diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9cf68f753214b4171d3b47fa8418fab8a41cb00a
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08_postprocess.srt
@@ -0,0 +1,1888 @@
+1
+00:00:00,000 --> 00:00:01,300
+موسيقى
+
+2
+00:00:19,070 --> 00:00:23,390
+بسم الله الرحمن الرحيم نعود إلى محاضرة الفترة
+
+3
+00:00:23,390 --> 00:00:27,430
+الصباحية طبعا ما بدأنا بال inverse Laplace
+
+4
+00:00:27,430 --> 00:00:31,430
+transform عطينا تعريف ل inverse Laplace transform
+
+5
+00:00:31,430 --> 00:00:36,850
+وعطينا على ذلك مثالا واحدا وهذا هو المثال رقم 2
+
+6
+00:00:37,480 --> 00:00:40,220
+يبقى المثال اللي بقول find the function that has
+
+7
+00:00:40,220 --> 00:00:44,600
+Laplace transform F of S يسوى S على S زائد واحد
+
+8
+00:00:44,600 --> 00:00:48,820
+لكل تربيع زائد أربعة بالشكل اللي قدامنا هنا
+
+9
+00:01:07,560 --> 00:01:11,840
+اللي هو بيعطيه هنا هذا أو اللي بيجينا في قائمة فيه
+
+10
+00:01:11,840 --> 00:01:17,800
+مع أسئلة الامتحان تمام طب بقولك كويس هذا لو في
+
+11
+00:01:17,800 --> 00:01:23,340
+عندي S زائد واحد في ال bus ليش؟ لأن عندي هنا S
+
+12
+00:01:23,340 --> 00:01:28,060
+زائد واحد كان قضيتي محلولة ومنتهية تماما إذا أنا
+
+13
+00:01:28,060 --> 00:01:33,340
+بتروح أخلك في ال bus S زائد واحد والله ناقص واحد
+
+14
+00:01:33,340 --> 00:01:39,660
+خليني أتأكد هذه S وين راحت؟س زائد واحد يبقى بدى س
+
+15
+00:01:39,660 --> 00:01:44,240
+زائد واحد يبقى بناء عليه مشان هيك ماعنديش partial
+
+16
+00:01:44,240 --> 00:01:48,700
+fraction حتى اقول partial fraction وانا قولت الصبح
+
+17
+00:01:48,700 --> 00:01:52,740
+اول خطوة بدي اعمل partial fraction مش كل مثل بقدر
+
+18
+00:01:52,740 --> 00:01:56,570
+اعمله partial هدف فيه ل partial fractionمالهاش
+
+19
+00:01:56,570 --> 00:02:02,390
+يبقى هذه جاهزة وخالصة تمام؟ إذا أنا بدي أحول هذه
+
+20
+00:02:02,390 --> 00:02:07,750
+إلى شكل من الأشكال اللي موجودة في الجدول إذا بقدر
+
+21
+00:02:07,750 --> 00:02:14,630
+أقول ال F of S اللي E تساوي لو روحت قولت S زائد
+
+22
+00:02:14,630 --> 00:02:20,370
+واحد ناقص واحد على S زائد واحد لكل تربيع زائد
+
+23
+00:02:20,370 --> 00:02:26,360
+أربعة عملت حاجة؟أضفت واحد واطرحت واحد بدي أفصل هذا
+
+24
+00:02:26,360 --> 00:02:33,060
+إلى مقدارين يبقى المقدار الأول هو S زائد واحد على
+
+25
+00:02:33,060 --> 00:02:41,400
+S زائد واحد لكل تربية زائد أربعة ناقص واحد على S
+
+26
+00:02:41,400 --> 00:02:49,170
+زائد واحد لكل تربية زائد أربعةالترم الأول صار
+
+27
+00:02:49,170 --> 00:02:53,390
+ماعنديش مشكلة لو روحت للجدول بلجيه عند وين في
+
+28
+00:02:53,390 --> 00:02:59,390
+الجدول هذا لسه لا يزال فيه مشكلة المشكلة أنه بده
+
+29
+00:02:59,390 --> 00:03:03,890
+اتنين هنا مدام هذه أربعة بد الجدر تبعها يكون وين
+
+30
+00:03:03,890 --> 00:03:11,370
+فور إذا بقدر أقول ال F of S بده يساوي ال S زائد
+
+31
+00:03:11,370 --> 00:03:18,350
+واحدعلى S زائد واحد لكل تربية زائد أربعة ناقص نص
+
+32
+00:03:18,350 --> 00:03:24,830
+في اتنين على S زائد واحد لكل تربية زائد أربعة
+
+33
+00:03:24,830 --> 00:03:32,500
+هيكسر كلامي صحيحالان انا بدي ال F of T F of T هي ل
+
+34
+00:03:32,500 --> 00:03:38,280
+plus inverse ل F of S يبقى ال F of T اللي انا بدور
+
+35
+00:03:38,280 --> 00:03:47,020
+عليها ال F of T هي ل plus inverse ل capital F of S
+
+36
+00:03:47,390 --> 00:03:54,250
+واللي هي بدها تساوي ل plus inverse لمين لل S plus
+
+37
+00:03:54,250 --> 00:04:02,470
+one على ال S plus one square plus four minus نص في
+
+38
+00:04:02,470 --> 00:04:08,690
+ال plus inverse ل الإتنين على S plus one لكل
+
+39
+00:04:08,690 --> 00:04:14,050
+square plus four بالشكل اللي عندنا هنا يبقى ال F
+
+40
+00:04:14,050 --> 00:04:19,760
+of T تساويبدي اجي على ال dialogue هادي و باجي على
+
+41
+00:04:19,760 --> 00:04:26,020
+الجدول اللي عندنا يبقى الجدول بدي ادور على الشكل
+
+42
+00:04:26,020 --> 00:04:30,880
+اللي ال S زائد واحد S زائد واحد لكل تربيع زائد
+
+43
+00:04:30,880 --> 00:04:32,400
+تربيع
+
+44
+00:04:34,010 --> 00:04:39,950
+طبعا لو جيت نظرت لهذا الجدول بلاحظ ان عندي هذا
+
+45
+00:04:39,950 --> 00:04:48,250
+الكلام موجود في النقطة رقم عشرة النقطة رقم عشرة
+
+46
+00:04:48,250 --> 00:04:56,040
+بتقول ليس نقص ال A على S نقص ال A لكل تربيع زي B
+
+47
+00:04:56,040 --> 00:05:01,440
+تربيع يعني بفرق بس بإشارة مين إشارة السالف لكن هذه
+
+48
+00:05:01,440 --> 00:05:08,310
+لو رجعت للأصل تبعها بلاقي E أس A T Cosبت يبقى
+
+49
+00:05:08,310 --> 00:05:12,550
+معناه هذا الكلام ان ال a اللي عندى هنا بإشارة بس a
+
+50
+00:05:12,550 --> 00:05:18,430
+سالب يبقى لو جيت على الجدول من part عشرة هذا
+
+51
+00:05:18,430 --> 00:05:25,110
+الكلام بدي ساوي a أس ال a عندى هنا بقداش بواحد
+
+52
+00:05:25,110 --> 00:05:33,030
+يبقى a أس ناقص T في cosine بت هذا بي تربيع يبقى
+
+53
+00:05:33,030 --> 00:05:37,300
+بيه بقداشباتنين لان P تربيه سوى ربع وانت بيه
+
+54
+00:05:37,300 --> 00:05:46,180
+باتنين يبقى E أس ناقص T في من في Cos 2T اللي بعدها
+
+55
+00:05:46,180 --> 00:05:52,220
+ناقص نص بداجي لهذه لو رجعت لخط و لجاب الخلف اللي
+
+56
+00:05:52,220 --> 00:05:57,620
+هو النقطة التاسعة بلجأ عندي P على S ناقص L كل
+
+57
+00:05:57,620 --> 00:06:04,650
+تربيع زائد P تربيعيبقى هذه بي هيب اتنين هي بي
+
+58
+00:06:04,650 --> 00:06:10,350
+تربيع باربعة زائد يبقى ال a بس بمين بسالب واحد
+
+59
+00:06:10,350 --> 00:06:18,530
+يبقى باجي بناقص نص في a أس سالب T ل sign اتنين T
+
+60
+00:06:18,530 --> 00:06:23,570
+انتهت مسألتنا يبقى كله اعتماد على الجدول كيف اطلع
+
+61
+00:06:23,570 --> 00:06:30,680
+من الجدول Laplace transform للدوال المختلفةمثال
+
+62
+00:06:30,680 --> 00:06:35,700
+ثلاثة
+
+63
+00:06:35,700 --> 00:06:43,740
+مثال ثلاثة بيقول ما ياتي بدنا
+
+64
+00:06:43,740 --> 00:06:48,720
+نجد مفعول
+
+65
+00:06:48,720 --> 00:06:53,460
+f of t with
+
+66
+00:06:55,610 --> 00:07:06,170
+اللي هو it's a type with Laplace transform
+
+67
+00:07:09,400 --> 00:07:15,960
+اللي لابلاس ترانسفورم إلها اللي هو capital F of S
+
+68
+00:07:15,960 --> 00:07:25,280
+بده يساوي تلاتة S ناقص اتنين على S تربيع ناقص
+
+69
+00:07:25,280 --> 00:07:28,680
+اتنين S زائد عشرة
+
+70
+00:07:33,040 --> 00:07:38,760
+بقول كويس اللي قال لو روحت على الجدول تابعنا هذا و
+
+71
+00:07:38,760 --> 00:07:46,560
+بلاجيش ولا term هشكل هذا لكن بده اعادة ايه ترتيب
+
+72
+00:07:46,560 --> 00:07:51,460
+هذا ال term كيف نقيت ترتيبه؟ بده اشوف المقام،
+
+73
+00:07:51,460 --> 00:07:56,000
+ماعنديش شغمة زي هيك كله بلاجي S زي واحد الكل تربيع
+
+74
+00:07:56,000 --> 00:08:01,440
+S نقص اتنين الكل تربيع زي رقم هنا رقم هنا S إلى
+
+75
+00:08:01,440 --> 00:08:06,100
+آخرينإذا بدي أعيد كتابة هذه ال function بطريقة
+
+76
+00:08:06,100 --> 00:08:12,260
+ثانية إذا بقدر أقول هذا الكلام يسوى ثلاثة S ناقص
+
+77
+00:08:12,260 --> 00:08:18,980
+اتنين على هذا S تربية ناقص اتنين S إذا هذا لازم
+
+78
+00:08:18,980 --> 00:08:24,660
+أعمله ايه مربع كامل مشان أعمل هذا مربع كامل جداش
+
+79
+00:08:24,660 --> 00:08:31,340
+بده S تربية زيدي اتنين S جداش بده رقمش هصير مربع
+
+80
+00:08:31,340 --> 00:08:40,770
+كامل2S ناقص
+
+81
+00:08:40,770 --> 00:08:47,170
+معامل X على أربع أمثال معامل X دربية يبقى هنا بقول
+
+82
+00:08:47,170 --> 00:08:55,850
+زائد 2S يبقى مش هين أحول بذكر مرتين و تلتة و عشرين
+
+83
+00:08:56,440 --> 00:09:02,060
+بدي اعمل اكمال المربع بضيف للطرفين و بطرح مربع
+
+84
+00:09:02,060 --> 00:09:07,200
+معامل X على اربع امثال معامل X تربيع اعطيتها لكم
+
+85
+00:09:07,200 --> 00:09:12,900
+في calculus P و يا محل نبع يبقى مربع معامل X على
+
+86
+00:09:12,900 --> 00:09:17,440
+اربع امثال معامل X تربيع يعني مربع معامل F على
+
+87
+00:09:17,440 --> 00:09:22,840
+اربع امثال معامل S تربيعيبقى هنا بيبقى داش بواحد
+
+88
+00:09:22,840 --> 00:09:27,940
+يبقى زائد اتنين اس زائد واحد الواحد موجود عند
+
+89
+00:09:27,940 --> 00:09:34,940
+الجيران عشرة باخد منها واحد بيبقى تسعة يبقى زائد
+
+90
+00:09:34,940 --> 00:09:43,110
+تسعة يبقى هذا الكلام يساويالمقام اللي عندنا هذا
+
+91
+00:09:43,110 --> 00:09:48,950
+الانصار مربع كامل صح يبقى هذا بقدر اقول اللي هو ال
+
+92
+00:09:48,950 --> 00:09:58,580
+S ناقص واحد لكل تربيع زائد تسعةأيوة إذن البث هذا
+
+93
+00:09:58,580 --> 00:10:05,160
+بيدخلك في مين S ناقص واحد بيدخلك في كاف S ناقص اما
+
+94
+00:10:05,160 --> 00:10:09,920
+هو تلاتة S ناقص اتنين الجثة بسيطة خالص بضيف سالب
+
+95
+00:10:09,920 --> 00:10:15,020
+واحد و بطرح واحد يعني بضيف واحد و بطرح سالب واحد
+
+96
+00:10:15,020 --> 00:10:21,200
+يبقى هذا لو حطيت سالب واحد كده بصير؟بقدر اخد تلاتة
+
+97
+00:10:21,200 --> 00:10:25,360
+عمل مشترك وبظل S ناقص واحد بيكون خلصت مسألة اتنين
+
+98
+00:10:25,360 --> 00:10:32,220
+اذا البسط هذا بقدر اكتب تلاتة S ناقص تلاتة زائد
+
+99
+00:10:32,220 --> 00:10:38,700
+واحديبقى أضفت سالب واحد وكذلك واحد يعني أضفت zero
+
+100
+00:10:38,700 --> 00:10:45,760
+مغيرتش ولا عالية يبقى بناء عليه أصبح شكل ال F of S
+
+101
+00:10:45,760 --> 00:10:54,100
+على الشكل التالي هذه تلاتةفى S ناقص واحد خدته
+
+102
+00:10:54,100 --> 00:11:02,020
+معامل مشترك وهنا زائد واحد على مين على S على S
+
+103
+00:11:02,020 --> 00:11:09,470
+ناقص واحد لكل تربية زائد تسعةممكن هذه أفصلها إلى
+
+104
+00:11:09,470 --> 00:11:18,670
+جزئين من الجزئين هاي تلاتة في S ناقص واحد S ناقص
+
+105
+00:11:18,670 --> 00:11:27,390
+واحد لكل تربية زائد تسعة ضال عندي زائد واحد على S
+
+106
+00:11:27,390 --> 00:11:33,350
+ناقص واحد لكل تربية زائد تسعة أظن صارت شبيهة
+
+107
+00:11:33,350 --> 00:11:40,390
+بمسألة هذه قبل قليلصح؟ وهذه شبيهة ابها بالضبط
+
+108
+00:11:40,390 --> 00:11:46,670
+تماماً يبقى تعالى نشوف كيف نسوي يبقى أنا هذه هاه
+
+109
+00:11:46,670 --> 00:11:52,550
+فدها بس فوق كده شمنهاكداش؟ تلاتة ممتاز يبقى بدي
+
+110
+00:11:52,550 --> 00:11:58,350
+اضرب في تلاتة و اجسم على تلاتة اذا بقدر اقول هذا
+
+111
+00:11:58,350 --> 00:12:05,190
+الكلام تلاتة في اس ناقص واحد على من على اس ناقص
+
+112
+00:12:05,190 --> 00:12:12,690
+واحد الكل تربية زائد تسعة زائد تلت في تلاتة على اس
+
+113
+00:12:12,690 --> 00:12:20,530
+ناقص واحد الكل تربية زائد تسعةيبقى ال F of T هي
+
+114
+00:12:20,530 --> 00:12:25,670
+Laplace inverse للطرفين يبقى تلاتة في Laplace
+
+115
+00:12:25,670 --> 00:12:32,870
+inverse لل S ناقص واحد S ناقص واحد لكل تربية زائد
+
+116
+00:12:32,870 --> 00:12:40,930
+تسعة زائد تلت Laplace inverse لتلاتة S ناقص واحد
+
+117
+00:12:40,930 --> 00:12:48,960
+لكل تربية زائد تسعةيبقى أصبح شكل ال F of T بيسوي
+
+118
+00:12:48,960 --> 00:12:56,240
+ثلاثة فيه نرجع بالذاكرة الوراء للجدول قبل قليل
+
+119
+00:12:56,240 --> 00:13:04,700
+كذلك إلى النقطة العاشرة بلاحظ عندي S ناقص A S ناقص
+
+120
+00:13:04,700 --> 00:13:10,560
+A لكل تربيع زائد B تربيع يبقى الأصل تبعها E أس AT
+
+121
+00:13:10,560 --> 00:13:20,600
+Cos BTقداش ال A عند هنا ال A بواحد طب و ال B؟تلاتة
+
+122
+00:13:20,600 --> 00:13:28,100
+لإن هذه بيه تربيع يبقى بناء عليه تلاتة E of T بدون
+
+123
+00:13:28,100 --> 00:13:35,060
+زالب تمام فاهمين فى cosine تلاتة T هذا ال term
+
+124
+00:13:35,060 --> 00:13:43,420
+الأول زائد طول هذه بنفس الطريقة E of T sine تلاتة
+
+125
+00:13:43,420 --> 00:13:48,120
+T يبقى هذه ال function اللى مطلوبة اللى عندنا
+
+126
+00:13:55,990 --> 00:14:00,830
+بنعطي كمان مثال مثال
+
+127
+00:14:00,830 --> 00:14:04,570
+تلاتة أو example أربعة
+
+128
+00:14:09,370 --> 00:14:16,690
+بيقول لي نفس القصة capital F of S بده يساوي E أس
+
+129
+00:14:16,690 --> 00:14:25,390
+ناقص S على S ناقص اتنين لكل تاربيع و بده مين؟ بده
+
+130
+00:14:25,390 --> 00:14:30,580
+نوجد لنا place transform اللي هالمعكوز تبعهبقول له
+
+131
+00:14:30,580 --> 00:14:35,340
+بسيطة جدا قبل ما توجد لبلاس ترانسفورم حاول ترتبها
+
+132
+00:14:35,340 --> 00:14:44,620
+بقول له يعني هذه لو كتبتها E أس ناقص S في واحد على
+
+133
+00:14:44,620 --> 00:14:52,860
+S ناقص اتنين لكل تربية عملنا حاجة طيب ايش رايك
+
+134
+00:14:52,860 --> 00:14:57,800
+الواحد هذا لو كتبت واحد factorial الشكل اللي عندنا
+
+135
+00:14:57,800 --> 00:14:58,020
+هذا
+
+136
+00:15:03,450 --> 00:15:09,810
+يبقى باجي بقول ال F of T اللي أنا بدور عليها هي
+
+137
+00:15:09,810 --> 00:15:17,810
+Laplace transform بالمعكوس تبعها لcapital F of S
+
+138
+00:15:17,810 --> 00:15:24,110
+ويساوي Laplace transform لل E أص ناقص S
+
+139
+00:15:39,210 --> 00:15:43,410
+يبقى ال F of T تساوي
+
+140
+00:15:52,230 --> 00:15:59,670
+طيب من فوق لتحت اكسبوننشيل اكسبوننشيل عندي رقم
+
+141
+00:15:59,670 --> 00:16:05,690
+اتناش اكسبوننشيل على اس انا عندي على اس ناقص كذا
+
+142
+00:16:06,430 --> 00:16:14,490
+طيب انا بلاحظ عندي الرقم تلتاش الرقم تلتاش اللي هو
+
+143
+00:16:14,490 --> 00:16:25,780
+E أس ناقص CS في capital F of Scapital F of S هذا
+
+144
+00:16:25,780 --> 00:16:32,100
+الاصل تبعها الاصل تبعها ده ال step function u C of
+
+145
+00:16:32,100 --> 00:16:39,260
+T فال F of T ناقص من ناقص ال C لكن لو رجعنا
+
+146
+00:16:39,260 --> 00:16:46,700
+للخاصية رقم 5 من section 9 3 تحيلي section 9 3
+
+147
+00:16:46,700 --> 00:16:48,040
+الخاصية رقم 5
+
+148
+00:16:50,690 --> 00:16:53,670
+يعني إذا عرفت تجيبيها من الجد والكرمها وماعرفتش
+
+149
+00:16:53,670 --> 00:17:00,490
+برجع للأصل هذه تبعها طلعيلي مشان أكتب هذه الدالة
+
+150
+00:17:00,490 --> 00:17:08,850
+بداجي للدالة بين القوسين هذه هي ال F of S قولي G
+
+151
+00:17:08,850 --> 00:17:15,490
+of S يساوي واحد factorial على S ناقص اتنين لكل
+
+152
+00:17:15,490 --> 00:17:20,650
+تربيعبقدر اجيب الاصل تبعها مين الاصل تبعها يا بنات
+
+153
+00:17:20,650 --> 00:17:26,510
+جي اوب تي يساوي هذه لو روحت جبت الاصل تبعها يبقى
+
+154
+00:17:26,510 --> 00:17:33,070
+الاصل تبعها هو عبارة عن تي في اي أس اتنين تي طبعا
+
+155
+00:17:33,070 --> 00:17:38,830
+من الجدول تي في اي أس اتنين تي لو روحت للخاصية رقم
+
+156
+00:17:38,830 --> 00:17:45,450
+خمسة اللي عندك بدي اعمل لهذه الدالة shift بمقدار
+
+157
+00:17:46,670 --> 00:17:52,430
+كداش؟ اتنين مش عندك هنا اتنين، هذا اتنين، انت بقى
+
+158
+00:17:52,430 --> 00:17:56,710
+ال exponential يبقى بدي اعمله shift بمقدار عفوا
+
+159
+00:17:56,710 --> 00:18:06,530
+بمقدار اللي هو الاتنين، بمقدار الواحد
+
+160
+00:18:06,530 --> 00:18:13,450
+وليس الاتنينطيب كيف ده جت كالتالي فباجي بقول يبقى
+
+161
+00:18:13,450 --> 00:18:20,110
+ال plus inverse لها يسوى أحد أمرين يا إما zero لما
+
+162
+00:18:20,110 --> 00:18:26,490
+ال T أكبر من ال zero أقل من واحد يا إما T ناقص
+
+163
+00:18:26,490 --> 00:18:34,630
+واحد E أس اتنين في T ناقص واحد وال T أكبر من
+
+164
+00:18:34,630 --> 00:18:35,430
+الواحد
+
+165
+00:18:38,640 --> 00:18:46,220
+خصية رقم خمسة الخاصية رقم خمسة من سكتشن تسعة تلاتة
+
+166
+00:18:48,480 --> 00:18:53,280
+خاصية رقم خمسة اللي بيقولي small q of t بدي ساوي
+
+167
+00:18:53,280 --> 00:18:56,860
+زيرو لما t محصورة بين ال zero و ال c او f of t
+
+168
+00:18:56,860 --> 00:19:02,140
+ناقص ال c لما t اكبر من ال c يبقى لبلاي ال
+
+169
+00:19:02,140 --> 00:19:08,240
+transform اللي هي E اص ناقص CS في capital F of S
+
+170
+00:19:08,240 --> 00:19:14,760
+يعني بدنا نجيب ال F of S للدلة اللي عندنا وين ال F
+
+171
+00:19:14,760 --> 00:19:23,510
+of S هىمظبوط؟ يبقى الدالة الأصلية تبعتها T في E
+
+172
+00:19:23,510 --> 00:19:29,870
+أُس 2T هيا جبناها هنا، كويس؟ الآن هذي بدي أعمل لها
+
+173
+00:19:29,870 --> 00:19:36,650
+shift بمقدار مين؟ بمقدار الواحد، مقدار الأُس اللي
+
+174
+00:19:36,650 --> 00:19:40,790
+عندي تبع ال exponential هنا، جداش المعامل اللي
+
+175
+00:19:40,790 --> 00:19:44,500
+هنا؟لأ سيبكي من السلب السلب تبع القانون موجود في
+
+176
+00:19:44,500 --> 00:19:50,120
+القانون صح موجود عندك أيه في النقطة رقم خمسة E و
+
+177
+00:19:50,120 --> 00:19:51,660
+سالب CS
+
+178
+00:19:54,070 --> 00:19:59,970
+خامسة أخر حاجة على اليمين يبقى E والسلب CS في ال F
+
+179
+00:19:59,970 --> 00:20:04,990
+of S يبقى أن المعامل هنا واحد إذا هذه الدلة بدي
+
+180
+00:20:04,990 --> 00:20:10,210
+أعمل لها shift بمقدار واحد يبقى صارت T ناقص واحد
+
+181
+00:20:10,210 --> 00:20:16,450
+في S اتنين T ناقص واحد لما T greater than zero
+
+182
+00:20:16,450 --> 00:20:21,990
+يبقى هذا باستخدام الخاصية رقم كم؟ رقم خمسة
+
+183
+00:20:24,770 --> 00:20:29,530
+لازلنا في نفس ال section و لما ننتهي بعد بدنا نعطي
+
+184
+00:20:29,530 --> 00:20:39,690
+تعريف صغير و مثال عليه كذلك تعريف
+
+185
+00:20:39,690 --> 00:20:44,390
+بيقول ما يأتي definition
+
+186
+00:20:44,390 --> 00:20:50,930
+the
+
+187
+00:20:50,930 --> 00:20:51,510
+function
+
+188
+00:20:54,110 --> 00:21:05,050
+F Star G F Star G As a function of T is called
+
+189
+00:21:05,050 --> 00:21:15,510
+بنسميه The Convolution The Convolution
+
+190
+00:21:15,510 --> 00:21:18,610
+Of
+
+191
+00:21:18,610 --> 00:21:20,990
+The
+
+192
+00:21:27,070 --> 00:21:30,490
+and denoted by
+
+193
+00:21:35,930 --> 00:21:44,890
+بنعرفها كالتالي ال f star g as a function of t بده
+
+194
+00:21:44,890 --> 00:21:53,950
+يسوي تكامل من zero إلى T لل F of T ناقص ال U ال G
+
+195
+00:21:53,950 --> 00:22:01,900
+of U دي Uواللي هي بدها تساوي تكامل من zero إلى T
+
+196
+00:22:01,900 --> 00:22:12,700
+لل F of U لل G of T ناقص ال U DU واللي هي بدها
+
+197
+00:22:12,700 --> 00:22:21,040
+تساوي G star F and
+
+198
+00:22:21,040 --> 00:22:32,660
+henceومن ثم لبلاسيت ترانسفورم لل F star G فال F
+
+199
+00:22:32,660 --> 00:22:42,980
+star G بده يساوي capital F of S في capital G of S
+
+200
+00:22:42,980 --> 00:22:46,480
+نعطي
+
+201
+00:22:46,480 --> 00:22:47,040
+مثال
+
+202
+00:22:53,540 --> 00:23:02,900
+معرفة مفهوم f*)g
+
+203
+00:23:02,900 --> 00:23:06,980
+كمفهوم من f
+
+204
+00:23:12,860 --> 00:23:22,700
+ال F of T بد يساوي ال E أس T وال G of T يساوي E أس
+
+205
+00:23:22,700 --> 00:23:23,980
+اتنين T
+
+206
+00:23:59,030 --> 00:24:03,430
+بنجي لتعريف ال convolution ل ال two functions ايش
+
+207
+00:24:03,430 --> 00:24:07,750
+بيقول دي؟ ال function f star g as a function of t
+
+208
+00:24:07,750 --> 00:24:12,710
+بنسميها ال convolution of ال function اللي هي ال
+
+209
+00:24:12,710 --> 00:24:16,710
+main of ال function f and g convolution في اللغة
+
+210
+00:24:16,710 --> 00:24:22,130
+العربية معناه التفاف يعني كأنه بيعمل التفاف يعني
+
+211
+00:24:22,130 --> 00:24:27,550
+ليهاعملت لدالة f ممكن اعمل لدالة g و التانية تظهر
+
+212
+00:24:27,550 --> 00:24:32,270
+زي ما هي بدون مشاكل من هنا سمينا convolution لمين
+
+213
+00:24:32,270 --> 00:24:37,690
+لتو functions بهمني هذا جدش بيساوي لإن أنا هذا هو
+
+214
+00:24:37,690 --> 00:24:42,290
+اللي بشتغل عليه إذا بدي بقول لدالة f star g أو f
+
+215
+00:24:42,290 --> 00:24:46,690
+convolution g as a function of tيتكوّن من zero إلى
+
+216
+00:24:46,690 --> 00:24:52,610
+T يا باجي على ال F اللي عنها دي بكتبها أو بشيل كل
+
+217
+00:24:52,610 --> 00:24:59,030
+T بحط بدلها T نقص U U real numberها يبقى F of T
+
+218
+00:24:59,030 --> 00:25:08,270
+نقص ال U في ال G of U في ال DUيبقى كوني الأن أخدت
+
+219
+00:25:08,270 --> 00:25:14,950
+الـDU يعني U هي اشتقاق وكأن الـT أنا ثبتها كأنه
+
+220
+00:25:14,950 --> 00:25:18,430
+خلت الـT مقدار ثابت لأن أنا كامل بالنسبة لـU إذا
+
+221
+00:25:18,430 --> 00:25:24,020
+الـT إيش تعتبر مقدارا ثابتاأريد أن أثبت الـ U
+
+222
+00:25:24,020 --> 00:25:28,580
+فأقول F of U يبقى الـ G فأقول G of T ناقص الـ U في
+
+223
+00:25:28,580 --> 00:25:33,380
+الـ DU وحسب الـ Definition هذه ستساوي عملت لهذه G
+
+224
+00:25:33,380 --> 00:25:39,300
+وهذه ثبتت فأقول G star F يبقى بناء عليه الـ F star
+
+225
+00:25:39,300 --> 00:25:46,500
+G هو G star F كلها as a function of T كلها كدالة
+
+226
+00:25:46,500 --> 00:25:50,200
+في D يبقى هذه والله هذه عملت للدالة الأولى والله
+
+227
+00:25:50,200 --> 00:25:55,120
+الدالة التانيةالاتنين are the same طب لو بده اجيب
+
+228
+00:25:55,120 --> 00:25:59,900
+Laplace transform لل convolution بقول Laplace
+
+229
+00:25:59,900 --> 00:26:05,040
+لدالة الأولى ضرب ضرب عادية Laplace لدالة التانية
+
+230
+00:26:05,040 --> 00:26:10,180
+هيها dot مضروبة ضرب فيها دي تمام؟ بدنا نروح نطبق
+
+231
+00:26:10,180 --> 00:26:14,790
+هذا الكلام بمثالجالي هاتلي الدالة هادى إذا كانت ال
+
+232
+00:26:14,790 --> 00:26:19,610
+F of T بده يساوي ال E of T وال G of T بده يساوي من
+
+233
+00:26:19,610 --> 00:26:25,110
+ال E أس اتنين إذا لما بداجي أحل بداجي أقوله ال F
+
+234
+00:26:25,110 --> 00:26:31,830
+star G كله as a function of T يساوي ال F of T يا
+
+235
+00:26:31,830 --> 00:26:38,130
+بنات اللي هي من E أس T ال G of T اللي هي E أس
+
+236
+00:26:38,130 --> 00:26:44,170
+اتنين T وهايهم function في Tطبقا للتعريف اللى فوق
+
+237
+00:26:44,170 --> 00:26:51,050
+يبقى تكامل من zero إلى T تمام عندك هذه الصيغة او
+
+238
+00:26:51,050 --> 00:26:56,450
+هذه سيان يبقى ال F اللى هى الدالة الاولى بدي اعمل
+
+239
+00:26:56,450 --> 00:27:04,810
+لها shift بمقدار جداش ال U يبقى E أس T ناقص ال U
+
+240
+00:27:04,810 --> 00:27:12,160
+ال G أبدا بدي اشيل ال T بس و اكتب مكانها جداشيوم
+
+241
+00:27:12,160 --> 00:27:22,580
+دي يوم تمام طيب إذا هذا بنيت بقدر أقول تساوي تكامل
+
+242
+00:27:22,580 --> 00:27:31,380
+من zero إلى T لمن لل E أوس T E أوس ناقص U E أوس
+
+243
+00:27:31,380 --> 00:27:37,570
+اتنين Uأظن الـ Eost مالهاش دعوة بالتكامل لإنه
+
+244
+00:27:37,570 --> 00:27:42,250
+يشتقق بالنسبة لمن يبقى بقدر أطلعها برا التكامل
+
+245
+00:27:42,250 --> 00:27:50,610
+يبقى هذه تساوي Eost تكامل من Zero إلى T لل E بجمع
+
+246
+00:27:50,610 --> 00:27:56,250
+الأسس لإن الأساسات زي بعض يبقى UDU
+
+247
+00:27:57,600 --> 00:28:04,640
+تمام؟ طيب هذا بيصير E Os T فيه تكامل ال E Os U بال
+
+248
+00:28:04,640 --> 00:28:10,480
+E Os U itself يبقى هذه ال E Os U من وين لوين؟ من
+
+249
+00:28:10,480 --> 00:28:17,800
+Zero لغاية T يبقى هذا الكلام بده يساوي اهه اللي هو
+
+250
+00:28:17,800 --> 00:28:26,970
+مين؟ E Os T في مين؟ في ال E Os T ناقص E Os ZeroE0
+
+251
+00:28:26,970 --> 00:28:34,490
+بيبقى داشر يبقى صار E of T في E of T ناقص واحد
+
+252
+00:28:34,490 --> 00:28:42,950
+يبقى E of 2T ناقص E of T إذا ال convolution اللي
+
+253
+00:28:42,950 --> 00:28:49,150
+حصل لل two functions F and G يسوى الدالة الأولى
+
+254
+00:28:49,150 --> 00:28:55,550
+الدالة الثانية ناقص الدالة الأولى بالمثللو أخذت
+
+255
+00:28:55,550 --> 00:29:01,830
+هذه الـ T عملت لها T ناقص الـ U وهذه خلّيت الـ U
+
+256
+00:29:01,830 --> 00:29:06,670
+كامل فهو يطلع نفس النتيجة اللي عندنا لحد هنا stop
+
+257
+00:29:06,670 --> 00:29:11,490
+and turn section إلى يكون أرقام المسائل يبقى
+
+258
+00:29:11,490 --> 00:29:20,370
+exercises تسعة أربعة المسائل واحد واتنين وأربعةبدأ
+
+259
+00:29:20,370 --> 00:29:30,170
+أخد الـ A و الـ C و سؤال 5 بدي ال A و ال B ال A و
+
+260
+00:29:30,170 --> 00:29:37,030
+ال B و ال A و ال F طيب
+
+261
+00:29:37,030 --> 00:29:45,050
+نيجي لآخر section اللي هو 9 5 يبقى 9 5 اللي هو ال
+
+262
+00:29:45,050 --> 00:29:46,190
+applications
+
+263
+00:29:49,160 --> 00:29:56,180
+applications to differential equations
+
+264
+00:29:58,370 --> 00:30:03,510
+تطبيقات على المعادلات التفاضلية ايش يعني المقصود
+
+265
+00:30:03,510 --> 00:30:07,730
+فيها المقصود استخدام Laplace transform لحل
+
+266
+00:30:07,730 --> 00:30:13,690
+المعادلة التفاضلية اظن حلنالكوا بدل المعادلة تنتين
+
+267
+00:30:13,690 --> 00:30:18,730
+مظبوط يبقى انا باعتمر ماشتغلتش بالمرة و بدي اشتغل
+
+268
+00:30:18,730 --> 00:30:26,490
+من جديد يبقى هنا بدي اقول to use السؤال بيجي كتالة
+
+269
+00:30:26,490 --> 00:30:42,450
+exampleتوضيحي example use Laplace transform to
+
+270
+00:30:42,450 --> 00:30:45,490
+solve
+
+271
+00:30:45,490 --> 00:30:51,590
+the
+
+272
+00:30:51,590 --> 00:30:54,690
+initial value problem
+
+273
+00:30:57,680 --> 00:31:05,600
+اللي هي ال x double prime زائد أربعة x بده ساوية
+
+274
+00:31:05,600 --> 00:31:13,320
+تمانية sign ال T وال x عند ال zero بدها تساوي zero
+
+275
+00:31:13,320 --> 00:31:20,440
+وال x prime عند ال zero بده ساوي اتنين solution
+
+276
+00:31:24,890 --> 00:31:28,750
+يبقى مدام أعطاني السؤال من هذا القبيل هو قيدني
+
+277
+00:31:28,750 --> 00:31:32,910
+بطريقة الحل أنا هذه معادلة من الرتبة الثانية إذا
+
+278
+00:31:32,910 --> 00:31:38,110
+لو بدي أرجع للي قبل المعاملات ثوابت ودالة بالصينيا
+
+279
+00:31:38,110 --> 00:31:41,050
+ممكن إذا بحلها بال undetermined coefficients بس هو
+
+280
+00:31:41,050 --> 00:31:43,730
+بدش ياني أحلها بال undetermined coefficients بدي
+
+281
+00:31:43,730 --> 00:31:48,130
+ياني أحلها بال a plus transform ويبقى أنا مقيد إذا
+
+282
+00:31:48,130 --> 00:31:52,490
+بال a plus transformاذا بروح اخد لبلاس ترانسفورم
+
+283
+00:31:52,490 --> 00:31:59,330
+للطرفين يبقى باجي بقول لبلاس ترانسفورم لل XW' زائد
+
+284
+00:31:59,330 --> 00:32:06,350
+أربعة لبلاس ترانسفورم لل X بدي ساوي تمانية لبلاس
+
+285
+00:32:06,350 --> 00:32:12,950
+ترانسفورم لصيتي لش؟ ان لبلاس ترانسفورم is a linear
+
+286
+00:32:12,950 --> 00:32:16,390
+function او linear operator يبقى التمانية بقدر
+
+287
+00:32:16,390 --> 00:32:25,560
+اطلع برابدي أطبق النظرية على هذه يبقى هذه S2 XS
+
+288
+00:32:25,560 --> 00:32:39,800
+ناقص S في X عند 0 ناقص X' عند 0 زائد 4XS بده ساوي
+
+289
+00:32:39,800 --> 00:32:45,890
+8صين الـ T مظبوط صين الـ T ولا صين اتنين T يبقى
+
+290
+00:32:45,890 --> 00:32:51,330
+صين الـ T مدام صين الـ T إذا هذه Laplace Transform
+
+291
+00:32:51,330 --> 00:32:58,970
+حسبناها عمليا يبقى هذا بقداش يا بناد بواحد على أس
+
+292
+00:32:58,970 --> 00:33:07,130
+تربيع زائد واحد مظبوططيب يبقى هنيجي طلعيلي لهذه
+
+293
+00:33:07,130 --> 00:33:14,310
+وهذه بقدر اخد X of S عامل مشترك بيظل عندي S
+
+294
+00:33:14,310 --> 00:33:21,630
+squared زائد 4 في capital X of Sالان ال X عندي
+
+295
+00:33:21,630 --> 00:33:25,470
+Zero يبقى
+
+296
+00:33:25,470 --> 00:33:32,970
+ناقص Zero ال X Prime باتنين يبقى ناقص اتنين يسوى
+
+297
+00:33:32,970 --> 00:33:40,710
+تمانية على استربيع زائد واحد او ان شئتم فقولوا ان
+
+298
+00:33:40,710 --> 00:33:48,370
+ال S Square زائد اربعةفي capital X of S بده يسوى
+
+299
+00:33:48,370 --> 00:33:55,790
+تمانية على S square plus one plus two بده واحد
+
+300
+00:33:55,790 --> 00:34:02,690
+المقامات يبقى بصير S square زائد أربعة في capital
+
+301
+00:34:02,690 --> 00:34:11,050
+X of S يسوى كله على S square plus one وهي تمانيةزي
+
+302
+00:34:11,050 --> 00:34:16,870
+دي اتنين S square زي دي اتنين تمام يبقى بيصير
+
+303
+00:34:16,870 --> 00:34:22,750
+عندنا مين بيصير عندنا S square plus four في
+
+304
+00:34:22,750 --> 00:34:30,970
+capital X of S يساويإتنين S Square زائد عشرة
+
+305
+00:34:30,970 --> 00:34:38,710
+مقسوما على S Square plus one طب أنا بدي X of S
+
+306
+00:34:38,710 --> 00:34:46,370
+يبقى ال X of S بده يساوي اتنين S Square زائد عشرة
+
+307
+00:34:46,370 --> 00:34:55,610
+على S Square plus one في S Square plus fourلو روحت
+
+308
+00:34:55,610 --> 00:35:01,010
+على الجدول بلاقي شغلة زي هذه في الشمكانية طب كيف
+
+309
+00:35:01,010 --> 00:35:04,870
+نسوي؟ بقولك بسيطة ال bus من الدرجة التانية و
+
+310
+00:35:04,870 --> 00:35:11,790
+المقام من الدرجةpartial fraction و الحمد لله جاهزة
+
+311
+00:35:11,790 --> 00:35:17,550
+يبقى بس احطها على شكل ايه شكل كسور يبقى هذا الكلام
+
+312
+00:35:17,550 --> 00:35:23,650
+بده يساوي هذا كسر وهذا ال S squared plus one وهذا
+
+313
+00:35:23,650 --> 00:35:29,110
+كسر تاني S squared plus four المعادلة من الدرجة
+
+314
+00:35:29,110 --> 00:35:33,790
+الثانية كل واحدة فيهم ولا يمكن تحليلها إذا بده أحط
+
+315
+00:35:33,790 --> 00:35:41,210
+فوق معادلة من الدرجةالأولى يبقى باجي بقوله AS زائد
+
+316
+00:35:41,210 --> 00:35:47,910
+B وهنا CS زائد D وبعد هيك بروح أحسب ال partial
+
+317
+00:35:47,910 --> 00:35:54,030
+fractions يبقى بقوله اتنين S Square زائد عشرة بده
+
+318
+00:35:54,030 --> 00:36:03,490
+يساوي AS زائد ال B في مين؟ في ال S Square زائد 4
+
+319
+00:36:03,490 --> 00:36:13,160
+زائد CSزي دي دي في ال S square plus oneطبعا بنفك
+
+320
+00:36:13,160 --> 00:36:19,960
+ونقرر مش هضيع وقت فيها هعطيك النتيجة مباشرة يبقى
+
+321
+00:36:19,960 --> 00:36:27,260
+بتطلع عندك هنا ال a تساوي zero ال a تساوي zero و
+
+322
+00:36:27,260 --> 00:36:36,660
+ال b تساوي ناقص تلتين و ال c بتطلع عندك ب zero و
+
+323
+00:36:36,660 --> 00:36:45,950
+ال d بتطلع عندى ب 8 على 3بناء عليه أصبحت المسألة
+
+324
+00:36:45,950 --> 00:36:47,770
+على الشكل التالي
+
+325
+00:37:00,950 --> 00:37:07,290
+يبقى أصبحت الـ X of S X as a function of S على
+
+326
+00:37:07,290 --> 00:37:12,390
+الشكل التالف طلعيه هنا كويسة يبقى بدأ دي أشيل ال A
+
+327
+00:37:12,390 --> 00:37:18,730
+و أحط مكانها Zero طارة ال B بدأ أحط بدل سالب تلتين
+
+328
+00:37:18,730 --> 00:37:25,450
+يبقى هاي سالب تلتين ضال واحد على S square زائد
+
+329
+00:37:25,450 --> 00:37:31,920
+واحدانتهينا منها الان ال c ب zero طارت يبقى ال d ب
+
+330
+00:37:31,920 --> 00:37:38,320
+تمانية على تلاتة زائد تمانية على تلاتة في جداش في
+
+331
+00:37:38,320 --> 00:37:46,370
+واحد على s square زائد اربعإذا أنا بدي ال X as a
+
+332
+00:37:46,370 --> 00:37:52,870
+function of T هي Laplace inverse لcapital X of S
+
+333
+00:37:52,870 --> 00:37:57,050
+بالشكل اللي عندنا هنا يبقى هذا بدي ساوي سالب
+
+334
+00:37:57,050 --> 00:38:02,630
+طولتين Laplace inverse للواحد على S squared plus
+
+335
+00:38:02,630 --> 00:38:11,680
+oneزائد تمانية على تلاتة وهنا لابلاس inverse لواحد
+
+336
+00:38:11,680 --> 00:38:18,620
+على اس square زائد اربع يبقى شكل ال X of T يساوي
+
+337
+00:38:18,620 --> 00:38:26,850
+سالب تلتين مين هذا يا بنات؟هى مين هذى؟ الصيني
+
+338
+00:38:26,850 --> 00:38:33,510
+التين يبقى سالف تلتين في صيني التين زائد تمانية
+
+339
+00:38:33,510 --> 00:38:41,370
+على تلاتة في مين كمان هذى؟ صيني التلتينهذا ليس ضبط
+
+340
+00:38:41,370 --> 00:38:49,710
+فقط اضرب في 2 و اقسم على 2 يبقى بيصير هنا تمانية
+
+341
+00:38:49,710 --> 00:38:57,070
+على تلاتة ل plus inverse ل نص و هنا اتنين على S
+
+342
+00:38:57,070 --> 00:39:03,030
+square زائد اربعة يعني بدك تظبط مسألتكدائما وابدا
+
+343
+00:39:03,030 --> 00:39:08,290
+بيعتقل تكون ما فعلا له في صورة الجدول يبقى النتيجة
+
+344
+00:39:08,290 --> 00:39:15,510
+ناقص تلتين sin t النص بيطلع برا وضل قداش عندي اربع
+
+345
+00:39:15,510 --> 00:39:25,270
+على تلاتة وهذه اللي هي مين sin اتنين T هذا هو الحل
+
+346
+00:39:25,270 --> 00:39:32,630
+تبع المعادلة X as a function of Tنعطي كمان مثال
+
+347
+00:39:32,630 --> 00:39:40,110
+أخير مثال
+
+348
+00:39:40,110 --> 00:39:48,430
+اثنين بيقول ال X double prime ناقص X بده يساوي ال
+
+349
+00:39:48,430 --> 00:39:56,900
+F of Tوالـ T أكبر من أو يساوي الـ Zero والـ X عند
+
+350
+00:39:56,900 --> 00:40:02,720
+ال Zero بده يساوي واحد والـ X' عند ال Zero بده
+
+351
+00:40:02,720 --> 00:40:10,520
+يساوي Zero و واحدحيث مين هي ال F of T هذه ال F of
+
+352
+00:40:10,520 --> 00:40:18,640
+T بده يساوي يا إما Zero لما T أكبر من Zero أقل من
+
+353
+00:40:18,640 --> 00:40:28,880
+واحد يا إما T ناقص واحد لما T greater than
+
+354
+00:40:28,880 --> 00:40:32,680
+one طيب
+
+355
+00:40:33,610 --> 00:40:39,750
+نبدأ ناخد Laplace transform للطرفين يبقى solution
+
+356
+00:40:39,750 --> 00:40:46,190
+واضح
+
+357
+00:40:46,190 --> 00:40:49,250
+أنه ماقدر أحلها بال undetermined coefficients
+
+358
+00:40:49,250 --> 00:40:56,590
+مظبوط؟ بس بديش ماجليش قال استخدم Laplace transform
+
+359
+00:40:56,590 --> 00:40:59,370
+لحل هذه المعادلة
+
+360
+00:41:04,040 --> 00:41:08,720
+أذا بدرح أخد Laplace للطرفين يبقى Laplace
+
+361
+00:41:08,720 --> 00:41:15,560
+transform لل X W prime as a function of T ناقص
+
+362
+00:41:15,560 --> 00:41:23,480
+Laplace transform لل X of T بدر يساوي Laplace لل F
+
+363
+00:41:23,480 --> 00:41:31,160
+of Tنعود لهذه الاختصار هذي S2 في capital X of S
+
+364
+00:41:31,160 --> 00:41:39,300
+ناقص S في مين؟ في الـ X عند Zero ناقص X prime of
+
+365
+00:41:39,300 --> 00:41:45,260
+Zero ناقص capital X of S يساوي نحتاج لـ plus
+
+366
+00:41:45,260 --> 00:41:51,040
+للدالة هذه تمام؟ نعود لمين للخواص اللي عندنا؟ تبع
+
+367
+00:41:51,040 --> 00:41:53,320
+ال section تسعة تلاتة
+
+368
+00:41:55,380 --> 00:42:03,500
+الخاصية رقم خمسة خاصية رقم خمسة الخاصية رقم خمسة
+
+369
+00:42:03,500 --> 00:42:03,700
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+370
+00:42:03,700 --> 00:42:04,180
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+371
+00:42:04,180 --> 00:42:04,840
+الخاصية رقم خمسة الخمسة الخاصية رقم خمسة الخمسة
+
+372
+00:42:04,840 --> 00:42:06,500
+الخاصية رقم خمسة الخمسة الخاصية رقم خمسة الخمسة
+
+373
+00:42:06,500 --> 00:42:10,700
+الخمسة الخاصية رقم
+
+374
+00:42:10,700 --> 00:42:13,260
+خمسة الخمسة الخمسة الخمسة الخمسة الخمسة الخمسة
+
+375
+00:42:13,260 --> 00:42:16,480
+الخمسة الخمسة الخمسة الخمسة الخمسة الخمسة الخمسة
+
+376
+00:42:16,480 --> 00:42:20,740
+الخمسة الخمسة
+
+377
+00:42:20,740 --> 00:42:26,610
+الخمسT لأن T مطروح من الواحد هو الواحد هذا الواحد
+
+378
+00:42:26,610 --> 00:42:33,050
+تمام اذا هذه لابلاس ترانسفورم لها حسب الخاصية رقم
+
+379
+00:42:33,050 --> 00:42:40,170
+خمسة هي عبارة عن مين عبارة عن ال E أثناق ال CS في
+
+380
+00:42:40,170 --> 00:42:46,070
+capital F of S تمام طيب أجيب أطلع قداش ال C
+
+381
+00:42:46,070 --> 00:42:54,770
+مقدارهايبقى E أس ناقص S بيصير بالدالة capital F of
+
+382
+00:42:54,770 --> 00:43:01,970
+S بدي أعرف كده إيش هذا اللي عندنا يبقى هذه Laplace
+
+383
+00:43:01,970 --> 00:43:10,240
+إلها بيصير عندي E أس ناقص Sفاهمين؟ في لابلاس ال
+
+384
+00:43:10,240 --> 00:43:15,980
+transfer حسب الخاصية رقم خمسة لدالة F of S الدالة
+
+385
+00:43:15,980 --> 00:43:21,780
+مين هذه قبل ال shift؟ T يبقى باجي بقول هنا لابلاس
+
+386
+00:43:21,780 --> 00:43:30,790
+ل T اللي همين واحد factorial على استربعيبقى هذه
+
+387
+00:43:30,790 --> 00:43:35,350
+بيصير EOS ناقص S بس على S تربيع و الله مشان ما
+
+388
+00:43:35,350 --> 00:43:41,690
+تقوليش كيف جابها هذه بنقولك هي EOS ناقص S في واحد
+
+389
+00:43:41,690 --> 00:43:47,810
+factorial على S تربيع من وين أجت؟ قولنا لـPlus لـT
+
+390
+00:43:47,810 --> 00:43:52,150
+يا واحد factorial على S أس واحد زائد وعدها يحط
+
+391
+00:43:52,150 --> 00:44:00,110
+نالك وين في الهامش طيب نكمل شغلناهذه أمانات مع هذه
+
+392
+00:44:00,110 --> 00:44:10,930
+عامل مشترك يبقى بيصير S²-1 XS نجي ال X عندي Zero
+
+393
+00:44:10,930 --> 00:44:18,730
+تسوى كده؟ تسوى واحد يبقى ناقص S في واحد ال X' بيه
+
+394
+00:44:18,730 --> 00:44:26,450
+Zero يبقى ناقص Zero يسوى E أس ناقص S على S تربيع
+
+395
+00:44:27,970 --> 00:44:35,430
+يبقى صارة المثال على الشكل التالي اللي هو من s²-1
+
+396
+00:44:35,430 --> 00:44:41,650
+في x of s بده يساوي ننقل هذه على الشجة التانية
+
+397
+00:44:41,650 --> 00:44:52,370
+بصير s زائد y ناقص s على من على s² بالشكل اللي
+
+398
+00:44:52,370 --> 00:45:01,250
+عندنا هذاطيب بدي أجسم كله على S²-1 هذا معناه ان X
+
+399
+00:45:01,250 --> 00:45:08,990
+of S هذا ال S²-1 مش عبارة عن فرق بين المربعين صح؟
+
+400
+00:45:08,990 --> 00:45:16,430
+يبقى هذا ايش بيصير؟ بيصير S على S ناقص واحد في S
+
+401
+00:45:16,860 --> 00:45:25,340
+زائد واحد، تمام؟ زائد إيص أو خلّي هذه إيص ناقص S
+
+402
+00:45:25,340 --> 00:45:33,180
+زي ما هي و بيبقى عندي واحد على S square في S ناقص
+
+403
+00:45:33,180 --> 00:45:40,740
+واحد في S زائد واحد بالشكل اللي عندنا اه بدنا
+
+404
+00:45:40,740 --> 00:45:46,080
+partial fraction هذهولا لأ يبقى بدنا نبدأ نحسب ال
+
+405
+00:45:46,080 --> 00:45:51,120
+part في ال fraction يبقى أخر ما توصلنا إليه هو ال
+
+406
+00:45:51,120 --> 00:45:58,000
+X of S يسوى S على S square minus ال one وديك S
+
+407
+00:45:58,000 --> 00:46:04,070
+square مظبوط تمام مئة مية الميةطب خلّينا نشوف هذه
+
+408
+00:46:04,070 --> 00:46:07,330
+اللي هي الأولى نعمل ال partial fraction و بعدين
+
+409
+00:46:07,330 --> 00:46:12,410
+بنشوف التاني نشوف الكبيرة هذه يبقى واحد على S
+
+410
+00:46:12,410 --> 00:46:19,430
+square في S minus ال one في S plus one يسوى S
+
+411
+00:46:19,430 --> 00:46:27,290
+square يجب لزمنا A S زائد B زائد S ناقص واحد C
+
+412
+00:46:27,290 --> 00:46:37,310
+زائد S زائد واحد يبقى Dأحسنتأو الواحد بده يساوي AS
+
+413
+00:46:37,310 --> 00:46:46,130
+زائد ال B ال AS زائد ال B في مين؟ في ال S square
+
+414
+00:46:46,130 --> 00:46:53,550
+minus ال one اللي هو حاصل ضربهما زائد C S square
+
+415
+00:46:53,550 --> 00:47:05,210
+في S plus one زائد D S square في S minus ال oneطيب
+
+416
+00:47:05,210 --> 00:47:13,130
+هذا الواحد يساوي A استكيب ناقص ال A S زائد B
+
+417
+00:47:13,130 --> 00:47:21,250
+استربيع ناقص ال B زائد C استكيب زائد C استربيع
+
+418
+00:47:21,250 --> 00:47:31,600
+زائد D استكيب ناقص D استربيعانجمع يبقى هذه فيها
+
+419
+00:47:31,600 --> 00:47:39,440
+تكييب وهذه تكييب وهذه تكييب يبقى A زائد C زائد D
+
+420
+00:47:39,440 --> 00:47:47,440
+كله في ال S تكييب زائد تعين التربيع يبقى هذه Bوهنا
+
+421
+00:47:47,440 --> 00:47:56,560
+C وهنا ناقص D كله في ال S تربيع نجلي فيهم S هنا
+
+422
+00:47:56,560 --> 00:48:03,320
+كله ماعنديش S ماعنديش اللي هاد يتيمة ناقص AS وهنا
+
+423
+00:48:03,320 --> 00:48:10,240
+ناقص B زيهتمام يبقى نعمل مقارنة بين الطرفين يبقى a
+
+424
+00:48:10,240 --> 00:48:18,740
+زيدي ال c زيدي ال d بده يساوي 0 و b زيدي ال c ناقص
+
+425
+00:48:18,740 --> 00:48:26,340
+ال d بده يساوي 0 و ناقص ال a بده يساوي 0 و ناقص ال
+
+426
+00:48:26,340 --> 00:48:31,770
+b يساوي 1يبقى الاتنين هدول اشباطون يا بنات ان ال a
+
+427
+00:48:31,770 --> 00:48:40,490
+تساوي zero و ال b تساوي سالب واحد يبقى
+
+428
+00:48:40,490 --> 00:48:45,630
+هدف بده يعطينا لو أخدت ال a ب zero بيظل قداش c
+
+429
+00:48:45,630 --> 00:48:51,270
+زائد d يساوي zero و لو أخدت ال b بسالب واحد بيصير
+
+430
+00:48:51,270 --> 00:48:59,510
+ال c ناقص d ساوي واحدمظبوط؟ اجمع هدول مع السلامة
+
+431
+00:48:59,510 --> 00:49:10,130
+يبقى 2C يساوي 1 يبقى C يساوي نص لما C يساوي نص و A
+
+432
+00:49:10,130 --> 00:49:18,870
+ب 0 يبقى D بسالف نصيبقى هيو C بنص يبقى D يساوي
+
+433
+00:49:18,870 --> 00:49:25,610
+سالب نص إذا أصبح ال term اللي عندنا هذا جاهز أيوة
+
+434
+00:49:25,610 --> 00:49:31,370
+بدنا نشوف التاني كمان للتاني على أي حالبدي اكتب
+
+435
+00:49:31,370 --> 00:49:35,490
+النتيجة دغري وانت بدك تروح تعملي partial fraction
+
+436
+00:49:35,490 --> 00:49:41,350
+بسيط انا سويتلك الصعب وخليت البسيط يبقى لو روحنا
+
+437
+00:49:41,350 --> 00:49:49,250
+عملنا بيكون على الشكل التالي يبقى ال X of S بده
+
+438
+00:49:49,250 --> 00:49:56,700
+يساويالـ S على S²-1 هذه لا نريد أن نعملها لها
+
+439
+00:49:56,700 --> 00:50:01,760
+خلّيها زي ما هي مش مشكلة يبقى S على S²-1 مافيهاش
+
+440
+00:50:01,760 --> 00:50:09,360
+مشكلة وهذه زائد E أس ناقص S في قداش في سالب واحد
+
+441
+00:50:09,360 --> 00:50:20,600
+على S² زائد نص في واحد على S ناقص واحد وهنايبقى
+
+442
+00:50:20,600 --> 00:50:25,980
+هذا ال exponential اللي عندنا طيب اروح نجمع و نشوف
+
+443
+00:50:25,980 --> 00:50:32,320
+وين بدنا نوصلهذه سأتركها كذلك لأنها سهلة و لا يوجد
+
+444
+00:50:32,320 --> 00:50:41,300
+فيها مشكلة يبقى هذه S على S²-1 هذه زائد EOS ناقص S
+
+445
+00:50:41,300 --> 00:50:49,440
+هذه سالب واحد على S² هذول بقدر اخد مين؟ زائد نص
+
+446
+00:50:49,440 --> 00:50:56,260
+عامل مشترك بظل عندنا مين؟ S ناقص واحد في S زائد
+
+447
+00:50:56,260 --> 00:51:03,690
+واحدبصير عندنا هنا S زائد واحد ناقص S زائد واحد
+
+448
+00:51:03,690 --> 00:51:09,670
+شكل لأن هذا أظن هذا كله مش لازم الآن
+
+449
+00:51:21,730 --> 00:51:27,930
+طيب يبقى أصبح شكل ال X as a function of S يساوي
+
+450
+00:51:38,130 --> 00:51:43,590
+هذه البنات بتروح سالب S وموجب S مع السلمة بيظل
+
+451
+00:51:43,590 --> 00:51:48,330
+واحد وواحد اتنين مع المص الله سهل عليه يبقى بيظل
+
+452
+00:51:48,330 --> 00:51:53,530
+عندي قداش بس واحد على S تربية ناقص واحد يبقى بيظل
+
+453
+00:51:53,530 --> 00:52:01,390
+عندي هنا اللي هو ناقص واحد على S تربية و هنا زائد
+
+454
+00:52:01,390 --> 00:52:05,110
+واحد على S تربية ناقص واحد
+
+455
+00:52:09,100 --> 00:52:17,980
+يبقى صرتي النتيجة S على S تربيع ناقص واحد ناقص E
+
+456
+00:52:17,980 --> 00:52:26,060
+أس ناقص S في واحد على S تربيع وهنا زائد E أس ناقص
+
+457
+00:52:26,060 --> 00:52:34,910
+S في واحد على S تربيع ناقص الواحدالان بقدر اجيب
+
+458
+00:52:34,910 --> 00:52:41,710
+main ل plus المعكوس تبعهم و اشوف كده بده يساوي هذا
+
+459
+00:52:41,710 --> 00:52:49,290
+بيصير ال X of .. بدي ال X of T ال solution X of T
+
+460
+00:52:49,290 --> 00:52:56,730
+يساوي ل plus inverse ل main ل capital X of S و
+
+461
+00:52:56,730 --> 00:53:04,730
+يساوي ل plus inverse ل ال Sعلى S square ناقص واحد
+
+462
+00:53:04,730 --> 00:53:13,630
+ناقص Laplace inverse لمين؟ لل E أس ناقص S في واحد
+
+463
+00:53:13,630 --> 00:53:22,290
+على S تربيع وهنا زائد Laplace inverse لل E أس ناقص
+
+464
+00:53:22,290 --> 00:53:28,490
+S في واحد على S تربيع ناقص واحد بالشكل اللي عندنا
+
+465
+00:53:30,740 --> 00:53:39,060
+هعطيك الجواب النهائي وانت تجيبيه لحالك ها طيب
+
+466
+00:53:39,060 --> 00:53:45,820
+مالكيش بلاش يبقى هذا الكلام يسامي بدالي الأن لل S
+
+467
+00:53:45,820 --> 00:53:51,520
+على S تربية ناقص واحد حد ممكن تقولي مين هي؟ مين
+
+468
+00:53:51,520 --> 00:53:57,180
+قالك ان ال cosine بالزائد المقام هذا منها قوش قوش
+
+469
+00:53:57,180 --> 00:54:04,690
+اتي و ال a بقدراشبواحد يبقى هذا بقدر اقول هذا ت
+
+470
+00:54:04,690 --> 00:54:08,410
+فقط
+
+471
+00:54:08,410 --> 00:54:16,770
+لا غير نيجي لناقص بدي ل plus inverse لل E أُس ناقص
+
+472
+00:54:16,770 --> 00:54:21,150
+S واحد على S تربيع يالا شوفيلي
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9cf68f753214b4171d3b47fa8418fab8a41cb00a
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08_raw.srt
@@ -0,0 +1,1888 @@
+1
+00:00:00,000 --> 00:00:01,300
+موسيقى
+
+2
+00:00:19,070 --> 00:00:23,390
+بسم الله الرحمن الرحيم نعود إلى محاضرة الفترة
+
+3
+00:00:23,390 --> 00:00:27,430
+الصباحية طبعا ما بدأنا بال inverse Laplace
+
+4
+00:00:27,430 --> 00:00:31,430
+transform عطينا تعريف ل inverse Laplace transform
+
+5
+00:00:31,430 --> 00:00:36,850
+وعطينا على ذلك مثالا واحدا وهذا هو المثال رقم 2
+
+6
+00:00:37,480 --> 00:00:40,220
+يبقى المثال اللي بقول find the function that has
+
+7
+00:00:40,220 --> 00:00:44,600
+Laplace transform F of S يسوى S على S زائد واحد
+
+8
+00:00:44,600 --> 00:00:48,820
+لكل تربيع زائد أربعة بالشكل اللي قدامنا هنا
+
+9
+00:01:07,560 --> 00:01:11,840
+اللي هو بيعطيه هنا هذا أو اللي بيجينا في قائمة فيه
+
+10
+00:01:11,840 --> 00:01:17,800
+مع أسئلة الامتحان تمام طب بقولك كويس هذا لو في
+
+11
+00:01:17,800 --> 00:01:23,340
+عندي S زائد واحد في ال bus ليش؟ لأن عندي هنا S
+
+12
+00:01:23,340 --> 00:01:28,060
+زائد واحد كان قضيتي محلولة ومنتهية تماما إذا أنا
+
+13
+00:01:28,060 --> 00:01:33,340
+بتروح أخلك في ال bus S زائد واحد والله ناقص واحد
+
+14
+00:01:33,340 --> 00:01:39,660
+خليني أتأكد هذه S وين راحت؟س زائد واحد يبقى بدى س
+
+15
+00:01:39,660 --> 00:01:44,240
+زائد واحد يبقى بناء عليه مشان هيك ماعنديش partial
+
+16
+00:01:44,240 --> 00:01:48,700
+fraction حتى اقول partial fraction وانا قولت الصبح
+
+17
+00:01:48,700 --> 00:01:52,740
+اول خطوة بدي اعمل partial fraction مش كل مثل بقدر
+
+18
+00:01:52,740 --> 00:01:56,570
+اعمله partial هدف فيه ل partial fractionمالهاش
+
+19
+00:01:56,570 --> 00:02:02,390
+يبقى هذه جاهزة وخالصة تمام؟ إذا أنا بدي أحول هذه
+
+20
+00:02:02,390 --> 00:02:07,750
+إلى شكل من الأشكال اللي موجودة في الجدول إذا بقدر
+
+21
+00:02:07,750 --> 00:02:14,630
+أقول ال F of S اللي E تساوي لو روحت قولت S زائد
+
+22
+00:02:14,630 --> 00:02:20,370
+واحد ناقص واحد على S زائد واحد لكل تربيع زائد
+
+23
+00:02:20,370 --> 00:02:26,360
+أربعة عملت حاجة؟أضفت واحد واطرحت واحد بدي أفصل هذا
+
+24
+00:02:26,360 --> 00:02:33,060
+إلى مقدارين يبقى المقدار الأول هو S زائد واحد على
+
+25
+00:02:33,060 --> 00:02:41,400
+S زائد واحد لكل تربية زائد أربعة ناقص واحد على S
+
+26
+00:02:41,400 --> 00:02:49,170
+زائد واحد لكل تربية زائد أربعةالترم الأول صار
+
+27
+00:02:49,170 --> 00:02:53,390
+ماعنديش مشكلة لو روحت للجدول بلجيه عند وين في
+
+28
+00:02:53,390 --> 00:02:59,390
+الجدول هذا لسه لا يزال فيه مشكلة المشكلة أنه بده
+
+29
+00:02:59,390 --> 00:03:03,890
+اتنين هنا مدام هذه أربعة بد الجدر تبعها يكون وين
+
+30
+00:03:03,890 --> 00:03:11,370
+فور إذا بقدر أقول ال F of S بده يساوي ال S زائد
+
+31
+00:03:11,370 --> 00:03:18,350
+واحدعلى S زائد واحد لكل تربية زائد أربعة ناقص نص
+
+32
+00:03:18,350 --> 00:03:24,830
+في اتنين على S زائد واحد لكل تربية زائد أربعة
+
+33
+00:03:24,830 --> 00:03:32,500
+هيكسر كلامي صحيحالان انا بدي ال F of T F of T هي ل
+
+34
+00:03:32,500 --> 00:03:38,280
+plus inverse ل F of S يبقى ال F of T اللي انا بدور
+
+35
+00:03:38,280 --> 00:03:47,020
+عليها ال F of T هي ل plus inverse ل capital F of S
+
+36
+00:03:47,390 --> 00:03:54,250
+واللي هي بدها تساوي ل plus inverse لمين لل S plus
+
+37
+00:03:54,250 --> 00:04:02,470
+one على ال S plus one square plus four minus نص في
+
+38
+00:04:02,470 --> 00:04:08,690
+ال plus inverse ل الإتنين على S plus one لكل
+
+39
+00:04:08,690 --> 00:04:14,050
+square plus four بالشكل اللي عندنا هنا يبقى ال F
+
+40
+00:04:14,050 --> 00:04:19,760
+of T تساويبدي اجي على ال dialogue هادي و باجي على
+
+41
+00:04:19,760 --> 00:04:26,020
+الجدول اللي عندنا يبقى الجدول بدي ادور على الشكل
+
+42
+00:04:26,020 --> 00:04:30,880
+اللي ال S زائد واحد S زائد واحد لكل تربيع زائد
+
+43
+00:04:30,880 --> 00:04:32,400
+تربيع
+
+44
+00:04:34,010 --> 00:04:39,950
+طبعا لو جيت نظرت لهذا الجدول بلاحظ ان عندي هذا
+
+45
+00:04:39,950 --> 00:04:48,250
+الكلام موجود في النقطة رقم عشرة النقطة رقم عشرة
+
+46
+00:04:48,250 --> 00:04:56,040
+بتقول ليس نقص ال A على S نقص ال A لكل تربيع زي B
+
+47
+00:04:56,040 --> 00:05:01,440
+تربيع يعني بفرق بس بإشارة مين إشارة السالف لكن هذه
+
+48
+00:05:01,440 --> 00:05:08,310
+لو رجعت للأصل تبعها بلاقي E أس A T Cosبت يبقى
+
+49
+00:05:08,310 --> 00:05:12,550
+معناه هذا الكلام ان ال a اللي عندى هنا بإشارة بس a
+
+50
+00:05:12,550 --> 00:05:18,430
+سالب يبقى لو جيت على الجدول من part عشرة هذا
+
+51
+00:05:18,430 --> 00:05:25,110
+الكلام بدي ساوي a أس ال a عندى هنا بقداش بواحد
+
+52
+00:05:25,110 --> 00:05:33,030
+يبقى a أس ناقص T في cosine بت هذا بي تربيع يبقى
+
+53
+00:05:33,030 --> 00:05:37,300
+بيه بقداشباتنين لان P تربيه سوى ربع وانت بيه
+
+54
+00:05:37,300 --> 00:05:46,180
+باتنين يبقى E أس ناقص T في من في Cos 2T اللي بعدها
+
+55
+00:05:46,180 --> 00:05:52,220
+ناقص نص بداجي لهذه لو رجعت لخط و لجاب الخلف اللي
+
+56
+00:05:52,220 --> 00:05:57,620
+هو النقطة التاسعة بلجأ عندي P على S ناقص L كل
+
+57
+00:05:57,620 --> 00:06:04,650
+تربيع زائد P تربيعيبقى هذه بي هيب اتنين هي بي
+
+58
+00:06:04,650 --> 00:06:10,350
+تربيع باربعة زائد يبقى ال a بس بمين بسالب واحد
+
+59
+00:06:10,350 --> 00:06:18,530
+يبقى باجي بناقص نص في a أس سالب T ل sign اتنين T
+
+60
+00:06:18,530 --> 00:06:23,570
+انتهت مسألتنا يبقى كله اعتماد على الجدول كيف اطلع
+
+61
+00:06:23,570 --> 00:06:30,680
+من الجدول Laplace transform للدوال المختلفةمثال
+
+62
+00:06:30,680 --> 00:06:35,700
+ثلاثة
+
+63
+00:06:35,700 --> 00:06:43,740
+مثال ثلاثة بيقول ما ياتي بدنا
+
+64
+00:06:43,740 --> 00:06:48,720
+نجد مفعول
+
+65
+00:06:48,720 --> 00:06:53,460
+f of t with
+
+66
+00:06:55,610 --> 00:07:06,170
+اللي هو it's a type with Laplace transform
+
+67
+00:07:09,400 --> 00:07:15,960
+اللي لابلاس ترانسفورم إلها اللي هو capital F of S
+
+68
+00:07:15,960 --> 00:07:25,280
+بده يساوي تلاتة S ناقص اتنين على S تربيع ناقص
+
+69
+00:07:25,280 --> 00:07:28,680
+اتنين S زائد عشرة
+
+70
+00:07:33,040 --> 00:07:38,760
+بقول كويس اللي قال لو روحت على الجدول تابعنا هذا و
+
+71
+00:07:38,760 --> 00:07:46,560
+بلاجيش ولا term هشكل هذا لكن بده اعادة ايه ترتيب
+
+72
+00:07:46,560 --> 00:07:51,460
+هذا ال term كيف نقيت ترتيبه؟ بده اشوف المقام،
+
+73
+00:07:51,460 --> 00:07:56,000
+ماعنديش شغمة زي هيك كله بلاجي S زي واحد الكل تربيع
+
+74
+00:07:56,000 --> 00:08:01,440
+S نقص اتنين الكل تربيع زي رقم هنا رقم هنا S إلى
+
+75
+00:08:01,440 --> 00:08:06,100
+آخرينإذا بدي أعيد كتابة هذه ال function بطريقة
+
+76
+00:08:06,100 --> 00:08:12,260
+ثانية إذا بقدر أقول هذا الكلام يسوى ثلاثة S ناقص
+
+77
+00:08:12,260 --> 00:08:18,980
+اتنين على هذا S تربية ناقص اتنين S إذا هذا لازم
+
+78
+00:08:18,980 --> 00:08:24,660
+أعمله ايه مربع كامل مشان أعمل هذا مربع كامل جداش
+
+79
+00:08:24,660 --> 00:08:31,340
+بده S تربية زيدي اتنين S جداش بده رقمش هصير مربع
+
+80
+00:08:31,340 --> 00:08:40,770
+كامل2S ناقص
+
+81
+00:08:40,770 --> 00:08:47,170
+معامل X على أربع أمثال معامل X دربية يبقى هنا بقول
+
+82
+00:08:47,170 --> 00:08:55,850
+زائد 2S يبقى مش هين أحول بذكر مرتين و تلتة و عشرين
+
+83
+00:08:56,440 --> 00:09:02,060
+بدي اعمل اكمال المربع بضيف للطرفين و بطرح مربع
+
+84
+00:09:02,060 --> 00:09:07,200
+معامل X على اربع امثال معامل X تربيع اعطيتها لكم
+
+85
+00:09:07,200 --> 00:09:12,900
+في calculus P و يا محل نبع يبقى مربع معامل X على
+
+86
+00:09:12,900 --> 00:09:17,440
+اربع امثال معامل X تربيع يعني مربع معامل F على
+
+87
+00:09:17,440 --> 00:09:22,840
+اربع امثال معامل S تربيعيبقى هنا بيبقى داش بواحد
+
+88
+00:09:22,840 --> 00:09:27,940
+يبقى زائد اتنين اس زائد واحد الواحد موجود عند
+
+89
+00:09:27,940 --> 00:09:34,940
+الجيران عشرة باخد منها واحد بيبقى تسعة يبقى زائد
+
+90
+00:09:34,940 --> 00:09:43,110
+تسعة يبقى هذا الكلام يساويالمقام اللي عندنا هذا
+
+91
+00:09:43,110 --> 00:09:48,950
+الانصار مربع كامل صح يبقى هذا بقدر اقول اللي هو ال
+
+92
+00:09:48,950 --> 00:09:58,580
+S ناقص واحد لكل تربيع زائد تسعةأيوة إذن البث هذا
+
+93
+00:09:58,580 --> 00:10:05,160
+بيدخلك في مين S ناقص واحد بيدخلك في كاف S ناقص اما
+
+94
+00:10:05,160 --> 00:10:09,920
+هو تلاتة S ناقص اتنين الجثة بسيطة خالص بضيف سالب
+
+95
+00:10:09,920 --> 00:10:15,020
+واحد و بطرح واحد يعني بضيف واحد و بطرح سالب واحد
+
+96
+00:10:15,020 --> 00:10:21,200
+يبقى هذا لو حطيت سالب واحد كده بصير؟بقدر اخد تلاتة
+
+97
+00:10:21,200 --> 00:10:25,360
+عمل مشترك وبظل S ناقص واحد بيكون خلصت مسألة اتنين
+
+98
+00:10:25,360 --> 00:10:32,220
+اذا البسط هذا بقدر اكتب تلاتة S ناقص تلاتة زائد
+
+99
+00:10:32,220 --> 00:10:38,700
+واحديبقى أضفت سالب واحد وكذلك واحد يعني أضفت zero
+
+100
+00:10:38,700 --> 00:10:45,760
+مغيرتش ولا عالية يبقى بناء عليه أصبح شكل ال F of S
+
+101
+00:10:45,760 --> 00:10:54,100
+على الشكل التالي هذه تلاتةفى S ناقص واحد خدته
+
+102
+00:10:54,100 --> 00:11:02,020
+معامل مشترك وهنا زائد واحد على مين على S على S
+
+103
+00:11:02,020 --> 00:11:09,470
+ناقص واحد لكل تربية زائد تسعةممكن هذه أفصلها إلى
+
+104
+00:11:09,470 --> 00:11:18,670
+جزئين من الجزئين هاي تلاتة في S ناقص واحد S ناقص
+
+105
+00:11:18,670 --> 00:11:27,390
+واحد لكل تربية زائد تسعة ضال عندي زائد واحد على S
+
+106
+00:11:27,390 --> 00:11:33,350
+ناقص واحد لكل تربية زائد تسعة أظن صارت شبيهة
+
+107
+00:11:33,350 --> 00:11:40,390
+بمسألة هذه قبل قليلصح؟ وهذه شبيهة ابها بالضبط
+
+108
+00:11:40,390 --> 00:11:46,670
+تماماً يبقى تعالى نشوف كيف نسوي يبقى أنا هذه هاه
+
+109
+00:11:46,670 --> 00:11:52,550
+فدها بس فوق كده شمنهاكداش؟ تلاتة ممتاز يبقى بدي
+
+110
+00:11:52,550 --> 00:11:58,350
+اضرب في تلاتة و اجسم على تلاتة اذا بقدر اقول هذا
+
+111
+00:11:58,350 --> 00:12:05,190
+الكلام تلاتة في اس ناقص واحد على من على اس ناقص
+
+112
+00:12:05,190 --> 00:12:12,690
+واحد الكل تربية زائد تسعة زائد تلت في تلاتة على اس
+
+113
+00:12:12,690 --> 00:12:20,530
+ناقص واحد الكل تربية زائد تسعةيبقى ال F of T هي
+
+114
+00:12:20,530 --> 00:12:25,670
+Laplace inverse للطرفين يبقى تلاتة في Laplace
+
+115
+00:12:25,670 --> 00:12:32,870
+inverse لل S ناقص واحد S ناقص واحد لكل تربية زائد
+
+116
+00:12:32,870 --> 00:12:40,930
+تسعة زائد تلت Laplace inverse لتلاتة S ناقص واحد
+
+117
+00:12:40,930 --> 00:12:48,960
+لكل تربية زائد تسعةيبقى أصبح شكل ال F of T بيسوي
+
+118
+00:12:48,960 --> 00:12:56,240
+ثلاثة فيه نرجع بالذاكرة الوراء للجدول قبل قليل
+
+119
+00:12:56,240 --> 00:13:04,700
+كذلك إلى النقطة العاشرة بلاحظ عندي S ناقص A S ناقص
+
+120
+00:13:04,700 --> 00:13:10,560
+A لكل تربيع زائد B تربيع يبقى الأصل تبعها E أس AT
+
+121
+00:13:10,560 --> 00:13:20,600
+Cos BTقداش ال A عند هنا ال A بواحد طب و ال B؟تلاتة
+
+122
+00:13:20,600 --> 00:13:28,100
+لإن هذه بيه تربيع يبقى بناء عليه تلاتة E of T بدون
+
+123
+00:13:28,100 --> 00:13:35,060
+زالب تمام فاهمين فى cosine تلاتة T هذا ال term
+
+124
+00:13:35,060 --> 00:13:43,420
+الأول زائد طول هذه بنفس الطريقة E of T sine تلاتة
+
+125
+00:13:43,420 --> 00:13:48,120
+T يبقى هذه ال function اللى مطلوبة اللى عندنا
+
+126
+00:13:55,990 --> 00:14:00,830
+بنعطي كمان مثال مثال
+
+127
+00:14:00,830 --> 00:14:04,570
+تلاتة أو example أربعة
+
+128
+00:14:09,370 --> 00:14:16,690
+بيقول لي نفس القصة capital F of S بده يساوي E أس
+
+129
+00:14:16,690 --> 00:14:25,390
+ناقص S على S ناقص اتنين لكل تاربيع و بده مين؟ بده
+
+130
+00:14:25,390 --> 00:14:30,580
+نوجد لنا place transform اللي هالمعكوز تبعهبقول له
+
+131
+00:14:30,580 --> 00:14:35,340
+بسيطة جدا قبل ما توجد لبلاس ترانسفورم حاول ترتبها
+
+132
+00:14:35,340 --> 00:14:44,620
+بقول له يعني هذه لو كتبتها E أس ناقص S في واحد على
+
+133
+00:14:44,620 --> 00:14:52,860
+S ناقص اتنين لكل تربية عملنا حاجة طيب ايش رايك
+
+134
+00:14:52,860 --> 00:14:57,800
+الواحد هذا لو كتبت واحد factorial الشكل اللي عندنا
+
+135
+00:14:57,800 --> 00:14:58,020
+هذا
+
+136
+00:15:03,450 --> 00:15:09,810
+يبقى باجي بقول ال F of T اللي أنا بدور عليها هي
+
+137
+00:15:09,810 --> 00:15:17,810
+Laplace transform بالمعكوس تبعها لcapital F of S
+
+138
+00:15:17,810 --> 00:15:24,110
+ويساوي Laplace transform لل E أص ناقص S
+
+139
+00:15:39,210 --> 00:15:43,410
+يبقى ال F of T تساوي
+
+140
+00:15:52,230 --> 00:15:59,670
+طيب من فوق لتحت اكسبوننشيل اكسبوننشيل عندي رقم
+
+141
+00:15:59,670 --> 00:16:05,690
+اتناش اكسبوننشيل على اس انا عندي على اس ناقص كذا
+
+142
+00:16:06,430 --> 00:16:14,490
+طيب انا بلاحظ عندي الرقم تلتاش الرقم تلتاش اللي هو
+
+143
+00:16:14,490 --> 00:16:25,780
+E أس ناقص CS في capital F of Scapital F of S هذا
+
+144
+00:16:25,780 --> 00:16:32,100
+الاصل تبعها الاصل تبعها ده ال step function u C of
+
+145
+00:16:32,100 --> 00:16:39,260
+T فال F of T ناقص من ناقص ال C لكن لو رجعنا
+
+146
+00:16:39,260 --> 00:16:46,700
+للخاصية رقم 5 من section 9 3 تحيلي section 9 3
+
+147
+00:16:46,700 --> 00:16:48,040
+الخاصية رقم 5
+
+148
+00:16:50,690 --> 00:16:53,670
+يعني إذا عرفت تجيبيها من الجد والكرمها وماعرفتش
+
+149
+00:16:53,670 --> 00:17:00,490
+برجع للأصل هذه تبعها طلعيلي مشان أكتب هذه الدالة
+
+150
+00:17:00,490 --> 00:17:08,850
+بداجي للدالة بين القوسين هذه هي ال F of S قولي G
+
+151
+00:17:08,850 --> 00:17:15,490
+of S يساوي واحد factorial على S ناقص اتنين لكل
+
+152
+00:17:15,490 --> 00:17:20,650
+تربيعبقدر اجيب الاصل تبعها مين الاصل تبعها يا بنات
+
+153
+00:17:20,650 --> 00:17:26,510
+جي اوب تي يساوي هذه لو روحت جبت الاصل تبعها يبقى
+
+154
+00:17:26,510 --> 00:17:33,070
+الاصل تبعها هو عبارة عن تي في اي أس اتنين تي طبعا
+
+155
+00:17:33,070 --> 00:17:38,830
+من الجدول تي في اي أس اتنين تي لو روحت للخاصية رقم
+
+156
+00:17:38,830 --> 00:17:45,450
+خمسة اللي عندك بدي اعمل لهذه الدالة shift بمقدار
+
+157
+00:17:46,670 --> 00:17:52,430
+كداش؟ اتنين مش عندك هنا اتنين، هذا اتنين، انت بقى
+
+158
+00:17:52,430 --> 00:17:56,710
+ال exponential يبقى بدي اعمله shift بمقدار عفوا
+
+159
+00:17:56,710 --> 00:18:06,530
+بمقدار اللي هو الاتنين، بمقدار الواحد
+
+160
+00:18:06,530 --> 00:18:13,450
+وليس الاتنينطيب كيف ده جت كالتالي فباجي بقول يبقى
+
+161
+00:18:13,450 --> 00:18:20,110
+ال plus inverse لها يسوى أحد أمرين يا إما zero لما
+
+162
+00:18:20,110 --> 00:18:26,490
+ال T أكبر من ال zero أقل من واحد يا إما T ناقص
+
+163
+00:18:26,490 --> 00:18:34,630
+واحد E أس اتنين في T ناقص واحد وال T أكبر من
+
+164
+00:18:34,630 --> 00:18:35,430
+الواحد
+
+165
+00:18:38,640 --> 00:18:46,220
+خصية رقم خمسة الخاصية رقم خمسة من سكتشن تسعة تلاتة
+
+166
+00:18:48,480 --> 00:18:53,280
+خاصية رقم خمسة اللي بيقولي small q of t بدي ساوي
+
+167
+00:18:53,280 --> 00:18:56,860
+زيرو لما t محصورة بين ال zero و ال c او f of t
+
+168
+00:18:56,860 --> 00:19:02,140
+ناقص ال c لما t اكبر من ال c يبقى لبلاي ال
+
+169
+00:19:02,140 --> 00:19:08,240
+transform اللي هي E اص ناقص CS في capital F of S
+
+170
+00:19:08,240 --> 00:19:14,760
+يعني بدنا نجيب ال F of S للدلة اللي عندنا وين ال F
+
+171
+00:19:14,760 --> 00:19:23,510
+of S هىمظبوط؟ يبقى الدالة الأصلية تبعتها T في E
+
+172
+00:19:23,510 --> 00:19:29,870
+أُس 2T هيا جبناها هنا، كويس؟ الآن هذي بدي أعمل لها
+
+173
+00:19:29,870 --> 00:19:36,650
+shift بمقدار مين؟ بمقدار الواحد، مقدار الأُس اللي
+
+174
+00:19:36,650 --> 00:19:40,790
+عندي تبع ال exponential هنا، جداش المعامل اللي
+
+175
+00:19:40,790 --> 00:19:44,500
+هنا؟لأ سيبكي من السلب السلب تبع القانون موجود في
+
+176
+00:19:44,500 --> 00:19:50,120
+القانون صح موجود عندك أيه في النقطة رقم خمسة E و
+
+177
+00:19:50,120 --> 00:19:51,660
+سالب CS
+
+178
+00:19:54,070 --> 00:19:59,970
+خامسة أخر حاجة على اليمين يبقى E والسلب CS في ال F
+
+179
+00:19:59,970 --> 00:20:04,990
+of S يبقى أن المعامل هنا واحد إذا هذه الدلة بدي
+
+180
+00:20:04,990 --> 00:20:10,210
+أعمل لها shift بمقدار واحد يبقى صارت T ناقص واحد
+
+181
+00:20:10,210 --> 00:20:16,450
+في S اتنين T ناقص واحد لما T greater than zero
+
+182
+00:20:16,450 --> 00:20:21,990
+يبقى هذا باستخدام الخاصية رقم كم؟ رقم خمسة
+
+183
+00:20:24,770 --> 00:20:29,530
+لازلنا في نفس ال section و لما ننتهي بعد بدنا نعطي
+
+184
+00:20:29,530 --> 00:20:39,690
+تعريف صغير و مثال عليه كذلك تعريف
+
+185
+00:20:39,690 --> 00:20:44,390
+بيقول ما يأتي definition
+
+186
+00:20:44,390 --> 00:20:50,930
+the
+
+187
+00:20:50,930 --> 00:20:51,510
+function
+
+188
+00:20:54,110 --> 00:21:05,050
+F Star G F Star G As a function of T is called
+
+189
+00:21:05,050 --> 00:21:15,510
+بنسميه The Convolution The Convolution
+
+190
+00:21:15,510 --> 00:21:18,610
+Of
+
+191
+00:21:18,610 --> 00:21:20,990
+The
+
+192
+00:21:27,070 --> 00:21:30,490
+and denoted by
+
+193
+00:21:35,930 --> 00:21:44,890
+بنعرفها كالتالي ال f star g as a function of t بده
+
+194
+00:21:44,890 --> 00:21:53,950
+يسوي تكامل من zero إلى T لل F of T ناقص ال U ال G
+
+195
+00:21:53,950 --> 00:22:01,900
+of U دي Uواللي هي بدها تساوي تكامل من zero إلى T
+
+196
+00:22:01,900 --> 00:22:12,700
+لل F of U لل G of T ناقص ال U DU واللي هي بدها
+
+197
+00:22:12,700 --> 00:22:21,040
+تساوي G star F and
+
+198
+00:22:21,040 --> 00:22:32,660
+henceومن ثم لبلاسيت ترانسفورم لل F star G فال F
+
+199
+00:22:32,660 --> 00:22:42,980
+star G بده يساوي capital F of S في capital G of S
+
+200
+00:22:42,980 --> 00:22:46,480
+نعطي
+
+201
+00:22:46,480 --> 00:22:47,040
+مثال
+
+202
+00:22:53,540 --> 00:23:02,900
+معرفة مفهوم f*)g
+
+203
+00:23:02,900 --> 00:23:06,980
+كمفهوم من f
+
+204
+00:23:12,860 --> 00:23:22,700
+ال F of T بد يساوي ال E أس T وال G of T يساوي E أس
+
+205
+00:23:22,700 --> 00:23:23,980
+اتنين T
+
+206
+00:23:59,030 --> 00:24:03,430
+بنجي لتعريف ال convolution ل ال two functions ايش
+
+207
+00:24:03,430 --> 00:24:07,750
+بيقول دي؟ ال function f star g as a function of t
+
+208
+00:24:07,750 --> 00:24:12,710
+بنسميها ال convolution of ال function اللي هي ال
+
+209
+00:24:12,710 --> 00:24:16,710
+main of ال function f and g convolution في اللغة
+
+210
+00:24:16,710 --> 00:24:22,130
+العربية معناه التفاف يعني كأنه بيعمل التفاف يعني
+
+211
+00:24:22,130 --> 00:24:27,550
+ليهاعملت لدالة f ممكن اعمل لدالة g و التانية تظهر
+
+212
+00:24:27,550 --> 00:24:32,270
+زي ما هي بدون مشاكل من هنا سمينا convolution لمين
+
+213
+00:24:32,270 --> 00:24:37,690
+لتو functions بهمني هذا جدش بيساوي لإن أنا هذا هو
+
+214
+00:24:37,690 --> 00:24:42,290
+اللي بشتغل عليه إذا بدي بقول لدالة f star g أو f
+
+215
+00:24:42,290 --> 00:24:46,690
+convolution g as a function of tيتكوّن من zero إلى
+
+216
+00:24:46,690 --> 00:24:52,610
+T يا باجي على ال F اللي عنها دي بكتبها أو بشيل كل
+
+217
+00:24:52,610 --> 00:24:59,030
+T بحط بدلها T نقص U U real numberها يبقى F of T
+
+218
+00:24:59,030 --> 00:25:08,270
+نقص ال U في ال G of U في ال DUيبقى كوني الأن أخدت
+
+219
+00:25:08,270 --> 00:25:14,950
+الـDU يعني U هي اشتقاق وكأن الـT أنا ثبتها كأنه
+
+220
+00:25:14,950 --> 00:25:18,430
+خلت الـT مقدار ثابت لأن أنا كامل بالنسبة لـU إذا
+
+221
+00:25:18,430 --> 00:25:24,020
+الـT إيش تعتبر مقدارا ثابتاأريد أن أثبت الـ U
+
+222
+00:25:24,020 --> 00:25:28,580
+فأقول F of U يبقى الـ G فأقول G of T ناقص الـ U في
+
+223
+00:25:28,580 --> 00:25:33,380
+الـ DU وحسب الـ Definition هذه ستساوي عملت لهذه G
+
+224
+00:25:33,380 --> 00:25:39,300
+وهذه ثبتت فأقول G star F يبقى بناء عليه الـ F star
+
+225
+00:25:39,300 --> 00:25:46,500
+G هو G star F كلها as a function of T كلها كدالة
+
+226
+00:25:46,500 --> 00:25:50,200
+في D يبقى هذه والله هذه عملت للدالة الأولى والله
+
+227
+00:25:50,200 --> 00:25:55,120
+الدالة التانيةالاتنين are the same طب لو بده اجيب
+
+228
+00:25:55,120 --> 00:25:59,900
+Laplace transform لل convolution بقول Laplace
+
+229
+00:25:59,900 --> 00:26:05,040
+لدالة الأولى ضرب ضرب عادية Laplace لدالة التانية
+
+230
+00:26:05,040 --> 00:26:10,180
+هيها dot مضروبة ضرب فيها دي تمام؟ بدنا نروح نطبق
+
+231
+00:26:10,180 --> 00:26:14,790
+هذا الكلام بمثالجالي هاتلي الدالة هادى إذا كانت ال
+
+232
+00:26:14,790 --> 00:26:19,610
+F of T بده يساوي ال E of T وال G of T بده يساوي من
+
+233
+00:26:19,610 --> 00:26:25,110
+ال E أس اتنين إذا لما بداجي أحل بداجي أقوله ال F
+
+234
+00:26:25,110 --> 00:26:31,830
+star G كله as a function of T يساوي ال F of T يا
+
+235
+00:26:31,830 --> 00:26:38,130
+بنات اللي هي من E أس T ال G of T اللي هي E أس
+
+236
+00:26:38,130 --> 00:26:44,170
+اتنين T وهايهم function في Tطبقا للتعريف اللى فوق
+
+237
+00:26:44,170 --> 00:26:51,050
+يبقى تكامل من zero إلى T تمام عندك هذه الصيغة او
+
+238
+00:26:51,050 --> 00:26:56,450
+هذه سيان يبقى ال F اللى هى الدالة الاولى بدي اعمل
+
+239
+00:26:56,450 --> 00:27:04,810
+لها shift بمقدار جداش ال U يبقى E أس T ناقص ال U
+
+240
+00:27:04,810 --> 00:27:12,160
+ال G أبدا بدي اشيل ال T بس و اكتب مكانها جداشيوم
+
+241
+00:27:12,160 --> 00:27:22,580
+دي يوم تمام طيب إذا هذا بنيت بقدر أقول تساوي تكامل
+
+242
+00:27:22,580 --> 00:27:31,380
+من zero إلى T لمن لل E أوس T E أوس ناقص U E أوس
+
+243
+00:27:31,380 --> 00:27:37,570
+اتنين Uأظن الـ Eost مالهاش دعوة بالتكامل لإنه
+
+244
+00:27:37,570 --> 00:27:42,250
+يشتقق بالنسبة لمن يبقى بقدر أطلعها برا التكامل
+
+245
+00:27:42,250 --> 00:27:50,610
+يبقى هذه تساوي Eost تكامل من Zero إلى T لل E بجمع
+
+246
+00:27:50,610 --> 00:27:56,250
+الأسس لإن الأساسات زي بعض يبقى UDU
+
+247
+00:27:57,600 --> 00:28:04,640
+تمام؟ طيب هذا بيصير E Os T فيه تكامل ال E Os U بال
+
+248
+00:28:04,640 --> 00:28:10,480
+E Os U itself يبقى هذه ال E Os U من وين لوين؟ من
+
+249
+00:28:10,480 --> 00:28:17,800
+Zero لغاية T يبقى هذا الكلام بده يساوي اهه اللي هو
+
+250
+00:28:17,800 --> 00:28:26,970
+مين؟ E Os T في مين؟ في ال E Os T ناقص E Os ZeroE0
+
+251
+00:28:26,970 --> 00:28:34,490
+بيبقى داشر يبقى صار E of T في E of T ناقص واحد
+
+252
+00:28:34,490 --> 00:28:42,950
+يبقى E of 2T ناقص E of T إذا ال convolution اللي
+
+253
+00:28:42,950 --> 00:28:49,150
+حصل لل two functions F and G يسوى الدالة الأولى
+
+254
+00:28:49,150 --> 00:28:55,550
+الدالة الثانية ناقص الدالة الأولى بالمثللو أخذت
+
+255
+00:28:55,550 --> 00:29:01,830
+هذه الـ T عملت لها T ناقص الـ U وهذه خلّيت الـ U
+
+256
+00:29:01,830 --> 00:29:06,670
+كامل فهو يطلع نفس النتيجة اللي عندنا لحد هنا stop
+
+257
+00:29:06,670 --> 00:29:11,490
+and turn section إلى يكون أرقام المسائل يبقى
+
+258
+00:29:11,490 --> 00:29:20,370
+exercises تسعة أربعة المسائل واحد واتنين وأربعةبدأ
+
+259
+00:29:20,370 --> 00:29:30,170
+أخد الـ A و الـ C و سؤال 5 بدي ال A و ال B ال A و
+
+260
+00:29:30,170 --> 00:29:37,030
+ال B و ال A و ال F طيب
+
+261
+00:29:37,030 --> 00:29:45,050
+نيجي لآخر section اللي هو 9 5 يبقى 9 5 اللي هو ال
+
+262
+00:29:45,050 --> 00:29:46,190
+applications
+
+263
+00:29:49,160 --> 00:29:56,180
+applications to differential equations
+
+264
+00:29:58,370 --> 00:30:03,510
+تطبيقات على المعادلات التفاضلية ايش يعني المقصود
+
+265
+00:30:03,510 --> 00:30:07,730
+فيها المقصود استخدام Laplace transform لحل
+
+266
+00:30:07,730 --> 00:30:13,690
+المعادلة التفاضلية اظن حلنالكوا بدل المعادلة تنتين
+
+267
+00:30:13,690 --> 00:30:18,730
+مظبوط يبقى انا باعتمر ماشتغلتش بالمرة و بدي اشتغل
+
+268
+00:30:18,730 --> 00:30:26,490
+من جديد يبقى هنا بدي اقول to use السؤال بيجي كتالة
+
+269
+00:30:26,490 --> 00:30:42,450
+exampleتوضيحي example use Laplace transform to
+
+270
+00:30:42,450 --> 00:30:45,490
+solve
+
+271
+00:30:45,490 --> 00:30:51,590
+the
+
+272
+00:30:51,590 --> 00:30:54,690
+initial value problem
+
+273
+00:30:57,680 --> 00:31:05,600
+اللي هي ال x double prime زائد أربعة x بده ساوية
+
+274
+00:31:05,600 --> 00:31:13,320
+تمانية sign ال T وال x عند ال zero بدها تساوي zero
+
+275
+00:31:13,320 --> 00:31:20,440
+وال x prime عند ال zero بده ساوي اتنين solution
+
+276
+00:31:24,890 --> 00:31:28,750
+يبقى مدام أعطاني السؤال من هذا القبيل هو قيدني
+
+277
+00:31:28,750 --> 00:31:32,910
+بطريقة الحل أنا هذه معادلة من الرتبة الثانية إذا
+
+278
+00:31:32,910 --> 00:31:38,110
+لو بدي أرجع للي قبل المعاملات ثوابت ودالة بالصينيا
+
+279
+00:31:38,110 --> 00:31:41,050
+ممكن إذا بحلها بال undetermined coefficients بس هو
+
+280
+00:31:41,050 --> 00:31:43,730
+بدش ياني أحلها بال undetermined coefficients بدي
+
+281
+00:31:43,730 --> 00:31:48,130
+ياني أحلها بال a plus transform ويبقى أنا مقيد إذا
+
+282
+00:31:48,130 --> 00:31:52,490
+بال a plus transformاذا بروح اخد لبلاس ترانسفورم
+
+283
+00:31:52,490 --> 00:31:59,330
+للطرفين يبقى باجي بقول لبلاس ترانسفورم لل XW' زائد
+
+284
+00:31:59,330 --> 00:32:06,350
+أربعة لبلاس ترانسفورم لل X بدي ساوي تمانية لبلاس
+
+285
+00:32:06,350 --> 00:32:12,950
+ترانسفورم لصيتي لش؟ ان لبلاس ترانسفورم is a linear
+
+286
+00:32:12,950 --> 00:32:16,390
+function او linear operator يبقى التمانية بقدر
+
+287
+00:32:16,390 --> 00:32:25,560
+اطلع برابدي أطبق النظرية على هذه يبقى هذه S2 XS
+
+288
+00:32:25,560 --> 00:32:39,800
+ناقص S في X عند 0 ناقص X' عند 0 زائد 4XS بده ساوي
+
+289
+00:32:39,800 --> 00:32:45,890
+8صين الـ T مظبوط صين الـ T ولا صين اتنين T يبقى
+
+290
+00:32:45,890 --> 00:32:51,330
+صين الـ T مدام صين الـ T إذا هذه Laplace Transform
+
+291
+00:32:51,330 --> 00:32:58,970
+حسبناها عمليا يبقى هذا بقداش يا بناد بواحد على أس
+
+292
+00:32:58,970 --> 00:33:07,130
+تربيع زائد واحد مظبوططيب يبقى هنيجي طلعيلي لهذه
+
+293
+00:33:07,130 --> 00:33:14,310
+وهذه بقدر اخد X of S عامل مشترك بيظل عندي S
+
+294
+00:33:14,310 --> 00:33:21,630
+squared زائد 4 في capital X of Sالان ال X عندي
+
+295
+00:33:21,630 --> 00:33:25,470
+Zero يبقى
+
+296
+00:33:25,470 --> 00:33:32,970
+ناقص Zero ال X Prime باتنين يبقى ناقص اتنين يسوى
+
+297
+00:33:32,970 --> 00:33:40,710
+تمانية على استربيع زائد واحد او ان شئتم فقولوا ان
+
+298
+00:33:40,710 --> 00:33:48,370
+ال S Square زائد اربعةفي capital X of S بده يسوى
+
+299
+00:33:48,370 --> 00:33:55,790
+تمانية على S square plus one plus two بده واحد
+
+300
+00:33:55,790 --> 00:34:02,690
+المقامات يبقى بصير S square زائد أربعة في capital
+
+301
+00:34:02,690 --> 00:34:11,050
+X of S يسوى كله على S square plus one وهي تمانيةزي
+
+302
+00:34:11,050 --> 00:34:16,870
+دي اتنين S square زي دي اتنين تمام يبقى بيصير
+
+303
+00:34:16,870 --> 00:34:22,750
+عندنا مين بيصير عندنا S square plus four في
+
+304
+00:34:22,750 --> 00:34:30,970
+capital X of S يساويإتنين S Square زائد عشرة
+
+305
+00:34:30,970 --> 00:34:38,710
+مقسوما على S Square plus one طب أنا بدي X of S
+
+306
+00:34:38,710 --> 00:34:46,370
+يبقى ال X of S بده يساوي اتنين S Square زائد عشرة
+
+307
+00:34:46,370 --> 00:34:55,610
+على S Square plus one في S Square plus fourلو روحت
+
+308
+00:34:55,610 --> 00:35:01,010
+على الجدول بلاقي شغلة زي هذه في الشمكانية طب كيف
+
+309
+00:35:01,010 --> 00:35:04,870
+نسوي؟ بقولك بسيطة ال bus من الدرجة التانية و
+
+310
+00:35:04,870 --> 00:35:11,790
+المقام من الدرجةpartial fraction و الحمد لله جاهزة
+
+311
+00:35:11,790 --> 00:35:17,550
+يبقى بس احطها على شكل ايه شكل كسور يبقى هذا الكلام
+
+312
+00:35:17,550 --> 00:35:23,650
+بده يساوي هذا كسر وهذا ال S squared plus one وهذا
+
+313
+00:35:23,650 --> 00:35:29,110
+كسر تاني S squared plus four المعادلة من الدرجة
+
+314
+00:35:29,110 --> 00:35:33,790
+الثانية كل واحدة فيهم ولا يمكن تحليلها إذا بده أحط
+
+315
+00:35:33,790 --> 00:35:41,210
+فوق معادلة من الدرجةالأولى يبقى باجي بقوله AS زائد
+
+316
+00:35:41,210 --> 00:35:47,910
+B وهنا CS زائد D وبعد هيك بروح أحسب ال partial
+
+317
+00:35:47,910 --> 00:35:54,030
+fractions يبقى بقوله اتنين S Square زائد عشرة بده
+
+318
+00:35:54,030 --> 00:36:03,490
+يساوي AS زائد ال B في مين؟ في ال S Square زائد 4
+
+319
+00:36:03,490 --> 00:36:13,160
+زائد CSزي دي دي في ال S square plus oneطبعا بنفك
+
+320
+00:36:13,160 --> 00:36:19,960
+ونقرر مش هضيع وقت فيها هعطيك النتيجة مباشرة يبقى
+
+321
+00:36:19,960 --> 00:36:27,260
+بتطلع عندك هنا ال a تساوي zero ال a تساوي zero و
+
+322
+00:36:27,260 --> 00:36:36,660
+ال b تساوي ناقص تلتين و ال c بتطلع عندك ب zero و
+
+323
+00:36:36,660 --> 00:36:45,950
+ال d بتطلع عندى ب 8 على 3بناء عليه أصبحت المسألة
+
+324
+00:36:45,950 --> 00:36:47,770
+على الشكل التالي
+
+325
+00:37:00,950 --> 00:37:07,290
+يبقى أصبحت الـ X of S X as a function of S على
+
+326
+00:37:07,290 --> 00:37:12,390
+الشكل التالف طلعيه هنا كويسة يبقى بدأ دي أشيل ال A
+
+327
+00:37:12,390 --> 00:37:18,730
+و أحط مكانها Zero طارة ال B بدأ أحط بدل سالب تلتين
+
+328
+00:37:18,730 --> 00:37:25,450
+يبقى هاي سالب تلتين ضال واحد على S square زائد
+
+329
+00:37:25,450 --> 00:37:31,920
+واحدانتهينا منها الان ال c ب zero طارت يبقى ال d ب
+
+330
+00:37:31,920 --> 00:37:38,320
+تمانية على تلاتة زائد تمانية على تلاتة في جداش في
+
+331
+00:37:38,320 --> 00:37:46,370
+واحد على s square زائد اربعإذا أنا بدي ال X as a
+
+332
+00:37:46,370 --> 00:37:52,870
+function of T هي Laplace inverse لcapital X of S
+
+333
+00:37:52,870 --> 00:37:57,050
+بالشكل اللي عندنا هنا يبقى هذا بدي ساوي سالب
+
+334
+00:37:57,050 --> 00:38:02,630
+طولتين Laplace inverse للواحد على S squared plus
+
+335
+00:38:02,630 --> 00:38:11,680
+oneزائد تمانية على تلاتة وهنا لابلاس inverse لواحد
+
+336
+00:38:11,680 --> 00:38:18,620
+على اس square زائد اربع يبقى شكل ال X of T يساوي
+
+337
+00:38:18,620 --> 00:38:26,850
+سالب تلتين مين هذا يا بنات؟هى مين هذى؟ الصيني
+
+338
+00:38:26,850 --> 00:38:33,510
+التين يبقى سالف تلتين في صيني التين زائد تمانية
+
+339
+00:38:33,510 --> 00:38:41,370
+على تلاتة في مين كمان هذى؟ صيني التلتينهذا ليس ضبط
+
+340
+00:38:41,370 --> 00:38:49,710
+فقط اضرب في 2 و اقسم على 2 يبقى بيصير هنا تمانية
+
+341
+00:38:49,710 --> 00:38:57,070
+على تلاتة ل plus inverse ل نص و هنا اتنين على S
+
+342
+00:38:57,070 --> 00:39:03,030
+square زائد اربعة يعني بدك تظبط مسألتكدائما وابدا
+
+343
+00:39:03,030 --> 00:39:08,290
+بيعتقل تكون ما فعلا له في صورة الجدول يبقى النتيجة
+
+344
+00:39:08,290 --> 00:39:15,510
+ناقص تلتين sin t النص بيطلع برا وضل قداش عندي اربع
+
+345
+00:39:15,510 --> 00:39:25,270
+على تلاتة وهذه اللي هي مين sin اتنين T هذا هو الحل
+
+346
+00:39:25,270 --> 00:39:32,630
+تبع المعادلة X as a function of Tنعطي كمان مثال
+
+347
+00:39:32,630 --> 00:39:40,110
+أخير مثال
+
+348
+00:39:40,110 --> 00:39:48,430
+اثنين بيقول ال X double prime ناقص X بده يساوي ال
+
+349
+00:39:48,430 --> 00:39:56,900
+F of Tوالـ T أكبر من أو يساوي الـ Zero والـ X عند
+
+350
+00:39:56,900 --> 00:40:02,720
+ال Zero بده يساوي واحد والـ X' عند ال Zero بده
+
+351
+00:40:02,720 --> 00:40:10,520
+يساوي Zero و واحدحيث مين هي ال F of T هذه ال F of
+
+352
+00:40:10,520 --> 00:40:18,640
+T بده يساوي يا إما Zero لما T أكبر من Zero أقل من
+
+353
+00:40:18,640 --> 00:40:28,880
+واحد يا إما T ناقص واحد لما T greater than
+
+354
+00:40:28,880 --> 00:40:32,680
+one طيب
+
+355
+00:40:33,610 --> 00:40:39,750
+نبدأ ناخد Laplace transform للطرفين يبقى solution
+
+356
+00:40:39,750 --> 00:40:46,190
+واضح
+
+357
+00:40:46,190 --> 00:40:49,250
+أنه ماقدر أحلها بال undetermined coefficients
+
+358
+00:40:49,250 --> 00:40:56,590
+مظبوط؟ بس بديش ماجليش قال استخدم Laplace transform
+
+359
+00:40:56,590 --> 00:40:59,370
+لحل هذه المعادلة
+
+360
+00:41:04,040 --> 00:41:08,720
+أذا بدرح أخد Laplace للطرفين يبقى Laplace
+
+361
+00:41:08,720 --> 00:41:15,560
+transform لل X W prime as a function of T ناقص
+
+362
+00:41:15,560 --> 00:41:23,480
+Laplace transform لل X of T بدر يساوي Laplace لل F
+
+363
+00:41:23,480 --> 00:41:31,160
+of Tنعود لهذه الاختصار هذي S2 في capital X of S
+
+364
+00:41:31,160 --> 00:41:39,300
+ناقص S في مين؟ في الـ X عند Zero ناقص X prime of
+
+365
+00:41:39,300 --> 00:41:45,260
+Zero ناقص capital X of S يساوي نحتاج لـ plus
+
+366
+00:41:45,260 --> 00:41:51,040
+للدالة هذه تمام؟ نعود لمين للخواص اللي عندنا؟ تبع
+
+367
+00:41:51,040 --> 00:41:53,320
+ال section تسعة تلاتة
+
+368
+00:41:55,380 --> 00:42:03,500
+الخاصية رقم خمسة خاصية رقم خمسة الخاصية رقم خمسة
+
+369
+00:42:03,500 --> 00:42:03,700
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+370
+00:42:03,700 --> 00:42:04,180
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+371
+00:42:04,180 --> 00:42:04,840
+الخاصية رقم خمسة الخمسة الخاصية رقم خمسة الخمسة
+
+372
+00:42:04,840 --> 00:42:06,500
+الخاصية رقم خمسة الخمسة الخاصية رقم خمسة الخمسة
+
+373
+00:42:06,500 --> 00:42:10,700
+الخمسة الخاصية رقم
+
+374
+00:42:10,700 --> 00:42:13,260
+خمسة الخمسة الخمسة الخمسة الخمسة الخمسة الخمسة
+
+375
+00:42:13,260 --> 00:42:16,480
+الخمسة الخمسة الخمسة الخمسة الخمسة الخمسة الخمسة
+
+376
+00:42:16,480 --> 00:42:20,740
+الخمسة الخمسة
+
+377
+00:42:20,740 --> 00:42:26,610
+الخمسT لأن T مطروح من الواحد هو الواحد هذا الواحد
+
+378
+00:42:26,610 --> 00:42:33,050
+تمام اذا هذه لابلاس ترانسفورم لها حسب الخاصية رقم
+
+379
+00:42:33,050 --> 00:42:40,170
+خمسة هي عبارة عن مين عبارة عن ال E أثناق ال CS في
+
+380
+00:42:40,170 --> 00:42:46,070
+capital F of S تمام طيب أجيب أطلع قداش ال C
+
+381
+00:42:46,070 --> 00:42:54,770
+مقدارهايبقى E أس ناقص S بيصير بالدالة capital F of
+
+382
+00:42:54,770 --> 00:43:01,970
+S بدي أعرف كده إيش هذا اللي عندنا يبقى هذه Laplace
+
+383
+00:43:01,970 --> 00:43:10,240
+إلها بيصير عندي E أس ناقص Sفاهمين؟ في لابلاس ال
+
+384
+00:43:10,240 --> 00:43:15,980
+transfer حسب الخاصية رقم خمسة لدالة F of S الدالة
+
+385
+00:43:15,980 --> 00:43:21,780
+مين هذه قبل ال shift؟ T يبقى باجي بقول هنا لابلاس
+
+386
+00:43:21,780 --> 00:43:30,790
+ل T اللي همين واحد factorial على استربعيبقى هذه
+
+387
+00:43:30,790 --> 00:43:35,350
+بيصير EOS ناقص S بس على S تربيع و الله مشان ما
+
+388
+00:43:35,350 --> 00:43:41,690
+تقوليش كيف جابها هذه بنقولك هي EOS ناقص S في واحد
+
+389
+00:43:41,690 --> 00:43:47,810
+factorial على S تربيع من وين أجت؟ قولنا لـPlus لـT
+
+390
+00:43:47,810 --> 00:43:52,150
+يا واحد factorial على S أس واحد زائد وعدها يحط
+
+391
+00:43:52,150 --> 00:44:00,110
+نالك وين في الهامش طيب نكمل شغلناهذه أمانات مع هذه
+
+392
+00:44:00,110 --> 00:44:10,930
+عامل مشترك يبقى بيصير S²-1 XS نجي ال X عندي Zero
+
+393
+00:44:10,930 --> 00:44:18,730
+تسوى كده؟ تسوى واحد يبقى ناقص S في واحد ال X' بيه
+
+394
+00:44:18,730 --> 00:44:26,450
+Zero يبقى ناقص Zero يسوى E أس ناقص S على S تربيع
+
+395
+00:44:27,970 --> 00:44:35,430
+يبقى صارة المثال على الشكل التالي اللي هو من s²-1
+
+396
+00:44:35,430 --> 00:44:41,650
+في x of s بده يساوي ننقل هذه على الشجة التانية
+
+397
+00:44:41,650 --> 00:44:52,370
+بصير s زائد y ناقص s على من على s² بالشكل اللي
+
+398
+00:44:52,370 --> 00:45:01,250
+عندنا هذاطيب بدي أجسم كله على S²-1 هذا معناه ان X
+
+399
+00:45:01,250 --> 00:45:08,990
+of S هذا ال S²-1 مش عبارة عن فرق بين المربعين صح؟
+
+400
+00:45:08,990 --> 00:45:16,430
+يبقى هذا ايش بيصير؟ بيصير S على S ناقص واحد في S
+
+401
+00:45:16,860 --> 00:45:25,340
+زائد واحد، تمام؟ زائد إيص أو خلّي هذه إيص ناقص S
+
+402
+00:45:25,340 --> 00:45:33,180
+زي ما هي و بيبقى عندي واحد على S square في S ناقص
+
+403
+00:45:33,180 --> 00:45:40,740
+واحد في S زائد واحد بالشكل اللي عندنا اه بدنا
+
+404
+00:45:40,740 --> 00:45:46,080
+partial fraction هذهولا لأ يبقى بدنا نبدأ نحسب ال
+
+405
+00:45:46,080 --> 00:45:51,120
+part في ال fraction يبقى أخر ما توصلنا إليه هو ال
+
+406
+00:45:51,120 --> 00:45:58,000
+X of S يسوى S على S square minus ال one وديك S
+
+407
+00:45:58,000 --> 00:46:04,070
+square مظبوط تمام مئة مية الميةطب خلّينا نشوف هذه
+
+408
+00:46:04,070 --> 00:46:07,330
+اللي هي الأولى نعمل ال partial fraction و بعدين
+
+409
+00:46:07,330 --> 00:46:12,410
+بنشوف التاني نشوف الكبيرة هذه يبقى واحد على S
+
+410
+00:46:12,410 --> 00:46:19,430
+square في S minus ال one في S plus one يسوى S
+
+411
+00:46:19,430 --> 00:46:27,290
+square يجب لزمنا A S زائد B زائد S ناقص واحد C
+
+412
+00:46:27,290 --> 00:46:37,310
+زائد S زائد واحد يبقى Dأحسنتأو الواحد بده يساوي AS
+
+413
+00:46:37,310 --> 00:46:46,130
+زائد ال B ال AS زائد ال B في مين؟ في ال S square
+
+414
+00:46:46,130 --> 00:46:53,550
+minus ال one اللي هو حاصل ضربهما زائد C S square
+
+415
+00:46:53,550 --> 00:47:05,210
+في S plus one زائد D S square في S minus ال oneطيب
+
+416
+00:47:05,210 --> 00:47:13,130
+هذا الواحد يساوي A استكيب ناقص ال A S زائد B
+
+417
+00:47:13,130 --> 00:47:21,250
+استربيع ناقص ال B زائد C استكيب زائد C استربيع
+
+418
+00:47:21,250 --> 00:47:31,600
+زائد D استكيب ناقص D استربيعانجمع يبقى هذه فيها
+
+419
+00:47:31,600 --> 00:47:39,440
+تكييب وهذه تكييب وهذه تكييب يبقى A زائد C زائد D
+
+420
+00:47:39,440 --> 00:47:47,440
+كله في ال S تكييب زائد تعين التربيع يبقى هذه Bوهنا
+
+421
+00:47:47,440 --> 00:47:56,560
+C وهنا ناقص D كله في ال S تربيع نجلي فيهم S هنا
+
+422
+00:47:56,560 --> 00:48:03,320
+كله ماعنديش S ماعنديش اللي هاد يتيمة ناقص AS وهنا
+
+423
+00:48:03,320 --> 00:48:10,240
+ناقص B زيهتمام يبقى نعمل مقارنة بين الطرفين يبقى a
+
+424
+00:48:10,240 --> 00:48:18,740
+زيدي ال c زيدي ال d بده يساوي 0 و b زيدي ال c ناقص
+
+425
+00:48:18,740 --> 00:48:26,340
+ال d بده يساوي 0 و ناقص ال a بده يساوي 0 و ناقص ال
+
+426
+00:48:26,340 --> 00:48:31,770
+b يساوي 1يبقى الاتنين هدول اشباطون يا بنات ان ال a
+
+427
+00:48:31,770 --> 00:48:40,490
+تساوي zero و ال b تساوي سالب واحد يبقى
+
+428
+00:48:40,490 --> 00:48:45,630
+هدف بده يعطينا لو أخدت ال a ب zero بيظل قداش c
+
+429
+00:48:45,630 --> 00:48:51,270
+زائد d يساوي zero و لو أخدت ال b بسالب واحد بيصير
+
+430
+00:48:51,270 --> 00:48:59,510
+ال c ناقص d ساوي واحدمظبوط؟ اجمع هدول مع السلامة
+
+431
+00:48:59,510 --> 00:49:10,130
+يبقى 2C يساوي 1 يبقى C يساوي نص لما C يساوي نص و A
+
+432
+00:49:10,130 --> 00:49:18,870
+ب 0 يبقى D بسالف نصيبقى هيو C بنص يبقى D يساوي
+
+433
+00:49:18,870 --> 00:49:25,610
+سالب نص إذا أصبح ال term اللي عندنا هذا جاهز أيوة
+
+434
+00:49:25,610 --> 00:49:31,370
+بدنا نشوف التاني كمان للتاني على أي حالبدي اكتب
+
+435
+00:49:31,370 --> 00:49:35,490
+النتيجة دغري وانت بدك تروح تعملي partial fraction
+
+436
+00:49:35,490 --> 00:49:41,350
+بسيط انا سويتلك الصعب وخليت البسيط يبقى لو روحنا
+
+437
+00:49:41,350 --> 00:49:49,250
+عملنا بيكون على الشكل التالي يبقى ال X of S بده
+
+438
+00:49:49,250 --> 00:49:56,700
+يساويالـ S على S²-1 هذه لا نريد أن نعملها لها
+
+439
+00:49:56,700 --> 00:50:01,760
+خلّيها زي ما هي مش مشكلة يبقى S على S²-1 مافيهاش
+
+440
+00:50:01,760 --> 00:50:09,360
+مشكلة وهذه زائد E أس ناقص S في قداش في سالب واحد
+
+441
+00:50:09,360 --> 00:50:20,600
+على S² زائد نص في واحد على S ناقص واحد وهنايبقى
+
+442
+00:50:20,600 --> 00:50:25,980
+هذا ال exponential اللي عندنا طيب اروح نجمع و نشوف
+
+443
+00:50:25,980 --> 00:50:32,320
+وين بدنا نوصلهذه سأتركها كذلك لأنها سهلة و لا يوجد
+
+444
+00:50:32,320 --> 00:50:41,300
+فيها مشكلة يبقى هذه S على S²-1 هذه زائد EOS ناقص S
+
+445
+00:50:41,300 --> 00:50:49,440
+هذه سالب واحد على S² هذول بقدر اخد مين؟ زائد نص
+
+446
+00:50:49,440 --> 00:50:56,260
+عامل مشترك بظل عندنا مين؟ S ناقص واحد في S زائد
+
+447
+00:50:56,260 --> 00:51:03,690
+واحدبصير عندنا هنا S زائد واحد ناقص S زائد واحد
+
+448
+00:51:03,690 --> 00:51:09,670
+شكل لأن هذا أظن هذا كله مش لازم الآن
+
+449
+00:51:21,730 --> 00:51:27,930
+طيب يبقى أصبح شكل ال X as a function of S يساوي
+
+450
+00:51:38,130 --> 00:51:43,590
+هذه البنات بتروح سالب S وموجب S مع السلمة بيظل
+
+451
+00:51:43,590 --> 00:51:48,330
+واحد وواحد اتنين مع المص الله سهل عليه يبقى بيظل
+
+452
+00:51:48,330 --> 00:51:53,530
+عندي قداش بس واحد على S تربية ناقص واحد يبقى بيظل
+
+453
+00:51:53,530 --> 00:52:01,390
+عندي هنا اللي هو ناقص واحد على S تربية و هنا زائد
+
+454
+00:52:01,390 --> 00:52:05,110
+واحد على S تربية ناقص واحد
+
+455
+00:52:09,100 --> 00:52:17,980
+يبقى صرتي النتيجة S على S تربيع ناقص واحد ناقص E
+
+456
+00:52:17,980 --> 00:52:26,060
+أس ناقص S في واحد على S تربيع وهنا زائد E أس ناقص
+
+457
+00:52:26,060 --> 00:52:34,910
+S في واحد على S تربيع ناقص الواحدالان بقدر اجيب
+
+458
+00:52:34,910 --> 00:52:41,710
+main ل plus المعكوس تبعهم و اشوف كده بده يساوي هذا
+
+459
+00:52:41,710 --> 00:52:49,290
+بيصير ال X of .. بدي ال X of T ال solution X of T
+
+460
+00:52:49,290 --> 00:52:56,730
+يساوي ل plus inverse ل main ل capital X of S و
+
+461
+00:52:56,730 --> 00:53:04,730
+يساوي ل plus inverse ل ال Sعلى S square ناقص واحد
+
+462
+00:53:04,730 --> 00:53:13,630
+ناقص Laplace inverse لمين؟ لل E أس ناقص S في واحد
+
+463
+00:53:13,630 --> 00:53:22,290
+على S تربيع وهنا زائد Laplace inverse لل E أس ناقص
+
+464
+00:53:22,290 --> 00:53:28,490
+S في واحد على S تربيع ناقص واحد بالشكل اللي عندنا
+
+465
+00:53:30,740 --> 00:53:39,060
+هعطيك الجواب النهائي وانت تجيبيه لحالك ها طيب
+
+466
+00:53:39,060 --> 00:53:45,820
+مالكيش بلاش يبقى هذا الكلام يسامي بدالي الأن لل S
+
+467
+00:53:45,820 --> 00:53:51,520
+على S تربية ناقص واحد حد ممكن تقولي مين هي؟ مين
+
+468
+00:53:51,520 --> 00:53:57,180
+قالك ان ال cosine بالزائد المقام هذا منها قوش قوش
+
+469
+00:53:57,180 --> 00:54:04,690
+اتي و ال a بقدراشبواحد يبقى هذا بقدر اقول هذا ت
+
+470
+00:54:04,690 --> 00:54:08,410
+فقط
+
+471
+00:54:08,410 --> 00:54:16,770
+لا غير نيجي لناقص بدي ل plus inverse لل E أُس ناقص
+
+472
+00:54:16,770 --> 00:54:21,150
+S واحد على S تربيع يالا شوفيلي
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270.srt
new file mode 100644
index 0000000000000000000000000000000000000000..af7b0187b517eb378ac57cd5768a4164b16c596d
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270.srt
@@ -0,0 +1,1614 @@
+1
+00:00:19,980 --> 00:00:25,880
+بسم الله الرحمن الرحيم في محاضرة الصبح اتكلمنا عن
+
+2
+00:00:25,880 --> 00:00:31,760
+بعض التعريفات قلنا لو الـ system star كان له حل
+
+3
+00:00:31,760 --> 00:00:36,680
+وحيد أو عدد لا نهائي من الحلول بنسمي consistent
+
+4
+00:00:36,680 --> 00:00:42,760
+وإذا كان مالوش حل بنسمي inconsistent وآخر حاجة
+
+5
+00:00:42,760 --> 00:00:47,600
+كتبناها two systems are equivalent اثنين بقول عنهم
+
+6
+00:00:47,600 --> 00:00:52,520
+اثنين متكافئين إذا كان لهم نفس الحلول إذا الـ system
+
+7
+00:00:52,520 --> 00:00:56,380
+الأول والـ system الثاني طلع لهم نفس الحلول إذا
+
+8
+00:00:56,380 --> 00:01:00,900
+بقول عن هذا الـ two systems are equivalent نجي ناخد 
+
+9
+00:01:00,900 --> 00:01:03,980
+مثال على ذلك بقول you show that the following two
+
+10
+00:01:03,980 --> 00:01:08,160
+systems are equivalent بينينا أن الـ two systems
+
+11
+00:01:08,160 --> 00:01:12,140
+هدول are equivalent بدل الـ system الأول بدي 
+
+12
+00:01:12,140 --> 00:01:16,760
+أحاول أحله بمعنى آخر بيطلع جدّيش قيمة x1 وجدّيش
+
+13
+00:01:16,760 --> 00:01:20,900
+قيمة x2 والـ system الثاني بيطلع جدّيش قيمة x1 وx2
+
+14
+00:01:20,900 --> 00:01:26,520
+بأي طريقة رياضية ممكن تقدر عليها بقول بسيطة جدًا
+
+15
+00:01:26,520 --> 00:01:33,740
+يبقى بمجرد النظر المعادلة الأولى 2x1-3x2 بدي أسميه
+
+16
+00:01:33,740 --> 00:01:38,100
+واحد المعادلة الثانية أظهر لو ضربناها في سالب 2 و
+
+17
+00:01:38,100 --> 00:01:41,680
+بنقدر نتخلص من أحد المجاهيل ونحصل على قيمة
+
+18
+00:01:41,680 --> 00:01:47,360
+المجهول الثاني يبقى لو روح ضربت هذه في سالب 2 بصير
+
+19
+00:01:47,360 --> 00:01:55,970
+سالب 2x1 سالب 8x2 يساوي سالب 12 لو جيت جمعت يبقى 
+
+20
+00:01:55,970 --> 00:02:00,710
+هدول مع السلامة بروح بصير أن سالب تلاتة وتمانية
+
+21
+00:02:00,710 --> 00:02:06,890
+أحد عشر X2 يساوي سالب أحد عشر ومنها X2 يساوي قداش
+
+22
+00:02:06,890 --> 00:02:12,070
+واحد لو رجعت على المعادلة الأولى وشلت X وحطيت
+
+23
+00:02:12,070 --> 00:02:16,810
+مكانها واحد بصير اثنين اكس وان ناقص ثلاثة يساوي
+
+24
+00:02:16,810 --> 00:02:22,970
+واحد ومنها two x one بده يساوي أربعة يبقى اكس وان
+
+25
+00:02:22,970 --> 00:02:27,750
+بده يساوي قداش اثنين يبقى the solution
+
+26
+00:02:31,500 --> 00:02:38,600
+X1 X2 X3
+
+27
+00:02:38,600 --> 00:02:39,840
+X4 X5 X6 X7 X8 X9 X10 X11 X12 X11 X12 X11 X11 X11
+
+28
+00:02:39,840 --> 00:02:40,240
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+29
+00:02:40,240 --> 00:02:40,560
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+30
+00:02:40,560 --> 00:02:42,500
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+31
+00:02:42,500 --> 00:02:44,960
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+32
+00:02:44,960 --> 00:02:47,460
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+33
+00:02:50,500 --> 00:02:55,860
+لو ضربت هذه في سالب بتروح مع هذه يبقى سالب بـ 2 X1
+
+34
+00:02:55,860 --> 00:03:02,200
+زائد 14 X2 بده يساوي قداش عشرة المعادلة الثانية
+
+35
+00:03:02,200 --> 00:03:09,920
+خلتها زي ما هي 2 X1 زائد 8 X2 يساوي 12 وروحت جامعة
+
+36
+00:03:10,330 --> 00:03:14,610
+يبقى لو روحت جامعة بصير هذا وهذا مع السلامة بـ 0
+
+37
+00:03:14,610 --> 00:03:21,670
+بظل عندنا 22 X2 يساوي 22 هذا بده يعطينا أن X2
+
+38
+00:03:21,670 --> 00:03:27,830
+يساوي 1 لو رجعت لأي من المعادلتين الأولى والثانية
+
+39
+00:03:27,830 --> 00:03:34,910
+وحطيت X2 بواحد بصير X1 ناقص سبعة بده يساوي ناقص
+
+40
+00:03:34,910 --> 00:03:45,450
+خمسة إذا X1 يساوي قداش اثنين يبقى the solution is x1 و
+
+41
+00:03:45,450 --> 00:03:52,150
+x2 يساوي 2 و 1 وهو نفس الحل اللي عندنا مادام طلع
+
+42
+00:03:52,150 --> 00:03:57,090
+نفس الحل يبقى الـ two systems هدول are equivalent
+
+43
+00:03:57,090 --> 00:04:06,990
+يبقى هنا so the two systems are equivalent
+
+44
+00:04:10,520 --> 00:04:27,060
+السبب because they have the same solution لأن
+
+45
+00:04:27,060 --> 00:04:31,900
+لهم نفس الحل ومن هنا الاثنين هذول are equivalent
+
+46
+00:04:31,900 --> 00:04:36,000
+بدنا
+
+47
+00:04:36,000 --> 00:04:37,580
+نيجي لـ remark
+
+48
+00:04:45,640 --> 00:04:56,400
+النظام الهوموجيني هو
+
+49
+00:04:56,400 --> 00:05:02,920
+دائمًا مستقل
+
+50
+00:05:02,920 --> 00:05:06,900
+دائمًا
+
+51
+00:05:06,900 --> 00:05:11,900
+مستقل لأن السبب
+
+52
+00:05:12,960 --> 00:05:22,880
+it has at least it has at least على الأقل the
+
+53
+00:05:22,880 --> 00:05:28,740
+trivial solution
+
+54
+00:05:30,550 --> 00:05:42,530
+اللي هو main x1 و x2 و xn بده يساوي zero و zero و
+
+55
+00:05:42,530 --> 00:05:51,970
+zero الآن
+
+56
+00:05:51,970 --> 00:05:59,270
+how to find بنطرح سؤال ونحاول نجاوب عليه and
+
+57
+00:06:01,280 --> 00:06:09,520
+equivalent how to find an
+
+58
+00:06:09,520 --> 00:06:12,680
+equivalent
+
+59
+00:06:12,680 --> 00:06:17,080
+how
+
+60
+00:06:17,080 --> 00:06:24,820
+to find an equivalent system for
+
+61
+00:06:24,820 --> 00:06:41,250
+a given system for a given system
+
+62
+00:06:41,250 --> 00:06:44,970
+هذا
+
+63
+00:06:44,970 --> 00:06:54,830
+سؤال الرجاء عليك التالي إذا واحد enter a change
+
+64
+00:06:57,980 --> 00:07:09,440
+interchange two equations النقطة الثانية multiply
+
+65
+00:07:09,440 --> 00:07:13,420
+both
+
+66
+00:07:13,420 --> 00:07:20,880
+sides of
+
+67
+00:07:20,880 --> 00:07:25,420
+an equation
+
+68
+00:07:27,350 --> 00:07:38,890
+by a number c والـ c does not equal to zero  نمرة
+
+69
+00:07:38,890 --> 00:07:46,090
+ثلاثة adding a
+
+70
+00:07:46,090 --> 00:07:50,370
+multiple of
+
+71
+00:07:50,370 --> 00:07:52,290
+one
+
+72
+00:07:53,730 --> 00:08:04,730
+equation to other equation لمعادلة أخرى in the
+
+73
+00:08:04,730 --> 00:08:13,270
+system these
+
+74
+00:08:13,270 --> 00:08:19,170
+operations هذه
+
+75
+00:08:19,170 --> 00:08:22,470
+العمليات are called
+
+76
+00:08:26,380 --> 00:08:38,860
+بنسميها elementary elementary
+
+77
+00:08:38,860 --> 00:08:42,480
+row operations
+
+78
+00:09:38,930 --> 00:09:44,530
+الآن بدي أعطي تعريف لكن نظرًا لأن هذا التعريف بدنا
+
+79
+00:09:44,530 --> 00:09:48,170
+نشتغله يعني كل شغل من الآن حتى نهاية الـ section
+
+80
+00:09:48,170 --> 00:09:52,890
+مركب عليه بدي أعطيه بالعربي حتى تعرف تشتغلي بعد
+
+81
+00:09:52,890 --> 00:09:56,410
+هيك مش لسه مستوعبيش التعريف الإنجليزي وبعدين يصير
+
+82
+00:09:56,410 --> 00:09:59,750
+صعب فجأة بدأت أقول تعريف
+
+83
+00:10:07,890 --> 00:10:17,270
+يقال للمصفوفة أيه؟ أنها على 
+
+84
+00:10:17,270 --> 00:10:23,270
+الشكل الـ Row echelon form
+
+85
+00:10:33,030 --> 00:10:40,210
+Row Echelon Form إذا تحققت 
+
+86
+00:10:40,210 --> 00:10:54,250
+الشروط التالية أول شرط من هذه الشروط إذا كان هناك
+
+87
+00:10:54,250 --> 00:11:00,270
+صف 
+
+88
+00:11:00,270 --> 00:11:12,100
+غير صفري إذا كان هناك صف غير صفري في المصفوفة
+
+89
+00:11:12,100 --> 00:11:25,360
+المصفوفة فإن الرقم الأول في هذا الصف الرقم الأول
+
+90
+00:11:25,360 --> 00:11:32,320
+في هذا الصف هو واحد صحيح ويسمى
+
+91
+00:11:33,750 --> 00:11:44,550
+هذا العنصر ويسمى هذا العنصر الـ leading leading
+
+92
+00:11:44,550 --> 00:11:51,970
+يعني زي القائد اللي بقود الباقي نمرة اثنين جميع
+
+93
+00:11:51,970 --> 00:12:01,210
+الصفوف الصفرية جميع الصفوف الصفرية
+
+94
+00:12:02,820 --> 00:12:16,260
+جميع الصفوف الصفرية تكون أسفل الصفوف الأخرى 
+
+95
+00:12:16,260 --> 00:12:22,880
+في المصفوفة نمرة
+
+96
+00:12:22,880 --> 00:12:28,880
+ثلاثة الرقم
+
+97
+00:12:30,940 --> 00:12:37,260
+واحد اللي هو الـ leading القائد
+
+98
+00:12:37,260 --> 00:12:52,200
+الـ leading هدف فيه الصفوف التالية لكل صف لكل صف
+
+99
+00:12:52,200 --> 00:13:08,710
+يقع على يمين يقع على يمين الرقم واحد اللي هو الـ
+
+100
+00:13:08,710 --> 00:13:12,610
+leading الـ
+
+101
+00:13:12,610 --> 00:13:25,270
+leading في الصفوف الأولى في الصفوف الأولى النقطة
+
+102
+00:13:25,270 --> 00:13:39,060
+الرابعة والأخيرة العمود الذي يحتوي على الواحد اللي 
+
+103
+00:13:39,060 --> 00:13:48,260
+هو الـ leading الـ leading تكون بقية
+
+104
+00:13:48,260 --> 00:13:51,800
+عناصره
+
+105
+00:13:51,800 --> 00:13:54,360
+أصفارًا
+
+106
+00:14:12,250 --> 00:14:17,110
+طيب نرجع للكلام اللي احنا كتبناه دي يا بنات ونفهم
+
+107
+00:14:17,110 --> 00:14:21,630
+كل كلمة فيه لأن دراستنا الآن أو الأمثلة منصبة على 
+
+108
+00:14:21,630 --> 00:14:25,310
+المعلومات اللي أعطانا إياها هنا الملاحظة بتقول الـ
+
+109
+00:14:25,310 --> 00:14:29,970
+homogeneous system is always consistent شو يعني
+
+110
+00:14:29,970 --> 00:14:35,510
+consistent؟ يعني في عنده حل أو عدد لا نهائي من الحلول
+
+111
+00:14:35,510 --> 00:14:39,750
+لكن احنا بيقولوا هنا consistently لأن هو على الأقل 
+
+112
+00:14:39,750 --> 00:14:44,870
+الهوموجيني الـ system له حل هو الحل الصفري صحيح
+
+113
+00:14:44,870 --> 00:14:48,430
+ولا لأ يعني لما يكون عندي معادلة اثنين اكس واحد 
+
+114
+00:14:48,430 --> 00:14:53,130
+ناقص ثلاثة اكس اثنين بيديه يساوي zero الحل البديهي
+
+115
+00:14:53,130 --> 00:14:56,720
+ليه إنه تخلي اكس واحد بـ zero اكس اثنين بـ zero إذا
+
+116
+00:14:56,720 --> 00:15:00,060
+لو كانت كل واحدة فيهم Zero هذا بيسمي الحل البديهي
+
+117
+00:15:00,060 --> 00:15:04,660
+واللي هو بيحقق من المعادلة يبقى هذا بالنسبة للـ 
+
+118
+00:15:04,660 --> 00:15:08,220
+homogeneous لو كان صفر لكن لما يكون عدد ليس
+
+119
+00:15:08,220 --> 00:15:12,040
+بالضرورة يبقى من هنا فصاعدًا بقول الـ homogeneous 
+
+120
+00:15:12,040 --> 00:15:18,920
+system هو consistent system لأنه على الأقل له الحل 
+
+121
+00:15:18,920 --> 00:15:25,720
+البديهي أو الحل الصفري لأنه له على الأقل الـ
+
+122
+00:15:25,720 --> 00:15:31,960
+solution اللي هو الـ 0,0,0 يبقى خذيها وأنت مغمضة الـ 
+
+123
+00:15:31,960 --> 00:15:36,900
+homogenous system هو consistent system لأنه على
+
+124
+00:15:36,900 --> 00:15:42,840
+الأقل له الحل الصفري السؤال هو كيف بدي أنا عندي 
+
+125
+00:15:42,840 --> 00:15:47,820
+system من هذا system بدي أولد system مكافئ له تمام
+
+126
+00:15:47,820 --> 00:15:52,300
+شو يعني مكافئ يعني الحل تبع هذا system هو نفس الحل 
+
+127
+00:15:52,300 --> 00:15:57,260
+تبع الـ system الآخر كما كما شفنا قبل قليل وينفي
+
+128
+00:15:57,260 --> 00:16:02,920
+هذا المثال أيوة بدنا نعمل بعض الخطوات هذه الخطوات
+
+129
+00:16:02,920 --> 00:16:07,500
+بتولد لي system يكافئ الـ system الأصلي يعني الحل 
+
+130
+00:16:07,500 --> 00:16:11,700
+تبع الـ system الجديد هو نفس تبع الحل تبع الـ system
+
+131
+00:16:11,700 --> 00:16:17,340
+الأصلي دون أن يكون اثنين لهم نفس الشكل بدنا نعمل 
+
+132
+00:16:17,340 --> 00:16:22,550
+بعض العمليات ماذا يسمى هذه العمليات؟ interchange two
+
+133
+00:16:22,550 --> 00:16:24,590
+equations interchange two equations يعني أن أنا في الـ
+
+134
+00:16:24,590 --> 00:16:27,730
+system لدي معادلة الأولى والثانية والثالثة والـ 
+
+135
+00:16:27,730 --> 00:16:31,410
+رابعة لو شيلت الرابعة وحطيتها الأولى والأولى و
+
+136
+00:16:31,410 --> 00:16:36,190
+خلتها الرابعة في مشكلة؟ بظل نفس الـ system تمام؟ 
+
+137
+00:16:36,190 --> 00:16:41,430
+يبقى هذه أول خطوة لو عملتها لا تتغير القيم الخطوة
+
+138
+00:16:41,430 --> 00:16:45,190
+الثانية multiply both sides of an equation by a
+
+139
+00:16:45,190 --> 00:16:49,430
+number c والـ c لا يساوي 0 لو جيت على أي معادلة
+
+140
+00:16:49,430 --> 00:16:55,190
+من المعادلات هذه وضربتها في رقم تبت كسري سالب
+
+141
+00:16:55,190 --> 00:17:01,270
+موجب بتفرقش عندنا تمام أي رقم بس ما يكونش صفر موجب
+
+142
+00:17:01,270 --> 00:17:06,010
+بسالب كسر ما عندنا مشكلة خالص يبقى بنضرب فيه بصير
+
+143
+00:17:06,010 --> 00:17:10,530
+عندنا معادلة بشكل جديد هيعمل لنا كمان حركة هذه الحركة 
+
+144
+00:17:10,530 --> 00:17:15,530
+لا تؤثر على شكل الـ system النوعي الآن الخطوة
+
+145
+00:17:15,530 --> 00:17:18,910
+الثالثة multiple of one equation to other equation
+
+146
+00:17:18,910 --> 00:17:22,770
+in the system يعني لو جت المعادلة هذه اللي ضربتها
+
+147
+00:17:22,770 --> 00:17:28,090
+في رقم زي هنا جت ضربتها في رقم وجت جمعت يعني جمعت
+
+148
+00:17:28,090 --> 00:17:32,580
+اثنين كأنه أضفت لجديد هذه لمين؟ للمعادلة فوق
+
+149
+00:17:32,580 --> 00:17:36,980
+وبالتالي لا يتغير بظل الـ system من ناحية الشكل
+
+150
+00:17:36,980 --> 00:17:40,760
+المختلف لكن من ناحية الحل له نفس الحل مثل الـ main
+
+151
+00:17:40,760 --> 00:17:46,640
+الـ system الأصلي ثلاث عمليات هذول بدّل صف مكان صف
+
+152
+00:17:46,640 --> 00:17:50,440
+يعني معادلة مكان معادلة اضربه لأي معادلة في مقدار 
+
+153
+00:17:50,440 --> 00:17:55,060
+ثابت أضف هذه المعادلة إلى معادلة أخرى هذه العمليات
+
+154
+00:17:55,060 --> 00:17:59,420
+بنسميها بنات elementary row operations عمليات الصف
+
+155
+00:17:59,420 --> 00:18:04,470
+البسيطة تذكروا في الثانوية أخذتو حل المصفوفات 
+
+156
+00:18:04,470 --> 00:18:09,670
+بجينا نحل المصفوفات بعمليات الصف البسيطة أو بواسطة
+
+157
+00:18:09,670 --> 00:18:14,210
+معكوس المصفوفة أو بواسطة grammar مظبوط يبجي هاي 
+
+158
+00:18:14,210 --> 00:18:18,530
+الثلاث طرق اللي كنا نحل فيها المعادلات المصفوفية
+
+159
+00:18:18,530 --> 00:18:22,890
+يبجي احنا بنتكلم اليوم بس على أول طريقة وهي طريقة
+
+160
+00:18:22,890 --> 00:18:28,330
+عمليات الصف البسيطة elementary row operation طيب
+
+161
+00:18:28,330 --> 00:18:32,930
+الحين أنا بدي أسوي elementary raw operation بس بدي 
+
+162
+00:18:32,930 --> 00:18:38,270
+أخليها شكلها درجية سلمية سلمية إذا بدنا نأتي
+
+163
+00:18:38,270 --> 00:18:43,670
+للتعريف الجديد إيش التعريف الجديد بقول المصفوفة 
+
+164
+00:18:43,670 --> 00:18:49,350
+بقول إنها على شكل row echelon form يعني مصفوفة
+
+165
+00:18:49,350 --> 00:18:55,580
+صفية على شكل درج أو سلم كيف هذا بيتم؟ بيتم بواسطة 
+
+166
+00:18:55,580 --> 00:19:01,480
+أربع خطوات لا خمسة لا شو الخطوة الأولى؟ بقول إذا
+
+167
+00:19:01,480 --> 00:19:06,320
+كان هناك صف غير صفري عناصر صفر مش كلهم صفر بعضهم
+
+168
+00:19:06,320 --> 00:19:10,400
+أصفار ممكن وممكن يكون فيش فيهم ولا صفر يبقى على 
+
+169
+00:19:10,400 --> 00:19:16,220
+الأقل بدي رقم فيهم يكون ماله عدد ما هو صفر فإن
+
+170
+00:19:16,220 --> 00:19:20,760
+الرقم الأول في هذا الصف هو واحد صحيح ويسمى هذا
+
+171
+00:19:20,760 --> 00:19:24,400
+العنصر بالـ leading يعني يا بنات لو جيت على مصروفة
+
+172
+00:19:24,400 --> 00:19:29,450
+خات الصف الأول بدي أول عنصر يكون جدّيش؟ واحد صحيح
+
+173
+00:19:29,450 --> 00:19:34,170
+بس بشرط الصف دي يكون غير صفري يبقى أول رقم بدي
+
+174
+00:19:34,170 --> 00:19:38,030
+هيكون واحد صحيح هي الخطوة الأولى الخطوة الثانية 
+
+175
+00:19:38,030 --> 00:19:41,950
+إذا كان هناك صف غير .. أه الخطوة الثانية جميع
+
+176
+00:19:41,950 --> 00:19:46,170
+الصفوف الصفرية بتكون تحت يعني لو أجى صف صفري ولا 
+
+177
+00:19:46,170 --> 00:19:51,990
+جيته فوق بقدر أنزله وأحطه تحت بدون مشاكل تمام؟
+
+178
+00:19:51,990 --> 00:19:55,250
+ليش؟ إنه في عمليات الصف البسيطة بقول بقدر أبدل صف
+
+179
+00:19:55,250 --> 00:19:59,730
+ما كان صف ما عنده مشكلة تمام؟ إذا ممكن إذا في صف
+
+180
+00:19:59,730 --> 00:20:03,010
+صفري بقول له خليك أنزل تحت ما لكش دعوة في الباقي
+
+181
+00:20:03,010 --> 00:20:06,890
+الخطوة الثالثة الرقم واحد
+
+201
+00:21:31,910 --> 00:21:36,630
+هذا الـ system مكافئ لمن؟ للـ system الأصلي وبالتالي
+
+202
+00:21:36,630 --> 00:21:42,610
+حل هذا الـ system هو حل نفس الـ system الأصلي تمامًا
+
+203
+00:21:42,610 --> 00:21:47,070
+بالضبط تمام، الكلام اللي بقوله، حد فيكم.. الآن مش
+
+204
+00:21:47,070 --> 00:21:49,930
+ضايل إلا أمثلة، دي لبالك على باقي الـ section كله
+
+205
+00:21:49,930 --> 00:21:55,760
+أمثلة، حد بتسألي سؤال؟ فالكلمتين النظريتين هدول بنطبقهم 
+
+206
+00:21:55,760 --> 00:22:00,880
+على أرض الواقع بالأمثلة العملية، حد بتسأل؟ طيب
+
+207
+00:22:00,880 --> 00:22:13,740
+نأتي إلى الأمثلة على هذا الموضوع، هذه
+
+208
+00:22:13,740 --> 00:22:19,460
+اللي كتبناها بالعرف الآن، ابنجل
+
+209
+00:22:19,460 --> 00:22:20,580
+أول مثال
+
+210
+00:22:27,800 --> 00:22:35,080
+example one, find
+
+211
+00:22:35,080 --> 00:22:38,220
+أو 
+
+212
+00:22:38,220 --> 00:22:43,900
+جاب الهدف، find the
+
+213
+00:22:43,900 --> 00:22:45,600
+solution
+
+214
+00:22:53,880 --> 00:23:04,900
+إذا كان موجود of the
+
+215
+00:23:04,900 --> 00:23:10,420
+following linear
+
+216
+00:23:10,420 --> 00:23:11,380
+systems
+
+217
+00:23:16,320 --> 00:23:27,180
+linear systems by reducing by reducing the matrix 
+
+218
+00:23:27,180 --> 00:23:31,840
+of
+
+219
+00:23:31,840 --> 00:23:43,280
+the system, the matrix of the system to
+
+220
+00:23:52,700 --> 00:24:02,400
+أول سؤال هو سؤال ثلاثة من الكتاب، نقص اثنين X1 زائد 
+
+221
+00:24:02,400 --> 00:24:13,200
+X2 يساوي خمسة، أربعة X1 ناقص اثنين X2 يساوي واحد
+
+222
+00:24:18,450 --> 00:24:28,130
+هذا الـ system بدي أسميه star solution، نرجع
+
+223
+00:24:28,130 --> 00:24:33,190
+لصيغة السؤال، نقرأ هذه الصيغة ونحاول نفهمها ثم 
+
+224
+00:24:33,190 --> 00:24:37,930
+نأتي لتطبيقها على أرض الواقع بأنواعها، بقول هات الـ solution
+
+225
+00:24:37,930 --> 00:24:42,410
+if it exist، إذا الـ solution موجود بدي إياه، مش
+
+226
+00:24:42,410 --> 00:24:46,510
+موجود، الله يسهل عليه، طيب، of the following linear
+
+227
+00:24:46,510 --> 00:24:51,290
+systems، للـ system الخطية التالية، by reducing the 
+
+228
+00:24:51,290 --> 00:24:56,510
+matrix، بتحويل الـ مصفوفة اللي عندنا of the system to 
+
+229
+00:24:56,510 --> 00:25:00,650
+row echelon form، إلى صيغة الـ row echelon form، يعني
+
+230
+00:25:00,650 --> 00:25:03,930
+إيش بقول له؟ الـ system اللي عندك، وإذا كتروح تجيب
+
+231
+00:25:03,930 --> 00:25:09,250
+الـ system المكافئ له، ومن ثم الـ system اللي نتاج 
+
+232
+00:25:09,250 --> 00:25:13,390
+الحل، تبقى هو حل مين؟ الـ system الأصلي، طبق للكلام
+
+233
+00:25:13,390 --> 00:25:17,830
+اللي كنت كتبينه قبل قليل، بقول لك كويس، يبقى أول مبدأ
+
+234
+00:25:17,830 --> 00:25:22,230
+يا بنات، ببدأ بالمصفوفة الموسعة، إيش المصفوفة
+
+235
+00:25:22,230 --> 00:25:26,390
+الموسعة؟ باخد مصفوفة المعاملين، فهي ناقص اثنين و
+
+236
+00:25:26,390 --> 00:25:31,210
+المعامل هنا واحد، أو هنا أربعة، وهنا ناقص اثنين، و
+
+237
+00:25:31,210 --> 00:25:36,990
+بروح بحط خطوة بس مشان أفصلهم عن بعض وبروح بحط
+
+238
+00:25:36,990 --> 00:25:44,110
+ثوابت، خمسة، واحد، بالشكل اللي عنها، طيب
+
+239
+00:25:44,110 --> 00:25:50,940
+أول شغلة بدي أعملها، بدي أخلي هذا قداش؟ واحد صحيح 
+
+240
+00:25:50,940 --> 00:25:56,800
+يعني بدي أروح أضرب الصف الأول في سالب نصف، بأطمئن أن
+
+241
+00:25:56,800 --> 00:26:03,680
+هذا واحد صحيح، يبقى هنا بجي بقول سالب نصف R1، هاي 
+
+242
+00:26:03,680 --> 00:26:07,710
+اللي بدي أعملها، اللي بدي أعمله بكتبه حتى لو رجعت أرجع
+
+243
+00:26:07,710 --> 00:26:11,770
+ثاني أعرف كيف جبت هدول، يبقاش بالصير المهادة عندنا 
+
+244
+00:26:11,770 --> 00:26:19,390
+سالب نصف، بيظل هنا قداش؟ واحد، وهنا سالب نصف، وهنا سالب
+
+245
+00:26:19,390 --> 00:26:25,030
+خمسة على اثنين، يعني ضربت هذا في سالب نصف، هذا زي ما
+
+246
+00:26:25,030 --> 00:26:30,410
+هو، هذه أربعة، وهذا سالب اثنين، وهذا واحد، بالشكل اللي
+
+247
+00:26:30,410 --> 00:26:34,940
+عندنا، هذا، هذا الحين صار مين يا بنات؟ اللي هو الـ
+
+248
+00:26:34,940 --> 00:26:41,560
+leading، القائد، اللي تحته إيش بدي يكون؟ صفر، لإنه 
+
+249
+00:26:41,560 --> 00:26:45,260
+قلنا العمود كله بدي يكونوا صفر مع الـ leading هذا،
+
+250
+00:26:45,260 --> 00:26:50,010
+كيف بدي أخلي هذا صفر؟ بقول بسيطة، بدي أضرب الصف 
+
+251
+00:26:50,010 --> 00:26:56,450
+هذا في سالب أربعة وأضيفه للصف الثاني، يبقى بروح
+
+252
+00:26:56,450 --> 00:27:04,310
+بقول ساهم هيك، سالب أربعة R1 + R2
+
+253
+00:27:11,070 --> 00:27:17,790
+يبقى الصف الأول يبقى كما هو، واحد، ناقص نصف، وهذا إيش؟
+
+254
+00:27:17,790 --> 00:27:22,870
+سالب خمسة على اثنين، ضربته في قداش؟ فيه سالب أربعة 
+
+255
+00:27:22,870 --> 00:27:27,670
+في واحد، سالب أربعة، بده يضيفه لهذا، قداش بيصير؟ Zero
+
+256
+00:27:29,180 --> 00:27:36,220
+سالب أربعة بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+257
+00:27:36,220 --> 00:27:36,720
+سالب اثنين بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+258
+00:27:36,720 --> 00:27:38,300
+سالب اثنين بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+259
+00:27:38,300 --> 00:27:41,240
+سالب اثنين بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+260
+00:27:41,240 --> 00:27:44,100
+سالب اثنين بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+261
+00:27:44,100 --> 00:27:46,920
+سالب اثنين بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+262
+00:27:46,920 --> 00:27:47,340
+سالب اثنين بيضل، اثنين، وسالب اثنين بيضل، اثنين، و
+
+263
+00:27:47,340 --> 00:27:53,190
+سيبقى، طلع الصف هذا كله أصفر، وهو طلع آخر حاجة تحت
+
+264
+00:27:53,190 --> 00:27:57,270
+طلع طبيعي، مش أنا بده أقوله طلع طبيعي، يبقى أكثر من 
+
+265
+00:27:57,270 --> 00:28:01,810
+هيك ما بقدرش أكتب، يبقى كل اللي بقدر أقول إن الـ
+
+266
+00:28:01,810 --> 00:28:07,010
+system هذا equivalent لمين؟ للـ system star، لإنه
+
+267
+00:28:07,010 --> 00:28:12,130
+استخدمت روشه،  هذا إيش بده يعطينا؟ بده يعطينا إن
+
+268
+00:28:12,130 --> 00:28:21,100
+ذا system الجديد، X1 ناقص نصف X2 يساوي ناقص خمسة على 
+
+269
+00:28:21,100 --> 00:28:28,940
+اثنين، و Zero X1 زائد Zero X2 يساوي قداش؟ هذا is 
+
+270
+00:28:28,940 --> 00:28:36,940
+equivalent to system
+
+271
+00:28:36,940 --> 00:28:39,080
+star
+
+272
+00:28:41,720 --> 00:28:46,600
+طيب، تعالوا نشوف، هي كانت الشغل اللي اشتغلته، تعالوا
+
+273
+00:28:46,600 --> 00:28:52,480
+نشوف هذا إيش معناه؟ هذا معناه 0 زائد 0 يساوي 1، 
+
+274
+00:28:52,480 --> 00:28:57,560
+ممكن هذا الكلام؟ يبقى هذا impossible، إيش معناه هذا
+
+275
+00:28:57,560 --> 00:29:02,740
+الكلام؟ أن الـ system of star has no solution، واحنا
+
+276
+00:29:02,740 --> 00:29:06,300
+في المحاضرة الصبح قلنا يا system مالوش حل، يا حل
+
+277
+00:29:06,300 --> 00:29:11,440
+واحد، يا عدد لا نهائي من الحلول، صحيح ولا لا؟ يبقى هذا 
+
+278
+00:29:11,440 --> 00:29:23,380
+معناه أن الـ system star has no solution، يبقى هذا
+
+279
+00:29:23,380 --> 00:29:31,060
+مثال بسيط وصغير، نعطيك مثال قليل شوية، يبقى مثال
+
+280
+00:29:31,060 --> 00:29:43,220
+رقم اثنين، هو سؤال ستة من الكتاب، بقول X1 - 2X2 + X3 
+
+281
+00:29:43,220 --> 00:29:52,080
+يساوي خمسة، المعادلة الثانية، ناقص X1 + X2 ناقص 
+
+282
+00:29:52,080 --> 00:29:59,240
+أربعة X3 يساوي ناقص سبعة، المعادلة بعدها، ثلاثة X
+
+283
+00:29:59,240 --> 00:30:06,820
+واحد زائد ثلاثة X اثنين زائد X ثلاثة كله يساوي
+
+284
+00:30:06,820 --> 00:30:11,220
+أربعة، وهذا الـ system عندنا اللي هو main، هو stop
+
+285
+00:30:11,220 --> 00:30:19,480
+بدأ أروح بالـ row echelon form، أحول هذا الـ system
+
+286
+00:30:19,480 --> 00:30:26,590
+إلى شكل جديد، بقوله كويس، solution، يبقى بنات، ببدأ
+
+287
+00:30:26,590 --> 00:30:32,830
+بمين؟ ببدأ بالمصفوفة الموسعة، يبقى باجي بقول هذا
+
+288
+00:30:32,830 --> 00:30:38,330
+المصفوفة الموسعة، معامل X واحد، واحد، معامل X اثنين
+
+289
+00:30:38,330 --> 00:30:43,970
+سالب اثنين، هنا واحد، سالب واحد، واحد، سالب أربعة
+
+290
+00:30:43,970 --> 00:30:49,950
+ثلاثة، ثلاثة، واحد، وبروح بقول هذه خمسة، سالب سبعة
+
+291
+00:30:49,950 --> 00:30:56,000
+أربعة، بالشكل اللي عندنا هنا، شوف إيش بدي أعمله، يوو
+
+292
+00:30:56,000 --> 00:31:00,340
+الحمد لله، هذا الأول واحد، الـ leading يبقى جاهز، يبقى
+
+293
+00:31:00,340 --> 00:31:07,060
+بدي أخلي عموده أصفار، يبقى بدي أضيفه لمين؟ للصف
+
+294
+00:31:07,060 --> 00:31:11,700
+اللي بعده، والخطوة الثانية بدي أضربه في سالب ثلاثة 
+
+295
+00:31:11,700 --> 00:31:20,640
+وأضيفه للصف الثالث، يبقى باجي بقوله هنا، إيش؟ R1 + R2
+
+296
+00:31:20,640 --> 00:31:29,000
+هاي الخطوة الأولى، اللي بعدها، سالب ثلاثة R1 + R3، R 
+
+297
+00:31:29,000 --> 00:31:33,960
+يا بنات، اللي كلمة row يعني الصف، أنا بأختصرها اختصار
+
+298
+00:31:33,960 --> 00:31:38,360
+لما أحط اثنين يبقى لصف الثاني، يبقى اللي بيتغير يا
+
+299
+00:31:38,360 --> 00:31:42,860
+بنات، مش اللي بنضرب فيه، المضاف اللي هو اللي بيتغير 
+
+300
+00:31:43,090 --> 00:31:48,770
+تمام، إذا هذه هتصبح المصفوفة على الشكل التالي، الصف 
+
+301
+00:31:48,770 --> 00:31:55,150
+الأول مافيش فيه أي حاجة، وهي لذاك، وهي هنا خمسة، الصف 
+
+302
+00:31:55,150 --> 00:31:58,930
+الثاني أضفته إليه، لما أضفته إليه صار هنا إيه يا عاش؟
+
+303
+00:31:58,930 --> 00:32:04,390
+Zero، صار هنا كده؟ سالب واحد، صار هنا كده؟ سالب
+
+304
+00:32:04,390 --> 00:32:09,810
+ثلاثة، صار هنا سالب اثنين، بعد هيك سالب ثلاثة وثلاثة
+
+305
+00:32:09,810 --> 00:32:15,290
+كده؟ Zero، سالب ثلاثة في اثنين بموجب ستة وثلاثة 
+
+306
+00:32:15,290 --> 00:32:22,210
+تسعة، سالب ثلاثة واحد بيظل سالب اثنين، سالب ثلاثة في 
+
+307
+00:32:22,210 --> 00:32:28,850
+خمسة بسالب خمسة عشر، وهنا بيظل سالب أحد عشر، مظبوط
+
+308
+00:32:28,850 --> 00:32:34,760
+هيك؟ مرة ثانية، ده جي جي معايا، سوف أضيف فضلة لهذا
+
+309
+00:32:34,760 --> 00:32:40,980
+بيصير zero، سالب واحد، سالب ثلاثة، هنا سالب اثنين، مش 
+
+310
+00:32:40,980 --> 00:32:45,000
+مشكلة، هنا سوف أضع في سالب ثلاثة وأضيف بيصير zero
+
+311
+00:32:45,000 --> 00:32:49,940
+سالب ثلاثة في سالب اثنين في ستة، وثلاثة تسعة، سالب 
+
+312
+00:32:49,940 --> 00:32:53,400
+ثلاثة في واحد في سالب ثلاثة، وواحد في سالب اثنين
+
+313
+00:32:53,400 --> 00:32:59,340
+سالب خمسة عشر، وأربعة بيضل كده سالب أحد عشر، تمام، تمام
+
+314
+00:32:59,620 --> 00:33:03,680
+يبقى هذه العمود اللي بعده يا شي أصفر، الآن بدي أجي 
+
+315
+00:33:03,680 --> 00:33:08,560
+للصف اللي بعده، بدي يكون الـ leading فين؟ هو على
+
+316
+00:33:08,560 --> 00:33:11,500
+يمين الـ leading الأولاني، ومنه التحت داخلي اللي 
+
+317
+00:33:11,500 --> 00:33:17,520
+همين، هذا بدي يا شي يكون واحد، يبقى بدي أضرب هذا الصف 
+
+318
+00:33:17,520 --> 00:33:25,860
+في سالب، يبقى باجي بقوله هنا هذا سهم، وهنا سالب R2 
+
+319
+00:33:26,450 --> 00:33:30,750
+تمام، يبقى بدها تصير المصفوفة على الشكل التالي، واحد
+
+320
+00:33:30,750 --> 00:33:37,850
+سالب اثنين، واحد، Zero، واحد، ثلاثة، وهنا اثنين، وهنا
+
+321
+00:33:37,850 --> 00:33:43,950
+خمسة، وصف الثالث زي ما هو، Zero، تسعة، ناقص اثنين، ناقص
+
+322
+00:33:43,950 --> 00:33:49,880
+أحد عشر، بالشكل اللي عندها، تمام، الآن بدي هذا يصير 
+
+323
+00:33:49,880 --> 00:33:55,380
+قداش؟ Zero، يبقى بدي أضرب هذا في سالب تسعة وأضيفه له 
+
+324
+00:33:55,380 --> 00:34:02,740
+يبقى باجي بقوله هنا سالب تسعة R2 + R3
+
+325
+00:34:02,740 --> 00:34:10,930
+بنحصل على ما يلي، الصف الأول كما هو، وهذه خمسة، والصف
+
+326
+00:34:10,930 --> 00:34:16,910
+الثاني كما هو، اثنين، الحين الصف المضروب تسعة في زيرو
+
+327
+00:34:16,910 --> 00:34:23,870
+بزيرو زائد الزيرو يبقى بزيرو، سالب تسعة مع تسعة بصير
+
+328
+00:34:23,870 --> 00:34:30,370
+زيرو، سالب سبعة وعشرين وسالب اثنين سالب تسعة وعشرين 
+
+329
+00:34:30,370 --> 00:34:37,010
+يبقى سالب تسعة وعشرين، سالب تسعة في اثنين بسالب
+
+330
+00:34:37,010 --> 00:34:41,970
+ثمانية عشر، سالب ثمانية عشر وسالب أحد عشر بسالب تسعة و
+
+331
+00:34:41,970 --> 00:34:50,030
+عشرين، يبقى سالب تسعة وعشرين، بعد هيك بدي أخلي هذا
+
+332
+00:34:50,030 --> 00:34:57,050
+واحد كذلك، تمام، يبقاش بعمل بضرب في سالب واحد على 
+
+333
+00:34:57,050 --> 00:35:03,930
+تسعة وعشرين الصف الثالث، يبقى هذا سالب واحد على 
+
+334
+00:35:03,930 --> 00:35:09,750
+تسعة وعشرين R ثلاثة، يبقى الصف الأول واحد، سالب 
+
+335
+00:35:09,750 --> 00:35:16,610
+اثنين، واحد، Zero، واحد، ثلاثة، Zero، Zero، واحد، وهنا
+
+336
+00:35:16,610 --> 00:35:25,190
+خمسة، اثنين، وهنا واحد، طبعًا طلع في السلم، واحد الـ 
+
+337
+00:35:25,190 --> 00:35:28,490
+leading الثاني على يمينه، الـ leading التالي على
+
+338
+00:35:28,490 --> 00:35:34,030
+شماله، العمود تبعه أصفر، هذا العمود تبعه مش أصفر
+
+339
+00:35:34,030 --> 00:35:43,390
+تمام، يبقى بدي أضرب الصف الثاني في اثنين وأضيفه لمن؟ 
+
+340
+00:35:43,390 --> 00:35:51,020
+للاول، يبقى باجي بقوله هنا اثنين R اثنين + R1
+
+341
+00:35:51,020 --> 00:35:57,580
+بده يصبح على الشكل التالي، هذا واحد زي ما هو، اثنين
+
+342
+00:35:57,580 --> 00:36:04,950
+وسالب اثنين بزيرو، هنا ضربنا اثنين في ثلاثة بستة، واحد
+
+343
+00:36:04,950 --> 00:36:10,330
+سبعة، هي مظبوط هيك، نضرب هنا في اثنين، وهنا اثنين في
+
+344
+00:36:10,330 --> 00:36:15,470
+اثنين بأربعة وخمسة هذه تسعة، وهذا الخط اللي عندنا
+
+345
+00:36:15,470 --> 00:36:23,370
+هذا بيظل زي ما هو، Zero، واحد، ثلاثة، اثنين، وده Zero
+
+346
+00:36:23,370 --> 00:36:29,590
+Zero، واحد، واحد، شكله لو ضربت هذا في السالب ثلاثة
+
+347
+00:36:29,590 --> 00:36:33,810
+وضفته لهذا، وضربته في سالب سبعة وضفته للي فوق، بقول
+
+348
+00:36:33,810 --> 00:36:40,090
+خلصت، تمام، يبقاش بيصير عندنا يا بنات، بيصير عندنا هذا
+
+349
+00:36:40,090 --> 00:36:50,630
+سهم، يبقى السالب سبعة R ثلاثة + R1، وسالب ثلاثة R 
+
+350
+00:36:50,630 --> 00:36:57,430
+ثلاثة + R2، بيحصل ما يلي، الواحد زي ما هو لن
+
+351
+00:36:57,430 --> 00:37:03,790
+يتأثر، وهذا الآن 
+
+352
+00:37:03,790 --> 00:37:11,670
+سالب سبعة R ثلاثة + R، هذا بيظل Zero زي ما هو، وهذا
+
+353
+00:37:11,670 --> 00:37:18,930
+بيصير Zero، وهنا سالب سبعة وعندك تسعة بيظل كده؟
+
+354
+00:37:18,930 --> 00:37:26,210
+بيظل اثنين فقط، لغير، الآن سالب ثلاثة R ثلاثة + R2
+
+355
+00:37:26,210 --> 00:37:31,550
+يبقى Zero، واحد زي ما هو، هنا بيجيكي الـ Zero، هنا
+
+356
+00:37:31,550 --> 00:37:36,870
+سالب ثلاثة واثنين بيصير سالب واحد، وهذا Zero، Zero
+
+357
+00:37:36,870 --> 00:37:43,630
+واحد، واحد، كما هو، الآن الـ system اللي بيطلع عندها يا
+
+358
+00:37:43,630 --> 00:37:49,690
+بناتي يكافئ من الـ system star اللي فوق، فبجي بقوله
+
+359
+00:37:49,690 --> 00:38:00,320
+هنا الـ system domain هنا x1 بدها تساوي 2 وهنا
+
+360
+00:38:00,320 --> 00:38:08,300
+ماعنديش إلا x2 بدها تساوي سالب واحد، وهنا الـ x3 بدها
+
+361
+00:38:08,300 --> 00:38:18,220
+تساوي الواحد، is equivalent to the system
+
+362
+00:38:20,530 --> 00:38:26,470
+يبقى هذا بكافئ الـ system star، معناته الحل تبع هذا هو
+
+363
+00:38:26,470 --> 00:38:31,990
+الحل تبع من؟ تبع الـ system star، فبروح وبقوله الآن
+
+364
+00:38:31,990 --> 00:38:43,090
+the solution of the system star is، لحظة
+
+365
+00:38:43,090 --> 00:38:45,010
+شوية، solution
+
+366
+00:38:
+
+401
+00:42:38,140 --> 00:42:45,340
+Zero واحد على تلاتة لأن ضرب في سالب تلاتة بيصير موجب وهنا
+
+402
+00:42:45,340 --> 00:42:48,700
+بيصير سالب سبعة على تلاتة
+
+403
+00:42:50,810 --> 00:43:00,450
+بقدر اخلي اللي فوق صفر كمان يبقى
+
+404
+00:43:00,450 --> 00:43:08,650
+هنا سالب R2 to R1 نحصل على ما يدينا واحد زي ما هو
+
+405
+00:43:08,650 --> 00:43:20,520
+وده صفر وده تلتين وهنا سالب سبعة على تلاتة وتلاتة 
+
+406
+00:43:20,520 --> 00:43:25,380
+بالموجب سبعة على تلاتة اللي هو اتنين وتلتين مظبوط
+
+407
+00:43:25,380 --> 00:43:28,780
+ولا اتنين وثلت، سبعة على تلاتة
+
+408
+00:43:34,250 --> 00:43:40,970
+تلتين بالموجب يبقى تلتين
+
+409
+00:43:40,970 --> 00:43:45,190
+بالموجب يبقى تلتين بالموجب يبقى تلتين بالموجب يبقى
+
+410
+00:43:45,190 --> 00:43:52,310
+تلتين بالموجب يبقى تلتين بالموجب يبقى تلتين 
+
+411
+00:43:52,310 --> 00:43:52,970
+بالموجب يبقى تلتين بالموجب يبقى تلتين بالموجب يبقى
+
+412
