يحسبونا أنهم .. أ يحسبونا .. أ يحسبونا
+
+479
+00:52:03,880 --> 00:52:13,320
+أنما نمدهم به .. لأ نمدهم به .. نمدهم به مال و بني
+
+480
+00:52:13,320 --> 00:52:18,920
+.. لأ نظبط .. نظبط أكتر عيد الآية أ يحسبونا أنما
+
+481
+00:52:18,920 --> 00:52:26,640
+نمدهم به مال ..بنقولش مين مالي و .. مين مالي و بني
+
+482
+00:52:26,640 --> 00:52:29,920
+.. غني .. لإن انت تركز على الغنى بتهيش معاك المد
+
+483
+00:52:29,920 --> 00:52:34,120
+اللي مش لازم .. مين مالي و بني .. هيحسبون أنما
+
+484
+00:52:34,120 --> 00:52:44,380
+نمدهم به مين مالي و بني .. هيحسبون أنما نمدهم به
+
+485
+00:52:44,380 --> 00:52:49,580
+.. نمدهم به .. غني .. نمد .. نمدهم .. نمدهم .. نمد
+
+486
+00:52:49,580 --> 00:52:57,580
+.. نمدهم به ..نمدهم، أيحسبوا لأننا نمدهم بهي
+
+487
+00:52:57,580 --> 00:53:05,800
+بالمال ومالين نسارع لهم في الخيرات بل لا يشعبون إن
+
+488
+00:53:05,800 --> 00:53:11,420
+الذين هم من خش .. هم قلني
+
+489
+00:53:11,420 --> 00:53:17,360
+إن الذين هم من خشية .. من خشية ربهم مشفقون ربهم
+
+490
+00:53:17,360 --> 00:53:26,910
+مشفقون اضغام؟ بيقول نعمإن الذين
+
+491
+00:53:26,910 --> 00:53:34,790
+هم من خشية ربهم يشرفون و الذين هم بآيات ربهم
+
+492
+00:53:34,790 --> 00:53:42,310
+يؤمنون و الذين هم بآيات ربهم يؤمنون و الذين هم
+
+493
+00:53:42,310 --> 00:53:47,150
+بربهم لا يشرفون هم بربهم انت حكاية الأخفاء الشفوي
+
+494
+00:53:47,150 --> 00:53:53,450
+أجت معاك كتيروالذين هم بربهم أرض أيضا اخفاء شفويح
+
+495
+00:53:53,450 --> 00:53:54,510
+الجيب الغنى
+
+496
+00:53:58,910 --> 00:54:03,610
+أحسنت يا هبة و بارك الله فيك ماشاء الله عليك صوتك
+
+497
+00:54:03,610 --> 00:54:07,410
+حلو كتير يا هبة صوتك حلو كتير بس إيش المشكلة أنك
+
+498
+00:54:07,410 --> 00:54:11,670
+أحيانا بتمدي في موضع لا يجيب فيه المد فإيش ..
+
+499
+00:54:11,670 --> 00:54:16,050
+فإحنا بدنا نظبط عشان نجيب .. عشان نظبط اللحن و
+
+500
+00:54:16,050 --> 00:54:19,930
+نجبط ال .. ال .. اه فعلى حساب الأحكام لأ فإحنا
+
+501
+00:54:19,930 --> 00:54:23,170
+بدنا نجيب الأحكام أولا فبيجي معنا إيش ان شاء الله
+
+502
+00:54:23,170 --> 00:54:27,240
+الصوت ال .. الحلوفركزي ع .. زي ما قلتلك أنا على
+
+503
+00:54:27,240 --> 00:54:30,800
+الأشياء اللي فيش فيها مدناش نمدها و الإخفاء الشفوي
+
+504
+00:54:30,800 --> 00:54:35,440
+الميم الساكنة بعدها بقى بدنا نغن نجيب إخفاء و
+
+505
+00:54:35,440 --> 00:54:42,300
+بعدها أياش غنة معاها غنة ميم بعد ربي يهم بيه أه ان
+
+506
+00:54:42,300 --> 00:54:49,540
+شاء الله و أحسنتي و ما شاء الله عليكي نيجي ل ..
+
+507
+00:54:49,540 --> 00:54:53,380
+موجودة ألاء حنون؟ يلا حبيت
+
+508
+00:54:59,890 --> 00:55:10,470
+يبتون ماء ماء و قلبهم ودلة أنهم إلى ربهم راجعون
+
+509
+00:55:10,470 --> 00:55:19,310
+أولئك يسارعون في الخيرات و هم لها سابحون و لا مكلف
+
+510
+00:55:19,310 --> 00:55:27,770
+نفسا إلا وسعها و لدينا كتاب إن ينطق بالحق و هم لا
+
+511
+00:55:27,770 --> 00:55:36,980
+يظلمونبل قلوبهم في غمرة من هذا ولهم أعمال من دون
+
+512
+00:55:36,980 --> 00:55:48,220
+ذلك هم لها عاملون حتى إذا أخذنا مصرفهم بالعذاب إذا
+
+513
+00:55:48,220 --> 00:55:58,580
+هم يجأرون لا تجأروا اليوم إنكم مننا لا تنصرون
+
+514
+00:55:59,170 --> 00:56:07,090
+قد كانت آياتي .. قد كانت آياتي تتلى عليكم فكنتم
+
+515
+00:56:07,090 --> 00:56:18,230
+على أعقابكم تنكسون مستكبرين به سامرا تهجرون أفلم
+
+516
+00:56:18,230 --> 00:56:28,090
+يتدبروا القول أم جاءهم ما لم يأتي آبائهم الأولينأم
+
+517
+00:56:28,090 --> 00:56:37,850
+لم يعرفوا رسولهم فهم له منكرون أم يقولون به جنة بل
+
+518
+00:56:37,850 --> 00:56:46,910
+جاءهم بالحق وأكثرهم للحق كارئون ولو اتبع الحق
+
+519
+00:56:46,910 --> 00:56:55,980
+أهواءهم لفسدت السماوات والأرض ومن فيهنبل أتيناهم
+
+520
+00:56:55,980 --> 00:57:05,100
+بذكرهم فهم عن ذكرهم معرضون أم تسألهم خرجا فخراج
+
+521
+00:57:05,100 --> 00:57:13,540
+ربك خير وهو خير الرازقين وإنك لتدعوهم إلى صراط
+
+522
+00:57:13,540 --> 00:57:22,310
+مستقيموإن الذين لا يؤمنون بالآخرة عن الصراط لنا
+
+523
+00:57:22,310 --> 00:57:27,890
+كيبوه أحسنتي ما شاء الله عليك رائعة مخارج تمام غنن
+
+524
+00:57:27,890 --> 00:57:32,570
+تمام حتى العرض المد العرض السكون برضك تمام أحسنتي
+
+525
+00:57:32,570 --> 00:57:37,370
+يعني ليس لنا إلا المدح والثناء على هذه القراءة
+
+526
+00:57:37,370 --> 00:57:40,750
+الأخت ألائي الفراه افضل حبتي
+
+527
+00:57:49,950 --> 00:57:56,890
+لأ مش هذي رحم انتبهي الحائش عليها كسرة و لو
+
+528
+00:57:56,890 --> 00:58:05,290
+راحمناهم و لو راحمناهم و كشفنا مابيهم من ضرر نلجوا
+
+529
+00:58:05,290 --> 00:58:12,050
+في عدو في طبيانهم يعمهم نعيد الآية و لو راحمناهم و
+
+530
+00:58:12,050 --> 00:58:17,930
+كشفنا مابيهم هنا و كشفنا .. مابدناش نقلق الفاء و
+
+531
+00:58:17,930 --> 00:58:19,250
+كشفنا ..
+
+532
+00:58:24,990 --> 00:58:42,230
+الغن أكتر للضرر للجو للجو
+
+533
+00:58:42,230 --> 00:58:45,610
+نجيب
+
+534
+00:58:45,610 --> 00:58:53,800
+للجو قوليأه مش ju دي ال aj تخرج من وسط اللسان مع
+
+535
+00:58:53,800 --> 00:58:57,160
+ميحذية من الحنق الأعلى مابدناش نجيب فيها إيش تفشي
+
+536
+00:58:57,160 --> 00:59:07,500
+اج اج للد جو جو ارجع سالك لورا شوية للد جو أكتر
+
+537
+00:59:07,500 --> 00:59:15,610
+شوية أصبح اج اج ايوة للد جوطيب، ضبطها في البيت
+
+538
+00:59:15,610 --> 00:59:23,110
+أكتر و لا قد أخذناهم بمعذار مش أخذناهم أخذناهم و
+
+539
+00:59:23,110 --> 00:59:32,490
+لا قد أخذناهم أخى و لذا ساكنة أخذ و لا قد أخذناهم
+
+540
+00:59:32,490 --> 00:59:40,110
+بمعذار أخى، الخى مفخمة أخذولقد أخذناهم بالعذاب ثم
+
+541
+00:59:40,110 --> 00:59:46,030
+استكانوا لربهم وما يطرعهم أخذناهم .. أخذناهم
+
+542
+00:59:46,030 --> 00:59:50,730
+بالعذاب أجت ال meme بعديها زي اللي مين أخطب أيوة
+
+543
+00:59:50,730 --> 00:59:57,950
+ال meme إخفاء شفوي هنقول ولقد أخذناهم بالعذاب هم
+
+544
+00:59:57,950 --> 01:00:05,770
+بالعذاب ولقد أخذناهم .. لأ قلت ذأ ولقد أخذناهم
+
+545
+01:00:05,770 --> 01:00:13,540
+بالعذابما فخمتيش الخطأ أخذناهم ولا قد أخذناهم
+
+546
+01:00:13,540 --> 01:00:24,100
+بالعذاب فما استكانوا لربهم وما يتضرعون حتى .. حتى
+
+547
+01:00:26,720 --> 01:00:33,500
+نفس الحياة زي اتنعت مين مانع مش فتحنا .. فتحنا حتى
+
+548
+01:00:33,500 --> 01:00:40,780
+إذا فتحنا عليهم .. فتحنا الحقيقة فيها رخاوة و فيها
+
+549
+01:00:40,780 --> 01:00:46,660
+إش و فيها همس و مش فيها قلقلق حتى إذا فتحنا .. لأ
+
+550
+01:00:46,660 --> 01:00:58,290
+حتى إذا فتحنا عليهم بابا .. بابا بعذاب شديدذا ذالع
+
+551
+01:00:58,290 --> 01:01:05,110
+شديد إذا هم فيه مبلسون بس هنا مافيش غنة هم فيه
+
+552
+01:01:05,110 --> 01:01:11,570
+إظهار هم فيه إظهار شفوي هألفظ الميم ظاهرة دون غنة
+
+553
+01:01:11,570 --> 01:01:19,470
+هقش أقول إذا هم في .. هم في .. هم في فقط إذا هم في
+
+554
+01:01:19,470 --> 01:01:31,040
+مبلسون و هو الذي أنه .. مددمدر و هو الذي .. و هو
+
+555
+01:01:31,040 --> 01:01:41,470
+الذي .. و هو الذي .. و هو الذي .. نعمبس مقولش و ..
+
+556
+01:01:41,470 --> 01:01:47,530
+و هو .. و هو .. ال و بس بجيب ال و فقط دون ألف و ..
+
+557
+01:01:47,530 --> 01:01:58,110
+و هو .. و هو الذي .. و هو الذي ..
+
+558
+01:01:58,110 --> 01:02:06,260
+نعم مش و هو .. و هو .. ضم تمك .. و هووهو الذي .. و
+
+559
+01:02:06,260 --> 01:02:12,800
+هو الذي أنشأ لكم السمعة و الابصار و الأدئة لأ عيدي
+
+560
+01:02:12,800 --> 01:02:18,640
+ثاني و هو اللذي .. و هو اللذي تخلفي أخوات صح تخلف
+
+561
+01:02:18,640 --> 01:02:27,500
+و هو عن و هو و هو الذي .. و هو الذي أنشأ لكم
+
+562
+01:02:27,500 --> 01:02:36,670
+السمعة و الأبصار و الأدئةوالأبيصار فخم الصاد و هو
+
+563
+01:02:36,670 --> 01:02:45,130
+الذي أنشأ له مستمع والأبصار والأفئده والأبيصار ..
+
+564
+01:02:45,130 --> 01:02:51,430
+صار .. نقول صار مفخمة والأبيصار والأفئده ..
+
+565
+01:02:51,430 --> 01:02:54,390
+والأبيصار والأفئده
+
+566
+01:02:56,810 --> 01:03:03,190
+لأ ممكن تفهم أكتر؟ و الأب يصار .. صا .. صا .. و
+
+567
+01:03:03,190 --> 01:03:07,670
+الأب يصار .. و الأفقلا .. لأ هيك مش تفخين و الأب
+
+568
+01:03:07,670 --> 01:03:12,290
+يصار .. صا .. صا .. و الأب يصار .. بدين .. بدين ..
+
+569
+01:03:12,290 --> 01:03:16,330
+يعني الهواء .. الفم ينتلق بالهواء صا .. و الأب
+
+570
+01:03:16,330 --> 01:03:17,310
+يصار ..
+
+571
+01:03:21,990 --> 01:03:27,530
+انسبتها في البيت تشكرون
+
+572
+01:03:27,530 --> 01:03:36,150
+مدي رول قليل ما تشكرون مش رول .. هذي إيش دي
+
+573
+01:03:36,150 --> 01:03:40,510
+الراهنة؟ الراهنة مليئة بالغنة ال wow اللي عندك
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+574
+01:03:40,510 --> 01:03:44,210
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+575
+01:03:44,210 --> 01:03:49,670
+بأتخلص من الغنة بإني أضمهضم شفايفي أكتر، هضم
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+576
+01:03:49,670 --> 01:03:54,950
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+577
+01:03:54,950 --> 01:03:59,570
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+578
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+579
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+
+580
+01:04:09,570 --> 01:04:12,970
+هنا روق من غير بطلعش .. بطلعش فيها غنة لو .. لو
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+581
+01:04:12,970 --> 01:04:19,350
+سكرتي أنفك روح روح روح وفتحتي روح نفس الحاجة روح
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+582
+01:04:19,350 --> 01:04:25,050
+يشكرون رون يالا
+
+583
+01:04:25,050 --> 01:04:35,680
+ضم و لا تزم يالا فين ما تشكرونرول .. رول .. رول ..
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+584
+01:04:35,680 --> 01:04:44,220
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
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+585
+01:04:44,220 --> 01:04:46,120
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+586
+01:04:46,120 --> 01:04:46,120
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+587
+01:04:46,120 --> 01:04:46,120
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+588
+01:04:46,120 --> 01:04:46,120
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+589
+01:04:46,120 --> 01:04:46,180
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+590
+01:04:46,180 --> 01:04:46,200
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
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+591
+01:04:46,200 --> 01:04:46,260
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
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+592
+01:04:46,260 --> 01:04:46,400
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+593
+01:04:46,400 --> 01:04:48,040
+رول .. رول .. رول .. رول .. رول .. رول .. رول ..
+
+594
+01:04:48,040 --> 01:05:00,480
+رول .. رول
+
+595
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+وهو الذي يحيي ويميت وله اختلاف الليل والنهار ده
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+596
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+597
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+598
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+..وهو الذي يحيي ويميت وله اختلاف الليل والنهاروهو
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+599
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+الذي يحي ويميد وله اختلاف الليل والنهار والنهار
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+600
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+601
+01:05:46,440 --> 01:05:56,720
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+602
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+تخرج من وسط الحلقة أحسنتى بل قالوا مثل ما قال
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+603
+01:06:01,920 --> 01:06:11,220
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+604
+01:06:11,220 --> 01:06:17,270
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+605
+01:06:17,270 --> 01:06:26,350
+أيذا ميتنا و كنا ترادا و عضادا أننا مابعدوا .. هذه
+
+606
+01:06:26,350 --> 01:06:30,850
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+
+607
+01:06:30,850 --> 01:06:34,090
+قالوا
+
+608
+01:06:34,090 --> 01:06:40,010
+أيذا .. أيذا ميتنا و كنا .. مش ميتنا .. ميتنا ..
+
+609
+01:06:40,010 --> 01:06:42,710
+ميتنا .. بس همس بسيط
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+610
+01:06:46,660 --> 01:06:52,580
+ما .. ما تمديش قالوا أذا ميتنا .. ميتنا .. ميتنا
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+611
+01:06:52,580 --> 01:07:02,180
+.. نعم قالوا أذا ميتنا و كنا جرادا و عظاما أإنا
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+612
+01:07:02,180 --> 01:07:08,800
+لمبعوثون لمبعوثون لمبعوثون
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+613
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+لقد وعدنا نحن و آذاؤنا لهذا منطلق إن هذا إلا
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+614
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+615
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+616
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+617
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+بعد اللام نفس
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+618
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+619
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+620
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+621
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+622
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+623
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+624
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+625
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+626
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+627
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+628
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+
+629
+01:08:43,890 --> 01:08:49,410
+الساكنة ما قبلها حرف مد .. بد إيش؟ أنا أفخمها
+
+630
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+النهار .. مبارك الله فيك ندوق على الأشياء الهادئ
+
+631
+01:08:52,930 --> 01:08:58,850
+وين في أرضها أخر واحدة معانا هتكون الأخت موجودة
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+632
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+فاطمة عدوان فاطمة .. فضلي فاطمة
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+633
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+قل لمن الأرض ومن فيها إن كنتم تعلمون سيقولون لله
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+634
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+635
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+636
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+ملكوت كل شيء و هو يجير .. و هو يجير و لا يجار عليه
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+637
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+638
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+آتيناهم لأ بل .. بل آتيناهم
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+639
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+640
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+قراءتك رائعة وجميلة فحاول تتخلص من الغنى في الأو
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+641
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+بضم التم، ضم الشفاية وإن هم لكاذبونبون أيوة ضم
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+642
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+أكتر فبتطلعش عندك القنة لأن قراءتك رائعة فهذه
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+643
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+644
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+أيوة شفتي كتلة عطها دي بون رائع من غير قلنا متخذا
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+645
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+646
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+كان معهم إله إذا لذهب كلكل إله .. كل إله بما خلق
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+647
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+648
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+هنا أشوف كيف إذا لذهب كل إله .. كل إلهلأ إيش ..
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+649
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+652
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+653
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+654
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+655
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+658
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+660
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+664
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+671
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+سوزان
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+672
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+673
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+هي الراء المكسورة نوري نوري نوري نوري أيوةوإن ..
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+ممكن
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+694
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+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
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+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
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+..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع ..ادفع
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+705
+01:16:27,270 --> 01:16:51,430
+مافيش فيها أقول لأ من همزات اعيدي
+
+706
+01:16:51,430 --> 01:16:51,770
+تاني
+
+707
+01:17:00,080 --> 01:17:05,340
+جاء في عندك إيش يا أخوات؟ مد واجب متصل لماذا أنا
+
+708
+01:17:05,340 --> 01:17:09,660
+أمد؟ لأقوى الضعيف حتى أتوصل إلى النطق القوي وهو
+
+709
+01:17:09,660 --> 01:17:14,220
+مين؟ الهمزة عشان هيك إذا إنت مد كويس أجيب الهمزة
+
+710
+01:17:14,220 --> 01:17:17,900
+إنت أحيانا .. إنت إيش عملت يا سوزان؟ أكلتي الهمزة
+
+711
+01:17:17,900 --> 01:17:24,790
+موضحتيهاش، محققتيهاش، هنقول إيش؟حتى إذا جاء أحدهم
+
+712
+01:17:24,790 --> 01:17:36,030
+جاء أحدهم جاء أحدهم جاء أحدهم
+
+713
+01:17:36,030 --> 01:17:40,370
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+714
+01:17:40,370 --> 01:17:42,050
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+715
+01:17:42,050 --> 01:17:45,410
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+716
+01:17:45,410 --> 01:17:47,670
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+717
+01:17:47,670 --> 01:17:47,730
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+718
+01:17:47,730 --> 01:17:47,850
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+719
+01:17:47,850 --> 01:17:49,430
+جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم جاء أحدهم
+
+720
+01:17:49,430 --> 01:17:58,520
+جاء أحدهم جاء أحدهم جلعلي أعمل صالحا فيما
+
+721
+01:17:58,520 --> 01:18:05,940
+تركت لعلي
+
+722
+01:18:05,940 --> 01:18:15,940
+أعمل صالحا فيما تركت لعلي
+
+723
+01:18:15,940 --> 01:18:18,840
+أعمل صالحا فيما تركت لعلي أعمل صالحا فيما تركت
+
+724
+01:18:18,840 --> 01:18:18,840
+لعلي أعمل صالحا فيما تركت لعلي أعمل صالحا فيما
+
+725
+01:18:18,840 --> 01:18:24,150
+تركت لعلي أعمل صالحا فيما تركتكلا إنها كلمة هو
+
+726
+01:18:24,150 --> 01:18:31,930
+قائلها حقق الإظهار كلا إنها كلمة هو قائلها حقق
+
+727
+01:18:31,930 --> 01:18:34,510
+الإظهار كلا إنها كلمة هو قائلها حقق الإظهار كلا
+
+728
+01:18:34,510 --> 01:18:35,930
+إنها كلمة هو قائلها حقق الإظهار كلا إنها كلمة هو
+
+729
+01:18:35,930 --> 01:18:36,130
+قائلها حقق الإظهار كلا إنها كلمة هو قائلها حقق
+
+730
+01:18:36,130 --> 01:18:36,450
+الإظهار كلا إنها كلمة هو قائلها حقق الإظهار كلا
+
+731
+01:18:36,450 --> 01:18:36,450
+إنها كلمة هو قائلها حقق الإظهار كلا إنها كلمة هو
+
+732
+01:18:36,450 --> 01:18:36,450
+قائلها حقق الإظهار كلا إنها كلمة هو قائلها حقق
+
+733
+01:18:36,450 --> 01:18:41,130
+الإظهار كلا إنها كلمة هو قائلها حقق الإظهار كلا
+
+734
+01:18:41,130 --> 01:18:46,150
+إنها كلمة هو قائلها حقق
+
+735
+01:18:48,100 --> 01:18:54,380
+أيوة أحسنت يبارك الله فيك ومن وراعيهم برزخ .. و من
+
+736
+01:18:54,380 --> 01:19:01,680
+وراعيهم برزخوا إلى يومي .. إلى يومي يبعثوا و من
+
+737
+01:19:01,680 --> 01:19:08,060
+وراعيهم برزخوا ال .. ها إيش قلنا؟ وراعيهم برزخوا
+
+738
+01:19:08,060 --> 01:19:11,560
+الميم الساكنة جاء بعدها بفهمنا حقق الإخفاء الشفوي
+
+739
+01:19:11,560 --> 01:19:13,700
+مع الغنى يلا؟
+
+740
+01:19:16,980 --> 01:19:25,140
+و من وراهم درزخ .. درزخ إلى يوم يبعته شايفة؟ درزخ
+
+741
+01:19:25,140 --> 01:19:34,440
+إلى أيضا إظهار نعم فإلى كيخ في الصور ثلاث .. ثلاث
+
+742
+01:19:34,440 --> 01:19:42,810
+ساب بينهم يوم إذا و لا يتساءلبعدين فلا أنساب نفسها
+
+743
+01:19:42,810 --> 01:19:49,030
+زي جهة حقق الهمزة بعد المد يلا أشوف فإذا نودي قربي
+
+744
+01:19:49,030 --> 01:19:53,830
+الصور فلا .. لأ هي كإنت مابينتيش الهمزة صح يا
+
+745
+01:19:53,830 --> 01:19:59,710
+أخوات؟ مابيناتش الهمزة لما نقول فلا أنساب .. فلا
+
+746
+01:19:59,710 --> 01:20:01,470
+أنساب
+
+747
+01:20:10,070 --> 01:20:14,150
+مدّي أكتر وحقق الهمزة في التساءل
+
+748
+01:20:28,800 --> 01:20:32,740
+شايف كيف؟ بدي أجيب الهمزة و بعدين يوم إذ و لا في
+
+749
+01:20:32,740 --> 01:20:40,770
+إضغام بيغنى حقيقي يوم إذ و لا يتساءلونأحسنت فنفق
+
+750
+01:20:40,770 --> 01:20:46,910
+لك موازينه فأولئك هم ال .. هم المفلحون
+
+751
+01:20:49,320 --> 01:20:58,440
+نفس الحاجة في عندك اظهر ومن .. ومن خفت ومن خفت
+
+752
+01:20:58,440 --> 01:21:04,780
+موازين .. سوزان ومن خفت ومن .. حقق النون مظهر يلا
+
+753
+01:21:04,780 --> 01:21:09,720
+ومن خفت .. لأ بس من غير غنى ظاهرة فيها بس أصل
+
+754
+01:21:09,720 --> 01:21:16,680
+الغنى، مدناش غنى ظاهرة ومن خفت موازينه ومن خفت
+
+755
+01:21:16,680 --> 01:21:17,600
+موازينه .. أيوة أحسنت
+
+756
+01:21:25,060 --> 01:21:36,540
+الذين خسروا أنفسهم في جهنم قالدون تلفح وجوههم
+
+757
+01:21:36,540 --> 01:21:45,360
+النار .. النار وهم فيها كائحون تلفح وجوههم النار
+
+758
+01:21:45,360 --> 01:21:48,640
+.. النار
+
+759
+01:21:48,640 --> 01:21:49,640
+وهم فيها كائحون
+
+760
+01:21:52,950 --> 01:22:00,930
+قولني أكتر وجوههم النار أنها .. لأ اعدي الآية تنفع
+
+761
+01:22:00,930 --> 01:22:07,620
+وجوههم النار فيها كرمأحسنت يا سيزان ماشاء الله
+
+762
+01:22:07,620 --> 01:22:10,500
+عليك يا سيزان ومبارك الله فيك يا حبيبتي بدنا بعض
+
+763
+01:22:10,500 --> 01:22:13,640
+الملاحظات اللي حكيناها الإظهار .. الإظهار في النون
+
+764
+01:22:13,640 --> 01:22:17,440
+الساكنة والتنوين إذا جاء بعدها أحد أحرف الإظهار
+
+765
+01:22:17,440 --> 01:22:21,080
+اللي هم مين؟ أخي هاكى علما، هزهوا وغيروا وخاسروا،
+
+766
+01:22:21,080 --> 01:22:24,540
+ست حروف إذا جاءت بعد النون الساكنة والتنوين، النون
+
+767
+01:22:24,540 --> 01:22:30,670
+فيها أصل الغنى فقط وهي مظهرة .. مظهرة من؟عمل .. من
+
+768
+01:22:30,670 --> 01:22:35,750
+عمل و في انها .. و من خفت .. و من خفت الحاجة
+
+769
+01:22:35,750 --> 01:22:38,690
+التانية اللي بدنا ندق عليها حكاية إيه؟ شقولنا يا
+
+770
+01:22:38,690 --> 01:22:46,030
+Suzanne اللي هوالاخفاء .. الاخفاء الشفوي .. الميم
+
+771
+01:22:46,030 --> 01:22:49,470
+الساكنة و بعدها باق .. و الباق .. بدنا نجيب اخفاء
+
+772
+01:22:49,470 --> 01:22:53,690
+شفوي .. نطبق الشفتين انتباقا يسيرا .. ثم ايش ..
+
+773
+01:22:53,690 --> 01:22:58,970
+ندخل على مخرج الباق .. فالاخفاء الشفوي .. و المدود
+
+774
+01:22:58,970 --> 01:23:02,650
+برضك .. انتبع المدود .. أخوات الكريمات انتهينا من
+
+775
+01:23:02,650 --> 01:23:05,330
+محاضرتنا الكريمة .. و الحمد لله رب العالمين ..
+
+776
+01:23:05,330 --> 01:23:08,210
+سبحانك اللهم و بحمدك أشهد أن لا إله إلا أنت
+
+777
+01:23:08,210 --> 01:23:11,210
+أستغفرك من كل ذنب و أتوب إليك .. بسم الله الرحمن
+
+778
+01:23:11,210 --> 01:23:15,600
+الرحيموالعصر إن الإنسان لا في خسر إلا الذين آمنوا
+
+779
+01:23:15,600 --> 01:23:20,200
+وعملوا الصالحات وتواصوا بالحق وتواصوا بالصبر شكرا
+
+780
+01:23:20,200 --> 01:23:22,820
+لكم والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/jeU4bIgAGkg_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/jeU4bIgAGkg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1048831abd2081bff0419c88b4a17b7fa4e83818
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/jeU4bIgAGkg_raw.srt
@@ -0,0 +1,732 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,340 --> 00:00:14,660
+أعوذ بالله من الشيطان الرجيم بسم الله الرحمن
+
+3
+00:00:14,660 --> 00:00:18,780
+الرحيم والصلاة والسلام على أشرف المرسلين سيدنا
+
+4
+00:00:18,780 --> 00:00:25,180
+محمد وعلى آله وصحبه أجمعين اللهم اللهم اشرحلي صدري
+
+5
+00:00:25,180 --> 00:00:29,260
+ويسرلي أمري وحل عقطة من لساني يفقه قولي اللهم
+
+6
+00:00:29,260 --> 00:00:33,600
+علمنا من القرآن ماينفعنا وانفعنا بما علمتنا وزدنا
+
+7
+00:00:33,600 --> 00:00:39,230
+اللهم علم أخوات الكريماتحبيبتي أخوات الكريمات بنات
+
+8
+00:00:39,230 --> 00:00:43,190
+الحبيبات وحييكنا بتحية الإسلام تحية أهل الجنة
+
+9
+00:00:43,190 --> 00:00:47,110
+جعلنا الله وإياكم من أهلها فالسلام عليكم ورحمة
+
+10
+00:00:47,110 --> 00:00:48,610
+الله تعالى وبركاته
+
+11
+00:00:51,150 --> 00:00:56,170
+قال رسول الله صلى الله عليه وسلم مجتمع قوم في بيت
+
+12
+00:00:56,170 --> 00:01:03,390
+من بيوت لا يتلون كتاب الله ويتدرسونه إلا .. إلا يا
+
+13
+00:01:03,390 --> 00:01:09,430
+أخواتي هيحصل لهم أربع أشياء، نزلت عليهم السكينةو
+
+14
+00:01:09,430 --> 00:01:14,670
+غشيتهم الرحمة و حفتهم الملائكة و ذكرهم الله في من
+
+15
+00:01:14,670 --> 00:01:18,470
+عنده فيا أخوتي بدنا نستشعر هذا الشعور أن الله
+
+16
+00:01:18,470 --> 00:01:23,990
+سبحانه و تعالى يذكر كل واحدة باسمها عنده عند مين؟
+
+17
+00:01:23,990 --> 00:01:28,090
+من الذي عند الله سبحانه و تعالى؟ الملائكة فنستشعر
+
+18
+00:01:28,090 --> 00:01:32,710
+هذا الشعور و الملائكة تحفنا و تدعو لنا فنبدأ
+
+19
+00:01:32,710 --> 00:01:36,270
+رحلتنا القرأنية الإيمانية مع الأخت
+
+20
+00:01:45,970 --> 00:01:55,930
+يلا يا مانار افتحيلي على صورة الحج صورة
+
+21
+00:01:55,930 --> 00:02:05,070
+الحج يا انتي اقرا
+
+22
+00:02:05,070 --> 00:02:08,590
+ايه من أولها؟
+
+23
+00:02:08,590 --> 00:02:16,450
+اعوذ بالله من الشيطان الراجلبسم الله الرحمن الرحيم
+
+24
+00:02:16,450 --> 00:02:25,550
+يا أيها الناس اتقوا ربكم إن فلفل ألف ساعة شيء عظيم
+
+25
+00:02:25,550 --> 00:02:33,310
+يوم دروسها تبهر كل موضعة عالم أربعة مضارة ..انت بي
+
+26
+00:02:33,310 --> 00:02:39,250
+أنت بي أعيد الآية يوم ..
+
+27
+00:02:44,300 --> 00:02:54,040
+هذه ايش؟ كله ولا كله؟ يوم تراونها تذهلوا كله عليها
+
+28
+00:02:54,040 --> 00:02:54,980
+ضمة يلا
+
+29
+00:03:00,440 --> 00:03:06,760
+لأ أعيد الآية من أولها يوم ترونها تذهب كل مرضعة
+
+30
+00:03:06,760 --> 00:03:14,940
+عما أرضعة و تضعوا كل ذات .. ذات حمل حملها و ترى
+
+31
+00:03:14,940 --> 00:03:21,590
+الناس .. و ترى الناس سكارةانتبهي يا منا يوم
+
+32
+00:03:21,590 --> 00:03:28,670
+تراونها تذهلوا كل مرضعة عامة الميم مشددة الميم
+
+33
+00:03:28,670 --> 00:03:33,410
+المشددة يا أخوات إيش عليها غنى مقدارها حركتين إذا
+
+34
+00:03:33,410 --> 00:03:39,230
+أنا بدي أغنى الميم المشددة مقدار حركتين عامة
+
+35
+00:03:40,670 --> 00:03:46,730
+عامة و بعدين بدي أمد المنفصل جاء حرف المد وجاء
+
+36
+00:03:46,730 --> 00:03:49,850
+بعدين الهمزة في كلمة الأخرى أو الكلمة اللي انت
+
+37
+00:03:49,850 --> 00:03:53,970
+تليها قدرش بدي أمد المنفصل؟ أربع أو خمس حركات من
+
+38
+00:03:53,970 --> 00:04:02,010
+طريق الشاطبية إذا بدي أقول عامة أرضعت بدي أمد قدرش
+
+39
+00:04:03,000 --> 00:04:10,980
+ما أربعت فإيش بدي أمد قداش أربع حركات وتضع كل ذات
+
+40
+00:04:10,980 --> 00:04:19,000
+حمل حملها هذه ذات عليها كسرة ذات ذات حمل حملها
+
+41
+00:04:19,000 --> 00:04:24,020
+وترى الناس سكارة وما هم بسكارة يبقى أعيد الآية
+
+42
+00:04:24,020 --> 00:04:29,420
+أختي وانتبهي للملاحظات اللي حكتلكيها يوم ترون أن
+
+43
+00:04:29,420 --> 00:04:36,010
+أنا كدهاه هنا أيضا في شيء كله يا أخوات عليها شدة
+
+44
+00:04:36,010 --> 00:04:40,130
+في عليها اللام غنة؟ لأ الحروف المشددة تنقسم إلى
+
+45
+00:04:40,130 --> 00:04:44,630
+قسمين حروف مشددة بغنة و حروف مشددة بغير غنة اللام
+
+46
+00:04:44,630 --> 00:04:48,950
+المشددة إيش؟ بغير غنة بغير غنة يبقى بدناش نقول كله
+
+47
+00:04:48,950 --> 00:04:55,250
+خاطئة كله لأ لازم أقول على طول هي كده كله كله بس
+
+48
+00:04:55,250 --> 00:05:01,210
+يا شده و بس يالا أحسنتي
+
+49
+00:05:05,390 --> 00:05:12,730
+مدي أكتر شوية و تضعوا
+
+50
+00:05:12,730 --> 00:05:21,560
+.. و تضعوا اش ع العين .. ع العينالضمة، إذا لا أشبه
+
+51
+00:05:21,560 --> 00:05:24,400
+حركتها الضمة عشان يصير بعدها wow، لا، انت إيش
+
+52
+00:05:24,400 --> 00:05:28,460
+قولتي؟ قولتي و تضعوا، جبتي wow، أشبعتي الضمة
+
+53
+00:05:28,460 --> 00:05:32,860
+بالحركة فأصبحت .. اتولد عندي wow، خطأ، هيك، لازم
+
+54
+00:05:32,860 --> 00:05:38,600
+أقول و تضعوا .. و تضعوا .. و تضعوا .. عادي، هل
+
+55
+00:05:38,600 --> 00:05:44,060
+أقنطي؟ و تضعوا كل .. صح؟ عادي، لأ عادي و تضعوا كل
+
+56
+00:05:44,060 --> 00:05:44,740
+.. أيوة
+
+57
+00:05:48,260 --> 00:05:54,260
+لأ هذه ذاتي إيش عليها؟ كثرة فقط يبقى هتقول كل ذاتي
+
+58
+00:05:54,260 --> 00:06:07,400
+حملن ذاتي حملن مش ذات حملن لأ ذاتي حملن نشوف
+
+59
+00:06:07,400 --> 00:06:14,300
+حملها هذه حملها حملها اللي لام عليها إيش فتحة
+
+60
+00:06:23,670 --> 00:06:28,310
+أيضا هناك أنت أشبعت الحركة في الوين؟ في الواو في
+
+61
+00:06:28,310 --> 00:06:32,610
+الضمة على التضعو أشبعت الحركة و هنا أكلتيها فإيش
+
+62
+00:06:32,610 --> 00:06:38,330
+بنقول هنا سكارا را في عندي مات طبيعي المقدار
+
+63
+00:06:38,330 --> 00:06:43,090
+حركتيها يلا و ترى الناس سكارا
+
+64
+00:06:45,350 --> 00:06:52,210
+طيب .. طيب هم بيسوكا رأيش فيها؟احسنتى اخفاء شفوي
+
+65
+00:06:52,210 --> 00:06:57,530
+اتى بعد الميم الساكنة با في الكلم اللى تليها اذا
+
+66
+00:06:57,530 --> 00:07:03,850
+اخفاء شفوي كيف بدى اخفي الاخفاء الشفوي هنا ايه وما
+
+67
+00:07:03,850 --> 00:07:13,010
+هم بسكارة هم بيه هم بيه اطبق شفتيه انطباقا يسيرا
+
+68
+00:07:13,010 --> 00:07:17,930
+على مين على الميم ثم ادخل على مخرج البا بانطباق
+
+69
+00:07:17,930 --> 00:07:27,630
+أشد ايش بنقولهم بي .. هم بي .. بدي أجيب الإخفاء و
+
+70
+00:07:27,630 --> 00:07:33,990
+أيضا إيش كمان؟ الغنى، ضروري حكاية الغنى، أعيدي وما
+
+71
+00:07:33,990 --> 00:07:42,370
+.. وما هم بسكرة .. وما هم بسك .. بسكرة كمان ماري
+
+72
+00:07:42,370 --> 00:07:53,400
+أنتي؟ وما هم بسك .. بسكرةوما هم بسكرة ولكن عذاب
+
+73
+00:07:53,400 --> 00:07:58,280
+الله شديد طيب، بدنا يا منارة نعيد الآية كلمة كلمة
+
+74
+00:07:58,280 --> 00:08:01,640
+مع الملاحظات اللي حكيناها و مع التعديلات اللي
+
+75
+00:08:01,640 --> 00:08:07,580
+أجريناها هيا اللي أنت كلمة كلمة يوم ترونها تدهل كل
+
+76
+00:08:07,580 --> 00:08:17,050
+مرضعة .. كل يوم ترونها تدهل كل مرضعة عمهيت الحمد
+
+77
+00:08:17,050 --> 00:08:21,330
+لله ال lab رائعة جبتيها من غير غنة و غنتي علمي من
+
+78
+00:08:21,330 --> 00:08:27,650
+المشددة و جبتي اللي هو مقدار قش المنفصل نعم و تضع
+
+79
+00:08:27,650 --> 00:08:36,770
+كل .. و تضع كل .. و تضع كل .. و تضع كل ذات حمل
+
+80
+00:08:36,770 --> 00:08:40,590
+حملها نعيد و كلمة كلمة يالا انتي
+
+81
+00:08:44,780 --> 00:08:53,480
+وتضع كل ذات حمل حملها احسنتى كل ذات حمل حملها
+
+82
+00:08:53,480 --> 00:08:59,220
+اللام بس شده بيضمه و اللام اللام اللام اللام اللام
+
+83
+00:08:59,220 --> 00:08:59,940
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+84
+00:08:59,940 --> 00:09:00,500
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+85
+00:09:00,500 --> 00:09:00,860
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+86
+00:09:00,860 --> 00:09:01,280
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+87
+00:09:01,280 --> 00:09:02,760
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+88
+00:09:02,760 --> 00:09:02,760
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+89
+00:09:02,760 --> 00:09:02,760
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+90
+00:09:02,760 --> 00:09:02,760
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+91
+00:09:02,760 --> 00:09:02,760
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+92
+00:09:02,760 --> 00:09:02,760
+اللام اللام اللام اللام اللام اللام اللام اللام
+
+93
+00:09:02,760 --> 00:09:13,740
+اللام اللام اللام اللام اللام اللام اللام
+
+94
+00:09:13,740 --> 00:09:17,830
+اللام اللبرضك ايش؟ عذاب الله هلاقيتي منارة؟ بدنا
+
+95
+00:09:17,830 --> 00:09:21,590
+نركز اليوم على اللام المشددة إنها تأتي من غير غنة
+
+96
+00:09:21,590 --> 00:09:26,450
+بقولش مثلا عذاب ال .. بقولش أنا عذاب .. عذاب ..
+
+97
+00:09:26,450 --> 00:09:31,590
+ولكن عذاب الله شديد بقولش عذاب الله .. خطأ اللام
+
+98
+00:09:31,590 --> 00:09:37,370
+المشددة قولنا تشديد من غير غنة يلا قولي أشوف ولكن
+
+99
+00:09:37,370 --> 00:09:41,110
+عذاب الله شديد
+
+100
+00:09:43,430 --> 00:09:51,890
+ولكن عذاب الله شديد أقولني عن المشددة ولكن عذاب
+
+101
+00:09:51,890 --> 00:10:01,910
+الله شديد ولكن عذاب الله شديد أحسنتي أكملي
+
+102
+00:10:04,830 --> 00:10:10,310
+و من الناس ما ي .. و من الناس ما يجادلوا في الله
+
+103
+00:10:10,310 --> 00:10:18,970
+بغير علم و يتبعوا ال .. و يتبعوا كل شيطان المريض
+
+104
+00:10:18,970 --> 00:10:23,970
+نعيد الآية أنتي و من الناس .. الناس النون مشددة
+
+105
+00:10:23,970 --> 00:10:31,630
+هون مقدار حركتين ما يجادلوا جاءت النون الساكنةو
+
+106
+00:10:31,630 --> 00:10:35,950
+أجى ورقة من ي .. إذا الحكم هنا إيش؟ إضغام بغنى ..
+
+107
+00:10:35,950 --> 00:10:40,330
+إضغام بغنى جبت الإضغام انت ولكن لم تأتي بالغنى إيش
+
+108
+00:10:40,330 --> 00:10:50,270
+بدأ أقول؟ و من الناس من يجادلوا في الله تكلم و من
+
+109
+00:10:50,270 --> 00:10:58,600
+الناس من يجادلوا في الله بغير علمويتبع كل شيطان
+
+110
+00:10:58,600 --> 00:11:04,240
+مريض يا مانارا بنظبط اللام من غير غنة اللام
+
+111
+00:11:04,240 --> 00:11:12,090
+المشددة مش فيها غنة نعيد تانىو في الله بغير علم و
+
+112
+00:11:12,090 --> 00:11:19,090
+يتبع كل شيطان مريض في الله .. في الله .. مش في
+
+113
+00:11:19,090 --> 00:11:27,110
+الله و يتبع كل .. كل شيطان .. كل شيطان .. كل شيطان
+
+114
+00:11:27,110 --> 00:11:35,500
+.. مش كل .. خطأ يالا أنتي و من الناس .. نعمو من
+
+115
+00:11:35,500 --> 00:11:42,100
+الناس .. لأ غني أكتر و من الناس من يجادلوا في الله
+
+116
+00:11:42,100 --> 00:11:48,360
+بغير علم .. بغيري .. الغاء مفخمة بغير علم .. أيوة
+
+117
+00:11:48,360 --> 00:11:55,260
+رائعة و يتبع كل شيطان مريض .. لأ جيبي إيش غنت ..
+
+118
+00:11:55,260 --> 00:12:05,180
+الإضغاء .. يلا و يتبع كل شيطان ..أحسنتي ويتبع كل
+
+119
+00:12:05,180 --> 00:12:17,320
+شيطان مريض شيطان مريض هم؟ يللا ويتبع كل .. لأ بس
+
+120
+00:12:17,320 --> 00:12:22,300
+ماتشدش كتير على .. يعني اتطوريش على الطول ويتبع ..
+
+121
+00:12:22,300 --> 00:12:34,380
+ويتبع كل شيطان مريض طيبكتب عليه أنه من تولاه فأنه
+
+122
+00:12:34,380 --> 00:12:42,620
+يظل .. فأنه يظله و يهديه إلى عذاب الصحير انت بيقعد
+
+123
+00:12:42,620 --> 00:12:50,580
+تشوفي كيف كتب عليه أنه من تولاه بس تولاه بالنسبة
+
+124
+00:12:50,580 --> 00:13:00,840
+لغنعلام المشددةكُتِب عليه أنه من تولاه فأنه يضله
+
+125
+00:13:00,840 --> 00:13:06,080
+يضله فأنه
+
+126
+00:13:06,080 --> 00:13:13,240
+يضله ويهديه إلى عذاب السعير فالمشدد يا أختي بدناش
+
+127
+00:13:13,240 --> 00:13:21,500
+نغن عليها يلا نعيد الآية كُتِب كُتِب عليه أنه من
+
+128
+00:13:21,500 --> 00:13:31,250
+تولاهفأنه يضله ويفديه إلى عذاب السعير مش يضله ..
+
+129
+00:13:31,250 --> 00:13:37,050
+الضاض هنا إيش؟ مش عليها ضمة عليها كسرة يضله .. يضي
+
+130
+00:13:37,050 --> 00:13:44,930
+.. يضي .. يلا فأنه يضله .. يضله ويهضل .. لأ ممكنش
+
+131
+00:13:44,930 --> 00:13:48,550
+أني أنحولها لضا .. يضي .. ضي .. ضي ..
+
+132
+00:13:54,820 --> 00:14:00,840
+طب إننا نجيب الصلة جاءت الهائل مضمومة بين متحركين
+
+133
+00:14:00,840 --> 00:14:06,380
+إيش الحكم؟ الصلة صغرة يبقى حاركة قداش حميدها قداش
+
+134
+00:14:06,380 --> 00:14:14,840
+حاركتين يلا شوف ها تقولي يضل و هو يهديه يضل و هو
+
+135
+00:14:14,840 --> 00:14:24,680
+يهديه يلا قنطيفأنه يضره .. فأنه يضره ويهدي إلى
+
+136
+00:14:24,680 --> 00:14:30,920
+عذاب الصحير طيب
+
+137
+00:14:30,920 --> 00:14:36,000
+يا انت .. يا مانار .. تقعدش أنحنا نركز على إيش؟
+
+138
+00:14:36,000 --> 00:14:41,080
+علامة مشددة لا غنّة فيها .. لا غنّة فيها .. بتجيبي
+
+139
+00:14:41,080 --> 00:14:49,830
+شدة فقطزي مين؟ تذهله كله مرضعة، كله مرضعة، كله
+
+140
+00:14:49,830 --> 00:14:53,150
+مرضعة، انتبهيلا يا aunty هذي، يعني أكتر إشي كانت
+
+141
+00:14:53,150 --> 00:14:59,270
+قرأتك فيها، فعيدي أشوف، تذهله كله مرضعة، كله
+
+142
+00:14:59,270 --> 00:15:06,490
+مرضعة، يوم تروناها تذهله كله مرضعة، الحمد لله
+
+143
+00:15:06,490 --> 00:15:10,370
+أحسن، أحسن كتير، وحنتدرب عليها في البيت أكتر،
+
+144
+00:15:10,370 --> 00:15:17,960
+وشكرا، وبرك الله فيك يا مانارولقيت مع الأخت حنين
+
+145
+00:15:17,960 --> 00:15:27,620
+شبات حنين شبات أكمل يا أنتي حرف
+
+146
+00:15:27,620 --> 00:15:34,200
+الجيم أيوة مش .. مش .. مش راجيم الجي .. الجي من
+
+147
+00:15:34,200 --> 00:15:38,120
+أين يخرج يا أخواتي من وسط اللسان مع ما يحذيه من
+
+148
+00:15:38,120 --> 00:15:42,380
+الحنق الأعلى إذا رجعي لسانك لورا شوية أجه
+
+149
+00:15:44,960 --> 00:15:50,380
+كمان مرة؟ أربع جيم أربع
+
+150
+00:15:50,380 --> 00:15:54,160
+جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم
+
+151
+00:15:54,160 --> 00:15:55,400
+أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع
+
+152
+00:15:55,400 --> 00:15:55,400
+جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم
+
+153
+00:15:55,400 --> 00:15:55,400
+أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع
+
+154
+00:15:55,400 --> 00:15:55,620
+جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم
+
+155
+00:15:55,620 --> 00:15:55,700
+أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع
+
+156
+00:15:55,700 --> 00:15:56,360
+جيم أربع جيم أربع جيم أربع جيم أربع جيم أربع جيم
+
+157
+00:15:56,360 --> 00:16:01,940
+أربع جيم أربع جيم أربع
+
+158
+00:16:01,940 --> 00:16:04,580
+جيم أربع ج
+
+159
+00:16:24,740 --> 00:16:28,480
+نعيد الآية نعيد الآية كلمة كلمة
+
+160
+00:16:32,500 --> 00:16:35,280
+أيوة بدنا نقول على مين؟ على نون المشددة في الناس
+
+161
+00:16:35,280 --> 00:16:54,860
+يا أيها الناس يلا بدنا
+
+162
+00:16:54,860 --> 00:17:02,860
+نقلقل القاف وين؟ في خلقناكم خلقواقولي خلقوناكم ..
+
+163
+00:17:02,860 --> 00:17:07,380
+خلقوناكم وانتبهي أن النام بدناش نفخمها، بدناش نقول
+
+164
+00:17:07,380 --> 00:17:14,740
+خلق .. خ .. خلا .. خلق .. خلق و القاف يا أخواتي
+
+165
+00:17:14,740 --> 00:17:18,180
+مقلقلة، قولنا أن القلقلة هي اضطراب في المخرج فبصير
+
+166
+00:17:18,180 --> 00:17:23,780
+إيش عنده؟ نبرة على مين؟في الحرف نبرة يعني بقوي صوت
+
+167
+00:17:23,780 --> 00:17:27,640
+شوية على الحرف ليش يا أخوتي حروف القلقلة هي حروف
+
+168
+00:17:27,640 --> 00:17:32,320
+فيها شدة لذلك أنا كنت أتخلص من هذه الشدة عن طريق
+
+169
+00:17:32,320 --> 00:17:40,180
+القلقلة عن طريق القلقلة خلقوا
+
+170
+00:17:40,180 --> 00:17:46,480
+بس بدناش نوقف بدناش نفصل يعني أحسنتي خلقوا ناكوا
+
+171
+00:18:02,190 --> 00:18:06,570
+بس نفعش هيك يعني نقرأ كلمتين و نوقف كلمتين و نوقف
+
+172
+00:18:06,570 --> 00:18:10,770
+كلمتين و نوقف المعنى متواصل مع بعضه هذه النقطة
+
+173
+00:18:10,770 --> 00:18:13,670
+النقطة الثانية ان لو بدي اوقف انا على الكلمة لازم
+
+174
+00:18:13,670 --> 00:18:18,730
+ايش لازم اسكنها و التنوينأو التأة المربوطة عند
+
+175
+00:18:18,730 --> 00:18:22,590
+السكون عليها عند الوقف عليها لازم اش تكون ساكنة
+
+176
+00:18:22,590 --> 00:18:26,970
+يبقى لو قفتي على مثلا علقة مدينك تقولي علقة ..
+
+177
+00:18:26,970 --> 00:18:36,300
+علقة .. علقةأعلي صوتك يالا .. أعلي صوتك و .. يالا
+
+178
+00:18:36,300 --> 00:18:40,940
+أشوف ثم
+
+179
+00:18:40,940 --> 00:18:52,300
+من نطفة ثم من علقة ثم من مضغه الهاء بتقع فعليها
+
+180
+00:18:52,300 --> 00:18:57,620
+الهاء المربوطة نقف عليها على هاء ساكنه يالا أعلي
+
+181
+00:18:57,620 --> 00:18:58,240
+صوتك شوية
+
+182
+00:19:07,640 --> 00:19:15,460
+لأ لما توقفى عليها عشان تقولى على ساكنة علقة يالا
+
+183
+00:19:15,460 --> 00:19:17,740
+اعطى ايوة
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/nbN9rguMoGc.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/nbN9rguMoGc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c4d1f9340c67510562056fdc37c89a8d51f78e81
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/nbN9rguMoGc.srt
@@ -0,0 +1,2087 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,950 --> 00:00:14,710
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن 
+
+3
+00:00:14,710 --> 00:00:19,370
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+4
+00:00:19,370 --> 00:00:23,310
+آله وصحبه وسلم أخذنا يا أخوات في المحاضرة الماضية
+
+5
+00:00:23,310 --> 00:00:28,930
+الصفات التي ليس لها ضد يعني غير المتضادة أخذنا صفة
+
+6
+00:00:28,930 --> 00:00:33,460
+الصفير وأخذنا صفة القلقلة،بقى علينا العديد من
+
+7
+00:00:33,460 --> 00:00:38,920
+الصفات غير المتضادة وهي صفة اللين وصفة الانحراف
+
+8
+00:00:38,920 --> 00:00:43,220
+والتكرير والاستطالة والتفشي والغنى والخفاء
+
+9
+00:00:43,220 --> 00:00:46,900
+عدة صفات هناخدها إن شاء الله في هذه المحاضرة
+
+10
+00:00:46,900 --> 00:00:51,310
+فالمحاضرة هذه نستكمل المحاضرة الصفات غير المتضادة
+
+11
+00:00:51,310 --> 00:00:56,710
+وأخذنا قبل ذلك الصفات المتضادة اللي هي الـ ... الهمس
+
+12
+00:00:56,710 --> 00:01:00,410
+ضدها الجهر، والشدة ضدها الرخاوة، وبينهم التوسط
+
+13
+00:01:00,410 --> 00:01:04,110
+والاستعلاء وضده الاستفال، والإطلاق وضده الانفتاح
+
+14
+00:01:04,110 --> 00:01:09,170
+والإذلاق وضده الإصمات، أما بالنسبة للصفير فهو ...
+
+15
+00:01:09,170 --> 00:01:13,920
+يعني من يعرف لنا الصفير؟انحصار الصوت بين طرف
+
+16
+00:01:13,920 --> 00:01:20,120
+اللسان وفوائق الثانية، وما هي حروف الصفير يا أخوات؟
+
+17
+00:01:20,120 --> 00:01:26,700
+الصين والصارت والزهر نقول أس أس از، طب صفة الصفير
+
+18
+00:01:26,700 --> 00:01:32,810
+هل هي صفة قوة ولا صفة ضعف؟صفة قوة، ممتاز صفة قوة
+
+19
+00:01:32,810 --> 00:01:38,410
+الصفة الثانية وهي صفة القلقلة، القلقلة هي اضطراب
+
+20
+00:01:38,410 --> 00:01:43,050
+المخرج عند النطق بأحد حروف القلقلة حتى يبدو له 
+
+21
+00:01:43,050 --> 00:01:49,110
+نبرة قوية، ما هي حروف القلقلة؟ مجموعة في قوله قطب
+
+22
+00:01:49,110 --> 00:01:55,040
+جد، كام حرف؟ خمسة أحرف، ق، ط، ب، ج، د، أي حرف من هذه
+
+23
+00:01:55,040 --> 00:01:58,960
+الحروف إذا عرضنا أن ننطقها سواء كانت ساكنة أو 
+
+24
+00:01:58,960 --> 00:02:05,640
+مشددة متطرفة ولا متوسطة بنسميها قلقلة نقول مثلًا
+
+25
+00:02:05,640 --> 00:02:11,380
+الحق، في النبرة هذه تسمى قلقلة، وأخذناها في المحاضرة
+
+26
+00:02:11,380 --> 00:02:16,280
+الماضية، والقلقلة بسبب يعني اجتماع صفتي الشدة
+
+27
+00:02:16,280 --> 00:02:20,000
+والجهر، صفة الشدة يعني نقولنا ما هي سبب القلقلة
+
+28
+00:02:21,190 --> 00:02:25,950
+اجتماع صفتي الشدة والجهر في الحرف، فالشدة فيها
+
+29
+00:02:25,950 --> 00:02:31,130
+انحباس الصوت والجهر فيها انحباس النفس عندما ننطق
+
+30
+00:02:31,130 --> 00:02:36,950
+بحرف القلق ده، قطب جد إب، نجد أن الصوت ينحبس والنفس
+
+31
+00:02:36,950 --> 00:02:45,980
+ينحبس، فتبدو بعد ذلك له نبرة قوية نقول إب إد أقالط
+
+32
+00:02:45,980 --> 00:02:49,980
+... هذه الحروف اللي هي مجموعة في قوله خطوب جد، وسبب
+
+33
+00:02:49,980 --> 00:02:54,140
+القلقلة إيش دي معاه صفتي الشدة والجهر؟ والقلقلة
+
+34
+00:02:54,140 --> 00:02:58,880
+تنقسم إلى كام قسم؟ تلات أقسام، القسم الأول هي
+
+35
+00:02:58,880 --> 00:03:03,420
+القلقلة الصغرى، والثاني قلقلة كبرى، والثاني
+
+36
+00:03:03,420 --> 00:03:07,060
+القلقلة الكبرى، من يأتي بمثل على القلقلة الصغرى
+
+37
+00:03:09,390 --> 00:03:16,430
+مقتدرة، مقتدرة، سبحان المجرمون ... المجرمون، حرف الجيم 
+
+38
+00:03:16,430 --> 00:03:21,230
+فيها قلقلة ولكن قلقلة صغيرة، سبحان البافية، قلقلة 
+
+39
+00:03:21,230 --> 00:03:26,450
+ولكن قلقلة صغيرة، مقتدرة القاف فيها قلقلة ولكنها
+
+40
+00:03:26,450 --> 00:03:29,590
+قلقلة صغيرة، القسم الثاني من أنواع ... من أقسام
+
+41
+00:03:29,590 --> 00:03:33,430
+القلقلة هي القلقلة الكبرى، وهو إذا جاء أحد حروف
+
+42
+00:03:33,430 --> 00:03:39,820
+القلقلة ساكن متطرف أو متطرف الكلمة، موقوف عليه نقول
+
+43
+00:03:39,820 --> 00:03:47,480
+مثلًا قل أعوذ برب الفلق، قل هو الله أحد، البروج، محيط 
+
+44
+00:03:47,480 --> 00:03:52,060
+فهذه قلقلة بنسميها كبرى لإنه جاء أحد حروف القلقلة
+
+45
+00:03:52,060 --> 00:03:58,440
+ساكن متطرف، موقوف عليه، يسمى قلقلة كبرى، طيب القسم 
+
+46
+00:03:58,440 --> 00:04:03,680
+الثالث يا أخوات ما هي القلقلة الكبرى؟ كون ساكن أو مش 
+
+47
+00:04:03,680 --> 00:04:07,160
+ساكن، إذا كان ... إذا جاء أحد حروف القلقلة ساكن 
+
+48
+00:04:07,160 --> 00:04:13,900
+سكونًا مثقلًا أو مشددًا نفسه متطرف، موقوف عليه يقلق
+
+49
+00:04:13,900 --> 00:04:18,940
+القلقلة الكبرى، من يأتي بمثال على ذلك؟ و تب ... تبت يا 
+
+50
+00:04:18,940 --> 00:04:27,340
+ده أبي لهب، و تب ... الحق ... الحج ... الحج، فهذه كلها
+
+51
+00:04:27,340 --> 00:04:33,400
+عبارة عن قلقلة يعني أكبر، أن هنا القلقلة، والآن 
+
+52
+00:04:33,400 --> 00:04:38,700
+ننتقل إلى الصفة الثالثة من الصفات التي ليس لها ضد 
+
+53
+00:04:38,700 --> 00:04:44,180
+وهي صفة اللين، اللين يا أخوات هنا لغة شيء لين بمعنى
+
+54
+00:04:44,180 --> 00:04:49,140
+إيه؟ سهل، فاللين في اللغة السهولة، وفي الاصطلاح هو 
+
+55
+00:04:49,140 --> 00:04:54,880
+إخراج الحرف من مخرجه بسهولة ويسر من غير كلفة على 
+
+56
+00:04:54,880 --> 00:04:59,960
+اللسان، يعني الحرف بيخرج بسهولة بدون ما يكون في نوع 
+
+57
+00:04:59,960 --> 00:05:06,120
+من الكلفة على اللسان، وحروف اللين هما حرفان، الواو
+
+58
+00:05:06,120 --> 00:05:11,340
+والياء، بس الواو الساكنة المفتوح ما قبلها والياء
+
+59
+00:05:11,340 --> 00:05:16,020
+الساكنة المفتوح ما قبلها، الآن لو قلنا الواو الياء،
+
+60
+00:05:16,020 --> 00:05:20,420
+هناك الواو المادية والياء المادية ليست من حروف 
+
+61
+00:05:20,420 --> 00:05:25,640
+اللين، لأن حروف اللين فقط هما حرفان، الواو الساكنة
+
+62
+00:05:25,640 --> 00:05:30,100
+المفتوح ما قبلها والياء الساكنة أيضًا المفتوح ما
+
+63
+00:05:30,100 --> 00:05:33,420
+قبلها، لو كانت الواو ساكنة مضمون ما قبلها، ماذا 
+
+64
+00:05:33,420 --> 00:05:39,040
+نسميه يا أخوات؟ الواو الساكنة المضمومة قبلها مثل 
+
+65
+00:05:39,040 --> 00:05:44,520
+المؤمنون ... مادية ... اه يعني بتسمى مادية ... المثلا 
+
+66
+00:05:44,520 --> 00:05:50,380
+المؤمنين ... مادية ... مادية، لكن نحن نريد الواو
+
+67
+00:05:50,380 --> 00:05:55,660
+الساكنة والياء ساكنة المفتوحة قبلهم ... وهم مثلًا ...