+00:43:52,970 --> 00:43:53,190
+تلتين بالموجب يبقى تلتين بالموجب يبقى تلتين
+
+413
+00:43:53,190 --> 00:43:53,770
+بالموجب يبقى تلتين بالموجب يبقى تلتين بالموجب يبقى
+
+414
+00:43:53,770 --> 00:43:59,540
+تلتين بالموجب يبقى تلتين بالموجب بقدر؟ مش إمكانية
+
+415
+00:43:59,540 --> 00:44:06,700
+يبقى الآن ال system الجديد بروح بقوله that the system
+
+416
+00:44:07,600 --> 00:44:14,180
+اللي هو مين X واحد زائد تلتين X تلاتة بيساوي
+
+417
+00:44:14,180 --> 00:44:22,780
+تلتين واللي بعده X اتنين زائد تلت X تلاتة بيساوي
+
+418
+00:44:22,780 --> 00:44:31,320
+سالب سبعة على تلاتة as equivalent to
+
+419
+00:44:31,320 --> 00:44:34,280
+the system
+
+420
+00:44:36,100 --> 00:44:41,860
+ستار الأصلي، إذا حل هذا ال system هو نفس حل ال
+
+421
+00:44:41,860 --> 00:44:48,560
+system star اللي فوق، طيب هدول معادلتين في تلاتة
+
+422
+00:44:48,560 --> 00:44:57,400
+مجاهيل، بقدرش إلا إذا أحط أحد المجاهيل من عندي، بروح
+
+423
+00:44:57,400 --> 00:45:02,980
+من عندها بحط أي قيمة لهذه اللواحد من المجاهيل
+
+424
+00:45:02,980 --> 00:45:07,460
+وبالتالي بجيب المجهولين للاتنين التانيات بدلالة
+
+425
+00:45:07,460 --> 00:45:12,620
+القيمة اللي أنا حطيتها، فمثلاً لو جيت قلت حط X
+
+426
+00:45:12,620 --> 00:45:18,620
+تلاتة بتلاتة أو حطيتها بتلاتة "أيه" تلاتة يعني حطيت
+
+427
+00:45:18,620 --> 00:45:22,960
+رقم محدد، لكن لما أقول تلاتة "أيه" في قيود على "أيه"
+
+428
+00:45:22,960 --> 00:45:30,980
+ماعنديش قيود يبقى هنا باجي بقوله FX تلاتة يساوي
+
+429
+00:45:30,980 --> 00:45:35,380
+تلاتة A، ثاني، X تلاتة يساوي تلاتة A، ثاني، X تلاتة
+
+430
+00:45:35,380 --> 00:45:38,700
+يساوي تلاتة A، ثاني، X تلاتة يساوي تلاتة A، ثاني، X
+
+431
+00:45:38,700 --> 00:45:40,400
+تلاتة يساوي تلاتة A، ثاني، X تلاتة يساوي تلاتة A
+
+432
+00:45:40,400 --> 00:45:40,840
+ثاني، X تلاتة يساوي تلاتة A، ثاني، X تلاتة يساوي
+
+433
+00:45:40,840 --> 00:45:41,380
+تلاتة A، ثاني، X تلاتة يساوي تلاتة A، ثاني، X تلاتة
+
+434
+00:45:41,380 --> 00:45:42,560
+يساوي تلاتة A، ثاني، X تلاتة يساوي تلاتة A، ثاني، X
+
+435
+00:45:42,560 --> 00:45:51,560
+تلاتة يساوي تلاتة A، ثاني، X تلاتة يساوي تلاتة A
+
+436
+00:45:51,560 --> 00:45:59,410
+ثاني، X تلاتة الحين X3 موجودة بقدر أجيب X1 يبقى بعدي
+
+437
+00:45:59,410 --> 00:46:08,830
+بقول X1 تساوي يبقى بعدي بقول X1 تساوي حطيت هذا
+
+438
+00:46:08,830 --> 00:46:15,050
+بالتلاتة يبقى بتروح التلاتة بضل أو X1 زائد
+
+439
+00:46:28,960 --> 00:46:35,300
+يبقى الـ General solution
+
+440
+00:46:37,770 --> 00:46:45,250
+X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15
+
+441
+00:46:45,250 --> 00:46:50,190
+X16 X17 X18 X19 X20 X21 X22 X23
+
+442
+00:46:50,190 --> 00:46:56,610
+X23 X23 X23 X23 X23 X23 X23
+
+443
+00:46:56,610 --> 00:47:02,670
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+444
+00:47:02,670 --> 00:47:02,810
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+445
+00:47:02,810 --> 00:47:02,910
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+446
+00:47:02,910 --> 00:47:05,470
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+447
+00:47:08,810 --> 00:47:17,510
+جد عددها أكتر شوية من هيك يعني نحط ال real number
+
+448
+00:47:17,510 --> 00:47:22,490
+اللي يجب بس بعيد عن الصفر تمام يبقى باجي بقوله أو
+
+449
+00:47:22,490 --> 00:47:25,850
+حتى لو حطيتها صفر بمشي الحل إنه ماعنديش قيود على
+
+450
+00:47:25,850 --> 00:47:32,970
+"أيه" تمام يبقى باجي بقوله this is infinite
+
+451
+00:47:34,760 --> 00:47:45,020
+أو this represents هذا يمثل this represents infinite
+
+452
+00:47:45,020 --> 00:47:56,900
+number of solutions يبقى هذا يمثل مالانهاية من
+
+453
+00:47:56,900 --> 00:48:02,160
+الحلول تمام، طيب خليني أسأل السؤال التالي احنا
+
+454
+00:48:02,160 --> 00:48:09,610
+ماكملناش لسه خليني أسأل السؤال التالي هل هذا ال
+
+455
+00:48:09,610 --> 00:48:14,210
+system consistent ولا inconsistent؟ Consistent
+
+456
+00:48:14,210 --> 00:48:18,750
+لأنه يحتوي على مالانهاية من الحلول، لا يزال هناك
+
+457
+00:48:18,750 --> 00:48:23,510
+المزيد من الأمثلة إلى المحاضرة القادمة إن شاء الله
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e1d8e521769fef09bc37d593e45b4c353ad75b33
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270_postprocess.srt
@@ -0,0 +1,1828 @@
+1
+00:00:19,980 --> 00:00:25,880
+بسم الله الرحمن الرحيم في محاضرة الصبح اتكلمنا عن
+
+2
+00:00:25,880 --> 00:00:31,760
+بعض التعريفات قلنا لو ال system star كان له حل
+
+3
+00:00:31,760 --> 00:00:36,680
+وحيد او عدد لا نهائي من الحلول بنسمي consistent
+
+4
+00:00:36,680 --> 00:00:42,760
+وإذا كان مالوش حل بنسمي inconsistent واخر حاجة
+
+5
+00:00:42,760 --> 00:00:47,600
+كتبناها two systems are equivalent اتنين بقول عنهم
+
+6
+00:00:47,600 --> 00:00:52,520
+اتنين متكافئينإذا كان لهم نفس الحلول إذا ال system
+
+7
+00:00:52,520 --> 00:00:56,380
+الأول و ال system التاني طلع لهم نفس الحلول إذا
+
+8
+00:00:56,380 --> 00:01:00,900
+بقول عن هذا ال two systems are equivalent نجي ناخد
+
+9
+00:01:00,900 --> 00:01:03,980
+مثال على ذلك بقول you show that the following two
+
+10
+00:01:03,980 --> 00:01:08,160
+systems are equivalentبينينا ان الـ two systems
+
+11
+00:01:08,160 --> 00:01:12,140
+هدول are equivalent بدالي للـ system الأول بدي
+
+12
+00:01:12,140 --> 00:01:16,760
+أحاول أحله بمعنى أخر بيطلع جديش قيمة x1 و جديش
+
+13
+00:01:16,760 --> 00:01:20,900
+قيمة x2 و ال system التاني بيطلع جديش قيمة x1 و x2
+
+14
+00:01:20,900 --> 00:01:26,520
+بأي طريقة رياضية ممكن تقدر عليهابقول بسيطة جدا
+
+15
+00:01:26,520 --> 00:01:33,740
+يبقى بمجرد النظر المعادلة الأولى 2x1-3x2 بدي اسيه
+
+16
+00:01:33,740 --> 00:01:38,100
+واحد المعادلة الثانية أظهر لو ضربناها في سالب 2 و
+
+17
+00:01:38,100 --> 00:01:41,680
+بنقدر نتخلص من أحد المجاهيل و نحصل على قيمة
+
+18
+00:01:41,680 --> 00:01:47,360
+المجهول الثاني يبقى لو روح ضربت هذه في سالب 2 بصير
+
+19
+00:01:47,360 --> 00:01:55,970
+سالب 2x1 سالب 8x2 يساوي سالب 12لو جيت جماعة يبقى
+
+20
+00:01:55,970 --> 00:02:00,710
+هدول مع السلامة بروحه بصير أن سالب تلاتة وتمانية
+
+21
+00:02:00,710 --> 00:02:06,890
+أحد عشر X2 يساوي سالب أحد عشر ومنها X2 يساوي قداش
+
+22
+00:02:06,890 --> 00:02:12,070
+واحد لو رجعت على المعادلة الأولى وشلت X وحطيت
+
+23
+00:02:12,070 --> 00:02:16,810
+مكانها واحدبصير اتنين اكس وان ناقص ثلاثة يساوي
+
+24
+00:02:16,810 --> 00:02:22,970
+واحد ومنها two x one بده يساوي اربعة يبقى اكس وان
+
+25
+00:02:22,970 --> 00:02:27,750
+بده يساوي قداش اتنين يبقى the solution
+
+26
+00:02:31,500 --> 00:02:38,600
+X1 X2 X3
+
+27
+00:02:38,600 --> 00:02:39,840
+X4 X5 X6 X7 X8 X9 X10 X11 X12 X11 X12 X11 X11 X11
+
+28
+00:02:39,840 --> 00:02:40,240
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+29
+00:02:40,240 --> 00:02:40,560
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+30
+00:02:40,560 --> 00:02:42,500
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+31
+00:02:42,500 --> 00:02:44,960
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+32
+00:02:44,960 --> 00:02:47,460
+X11 X11 X11 X11 X11 X11 X11 X11 X11 X11 X11
+
+33
+00:02:50,500 --> 00:02:55,860
+لو ضربت هذه في سالي بتروح مع هذه يبقى سالي ب2 X1
+
+34
+00:02:55,860 --> 00:03:02,200
+زائد 14 X2 بده يسوى قداش عشرة المعادلة التانية
+
+35
+00:03:02,200 --> 00:03:09,920
+خلتها زي ما هي 2 X1 زائد 8 X2 يسوى 12 وروحت جامعة
+
+36
+00:03:10,330 --> 00:03:14,610
+يبقى لو روحت جامعة بصير هذا وهذا مع السلامة بـ 0
+
+37
+00:03:14,610 --> 00:03:21,670
+بظل عندنا 22 X2 يساوي 22 هذا بده يعطينا ان X2
+
+38
+00:03:21,670 --> 00:03:27,830
+يساوي 1 لو رجعت لأي من المعادلتين الأولى والثانية
+
+39
+00:03:27,830 --> 00:03:34,910
+وحطيت X2 بواحد بصير X1 ناقص سبعة بده يساوي ناقص
+
+40
+00:03:34,910 --> 00:03:45,450
+خمسة إذا X1 يساوي قداشتينيبقى the solution is x1 و
+
+41
+00:03:45,450 --> 00:03:52,150
+x2 يساوي 2 و 1 وهو نفس الحل اللي عندنا مادام طلع
+
+42
+00:03:52,150 --> 00:03:57,090
+نفس الحل يبقى ال two systems هدول are equivalent
+
+43
+00:03:57,090 --> 00:04:06,990
+يبقى هنا so the two systems are equivalent
+
+44
+00:04:10,520 --> 00:04:27,060
+السبب because they have the same solution لأن
+
+45
+00:04:27,060 --> 00:04:31,900
+لهم نفس الحل ومن هنا الاتنين هذول are equivalent
+
+46
+00:04:31,900 --> 00:04:36,000
+بدنا
+
+47
+00:04:36,000 --> 00:04:37,580
+نيجي ل remark
+
+48
+00:04:45,640 --> 00:04:56,400
+النظام الهوموجيني هو
+
+49
+00:04:56,400 --> 00:05:02,920
+دائما مستقل
+
+50
+00:05:02,920 --> 00:05:06,900
+دائما
+
+51
+00:05:06,900 --> 00:05:11,900
+مستقل لأن السبب
+
+52
+00:05:12,960 --> 00:05:22,880
+it has at least it has at least على الأقل the
+
+53
+00:05:22,880 --> 00:05:28,740
+trivial solution
+
+54
+00:05:30,550 --> 00:05:42,530
+اللي هو main x1 و x2 و xn بده يساوي zero و zero و
+
+55
+00:05:42,530 --> 00:05:51,970
+zero الان
+
+56
+00:05:51,970 --> 00:05:59,270
+how to find بنطرح سؤال و نحاول نجاوب عليه and
+
+57
+00:06:01,280 --> 00:06:09,520
+equivalent how to find an
+
+58
+00:06:09,520 --> 00:06:12,680
+equivalent
+
+59
+00:06:12,680 --> 00:06:17,080
+how
+
+60
+00:06:17,080 --> 00:06:24,820
+to find an equivalent system for
+
+61
+00:06:24,820 --> 00:06:41,250
+a given system fora given system
+
+62
+00:06:41,250 --> 00:06:44,970
+هذا
+
+63
+00:06:44,970 --> 00:06:54,830
+سؤال الرجاب عليك التالي اذا واحد enter a change
+
+64
+00:06:57,980 --> 00:07:09,440
+interchange two equations النقطة الثانية multiply
+
+65
+00:07:09,440 --> 00:07:13,420
+both
+
+66
+00:07:13,420 --> 00:07:20,880
+sides of
+
+67
+00:07:20,880 --> 00:07:25,420
+an equation
+
+68
+00:07:27,350 --> 00:07:38,890
+by a number c و الـ c does not equal to zero نمرة
+
+69
+00:07:38,890 --> 00:07:46,090
+تلاتة adding a
+
+70
+00:07:46,090 --> 00:07:50,370
+multiple of
+
+71
+00:07:50,370 --> 00:07:52,290
+n
+
+72
+00:07:53,730 --> 00:08:04,730
+equation to other equation لمعادلة أخرى in the
+
+73
+00:08:04,730 --> 00:08:13,270
+system these
+
+74
+00:08:13,270 --> 00:08:19,170
+operations هذه
+
+75
+00:08:19,170 --> 00:08:22,470
+العمليات are called
+
+76
+00:08:26,380 --> 00:08:38,860
+بنسميها elementary elementary
+
+77
+00:08:38,860 --> 00:08:42,480
+raw operations
+
+78
+00:09:38,930 --> 00:09:44,530
+الان بدى اعطى تعريف لكن نظرا لإن هذا التعريف بدنا
+
+79
+00:09:44,530 --> 00:09:48,170
+نشتغله يعني كل شغل من الآن حتى نهاية ال section
+
+80
+00:09:48,170 --> 00:09:52,890
+مركب عليه بدى اعطيه بالعربي حتى تعرف تشتغلي بعد
+
+81
+00:09:52,890 --> 00:09:56,410
+هيك مش لسه مستوعبيش التعريف الإنجليزي و بعدين يصير
+
+82
+00:09:56,410 --> 00:09:59,750
+صعب يفجأة بدأت أقول تعريف
+
+83
+00:10:07,890 --> 00:10:17,270
+يقالوا للمصفوفة أيه؟ أنها على
+
+84
+00:10:17,270 --> 00:10:23,270
+الشكل الـ Raw echelon form
+
+85
+00:10:33,030 --> 00:10:40,210
+Row Echelon Form إذا تحققت
+
+86
+00:10:40,210 --> 00:10:54,250
+الشروط التالية أول شرط من هذه الشروط إذا كان هناك
+
+87
+00:10:54,250 --> 00:11:00,270
+صفر
+
+88
+00:11:00,270 --> 00:11:12,100
+غير صفريإذا كان هناك صف غير صفري في المصفوفة
+
+89
+00:11:12,100 --> 00:11:25,360
+المصفوفة فإن الرقم الأول في هذا الصف الرقم الأول
+
+90
+00:11:25,360 --> 00:11:32,320
+في هذا الصف هو واحد صحيح ويسمى
+
+91
+00:11:33,750 --> 00:11:44,550
+هذا العنصر و يسمى هذا العنصر ال leading leading
+
+92
+00:11:44,550 --> 00:11:51,970
+يعني زي القائد اللي بقود الباقي نمر اتنين جميع
+
+93
+00:11:51,970 --> 00:12:01,210
+الصفوف الصفرية جميع الصفوف الصفرية
+
+94
+00:12:02,820 --> 00:12:16,260
+جميع الصفوف الصفرية تكون أسفل الصفوف الأخرى
+
+95
+00:12:16,260 --> 00:12:22,880
+في المصفوفة نمر
+
+96
+00:12:22,880 --> 00:12:28,880
+تلاتة الرقم
+
+97
+00:12:30,940 --> 00:12:37,260
+واحد اللي هو ال leading القائد
+
+98
+00:12:37,260 --> 00:12:52,200
+ال leading هدف فيه الصفوف التالية لكل صف لكل صف
+
+99
+00:12:52,200 --> 00:13:08,710
+يقع على يمين يقع علىيمين الرقم واحد اللي هو ال
+
+100
+00:13:08,710 --> 00:13:12,610
+leading ال
+
+101
+00:13:12,610 --> 00:13:25,270
+leading في الصفوف الأولى في الصفوف الأولى النقطة
+
+102
+00:13:25,270 --> 00:13:39,060
+الرابعةوالاخيرة العمود الذي يحتوي على الواحد اللي
+
+103
+00:13:39,060 --> 00:13:48,260
+هو ال leading ال leading تكون بقية
+
+104
+00:13:48,260 --> 00:13:51,800
+عناصره
+
+105
+00:13:51,800 --> 00:13:54,360
+أصفرا
+
+106
+00:14:12,250 --> 00:14:17,110
+طيب نرجع الكلام اللي احنا كتبناه دي يا بنات و نفهم
+
+107
+00:14:17,110 --> 00:14:21,630
+كل كلمة فيه لإن دراستنا الآن أو الأمثلة منصبة على
+
+108
+00:14:21,630 --> 00:14:25,310
+المعلومات اللي اعطاناها هنا الملاحظة بتقول ال
+
+109
+00:14:25,310 --> 00:14:29,970
+homogeneous system is always consistent شو يعني
+
+110
+00:14:29,970 --> 00:14:35,510
+consistent؟يعني في عنده حل أو عدد لنهائي من الحلول
+
+111
+00:14:35,510 --> 00:14:39,750
+لكن احنا بيقولوا هنا consistently لإن هو على الأقل
+
+112
+00:14:39,750 --> 00:14:44,870
+الهوموجينية ال system له حل هو الحل الصفري صحيح
+
+113
+00:14:44,870 --> 00:14:48,430
+ولا لأ يعني لما يكون عندي معادلة اتنين اكس واحد
+
+114
+00:14:48,430 --> 00:14:53,130
+نقص ثلاث اكس اتنين بيديه ساوي zero الحل البديهي
+
+115
+00:14:53,130 --> 00:14:56,720
+ليه انه تكبر اكس واحد ب zero اكس اتنين ب zeroأذا
+
+116
+00:14:56,720 --> 00:15:00,060
+لو كانت كل واحدة فيهم Zero هذا بيسمي الحل البديهي
+
+117
+00:15:00,060 --> 00:15:04,660
+و اللي هو بيحقق من المعادلة يبقى هذا بالنسبة لل
+
+118
+00:15:04,660 --> 00:15:08,220
+homogeneous لو كان صفر لكن لما يكون عدد ليس
+
+119
+00:15:08,220 --> 00:15:12,040
+بالضرورة يبقى من هنا فصاعدا بقول ال homogeneous
+
+120
+00:15:12,040 --> 00:15:18,920
+systemهو consistent system لأنه على الأقل له الحل
+
+121
+00:15:18,920 --> 00:15:25,720
+البديهي أو الحل الصفري لأن له على الأقل ال
+
+122
+00:15:25,720 --> 00:15:31,960
+solution الهو الـ 0,0,0 يبقى خديها و أنت مغمضة ال
+
+123
+00:15:31,960 --> 00:15:36,900
+homogenous system هو consistent system لأنه على
+
+124
+00:15:36,900 --> 00:15:42,840
+الأقل له الحل الصفري السؤال هوكيف بدي انا عندي
+
+125
+00:15:42,840 --> 00:15:47,820
+system من هذا system بدي اولد system مكافئ له تمام
+
+126
+00:15:47,820 --> 00:15:52,300
+شو يعني مكافئ يعني الحل تبع هذا system هو نفس الحل
+
+127
+00:15:52,300 --> 00:15:57,260
+تبع ال system الاخر كما كما شفنا قبل قليل وينفي
+
+128
+00:15:57,260 --> 00:16:02,920
+هذا المثال ايوة بدنا نعمل بعض الخطوات هذه الخطوات
+
+129
+00:16:02,920 --> 00:16:07,500
+بتولدلي system يكافئ ال system الأصلي يعني الحل
+
+130
+00:16:07,500 --> 00:16:11,700
+تبع ال system الجديد هو نفس تبع الحل تبع ال system
+
+131
+00:16:11,700 --> 00:16:17,340
+الأصلي دون أن يكون اتنين لهم نفس الشكل بدنا نعمل
+
+132
+00:16:17,340 --> 00:16:22,550
+بعض عملياتماذا يسمى هذه العمليات ؟ انترتشينتو
+
+133
+00:16:22,550 --> 00:16:24,590
+اكويشنز انترتشينتو اكويشنز يعني ان انا في ال
+
+134
+00:16:24,590 --> 00:16:27,730
+system لدي معادلة الأولى و التانية و التالتة و
+
+135
+00:16:27,730 --> 00:16:31,410
+الرابعة لو شيلت الرابعة و حطيتها الأولى و الأولى و
+
+136
+00:16:31,410 --> 00:16:36,190
+خلتها الرابعة في مشكلة؟ بظل نفس ال system تمام؟
+
+137
+00:16:36,190 --> 00:16:41,430
+يبقى هذه أول خطوة لو عملتها لا تتغير القيمالخطوة
+
+138
+00:16:41,430 --> 00:16:45,190
+التانية multiply both sides of an equation by a
+
+139
+00:16:45,190 --> 00:16:49,430
+number c و الـ c لا يساوي 0 لو جيت على أي معادلة
+
+140
+00:16:49,430 --> 00:16:55,190
+من المعادلات هذه و ضربتها في رقم تبت كسري سالب
+
+141
+00:16:55,190 --> 00:17:01,270
+موجة بتفريقش عندنا تمام اي رقم بس مايكونش صفر موجة
+
+142
+00:17:01,270 --> 00:17:06,010
+بسالب كسر ماعنا مشكلة خالص يبقى بنضرب فيه بصير
+
+143
+00:17:06,010 --> 00:17:10,530
+عندنا معادلة بشكل جديد هيعملنا كمان حركةهذه الحركة
+
+144
+00:17:10,530 --> 00:17:15,530
+لا تؤثر على شكل ال system النعية الآن الخطوة
+
+145
+00:17:15,530 --> 00:17:18,910
+الثالثة multiple of one equation to other equation
+
+146
+00:17:18,910 --> 00:17:22,770
+in the system يعني لو جت المعادلة هذه اللي ضربتها
+
+147
+00:17:22,770 --> 00:17:28,090
+في رقم زي هنا جت ضربتها في رقم وجت جمعت يعني جمعت
+
+148
+00:17:28,090 --> 00:17:32,580
+اتنين كأنه اضفت لجديد هذه لمينللمعادلة فوق
+
+149
+00:17:32,580 --> 00:17:36,980
+وبالتالي لا يتغير بظل ال system من ناحية الشكل
+
+150
+00:17:36,980 --> 00:17:40,760
+المختلف لكن من ناحية الحل له نفس الحل مثل ال main
+
+151
+00:17:40,760 --> 00:17:46,640
+ال system الأصلي تلت عمليات هذون بديل صف مكان صف
+
+152
+00:17:46,640 --> 00:17:50,440
+يعني معادلة مكان معادلة اضربيه لأي معادلة في مقدار
+
+153
+00:17:50,440 --> 00:17:55,060
+ثابت ضيف هذه المعادلة إلى معادلة أخرى هذه العمليات
+
+154
+00:17:55,060 --> 00:17:59,420
+بنسميها بنات elementary row operations عمليات الصف
+
+155
+00:17:59,420 --> 00:18:04,470
+البسيطةتذكروا في الثانوية أخدتوا حل المصفوفات
+
+156
+00:18:04,470 --> 00:18:09,670
+بجينا نحل المصفوفات بعمليات الصف البسيطة أو بواسطة
+
+157
+00:18:09,670 --> 00:18:14,210
+معكوس المصفوفة أو بواسطة grammar مظبوط يبجي هاي
+
+158
+00:18:14,210 --> 00:18:18,530
+التلات الطرق اللي كنا نحل فيها المعادلات المصفوفية
+
+159
+00:18:18,530 --> 00:18:22,890
+يبجي احنا بنتكلم اليوم بس على أول طريقة وهي طريقة
+
+160
+00:18:22,890 --> 00:18:28,330
+عمليات الصف البسيطة elementary row operationطيب
+
+161
+00:18:28,330 --> 00:18:32,930
+الحين أنا بدي أسوي elementary raw operation بس بدي
+
+162
+00:18:32,930 --> 00:18:38,270
+أخليها شكلة درجية سلمية سلمية إذا بدنا نأتي
+
+163
+00:18:38,270 --> 00:18:43,670
+للتعريف الجديد إيش التعريف الجديد بقول المصفوفة
+
+164
+00:18:43,670 --> 00:18:49,350
+بقول إنها على شكل raw echelon form يعني مصفوفة
+
+165
+00:18:49,350 --> 00:18:55,580
+صفية على شكل درج أو سلمكيف هذا بيتم؟ بيتم بواسطة
+
+166
+00:18:55,580 --> 00:19:01,480
+أربعة خطوات لا خامسة لا شو الخطوة الأولى؟بقول إذا
+
+167
+00:19:01,480 --> 00:19:06,320
+كان هناك صف غير صفري عناصر صفر مش كلهم صفر بعضهم
+
+168
+00:19:06,320 --> 00:19:10,400
+أصفر ممكن و ممكن يكون فيش فيهم ولا صفر يبقى على
+
+169
+00:19:10,400 --> 00:19:16,220
+الأقل بدي رقم فيهم يكون ماله عدد ما هوش صفر فإن
+
+170
+00:19:16,220 --> 00:19:20,760
+الرقم الأول في هذا الصفر هو واحد صحيح و يسمى هذا
+
+171
+00:19:20,760 --> 00:19:24,400
+العنصر بال leading يعني يا بنات لو جيت على مصروفة
+
+172
+00:19:24,400 --> 00:19:29,450
+خات الصف الأول بدي أول عنصر يكون جدياشيواحد صحيح
+
+173
+00:19:29,450 --> 00:19:34,170
+بس بشرط الصفة دي يكون غير صفري يبقى أول رقم بدي
+
+174
+00:19:34,170 --> 00:19:38,030
+هيكون واحد صحيح هي الخطوة الأولى الخطوة التانية
+
+175
+00:19:38,030 --> 00:19:41,950
+إذا كان هناك صف غير .. أه الخطوة التانية جميع
+
+176
+00:19:41,950 --> 00:19:46,170
+الصفر في الصفرية بتكون تاعةيعني لو أجى صف صفري ولا
+
+177
+00:19:46,170 --> 00:19:51,990
+جيته فوق بقدر أنزله و أحطه تحت بدون مشاكل تمام؟
+
+178
+00:19:51,990 --> 00:19:55,250
+ليش؟ إنه في عمليات الصف البسيطة بقول بقدر أبدل صف
+
+179
+00:19:55,250 --> 00:19:59,730
+ما كان صف ماعناه مشكلة تمام؟ إذا ممكن إذا في صف
+
+180
+00:19:59,730 --> 00:20:03,010
+صفري بقوله خليك أنزل تحت مالكش دعوة في الباقى
+
+181
+00:20:03,010 --> 00:20:06,890
+الخطوة التالتة الرقم واحد الينج في الصفوف التالية
+
+182
+00:20:06,890 --> 00:20:11,860
+يعني أنا جيت على الصف الأول خليت الرقم إيش واحدبدي
+
+183
+00:20:11,860 --> 00:20:16,580
+اجي للصف اللي تحتي الرقم واحد مايكون تحتي بدي يكون
+
+184
+00:20:16,580 --> 00:20:21,420
+العنصر اللي عيمينه منه تحت مباشرة يكبش عاملنا سلة
+
+185
+00:20:21,420 --> 00:20:26,860
+درجة من هنا اشلون form يبقى الصف الأول اللي واحد
+
+186
+00:20:26,860 --> 00:20:30,100
+بدي يكون اول عنصر الصف التاني اللي واحد بدي يكون
+
+187
+00:20:30,100 --> 00:20:35,720
+ماله تاني عنصر بسميه اللي قبله سفرواللي بعده يمكن
+
+188
+00:20:35,720 --> 00:20:40,000
+أصفر ويمكن لا الله أعلم يبقى هيسونا الخطوة مين
+
+189
+00:20:40,000 --> 00:20:43,400
+الخطوة التالتة الرقم واحد ال leading في الصفوف
+
+190
+00:20:43,400 --> 00:20:47,360
+التالية اللي كل صف يقع على يمين الرقم واحد ال
+
+191
+00:20:47,360 --> 00:20:51,040
+leading في الصفوف الأولى يعني الصف الأول كان واحد
+
+192
+00:20:51,040 --> 00:20:54,960
+التاني على يمين و بس تحت دوري يبقى هذا خطوة
+
+193
+00:20:54,960 --> 00:20:58,560
+التالتة الخطوة الرابعة العمود اللي بيحتوي على ال
+
+194
+00:20:58,560 --> 00:21:02,800
+leading بدي يكون عناصره كله أصفر ما عدا هذا ال
+
+195
+00:21:02,800 --> 00:21:07,270
+leadingمتذكرين مصفوف الوحدة يا بنات؟ يبقى مصفوف
+
+196
+00:21:07,270 --> 00:21:11,290
+الواحد واحد زيرو زيرو، زيرو واحد زيرو زيرو، زيرو
+
+197
+00:21:11,290 --> 00:21:15,070
+زيرو واحد، و هكذا، تمام؟ يعني ولا تشبه زي مصفوف
+
+198
+00:21:15,070 --> 00:21:21,250
+تمين الواحدة يبقى الشغل نزل على شكل درج أو سلم
+
+199
+00:21:21,250 --> 00:21:26,810
+فسمناها ال raw echelon formطيب بعد ما سويها
+
+200
+00:21:26,810 --> 00:21:31,910
+الحركات دي بروح بكتب نظام المعادلات الجديد بيكون
+
+201
+00:21:31,910 --> 00:21:36,630
+ال system هذا مكافئ لمن؟ لل system الأصلي وبالتالي
+
+202
+00:21:36,630 --> 00:21:42,610
+حل هذا ال system هو حل نفس ال system الأصلي تمام
+
+203
+00:21:42,610 --> 00:21:47,070
+بالضبط تمام الكلام اللي بقوله حد فيكم ..الان مش
+
+204
+00:21:47,070 --> 00:21:49,930
+ضايل إلا أمثلة دي لبالك على باقي ال section كله
+
+205
+00:21:49,930 --> 00:21:55,760
+أمثلة حد بتسألي سؤال فالكلمتين النظري هدولبنطبقهم
+
+206
+00:21:55,760 --> 00:22:00,880
+على أرض الواقع بالأمثلة العاملية حد بتسأل؟ طيب
+
+207
+00:22:00,880 --> 00:22:13,740
+نأتي إلى الأمثلة على هذا الموضوع هذه
+
+208
+00:22:13,740 --> 00:22:19,460
+اللي كتبناها بالعرف الآن ابنجل
+
+209
+00:22:19,460 --> 00:22:20,580
+أول مثال
+
+210
+00:22:27,800 --> 00:22:35,080
+example one find
+
+211
+00:22:35,080 --> 00:22:38,220
+او
+
+212
+00:22:38,220 --> 00:22:43,900
+جاب الهدف find the
+
+213
+00:22:43,900 --> 00:22:45,600
+solution
+
+214
+00:22:53,880 --> 00:23:04,900
+إذا كان موجود of the
+
+215
+00:23:04,900 --> 00:23:10,420
+following linear
+
+216
+00:23:10,420 --> 00:23:11,380
+systems
+
+217
+00:23:16,320 --> 00:23:27,180
+linear systems by reducing by reducing the matrix
+
+218
+00:23:27,180 --> 00:23:31,840
+of
+
+219
+00:23:31,840 --> 00:23:43,280
+the system the matrix of the system to
+
+220
+00:23:52,700 --> 00:24:02,400
+أول سؤال هو سؤال تلاتة من الكتاب نقص اتنين X1 زائد
+
+221
+00:24:02,400 --> 00:24:13,200
+X2 يساوي خمسة أربعة X1 ناقص اتنين X2 يساوي واحدة
+
+222
+00:24:18,450 --> 00:24:28,130
+هذا الـ system بدي أسميه star solution نرجع
+
+223
+00:24:28,130 --> 00:24:33,190
+لصيفة السؤال نقرأ هذه الصيغة و نحاول نفهمها ثم
+
+224
+00:24:33,190 --> 00:24:37,930
+نأتي لتطبيقها على أرض أنواعها بقول هات ال solution
+
+225
+00:24:37,930 --> 00:24:42,410
+if it exist إذا ال solution موجود بدي إياه مش
+
+226
+00:24:42,410 --> 00:24:46,510
+موجود الله سهل عليهطيب of the following linear
+
+227
+00:24:46,510 --> 00:24:51,290
+systems لسystem الخطية التالية by reducing the
+
+228
+00:24:51,290 --> 00:24:56,510
+matrix بتحويل المصموفة اللي عندنا of the system to
+
+229
+00:24:56,510 --> 00:25:00,650
+raw echelon form إلى صيغة ال raw echelon form يعني
+
+230
+00:25:00,650 --> 00:25:03,930
+إيش بقول ليه؟الـ system اللى عندك و إذا كتروح تجيب
+
+231
+00:25:03,930 --> 00:25:09,250
+الـ system المكافئ له و من ثم ال system اللى نتاج
+
+232
+00:25:09,250 --> 00:25:13,390
+الحل تبقى هو حل مين ال system الأصلي طبق للكلام
+
+233
+00:25:13,390 --> 00:25:17,830
+اللى كنت كتبينه قبل قليل بقولك كويس يبجي أول مبدأ
+
+234
+00:25:17,830 --> 00:25:22,230
+يا بنات ببدأ بالمصفوفة الموسعة إيش المصفوفة
+
+235
+00:25:22,230 --> 00:25:26,390
+الموسعة باخد مصفوفة المعاملين فهي ناقص اتنين و
+
+236
+00:25:26,390 --> 00:25:31,210
+المعامل هنا واحد أو هنا أربع و هنا ناقص اتنينو
+
+237
+00:25:31,210 --> 00:25:36,990
+بروح بحط خطوه بس مشان افصلهم عن بعض و بروح بحط
+
+238
+00:25:36,990 --> 00:25:44,110
+ثوابت خمسة واحد بالشكل اللي عنها طيب
+
+239
+00:25:44,110 --> 00:25:50,940
+اول شغلة بدي اعملهابدي أخلي هذا جداش واحد صحيح
+
+240
+00:25:50,940 --> 00:25:56,800
+يعني بدي أروح أضرب الصف الأول في سالب نص باطمن أن
+
+241
+00:25:56,800 --> 00:26:03,680
+هذا واحد صحيح يبقى هنا بجي بقول سالب نص R1 هاي
+
+242
+00:26:03,680 --> 00:26:07,710
+اللي بدي أعملاللي بدي أعمله بكتبه حتى لو رجعت أرجع
+
+243
+00:26:07,710 --> 00:26:11,770
+تاني أعرف كيف جبت هدول يبقاش بالصير المهادة عندنا
+
+244
+00:26:11,770 --> 00:26:19,390
+سالب نص بيظل هنا قداش واحد وهنا سالب نص وهنا سالب
+
+245
+00:26:19,390 --> 00:26:25,030
+خمسة على اتنين يعني ضربت هذا في سالب نص هذا زي ما
+
+246
+00:26:25,030 --> 00:26:30,410
+هو هذه أربعة وهذا سالب اتنين وهذا واحد بالشكل اللي
+
+247
+00:26:30,410 --> 00:26:34,940
+عندنا هذاهذا الحين صار مين يا بناتي؟ اللي هو ال
+
+248
+00:26:34,940 --> 00:26:41,560
+leading، القائد، اللي تحته إيش بدي يكون؟ صفر، لإنه
+
+249
+00:26:41,560 --> 00:26:45,260
+قلنا العمود كله بدي يكونوا صفر مع ال leading هذا،
+
+250
+00:26:45,260 --> 00:26:50,010
+كيف بدي أخلي هذا الصفر؟ بقول بسيطةبدي اضرب الصف
+
+251
+00:26:50,010 --> 00:26:56,450
+هذا في سالب اربعة واضيفه للصف الثاني يبقى بروح
+
+252
+00:26:56,450 --> 00:27:04,310
+بقول ساهم هيك سالب اربعة R one two R two
+
+253
+00:27:11,070 --> 00:27:17,790
+يبقى الصف الأول يبقى كما هو واحد ناقص نص وهذا ايش
+
+254
+00:27:17,790 --> 00:27:22,870
+سالب خمسة على اتنين ضربته في قداش فيه سالب اربعة
+
+255
+00:27:22,870 --> 00:27:27,670
+في واحد سالب اربعة بده يضيفه لهذا قداش بيصير Zero
+
+256
+00:27:29,180 --> 00:27:36,220
+سالب اربعة بيضال اتنين و سالب اتنين بيضال اتنين و
+
+257
+00:27:36,220 --> 00:27:36,720
+سالب اتنين بيضال اتنين و سالب اتنين بيضال اتنين و
+
+258
+00:27:36,720 --> 00:27:38,300
+سالب اتنين بيضال اتنين و سالب اتنين بيضال اتنين و
+
+259
+00:27:38,300 --> 00:27:41,240
+سالب اتنين بيضال اتنين و سالب اتنين بيضال اتنين و
+
+260
+00:27:41,240 --> 00:27:44,100
+سالب اتنين بيضال اتنين و سالب اتنين بيضال اتنين و
+
+261
+00:27:44,100 --> 00:27:46,920
+سالب اتنين بيضال اتنين و سالب اتنين بيضال اتنين و
+
+262
+00:27:46,920 --> 00:27:47,340
+سالب اتنين بيضال اتنين و سالب اتنين بيضال اتنين و
+
+263
+00:27:47,340 --> 00:27:53,190
+سيبقى طلع الصف هذا كله أصفر و هو طلع أخر حاجة تحت
+
+264
+00:27:53,190 --> 00:27:57,270
+طلع طبيعي مش أنا بده أقوله طلع طبيعي يبقى أكتر من
+
+265
+00:27:57,270 --> 00:28:01,810
+هيك ما بقدرش أكتب يبقى كل اللي بقدر أقول إن ال
+
+266
+00:28:01,810 --> 00:28:07,010
+system هذا equivalent لمين ل system star لإنه
+
+267
+00:28:07,010 --> 00:28:12,130
+استخدمت روشنلوه هذا إيش بده يعطينا بده يعطينا إن
+
+268
+00:28:12,130 --> 00:28:21,100
+ذا systemالجديد X1 ناقص نص X2 يساوي ناقص خمس على
+
+269
+00:28:21,100 --> 00:28:28,940
+اتنين و Zero X1 زائد Zero X2 يساوي احداش هذا is
+
+270
+00:28:28,940 --> 00:28:36,940
+equivalent to system
+
+271
+00:28:36,940 --> 00:28:39,080
+star
+
+272
+00:28:41,720 --> 00:28:46,600
+طيب تعالوا نشوف هي كانت الشغل اللي اشتغلته تعالوا
+
+273
+00:28:46,600 --> 00:28:52,480
+نشوف هذا ايش معناه هذا معناه 0 زائد 0 يساوي 11
+
+274
+00:28:52,480 --> 00:28:57,560
+ممكن هذا الكلام يبقى هذا impossible ايش معناه هذا
+
+275
+00:28:57,560 --> 00:29:02,740
+الكلام ان ال system of star has no solution واحنا
+
+276
+00:29:02,740 --> 00:29:06,300
+في المحاضرة الصبح قلنا يا system مالوش حل يا حل
+
+277
+00:29:06,300 --> 00:29:11,440
+واحد يا عدد لنهائي من الحلول صحيح ولا لايبقى هذا
+
+278
+00:29:11,440 --> 00:29:23,380
+معناه ان ال system star has no solution يبقى هذا
+
+279
+00:29:23,380 --> 00:29:31,060
+مثال بسيط و صغير نعطيك مثالة قليل شوية يبقى مثال
+
+280
+00:29:31,060 --> 00:29:43,220
+رقم اتنين هو سؤال ستة من الكتاببقول X1-2X2 زائد X3
+
+281
+00:29:43,220 --> 00:29:52,080
+يساوي خمسة المعادلة التانية ناقص X1 زائد X2 ناقص
+
+282
+00:29:52,080 --> 00:29:59,240
+أربعة X3 يساوي ناقص سبعةالمعادلة بعدها تلاتة اكس
+
+283
+00:29:59,240 --> 00:30:06,820
+واحد زائد تلاتة اكس اتنين زائد اكس تلاتة كله يساوي
+
+284
+00:30:06,820 --> 00:30:11,220
+اربعة وهذا ال system عندنا اللي هو main هو stop
+
+285
+00:30:11,220 --> 00:30:19,480
+بدأ اروح بال row echelon four احول هذا ال system
+
+286
+00:30:19,480 --> 00:30:26,590
+إلى شكل جديد بقوله كويس solutionيبقى بنات ببدأ
+
+287
+00:30:26,590 --> 00:30:32,830
+بمين؟ ببدأ بالمصفوفة الموسعة يبقى باجي بقول هذا
+
+288
+00:30:32,830 --> 00:30:38,330
+المصفوفة الموسعة معامل X واحد واحد معامل X اتنين
+
+289
+00:30:38,330 --> 00:30:43,970
+سالب اتنين هنا واحد سالب واحد واحد سالب اربعة
+
+290
+00:30:43,970 --> 00:30:49,950
+تلاتة تلاتة واحد و بروح بقول هذه خمسة سالب سبعة
+
+291
+00:30:49,950 --> 00:30:56,000
+اربعة بالشكل اللي عندنا هنا شوف ايش بدني اعملهيو
+
+292
+00:30:56,000 --> 00:31:00,340
+الحمد لله هذا الأول واحد ال leading يبقى جاهز يبقى
+
+293
+00:31:00,340 --> 00:31:07,060
+بدي أخلي عموده أصفرا يبقى بدي أضيفه للمين للصف
+
+294
+00:31:07,060 --> 00:31:11,700
+اللي بعده و الخطوة التانية بدي أضربه في سالب تلاتة
+
+295
+00:31:11,700 --> 00:31:20,640
+و أضيفه للصف التالت يبقى باجي بقوله هنا اشR1 to R2
+
+296
+00:31:20,640 --> 00:31:29,000
+هاي الخطوة الأولى اللى بعدها سالب تلاتة R1 to R3 R
+
+297
+00:31:29,000 --> 00:31:33,960
+يا بنات اللى كلمة رو يعني الصف انا باختصرها اختصار
+
+298
+00:31:33,960 --> 00:31:38,360
+لما احط اتنين يبقى لصف التاني يبقى اللى يتغير يا
+
+299
+00:31:38,360 --> 00:31:42,860
+بنات مش اللى بنضرب فيه المضاف اللى هو اللى بيتغير
+
+300
+00:31:43,090 --> 00:31:48,770
+تمام إذا هذه هتصبح المصفوفة على الشكل التالي الصف
+
+301
+00:31:48,770 --> 00:31:55,150
+الأول مافيش فيه أي حاجة وهي لذاك وهي هنا خمسة الصف
+
+302
+00:31:55,150 --> 00:31:58,930
+التاني أضفته إليه لما أضفته إليه صار هنا إيه عاش؟
+
+303
+00:31:58,930 --> 00:32:04,390
+Zero صار هنا كده؟ سالب واحد صار هنا كده؟ سالب
+
+304
+00:32:04,390 --> 00:32:09,810
+تلاتة صار هنا سالب اتنين بعد هيكسالب تلاتة و تلاتة
+
+305
+00:32:09,810 --> 00:32:15,290
+كده؟ Zero سالب تلاتة في اتنين بموجة بستة وتلاتة
+
+306
+00:32:15,290 --> 00:32:22,210
+تسعة سالب تلاتة واحد بيظل سالب اتنين سالب تلاتة في
+
+307
+00:32:22,210 --> 00:32:28,850
+خمسة بسالب خمستاشر وهنا بيظل سالب احداشر مظبوط
+
+308
+00:32:28,850 --> 00:32:34,760
+هيك؟ مرة تانية ده جيجي معاياسوف أضيف فضلة لهذا
+
+309
+00:32:34,760 --> 00:32:40,980
+بصير zero سالب واحد سالب تلاتة هنا سالب اتنين مش
+
+310
+00:32:40,980 --> 00:32:45,000
+مشكلة هنا سوف أضع في سالب تلاتة و أضيف بصير zero
+
+311
+00:32:45,000 --> 00:32:49,940
+سالب تلاتة في سالب اتنين في ستة و تلاتة تسعة سالب
+
+312
+00:32:49,940 --> 00:32:53,400
+تلاتة في واحد في سالب تلاتة و واحد في سالب اتنين
+
+313
+00:32:53,400 --> 00:32:59,340
+سالب خمستاشر وأربعة بضل كده سالب احداشر تمام تمام
+
+314
+00:32:59,620 --> 00:33:03,680
+يبقى هذه العمود اللي بعده ياشي أصفر الآن بدي أجي
+
+315
+00:33:03,680 --> 00:33:08,560
+للصف اللي بعده بدي يكون ال leading فين؟ هو على
+
+316
+00:33:08,560 --> 00:33:11,500
+يمين ال leading الأولاني ومنه التحت داخلي اللي
+
+317
+00:33:11,500 --> 00:33:17,520
+همين هذا بدي ياشي يكون واحد يبقى بدي أضرب هذا الصف
+
+318
+00:33:17,520 --> 00:33:25,860
+في سالب يبقى باجي بقوله هنا هذا سهم وهنا سالب R2
+
+319
+00:33:26,450 --> 00:33:30,750
+تمام يبقى بدها صير المصوفة على الشكل تالي واحد
+
+320
+00:33:30,750 --> 00:33:37,850
+سالب اتنين واحد zero واحد تلاتة وهنا اتنين وهنا
+
+321
+00:33:37,850 --> 00:33:43,950
+خمسة وصف التالت زي ما هو zero تسعة ناقص اتنين ناقص
+
+322
+00:33:43,950 --> 00:33:49,880
+احداشر بالشكل اللي عندها تمامالان بدى هذا يصير
+
+323
+00:33:49,880 --> 00:33:55,380
+قداش Zero يبقى بدى اغرب هذا في سلب تسعة واضفه له
+
+324
+00:33:55,380 --> 00:34:02,740
+يبقى باجي بقوله هنا سالب تسعة R two to R three
+
+325
+00:34:02,740 --> 00:34:10,930
+بنحصل على ماتالصف الأول كما هو وهذه خمسة والصف
+
+326
+00:34:10,930 --> 00:34:16,910
+الثاني كما هو اتنين الحين الصف المضرب تسعة في زيرو
+
+327
+00:34:16,910 --> 00:34:23,870
+بزيرو زائد الزيرو يبقى بزيرو سلب تسعة مع تسعة بصير
+
+328
+00:34:23,870 --> 00:34:30,370
+زيرو سلب سبعة وعشرين وسلب اتنينسالب تسعة و عشرين
+
+329
+00:34:30,370 --> 00:34:37,010
+يبقى سالب تسعة و عشرين سالب تسعة في اتنين بسالب
+
+330
+00:34:37,010 --> 00:34:41,970
+تمانتاش سالب تمانتاش و سالب احداشر بسالب تسعة و
+
+331
+00:34:41,970 --> 00:34:50,030
+عشرين يبقى سالب تسعة و عشرين بعد هيك بدي اخلي هذا
+
+332
+00:34:50,030 --> 00:34:57,050
+واحد كذلك تمام يبقاش بعملبضرب في سالب واحد على
+
+333
+00:34:57,050 --> 00:35:03,930
+تسعة وعشرين الصف التالت يبقى هذا سالب واحد على
+
+334
+00:35:03,930 --> 00:35:09,750
+تسعة وعشرين R تلاتة يبقى الصف الأول واحد سالب
+
+335
+00:35:09,750 --> 00:35:16,610
+اتنين واحد Zero واحد تلاتة Zero Zero واحد و هنا
+
+336
+00:35:16,610 --> 00:35:25,190
+خمسة اتنين و هنا واحدطبعا طلع في السلم واحد ال
+
+337
+00:35:25,190 --> 00:35:28,490
+leading التاني على يمينه ال leading التالي على
+
+338
+00:35:28,490 --> 00:35:34,030
+شماله العمود تبعه أصفر هذا العمود تبعه مش أصفر
+
+339
+00:35:34,030 --> 00:35:43,390
+تمام يبقى بدي أضرب الصف تاني في تنين و أضيفه لمن؟
+
+340
+00:35:43,390 --> 00:35:51,020
+للأوليبقى باجي بقوله هنا اتنين R اتنين to R one
+
+341
+00:35:51,020 --> 00:35:57,580
+بده يصبح على الشكل التالف هذا واحد زي ما هو اتنين
+
+342
+00:35:57,580 --> 00:36:04,950
+وسلب اتنين بزيروهنا ضربنا اتنين في تلاتة بستة واحد
+
+343
+00:36:04,950 --> 00:36:10,330
+سبعة هي مظبوط هيك نضرب هنا في اتنين و هنا اتنين في
+
+344
+00:36:10,330 --> 00:36:15,470
+اتنين باربعة و خمسة هذه تسعة و هذا الخط اللي عندنا
+
+345
+00:36:15,470 --> 00:36:23,370
+هذا بيظل زي ما هو Zero واحد تلاتة اتنين و ده Zero
+
+346
+00:36:23,370 --> 00:36:29,590
+Zero واحد واحدشكله لو ضربت هذا في السلب تلاتة
+
+347
+00:36:29,590 --> 00:36:33,810
+وضفته لهذا وضربته في سلب سبعة وضفته للي فوق بقول
+
+348
+00:36:33,810 --> 00:36:40,090
+خلصت تمام يبقاش بصير عندنا يا بنات بصير عندنا هذا
+
+349
+00:36:40,090 --> 00:36:50,630
+سهم يبقى السلب سبعة R تلاتة to R one وسلب تلاتة R
+
+350
+00:36:50,630 --> 00:36:57,430
+تلاتة to R twoبيحصل ما ياتي الواحد زي ما هو لن
+
+351
+00:36:57,430 --> 00:37:03,790
+يتأثر وهذا الان
+
+352
+00:37:03,790 --> 00:37:11,670
+سالب سبعة R ثلاثة R هذا بيظل Zero زي ما هو وهذا
+
+353
+00:37:11,670 --> 00:37:18,930
+بيصير Zero وهنا سالب سبعة و عندك تسعة بيظل كده؟
+
+354
+00:37:18,930 --> 00:37:26,210
+بيظل اتنين فقط لغيرالأن سالب تلاتة R تلاتة ل R2
+
+355
+00:37:26,210 --> 00:37:31,550
+يبقى Zero واحد زي ما هو هنا بيجيكي ال Zero هنا
+
+356
+00:37:31,550 --> 00:37:36,870
+سالب تلاتة و اتنين بيصير سالب واحد و هذا Zero Zero
+
+357
+00:37:36,870 --> 00:37:43,630
+واحد واحد كما هو الان ال system اللي بطلع عندها يا
+
+358
+00:37:43,630 --> 00:37:49,690
+بناتي يكافئ من ال system star اللي فوق فبجي بقوله
+
+359
+00:37:49,690 --> 00:38:00,320
+هناsystem الـ domain هنا x1 بدها تساوي 2 وهنا
+
+360
+00:38:00,320 --> 00:38:08,300
+ماعنديش إلا x2 بده يساوي سالب واحد وهنا ال x3 بده
+
+361
+00:38:08,300 --> 00:38:18,220
+يساوي الواحد is equivalent to the system
+
+362
+00:38:20,530 --> 00:38:26,470
+يبقى هذا بكافئة system star معناته الحل تبع هذا هو
+
+363
+00:38:26,470 --> 00:38:31,990
+الحل تبع من؟ تبع ال system star فبروح و بقوله الآن
+
+364
+00:38:31,990 --> 00:38:43,090
+the solution of the system star is لحظة
+
+365
+00:38:43,090 --> 00:38:45,010
+شوية solution
+
+366
+00:38:48,920 --> 00:39:03,620
+of the system star is x1 و x2 و x3 يساوي اتنين
+
+367
+00:39:03,620 --> 00:39:08,060
+سالب واحد واحد اتنين و سالب واحد واحد مين اللي
+
+368
+00:39:08,060 --> 00:39:13,820
+بتسأل؟ ايوة خلت
+
+369
+00:39:13,820 --> 00:39:20,910
+صحيحلما هو طالع الصف كل أصفار اللي تحت ماقدرش
+
+370
+00:39:20,910 --> 00:39:27,010
+اتحرك ولا حاجة لما يطلع كل أصفار يقفق كما هو عجيب
+
+371
+00:39:27,010 --> 00:39:30,670
+لك الحين بس أصبح احنا لسه في البداية تستعيدليش في
+
+372
+00:39:30,670 --> 00:39:37,530
+حد بتسأل تاني طب نعطي كمان مثال المثال رقم تلاتة
+
+373
+00:39:37,530 --> 00:39:40,990
+بس
+
+374
+00:39:40,990 --> 00:39:46,670
+قبل المثال رقم تلاتةماذا رأيك في المثال هذا؟ إذا
+
+375
+00:39:46,670 --> 00:39:50,170
+طلعنا two systems are equivalent وبالتالي الحل هذا
+
+376
+00:39:50,170 --> 00:39:54,090
+هو حل ال system الأولاني يبقى ال system الأولاني
+
+377
+00:39:54,090 --> 00:39:59,310
+consistent ولا inconsistent؟ inconsistent على طول
+
+378
+00:39:59,310 --> 00:40:04,410
+الخط لأن قلنا consistent له حل وحيد أو عدد لنهائي
+
+379
+00:40:04,410 --> 00:40:10,940
+من الحلولنعطي كمان مثال يبقى سؤال تلت عشر من
+
+380
+00:40:10,940 --> 00:40:19,360
+الكتاب نعطيني اتنين X one ناقص X two زائد X three
+
+381
+00:40:19,360 --> 00:40:27,660
+يساوي سالب واحد و X واحد زائد X اتنين زائد X تلاتة
+
+382
+00:40:27,660 --> 00:40:35,320
+يساوي من؟ يساوي تلاتةهذا هو الـ system start
+
+383
+00:40:35,320 --> 00:40:41,220
+solution يبقى انا بدى اروح اخد المصفوفة الموسعة
+
+384
+00:40:41,220 --> 00:40:47,430
+لاحظى ان انا ماعنديش الا معادلتين والمجاهيلتلاتة
+
+385
+00:40:47,430 --> 00:41:04,170
+تلاتة
+
+386
+00:41:04,170 --> 00:41:09,600
+تلاتةأظن لو بدلت الصف الأول و خلّيته هو الصف
+
+387
+00:41:09,600 --> 00:41:13,240
+التاني والتاني هو الأول مافيش مشكلة نفس الخواص
+
+388
+00:41:13,240 --> 00:41:18,400
+اللي كنا بشتغل فيها قبل هيك إذا هادي هاها بدي أعمل
+
+389
+00:41:18,400 --> 00:41:19,380
+replace
+
+390
+00:41:21,600 --> 00:41:31,720
+replace r1 and r2 بدّل او exchange r1 and r2 يبقى
+
+391
+00:41:31,720 --> 00:41:32,980
+بنحصل على
+
+392
+00:41:41,850 --> 00:41:46,530
+بدأ أخلّي هذا الـ zero يبقى بضرب الصف الأول في
+
+393
+00:41:46,530 --> 00:41:51,830
+سالب اتنين وبضيفه للصف الثاني يبقى هنا بروح بقوله
+
+394
+00:41:51,830 --> 00:41:59,400
+سالب اتنين R one two R two نحصل على ما يدىواحد
+
+395
+00:41:59,400 --> 00:42:04,780
+واحد واحد تلاتة مافيش فيها تغيير سالب اتنين بصير
+
+396
+00:42:04,780 --> 00:42:09,380
+ال zero سالب اتنين و سالب واحد يبقى سالب تلاتة
+
+397
+00:42:09,380 --> 00:42:14,220
+سالب اتنين و واحد يبقى سالب واحد سالب ستة و هذا
+
+398
+00:42:14,220 --> 00:42:21,960
+بصير اه سالب سبعة بعد هيك بدي اخلي هذا كده واحد
+
+399
+00:42:21,960 --> 00:42:30,320
+صحيح يبقىبضرب في سالب تلت يبقى لو ضربت في سالب تلت
+
+400
+00:42:30,320 --> 00:42:38,140
+بقوله سالب تلت قاري اتنين واحد واحد واحد تلاتة
+
+401
+00:42:38,140 --> 00:42:45,340
+Zero واحد تلت لان ضرب في سالب تلت بيصير موجب وهنا
+
+402
+00:42:45,340 --> 00:42:48,700
+بيصير السابعة على تلاتة
+
+403
+00:42:50,810 --> 00:43:00,450
+بقدر اخل اللي فوق صفر كمان يبقى
+
+404
+00:43:00,450 --> 00:43:08,650
+هنا سالب R2 to R1 نحصل على ما يدى واحد زي ما هو
+
+405
+00:43:08,650 --> 00:43:20,520
+وده zero وده تلتينوهنا سالب سبعة على تلاتة و تلاتة
+
+406
+00:43:20,520 --> 00:43:25,380
+بالموجة سبعة على تلاتة اللي هو اتنين و تلتين مظبوط
+
+407
+00:43:25,380 --> 00:43:28,780
+ولا اتنين و تلت سبعة على تلاتة
+
+408
+00:43:34,250 --> 00:43:40,970
+تلتين بالموجب يبقى تلتين
+
+409
+00:43:40,970 --> 00:43:45,190
+بالموجب يبقى تلتين بالموجب يبقى تلتين بالموجب يبقى
+
+410
+00:43:45,190 --> 00:43:52,310
+تلتين بالموجب يبقى تلتين بالموجب يبقى تلتين
+
+411
+00:43:52,310 --> 00:43:52,970
+بالموجب يبقى تلتين بالموجب يبقى تلتين بالموجب يبقى
+
+412
+00:43:52,970 --> 00:43:53,190
+تلتين بالموجب يبقى تلتين بالموجب يبقى تلتين
+
+413
+00:43:53,190 --> 00:43:53,770
+بالموجب يبقى تلتين بالموجب يبقى تلتين بالموجب يبقى
+
+414
+00:43:53,770 --> 00:43:59,540
+تلتين بالموجب يبقى تلتين بالموجببقدر؟ مش إمكانية
+
+415
+00:43:59,540 --> 00:44:06,700
+يبقى الآن ال system الجديد بروح بقوله that system
+
+416
+00:44:07,600 --> 00:44:14,180
+اللي هو مين X واحد زائد تلتين X تلاتة بده يساوي
+
+417
+00:44:14,180 --> 00:44:22,780
+تلتين واللي بعده X اتنين زائد تلت X تلاتة بده
+
+418
+00:44:22,780 --> 00:44:31,320
+يساوي سبعة على تلاتة as equivalent to
+
+419
+00:44:31,320 --> 00:44:34,280
+the system
+
+420
+00:44:36,100 --> 00:44:41,860
+ستار الأصلي إذا حل هذا ال system هو نفس حل ال
+
+421
+00:44:41,860 --> 00:44:48,560
+system star اللي فوق طيب هدول معادلتين في ثلاثة
+
+422
+00:44:48,560 --> 00:44:57,400
+مجاهيل بقدرش إلا إذا أحط أحد المجاهيل من عندى بروح
+
+423
+00:44:57,400 --> 00:45:02,980
+من عندهابحط أي قيمة لهذه اللواحد من المجاهيل
+
+424
+00:45:02,980 --> 00:45:07,460
+وبالتالي بجيب المجهولين للاتنين التانيات بدلالة
+
+425
+00:45:07,460 --> 00:45:12,620
+القيمة اللي انا حطيتها فمثلا لو جاتي قولت حط X
+
+426
+00:45:12,620 --> 00:45:18,620
+تلاتة بتلاتة او حطيتها بتلاتة ايه تلاتة يعني حطيت
+
+427
+00:45:18,620 --> 00:45:22,960
+رقم محدد لكن لما اقول تلاتة ايه في قيود على ايه
+
+428
+00:45:22,960 --> 00:45:30,980
+ماعنديش قيود يبقى هنا باجي بقوله FX تلاتة يساوي
+
+429
+00:45:30,980 --> 00:45:35,380
+تلاتة A ثاني X تلاتة يساوي تلاتة A ثاني X تلاتة
+
+430
+00:45:35,380 --> 00:45:38,700
+يساوي تلاتة A ثاني X تلاتة يساوي تلاتة A ثاني X
+
+431
+00:45:38,700 --> 00:45:40,400
+تلاتة يساوي تلاتة A ثاني X تلاتة يساوي تلاتة A
+
+432
+00:45:40,400 --> 00:45:40,840
+ثاني X تلاتة يساوي تلاتة A ثاني X تلاتة يساوي
+
+433
+00:45:40,840 --> 00:45:41,380
+تلاتة A ثاني X تلاتة يساوي تلاتة A ثاني X تلاتة
+
+434
+00:45:41,380 --> 00:45:42,560
+يساوي تلاتة A ثاني X تلاتة يساوي تلاتة A ثاني X
+
+435
+00:45:42,560 --> 00:45:51,560
+تلاتة يساوي تلاتة A ثاني X تلاتة يساوي تلاتة A
+
+436
+00:45:51,560 --> 00:45:59,410
+ثاني X تلالحين X3 موجودة بقدر أجيب X1 يبقى بعدي
+
+437
+00:45:59,410 --> 00:46:08,830
+بقول X1 تساوي يبقى بعدي بقول X1 تساوي حطيت هذا
+
+438
+00:46:08,830 --> 00:46:15,050
+بالتلاتة يبقى بتروح التلاتة بضل أو X1 زائد
+
+439
+00:46:28,960 --> 00:46:35,300
+يبقى الـ General solution
+
+440
+00:46:37,770 --> 00:46:45,250
+X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15
+
+441
+00:46:45,250 --> 00:46:50,190
+X16 X17 X18 X19 X20 X21 X22 X23
+
+442
+00:46:50,190 --> 00:46:56,610
+X23 X23 X23 X23 X23 X23 X23
+
+443
+00:46:56,610 --> 00:47:02,670
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+444
+00:47:02,670 --> 00:47:02,810
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+445
+00:47:02,810 --> 00:47:02,910
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+446
+00:47:02,910 --> 00:47:05,470
+X23 X23 X23 X23 X23 X23 X23 X23 X23 X23
+
+447
+00:47:08,810 --> 00:47:17,510
+جد عددكوا اكتر شوية مالا يعني نحط ال real number
+
+448
+00:47:17,510 --> 00:47:22,490
+اللي يجب بس بعيد عن الصفر تمام يبقى باجي بقوله او
+
+449
+00:47:22,490 --> 00:47:25,850
+حتى لو حطيتها صفر بمشي الحل انه ماعنديش قيود على
+
+450
+00:47:25,850 --> 00:47:32,970
+ايه تمام يبقى باجي بقوله this is infinite
+
+451
+00:47:34,760 --> 00:47:45,020
+أو this represent هذا يمثل this represent infinite
+
+452
+00:47:45,020 --> 00:47:56,900
+number of solutions يبقى هذا يمثلي مالة نهاية من
+
+453
+00:47:56,900 --> 00:48:02,160
+الحلول تمام طيب خليني أسأل السؤال التالف احنا
+
+454
+00:48:02,160 --> 00:48:09,610
+ماكملناش لسهخلّيني أسأل السؤال التالي هل هذا ال
+
+455
+00:48:09,610 --> 00:48:14,210
+system consistent و لا inconsistent؟ Consistent
+
+456
+00:48:14,210 --> 00:48:18,750
+لأنه يحتوي على مالة نهاية من الحلول، لا يزال هناك
+
+457
+00:48:18,750 --> 00:48:23,510
+المزيد من الأمثلة إلى المحاضرة القادمة إن شاء الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8cc3326f9e4fd24f41dfd3b26ebe84a6d7bad09c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0pV1qTRy270_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4916, "start": 19.98, "end": 49.16, "text": "بسم الله الرحمن الرحيم في محاضرة الصبح اتكلمنا عن بعض التعريفات قلنا لو ال system star كان له حل وحيد او عدد لا نهائي من الحلول بنسمي consistent وإذا كان مالوش حل بنسمي inconsistent واخر حاجة كتبناها two systems are equivalent اتنين بقول عنهم اتنين متكافئين", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 3714, 5016, 46958, 25720, 31767, 49628, 1975, 2655, 4117, 19528, 8315, 18871, 45030, 11242, 16712, 3615, 16572, 5172, 9307, 12174, 1211, 8315, 45164, 2423, 1185, 3543, 25961, 46740, 11331, 1211, 4032, 5016, 25708, 1975, 2407, 6225, 3215, 3215, 20193, 8717, 3224, 16373, 1829, 9154, 21542, 1211, 12610, 44945, 38251, 1829, 8398, 4032, 28814, 15730, 25961, 3714, 6027, 2407, 8592, 11331, 1211, 44945, 38251, 1829, 36891, 4032, 47283, 2288, 11331, 26108, 3660, 9122, 2655, 3555, 8315, 11296, 732, 3652, 366, 10344, 1975, 2655, 1863, 9957, 4724, 39648, 18871, 16095, 1975, 2655, 1863, 9957, 44650, 4117, 31845, 19986, 9957], "avg_logprob": -0.13693576830404777, "compression_ratio": 1.7178423236514522, "no_speech_prob": 0.0, "words": [{"start": 19.98, "end": 20.28, "word": "بسم", "probability": 0.907958984375}, {"start": 20.28, "end": 20.48, "word": " الله", "probability": 0.96923828125}, {"start": 20.48, "end": 20.88, "word": " الرحمن", "probability": 0.9484049479166666}, {"start": 20.88, "end": 21.4, "word": " الرحيم", "probability": 0.9931640625}, {"start": 21.4, "end": 22.84, "word": " في", "probability": 0.82568359375}, {"start": 22.84, "end": 23.58, "word": " محاضرة", "probability": 0.981689453125}, {"start": 23.58, "end": 24.68, "word": " الصبح", "probability": 0.96875}, {"start": 24.68, "end": 25.7, "word": " اتكلمنا", "probability": 0.84013671875}, {"start": 25.7, "end": 25.88, "word": " عن", "probability": 0.99267578125}, {"start": 25.88, "end": 26.22, "word": " بعض", "probability": 0.994384765625}, {"start": 26.22, "end": 27.28, "word": " التعريفات", "probability": 0.99130859375}, {"start": 27.28, "end": 27.94, "word": " قلنا", "probability": 0.6551920572916666}, {"start": 27.94, "end": 28.2, "word": " لو", "probability": 0.92724609375}, {"start": 28.2, "end": 28.46, "word": " ال", "probability": 0.9658203125}, {"start": 28.46, "end": 29.02, "word": " system", "probability": 0.943359375}, {"start": 29.02, "end": 29.7, "word": " star", "probability": 0.359375}, {"start": 29.7, "end": 31.06, "word": " كان", "probability": 0.97509765625}, {"start": 31.06, "end": 31.34, "word": " له", "probability": 0.480224609375}, {"start": 31.34, "end": 31.76, "word": " حل", "probability": 0.9775390625}, {"start": 31.76, "end": 32.4, "word": " وحيد", "probability": 0.8470052083333334}, {"start": 32.4, "end": 32.72, "word": " او", "probability": 0.8798828125}, {"start": 32.72, "end": 33.1, "word": " عدد", "probability": 0.9851888020833334}, {"start": 33.1, "end": 33.26, "word": " لا", "probability": 0.404052734375}, {"start": 33.26, "end": 33.66, "word": " نهائي", "probability": 0.8916015625}, {"start": 33.66, "end": 33.8, "word": " من", "probability": 0.98193359375}, {"start": 33.8, "end": 34.18, "word": " الحلول", "probability": 0.9947916666666666}, {"start": 34.18, "end": 35.12, "word": " بنسمي", "probability": 0.9278971354166666}, {"start": 35.12, "end": 36.68, "word": " consistent", "probability": 0.6640625}, {"start": 36.68, "end": 37.66, "word": " وإذا", "probability": 0.8240559895833334}, {"start": 37.66, "end": 38.1, "word": " كان", "probability": 0.9833984375}, {"start": 38.1, "end": 38.72, "word": " مالوش", "probability": 0.78955078125}, {"start": 38.72, "end": 39.0, "word": " حل", "probability": 0.96875}, {"start": 39.0, "end": 39.64, "word": " بنسمي", "probability": 0.95458984375}, {"start": 39.64, "end": 40.76, "word": " inconsistent", "probability": 0.5146484375}, {"start": 40.76, "end": 42.44, "word": " واخر", "probability": 0.7578938802083334}, {"start": 42.44, "end": 42.76, "word": " حاجة", "probability": 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ال two systems are equivalent نجي ناخد مثال على ذلك بقول you show that the following two systems are equivalent", "tokens": [28814, 15730, 25961, 5296, 16095, 8717, 36178, 21542, 1211, 12610, 11933, 15730, 2423, 1185, 16247, 12610, 4032, 2423, 1185, 16712, 7649, 1829, 23032, 1211, 3615, 5296, 16095, 8717, 36178, 21542, 1211, 12610, 11933, 15730, 4724, 39648, 18871, 23758, 2423, 732, 3652, 366, 10344, 8717, 7435, 1829, 8717, 47283, 3215, 50113, 6027, 15844, 29910, 23275, 4724, 39648, 291, 855, 300, 264, 3480, 732, 3652, 366, 10344], "avg_logprob": -0.21496211940591986, "compression_ratio": 1.7664670658682635, "no_speech_prob": 0.0, "words": [{"start": 49.44, "end": 49.9, "word": "إذا", "probability": 0.75634765625}, {"start": 49.9, "end": 50.3, "word": " كان", "probability": 0.90087890625}, {"start": 50.3, "end": 50.76, "word": " لهم", "probability": 0.85302734375}, {"start": 50.76, "end": 51.36, "word": " نفس", "probability": 0.98828125}, {"start": 51.36, "end": 51.82, "word": " الحلول", "probability": 0.9931640625}, {"start": 51.82, "end": 52.04, "word": " إذا", "probability": 0.6912841796875}, {"start": 52.04, "end": 52.18, "word": " ال", "probability": 0.80615234375}, {"start": 52.18, "end": 52.52, "word": " system", "probability": 0.56494140625}, {"start": 52.52, "end": 53.12, "word": " الأول", "probability": 0.95556640625}, {"start": 53.12, "end": 53.62, "word": " و", "probability": 0.634765625}, {"start": 53.62, "end": 53.76, "word": " ال", "probability": 0.779296875}, {"start": 53.76, "end": 54.08, "word": " system", "probability": 0.87939453125}, {"start": 54.08, "end": 54.46, "word": " التاني", "probability": 0.7740885416666666}, {"start": 54.46, "end": 54.78, "word": " طلع", "probability": 0.8951822916666666}, {"start": 54.78, "end": 55.0, "word": " لهم", "probability": 0.925537109375}, {"start": 55.0, "end": 55.36, "word": " نفس", "probability": 0.9921875}, {"start": 55.36, "end": 55.96, "word": " الحلول", "probability": 0.6764933268229166}, {"start": 55.96, "end": 56.38, "word": " إذا", "probability": 0.698486328125}, {"start": 56.38, "end": 56.72, "word": " بقول", "probability": 0.861572265625}, {"start": 56.72, "end": 56.94, "word": " عن", "probability": 0.9111328125}, {"start": 56.94, "end": 57.36, "word": " هذا", "probability": 0.93408203125}, {"start": 57.36, "end": 57.76, "word": " ال", "probability": 0.798828125}, {"start": 57.76, "end": 57.94, "word": " two", "probability": 0.759765625}, {"start": 57.94, "end": 58.56, "word": " systems", "probability": 0.939453125}, {"start": 58.56, "end": 59.1, "word": " are", "probability": 0.9560546875}, {"start": 59.1, "end": 59.84, "word": " equivalent", "probability": 0.9404296875}, {"start": 59.84, "end": 60.58, "word": " نجي", "probability": 0.5941975911458334}, {"start": 60.58, "end": 60.9, "word": " ناخد", "probability": 0.9775390625}, {"start": 60.9, "end": 61.34, "word": " مثال", "probability": 0.971923828125}, {"start": 61.34, "end": 61.54, "word": " على", 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هدول are equivalent بدالي للـ system الأول بدي أحاول أحله بمعنى أخر بيطلع جديش قيمة x1 و جديش قيمة x2 و ال system التاني بيطلع جديش قيمة x1 و x2 بأي طريقة رياضية ممكن تقدر عليها", "tokens": [3555, 9957, 1829, 8315, 16472, 2423, 39184, 732, 3652, 8032, 3215, 12610, 366, 10344, 47525, 6027, 1829, 24976, 39184, 1185, 16247, 12610, 4724, 16254, 5551, 5016, 995, 12610, 5551, 5016, 43761, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 4724, 1829, 9566, 1211, 3615, 10874, 16254, 8592, 12174, 32640, 3660, 2031, 16, 4032, 10874, 16254, 8592, 12174, 32640, 3660, 2031, 17, 4032, 2423, 1185, 16712, 7649, 1829, 4724, 1829, 9566, 1211, 3615, 10874, 16254, 8592, 12174, 32640, 3660, 2031, 16, 4032, 2031, 17, 4724, 10721, 1829, 23032, 16572, 28671, 12602, 1829, 46958, 10632, 3714, 43020, 6055, 28543, 2288, 25894, 11296], "avg_logprob": -0.20515625596046447, "compression_ratio": 1.708994708994709, "no_speech_prob": 0.0, "words": [{"start": 65.94, "end": 66.96, "word": "بينينا", "probability": 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" number", "probability": 0.9775390625}, {"start": 451.17, "end": 453.93, "word": " c", "probability": 0.349853515625}, {"start": 453.93, "end": 454.55, "word": " و", "probability": 0.327880859375}, {"start": 454.55, "end": 454.79, "word": " الـ", "probability": 0.594970703125}, {"start": 454.79, "end": 455.03, "word": " c", "probability": 0.7041015625}, {"start": 455.03, "end": 455.43, "word": " does", "probability": 0.501953125}, {"start": 455.43, "end": 455.79, "word": " not", "probability": 0.96923828125}, {"start": 455.79, "end": 456.35, "word": " equal", "probability": 0.931640625}, {"start": 456.35, "end": 456.71, "word": " to", "probability": 0.91162109375}, {"start": 456.71, "end": 457.05, "word": " zero", "probability": 0.45703125}, {"start": 457.05, "end": 458.89, "word": " نمرة", "probability": 0.679931640625}, {"start": 458.89, "end": 460.09, "word": " تلاتة", "probability": 0.94970703125}, {"start": 460.09, "end": 462.03, "word": " adding", "probability": 0.80419921875}, {"start": 462.03, "end": 466.09, "word": " a", "probability": 0.712890625}, {"start": 466.09, "end": 467.23, "word": " multiple", "probability": 0.91455078125}, {"start": 467.23, "end": 470.37, "word": " of", "probability": 0.97509765625}, {"start": 470.37, "end": 472.29, "word": " n", "probability": 0.66845703125}], "temperature": 1.0}, {"id": 19, "seek": 50247, "start": 473.73, "end": 502.47, "text": "equation to other equation لمعادلة أخرى in the system these operations هذه العمليات are called", "tokens": [12816, 399, 281, 661, 5367, 32767, 3615, 18513, 37977, 5551, 34740, 7578, 294, 264, 1185, 613, 7705, 29538, 18863, 2304, 20292, 9307, 366, 1219], "avg_logprob": -0.18171874523162843, "compression_ratio": 1.0740740740740742, "no_speech_prob": 0.0, "words": [{"start": 473.73, "end": 475.05, "word": "equation", "probability": 0.707763671875}, {"start": 475.05, "end": 476.49, "word": " to", "probability": 0.70263671875}, {"start": 476.49, "end": 478.41, "word": " other", 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{"start": 715.27, "end": 717.75, "word": " الصفوف", "probability": 0.9894205729166666}, {"start": 717.75, "end": 721.21, "word": " الصفرية", "probability": 0.9947509765625}], "temperature": 1.0}, {"id": 26, "seek": 74888, "start": 722.82, "end": 748.88, "text": "جميع الصفوف الصفرية تكون أسفل الصفوف الأخرى في المصفوفة نمر تلاتة الرقم", "tokens": [7435, 2304, 40228, 31767, 5172, 38688, 31767, 5172, 2288, 10632, 6055, 30544, 5551, 3794, 5172, 1211, 31767, 5172, 38688, 16247, 34740, 7578, 8978, 9673, 9381, 5172, 38688, 3660, 8717, 29973, 6055, 1211, 9307, 3660, 34892, 4587, 2304], "avg_logprob": -0.08470394403526657, "compression_ratio": 1.4719101123595506, "no_speech_prob": 0.0, "words": [{"start": 722.82, "end": 723.32, "word": "جميع", "probability": 0.8328450520833334}, {"start": 723.32, "end": 723.88, "word": " الصفوف", "probability": 0.9892578125}, {"start": 723.88, "end": 724.82, "word": " الصفرية", "probability": 0.9727783203125}, {"start": 724.82, "end": 726.76, "word": " تكون", 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"seek": 80575, "start": 779.59, "end": 805.75, "text": "يمين الرقم واحد اللي هو ال leading ال leading في الصفوف الأولى في الصفوف الأولى النقطة الرابعة", "tokens": [32640, 9957, 34892, 4587, 2304, 36764, 24401, 13672, 1829, 31439, 2423, 5775, 2423, 5775, 8978, 31767, 5172, 38688, 16247, 12610, 7578, 8978, 31767, 5172, 38688, 16247, 12610, 7578, 28239, 47432, 3660, 34892, 16758, 27884], "avg_logprob": -0.06941964030265808, "compression_ratio": 1.5643564356435644, "no_speech_prob": 0.0, "words": [{"start": 779.59, "end": 780.67, "word": "يمين", "probability": 0.870361328125}, {"start": 780.67, "end": 782.93, "word": " الرقم", "probability": 0.9493815104166666}, {"start": 782.93, "end": 785.39, "word": " واحد", "probability": 0.955810546875}, {"start": 785.39, "end": 786.57, "word": " اللي", "probability": 0.93212890625}, {"start": 786.57, "end": 787.59, "word": " هو", "probability": 0.98974609375}, {"start": 787.59, "end": 788.71, "word": " ال", "probability": 0.82958984375}, {"start": 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"والاخيرة العمود الذي يحتوي على الواحد اللي هو ال leading ال leading تكون بقية عناصره أصفرا", "tokens": [2407, 6027, 47283, 48923, 18863, 2304, 23328, 43527, 7251, 33753, 45865, 15844, 2423, 14407, 24401, 13672, 1829, 31439, 2423, 5775, 2423, 5775, 6055, 30544, 4724, 4587, 10632, 18871, 33546, 2288, 3224, 5551, 9381, 5172, 23557], "avg_logprob": -0.0985785625461075, "compression_ratio": 1.3130434782608695, "no_speech_prob": 0.0, "words": [{"start": 807.06, "end": 808.36, "word": "والاخيرة", "probability": 0.864990234375}, {"start": 808.36, "end": 810.18, "word": " العمود", "probability": 0.9599609375}, {"start": 810.18, "end": 812.3, "word": " الذي", "probability": 0.544921875}, {"start": 812.3, "end": 814.54, "word": " يحتوي", "probability": 0.9812825520833334}, {"start": 814.54, "end": 816.36, "word": " على", "probability": 0.89599609375}, {"start": 816.36, "end": 818.16, "word": " الواحد", "probability": 0.9853515625}, {"start": 818.16, "end": 819.06, "word": " اللي", "probability": 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is always consistent شو يعني consistent؟", "tokens": [9566, 1829, 3555, 8717, 47341, 3615, 2423, 28820, 10943, 13672, 1829, 1975, 5016, 8315, 9122, 2655, 3555, 8315, 3224, 11778, 1829, 35186, 4724, 8315, 2655, 4032, 8717, 5172, 16095, 28242, 9122, 19528, 3660, 8978, 3224, 5296, 28814, 1863, 11778, 23557, 14851, 8315, 6024, 48506, 34051, 16247, 2304, 12984, 37977, 9154, 9381, 49401, 15844, 9673, 30241, 20498, 9307, 13672, 1829, 1975, 3615, 9566, 7649, 995, 11296, 34105, 9673, 15040, 5016, 19913, 3660, 39894, 39648, 2423, 42632, 1185, 307, 1009, 8398, 13412, 2407, 37495, 22653, 8398, 22807], "avg_logprob": -0.16397165870943733, "compression_ratio": 1.5885167464114833, "no_speech_prob": 0.0, "words": [{"start": 852.25, "end": 853.15, "word": "طيب", "probability": 0.8523763020833334}, {"start": 853.15, "end": 853.73, "word": " نرجع", "probability": 0.8544921875}, {"start": 853.73, "end": 854.11, "word": " الكلام", "probability": 0.764892578125}, {"start": 854.11, "end": 854.25, "word": " 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"probability": 0.904296875}, {"start": 1385.72, "end": 1390.42, "word": " linear", "probability": 0.8564453125}, {"start": 1390.42, "end": 1391.38, "word": " systems", "probability": 0.95703125}], "temperature": 1.0}, {"id": 53, "seek": 142328, "start": 1396.32, "end": 1423.28, "text": "linear systems by reducing by reducing the matrix of the system the matrix of the system to", "tokens": [28263, 3652, 538, 12245, 538, 12245, 264, 8141, 295, 264, 1185, 264, 8141, 295, 264, 1185, 281], "avg_logprob": -0.3745659705665376, "compression_ratio": 1.6545454545454545, "no_speech_prob": 0.0, "words": [{"start": 1396.32, "end": 1396.82, "word": "linear", "probability": 0.07867431640625}, {"start": 1396.82, "end": 1397.58, "word": " systems", "probability": 0.7509765625}, {"start": 1397.58, "end": 1398.62, "word": " by", "probability": 0.58642578125}, {"start": 1398.62, "end": 1399.62, "word": " reducing", "probability": 0.880859375}, {"start": 1399.62, "end": 1401.14, "word": " by", 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15040, 2031, 17, 47525, 3224, 7251, 3794, 995, 45865, 8608, 6027, 3555, 36764, 24401, 37037, 8315, 2423, 2031, 18, 47525, 3224, 7251, 3794, 995, 45865, 2423, 14407, 24401, 307, 10344, 281, 264, 1185], "avg_logprob": -0.2384207583963871, "compression_ratio": 1.4244604316546763, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2272.2999999999997, "end": 2273.7, "word": "system", "probability": 0.11376953125}, {"start": 2273.7, "end": 2275.1, "word": " الـ", "probability": 0.4561767578125}, {"start": 2275.1, "end": 2275.54, "word": " domain", "probability": 0.21875}, {"start": 2275.54, "end": 2276.02, "word": " هنا", "probability": 0.666015625}, {"start": 2276.02, "end": 2277.26, "word": " x1", "probability": 0.4971923828125}, {"start": 2277.26, "end": 2278.12, "word": " بدها", "probability": 0.626220703125}, {"start": 2278.12, "end": 2278.76, "word": " تساوي", "probability": 0.9088134765625}, {"start": 2278.76, "end": 2279.12, "word": " 2", "probability": 0.82568359375}, {"start": 2279.12, "end": 2280.32, "word": " وهنا", "probability": 0.80029296875}, {"start": 2280.32, "end": 2281.16, "word": " ماعنديش", "probability": 0.925}, {"start": 2281.16, "end": 2281.54, "word": " إلا", "probability": 0.800537109375}, {"start": 2281.54, "end": 2282.94, "word": " x2", "probability": 0.888427734375}, {"start": 2282.94, "end": 2283.72, "word": " بده", "probability": 0.8896484375}, {"start": 2283.72, "end": 2284.16, "word": " يساوي", "probability": 0.9498291015625}, {"start": 2284.16, "end": 2284.78, "word": " سالب", "probability": 0.7626953125}, {"start": 2284.78, "end": 2285.28, "word": " واحد", "probability": 0.845703125}, {"start": 2285.28, "end": 2286.1, "word": " وهنا", "probability": 0.88720703125}, {"start": 2286.1, "end": 2286.32, "word": " ال", "probability": 0.67822265625}, {"start": 2286.32, "end": 2287.4, "word": " x3", "probability": 0.788818359375}, {"start": 2287.4, "end": 2288.3, "word": " بده", "probability": 0.970947265625}, {"start": 2288.3, "end": 2288.82, "word": " يساوي", "probability": 0.983154296875}, {"start": 2288.82, "end": 2289.42, "word": " الواحد", "probability": 0.8816731770833334}, {"start": 2289.42, "end": 2290.46, "word": " is", "probability": 0.79052734375}, {"start": 2290.46, "end": 2292.32, "word": " equivalent", "probability": 0.93017578125}, {"start": 2292.32, "end": 2294.72, "word": " to", "probability": 0.9521484375}, {"start": 2294.72, "end": 2295.26, "word": " the", "probability": 0.904296875}, {"start": 2295.26, "end": 2298.22, "word": " system", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 90, "seek": 232501, "start": 2300.53, "end": 2325.01, "text": "يبقى هذا بكافئة system star معناته الحل تبع هذا هو الحل تبع من؟ تبع ال system star فبروح و بقوله الآن the solution of the system star is لحظة شوية solution", "tokens": [1829, 3555, 4587, 7578, 23758, 4724, 4117, 31845, 19986, 3660, 1185, 3543, 20449, 8315, 47395, 21542, 1211, 6055, 3555, 3615, 23758, 31439, 21542, 1211, 6055, 3555, 3615, 9154, 22807, 6055, 3555, 3615, 2423, 1185, 3543, 6156, 26890, 2407, 5016, 4032, 4724, 39648, 3224, 6024, 48506, 264, 3827, 295, 264, 1185, 3543, 307, 5296, 5016, 19913, 3660, 13412, 2407, 10632, 3827], "avg_logprob": -0.33657786298970704, "compression_ratio": 1.5342465753424657, "no_speech_prob": 0.0, "words": [{"start": 2300.53, "end": 2301.69, "word": "يبقى", "probability": 0.6846694946289062}, {"start": 2301.69, "end": 2301.95, "word": " هذا", "probability": 0.3173828125}, {"start": 2301.95, "end": 2302.71, "word": " بكافئة", "probability": 0.757373046875}, {"start": 2302.71, "end": 2303.09, "word": " system", "probability": 0.417236328125}, {"start": 2303.09, "end": 2303.67, "word": " star", "probability": 0.216796875}, {"start": 2303.67, "end": 2304.63, "word": " معناته", "probability": 0.7097981770833334}, {"start": 2304.63, "end": 2305.31, "word": " الحل", "probability": 0.781982421875}, {"start": 2305.31, "end": 2305.77, "word": " تبع", "probability": 0.8811848958333334}, 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"text": "of the system star is x1 و x2 و x3 يساوي اتنين سالب واحد واحد اتنين و سالب واحد واحد مين اللي بتسأل؟ ايوة خلت صحيح", "tokens": [2670, 264, 1185, 3543, 307, 2031, 16, 4032, 2031, 17, 4032, 2031, 18, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 1975, 2655, 1863, 9957, 4032, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 3714, 9957, 13672, 1829, 39894, 3794, 10721, 1211, 22807, 1975, 1829, 2407, 3660, 16490, 1211, 2655, 20328, 5016, 1829, 5016], "avg_logprob": -0.2651127049180328, "compression_ratio": 1.4285714285714286, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2328.92, "end": 2329.46, "word": "of", "probability": 0.10552978515625}, {"start": 2329.46, "end": 2331.12, "word": " the", "probability": 0.86474609375}, {"start": 2331.12, "end": 2332.98, "word": " system", "probability": 0.958984375}, {"start": 2332.98, "end": 2335.4, "word": " star", "probability": 0.17919921875}, {"start": 2335.4, "end": 2336.44, "word": " is", "probability": 0.7431640625}, {"start": 2336.44, "end": 2338.06, "word": " x1", "probability": 0.674072265625}, {"start": 2338.06, "end": 2338.72, "word": " و", "probability": 0.5009765625}, {"start": 2338.72, "end": 2339.64, "word": " x2", "probability": 0.7783203125}, {"start": 2339.64, "end": 2340.3, "word": " و", "probability": 0.9794921875}, {"start": 2340.3, "end": 2341.4, "word": " x3", "probability": 0.959228515625}, {"start": 2341.4, "end": 2342.76, "word": " يساوي", "probability": 0.79754638671875}, {"start": 2342.76, "end": 2343.62, "word": " اتنين", "probability": 0.81011962890625}, {"start": 2343.62, "end": 2344.1, "word": " سالب", "probability": 0.84765625}, {"start": 2344.1, "end": 2344.42, "word": " واحد", "probability": 0.988037109375}, {"start": 2344.42, "end": 2344.82, "word": " واحد", "probability": 0.9619140625}, {"start": 2344.82, "end": 2345.92, "word": " اتنين", "probability": 0.9654541015625}, {"start": 2345.92, "end": 2346.54, "word": " و", 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لسه في البداية تستعيدليش في حد بتسأل تاني طب نعطي كمان مثال المثال رقم تلاتة بس قبل المثال رقم تلاتة", "tokens": [1211, 15042, 31439, 23032, 6027, 3615, 31767, 5172, 28242, 5551, 9381, 5172, 9640, 13672, 1829, 6055, 33753, 19446, 28543, 2288, 8592, 1975, 2655, 5016, 31747, 49429, 11331, 26108, 3660, 5296, 15042, 7251, 9566, 1211, 3615, 28242, 5551, 9381, 5172, 9640, 7251, 4587, 5172, 4587, 9122, 15042, 31439, 6225, 7435, 1829, 3555, 5296, 4117, 21542, 9957, 4724, 3794, 5551, 9381, 49628, 1975, 5016, 8315, 5296, 3794, 3224, 8978, 29739, 28259, 10632, 6055, 14851, 3615, 25708, 20292, 8592, 8978, 11331, 3215, 39894, 3794, 10721, 1211, 6055, 7649, 1829, 23032, 3555, 8717, 3615, 9566, 1829, 9122, 2304, 7649, 50113, 6027, 9673, 12984, 6027, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 4724, 3794, 12174, 36150, 9673, 12984, 6027, 12602, 4587, 2304, 6055, 1211, 9307, 3660], "avg_logprob": -0.19454405053717191, "compression_ratio": 1.9492385786802031, "no_speech_prob": 5.960464477539063e-08, 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كمان", "probability": 0.8974609375}, {"start": 2374.17, "end": 2374.73, "word": " مثال", "probability": 0.889892578125}, {"start": 2374.73, "end": 2375.33, "word": " المثال", "probability": 0.74853515625}, {"start": 2375.33, "end": 2375.91, "word": " رقم", "probability": 0.9840494791666666}, {"start": 2375.91, "end": 2377.53, "word": " تلاتة", "probability": 0.8599853515625}, {"start": 2377.53, "end": 2380.99, "word": " بس", "probability": 0.98583984375}, {"start": 2380.99, "end": 2381.25, "word": " قبل", "probability": 0.987060546875}, {"start": 2381.25, "end": 2381.73, "word": " المثال", "probability": 0.9931640625}, {"start": 2381.73, "end": 2382.21, "word": " رقم", "probability": 0.95556640625}, {"start": 2382.21, "end": 2382.83, "word": " تلاتة", "probability": 0.982666015625}], "temperature": 1.0}, {"id": 93, "seek": 240565, "start": 2383.31, "end": 2405.65, "text": "ماذا رأيك في المثال هذا؟ إذا طلعنا two systems are equivalent وبالتالي الحل هذا هو حل ال system الأولاني يبقى ال 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3714, 6027, 3660, 8717, 11296, 10632, 9154, 21542, 1211, 12610, 46811, 10943, 23032, 1829, 3555, 16490, 1211, 9957, 1829, 5551, 3794, 10721, 1211, 21136, 33604, 6027, 16712, 6027, 5172, 1975, 5016, 8315, 19446, 24793, 1211, 1863, 33599, 5296, 3794, 3224], "avg_logprob": -0.24314903846153846, "compression_ratio": 1.5031446540880504, "no_speech_prob": 0.0, "words": [{"start": 2854.76, "end": 2855.08, "word": "أو", "probability": 0.58221435546875}, {"start": 2855.08, "end": 2855.32, "word": " this", "probability": 0.438720703125}, {"start": 2855.32, "end": 2856.58, "word": " represent", "probability": 0.3671875}, {"start": 2856.58, "end": 2858.0, "word": " هذا", "probability": 0.65087890625}, {"start": 2858.0, "end": 2858.9, "word": " يمثل", "probability": 0.9661865234375}, {"start": 2858.9, "end": 2859.92, "word": " this", "probability": 0.432373046875}, {"start": 2859.92, "end": 2861.7, "word": " represent", "probability": 0.71875}, {"start": 2861.7, "end": 2865.02, "word": " infinite", "probability": 0.57861328125}, {"start": 2865.02, "end": 2867.84, "word": " number", "probability": 0.96533203125}, {"start": 2867.84, "end": 2870.62, "word": " of", "probability": 0.93701171875}, {"start": 2870.62, "end": 2872.6, "word": " solutions", "probability": 0.931640625}, {"start": 2872.6, "end": 2873.7, "word": " يبقى", "probability": 0.916015625}, {"start": 2873.7, "end": 2874.04, "word": " هذا", "probability": 0.9365234375}, {"start": 2874.04, "end": 2874.96, "word": " يمثلي", "probability": 0.82781982421875}, {"start": 2874.96, "end": 2875.56, "word": " مالة", "probability": 0.7361653645833334}, {"start": 2875.56, "end": 2876.24, "word": " نهاية", "probability": 0.8082682291666666}, {"start": 2876.24, "end": 2876.9, "word": " من", "probability": 0.990234375}, {"start": 2876.9, "end": 2877.96, "word": " الحلول", "probability": 0.9601236979166666}, {"start": 2877.96, "end": 2879.0, "word": " تمام", "probability": 0.7890625}, {"start": 2879.0, "end": 2880.36, "word": " طيب", "probability": 0.7452392578125}, {"start": 2880.36, "end": 2880.88, "word": " خليني", "probability": 0.74920654296875}, {"start": 2880.88, "end": 2881.16, "word": " أسأل", "probability": 0.8448486328125}, {"start": 2881.16, "end": 2881.58, "word": " السؤال", "probability": 0.9755859375}, {"start": 2881.58, "end": 2881.98, "word": " التالف", "probability": 0.7977701822916666}, {"start": 2881.98, "end": 2882.16, "word": " احنا", "probability": 0.904296875}, {"start": 2882.16, "end": 2882.98, "word": " ماكملناش", "probability": 0.85654296875}, {"start": 2882.98, "end": 2883.5, "word": " لسه", "probability": 0.986328125}], "temperature": 1.0}, {"id": 115, "seek": 290351, "start": 2884.21, "end": 2903.51, "text": "خلّيني أسأل السؤال التالي هل هذا ال system consistent و لا inconsistent؟ Consistent لأنه يحتوي على مالة نهاية من الحلول، لا يزال هناك المزيد من الأمثلة إلى المحاضرة القادمة إن شاء الله", "tokens": [9778, 1211, 11703, 9957, 1829, 5551, 3794, 10721, 1211, 21136, 33604, 6027, 16712, 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0.9073893229166666}, {"start": 2896.33, "end": 2896.69, "word": " من", "probability": 0.97705078125}, {"start": 2896.69, "end": 2897.77, "word": " الحلول،", "probability": 0.85162353515625}, {"start": 2897.77, "end": 2897.91, "word": " لا", "probability": 0.625}, {"start": 2897.91, "end": 2898.29, "word": " يزال", "probability": 0.990234375}, {"start": 2898.29, "end": 2898.75, "word": " هناك", "probability": 0.987060546875}, {"start": 2898.75, "end": 2899.51, "word": " المزيد", "probability": 0.9920247395833334}, {"start": 2899.51, "end": 2899.81, "word": " من", "probability": 0.98095703125}, {"start": 2899.81, "end": 2900.63, "word": " الأمثلة", "probability": 0.9847412109375}, {"start": 2900.63, "end": 2900.95, "word": " إلى", "probability": 0.794921875}, {"start": 2900.95, "end": 2901.69, "word": " المحاضرة", "probability": 0.9881591796875}, {"start": 2901.69, "end": 2902.37, "word": " القادمة", "probability": 0.9943033854166666}, {"start": 2902.37, "end": 2902.71, "word": " إن", "probability": 0.7333984375}, {"start": 2902.71, "end": 2903.19, "word": " شاء", "probability": 0.981689453125}, {"start": 2903.19, "end": 2903.51, "word": " الله", "probability": 0.96044921875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2904.77, "duration_after_vad": 2735.4281249999935}
\ No newline at end of file
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@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4047, "start": 20.96, "end": 40.48, "text": "بسم الله الرحمن الرحيم ابتدأنا المرة الماضية بال eigenvalues وال eigenvectors عرفنا ال eigenvalue وال eigenvector واخدنا على ذلك ثلاثة أمثلة ولاحظنا أن ال eigenvalues قد تكون real وقد تكون complex", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 48127, 2655, 3215, 10721, 8315, 9673, 25720, 9673, 46958, 10632, 20666, 10446, 46033, 16070, 10446, 303, 5547, 6225, 28480, 8315, 2423, 10446, 29155, 16070, 10446, 303, 1672, 4032, 47283, 3215, 8315, 15844, 29910, 23275, 38637, 1211, 5718, 104, 3660, 5551, 2304, 12984, 37977, 4032, 15040, 5016, 19913, 8315, 14739, 2423, 10446, 46033, 12174, 3215, 6055, 30544, 957, 4032, 28543, 6055, 30544, 3997], "avg_logprob": -0.1609157942649391, "compression_ratio": 1.7411764705882353, "no_speech_prob": 0.0, "words": [{"start": 20.96, "end": 21.26, "word": "بسم", "probability": 0.83203125}, {"start": 21.26, "end": 21.52, "word": " الله", "probability": 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0.91455078125}, {"start": 29.98, "end": 30.2, "word": " وال", "probability": 0.853515625}, {"start": 30.2, "end": 31.02, "word": " eigenvector", "probability": 0.9044596354166666}, {"start": 31.02, "end": 32.02, "word": " واخدنا", "probability": 0.8846435546875}, {"start": 32.02, "end": 32.2, "word": " على", "probability": 0.86865234375}, {"start": 32.2, "end": 32.66, "word": " ذلك", "probability": 0.992919921875}, {"start": 32.66, "end": 33.46, "word": " ثلاثة", "probability": 0.96943359375}, {"start": 33.46, "end": 34.1, "word": " أمثلة", "probability": 0.94091796875}, {"start": 34.1, "end": 35.52, "word": " ولاحظنا", "probability": 0.91123046875}, {"start": 35.52, "end": 35.98, "word": " أن", "probability": 0.462158203125}, {"start": 35.98, "end": 36.18, "word": " ال", "probability": 0.93701171875}, {"start": 36.18, "end": 37.08, "word": " eigenvalues", "probability": 0.94580078125}, {"start": 37.08, "end": 37.5, "word": " قد", "probability": 0.99267578125}, {"start": 37.5, "end": 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الأول ال eigenvalues و ال eigenvectors ل ال matrix A المطلوب الثاني قال هاتلي basis لكل eigenvector space بطلع عندنا بنقوله بسيطة تعالى نجيب اللي في الأول ال eigenvalues و ال eigenvectors اللي عندنا فبنجيب و نقول solution", "tokens": [1829, 3555, 4587, 7578, 9673, 12984, 6027, 4724, 33911, 2655, 43042, 16472, 3224, 18871, 16254, 9673, 9381, 5172, 38688, 3660, 316, 30767, 1829, 19446, 16472, 2655, 14407, 13412, 995, 33911, 9957, 4032, 9566, 46152, 16472, 1829, 9673, 9566, 1211, 37746, 16247, 12610, 2423, 10446, 46033, 4032, 2423, 10446, 303, 5547, 5296, 2423, 8141, 316, 9673, 9566, 1211, 37746, 6024, 104, 7649, 1829, 50239, 8032, 9307, 20292, 5143, 5296, 28820, 10446, 303, 1672, 1901, 4724, 9566, 1211, 3615, 43242, 8315, 44945, 39648, 3224, 4724, 3794, 1829, 9566, 3660, 37279, 6027, 7578, 8717, 7435, 1829, 3555, 13672, 1829, 8978, 16247, 12610, 2423, 10446, 46033, 4032, 2423, 10446, 303, 5547, 13672, 1829, 43242, 8315, 6156, 3555, 1863, 7435, 1829, 3555, 4032, 8717, 39648, 3827], 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ناقص واحد ناقص واحد هنا واحد فقط هنا ال land ناقص واحد وهنا ناقص واحد الصف التالت الصف التالت اللي هو واحد وهنا سالب واحد", "tokens": [2407, 16, 28239, 31371, 7435, 3660, 9122, 6027, 2655, 6027, 1829, 7251, 3555, 4587, 7578, 2423, 2117, 9122, 15042, 39896, 34105, 8717, 995, 4587, 9381, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 34105, 36764, 24401, 6156, 47432, 34105, 2423, 2117, 8717, 995, 4587, 9381, 36764, 24401, 37037, 8315, 8717, 995, 4587, 9381, 36764, 24401, 31767, 5172, 16712, 6027, 2655, 31767, 5172, 16712, 6027, 2655, 13672, 1829, 31439, 36764, 24401, 37037, 8315, 8608, 6027, 3555, 36764, 24401], "avg_logprob": -0.12650240403719437, "compression_ratio": 2.234375, "no_speech_prob": 0.0, "words": [{"start": 116.3, "end": 117.04, "word": "و1", "probability": 0.3875732421875}, {"start": 117.04, "end": 118.16, "word": " النتيجة", "probability": 0.8583984375}, {"start": 118.16, "end": 119.1, "word": " كالتالي", "probability": 0.83408203125}, {"start": 119.1, "end": 120.18, 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{"start": 614.38, "end": 615.08, "word": " لو", "probability": 0.8681640625}, {"start": 615.08, "end": 615.84, "word": " كانت", "probability": 0.94921875}, {"start": 615.84, "end": 616.52, "word": " مثلا", "probability": 0.956298828125}, {"start": 616.52, "end": 617.38, "word": " X3", "probability": 0.569580078125}, {"start": 617.38, "end": 617.76, "word": " بيه", "probability": 0.6387939453125}, {"start": 617.76, "end": 618.04, "word": " او", "probability": 0.821044921875}, {"start": 618.04, "end": 618.72, "word": " X2", "probability": 0.989990234375}, {"start": 618.72, "end": 619.1, "word": " بيه", "probability": 0.9915364583333334}, {"start": 619.1, "end": 619.76, "word": " سيان", "probability": 0.5779622395833334}, {"start": 619.76, "end": 620.66, "word": " يبقى", "probability": 0.9443359375}, {"start": 620.66, "end": 621.0, "word": " باجي", "probability": 0.9016927083333334}, {"start": 621.0, "end": 621.44, "word": " بقول", "probability": 0.950927734375}, {"start": 621.44, "end": 622.42, "word": " هنا", "probability": 0.97265625}, {"start": 622.42, "end": 623.1, "word": " if", "probability": 0.3603515625}, {"start": 623.1, "end": 624.2, "word": " ال", "probability": 0.49755859375}, {"start": 624.2, "end": 625.58, "word": " X3", "probability": 0.864501953125}, {"start": 625.58, "end": 626.14, "word": " بده", "probability": 0.629638671875}, {"start": 626.14, "end": 626.54, "word": " يسوي", "probability": 0.7525227864583334}, {"start": 626.54, "end": 627.04, "word": " ايه", "probability": 0.7649739583333334}, {"start": 627.04, "end": 627.96, "word": " then", "probability": 0.76953125}, {"start": 627.96, "end": 629.78, "word": " the", "probability": 0.8271484375}, {"start": 629.78, "end": 631.58, "word": " eigen", "probability": 0.76318359375}, {"start": 631.58, "end": 634.14, "word": " vectors", "probability": 0.58544921875}], "temperature": 1.0}, {"id": 27, "seek": 63949, "start": 635.83, "end": 639.49, "text": "يبقى الـ eigenvectors بتكون على الشكل التالي", "tokens": [1829, 3555, 4587, 7578, 2423, 39184, 10446, 303, 5547, 39894, 30544, 15844, 25124, 28820, 16712, 6027, 1829], "avg_logprob": -0.3268229116996129, "compression_ratio": 1.044776119402985, "no_speech_prob": 0.0, "words": [{"start": 635.83, "end": 636.45, "word": "يبقى", "probability": 0.815673828125}, {"start": 636.45, "end": 636.57, "word": " الـ", "probability": 0.534423828125}, {"start": 636.57, "end": 637.37, "word": " eigenvectors", "probability": 0.7112630208333334}, {"start": 637.37, "end": 637.87, "word": " بتكون", "probability": 0.6605224609375}, {"start": 637.87, "end": 638.11, "word": " على", "probability": 0.685546875}, {"start": 638.11, "end": 638.71, "word": " الشكل", "probability": 0.96337890625}, {"start": 638.71, "end": 639.49, "word": " التالي", "probability": 0.9861653645833334}], "temperature": 1.0}, {"id": 28, "seek": 66874, "start": 649.18, "end": 668.74, "text": "يبقى x1 أطلع عنها بالـ zero وهذا الـ zero و x2 يبقى ناقص a و a بالشكل هذا أو a في zero سالب واحد واحد بالشكل اللي عندنا هنا", "tokens": [1829, 3555, 4587, 7578, 2031, 16, 5551, 9566, 1211, 3615, 18871, 11296, 20666, 39184, 4018, 37037, 15730, 2423, 39184, 4018, 4032, 2031, 17, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 257, 4032, 257, 20666, 8592, 28820, 23758, 34051, 257, 8978, 4018, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105], "avg_logprob": -0.41810343491620033, "compression_ratio": 1.5426356589147288, "no_speech_prob": 0.0, "words": [{"start": 649.18, "end": 649.7, "word": "يبقى", "probability": 0.81427001953125}, {"start": 649.7, "end": 650.18, "word": " x1", "probability": 0.54150390625}, {"start": 650.18, "end": 650.56, "word": " أطلع", "probability": 0.477447509765625}, {"start": 650.56, "end": 650.92, "word": " عنها", "probability": 0.767822265625}, {"start": 650.92, "end": 651.12, "word": " بالـ", "probability": 0.4686279296875}, {"start": 651.12, "end": 651.38, "word": " zero", "probability": 0.2802734375}, 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eigenvectors اللي أصمصوه في ايه؟ بعدين جالي هاتلي basis for each eigenvector space يبقى نمرأ بإيه؟ السؤال هو مش هذا كل ال eigenvectors على الشكل اللي قدامي هذا يا بنات؟ يبقى مين اللي بيجيب ال eigenvectors كلها؟", "tokens": [9566, 1829, 3555, 23758, 28242, 3224, 11331, 49975, 6024, 48506, 31439, 9673, 9566, 1211, 37746, 1975, 1829, 3224, 9154, 9673, 12984, 1211, 22807, 10874, 6027, 1829, 8032, 9307, 20292, 2423, 10446, 46033, 4032, 2423, 10446, 303, 5547, 13672, 1829, 5551, 9381, 2304, 9381, 2407, 3224, 8978, 1975, 1829, 3224, 22807, 39182, 9957, 10874, 6027, 1829, 8032, 9307, 20292, 5143, 337, 1184, 10446, 303, 1672, 1901, 7251, 3555, 4587, 7578, 8717, 29973, 10721, 4724, 28814, 1829, 3224, 22807, 21136, 33604, 6027, 31439, 37893, 23758, 28242, 2423, 10446, 303, 5547, 15844, 25124, 28820, 13672, 1829, 12174, 3215, 10943, 1829, 23758, 35186, 4724, 8315, 2655, 22807, 7251, 3555, 4587, 7578, 3714, 9957, 13672, 1829, 4724, 1829, 7435, 1829, 3555, 2423, 10446, 303, 5547, 28242, 11296, 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similar", "probability": 0.8857421875}, {"start": 2433.09, "end": 2435.51, "word": " to", "probability": 0.96337890625}, {"start": 2435.51, "end": 2436.37, "word": " be", "probability": 0.55810546875}, {"start": 2436.37, "end": 2437.49, "word": " هدا", "probability": 0.3228759765625}, {"start": 2437.49, "end": 2438.07, "word": " معناته", "probability": 0.9363606770833334}, {"start": 2438.07, "end": 2438.85, "word": " ايش؟", "probability": 0.68609619140625}, {"start": 2438.85, "end": 2439.31, "word": " there", "probability": 0.77001953125}, {"start": 2439.31, "end": 2440.11, "word": " exist", "probability": 0.5810546875}, {"start": 2440.11, "end": 2440.99, "word": " a", "probability": 0.85009765625}, {"start": 2440.99, "end": 2442.07, "word": " there", "probability": 0.350341796875}, {"start": 2442.07, "end": 2442.73, "word": " exist", "probability": 0.96435546875}, {"start": 2442.73, "end": 2443.23, "word": " a", "probability": 0.9775390625}, {"start": 2443.23, "end": 2443.99, "word": " non", "probability": 0.88330078125}, {"start": 2443.99, "end": 2445.71, "word": " singular", "probability": 0.7783203125}, {"start": 2445.71, "end": 2449.21, "word": " matrix", "probability": 0.9599609375}, {"start": 2449.21, "end": 2453.07, "word": " K", "probability": 0.501953125}, {"start": 2453.07, "end": 2454.03, "word": " such", "probability": 0.9462890625}, {"start": 2454.03, "end": 2454.73, "word": " that", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 104, "seek": 246311, "start": 2455.95, "end": 2463.11, "text": "بحيث ان الـ B بدي ساوي K inverse AK", "tokens": [3555, 5016, 1829, 12984, 16472, 2423, 39184, 363, 4724, 16254, 8608, 995, 45865, 591, 17340, 24789], "avg_logprob": -0.6957720588235294, "compression_ratio": 0.9107142857142857, "no_speech_prob": 0.0, "words": [{"start": 2455.95, "end": 2456.69, "word": "بحيث", "probability": 0.81805419921875}, {"start": 2456.69, "end": 2457.11, "word": " ان", "probability": 0.52099609375}, {"start": 2457.11, "end": 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الاولى inverse والتانية بدون مظبوط لكن ك هادى بقدر اكتبها ك inverse inverse صح ولا لأ مش المصفوفة ايه تسوى a inverse inverse يبقى بقدر اكتب هادي على الشكل التالى ان ال a يسوى ك inverse", "tokens": [3555, 6027, 8592, 28820, 23758, 5296, 10721, 1975, 8315, 4724, 16254, 42963, 12610, 7578, 17340, 16070, 2655, 7649, 10632, 47525, 11536, 3714, 19913, 3555, 2407, 9566, 44381, 9122, 8032, 18513, 7578, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 9122, 17340, 17340, 20328, 5016, 49429, 5296, 10721, 37893, 9673, 9381, 5172, 38688, 3660, 1975, 1829, 3224, 6055, 3794, 2407, 7578, 257, 17340, 17340, 7251, 3555, 4587, 7578, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 8032, 995, 16254, 15844, 25124, 28820, 16712, 6027, 7578, 16472, 2423, 257, 7251, 3794, 2407, 7578, 9122, 17340], "avg_logprob": -0.2511760752688172, "compression_ratio": 1.8531073446327684, "no_speech_prob": 0.0, "words": [{"start": 2534.69, "end": 2535.27, "word": "بالشكل", "probability": 0.8223876953125}, {"start": 2535.27, 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"end": 2609.46, "word": " مثال", "probability": 0.978271484375}, {"start": 2609.46, "end": 2610.16, "word": " توضيحي", "probability": 0.94453125}, {"start": 2610.16, "end": 2610.36, "word": " على", "probability": 0.8427734375}, {"start": 2610.36, "end": 2610.96, "word": " ذلك", "probability": 0.994384765625}, {"start": 2610.96, "end": 2612.06, "word": " يبقى", "probability": 0.984375}, {"start": 2612.06, "end": 2612.78, "word": " example", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 111, "seek": 264229, "start": 2615.25, "end": 2642.29, "text": "المثال بيقول let المصوفة a تساوي واحد واحد سلبي اتنين اربعة and المصوفة k تساوي واحد واحد واحد اتنين find a matrix بي find a matrix", "tokens": [45340, 12984, 6027, 4724, 1829, 39648, 718, 9673, 9381, 38688, 3660, 257, 6055, 3794, 995, 45865, 36764, 24401, 36764, 24401, 8608, 1211, 21292, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 293, 9673, 9381, 38688, 3660, 350, 6055, 3794, 995, 45865, 36764, 24401, 36764, 24401, 36764, 24401, 1975, 2655, 1863, 9957, 915, 257, 8141, 4724, 1829, 915, 257, 8141], "avg_logprob": -0.20272774969117116, "compression_ratio": 1.6967213114754098, "no_speech_prob": 0.0, "words": [{"start": 2615.25, "end": 2615.95, "word": "المثال", "probability": 0.9111328125}, {"start": 2615.95, "end": 2616.59, "word": " بيقول", "probability": 0.7963053385416666}, {"start": 2616.59, "end": 2617.57, "word": " let", "probability": 0.3681640625}, {"start": 2617.57, "end": 2619.97, "word": " المصوفة", "probability": 0.80181884765625}, {"start": 2619.97, "end": 2620.33, "word": " a", "probability": 0.32177734375}, {"start": 2620.33, "end": 2621.29, "word": " تساوي", "probability": 0.8919677734375}, {"start": 2621.29, "end": 2623.31, "word": " واحد", "probability": 0.63623046875}, {"start": 2623.31, "end": 2623.85, "word": " واحد", "probability": 0.921875}, {"start": 2623.85, "end": 2624.49, "word": " سلبي", "probability": 0.6949462890625}, {"start": 2624.49, "end": 2625.21, "word": " اتنين", "probability": 0.9681396484375}, {"start": 2625.21, "end": 2626.15, "word": " اربعة", "probability": 0.7547200520833334}, {"start": 2626.15, "end": 2627.35, "word": " and", "probability": 0.7138671875}, {"start": 2627.35, "end": 2629.87, "word": " المصوفة", "probability": 0.974365234375}, {"start": 2629.87, "end": 2630.29, "word": " k", "probability": 0.58837890625}, {"start": 2630.29, "end": 2631.75, "word": " تساوي", "probability": 0.9775390625}, {"start": 2631.75, "end": 2633.41, "word": " واحد", "probability": 0.984375}, {"start": 2633.41, "end": 2634.27, "word": " واحد", "probability": 0.982421875}, {"start": 2634.27, "end": 2635.19, "word": " واحد", "probability": 0.91943359375}, {"start": 2635.19, "end": 2636.41, "word": " اتنين", "probability": 0.9700927734375}, {"start": 2636.41, "end": 2637.55, "word": " find", "probability": 0.830078125}, {"start": 2637.55, "end": 2637.81, "word": " a", "probability": 0.97314453125}, {"start": 2637.81, "end": 2638.41, "word": " matrix", "probability": 0.96240234375}, {"start": 2638.41, "end": 2638.83, "word": " بي", "probability": 0.604736328125}, {"start": 2638.83, "end": 2639.85, "word": " find", "probability": 0.8779296875}, {"start": 2639.85, "end": 2641.39, "word": " a", "probability": 0.9677734375}, {"start": 2641.39, "end": 2642.29, "word": " matrix", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 112, "seek": 266435, "start": 2645.39, "end": 2664.35, "text": "ب such that ال a is similar to b يعني similar to b ماشي اقوله solution", "tokens": [3555, 1270, 300, 2423, 257, 307, 2531, 281, 272, 37495, 22653, 2531, 281, 272, 3714, 33599, 1829, 1975, 39648, 3224, 3827], "avg_logprob": -0.5241477191448212, "compression_ratio": 1.0617283950617284, "no_speech_prob": 0.0, "words": [{"start": 2645.39, "end": 2646.79, "word": "ب", "probability": 0.458740234375}, {"start": 2646.79, "end": 2648.19, "word": " such", "probability": 0.2147216796875}, {"start": 2648.19, "end": 2649.25, "word": " that", "probability": 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{"start": 2663.75, "end": 2664.35, "word": " solution", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 113, "seek": 267750, "start": 2667.92, "end": 2677.5, "text": "يبقى يعطيني مصحوفة A ومصحوفة K وقال هاتلي matrix B بحيث ال A تبقى similar to B", "tokens": [1829, 3555, 4587, 7578, 37495, 9566, 1829, 22653, 3714, 9381, 5016, 38688, 3660, 316, 4032, 2304, 9381, 5016, 38688, 3660, 591, 4032, 4587, 6027, 8032, 9307, 20292, 8141, 363, 4724, 5016, 1829, 12984, 2423, 316, 6055, 3555, 4587, 7578, 2531, 281, 363], "avg_logprob": -0.38880814092103827, "compression_ratio": 1.1538461538461537, "no_speech_prob": 0.0, "words": [{"start": 2667.92, "end": 2668.36, "word": "يبقى", "probability": 0.66900634765625}, {"start": 2668.36, "end": 2668.94, "word": " يعطيني", "probability": 0.5395355224609375}, {"start": 2668.94, "end": 2669.72, "word": " مصحوفة", "probability": 0.7903076171875}, {"start": 2669.72, "end": 2670.06, "word": " A", "probability": 0.46923828125}, {"start": 2670.06, "end": 2671.96, "word": " ومصحوفة", "probability": 0.8210042317708334}, {"start": 2671.96, "end": 2672.4, "word": " K", "probability": 0.93310546875}, {"start": 2672.4, "end": 2673.28, "word": " وقال", "probability": 0.7119140625}, {"start": 2673.28, "end": 2673.84, "word": " هاتلي", "probability": 0.6861979166666666}, {"start": 2673.84, "end": 2674.54, "word": " matrix", "probability": 0.6796875}, {"start": 2674.54, "end": 2674.86, "word": " B", "probability": 0.73681640625}, {"start": 2674.86, "end": 2675.46, "word": " بحيث", "probability": 0.9173583984375}, {"start": 2675.46, "end": 2675.66, "word": " ال", "probability": 0.77294921875}, {"start": 2675.66, "end": 2675.88, "word": " A", "probability": 0.71337890625}, {"start": 2675.88, "end": 2676.44, "word": " تبقى", "probability": 0.950439453125}, {"start": 2676.44, "end": 2676.86, "word": " similar", "probability": 0.7236328125}, {"start": 2676.86, "end": 2677.22, "word": " to", "probability": 0.86572265625}, {"start": 2677.22, "end": 2677.5, "word": " B", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 114, "seek": 269822, "start": 2691.96, "end": 2698.22, "text": "أول خطوة باخد من ال determinant لل K", "tokens": [10721, 12610, 16490, 9566, 2407, 3660, 4724, 47283, 3215, 9154, 2423, 41296, 24976, 591], "avg_logprob": -0.525781226158142, "compression_ratio": 0.8833333333333333, "no_speech_prob": 0.0, "words": [{"start": 2691.96, "end": 2693.36, "word": "أول", "probability": 0.28192138671875}, {"start": 2693.36, "end": 2694.76, "word": " خطوة", "probability": 0.9771728515625}, {"start": 2694.76, "end": 2695.3, "word": " باخد", "probability": 0.679443359375}, {"start": 2695.3, "end": 2695.54, "word": " من", "probability": 0.86669921875}, {"start": 2695.54, "end": 2695.72, "word": " ال", "probability": 0.5185546875}, {"start": 2695.72, "end": 2696.7, "word": " determinant", "probability": 0.431640625}, {"start": 2696.7, "end": 2697.7, "word": " لل", "probability": 0.32373046875}, {"start": 2697.7, "end": 2698.22, "word": " K", "probability": 0.439208984375}], "temperature": 1.0}, {"id": 115, "seek": 272503, "start": 2698.97, "end": 2725.03, "text": "بدي أخد determinant للـ K أشوفه كده بده يساوي يبقى واحد واحد اتنين يبقى اتنين ناقص يساوي واحد لا يساوي ال zero يبقى هنا ال K هذه ال K is non singular", "tokens": [3555, 16254, 5551, 9778, 3215, 41296, 24976, 39184, 591, 5551, 8592, 38688, 3224, 9122, 3215, 3224, 47525, 3224, 7251, 3794, 995, 45865, 7251, 3555, 4587, 7578, 36764, 24401, 36764, 24401, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 8717, 995, 4587, 9381, 7251, 3794, 995, 45865, 36764, 24401, 20193, 7251, 3794, 995, 45865, 2423, 4018, 7251, 3555, 4587, 7578, 34105, 2423, 591, 29538, 2423, 591, 307, 2107, 20010], "avg_logprob": -0.2733304729200389, "compression_ratio": 1.5733333333333333, "no_speech_prob": 0.0, "words": [{"start": 2698.97, "end": 2699.37, "word": "بدي", "probability": 0.239715576171875}, {"start": 2699.37, "end": 2699.69, "word": " أخد", "probability": 0.6827799479166666}, {"start": 2699.69, "end": 2700.41, "word": " determinant", "probability": 0.802734375}, {"start": 2700.41, "end": 2701.15, "word": " للـ", "probability": 0.3958740234375}, {"start": 2701.15, "end": 2701.49, "word": " K", "probability": 0.349365234375}, {"start": 2701.49, "end": 2702.37, "word": " أشوفه", "probability": 0.720703125}, {"start": 2702.37, "end": 2702.67, "word": " كده", "probability": 0.7347005208333334}, {"start": 2702.67, "end": 2703.05, "word": " بده", "probability": 0.59222412109375}, {"start": 2703.05, "end": 2703.61, "word": " يساوي", "probability": 0.9727783203125}, {"start": 2703.61, "end": 2704.37, "word": " يبقى", "probability": 0.9493408203125}, {"start": 2704.37, "end": 2704.79, "word": " واحد", "probability": 0.749267578125}, {"start": 2704.79, "end": 2705.39, "word": " واحد", "probability": 0.884521484375}, {"start": 2705.39, "end": 2706.11, "word": " اتنين", "probability": 0.9429931640625}, {"start": 2706.11, 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0.83837890625}, {"start": 2921.5, "end": 2921.72, "word": " دول", "probability": 0.883056640625}, {"start": 2921.72, "end": 2922.32, "word": " مين", "probability": 0.772705078125}, {"start": 2922.32, "end": 2922.74, "word": " هم", "probability": 0.852783203125}, {"start": 2922.74, "end": 2923.54, "word": " هدول", "probability": 0.8387044270833334}, {"start": 2923.54, "end": 2924.34, "word": " باللي", "probability": 0.38720703125}, {"start": 2924.34, "end": 2924.62, "word": " جيهم", "probability": 0.7862955729166666}, {"start": 2924.62, "end": 2924.96, "word": " هم", "probability": 0.935791015625}, {"start": 2924.96, "end": 2925.12, "word": " ال", "probability": 0.9130859375}, {"start": 2925.12, "end": 2926.56, "word": " eigenvalues", "probability": 0.4149169921875}, {"start": 2926.56, "end": 2927.42, "word": " اول", "probability": 0.792236328125}, {"start": 2927.42, "end": 2927.58, "word": " ما", "probability": 0.82958984375}, {"start": 2927.58, "end": 2927.92, "word": " بدينا", "probability": 0.7410481770833334}, {"start": 2927.92, "end": 2928.04, "word": " ال", "probability": 0.9453125}, {"start": 2928.04, "end": 2928.86, "word": " eigenvalues", "probability": 0.90673828125}, {"start": 2928.86, "end": 2929.74, "word": " اخدنا", "probability": 0.8570556640625}, {"start": 2929.74, "end": 2930.1, "word": " اول", "probability": 0.9404296875}, {"start": 2930.1, "end": 2930.54, "word": " مثال", "probability": 0.97802734375}, {"start": 2930.54, "end": 2930.66, "word": " و", "probability": 0.96826171875}, {"start": 2930.66, "end": 2931.32, "word": " طلعناهم", "probability": 0.7994140625}, {"start": 2931.32, "end": 2931.9, "word": " اتنين", "probability": 0.78485107421875}, {"start": 2931.9, "end": 2932.26, "word": " تين", "probability": 0.528564453125}, {"start": 2932.26, "end": 2932.68, "word": " real", "probability": 0.63427734375}, {"start": 2932.68, "end": 2933.58, "word": " فكانت", "probability": 0.7840169270833334}, {"start": 2933.58, "end": 2933.92, "word": " واحدة", "probability": 0.94384765625}, {"start": 2933.92, "end": 2934.42, "word": " اتنين", "probability": 0.9798583984375}, {"start": 2934.42, "end": 2935.56, "word": " واحدة", "probability": 0.84716796875}, {"start": 2935.56, "end": 2936.48, "word": " تلاتة", "probability": 0.978515625}, {"start": 2936.48, "end": 2937.2, "word": " يبقى", "probability": 0.9635009765625}, {"start": 2937.2, "end": 2937.42, "word": " نفس", "probability": 0.997802734375}, {"start": 2937.42, "end": 2937.8, "word": " الشيء", "probability": 0.9617513020833334}, {"start": 2937.8, "end": 2938.08, "word": " ما", "probability": 0.841796875}, {"start": 2938.08, "end": 2938.72, "word": " علينا", "probability": 0.923583984375}], "temperature": 1.0}, {"id": 125, "seek": 295971, "start": 2940.33, "end": 2959.71, "text": "بعد قليل هروح نحط تعريف لل diagonalizable matrix ونبدأ نشتغل كيف بدي أخلي المصوف اللي عندي تبقى diagonal matrix هذا ما سنتعرضله في المحاضرة القادمة ان شاء الله تعالى اعطيكوا العافية", "tokens": [3555, 22488, 12174, 20292, 1211, 8032, 32887, 5016, 8717, 5016, 9566, 37279, 16572, 5172, 24976, 21539, 22395, 8141, 4032, 1863, 44510, 10721, 8717, 8592, 2655, 17082, 1211, 9122, 33911, 4724, 16254, 5551, 9778, 20292, 9673, 9381, 38688, 13672, 1829, 18871, 16254, 6055, 3555, 4587, 7578, 21539, 8141, 23758, 19446, 8608, 29399, 3615, 43042, 43761, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 1975, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.17533624096761777, "compression_ratio": 1.568421052631579, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2940.33, "end": 2940.73, "word": "بعد", "probability": 0.872802734375}, {"start": 2940.73, "end": 2941.43, "word": " قليل", "probability": 0.96435546875}, {"start": 2941.43, "end": 2942.01, "word": " هروح", "probability": 0.76123046875}, {"start": 2942.01, "end": 2942.41, "word": " نحط", "probability": 0.86767578125}, {"start": 2942.41, "end": 2943.13, "word": " تعريف", "probability": 0.9778645833333334}, {"start": 2943.13, "end": 2943.47, "word": " لل", "probability": 0.75439453125}, {"start": 2943.47, "end": 2944.91, "word": " diagonalizable", "probability": 0.6151123046875}, {"start": 2944.91, "end": 2946.29, "word": " matrix", "probability": 0.94384765625}, {"start": 2946.29, "end": 2947.33, "word": " ونبدأ", "probability": 0.8590087890625}, {"start": 2947.33, "end": 2947.99, "word": " نشتغل", "probability": 0.98642578125}, {"start": 2947.99, "end": 2948.67, "word": " كيف", "probability": 0.976318359375}, {"start": 2948.67, "end": 2948.99, "word": " بدي", "probability": 0.6993408203125}, {"start": 2948.99, "end": 2949.45, "word": " أخلي", "probability": 0.675537109375}, {"start": 2949.45, "end": 2949.97, "word": " المصوف", "probability": 0.8004557291666666}, {"start": 2949.97, "end": 2950.17, "word": " اللي", "probability": 0.869384765625}, {"start": 2950.17, "end": 2950.61, "word": " عندي", "probability": 0.86279296875}, {"start": 2950.61, "end": 2951.63, "word": " تبقى", "probability": 0.9637451171875}, {"start": 2951.63, "end": 2952.35, "word": " diagonal", "probability": 0.84716796875}, {"start": 2952.35, "end": 2953.39, "word": " matrix", "probability": 0.8486328125}, {"start": 2953.39, "end": 2953.99, "word": " هذا", "probability": 0.69970703125}, {"start": 2953.99, "end": 2954.27, "word": " ما", "probability": 0.943359375}, {"start": 2954.27, "end": 2955.19, "word": " سنتعرضله", "probability": 0.89130859375}, {"start": 2955.19, "end": 2955.63, "word": " في", "probability": 0.9365234375}, {"start": 2955.63, "end": 2956.29, "word": " المحاضرة", "probability": 0.974609375}, {"start": 2956.29, "end": 2957.05, "word": " القادمة", "probability": 0.9915364583333334}, {"start": 2957.05, "end": 2957.45, "word": " ان", "probability": 0.75341796875}, {"start": 2957.45, "end": 2957.73, "word": " شاء", "probability": 0.985595703125}, {"start": 2957.73, "end": 2957.93, "word": " الله", "probability": 0.93212890625}, {"start": 2957.93, "end": 2958.77, "word": " تعالى", "probability": 0.7689615885416666}, {"start": 2958.77, "end": 2959.31, "word": " اعطيكوا", "probability": 0.75390625}, {"start": 2959.31, "end": 2959.71, "word": " العافية", "probability": 0.955078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2960.45125, "duration_after_vad": 2795.7531249999934}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0psUrzQdG-A_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0psUrzQdG-A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bf14a55282a25cb84b037a879405f06ae138d633
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0psUrzQdG-A_raw.srt
@@ -0,0 +1,1748 @@
+1
+00:00:20,960 --> 00:00:24,900
+بسم الله الرحمن الرحيم ابتدأنا المرة الماضية بال
+
+2
+00:00:24,900 --> 00:00:29,980
+eigenvalues وال eigenvectors عرفنا ال eigenvalue
+
+3
+00:00:29,980 --> 00:00:35,520
+وال eigenvector واخدنا على ذلك ثلاثة أمثلة ولاحظنا
+
+4
+00:00:35,520 --> 00:00:42,140
+أن ال eigenvalues قد تكون real وقد تكون complexوفي
+
+5
+00:00:42,140 --> 00:00:47,800
+المثال الثاني طلعنا أن لاندا كانت real وفي المثال
+
+6
+00:00:47,800 --> 00:00:53,660
+الثالث طلعنا لاندا complex وقد تكون مزيجا من ال
+
+7
+00:00:53,660 --> 00:00:58,700
+complex و real في نفس المثلة كما سنرى بعد قليل من
+
+8
+00:00:58,700 --> 00:01:03,500
+خلال هذا المثاليبقى المثال بيفترض انه عندي
+
+9
+00:01:03,500 --> 00:01:08,000
+المصفوفة A زي ما انتوا شايفين وطلب اني المطلوب
+
+10
+00:01:08,000 --> 00:01:11,260
+الأول ال eigenvalues و ال eigenvectors ل ال matrix
+
+11
+00:01:11,260 --> 00:01:16,340
+A المطلوب الثاني قال هاتلي basis لكل eigenvector
+
+12
+00:01:16,340 --> 00:01:21,020
+space بطلع عندنا بنقوله بسيطة تعالى نجيب اللي في
+
+13
+00:01:21,020 --> 00:01:25,260
+الأول ال eigenvalues و ال eigenvectors اللي عندنا
+
+14
+00:01:25,260 --> 00:01:30,840
+فبنجيب و نقول solutionيبقى أول شغلة بروح نجيب
+
+15
+00:01:30,840 --> 00:01:39,000
+المصوفة لاندا I ناقص ال A وتساوي هاي لاندا Zero
+
+16
+00:01:39,000 --> 00:01:44,860
+Zero Zero لاندا Zero Zero لاندا بالشكل اللي عندنا
+
+17
+00:01:44,860 --> 00:01:50,220
+هذا فاهمين في مصوفة الواحدة اللي هي I مطروح منها
+
+18
+00:01:50,220 --> 00:01:57,040
+المصوفة Zero واحد واحد سالب واحد واحد سالب واحدو1
+
+19
+00:01:57,040 --> 00:02:04,500
+النتيجة كالتالي يبقى ال land كما هي هنا ناقص واحد
+
+20
+00:02:04,500 --> 00:02:12,800
+ناقص واحد هنا واحد فقط هنا ال land ناقص واحد وهنا
+
+21
+00:02:12,800 --> 00:02:19,600
+ناقص واحد الصف التالت الصف التالت اللي هو واحد
+
+22
+00:02:19,600 --> 00:02:28,180
+وهنا سالب واحدوهنا لندن اقص واحد بالشكل اللي عندنا
+
+23
+00:02:28,180 --> 00:02:36,210
+هذابعد ذلك نجيب الـ determinant لمن؟ لـ lambda I
+
+24
+00:02:36,210 --> 00:02:43,770
+ناقص الـ A يبقى نجيب المحدد لـ lambda I ناقص الـ A
+
+25
+00:02:43,770 --> 00:02:49,710
+و من خلال فك هذا المحدد اللي سنفعله بالصفر نطلع
+
+26
+00:02:49,710 --> 00:02:54,190
+القيم المختلفة لمن؟ لـ lambda I اللي عندنا يبقى
+
+27
+00:02:54,190 --> 00:02:59,510
+هذا الكلام يجب أن يكون zero impliesالمحدد اللي
+
+28
+00:02:59,510 --> 00:03:06,010
+قلناه يبقى هذه ال land فيه المحدد الأصغر المناظر
+
+29
+00:03:06,010 --> 00:03:13,230
+له يبقى land ناقص واحد الكل تربيع ناقص واحد هذا
+
+30
+00:03:13,230 --> 00:03:19,650
+الترم الأول الترم اللي بعده زائد واحد فيه نشطب صفه
+
+31
+00:03:19,650 --> 00:03:27,080
+و عموده بيصير land ناقص واحدهيشطبنه صف و عموده
+
+32
+00:03:27,080 --> 00:03:33,320
+لاندا ناقص واحد زائد واحد الترم الأخير ناقص واحد
+
+33
+00:03:33,320 --> 00:03:38,620
+فيه نشطب صف و عموده بيصير سالب واحد سالب لاندا
+
+34
+00:03:38,620 --> 00:03:45,520
+زائد واحد كل هذا الكلام بده يساوي zeroيبقى هذه
+
+35
+00:03:45,520 --> 00:03:50,920
+لاندا في لاندا تربيع ناقص اتنين لاندا زائد واحد
+
+36
+00:03:50,920 --> 00:03:58,200
+ناقص واحد وهنا زائد لاندا وهنا زائد لاندا كمان بده
+
+37
+00:03:58,200 --> 00:04:04,750
+يساوي مين؟ بده يساوي Zeroطبعا ناقص واحد وزائد واحد
+
+38
+00:04:04,750 --> 00:04:11,770
+مع السلامة يبقى صارت عندنا لاندا تكييب ناقص اتنية
+
+39
+00:04:11,770 --> 00:04:17,890
+لاندا تربيع زائد اتنية لاندا بده يسوي كدهاش؟ Zero
+
+40
+00:04:17,890 --> 00:04:23,430
+لو أخدنا لاندا عامل مشترك بيظل عندنا مين؟ بيظل
+
+41
+00:04:23,430 --> 00:04:29,680
+عندنا لاندا تربيع ناقص اتنية لاندازائد اتنين كل
+
+42
+00:04:29,680 --> 00:04:34,340
+هذا الكلام يبدو يساوي زيرو طبعا هذا لا نستطيع ان
+
+43
+00:04:34,340 --> 00:04:39,760
+نحله اكواسي يبقى نروح ونستخدم القانون يبقى هذا
+
+44
+00:04:39,760 --> 00:04:47,420
+يعطينا اما لاندا تساوي زيرو او لاندا تساوي ناقص با
+
+45
+00:04:47,420 --> 00:04:54,140
+يبقى زائد او ناقص الجدر التربية لبا تربية ناقص
+
+46
+00:04:54,140 --> 00:05:01,970
+اربعة الف بواحدgen بتنين كله على الاتنين في واحد
+
+47
+00:05:01,970 --> 00:05:08,750
+ويساوي اتنين زائد او ناقص طبعا تمانية بشيل منها
+
+48
+00:05:08,750 --> 00:05:13,530
+اربعة بظل اربعة بالسالب لو طلعت الأربعة برا بصير
+
+49
+00:05:13,530 --> 00:05:18,990
+بتنين الجدر التربية لسالب واحد اللي هو ب I كله على
+
+50
+00:05:18,990 --> 00:05:25,700
+اتنين يبقى واحد زائد او ناقص Iإذا صار عندى lambda
+
+51
+00:05:25,700 --> 00:05:30,400
+real اللى هو بالزيرو و lambda complex اللى هو I
+
+52
+00:05:30,400 --> 00:05:34,100
+زائد واحد و I ناقص واحد و زى ما انتوا شايفين
+
+53
+00:05:34,100 --> 00:05:42,120
+الجذران تخيليان و مترافقان في نفس الوقت فمن فكرة
+
+54
+00:05:42,120 --> 00:05:48,060
+المحدد العنصر التالى كده من فكرة المحدد العنصر
+
+55
+00:05:48,060 --> 00:05:51,740
+التالى صح يعنى بساطة ال lambda واحد في lambda ناقص
+
+56
+00:05:51,740 --> 00:05:52,740
+واحد زائد واحد
+
+57
+00:05:56,640 --> 00:06:03,200
+هذه طيب نمشي معاك و بنعتبر كلامك صحيح و كلامك صحيح
+
+58
+00:06:03,200 --> 00:06:09,540
+لغاية ما يثبت العكس 100% كيف؟ احنا بنفك باستخدام
+
+59
+00:06:09,540 --> 00:06:14,160
+عناصر الصف الأول لهذا المحدد نقول لك ال
+
+60
+00:06:14,160 --> 00:06:19,880
+determinant تمام؟ يبقى حسب شرط القاتل شرط شرط هذا
+
+61
+00:06:19,880 --> 00:06:25,940
+مع السالبيبقى هذا الإشارة الموجة بيصار واحد بعد
+
+62
+00:06:25,940 --> 00:06:31,580
+ذلك أشط بصفه و عموده بيصير واحد فلان ده ناقص واحد
+
+63
+00:06:31,580 --> 00:06:37,140
+ناقص ناقص اش بيصير زاد يبقى لان ده ناقص واحد زاد
+
+64
+00:06:37,140 --> 00:06:42,640
+واحد يبقى كلامي ولا كلامك مش مشكلة وجهات النظر قد
+
+65
+00:06:42,640 --> 00:06:49,360
+تكون صحية و قد تكون غير صحيةيبقى النتيجة تماماً
+
+66
+00:06:49,360 --> 00:06:52,200
+بيبقى من المياه ثلاث قيم واحدة الواحدة الواحدة
+
+67
+00:06:52,200 --> 00:06:54,400
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+68
+00:06:54,400 --> 00:06:56,320
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+69
+00:06:56,320 --> 00:06:59,280
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+70
+00:06:59,280 --> 00:07:00,340
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+71
+00:07:00,340 --> 00:07:03,840
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+72
+00:07:03,840 --> 00:07:03,980
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+73
+00:07:03,980 --> 00:07:03,980
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+74
+00:07:03,980 --> 00:07:12,480
+الواحدة الواحدة الواحدة الواحدة
+
+75
+00:07:12,480 --> 00:07:20,240
+الوايبقى احنا لاندا اي ناقص ال a كله في ال vector
+
+76
+00:07:20,240 --> 00:07:24,000
+x بدى يساوي zero مش هذه المعادلة الأساسية اللى
+
+77
+00:07:24,000 --> 00:07:27,640
+عندنا دايما وابدا اذا بدنا نروح نطبقها على أرض
+
+78
+00:07:27,640 --> 00:07:32,850
+الواقع لاندا اي ناقص a هي المصوفة هذهيبقى هذه
+
+79
+00:07:32,850 --> 00:07:37,470
+المصحوفة اللي عندنا هذه اللي هي lambda وهنا ناقص
+
+80
+00:07:37,470 --> 00:07:44,450
+واحد ناقص واحد واحد lambda ناقص واحد ناقص واحد
+
+81
+00:07:44,450 --> 00:07:51,130
+واحد ناقص واحد lambda ناقص واحد في x اللي هي x
+
+82
+00:07:51,130 --> 00:07:59,190
+واحد x اتنين x تلاتة بده يساوي zero zero zero بيد
+
+83
+00:07:59,190 --> 00:08:05,510
+الشكلالان بدى ابدأ احط لاندا تساوي Zero لو لاندا
+
+84
+00:08:05,510 --> 00:08:09,750
+حطناها ب Zero بصير المعادلة على الشكل التالي هاي
+
+85
+00:08:09,750 --> 00:08:15,690
+Zero وهنا ناقص واحد وهنا ناقص واحد وهنا واحد وهنا
+
+86
+00:08:15,690 --> 00:08:20,990
+ناقص واحد وهنا ناقص واحد وهنا واحد وهنا ناقص واحد
+
+87
+00:08:20,990 --> 00:08:27,690
+وهنا ناقص واحد كله في من؟ في X واحد X اتنين X
+
+88
+00:08:27,690 --> 00:08:35,720
+تلاتة بده يساوي Zero و Zeroهذا الانبناط بيعطيني لو
+
+89
+00:08:35,720 --> 00:08:41,400
+ضربت ثلاث معادلات المعادلة الأولى x واحد بتروح بال
+
+90
+00:08:41,400 --> 00:08:47,580
+zero يبقى ناقص x اتنين ناقص x تلاتة بده يساوي zero
+
+91
+00:08:48,300 --> 00:08:57,500
+المعادلة التانية بتعطيني x1-x2-x3 بده يساوي 0
+
+92
+00:08:57,500 --> 00:09:07,060
+المعادلة التالتة x1-x2-x3 بده يساوي 0
+
+93
+00:09:10,090 --> 00:09:15,910
+تلات معادلة لكن في الحقيقة تنتين فقط لغير لأن
+
+94
+00:09:15,910 --> 00:09:20,470
+المعادلة التانية والمعادلة التالتة نفس الشيء يبقى
+
+95
+00:09:20,470 --> 00:09:27,390
+بناء عليه بقدر استنتج من هذا الكلام ان هذي X2 زائد
+
+96
+00:09:27,390 --> 00:09:32,010
+X3 بده يساوي Zero يعني باعتبار ضربت في سالب واحد
+
+97
+00:09:32,380 --> 00:09:42,040
+وهذه سنزيلها كما هي لـ X1-X2-X3 يبدو يساوي 0 لو
+
+98
+00:09:42,040 --> 00:09:46,960
+جيت جماعة يبقى هدول و هدول مع السلامة يبقى X1
+
+99
+00:09:46,960 --> 00:09:54,210
+تساوي كم؟تساوي 0 إذا لو كانت x واحد تساوي 0 بظل x
+
+100
+00:09:54,210 --> 00:10:00,310
+اتنين زاد x تلاتة يساوي 0 إذا بصير عند هنا x اتنين
+
+101
+00:10:00,310 --> 00:10:07,450
+زاد x تلاتة بدي ساوي 0 يبقى x اتنين بدي ساوي سالب
+
+102
+00:10:07,450 --> 00:10:15,840
+x تلاتةإذا مادام جبت هذه القيام بقدر اقول لو كانت
+
+103
+00:10:15,840 --> 00:10:23,100
+مثلا X3 بيه او X2 بيه سيان يبقى باجي بقول هنا if
+
+104
+00:10:23,100 --> 00:10:34,140
+ال X3 بده يسوي ايه then the eigen vectors
+
+105
+00:10:35,830 --> 00:10:39,490
+يبقى الـ eigenvectors بتكون على الشكل التالي
+
+106
+00:10:49,180 --> 00:10:54,240
+يبقى x1 أطلع عنها بالـ zero وهذا الـ zero و x2
+
+107
+00:10:54,240 --> 00:10:59,560
+يبقى
+
+108
+00:10:59,560 --> 00:11:07,560
+ناقص a و a بالشكل هذا أو a في zero سالب واحد واحد
+
+109
+00:11:07,560 --> 00:11:12,440
+بالشكل اللي عندنا هناطيب هذا كله حتى الآن هو
+
+110
+00:11:12,440 --> 00:11:18,280
+المطلوب ايه من المثل؟ جالي هاتلي ال eigenvalues و
+
+111
+00:11:18,280 --> 00:11:21,460
+ال eigenvectors اللي أصمصوه في ايه؟ بعدين جالي
+
+112
+00:11:21,460 --> 00:11:26,680
+هاتلي basis for each eigenvector space يبقى نمرأ
+
+113
+00:11:26,680 --> 00:11:32,360
+بإيه؟ السؤال هو مش هذا كل ال eigenvectors على
+
+114
+00:11:32,360 --> 00:11:35,800
+الشكل اللي قدامي هذا يا بنات؟ يبقى مين اللي بيجيب
+
+115
+00:11:35,800 --> 00:11:40,430
+ال eigenvectors كلها؟هو ال element اللي عندنا هذا
+
+116
+00:11:40,430 --> 00:11:44,150
+هو اللي بولده مدى كله اضرب فيها مين ما يكون ايه
+
+117
+00:11:44,150 --> 00:11:49,070
+يكون any real number يبقى كل ال eigen vectors على
+
+118
+00:11:49,070 --> 00:11:52,650
+الشكل اللي عندنا هذا يبقى هدول اللي بيكونون ال
+
+119
+00:11:52,650 --> 00:11:56,930
+eigen vector space طب لما يكون عندي element واحد
+
+120
+00:11:56,930 --> 00:12:00,650
+يكون linearly dependent ولا linearly independent
+
+121
+00:12:00,650 --> 00:12:07,990
+vector واحدLinearly Dependent ولا Linearly
+
+122
+00:12:07,990 --> 00:12:11,250
+Independent؟ إذا كنت تقول لي إنه Linearly
+
+123
+00:12:11,250 --> 00:12:14,370
+Dependent، سأقول لك إنه يعتمد على من؟ طب هم فيش
+
+124
+00:12:14,370 --> 00:12:18,570
+غيره، تمام؟ يبقى واش بيكون؟ Linearly Independent
+
+125
+00:12:18,570 --> 00:12:23,370
+مستقل تماماً وبالتالي هذا ال element هو ال basis
+
+126
+00:12:23,370 --> 00:12:28,830
+لكل ال eigen vector space إذا باجي بقول له هنا the
+
+127
+00:12:28,830 --> 00:12:45,540
+basis for the eigenVector space corresponding to
+
+128
+00:12:45,540 --> 00:12:53,720
+lambda تساوي zero as ال vector اللي عندنا zero
+
+129
+00:12:53,720 --> 00:12:58,020
+سالب واحد واحد بالشكل اللي عندنا
+
+130
+00:13:00,790 --> 00:13:06,790
+خلصنا لو كانت مين؟ لو كانت lambda تساوي zero الان
+
+131
+00:13:06,790 --> 00:13:11,290
+بدنا نيجي يا بنات لو كانت ال lambda تساوي قدرش
+
+132
+00:13:11,290 --> 00:13:17,030
+العنصر التاني هو واحد زائد Iالشكل اللي عندنا هنا
+
+133
+00:13:17,030 --> 00:13:20,590
+إذا بدي أجي إلى مين؟ بدي أجي إلى المعادلة اللي
+
+134
+00:13:20,590 --> 00:13:27,830
+عندنا هذه بدي أشيل كلها و أحط مكانها 1 زائد I لما
+
+135
+00:13:27,830 --> 00:13:34,350
+أحط 1 زائد I مكان هذه يبقى و بدنا نيجي نكوّن
+
+136
+00:13:34,350 --> 00:13:38,670
+المعادلة اللي عندنا هذه و نشوف إيش اللي بده يصير
+
+137
+00:13:39,400 --> 00:13:45,360
+يبقى هذه نتجة لما حطيت لاندا تساوي zero الحين انا
+
+138
+00:13:45,360 --> 00:13:51,740
+بده اشيل لاندا واحط مكانها واحد زائد I يبقى if
+
+139
+00:13:51,740 --> 00:14:00,500