+
+68
+00:05:55,660 --> 00:06:01,870
+مثلًا حرف خوف، خوف هنا نجد أن الواو ساكنة وما 
+
+69
+00:06:01,870 --> 00:06:09,270
+قبلها مفتوح فهو يعني حرف لين، كذلك كلمة إيه؟ فرعون
+
+70
+00:06:09,270 --> 00:06:14,690
+... فرعون، الواو ساكنة وما قبلها الحرف العين مفتوح
+
+71
+00:06:14,690 --> 00:06:20,790
+كذلك بيت ... بيت، الياء ساكنة وما قبلها مفتوح حرف
+
+72
+00:06:20,790 --> 00:06:27,210
+الباء يسمى حرف لين، وكذلك قريش، وهذا كله ما يسمى
+
+73
+00:06:27,210 --> 00:06:31,750
+بالمد ... ما هو نوع المد الموجود في هذه الكلمات؟ مد
+
+74
+00:06:31,750 --> 00:06:38,910
+اللين، لو كان هنا ليس حرف لين وإنما حرف مد مثل 
+
+75
+00:06:38,910 --> 00:06:44,000
+المؤمنون، المؤمنين، الرحمن، ماذا نسميه مد اللين؟ مد
+
+76
+00:06:44,000 --> 00:06:49,100
+... عارض ... لسكون ... لسكون ... لنتقل إلى ... طب صفة
+
+77
+00:06:49,100 --> 00:06:51,740
+اللين لي أخواتها؟ اللي هي صفة قوة ولا صفة ضعف؟ صفة
+
+78
+00:06:51,740 --> 00:06:55,840
+ضعف ... صفة ضعف ... الآن إحنا أخذنا صفتين وده الصفة
+
+79
+00:06:55,840 --> 00:07:00,070
+التالتة، الصفة الأولى صفة الصفير وهي صفة قوة، الصفة
+
+80
+00:07:00,070 --> 00:07:04,110
+الثانية صفة القلقلة وهي صفة قوة، الصفة الثالثة هذه
+
+81
+00:07:04,110 --> 00:07:08,190
+اللي هي صفة اللين، صفة ضعف هو اللي بمعنى السهولة هو 
+
+82
+00:07:08,190 --> 00:07:11,410
+اللي ياخد الحرف سهولة ويسر من غير كلفة على اللسان
+
+83
+00:07:11,410 --> 00:07:14,470
+وحروف الواو والياء اللي ساكنين المفتوح ما قبلهما
+
+84
+00:07:14,470 --> 00:07:21,730
+يعدوا حرف ضعيف أو صفة ... صفة ضعف، الصفة الرابعة من 
+
+85
+00:07:21,730 --> 00:07:26,910
+الصفات التي ليس لها ضد هي صفة الانحراف، والانحراف
+
+86
+00:07:26,910 --> 00:07:30,990
+شيء يعني انحرف عن مساره، ميلو ... الميل عن الشيء و
+
+87
+00:07:30,990 --> 00:07:36,850
+العدول عنه، نقول انحرف السهم عن مساره، يعني المالة 
+
+88
+00:07:36,850 --> 00:07:41,170
+عن الجهة التي كان متجه لها، والانحراف في الاصطلاح 
+
+89
+00:07:41,170 --> 00:07:46,670
+يا أخوات، هو ميل الحرف عن مخرجه بعد النطق به، حتى 
+
+90
+00:07:46,670 --> 00:07:53,330
+يتصل بمخرج غيره، ميل الحرف عن مخرجه بعد نطقه حتى
+
+91
+00:07:53,330 --> 00:07:57,730
+يتصل بمخرج غيره، بعد ما ننطق بالحرف بنجد أن اللسان
+
+92
+00:07:57,730 --> 00:08:05,730
+يقف عند مخرج حرف آخر، وحرفاء اللين ... أقصد الانحراف
+
+93
+00:08:05,730 --> 00:08:10,770
+هو اللام والراء، إذا ما هي حروف الانحراف يا أخوات؟
+
+94
+00:08:10,770 --> 00:08:16,710
+اللام والراء هما حرفان، اللام والراء، اللام ينحرف بعد
+
+95
+00:08:16,710 --> 00:08:21,370
+النطق به حتى يتصل بمخرج حرف النون، عندما أقول أنا 
+
+96
+00:08:21,370 --> 00:08:27,370
+مثلًا الـ ... الـ ... بنجد أن اللام ... مخرج اللام
+
+97
+00:08:27,370 --> 00:08:34,510
+يتحرك وبيقف طرف اللسان عند مخرج حرف الـ N، لذلك إن
+
+98
+00:08:34,510 --> 00:08:39,950
+لم يحضر الإنسان من حرف اللام قد يصل إلى أو قد ينطق
+
+99
+00:08:39,950 --> 00:08:45,670
+حرف اللام N، مثال ذلك عندما يقول وجعلنا الليلة لباسة
+
+100
+00:08:45,670 --> 00:08:50,890
+ممكن واحد يقرأها وجعلنا ... وجعلنا الليلة لباسة لأن
+
+101
+00:08:50,890 --> 00:08:56,390
+اللام ينحرف عن مساره حتى يتصل بمخرج حرف النون، لذلك
+
+102
+00:08:56,390 --> 00:09:01,270
+لابد من الحذر عند النطق بحرف اللام حتى لا ينطقه 
+
+103
+00:09:01,270 --> 00:09:06,830
+نون مثل كلمة وجعلنا، ينطقها الـ ... الـ ... الذي يقرأ
+
+104
+00:09:06,830 --> 00:09:11,150
+وجعلنا ... ممكن ولد صغير يـ ... ينطق بهذا الحرف، يقول
+
+105
+00:09:11,150 --> 00:09:16,070
+وجعلنا، لكن دا بد أن يحذر القارئ من أن ينطق حرف 
+
+106
+00:09:16,070 --> 00:09:21,070
+اللام نون، لأن اللام بينحرف عن مساره بعد النطق به
+
+107
+00:09:21,070 --> 00:09:26,760
+حتى يتصل بمخرج غيره، الحرف الثاني أخوات هو مخرج حرف
+
+108
+00:09:26,760 --> 00:09:31,740
+الـ إيه؟ الـ لا ... الـ ... الـ ر، أقصد حرف الـ ر ينحرف عن
+
+109
+00:09:31,740 --> 00:09:38,820
+مخرجه حتى يتصل بمخرج حرف اللام، الراء بينحرف عن مساره
+
+110
+00:09:38,820 --> 00:09:44,360
+حتى يتصل بمخرج حرف اللام، مثلًا عندما يقرأ ... يقول
+
+111
+00:09:44,360 --> 00:09:49,120
+إنسان الرحمن الرحيم، ممكن لو إن لم يحضر القارئ يقول
+
+112
+00:09:49,120 --> 00:09:54,180
+اللحمان اللحيم، وهذا طبعًا يخطئ لأنه انحرف اللام عن
+
+113
+00:09:54,180 --> 00:09:58,560
+مساره حتى يعني يتصل بمخرج حرف النون، والراء بتنحرف
+
+114
+00:09:58,560 --> 00:10:02,920
+عن مسارها حتى يتصل بحرف اللام
+
+115
+00:10:04,360 --> 00:10:07,960
+طيب، هذه يا أخوات صفة الانحراف، ما هما حرفا
+
+116
+00:10:07,960 --> 00:10:13,020
+الانحراف؟ اللام والراء، اللام والراء، اللام والراء، 
+
+117
+00:10:13,020 --> 00:10:15,440
+اللام والراء، اللام والراء، اللام والراء، 
+
+118
+00:10:15,440 --> 00:10:18,100
+اللام والراء، اللام والراء، اللام والراء،
+
+119
+00:10:18,100 --> 00:10:20,840
+اللام والراء، اللام والراء، اللام والراء،
+
+120
+00:10:20,840 --> 00:10:21,020
+اللام والراء، اللام والراء، اللام والراء،
+
+121
+00:10:21,020 --> 00:10:29,080
+اللام والراء، اللام والراء، اللام والراء،
+
+122
+00:10:29,330 --> 00:10:32,790
+نقول كررتوا الشاي بمعنى إيش يا إخوان؟ إعادة
+
+123
+00:10:32,790 --> 00:10:38,850
+فتكريره لغة الإعادة، وفي الاصطلاح هو ارتعاد رأس
+
+124
+00:10:38,850 --> 00:10:46,080
+اللسان عند النطق بحرف الراء، ارتعاد رأس اللسان عند
+
+125
+00:10:46,080 --> 00:10:50,740
+النطق بحرف الراء يسمى إيه؟ يعني تكرير، نجد أن القارئ
+
+126
+00:10:50,740 --> 00:10:55,600
+أو الذي يلفظ حرف الراء يبقى نجد أن اللسان أو رأس 
+
+127
+00:10:55,600 --> 00:11:00,400
+اللسان يرتعد، يقول ار ... ار، فهذا يسمى إيه اللي هو
+
+128
+00:11:00,400 --> 00:11:06,340
+التكرير، فصفة التكرير هي صفة ملازمة لحرف الراء تظهر
+
+129
+00:11:06,340 --> 00:11:10,990
+في حالة التشديد أكثر شيء، مثل الرحمن ... الرحمن، ولكن 
+
+130
+00:11:10,990 --> 00:11:16,110
+على القارئ ألا يجعل اللسان يتكرر أكثر من مرة
+
+131
+00:11:16,110 --> 00:11:21,690
+وإن زادت مرة ونصف، يعني ما بنفع يقول الرحمن أو
+
+132
+00:11:21,690 --> 00:11:27,880
+الرأيتك أو الرحمان، هذا خطأ وإنما الرحمان يعني
+
+133
+00:11:27,880 --> 00:11:34,580
+ارتعاد اللسان مرة واحدة، كذلك الرحمان رحيم وليس 
+
+134
+00:11:34,580 --> 00:11:39,200
+نوع من التكرير، لذلك صفة التكرير يا أخوات نحن
+
+135
+00:11:39,200 --> 00:11:45,300
+ندرسها حتى نتجنب المبالغة فيها، يعني ندرس هذه الصفة
+
+136
+00:11:45,300 --> 00:11:49,980
+ليس لأن نحقق صفر التكرير فيها ونضلنا نتكرر، وإنما
+
+137
+00:11:49,980 --> 00:11:55,660
+ندرسها حتى نتجنب المبالغة فيها، فالغرض من معرفة صفة
+
+138
+00:11:55,660 --> 00:11:59,640
+التكرير عدم المبالغة فيها، فيجب على القارئ أن يخفي
+
+139
+00:11:59,640 --> 00:12:03,720
+التكرير ولا يبادر فيه ويكتفي بارتعاد واحدة عند 
+
+140
+00:12:03,720 --> 00:12:10,060
+النطق بحرف الراء، وحتى يعني يتخلص من التكرير، في 
+
+141
+00:12:10,060 --> 00:12:13,060
+عندنا نتخلص .. نتخلص من التكرير في حالة التفخيم
+
+142
+00:12:13,060 --> 00:12:18,400
+ونتخلص من التكرير في حالة إيش؟ الترقيم عند حالة
+
+143
+00:12:18,400 --> 00:12:22,520
+التفخيم مثل الرحمن، إذا أردنا أن نتخلص أو يجب
+
+144
+00:12:22,520 --> 00:12:27,400
+علينا أن نتخلص من التكرير ولا نسمح للإنسان يرتعد 
+
+145
+00:12:27,400 --> 00:12:35,570
+أكثر من مرة، فنوقف طرف اللسان نجعله يعني يقف عند
+
+146
+00:12:35,570 --> 00:12:40,630
+الحنك الأعلى فنقول الرحمن .. الرحمن إذا يلسق ظهر 
+
+147
+00:12:40,630 --> 00:12:46,190
+طرف اللسان بوسط الحنك الأعلى عند النطق بحرف الراء
+
+148
+00:12:46,190 --> 00:12:52,090
+المفخم نقول الرحمن .. الرحمن ولا نسمح لللسان إيه
+
+149
+00:12:52,090 --> 00:12:58,370
+يرتعد لا نقول الرحمن إنما نقول الرحمن يعني نجعل
+
+150
+00:12:58,370 --> 00:13:03,070
+اللسان يلتصق بالحنك الأعلى عند النطق بحرف الراء
+
+151
+00:13:03,070 --> 00:13:08,290
+المفخمة أما بالنسبة لِكيفية تتخلص من التكرير في حالة
+
+152
+00:13:08,290 --> 00:13:13,050
+الراء المرققة أن يلتصق ظهر طرف اللسان بلثة الثنايا
+
+153
+00:13:13,050 --> 00:13:21,290
+العليا نقول مثلًا بريح أو بيكيكD يعني نجعل طرف 
+
+154
+00:13:21,290 --> 00:13:26,170
+اللسان يلتصق بلثة الثنايا العليا على أساس أنه نريد 
+
+155
+00:13:26,170 --> 00:13:31,570
+أن نخرج حرف الراء مرققًا وبدون تكرير إذا في حالة
+
+156
+00:13:31,570 --> 00:13:37,210
+التفخيم نجعل طرف اللسان يلتصق بالحنك الأعلى حتى لا
+
+157
+00:13:37,210 --> 00:13:41,990
+تظهر صفة التكرير على حرف الراء نقول الرحمن أما 
+
+158
+00:13:41,990 --> 00:13:45,990
+بالنسبة إذا كان حرف الراء مرققًا نجعل طرف اللسان 
+
+159
+00:13:45,990 --> 00:13:50,360
+يلتصق بلثة الثنايا العليا كي لا يرتعد رأس اللسان
+
+160
+00:13:50,360 --> 00:13:55,880
+أكثر من مرة الصفة السادسة يا إخوان طبعًا صفة
+
+161
+00:13:55,880 --> 00:14:02,070
+التكرير صفة قوة صفة اللين صفات بعض، صفة الانحراف
+
+162
+00:14:02,070 --> 00:14:07,610
+صفات قوة، صفة القلقلة صفات .. الانحراف صفات قوة،
+
+163
+00:14:07,610 --> 00:14:12,370
+القلقلة صفات قوة، الصفير صفات قوة، إذا من الصفات
+
+164
+00:14:12,370 --> 00:14:16,190
+التي أخذناها آخر شيء اللي هي الصفير، القلقلة،
+
+165
+00:14:16,190 --> 00:14:21,150
+الانحراف، التكرير، كلها صفات قوة وصفة الانحراف مش
+
+166
+00:14:21,150 --> 00:14:27,490
+قوة الانحراف صفة قوة .. الانحراف صفة قوة .. الليل
+
+167
+00:14:27,490 --> 00:14:33,860
+فقط هو الذي يعده صفة ضعف ننتقل للصفة السادسة يا
+
+168
+00:14:33,860 --> 00:14:40,400
+أخوات وهي صفة التفشي صفة التفشي نقول تفشّي المرض،
+
+169
+00:14:40,400 --> 00:14:46,560
+تفشّي الوباء بمعنى انتشر من حيث اللغة فالتفشي لغةً ما
+
+170
+00:14:46,560 --> 00:14:51,840
+هو يا أخوات الانتشار والاتساع وفي الاصطلاح من يعرف 
+
+171
+00:14:51,840 --> 00:14:53,740
+لنا التفشي اصطلاحًا
+
+172
+00:14:57,960 --> 00:15:02,220
+انتشار الريح في الفم عند النطق بحرف الشين
+
+173
+00:15:04,950 --> 00:15:10,230
+فنجد بأنه الـ .. الريح ينتشر بالفم عند النطق بهذا
+
+174
+00:15:10,230 --> 00:15:15,390
+الحرف، إذا ما هي حروف التفشي؟ حرف واحد فقط وهو
+
+175
+00:15:15,390 --> 00:15:19,510
+الشين، فانتشار الريح في الفم عند النطق بحرف
+
+176
+00:15:19,510 --> 00:15:25,850
+التفشي وهو الشين يسمى هذا اللي هو التفشي وتثبت صفة 
+
+177
+00:15:25,850 --> 00:15:30,390
+التفشي لحرف الشين في جميع أحواله سواء كان ساكنًا أو
+
+178
+00:15:30,390 --> 00:15:36,590
+متحركًا متطرفًا أو متوسطًا ولكن تظهر بشكل واضح إذا
+
+179
+00:15:36,590 --> 00:15:41,790
+كان حرف الشين ساكنًا أو مشددًا تظهر صفة التفشي بشكل
+
+180
+00:15:41,790 --> 00:15:49,590
+واضح مثل ذلك مشربهم عشرة أو مثلًا بُشراكم تظهر صفة
+
+181
+00:15:49,590 --> 00:15:53,770
+الإش أو صفة حرف الشين للإش اللي هي صفة التفشي
+
+182
+00:15:53,770 --> 00:16:00,150
+بُشراكم عشرة مشربهم هذه كلها فيها حروف تفشي وصفة
+
+183
+00:16:00,150 --> 00:16:05,770
+التفشي أيضًا تعد صفة إش أخوات صفة قوة ننتقل إلى
+
+184
+00:16:05,770 --> 00:16:11,790
+الصفة السابعة وهي صفة الاستطالة أيضًا يا أخوات 
+
+185
+00:16:11,790 --> 00:16:16,670
+الاستطالة هي صفة قوة نقول استطالت الطريق بمعنى
+
+186
+00:16:16,670 --> 00:16:23,050
+امتدت فالاستطالة في اللغة الامتداد الاستطالة لغةً
+
+187
+00:16:23,050 --> 00:16:28,710
+الامتداد وفي الاصطلاح امتداد الصوت من أول حافة
+
+188
+00:16:28,710 --> 00:16:34,050
+اللسان إلى آخره عند النطق بحرف واحد وهو الضاد
+
+189
+00:16:34,050 --> 00:16:39,110
+امتداد الصوت من أول حافة اللسان إلى آخره عند النطق 
+
+190
+00:16:39,110 --> 00:16:45,390
+بحرف الضاد لو سألنا الأخوات من أين يخرج حرف الضاد؟
+
+191
+00:16:45,390 --> 00:16:55,450
+إحدى .. فضلي إحدى 
+
+192
+00:16:55,450 --> 00:17:00,430
+حفتي اللسان اليمنى أو اليسرى ومن اليسرى أيسر مع ما
+
+193
+00:17:00,430 --> 00:17:05,690
+يليها من أدراس الجهة العليا لو قالت واحدة مثلًا مع 
+
+194
+00:17:05,690 --> 00:17:11,450
+الثنايا العليا صحيح ولا غلط؟ غلط، أين تقع الثنايا 
+
+195
+00:17:11,450 --> 00:17:15,570
+العليا؟ الثنايا العليا هذه السنين، هذول، لو ..
+
+196
+00:17:15,570 --> 00:17:19,830
+وبالتالي خطأ أن أقول الثنايا العليا، فلابد أن 
+
+197
+00:17:19,830 --> 00:17:22,590
+أدراس .. الأدراس اللي هي الجهة العليا اللي احنا
+
+198
+00:17:22,590 --> 00:17:26,190
+نسميها الطواحين، اليمنى أو اليسرى، ولكن من اليسرى
+
+199
+00:17:26,190 --> 00:17:31,030
+أيسر، إذا حرف الضاد يخرج من إحدى حفتي اللسان، اليمنى 
+
+200
+00:17:31,290 --> 00:17:36,350
+أو اليسرى واليسرى أيسر مع ما يليها من أدراس الجهة
+
+201
+00:17:36,350 --> 00:17:41,690
+اليسرى فعندما نقول فيها صفة الاستطالة بمعنى أنه
+
+202
+00:17:41,690 --> 00:17:45,870
+عندما نقول او او نجد أن الصفة الاستطالة اللي هو الـ
+
+203
+00:17:45,870 --> 00:17:51,350
+او يمتد من أول حافة اللسان إلى آخرها هل يصح لنا أن
+
+204
+00:17:51,350 --> 00:17:58,350
+نقول رب السماوات والأرض يعني اض ا .. نطلع النبرة،
+
+205
+00:17:58,350 --> 00:18:04,140
+بنفع؟ ليش؟ لأنه أنا عندما أقول رب السماوات والأرض
+
+206
+00:18:04,140 --> 00:18:08,120
+فيها قلقة، لكن هذا يعني أنا قلقلت الآن، وهذا خطأ، 
+
+207
+00:18:08,120 --> 00:18:13,840
+لابد أن أقول رب السماوات والأرض فيها يعني نوع من
+
+208
+00:18:13,840 --> 00:18:18,960
+استطالة وصفة الاستطالة هو امتداد .. امتداد الصوت
+
+209
+00:18:18,960 --> 00:18:24,380
+من أول حافة اللسان إلى آخره عند النطق بحرف الـ ..
+
+210
+00:18:24,380 --> 00:18:30,520
+حرف الضاد وتثبت طبعًا صفة الاستطالة لحرف الضاد في
+
+211
+00:18:30,520 --> 00:18:34,980
+عندما كان ساكنًا أو مشددًا مثال ذلك هنا .. مثال ذلك ما
+
+212
+00:18:34,980 --> 00:18:40,020
+اللي يقرأ الكلمة؟ فضلي .. أضّالي .. أضّالي ..
+
+213
+00:18:40,020 --> 00:18:46,640
+أضّالي .. ففيها استطالة كذلك يضرب .. يضرب في صفة
+
+214
+00:18:46,640 --> 00:18:52,660
+الاستطالة الأولى حرف الضاد مشدد والثانية يضرب حرف
+
+215
+00:18:52,660 --> 00:18:59,060
+الضاد ساكنة ونشاهد هنا إن حرف الضاد عند نطقه له
+
+216
+00:18:59,060 --> 00:19:04,130
+امتداد للصوت من أول حافة اللسان إلى آخره ويجب
+
+217
+00:19:04,130 --> 00:19:09,530
+الحذر يا أخوات من أن نلفظ حرف الضاد ضا يعني هناك
+
+218
+00:19:09,530 --> 00:19:14,410
+بعض الدول أو بعض المجتمعات ابتدوا يلفظون حرف الضاد 
+
+219
+00:19:14,410 --> 00:19:19,090
+ضا يعني بدلًا من أن يقول غير المغضوب عليهم يقولون 
+
+220
+00:19:19,090 --> 00:19:24,410
+غير المغضوب عليهم ليس المغضوب .. المغضوب هي اللي هي
+
+221
+00:19:24,410 --> 00:19:28,150
+حرف .. بيصير حرف آخر اللي هو ضا .. يعني بيصير
+
+222
+00:19:28,150 --> 00:19:33,370
+عندنا لحن جليّ بدّلنا حرفًا محال إيه؟ محال حرفًا 
+
+223
+00:19:33,370 --> 00:19:38,090
+وبالتالي هذا خطأ وإنما نقول غير المغضوب عليهم لو
+
+224
+00:19:38,090 --> 00:19:45,340
+قلنا مثلًا في قوله تعالى ضلّ ما تدعون إلا إياه ضلّةً،
+
+225
+00:19:45,340 --> 00:19:52,780
+لو واحد لفظ حرف الظاء، ده، فقرأ ضلّ ما تدعون إلا
+
+226
+00:19:52,780 --> 00:19:58,020
+إياه، إيش بصير عنها؟ تغيّر المعنى، أول شيء لحن
+
+227
+00:19:58,020 --> 00:20:03,860
+جليّ وكذلك غير المعنى وقنّر، عندما أقول ضلّة من
+
+228
+00:20:03,860 --> 00:20:09,170
+الضلال يعني ضلّت جميع الآلهة إلا الله سبحانه وتعالى
+
+229
+00:20:09,170 --> 00:20:14,490
+فهو الإله بحق لكن الذين يعبدون الأصنام والحجارة 
+
+230
+00:20:14,490 --> 00:20:18,430
+وغير ذلك هي ضلّ .. ضلّ هؤلاء الناس وضَلّوا الطريق
+
+231
+00:20:18,430 --> 00:20:22,790
+وانحرفوا عن المسار الذين يعبدون غير الله عز وجل إلا
+
+232
+00:20:22,790 --> 00:20:26,650
+إياه إلا المسلمين الذين يعبدون الله سبحانه وتعالى
+
+233
+00:20:26,650 --> 00:20:32,150
+فهذا صحيح ضلّ ما تدعون إلا إياه لكن لو واحد قرأ
+
+234
+00:20:32,150 --> 00:20:39,320
+مثلًا ظلة بمعنى بقية اختلّ المعنى وانقلبت رأسًا
+
+235
+00:20:39,320 --> 00:20:43,580
+على العقل يعني نقول ظلة يعني بقية من تدعون إلا 
+
+236
+00:20:43,580 --> 00:20:47,160
+إياها يعني كل الأصنام بقيت إلا الله غير بقى وهذا 
+
+237
+00:20:47,160 --> 00:20:52,040
+انحراف وهذا لا يجوز لذلك لابد أن ننطق بالحرف و
+
+238
+00:20:52,040 --> 00:20:57,140
+نخرجه من مخرجه الصحيح فحرف الضاد يخرج من إحدى 
+
+239
+00:20:57,140 --> 00:21:01,020
+حفتي اللسان اليمنى أو اليسرى مع ما يليها من أدراس 
+
+240
+00:21:01,020 --> 00:21:07,420
+الجهة اليسرى يعني بيخرج من رأس اللسان بالتساقط مع
+
+241
+00:21:07,420 --> 00:21:12,080
+أطراف الثنايا العليا الـ أو والـ اث والـ اذ مخرجهم
+
+242
+00:21:12,080 --> 00:21:17,300
+واحد فلا يجوز لنا أن نخرج حرف الضاد من مخرج حرف الظاء 
+
+243
+00:21:18,570 --> 00:21:23,010
+طيب مثلًا الفرق ما بين الاستطالة والمد إحنا بنقول
+
+244
+00:21:23,010 --> 00:21:26,750
+امتداد صوت الحرف من أول حافة اللسان إلى آخره هذا 
+
+245
+00:21:26,750 --> 00:21:31,270
+الاستطالة امتداد صوت الحرف من أول حافة اللسان إلى
+
+246
+00:21:31,270 --> 00:21:35,890
+آخره عند النطق بحرف إيه؟ بحرف الضاد والامتداد
+
+247
+00:21:35,890 --> 00:21:39,350
+والمد نفسه هو امتداد الصوت لكن ما الفرق بين 
+
+248
+00:21:39,350 --> 00:21:45,430
+الاستطالة و .. أو .. و .. والمد ما رأيكم يا بنات؟
+
+249
+00:21:45,430 --> 00:21:47,770
+ما هي الاستطالة؟ فضل الأخت الوراق 
+
+250
+00:21:52,350 --> 00:21:56,830
+صحيح، يعني هنا مثلًا جريان الصوت في مخرج الحرف بقدر 
+
+251
+00:21:56,830 --> 00:22:02,010
+طوله دون أن يتجاوز المخرج، يعني أقول .. يعني هذا
+
+252
+00:22:02,010 --> 00:22:06,370
+امتداد الصوت، بس في اللسان، لكن حرف المد .. حرف
+
+253
+00:22:06,370 --> 00:22:10,310
+المد، جريان الصوت في ذات الحرف، ولا ينقطع الصوت
+
+254
+00:22:10,310 --> 00:22:15,130
+إلا من قطاع النفس، يعني هيظل يقول .. لما .. لما
+
+255
+00:22:15,130 --> 00:22:22,510
+ينتهي نفسه أو أو إيه؟ هذه حروف المد الثلاثة وهي
+
+256
+00:22:22,510 --> 00:22:27,670
+ليس لها حيز تنتهي إليه بل انتهاؤها بانتهاء .. 
+
+257
+00:22:27,670 --> 00:22:31,470
+بانتهاء النفس لكن بالنسبة لحرف الضاد فهو جريان
+
+258
+00:22:31,470 --> 00:22:36,760
+الصوت في مخرج حرف الضاد بقدر طوله يعني أوروب
+
+259
+00:22:36,760 --> 00:22:43,360
+السماوات والأرض بس مش الأرض تمشي معنا لأنه ليس
+
+260
+00:22:43,360 --> 00:22:47,320
+مثل حرف المد، إذا جريان الصوت في مخرج الحرف بقدر
+
+261
+00:22:47,320 --> 00:22:50,980
+طوله دون أن يتجاوز مخرج الحرف، هذا بالنسبة 
+
+262
+00:22:50,980 --> 00:22:53,980
+للاستطالة، لكن بالنسبة للمد، هو جريان الصوت في
+
+263
+00:22:53,980 --> 00:22:59,320
+ذات الحرف ولا ينقطع الصوت إلا بانقطاع النفس، لأن
+
+264
+00:22:59,320 --> 00:23:03,780
+حرف المد ليس له حيز ينتهي إليه، بل انتهاؤها 
+
+265
+00:23:03,780 --> 00:23:10,200
+بانتهاء النفس صفة الاستطالة ليه هي صفة قوة ولا ضعف؟ 
+
+266
+00:23:10,200 --> 00:23:15,580
+صفة قوة ننتقل للصفة الثامنة وهي صفة الخفاء
+
+267
+00:23:15,580 --> 00:23:22,020
+والخفاء لغةً من الشيء المخفي بمعنى الاستطارة الخفاء
+
+268
+00:23:22,020 --> 00:23:27,440
+لغةً الاستطارة وعدم الوضوح وفي الاصطلاح هنا استطارة
+
+269
+00:23:27,440 --> 00:23:32,480
+صوت الحرف عند النطق بأحد حروف الخفاء فما هي حروف 
+
+270
+00:23:32,480 --> 00:23:38,510
+الخفاء؟ حروف الخفاء أربعة هي حروف المد الثلاثة زي
+
+271
+00:23:38,510 --> 00:23:44,710
+الحرف الها اللي هي مجموعة في قوله هاوي هالف واو يا
+
+272
+00:23:44,710 --> 00:23:49,910
+حروف المد الثلاثة زي الحرف الها هذه حروف هاوي
+
+273
+00:23:49,910 --> 00:23:55,030
+وهي حروف الخفاء وهي استطارة صوت الحرف عند نطقه بأحد
+
+274
+00:23:55,030 --> 00:24:00,240
+حروف الخفاء وهي مجموعة في قوله هاوي سُميت حروف 
+
+275
+00:24:00,240 --> 00:24:05,260
+الخفاء بهذا الاسم لأنها تخفى في اللفظ عند النطق 
+
+276
+00:24:05,260 --> 00:24:10,880
+بها يعني ممكن تخفى ولا طول فاض ممكن تخفى ولا طول
+
+277
+00:24:10,880 --> 00:24:16,440
+فاض حروف المد الثلاثة لأنه طبعًا تخفى لأنه لو
+
+278
+00:24:16,440 --> 00:24:21,060
+أعطيناها حركة واحدة بتصير فتحة لو أعطيناها .. لو
+
+279
+00:24:21,060 --> 00:24:28,130
+أعطينا .. حرف المد حركة واحدة A O E بتصير فتحة لكن 
+
+280
+00:24:28,130 --> 00:24:31,930
+لابد أن نعطيها حركتين يعني نمدهم بمعنى أن نعطيهم 
+
+281
+00:24:31,930 --> 00:24:37,590
+زمن الصوت معناه مقدار حركتين فلأن مخرجها واسع وليس
+
+282
+00:24:37,590 --> 00:24:40,870
+لها حيز تنتهي إليه اللي هي حروف المد الثلاثة ليس 
+
+283
+00:24:40,870 --> 00:24:47,300
+لها حيز تنتهي إليه ومخرجها واسع لذلك ممكن تخفى مثلا
+
+284
+00:24:47,300 --> 00:24:52,800
+عندما نقول واضحة فلابد أن أقول واضحة والليل إذا 
+
+285
+00:24:52,800 --> 00:24:58,320
+سجى أو بين الألف لو قلت مثلا واضحة والليل إذا سجا
+
+286
+00:24:58,320 --> 00:25:02,960
+إيش بيصير؟ بيصير عبارة عن ضحة والحال عليها فتحة
+
+287
+00:25:02,960 --> 00:25:08,060
+يبقى الألف أخفيت لأن مخرج الألف واسع لا تكفيها
+
+288
+00:25:08,060 --> 00:25:13,640
+حركة بل لابد أن نعطيها كم؟ حركتين نقول واضحة
+
+289
+00:25:13,640 --> 00:25:20,100
+والليل إذا سجى .. لأ أقول والضحى والليل إذا سجى
+
+290
+00:25:20,100 --> 00:25:25,960
+إذا ممكن حرف المد يُخفى كذلك إن أنزلناه في ليلة
+
+291
+00:25:25,960 --> 00:25:31,100
+القدر يعني ممكن أن .. أنزلناه في الألف بيختلف أو
+
+292
+00:25:31,100 --> 00:25:36,800
+إن أنزلناه لو قال إن أنزلناه .. إن أنزلناه كأن
+
+293
+00:25:36,800 --> 00:25:42,340
+النون بس عليها شدة هي مش إننا أنزلناه، إننا 
+
+294
+00:25:42,340 --> 00:25:47,920
+أنزلناه، لابد أن نمد حرف المد لأنه لو لم نمدها
+
+295
+00:25:47,920 --> 00:25:51,960
+ممكن يكون هذا الحرف قابل لإيش يا أخوات؟ قابل
+
+296
+00:25:51,960 --> 00:25:57,460
+للخفاء، فيقفأ لأنه .. يعني لو سألنا سؤال لماذا 
+
+297
+00:25:57,460 --> 00:26:00,820
+حروف المد الثلاثة الألف الساكنة المفتوحة ما قبلها
+
+298
+00:26:00,820 --> 00:26:03,220
+و اللي هو الساكنة المضمون ما قبلها و اللي هي 
+
+299
+00:26:03,220 --> 00:26:07,820
+ال ساكنة المكسورة ما قبلها تقفأ؟ لأن مخرجها واسع 
+
+300
+00:26:07,820 --> 00:26:12,240
+وليس لها حيز تنتهي إليه بل انتهاءه بانتهاء النفس
+
+301
+00:26:12,240 --> 00:26:18,100
+ولأنها ممكن تقفأ إذا أعطيت حركة نقول وضحا فلابد أن
+
+302
+00:26:18,100 --> 00:26:24,340
+نعطيها حركتين نقول وضحا والليل إذا سجا وهكذا باقي
+
+303
+00:26:24,340 --> 00:26:30,150
+حروف المد الثلاثة أما بالنسبة للهاء فهي تُخفى أيضًا
+
+304
+00:26:30,150 --> 00:26:36,130
+لأن حروف صفاتها كلها ضعيفة و لأن حرف الهاء حرف ضعيف 
+
+305
+00:26:36,130 --> 00:26:40,990
+لا تكفي أن نعطيه حركة ممكن يُخفى فلابد أن نحقق
+
+306
+00:26:40,990 --> 00:26:46,610
+الهاء يعني حتى أحيان التال مربوطة لو وقفنا عليها
+
+307
+00:26:46,610 --> 00:26:53,870
+بتصبح إيه؟ تصبح هاء يعني مثلًا نعمة، رحمة، حكمة،
+
+308
+00:26:53,870 --> 00:27:01,020
+ماذا نقول؟ نعمة، رحمة، حكمة، فلو واحد مثلا قال نعمة،
+
+309
+00:27:01,020 --> 00:27:05,660
+رحمة، حكمة، كأنه الميم والعين مفتوحة، يعني مثلا
+
+310
+00:27:05,660 --> 00:27:13,630
+نعمة هي أصلا نعمة ده أحقق الهاء نعمة طيب لو واحد
+
+311
+00:27:13,630 --> 00:27:17,810
+أسرع فقال نعمة بس عبارة عن ن و أ و م و على 
+
+312
+00:27:17,810 --> 00:27:24,310
+الميم فاتحة إذا أسرع في الهاء أخفيها رحمة بيصير رحمة
+
+313
+00:27:24,310 --> 00:27:29,950
+لو أسرع فيها بيصير رحمة عبارة عن ميم عليها فتحة
+
+314
+00:27:29,950 --> 00:27:36,630
+حكمة هي أصلا حكمة التي لو وقفنا عليها تبدأ إلى هـ
+
+315
+00:27:36,630 --> 00:27:44,370
+فبتقرأ حكمة ونحقق الهاء لو واحد قصها إيش يصير؟ حكمة
+
+316
+00:27:44,370 --> 00:27:48,690
+يعني كأنها الميم يعني عليها فتحة إذا هذه الخفقة
+
+317
+00:27:48,690 --> 00:27:52,510
+تُخفى إذا ما هي الحروف التي تُخفى؟ حروف المادية
+
+318
+00:27:52,510 --> 00:27:56,470
+الثلاثة يا أخوات زائد حرف الهاء لماذا تُخفى حروف 
+
+319
+00:27:56,470 --> 00:28:02,550
+المادية الثلاثة؟ لأن مخرجها واسع لا تكفيها حركة بل
+
+320
+00:28:02,550 --> 00:28:09,660
+نعطيها حركتين فنقول وضحا سجى وغير ذلك من الكلمات
+
+321
+00:28:09,660 --> 00:28:16,620
+بالنسبة لحرف الهاء الهاء أيضا صفاتها كلها ضعيفة لذلك
+
+322
+00:28:16,620 --> 00:28:21,020
+ممكن أن يُخفى بسهولة فحتى إذا جاءت في آخر كلمة
+
+323
+00:28:21,020 --> 00:28:28,760
+لابد أن نحققها فنقول نعمة حكمة رحمة طيب صفة الخفاء
+
+324
+00:28:28,760 --> 00:28:34,570
+يا أخوات هل هي صفة قوة ولا صفة ضعف؟ صفة الخفاء يا 
+
+325
+00:28:34,570 --> 00:28:38,970
+أخوات صفة ضعف، الخفاء صفة ضعف و كذلك الـ lean اللي 
+
+326
+00:28:38,970 --> 00:28:43,250
+أخذنا صفة ضعف، هدول الصفتين بس صفة الخفاء و صفة الـ
+
+327
+00:28:43,250 --> 00:28:48,670
+lean هما الصفتين الضعيفتين في الصفات الغير متضادة
+
+328
+00:28:48,670 --> 00:28:54,670
+و ليس لها ضد طبعا طيب صفة الخفاء يعني الهاء هذه
+
+329
+00:28:54,670 --> 00:28:58,410
+إذا وقعت بين .. يعني في نهاية الكلمة و وقعت بين
+
+330
+00:28:58,410 --> 00:29:04,320
+حرفين متحركين تمدتُعطى .. لو كان .. ممكن تُمدها و
+
+331
+00:29:04,320 --> 00:29:08,860
+تسميها مادّة صلة صغرى إذا وقعت حرف الهاء بين حرفين
+
+332
+00:29:08,860 --> 00:29:14,700
+متحركين ولم يكن المتحرك الثاني همزة من سمي صلة ..