+لاندا we have ان لاندا I ناقص ال A في ال X بده
+
+140
+00:14:00,500 --> 00:14:06,020
+تساويطلع لي هنا كويس هذي اللاندا بده اشيلها و اكتب
+
+141
+00:14:06,020 --> 00:14:13,060
+بدالها واحد زائد I و عندك هنا ناقص واحد و هنا ناقص
+
+142
+00:14:13,060 --> 00:14:21,840
+واحد و هنا واحد و هنا I زائد واحد و عندك ناقص واحد
+
+143
+00:14:21,840 --> 00:14:27,850
+بيضل عندى بس هنا جدرش بس Iوعندك هنا ناقص واحد كما
+
+144
+00:14:27,850 --> 00:14:34,230
+هي وهنا واحد وهنا ناقص واحد وهنا كمان واحد زائد I
+
+145
+00:14:34,230 --> 00:14:41,730
+بيظل I فقط لا غير في X واحد X اتنين X تلاتة بده
+
+146
+00:14:41,730 --> 00:14:49,730
+يساوي Zero Zero Zeroيبقى الشلط كلها ده وحطيت
+
+147
+00:14:49,730 --> 00:14:55,170
+مكانها واحد زائد I وبدنا نيجي نكون ال system of
+
+148
+00:14:55,170 --> 00:14:59,870
+linear equations لو ضربنا وفكنا بصير المعادلة
+
+149
+00:14:59,870 --> 00:15:10,740
+الأولى اللي هو X واحد زائد I في X واحدناقص X2 ناقص
+
+150
+00:15:10,740 --> 00:15:22,290
+X3 بيساوي 0 المعادلة التانية X1زائد I X2 اللي
+
+151
+00:15:22,290 --> 00:15:31,250
+بعدها ناقص X3 بده يسوى Zero المعادلة التالتة X1 X1
+
+152
+00:15:31,250 --> 00:15:42,890
+ناقص X2 X1 ناقص X2 زائد I X3 بده يسوى Zero
+
+153
+00:15:46,690 --> 00:15:52,410
+بدا نحل المعادلات مع بعضها و نطلع قيم ممكن بالروشن
+
+154
+00:15:52,410 --> 00:15:58,570
+فورم أو بجاوسين او بأي طريقة كانت انا بفضل الان
+
+155
+00:15:58,570 --> 00:16:04,150
+الطريقة التالية لو جيت ضربت هذه في سالب واحد بيصير
+
+156
+00:16:04,150 --> 00:16:15,000
+سالب X واحدسالب I X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
+
+157
+00:16:15,000 --> 00:16:18,620
+X11 X12 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+158
+00:16:18,620 --> 00:16:18,620
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+159
+00:16:18,620 --> 00:16:18,760
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+160
+00:16:18,760 --> 00:16:19,040
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+161
+00:16:19,040 --> 00:16:19,040
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+162
+00:16:19,040 --> 00:16:19,040
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+163
+00:16:19,040 --> 00:16:19,040
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+164
+00:16:19,040 --> 00:16:20,000
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+165
+00:16:20,000 --> 00:16:32,230
+X13 X13 X13 X13زائد I X2 وناقص X تلاتة يسوى من الـ
+
+166
+00:16:32,230 --> 00:16:32,470
+Zero
+
+167
+00:16:38,270 --> 00:16:46,390
+يبقى هذه باقية لوحدها اللي همين ناقص I X 1 زائد I
+
+168
+00:16:46,390 --> 00:16:54,030
+زائد 1 في X2 بدري يساوي 0 هذا بدري يعطينا ان I
+
+169
+00:16:54,030 --> 00:17:05,570
+زائد 1 في X2 بدري يساوي I X1 مرة تانية بقولالان
+
+170
+00:17:05,570 --> 00:17:09,510
+جيه ضربت المعادلة الأولى في سالب واحد والمعادلة
+
+171
+00:17:09,510 --> 00:17:15,130
+الثانية كما هي مغيرتش فيها ولا حاجة يبقى هذه
+
+172
+00:17:15,130 --> 00:17:20,270
+وصلتني لإيه صار هنا سالب هنا سالب هنا موجب هنا
+
+173
+00:17:20,270 --> 00:17:24,700
+موجب المعادلة التانية نزلتها زي ما هيهذول بروحوا
+
+174
+00:17:24,700 --> 00:17:30,360
+مع بعض و هذول بروحوا هدى و هدى بياخد X2 عامل مشترك
+
+175
+00:17:30,360 --> 00:17:35,740
+بيظل I زياد واحد وهدى نزلتها زي ما هى نجلتها على
+
+176
+00:17:35,740 --> 00:17:40,800
+الشجرة التانية صار I زياد واحد X2 بده يساوي I X
+
+177
+00:17:40,800 --> 00:17:46,430
+واحدالان اللى عملته هنا بدي اعمله مرة تانية ما بين
+
+178
+00:17:46,430 --> 00:17:51,290
+المعادلة الاولى والمعادلة التالتة يبقى لو جيتلى
+
+179
+00:17:51,290 --> 00:17:58,770
+المعادلة الاولى ضربتها في سالب يبقى سالب X1 سالب I
+
+180
+00:17:58,770 --> 00:18:07,150
+X1 زائد X2 زائد X3 بده يساوي Zeroجت للمعادلة هذه
+
+181
+00:18:07,150 --> 00:18:14,870
+التالتة و نزلتها زي ما هي يبقى ناقص X2 وعندك هنا
+
+182
+00:18:14,870 --> 00:18:22,950
+X1 بالموجب وزائد I X3 بده يساوي Zero جي الجماعة
+
+183
+00:18:22,950 --> 00:18:30,530
+يبقى هدول و هدول مالهم مع السلامة يبقى ناقص I X1
+
+184
+00:18:30,530 --> 00:18:34,230
+زائد I زائد 1
+
+185
+00:18:38,010 --> 00:18:46,390
+بناء عليه بقدر اقول يبقى I زائد واحد X تلاتة بده
+
+186
+00:18:46,390 --> 00:18:53,620
+يسوى I X oneطب ما رأيك في التنتين هذول؟ مش الطرف
+
+187
+00:18:53,620 --> 00:18:58,160
+اليمين هو نفس الطرف اليمين إذا الطرف الشمال هو نفس
+
+188
+00:18:58,160 --> 00:19:04,540
+الطرف الشمال يبقى بداجي أقول هذا بدي يعطينا ان I
+
+189
+00:19:04,540 --> 00:19:12,540
+زائد واحد في X2 يساوي I زائد واحد في من؟ في X3
+
+190
+00:19:12,540 --> 00:19:19,040
+يبقى هذا بدي يعطينا ان X2 يساوي من يا بنات؟ X3
+
+191
+00:19:19,700 --> 00:19:25,900
+عندما أخذت المعادلة الأولى والثانية والثالثة
+
+192
+00:19:25,900 --> 00:19:26,920
+والأولى والأولى والثالثة والأولى والثالثة والأولى
+
+193
+00:19:26,920 --> 00:19:27,780
+والثالثة والأولى والثالثة والأولى والثالثة والأولى
+
+194
+00:19:27,780 --> 00:19:29,140
+والثالثة والأولى والثالثة والأولى والثالثة والأولى
+
+195
+00:19:29,140 --> 00:19:33,000
+والثالثة والأولى والثالثة والأولى والثالثة والأولى
+
+196
+00:19:33,000 --> 00:19:35,160
+والثالثة والأولى والثالثة والأولى والثالثة والأولى
+
+197
+00:19:35,160 --> 00:19:35,160
+والثالثة والأولى والثالثة والأولى والثالثة والأولى
+
+198
+00:19:35,160 --> 00:19:41,190
+والثالثة والأولى والثالثة والأولى واللو جيت
+
+199
+00:19:41,190 --> 00:19:44,710
+للمعادلة
+
+200
+00:19:44,710 --> 00:19:49,550
+التانية والتالتة دي بالشكل هذا هاي X واحد زي ما هي
+
+201
+00:19:49,550 --> 00:19:57,390
+وزائد I X اتنين و X تلاتة اليمينة بناتاكس اتنين مش
+
+202
+00:19:57,390 --> 00:20:00,650
+طالع انا اكس اتنين يسوي اكس تلاتة اذا بدى اعوض هنا
+
+203
+00:20:00,650 --> 00:20:05,950
+عن كل من اكس تلاتة بمين باكس اتنين يبقى اكس واحد
+
+204
+00:20:05,950 --> 00:20:11,130
+زائد اي اكس اتنين ناقص اكس اتنين بده يسوي زيرو
+
+205
+00:20:11,130 --> 00:20:19,650
+الان كمان اكس واحد ناقص اكس اتنين زائد اي اكس
+
+206
+00:20:19,650 --> 00:20:25,320
+اتنين بده يسوي مين بده يسوي زيروهذا الكلام بدّى
+
+207
+00:20:25,320 --> 00:20:30,480
+يعطينا ما يأتي هل المعادلة اللى فوق هي نفس
+
+208
+00:20:30,480 --> 00:20:36,020
+المعادلة اللى تحت؟مظبوط؟ يبقى هي نفسها حرفيا يبقى
+
+209
+00:20:36,020 --> 00:20:40,040
+هذول مش معادلتين وإنما مين؟ معادلة واحدة مدام
+
+210
+00:20:40,040 --> 00:20:45,980
+معادلة واحدة إذا بقدر أقول هنا عندنا بدي يكون x
+
+211
+00:20:45,980 --> 00:20:53,480
+واحد زائد اللي هو I ناقص واحد في ال x اتنين بدي
+
+212
+00:20:53,480 --> 00:21:01,720
+يساوي zeroأو الـ X1 بده يساوي 1 ناقص I في main
+
+213
+00:21:01,720 --> 00:21:07,000
+بالـ X2 نجلناها على الشجة التانية وأجى بإشارة main
+
+214
+00:21:07,000 --> 00:21:09,340
+بإشارة سالب
+
+215
+00:21:29,010 --> 00:21:34,170
+بناء اللي عليها بقدر أجيب الـ eigenvectors يبقى
+
+216
+00:21:34,170 --> 00:21:39,490
+باجي بقول هنا the eigenvectors
+
+217
+00:21:39,490 --> 00:21:46,550
+corresponding to
+
+218
+00:21:48,910 --> 00:21:56,050
+cross bonding two lambda يساوي I زائد واحد والله
+
+219
+00:21:56,050 --> 00:22:05,450
+واحد زائد I are in the four على الشكل التالي اللي
+
+220
+00:22:05,450 --> 00:22:11,800
+هو manالحد الأولاني او X واحد كانت بواحد ناقص I
+
+221
+00:22:11,800 --> 00:22:18,060
+اللي هو واحد اه استنى شوية ماحطناش رموز احنا احنا
+
+222
+00:22:18,060 --> 00:22:25,670
+قولنا بس يبقى هذه باجي بقوله هنا Fمثلا اكس اتنين
+
+223
+00:22:25,670 --> 00:22:33,450
+تساوي ايه اذا اكتب
+
+224
+00:22:33,450 --> 00:22:40,110
+هالك اوضع شوية فباجي بقول اكس واحد و اكس اتنين و
+
+225
+00:22:40,110 --> 00:22:46,630
+اكس تلاتة بده يساوي اكس واحدطلعناها عنا بقدرش
+
+226
+00:22:46,630 --> 00:22:54,070
+بواحد ناقص I في X اتنين يبقى واحد ناقص I في A و X
+
+227
+00:22:54,070 --> 00:23:00,270
+اتنين ب A و X تلاتة ب A كذلك اللي هو بده يساوي A
+
+228
+00:23:00,270 --> 00:23:06,390
+في واحد ناقص I و هنا واحد واحد بالشكل اللي عندنا
+
+229
+00:23:06,390 --> 00:23:06,610
+هنا
+
+230
+00:23:24,200 --> 00:23:32,100
+هي المجموعة اللي همين واحد ناقص I وهنا واحد وهنا
+
+231
+00:23:32,100 --> 00:23:37,710
+واحد الشكل اللي عندنا هنايبقى اللي عملته لل ايجن
+
+232
+00:23:37,710 --> 00:23:42,070
+فاليو I زي واحد بيروح اعمله ال ايجن فاليو الأخيرة
+
+233
+00:23:42,070 --> 00:23:48,310
+اللي هي واحد ناقص I يبقى باجي بقوله if لاندا تساوي
+
+234
+00:23:48,310 --> 00:23:57,790
+واحد ناقص I then لاندا I ناقص ال A في ال X يساوي
+
+235
+00:23:57,790 --> 00:23:59,090
+Zero implies
+
+236
+00:24:01,550 --> 00:24:08,510
+هذا الكلام يبقى مكان اللي بدي اضافه مين واحد ناقص
+
+237
+00:24:08,510 --> 00:24:14,910
+I يبقى I واحد ناقص I وهنا ناقص واحد وهنا ناقص واحد
+
+238
+00:24:14,910 --> 00:24:26,020
+واحد وهنا واحد ناقص Iبصير هنا ناقص I وهنا ناقص
+
+239
+00:24:26,020 --> 00:24:33,620
+واحد كما هي وهنا واحد ناقص واحد وهنا واحد ناقص I
+
+240
+00:24:33,620 --> 00:24:41,620
+يبقى كمان ناقص I في X واحد X اتنين X تلاتة بده
+
+241
+00:24:41,620 --> 00:24:46,440
+يساوي Zero و Zero و Zeroيبقى هذه المعادلة اللي
+
+242
+00:24:46,440 --> 00:24:49,900
+عندي كتبت على الشكل هذا يبقى الأن بدي أضرو
+
+243
+00:24:49,900 --> 00:24:56,020
+المصفتين وساوي الطرفين ببعض في خطوة واحدة إذا
+
+244
+00:24:56,020 --> 00:25:03,940
+المعادلة الأولى x واحد ناقص I x اتنين يبقى x واحد
+
+245
+00:25:03,940 --> 00:25:22,860
+ناقص IX1-IX1-X2-X3 == 0 المعادلة X1-IX2
+
+246
+00:25:22,860 --> 00:25:25,760
+-IX2
+
+247
+00:25:27,710 --> 00:25:36,930
+ناقص x3 بده يساوي 0 المعادلة التالتة اللي هو x1
+
+248
+00:25:36,930 --> 00:25:46,070
+ناقص x2 ناقص i x3 بده يساوي مين؟ بده يساوي الـ 0
+
+249
+00:25:50,270 --> 00:25:57,590
+طيب ايش رأيك لو جينا ضربنا المعادلة الأولى في I لو
+
+250
+00:25:57,590 --> 00:26:04,590
+جيت ضربت المعادلة هذه في I ايش بصير؟ I X 1 هذي
+
+251
+00:26:04,590 --> 00:26:10,730
+بنيت I في I I تربية I تربية ناقص واحد مع ناقص بصير
+
+252
+00:26:10,730 --> 00:26:20,790
+زائد X واحدناقص I X 2 ناقص I X 3 بده يسوي 0 هذه
+
+253
+00:26:20,790 --> 00:26:32,070
+المعادلة بدي أخليها زي ما هي X 1 ناقص I X 2 ناقص X
+
+254
+00:26:32,070 --> 00:26:41,990
+3 بده يسوي 0 إيش عملتلي هذه؟ كيه؟ هذه؟
+
+255
+00:26:43,220 --> 00:26:52,160
+هذه I X 1 هنا زائد X 1 مظبوط وهنا ناقص I X 2 ناقص
+
+256
+00:26:52,160 --> 00:27:02,280
+I X 3 بده يساوي Zero هذه X 1 ناقص I X 2 ناقص X 3
+
+257
+00:27:02,280 --> 00:27:08,360
+مظبوط الدرب لكن هل جابلي هذا نتيجة ام لا ما جابليش
+
+258
+00:27:08,360 --> 00:27:16,200
+ولا حاجة الا اذا كانضربت الثانية في سالب واحد اه
+
+259
+00:27:16,200 --> 00:27:19,700
+لو ضربت الثانية في سالب واحد بمشي الحال يبقى اضرب
+
+260
+00:27:19,700 --> 00:27:23,960
+التانية في سالب واحد يبقى ايه السالب واحد وهي موجب
+
+261
+00:27:23,960 --> 00:27:28,960
+وهي موجب هيك جبنا نتيجة صحية تمام؟ يبقى لو جيت
+
+262
+00:27:28,960 --> 00:27:30,280
+جماعة يا بنات
+
+263
+00:27:33,000 --> 00:27:38,400
+بتروح هدى و هدى و هدى و هدى مع السلامة بظل عندنا
+
+264
+00:27:38,400 --> 00:27:46,760
+مين بظل عندنا ما يأتين اللى هو I X 1 و بظل عندنا
+
+265
+00:27:46,760 --> 00:27:55,920
+هنا ناقص I ناقص واحد X 3 بده يسوى Zero يبقى بناء
+
+266
+00:27:55,920 --> 00:27:58,460
+عليه I ناقص واحد
+
+267
+00:28:12,940 --> 00:28:16,020
+هذا الكلام كله مش لازم الآن
+
+268
+00:28:20,410 --> 00:28:26,870
+يبقى المعادلة الثانية هذي لو جيت ضربتها كمان في
+
+269
+00:28:26,870 --> 00:28:37,710
+سالب ا في I يبقى بصير I X 1 زائد X 1 هنا زائد
+
+270
+00:28:37,710 --> 00:28:45,260
+والله ناقص I X 2 ناقص I X 3 بده يسوى Zeroهذه هنا
+
+271
+00:28:45,260 --> 00:28:53,380
+بدها ضربها في ناقص يبقى ناقص X1 زائد X2 هنا
+
+272
+00:28:53,380 --> 00:29:00,040
+ضربناها في ناقص بيصير زائد I X3 بده يساوي Zero
+
+273
+00:29:00,040 --> 00:29:09,440
+هدول مع السلامة طيبهو I X 3 و سالب I X 3 مع
+
+274
+00:29:09,440 --> 00:29:18,620
+السلامة يبقى ضال عندنا هنا مين؟ اللي هو سالب
+
+275
+00:29:18,620 --> 00:29:29,700
+Iزاء ناقص واحد X2 زائد I X1 بدري ساوي Zero او اللي
+
+276
+00:29:29,700 --> 00:29:37,810
+همين I ناقص واحد في ال X2 بدري ساوي I X1طلعولي في
+
+277
+00:29:37,810 --> 00:29:41,590
+الاتنين هذول يا بنات النتيجة اللي وصلنا لإينا و
+
+278
+00:29:41,590 --> 00:29:45,090
+النتيجة اللي وصلنا إلينا يبقى اتنين هذول ما لهم
+
+279
+00:29:45,090 --> 00:29:50,390
+بيساووا بعض يبقى مادام بيساووا بعض يبقى هذا بد
+
+280
+00:29:50,390 --> 00:29:56,450
+يظهر ان I ناقص واحد في ال X اتنين يساوي I ناقص
+
+281
+00:29:56,450 --> 00:30:03,030
+واحد في ال X تلاتة يبقى كمان X اتنين بد يساوي من؟
+
+282
+00:30:03,030 --> 00:30:10,710
+بد يساوي X تلاتةبداية للمعادلة التانية والتالتة
+
+283
+00:30:10,710 --> 00:30:16,030
+تمام زي المرة الماضية يبقى المعادلة التانية ها دي
+
+284
+00:30:16,030 --> 00:30:22,690
+ها ها بالضبط تماما باجي بقول هاي X واحد ناقص I X
+
+285
+00:30:22,690 --> 00:30:28,490
+اتنين ناقص X اتنين شيلنا X تلاتة وحطينا بدلها X
+
+286
+00:30:28,490 --> 00:30:36,640
+اتنين يساوي Zero والمعادلة التانية X واحدناقص X2
+
+287
+00:30:36,640 --> 00:30:44,900
+ناقص I X2 كله بده ساوي Zero لاحظ ان المعادلة هذه
+
+288
+00:30:44,900 --> 00:30:49,380
+هي نفس المعادلة فوق يبقى هدول معادلتين اذا هدول
+
+289
+00:30:49,380 --> 00:30:58,560
+التنتين في الحقيقة هي معادلة واحدة وهي X واحدناقص
+
+290
+00:30:58,560 --> 00:31:05,600
+I زائد واحد X اتنين بده يساوي Zero إذا هذا الكلام
+
+291
+00:31:05,600 --> 00:31:12,640
+بده يعطينا ان X واحد بده يساوي I زائد واحد في X
+
+292
+00:31:12,640 --> 00:31:19,580
+اتنين إذا بالمثل لو جيت قولت لو كانت X اتنين تساوي
+
+293
+00:31:19,580 --> 00:31:20,240
+A
+
+294
+00:31:22,840 --> 00:31:32,020
+الـ X1 بدر يساوي I زائد واحد في الـ A والـ X2 بدر
+
+295
+00:31:32,020 --> 00:31:40,040
+يساوي A والـ X3 بدر يساوي الـ A إذا بقدر أجيب اللي
+
+296
+00:31:40,040 --> 00:31:47,740
+هو ال Eigen vector Z يبقى باجي بقوله هنا
+
+297
+00:31:53,120 --> 00:32:03,600
+Eigel vectors corresponding to
+
+298
+00:32:03,600 --> 00:32:17,240
+lambda تساوي الواحد ناقص I واحد ناقص I are
+
+299
+00:32:17,240 --> 00:32:28,460
+in the formبالشكل التالي اكس واحد اكس اتنين اكس
+
+300
+00:32:28,460 --> 00:32:35,300
+تلاتة تساوي اكس واحد اتفاجنا اللي هي بقدرش اي زائد
+
+301
+00:32:35,300 --> 00:32:43,840
+واحد في اي اي زائد واحد في اي و اي و اي بشكل لأن
+
+302
+00:32:43,840 --> 00:32:51,140
+هذا او بنقدر نقول ال اي في اي زائد واحد واحد واحد
+
+303
+00:32:51,910 --> 00:32:58,290
+يبقى كإنه تماما زي مين زي اللي عندنا هذا مع الفارق
+
+304
+00:32:58,290 --> 00:33:03,570
+المركبة الأولى بدل ما هي واحد زي die المرافق لها
+
+305
+00:33:03,570 --> 00:33:09,590
+وهي واحد ناقص I يبقى باجي بقوله هنا نمره بيه the
+
+306
+00:33:09,590 --> 00:33:19,390
+basis for the eigen vector space
+
+307
+00:33:21,390 --> 00:33:27,530
+Is the set هي عبارة عن ال set اللي فيها vector
+
+308
+00:33:27,530 --> 00:33:35,390
+واحد I زائد واحد واحد بالشكل اللي عندنا هنا حد
+
+309
+00:33:35,390 --> 00:33:37,990
+فيكم لأي تساؤل هنا؟
+
+310
+00:33:40,590 --> 00:33:45,490
+على أي حال، هذه السؤالة ربط بين المثالين السابقين
+
+311
+00:33:45,490 --> 00:33:51,790
+المثال الرقم اتنين كان كله الانظار الحقيقي والمثال
+
+312
+00:33:51,790 --> 00:33:56,550
+الثالث كان كله الانظار التخيلي إذا قد يكون الانظار
+
+313
+00:33:56,550 --> 00:34:01,050
+الـEigenvalues هي مزيج بين القيم الحقيقية والقيم
+
+314
+00:34:01,050 --> 00:34:06,380
+التخيلية كما في المثال اللي بين إيدينا هذاعلى اي
+
+315
+00:34:06,380 --> 00:34:12,840
+حالة هنا stop انتهى هذا section وبانتهى هذا
+
+316
+00:34:12,840 --> 00:34:18,980
+section ناخد الأسئلة تبعته ثم نذهب الى ال section
+
+317
+00:34:18,980 --> 00:34:26,060
+اللذي يليه يبقى بدنا المسائل من 1 ل 15 يبقى
+
+318
+00:34:26,060 --> 00:34:33,480
+exercises اربعة واحد المسائل من 1 ل 15
+
+319
+00:34:37,360 --> 00:34:41,980
+أنت انا مااسكش اربعة واحد اربعة اتنين مش لازمنا
+
+320
+00:34:41,980 --> 00:34:45,360
+بنروح لاربعة تلاتة
+
+321
+00:35:05,760 --> 00:35:10,080
+يبقى section اربعة تلاتة اللي هو ال
+
+322
+00:35:10,080 --> 00:35:12,380
+diagonalization
+
+323
+00:35:19,230 --> 00:35:25,430
+هيش diagonalization جاء من كلمة diagonal تمام
+
+324
+00:35:25,430 --> 00:35:29,430
+diagonal اللي هو قطري diagonalization كيف بيدخلي
+
+325
+00:35:29,430 --> 00:35:34,990
+المصوفات اللي عندنا مصوفة قطرية فقط يعني كيف جميع
+
+326
+00:35:34,990 --> 00:35:40,790
+العناصر أسفرا ما عدا عناصر القطر الرئيسي هنعطي
+
+327
+00:35:40,790 --> 00:35:46,090
+definition ونشوف كيف نطبق هذا ال definition يبقى
+
+328
+00:35:46,090 --> 00:36:03,280
+definitionبقول if a and b are two n by n matrices
+
+329
+00:36:03,280 --> 00:36:06,300
+مصفات
+
+330
+00:36:06,300 --> 00:36:15,600
+نظام n في n we say that we say that ان ال a is
+
+331
+00:36:15,600 --> 00:36:17,700
+similar
+
+332
+00:36:21,820 --> 00:36:29,300
+similar to be if there exists a non singular
+
+333
+00:36:29,300 --> 00:36:41,920
+matrix if there exists a non singular matrix
+
+334
+00:36:41,920 --> 00:36:45,180
+capital
+
+335
+00:36:45,180 --> 00:36:49,120
+K such that
+
+336
+00:36:53,440 --> 00:37:08,360
+بساطش ذات ان ال B بده يساوي K inverse اك فري
+
+337
+00:37:08,360 --> 00:37:14,740
+مارك نمر
+
+338
+00:37:14,740 --> 00:37:35,070
+واحدif ال a if ال a is similar to b then b is
+
+339
+00:37:35,070 --> 00:37:52,040
+similar to a نمرا اتنين a issimilar to itself
+
+340
+00:38:24,360 --> 00:38:29,880
+هنعمل عملية ال diagonalization ببعض التعريفات
+
+341
+00:38:29,880 --> 00:38:32,740
+التعريف الأول اللي عندنا بيقول
+
+342
+00:38:55,670 --> 00:39:03,170
+ماذا نقول احنا؟ ايوة انت، ماذا نقول؟ خليك معانا
+
+343
+00:39:03,170 --> 00:39:08,250
+وإلا، دينا بالك، بضلك برا تفكري برا براعتك، تصريش،
+
+344
+00:39:08,250 --> 00:39:13,050
+خليكي معانا، تصريش من بني سرحان، طيب، نيجي الآن
+
+345
+00:39:13,050 --> 00:39:18,470
+مرة تانية بقولمرة تانى لكي يخد باله الجميع بقول
+
+346
+00:39:18,470 --> 00:39:24,430
+الان عندي مصففتين A وB تنتين هذول نظامهم infinite
+
+347
+00:39:24,430 --> 00:39:29,590
+تنتين من نفس النظام بقول ان ال A هي similar to B
+
+348
+00:39:29,590 --> 00:39:35,470
+إذا قدرت تلاقي مصفوفة أخرى K بحيث المصفوفة هذه ايش
+
+349
+00:39:35,470 --> 00:39:42,190
+كتب عليها؟ non singular يعني ايش؟يعني المحدد ده
+
+350
+00:39:42,190 --> 00:39:47,050
+يساوي zero يعني المعكوس موجود تبعها تمام؟ إذا كنت
+
+351
+00:39:47,050 --> 00:39:51,730
+لاجي مصفوفة K بحيث المعكوس هيكون موجود وبالتالي
+
+352
+00:39:51,730 --> 00:39:58,090
+تبقى B تساوي K inverse في A كإن حدث ذلك بقول يبقى
+
+353
+00:39:58,090 --> 00:40:04,680
+A similar to Bطيب كويس ال remark بتقول لو كانت ال
+
+354
+00:40:04,680 --> 00:40:10,780
+a similar to b then be similar to a لحظة ما ياتي
+
+355
+00:40:10,780 --> 00:40:15,340
+لما تبقى هذه ك .. هذه بدي تكون main المعكوث تبعي
+
+356
+00:40:15,340 --> 00:40:19,300
+يعني أيش ما تكون المصروفة هذه بديها تكون هذه main
+
+357
+00:40:19,300 --> 00:40:23,660
+هذه المعكوث تبعها طيب بدنا نثبت ان لو كانت ال a
+
+358
+00:40:23,660 --> 00:40:28,840
+similar to b then be similar to a يبقى بداجي اقول
+
+359
+00:40:28,840 --> 00:40:39,310
+لات ال abe similar to be هدا معناته ايش؟ there
+
+360
+00:40:39,310 --> 00:40:49,210
+exist a there exist a non singular matrix
+
+361
+00:40:49,210 --> 00:40:53,070
+K
+
+362
+00:40:53,070 --> 00:41:04,920
+such thatبحيث ان الـ B بدي ساوي K inverse AKيبقى
+
+363
+00:41:04,920 --> 00:41:10,660
+انا طبقنا التعريف مباشرة هذه تقرا من ان a similar
+
+364
+00:41:10,660 --> 00:41:16,520
+to b انا بدى اثبت من ان b similar to a طب كويسة من
+
+365
+00:41:16,520 --> 00:41:20,800
+ات ايه اش رايكوا؟ بالداجل المصوفة هذه اضربها من
+
+366
+00:41:20,800 --> 00:41:25,040
+جهة اليمين في k inverse واضربها من جهة الشمال في
+
+367
+00:41:25,040 --> 00:41:35,450
+من؟ في k يبقى بناء عليه بصير عند هنا kبك انفرس بده
+
+368
+00:41:35,450 --> 00:41:45,850
+يساوي ك في ال ك انفرس في ال a في ال k ك انفرس
+
+369
+00:41:45,850 --> 00:41:50,070
+الشكل اللي عندنا هذا ايش بيعطينا؟
+
+370
+00:41:52,890 --> 00:41:56,130
+و مصفوفة الواحدة تضربها في أي مصفوفة، ماذا بتعطيك؟
+
+371
+00:41:56,130 --> 00:42:04,030
+نفس المصفوفة يبقى بصير عندنا ال A تساوي K في ال B
+
+372
+00:42:04,030 --> 00:42:10,210
+في ال K inverse الشكل اللي عندنا هذا هذا معناه ان
+
+373
+00:42:10,210 --> 00:42:16,530
+B similar to A؟ لأ مش صحيحبالشكل هذا لأ انا بدي
+
+374
+00:42:16,530 --> 00:42:22,730
+الاولى inverse والتانية بدون مظبوط لكن ك هادى بقدر
+
+375
+00:42:22,730 --> 00:42:27,650
+اكتبها ك inverse inverse صح ولا لأ مش المصفوفة ايه
+
+376
+00:42:27,650 --> 00:42:32,350
+تسوى a inverse inverse يبقى بقدر اكتب هادي على
+
+377
+00:42:32,350 --> 00:42:41,240
+الشكل التالى ان ال a يسوى ك inverseInverse بي
+
+378
+00:42:41,240 --> 00:42:47,220
+كإنفرس يبقى أنا جيت على المصوفة هذه واخدت من هنا
+
+379
+00:42:47,220 --> 00:42:51,300
+معكوسة يبقى هذا ينطمق على من؟ على التعريف اللي هو
+
+380
+00:42:51,300 --> 00:42:57,640
+هذا؟ إذا هذا معناه أن بي similar to ايه؟ هذا معناه
+
+381
+00:42:57,640 --> 00:43:09,220
+أن بي similar to ايه؟ وهو المطموقأظن نمرة اتنين هي
+
+382
+00:43:09,220 --> 00:43:15,040
+نفس نمرة واحد بس بدل بيحط مكانها مين ايه فقط لا
+
+383
+00:43:15,040 --> 00:43:21,800
+غير يبقى هنا similarly as
+
+384
+00:43:21,800 --> 00:43:29,460
+a زيها بالحرف الواحد لا تغير ولا تبديل نعطي مثال
+
+385
+00:43:29,460 --> 00:43:32,780
+توضيحي على ذلك يبقى example
+
+386
+00:43:35,250 --> 00:43:44,490
+المثال بيقول let المصوفة a تساوي واحد واحد سلبي
+
+387
+00:43:44,490 --> 00:43:55,190
+اتنين اربعة and المصوفة k تساوي واحد واحد واحد
+
+388
+00:43:55,190 --> 00:44:02,290
+اتنين find a matrix بي find a matrix
+
+389
+00:44:05,390 --> 00:44:12,850
+ب such that ال
+
+390
+00:44:12,850 --> 00:44:23,750
+a is similar to b يعني similar to b ماشي اقوله
+
+391
+00:44:23,750 --> 00:44:24,350
+solution
+
+392
+00:44:27,920 --> 00:44:34,860
+يبقى يعطيني مصحوفة A ومصحوفة K وقال هاتلي matrix B
+
+393
+00:44:34,860 --> 00:44:37,500
+بحيث ال A تبقى similar to B
+
+394
+00:44:51,960 --> 00:44:59,690
+أول خطوة باخد من ال determinant لل Kبدي أخد
+
+395
+00:44:59,690 --> 00:45:04,790
+determinant للـ K أشوفه كده بده يساوي يبقى واحد
+
+396
+00:45:04,790 --> 00:45:11,290
+واحد اتنين يبقى اتنين ناقص يساوي واحد لا يساوي ال
+
+397
+00:45:11,290 --> 00:45:22,830
+zero يبقى هنا ال K هذه ال K is non
+
+398
+00:45:22,830 --> 00:45:25,030
+singular
+
+399
+00:45:29,010 --> 00:45:32,890
+Madame non-singular إيه؟ بيظلمني مين؟ بده يظلمني
+
+400
+00:45:32,890 --> 00:45:40,030
+المعكوس تبعها، يبقى بده أروح أجيبله كinverse، why؟
+
+401
+00:45:40,280 --> 00:45:45,120
+يبقى هذه واحدة على المحدد التابعي المحدد التابعي
+
+402
+00:45:45,120 --> 00:45:50,960
+يبقى ده بواحد وباجي على كيف ببدل عناصر القطر
+
+403
+00:45:50,960 --> 00:45:57,820
+الرئيسي مكان بعض وبغير إشارات عناصر القطر الثانوي
+
+404
+00:45:57,820 --> 00:46:04,850
+بهذا الشكليبقى ده شو بده تصير اتنين سالب واحد سالب
+
+405
+00:46:04,850 --> 00:46:10,570
+واحد واحد هذا معكوس من معكوس ال K السؤال قال يهتلي
+
+406
+00:46:10,570 --> 00:46:16,690
+المصوفة B بحيث A تبقى similar to B اذا بروح بقوله
+
+407
+00:46:16,690 --> 00:46:24,070
+الان B اللي بدنا ياها هي عبارة عن K inverseاك
+
+408
+00:46:24,070 --> 00:46:31,010
+ويساول ك انفرستطلعناها اتنين سالب واحد سالب واحد
+
+409
+00:46:31,010 --> 00:46:39,410
+واحد في مين في اللي هو ال a واحد واحد ناقص اتنين
+
+410
+00:46:39,410 --> 00:46:44,950
+اربع في المصوفة ك itself بالشكل اللي عندنا هنا
+
+411
+00:46:44,950 --> 00:46:51,110
+اللي انا اقولش اللي احنا رفعينهdiagonalization
+
+412
+00:46:51,110 --> 00:46:55,730
+عارفين حصل الضرب لازم يعطيني ال diagonal matrix
+
+413
+00:46:55,730 --> 00:47:00,550
+وإلا بصير في عندي غلطة يبقى تأكد أن اللي بدي يطلع
+
+414
+00:47:00,550 --> 00:47:06,070
+عندي هو diagonal matrix يبقى هذا الكلام بده يساوي
+
+415
+00:47:06,070 --> 00:47:10,490
+هذه المصوفة الأولى اللي اتنين سالب واحد سالب واحد
+
+416
+00:47:10,490 --> 00:47:15,550
+واحد بدي أضرب هدول في بعض منها الصف الأول في
+
+417
+00:47:15,550 --> 00:47:18,370
+العمود الأول أظن بيعطيني اتنين هيك صح؟
+
+418
+00:47:37,200 --> 00:47:42,820
+مظبوط حصلت ضربك؟ يساوي
+
+419
+00:47:43,600 --> 00:47:46,700
+مصوفة اللي عندنا هذا برضه الصف الأول في العمود
+
+420
+00:47:46,700 --> 00:47:52,700
+الأول هي أربعة ونقص اتنين بطلع اتنين الصف الثاني
+
+421
+00:47:52,700 --> 00:47:57,320
+في العمود الاتنين في تلاتة بستة ونقص ستة بجداش
+
+422
+00:47:57,320 --> 00:48:02,320
+بزيرو الصف الثاني في العمود الأول نقص اتنين وزايد
+
+423
+00:48:02,320 --> 00:48:07,580
+اتنين يبقى زيرو الصف الثاني في العمود التاني يبقى
+
+424
+00:48:07,580 --> 00:48:13,270
+سالب تلاتة وزايد ستة بجداشبتلاتة بالشكل اللى عندنا
+
+425
+00:48:13,270 --> 00:48:19,470
+هذا يبقى أسوحة المصفوف اللى عندنا 2003 لحظة هذا
+
+426
+00:48:19,470 --> 00:48:24,590
+مين هذا هو ال diagonal matrix يبقى هذا هو ال
+
+427
+00:48:24,590 --> 00:48:28,310
+diagonal ال matrix اللى عندنا بالضبط تماما يبقى
+
+428
+00:48:28,310 --> 00:48:34,390
+شغلنا خلال هذا ال section كله كيف أحول المصفوفة
+
+429
+00:48:34,390 --> 00:48:40,400
+إلى مين إلى diagonal matrixلحظة لو رحنا ندور على
+
+430
+00:48:40,400 --> 00:48:45,120
+اتنين والتلاتة دول مين هم هدول باللي جيهم هم ال
+
+431
+00:48:45,120 --> 00:48:50,100
+eigenvalues اول ما بدينا ال eigenvalues اخدنا اول
+
+432
+00:48:50,100 --> 00:48:54,420
+مثال و طلعناهم اتنين تين real فكانت واحدة اتنين
+
+433
+00:48:54,420 --> 00:49:02,010
+واحدة تلاتة يبقى نفس الشيء ما علينابعد قليل هروح
+
+434
+00:49:02,010 --> 00:49:08,670
+نحط تعريف لل diagonalizable matrix ونبدأ نشتغل كيف
+
+435
+00:49:08,670 --> 00:49:13,990
+بدي أخلي المصوف اللي عندي تبقى diagonal matrix هذا
+
+436
+00:49:13,990 --> 00:49:18,770
+ما سنتعرضله في المحاضرة القادمة ان شاء الله تعالى
+
+437
+00:49:18,770 --> 00:49:19,710
+اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3eQp6W53jbo.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3eQp6W53jbo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2bcf268dabf2d46cf6ddd84e6b10a8229a7002ab
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3eQp6W53jbo.srt
@@ -0,0 +1,1665 @@
+1
+00:00:00,000 --> 00:00:01,260
+موسيقى
+
+2
+00:00:19,490 --> 00:00:23,670
+بسم الله الرحمن الرحيم نعود الآن لإكمال ما ابتدأنا
+
+3
+00:00:23,670 --> 00:00:28,950
+في المحاضرة الماضية وهو section 5-7 الذي يتحدث عن
+
+4
+00:00:28,950 --> 00:00:32,350
+الـundetermined coefficients اللي هي طريقة
+
+5
+00:00:32,350 --> 00:00:38,110
+المعاملات المجهولة لحل المعادلة التفاضلية بنحل بهذه 
+
+6
+00:00:38,110 --> 00:00:42,370
+الطريقة إذا تحقق في المعادلة أمران الأمر الأول
+
+7
+00:00:42,370 --> 00:00:48,210
+كانت المعاملات كلها ثوابت للمعادلة التفاضلية الأمر 
+
+8
+00:00:48,210 --> 00:00:53,450
+الثاني شكل الـ F of X يبقى على شكل معين ما هو هذا
+
+9
+00:00:53,450 --> 00:00:57,810
+الشكل؟ أحد ثلاثة أمور الأمر الأول أن يكون polynomial
+
+10
+00:00:57,810 --> 00:01:01,930
+الأمر الثاني polynomial في exponential الأمر 
+
+11
+00:01:01,930 --> 00:01:07,170
+الثالث polynomial في exponential في sin x أو cos x
+
+12
+00:01:07,170 --> 00:01:12,390
+أو مجموعهما أو الفرق فيما بينهما وعطينا على ذلك في 
+
+13
+00:01:12,390 --> 00:01:17,270
+المرة الماضية مثالين وهذا هو المثال رقم ثلاثة يبقى 
+
+14
+00:01:17,270 --> 00:01:21,270
+بدنا نحل المعادلة التفاضلية اللي عندنا هذه ذكرنا 
+
+15
+00:01:21,270 --> 00:01:24,830
+في المرة الماضية بنجزئها إلى جزئين بناخد الـ 
+
+16
+00:01:24,830 --> 00:01:28,730
+homogeneous ومن ثم الـ non homogeneous differential 
+
+17
+00:01:28,730 --> 00:01:34,790
+equation يبقى بداجي أقوله افترض أن Y تساوي E أس RX
+
+18
+00:01:34,790 --> 00:01:45,450
+بيه solution of the homogeneous differential
+
+19
+00:01:45,450 --> 00:01:51,890
+equation اللي هي المعادلة التالية Y W Prime زائد Y 
+
+20
+00:01:51,890 --> 00:01:57,450
+يساوي Zero then the characteristic equation 
+
+21
+00:02:12,070 --> 00:02:18,010
+الحل المتجانس يبقى 
+
+22
+00:02:22,280 --> 00:02:32,080
+The Homogeneous Differential Equation is يساوي 
+
+23
+00:02:32,080 --> 00:02:40,580
+يساوي يساوي
+
+24
+00:02:40,580 --> 00:02:44,700
+يساوي يساوي يساوي يساوي يساوي يساوي يساوي يساوي
+
+25
+00:02:44,700 --> 00:02:45,880
+يساوي يساوي يساوي يساوي يساوي يساوي يساوي يساوي
+
+26
+00:02:45,880 --> 00:02:47,560
+يساوي يساوي يساوي يساوي يساوي يساوي يساوي يساوي
+
+27
+00:02:47,560 --> 00:02:47,620
+يساوي يساوي يساوي يساوي يساوي يساوي يساوي يساوي
+
+28
+00:02:47,620 --> 00:02:51,060
+يساوي يساوي
+
+29
+00:02:51,060 --> 00:02:56,550
+يبقى أروح أدور على particular solution لحل 
+
+30
+00:02:56,550 --> 00:03:01,730
+المعادلة اللي هي non homogeneous فباجي بقوله the 
+
+31
+00:03:01,730 --> 00:03:07,970
+particular solution
+
+32
+00:03:07,970 --> 00:03:17,010
+of the Differential equation start وبروح اللي فوق
+
+33
+00:03:17,010 --> 00:03:24,150
+الأساسية هذه بسميها star (S) مديله الرمز YP وبدي
+
+34
+00:03:24,150 --> 00:03:31,510
+بقول كتالي X to the power S V بأجي على شكل اللي هو
+
+35
+00:03:31,510 --> 00:03:35,650
+الدالة اللي عندنا هذه رقم في sign يعني polynomial
+
+36
+00:03:35,650 --> 00:03:39,790
+من الدرجة الصفرية مضروبة في sign إذا بدي أكتب
+
+37
+00:03:39,790 --> 00:03:43,630
+polynomial من الدرجة الصفرية في sign زائد
+
+38
+00:03:43,630 --> 00:03:49,090
+polynomial في cosine يبقى بقدر أقول هذه عبارة عن a 
+
+39
+00:03:49,090 --> 00:03:55,610
+في cosine الـ x زائد b في sine الـ x بالشكل اللي
+
+40
+00:03:55,610 --> 00:04:04,280
+عندنا هذا عندما أبحث عن قيمة S هل هي 0 أو 1 أو 2 أو 
+
+41
+00:04:04,280 --> 00:04:06,980
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 
+
+42
+00:04:06,980 --> 00:04:10,500
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 
+
+43
+00:04:10,500 --> 00:04:10,560
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو
+
+44
+00:04:10,560 --> 00:04:10,600
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو
+
+45
+00:04:10,600 --> 00:04:11,400
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو
+
+46
+00:04:11,400 --> 00:04:11,720
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو
+
+47
+00:04:11,720 --> 00:04:21,600
+3 أو 3 أو 3 أو 3 أو 3 أو 3 أو 3 أو
+
+48
+00:04:24,720 --> 00:04:28,780
+بواحد وشوف لو حطيتها بواحد بيظل فيه تشابه ولا بيكون
+
+49
+00:04:28,780 --> 00:04:34,980
+انتهى هذا التشابه إذا لو حطيت S بواحد بيصير AX Cos
+
+50
+00:04:34,980 --> 00:04:41,400
+وهنا BX Sin هل في أي term هنا يشبه أي term هنا
+
+51
+00:04:41,400 --> 00:04:48,920
+طبعا لأ يبقى هنا here هنا الـ S تساوي واحد لما حط الـ
+
+52
+00:04:48,920 --> 00:04:53,740
+S تساوي واحد بيكون أزلنا الشبه اللي موجود تماما ما
+
+53
+00:04:53,740 --> 00:04:56,880
+بين الـ complementary solution و الـ particular
+
+54
+00:04:56,880 --> 00:05:02,600
+solution يبقى بناء عليه هيصبح YP على الشكل التالي
+
+55
+00:05:02,600 --> 00:05:12,510
+AX في cosine X زائد BX في sine X الآن بدنا نحدد
+
+56
+00:05:12,510 --> 00:05:19,010
+قيمتين ثوابت الـ A و الـ B لذلك بدي اشتق مرة و اثنين
+
+57
+00:05:19,010 --> 00:05:26,590
+و أعوض في المعادلة الأصلية يبقى بدي أخد Y P Prime
+
+58
+00:05:26,930 --> 00:05:34,310
+هذه المشتقة حصل ضرب دالتين يبقى a في cos x ناقص ax 
+
+59
+00:05:34,310 --> 00:05:41,070
+في sin x زائد كمان هذه حصل ضرب دالتين يبقى b في 
+
+60
+00:05:41,070 --> 00:05:50,100
+sin x زائد bx في cos x يبقى اشتقنا كله من X و Cos X
+
+61
+00:05:50,100 --> 00:05:56,040
+و X و Sin X كحاصل ضرب دالتين هذا حصلنا على Y' طبعا 
+
+62
+00:05:56,040 --> 00:06:00,020
+ما فيش ولا term زي الثاني يبقى بيخلي كل شيء زي ما 
+
+63
+00:06:00,020 --> 00:06:06,500
+هو بدنا نروح نجيب YPW' يبقى بدنا نشتق هذه بالسالب
+
+64
+00:06:06,500 --> 00:06:16,830
+A Sin X وهذه السالب A Sin X بعد ذلك السالب ax في
+
+65
+00:06:16,830 --> 00:06:23,190
+cos x اشتقت هذه حصل ضرب دالتين بنانيج اللي بعدها
+
+66
+00:06:23,190 --> 00:06:29,610
+يبقى زائد b في cos x خلصنا منها بدأت أشتق هذه حصل
+
+67
+00:06:29,610 --> 00:06:38,190
+ضرب دالتين يبقى زائد b في cos x ناقص bx في sin x
+
+68
+00:06:38,620 --> 00:06:42,780
+يبقى اشتقناه حصل ضرب دالتين هنا في بعض العناصر 
+
+69
+00:06:42,780 --> 00:06:50,640
+متشابهة هي عند هنا سالب اثنين a في sine الـ X وعندي 
+
+70
+00:06:50,640 --> 00:06:56,880
+كمان زائد اثنين b في cosine الـ X هدول اثنين مع بعض
+
+71
+00:06:56,880 --> 00:07:03,720
+وهدول اثنين مع بعض باقي عندي ناقص ax في cosine الـ 
+
+72
+00:07:03,720 --> 00:07:10,180
+X وناقص bx في sine الـ X بعد ذلك اخذ المعلومات اللي 
+
+73
+00:07:10,180 --> 00:07:15,040
+حصلت عليها و أعوض في المعادلة star يبقى هنا 
+
+74
+00:07:15,040 --> 00:07:23,320
+substitute in 
+
+75
+00:07:23,320 --> 00:07:33,740
+the differential equation star we get بنحصل على ما 
+
+76
+00:07:33,740 --> 00:07:34,200
+يأتي
+
+77
+00:07:40,110 --> 00:07:43,630
+يجب أن ازالة وي دابلي برايم واحط قيمتها وي دابلي 
+
+78
+00:07:43,630 --> 00:07:48,950
+برايم هي حصلنا عليها يبقى ناقص اثنين اف صين
+
+79
+00:07:48,950 --> 00:07:55,980
+الزاوية ثتا صين الزاوية X تمام؟ اللي بعدها زائد
+
+80
+00:07:55,980 --> 00:08:04,340
+اثنين B في cosine الـ X اللي بعدها ناقص الـ AX في
+
+81
+00:08:04,340 --> 00:08:11,080
+cosine الـ X ناقص الـ BX في sine الـ X هذا كله اللي
+
+82
+00:08:11,080 --> 00:08:17,400
+أخدته مين؟ YW prime ضايق لنا مين؟ Y وين Y هايها؟ 
+
+83
+00:08:17,400 --> 00:08:24,560
+بده أجمعهم هدول يبقى زائدهه اللي هو مين ax في cos
+
+84
+00:08:24,560 --> 00:08:33,520
+x وبعد هي كده زائد bx في sin x كله بيساوي الطرف
+
+85
+00:08:33,520 --> 00:08:40,300
+اللي يتبع المعادلة اللي هو 4 في sin x بنجي نجمع عن 
+
+86
+00:08:40,300 --> 00:08:47,940
+ax cos بالسالب و ax cos بالموجب عنا bx sin بالسالب 
+
+87
+00:08:47,940 --> 00:08:53,220
+و bx بيمين بالموجب يبقى صفة المعادلة على الشكل
+
+88
+00:08:53,220 --> 00:09:00,740
+التالي ناقص اثنين a sin x زائدي اثنين b cos x كله 
+
+89
+00:09:00,740 --> 00:09:07,540
+بده يساوي أربع sin x بعد ذلك نقرر المعاملات في
+
+90
+00:09:07,540 --> 00:09:13,340
+الطرفين إذا لو قررنا المعاملات في الطرفين بسنا نقص
+
+91
+00:09:13,340 --> 00:09:19,580
+اثنين a بدي أساوي قداش؟ أربع وعندك اثنين b بدي عندي 
+
+92
+00:09:19,580 --> 00:09:26,520
+cosine هنا ما عندناش يبقى بيه Zero هذا معناه أن الـ a
+
+93
+00:09:26,520 --> 00:09:33,330
+تساوي سالب اثنين و الـ b تساوي Zero يبقى أصبح شكل الـ 
+
+94
+00:09:33,330 --> 00:09:46,570
+YP على الشكل التالي يبقى
+
+95
+00:09:46,570 --> 00:09:50,570
+أصبح هذا شكل الـ YP
+
+96
+00:10:01,840 --> 00:10:11,150
+Y يساوي YC زائد YP يبقى بناء عليه يصبح y يساوي yc هي 
+
+97
+00:10:11,150 --> 00:10:20,070
+الموجودة عندي يبقى c1 cos x زائد c2 في sin x وزائد 
+
+98
+00:10:20,070 --> 00:10:28,010
+yp ناقص 2x في cos x يبقى هذا الحل النهائي تبع من؟
+
+99
+00:10:28,010 --> 00:10:32,990
+تبع المعادلة لاحظي ولا term من الثلاث termات زي
+
+100
+00:10:32,990 --> 00:10:38,240
+الثاني ما فيش تشابه بين أي term والـ term الثاني
+
+101
+00:10:38,240 --> 00:10:46,440
+المثال رقم أربعة يبقى example أربعة 
+
+102
+00:10:46,440 --> 00:10:50,720
+بقول
+
+103
+00:10:50,720 --> 00:10:56,260
+دي term a suitable 
+
+104
+00:10:56,260 --> 00:11:03,480
+form شكل
+
+105
+00:11:03,480 --> 00:11:09,990
+مناسب For the 
+
+106
+00:11:09,990 --> 00:11:19,330
+particular solution
+
+107
+00:11:19,330 --> 00:11:23,490
+of the
+
+108
+00:11:23,960 --> 00:11:32,520
+Differential equation للمعادلة التفاضلية YW' ناقص
+
+109
+00:11:32,520 --> 00:11:49,540
+4Y' زائد 4Y يساوي 2X تربيع زائد 4X E أس 2X زائد X
+
+110
+00:11:49,540 --> 00:11:55,100
+في Sin 2X وهذه بدي اسميها المعادلة هي من 
+
+111
+00:11:55,100 --> 00:12:00,960
+الـ star وبين جسين don't
+
+112
+00:12:00,960 --> 00:12:07,800
+don't evaluate the 
+
+113
+00:12:07,800 --> 00:12:08,620
+constants
+
+114
+00:12:38,460 --> 00:12:43,640
+قالب الكوينة تانينقرأ السؤال مرة ثانية ونشوف شو
+
+115
+00:12:43,640 --> 00:12:51,120
+المطلوب بيقول لي حدد حل في شكل مناسب للـ particular
+
+116
+00:12:51,120 --> 00:12:54,400
+solution y, z تبع الـ differential equation هذا
+
+117
+00:12:54,400 --> 00:12:57,020
+يبقى الناس بتحدد شكل الـ particular solution
+
+118
+00:12:57,020 --> 00:13:00,840
+ويقول لي ما تحسبش الثوابت اضايع شواجدك وأنت بتجيب
+
+119
+00:13:00,840 --> 00:13:04,120
+المشتقة الأولى والثانية وتعوض في المعادلة وتجيب
+
+120
+00:13:04,120 --> 00:13:07,940
+ليه قد ايش قيمة a و b أو a و b و c وما إلا بتديش قيمة
+
+121
+00:13:07,940 --> 00:13:11,650
+ثوابت بس هتلي شكل الـ main الـ Particular solution ليس
+
+122
+00:13:11,650 --> 00:13:15,790
+لازم يكون قيمته ثابتة بقوله كويس يبقى يحتاج
+
+123
+00:13:15,790 --> 00:13:20,350
+للمعادلة يحتاج أن يأخذ الـ Homogeneous differential
+
+124
+00:13:20,350 --> 00:13:24,550
+equation يبقى يبدأ كما بدأت في المثال اللي قبله
+
+125
+00:13:24,550 --> 00:13:29,290
+let Y تساوي E أس RX بإيه؟ 
+
+126
+00:13:41,220 --> 00:13:50,680
+يبقى باجي بقوله the characteristic Equation is R
+
+127
+00:13:50,680 --> 00:13:56,060
+تربيع ناقص أربعة R زائد أربعة يساوي Zero أو أن 
+
+128
+00:13:56,060 --> 00:14:02,560
+شئتم فقولوا R ناقص اثنين لكل تربيع تساوي Zero أو 
+
+129
+00:14:02,560 --> 00:14:09,370
+الـ R تساوي اثنين والحل هذا مكبر كم مرة؟ يبقى مرتين
+
+130
+00:14:09,370 --> 00:14:12,850
+يبقى of multiplicity two
+
+131
+00:14:19,800 --> 00:14:25,640
+2 يعني الحل مكرر مرتين بناء عليه بروح بقوله هنا
+
+132
+00:14:25,640 --> 00:14:32,220
+يبقى solution yc بده يساوي الحل real ومكرر مرتين
+
+133
+00:14:32,220 --> 00:14:38,680
+يبقى c1 زائد c2x e أس r
+
+134
+00:14:44,740 --> 00:14:49,820
+بنبروز هذا الحل وبنسيبه وبنروح نرجع له بعد قليل
+
+135
+00:14:49,820 --> 00:14:52,800
+الآن بدنا نيجي للـ non homogeneous differential
+
+136
+00:14:52,800 --> 00:14:56,280
+equation اللي الـ star اللي عندنا بدنا نتطلع على
+
+137
+00:14:56,280 --> 00:15:00,240
+شكل الـ F of X اللي هو الشكل اللي عندنا هذا هل هي 
+
+138
+00:15:00,240 --> 00:15:05,740
+polynomial فقط؟ أو polynomial في exponential أو
+
+139
+00:15:05,740 --> 00:15:09,360
+polynomial في sin أو cos المجموعة الحمد لله جايبة 
+
+140
+00:15:09,360 --> 00:15:13,720
+الثلاث حالات كلهم بسؤال انواعي هي polynomial من
+
+141
+00:15:13,720 --> 00:15:17,180
+الدرجة الثانية polynomial من الدرجة الأولى في 
+
+142
+00:15:17,180 --> 00:15:21,820
+exponential polynomial من الدرجة الأولى في sin إذا 
+
+143
+00:15:21,820 --> 00:15:27,630
+إيش هأعمل في المعادلة اللي عندي؟ هأجزقها إلى ثلاث
+
+144
+00:15:27,630 --> 00:15:31,690
+معادلات تمام؟ و أحل كل واحدة فيهم و أجيب الـ
+
+145
+00:15:31,690 --> 00:15:35,390
+particular solution تبعها وأجمع الحلول الثلاثة
+
+146
+00:15:35,390 --> 00:15:38,810
+بيعطيني الـ particular solution لمين؟ للمعادلة 
+
+147
+00:15:38,810 --> 00:15:43,970
+طبقا للنظرية اللي أعطانيها لكم في أول section في 
+
+148
+00:15:43,970 --> 00:15:46,970
+الـ non homogeneous differential equation قولنا لكم
+
+149
+00:15:46,970 --> 00:15:53,150
+هذا بيلزمنا لمين؟ للـ sections القادمة تمام؟ يبقى 
+
+150
+00:15:53,150 --> 00:16:01,260
+بداجي أقوله هنا differential equation star is
+
+151
+00:16:01,260 --> 00:16:08,360
+written as يمكننا أن نكتبها على الشكل التالي الـ y 
+
+152
+00:16:08,360 --> 00:16:14,460
+double prime ناقص أربعة y prime زائد أربعة y يساوي 
+
+153
+00:16:14,460 --> 00:16:20,580
+كم؟ يساوي اثنين x تربيع المعادلة الثانية اللي هي 
+
+154
+00:16:20,580 --> 00:16:33,690
+مين؟ YW'-4Y' زائد 4Y يساوي 4XE2X 
+
+155
+00:16:33,690 --> 00:16:45,370
+المعادلة الثالثة YW'-4Y' زائد 4Y يساوي XSIN2X يساوي
+
+156
+00:16:45,370 --> 00:16:50,350
+X في SIN2X بالشكل اللي عندنا هذا
+
+157
+00:16:58,280 --> 00:17:03,840
+طيب، الآن يعني كأنه صار عندي مش مسألة واحدة، ثلاث 
+
+158
+00:17:03,840 --> 00:17:07,120
+مسائل، بدي أحل كل واحد أجيب الـ particle solution
+
+159
+00:17:07,120 --> 00:17:12,980
+كأنه لا علاقة لها بمين؟ بالأخرى، يبقى هنا بدي أجيب
+
+160
+00:17:12,980 --> 00:17:20,180
+الـ YP1 يبقى YP1 يساوي X to the power S فيه، هذه 
+
+161
+00:17:20,180 --> 00:17:21,740
+polynomial من الدرجة 
+
+162
+00:17:34,810 --> 00:17:40,490
+هل أي term من هنا يشبه
+
+163
+00:17:40,490 --> 00:17:42,250
+أي term فوق؟
+
+164
+00:17:45,280 --> 00:17:52,060
+مضروبة يعني هذا C1 E2 X و C2 X E2 فيه؟ ما عنديش 
+
+165
+00:17:52,060 --> 00:17:56,020
+exponential هناك بما فيش يبقى هنا S بقدر إيه؟ ب
+
+166
+00:17:56,020 --> 00:18:03,680
+Zero يبقى here الـ S تساوي Zero يبقى أصبح Y P1 بده 
+
+167
+00:18:03,680 --> 00:18:11,780
+يساوي A0 X تربيع زائد A1 X زائد A2 سيبونا من هذا
+
+168
+00:18:11,780 --> 00:18:20,370
+ننتقل على اللي بعدها يبقى بدي أكتب يبقى
+
+169
+00:18:20,370 --> 00:18:23,230
+بدي أكتب polynomial من الدرجة الأولى في الـ 
+
+170
+00:18:23,230 --> 00:18:26,990
+exponential يبقى بدي أكتب polynomial من الدرجة 
+
+171
+00:18:26,990 --> 00:18:32,070
+الأولى في الـ exponential يبقى بدي أكتب polynomial
+
+172
+00:18:32,070 --> 00:18:34,410
+من الدرجة الأولى في الـ exponential يبقى بدي أكتب 
+
+173
+00:18:34,410 --> 00:18:37,350
+polynomial من الدرجة الأولى في الـ exponential
+
+174
+00:18:37,350 --> 00:18:37,390
+exponential يبقى بدي أكتب polynomial من الدرجة
+
+175
+00:18:37,390 --> 00:18:38,650
+الأولى في الـ exponential يبقى بدي أكتب polynomial
+
+176
+0
+
+201
+00:20:37,040 --> 00:20:47,000
+كل هذا الكلام مضروب في cos 2x زائد e<sup>x</sup>
+
+202
+00:20:47,000 --> 00:20:53,980
+زائد e<sup>x</sup> كله مضروب في sin 2x و exponential ماعنديش
+
+203
+00:20:56,240 --> 00:21:03,100
+هل أي term من المستطيل اللي فوق هذا يشبه أي term
+
+204
+00:21:03,100 --> 00:21:07,720
+من المستطيل اللي فوق هذا؟ لأ ولا فيه sign ولا cos
+
+205
+00:21:07,720 --> 00:21:08,120
+ساين
+
+206
+00:21:13,370 --> 00:21:20,650
+الـ S بدها تساوي 0 يبقى أصبح YP3 بدها تساوي D e<sup>x</sup>
+
+207
+00:21:20,650 --> 00:21:32,590
+X زائد D1 في Cos 2X زائد E e<sup>x</sup> زائد E1 في Sin
+
+208
+00:21:32,590 --> 00:21:38,120
+2X يبقى الـ Particular solution اللي بدنا يا بنات
+
+209
+00:21:38,120 --> 00:21:47,060
+يبقى يساوي YP1 زائد YP2 زائد YP3 يبقى أصبح YP
+
+210
+00:21:47,060 --> 00:21:55,380
+يساوي YP1 هاي و بنزله زي ما هو A0 X تربيع A1X زائد
+
+211
+00:21:55,380 --> 00:21:57,580
+A2 زائد
+
+212
+00:22:19,860 --> 00:22:21,260
+YP2 YP3 YP4 YP5 YP6 YP7
+
+213
+00:22:29,550 --> 00:22:36,330
+يبقى هذا كله يعتبر من ال particular solution اللي
+
+214
+00:22:36,330 --> 00:22:41,990
+مطلوب عنها حد فيكوا له أي تساؤل هنا في هذا السؤال؟
+
+215
+00:22:41,990 --> 00:22:48,270
+في أي تساؤل؟ طيب على هيك انتهى هذا ال section وإلى
+
+216
+00:22:48,270 --> 00:22:55,590
+يكون أرقام المسائل يبقى exercises خمسة سبعة
+
+217
+00:22:55,590 --> 00:23:01,730
+المسائل التالية من واحد لغاية عشرين ومن خمسة
+
+218
+00:23:01,730 --> 00:23:08,730
+وعشرين لغاية ثلاثين مرني
+
+219
+00:23:08,730 --> 00:23:13,530
+أديكي قد ما تقدري بتصير هذا الموضوع بصير جدا
+
+220
+00:23:26,290 --> 00:23:49,450
+اللي فوق هذا انتهينا منه أظن خلاص؟
+
+221
+00:23:49,450 --> 00:23:55,440
+طيب لما ننتقل إلى ال section الأخير من هذا ال
+
+222
+00:23:55,440 --> 00:24:00,320
+chapter وهي الطريقة الثانية من طرق حل ال non
+
+223
+00:24:00,320 --> 00:24:03,800
+homogeneous differential equation وهي طريقة ال
+
+224
+00:24:03,800 --> 00:24:11,280
+variation of parameters تغيير الوسيطات يبقى 85 أو
+
+225
+00:24:11,280 --> 00:24:19,340
+58 اللي هو variation of
+
+226
+00:24:20,530 --> 00:24:29,030
+Parameters نستخدم
+
+227
+00:24:29,030 --> 00:24:39,410
+هذه الطريقة نستخدم هذه الطريقة to find a
+
+228
+00:24:39,410 --> 00:24:45,850
+particular solution to find a particular
+
+229
+00:24:54,020 --> 00:24:58,120
+YP الرمز للإيقاع
+
+230
+00:25:01,140 --> 00:25:07,280
+Differential equation للمعادلة التفاضلية a<sub>0</sub> as a
+
+231
+00:25:07,280 --> 00:25:14,040
+function of x زائد ال a<sub>1</sub> as a function of x لل
+
+232
+00:25:14,040 --> 00:25:21,470
+derivative n-1 زائد نبقى ماشي لغاية a<sub>n</sub>
+
+233
+00:25:21,470 --> 00:25:27,750
+-1 as a function of x y' زائد a<sub>n</sub> as a
+
+234
+00:25:27,750 --> 00:25:33,130
+function of x في ال y بده يساوي  F(x)
+
+235
+00:25:33,130 --> 00:25:36,790
+وهذه اللي كنا بنطلق عليها المعادلة الأصلية اللي هي
+
+236
+00:25:36,790 --> 00:25:46,210
+star where حيث ال a<sub>0</sub>(x) و ال a<sub>1</sub>(x) و
+
+237
+00:25:46,210 --> 00:25:54,330
+لغاية ال a<sub>n</sub>(x) هدول كلهم need not need not
+
+238
+00:25:54,330 --> 00:26:00,510
+constants need
+
+239
+00:26:00,510 --> 00:26:09,410
+not constants and no restriction ماعنديش قيود
+
+240
+00:26:09,410 --> 00:26:24,010
+ماعنديش
+
+241
+00:26:24,010 --> 00:26:24,850
+قيود عليها
+
+242
+00:26:33,720 --> 00:26:46,600
+YC يبدو يساوي C<sub>1</sub>Y<sub>1</sub> زائد C<sub>2</sub>Y<sub>2</sub> زائد C<sub>n</sub>Y<sub>n</sub> Assume that
+
+243
+00:26:46,600 --> 00:26:57,440
+is a solution of the homo
+
+244
+00:27:10,960 --> 00:27:16,840
+زائد زائد a<sub>n-1</sub> as a function of x في ال y
+
+245
+00:27:16,840 --> 00:27:23,680
+prime زائد a<sub>n</sub>(x) y بده يساوي كده؟ بده يساوي 0
+
+246
+00:27:29,020 --> 00:27:32,880
+to get a
+
+247
+00:27:32,880 --> 00:27:37,540
+particular solution
+
+248
+00:27:37,540 --> 00:27:46,180
+to get a particular solution yp of the
+
+249
+00:27:46,180 --> 00:27:56,140
+differential equation star by the method
+
+250
+00:27:59,990 --> 00:28:07,590
+of variation of
+
+251
+00:28:07,590 --> 00:28:20,570
+parameters replace
+
+252
+00:28:20,570 --> 00:28:32,010
+استبدل replace the above constants above constants
+
+253
+00:28:32,010 --> 00:28:42,250
+in
+
+254
+00:28:42,250 --> 00:28:48,930
+the solution yc
+
+255
+00:28:48,930 --> 00:28:52,550
+by the functions
+
+256
+00:28:55,020 --> 00:29:10,660
+The functions C<sub>1</sub>(X) C<sub>2</sub>(X) و لغاية C<sub>n</sub>(X) That
+
+257
+00:29:10,660 --> 00:29:11,060
+is
+
+258
+00:29:15,470 --> 00:29:25,490
+YP يصبح على الشكل التالي C<sub>1</sub>(X)Y<sub>1</sub> C<sub>2</sub>(X)Y<sub>2</sub> زائد
+
+259
+00:29:25,490 --> 00:29:29,470
+C<sub>n</sub>(X)Y<sub>n</sub>
+
+260
+00:29:35,370 --> 00:29:44,010
+الـ C<sub>m</sub> as a function of X يسوي تكامل الورنسكين m
+
+261
+00:29:44,010 --> 00:29:51,350
+as a function of X في F<sub>1</sub>(X) على
+
+262
+00:29:51,350 --> 00:29:59,090
+الورنسكين (X) كله بالنسبة إلى DX والـ M
+
+263
+00:30:02,270 --> 00:30:09,990
+و لغاية ال N و
+
+264
+00:30:09,990 --> 00:30:14,950
+لغاية
+
+265
+00:30:14,950 --> 00:30:21,750
+ال N و لغاية ال N و لغاية ال N و لغاية ال N
+
+266
+00:30:28,070 --> 00:30:34,350
+is the determinant المحدد
+
+267
+00:30:34,350 --> 00:30:41,370
+obtained from
+
+268
+00:30:41,370 --> 00:30:46,810
+الوانسكين
+
+269
+00:30:46,810 --> 00:30:52,130
+of X by replacing
+
+270
+00:30:58,290 --> 00:31:15,810
+By replacing the m column By the column By
+
+271
+00:31:15,810 --> 00:31:26,730
+the column Zero Zero ونظل ماشيين لغاية الواحد and
+
+272
+00:31:30,230 --> 00:31:42,150
+الـ F<sub>1</sub>(X) تساوي الـ F(X) مقسومة على A<sub>0</sub>(X)
+
+273
+00:31:42,150 --> 00:31:45,550
+Note
+
+274
+00:31:45,550 --> 00:31:50,310
+When
+
+275
+00:31:50,310 --> 00:32:00,490
+we use the method when we use the method of
+
+276
+00:32:00,490 --> 00:32:05,590
+variation
+
+277
+00:32:05,590 --> 00:32:15,910
+of parameters عندما
+
+278
+00:32:15,910 --> 00:32:23,110
+نستخدم هذه الطريقة variation of parameters the
+
+279
+00:32:23,110 --> 00:32:23,850
+coefficient
+
+280
+00:32:33,870 --> 00:32:45,010
+يجب أن يكون يومي يومي
+
+281
+00:32:45,010 --> 00:32:47,290
+يومي يومي يومي يومي يومي يومي يومي
+
+282
+00:32:58,790 --> 00:33:11,670
+is of the second order
+
+283
+00:33:11,670 --> 00:33:14,970
+that
+
+284
+00:33:14,970 --> 00:33:18,690
+is
+
+285
+00:33:20,880 --> 00:33:30,340
+الـ A<sub>0</sub>(x) y'' A<sub>1</sub>(x) y' A<sub>2</sub>(x) y
+
+286
+00:33:30,340 --> 00:33:35,420
+بدها تساوي f
+
+287
+00:33:35,420 --> 00:33:50,710
+of x and f y<sub>1</sub> and y<sub>2</sub> are two solutions are two
+
+288
+00:33:50,710 --> 00:33:57,990
+solutions of
+
+289
+00:33:57,990 --> 00:34:12,570
+the homogeneous equation A<sub>0</sub>(x) y'' A<sub>1</sub>(x) 
+
+290
+00:34:12,570 --> 00:34:18,570
+y' A<sub>2</sub>(x) y بدو يساوي zero then
+
+291
+00:34:23,050 --> 00:34:33,070
+الـ C<sub>1</sub>(X) هو تكامل لناقص Y<sub>2</sub> as a function of X
+
+292
+00:34:33,070 --> 00:34:39,550
+في الـ F<sub>1</sub>(X) على W(X) DX
+
+293
+00:34:43,770 --> 00:34:51,950
+الـ C<sub>2</sub> as a function of X بده يساوي تكامل لمين؟
+
+294
+00:34:51,950 --> 00:34:58,690
+بده يساوي تكامل للـ Y<sub>1</sub> as a function of X في الـ
+
+295
+00:34:58,690 --> 00:35:05,170
+F<sub>1</sub>(X) كله على الـ W(X) في الـ DX
+
+296
+00:35:05,170 --> 00:35:10,030
+example
+
+297
+00:35:10,030 --> 00:35:10,490
+1
+
+298
+00:35:15,200 --> 00:35:26,200
+Find the general solution of
+
+299
+00:35:26,200 --> 00:35:32,340
+the differential equation للمعادلة
+
+300
+00:35:32,340 --> 00:35:38,340
+التفاضلية Y'''-2Y
+
+301
+00:35:43,090 --> 00:35:51,990
+للمعاملة التحوي عضلية y
+
+302
+00:35:51,990 --> 00:36:03,650
+''' زائد y' بدي يساوي x يساوي
+
+303
+00:36:03,650 --> 00:36:12,610
+x و ناقص y على 2 أقل من x أقل من y على 2
+
+304
+00:37:01,140 --> 00:37:06,600
+الطريقة الثانية من حل المعادلة التفاضلية غير
+
+305
+00:37:06,600 --> 00:37:11,260
+المتجانسة هذه الطريقة سمنها ال variation of
+
+306
+00:37:11,260 --> 00:37:14,940
+parameters يبقى أول طريقة طريقة ال undetermined
+
+307
+00:37:14,940 --> 00:37:18,380
+coefficients والطريقة الثانية التي هي طريقة ال
+
+308
+00:37:18,380 --> 00:37:23,200
+variation of parameters تغيير الوسيطات تتلخص هذه
+
+309
+00:37:23,200 --> 00:37:26,740
+الطريقة فيما يأتي طبعا الـ Undetermined
+
+310
+00:37:26,740 --> 00:37:30,880
+coefficients قلنا مشان نشتغل بها بدي شرطين أن
+
+311
+00:37:30,880 --> 00:37:34,860
+المعاملة ثابتة و ال F(x) تبقى على شكل معين حسب
+
+312
+00:37:34,860 --> 00:37:37,660
+الجدول اللي اعطاناكوا يعني، مظبوط؟ هنا ال
+
+313
+00:37:37,660 --> 00:37:41,460
+variation بيقولي لأ المعاملة ثابتة و الله متغيرة
+
+314
+00:37:41,460 --> 00:37:45,660
+ماعنديش مشكلة ال F(x) اللي في الطرف اليمين هذه
+
+315
+00:37:45,660 --> 00:37:49,180
+ال F(x) كانت على شكل معين و الله غير عليها شكل
+
+316
+00:37:49,180 --> 00:37:53,590
+معين ماعنديش مشكلة يعني أيش ما يكون شكل ال F يكون و
+
+317
+00:37:53,590 --> 00:37:56,590
+ايش ما يكون المعاملة ثوابت أو متغيرات ماعنديش
+
+318
+00:37:56,590 --> 00:38:00,970
+مشكلة يبقى هذا الشكل العام للمعادلة (*) حيث هدول
+
+319
+00:38:00,970 --> 00:38:05,350
+الدوال need not constants ليس بالضرورة يكونوا constants يعني
+
+320
+00:38:05,350 --> 00:38:08,470
+ممكن يكونوا constants وممكن يكونوا متغيرات ماعنديش
+
+321
+00:38:08,470 --> 00:38:12,070
+مشكلة في هذه الحالة and
+
+322
+00:38:13,430 --> 00:38:18,250
+and no restrictions
+
+323
+00:38:18,250 --> 00:38:23,170
+ماعنديش قيود على شكل ال F(x) في ال Undetermined
+
+324
+00:38:23,170 --> 00:38:25,650
+قلت يابولينوميال يابولينوميال في الاكسبوننشيل
+
+325
+00:38:25,650 --> 00:38:28,830
+يابولينوميال في اكسبوننشيل في الاكسبوننشيل في
+
+326
+00:38:28,830 --> 00:38:33,850
+الاكسبوننشيل في الاكسبوننشيل في الاكسبوننشيل في
+
+327
+00:38:33,850 --> 00:38:35,710
+الاكسبوننشيل في الاكسبوننشيل في الاكسبوننشيل في
+
+328
+00:38:35,710 --> 00:38:36,610
+الاكسبوننشيل في الاكسبوننشيل في الاكسبوننشيل في
+
+329
+00:38:36,610 --> 00:38:37,770
+الاكسبوننشيل في الاكسبوننشيل في الاكسبوننشيل في
+
+330
+00:38:37,770 --> 00:38:38,170
+الاكسبوننشيل في الاكسبوننشيل في الاكسبوننشيل في
+
+331
+00:38:38,170 --> 00:38:40,250
+الاكسبوننشيل في الاكسبوننشيل في الاكسبوننشيل في
+
+332
+00:38:40,250 --> 00:38:45,310
+الاكسبوننشيل في الاكس هذا الشغل الوحيد اللي هو الحل
+
+333
+00:38:45,310 --> 00:38:47,610
+الـComplementary Solution بدي أدور على الـ
+
+334
+00:38:47,610 --> 00:38:51,270
+Particular Solution تبع المعادلة مين؟ تبع المعادلة
+
+335
+00:38:51,270 --> 00:38:55,570
+(*) فبجي بقول بدي أفترض الحل بطريقة ال version of
+
+336
+00:38:55,570 --> 00:38:59,870
+parameters هو نفس الحل هذا بس بدي أشيل ثوابت و
+
+337
+00:38:59,870 --> 00:39:04,230
+أضع بدلهم دوال في X يبقى (*) شكل ال Particular
+
+338
+00:39:04,230 --> 00:39:09,490
+Solution هو C<sub>1</sub>(X) Y<sub>1</sub> زائد C<sub>2</sub>(X) Y<sub>2</sub> زائد زائد
+
+339
+00:39:09,490 --> 00:39:14,560
+C<sub>n</sub>(X)Y<sub>n</sub> طيب مين هي الـC هات كيف بدي أحسبها
+
+340
+00:39:14,560 --> 00:39:19,980
+هذه؟ بعد شوية حسابات لجينا في قاعدة بواسطتها بجيب
+
+341
+00:39:19,980 --> 00:39:25,320
+كل دالة من هذه الدوال مين هي؟ قاعدة C<sub>m</sub>(X) طبعا
+
+342
+00:39:25,320 --> 00:39:29,500
+بواحد واثنين لغاية ال N يعني بC واحد وC اتنين وC
+
+343
+00:39:29,500 --> 00:39:34,890
+ثلاثة كده إلى الآخر يساوي الـ W(m) F<sub>1</sub>(X) على
+
+344
+00:39:34,890 --> 00:39:38,530
+W(X) DX نجي على الـ W(X) الـ
+
+345
+00:39:38,530 --> 00:39:42,330
+W(X) هذا تابع للحلول اللي في الحالة الأولى
+
+346
+00:39:42,330 --> 00:39:46,190
+Y<sub>1</sub> و Y<sub>2</sub> و Y<sub>n</sub> بجيب اللي هم الـ W(X) بيكون هذا
+
+347
+00:39:46,190 --> 00:39:50,140
+هو الـ W(X) تابع لحصوف على شجرة بدي W(1) و
+
+348
+00:39:50,140 --> 00:39:54,760
+W(2) و W(3) لغاية W(n) مين هو هذا؟
+
+349
+00:39:54,760 --> 00:39:58,720
+هذا ال W(1) باجي على ال W(X) دي بشيل
+
+350
+00:39:58,720 --> 00:40:02,880
+العمود الأول و بحط بداله العمود هذا و بحسب قداش
+
+351
+00:40:02,880 --> 00:40:07,890
+قيمة ال W(X) طب بدي W(2) بسيب ال W(X) هذا
+
+352
+00:40:07,890 --> 00:40:13,670
+زي ما هو و بجي على العمود الثاني بشيله كله و بحط
+
+353
+00:40:13,670 --> 00:40:16,810
+بداله العمود هذا و هكذا W(3) W(X)
+
+354
+00:40:16,810 --> 00:40:21,210
+لغاية بكملهم كلهم يبقى في هذه الحالة جبتها طب مين
+
+355
+00:40:21,210 --> 00:40:25,850
+هي ال F<sub>1</sub>(X) هذه؟ اه ال F<sub>1</sub>(X) هذه لما تيجي المعادلة بد
+
+356
+00:40:25,850 --> 00:40:30,310
+المعادلة هنا المعامل تبعي يكون جديشهذا يعني أنني
+
+357
+00:40:30,310 --> 00:40:36,110
+أقسم الطرفين على مين على A<sub>0</sub>(X) يبقى ال F<sub>1</sub> هي
+
+358
+00:40:36,110 --> 00:40:42,270
+عبارة عن F(x) مقسومة على ال A<sub>0</sub>(X) يبقى ال F<sub>1</sub>
+
+359
+00:40:42,270 --> 00:40:47,270
+(X) هي ال F(X) مقسومة على مين على ال A<sub>0</sub>(X)
+
+360
+00:40:47,270 --> 00:40:52,490
+أصلا واضح كلام هذا طيب الآن في ملاحظة بدنا نشير
+
+361
+00:40:52,490 --> 00:40:57,290
+إليها الملاحظة كانت التالية قلتها بس بدنا نعيدها هيا
+
+362
+00:40:57,290 --> 00:41:00,590
+عندما نستخدم ال variation of parameters لازم يكون
+
+363
+00:41:00,590 --> 00:41:05,610
+المعامل تبع Y'' هو مين و نسيت و حطيت ال F(x)
+
+364
+00:41:05,610 --> 00:41:11,110
+هذه بدل هذه بصي كلامك غلط بصي تحققش و ما تقدرش
+
+365
+00:41:11,110 --> 00:41:16,250
+تتكاملي تمام يبقى تتأكدي عندما بدك تستخدم التكامل
+
+366
+00:41:16,250 --> 00:41:20,390
+بتخلي المعامل تبع Y to the derivative أن هو واحد
+
+367
+00:41:20,390 --> 00:41:24,610
+صحيح تمام هي نقطة الأولى بعدين فينا ملاحظة ثانية
+
+368
+00:41:25,260 --> 00:41:28,720
+بيقول ال equation (*) هذه لو كانت من الرتبة
+
+369
+00:41:28,720 --> 00:41:32,680
+الثانية يبقى بدل ال W(1) و نص كنتوا محسبينه و
+
+370
+00:41:32,680 --> 00:41:38,320
+خلصينه و جاهزين ايش بيقول ال C<sub>1</sub>(X) بتحطي للحل
+
+371
+00:41:38,320 --> 00:41:42,940
+الثاني بإشارة سالب في ال F<sub>1</sub>(X) على ال W(X)
+
+372
+00:41:42,940 --> 00:41:48,260
+طيب و ال C<sub>2</sub>؟ و ال C<sub>2</sub> هي الحل الأول في ال Y<sub>1</sub>(X)
+
+373
+00:41:48,260 --> 00:41:51,850
+على مين؟ على ال W(X) يبقى كمان لابد تحسب
+
+374
+00:41:51,850 --> 00:41:54,950
+ال W(X) لأ هذا إن كانت من الرتبة الثانية، من
+
+375
+00:41:54,950 --> 00:41:59,930
+الرتبة الثالثة، بدي أرجع عالميا للكلام الأول، واضح
+
+376
+00:41:59,930 --> 00:42:03,590
+كلام هيك؟ الأمن اللي حطوه على أرض واقعة جالي يحل
+
+377
+00:42:03,590 --> 00:42:08,430
+المعادلة هذه بقوله تمام يبقى أنا بدي أبدأ بحل ال
+
+378
+00:42:08,430 --> 00:42:12,190
+homogeneous differential equation كما كنا من قبل
+
+379
+00:42:12,190 --> 
+
+401
+00:44:50,280 --> 00:44:58,140
+كمان مرة Zero ناقص Cos X ناقص Sine X بدي أفكه
+
+402
+00:44:58,140 --> 00:45:05,170
+باستخدام عناصر العمود الأول يبقى واحد فيه قشط بصفه
+
+403
+00:45:05,170 --> 00:45:11,630
+عموده يبقى Sin تربيع ال X زائد Cosine تربيع ال X
+
+404
+00:45:11,630 --> 00:45:16,650
+اللي هو قداش الواحد بدي أجيب الـ Ronskian 1 as a
+
+405
+00:45:16,650 --> 00:45:20,810
+function of X بدي أشيل العمود هذا و أستبدله 
+
+406
+00:45:20,810 --> 00:45:31,390
+بالعمود 001 والاتنين هدول زي ما هم Cos X Sin X -Sin
+
+407
+00:45:31,390 --> 00:45:41,050
+X Cos X - Cos X - Sin X ويساوي بدي أفكه برضه باستخدام
+
+408
+00:45:41,050 --> 00:45:46,830
+العمود الأول يبقى Zero ناقص Zero زائد واحد في قشط
+
+409
+00:45:46,830 --> 00:45:51,250
+بصفه عموده Cosine تربيع زائد Sine تربيع Cosine
+
+410
+00:45:51,250 --> 00:45:57,430
+تربيع ال X زائد Sine تربيع ال X كله بقداش بواحد
+
+411
+00:45:57,910 --> 00:46:02,810
+يبقى بناء عليه بدي أجيب الـ Ronskian 2 as a
+
+412
+00:46:02,810 --> 00:46:05,910
+function of x يبقى العمودي اللي اللي هو بدي أرجع
+
+413
+00:46:05,910 --> 00:46:09,970
+كما كان يا بنات أي واحد Zero Zero العمودي الثاني
+
+414
+00:46:09,970 --> 00:46:13,550
+هو اللي بدي أستبدله ب Zero Zero واحد والعمودي 
+
+415
+00:46:13,550 --> 00:46:20,110
+الثالث كما كان Sine ال X Cosine ال X ناقص Sine ال
+
+416
+00:46:20,110 --> 00:46:25,970
+X يبقى بناء عليه هذا الكلام يساوي بدي أفكه باستخدام
+
+417
+00:46:25,970 --> 00:46:31,590
+عناصر العمود الأول يبقى قشط بصفه وعموده Zero ناقص 
+
+418
+00:46:31,590 --> 00:46:36,470
+Cosine ال X يبقى ناقص Cosine ال X خلينا نجيب
+
+419
+00:46:36,470 --> 00:46:43,350
+الـ Ronskian 3 as a function of X يساوي 1 0 0 العمود
+
+420
+00:46:43,350 --> 00:46:50,590
+الثاني كما هو Cosine ال X ناقص Sine ال X وهنا ناقص 
+
+421
+00:46:50,590 --> 00:46:58,270
+Cosine ال X وهنا 001 بالشكل اللي اقنعناه بدي أفكه
+
+422
+00:46:58,270 --> 00:47:02,590
+باستخدام عناصر العمود الأول بقشط بصف وعموده ناقص 
+
+423
+00:47:02,590 --> 00:47:11,780
+Sin X خلصنا منه، سأحصل على الـ C1 as a function of
+
+424
+00:47:11,780 --> 00:47:19,880
+X التكامل من أين؟ التكامل للـ Ronskian 1 of X في 
+
+425
+00:47:19,880 --> 00:47:24,260
+الـ F of X لا يوجد فيها تغيير كما هي على الـ 
+
+426
+00:47:24,260 --> 00:47:30,180
+Ronskian of X كله بالنسبة إلى DX يساوي تكامل Ronskian 
+
+427
+00:47:30,180 --> 00:47:35,670
+1 طلعناه بقداش بواحد يبقى هذا واحد فيه الـ F of X
+
+428
+00:47:35,670 --> 00:47:41,410
+اللي يبقى دهشة بنات Sec ال X ازاي على Sec ال X على 
+
+429
+00:47:41,410 --> 00:47:47,270
+الـ Ronskian of X الأول برضه واحد كله DX يبقى تكامل
+
+430
+00:47:47,270 --> 00:47:53,190
+الـ Sec لين Absolute value لـ Sec ال X زائد Tan ال X 
+
+431
+00:47:53,190 --> 00:47:59,710
+بدنا نجيب C2 as a function of X يبقى تكامل Ronskian 2
+
+432
+00:47:59,710 --> 00:48:06,470
+of x في f of x على Ronskian of x dx يساوي تكامل
+
+433
+00:48:06,470 --> 00:48:11,790
+Ronskian 2 هو بناقص Cos x
+
+434
+00:48:22,510 --> 00:48:28,490
+يبقى تكامل لناقص DX يبقى بناقص X ولا تكتبي
+
+435
+00:48:28,490 --> 00:48:33,650
+Constants لأن كل صلاة وكتاب يعملوا ليه تكرار يبقى
+
+436
+00:48:33,650 --> 00:48:38,510
+سيبين من التكرار يبقى بكتبها فقط زي هيك بدأ ياخد 
+
+437
+00:48:38,510 --> 00:48:39,590
+C3
+
+438
+00:48:46,760 --> 00:48:54,240
+يبقى بيدي C3A of X يبقى يساوي تكامل Ronskian 3 of X
+
+439
+00:48:54,240 --> 00:49:00,900
+في F of X على Ronskian of X DX Y يساوي الـ Ronskian 3
+
+440
+00:49:00,900 --> 00:49:09,010
+له سالب Sin X والدالة Sec ال X والرمز كان واحد DX
+
+441
+00:49:09,010 --> 00:49:15,810
+يبقى يساوي تكامل سالب Sin X الـ Sec مقلوب الـ Cos X DX
+
+442
+00:49:15,810 --> 00:49:20,570
+أظن البسطة فاضل المقام يبقى الجواب لين Absolute 
+
+443
+00:49:20,570 --> 00:49:28,570
+value لـ Cos X يبقى جبت الـ C الثلاث يبقى سار YP 
+
+444
+00:49:28,570 --> 00:49:33,720
+يساوي وين YP يا بناتهيه بدي أشيل الـ C1 الـ C1
+
+445
+00:49:33,720 --> 00:49:38,720
+جيبناها اللي هي قداش اللي هي الـ Ln Absolute value 
+
+446
+00:49:38,720 --> 00:49:47,480
+لـ Sec ال X زائد Tan ال X زائد C2 وين C2 هيو زائد
+
+447
+00:49:47,480 --> 00:49:52,280
+اللي هي ناقص X في مين؟ في Cosine ال X
+
+448
+00:50:04,270 --> 00:50:12,930
+يبقى y يساوي yc هي
+
+449
+00:50:12,930 --> 00:50:23,580
+تحت يبقى c واحد زائد C2 Cos X زائد C3 Sin X زائد YP 
+
+450
+00:50:23,580 --> 00:50:28,540
+هاي وبدي أنزله زي ما هو بس ليه خاطر أرتبه يبقى هاي
+
+451
+00:50:28,540 --> 00:50:36,820
+Sin X في Ln Absolute value لـ Cos X ناقص X في Cos 
+
+452
+00:50:36,820 --> 00:50:45,600
+X زائد Ln Absolute value لـ Sec X زائد Tan ال X وكان
+
+453
+00:50:45,600 --> 00:50:50,160
+الله بالسر علينا يبقى هذا حل السؤال اللي عندنا 
+
+454
+00:50:50,160 --> 00:50:54,780
+تمام وهكذا يعني الشغل بهذه الطريقة طبعا لو جيبناك 
+
+455
+00:50:54,780 --> 00:50:58,200
+سؤال في الامتحان لن يزيد عن الرتبة الثالثة أن 
+
+456
+00:50:58,200 --> 00:51:01,780
+دخلنا في الرتبة الرابعة بدك محدد من الدرجة الرابعة
+
+457
+00:51:01,780 --> 00:51:05,760
+بياخد وقت كتير وانت تحل فيه يبقى فقط من الدرجة
+
+458
+00:51:05,760 --> 00:51:11,260
+الثالثة أو الدرجة الثانية إن شاء الله لازلنا في 
+
+459
+00:51:11,260 --> 00:51:15,600
+نفس الـ Section ولما ننتهي بعد في عندي بعض الأمثلة
+
+460
+00:51:15,600 --> 00:51:20,060
+على نفس الموضوع بالإضافة إلى آخر طريقة اللي هي
+
+461
+00:51:20,060 --> 00:51:24,340
+طريقة Reduction of Order لاختزال الرتبة للمحاضرة 
+
+462
+00:51:24,340 --> 00:51:26,760
+اليوم بعد الظهر إن شاء الله وتعالى 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3eQp6W53jbo_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3eQp6W53jbo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5692689130e164f2ede428a80ead8439d8919ba2
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3eQp6W53jbo_raw.json
@@ -0,0 +1 @@
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1275.11, "word": " تساوي", "probability": 0.935546875}, {"start": 1275.11, "end": 1275.59, "word": " 0", "probability": 0.393310546875}, {"start": 1275.59, "end": 1276.39, "word": " يبقى", "probability": 0.9437255859375}, {"start": 1276.39, "end": 1276.95, "word": " أصبح", "probability": 0.9127604166666666}, {"start": 1276.95, "end": 1278.15, "word": " YP3", "probability": 0.7589518229166666}, {"start": 1278.15, "end": 1278.91, "word": " بدها", "probability": 0.65771484375}, {"start": 1278.91, "end": 1279.41, "word": " تساوي", "probability": 0.9365234375}, {"start": 1279.41, "end": 1279.95, "word": " D", "probability": 0.58935546875}, {"start": 1279.95, "end": 1280.65, "word": " node", "probability": 0.16650390625}, {"start": 1280.65, "end": 1281.19, "word": " X", "probability": 0.91064453125}, {"start": 1281.19, "end": 1281.91, "word": " زائد", "probability": 0.646484375}, {"start": 1281.91, "end": 1282.81, "word": " D1", "probability": 0.93017578125}, {"start": 1282.81, "end": 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"seek": 131758, "start": 1294.46, "end": 1317.58, "text": "يبقى الـ Particular solution اللي بدنا يا بنات يبقى يساوي YP1 زائد YP2 زائد YP3 يبقى أصبح YP يساوي YP1 هاي و بنزله زي ما هو A0 X تربيع A1X زائد A2 زائد", "tokens": [1829, 3555, 4587, 7578, 2423, 39184, 4100, 14646, 3827, 13672, 1829, 47525, 8315, 35186, 4724, 8315, 2655, 7251, 3555, 4587, 7578, 7251, 3794, 995, 45865, 398, 47, 16, 30767, 16373, 3215, 398, 47, 17, 30767, 16373, 3215, 398, 47, 18, 7251, 3555, 4587, 7578, 5551, 9381, 49628, 398, 47, 7251, 3794, 995, 45865, 398, 47, 16, 8032, 47302, 4032, 44945, 11622, 43761, 30767, 1829, 19446, 31439, 316, 15, 1783, 6055, 2288, 21292, 3615, 316, 16, 55, 30767, 16373, 3215, 316, 17, 30767, 16373, 3215], "avg_logprob": -0.2654411652508904, "compression_ratio": 1.4838709677419355, "no_speech_prob": 0.0, "words": [{"start": 1294.46, "end": 1295.06, "word": "يبقى", "probability": 0.8399658203125}, {"start": 1295.06, "end": 1295.18, "word": " الـ", "probability": 0.3834228515625}, {"start": 1295.18, "end": 1295.84, "word": " Particular", "probability": 0.79052734375}, {"start": 1295.84, "end": 1296.58, "word": " solution", "probability": 0.5849609375}, {"start": 1296.58, "end": 1296.86, "word": " اللي", "probability": 0.681396484375}, {"start": 1296.86, "end": 1297.2, "word": " بدنا", "probability": 0.93603515625}, {"start": 1297.2, "end": 1297.44, "word": " يا", "probability": 0.33984375}, {"start": 1297.44, "end": 1298.12, "word": " بنات", "probability": 0.84228515625}, {"start": 1298.12, "end": 1298.66, "word": " يبقى", "probability": 0.70263671875}, {"start": 1298.66, "end": 1299.0, "word": " يساوي", "probability": 0.69219970703125}, {"start": 1299.0, "end": 1300.08, "word": " YP1", "probability": 0.656494140625}, {"start": 1300.08, "end": 1300.94, "word": " زائد", "probability": 0.5433146158854166}, {"start": 1300.94, "end": 1302.04, "word": " YP2", "probability": 0.9747721354166666}, {"start": 1302.04, "end": 1302.9, "word": " زائد", "probability": 0.9480794270833334}, {"start": 1302.9, "end": 1304.66, "word": " YP3", "probability": 0.98486328125}, {"start": 1304.66, "end": 1305.58, "word": " يبقى", "probability": 0.967041015625}, {"start": 1305.58, "end": 1306.18, "word": " أصبح", "probability": 0.8592122395833334}, {"start": 1306.18, "end": 1307.06, "word": " YP", "probability": 0.892822265625}, {"start": 1307.06, "end": 1307.8, "word": " يساوي", "probability": 0.9306640625}, {"start": 1307.8, "end": 1309.18, "word": " YP1", "probability": 0.8821614583333334}, {"start": 1309.18, "end": 1309.6, "word": " هاي", "probability": 0.5850830078125}, {"start": 1309.6, "end": 1309.7, "word": " و", "probability": 0.296875}, {"start": 1309.7, "end": 1310.24, "word": " بنزله", "probability": 0.7561848958333334}, {"start": 1310.24, "end": 1310.62, "word": " زي", "probability": 0.9404296875}, {"start": 1310.62, "end": 1310.8, "word": " ما", "probability": 0.9345703125}, {"start": 1310.8, "end": 1311.02, "word": " هو", "probability": 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هنا", "probability": 0.7939453125}, {"start": 1360.05, "end": 1360.25, "word": " في", "probability": 0.96533203125}, {"start": 1360.25, "end": 1360.55, "word": " هذا", "probability": 0.9560546875}, {"start": 1360.55, "end": 1361.99, "word": " السؤال؟", "probability": 0.9400634765625}, {"start": 1361.99, "end": 1362.67, "word": " في", "probability": 0.80615234375}, {"start": 1362.67, "end": 1362.89, "word": " اي", "probability": 0.8388671875}, {"start": 1362.89, "end": 1363.77, "word": " تساؤل؟", "probability": 0.8863118489583334}], "temperature": 1.0}, {"id": 60, "seek": 139353, "start": 1365.29, "end": 1393.53, "text": "طيب على هيك انتهى هذا ال section وإلى يكون أرقام المسائل يبقى exercises خمسة سبعة المسائل التالية من واحد لغاية عشرين ومن خمسة وعشرين لغاية تلاتين مرني أديكي قد ما تقدري بتصير هذا الموضوع بصير جدا", "tokens": [9566, 1829, 3555, 15844, 39896, 4117, 16472, 47395, 7578, 23758, 2423, 3541, 4032, 28814, 23942, 7251, 30544, 5551, 2288, 4587, 10943, 9673, 3794, 16373, 1211, 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3079.94, "end": 3080.06, "word": " هي", "probability": 0.68505859375}, {"start": 3080.06, "end": 3080.42, "word": " طريقة", "probability": 0.9200846354166666}, {"start": 3080.42, "end": 3080.88, "word": " reduction", "probability": 0.83740234375}, {"start": 3080.88, "end": 3081.28, "word": " of", "probability": 0.95458984375}, {"start": 3081.28, "end": 3081.8, "word": " order", "probability": 0.95751953125}, {"start": 3081.8, "end": 3082.72, "word": " لاختزال", "probability": 0.86767578125}, {"start": 3082.72, "end": 3083.28, "word": " الرتبة", "probability": 0.8636067708333334}, {"start": 3083.28, "end": 3084.34, "word": " للمحاضرة", "probability": 0.966796875}, {"start": 3084.34, "end": 3084.66, "word": " اليوم", "probability": 0.95361328125}, {"start": 3084.66, "end": 3084.98, "word": " بعد", "probability": 0.9580078125}, {"start": 3084.98, "end": 3085.52, "word": " الظهر", "probability": 0.91552734375}, {"start": 3085.52, "end": 3085.82, "word": " ان", "probability": 0.90087890625}, {"start": 3085.82, "end": 3086.1, "word": " شاء", "probability": 0.981689453125}, {"start": 3086.1, "end": 3086.3, "word": " الله", "probability": 0.95849609375}, {"start": 3086.3, "end": 3086.48, "word": " و", "probability": 0.6982421875}, {"start": 3086.48, "end": 3086.76, "word": " تعالى", "probability": 0.81005859375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3088.161, "duration_after_vad": 2887.30534374999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3zZhd_x-pt0_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3zZhd_x-pt0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4b5e8256753a622bde0d5652153eb8c388d5942c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/3zZhd_x-pt0_raw.srt
@@ -0,0 +1,1952 @@
+1
+00:00:00,000 --> 00:00:01,260
+موسيقى
+
+2
+00:00:20,000 --> 00:00:25,800
+بسم الله الرحمن الرحيم نواصل سيكشن تسعة تلاتة وهي
+
+3
+00:00:25,800 --> 00:00:29,440
+Properties of Laplace Transforms المرة اللي فاتت
+
+4
+00:00:29,440 --> 00:00:34,400
+ذكرنا خواص Laplace Transform وشرحنا هذه الخواص وهي
+
+5
+00:00:34,400 --> 00:00:37,980
+الخواص كتبتها قدامكوا على اللوح بالاضافة الخاصية
+
+6
+00:00:37,980 --> 00:00:42,580
+الأولى هي خاصية ال linearity والخاصية السادسة وهي
+
+7
+00:00:42,580 --> 00:00:46,840
+خاصية Laplace La differentiationهذه المقالات
+
+8
+00:00:46,840 --> 00:00:51,220
+ذكرتها في قسم قبله يبقى لا داعي لإعادة كتابتها
+
+9
+00:00:51,220 --> 00:00:56,760
+الآن سأحاول كيف أستخدم هذه الخواص سأخد أمثلة على
+
+10
+00:00:56,760 --> 00:01:02,440
+كيفية استخدام هذه الخواص بيقول المثل هو find a
+
+11
+00:01:02,440 --> 00:01:05,880
+place to transform لكل من الدوال التالي واحنا الآن
+
+12
+00:01:05,880 --> 00:01:10,240
+سناخد بدل دل عشر دوالوالله تسعة نوجد لبلاس
+
+13
+00:01:10,240 --> 00:01:14,800
+ترانسفورم لهم بس كل دالة مختلفة عن مين عن الدالة a
+
+14
+00:01:14,800 --> 00:01:24,700
+الثانية إذا بدي أخد لبلاس ترانسفورم لدالة F of T
+
+15
+00:01:25,400 --> 00:01:29,600
+أول خاصية خاصية ال linear تبقى linear للابلاسلا
+
+16
+00:01:29,600 --> 00:01:34,680
+الأول زي دابلاسلا ثانى زي دابلاسلا ثانى مضروبة في
+
+17
+00:01:34,680 --> 00:01:39,760
+كونصة تبقى كونصة بتطلعها برا تبقى للخاصية الأولى
+
+18
+00:01:39,760 --> 00:01:46,720
+يبقى هذا بتسوى تلاتة Laplace transform لل Eostنقص
+
+19
+00:01:46,720 --> 00:01:53,320
+اتنين لبلاس ترانسفورم لإيه سالب T زائد اربعة لبلاس
+
+20
+00:01:53,320 --> 00:02:00,220
+ترانسفورم لصين تلاتة T هذه لبلاس ال F of T قولنا
+
+21
+00:02:00,220 --> 00:02:07,760
+بنعطيها رمز capital F of S هذه تساوي تلاتة فيه ال
+
+22
+00:02:07,760 --> 00:02:13,200
+exponential E of T لبلاس ترانسفورم واحد على S ناقص
+
+23
+00:02:13,200 --> 00:02:19,170
+المعامل تبعتي اللي هو جداشواحد صحيح هنا ناقص اتنين
+
+24
+00:02:19,170 --> 00:02:24,990
+وهنا واحد على اس ناقص ناقص واحد يبقى بيصير جداش
+
+25
+00:02:24,990 --> 00:02:31,150
+زائد واحد وهنا زائد اربعة فيه ل plus ل sin تلاتة
+
+26
+00:02:31,150 --> 00:02:38,250
+تين وقولنا هو عبارة عن تلاتة على اس تربيع زائد
+
+27
+00:02:38,250 --> 00:02:42,930
+مربع التلاتة اليومين اللي هو تسعةيبقى يجب ان انا
+
+28
+00:02:42,930 --> 00:02:47,090
+اخد عوامل مشتركة و اجمع بهمنيتش هذا كل شغل تحصيل
+
+29
+00:02:47,090 --> 00:02:52,910
+حاصل شغل رابع ابتدائي يبقى جمع زي ما بدك ماعندكش
+
+30
+00:02:52,910 --> 00:02:58,790
+مشكلة ابنجي الان للمثال اللذي يليه المثال اللذي
+
+31
+00:02:58,790 --> 00:03:07,150
+يليه نمره اتنين بيقول ال HRT بدها تساوي ال E أس
+
+32
+00:03:07,150 --> 00:03:14,000
+اتنين T في Sin تلاتة Tبدي احسب لبلاس ال transform
+
+33
+00:03:14,000 --> 00:03:21,160
+لها فبجي بقول لبلاس لل H of T او بقول capital H of
+
+34
+00:03:21,160 --> 00:03:28,840
+T يبقى هو عبارة عن capital H of T H of S capital H
+
+35
+00:03:28,840 --> 00:03:34,320
+of S بال D7بدأت أطلع على الدالة اللي عندناها دي
+
+36
+00:03:34,320 --> 00:03:39,780
+بدلا plus inها exponential في sign بقى دي بطلع في
+
+37
+00:03:39,780 --> 00:03:45,040
+هدول كلهم فش exponential في sign لكن في عندي
+
+38
+00:03:45,040 --> 00:03:49,530
+exponentialفى الـ function مين ما يكون شكلها يكون
+
+39
+00:03:49,530 --> 00:03:54,490
+تمام؟ يبقى الـ function عندي مهم اللى هى الـ sine
+
+40
+00:03:54,490 --> 00:03:59,550
+ايش بيقولى؟ بيقولى بدك اللى هى ال F of S ناقص الـC
+
+41
+00:03:59,550 --> 00:04:04,430
+يعنى بدي اجيب لل F of T اجيب لها plus ال transform
+
+42
+00:04:04,430 --> 00:04:09,870
+لها و بعدها اعمل لها shift بمقدار من؟ بمقدار الـC
+
+43
+00:04:10,300 --> 00:04:18,100
+إذا أنا هذه بدي أجيب لابلاس ترانسفورم لها على شجة
+
+44
+00:04:18,100 --> 00:04:24,700
+لو جيت قولت هذا لابلاس ترانسفورم أو هذا capital F
+
+45
+00:04:24,700 --> 00:04:30,680
+of S و الله بدي أخد مين؟بدي اخد ال F of T اللي
+
+46
+00:04:30,680 --> 00:04:37,400
+عندى ال F of T اللي هي من صين تلاتة T يبجى capital
+
+47
+00:04:37,400 --> 00:04:43,040
+F of S اللي هو من تلاتة على اس تربيه زائد تسعة
+
+48
+00:04:43,040 --> 00:04:45,880
+مظبوط الان هذه
+
+49
+00:04:45,880 --> 00:04:49,920
+هههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+50
+00:04:59,220 --> 00:05:06,680
+يبقى هذا الكلام بده يساوي تلاتة على S ناقص اتنين
+
+51
+00:05:06,680 --> 00:05:11,220
+الكل تربية زي التسعة انت هنا من المثلة يبقى أنا
+
+52
+00:05:11,220 --> 00:05:14,720
+بمسك القاعدة و بطبق القاعدة حرفيا
+
+53
+00:05:19,430 --> 00:05:28,890
+السؤال الرقم تلاتة بيقول ال H of T بيساوي E أص
+
+54
+00:05:28,890 --> 00:05:37,000
+ناقص تلاتة T في من في T أص أربعةبدي لبلاس
+
+55
+00:05:37,000 --> 00:05:40,860
+ترانسفورم لهذه الدالة باجي بتطلع exponential
+
+56
+00:05:40,860 --> 00:05:45,860
+بالسلب ماعنديش ماني ماشترطش ل C تكون هادي موجبة
+
+57
+00:05:45,860 --> 00:05:50,960
+يعني ممكن تكون موجبة و ممكن تكون سالبة يبقى هاي ال
+
+58
+00:05:50,960 --> 00:05:54,340
+exponential موجود غطيت ال exponential مين بيظل ال
+
+59
+00:05:54,340 --> 00:06:01,780
+F of T؟توس أربعة يبقى انا عند ال F of T بده ساوي T
+
+60
+00:06:01,780 --> 00:06:06,680
+أس أربعة لو جبتلها Laplace transform اللي هو
+
+61
+00:06:06,680 --> 00:06:11,840
+capital F of S اللي هبدي Laplace transform ل T أس
+
+62
+00:06:11,840 --> 00:06:16,800
+أربعة اعطيتها لك المرة اللي فاتت في الجدول، مظبوط؟
+
+63
+00:06:16,800 --> 00:06:21,530
+اتطلع عندك في الجدول اللي هو أبو التسع نقاطباجي
+
+64
+00:06:21,530 --> 00:06:26,710
+باطل على الجدول أبو تسعة نقاط، بلاقي عند النقطة
+
+65
+00:06:26,710 --> 00:06:32,420
+الأولىاللي T to the power N مكتوب عندك عنوان some
+
+66
+00:06:32,420 --> 00:06:36,580
+basic Laplace transform اللي همين عندك T to the
+
+67
+00:06:36,580 --> 00:06:40,260
+power N طبعا احنا في الامتحان هتجيك الورقة هذه
+
+68
+00:06:40,260 --> 00:06:47,260
+مصورة تمنتاشر دالة و Laplace transform لمين لهذه
+
+69
+00:06:47,260 --> 00:06:50,680
+الدولة يبقى بتوجب الدولة زي ما احنا بندور هيك الآن
+
+70
+00:06:51,140 --> 00:06:54,280
+أنا عندي T to the power N مش بتروح أحسبها من أول و
+
+71
+00:06:54,280 --> 00:06:58,220
+جديد لأ بروح على الجدول بلاقي ال place transform
+
+72
+00:06:58,220 --> 00:07:01,380
+اللي مكتوب معاكي المرة اللي فاتت أول واحدة فيهم
+
+73
+00:07:01,380 --> 00:07:07,260
+اللي هو N factorial على S أس N زائد واحد يبقى هنا
+
+74
+00:07:07,260 --> 00:07:13,590
+جديش ال N عندي يا بناتيبقى هاي أربعة factorial على
+
+75
+00:07:13,590 --> 00:07:20,250
+S أس أربعة زائد واحد يعني أربعة factorial على S أس
+
+76
+00:07:20,250 --> 00:07:25,530
+خمسة تمام؟ الحين نيجي هادي لل exponential في ال F
+
+77
+00:07:25,530 --> 00:07:31,810
+of T بيقول ال F of S ناقص ال C هادي ال F of Sإذا
+
+78
+00:07:31,810 --> 00:07:42,390
+بدي أشيل كل S و أكتب مدالها مين S ناقص الـC S ناقص
+
+79
+00:07:42,390 --> 00:07:47,930
+ناقص ثلاثة يعني S زائد تلاتة يبقى هذا الكلام بده
+
+80
+00:07:47,930 --> 00:07:53,670
+يساوي أربعة factorial على S زائد تلاتة كله to the
+
+81
+00:07:53,670 --> 00:07:56,630
+power five بالشكل اللي عندنا هذا
+
+82
+00:08:00,670 --> 00:08:06,470
+الان بدنا نيجي ل ال exercises رقم اللي هو تلاتة
+
+83
+00:08:06,470 --> 00:08:18,090
+أربعة بدنا لو كانت ال H of T هي عبارة عن T في E أس
+
+84
+00:08:18,090 --> 00:08:25,570
+ثلاثة T في Cos تربيع T هذا السؤال أجي في امتحان
+
+85
+00:08:25,570 --> 00:08:26,230
+2005
+
+86
+00:08:28,770 --> 00:08:33,410
+طبعا سؤال مش بسيط و بدنا لبلاس ترانسوفار لانه تمسك
+
+87
+00:08:33,410 --> 00:08:37,570
+ال list من أولها لأخرها بتلاقيش اللي هو الشكل اللي
+
+88
+00:08:37,570 --> 00:08:42,850
+عندي انا لكن دبر حالك باجي بقولك وصين تربيه انا
+
+89
+00:08:42,850 --> 00:08:49,680
+بدي حاول اتخلص منهاماذا يعني كوصين تربية؟ هي عبارة
+
+90
+00:08:49,680 --> 00:08:56,740
+عن T في E أس ثلاثة T في نص في واحد زائد كوصين
+
+91
+00:08:56,740 --> 00:09:03,060
+اتنين T الشكل اللي عندنا هذا أو ان شئتم فقولوا هي
+
+92
+00:09:03,060 --> 00:09:12,770
+نص في T في E أس ثلاثة Tزائد كمان نص T E أس تلاتة T
+
+93
+00:09:12,770 --> 00:09:19,130
+في main في cos اتنين T طب إن Laplace transform
+
+94
+00:09:19,130 --> 00:09:27,590
+لهذه الدالة يبقى هذه H of S بده يساوي نص في
+
+95
+00:09:27,590 --> 00:09:36,900
+Laplace transform لT في E أس تلاتة Tزائد كمان نص
+
+96
+00:09:36,900 --> 00:09:45,740
+في Laplace transform لT في E أس 3T في Cos 2T بهذا
+
+97
+00:09:45,740 --> 00:09:52,550
+الشكليبقى انا بدي لبلاس ال transfer لمجموع دالتين
+
+98
+00:09:52,550 --> 00:09:57,350
+و ليس لدلة واحدة، اذا اول خاصية خاصية main ال
+
+99
+00:09:57,350 --> 00:10:00,870
+linearity يبقى all constant في لبلاس الا زي ال
+
+100
+00:10:00,870 --> 00:10:06,050
+constant في لبلاس الثانية، اذا هي نص في لبلاس
+
+101
+00:10:06,050 --> 00:10:11,150
+الأولى زي نص في لبلاس الثانيةبالدالي هذه التي في
+
+102
+00:10:11,150 --> 00:10:16,930
+ال exponential لازلت مع مين؟ مع الأولى هذا ال
+
+103
+00:10:16,930 --> 00:10:22,410
+exponential في مين؟ في ال F of T يبقى F of T هنا
+
+104
+00:10:22,410 --> 00:10:28,240
+بمين يا بنات؟الـ T وهي الـ exponential يبقى هنا ال
+
+105
+00:10:28,240 --> 00:10:32,960
+F of T اللي هي الدالة اللي عندنا هذه يبقى للجزء
+
+106
+00:10:32,960 --> 00:10:39,920
+الأول هدهها لبلاس ترانسفورم اللي همين؟ واحد
+
+107
+00:10:39,920 --> 00:10:47,350
+factorial على استربيعطالع عندك برضه من أول خاصية
+
+108
+00:10:47,350 --> 00:10:51,810
+من الخواص T to the power N هنا ال N بجدهش واحد
+
+109
+00:10:51,810 --> 00:10:57,670
+يبقى بطبق اللي هو التسعة بعد الست خواص اللي هو sum
+
+110
+00:10:57,670 --> 00:11:02,070
+basic ل place transform أول واحدة فيهميبقى ال N
+
+111
+00:11:02,070 --> 00:11:06,470
+بواحد يبقى واحد factorial على مين على S تربيع
+
+112
+00:11:06,470 --> 00:11:11,030
+مضروبة في ال exponential يبقى بدي اكتف هايلا plus
+
+113
+00:11:11,030 --> 00:11:15,910
+للدالة ال F of T جبته بدي اشيل كل S و اكتف مكانها
+
+114
+00:11:15,910 --> 00:11:23,100
+ال S ناقص ال C ال C عندي قداش؟ بتلاتةيبقى هذا
+
+115
+00:11:23,100 --> 00:11:28,260
+الكلام بده يساوي نص في مين؟ في واحد factorial اللي
+
+116
+00:11:28,260 --> 00:11:35,380
+هو بواحد على S ناقص تلاتة لكل تربيع خلصنا منه زاد
+
+117
+00:11:35,380 --> 00:11:43,170
+نص واستنى شويةهذه ليست دلتين، هي تلت دوال لكن واضح
+
+118
+00:11:43,170 --> 00:11:47,910
+خد ال exponential على الشجة اللي بيظل هو من؟ هو ال
+
+119
+00:11:47,910 --> 00:11:54,170
+F of T يبقى ال F of T عندي في ال H مش هيك F of T
+
+120
+00:11:54,170 --> 00:12:01,730
+اللي هي T في cosine اتنين T بظبط؟ T في cosine
+
+121
+00:12:01,730 --> 00:12:09,610
+اتنين Tنعود للجدول لانه يوجد هنا T to the power of
+
+122
+00:12:09,610 --> 00:12:11,550
+N في X بوننشيل ولا لا
+
+123
+00:12:21,240 --> 00:12:28,780
+T في ال cosine يبقى T في ال cosine بتطلع في الجودة
+
+124
+00:12:28,780 --> 00:12:33,040
+اللي احنا كتبنا فيها ان ال cosine صحيح بس مافيش
+
+125
+00:12:33,040 --> 00:12:37,880
+فيها T ولا exponential ولا غيره لكن لو روحت
+
+126
+00:12:37,880 --> 00:12:44,350
+للخاصية رقم 4سابت التسعة نقاط و راحت للخاصية الرقم
+
+127
+00:12:44,350 --> 00:12:48,470
+أربعة الخاصية الرقم أربعة اللي بتقول لي T to the
+
+128
+00:12:48,470 --> 00:12:55,230
+power N في ال F of T مش ينطبق عليها هذه ولا لا؟T
+
+129
+00:12:55,230 --> 00:13:05,770
+to the power of N في F of
+
+130
+00:13:05,770 --> 00:13:24,690
+T
+
+131
+00:13:24,800 --> 00:13:31,980
+يبقى ما تصير هذه هي ال F of T مظبوط؟ يبقى لما أجي
+
+132
+00:13:31,980 --> 00:13:38,940
+أقول هذه هي ال F of T بدي ال F of S يبقى ال F of S
+
+133
+00:13:38,940 --> 00:13:46,100
+في هذه الحالة ال F of S يساوي ال cosine اللي عبارة
+
+134
+00:13:46,100 --> 00:13:53,890
+عن S على S تربيع زائد 4مظبوط؟ طب هذا إيش بيقوللي؟
+
+135
+00:13:53,890 --> 00:13:58,870
+بيقول إن أقص واحد to the power n في مشتقة ال F of
+
+136
+00:13:58,870 --> 00:14:08,070
+S يبقى أنا لما نبدي ال G of S بده يساويبدي اجعل
+
+137
+00:14:08,070 --> 00:14:14,470
+هذه و اقول سلب واحد to the power n يبقى هذا سلب
+
+138
+00:14:14,470 --> 00:14:22,330
+واحد أس كده واحد في مشتقة مين هذه؟ في D على DS
+
+139
+00:14:22,330 --> 00:14:33,180
+لمن؟ لل S على S تربيع زائد أربعةهذه بدأت تساوي هي
+
+140
+00:14:33,180 --> 00:14:41,160
+السالب برا وهذه المقام في مشتقة البصد ناقص البصد
+
+141
+00:14:41,160 --> 00:14:48,760
+في مشتقة المقام على مربع المقام الأصلي الشكل اللي
+
+142
+00:14:48,760 --> 00:14:49,320
+عندنا هنا
+
+143
+00:14:52,890 --> 00:14:58,350
+طيب نيجي نكمل، خلي بالكوا هنا هذه يا بنات ناقص
+
+144
+00:14:58,350 --> 00:15:03,830
+اتنين استربيع و استربيع بيظل كده؟ ناقص استربيع،
+
+145
+00:15:03,830 --> 00:15:09,230
+وعندي ناقص برا، بيظل استربيع بالموجة هذه الأربعة
+
+146
+00:15:09,230 --> 00:15:14,890
+في الشغل، لو في ناقص برا، بيصير ناقص أربعة المقام
+
+147
+00:15:14,890 --> 00:15:22,580
+اللي هو الاستربيعزائد أربعة لكل تاربيع يبقى هذا G
+
+148
+00:15:22,580 --> 00:15:29,440
+of S يبقى Laplace transform لهذه الدالة طيب نرجع
+
+149
+00:15:29,440 --> 00:15:36,520
+لمين لمسألتنا مسألتنا قلنا ال G of T اللي هي T في
+
+150
+00:15:36,520 --> 00:15:43,060
+Cos T يعني كأن المسألة هذه زائد نص Laplace
+
+151
+00:15:43,060 --> 00:15:49,910
+transform لل E أس تلاتة Tفى T فى cosine اتنين T
+
+152
+00:15:49,910 --> 00:15:56,370
+كاينة هذه كلها اللى هى main الـG of T يبقى صارت
+
+153
+00:15:56,370 --> 00:16:01,490
+هذه كلها G of T وهذه E أس ثلاثة T برجع للخاصية
+
+154
+00:16:01,490 --> 00:16:06,710
+اللى exponential فى function يبقى اللى اللى بده
+
+155
+00:16:06,710 --> 00:16:11,770
+يجيب Laplace transform لهذه ال function وقد اتيته
+
+156
+00:16:11,770 --> 00:16:16,910
+بيه يبقى ده اللى عمله بس ايشبكون حصلت على المطلوب
+
+157
+00:16:16,910 --> 00:16:22,530
+يبقى هذا بدي أعمله shift بمقدار كده؟ بمقدار تلاتة
+
+158
+00:16:22,530 --> 00:16:29,770
+يبقى هذا الكلام زائد نص في ال S ناقص تلاتة لكل
+
+159
+00:16:29,770 --> 00:16:38,230
+تربيع ناقص أربعة على S ناقص تلاتة لكل تربيع زائد
+
+160
+00:16:38,230 --> 00:16:42,570
+أربعة لكل تربيع بالشكل اللي عندنا هنا
+
+161
+00:16:45,650 --> 00:16:51,190
+يبقى هذا الـ placid transform لهذه الدالة، اه دي
+
+162
+00:16:51,190 --> 00:16:54,430
+لبالك يعني، هذا مش سؤال أجيب، بس مش أنا اللي جبته،
+
+163
+00:16:54,430 --> 00:16:58,510
+حط السؤال لدكتور هشام مادى، قال ليه؟ أما كنتش أنا
+
+164
+00:16:58,510 --> 00:17:02,910
+شريك كل حاله في المساق، فقام حط السؤال هذا في
+
+165
+00:17:02,910 --> 00:17:04,890
+الامتحان النهائي
+
+166
+00:17:08,380 --> 00:17:18,900
+ننتقل للنقطة الرقم 4 والنقطة الرقم 5يبقى النقطة
+
+167
+00:17:18,900 --> 00:17:25,780
+رقم خمسة أو السؤال المثال رقم خمسة بيقول لمين؟
+
+168
+00:17:25,780 --> 00:17:33,320
+بيقول الدالة K of T بدها سوى تكامل من Zero إلى T
+
+169
+00:17:33,320 --> 00:17:41,220
+لصين اتنين U دي U علي
+
+170
+00:17:41,220 --> 00:17:47,710
+بالك هناالان انا لدي K of T بدي أسوي تكامل من 0
+
+171
+00:17:47,710 --> 00:17:54,290
+إلى T لصيني 2U DU بدي لبلاس ترانسفورم لهذه الدالة
+
+172
+00:17:54,290 --> 00:17:59,830
+برجع لخواصة اللي عندنا تكامل من 0 إلى T ل F of U
+
+173
+00:17:59,830 --> 00:18:06,080
+DUبتقول 1 على S في capital F of S يعني انت بتاخد
+
+174
+00:18:06,080 --> 00:18:11,000
+ال F of U بتروح تجيبلها ل plus transform و تضرب
+
+175
+00:18:11,000 --> 00:18:16,180
+فاهمين 1 على S يبقى احنا الدالة اللي عندنا ال F of
+
+176
+00:18:16,180 --> 00:18:23,460
+T هي ال F of U او بيدي اسمها ال F of T لصيني 2T
+
+177
+00:18:23,460 --> 00:18:29,820
+اذا باجي بقوله في الهامش هنا F of T بده يساوي صيني
+
+178
+00:18:29,820 --> 00:18:36,810
+2Tبدي capital F of S اللي هو Laplace transform لها
+
+179
+00:18:36,810 --> 00:18:41,590
+يساوي هذه محسوبة معانا وموجودة في التسعة يبقى هذه
+
+180
+00:18:41,590 --> 00:18:48,890
+اتنين على S تربيع زائد اربعطب هنا ايش بيقولي؟
+
+181
+00:18:48,890 --> 00:18:54,170
+بيقولي بتخليها زي ما هي بس بتضرب في جداش في واحد
+
+182
+00:18:54,170 --> 00:19:00,410
+على اس اذا capital K of S اللي هو ال plus
+
+183
+00:19:00,410 --> 00:19:06,650
+transform لهذه الدالة يسوى واحد على اس في اتنين
+
+184
+00:19:06,650 --> 00:19:13,050
+على اس تربيع زائد اربع انت هنا من المثالة
+
+185
+00:19:28,630 --> 00:19:32,950
+نماذج الامتحانات اللى صورناهم لكوا في نهاية كل
+
+186
+00:19:32,950 --> 00:19:38,190
+نموذج في الورقة المصورة هذه وستأتيكوا ان شاء الله
+
+187
+00:19:38,190 --> 00:19:43,230
+يقولوا لكوا تمنتعشر دالة و تمنتعشر لبلاس ترانسفورم
+
+188
+00:19:43,230 --> 00:19:47,890
+لهم وبالتالي كل شىء بيجيكي معاكوا بس تعرفوا الدور
+
+189
+00:19:47,890 --> 00:19:54,420
+نيات منهم زى ما احنا قاعدين ندور الحينطيب هذه نمرة
+
+190
+00:19:54,420 --> 00:20:03,140
+ست نمرة خمسة بدنا نروح لنمرة ستة يبقى نمرة ستة
+
+191
+00:20:03,140 --> 00:20:12,000
+بيقول ال K of T يسوى تكامل من Zero إلى T لل X
+
+192
+00:20:12,000 --> 00:20:17,160
+تربية E أس X كله منين؟ كله ل DX
+
+193
+00:20:23,740 --> 00:20:29,420
+بنجيب لابلس ترانسفورم لهذه الدالة يبقى باجي بقوله
+
+194
+00:20:29,420 --> 00:20:35,520
+capital K of S بديه ساوي اللي هو من لابلس
+
+195
+00:20:35,520 --> 00:20:41,180
+ترانسفورم لتكامل من zero إلى T لل X تربية E أس X
+
+196
+00:20:41,180 --> 00:20:46,560
+كله بالنسبة لمين إلى DX وإن التكامل ماعنديش اللي
+
+197
+00:20:46,560 --> 00:20:54,700
+هذايبقى هذا بقول واحد على S لمين للدالة F of S لكن
+
+198
+00:20:54,700 --> 00:21:01,060
+أنا عندي هنا من اللي هو الدالة لل X تربيع في من؟
+
+199
+00:21:01,060 --> 00:21:08,860
+في E أوس X يعني كأن النتيجة هذه هي واحد على S في
+
+200
+00:21:08,860 --> 00:21:16,060
+لبلاس ترانسفورم لمين؟ هذه بقدر أقوله T تربيع E أوس
+
+201
+00:21:16,060 --> 00:21:23,360
+T بصبوط؟طلع هنا بيقول بتاخدي الدالة هذه و
+
+202
+00:21:23,360 --> 00:21:27,040
+بتجيبليها لبلاس ترانسفورم تضربها في واحد علي اسم
+
+203
+00:21:27,040 --> 00:21:31,820
+يبقى هاي ضربت في واحد علي اسم وهي لبلاس ترانسفورم
+
+204
+00:21:31,820 --> 00:21:36,730
+لهذه الدالة الشكل الآن أنا بتضربه وحاح اسمهيبقى
+
+205
+00:21:36,730 --> 00:21:42,190
+هذا T to the power N في ال exponential باجي بطلع
+
+206
+00:21:42,190 --> 00:21:46,650
+عندي T to the power في ال exponential ماعنديش T to
+
+207
+00:21:46,650 --> 00:21:50,430
+the power N في ال exponential لكن لو روحنا على
+
+208
+00:21:50,430 --> 00:21:55,610
+الجدول اللي أعطاناكوا ياه المرة اللي فاتت T to the
+
+209
+00:21:55,610 --> 00:22:03,740
+power N في ال exponential رقم 9مظبوط يبقى T to the
+
+210
+00:22:03,740 --> 00:22:08,320
+power N في ال exponential اللي هي main N factorial
+
+211
+00:22:08,320 --> 00:22:13,580
+على S ناقص A to the power N plus one وال N قولنا
+
+212
+00:22:13,580 --> 00:22:20,290
+is a positive integer طبعا هذه رقمهاT to the power
+
+213
+00:22:20,290 --> 00:22:25,190
+inflex هو رقمها في الجدولة رقم 11 في الجدولة هيوزع
+
+214
+00:22:25,190 --> 00:22:28,390
+عليكم هذه لكن احنا في الخواصة رقم 9 بهمنيش ان
+
+215
+00:22:28,390 --> 00:22:32,330
+الرقم بهمني الدالة وين الاقي الدالة وكيف اطبقها
+
+216
+00:22:32,330 --> 00:22:38,930
+يبقى باجي هذه هه هذا الكلام بده يساوي واحد على اس
+
+217
+00:22:38,930 --> 00:22:43,730
+لبلاس ترانسوفر من T to the power يبقى N factorial
+
+218
+00:22:43,730 --> 00:22:49,730
+جدش ال N عندنا منهايبقى اتنين factorial على مين
+
+219
+00:22:49,730 --> 00:22:55,590
+على S ناقص ال A يبقى ال S ناقص ال A اللي هو
+
+220
+00:22:55,590 --> 00:23:01,570
+المعامل تبع ال T يبقى اللي هو واحد وهنا بقول اس
+
+221
+00:23:01,570 --> 00:23:06,530
+كده اس تلاتة بالشكل اللي عندنا هذا او ان شئتوا
+
+222
+00:23:06,530 --> 00:23:09,910
+فبقولوا مضروب اتنين اللي هو اتنين في واحد باتنين
+
+223
+00:23:09,910 --> 00:23:13,710
+على S في S ناقص واحد لكل
+
+224
+00:23:19,340 --> 00:23:22,140
+النقطة السابعة
+
+225
+00:23:23,850 --> 00:23:29,790
+النقطة السابعة بدنا ال F of T بدنا نغيرلكوا الشكل
+
+226
+00:23:29,790 --> 00:23:37,650
+شوية بد يعطيني يا إما Zero لما T أكبر من Zero أقل
+
+227
+00:23:37,650 --> 00:23:47,410
+من Pi يا إما ال Sin T ناقص ال Pi لما ال T greater
+
+228
+00:23:47,410 --> 00:23:54,610
+than Piبدي لبلاس ترانسفورم لهذه الدالة المجزقة إلى
+
+229
+00:23:54,610 --> 00:24:01,160
+جزءين بدي بطلع فيه عندى، اه فيه هي موجودةمعمول لها
+
+230
+00:24:01,160 --> 00:24:05,120
+shift يبقى
+
+231
+00:24:05,120 --> 00:24:11,760
+هذه الصورة طبق الأصل من المثلة اللي عندنا هذه يبقى
+
+232
+00:24:11,760 --> 00:24:17,160
+باجي على الخاصية اللي عندنا هذه يبقى باجي على
+
+233
+00:24:17,160 --> 00:24:22,120
+الخاصية اللي عندنا هذه و بدي أخد لبلاس ترانسفورم
+
+234
+00:24:22,120 --> 00:24:30,100
+لها يبقى لبلاس ترانسفورم لل F of TF of S بالشكل
+
+235
+00:24:30,100 --> 00:24:34,840
+اللي عندنا هذا نيجي لبلاس لهذه ال exponential
+
+236
+00:24:34,840 --> 00:24:40,520
+quiet يبقى ايش بيقولي بتقولي ال exponential في ال
+
+237
+00:24:40,520 --> 00:24:45,820
+F of S يعني بتيجي على الدالة هذه و بتجردها من ال C
+
+238
+00:24:45,820 --> 00:24:51,600
+و بضلب اسمين F of T يبقى بالداجي اقوله هذه تساوي
+
+239
+00:24:51,600 --> 00:25:00,550
+اقص ناقص ال C عندي بقدراشبي باي و هاد ال S و بدي ل
+
+240
+00:25:00,550 --> 00:25:10,060
+place transform ل sign ال Tأنا بطبق الخاصية رقم
+
+241
+00:25:10,060 --> 00:25:14,480
+خمسة دالة مجزاة بالشكل هذا يبقى exponential
+
+242
+00:25:14,480 --> 00:25:19,960
+المعامل تبع ال S اللي هو مقدار ال shift اللي عندنا
+
+243
+00:25:19,960 --> 00:25:26,080
+مقدار ال C يبقى هذا E أوس ناقص by S في ال F of S
+
+244
+00:25:26,080 --> 00:25:31,540
+بتجيب Laplace لدالة هذه بدون C يبقى هي Laplace هذه
+
+245
+00:25:31,540 --> 00:25:39,260
+لدالة بدون Shiftتمام؟ إذن النتيجة تساوي EOS ناقص
+
+246
+00:25:39,260 --> 00:25:46,760
+by S لبلاسترانسفورم للصين اللي هو واحد على S تربيه
+
+247
+00:25:46,760 --> 00:25:51,020
+زائد واحد لأن المعامل تبع ال T هنا واحد يبقى
+
+248
+00:25:51,020 --> 00:25:56,760
+انتهينا منها أو إن حبيت تقولي EOS ناقص by S على S
+
+249
+00:25:56,760 --> 00:26:00,580
+تربيه زائد واحد مافي مشكلة دي والله دي نفس الشيء
+
+250
+00:26:00,930 --> 00:26:05,330
+لكن يا بنات احيانا في المسألة بيجي ال shift زيك
+
+251
+00:26:05,330 --> 00:26:10,390
+انت بدك تخلق shift في المسألة انت لوحدك مش هنقدر
+
+252
+00:26:10,390 --> 00:26:16,110
+نطبق منهم هذه الخاصية زي ايش مثلا خديلك السؤال رقم
+
+253
+00:26:16,110 --> 00:26:25,370
+8يبقى تمانية بيقول ال F of T بدي سوى أحد أمرين، يا
+
+254
+00:26:25,370 --> 00:26:31,910
+إما Zero لما T أكبر من Zero أقل من واحد، يا إما T
+
+255
+00:26:31,910 --> 00:26:35,930
+تربيع لما T greater than one
+
+256
+00:26:42,460 --> 00:26:49,060
+مشكلة ان دالة مجزئة لجزئين مثل ما هي عندنا بس هذه
+
+257
+00:26:49,060 --> 00:26:53,800
+معمولة لها shift وهذه مش معمولة لها shift عند
+
+258
+00:26:53,800 --> 00:26:59,270
+الواحديبقى مشان اقدر اطبق هذه القصة يبقى انا بدى
+
+259
+00:26:59,270 --> 00:27:04,590
+اعمل الهاشفت عند الواحد هقول كويس هدى مشان اعمل
+
+260
+00:27:04,590 --> 00:27:12,070
+الهاشفت بدها تبقى T ناقص واحد لكل تربية طب T ناقص
+
+261
+00:27:12,070 --> 00:27:17,470
+واحد لكل تربية ليه T تربية ناقص اتنين T زائد واحد
+
+262
+00:27:17,730 --> 00:27:24,370
+يعني بقدر أقول هذه على صيغة zero لما T أكبر من
+
+263
+00:27:24,370 --> 00:27:31,510
+zero أقل من واحد T تربيع ناقص اتنين T زائد واحد
+
+264
+00:27:31,510 --> 00:27:36,790
+هذه الدالة هي هذه الدالة؟ لأاللي روح اضفته بدك
+
+265
+00:27:36,790 --> 00:27:44,330
+تروح تطرحه يبقى باجي بقوله زائد اتنين T ناقص واحد
+
+266
+00:27:44,330 --> 00:27:51,230
+وT اكبر من الواحد عملت حاجة؟ لأ يبقى ناقص اتنين T
+
+267
+00:27:51,230 --> 00:27:55,870
+هي زائد اتنين T زائد واحد هي ناقص واحد يبقى اضفت
+
+268
+00:27:55,870 --> 00:28:00,770
+Zero يبقى انا مغيرتش ولا حاجة من هنا فضلي
+
+269
+00:28:03,080 --> 00:28:09,480
+عن ال shift عندى شايف الواحد هذا مظبوط سألت قولتلك
+
+270
+00:28:09,480 --> 00:28:14,740
+هذه مشان يكون لها shift عند الواحد بتبقى T ناقص
+
+271
+00:28:14,740 --> 00:28:19,940
+واحد لكل تربية تي ناقص واحد لكل تربية مين هى اللى
+
+272
+00:28:19,940 --> 00:28:24,620
+تي تربية ناقص اتنين T زائد واحد يبقى بالزمن ناقص
+
+273
+00:28:24,620 --> 00:28:29,580
+اتنين T زائد الواحد يبقى روحت اضافت ناقص اتنين T
+
+274
+00:28:29,580 --> 00:28:33,870
+زائد واحد اللى اضافته بدي اروح اطرحهيبقى بصير زائد
+
+275
+00:28:33,870 --> 00:28:39,550
+اتنين T ناقص الواحد، واضحة؟ طيب، حد بتسأل تاني؟
+
+276
+00:28:39,550 --> 00:28:44,150
+لسه ماكملناش، لسه فيكمال لعبة تاني، مش على جد هيك
+
+277
+00:28:44,150 --> 00:28:48,570
+T تربية
+
+278
+00:28:48,570 --> 00:28:52,790
+لحال ناقص واحد بتكون جبتي صيغة ال shift اللي عندك
+
+279
+00:28:52,790 --> 00:28:59,750
+هذا؟أنا بدي T تربيع ناقص اتنين T زي واحد لأن هذي
+
+280
+00:28:59,750 --> 00:29:04,410
+عبارة عن T ناقص واحد لكل تربيع مش T تربيع ناقص
+
+281
+00:29:04,410 --> 00:29:10,350
+واحد بدي T ناقص واحد لكل تربيع تصير كلام صحيح بكون
+
+282
+00:29:10,350 --> 00:29:14,310
+فعلا عملنا shift لمين لدالة اللي عندنا هذا مش T
+
+283
+00:29:14,310 --> 00:29:18,130
+تربيع ناقص واحد هذا هو ال shift لأ مش هيك هذي
+
+284
+00:29:18,130 --> 00:29:24,600
+بتكون T ناقص واحد لكل تربيع تمام؟طيب يبقى المثال
+
+285
+00:29:24,600 --> 00:29:30,920
+هذه صارت على الشكل التالي ال F of T لازالت تساوي
+
+286
+00:29:30,920 --> 00:29:37,560
+يا اما Zero لما T اكبر من Zero اقل من واحد هذه يا
+
+287
+00:29:37,560 --> 00:29:42,840
+بنات اللي هي مين اللي هي T ناقص واحد لكل تربية
+
+288
+00:29:42,840 --> 00:29:47,320
+بيظلوا هدول هل هدول جابولي shift؟
+
+289
+00:29:51,280 --> 00:29:57,560
+هذه شفت تماما وهذه لا تزال فيها مشكلة اه لكن لو
+
+290
+00:29:57,560 --> 00:30:03,540
+كانت هذه اتنين لصرت قصتي محلولة يبقى معناته بدي
+
+291
+00:30:03,540 --> 00:30:08,820
+اطرح واحد واضيف واحد انتبه ان حلت المشكلة صحيح ولا
+
+292
+00:30:08,820 --> 00:30:16,900
+لا يبقى هذه ايش بيصير يبقى زائد اتنين T ناقص اتنين
+
+293
+00:30:16,900 --> 00:30:22,520
+زائد واحديبقى شامل ضفت واحد سالب واحد موجب
+
+294
+00:30:22,520 --> 00:30:28,300
+وبالتالي مشكلة انحلت وبالتالي هذا الكلام لم تي
+
+295
+00:30:28,300 --> 00:30:34,440
+اكبر من الواحد يبقى الشكل الجديد للدالة هو zero
+
+296
+00:30:35,120 --> 00:30:43,880
+وهنا لما T أكبر من Zero أقل من واحد هذا T ناقص
+
+297
+00:30:43,880 --> 00:30:50,100
+واحد لكل تربية هنا لو أخدت اتنين عامل مشترك بيظل
+
+298
+00:30:50,100 --> 00:30:57,660
+عندي T ناقص واحد وهنا زائد واحد وهنا T أكبر من
+
+299
+00:30:57,660 --> 00:31:02,750
+الواحديبقى هذه الدالة معمولة لها shift الآن،
+
+300
+00:31:02,750 --> 00:31:09,290
+مظبوط، يبقى صار الدالة هذه تكافئ الدالة الأصلية،
+
+301
+00:31:09,290 --> 00:31:15,010
+بس معمولة لها ال shift تماما و بدون أي مشكلة، كلام
+
+302
+00:31:15,010 --> 00:31:20,280
+سليم مئة بالمئةيبقى الدالة مش معمولة لها shift انت
+
+303
+00:31:20,280 --> 00:31:24,560
+بدك تعمليها shift طب shift علي اعمل بمزاجي؟ لأ انت
+
+304
+00:31:24,560 --> 00:31:29,660
+مقيد بالرقم اللي عندك يعني انا بده اطلع الرقم اللي
+
+305
+00:31:29,660 --> 00:31:34,480
+عندى يكون وين في المثلة او ال shift بمقدار هذا
+
+306
+00:31:34,480 --> 00:31:40,820
+الرقم يبقى عملنا هذا shift اذابرجع بقول هاي الدالة
+
+307
+00:31:40,820 --> 00:31:45,020
+ومعمولة لها shift يبقى ال exponential في Laplace
+
+308
+00:31:45,020 --> 00:31:50,120
+ال transform للدالة إذا بيداجي للدالة الأصلية اللي
+
+309
+00:31:50,120 --> 00:31:54,200
+عندنا مين تقدر تقولي مين هي الدالة الأصلية اللي
+
+310
+00:31:54,200 --> 00:32:01,560
+عندنا هنا يا بنات G of T تساوي إيش الدالة هذه قبل
+
+311
+00:32:01,560 --> 00:32:06,900
+ال shift مين الدالة هذه قبل ال shift T تربيع أي
+
+312
+00:32:06,900 --> 00:32:13,920
+واحدزائدي اتنين T زائد واحد يعني ال shift اللي
+
+313
+00:32:13,920 --> 00:32:18,980
+عندي يبقى هذه تضالة بدي لبلاس ترانسفورم لها بروح
+
+314
+00:32:18,980 --> 00:32:25,780
+بقوله يبقى ال G of S يساوي T تربية اللي هي اتنين
+
+315
+00:32:25,780 --> 00:32:34,330
+factorial على S تكعيبمظبوط؟ وهنا زائد اتنين في
+
+316
+00:32:34,330 --> 00:32:43,390
+واحد factorial على كده اش؟ على T على S تربيع على S
+
+317
+00:32:43,390 --> 00:32:53,020
+تربيع وهذه واحد الواحد على Sطبعا 1 على S بالشكل
+
+318
+00:32:53,020 --> 00:32:57,600
+اللي قلنا عنه يبقى هاي جيب G of S ايش بيقوللي هاي
+
+319
+00:32:57,600 --> 00:33:02,420
+الدالة exponential في ال F of S يبقى هذه بتضروفها
+
+320
+00:33:02,420 --> 00:33:07,380
+بس في ال exponential ال exponential قداش مقدار ال
+
+321
+00:33:07,380 --> 00:33:16,320
+C في مسألة هذه1 يبقى بصير أن هنا capital F of S
+
+322
+00:33:16,320 --> 00:33:25,220
+بده يساوي اللي هو مين؟ اللي هو E أس سالب S لإن ال
+
+323
+00:33:25,220 --> 00:33:33,440
+C عندي بده يشبه 1 في مين؟ في 2 على S تكيب زائد 2
+
+324
+00:33:33,440 --> 00:33:39,020
+على S تربيع زائد 1 على S
+
+325
+00:33:41,810 --> 00:33:46,990
+أه يعني القضية مش سهلة مش تطلع بس قرص مرسم لكن
+
+326
+00:33:46,990 --> 00:33:50,810
+شغلي مخك حتى توصل لنصيغة و من ثم ترسم رسم
+
+327
+00:33:59,190 --> 00:34:06,750
+عشان هذا هو السؤال الثامن بدنا نروح لسؤال التاسع
+
+328
+00:34:06,750 --> 00:34:15,530
+سؤال التاسع بيقول ما يأتي find Laplace
+
+329
+00:34:15,530 --> 00:34:19,630
+غالبهم أسلة في الكتاب دي ريبالك هدول يعني ماجيبش
+
+330
+00:34:19,630 --> 00:34:25,890
+انهم غالبهم أسلة من أسلة التمرين يبقى find Laplace
+
+331
+00:34:25,890 --> 00:34:28,150
+transform
+
+332
+00:34:32,650 --> 00:34:42,910
+four المشتق الرابع ل F إذا
+
+333
+00:34:42,910 --> 00:34:51,790
+كان ال
+
+334
+00:34:51,790 --> 00:34:59,500
+F of zero بدي ساوي اتنينالـ F of 0 بده يساوي 2
+
+335
+00:34:59,500 --> 00:35:05,440
+والـ F prime of 0 بده يساوي الـ F double prime of
+
+336
+00:35:05,440 --> 00:35:11,260
+0 بده يساوي الـ F triple prime of 0 بده يساوي قداش
+
+337
+00:35:11,260 --> 00:35:16,620
+بده يساوي 0 طيب
+
+338
+00:35:16,620 --> 00:35:24,780
+خدي بالك هنا الأن أنا بدي solutionبدي لبلاس
+
+339
+00:35:24,780 --> 00:35:33,180
+transform لمن؟ للمشتقة الرابعة as a function of T
+
+340
+00:35:33,180 --> 00:35:38,340
+بدالي
+
+341
+00:35:38,340 --> 00:35:43,820
+لخاصية السادسة اللي عندنا لبعد هذه يبقى باجي بقول
+
+342
+00:35:43,820 --> 00:35:52,520
+هذه تساوي S أس كدهش؟ S و أس أربع طلع عندك خاصية
+
+343
+00:35:52,520 --> 00:35:58,560
+السادسةطبعا هذه في الملزمة مناطق الصورة موجودة اخر
+
+344
+00:35:58,560 --> 00:36:03,560
+واحدة رقم 18 تعالىيعني هتجيك في الامتحان جاهزة
+
+345
+00:36:03,560 --> 00:36:11,500
+معاكي يبقى هذه S أُس أربعة في مين؟ في capital F of
+
+346
+00:36:11,500 --> 00:36:21,420
+S ناقص استكيب في ال F of Zero ناقص استربيع في ال F
+
+347
+00:36:21,420 --> 00:36:29,660
+prime of Zero ناقص S في ال F double prime of Zero
+
+348
+00:36:34,240 --> 00:36:41,680
+نقص ال F triple prime
+
+349
+00:36:41,680 --> 00:36:48,470
+of 0 هيك مكتوب معاكي؟أصبح رقم ستة مظبوط يبقى احنا
+
+350
+00:36:48,470 --> 00:36:56,170
+طبقنا حرفيا النتيجة تساوي S أس أربعة زي ما هي في
+
+351
+00:36:56,170 --> 00:37:04,270
+capital F of S ناقص استكيب ال F of Zero مطاب قداش
+
+352
+00:37:04,270 --> 00:37:10,370
+باتنين اظن الباقى ناقص Zero ناقص Zero ناقص Zero
+
+353
+00:37:10,370 --> 00:37:19,220
+كله مرة واحدةيبقى النتيجة تساوي S أُس أربعة في F
+
+354
+00:37:19,220 --> 00:37:26,200
+of S ناقص اتنين S تكيب بالشكل اللي عندنا هذا
+
+355
+00:37:28,830 --> 00:37:34,470
+طبعا لو كنت بعرف ما هو شكل ال F كان حسب تاني ما
+
+356
+00:37:34,470 --> 00:37:39,190
+بعرفش خلاص خلّيها زي ما هي هكذا على هيك انتهى هذا
+
+357
+00:37:39,190 --> 00:37:44,230
+ال section اللي هيكون أرقام المسائل يبقى هيها بده
+
+358
+00:37:44,230 --> 00:37:50,870
+اكتبها لك فوق يبقى بالدالي ل exercises تسعة تلاتة
+
+359
+00:37:50,870 --> 00:38:02,070
+المسائل اللي هو اتنينوتلاتة تلاتة تلاتة
+
+360
+00:38:02,070 --> 00:38:05,870
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+361
+00:38:05,870 --> 00:38:06,670
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+362
+00:38:06,670 --> 00:38:06,890
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+363
+00:38:06,890 --> 00:38:07,130
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+364
+00:38:07,130 --> 00:38:07,210
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+365
+00:38:07,210 --> 00:38:07,210
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+366
+00:38:07,210 --> 00:38:22,050
+تلاتة تلاتة تلاتة تلاتة تلاتة
+
+367
+00:38:27,330 --> 00:38:33,910
+بدا نتابر الان الى section 9-4 اللى هو معكوس ل
+
+368
+00:38:33,910 --> 00:38:42,350
+place transform اللى هو ال inverse transforms
+
+369
+00:38:42,350 --> 00:38:46,570
+بقدروا
+
+370
+00:38:46,570 --> 00:38:51,650
+اعطيها definition ونشوف كيف بدنا نطبق هذا اللى هو
+
+371
+00:38:51,650 --> 00:38:52,450
+ال definition
+
+372
+00:39:00,090 --> 00:39:06,590
+يبقى ال definition بيقول ما يأتي definition if
+
+373
+00:39:06,590 --> 00:39:17,190
+Laplace transform لل F of T بده يساوي capital F of
+
+374
+00:39:17,190 --> 00:39:27,980
+S then Laplace inverse ل F of SLaplace inverse لل
+
+375
+00:39:27,980 --> 00:39:36,520
+F of S بده ساوي اللي هو F of T is called هذا اللي
+
+376
+00:39:36,520 --> 00:39:45,580
+هو بنسمي the inverse Laplace transform Laplace
+
+377
+00:39:45,580 --> 00:39:48,660
+transform
+
+378
+00:39:48,660 --> 00:40:02,440
+of L and we writeAnd we write بروح نكتب أنه ل plus
+
+379
+00:40:02,440 --> 00:40:11,840
+inverse لل F لل F of SLaplace inverse لل F of S
+
+380
+00:40:11,840 --> 00:40:22,420
+بدي ساوي F of T F and only F Laplace لل F of T بدي
+
+381
+00:40:22,420 --> 00:40:30,400
+ساوي مين اللي هو ال F of S نطرح السؤال التالي How
+
+382
+00:40:30,400 --> 00:40:41,170
+to findكيف بدنا نوجد ل plus inverse لمين لل
+
+383
+00:40:41,170 --> 00:40:48,290
+capital F of S هذا هو السؤال الإجابة الخطوة
+
+384
+00:40:48,290 --> 00:40:57,210
+التالية answer بدنا نعمل الخطوة الأولى use partial
+
+385
+00:40:57,210 --> 00:40:59,330
+fractions
+
+386
+00:41:01,390 --> 00:41:11,610
+استخدم الكثور الجزية نمر اتنين use the table
+
+387
+00:41:11,610 --> 00:41:17,850
+الجدول اللي اعطاناك فيها المرة اللي فاتت of some
+
+388
+00:41:17,850 --> 00:41:27,190
+basic some basic Laplace transforms
+
+389
+00:41:30,230 --> 00:41:43,710
+transforms in section تسعة تلاتة نمرة تلاتة use
+
+390
+00:41:43,710 --> 00:41:53,590
+the linear property linear
+
+391
+00:41:53,590 --> 00:42:01,190
+property ofالإنفرس يعني زي ما الابلاس ترانسفورم لو
+
+392
+00:42:01,190 --> 00:42:06,170
+خاصية ال linearity فجذلك معكوسه لو خاصية ال
+
+393
+00:42:06,170 --> 00:42:21,070
+linearity يبقى example one find the function f of
+
+394
+00:42:21,070 --> 00:42:34,340
+t that isfor if its
+
+395
+00:42:34,340 --> 00:42:42,180
+Laplace transform is
+
+396
+00:42:42,180 --> 00:42:48,800
+ال
+
+397
+00:42:48,800 --> 00:43:00,120
+F of Sبتساوي واحد على اس في اس زائد اتنين لكل
+
+398
+00:43:00,120 --> 00:43:01,020
+تربيع
+
+399
+00:43:20,540 --> 00:43:25,020
+مرة تانية مانا اقعد تعريف ال inverse Laplace
+
+400
+00:43:25,020 --> 00:43:30,120
+transform Laplace transform لو كان الدالة f of t
+
+401
+00:43:30,120 --> 00:43:36,840
+يساوي f of s يعني exist يبقى then Laplace inverse
+
+402
+00:43:36,840 --> 00:43:42,180
+لهذه الدالة كذلك exist وشكله بيعطيني يعني الدالة
+
+403
+00:43:42,180 --> 00:43:47,020
+الأصلية قبل ما ناخد لها Laplace transform هذا اللي
+
+404
+00:43:47,020 --> 00:43:50,930
+هو بيسميه ال inverse Laplace transformبصيغ السطرين
+
+405
+00:43:50,930 --> 00:43:54,570
+مرة تانية بقول لبلاس inverse لل F of S بدي ساوي F
+
+406
+00:43:54,570 --> 00:44:00,410
+of T إذا كان لبلاس لل F of T عبارة عن main F of S
+
+407
+00:44:00,410 --> 00:44:09,090
+بهمنا التطبيق اللي عمله كيف بدي أحسب اللي هو معكوس
+
+408
+00:44:09,090 --> 00:44:13,810
+لبلاس ال transform لدا اللي تمها يعنيلو ماعطيني
+
+409
+00:44:13,810 --> 00:44:18,730
+الدالة بدللة F of S يعني ماعطيني لبلاس ترانسفورم
+
+410
+00:44:18,730 --> 00:44:24,750
+لدالة ما هل بنقدر نجيب الأصل ولا لأ هو هذا الموضوع
+
+411
+00:44:24,750 --> 00:44:28,890
+تبع هذا ال section بقول مش هنجيب الأصل بدك تتبع
+
+412
+00:44:28,890 --> 00:44:33,200
+ثلاث خطواتالخطوة اللى بيجي تعمل partial fractions
+
+413
+00:44:33,200 --> 00:44:38,200
+ممكن ماجدرش تعمل partial fractions أحيانا يبقى
+
+414
+00:44:38,200 --> 00:44:42,980
+تدبر حالك من خلال المثال اللى قدامك وسأعطيك بدل
+
+415
+00:44:42,980 --> 00:44:47,390
+المثال اتنين على ذلك بعد قليل ان شاء اللهالتانى
+
+416
+00:44:47,390 --> 00:44:49,590
+يستخدم الاسم الـ table of values اذا كنت مابدي
+
+417
+00:44:49,590 --> 00:44:52,570
+ارجع للجدول اللي قلنا بيجيك في الامتحان النمرة
+
+418
+00:44:52,570 --> 00:44:56,890
+التلاتة بدي استخدم خاصية او الخاصية الخطية ل
+
+419
+00:44:56,890 --> 00:45:00,690
+Laplace transform و معاكوس Laplace transform اول
+
+420
+00:45:00,690 --> 00:45:03,970
+مثال قال لي هاتلي الدالة F of D ل Laplace
+
+421
+00:45:03,970 --> 00:45:08,930
+transform اللي همواطعة بقولكوا يا أسباجي بتطلع لو
+
+422
+00:45:08,930 --> 00:45:13,430
+روحت على الجدول مالاجيش ولا واحدة بالشكل هذايبقى
+
+423
+00:45:13,430 --> 00:45:18,130
+أول خطش بدي ايه؟ بدي أفصلهم عن بعض، مشان أفصلهم عن
+
+424
+00:45:18,130 --> 00:45:22,910
+بعض، بدي أجي أقول هذا الكلام يساوي، بدي أعمله
+
+425
+00:45:22,910 --> 00:45:26,830
+Laplace Transform تبع Calculus بيه، يبقى باجي
+
+426
+00:45:26,830 --> 00:45:34,730
+بقوله هذا جوس اللي هو S وهذا مين؟ جوس تاني، اه هذا
+
+427
+00:45:34,730 --> 00:45:42,360
+الجوس مكرر جديشمرتين إذا بدي أقول S زائد اتنين و
+
+428
+00:45:42,360 --> 00:45:48,740
+بدي أعمل كمان جوة S S زائد اتنين الكل تربيع هذا من
+
+429
+00:45:48,740 --> 00:45:53,420
+الدرجة الأولى بقول A هذا من الدرجة الأولى بقول B
+
+430
+00:45:53,420 --> 00:46:01,900
+هذا من الدرجة الأولى و مكرر بقول Cطيب إذا بروح
+
+431
+00:46:01,900 --> 00:46:05,360
+اوجد ال a و ال b و ال c مش هان اوجد ال a و ال b و
+
+432
+00:46:05,360 --> 00:46:09,940
+ال c باجي على ال term اللي عندنا هذا هك كله من
+
+433
+00:46:09,940 --> 00:46:13,760
+الأول للآخر بضربه في هذا الرقم مش هان اتخلص من
+
+434
+00:46:13,760 --> 00:46:18,240
+مين؟ من الكثور يبقى لو ضربت في هذا الرقم بضلي
+
+435
+00:46:18,240 --> 00:46:26,120
+الشمال كده؟واليمين AS زائد اتنين لكل تربيع وهنا
+
+436
+00:46:26,120 --> 00:46:35,640
+زائد BS في S زائد اتنين وهنا زائد C في Sمظبوط؟
+
+437
+00:46:35,640 --> 00:46:40,240
+يبقى هذه لو جيت فكيتها بدى تصير على الشكل التالي
+
+438
+00:46:40,240 --> 00:46:48,920
+واحد تساوي اللي قول A S ترميع زائد أربعة A S زائد
+
+439
+00:46:48,920 --> 00:46:55,740
+أربعة A فكيت الجثه و ضربت في A زائد B S ترميع
+
+440
+00:46:56,220 --> 00:47:03,700
+بستربية زائد اتنين باس واخد
+
+441
+00:47:03,700 --> 00:47:10,620
+term زائد CS يبقى هذا الكلام بده يساوي هدى عندك
+
+442
+00:47:10,620 --> 00:47:17,520
+تربية و هنا تربية يبقى A زائد B في ال S تربيةهو
+
+443
+00:47:17,520 --> 00:47:24,260
+عندك هنا زائد 4A في ال S وهذا كله في S وهذا كله في
+
+444
+00:47:24,260 --> 00:47:33,320
+S يبقى 4A زائد 2B زائد C كله في ال S ولم يقطع عندك
+
+445
+00:47:33,320 --> 00:47:39,310
+إلا من 4Aكله يبدو يساوي واحد، بنقعد مقارنة ما بين
+
+446
+00:47:39,310 --> 00:47:44,990
+الطرفين يبقى الـA زائد الـB يساوي جداش Zero لإن
+
+447
+00:47:44,990 --> 00:47:50,730
+ماعنديش على الشمال استربيع كذلك عندي أربعة A زائد
+
+448
+00:47:50,730 --> 00:47:55,530
+اتنين B زائد C يساوي Zero ماعنديش S ال constant
+
+449
+00:47:55,530 --> 00:47:59,770
+هذا هو ال constant هذا يبقى أربعة A يساوي واحد
+
+450
+00:47:59,770 --> 00:48:06,280
+يبقى ال A تساوي ربعلما الـ A تساوي ربع يبقى B
+
+451
+00:48:06,280 --> 00:48:12,520
+تساوي سالب ربع ناخد المعلومات هذه و نعوض بها في
+
+452
+00:48:12,520 --> 00:48:17,200
+المعادلة هذه يبقى لما أضرب أربعة في ربع يبقى هنا
+
+453
+00:48:17,200 --> 00:48:24,340
+كده؟ واحدوهنا ناقص اتنين في ربع اللي هو بنص وزائد
+
+454
+00:48:24,340 --> 00:48:30,840
+C يبجى هذا بده يعطيك انه C يساوي واحد ناقص نص بيظل
+
+455
+00:48:30,840 --> 00:48:36,560
+زائد نص وديه على الشجة التانية بصير سالب نص يبجى
+
+456
+00:48:36,560 --> 00:48:44,950
+أصبح شكل ال F of S على الشكل التالي ال A بربععلى S
+
+457
+00:48:44,950 --> 00:48:53,310
+تمام و ال B بسالب ربع يبقى سالب و هذا الربع على S
+
+458
+00:48:53,310 --> 00:49:01,850
+زائد 2 و ال C اللي هو بالنص يبقى ناقص نص على S
+
+459
+00:49:01,850 --> 00:49:09,600
+زائد 2 لكل تربيعتعالى نشوف هذه بقدر اقول ربع في
+
+460
+00:49:09,600 --> 00:49:17,500
+واحد على اس ناقص ربع في واحد على اس زائد اتنين و
+
+461
+00:49:17,500 --> 00:49:25,100
+هنا ناقص نص في واحد على اس زائد اتنين لكل تربيع
+
+462
+00:49:25,100 --> 00:49:31,090
+الواحد هذه يا بنات بقدر اقول هي واحد factorialفي
+
+463
+00:49:31,090 --> 00:49:36,470
+مشكلة واحد واحد factorial ما هي واحد يبقى هذه واحد
+
+464
+00:49:36,470 --> 00:49:41,130
+factorial بالشكل اللي عندنا الان انا بدي الدالة
+
+465
+00:49:41,130 --> 00:49:47,390
+الاصلية يبقى F of T دالة اللي بديها هي ل plus
+
+466
+00:49:47,390 --> 00:49:54,010
+inverse لمين ل capital F of Sالـ F of T هي Laplace
+
+467
+00:49:54,010 --> 00:49:58,550
+inverse للـ F of S يعني معناته ياخد Laplace
+
+468
+00:49:58,550 --> 00:50:03,350
+inverse لكل طرف من هذه الأعطراف الثلاثة يبقى هذا
+
+469
+00:50:03,350 --> 00:50:10,510
+الرابع في Laplace inverse للواحد على S ناقص رابع
+
+470
+00:50:10,510 --> 00:50:17,970
+في Laplace inverse للواحد على S زائد اتنيننقص نص
+
+471
+00:50:17,970 --> 00:50:24,350
+في Laplace inverse للواحد factorial على S زائد
+
+472
+00:50:24,350 --> 00:50:31,390
+اتنين لكل تربيع يبقى ال F of T اللي انا بديها بدي
+
+473
+00:50:31,390 --> 00:50:35,390
+ساوي ربع بيداجي لواحد عليه السادس ل Laplace تبعت
+
+474
+00:50:35,390 --> 00:50:39,190
+مين اذا Laplace inverse اللي واحدة لسه بدي رجعها
+
+475
+00:50:39,190 --> 00:50:44,970
+لاصلها اصلها مينواحد صحيح يبقى هذه في واحد صحيح
+
+476
+00:50:44,970 --> 00:50:51,110
+وهنا ناقص ربع واحد علاش زي اتنين هذه plus تبع
+
+477
+00:50:51,110 --> 00:50:52,130
+اتمين
+
+478
+00:50:57,600 --> 00:51:03,240
+طلع في الجدول اللي عندك يبقى ناقص اتنين T يبقى هذه
+
+479
+00:51:03,240 --> 00:51:11,980
+ال A أس ناقص اتنين T وهنا ناقص نص نجي للي عندنا
+
+480
+00:51:11,980 --> 00:51:16,940
+هذه اطلعيلي في الجدول اللي عندك انا في الجدول اللي
+
+481
+00:51:16,940 --> 00:51:22,600
+عندي هذه في الجدول اللي عندي اللي هي من factorial
+
+482
+00:51:22,600 --> 00:51:26,060
+اللي هي رقم 11 اعتقد عندك رقم 9
+
+483
+00:51:33,970 --> 00:51:39,570
+أخر واحدة التاسعة اللي هو عندك N factorial على S
+
+484
+00:51:39,570 --> 00:51:47,470
+ناقص A to the power M زائد واحد نميه T أس N E أس
+
+485
+00:51:47,470 --> 00:51:56,460
+ATيبقى T أس N بقوله هاي T ال N عندي بقداش واحد
+
+486
+00:51:56,460 --> 00:52:02,440
+يبقى T فقط لغيره وال exponential E وال E هنا بقداش
+
+487
+00:52:02,440 --> 00:52:09,260
+بناقص اتنين T يبقى هذه شكل الدالة ال همين اللي هو
+
+488
+00:52:09,260 --> 00:52:11,300
+بده يعني تمام؟
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ccd9cb79a3164d63611273e6f782deb38cfa83d7
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI.srt
@@ -0,0 +1,1718 @@
+1
+00:00:21,230 --> 00:00:25,470
+بسم الله الرحمن الرحيم ابتدأنا في المرة الماضية
+
+2
+00:00:25,470 --> 00:00:28,130
+بالـ system of linear equations اللي هو section 
+
+3
+00:00:28,130 --> 00:00:33,070
+2.1 ولما ننتهي بعد و ابتدأنا في أخذ أمثلة
+
+4
+00:00:33,070 --> 00:00:38,070
+على هذا الـ section  و أعطينا على ذلك ثلاثة أمثلة 
+
+5
+00:00:38,070 --> 00:00:42,930
+تمام؟ و هذا هو المثال الرابع اللي بين إيدنا الآن
+
+6
+00:00:43,470 --> 00:00:48,850
+المثال بيقول استخدم الـ Echelon Form أو الـ Row 
+
+7
+00:00:48,850 --> 00:00:53,450
+Echelon Form عشان نحل المعادلة اللي عندنا هذه يبقى
+
+8
+00:00:53,450 --> 00:00:57,170
+الخطوة الأولى يقول بناخد الـ Augmented Matrix يعني
+
+9
+00:00:57,170 --> 00:01:02,010
+المصفوفة الموسعة المصوفة الموسعة عندنا على هذا 
+
+10
+00:01:02,010 --> 00:01:09,690
+الشكل اللي هو 1 1 -1 1 2 1
+
+11
+00:01:09,690 --> 00:01:18,930
+-1 1  و هنا 0  و هنا 1 1 0 و
+
+12
+00:01:18,930 --> 00:01:28,910
+هنا الصف الرابع هو عبارة عن 0 و كذلك 1 و
+
+13
+00:01:28,910 --> 00:01:36,130
+0 و 2 و بنروح نحط هنا مصفوفة المعاملات أو
+
+14
+00:01:36,130 --> 00:01:44,190
+الثوابت اللي هو 4 -5 -1 4
+
+15
+00:01:44,190 --> 00:01:50,930
+الشكل اللي عندنا طبعا إيش 
+
+16
+00:01:50,930 --> 00:01:58,490
+5؟ 4 صفوف هي المعادلة 
+
+17
+00:01:58,490 --> 00:02:04,330
+الثانية 5 بالموجب 5 بالموجب فعلا يبقى هي ..
+
+18
+00:02:04,330 --> 00:02:09,710
+هي كتبنا اللي هو مصفوفة المعاملات وكذلك أضفنا لها
+
+19
+00:02:09,710 --> 00:02:16,090
+عمود الثوابت وسميت لذلك بالمصوفة الموسعة الآن واضح
+
+20
+00:02:16,090 --> 00:02:20,330
+عندي هنا صفرين يبقى دول بقدرش أعمل فيهم ولا حاجة 
+
+21
+00:02:20,570 --> 00:02:26,270
+يبقى باجي على الاثنين هذه و بتخليها 1 صحيح إذا
+
+22
+00:02:26,270 --> 00:02:33,850
+بقدر أضرب الصف الأول في سالب 2 و أضيفه للصف
+
+23
+00:02:33,850 --> 00:02:39,510
+الثاني يبقى هذا بدي أعمل سالب 2 R1
+
+24
+00:02:42,510 --> 00:02:49,830
+بأحصل على المصفوفة الثانية الصف الأول كما هو 1
+
+25
+00:02:49,830 --> 00:02:56,050
+1 -1 1 وهي الـ 4 الصف الثاني بيصير
+
+26
+00:02:56,050 --> 00:03:00,210
+0 -2 1 بيصير -1 
+
+27
+00:03:14,240 --> 00:03:20,850
+الصفرين يبقوا كما هم الاثنين يبقى هاي 0 وهي 0
+
+28
+00:03:20,850 --> 00:03:27,450
+وهي 1 1 وهنا 1 0 وهنا 0 2 وهنا 
+
+29
+00:03:27,450 --> 00:03:32,890
+-1 وهي الـ 4 وهي المصفوفة الجديدة اللي 
+
+30
+00:03:32,890 --> 00:03:39,150
+عندنا الآن هذا الـ leading اللي عندنا له 1 تمام
+
+31
+00:03:39,150 --> 00:03:43,630
+إذا بالضبط للصف اللي بعده العصر صحته لأ اللي على 
+
+32
+00:03:43,630 --> 00:03:48,090
+يمينه بالضبط لازم يكون الـ leading هذا جداش 1 صح
+
+33
+00:03:48,090 --> 00:03:50,930
+يبقى بروح بضرب الصف الأول هذا في جد إيه الصف 
+
+34
+00:03:50,930 --> 00:03:55,090
+الثاني في جد إيه في -1 يبقى باجي بقوله بدي
+
+35
+00:03:55,090 --> 00:04:02,610
+أعمل - R2 فقط لغة يبقى باجي بقول المصفوفة 
+
+36
+00:04:02,610 --> 00:04:09,250
+هتأخذ الشكل التالي 1 1 -1 وهنا كمان
+
+37
+00:04:09,250 --> 00:04:15,760
+1 وهذا عمودي الثوابت اللي هو 4 وهنا 0
+
+38
+00:04:15,760 --> 00:04:22,940
+وهنا 1 وهنا -1 وهنا 1 وهنا 3
+
+39
+00:04:22,940 --> 00:04:28,240
+والصفين التانيات الاثنين اللي صفلين زي ما هم 1
+
+40
+00:04:28,240 --> 00:04:36,380
+1 وهنا 1 0 وهنا 0 2 وهنا -1 
+
+41
+00:04:36,380 --> 00:04:44,100
+وهنا كداش اللي هو 4 بعد هيك بدي أعمل هنا 0
+
+42
+00:04:44,100 --> 00:04:49,220
+وهنا 0 إذا بضرب الصف الثاني في -1 و
+
+43
+00:04:49,220 --> 00:04:56,100
+بضيفه للصف الثالث و كذلك للصف الرابع يبقى عملتين 
+
+44
+00:04:56,100 --> 00:05:02,880
+هعملهم في الـ 1 يبقى بدي أعمل ما يأتي - اللي
+
+45
+00:05:02,880 --> 00:05:06,220
+هو R2 to R3
+
+46
+00:05:19,380 --> 00:05:26,280
+يبقى أول صفين يبقوا كما هم يبقى باجي بقول الصف
+
+47
+00:05:26,280 --> 00:05:34,180
+الأول هذا اللي هو 1 1 -1 وهنا 1 هنا
+
+48
+00:05:34,180 --> 00:05:40,940
+4 كما هو وهنا 0 وهنا 1 وسالب 1 1
+
+49
+00:05:40,940 --> 00:05:46,780
+وهنا 3 الآن بدي أضربه في -1 وأضيفه هنا 
+
+50
+00:05:46,780 --> 00:05:51,820
+بدي يجيني هنا هذا 0 0 زي ما هو بدي يجيكي هنا
+
+51
+00:05:51,820 --> 00:05:57,280
+0 0 تمام؟ الآن هذا أنا ضربته في -1
+
+52
+00:05:57,280 --> 00:06:02,810
+يبقى هنا كداش 1 1 بيصير 2 وهنا 1 يبقى
+
+53
+00:06:02,810 --> 00:06:08,510
+هنا 2 وهنا 1 هنا صار هذا -1 أضيفه
+
+54
+00:06:08,510 --> 00:06:14,510
+هنا يبقى بيصير -1 و 1 يبقى -1 و
+
+55
+00:06:14,510 --> 00:06:19,490
+1 فقط لغير بقول -1 زي 2 اللي هو اب
+
+56
+00:06:19,490 --> 00:06:24,330
+1 لأ إذا عرفت أن -1 بيصير -3
+
+57
+00:06:24,330 --> 00:06:29,980
+يبقى بيصير هذه -4 وهذه 1 يبقى هذه سالف
+
+58
+00:06:29,980 --> 00:06:36,000
+4 وهذه 1 بالشكل اللي عندنا هذا، تمام؟ الآن
+
+59
+00:06:36,000 --> 00:06:42,320
+بالذالك لمين؟ لصف الثالث، بدي هذا يكون 1، صحيح،
+
+60
+00:06:42,320 --> 00:06:46,600
+يبقى بروح بضرب هذا الكلام في قداش، في ½، يبقى بدي
+
+61
+00:06:46,600 --> 00:06:55,170
+النص R3 يبقى بالده ياخد هنا النص R3 ينثب
+
+62
+00:06:55,170 --> 00:07:01,890
+على الشكل ثالث أول صفين زي ما هما 1 1 وكمان
+
+63
+00:07:01,890 --> 00:07:04,670
+-1 وهنا 1
+
+64
+00:07:14,780 --> 00:07:20,920
+والعمود هذا هذا 1 وهنا 4 وهنا 0 وهنا 
+
+65
+00:07:20,920 --> 00:07:27,120
+1 -1 1 3 الآن بدي أضرب هدف ½ 
+
+66
+00:07:27,120 --> 00:07:32,280
+يبقى 0 0 زي ما هو وهنا -½ وهنا -
+
+67
+00:07:32,280 --> 00:07:41,220
+2 والصفة الرابعة زي ما هو 1 1 1 الآن 
+
+68
+00:07:41,730 --> 00:07:50,010
+بدي أخلي هذا 0 يبقى بداتي أقوله -R3 to R4
+
+69
+00:07:50,010 --> 00:07:55,050
+ونشوف إيش بدنا نعمل في هذا يبقى هذا الكلام بده 
+
+70
+00:07:55,050 --> 00:08:01,410
+يعطينا المصفوفة التالية الآن 1 1 -1
+
+71
+00:08:01,410 --> 00:08:10,710
+1 0 1 -1 1 0 0 1 -
+
+72
+00:08:10,710 --> 00:08:18,310
+½ هنا موجبة وهنا موجبة وهنا موجبة وهنا موجبة وهنا
+
+73
+00:08:18,310 --> 00:08:22,250
+موجبة 
+
+74
+00:08:22,250 --> 00:08:32,410
+وهنا موجبة
+
+75
+00:08:36,410 --> 00:08:44,730
+بدي هذا يكون كمان جداشر بدي 1 صحيح طيب إيش رأيك
+
+76
+00:08:44,730 --> 00:08:51,350
+يا بنات لو عملت ما يأتي بدي أحاول أخفف الخطوات
+
+77
+00:08:51,350 --> 00:08:57,470
+شوية يبقى بدي أعمل ما يأتي بدي أضرب هذا في سالب 
+
+78
+00:08:57,470 --> 00:09:02,830
+1 و أضيفه فوق هاي الخطوة الأولى الخطوة الثانية
+
+79
+00:09:03,120 --> 00:09:11,260
+بدي أضغط هدف قداش ⅔ يبقى بدي أجي R2
+
+80
+00:09:11,260 --> 00:09:17,720
+بالسالب -R2 to R1 هاي واحدة الثانية
+
+81
+00:09:17,720 --> 00:09:25,300
+بدي ⅔ R4 مرة واحدة خطوة واحدة يبقى بتاخد 
+
+82
+00:09:25,300 --> 00:09:32,920
+الشكل التالي هادي 1 وهذا 0 وهذا هنا ضربنا فيه
+
+83
+00:09:32,920 --> 00:09:37,940
+-1 بيصير موجبة 1 بيصير 0 وهنا كمان 
+
+84
+00:09:37,940 --> 00:09:42,520
+0 وهنا ضربنا فيه -1 بيصير -3
+
+85
+00:09:42,520 --> 00:09:48,220
+يبقى هنا ويبقى القداش 1 هذا 0 1 -1
+
+86
+00:09:48,220 --> 00:09:57,290
+1 كما هو وهذه 3 كما هي وهنا 0 0 1 0 0 وهنا
+
+87
+00:09:57,290 --> 00:10:00,590
+0 0 0 1
+
+88
+00:10:00,590 --> 00:10:08,050
+صحيح لإن أنا ضربت جدًّا في ⅔ وهذا يصبح 2 و
+
+89
+00:10:08,050 --> 00:10:13,890
+اللي قبلها -2 زي مين يبقى هذه -2 و
+
+90
+00:10:13,890 --> 00:10:19,870
+هذه اللي هي مين 2 بالشكل اللي عندنا هذا طيب أنا 
+
+91
+00:10:19,870 --> 00:10:28,150
+ممكن أخلي هنا هذا 0 و أخلي هذا 0 يبقى بدأ 
+
+92
+00:10:28,150 --> 00:10:34,270
+أضيف الصف الثالث إلى الصف الثاني بخلق 0 فوق 
+
+93
+00:10:34,270 --> 00:10:41,210
+يبقى هنا بدنا نعمل ما يأتي بدأ أحط سهم و أقول هنا
+
+94
+00:10:41,210 --> 00:10:50,530
+-R3 to R2 يبقى بدى يصير عندي ما يأتي
+
+95
+00:10:50,530 --> 00:10:55,410
+R3
+
+96
+00:10:55,410 --> 00:11:03,710
+to R2 وهذا شو رأيك كمان أضربه في ½ و أضيفه للي
+
+97
+00:11:03,710 --> 00:11:06,890
+فوق بالمرة كويس؟
+
+98
+00:11:10,320 --> 00:11:18,100
+طيب نعملها خطوة واحدة يبقى -R3 to R2 
+
+99
+00:11:18,100 --> 00:11:30,380
+وكذلك ½ R4 to R3 مرة واحدة يبقى بيصير 
+
+100
+00:11:30,380 --> 00:11:38,510
+عندنا هنا 1 0 0 0 1 هنا -R3 
+
+101
+00:11:38,510 --> 00:11:44,050
+to R2 سالب 
+
+102
+00:11:44,050 --> 00:11:48,990
+R3 .. لا لا R3 بدون سالب صحيح R3
+
+103
+00:11:48,990 --> 00:11:55,030
+بدي أضيفه لـ R2 مباشرة يبقى 0 وهنا 1
+
+104
+00:11:55,030 --> 00:12:04,270
+وهنا 0 وهنا ½ وهنا 1 أضفنا إضافة بعدين ½ R
+
+105
+00:12:04,270 --> 00:12:12,620
+4 بدي أضيفه لـ R3 بيصير 0 0 1 وهنا 
+
+106
+00:12:12,620 --> 00:12:18,740
+½ بيصير 0 وهنا ½ فيه 2 اللي هو بـ 1
+
+107
+00:12:18,740 --> 00:12:23,560
+بيبقى اللي عندنا هنا جدًّا -1 وهذا 0 0
+
+108
+00:12:23,560 --> 00:12:29,040
+وهنا 1 وهنا 2 بالشكل اللي عندنا هو ضايل
+
+109
+00:12:29,040 --> 00:12:33,830
+علينا بس خطوة واحدة اللي هتخلص من النص اللي عندنا
+
+110
+00:12:33,830 --> 00:12:38,550
+هذا يبقى بقى أضرب الصف الرابع في -½ وأضيفه 
+
+111
+00:12:38,550 --> 00:12:47,170
+للصف الثاني يبقى هذا بده يعطينا -½ R4 to 
+
+112
+00:12:47,170 --> 00:12:55,670
+R3 بنحصل على ما يأتي هاي 1 0 0 0
+
+113
+00:12:55,670 --> 00:13:04,810
+1 أو هنا 0 1 زيرو زيرو وهنا آه استني 
+
+114
+00:13:04,810 --> 00:13:09,990
+شوية إحنا بقول -½ آه 4 يبقى هنا بيصير قدير
+
+115
+00:13:09,990 --> 00:13:16,630
+-1 مع 1 بيصير 0 مظبوط هيك مرة ثانية
+
+116
+00:13:16,630 --> 00:13:22,020
+بالأول مالكم معاك الصف الأول حاطيته زي ما هو صفى 
+
+117
+00:13:22,020 --> 00:13:29,320
+الثاني بقول -½ أقل .. لأ صفى الثاني .. سالب 
+
+118
+00:13:29,320 --> 00:13:35,640
+½ .. لأ هذا -½ أقل 4 و قاري 2 .. 
+
+119
+00:13:35,640 --> 00:13:41,450
+أيوه لقاري 2 يبقى لـ R2 بيصير عندنا هنا 0 0
+
+120
+00:13:41,450 --> 00:13:46,950
+مظبوط وهذا 0 0 1 0
+
+121
+00:13:46,950 --> 00:13:53,850
+-1 وهنا 0 0 0 2
+
+122
+00:13:53,850 --> 00:13:59,070
+الشكل اللي عندنا إذاً الـ System اللي وصلته يا بنات 
+
+123
+00:13:59,070 --> 00:14:03,890
+هذا اللي هو X1 = 1 و X2 = 0 و X3
+
+124
+00:14:03,890 --> 00:14:08,030
+= -1 و X4 = 2 مكافئ للـ System 
+
+125
+00:14:08,030 --> 00:14:12,710
+الأصل اللي همين الـ Star اللي عندنا يبقى أصبح حل 
+
+126
+00:14:12,710 --> 00:14:16,630
+المعادلة الـ Star أو الـ System الـ Star هو حل هذا 
+
+127
+00:14:16,630 --> 00:14:23,790
+الـ System لذلك برفض أقول له solution of
+
+128
+00:14:23,790 --> 00:14:39,520
+the system star with x1 و x2 و x3 و x4 بيبقى يساوي
+
+129
+00:14:39,520 --> 00:14:47,880
+يعني four triple من 1 0 سالب 1 2
+
+130
+00:14:47,880 --> 00:14:54,800
+بالشكل اللي عندنا هذا خلينا نسأل السؤال التالي الآن
+
+131
+00:14:54,800 --> 00:15:01,240
+هل الـ system star هذا Consistent ولا Inconsistent؟
+
+132
+00:15:01,240 --> 00:15:06,240
+Consistent لأنه لجيت حل مرة ليه فده أقول أن لو كان
+
+133
+00:15:06,240 --> 00:15:11,000
+حل أو عدد لا نهائي من الحلول يبقى بسمي الـ system
+
+134
+00:15:11,000 --> 00:15:13,400
+Consistent؟
+
+135
+00:15:15,600 --> 00:15:19,720
+طيب إحنا لغاية أخذنا 4 أمثلة زي ما أنتم شايفين 
+
+136
+00:15:19,720 --> 00:15:26,600
+وكل واحد فيهم شكل واتساب درجنا من المعادلتين في
+
+137
+00:15:26,600 --> 00:15:31,760
+مجهولين لغاية ما وصلنا إلى 4 معادلات في 4 
+
+138
+00:15:31,760 --> 00:15:39,390
+مجهولين بنجي ناخد مثال بيختلف شكلاً عن الأمثلة اللي
+
+139
+00:15:39,390 --> 00:15:47,190
+فاتت لكن بيحمل نفس الفكرة يبقى مثال رقم 5 هذا
+
+140
+00:15:47,190 --> 00:15:53,050
+من الكتاب سؤال 19 نمرة إيه بيقول For what
+
+141
+00:15:53,050 --> 00:16:02,890
+values For what values ما هي القيم اللي بتاخدها a 
+
+142
+00:16:02,890 --> 00:16:11,530
+and b بحيث أن For what value of a does the system
+
+143
+00:16:11,530 --> 00:16:19,910
+does the system does 
+
+144
+00:16:33,010 --> 00:16:41,970
+اللي هو x1 - 2x2 = a و - 
+
+145
+00:16:41,970 --> 00:16:49,270
+3x1 + 6x2 بده يساوي b هذا هو الـ
+
+146
+00:16:49,270 --> 00:16:57,110
+system have a solution have a 
+
+147
+00:16:57,110 --> 00:16:58,690
+solution
+
+148
+00:17:33,750 --> 00:17:39,630
+سؤال مرة ثانية يقول لي ما هي القيم التي تأخذها كل 
+
+149
+00:17:39,630 --> 00:17:46,010
+من a و b بحيث أن هذا الـ system يكون له حل تمام
+
+150
+00:17:46,010 --> 00:17:52,530
+لما أقول حل ما قلتش حل وحيد قد يكون حل وحيد وقد يكون
+
+151
+00:17:52,530 --> 00:17:57,790
+عدد لا نهائي من الحلول المهم أن يكون هناك حل بغض 
+
+152
+00:17:57,790 --> 00:18:01,830
+النظر عن شكل الحل يعني بدي إيش القلم تأخذها a
+
+153
+00:18:01,830 --> 00:18:06,090
+و b إذا بروح ببدأ بالمصفوفة الموسعة زي ما كنت 
+
+154
+00:18:06,090 --> 00:18:11,630
+بشتغل في الأربعة أمثلة الماضية يبقى هنا بقوله 
+
+155
+00:18:11,630 --> 00:18:12,610
+solution
+
+156
+00:18:14,930 --> 00:18:24,930
+بعدين للمصفوفة الموسعة 1 -2 3 6 وهنا a وهنا b
+
+157
+00:18:24,930 --> 00:18:30,870
+بالشكل اللي عندناها تمام؟ بدي أحاول أخلي هذا 0 
+
+158
+00:18:30,870 --> 00:18:36,910
+يبقى بضرب الصف الأول فيه 3 و بضيفه للصف الثاني 
+
+159
+00:18:36,910 --> 00:18:45,940
+يبقى هنا 3 R1 to R2 نفس العدد الصف الأول زي ما
+
+160
+00:18:45,940 --> 00:18:53,160
+هو 1 سالب 2 a الصف الثاني 0 يعني ضربنا
+
+161
+00:18:53,160 --> 00:18:59,120
+فيه 3 في سالب 6 مع 6 في 0 هنا ضربنا فيه
+
+162
+00:18:59,120 --> 00:19:05,560
+3 اللي بيصير 3a + الـ b بالشكل اللي 
+
+163
+00:19:05,560 --> 00:19:08,440
+عندنا تمام
+
+164
+00:19:09,470 --> 00:19:13,430
+من هذا الكلام ماذا نستنتج يا بنات أن 3a + 
+
+165
+00:19:13,430 --> 00:19:20,110
+b كده 0 أصلاً الله يرضى يعني كأنه هنا 0 X
+
+166
+00:19:20,110 --> 00:19:26,290
+1 + 0 X2 + 3a + b وهنا X
+
+167
+00:19:26,290 --> 00:19:30,630
+1 - 2 X2 + a المعادلة الأولى
+
+168
+00:19:30,630 --> 00:19:37,190
+تمام يبقى باجي بقول له The above system
+
+169
+00:19:39,090 --> 00:19:50,930
+has a solution of الـ 3a + الـ b بدل ساوية 0
+
+170
+00:19:51,930 --> 00:19:57,110
+يعني أي قيمتين أخدهم لـ a و b بيخلوه للمعادلة
+
+171
+00:19:57,110 --> 00:20:03,150
+تساوي 0 بتبقى هي عبارة عن القيم اللي بتخلي لهذا
+
+172
+00:20:03,150 --> 00:20:06,950
+الـ system حل بس ما قاليش هات الحل لو قالي هات
+
+173
+00:20:06,950 --> 00:20:12,190
+الحل بدي أروح القيمة اللي بدي أحطها وبدي أطبقها 
+
+174
+00:20:12,190 --> 00:20:16,390
+وبالتالي كل واحد بيطلع عنده إيه حل الشكل يعني كام
+
+175
+00:20:1
+
+201
+00:23:14,080 --> 00:23:18,540
+a system
+
+202
+00:23:18,540 --> 00:23:22,260
+in the form
+
+203
+00:23:28,810 --> 00:23:37,730
+A11X1 A12X2 A1NXN0
+
+204
+00:23:37,730 --> 00:23:42,170
+A21X1
+
+205
+00:23:42,170 --> 00:23:45,470
+A22X2
+
+206
+00:23:45,470 --> 00:23:49,710
+A2NXN0
+
+207
+00:23:49,710 --> 00:23:54,630
+AM1X1
+
+208
+00:23:57,270 --> 00:24:04,530
+AM2X2 + + AMNXN
+
+209
+00:24:04,530 --> 00:24:09,770
++ + AMNXN + + AMNXN
+
+210
+00:24:09,770 --> 00:24:16,310
++ AMNXN + AMNXN
+
+211
+00:24:16,310 --> 00:24:18,990
++ AMNXN + AMNXN + AMNXN + AMNXN +
+
+212
+00:24:18,990 --> 00:24:22,290
+AMNXN + AMNXN + AMNXN
+
+213
+00:24:22,290 --> 00:24:27,410
+يبقى هتقسم هذه الـ remark إلى نقطتين النقطة
+
+214
+00:24:27,410 --> 00:24:36,570
+الأولى The homogeneous system استعارة اللي عندنا
+
+215
+00:24:36,570 --> 00:24:46,810
+هذا is always has a solution is always has a
+
+216
+00:24:46,810 --> 00:24:51,650
+solution دائما بلقيله حل because
+
+217
+00:24:55,830 --> 00:25:00,410
+it has because
+
+218
+00:25:00,410 --> 00:25:08,490
+it has at least the
+
+219
+00:25:08,490 --> 00:25:17,750
+trivial solution ايش
+
+220
+00:25:17,750 --> 00:25:23,550
+ال trivial solution الو x واحد و x اتنين ونظل
+
+221
+00:25:23,550 --> 00:25:31,410
+ماشيين لغاية xn بدي يساوي zero و zero و كذلك zero
+
+222
+00:25:31,410 --> 00:25:39,510
+النقطة الثانية the homogeneous system يبقى هنضيف
+
+223
+00:25:39,510 --> 00:25:45,630
+عليها كمان عبارة قبل ما نبدأ النقطة التانية يبقى
+
+224
+00:25:45,630 --> 00:25:55,070
+باجي بقول sir the homogeneous system
+
+225
+00:25:56,240 --> 00:26:04,940
+a star is consistent is consistent
+
+226
+00:26:04,940 --> 00:26:12,420
+بنجي إلى النقطة الثانية the homogeneous system a
+
+227
+00:26:12,420 --> 00:26:23,740
+star the homogeneous system a star of m equations
+
+228
+00:26:23,740 --> 00:26:41,630
+of m equations and n unknowns has
+
+229
+00:26:41,630 --> 00:26:45,830
+infinite
+
+230
+00:26:45,830 --> 00:26:55,190
+number of solutions infinite number of
+
+231
+00:26:57,200 --> 00:27:03,940
+Solutions Infinite number of solutions that
+
+232
+00:27:03,940 --> 00:27:07,140
+contains
+
+233
+00:27:07,140 --> 00:27:16,640
+the trivial solution that
+
+234
+00:27:16,640 --> 00:27:21,440
+contains the trivial solution
+
+235
+00:27:28,560 --> 00:27:32,740
+m أقل من n
+
+236
+00:27:58,990 --> 00:28:14,570
+كذبت one find the solution of the system x
+
+237
+00:28:14,570 --> 00:28:24,550
+واحد ناقص x اتنين ناقص تلاتة x تلاتة بيساوي زيرو
+
+238
+00:28:24,550 --> 00:28:32,040
+واحد x واحد زي x اتنين زائد x تلاتة بيساوي زيرو
+
+239
+00:28:32,040 --> 00:28:41,120
+اتنين x واحد زائد اتنين x اتنين زائد x تلاتة
+
+240
+00:28:41,120 --> 00:28:44,740
+كله بيساوي زيرو
+
+241
+00:29:18,390 --> 00:29:23,190
+النقطة الأولى هو تعريف الـ homogeneous system
+
+242
+00:29:23,190 --> 00:29:28,450
+النقطة الثانية هي الملاحظة التي تتكون من نقطتين
+
+243
+00:29:28,450 --> 00:29:32,610
+وهذه تعطينا مؤشر لحل الـ homogeneous system
+
+244
+00:29:33,240 --> 00:29:37,060
+الدفينيشن بيقول الـ homogeneous literal system is
+
+245
+00:29:37,060 --> 00:29:41,800
+a system in the form يبقى معادلات قطية بس الثوابت
+
+246
+00:29:41,800 --> 00:29:49,080
+كلها أصفار لو كان استبدلنا أحد الأصفار برقم بيبطل
+
+247
+00:29:49,080 --> 00:29:52,980
+يصير homogeneous system بيصير non homogeneous
+
+248
+00:29:52,980 --> 00:29:57,320
+system على أي حال ، أنا مدير الـ System بهذا الشكل
+
+249
+00:29:57,320 --> 00:30:01,880
+ما هي أخبار الحلول بتابعته بروح بقول النقطة الأولى
+
+250
+00:30:01,880 --> 00:30:06,780
+اللي هو مدير الـ System Star دائماً و أبداً له حل
+
+251
+00:30:06,780 --> 00:30:13,520
+على الأقل هو الحل الصفري لأن لو شيلت X1 و X2 و Xn
+
+252
+00:30:13,520 --> 00:30:18,320
+في كل من المعادلة و حطيت بدلها صفر بصير الـ System
+
+253
+00:30:18,320 --> 00:30:24,320
+صحية بصير 00000 بتحقق أي معادلة أو بتحقق كل
+
+254
+00:30:24,320 --> 00:30:28,140
+المعادلات اللي موجودة ورا في هذا ال system ومن هنا
+
+255
+00:30:28,140 --> 00:30:32,700
+بروح بقول له ال homogenous system على الأقل له
+
+256
+00:30:32,700 --> 00:30:38,660
+الحل الصفري تمام تمام يعني معنى هذا الكلام أن هذا
+
+257
+00:30:38,660 --> 00:30:43,940
+ال system دائما و أبدا Consistent عمروش بيكون
+
+258
+00:30:43,940 --> 00:30:48,940
+inconsistent على الإطلاق دائما و أبدا consistent
+
+259
+00:30:48,940 --> 00:30:54,460
+لأنه بيحتوي على أو له الحل الصفري أو الحل البديهي
+
+260
+00:30:54,460 --> 00:31:00,160
+أو الحل التافعي ال trivial solution 000 هذا النقطة
+
+261
+00:31:00,160 --> 00:31:03,920
+الأولى النقطة الثانية ال homogenous system star
+
+262
+00:31:03,920 --> 00:31:10,260
+اللي في M من المعادلات و N من المجاهيل شايفة M من
+
+263
+00:31:10,260 --> 00:31:15,860
+المعادلات وعندي N من المجاهيل يبقى عندي X1 و X2
+
+264
+00:31:15,860 --> 00:31:23,500
+لغاية XN وعندي عدد من المعادلات يساوي M يمكن هدول
+
+265
+00:31:23,500 --> 00:31:27,680
+يكونوا جد بعض زي ما احنا جايلين هنا ويمكن يكونوا
+
+266
+00:31:27,680 --> 00:31:33,700
+مختلفات طيب تعالى نشوف ايش بيقول هنا ال homogenous
+
+267
+00:31:33,700 --> 00:31:39,030
+system of M equations and N unknowns لديها عدد محدد
+
+268
+00:31:39,030 --> 00:31:43,230
+من الحلول التي تحتوي على هذه الحلول التعريفة إذا
+
+269
+00:31:43,230 --> 00:31:48,450
+كانت يعني يا بنات لو عندي عدد لا نهائي من الحلول
+
+270
+00:31:48,450 --> 00:31:53,110
+لهذا ال system فإن هذا العدد النهائي دائما و أبدا
+
+271
+00:31:53,110 --> 00:31:58,620
+يجتمع على مين؟ على الحل الصفري يعني يا بيكون الحل
+
+272
+00:31:58,620 --> 00:32:03,680
+الصفري مستقل لحاله مافيش غيره يا إما بكون عندي عدد
+
+273
+00:32:03,680 --> 00:32:08,540
+لا نهائي من الحلول تجتمل على الحل الصفري اللي موجود
+
+274
+00:32:08,540 --> 00:32:12,820
+تمام يبقى هيك بيقول النظام اللي عندنا بقوله كويس
+
+275
+00:32:12,820 --> 00:32:17,160
+طيب يا بنات خليني أسأل قبل ما أكمل السؤال التالي
+
+276
+00:32:17,160 --> 00:32:21,900
+هل ال non homogeneous system يحتوي على الحل
+
+277
+00:32:21,900 --> 00:32:29,190
+الصفري؟ يعني هل الحل الصفري أحد حلول الـ non
+
+278
+00:32:29,190 --> 00:32:34,310
+-homogeneous system؟ ولا
+
+279
+00:32:34,310 --> 00:32:39,350
+عمره بيحصل ولا عمره بيحصل ليش؟ لأن لو قلت الكلام
+
+280
+00:32:39,350 --> 00:32:44,150
+هذا صاحب بدي أشيل كل ال axis و أحط بدلها أصفرًا
+
+281
+00:32:44,150 --> 00:32:48,790
+صار الطرف الشمال كله أصفر بس الطرف اليمين أعداد
+
+282
+00:32:48,790 --> 00:32:53,750
+بنفع الصفر يستوي أعداد؟ يعني ماعنديش حل يبقى بناء
+
+283
+00:32:53,750 --> 00:32:59,010
+عليه الـ Non-homogeneous system لا يمكن أن يكون
+
+284
+00:32:59,010 --> 00:33:04,990
+الحل الصفري هو أحد الحلول له لكن الحل الصفري يكون
+
+285
+00:33:04,990 --> 00:33:10,990
+حلا للـ homogeneous system فقط لا غير قد تأتي هذا
+
+286
+00:33:10,990 --> 00:33:16,210
+إذا جبنا صح وخطأ دلوقتي يبقى ركزي على هذه النقطة
+
+287
+00:33:16,480 --> 00:33:21,240
+بدي أرجع للنقطة الثانية مرة ثانية «شولي» يضمن لي
+
+288
+00:33:21,240 --> 00:33:26,700
+أن في عندي عدد لا نهائي من الحلول الذاتي يجتمل على
+
+289
+00:33:26,700 --> 00:33:33,800
+الحل الصفري شرط واحد فقط أن عدد المعادلات أقل من
+
+290
+00:33:33,800 --> 00:33:38,480
+عدد المجاهيل يعني ممكن يكون عندي معادلتين و تلت
+
+291
+00:33:38,480 --> 00:33:45,590
+مجاهيل ممكن يكون عندى 3 معادلات و 5 مجاهيل ممكن
+
+292
+00:33:45,590 --> 00:33:51,090
+يكون عندى 10 معادلات و 11 مجهول يعني دائما و أبدا
+
+293
+00:33:51,090 --> 00:33:55,630
+إذا كان عدد المعادلات أقل من عدد المجاهيل
+
+294
+00:33:55,630 --> 00:34:02,510
+automatic لازم يحصل عندى عدد لا نهائي من الحلول هي
+
+295
+00:34:02,510 --> 00:34:07,020
+هذه اللى بتقوله النقطة اللى عندها تمام طب نرجع الآن
+
+296
+00:34:07,020 --> 00:34:13,260
+نحاول نطبق ما نقوله على أرض الواقع طيب يا بنات لما
+
+297
+00:34:13,260 --> 00:34:17,160
+يكون عندي عدد لا نهائي من الحلول تجتمل على الحل
+
+298
+00:34:17,160 --> 00:34:22,480
+الصفري يعني هذا الحل بيكون أعداد ولا أصفار
+
+299
+00:34:26,360 --> 00:34:30,980
+قد يكون أعداد وقد يكون أصفار صح ولا لأ مش احنا بنقول
+
+300
+00:34:30,980 --> 00:34:35,340
+يعني إذا يحتوي على الحل الصفري إذا الحل ال zero
+
+301
+00:34:35,340 --> 00:34:39,540
+أحد هذه الحلول وبعدها تتأعدى لكن الأعداد هل بقدر
+
+302
+00:34:39,540 --> 00:34:45,280
+أجيبهم بالضبط كلهم لا بقدرش ممكن أجيبهم صحيح كلهم و
+
+303
+00:34:45,280 --> 00:34:50,920
+ممكن ماقدرش فبتظهر الحل بدلالة رموز يعني أنا بفرض
+
+304
+00:34:50,920 --> 00:34:55,340
+هذه رموز وبالتالي الرموز هذه قد ما بدك حط وبالتالي
+
+305
+00:34:55,340 --> 00:35:00,310
+بيطلع عندك معلنها من الحلول نبدأ بتطبيق هذا على أرض
+
+306
+00:35:00,310 --> 00:35:03,950
+الواقع بيقول هاتلي حل ال system اللي قدامنا هذا
+
+307
+00:35:03,950 --> 00:35:10,070
+يبقى بدي أبدأ بمين بالمصوفة الموسعة اللي قلنا
+
+308
+00:35:10,070 --> 00:35:15,060
+عليها يبقى المصوفة الموسعة على الشكل التالي هذا
+
+309
+00:35:15,060 --> 00:35:21,060
+واحد و هنا سالب واحد و هنا سالب تلاتة و هنا زيرو و
+
+310
+00:35:21,060 --> 00:35:27,320
+هنا واحد و هنا واحد و هنا اتنين اتنين واحد و هنا
+
+311
+00:35:27,320 --> 00:35:30,620
+زيرو زيرو زيرو بالشكل اللي عندنا
+
+312
+00:35:33,400 --> 00:35:45,920
+بنخلق هنا أسطار نقص R1 to R2 ونقص R1 to R3 نحصل
+
+313
+00:35:45,920 --> 00:35:52,440
+على ما يأتي الصف الأول زي ما هو 1 سالب 1 سالب 3
+
+314
+00:35:52,440 --> 00:36:01,740
+زيرو الصف التاني زيرو وهنا اتنين وهنا اربعة و هنا
+
+315
+00:36:01,740 --> 00:36:07,860
+زيرو وهنا زيرو وهنا ضربنا في سالب اتنين بصير
+
+316
+00:36:07,860 --> 00:36:14,180
+اتنين يبقى اربعة وهنا ضربنا في سالب اتنين بصير
+
+317
+00:36:14,180 --> 00:36:21,640
+ستة واحد سبعة وهنا زيرو وضحكوابعدين بدي هذا
+
+318
+00:36:21,640 --> 00:36:28,700
+قداش واحد صحيح يبقى بدي نص قاري اتنين يبقى هذا
+
+319
+00:36:28,700 --> 00:36:35,420
+ناخد نص قاري اتنين تصبح المفروفة على الشكل التالي
+
+320
+00:36:35,420 --> 00:36:41,680
+واحد سالب واحد سالب تلاتة زيرو وهنا زيرو واحد
+
+321
+00:36:41,680 --> 00:36:48,880
+اتنين زيرو وهنا زيرو اربع سبعة زيرو بالشكل اللي
+
+322
+00:36:48,880 --> 00:36:54,030
+عندنا يبقى هذا بده يعطينا الصف الأول ماليش علاقة
+
+323
+00:36:54,030 --> 00:36:59,590
+فيه بدي على الصف التاني بقول ناقص اربعة R اتنين to
+
+324
+00:36:59,590 --> 00:37:07,830
+R تلت وابتدي تصبح على طبيعي ايش رأيك لو أضفنا كمان
+
+325
+00:37:07,830 --> 00:37:13,550
+الصف الثاني الى الصف الأول بالمرة ماحدش أحسن من
+
+326
+00:37:13,550 --> 00:37:21,840
+هذا إذا لو قل R اتنين to R one خطوة واحدة يفجأش
+
+327
+00:37:21,840 --> 00:37:25,840
+اللي بده يصير R اتنين ل R one بيظل هنا واحد و
+
+328
+00:37:25,840 --> 00:37:30,120
+بيصير هنا زيرو وهنا سالب واحد و هذا زيرو واحد
+
+329
+00:37:30,120 --> 00:37:36,520
+اتنين وهنا زيرو زيرو زي ما هو تمام و هذا زيرو زي
+
+330
+00:37:36,520 --> 00:37:42,180
+ما هو ضربته في سالب اربع بيصير زيرو بيصير هنا سالب
+
+331
+00:37:42,180 --> 00:37:48,310
+واحد وهنا جداش زيرو بالشكل اللي عندنا هذا أنا بديش
+
+332
+00:37:48,310 --> 00:37:52,070
+هذا سالب بدي إياه بالموجب حتى لو ضال بالسالب
+
+333
+00:37:52,070 --> 00:37:57,310
+ماعنديش إياه ماعنديش مشكلة مشكلتنا بدي أخلي هذا ب
+
+334
+00:37:57,310 --> 00:38:02,430
+زيرو و بدي أخلي هذا ب إياه ب زيرو يبقى بدي أجي ل R
+
+335
+00:38:02,430 --> 00:38:07,510
+تلاتة أضربه في سالب واحد و أضيفه للصف الأول و
+
+336
+00:38:07,510 --> 00:38:13,510
+أضربه في اتنين و أضيفه للصف الثاني يبقى هذا بدي
+
+337
+00:38:13,510 --> 00:38:22,220
+يعطينا اللي هو من سالب R ثلاثة to R one و بعد هيك
+
+338
+00:38:22,220 --> 00:38:29,760
+سالب اتنين والله موجة باتنين موجة باتنين R ثلاثة
+
+339
+00:38:29,760 --> 00:38:37,020
+to R two نفس العالمية هذا واحد وهذا زيرو زي ما هو
+
+340
+00:38:37,020 --> 00:38:44,530
+لأنني باضيف سالب R ثلاثة to R one وهنا بيصير زيرو و
+
+341
+00:38:44,530 --> 00:38:52,770
+هنا زيرو وهنا اتنين R three ل R two يبقى هنا زيرو
+
+342
+00:38:52,770 --> 00:38:58,970
+وهنا واحد وهنا زيرو وهنا زيرو وهنا زيرو و زيرو
+
+343
+00:38:58,970 --> 00:39:07,230
+سالب واحد و زيرو بقدر اقوله اخر خطوة سالب R ثلاثة
+
+344
+00:39:07,230 --> 00:39:17,840
+وبالتالي بتصبح المصوفة 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
+
+345
+00:39:17,840 --> 00:39:32,680
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+
+346
+00:39:46,770 --> 00:39:51,470
+solution لا مشكلة فيه بقى solution والله غيره
+
+347
+00:39:51,470 --> 00:39:55,970
+مافيش مشكلة طب
+
+348
+00:39:55,970 --> 00:40:01,730
+ليش ما طلع الشبنات هنا عدد لا نهائي من الحلول أيوة
+
+349
+00:40:01,730 --> 00:40:08,140
+لأن عدد المعادلات بيساوي عدد المجاهديبقى إذا كان
+
+350
+00:40:08,140 --> 00:40:12,560
+عدد المعادلات يساوي عدد المجاهيل يطلع عندي الحل
+
+351
+00:40:12,560 --> 00:40:19,260
+الصفري يطلع عندي عدد عادي عدد عادي غير هيك بصير
+
+352
+00:40:19,260 --> 00:40:23,760
+عدد المعادلات أقل من عدد المجاهيل بصير عندي عدد
+
+353
+00:40:23,760 --> 00:40:32,040
+لا نهائي من الحلول طيب نجي ناخد كمان مثال يبقى
+
+354
+00:40:32,040 --> 00:40:34,900
+المثال رقم اتنين exactly two
+
+355
+00:40:40,600 --> 00:40:49,100
+solve the system solve the system خلص ال system
+
+356
+00:40:49,100 --> 00:40:58,260
+اللي هو اتنين x واحد ناقص اتنين x اتنين ناقص
+
+357
+00:40:58,260 --> 00:41:07,320
+x تلاتة زائد x اربعة بيساوي زيرو المعادلة
+
+358
+00:41:07,320 --> 00:41:16,230
+التالية ناقص x واحد زائد x اتنين زائد x تلاتة
+
+359
+00:41:16,230 --> 00:41:19,930
+ناقص اتنين x اربع زائد x اربع زائد x اربع
+
+360
+00:41:19,930 --> 00:41:21,710
+زائد x اربع زائد x اربع زائد x اربع زائد x
+
+361
+00:41:21,710 --> 00:41:23,890
+اربع زائد x اربع زائد x اربع زائد x اربع
+
+362
+00:41:23,890 --> 00:41:24,010
+اربع زائد x اربع زائد x اربع زائد x اربع
+
+363
+00:41:24,010 --> 00:41:29,190
+زائد x اربع زائد x اربع زائد x اربع زائد x
+
+364
+00:41:29,190 --> 00:41:34,930
+اربع زائد x اربع ز
+
+365
+00:41:45,650 --> 00:41:51,590
+-2x2 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 
+
+366
+00:41:51,590 --> 00:41:51,630
+-2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4
+
+367
+00:41:51,630 --> 00:41:53,310
+-2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4
+
+368
+00:41:53,310 --> 00:41:56,150
+-2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4
+
+369
+00:41:56,150 --> 00:41:59,510
+-2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4 - 2x4
+
+370
+00:42:08,180 --> 00:42:13,520
+بالنسبة لل system اللي عندنا تتوقعوا أن يكون عندي
+
+371
+00:42:13,520 --> 00:42:20,920
+حل صفري فقط لغير قد يكون وقد لا يكون طب ممكن يكون
+
+372
+00:42:20,920 --> 00:42:29,930
+عدد لا نهائي من
+
+401
+00:45:12,220 --> 00:45:18,440
+and R2 بدي أبدلهم والباقي بدي أخليه مكانه زي ما 
+
+402
+00:45:18,440 --> 00:45:23,900
+يبقى بيجيكي عندك هنا هاي سالب واحد وهنا واحد وهنا
+
+403
+00:45:23,900 --> 00:45:29,530
+واحد وهنا سالب اثنين وهنا زيرو هنا سالب اثنين
+
+404
+00:45:29,530 --> 00:45:36,170
+سالب واحد واحد صفر ثلاثة سالب ثلاثة واحد سالب ستة
+
+405
+00:45:36,170 --> 00:45:41,330
+صفر هنا الصف الرابع والأخير اثنين سالب اثنين
+
+406
+00:45:41,330 --> 00:45:49,590
+صفر سالب اثنين صفر بالشكل هذا الآن هذا بعمل
+
+407
+00:45:49,590 --> 00:45:53,870
+كتابة يرجى بالداجة على الصف الأول أو الأخير وكله
+
+408
+00:45:53,870 --> 00:46:00,220
+فات بسالب واحد يبقى ايش بصير عندنا هنا اللي هو سالب
+
+409
+00:46:00,220 --> 00:46:06,200
+أصفار فقط لا غير يبقى بالصبح المصفوفة على الشكل
+
+410
+00:46:06,200 --> 00:46:13,480
+التالي واحد سالب واحد سالب واحد سالب واحد سالب
+
+411
+00:46:13,480 --> 00:46:21,000
+واحد اثنين هذه فقط لا غير وهذه zero وهذه اثنين
+
+412
+00:46:21,000 --> 00:46:27,710
+سالب اثنين سالب واحد واحد ثلاثة سالب ثلاثة واحد سالب ستة
+
+413
+00:46:27,710 --> 00:46:33,930
+اثنين سالب اثنين صفر سالب اثنين صفر صفر صفر 
+
+414
+00:46:33,930 --> 00:46:40,770
+بالشكل اللي عندنا الآن بدي أعمل ثلاث خطوات مرة
+
+415
+00:46:40,770 --> 00:46:47,850
+واحدة هتخلق هنا صفر وهنا صفر وهنا صفر يبقى سالب 
+
+416
+00:46:47,850 --> 00:46:57,030
+اثنين R1 إلى R2 وإلى R4 يبقى بداشي أقوله
+
+417
+00:46:57,030 --> 00:47:08,430
+ما يأتي بدي آخذ سالب R1 to R2 and R4 له أربعة وبعد
+
+418
+00:47:08,430 --> 00:47:18,430
+هيك طبعاً سالب اثنين هنا هذه 
+
+419
+00:47:18,430 --> 00:47:25,680
+سالب اثنين R1 لها وبعد هيك سالب ثلاثة R1 two are
+
+420
+00:47:25,680 --> 00:47:32,140
+three كله مرة واحدة يبقى الصف الأول زي ما هو واحد
+
+421
+00:47:32,140 --> 00:47:38,840
+سالب واحد سالب واحد اثنين zero الصف الثاني هذا صار
+
+422
+00:47:38,840 --> 00:47:45,260
+zero وهذا ضربته في سالب اثنين بصير هنا zero وهذا
+
+423
+00:47:45,260 --> 00:47:50,200
+ضربته في سالب اثنين بصير هنا واحد وهنا هذا بصير
+
+424
+00:47:50,200 --> 00:47:56,160
+سالب ثلاثة وهذه zero هذا ضربت في سالب ثلاثة بصير
+
+425
+00:47:56,160 --> 00:48:02,740
+zero هذا بصير ثلاثة وسالب ثلاثة كمان zero هذا 
+
+426
+00:48:02,740 --> 00:48:08,420
+ضربت في سالب ثلاثة بصير ثلاثة واحد أربعة هذا سالب 
+
+427
+00:48:08,420 --> 00:48:16,170
+ستة وسالب ستة بصير سالب أتماشى وهنا zero وهذا
+
+428
+00:48:16,170 --> 00:48:21,750
+zero هنا وهذا ربطه في سالب اثنين بصير هنا zero
+
+429
+00:48:21,750 --> 00:48:27,430
+وهذا بيصير هنا اثنين وهذا ربطه في سالب اثنين بيصير
+
+430
+00:48:27,430 --> 00:48:34,750
+سالب أربعة يفجر سالب ستة وهنا اثنين وهنا zero اللي
+
+431
+00:48:34,750 --> 00:48:38,590
+ماصارش عندي leading هنا واحد أمان طالع صار في
+
+432
+00:48:38,590 --> 00:48:43,150
+أصفار اللي بيجرّش أسوي فيها حاجة إذا مداجي على مين؟
+
+433
+00:48:43,470 --> 00:48:51,110
+على الصف الثالث واضربه في ربع تمام؟ يبقى باجي
+
+434
+00:48:51,110 --> 00:48:58,430
+بقوله هنا أنا بدي ربع فهعرف ثلاثة بصيله إنما يعني
+
+435
+00:48:58,430 --> 00:49:05,250
+اللي هو واحد سالب واحد سالب واحد اثنين zero zero
+
+436
+00:49:05,250 --> 00:49:13,430
+zero واحد سالب ثلاثة zero وهنا zero .. zero ..
+
+437
+00:49:13,430 --> 00:49:20,690
+واحد .. وهنا سالب ثلاثة .. zero .. وهنا zero ..
+
+438
+00:49:20,690 --> 00:49:29,030
+zero .. اثنين .. سالب ستة .. zero .. بالشكل هذا طب
+
+439
+00:49:29,030 --> 00:49:35,170
+ايش رأيك تخلص من الصف الثالث والرابع مرة واحدة
+
+440
+00:49:35,170 --> 00:49:40,750
+نبدأ دي على الصف الثاني أضربه في سالب واحد وأضيفه
+
+441
+00:49:40,750 --> 00:49:45,730
+للصف الثالث واضربه في سالب اثنين وأضيفه للصف
+
+442
+00:49:45,730 --> 00:49:55,130
+الرابع يبقى باقي بقوله هنا سالب R2 to
+
+443
+00:49:55,130 --> 00:50:03,750
+R3 وسالب اثنين R2 to R4 الشكل اللي 
+
+444
+00:50:03,750 --> 00:50:08,860
+عليه هذا يبقى بتصبح على الشكل التالي هنا واحد وهنا
+
+445
+00:50:08,860 --> 00:50:15,280
+سالب واحد وهنا سالب واحد وهنا اثنين وهنا zero وهنا
+
+446
+00:50:15,280 --> 00:50:23,140
+zero zero وهنا واحد سالب ثلاثة وهنا zero وهنا zero
+
+447
+00:50:23,140 --> 00:50:29,480
+zero zero zero وهنا zero zero zero zero zero zero
+
+448
+00:50:29,480 --> 00:50:34,940
+zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero zero
+
+449
+00:50:36,150 --> 00:50:43,210
+كمان خطوة هذا ال system هنا بدأ الحل يبقى هذا بقدر
+
+450
+00:50:43,210 --> 00:50:55,790
+أشيله بالشكل إن أنا بدي 
+
+451
+00:50:55,790 --> 00:51:05,860
+أضيف الصف الثاني للصف الأول يبقى R2 والله ايش رأيك
+
+452
+00:51:05,860 --> 00:51:11,640
+إنك دلوقت نعملهم لو عملناها مع الخطوة الأولى هذه
+
+453
+00:51:11,640 --> 00:51:19,540
+لها بلاش خطوة جديدة and R2
+
+454
+00:51:19,540 --> 00:51:29,140
+to R1 يبقى هذه بالصير zero وهذه بالصير سالب واحد 
+
+455
+00:51:29,140 --> 00:51:30,320
+فقط ده غير
+
+456
+00:51:35,780 --> 00:51:42,720
+أكثر من هيك بنقدر نعمل؟ لأ يبقى ال system بأربع
+
+457
+00:51:42,720 --> 00:51:49,180
+معادلات إلى مين إلى معادلتين المعادلة الأولى x
+
+458
+00:51:49,180 --> 00:51:56,960
+واحد ناقص x اثنين ناقص x أربعة بده يساوي zero
+
+459
+00:51:56,960 --> 00:52:03,380
+والمعادلة الثانية أصبح x واحد على x ثلاثة
+
+460
+00:52:16,330 --> 00:52:24,200
+معادلتين في أربعة مجاهيل يبقى فيش إمكانية إلا أحط
+
+461
+00:52:24,200 --> 00:52:29,680
+قيمتين من عندي تمام يبقى بعدي أختار اللي بدكيها أي 
+
+462
+00:52:29,680 --> 00:52:34,080
+قيمة أحطيها من عندك وأشوف ايش اللي بده يحصل يبقى
+
+463
+00:52:34,080 --> 00:52:43,380
+أنا لو روحت جيب main goal put مثلاً x4 تساوي اللي
+
+464
+00:52:43,380 --> 00:52:52,290
+بدكيها x4 نحطها بواحد أو الـ x4 بـ ax4 تساوي a مثلاً
+
+465
+00:52:52,290 --> 00:53:03,290
+and x2 تساوي b نحن نحن نحن نحن نحن نحن نحن نحن
+
+466
+00:53:03,290 --> 00:53:03,310
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+467
+00:53:03,310 --> 00:53:06,630
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+468
+00:53:06,630 --> 00:53:06,650
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+469
+00:53:06,650 --> 00:53:16,530
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+470
+00:53:21,350 --> 00:53:27,450
+يبقى الـ x ثلاثة والـ x أربعة نحطوها بـ A يبقى بده
+
+471
+00:53:27,450 --> 00:53:37,990
+يساوي ثلاثة A يبقى أصبح that solution is x واحد x
+
+472
+00:53:37,990 --> 00:53:45,850
+اثنين x ثلاثة x أربعة تساوي x واحد اللي هي بقداش
+
+473
+00:53:45,850 --> 00:53:59,850
+طلعناها a زائد الـ b x2 حطيناها b x3 ثلاثة a x4 دي 
+
+474
+00:53:59,850 --> 00:54:06,490
+a بالشكل اللي عندنا يبقى هذا أصبح الحل طب هل هذا
+
+475
+00:54:06,490 --> 00:54:11,810
+يحتوي على الـ trivial solution الإجابة نعم حطيت
+
+476
+00:54:11,810 --> 00:54:12,990
+قيود على a وb
+
+477
+00:54:16,070 --> 00:54:22,410
+بحصل على حل الصفري إذا 
+
+478
+00:54:22,410 --> 00:54:31,390
+صار عندي عدد لا نهائي من الحلول system has
+
+479
+00:54:31,390 --> 00:54:41,510
+infinite number of solutions
+
+480
+00:54:42,440 --> 00:54:54,640
+that is this system this system is consistent
+
+481
+00:54:54,640 --> 00:54:58,600
+لازلنا
+
+482
+00:54:58,600 --> 00:55:03,400
+في نفس ال section ولما ننتهي بعد للمرة القادمة
+
+483
+00:55:03,400 --> 00:55:05,080
+إن شاء الله تعالى
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1032f34168657da9eadce0c37bcee9b9e47c7bb1
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_postprocess.srt
@@ -0,0 +1,1932 @@
+1
+00:00:21,230 --> 00:00:25,470
+بسم الله الرحمن الرحيم ابتدأنا في المرة الماضية
+
+2
+00:00:25,470 --> 00:00:28,130
+بال system of linear equations اللي هو section
+
+3
+00:00:28,130 --> 00:00:33,070
+اتنين واحد و لما ننتهي بعد و ابتدأنا في أخذ أمثلة
+
+4
+00:00:33,070 --> 00:00:38,070
+على هذا ال section و أعطينا على ذلك ثلاثة أمثلة
+
+5
+00:00:38,070 --> 00:00:42,930
+تمام؟ و هذا هو المثال الرابع اللي بين إيدنا الآن
+
+6
+00:00:43,470 --> 00:00:48,850
+المثال بيقول استخدم الـ Echelon Form او الـ Raw
+
+7
+00:00:48,850 --> 00:00:53,450
+Echelon Form عشان نحل المعادلة اللي عندنا هذه يبقى
+
+8
+00:00:53,450 --> 00:00:57,170
+الخطوة الأولى يقول بناخد الـ Agumented Matrix يعني
+
+9
+00:00:57,170 --> 00:01:02,010
+المصوفة الموسعة المصوفة الموسعة عندنا على هذا
+
+10
+00:01:02,010 --> 00:01:09,690
+الشكل اللي هو واحد واحد سالب واحد واحد اتنين واحد
+
+11
+00:01:09,690 --> 00:01:18,930
+سالب واحد واحدو هنا zero و هنا واحد واحد zero و
+
+12
+00:01:18,930 --> 00:01:28,910
+هنا الصف الرابع هو عبارة عن zero و كذلك واحد و
+
+13
+00:01:28,910 --> 00:01:36,130
+zeroو اتنين و بنروح نحط هنا مصوفة المعاملة او
+
+14
+00:01:36,130 --> 00:01:44,190
+الثوابت اللي هو اربعة سالب خمسة سالب واحد اربعة
+
+15
+00:01:44,190 --> 00:01:50,930
+الشكل اللي عندنا طبعا ايش
+
+16
+00:01:50,930 --> 00:01:58,490
+خمسة؟أربعة صفوف هى المعادلة
+
+17
+00:01:58,490 --> 00:02:04,330
+التانية خمسة بالموجب خمسة بالموجب فعلا يبقى هى ..
+
+18
+00:02:04,330 --> 00:02:09,710
+هى كتبنا اللى هو مصوفة المعاملات وكذلك أضفنا لها
+
+19
+00:02:09,710 --> 00:02:16,090
+عمود الثوابط وسميت لذلك بالمصوفة الموسعة الان واضح
+
+20
+00:02:16,090 --> 00:02:20,330
+عندى هنا صفرين يبقى دول بقدرش أعمل فيهم ولا حاجة
+
+21
+00:02:20,570 --> 00:02:26,270
+يبقى باجي على الاتنين هذي و بتخليها واحد صحيح اذا
+
+22
+00:02:26,270 --> 00:02:33,850
+بقدر اضرب الصف الأول في سالي باتنين و اضيفه للصف
+
+23
+00:02:33,850 --> 00:02:39,510
+الثاني يبقى هذا بدي اعمل سالي باتنين R1
+
+24
+00:02:42,510 --> 00:02:49,830
+بحصل على المصفوفة التانية الصف الأول كما هو واحد
+
+25
+00:02:49,830 --> 00:02:56,050
+واحد سالب واحد واحد وهي الأربعة الصف التاني بصير
+
+26
+00:02:56,050 --> 00:03:00,210
+zero سالب اتنين واحد بصير سالب واحد
+
+27
+00:03:14,240 --> 00:03:20,850
+الصفرين يبقوا كما هم الاتنينيبقى هاي Zero وهي Zero
+
+28
+00:03:20,850 --> 00:03:27,450
+وهي واحد واحد وهنا واحد Zero وهنا Zero اتنين وهنا
+
+29
+00:03:27,450 --> 00:03:32,890
+سالب واحد وهي الأربعة وهي المصفوفة الجديدة اللي
+
+30
+00:03:32,890 --> 00:03:39,150
+عندنا الان هذا ال leading اللي عندنا له واحد تمام
+
+31
+00:03:39,150 --> 00:03:43,630
+اذا بالضبط للصف اللي بعده العمصر صحته لأ اللي على
+
+32
+00:03:43,630 --> 00:03:48,090
+يمينه بالضبط لازم يكون ال leading هذا جداشواحد صح
+
+33
+00:03:48,090 --> 00:03:50,930
+يبقى بروح بضرب الصف الأول هذا في جد إيه الصف
+
+34
+00:03:50,930 --> 00:03:55,090
+الثاني في جد إيه في سالب واحد يبقى باجي بقوله بدي
+
+35
+00:03:55,090 --> 00:04:02,610
+أعمل سالب are two فقط لغة يبقى باجي بقول المصطفة
+
+36
+00:04:02,610 --> 00:04:09,250
+هتأخد الشكل التالي واحد واحد سالب واحد وهنا كمان
+
+37
+00:04:09,250 --> 00:04:15,760
+واحدوهذا عمودي الثوابت اللي هو أربعة وهنا zero
+
+38
+00:04:15,760 --> 00:04:22,940
+وهنا واحد وهنا سالب واحد وهنا واحد وهنا تلاتة
+
+39
+00:04:22,940 --> 00:04:28,240
+والصفين التانيات الاتنين اللي صفلين زي ما هم واحد
+
+40
+00:04:28,240 --> 00:04:36,380
+واحد وهنا واحد zero وهنا zero اتنين وهنا سالب واحد
+
+41
+00:04:36,380 --> 00:04:44,100
+وهنا كداش اللي هو أربعةبعد هيك بدي أعمل هنا zero
+
+42
+00:04:44,100 --> 00:04:49,220
+وهنا zero إذا بضرب الصف الثاني في سالب واحد و
+
+43
+00:04:49,220 --> 00:04:56,100
+بضيفه للصف التالت و كذلك للصف الرابع يبقى عملتين
+
+44
+00:04:56,100 --> 00:05:02,880
+هعملهم في آل واحد يبقى بدي أعمل ما ياتي سالب اللي
+
+45
+00:05:02,880 --> 00:05:06,220
+هو R2 to R3
+
+46
+00:05:19,380 --> 00:05:26,280
+يبقى أول صفين يبقوا كما هم يبقى باجي بقول الصف
+
+47
+00:05:26,280 --> 00:05:34,180
+الأول هذا اللي هو واحد واحد سالب واحد وهنا واحدهنا
+
+48
+00:05:34,180 --> 00:05:40,940
+أربعة كما هو وهنا زيرو وهنا واحد وسالب واحد واحد
+
+49
+00:05:40,940 --> 00:05:46,780
+وهنا تلاتة الآن بدي أضربه في سالب واحد واضيفه هنا
+
+50
+00:05:46,780 --> 00:05:51,820
+بدي يجيني هنا هذا زيرو زيرو زي ما هو بدي يجيكي هنا
+
+51
+00:05:51,820 --> 00:05:57,280
+زيرو زيرو تمام؟ الآن هذا أنا ضربته في سالب واحد
+
+52
+00:05:57,280 --> 00:06:02,810
+يبقى هنا كدهش واحد واحد بصير اتنين وهنا واحديبقى
+
+53
+00:06:02,810 --> 00:06:08,510
+هنا اتنين و هنا واحد هنا صار هذا سالب واحد اضيفه
+
+54
+00:06:08,510 --> 00:06:14,510
+هنا يبقى بيصير سالب واحد و واحد يبقى سالب واحد و
+
+55
+00:06:14,510 --> 00:06:19,490
+واحد فقط لغير بقول سالب واحد زي اتنين اللي هو اب
+
+56
+00:06:19,490 --> 00:06:24,330
+واحد لأ اذا عرفت ان سالب واحد بيصير سالب تلاتة
+
+57
+00:06:24,330 --> 00:06:29,980
+يبقى بيصير هذه سالب اربعة و هذه واحدةيبقى هذه سالف
+
+58
+00:06:29,980 --> 00:06:36,000
+أربعة وهذه واحد بالشكل اللي عندنا هذا، تمام؟ الآن
+
+59
+00:06:36,000 --> 00:06:42,320
+بالذالك لمين؟ لصف التالت، بدي هذا يكون واحد، صحيح،
+
+60
+00:06:42,320 --> 00:06:46,600
+يبقى بروح بضرب هذا الكلام في قداش، في نص، يبقى بدي
+
+61
+00:06:46,600 --> 00:06:55,170
+النص R تلاتةيبقى بالده ياخد هنا النص R ثلاثة ينثب
+
+62
+00:06:55,170 --> 00:07:01,890
+على الشكل ثالث أول صفين زي ما هما واحد واحد وكمان
+
+63
+00:07:01,890 --> 00:07:04,670
+سالب واحد وهنا واحد
+
+64
+00:07:14,780 --> 00:07:20,920
+والعمود هذا هذا واحد وهنا اربعة وهنا zero وهنا
+
+65
+00:07:20,920 --> 00:07:27,120
+واحد سالب واحد واحد تلاتة الان بدي اضرب هدف نص
+
+66
+00:07:27,120 --> 00:07:32,280
+يبقى zero zero زي ما هو وهنا ناقص نص وهنا ناقص
+
+67
+00:07:32,280 --> 00:07:41,220
+اتنين والصفة الرابعة زي ما هو واحد واحد واحد الان
+
+68
+00:07:41,730 --> 00:07:50,010
+بدي اخلي هذا zero يبقى بداتي اقوله سالب R3 to R4
+
+69
+00:07:50,010 --> 00:07:55,050
+ونشوف ايش بدنا نعمل في هذا يبقى هذا الكلام بده
+
+70
+00:07:55,050 --> 00:08:01,410
+يعطينا المصفوفة التالية الان واحد واحد سالب واحد
+
+71
+00:08:01,410 --> 00:08:10,710
+واحد zero واحد سالب واحد واحد zero zero واحد سالب
+
+72
+00:08:10,710 --> 00:08:18,310
+نصهنا موجة و هنا موجة و هنا موجة و هنا موجة و هنا
+
+73
+00:08:18,310 --> 00:08:22,250
+موجة
+
+74
+00:08:22,250 --> 00:08:32,410
+و هنا موجة
+
+75
+00:08:36,410 --> 00:08:44,730
+بدي هذا يكون كمان جداشر بدي واحد صحيح طيب إيش رأيك
+
+76
+00:08:44,730 --> 00:08:51,350
+يا بنات لو عملت ما يأتي بدي أحاول أخفف الخطوات
+
+77
+00:08:51,350 --> 00:08:57,470
+شوية يبقى بدي أعمل ما يأتي بدي أضرب هذا في سالب
+
+78
+00:08:57,470 --> 00:09:02,830
+واحد و أضيفه فوق هاي الخطوة الأولى الخطوة الثانية
+
+79
+00:09:03,120 --> 00:09:11,260
+بدي اضغط هدف يقداش تلتين يبقى بدي اجي R اتنين
+
+80
+00:09:11,260 --> 00:09:17,720
+بالسالب سالب R اتنين to R one هاي واحدة التانية
+
+81
+00:09:17,720 --> 00:09:25,300
+بدي تلتين R أربع مرة واحدة خطوة واحدة يبقى بتاخد
+
+82
+00:09:25,300 --> 00:09:32,920
+الشكل التالي هادي واحدوهذا زيرو وهذا هنا ضربنا فيه
+
+83
+00:09:32,920 --> 00:09:37,940
+سالب واحد بيصير موجة واحد بيصير زيرو وهنا كمان
+
+84
+00:09:37,940 --> 00:09:42,520
+زيرو وهنا ضربنا فيه سالب واحد بيصير سالب تلاتة
+
+85
+00:09:42,520 --> 00:09:48,220
+يبقى هنا ويبقى القداش واحد هذا زيرو واحد سالب واحد
+
+86
+00:09:48,220 --> 00:09:57,290
+واحد كما هوو هذه تلاتة كما هي و هنا 001000 و هنا
+
+87
+00:09:57,290 --> 00:10:00,590
+0001
+
+88
+00:10:00,590 --> 00:10:08,050
+صحيح لإن أنا ضارف جدا في تلتين و هذا يصبح اتنين و
+
+89
+00:10:08,050 --> 00:10:13,890
+اللي قبلها سالب اتنين زي مين يبقى هذه سالب اتنين و
+
+90
+00:10:13,890 --> 00:10:19,870
+هذه اللي هي مين اتنين بالشكل اللي عندنا هذا طيبأنا
+
+91
+00:10:19,870 --> 00:10:28,150
+ممكن أخلي هنا هذا zero و أخلي هذا zero يبقى بدأ
+
+92
+00:10:28,150 --> 00:10:34,270
+أضيف الصف التالت إلى الصف الثاني بخلق zero فوق
+
+93
+00:10:34,270 --> 00:10:41,210
+يبقى هنا بدنا نعمل ما يأتي بدأ أحط سهم و أقول هنا
+
+94
+00:10:41,210 --> 00:10:50,530
+سالب R تلاتة to R اتنينيبقى بدى يصير عندى ما يأتي
+
+95
+00:10:50,530 --> 00:10:55,410
+R3
+
+96
+00:10:55,410 --> 00:11:03,710
+to R2 و هذا شو رأيك كمان اضربه في نص و اضيفه للي
+
+97
+00:11:03,710 --> 00:11:06,890
+فوق بالمرة كويس؟
+
+98
+00:11:10,320 --> 00:11:18,100
+طيب نعملها خطوة واحدة يبقى سالب R تلاتة to R اتنين
+
+99
+00:11:18,100 --> 00:11:30,380
+وكذلك نص R اربعة to R تلاتة مرة واحدة يبقى بصير
+
+100
+00:11:30,380 --> 00:11:38,510
+عندنا هنا one zero zero zero واحدهنا سالب R ثلاثة
+
+101
+00:11:38,510 --> 00:11:44,050
+to R اتنين سالب
+
+102
+00:11:44,050 --> 00:11:48,990
+R ثلاثة .. لا لا R ثلاثة بدون سالب صحيح R ثلاثة
+
+103
+00:11:48,990 --> 00:11:55,030
+بدي اضيفه ل R اتنين مباشرة يبقى Zero وهنا واحد
+
+104
+00:11:55,030 --> 00:12:04,270
+وهنا Zero وهنا نص وهنا واحد اضفنا اضافة بعدين نص R
+
+105
+00:12:04,270 --> 00:12:12,620
+اربعةبدي أضيفه ل R ثلاثة بيصير Zero Zero واحد وهنا
+
+106
+00:12:12,620 --> 00:12:18,740
+نص بيصير Zero وهنا نص فيه اتنين اللي هو بواحد
+
+107
+00:12:18,740 --> 00:12:23,560
+بيبقى اللي عندنا هنا جدا سالب واحد وهذا Zero Zero
+
+108
+00:12:23,560 --> 00:12:29,040
+وهنا واحد وهنا اتنين بالشكل اللي عندنا هو ضايل
+
+109
+00:12:29,040 --> 00:12:33,830
+علينا بس خطوة واحدةاللي هتخلص من النص اللي عندنا
+
+110
+00:12:33,830 --> 00:12:38,550
+هذا يبقى بقى اضرب الصف الرابع في سلب نص واضيبه
+
+111
+00:12:38,550 --> 00:12:47,170
+للصف الثاني يبقى هذا بده يعطينا سالب نص R أربعة to
+
+112
+00:12:47,170 --> 00:12:55,670
+R تلاتة بنحصل على ما يأتي هاي واحد zero zero zero
+
+113
+00:12:55,670 --> 00:13:04,810
+واحد او هنا zero واحدزي رو زي رو و هنا اه استني
+
+114
+00:13:04,810 --> 00:13:09,990
+شوية احنا بقول سالب نص اه اربع يبقى هنا بيصير قدير
+
+115
+00:13:09,990 --> 00:13:16,630
+سالب واحد مع واحد بيصير زي رو مظبوط هيك مرة تانية
+
+116
+00:13:16,630 --> 00:13:22,020
+بالأول ماليكم معاك الصف الأول حاطيته زي ما هوصفى
+
+117
+00:13:22,020 --> 00:13:29,320
+التانى بقول سالب نص اقل .. لأ صفى التانى .. سالب
+
+118
+00:13:29,320 --> 00:13:35,640
+نص .. لأ هذا سالب نص اقل اربعة و قارى اتنين ..
+
+119
+00:13:35,640 --> 00:13:41,450
+ايوة لقارى اتنينيبقى لارتنين بيصير عندنا هنا 00
+
+120
+00:13:41,450 --> 00:13:46,950
+مظبوط وهذا 0010
+
+121
+00:13:46,950 --> 00:13:53,850
+-1 وهنا 00012
+
+122
+00:13:53,850 --> 00:13:59,070
+الشكل اللي عندناإذاً الـ System اللي وصلته يا بنات
+
+123
+00:13:59,070 --> 00:14:03,890
+هذا اللي هو X1 يساوي واحد و X2 يساوي Zero و X3
+
+124
+00:14:03,890 --> 00:14:08,030
+يساوي سالب واحد و X4 يساوي اتنين مكافئ للـ System
+
+125
+00:14:08,030 --> 00:14:12,710
+الأصل اللي همين الـ Star اللي عندنا يبقى أصبح حل
+
+126
+00:14:12,710 --> 00:14:16,630
+المعادلة الـ Star أو الـ System الـ Star هو حل هذا
+
+127
+00:14:16,630 --> 00:14:23,790
+الـ System لذلك برفض أقول له solution of
+
+128
+00:14:23,790 --> 00:14:39,520
+thesystem start with x1 و x2 و x3 و x4 بيبقى يساوي
+
+129
+00:14:39,520 --> 00:14:47,880
+يعني four triple من واحد زيرو سالف واحد اتنين
+
+130
+00:14:47,880 --> 00:14:54,800
+بالشكل اللي عندنا هذا خلينا نسأل السؤال التاليالان
+
+131
+00:14:54,800 --> 00:15:01,240
+هل ال system star هذا consistent ولا inconsistent؟
+
+132
+00:15:01,240 --> 00:15:06,240
+consistent لأنه لجيت حل مرة ليه فده اقول ان لو كان
+
+133
+00:15:06,240 --> 00:15:11,000
+حل او عدد لنهائي من الحلول يبقى بسمي ال system
+
+134
+00:15:11,000 --> 00:15:13,400
+consistent؟
+
+135
+00:15:15,600 --> 00:15:19,720
+طيب إحنا لغا ناخدنا أربعة أمثلة زي ما انتوا شايفين
+
+136
+00:15:19,720 --> 00:15:26,600
+وكل واحد فيهم شكل واتساب درجنا من المعادلتين في
+
+137
+00:15:26,600 --> 00:15:31,760
+مجهولين لغا ما وصلنا إلى أربعة معادلات في أربعة
+
+138
+00:15:31,760 --> 00:15:39,390
+مجاهينبنجي ناخد مثال بيختلف شكلا عن الأمثلة اللي
+
+139
+00:15:39,390 --> 00:15:47,190
+فاتت لكن بيحمل نفس الفكرة يبقى مثال رقم خمسة هذا
+
+140
+00:15:47,190 --> 00:15:53,050
+من الكتاب سؤال تسعة عشر نمرة ايه بيقول four what
+
+141
+00:15:53,050 --> 00:16:02,890
+values four what values ما هي القيم اللي بتاخدها a
+
+142
+00:16:02,890 --> 00:16:11,530
+andb بحيث أن for what value of a does the system
+
+143
+00:16:11,530 --> 00:16:19,910
+does the system does
+
+144
+00:16:33,010 --> 00:16:41,970
+اللي هو x واحد ناقص اتنين x اتنين يسوي a وناقص
+
+145
+00:16:41,970 --> 00:16:49,270
+تلاتة x واحد زائد ستة x اتنين بده يسوي b هذا هو ال
+
+146
+00:16:49,270 --> 00:16:57,110
+system have a solution have a
+
+147
+00:16:57,110 --> 00:16:58,690
+solution
+
+148
+00:17:33,750 --> 00:17:39,630
+سؤال مرة تانية يقول لي ما هي القيم التي تاخدها كل
+
+149
+00:17:39,630 --> 00:17:46,010
+من إيوا بي بحيث أن هذا ال system يكون له حل تمام
+
+150
+00:17:46,010 --> 00:17:52,530
+لما قول حل ما قلتش حل وحيدقد يكون حل وحيد وقد يكون
+
+151
+00:17:52,530 --> 00:17:57,790
+عدد لا نهائي من الحلول المهم أن يكون هناك حل بغض
+
+152
+00:17:57,790 --> 00:18:01,830
+النظر عن شكل الحل يعني بدي ايش القلم تاخدها ايه
+
+153
+00:18:01,830 --> 00:18:06,090
+وبين اذا بروح ببدأ بالمصفوفة المؤسسة زي ما كنت
+
+154
+00:18:06,090 --> 00:18:11,630
+بشتغل في الأربعة أمثلة الماضية يبقى هنا بقوله
+
+155
+00:18:11,630 --> 00:18:12,610
+solution
+
+156
+00:18:14,930 --> 00:18:24,930
+بعدين للمصوفة الموسعى 1-2-3-6 و هنا A و هنا B
+
+157
+00:18:24,930 --> 00:18:30,870
+بالشكل اللي عناها تمام؟ بدي أحاول أخلي هذا Zero
+
+158
+00:18:30,870 --> 00:18:36,910
+يبقى بضرب الصف الأول فيه تلاتة و بضيفه للصف التاني
+
+159
+00:18:36,910 --> 00:18:45,940
+يبقى هنا تلاتة R1 to R2 نفس العددالصف الأول زي ما
+
+160
+00:18:45,940 --> 00:18:53,160
+هو واحد سالف اتنين a الصف التاني zero يعني ضربنا
+
+161
+00:18:53,160 --> 00:18:59,120
+فيه تلاتة في سالف ستة مع ستة في zero هنا ضربنا فيه
+
+162
+00:18:59,120 --> 00:19:05,560
+تلاتة اللي بيصير تلاتة a زائد ال b بالشكل اللي
+
+163
+00:19:05,560 --> 00:19:08,440
+عندنا تمام
+
+164
+00:19:09,470 --> 00:19:13,430
+من هذا الكلام ماذا نستنتج يا بنات ان ثلاثة a زائد
+
+165
+00:19:13,430 --> 00:19:20,110
+بي كده Zero اصلا الله يرضى يعني كأنه هنا Zero X
+
+166
+00:19:20,110 --> 00:19:26,290
+واحد زائد Zero X اتنين زائد ثلاثة a زائد بي وهنا X
+
+167
+00:19:26,290 --> 00:19:30,630
+واحد نقص اتنين X اتنين زائد ايه المعادلة الأولى
+
+168
+00:19:30,630 --> 00:19:37,190
+تمام يبقى باجي بقول له the above system
+
+169
+00:19:39,090 --> 00:19:50,930
+has a solution of التلاتة a زائد ال V بدل ساوية U
+
+170
+00:19:51,930 --> 00:19:57,110
+يعني أي قيمتين أخدهم لأي و بي بيخلوه للمعادلة
+
+171
+00:19:57,110 --> 00:20:03,150
+تساوي zero بتبقى هي عبارة عن القيم اللي بتخلي لهذا
+
+172
+00:20:03,150 --> 00:20:06,950
+ال system حل بس ماقالليش هات الحل لو قاللي هات
+
+173
+00:20:06,950 --> 00:20:12,190
+الحل بدي أروحالقيمة اللى بدى أحطها وبدى أطبقها
+
+174
+00:20:12,190 --> 00:20:16,390
+وبالتالي كل واحد بيطلع عنده إيه حل الشكل يعني كام
+
+175
+00:20:16,390 --> 00:20:21,830
+حل لهذه أو لهذا ال system بيصير عدد لانهائي من
+
+176
+00:20:21,830 --> 00:20:27,370
+الحلول طب حدا فيكم بتقدر تعطيني قيمة لإيه وقيمة
+
+177
+00:20:27,370 --> 00:20:34,480
+لبيه بتخلي لهذا ال system حل واحد أسالب تلاتةراحت
+
+178
+00:20:34,480 --> 00:20:39,560
+أخدت إحدى الأخوات A بواحد و أخدت B بسالب تلاتة
+
+179
+00:20:39,560 --> 00:20:45,860
+كلام مظبوطواحدة راحت أخدت الـ A بتلت وB بسالب واحد
+
+180
+00:20:45,860 --> 00:20:51,300
+وواحدة أخدت الـ A باثنين وواحدة أخدت الـ B بسالب
+
+181
+00:20:51,300 --> 00:20:55,940
+ستة يعني قيم كثيرة إيش بيجي في بالك قيم اتحقق
+
+182
+00:20:55,940 --> 00:21:00,880
+المعادلة بتخلي لهذا solution حل يبقى the above
+
+183
+00:21:00,880 --> 00:21:05,060
+system has a solution إذا كانت ثلاثة A زائد B
+
+184
+00:21:05,060 --> 00:21:09,920
+يساوي Zero و بعدين حط القيم اللي بدك إياهاعلى أي
+
+185
+00:21:09,920 --> 00:21:15,960
+حال الان وصلنا الى نهاية هذا ال section و لذلك
+
+186
+00:21:15,960 --> 00:21:22,600
+وصلنا الى exercises اتنين واحد المسائل التالية
+
+187
+00:21:22,600 --> 00:21:31,810
+اتنين وخمسة وسبعةو تسعة و احداش و تلتاش و ستاش و
+
+188
+00:21:31,810 --> 00:21:40,790
+سبعتاش و كذلك تمانتاش و تسعة و تاشر بيه طبعا احنا
+
+189
+00:21:40,790 --> 00:21:46,310
+حلنالك انت بتروح تحلي من اللي هو بيه من هذا
+
+190
+00:21:58,750 --> 00:22:04,890
+بننتقل الان الى section 222 اللى هو ال homogenous
+
+191
+00:22:04,890 --> 00:22:13,010
+system اللى هو المعادلات او الأنظمة المتجانسة يبقى
+
+192
+00:22:13,010 --> 00:22:19,250
+section 222 اللى هى ال homogeneous
+
+193
+00:22:27,750 --> 00:22:32,550
+يبقى الـ homogeneous systems
+
+194
+00:22:32,550 --> 00:22:36,650
+الأنظمة
+
+195
+00:22:36,650 --> 00:22:42,510
+المتجانسة بتذكروا ذكرنا لها تعريف قبل ذلك ولذلك
+
+196
+00:22:42,510 --> 00:22:47,470
+بدنا نروح بس نكرر تكرار لهذا التعريف هو ال system
+
+197
+00:22:47,470 --> 00:22:53,010
+للعمود الثوابط هذا بيكون كله أسفارا يبقى
+
+198
+00:22:53,010 --> 00:22:53,670
+definition
+
+199
+00:22:58,620 --> 00:23:10,360
+The homogeneous linear system
+
+200
+00:23:10,360 --> 00:23:14,080
+is
+
+201
+00:23:14,080 --> 00:23:18,540
+a system
+
+202
+00:23:18,540 --> 00:23:22,260
+in the form
+
+203
+00:23:28,810 --> 00:23:37,730
+A11X1 A12X2 A1NXN0
+
+204
+00:23:37,730 --> 00:23:42,170
+A21X1
+
+205
+00:23:42,170 --> 00:23:45,470
+A22X2
+
+206
+00:23:45,470 --> 00:23:49,710
+A2NXN0
+
+207
+00:23:49,710 --> 00:23:54,630
+A M1X1
+
+208
+00:23:57,270 --> 00:24:04,530
+AM2X2 زائد زائد AMNXN
+
+209
+00:24:04,530 --> 00:24:09,770
+زائد زائد AMNXN زائد زائد AMNXN
+
+210
+00:24:09,770 --> 00:24:16,310
+زائد AMNXN زائد AMNXN
+
+211
+00:24:16,310 --> 00:24:18,990
+زائد AMNXN زائد AMNXN زائد AMNXN زائد AMNXN زائد
+
+212
+00:24:18,990 --> 00:24:22,290
+AMNXN زائد AMNXN زائد AMNXN
+
+213
+00:24:22,290 --> 00:24:27,410
+زيبقى هتقسم هذه الـ remark إلى نقطتين النقطة
+
+214
+00:24:27,410 --> 00:24:36,570
+الأولى The homogeneous system استعارة اللي عندنا
+
+215
+00:24:36,570 --> 00:24:46,810
+هذا is always has a solution is always has a
+
+216
+00:24:46,810 --> 00:24:51,650
+solution دائما بلقيله حل because
+
+217
+00:24:55,830 --> 00:25:00,410
+it has because
+
+218
+00:25:00,410 --> 00:25:08,490
+it has at least the
+
+219
+00:25:08,490 --> 00:25:17,750
+trivial solution ايش
+
+220
+00:25:17,750 --> 00:25:23,550
+ال trivial solution الو x واحد و x اتنين ونظل
+
+221
+00:25:23,550 --> 00:25:31,410
+ماشيين لغاية xnبدي يساوي zero و zero و كذلك zero
+
+222
+00:25:31,410 --> 00:25:39,510
+النقطة الثانية the homogeneous system يبقى هنضيف
+
+223
+00:25:39,510 --> 00:25:45,630
+عليها كمان عبارة قبل ما نبدأ النقطة التانية يبقى
+
+224
+00:25:45,630 --> 00:25:55,070
+باجي بقول sir the homogeneous system
+
+225
+00:25:56,240 --> 00:26:04,940
+a star is consistent is consistent
+
+226
+00:26:04,940 --> 00:26:12,420
+بنجي إلى النقطة الثانية the homogeneous system a
+
+227
+00:26:12,420 --> 00:26:23,740
+star the homogeneous system a star of m equations
+
+228
+00:26:23,740 --> 00:26:41,630
+ofm equations and n unknowns has
+
+229
+00:26:41,630 --> 00:26:45,830
+infinite
+
+230
+00:26:45,830 --> 00:26:55,190
+number of solutions infinite number of
+
+231
+00:26:57,200 --> 00:27:03,940
+Solutions Infinite number of solutions that
+
+232
+00:27:03,940 --> 00:27:07,140
+contains
+
+233
+00:27:07,140 --> 00:27:16,640
+the trivial solution that
+
+234
+00:27:16,640 --> 00:27:21,440
+contains the trivial solution
+
+235
+00:27:28,560 --> 00:27:32,740
+FM أقل من N
+
+236
+00:27:58,990 --> 00:28:14,570
+كذبت one find the solution of the system x
+
+237
+00:28:14,570 --> 00:28:24,550
+واحد ناقص x اتنين ناقص تلاتة x تلاتة بيساوي زي
+
+238
+00:28:24,550 --> 00:28:32,040
+واحد x واحد زي x اتنينزائد اكس تلاتة بدل ساوي زيرو
+
+239
+00:28:32,040 --> 00:28:41,120
+اتنين اكس واحد زائد اتنين اكس اتنين زائد اكس تلاتة
+
+240
+00:28:41,120 --> 00:28:44,740
+كله بدل ساوي زيرو
+
+241
+00:29:18,390 --> 00:29:23,190
+النقطة الأولى هو تعريف الـ homogeneous system
+
+242
+00:29:23,190 --> 00:29:28,450
+النقطة الثانية هي الملاحظة التي تتكون من نقطتين
+
+243
+00:29:28,450 --> 00:29:32,610
+وهذه تعطينا مؤشر لحل الـ homogeneous system
+
+244
+00:29:33,240 --> 00:29:37,060
+الدفينيشن بيقول الـ homogeneous literal system is
+
+245
+00:29:37,060 --> 00:29:41,800
+a system in the form يبقى معادلات قطية بس الثوابط
+
+246
+00:29:41,800 --> 00:29:49,080
+كلها أصفار لو كان استبدلنا أحد الأصفار برقم بيبطل
+
+247
+00:29:49,080 --> 00:29:52,980
+يصير homogeneous system بيصير non homogeneous
+
+248
+00:29:52,980 --> 00:29:57,320
+systemعلى أي حال ، أنا مدير الـ System بهذا الشكل
+
+249
+00:29:57,320 --> 00:30:01,880
+ما هي أخبار الحلول بتابعته بروح بقول النقطة الأولى
+
+250
+00:30:01,880 --> 00:30:06,780
+اللي هو مدير الـ System Star دائماً و أبداً له حل
+
+251
+00:30:06,780 --> 00:30:13,520
+على الأقل هو الحل الصفري لأن لو شيلت X1 و X2 و Xn
+
+252
+00:30:13,520 --> 00:30:18,320
+في كل من المعادلة و حطيت بدلها صفر بصير الـ System
+
+253
+00:30:18,320 --> 00:30:24,320
+صحية بصير 00000 بتحقق أي معادلةأو بتحقق كل
+
+254
+00:30:24,320 --> 00:30:28,140
+المعادلات اللي موجودة ورا في هذا ال system ومن هنا
+
+255
+00:30:28,140 --> 00:30:32,700
+بروح بقول له ال homogenous system على الأقل له
+
+256
+00:30:32,700 --> 00:30:38,660
+الحل الصفري تمام تمام يعني معنى هذا الكلام أن هذا
+
+257
+00:30:38,660 --> 00:30:43,940
+ال system دائما و أبداConsistent عمروش بيكون
+
+258
+00:30:43,940 --> 00:30:48,940
+inconsistent على الإطلاق دائما و أبدا consistent
+
+259
+00:30:48,940 --> 00:30:54,460
+لأنه بيحتوي على أو له الحل الصفري أو الحل البديهي
+
+260
+00:30:54,460 --> 00:31:00,160
+أو الحل التافعي ال trivial solution 000 هذا النقطة
+
+261
+00:31:00,160 --> 00:31:03,920
+الأولى النقطة الثانية ال homogenous system star
+
+262
+00:31:03,920 --> 00:31:10,260
+اللي في M من المعادلات و N من المجاهدشايفة M من
+
+263
+00:31:10,260 --> 00:31:15,860
+المعادلات وعندي N من المجاهد يبقى عندي X1 و X2
+
+264
+00:31:15,860 --> 00:31:23,500
+لغاية XN وعندي عدد من المعادلات يساوي M يمكن هدول
+
+265
+00:31:23,500 --> 00:31:27,680
+يكونوا جد بعض زي ما احنا جايلين هنا ويمكن يكونوا
+
+266
+00:31:27,680 --> 00:31:33,700
+مختلفات طيب تعالى نشوف ايش بيقول هنا ال homogenous
+
+267
+00:31:33,700 --> 00:31:39,030
+system of M equations and N unknownsلديها عدد محدد
+
+268
+00:31:39,030 --> 00:31:43,230
+من الحلول التي تحتوي على هذه الحلول التعريفة إذا
+
+269
+00:31:43,230 --> 00:31:48,450
+كانت يعني يا بنات لو عندي عدد لنهائي من الحلول
+
+270
+00:31:48,450 --> 00:31:53,110
+لهذا ال system فإن هذا العدد النهائي دائما و أبدا
+
+271
+00:31:53,110 --> 00:31:58,620
+يجتمع على مين؟على الحل الصفري يعني يا بيكون الحل
+
+272
+00:31:58,620 --> 00:32:03,680
+الصفري مستقل لحاله مافيش غيره يا إما بكون عندي عدد
+
+273
+00:32:03,680 --> 00:32:08,540
+لنهائي من الحلول تجتمل على الحل الصفري اللي موجود
+
+274
+00:32:08,540 --> 00:32:12,820
+تمام يبقى هيك بيقول النظام اللي عندنا بقوله كويس
+
+275
+00:32:12,820 --> 00:32:17,160
+طيب يا بنات خليني أسأل قبل ما أكمل السؤال التالي
+
+276
+00:32:17,160 --> 00:32:21,900
+هل ال non homogeneous system يحتوي على الحل
+
+277
+00:32:21,900 --> 00:32:29,190
+الصفري؟يعني هل الحل الصفري أحد حلول الـ non
+
+278
+00:32:29,190 --> 00:32:34,310
+-homogeneous system؟ ولا
+
+279
+00:32:34,310 --> 00:32:39,350
+عمره بيحصل ولا عمره بيحصل ليش؟ لأن لو قلت الكلام
+
+280
+00:32:39,350 --> 00:32:44,150
+هذا صاحب بدي أشيل كل ال axis و أحط بدلها أصفرًا
+
+281
+00:32:44,150 --> 00:32:48,790
+صار الطرف الشمال كله أصفر بس الطرف اليمين أعداد
+
+282
+00:32:48,790 --> 00:32:53,750
+بنفع الصفر يستوي أعداد؟يعني ماعنديش حل يبقى بناء
+
+283
+00:32:53,750 --> 00:32:59,010
+عليه الـ Non-homogeneous system لا يمكن أن يكون
+
+284
+00:32:59,010 --> 00:33:04,990
+الحل الصفري هو أحد الحلول له لكن الحل الصفري يكون
+
+285
+00:33:04,990 --> 00:33:10,990
+حلا للـ homogeneous system فقط لا غير قد تأتي هذا
+
+286
+00:33:10,990 --> 00:33:16,210
+إذا جبنا صح وخطأ دلوقتي يبقى ركزي على هذه النقطة
+
+287
+00:33:16,480 --> 00:33:21,240
+بدي أرجع للنقطة الثانية مرة ثانية «شولي» يضمن لي
+
+288
+00:33:21,240 --> 00:33:26,700
+أن في عندي عدد لنهائي من الحلول الذاتي يجتمل على
+
+289
+00:33:26,700 --> 00:33:33,800
+الحل الصفري شرط واحد فقط أن عدد المعادلات أقل من
+
+290
+00:33:33,800 --> 00:33:38,480
+عدد المجاهيل يعني ممكن يكون عندي معادلتين و تلت
+
+291
+00:33:38,480 --> 00:33:45,590
+مجاهيلممكن يكون عندى 3 معادلات و 5 مجاهيل ممكن
+
+292
+00:33:45,590 --> 00:33:51,090
+يكون عندى 10 معادلات و 11 مجهول يعني دائما و أبدا
+
+293
+00:33:51,090 --> 00:33:55,630
+إذا كان عدد المعادلات أقل من عدد المجاهيل
+
+294
+00:33:55,630 --> 00:34:02,510
+automatic لازم يحصل عندى عدد لانهائي من الحلول هي
+
+295
+00:34:02,510 --> 00:34:07,020
+هذه اللى بتقوله النقطة اللى عندها تمامطب نرجع الآن
+
+296
+00:34:07,020 --> 00:34:13,260
+نحاول نطبق ما نقوله على أرض الواقع طيب يا بنات لما
+
+297
+00:34:13,260 --> 00:34:17,160
+يكون عندي عدد لا نهائم الحلول تجتمل على الحل
+
+298
+00:34:17,160 --> 00:34:22,480
+الصفري يعني هذا الحل بيكون أعداد ولا أصفار
+
+299
+00:34:26,360 --> 00:34:30,980
+قد يكون أدد وقد يكون أصفر صح ولا لأ مش احنا بنقول
+
+300
+00:34:30,980 --> 00:34:35,340
+يعني إذا يحتوي على الحل الصفري إذا الحل ال zero
+
+301
+00:34:35,340 --> 00:34:39,540
+أحد هذه الحلول وبعدها تتأعدى لكن الأعداد هل بقدر
+
+302
+00:34:39,540 --> 00:34:45,280
+أجيبهم بالضبط كلهملا بقدرش ممكن أجيبهم صحيح كلهم و
+
+303
+00:34:45,280 --> 00:34:50,920
+ممكن ماقدرش فبتظهر الحل بدلالة رموز يعني أنا بفرض
+
+304
+00:34:50,920 --> 00:34:55,340
+هذه رموز وبالتالي الرموز هذه قد ما بدك حط وبالتالي
+
+305
+00:34:55,340 --> 00:35:00,310
+بيطلع عندك معلنها من الحلولنبدأ بتطبيق هذا على أرض
+
+306
+00:35:00,310 --> 00:35:03,950
+الواقع بيقول هاتلي حل ال system اللي قدامنا هذا
+
+307
+00:35:03,950 --> 00:35:10,070
+يبقى بدي أبدأ بمين بالمصوفة الموسعة اللي قلنا
+
+308
+00:35:10,070 --> 00:35:15,060
+عليها يبقى المصوفة الموسعة على الشكل التانيهذا
+
+309
+00:35:15,060 --> 00:35:21,060
+واحد و هنا سالب واحد و هنا سالب تلاتة و هنا واحد و
+
+310
+00:35:21,060 --> 00:35:27,320
+هنا واحد و هنا واحد و هنا اتنين اتنين واحد و هنا
+
+311
+00:35:27,320 --> 00:35:30,620
+زيرو زيرو زيرو بالشكل اللي عندنا
+
+312
+00:35:33,400 --> 00:35:45,920
+بنخلق هنا أسطار نقص R1 to R2 ونقص R1 to R3 نحصل
+
+313
+00:35:45,920 --> 00:35:52,440
+على ما يأتي الصف الأول زي ما هو 1 سالب 1 سالب 3
+
+314
+00:35:52,440 --> 00:36:01,740
+زيرو الصف التاني زيروو هنا اتنين و هنا اربعة و هنا
+
+315
+00:36:01,740 --> 00:36:07,860
+zero و هنا zero و هنا ضربنا في سالب اتنين بصير
+
+316
+00:36:07,860 --> 00:36:14,180
+اتنين يبقى اربعة و هنا ضربنا في سالب اتنين بصير
+
+317
+00:36:14,180 --> 00:36:21,640
+ستة واحد سبعة و هنا zero و اضحكوابعدين بدي هذا
+
+318
+00:36:21,640 --> 00:36:28,700
+قداش واحد صحيح يبقى بدي نص قاري اتنين يبقى هذا
+
+319
+00:36:28,700 --> 00:36:35,420
+ناخد نص قاري اتنين تصبح المفروفة على الشكل التالي
+
+320
+00:36:35,420 --> 00:36:41,680
+واحد سالب واحد سالب تلاتة زيرو وهنا زيرو واحد
+
+321
+00:36:41,680 --> 00:36:48,880
+اتنين زيرو وهنا زيرو اربع سبعة زيرو بالشكل اللي
+
+322
+00:36:48,880 --> 00:36:54,030
+عندنايبقى هذا بده يعطينا الصف الأول ماليش علاقة
+
+323
+00:36:54,030 --> 00:36:59,590
+فيه بدي على الصف التاني بقول ناقص اربعة R اتنين to
+
+324
+00:36:59,590 --> 00:37:07,830
+R تلت وابتدي تصبح على طبيعي ايش رأيك لو أضفنا كمان
+
+325
+00:37:07,830 --> 00:37:13,550
+الصف الثاني الى الصف الأول بالمرة ماحدش أحسن من
+
+326
+00:37:13,550 --> 00:37:21,840
+هذا إذا لو قل R اتنين to R oneخطوة واحدة يفجأش
+
+327
+00:37:21,840 --> 00:37:25,840
+اللي بده يصير R اتنين ل R one بيظل هنا واحد و
+
+328
+00:37:25,840 --> 00:37:30,120
+بيصير هنا Zero و هنا سالب واحد و هذا Zero واحد
+
+329
+00:37:30,120 --> 00:37:36,520
+اتنين و هنا Zero Zero زي ما هو تمام و هذا Zero زي
+
+330
+00:37:36,520 --> 00:37:42,180
+ما هو ضربته في سالب اربع بيصير Zero بيصير هنا سالب
+
+331
+00:37:42,180 --> 00:37:48,310
+واحد و هنا جداش Zero بالشكل اللي عندنا هذاأنا بديش
+
+332
+00:37:48,310 --> 00:37:52,070
+هذا سالب بدي إياه بالموجب حتى لو ضال بالسالب
+
+333
+00:37:52,070 --> 00:37:57,310
+ماعنديش إياه ماعنديش مشكلة مشكلتنا بدي أخلي هذا ب
+
+334
+00:37:57,310 --> 00:38:02,430
+zero و بدي أخلي هذا ب إياه ب zero يبقى بدي أجي ل R
+
+335
+00:38:02,430 --> 00:38:07,510
+تلاتة أضربه في سالب واحد و أضيفه للصف الأول و
+
+336
+00:38:07,510 --> 00:38:13,510
+أضربه في اتنين و أضيفه للصف الثاني يبقى هذا بدي
+
+337
+00:38:13,510 --> 00:38:22,220
+يعطينااللي هو من سالف R ثلاثة to R one و بعد هيك
+
+338
+00:38:22,220 --> 00:38:29,760
+سالف اتنين والله موجة باتنين موجة باتنين R ثلاثة
+
+339
+00:38:29,760 --> 00:38:37,020
+to R two نفس العالمية هذا واحد وهذا Zero زي ما هو
+
+340
+00:38:37,020 --> 00:38:44,530
+لأنني باضيف سالف R ثلاثة to R oneوهنا بيصير zero و
+
+341
+00:38:44,530 --> 00:38:52,770
+هنا zero و هنا اتنين R three ل R two يبقى هنا zero
+
+342
+00:38:52,770 --> 00:38:58,970
+و هنا واحد و هنا zero و هنا zero و هنا zero و zero
+
+343
+00:38:58,970 --> 00:39:07,230
+سالب واحد و zero بقدر اقوله اخر خطوة سالب R ثلاثة
+
+344
+00:39:07,230 --> 00:39:17,840
+وبالتالي بتصبح المصوفة واحد zero0 1 0 0 0 1 0 0 0
+
+345
+00:39:17,840 --> 00:39:32,680
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+
+346
+00:39:46,770 --> 00:39:51,470
+solution لا مشكلة فيه بقى solution و الله غيره
+
+347
+00:39:51,470 --> 00:39:55,970
+مافيش مشكلة طب
+
+348
+00:39:55,970 --> 00:40:01,730
+ليش ما طلع الشبنات هنا عدد لنهائي من الحلول ايوة
+
+349
+00:40:01,730 --> 00:40:08,140
+لان عدد المعادلات بساوي عدد المجاهديبقى إذا كان
+
+350
+00:40:08,140 --> 00:40:12,560
+عدد المعادلات يسوي عدد المجاهد يطلع عندي الحل
+
+351
+00:40:12,560 --> 00:40:19,260
+الصفري يطلع عندي عدد عادي عدد عادي غير هيك بصير
+
+352
+00:40:19,260 --> 00:40:23,760
+عدد المعادلات أقل من عدد المجاهد بصير عندي عدد
+
+353
+00:40:23,760 --> 00:40:32,040
+لنهائي من الحلول طيب نجي ناخد كمان مثال يبقى
+
+354
+00:40:32,040 --> 00:40:34,900
+المثال رقم اتنين exactly two
+
+355
+00:40:40,600 --> 00:40:49,100
+solve the system solve the system خلص ال system
+
+356
+00:40:49,100 --> 00:40:58,260
+اللي هو اتنين اكس واحد ناقص اتنين اكس اتنين ناقص
+
+357
+00:40:58,260 --> 00:41:07,320
+اكس تلاتة زائد اكس اربعة بده ساوي زيرو المعادلة
+
+358
+00:41:07,320 --> 00:41:16,230
+التالية ناقص اكس واحدزائد اكس اتنين زائد اكس تلاتة
+
+359
+00:41:16,230 --> 00:41:19,930
+ناقص اتنين اكس اربع زائد اكس اربع زائد اكس اربع
+
+360
+00:41:19,930 --> 00:41:21,710
+زائد اكس اربع زائد اكس اربع زائد اكس اربع زائد اكس
+
+361
+00:41:21,710 --> 00:41:23,890
+اربع زائد اكس اربع زائد اكس اربع زائد اكس اربع
+
+362
+00:41:23,890 --> 00:41:24,010
+اربع زائد اكس اربع زائد اكس اربع زائد اكس اربع
+
+363
+00:41:24,010 --> 00:41:29,190
+زائد اكس اربع زائد اكس اربع زائد اكس اربع زائد اكس
+
+364
+00:41:29,190 --> 00:41:34,930
+اربع زائد اكس اربع ز
+
+365
+00:41:45,650 --> 00:41:51,590
+-2x2-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+366
+00:41:51,590 --> 00:41:51,630
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+367
+00:41:51,630 --> 00:41:53,310
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+368
+00:41:53,310 --> 00:41:56,150
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+369
+00:41:56,150 --> 00:41:59,510
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+370
+00:42:08,180 --> 00:42:13,520
+بالنسبة لل system اللى عندنا تتوقعوا ان يكون عندى
+
+371
+00:42:13,520 --> 00:42:20,920
+حل صفري فقط لغير قد يكون و قد لا يكون طب ممكن يكون
+
+372
+00:42:20,920 --> 00:42:29,930
+عدد لنهائي من الحلول يعني مش معقوللا قد يكون عدد
+
+373
+00:42:29,930 --> 00:42:35,690
+المعادلات مشرطناش لم نضع شرطا انه اذا كان عدد
+
+374
+00:42:35,690 --> 00:42:40,490
+المعادلات يساوي عدد المجاهيل فانه لا يوجد الا حلا
+
+375
+00:42:40,490 --> 00:42:45,230
+واحدا ماقلناش هذا الكلام احنا يعني لو جيت انا
+
+376
+00:42:45,230 --> 00:42:50,070
+جامعت و سويت و ضربت و بالاخر طالع عندى الصف كله
+
+377
+00:42:50,070 --> 00:42:58,390
+أصفاراأو صفر طلع أسفارا كيف بدي أجيب قيم x1, x2,
+
+378
+00:42:58,610 --> 00:43:03,070
+x3, x4؟ مش إمكانية إذا في هذه الحلقة بيكون عندي
+
+379
+00:43:03,070 --> 00:43:08,590
+عدد لنهائي من الحلول وهذا العدد يحتوي على الحل
+
+380
+00:43:08,590 --> 00:43:14,950
+الصفري تمام تعالى نشوف هل سؤالنا هذا له حل واحد و
+
+381
+00:43:14,950 --> 00:43:20,990
+الله حل الصفريوالله في عندي عدد لنهائي من الحلول و
+
+382
+00:43:20,990 --> 00:43:26,130
+الله حل قيم عددية عادية فعلا شوف يفجأ أنا بدي أبدأ
+
+383
+00:43:26,130 --> 00:43:33,730
+بالمصوفة الموسعة يفجأ المصوفة الموسعة للشكل التالت
+
+384
+00:43:33,730 --> 00:43:40,270
+هذا اتنين هي سالم اتنين وهي سالم واحد وهنا واحد
+
+385
+00:43:40,500 --> 00:43:46,180
+وهنا سالب واحد واحد واحد سالب اتنين وهنا تلاتة
+
+386
+00:43:46,180 --> 00:43:54,020
+سالب تلاتة وهنا واحد وهنا سالب ستة وهنا اتنين سالب
+
+387
+00:43:54,020 --> 00:44:00,940
+اتنين وهنا Zero وهنا سالب اتنين وهي Zero Zero و
+
+388
+00:44:00,940 --> 00:44:06,320
+Zero بالشكل اللي عندنا شوف يا بنات لما نكتب
+
+389
+00:44:06,320 --> 00:44:11,690
+المعادلاتإذا كان عندى term غيب بروحش أصفه من جانب
+
+390
+00:44:11,690 --> 00:44:15,790
+بعض بخلي واسع مكان غيب حتى لما أجى أكتب مصفوطة
+
+391
+00:44:15,790 --> 00:44:19,490
+المعاملة ماروحش أتلخبط فيها زى عندى هنا في
+
+392
+00:44:19,490 --> 00:44:24,610
+المعادلة 4 X3 مفقودة يبغى أروحش أحط ناقص الدنيا X4
+
+393
+00:44:24,610 --> 00:44:28,210
+جانب ناقص الدنيا بخلي فيه واسع عشان نعرف إن هنا
+
+394
+00:44:28,210 --> 00:44:33,590
+فيه term مفقود وبالتالي هذا المعامل بحطه P0 طيب
+
+395
+00:44:33,590 --> 00:44:39,950
+شوفوا يا عمان الله يبقى أول خطوةبدي أروح أخلي الحد
+
+396
+00:44:39,950 --> 00:44:44,830
+اللي عندنا هذا الأول مجدد واحد صحيح يبقى إلي كل
+
+397
+00:44:44,830 --> 00:44:53,770
+خيار تمام؟ يا إما بضرب هدف ناصر يا إما بطلع هدفه و
+
+398
+00:44:53,770 --> 00:44:58,770
+بروح بضربه في واحد صحيح مش حسن؟ و بت .. ليه بصير
+
+399
+00:44:58,770 --> 00:45:05,440
+عملية صحيح؟ يبقى أنا بدي أبدل R2 مع R1يبقى هاي
+
+400
+00:45:05,440 --> 00:45:12,220
+القطوة اللى عندنا يبقى هنا replace R1
+
+401
+00:45:12,220 --> 00:45:18,440
+and R2 بدي أبدلهم و الباقى بدي أخليه مكانه زي ما
+
+402
+00:45:18,440 --> 00:45:23,900
+يبقى بيجيكي عندك هنا هاي سالف واحد وهنا واحد وهنا
+
+403
+00:45:23,900 --> 00:45:29,530
+واحد وهنا سالف اتنين وهنا زيرهنا اتنين سالب اتنين
+
+404
+00:45:29,530 --> 00:45:36,170
+سالب واحد واحد زيرو تلاتة سالب تلاتة واحد سالب ستة
+
+405
+00:45:36,170 --> 00:45:41,330
+زيرو هنا الصفة الرابعة والاخيرة اتنين سالب اتنين
+
+406
+00:45:41,330 --> 00:45:49,590
+زيرو سالب اتنين زيرو بالشكل هذا الآن هذا بعمل
+
+407
+00:45:49,590 --> 00:45:53,870
+كتابة يرجى بالداجة على الصف الأول أو الأخر وكله
+
+408
+00:45:53,870 --> 00:46:00,220
+فات بسالب واحديبقى ايش بصير عندنا هنا اللي هو سالب
+
+409
+00:46:00,220 --> 00:46:06,200
+اروان فقط لا غير يبقى بالصبح المصوفة على الشكل
+
+410
+00:46:06,200 --> 00:46:13,480
+التالي واحد سالب واحد سالب واحد سالب واحد سالب
+
+411
+00:46:13,480 --> 00:46:21,000
+واحد اتنين هذه فقط لا غير وهذه zero وهذه اتنين
+
+412
+00:46:21,000 --> 00:46:27,710
+سالب اتنين سالب واحد واحد تلاتة سالب تلاتة1 سالب 6
+
+413
+00:46:27,710 --> 00:46:33,930
+اتنين سالب اتنين زيرو سالب اتنين زيرو زيرو زيرو
+
+414
+00:46:33,930 --> 00:46:40,770
+بالشكل اللي عندنا الان بدي اعمل ثلاث خطوات مرة
+
+415
+00:46:40,770 --> 00:46:47,850
+واحدة هتخلق هنا زيرو وهنا زيرو وهنا زيرو يبقى سالب
+
+416
+00:46:47,850 --> 00:46:57,030
+اتنين R واحد ل R اتنين و ل R اربعيبقى بداشي أقوله
+
+417
+00:46:57,030 --> 00:47:08,430
+ما يأتي بدي أخد سالب R1 to R2 and R4 له أربع و بعد
+
+418
+00:47:08,430 --> 00:47:18,430
+هيك طبعا سالب اتنين هنا هذه
+
+419
+00:47:18,430 --> 00:47:25,680
+سالب اتنين R1 لها و بعد هيك سالب تلاتة R1two are
+
+420
+00:47:25,680 --> 00:47:32,140
+three كله مرة واحدة يبقى الصف الأول زي ما هو واحد
+
+421
+00:47:32,140 --> 00:47:38,840
+سالب واحد سالب واحد اتنين Zero الصف التاني هذا صار
+
+422
+00:47:38,840 --> 00:47:45,260
+Zero وهذا ضربته في سالب اتنين بصير هنا Zero وهذا
+
+423
+00:47:45,260 --> 00:47:50,200
+ضربته في سالب اتنين بصير هنا واحد وهنا هذا بصير
+
+424
+00:47:50,200 --> 00:47:56,160
+سالب تلاتة وهذه Zeroهذا ضربت في سالب تلاتة بصير
+
+425
+00:47:56,160 --> 00:48:02,740
+Zero هذا بصير تلاتة و سالب تلاتة كمان Zero هذا
+
+426
+00:48:02,740 --> 00:48:08,420
+ضربت في سالب تلاتة بصير تلاتة واحد أربعة هذا سالب
+
+427
+00:48:08,420 --> 00:48:16,170
+ستة و سالب ستة بصير سالب أتماشى و هنا Zeroوهذا
+
+428
+00:48:16,170 --> 00:48:21,750
+zero هنا وهذا ربطه في سالف اتنين بصير هنا zero
+
+429
+00:48:21,750 --> 00:48:27,430
+وهذا بيصير هنا اتنين وهذا ربطه في سالف اتنين بيصير
+
+430
+00:48:27,430 --> 00:48:34,750
+سالف اربعة يفجر سالف ستة وهنا اتنين وهنا zero اللي
+
+431
+00:48:34,750 --> 00:48:38,590
+ماصارش عندي leading هنا واحد امان طالع صار في
+
+432
+00:48:38,590 --> 00:48:43,150
+أسرار اللي بجهرش أسوي فيها حاجة إذا مداجي على مين؟
+
+433
+00:48:43,470 --> 00:48:51,110
+على الصف التالت و اضربه في ربع تمام؟ يبقى باجي
+
+434
+00:48:51,110 --> 00:48:58,430
+بقوله هنا انا بدي ربع فهعرف تلاتة بصيله انما يعني
+
+435
+00:48:58,430 --> 00:49:05,250
+اللي هو واحد سالب واحد سالب واحد اتنين Zero Zero
+
+436
+00:49:05,250 --> 00:49:13,430
+Zero واحد سالب تلاتة Zeroو هنا zero .. zero ..