+
+333
+00:29:14,700 --> 00:29:22,560
+مادّة صلة صغرى مثال ذلك بلى إن ربه كان به بصيرة هنا
+
+334
+00:29:22,560 --> 00:29:28,880
+بلى إن ربه الهاء هنا بتاعة ربه وقعت أخوات بين إيه؟ 
+
+335
+00:29:29,020 --> 00:29:34,740
+بين حرفين متحركين حرف الـ ب مفتوح و حرف الـ ك مفتوح
+
+336
+00:29:34,740 --> 00:29:40,460
+بيتولد عن حركة الهاء و أو مادية لو كانت مضمومة هنا
+
+337
+00:29:40,460 --> 00:29:46,700
+الـ ه عليها ضمة ولا فتحة ولا كسرة؟ ضمة فمنشبع الضمة
+
+338
+00:29:46,700 --> 00:29:50,800
+منشبع يعني بنعطيها حركتين يعني بيتولد عنها و أو 
+
+339
+00:29:50,800 --> 00:29:58,110
+مادية فنقول بلى إن ربه كان .. ربه كانما يمكن نقول
+
+340
+00:29:58,110 --> 00:30:03,030
+ربه كان .. ما يمكن نقول بلى إن ربه كان .. لو قلنا
+
+341
+00:30:03,030 --> 00:30:10,110
+ربه كان .. حرف الهاء اختفت والواو اللي بتولد عن
+
+342
+00:30:10,110 --> 00:30:15,330
+حرف الواو أيضا اختفت .. اختفت لذلك ربه كان به
+
+343
+00:30:15,330 --> 00:30:21,050
+بصيرة كذلك حرف الـ .. الهاء في به بلى إن ربه كان
+
+344
+00:30:21,050 --> 00:30:25,710
+به بصيرة الهاء في به .. أيش الحركة اللي عليها يا 
+
+345
+00:30:25,710 --> 00:30:30,860
+أخوانك؟ كسرة فالكسرة نشبع الكسرة طبعا وقعت لها
+
+346
+00:30:30,860 --> 00:30:35,360
+متحركة بين حرفين متحركين اللي هي الـ ب و الـ ب الـ ب
+
+347
+00:30:35,360 --> 00:30:40,820
+الأولى مكسورة به و الباء الثانية مفتوحة نشبع 
+
+348
+00:30:40,820 --> 00:30:47,160
+الكسرة فنعطيها حركتين بتسيريا فنقول به بصيرة هذا
+
+349
+00:30:47,160 --> 00:30:50,560
+لو كان اللي هو مادة الصلة الصغرى أما إذا كان
+
+350
+00:30:50,560 --> 00:30:57,520
+المتحرك الثاني بدل حرف الباء وضعنا همزة بتصير بهي و
+
+351
+00:30:57,520 --> 00:31:00,840
+وراها همزة .. يعني زي مثلا بيشبه المد الجاز
+
+352
+00:31:00,840 --> 00:31:05,140
+المنفصل، من مده من أربعة إلى خمس حركات و بنسميه
+
+353
+00:31:05,140 --> 00:31:11,280
+مدّ صلة كبرى، هن مدّ صلة صغرى، لكن في قوله تعالى يحسب
+
+354
+00:31:11,280 --> 00:31:18,980
+أنّ ما له أخلاده، ما له أخلاده، هنا بنجد يا أخوات
+
+355
+00:31:18,980 --> 00:31:25,180
+أنّ حرف الـ ه عليه ضمة وأشبعنا الضمة يعني أعطناها 
+
+356
+00:31:25,180 --> 00:31:31,300
+حركتين فصارت الضمة واو ولما وقعت الواو ربه أو
+
+357
+00:31:31,300 --> 00:31:37,000
+ما له ووراها حرف الهمزة صار في عندنا كأنها مدّ
+
+358
+00:31:37,000 --> 00:31:42,040
+جائز منفصل فمنمدها من أربع إلى خمس حركات و بنقول
+
+359
+00:31:42,040 --> 00:31:47,940
+يحسبوا أنّ ما له أخلاده و بنسميها اسم ما هو اسم 
+
+360
+00:31:47,940 --> 00:31:55,130
+المدّ في هذه الحالة؟ ممتازة مدّ صلة كبيرة وصفة الخفاء
+
+361
+00:31:55,130 --> 00:31:59,570
+احنا قلنا هي صفة ضعف آخر صفة يا أخوات من الصفات 
+
+362
+00:31:59,570 --> 00:32:05,910
+التي ليس لها ضد هي صفة الغنّة والغنّة هو صوت له
+
+363
+00:32:05,910 --> 00:32:10,610
+رنين يخرج من الخيشوم، يعني صوت أغنية له رنين يخرج
+
+364
+00:32:10,610 --> 00:32:15,530
+من الخيشوم مقداره حركتين ولا عمل لللسان به، وهي
+
+365
+00:32:15,530 --> 00:32:21,010
+صفة ملازمة لحرفين الميم والنون، إذا من يعرف لنا 
+
+366
+00:32:21,010 --> 00:32:26,870
+الغنّة يا أخوان؟ تفضلي هو صوت أغنية يخرج من الخيشوم
+
+367
+00:32:26,870 --> 00:32:32,140
+مقداره حركتين لعمل اللسان أحسنتي هو صوت أغنية يخرج
+
+368
+00:32:32,140 --> 00:32:37,600
+من الخشوم مقداره حركتين لا عمل لللسان به وهو صفة
+
+369
+00:32:37,600 --> 00:32:42,940
+ملازمة لحرفي الميم والنون ماذا نعني بقولنا لا عمل 
+
+370
+00:32:42,940 --> 00:32:49,020
+لللسان به؟ يعني واحد ممكن يغلق فمه ويغنّي في الغنّة
+
+371
+00:32:49,020 --> 00:32:56,070
+فلما .. فأنا قلت فلمّا أغلقت الفم، يعني العقل، الآن
+
+372
+00:32:56,070 --> 00:33:00,310
+لأعمل لسان به، وخرجت صفة الغنّة من الخيشوم لأنها
+
+373
+00:33:00,310 --> 00:33:04,290
+صفة ملازمة لحرف الميم، وش كمان؟ وحرف النون، مثلا
+
+374
+00:33:04,290 --> 00:33:12,240
+إنّ إن الله وملأيكته إنّ أيضًا لا عمل 
+
+375
+00:33:12,240 --> 00:33:16,440
+لللسان به والصوت كله بيخرج من الخشوم إذا صفة
+
+376
+00:33:16,440 --> 00:33:22,240
+الغنّة هي صوت أغنية مركّم في جسمه يعني صوت أغنية
+
+377
+00:33:22,240 --> 00:33:27,160
+بيخرج من الخشوم مقدره حركتين وهو لا عمل اللسان به
+
+378
+00:33:27,160 --> 00:33:33,960
+وهو صفة ملازمة لحرفي الميم والنون حروف الغنّة اللي 
+
+379
+00:33:33,960 --> 00:33:38,240
+هي الميم والنون في جميع أحوالها ولكن أكثر شيء 
+
+380
+00:33:38,240 --> 00:33:44,040
+بيكون في الميم والنون المشددتين أو المضغمتين ومن
+
+381
+00:33:44,040 --> 00:33:49,400
+هنا نقول في عندنا غنّة قوية جدًا وغنّة أضعف وأضعف و
+
+382
+00:33:49,400 --> 00:33:55,400
+أضعف وهو ما يسمى بمراتب الغنّة فما هي مراتب الغنّة
+
+383
+00:33:55,400 --> 00:33:59,730
+يا أخواتي؟ أربع مراتب المراتب الأولى وهي أقوى
+
+384
+00:33:59,730 --> 00:34:04,930
+المراتب وهو الميم والنون المشددتين وصلًا ووقفًا
+
+385
+00:34:04,930 --> 00:34:13,410
+وهي أوضاع .. يعني أقوى المراتب الغنّة مثال ذلك إنّ
+
+386
+00:34:13,410 --> 00:34:21,460
+أو فلم أو إنما فالغنّة إيش فيها يا أخوات؟ بينة في
+
+387
+00:34:21,460 --> 00:34:28,340
+النون والميم المشددتين وهي أقوى مراتب الغنّة و
+
+388
+00:34:28,340 --> 00:34:33,280
+يلحق بها كذلك الإضغام يعني عندما يضغم الميم مع 
+
+389
+00:34:33,280 --> 00:34:41,660
+الميم مثل ولهم يشتهون .. لهم .. الميم مع الميم
+
+390
+00:34:41,660 --> 00:34:45,940
+يعني أضغمت الميم الساكنة بالميم المتحركة فصاروا
+
+391
+00:34:45,940 --> 00:34:51,420
+كأنهم ميمًا واحدة مشددة يعني ميم مشددة أقوى أنواع
+
+392
+00:34:51,420 --> 00:34:59,260
+الغنّة كذلك وما بكم من نعمة هنا وما بكم من نعمة
+
+393
+00:34:59,260 --> 00:35:03,180
+فيها عندنا إدغامين أيضًا الإدغامين يا أخوات الميم
+
+394
+00:35:03,180 --> 00:35:07,280
+والميم إدغام شفوي؟ أيوة الميم مع الميم وما بكم 
+
+395
+00:35:07,280 --> 00:35:13,540
+من هنا في عندنا إدغام شفوي وبعدين من نعمة النون
+
+396
+00:35:13,540 --> 00:35:19,590
+والنون أيضًا إدغام بغنة وبالتالي هو إدغام أضغمها
+
+397
+00:35:19,590 --> 00:35:23,090
+الحرف الأول في الحرف الثاني بحيث يصيراني حرفا
+
+398
+00:35:23,090 --> 00:35:27,470
+واحدة مشددة وبالتالي هذا صار حرف النون مشدد أو
+
+399
+00:35:27,470 --> 00:35:30,690
+الميم المشدد ناتج عن الإضغام سواء كان إضغام شفوي
+
+400
+00:35:30,690 --> 00:35:37,470
+ولا إضغام غنّي هذه المرتبة الأولى وهي الميم والنون
+
+401
+00:35:37,470 --> 00:35:44,200
+المشددتين أو الميم .. مع الميم إضغام ب .. شفوي 
+
+402
+00:35:44,200 --> 00:35:48,700
+أو النون مع النون إضغام أيضًا ب .. بغنة هذه المرتبة 
+
+403
+00:35:48,700 --> 00:35:52,300
+الأولى وهي أقوى أنواع المراتب يعني أقوى مرتبة
+
+404
+00:35:53,010 --> 00:35:56,790
+المرتبة التي تليها يا أخوات هي مرتبة أقل منها وهي
+
+405
+00:35:56,790 --> 00:36:01,150
+غنّة الميم الساكنة أو التنوين عندما أو عند إضغامها
+
+406
+00:36:01,150 --> 00:36:06,310
+بالواو والياء إضغام بغنة اسمه ولكن ليس مثل المرتبة 
+
+407
+00:36:06,310 --> 00:36:10,370
+الأولى اللي هي مرتبة الميم والنون المشددتين مثال
+
+408
+00:36:10,370 --> 00:36:15,770
+ذلك أن تضغم النون مع الياء أو الواو فنقول هنا من 
+
+409
+00:36:15,770 --> 00:36:19,130
+يأتي بالمثال على الإضغام اللي بغنة مع الواو أو
+
+410
+00:36:19,130 --> 00:36:22,470
+الياء؟ ميموال
+
+411
+00:36:22,730 --> 00:36:30,230
+ميموال أو ميموال ميموال هنا أضغمة النون مع الواو
+
+412
+00:36:30,230 --> 00:36:37,050
+فنقول ميموال من يعرف لنا الإضغام يا أخوان؟ إدخال 
+
+413
+00:36:37,050 --> 00:36:42,990
+حرف ساكن لحرف متحرك لحييط يسيران حرفا واحدة مشددة
+
+414
+00:36:42,990 --> 00:36:48,410
+من جنس ثاني فعندما أضغمنا النون مع الواو يعني
+
+415
+00:36:48,410 --> 00:36:55,310
+أضغمة النون كلها بالواو وتقرأ ميموال يعني الذي يلفظ
+
+416
+00:36:55,310 --> 00:36:59,530
+حرف الواو المشدد مع مراعاة الغنّة لأن الغنّة هي 
+
+417
+00:36:59,530 --> 00:37:03,770
+بيسمّوه إدغام ناقص بيدخل نصف النون ذات النون وتبقى
+
+418
+00:37:03,770 --> 00:37:08,290
+صفات الغنّة موجودة فيها كذلك ما يعمل أيضًا النون
+
+419
+00:37:08,290 --> 00:37:14,030
+أدخلت وأضغمت في الياء فصار عندنا إدغام بغنة وهذا هي 
+
+420
+00:37:14,030 --> 00:37:18,690
+المرتبة الثانية ننتقل لمرتبة الثالثة يا أخوات هي 
+
+421
+00:37:18,690 --> 00:37:23,510
+الغنى الناتج عن إخفاء النون الساكنة أو التنوين
+
+422
+00:37:23,510 --> 00:37:27,390
+محروف الإخفاء ما هي حروف الإخفاء؟ مين ذاكر حروف
+
+423
+00:37:27,390 --> 00:37:33,620
+الإخفاء يا أخوات؟ حرف الإخفاء مجموعة في قوله صف ده
+
+424
+00:37:33,620 --> 00:37:38,980
+ثنى، كم جاد شخص قد سمى دم طيبا زد في تخن ضع ضلمة،
+
+425
+00:37:38,980 --> 00:37:44,840
+كم حرف هذه؟ خمس عشرة حرفا حرف النون أو التنوين
+
+426
+00:37:44,840 --> 00:37:48,380
+إذا جاء بعده أي حرف من حروف هذا البيت اللي هي
+
+427
+00:37:48,380 --> 00:37:53,540
+حروف الإخفاء يعني تخفى، يعني وهي أعطاه صفة للنون ما
+
+428
+00:37:53,540 --> 00:37:58,000
+بين الإضغام والإظهار مع مراعاة الغنى، ولكن الغنى
+
+429
+00:37:58,000 --> 00:38:01,340
+اللي فيه بتكون مرتبتها مرتبة إيه يا أخوات؟ مرتبة
+
+430
+00:38:01,340 --> 00:38:04,880
+ثالثة، مثال ذلك مثلًا الإنسان
+
+431
+00:38:06,610 --> 00:38:12,290
+الإنسان، نوّف وراسين، إيش الحكم هنا؟ إخفاء حقيقي،
+
+432
+00:38:12,290 --> 00:38:17,010
+إخفاء حقيقي، نقول الإنسان، فيها غنة ولا ما فيها
+
+433
+00:38:17,010 --> 00:38:24,270
+غنة؟ فيها غنة، الإنسان، كذلك وقضي بينهم بالحق، هنا
+
+434
+00:38:24,270 --> 00:38:28,070
+ميم ساكنة وراها حرف الباء، ويكون فيه عندنا إخفاء
+
+435
+00:38:28,070 --> 00:38:33,110
+شهوي، نقول وقضي بينهم بالحق، فيها إخفاء، ولكن من
+
+436
+00:38:33,110 --> 00:38:37,590
+الترتيب... بيكون الترتيب رقمها رقم؟ ثلاتة أو وقود
+
+437
+00:38:37,590 --> 00:38:42,390
+يبينهم بالحق تعريفهم بسماه وهكذا آخر مرتبة من
+
+438
+00:38:42,390 --> 00:38:47,210
+المراتب الغنى وهي المرتبة الرابعة وهي غنة أو الغنى
+
+439
+00:38:47,210 --> 00:38:51,430
+الظاهرة غنة النون الساكنة أو التنوين حال الإظهار
+
+440
+00:38:51,430 --> 00:38:56,030
+أو الميم الساكنة أيضًا حال الإظهار مثال ذلك يعني
+
+441
+00:38:56,030 --> 00:39:06,150
+ينأون ينهون أو ألم ترا ألم تراميم وراها حرف التاء فيها
+
+442
+00:39:06,150 --> 00:39:11,030
+إظهار إيش اسمه؟ إظهار شفوي لكن عندما أقول ألم ترا
+
+443
+00:39:11,030 --> 00:39:15,670
+فيها أصل الغنى وكذلك الميم المتحركة أو النون
+
+444
+00:39:15,670 --> 00:39:20,150
+المتحركة فيها أصل الغنى ألم ترا يعني ليس... يعني
+
+445
+00:39:20,150 --> 00:39:26,210
+لا نقول مثلًا ألم ترا لنقولها كذا إنما تلفظ بشكل
+
+446
+00:39:26,210 --> 00:39:31,350
+سريع ألم ترا أظهرنا ال... الميم وأخرجنا الميم من
+
+447
+00:39:31,350 --> 00:39:37,290
+مخرجها كذلك النون في قوله مثلًا ينأون... ينهون
+
+448
+00:39:37,290 --> 00:39:42,010
+أيضًا في عندنا إظهار... إظهار حلقي وهي مرتبة...
+
+449
+00:39:42,010 --> 00:39:45,430
+مرتبتها مرتبة رابعة الثلاتة... المرتبة الثالثة
+
+450
+00:39:45,430 --> 00:39:49,030
+الأولى يا أخوتي هي فيها غنى واضحة وتسمى مرتبة
+
+451
+00:39:49,030 --> 00:39:53,330
+الكمال في الغنى أما المرتبة الرابعة سواء كانت
+
+452
+00:39:53,330 --> 00:39:58,270
+النون أو الميم المظهرتين أو المتحركتين هي فيها أصل
+
+453
+00:39:58,270 --> 00:40:05,130
+الغنى طبعًا فينا خلصنا الآن الصفات كلها... آه...
+
+454
+00:40:05,130 --> 00:40:08,590
+الآن بس نمر سريعًا على الصفات القوية والضعيفة احنا
+
+455
+00:40:08,590 --> 00:40:13,050
+أظهرناهم لوحدنا أولًا بأول مثلًا الصفات القوية هي
+
+456
+00:40:13,050 --> 00:40:16,970
+صفة الجهر والشدة والاستعلاء والإطباق والصفير
+
+457
+00:40:16,970 --> 00:40:21,110
+والقلقلة والانحراف والتكرير والتفشي والاستطالة
+
+458
+00:40:21,110 --> 00:40:25,090
+والغنى هذه الصفات كلها من العشرين صفة يعني احنا
+
+459
+00:40:25,090 --> 00:40:29,770
+خلصنا يا أخوات الآن كم صفة؟ عشرين صفة الصفات
+
+460
+00:40:29,770 --> 00:40:34,870
+الصفات القوية الصفات الضعيفة هي الهمس والرخاوة
+
+461
+00:40:34,870 --> 00:40:39,250
+والاستفال والانفتاح والنّين والخفاء وفي عندنا صفات
+
+462
+00:40:39,250 --> 00:40:43,970
+متوسطة لا تحسب لا مع القوية ولا مع الضعيفة اللي هي
+
+463
+00:40:43,970 --> 00:40:48,670
+صفة الإذلاق والإصغاء والتوسط هذه لا تحسب لا 
+
+464
+00:40:48,670 --> 00:40:51,690
+بالضعيفة ولا بالقوية في عندنا كذلك حروف احنا لو
+
+465
+00:40:51,690 --> 00:40:56,350
+بدنا نتعرف على مخرج حرف أو صفة حرف من الحروف بنشوف
+
+466
+00:40:56,350 --> 00:41:00,970
+ما هي الصفات الموجودة مثلًا في حرف الألف مثلًا حلق
+
+467
+00:41:00,970 --> 00:41:06,530
+الصفات اللي في حرف الألف هل هي همس ولا جهر؟ حلق
+
+468
+00:41:06,530 --> 00:41:11,990
+فيها همس أم نكتب همسة هل هي شدة ولا رخاوة ولا توسط
+
+469
+00:41:11,990 --> 00:41:16,410
+في حرف الفاء؟ هنلاقيها رخاوة، طيب؟ هل هي استعلاء
+
+470
+00:41:16,410 --> 00:41:20,530
+ولا استفال؟ استفال هنلاقيها استفال، هنلاقي فيها همس
+
+471
+00:41:20,530 --> 00:41:25,310
+ورخاوة واستفال؟ ضعيفة، هل... نشوف كمان، هل فيها
+
+472
+00:41:25,310 --> 00:41:30,820
+إطباق ولا انفتاح؟ هنلاقيها انفتاح، هي صفة الانفتاح،
+
+473
+00:41:30,820 --> 00:41:35,280
+هل هي إذلاق ولا إصمات؟ هنلاقيها اذلاق، لأنه فرح...
+
+474
+00:41:35,280 --> 00:41:38,840
+فرح عرفت فات، main لغة، إذن الصفات اللي في الألف
+
+475
+00:41:38,840 --> 00:41:43,400
+عشان نحسبها، عندنا صفات ال... الهمس والرخاوة
+
+476
+00:41:43,400 --> 00:41:49,880
+والانفتاح وال... والاستفال والإذلاق، وجميع هذه
+
+477
+00:41:49,880 --> 00:41:54,400
+الصفات صفات ضعيفة والانفتاح وال... أقصد الإذلاق
+
+478
+00:41:54,400 --> 00:42:00,230
+صفة متوسطة إذن حرف الألف ضعيف جدًا لأن جميع الصفات
+
+479
+00:42:00,230 --> 00:42:05,950
+ضعيفة نشوف مثلًا حرف الطاء... حرف الطاء... احنا بنكون
+
+480
+00:42:05,950 --> 00:42:11,930
+حافظين الصفات العشرين حرف الطاء... هل هو حرف من صفة
+
+481
+00:42:11,930 --> 00:42:18,820
+the hence ولا جهر؟ هنلاقي جهر حرف الطاء فيه شدة ولا
+
+482
+00:42:18,820 --> 00:42:24,460
+رخاوة ولا توسط؟ هنلاقي الطاء فيها شدة حرف الطاء فيه
+
+483
+00:42:24,460 --> 00:42:27,980
+استعلاء تقص ضغط قذر ولا استفال باقي الحروف؟
+
+484
+00:42:27,980 --> 00:42:33,440
+هنلاقي استعلاء، هنلاقي عنه، اللي هو جهر وشدة و
+
+485
+00:42:33,440 --> 00:42:37,720
+استعلاء، هل هو انفتاح ولا إطباق، صدر، طهضة،
+
+486
+00:42:37,720 --> 00:42:41,660
+إطباق، هل هو إذلاق ولا إصلاق؟ إيه اللي هو إيه؟
+
+487
+00:42:41,660 --> 00:42:46,080
+إصمات طيب في كمان صفات من الصفات المتضادة، هل هو
+
+488
+00:42:46,080 --> 00:42:52,900
+صفير؟ لا، قلقلة؟ قطب جد؟ قلقلة إيش كمان في عندنا؟
+
+489
+00:42:52,900 --> 00:42:56,180
+فيش... فيش عندنا لا تفشي ولا أي شيء إذن في قلقلة
+
+490
+00:42:56,180 --> 00:43:01,300
+وفي الخمس صفات الشدة والقوية... إذن كلهم... كل
+
+491
+00:43:01,300 --> 00:43:05,840
+صفات حرف الطاء قوية عشان هيك... بنعتبر يا أخوات إن
+
+492
+00:43:05,840 --> 00:43:12,440
+في عندنا صفات كلها يعني حروف كل صفات قوية ومن سوي
+
+493
+00:43:12,440 --> 00:43:18,340
+... منسميه قوي جدًا وهذا متوفر في حرف الطاء والضاد و
+
+494
+00:43:18,340 --> 00:43:22,480
+الظاء والقاف كل الحروف أو كل الصفات اللي فيه صفات
+
+495
+00:43:22,480 --> 00:43:27,300
+قوية... نسميها قوية جدًا وفي عندنا صفات ضعيفة جدًا
+
+496
+00:43:27,300 --> 00:43:31,440
+لأن كل الصفات اللي فيها إيه ضعيفة مثل حرف الثاء
+
+497
+00:43:31,440 --> 00:43:38,430
+والحاء والواو والهاء وفي عندنا حروف متوسطة يعني... يعني
+
+498
+00:43:38,430 --> 00:43:42,370
+فيها... فيها ضعف وفيها قوة مثل حرف الهمزة والغين
+
+499
+00:43:42,370 --> 00:43:46,150
+واللام والميم والنون وفي عندنا حروف قوية يعني
+
+500
+00:43:46,150 --> 00:43:49,970
+صفات القوة أكثر من صفات الضعف مثل حرف الجيم والإدغام 
+
+501
+00:43:49,970 --> 00:43:53,470
+والدال وفي عندنا حروف ضعيفة يعني صفات الضعف أكثر
+
+502
+00:43:53,470 --> 00:43:58,740
+من صفات القوة آخر شيء عندنا عشان ننهي بعض الحروف يا
+
+503
+00:43:58,740 --> 00:44:03,420
+أخوات... بعض الحروف... بعض الناس بيلفظها غلط مثلها
+
+504
+00:44:03,420 --> 00:44:09,400
+ذلك حرف الألف بيلفظ... بيلفظ فا فيقول أفضل
+
+505
+00:44:09,400 --> 00:44:14,760
+فلان أفضل من فلان لا نقول أفضل هي أفضل... أفضل
+
+506
+00:44:14,760 --> 00:44:20,880
+كذلك حرف الصّاد بعض الناس بيلفظ اس يقول يصدر مش
+
+507
+00:44:20,880 --> 00:44:26,760
+يصدر هي يصدر حرف الصّاد كذلك حرف ال... الاس أو ال
+
+508
+00:44:26,760 --> 00:44:32,290
+gene السين يُرفض ببعض الكلمات as عند الناس، يقول as
+
+509
+00:44:32,290 --> 00:44:36,410
+you do... as you do، مش as you do، هي as you do،
+
+510
+00:44:36,410 --> 00:44:42,630
+حرف السين يُرفض as، حرف الدال... يُرفض حرف التاء
+
+511
+00:44:42,630 --> 00:44:48,420
+دال، يقول مداعهي أصلًا متاع، متاع بالـ taa وليس مذاع
+
+512
+00:44:48,420 --> 00:44:55,120
+حرف التاء بيلفظه بعض الناس السيء اس كذلك ذلك
+
+513
+00:44:55,120 --> 00:45:01,420
+بيلفظ أحيانًا ذلك، ده خطأ جاء بيلفظ جاء وجاء رجل
+
+514
+00:45:01,420 --> 00:45:07,340
+خطأ طبعًا هذا قال ممكن يلفظ كان أنا كنتله مثلًا بعض
+
+515
+00:45:07,340 --> 00:45:14,000
+الخبائث عندنا القرى حرف القاف بيلفظ ك... أو حتى بعض
+
+516
+00:45:14,000 --> 00:45:18,420
+الناس بيقول قاله بدل من أن يقول قاله يقول قاله هو
+
+517
+00:45:18,420 --> 00:45:22,300
+اللي قال وأنا قلت له وهو اللي قال لي طبعًا هذا خطأ
+
+518
+00:45:22,300 --> 00:45:28,360
+كذلك حرف ال... ال... ده بيلفظظاه ولا الظالمين وهذا
+
+519
+00:45:28,360 --> 00:45:33,160
+طبعًا بيكون إيش خطأ احنا أنهينا الآن كل المخارج
+
+520
+00:45:33,160 --> 00:45:36,080
+والصفات ونكتفي بهذا القدر ونكون إن شاء الله في
+
+521
+00:45:36,080 --> 00:45:38,640
+الموضوع الآخر في اللقاء القادم بارك الله فيكم
+
+522
+00:45:38,640 --> 00:45:41,200
+جميعًا السلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/nbN9rguMoGc_raw.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/nbN9rguMoGc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..57c3546adbeecdeae2dbd6e2084c3a6a04aee597
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/nbN9rguMoGc_raw.srt
@@ -0,0 +1,2096 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,950 --> 00:00:14,710
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+3
+00:00:14,710 --> 00:00:19,370
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+4
+00:00:19,370 --> 00:00:23,310
+آله وصحبه وسلم أخذنا يا أخوات في المحاضرة الماضية
+
+5
+00:00:23,310 --> 00:00:28,930
+الصفات التي ليس لها ضد يعني غير المتضادة أخذنا صفة
+
+6
+00:00:28,930 --> 00:00:33,460
+الصفير وأخذنا صفة القلقلةبقى علينا العديد من
+
+7
+00:00:33,460 --> 00:00:38,920
+الصفات الغير متضادة و هي صفة اللين و صفة الانحراف
+
+8
+00:00:38,920 --> 00:00:43,220
+و التكرير و الاستطالة و التفشي و الغنى و الخفاء
+
+9
+00:00:43,220 --> 00:00:46,900
+عدة صفات هناخدها ان شاء الله في هذه المحاضرة
+
+10
+00:00:46,900 --> 00:00:51,310
+فالمحاضرة هذه استكملالمحاضرة الصفات غير المتضادة
+
+11
+00:00:51,310 --> 00:00:56,710
+واخدنا قبل ذلك الصفات المتضادة اللي هي ال .. الهمس
+
+12
+00:00:56,710 --> 00:01:00,410
+ضدها الجهر والشدة ضدها الرخاوة وبينهم التوسط
+
+13
+00:01:00,410 --> 00:01:04,110
+والاستعلاء وضده الاستفال والاطلاق وضده الانفتاح
+
+14
+00:01:04,110 --> 00:01:09,170
+والاذلاق وضده الاصمت أما بالنسبة للصفير فهو ..