+
+437
+00:49:13,430 --> 00:49:20,690
+واحد .. و هنا سالب تلاتة .. zero .. و هنا zero ..
+
+438
+00:49:20,690 --> 00:49:29,030
+zero .. اتنين .. سالب ستة .. zero .. بالشكل هذا طب
+
+439
+00:49:29,030 --> 00:49:35,170
+ايش رأيك تخلص من الصف التالت و الراجل مرة واحدة
+
+440
+00:49:35,170 --> 00:49:40,750
+نبدأ دي على الصف الثانيأضربه في سالب واحد و أضيفه
+
+441
+00:49:40,750 --> 00:49:45,730
+للصف التالت و أضربه في سالب اتنين و أضيفه للصف
+
+442
+00:49:45,730 --> 00:49:55,130
+الرابع يبقى باقي بقوله هنا سالب R اتنين R اتنين to
+
+443
+00:49:55,130 --> 00:50:03,750
+R تلت و سالب اتنين R اتنين to R اربع الشكل اللي
+
+444
+00:50:03,750 --> 00:50:08,860
+علناه هذا يبقى بتصبح على الشكل التالتهنا واحد وهنا
+
+445
+00:50:08,860 --> 00:50:15,280
+سالب واحد وهنا سالب واحد وهنا اتنين وهنا زيرو وهنا
+
+446
+00:50:15,280 --> 00:50:23,140
+زيرو زيرو وهنا واحد سالب تلاتة وهنا زيرو وهنا زيرو
+
+447
+00:50:23,140 --> 00:50:29,480
+زيرو زيرو زيرو وهنا زيرو زيرو زيرو زيرو زيرو زيرو
+
+448
+00:50:29,480 --> 00:50:34,940
+زيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزير
+
+449
+00:50:36,150 --> 00:50:43,210
+كمان خطوة هذا ال system هنا بدأ الحل يبقى هذا بقدر
+
+450
+00:50:43,210 --> 00:50:55,790
+اشيله بالشكل ان انا بدي
+
+451
+00:50:55,790 --> 00:51:05,860
+اضيف الصف التاني للصف الاول يبقى R2والله ايش رايك
+
+452
+00:51:05,860 --> 00:51:11,640
+انك دلوقت نعملهم لو عملناها مع الخطوة الأولى هذه
+
+453
+00:51:11,640 --> 00:51:19,540
+ليها بلاش خطوة جديدة and r2
+
+454
+00:51:19,540 --> 00:51:29,140
+to r1 يبقى هذه بالصير zero وهذه بالصير سالب واحد
+
+455
+00:51:29,140 --> 00:51:30,320
+فقط ده غير
+
+456
+00:51:35,780 --> 00:51:42,720
+أكتر من هيك بنقدر نعمل؟ لأ يبقى ال system باربع
+
+457
+00:51:42,720 --> 00:51:49,180
+معادلات الى مين الى معادلتين المعادلة الأولى x
+
+458
+00:51:49,180 --> 00:51:56,960
+واحد ناقص x اتنين ناقص x أربعة بده يسوي zero
+
+459
+00:51:56,960 --> 00:52:03,380
+والمعادلة التانية اصبح x واحد على x تلاتة
+
+460
+00:52:16,330 --> 00:52:24,200
+معادلتين في أربعة مجهوليبقى فيش إمكانية إلا أحط
+
+461
+00:52:24,200 --> 00:52:29,680
+قيمتين من عندي تمام يبقى بعدي أختار اللي بدكيها أي
+
+462
+00:52:29,680 --> 00:52:34,080
+قيمة أحطيها من عندك و أشوف إيش اللي بده يحصل يبقى
+
+463
+00:52:34,080 --> 00:52:43,380
+أنا لو روحت جيب main goal put مثلا x4 تساوي اللي
+
+464
+00:52:43,380 --> 00:52:52,290
+بدكيها x4 نحطها بواحد او الا x4 ب ax4 تساوي a مثلا
+
+465
+00:52:52,290 --> 00:53:03,290
+and x2 تساوي b نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+466
+00:53:03,290 --> 00:53:03,310
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+467
+00:53:03,310 --> 00:53:06,630
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+468
+00:53:06,630 --> 00:53:06,650
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+469
+00:53:06,650 --> 00:53:16,530
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+470
+00:53:21,350 --> 00:53:27,450
+يبقى ال X تلاتة و X أربعة نحطوها بـ A يبقى بده
+
+471
+00:53:27,450 --> 00:53:37,990
+ساوي تلاتة A يبقى أصبح that solution is X واحد X
+
+472
+00:53:37,990 --> 00:53:45,850
+اتنين X تلاتة X أربعة أساوية X واحداللي هي بقداش
+
+473
+00:53:45,850 --> 00:53:59,850
+طلعناها A زائد الـ B X2 حطناها V X3 ثلاثة A X4 دي
+
+474
+00:53:59,850 --> 00:54:06,490
+A بالشكل اللي عندنا يبقى هذا أصبح الحل طب هل هذا
+
+475
+00:54:06,490 --> 00:54:11,810
+يحتوي على ال trivial solution الإجابة نعم حطيت
+
+476
+00:54:11,810 --> 00:54:12,990
+قيود على A وB
+
+477
+00:54:16,070 --> 00:54:22,410
+بحصل على حل الصفري اذا
+
+478
+00:54:22,410 --> 00:54:31,390
+صار عندي عدد لنهائي من الحلول system has
+
+479
+00:54:31,390 --> 00:54:41,510
+infinite number of solutions
+
+480
+00:54:42,440 --> 00:54:54,640
+that is this system this system is consistent
+
+481
+00:54:54,640 --> 00:54:58,600
+لازلنا
+
+482
+00:54:58,600 --> 00:55:03,400
+في نفس ال section و لمّا ننتهي بعد للمرة القادمة
+
+483
+00:55:03,400 --> 00:55:05,080
+ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2174ec625a171176f1318dcd3913687ee790f493
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_raw.srt
@@ -0,0 +1,1968 @@
+1
+00:00:21,230 --> 00:00:25,470
+بسم الله الرحمن الرحيم ابتدأنا في المرة الماضية
+
+2
+00:00:25,470 --> 00:00:28,130
+بال system of linear equations اللي هو section
+
+3
+00:00:28,130 --> 00:00:33,070
+اتنين واحد و لما ننتهي بعد و ابتدأنا في أخذ أمثلة
+
+4
+00:00:33,070 --> 00:00:38,070
+على هذا ال section و أعطينا على ذلك ثلاثة أمثلة
+
+5
+00:00:38,070 --> 00:00:42,930
+تمام؟ و هذا هو المثال الرابع اللي بين إيدنا الآن
+
+6
+00:00:43,470 --> 00:00:48,850
+المثال بيقول استخدم الـ Echelon Form او الـ Raw
+
+7
+00:00:48,850 --> 00:00:53,450
+Echelon Form عشان نحل المعادلة اللي عندنا هذه يبقى
+
+8
+00:00:53,450 --> 00:00:57,170
+الخطوة الأولى يقول بناخد الـ Agumented Matrix يعني
+
+9
+00:00:57,170 --> 00:01:02,010
+المصوفة الموسعة المصوفة الموسعة عندنا على هذا
+
+10
+00:01:02,010 --> 00:01:09,690
+الشكل اللي هو واحد واحد سالب واحد واحد اتنين واحد
+
+11
+00:01:09,690 --> 00:01:18,930
+سالب واحد واحدو هنا zero و هنا واحد واحد zero و
+
+12
+00:01:18,930 --> 00:01:28,910
+هنا الصف الرابع هو عبارة عن zero و كذلك واحد و
+
+13
+00:01:28,910 --> 00:01:36,130
+zeroو اتنين و بنروح نحط هنا مصوفة المعاملة او
+
+14
+00:01:36,130 --> 00:01:44,190
+الثوابت اللي هو اربعة سالب خمسة سالب واحد اربعة
+
+15
+00:01:44,190 --> 00:01:50,930
+الشكل اللي عندنا طبعا ايش
+
+16
+00:01:50,930 --> 00:01:58,490
+خمسة؟أربعة صفوف هى المعادلة
+
+17
+00:01:58,490 --> 00:02:04,330
+التانية خمسة بالموجب خمسة بالموجب فعلا يبقى هى ..
+
+18
+00:02:04,330 --> 00:02:09,710
+هى كتبنا اللى هو مصوفة المعاملات وكذلك أضفنا لها
+
+19
+00:02:09,710 --> 00:02:16,090
+عمود الثوابط وسميت لذلك بالمصوفة الموسعة الان واضح
+
+20
+00:02:16,090 --> 00:02:20,330
+عندى هنا صفرين يبقى دول بقدرش أعمل فيهم ولا حاجة
+
+21
+00:02:20,570 --> 00:02:26,270
+يبقى باجي على الاتنين هذي و بتخليها واحد صحيح اذا
+
+22
+00:02:26,270 --> 00:02:33,850
+بقدر اضرب الصف الأول في سالي باتنين و اضيفه للصف
+
+23
+00:02:33,850 --> 00:02:39,510
+الثاني يبقى هذا بدي اعمل سالي باتنين R1
+
+24
+00:02:42,510 --> 00:02:49,830
+بحصل على المصفوفة التانية الصف الأول كما هو واحد
+
+25
+00:02:49,830 --> 00:02:56,050
+واحد سالب واحد واحد وهي الأربعة الصف التاني بصير
+
+26
+00:02:56,050 --> 00:03:00,210
+zero سالب اتنين واحد بصير سالب واحد
+
+27
+00:03:14,240 --> 00:03:20,850
+الصفرين يبقوا كما هم الاتنينيبقى هاي Zero وهي Zero
+
+28
+00:03:20,850 --> 00:03:27,450
+وهي واحد واحد وهنا واحد Zero وهنا Zero اتنين وهنا
+
+29
+00:03:27,450 --> 00:03:32,890
+سالب واحد وهي الأربعة وهي المصفوفة الجديدة اللي
+
+30
+00:03:32,890 --> 00:03:39,150
+عندنا الان هذا ال leading اللي عندنا له واحد تمام
+
+31
+00:03:39,150 --> 00:03:43,630
+اذا بالضبط للصف اللي بعده العمصر صحته لأ اللي على
+
+32
+00:03:43,630 --> 00:03:48,090
+يمينه بالضبط لازم يكون ال leading هذا جداشواحد صح
+
+33
+00:03:48,090 --> 00:03:50,930
+يبقى بروح بضرب الصف الأول هذا في جد إيه الصف
+
+34
+00:03:50,930 --> 00:03:55,090
+الثاني في جد إيه في سالب واحد يبقى باجي بقوله بدي
+
+35
+00:03:55,090 --> 00:04:02,610
+أعمل سالب are two فقط لغة يبقى باجي بقول المصطفة
+
+36
+00:04:02,610 --> 00:04:09,250
+هتأخد الشكل التالي واحد واحد سالب واحد وهنا كمان
+
+37
+00:04:09,250 --> 00:04:15,760
+واحدوهذا عمودي الثوابت اللي هو أربعة وهنا zero
+
+38
+00:04:15,760 --> 00:04:22,940
+وهنا واحد وهنا سالب واحد وهنا واحد وهنا تلاتة
+
+39
+00:04:22,940 --> 00:04:28,240
+والصفين التانيات الاتنين اللي صفلين زي ما هم واحد
+
+40
+00:04:28,240 --> 00:04:36,380
+واحد وهنا واحد zero وهنا zero اتنين وهنا سالب واحد
+
+41
+00:04:36,380 --> 00:04:44,100
+وهنا كداش اللي هو أربعةبعد هيك بدي أعمل هنا zero
+
+42
+00:04:44,100 --> 00:04:49,220
+وهنا zero إذا بضرب الصف الثاني في سالب واحد و
+
+43
+00:04:49,220 --> 00:04:56,100
+بضيفه للصف التالت و كذلك للصف الرابع يبقى عملتين
+
+44
+00:04:56,100 --> 00:05:02,880
+هعملهم في آل واحد يبقى بدي أعمل ما ياتي سالب اللي
+
+45
+00:05:02,880 --> 00:05:06,220
+هو R2 to R3
+
+46
+00:05:19,380 --> 00:05:26,280
+يبقى أول صفين يبقوا كما هم يبقى باجي بقول الصف
+
+47
+00:05:26,280 --> 00:05:34,180
+الأول هذا اللي هو واحد واحد سالب واحد وهنا واحدهنا
+
+48
+00:05:34,180 --> 00:05:40,940
+أربعة كما هو وهنا زيرو وهنا واحد وسالب واحد واحد
+
+49
+00:05:40,940 --> 00:05:46,780
+وهنا تلاتة الآن بدي أضربه في سالب واحد واضيفه هنا
+
+50
+00:05:46,780 --> 00:05:51,820
+بدي يجيني هنا هذا زيرو زيرو زي ما هو بدي يجيكي هنا
+
+51
+00:05:51,820 --> 00:05:57,280
+زيرو زيرو تمام؟ الآن هذا أنا ضربته في سالب واحد
+
+52
+00:05:57,280 --> 00:06:02,810
+يبقى هنا كدهش واحد واحد بصير اتنين وهنا واحديبقى
+
+53
+00:06:02,810 --> 00:06:08,510
+هنا اتنين و هنا واحد هنا صار هذا سالب واحد اضيفه
+
+54
+00:06:08,510 --> 00:06:14,510
+هنا يبقى بيصير سالب واحد و واحد يبقى سالب واحد و
+
+55
+00:06:14,510 --> 00:06:19,490
+واحد فقط لغير بقول سالب واحد زي اتنين اللي هو اب
+
+56
+00:06:19,490 --> 00:06:24,330
+واحد لأ اذا عرفت ان سالب واحد بيصير سالب تلاتة
+
+57
+00:06:24,330 --> 00:06:29,980
+يبقى بيصير هذه سالب اربعة و هذه واحدةيبقى هذه سالف
+
+58
+00:06:29,980 --> 00:06:36,000
+أربعة وهذه واحد بالشكل اللي عندنا هذا، تمام؟ الآن
+
+59
+00:06:36,000 --> 00:06:42,320
+بالذالك لمين؟ لصف التالت، بدي هذا يكون واحد، صحيح،
+
+60
+00:06:42,320 --> 00:06:46,600
+يبقى بروح بضرب هذا الكلام في قداش، في نص، يبقى بدي
+
+61
+00:06:46,600 --> 00:06:55,170
+النص R تلاتةيبقى بالده ياخد هنا النص R ثلاثة ينثب
+
+62
+00:06:55,170 --> 00:07:01,890
+على الشكل ثالث أول صفين زي ما هما واحد واحد وكمان
+
+63
+00:07:01,890 --> 00:07:04,670
+سالب واحد وهنا واحد
+
+64
+00:07:14,780 --> 00:07:20,920
+والعمود هذا هذا واحد وهنا اربعة وهنا zero وهنا
+
+65
+00:07:20,920 --> 00:07:27,120
+واحد سالب واحد واحد تلاتة الان بدي اضرب هدف نص
+
+66
+00:07:27,120 --> 00:07:32,280
+يبقى zero zero زي ما هو وهنا ناقص نص وهنا ناقص
+
+67
+00:07:32,280 --> 00:07:41,220
+اتنين والصفة الرابعة زي ما هو واحد واحد واحد الان
+
+68
+00:07:41,730 --> 00:07:50,010
+بدي اخلي هذا zero يبقى بداتي اقوله سالب R3 to R4
+
+69
+00:07:50,010 --> 00:07:55,050
+ونشوف ايش بدنا نعمل في هذا يبقى هذا الكلام بده
+
+70
+00:07:55,050 --> 00:08:01,410
+يعطينا المصفوفة التالية الان واحد واحد سالب واحد
+
+71
+00:08:01,410 --> 00:08:10,710
+واحد zero واحد سالب واحد واحد zero zero واحد سالب
+
+72
+00:08:10,710 --> 00:08:18,310
+نصهنا موجة و هنا موجة و هنا موجة و هنا موجة و هنا
+
+73
+00:08:18,310 --> 00:08:22,250
+موجة
+
+74
+00:08:22,250 --> 00:08:32,410
+و هنا موجة
+
+75
+00:08:36,410 --> 00:08:44,730
+بدي هذا يكون كمان جداشر بدي واحد صحيح طيب إيش رأيك
+
+76
+00:08:44,730 --> 00:08:51,350
+يا بنات لو عملت ما يأتي بدي أحاول أخفف الخطوات
+
+77
+00:08:51,350 --> 00:08:57,470
+شوية يبقى بدي أعمل ما يأتي بدي أضرب هذا في سالب
+
+78
+00:08:57,470 --> 00:09:02,830
+واحد و أضيفه فوق هاي الخطوة الأولى الخطوة الثانية
+
+79
+00:09:03,120 --> 00:09:11,260
+بدي اضغط هدف يقداش تلتين يبقى بدي اجي R اتنين
+
+80
+00:09:11,260 --> 00:09:17,720
+بالسالب سالب R اتنين to R one هاي واحدة التانية
+
+81
+00:09:17,720 --> 00:09:25,300
+بدي تلتين R أربع مرة واحدة خطوة واحدة يبقى بتاخد
+
+82
+00:09:25,300 --> 00:09:32,920
+الشكل التالي هادي واحدوهذا زيرو وهذا هنا ضربنا فيه
+
+83
+00:09:32,920 --> 00:09:37,940
+سالب واحد بيصير موجة واحد بيصير زيرو وهنا كمان
+
+84
+00:09:37,940 --> 00:09:42,520
+زيرو وهنا ضربنا فيه سالب واحد بيصير سالب تلاتة
+
+85
+00:09:42,520 --> 00:09:48,220
+يبقى هنا ويبقى القداش واحد هذا زيرو واحد سالب واحد
+
+86
+00:09:48,220 --> 00:09:57,290
+واحد كما هوو هذه تلاتة كما هي و هنا 001000 و هنا
+
+87
+00:09:57,290 --> 00:10:00,590
+0001
+
+88
+00:10:00,590 --> 00:10:08,050
+صحيح لإن أنا ضارف جدا في تلتين و هذا يصبح اتنين و
+
+89
+00:10:08,050 --> 00:10:13,890
+اللي قبلها سالب اتنين زي مين يبقى هذه سالب اتنين و
+
+90
+00:10:13,890 --> 00:10:19,870
+هذه اللي هي مين اتنين بالشكل اللي عندنا هذا طيبأنا
+
+91
+00:10:19,870 --> 00:10:28,150
+ممكن أخلي هنا هذا zero و أخلي هذا zero يبقى بدأ
+
+92
+00:10:28,150 --> 00:10:34,270
+أضيف الصف التالت إلى الصف الثاني بخلق zero فوق
+
+93
+00:10:34,270 --> 00:10:41,210
+يبقى هنا بدنا نعمل ما يأتي بدأ أحط سهم و أقول هنا
+
+94
+00:10:41,210 --> 00:10:50,530
+سالب R تلاتة to R اتنينيبقى بدى يصير عندى ما يأتي
+
+95
+00:10:50,530 --> 00:10:55,410
+R3
+
+96
+00:10:55,410 --> 00:11:03,710
+to R2 و هذا شو رأيك كمان اضربه في نص و اضيفه للي
+
+97
+00:11:03,710 --> 00:11:06,890
+فوق بالمرة كويس؟
+
+98
+00:11:10,320 --> 00:11:18,100
+طيب نعملها خطوة واحدة يبقى سالب R تلاتة to R اتنين
+
+99
+00:11:18,100 --> 00:11:30,380
+وكذلك نص R اربعة to R تلاتة مرة واحدة يبقى بصير
+
+100
+00:11:30,380 --> 00:11:38,510
+عندنا هنا one zero zero zero واحدهنا سالب R ثلاثة
+
+101
+00:11:38,510 --> 00:11:44,050
+to R اتنين سالب
+
+102
+00:11:44,050 --> 00:11:48,990
+R ثلاثة .. لا لا R ثلاثة بدون سالب صحيح R ثلاثة
+
+103
+00:11:48,990 --> 00:11:55,030
+بدي اضيفه ل R اتنين مباشرة يبقى Zero وهنا واحد
+
+104
+00:11:55,030 --> 00:12:04,270
+وهنا Zero وهنا نص وهنا واحد اضفنا اضافة بعدين نص R
+
+105
+00:12:04,270 --> 00:12:12,620
+اربعةبدي أضيفه ل R ثلاثة بيصير Zero Zero واحد وهنا
+
+106
+00:12:12,620 --> 00:12:18,740
+نص بيصير Zero وهنا نص فيه اتنين اللي هو بواحد
+
+107
+00:12:18,740 --> 00:12:23,560
+بيبقى اللي عندنا هنا جدا سالب واحد وهذا Zero Zero
+
+108
+00:12:23,560 --> 00:12:29,040
+وهنا واحد وهنا اتنين بالشكل اللي عندنا هو ضايل
+
+109
+00:12:29,040 --> 00:12:33,830
+علينا بس خطوة واحدةاللي هتخلص من النص اللي عندنا
+
+110
+00:12:33,830 --> 00:12:38,550
+هذا يبقى بقى اضرب الصف الرابع في سلب نص واضيبه
+
+111
+00:12:38,550 --> 00:12:47,170
+للصف الثاني يبقى هذا بده يعطينا سالب نص R أربعة to
+
+112
+00:12:47,170 --> 00:12:55,670
+R تلاتة بنحصل على ما يأتي هاي واحد zero zero zero
+
+113
+00:12:55,670 --> 00:13:04,810
+واحد او هنا zero واحدزي رو زي رو و هنا اه استني
+
+114
+00:13:04,810 --> 00:13:09,990
+شوية احنا بقول سالب نص اه اربع يبقى هنا بيصير قدير
+
+115
+00:13:09,990 --> 00:13:16,630
+سالب واحد مع واحد بيصير زي رو مظبوط هيك مرة تانية
+
+116
+00:13:16,630 --> 00:13:22,020
+بالأول ماليكم معاك الصف الأول حاطيته زي ما هوصفى
+
+117
+00:13:22,020 --> 00:13:29,320
+التانى بقول سالب نص اقل .. لأ صفى التانى .. سالب
+
+118
+00:13:29,320 --> 00:13:35,640
+نص .. لأ هذا سالب نص اقل اربعة و قارى اتنين ..
+
+119
+00:13:35,640 --> 00:13:41,450
+ايوة لقارى اتنينيبقى لارتنين بيصير عندنا هنا 00
+
+120
+00:13:41,450 --> 00:13:46,950
+مظبوط وهذا 0010
+
+121
+00:13:46,950 --> 00:13:53,850
+-1 وهنا 00012
+
+122
+00:13:53,850 --> 00:13:59,070
+الشكل اللي عندناإذاً الـ System اللي وصلته يا بنات
+
+123
+00:13:59,070 --> 00:14:03,890
+هذا اللي هو X1 يساوي واحد و X2 يساوي Zero و X3
+
+124
+00:14:03,890 --> 00:14:08,030
+يساوي سالب واحد و X4 يساوي اتنين مكافئ للـ System
+
+125
+00:14:08,030 --> 00:14:12,710
+الأصل اللي همين الـ Star اللي عندنا يبقى أصبح حل
+
+126
+00:14:12,710 --> 00:14:16,630
+المعادلة الـ Star أو الـ System الـ Star هو حل هذا
+
+127
+00:14:16,630 --> 00:14:23,790
+الـ System لذلك برفض أقول له solution of
+
+128
+00:14:23,790 --> 00:14:39,520
+thesystem start with x1 و x2 و x3 و x4 بيبقى يساوي
+
+129
+00:14:39,520 --> 00:14:47,880
+يعني four triple من واحد زيرو سالف واحد اتنين
+
+130
+00:14:47,880 --> 00:14:54,800
+بالشكل اللي عندنا هذا خلينا نسأل السؤال التاليالان
+
+131
+00:14:54,800 --> 00:15:01,240
+هل ال system star هذا consistent ولا inconsistent؟
+
+132
+00:15:01,240 --> 00:15:06,240
+consistent لأنه لجيت حل مرة ليه فده اقول ان لو كان
+
+133
+00:15:06,240 --> 00:15:11,000
+حل او عدد لنهائي من الحلول يبقى بسمي ال system
+
+134
+00:15:11,000 --> 00:15:13,400
+consistent؟
+
+135
+00:15:15,600 --> 00:15:19,720
+طيب إحنا لغا ناخدنا أربعة أمثلة زي ما انتوا شايفين
+
+136
+00:15:19,720 --> 00:15:26,600
+وكل واحد فيهم شكل واتساب درجنا من المعادلتين في
+
+137
+00:15:26,600 --> 00:15:31,760
+مجهولين لغا ما وصلنا إلى أربعة معادلات في أربعة
+
+138
+00:15:31,760 --> 00:15:39,390
+مجاهينبنجي ناخد مثال بيختلف شكلا عن الأمثلة اللي
+
+139
+00:15:39,390 --> 00:15:47,190
+فاتت لكن بيحمل نفس الفكرة يبقى مثال رقم خمسة هذا
+
+140
+00:15:47,190 --> 00:15:53,050
+من الكتاب سؤال تسعة عشر نمرة ايه بيقول four what
+
+141
+00:15:53,050 --> 00:16:02,890
+values four what values ما هي القيم اللي بتاخدها a
+
+142
+00:16:02,890 --> 00:16:11,530
+andb بحيث أن for what value of a does the system
+
+143
+00:16:11,530 --> 00:16:19,910
+does the system does
+
+144
+00:16:19,910 --> 00:16:19,910
+the system
+
+145
+00:16:33,010 --> 00:16:41,970
+اللي هو x واحد ناقص اتنين x اتنين يسوي a وناقص
+
+146
+00:16:41,970 --> 00:16:49,270
+تلاتة x واحد زائد ستة x اتنين بده يسوي b هذا هو ال
+
+147
+00:16:49,270 --> 00:16:57,110
+system have a solution have a
+
+148
+00:16:57,110 --> 00:16:58,690
+solution
+
+149
+00:17:33,750 --> 00:17:39,630
+سؤال مرة تانية يقول لي ما هي القيم التي تاخدها كل
+
+150
+00:17:39,630 --> 00:17:46,010
+من إيوا بي بحيث أن هذا ال system يكون له حل تمام
+
+151
+00:17:46,010 --> 00:17:52,530
+لما قول حل ما قلتش حل وحيدقد يكون حل وحيد وقد يكون
+
+152
+00:17:52,530 --> 00:17:57,790
+عدد لا نهائي من الحلول المهم أن يكون هناك حل بغض
+
+153
+00:17:57,790 --> 00:18:01,830
+النظر عن شكل الحل يعني بدي ايش القلم تاخدها ايه
+
+154
+00:18:01,830 --> 00:18:06,090
+وبين اذا بروح ببدأ بالمصفوفة المؤسسة زي ما كنت
+
+155
+00:18:06,090 --> 00:18:11,630
+بشتغل في الأربعة أمثلة الماضية يبقى هنا بقوله
+
+156
+00:18:11,630 --> 00:18:12,610
+solution
+
+157
+00:18:14,930 --> 00:18:24,930
+بعدين للمصوفة الموسعى 1-2-3-6 و هنا A و هنا B
+
+158
+00:18:24,930 --> 00:18:30,870
+بالشكل اللي عناها تمام؟ بدي أحاول أخلي هذا Zero
+
+159
+00:18:30,870 --> 00:18:36,910
+يبقى بضرب الصف الأول فيه تلاتة و بضيفه للصف التاني
+
+160
+00:18:36,910 --> 00:18:45,940
+يبقى هنا تلاتة R1 to R2 نفس العددالصف الأول زي ما
+
+161
+00:18:45,940 --> 00:18:53,160
+هو واحد سالف اتنين a الصف التاني zero يعني ضربنا
+
+162
+00:18:53,160 --> 00:18:59,120
+فيه تلاتة في سالف ستة مع ستة في zero هنا ضربنا فيه
+
+163
+00:18:59,120 --> 00:19:05,560
+تلاتة اللي بيصير تلاتة a زائد ال b بالشكل اللي
+
+164
+00:19:05,560 --> 00:19:08,440
+عندنا تمام
+
+165
+00:19:09,470 --> 00:19:13,430
+من هذا الكلام ماذا نستنتج يا بنات ان ثلاثة a زائد
+
+166
+00:19:13,430 --> 00:19:20,110
+بي كده Zero اصلا الله يرضى يعني كأنه هنا Zero X
+
+167
+00:19:20,110 --> 00:19:26,290
+واحد زائد Zero X اتنين زائد ثلاثة a زائد بي وهنا X
+
+168
+00:19:26,290 --> 00:19:30,630
+واحد نقص اتنين X اتنين زائد ايه المعادلة الأولى
+
+169
+00:19:30,630 --> 00:19:37,190
+تمام يبقى باجي بقول له the above system
+
+170
+00:19:39,090 --> 00:19:50,930
+has a solution of التلاتة a زائد ال V بدل ساوية U
+
+171
+00:19:51,930 --> 00:19:57,110
+يعني أي قيمتين أخدهم لأي و بي بيخلوه للمعادلة
+
+172
+00:19:57,110 --> 00:20:03,150
+تساوي zero بتبقى هي عبارة عن القيم اللي بتخلي لهذا
+
+173
+00:20:03,150 --> 00:20:06,950
+ال system حل بس ماقالليش هات الحل لو قاللي هات
+
+174
+00:20:06,950 --> 00:20:12,190
+الحل بدي أروحالقيمة اللى بدى أحطها وبدى أطبقها
+
+175
+00:20:12,190 --> 00:20:16,390
+وبالتالي كل واحد بيطلع عنده إيه حل الشكل يعني كام
+
+176
+00:20:16,390 --> 00:20:21,830
+حل لهذه أو لهذا ال system بيصير عدد لانهائي من
+
+177
+00:20:21,830 --> 00:20:27,370
+الحلول طب حدا فيكم بتقدر تعطيني قيمة لإيه وقيمة
+
+178
+00:20:27,370 --> 00:20:34,480
+لبيه بتخلي لهذا ال system حل واحد أسالب تلاتةراحت
+
+179
+00:20:34,480 --> 00:20:39,560
+أخدت إحدى الأخوات A بواحد و أخدت B بسالب تلاتة
+
+180
+00:20:39,560 --> 00:20:45,860
+كلام مظبوطواحدة راحت أخدت الـ A بتلت وB بسالب واحد
+
+181
+00:20:45,860 --> 00:20:51,300
+وواحدة أخدت الـ A باثنين وواحدة أخدت الـ B بسالب
+
+182
+00:20:51,300 --> 00:20:55,940
+ستة يعني قيم كثيرة إيش بيجي في بالك قيم اتحقق
+
+183
+00:20:55,940 --> 00:21:00,880
+المعادلة بتخلي لهذا solution حل يبقى the above
+
+184
+00:21:00,880 --> 00:21:05,060
+system has a solution إذا كانت ثلاثة A زائد B
+
+185
+00:21:05,060 --> 00:21:09,920
+يساوي Zero و بعدين حط القيم اللي بدك إياهاعلى أي
+
+186
+00:21:09,920 --> 00:21:15,960
+حال الان وصلنا الى نهاية هذا ال section و لذلك
+
+187
+00:21:15,960 --> 00:21:22,600
+وصلنا الى exercises اتنين واحد المسائل التالية
+
+188
+00:21:22,600 --> 00:21:31,810
+اتنين وخمسة وسبعةو تسعة و احداش و تلتاش و ستاش و
+
+189
+00:21:31,810 --> 00:21:40,790
+سبعتاش و كذلك تمانتاش و تسعة و تاشر بيه طبعا احنا
+
+190
+00:21:40,790 --> 00:21:46,310
+حلنالك انت بتروح تحلي من اللي هو بيه من هذا
+
+191
+00:21:58,750 --> 00:22:04,890
+بننتقل الان الى section 222 اللى هو ال homogenous
+
+192
+00:22:04,890 --> 00:22:13,010
+system اللى هو المعادلات او الأنظمة المتجانسة يبقى
+
+193
+00:22:13,010 --> 00:22:19,250
+section 222 اللى هى ال homogeneous
+
+194
+00:22:27,750 --> 00:22:32,550
+يبقى الـ homogeneous systems
+
+195
+00:22:32,550 --> 00:22:36,650
+الأنظمة
+
+196
+00:22:36,650 --> 00:22:42,510
+المتجانسة بتذكروا ذكرنا لها تعريف قبل ذلك ولذلك
+
+197
+00:22:42,510 --> 00:22:47,470
+بدنا نروح بس نكرر تكرار لهذا التعريف هو ال system
+
+198
+00:22:47,470 --> 00:22:53,010
+للعمود الثوابط هذا بيكون كله أسفارا يبقى
+
+199
+00:22:53,010 --> 00:22:53,670
+definition
+
+200
+00:22:58,620 --> 00:23:10,360
+The homogeneous linear system
+
+201
+00:23:10,360 --> 00:23:14,080
+is
+
+202
+00:23:14,080 --> 00:23:18,540
+a system
+
+203
+00:23:18,540 --> 00:23:22,260
+in the form
+
+204
+00:23:28,810 --> 00:23:37,730
+A11X1 A12X2 A1NXN0
+
+205
+00:23:37,730 --> 00:23:42,170
+A21X1
+
+206
+00:23:42,170 --> 00:23:45,470
+A22X2
+
+207
+00:23:45,470 --> 00:23:49,710
+A2NXN0
+
+208
+00:23:49,710 --> 00:23:54,630
+A M1X1
+
+209
+00:23:57,270 --> 00:24:04,530
+AM2X2 زائد زائد AMNXN
+
+210
+00:24:04,530 --> 00:24:09,770
+زائد زائد AMNXN زائد زائد AMNXN
+
+211
+00:24:09,770 --> 00:24:16,310
+زائد AMNXN زائد AMNXN
+
+212
+00:24:16,310 --> 00:24:18,990
+زائد AMNXN زائد AMNXN زائد AMNXN زائد AMNXN زائد
+
+213
+00:24:18,990 --> 00:24:18,990
+AMNXN زائد AMNXN زائد AMNXN زائد AMNXN زائد AMNXN
+
+214
+00:24:18,990 --> 00:24:18,990
+زائد AMNXN زائد AMNXN زائد AMNXN زائد AMNXN زائد
+
+215
+00:24:18,990 --> 00:24:18,990
+AMNXN زائد AMNXN زائد AMNXN زائد AMNXN زائد AMNXN
+
+216
+00:24:18,990 --> 00:24:18,990
+زائد AMNXN زائد AMNXN زائد AMNXN زائد AMNXN زائد
+
+217
+00:24:18,990 --> 00:24:22,290
+AMNXN زائد AMNXN زائد AMNXN
+
+218
+00:24:22,290 --> 00:24:27,410
+زيبقى هتقسم هذه الـ remark إلى نقطتين النقطة
+
+219
+00:24:27,410 --> 00:24:36,570
+الأولى The homogeneous system استعارة اللي عندنا
+
+220
+00:24:36,570 --> 00:24:46,810
+هذا is always has a solution is always has a
+
+221
+00:24:46,810 --> 00:24:51,650
+solution دائما بلقيله حل because
+
+222
+00:24:55,830 --> 00:25:00,410
+it has because
+
+223
+00:25:00,410 --> 00:25:08,490
+it has at least the
+
+224
+00:25:08,490 --> 00:25:17,750
+trivial solution ايش
+
+225
+00:25:17,750 --> 00:25:23,550
+ال trivial solution الو x واحد و x اتنين ونظل
+
+226
+00:25:23,550 --> 00:25:31,410
+ماشيين لغاية xnبدي يساوي zero و zero و كذلك zero
+
+227
+00:25:31,410 --> 00:25:39,510
+النقطة الثانية the homogeneous system يبقى هنضيف
+
+228
+00:25:39,510 --> 00:25:45,630
+عليها كمان عبارة قبل ما نبدأ النقطة التانية يبقى
+
+229
+00:25:45,630 --> 00:25:55,070
+باجي بقول sir the homogeneous system
+
+230
+00:25:56,240 --> 00:26:04,940
+a star is consistent is consistent
+
+231
+00:26:04,940 --> 00:26:12,420
+بنجي إلى النقطة الثانية the homogeneous system a
+
+232
+00:26:12,420 --> 00:26:23,740
+star the homogeneous system a star of m equations
+
+233
+00:26:23,740 --> 00:26:41,630
+ofm equations and n unknowns has
+
+234
+00:26:41,630 --> 00:26:45,830
+infinite
+
+235
+00:26:45,830 --> 00:26:55,190
+number of solutions infinite number of
+
+236
+00:26:57,200 --> 00:27:03,940
+Solutions Infinite number of solutions that
+
+237
+00:27:03,940 --> 00:27:07,140
+contains
+
+238
+00:27:07,140 --> 00:27:16,640
+the trivial solution that
+
+239
+00:27:16,640 --> 00:27:21,440
+contains the trivial solution
+
+240
+00:27:28,560 --> 00:27:32,740
+FM أقل من N
+
+241
+00:27:58,990 --> 00:28:14,570
+كذبت one find the solution of the system x
+
+242
+00:28:14,570 --> 00:28:24,550
+واحد ناقص x اتنين ناقص تلاتة x تلاتة بيساوي زي
+
+243
+00:28:24,550 --> 00:28:32,040
+واحد x واحد زي x اتنينزائد اكس تلاتة بدل ساوي زيرو
+
+244
+00:28:32,040 --> 00:28:41,120
+اتنين اكس واحد زائد اتنين اكس اتنين زائد اكس تلاتة
+
+245
+00:28:41,120 --> 00:28:44,740
+كله بدل ساوي زيرو
+
+246
+00:29:18,390 --> 00:29:23,190
+النقطة الأولى هو تعريف الـ homogeneous system
+
+247
+00:29:23,190 --> 00:29:28,450
+النقطة الثانية هي الملاحظة التي تتكون من نقطتين
+
+248
+00:29:28,450 --> 00:29:32,610
+وهذه تعطينا مؤشر لحل الـ homogeneous system
+
+249
+00:29:33,240 --> 00:29:37,060
+الدفينيشن بيقول الـ homogeneous literal system is
+
+250
+00:29:37,060 --> 00:29:41,800
+a system in the form يبقى معادلات قطية بس الثوابط
+
+251
+00:29:41,800 --> 00:29:49,080
+كلها أصفار لو كان استبدلنا أحد الأصفار برقم بيبطل
+
+252
+00:29:49,080 --> 00:29:52,980
+يصير homogeneous system بيصير non homogeneous
+
+253
+00:29:52,980 --> 00:29:57,320
+systemعلى أي حال ، أنا مدير الـ System بهذا الشكل
+
+254
+00:29:57,320 --> 00:30:01,880
+ما هي أخبار الحلول بتابعته بروح بقول النقطة الأولى
+
+255
+00:30:01,880 --> 00:30:06,780
+اللي هو مدير الـ System Star دائماً و أبداً له حل
+
+256
+00:30:06,780 --> 00:30:13,520
+على الأقل هو الحل الصفري لأن لو شيلت X1 و X2 و Xn
+
+257
+00:30:13,520 --> 00:30:18,320
+في كل من المعادلة و حطيت بدلها صفر بصير الـ System
+
+258
+00:30:18,320 --> 00:30:24,320
+صحية بصير 00000 بتحقق أي معادلةأو بتحقق كل
+
+259
+00:30:24,320 --> 00:30:28,140
+المعادلات اللي موجودة ورا في هذا ال system ومن هنا
+
+260
+00:30:28,140 --> 00:30:32,700
+بروح بقول له ال homogenous system على الأقل له
+
+261
+00:30:32,700 --> 00:30:38,660
+الحل الصفري تمام تمام يعني معنى هذا الكلام أن هذا
+
+262
+00:30:38,660 --> 00:30:43,940
+ال system دائما و أبداConsistent عمروش بيكون
+
+263
+00:30:43,940 --> 00:30:48,940
+inconsistent على الإطلاق دائما و أبدا consistent
+
+264
+00:30:48,940 --> 00:30:54,460
+لأنه بيحتوي على أو له الحل الصفري أو الحل البديهي
+
+265
+00:30:54,460 --> 00:31:00,160
+أو الحل التافعي ال trivial solution 000 هذا النقطة
+
+266
+00:31:00,160 --> 00:31:03,920
+الأولى النقطة الثانية ال homogenous system star
+
+267
+00:31:03,920 --> 00:31:10,260
+اللي في M من المعادلات و N من المجاهدشايفة M من
+
+268
+00:31:10,260 --> 00:31:15,860
+المعادلات وعندي N من المجاهد يبقى عندي X1 و X2
+
+269
+00:31:15,860 --> 00:31:23,500
+لغاية XN وعندي عدد من المعادلات يساوي M يمكن هدول
+
+270
+00:31:23,500 --> 00:31:27,680
+يكونوا جد بعض زي ما احنا جايلين هنا ويمكن يكونوا
+
+271
+00:31:27,680 --> 00:31:33,700
+مختلفات طيب تعالى نشوف ايش بيقول هنا ال homogenous
+
+272
+00:31:33,700 --> 00:31:39,030
+system of M equations and N unknownsلديها عدد محدد
+
+273
+00:31:39,030 --> 00:31:43,230
+من الحلول التي تحتوي على هذه الحلول التعريفة إذا
+
+274
+00:31:43,230 --> 00:31:48,450
+كانت يعني يا بنات لو عندي عدد لنهائي من الحلول
+
+275
+00:31:48,450 --> 00:31:53,110
+لهذا ال system فإن هذا العدد النهائي دائما و أبدا
+
+276
+00:31:53,110 --> 00:31:58,620
+يجتمع على مين؟على الحل الصفري يعني يا بيكون الحل
+
+277
+00:31:58,620 --> 00:32:03,680
+الصفري مستقل لحاله مافيش غيره يا إما بكون عندي عدد
+
+278
+00:32:03,680 --> 00:32:08,540
+لنهائي من الحلول تجتمل على الحل الصفري اللي موجود
+
+279
+00:32:08,540 --> 00:32:12,820
+تمام يبقى هيك بيقول النظام اللي عندنا بقوله كويس
+
+280
+00:32:12,820 --> 00:32:17,160
+طيب يا بنات خليني أسأل قبل ما أكمل السؤال التالي
+
+281
+00:32:17,160 --> 00:32:21,900
+هل ال non homogeneous system يحتوي على الحل
+
+282
+00:32:21,900 --> 00:32:29,190
+الصفري؟يعني هل الحل الصفري أحد حلول الـ non
+
+283
+00:32:29,190 --> 00:32:34,310
+-homogeneous system؟ ولا
+
+284
+00:32:34,310 --> 00:32:39,350
+عمره بيحصل ولا عمره بيحصل ليش؟ لأن لو قلت الكلام
+
+285
+00:32:39,350 --> 00:32:44,150
+هذا صاحب بدي أشيل كل ال axis و أحط بدلها أصفرًا
+
+286
+00:32:44,150 --> 00:32:48,790
+صار الطرف الشمال كله أصفر بس الطرف اليمين أعداد
+
+287
+00:32:48,790 --> 00:32:53,750
+بنفع الصفر يستوي أعداد؟يعني ماعنديش حل يبقى بناء
+
+288
+00:32:53,750 --> 00:32:59,010
+عليه الـ Non-homogeneous system لا يمكن أن يكون
+
+289
+00:32:59,010 --> 00:33:04,990
+الحل الصفري هو أحد الحلول له لكن الحل الصفري يكون
+
+290
+00:33:04,990 --> 00:33:10,990
+حلا للـ homogeneous system فقط لا غير قد تأتي هذا
+
+291
+00:33:10,990 --> 00:33:16,210
+إذا جبنا صح وخطأ دلوقتي يبقى ركزي على هذه النقطة
+
+292
+00:33:16,480 --> 00:33:21,240
+بدي أرجع للنقطة الثانية مرة ثانية «شولي» يضمن لي
+
+293
+00:33:21,240 --> 00:33:26,700
+أن في عندي عدد لنهائي من الحلول الذاتي يجتمل على
+
+294
+00:33:26,700 --> 00:33:33,800
+الحل الصفري شرط واحد فقط أن عدد المعادلات أقل من
+
+295
+00:33:33,800 --> 00:33:38,480
+عدد المجاهيل يعني ممكن يكون عندي معادلتين و تلت
+
+296
+00:33:38,480 --> 00:33:45,590
+مجاهيلممكن يكون عندى 3 معادلات و 5 مجاهيل ممكن
+
+297
+00:33:45,590 --> 00:33:51,090
+يكون عندى 10 معادلات و 11 مجهول يعني دائما و أبدا
+
+298
+00:33:51,090 --> 00:33:55,630
+إذا كان عدد المعادلات أقل من عدد المجاهيل
+
+299
+00:33:55,630 --> 00:34:02,510
+automatic لازم يحصل عندى عدد لانهائي من الحلول هي
+
+300
+00:34:02,510 --> 00:34:07,020
+هذه اللى بتقوله النقطة اللى عندها تمامطب نرجع الآن
+
+301
+00:34:07,020 --> 00:34:13,260
+نحاول نطبق ما نقوله على أرض الواقع طيب يا بنات لما
+
+302
+00:34:13,260 --> 00:34:17,160
+يكون عندي عدد لا نهائم الحلول تجتمل على الحل
+
+303
+00:34:17,160 --> 00:34:22,480
+الصفري يعني هذا الحل بيكون أعداد ولا أصفار
+
+304
+00:34:26,360 --> 00:34:30,980
+قد يكون أدد وقد يكون أصفر صح ولا لأ مش احنا بنقول
+
+305
+00:34:30,980 --> 00:34:35,340
+يعني إذا يحتوي على الحل الصفري إذا الحل ال zero
+
+306
+00:34:35,340 --> 00:34:39,540
+أحد هذه الحلول وبعدها تتأعدى لكن الأعداد هل بقدر
+
+307
+00:34:39,540 --> 00:34:45,280
+أجيبهم بالضبط كلهملا بقدرش ممكن أجيبهم صحيح كلهم و
+
+308
+00:34:45,280 --> 00:34:50,920
+ممكن ماقدرش فبتظهر الحل بدلالة رموز يعني أنا بفرض
+
+309
+00:34:50,920 --> 00:34:55,340
+هذه رموز وبالتالي الرموز هذه قد ما بدك حط وبالتالي
+
+310
+00:34:55,340 --> 00:35:00,310
+بيطلع عندك معلنها من الحلولنبدأ بتطبيق هذا على أرض
+
+311
+00:35:00,310 --> 00:35:03,950
+الواقع بيقول هاتلي حل ال system اللي قدامنا هذا
+
+312
+00:35:03,950 --> 00:35:10,070
+يبقى بدي أبدأ بمين بالمصوفة الموسعة اللي قلنا
+
+313
+00:35:10,070 --> 00:35:15,060
+عليها يبقى المصوفة الموسعة على الشكل التانيهذا
+
+314
+00:35:15,060 --> 00:35:21,060
+واحد و هنا سالب واحد و هنا سالب تلاتة و هنا واحد و
+
+315
+00:35:21,060 --> 00:35:27,320
+هنا واحد و هنا واحد و هنا اتنين اتنين واحد و هنا
+
+316
+00:35:27,320 --> 00:35:30,620
+زيرو زيرو زيرو بالشكل اللي عندنا
+
+317
+00:35:33,400 --> 00:35:45,920
+بنخلق هنا أسطار نقص R1 to R2 ونقص R1 to R3 نحصل
+
+318
+00:35:45,920 --> 00:35:52,440
+على ما يأتي الصف الأول زي ما هو 1 سالب 1 سالب 3
+
+319
+00:35:52,440 --> 00:36:01,740
+زيرو الصف التاني زيروو هنا اتنين و هنا اربعة و هنا
+
+320
+00:36:01,740 --> 00:36:07,860
+zero و هنا zero و هنا ضربنا في سالب اتنين بصير
+
+321
+00:36:07,860 --> 00:36:14,180
+اتنين يبقى اربعة و هنا ضربنا في سالب اتنين بصير
+
+322
+00:36:14,180 --> 00:36:21,640
+ستة واحد سبعة و هنا zero و اضحكوابعدين بدي هذا
+
+323
+00:36:21,640 --> 00:36:28,700
+قداش واحد صحيح يبقى بدي نص قاري اتنين يبقى هذا
+
+324
+00:36:28,700 --> 00:36:35,420
+ناخد نص قاري اتنين تصبح المفروفة على الشكل التالي
+
+325
+00:36:35,420 --> 00:36:41,680
+واحد سالب واحد سالب تلاتة زيرو وهنا زيرو واحد
+
+326
+00:36:41,680 --> 00:36:48,880
+اتنين زيرو وهنا زيرو اربع سبعة زيرو بالشكل اللي
+
+327
+00:36:48,880 --> 00:36:54,030
+عندنايبقى هذا بده يعطينا الصف الأول ماليش علاقة
+
+328
+00:36:54,030 --> 00:36:59,590
+فيه بدي على الصف التاني بقول ناقص اربعة R اتنين to
+
+329
+00:36:59,590 --> 00:37:07,830
+R تلت وابتدي تصبح على طبيعي ايش رأيك لو أضفنا كمان
+
+330
+00:37:07,830 --> 00:37:13,550
+الصف الثاني الى الصف الأول بالمرة ماحدش أحسن من
+
+331
+00:37:13,550 --> 00:37:21,840
+هذا إذا لو قل R اتنين to R oneخطوة واحدة يفجأش
+
+332
+00:37:21,840 --> 00:37:25,840
+اللي بده يصير R اتنين ل R one بيظل هنا واحد و
+
+333
+00:37:25,840 --> 00:37:30,120
+بيصير هنا Zero و هنا سالب واحد و هذا Zero واحد
+
+334
+00:37:30,120 --> 00:37:36,520
+اتنين و هنا Zero Zero زي ما هو تمام و هذا Zero زي
+
+335
+00:37:36,520 --> 00:37:42,180
+ما هو ضربته في سالب اربع بيصير Zero بيصير هنا سالب
+
+336
+00:37:42,180 --> 00:37:48,310
+واحد و هنا جداش Zero بالشكل اللي عندنا هذاأنا بديش
+
+337
+00:37:48,310 --> 00:37:52,070
+هذا سالب بدي إياه بالموجب حتى لو ضال بالسالب
+
+338
+00:37:52,070 --> 00:37:57,310
+ماعنديش إياه ماعنديش مشكلة مشكلتنا بدي أخلي هذا ب
+
+339
+00:37:57,310 --> 00:38:02,430
+zero و بدي أخلي هذا ب إياه ب zero يبقى بدي أجي ل R
+
+340
+00:38:02,430 --> 00:38:07,510
+تلاتة أضربه في سالب واحد و أضيفه للصف الأول و
+
+341
+00:38:07,510 --> 00:38:13,510
+أضربه في اتنين و أضيفه للصف الثاني يبقى هذا بدي
+
+342
+00:38:13,510 --> 00:38:22,220
+يعطينااللي هو من سالف R ثلاثة to R one و بعد هيك
+
+343
+00:38:22,220 --> 00:38:29,760
+سالف اتنين والله موجة باتنين موجة باتنين R ثلاثة
+
+344
+00:38:29,760 --> 00:38:37,020
+to R two نفس العالمية هذا واحد وهذا Zero زي ما هو
+
+345
+00:38:37,020 --> 00:38:44,530
+لأنني باضيف سالف R ثلاثة to R oneوهنا بيصير zero و
+
+346
+00:38:44,530 --> 00:38:52,770
+هنا zero و هنا اتنين R three ل R two يبقى هنا zero
+
+347
+00:38:52,770 --> 00:38:58,970
+و هنا واحد و هنا zero و هنا zero و هنا zero و zero
+
+348
+00:38:58,970 --> 00:39:07,230
+سالب واحد و zero بقدر اقوله اخر خطوة سالب R ثلاثة
+
+349
+00:39:07,230 --> 00:39:17,840
+وبالتالي بتصبح المصوفة واحد zero0 1 0 0 0 1 0 0 0
+
+350
+00:39:17,840 --> 00:39:32,680
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+
+351
+00:39:32,680 --> 00:39:32,680
+0
+
+352
+00:39:46,770 --> 00:39:51,470
+solution لا مشكلة فيه بقى solution و الله غيره
+
+353
+00:39:51,470 --> 00:39:55,970
+مافيش مشكلة طب
+
+354
+00:39:55,970 --> 00:40:01,730
+ليش ما طلع الشبنات هنا عدد لنهائي من الحلول ايوة
+
+355
+00:40:01,730 --> 00:40:08,140
+لان عدد المعادلات بساوي عدد المجاهديبقى إذا كان
+
+356
+00:40:08,140 --> 00:40:12,560
+عدد المعادلات يسوي عدد المجاهد يطلع عندي الحل
+
+357
+00:40:12,560 --> 00:40:19,260
+الصفري يطلع عندي عدد عادي عدد عادي غير هيك بصير
+
+358
+00:40:19,260 --> 00:40:23,760
+عدد المعادلات أقل من عدد المجاهد بصير عندي عدد
+
+359
+00:40:23,760 --> 00:40:32,040
+لنهائي من الحلول طيب نجي ناخد كمان مثال يبقى
+
+360
+00:40:32,040 --> 00:40:34,900
+المثال رقم اتنين exactly two
+
+361
+00:40:40,600 --> 00:40:49,100
+solve the system solve the system خلص ال system
+
+362
+00:40:49,100 --> 00:40:58,260
+اللي هو اتنين اكس واحد ناقص اتنين اكس اتنين ناقص
+
+363
+00:40:58,260 --> 00:41:07,320
+اكس تلاتة زائد اكس اربعة بده ساوي زيرو المعادلة
+
+364
+00:41:07,320 --> 00:41:16,230
+التالية ناقص اكس واحدزائد اكس اتنين زائد اكس تلاتة
+
+365
+00:41:16,230 --> 00:41:19,930
+ناقص اتنين اكس اربع زائد اكس اربع زائد اكس اربع
+
+366
+00:41:19,930 --> 00:41:21,710
+زائد اكس اربع زائد اكس اربع زائد اكس اربع زائد اكس
+
+367
+00:41:21,710 --> 00:41:23,890
+اربع زائد اكس اربع زائد اكس اربع زائد اكس اربع
+
+368
+00:41:23,890 --> 00:41:23,890
+زائد اكس اربع زائد اكس اربع زائد اكس اربع زائد اكس
+
+369
+00:41:23,890 --> 00:41:24,010
+اربع زائد اكس اربع زائد اكس اربع زائد اكس اربع
+
+370
+00:41:24,010 --> 00:41:29,190
+زائد اكس اربع زائد اكس اربع زائد اكس اربع زائد اكس
+
+371
+00:41:29,190 --> 00:41:34,930
+اربع زائد اكس اربع ز
+
+372
+00:41:45,650 --> 00:41:51,590
+-2x2-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+373
+00:41:51,590 --> 00:41:51,630
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+374
+00:41:51,630 --> 00:41:53,310
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+375
+00:41:53,310 --> 00:41:56,150
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+376
+00:41:56,150 --> 00:41:59,510
+-2x4-2x4-2x4-2x4-2x4-2x4-2x4-2x4
+
+377
+00:42:08,180 --> 00:42:13,520
+بالنسبة لل system اللى عندنا تتوقعوا ان يكون عندى
+
+378
+00:42:13,520 --> 00:42:20,920
+حل صفري فقط لغير قد يكون و قد لا يكون طب ممكن يكون
+
+379
+00:42:20,920 --> 00:42:29,930
+عدد لنهائي من الحلول يعني مش معقوللا قد يكون عدد
+
+380
+00:42:29,930 --> 00:42:35,690
+المعادلات مشرطناش لم نضع شرطا انه اذا كان عدد
+
+381
+00:42:35,690 --> 00:42:40,490
+المعادلات يساوي عدد المجاهيل فانه لا يوجد الا حلا
+
+382
+00:42:40,490 --> 00:42:45,230
+واحدا ماقلناش هذا الكلام احنا يعني لو جيت انا
+
+383
+00:42:45,230 --> 00:42:50,070
+جامعت و سويت و ضربت و بالاخر طالع عندى الصف كله
+
+384
+00:42:50,070 --> 00:42:58,390
+أصفاراأو صفر طلع أسفارا كيف بدي أجيب قيم x1, x2,
+
+385
+00:42:58,610 --> 00:43:03,070
+x3, x4؟ مش إمكانية إذا في هذه الحلقة بيكون عندي
+
+386
+00:43:03,070 --> 00:43:08,590
+عدد لنهائي من الحلول وهذا العدد يحتوي على الحل
+
+387
+00:43:08,590 --> 00:43:14,950
+الصفري تمام تعالى نشوف هل سؤالنا هذا له حل واحد و
+
+388
+00:43:14,950 --> 00:43:20,990
+الله حل الصفريوالله في عندي عدد لنهائي من الحلول و
+
+389
+00:43:20,990 --> 00:43:26,130
+الله حل قيم عددية عادية فعلا شوف يفجأ أنا بدي أبدأ
+
+390
+00:43:26,130 --> 00:43:33,730
+بالمصوفة الموسعة يفجأ المصوفة الموسعة للشكل التالت
+
+391
+00:43:33,730 --> 00:43:40,270
+هذا اتنين هي سالم اتنين وهي سالم واحد وهنا واحد
+
+392
+00:43:40,500 --> 00:43:46,180
+وهنا سالب واحد واحد واحد سالب اتنين وهنا تلاتة
+
+393
+00:43:46,180 --> 00:43:54,020
+سالب تلاتة وهنا واحد وهنا سالب ستة وهنا اتنين سالب
+
+394
+00:43:54,020 --> 00:44:00,940
+اتنين وهنا Zero وهنا سالب اتنين وهي Zero Zero و
+
+395
+00:44:00,940 --> 00:44:06,320
+Zero بالشكل اللي عندنا شوف يا بنات لما نكتب
+
+396
+00:44:06,320 --> 00:44:11,690
+المعادلاتإذا كان عندى term غيب بروحش أصفه من جانب
+
+397
+00:44:11,690 --> 00:44:15,790
+بعض بخلي واسع مكان غيب حتى لما أجى أكتب مصفوطة
+
+398
+00:44:15,790 --> 00:44:19,490
+المعاملة ماروحش أتلخبط فيها زى عندى هنا في
+
+399
+00:44:19,490 --> 00:44:24,610
+المعادلة 4 X3 مفقودة يبغى أروحش أحط ناقص الدنيا X4
+
+400
+00:44:24,610 --> 00:44:28,210
+جانب ناقص الدنيا بخلي فيه واسع عشان نعرف إن هنا
+
+401
+00:44:28,210 --> 00:44:33,590
+فيه term مفقود وبالتالي هذا المعامل بحطه P0 طيب
+
+402
+00:44:33,590 --> 00:44:39,950
+شوفوا يا عمان الله يبقى أول خطوةبدي أروح أخلي الحد
+
+403
+00:44:39,950 --> 00:44:44,830
+اللي عندنا هذا الأول مجدد واحد صحيح يبقى إلي كل
+
+404
+00:44:44,830 --> 00:44:53,770
+خيار تمام؟ يا إما بضرب هدف ناصر يا إما بطلع هدفه و
+
+405
+00:44:53,770 --> 00:44:58,770
+بروح بضربه في واحد صحيح مش حسن؟ و بت .. ليه بصير
+
+406
+00:44:58,770 --> 00:45:05,440
+عملية صحيح؟ يبقى أنا بدي أبدل R2 مع R1يبقى هاي
+
+407
+00:45:05,440 --> 00:45:12,220
+القطوة اللى عندنا يبقى هنا replace R1
+
+408
+00:45:12,220 --> 00:45:18,440
+and R2 بدي أبدلهم و الباقى بدي أخليه مكانه زي ما
+
+409
+00:45:18,440 --> 00:45:23,900
+يبقى بيجيكي عندك هنا هاي سالف واحد وهنا واحد وهنا
+
+410
+00:45:23,900 --> 00:45:29,530
+واحد وهنا سالف اتنين وهنا زيرهنا اتنين سالب اتنين
+
+411
+00:45:29,530 --> 00:45:36,170
+سالب واحد واحد زيرو تلاتة سالب تلاتة واحد سالب ستة
+
+412
+00:45:36,170 --> 00:45:41,330
+زيرو هنا الصفة الرابعة والاخيرة اتنين سالب اتنين
+
+413
+00:45:41,330 --> 00:45:49,590
+زيرو سالب اتنين زيرو بالشكل هذا الآن هذا بعمل
+
+414
+00:45:49,590 --> 00:45:53,870
+كتابة يرجى بالداجة على الصف الأول أو الأخر وكله
+
+415
+00:45:53,870 --> 00:46:00,220
+فات بسالب واحديبقى ايش بصير عندنا هنا اللي هو سالب
+
+416
+00:46:00,220 --> 00:46:06,200
+اروان فقط لا غير يبقى بالصبح المصوفة على الشكل
+
+417
+00:46:06,200 --> 00:46:13,480
+التالي واحد سالب واحد سالب واحد سالب واحد سالب
+
+418
+00:46:13,480 --> 00:46:21,000
+واحد اتنين هذه فقط لا غير وهذه zero وهذه اتنين
+
+419
+00:46:21,000 --> 00:46:27,710
+سالب اتنين سالب واحد واحد تلاتة سالب تلاتة1 سالب 6
+
+420
+00:46:27,710 --> 00:46:33,930
+اتنين سالب اتنين زيرو سالب اتنين زيرو زيرو زيرو
+
+421
+00:46:33,930 --> 00:46:40,770
+بالشكل اللي عندنا الان بدي اعمل ثلاث خطوات مرة
+
+422
+00:46:40,770 --> 00:46:47,850
+واحدة هتخلق هنا زيرو وهنا زيرو وهنا زيرو يبقى سالب
+
+423
+00:46:47,850 --> 00:46:57,030
+اتنين R واحد ل R اتنين و ل R اربعيبقى بداشي أقوله
+
+424
+00:46:57,030 --> 00:47:08,430
+ما يأتي بدي أخد سالب R1 to R2 and R4 له أربع و بعد
+
+425
+00:47:08,430 --> 00:47:18,430
+هيك طبعا سالب اتنين هنا هذه
+
+426
+00:47:18,430 --> 00:47:25,680
+سالب اتنين R1 لها و بعد هيك سالب تلاتة R1two are
+
+427
+00:47:25,680 --> 00:47:32,140
+three كله مرة واحدة يبقى الصف الأول زي ما هو واحد
+
+428
+00:47:32,140 --> 00:47:38,840
+سالب واحد سالب واحد اتنين Zero الصف التاني هذا صار
+
+429
+00:47:38,840 --> 00:47:45,260
+Zero وهذا ضربته في سالب اتنين بصير هنا Zero وهذا
+
+430
+00:47:45,260 --> 00:47:50,200
+ضربته في سالب اتنين بصير هنا واحد وهنا هذا بصير
+
+431
+00:47:50,200 --> 00:47:56,160
+سالب تلاتة وهذه Zeroهذا ضربت في سالب تلاتة بصير
+
+432
+00:47:56,160 --> 00:48:02,740
+Zero هذا بصير تلاتة و سالب تلاتة كمان Zero هذا
+
+433
+00:48:02,740 --> 00:48:08,420
+ضربت في سالب تلاتة بصير تلاتة واحد أربعة هذا سالب
+
+434
+00:48:08,420 --> 00:48:16,170
+ستة و سالب ستة بصير سالب أتماشى و هنا Zeroوهذا
+
+435
+00:48:16,170 --> 00:48:21,750
+zero هنا وهذا ربطه في سالف اتنين بصير هنا zero
+
+436
+00:48:21,750 --> 00:48:27,430
+وهذا بيصير هنا اتنين وهذا ربطه في سالف اتنين بيصير
+
+437
+00:48:27,430 --> 00:48:34,750
+سالف اربعة يفجر سالف ستة وهنا اتنين وهنا zero اللي
+
+438
+00:48:34,750 --> 00:48:38,590
+ماصارش عندي leading هنا واحد امان طالع صار في
+
+439
+00:48:38,590 --> 00:48:43,150
+أسرار اللي بجهرش أسوي فيها حاجة إذا مداجي على مين؟
+
+440
+00:48:43,470 --> 00:48:51,110
+على الصف التالت و اضربه في ربع تمام؟ يبقى باجي
+
+441
+00:48:51,110 --> 00:48:58,430
+بقوله هنا انا بدي ربع فهعرف تلاتة بصيله انما يعني
+
+442
+00:48:58,430 --> 00:49:05,250
+اللي هو واحد سالب واحد سالب واحد اتنين Zero Zero
+
+443
+00:49:05,250 --> 00:49:13,430
+Zero واحد سالب تلاتة Zeroو هنا zero .. zero ..
+
+444
+00:49:13,430 --> 00:49:20,690
+واحد .. و هنا سالب تلاتة .. zero .. و هنا zero ..
+
+445
+00:49:20,690 --> 00:49:29,030
+zero .. اتنين .. سالب ستة .. zero .. بالشكل هذا طب
+
+446
+00:49:29,030 --> 00:49:35,170
+ايش رأيك تخلص من الصف التالت و الراجل مرة واحدة
+
+447
+00:49:35,170 --> 00:49:40,750
+نبدأ دي على الصف الثانيأضربه في سالب واحد و أضيفه
+
+448
+00:49:40,750 --> 00:49:45,730
+للصف التالت و أضربه في سالب اتنين و أضيفه للصف
+
+449
+00:49:45,730 --> 00:49:55,130
+الرابع يبقى باقي بقوله هنا سالب R اتنين R اتنين to
+
+450
+00:49:55,130 --> 00:50:03,750
+R تلت و سالب اتنين R اتنين to R اربع الشكل اللي
+
+451
+00:50:03,750 --> 00:50:08,860
+علناه هذا يبقى بتصبح على الشكل التالتهنا واحد وهنا
+
+452
+00:50:08,860 --> 00:50:15,280
+سالب واحد وهنا سالب واحد وهنا اتنين وهنا زيرو وهنا
+
+453
+00:50:15,280 --> 00:50:23,140
+زيرو زيرو وهنا واحد سالب تلاتة وهنا زيرو وهنا زيرو
+
+454
+00:50:23,140 --> 00:50:29,480
+زيرو زيرو زيرو وهنا زيرو زيرو زيرو زيرو زيرو زيرو
+
+455
+00:50:29,480 --> 00:50:29,480
+زيرو
+
+456
+00:50:29,480 --> 00:50:34,940
+زيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزيروزير
+
+457
+00:50:36,150 --> 00:50:43,210
+كمان خطوة هذا ال system هنا بدأ الحل يبقى هذا بقدر
+
+458
+00:50:43,210 --> 00:50:55,790
+اشيله بالشكل ان انا بدي
+
+459
+00:50:55,790 --> 00:51:05,860
+اضيف الصف التاني للصف الاول يبقى R2والله ايش رايك
+
+460
+00:51:05,860 --> 00:51:11,640
+انك دلوقت نعملهم لو عملناها مع الخطوة الأولى هذه
+
+461
+00:51:11,640 --> 00:51:19,540
+ليها بلاش خطوة جديدة and r2
+
+462
+00:51:19,540 --> 00:51:29,140
+to r1 يبقى هذه بالصير zero وهذه بالصير سالب واحد
+
+463
+00:51:29,140 --> 00:51:30,320
+فقط ده غير
+
+464
+00:51:35,780 --> 00:51:42,720
+أكتر من هيك بنقدر نعمل؟ لأ يبقى ال system باربع
+
+465
+00:51:42,720 --> 00:51:49,180
+معادلات الى مين الى معادلتين المعادلة الأولى x
+
+466
+00:51:49,180 --> 00:51:56,960
+واحد ناقص x اتنين ناقص x أربعة بده يسوي zero
+
+467
+00:51:56,960 --> 00:52:03,380
+والمعادلة التانية اصبح x واحد على x تلاتة
+
+468
+00:52:16,330 --> 00:52:24,200
+معادلتين في أربعة مجهوليبقى فيش إمكانية إلا أحط
+
+469
+00:52:24,200 --> 00:52:29,680
+قيمتين من عندي تمام يبقى بعدي أختار اللي بدكيها أي
+
+470
+00:52:29,680 --> 00:52:34,080
+قيمة أحطيها من عندك و أشوف إيش اللي بده يحصل يبقى
+
+471
+00:52:34,080 --> 00:52:43,380
+أنا لو روحت جيب main goal put مثلا x4 تساوي اللي
+
+472
+00:52:43,380 --> 00:52:52,290
+بدكيها x4 نحطها بواحد او الا x4 ب ax4 تساوي a مثلا
+
+473
+00:52:52,290 --> 00:53:03,290
+and x2 تساوي b نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+474
+00:53:03,290 --> 00:53:03,310
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+475
+00:53:03,310 --> 00:53:06,630
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+476
+00:53:06,630 --> 00:53:06,630
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+477
+00:53:06,630 --> 00:53:06,650
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+478
+00:53:06,650 --> 00:53:16,530
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+479
+00:53:21,350 --> 00:53:27,450
+يبقى ال X تلاتة و X أربعة نحطوها بـ A يبقى بده
+
+480
+00:53:27,450 --> 00:53:37,990
+ساوي تلاتة A يبقى أصبح that solution is X واحد X
+
+481
+00:53:37,990 --> 00:53:45,850
+اتنين X تلاتة X أربعة أساوية X واحداللي هي بقداش
+
+482
+00:53:45,850 --> 00:53:59,850
+طلعناها A زائد الـ B X2 حطناها V X3 ثلاثة A X4 دي
+
+483
+00:53:59,850 --> 00:54:06,490
+A بالشكل اللي عندنا يبقى هذا أصبح الحل طب هل هذا
+
+484
+00:54:06,490 --> 00:54:11,810
+يحتوي على ال trivial solution الإجابة نعم حطيت
+
+485
+00:54:11,810 --> 00:54:12,990
+قيود على A وB
+
+486
+00:54:16,070 --> 00:54:22,410
+بحصل على حل الصفري اذا
+
+487
+00:54:22,410 --> 00:54:31,390
+صار عندي عدد لنهائي من الحلول system has
+
+488
+00:54:31,390 --> 00:54:41,510
+infinite number of solutions
+
+489
+00:54:42,440 --> 00:54:54,640
+that is this system this system is consistent
+
+490
+00:54:54,640 --> 00:54:58,600
+لازلنا
+
+491
+00:54:58,600 --> 00:55:03,400
+في نفس ال section و لمّا ننتهي بعد للمرة القادمة
+
+492
+00:55:03,400 --> 00:55:05,080
+ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6wYdmeO7zro_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6wYdmeO7zro_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..11cb1147b8018646d05f973da3f1861c5d8b624b
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6wYdmeO7zro_postprocess.srt
@@ -0,0 +1,1404 @@
+1
+00:00:21,160 --> 00:00:26,220
+بسم الله الرحمن الرحيم نعود الآن إلى نهاية
+
+2
+00:00:26,220 --> 00:00:29,920
+المحاضرة الماضية المحاضرة الماضية بدأنا بموضوع ال
+
+3
+00:00:29,920 --> 00:00:37,240
+diagonalization وكيف نعمل الهو diagonalize للمصوفة
+
+4
+00:00:37,240 --> 00:00:41,780
+بمعنى خليها مصوفة قطرية ابتدنا بتعريف ال similar
+
+5
+00:00:41,780 --> 00:00:47,180
+matrix فقلنا ان ال similar matrix بإذا جدرت لاجي
+
+6
+00:00:47,180 --> 00:00:53,710
+مصوفة تانية Kبحيث الكي هذه non zero matrix يعني او
+
+7
+00:00:53,710 --> 00:00:57,610
+non singular matrix ايش يعني يعني المعكوس تبعها
+
+8
+00:00:57,610 --> 00:01:02,470
+موجود بحيث اللي بيبدأ يسوي ال K inverse في ال A في
+
+9
+00:01:02,470 --> 00:01:06,750
+الكي تمام؟ واخدنا على ذلك مثالا واحدا بعد ما
+
+10
+00:01:06,750 --> 00:01:11,440
+أثبتناإن إذا كانت ال A similar ل B فإن B similar ل
+
+11
+00:01:11,440 --> 00:01:14,940
+A وفي نفس اللغة وفي نفس الوقت A is similar to
+
+12
+00:01:14,940 --> 00:01:18,580
+itself تمام يبقى هذا اللي خدناه المحاضرة الماضية و
+
+13
+00:01:18,580 --> 00:01:23,160
+الآن بدنا نضيق .. أخدنا طبعا مثال واحد لسه ياما
+
+14
+00:01:23,160 --> 00:01:27,500
+ناخد أمثلة فبدنا نبدأ نحط بعض المعلومات النظرية
+
+15
+00:01:27,500 --> 00:01:33,160
+الأساسية أو العمودي الفقري في هذا sectionبيقول لي
+
+16
+00:01:33,160 --> 00:01:37,540
+to show that the given n by n matrix is a is
+
+17
+00:01:37,540 --> 00:01:41,120
+similar to a diagonal matrix و ال diagonal matrix
+
+18
+00:01:41,120 --> 00:01:44,180
+هي بكتوبها بالشكل هذا من حد ما تشوفيها دي يعني
+
+19
+00:01:44,180 --> 00:01:49,800
+مصوفة قطرية جميع عناصرها أصفرا معادة عناصرالقطر
+
+20
+00:01:49,800 --> 00:01:57,540
+الرئيسي نأخذ النظرية التالية طبعا من اللمدات هذول
+
+21
+00:01:57,540 --> 00:02:00,400
+اللمدة واحد و اللمدة اتنين و اللمدة ان هي ال eigen
+
+22
+00:02:00,400 --> 00:02:07,440
+values مش حياله مش اي ارقام يبقى ارقام محددةطيب
+
+23
+00:02:07,440 --> 00:02:11,480
+النظرية بتقول إيه؟ the n by n matrix A is similar
+
+24
+00:02:11,480 --> 00:02:16,420
+to a diagonal matrix ملاحظي المرة اللي فاتت بدينا
+
+25
+00:02:16,420 --> 00:02:21,060
+canvas A K طلت عني مصروفة قطرية في الآخر، مصبوط
+
+26
+00:02:21,060 --> 00:02:24,920
+ولا لأ؟ المصروف القطرية العمودي الفقري قيمة ال two
+
+27
+00:02:24,920 --> 00:02:28,870
+landers اللي طلوا عندي بالضبطيبقى هنا لما أقول الـ
+
+28
+00:02:28,870 --> 00:02:32,650
+A is similar to a diagonal matrix if and only if
+
+29
+00:02:32,650 --> 00:02:36,350
+it has a set of linearly independent eigenvectors
+
+30
+00:02:36,350 --> 00:02:43,250
+K1 وK2 لغاية KM الكلام هذا بدي أعيد صياغته مرة
+
+31
+00:02:43,250 --> 00:02:48,750
+تانية باجي بقول that is لو كان عند المصوفة K هذه
+
+32
+00:02:48,750 --> 00:02:53,670
+مصوفة K K1 هو العمود الأول K2 العمود التالت KN
+
+33
+00:02:53,670 --> 00:03:01,400
+العمود رقم Mوكل eigen vector هذا مناظر لمن؟ مناظر
+
+34
+00:03:01,400 --> 00:03:04,500
+لل eigen value اللي هي لاندا واحد والتاني لاندا
+
+35
+00:03:04,500 --> 00:03:08,920
+اتنين والتالتة لاندا تلاتة والاخر لاندا in them ال
+
+36
+00:03:08,920 --> 00:03:14,340
+K inverse A في ال K بده يساوي المصوفة اللي عندها
+
+37
+00:03:14,340 --> 00:03:18,880
+دي يعني بده يساوي المصوفة لجميع عناصرها أصفرا ما
+
+38
+00:03:18,880 --> 00:03:25,450
+عدا عناصر قطة الرئيسي بيكونوا على أسرها هو من؟هذه
+
+39
+00:03:25,450 --> 00:03:29,090
+النظرية بتحكي بالكارشاكل انها ده يبقى لو اعطاني
+
+40
+00:03:29,090 --> 00:03:35,010
+مصفوفة ايه بدي اجيب ال diagonal matrix بتاعها بحيث
+
+41
+00:03:35,010 --> 00:03:40,090
+العناصر تبع ال diagonal matrix يكونوا هم ال eigen
+
+42
+00:03:40,090 --> 00:03:46,120
+values يبقى بدي احاول اجيبالـEigenvectors اللي
+
+43
+00:03:46,120 --> 00:03:50,260
+عندنا والـEigenvectors بس بيشرّنوا كلهم linearly
+
+44
+00:03:50,260 --> 00:03:54,260
+independent لأنه جالي linearly independent ولو
+
+45
+00:03:54,260 --> 00:03:58,420
+واحد يعتمد على التاني كلهم مستقلات عن بعض تمام
+
+46
+00:03:58,420 --> 00:04:02,220
+الاستقلال يبقى بحص العالمين على ال diagonal matrix
+
+47
+00:04:03,840 --> 00:04:07,760
+الان بدأجي للعنوان اللي انا رافعه المرة اللي فاتت
+
+48
+00:04:07,760 --> 00:04:11,780
+كنا بنتكلم عن ال similar matrix فقط و لم نتكلم عن
+
+49
+00:04:11,780 --> 00:04:15,460
+ال diagonalization تمام؟ هذا الكلام اللي احنا
+
+50
+00:04:15,460 --> 00:04:19,140
+بنحكي هو ال diagonalization و احنا مش ذارين طلع
+
+51
+00:04:19,140 --> 00:04:20,120
+التريفش بقول
+
+52
+00:04:24,300 --> 00:04:28,980
+التعريف اللي جابله if a is a similar to a diagonal
+
+53
+00:04:28,980 --> 00:04:34,880
+matrix يعني هالكلام هذا صحيح then a is said to be
+
+54
+00:04:34,880 --> 00:04:40,130
+diagonalizableيبقى المصوفة ايه بنقدر نعملها على
+
+55
+00:04:40,130 --> 00:04:46,770
+شكل مصوفة قطرية يبقى لو كانت المصوفة similar to a
+
+56
+00:04:46,770 --> 00:04:50,330
+diagonal matrix automatic بقول ان ال a دي
+
+57
+00:04:50,330 --> 00:04:55,180
+diagonalizableطيب التعريف التاني بيقول لو كانت ال
+
+58
+00:04:55,180 --> 00:05:00,600
+a diagonalizable matrix then it processes يتفترض
+
+59
+00:05:00,600 --> 00:05:05,100
+in linearly independent eigenvectors يبقى ال
+
+60
+00:05:05,100 --> 00:05:08,140
+eigenvectors اللي عندنا عددهم يساوي in بدهم يكونوا
+
+61
+00:05:08,140 --> 00:05:15,240
+linearly independentوهذه الستة نسميها complete set
+
+62
+00:05:15,240 --> 00:05:20,380
+of eigenvectors يبقى هذه المجموعة الكاملة لمين لل
+
+63
+00:05:20,380 --> 00:05:24,040
+eigenvectors اللي عندنا على أي حال التعريف
+
+64
+00:05:24,040 --> 00:05:29,380
+الأولاني دقيق جدا لأنه هيقولك كيف بدك تخلي المصوفة
+
+65
+00:05:29,380 --> 00:05:34,920
+دي diagonal matrix صح السؤال ممكنطلع هنا نطرح حدث
+
+66
+00:05:34,920 --> 00:05:39,440
+و نحاول الإجابة عليه نمشي خطوات محددة الآن بعد
+
+67
+00:05:39,440 --> 00:05:44,080
+قليل فتجيجي معايا بقول how to diagonalize an n by
+
+68
+00:05:44,080 --> 00:05:48,180
+n matrix انا بعطيك مصفوفة لما اعطيك مصفوفة كيف
+
+69
+00:05:48,180 --> 00:05:55,500
+المصفوفة ديبتكتب عليها على شكل قطري فقط وبحيث
+
+70
+00:05:55,500 --> 00:06:00,480
+عناصر القطر الرئيسي هما الـEigenvalues فقط لا غير
+
+71
+00:06:00,480 --> 00:06:04,360
+بقول لها بدي أمشي تلت خطوات اللي عندنا خطوة الأولى
+
+72
+00:06:06,680 --> 00:06:10,320
+Find in linearly independent eigenvectors of the
+
+73
+00:06:10,320 --> 00:06:15,720
+matrix A,C,K1,K2 لغاية KN وهذا الكلام بجيناه احنا
+
+74
+00:06:15,720 --> 00:06:20,020
+بنوجده في الأمثلة السابقة كل أربع section واحد كان
+
+75
+00:06:20,020 --> 00:06:24,310
+ال eigenvalues و ال eigenvectorsإذا الخطوة الأولى
+
+76
+00:06:24,310 --> 00:06:30,090
+تحصيل حاصل في كل الأمثلة اللى فاتت سواء كانت
+
+77
+00:06:30,090 --> 00:06:33,530
+complex اللى اللى لعنها كانت complex أو real صحيح
+
+78
+00:06:33,530 --> 00:06:37,830
+ولا لا يجب الخطوة الأولى لم نأتي بجديد نجي الخطوة
+
+79
+00:06:37,830 --> 00:06:42,690
+التانية finally matrix Kاللي هي عناصر هم اللي عمود
+
+80
+00:06:42,690 --> 00:06:48,090
+الأول كواحد كتنين كام يبجى هذه برضه كنا بنكتبها
+
+81
+00:06:48,090 --> 00:06:50,930
+اللي هو العناصر اللي عندنا هذه تبعت ال
+
+82
+00:06:50,930 --> 00:06:54,870
+eigenvectors لما نقول الست هذه تُسمّت ال bases لل
+
+83
+00:06:54,870 --> 00:07:00,260
+eigen spaces تمام؟ يبجى، إيه المصروف في هذه؟Where
+
+84
+00:07:00,260 --> 00:07:04,840
+الكهات هذول are called eigenvectors يبقى جيبنا له
+
+85
+00:07:04,840 --> 00:07:09,820
+المصوفة تحصيل حاصل كمان هذه يعني ال eigenvectors
+
+86
+00:07:09,820 --> 00:07:13,560
+اللي جيبناهم بدك تكتبهم بس على شكل المصوفة هي اللي
+
+87
+00:07:13,560 --> 00:07:17,900
+بتقوله منهم الخطوة الثانيةيبقى الخطوة الأولى بدي
+
+88
+00:07:17,900 --> 00:07:21,100
+أجيب ال eigenvalues و ال eigenvectors الخطوة
+
+89
+00:07:21,100 --> 00:07:24,660
+التانية بدي أكتب ال eigenvectors على شكل مصفوفة
+
+90
+00:07:24,660 --> 00:07:30,820
+الخطوة التالتة دي matrix المصففة كإنفرس A كي والب
+
+91
+00:07:30,820 --> 00:07:35,080
+A دياجونال matrix حديها الرمز دي يبقى بتطلع عندك
+
+92
+00:07:35,080 --> 00:07:39,180
+ال diagonal يعني بدي أضربمعكوس المصفوفة K اللي
+
+93
+00:07:39,180 --> 00:07:43,240
+طلعت هنا هنا في اتنين في المصفوفة A الأصلي اللي
+
+94
+00:07:43,240 --> 00:07:48,180
+عندي في المصفوفة K النتج لازم يطلع المصفوفة اللي
+
+95
+00:07:48,180 --> 00:07:51,460
+عندنا هذه where lambda I the eigenvector the
+
+96
+00:07:51,460 --> 00:07:56,580
+eigenvalue corresponding to Ki والI من واحد لغاية
+
+97
+00:07:56,580 --> 00:08:01,200
+مين لغاية ال N طب حد فيكم بتحب تسأل أي سؤال في
+
+98
+00:08:01,200 --> 00:08:05,120
+الكلمتين انا اضغطيك قبل ان نذهب للتطبيق العاملي
+
+99
+00:08:05,120 --> 00:08:11,690
+لهذا الكلامحدث فيكوا تحب تسألوا اي سؤال؟ جاهزين؟
+
+100
+00:08:11,690 --> 00:08:16,010
+طيب طبعا تعرفوا الامتحان وجه اليوم 24 اللي هو يوم
+
+101
+00:08:16,010 --> 00:08:20,750
+الثلاثاء مش بكرا الثلاثاء اللي بعدها الأربعة ولا
+
+102
+00:08:20,750 --> 00:08:25,470
+الثلاثة؟ الأربعة الأربعة مافيش مشكلة عادي جدا يبقى
+
+103
+00:08:25,470 --> 00:08:29,910
+الامتحان يوم الأربعاء اللي هو القادم ساعة قد أيش؟
+
+104
+00:08:29,910 --> 00:08:35,140
+ساعتين تانية بعد ما نخلص محاضرتنابس عند الطلاب مش
+
+105
+00:08:35,140 --> 00:08:41,920
+عندكم. طيب على أي حال ما علينا يبقى الامتحان كما
+
+106
+00:08:41,920 --> 00:08:47,280
+هو في chapter 3 و باقي chapter 2 مش هنضيف زيادة
+
+107
+00:08:47,280 --> 00:08:53,290
+للمتحان انطبعه جاهز.هذا هو المثال اللي عندنا بيقول
+
+108
+00:08:53,290 --> 00:08:57,430
+خد المصوفة نظامها اتنين في اتنين زي ما انت شايف
+
+109
+00:08:57,430 --> 00:09:01,190
+هاتل ال eigen value و ال eigen vectors يبقى هذا
+
+110
+00:09:01,190 --> 00:09:04,070
+اللي كنا بنجيبه المرة الماضية في ال section اربعة
+
+111
+00:09:04,070 --> 00:09:08,510
+واحد بعدين تبيني ان ال a is diagonalizable يبقى
+
+112
+00:09:08,510 --> 00:09:15,340
+بعدين تبيني ان المصوفة aبقدر استبدلها بمصفوفة
+
+113
+00:09:15,340 --> 00:09:21,180
+قطرية عناصرها هما عناصر من الـ eigenvalues إذا بدي
+
+114
+00:09:21,180 --> 00:09:28,300
+أبدأ زي ما كنت ببدأ هناك بدي أخد lambda I ناقص
+
+115
+00:09:28,300 --> 00:09:36,080
+المصفوفة A وتساوي I Lambda و هنا Zero Zero Lambda
+
+116
+00:09:36,080 --> 00:09:38,540
+ناقص المصفوفة A
+
+117
+00:09:41,740 --> 00:09:46,140
+بالشكل اللي عندنا هذا هذي بتصبح على الشكل التالي
+
+118
+00:09:46,140 --> 00:09:53,160
+هنا لندن مافيش غيرها و هنا ناقص واحد و هنا ناقص
+
+119
+00:09:53,160 --> 00:09:59,820
+اتنين و هنا لندن ناقص واحد بالشكل اللي عندنا هنا
+
+120
+00:10:00,650 --> 00:10:04,650
+بعد ذلك سأحصل على determinant من خلال الـ
+
+121
+00:10:04,650 --> 00:10:08,250
+determinant أو المحدد سأحصل على قيم الـ
+
+122
+00:10:08,250 --> 00:10:14,090
+eigenvalues يبقى سأحصل على determinant لمن ل
+
+123
+00:10:14,090 --> 00:10:20,330
+lambda I ناقص الـ A و أسوي بالزيرو يبقى هذا معناه
+
+124
+00:10:20,330 --> 00:10:26,570
+ان المحدد lambda سالب واحد سالب اتنين lambda سالب
+
+125
+00:10:26,570 --> 00:10:33,390
+واحد سيسوىبتفك هذا يبقى لاندا في لاندا ناقص واحد
+
+126
+00:10:33,390 --> 00:10:39,450
+ناقص اتنين يساوي مين؟ يساوي Zero يبقى المحدد هذا
+
+127
+00:10:39,450 --> 00:10:46,370
+في لاندا تربيع ناقص لاندا ناقص اتنين يساوي Zero
+
+128
+00:10:46,370 --> 00:10:52,770
+بدي احلل هذا كحصل ضرب قوسين يبقى او حصل ضرب عاملين
+
+129
+00:10:52,770 --> 00:11:00,050
+يساوي Zeroهنا lambda هنا lambda هنا واحد هنا اتنين
+
+130
+00:11:00,050 --> 00:11:04,930
+هنا ناقص هنا زائد يبقى زائد lambda او ناقص اتنين
+
+131
+00:11:04,930 --> 00:11:08,190
+lambda بيبقى ناقص lambda واحدة هي موجودة عندنا
+
+132
+00:11:08,190 --> 00:11:13,730
+يبقى تحليلنا سليم يبقى بناء عليه lambda تساوي سالب
+
+133
+00:11:13,730 --> 00:11:17,910
+واحد و lambda تساوي اتنين من هذول البنات
+
+134
+00:11:21,730 --> 00:11:29,470
+يبقى هذول are the eigenvalues
+
+135
+00:11:29,470 --> 00:11:39,530
+of the matrix A يبقى هذول اللي هم ال eigenvalues
+
+136
+00:11:57,290 --> 00:12:02,270
+بعد ذلك نجيب الـEigenvectors يبقى احنا حتى الآن في
+
+137
+00:12:02,270 --> 00:12:06,390
+الخطوة الأولى لسه جيبنا الـEigenvalues وبعد ذلك
+
+138
+00:12:06,390 --> 00:12:09,930
+نجيب الـEigenvectors
+
+139
+00:12:09,930 --> 00:12:16,490
+يبقى بالده دي للمصوفة او لحاصل الضرب اللي هو مين
+
+140
+00:12:18,900 --> 00:12:22,260
+هذا كله من أول ومبتدأ الحلقة تعتبر النقطة الأولى
+
+141
+00:12:22,260 --> 00:12:29,560
+نمرة a احنا اننا lambda I ناقص ال a في ال X بيساوي
+
+142
+00:12:29,560 --> 00:12:32,660
+zero هذه المعادلة الأصلية اللي بنشتغل عليها
+
+143
+00:12:32,660 --> 00:12:40,440
+ابتدائها من section 4-1 هي هي ماغيرناش هذا معناهم
+
+144
+00:12:42,120 --> 00:12:47,200
+لاند اي ناقص اتنين هي هجازة المصوفة لانها ناقص
+
+145
+00:12:47,200 --> 00:12:52,320
+واحد لاند اي ناقص اتنين لاند اي ناقص واحد لاند اي
+
+146
+00:12:52,320 --> 00:12:54,480
+ناقص اتنين لاند اي ناقص اتنين لاند اي ناقص اتنين
+
+147
+00:12:54,480 --> 00:12:55,100
+لاند اي ناقص اتنين لاند اي ناقص اتنين لاند اي ناقص
+
+148
+00:12:55,100 --> 00:12:55,320
+اتنين لاند اي ناقص اتنين لاند اي ناقص اتنين لاند
+
+149
+00:12:55,320 --> 00:12:55,620
+اي ناقص اتنين لاند اي ناقص اتنين لاند اي ناقص
+
+150
+00:12:55,620 --> 00:12:59,240
+اتنين لاند اي ناقص اتنين لاند اي ناقص اتنين
+
+151
+00:12:59,350 --> 00:13:05,730
+بتاخد الحالة الأولى لو كانت Lambda تساوي سالب واحد
+
+152
+00:13:05,730 --> 00:13:09,410
+مافيش اللي بده يصير يبقى بده أشيل كل Lambda و أحط
+
+153
+00:13:09,410 --> 00:13:14,570
+مكانها سالب واحد يبقى بصير عنه هنا سالب واحد سالب
+
+154
+00:13:14,570 --> 00:13:22,530
+واحد و هنا سالب اتنين سالب اتنين في X واحد X اتنين
+
+155
+00:13:22,530 --> 00:13:27,650
+كله بده يساوي من Zero و Zeroهذا المعادل يجب أن
+
+156
+00:13:27,650 --> 00:13:32,270
+أفكر المعادلة هذه و أحولها إلى معادلات يعني
+
+157
+00:13:32,270 --> 00:13:35,070
+المعادلة المصفوهية يجب أن أضربها و أحولها إلى
+
+158
+00:13:35,070 --> 00:13:41,890
+معادلتين فأقول له ناقص X1 ناقص X2 سيكون Zero وهنا
+
+159
+00:13:41,890 --> 00:13:49,210
+ناقص 2 X1 ناقص 2 X2 سيكون Zero هذه كانت معادلة يا
+
+160
+00:13:49,210 --> 00:13:54,000
+بناتمعادلة واحدة تنتهي لك في الحقيقة معادلة واحدة
+
+161
+00:13:54,000 --> 00:14:00,860
+إذا هذه المعادلة الواحدة X1 زائد X2 بده يساوي Zero
+
+162
+00:14:00,860 --> 00:14:08,820
+ومنها X1 بده يساوي من سالب X2 أو X2 بده يساوي سالب
+
+163
+00:14:08,820 --> 00:14:17,060
+X1يبقى باجي بقوله لو كانت ال X2 بدي ساوي A then X1
+
+164
+00:14:17,060 --> 00:14:25,760
+بدي مين سالب A هذا بدي يعطيني the eigen vectors
+
+165
+00:14:26,750 --> 00:14:37,190
+are in the form على الشكل التالي اللي هما من X1 X2
+
+166
+00:14:37,190 --> 00:14:47,310
+بده يساوي X1 اللي هي ناقص A و X2 اللي هي A بالشكل
+
+167
+00:14:47,310 --> 00:14:51,590
+اللي عندنا او A في سالب واحد واحد
+
+168
+00:14:54,310 --> 00:15:00,330
+يبقى طالع عندي هذا هو يمثل mean bases لل eigen
+
+169
+00:15:00,330 --> 00:15:06,510
+vector space المناظر لل eigen value لمن lambda
+
+170
+00:15:06,510 --> 00:15:08,590
+تساوي سالب واحد
+
+171
+00:15:17,540 --> 00:15:22,440
+الان بدنا نجي لمين؟ ناخد لان ده التانية يبقى باجي
+
+172
+00:15:22,440 --> 00:15:29,200
+بقوله هنا F لان ده تزاوي التانية طلت معانا اتنين
+
+173
+00:15:29,200 --> 00:15:34,970
+يبقى thenلما طلعت لاندا تساوي اتنين يبقى المعادلة
+
+174
+00:15:34,970 --> 00:15:39,390
+المصففية هتكون عليه الشكل التالي هشيل كل لاندا و
+
+175
+00:15:39,390 --> 00:15:45,330
+احط مكانها اتنين يبقى اتنين ناقص واحد هنا ناقص
+
+176
+00:15:45,330 --> 00:15:50,690
+اتنين و اتنين ناقص واحد اللي يبقى درجة اب واحد
+
+177
+00:15:50,690 --> 00:15:55,830
+بالشكل اللي عندنا هذا X واحد X اتنين بدها تساوي
+
+178
+00:15:55,830 --> 00:16:02,120
+Zero Zeroهذول هتعطيني معادلتين المعادلة الأولى
+
+179
+00:16:02,120 --> 00:16:08,520
+اللى هى 2x1-x2 بده يسوى zero والمعادلة التانية
+
+180
+00:16:08,520 --> 00:16:16,600
+الناقصى 2x1 زائد x2 برضه يسوى zero هذول كام معادلة
+
+181
+00:16:16,600 --> 00:16:21,210
+يا بنات؟معادلة واحدة لأن لو ضربت التانية فى سالب
+
+182
+00:16:21,210 --> 00:16:26,270
+بيصير هي المعادلة الأولى يبقى هذا معناه انه اتنين
+
+183
+00:16:26,270 --> 00:16:31,910
+اكس واحد ناقص اكس اتنين بده يساوي Zero هذا معناه
+
+184
+00:16:31,910 --> 00:16:36,970
+ان اكس اتنين بده يساوي اتنين اكس واحد يبقى هذا
+
+185
+00:16:36,970 --> 00:16:44,750
+معناه ان لو كانت ال X واحد تساوي ايه والله بي مثلا
+
+186
+00:16:44,750 --> 00:16:57,200
+thenبعد ذلك X2 يكون 2B وبالتالي اصبحت هنا من the
+
+187
+00:16:57,200 --> 00:17:08,180
+Eigen vectors are inthe form صار على الشكل التالي
+
+188
+00:17:08,180 --> 00:17:16,540
+ال X1 ب B و هنا ب 2B يعني بيه برا و هنا واحد اتنين
+
+189
+00:17:16,540 --> 00:17:23,720
+بالشكل اللي عندنا هذا طبعا هذا يمثل bases لمين لل
+
+190
+00:17:23,720 --> 00:17:30,380
+eigen vector space اللي عندنا طيب الآن خلصت اللي
+
+191
+00:17:30,380 --> 00:17:35,760
+هو المطلوب الأولالمطلوب التالي جالي هتل المصفوفة K
+
+192
+00:17:35,760 --> 00:17:43,320
+باجي بقولها المصفوفة K هي عبارة عن مين؟ هي عبارة
+
+193
+00:17:43,320 --> 00:17:49,460
+عن K واحد و K اتنين في عندي غيرهم؟ ماعنديش غيرهم K
+
+194
+00:17:49,460 --> 00:17:56,860
+واحد اللي هو من سالب واحد و واحد و K اتنين K اتنين
+
+195
+00:17:56,860 --> 00:18:03,570
+هي عبارة عن العمود واحد و اتنينلاحظ ان اتنين هدول
+
+196
+00:18:03,570 --> 00:18:07,870
+linearly dependent ولا linearly independent
+
+197
+00:18:07,870 --> 00:18:14,010
+اندبندنت ليش ان ولا واحد فيهم مضاعفات الآخر يبقى
+
+198
+00:18:14,010 --> 00:18:21,290
+هنا باجي بقولك بين جثين نوتthat لحظة أن السالب
+
+199
+00:18:21,290 --> 00:18:29,110
+واحد وواحد and التاني واحد واتنين are linearly
+
+200
+00:18:29,110 --> 00:18:30,390
+independent
+
+201
+00:18:34,060 --> 00:18:40,500
+الخطوة التالتة هي المطلوب نمر بيه من المسألة بيّلي
+
+202
+00:18:40,500 --> 00:18:44,960
+ان a is diagonalizable يعني احنا حتى اللي هنجيبنا
+
+203
+00:18:44,960 --> 00:18:48,640
+ال eigenvalues و ال eigenvectors اللي عندنا و
+
+204
+00:18:48,640 --> 00:18:54,840
+حطناهم على شكل مصفوفة اذا بيداجي لنمر بيه من
+
+205
+00:18:54,840 --> 00:19:00,110
+السؤالمش هنجيب نمرة بيه بدي أجي للمصفوفة K و أجيب
+
+206
+00:19:00,110 --> 00:19:05,170
+من المعكوث سبعها مش هنجيب المعكوث سبعها بدي أعرف
+
+207
+00:19:05,170 --> 00:19:11,510
+قداش ال determinant لل K تمام يبقى المحدد سالب
+
+208
+00:19:11,510 --> 00:19:18,910
+واحد واحد اتنين ويساوي سالب اتنين سالب واحد ويساوي
+
+209
+00:19:18,910 --> 00:19:24,870
+قداش سالب تلاتة وزي ما انتوا شايفينلا يساوي zero
+
+210
+00:19:24,870 --> 00:19:31,350
+يعني هذه المصفوفة non singular matrix يبجى هذا
+
+211
+00:19:31,350 --> 00:19:40,570
+معناه انك is a non singular matrix
+
+212
+00:19:41,270 --> 00:19:46,830
+ما دام non singular matrix إذا إيه اللي هي معكوس
+
+213
+00:19:46,830 --> 00:19:52,310
+بدنا نروح نجيب المعكوس تبع هذه المصفوفة و نضربه في
+
+214
+00:19:52,310 --> 00:19:59,650
+المصفوفة A و كذلك في المصفوفة K تسلم يبقى الان K
+
+215
+00:19:59,650 --> 00:20:05,730
+inverse AK إيش بده تعمل إيش الناتج يا بنات حتى
+
+216
+00:20:05,730 --> 00:20:07,450
+بتجري تقولي جديش الناتج
+
+217
+00:20:09,990 --> 00:20:15,550
+هما المصوفة نظام اتنين في اتنين بحيث القطر الرئيسي
+
+218
+00:20:15,550 --> 00:20:19,910
+هو ناقص واحد واتنين والقطر الرئيسي الثانوي يبقى
+
+219
+00:20:19,910 --> 00:20:24,270
+أسفار يعني جاب المبدأ لإن هذه المصوفة هي اللي
+
+220
+00:20:24,270 --> 00:20:28,830
+بتعملي ال diagonalization للميم للمصوفة A وبالتالي
+
+221
+00:20:28,830 --> 00:20:34,850
+بقول ال A is diagonalizable طيب هذا معناه طبعا
+
+222
+00:20:34,850 --> 00:20:39,970
+هتعرفيش مين يا بنات؟النتج المصوفة اللي بتطلعيش
+
+223
+00:20:39,970 --> 00:20:44,610
+بقول عليها similar to a مش هتعرف ال similar وكأنه
+
+224
+00:20:44,610 --> 00:20:48,850
+ال similar هي من؟ هي ال diagonalization هي نفس
+
+225
+00:20:48,850 --> 00:20:53,350
+العملية بس هنا حطنا لها شغل و كده هناك ماكناش
+
+226
+00:20:53,350 --> 00:20:57,190
+بنعرف هذا الكلام في المثال اللي اطرحناه المحاضرة
+
+227
+00:20:57,190 --> 00:21:02,010
+الماضيةيبقى هذا الكلام يساوي بالداخل لمعكوس
+
+228
+00:21:02,010 --> 00:21:08,010
+المصوفة K بنبدل عناصر القطر الرئيسي مكان بعض
+
+229
+00:21:08,010 --> 00:21:14,130
+وبنغير إشارات عناصر القطر الثانوي وبنجسم على محدد
+
+230
+00:21:14,130 --> 00:21:19,730
+هذه المصوفة المحدد هذا كده؟ سالب تلاتة يبقى هاي
+
+231
+00:21:19,730 --> 00:21:26,640
+واحد على سالب تلاتةبتداجي هنا هذا اتنين وهنا سالب
+
+232
+00:21:26,640 --> 00:21:32,020
+واحد وهنا سالب واحد وهنا سالب واحد غيرت اشارات
+
+233
+00:21:32,020 --> 00:21:36,060
+عناصر القطر الثانوي وبدلت عناصر القطر الرئيسي مكان
+
+234
+00:21:36,060 --> 00:21:43,500
+بعض ال a باجي بنزلها كما كانت له zero واحد اتنين
+
+235
+00:21:43,500 --> 00:21:52,120
+واحد مصوفة ك كما هي واحد اتنين ويساويسالب تلت
+
+236
+00:21:52,120 --> 00:21:57,980
+خلّيك برا تمام؟ بيضل لإن هنا بدي أدرب المصفتين
+
+237
+00:21:57,980 --> 00:22:04,800
+مثلا هذا اتنين سالب واحد سالب واحد سالب واحد فيه
+
+238
+00:22:04,800 --> 00:22:09,880
+بدي أضرب هدول المصفتين في بعض يبقى Zero واحد اللي
+
+239
+00:22:09,880 --> 00:22:15,740
+هو بواحد يبقى Zero واتنين يبقى في اتنينيبقى سالب
+
+240
+00:22:15,740 --> 00:22:21,440
+اتنين و واحد يبقى سالب واحد اتنين و اتنين يبقى كده
+
+241
+00:22:21,440 --> 00:22:26,040
+اش؟ اربعة بالشكل اللي عندنا هنا يبقى هذا الكلام
+
+242
+00:22:26,040 --> 00:22:32,080
+بده يساوي سالب طول فيه نضرب المصفتين هدول في بعض
+
+243
+00:22:32,080 --> 00:22:39,630
+يبقى هنا اتنين و هنا واحد يبقى تلاتةهنا أربعة
+
+244
+00:22:39,630 --> 00:22:46,750
+وناقص أربعة يبقى zero تمام هنا صف ثاني سالب واحد
+
+245
+00:22:46,750 --> 00:22:51,510
+وموجب واحد يبقى zero الصف الثاني في العمود التاني
+
+246
+00:22:51,510 --> 00:22:57,610
+سالب اتنين وسالب أربعة يبقى سالب ستة بالشكل اللي
+
+247
+00:22:57,610 --> 00:23:03,690
+عندنا دهبدي اضرب كل العناصر في سالب طول يبقى هذا
+
+248
+00:23:03,690 --> 00:23:08,970
+بيعطيكوا جداش سالب واحد و هنا zero و هنا zero سالب
+
+249
+00:23:08,970 --> 00:23:14,230
+مع سالب موجب و هنا باتنين اطلعلي عناصر القطرة
+
+250
+00:23:14,230 --> 00:23:18,810
+رئيسي سالب واحد و اتنين هي قيم main ال eigen value
+
+251
+00:23:18,810 --> 00:23:23,970
+المعنى هذا الكلام ان ال a is diagonalizable يبقى
+
+252
+00:23:23,970 --> 00:23:31,720
+هناالـ A is diagonalizable
+
+253
+00:23:31,720 --> 00:23:34,040
+وهو المطلوب
+
+254
+00:24:01,920 --> 00:24:11,060
+ناخد الملاحظة هذه remark it
+
+255
+00:24:11,060 --> 00:24:22,540
+should be noted that it should be noted that يجب
+
+256
+00:24:22,540 --> 00:24:29,060
+ملاحظة ان not every square matrix not every
+
+257
+00:24:32,360 --> 00:24:45,100
+square matrix مش كل مصوفة مربعة is similar to
+
+258
+00:24:45,100 --> 00:24:51,880
+a diagonal matrix
+
+259
+00:24:51,880 --> 00:24:58,860
+because السبب
+
+260
+00:25:01,690 --> 00:25:11,770
+بسبب ان ليس كل مقاطع كل مقاطعة
+
+261
+00:25:11,770 --> 00:25:19,870
+لديها
+
+262
+00:25:19,870 --> 00:25:26,650
+مقاطعة كاملة كمقاطعة
+
+263
+00:25:31,150 --> 00:25:38,230
+complicit of eigenvectors
+
+264
+00:25:38,230 --> 00:25:41,450
+example
+
+265
+00:25:41,450 --> 00:25:48,430
+is
+
+266
+00:25:48,430 --> 00:25:57,750
+the matrix A تساوي
+
+267
+00:25:58,890 --> 00:26:07,490
+ايتنين تلاتة زيرو اتنين Similar to
+
+268
+00:26:07,490 --> 00:26:10,890
+a diagonal matrix
+
+269
+00:26:36,780 --> 00:27:04,360
+العمود هذا لازم خلاص خلي
+
+270
+00:27:04,360 --> 00:27:10,490
+بالكمالملاحظة اللى كتبناها المثال اللى جاب لو كان
+
+271
+00:27:10,490 --> 00:27:13,810
+هنا مصحوف مربع نظام اتنين في اتنين لقناها
+
+272
+00:27:13,810 --> 00:27:18,010
+diagonalizable لما نسأل هل المصحوف دي
+
+273
+00:27:18,010 --> 00:27:22,370
+diagonalizable ولا لا انا بفهم منها شغلتين الشغل
+
+274
+00:27:22,370 --> 00:27:26,130
+الاولى قد تكون diagonalizable وقد لا تكون
+
+275
+00:27:26,130 --> 00:27:31,060
+diagonalizableإذا ما بنقدر نقول مش كل مصفوفة
+
+276
+00:27:31,060 --> 00:27:36,100
+similar to اي مصفوفة أخرى ليس بالضرورة أو بمعنى
+
+277
+00:27:36,100 --> 00:27:41,760
+أخر مش كل مصفوفة بتكون diagonalizable طيب كيه بدنا
+
+278
+00:27:41,760 --> 00:27:46,300
+نثبت صحة هذا الكلام أو كيه بدنا نبين هذا الكلام؟
+
+279
+00:27:46,300 --> 00:27:49,120
+إيش بقولي هنا في الملاحظة دي؟
+
+280
+00:27:57,900 --> 00:28:07,700
+مش كل مصفوفة مربعة مشكلة مش كل مصفوفة
+
+281
+00:28:07,700 --> 00:28:11,600
+مربعة مشكلة
+
+282
+00:28:11,600 --> 00:28:12,280
+مش كل
+
+283
+00:28:14,720 --> 00:28:18,640
+square matrix المصحوفة مربعية و complete set of
+
+284
+00:28:18,640 --> 00:28:24,120
+eigenvalues تعالى نترجم هذا الكلام على أرض الواقع
+
+285
+00:28:24,120 --> 00:28:27,100
+المعطيني المصحوفة وجالى يشوف لي هل هذه
+
+286
+00:28:27,100 --> 00:28:32,180
+diagonalizable ولا not diagonalizable إذا بدي أمشي
+
+287
+00:28:32,180 --> 00:28:35,940
+مثل ما مشيت في المثال اللى طوى شوف حالي إلى وين
+
+288
+00:28:35,940 --> 00:28:41,280
+بدي أوصل هل بقدر أكمل ولا بقدرش أكملوإذا ماقدرش
+
+289
+00:28:41,280 --> 00:28:45,360
+أكمل إيش الشيء اللي خلاني ماقدرش أكمل الحكي تبعي
+
+290
+00:28:45,360 --> 00:28:52,280
+بقوله بسيطة إذا أنا بدي أبدأ ب lambda I ناقص ال a
+
+291
+00:28:52,280 --> 00:29:02,480
+يبقى اللي هي mean lambda 00 lambda ناقص ال a 2302
+
+292
+00:29:02,480 --> 00:29:10,830
+ويساويهنا لاندا ناقص اتنين وهنا ناقص ثلاثة و zero
+
+293
+00:29:10,830 --> 00:29:16,590
+كزي ما هو وهنا لاندا ناقص اتنين بشكل اللي عندنا
+
+294
+00:29:16,590 --> 00:29:25,080
+هذابدى اخد المحدد يبقى determinant لlanda i ناقص
+
+295
+00:29:25,080 --> 00:29:32,580
+ال a ويسوى المحدد landa ناقص اتنين ناقص ثلاثة zero
+
+296
+00:29:32,580 --> 00:29:39,270
+landa ناقص اتنينيبقى هذا lambda ناقص اتنين لكل
+
+297
+00:29:39,270 --> 00:29:45,470
+تربيع ناقص ال zero هذا الكلام بده يساوي zero يبقى
+
+298
+00:29:45,470 --> 00:29:51,210
+هذا معناه ان ال lambda ناقص اتنين لكل تربيع يساوي
+
+299
+00:29:51,210 --> 00:29:56,410
+zero هذه معادلة من اي درجة من درجة ان يبقى لها كم
+
+300
+00:29:56,410 --> 00:30:00,890
+حل حلين يبقى هذه المعادلة لك الحلان
+
+301
+00:30:05,540 --> 00:30:12,540
+يبقى هذا الكلام بناء عليه ان لاندا واحد تساوي
+
+302
+00:30:12,540 --> 00:30:19,850
+لاندا اتنين تساوي اتنينبناء عليه سأحصل على
+
+303
+00:30:19,850 --> 00:30:27,190
+الـEigenvectors المناظرة لمن؟ لـLanda تساوي اتنين
+
+304
+00:30:27,190 --> 00:30:32,930
+يبقى باجي بقول هنا لو أخدنا لاندا واحد تساوي اتنين
+
+305
+00:30:32,930 --> 00:30:40,090
+تمام؟ بدي أروح أخد من؟ لاندا I ناقص الـA في الـX
+
+306
+00:30:40,090 --> 00:30:47,130
+كل هذا الكلام بدي يساوي Zero هذا بدي يعطينالاندا
+
+307
+00:30:47,130 --> 00:30:52,150
+اي ناقص ليها هذه المصوفة هشيل لاندا هذه و اكتب
+
+308
+00:30:52,150 --> 00:30:58,540
+مكانها جداشو اكتب مكانها اتنين بيصير هايها هاي
+
+309
+00:30:58,540 --> 00:31:02,240
+لاندا ناقص اتنين ولا شي تقولي من وين اجت و هنا
+
+310
+00:31:02,240 --> 00:31:10,760
+ناقص تلاتة و هنا zero و هنا لاندا ناقص اتنين و هاد
+
+311
+00:31:10,760 --> 00:31:16,820
+ال X واحد X اتنين بدها ساوي zero و zero بالشكل
+
+312
+00:31:16,820 --> 00:31:21,810
+اللي عندنا هنايبقى لما لاندا تساوي اتنين بيصير
+
+313
+00:31:21,810 --> 00:31:26,970
+المصفوفة لانها تبقى كم؟ Zero وهذه سالب تلاتة وهذه
+
+314
+00:31:26,970 --> 00:31:33,690
+Zero وهذه Zero في X واحد X اتنين بده يساوي Zero و
+
+315
+00:31:33,690 --> 00:31:39,730
+Zero يبقى الصف الأول في العمود الأول بيعطينا مين؟
+
+316
+00:31:39,730 --> 00:31:45,130
+بيعطينا سالب تلاتة X اتنين يساوي Zero في غير هي
+
+317
+00:31:45,130 --> 00:31:51,940
+كده؟ما اعطانيش الا معادلة واحدة بمجهول واحد كل
+
+318
+00:31:51,940 --> 00:31:57,060
+اللي بقدر اقوله من هذه المعادلة ان ال X2 بده ساوي
+
+319
+00:31:57,060 --> 00:32:05,550
+قداش طب و ال X1 اي رقم؟ مين مكان يكونيبقى باجي
+
+320
+00:32:05,550 --> 00:32:14,170
+بقوله and اكس اتنين بده يسوي ال a say مثلا يعني اه
+
+321
+00:32:14,170 --> 00:32:17,270
+وقع كيف؟ بسمع
+
+322
+00:32:19,810 --> 00:32:31,730
+يبقى X1 يبقى X1 يبقى X1
+
+323
+00:32:31,730 --> 00:32:40,890
+يبقى X1 يبقى X1 يبقى X1 يبقى X1 يبقى X1 يبقى X1
+
+324
+00:32:40,890 --> 00:32:43,450
+يبقى X1 يبقى
+
+325
+00:32:46,580 --> 00:32:55,980
+تو لاندا واحد يساوي اتنين are in the form على
+
+326
+00:32:55,980 --> 00:33:04,040
+الشكل التالي X واحد X اتنين يساوي X واحد اللي هو ب
+
+327
+00:33:04,040 --> 00:33:09,700
+A و X اتنين اللي هو بقداش ب Zero اللي يساوي A في
+
+328
+00:33:09,700 --> 00:33:14,260
+واحد Zero طب
+
+329
+00:33:14,260 --> 00:33:21,480
+لاندا مكررةيبقى التانية زيها صح ولا لأ يبقى also
+
+330
+00:33:21,480 --> 00:33:28,240
+the eigenvectors
+
+331
+00:33:28,240 --> 00:33:35,900
+corresponding to
+
+332
+00:33:35,900 --> 00:33:45,480
+land اتنين تساوي اتنين are in the four
+
+333
+00:33:47,770 --> 00:33:54,870
+يبقى أصبحت على الشكل التالي اللي هو بي مثلا لكن هي
+
+334
+00:33:54,870 --> 00:34:00,370
+هي نفسها ماتغيرتش يبقى ليس بي وإنما ايه في واحد
+
+335
+00:34:00,370 --> 00:34:01,070
+زيرو
+
+336
+00:34:04,190 --> 00:34:09,650
+طيب تعالى نشوف في هذه الحالة شو شكل المصوفة K
+
+337
+00:34:09,650 --> 00:34:14,310
+المصوفة K بحط فيها ال Eigen vectors مظبوطة ولا لأ
+
+338
+00:34:14,310 --> 00:34:24,210
+يبقى بناء عليه المصوفة K بدها تساوي 1010
+
+339
+00:34:24,210 --> 00:34:26,070
+تمام
+
+340
+00:34:28,060 --> 00:34:32,700
+لو رجعنا ل a similar to b يقولنا if there exists a
+
+341
+00:34:32,700 --> 00:34:38,620
+non singular matrix K such that تمام؟ بدنا نشوف هل
+
+342
+00:34:38,620 --> 00:34:42,220
+هذه singular ولا non singular
+
+343
+00:34:44,480 --> 00:34:49,600
+يبقى احنا بنات هنا طلعنا المصوفة K تبعت ال
+
+344
+00:34:49,600 --> 00:34:54,480
+eigenvectors على الشكل اللي عندنا هذا جينا اخدنا
+
+345
+00:34:54,480 --> 00:34:59,300
+المحدد اللي لها وجينا المحدد اللي يساوي مين؟ Zero
+
+346
+00:34:59,300 --> 00:35:03,780
+مدام المحدد Zero يعني ال K inverse does not exist
+
+347
+00:35:03,780 --> 00:35:09,760
+لأن المصوفة اللي لها ماكوس هي المصوفة اللي محددها
+
+348
+00:35:09,760 --> 00:35:15,700
+لا يساوي Zero تمام؟يساوي زي رويب جهدي مش موجودة،
+
+349
+00:35:15,700 --> 00:35:20,980
+مدن مش موجودة، إذا لا يمكن تبقى المصوفة similar to
+
+350
+00:35:20,980 --> 00:35:24,560
+a diagonal matrix أو المصوفة بقول عنها هي
+
+351
+00:35:24,560 --> 00:35:29,160
+diagonalizable يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6wYdmeO7zro_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6wYdmeO7zro_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e6bfd37411ad05a635265080c6737ccfa7e95f8f
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6wYdmeO7zro_raw.srt
@@ -0,0 +1,1408 @@
+1
+00:00:21,160 --> 00:00:26,220
+بسم الله الرحمن الرحيم نعود الآن إلى نهاية
+
+2
+00:00:26,220 --> 00:00:29,920
+المحاضرة الماضية المحاضرة الماضية بدأنا بموضوع ال
+
+3
+00:00:29,920 --> 00:00:37,240
+diagonalization وكيف نعمل الهو diagonalize للمصوفة
+
+4
+00:00:37,240 --> 00:00:41,780
+بمعنى خليها مصوفة قطرية ابتدنا بتعريف ال similar
+
+5
+00:00:41,780 --> 00:00:47,180
+matrix فقلنا ان ال similar matrix بإذا جدرت لاجي
+
+6
+00:00:47,180 --> 00:00:53,710
+مصوفة تانية Kبحيث الكي هذه non zero matrix يعني او
+
+7
+00:00:53,710 --> 00:00:57,610
+non singular matrix ايش يعني يعني المعكوس تبعها
+
+8
+00:00:57,610 --> 00:01:02,470
+موجود بحيث اللي بيبدأ يسوي ال K inverse في ال A في
+
+9
+00:01:02,470 --> 00:01:06,750
+الكي تمام؟ واخدنا على ذلك مثالا واحدا بعد ما
+
+10
+00:01:06,750 --> 00:01:11,440
+أثبتناإن إذا كانت ال A similar ل B فإن B similar ل
+
+11
+00:01:11,440 --> 00:01:14,940
+A وفي نفس اللغة وفي نفس الوقت A is similar to
+
+12
+00:01:14,940 --> 00:01:18,580
+itself تمام يبقى هذا اللي خدناه المحاضرة الماضية و
+
+13
+00:01:18,580 --> 00:01:23,160
+الآن بدنا نضيق .. أخدنا طبعا مثال واحد لسه ياما
+
+14
+00:01:23,160 --> 00:01:27,500
+ناخد أمثلة فبدنا نبدأ نحط بعض المعلومات النظرية
+
+15
+00:01:27,500 --> 00:01:33,160
+الأساسية أو العمودي الفقري في هذا sectionبيقول لي
+
+16
+00:01:33,160 --> 00:01:37,540
+to show that the given n by n matrix is a is
+
+17
+00:01:37,540 --> 00:01:41,120
+similar to a diagonal matrix و ال diagonal matrix
+
+18
+00:01:41,120 --> 00:01:44,180
+هي بكتوبها بالشكل هذا من حد ما تشوفيها دي يعني
+
+19
+00:01:44,180 --> 00:01:49,800
+مصوفة قطرية جميع عناصرها أصفرا معادة عناصرالقطر
+
+20
+00:01:49,800 --> 00:01:57,540
+الرئيسي نأخذ النظرية التالية طبعا من اللمدات هذول
+
+21
+00:01:57,540 --> 00:02:00,400
+اللمدة واحد و اللمدة اتنين و اللمدة ان هي ال eigen
+
+22
+00:02:00,400 --> 00:02:07,440
+values مش حياله مش اي ارقام يبقى ارقام محددةطيب
+
+23
+00:02:07,440 --> 00:02:11,480
+النظرية بتقول إيه؟ the n by n matrix A is similar
+
+24
+00:02:11,480 --> 00:02:16,420
+to a diagonal matrix ملاحظي المرة اللي فاتت بدينا
+
+25
+00:02:16,420 --> 00:02:21,060
+canvas A K طلت عني مصروفة قطرية في الآخر، مصبوط
+
+26
+00:02:21,060 --> 00:02:24,920
+ولا لأ؟ المصروف القطرية العمودي الفقري قيمة ال two
+
+27
+00:02:24,920 --> 00:02:28,870
+landers اللي طلوا عندي بالضبطيبقى هنا لما أقول الـ
+
+28
+00:02:28,870 --> 00:02:32,650
+A is similar to a diagonal matrix if and only if
+
+29
+00:02:32,650 --> 00:02:36,350
+it has a set of linearly independent eigenvectors
+
+30
+00:02:36,350 --> 00:02:43,250
+K1 وK2 لغاية KM الكلام هذا بدي أعيد صياغته مرة
+
+31
+00:02:43,250 --> 00:02:48,750
+تانية باجي بقول that is لو كان عند المصوفة K هذه
+
+32
+00:02:48,750 --> 00:02:53,670
+مصوفة K K1 هو العمود الأول K2 العمود التالت KN
+
+33
+00:02:53,670 --> 00:03:01,400
+العمود رقم Mوكل eigen vector هذا مناظر لمن؟ مناظر
+
+34
+00:03:01,400 --> 00:03:04,500
+لل eigen value اللي هي لاندا واحد والتاني لاندا
+
+35
+00:03:04,500 --> 00:03:08,920
+اتنين والتالتة لاندا تلاتة والاخر لاندا in them ال
+
+36
+00:03:08,920 --> 00:03:14,340
+K inverse A في ال K بده يساوي المصوفة اللي عندها
+
+37
+00:03:14,340 --> 00:03:18,880
+دي يعني بده يساوي المصوفة لجميع عناصرها أصفرا ما
+
+38
+00:03:18,880 --> 00:03:25,450
+عدا عناصر قطة الرئيسي بيكونوا على أسرها هو من؟هذه
+
+39
+00:03:25,450 --> 00:03:29,090
+النظرية بتحكي بالكارشاكل انها ده يبقى لو اعطاني
+
+40
+00:03:29,090 --> 00:03:35,010
+مصفوفة ايه بدي اجيب ال diagonal matrix بتاعها بحيث
+
+41
+00:03:35,010 --> 00:03:40,090
+العناصر تبع ال diagonal matrix يكونوا هم ال eigen
+
+42
+00:03:40,090 --> 00:03:46,120
+values يبقى بدي احاول اجيبالـEigenvectors اللي
+
+43
+00:03:46,120 --> 00:03:50,260
+عندنا والـEigenvectors بس بيشرّنوا كلهم linearly
+
+44
+00:03:50,260 --> 00:03:54,260
+independent لأنه جالي linearly independent ولو
+
+45
+00:03:54,260 --> 00:03:58,420
+واحد يعتمد على التاني كلهم مستقلات عن بعض تمام
+
+46
+00:03:58,420 --> 00:04:02,220
+الاستقلال يبقى بحص العالمين على ال diagonal matrix
+
+47
+00:04:03,840 --> 00:04:07,760
+الان بدأجي للعنوان اللي انا رافعه المرة اللي فاتت
+
+48
+00:04:07,760 --> 00:04:11,780
+كنا بنتكلم عن ال similar matrix فقط و لم نتكلم عن
+
+49
+00:04:11,780 --> 00:04:15,460
+ال diagonalization تمام؟ هذا الكلام اللي احنا
+
+50
+00:04:15,460 --> 00:04:19,140
+بنحكي هو ال diagonalization و احنا مش ذارين طلع
+
+51
+00:04:19,140 --> 00:04:20,120
+التريفش بقول
+
+52
+00:04:24,300 --> 00:04:28,980
+التعريف اللي جابله if a is a similar to a diagonal
+
+53
+00:04:28,980 --> 00:04:34,880
+matrix يعني هالكلام هذا صحيح then a is said to be
+
+54
+00:04:34,880 --> 00:04:40,130
+diagonalizableيبقى المصوفة ايه بنقدر نعملها على
+
+55
+00:04:40,130 --> 00:04:46,770
+شكل مصوفة قطرية يبقى لو كانت المصوفة similar to a
+
+56
+00:04:46,770 --> 00:04:50,330
+diagonal matrix automatic بقول ان ال a دي
+
+57
+00:04:50,330 --> 00:04:55,180
+diagonalizableطيب التعريف التاني بيقول لو كانت ال
+
+58
+00:04:55,180 --> 00:05:00,600
+a diagonalizable matrix then it processes يتفترض
+
+59
+00:05:00,600 --> 00:05:05,100
+in linearly independent eigenvectors يبقى ال
+
+60
+00:05:05,100 --> 00:05:08,140
+eigenvectors اللي عندنا عددهم يساوي in بدهم يكونوا
+
+61
+00:05:08,140 --> 00:05:15,240
+linearly independentوهذه الستة نسميها complete set
+
+62
+00:05:15,240 --> 00:05:20,380
+of eigenvectors يبقى هذه المجموعة الكاملة لمين لل
+
+63
+00:05:20,380 --> 00:05:24,040
+eigenvectors اللي عندنا على أي حال التعريف
+
+64
+00:05:24,040 --> 00:05:29,380
+الأولاني دقيق جدا لأنه هيقولك كيف بدك تخلي المصوفة
+
+65
+00:05:29,380 --> 00:05:34,920
+دي diagonal matrix صح السؤال ممكنطلع هنا نطرح حدث
+
+66
+00:05:34,920 --> 00:05:39,440
+و نحاول الإجابة عليه نمشي خطوات محددة الآن بعد
+
+67
+00:05:39,440 --> 00:05:44,080
+قليل فتجيجي معايا بقول how to diagonalize an n by
+
+68
+00:05:44,080 --> 00:05:48,180
+n matrix انا بعطيك مصفوفة لما اعطيك مصفوفة كيف
+
+69
+00:05:48,180 --> 00:05:55,500
+المصفوفة ديبتكتب عليها على شكل قطري فقط وبحيث
+
+70
+00:05:55,500 --> 00:06:00,480
+عناصر القطر الرئيسي هما الـEigenvalues فقط لا غير
+
+71
+00:06:00,480 --> 00:06:04,360
+بقول لها بدي أمشي تلت خطوات اللي عندنا خطوة الأولى
+
+72
+00:06:06,680 --> 00:06:10,320
+Find in linearly independent eigenvectors of the
+
+73
+00:06:10,320 --> 00:06:15,720
+matrix A,C,K1,K2 لغاية KN وهذا الكلام بجيناه احنا
+
+74
+00:06:15,720 --> 00:06:20,020
+بنوجده في الأمثلة السابقة كل أربع section واحد كان
+
+75
+00:06:20,020 --> 00:06:24,310
+ال eigenvalues و ال eigenvectorsإذا الخطوة الأولى
+
+76
+00:06:24,310 --> 00:06:30,090
+تحصيل حاصل في كل الأمثلة اللى فاتت سواء كانت
+
+77
+00:06:30,090 --> 00:06:33,530
+complex اللى اللى لعنها كانت complex أو real صحيح
+
+78
+00:06:33,530 --> 00:06:37,830
+ولا لا يجب الخطوة الأولى لم نأتي بجديد نجي الخطوة
+
+79
+00:06:37,830 --> 00:06:42,690
+التانية finally matrix Kاللي هي عناصر هم اللي عمود
+
+80
+00:06:42,690 --> 00:06:48,090
+الأول كواحد كتنين كام يبجى هذه برضه كنا بنكتبها
+
+81
+00:06:48,090 --> 00:06:50,930
+اللي هو العناصر اللي عندنا هذه تبعت ال
+
+82
+00:06:50,930 --> 00:06:54,870
+eigenvectors لما نقول الست هذه تُسمّت ال bases لل
+
+83
+00:06:54,870 --> 00:07:00,260
+eigen spaces تمام؟ يبجى، إيه المصروف في هذه؟Where
+
+84
+00:07:00,260 --> 00:07:04,840
+الكهات هذول are called eigenvectors يبقى جيبنا له
+
+85
+00:07:04,840 --> 00:07:09,820
+المصوفة تحصيل حاصل كمان هذه يعني ال eigenvectors
+
+86
+00:07:09,820 --> 00:07:13,560
+اللي جيبناهم بدك تكتبهم بس على شكل المصوفة هي اللي
+
+87
+00:07:13,560 --> 00:07:17,900
+بتقوله منهم الخطوة الثانيةيبقى الخطوة الأولى بدي
+
+88
+00:07:17,900 --> 00:07:21,100
+أجيب ال eigenvalues و ال eigenvectors الخطوة
+
+89
+00:07:21,100 --> 00:07:24,660
+التانية بدي أكتب ال eigenvectors على شكل مصفوفة
+
+90
+00:07:24,660 --> 00:07:30,820
+الخطوة التالتة دي matrix المصففة كإنفرس A كي والب
+
+91
+00:07:30,820 --> 00:07:35,080
+A دياجونال matrix حديها الرمز دي يبقى بتطلع عندك
+
+92
+00:07:35,080 --> 00:07:39,180
+ال diagonal يعني بدي أضربمعكوس المصفوفة K اللي
+
+93
+00:07:39,180 --> 00:07:43,240
+طلعت هنا هنا في اتنين في المصفوفة A الأصلي اللي
+
+94
+00:07:43,240 --> 00:07:48,180
+عندي في المصفوفة K النتج لازم يطلع المصفوفة اللي
+
+95
+00:07:48,180 --> 00:07:51,460
+عندنا هذه where lambda I the eigenvector the
+
+96
+00:07:51,460 --> 00:07:56,580
+eigenvalue corresponding to Ki والI من واحد لغاية
+
+97
+00:07:56,580 --> 00:08:01,200
+مين لغاية ال N طب حد فيكم بتحب تسأل أي سؤال في
+
+98
+00:08:01,200 --> 00:08:05,120
+الكلمتين انا اضغطيك قبل ان نذهب للتطبيق العاملي
+
+99
+00:08:05,120 --> 00:08:11,690
+لهذا الكلامحدث فيكوا تحب تسألوا اي سؤال؟ جاهزين؟
+
+100
+00:08:11,690 --> 00:08:16,010
+طيب طبعا تعرفوا الامتحان وجه اليوم 24 اللي هو يوم
+
+101
+00:08:16,010 --> 00:08:20,750
+الثلاثاء مش بكرا الثلاثاء اللي بعدها الأربعة ولا
+
+102
+00:08:20,750 --> 00:08:25,470
+الثلاثة؟ الأربعة الأربعة مافيش مشكلة عادي جدا يبقى
+
+103
+00:08:25,470 --> 00:08:29,910
+الامتحان يوم الأربعاء اللي هو القادم ساعة قد أيش؟
+
+104
+00:08:29,910 --> 00:08:35,140
+ساعتين تانية بعد ما نخلص محاضرتنابس عند الطلاب مش
+
+105
+00:08:35,140 --> 00:08:41,920
+عندكم. طيب على أي حال ما علينا يبقى الامتحان كما
+
+106
+00:08:41,920 --> 00:08:47,280
+هو في chapter 3 و باقي chapter 2 مش هنضيف زيادة
+
+107
+00:08:47,280 --> 00:08:53,290
+للمتحان انطبعه جاهز.هذا هو المثال اللي عندنا بيقول
+
+108
+00:08:53,290 --> 00:08:57,430
+خد المصوفة نظامها اتنين في اتنين زي ما انت شايف
+
+109
+00:08:57,430 --> 00:09:01,190
+هاتل ال eigen value و ال eigen vectors يبقى هذا
+
+110
+00:09:01,190 --> 00:09:04,070
+اللي كنا بنجيبه المرة الماضية في ال section اربعة
+
+111
+00:09:04,070 --> 00:09:08,510
+واحد بعدين تبيني ان ال a is diagonalizable يبقى
+
+112
+00:09:08,510 --> 00:09:15,340
+بعدين تبيني ان المصوفة aبقدر استبدلها بمصفوفة
+
+113
+00:09:15,340 --> 00:09:21,180
+قطرية عناصرها هما عناصر من الـ eigenvalues إذا بدي
+
+114
+00:09:21,180 --> 00:09:28,300
+أبدأ زي ما كنت ببدأ هناك بدي أخد lambda I ناقص
+
+115
+00:09:28,300 --> 00:09:36,080
+المصفوفة A وتساوي I Lambda و هنا Zero Zero Lambda
+
+116
+00:09:36,080 --> 00:09:38,540
+ناقص المصفوفة A
+
+117
+00:09:41,740 --> 00:09:46,140
+بالشكل اللي عندنا هذا هذي بتصبح على الشكل التالي
+
+118
+00:09:46,140 --> 00:09:53,160
+هنا لندن مافيش غيرها و هنا ناقص واحد و هنا ناقص
+
+119
+00:09:53,160 --> 00:09:59,820
+اتنين و هنا لندن ناقص واحد بالشكل اللي عندنا هنا
+
+120
+00:10:00,650 --> 00:10:04,650
+بعد ذلك سأحصل على determinant من خلال الـ
+
+121
+00:10:04,650 --> 00:10:08,250
+determinant أو المحدد سأحصل على قيم الـ
+
+122
+00:10:08,250 --> 00:10:14,090
+eigenvalues يبقى سأحصل على determinant لمن ل
+
+123
+00:10:14,090 --> 00:10:20,330
+lambda I ناقص الـ A و أسوي بالزيرو يبقى هذا معناه
+
+124
+00:10:20,330 --> 00:10:26,570
+ان المحدد lambda سالب واحد سالب اتنين lambda سالب
+
+125
+00:10:26,570 --> 00:10:33,390
+واحد سيسوىبتفك هذا يبقى لاندا في لاندا ناقص واحد
+
+126
+00:10:33,390 --> 00:10:39,450
+ناقص اتنين يساوي مين؟ يساوي Zero يبقى المحدد هذا
+
+127
+00:10:39,450 --> 00:10:46,370
+في لاندا تربيع ناقص لاندا ناقص اتنين يساوي Zero
+
+128
+00:10:46,370 --> 00:10:52,770
+بدي احلل هذا كحصل ضرب قوسين يبقى او حصل ضرب عاملين
+
+129
+00:10:52,770 --> 00:11:00,050
+يساوي Zeroهنا lambda هنا lambda هنا واحد هنا اتنين
+
+130
+00:11:00,050 --> 00:11:04,930
+هنا ناقص هنا زائد يبقى زائد lambda او ناقص اتنين
+
+131
+00:11:04,930 --> 00:11:08,190
+lambda بيبقى ناقص lambda واحدة هي موجودة عندنا
+
+132
+00:11:08,190 --> 00:11:13,730
+يبقى تحليلنا سليم يبقى بناء عليه lambda تساوي سالب
+
+133
+00:11:13,730 --> 00:11:17,910
+واحد و lambda تساوي اتنين من هذول البنات
+
+134
+00:11:21,730 --> 00:11:29,470
+يبقى هذول are the eigenvalues
+
+135
+00:11:29,470 --> 00:11:39,530
+of the matrix A يبقى هذول اللي هم ال eigenvalues
+
+136
+00:11:57,290 --> 00:12:02,270
+بعد ذلك نجيب الـEigenvectors يبقى احنا حتى الآن في
+
+137
+00:12:02,270 --> 00:12:06,390
+الخطوة الأولى لسه جيبنا الـEigenvalues وبعد ذلك
+
+138
+00:12:06,390 --> 00:12:09,930
+نجيب الـEigenvectors
+
+139
+00:12:09,930 --> 00:12:16,490
+يبقى بالده دي للمصوفة او لحاصل الضرب اللي هو مين
+
+140
+00:12:18,900 --> 00:12:22,260
+هذا كله من أول ومبتدأ الحلقة تعتبر النقطة الأولى
+
+141
+00:12:22,260 --> 00:12:29,560
+نمرة a احنا اننا lambda I ناقص ال a في ال X بيساوي
+
+142
+00:12:29,560 --> 00:12:32,660
+zero هذه المعادلة الأصلية اللي بنشتغل عليها
+
+143
+00:12:32,660 --> 00:12:40,440
+ابتدائها من section 4-1 هي هي ماغيرناش هذا معناهم
+
+144
+00:12:42,120 --> 00:12:47,200
+لاند اي ناقص اتنين هي هجازة المصوفة لانها ناقص
+
+145
+00:12:47,200 --> 00:12:52,320
+واحد لاند اي ناقص اتنين لاند اي ناقص واحد لاند اي
+
+146
+00:12:52,320 --> 00:12:54,480
+ناقص اتنين لاند اي ناقص اتنين لاند اي ناقص اتنين
+
+147
+00:12:54,480 --> 00:12:55,100
+لاند اي ناقص اتنين لاند اي ناقص اتنين لاند اي ناقص
+
+148
+00:12:55,100 --> 00:12:55,320
+اتنين لاند اي ناقص اتنين لاند اي ناقص اتنين لاند
+
+149
+00:12:55,320 --> 00:12:55,620
+اي ناقص اتنين لاند اي ناقص اتنين لاند اي ناقص
+
+150
+00:12:55,620 --> 00:12:59,240
+اتنين لاند اي ناقص اتنين لاند اي ناقص اتنين
+
+151
+00:12:59,350 --> 00:13:05,730
+بتاخد الحالة الأولى لو كانت Lambda تساوي سالب واحد
+
+152
+00:13:05,730 --> 00:13:09,410
+مافيش اللي بده يصير يبقى بده أشيل كل Lambda و أحط
+
+153
+00:13:09,410 --> 00:13:14,570
+مكانها سالب واحد يبقى بصير عنه هنا سالب واحد سالب
+
+154
+00:13:14,570 --> 00:13:22,530
+واحد و هنا سالب اتنين سالب اتنين في X واحد X اتنين
+
+155
+00:13:22,530 --> 00:13:27,650
+كله بده يساوي من Zero و Zeroهذا المعادل يجب أن
+
+156
+00:13:27,650 --> 00:13:32,270
+أفكر المعادلة هذه و أحولها إلى معادلات يعني
+
+157
+00:13:32,270 --> 00:13:35,070
+المعادلة المصفوهية يجب أن أضربها و أحولها إلى
+
+158
+00:13:35,070 --> 00:13:41,890
+معادلتين فأقول له ناقص X1 ناقص X2 سيكون Zero وهنا
+
+159
+00:13:41,890 --> 00:13:49,210
+ناقص 2 X1 ناقص 2 X2 سيكون Zero هذه كانت معادلة يا
+
+160
+00:13:49,210 --> 00:13:54,000
+بناتمعادلة واحدة تنتهي لك في الحقيقة معادلة واحدة
+
+161
+00:13:54,000 --> 00:14:00,860
+إذا هذه المعادلة الواحدة X1 زائد X2 بده يساوي Zero
+
+162
+00:14:00,860 --> 00:14:08,820
+ومنها X1 بده يساوي من سالب X2 أو X2 بده يساوي سالب
+
+163
+00:14:08,820 --> 00:14:17,060
+X1يبقى باجي بقوله لو كانت ال X2 بدي ساوي A then X1
+
+164
+00:14:17,060 --> 00:14:25,760
+بدي مين سالب A هذا بدي يعطيني the eigen vectors
+
+165
+00:14:26,750 --> 00:14:37,190
+are in the form على الشكل التالي اللي هما من X1 X2
+
+166
+00:14:37,190 --> 00:14:47,310
+بده يساوي X1 اللي هي ناقص A و X2 اللي هي A بالشكل
+
+167
+00:14:47,310 --> 00:14:51,590
+اللي عندنا او A في سالب واحد واحد
+
+168
+00:14:54,310 --> 00:15:00,330
+يبقى طالع عندي هذا هو يمثل mean bases لل eigen
+
+169
+00:15:00,330 --> 00:15:06,510
+vector space المناظر لل eigen value لمن lambda
+
+170
+00:15:06,510 --> 00:15:08,590
+تساوي سالب واحد
+
+171
+00:15:17,540 --> 00:15:22,440
+الان بدنا نجي لمين؟ ناخد لان ده التانية يبقى باجي
+
+172
+00:15:22,440 --> 00:15:29,200
+بقوله هنا F لان ده تزاوي التانية طلت معانا اتنين
+
+173
+00:15:29,200 --> 00:15:34,970
+يبقى thenلما طلعت لاندا تساوي اتنين يبقى المعادلة
+
+174
+00:15:34,970 --> 00:15:39,390
+المصففية هتكون عليه الشكل التالي هشيل كل لاندا و
+
+175
+00:15:39,390 --> 00:15:45,330
+احط مكانها اتنين يبقى اتنين ناقص واحد هنا ناقص
+
+176
+00:15:45,330 --> 00:15:50,690
+اتنين و اتنين ناقص واحد اللي يبقى درجة اب واحد
+
+177
+00:15:50,690 --> 00:15:55,830
+بالشكل اللي عندنا هذا X واحد X اتنين بدها تساوي
+
+178
+00:15:55,830 --> 00:16:02,120
+Zero Zeroهذول هتعطيني معادلتين المعادلة الأولى
+
+179
+00:16:02,120 --> 00:16:08,520
+اللى هى 2x1-x2 بده يسوى zero والمعادلة التانية
+
+180
+00:16:08,520 --> 00:16:16,600
+الناقصى 2x1 زائد x2 برضه يسوى zero هذول كام معادلة
+
+181
+00:16:16,600 --> 00:16:21,210
+يا بنات؟معادلة واحدة لأن لو ضربت التانية فى سالب
+
+182
+00:16:21,210 --> 00:16:26,270
+بيصير هي المعادلة الأولى يبقى هذا معناه انه اتنين
+
+183
+00:16:26,270 --> 00:16:31,910
+اكس واحد ناقص اكس اتنين بده يساوي Zero هذا معناه
+
+184
+00:16:31,910 --> 00:16:36,970
+ان اكس اتنين بده يساوي اتنين اكس واحد يبقى هذا
+
+185
+00:16:36,970 --> 00:16:44,750
+معناه ان لو كانت ال X واحد تساوي ايه والله بي مثلا
+
+186
+00:16:44,750 --> 00:16:57,200
+thenبعد ذلك X2 يكون 2B وبالتالي اصبحت هنا من the
+
+187
+00:16:57,200 --> 00:17:08,180
+Eigen vectors are inthe form صار على الشكل التالي
+
+188
+00:17:08,180 --> 00:17:16,540
+ال X1 ب B و هنا ب 2B يعني بيه برا و هنا واحد اتنين
+
+189
+00:17:16,540 --> 00:17:23,720
+بالشكل اللي عندنا هذا طبعا هذا يمثل bases لمين لل
+
+190
+00:17:23,720 --> 00:17:30,380
+eigen vector space اللي عندنا طيب الآن خلصت اللي
+
+191
+00:17:30,380 --> 00:17:35,760
+هو المطلوب الأولالمطلوب التالي جالي هتل المصفوفة K
+
+192
+00:17:35,760 --> 00:17:43,320
+باجي بقولها المصفوفة K هي عبارة عن مين؟ هي عبارة
+
+193
+00:17:43,320 --> 00:17:49,460
+عن K واحد و K اتنين في عندي غيرهم؟ ماعنديش غيرهم K
+
+194
+00:17:49,460 --> 00:17:56,860
+واحد اللي هو من سالب واحد و واحد و K اتنين K اتنين
+
+195
+00:17:56,860 --> 00:18:03,570
+هي عبارة عن العمود واحد و اتنينلاحظ ان اتنين هدول
+
+196
+00:18:03,570 --> 00:18:07,870
+linearly dependent ولا linearly independent
+
+197
+00:18:07,870 --> 00:18:14,010
+اندبندنت ليش ان ولا واحد فيهم مضاعفات الآخر يبقى
+
+198
+00:18:14,010 --> 00:18:21,290
+هنا باجي بقولك بين جثين نوتthat لحظة أن السالب
+
+199
+00:18:21,290 --> 00:18:29,110
+واحد وواحد and التاني واحد واتنين are linearly
+
+200
+00:18:29,110 --> 00:18:30,390
+independent
+
+201
+00:18:34,060 --> 00:18:40,500
+الخطوة التالتة هي المطلوب نمر بيه من المسألة بيّلي
+
+202
+00:18:40,500 --> 00:18:44,960
+ان a is diagonalizable يعني احنا حتى اللي هنجيبنا
+
+203
+00:18:44,960 --> 00:18:48,640
+ال eigenvalues و ال eigenvectors اللي عندنا و
+
+204
+00:18:48,640 --> 00:18:54,840
+حطناهم على شكل مصفوفة اذا بيداجي لنمر بيه من
+
+205
+00:18:54,840 --> 00:19:00,110
+السؤالمش هنجيب نمرة بيه بدي أجي للمصفوفة K و أجيب
+
+206
+00:19:00,110 --> 00:19:05,170
+من المعكوث سبعها مش هنجيب المعكوث سبعها بدي أعرف
+
+207
+00:19:05,170 --> 00:19:11,510
+قداش ال determinant لل K تمام يبقى المحدد سالب
+
+208
+00:19:11,510 --> 00:19:18,910
+واحد واحد اتنين ويساوي سالب اتنين سالب واحد ويساوي
+
+209
+00:19:18,910 --> 00:19:24,870
+قداش سالب تلاتة وزي ما انتوا شايفينلا يساوي zero
+
+210
+00:19:24,870 --> 00:19:31,350
+يعني هذه المصفوفة non singular matrix يبجى هذا
+
+211
+00:19:31,350 --> 00:19:40,570
+معناه انك is a non singular matrix
+
+212
+00:19:41,270 --> 00:19:46,830
+ما دام non singular matrix إذا إيه اللي هي معكوس
+
+213
+00:19:46,830 --> 00:19:52,310
+بدنا نروح نجيب المعكوس تبع هذه المصفوفة و نضربه في
+
+214
+00:19:52,310 --> 00:19:59,650
+المصفوفة A و كذلك في المصفوفة K تسلم يبقى الان K
+
+215
+00:19:59,650 --> 00:20:05,730
+inverse AK إيش بده تعمل إيش الناتج يا بنات حتى
+
+216
+00:20:05,730 --> 00:20:07,450
+بتجري تقولي جديش الناتج
+
+217
+00:20:09,990 --> 00:20:15,550
+هما المصوفة نظام اتنين في اتنين بحيث القطر الرئيسي
+
+218
+00:20:15,550 --> 00:20:19,910
+هو ناقص واحد واتنين والقطر الرئيسي الثانوي يبقى
+
+219
+00:20:19,910 --> 00:20:24,270
+أسفار يعني جاب المبدأ لإن هذه المصوفة هي اللي
+
+220
+00:20:24,270 --> 00:20:28,830
+بتعملي ال diagonalization للميم للمصوفة A وبالتالي
+
+221
+00:20:28,830 --> 00:20:34,850
+بقول ال A is diagonalizable طيب هذا معناه طبعا
+
+222
+00:20:34,850 --> 00:20:39,970
+هتعرفيش مين يا بنات؟النتج المصوفة اللي بتطلعيش
+
+223
+00:20:39,970 --> 00:20:44,610
+بقول عليها similar to a مش هتعرف ال similar وكأنه
+
+224
+00:20:44,610 --> 00:20:48,850
+ال similar هي من؟ هي ال diagonalization هي نفس
+
+225
+00:20:48,850 --> 00:20:53,350
+العملية بس هنا حطنا لها شغل و كده هناك ماكناش
+
+226
+00:20:53,350 --> 00:20:57,190
+بنعرف هذا الكلام في المثال اللي اطرحناه المحاضرة
+
+227
+00:20:57,190 --> 00:21:02,010
+الماضيةيبقى هذا الكلام يساوي بالداخل لمعكوس
+
+228
+00:21:02,010 --> 00:21:08,010
+المصوفة K بنبدل عناصر القطر الرئيسي مكان بعض
+
+229
+00:21:08,010 --> 00:21:14,130
+وبنغير إشارات عناصر القطر الثانوي وبنجسم على محدد
+
+230
+00:21:14,130 --> 00:21:19,730
+هذه المصوفة المحدد هذا كده؟ سالب تلاتة يبقى هاي
+
+231
+00:21:19,730 --> 00:21:26,640
+واحد على سالب تلاتةبتداجي هنا هذا اتنين وهنا سالب
+
+232
+00:21:26,640 --> 00:21:32,020
+واحد وهنا سالب واحد وهنا سالب واحد غيرت اشارات
+
+233
+00:21:32,020 --> 00:21:36,060
+عناصر القطر الثانوي وبدلت عناصر القطر الرئيسي مكان
+
+234
+00:21:36,060 --> 00:21:43,500
+بعض ال a باجي بنزلها كما كانت له zero واحد اتنين
+
+235
+00:21:43,500 --> 00:21:52,120
+واحد مصوفة ك كما هي واحد اتنين ويساويسالب تلت
+
+236
+00:21:52,120 --> 00:21:57,980
+خلّيك برا تمام؟ بيضل لإن هنا بدي أدرب المصفتين
+
+237
+00:21:57,980 --> 00:22:04,800
+مثلا هذا اتنين سالب واحد سالب واحد سالب واحد فيه
+
+238
+00:22:04,800 --> 00:22:09,880
+بدي أضرب هدول المصفتين في بعض يبقى Zero واحد اللي
+
+239
+00:22:09,880 --> 00:22:15,740
+هو بواحد يبقى Zero واتنين يبقى في اتنينيبقى سالب
+
+240
+00:22:15,740 --> 00:22:21,440
+اتنين و واحد يبقى سالب واحد اتنين و اتنين يبقى كده
+
+241
+00:22:21,440 --> 00:22:26,040
+اش؟ اربعة بالشكل اللي عندنا هنا يبقى هذا الكلام
+
+242
+00:22:26,040 --> 00:22:32,080
+بده يساوي سالب طول فيه نضرب المصفتين هدول في بعض
+
+243
+00:22:32,080 --> 00:22:39,630
+يبقى هنا اتنين و هنا واحد يبقى تلاتةهنا أربعة
+
+244
+00:22:39,630 --> 00:22:46,750
+وناقص أربعة يبقى zero تمام هنا صف ثاني سالب واحد
+
+245
+00:22:46,750 --> 00:22:51,510
+وموجب واحد يبقى zero الصف الثاني في العمود التاني
+
+246
+00:22:51,510 --> 00:22:57,610
+سالب اتنين وسالب أربعة يبقى سالب ستة بالشكل اللي
+
+247
+00:22:57,610 --> 00:23:03,690
+عندنا دهبدي اضرب كل العناصر في سالب طول يبقى هذا
+
+248
+00:23:03,690 --> 00:23:08,970
+بيعطيكوا جداش سالب واحد و هنا zero و هنا zero سالب
+
+249
+00:23:08,970 --> 00:23:14,230
+مع سالب موجب و هنا باتنين اطلعلي عناصر القطرة
+
+250
+00:23:14,230 --> 00:23:18,810
+رئيسي سالب واحد و اتنين هي قيم main ال eigen value
+
+251
+00:23:18,810 --> 00:23:23,970
+المعنى هذا الكلام ان ال a is diagonalizable يبقى
+
+252
+00:23:23,970 --> 00:23:31,720
+هناالـ A is diagonalizable
+
+253
+00:23:31,720 --> 00:23:34,040
+وهو المطلوب
+
+254
+00:24:01,920 --> 00:24:11,060
+ناخد الملاحظة هذه remark it
+
+255
+00:24:11,060 --> 00:24:22,540
+should be noted that it should be noted that يجب
+
+256
+00:24:22,540 --> 00:24:29,060
+ملاحظة ان not every square matrix not every
+
+257
+00:24:32,360 --> 00:24:45,100
+square matrix مش كل مصوفة مربعة is similar to
+
+258
+00:24:45,100 --> 00:24:51,880
+a diagonal matrix
+
+259
+00:24:51,880 --> 00:24:58,860
+because السبب
+
+260
+00:25:01,690 --> 00:25:11,770
+بسبب ان ليس كل مقاطع كل مقاطعة
+
+261
+00:25:11,770 --> 00:25:19,870
+لديها
+
+262
+00:25:19,870 --> 00:25:26,650
+مقاطعة كاملة كمقاطعة
+
+263
+00:25:26,650 --> 00:25:26,650
+كاملة
+
+264
+00:25:31,150 --> 00:25:38,230
+complicit of eigenvectors
+
+265
+00:25:38,230 --> 00:25:41,450
+example
+
+266
+00:25:41,450 --> 00:25:48,430
+is
+
+267
+00:25:48,430 --> 00:25:57,750
+the matrix A تساوي
+
+268
+00:25:58,890 --> 00:26:07,490
+ايتنين تلاتة زيرو اتنين Similar to
+
+269
+00:26:07,490 --> 00:26:10,890
+a diagonal matrix
+
+270
+00:26:36,780 --> 00:27:04,360
+العمود هذا لازم خلاص خلي
+
+271
+00:27:04,360 --> 00:27:10,490
+بالكمالملاحظة اللى كتبناها المثال اللى جاب لو كان
+
+272
+00:27:10,490 --> 00:27:13,810
+هنا مصحوف مربع نظام اتنين في اتنين لقناها
+
+273
+00:27:13,810 --> 00:27:18,010
+diagonalizable لما نسأل هل المصحوف دي
+
+274
+00:27:18,010 --> 00:27:22,370
+diagonalizable ولا لا انا بفهم منها شغلتين الشغل
+
+275
+00:27:22,370 --> 00:27:26,130
+الاولى قد تكون diagonalizable وقد لا تكون
+
+276
+00:27:26,130 --> 00:27:31,060
+diagonalizableإذا ما بنقدر نقول مش كل مصفوفة
+
+277
+00:27:31,060 --> 00:27:36,100
+similar to اي مصفوفة أخرى ليس بالضرورة أو بمعنى
+
+278
+00:27:36,100 --> 00:27:41,760
+أخر مش كل مصفوفة بتكون diagonalizable طيب كيه بدنا
+
+279
+00:27:41,760 --> 00:27:46,300
+نثبت صحة هذا الكلام أو كيه بدنا نبين هذا الكلام؟
+
+280
+00:27:46,300 --> 00:27:49,120
+إيش بقولي هنا في الملاحظة دي؟
+
+281
+00:27:57,900 --> 00:28:07,700
+مش كل مصفوفة مربعة مشكلة مش كل مصفوفة
+
+282
+00:28:07,700 --> 00:28:11,600
+مربعة مشكلة
+
+283
+00:28:11,600 --> 00:28:12,280
+مش كل
+
+284
+00:28:14,720 --> 00:28:18,640
+square matrix المصحوفة مربعية و complete set of
+
+285
+00:28:18,640 --> 00:28:24,120
+eigenvalues تعالى نترجم هذا الكلام على أرض الواقع
+
+286
+00:28:24,120 --> 00:28:27,100
+المعطيني المصحوفة وجالى يشوف لي هل هذه
+
+287
+00:28:27,100 --> 00:28:32,180
+diagonalizable ولا not diagonalizable إذا بدي أمشي
+
+288
+00:28:32,180 --> 00:28:35,940
+مثل ما مشيت في المثال اللى طوى شوف حالي إلى وين
+
+289
+00:28:35,940 --> 00:28:41,280
+بدي أوصل هل بقدر أكمل ولا بقدرش أكملوإذا ماقدرش
+
+290
+00:28:41,280 --> 00:28:45,360
+أكمل إيش الشيء اللي خلاني ماقدرش أكمل الحكي تبعي
+
+291
+00:28:45,360 --> 00:28:52,280
+بقوله بسيطة إذا أنا بدي أبدأ ب lambda I ناقص ال a
+
+292
+00:28:52,280 --> 00:29:02,480
+يبقى اللي هي mean lambda 00 lambda ناقص ال a 2302
+
+293
+00:29:02,480 --> 00:29:10,830
+ويساويهنا لاندا ناقص اتنين وهنا ناقص ثلاثة و zero
+
+294
+00:29:10,830 --> 00:29:16,590
+كزي ما هو وهنا لاندا ناقص اتنين بشكل اللي عندنا
+
+295
+00:29:16,590 --> 00:29:25,080
+هذابدى اخد المحدد يبقى determinant لlanda i ناقص
+
+296
+00:29:25,080 --> 00:29:32,580
+ال a ويسوى المحدد landa ناقص اتنين ناقص ثلاثة zero
+
+297
+00:29:32,580 --> 00:29:39,270
+landa ناقص اتنينيبقى هذا lambda ناقص اتنين لكل
+
+298
+00:29:39,270 --> 00:29:45,470
+تربيع ناقص ال zero هذا الكلام بده يساوي zero يبقى
+
+299
+00:29:45,470 --> 00:29:51,210
+هذا معناه ان ال lambda ناقص اتنين لكل تربيع يساوي
+
+300
+00:29:51,210 --> 00:29:56,410
+zero هذه معادلة من اي درجة من درجة ان يبقى لها كم
+
+301
+00:29:56,410 --> 00:30:00,890
+حل حلين يبقى هذه المعادلة لك الحلان
+
+302
+00:30:05,540 --> 00:30:12,540
+يبقى هذا الكلام بناء عليه ان لاندا واحد تساوي
+
+303
+00:30:12,540 --> 00:30:19,850
+لاندا اتنين تساوي اتنينبناء عليه سأحصل على
+
+304
+00:30:19,850 --> 00:30:27,190
+الـEigenvectors المناظرة لمن؟ لـLanda تساوي اتنين
+
+305
+00:30:27,190 --> 00:30:32,930
+يبقى باجي بقول هنا لو أخدنا لاندا واحد تساوي اتنين
+
+306
+00:30:32,930 --> 00:30:40,090
+تمام؟ بدي أروح أخد من؟ لاندا I ناقص الـA في الـX
+
+307
+00:30:40,090 --> 00:30:47,130
+كل هذا الكلام بدي يساوي Zero هذا بدي يعطينالاندا
+
+308
+00:30:47,130 --> 00:30:52,150
+اي ناقص ليها هذه المصوفة هشيل لاندا هذه و اكتب
+
+309
+00:30:52,150 --> 00:30:58,540
+مكانها جداشو اكتب مكانها اتنين بيصير هايها هاي
+
+310
+00:30:58,540 --> 00:31:02,240
+لاندا ناقص اتنين ولا شي تقولي من وين اجت و هنا
+
+311
+00:31:02,240 --> 00:31:10,760
+ناقص تلاتة و هنا zero و هنا لاندا ناقص اتنين و هاد
+
+312
+00:31:10,760 --> 00:31:16,820
+ال X واحد X اتنين بدها ساوي zero و zero بالشكل
+
+313
+00:31:16,820 --> 00:31:21,810
+اللي عندنا هنايبقى لما لاندا تساوي اتنين بيصير
+
+314
+00:31:21,810 --> 00:31:26,970
+المصفوفة لانها تبقى كم؟ Zero وهذه سالب تلاتة وهذه
+
+315
+00:31:26,970 --> 00:31:33,690
+Zero وهذه Zero في X واحد X اتنين بده يساوي Zero و
+
+316
+00:31:33,690 --> 00:31:39,730
+Zero يبقى الصف الأول في العمود الأول بيعطينا مين؟
+
+317
+00:31:39,730 --> 00:31:45,130
+بيعطينا سالب تلاتة X اتنين يساوي Zero في غير هي
+
+318
+00:31:45,130 --> 00:31:51,940
+كده؟ما اعطانيش الا معادلة واحدة بمجهول واحد كل
+
+319
+00:31:51,940 --> 00:31:57,060
+اللي بقدر اقوله من هذه المعادلة ان ال X2 بده ساوي
+
+320
+00:31:57,060 --> 00:32:05,550
+قداش طب و ال X1 اي رقم؟ مين مكان يكونيبقى باجي
+
+321
+00:32:05,550 --> 00:32:14,170
+بقوله and اكس اتنين بده يسوي ال a say مثلا يعني اه
+
+322
+00:32:14,170 --> 00:32:17,270
+وقع كيف؟ بسمع
+
+323
+00:32:19,810 --> 00:32:31,730
+يبقى X1 يبقى X1 يبقى X1
+
+324
+00:32:31,730 --> 00:32:40,890
+يبقى X1 يبقى X1 يبقى X1 يبقى X1 يبقى X1 يبقى X1
+
+325
+00:32:40,890 --> 00:32:43,450
+يبقى X1 يبقى
+
+326
+00:32:46,580 --> 00:32:55,980
+تو لاندا واحد يساوي اتنين are in the form على
+
+327
+00:32:55,980 --> 00:33:04,040
+الشكل التالي X واحد X اتنين يساوي X واحد اللي هو ب
+
+328
+00:33:04,040 --> 00:33:09,700
+A و X اتنين اللي هو بقداش ب Zero اللي يساوي A في
+
+329
+00:33:09,700 --> 00:33:14,260
+واحد Zero طب
+
+330
+00:33:14,260 --> 00:33:21,480
+لاندا مكررةيبقى التانية زيها صح ولا لأ يبقى also
+
+331
+00:33:21,480 --> 00:33:28,240
+the eigenvectors
+
+332
+00:33:28,240 --> 00:33:35,900
+corresponding to
+
+333
+00:33:35,900 --> 00:33:45,480
+land اتنين تساوي اتنين are in the four
+
+334
+00:33:47,770 --> 00:33:54,870
+يبقى أصبحت على الشكل التالي اللي هو بي مثلا لكن هي
+
+335
+00:33:54,870 --> 00:34:00,370
+هي نفسها ماتغيرتش يبقى ليس بي وإنما ايه في واحد
+
+336
+00:34:00,370 --> 00:34:01,070
+زيرو
+
+337
+00:34:04,190 --> 00:34:09,650
+طيب تعالى نشوف في هذه الحالة شو شكل المصوفة K
+
+338
+00:34:09,650 --> 00:34:14,310
+المصوفة K بحط فيها ال Eigen vectors مظبوطة ولا لأ
+
+339
+00:34:14,310 --> 00:34:24,210
+يبقى بناء عليه المصوفة K بدها تساوي 1010
+
+340
+00:34:24,210 --> 00:34:26,070
+تمام
+
+341
+00:34:28,060 --> 00:34:32,700
+لو رجعنا ل a similar to b يقولنا if there exists a
+
+342
+00:34:32,700 --> 00:34:38,620
+non singular matrix K such that تمام؟ بدنا نشوف هل
+
+343
+00:34:38,620 --> 00:34:42,220
+هذه singular ولا non singular
+
+344
+00:34:44,480 --> 00:34:49,600
+يبقى احنا بنات هنا طلعنا المصوفة K تبعت ال
+
+345
+00:34:49,600 --> 00:34:54,480
+eigenvectors على الشكل اللي عندنا هذا جينا اخدنا
+
+346
+00:34:54,480 --> 00:34:59,300
+المحدد اللي لها وجينا المحدد اللي يساوي مين؟ Zero
+
+347
+00:34:59,300 --> 00:35:03,780
+مدام المحدد Zero يعني ال K inverse does not exist
+
+348
+00:35:03,780 --> 00:35:09,760
+لأن المصوفة اللي لها ماكوس هي المصوفة اللي محددها
+
+349
+00:35:09,760 --> 00:35:15,700
+لا يساوي Zero تمام؟يساوي زي رويب جهدي مش موجودة،
+
+350
+00:35:15,700 --> 00:35:20,980
+مدن مش موجودة، إذا لا يمكن تبقى المصوفة similar to
+
+351
+00:35:20,980 --> 00:35:24,560
+a diagonal matrix أو المصوفة بقول عنها هي
+
+352
+00:35:24,560 --> 00:35:29,160
+diagonalizable يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..86692b672c4f3b0ece93013a6ed9a89a9cb32b38
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ.srt
@@ -0,0 +1,1381 @@
+1
+00:00:19,390 --> 00:00:23,870
+بسم الله الرحمن الرحيم انتهينا في أول chapter من 
+
+2
+00:00:23,870 --> 00:00:27,410
+الجبر الخطي و هو chapter 2 والآن بنروح لل
+
+3
+00:00:27,410 --> 00:00:31,030
+chapter الثاني من الجبر الخطي و هو chapter 3
+
+4
+00:00:31,030 --> 00:00:35,870
+من الكتاب المقرر هذا ال chapter يتحدث عن نقطتين 
+
+5
+00:00:35,870 --> 00:00:39,910
+رئيسيتين النقطة الأولى هي ال vector spaces و
+
+6
+00:00:39,910 --> 00:00:43,890
+النقطة الثانية هي ال linear transformations يعني
+
+7
+00:00:43,890 --> 00:00:48,830
+التحويلات الخطية موضوعنا اليوم موضوع ال vector
+
+8
+00:00:48,830 --> 00:00:54,070
+spaces وعلى مدار الأيام القادمة كذلك لكننا في هذا
+
+9
+00:00:54,070 --> 00:00:58,550
+ال section فقط سنعطي تعريف لل vector space ونعطي
+
+10
+00:00:58,550 --> 00:01:04,670
+بعض الأمثلة عليه فقط لا غير ومن ثم ننتقل إلى بقية 
+
+11
+00:01:04,670 --> 00:01:09,450
+الأجزاء التي تتعلق بال vector spaces يبقى احنا
+
+12
+00:01:09,450 --> 00:01:16,950
+عندنا vector spaces يعني الفضاءات الاتجاهية بدنا 
+
+13
+00:01:16,950 --> 00:01:22,530
+نعطي تعريف للفضاء الاتجاهي ونشوف كيف نطبق التعريف
+
+14
+00:01:22,530 --> 00:01:28,090
+على الأمثلة المختلفة بقول افترض أن capital V عبارة
+
+15
+00:01:28,090 --> 00:01:32,370
+عن non-empty set of objects يبقى أنا عندي capital
+
+16
+00:01:32,370 --> 00:01:37,650
+V هي عبارة عن مجموعة وهذه المجموعة تحتوي على عدد
+
+17
+00:01:37,650 --> 00:01:41,750
+من العناصر in which two operations addition and
+
+18
+00:01:41,750 --> 00:01:45,610
+multiplication by scalars are defined وعليها
+
+19
+00:01:45,610 --> 00:01:50,030
+عمليتين معرفتين عملية بنسميها عملية الجمع والثانية
+
+20
+00:01:50,030 --> 00:01:54,650
+عملية الضرب في مقدار قياسي أو مقدار ثابت لما نقول
+
+21
+00:01:54,650 --> 00:01:58,930
+vector يبقى لو ضربناها في رقم نقول هذا هو scalar
+
+22
+00:01:58,930 --> 00:02:04,130
+multiplication يعني ضرب قياسي يبقى احنا في عندنا
+
+23
+00:02:04,130 --> 00:02:08,670
+set V الـ V هذا بدأ أضع عليها عمليتين العملية 
+
+24
+00:02:08,670 --> 00:02:14,070
+الأولى عملية الجمع بين المتجهات الموجودة في V
+
+25
+00:02:14,070 --> 00:02:18,870
+العملية الثانية أخد رقم من set of real numbers R
+
+26
+00:02:18,870 --> 00:02:25,370
+وضربه في أي من المتجهات تبعات ال vector V يبقى هاي 
+
+27
+00:02:25,370 --> 00:02:28,970
+العمليتين اللي أنا بقول عليهم معرفتين كانوا معرفة 
+
+28
+00:02:28,970 --> 00:02:29,550
+ذاتي 
+
+29
+00:02:46,650 --> 00:02:52,470
+عملية جمع متجهين من V هو متجه جديد موجود في V
+
+30
+00:02:52,470 --> 00:02:58,210
+عملية ضرب scalar A في U هو بيعطيني متجه جديد هذا
+
+31
+00:02:58,210 --> 00:03:04,030
+المتجه موجود في V كذلك R defined يبقى في هذه الحالة
+
+32
+00:03:04,030 --> 00:03:08,170
+بيقول إن ال V وعليها عملية الجمع وعليها عملية 
+
+33
+00:03:08,170 --> 00:03:13,390
+الضرب base color is a vector space أو linear space
+
+34
+00:03:13,390 --> 00:03:16,830
+بعض الكتب بتقول عنه vector space و بعض الكتب بتقول 
+
+35
+00:03:16,830 --> 00:03:19,890
+عنه linear space if the following properties are
+
+36
+00:03:19,890 --> 00:03:26,080
+satisfied على V يبقى إذا تحقق الشروط العشرة التالية
+
+37
+00:03:26,080 --> 00:03:31,540
+على هذه الست بقول الست هذي vector space إذا لم 
+
+38
+00:03:31,540 --> 00:03:36,640
+يتحقق ولو شرط واحد يبقى بيبطل يصير vector space
+
+39
+00:03:36,640 --> 00:03:40,520
+يبقى يبين لي أن هذا ما هو  vector space يكفي
+
+40
+00:03:40,520 --> 00:03:47,060
+ألغي شرط من الشروط العشرة نأتي للشرط الأول أو
+
+41
+00:03:47,060 --> 00:03:51,080
+الخاصية اللي هو لو أخدت عنصرين من V يبقى حاصل 
+
+42
+00:03:51,080 --> 00:03:56,420
+الجمع مش بده يكون موجود في V وليس خارج V طالع 
+
+43
+00:03:56,420 --> 00:04:00,240
+خارج V فبتبطل يصير vector space يبقى بدّه المجموع
+
+44
+00:04:00,240 --> 00:04:05,480
+يكون داخل V ال condition التاني ال U زائد ال V
+
+45
+00:04:05,480 --> 00:04:10,020
+يساوي ال V زائد ال U يعني عملية عملية جمع المنتجات
+
+46
+00:04:10,020 --> 00:04:14,690
+عملية إبدالية لو ما كانت إبدالية it is not a vector
+
+47
+00:04:14,690 --> 00:04:19,210
+space طيب الخاصيتين اللي اثنينهم تحققا بروحنا
+
+48
+00:04:19,210 --> 00:04:23,210
+الخاصية الثالثة و هي خاصية ال associativity لو
+
+49
+00:04:23,210 --> 00:04:29,230
+جمعت ال U إلى V زائد ال W تماما كما لو جمعت ال U
+
+50
+00:04:29,230 --> 00:04:34,530
+زائد ال V إلى من إلى ال W و دي بيسميه خاصية الدمج 
+
+51
+00:04:34,530 --> 00:04:38,830
+associative law أو associative property الآن أنتَ
+
+52
+00:04:38,830 --> 00:04:42,630
+حققت الخواص الثلاث بروح لخاصية رابعة الخاصية
+
+53
+00:04:42,630 --> 00:04:46,450
+الرابعة تقول لي في عندك عنصر اللي هو ال zero
+
+54
+00:04:46,450 --> 00:04:51,450
+المُتّصل هذا موجود في V إذا والله كان Zero زائد V
+
+55
+00:04:51,450 --> 00:04:57,230
+يساوي V زائد Zero يساوي V لكل ال V يبقى هذا بسميه
+
+56
+00:04:57,230 --> 00:05:01,970
+Zero vector لمين؟ لل vector space V يعني بمعنى آخر 
+
+57
+00:05:01,970 --> 00:05:07,070
+أن ال vector space V لازم يحتوي على العنصر الصفري 
+
+58
+00:05:07,070 --> 00:05:13,410
+بالنسبة لعملية الجمع يبقى الـ zero هذا vector يبقى
+
+59
+00:05:13,410 --> 00:05:20,130
+مش scalar يعني مش number وإنما هو vector تمام بحيث
+
+60
+00:05:20,130 --> 00:05:24,030
+هذا ال zero vector لو جمعته إلى أي vector آخر من
+
+61
+00:05:24,030 --> 00:05:28,590
+اليمين أو من الشمال بده يعطيني نفس ال vector هذا
+
+62
+00:05:28,590 --> 00:05:32,850
+ال element بقول عليه ال zero vector خاصية الخامسة 
+
+63
+00:05:32,850 --> 00:05:37,470
+لأي u موجود في capital V there exists لازم اللي
+
+64
+00:05:37,470 --> 00:05:42,980
+أجي أسألي بـ U موجود في V يعني يعني إذا العنصر أو ال
+
+65
+00:05:42,980 --> 00:05:48,560
+vector موجود في V لازم ألاقي سالب هذا العنصر موجود
+
+66
+00:05:48,560 --> 00:05:54,560
+في V بحيث لو جمعت ال U وسالب U تماما كما لو جمعت 
+
+67
+00:05:54,560 --> 00:05:58,740
+سالب U و U لأنه قال هنا commutative وندش بده
+
+68
+00:05:58,740 --> 00:06:02,830
+يعطينا الـ zero vector مش الـ zero scalar لأن احنا
+
+69
+00:06:02,830 --> 00:06:09,790
+بنجمع vectors سالب U هو vector يبقى U زائد ناقص U
+
+70
+00:06:09,790 --> 00:06:14,910
+يساوي تماما ناقص الـ U زائد الـ U بده يساوي من الـ 
+
+71
+00:06:14,910 --> 00:06:19,180
+zero vector هذه الخامسة الخاصية السادسة لو أخدت أي 
+
+72
+00:06:19,180 --> 00:06:23,740
+scalar من ال set of real number A أخدت عنصر A من
+
+73
+00:06:23,740 --> 00:06:27,900
+ال set of real number و أخدت ال U vector موجود في 
+
+74
+00:06:27,900 --> 00:06:35,880
+V إذا حصل ضرب ل 2A في U بده يكون موجود في V تماما 
+
+75
+00:06:35,880 --> 00:06:40,070
+تحققت الخاصية ده نروح بالخاصية اللي بعدها لو كان
+
+76
+00:06:40,070 --> 00:06:45,170
+الـ A scalar و أخدت two vectors من V و روح ضرب كاسكلر 
+
+77
+00:06:45,170 --> 00:06:51,550
+الـ A ضد الـ U زائد الـ V خضعت هذه لعمليات التوزيع
+
+78
+00:06:51,550 --> 00:06:56,850
+أو distributive property خاصية التوزيع صارت هذه A
+
+79
+00:06:56,850 --> 00:07:03,190
+ضد الـ U زائد A ضد الـ V مش عاجز هك و بس ضرب scalar
+
+80
+00:07:03,190 --> 00:07:08,090
+مع جامعة و vector لأ جامعة و scalars مع ضرب مع مين
+
+81
+00:07:08,090 --> 00:07:12,750
+مع vector الخاصية اللي بعدها لو كان ال a و ال b
+
+82
+00:07:12,750 --> 00:07:16,930
+موجودة في R و ال u موجودة في V يبقى ال a زائد ال b
+
+83
+00:07:16,930 --> 00:07:21,450
+و dot ال u بيساوي a dot ال u زائد ال b dot ال u كل
+
+84
+00:07:21,450 --> 00:07:28,160
+هذا بيكون موجود في V طبعا يبقى بنجي للخاصية التاسعة
+
+85
+00:07:28,160 --> 00:07:34,580
+لو كان عندي scalar A وعندي scalar B ضربت ال B في
+
+86
+00:07:34,580 --> 00:07:39,000
+ال U والنتج روحت ضربت في A تماما كما لو ضربت ال
+
+87
+00:07:39,000 --> 00:07:43,360
+two scalars من البداية في من في ال vector V بده
+
+88
+00:07:43,360 --> 00:07:48,960
+يطلع عندي vector اسمه A B ضد ال U وهذا بيكون vector
+
+89
+00:07:48,960 --> 00:07:53,220
+موجود في الـ vector الأصلي طبقًا للخاصية اللي 
+
+90
+00:07:53,220 --> 00:07:57,640
+عندنا هذه تمام تحقق الخاصية التاسعة بيروح الخاصية 
+
+91
+00:07:57,640 --> 00:08:02,860
+العاشرة لو أخدت الواحد as a scalar يعني كأنه
+
+92
+00:08:02,860 --> 00:08:08,400
+الخاصية دي حالة خاصة من من اللي فوق أخدت ال U هو 
+
+93
+00:08:08,400 --> 00:08:12,180
+vector و أخدت الواحد as a scalar ضربت الواحد في U
+
+94
+00:08:12,180 --> 00:08:18,850
+بيطلع النتج يساوي U اللي هو موجود في V يبقى إذا
+
+95
+00:08:18,850 --> 00:08:23,930
+تحققت هذه الخواص العشر في هذه الحالة بقول يبقى
+
+96
+00:08:23,930 --> 00:08:28,430
+اللي في عندي هذا ماله vector space بدنا نبدأ نطبق
+
+97
+00:08:28,430 --> 00:08:31,710
+الكلام اللي احنا بنقوله على أرض الواقع بأمثلة
+
+98
+00:08:31,710 --> 00:08:35,950
+مختلفة ونشوف مين ممكن يطلع vector space أو ممكن
+
+99
+00:08:35,950 --> 00:08:42,150
+ما يطلعش vector space وإذا ما طلعش مين من الخواص لا
+
+100
+00:08:42,150 --> 00:08:46,790
+تتحقق في هذه الحالة بقيت يصير ما هو  vector
+
+101
+00:08:46,790 --> 00:08:52,980
+space  جاء ياخد المثال الأول افترض ال V كل العناصر
+
+102
+00:08:52,980 --> 00:08:59,700
+الـ zero X1 و X2 بحيث X1 و X2 موجود في R يعني ايش؟ 
+
+103
+00:08:59,700 --> 00:09:04,700
+يعني بدي اخذ كل ال vectors اللي كل vector مكون من
+
+104
+00:09:04,700 --> 00:09:08,560
+ال three components بحيث المركبة الأولى دائما و
+
+105
+00:09:08,560 --> 00:09:12,920
+أبدأ zero لو ما هي zero إذا مش عندنا برا مالناش 
+
+106
+00:09:12,920 --> 00:09:17,560
+علاقة فيها يبقى احنا بدنا نجمع يعني مثلا لو جيت
+
+107
+00:09:17,560 --> 00:09:22,140
+قلت يا بنات هذا كل واحدة فيكو عبارة عن عنصر في ال
+
+108
+00:09:22,140 --> 00:09:26,560
+vector space الشكل هذي تمام جيت قلت للبنات السطر
+
+109
+00:09:26,560 --> 00:09:30,930
+هذا كله انتج للناحية الثانية يبقى كأنه أنا أخدت 
+
+110
+00:09:30,930 --> 00:09:35,490
+حالة خاصة من الأصلية المركبة الأولى كلها zero في 
+
+111
+00:09:35,490 --> 00:09:42,390
+كل three tuple تمام؟ بدأت أشوف هل هذا تحت عملية
+
+112
+00:09:42,390 --> 00:09:47,030
+الجمع العادية وتحت عملية الضرب العادية هل هو
+
+113
+00:09:47,030 --> 00:09:52,990
+vector space أم لا طلع هنا كل العناصر اللي المركبة
+
+114
+00:09:52,990 --> 00:09:56,610
+الأولى دائما و أبدا ب zero طب و المركبة الثانية و
+
+115
+00:09:56,610 --> 00:10:01,430
+الثالثة  أش ما كان يكون وما حطيتش عليهم قيود يمكن 
+
+116
+00:10:01,430 --> 00:10:06,250
+سالب يمكن موجب يمكن Zero كل أنا مقيد بالمركبة 
+
+117
+00:10:06,250 --> 00:10:10,510
+الأولى لازم تكون Zero و قلت لك X1 و X2 موجودة في
+
+118
+00:10:10,510 --> 00:10:14,510
+R موجودة بسالب كسر مش عارف ايه Zero ماليش علاقة بيه
+
+119
+00:10:14,510 --> 00:10:17,210
+أش ما يكون شكله ما يكون إن شاء الله يكون جذور
+
+120
+00:10:17,210 --> 00:10:22,210
+تربيعية وجذور تكعيبية لأنها set أي عناصر موجودة في 
+
+121
+00:10:22,210 --> 00:10:27,060
+ال set of real number طيب under the usual addition
+
+122
+00:10:27,060 --> 00:10:33,680
+عملية الجمع العادية تبع ال vectors and the usual
+
+123
+00:10:33,680 --> 00:10:38,040
+multiplication of scalar وعملية الضرب العادي لل
+
+124
+00:10:38,040 --> 00:10:42,280
+vectors في scalar و أخذنا سابقا إنه عملية لو ضربت 
+
+125
+00:10:42,280 --> 00:10:47,160
+element في vector بدّي أضربه في جميع ال components مش
+
+126
+00:10:47,160 --> 00:10:51,720
+هيك يبقى ده اسمه الضرب العادي والجمع بجمع
+
+127
+00:10:51,720 --> 00:10:57,070
+component was كل عنصر مع نظيره بيقول then ال V is
+
+128
+00:10:57,070 --> 00:11:02,490
+a vector space because يبقى هذا اللي فوق تحت عملية 
+
+129
+00:11:02,490 --> 00:11:06,010
+الجمع العادية والضرب العادية دي بيكون vector
+
+130
+00:11:06,010 --> 00:11:10,030
+space ما هو السبب بيقول لو أخدت three vectors
+
+131
+00:11:10,030 --> 00:11:15,770
+موجودة في V طلعي المركبة طلعي كلّه المركبة الأولى
+
+132
+00:11:15,770 --> 00:11:25,990
+والمركبة الأولى والمركب الأولى كلّه بأسفار موجودة 
+
+133
+00:11:25,990 --> 00:11:31,690
+في V بداية أشوف الخواص العاشرة هل ال U زائد ال V
+
+134
+00:11:31,690 --> 00:11:37,070
+موجود في V ولا لأ يبقى بداية للخاصية الأولى نمر 
+
+135
+00:11:37,070 --> 00:11:42,370
+واحد بياخذ ال U زائد ال V يبقى هذا بده يعطيني 
+
+136
+00:11:42,370 --> 00:11:48,130
+Zero و X واحد و X اثنين زائد Zero و Y واحد و Y
+
+137
+00:11:48,130 --> 00:11:55,140
+اثنين و Y يساوي احنا قلنا هذه عملية الجمع عادية لمين؟
+
+138
+00:11:55,140 --> 00:11:59,040
+للـ vectors يبقى عملية الجمع العادية بجمع
+
+139
+00:11:59,040 --> 00:12:08,440
+component y 0 مع 0 بقدرش 0 X1 زائد Y1 X2 زائد Y2
+
+140
+00:12:08,440 --> 00:12:12,630
+موجودة في V ولا يا بنات؟ موجود في V ليش؟ لأن الـ
+
+141
+00:12:12,630 --> 00:12:17,290
+element الأول أو المركبة الأولى في كل vector يساوي
+
+142
+00:12:17,290 --> 00:12:23,030
+0 إذا تحقق الخاصية الأولى بدّي أجرب الخاصية
+
+143
+00:12:23,030 --> 00:12:28,750
+الثانية نمرة 2 بدي أخد ال U زائد ال V يبقى .. بدّي 
+
+144
+00:12:28,750 --> 00:12:33,970
+أجمعه لغاية يا بنات يبقى هنا 0 زائد 0 ب 0 X1 زائد 
+
+145
+00:12:33,970 --> 00:12:44,370
+Y1 X2 زائد Y2 موجودة في V موجودة في V أنا بدي خاصية 
+
+146
+00:12:44,370 --> 00:12:51,790
+الإبدال أليس التهادي تساوي Zero one الآن X واحد زائد
+
+147
+00:12:51,790 --> 00:12:57,030
+Y واحد مش هدول X واحد و Y واحد أعداد موجودة في 
+
+148
+00:12:57,030 --> 00:13:01,810
+الست في real numbers عملية جمع الأعداد العادية هذه
+
+149
+00:13:01,810 --> 00:13:05,210
+عملية إبدالية ولا لا؟ أنا بقول خمسة زائد ستة و
+
+150
+00:13:05,210 --> 00:13:09,030
+الله ستة زائد خمسة ما هي نفس الشيء إذا باجي بقول
+
+151
+00:13:09,030 --> 00:13:16,210
+هذا Y واحد زائد X واحد و Y اثنين زائد X اثنين اللي 
+
+152
+00:13:16,210 --> 00:13:23,350
+بقدر أقول هذه Zero و Y واحد و Y اثنين زائد Zero X
+
+153
+00:13:23,350 --> 00:13:28,490
+واحد و X اثنين صحيح ولا لأ؟ يعني فصلت هذا ال vector
+
+154
+00:13:28,490 --> 00:13:32,710
+إلى مجموع two vectors طب الأول مين هو؟ مش V
+
+155
+00:13:32,710 --> 00:13:38,930
+و الثاني يبقى V زائد ال U يبقى بدأت ب U زائد ال V
+
+156
+00:13:38,930 --> 00:13:44,130
+وصلت إلى V زائد ال U يبقى تحقق الخاصية الأولى
+
+157
+00:13:44,130 --> 00:13:48,800
+والخاصية الثانية عندنا بدنا نروح لمين؟ للخاصية 
+
+158
+00:13:48,800 --> 00:13:54,360
+الثالثة يبقى باخذ U زائد V زائد W
+
+159
+00:13:59,340 --> 00:14:04,300
+و X1 و X2 زائد ال V زائد ال W بدّي أجمع على طول 
+
+160
+00:14:04,300 --> 00:14:10,640
+الخط هاي عند ال V وهذه ال W بدي أجمعها مباشرة يبقى
+
+161
+00:14:10,640 --> 00:14:22,570
+Zero Y1 زائد Z1 و Y2 زائد Z2 الآن بدأجي أجمع صار
+
+162
+00:14:22,570 --> 00:14:25,650
+عندي vector وعندي vector ثاني بدأ أجمع component
+
+163
+00:14:25,650 --> 00:14:33,650
+twice 00 ب 0 يبقى بيصير عندي X واحد زائد Y واحد
+
+164
+00:14:33,650 --> 00:14:46,190
+زائد Z واحد و X اثنين زائد Y اثنين زائد Z اثنين 
+
+165
+00:14:46,190 --> 00:14:54,460
+بالشكل اللي عندنا طيب هذا الكلام بده يساوي بدأجي 
+
+166
+00:14:54,460 --> 00:14:59,700
+للي وصلت له هذا هدول كلهم real number عملية الجمع 
+
+167
+00:14:59,700 --> 00:15:04,160
+على ال real number إدماجية ولا لا؟ يبقى خلاص إذا
+
+168
+00:15:04,160 --> 00:15:09,860
+بقدر أكتب هذه على الشكل التالي هي عبارة عن Zero و
+
+169
+00:15:09,860 --> 00:15:17,480
+X واحد زائد Y واحد زائد Z واحد تمام هذا ال term
+
+170
+00:15:17,480 --> 00:15:25,640
+الأول و ال term الثاني بقدر اقول X واحد زائد Y
+
+171
+00:15:25,640 --> 00:15:30,840
+واحد زائد Z واحد وهذه بقول X اثنين زائد Y اثنين 
+
+172
+00:15:30,840 --> 00:15:39,220
+زائد Z اثنين تمام إذا هذه بقدر أقول تساوي بدأت 
+
+173
+00:15:39,220 --> 00:15:44,300
+أحطها على شكل مجموع two vectors إذا بقدر أقول هذا
+
+174
+00:15:44,300 --> 00:15:54,100
+Zero و X واحد زائد Y واحد و X اثنين زائد Y اثنين
+
+175
+00:15:54,100 --> 00:16:00,580
+زائد ضال عندي Zero و ضال عندي Z واحد و ضال عندي Z
+
+1
+
+201
+00:18:48,400 --> 00:18:58,430
+أقول له  U + (-U) = 0 
+
+202
+00:18:58,430 --> 00:19:10,130
+X1 + X2 + 0  -X1 - X2 تمام نجمع 0 مع 0 ب 0
+
+203
+00:19:10,130 --> 00:19:18,110
+X1 و نقص X1 ب 0 X2 و نقص X2 ب 0 مين هو هذا؟ هذا ال
+
+204
+00:19:18,110 --> 00:19:27,610
+zero vector. Similarly بنفس الطريقة سالب
+
+205
+00:19:27,610 --> 00:19:33,810
+U + (-U) = the zero vector إذا تحققت الخاصية
+
+206
+00:19:33,810 --> 00:19:39,590
+رقم خمسة بدنا نحقق باقي الخواص خليني أمسح اللي فوق
+
+207
+00:19:39,590 --> 00:19:45,610
+هذا طيب هذا اللي مالهوش لزوم من هنا وفوق نمسحه
+
+208
+00:19:56,930 --> 00:20:01,810
+خلصنا الخاصية الخامسة وانتقلنا للخاصية السادسة، خاصية
+
+209
+00:20:01,810 --> 00:20:06,230
+السادسة بيقول لو كان أخذت scalar موجود في R و U 
+
+210
+00:20:06,230 --> 00:20:11,430
+موجود في V فحصل ضربه ما بدي يكون موجود في V يبقى 
+
+211
+00:20:11,430 --> 00:20:18,390
+بدي أخد هنا F ، الـ A موجود في R scalar و الـ U اللي
+
+212
+00:20:18,390 --> 00:20:25,310
+هي يساوي (0, X1, X2) موجودات في V then
+
+213
+00:20:25,310 --> 00:20:33,740
+بدي أخد الـ A في الـ U يبقى هذه A بدي أضربها في الـ 0 
+
+214
+00:20:33,740 --> 00:20:39,420
+X1 و X2 يساوي الـ A في الـ 0 بقداش يا بنات؟
+
+215
+00:20:39,420 --> 00:20:46,200
+Zero وهنا A X1 وهنا A X2، إيش رأيك في ال vector 
+
+216
+00:20:46,200 --> 00:20:50,120
+اللي طلع موجود في V ولا لأ؟ لأن المركبة الأولى
+
+217
+00:20:50,620 --> 00:20:55,820
+والباقية في نفس المكان،  يكون يبقى هذا موجود في ال vector
+
+218
+00:20:55,820 --> 00:21:01,020
+space V وبالتالي اتحققت الخاصية السادسة بدنا نروح 
+
+219
+00:21:01,020 --> 00:21:05,700
+للخاصية السابعة، الخاصية السابعة بيقول لو كان A 
+
+220
+00:21:05,700 --> 00:21:13,980
+موجود في R و U و V موجودة في U يبقى هنا F الـ A
+
+221
+00:21:13,980 --> 00:21:21,940
+موجودة في R and الـ U اللي هي (0, 0, X1, X2) 
+
+222
+00:21:21,940 --> 00:21:30,080
+و الـ V (0, Y1, Y2) موجودات في
+
+223
+00:21:30,080 --> 00:21:40,020
+V then بدي أخد الـ A Dot الـ U زائدي الـ V يبقى الـ A
+
+224
+00:21:40,020 --> 00:21:46,430
+Dot الـ U زائد الـ V بدي أجمع component twice يبقى 
+
+225
+00:21:46,430 --> 00:21:55,970
+(0, X1 + Y1, X2 + Y2) بدي 
+
+226
+00:21:55,970 --> 00:22:05,350
+أضرب يبقى هاد 0 و a في (x1 + y1) و a 
+
+227
+00:22:05,350 --> 00:22:17,030
+في (x2 + y2) ليش ضربتك؟ لأن ضرب عادي طيب
+
+228
+00:22:17,030 --> 00:22:27,330
+هذا الكلام بده يساوي بدو يساوي (0, ax1 + ay1, 
+
+229
+00:22:27,330 --> 00:22:32,650
+ax2 + ay2) 
+
+230
+00:22:32,650 --> 00:22:39,820
+هذا صار vector واحد، شو رأيك
+
+231
+00:22:39,820 --> 00:22:45,900
+ممكن أجزه الى two vectors، إيش ال two vectors يعني؟
+
+232
+00:22:45,900 --> 00:22:53,700
+ممكن أقول هذا (0, ax1, ax2) زائد
+
+233
+00:22:53,700 --> 00:23:02,480
+(0, ay1, ay2) لو جمعتهم بيطلع عندي هذا
+
+234
+00:23:02,480 --> 00:23:08,260
+مرة ثانية طيب بدي أركز على خواص ال scalar أظن بقدر أخد 
+
+235
+00:23:08,260 --> 00:23:19,160
+a عامل مشترك من الكل برا بيظل (0, x1, x2) زائد a (0, y1,
+
+236
+00:23:19,160 --> 00:23:29,950
+y2) يبقى هذا A الأولاني هو الـ U والتاني A في الـ V 
+
+237
+00:23:29,950 --> 00:23:36,290
+الشكل اللي عنها يبقى بناء على A ضد U زائد V يبقى A 
+
+238
+00:23:36,290 --> 00:23:44,270
+ضد U زائد A ضد V وبالتالي تحققت الخاصية السابعة
+
+239
+00:23:44,750 --> 00:23:51,810
+بنروح للخاصية الثامنة يبقى باجي بقوله ثمانية if
+
+240
+00:23:51,810 --> 00:24:00,710
+الـ A و الـ B موجودة في R and الـ U (0, X1, X
+
+241
+00:24:00,710 --> 00:24:09,870
+2) موجودة في V then بدي أخد الـ A زائد الـ B Dot
+
+242
+00:24:09,870 --> 00:24:20,230
+من Dot الـ U يساوي A زائد B ضات الـ U
+
+243
+00:24:26,050 --> 00:24:29,870
+هذا مجموع two real numbers يبقى real number واحد
+
+244
+00:24:29,870 --> 00:24:35,310
+يبقى بدي أضرب جوبه حسب الضرب العادي يبقى هذا بقداش؟
+
+245
+00:24:35,310 --> 00:24:44,530
+بـ 0، نجي للي بعدها هذه a زائد الـ B في الـ X1 وهنا 
+
+246
+00:24:44,530 --> 00:24:51,770
+a زائد الـ B في من؟ في الـ X2 وهيقفلنا الجزء، هذه بقدر
+
+247
+00:24:51,770 --> 00:24:57,750
+أقول عليها ما يأتي، يساوي هاي 0 زي ما هي وهذه
+
+248
+00:24:57,750 --> 00:25:01,930
+بقدر أفكها لأن الـ X1 والـ X2 real number
+
+249
+00:25:01,930 --> 00:25:08,270
+والـ A و الـ B real number يبقى A X1 زائد B X
+
+250
+00:25:08,270 --> 00:25:18,280
+1 , A X2 زائد B X2 ممكن أجزه إلى two 
+
+251
+00:25:18,280 --> 00:25:28,180
+vectors يبقى هذه بقدر أقول (0, ax1, ax2) زائد 
+
+252
+00:25:28,180 --> 00:25:39,510
+(0, bx1, bx2) ممكن أخد الـ A برا يبقى الـ A في 
+
+253
+00:25:39,510 --> 00:25:50,050
+(0, X1, X2) زائد B في (0, X1, X
+
+254
+00:25:50,050 --> 00:25:57,030
+2) يبقى هذه بدأت تساوي A ضد الـ U زائد B ضد الـ
+
+255
+00:25:57,030 --> 00:26:03,150
+U وبالتالي تحققت الخاصية رقم ثمانية يبقى ثمانية
+
+256
+00:26:07,780 --> 00:26:18,160
+الخاصية التاسعة يبقى الفرض
+
+257
+00:26:18,160 --> 00:26:28,520
+التاسعة، بدأت أخد F الـ A والـ B موجودة في R and الـ
+
+258
+00:26:28,520 --> 00:26:36,780
+U (0, X1, X2) موجودة في V then بدأت أخد الـ
+
+259
+00:26:36,780 --> 00:26:46,120
+A في الـ B ضد الـ U يساوي A في ض ضد الـ U يبقى بدي اضرب
+
+260
+00:26:46,120 --> 00:26:52,220
+B في كل عنصر من العناصر اللي عندنا يبقى هاي 0 و
+
+261
+00:26:52,220 --> 00:27:00,280
+B X1 و B X2، الشكل اللي عندنا هنا الآن بدي 
+
+262
+00:27:00,280 --> 00:27:07,280
+اضرب الـ A يبقى هذا الكلام بدي يساوي A في 0 ب
+
+263
+00:27:07,280 --> 00:27:17,690
+0 يبقى A B X1 و A B X2 بالشكل اللي عندنا
+
+264
+00:27:17,690 --> 00:27:24,790
+هنا، هذا الكلام بده يساوي الآن الـ A و الـ B و الـ X1 
+
+265
+00:27:24,790 --> 00:27:29,830
+كلهم real numbers وكذلك الـ A و الـ B و الـ X2 كله
+
+266
+00:27:29,830 --> 00:27:36,350
+real numbers يبقى بقدر أقول هذا 0 وهذا A B X1
+
+267
+00:27:36,350 --> 00:27:43,980
+وفي نفس الوقت A B X2 بقدر أخد الـ a B برا يبقى 
+
+268
+00:27:43,980 --> 00:27:51,160
+هذا a B برا كله في مين؟ في الـ (0, x1, x2)
+
+269
+00:27:51,160 --> 00:27:59,360
+يبقى هذا a B ضد الـ U يبقى تحققت الخاصية رقم 9
+
+270
+00:27:59,360 --> 00:28:07,540
+بنانتقل للخاصية رقم 10 الأخيرة بدي 1. (0, x1, x2) يبقى 1 
+
+271
+00:28:07,540 --> 00:28:12,520
+في (0, x1, x2) 
+
+272
+00:28:13,880 --> 00:28:17,600
+الواحد لما نضربه في 0 بيبقى ده جمناته بـ 0 
+
+273
+00:28:17,600 --> 00:28:23,660
+الواحد في الـ X1 بالـ X1، الواحد في الـ X2 بالـ X2 يبقى 
+
+274
+00:28:23,660 --> 00:28:29,940
+هذا أعطاني مين؟ الـ U يبقى قلنالك من البداية أن هذا
+
+275
+00:28:29,940 --> 00:28:35,040
+vector space ليش قلنا؟ because وروحنا وجينا العشر
+
+276
+00:28:35,040 --> 00:28:39,660
+خواص كلها محققة يبقى أصبح هذا اللي عندنا اللي هو
+
+277
+00:28:39,660 --> 00:28:45,840
+vector space، طبعاً مش كل ستة بنعطيها لك بتكون vector
+
+278
+00:28:45,840 --> 00:28:51,660
+space و بضروح أبدأ أطبق الخواص العشرة، تمام؟ يعني
+
+279
+00:28:51,660 --> 00:28:56,840
+ليس بالضرورة إن راح أطول خاصية ما تحققش، يبقى أروح
+
+280
+00:28:56,840 --> 00:29:00,240
+أدور على الباقي، ما أدورش على الباقي، خلاص، not vector
+
+281
+00:29:00,240 --> 00:29:03,940
+space وباس، لقيت الأولى اتحققت بروح للتانية وما 
+
+282
+00:29:03,940 --> 00:29:07,400
+اتحققتش، الثانية not vector space وبسيب الباقي و
+
+283
+00:29:07,400 --> 00:29:12,520
+هكذا يعني، وين خاصية بتتحققش بقول يبقى هذا ماهو 
+
+284
+00:29:12,520 --> 00:29:16,880
+vector space وبنتهي، الدلة الثانية الأولى اتحققت
+
+285
+00:29:16,880 --> 00:29:20,680
+إنها بروح للتالت بروح للرابع لما إذا اتحققوا 
+
+286
+00:29:20,680 --> 00:29:24,400
+العشرة كلهم يبقى هو vector space، يبقى إذا اختلت أي 
+
+287
+00:29:24,400 --> 00:29:28,320
+خاصية من الخاصة العشر بكون معله ماهو vector
+
+288
+00:29:28,320 --> 00:29:35,680
+space هذا أول مثال على هذا الموضوع، لا يزال عندنا 
+
+289
+00:29:35,680 --> 00:29:45,140
+العديد من الأمثلة، دي المثال رقم اثنين هذا 
+
+290
+00:29:45,140 --> 00:29:50,320
+إذا طلع vector space إذا ما طلعش vector space 
+
+291
+00:29:50,320 --> 00:29:55,990
+يمكن تسوي خطوة واحدة ولا لا؟ وإذا أنت دقيقة نظر
+
+292
+00:29:55,990 --> 00:30:00,090
+وشاطرة في الحسابات ومجرد النظر بتقولي هذه البرشم
+
+293
+00:30:00,090 --> 00:30:04,230
+تنفعش للخاصية الفلانية على طول من دون مجرمي وتروح
+
+294
+00:30:04,230 --> 00:30:09,030
+تكتبي ليها وبتكشف الباقي 100% تمام، نعطي المثال 
+
+295
+00:30:09,030 --> 00:30:17,970
+رقم اثنين example two هذا سؤال خمسة من الكتاب 
+
+296
+00:30:17,970 --> 00:30:20,690
+بيقول let V to sound
+
+297
+00:30:24,960 --> 00:30:34,460
+كل العناصر على الشكل (1, X, Y) بحيث X و Y 
+
+298
+00:30:34,460 --> 00:30:39,800
+موجودة في set of real numbers under usual addition 
+
+299
+00:30:40,930 --> 00:30:49,930
+under usual addition تحت عملية الجمع العادية and
+
+300
+00:30:49,930 --> 00:30:57,030
+وفي نفس الوقت usual scalar multiplication، usual
+
+301
+00:30:57,030 --> 00:31:03,250
+scalar multiplication 
+
+302
+00:31:03,250 --> 00:31:06,370
+تحت 
+
+303
+00:31:06,370 --> 00:31:18,190
+عملية الضرب والجمع العادية then is not
+
+304
+00:31:18,190 --> 00:31:26,430
+a vector space
+
+305
+00:31:32,720 --> 00:31:37,520
+ومجرد النظر هذا الـ V اللي عندنا هذه تحت عملية
+
+306
+00:31:37,520 --> 00:31:40,760
+الجمع العادية والضرب العادية ليست في الاقتراضية 
+
+307
+00:31:40,760 --> 00:31:44,520
+ليه؟ بدي واحدة تحكي، بس واحدة ترفع أيديها وتحكي 
+
+308
+00:31:44,520 --> 00:31:49,680
+أنا بقول فيش zero element ما عنديش الحالة هذا وجهة 
+
+309
+00:31:49,680 --> 00:31:55,200
+نظر، في وجهة نظر ثانية؟ قبل الـ zero طيب شوفي اللي
+
+310
+00:31:55,200 --> 00:32:01,520
+قبل الـ zero، اجمع اثنين، اجمع لو جمعت اثنين ايش 
+
+311
+00:32:01,520 --> 00:32:02,100
+بيطلع؟ 
+
+312
+00:32:06,540 --> 00:32:11,420
+يبقى عملية الجمع لا تتحقق، صحيح ولا لأ؟ بروح بقوله 
+
+313
+00:32:11,420 --> 00:32:15,500
+هذا is not a vector space because
+
+314
+00:32:19,270 --> 00:32:26,570
+الـ U بدها تساوي (1, X1, Y1) و الـ V
+
+315
+00:32:26,570 --> 00:32:33,150
+دوسر (1, X2, Y2) موجودة في capital V
+
+316
+00:32:33,150 --> 00:32:42,170
+then الـ U زائد الـ V بدو يساوي (2, X1 + 
+
+317
+00:32:42,170 --> 00:32:48,860
+X2, X1 خليها بس لسهولة يا بنات خليها X
+
+318
+00:32:48,860 --> 00:32:57,060
+1 و X2، وهذي Y1 و Y2 تمام يبقى X
+
+319
+00:32:57,060 --> 00:33:04,800
+1 + Y1، X2 + Y2) does not
+
+320
+00:33:04,800 --> 00:33:09,740
+belong to V مش موجودة في V لأن أنا بدي ال
+
+321
+00:33:09,740 --> 00:33:14,550
+component اللي قداش تكون يبقى في حالة ال zero ينفع
+
+322
+00:33:14,550 --> 00:33:18,830
+يصير vector space لكن في حالة الواحد ما نفعش يكون
+
+323
+00:33:18,830 --> 00:33:24,230
+vector space، ماهو vector space، طيب مثال ثلاثة 
+
+324
+00:33:24,230 --> 00:33:32,530
+مثال ثلاثة له سؤال سبعة من الكتاب كذلك سؤال سبعة 
+
+325
+00:33:32,530 --> 00:33:42,530
+بيقول let الـ V تساوي كل المصفوفات A بحيث الـ A is
+
+326
+00:33:42,530 --> 00:33:48,370
+two by two matrix، كل المصفوفات اللي نظامها اثنين 
+
+327
+00:33:48,370 --> 00:33:56,450
+في اثنين with determinant للـ A لا يساوي 0
+
+328
+00:33:56,450 --> 00:34:02,970
+under usual
+
+329
+00:34:09,830 --> 00:34:19,150
+addition and scalar multiplication 
+
+330
+00:34:19,150 --> 00:34:26,610
+of
+
+331
+00:34:26,610 --> 00:34:38,460
+matrices then إيش رأيك؟ الـ V مش عارف اكتب هي
+
+332
+00:34:38,460 --> 00:34:42,420
+vector space ولا not vector space، نيجي مين هي الـ V
+
+333
+00:34:42,420 --> 00:34:51,200
+في الأول الـ V كل المصفوفات A اللي نظامها 2 في 2 و
+
+334
+00:34:51,200 --> 00:34:55,760
+اللي محددها ما له لا يساوي 0 اللي محدد فيها لا 
+
+335
+00:34:55,760 --> 00:34:59,550
+يساوي 0 يبقى كل المصوات اللي نظامها اثنين في اثنين
+
+336
+00:34:59,550 --> 00:35:04,850
+و اللي محددة لا يساوي تجمعتهم وحطيتهم في V، عرفت
+
+337
+00:35:04,850 --> 00:35:09,510
+عليها عملية جمع المصوفات العادي وهو جمع component
+
+338
+00:35:09,510 --> 00:35:14,630
+-wise وعرفت عليها ضرب المصوفة في scalar وهو ضرب ال
+
+339
+00:35:14,630 --> 00:35:17,730
+real number في كل عنصر من العناصر المصوفة اللي 
+
+340
+00:35:17,730 --> 00:35:21,670
+كانت usual addition and usual multiplication تمام 
+
+341
+00:35:21,990 --> 00:35:27,530
+تحت العمليتين الاثنين هدول هل الـ V Vector Space أم
+
+342
+00:35:27,530 --> 00:35:35,990
+لا؟ طبعاً لأ أبسط شغلة بدي Zero Matrix، هل الـ Zero
+
+343
+00:35:35,990 --> 00:35:40,270
+Matrix المحدد تبعها لا يساوي 0؟ لأ طبعاً، يبقى جد
+
+344
+00:35:40,270 --> 00:35:48,990
+إن الـ V is not a vector space because
+
+345
+00:35:54,180 --> 00:36:10,760
+it does not contain the zero matrix since 
+
+346
+00:36:15,640 --> 00:36:23,320
+الـ Determinant للمصفوفة 0 يبقى 0 يبقى
+
+347
+00:36:23,320 --> 00:36:28,760
+الخاصية تبع العنصر الصفري لم تتحقق لذلك هذا ليس
+
+348
+00:36:28,760 --> 00:36:37,320
+Vector Space فبالمثال 
+
+349
+00:36:37,320 --> 00:36:47,640
+رقم أربعة بقول Let capital V كل العناصر على الشكل (X
+
+350
+00:36:47,640 --> 00:36:57,480
+، Y ، Z) بحيث إن الـ X و Y و Z موجودة في set of real 
+
+351
+00:36:57,480 --> 00:37:03,900
+numbers، define addition
+
+352
+00:37:03,900 --> 00:37:07,380
+define 
+
+353
+00:37:07,380 --> 00:37:09,780
+addition and 
+
+354
+00:37:16,800 --> 00:37:26,020
+multiplication on the by الـ
+
+355
+00:37:26,020 --> 00:37:40,400
+(X1, Y1, Z1) زائد (X2, Y2, Z2) بده يساوي اللي 
+
+356
+00:37:40,400 --> 00:37:54,760
+هو (X1, Y1, Z1) وهنا (X2, Y2, Z2)، X1 + X2، Y1
+
+357
+00:37:54,760 --> 00:38:06,920
++ Y2 وهنا Z1 + Z2، هذا الجمع and 
+
+358
+00:38:06,920 --> 00:38:11,000
+ال
+
+359
+00:38:11,000 --> 00:38:25,540
+a في (x, y, z) يساوي (ax, y, z)، then الـ V 
+
+360
+00:38:25,540 --> 00:38:28,580
+is الله أعلم
+
+361
+00:38:40,130 --> 00:38:46,110
+كيف؟ آه بس بنضربها في المركبة الأولى، يعني عملية 
+
+362
+00:38:46,110 --> 00:38:50,690
+الجمع كما هي component-wise والإيه بس بنضربها في 
+
+363
+00:38:50,690 --> 00:38:59,410
+المركبة الأولى فقط لا غير، تمام؟ يعني إنه هذه ال
+
+364
+00:38:59,410 --> 00:39:07,410
+Sid هي هيك قصيرة، فاهم
+
+365
+00:39:07,410 --> 00:39:13,190
+يعني هذه ال Sid خاص فيه لأنه .. خاص فيه .. فاهم
+
+366
+00:39:17,540 --> 00:39:21,240
+هل هذا vector space ولا ماهو vector space، بتخيل
+
+367
+00:39:21,240 --> 00:39:28,220
+أنه ماهو vector space سبق because لو أخذت يبقى 
+
+368
+00:39:28,220 --> 00:39:40,920
+هذا is not a vector space because لو 
+
+369
+00:39:40,920 --> 00:39:47,910
+أخذت يا مناد (a + b) في من؟ في U يبقى هذا 
+
+370
+00:39:47,910 --> 00:39:57,190
+بيصير (a + b) في
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5d60b62bab8243ec03839020ad4549159061b0d4
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0.srt
@@ -0,0 +1,1365 @@
+
+1
+00:00:19,490 --> 00:00:25,010
+بسم الله الرحمن الرحيم نعود الآن إلى محاضرة الصباح
+
+2
+00:00:25,010 --> 00:00:30,130
+بدأنا في محاضرة الصباح بـ Cauchy Euler equation
+
+3
+00:00:30,130 --> 00:00:34,290
+حطينا الصيغة العامة لها وبعدين خدنا حالة منها
+
+4
+00:00:34,290 --> 00:00:36,850
+خاصة اللي هو كانت من
+
+5
+00:00:48,230 --> 00:00:52,730
+المعادلة الأصلية لـ كوشي  أن هناك
+
+6
+00:00:52,730 --> 00:00:58,380
+طريقان للحل، الطريق الأول اللي هو بالتعويض قلنا لو
+
+7
+00:00:58,380 --> 00:01:04,980
+حطينا التعويضة X يساوي E أُس T، خدنا ln للطرفين فصار
+
+8
+00:01:04,980 --> 00:01:11,080
+T تساوي ln X، اشتقينا DT على DX يساوي 1 على X، ثم 
+
+9
+00:01:11,080 --> 00:01:15,880
+بعد ذلك روحنا جيبنا Y' و Y'' بدل ما نشتق
+
+10
+00:01:15,880 --> 00:01:20,260
+بالنسبة لـ X، حولنا الاشتقاق بالنسبة إلى T وبالتالي
+
+11
+00:01:20,260 --> 00:01:24,490
+عوضنا  الـ Variables وسمينا هذه هي الطريقة
+
+12
+00:01:24,490 --> 00:01:29,270
+الأولى، يعني الطريقة الأولى بواسطه تعويضة بتبعدنا
+
+13
+00:01:29,270 --> 00:01:35,110
+حولنا المعادلة من معادلة بمعاملات متغيرة إلى
+
+14
+00:01:35,110 --> 00:01:39,670
+معادلة بمعاملات ثابتة وبالتالي بنروح نحل هذه كما 
+
+15
+00:01:39,670 --> 00:01:44,090
+كنا بنحل في الـ sections الماضية، انتقلنا الآن إلى
+
+16
+00:01:44,090 --> 00:01:49,970
+الطريقة الثانية اللي كتبناها قبل ساعتين من الآن 
+
+17
+00:01:49,970 --> 00:01:56,510
+طريقة نفترض أن Y يساوي X أُس R عبارة عن solution و
+
+18
+00:01:56,510 --> 00:02:00,170
+رحنا اشتغلنا مرة مرتين ثلاثة N من المرات وعوضنا
+
+19
+00:02:00,170 --> 00:02:07,400
+في المعادلة، حصلنا على المعادلة المساعدة
+
+20
+00:02:07,400 --> 00:02:13,440
+أو المعادلة المميزة للمعادلة الأصلية ورحنا هذه 
+
+21
+00:02:13,440 --> 00:02:17,880
+المعادلة لما جينا نحل هذه المعادلة صار عندي أحد
+
+22
+00:02:17,880 --> 00:02:22,780
+ثلاثة احتمالات، الاحتمال الأول، الاحتمال الثاني، 
+
+23
+00:02:22,780 --> 00:02:26,760
+الاحتمال الثالث، سميتها ثلاث حالات نجي للحالة
+
+24
+00:02:26,760 --> 00:02:30,800
+الأولى لو equation double star هذه المعادلة
+
+25
+00:02:30,800 --> 00:02:35,900
+المميزة has distinct roots يبقى صار عندي R واحد
+
+26
+00:02:35,900 --> 00:02:40,700
+لا يساوي R اثنين، لا يساوي R ثلاثة، لا يساوي... لا يساوي RN 
+
+27
+00:02:40,700 --> 00:02:45,220
+ولا واحد زي الثاني، ما هو الشكل العام للحل يبقى 
+
+28
+00:02:45,220 --> 00:02:48,160
+الشكل العام للحل C1 في X أُس R1
+
+29
+00:02:56,780 --> 00:03:01,000
+الحلول يبقى كونصا في الأول، و كونصا في الثاني، و
+
+30
+00:03:01,000 --> 00:03:05,420
+يمثل الـ general solution إذا الحلول كانوا real and
+
+31
+00:03:05,420 --> 00:03:11,030
+different، بنجي للحالة الثانية لو equation star has
+
+32
+00:03:11,030 --> 00:03:16,070
+complex roots، المعادلة طالعة عندما فيها جذور
+
+33
+00:03:16,070 --> 00:03:20,890
+تخيلية، فعلى سبيل المثال لو أخدنا جذرين منهم ماذا
+
+34
+00:03:20,890 --> 00:03:25,330
+يكون شكل الحل؟ يبقى باجي بقول الحل بيكون X to the
+
+35
+00:03:25,330 --> 00:03:31,390
+power إيه؟ ليش؟ لأنه بدي يطلع اللي هو الـ R يساوي A
+
+36
+00:03:31,390 --> 00:03:37,450
+زائد IB، تمام؟ A زائد و الـ conjugate تبعه A ناقص IB
+
+37
+00:03:37,450 --> 00:03:41,470
+الحل الأول R واحد A زائد IB والحل الثاني R اثنين
+
+38
+00:03:41,470 --> 00:03:47,510
+بديه يساوي A ناقص IB، يبقى الـ E الـ X أُس A في مين؟ في
+
+39
+00:03:47,510 --> 00:03:53,230
+C واحد cos B ln X زائد C اثنين sin B ln
+
+40
+00:03:53,230 --> 00:03:59,050
+X، يعني يا بنات هنا كنا نقول هناك في الحقيقي في 
+
+41
+00:03:59,050 --> 00:04:04,550
+التخيلة لما كانوا المعاملات حقيقية، بقى نقول C1 Cos
+
+42
+00:04:04,550 --> 00:04:11,050
+Bx ماعنديش ln لكن هنا جانبين ln X زي C2 Sin B
+
+43
+00:04:11,050 --> 00:04:16,140
+ln X، الحالة الثالثة، الحالة الثالثة لحالة الـ real 
+
+44
+00:04:16,140 --> 00:04:20,000
+قد يكون real و repeated وقد يكون complex و
+
+45
+00:04:20,000 --> 00:04:24,300
+repeated، فكيف نسوي في هذه الحالة؟ يبقى باجي للحالة 
+
+46
+00:04:24,300 --> 00:04:27,780
+الأولى الـ equation اثنين has real repeated roots of
+
+47
+00:04:27,780 --> 00:04:33,000
+multiplicity S، عدد مرات التكرار S والباقي يمكن
+
+48
+00:04:33,000 --> 00:04:38,320
+يكون real يا إما S ممكن يكون كله complex وتساوي N 
+
+49
+00:04:38,320 --> 00:04:43,740
+بس بشرط أن الـ N عدد زوجي، يبقى بيصير R واحد يساوي R
+
+50
+00:04:43,740 --> 00:04:48,700
+الثاني يساوي RS يساوي R، يبقى في هذه الحالة شكل الـ
+
+51
+00:04:48,700 --> 00:04:52,400
+general solution زي شكله with constant
+
+52
+00:04:52,400 --> 00:04:57,720
+coefficients، ما عدل X بشيله وبحط بداله ln X 
+
+53
+00:04:57,720 --> 00:05:02,240
+والباقي كل شيء زي ما هو، تطلع C1، C2 ln X، C3 ln X
+
+54
+00:05:02,240 --> 00:05:07,700
+نرويها C4 ln X تكريم لغاية ما وصل لـ CS ln X أُس S
+
+55
+00:05:07,700 --> 00:05:15,890
+-1 في X أُس R لأن الأُس هذا صار مكرر، تمام؟ طيب لو
+
+56
+00:05:15,890 --> 00:05:20,210
+كانوا الـ roots are repeated complex conjugate لو
+
+57
+00:05:20,210 --> 00:05:24,610
+كانوا هذا real لو كانوا complex يبقى بدي يصير الحل
+
+58
+00:05:24,610 --> 00:05:29,450
+X أُس A زي ما هي تبعيتي تبع الـ complex بس ايش بدي
+
+59
+00:05:29,450 --> 00:05:32,930
+يصير؟ A واحد زي دي اثنين ln X زي دي A أُس ln
+
+60
+00:05:41,450 --> 00:05:48,130
+الثوابت المتغيرات C1 وC2 لغاية CS كلها في Sin B ln
+
+61
+00:05:48,130 --> 00:05:54,460
+X، يبقى هذه بدي أفهمها إنها عبارة عن مين؟ عبارة عن
+
+62
+00:05:54,460 --> 00:06:00,000
+الحل X أُس A في الـ polynomial الكبير هذا من 
+
+63
+00:06:00,000 --> 00:06:05,540
+الدرجة لأن S ناقص واحد في الـ cosine P ln X زي الـ
+
+64
+00:06:05,540 --> 00:06:09,000
+polynomial من نفس الدرجة Sin P ln X في حتة الـ
+
+65
+00:06:09,000 --> 00:06:13,340
+complex لكن في حالتها الـ real لا عندي Cosine ولا
+
+66
+00:06:13,340 --> 00:06:19,360
+عندي Sin polynomial فقط لغير في X أُس A، هل بتحب تسأل
+
+67
+00:06:19,360 --> 00:06:24,660
+أي سؤال هنا قبل أن ندخل الأمثلة؟
+
+68
+00:06:31,850 --> 00:06:35,070
+ماشي، المثال الأول طبعًا احنا حققنا معانا طريقتين يا
+
+69
+00:06:35,070 --> 00:06:39,290
+بنات أن قيدني بطريقة بدي التزم في انجل يوز the
+
+70
+00:06:39,290 --> 00:06:44,330
+substitution X يساوي E أُس T، يعني بده مين؟ بده
+
+71
+00:06:44,330 --> 00:06:48,450
+يحول المعلق، يمكن يقول لي كمان اجيب لي السؤال بطريقة
+
+72
+00:06:48,450 --> 00:06:52,690
+ثانية يعطي المعلق ويقول لي change او use the 
+
+73
+00:06:52,690 --> 00:06:57,630
+substitution X يساوي E أُس T to change، هذه هي 
+
+74
+00:06:57,630 --> 00:06:59,670
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار 
+
+75
+00:06:59,670 --> 00:07:00,610
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار 
+
+76
+00:07:00,610 --> 00:07:01,190
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار
+
+77
+00:07:01,190 --> 00:07:01,570
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار
+
+78
+00:07:01,570 --> 00:07:04,430
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار
+
+79
+00:07:04,430 --> 00:07:09,830
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار
+
+80
+00:07:09,830 --> 00:07:12,630
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار
+
+81
+00:07:12,630 --> 00:07:14,450
+الاختصار، الاختصار، الاختصار، الاختصار، الاختصار
+
+82
+00:07:14,450 --> 00:07:20,360
+الاختصار، الاختصار، الاختصار، الاختصار، يبقى أول
+
+83
+00:07:20,360 --> 00:07:23,180
+مثال يقول Find the general solution of the 
+
+84
+00:07:23,180 --> 00:07:27,580
+differential equation ولم يقيدني، ما قيدنيش، لكن أنا
+
+85
+00:07:27,580 --> 00:07:30,720
+كونه أول مثال بدي أحله بالطريقتين وبدي أبين أن 
+
+86
+00:07:30,720 --> 00:07:35,380
+الطريقتين ما لهما نفس الشيء، ما بتغيرش فيها ايه ولا 
+
+87
+00:07:35,380 --> 00:07:39,260
+حاجة، يبقى بدي أجي للحل الأول اللي عندنا هذا 
+
+88
+00:07:43,620 --> 00:07:51,100
+يبقى بداجة أقول استخدم التعويضة Put X يساوي E أُس
+
+89
+00:07:51,100 --> 00:07:58,260
+T، هذا بتعطيك T يساوي ln X، هذا بتعطيك الـ DT على DX
+
+90
+00:07:58,260 --> 00:08:05,720
+يساوي 1 على X and الـ Y' يا بنات كده ايش طلعت؟ مش 1
+
+91
+00:08:05,720 --> 00:08:12,120
+على X في الـ DY على DT صح؟ طب والـ Y''
+
+92
+00:08:17,770 --> 00:08:26,430
+D²Y على DT²، أيوة، ناقص DY على
+
+93
+00:08:26,430 --> 00:08:35,000
+DT، طب الحمد لله، بس أنت بتفرض التعويضة وتقول إذا
+
+94
+00:08:35,000 --> 00:08:37,700
+كذا ما عنديش مشكلة، ما عندك تروح تستنتجيها من أول و
+
+95
+00:08:37,700 --> 00:08:41,760
+جديد، لكن إذا كنت نسيتها بديك تروح تستنتجيها من أول
+
+96
+00:08:41,760 --> 00:08:46,560
+و جديد، طيب يبقى الآن بدي أمسك المعلومات هذه واعوض
+
+97
+00:08:46,560 --> 00:08:51,120
+وين؟ في المعادلة اللي هي أصلية اللي هي star يبقى
+
+98
+00:08:51,120 --> 00:08:55,000
+باجي بقول المعادلة star بصير X تربيع في الـ Y''
+
+99
+00:08:55,000 --> 00:09:03,930
+هي هي 1 على X تربيع في D²Y على DT² ناقص DY
+
+100
+00:09:03,930 --> 00:09:10,050
+على DT بالشكل اللي عندنا هنا اللي بعدها ناقص 3X 
+
+101
+00:09:10,050 --> 00:09:16,170
+فيه بدي أشيل الـ Y' وأحط قيمة التالي 1 على X في DY 
+
+102
+00:09:16,170 --> 00:09:24,510
+على DT، خلصنا منها، زائد 4Y، مش غيرها، تمام؟ كل هذا
+
+103
+00:09:24,510 --> 00:09:29,590
+الكلام يساوي كده؟ Zero، أظن X تربيع مع X تربيع راحت
+
+104
+00:09:29,590 --> 00:09:35,010
+مع السلامة، يبقى D Square Y على DT Square ناقص DY
+
+105
+00:09:35,010 --> 00:09:42,650
+على DT ناقص ثلاثة DY على DT زائد أربعة Y بدأت تساوي
+
+106
+00:09:42,650 --> 00:09:52,040
+Zero، لو روحنا جماعة مهدول بصير D2Y على DT2 ناقص 4DY
+
+107
+00:09:52,040 --> 00:10:00,600
+على DT زائد 4Y بده يساوي قداش؟ Zero، أطلع في المعادلة
+
+108
+00:10:00,600 --> 00:10:04,680
+star واطلع في المعادلة بعد التعويض كيف صارت
+
+109
+00:10:04,680 --> 00:10:09,820
+المعادلة star، المعاملات عندي متغيرات بدلالة الـ X
+
+110
+00:10:09,820 --> 00:10:15,400
+لكن لما حطيت التعويض هذه حولت إلى معادلة بمعاملات 
+
+111
+00:10:15,400 --> 00:10:21,460
+ثابتة، إذا بتروح أحلّي المعادلة هذه بمين؟ بالمعاملات 
+
+112
+00:10:21,460 --> 00:10:29,110
+الثابتة، كيف بنحلي الحل؟ let Y تساوي E أُس RT، ما عنديش
+
+113
+00:10:29,110 --> 00:10:33,250
+X هنا بطل يصير عندي X، الشغل نتوهّل من دلالة X إلى
+
+114
+00:10:33,250 --> 00:10:38,810
+دلالة T، يبقى بداجة أقول له let وسمّيلي هذه 
+
+115
+00:10:38,810 --> 00:10:47,970
+المعادلة رقم Star، let Y تساوي E أُس RT بـ A
+
+116
+00:10:47,970 --> 00:11:00,120
+solution of إذا كانت المقارنة مربوطة ثم المقارنة
+
+117
+00:11:00,120 --> 00:11:05,500
+الخاصة هي 
+
+118
+00:11:06,540 --> 00:11:14,900
+R تربيع ناقص أربعة R زائد أربعة يساوي Zero، يعني هذه
+
+119
+00:11:14,900 --> 00:11:21,440
+مالها R ناقص اثنين لكل تربيع يساوي Zero، يبقى الجذور 
+
+120
+00:11:21,440 --> 00:11:31,280
+حقيقية ومكررة كم مرة؟ مرتين، يبقى هذا معناه أن R
+
+121
+00:11:31,280 --> 00:11:41,750
+تساوي اثنين of multiplicity، بالإضافة لـ ECT، كررت مرتين 
+
+122
+00:11:41,750 --> 00:11:52,930
+إذا بدأت أقول له The general solution of equation
+
+123
+00:11:52,930 --> 00:12:00,880
+double star is Y تساوي، مش طبعًا أنا كنت ملاّعب
+
+124
+00:12:00,880 --> 00:12:04,660
+بدلالة text احنا راهيب نشتغل على T، يبقى شو بدي يصير 
+
+125
+00:12:04,660 --> 00:12:16,560
+تكرار مرتين يبقى C1 زي C2T في قداش؟ في E أُس اثنين T
+
+126
+00:12:16,560 --> 00:12:19,620
+طب
+
+127
+00:12:19,620 --> 00:12:27,050
+الجواب ايش طلعناه؟ بدلالة ايش؟ T،  والأصل بدرجة أو
+
+128
+00:12:27,050 --> 00:12:30,370
+بدلالة X، بكون جيب تحليل المعادلة الأصلية اللي هو
+
+129
+00:12:30,370 --> 00:12:34,970
+star، يبقى باجي بقوله The general solution of
+
+130
+00:12:34,970 --> 00:12:44,730
+equation A star is الـ Y يساوي C1 زائد C2 قداش؟ الـ 
+
+131
+00:12:44,730 --> 00:12:57,360
+T حطيناها قداش؟ لأن الـ X في E أُس 2T، لأن الـ X مظبوط
+
+132
+00:12:57,360 --> 00:13:03,480
+يبقى ايه صارت بدل لثمين X هذه؟ هذه يا بنات هي C1 
+
+133
+00:13:03,480 --> 00:13:12,320
+زائد C2 ln X، نجي هذه مش هذه E ln X تربيع اثنين
+
+134
+00:13:12,320 --> 00:13:17,420
+بدخلها جوا الـ ln الـ E والـ L عكس بعض يبقى صار جداش؟
+
+135
+00:13:17,420 --> 00:13:23,860
+X تربيع، يبقى هذا الحل بالطريقة الأولى، بدنا نروح
+
+136
+00:13:23,860 --> 00:13:30,980
+نحله بالطريقة، بالطريقة الثانية، نجربها لأنه ما قال لي 
+
+137
+00:13:30,980 --> 00:13:34,980
+احنا اثنين في الامتحان، أنا أجيب بالي الطريقة 
+
+138
+00:13:34,980 --> 00:13:37,080
+الأولى ورحت حلّ التباهي، أنت اجيب بالي الطريقة
+
+139
+00:13:37,080 --> 00:13:41,200
+الثانية، بنشوف هل الطريقتين بيعطوني نفس الحل ولا كل
+
+140
+00:13:41,200 --> 00:13:48,100
+واحد بتعطيني حل شكل الله أعلم، تعالي نشوف، أيوة مين 
+
+141
+00:13:48,100 --> 00:13:52,420
+اللي بتسأل احنا؟ طيب بنفعل الحل اللي هي الـ
+
+142
+00:13:52,420 --> 00:13:54,060
+differential equation 
+
+143
+00:13:56,980 --> 00:14:00,120
+بايش؟ كيف كنا بنحلها في الشفتر الأول؟ مش هي احنا 
+
+144
+00:14:00,120 --> 00:14:04,320
+قلنا little y ساوي E أُس RT هي طريقة... لأ لأ
+
+145
+00:14:04,320 --> 00:14:07,660
+هي الـ equation star two stars هذه بنحلها زي ما كنا
+
+146
+00:14:07,660 --> 00:14:10,420
+نحلها سابقًا، star ولا double star؟ double star، و
+
+147
+00:14:10,420 --> 00:14:13,560
+double star، ما احنا بنحلها زي قبل، لأ، زي أي هم شفتر
+
+148
+00:14:13,560 --> 00:14:16,520
+واحد، Second order differential equation أخدنا two
+
+149
+00:14:16,520 --> 00:14:20,990
+cases special cases T missing و X missing فيش مشكلة
+
+150
+00:14:20,990 --> 00:14:24,030
+أحديها بأي طريقة، لكن مين اللي أسأله؟ هذه والله 
+
+151
+00:14:24,030 --> 00:14:27,190
+الـ X مسجد والـ T مسجد، هذه بيخليّجي بلها الدورة،
+
+152
+00:14:27,190 --> 00:14:30,650
+وأنت حر بقى، تروح وترجع، تتعقز في الكلام اللي
+
+153
+00:14:30,650 --> 00:14:34,210
+عطيك، أنت حر، هذا شأنك، أنا بدي شغل، بس الشغل يكون
+
+154
+00:14:34,210 --> 00:14:39,330
+صحيح بأي طريقة تشتي، ما لم أقيدك، فيش تقييد،
+
+155
+00:14:39,330 --> 00:14:43,310
+خلاص، شغل اللي بديكي يعني، ماشي؟ طب لو صار 
+
+156
+00:14:43,310 --> 00:14:47,990
+الـ third order يبقى نفعش الكلام اللي إتيه يبقى
+
+157
+00:14:47,990 --> 00:14:51,590
+يخليه يتعود كل طريقة بناخدها نتعودها مش نهملها و
+
+158
+00:14:51,590 --> 00:14:58,030
+نسيبها، طيب بنيجي نكمل، يبقى هذا بالشكل اللي عندنا
+
+159
+00:14:58,030 --> 00:15:02,970
+هذا وخلي كيس ثلاثة يمكن تلزم، يبقى بالدهجة اللي 
+
+160
+00:15:02,970 --> 00:15:07,570
+أقول الآن a second solution
+
+161
+00:15:09,270 --> 00:15:20,410
+بعد ذلك أقول let Y تساوي X أُس R بيه solution of the
+
+162
+00:15:20,410 --> 00:15:23,770
+equation star
+
+163
+00:15:26,940 --> 00:15:32,660
+بدا أجيب Y' اللي هو مين؟ R X أُس R ناقص الواحد
+
+164
+00:15:32,660 --> 00:15:39,260
+بعدين بدي أجيب الـ Y'' R في R ناقص الواحد في X
+
+165
+00:15:39,260 --> 00:15:45,010
+أُس R ناقص الاثنين، بتاخد المعلومات وروح اعوض وين
+
+166
+00:15:45,010 --> 00:15:53,470
+في هذه المعادلة، يبقى يا بنات ايش بيصير؟ XY''-3XY'
+
+167
+00:15:53,470 --> 00:15:57,030
+زائد 4Y يساوي 
+
+168
+00:16:03,280 --> 00:16:14,800
+يبقى X تربيع في الـ Y'' هي R في R-1 في X أُس R-2
+
+169
+00:16:15,220 --> 00:16:22,500
+ناقص ثلاثة X في الـ Y'
+
+201
+00:19:45,810 --> 00:19:53,290
+هذا أول مثال له سؤال 6 من الكتاب المثال الثاني له
+
+202
+00:19:53,290 --> 00:20:02,450
+سؤال 10 من الكتاب مثال 2 هذا سؤال 10 من الكتاب
+
+203
+00:20:02,450 --> 00:20:09,790
+يقول السؤال The differential equation of x تربيع و
+
+204
+00:20:09,790 --> 00:20:18,490
+y double prime ناقص خمسة x y prime زائد ثلاثة عشر y
+
+205
+00:20:18,490 --> 00:20:22,810
+بده يساوي zero وهذا اللي بدي أسميها main واللي
+
+206
+00:20:22,810 --> 00:20:31,170
+بدي أسميها ال start يبقى 
+
+207
+00:20:31,170 --> 00:20:32,990
+بدي أبدأ solution
+
+208
+00:20:36,130 --> 00:20:39,630
+أظن أنه لا يوجد دا على الطريقين بيكفيني واحدة لكن
+
+209
+00:20:39,630 --> 00:20:44,230
+التان تان اتعلمناهم تاني أسهلي خلاص بالتاني يبقى
+
+210
+00:20:44,230 --> 00:20:50,270
+باجي بيقول في الطريق أن ال Y يساوي X أُس R 
+
+211
+00:20:50,270 --> 00:21:01,410
+solution of equation A star with X greater than 0
+
+212
+00:21:01,410 --> 00:21:09,400
+يبقى then الـ Y' بدي يساوي R X أُس R ناقص الـ 1
+
+213
+00:21:09,400 --> 00:21:17,620
+و y double prime R في R ناقص الـ 1 في X أُس R ناقص الـ 2
+
+214
+00:21:17,620 --> 00:21:28,040
+الآن بدي بقوله Substitute in equation star we get
+
+215
+00:21:28,860 --> 00:21:34,600
+نحصل على ما يلي هي ال X تربيع برا وهذه R في R
+
+216
+00:21:34,600 --> 00:21:40,120
+في R ناقص ال one في X أُس R ناقص ال two
+
+217
+00:21:40,120 --> 00:21:46,900
+اللي بعدها ناقص خمسة X في ال Y prime R X أُس R 
+
+218
+00:21:46,900 --> 00:21:53,600
+ناقص ال one اللي بعدها زائد ثلاثة عشر X أُس R كله
+
+219
+00:21:53,600 --> 00:22:01,500
+بده يساوي Zero هذه لو فكتها R في R ناقص ال one في
+
+220
+00:22:01,500 --> 00:22:10,460
+X أُس R ناقص خمسة R X أُس R زائد ثلاثة عشر X أُس R
+
+221
+00:22:10,460 --> 00:22:16,630
+بده يساوي Zero أظن لو جسمنا على الـ X أُس R بنحصل
+
+222
+00:22:16,630 --> 00:22:21,650
+على الـ characteristic equation على الصيغة التالية
+
+223
+00:22:21,650 --> 00:22:30,480
+R تربيع ناقص خمسة R زائد ثلاثة عشر يساوي Zero أو بمعنى آخر R 
+
+224
+00:22:30,480 --> 00:22:39,100
+تربيع ناقص R ناقص خمسة R زائد ثلاثة عشر يساوي Zero أو
+
+225
+00:22:39,100 --> 00:22:49,260
+R تربيع ناقص ستة R زائد ثلاثة عشر بده يساوي Zero وهذه 
+
+226
+00:22:49,260 --> 00:22:52,320
+اللي بنسميها ال characteristic
+
+227
+00:22:59,700 --> 00:23:04,580
+بعد إنجاز الشغل الروتيني بدي أحلل المعادلة هذه هل
+
+228
+00:23:04,580 --> 00:23:10,740
+يمكن تحليل هذه المعادلة؟ في إمكانية لكن كلها من
+
+229
+00:23:10,740 --> 00:23:14,120
+الدرجة الثانية مش قادرة أحللها بروحي بحل بالقانون 
+
+230
+00:23:14,120 --> 00:23:19,260
+واللي الله سبحانه وتعالى يفرجها تمام؟ يبقى باجي
+
+231
+00:23:19,260 --> 00:23:25,160
+بيقول هذا R وأنا متأكد أنه سيفرجها سيفرجها إذا الله 
+
+232
+00:23:25,160 --> 00:23:28,920
+ما فرجهاش مين بده يفرجها؟ يبقى هاي ناقص بقى بيصير
+
+233
+00:23:28,920 --> 00:23:33,340
+ستة زائد أو ناقص الجذر التربيعي ستة في ستة 
+
+234
+00:23:51,950 --> 00:24:02,040
+أربعة في ثلاثة باتنين وخمسين 52 مضروب
+
+235
+00:24:02,040 --> 00:24:13,460
+قداش سالب 16 على 2 يعني 6 زائد أو ناقص اللي هو 4I
+
+236
+00:24:13,460 --> 00:24:21,360
+كله مقسوم على قداش 2 يبقى بده يساوي 3 زائد أو ناقص
+
+237
+00:24:21,360 --> 00:24:29,050
+2I يبقى عندنا ال a هنا بقداش يا بنات وال b تساوي كده 
+
+238
+00:24:29,050 --> 00:24:34,850
+إذا بقدر أجيب ال general solution يبقى بروح بقوله
+
+239
+00:24:34,850 --> 00:24:46,270
+the general solution of the differential equation
+
+240
+00:24:46,270 --> 00:24:57,330
+star is y تساوي X أُس R يبقى X أُس كده؟ أُس ثلاثة،
+
+241
+00:24:57,330 --> 00:25:03,850
+X أُس إيه؟ فيه عندنا جذرين، اثنين are conjugate
+
+242
+00:25:03,850 --> 00:25:10,310
+وما فيش غيرهم، يبقى بش باجي بقول C واحد كوسين، كده يا
+
+243
+00:25:10,310 --> 00:25:14,130
+بنات؟ اثنين، اثنين، اثنين، اثنين، اثنين، اثنين، 
+
+244
+00:25:23,910 --> 00:25:30,470
+كفى الله المؤمنين القتال هذا كان المثال رقم اثنين
+
+245
+00:25:30,470 --> 00:25:37,330
+بدنا نروح للمثال رقم ثلاثة مثال رقم ثلاثة بيقول ما
+
+246
+00:25:37,330 --> 00:25:46,280
+يأتي solve the Differential Equation مثل المعادلة
+
+247
+00:25:46,280 --> 00:25:53,260
+التفاضلية X تكعيب Y triple prime Y triple prime 
+
+248
+00:25:53,260 --> 00:26:00,240
+ناقص X تربيع و Y double prime زائد X في Y prime
+
+249
+00:26:00,240 --> 00:26:05,920
+بده يساوي كم؟ بده يساوي Zero وهذه هي المعادلة رقم
+
+250
+00:26:05,920 --> 00:26:09,520
+start خليني 
+
+251
+00:26:09,520 --> 00:26:20,060
+أسأل السؤال التالي هل هذه كوشي أويلر equation؟ هل
+
+252
+00:26:20,060 --> 00:26:25,460
+هذه كوشي أويلر equation؟ هل 
+
+253
+00:26:25,460 --> 00:26:32,080
+هذه كوشي أويلر equation؟ هل هذه كوشي
+
+254
+00:26:32,080 --> 00:26:38,050
+أويلر equation؟ هل هذه كوشي أويلر equation؟ أنا كنت
+
+255
+00:26:38,050 --> 00:26:41,650
+بسألها سؤال مش شايفة، كنت شايفة المكتوب على 
+
+256
+00:26:41,650 --> 00:26:44,270
+الدافع، بس أنا .. ايه مكتوب؟ هي فوق وقدامك أنا 
+
+257
+00:26:44,270 --> 00:26:53,690
+بسأل فيه هذا، هذه كوشي أويلر equation؟ طلع
+
+258
+00:26:53,690 --> 00:26:57,190
+في القصة تبع ال X وطلع في المشتقة، زي بعض والله 
+
+259
+00:26:57,190 --> 00:27:03,800
+بيختلفوا كلهم زي بعض حتى وإن غاب term حتى وإن غاب
+
+260
+00:27:03,800 --> 00:27:09,220
+two terms يعني إحنا لو شيلنا كمان هذا بتظهر كوشي
+
+261
+00:27:09,220 --> 00:27:12,580
+أو أويلر equation حتى لو شيلنا اثنين هذول بتظهر
+
+262
+00:27:12,580 --> 00:27:18,780
+كوشي أو أويلر equation بهمان الأس تبع ال X يكون جد
+
+263
+00:27:18,780 --> 00:27:23,580
+المشتقة بالضمن تكعيب يجب على المشتقة الثالثة تربيع 
+
+264
+00:27:23,580 --> 00:27:26,140
+يجب على المشتقة الثانية يجب على الصحة صوتين
+
+265
+00:27:26,140 --> 00:27:31,310
+غاليكم معايا كويس دينا بالكم يبقى بدنا نجي لمن؟ لـ
+
+266
+00:27:31,310 --> 00:27:34,890
+الحل يبقى بدي أفترض بنفس الطريقة التكتيكي اللي 
+
+267
+00:27:34,890 --> 00:27:44,390
+اتبعته هنا بدأشي أقوله افترض أن ال Y تساوي X أُس R 
+
+268
+00:27:44,390 --> 00:27:49,870
+ب solution of
+
+269
+00:27:49,870 --> 00:27:58,510
+equation star with X greater than 0 يبقى بدنا نكتب
+
+270
+00:27:58,510 --> 00:28:01,050
+ال characteristic equation دغري يا بنات والله ايش 
+
+271
+00:28:01,050 --> 00:28:09,330
+رأيكوا يبقى the characteristic equation is طب يلا
+
+272
+00:28:09,330 --> 00:28:12,490
+مدام دغري ينجلوني كدهش ال characteristic equation
+
+273
+00:28:12,490 --> 00:28:18,310
+اللي هي دي R في كدهش في R ناقص واحد في R ناقص
+
+274
+00:28:18,310 --> 00:28:28,010
+اثنين مظبوط وهنا ناقص هذه قدرات R في R ناقص واحد
+
+275
+00:28:28,010 --> 00:28:35,910
+وهذه زائد R كله بده يساوي قداش زي يعني كأنه عوض
+
+276
+00:28:35,910 --> 00:28:40,590
+واشتق وقسم على X plus R وصلت زي ما كنا بنعمل في
+
+277
+00:28:40,590 --> 00:28:45,070
+حالة ال equations with constant coefficients
+
+278
+00:28:45,070 --> 00:28:49,230
+بالضبط تماما طيب ضايق أفكك هذه المعادلة أظن أن
+
+279
+00:28:49,230 --> 00:28:54,070
+عندي هنا R وعندي هنا R وعندي هنا R بقدر آخذها برا 
+
+280
+00:28:54,070 --> 00:28:58,630
+عامل مشترك إذا لو أخذت ال R برا عامل مشترك كده
+
+281
+00:28:58,630 --> 00:29:03,210
+بيظل عندي؟ حصل ضرب الاثنين هذول اللي هو R تربيع
+
+282
+00:29:03,210 --> 00:29:11,350
+ناقص ثلاثة R زائد اثنين صح؟ وهنا هذه بيصير ناقص R
+
+283
+00:29:11,350 --> 00:29:16,370
+زائد واحد وهذه بيظل عندي كدهش لما أخذت منها R بظل
+
+284
+00:29:16,370 --> 00:29:19,710
+واحد مظبوط هيك؟ أه 
+
+285
+00:29:23,260 --> 00:29:32,360
+هذه R في R تربيع عندك ناقص 3R وناقص 4R ناقص 4R دل
+
+286
+00:29:32,360 --> 00:29:37,740
+عندك اثنين واثنين كمان كده أربعة كله بده يساوي 0
+
+287
+00:29:37,740 --> 00:29:42,780
+إذا شكل ال characteristic equation صارت R في R
+
+288
+00:29:42,780 --> 00:29:51,330
+ناقص اثنين لكل تربيع يبقى الـ roots واحد 
+
+289
+00:29:51,330 --> 00:29:55,070
+منهم مكرر مرتين ممتاز جدا
+
+290
+00:30:17,600 --> 00:30:35,540
+Y ثم Y ساعة يبقى C1 في X أُس 0 C2
+
+291
+00:30:35,540 --> 00:30:46,940
+زائد C3 لأن X في X أُس 2 يبقى هذا شكل ال general
+
+292
+00:30:46,940 --> 00:30:51,420
+solution اللي عندك حد فيكم لأي استفسار قبل أن أذهب
+
+293
+00:30:51,420 --> 00:30:58,580
+إلى المثال الذي يليه في أي تساؤل؟ هاي، أروح الآن
+
+294
+00:30:58,580 --> 00:31:05,280
+للمثال اللي بعده
+
+295
+00:31:05,280 --> 00:31:14,740
+يبقى
+
+296
+00:31:14,740 --> 00:31:16,280
+باجي لـ Example 4
+
+297
+00:31:27,600 --> 00:31:28,860
+Solve the equation
+
+298
+00:31:34,610 --> 00:31:43,150
+Equation المعادلة X ناقص ثلاثة لكل تربيع في ال Y
+
+299
+00:31:43,150 --> 00:31:51,090
+double prime زائد ثلاثة في X ناقص ثلاثة في ال Y
+
+300
+00:31:51,090 --> 00:31:57,950
+prime زائد Y بده يساوي Zero وال X greater than 
+
+301
+00:31:57,950 --> 00:31:58,770
+ثلاثة
+
+302
+00:32:30,510 --> 00:32:37,270
+السؤال الذي سألناه قبل قليل قائماً ولكما Is it a 
+
+303
+00:32:37,270 --> 00:32:39,170
+Cauchy-Euler equation؟
+
+304
+00:32:43,960 --> 00:32:53,640
+هو مضمون أن X أكبر من 3 لأن X أكبر من 0 لأن X أكبر
+
+305
+00:32:53,640 --> 00:32:57,360
+من 3 لأن X أكبر من 100 لأن X أكبر 
+
+306
+00:32:57,360 --> 00:33:01,020
+من 3 لأن 
+
+307
+00:33:01,020 --> 00:33:01,640
+X أكبر من 3 لأن X أكبر من 3 لأن X أكبر من 100 لأن
+
+308
+00:33:01,640 --> 00:33:02,100
+X أكبر من 3 لأن X أكبر من 3 لأن X أكبر من 3 لأن X
+
+309
+00:33:02,100 --> 00:33:05,140
+أكبر من 3 لأن X أكبر من 3 لأن X أكبر من 3 لأن X 
+
+310
+00:33:05,140 --> 00:33:06,740
+أكبر من 3 لأن X أكبر من 3 لأن X أكبر من 3 لأن X
+
+311
+00:33:06,740 --> 00:33:06,840
+أكبر من 3 لأن X أكبر من 3 لأن X أكبر من 3 لأن X
+
+312
+00:33:06,840 --> 00:33:08,880
+أكبر من 3 لأن X أكبر من 3 لأن X أكبر من 3 لأن X 
+
+313
+00:33:19,830 --> 00:33:25,030
+يبقى افترض الحل على الشكل طبعا أطلّعي الأس اللي 
+
+314
+00:33:25,030 --> 00:33:28,530
+هنا هو نفس المشتقة الأس اللي هنا هو نفس المشتقة و
+
+315
+00:33:28,530 --> 00:33:33,010
+هكذا تمام إذا هذه كوشي أويلر equation يبقى بدأ
+
+316
+00:33:33,010 --> 00:33:41,980
+أقوله little y تساوي X ناقص ثلاثة أُس R با solution
+
+317
+00:33:41,980 --> 00:33:53,300
+of the above differential equation طب
+
+318
+00:33:53,300 --> 00:33:59,220
+لو جئت بدي أجيب ال Y' يبقى R في ال X ناقص ثلاثة و
+
+319
+00:33:59,220 --> 00:34:02,920
+R ناقص واحد في مشتقة مداخل القوس 
+
+320
+00:34:05,730 --> 00:34:15,870
+عن طريق الـ Y double prime يبقى R في R-1 في X ناقص 3 أُس R-2
+
+321
+00:34:15,870 --> 00:34:21,400
+في مشتقة مداخل القوس اللي هو الواحد اعوض في المعادلة 
+
+322
+00:34:21,400 --> 00:34:26,080
+اللي فوق لو جئت عوض في المعادلة اللي فوق بيصير X
+
+323
+00:34:26,080 --> 00:34:32,040
+ناقص ثلاثة لكل تربيع في ال Y double prime اللي هو R في R
+
+324
+00:34:32,040 --> 00:34:37,320
+ناقص ال one في X ناقص ثلاثة to the power R ناقص
+
+325
+00:34:37,320 --> 00:34:44,420
+two زائد ثلاثة X ناقص ثلاثة في ال Y prime اللي هي R
+
+326
+00:34:44,420 --> 00:34:50,500
+X ناقص ثلاثة to the power R ناقص one زائد Y اللي 
+
+327
+00:34:50,500 --> 00:34:54,560
+هي X ناقص ثلاثة to the power R كله بده يساوي Zero
+
+328
+00:34:55,280 --> 00:35:00,200
+بتعيد كتابتها يبقى R في R ناقص واحد في X ناقص
+
+329
+00:35:00,200 --> 00:35:09,520
+ثلاثة أُس R زائد ثلاثة R زائد ثلاثة R فاهمين في ال
+
+330
+00:35:09,520 --> 00:35:16,820
+X ناقص ثلاثة أُس R زائد X ناقص ثلاثة أُس R كله بده
+
+331
+00:35:16,820 --> 00:35:24,240
+يساوي Zero الـ X ناقص ثلاثة هذا مقدار أكبر من الـ
+
+332
+00:35:24,240 --> 00:35:28,480
+Zero إذا موجب بقدر أقسم عليه بدون مشاكل يبقى لو 
+
+333
+00:35:28,480 --> 00:35:33,020
+قسمت كله على X ناقص ثلاثة أُس R بنحصل على ال
+
+334
+00:35:33,020 --> 00:35:39,060
+characteristic equation بالشكل التالي هذه دي mean R
+
+335
+00:35:39,060 --> 00:35:45,320
+في R ناقص ال one زائد ثلاثة R زائد واحد بده يساوي
+
+336
+00:35:45,320 --> 00:35:51,640
+Zero أو إن شئتم فقولوا R تربيع وعندك ناقص R زائد
+
+337
+00:35:51,640 --> 00:35:56,860
+ثلاثة R بيظل زائد اثنين R زائد واحد يساوي Zero
+
+338
+00:35:56,860 --> 00:36:04,260
+يبقى هذه R زائد واحد لكل تربيع يساوي Zero يبقى ال R
+
+339
+00:36:04,260 --> 00:36:10,540
+تساوي سالب واحد of Multiplicity
+
+340
+00:36:10,540 --> 00:36:16,680
+كدهش؟ اثنين اثنين مكررة مرتين يبقى أصبح The
+
+341
+00:36:16,680 --> 00:36:32,860
+General Solution Of The Equation Is Y تساوي X و C
+
+342
+00:36:32,860 --> 00:36:40,540
+ايه يا بنات هنا؟ والله مش بنكتب كرر مرتين يبقى ايش
+
+343
+00:36:40,540 --> 00:36:54,040
+بدي أقوله؟ C1 زائد C2 لأن كده؟ X ناقص ثلاثة يبقى X
+
+344
+00:36:54,040 --> 00:37:02,540
+ناقص ثلاثة مضروب في ال X ناقص ثلاثة أُس اللي هو 
+
+345
+00:37:02,540 --> 00:37:11,080
+قداش؟ اثنين هيك ماشي للحل صحيح بالمئة ال X أُس مش
+
+346
+00:37:11,080 --> 00:37:18,060
+اثنين سالب واحد احنا طلعناها ال R أُس سالب واحد لحد
+
+347
+00:37:18,060 --> 00:37:21,380
+هنا stop in the intersection ولا يكون أرقام
+
+348
+00:37:21,380 --> 00:37:29,420
+المسائل يبقى أرقام المسائل exercises خمسة خمسة
+
+349
+00:37:29,420 --> 00:37:37,200
+بدنا المسائل من واحد إلى خمسة عشر وكذلك سؤال واحد
+
+350
+00:37:37,200 --> 00:37:38,080
+وعشرين
+
+351
+00:37:43,580 --> 00:37:46,960
+في كلمتين حابين نقولهم في ال section اللي بعده 
+
+352
+00:37:46,960 --> 00:37:52,500
+بدون ما نعطي ولا مثال ولا نطلب منكوا تحلوا مثالين 
+
+353
+00:37:52,500 --> 00:37:58,400
+مقدمة شيء إحنا بنجي نشتغل يا بنات على ال
+
+354
+00:37:58,400 --> 00:38:01,900
+homogeneous differential equation بدنا نبدأ الآن
+
+355
+00:38:01,900 --> 00:38:06,160
+الشغل على ال homogeneous differential equation
+
+356
+00:38:06,160 --> 00:38:14,410
+فاكتبي لي ال section خمسة ستة خمسة ستة هذه non
+
+357
+00:38:14,410 --> 00:38:32,010
+homogeneous differential equations definition
+
+358
+00:38:32,010 --> 00:38:35,730
+they none
+
+359
+00:38:37,570 --> 00:38:46,150
+Homogenous differential equation is
+
+360
+00:38:46,150 --> 00:38:54,530
+an equation in the form طبعا كل شغل non 
+
+361
+00:38:54,530 --> 00:39:01,390
+homogeneous linear differential equation على الشكل 
+
+362
+00:39:01,390 --> 00:39:03,810
+التالي A0
+
+363
+00:39:28,500 --> 00:39:29,900
+Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y11 Y12 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11 Y11
+
+364
+00:39:31,410 --> 00:39:40,310
+Where حيث capital F of X لا يمكن أن تساوي zero عند
+
+365
+00:39:40,310 --> 00:39:50,190
+ال a naught وال a one ولغاية ال a n may or may
+
+366
+00:39:50,190 --> 00:39:53,970
+not or may not
+
+
+401
+00:45:12,430 --> 00:45:19,970
+الإجازة يعني بقى لإن بقينا طيبين بناخد من؟ بناخد
+
+402
+00:45:19,970 --> 00:45:25,710
+الـ two sections اللي ضالت في هذا ال chapter ومحل
+
+403
+00:45:25,710 --> 00:45:30,570
+لـ non homogeneous differential equation بإحدى
+
+404
+00:45:30,570 --> 00:45:34,970
+طريقتين الأولى الـ undetermined coefficients و
+
+405
+00:45:34,970 --> 00:45:39,810
+الطريقة الثانية الـ variation of parameters إن شاء
+
+406
+00:45:39,810 --> 00:45:39,990
+الله
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7cd3dddadefd44f88d06efd7c083b48ef8303880
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0_postprocess.srt
@@ -0,0 +1,1624 @@
+1
+00:00:19,490 --> 00:00:25,010
+بسم الله الرحمن الرحيم نعود الآن إلى محاضرة الصباح
+
+2
+00:00:25,010 --> 00:00:30,130
+بدأنا في محاضرة الصباح ب Koshi Euler equation
+
+3
+00:00:30,130 --> 00:00:34,290
+حطينا الصيغة العامة لها و بعدين خدنا حالة منها
+
+4
+00:00:34,290 --> 00:00:36,850
+خاصة اللي هو كانت من
+
+5
+00:00:48,230 --> 00:00:52,730
+المعادلة الأصلية تبعت كوشي ولا ريكوشي ان هناك
+
+6
+00:00:52,730 --> 00:00:58,380
+طريقان للحلالطريق الأول اللي هو بالتعويض قلنا لو
+
+7
+00:00:58,380 --> 00:01:04,980
+حطينا التعويضة X يساوي E قص T خدنا لن للطرفين فصار
+
+8
+00:01:04,980 --> 00:01:11,080
+T تساوي لنا X اشتقنا DT على DX يساوي 1 على X ثم
+
+9
+00:01:11,080 --> 00:01:15,880
+بعد ذلك روحنا جيبنا Y' وYW' بدل ما الاشتقاق
+
+10
+00:01:15,880 --> 00:01:20,260
+بالنسبة لX حولنا الاشتقاق بالنسبة إلى T وبالتالي
+
+11
+00:01:20,260 --> 00:01:24,490
+عوضنا طارمينالـ Variables وسمينا هذه هي الطريقة
+
+12
+00:01:24,490 --> 00:01:29,270
+الأولى يعني الطريقة الأولى بوسط تعويضة بتبعدنا
+
+13
+00:01:29,270 --> 00:01:35,110
+حولنا المعادلة من معادلة بمعاملات متغيرة إلى
+
+14
+00:01:35,110 --> 00:01:39,670
+معادلة بمعاملات ثابتة وبالتالي بنروح نحل هذه كما
+
+15
+00:01:39,670 --> 00:01:44,090
+كنا بنحل في ال sections الماضيةانتقلنا الان الى
+
+16
+00:01:44,090 --> 00:01:49,970
+الطريقة الاولى اللى كتبناها قبل ساعتين من الان
+
+17
+00:01:49,970 --> 00:01:56,510
+طريقة يفترض ان Y يسوى X أس R عبارة عن solution و
+
+18
+00:01:56,510 --> 00:02:00,170
+رحنا اشتغلنا مرة مرتين تلاتة N من المرات و عوضنا
+
+19
+00:02:00,170 --> 00:02:07,400
+في المعادلةحصلنا على المعادلة المساعدة
+
+20
+00:02:07,400 --> 00:02:13,440
+أو المعادلة المميزة للمعادلة الأصلية و رحلنا هذه
+
+21
+00:02:13,440 --> 00:02:17,880
+المعادلة لما جينا نحل هذه المعادلة صار عندي أحد
+
+22
+00:02:17,880 --> 00:02:22,780
+ثلاثة احتمالاتالاحتمال الأول الاحتمال التاني
+
+23
+00:02:22,780 --> 00:02:26,760
+الاحتمال التالت سميتها ثلاث حالات نجي للحالة
+
+24
+00:02:26,760 --> 00:02:30,800
+الأولى لو question double star هذه المعادلة
+
+25
+00:02:30,800 --> 00:02:35,900
+المميزة has indifferent roots يبقى صار عندي R واحد
+
+26
+00:02:35,900 --> 00:02:40,700
+لا يسوى R اتنين لا يسوى R ثلاثة لا يسوى لا يسوى RN
+
+27
+00:02:40,700 --> 00:02:45,220
+ولا واحد زي التاني ما هو الشكل العام للحل يبقى
+
+28
+00:02:45,220 --> 00:02:48,160
+الشكل العام للحل C1 في X وسط R1
+
+29
+00:02:56,780 --> 00:03:01,000
+الحلوق يبقى كونصا في الأول و كونصا في التاريب و
+
+30
+00:03:01,000 --> 00:03:05,420
+يمثل ال general solution إذا الحلوق كانوا real and
+
+31
+00:03:05,420 --> 00:03:11,030
+differentبنجي للحالة التانية لو equation star has
+
+32
+00:03:11,030 --> 00:03:16,070
+complex roots المعادلة طالعة عندما فيها جذور
+
+33
+00:03:16,070 --> 00:03:20,890
+تخيلية فعلى سبيل المثال لو أخد جذرين منهم ماذا
+
+34
+00:03:20,890 --> 00:03:25,330
+يكون شكل الحل يبقى باجي بقول الحل بيكون x to the
+
+35
+00:03:25,330 --> 00:03:31,390
+power إيه؟ ليش؟لأنه بدي يطلع اللي هو ال R يسوي A
+
+36
+00:03:31,390 --> 00:03:37,450
+زائد IB تمام؟ A زائد و ال conduct تبعه A ناقص IB
+
+37
+00:03:37,450 --> 00:03:41,470
+الحل الأول R واحد A زائد IB و الحل التاني R اتنين
+
+38
+00:03:41,470 --> 00:03:47,510
+بديه يسوي A ناقص IB يبقى ال E ال X قص A في مين؟ في
+
+39
+00:03:47,510 --> 00:03:53,230
+C واحد cosine B لن ال X زائد C اتنين sine B لن ال
+
+40
+00:03:53,230 --> 00:03:59,050
+X يعني يا بناتهنا كنا نقول هناك في الحقيقي في
+
+41
+00:03:59,050 --> 00:04:04,550
+التخيلة لما كانوا المعاملات حقيقية بقى نقول C1 Cos
+
+42
+00:04:04,550 --> 00:04:11,050
+Bx ماعنديش Lin لكن هنا جانبين Lin X زي C2 Sin B
+
+43
+00:04:11,050 --> 00:04:16,140
+Lin X الحالة التالتةالحالة التالتة لحالة الـ real
+
+44
+00:04:16,140 --> 00:04:20,000
+قد يكون real و repeated و قد يكون complex و
+
+45
+00:04:20,000 --> 00:04:24,300
+repeated فكيف بنسوي في هذه الحالة يبقى باجي للحالة
+
+46
+00:04:24,300 --> 00:04:27,780
+الأولى ال equation اتنين has real repeated rows of
+
+47
+00:04:27,780 --> 00:04:33,000
+multiplicity S عدد مرات التكرار S والباقي يمكن
+
+48
+00:04:33,000 --> 00:04:38,320
+يكون real يا اما S ممكن يكون كله complex وتساوي N
+
+49
+00:04:38,320 --> 00:04:43,740
+بس بشرط ان ال N عدد زوجييبقى بيصير R واحد يساوي R
+
+50
+00:04:43,740 --> 00:04:48,700
+التاني يساوي RS يساوي R يبقى في هذه الحالة شكل ال
+
+51
+00:04:48,700 --> 00:04:52,400
+general solution زي شكله with constant
+
+52
+00:04:52,400 --> 00:04:57,720
+coefficients ما عدل X بشيله و بحط بدالهالن ال X
+
+53
+00:04:57,720 --> 00:05:02,240
+والباقي كل شيء زي ما هو تطلع C1 C2 لن X C3 لن X
+
+54
+00:05:02,240 --> 00:05:07,700
+نرويها C4 لن X تكريم لغاية ما وصل ل CS لن X أُس S
+
+55
+00:05:07,700 --> 00:05:15,890
+-1 في X أُس R لأن الأُس هذا صار مكرر تمام؟طيب لو
+
+56
+00:05:15,890 --> 00:05:20,210
+كانوا ال roots are repeated complex conjugate لو
+
+57
+00:05:20,210 --> 00:05:24,610
+كانوا هذا real لو كانوا complex يبقى بدي يصير الحل
+
+58
+00:05:24,610 --> 00:05:29,450
+X أس A زي ما هي تبعتي تبعت ال complex بس ايش بدي
+
+59
+00:05:29,450 --> 00:05:32,930
+يصير A واحد زي دي اتنية لن ال X زي دي A أس لن
+
+60
+00:05:41,450 --> 00:05:48,130
+الثوابت المتغيرات C1 وC2 لغاية CS كلها في SIN BLN
+
+61
+00:05:48,130 --> 00:05:54,460
+Xيبقى هذه بدي أفهمها إنها عبارة عن مين عبارة عن
+
+62
+00:05:54,460 --> 00:06:00,000
+الحل X أس A في الجوس الكبير هذا polynomial من
+
+63
+00:06:00,000 --> 00:06:05,540
+الدرجة لأن S ناقص واحد في ال cosine P لن X زي ال
+
+64
+00:06:05,540 --> 00:06:09,000
+polynomial من نفس الدرجة sin P لن X في حتة ال
+
+65
+00:06:09,000 --> 00:06:13,340
+complex لكن في حالتها ال real لا عندي cosine ولا
+
+66
+00:06:13,340 --> 00:06:19,360
+عندي sin polynomial فقط لغير في X أس Aهل بتحب تسأل
+
+67
+00:06:19,360 --> 00:06:24,660
+اي سؤال هنا قبل ان ندخل الامثلة؟
+
+68
+00:06:31,850 --> 00:06:35,070
+ماشي المثال الأول طبعا احنا حققنا معانا طريقتين يا
+
+69
+00:06:35,070 --> 00:06:39,290
+بنات ان قيدني بطريقة بدي التزم في انجل يوز the
+
+70
+00:06:39,290 --> 00:06:44,330
+substitution X يساوي E يساوي T يعني بده مين؟ بده
+
+71
+00:06:44,330 --> 00:06:48,450
+يحول المعلق يمكن يقول لي كمان اجيبلي السؤال بطريقة
+
+72
+00:06:48,450 --> 00:06:52,690
+ثانية يعطي المعلق ويقول لي change او use the
+
+73
+00:06:52,690 --> 00:06:57,630
+substitution X يساوي E يساوي T to changeهذه هي
+
+74
+00:06:57,630 --> 00:06:59,670
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+75
+00:06:59,670 --> 00:07:00,610
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+76
+00:07:00,610 --> 00:07:01,190
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+77
+00:07:01,190 --> 00:07:01,570
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+78
+00:07:01,570 --> 00:07:04,430
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+79
+00:07:04,430 --> 00:07:09,830
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+80
+00:07:09,830 --> 00:07:12,630
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+81
+00:07:12,630 --> 00:07:14,450
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+82
+00:07:14,450 --> 00:07:20,360
+الاختصار الاختصار الاختصار الاختصار اليبقى اول
+
+83
+00:07:20,360 --> 00:07:23,180
+مثال يقول find the general solution of the
+
+84
+00:07:23,180 --> 00:07:27,580
+differential equation ولم يقيدني ما قيدنيش لكن انا
+
+85
+00:07:27,580 --> 00:07:30,720
+كونه اول مثال بدي احله بالطريقتين و بدي ابين ان
+
+86
+00:07:30,720 --> 00:07:35,380
+الطريقتين ما لها نفس الشيء مابتغيرش فيها ايه ولا
+
+87
+00:07:35,380 --> 00:07:39,260
+حاجة يبقى بدي اجي للحل الأول اللي عندنا هذا
+
+88
+00:07:43,620 --> 00:07:51,100
+يبقى بداجة اقول استخدم التعويضة put X يساوي E أُس
+
+89
+00:07:51,100 --> 00:07:58,260
+T هذا بتعطيك T يساوي لن X هذا بتعطيك الـDT على DX
+
+90
+00:07:58,260 --> 00:08:05,720
+يساوي 1 على X and الـY' يا بنات كده اش طلعت؟ مش 1
+
+91
+00:08:05,720 --> 00:08:12,120
+على X في الـDY على DT صح؟ طب والـY W'
+
+92
+00:08:17,770 --> 00:08:26,430
+دي سكوير واي على دي تي سكوير ايوة ناقص دي واي على
+
+93
+00:08:26,430 --> 00:08:35,000
+دي تيطب الحمد لله بس انت بتفرض التعويضة و تقول اذا
+
+94
+00:08:35,000 --> 00:08:37,700
+كذا ماعنديش مشكلة ماعنديك تروح تستنتجيها من أول و
+
+95
+00:08:37,700 --> 00:08:41,760
+جديد لكن اذا كنت نسيها بديك تروح تستنتجيها من أول
+
+96
+00:08:41,760 --> 00:08:46,560
+و جديد طيب يبقى الان بدي امسك المعلومات هذه و اعوض
+
+97
+00:08:46,560 --> 00:08:51,120
+وين في المعادلة اللي هي أصلي اللي هي star يبقى
+
+98
+00:08:51,120 --> 00:08:55,000
+باجي بقول المعادلة star بصير x تربية في ال y w
+
+99
+00:08:55,000 --> 00:09:03,930
+prime هيهي 1 على X تربيع في D²Y على DT² ناقص DY
+
+100
+00:09:03,930 --> 00:09:10,050
+على DT بالشكل اللي عندنا هنا اللي بعدها ناقص 3X
+
+101
+00:09:10,050 --> 00:09:16,170
+فيه بدي أشيل ال Y' و أحط قيمة تالية 1 على X في DY
+
+102
+00:09:16,170 --> 00:09:24,510
+على DT خلصنا منها زائد 4Y مش غيرهاتمام كل هذا
+
+103
+00:09:24,510 --> 00:09:29,590
+الكلام يساوي كده؟ Zero اظن X تربيه مع X تربيه راحت
+
+104
+00:09:29,590 --> 00:09:35,010
+مع السلامة يبقى D Square Y على DT Square ناقص DY
+
+105
+00:09:35,010 --> 00:09:42,650
+على DT ناقص تلاتة DY على DT زائد أربع Y بدأت ساوي
+
+106
+00:09:42,650 --> 00:09:52,040
+Zeroلو روحت جماعة تمهدول بصير D2Y على DT2 ناقص 4DY
+
+107
+00:09:52,040 --> 00:10:00,600
+على DT زائد 4Y بده يسوي قداش Zeroأطلع في المعادلة
+
+108
+00:10:00,600 --> 00:10:04,680
+star واطلع في المعادلة بعد التعويض كيف صارت
+
+109
+00:10:04,680 --> 00:10:09,820
+المعادلة star المعاملات عندي متغيرات بدلالة ال X
+
+110
+00:10:09,820 --> 00:10:15,400
+لكن لما حطيت التعويض هذه حولت إلى معادلة بمعاملات
+
+111
+00:10:15,400 --> 00:10:21,460
+ثابتة إذا بتروح أحلي المعادلة هذه بمين؟ بالمعاملات
+
+112
+00:10:21,460 --> 00:10:29,110
+الثابتة كيف بنين الحل؟ let Y تساوي E أسار Tماعنديش
+
+113
+00:10:29,110 --> 00:10:33,250
+X هنا بطل يصير عندي X الشغل نتهوّل من دلالة X إلى
+
+114
+00:10:33,250 --> 00:10:38,810
+دلالة T يبقى بداجي أقول له let وسمّيلي هذه
+
+115
+00:10:38,810 --> 00:10:47,970
+المعادلة رقم Star let Y تساوي E أُس RT ب A
+
+116
+00:10:47,970 --> 00:11:00,120
+solution ofإذا كانت المقارنة مربوطة ثم المقارنة
+
+117
+00:11:00,120 --> 00:11:05,500
+الخاصة هي
+
+118
+00:11:06,540 --> 00:11:14,900
+R تربيع نقص اربعة R زائد اربعة يساوي Zero يعني هذه
+
+119
+00:11:14,900 --> 00:11:21,440
+مالها R نقص اتنين لكل تربيع يساوي Zero يبقى الجذور
+
+120
+00:11:21,440 --> 00:11:31,280
+حقيقية ومكررة كم مرة مرتين يبقى هذا معناه ان R
+
+121
+00:11:31,280 --> 00:11:41,750
+تساوي اتنين of multiبالإضافة لـ ECT2 كرّرة مرتين
+
+122
+00:11:41,750 --> 00:11:52,930
+إذا بدأت أقول له the general solution of equation
+
+123
+00:11:52,930 --> 00:12:00,880
+double star is Y to sevenمش طبعا انا كنت ملعب
+
+124
+00:12:00,880 --> 00:12:04,660
+دلالة text احنا راهيب نشغل على T يبقى شو بدي يصير
+
+125
+00:12:04,660 --> 00:12:16,560
+تكرار مرتين يبقى C1 زي C2T في قداش في E أس اتنين T
+
+126
+00:12:16,560 --> 00:12:19,620
+طب
+
+127
+00:12:19,620 --> 00:12:27,050
+الجواب ايش طلعناه؟دلالة ايش؟ T و الاصل بدرجة او
+
+128
+00:12:27,050 --> 00:12:30,370
+بدلالة X بكون جيب تحليل المعادلة الأصلية اللي هو
+
+129
+00:12:30,370 --> 00:12:34,970
+Star يبقى باجي بقوله The general solution of
+
+130
+00:12:34,970 --> 00:12:44,730
+equation A star is ال Y يساوي C1 زائد C2 مقداش ال
+
+131
+00:12:44,730 --> 00:12:57,360
+T حطناها مقداش؟لأن الـ X في E أُس 2 لأن الـ Xمظبوط
+
+132
+00:12:57,360 --> 00:13:03,480
+يبقى ايه صارت بدلة لثمين ال X هذهها يا بنات هي C1
+
+133
+00:13:03,480 --> 00:13:12,320
+زائد C2 لن X نجي هذه مش هذه E لن X تربيع اتنين
+
+134
+00:13:12,320 --> 00:13:17,420
+بدخلها جوا اللم ال E و ال L عكس بعض يبقى صار جداش
+
+135
+00:13:17,420 --> 00:13:23,860
+X تربيع يبقى هذا الحل بالطريقة الأولى بدنا نروح
+
+136
+00:13:23,860 --> 00:13:30,980
+نحل بالطريقةبالطريقة الثانية نجربها لأنه ماقاليش
+
+137
+00:13:30,980 --> 00:13:34,980
+احنا اتنين في الامتحان انا اجيب بالي الطريقة
+
+138
+00:13:34,980 --> 00:13:37,080
+الأولى و روحت حل التباهي انت اجيب بالي الطريقة
+
+139
+00:13:37,080 --> 00:13:41,200
+الثانية بنشوف هل الطريقتين بيعطوني نفس الحل ولا كل
+
+140
+00:13:41,200 --> 00:13:48,100
+واحد بتعطيني حل شكل الله أعلم تعالي نشوف ايوة مين
+
+141
+00:13:48,100 --> 00:13:52,420
+اللي بتسأل احنا؟ طيب بنفعل الحل اللي هي ال
+
+142
+00:13:52,420 --> 00:13:54,060
+differential equation
+
+143
+00:13:56,980 --> 00:14:00,120
+بإيش؟ كيف كنا بنحلها في الشفتر الأول؟ مش هاي احنا
+
+144
+00:14:00,120 --> 00:14:04,320
+قولنا little y ساوي E أقصر R T هي طريقة .. لأ لأ
+
+145
+00:14:04,320 --> 00:14:07,660
+هي ال equation star two stars هذي بنحلها زي ما كنا
+
+146
+00:14:07,660 --> 00:14:10,420
+نحلها سابقا star ولا double star? double star و
+
+147
+00:14:10,420 --> 00:14:13,560
+double star ما احنا بنحلها زي قبل لأ زي اي هم شفتر
+
+148
+00:14:13,560 --> 00:14:16,520
+واحد second order differential equation أخدنا two
+
+149
+00:14:16,520 --> 00:14:20,990
+cases special cases T missing و X missingفيش مشكلة
+
+150
+00:14:20,990 --> 00:14:24,030
+أحديها بأي طريقة، لكن مين اللي أسأله؟ هذي والله
+
+151
+00:14:24,030 --> 00:14:27,190
+الـx مسجد و الـt مسجد، هذي بيخلّجي بلها الدورة،
+
+152
+00:14:27,190 --> 00:14:30,650
+وانت حر بقى، تروح و ترجع، تتعقز في الكلام اللي
+
+153
+00:14:30,650 --> 00:14:34,210
+عطيك، انت حر، هذا شأنك، أنا بدي شغل، بس الشغل يكون
+
+154
+00:14:34,210 --> 00:14:39,330
+صحيح، بأي طريقة تشتي، ما لم أقيدكي، فيش تقييد،
+
+155
+00:14:39,330 --> 00:14:43,310
+خلاص، شغل اللي بديكي يعني، ماشي؟ طب لو صار
+
+156
+00:14:43,310 --> 00:14:47,990
+الـthird orderيبقى نفعش الكلام اللي اتيه يبقى
+
+157
+00:14:47,990 --> 00:14:51,590
+يخليه يتعود كل طريقة بناخدها نتعودها مش نهملها و
+
+158
+00:14:51,590 --> 00:14:58,030
+نسيبها طيب بنيجي نكمل يبقى هذا بالشكل اللي عندنا
+
+159
+00:14:58,030 --> 00:15:02,970
+هذا و خلي كيس تلاتة يمكن تلزم يبقى بالدهجة اللي
+
+160
+00:15:02,970 --> 00:15:07,570
+اقول الان a second solution
+
+161
+00:15:09,270 --> 00:15:20,410
+بعد ذلك اقول لت Y تسوى X أُس R بيه solution of the
+
+162
+00:15:20,410 --> 00:15:23,770
+equation star
+
+163
+00:15:26,940 --> 00:15:32,660
+بدا اجيب Y' اللي هو مين؟ R X أُس R ماينوس الوان
+
+164
+00:15:32,660 --> 00:15:39,260
+بعدين بدي اجيب ال Y W' R في R ماينوس الوان في X
+
+165
+00:15:39,260 --> 00:15:45,010
+أُس R ماينوس الاتونبتاخد المعلومات وروح اعوض وين
+
+166
+00:15:45,010 --> 00:15:53,470
+في هذه المعادلة يبقى يا بنات ايش بيصير؟ XYW'-3XY
+
+167
+00:15:53,470 --> 00:15:57,030
+'زائد 4Y يساوي
+
+168
+00:16:03,280 --> 00:16:14,800
+يبقى X تربية في الـ YW' هي R في R-1 في X أُس R-2
+
+169
+00:16:15,220 --> 00:16:22,500
+ناقص ثلاثة X في الـ Y' هيها اللي هي R في X أُس R
+
+170
+00:16:22,500 --> 00:16:30,200
+minus ال 1 زائد أربعة ال Y أنا فرضها بقداش ب X أُس
+
+171
+00:16:30,200 --> 00:16:35,880
+R X أُس R كله بده يساوي Zero تعالى نشوف في هذه كيف
+
+172
+00:16:35,880 --> 00:16:39,420
+صارت هل هي X ترميل لما تدخل جيوب الصين هذي X أُس
+
+173
+00:16:39,420 --> 00:16:45,340
+قداشأس ار ار نقص اتنين و عندك كده اتنين بيصير أس
+
+174
+00:16:45,340 --> 00:16:51,200
+ار يبقى هذه بيصير الار في الار minus ال one في ال
+
+175
+00:16:51,200 --> 00:16:57,760
+X أس ار ناقص تلاتة تلاتة
+
+176
+00:16:57,760 --> 00:17:05,780
+X أس واحد مع X أس R يبقى تلاتة R X أس R زائد أربعة
+
+177
+00:17:05,780 --> 00:17:12,770
+X أس R يسوى كده؟ Zeroأحنا فرضنا هذا الـ solution
+
+178
+00:17:12,770 --> 00:17:17,490
+علما بأن الـ X هنا بنات جداش قلنا من Zero إلى
+
+179
+00:17:17,490 --> 00:17:20,570
+Infinity في الجزء النظري يعني دائما وابدا أكبر من
+
+180
+00:17:20,570 --> 00:17:26,090
+مين أكبر من الـ Zero إذا ممكن قسمت هذه الطرفين كله
+
+181
+00:17:26,090 --> 00:17:31,830
+على مين؟ على X أُس R يبقى بصير عنا R في R ناقص
+
+182
+00:17:31,830 --> 00:17:40,820
+واحد زائد تلاتة R زائد أربع يساوي ZeroR في R ناقص
+
+183
+00:17:40,820 --> 00:17:49,120
+واحد عندك هنا ناقص اهينا ناقص اهي ناقص R وهذه ايه
+
+184
+00:17:49,120 --> 00:17:52,940
+اللي هي ناقص بالشكل اللي عندنا هنا يبقى بناء صلة
+
+185
+00:17:52,940 --> 00:17:59,860
+المعادلة على الشكل R تربية ناقص R ناقص 3R زائد 4
+
+186
+00:17:59,860 --> 00:18:06,240
+بده يساوي 0 يبقى R تربية ناقص 4R زائد 4 تساوي 0
+
+187
+00:18:06,240 --> 00:18:13,030
+مين هي هذه؟characteristic equation يبقى هذا معناه
+
+188
+00:18:13,030 --> 00:18:18,890
+ان الار ناقص اتنين لكل تربية يساوي zero هذا معناته
+
+189
+00:18:18,890 --> 00:18:25,110
+ان الار بدي ساوي اتنين و مكررة كده مرتين اذا بدي
+
+190
+00:18:25,110 --> 00:18:33,650
+اطبق عليها اتكرار فبجي بقوله the general solution
+
+191
+00:18:33,650 --> 00:18:35,630
+is
+
+192
+00:18:37,660 --> 00:18:47,800
+Y تساوي C1 زي C2 من X، هل في أكتر من ذلك؟ هؤلاء
+
+193
+00:18:47,800 --> 00:18:52,920
+المقارنة مرتين حطيت حالين، في من؟ في X أُس R، R
+
+194
+00:18:52,920 --> 00:18:58,860
+بقدرش؟ ب2، طلع إلى الحل هذا و الحل هناك هو
+
+195
+00:18:58,860 --> 00:19:04,660
+الاختلافيبقى لي اتنين ار داسيم سواء كان الحل اللى
+
+196
+00:19:04,660 --> 00:19:08,560
+عندي هذا او الحل اللى عندي هذا، مادام ما قيدنيش
+
+197
+00:19:08,560 --> 00:19:12,700
+اللى بتحل بالحل الثاني ماشي، بتحل بالحل الأول،
+
+198
+00:19:12,700 --> 00:19:19,340
+ماشي طبعا الحل الثاني أسهل، خلاص انت حرة، بس إذا
+
+199
+00:19:19,340 --> 00:19:24,020
+قيدتك بدك تلتجي مين، أحيانا بنقيد و أحيانا لا، انت
+
+200
+00:19:24,020 --> 00:19:24,860
+و بختك عندك
+
+201
+00:19:45,810 --> 00:19:53,290
+هذا اول مثال له سؤال 6 من الكتاب المثال الثاني له
+
+202
+00:19:53,290 --> 00:20:02,450
+سؤال 10 من الكتاب مثال 2 هذا سؤال 10 من الكتاب
+
+203
+00:20:02,450 --> 00:20:09,790
+يقول السؤالThe differential equation of x تربيع و
+
+204
+00:20:09,790 --> 00:20:18,490
+y double prime ناقص خمسة x y prime زائد تلتاشر y
+
+205
+00:20:18,490 --> 00:20:22,810
+بده يساوي zero وهذا اللي بدي أسميها main و اللي
+
+206
+00:20:22,810 --> 00:20:31,170
+بدي أسميها ال start يبقى
+
+207
+00:20:31,170 --> 00:20:32,990
+بدي أبدأ solution
+
+208
+00:20:36,130 --> 00:20:39,630
+أظن أنه لا يوجد دا على الطريقين بيكفيني واحدة لكن
+
+209
+00:20:39,630 --> 00:20:44,230
+التان تان اتعلمناهم تاني أسهلي خلاص بالتاني يبقى
+
+210
+00:20:44,230 --> 00:20:50,270
+باجي بيقول في الطريق ان ال Y يسوى X أُس A ب
+
+211
+00:20:50,270 --> 00:21:01,410
+solution of equation A star with X greater than 0
+
+212
+00:21:01,410 --> 00:21:09,400
+يبقى thenالـ Y' بدي يسوى R X أُس R مينوس الـ 1
+
+213
+00:21:09,400 --> 00:21:17,620
+وYW' R في R مينوس الـ 1 في X أُس R مينوس الـ 2
+
+214
+00:21:17,620 --> 00:21:28,040
+الآن بدي بقوله Substitute in equation star we get
+
+215
+00:21:28,860 --> 00:21:34,600
+نحصل على ما يدى هى ال X تربيه برا وهى هدى R W
+
+216
+00:21:34,600 --> 00:21:40,120
+Prime R في R minus ال one في X أُس R minus ال two
+
+217
+00:21:40,120 --> 00:21:46,900
+اللى بعدها ناقص خمسة X في ال Y Prime R X أُس R
+
+218
+00:21:46,900 --> 00:21:53,600
+minus ال one اللى بعدها زائد تلتاشر X أُس R كله
+
+219
+00:21:53,600 --> 00:22:01,500
+بده يساوي Zeroهذه لو فكتها R في R minus ال one في
+
+220
+00:22:01,500 --> 00:22:10,460
+X أُس R ناقص خمسة R X أُس R زائد تلتاشر X أُس R
+
+221
+00:22:10,460 --> 00:22:16,630
+بده يساوي Zeroأظن لو جسمنا على الـ X أُس R بنحصل
+
+222
+00:22:16,630 --> 00:22:21,650
+على الـ characteristic equation على الصيغة التالية
+
+223
+00:22:21,650 --> 00:22:30,480
+ناقص خمسة R زائد تلتاشر يساوي Zeroأو بمعنى آخر R
+
+224
+00:22:30,480 --> 00:22:39,100
+تربيع ناقص R ناقص خمسة R زائد تلتاشر يساوي Zero أو
+
+225
+00:22:39,100 --> 00:22:49,260
+R تربيع ناقص ستة R زائد تلتاشر بده يساوي Zero وهذه
+
+226
+00:22:49,260 --> 00:22:52,320
+اللي بنسميها ال characteristic
+
+227
+00:22:59,700 --> 00:23:04,580
+بعد إكسار الشغل الروتيني بدي أحلل المعادلة هذه هل
+
+228
+00:23:04,580 --> 00:23:10,740
+يمكن تحليل هذه المعادلة؟في إمكانية لكن كلها من
+
+229
+00:23:10,740 --> 00:23:14,120
+الدرجة الثانية مش قادرة أحللها بروح بحل بالقانون
+
+230
+00:23:14,120 --> 00:23:19,260
+واللي الله سبحانه وتعالى يفرجها تمام؟ يبقى باجي
+
+231
+00:23:19,260 --> 00:23:25,160
+بيقول هذا R وانا متأكد انه سيفرج سيفرجها إذا الله
+
+232
+00:23:25,160 --> 00:23:28,920
+مافرجهاش مين بده يفرجها؟ يبقى هاي ناقص بقى بيصير
+
+233
+00:23:28,920 --> 00:23:33,340
+ستة زايدة أو ناقص الجدرى التربية ستة في ستة
+
+234
+00:23:51,950 --> 00:24:02,040
+أربعة في تلاتاش باتنين وخمسين52 مضال
+
+235
+00:24:02,040 --> 00:24:13,460
+قداش سالب 16 على 2 يعني 6 زائد او ناقص اللي هو 4I
+
+236
+00:24:13,460 --> 00:24:21,360
+كله مقسم على قداش 2 يبقى بده يساوي 3 زائد او ناقص
+
+237
+00:24:21,360 --> 00:24:29,050
+2Iيبقى عنا ال a هنا بقدش يا بنات و ال b تساوي كده
+
+238
+00:24:29,050 --> 00:24:34,850
+اذا بقدر اجيب ال general solution يبقى بروح بقوله
+
+239
+00:24:34,850 --> 00:24:46,270
+the general solution of the differential equation
+
+240
+00:24:46,270 --> 00:24:57,330
+star is y تساوي x أُس rيبقى X أُس كده؟ أُس تلاتة،
+
+241
+00:24:57,330 --> 00:25:03,850
+X أُس إيه؟ فيه عندنا جذرين، اتنين are conjugate
+
+242
+00:25:03,850 --> 00:25:10,310
+ومافيش غيرهم، يبقاش باجي بقول C واحد كوصين، كده يا
+
+243
+00:25:10,310 --> 00:25:14,130
+بنات؟ اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+244
+00:25:23,910 --> 00:25:30,470
+كف الله المؤمنين والقتال هذا كان المثال رقم اتنين
+
+245
+00:25:30,470 --> 00:25:37,330
+بدنا نروح للمثال رقم تلاتة مثال رقم تلاتة بيقول ما
+
+246
+00:25:37,330 --> 00:25:46,280
+يأتي solve ذاDifferential Equation مثل المعادلة
+
+247
+00:25:46,280 --> 00:25:53,260
+التفاضلية X تكيب Y triple A prime Y triple A prime
+
+248
+00:25:53,260 --> 00:26:00,240
+ناقص X تربيع و Y double A prime زائد X في Y prime
+
+249
+00:26:00,240 --> 00:26:05,920
+بده يساوي كم؟ بده يساوي Zero وهذه هي المعادلة رقم
+
+250
+00:26:05,920 --> 00:26:09,520
+start خليني
+
+251
+00:26:09,520 --> 00:26:20,060
+أسأل السؤال التاليهل هذه كوشي اويلر اكويشن؟ هل
+
+252
+00:26:20,060 --> 00:26:25,460
+هذه كوشي اويلر اكويشن؟ هل
+
+253
+00:26:25,460 --> 00:26:32,080
+هذه كوشي اويلر اكويشن؟ هل هذه كوشي
+
+254
+00:26:32,080 --> 00:26:38,050
+اويلر اكويشن؟ هل هذه كوشي اويلر اكويشن؟أنا كنت
+
+255
+00:26:38,050 --> 00:26:41,650
+بسألها سؤال مش شايفة، كنت شايفة المكتوب على
+
+256
+00:26:41,650 --> 00:26:44,270
+الدافع، بس أنا .. ايه مكتوب؟ هي فوق و قدامك أنا
+
+257
+00:26:44,270 --> 00:26:53,690
+بسأل فيه هذا، هذي كوشويلة equation؟ طلع
+
+258
+00:26:53,690 --> 00:26:57,190
+في القصة تبع ال X و طلع في المشتقة، زي بعض و الله
+
+259
+00:26:57,190 --> 00:27:03,800
+بختلفواكلهم زي بعض حتى وان غاب term حتى وان غاب
+
+260
+00:27:03,800 --> 00:27:09,220
+two terms يعني احنا لو شيلنا كمان هذا بتظهر كوشي
+
+261
+00:27:09,220 --> 00:27:12,580
+او ايلار اكويشين حتى لو شيلنا اتنين هذول بتظهر
+
+262
+00:27:12,580 --> 00:27:18,780
+كوشي او ايلار اكويشين بهمن الأس تبع ال X يكون جد
+
+263
+00:27:18,780 --> 00:27:23,580
+المشتقة بالضمن تكييب يجب علي المشتقة التالتة تربية
+
+264
+00:27:23,580 --> 00:27:26,140
+يجب علي المشتقة التانية يجب علي الصحة صوتنتين
+
+265
+00:27:26,140 --> 00:27:31,310
+غاليكم معايا كويس دينا بالكميبقى بدنا نجي لمن؟ ل
+
+266
+00:27:31,310 --> 00:27:34,890
+الحل يبقى بدي افترض بنفس الطريقة التكتيكي اللي
+
+267
+00:27:34,890 --> 00:27:44,390
+اتبعته هنا بداشي اقوله افترض ان ال Y تساوي X أُس R
+
+268
+00:27:44,390 --> 00:27:49,870
+ب solution of
+
+269
+00:27:49,870 --> 00:27:58,510
+equation star with X greater than 0يبقى بدنا اكتب
+
+270
+00:27:58,510 --> 00:28:01,050
+ال characteristic equation دغري يا بنات و الله ايش
+
+271
+00:28:01,050 --> 00:28:09,330
+رايكوا يبقى the characteristic equation is طب يالا
+
+272
+00:28:09,330 --> 00:28:12,490
+مدام دغري ينجلوني كدهش ال characteristic equation
+
+273
+00:28:12,490 --> 00:28:18,310
+اللي هي دي R في كدهش في R ناقص واحد في R ناقص
+
+274
+00:28:18,310 --> 00:28:28,010
+اتنين مظبوط و هنا ناقصهذه قدرات R في R ناقص واحد
+
+275
+00:28:28,010 --> 00:28:35,910
+وهذه زائد R كله بده يساوي قدر زيب يعني كأنه عوّط
+
+276
+00:28:35,910 --> 00:28:40,590
+واشتقت وقسمت على X plus R وصلت زي ما كنا بنعمل في
+
+277
+00:28:40,590 --> 00:28:45,070
+حالة ال equations with constant coefficients
+
+278
+00:28:45,070 --> 00:28:49,230
+بالضبط تماما طيب ضايق افكك هذه المعادلة اظن ان
+
+279
+00:28:49,230 --> 00:28:54,070
+عندي هنا Rوعندي هنا R وعندي هنا R بقدر أخدها برا
+
+280
+00:28:54,070 --> 00:28:58,630
+عامل مشترك إذا لو أخدت ال R برا عامل مشترك كده
+
+281
+00:28:58,630 --> 00:29:03,210
+بيظل عندي؟ حصل ضرب الأثنين هذول اللي هو R تربية
+
+282
+00:29:03,210 --> 00:29:11,350
+ناقص ثلاثة R زائد اتنين صح؟ وهنا هذي بيصير ناقص R
+
+283
+00:29:11,350 --> 00:29:16,370
+زائد واحد وهذه بيظل عندي كدهش لما أخدت منها R بظل
+
+284
+00:29:16,370 --> 00:29:19,710
+واحد مظبوط هيك؟ أه
+
+285
+00:29:23,260 --> 00:29:32,360
+هذه R في R تربية عندك ناقص 3R و ناقص 4R ناقص 4R دل
+
+286
+00:29:32,360 --> 00:29:37,740
+عندك اتنين و اتنين كمان كده اربعة كله بده يساوي 0
+
+287
+00:29:37,740 --> 00:29:42,780
+اذا شكل ال characteristic equation صارت R في R
+
+288
+00:29:42,780 --> 00:29:51,330
+ناقص اتنين لكل تربيةيبقى الـ roots واحد
+
+289
+00:29:51,330 --> 00:29:55,070
+منهم مكرر مرتين ممتاز جدا
+
+290
+00:30:17,600 --> 00:30:35,540
+Y ثم Y ساعةيبقى C1 في X أُس 0 C2
+
+291
+00:30:35,540 --> 00:30:46,940
+زائد C3 لأن X في X أُس 2 يبقى هذا شكل ال general
+
+292
+00:30:46,940 --> 00:30:51,420
+solution اللي عندكحد فيكم لأي استفسار قبل أن أذهب
+
+293
+00:30:51,420 --> 00:30:58,580
+إلى المثال الذي يليه في أي تساؤل؟ هاي، أروح الآن
+
+294
+00:30:58,580 --> 00:31:05,280
+للمثال اللي بعده
+
+295
+00:31:05,280 --> 00:31:14,740
+يبقى
+
+296
+00:31:14,740 --> 00:31:16,280
+بداجي لـExample 4
+
+297
+00:31:27,600 --> 00:31:28,860
+Solve the equation
+
+298
+00:31:34,610 --> 00:31:43,150
+Equation المعادلة X ناقص تلاتة لكل ترابية في ال Y
+
+299
+00:31:43,150 --> 00:31:51,090
+double prime زائد تلاتة في X ناقص تلاتة في ال Y
+
+300
+00:31:51,090 --> 00:31:57,950
+prime زائد Y بده يساوي Zero وال X greater than
+
+301
+00:31:57,950 --> 00:31:58,770
+تلاتة
+
+302
+00:32:30,510 --> 00:32:37,270
+السؤال الذي سألناه قبل قليل قائماً ولكما Is it a
+
+303
+00:32:37,270 --> 00:32:39,170
+Cauchy-Euler equation؟
+
+304
+00:32:43,960 --> 00:32:53,640
+هو مضمون ان X أكبر من 3 لان X أكبر من 0 لان X أكبر
+
+305
+00:32:53,640 --> 00:32:57,360
+من 3 لان X أكبر من 100 لان X أكبر من 3 لان X أكبر
+
+306
+00:32:57,360 --> 00:33:01,020
+من 100 لان
+
+307
+00:33:01,020 --> 00:33:01,640
+X أكبر من 3 لان X أكبر من 3 لان X أكبر من 100 لان
+
+308
+00:33:01,640 --> 00:33:02,100
+X أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+309
+00:33:02,100 --> 00:33:05,140
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+310
+00:33:05,140 --> 00:33:06,740
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+311
+00:33:06,740 --> 00:33:06,840
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+312
+00:33:06,840 --> 00:33:08,880
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+313
+00:33:19,830 --> 00:33:25,030
+يبقى افترض الحل على الشكل طبعا اتطلعي الأس اللي
+
+314
+00:33:25,030 --> 00:33:28,530
+هنا هو نفس المشتقة الأس اللي هنا هو نفس المشتقة و
+
+315
+00:33:28,530 --> 00:33:33,010
+هكذا تمام اذا هذه كوشي أولى equation يبقى بدأ
+
+316
+00:33:33,010 --> 00:33:41,980
+اقوله little y تساوي x ناقص تلاتة أس Rبا solution
+
+317
+00:33:41,980 --> 00:33:53,300
+of the above differential equation طب
+
+318
+00:33:53,300 --> 00:33:59,220
+لو جيت بدي أجيب ال Y' يبقى R في ال X ناقص تلاتة و
+
+319
+00:33:59,220 --> 00:34:02,920
+ر ناقص واحد في مشتقة مداخل القوس
+
+320
+00:34:05,730 --> 00:34:15,870
+عن طريق الـ YW' يبقى R في R-1 في X ناقص 3 أُس R-2
+
+321
+00:34:15,870 --> 00:34:21,400
+في مشتقة مداخل القصر اللي هو الجداجعوض في المعادل
+
+322
+00:34:21,400 --> 00:34:26,080
+اللي فوق لو جيت عوض في المعادل اللي فوق بصير X
+
+323
+00:34:26,080 --> 00:34:32,040
+ناقص تلاتة لكل تربيع في ال YW prime اللي هو R في R
+
+324
+00:34:32,040 --> 00:34:37,320
+minus ال one في X ناقص تلاتة to the power R minus
+
+325
+00:34:37,320 --> 00:34:44,420
+twoزائد تلاتة X ناقص تلاتة في ال Y prime اللي هي R
+
+326
+00:34:44,420 --> 00:34:50,500
+X ناقص تلاتة to the power R minus one زائد Y اللي
+
+327
+00:34:50,500 --> 00:34:54,560
+هي X ناقص تلاتة to the power R كله بده يساوي Zero
+
+328
+00:34:55,280 --> 00:35:00,200
+بتعيد كتابتها يبقى R في R ناقص واحد في X ناقص
+
+329
+00:35:00,200 --> 00:35:09,520
+تلاتة أس R زائد تلاتة R زائد تلاتة R فاهمين في ال
+
+330
+00:35:09,520 --> 00:35:16,820
+X ناقص تلاتة أس R زائد X ناقص تلاتة أس R كله بده
+
+331
+00:35:16,820 --> 00:35:24,240
+يساوي Zeroالـ X ناقص تلاتة هذا مقدار أكبر من الـ
+
+332
+00:35:24,240 --> 00:35:28,480
+Zero إذا موجب بقدر أقسم عليه بدون مشاكل يبقى لو
+
+333
+00:35:28,480 --> 00:35:33,020
+قسمت كله على X ناقص تلاتة أس R بحصل على ال
+
+334
+00:35:33,020 --> 00:35:39,060
+characteristic equationبالشكل التالي اله دي mean R
+
+335
+00:35:39,060 --> 00:35:45,320
+في R minus ال one زائد تلاتة R زائد واحد بده يساوي
+
+336
+00:35:45,320 --> 00:35:51,640
+Zero او ان شئتم فقولوا R تربيع و عندك ناقص R زائد
+
+337
+00:35:51,640 --> 00:35:56,860
+تلاتة R بيظل زائد اتنين R زائد واحد يساوي Zero
+
+338
+00:35:56,860 --> 00:36:04,260
+يبقى هدى R زائد واحد لكل تربيعيساوي Zero يبقى ال R
+
+339
+00:36:04,260 --> 00:36:10,540
+تساوي سالف واحد of Multiplicity
+
+340
+00:36:10,540 --> 00:36:16,680
+كدهش؟ اتنين اتنين مكررة مرتين يبقى أصبح The
+
+341
+00:36:16,680 --> 00:36:32,860
+General Solution Of The Equation Is Y تساويX وC
+
+342
+00:36:32,860 --> 00:36:40,540
+ايه يا بنات هنا؟ والله مش بنكتب كرر مرتين يبقى إيش
+
+343
+00:36:40,540 --> 00:36:54,040
+بدي أقوله؟ C1 زائد C2 لإن كده؟X ناقص ثلاثة يبقى X
+
+344
+00:36:54,040 --> 00:37:02,540
+ناقص ثلاثة تمين في ال X ناقص ثلاثة أس اللي هو
+
+345
+00:37:02,540 --> 00:37:11,080
+قداشر اتنين هك ماشي للحل صحيح بالمية ال X أس مش
+
+346
+00:37:11,080 --> 00:37:18,060
+اتنين سالب واحد احنا طلعناها ال R أس سالب واحدلحد
+
+347
+00:37:18,060 --> 00:37:21,380
+هنا stop in the intersection ولا يكون أرقام
+
+348
+00:37:21,380 --> 00:37:29,420
+المسائل يبقى أرقام المسائل exercises خمسة خمسة
+
+349
+00:37:29,420 --> 00:37:37,200
+بدنا المسائل من واحد إلى خمستاشر وكذلك سؤال واحد
+
+350
+00:37:37,200 --> 00:37:38,080
+وعشرين
+
+351
+00:37:43,580 --> 00:37:46,960
+في كلمتين حابين نقولهم في ال section اللي بعده
+
+352
+00:37:46,960 --> 00:37:52,500
+بدون ما نعطي ولا مثال ولا نطلب منكوا تحلوا مثالين
+
+353
+00:37:52,500 --> 00:37:58,400
+مقدمة اشي احنا بجينا نشتغل يا بنات على ال
+
+354
+00:37:58,400 --> 00:38:01,900
+homogeneous differential equation بدنا نبدأ الآن
+
+355
+00:38:01,900 --> 00:38:06,160
+الشغل على ال homogeneous differential equation
+
+356
+00:38:06,160 --> 00:38:14,410
+فاكتبلي ال section خمسة ستةخمسة ستة الهي non
+
+357
+00:38:14,410 --> 00:38:32,010
+homogeneous differential equations definition
+
+358
+00:38:32,010 --> 00:38:35,730
+they none
+
+359
+00:38:37,570 --> 00:38:46,150
+Homogenous differential equation is
+
+360
+00:38:46,150 --> 00:38:54,530
+an equation in the form طبعا كل شغل non
+
+361
+00:38:54,530 --> 00:39:01,390
+homogeneous linear differential equation على الشكل
+
+362
+00:39:01,390 --> 00:39:03,810
+التالي A0
+
+363
+00:39:28,500 --> 00:39:29,900
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y11Y12Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11
+
+364
+00:39:31,410 --> 00:39:40,310
+Where حيث capital F of X لا يمكن أن تساوي zero عند
+
+365
+00:39:40,310 --> 00:39:50,190
+ال a naught وال a one و لغاية ال a n may or may
+
+366
+00:39:50,190 --> 00:39:53,970
+not or may not
+
+367
+00:39:58,640 --> 00:40:04,740
+بـColostans يعني ممكن يكونوا ثوابت وممكن يكونوش
+
+368
+00:40:04,740 --> 00:40:15,880
+ثوابت يبقى باجي بقوله F YC يساوي واحد Y واحد C
+
+369
+00:40:15,880 --> 00:40:24,640
+اتنين Y اتنين CNYN is the
+
+370
+00:40:31,990 --> 00:40:44,230
+complimentary solution of
+
+371
+00:40:44,230 --> 00:40:50,090
+the
+
+372
+00:40:50,090 --> 00:40:53,570
+homogenous
+
+373
+00:40:54,300 --> 00:41:01,900
+Differential Equation لـ a0 y to the derivative n
+
+374
+00:41:01,900 --> 00:41:10,100
+زائد a1 y to the derivative n minus one زائد زائد
+
+375
+00:41:10,100 --> 00:41:20,800
+a n minus one y prime زائد a ny بدو يساوي zero and
+
+376
+00:41:20,800 --> 00:41:33,910
+ifYP هو مصطلح مصطلح
+
+377
+00:41:33,910 --> 00:41:40,090
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+378
+00:41:40,090 --> 00:41:40,270
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+379
+00:41:40,270 --> 00:41:45,030
+مصطلح مصطلح
+
+380
+00:41:45,030 --> 00:41:46,410
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+381
+00:41:46,410 --> 00:41:46,450
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+382
+00:41:46,450 --> 00:41:48,730
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح م
+
+383
+00:41:52,260 --> 00:42:00,500
+The general solution
+
+384
+00:42:00,500 --> 00:42:06,140
+of the differential
+
+385
+00:42:06,980 --> 00:42:18,600
+Equation star is y يساوي yc زائد yp ولو بدي ساوي
+
+386
+00:42:18,600 --> 00:42:30,280
+c1 y1 c2 y2 زائد cn yn زائد yp
+