+
+15
+00:01:09,170 --> 00:01:13,920
+يعني من يعرف لنا الصفير؟انحصار الصوت بين طرف
+
+16
+00:01:13,920 --> 00:01:20,120
+اللسان وفوائق الثانية وما هي حروف الصفير يا أخوات؟
+
+17
+00:01:20,120 --> 00:01:26,700
+الصين و الصارت و الزهر نقول اس أس از طب صفة الصفير
+
+18
+00:01:26,700 --> 00:01:32,810
+هل هي صفة قوة ولا صفة ضعف؟صفة قوة ممتاز صفة قوة
+
+19
+00:01:32,810 --> 00:01:38,410
+الصفة الثانية وهي صفة القلقلة القلقلة هي اضطراب
+
+20
+00:01:38,410 --> 00:01:43,050
+المخرج عند النطق بأحد حروف القلقلة حتى يبدو له
+
+21
+00:01:43,050 --> 00:01:49,110
+نبرة قوية ما هي حروف القلقلة؟ مجموعة في قوله قطب
+
+22
+00:01:49,110 --> 00:01:55,040
+جد كام حرف؟خمسة أحرف قطة باجيم ذان أي حرف من هذه
+
+23
+00:01:55,040 --> 00:01:58,960
+الحروف إذا عرضنا أن ننطقها سواء كانت ساكنة أو
+
+24
+00:01:58,960 --> 00:02:05,640
+مشددة متطرفة ولا متوسطة بنسميها قلقلة نقول مثلا
+
+25
+00:02:05,640 --> 00:02:11,380
+الحق في النبرة هذه تسمى قلقلة وأخدناها في المحاضرة
+
+26
+00:02:11,380 --> 00:02:16,280
+الماضية و القلقلة بسبب يعني اجتماع صفتي الشدة
+
+27
+00:02:16,280 --> 00:02:20,000
+والجهر صفة الشدة يعني نقولنا ما هي سبب القلقلة
+
+28
+00:02:21,190 --> 00:02:25,950
+اجتماع صفتي الشدة والجهر في الحرف فالشدة فيها
+
+29
+00:02:25,950 --> 00:02:31,130
+انحباس الصوت والجهر فيها انحباس النفس عندما ننطق
+
+30
+00:02:31,130 --> 00:02:36,950
+بحرف القلق ده قطب جد إب نجد أن الصوت ينحبس والنفس
+
+31
+00:02:36,950 --> 00:02:45,980
+ينحبس فتبدو بعد ذلك له نبرة قوية نقول إب إد أقالط
+
+32
+00:02:45,980 --> 00:02:49,980
+.. هذه الحروف اللي هي مجموعة في قوله خطوب جد وسبب
+
+33
+00:02:49,980 --> 00:02:54,140
+القلقلة ايش دي معاه صفتي الشدة والجهد؟ والقلقلة
+
+34
+00:02:54,140 --> 00:02:58,880
+تنقسم إلى كام قسم؟ تلات أقسام، القسم الأول هي
+
+35
+00:02:58,880 --> 00:03:03,420
+القلقلة الصغرة، والثاني قلقلة كبرى، والثاني
+
+36
+00:03:03,420 --> 00:03:07,060
+القلقلة أكبر، من يأتي بمثل على القلقلة الصغرة
+
+37
+00:03:09,390 --> 00:03:16,430
+مقتدرة مقتدرة سبحان المجرمون .. المجرمون حرف الجين
+
+38
+00:03:16,430 --> 00:03:21,230
+فيها قلقلة ولكن قلقلة صغيرة سبحان البافية قلقلة
+
+39
+00:03:21,230 --> 00:03:26,450
+ولكن قلقلة صغيرة مقتدرة القاف فيها قلقلة ولكنها
+
+40
+00:03:26,450 --> 00:03:29,590
+قلقلة صغيرة القسم الثاني من أنواع .. من أقسم
+
+41
+00:03:29,590 --> 00:03:33,430
+القلقلة هي القلقلة الكبرى وهو إذا جاء أحد حروف
+
+42
+00:03:33,430 --> 00:03:39,820
+القلقلة ساكن متطرفأو متطرف الكلمة موقوف عليه نقول
+
+43
+00:03:39,820 --> 00:03:47,480
+مثلا قل أعوذ برب الفلقق قل هو الله أحد البروج محيط
+
+44
+00:03:47,480 --> 00:03:52,060
+فهذه قلقلة بنسميها كبرى لإنه جاء أحد حروف القلقلة
+
+45
+00:03:52,060 --> 00:03:58,440
+ساكن متطرف موقوف عليه يسمى قلقلة كبرى طيب القسم
+
+46
+00:03:58,440 --> 00:04:03,680
+الثالث يا أخوات ما هي القلقلة الأكبركون ساكن أو مش
+
+47
+00:04:03,680 --> 00:04:07,160
+ساكن إذا كان .. إذا جاء أحد حروف القلقلة ساكن
+
+48
+00:04:07,160 --> 00:04:13,900
+سكونا مثقلا أو مشددا نفسه متطرف موقوف عليه يقلق
+
+49
+00:04:13,900 --> 00:04:18,940
+القلقلة كبرى من يأتي بمثال على ذلك؟ و تب .. تبت يا
+
+50
+00:04:18,940 --> 00:04:27,340
+ده أبي لهب و تب .. الحق .. الحج .. الحج فهذه كلها
+
+51
+00:04:27,340 --> 00:04:33,400
+عبارة عن قلقلة يعني أكبرأن هنا القلقلة و الأن
+
+52
+00:04:33,400 --> 00:04:38,700
+ننتقل إلى الصفة الثالثة من الصفات التي ليست لها ضد
+
+53
+00:04:38,700 --> 00:04:44,180
+وهي صفة اللين اللين يا أخوات هنا لغة شيء لين بمعنى
+
+54
+00:04:44,180 --> 00:04:49,140
+إيه سهل فاللين في اللغة السهولة وفي الإصطلاح هو
+
+55
+00:04:49,140 --> 00:04:54,880
+إخراج الحرف من مخرجه بسهولة و يسر من غير كلفة على
+
+56
+00:04:54,880 --> 00:04:59,960
+اللسانيعني الحرب بيخرج بسهولة بدون ما يكون في نوع
+
+57
+00:04:59,960 --> 00:05:06,120
+من الكلفة على اللسان وحروف اللين هما حرفان ال wow
+
+58
+00:05:06,120 --> 00:05:11,340
+و ال ya بس ال wow الساكنة المفتوح ما قبلها و ال ya
+
+59
+00:05:11,340 --> 00:05:16,020
+الساكنة المفتوح ما قبلهالأن لو قلنا الواو الياه،
+
+60
+00:05:16,020 --> 00:05:20,420
+هناك الواو المادية والياء المادية ليست من حروف
+
+61
+00:05:20,420 --> 00:05:25,640
+اللين، لأن حروف اللين فقط هما حرفان الواو الساكنة
+
+62
+00:05:25,640 --> 00:05:30,100
+المفتوح ما قبلها والياء الساكنة أيضًا المفتوح ما
+
+63
+00:05:30,100 --> 00:05:33,420
+قبلها، لو كانت الواو ساكنة مضمون ما قبلها، ماذا
+
+64
+00:05:33,420 --> 00:05:39,040
+نسميه يا أخوات؟الواو الساكنة المضمومة قبلها مثل
+
+65
+00:05:39,040 --> 00:05:44,520
+المؤمنون .. مادية .. اه يعني بتسمى مادية .. المثلا
+
+66
+00:05:44,520 --> 00:05:50,380
+المؤمنين .. مادية .. مادية لكن نحن نريد الواو
+
+67
+00:05:50,380 --> 00:05:55,660
+الساكنة واليأس ساكنة المفتوحة قبلهم .. وهم مثلا ..
+
+68
+00:05:55,660 --> 00:06:01,870
+مثلا حرف خوفخوف هنا نجهد انه الواو ساكنة و ما
+
+69
+00:06:01,870 --> 00:06:09,270
+قبلها مفتوح فهو يعني حرف لين كذلك كلمة ايه؟ فرعون
+
+70
+00:06:09,270 --> 00:06:14,690
+.. فرعون الواو ساكنة و ما قبلها الحرف العين مفتوح
+
+71
+00:06:14,690 --> 00:06:20,790
+كذلكبيت .. بيت الياق ساكنها وما قبلها مفتوح حرف
+
+72
+00:06:20,790 --> 00:06:27,210
+البا يسمى حرف لين و كذلك قريش و هذا كله ما يسمى
+
+73
+00:06:27,210 --> 00:06:31,750
+بالمد .. ما هو نوع المد الموجود في هذه الكلمات؟ مد
+
+74
+00:06:31,750 --> 00:06:38,910
+اللين لو كان هنا ليس حرف لين و انما حرف مد مثل
+
+75
+00:06:38,910 --> 00:06:44,000
+المؤمنون، المؤمنين، الرحمن، ماذا نسميه مد اللين؟مد
+
+76
+00:06:44,000 --> 00:06:49,100
+.. عارض .. لسكون .. لسكون .. لنتقل إلى .. طب صفة
+
+77
+00:06:49,100 --> 00:06:51,740
+اللي لي أخوتها؟ اللي هي صفة قوة ولا صفة ضعف؟ صفة
+
+78
+00:06:51,740 --> 00:06:55,840
+ضعف .. صفة ضعف .. الآن احنا أخدنا صفتين و ده الصفة
+
+79
+00:06:55,840 --> 00:07:00,070
+التالتة الصفة الأولى صفة الصفير و هي صفة قوةالصفة
+
+80
+00:07:00,070 --> 00:07:04,110
+الثانية صفة القلقل وهي صفة قوة الصفة الثالثة هذه
+
+81
+00:07:04,110 --> 00:07:08,190
+اللي هي صفة النيل صفة ضعف هو اللي بمعنى السهولة هو
+
+82
+00:07:08,190 --> 00:07:11,410
+اللي ياخد الحرف سهولة ويسر من غير كلفة على اللسان
+
+83
+00:07:11,410 --> 00:07:14,470
+وحروف الواو والياء اللي ساكنين المفتوح ما قبلهما
+
+84
+00:07:14,470 --> 00:07:21,730
+يعدوا حرف ضعيف أو صفة .. صفة ضعف الصفة الرابعة من
+
+85
+00:07:21,730 --> 00:07:26,910
+الصفات التي ليس لها ضد هي صفة الانحرافوالانحراف
+
+86
+00:07:26,910 --> 00:07:30,990
+شيء يعني انحرف عن مساره، ميلو .. الميلو عن الشيء و
+
+87
+00:07:30,990 --> 00:07:36,850
+العدول عنه، نقول انحرف السهم عن مساره، يعني المالة
+
+88
+00:07:36,850 --> 00:07:41,170
+عن الجهة التي كان متجه لها والانحراف في الاصطلاح
+
+89
+00:07:41,170 --> 00:07:46,670
+يا أخوات، هو ميلو الحرف عن مخرجه بعد النط به، حتى
+
+90
+00:07:46,670 --> 00:07:53,330
+يتصل بمخرج غيرهميل الحرف عن مخرجه بعد نطقله حتى
+
+91
+00:07:53,330 --> 00:07:57,730
+يتصل بمخرج غيره بعد ما ننطق بالحرف بنجد أن اللسان
+
+92
+00:07:57,730 --> 00:08:05,730
+يقف عند مخرج حرف آخر وحرفاء اللين .. اقصد الانحراف
+
+93
+00:08:05,730 --> 00:08:10,770
+هو اللام والرا إذا ما هي حروف الانحراف يا أخوات؟
+
+94
+00:08:10,770 --> 00:08:16,710
+اللام والرا هما حرفاناللام والرا اللام ينحرف بعد
+
+95
+00:08:16,710 --> 00:08:21,370
+النطق به حتى يتصل بمخرج حرف النون عندما أقول أنا
+
+96
+00:08:21,370 --> 00:08:27,370
+مثلا ال .. ال .. باجد أن اللام .. المخرج اللام
+
+97
+00:08:27,370 --> 00:08:34,510
+يتحرك وبيقف طرف اللسان عند مخرج حرف ال N لذلك إن
+
+98
+00:08:34,510 --> 00:08:39,950
+لم يحضر إنسان من حرف اللام قد يصل إلى أو قد ينطق
+
+99
+00:08:39,950 --> 00:08:45,670
+حرف اللام Nمثال ذلك عندما يقول وجعلنا الليلة لباسة
+
+100
+00:08:45,670 --> 00:08:50,890
+ممكن واحد يقرأها وجعلنا .. وجعلنا الليلة لباسة لأن
+
+101
+00:08:50,890 --> 00:08:56,390
+اللام ينحرف عن مساره حتى يتصل بمخرج حرف النون لذلك
+
+102
+00:08:56,390 --> 00:09:01,270
+لابد من الحضر عند النطق بحرف اللام حتى لا ينطقه
+
+103
+00:09:01,270 --> 00:09:06,830
+نون مثل كلمة وجعلناينطقها ال .. ال .. الذي يقرأ
+
+104
+00:09:06,830 --> 00:09:11,150
+وجعلنا .. ممكن ولد صغير ي .. ينطق بهذا الحرف، يقول
+
+105
+00:09:11,150 --> 00:09:16,070
+وجعلنا، لكن دا بد أن يحضر القارئ من أن ينطق حرف
+
+106
+00:09:16,070 --> 00:09:21,070
+اللام نون، لأن اللام بينحرف عن مساره بعد النطق به
+
+107
+00:09:21,070 --> 00:09:26,760
+حتى يتصل بمخرج غيرهالحرف الثاني أخوات هو مخرج حرف
+
+108
+00:09:26,760 --> 00:09:31,740
+ال إيه؟ ال لا .. ال .. ال ر أقصد حرف ال ر ينحلف عن
+
+109
+00:09:31,740 --> 00:09:38,820
+مخرجه حتى يتصل بمخرج حرف ال لاالرا بينحرف عن مساره
+
+110
+00:09:38,820 --> 00:09:44,360
+حتى يتصل بمخرج حرف اللام مثلا عندما يقرأ .. يقول
+
+111
+00:09:44,360 --> 00:09:49,120
+إنسان الرحمن الرحيم ممكن لو إن لم يحضر القارئ يقول
+
+112
+00:09:49,120 --> 00:09:54,180
+اللحمان اللحيم وهذا طبعا يخطئ لأنه انحرف اللام عن
+
+113
+00:09:54,180 --> 00:09:58,560
+مساره حتى يعني يتصل بمخرج حرف النون والرا بتنحرف
+
+114
+00:09:58,560 --> 00:10:02,920
+عن مسارها حتى يتصل بحرف اللام
+
+115
+00:10:04,360 --> 00:10:07,960
+طيب، هذه يا أخوات صفة الانحراف، ما هما حرفاء
+
+116
+00:10:07,960 --> 00:10:13,020
+الانحراف اللمرة، اللامورة، اللامورة، اللامورة،
+
+117
+00:10:13,020 --> 00:10:15,440
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+118
+00:10:15,440 --> 00:10:15,440
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+119
+00:10:15,440 --> 00:10:15,440
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+120
+00:10:15,440 --> 00:10:18,100
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+121
+00:10:18,100 --> 00:10:20,840
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+122
+00:10:20,840 --> 00:10:21,020
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+123
+00:10:21,020 --> 00:10:29,080
+اللامورة، اللامورة، اللامورة، اللامورة، اللامورة،
+
+124
+00:10:29,330 --> 00:10:32,790
+نقول كررتوا الشاي بمعنى إيش يا أخوان؟ اعادة
+
+125
+00:10:32,790 --> 00:10:38,850
+فتكريره لغة الإعادة وفي الاصطلاح هو ارتعاده رأس
+
+126
+00:10:38,850 --> 00:10:46,080
+اللسان عند النطب بحرف الرأس، ارتعاد رأس اللسانعند
+
+127
+00:10:46,080 --> 00:10:50,740
+النطق بحرف الرا يسمى إيه يعني تكرير ناجد أن القارئ
+
+128
+00:10:50,740 --> 00:10:55,600
+أو الذي يلفظ حرف الرا يبقى ناجد أن اللسان أو رأس
+
+129
+00:10:55,600 --> 00:11:00,400
+اللسان يرتعد، يقول ار .. ار فهذا يسمى إيه اللي هو
+
+130
+00:11:00,400 --> 00:11:06,340
+التكرير فصفة التكرير هي صفة ملازمة لحرف الرا تظهر
+
+131
+00:11:06,340 --> 00:11:10,990
+في حالة التشديد أكتر شيء مثل الرحمن .. الرحمنولكن
+
+132
+00:11:10,990 --> 00:11:16,110
+على القارئ ألا يجعل اللسان يتكرر أكتر من مرة
+
+133
+00:11:16,110 --> 00:11:21,690
+وانزادت مرة ونصف يعني ما بنفع يقول الرحمن أو
+
+134
+00:11:21,690 --> 00:11:27,880
+الرأيتكأو الرحمان هذا خطأ وإنما الرحمان يعني
+
+135
+00:11:27,880 --> 00:11:34,580
+ارتعادة اللسان مرة واحدة كذلك الرحمان رحيم وليس
+
+136
+00:11:34,580 --> 00:11:39,200
+نوع من التكرير لذلك صفة التكرير يا أخوات نحن
+
+137
+00:11:39,200 --> 00:11:45,300
+ندرسها حتى نتجنب المبالغة فيها يعني ندرس هذه الصفة
+
+138
+00:11:45,300 --> 00:11:49,980
+ليس لأن نحقق صفر التكرير فيها ونضلنا نتكرروانما
+
+139
+00:11:49,980 --> 00:11:55,660
+ندرسها حتى نتجنب المبالغة فيها فالغرض من معرفة صفة
+
+140
+00:11:55,660 --> 00:11:59,640
+التكرير عدم المبالغة فيها فيجب على القارئ أن يخفي
+
+141
+00:11:59,640 --> 00:12:03,720
+التكرير ولا يبادر فيه ويكتفي بارتعادة واحدة عند
+
+142
+00:12:03,720 --> 00:12:10,060
+النطق بحرف الراوحتى يعني يتخلص من التكرير، في
+
+143
+00:12:10,060 --> 00:12:13,060
+عندنا نتخلص .. نتخلص من التكرير في حالة التفخيم
+
+144
+00:12:13,060 --> 00:12:18,400
+ونتخلص من التكرير في حالة إيش؟ الترقيم عند حالة
+
+145
+00:12:18,400 --> 00:12:22,520
+التفخيم مثل الرحمن، إذا أردنا أن نتخلص أو يجب
+
+146
+00:12:22,520 --> 00:12:27,400
+علينا أن نتخلص من التكرير و لا نسمح للإنسان يرتعد
+
+147
+00:12:27,400 --> 00:12:35,570
+أكثر من مرة، فنوقفطرف اللسان نجعله يعني يقف عند
+
+148
+00:12:35,570 --> 00:12:40,630
+الحنك الأعلى فنقول الرحمن .. الرحمن إذا يلسق ظهر
+
+149
+00:12:40,630 --> 00:12:46,190
+طرف اللسان بوسط الحنك الأعلى عند النطق بحرف الرا
+
+150
+00:12:46,190 --> 00:12:52,090
+المفخم نقول الرحمن .. الرحمن ولا نسمح لللسان إيه
+
+151
+00:12:52,090 --> 00:12:58,370
+يرتعد لا نقول الرحمن إنما نقولالرحمان يعني نجعل
+
+152
+00:12:58,370 --> 00:13:03,070
+اللسان يلثثق بالحنك الأعلى عند النطق بحر الراء
+
+153
+00:13:03,070 --> 00:13:08,290
+المفخرة أما بالنسبة كيفية تتخلص من التكرير في حالة
+
+154
+00:13:08,290 --> 00:13:13,050
+الراء المراققة أن يلثق ظهر طرف اللسان بلثة الثنايا
+
+155
+00:13:13,050 --> 00:13:21,290
+العليا نقول مثلا بريح أو بيكيكD يعني نجعل طرف
+
+156
+00:13:21,290 --> 00:13:26,170
+اللسان يلتسق بلثة الثناية العليا على أساس أنه نريد
+
+157
+00:13:26,170 --> 00:13:31,570
+أن نخرج حرف الرا مراققا و بدون تكرير إذا في حالة
+
+158
+00:13:31,570 --> 00:13:37,210
+التفخيم نجعل طرف اللسان يلتسق بالحنك الأعلى حتى لا
+
+159
+00:13:37,210 --> 00:13:41,990
+تظهر صفة التكرير على حرف الرا نقول الرحمن أما
+
+160
+00:13:41,990 --> 00:13:45,990
+بالنسبة إذا كان حرف الرا مراققا نجعل طرف اللسان
+
+161
+00:13:45,990 --> 00:13:50,360
+يلتسق بلثة الثناية العلياكي لا يرتعد رأس اللسان
+
+162
+00:13:50,360 --> 00:13:55,880
+أكثر من مرة الصفة السادسة يا اخوان طبعا صفة
+
+163
+00:13:55,880 --> 00:14:02,070
+التكرير صفة قوةصفة الين صفات بعض، صفة الانحراف
+
+164
+00:14:02,070 --> 00:14:07,610
+صفات قوة، صفة القلقلة صفات .. الانحراف صفات قوة،
+
+165
+00:14:07,610 --> 00:14:12,370
+القلقلة صفات قوة، الصفير صفات قوة، إذا من الصفات
+
+166
+00:14:12,370 --> 00:14:16,190
+التي أخذناها أخر شيء اللي هي الصفير، القلقلة،
+
+167
+00:14:16,190 --> 00:14:21,150
+الانحراف، التكرير، كلها صفات قوة وصفة الانحراف مش
+
+168
+00:14:21,150 --> 00:14:27,490
+قوةالانحراف صفة قوة .. الانحراف صفة قوة .. الليل
+
+169
+00:14:27,490 --> 00:14:33,860
+فقط هو الذي يعده صفة ضعفننتقل الصفة السادسة يا
+
+170
+00:14:33,860 --> 00:14:40,400
+أخوات و هي صفة التفشي صفة التفشي نقول تفش المرض،
+
+171
+00:14:40,400 --> 00:14:46,560
+تفش الوباء بمعنى انتشر من حيث اللغة فالتفشي لغة ما
+
+172
+00:14:46,560 --> 00:14:51,840
+هو يا أخوات الانتشار والاتساع وفي الاصطلاح من يعرف
+
+173
+00:14:51,840 --> 00:14:53,740
+لنا التفشي اصطلاحا
+
+174
+00:14:57,960 --> 00:15:02,220
+انتشار الريح في الفم عند النطق بحرف الشين
+
+175
+00:15:04,950 --> 00:15:10,230
+فنجد بأنه ال .. الريح ينتشر بالفمي عند النطب بهذا
+
+176
+00:15:10,230 --> 00:15:15,390
+الحرف، إذا ما هي حروف التفشي؟ حرف واحد فقط وهو
+
+177
+00:15:15,390 --> 00:15:19,510
+الشين، فانتشار الريح في الفمي عند النطب بحرف
+
+178
+00:15:19,510 --> 00:15:25,850
+التفشي وهو الشين يسمى هذا اللي هو التفشيوتثبت صفة
+
+179
+00:15:25,850 --> 00:15:30,390
+التفشي لحرف الشين في جميع أحواله سواء كان ساكنا أو
+
+180
+00:15:30,390 --> 00:15:36,590
+متحركا متطرفا أو متوسطا ولكن تظهر بشكل واضح إذا
+
+181
+00:15:36,590 --> 00:15:41,790
+كان حرف الشين ساكنا أو مشددا تظهر صفة التفشي بشكل
+
+182
+00:15:41,790 --> 00:15:49,590
+واضح مثل ذلك مشربهمعشرة أو مثلا بُشراكم تظهر صفة
+
+183
+00:15:49,590 --> 00:15:53,770
+الاش أو صفة حرف الشين لإش اللي هي صفة التفشي
+
+184
+00:15:53,770 --> 00:16:00,150
+بُشراكم عشرة مشربهم هذه كلها فيها حروف تفشي وصفة
+
+185
+00:16:00,150 --> 00:16:05,770
+التفش أيضا تعد صفة إش أخوات صفة قوة ننتقل إلى
+
+186
+00:16:05,770 --> 00:16:11,790
+الصفة السابعة وهي صفة الاستطالة أيضا يا أخوات
+
+187
+00:16:11,790 --> 00:16:16,670
+الاستطالة هي صفة قوةنقول استطالت الطريق بمعنى
+
+188
+00:16:16,670 --> 00:16:23,050
+امتدت فالاستطالة في اللغة الامتداد الاستطالة لغة
+
+189
+00:16:23,050 --> 00:16:28,710
+الامتداد وفي الإصطلاح امتداد الصوت من أول حافة
+
+190
+00:16:28,710 --> 00:16:34,050
+اللسان إلى آخره عند النطق بحرف واحد وهو الضغط
+
+191
+00:16:34,050 --> 00:16:39,110
+امتداد الصوت من أول حافة اللسان إلى آخره عند النطق
+
+192
+00:16:39,110 --> 00:16:45,390
+بحرف الضغط لو سألنا الأخواتمن أين يخرج حرف الضاب؟
+
+193
+00:16:45,390 --> 00:16:55,450
+إحدى .. فضلي إحدى
+
+194
+00:16:55,450 --> 00:17:00,430
+حفتي اللسان اليمنى أو اليسرى ومن اليسرى أيسر مع ما
+
+195
+00:17:00,430 --> 00:17:05,690
+يليها من أدراس الجهة العليا لو قالت واحدة مثلا مع
+
+196
+00:17:05,690 --> 00:17:11,450
+الثنائي العلياصح ولا غلط؟ غلط، أين تقع الثانية
+
+197
+00:17:11,450 --> 00:17:15,570
+العليا؟ الثانية العليا هذه السنين، هذول، لو ..
+
+198
+00:17:15,570 --> 00:17:19,830
+وبالتالي خطأ أن أقول الثانية العليا، فلابد أن
+
+199
+00:17:19,830 --> 00:17:22,590
+أدراس .. الأدراس اللي هي الجهة العليا اللي احنا
+
+200
+00:17:22,590 --> 00:17:26,190
+نسميها الطواحين، اليمنى أو اليسرى، ولكن من اليسرى
+
+201
+00:17:26,190 --> 00:17:31,030
+أيسر، إذا حرف الضد يخرج من إحدى حفتين لسان، اليمنى
+
+202
+00:17:31,290 --> 00:17:36,350
+أو اليسرة و اليسرة أيسر مع ما يليها من أدراس الجهة
+
+203
+00:17:36,350 --> 00:17:41,690
+اليسرة فعندما نقول فيها صفة الاستطالة بمعنى أنه
+
+204
+00:17:41,690 --> 00:17:45,870
+عندما نقول او او نجد أن الصفة الاستطالة اللي هو ال
+
+205
+00:17:45,870 --> 00:17:51,350
+او يمتد من أول حفة اللساني إلى آخرها هل يصح لنا أن
+
+206
+00:17:51,350 --> 00:17:58,350
+نقول رب السماوات والأرض يعني اض ا .. نطلع النبرة،
+
+207
+00:17:58,350 --> 00:18:04,140
+بنفع؟ ليش؟لأنه أنا عندما أقول رب السماوات والأرض
+
+208
+00:18:04,140 --> 00:18:08,120
+فيها قلقة، لكن هذا يعني أنا قلقلت الآن، وهذا خطأ،
+
+209
+00:18:08,120 --> 00:18:13,840
+لابد أن أقول رب السماوات والأرضفيها يعني نوع من
+
+210
+00:18:13,840 --> 00:18:18,960
+استطالة وصفة الاستطالة هو امتداد .. امتداد الصوت
+
+211
+00:18:18,960 --> 00:18:24,380
+من أول حافة اللساني إلى آخره عند النطب بحرف ال ..
+
+212
+00:18:24,380 --> 00:18:30,520
+حرف الضاب وتثبت طبعا صفة الاستطالة لحرف الضاب في
+
+213
+00:18:30,520 --> 00:18:34,980
+عند كان ساكن أو مشددا مثال ذلك هنا .. مثال ذلك ما
+
+214
+00:18:34,980 --> 00:18:40,020
+اللي يقرأ الكلمة؟فضلي .. أضّالي .. أضّالي ..
+
+215
+00:18:40,020 --> 00:18:46,640
+أضّالي .. ففيها استقالة كذلك يضرب .. يضرب في صفة
+
+216
+00:18:46,640 --> 00:18:52,660
+الاستقالة الأولى حرف الضاب مشدد والثانية يضرب حرف
+
+217
+00:18:52,660 --> 00:18:59,060
+الضاب ساكنة ونشاهد هنا إن حرف الضاب عند نطبه له
+
+218
+00:18:59,060 --> 00:19:04,130
+امتداد للصوت من أول حافة اللساني إلى آخرهو يجب
+
+219
+00:19:04,130 --> 00:19:09,530
+الحضرة يا أخوات من أن نلفظ حرف الضاد ضا يعني هناك
+
+220
+00:19:09,530 --> 00:19:14,410
+بعض الدول أو بعض المجتمعات ابتدوا تلفظ حرف الضاد
+
+221
+00:19:14,410 --> 00:19:19,090
+ضا يعني بدلا من أن يقول غير المغضوب عليهم يقولون
+
+222
+00:19:19,090 --> 00:19:24,410
+غير المغضوب عليهمليس المغضوب .. المغضوب هي اللي هي
+
+223
+00:19:24,410 --> 00:19:28,150
+حرف .. بيصير حرف آخر اللي هو اض .. يعني بيصير
+
+224
+00:19:28,150 --> 00:19:33,370
+عندنا لحن جنيه أبدلنا حرف محال إيه؟ محال حرف
+
+225
+00:19:33,370 --> 00:19:38,090
+وبالتالي هذا خطأ وإنما نقول غير المغضوب عليهم لو
+
+226
+00:19:38,090 --> 00:19:45,340
+قلنا مثلا في قوله تعالى ضل ما تدعون إلا إياهظلة،
+
+227
+00:19:45,340 --> 00:19:52,780
+لو واحد لفظ حرف الظال، ده، فقرأ ضل ما تدعون إلا
+
+228
+00:19:52,780 --> 00:19:58,020
+إياه، إيش بصيتي عنها؟ تغير المعنى، أول شيء لحن
+
+229
+00:19:58,020 --> 00:20:03,860
+جليه و كذلك غير المعنى و قنره، عندما أقول ضلة من
+
+230
+00:20:03,860 --> 00:20:09,170
+الضلاليعني ضلت جميع الآلهة إلا الله سبحانه وتعالى
+
+231
+00:20:09,170 --> 00:20:14,490
+فهو الإله بحق لكن الذين يعبدون الأصنام والحجارة
+
+232
+00:20:14,490 --> 00:20:18,430
+وغير ذلك هي ضل .. ضل هؤلاء الناس وضلوا الطريق
+
+233
+00:20:18,430 --> 00:20:22,790
+ونحرفوا عن المسار الذين يعبدون غير الله عزوجل إلا
+
+234
+00:20:22,790 --> 00:20:26,650
+إياه إلا المسلمين الذين يعبدون الله سبحانه وتعالى
+
+235
+00:20:26,650 --> 00:20:32,150
+فهذا صحيح ضل ما تدعون إلا إياه لكن لو واحد قرأ
+
+236
+00:20:32,150 --> 00:20:39,320
+مثلا غلىظلة بمعنى بقية اختلل المعنى وانقلبها رأسنا
+
+237
+00:20:39,320 --> 00:20:43,580
+على العقل يعني نقول ظلة يعني بقية من تدعون إلا
+
+238
+00:20:43,580 --> 00:20:47,160
+إياها يعني كل الأصنام بقيت إلا الله غير بقى و هذا
+
+239
+00:20:47,160 --> 00:20:52,040
+انحراف و هذا لا يجوز لذلك لابد أن ننطق بالحرف و
+
+240
+00:20:52,040 --> 00:20:57,140
+نخرجه من مخرجه الصحيح فحرف الضاد يخرج من إحدى
+
+241
+00:20:57,140 --> 00:21:01,020
+حرفتين لسان اليمنى أو اليسرى مع ما يليها من أدراس
+
+242
+00:21:01,020 --> 00:21:07,420
+الجهة اليسرىيعني بيخرج من رأس اللسان بالتساقه مع
+
+243
+00:21:07,420 --> 00:21:12,080
+أطلاف الثلاثة العليا ال او وال اث وال اذ مخرجهم
+
+244
+00:21:12,080 --> 00:21:17,300
+واحد فلا يجود لنا أن نخرج حرف الض من مخرج حرف الض
+
+245
+00:21:18,570 --> 00:21:23,010
+طيب مثلا الفرق ما بين الاستطالة والمد احنا بنقول
+
+246
+00:21:23,010 --> 00:21:26,750
+امتداد صوت الحرف من أول حرفة اللساني إلى آخره هذا
+
+247
+00:21:26,750 --> 00:21:31,270
+الاستطالة امتداد صوت الحرف من أول حرفة اللساني إلى
+
+248
+00:21:31,270 --> 00:21:35,890
+آخره عند النطق بحرف ايه؟ بحرف الضابط والامتداد
+
+249
+00:21:35,890 --> 00:21:39,350
+والمد نفسه هو امتداد الصوت لكن ما الفرق بين
+
+250
+00:21:39,350 --> 00:21:45,430
+الاستطالة و .. او .. و .. والمد ما رأيكم يا بنات؟
+
+251
+00:21:45,430 --> 00:21:47,770
+ما هي الاستطالة؟ فضل الأخت الوراق
+
+252
+00:21:52,350 --> 00:21:56,830
+صحيح، يعني هنا مثلا جريان الصوت في مخرج الحرف بقدر
+
+253
+00:21:56,830 --> 00:22:02,010
+طوله دون أن يتجاوز المخرج، يعني أقول .. يعني هذا
+
+254
+00:22:02,010 --> 00:22:06,370
+امتداد الصوت، بس في اللسان، لكن حرف المد .. حرف
+
+255
+00:22:06,370 --> 00:22:10,310
+المد، جريان الصوت في ذات الحرف، ولا ينقطع الصوت
+
+256
+00:22:10,310 --> 00:22:15,130
+إلا من قطاع النفس، يعني هيظل يقول ..لما .. لما
+
+257
+00:22:15,130 --> 00:22:22,510
+ينتهي نفسه أو او ايه؟ هذه حروف المادة الثلاثة وهي
+
+258
+00:22:22,510 --> 00:22:27,670
+ليس لها حيز تنتهي إليه بل انتهاؤها بانتهاء ..