+387
+00:42:52,970 --> 00:43:10,410
+فيرم F U P F U P SA particle is a particular
+
+388
+00:43:10,410 --> 00:43:14,970
+solution
+
+389
+00:43:14,970 --> 00:43:28,270
+of the differential equation
+
+390
+00:43:28,270 --> 00:43:30,710
+L of Y
+
+391
+00:43:33,500 --> 00:43:48,680
+الـ F of X and if ال V P is a particular solution
+
+392
+00:43:48,680 --> 00:44:03,080
+of the differential equation L of Y يساوي G of X
+
+393
+00:44:06,330 --> 00:44:13,930
+ثم مفهوم YP
+
+394
+00:44:13,930 --> 00:44:28,490
+يساوي UP زائد في P هو مفهوم محدد مفهوم
+
+395
+00:44:28,490 --> 00:44:31,450
+محدد من
+
+396
+00:44:34,590 --> 00:44:43,730
+Differential Equation L of Y بده ساوي ال F of X
+
+397
+00:44:43,730 --> 00:44:55,730
+زاد ال G of X يا
+
+398
+00:44:55,730 --> 00:44:59,990
+حد هنا ماتكتبش اسمها باللجاعدات؟ خلاص؟
+
+399
+00:45:02,010 --> 00:45:05,890
+بيعطيكوا العافية لحد هنا انتهى هذا ال section
+
+400
+00:45:05,890 --> 00:45:12,430
+المرة القادمة ان شاء الله اللي هو بعد العيد بعد
+
+401
+00:45:12,430 --> 00:45:19,970
+الإجازة يعني بقى لإن بقينا طيبين بناخد من؟ بناخد
+
+402
+00:45:19,970 --> 00:45:25,710
+ال two sections اللي ضالات في هذا ال chapter ومحل
+
+403
+00:45:25,710 --> 00:45:30,570
+لل non homogeneous differential equationبإحدى
+
+404
+00:45:30,570 --> 00:45:34,970
+طريقتين الأولى ال undetermined coefficients و
+
+405
+00:45:34,970 --> 00:45:39,810
+الطريقة الثانية ال variation of parameters ان شاء
+
+406
+00:45:39,810 --> 00:45:39,990
+الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ddfd2f806d6d4faee965de4cd7cff946702dcd6
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7KldLDfPxv0_raw.srt
@@ -0,0 +1,1644 @@
+1
+00:00:19,490 --> 00:00:25,010
+بسم الله الرحمن الرحيم نعود الآن إلى محاضرة الصباح
+
+2
+00:00:25,010 --> 00:00:30,130
+بدأنا في محاضرة الصباح ب Koshi Euler equation
+
+3
+00:00:30,130 --> 00:00:34,290
+حطينا الصيغة العامة لها و بعدين خدنا حالة منها
+
+4
+00:00:34,290 --> 00:00:36,850
+خاصة اللي هو كانت من
+
+5
+00:00:48,230 --> 00:00:52,730
+المعادلة الأصلية تبعت كوشي ولا ريكوشي ان هناك
+
+6
+00:00:52,730 --> 00:00:58,380
+طريقان للحلالطريق الأول اللي هو بالتعويض قلنا لو
+
+7
+00:00:58,380 --> 00:01:04,980
+حطينا التعويضة X يساوي E قص T خدنا لن للطرفين فصار
+
+8
+00:01:04,980 --> 00:01:11,080
+T تساوي لنا X اشتقنا DT على DX يساوي 1 على X ثم
+
+9
+00:01:11,080 --> 00:01:15,880
+بعد ذلك روحنا جيبنا Y' وYW' بدل ما الاشتقاق
+
+10
+00:01:15,880 --> 00:01:20,260
+بالنسبة لX حولنا الاشتقاق بالنسبة إلى T وبالتالي
+
+11
+00:01:20,260 --> 00:01:24,490
+عوضنا طارمينالـ Variables وسمينا هذه هي الطريقة
+
+12
+00:01:24,490 --> 00:01:29,270
+الأولى يعني الطريقة الأولى بوسط تعويضة بتبعدنا
+
+13
+00:01:29,270 --> 00:01:35,110
+حولنا المعادلة من معادلة بمعاملات متغيرة إلى
+
+14
+00:01:35,110 --> 00:01:39,670
+معادلة بمعاملات ثابتة وبالتالي بنروح نحل هذه كما
+
+15
+00:01:39,670 --> 00:01:44,090
+كنا بنحل في ال sections الماضيةانتقلنا الان الى
+
+16
+00:01:44,090 --> 00:01:49,970
+الطريقة الاولى اللى كتبناها قبل ساعتين من الان
+
+17
+00:01:49,970 --> 00:01:56,510
+طريقة يفترض ان Y يسوى X أس R عبارة عن solution و
+
+18
+00:01:56,510 --> 00:02:00,170
+رحنا اشتغلنا مرة مرتين تلاتة N من المرات و عوضنا
+
+19
+00:02:00,170 --> 00:02:07,400
+في المعادلةحصلنا على المعادلة المساعدة
+
+20
+00:02:07,400 --> 00:02:13,440
+أو المعادلة المميزة للمعادلة الأصلية و رحلنا هذه
+
+21
+00:02:13,440 --> 00:02:17,880
+المعادلة لما جينا نحل هذه المعادلة صار عندي أحد
+
+22
+00:02:17,880 --> 00:02:22,780
+ثلاثة احتمالاتالاحتمال الأول الاحتمال التاني
+
+23
+00:02:22,780 --> 00:02:26,760
+الاحتمال التالت سميتها ثلاث حالات نجي للحالة
+
+24
+00:02:26,760 --> 00:02:30,800
+الأولى لو question double star هذه المعادلة
+
+25
+00:02:30,800 --> 00:02:35,900
+المميزة has indifferent roots يبقى صار عندي R واحد
+
+26
+00:02:35,900 --> 00:02:40,700
+لا يسوى R اتنين لا يسوى R ثلاثة لا يسوى لا يسوى RN
+
+27
+00:02:40,700 --> 00:02:45,220
+ولا واحد زي التاني ما هو الشكل العام للحل يبقى
+
+28
+00:02:45,220 --> 00:02:48,160
+الشكل العام للحل C1 في X وسط R1
+
+29
+00:02:56,780 --> 00:03:01,000
+الحلوق يبقى كونصا في الأول و كونصا في التاريب و
+
+30
+00:03:01,000 --> 00:03:05,420
+يمثل ال general solution إذا الحلوق كانوا real and
+
+31
+00:03:05,420 --> 00:03:11,030
+differentبنجي للحالة التانية لو equation star has
+
+32
+00:03:11,030 --> 00:03:16,070
+complex roots المعادلة طالعة عندما فيها جذور
+
+33
+00:03:16,070 --> 00:03:20,890
+تخيلية فعلى سبيل المثال لو أخد جذرين منهم ماذا
+
+34
+00:03:20,890 --> 00:03:25,330
+يكون شكل الحل يبقى باجي بقول الحل بيكون x to the
+
+35
+00:03:25,330 --> 00:03:31,390
+power إيه؟ ليش؟لأنه بدي يطلع اللي هو ال R يسوي A
+
+36
+00:03:31,390 --> 00:03:37,450
+زائد IB تمام؟ A زائد و ال conduct تبعه A ناقص IB
+
+37
+00:03:37,450 --> 00:03:41,470
+الحل الأول R واحد A زائد IB و الحل التاني R اتنين
+
+38
+00:03:41,470 --> 00:03:47,510
+بديه يسوي A ناقص IB يبقى ال E ال X قص A في مين؟ في
+
+39
+00:03:47,510 --> 00:03:53,230
+C واحد cosine B لن ال X زائد C اتنين sine B لن ال
+
+40
+00:03:53,230 --> 00:03:59,050
+X يعني يا بناتهنا كنا نقول هناك في الحقيقي في
+
+41
+00:03:59,050 --> 00:04:04,550
+التخيلة لما كانوا المعاملات حقيقية بقى نقول C1 Cos
+
+42
+00:04:04,550 --> 00:04:11,050
+Bx ماعنديش Lin لكن هنا جانبين Lin X زي C2 Sin B
+
+43
+00:04:11,050 --> 00:04:16,140
+Lin X الحالة التالتةالحالة التالتة لحالة الـ real
+
+44
+00:04:16,140 --> 00:04:20,000
+قد يكون real و repeated و قد يكون complex و
+
+45
+00:04:20,000 --> 00:04:24,300
+repeated فكيف بنسوي في هذه الحالة يبقى باجي للحالة
+
+46
+00:04:24,300 --> 00:04:27,780
+الأولى ال equation اتنين has real repeated rows of
+
+47
+00:04:27,780 --> 00:04:33,000
+multiplicity S عدد مرات التكرار S والباقي يمكن
+
+48
+00:04:33,000 --> 00:04:38,320
+يكون real يا اما S ممكن يكون كله complex وتساوي N
+
+49
+00:04:38,320 --> 00:04:43,740
+بس بشرط ان ال N عدد زوجييبقى بيصير R واحد يساوي R
+
+50
+00:04:43,740 --> 00:04:48,700
+التاني يساوي RS يساوي R يبقى في هذه الحالة شكل ال
+
+51
+00:04:48,700 --> 00:04:52,400
+general solution زي شكله with constant
+
+52
+00:04:52,400 --> 00:04:57,720
+coefficients ما عدل X بشيله و بحط بدالهالن ال X
+
+53
+00:04:57,720 --> 00:05:02,240
+والباقي كل شيء زي ما هو تطلع C1 C2 لن X C3 لن X
+
+54
+00:05:02,240 --> 00:05:07,700
+نرويها C4 لن X تكريم لغاية ما وصل ل CS لن X أُس S
+
+55
+00:05:07,700 --> 00:05:15,890
+-1 في X أُس R لأن الأُس هذا صار مكرر تمام؟طيب لو
+
+56
+00:05:15,890 --> 00:05:20,210
+كانوا ال roots are repeated complex conjugate لو
+
+57
+00:05:20,210 --> 00:05:24,610
+كانوا هذا real لو كانوا complex يبقى بدي يصير الحل
+
+58
+00:05:24,610 --> 00:05:29,450
+X أس A زي ما هي تبعتي تبعت ال complex بس ايش بدي
+
+59
+00:05:29,450 --> 00:05:32,930
+يصير A واحد زي دي اتنية لن ال X زي دي A أس لن
+
+60
+00:05:41,450 --> 00:05:48,130
+الثوابت المتغيرات C1 وC2 لغاية CS كلها في SIN BLN
+
+61
+00:05:48,130 --> 00:05:54,460
+Xيبقى هذه بدي أفهمها إنها عبارة عن مين عبارة عن
+
+62
+00:05:54,460 --> 00:06:00,000
+الحل X أس A في الجوس الكبير هذا polynomial من
+
+63
+00:06:00,000 --> 00:06:05,540
+الدرجة لأن S ناقص واحد في ال cosine P لن X زي ال
+
+64
+00:06:05,540 --> 00:06:09,000
+polynomial من نفس الدرجة sin P لن X في حتة ال
+
+65
+00:06:09,000 --> 00:06:13,340
+complex لكن في حالتها ال real لا عندي cosine ولا
+
+66
+00:06:13,340 --> 00:06:19,360
+عندي sin polynomial فقط لغير في X أس Aهل بتحب تسأل
+
+67
+00:06:19,360 --> 00:06:24,660
+اي سؤال هنا قبل ان ندخل الامثلة؟
+
+68
+00:06:31,850 --> 00:06:35,070
+ماشي المثال الأول طبعا احنا حققنا معانا طريقتين يا
+
+69
+00:06:35,070 --> 00:06:39,290
+بنات ان قيدني بطريقة بدي التزم في انجل يوز the
+
+70
+00:06:39,290 --> 00:06:44,330
+substitution X يساوي E يساوي T يعني بده مين؟ بده
+
+71
+00:06:44,330 --> 00:06:48,450
+يحول المعلق يمكن يقول لي كمان اجيبلي السؤال بطريقة
+
+72
+00:06:48,450 --> 00:06:52,690
+ثانية يعطي المعلق ويقول لي change او use the
+
+73
+00:06:52,690 --> 00:06:57,630
+substitution X يساوي E يساوي T to changeهذه هي
+
+74
+00:06:57,630 --> 00:06:59,670
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+75
+00:06:59,670 --> 00:07:00,610
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+76
+00:07:00,610 --> 00:07:01,190
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+77
+00:07:01,190 --> 00:07:01,570
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+78
+00:07:01,570 --> 00:07:04,430
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+79
+00:07:04,430 --> 00:07:09,830
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+80
+00:07:09,830 --> 00:07:12,630
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+81
+00:07:12,630 --> 00:07:14,450
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+82
+00:07:14,450 --> 00:07:20,360
+الاختصار الاختصار الاختصار الاختصار اليبقى اول
+
+83
+00:07:20,360 --> 00:07:23,180
+مثال يقول find the general solution of the
+
+84
+00:07:23,180 --> 00:07:27,580
+differential equation ولم يقيدني ما قيدنيش لكن انا
+
+85
+00:07:27,580 --> 00:07:30,720
+كونه اول مثال بدي احله بالطريقتين و بدي ابين ان
+
+86
+00:07:30,720 --> 00:07:35,380
+الطريقتين ما لها نفس الشيء مابتغيرش فيها ايه ولا
+
+87
+00:07:35,380 --> 00:07:39,260
+حاجة يبقى بدي اجي للحل الأول اللي عندنا هذا
+
+88
+00:07:43,620 --> 00:07:51,100
+يبقى بداجة اقول استخدم التعويضة put X يساوي E أُس
+
+89
+00:07:51,100 --> 00:07:58,260
+T هذا بتعطيك T يساوي لن X هذا بتعطيك الـDT على DX
+
+90
+00:07:58,260 --> 00:08:05,720
+يساوي 1 على X and الـY' يا بنات كده اش طلعت؟ مش 1
+
+91
+00:08:05,720 --> 00:08:12,120
+على X في الـDY على DT صح؟ طب والـY W'
+
+92
+00:08:17,770 --> 00:08:26,430
+دي سكوير واي على دي تي سكوير ايوة ناقص دي واي على
+
+93
+00:08:26,430 --> 00:08:35,000
+دي تيطب الحمد لله بس انت بتفرض التعويضة و تقول اذا
+
+94
+00:08:35,000 --> 00:08:37,700
+كذا ماعنديش مشكلة ماعنديك تروح تستنتجيها من أول و
+
+95
+00:08:37,700 --> 00:08:41,760
+جديد لكن اذا كنت نسيها بديك تروح تستنتجيها من أول
+
+96
+00:08:41,760 --> 00:08:46,560
+و جديد طيب يبقى الان بدي امسك المعلومات هذه و اعوض
+
+97
+00:08:46,560 --> 00:08:51,120
+وين في المعادلة اللي هي أصلي اللي هي star يبقى
+
+98
+00:08:51,120 --> 00:08:55,000
+باجي بقول المعادلة star بصير x تربية في ال y w
+
+99
+00:08:55,000 --> 00:09:03,930
+prime هيهي 1 على X تربيع في D²Y على DT² ناقص DY
+
+100
+00:09:03,930 --> 00:09:10,050
+على DT بالشكل اللي عندنا هنا اللي بعدها ناقص 3X
+
+101
+00:09:10,050 --> 00:09:16,170
+فيه بدي أشيل ال Y' و أحط قيمة تالية 1 على X في DY
+
+102
+00:09:16,170 --> 00:09:24,510
+على DT خلصنا منها زائد 4Y مش غيرهاتمام كل هذا
+
+103
+00:09:24,510 --> 00:09:29,590
+الكلام يساوي كده؟ Zero اظن X تربيه مع X تربيه راحت
+
+104
+00:09:29,590 --> 00:09:35,010
+مع السلامة يبقى D Square Y على DT Square ناقص DY
+
+105
+00:09:35,010 --> 00:09:42,650
+على DT ناقص تلاتة DY على DT زائد أربع Y بدأت ساوي
+
+106
+00:09:42,650 --> 00:09:52,040
+Zeroلو روحت جماعة تمهدول بصير D2Y على DT2 ناقص 4DY
+
+107
+00:09:52,040 --> 00:10:00,600
+على DT زائد 4Y بده يسوي قداش Zeroأطلع في المعادلة
+
+108
+00:10:00,600 --> 00:10:04,680
+star واطلع في المعادلة بعد التعويض كيف صارت
+
+109
+00:10:04,680 --> 00:10:09,820
+المعادلة star المعاملات عندي متغيرات بدلالة ال X
+
+110
+00:10:09,820 --> 00:10:15,400
+لكن لما حطيت التعويض هذه حولت إلى معادلة بمعاملات
+
+111
+00:10:15,400 --> 00:10:21,460
+ثابتة إذا بتروح أحلي المعادلة هذه بمين؟ بالمعاملات
+
+112
+00:10:21,460 --> 00:10:29,110
+الثابتة كيف بنين الحل؟ let Y تساوي E أسار Tماعنديش
+
+113
+00:10:29,110 --> 00:10:33,250
+X هنا بطل يصير عندي X الشغل نتهوّل من دلالة X إلى
+
+114
+00:10:33,250 --> 00:10:38,810
+دلالة T يبقى بداجي أقول له let وسمّيلي هذه
+
+115
+00:10:38,810 --> 00:10:47,970
+المعادلة رقم Star let Y تساوي E أُس RT ب A
+
+116
+00:10:47,970 --> 00:11:00,120
+solution ofإذا كانت المقارنة مربوطة ثم المقارنة
+
+117
+00:11:00,120 --> 00:11:05,500
+الخاصة هي
+
+118
+00:11:06,540 --> 00:11:14,900
+R تربيع نقص اربعة R زائد اربعة يساوي Zero يعني هذه
+
+119
+00:11:14,900 --> 00:11:21,440
+مالها R نقص اتنين لكل تربيع يساوي Zero يبقى الجذور
+
+120
+00:11:21,440 --> 00:11:31,280
+حقيقية ومكررة كم مرة مرتين يبقى هذا معناه ان R
+
+121
+00:11:31,280 --> 00:11:41,750
+تساوي اتنين of multiبالإضافة لـ ECT2 كرّرة مرتين
+
+122
+00:11:41,750 --> 00:11:52,930
+إذا بدأت أقول له the general solution of equation
+
+123
+00:11:52,930 --> 00:12:00,880
+double star is Y to sevenمش طبعا انا كنت ملعب
+
+124
+00:12:00,880 --> 00:12:04,660
+دلالة text احنا راهيب نشغل على T يبقى شو بدي يصير
+
+125
+00:12:04,660 --> 00:12:16,560
+تكرار مرتين يبقى C1 زي C2T في قداش في E أس اتنين T
+
+126
+00:12:16,560 --> 00:12:19,620
+طب
+
+127
+00:12:19,620 --> 00:12:27,050
+الجواب ايش طلعناه؟دلالة ايش؟ T و الاصل بدرجة او
+
+128
+00:12:27,050 --> 00:12:30,370
+بدلالة X بكون جيب تحليل المعادلة الأصلية اللي هو
+
+129
+00:12:30,370 --> 00:12:34,970
+Star يبقى باجي بقوله The general solution of
+
+130
+00:12:34,970 --> 00:12:44,730
+equation A star is ال Y يساوي C1 زائد C2 مقداش ال
+
+131
+00:12:44,730 --> 00:12:57,360
+T حطناها مقداش؟لأن الـ X في E أُس 2 لأن الـ Xمظبوط
+
+132
+00:12:57,360 --> 00:13:03,480
+يبقى ايه صارت بدلة لثمين ال X هذهها يا بنات هي C1
+
+133
+00:13:03,480 --> 00:13:12,320
+زائد C2 لن X نجي هذه مش هذه E لن X تربيع اتنين
+
+134
+00:13:12,320 --> 00:13:17,420
+بدخلها جوا اللم ال E و ال L عكس بعض يبقى صار جداش
+
+135
+00:13:17,420 --> 00:13:23,860
+X تربيع يبقى هذا الحل بالطريقة الأولى بدنا نروح
+
+136
+00:13:23,860 --> 00:13:30,980
+نحل بالطريقةبالطريقة الثانية نجربها لأنه ماقاليش
+
+137
+00:13:30,980 --> 00:13:34,980
+احنا اتنين في الامتحان انا اجيب بالي الطريقة
+
+138
+00:13:34,980 --> 00:13:37,080
+الأولى و روحت حل التباهي انت اجيب بالي الطريقة
+
+139
+00:13:37,080 --> 00:13:41,200
+الثانية بنشوف هل الطريقتين بيعطوني نفس الحل ولا كل
+
+140
+00:13:41,200 --> 00:13:48,100
+واحد بتعطيني حل شكل الله أعلم تعالي نشوف ايوة مين
+
+141
+00:13:48,100 --> 00:13:52,420
+اللي بتسأل احنا؟ طيب بنفعل الحل اللي هي ال
+
+142
+00:13:52,420 --> 00:13:54,060
+differential equation
+
+143
+00:13:56,980 --> 00:14:00,120
+بإيش؟ كيف كنا بنحلها في الشفتر الأول؟ مش هاي احنا
+
+144
+00:14:00,120 --> 00:14:04,320
+قولنا little y ساوي E أقصر R T هي طريقة .. لأ لأ
+
+145
+00:14:04,320 --> 00:14:07,660
+هي ال equation star two stars هذي بنحلها زي ما كنا
+
+146
+00:14:07,660 --> 00:14:10,420
+نحلها سابقا star ولا double star? double star و
+
+147
+00:14:10,420 --> 00:14:13,560
+double star ما احنا بنحلها زي قبل لأ زي اي هم شفتر
+
+148
+00:14:13,560 --> 00:14:16,520
+واحد second order differential equation أخدنا two
+
+149
+00:14:16,520 --> 00:14:20,990
+cases special cases T missing و X missingفيش مشكلة
+
+150
+00:14:20,990 --> 00:14:24,030
+أحديها بأي طريقة، لكن مين اللي أسأله؟ هذي والله
+
+151
+00:14:24,030 --> 00:14:27,190
+الـx مسجد و الـt مسجد، هذي بيخلّجي بلها الدورة،
+
+152
+00:14:27,190 --> 00:14:30,650
+وانت حر بقى، تروح و ترجع، تتعقز في الكلام اللي
+
+153
+00:14:30,650 --> 00:14:34,210
+عطيك، انت حر، هذا شأنك، أنا بدي شغل، بس الشغل يكون
+
+154
+00:14:34,210 --> 00:14:39,330
+صحيح، بأي طريقة تشتي، ما لم أقيدكي، فيش تقييد،
+
+155
+00:14:39,330 --> 00:14:43,310
+خلاص، شغل اللي بديكي يعني، ماشي؟ طب لو صار
+
+156
+00:14:43,310 --> 00:14:47,990
+الـthird orderيبقى نفعش الكلام اللي اتيه يبقى
+
+157
+00:14:47,990 --> 00:14:51,590
+يخليه يتعود كل طريقة بناخدها نتعودها مش نهملها و
+
+158
+00:14:51,590 --> 00:14:58,030
+نسيبها طيب بنيجي نكمل يبقى هذا بالشكل اللي عندنا
+
+159
+00:14:58,030 --> 00:15:02,970
+هذا و خلي كيس تلاتة يمكن تلزم يبقى بالدهجة اللي
+
+160
+00:15:02,970 --> 00:15:07,570
+اقول الان a second solution
+
+161
+00:15:09,270 --> 00:15:20,410
+بعد ذلك اقول لت Y تسوى X أُس R بيه solution of the
+
+162
+00:15:20,410 --> 00:15:23,770
+equation star
+
+163
+00:15:26,940 --> 00:15:32,660
+بدا اجيب Y' اللي هو مين؟ R X أُس R ماينوس الوان
+
+164
+00:15:32,660 --> 00:15:39,260
+بعدين بدي اجيب ال Y W' R في R ماينوس الوان في X
+
+165
+00:15:39,260 --> 00:15:45,010
+أُس R ماينوس الاتونبتاخد المعلومات وروح اعوض وين
+
+166
+00:15:45,010 --> 00:15:53,470
+في هذه المعادلة يبقى يا بنات ايش بيصير؟ XYW'-3XY
+
+167
+00:15:53,470 --> 00:15:57,030
+'زائد 4Y يساوي
+
+168
+00:16:03,280 --> 00:16:14,800
+يبقى X تربية في الـ YW' هي R في R-1 في X أُس R-2
+
+169
+00:16:15,220 --> 00:16:22,500
+ناقص ثلاثة X في الـ Y' هيها اللي هي R في X أُس R
+
+170
+00:16:22,500 --> 00:16:30,200
+minus ال 1 زائد أربعة ال Y أنا فرضها بقداش ب X أُس
+
+171
+00:16:30,200 --> 00:16:35,880
+R X أُس R كله بده يساوي Zero تعالى نشوف في هذه كيف
+
+172
+00:16:35,880 --> 00:16:39,420
+صارت هل هي X ترميل لما تدخل جيوب الصين هذي X أُس
+
+173
+00:16:39,420 --> 00:16:45,340
+قداشأس ار ار نقص اتنين و عندك كده اتنين بيصير أس
+
+174
+00:16:45,340 --> 00:16:51,200
+ار يبقى هذه بيصير الار في الار minus ال one في ال
+
+175
+00:16:51,200 --> 00:16:57,760
+X أس ار ناقص تلاتة تلاتة
+
+176
+00:16:57,760 --> 00:17:05,780
+X أس واحد مع X أس R يبقى تلاتة R X أس R زائد أربعة
+
+177
+00:17:05,780 --> 00:17:12,770
+X أس R يسوى كده؟ Zeroأحنا فرضنا هذا الـ solution
+
+178
+00:17:12,770 --> 00:17:17,490
+علما بأن الـ X هنا بنات جداش قلنا من Zero إلى
+
+179
+00:17:17,490 --> 00:17:20,570
+Infinity في الجزء النظري يعني دائما وابدا أكبر من
+
+180
+00:17:20,570 --> 00:17:26,090
+مين أكبر من الـ Zero إذا ممكن قسمت هذه الطرفين كله
+
+181
+00:17:26,090 --> 00:17:31,830
+على مين؟ على X أُس R يبقى بصير عنا R في R ناقص
+
+182
+00:17:31,830 --> 00:17:40,820
+واحد زائد تلاتة R زائد أربع يساوي ZeroR في R ناقص
+
+183
+00:17:40,820 --> 00:17:49,120
+واحد عندك هنا ناقص اهينا ناقص اهي ناقص R وهذه ايه
+
+184
+00:17:49,120 --> 00:17:52,940
+اللي هي ناقص بالشكل اللي عندنا هنا يبقى بناء صلة
+
+185
+00:17:52,940 --> 00:17:59,860
+المعادلة على الشكل R تربية ناقص R ناقص 3R زائد 4
+
+186
+00:17:59,860 --> 00:18:06,240
+بده يساوي 0 يبقى R تربية ناقص 4R زائد 4 تساوي 0
+
+187
+00:18:06,240 --> 00:18:13,030
+مين هي هذه؟characteristic equation يبقى هذا معناه
+
+188
+00:18:13,030 --> 00:18:18,890
+ان الار ناقص اتنين لكل تربية يساوي zero هذا معناته
+
+189
+00:18:18,890 --> 00:18:25,110
+ان الار بدي ساوي اتنين و مكررة كده مرتين اذا بدي
+
+190
+00:18:25,110 --> 00:18:33,650
+اطبق عليها اتكرار فبجي بقوله the general solution
+
+191
+00:18:33,650 --> 00:18:35,630
+is
+
+192
+00:18:37,660 --> 00:18:47,800
+Y تساوي C1 زي C2 من X، هل في أكتر من ذلك؟ هؤلاء
+
+193
+00:18:47,800 --> 00:18:52,920
+المقارنة مرتين حطيت حالين، في من؟ في X أُس R، R
+
+194
+00:18:52,920 --> 00:18:58,860
+بقدرش؟ ب2، طلع إلى الحل هذا و الحل هناك هو
+
+195
+00:18:58,860 --> 00:19:04,660
+الاختلافيبقى لي اتنين ار داسيم سواء كان الحل اللى
+
+196
+00:19:04,660 --> 00:19:08,560
+عندي هذا او الحل اللى عندي هذا، مادام ما قيدنيش
+
+197
+00:19:08,560 --> 00:19:12,700
+اللى بتحل بالحل الثاني ماشي، بتحل بالحل الأول،
+
+198
+00:19:12,700 --> 00:19:19,340
+ماشي طبعا الحل الثاني أسهل، خلاص انت حرة، بس إذا
+
+199
+00:19:19,340 --> 00:19:24,020
+قيدتك بدك تلتجي مين، أحيانا بنقيد و أحيانا لا، انت
+
+200
+00:19:24,020 --> 00:19:24,860
+و بختك عندك
+
+201
+00:19:45,810 --> 00:19:53,290
+هذا اول مثال له سؤال 6 من الكتاب المثال الثاني له
+
+202
+00:19:53,290 --> 00:20:02,450
+سؤال 10 من الكتاب مثال 2 هذا سؤال 10 من الكتاب
+
+203
+00:20:02,450 --> 00:20:09,790
+يقول السؤالThe differential equation of x تربيع و
+
+204
+00:20:09,790 --> 00:20:18,490
+y double prime ناقص خمسة x y prime زائد تلتاشر y
+
+205
+00:20:18,490 --> 00:20:22,810
+بده يساوي zero وهذا اللي بدي أسميها main و اللي
+
+206
+00:20:22,810 --> 00:20:31,170
+بدي أسميها ال start يبقى
+
+207
+00:20:31,170 --> 00:20:32,990
+بدي أبدأ solution
+
+208
+00:20:36,130 --> 00:20:39,630
+أظن أنه لا يوجد دا على الطريقين بيكفيني واحدة لكن
+
+209
+00:20:39,630 --> 00:20:44,230
+التان تان اتعلمناهم تاني أسهلي خلاص بالتاني يبقى
+
+210
+00:20:44,230 --> 00:20:50,270
+باجي بيقول في الطريق ان ال Y يسوى X أُس A ب
+
+211
+00:20:50,270 --> 00:21:01,410
+solution of equation A star with X greater than 0
+
+212
+00:21:01,410 --> 00:21:09,400
+يبقى thenالـ Y' بدي يسوى R X أُس R مينوس الـ 1
+
+213
+00:21:09,400 --> 00:21:17,620
+وYW' R في R مينوس الـ 1 في X أُس R مينوس الـ 2
+
+214
+00:21:17,620 --> 00:21:28,040
+الآن بدي بقوله Substitute in equation star we get
+
+215
+00:21:28,860 --> 00:21:34,600
+نحصل على ما يدى هى ال X تربيه برا وهى هدى R W
+
+216
+00:21:34,600 --> 00:21:40,120
+Prime R في R minus ال one في X أُس R minus ال two
+
+217
+00:21:40,120 --> 00:21:46,900
+اللى بعدها ناقص خمسة X في ال Y Prime R X أُس R
+
+218
+00:21:46,900 --> 00:21:53,600
+minus ال one اللى بعدها زائد تلتاشر X أُس R كله
+
+219
+00:21:53,600 --> 00:22:01,500
+بده يساوي Zeroهذه لو فكتها R في R minus ال one في
+
+220
+00:22:01,500 --> 00:22:10,460
+X أُس R ناقص خمسة R X أُس R زائد تلتاشر X أُس R
+
+221
+00:22:10,460 --> 00:22:16,630
+بده يساوي Zeroأظن لو جسمنا على الـ X أُس R بنحصل
+
+222
+00:22:16,630 --> 00:22:21,650
+على الـ characteristic equation على الصيغة التالية
+
+223
+00:22:21,650 --> 00:22:30,480
+ناقص خمسة R زائد تلتاشر يساوي Zeroأو بمعنى آخر R
+
+224
+00:22:30,480 --> 00:22:39,100
+تربيع ناقص R ناقص خمسة R زائد تلتاشر يساوي Zero أو
+
+225
+00:22:39,100 --> 00:22:49,260
+R تربيع ناقص ستة R زائد تلتاشر بده يساوي Zero وهذه
+
+226
+00:22:49,260 --> 00:22:52,320
+اللي بنسميها ال characteristic
+
+227
+00:22:59,700 --> 00:23:04,580
+بعد إكسار الشغل الروتيني بدي أحلل المعادلة هذه هل
+
+228
+00:23:04,580 --> 00:23:10,740
+يمكن تحليل هذه المعادلة؟في إمكانية لكن كلها من
+
+229
+00:23:10,740 --> 00:23:14,120
+الدرجة الثانية مش قادرة أحللها بروح بحل بالقانون
+
+230
+00:23:14,120 --> 00:23:19,260
+واللي الله سبحانه وتعالى يفرجها تمام؟ يبقى باجي
+
+231
+00:23:19,260 --> 00:23:25,160
+بيقول هذا R وانا متأكد انه سيفرج سيفرجها إذا الله
+
+232
+00:23:25,160 --> 00:23:28,920
+مافرجهاش مين بده يفرجها؟ يبقى هاي ناقص بقى بيصير
+
+233
+00:23:28,920 --> 00:23:33,340
+ستة زايدة أو ناقص الجدرى التربية ستة في ستة
+
+234
+00:23:51,950 --> 00:24:02,040
+أربعة في تلاتاش باتنين وخمسين52 مضال
+
+235
+00:24:02,040 --> 00:24:13,460
+قداش سالب 16 على 2 يعني 6 زائد او ناقص اللي هو 4I
+
+236
+00:24:13,460 --> 00:24:21,360
+كله مقسم على قداش 2 يبقى بده يساوي 3 زائد او ناقص
+
+237
+00:24:21,360 --> 00:24:29,050
+2Iيبقى عنا ال a هنا بقدش يا بنات و ال b تساوي كده
+
+238
+00:24:29,050 --> 00:24:34,850
+اذا بقدر اجيب ال general solution يبقى بروح بقوله
+
+239
+00:24:34,850 --> 00:24:46,270
+the general solution of the differential equation
+
+240
+00:24:46,270 --> 00:24:57,330
+star is y تساوي x أُس rيبقى X أُس كده؟ أُس تلاتة،
+
+241
+00:24:57,330 --> 00:25:03,850
+X أُس إيه؟ فيه عندنا جذرين، اتنين are conjugate
+
+242
+00:25:03,850 --> 00:25:10,310
+ومافيش غيرهم، يبقاش باجي بقول C واحد كوصين، كده يا
+
+243
+00:25:10,310 --> 00:25:14,130
+بنات؟ اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+244
+00:25:14,130 --> 00:25:14,130
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+245
+00:25:14,130 --> 00:25:14,130
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+246
+00:25:14,130 --> 00:25:14,130
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+247
+00:25:14,130 --> 00:25:14,130
+اتنين، اتنين، اتن
+
+248
+00:25:23,910 --> 00:25:30,470
+كف الله المؤمنين والقتال هذا كان المثال رقم اتنين
+
+249
+00:25:30,470 --> 00:25:37,330
+بدنا نروح للمثال رقم تلاتة مثال رقم تلاتة بيقول ما
+
+250
+00:25:37,330 --> 00:25:46,280
+يأتي solve ذاDifferential Equation مثل المعادلة
+
+251
+00:25:46,280 --> 00:25:53,260
+التفاضلية X تكيب Y triple A prime Y triple A prime
+
+252
+00:25:53,260 --> 00:26:00,240
+ناقص X تربيع و Y double A prime زائد X في Y prime
+
+253
+00:26:00,240 --> 00:26:05,920
+بده يساوي كم؟ بده يساوي Zero وهذه هي المعادلة رقم
+
+254
+00:26:05,920 --> 00:26:09,520
+start خليني
+
+255
+00:26:09,520 --> 00:26:20,060
+أسأل السؤال التاليهل هذه كوشي اويلر اكويشن؟ هل
+
+256
+00:26:20,060 --> 00:26:25,460
+هذه كوشي اويلر اكويشن؟ هل
+
+257
+00:26:25,460 --> 00:26:32,080
+هذه كوشي اويلر اكويشن؟ هل هذه كوشي
+
+258
+00:26:32,080 --> 00:26:38,050
+اويلر اكويشن؟ هل هذه كوشي اويلر اكويشن؟أنا كنت
+
+259
+00:26:38,050 --> 00:26:41,650
+بسألها سؤال مش شايفة، كنت شايفة المكتوب على
+
+260
+00:26:41,650 --> 00:26:44,270
+الدافع، بس أنا .. ايه مكتوب؟ هي فوق و قدامك أنا
+
+261
+00:26:44,270 --> 00:26:53,690
+بسأل فيه هذا، هذي كوشويلة equation؟ طلع
+
+262
+00:26:53,690 --> 00:26:57,190
+في القصة تبع ال X و طلع في المشتقة، زي بعض و الله
+
+263
+00:26:57,190 --> 00:27:03,800
+بختلفواكلهم زي بعض حتى وان غاب term حتى وان غاب
+
+264
+00:27:03,800 --> 00:27:09,220
+two terms يعني احنا لو شيلنا كمان هذا بتظهر كوشي
+
+265
+00:27:09,220 --> 00:27:12,580
+او ايلار اكويشين حتى لو شيلنا اتنين هذول بتظهر
+
+266
+00:27:12,580 --> 00:27:18,780
+كوشي او ايلار اكويشين بهمن الأس تبع ال X يكون جد
+
+267
+00:27:18,780 --> 00:27:23,580
+المشتقة بالضمن تكييب يجب علي المشتقة التالتة تربية
+
+268
+00:27:23,580 --> 00:27:26,140
+يجب علي المشتقة التانية يجب علي الصحة صوتنتين
+
+269
+00:27:26,140 --> 00:27:31,310
+غاليكم معايا كويس دينا بالكميبقى بدنا نجي لمن؟ ل
+
+270
+00:27:31,310 --> 00:27:34,890
+الحل يبقى بدي افترض بنفس الطريقة التكتيكي اللي
+
+271
+00:27:34,890 --> 00:27:44,390
+اتبعته هنا بداشي اقوله افترض ان ال Y تساوي X أُس R
+
+272
+00:27:44,390 --> 00:27:49,870
+ب solution of
+
+273
+00:27:49,870 --> 00:27:58,510
+equation star with X greater than 0يبقى بدنا اكتب
+
+274
+00:27:58,510 --> 00:28:01,050
+ال characteristic equation دغري يا بنات و الله ايش
+
+275
+00:28:01,050 --> 00:28:09,330
+رايكوا يبقى the characteristic equation is طب يالا
+
+276
+00:28:09,330 --> 00:28:12,490
+مدام دغري ينجلوني كدهش ال characteristic equation
+
+277
+00:28:12,490 --> 00:28:18,310
+اللي هي دي R في كدهش في R ناقص واحد في R ناقص
+
+278
+00:28:18,310 --> 00:28:28,010
+اتنين مظبوط و هنا ناقصهذه قدرات R في R ناقص واحد
+
+279
+00:28:28,010 --> 00:28:35,910
+وهذه زائد R كله بده يساوي قدر زيب يعني كأنه عوّط
+
+280
+00:28:35,910 --> 00:28:40,590
+واشتقت وقسمت على X plus R وصلت زي ما كنا بنعمل في
+
+281
+00:28:40,590 --> 00:28:45,070
+حالة ال equations with constant coefficients
+
+282
+00:28:45,070 --> 00:28:49,230
+بالضبط تماما طيب ضايق افكك هذه المعادلة اظن ان
+
+283
+00:28:49,230 --> 00:28:54,070
+عندي هنا Rوعندي هنا R وعندي هنا R بقدر أخدها برا
+
+284
+00:28:54,070 --> 00:28:58,630
+عامل مشترك إذا لو أخدت ال R برا عامل مشترك كده
+
+285
+00:28:58,630 --> 00:29:03,210
+بيظل عندي؟ حصل ضرب الأثنين هذول اللي هو R تربية
+
+286
+00:29:03,210 --> 00:29:11,350
+ناقص ثلاثة R زائد اتنين صح؟ وهنا هذي بيصير ناقص R
+
+287
+00:29:11,350 --> 00:29:16,370
+زائد واحد وهذه بيظل عندي كدهش لما أخدت منها R بظل
+
+288
+00:29:16,370 --> 00:29:19,710
+واحد مظبوط هيك؟ أه
+
+289
+00:29:23,260 --> 00:29:32,360
+هذه R في R تربية عندك ناقص 3R و ناقص 4R ناقص 4R دل
+
+290
+00:29:32,360 --> 00:29:37,740
+عندك اتنين و اتنين كمان كده اربعة كله بده يساوي 0
+
+291
+00:29:37,740 --> 00:29:42,780
+اذا شكل ال characteristic equation صارت R في R
+
+292
+00:29:42,780 --> 00:29:51,330
+ناقص اتنين لكل تربيةيبقى الـ roots واحد
+
+293
+00:29:51,330 --> 00:29:55,070
+منهم مكرر مرتين ممتاز جدا
+
+294
+00:30:17,600 --> 00:30:35,540
+Y ثم Y ساعةيبقى C1 في X أُس 0 C2
+
+295
+00:30:35,540 --> 00:30:46,940
+زائد C3 لأن X في X أُس 2 يبقى هذا شكل ال general
+
+296
+00:30:46,940 --> 00:30:51,420
+solution اللي عندكحد فيكم لأي استفسار قبل أن أذهب
+
+297
+00:30:51,420 --> 00:30:58,580
+إلى المثال الذي يليه في أي تساؤل؟ هاي، أروح الآن
+
+298
+00:30:58,580 --> 00:31:05,280
+للمثال اللي بعده
+
+299
+00:31:05,280 --> 00:31:14,740
+يبقى
+
+300
+00:31:14,740 --> 00:31:16,280
+بداجي لـExample 4
+
+301
+00:31:27,600 --> 00:31:28,860
+Solve the equation
+
+302
+00:31:34,610 --> 00:31:43,150
+Equation المعادلة X ناقص تلاتة لكل ترابية في ال Y
+
+303
+00:31:43,150 --> 00:31:51,090
+double prime زائد تلاتة في X ناقص تلاتة في ال Y
+
+304
+00:31:51,090 --> 00:31:57,950
+prime زائد Y بده يساوي Zero وال X greater than
+
+305
+00:31:57,950 --> 00:31:58,770
+تلاتة
+
+306
+00:32:30,510 --> 00:32:37,270
+السؤال الذي سألناه قبل قليل قائماً ولكما Is it a
+
+307
+00:32:37,270 --> 00:32:39,170
+Cauchy-Euler equation؟
+
+308
+00:32:43,960 --> 00:32:53,640
+هو مضمون ان X أكبر من 3 لان X أكبر من 0 لان X أكبر
+
+309
+00:32:53,640 --> 00:32:57,360
+من 3 لان X أكبر من 100 لان X أكبر من 3 لان X أكبر
+
+310
+00:32:57,360 --> 00:33:01,020
+من 100 لان
+
+311
+00:33:01,020 --> 00:33:01,640
+X أكبر من 3 لان X أكبر من 3 لان X أكبر من 100 لان
+
+312
+00:33:01,640 --> 00:33:02,100
+X أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+313
+00:33:02,100 --> 00:33:05,140
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+314
+00:33:05,140 --> 00:33:06,740
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+315
+00:33:06,740 --> 00:33:06,840
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+316
+00:33:06,840 --> 00:33:06,840
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+317
+00:33:06,840 --> 00:33:08,880
+أكبر من 3 لان X أكبر من 3 لان X أكبر من 3 لان X
+
+318
+00:33:19,830 --> 00:33:25,030
+يبقى افترض الحل على الشكل طبعا اتطلعي الأس اللي
+
+319
+00:33:25,030 --> 00:33:28,530
+هنا هو نفس المشتقة الأس اللي هنا هو نفس المشتقة و
+
+320
+00:33:28,530 --> 00:33:33,010
+هكذا تمام اذا هذه كوشي أولى equation يبقى بدأ
+
+321
+00:33:33,010 --> 00:33:41,980
+اقوله little y تساوي x ناقص تلاتة أس Rبا solution
+
+322
+00:33:41,980 --> 00:33:53,300
+of the above differential equation طب
+
+323
+00:33:53,300 --> 00:33:59,220
+لو جيت بدي أجيب ال Y' يبقى R في ال X ناقص تلاتة و
+
+324
+00:33:59,220 --> 00:34:02,920
+ر ناقص واحد في مشتقة مداخل القوس
+
+325
+00:34:05,730 --> 00:34:15,870
+عن طريق الـ YW' يبقى R في R-1 في X ناقص 3 أُس R-2
+
+326
+00:34:15,870 --> 00:34:21,400
+في مشتقة مداخل القصر اللي هو الجداجعوض في المعادل
+
+327
+00:34:21,400 --> 00:34:26,080
+اللي فوق لو جيت عوض في المعادل اللي فوق بصير X
+
+328
+00:34:26,080 --> 00:34:32,040
+ناقص تلاتة لكل تربيع في ال YW prime اللي هو R في R
+
+329
+00:34:32,040 --> 00:34:37,320
+minus ال one في X ناقص تلاتة to the power R minus
+
+330
+00:34:37,320 --> 00:34:44,420
+twoزائد تلاتة X ناقص تلاتة في ال Y prime اللي هي R
+
+331
+00:34:44,420 --> 00:34:50,500
+X ناقص تلاتة to the power R minus one زائد Y اللي
+
+332
+00:34:50,500 --> 00:34:54,560
+هي X ناقص تلاتة to the power R كله بده يساوي Zero
+
+333
+00:34:55,280 --> 00:35:00,200
+بتعيد كتابتها يبقى R في R ناقص واحد في X ناقص
+
+334
+00:35:00,200 --> 00:35:09,520
+تلاتة أس R زائد تلاتة R زائد تلاتة R فاهمين في ال
+
+335
+00:35:09,520 --> 00:35:16,820
+X ناقص تلاتة أس R زائد X ناقص تلاتة أس R كله بده
+
+336
+00:35:16,820 --> 00:35:24,240
+يساوي Zeroالـ X ناقص تلاتة هذا مقدار أكبر من الـ
+
+337
+00:35:24,240 --> 00:35:28,480
+Zero إذا موجب بقدر أقسم عليه بدون مشاكل يبقى لو
+
+338
+00:35:28,480 --> 00:35:33,020
+قسمت كله على X ناقص تلاتة أس R بحصل على ال
+
+339
+00:35:33,020 --> 00:35:39,060
+characteristic equationبالشكل التالي اله دي mean R
+
+340
+00:35:39,060 --> 00:35:45,320
+في R minus ال one زائد تلاتة R زائد واحد بده يساوي
+
+341
+00:35:45,320 --> 00:35:51,640
+Zero او ان شئتم فقولوا R تربيع و عندك ناقص R زائد
+
+342
+00:35:51,640 --> 00:35:56,860
+تلاتة R بيظل زائد اتنين R زائد واحد يساوي Zero
+
+343
+00:35:56,860 --> 00:36:04,260
+يبقى هدى R زائد واحد لكل تربيعيساوي Zero يبقى ال R
+
+344
+00:36:04,260 --> 00:36:10,540
+تساوي سالف واحد of Multiplicity
+
+345
+00:36:10,540 --> 00:36:16,680
+كدهش؟ اتنين اتنين مكررة مرتين يبقى أصبح The
+
+346
+00:36:16,680 --> 00:36:32,860
+General Solution Of The Equation Is Y تساويX وC
+
+347
+00:36:32,860 --> 00:36:40,540
+ايه يا بنات هنا؟ والله مش بنكتب كرر مرتين يبقى إيش
+
+348
+00:36:40,540 --> 00:36:54,040
+بدي أقوله؟ C1 زائد C2 لإن كده؟X ناقص ثلاثة يبقى X
+
+349
+00:36:54,040 --> 00:37:02,540
+ناقص ثلاثة تمين في ال X ناقص ثلاثة أس اللي هو
+
+350
+00:37:02,540 --> 00:37:11,080
+قداشر اتنين هك ماشي للحل صحيح بالمية ال X أس مش
+
+351
+00:37:11,080 --> 00:37:18,060
+اتنين سالب واحد احنا طلعناها ال R أس سالب واحدلحد
+
+352
+00:37:18,060 --> 00:37:21,380
+هنا stop in the intersection ولا يكون أرقام
+
+353
+00:37:21,380 --> 00:37:29,420
+المسائل يبقى أرقام المسائل exercises خمسة خمسة
+
+354
+00:37:29,420 --> 00:37:37,200
+بدنا المسائل من واحد إلى خمستاشر وكذلك سؤال واحد
+
+355
+00:37:37,200 --> 00:37:38,080
+وعشرين
+
+356
+00:37:43,580 --> 00:37:46,960
+في كلمتين حابين نقولهم في ال section اللي بعده
+
+357
+00:37:46,960 --> 00:37:52,500
+بدون ما نعطي ولا مثال ولا نطلب منكوا تحلوا مثالين
+
+358
+00:37:52,500 --> 00:37:58,400
+مقدمة اشي احنا بجينا نشتغل يا بنات على ال
+
+359
+00:37:58,400 --> 00:38:01,900
+homogeneous differential equation بدنا نبدأ الآن
+
+360
+00:38:01,900 --> 00:38:06,160
+الشغل على ال homogeneous differential equation
+
+361
+00:38:06,160 --> 00:38:14,410
+فاكتبلي ال section خمسة ستةخمسة ستة الهي non
+
+362
+00:38:14,410 --> 00:38:32,010
+homogeneous differential equations definition
+
+363
+00:38:32,010 --> 00:38:35,730
+they none
+
+364
+00:38:37,570 --> 00:38:46,150
+Homogenous differential equation is
+
+365
+00:38:46,150 --> 00:38:54,530
+an equation in the form طبعا كل شغل non
+
+366
+00:38:54,530 --> 00:39:01,390
+homogeneous linear differential equation على الشكل
+
+367
+00:39:01,390 --> 00:39:03,810
+التالي A0
+
+368
+00:39:28,500 --> 00:39:29,900
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y11Y12Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11Y11
+
+369
+00:39:31,410 --> 00:39:40,310
+Where حيث capital F of X لا يمكن أن تساوي zero عند
+
+370
+00:39:40,310 --> 00:39:50,190
+ال a naught وال a one و لغاية ال a n may or may
+
+371
+00:39:50,190 --> 00:39:53,970
+not or may not
+
+372
+00:39:58,640 --> 00:40:04,740
+بـColostans يعني ممكن يكونوا ثوابت وممكن يكونوش
+
+373
+00:40:04,740 --> 00:40:15,880
+ثوابت يبقى باجي بقوله F YC يساوي واحد Y واحد C
+
+374
+00:40:15,880 --> 00:40:24,640
+اتنين Y اتنين CNYN is the
+
+375
+00:40:31,990 --> 00:40:44,230
+complimentary solution of
+
+376
+00:40:44,230 --> 00:40:50,090
+the
+
+377
+00:40:50,090 --> 00:40:53,570
+homogenous
+
+378
+00:40:54,300 --> 00:41:01,900
+Differential Equation لـ a0 y to the derivative n
+
+379
+00:41:01,900 --> 00:41:10,100
+زائد a1 y to the derivative n minus one زائد زائد
+
+380
+00:41:10,100 --> 00:41:20,800
+a n minus one y prime زائد a ny بدو يساوي zero and
+
+381
+00:41:20,800 --> 00:41:33,910
+ifYP هو مصطلح مصطلح
+
+382
+00:41:33,910 --> 00:41:40,090
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+383
+00:41:40,090 --> 00:41:40,270
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+384
+00:41:40,270 --> 00:41:45,030
+مصطلح مصطلح
+
+385
+00:41:45,030 --> 00:41:46,410
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+386
+00:41:46,410 --> 00:41:46,450
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح
+
+387
+00:41:46,450 --> 00:41:48,730
+مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح مصطلح م
+
+388
+00:41:52,260 --> 00:42:00,500
+The general solution
+
+389
+00:42:00,500 --> 00:42:06,140
+of the differential
+
+390
+00:42:06,980 --> 00:42:18,600
+Equation star is y يساوي yc زائد yp ولو بدي ساوي
+
+391
+00:42:18,600 --> 00:42:30,280
+c1 y1 c2 y2 زائد cn yn زائد yp
+
+392
+00:42:52,970 --> 00:43:10,410
+فيرم F U P F U P SA particle is a particular
+
+393
+00:43:10,410 --> 00:43:14,970
+solution
+
+394
+00:43:14,970 --> 00:43:28,270
+of the differential equation
+
+395
+00:43:28,270 --> 00:43:30,710
+L of Y
+
+396
+00:43:33,500 --> 00:43:48,680
+الـ F of X and if ال V P is a particular solution
+
+397
+00:43:48,680 --> 00:44:03,080
+of the differential equation L of Y يساوي G of X
+
+398
+00:44:06,330 --> 00:44:13,930
+ثم مفهوم YP
+
+399
+00:44:13,930 --> 00:44:28,490
+يساوي UP زائد في P هو مفهوم محدد مفهوم
+
+400
+00:44:28,490 --> 00:44:31,450
+محدد من
+
+401
+00:44:34,590 --> 00:44:43,730
+Differential Equation L of Y بده ساوي ال F of X
+
+402
+00:44:43,730 --> 00:44:55,730
+زاد ال G of X يا
+
+403
+00:44:55,730 --> 00:44:59,990
+حد هنا ماتكتبش اسمها باللجاعدات؟ خلاص؟
+
+404
+00:45:02,010 --> 00:45:05,890
+بيعطيكوا العافية لحد هنا انتهى هذا ال section
+
+405
+00:45:05,890 --> 00:45:12,430
+المرة القادمة ان شاء الله اللي هو بعد العيد بعد
+
+406
+00:45:12,430 --> 00:45:19,970
+الإجازة يعني بقى لإن بقينا طيبين بناخد من؟ بناخد
+
+407
+00:45:19,970 --> 00:45:25,710
+ال two sections اللي ضالات في هذا ال chapter ومحل
+
+408
+00:45:25,710 --> 00:45:30,570
+لل non homogeneous differential equationبإحدى
+
+409
+00:45:30,570 --> 00:45:34,970
+طريقتين الأولى ال undetermined coefficients و
+
+410
+00:45:34,970 --> 00:45:39,810
+الطريقة الثانية ال variation of parameters ان شاء
+
+411
+00:45:39,810 --> 00:45:39,990
+الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/9ztjtNMsYXg_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/9ztjtNMsYXg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..debccaa97fe5441576f07d8ebad6b8683e1f8dc1
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/9ztjtNMsYXg_postprocess.srt
@@ -0,0 +1,1888 @@
+1
+00:00:19,760 --> 00:00:25,200
+بسم الله الرحمن الرحيم ننتقل الان إلى شبتر تسعة
+
+2
+00:00:25,200 --> 00:00:31,020
+شبتر تسعة بتحدث عن لبلاسي transforms تحويلات
+
+3
+00:00:31,020 --> 00:00:36,440
+لبلاسيليش التحويلات هذه؟ هذه أحياناً بيكون الدالة
+
+4
+00:00:36,440 --> 00:00:41,860
+صعبة التعامل معاها فبنحولها إلى صورة مكافئة لها
+
+5
+00:00:41,860 --> 00:00:46,520
+سهل التعامل معاها هذه التحويلة بنسميها تحويلة
+
+6
+00:00:46,520 --> 00:00:51,580
+Laplace لإن هو اللي اكتشف الشغل هذهبنأخد أول
+
+7
+00:00:51,580 --> 00:00:55,340
+section في هذا الشبتر اللي هو the place transform
+
+8
+00:00:55,340 --> 00:01:00,700
+هنعطي تعريف ومن ثم ناخد أمثلة مختلفة على كيفية
+
+9
+00:01:00,700 --> 00:01:07,060
+حساب the place transform للدوال المختلفة بيقول
+
+10
+00:01:07,060 --> 00:01:11,000
+افترض ان ال f of t بيه function معرفة على الفترة
+
+11
+00:01:11,000 --> 00:01:15,830
+من zero ل infinityLaplace transform the function f
+
+12
+00:01:15,830 --> 00:01:20,670
+of t denoted by يبقى Laplace transform لدالة f of
+
+13
+00:01:20,670 --> 00:01:26,870
+t يا بعطيله رمز L of f of t يعني Laplace ل F of T
+
+14
+00:01:26,870 --> 00:01:32,330
+ال L هذه الحرف الأول ما كلمت Laplace or capital F
+
+15
+00:01:32,330 --> 00:01:36,650
+of S يعني باعتبره function في من؟ function في S
+
+16
+00:01:36,650 --> 00:01:41,010
+ليش function في S؟ هذا مثلا نجيب عليه بعد قليل
+
+17
+00:01:41,580 --> 00:01:45,760
+بيقول للابلايسترانسون ال F of T او ال F of S is
+
+18
+00:01:45,760 --> 00:01:52,680
+defined by كابتال F of S يسوى تكامل من 0 لإنفينيتي
+
+19
+00:01:52,680 --> 00:01:58,620
+لل E نقص ST لل F of T دي T حيث S parameter او any
+
+20
+00:01:58,620 --> 00:02:03,100
+real number هذا الان واضح انه improper integral
+
+21
+00:02:03,100 --> 00:02:04,340
+بسبب وجود man
+
+22
+00:02:12,050 --> 00:02:16,210
+عن طريق الـ Limit بيبدأ تذهب إلى الـ Infinity لمن؟
+
+23
+00:02:16,210 --> 00:02:17,850
+لتكمل من Zero إلى B
+
+24
+00:02:21,360 --> 00:02:26,240
+بنخلّي P تروح ل Infinity وبالتالي اوجدنا لـ Placid
+
+25
+00:02:26,240 --> 00:02:31,460
+transform نتيجتي التكامل لازم تطلع function في S
+
+26
+00:02:31,460 --> 00:02:37,320
+ومن هنا قولنا F of S ضروري جدا لازم تطلع function
+
+27
+00:02:37,320 --> 00:02:41,650
+في S زي ما هنشوف الآنأول مثال قال لي خد لل F of T
+
+28
+00:02:41,650 --> 00:02:45,450
+و سوى E أس AT و T greater than or equal to zero
+
+29
+00:02:45,450 --> 00:02:49,770
+قال لي هاتي لأ plus لل E أس AT طبعا ال area number
+
+30
+00:02:49,770 --> 00:02:54,470
+و هاتي لأ plus لل واحد و لأ plus ل E أس ناقص AT و
+
+31
+00:02:54,470 --> 00:02:58,630
+لأ plus ل E أس ناقص خمسة T يعني تطبيق مباشر دي
+
+32
+00:02:58,630 --> 00:03:05,000
+تطبيق مباشر على Cإذا بدنا نحسب لبلاس ترانسفورم
+
+33
+00:03:05,000 --> 00:03:11,760
+لدالة الأولى يبقى هذا لبلاس ترانسفورم لل E أُس AT
+
+34
+00:03:11,760 --> 00:03:16,520
+بدي أرجع للتعريف يبقى هو تكامل من Zero إلى
+
+35
+00:03:16,520 --> 00:03:23,180
+Infinity لل E أُس ناقص ST ال F of T أنا ماخدها E
+
+36
+00:03:23,180 --> 00:03:26,340
+أُس AT كله في DT
+
+37
+00:03:34,330 --> 00:03:40,950
+يبقى هذا الكلام بده يساوي limit و هي تكامل من zero
+
+38
+00:03:40,950 --> 00:03:49,630
+إلى B لما B tends to infinity لل E أس ناقص S ناقص
+
+39
+00:03:49,630 --> 00:03:57,170
+A كله في T dtيبقى كتابت هذا التكامل على شكل limit
+
+40
+00:03:57,170 --> 00:04:02,750
+يعني بدي أكامل هذه الدالة ثم أروح أخدلها ال limit
+
+41
+00:04:02,750 --> 00:04:10,770
+هذا الكلام بده يساوي يبقى ال plus لل E أُس AT بده
+
+42
+00:04:10,770 --> 00:04:15,490
+يساوي هي ال limit وهذا ال B بدها تروح لل infinity
+
+43
+00:04:16,130 --> 00:04:20,470
+أظن يا بنات تكامل ال exponential بنفس ال
+
+44
+00:04:20,470 --> 00:04:26,830
+exponential itself مقسوما على تفاضل S إن كانت الـS
+
+45
+00:04:26,830 --> 00:04:30,710
+من الدرجة الأولى وزي ما انتوا شايفين هو من الدرجة
+
+46
+00:04:30,710 --> 00:04:37,230
+الأولى في T يبقى مقسوما على ناقص ال S ناقص ال A
+
+47
+00:04:37,230 --> 00:04:43,240
+والحكي هذا كله من Zero لوين؟ من Zero لغاية Bإذا
+
+48
+00:04:43,240 --> 00:04:48,160
+بدنا نعوض بحدود التكامل يبقى هذا الكلام بده يساوي
+
+49
+00:04:48,160 --> 00:04:54,100
+ال limit لما B tends to infinity لل E أس ناقص S
+
+50
+00:04:54,100 --> 00:05:01,260
+ناقص ال A في B على مين على ناقص ال S ناقص ال A
+
+51
+00:05:01,260 --> 00:05:06,850
+ناقص مع ناقص بالصير زائدبدي أشيل الـ T و أضع
+
+52
+00:05:06,850 --> 00:05:10,950
+مكانها Zero يبقى هذا الـ Plus يصبح E و ال Zero
+
+53
+00:05:10,950 --> 00:05:19,350
+يبقى داشر بواحد يبقى زائد واحد على S ناقص الـ A
+
+54
+00:05:19,350 --> 00:05:24,630
+بالشكل اللي عندنا هنا يبقى أصبح لبلاس Transform
+
+55
+00:05:24,630 --> 00:05:32,370
+لدلة E أس A T بدي أساوي طبعا هذا الـ O السالبممكن
+
+56
+00:05:32,370 --> 00:05:37,110
+انازله تحت ايش بيصير؟ بيصير موجب يبقى بيصير limit
+
+57
+00:05:37,110 --> 00:05:45,870
+لما B tends to infinity لواحد على ناقص ال S ناقص
+
+58
+00:05:45,870 --> 00:05:55,990
+ال A في E أس S ناقص ال A كله في B زائد واحد على S
+
+59
+00:05:55,990 --> 00:06:01,940
+ناقص ال Aالحين لما بيبدأ تروح ل zero هذا المقدار
+
+60
+00:06:01,940 --> 00:06:09,220
+كله بقداش؟ لما تروح ل مالة نهاية هذا المقدار كله
+
+61
+00:06:09,220 --> 00:06:10,940
+مالة نهاية في رقم
+
+62
+00:06:14,430 --> 00:06:19,930
+يبقى هذا كله راح بزيرو يبقى ضلة النتيجة واحد على S
+
+63
+00:06:19,930 --> 00:06:25,550
+نقص ال A بشرط ان ال S is greater than A يبقى بناء
+
+64
+00:06:25,550 --> 00:06:29,510
+عليه من الآن فا ساعدا Laplace transform لل
+
+65
+00:06:29,510 --> 00:06:34,490
+exponential function E أس AT هو عبارة عن واحد على
+
+66
+00:06:34,490 --> 00:06:39,880
+S ناقص ال A انتهينا منهاطيب ان المطلوب الأول
+
+67
+00:06:39,880 --> 00:06:45,820
+بيداجي للمطلوب الثاني نمرا بي نمرا بي ايوة اخر شرط
+
+68
+00:06:45,820 --> 00:06:49,820
+نقصنا اكتر من ايه؟ بدي مشان اضمن انه ماصلتش سالبة
+
+69
+00:06:49,820 --> 00:06:54,880
+دائما انا بدي نقص سجريتر ده نقصه طيب الان بيداجي
+
+70
+00:06:54,880 --> 00:07:00,180
+لنمرا بي نمرا بي بدي ل plus لل one هل بقدر اجرب ان
+
+71
+00:07:00,180 --> 00:07:07,320
+اتجيب الواحد الصحيح من ال E أس ET هذي
+
+72
+00:07:07,320 --> 00:07:13,490
+نقدر؟لو حطينا ال a بقدرش؟ Zero يبقى باجي بقوله هنا
+
+73
+00:07:13,490 --> 00:07:22,130
+F ال a تساوي zero then Laplace transform لل e او
+
+74
+00:07:22,130 --> 00:07:27,850
+ال zero هو Laplace transform لمن؟ لل واحد يعني هنا
+
+75
+00:07:27,850 --> 00:07:33,830
+هشيل ال a و أحط مكانها zero يبقى واحد على s ناقص
+
+76
+00:07:33,830 --> 00:07:40,620
+ال zero يبقى بهوله بقدرش1 على S إذا من الآن فصاعدا
+
+77
+00:07:40,620 --> 00:07:48,480
+ل plus transform للواحد الصحيح هي 1 على S طيب نمرى
+
+78
+00:07:48,480 --> 00:07:57,560
+C جال بيده ل plus transform لل E أس ناقص AT هذه
+
+79
+00:07:57,560 --> 00:08:03,340
+نمرى C شو بتفرج عن ال A؟بس الـ A بالسالب. إذا بدي
+
+80
+00:08:03,340 --> 00:08:06,620
+أخد الإجابة اللي حصلت عليها فوق و أحط الـ A
+
+81
+00:08:06,620 --> 00:08:12,860
+بالسالب. يبقى هذا الكلام دي سواء 1 على S ناقص بدل
+
+82
+00:08:12,860 --> 00:08:20,310
+الـ A اجانب ناقص A يبقى 1 على S زائد الـ A.نمر دي
+
+83
+00:08:20,310 --> 00:08:27,310
+جالي هتلي plus transform ل E أس ناقص خمسة T يبقى
+
+84
+00:08:27,310 --> 00:08:33,330
+واحد على S زائد خمسة لأن هذا هو حالة خاصة للي
+
+85
+00:08:33,330 --> 00:08:39,110
+عندنا هذا ايه بهي حسبنا plus transform لدوالين
+
+86
+00:08:39,110 --> 00:08:41,670
+مختلفة example two
+
+87
+00:08:51,800 --> 00:08:57,540
+بقول find نمرا
+
+88
+00:08:57,540 --> 00:09:10,360
+A لبلاس ترانسفورم لصين AT نمرا B لبلاس ترانسفورم
+
+89
+00:09:10,360 --> 00:09:24,710
+لكو صين ATنمر ال c ل plus transform ل cos cos 5t
+
+90
+00:09:24,710 --> 00:09:35,410
+خلي
+
+91
+00:09:35,410 --> 00:09:43,800
+بركتيبدّى اخد نمرة ايه بدي لبلاس ترانسفورم لصين اي
+
+92
+00:09:43,800 --> 00:09:48,580
+تي بدي ارجع للتعريف اللى عندنا يبقى هو تكامل من
+
+93
+00:09:48,580 --> 00:09:58,520
+zero ل infinity لل E أس ناقص ST لصين اي تي دي تي
+
+94
+00:09:58,520 --> 00:10:06,480
+طبعا يبقى هذا هو عبارة عن مين عبارة عن limitلما B
+
+95
+00:10:06,480 --> 00:10:13,320
+tends to infinity لتكمل من zero ل B ل E أس ناقص ST
+
+96
+00:10:13,320 --> 00:10:24,340
+cosine AT sin AT DT sin AT DT
+
+97
+00:10:24,340 --> 00:10:28,380
+طب
+
+98
+00:10:28,380 --> 00:10:34,340
+كيف بنكمل هذا يا مناسي؟ شو الطريقة؟ بن calculate B
+
+99
+00:10:36,410 --> 00:10:39,210
+بدي واحدة تحكي انا ماتديش الهمامات بدي واحدة ترفع
+
+100
+00:10:39,210 --> 00:10:41,950
+أيديها و تحكي اه integration by parts integration
+
+101
+00:10:41,950 --> 00:10:45,370
+by parts تمام؟ و هنا زي ما يقولوا ضرب العميان
+
+102
+00:10:45,370 --> 00:10:49,110
+الصيف ايش ما تاخد صح ان اخدت ال U تساوي ال
+
+103
+00:10:49,110 --> 00:10:53,150
+exponential و ال DV تساوي ال cosine ماشي ان اعملت
+
+104
+00:10:53,150 --> 00:10:58,270
+العملية العكسية اخدت ال U هي ال sine و ال DV هي ال
+
+105
+00:10:58,270 --> 00:11:02,600
+exponential ماعناش مشكلةيبقى كل ما تاخد الاتنين
+
+106
+00:11:02,600 --> 00:11:10,140
+صحيح يبقى انا بدي اخد ال U تساوي E أس ناقص ST و
+
+107
+00:11:10,140 --> 00:11:19,820
+بدي اخد ال DV Sin AT بدي ال DU يبقى ناقص S E أس
+
+108
+00:11:19,820 --> 00:11:32,010
+ناقص ST DT بدي ال V ناقص Cos AT على Aيبقى النتيجة
+
+109
+00:11:32,010 --> 00:11:39,290
+هذه بدها تساوي limit لما B tends to infinity لمن؟
+
+110
+00:11:39,290 --> 00:11:44,510
+ل ال U في ال V يبقى هي ال U و ال V اللي هو ناقص
+
+111
+00:11:44,510 --> 00:11:56,510
+واحد على A في A أس ناقص ST في cosine AT هذا ال U
+
+112
+00:11:56,510 --> 00:12:06,050
+في ال V ناقص تكامل V ده UV ناقص cosine AT على A
+
+113
+00:12:06,050 --> 00:12:16,750
+داليه ناقص S يوس ناقص ST كله بالنسبة الى DTطبعا
+
+114
+00:12:16,750 --> 00:12:21,910
+كوني كامل تبقى حدود التكامل هذه هتبقى من وين لوين؟
+
+115
+00:12:21,910 --> 00:12:30,010
+من zero لغاية B وهذا كمان تكامل من zero لغاية B و
+
+116
+00:12:30,010 --> 00:12:34,570
+limit للكل من هنا لما نكمل من هنا
+
+117
+00:12:42,160 --> 00:12:47,560
+بتعوض بالقيمة اللى فوق ناقص القيمة اللى اتاها يبقى
+
+118
+00:12:47,560 --> 00:12:59,450
+هنا ناقص cosine a b على a في a أس Sbنزلت ال
+
+119
+00:12:59,450 --> 00:13:03,910
+exponential تحت بإشارة موجبة هذا التعييل الأول
+
+120
+00:13:03,910 --> 00:13:11,630
+ناقص مع ناقص بصير زائد كسين صفر بواحد و E of zero
+
+121
+00:13:11,630 --> 00:13:19,020
+بواحد بظل عندى هنا بس كدهش واحد على ايهو أي limit
+
+122
+00:13:19,020 --> 00:13:24,280
+للكل نجي للي بعد هذه عندك هنا ناقص و هنا ناقص و
+
+123
+00:13:24,280 --> 00:13:31,160
+هنا ناقص يبقى تلاتة بالناقص عندك S و هنا A مقادير
+
+124
+00:13:31,160 --> 00:13:36,540
+ثابتة يبقى بقدر اخدها برا التكامل و بصير تكامل من
+
+125
+00:13:36,540 --> 00:13:44,920
+zero إلى B لل E أس ناقص ST ل cosine ATDT
+
+126
+00:13:47,530 --> 00:13:50,510
+خلّي بالك هنا طبعا هذا حالنا فيكال كلاصي بس أنا
+
+127
+00:13:50,510 --> 00:13:55,190
+بدكر تذكير يبقى أنا أخدت ال U هنا بال exponential
+
+128
+00:13:55,190 --> 00:14:02,450
+و أخدت ال DV بsin 80 اشتقت و هنا كامل يبقى هذه ال
+
+129
+00:14:02,450 --> 00:14:10,330
+U في ال Vماقص تكامل Vداليون بدي أعيد الترتيب و
+
+130
+00:14:10,330 --> 00:14:13,530
+أعوض بالقيمة اللي فوق ناقص القيمة اللي فوق هذه
+
+131
+00:14:13,530 --> 00:14:18,410
+السلة اللي بدي أنزلها تحت بصير مجبرة بيبقى Cos AB
+
+132
+00:14:18,410 --> 00:14:24,540
+على A في Sهنا ناقص مع ناقص زائد بدي أشيل ال T و
+
+133
+00:14:24,540 --> 00:14:27,900
+أضع مكانها Zero و ال cosine صفر بواحد E و ال Zero
+
+134
+00:14:27,900 --> 00:14:33,380
+بواحد بيضل بس كدهش واحد على A هنا عندنا S على A
+
+135
+00:14:33,380 --> 00:14:38,780
+برا عندك ناقص ناقص ناقص يبقى تلاتة بالناقص بيصير
+
+136
+00:14:38,780 --> 00:14:43,500
+عندنا ناقص S على A تكمل من Zero ل B لل E و ناقص ال
+
+137
+00:14:43,500 --> 00:14:48,840
+T cosine ATDTتعالى نحسب الحسبة اللى عندنا هذه هذا
+
+138
+00:14:48,840 --> 00:14:53,740
+الكلام يساوي لو أخدت limit لهذا المقدار يابانات
+
+139
+00:14:53,740 --> 00:15:00,060
+كدهش بطلع يلا ايه اشوف على السريع كدهش واحد على
+
+140
+00:15:00,060 --> 00:15:07,480
+ايه هذا term الاول term الاول كصينمه محصر من واحد
+
+141
+00:15:07,480 --> 00:15:12,510
+و سالب واحد و هذا بين بيروحما لا لا يبقى على جد
+
+142
+00:15:12,510 --> 00:15:16,030
+ياشف زيرو على طول الخط او بتقولوا ليه cos a b
+
+143
+00:15:16,030 --> 00:15:19,590
+محصور من واحد و سالب واحد و بدي اضرب الطرفين في
+
+144
+00:15:19,590 --> 00:15:24,410
+واحد على a في e أس s a b و اخد اللي ما بصير هنا
+
+145
+00:15:24,410 --> 00:15:27,110
+زيرو هنا زيرو و بيجيب ساندوشتين و اللي في النص
+
+146
+00:15:27,110 --> 00:15:32,130
+بيزيروإذا هذا ال limit اللي هو كله بـ0 واحد على
+
+147
+00:15:32,130 --> 00:15:36,250
+إيه مقدار ثابت، مالوش دعوة بال limit تمام، وانهيت
+
+148
+00:15:36,250 --> 00:15:40,230
+المقدار الثابت بالمقدار الثابت itself يبقى واحد
+
+149
+00:15:40,230 --> 00:15:46,450
+على إيه ناقص S على إيه في limit لما B tends to
+
+150
+00:15:46,450 --> 00:15:52,970
+infinity لتكامل من zero إلى B لل E أس ناقص ST
+
+151
+00:15:52,970 --> 00:15:56,190
+cosine ATDT
+
+152
+00:16:12,880 --> 00:16:18,440
+الان برضه بنعمل هذه integration by parts تمام؟
+
+153
+00:16:18,440 --> 00:16:21,940
+برضه نفس التعويض اللي أخدت U هنا بدي أخدها U هنا
+
+154
+00:16:21,940 --> 00:16:25,760
+بالضبط لإن لو عملت العملية العكسية ماعرفش اللي
+
+155
+00:16:25,760 --> 00:16:29,100
+اشتغلت و خربت و رجعت و ماسويش شيء شيءيبقى بضالة
+
+156
+00:16:29,100 --> 00:16:35,180
+الماشي بنفس الاتجاه إذا بدي أخد ال U تساوي E أس
+
+157
+00:16:35,180 --> 00:16:47,130
+ناقص ST و DV ليه cosine ATDTيبقى الـ DU يكون ناقص
+
+158
+00:16:47,130 --> 00:16:56,610
+SE أُس ناقص ST في DT والـ V بـSin AT على A يبقى
+
+159
+00:16:56,610 --> 00:17:01,630
+أصبح عندي اللي هو من لبلاسر ترانسفورم اللي هي
+
+160
+00:17:01,630 --> 00:17:07,330
+الـSin AT بدي سوية واحد على A الثابت اللي عندنا
+
+161
+00:17:07,330 --> 00:17:16,080
+ناقصS على A في الـ limit لما B tends to infinity و
+
+162
+00:17:16,080 --> 00:17:21,480
+هذا الـ goose اللي عندنا بنروح نكتب U في V هذا الـ
+
+163
+00:17:21,480 --> 00:17:29,680
+U و هذا الـ V يبقى E أس ناقص ST في Sin AT كله على
+
+164
+00:17:29,680 --> 00:17:40,940
+جداش على A ناقص تكاملV التي هي الـSin AT على A W
+
+165
+00:17:40,940 --> 00:17:50,160
+التي هي ناقص SEOS ناقص ST كل هذا الكلام بالنسبة
+
+166
+00:17:50,160 --> 00:17:57,360
+إلى مين إلى DT وهيجفلنا الجوز بالشكل اللي عندناهذا
+
+167
+00:17:57,360 --> 00:18:02,800
+الكلام يبدو يساوي 1 على a نزلناها زي ما هي ناقص s
+
+168
+00:18:02,800 --> 00:18:07,600
+على a زي ما هي و جينا بدنا ناخد a بس هذه يا بنات
+
+169
+00:18:07,600 --> 00:18:13,460
+بنعود بحدود التكامل من zero إلى b وهذه من zero إلى
+
+170
+00:18:13,460 --> 00:18:20,680
+b كذلك يبقى هذه بدها الصيرة اللي ماتلما الـ B بدها
+
+171
+00:18:20,680 --> 00:18:24,920
+تروح إلى infinity للجوز، بتعوض بالقيمة اللى فوق
+
+172
+00:18:24,920 --> 00:18:35,350
+ناقص اللى تحتى بجا صين A B على A في E أس S Bنقص
+
+173
+00:18:35,350 --> 00:18:43,130
+نقص
+
+174
+00:18:43,130 --> 00:18:46,250
+نقص
+
+175
+00:18:46,250 --> 00:18:53,490
+نقص نقص
+
+176
+00:18:53,490 --> 00:18:57,730
+نقص
+
+177
+00:18:57,730 --> 00:19:03,650
+نقص نقص نقص
+
+178
+00:19:05,270 --> 00:19:11,130
+طيب هذا اللي ما تقزش بتعطيني ابنات كمان0 يبقى صارة
+
+179
+00:19:11,130 --> 00:19:18,530
+إن النتيجة 1 على a ناقص s على a ب a في s على a s
+
+180
+00:19:18,530 --> 00:19:25,790
+تربيع على a تربيع تمام؟ في limit لمن؟ لما ال b
+
+181
+00:19:25,790 --> 00:19:32,550
+tends to infinity لتكامل من 0 إلى b لل e أس ناقص
+
+182
+00:19:32,550 --> 00:19:42,530
+st في sin a t في dtأو ان شئتنا فقولنا واحد على إيه
+
+183
+00:19:42,530 --> 00:19:48,150
+ناقص S تربيع على إيه تربيع مش هذه هي التعريف
+
+184
+00:19:48,150 --> 00:19:53,470
+الأساسي اللي موجود عندنا اللي هو هذا يعني هذه بقدر
+
+185
+00:19:53,470 --> 00:20:00,090
+أقول هي تكامل من zero إلى infinity لل E أس ناقص ST
+
+186
+00:20:00,090 --> 00:20:03,810
+ل sign ATDT
+
+187
+00:20:06,160 --> 00:20:11,660
+مصبوط؟ هذه ليلا plus لهذه إذا بده أرجعها يعني صار
+
+188
+00:20:11,660 --> 00:20:18,140
+هذا عندنا كالتالي صار عندنا بالشكل التالي هذه هو
+
+189
+00:20:19,660 --> 00:20:25,980
+اللي هي S تربيع على A تربيع وهي الناقص وهي واحد
+
+190
+00:20:25,980 --> 00:20:31,260
+على A تساوي تساوي اللي هي تكامل من Zero إلى
+
+191
+00:20:31,260 --> 00:20:40,480
+Infinity لل E أُس ناقص ST لـSin ATDT هي اللي بدأت
+
+192
+00:20:40,480 --> 00:20:45,580
+فيها مش هي التعريف هذا لإن كتبته زي ما هو طب إيش
+
+193
+00:20:45,580 --> 00:20:51,300
+رأيك ال term هذا مش هو ال term هذايبقى خليني أنقله
+
+194
+00:20:51,300 --> 00:20:57,920
+عنده بيجيني بشرط مين؟ موجة يبقى بصير عنا هنا واحد
+
+195
+00:20:57,920 --> 00:21:07,080
+زائد اللي هو S تربيع على A تربيع كله هدفي لابلاس
+
+196
+00:21:07,080 --> 00:21:15,320
+ترانسفورم لصين AT بده يسوي قداش1 على a يبقى هذا
+
+197
+00:21:15,320 --> 00:21:23,240
+معناه ان a تربيع زائد s تربيع على a تربيع كل هذا
+
+198
+00:21:23,240 --> 00:21:30,000
+الكلام في لابلاسي ترانس فورم لصين at سوى 1 على a
+
+199
+00:21:30,510 --> 00:21:37,050
+يبقى بناء أن علي أصبح لبلاس ال transform ل sign AT
+
+200
+00:21:37,050 --> 00:21:44,690
+أضرب A بصير ال A على S تربيع زائد A تربيع مين اللي
+
+201
+00:21:44,690 --> 00:21:51,110
+بدها تسأل؟ اه ايوة لماذا؟
+
+202
+00:21:51,110 --> 00:21:55,170
+طب انا بجزر و لسه بتناقش انا وياك و انا باشرع
+
+203
+00:21:55,170 --> 00:22:01,800
+التكامل هذاتكامل هذا كالكلصبية بنت الحلال و اصولك
+
+204
+00:22:01,800 --> 00:22:05,940
+تبقى عرفاة و اصول حفظك النتيجة وامشي لكن انا بحصلك
+
+205
+00:22:05,940 --> 00:22:09,280
+اتفصيل و بذكر تذكير لان العقل مش دايما موجود
+
+206
+00:22:09,280 --> 00:22:17,330
+عبدالله بيجي بيعدرطيب يبقى مرة تانية بقول احنا
+
+207
+00:22:17,330 --> 00:22:21,650
+خلصنا الحل شو اللي عملناه و اين توصلنا احنا بدنا
+
+208
+00:22:21,650 --> 00:22:26,450
+لبلاس ترانسفورم لصين اتي انا ماعنديش الا التعريف
+
+209
+00:22:26,450 --> 00:22:31,410
+يبقى بدي اضرب هدف E والسالم ST وكمل من Zero الى
+
+210
+00:22:31,410 --> 00:22:35,580
+Infinity الشكل اللي عندهاالان هذا الـ improper
+
+211
+00:22:35,580 --> 00:22:39,540
+integral يبقى خاتل و limit integration by parts
+
+212
+00:22:39,540 --> 00:22:44,480
+بدي اعملها مرتين إذا عملتها مرتين بتبقى مسألة T
+
+213
+00:22:44,480 --> 00:22:49,580
+خلصت وهذا كان معنا سؤال في calculus B إذا مذاكرين
+
+214
+00:22:49,580 --> 00:22:53,380
+موجود كان معنا في calculus B في ال integration by
+
+215
+00:22:53,380 --> 00:22:56,920
+parts بس ده مجنون integration by parts مع ال
+
+216
+00:22:56,920 --> 00:23:02,640
+improper integralيبقى هذا التكامل بدي أخد هذه U و
+
+217
+00:23:02,640 --> 00:23:08,940
+هذه DV وبالتالي سلمت U في V ناقص تكامل V داليو
+
+218
+00:23:08,940 --> 00:23:14,500
+الان بدي أعيد الترتيب هذه بدي أعوض بالقيم اللي فوق
+
+219
+00:23:14,500 --> 00:23:18,480
+ناقص اللي تحتي بدي أشيل كل T و أحط مكانها
+
+220
+00:23:25,040 --> 00:23:31,240
+نقص نقص نقص يبقى تلاتة بالسالب بصير عندنا سالب S
+
+221
+00:23:31,240 --> 00:23:35,860
+على A ثابت بدي أخده برا بضال تكابل من Zero إلى B
+
+222
+00:23:35,860 --> 00:23:42,890
+لإيه؟ و اذا ناقص ST Cos ATDTبعد ذلك بدي نزل هذه زي
+
+223
+00:23:42,890 --> 00:23:47,610
+ما هي هذه زي ما هي وهي ال limit ال exponential
+
+224
+00:23:47,610 --> 00:23:53,150
+اللي عندنا يعني انتقلنا من E أس سالب ST ل sine AT
+
+225
+00:23:53,150 --> 00:23:59,550
+إلى تكامل لل E أس نقل ST cosine AT يبقى لو كملت
+
+226
+00:23:59,550 --> 00:24:04,250
+كمان مرة برجع لراسي المسألة اللي فوق إذا بدي أروح
+
+227
+00:24:04,250 --> 00:24:08,330
+كامل كمان مرة بدي أخد هذه U وهذه DV
+
+228
+00:24:15,840 --> 00:24:22,700
+هذه تكاملها بـsin at عليها بنقسم على تفاضل الزاوية
+
+229
+00:24:22,700 --> 00:24:28,810
+إن كانت الزاوية من الدرجة الأولىطيب بدنا نبدأ نعوض
+
+230
+00:24:28,810 --> 00:24:34,090
+يبقى 1 على a ناقص s على a في limit اللي هي موجودة
+
+231
+00:24:34,090 --> 00:24:39,670
+عندنا هنا بالضغط تماما الان بداجي اقوله ال U في ال
+
+232
+00:24:39,670 --> 00:24:46,290
+V أيها من a من zero ل b ناقص تكمل من zero ل b لل V
+
+233
+00:24:46,290 --> 00:24:52,090
+ده ال U هذا ال V وهذه ده ال U كتبتها زي مانيطيب 1
+
+234
+00:24:52,090 --> 00:24:56,930
+على a نزلت سالب s a على a نزلت ال limit كما هي هذه
+
+235
+00:24:56,930 --> 00:25:01,890
+لما تنزل بي تحت بصير sin a بي على a في ال s بي
+
+236
+00:25:01,890 --> 00:25:05,730
+طبعا هذه ال limit اللي هبزير وانما بي تروح لما لا
+
+237
+00:25:05,730 --> 00:25:09,790
+نهاية ليش انو ال sin a بي محصور من واحد وسالب واحد
+
+238
+00:25:09,790 --> 00:25:13,910
+ضربنا في واحد على ال exponential وخلت بي تروح لما
+
+239
+00:25:13,910 --> 00:25:19,550
+لا نهاية بصير عدد على ما لا نهاية لهوبزيرو يبقى
+
+240
+00:25:19,550 --> 00:25:25,410
+هذه zero دائما و أبدا الان ناقص بدي أضع هنا zero
+
+241
+00:25:25,410 --> 00:25:31,210
+وهنا zero هذه واحد وهذه زيرو على أي عدد بقدر بزيرو
+
+242
+00:25:31,210 --> 00:25:37,330
+وصلنا لهذه ال S على A برة وناقص مع ناقص بصير زاد
+
+243
+00:25:37,330 --> 00:25:45,330
+وE أقص ناقص ST sin ATDT هي كما هيإذا انصرت المسألة
+
+244
+00:25:45,330 --> 00:25:50,690
+التكامل الأساسي elemental والـsin AT هذا بدي أساوي
+
+245
+00:25:50,690 --> 00:25:54,430
+مين؟ بدي أساوي واحد على إيه؟ ناقص، فعندك هنا S
+
+246
+00:25:54,430 --> 00:25:59,090
+عليّ وهنا S علي إيه؟ S تربيع علي تربيع limit لما
+
+247
+00:25:59,090 --> 00:26:04,030
+الـP بدأ تروح لل infinity للتكامل اللي عندنا هذا
+
+248
+00:26:04,340 --> 00:26:09,480
+التكامل لأن هذا هو نفس التكامل هذا تمام بس بده
+
+249
+00:26:09,480 --> 00:26:13,700
+أرجع هذا إلى أصله قبل ال limit يبقى رجعته إلى أصله
+
+250
+00:26:13,700 --> 00:26:17,340
+بدل ما هو limit شيلته و كتبت تكامل من zero إلى
+
+251
+00:26:17,340 --> 00:26:23,420
+infinity لل EOS ناقص STDD هذا هو الطرف الشمال يبقى
+
+252
+00:26:23,420 --> 00:26:27,640
+بده أديه عنده و أجمع بدل ما كانت شرطه سلمة بصيري
+
+253
+00:26:27,640 --> 00:26:33,560
+شرطه موجبة يبقى بظل هنا واحدوهنا بيظل S تربيع على
+
+254
+00:26:33,560 --> 00:26:36,820
+A تربيع كله في التكامل هذا اللي هو Laplace
+
+255
+00:26:36,820 --> 00:26:41,240
+transform لsin A T بيظل الطرف اليمين فقط اللي هو
+
+256
+00:26:41,240 --> 00:26:47,500
+جداش 1 على Aالأن وحدنا المقامات لهذه صورة a تربية
+
+257
+00:26:47,500 --> 00:26:52,780
+زائد s تربية على a تربية بده يساوي واحد على a الان
+
+258
+00:26:52,780 --> 00:26:59,260
+بدنا نجسم على هذي بيصير a تربية على s تربية زائد a
+
+259
+00:26:59,260 --> 00:27:04,260
+تربية في a تربية بتروح ال a مع ال a بيظهر أن a في
+
+260
+00:27:04,260 --> 00:27:09,960
+s تربية عال زائد a تربية هذا ل plus transform ل
+
+261
+00:27:09,960 --> 00:27:16,650
+sign atلذلك كملنا مرتين و توصلنا إلى تيت التكامل و
+
+262
+00:27:16,650 --> 00:27:19,750
+قبل شوية لما دي انا اعطينا تعريف لبلايسترانسونه
+
+263
+00:27:19,750 --> 00:27:25,690
+اقول لك يا بقول L of F of T يا اما F of S لحظة من
+
+264
+00:27:25,690 --> 00:27:30,750
+حد ما انكمل بطلع عندي دالة في مين؟دالة في S و هنا
+
+265
+00:27:30,750 --> 00:27:34,250
+دالة في S و هنا دالة في S و هنا دالة في S و كله
+
+266
+00:27:34,250 --> 00:27:39,090
+دالة في S و سألتك هذا السؤال ليش ال F of S يبقى
+
+267
+00:27:39,090 --> 00:27:43,030
+النتيجة بعد ما نكمل و نعوض كلها بتطلع function في
+
+268
+00:27:43,030 --> 00:27:48,170
+S فقط مضالش عند من T و بالتالي جيب دالة كافة من
+
+269
+00:27:48,170 --> 00:27:52,330
+الدالة الأصلية طب احنا الأن جيبنا
+
+270
+00:27:59,930 --> 00:28:04,430
+بتعملي الخطوات اللي عملتها بس بدل الصين بتحط معها
+
+271
+00:28:04,430 --> 00:28:05,530
+كوصين
+
+272
+00:28:11,800 --> 00:28:18,920
+هذه نمر بيه Similarly اللي هو Laplace transform La
+
+273
+00:28:18,920 --> 00:28:27,400
+cosine AT بديه ساوية بنات S على S تربيع زائد A
+
+274
+00:28:27,400 --> 00:28:33,190
+تربيعهذه الـSin بدل الـConstant بيجيني S وليس
+
+275
+00:28:33,190 --> 00:28:37,470
+Constant، بس هنا كانت إعادة الـSin Constant وهنا S
+
+276
+00:28:37,470 --> 00:28:44,050
+وهذه تشك براحتك، روح أعملها في الدار، شيك عليهاطيب
+
+277
+00:28:44,050 --> 00:28:49,850
+من B بده أروح أجيب C يبقى بدي C بدي ل plus
+
+278
+00:28:49,850 --> 00:28:58,630
+transform ل cosine 5T اللي عبارة عن S على S تربيع
+
+279
+00:28:58,630 --> 00:29:07,570
+زائد خمسة لكل تربيع يعني S على S تربيع زائد خمسة
+
+280
+00:29:07,570 --> 00:29:16,620
+وعشرين حد فيكم بتحب تسأل أسئلة هنا؟خلاص؟ ها يا بنت
+
+281
+00:29:16,620 --> 00:29:21,540
+الحلال انت لعبتي تقصبي ولا لا؟ خلاص يعني؟ فرجت
+
+282
+00:29:21,540 --> 00:29:23,640
+وكنت وقنوها تفرجوا؟
+
+283
+00:29:42,720 --> 00:29:48,600
+ما بعد الضيقة بنات إلا الوسعة، وما بعد العسر إلا
+
+284
+00:29:48,600 --> 00:29:55,240
+اليسر، ولهذا قال الله تعالى فإن مع العسر يسرا، وإن
+
+285
+00:29:55,240 --> 00:29:59,660
+مع العسر يسرا، ولن يغلب عسرا يسرين أو كما قال صلى
+
+286
+00:29:59,660 --> 00:30:03,470
+الله عليه وسلم.يعني قدش بتدايق في لحظة تمام و بعد
+
+287
+00:30:03,470 --> 00:30:07,830
+شوية بتتوسع و هذه طبيعة الدنيا بضلش الواحد عنده
+
+288
+00:30:07,830 --> 00:30:13,030
+عصر على طول ولا بضل عنده انفراجة على طول الله يخفض
+
+289
+00:30:13,030 --> 00:30:18,670
+القصة و يرفعها و هذه طبعا من بدهيات اللي هو عمل
+
+290
+00:30:18,670 --> 00:30:26,550
+الله سبحانه و تعالى طيب نرجع الآن و نكمل في عندنا
+
+291
+00:30:26,550 --> 00:30:30,170
+نظرية بتقول ما يأتي theorem
+
+292
+00:30:34,330 --> 00:30:44,450
+لابلاس تحويل لابلاس لابلاس لابلاس لابلاس لابلاس
+
+293
+00:30:44,450 --> 00:30:53,230
+لابلاس
+
+294
+00:30:53,230 --> 00:30:53,550
+لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس
+
+295
+00:30:53,550 --> 00:30:53,930
+لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس
+
+296
+00:30:53,930 --> 00:30:54,070
+لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس
+
+297
+00:30:54,070 --> 00:30:54,690
+لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس لابلاس
+
+298
+00:31:04,380 --> 00:31:14,120
+لو لابلاس ترانسفورم لل F1 and لابلاس ترانسفورم لل
+
+299
+00:31:14,120 --> 00:31:27,260
+F2 are both exist لو كانوا exist for لل S اللي
+
+300
+00:31:27,260 --> 00:31:30,320
+أكبر من S node then
+
+301
+00:31:52,040 --> 00:31:59,900
+أو بقدر أقول C1 F1
+
+302
+00:31:59,900 --> 00:32:16,940
+of Sزائد C2 capital F2 of S example نمرة
+
+303
+00:32:16,940 --> 00:32:30,900
+A find Laplace transform ل تمانية هذا نمرة A نمرة
+
+304
+00:32:30,900 --> 00:32:45,060
+Bنبدأ بالـ Plastic Transform لـ 3 Cos 2T 3 Cos 2T
+
+305
+00:32:45,060 --> 00:32:59,120
+ناقص خمسة E أس ناقص تلاتة T نمرى C Find
+
+306
+00:33:01,390 --> 00:33:12,550
+Laplace transform La cosine تربيع AT Cosine تربيع
+
+307
+00:33:12,550 --> 00:33:26,770
+اتنين T نمرة D find Laplace transform Lagosh AT
+
+308
+00:33:39,130 --> 00:33:45,090
+خلّي بالك هنا، اللي بتحكي هناك، خلّي بالك هنا يبقى
+
+309
+00:33:45,090 --> 00:33:51,050
+باجي و بقول بدنا الآن نجلع نظرية هذه و نحاول نطبق
+
+310
+00:33:51,050 --> 00:33:54,930
+هذه النظرية، هذه النظرية بتقول لي أن الـplacid
+
+311
+00:33:54,930 --> 00:34:00,430
+transform عبارة عن مؤثر خطي، شو يعني مؤثر خطي؟ هذا
+
+312
+00:34:00,430 --> 00:34:05,200
+اللي بدنا نعرفبيقول هنا لأ بلاس ترانسفورم is a
+
+313
+00:34:05,200 --> 00:34:11,000
+linear operator مؤثر خطي ذاتي an لو كان لابلاس
+
+314
+00:34:11,000 --> 00:34:15,640
+ترانسفورم لداله f1 و لابلاس ترانسفورم لداله f2
+
+315
+00:34:15,640 --> 00:34:21,920
+اتنين معرفين يبقى في هذه الحالة بدي لابلاس ل c1 f1
+
+316
+00:34:21,920 --> 00:34:28,660
+زاد c2 f2 لما اقول مؤثر خطي معناته لابلاس بدي يدخل
+
+317
+00:34:28,660 --> 00:34:33,120
+على كل term من هذين الtermينيبقى بصير Laplace
+
+318
+00:34:33,120 --> 00:34:37,960
+للأول زي Laplace للثانى ال constant بنقدر نطلعه
+
+319
+00:34:37,960 --> 00:34:43,600
+برا Laplace يبقى C1 Laplace لل F1 زي C2 Laplace لل
+
+320
+00:34:43,600 --> 00:34:48,880
+F2 Laplace لل F1 لو عديتها رمز capital F1 of S
+
+321
+00:34:48,880 --> 00:34:56,310
+يبقى بصير C1 F1 of S والتانية C2 F2 of Sبنروح
+
+322
+00:34:56,310 --> 00:35:00,030
+نستخدم هذا الكلام في إيجاد Laplace ال transform
+
+323
+00:35:00,030 --> 00:35:07,190
+للدوالي المختلفة و كذلك باستخدام المثالين السابقين
+
+324
+00:35:07,190 --> 00:35:14,310
+اللي أخذناهم قبل قليل يبقى بدايجي لنمرة A بيقول
+
+325
+00:35:14,310 --> 00:35:19,110
+لها Laplace ل تمانيةبقول مش بعرفني ال place أنا
+
+326
+00:35:19,110 --> 00:35:24,730
+بعرف ال place للواحد صح بقدر أقول له هذه ال place
+
+327
+00:35:24,730 --> 00:35:32,400
+ل تمانية في واحد مظبوطالتمانية هي المقدار الثابت
+
+328
+00:35:32,400 --> 00:35:38,100
+بقدر اطلعه برا ياش برا Laplace يبقى هذه تمانية في
+
+329
+00:35:38,100 --> 00:35:44,440
+Laplace للواحد تمانية قداش Laplace للواحد واحد على
+
+330
+00:35:44,440 --> 00:35:52,260
+اس فقط لغير يبقى تمانية على اس هذا Laplace لتمانية
+
+331
+00:35:52,260 --> 00:35:57,080
+طب Laplace Laplace لمية منهامية ليس حط الرقم اللي
+
+332
+00:35:57,080 --> 00:36:00,560
+بدك اياه بس انا كنت باعلي اسمك و جبت ال plus ايه
+
+333
+00:36:00,560 --> 00:36:04,740
+اللي؟ هذا بالنسبالي ايه؟ بدنا نمرأ بيه نمرأ بيه
+
+334
+00:36:04,740 --> 00:36:10,680
+قلي ال plus ايوة هذه اللي هي ال plus لمين؟ اللي
+
+335
+00:36:10,680 --> 00:36:18,140
+تلاتة cosine اتنين T ناقص خمسة E أس ناقص تلاتة T
+
+336
+00:36:18,140 --> 00:36:26,670
+وتساوي هذه هي هذه بالضبط صح؟مظبوط؟ يبقى بدأ أقول
+
+337
+00:36:26,670 --> 00:36:29,690
+الـconstant في Laplace للدالة الأولى، ناقص
+
+338
+00:36:29,690 --> 00:36:33,310
+الـconstant في Laplace للدالة الثانية، يبقى هذا
+
+339
+00:36:33,310 --> 00:36:42,950
+عبارة عن تلاتة Laplace لمين؟ ليه؟ Cos 2T ناقص خمسة
+
+340
+00:36:42,950 --> 00:36:49,600
+في Laplace للإيقوس ناقص تلاتة Tهذا الكلام يسوى
+
+341
+00:36:49,600 --> 00:36:55,320
+تلاتة فيه بديلا بلاسلا كوصين اتنين T اللي هي عبارة
+
+342
+00:36:55,320 --> 00:37:04,940
+عن S على S تربيع زائد كم؟ اتنين تربيع حسبناها قبل
+
+343
+00:37:04,940 --> 00:37:11,210
+قليل، مظبوط؟ وقلنا لك تشكها يعنيمظبوط؟ يبقى شيلنا
+
+344
+00:37:11,210 --> 00:37:15,050
+ال a وحطينا اللي هو الرقم اللي مضروه في الزاوية
+
+345
+00:37:15,050 --> 00:37:20,910
+اللي هو الأثنين هذه الأولى، التانية ناقص خمسة في
+
+346
+00:37:20,910 --> 00:37:30,430
+نيجي لهذه ال exponential اللي هو واحد على Sإذا
+
+347
+00:37:30,430 --> 00:37:38,350
+صارت المسألة هي تلاتة S على S ترابيع زائد أربعة
+
+348
+00:37:38,350 --> 00:37:46,270
+ناقص خمسة على S زائد تلاتةأظن أن هذا هو المضاعف
+
+349
+00:37:46,270 --> 00:37:54,610
+المشترك كله S تربيع زائد أربعة في S زائد تلاتة هذي
+
+350
+00:37:54,610 --> 00:38:05,470
+بيصير تلاتة S في S زائد تلاتة ناقص خمسة في S تربيع
+
+351
+00:38:05,470 --> 00:38:13,940
+زائد أربعةالنتيجة على الشكل التالي تساوي هذه تلاتة
+
+352
+00:38:13,940 --> 00:38:23,180
+أس تربيع زائد تسعة أسالـ term التاني ناقص خمسة
+
+353
+00:38:23,180 --> 00:38:31,260
+استربيع ناقص عشرين كله على المقام اللي هو استربيع
+
+354
+00:38:31,260 --> 00:38:38,340
+زائد أربعة في S زائد تلاتة يبقى النتيجة على الوجه
+
+355
+00:38:38,340 --> 00:38:47,870
+التالي ناقص اتنين استربيعوهنا زائد تسعة S وهنا
+
+356
+00:38:47,870 --> 00:38:57,130
+ناقص عشرين كله مقسوما على S تربيع زائد أربع في مين
+
+357
+00:38:57,130 --> 00:39:03,770
+في S زائد تلاتة يبقى هذا ل plus transform للدالة
+
+358
+00:39:03,770 --> 00:39:08,370
+هذه طب هذه يا بنات لو عملتلها partial fraction
+
+359
+00:39:08,370 --> 00:39:16,730
+كسور جزء يمين بطلع بطلع هذاصح؟ مش هذا وحدنا
+
+360
+00:39:16,730 --> 00:39:20,510
+المقامات، يبقى لو بدى أعمل كسورز بتكون عندي هذه
+
+361
+00:39:20,510 --> 00:39:24,650
+بالدرجة على الأصل تبعها، يبقى هذا هو الأصل تبعها
+
+362
+00:39:24,650 --> 00:39:30,130
+طبعا ليش هو بيقولك كده الكلام أنه سيلزمنا بعد شوية
+
+363
+00:39:30,130 --> 00:39:35,350
+ان شاء الله نضطر نعمل كسور جزئية لمقدار مثل هذا
+
+364
+00:39:35,350 --> 00:39:40,310
+المقدار مش هنقدر نوجد Laplace transform له أو نوجد
+
+365
+00:39:40,310 --> 00:39:42,710
+معكوس Laplace transform
+
+366
+00:39:55,960 --> 00:40:03,920
+هذا نمرة بيبدأ يجي لنمرة C نمرة C بيقول اللي بده
+
+367
+00:40:03,920 --> 00:40:10,760
+لبلاس ترانس ويراهد C لبلاس لكوسين تربيع بدنا لبلاس
+
+368
+00:40:10,760 --> 00:40:19,240
+لكوسين تربيع اتنين T يبقى هذه لبلاس ترانس فورم لمص
+
+369
+00:40:19,240 --> 00:40:27,020
+في واحد زائد كوسين كده شابنات؟أربعة T من حساب
+
+370
+00:40:27,020 --> 00:40:35,300
+المثلثات يبقى هذه كأنها Laplace transform لنص زائد
+
+371
+00:40:35,300 --> 00:40:43,960
+نص كوساين أربعة Tهذا الكلام بدي يسوي نص ل plus
+
+372
+00:40:43,960 --> 00:40:51,620
+transform للواحد زائد نص ل plus transform ل cosine
+
+373
+00:40:51,620 --> 00:40:58,860
+أربعة T ويسوي هذا نص و ل plus transform للواحد
+
+374
+00:40:58,860 --> 00:41:06,880
+اللي هو بقداش بواحد على S تهيئنا منه زائد كمان نص
+
+375
+00:41:07,510 --> 00:41:13,630
+هذه كوصينة أربعة ت اللي باس على اس تربية زائد
+
+376
+00:41:13,630 --> 00:41:18,860
+أربعة تربية اللي بقداش بستاشةلو حبيت احطها في
+
+377
+00:41:18,860 --> 00:41:24,560
+الصيغة النهائية يبقى نص عامل مشترك بيظل المقام S
+
+378
+00:41:24,560 --> 00:41:34,380
+في S تربيع زائد 16 يبقى هنا S تربيع زائد 16 زائد
+
+379
+00:41:34,380 --> 00:41:42,180
+اللي هو من S تربيع الشكل اللي عندنايبقى هذا يصير
+
+380
+00:41:42,180 --> 00:41:52,840
+نصف اتنين استربيع زائد ستاش على اس في استربيع زائد
+
+381
+00:41:52,840 --> 00:41:54,880
+ستاش ويساوي
+
+382
+00:42:09,410 --> 00:42:17,350
+هذا لبلاس ترانسورم للقوساين تيرفيا نمرأ دين نمرأ
+
+383
+00:42:17,350 --> 00:42:27,630
+دي كان لبلاس للقوش AT بدي لبلاس للقوش AT طبعا
+
+384
+00:42:27,630 --> 00:42:33,810
+إذا بدي أبدأ زي ما جيب لبلاس للصين صح؟يعني بدي
+
+385
+00:42:33,810 --> 00:42:39,210
+أقول EOS نقص ST في جوش AT وكامل مرتين integration
+
+386
+00:42:39,210 --> 00:42:46,130
+by parts لكن اللي عارف النظرية في عندها طريقة أسهل
+
+387
+00:42:46,130 --> 00:42:53,600
+من ذلك وهو كتابة الجوش بدلالةExponential تمام يبقى
+
+388
+00:42:53,600 --> 00:42:59,320
+بتقدر تقولي هذا الكلام بده يساوي Laplace transform
+
+389
+00:42:59,320 --> 00:43:09,580
+لل E أس AT زائد ال E أس ناقص AT كله على اتنين او
+
+390
+00:43:10,140 --> 00:43:16,980
+تقول لي هذا الكلام نص برا وهي نص برا وبظل انمين
+
+391
+00:43:16,980 --> 00:43:25,080
+لبلاس ترانسفورم لل E أس AT زائد لبلاس ترانسفورم لل
+
+392
+00:43:25,080 --> 00:43:34,580
+E أس ناقص AT وهي قفلنا الجزءهذا الكلام يساوي هي نص
+
+393
+00:43:34,580 --> 00:43:41,720
+برا مالوش دعوة ل plus لل E أس AT له من واحد على S
+
+394
+00:43:41,720 --> 00:43:51,370
+ناقص ال A زائد واحد على S زائد ال Aيبقى هذا الكلام
+
+395
+00:43:51,370 --> 00:44:00,550
+مُص واحد المقامات S ناقص الـA S زائد الـA لو جيت
+
+396
+00:44:00,550 --> 00:44:07,970
+جمعت بصير الـS زائد الـA زائد الـS ناقص الـA
+
+397
+00:44:07,970 --> 00:44:16,210
+ويساوي اظن زائد A وناقص A مع السلامةبيظل نصف اتنين
+
+398
+00:44:16,210 --> 00:44:22,410
+اس عالمين مش هذا فرق بين المربعين يا بناتيبقى S
+
+399
+00:44:22,410 --> 00:44:28,170
+تربيع ناقص ال A تربيع نص مع اتنين الله سهل عليها
+
+400
+00:44:28,170 --> 00:44:36,470
+يبقى النتيجة S على S تربيع ناقص A تربيع اظن زي ال
+
+401
+00:44:36,470 --> 00:44:45,150
+cosine بس الإشارة في المقام بالسالب وليس بالموجة
+
+402
+00:44:45,150 --> 00:44:49,790
+كيف
+
+403
+00:44:49,790 --> 00:44:50,390
+كيف؟
+
+404
+00:44:53,080 --> 00:44:58,040
+لا تحفظيش و هنصورها لك ان شاء الله كل ال aplasia
+
+405
+00:44:58,040 --> 00:45:02,880
+transform بدل الدالة عشرين دالة و نعطيك يا فيلم
+
+406
+00:45:02,880 --> 00:45:08,460
+تعالى اتفضلي هيها معاكي استخدميها متى لازم الأمر
+
+407
+00:45:08,460 --> 00:45:13,220
+يعني الصفحة الأخيرة في ورقة الأسئلة بتكون ال
+
+408
+00:45:13,220 --> 00:45:17,220
+aplasia transform للدوال كلها اللي بتلزمك و زيادة
+
+409
+00:45:17,220 --> 00:45:23,250
+شويةبس بدي تعرفي لو قلتلك use the definition to
+
+410
+00:45:23,250 --> 00:45:26,850
+find Laplace transform لدلة فلانية و أعطيتك دلة
+
+411
+00:45:26,850 --> 00:45:32,990
+يبقى بدك تروح تشتغلي الشغل هذا، تمام؟ لكن إذا ما
+
+412
+00:45:32,990 --> 00:45:36,850
+قلتش هذا الكلام و لزمن Laplace لاي دلة بجيبها من
+
+413
+00:45:36,850 --> 00:45:40,990
+الجدول دوري، الجدول هذا هنعطيكوا يومي ذلكالمرة
+
+414
+00:45:40,990 --> 00:45:44,270
+القادمة دا من المرة القادمة دي كل واحد أفيكوا يكون
+
+415
+00:45:44,270 --> 00:45:47,570
+اكتبها معاها لإنه في جدول بدي أقولك يالا عشان
+
+416
+00:45:47,570 --> 00:45:52,390
+تتعودي تفتشي و تعرفي كيف تقولي من الجدول ل place
+
+417
+00:45:52,390 --> 00:45:56,510
+transform لدالة ما كل واحد المرة الجاية يكون
+
+418
+00:45:56,510 --> 00:45:57,810
+اكتبها معاها دي ربالكم
+
+419
+00:46:01,630 --> 00:46:06,770
+طيب فينا كمان نظرية بنات بتجيب لبلاس ترانسفورم
+
+420
+00:46:06,770 --> 00:46:12,390
+للمشتقات يعني لو اشتقنا ده اللي بدي لبلاس للمشتقة
+
+421
+00:46:12,390 --> 00:46:16,150
+هذه النظرية تنص على ما يقيل
+
+422
+00:46:19,780 --> 00:46:24,840
+طب ليش بدنا Laplace transform لهذه المشتقد؟ لإن
+
+423
+00:46:24,840 --> 00:46:29,940
+موضوعنا موضوع معادلات تفاضلية بدنا نجيب حل
+
+424
+00:46:29,940 --> 00:46:36,120
+المعادلة التفاضلية باستخدام Laplace transform يبقى
+
+425
+00:46:36,120 --> 00:46:43,560
+النظرية بتقول ما ياتي theorem f
+
+426
+00:46:43,560 --> 00:47:00,950
+f of tis a function such that بحيث ان both Laplace
+
+427
+00:47:00,950 --> 00:47:12,190
+transform both Laplace transform لل F of T and
+
+428
+00:47:12,190 --> 00:47:27,640
+Laplace transformللـ F' of T exists then
+
+429
+00:47:27,640 --> 00:47:31,240
+بدنا
+
+430
+00:47:31,240 --> 00:47:40,380
+Laplace transform لل F' of T بنعرف على إنها S في
+
+431
+00:47:40,380 --> 00:47:52,260
+Laplace transform لل F of Tناقص ال F of Zero هذه
+
+432
+00:47:52,260 --> 00:47:59,940
+لها صيغة تانية كمان وهي S في مين؟ في capital X as
+
+433
+00:47:59,940 --> 00:48:07,640
+a function of S ناقص ال F of Zero هذه لو كانت
+
+434
+00:48:07,640 --> 00:48:13,320
+المشتقة الأولى لو جينا للمشتقة الثانية Similarly
+
+435
+00:48:15,900 --> 00:48:22,260
+لبلاس ترانسفورم للمشتقة الثانية as a function of T
+
+436
+00:48:22,260 --> 00:48:34,360
+بدي ساوي S squared لبلاس لل F of T ناقص ال S في ال
+
+437
+00:48:34,360 --> 00:48:42,800
+F of Zero ناقص ال F prime of Zero in general
+
+438
+00:48:46,850 --> 00:48:53,970
+على وجه العموم لابلاس ترانسفورم للتفاضل النوني as
+
+439
+00:48:53,970 --> 00:48:55,690
+a function of T
+
+440
+00:49:02,760 --> 00:49:13,960
+ناقص SN ناقص واحد في ال F of Zero ناقص SN ناقص
+
+441
+00:49:13,960 --> 00:49:23,220
+اتنين في ال F prime of Zero ناقص ناقص اللي هو ال S
+
+442
+00:49:24,240 --> 00:49:30,300
+فى ال F to the derivative of N minus two عند ال
+
+443
+00:49:30,300 --> 00:49:37,560
+zero ناقص F to the derivative of N minus one عند
+
+444
+00:49:37,560 --> 00:49:38,160
+ال zero
+
+445
+00:49:57,000 --> 00:50:02,900
+الحسابات اللي فاتت كانت كلها حسابات لبلاس للدوال
+
+446
+00:50:02,900 --> 00:50:09,080
+لكن هنا بيجي حسابات لبلاس لمشتقات الدوال هناخد
+
+447
+00:50:09,080 --> 00:50:12,820
+لبلاس المشتقة الأولى لبلاس المشتقة الثانية ومن ثم
+
+448
+00:50:12,820 --> 00:50:18,280
+انعمم لبلاس المشتقة النونية لو جينا الجدول هذا
+
+449
+00:50:18,280 --> 00:50:24,200
+فتحت فيه في الكتاب بتلاقي هذهها أخر لبلاس في
+
+450
+00:50:24,200 --> 00:50:30,760
+الجدول أسفله أخر واحدةأيش بيقول النظرية؟ بيقول لي
+
+451
+00:50:30,760 --> 00:50:36,020
+ما يأتي f of t هي ال function بحيث لابلسة ل f of t
+
+452
+00:50:36,020 --> 00:50:41,340
+و لابلسة المشتقة exist ان حدث ذلك يعني ايه بقدر
+
+453
+00:50:41,340 --> 00:50:45,640
+اجيب لابلسة للمشتقة بدلالة لابلسة للدالة كيف؟
+
+454
+00:50:45,640 --> 00:50:51,000
+كالتالي بقول s في لابلسة ل f of t ناقص ال f of
+
+455
+00:50:51,000 --> 00:50:56,270
+zeroأو ال F of T ل plus اللي هبقى عبّره عنه بصيغة
+
+456
+00:50:56,270 --> 00:51:02,430
+X of S يعني هذه أمانات function كلها في S capital
+
+457
+00:51:02,430 --> 00:51:08,190
+X of S و هنا ناقص ال F of Zero لو عندي المشتقة
+
+458
+00:51:08,190 --> 00:51:12,350
+الثانية و بدي أجيبلها ل plus يبقى بابدأ ال S الأس
+
+459
+00:51:12,350 --> 00:51:17,940
+تابعه هنا كده كانلأن المشتقة واحد هنا مشتقة تانية
+
+460
+00:51:17,940 --> 00:51:22,640
+بدأت ب S تربيع S بعدها تعدى من ال S بصير S of Zero
+
+461
+00:51:22,640 --> 00:51:27,660
+يبقى S تربيع ل plus F of T ناقص ال S في F of Zero
+
+462
+00:51:27,660 --> 00:51:34,380
+ناقص F prime of Zeroوهكذا الان لو جينا نعممها يبقى
+
+463
+00:51:34,380 --> 00:51:40,300
+ال plus المشتق قانونية ل F هو S to the power N هذا
+
+464
+00:51:40,300 --> 00:51:44,620
+derivative وهذا أس في X to the power S ك function
+
+465
+00:51:44,620 --> 00:51:49,700
+ناقص ال S بده ينجس الأس تبعها واحد في ال F of Zero
+
+466
+00:51:49,700 --> 00:51:54,300
+ناقص ال S ال N بده ينجس واحد هنا عن اللي جابلهفى
+
+467
+00:51:54,300 --> 00:51:58,800
+ال F prime of 0 نظل ماشي لغاية ما نوصل S و S واحد
+
+468
+00:51:58,800 --> 00:52:05,600
+المشتقة N نقص اتنين نقص ال F N minus ال one عند Z
+
+469
+00:52:05,600 --> 00:52:10,340
+المرة القادمة ان شاء الله بدنا ناخد امثلة على كيف
+
+470
+00:52:10,340 --> 00:52:15,540
+نحيل معادلة تفاضلية بواسطة Laplace transform
+
+471
+00:52:15,540 --> 00:52:20,360
+وباستخدام هذه النظرية ان شاء الله تعالى اعطيكوا
+
+472
+00:52:20,360 --> 00:52:20,580
+العفو
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Ajp3L7L9scU.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Ajp3L7L9scU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f36023d569e4f5deb70d4ea0b196b8164972bd55
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Ajp3L7L9scU.srt
@@ -0,0 +1,1362 @@
+1
+00:00:21,140 --> 00:00:25,860
+بسم الله الرحمن الرحيم نعود الآن إلى ما ابتدأنا به
+
+2
+00:00:25,860 --> 00:00:30,980
+محاضرتنا في الفترة الصباحية وهو آخر جزء نظري من 
+
+3
+00:00:30,980 --> 00:00:36,940
+section 4-3 النظرية بتقول ما يتيف ترضي أن ال eigenvalues
+
+4
+00:00:36,940 --> 00:00:39,500
+للمصفوفة n×n A  distinct
+
+5
+00:00:39,500 --> 00:00:45,260
+eigenvalues of n by n matrix A يبقى احنا عندنا عدد
+
+6
+00:00:45,260 --> 00:00:49,860
+من ال eigenvalues وعددهم يساوي R ولا واحدة فيهم زي
+
+7
+00:00:49,860 --> 00:00:54,820
+التانية distinct معناته منفصلين يعني غير متساوين
+
+8
+00:00:54,820 --> 00:00:59,820
+ولا واحدة فيهم متساوية يعني مافيش تكرار في هدول
+
+9
+00:00:59,820 --> 00:01:06,570
+طيب المصروفة نظامها N في N طيب ال R هذه شو علاقتها
+
+10
+00:01:06,570 --> 00:01:14,050
+ب M؟ أما ال R تساوي N أو ال R أقل من N دائما وأبدا
+
+11
+00:01:14,050 --> 00:01:20,570
+يبقى بناء عليه بقول افترض أن K1 و K2 و KR هما ال
+
+12
+00:01:20,570 --> 00:01:26,110
+eigen vectors المناظرة لمن؟ لل Eigen values then
+
+13
+00:01:26,110 --> 00:01:30,370
+these vectors are linearly independent يعني ما نتش
+
+14
+00:01:30,370 --> 00:01:35,920
+قصد يقول هو يقول إذا كان لديك distinct eigenvalues،
+
+15
+00:01:35,920 --> 00:01:38,820
+فكل الـEigenvectors اللي بيطلعوا مناضرات اللي
+
+16
+00:01:38,820 --> 00:01:43,340
+بيكونوا مالهم، linearly independent، ولا واحد له
+
+17
+00:01:43,340 --> 00:01:49,340
+اعتماد على الثاني، بس لمين؟ لل eigenvalues الغير مكررات،
+
+18
+00:01:49,340 --> 00:01:55,300
+دي برضو كلام لو وضعهذه هي النظرية اللي بتقولها
+
+19
+00:01:55,300 --> 00:02:04,000
+أنها نظام n×n وأنها in distinct eigenvalues
+
+20
+00:02:06,880 --> 00:02:12,940
+يساوي نظام تبع نص المصفوفة N يبقى العدد يساوي N
+
+21
+00:02:12,940 --> 00:02:21,120
+ثم يبقى هناك complete set of eigenvectors والمصفوفة
+
+22
+00:02:21,120 --> 00:02:27,530
+A مستقلة مستقلة مستقلة مستقلة مستقلة مستقلة بتقول لو أنت
+
+23
+00:02:27,530 --> 00:02:31,450
+عندك جة المصفوفة نظامها مثلاً تلاتة في تلاتة أو
+
+24
+00:02:31,450 --> 00:02:35,730
+اتنين في اتنين أو أربعة في أربعة إذا نظامها أربعة
+
+25
+00:02:35,730 --> 00:02:42,190
+في أربعة وطلع عندي أربعة distinct eigenvalues يبقى
+
+26
+00:02:42,190 --> 00:02:46,610
+على طول الخط هذه diagonalizable يبقى المصفوفة اللي
+
+27
+00:02:46,610 --> 00:02:52,770
+عندي إذا ساوى عدد الـ distinct eigenvalues نظام
+
+28
+00:02:52,770 --> 00:02:57,770
+المصفوفة أوتوماتيك هذه بتبقى diagonalizable يعني
+
+29
+00:02:57,770 --> 00:03:02,310
+بقدر أكتبها على صيغة مصفوفة قطرية وعناصر القطر
+
+30
+00:03:02,310 --> 00:03:07,870
+الرئيسي فيها هم ال eigenvalues كويس والله دي بيسهل
+
+31
+00:03:07,870 --> 00:03:11,050
+الشغل كتير يعني بدل لسه ما أروح أثبت وأجيب
+
+32
+00:03:11,050 --> 00:03:14,510
+ال eigenvectors وأحسب لا داعي ال eigenvectors
+
+33
+00:03:14,510 --> 00:03:17,670
+يبقى بس بدي أشوف عدد
+
+34
+00:03:20,480 --> 00:03:25,720
+هل يساوي نظام المصفوفة أو لا؟ أو هل يساوي رتبة
+
+35
+00:03:25,720 --> 00:03:29,620
+المصفوفة أو لا؟ إذا ساوى بيقول خلاصنا يبقى المصفوفة
+
+36
+00:03:29,620 --> 00:03:34,060
+هذه، دا يقننا، لا يزيبنا، دا مهم جدا في الشغل بعد
+
+37
+00:03:34,060 --> 00:03:43,260
+قليلالملحوظة التالية بيقول لـ An n by n matrix
+
+38
+00:03:43,260 --> 00:03:47,980
+need not have distinct eigenvalues زي ما شفنا
+
+39
+00:03:47,980 --> 00:03:53,100
+قبل قليل في محاضرة الصباح اللي هو المصفوفة اللي
+
+40
+00:03:53,100 --> 00:03:58,040
+عندي طالعة two eigenvalues بيساووا بعض، مظبوط؟ إذا 
+
+41
+00:03:58,040 --> 00:04:03,610
+ليس بالضرورة أن يكونوا كلهم منفصلات عن بعض المهم هو
+
+42
+00:04:03,610 --> 00:04:07,490
+لا يكون هناك eigenvalue ممكن أن يكون هناك eigenvalue
+
+43
+00:04:07,490 --> 00:04:08,370
+eigenvalue ممكن أن يكون هناك eigenvalue ممكن أن
+
+44
+00:04:08,370 --> 00:04:11,710
+يكون هناك eigenvalue ممكن أن يكون هناك eigenvalue ممكن
+
+45
+00:04:11,710 --> 00:04:13,190
+أن يكون هناك eigenvalue ممكن أن يكون هناك eigenvalue
+
+46
+00:04:13,190 --> 00:04:15,290
+eigenvalue ممكن أن يكون هناك eigenvalue ممكن أن
+
+47
+00:04:15,290 --> 00:04:17,970
+يكون هناك eigenvalue ممكن أن يكون هناك eigenvalue ممكن
+
+48
+00:04:17,970 --> 00:04:18,890
+أن يكون هناك eigenvalue ممكن أن يكون هناك eigenvalue
+
+49
+00:04:18,890 --> 00:04:21,270
+eigenvalue ممكن أن يكون هناك eigenvalue ممكن أن
+
+50
+00:04:21,270 --> 00:04:25,130
+يكون هناك eigenvalue ممكن أن يكون هناك eigenvalue ممكن
+
+51
+00:04:25,130 --> 00:04:28,650
+أن
+
+52
+00:04:28,650 --> 00:04:31,000
+يكون هناك eigenvalue النقطة الثانية بيقول لو كان 
+
+53
+00:04:31,000 --> 00:04:33,080
+λ1 و λ2 و λR are the
+
+54
+00:04:33,080 --> 00:04:39,360
+distinct eigenvalues للمين؟ لـ ال n by n matrix A
+
+55
+00:04:39,360 --> 00:04:46,600
+لحظة R أقل من أو تساوي N زي ما قلنا قبل قليل يبقى
+
+56
+00:04:46,600 --> 00:04:51,180
+هذول ال distinct لمين؟ للمصفوفة the characteristic
+
+57
+00:04:51,180 --> 00:04:55,820
+polynomial بقدر أكتبها على ميم على الشكل التالي
+
+58
+00:04:55,820 --> 00:05:01,380
+يعني مش أقوى أسسهم n لأن أقوى أسسهم n معناته
+
+59
+00:05:01,380 --> 00:05:06,340
+أن عندي n من اللاندات بعضهم هيكون مكرر يعني هيطلع
+
+60
+00:05:06,340 --> 00:05:10,640
+λ - λ1 مثلاً تربيع هذه تكعيب دلوقتي
+
+61
+00:05:10,640 --> 00:05:14,680
+ما وصل لل λR ممكن لوس واحد ممكن كله لوس اتنين
+
+62
+00:05:14,680 --> 00:05:18,360
+ممكن تلاتة إذا كان مجموعي الأسس هذه كلها مدوسة
+
+63
+00:05:18,360 --> 00:05:24,730
+بدوساوي n إيش سبب الأسس دي؟ سببه التكرار ال
+
+64
+00:05:24,730 --> 00:05:30,470
+multiplicity جالكة the integer mi يعني أي واحد من
+
+65
+00:05:30,470 --> 00:05:34,210
+هدول is called the multiplicity of the eigenvalue
+
+66
+00:05:34,210 --> 00:05:38,970
+λi يعني هذا الرقم يدل على أن ال λi
+
+67
+00:05:38,970 --> 00:05:44,290
+مكررة مرتين تلاتة أربعة جد ما يكون يبقى يا بنات،
+
+68
+00:05:44,290 --> 00:05:50,730
+هذا الـM اللي عندنا يدل على عدد مرات تكرار قيمة 
+
+69
+00:05:50,730 --> 00:05:56,350
+λ، اللي هي ال eigenvalue، هنا وضع الحد هنا،
+
+70
+00:05:56,350 --> 00:06:01,700
+جاب المفروض، حد يلاقي استفسار هنا؟ لما بتسأل تسأل
+
+71
+00:06:01,700 --> 00:06:06,380
+مش عيب تسأليه وخذ السؤال اللي بدك إياه فيه أي نقطة
+
+72
+00:06:06,380 --> 00:06:10,080
+بدك إياه لإنه بعد قليل بدنا نطبق هذا على أرض الواقع
+
+73
+00:06:10,080 --> 00:06:15,760
+نطبق الـ characteristic polynomial لإيش؟ مش .. مش 
+
+74
+00:06:15,760 --> 00:06:20,720
+أخدنا في أول مبادئنا هذا الـ section قلنا فيه حاجة
+
+75
+00:06:20,720 --> 00:06:24,340
+اسمها الـ characteristics polynomial المحدد تبع ال
+
+76
+00:06:24,340 --> 00:06:27,380
+λI - A مش سميناها الـ characteristics
+
+77
+00:06:27,380 --> 00:06:31,120
+polynomial هذه اللي هي ال λ تربيع ال λ تكعيب
+
+78
+00:06:31,120 --> 00:06:34,220
+زائد مش عارفين اللي هي المعادلة الطويلة هذه هذه
+
+79
+00:06:34,220 --> 00:06:37,640
+اللي هي الحلول اللي هي ال λI المعادلة هذه راحت
+
+80
+00:06:37,640 --> 00:06:42,130
+حطيتها على الشكل اللي قدامنا هذا من λ لغاية λ
+
+81
+00:06:42,130 --> 00:06:45,830
+واحد لغاية λ آخر طب ليش ممكن تشيل λn لو
+
+82
+00:06:45,830 --> 00:06:50,090
+قلت لـ λn معناته ولا واحدة مكررة صح ولا لا؟ كل
+
+83
+00:06:50,090 --> 00:06:53,890
+واحدة بس مرة واحدة وكله distinct لكن ما دام
+
+84
+00:06:53,890 --> 00:06:58,310
+تساوي إذا هيصير فيه تكرار يبقى عدد الأقواس لا يمكن
+
+85
+00:06:58,310 --> 00:07:03,290
+أن يساوي n بساوي R جد ما يكون بشرط R قد تكون
+
+86
+00:07:03,290 --> 00:07:07,470
+تساوي n أو أقل منها إن ساوى n يبقى كل واحد من
+
+87
+00:07:07,470 --> 00:07:11,350
+الأسس هدول بقد إيش؟ يبقى حصتها غير هيك بدي أزيد عنها
+
+88
+00:07:11,350 --> 00:07:14,970
+يعني بعضهم قد يكون واحد بعضهم اتنين بعضهم تلاتة
+
+89
+00:07:14,970 --> 00:07:20,630
+إلى آخره طيب بنجي لـ remark بقولي the number of mi
+
+90
+00:07:20,630 --> 00:07:25,230
+of multiplicity of the eigenvalue of λi
+
+91
+00:07:25,230 --> 00:07:28,230
+equal the number of linearly independent eigen
+
+92
+00:07:28,230 --> 00:07:36,170
+vectors كويس الآن أنا جيت على ال mi افترض ال mi
+
+93
+00:07:36,170 --> 00:07:41,350
+كانت بقد إيش؟ يعني الأس باتنين يعني λ ده مكرر رقم
+
+94
+00:07:41,350 --> 00:07:46,510
+مرة مرتين يبقى بيقول the number of multiplicity of
+
+95
+00:07:46,510 --> 00:07:52,230
+the eigenvalue λ is equal العدد اللينياري
+
+96
+00:07:52,230 --> 00:07:55,910
+الـ independent اللي هو eigenvalue يبقى في هذه الحالة
+
+97
+00:07:55,910 --> 00:08:00,790
+بطل عندي كام eigenvector؟ اتنين اتنين اتنين اتنين اتنين
+
+98
+00:08:00,790 --> 00:08:02,650
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+99
+00:08:02,650 --> 00:08:04,110
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+100
+00:08:04,110 --> 00:08:07,330
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+101
+00:08:07,330 --> 00:08:15,170
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتن
+
+102
+00:08:15,190 --> 00:08:18,770
+الكلام اللي بنقوله هذا بنروح نحطه على أرض الواقع
+
+103
+00:08:18,770 --> 00:08:25,750
+بأمثلة كثيرة توضح الكلام هذا كله عملياً جالي هل ال
+
+104
+00:08:25,750 --> 00:08:33,470
+matrix دي diagonalizable أم لا؟ نعرفش هذه بتقولي
+
+105
+00:08:33,470 --> 00:08:42,430
+بيكون diagonalizable إذا كان نظام المصفوفة أو رتبة
+
+106
+00:08:42,430 --> 00:08:47,870
+المصفوفة بده يساوي عدد ال characteristic values
+
+107
+00:08:49,860 --> 00:08:56,060
+characteristic values يبقى بتجي تقول بده أخد
+
+108
+00:08:56,060 --> 00:09:03,480
+ال λI اللي هو مين؟ λI - A بده يساوي هذه
+
+109
+00:09:03,480 --> 00:09:07,960
+تلاتة في تلاتة يبقى λ 0 0 λ 0
+
+110
+00:09:07,960 --> 00:09:14,680
+0 λ - A 3 0 0 2 1
+
+111
+00:09:14,680 --> 00:09:19,970
+0 -1 -2 -1 بالشكل اللي
+
+112
+00:09:19,970 --> 00:09:27,030
+عندنا يبقى هذا بدي يعطينا λ - 3 وهنا 
+
+113
+00:09:27,030 --> 00:09:31,970
+0 0 زي ما هي هذا بدي يعطينا -2 هذا 
+
+114
+00:09:31,970 --> 00:09:38,870
+λ - 1 هذا 0 زي ما هو هذا 1 2
+
+115
+00:09:38,870 --> 00:09:47,930
+λ + 1 فبقى كويس أنا سميت حلم مش عارف ولا
+
+116
+00:09:47,930 --> 00:09:51,710
+حاجة وقاعد بشتغل زي ما كنت بشتغل الصبح وزي ما 
+
+117
+00:09:51,710 --> 00:09:55,750
+كنت بشتغل المرة اللي فاتت كويس لكن لو واحدة صحى
+
+118
+00:09:55,750 --> 00:10:04,000
+شوية يكون فاتحة بتقولي هذه مصفوفة مثلثة سفلى صح ولا 
+
+119
+00:10:04,000 --> 00:10:09,800
+لا؟ إذا المحدد تبعها بدي يساوي حاصل ضرب عناصر القطر
+
+120
+00:10:09,800 --> 00:10:14,840
+الرئيسي، مافيش دا تروح تفكي، خلاص حاصل ضرب وجاهزة
+
+121
+00:10:14,840 --> 00:10:19,580
+وخلاص، ماشي بقولها، بقول والله كويس، إذا ال
+
+122
+00:10:19,580 --> 00:10:26,000
+determinant ل λI - A بدي يساوي ال
+
+123
+00:10:26,000 --> 00:10:35,660
+λ λ - 3 في λ - 1 في λ
+
+124
+00:10:35,660 --> 00:10:42,160
++ 1 وده يساوي 0 صحيح ولا لا؟ يبقى يساوي the
+
+125
+00:10:42,160 --> 00:10:49,940
+characteristic values أو ال eigenvalues are λ
+
+126
+00:10:49,940 --> 00:10:55,860
+تساوي -1 و λ تساوي 1 و λ تساوي
+
+127
+00:10:55,860 --> 00:10:56,980
+3
+
+128
+00:10:59,830 --> 00:11:05,150
+هؤلاء distinct ولا لا؟ ونظام المصفوفة إذا ده يكون
+
+129
+00:11:05,150 --> 00:11:09,470
+لازم يبل طب خلّال ال crawler اللي خلّصنا بدون أن 
+
+130
+00:11:09,470 --> 00:11:12,870
+تروح تدور ولا تجيب ال eigenvectors ولا تغلب شحالك
+
+131
+00:11:12,870 --> 00:11:21,490
+يبقى باجي بقول هنا since the eigenvalues
+
+132
+00:11:21,490 --> 00:11:27,730
+are distinct 
+
+133
+00:11:31,680 --> 00:11:48,960
+and equal 3 عددهم تلاتة and the system of the
+
+134
+00:11:48,960 --> 00:12:08,110
+matrix A is 3×3 by the above crawlery we
+
+135
+00:12:08,110 --> 00:12:18,270
+have that the A is diagonalizable
+
+136
+00:12:18,270 --> 00:12:23,530
+زيبل diagonalizable
+
+137
+00:12:23,530 --> 00:12:30,390
+والله كويس هذه وسيلة طريقة مبسطة بتسهل هالشغل هذه
+
+138
+00:12:40,990 --> 00:12:47,810
+بناخد كمان مثال حد ما نقت معلمة شيكبال اسمها
+
+139
+00:12:47,810 --> 00:12:56,010
+example
+
+140
+00:12:56,010 --> 00:13:04,950
+2 بيقول 
+
+141
+00:13:04,950 --> 00:13:15,490
+إن المصفوفة A تساوي 2 2 3 1 2 
+
+142
+00:13:15,490 --> 00:13:23,050
+1 2 -2 1 2 -2 1
+
+143
+00:13:23,050 --> 00:13:34,290
+بيقول is the matrix A diagonalizable
+
+144
+00:13:56,840 --> 00:13:58,240
+السلام عليكم
+
+145
+00:14:07,940 --> 00:14:12,040
+هذه السؤال مختلفة عن السؤال السابق لأن السؤال
+
+146
+00:14:12,040 --> 00:14:17,040
+السابق كان سهل لأنه كان lower triangular matrix تمام
+
+147
+00:14:17,040 --> 00:14:21,280
+هذه الأبناء لا lower ولا upper هذه مصفوفة عادية
+
+148
+00:14:21,280 --> 00:14:28,040
+وبالتالي نحسب الحسابات هذه بالتفصيل ناخد ال λ
+
+149
+00:14:28,040 --> 00:14:37,590
+I - A يبدو يساوي λ 0 0 λ 0 0
+
+150
+00:14:37,590 --> 00:14:44,330
+λ - اللي هو 2 2 3 1 2
+
+151
+00:14:44,330 --> 00:14:52,010
+1 2 -2 1 ويساوي λ - 2
+
+152
+00:14:52,010 --> 00:14:59,030
+وهنا -2 -3 وهنا -1 وهنا
+
+153
+00:14:59,030 --> 00:15:05,250
+λ - 2 وهنا -1 -2 2
+
+154
+00:15:05,480 --> 00:15:11,960
+وهنا λ - 1 شكل اللي عندنا هنا بعد هيك
+
+155
+00:15:11,960 --> 00:15:17,780
+مشان نجيب قيم λ بدنا نروح ناخد المحدد تبع هذه
+
+156
+00:15:17,780 --> 00:15:24,780
+المصفوفة يبقى بدي آخد ال determinant تبع λI
+
+157
+00:15:24,780 --> 00:15:32,290
+- A يبقى المحدد λ - 2 -2
+
+158
+00:15:32,290 --> 00:15:40,050
+-3 -1 λ - 2 -1
+
+159
+00:15:40,050 --> 00:15:47,600
+-2 2 λ - 1 يبقى هاي روحنا 
+
+160
+00:15:47,600 --> 00:15:52,200
+أخدنا المحدد اللي عندنا هذا وبدنا نيجي نفك المحدد
+
+161
+00:15:52,200 --> 00:15:58,800
+باستخدام عناصر أي صف أو أي عمود فيه فمثلاً لو جيت
+
+162
+00:15:58,800 --> 00:16:04,100
+قلت بدي أفكه باستخدام عناصر الصف الأول يبقى λ
+
+163
+00:16:04,100 --> 00:16:11,080
+- 2 فيه الرئيسي -2 ويبقى λ -
+
+164
+00:16:11,080 --> 00:16:19,720
+2 في λ - 1 + 2 هذا من هذا لسه
+
+165
+00:16:19,720 --> 00:16:24,160
+الحد الأول اللي بعده حسب قاعدة الإشارات إشارته
+
+166
+00:16:24,160 --> 00:16:30,900
+سالبة وسالب بيصير موجب 2 فيه أشطر بصفه و
+
+167
+00:16:30,900 --> 00:16:37,140
+عموده يبقى هذا المقدار اللي هو بيصير 1 -
+
+168
+00:16:37,140 --> 00:16:42,820
+λ لإنه بيشار السالب -2 الشكل اللي 
+
+169
+00:16:42,820 --> 00:16:49,550
+عندنا هذا اللي بعده -3 فيه أشطر بصفه عموده
+
+170
+00:16:49,550 --> 00:16:57,970
+يبقى -2 + 2λ - 4 كل هذا
+
+171
+00:16:57,970 --> 00:17:03,890
+الكلام بده يساوي 0 مرة ثانية قليكي معايا ثانية
+
+172
+00:17:04,670 --> 00:17:09,150
+بقول هذا ال term الأول المحدد الأصغر ماضي راح حصل
+
+173
+00:17:09,150 --> 00:17:14,910
+ضرب هدول - مع - بصير + 2 حسب قاله شرط
+
+174
+00:17:14,910 --> 00:17:20,790
+الشرط السلبية بصير موجبة تمشيط بصفه عموده بصير -
+
+175
+00:17:20,790 --> 00:17:27,670
+λ + 1 يبقى -λ + 1 - مع
+
+176
+00:17:27,670 --> 00:17:33,150
+ضابل - بيبقى - قد إيش؟ -2 - 3 وشت
+
+177
+00:17:33,150 --> 00:17:38,810
+بيصفوا عموده بيصير -2 وهنا - مع -
+
+178
+00:17:38,810 --> 00:17:43,510
+بيصير + 2λ - 4 كل هذا الكلام
+
+179
+00:17:43,510 --> 00:17:49,530
+بده يساوي قد إيش؟ 0 هذا الكلام بده يساوي λ -
+
+180
+00:17:49,530 --> 00:17:57,530
+
+201
+00:20:17,250 --> 00:20:24,950
+بالموجة يبقى هاي سالب ثمانية بيظل سالب اثنين بيظل
+
+202
+00:20:24,950 --> 00:20:32,150
+زائد اثنين لإن مظبوط إيه يا بنات؟ أربعة و ستة عشر
+
+203
+00:20:32,150 --> 00:20:36,070
+موجب و اثنين و ستة ثمانية بيظل اثنين بالموجب بيظل
+
+204
+00:20:36,070 --> 00:20:40,590
+لنا من هنا سالب ثمانية و سالب اثنين سالب عشرة و
+
+205
+00:20:40,590 --> 00:20:47,110
+زائد ع ثمان عشرة بيظل زائد ثمانية يساوي Zero
+
+206
+00:21:06,420 --> 00:21:13,380
+في حد الاعتراض؟ كيف؟
+
+207
+00:21:13,380 --> 00:21:18,000
+المعادلة سليمة مائة بالمائة طب بدنا نحل هذه لا في
+
+208
+00:21:18,000 --> 00:21:23,280
+عوامل مشتركة ولا في غيره يبقى أنا المعادلة منها
+
+209
+00:21:23,280 --> 00:21:27,600
+الدرجة الثالثة لما بدي أحل هيك و تبقى صعبة بروح
+
+210
+00:21:27,600 --> 00:21:35,580
+بدور على قواسم الثمانية مين؟ 1 و سالب 1 
+
+211
+00:21:35,580 --> 00:21:44,940
+2 سالب 2 4 سالب 4 8 سالب 8 يعني عندي 8 قواسم تمام
+
+212
+00:21:44,940 --> 00:21:50,630
+خليني نبدأ بالأول لو حطيت لإن ده بواحد بيصير هنا
+
+213
+00:21:50,630 --> 00:21:57,350
+واحد و اثنين ثلاثة ثلاثة و ثمانية أحد عشر أحد عشر
+
+214
+00:21:57,350 --> 00:22:01,730
+هنا بواحد بيصير ناقص خمسة يبعتك الله يبقى لإن ده
+
+215
+00:22:01,730 --> 00:22:07,030
+بواحد لأ بدي احط لإن ده بقداش سالب واحد لو حطيت 
+
+216
+00:22:07,030 --> 00:22:12,650
+سالب واحد بيصير هنا سالب واحد و سالب خمسة سالب ستة
+
+217
+00:22:12,650 --> 00:22:17,650
+سالب ستة و اثنين سالب ثمانية و ثمانية زيرو تمام
+
+218
+00:22:17,650 --> 00:22:22,390
+تمام يبقى ال lambda تساوي سالب واحد هي عبارة عن مين
+
+219
+00:22:22,390 --> 00:22:27,910
+عن حل هذه المعادلة يعني ال lambda زائد واحد هي أحد
+
+220
+00:22:27,910 --> 00:22:34,990
+عوامل المعادلة هذه يبقى باجي بقوله since بما أن
+
+221
+00:22:36,230 --> 00:22:47,810
+Lambda تساوي سالب واحد is a solution of 
+
+222
+00:22:47,810 --> 00:22:58,330
+the equation A star يبقى 
+
+223
+00:22:58,330 --> 00:23:11,910
+Lambda زائد واحد is a factor of equation star يعني
+
+224
+00:23:11,910 --> 00:23:16,410
+المعادلة تقسم على هذا المقدار بدون باقي
+
+225
+00:23:23,490 --> 00:23:29,970
+وهنا عندك ناقص خمسة lambda تربيع ناقص خمسة زائد
+
+226
+00:23:29,970 --> 00:23:35,570
+اثنين lambda زائد ثمانية بدي أقسمها قسمة طويلة 
+
+227
+00:23:35,570 --> 00:23:41,350
+عادية على lambda زائد واحد فيها قداش lambda تربيع في
+
+228
+00:23:41,350 --> 00:23:48,610
+lambda lambda تكعيب زائد lambda تربيع تمام؟ بأجي بغير
+
+229
+00:23:48,610 --> 00:23:54,810
+الإشارات وبجمع مع السلامة فالناقص ستة lambda تربيع
+
+230
+00:23:54,810 --> 00:24:00,330
+زائد اثنين lambda زائد ثمانية الباقي من الدرجة 
+
+231
+00:24:00,330 --> 00:24:04,850
+الثانية والمقسوم عليه من الدرجة الأولى بواصل عملية
+
+232
+00:24:04,850 --> 00:24:10,230
+القسمة يبقى ناقص ستة lambda تربيع على lambda بطلع
+
+233
+00:24:10,230 --> 00:24:20,080
+قداش ناقص ستة lambda تربيع
+
+234
+00:24:20,080 --> 00:24:24,120
+ناقص ستة lambda تربيع ناقص ستة lambda تربيع ناقص ستة 
+
+235
+00:24:24,120 --> 00:24:24,160
+lambda تربيع ناقص ستة lambda تربيع ناقص ستة lambda
+
+236
+00:24:24,160 --> 00:24:24,740
+ستة lambda تربيع ناقص ستة lambda تربيع ناقص ستة lambda
+
+237
+00:24:24,740 --> 00:24:24,820
+تربيع ناقص ستة lambda تربيع ناقص ستة lambda تربيع ناقص
+
+238
+00:24:24,820 --> 00:24:27,680
+ستة lambda تربيع ناقص ستة lambda تربيع ناقص ستة lambda
+
+239
+00:24:27,680 --> 00:24:33,620
+تربيع ناقص ستة lambda تربيع ناقص الباقي من الدرجة
+
+240
+00:24:33,620 --> 00:24:37,500
+الأولى والمقسوم عليه من الدرجة الأولى بواصل عملية
+
+241
+00:24:37,500 --> 00:24:42,580
+القسمة يبقى ثمانية lambda على lambda فيها قداش هي
+
+242
+00:24:42,580 --> 00:24:50,240
+ثمانية ثمانية lambda وهنا زائد ثمانية غير الإشارات
+
+243
+00:24:50,240 --> 00:24:57,060
+وجمعي بيصير هنا قداش بيصير هذه بالذات بيصير ناقص يبقى
+
+244
+00:24:57,060 --> 00:25:03,300
+zero و zero يبقى بناء عليه المعادلة star يبقى 
+
+245
+00:25:03,300 --> 00:25:10,480
+equation star take the four يبقى بتاخد الشكل الجديد
+
+246
+00:25:10,480 --> 00:25:15,240
+اللي عندي خارج القسمة اللي هو مضروب في المقسوم
+
+247
+00:25:15,240 --> 00:25:21,760
+عليه lambda تربيع ناقص ستة lambda زائد ثمانية يساوي 
+
+248
+00:25:21,760 --> 00:25:27,820
+زيرو الآن هذه بقدر أقول lambda زائد واحد هذه بقدر
+
+249
+00:25:27,820 --> 00:25:35,340
+أحللها كحاصل ضرب قوسين هنا lambda هنا lambda وهنا
+
+250
+00:25:35,340 --> 00:25:41,400
+اثنين وهنا أربعة وهنا ناقص وهنا ناقص يبقى بناء
+
+251
+00:25:41,400 --> 00:25:46,560
+عليه lambda تساوي سالب واحد و lambda تساوي اثنين
+
+252
+00:25:46,560 --> 00:25:56,060
+و lambda تساوي قداش أربعة هدول مالهم are distinct
+
+253
+00:25:56,060 --> 00:25:59,380
+eigen
+
+254
+00:25:59,380 --> 00:26:02,100
+values
+
+255
+00:26:03,990 --> 00:26:08,370
+يبقى هدول الـ distinct eigenvalues إذا بناء على
+
+256
+00:26:08,370 --> 00:26:13,030
+المصفوفة عند الأصلية قداش نظامها ثلاثة في ثلاثة
+
+257
+00:26:13,030 --> 00:26:18,130
+يبقى هذه مالها؟ Diagonalizable يبقى هنا الـ sense
+
+258
+00:26:18,130 --> 00:26:24,230
+اللي دي Matrix A
+
+259
+00:26:24,230 --> 00:26:41,130
+is of the system ثلاثة في ثلاثة and we have three 
+
+260
+00:26:41,130 --> 00:26:49,950
+distinct eigenvalues
+
+261
+00:26:49,950 --> 00:26:57,170
+we have the a is
+
+262
+00:27:06,400 --> 00:27:10,280
+Diagonalizable يبقى الوقت لو جابلتك معادلة من
+
+263
+00:27:10,280 --> 00:27:14,800
+الدرجة الثالثة كيف بدك تحليها بتشوفي قواسم ال
+
+264
+00:27:14,800 --> 00:27:20,460
+constant بالدور على رقم يصفر المعادلة وبعد هيك
+
+265
+00:27:20,460 --> 00:27:24,460
+بنجيب الرقم هذا على الشجرة الثانية وبالتالي يكون
+
+266
+00:27:24,460 --> 00:27:28,500
+هذا أحد عوامل المعادلة وبالتالي بننزل رتبها من 
+
+267
+00:27:28,500 --> 00:27:31,260
+الدرجة الثالثة إلى الدرجة الثانية وبالتالي بقدر
+
+268
+00:27:31,260 --> 00:27:36,480
+أحلها يا إما تحليها بالقوسين أو بالقانون وبطلع قداش 
+
+269
+00:27:36,480 --> 00:27:40,460
+اللي هو قيم lambda المختلفة
+
+270
+00:28:01,410 --> 00:28:11,690
+مثال ثلاثة بيقول
+
+271
+00:28:11,690 --> 00:28:22,350
+is the matrix is the matrix قليلة مصفوفة إيه تساوي؟
+
+272
+00:28:22,350 --> 00:28:29,410
+Zero و Zero و واحد و Zero واحد و اثنين و Zero و
+
+273
+00:28:29,410 --> 00:28:49,510
+Zero و واحد دقيقة diagonalizable كيف؟
+
+274
+00:28:54,850 --> 00:28:59,810
+المحدد صحيح يساوي زيرو لكن إحنا ما قلناش حاجة 
+
+275
+00:28:59,810 --> 00:29:03,990
+إحنا قلنا ابحثوا ودوروا خلاص لكن هل حطينا شرطنا لو 
+
+276
+00:29:03,990 --> 00:29:09,010
+كان المحدد يساوي زيرو ممنوع؟ لا المصفوفة الأخرى
+
+277
+00:29:09,010 --> 00:29:12,450
+اللي بدي أضربها فيها بدي أياها المحدد تبعها هيكون
+
+278
+00:29:12,450 --> 00:29:15,910
+مانع لو ساوى إن ماتكلمناش عليها دي ولا حاجة إحنا 
+
+279
+00:29:15,910 --> 00:29:22,290
+بقول قد تكون وقد لا تكون تمام؟ إذا بدي أروح نفس
+
+280