+
+259
+00:22:27,670 --> 00:22:31,470
+بانتهاء النفس لكن بالنسبة لحرف الضغط فهو جريان
+
+260
+00:22:31,470 --> 00:22:36,760
+الصوت في مخرج حرف الضغط بقدر طوله يعني اورب
+
+261
+00:22:36,760 --> 00:22:43,360
+السماوات والأرض بس مش الأرض تمشيشي معانا لأنه ليس
+
+262
+00:22:43,360 --> 00:22:47,320
+مثل حرف الماد، إذا جريان الصوت في مخرج الحرف بقدر
+
+263
+00:22:47,320 --> 00:22:50,980
+طوله دون أن يتجاوز مخرج الحرف، هذا بالنسبة
+
+264
+00:22:50,980 --> 00:22:53,980
+للاستطلاع، لكن بالنسبة للماد، هو جريان الصوت في
+
+265
+00:22:53,980 --> 00:22:59,320
+ذات الحرف ولا ينقطع الصوت إلا بانقطاع النفس، لأن
+
+266
+00:22:59,320 --> 00:23:03,780
+حرف الماد ليس له حيث ينتهي إليه، بل انتهاؤها
+
+267
+00:23:03,780 --> 00:23:10,200
+بانتهاء النفسصفة الاستطار ليه هو صفة قوة ولا ضعف؟
+
+268
+00:23:10,200 --> 00:23:15,580
+صفة قوة ننتقل إلى الصفة الثامنة وهي صفة الخفاء
+
+269
+00:23:15,580 --> 00:23:22,020
+والخفاء لغة من الشيء المخفي بمعنى الاستطار الخفاء
+
+270
+00:23:22,020 --> 00:23:27,440
+لغة الاستطار وعدم الوضوح وفي الاصطلاح هنا استطار
+
+271
+00:23:27,440 --> 00:23:32,480
+صوت الحرفي عند النط بأحد حروف الخفاء فما هي حروف
+
+272
+00:23:32,480 --> 00:23:38,510
+الخفاء؟حروف الخفاء أربعة هي حروف المادة الثلاثة زي
+
+273
+00:23:38,510 --> 00:23:44,710
+الحرف الها اللي هي مجموعة في قوله هاوي هالف واو يا
+
+274
+00:23:44,710 --> 00:23:49,910
+حروف المادة الثلاثة زي الحرف الها هذه حروف هاوي
+
+275
+00:23:49,910 --> 00:23:55,030
+وهي حروف الخفاء وهي استطار صوت الحرف عند نطمي بأحد
+
+276
+00:23:55,030 --> 00:24:00,240
+حروف الخفاء وهي مجموعة في قوله هاويوسميت حروف
+
+277
+00:24:00,240 --> 00:24:05,260
+الخفاء بهذا الاسم لأنها تخفى في اللفظ عند النقطة
+
+278
+00:24:05,260 --> 00:24:10,880
+بيها يعني ممكن تخفى ولا طول فاض ممكن تخفى ولا طول
+
+279
+00:24:10,880 --> 00:24:16,440
+فاض حروف المادة الثلاثة لأنه طبعا تخفى لأنه لو
+
+280
+00:24:16,440 --> 00:24:21,060
+أعطيناها حركة واحدة بتصير فتحة لو أعطيناها .. لو
+
+281
+00:24:21,060 --> 00:24:28,130
+أعطينا ..حرف المد حركة واحدة A O E بتصير فتحة لكن
+
+282
+00:24:28,130 --> 00:24:31,930
+لابد أن نعطيها حركتين يعني نمدهم بمعنى أن نعطيهم
+
+283
+00:24:31,930 --> 00:24:37,590
+زمن الصوت معناه مقدار حركتين فلأن مخرجها واسع وليس
+
+284
+00:24:37,590 --> 00:24:40,870
+لها حيز تنتهي إليه اللي هي حروف المد الثلاثة ليس
+
+285
+00:24:40,870 --> 00:24:47,300
+لها حيز تنتهي إليه ومخرجها واسع لذلك ممكن تخفىمثلا
+
+286
+00:24:47,300 --> 00:24:52,800
+عندما نقول واضحة فلبد أن أقول واضحة والليل إذا
+
+287
+00:24:52,800 --> 00:24:58,320
+سجاء أو بين الألف لو قلت مثلا واضحة والليل إذا سجا
+
+288
+00:24:58,320 --> 00:25:02,960
+إيش بيصير؟ بيصير عبارة عن ضحة الحال عليها فتحة
+
+289
+00:25:02,960 --> 00:25:08,060
+يبقى الألف أخفيت لأن مخرج الألف واسع لا تكفيها
+
+290
+00:25:08,060 --> 00:25:13,640
+حركة بل لابد أن نعطيها كم؟ حركتين نقول واضحة
+
+291
+00:25:13,640 --> 00:25:20,100
+والليل إذا سجالأ .. لأ أقول والضحى والليل إذا سجى
+
+292
+00:25:20,100 --> 00:25:25,960
+إذا ممكن الحرف المد يُخفى كذلك إن أنزلناه في ليلة
+
+293
+00:25:25,960 --> 00:25:31,100
+القدر يعني ممكن أن .. أنزلناه في الألف بيختلف أو
+
+294
+00:25:31,100 --> 00:25:36,800
+إن أنزلناه لو قال إن أنزلناه .. إن أنزلناه كأن
+
+295
+00:25:36,800 --> 00:25:42,340
+النون بس عليها شدةهي مش اننا أنزلناه، اننا
+
+296
+00:25:42,340 --> 00:25:47,920
+أنزلناه، لابد أن نمد حرف المد لأنه لو لم نمدها
+
+297
+00:25:47,920 --> 00:25:51,960
+ممكن يكون هذا الحرف قابل لإيش يا أخوات؟ قابل
+
+298
+00:25:51,960 --> 00:25:57,460
+للخفاء، فيقفأ لأنه .. يعني لو سألنا سؤال لماذا
+
+299
+00:25:57,460 --> 00:26:00,820
+حروف المد الثلاثة الألف الساكنة المفتوحة ما قبلها
+
+300
+00:26:00,820 --> 00:26:03,220
+و اللي هو الساكنة المضمون ما قبلها و اللي هي
+
+301
+00:26:03,220 --> 00:26:07,820
+الساكنة المكسورة ما قبلها تقفأ؟لأن مخرجها واسع
+
+302
+00:26:07,820 --> 00:26:12,240
+وليس لها حيز تنتهي إليه بل انتهاءه بانتهاء النفس
+
+303
+00:26:12,240 --> 00:26:18,100
+ولأنها ممكن تقفأ إذا أعطيت حركة نقول وضحا فلابد أن
+
+304
+00:26:18,100 --> 00:26:24,340
+نعطيها حركتين نقول وضحا والليل إذا سجا وهكذا باقي
+
+305
+00:26:24,340 --> 00:26:30,150
+حروف المد التلاتةأما بالنسبة للها فهي تُخف أيضًا
+
+306
+00:26:30,150 --> 00:26:36,130
+لأن حروف صفاتها كلها ضعيفة و لأن حرف الها حرف ضعيف
+
+307
+00:26:36,130 --> 00:26:40,990
+لا تكفي أن نعطيه حركة ممكن يُخفى فلابد أن نحقق
+
+308
+00:26:40,990 --> 00:26:46,610
+الها يعني حتى أحيان التال مربوطة لو وقفنا عليها
+
+309
+00:26:46,610 --> 00:26:53,870
+بتصبح إيه؟ تصبح ها يعني مثلًا نعمة، رحمة، حكمة،
+
+310
+00:26:53,870 --> 00:27:01,020
+ماذا نقول؟ نعمة، رحمةحكمة، فلو واحد مثلا قال نعمة،
+
+311
+00:27:01,020 --> 00:27:05,660
+رحمة، حكمة، كأنه الميم والعين مفتوحة، يعني مثلا
+
+312
+00:27:05,660 --> 00:27:13,630
+نعمة هي أصلا نعمةده أحقق الها نعمة طيب لو واحد
+
+313
+00:27:13,630 --> 00:27:17,810
+أسرع فقال نعمة بس عبارة عن ان و اع و ام و على
+
+314
+00:27:17,810 --> 00:27:24,310
+الميم فاتحة إذا أسرع في الها أخفيا رحمة بيصير رحمة
+
+315
+00:27:24,310 --> 00:27:29,950
+لو أسرع فيها بيصير رحمة عبارة عن ميم عليها فتحة
+
+316
+00:27:29,950 --> 00:27:36,630
+حكمة هي أصلا حكمة التى لو وقفنا عليها تبدأ إلى ه
+
+317
+00:27:36,630 --> 00:27:44,370
+فبتقرأ حكمةوانحقق الها لو واحد قصها إيش يصير؟ حكمة
+
+318
+00:27:44,370 --> 00:27:48,690
+يعني كأنها ال meme يعني عليه فتحة إذا هذه الخفقة
+
+319
+00:27:48,690 --> 00:27:52,510
+تُخفى إذا ما هي الحروف التي تُخفى؟ حروف المادية
+
+320
+00:27:52,510 --> 00:27:56,470
+الثلاثة يا أخوات زائد حرف الها لماذا تُخفى حروف
+
+321
+00:27:56,470 --> 00:28:02,550
+المادية الثلاثة؟ لأن مخرجها واسع لا تكفيها حركة بل
+
+322
+00:28:02,550 --> 00:28:09,660
+نعطيها حركتين فنقول وضحاسجال وغير ذلك من الكلمات
+
+323
+00:28:09,660 --> 00:28:16,620
+بالنسبة لحرف الها الها أيضا صفاته كلها ضعيفة لذلك
+
+324
+00:28:16,620 --> 00:28:21,020
+ممكن أن يُخفى بسهولة فحتى إذا جاءت في آخر كلمة
+
+325
+00:28:21,020 --> 00:28:28,760
+لابد أن نحققها فنقول نعمة حكمة رحمة طيب صفة الخفاء
+
+326
+00:28:28,760 --> 00:28:34,570
+يا أخوات هل هي صفة قوة ولا صفة ضعف؟صفة الخفاء يا
+
+327
+00:28:34,570 --> 00:28:38,970
+أخوات صفة ضعف، الخفاء صفة ضعف و كذلك ال lean اللي
+
+328
+00:28:38,970 --> 00:28:43,250
+أخدنا صفة ضعف، هدول الصفتين بس صفة الخفاء و صفة ال
+
+329
+00:28:43,250 --> 00:28:48,670
+lean هما الصفاتين الضعيفتين في الصفات الغير متضادة
+
+330
+00:28:48,670 --> 00:28:54,670
+و ليس لها ضد طبعا طيب صفة الخفاء يعني الهاء هذه
+
+331
+00:28:54,670 --> 00:28:58,410
+إذا وقعت بين .. يعني في نهاية الكلمة و وقعت بين
+
+332
+00:28:58,410 --> 00:29:04,320
+حرفين متحركين تمدتُعطى .. لو كان .. ممكن تُمدّه و
+
+333
+00:29:04,320 --> 00:29:08,860
+تسميها ماد صلة صغرى إذا وقعت حرف الها بين حرفين
+
+334
+00:29:08,860 --> 00:29:14,700
+متحركين ولم يكن المتحرك الثاني همزة من سمي صلة ..
+
+335
+00:29:14,700 --> 00:29:22,560
+ماد صلة صغرى مثال ذلك بلى إن ربه كان بيه بصيرة هنا
+
+336
+00:29:22,560 --> 00:29:28,880
+بلى إن ربه الها هنا بتاعة ربه وقعت أخوات بين إيه؟
+
+337
+00:29:29,020 --> 00:29:34,740
+بين حرفين متحركين حرف ال ب مفتوح و حرف ال ك مفتوح
+
+338
+00:29:34,740 --> 00:29:40,460
+بيتولد عن حركة ال ه و او مادية لو كانت مضمومة هنا
+
+339
+00:29:40,460 --> 00:29:46,700
+ال ه عليها ضمة ولا فتحة ولا كسرة؟ ضمة فمنشبع الضمة
+
+340
+00:29:46,700 --> 00:29:50,800
+منشبع يعني بنعطيها حركتين يعني بيتولد عنها و او
+
+341
+00:29:50,800 --> 00:29:58,110
+مادية فنقول بلى إن ربه كان .. ربه كانما يمكن نقول
+
+342
+00:29:58,110 --> 00:30:03,030
+ربه كان .. ما يمكن نقول بلى إن ربه كان .. لو قلنا
+
+343
+00:30:03,030 --> 00:30:10,110
+ربه كان .. حرف الها اختفت و ال wow اللي بتولد عن
+
+344
+00:30:10,110 --> 00:30:15,330
+حرف ال wow أيضا اختفت .. اختفت لذلك ربه كان بيه
+
+345
+00:30:15,330 --> 00:30:21,050
+باصيرة كذلك حرف ال .. الها في بيه بلى إن ربه كان
+
+346
+00:30:21,050 --> 00:30:25,710
+بيه باصيرة الها في بيه .. أيش الحركة اللي عليها يا
+
+347
+00:30:25,710 --> 00:30:30,860
+أخوانك؟كسرة فالكسرة نشبع الكسرة طبعا وقعت لها
+
+348
+00:30:30,860 --> 00:30:35,360
+متحركة بين حرفين متحركين اللي هي ال با و البا البا
+
+349
+00:30:35,360 --> 00:30:40,820
+الأولى مكسورة بهي و البا الثانية مفتوحة نشبع
+
+350
+00:30:40,820 --> 00:30:47,160
+الكسرة فنعطيها حركتين بتسيريا فنقول بهي باسيرة هذا
+
+351
+00:30:47,160 --> 00:30:50,560
+لو كان اللي هو مادة الصلة الصغرى أما إذا كان
+
+352
+00:30:50,560 --> 00:30:57,520
+المتحرك الثاني بدل حرف البا وضعنا همزةبتصير هديا و
+
+353
+00:30:57,520 --> 00:31:00,840
+وراها همزا .. يعني زي مثلا بيشبه المد الجاز
+
+354
+00:31:00,840 --> 00:31:05,140
+المنفصل، من مده من أربعة إلى خمس حركات و بنسميه
+
+355
+00:31:05,140 --> 00:31:11,280
+مدصلة كبرى، هن مدصلة صغرى، لكن في قوله تعالى يحسب
+
+356
+00:31:11,280 --> 00:31:18,980
+أن ما له أخلاده، ما له أخلاده، هنا بنجد يا أخوات
+
+357
+00:31:18,980 --> 00:31:25,180
+أن حرف ال ه عليه ضمةو أشبعنا الضمّة يعني أعطناها
+
+358
+00:31:25,180 --> 00:31:31,300
+حركتين فصارت الضمّة wow و لما وقعت ال wow ربه أو
+
+359
+00:31:31,300 --> 00:31:37,000
+ما له و وراها حرف الهمزة صار في عندنا كأنها مد
+
+360
+00:31:37,000 --> 00:31:42,040
+جائز منفصل فمنمدها من أربع إلى خمس حركات و بنقول
+
+361
+00:31:42,040 --> 00:31:47,940
+يحسبوا أن ما له أخلة ده و بنسميها اسم ما هو اسم
+
+362
+00:31:47,940 --> 00:31:55,130
+المد في هذه الحالة؟ممتازة مد صلة كبيرة وصفة الخفاء
+
+363
+00:31:55,130 --> 00:31:59,570
+احنا قلنا هي صفة ضعف اخر صفة يا اخوات من الصفات
+
+364
+00:31:59,570 --> 00:32:05,910
+التي ليس لها ضبط هي صفة الغنىوالغنة هو صوت له
+
+365
+00:32:05,910 --> 00:32:10,610
+رانين يخرج من الخيشوم، يعني صوت أغنن له رانين يخرج
+
+366
+00:32:10,610 --> 00:32:15,530
+من الخيشوم مقداره حركتين ولا عمل لللسان به، وهي
+
+367
+00:32:15,530 --> 00:32:21,010
+صفة ملازمة لحرفين ال م و ال ن، إذا من يعرف لنا
+
+368
+00:32:21,010 --> 00:32:26,870
+الغنة يا أخوان؟ تفضلي هو صوت أغن يخرج من الخيشوم
+
+369
+00:32:26,870 --> 00:32:32,140
+مقداره حركتين لعمل اللسانأحسنتي هو صوت أغنن يخرج
+
+370
+00:32:32,140 --> 00:32:37,600
+من الخشوم مقداره حركتين لا عمل لللسان به وهو صفة
+
+371
+00:32:37,600 --> 00:32:42,940
+ملازمة لحرفي الميم والنوم ماذا نعني بقولنا لا عمل
+
+372
+00:32:42,940 --> 00:32:49,020
+لللسان به؟ يعني واحد ممكن يغلق فمه ويقن في الغنة
+
+373
+00:32:49,020 --> 00:32:56,070
+فلما ..فأنا قلت فلمّا أغلقت الفم، يعني العقل، الآن
+
+374
+00:32:56,070 --> 00:33:00,310
+لأعمل لسان بيه، وخرجت صفة الغنّة من الفيشوف لأنها
+
+375
+00:33:00,310 --> 00:33:04,290
+صفة ملازمة لحرف المين، وش كمان؟ وحرف النون، مثلا
+
+376
+00:33:04,290 --> 00:33:12,240
+إنإِنَّ اللَّهَ وَمَلَائِكَتَهُ إن أيضًا لاعمل
+
+377
+00:33:12,240 --> 00:33:16,440
+اللسان به و الصوت كله بيخرج من الخشوم إذا صفة
+
+378
+00:33:16,440 --> 00:33:22,240
+الغنى هي صوت أغنم مركّم في جسمه يعني صوت أغنم
+
+379
+00:33:22,240 --> 00:33:27,160
+بيخرج من الخشوم مقدره حركتين وهو لاعمل اللسان به
+
+380
+00:33:27,160 --> 00:33:33,960
+وهو صفة ملازمة لحرفي الميم والنومحرفاء الغنى اللي
+
+381
+00:33:33,960 --> 00:33:38,240
+هي ال meme والنون في جميع أحوالها ولكن أكتر شيء
+
+382
+00:33:38,240 --> 00:33:44,040
+بيكون في ال meme والنون المشددتين أو المضغمتين ومن
+
+383
+00:33:44,040 --> 00:33:49,400
+هنا نقول في عندنا غنى قوية جدا وغنى أضعف و أضعف و
+
+384
+00:33:49,400 --> 00:33:55,400
+أضعف وهو ما يسمى بمراتب الغنى فما هي مراتب الغنى
+
+385
+00:33:55,400 --> 00:33:59,730
+يا أخواتي؟أربع مراتب المراتب الأولى و هي أقوى
+
+386
+00:33:59,730 --> 00:34:04,930
+المراتب و هو الـ Me و النون المشددتين وصلا و وقفا
+
+387
+00:34:04,930 --> 00:34:13,410
+و هي أوضاع .. يعني أقوى المراتب الغنى مثال ذلك إن
+
+388
+00:34:13,410 --> 00:34:21,460
+أو فلم أو إنما فالغنى إيش فيها يا أخوات؟بينة في
+
+389
+00:34:21,460 --> 00:34:28,340
+النون والميم المشددتين و هي أقوى مراتب الغنى و
+
+390
+00:34:28,340 --> 00:34:33,280
+يلحق بها كذلك الإضغام يعني عندما يضغم ال ميم مع
+
+391
+00:34:33,280 --> 00:34:41,660
+الميم مثل و لهم يشتهون .. لهم .. الميم مع الميم
+
+392
+00:34:41,660 --> 00:34:45,940
+يعني اضغمت الميم الساكنة بالميم المتحركة فصاروا
+
+393
+00:34:45,940 --> 00:34:51,420
+كأنهم ميما واحدة مشددة يعني ميم مشددةأقوى أنواع
+
+394
+00:34:51,420 --> 00:34:59,260
+الغنى كذلك وما بيكم من نعمة هنا وما بيكم من نعمة
+
+395
+00:34:59,260 --> 00:35:03,180
+فيها عندنا إدغامين أيضا الإدغامين يا أخوات الميم
+
+396
+00:35:03,180 --> 00:35:07,280
+والميم إدغام شافون؟ أيوة الميم مع الميم وما بيكم
+
+397
+00:35:07,280 --> 00:35:13,540
+من هنا في عندنا إدغام شافون و بعدين من نعمة النوم
+
+398
+00:35:13,540 --> 00:35:19,590
+والنون أيضا إدغام بغنى وبالتالي هو إدغاماضغمها
+
+399
+00:35:19,590 --> 00:35:23,090
+الحرف الأول في الحرف الثاني بحيث يصيراني حرفا
+
+400
+00:35:23,090 --> 00:35:27,470
+واحدة المشددة وبالتالي هذا صار حرف النون مشدد أو
+
+401
+00:35:27,470 --> 00:35:30,690
+الميم المشدد ناتج عن الإضغام سواء كان إضغام الشفوي
+
+402
+00:35:30,690 --> 00:35:37,470
+ولا إضغام جغنم هذه المرتبة الأولى وهي الميم والنون
+
+403
+00:35:37,470 --> 00:35:44,200
+المشددتينأو ال meme .. مع ال meme اضغام ب .. شفوي
+
+404
+00:35:44,200 --> 00:35:48,700
+أو النون مع النون اضغام أيضا ب .. بغنى هذه المرتبة
+
+405
+00:35:48,700 --> 00:35:52,300
+الأولى و هي أقوى أنواع المراتب يعني أقوى مرتبة
+
+406
+00:35:53,010 --> 00:35:56,790
+المرتبة التي تليها يا أخوات هي مرتبة أقل منها وهي
+
+407
+00:35:56,790 --> 00:36:01,150
+غنّة الميم الساكنة أو التنوين عندما أو عند إضغامها
+
+408
+00:36:01,150 --> 00:36:06,310
+بالواو واليا إضغام بغنى اسمه ولكن ليس مثل المرتبة
+
+409
+00:36:06,310 --> 00:36:10,370
+الأولى اللي هي مرتبة الميم والنون المشددتين مثال
+
+410
+00:36:10,370 --> 00:36:15,770
+ذلك أن تضغم النون مع اليا أو الواو فنقول هنا من
+
+411
+00:36:15,770 --> 00:36:19,130
+يأتي بالمثال على الإضغام اللي بغنى مع الواو أو
+
+412
+00:36:19,130 --> 00:36:22,470
+اليا؟ ميعمل
+
+413
+00:36:22,730 --> 00:36:30,230
+ميووال أو ميووال ميووال هنا أضغمة النون مع الواو
+
+414
+00:36:30,230 --> 00:36:37,050
+فنقول ميووال من يعرف لنا الإضغام يا أخوان؟ ادخال
+
+415
+00:36:37,050 --> 00:36:42,990
+حرف ساكن لحرف متحرك لحيط يسيران حرفا واحدة مشددة
+
+416
+00:36:42,990 --> 00:36:48,410
+من جنس تاني فعندما أضغمنا النون مع الواو يعني
+
+417
+00:36:48,410 --> 00:36:55,310
+أضغمة النون كلها بالواووتقرأ ميووال يعني الذي يلفظ
+
+418
+00:36:55,310 --> 00:36:59,530
+حرف الواو المشدد مع مراعاة الغنى لأن الغنى هي
+
+419
+00:36:59,530 --> 00:37:03,770
+بيسموه ادغام ناخص بيدخل نصف النون ذات النون وتبقى
+
+420
+00:37:03,770 --> 00:37:08,290
+صفات الغنى موجودة فيها كذلك ما يعمل ايضا النون
+
+421
+00:37:08,290 --> 00:37:14,030
+ادخلت وادغمت في اليا فصار عندنا ادغام بغنى وهذا هي
+
+422
+00:37:14,030 --> 00:37:18,690
+المرتبة الثانيةننتقل لمرتبة التالتة يا أخوات هي
+
+423
+00:37:18,690 --> 00:37:23,510
+الغنى الناتج عن إخفاء النون الساكنة أو التنوين
+
+424
+00:37:23,510 --> 00:37:27,390
+محروف الإخفاء ما هي حروف الإخفاء؟ مين ذاكر حروف
+
+425
+00:37:27,390 --> 00:37:33,620
+الإخفاء يا أخوات؟حرف الأخفاء مجموعة في قوله صف ده
+
+426
+00:37:33,620 --> 00:37:38,980
+ثنى، كم جاد شخص قد سمى دم طيبا زد في تخن ضع ضلمة،
+
+427
+00:37:38,980 --> 00:37:44,840
+كم حرف هذه؟ خمس و عشرة حرفة حرف النون أو التنوين
+
+428
+00:37:44,840 --> 00:37:48,380
+إذا جاء بعده أي حرف من حروف هذا البيتحن اللي هي
+
+429
+00:37:48,380 --> 00:37:53,540
+حرف الأخفاءيعني تخفى، يعني و هي أعطاه صفة للنوم ما
+
+430
+00:37:53,540 --> 00:37:58,000
+بين الإضغام والإظهار مع مراعاة الغنى، ولكن الغنى
+
+431
+00:37:58,000 --> 00:38:01,340
+اللي فيه بتكون مرتبتها مرتبة إيه يا أخوات؟ مرتبة
+
+432
+00:38:01,340 --> 00:38:04,880
+تالتة، مثال ذلك مثلا الإنسان
+
+433
+00:38:06,610 --> 00:38:12,290
+الإنسان، نوف وراسين، إيش الحكم هنا؟ إخفاء حقيقي،
+
+434
+00:38:12,290 --> 00:38:17,010
+إخفاء حقيقي، نقول الإنسان، فيها غنة ولا ما فيها
+
+435
+00:38:17,010 --> 00:38:24,270
+غنة؟ فيها غنة، الإنسان، كذلك وقضي بينهم بالحق، هنا
+
+436
+00:38:24,270 --> 00:38:28,070
+ميم ساكنة وراها حرف البا، وكون فيه عندنا إخفاء
+
+437
+00:38:28,070 --> 00:38:33,110
+شهوي، نقول وقضي بينهم بالحق، فيها إخفاء، ولكن من
+
+438
+00:38:33,110 --> 00:38:37,590
+المرتب .. بكون المرتب رقمها رقم؟تلاتة او وقود
+
+439
+00:38:37,590 --> 00:38:42,390
+يبينهم بالحق تعريفهم بسماه و هكذا اخر مرتبة من
+
+440
+00:38:42,390 --> 00:38:47,210
+المراتب الغنى وهي المرتبة الرابعة وهي غنة او الغنى
+
+441
+00:38:47,210 --> 00:38:51,430
+الظاهرة غنة النون الساكنة او التنوين حال الإظهار
+
+442
+00:38:51,430 --> 00:38:56,030
+او الميم الساكنة ايضا حال الإظهار مثال ذلك يعني
+
+443
+00:38:56,030 --> 00:39:06,150
+ينأون ينهون او ألم ترا ألم تراميم وراها حرف ت فيها
+
+444
+00:39:06,150 --> 00:39:11,030
+إظهار إيش اسمه؟ إظهار شفه لكن عندما أقول ألم ترا
+
+445
+00:39:11,030 --> 00:39:15,670
+فيها أصل الغنى و كذلك الميم المتحركة أو النون
+
+446
+00:39:15,670 --> 00:39:20,150
+المتحركة فيها أصل الغنى ألم ترا يعني ليس .. يعني
+
+447
+00:39:20,150 --> 00:39:26,210
+لا نقول مثلا ألم ترا لنقولها كذا إنما تلفظ شكل
+
+448
+00:39:26,210 --> 00:39:31,350
+سريع ألم ترا أظهرنا ال .. ال ميم و أخرجنا الميم من
+
+449
+00:39:31,350 --> 00:39:37,290
+مخرجها كذلك النونفي قوله مثلا ينأونا .. ينهونا
+
+450
+00:39:37,290 --> 00:39:42,010
+أيضا في عندنا اظهار .. اظهار حلقي وهي مرتبة ..
+
+451
+00:39:42,010 --> 00:39:45,430
+مرتبتها مرتبة رابعة التلاتة .. المرتبة التلاتة
+
+452
+00:39:45,430 --> 00:39:49,030
+الأولى يا اخوتي هي فيها غنى واضحة واتسمى مرتبة
+
+453
+00:39:49,030 --> 00:39:53,330
+الكمال في الغنى أما المرتبة الرابعة سواء كانت
+
+454
+00:39:53,330 --> 00:39:58,270
+النون أو الميم المظهرتين أو المتحركتين هي فيها أصل
+
+455
+00:39:58,270 --> 00:40:05,130
+الغنىطبعا فينا خلصنا الآن الصفات كلها .. أه ..
+
+456
+00:40:05,130 --> 00:40:08,590
+الآن بس نمر سريعا على الصفات القوية والضعيفة احنا
+
+457
+00:40:08,590 --> 00:40:13,050
+أظهرناهم لوحدنا أولا بأول مثلا الصفات القوية هي
+
+458
+00:40:13,050 --> 00:40:16,970
+صفة الجهر والشدة والاستعلاء والاطباق والصفير
+
+459
+00:40:16,970 --> 00:40:21,110
+والقلقلة والانحراف والتكرير والتفشي والاستطالة
+
+460
+00:40:21,110 --> 00:40:25,090
+والغنى هذه الصفات كلها من العشرين صفات يعني احنا
+
+461
+00:40:25,090 --> 00:40:29,770
+ذلصنا يا أخوات الآن كام صفة؟عشرين صفات الصفات
+
+462
+00:40:29,770 --> 00:40:34,870
+الصفات القوية الصفات الضعيفة هي الهمس والرخاوة
+
+463
+00:40:34,870 --> 00:40:39,250
+والاستفال والانفتاح والنين والخفاة وفي عندنا صفات
+
+464
+00:40:39,250 --> 00:40:43,970
+متوسطة لا تحسب لا مع القوية ولا مع الضعيفة اللي هي
+
+465
+00:40:43,970 --> 00:40:48,670
+صفة الإذلاق والاصناع والتوسطفهذه لا حلصة بلا
+
+466
+00:40:48,670 --> 00:40:51,690
+بالضعيفة ولا بالقوي في عندنا كذلك حروف احنا لو
+
+467
+00:40:51,690 --> 00:40:56,350
+بدنا نتعرف على مخرج حرف او صفة حرف من الحروف بنشوف
+
+468
+00:40:56,350 --> 00:41:00,970
+ما هي الصفات الموجودة مثلا في حرف الفا مثلا حلق
+
+469
+00:41:00,970 --> 00:41:06,530
+الصفات اللي في حرف الفا هل هي همس ولا جهر؟ حلق
+
+470
+00:41:06,530 --> 00:41:11,990
+فيها همس ام نكتب همسهل هي شدة ولا رخاوة ولا توسط
+
+471
+00:41:11,990 --> 00:41:16,410
+في حرف الفاء؟ هلاجيها رخاوة، طيب؟ هل هي استعلاء
+
+472
+00:41:16,410 --> 00:41:20,530
+ولا استفال؟ استفال هلاجيها استفال، هلجيت فيها همس
+
+473
+00:41:20,530 --> 00:41:25,310
+ورخاوة واستفال؟ ضعيفة، هل .. نشوف كمان، هل فيها
+
+474
+00:41:25,310 --> 00:41:30,820
+إطباق ولا انفتاح؟حنلاقيها انفتاح، هي صفة الانفتاح،
+
+475
+00:41:30,820 --> 00:41:35,280
+هل هي اذلاء ولا اصمات؟ حنلاقيها اذلاب، لأنه فرح ..
+
+476
+00:41:35,280 --> 00:41:38,840
+فرح عرفت فات، main لغة، اذا الصفات اللي في الفا
+
+477
+00:41:38,840 --> 00:41:43,400
+عشان نحسبها، عندنا صفات ال .. الهمس والرخاوة
+
+478
+00:41:43,400 --> 00:41:49,880
+والانفتاح وال .. والاستفال والاذلاء، وجميع هذه
+
+479
+00:41:49,880 --> 00:41:54,400
+الصفات صفات ضعيفة والانفتاح وال .. اقصد الاذلاء
+
+480
+00:41:54,400 --> 00:42:00,230
+صفة متوسطةإذا حرف الفا ضعيف جدا لأن جميع الصفات
+
+481
+00:42:00,230 --> 00:42:05,950
+ضعيفة نشوف مثلا حرف الط .. حرف الاط .. احنا بنكون
+
+482
+00:42:05,950 --> 00:42:11,930
+حافظين الصفات العشرين حرف الاط .. هل هو حرف من صفة
+
+483
+00:42:11,930 --> 00:42:18,820
+the hence ولا جهر؟ هنلاقي جهرحرف القط فيه شدة و لا
+
+484
+00:42:18,820 --> 00:42:24,460
+رخاوة و لا توسط؟ أجد قط بكت فيه شدة حرف القط فيه
+
+485
+00:42:24,460 --> 00:42:27,980
+استعلاء تقص ضغط قذر و لا استفال باقي الحروف؟
+
+486
+00:42:27,980 --> 00:42:33,440
+هنلاقي استعلاء، هاجأت عنه، اللي هو جهر و شدة و
+
+487
+00:42:33,440 --> 00:42:37,720
+استعلاء، هل هو انفتاح و لا إطباق، صدر، طهضة،
+
+488
+00:42:37,720 --> 00:42:41,660
+إطباق، هل هو إذلاق و لا إصلاق؟ايه اللي هو ايه؟
+
+489
+00:42:41,660 --> 00:42:46,080
+اصمار طيب في كمان صفات من الصفات المتضادة، هل هو
+
+490
+00:42:46,080 --> 00:42:52,900
+صفير؟ لأ، قلقلة؟ قطب جد؟قلقلة إيش كمان في عندنا؟
+
+491
+00:42:52,900 --> 00:42:56,180
+فيش .. فيش عندنا لا تفشي ولا أي شيء إذا في قلقلة
+
+492
+00:42:56,180 --> 00:43:01,300
+وفي الخمس صفات الشدة و القويات .. إذا كلهم .. كل
+
+493
+00:43:01,300 --> 00:43:05,840
+صفات حرف الطا قوية عشان هيك .. بنعتبر يا أخوات إن
+
+494
+00:43:05,840 --> 00:43:12,440
+في عندنا صفات كلها يعني حروف كل صفات قوية ومن سوي
+
+495
+00:43:12,440 --> 00:43:18,340
+.. منسميه قوي جدا وهذا متوفر في حرف الطاوالضاد و
+
+496
+00:43:18,340 --> 00:43:22,480
+الضا و القاف كل الحروف أو كل الصفات اللي فيه صفات
+
+497
+00:43:22,480 --> 00:43:27,300
+قوية .. نسميها قوية جدا وفي عندنا صفات ضعيفة جدا
+
+498
+00:43:27,300 --> 00:43:31,440
+لأن كل الصفات اللي فيها ايه ضعيفة مثل حرفة الث
+
+499
+00:43:31,440 --> 00:43:38,430
+والح والف واله وفي عندنا حروف متوسطةيعني .. يعني
+
+500
+00:43:38,430 --> 00:43:42,370
+فيها .. فيها ضعف و فيها قوة مثل حرف الهنزة و الغين
+
+501
+00:43:42,370 --> 00:43:46,150
+و اللام و الميم و النون و في عندنا حروف قوية يعني
+
+502
+00:43:46,150 --> 00:43:49,970
+صفات القوة أكتر من صفات الضعف مثل حرف الإجأ و
+
+503
+00:43:49,970 --> 00:43:53,470
+الإدء و في عندنا حروف ضعيفة يعني صفات الضعف أكتر
+
+504
+00:43:53,470 --> 00:43:58,740
+من صفات القوة أخر شي عندنا عشان ننهيبعض الحروف يا
+
+505
+00:43:58,740 --> 00:44:03,420
+أخوات .. بعض الحروف .. بعض الناس بيلفظها غلط مثاله
+
+506
+00:44:03,420 --> 00:44:09,400
+ذلك حرف ال .. الفا بيلفظ .. بيلفظ فا فيقول أفضل
+
+507
+00:44:09,400 --> 00:44:14,760
+فلان أفضل من فلان لا نقول أفضل هي أفضل .. أفضل
+
+508
+00:44:14,760 --> 00:44:20,880
+كذلك حرف الصاب بعض الناس بيلفظ اس يقول يصدر مش
+
+509
+00:44:20,880 --> 00:44:26,760
+يصدر هي يصدر حرف الصاب كذلك حرف ال .. ال اس أو ال
+
+510
+00:44:26,760 --> 00:44:32,290
+geneالسين يُرفض ببعض الكلمات as عند الناس، يقول as
+
+511
+00:44:32,290 --> 00:44:36,410
+you do .. as you do، مش as you do، هي as you do،
+
+512
+00:44:36,410 --> 00:44:42,630
+حرف السين يُرفض as، حرف الدال .. يُرفض حرف التا
+
+513
+00:44:42,630 --> 00:44:48,420
+دال، يقول مداعهي أصلا متاع، متاع بالtaa وليس مذاع
+
+514
+00:44:48,420 --> 00:44:55,120
+حرف الtaa بيلفظه بعض الناس السي باد اس كذلك ذالك
+
+515
+00:44:55,120 --> 00:45:01,420
+بيلفظ أحيانا ذالك، ده خطأ جاء بيلفظ جاء و جاء رجل
+
+516
+00:45:01,420 --> 00:45:07,340
+خطأ طبعا هذا قال ممكن يلفظ كان أنا كنتله مثلا بعض
+
+517
+00:45:07,340 --> 00:45:14,000
+الخبائع عندنا القرى حرف القافبيلفظ ك .. او حتى بعض
+
+518
+00:45:14,000 --> 00:45:18,420
+الناس بيقول قاله بدل من ان يقول قاله يقول قاله هو
+
+519
+00:45:18,420 --> 00:45:22,300
+اللي قال و انا قلتله و هو اللي قاللي طبعا هذا خطأ
+
+520
+00:45:22,300 --> 00:45:28,360
+كذلك حرف ال .. ال .. ده بيلفظظاه ولا الظالين وهذا
+
+521
+00:45:28,360 --> 00:45:33,160
+طبعا بكون ايش خطأ احنا نهينا الان كل المخارج
+
+522
+00:45:33,160 --> 00:45:36,080
+والصفات ونكتفي بهذا القدر ونكون ان شاء الله في
+
+523
+00:45:36,080 --> 00:45:38,640
+الموضوع الآخر في اللقاء القادم بارك الله فيكم
+
+524
+00:45:38,640 --> 00:45:41,200
+جميعا السلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/ph1VHLnLb3M_raw.json b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/ph1VHLnLb3M_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0af62564e990a5189b0d0d9a5bfd0b3e9449a4c9
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/ph1VHLnLb3M_raw.json
@@ -0,0 +1 @@
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يمكن أن يكون في الحرف الواحد أكثر من صفة يعني ممكن الحرف الواحد يكون فيه تلت أربع خمس ست صفات", "tokens": [4117, 15040, 3224, 15042, 44650, 41779, 9566, 3660, 11933, 15730, 19446, 39896, 21542, 32887, 5172, 9673, 2655, 41779, 9566, 3660, 43242, 8315, 9154, 31767, 5172, 9307, 38392, 5551, 9778, 8848, 8315, 11296, 19446, 39896, 31767, 5172, 9307, 9673, 2655, 41779, 9566, 3660, 16712, 41779, 9566, 39896, 36764, 24401, 33688, 8848, 15040, 4587, 16070, 28814, 9381, 2304, 9307, 28242, 11296, 20328, 5172, 9307, 33427, 3794, 9566, 19446, 39896, 20328, 5172, 9307, 25062, 2407, 3660, 38392, 5551, 9778, 8848, 8315, 11296, 25124, 41891, 16070, 7435, 3224, 2288, 16070, 995, 14851, 30241, 16606, 16070, 41193, 3555, 995, 4587, 4724, 3794, 29538, 31767, 5172, 9307, 16247, 25513, 3615, 8032, 1211, 7251, 43020, 14739, 7251, 30544, 8978, 21542, 28480, 2423, 14407, 24401, 5551, 4117, 49115, 9154, 20328, 5172, 3660, 37495, 22653, 3714, 43020, 21542, 28480, 2423, 14407, 24401, 7251, 30544, 8978, 3224, 6055, 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"end": 1901.85, "word": " مكسور", "probability": 0.9775390625}, {"start": 1901.85, "end": 1902.59, "word": " فبتكون", "probability": 0.9677734375}, {"start": 1902.59, "end": 1902.77, "word": " في", "probability": 0.85693359375}, {"start": 1902.77, "end": 1903.21, "word": " عندنا", "probability": 0.99609375}, {"start": 1903.21, "end": 1903.63, "word": " مائل", "probability": 0.9583333333333334}, {"start": 1903.63, "end": 1903.79, "word": " إلا", "probability": 0.940185546875}, {"start": 1903.79, "end": 1904.11, "word": " كسر", "probability": 0.9803059895833334}, {"start": 1904.11, "end": 1904.63, "word": " هدول", "probability": 0.7552083333333334}, {"start": 1904.63, "end": 1904.75, "word": " يا", "probability": 0.947265625}, {"start": 1904.75, "end": 1905.03, "word": " أخوات", "probability": 0.9073486328125}, {"start": 1905.03, "end": 1905.27, "word": " هو", "probability": 0.90234375}, {"start": 1905.27, "end": 1905.63, "word": " ال", "probability": 0.802734375}, {"start": 1905.63, 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1920.61, "word": " هي", "probability": 0.9228515625}, {"start": 1920.61, "end": 1921.35, "word": " الصفير", "probability": 0.93603515625}, {"start": 1921.35, "end": 1921.47, "word": " و", "probability": 0.4228515625}, {"start": 1921.47, "end": 1921.61, "word": " هي", "probability": 0.92236328125}, {"start": 1921.61, "end": 1921.89, "word": " صفة", "probability": 0.99267578125}, {"start": 1921.89, "end": 1922.37, "word": " قوة", "probability": 0.9933268229166666}, {"start": 1922.37, "end": 1922.81, "word": " و", "probability": 0.6494140625}, {"start": 1922.81, "end": 1923.43, "word": " القلقلة", "probability": 0.82928466796875}, {"start": 1923.43, "end": 1923.79, "word": " هي", "probability": 0.85546875}, {"start": 1923.79, "end": 1924.25, "word": " صفة", "probability": 0.9905598958333334}, {"start": 1924.25, "end": 1924.61, "word": " ضعف", "probability": 0.8455403645833334}, {"start": 1924.61, "end": 1924.97, "word": " ان", "probability": 0.60302734375}, {"start": 1924.97, "end": 1925.15, "word": " شاء", "probability": 0.983154296875}, {"start": 1925.15, "end": 1925.25, "word": " الله", "probability": 0.93896484375}, {"start": 1925.25, "end": 1925.39, "word": " في", "probability": 0.88037109375}, {"start": 1925.39, "end": 1925.89, "word": " المحاضرات", "probability": 0.957421875}, {"start": 1925.89, "end": 1926.41, "word": " القادمة", "probability": 0.9947916666666666}, {"start": 1926.41, "end": 1927.21, "word": " نكمل", "probability": 0.98828125}, {"start": 1927.21, "end": 1927.79, "word": " الصفات", "probability": 0.9934895833333334}, {"start": 1927.79, "end": 1928.77, "word": " المتضادة", "probability": 0.9841796875}, {"start": 1928.77, "end": 1929.09, "word": " و", "probability": 0.98046875}, {"start": 1929.09, "end": 1929.47, "word": " نكتفي", "probability": 0.9271240234375}, {"start": 1929.47, "end": 1929.79, "word": " بهذا", "probability": 0.978515625}, {"start": 1929.79, "end": 1930.33, "word": " القدر", "probability": 0.99462890625}, {"start": 1930.33, 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" السلام", "probability": 0.966796875}, {"start": 1933.73, "end": 1934.03, "word": " عليكم", "probability": 0.94091796875}, {"start": 1934.03, "end": 1934.13, "word": " و", "probability": 0.9990234375}, {"start": 1934.13, "end": 1934.37, "word": " رحمة", "probability": 0.9007161458333334}, {"start": 1934.37, "end": 1934.63, "word": " الله", "probability": 0.97119140625}, {"start": 1934.63, "end": 1935.01, "word": " و", "probability": 0.99755859375}, {"start": 1935.01, "end": 1935.49, "word": " بركاته", "probability": 0.9105224609375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1936.033375, "duration_after_vad": 1887.7528437499964}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/rHV0Kj8bHwQ.srt b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/rHV0Kj8bHwQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9a6ef8d8ebb7068b97fc6f776784f31dd6af708
--- /dev/null
+++ b/PL9fwy3NUQKwbfMrmJBRbdEavuwd9NDKwu/rHV0Kj8bHwQ.srt
@@ -0,0 +1,1479 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:11,980 --> 00:00:14,400
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+3
+00:00:14,400 --> 00:00:18,640
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+4
+00:00:18,640 --> 00:00:23,520
+آله وصحبه وسلم استكمالا للموضوع السابق في المخارج
+
+5
+00:00:23,520 --> 00:00:28,240
+والصفات نتحدث اليوم عن الرأي رأي ابن الجزري وهو
+
+6
+00:00:28,240 --> 00:00:34,340
+الرأي الذي نتبناه نحن أن مخارج الحروف العامة خمسة
+
+7
+00:00:34,340 --> 00:00:40,320
+يتفرع عنها سبعة عشر مخرجا فرعيا نتحدث اليوم عن
+
+8
+00:00:40,320 --> 00:00:44,820
+تفصيل هذه المخارج إحنا قلنا أن المخارج الخامسة ما
+
+9
+00:00:44,820 --> 00:00:51,070
+هي يا أخوات المخرج الأول الجوف واللسان والحلق
+
+10
+00:00:51,070 --> 00:00:58,230
+اللسان الشفتان الخيشوم بيخرج منها سبعة عشر مخرجا
+
+11
+00:00:58,230 --> 00:01:04,200
+فرعيا مخرج واحد من الجوف وثلاثة خارج من الحلق و
+
+12
+00:01:04,200 --> 00:01:09,560
+عشرة مخارج من اللسان ومخرجان من الشفتين ومخرج من 
+
+13
+00:01:09,560 --> 00:01:13,920
+الخشوم هذه هي المخارج السبعة عشر مخرجا فرعيا
+
+14
+00:01:13,920 --> 00:01:20,000
+المخرج الأول هو الجوف والجوف في اللغة الخلاء وفي
+
+15
+00:01:20,000 --> 00:01:25,440
+الاصطلاح الخلاء الواقع في الفم والحلق يبقى الجوف
+
+16
+00:01:25,440 --> 00:01:29,920
+والخلاء نعرفه أن الهواء يخرج من الرئتين على
+
+17
+00:01:29,920 --> 00:01:34,820
+القصبة الهوائية يحتك في الحنجرة بأحبال الصوتية في
+
+18
+00:01:34,820 --> 00:01:40,180
+الحنجرة تخرج الصوت وبعد ذلك يخرج إلى الحلق وإلى
+
+19
+00:01:40,180 --> 00:01:45,500
+الفم هذا الخلاء كله يسمى اللي هو الجوف فالجوف من
+
+20
+00:01:45,500 --> 00:01:50,820
+حيث الاصطلاح هو الخلاء الواقع في الفم والحلق  وله
+
+21
+00:01:50,820 --> 00:01:56,180
+حروف ما هي حروف الجوف؟ طبعا في إن الجوف العام كمخرج
+
+22
+00:01:56,180 --> 00:02:00,460
+عامة وفي نفسه مخرج فرع يعني المخرج العام اللي هو
+
+23
+00:02:00,460 --> 00:02:06,360
+الجوف كم مخرج فرع يخرج منه؟ بس مخرج واحد وبيخرج من
+
+24
+00:02:06,360 --> 00:02:10,740
+المخرج الواحد اللي بنسميه أيضا الجوف ثلاث حروف ما
+
+25
+00:02:10,740 --> 00:02:14,480
+هي الحروف الثلاثة التي تخرج من الجوف تفضل
+
+26
+00:02:14,480 --> 00:02:14,780
+اختير
+
+27
+00:02:20,360 --> 00:02:24,540
+صحيح يعني حروف المادة الثلاثة وحتى نكون دقيقين جدا
+
+28
+00:02:24,540 --> 00:02:29,760
+هو الألف الساكنة المفتوح ما قبلها والواو الساكنة 
+
+29
+00:02:29,760 --> 00:02:34,380
+المضمون ما قبلها والياء الساكنة المكسور ما قبلها هل
+
+30
+00:02:34,380 --> 00:02:39,940
+يصح لنا أن نقول الألف والواو والياء فقط؟ طبعا لا لأن
+
+31
+00:02:39,940 --> 00:02:47,560
+هناك واو متحركة مثل حرف و وي يعني الحروف
+
+32
+00:02:47,560 --> 00:02:53,860
+المتحركة ليست حروف جوفية كذلك الياء يو إذا ليس من
+
+33
+00:02:53,860 --> 00:02:58,860
+الصواب أن نقول حروف المد الألف والواو والياء لابد أن
+
+34
+00:02:58,860 --> 00:03:02,840
+نقول حروف المد الألف الساكنة المفتوح ما قبلها والواو 
+
+35
+00:03:02,840 --> 00:03:05,740
+اللي هي الساكنة المضمون ما قبلها والياء هي الساكنة
+
+36
+00:03:05,740 --> 00:03:11,160
+المكسور ما قبلها هذه هي حروف المادة لكن تسمية حروف
+
+37
+00:03:11,160 --> 00:03:15,540
+المادة تسمى بالحروف المادية وحروف الجوفية وحروف 
+
+38
+00:03:15,540 --> 00:03:20,940
+العلة أما بالنسبة للجوف وهي طبعا لقب هذه الحروف
+
+39
+00:03:20,940 --> 00:03:26,180
+حروف المادة الثلاثة لقبها إيش يا أخوات؟ جوفية لماذا
+
+40
+00:03:26,180 --> 00:03:31,060
+تلقب هذه الحروف الثلاثة بالجوفية؟ لأنها تخرج من
+
+41
+00:03:31,060 --> 00:03:34,580
+الجوف وتسمى
+
+42
+00:03:34,580 --> 00:03:39,880
+حروف جوفية وتلقب بأنها حروف جوفية كذلك يطلق عليها
+
+43
+00:03:39,880 --> 00:03:43,420
+أيضا حروف العلة لماذا تسمى حروف علة؟
+
+44
+00:03:46,470 --> 00:03:50,630
+تسمى حروف العلة لتأوه العليل أي المريض إذا اشتكى من
+
+45
+00:03:50,630 --> 00:03:51,030
+ألم
+
+46
+00:04:17,860 --> 00:04:22,820
+ويمتد الصوت إذا هي تسمى حروف الجوف لأنها تخرج من
+
+47
+00:04:22,820 --> 00:04:27,560
+الجوف وتلقب بيه تسمى حروف المد لامتداد الصوت معها
+
+48
+00:04:27,560 --> 00:04:32,540
+بسهولة ويسر عند النطق بحروف المد الثلاثة كذلك
+
+49
+00:04:32,540 --> 00:04:38,080
+تسمى حروف علة لأن المريض يتأوه بهذه الحروف يقول آه
+
+50
+00:04:38,570 --> 00:04:44,730
+و إي عندما يتأوه وحروف الجوفية يا أخوات هي نفسها
+
+51
+00:04:44,730 --> 00:04:49,810
+حروف هوائية لماذا تسمى الحروف الجوفية أو الحروف
+
+52
+00:04:49,810 --> 00:04:53,130
+العلة أو حروف المد حروف جوفية أو حروف هوائية
+
+53
+00:04:53,130 --> 00:04:56,050
+لأنه فضل أخت
+
+54
+00:04:59,610 --> 00:05:05,230
+أحسنتي لأن حروف المادة ليس لها حيز تنتهي إليه بل 
+
+55
+00:05:05,230 --> 00:05:10,450
+انتهاؤها بانتهاء النفس ما معنى هذه الجملة أن حروف 
+
+56
+00:05:10,450 --> 00:05:15,510
+المادة أو الحروف الجوفية ليس لها حيز تنتهي إليه بل 
+
+57
+00:05:15,510 --> 00:05:23,610
+انتهاؤها بانتهاء النفس يعني الواحد ممكن يقول آه
+
+58
+00:05:23,610 --> 00:05:26,910
+لما ينتهي نفسه
+
+59
+00:05:30,710 --> 00:05:37,740
+بنت نفسه نفس الموضوع إذا حروف المادة الثلاثة الألف 
+
+60
+00:05:37,740 --> 00:05:40,680
+الساكنة المفتوح ما قبلها والواو الساكنة المضمون ما
+
+61
+00:05:40,680 --> 00:05:44,280
+قبلها والياء الساكنة المكسور ما قبلها هي حروف 
+
+62
+00:05:44,280 --> 00:05:48,940
+هوائية لأن ليس لها حيز تنتهي إليه بل انتهاؤها
+
+63
+00:05:48,940 --> 00:05:53,780
+بانتهاء النفس ولذلك تسمى هذه الحروف من حروف الخفاء
+
+64
+00:05:53,780 --> 00:05:57,760
+المجموعة في قوله تعالى والتي سنأخذه إن شاء الله في
+
+65
+00:05:57,760 --> 00:06:02,100
+دروس قادمة هذا المخرج الأول يا أخوات المخرج الثاني
+
+66
+00:06:02,760 --> 00:06:09,020
+أين ما هو؟ الحلق وقلنا إن المخرج خمسة الجوف الحلق 
+
+67
+00:06:09,020 --> 00:06:13,020
+الحلق طبعا الحلق اللي هو بعد ما بعد الحنجرة يعني
+
+68
+00:06:13,020 --> 00:06:18,220
+قبل اللسان فيه هناك يعني جزء من أجزاء الفم ويسمى
+
+69
+00:06:18,220 --> 00:06:24,630
+الحلق وهذا الحلق يشتمل على كم مخرج فرعي؟ على ثلاثة
+
+70
+00:06:24,630 --> 00:06:29,450
+مخارج فرعية اللي هي أقصى الحلق من الآخر يعني مما
+
+71
+00:06:29,450 --> 00:06:33,570
+يلي الحنجرة أو نهاية القصبة الهوائية وسط الحلق
+
+72
+00:06:33,570 --> 00:06:38,810
+وأدنى الحلق أقصى الحلق وسط الحلق أدنى الحلق كأنه
+
+73
+00:06:38,810 --> 00:06:44,810
+في عندنا سلم بثلاث درجات أقصى الحلق وهو آخر شيء
+
+74
+00:06:44,810 --> 00:06:50,820
+أقصى شيء من جهة الفم الخارج كذلك يلي وسط الحلق و
+
+75
+00:06:50,820 --> 00:06:55,740
+بعد ذلك في عندنا أدنى الحلق أقصى الحلق بيخرج منه
+
+76
+00:06:55,740 --> 00:07:03,120
+حرفان ما هما الهمزة والهاء ووسط الحلق بيخرج منه أيضا 
+
+77
+00:07:03,120 --> 00:07:08,340
+حرفان وهما العين والهاء أدنى الحلق بيخرج منه حرفان
+
+78
+00:07:08,340 --> 00:07:12,260
+الغين والخاء أما بالنسبة لأقصى الحلق يخرج منه 
+
+79
+00:07:12,260 --> 00:07:16,780
+الهمزة والهاء إذا أردنا أن نتعرف على مخرج أي حرف 
+
+80
+00:07:16,780 --> 00:07:23,770
+أخوات ماذا نفعل؟ نأتي بالحرف ساكنة مسبوق بهمزة نقول ا
+
+81
+00:07:23,770 --> 00:07:30,290
+ا من أين خرج حرف الـ ا؟ أما نشعر نشعر أثناء النطق ا
+
+82
+00:07:30,290 --> 00:07:36,030
+أو اه اه من أقصى الحلق يعني من آخر شيء في الحلق
+
+83
+00:07:37,250 --> 00:07:42,070
+ووسط الحلق بيخرج منه حرف الـ  اع والـ  اح بنشوف أنه
+
+84
+00:07:42,070 --> 00:07:48,170
+يطلع درجة يعني أقصى شيء ا واه من أقصى الحلق اع و
+
+85
+00:07:48,170 --> 00:07:56,470
+اح ووسط الحلق اغ واخ من أقصى الحلق هذه الست حروف 
+
+86
+00:07:56,470 --> 00:08:00,510
+حرفان الهمزة والهاء بيخرجوا من أقصى الحلق العين و
+
+87
+00:08:00,510 --> 00:08:04,350
+الهاء بيخرجوا من وسط الحلق الغين والخاء بيخرجوا من
+
+88
+00:08:04,350 --> 00:08:11,390
+أدنى الحلق لقب هذه الحروف ما هي؟ حروف حروف الحلق أو 
+
+89
+00:08:11,390 --> 00:08:15,430
+حروف الحلقية مثل ما لقبنا حروف المادة الثلاثة
+
+90
+00:08:15,430 --> 00:08:20,190
+بالحروف الجوفية هذه الحروف نلقبها بالحروف الحلقية
+
+91
+00:08:20,190 --> 00:08:25,050
+هناك سبب لقبها بالحروف الجوفية لأنها تخرج من الجوف
+
+92
+00:08:25,050 --> 00:08:29,230
+وهنا الحروف الحلقية تلقب بالحروف الحلقية لأنها 
+
+93
+00:08:29,230 --> 00:08:34,430
+تخرج من أين؟ من الحلق هذا هو المخرج الثاني يعني لو 
+
+94
+00:08:34,430 --> 00:08:40,830
+سألناكم حرف العين من أين هي الخرج؟ وسط الحلق حرف
+
+95
+00:08:40,830 --> 00:08:48,090
+الهاء من أين يخرج؟ أقصى الحلق حرف الخاء يخرج من أدنى
+
+96
+00:08:48,090 --> 00:08:53,750
+الحلق ننتقل إلى المخرج العام الثالث وهو اللسان 
+
+97
+00:08:53,750 --> 00:08:58,770
+وهذا اللسان يعني بيخرج منه 18 حرف يعني عشرة مخارج 
+
+98
+00:08:58,770 --> 00:09:03,740
+لثمانية عشر حرفا يعني معظم حروف اللغة العربية تخرج
+
+99
+00:09:03,740 --> 00:09:08,360
+من وين؟ من اللسان لذلك اللسان مهم جدا وأصعب شيء 
+
+100
+00:09:08,360 --> 00:09:13,880
+أصلا لأن في عندنا عشرة مخارج فرعية بتخرج من اللسان
+
+101
+00:09:13,880 --> 00:09:19,820
+بـ 18 حرف من حروف اللغة العربية لكن قبل أن ندخل على 
+
+102
+00:09:19,820 --> 00:09:24,440
+اللسان نتعرف على أجزاء اللسان اللسان طبعا في عندنا 
+
+103
+00:09:24,440 --> 00:09:29,040
+طرف اللسان وهو مما يلي الشفتين اللي هو رأس اللسان
+
+104
+00:09:29,040 --> 00:09:32,850
+طرف اللسان اللي هو طرف اللسان هذا الجزء الأول يعني 
+
+105
+00:09:32,850 --> 00:09:38,550
+في عندنا حفتي اللسان لو قلنا نعتبر أن يدي هذه هي 
+
+106
+00:09:38,550 --> 00:09:43,000
+اللسان طرف اللسان هي المنطقة هذه اللي هي رأس
+
+107
+00:09:43,000 --> 00:09:49,780
+اللسان، طرف اللسان أو الطرف، حفتي اللسان له حافة
+
+108
+00:09:49,780 --> 00:09:54,820
+يمنى، هي حافة يمنى وحافة يسرة، اسمه حافتي اللسان،
+
+109
+00:09:54,820 --> 00:09:59,380
+حافة يمنى وحافة يسرة، وسط اللسان اللي هي المنطقة
+
+110
+00:09:59,380 --> 00:10:04,280
+هذه، نعتبر أن هذا وسط اللسان في عندنا أقصى اللسان
+
+111
+00:10:04,280 --> 00:10:07,840
+اللي هو المنطقة هذه أقصى اللسان مثلا هذا اللسان
+
+112
+00:10:07,840 --> 00:10:12,420
+أقصى اللسان وسط اللسان رأس اللسان حافة اللسان 
+
+113
+00:10:12,420 --> 00:10:16,440
+اليمنى حافة اللسان اليسرى في عندنا يا أخوات ظهر
+
+114
+00:10:16,440 --> 00:10:22,000
+اللسان اللي هي المنطقة هذه فوق ظهر اللسان بطن
+
+115
+00:10:22,000 --> 00:10:26,200
+اللسان اللي هي اللي اتحاد في عندنا الحنك الأعلى 
+
+116
+00:10:26,200 --> 00:10:30,400
+والحنك الأسفل الحنك الأعلى اللي هو ما يعلي اللسان
+
+117
+00:10:30,400 --> 00:10:34,700
+من العضمة التي في سقف الحلق نسميها سقف الحلق أو
+
+118
+00:10:34,700 --> 00:10:40,370
+مثلا الحنك الأعلى يسمى الذي يغطي اللسان يسمى الحنك
+
+119
+00:10:40,370 --> 00:10:44,890
+الأعلى وفي عندنا حنك أسفل اللي هو إلى أسفل اللسان
+
+120
+00:10:44,890 --> 00:10:50,710
+إذا هذه أجزاء اللسان والحنك الأعلى والحنك الأسفل
+
+121
+00:10:50,710 --> 00:10:55,830
+من هذه الأجزاء يا أخوات تخرج المخارج الخاصة أو
+
+122
+00:10:55,830 --> 00:11:00,810
+الفرعية من اللسان اللسان قلنا كم مخرج فرعي بيخرج 
+
+123
+00:11:00,810 --> 00:11:07,040
+من اللسان عشرة مخارج فرعية نبدأ بالمخرج الأول المخرج 
+
+124
+00:11:07,040 --> 00:11:11,040
+الأول لن نبدأه من طرف سنبدأ من الأقصى وننزل تحت 
+
+125
+00:11:11,040 --> 00:11:15,940
+نعتبر أن هذه إيدي هي اللسان لو كان في عندنا صور أفضل 
+
+126
+00:11:15,940 --> 00:11:20,900
+أقصى اللسان المنطقة هذه مثلا مع ما يحاذيها من 
+
+127
+00:11:20,900 --> 00:11:24,740
+الحنك الأعلى الحنك الأعلى اللي هو سقف الحلق 
+
+128
+00:11:24,740 --> 00:11:28,460
+الحنك الأعلى سقف الحلق فعندما أقول أقصى اللسان مع 
+
+129
+00:11:28,460 --> 00:11:33,260
+ما يحاذيها من الحنك الأعلى بيخرج منه حرف القاف حرف
+
+130
+00:11:33,260 --> 00:11:39,580
+الـ ق حتى نحن عندما نقول اقق اقق نجد أن أقصى 
+
+131
+00:11:39,580 --> 00:11:45,100
+اللسان التثقية بالحنك الأعلى فحصر الصوت وكذلك
+
+132
+00:11:45,100 --> 00:11:50,520
+النفس ثم انفتح المخرج فخرجت منه النبرة التي نسميها 
+
+133
+00:11:50,520 --> 00:11:55,160
+القلقلة إذا أقصى اللسان مع ما يحاذيه من الحنك
+
+134
+00:11:55,160 --> 00:12:03,540
+الأعلى يخرج منه حرف القاف نقول أنه أقصى اللسان مع
+
+135
+00:12:03,540 --> 00:12:07,220
+ما يحاذيه من الحنك الأعلى بيخرج منه حرف واحد وهو 
+
+136
+00:12:07,220 --> 00:12:13,860
+حرف القاف بعد ذلك يأتي الحرف الذي يليه وهو نقول 
+
+137
+00:12:13,860 --> 00:12:19,960
+اك اك بيخرج أيضا حرف الكاف من أقصى اللسان أسفل 
+
+138
+00:12:19,960 --> 00:12:24,140
+مخرج حرف القاف مع ما يحاذيه من الحنك الأعلى نقول
+
+139
+00:12:24,140 --> 00:12:30,230
+اكو نحن نجد هنا أن اقط اول شي أقصى اللسان مع ما
+
+140
+00:12:30,230 --> 00:12:35,510
+يحاذيها من الحنك الأعلى بعد ذلك المخرج الذي يليه 
+
+141
+00:12:35,510 --> 00:12:41,190
+بيأتي حرف الكاف وبيخرج من أقصى اللسان ولكن لابد أن 
+
+142
+00:12:41,190 --> 00:12:45,630
+نقول أسفل مخرج حرف القاف مع ما يحاذيه من الحنك
+
+143
+00:12:45,630 --> 00:12:50,450
+الأعلى وبيخرج منه حرف الكاف يعني لو صورنا أن هذه
+
+144
+00:12:50,450 --> 00:12:54,070
+يد اللسان أقصى اللسان من الجهة هذه و هذا الحنك
+
+145
+00:12:54,070 --> 00:12:58,600
+الأعلى نقولها أقصى اللسان يعني أقصى اللسان مع
+
+146
+00:12:58,600 --> 00:13:02,920
+ما يحاذيه من الحنك الأعلى الكاف أقصى اللسان أسفل مخرج
+
+147
+00:13:02,920 --> 00:13:08,880
+حرف القاف يعني المنطقة هذه نقولها كبنجد أن أقصى
+
+148
+00:13:08,880 --> 00:13:12,360
+اللسان أسفل مخرج حرف القاف المتصل بالحنك الأعلى
+
+149
+00:13:12,360 --> 00:13:17,380
+فخرج منه حرف الكاف هي المخرج الثاني وهذا الحرفان
+
+150
+00:13:17,380 --> 00:13:21,760
+يا أخوات اللي هو حرف القاف وحرف الكاف يطلق عليهم
+
+151
+00:13:21,760 --> 00:13:26,800
+أو يلقبان بالحرفين اللّهويين لماذا يطلق عليهم
+
+152
+00:13:26,800 --> 00:13:33,090
+بالحرفين اللّهويين؟ فضل أختي يخرجان بالقرب من اللهاة
+
+153
+00:13:33,090 --> 00:13:37,150
+واللهاة هي اللحمية التي تكون في أقصى الحنك الأعلى
+
+154
+00:13:37,150 --> 00:13:42,490
+والملتصق فيها لسان المزمار هذه اللهاة فلأن حرف
+
+155
+00:13:42,490 --> 00:13:47,830
+القاف وحرف الكاف يخرجان بالقرب من اللهاة يطلق على
+
+156
+00:13:47,830 --> 00:13:52,710
+حرف القاف والكاف الحرفان اللّهويان هذه عندنا المخرج
+
+157
+00:13:52,710 --> 00:13:56,930
+الثاني والمخرج الثالث يا أخوات بيخرج منه ما هي 
+
+158
+00:13:56,930 --> 00:14:00,720
+الحروف اللي تخرج من المخرج الثالث؟ اللي هي الجيم
+
+159
+00:14:00,720 --> 00:14:07,180
+والشين والياء وتخرج من وسط اللسان مع ما يحاذيه من
+
+160
+00:14:07,180 --> 00:14:15,320
+الحنك الأعلى نقول جا جا ولنحضر من أن نقوله جا جلو
+
+161
+00:14:15,320 --> 00:14:31,860
+شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا شا 
+
+162
+00:14:43,470 --> 00:14:46,830
+الياء المتحركة وليس الياء المادية الياء المادية
+
+163
+00:14:46,830 --> 00:14:53,550
+بتخرج كما قلنا من الجوف نقول المؤمنين لكن الياء
+
+164
+00:14:53,550 --> 00:15:00,930
+المتحركة مثل كلمة يأكل يلعب ينام يعملون هذا حرف
+
+165
+00:15:00,930 --> 00:15:06,370
+الياء متحركة وليس فيها مادية ليس حرف مدٍّ وإنما حرف
+
+166
+00:15:06,370 --> 00:15:09,920
+يخرجه من وسط اللسان مع ما يحاذيه من الحنك الأعلى
+
+167
+00:15:09,920 --> 00:15:16,200
+وهذا لقبه شجرية لأن الحروف التي تخرج من وسط اللسان
+
+168
+00:15:16,200 --> 00:15:21,100
+مع ما يحاذيه من الحنك الأعلى لقبها نلقبها شجرية
+
+169
+00:15:21,100 --> 00:15:26,060
+لأنها تخرج من شجر الفم يعني أوسع جزء بالفم يعني
+
+170
+00:15:26,060 --> 00:15:31,820
+متسعة من الفم إذا حروف هذه المخرج الثالث وسط
+
+171
+00:15:31,820 --> 00:15:32,780
+اللسان ال
+
+172
+00:15:35,550 --> 00:15:40,150
+الياء .. طب عندنا نقول شين وعندنا نقول ياء لأنه 
+
+173
+00:15:40,150 --> 00:15:43,810
+إذا أردنا نتعرف على مخرج أي حرف ماذا نفعل يا أخوات
+
+174
+00:15:43,810 --> 00:15:49,010
+نأتي بالحرف الساكن أو مشددا مسبوقا بهمزٍ وننطق 
+
+175
+00:15:49,010 --> 00:15:53,790
+الحرف فحيثما انحصر الصوت فهو مخرجه فأنا عندما أقول 
+
+176
+00:15:53,790 --> 00:15:59,030
+ياء أجد أن الريح ينتشر في الفم لكن المخرج يكون من
+
+177
+00:15:59,030 --> 00:16:06,870
+وسط الفم الياء جا جا وياء و ياء يو يعني الياء المتحركة
+
+178
+00:16:06,870 --> 00:16:10,650
+وهذه الحروف الثلاثة التي تخرج من وسط اللسان مع ما 
+
+179
+00:16:10,650 --> 00:16:14,470
+يحدث من حنك الأعلى نسميها أو نلقبها بالحروف
+
+180
+00:16:14,470 --> 00:16:20,500
+الشجرية المخرج الرابع يا أخوات من مخرج حرف الضاد أو
+
+181
+00:16:20,500 --> 00:16:25,080
+من مخرج اللسان طبعًا اللسان مخرج وعام له عشرة مخارج
+
+182
+00:16:25,080 --> 00:16:28,080
+أخذنا أقصى اللسان مع ما يحاذيه من الحنك الأعلى
+
+183
+00:16:28,080 --> 00:16:31,880
+بيخرج منه حرف القاف أقصى اللسان أسفل مخرج حرف 
+
+184
+00:16:31,880 --> 00:16:35,680
+القاف مع ما يحاذيه من الحنك الأعلى وبيخرج منه حرف
+
+185
+00:16:35,680 --> 00:16:40,400
+الكاف الكاف ووسط اللسان مع ما يحاذيه من الحنك
+
+186
+00:16:40,400 --> 00:16:44,880
+الأعلى وبيخرج منه ثلاثة حروف اللي هي الجيم والشين 
+
+187
+00:16:44,880 --> 00:16:51,650
+والياء أما المخرج الرابع فهو مخرج حرف الضاد والضاد
+
+188
+00:16:51,650 --> 00:16:56,130
+هي يعني امتازت فيها اللغة العربية التي تسمى أو تطلق
+
+189
+00:16:56,130 --> 00:17:00,770
+عليها بلغة الضاد لأنه لا يوجد أي لغة في العالم 
+
+190
+00:17:00,770 --> 00:17:04,450
+فيها حرف الضاد يعني أي لغة في العالم ينطق حرف 
+
+191
+00:17:04,450 --> 00:17:09,770
+الضاد ظال واحد لو اسمه ظاهر نقول ظاهر يكتب حرف 
+
+192
+00:17:09,770 --> 00:17:13,970
+الدال لكن حرف الضاد هو حرف امتازت فيه اللغة العربية
+
+193
+00:17:13,970 --> 00:17:19,190
+فهي لغة الضاد إذا مخرج حرف الضاد يخرجه من إحدى
+
+194
+00:17:19,190 --> 00:17:24,950
+حافتي اللسان اليمنى أو اليسرى ومن اليسرى أسهل مع
+
+195
+00:17:24,950 --> 00:17:28,570
+ما يليها من أضراس الجهة العليا يعني هي اللسان مثلًا
+
+196
+00:17:28,570 --> 00:17:32,880
+يدي اللسان الجهة اليمنى هي الجهة اليمنى أو الجهة 
+
+197
+00:17:32,880 --> 00:17:37,980
+اليسرى إحدى حافتي لسان اليمنى أو اليسرى ولكن من 
+
+198
+00:17:37,980 --> 00:17:41,960
+اليسرى أيسر مع ما يليها من أضراس الجهة العليا
+
+199
+00:17:41,960 --> 00:17:49,710
+فنقول ض ض ض فو هكذا ولا نقول د ولا ضّ إنما هي 
+
+200
+00:17:49,710 --> 00:17:54,550
+أب ولا الضالين يعني الحافة اليمنى أو الحافة 
+
+201
+00:17:54,550 --> 00:17:59,250
+اليسرى ويجب أن نخرجها من الحافتين ولكن الأيسر 
+
+202
+00:17:59,250 --> 00:18:04,710
+الحافة اليسرى أو يخرج منه حرف الأب اللي هو مثل ولا 
+
+203
+00:18:04,710 --> 00:18:11,770
+الضالين وحرف حرف الضاد يا أخوات قال بعض العلماء
+
+204
+00:18:11,770 --> 00:18:18,330
+أن لقبه يعني يلحق بالحروف الشجرية وليس هناك إجماع
+
+205
+00:18:18,330 --> 00:18:22,230
+ما بين العلماء يعني لو سألنا .. لو سألنا سؤال أن 
+
+206
+00:18:22,230 --> 00:18:28,220
+أجمع العلماء على أن حرف الضاد شجري يعني من الحروف
+
+207
+00:18:28,220 --> 00:18:32,900
+الشجرية نقول هذا خطأ لأنها ليست إجماعًا وإنما ذكر
+
+208
+00:18:32,900 --> 00:18:38,620
+بعض العلماء أن لقب حرف الضاد شجري لأنه بيخرج من وسط
+
+209
+00:18:38,620 --> 00:18:42,560
+اللسان تقريبًا إحدى حافتي لسان اليمنى أو اليسرى ومن
+
+210
+00:18:42,560 --> 00:18:47,660
+اليسرى أيسر قالوا أن لقبه شجري وليس هناك إجماع على
+
+211
+00:18:47,660 --> 00:18:52,870
+ذلك هذا يا أخوات هو المخرج الرابع من مخرج اللسان
+
+212
+00:18:52,870 --> 00:18:59,830
+ننزل قليلًا هنجد أن هناك المخرج الخامس وهو مخرج حرف 
+
+213
+00:18:59,830 --> 00:19:05,490
+اللام مخرج حرف اللام من أين يخرج؟ يخرج من أدنى
+
+214
+00:19:05,490 --> 00:19:11,510
+حافتي اللسان مع ما يحاذيه من لثة الأسنان العليا أدنى
+
+215
+00:19:11,510 --> 00:19:14,710
+حافتي لسان يعني اعتبرنا أن هذا اللسان أدنى
+
+216
+00:19:14,710 --> 00:19:18,590
+الحافتين هذه الحافة اليمنى وهذه الحافة اليسرى أدنى
+
+217
+00:19:18,590 --> 00:19:21,690
+الحافتين يعني أقرب الحافتين يعني المنطقة هذه
+
+218
+00:19:21,690 --> 00:19:27,530
+المنطقة هذه كلها تسمى أدنى حافتي لسان مع ما يليها 
+
+219
+00:19:27,530 --> 00:19:32,110
+من لثة الأسنان العليا الأسنان العليا عندما نقول يا
+
+220
+00:19:32,110 --> 00:19:38,770
+أخوات الأسنان العليا ماذا تشمل؟ تشمل الثنايا اللي
+
+221
+00:19:38,770 --> 00:19:44,050
+هم الأسنان هدول، الثنايا، وتشمل الرباعيات اللي
+
+222
+00:19:44,050 --> 00:19:49,390
+بعد الثانية، وتشمل النابين، الناب هذا والناب هذا، 
+
+223
+00:19:49,390 --> 00:19:55,020
+وتشمل الضحكين اللي هو أول درس بعد الناب إذا هذه
+
+224
+00:19:55,020 --> 00:20:01,540
+تسمى الأسنان العليا فعندما نقول حرف ال لام لام نجد
+
+225
+00:20:01,540 --> 00:20:07,220
+أنه أدنى حافتي لسان المتصلتين بلثة الأسنان العليا 
+
+226
+00:20:07,220 --> 00:20:12,620
+فخرج منه حرف اللام لام يعني ليس رأس اللسان إنما ال
+
+227
+00:20:12,620 --> 00:20:17,240
+أدنى حافتي لسان مع ما يليها من لثة الأسنان العليا
+
+228
+00:20:17,240 --> 00:20:20,440
+التي تجتمل على الثنايا
+
+229
+00:20:22,630 --> 00:20:29,010
+زاد رباعيات اللي بعدها زاد النابين زاد الضحكين
+
+230
+00:20:29,010 --> 00:20:33,870
+وهو أول درس بعد الناب لماذا يطلق على الضحكين
+
+231
+00:20:33,870 --> 00:20:39,810
+بالضحكين؟ لأنهما لا يبدوان إلا عند الضحك يعني 
+
+232
+00:20:39,810 --> 00:20:43,810
+عندما يتكلم الإنسان أكثر شيء بيظهر الناب بيظهر
+
+233
+00:20:43,810 --> 00:20:49,010
+الرباعية أو الأسنان لكن متى يظهر الضحكين عندما 
+
+234
+00:20:49,010 --> 00:20:54,730
+يضحك الإنسان تنفتح الشفتين فيظهر الضحكين لذلك لأن
+
+235
+00:20:54,730 --> 00:20:59,570
+هما لا يبدوان إلا عند الضحك يطلق على هذين الدرسين
+
+236
+00:20:59,570 --> 00:21:06,160
+اللذين يلي الناب يطلق عليهما إيش الضحكين هذا المخرج
+
+237
+00:21:06,160 --> 00:21:11,520
+الخامس المخرج السادس يا أخوات وهو مخرج حرف النون 
+
+238
+00:21:11,520 --> 00:21:18,420
+ومخرج حرف النون يخرج من طرف اللسان أسفل مخرج حرف
+
+239
+00:21:18,420 --> 00:21:23,760
+اللام مع ما يحاذيه من لثة الثنايا العليا الثنايا
+
+240
+00:21:23,760 --> 00:21:28,940
+العليا هدول الأسنان القواطع يسمى الثنايا العليا
+
+241
+00:21:29,500 --> 00:21:34,360
+اللثة اللي هي اللحمية التي تنغرز فيها الثناية
+
+242
+00:21:34,360 --> 00:21:37,880
+العليا يعني اللحمية من الداخل لحمة الفم من الداخل 
+
+243
+00:21:37,880 --> 00:21:43,600
+حول الثناية العليا يسمى لثة الثناية العليا ويخرج
+
+244
+00:21:43,600 --> 00:21:47,660
+منه حرف النون يبقى طرف اللسان مع ما يليه من لثة
+
+245
+00:21:47,660 --> 00:21:52,980
+الثناية العليا أسفل مخرج حرف اللام لازم نقول أسفل
+
+246
+00:21:52,980 --> 00:22:00,050
+مخرج حرف اللام بيخرج منه حرف النون فقول نن أنا 
+
+247
+00:22:00,050 --> 00:22:05,450
+عندما أقول نن أجد أنه طرف اللسان المتصل بلثة
+
+248
+00:22:05,450 --> 00:22:11,630
+الثنايا العليا فخرج منه حرف النون وحرف النون أسفل
+
+249
+00:22:11,630 --> 00:22:17,350
+مخرج حرف اللام المخرج الذي يليه هو المخرج السابع
+
+250
+00:22:17,350 --> 00:22:23,150
+وهو مخرج حرف الراء حرف الراء يخرج من ظهر طرف اللسان 
+
+251
+00:22:23,150 --> 00:22:28,530
+أسفل مخرج حرف النون مع ما يليه من لثة الثنايا
+
+252
+00:22:28,530 --> 00:22:36,010
+العليا يعني بالترتيب اللام نون راء اللام أدنى حافتي
+
+253
+00:22:36,010 --> 00:22:41,870
+لسان مع لثة الثنايا العليا كلها النون أسفل رأس
+
+254
+00:22:41,870 --> 00:22:46,170
+اللسان أو طرف اللسان أسفل مخرج حرف اللام مع ما
+
+255
+00:22:46,170 --> 00:22:51,970
+يليه من لثة الثنايا العليا وليست الأسنان العليا 
+
+256
+00:22:51,970 --> 00:22:57,160
+وهذا المخرج الخامس المخرج السابع أسفل المخرج السابع
+
+257
+00:22:57,160 --> 00:23:01,060
+اللي هي ظهر طرف اللسان أو طرف اللسان مائلًا إلى 
+
+258
+00:23:01,060 --> 00:23:06,480
+الظهر أسفل مخرج حرف النون مع ما يليه من لثة
+
+259
+00:23:06,480 --> 00:23:12,960
+الثنايا العليا بيخرج منه حرف الراء راء راء هذا المخرج
+
+260
+00:23:12,960 --> 00:23:16,700
+الثلاثة هذه الحروف الثلاثة اللي هو مخرج اللام
+
+261
+00:23:16,700 --> 00:23:22,220
+والنون والراء هي عندنا ثلاثة مخارج عند الشاطبي
+
+262
+00:23:22,220 --> 00:23:26,780
+اعتبارها مخرج واحد أو عند الفراء اعتبارها مخرج
+
+263
+00:23:26,780 --> 00:23:32,620
+واحد لذلك دمج هذه المخارج الثلاثة قال بدل أن يقول
+
+264
+00:23:34,040 --> 00:23:39,000
+طرف أدنى حافتي اللسان وطرف اللسان واللام والنون 
+
+265
+00:23:39,000 --> 00:23:43,000
+والراء اعتبارها كلها طرف اللسان مع لثة
+
+266
+00:23:43,000 --> 00:23:46,760
+الثنايا العليا أو الأسنان العليا واعتبارها كلها
+
+267
+00:23:46,760 --> 00:23:50,880
+مخرج واحد لكن عندنا .. عندنا نحن على حسب ابن 
+
+268
+00:23:50,880 --> 00:23:57,360
+الجزري اعتبارها أن ثلاثة مخارج مخرج لللام مخرج للنون
+
+269
+00:23:57,360 --> 00:24:03,300
+مخرج للراء اللام أدنى حافتي لسان مع ما يليه من لثة
+
+270
+00:24:03,300 --> 00:24:08,700
+الأسنان العليا النون طرف اللسان مع ما يليه من لثة
+
+271
+00:24:08,700 --> 00:24:14,850
+الثنايا العليا أسفل مخرج حرف اللام الراء ظهر طرف 
+
+272
+00:24:14,850 --> 00:24:18,990
+اللسان أو طرف اللسان مائلًا إلى الظهر أسفل مخرج
+
+273
+00:24:18,990 --> 00:24:23,090
+حرف النون بالترتيب مع ما يليه من لثة الثنايا العليا
+
+274
+00:24:23,090 --> 00:24:28,310
+ويخرج منه حرف الراء وهذه الحروف الثلاثة كلها التي
+
+275
+00:24:28,310 --> 00:24:32,550
+هي ثلاثة مخارج يعني يطلق عليها أو يلقب بالحروف
+
+276
+00:24:32,550 --> 00:24:37,810
+الذلقية لأنها تخرج من ذلق اللسان اللي هو طرف 
+
+277
+00:24:37,810 --> 00:24:42,890
+اللسان ننتقل يا أخوات إلى المخرج الثامن والمخرج
+
+278
+00:24:42,890 --> 00:24:50,050
+الثامن يخرج منه حرف التاء والدال والطاء وهي من ظهر طرف 
+
+279
+00:24:50,050 --> 00:24:55,310
+اللسان مع ما يليه من أصول الثنايا العليا ما معنى يا
+
+280
+00:24:55,310 --> 00:24:59,510
+أخوات أصول الثنايا العليا؟ أصول الثنايا العليا ليست 
+
+281
+00:24:59,510 --> 00:25:06,850
+الأطراف هذه وإنما الثنايا العليا عندما تنغرز بالفك
+
+282
+00:25:06,850 --> 00:25:10,170
+العلوي هذا هو أصول الثنايا العليا يعني الجذر نفسه
+
+283
+00:25:10,170 --> 00:25:14,150
+جذر الثنايا العليا يعني جذر الثنايا وهو المكان
+
+284
+00:25:14,150 --> 00:25:18,230
+الذي ينغرز به في الفك يسمى أصول الثنايا العليا
+
+285
+00:25:18,230 --> 00:25:25,100
+فعندما أقول ات و اطو إد أجد أنه ظهر طرف اللسان
+
+286
+00:25:25,100 --> 00:25:29,820
+متساقيًا مع أصول الثنايا العليا وخرجت منه هذه الحروف
+
+287
+00:25:29,820 --> 00:25:36,620
+حرف الات والأت والإد إذا هذا هو المخرج رقم ثمانية
+
+288
+00:25:36,620 --> 00:25:45,670
+كذلك لقب هذه الحروف تسمى نطعية، يعني الات والاط
+
+289
+00:25:45,670 --> 00:25:52,050
+والاد تسمى أو تُلقب بالحروف النطعية لأنها تخرج من
+
+290
+00:25:52,050 --> 00:25:58,320
+نطع الفم وهي بداية انفتاح الفم فإني عندما أقول يعني
+
+291
+00:25:58,320 --> 00:26:06,100
+يضيق فمي، فبداية انفتاح الفم يُسمى نطع الفم، فلأن 
+
+292
+00:26:06,100 --> 00:26:11,480
+حرف ال it و ال it و ال it بتخرج عندما تضيق فترة
+
+293
+00:26:11,480 --> 00:26:16,080
+الشفتين ويخرج ويُسمى نطع الفم يعني بداية انفتاح
+
+294
+00:26:16,080 --> 00:26:21,000
+الفم تُلقب بهذه الحروف، وحرف ال it و ال it و ال it 
+
+295
+00:26:21,000 --> 00:26:26,260
+تُلقب بالحروف النطعية هذا يا أخوات هو المخرج رقم 8
+
+296
+00:26:27,020 --> 00:26:34,980
+المخرج التاسع وهو مخرج حرف السين والصاد والزاي (S) و
+
+297
+00:26:34,980 --> 00:26:43,200
+(S) و (IZ) هذه الحروف تُسمى الحروف الأسلية وتخرج من طرف
+
+298
+00:26:43,200 --> 00:26:48,500
+اللسان مع ما بين أطراف الثنايا العليا والسفلى يعني
+
+299
+00:26:48,500 --> 00:26:52,980
+تخرج من طرف اللسان أو من أسل اللسان ومع ما بين
+
+300
+00:26:52,980 --> 00:26:58,820
+أطراف الثنايا العليا والسفلى مع بقاء فرجة بسيطة ما
+
+301
+00:26:58,820 --> 00:27:06,230
+بين الأسنان تخرج منها ال S والأس والز و هذه
+
+302
+00:27:06,230 --> 00:27:10,610
+الحروف تُلقب بالحروف الأسلية لأنها تخرج من أسل
+
+303
+00:27:10,610 --> 00:27:16,710
+اللسان أو من أسل الفم يعني بمعنى ما استدق من
+
+304
+00:27:16,710 --> 00:27:22,300
+اللسان هذا مخرج رقم تسعة إذا المخرج التاسع يخرجوا
+
+305
+00:27:22,300 --> 00:27:29,040
+حرف السين والزاي والصاد يخرجوا من طرف اللسان أو ما
+
+306
+00:27:29,040 --> 00:27:34,120
+استدق من طرف اللسان بين أطراف الثنايا العليا
+
+307
+00:27:34,120 --> 00:27:40,940
+والسفلة فيخرج منها حرف الاس والأس والإز وتُلقب هذه
+
+308
+00:27:40,940 --> 00:27:45,380
+الحروف بالحروف الأسلية لأنها تخرج من أين يا أخوات؟
+
+309
+00:27:45,380 --> 00:27:51,170
+من أسل اللسان ما معنى أسل اللسان؟يعني ما استدق من طرف
+
+310
+00:27:51,170 --> 00:27:56,410
+اللسان يعني طرف طرف اللسان أو رأس اللسان فإني
+
+311
+00:27:56,410 --> 00:28:00,030
+عندما يعني أقول إن هذا هو طرف اللسان ما استدق من طرف
+
+312
+00:28:00,030 --> 00:28:03,290
+اللسان يعني رأس اللسان رأس الدبوس مثلا رأس الدبوس
+
+313
+00:28:03,290 --> 00:28:10,680
+بالنسبة للدبوس فأقول مثلا أس إذ هذه الحروف التي هي
+
+314
+00:28:10,680 --> 00:28:15,340
+تخرج من أس اللسان أو ما استدق من طرف اللسان مع ما
+
+315
+00:28:15,340 --> 00:28:18,700
+بين أطراف الثنايا العليا والسفلة فيخرج منها حرف
+
+316
+00:28:18,700 --> 00:28:25,560
+الاس والأس والإذ ننتقل إلى آخر مخرج من مخارج
+
+317
+00:28:25,560 --> 00:28:32,450
+اللسان الفرعية وهو مخرج حرف الـ ث والـ ذ والـ ض و
+
+318
+00:28:32,450 --> 00:28:37,230
+يخرجوا من ظهر طرف اللسان متساقيًا مع أطراف 
+
+319
+00:28:37,230 --> 00:28:43,840
+أطراف الثنايا العليا والسفلة فنقول ذ و ظ و ث
+
+320
+00:28:43,840 --> 00:28:48,980
+وهذه الحروف التي نجد أن كثيرًا من الناس لا يخرجها من
+
+321
+00:28:48,980 --> 00:28:56,080
+مخرجها فيقول عن حرف الـ ذ أيش ذ يقولون ذلك الكتاب
+
+322
+00:28:56,080 --> 00:29:02,940
+أو الذهب ليس ذهب وليس ذلك خطأ إنما هي ذلك الكتاب
+
+323
+00:29:02,940 --> 00:29:09,370
+كذلك حرف الـ ث بيخرجونه من مخرج حرف الـ س فيقول ثمة
+
+324
+00:29:09,370 --> 00:29:14,910
+ثيبات وأبكارة وهذا خطأ هي ثيبات وأبكارة أو نقول
+
+325
+00:29:14,910 --> 00:29:22,210
+ثمة كذلك حرف الأض يقولون ظهر الحق يخرجون حرف الأض
+
+326
+00:29:22,210 --> 00:29:28,170
+من مخرج حرف الزاي طبعًا ليس لنقول زهرة وإنما ظهرة
+
+327
+00:29:28,170 --> 00:29:33,110
+إذا هذه الحروف تخرجوا من طرف اللسان متساقيًا مع
+
+328
+00:29:33,110 --> 00:29:40,080
+أطراف الثنايا العليا فيقول ذ و ظ و ث حتى أنه
+
+329
+00:29:40,080 --> 00:29:47,680
+يبدو جزء بسيط من اللسان خارج الأسنان وهذه الحروف
+
+330
+00:29:47,680 --> 00:29:53,020
+الثلاثة الذال والظاء والثاء تُلقب بالحروف اللثوية
+
+331
+00:29:53,020 --> 00:29:58,210
+انتهينا يا أخوات من مخرج اللسان في عندنا آخر شيء
+
+332
+00:29:58,210 --> 00:30:03,610
+الذي هو مخرج الشفتين والشفتين له مخرجان مخرج واحد
+
+333
+00:30:03,610 --> 00:30:07,730
+يخرج منه حرف الف وهو من أطراف عند وضع أطراف
+
+334
+00:30:07,730 --> 00:30:15,140
+الثنايا العليا على بطن الشفة السفلى فنقول F إذا
+
+335
+00:30:15,140 --> 00:30:19,360
+الشفتين وهو المخرج رقم أربعة من المخرج العامة
+
+336
+00:30:19,360 --> 00:30:24,320
+يخرج منه مخرجين فرعيين والمخرج الأول عند وضع
+
+337
+00:30:24,320 --> 00:30:28,720
+أطراف الثنايا العليا هذول على بطن الشفة السفلى
+
+338
+00:30:28,720 --> 00:30:35,650
+فنقول if if وهذا مخرج حرف الف والمخرج الثاني
+
+339
+00:30:35,650 --> 00:30:41,150
+يخرج أخوات من بين الشفتين ويخرج منه الميم والباء
+
+340
+00:30:41,150 --> 00:30:46,990
+والواو الميم نقول ام عند انطباق الشفتين إلى
+
+341
+00:30:46,990 --> 00:30:52,910
+الخارج واب عند انطباق الشفتين إلى الداخل فنقول ام
+
+342
+00:30:52,910 --> 00:30:58,680
+وبالـ B عند الذاكرة B والـ M إلى الخارج حرف ال
+
+343
+00:30:58,680 --> 00:31:03,300
+ميم والباء أما الواو أيضًا بيخرج من بين الشفتين ولكن
+
+344
+00:31:03,300 --> 00:31:07,640
+عند ضم الشفتين وانفراجهما ويخرج منه الواو
+
+345
+00:31:07,640 --> 00:31:13,920
+المتحركة هذه الحروف كلها ألف والواو والميم والباء
+
+346
+00:31:13,920 --> 00:31:18,980
+تُلقب شفوية إذا ما هي ألقاب حرف الميم والباء
+
+347
+00:31:18,980 --> 00:31:23,420
+والواو والميم؟ شفوية، إذا في عندنا مخرجين يخرج من
+
+348
+00:31:23,420 --> 00:31:29,040
+الشفتين، مخرج للف ومخرج للميم والباء والواو،
+
+349
+00:31:29,040 --> 00:31:33,860
+المدية ولا المتحركة؟ المتحركة لأن أنا أنا أقول و
+
+350
+00:31:33,860 --> 00:31:41,610
+ويطبعًا في عندنا مثلًا المخرج الأخير وهو مخرج
+
+351
+00:31:41,610 --> 00:31:47,190
+الخيشوم ومخرج الخيشوم هو أقصى الأنف من الداخل و
+
+352
+00:31:47,190 --> 00:31:53,690
+يُجمل على مخرج واحد وهو عبارة عن صفة وليس له
+
+353
+00:31:53,690 --> 00:31:58,350
+حروف يعني لا نقول إن حرف النون والميم تخرج من
+
+354
+00:31:58,350 --> 00:32:02,750
+الخيشوم وإنما هي صفة إذا ما هي الحروف التي تخرج
+
+355
+00:32:02,750 --> 00:32:09,070
+من الخيشوم؟ ليس هناك حرفًا وإنما هي صفة ويُسمى الغنّة
+
+356
+00:32:09,070 --> 00:32:15,150
+صفة الغنّة وصوت وهو صوت أغنّ يخرج من الخيشوم لعمل
+
+357
+00:32:15,150 --> 00:32:20,810
+اللسان به مقدار حركتين وهو صفة ملازمة لحرفي ال
+
+358
+00:32:20,810 --> 00:32:27,050
+ميم والنون إذا المخرج الخامس هو مخرج الخيشوم وهو
+
+359
+00:32:27,050 --> 00:32:32,970
+أعلى الأنف بيخرج منه صفة صفة الغنّة وصفة الغنّة
+
+360
+00:32:32,970 --> 00:32:38,750
+ليست حرفًا بل هي صفة ملازمة للميم والنون والغنّة
+
+361
+00:32:38,750 --> 00:32:43,610
+كما يعرفها العلماء هي صوت أغنّ يخرج من الخيشوم
+
+362
+00:32:43,610 --> 00:32:49,970
+مُركّب في جسمي الميم والنون مقداره حركتين عندما
+
+363
+00:32:49,970 --> 00:32:59,100
+نقول فلمّا فكلمة الغنّة أو عندما نقول إن الله إن
+
+364
+00:32:59,100 --> 00:33:04,460
+الله إن لأنها تخرج من الخيشوم تكون هي صفات إيه
+
+365
+00:33:04,460 --> 00:33:12,100
+صفات الغنّة طبعًا الغنّة طبعًا هي يعني عبارة عن صوت غنّ
+
+366
+00:33:12,100 --> 00:33:17,280
+مُركّب في جسمي الميم والنون انتهينا يا أخوات من مخرج
+
+367
+00:33:17,280 --> 00:33:22,540
+الحروف كلها الخمس مخرج عامة والمخرج الفرعية بقى
+
+368
+00:33:22,540 --> 00:33:27,380
+علينا صفات الحروف والتي سوف نأخذها إن شاء الله في
+
+369
+00:33:27,380 --> 00:33:30,780
+المحاضرة القادمة بارك الله فيكم وجزاكم الله خيرًا
+
+370
+00:33:30,780 --> 00:33:33,160
+والسلام عليكم ورحمة الله وبركاته