+00:29:22,290 --> 00:29:27,150
+القصة بدي أمشي زي ما كنت بمشي قبل قليل طب باجي
+
+281
+00:29:27,150 --> 00:29:32,410
+بسأل نفسي هذه upper ولا lower triangle؟ upper
+
+282
+00:29:32,410 --> 00:29:36,850
+يبقى معناتها و ال Zero و ال واحد و الواحد هم من
+
+283
+00:29:36,850 --> 00:29:42,950
+ال lambdas وبالتالي ال lambdas تكررت كده؟ مرتين يبقى بناء
+
+284
+00:29:42,950 --> 00:29:43,750
+عليه
+
+285
+00:29:46,400 --> 00:29:53,620
+الـ Determinant لـ Lambda I ناقص الـ A هو المحدد
+
+286
+00:29:53,620 --> 00:30:03,240
+تبع Lambda و Zero و ناقص واحد و Zero و هنا Lambda
+
+287
+00:30:03,240 --> 00:30:09,860
+ناقص واحد و ناقص اثنين و Zero Zero Lambda ناقص
+
+288
+00:30:09,860 --> 00:30:10,540
+واحد
+
+289
+00:30:13,120 --> 00:30:20,760
+وهذا يقوم بإضافة لـLambda ناقص واحد لـLambda ناقص
+
+290
+00:30:20,760 --> 00:30:22,260
+واحد لـLambda ناقص واحد لـLambda ناقص واحد
+
+291
+00:30:22,260 --> 00:30:31,000
+لـLambda ناقص واحد لـLambda ناقص 
+
+292
+00:30:31,000 --> 00:30:37,450
+واحد يبقى إيه جبت له مان جبت له اللي هو الـ ال
+
+293
+00:30:37,450 --> 00:30:43,230
+eigenvalues لكن فيه اثنتين are repeated يعني يا
+
+294
+00:30:43,230 --> 00:30:47,410
+بنات لو فكيت الجملة دي إيه بيصير lambda في lambda ناقص
+
+295
+00:30:47,410 --> 00:30:53,330
+واحد لكل تربيع يساوي zero لإن lambda بواحد والقوس بأسي
+
+296
+00:30:53,330 --> 00:30:58,550
+اثنين يبقى مجموع درجات يساوي الـ N الدرجة
+
+297
+00:30:58,550 --> 00:31:02,730
+تبع المصفوفة هذه تمام وبالتالي هذا اللي كنا
+
+298
+00:31:02,730 --> 00:31:06,730
+كاتبينه قبل قليل M واحد زي M اثنين زي M ثلاثة زي M
+
+299
+00:31:06,730 --> 00:31:13,390
+N بده يساوي N مظبوط يبقى هي تنطبق عليها تمام طيب
+
+300
+00:31:13,390 --> 00:31:17,670
+هايجيبنا ال lambdas اللي عندنا بس هدول مش distinct
+
+301
+00:31:17,670 --> 00:31:25,330
+طلعوا فيهم الاثنتين هدول مالهم مكررات تمام باجي
+
+302
+00:31:25,330 --> 00:31:31,190
+بقول والله ما أنا عارف الحين اختلفت عن الرقم ثلاثة
+
+303
+00:31:31,190 --> 00:31:34,650
+اللي عندنا هل تطلع دي يقول اللي يزبل والله ميزبل 
+
+304
+00:31:34,650 --> 00:31:41,570
+يقول الله أعلم يبقى باجي بقوله هنا F lambda تساوي 
+
+305
+00:31:41,570 --> 00:31:46,890
+زيرو lambda
+
+306
+00:31:46,890 --> 00:31:54,270
+I ناقص الـ A في الـ X بده يساوي زيرو M Plus lambda I
+
+307
+00:31:54,270 --> 00:32:01,150
+ناقص الـ A هي يبقى هي عند مين؟ هي lambda وزيرو وسالب
+
+308
+00:32:01,150 --> 00:32:07,010
+واحد وزيرو و lambda ناقص واحد وناقص اثنين وزيرو زيرو
+
+309
+00:32:07,010 --> 00:32:17,390
+lambda ناقص واحد في X1, X2, X3 بدي يساوي 000 بدي
+
+310
+00:32:17,390 --> 00:32:21,870
+أشيل كل lambda وأحط مكانها Zero يبقى بلاش هاد
+
+311
+00:32:21,870 --> 00:32:28,270
+نكتبها هنا مش هيكون أرتب بس F lambda تساوي Zero
+
+312
+00:32:28,270 --> 00:32:34,310
+then بدي أجعل هذه وأشيل كل lambda وأحط مكانها 
+
+313
+00:32:34,310 --> 00:32:42,620
+Zero يبقى Zero وهنا zero وهنا سالب واحد وهنا zero
+
+314
+00:32:42,620 --> 00:32:49,980
+سالب واحد سالب اثنين zero zero سالب واحد X واحد X
+
+315
+00:32:49,980 --> 00:32:55,440
+اثنين X ثلاثة بده يساوي zero zero zero هذا بده
+
+316
+00:32:55,440 --> 00:33:00,810
+يعطينا نبدأ أكتب المعادلات اللي عندي يبقى المعادلات
+
+317
+00:33:00,810 --> 00:33:06,950
+اللي عندي سالب X واحد بده يساوي قداش zero و سالب X
+
+318
+00:33:06,950 --> 00:33:13,550
+اثنين سالب اثنين X ثلاثة بده يساوي zero و الـ X
+
+319
+00:33:13,550 --> 00:33:23,110
+ثلاثة بده يساوي قداش بده يساوي zero تمام هذا معناه و
+
+320
+00:33:23,110 --> 00:33:31,390
+الـ X ثلاثة أو سالب X ثلاثة سالب X ثلاثة بده يساوي 
+
+321
+00:33:31,390 --> 00:33:32,250
+زيرو
+
+322
+00:33:40,120 --> 00:33:45,880
+سالب X ثلاثة مظبوط هذا سالب X ثلاثة وهذا سالب 
+
+323
+00:33:45,880 --> 00:33:51,100
+X اثنين سالب اثنين X ثلاثة بده يساوي Zero وهذا
+
+324
+00:33:51,100 --> 00:33:55,220
+سالب X ثلاثة بده يساوي مظبوط يبقى هذا معناه إن
+
+325
+00:33:55,220 --> 00:34:00,670
+X ثلاثة بده يساوي جبناها بديوا يساوي Zero لما 
+
+326
+00:34:00,670 --> 00:34:05,810
+الـ X ثلاثة بديوا يساوي Zero X اثنين كمان بديوا
+
+327
+00:34:05,810 --> 00:34:10,290
+يساوي مين؟ Zero لمشان يكون Eigen vector X واحد
+
+328
+00:34:10,290 --> 00:34:19,070
+ممكن تبقى الرقم غير Zero يبقى باجي بقوله هنا F X
+
+329
+00:34:19,070 --> 00:34:26,810
+واحد بديوا يساوي الـ A then the Eigen vectors
+
+330
+00:34:34,960 --> 00:34:48,020
+Lambda تساوي زيرو are in the form بالشكل التالي X
+
+331
+00:34:48,020 --> 00:34:55,140
+واحد بـ a واللي بعده بـ zero zero يبقى a في واحد
+
+332
+00:34:55,140 --> 00:35:02,960
+zero zero بالشكل اللي عندنا يبقى جبت هذا الـ eigen 
+
+333
+00:35:02,960 --> 00:35:07,880
+vector اللي عندنا إيه هنا zero zero
+
+334
+00:35:22,560 --> 00:35:28,320
+طيب بدنا نروح نجي ناخد اللي هو الحالة الثانية لو 
+
+335
+00:35:28,320 --> 00:35:33,260
+كان Lambda تساوي اثنين أو تساوي القيمة الثانية
+
+336
+00:35:43,490 --> 00:35:55,310
+بادئ بقول هنا F lambda تساوي lambda اثنين أو تساوي 
+
+337
+00:35:55,310 --> 00:36:00,090
+lambda ثلاثة تساوي واحد then هذه المصموفة اللي 
+
+338
+00:36:00,090 --> 00:36:03,430
+عندنا بدي أشيل lambda واحطه مكانها واحد يا بنات
+
+339
+00:36:03,430 --> 00:36:12,270
+يبقاش بيصير اي واحد zero سالب واحد zero zero هنا
+
+340
+00:36:12,270 --> 00:36:20,610
+ناقص اثنين وهنا زيرو زيرو وهنا كمان زيرو بالشكل 
+
+341
+00:36:20,610 --> 00:36:25,650
+اللي عندنا هذا يبقى X واحد X اثنين X ثلاثة
+
+342
+00:36:25,650 --> 00:36:33,930
+يساوي زيرو وزيرو وزيرو يبقى المعادلات X واحد ناقص
+
+343
+00:36:33,930 --> 00:36:41,750
+X ثلاثة بده يساوي زيرو وناقص اثنين X 
+
+344
+00:36:41,750 --> 00:36:50,760
+ثلاثة بده يساوي Zero يبقى بناء عليه هذا معناه إيه
+
+345
+00:36:50,760 --> 00:36:57,780
+معناه إن X ثلاثة بده يساوي زيرو لما X ثلاثة بده يساوي زيرو
+
+346
+00:36:57,780 --> 00:37:07,220
+يكبر X واحد بده يساوي زيرو معناته إن X اثنين بده يساوي b مثلاً 
+
+347
+00:37:07,220 --> 00:37:13,100
+يبقى أصبح Eigen 
+
+348
+00:37:13,100 --> 00:37:15,060
+vectors
+
+349
+00:37:20,700 --> 00:37:31,840
+corresponding the eigen vector eigen value الـ lambda
+
+350
+00:37:31,840 --> 00:37:42,920
+تساوي واحد are in the form بالشكل التالي اللي هو من
+
+351
+00:37:42,920 --> 00:37:54,240
+X1 X2 X3 بده يساوي X1 بـ 0 و X3 بـ 0 و هذه بي بي
+
+352
+00:37:54,240 --> 00:38:01,860
+اللي هي بدها تساوي بي في Zero واحد Zero كده عدد
+
+353
+00:38:01,860 --> 00:38:03,820
+مرات تكرار الـ lambda ده؟
+
+354
+00:38:21,090 --> 00:38:27,910
+إن حدث ذلك بيقول Diagonalizable ما حدث يبقى الـ 
+
+355
+00:38:27,910 --> 00:38:33,910
+not diagonalizable يبقى since
+
+356
+00:38:35,540 --> 00:38:42,840
+lambda تساوي واحد has multiplicity
+
+357
+00:38:42,840 --> 00:38:59,640
+two and we have one اللي هو one eigen vector only
+
+358
+00:38:59,640 --> 00:39:11,770
+for lambda تساوي واحد The matrix A is not
+
+359
+00:39:11,770 --> 00:39:15,350
+diagonalizable
+
+360
+00:39:25,990 --> 00:39:30,550
+طب يعطيكم العفو ونكمل المرة القادمة لسه لا يزال 
+
+361
+00:39:30,550 --> 00:39:34,370
+عندنا مزيد من الأمثلة
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/BZBTTMoYXDc_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/BZBTTMoYXDc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..05f0ae1f7125a2dd4b0b21817dbfaeff7b590228
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/BZBTTMoYXDc_postprocess.srt
@@ -0,0 +1,1952 @@
+1
+00:00:20,890 --> 00:00:25,630
+بسم الله الرحمن الرحيم عود على بدء المرة اللي فاتت
+
+2
+00:00:25,630 --> 00:00:29,790
+بدأنا بال linear transformation و بعد ذلك أخدنا
+
+3
+00:00:29,790 --> 00:00:34,910
+عدة تمثيل عليها ثم أخدنا بعض النظريات أثبتنا أن ال
+
+4
+00:00:34,910 --> 00:00:39,010
+kernel linear transformation is a subspace و
+
+5
+00:00:39,010 --> 00:00:43,330
+أثبتنا أن ال range لل linear transformation is a
+
+6
+00:00:43,330 --> 00:00:49,020
+subspace و أخدنا على ذلك المثال الأولطبعا اعطينا
+
+7
+00:00:49,020 --> 00:00:54,920
+function معرفة بالشكل التالي T of A بتسوي A زائد A
+
+8
+00:00:54,920 --> 00:01:00,840
+Transpose تمام؟ و قولنا هاتينا ال range تبع من ال
+
+9
+00:01:00,840 --> 00:01:05,380
+T ال kernel طبعا وجدناه المرة اللي فاتت و قولنا
+
+10
+00:01:05,380 --> 00:01:10,820
+the set of all skew symmetric matrices هذا اخر ما
+
+11
+00:01:10,820 --> 00:01:15,280
+اخدناه المحاضرة الماضية تمام؟ إذا نفني جيب نكمل
+
+12
+00:01:15,280 --> 00:01:19,750
+حديثناو بدنا نوجد من ال R of T
+
+13
+00:01:24,660 --> 00:01:31,440
+اللي هي عبارة عن مين؟ كل العناصر Y او احنا كانت T
+
+14
+00:01:31,440 --> 00:01:40,880
+من كل العناصر ايش بجينا نقول هي T من A الى او T
+
+15
+00:01:40,880 --> 00:01:45,660
+كانت من وين الى وين من مصممة M22 الى M22 مش هيك؟
+
+16
+00:01:45,660 --> 00:01:54,760
+من M22 لل M22بقى باجي بقول كل المصفات بي اللي
+
+17
+00:01:54,760 --> 00:02:04,580
+موجودة في ال M22 such that ال B تساوي T of A for
+
+18
+00:02:04,580 --> 00:02:09,200
+some A
+
+19
+00:02:09,200 --> 00:02:16,080
+اللي موجودة في ال M22 مش شكت عارف ال range؟يبقى كل
+
+20
+00:02:16,080 --> 00:02:21,260
+المصفوفات اللي موجودة في مجموعة المصفوفات M22
+
+21
+00:02:21,260 --> 00:02:27,120
+واللي صورتها تكون main T of A بحيث الـA some
+
+22
+00:02:27,120 --> 00:02:32,980
+element موجود في M22 يبقى هذا التعريف العام لمين؟
+
+23
+00:02:32,980 --> 00:02:37,200
+لل range تبعتي بدنا نيجي نطبق هذا التعريف و نشوف
+
+24
+00:02:37,200 --> 00:02:42,000
+بدي وصلني إلى وينيبقى هذا الكلام بده يساوي كل
+
+25
+00:02:42,000 --> 00:02:48,420
+المصفات B اللي موجودة في ال M22 such that ان ال B
+
+26
+00:02:48,420 --> 00:02:55,380
+تساوي T of A حسب التعريف هيها فوق اللي هو A زائد A
+
+27
+00:02:55,380 --> 00:03:02,720
+transpose for some A اللي موجودة في ال M22
+
+28
+00:03:04,900 --> 00:03:10,560
+طيب بدي أعرف مين هي ال B هذه طيب
+
+29
+00:03:10,560 --> 00:03:15,800
+إيش رايك لو أخدت transpose للطرفين يبقى هذه بدأت
+
+30
+00:03:15,800 --> 00:03:21,200
+ساوي كل المصفوفات B اللي موجودة في ال M22 such
+
+31
+00:03:21,200 --> 00:03:28,420
+that B transpose بده يساوي A زائد A transpose لكل
+
+32
+00:03:28,420 --> 00:03:34,320
+ال transpose يبقى for some A اللي موجودة في ال B22
+
+33
+00:03:34,980 --> 00:03:39,520
+يبقى هذا الكلام بده يساوي كل المصففات بيه اللي
+
+34
+00:03:39,520 --> 00:03:46,400
+موجودة في ال M22 such that ال BT تساوي لترانسبوز
+
+35
+00:03:46,400 --> 00:03:50,900
+بتجي ترانسبوز على الأولى زائد ترانسبوز على من؟ على
+
+36
+00:03:50,900 --> 00:03:57,060
+التانية يبقى ال A transpose زائدهذه a ترانسبوز
+
+37
+00:03:57,060 --> 00:04:01,560
+ترانسبوز اللي هي عبارة عن مين ال a itself يبقى ال
+
+38
+00:04:01,560 --> 00:04:07,940
+a itself طيب هذه ال a زي a ترانسبوز مش هي هذه اللي
+
+39
+00:04:07,940 --> 00:04:14,050
+فوقيبقى كأنه بي ترانسفوس بدي تسوي من بي يبقى
+
+40
+00:04:14,050 --> 00:04:19,130
+معناته كل مجموعة ال symmetric matrices يبقى ال
+
+41
+00:04:19,130 --> 00:04:24,250
+kernel هو ال skew ال symmetric matrices و ال range
+
+42
+00:04:24,250 --> 00:04:29,610
+هو ال symmetric matrices يبقى for some a اللي
+
+43
+00:04:29,610 --> 00:04:37,240
+موجودة في b22 يبقى هذا بدي يسوي the setof all
+
+44
+00:04:37,240 --> 00:04:41,740
+symmetric
+
+45
+00:04:41,740 --> 00:04:53,260
+matrices in M22 يبقى مجموعة الـ symmetric matrices
+
+46
+00:04:53,260 --> 00:04:58,460
+في M22 انتهينا من المثال الأول بدنا نروح الآن
+
+47
+00:04:58,460 --> 00:05:03,140
+للمثال الثاني يبقى بالداجل example 2
+
+48
+00:05:07,440 --> 00:05:19,080
+المثال الثاني بيقول let ال a بي an m في n matrix
+
+49
+00:05:19,080 --> 00:05:23,040
+define
+
+50
+00:05:23,040 --> 00:05:32,300
+عرفونا ايه mapping define
+
+51
+00:05:32,300 --> 00:05:33,280
+ايه mapping
+
+52
+00:05:36,620 --> 00:05:46,920
+من RN إلى RM by T
+
+53
+00:05:46,920 --> 00:05:57,420
+of X بده يساوي اللي هو ال AX where ال X اللي هو ال
+
+54
+00:05:57,420 --> 00:06:05,400
+call matrix X1 X2 وانضل ماشيين لغاية ال XN
+
+55
+00:06:07,700 --> 00:06:20,100
+is a calm vector المطلوب
+
+56
+00:06:20,100 --> 00:06:31,360
+نمرأ a show that بينون ان ال T is a linear
+
+57
+00:06:31,360 --> 00:06:45,120
+transformation نمرأ بيهFind الـ kernel للـ T نمرة
+
+58
+00:06:45,120 --> 00:06:50,620
+C Find
+
+59
+00:06:50,620 --> 00:06:54,240
+the
+
+60
+00:06:54,240 --> 00:07:06,000
+range of T اللي هو R of T نمرة
+
+61
+00:07:06,000 --> 00:07:15,580
+Dshow that ان
+
+62
+00:07:15,580 --> 00:07:23,860
+الـ T of X بده يساوي ال A X و
+
+63
+00:07:23,860 --> 00:07:35,620
+الله define a linear transformation from R
+
+64
+00:07:35,620 --> 00:07:36,200
+N
+
+65
+00:08:01,390 --> 00:08:10,350
+RM سؤال مرة تانيةبنقول افترض ان T من Rn إلى Rm
+
+66
+00:08:10,350 --> 00:08:16,350
+عرفناها اولت ال A ب M by N matrix يبقى اخدنا مصوفة
+
+67
+00:08:16,350 --> 00:08:22,490
+نظامها M في N define a mapping عرفنا function من
+
+68
+00:08:22,490 --> 00:08:27,970
+ال vector space Rn إلى ال vector space Rm by T of
+
+69
+00:08:27,970 --> 00:08:33,970
+capital X بدو يساوي Ax الشكل هنا يعني حاصل ضرب
+
+70
+00:08:34,480 --> 00:08:39,860
+المصوفة اللى نضامها M فى N فى المصوفة العمودية
+
+71
+00:08:39,860 --> 00:08:45,060
+اللى هى X مى المصوفة العمودية مصوفة مكونة من N من
+
+72
+00:08:45,060 --> 00:08:50,340
+الصفوف وعمود واحد يبقى هنا قولنا ال X دى is a
+
+73
+00:08:50,340 --> 00:08:55,080
+column vector يبقى متجه عمودي يعنى مصوفة مكونة من
+
+74
+00:08:55,080 --> 00:09:00,230
+عمود واحد لكنها مجموعة من الصفوفبناء على هذا
+
+75
+00:09:00,230 --> 00:09:03,790
+التعريف بدي أثبت أن T هي linear transformation
+
+76
+00:09:03,790 --> 00:09:08,270
+يعني إيش بدي أحقق؟ الشرطين تبعات ال linear
+
+77
+00:09:08,270 --> 00:09:12,530
+transformation أمر تاني بدي أجيبها لل kernel بدي
+
+78
+00:09:12,530 --> 00:09:16,770
+أعرف قداش الأمر التالف بدي أعرف قداش ال range تبع
+
+79
+00:09:16,770 --> 00:09:22,260
+T اللي بجي نربزله R of T تلاتةبتبين Any Linear
+
+80
+00:09:22,260 --> 00:09:29,000
+Transformation من الـ RN إلى ال RM من ال RN إلى ال
+
+81
+00:09:29,000 --> 00:09:34,100
+RM هي على الشكل اللي عندنا دائما او بدا T of X بدي
+
+82
+00:09:34,100 --> 00:09:40,700
+سوى حصل ضرب المصوفة A في المصوفة العمودية X يبقى
+
+83
+00:09:40,700 --> 00:09:44,820
+عندنا أربعة مطاليب بدنا نبدأ نحسب كل مطلوب من هذه
+
+84
+00:09:44,820 --> 00:09:51,110
+المطاليب الأربعةبنجي للمطلوب الأول اللي هو بدي
+
+85
+00:09:51,110 --> 00:09:56,430
+أثبت أن T عبارة عن Linear Transformation
+
+86
+00:10:05,420 --> 00:10:08,340
+يبقى بدى اثبت اول شىء ان هاد الـ T Linear
+
+87
+00:10:08,340 --> 00:10:12,340
+Transformation يبقى بدى اخد element من ال set of
+
+88
+00:10:12,340 --> 00:10:15,980
+real numbers الـ scalar يعني و element من ال
+
+89
+00:10:15,980 --> 00:10:21,680
+vector اللي هو main RN و اشوف حصل ضربه معاه وين
+
+90
+00:10:21,680 --> 00:10:29,040
+بدى يوديني يبقى باجي بقول هنا Fالـ C موجودة في الـ
+
+91
+00:10:29,040 --> 00:10:39,260
+R and على سبيل المثال الـ X موجودة في الـ RNالـ X
+
+92
+00:10:39,260 --> 00:10:48,280
+هذا بقدر اكتبه على شكل X1 و X2 و لغاية XN او بقدر
+
+93
+00:10:48,280 --> 00:10:56,000
+اكتبه على شكل مصفوفة عمودية X1 X2 لغاية XN بالشكل
+
+94
+00:10:56,000 --> 00:11:05,790
+اللي عندنا هناطيب انا بدي اخد T of CX بدي احاول
+
+95
+00:11:05,790 --> 00:11:13,010
+اثبت ان هذا بدي يسوى C في T of X برجع للتعريف اللي
+
+96
+00:11:13,010 --> 00:11:17,850
+انا قايله يبقى طبقا لهذا التعريف هذا بدي يسوى
+
+97
+00:11:17,850 --> 00:11:26,600
+المصوفة A في C of Xلأن C هذا scalar إذا بقدر أطلعه
+
+98
+00:11:26,600 --> 00:11:32,980
+برا ال T أو بقدر أطلعه برا حصل ضرب المصوفين يبقى
+
+99
+00:11:32,980 --> 00:11:39,290
+هذا C في ال AX بالشكل اللي عندنا هذايبقى هذا
+
+100
+00:11:39,290 --> 00:11:44,390
+الكلام بدي يساوي C ال AX عبارة عن مين حسب ال
+
+101
+00:11:44,390 --> 00:11:50,290
+definition اللي عندلي T of X يبقى C في T of X
+
+102
+00:11:54,650 --> 00:11:59,950
+يبقى T of X يبقى بناء عليه أصبح T في C of X يساوي
+
+103
+00:11:59,950 --> 00:12:03,910
+C في T of X إذا انتحقق ال condition الأول أو
+
+104
+00:12:03,910 --> 00:12:08,090
+الخاصية الأولى من خاصة Linear Transformation يبقى
+
+105
+00:12:08,090 --> 00:12:12,350
+هذه من هذه الخاصية الأولى بدأجي للخاصية الثانية
+
+106
+00:12:12,350 --> 00:12:17,630
+بدأ أخد two vectors يبقى بدأجي أقوله let X وY
+
+107
+00:12:17,630 --> 00:12:23,830
+موجودة في ال vector space RN
+
+108
+00:12:25,570 --> 00:12:32,460
+بتاخد T of X زائد Y يساويبناء على الـ definition
+
+109
+00:12:32,460 --> 00:12:37,080
+تابعناها هذا بيكون المصفوفة a في ال vector x زائد
+
+110
+00:12:37,080 --> 00:12:45,220
+y يبقى a في ال vector x زائد y هذا حسب خواص عملية
+
+111
+00:12:45,220 --> 00:12:52,720
+التوزيع على المصفوفات يبقى هذا بيكون ax زائد ay
+
+112
+00:12:52,720 --> 00:13:00,820
+هذا تعريف من ال T of x وهذا تعريف ال T of yيبقى
+
+113
+00:13:00,820 --> 00:13:05,420
+تحقق ال condition الثاني ولا لا يبقى بناء عليه so
+
+114
+00:13:05,420 --> 00:13:12,940
+T is a linear transformationإذا انتهينا من المطلوب
+
+115
+00:13:12,940 --> 00:13:17,780
+الأول اللي هو نمرا A نمرا B قال هاتل ال kernel
+
+116
+00:13:17,780 --> 00:13:24,300
+التي باجي بقوله ال kernel التي حسب ال definition
+
+117
+00:13:24,300 --> 00:13:30,020
+هو مين؟ هو كل ال X اللي موجودة في ال vector space
+
+118
+00:13:30,020 --> 00:13:37,820
+RN بحيث أن T of X بدي تساوي 100 ال 0، 0 تبع مين؟
+
+119
+00:13:39,260 --> 00:13:45,800
+تبع RM مش هيك عرفنا ال kernel كل ال vectors اللي
+
+120
+00:13:45,800 --> 00:13:49,240
+في ال vector space الأول و اللي صورتهم بيكون ال
+
+121
+00:13:49,240 --> 00:13:54,920
+zero تبع ال vector space الثاني تمام يبقى هنا كل
+
+122
+00:13:54,920 --> 00:13:59,940
+ال X اللي موجودة في RN بحيث ان T of X بده يساوي
+
+123
+00:13:59,940 --> 00:14:05,510
+zeroيبقى هذا بدى يساوي كل ال X اللى موجودة في RN
+
+124
+00:14:05,510 --> 00:14:09,730
+such that
+
+125
+00:14:09,730 --> 00:14:15,570
+ال T of X حسب ال definition مين ال A X بدى يساوي
+
+126
+00:14:15,570 --> 00:14:19,570
+Zero بالشكل اللى عندنا هذا يبقى هذا ايش معناه يا
+
+127
+00:14:19,570 --> 00:14:29,800
+بنات كل ال Xهه اللي موجودة في RN يعني call vectors
+
+128
+00:14:29,800 --> 00:14:34,740
+ما لهم بحيث ال X يساوي Zero يعني هذا بيعطينا مين
+
+129
+00:14:34,740 --> 00:14:41,020
+مجموعة الحلول ال homogenous system مظبوط يبقى هذا
+
+130
+00:14:41,020 --> 00:14:52,500
+معناه اللي هو the set of all solutions of the
+
+131
+00:14:54,210 --> 00:15:04,170
+هوموجينيا سيستم الهو ax بده يساوي من زرع شو شكلهم
+
+132
+00:15:04,170 --> 00:15:09,510
+اش ما يكون يكون يبقى ملموعة كل الحلول للهوموجينيا
+
+133
+00:15:09,510 --> 00:15:15,170
+سيستم اكم حلله الهوموجينيا سيستمأما حل واحد هو
+
+134
+00:15:15,170 --> 00:15:20,370
+الحل الصفري أو عدد لانهائي من الحلول وهذا العدد
+
+135
+00:15:20,370 --> 00:15:24,550
+النهائي يجتمع عالميا على الحل الصفري نفسه طيب ما
+
+136
+00:15:24,550 --> 00:15:29,470
+علينا يبقى حسبنا له كيرنل يبقى كيرنل تبع هذه ال
+
+137
+00:15:29,470 --> 00:15:35,710
+function هو كل الحلول لل homogenous system X بده
+
+138
+00:15:35,710 --> 00:15:42,480
+يساوي مان؟ بده يساوي Zero طيب نمرى ال Cنمرا سيجا
+
+139
+00:15:42,480 --> 00:15:46,460
+اللي هتل ال range تبع ال T باجي بقول له ال range
+
+140
+00:15:46,460 --> 00:15:55,530
+تبع ال T هو مين؟كل العناصر اللي موجودة في الـ RM
+
+141
+00:15:55,530 --> 00:16:02,990
+يبقى كل ال vectors Y اللي موجودة في الـ RM بحيث ان
+
+142
+00:16:02,990 --> 00:16:12,250
+الـ Y هذه بدها تساوي T of X for some X اللي موجودة
+
+143
+00:16:12,250 --> 00:16:19,660
+في الـ RN مش هيك تعريف ال rangeمظبوط كل العناصر
+
+144
+00:16:19,660 --> 00:16:27,220
+اللي موجودة في ال domain RM و اللي إلها أصل في ال
+
+145
+00:16:27,220 --> 00:16:33,980
+domain RM طيب تمام تمام يبقى هذي بده أعيد صياغتها
+
+146
+00:16:33,980 --> 00:16:40,080
+مرة تانية فبقول كل ال Y اللي موجودة في RM such
+
+147
+00:16:40,080 --> 00:16:44,680
+that ال Y بده يساوي T of X حسب ال definition بده
+
+148
+00:16:44,680 --> 00:16:55,850
+يساوي مين؟الـ AX هي
+
+149
+00:16:55,850 --> 00:17:03,470
+نكمل for some X
+
+150
+00:17:03,470 --> 00:17:10,830
+اللي موجودة في الـ RNإذاً كل ال Y اللي موجودة في
+
+151
+00:17:10,830 --> 00:17:16,610
+ال RM بحيث ال Y على الشكل A of X for some X اللي
+
+152
+00:17:16,610 --> 00:17:23,220
+موجودة في ال RN يعني إيش قصدا نقول؟يبقى كل القيم
+
+153
+00:17:23,220 --> 00:17:28,840
+اللي هي Y بحيث الـ non homogeneous system has a
+
+154
+00:17:28,840 --> 00:17:35,440
+solution ماقلتش حلول هذا ال system لأ يبقى باجي
+
+155
+00:17:35,440 --> 00:17:43,740
+بقول هذا الكلام بده يساوي the set of all elements
+
+156
+00:17:45,790 --> 00:17:58,650
+Y الموجودة في الـ RM such that بحيث ان ال system
+
+157
+00:17:58,650 --> 00:18:05,290
+X يساوي Y has a solution
+
+158
+00:18:12,620 --> 00:18:17,080
+يعني المقصود بهذا الحل الـ Y's و لا الـ X's
+
+159
+00:18:17,080 --> 00:18:23,820
+الإجابة الـ Y's لأن هذا الـ non homogeneous system
+
+160
+00:18:23,820 --> 00:18:27,720
+قد يكون له حل و قد لا يكون له حل مش هيك ده اللي
+
+161
+00:18:27,720 --> 00:18:31,320
+أخدناه قبلك ان الـ non homogeneous system ممكن
+
+162
+00:18:31,320 --> 00:18:36,320
+يكون مالوش حلول و ممكن يكون حل وحيد و ممكن يكون
+
+163
+00:18:36,320 --> 00:18:41,770
+عدد لا نهائي من الحلولهذا ما تقوله؟ كل العناصر Y
+
+164
+00:18:41,770 --> 00:18:45,670
+بحيث ال system هذا له حلول يبقى لو مالهوش حلول
+
+165
+00:18:45,670 --> 00:18:51,910
+مالهم مستبعدة كليا يبقى سواء كان حل واحد أو عدد
+
+166
+00:18:51,910 --> 00:18:55,510
+لنهائي من الحلول على كل الأمرين الأمر الجوابي لأن
+
+167
+00:18:55,510 --> 00:19:02,630
+هذا ماله جواب صحيح إذا طلع الفرج ما بين A وB ال B
+
+168
+00:19:02,630 --> 00:19:10,830
+يا ترى صبصت من RN و لا RMمن مين؟ من RN هذا ال
+
+169
+00:19:10,830 --> 00:19:16,530
+kernel طيب ال range subset من مين؟ من RM لأن ال
+
+170
+00:19:16,530 --> 00:19:22,110
+range المدى الصور تبعت العناصر يبقى في الحلقة كل
+
+171
+00:19:22,110 --> 00:19:25,910
+ال solutions تبع ال homogeneous system ال solution
+
+172
+00:19:25,910 --> 00:19:30,750
+يعني قيم X وال X قولنا وين موجودةبالنسبة للـ RM
+
+173
+00:19:30,750 --> 00:19:34,810
+يبقى هذا يتفق وكلمنا تماما الـ range قولنا هو جزء
+
+174
+00:19:34,810 --> 00:19:38,490
+من الـ RM لذلك قولنا الـ range كل العناصر اللي
+
+175
+00:19:38,490 --> 00:19:43,690
+موجودة في RM يبقى كل العناصر اللي موجودة في RM
+
+176
+00:19:43,690 --> 00:19:48,330
+بحيث الـ non homogeneous system هذا له solution
+
+177
+00:19:48,330 --> 00:19:55,480
+يبقى انتهينا من النقطة C بدنا نروح للنقطة ديالنقطة
+
+178
+00:19:55,480 --> 00:20:00,140
+دي بيقوللي اثبتلي ان ال T of X سوى X defined a
+
+179
+00:20:00,140 --> 00:20:03,720
+Linear Transformation يعني Linear Transformation
+
+180
+00:20:03,720 --> 00:20:08,540
+من ال RN للRM دائما و أبدا تاخد الشكل اللي عندنا
+
+181
+00:20:08,540 --> 00:20:14,240
+هذا بقولك كويس اذا بدنا نبدأ الحل كتالي بده اجي
+
+182
+00:20:14,240 --> 00:20:19,760
+علمين على ال RN و اروح اخد ال basis تبعه و نتفهم
+
+183
+00:20:19,760 --> 00:20:26,220
+عليه بعد هيكيبقى هنا بجي بقول له let E1 يبقى يساوي
+
+184
+00:20:26,220 --> 00:20:36,640
+1 و 0 و 0 و لغاية 0 و E2 يساوي 0 و 1 و 0 لغاية 0 و
+
+185
+00:20:36,640 --> 00:20:43,880
+نظل ماشيين لغاية ما نصل الى EN 001
+
+186
+00:20:43,880 --> 00:20:50,500
+بالشكل اللي عندنا هنايبقى خدت هدول مين هدول ال
+
+187
+00:20:50,500 --> 00:20:56,880
+bases تبعات مين تبعات العناصر ال bases تبعات ال RN
+
+188
+00:20:56,880 --> 00:21:09,740
+يبقى هدول العناصر لت بي the standard bases
+
+189
+00:21:09,740 --> 00:21:13,780
+for RN
+
+190
+00:21:15,360 --> 00:21:31,020
+يبقى دول عناصر ال standard basis لمن؟ لل RN كويس
+
+191
+00:21:31,020 --> 00:21:42,660
+بدا أفترض برضه suppose that افترض ان ال T of E1
+
+192
+00:21:42,660 --> 00:21:54,590
+بده يسوي E1و T of E2 هو A2 وانظر لغاية T of EN هو
+
+193
+00:21:54,590 --> 00:21:59,330
+AN خليني
+
+194
+00:21:59,330 --> 00:22:04,890
+أسألكم السؤال التالي ال A1 و ال A2 و ال A3 و ال AN
+
+195
+00:22:04,890 --> 00:22:11,540
+شم هدول؟يعني answer real number والله vector يعني
+
+196
+00:22:11,540 --> 00:22:18,600
+مصفوفة والله ايه شو a1 هذا؟ vector ليش؟ لأن T of
+
+197
+00:22:18,600 --> 00:22:24,540
+E1 E1 موجود في ال R in صورة وين؟ في ال R M يبقى
+
+198
+00:22:24,540 --> 00:22:28,360
+هذا vector و ال vector عليها شكل مصفوفة عمودية
+
+199
+00:22:28,360 --> 00:22:35,620
+فيها M من الصفوف و عمود واحد يبقى هنا where
+
+200
+00:22:38,960 --> 00:22:52,300
+حيث ال A1 و ال A2 و لغاية ال AM RM في one matrices
+
+201
+00:22:52,300 --> 00:22:59,260
+يعني وين موجود كل واحد فيهم؟فى ال R M يعني كأنه
+
+202
+00:22:59,260 --> 00:23:05,500
+ايش A1 و A2 مجصدي ال A1 بده يساوي X1 و X2 لغاية X
+
+203
+00:23:05,500 --> 00:23:11,640
+M تمام يعني موجود فى ال R M تمام التمام طيب كويس
+
+204
+00:23:11,640 --> 00:23:17,420
+احنا عايزا الان كيف ANA مش سامع ليه حطت هنا AN مش
+
+205
+00:23:17,420 --> 00:23:24,320
+Mم في واحد لماذا الموجودة في الار ام كل element
+
+206
+00:23:24,320 --> 00:23:30,000
+مكون من ام من العناصر بدل ما هو الرقم الأول فاصل
+
+207
+00:23:30,000 --> 00:23:34,060
+الرقم اللي كتبته على شكل عمود مكون من ام من الصفوف
+
+208
+00:23:34,060 --> 00:23:43,060
+و عمود واحد فقط يبقى اقول ان كل الان ان كلهم ار ام
+
+209
+00:23:43,060 --> 00:23:44,800
+في one matrices
+
+210
+00:23:50,880 --> 00:23:57,880
+belongs to RM يبقى كلها موجودة في الـ RM بالشكل
+
+211
+00:23:57,880 --> 00:24:04,180
+اللي عندنا هناأيش بقولي بقولي هذه ال T اللي أنت
+
+212
+00:24:04,180 --> 00:24:09,300
+أخدتها من ال RN لل RM بدي أثبت إنه دايما و أبدا
+
+213
+00:24:09,300 --> 00:24:12,440
+بقدر أكتبها على مين على الشكل اللي عندنا هذا
+
+214
+00:24:12,440 --> 00:24:18,120
+يمكنني أن أروح أخد element X موجود في RN و أشوف شو
+
+215
+00:24:18,120 --> 00:24:23,600
+بدي أساوي أنا إذا لو جيت قلت خدلي ال X اللي هو بدي
+
+216
+00:24:23,600 --> 00:24:31,340
+أساوي من X1 و X2 و لغاية XMالإنسان موجود في كل
+
+217
+00:24:31,340 --> 00:24:38,430
+مكانبالـ RN يعني T بيقدر يؤثر عليه حتى أقول T of X
+
+218
+00:24:38,430 --> 00:24:44,210
+بدي أثبت أنه بدي يسوى main X طيب هذا مش يسوى
+
+219
+00:24:44,210 --> 00:24:52,030
+مجموعة من ال vector X 1 و 0 و 0 لغاية الـ 0 زائد 0
+
+220
+00:24:52,030 --> 00:24:59,490
+و X 2 و 0 و 0 زائد و تبقى ماشية لغاية ما توصل إلى
+
+221
+00:24:59,490 --> 00:25:07,910
+0و 0 و XN ولا لأيبقى هذا العنصر كتبته على شكل
+
+222
+00:25:07,910 --> 00:25:13,970
+مجموعة من مين؟ من العناصر يبقى لو جيت اخدت x1 عامل
+
+223
+00:25:13,970 --> 00:25:24,070
+مشترك بيظل كده؟ 100 زيد x2 0 و 1 و 0 و 0 زيد ان
+
+224
+00:25:24,070 --> 00:25:32,910
+بيظل ماشيين xn 0 و 0 و 1 بالشكل اللي عندنا هذايبقى
+
+225
+00:25:32,910 --> 00:25:38,350
+واحد وهيجفلنا مين؟ الجوز لعلكوا الآن أدركتوا ما هو
+
+226
+00:25:38,350 --> 00:25:43,410
+السر اللي خلاني أبدأ بمين بالفرضية اللي عندنا هذه
+
+227
+00:25:43,410 --> 00:25:50,630
+تمام؟ يبقى هذه كإنه إيه يا شبنات؟ كإنه X1E1 وهذه
+
+228
+00:25:50,630 --> 00:26:00,820
+X2E2 وضلت ماشي إلى غاية XNEN هذا مين؟الـ X يبقى
+
+229
+00:26:00,820 --> 00:26:06,600
+الـ X اللي عندي هذا كتبته على شكل linear
+
+230
+00:26:06,600 --> 00:26:12,100
+combination من عناصر ال bases تمام الان T linear
+
+231
+00:26:12,100 --> 00:26:17,560
+transformation بدي أخليها تأثر على مين؟على X يبقى
+
+232
+00:26:17,560 --> 00:26:22,800
+بالداجي هاخدله T of X اللي أنا بدور عليها يبقى
+
+233
+00:26:22,800 --> 00:26:28,780
+بتثوي T للمقدار هذا كله ونظرا لأنها T Linear
+
+234
+00:26:28,780 --> 00:26:36,600
+Transformation يبقى بتصير T of X1 E1 زائد T of X2
+
+235
+00:26:36,600 --> 00:26:46,120
+E2 زائد زائدT of X N E N ليش الكلام هذا since لأن
+
+236
+00:26:46,120 --> 00:26:54,420
+T is a linear transformation طيب من خواصة ال
+
+237
+00:26:54,420 --> 00:26:59,240
+linear transformation الأن ال E1 vector طب و ال X1
+
+238
+00:26:59,240 --> 00:27:14,240
+vector ولا scalarأول خاصية يبقى هنا X1 في T of E1
+
+239
+00:27:14,240 --> 00:27:25,130
+زائد X2 في T of E2 زائد زائد XN في T of ENيبقى هذا
+
+240
+00:27:25,130 --> 00:27:33,850
+الكلام بدي يساوي X1A1 زي ال X2A2 زي ال XNAN حسب ما
+
+241
+00:27:33,850 --> 00:27:39,110
+نفرض فوق صحيح ولا لأ؟ طيب وقولنا ال اهات مالهم
+
+242
+00:27:39,110 --> 00:27:46,790
+هدول؟ مصفوفات يبقى هدول ماله مصفوفات طيب سؤال أليس
+
+243
+00:27:46,790 --> 00:27:55,080
+هذا هو حاصل الضرب AX؟صح ولا لأ؟ لأن هذه الـA
+
+244
+00:27:55,080 --> 00:28:00,860
+مصوفات اللي عندنا هذه تمام؟ كأنه ايش؟ كأن الـE1
+
+245
+00:28:00,860 --> 00:28:04,740
+مصوفة عمود الـA2 مصوفة عمود الـA3 ماصوفة عمود
+
+246
+00:28:04,740 --> 00:28:05,160
+الـA4 ماصوفة عمود الـA5 ماصوفة عمود الـA6 ماصوفة
+
+247
+00:28:05,160 --> 00:28:05,180
+عمود الـA7 ماصوفة عمود الـA8 ماصوفة عمود الـA9
+
+248
+00:28:05,180 --> 00:28:06,220
+ماصوفة عمود الـA9 ماصوفة عمود الـA9 ماصوفة عمود
+
+249
+00:28:06,220 --> 00:28:06,480
+الـA9 ماصوفة عمود الـA9 ماصوفة عمود الـA9 ماصوفة
+
+250
+00:28:06,480 --> 00:28:09,080
+عمود الـA9 ماصوفة عمود الـA9 ماصوفة عمود الـA9
+
+251
+00:28:09,080 --> 00:28:17,640
+ماصوفة عمود الـA9مظبوط يبقى هذا ال ax where حيث ال
+
+252
+00:28:17,640 --> 00:28:25,440
+a هي المصحوفة لعمودي a1 و a2 و لغاية an بالشكل
+
+253
+00:28:25,440 --> 00:28:31,230
+اللي عندنايعني كل واحد من A1 و A2 و AN هو عمود
+
+254
+00:28:31,230 --> 00:28:37,530
+لمن؟ للمصوفة A يبقى من الأنفا ساعدا أي linear
+
+255
+00:28:37,530 --> 00:28:41,930
+transformation من ال RN إلى ال RM تكون دائما و
+
+256
+00:28:41,930 --> 00:28:48,150
+أبدا على الشكل T of X بيساوي 100 يساوي AX و هكذا
+
+257
+00:28:48,150 --> 00:28:54,340
+حد فيكم بتحب تسأل أي سؤال هنا؟طيب انتهينا من
+
+258
+00:28:54,340 --> 00:28:59,160
+المثال الثاني بدنا نروح للمثال الثالث
+
+259
+00:29:31,620 --> 00:29:39,580
+Example 3 بيقول
+
+260
+00:29:39,580 --> 00:29:52,620
+LED T من R3 لغاية R3 بـ A linear transformation
+
+261
+00:29:52,620 --> 00:30:05,450
+defined by معرفة على الشكل التاليفى ofX هو عبارة
+
+262
+00:30:05,450 --> 00:30:16,090
+عن TR X1 و X2 و X3 بالشكل اللي عندنا هذا بده يساوي
+
+263
+00:30:16,090 --> 00:30:25,630
+حصل ضرب 101 112213
+
+264
+00:30:25,630 --> 00:30:36,400
+في X1 X2 X3الشكل اللي عندنا هذا المطلوب الأول نمر
+
+265
+00:30:36,400 --> 00:30:49,960
+ايه find ال kernel التي and ال dimension لل kernel
+
+266
+00:30:49,960 --> 00:31:01,420
+التي نمر بيه find a bases
+
+267
+00:31:07,180 --> 00:31:20,940
+Find a basis for R of T and الـ dimension للـ R of
+
+268
+00:31:20,940 --> 00:31:24,660
+T نمره
+
+269
+00:31:24,660 --> 00:31:37,560
+C Find T of واحد و اتنين و تلاتة نمره Dis the
+
+270
+00:31:37,560 --> 00:31:44,220
+element
+
+271
+00:31:44,220 --> 00:31:53,860
+اتنين وخمسة وسبعة موجود في ال R of T ام لا؟
+
+272
+00:32:14,190 --> 00:32:19,150
+سؤال مرة تانيةطبعا زي ما انت شايفين من سؤال إلى
+
+273
+00:32:19,150 --> 00:32:25,570
+سؤال بتختلف الفكرة شوية بيقول افترض T من R3 إلى R3
+
+274
+00:32:25,570 --> 00:32:31,130
+بيه Linear Transformation واضح من RN إلى RM ايش
+
+275
+00:32:31,130 --> 00:32:35,970
+اتفاجنا النصيقه دايما من T of X بديه سوى من؟ بديه
+
+276
+00:32:35,970 --> 00:32:40,310
+سوى X من المثال اللي جابله يعني كأنه سؤالنا هذا هو
+
+277
+00:32:40,310 --> 00:32:45,150
+تطبيق عملي على من؟ على المثال اللي جابله، مظبوط؟
+
+278
+00:32:45,410 --> 00:32:49,930
+يبقى كأن احنا بناطل أن مثال عددي تطبيق على المثال
+
+279
+00:32:49,930 --> 00:32:55,350
+النظري اللي جابله يبقى معرفة كالتالي T of X الـ X
+
+280
+00:32:55,350 --> 00:32:59,390
+هو اللي موجود في R3 يعني T of X واحد و X اتنين و X
+
+281
+00:32:59,390 --> 00:33:04,230
+تلاتة بتكتبهم على شكل عمود يبقى يقول T of X واحد X
+
+282
+00:33:04,230 --> 00:33:10,470
+اتنين X تلاتة بده يساوي حاصل ضرب المصوفة A أخدناها
+
+283
+00:33:10,470 --> 00:33:14,430
+بالشكل هذا في X اللي هو X واحد و X اتنين و X تلاتة
+
+284
+00:33:14,640 --> 00:33:17,780
+يبقى هذه الـ Linear Transformation اللي عندنا
+
+285
+00:33:17,780 --> 00:33:21,580
+مطلوب من هذه الـ Linear Transformation هي تبدأ الـ
+
+286
+00:33:21,580 --> 00:33:25,730
+Kernelو بدي ال dimension للكيرنل لان كيرنل ماله
+
+287
+00:33:25,730 --> 00:33:31,790
+sub space يعني space بدي ال dimension له جداش تنين
+
+288
+00:33:31,790 --> 00:33:38,350
+بدي basis لل range بدي ال vectors اللي بوالدولي ال
+
+289
+00:33:38,350 --> 00:33:42,650
+range تبع من ال subspace R of T و بعد هيك بدي ال
+
+290
+00:33:42,650 --> 00:33:47,570
+dimension كمان لل R of T يعني كل نقطة زي ما تلاحظت
+
+291
+00:33:47,570 --> 00:33:50,730
+ب main بمطلبين لكن إذا جبت المطلب الأول بصير
+
+292
+00:33:50,730 --> 00:33:55,160
+المطلب التاني السهل تحصيل حصلالمطلوب نمرى C بيقول
+
+293
+00:33:55,160 --> 00:33:58,840
+لي هاتلي T of واحد واثنين وثلاث بتعرف قداش صورة
+
+294
+00:33:58,840 --> 00:34:03,340
+واحد واثنين وثلاث شو بتعطيني الأمر الرابع بيقول لي
+
+295
+00:34:03,340 --> 00:34:08,100
+هل العنصر هذا موجود في ال range أم لا؟ بيقول له
+
+296
+00:34:08,100 --> 00:34:13,400
+الله أعلم يبقى بداجي للنقطة الأولى اللي هي A قال
+
+297
+00:34:13,400 --> 00:34:18,280
+لي هاتلي ال kernelبقول له قبل ال kernel خلّيني أحط
+
+298
+00:34:18,280 --> 00:34:24,740
+هذه في شكل ألطف من هيك شوية بقوله كيف بقوله هيتي
+
+299
+00:34:24,740 --> 00:34:35,180
+of X1 X2 X3 كمصفوفة الشكل اللي عندنا تمام؟ بده
+
+300
+00:34:35,180 --> 00:34:41,490
+يساوي حاصل ضرب هدول طب مضربهم في بعضماشي يبقى لو
+
+301
+00:34:41,490 --> 00:34:45,690
+روحت ضربتم في بعض بيقول لمين الصف الأول في العمود
+
+302
+00:34:45,690 --> 00:34:54,690
+الأول يبقى x1 زائد x3 الصف الثاني يبقى x1 زائد x2
+
+303
+00:34:54,690 --> 00:35:08,130
+زائد 2x3 الصف التالت 2x1 زائد x2 زائد 3x3 هاي
+
+304
+00:35:08,130 --> 00:35:13,070
+ضربنايبقى هذا الـlinear transformation المعرفة عنه
+
+305
+00:35:13,070 --> 00:35:21,360
+جالي هاتل الكيرنل باجي بقوله اه الكيرنلالتي هو كل
+
+306
+00:35:21,360 --> 00:35:26,880
+ال X's اللي موجودة في ال R3 اللي عندها و اللي
+
+307
+00:35:26,880 --> 00:35:33,580
+صورتها T of X بده يساوي مين؟ بده يساوي Zero يبقى
+
+308
+00:35:33,580 --> 00:35:39,660
+هذه كل ال X's ال X هذه اللي هي مين؟ X واحد و X
+
+309
+00:35:39,660 --> 00:35:45,650
+اتنين و X تلاتة اللي موجودة في ال R3 صتش دهلما
+
+310
+00:35:45,650 --> 00:35:49,810
+أقول هذا الـT of X ساوي 0، الـT of X ساوي مين؟
+
+311
+00:35:49,810 --> 00:35:54,170
+يساوي هذا كله، معناته هذه بدها تساوي مين؟ بدها
+
+312
+00:35:54,170 --> 00:36:00,630
+تساوي المصوفة الصفرية يبقى ده such that المصوفة دي
+
+313
+00:36:00,630 --> 00:36:12,850
+X1 زائد X3وهنا X1 زائد X2 زائد 2 X3 وهنا 2 X1 زائد
+
+314
+00:36:12,850 --> 00:36:20,570
+X2 ثلاثة X3 كله بيساوي المصفوفة الصفرية اللي عندنا
+
+315
+00:36:20,570 --> 00:36:27,790
+بالشكل هذا تمام؟ اذا انا طبقت حتى الان تعريف من ال
+
+316
+00:36:27,790 --> 00:36:33,830
+kernel هذا يا بنات بيقودنا الى كام معادلة؟يعني هو
+
+317
+00:36:33,830 --> 00:36:38,630
+homogeneous system صح ولا لأ؟ يبقى هذا يقودنا إلى
+
+318
+00:36:38,630 --> 00:36:48,330
+ما يأتي ان X1 زائد X3 يسوى 0 و X1 زائد X2 زائد 2
+
+319
+00:36:48,330 --> 00:36:58,590
+X3 يسوى 0 و 2X1 زائد X2 زائد 3X3 يسوى 0 هذا عبارة
+
+320
+00:36:58,590 --> 00:37:03,230
+عن ماذا؟Homogeneous System بحاول نحل الـ
+
+321
+00:37:03,230 --> 00:37:07,270
+Homogeneous System بأي طريقة من الطرق التي سبقت
+
+322
+00:37:07,270 --> 00:37:11,870
+دراستها طبعا الـ Homogeneous أسهل من الـ Non
+
+323
+00:37:11,870 --> 00:37:14,890
+-Homogeneous في الحل وبالتالي ممكن نجيب الحل
+
+324
+00:37:14,890 --> 00:37:19,930
+بسهولة بدون ملجأ لـ Gaussian ولا لـ Rho Epsilon
+
+325
+00:37:19,930 --> 00:37:24,790
+Form إلى آخرى فمثلا لو جيت قلت هنا X واحد تتساوي
+
+326
+00:37:24,790 --> 00:37:32,000
+مين يا بنات؟بدي يساوي سالب X3 مظبوط طيب إذا لو جيت
+
+327
+00:37:32,000 --> 00:37:38,640
+على المعدل التاني هذا إيش بيصير سالب X3 زائد X2
+
+328
+00:37:38,640 --> 00:37:48,770
+زائد 2 X3 بدي يساوي Zero وهنا سالب 2 X3زائد X2
+
+329
+00:37:48,770 --> 00:37:51,710
+زائد X3 زائد X2 زائد X2 زائد X3 زائد X2 زائد X2
+
+330
+00:37:51,710 --> 00:37:52,070
+زائد X2 زائد X2 زائد X2 زائد X2 زائد X2 زائد X2
+
+331
+00:37:52,070 --> 00:37:55,290
+زائد X2 زائد X2 زائد X2 زائد X2 زائد X2 زائد X2
+
+332
+00:37:55,290 --> 00:37:58,550
+زائد X2 زائد X2 زائد X2 زائد X2 زائد X2 زائد X2
+
+333
+00:37:58,550 --> 00:38:01,530
+زائد X2 زائد X2 زائد X2 زائد X2 زائد X2 زائد X2
+
+334
+00:38:01,530 --> 00:38:11,710
+زائد X2 زائد X
+
+335
+00:38:11,740 --> 00:38:21,720
+بتبقى x2 زائد x3 يساوي 0 و هذه بتعطيني x2 زائد x3
+
+336
+00:38:21,720 --> 00:38:28,280
+يساوي 0 يعني بتعطيني مين؟ نفس المعادلة إذا من
+
+337
+00:38:28,280 --> 00:38:36,720
+الاتنين هدول بقدر أقول ان x2 بده يساوي سالب x3يبقى
+
+338
+00:38:36,720 --> 00:38:44,160
+بناء عليه لو كانت x تلاتة تساوي a then x واحد كده
+
+339
+00:38:44,160 --> 00:38:52,920
+بده يساويو X2 بده يسوي كده؟ سالب A يبقى أصبح الـ
+
+340
+00:38:52,920 --> 00:38:59,340
+Kernel لمن؟ لـ Linear Transformation T هو عبارة عن
+
+341
+00:38:59,340 --> 00:39:05,920
+من؟ The set of all elements X1 اللي يبقى كده؟ سالب
+
+342
+00:39:05,920 --> 00:39:15,850
+A و X2 اللي هو سالب A و X3 اوهذا اللي بقدر اكتب
+
+343
+00:39:15,850 --> 00:39:21,690
+عليه الشكل التالي كل المصوف اللي ع شكل ناقص ايه
+
+344
+00:39:21,690 --> 00:39:27,870
+ناقص ايه و ايه such that او هذا اللي بده يساوي
+
+345
+00:39:27,870 --> 00:39:33,910
+كمان ايه لو أخدت عامل مشترك بده يكون مين ناقص واحد
+
+346
+00:39:33,910 --> 00:39:39,570
+ناقص واحد واحد such that ال a موجودة في ال set of
+
+347
+00:39:39,570 --> 00:39:44,330
+real numbersيعني ماحطيتش عليها أي قيود لأي عدد
+
+348
+00:39:44,330 --> 00:39:52,070
+حقيقي من مكان يكون تمام؟ إذا أصبح ال kernel من هو؟
+
+349
+00:39:52,070 --> 00:39:58,590
+هو كل ال vectors اللي المركبة الأولى تساوي المركبة
+
+350
+00:39:58,590 --> 00:40:03,070
+الثانية و المركبة التالتة باس تساويهم لكنها تخلفهم
+
+351
+00:40:03,070 --> 00:40:07,990
+في من؟ الإشارة يبقى ال vector هذا منات إيش علاقته
+
+352
+00:40:07,990 --> 00:40:17,040
+بال kernel؟بجيب بعض عناصر الكرنن ولا كلهم؟ يعني
+
+353
+00:40:17,040 --> 00:40:23,300
+إيش بينفع يكون؟bases لأنه مستقل حاله لينياري مش
+
+354
+00:40:23,300 --> 00:40:28,720
+معتمد على غيره يبقى هذا لينياري independent اثنين
+
+355
+00:40:28,720 --> 00:40:33,780
+كل أنصر في ال kernel بقدر اكتب دلته حطيت قيود على
+
+356
+00:40:33,780 --> 00:40:39,340
+ايه لأ يبقى حط الرقم اللي يجبك وهذا ثابت يبقى هذا
+
+357
+00:40:39,340 --> 00:40:43,800
+معناته ال bases للكيرنل هو مين ال vector اللي
+
+358
+00:40:43,800 --> 00:40:53,340
+عندنا هذا يبقى هذا معناه ايش معناه ذاVector لحاله
+
+359
+00:40:53,340 --> 00:41:01,200
+أو the set هذا معناته ال vector
+
+360
+00:41:01,200 --> 00:41:08,220
+على الشكل هذا سالب واحد سالب واحد هذا is a basis
+
+361
+00:41:08,220 --> 00:41:24,320
+for ال kernel التيهذا معناته ان ال dimension لل
+
+362
+00:41:24,320 --> 00:41:29,660
+kernel of T يساوي جداش يا بنات خلصنا المطلوب الأول
+
+363
+00:41:30,630 --> 00:41:33,890
+قال لي هتل ال kernel و في نفس الوقت هتل ال
+
+364
+00:41:33,890 --> 00:41:40,770
+dimension تمام؟ إذا هيجب ناله ال kernel من هو كل
+
+365
+00:41:40,770 --> 00:41:45,050
+ال vectors اللي المركبة الأولى تساوي المركبة
+
+366
+00:41:45,050 --> 00:41:50,010
+التانية تساوي المركبة التالتة بإشارة مخالفة يبقى
+
+367
+00:41:50,010 --> 00:41:55,010
+هذا كل ال kernel إذا بقدر أحدد منهما كم vector
+
+368
+00:41:55,010 --> 00:42:03,880
+هدول يا بنات؟2 3 4 10 100 عدد لا نهائي لأن الـ a
+
+369
+00:42:03,880 --> 00:42:11,100
+هو عدد لا نهائي من الـ vector تمام إذا جلبنا الـ
+
+370
+00:42:11,100 --> 00:42:14,940
+main جلبنا ال basis اللي هو بالتالي جلبنا ال
+
+371
+00:42:14,940 --> 00:42:19,540
+dimension لـ main لل kernel بالمثل بدنا نروح نجلب
+
+372
+00:42:19,540 --> 00:42:23,540
+mainالمطلب الثاني المطلب الثاني بال domain ال
+
+373
+00:42:23,540 --> 00:42:29,280
+bases لل range تمام؟ إذا بروح أجيب له ال bases لل
+
+374
+00:42:29,280 --> 00:42:34,720
+range يبقى هذا ال element موجود في ال range ولا
+
+375
+00:42:34,720 --> 00:42:41,320
+لا؟ صح ولا لا؟ يبقى هذا ال element موجود في ال
+
+376
+00:42:41,320 --> 00:42:47,720
+range يبقى باجي بقوله هنا هذا نمرا a نمرا b the b
+
+377
+00:42:47,720 --> 00:42:48,980
+أو the element
+
+378
+00:42:51,600 --> 00:43:00,500
+اللي هو على الشكل التالي X1 زائد X3 و X1 زائد X2
+
+379
+00:43:00,500 --> 00:43:14,940
+زائد 2 X3 و 2 X1 زائد X2 زائد 3 X3 موجود في R of D
+
+380
+00:43:14,940 --> 00:43:20,220
+طب بدى أشوف ال element هذا إيش بقدر أعمل منه
+
+381
+00:43:33,550 --> 00:43:36,010
+تعالى نشوف ال element هذا اللى موجود فى ال range
+
+382
+00:43:36,010 --> 00:43:43,650
+شو شكله يبقى باجي بقولهم ال element هذا x1 زائد x3
+
+383
+00:43:43,650 --> 00:43:57,150
+اللى بعده x1 زائد x2 زائد 2x3 2x1 زائد x2 زائد 3x3
+
+384
+00:43:57,150 --> 00:44:03,470
+ويسوىهذا ال element أخدته من ال R of T يعني من ال
+
+385
+00:44:03,470 --> 00:44:07,490
+range طبعا هيش قاللي ماجلليش هاترين قاللي هاتلي
+
+386
+00:44:07,490 --> 00:44:13,170
+basis لل range بقوله كويس طيب هذا يا بنات بقدر
+
+387
+00:44:13,170 --> 00:44:20,770
+أكتبه على شكل مجموع تلاتة vectorsأه بنقدر، كيف كان
+
+388
+00:44:20,770 --> 00:44:31,360
+التالي؟ بداخل هنا x1 وهنا x1 وهنا 2x1هو اجي اقول
+
+389
+00:44:31,360 --> 00:44:36,320
+زاد المصفوف التاني اكس اتنين ماعنديش يبقى بزيرو
+
+390
+00:44:36,320 --> 00:44:43,140
+وهي اكس اتنين وهي اكس اتنين زاد بدهاجي لمين للي
+
+391
+00:44:43,140 --> 00:44:50,220
+بعده اكس تلاتة اتنين اكس تلاتة تلاتة اكس تلاتة
+
+392
+00:44:50,220 --> 00:44:57,420
+مظبوط هيك؟طيب بقدر اقول هذا الكلام لو اخدت x واحد
+
+393
+00:44:57,420 --> 00:45:04,220
+بصير واحد واحد اتنين زائد zero واحد واحد و هنا x
+
+394
+00:45:04,220 --> 00:45:10,660
+اتنين زائد x اتنين و جينا اللي بعده زائد x تلاتة
+
+395
+00:45:10,660 --> 00:45:17,230
+في واحد اتنين تلاتة بالشكل اللي عندنا هذايبقى ال
+
+396
+00:45:17,230 --> 00:45:21,070
+element اللى موجود فى ال range حطيته على صيغة
+
+397
+00:45:21,070 --> 00:45:27,950
+linear combination من من ال vectors التلاتة اللى
+
+398
+00:45:27,950 --> 00:45:32,790
+عندنا يبقى أي element فى ال range كتبته على صيغة
+
+399
+00:45:32,790 --> 00:45:36,970
+linear combination من three vectors x1 فى ال
+
+400
+00:45:36,970 --> 00:45:41,010
+vector زاد x2 فى ال vector زاد x3 فى ال vector
+
+401
+00:45:41,010 --> 00:45:47,950
+التالىلو طلعوا هدول linearly independent بيصير هم
+
+402
+00:45:47,950 --> 00:45:53,610
+ال bases طب لو طلعوا linearly dependent بدك تدور
+
+403
+00:45:53,610 --> 00:46:00,010
+على ال bases تعالوا نطلع هك ندجج النظر لو جمعت ال
+
+404
+00:46:00,010 --> 00:46:07,150
+two vectors هدول قدش بيعطيني ايه التالت بيعطيني
+
+405
+00:46:07,150 --> 00:46:13,280
+التالتو 1 زي 0 ب1 و 1 ب1 ب2 ب2 ب1 ب3 ب3 ب3 ب3 ب3
+
+406
+00:46:13,280 --> 00:46:13,760
+ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3
+
+407
+00:46:13,760 --> 00:46:14,000
+ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3
+
+408
+00:46:14,000 --> 00:46:16,760
+ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3
+
+409
+00:46:16,760 --> 00:46:17,760
+ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3
+
+410
+00:46:17,760 --> 00:46:26,640
+ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3 ب3
+
+411
+00:46:26,640 --> 00:46:33,340
+بوبالتالي الاتنين هذول بيوضول بيوضولي جميع أناصر
+
+412
+00:46:33,340 --> 00:46:37,740
+ال vector of space أو ال subspace R of T طب و
+
+413
+00:46:37,740 --> 00:46:40,480
+التلت مش جزء و التلت ما هو linear combination من
+
+414
+00:46:40,480 --> 00:46:44,100
+الاتنين صحيح ولا يعني ايه بقدر اخلي هذا في شجة و
+
+415
+00:46:44,100 --> 00:46:46,660
+ادى هذول على شجة تانية ساوة زيرة و اخليها سالب
+
+416
+00:46:46,660 --> 00:46:49,240
+سالب و انت ايه رأي منهم يبقى ده اسم linearly
+
+417
+00:46:49,240 --> 00:46:55,200
+dependent لكن اتنين هذول linearly independent يبقى
+
+418
+00:46:55,200 --> 00:47:04,320
+باجي بقول هناالان الواحد والواحد واثنين زائد زيرو
+
+419
+00:47:04,320 --> 00:47:11,940
+واحد واحد بده يساوي واحد اتنين تلاتة اذا لا يمكن
+
+420
+00:47:11,940 --> 00:47:17,460
+اقول ان التلاتة دول linearly independent لكن يا
+
+421
+00:47:17,460 --> 00:47:25,480
+بنات بقدر اقول هنا the vectorsv1 اللي هو بده يساوي
+
+422
+00:47:25,480 --> 00:47:33,560
+11e2 وv2 بده يساوي 011r
+
+423
+00:47:33,560 --> 00:47:44,700
+ماله linearly independent السبب because anyone of
+
+424
+00:47:44,700 --> 00:47:59,140
+v1 and v2 is notmultiple of the other ولا واحد
+
+425
+00:47:59,140 --> 00:48:04,660
+فيهم مضاعفات التانية يبقى هدول إيش بيشكلولي؟
+
+426
+00:48:04,660 --> 00:48:09,660
+بالنسبة ل R2 بيبقى هنا ساعة
+
+427
+00:48:17,300 --> 00:48:34,460
+V1 V2 V3
+
+428
+00:48:34,460 --> 00:48:34,620
+V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V12 V13 V12 V12
+
+429
+00:48:34,620 --> 00:48:35,020
+V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12
+
+430
+00:48:35,020 --> 00:48:35,080
+V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12
+
+431
+00:48:35,080 --> 00:48:35,180
+V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12
+
+432
+00:48:35,180 --> 00:48:39,590
+V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V122 عدد
+
+433
+00:48:39,590 --> 00:48:44,570
+العناصر في الـ Basel إذا خلصنا من المطلوب الثاني
+
+434
+00:48:44,570 --> 00:48:50,270
+قال لي هاتلي Basel لل R of T of 2 of T جيبناله و
+
+435
+00:48:50,270 --> 00:48:53,130
+قاللي هاتلي ال dimension جيبناله ال dimension
+
+436
+00:48:53,130 --> 00:48:58,810
+قاللي بعدين هاتلي صورة العنصر T of 1 و 2 و 3 إذا
+
+437
+00:48:58,810 --> 00:49:02,850
+بيداجي للمطلوب التالد
+
+438
+00:49:15,200 --> 00:49:21,440
+إذا المطلوب التالت نمرى الـC بدنا T of واحد واتنين
+
+439
+00:49:21,440 --> 00:49:29,300
+وتلاتة من وين بده أجيب له هذا؟
+
+440
+00:49:29,300 --> 00:49:38,550
+من وين بده أجيب له؟ وين هي؟ مش هذه؟مش T of element
+
+441
+00:49:38,550 --> 00:49:42,250
+يساوي أي عنصر في ال range على الشكل اللي عندنا هذا
+
+442
+00:49:42,250 --> 00:49:47,550
+يبقى ده يقول X1 زي X3 كذا يبقى بناء ان عليه هذا
+
+443
+00:49:47,550 --> 00:49:54,210
+الكلام بده يساوي بده يساوي من X1 زي X3 يبقى 1 زي 3
+
+444
+00:49:56,030 --> 00:50:05,930
+العنصر التاني X1 زي X2 زي 2X3 يبقى 1 زي 2 زي 3
+
+445
+00:50:11,050 --> 00:50:21,370
+يبقى هذا العنصر التالت 2x1 يبقى 2 في 1 زائد 2 زائد
+
+446
+00:50:21,370 --> 00:50:28,010
+3 في 3 بالشكل اللي عندنا هذاتمام واحد زي التلاتة
+
+447
+00:50:28,010 --> 00:50:33,010
+كداش اربعة هنا اتنين في التلاتة بستة و تلاتة تسعة
+
+448
+00:50:33,010 --> 00:50:38,850
+تسعة و اتنين احداش و اتنين تلتاش اذا صورة العنصر
+
+449
+00:50:38,850 --> 00:50:44,370
+واحد و اتنين و تلاتة هي اربعة و تسعة و تلتاش اظن
+
+450
+00:50:44,370 --> 00:50:48,210
+واضح ادى كيف جيبناها جيبناها من خلال التعريف لما
+
+451
+00:50:48,210 --> 00:50:51,430
+قلنا T of X واحد و X اتنين لما ضربنا المصفوف T
+
+452
+00:50:51,430 --> 00:50:56,330
+الاتنين هادول طلعت على الشكل اللى قدامنا هذاطيب
+
+453
+00:50:56,330 --> 00:51:00,550
+بسأل كمان سؤال بقول لي هل العنصر هذا موجود في ال
+
+454
+00:51:00,550 --> 00:51:05,450
+range أم لا؟ بقول له الله أعلم تعالى نشوف يعني هل
+
+455
+00:51:05,450 --> 00:51:09,970
+العنصر اتنين و خمسة و سبعة موجود في ال range تبع
+
+456
+00:51:09,970 --> 00:51:16,130
+ال T باجي بسأل مين هو ال business تبع ال T؟إذا
+
+457
+00:51:16,130 --> 00:51:20,610
+قدرنا نكتب العنصر هذا على صورة linear combination
+
+458
+00:51:20,610 --> 00:51:25,050
+من الاتنين هذول بصير موجود في ال range صح ولا لأ
+
+459
+00:51:25,050 --> 00:51:30,580
+وإذا ماقدرناش يبقى مكون برا ال rangeطبعا إذا بداجي
+
+460
+00:51:30,580 --> 00:51:35,540
+لمن؟ لنمردي بداجي أخد العنصر اللي هو اتنين وخمسة
+
+461
+00:51:35,540 --> 00:51:41,680
+وسبعة يبقى اتنين وخمسة وسبعة بقدر اكتبه على شكل
+
+462
+00:51:41,680 --> 00:51:48,080
+مصوف اتنين خمسة سبعة مش هيك قولنا هذا if and قولي
+
+463
+00:51:48,080 --> 00:51:55,390
+if و بقدر اكتبه فوقي كمان طب إيش رأيك؟أنا بدي أكتب
+
+464
+00:51:55,390 --> 00:51:59,970
+عليه شكلًا يعني بدي الرقم الأول جد الرقم الثاني
+
+465
+00:51:59,970 --> 00:52:06,010
+الرقم الأول عندي مقداش اتنين والرقم الثاني بدي
+
+466
+00:52:06,010 --> 00:52:13,250
+يكون زيه اتنين والرقم التالت باتنين يبقى بدي أكتب
+
+467
+00:52:13,250 --> 00:52:16,170
+أربعة زاد
+
+468
+00:52:17,970 --> 00:52:22,250
+أيش بيظل عندي؟ بدي أكتبه الحين من اتنين أخدت اتنين
+
+469
+00:52:22,250 --> 00:52:26,910
+بيظل كده؟ Zero من الخمسة أخدت اتنين بيظل كده؟
+
+470
+00:52:26,910 --> 00:52:32,170
+تلاتة من السبعة أخدت أربعة بيظل كده؟ تلاتة يبقى
+
+471
+00:52:32,170 --> 00:52:36,670
+هذا الكلام .. بقدر أخدي اتنين عامل مشترك أيش بيظل
+
+472
+00:52:36,670 --> 00:52:41,890
+عندي؟ واحد واحد اتنين بقدر أخد تلاتة عامل مشترك
+
+473
+00:52:41,890 --> 00:52:46,910
+Zero واحد واحد linear combination من الاتنين؟يبقى
+
+474
+00:52:46,910 --> 00:52:50,950
+موجود في ال range ولا لا لإنه يبقى كتبت هذا ال
+
+475
+00:52:50,950 --> 00:52:56,390
+element بواسط عناصر البذل لو ما جدرتش يبقى بنقول
+
+476
+00:52:56,390 --> 00:53:00,930
+مش موجود طبعا هذه طريقة سهلة جدا بمجرد النظر لكن
+
+477
+00:53:00,930 --> 00:53:04,590
+الأصل ان اقول اتنين وخمسة وسبعة يساوي يكون اصلا في
+
+478
+00:53:04,590 --> 00:53:07,470
+الأول ويكون اصلا في التاني واروح احل ال non
+
+479
+00:53:07,470 --> 00:53:15,710
+homogeneous system تمام يبقى هذا معناه هذا يبقى
+
+480
+00:53:16,490 --> 00:53:26,090
+إتنين وخمسة وسبعة is a linear combination of the
+
+481
+00:53:26,090 --> 00:53:41,660
+elements of the basesof R of T Thus و هكذا اتنين
+
+482
+00:53:41,660 --> 00:53:53,540
+خمسة سبعة و عنصر موجود في R of T و هو المطلوب حد
+
+483
+00:53:53,540 --> 00:53:58,980
+فيكم بتحب تسأل اي سؤال هنا يا مانال؟ اي سؤال؟طب
+
+484
+00:53:58,980 --> 00:54:03,480
+لازلنا في نفس ال section و هناك بدل المثال اتنين
+
+485
+00:54:03,480 --> 00:54:07,880
+لسه كمان لإن الموضوع هذا قلتلكوا هذا ال section
+
+486
+00:54:07,880 --> 00:54:13,000
+بالذات very important و لازم ييجي عليه سؤال في
+
+487
+00:54:13,000 --> 00:54:17,720
+امتحان أعمال الفصل و كذلك النهاية وضع طبيعي لازم
+
+488
+00:54:17,720 --> 00:54:19,620
+يكون هذا يعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/BZBTTMoYXDc_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/BZBTTMoYXDc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..288092a81d77f0dde96f79a9748151d1f708876c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/BZBTTMoYXDc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4719, "start": 20.89, "end": 47.19, "text": "بسم الله الرحمن الرحيم عود على بدء المرة اللي فاتت بدأنا بال linear transformation و بعد ذلك أخدنا عدة تمثيل عليها ثم أخدنا بعض النظريات أثبتنا أن ال kernel linear transformation is a subspace و أثبتنا أن ال range لل linear transformation is a subspace و أخدنا على ذلك المثال الأول", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 6225, 23328, 15844, 47525, 38207, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 47525, 10721, 8315, 20666, 8213, 9887, 4032, 39182, 29910, 23275, 5551, 9778, 3215, 8315, 6225, 41891, 46811, 12984, 26895, 25894, 11296, 38637, 2304, 5551, 9778, 3215, 8315, 45030, 11242, 28239, 19913, 16572, 9307, 5551, 12984, 3555, 2655, 8315, 14739, 2423, 28256, 8213, 9887, 307, 257, 2090, 17940, 4032, 5551, 12984, 3555, 2655, 8315, 14739, 2423, 3613, 24976, 8213, 9887, 307, 257, 2090, 17940, 4032, 5551, 9778, 3215, 8315, 15844, 29910, 23275, 9673, 12984, 6027, 16247, 12610], "avg_logprob": -0.16836734222514288, "compression_ratio": 1.9671361502347418, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.89, "end": 21.23, "word": "بسم", "probability": 0.6444091796875}, {"start": 21.23, "end": 21.41, "word": " الله", "probability": 0.9599609375}, {"start": 21.41, "end": 21.81, "word": " الرحمن", "probability": 0.9627278645833334}, {"start": 21.81, "end": 22.33, "word": " الرحيم", "probability": 0.9925130208333334}, {"start": 22.33, "end": 23.49, "word": " عود", "probability": 0.833740234375}, {"start": 23.49, "end": 23.95, "word": " على", "probability": 0.4140625}, {"start": 23.95, "end": 24.49, "word": " بدء", "probability": 0.589599609375}, {"start": 24.49, "end": 25.01, "word": " المرة", "probability": 0.7330322265625}, {"start": 25.01, "end": 25.17, "word": " اللي", "probability": 0.61865234375}, {"start": 25.17, "end": 25.63, "word": " فاتت", "probability": 0.9615885416666666}, {"start": 25.63, "end": 26.41, "word": " بدأنا", "probability": 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يبقى هذا التعريف العام لمين؟ لل range تبعتي بدنا نيجي نطبق هذا التعريف و نشوف بدي وصلني إلى وين", "tokens": [1829, 3555, 4587, 7578, 28242, 9673, 9381, 5172, 38688, 9307, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 3714, 7435, 2304, 2407, 27884, 9673, 9381, 5172, 38688, 9307, 376, 7490, 4032, 6027, 20292, 20328, 13063, 2655, 11296, 6055, 30544, 2135, 314, 295, 316, 4724, 5016, 1829, 12984, 2423, 39184, 32, 512, 4478, 3714, 29245, 23328, 8978, 376, 7490, 7251, 3555, 4587, 7578, 23758, 16712, 3615, 16572, 5172, 18863, 10943, 5296, 2304, 9957, 22807, 24976, 3613, 6055, 3555, 3615, 31371, 47525, 8315, 8717, 1829, 7435, 1829, 8717, 9566, 3555, 4587, 23758, 16712, 3615, 16572, 5172, 4032, 8717, 8592, 38688, 4724, 16254, 4032, 36520, 22653, 30731, 4032, 9957], "avg_logprob": -0.2463148576471041, "compression_ratio": 1.6199095022624435, "no_speech_prob": 0.0, "words": [{"start": 135.06, "end": 135.66, "word": "يبقى", "probability": 0.83251953125}, {"start": 135.66, "end": 136.08, "word": " 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"word": " اللي", "probability": 0.884765625}, {"start": 219.52, "end": 220.16, "word": " موجودة", "probability": 0.9857177734375}, {"start": 220.16, "end": 220.34, "word": " في", "probability": 0.8095703125}, {"start": 220.34, "end": 220.5, "word": " ال", "probability": 0.8818359375}, {"start": 220.5, "end": 221.2, "word": " M22", "probability": 0.50341796875}, {"start": 221.2, "end": 221.7, "word": " such", "probability": 0.4384765625}, {"start": 221.7, "end": 222.28, "word": " that", "probability": 0.92626953125}, {"start": 222.28, "end": 222.94, "word": " ال", "probability": 0.85400390625}, {"start": 222.94, "end": 223.44, "word": " BT", "probability": 0.26806640625}, {"start": 223.44, "end": 224.48, "word": " تساوي", "probability": 0.9398193359375}, {"start": 224.48, "end": 226.4, "word": " لترانسبوز", "probability": 0.7220982142857143}, {"start": 226.4, "end": 226.8, "word": " بتجي", "probability": 0.6539306640625}, {"start": 226.8, "end": 227.66, "word": " ترانسبوز", 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{"start": 261.73, "end": 262.61, "word": " و", "probability": 0.66064453125}, {"start": 262.61, "end": 263.27, "word": " ال", "probability": 0.67333984375}, {"start": 263.27, "end": 264.25, "word": " range", "probability": 0.787109375}, {"start": 264.25, "end": 264.65, "word": " هو", "probability": 0.93408203125}, {"start": 264.65, "end": 265.23, "word": " ال", "probability": 0.8984375}, {"start": 265.23, "end": 265.75, "word": " symmetric", "probability": 0.8642578125}, {"start": 265.75, "end": 266.81, "word": " matrices", "probability": 0.978515625}, {"start": 266.81, "end": 268.07, "word": " يبقى", "probability": 0.989990234375}, {"start": 268.07, "end": 268.55, "word": " for", "probability": 0.53955078125}, {"start": 268.55, "end": 269.07, "word": " some", "probability": 0.82080078125}, {"start": 269.07, "end": 269.47, "word": " a", "probability": 0.87255859375}, {"start": 269.47, "end": 269.61, "word": " اللي", "probability": 0.835205078125}, {"start": 269.61, "end": 270.11, 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"probability": 0.70751953125}, {"start": 511.31, "end": 512.01, "word": " الشكل", "probability": 0.6031494140625}, {"start": 512.01, "end": 512.29, "word": " هنا", "probability": 0.2337646484375}, {"start": 512.29, "end": 512.71, "word": " يعني", "probability": 0.78955078125}, {"start": 512.71, "end": 513.59, "word": " حاصل", "probability": 0.88671875}, {"start": 513.59, "end": 513.97, "word": " ضرب", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 20, "seek": 53878, "start": 514.48, "end": 538.78, "text": "المصوفة اللى نضامها M فى N فى المصوفة العمودية اللى هى X مى المصوفة العمودية مصوفة مكونة من N من الصفوف وعمود واحد يبقى هنا قولنا ال X دى is a column vector يبقى متجه عمودي يعنى مصوفة مكونة من عمود واحد لكنها مجموعة من الصفوف", "tokens": [45340, 9381, 38688, 3660, 13672, 7578, 8717, 11242, 10943, 11296, 376, 6156, 7578, 426, 6156, 7578, 9673, 9381, 38688, 3660, 18863, 2304, 23328, 10632, 13672, 7578, 8032, 7578, 1783, 3714, 7578, 9673, 9381, 38688, 3660, 18863, 2304, 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524.3, "word": " من", "probability": 0.97265625}, {"start": 524.3, "end": 524.72, "word": " N", "probability": 0.8037109375}, {"start": 524.72, "end": 525.06, "word": " من", "probability": 0.958984375}, {"start": 525.06, "end": 525.8, "word": " الصفوف", "probability": 0.9827473958333334}, {"start": 525.8, "end": 526.68, "word": " وعمود", "probability": 0.9078776041666666}, {"start": 526.68, "end": 527.22, "word": " واحد", "probability": 0.7181396484375}, {"start": 527.22, "end": 528.02, "word": " يبقى", "probability": 0.9642333984375}, {"start": 528.02, "end": 528.3, "word": " هنا", "probability": 0.890625}, {"start": 528.3, "end": 528.96, "word": " قولنا", "probability": 0.8694661458333334}, {"start": 528.96, "end": 529.22, "word": " ال", "probability": 0.62646484375}, {"start": 529.22, "end": 529.46, "word": " X", "probability": 0.91796875}, {"start": 529.46, "end": 529.8, "word": " دى", "probability": 0.603759765625}, {"start": 529.8, "end": 530.02, "word": " is", "probability": 0.3828125}, {"start": 530.02, "end": 530.34, "word": " a", "probability": 0.9228515625}, {"start": 530.34, "end": 530.62, "word": " column", "probability": 0.79638671875}, {"start": 530.62, "end": 531.12, "word": " vector", "probability": 0.9521484375}, {"start": 531.12, "end": 531.76, "word": " يبقى", "probability": 0.94140625}, {"start": 531.76, "end": 532.36, "word": " متجه", "probability": 0.9786783854166666}, {"start": 532.36, "end": 533.18, "word": " عمودي", "probability": 0.978759765625}, {"start": 533.18, "end": 533.82, "word": " يعنى", "probability": 0.8338216145833334}, {"start": 533.82, "end": 534.4, "word": " مصوفة", "probability": 0.977783203125}, {"start": 534.4, "end": 534.92, "word": " مكونة", "probability": 0.9480794270833334}, {"start": 534.92, "end": 535.08, "word": " من", "probability": 0.9892578125}, {"start": 535.08, "end": 535.38, "word": " عمود", "probability": 0.9664713541666666}, {"start": 535.38, "end": 535.74, "word": " واحد", "probability": 0.9794921875}, {"start": 535.74, "end": 536.4, "word": " لكنها", "probability": 0.907958984375}, {"start": 536.4, "end": 537.1, "word": " مجموعة", "probability": 0.9904296875}, {"start": 537.1, "end": 537.9, "word": " من", "probability": 0.99462890625}, {"start": 537.9, "end": 538.78, "word": " الصفوف", "probability": 0.9856770833333334}], "temperature": 1.0}, {"id": 21, "seek": 56009, "start": 539.27, "end": 560.09, "text": "بناء على هذا التعريف بدي أثبت أن T هي linear transformation يعني إيش بدي أحقق؟ الشرطين تبعات ال linear transformation أمر تاني بدي أجيبها لل kernel بدي أعرف قداش الأمر التالف بدي أعرف قداش ال range تبع T اللي بجي نربزله R of T تلاتة", "tokens": [3555, 1863, 16606, 15844, 23758, 16712, 3615, 16572, 5172, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 314, 39896, 8213, 9887, 37495, 22653, 11933, 1829, 8592, 4724, 16254, 5551, 5016, 4587, 4587, 22807, 25124, 2288, 9566, 9957, 6055, 3555, 3615, 9307, 2423, 8213, 9887, 5551, 29973, 6055, 7649, 1829, 4724, 16254, 5551, 7435, 1829, 3555, 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"word": " T", "probability": 0.73388671875}, {"start": 542.03, "end": 542.29, "word": " هي", "probability": 0.86572265625}, {"start": 542.29, "end": 542.59, "word": " linear", "probability": 0.35986328125}, {"start": 542.59, "end": 543.79, "word": " transformation", "probability": 0.88037109375}, {"start": 543.79, "end": 544.61, "word": " يعني", "probability": 0.859619140625}, {"start": 544.61, "end": 544.79, "word": " إيش", "probability": 0.7460123697916666}, {"start": 544.79, "end": 544.99, "word": " بدي", "probability": 0.73583984375}, {"start": 544.99, "end": 546.21, "word": " أحقق؟", "probability": 0.824462890625}, {"start": 546.21, "end": 547.25, "word": " الشرطين", "probability": 0.9708251953125}, {"start": 547.25, "end": 547.93, "word": " تبعات", "probability": 0.9010009765625}, {"start": 547.93, "end": 548.03, "word": " ال", "probability": 0.74755859375}, {"start": 548.03, "end": 548.27, "word": " linear", "probability": 0.48876953125}, {"start": 548.27, "end": 549.37, "word": " transformation", "probability": 0.88427734375}, {"start": 549.37, "end": 549.85, "word": " أمر", "probability": 0.75390625}, {"start": 549.85, "end": 550.37, "word": " تاني", "probability": 0.8458658854166666}, {"start": 550.37, "end": 550.89, "word": " بدي", "probability": 0.743408203125}, {"start": 550.89, "end": 551.27, "word": " أجيبها", "probability": 0.788232421875}, {"start": 551.27, "end": 551.47, "word": " لل", "probability": 0.31640625}, {"start": 551.47, "end": 552.03, "word": " kernel", "probability": 0.2841796875}, {"start": 552.03, "end": 552.53, "word": " بدي", "probability": 0.7861328125}, {"start": 552.53, "end": 552.73, "word": " أعرف", "probability": 0.9796549479166666}, {"start": 552.73, "end": 553.27, "word": " قداش", "probability": 0.8033854166666666}, {"start": 553.27, "end": 554.09, "word": " الأمر", "probability": 0.8505859375}, {"start": 554.09, "end": 554.63, "word": " التالف", "probability": 0.7447916666666666}, {"start": 554.63, "end": 554.99, "word": " بدي", "probability": 0.914306640625}, {"start": 554.99, "end": 555.23, "word": " أعرف", "probability": 0.98486328125}, {"start": 555.23, "end": 555.73, "word": " قداش", "probability": 0.9767252604166666}, {"start": 555.73, "end": 555.95, "word": " ال", "probability": 0.89013671875}, {"start": 555.95, "end": 556.31, "word": " range", "probability": 0.96337890625}, {"start": 556.31, "end": 556.77, "word": " تبع", "probability": 0.9290364583333334}, {"start": 556.77, "end": 557.27, "word": " T", "probability": 0.2158203125}, {"start": 557.27, "end": 557.49, "word": " اللي", "probability": 0.607177734375}, {"start": 557.49, "end": 557.71, "word": " بجي", "probability": 0.8024088541666666}, {"start": 557.71, "end": 558.45, "word": " نربزله", "probability": 0.63604736328125}, {"start": 558.45, "end": 558.97, "word": " R", "probability": 0.87939453125}, {"start": 558.97, "end": 559.19, "word": " of", "probability": 0.372314453125}, {"start": 559.19, "end": 559.37, "word": " T", "probability": 0.9892578125}, {"start": 559.37, "end": 560.09, "word": " تلاتة", "probability": 0.837890625}], "temperature": 1.0}, {"id": 22, "seek": 58650, "start": 560.58, "end": 586.5, "text": "بتبين Any Linear Transformation من الـ RN إلى ال RM من ال RN إلى ال RM هي على الشكل اللي عندنا دائما او بدا T of X بدي سوى حصل ضرب المصوفة A في المصوفة العمودية X يبقى عندنا أربعة مطاليب بدنا نبدأ نحسب كل مطلوب من هذه المطاليب الأربعة", "tokens": [3555, 2655, 3555, 9957, 2639, 14670, 289, 6531, 8663, 9154, 2423, 39184, 45702, 30731, 2423, 23790, 9154, 2423, 45702, 30731, 2423, 23790, 39896, 15844, 25124, 28820, 13672, 1829, 43242, 8315, 11778, 16373, 15042, 1975, 2407, 4724, 28259, 314, 295, 1783, 4724, 16254, 8608, 2407, 7578, 11331, 9381, 1211, 48812, 25513, 9673, 9381, 38688, 3660, 316, 8978, 9673, 9381, 38688, 3660, 18863, 2304, 23328, 10632, 1783, 7251, 3555, 4587, 7578, 43242, 8315, 5551, 25513, 27884, 3714, 9566, 6027, 1829, 3555, 47525, 8315, 8717, 44510, 10721, 8717, 5016, 35457, 28242, 3714, 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0.45703125}, {"start": 566.78, "end": 567.28, "word": " من", "probability": 0.3671875}, {"start": 567.28, "end": 567.62, "word": " ال", "probability": 0.9345703125}, {"start": 567.62, "end": 568.36, "word": " RN", "probability": 0.94775390625}, {"start": 568.36, "end": 568.8, "word": " إلى", "probability": 0.97216796875}, {"start": 568.8, "end": 569.0, "word": " ال", "probability": 0.96728515625}, {"start": 569.0, "end": 569.7, "word": " RM", "probability": 0.96533203125}, {"start": 569.7, "end": 570.28, "word": " هي", "probability": 0.79052734375}, {"start": 570.28, "end": 570.52, "word": " على", "probability": 0.89453125}, {"start": 570.52, "end": 570.96, "word": " الشكل", "probability": 0.968017578125}, {"start": 570.96, "end": 571.12, "word": " اللي", "probability": 0.85888671875}, {"start": 571.12, "end": 571.48, "word": " عندنا", "probability": 0.8349609375}, {"start": 571.48, "end": 572.24, "word": " دائما", "probability": 0.8857421875}, {"start": 572.24, "end": 572.4, "word": " او", "probability": 0.6529541015625}, {"start": 572.4, "end": 572.72, "word": " بدا", "probability": 0.585693359375}, {"start": 572.72, "end": 573.28, "word": " T", "probability": 0.2476806640625}, {"start": 573.28, "end": 573.6, "word": " of", "probability": 0.5517578125}, {"start": 573.6, "end": 573.82, "word": " X", "probability": 0.9775390625}, {"start": 573.82, "end": 574.1, "word": " بدي", "probability": 0.59814453125}, {"start": 574.1, "end": 574.36, "word": " سوى", "probability": 0.5045572916666666}, {"start": 574.36, "end": 574.78, "word": " حصل", "probability": 0.6507161458333334}, {"start": 574.78, "end": 575.06, "word": " ضرب", "probability": 0.969970703125}, {"start": 575.06, "end": 575.78, "word": " المصوفة", "probability": 0.790435791015625}, {"start": 575.78, "end": 576.04, "word": " A", "probability": 0.49951171875}, {"start": 576.04, "end": 576.56, "word": " في", "probability": 0.81787109375}, {"start": 576.56, "end": 577.6, "word": " المصوفة", "probability": 0.802001953125}, {"start": 577.6, "end": 578.5, "word": " العمودية", "probability": 0.9129638671875}, {"start": 578.5, "end": 579.98, "word": " X", "probability": 0.483154296875}, {"start": 579.98, "end": 580.7, "word": " يبقى", "probability": 0.8916015625}, {"start": 580.7, "end": 581.02, "word": " عندنا", "probability": 0.925537109375}, {"start": 581.02, "end": 581.38, "word": " أربعة", "probability": 0.6278483072916666}, {"start": 581.38, "end": 582.08, "word": " مطاليب", "probability": 0.92529296875}, {"start": 582.08, "end": 582.68, "word": " بدنا", "probability": 0.71923828125}, {"start": 582.68, "end": 583.02, "word": " نبدأ", "probability": 0.9254557291666666}, {"start": 583.02, "end": 583.44, "word": " نحسب", "probability": 0.9923502604166666}, {"start": 583.44, "end": 583.82, "word": " كل", "probability": 0.98291015625}, {"start": 583.82, "end": 584.32, "word": " مطلوب", "probability": 0.927001953125}, {"start": 584.32, "end": 584.5, "word": " من", "probability": 0.978515625}, {"start": 584.5, "end": 584.82, "word": " هذه", "probability": 0.8935546875}, {"start": 584.82, "end": 585.76, "word": " المطاليب", "probability": 0.9755859375}, {"start": 585.76, "end": 586.5, "word": " الأربعة", "probability": 0.95703125}], "temperature": 1.0}, {"id": 23, "seek": 59642, "start": 587.11, "end": 596.43, "text": "بنجي للمطلوب الأول اللي هو بدي أثبت أن T عبارة عن Linear Transformation", "tokens": [3555, 1863, 7435, 1829, 5296, 19528, 9566, 1211, 37746, 16247, 12610, 13672, 1829, 31439, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 314, 6225, 3555, 9640, 3660, 18871, 14670, 289, 6531, 8663], "avg_logprob": -0.27075194753706455, "compression_ratio": 1.0792079207920793, "no_speech_prob": 0.0, "words": [{"start": 587.11, "end": 587.73, "word": "بنجي", "probability": 0.66790771484375}, {"start": 587.73, "end": 588.53, "word": " للمطلوب", "probability": 0.87607421875}, {"start": 588.53, "end": 589.43, "word": " الأول", "probability": 0.895263671875}, {"start": 589.43, "end": 590.21, "word": " اللي", "probability": 0.67431640625}, {"start": 590.21, "end": 590.59, "word": " هو", "probability": 0.982421875}, {"start": 590.59, "end": 591.11, "word": " بدي", "probability": 0.58819580078125}, {"start": 591.11, "end": 591.61, "word": " أثبت", "probability": 0.932373046875}, {"start": 591.61, "end": 591.77, "word": " أن", "probability": 0.436767578125}, {"start": 591.77, "end": 592.09, "word": " T", "probability": 0.6630859375}, {"start": 592.09, "end": 592.57, "word": " عبارة", "probability": 0.9833984375}, {"start": 592.57, "end": 592.71, "word": " عن", "probability": 0.94287109375}, {"start": 592.71, "end": 594.57, "word": " Linear", "probability": 0.6456298828125}, {"start": 594.57, "end": 596.43, "word": " Transformation", "probability": 0.90869140625}], "temperature": 1.0}, {"id": 24, "seek": 62504, "start": 605.42, "end": 625.04, "text": "يبقى بدى اثبت اول شىء ان هاد الـ T Linear Transformation يبقى بدى اخد element من ال set of real numbers الـ scalar يعني و element من ال vector اللي هو main RN و اشوف حصل ضربه معاه وين بدى يوديني يبقى باجي بقول هنا F", "tokens": [1829, 3555, 4587, 7578, 47525, 7578, 1975, 12984, 3555, 2655, 1975, 12610, 13412, 7578, 38207, 16472, 8032, 18513, 2423, 39184, 314, 14670, 289, 6531, 8663, 7251, 3555, 4587, 7578, 47525, 7578, 1975, 9778, 3215, 4478, 9154, 2423, 992, 295, 957, 3547, 2423, 39184, 39684, 37495, 22653, 4032, 4478, 9154, 2423, 8062, 13672, 1829, 31439, 2135, 45702, 4032, 1975, 8592, 38688, 11331, 36520, 48812, 25513, 3224, 20449, 40294, 4032, 9957, 47525, 7578, 7251, 2407, 16254, 22653, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 34105, 479], "avg_logprob": -0.3141163854763426, "compression_ratio": 1.5217391304347827, "no_speech_prob": 0.0, "words": [{"start": 605.42, "end": 605.84, "word": "يبقى", "probability": 0.674102783203125}, {"start": 605.84, "end": 606.08, "word": " بدى", "probability": 0.529052734375}, {"start": 606.08, "end": 606.58, "word": " اثبت", 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"probability": 0.6668701171875}, {"start": 621.96, "end": 622.56, "word": " يوديني", "probability": 0.6719970703125}, {"start": 622.56, "end": 623.34, "word": " يبقى", "probability": 0.921875}, {"start": 623.34, "end": 623.7, "word": " باجي", "probability": 0.8297526041666666}, {"start": 623.7, "end": 624.14, "word": " بقول", "probability": 0.97021484375}, {"start": 624.14, "end": 624.6, "word": " هنا", "probability": 0.97119140625}, {"start": 624.6, "end": 625.04, "word": " F", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 25, "seek": 63626, "start": 626.52, "end": 636.26, "text": "الـ C موجودة في الـ R and على سبيل المثال الـ X موجودة في الـ RN", "tokens": [6027, 39184, 383, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 497, 293, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 2423, 39184, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 45702], "avg_logprob": -0.18409778514216024, "compression_ratio": 1.4583333333333333, "no_speech_prob": 5.960464477539063e-08, "words": 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"word": " موجودة", "probability": 0.9913330078125}, {"start": 635.02, "end": 635.24, "word": " في", "probability": 0.986328125}, {"start": 635.24, "end": 635.6, "word": " الـ", "probability": 0.96337890625}, {"start": 635.6, "end": 636.26, "word": " RN", "probability": 0.283447265625}], "temperature": 1.0}, {"id": 26, "seek": 65676, "start": 638.5, "end": 656.76, "text": "الـ X هذا بقدر اكتبه على شكل X1 و X2 و لغاية XN او بقدر اكتبه على شكل مصفوفة عمودية X1 X2 لغاية XN بالشكل اللي عندنا هنا", "tokens": [6027, 39184, 1783, 23758, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 3224, 15844, 13412, 28820, 1783, 16, 4032, 1783, 17, 4032, 5296, 17082, 995, 10632, 1783, 45, 1975, 2407, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 3224, 15844, 13412, 28820, 3714, 9381, 5172, 38688, 3660, 6225, 2304, 23328, 10632, 1783, 16, 1783, 17, 5296, 17082, 995, 10632, 1783, 45, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105], "avg_logprob": -0.13821231004069834, "compression_ratio": 1.6260162601626016, 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بدنا", "probability": 0.924072265625}, {"start": 1211.14, "end": 1211.5, "word": " نبدأ", "probability": 0.9900716145833334}, {"start": 1211.5, "end": 1212.08, "word": " الحل", "probability": 0.984375}, {"start": 1212.08, "end": 1213.06, "word": " كتالي", "probability": 0.83685302734375}, {"start": 1213.06, "end": 1214.1, "word": " بده", "probability": 0.354248046875}, {"start": 1214.1, "end": 1214.24, "word": " اجي", "probability": 0.7564290364583334}, {"start": 1214.24, "end": 1214.86, "word": " علمين", "probability": 0.6516927083333334}, {"start": 1214.86, "end": 1215.48, "word": " على", "probability": 0.703125}, {"start": 1215.48, "end": 1215.7, "word": " ال", "probability": 0.9609375}, {"start": 1215.7, "end": 1216.34, "word": " RN", "probability": 0.95947265625}, {"start": 1216.34, "end": 1216.7, "word": " و", "probability": 0.9853515625}, {"start": 1216.7, "end": 1217.04, "word": " اروح", "probability": 0.7254231770833334}, {"start": 1217.04, "end": 1217.58, "word": " اخد", "probability": 0.8948567708333334}, {"start": 1217.58, "end": 1217.78, "word": " ال", "probability": 0.98681640625}, {"start": 1217.78, "end": 1218.24, "word": " basis", "probability": 0.479248046875}, {"start": 1218.24, "end": 1219.08, "word": " تبعه", "probability": 0.9033203125}, {"start": 1219.08, "end": 1219.2, "word": " و", "probability": 0.9482421875}, {"start": 1219.2, "end": 1219.76, "word": " نتفهم", "probability": 0.8836669921875}, {"start": 1219.76, "end": 1220.12, "word": " عليه", "probability": 0.97802734375}, {"start": 1220.12, "end": 1220.38, "word": " بعد", "probability": 0.96142578125}, {"start": 1220.38, "end": 1220.7, "word": " هيك", "probability": 0.814208984375}], "temperature": 1.0}, {"id": 52, "seek": 124548, "start": 1221.14, "end": 1245.48, "text": "يبقى هنا بجي بقول له let E1 يبقى يساوي 1 و 0 و 0 و لغاية 0 و E2 يساوي 0 و 1 و 0 لغاية 0 و نظل ماشيين لغاية ما نصل الى EN 001 بالشكل اللي عندنا هنا", "tokens": [1829, 3555, 4587, 7578, 34105, 4724, 7435, 1829, 4724, 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"probability": 0.431640625}, {"start": 1223.68, "end": 1224.84, "word": " E1", "probability": 0.6319580078125}, {"start": 1224.84, "end": 1225.64, "word": " يبقى", "probability": 0.593658447265625}, {"start": 1225.64, "end": 1226.22, "word": " يساوي", "probability": 0.6826171875}, {"start": 1226.22, "end": 1226.7, "word": " 1", "probability": 0.39990234375}, {"start": 1226.7, "end": 1227.06, "word": " و", "probability": 0.59130859375}, {"start": 1227.06, "end": 1227.46, "word": " 0", "probability": 0.63720703125}, {"start": 1227.46, "end": 1227.82, "word": " و", "probability": 0.9208984375}, {"start": 1227.82, "end": 1228.34, "word": " 0", "probability": 0.88330078125}, {"start": 1228.34, "end": 1228.88, "word": " و", "probability": 0.806640625}, {"start": 1228.88, "end": 1229.3, "word": " لغاية", "probability": 0.9239501953125}, {"start": 1229.3, "end": 1229.8, "word": " 0", "probability": 0.71337890625}, {"start": 1229.8, "end": 1230.42, "word": " و", "probability": 0.64404296875}, 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standard bases for RN", "tokens": [1829, 3555, 4587, 7578, 16490, 3215, 2655, 8032, 3215, 12610, 3714, 9957, 8032, 3215, 12610, 2423, 17949, 6055, 3555, 3615, 9307, 3714, 9957, 6055, 3555, 3615, 9307, 18863, 1863, 33546, 2288, 2423, 17949, 6055, 3555, 3615, 9307, 2423, 45702, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 18863, 1863, 33546, 2288, 5296, 2655, 4724, 1829, 264, 3832, 17949, 337, 45702], "avg_logprob": -0.2963541656732559, "compression_ratio": 1.603305785123967, "no_speech_prob": 0.0, "words": [{"start": 1247.42, "end": 1247.76, "word": "يبقى", "probability": 0.67095947265625}, {"start": 1247.76, "end": 1248.28, "word": " خدت", "probability": 0.5442708333333334}, {"start": 1248.28, "end": 1248.58, "word": " هدول", "probability": 0.6773274739583334}, {"start": 1248.58, "end": 1248.98, "word": " مين", "probability": 0.60955810546875}, {"start": 1248.98, "end": 1250.02, "word": " هدول", "probability": 0.81494140625}, {"start": 1250.02, "end": 1250.5, "word": " ال", "probability": 0.97216796875}, {"start": 1250.5, "end": 1250.92, "word": " bases", "probability": 0.56201171875}, {"start": 1250.92, "end": 1251.5, "word": " تبعات", "probability": 0.80413818359375}, {"start": 1251.5, "end": 1251.86, "word": " مين", "probability": 0.785888671875}, {"start": 1251.86, "end": 1253.78, "word": " تبعات", "probability": 0.785675048828125}, {"start": 1253.78, "end": 1254.84, "word": " العناصر", "probability": 0.8365478515625}, {"start": 1254.84, "end": 1255.04, "word": " ال", "probability": 0.97265625}, {"start": 1255.04, "end": 1255.4, "word": " bases", "probability": 0.68701171875}, {"start": 1255.4, "end": 1256.02, "word": " تبعات", "probability": 0.95263671875}, {"start": 1256.02, "end": 1256.22, "word": " ال", "probability": 0.85400390625}, {"start": 1256.22, "end": 1256.88, "word": " RN", "probability": 0.54931640625}, {"start": 1256.88, "end": 1258.28, "word": " يبقى", "probability": 0.9654541015625}, {"start": 1258.28, "end": 1258.76, "word": " هدول", "probability": 0.9871419270833334}, {"start": 1258.76, "end": 1259.66, "word": " العناصر", "probability": 0.9642333984375}, {"start": 1259.66, "end": 1260.02, "word": " لت", "probability": 0.6015625}, {"start": 1260.02, "end": 1261.38, "word": " بي", "probability": 0.89599609375}, {"start": 1261.38, "end": 1263.2, "word": " the", "probability": 0.392822265625}, {"start": 1263.2, "end": 1265.88, "word": " standard", "probability": 0.87841796875}, {"start": 1265.88, "end": 1269.74, "word": " bases", "probability": 0.5107421875}, {"start": 1269.74, "end": 1271.92, "word": " for", "probability": 0.96337890625}, {"start": 1271.92, "end": 1273.78, "word": " RN", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 54, "seek": 130428, "start": 1275.36, "end": 1304.28, "text": "يبقى دول عناصر ال standard basis لمن؟ لل RN كويس بدا أفترض برضه suppose that افترض ان ال T of E1 بده يسوي E1", "tokens": [1829, 3555, 4587, 7578, 11778, 12610, 18871, 33546, 2288, 2423, 3832, 5143, 5296, 27842, 22807, 24976, 45702, 9122, 45865, 3794, 4724, 28259, 5551, 5172, 2655, 43042, 4724, 43042, 3224, 7297, 300, 1975, 5172, 2655, 43042, 16472, 2423, 314, 295, 462, 16, 47525, 3224, 7251, 3794, 45865, 462, 16], "avg_logprob": -0.3788265306122449, "compression_ratio": 1.1594202898550725, "no_speech_prob": 0.0, "words": [{"start": 1275.36, "end": 1275.88, "word": "يبقى", "probability": 0.8428955078125}, {"start": 1275.88, "end": 1276.18, "word": " دول", "probability": 0.5118408203125}, {"start": 1276.18, "end": 1276.96, "word": " عناصر", "probability": 0.8684895833333334}, {"start": 1276.96, "end": 1277.14, "word": " ال", "probability": 0.7333984375}, {"start": 1277.14, "end": 1277.56, "word": " standard", "probability": 0.418212890625}, {"start": 1277.56, "end": 1278.12, "word": " basis", "probability": 0.52978515625}, {"start": 1278.12, "end": 1279.26, "word": " لمن؟", "probability": 0.6370442708333334}, {"start": 1279.26, "end": 1279.6, "word": " لل", "probability": 0.64794921875}, {"start": 1279.6, "end": 1280.76, "word": " RN", "probability": 0.292724609375}, {"start": 1280.76, "end": 1291.02, "word": " كويس", "probability": 0.8924153645833334}, {"start": 1291.02, "end": 1292.1, "word": " بدا", "probability": 0.466796875}, {"start": 1292.1, "end": 1292.9, "word": " أفترض", "probability": 0.7725830078125}, {"start": 1292.9, "end": 1294.98, "word": " برضه", "probability": 0.9415690104166666}, {"start": 1294.98, "end": 1295.64, "word": " suppose", "probability": 0.391845703125}, {"start": 1295.64, "end": 1297.3, "word": " that", "probability": 0.8671875}, {"start": 1297.3, "end": 1299.04, "word": " افترض", "probability": 0.80242919921875}, {"start": 1299.04, "end": 1299.48, "word": " ان", "probability": 0.68603515625}, {"start": 1299.48, "end": 1300.56, "word": " ال", "probability": 0.76953125}, {"start": 1300.56, "end": 1301.02, "word": " T", "probability": 0.82373046875}, {"start": 1301.02, "end": 1301.64, "word": " of", "probability": 0.728515625}, {"start": 1301.64, "end": 1302.66, "word": " E1", "probability": 0.828369140625}, {"start": 1302.66, "end": 1303.3, "word": " بده", "probability": 0.33172607421875}, {"start": 1303.3, "end": 1303.7, "word": " يسوي", "probability": 0.7963053385416666}, {"start": 1303.7, "end": 1304.28, "word": " E1", "probability": 0.758544921875}], "temperature": 1.0}, {"id": 55, "seek": 132613, "start": 1304.81, "end": 1326.13, "text": "و T of E2 هو A2 وانظر لغاية T of EN هو AN خليني أسألكم السؤال التالي ال A1 و ال A2 و ال A3 و ال AN شم هدول؟", "tokens": [2407, 314, 295, 462, 17, 31439, 316, 17, 4032, 7649, 19913, 2288, 5296, 17082, 995, 10632, 314, 295, 15244, 31439, 5252, 16490, 1211, 9957, 1829, 5551, 3794, 10721, 23275, 2304, 21136, 33604, 6027, 16712, 6027, 1829, 2423, 316, 16, 4032, 2423, 316, 17, 4032, 2423, 316, 18, 4032, 2423, 5252, 13412, 2304, 8032, 3215, 12610, 22807], "avg_logprob": -0.3977522055308024, "compression_ratio": 1.3583333333333334, "no_speech_prob": 0.0, "words": [{"start": 1304.81, "end": 1305.17, "word": "و", "probability": 0.36376953125}, {"start": 1305.17, "end": 1305.71, "word": " T", "probability": 0.357177734375}, {"start": 1305.71, "end": 1306.35, "word": " of", "probability": 0.2362060546875}, {"start": 1306.35, "end": 1307.27, "word": " E2", "probability": 0.87890625}, {"start": 1307.27, "end": 1307.89, "word": " هو", "probability": 0.021026611328125}, {"start": 1307.89, "end": 1309.23, "word": " A2", "probability": 0.5302734375}, {"start": 1309.23, "end": 1310.57, "word": " وانظر", "probability": 0.597808837890625}, {"start": 1310.57, "end": 1311.61, "word": " لغاية", "probability": 0.72412109375}, {"start": 1311.61, "end": 1312.15, "word": " T", "probability": 0.5380859375}, {"start": 1312.15, "end": 1312.89, "word": " of", "probability": 0.90625}, {"start": 1312.89, "end": 1313.73, "word": " EN", "probability": 0.546875}, {"start": 1313.73, "end": 1314.59, "word": " هو", "probability": 0.59375}, {"start": 1314.59, "end": 1316.23, "word": " AN", "probability": 0.59033203125}, {"start": 1316.23, "end": 1319.33, "word": " خليني", "probability": 0.72430419921875}, {"start": 1319.33, "end": 1319.79, "word": " أسألكم", "probability": 0.74755859375}, {"start": 1319.79, "end": 1320.19, "word": " السؤال", "probability": 0.9641927083333334}, {"start": 1320.19, "end": 1320.97, "word": " التالي", "probability": 0.97607421875}, {"start": 1320.97, "end": 1322.01, "word": " ال", "probability": 0.55029296875}, {"start": 1322.01, "end": 1322.63, "word": " A1", "probability": 0.90478515625}, {"start": 1322.63, "end": 1322.83, "word": " و", "probability": 0.59228515625}, {"start": 1322.83, "end": 1322.97, "word": " ال", "probability": 0.422607421875}, {"start": 1322.97, "end": 1323.53, "word": " A2", "probability": 0.972412109375}, {"start": 1323.53, "end": 1323.71, "word": " و", "probability": 0.9814453125}, {"start": 1323.71, "end": 1323.81, "word": " ال", "probability": 0.958984375}, {"start": 1323.81, "end": 1324.17, "word": " A3", "probability": 0.98876953125}, {"start": 1324.17, "end": 1324.35, "word": " و", "probability": 0.97705078125}, {"start": 1324.35, "end": 1324.53, "word": " ال", "probability": 0.931640625}, {"start": 1324.53, "end": 1324.89, "word": " AN", "probability": 0.869140625}, {"start": 1324.89, "end": 1325.33, "word": " شم", "probability": 0.4573974609375}, {"start": 1325.33, "end": 1326.13, "word": " هدول؟", "probability": 0.77532958984375}], "temperature": 1.0}, {"id": 56, "seek": 135562, "start": 1327.54, "end": 1355.62, "text": "يعني answer real number والله vector يعني مصفوفة والله ايه شو a1 هذا؟ vector ليش؟ لأن T of E1 E1 موجود في ال R in صورة وين؟ في ال R M يبقى هذا vector و ال vector عليها شكل مصفوفة عمودية فيها M من الصفوف و عمود واحد يبقى هنا where", "tokens": [40228, 22653, 1867, 957, 1230, 16070, 43761, 8062, 37495, 22653, 3714, 9381, 5172, 38688, 3660, 16070, 43761, 1975, 1829, 3224, 13412, 2407, 257, 16, 23758, 22807, 8062, 32239, 8592, 22807, 5296, 33456, 314, 295, 462, 16, 462, 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"end": 1331.54, "word": " يعني", "probability": 0.96044921875}, {"start": 1331.54, "end": 1332.62, "word": " مصفوفة", "probability": 0.9013671875}, {"start": 1332.62, "end": 1333.36, "word": " والله", "probability": 0.82958984375}, {"start": 1333.36, "end": 1333.54, "word": " ايه", "probability": 0.642333984375}, {"start": 1333.54, "end": 1333.8, "word": " شو", "probability": 0.80859375}, {"start": 1333.8, "end": 1334.3, "word": " a1", "probability": 0.564453125}, {"start": 1334.3, "end": 1335.1, "word": " هذا؟", "probability": 0.2930908203125}, {"start": 1335.1, "end": 1336.3, "word": " vector", "probability": 0.77587890625}, {"start": 1336.3, "end": 1337.4, "word": " ليش؟", "probability": 0.8390299479166666}, {"start": 1337.4, "end": 1337.82, "word": " لأن", "probability": 0.796142578125}, {"start": 1337.82, "end": 1338.26, "word": " T", "probability": 0.485107421875}, {"start": 1338.26, "end": 1338.6, "word": " of", "probability": 0.87548828125}, {"start": 1338.6, "end": 1339.06, "word": " E1", "probability": 0.43505859375}, {"start": 1339.06, "end": 1339.58, "word": " E1", "probability": 0.75830078125}, {"start": 1339.58, "end": 1340.06, "word": " موجود", "probability": 0.9855143229166666}, {"start": 1340.06, "end": 1340.22, "word": " في", "probability": 0.935546875}, {"start": 1340.22, "end": 1340.4, "word": " ال", "probability": 0.93212890625}, {"start": 1340.4, "end": 1340.7, "word": " R", "probability": 0.48388671875}, {"start": 1340.7, "end": 1341.08, "word": " in", "probability": 0.1898193359375}, {"start": 1341.08, "end": 1341.54, "word": " صورة", "probability": 0.7373046875}, {"start": 1341.54, "end": 1342.36, "word": " وين؟", "probability": 0.9095052083333334}, {"start": 1342.36, "end": 1342.88, "word": " في", "probability": 0.8603515625}, {"start": 1342.88, "end": 1343.08, "word": " ال", "probability": 0.951171875}, {"start": 1343.08, "end": 1343.5, "word": " R", "probability": 0.9638671875}, {"start": 1343.5, "end": 1344.04, "word": " M", "probability": 0.286376953125}, {"start": 1344.04, "end": 1344.54, "word": " يبقى", "probability": 0.91796875}, {"start": 1344.54, "end": 1344.92, "word": " هذا", "probability": 0.8212890625}, {"start": 1344.92, "end": 1345.38, "word": " vector", "probability": 0.8408203125}, {"start": 1345.38, "end": 1345.58, "word": " و", "probability": 0.46630859375}, {"start": 1345.58, "end": 1345.66, "word": " ال", "probability": 0.437255859375}, {"start": 1345.66, "end": 1345.9, "word": " vector", "probability": 0.98193359375}, {"start": 1345.9, "end": 1346.24, "word": " عليها", "probability": 0.6630859375}, {"start": 1346.24, "end": 1346.52, "word": " شكل", "probability": 0.950927734375}, {"start": 1346.52, "end": 1347.34, "word": " مصفوفة", "probability": 0.98642578125}, {"start": 1347.34, "end": 1348.36, "word": " عمودية", "probability": 0.8841796875}, {"start": 1348.36, "end": 1349.16, "word": " فيها", "probability": 0.95751953125}, {"start": 1349.16, "end": 1349.66, "word": " M", "probability": 0.96533203125}, {"start": 1349.66, "end": 1350.02, "word": " من", "probability": 0.96142578125}, {"start": 1350.02, "end": 1350.94, "word": " الصفوف", "probability": 0.986328125}, {"start": 1350.94, "end": 1351.9, "word": " و", "probability": 0.9775390625}, {"start": 1351.9, "end": 1352.28, "word": " عمود", "probability": 0.8230794270833334}, {"start": 1352.28, "end": 1352.92, "word": " واحد", "probability": 0.90869140625}, {"start": 1352.92, "end": 1353.42, "word": " يبقى", "probability": 0.959716796875}, {"start": 1353.42, "end": 1355.06, "word": " هنا", "probability": 0.8662109375}, {"start": 1355.06, "end": 1355.62, "word": " where", "probability": 0.86328125}], "temperature": 1.0}, {"id": 57, "seek": 137584, "start": 1358.96, "end": 1375.84, "text": "حيث ال A1 و ال A2 و لغاية ال AM RM في one matrices يعني وين موجود كل واحد فيهم؟", "tokens": [5016, 1829, 12984, 2423, 316, 16, 4032, 2423, 316, 17, 4032, 5296, 17082, 995, 10632, 2423, 6475, 23790, 8978, 472, 32284, 37495, 22653, 4032, 9957, 3714, 29245, 23328, 28242, 36764, 24401, 8978, 16095, 22807], "avg_logprob": -0.233482141154153, "compression_ratio": 1.1214953271028036, "no_speech_prob": 0.0, "words": [{"start": 1358.96, "end": 1359.64, "word": "حيث", "probability": 0.81982421875}, {"start": 1359.64, "end": 1360.5, "word": " ال", "probability": 0.54345703125}, {"start": 1360.5, "end": 1361.38, "word": " A1", "probability": 0.6885986328125}, {"start": 1361.38, "end": 1361.86, "word": " و", "probability": 0.50830078125}, {"start": 1361.86, "end": 1362.04, "word": " ال", "probability": 0.33642578125}, {"start": 1362.04, "end": 1362.88, "word": " A2", "probability": 0.98583984375}, {"start": 1362.88, "end": 1363.44, "word": " و", "probability": 0.87646484375}, {"start": 1363.44, "end": 1364.16, "word": " لغاية", "probability": 0.9620361328125}, {"start": 1364.16, "end": 1364.58, "word": " ال", "probability": 0.958984375}, {"start": 1364.58, "end": 1365.54, "word": " AM", "probability": 0.64404296875}, {"start": 1365.54, "end": 1367.66, "word": " RM", "probability": 0.625}, {"start": 1367.66, "end": 1368.96, "word": " في", "probability": 0.89990234375}, {"start": 1368.96, "end": 1369.52, "word": " one", "probability": 0.60546875}, {"start": 1369.52, "end": 1372.3, "word": " matrices", "probability": 0.93798828125}, {"start": 1372.3, "end": 1373.94, "word": " يعني", "probability": 0.915771484375}, {"start": 1373.94, "end": 1374.2, "word": " وين", "probability": 0.491455078125}, {"start": 1374.2, "end": 1374.58, "word": " موجود", "probability": 0.9720052083333334}, {"start": 1374.58, "end": 1374.78, "word": " كل", "probability": 0.9677734375}, {"start": 1374.78, "end": 1375.08, "word": " واحد", "probability": 0.99365234375}, {"start": 1375.08, "end": 1375.84, "word": " فيهم؟", "probability": 0.9363606770833334}], "temperature": 1.0}, {"id": 58, "seek": 139772, "start": 1376.66, "end": 1397.72, "text": "فى ال R M يعني كأنه ايش A1 و A2 مجصدي ال A1 بده يساوي X1 و X2 لغاية 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"word": " هذا", "probability": 0.830078125}, {"start": 3247.46, "end": 3247.6, "word": " ال", "probability": 0.73828125}, {"start": 3247.6, "end": 3247.88, "word": " section", "probability": 0.80419921875}, {"start": 3247.88, "end": 3248.48, "word": " بالذات", "probability": 0.7498372395833334}, {"start": 3248.48, "end": 3249.46, "word": " very", "probability": 0.87158203125}, {"start": 3249.46, "end": 3250.38, "word": " important", "probability": 0.970703125}, {"start": 3250.38, "end": 3250.7, "word": " و", "probability": 0.82373046875}, {"start": 3250.7, "end": 3251.2, "word": " لازم", "probability": 0.9816080729166666}, {"start": 3251.2, "end": 3251.54, "word": " ييجي", "probability": 0.8570556640625}, {"start": 3251.54, "end": 3252.0, "word": " عليه", "probability": 0.98193359375}, {"start": 3252.0, "end": 3252.84, "word": " سؤال", "probability": 0.9921875}, {"start": 3252.84, "end": 3253.0, "word": " في", "probability": 0.7919921875}, {"start": 3253.0, "end": 3253.62, "word": " امتحان", "probability": 0.97958984375}, {"start": 3253.62, "end": 3254.12, "word": " أعمال", "probability": 0.8252766927083334}, {"start": 3254.12, "end": 3254.72, "word": " الفصل", "probability": 0.937255859375}, {"start": 3254.72, "end": 3255.42, "word": " و", "probability": 0.9921875}, {"start": 3255.42, "end": 3255.92, "word": " كذلك", "probability": 0.97412109375}, {"start": 3255.92, "end": 3256.62, "word": " النهاية", "probability": 0.8733723958333334}, {"start": 3256.62, "end": 3256.94, "word": " وضع", "probability": 0.86865234375}, {"start": 3256.94, "end": 3257.32, "word": " طبيعي", "probability": 0.95654296875}, {"start": 3257.32, "end": 3257.72, "word": " لازم", "probability": 0.9938151041666666}, {"start": 3257.72, "end": 3258.04, "word": " يكون", "probability": 0.98583984375}, {"start": 3258.04, "end": 3258.4, "word": " هذا", "probability": 0.3154296875}, {"start": 3258.4, "end": 3259.36, "word": " يعطيكوا", "probability": 0.82021484375}, {"start": 3259.36, "end": 3259.62, "word": " العفو", "probability": 0.695068359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3260.1745, "duration_after_vad": 3072.4337499999897}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOFH4XnuduE.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOFH4XnuduE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7df32e8ebe5e588b0ebfb42cdace2f6f4880c16e
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOFH4XnuduE.srt
@@ -0,0 +1,1360 @@
+1
+00:00:19,490 --> 00:00:24,690
+بسم الله الرحمن الرحيم في حديثنا السابق في ال
+
+2
+00:00:24,690 --> 00:00:28,850
+sections الماضي من خمسة واحد لغاية خمسة خمسة كنا 
+
+3
+00:00:28,850 --> 00:00:33,130
+بنتكلم على ال homogeneous
+
+4
+00:00:33,130 --> 00:00:38,000
+differential equation في خمسة ستة اعطينا مقدمة
+
+5
+00:00:38,000 --> 00:00:41,860
+بسيطة أنه أنا لو بده اجيب حل ال non homogeneous
+
+6
+00:00:41,860 --> 00:00:46,540
+equation  star هذا بده اقسم المسألة الى جزئين ال
+
+7
+00:00:46,540 --> 00:00:49,540
+homogeneous و ال non homogeneous ال homogeneous
+
+8
+00:00:49,540 --> 00:00:53,320
+بحلها زي ما كنت حل في ال sections الماضية و بده
+
+9
+00:00:53,320 --> 00:00:57,340
+اسميه ال complementary solution الحل المتمم وبديله
+
+10
+00:00:57,340 --> 00:01:01,840
+رمز Y<sub>c</sub> بعد هيك هو يقول لو عندي particular solution
+
+11
+00:01:01,840 --> 00:01:07,400
+حل خاص للمعادلة هذه a star باجمع الحلين تبع ال
+
+12
+00:01:07,400 --> 00:01:10,400
+homogeneous وال non homogeneous بيعطيني حل محترم
+
+13
+00:01:10,400 --> 00:01:14,640
+لمين؟ للمعادلة اللي هي رقم a star يبقى هذه اللي
+
+14
+00:01:14,640 --> 00:01:20,860
+قلناها في المرة الماضية الآن بدي انتقل الى هذا ال
+
+15
+00:01:20,860 --> 00:01:24,540
+section وهو طريقة ال undetermined coefficients
+
+16
+00:01:24,540 --> 00:01:28,400
+المعادلات اللي من هذا القبيل يا بنات إنّهـا ثلاث طرق
+
+17
+00:01:28,400 --> 00:01:32,240
+للحل الطريقة الأولى ال undetermined coefficients
+
+18
+00:01:32,240 --> 00:01:36,940
+الطريقة الثانية ال variation of parameters الطريقة
+
+19
+00:01:36,940 --> 00:01:40,400
+الثالثة ال reduction of order والتلت طرق سنأخذهم
+
+20
+00:01:40,400 --> 00:01:44,040
+في هذا ال section وال section الذي يليه له خمسة 
+
+21
+00:01:44,040 --> 00:01:48,780
+ثمانية إن شاء الله تبارك وتعالى اليوم فقط هناخد ال
+
+22
+00:01:48,780 --> 00:01:51,760
+undetermined coefficients كل المعلومات النظرية 
+
+23
+00:01:51,760 --> 00:01:54,200
+اللي بنبنيها من هذا ال section هي قدامك على اللوح
+
+24
+00:01:54,200 --> 00:01:59,440
+ولم يبقى إلا مجموعة من الأمثلة طيب نيجي للطريقة 
+
+25
+00:01:59,440 --> 00:02:02,780
+هذه بيقولي هذه المعادلة الأصلية اللي هي non
+
+26
+00:02:02,780 --> 00:02:07,600
+homogeneous المعاملات دول يا بنات كلهم ثوابت تمام؟ 
+
+27
+00:02:07,710 --> 00:02:12,210
+هذه المعادلة سأقوم بتقسيمها لـ homogeneous و non
+
+28
+00:02:12,210 --> 00:02:15,830
+homogeneous سأقوم بتقسيم الـ homogeneous بالأول اللي هي 
+
+29
+00:02:15,830 --> 00:02:20,510
+المعادلة اللي عندنا هذه بدون f(x) لو كانت تساوي
+
+30
+00:02:20,510 --> 00:02:24,750
+زيرو يبقى الحل تبعها هيكون على الشكل اللي احنا كنا
+
+31
+00:02:24,750 --> 00:02:28,770
+بنطلعه في ال sections الماضية سواء كان ال complex
+
+32
+00:02:28,770 --> 00:02:34,130
+roots or repeated roots ال roots are all different 
+
+33
+00:02:34,130 --> 00:02:37,090
+يبقى بالطرق التلاتة السابقة اللي كنا بنعملها
+
+34
+00:02:37,090 --> 00:02:41,630
+وقلعنا هذا الحل تمام؟ الآن بدأ افترض ان هذا الحل 
+
+35
+00:02:41,630 --> 00:02:45,630
+هو لـ هذه المعادلة نفرض Y تساوي e<sup>ax</sup> ونجيب ال
+
+36
+00:02:45,630 --> 00:02:50,050
+characteristic equation ونجيبها ونذهب للحل هنا ونجيبها خلصنا 
+
+37
+00:02:50,050 --> 00:02:54,530
+حل ال homogeneous بدي اجي للحل الخاص تبع ال non
+
+38
+00:02:54,530 --> 00:02:57,670
+homogeneous اللي إنّهـا دي فباجي بقول we use the
+
+39
+00:02:57,670 --> 00:03:01,030
+method of undetermined coefficients بدنا نستخدم
+
+40
+00:03:01,030 --> 00:03:05,870
+طريقة المعاملات المجهولة والحين هنقول لك لسه منها
+
+41
+00:03:05,870 --> 00:03:12,140
+معادلات مجهولة عن طريق البحث عن حل لإيجاد
+
+42
+00:03:12,140 --> 00:03:16,420
+حل خاص لـ non homogeneous differential equation من
+
+43
+00:03:16,420 --> 00:03:20,540
+ال start اللي فوق اللي هي ال non homogenous احنا
+
+44
+00:03:20,540 --> 00:03:24,100
+هذا جبنا له ال homogeneous بدنا ال non homogeneous
+
+45
+00:03:24,100 --> 00:03:29,560
+يعطيه رمز Y<sub>p</sub> كيف بنجيبه؟ بنستخدم طريقة ال
+
+46
+00:03:29,560 --> 00:03:33,060
+undetermined coefficients إذا تحقق في المعادلة
+
+47
+00:03:33,060 --> 00:03:38,040
+أمران ما هما الأمران هذه؟ الأمر الأول ذكرناه إنّ
+
+48
+00:03:38,040 --> 00:03:43,480
+المعاملات هذول كلهم ثوابت الأمر الثاني يجب أن يكون 
+
+49
+00:03:43,480 --> 00:03:49,420
+الـ f(x) على شكل معين ما هو هذا الشكل المعين اللي 
+
+50
+00:03:49,420 --> 00:03:53,700
+لو تحقق في ال f(x) بقدر استخدم ال undetermined
+
+51
+00:03:53,700 --> 00:04:00,550
+coefficients دون غيرها بقول بسيطة جدا لو جيت على 
+
+52
+00:04:00,550 --> 00:04:05,690
+الـ f(x) لاجيتها polynomial بدي اكتب شكل ال
+
+53
+00:04:05,690 --> 00:04:09,690
+particular solution على polynomial زيها من نفس
+
+54
+00:04:09,690 --> 00:04:15,050
+الدرجة بس المعاملات مش هم يبقى هذول هم ال
+
+55
+00:04:15,050 --> 00:04:19,450
+undetermined coefficients تبعت طريقتنا هذه مضروبة
+
+56
+00:04:19,450 --> 00:04:23,830
+كلها في x<sup>s</sup> مين ال x<sup>s</sup>
+
+57
+00:04:23,830 --> 00:04:29,250
+هذا ما سنجيب عليه بعد قليل يبقى خليكوا صحين معانا
+
+58
+00:04:29,250 --> 00:04:34,890
+لأن هذا very important مين هي ال x<sup>s</sup> هذا very
+
+59
+00:04:34,890 --> 00:04:41,680
+important وهي عمود في قريف الحل والإجابة لو كانت ال
+
+60
+00:04:41,680 --> 00:04:45,460
+f(x) هذه على شكل polynomial في exponential 
+
+61
+00:04:45,460 --> 00:04:49,620
+polynomial من الدرجة النونية في exponential إذا
+
+62
+00:04:49,620 --> 00:04:53,620
+شكل الحل الخاص بدي يكون x<sup>s</sup> 
+
+63
+00:04:53,620 --> 00:04:57,460
+polynomial من الدرجة النونية زي ال polynomial هذه
+
+64
+00:04:57,460 --> 00:05:02,380
+بالضبط في نفس ال exponential اللي عندي طيب الحالة
+
+65
+00:05:02,380 --> 00:05:07,300
+التالتة و الأخيرة لو كانت ال f(x) اللي عندي
+
+66
+00:05:07,900 --> 00:05:15,700
+polynomial في exponential في cos bx أو sin
+
+67
+00:05:15,700 --> 00:05:24,620
+bx أو مجموعهما أو الفرق فيما بينهما يبقى عندي
+
+68
+00:05:24,620 --> 00:05:30,930
+polynomial في exponential في ال cos bx أو ال
+
+69
+00:05:30,930 --> 00:05:35,510
+polynomial في ال exponential في ال sin bx أو ال
+
+70
+00:05:35,510 --> 00:05:39,290
+polynomial في ال exponential في ال cos bx زي
+
+71
+00:05:39,290 --> 00:05:45,010
+ال sin bx الحالات هذول كلهم ذكرتهم لهم نفس ال
+
+72
+00:05:45,010 --> 00:05:48,390
+particular solution شو ال particular solution بحط 
+
+73
+00:05:48,390 --> 00:05:52,260
+ال x<sup>s</sup> كما في الحالتين السابقتين بعد
+
+74
+00:05:52,260 --> 00:05:55,740
+ذلك بكتب polynomial من الدرجة النونية في cos
+
+75
+00:05:55,740 --> 00:06:00,620
+bx زائد polynomial أخرى من الدرجة النونية في sin
+
+76
+00:06:00,620 --> 00:06:04,340
+bx وكله بضربه في مين؟ في ال exponential اللي
+
+77
+00:06:04,340 --> 00:06:10,080
+عندنا خلصنا؟ خلصنا يبقى من حد ما جاهل بده أطلع على
+
+78
+00:06:10,080 --> 00:06:13,840
+الشكل لفه فيك مش هان أشوف هل بنفعل هال polynomial
+
+79
+00:06:13,840 --> 00:06:18,800
+هل بنفعل هال undetermined coefficients أم لا تمام
+
+80
+00:06:18,800 --> 00:06:24,010
+بعد ما عرفت إنّهـ معاملات ثوابت باجي بتطلّع هذا ال f
+
+81
+00:06:24,010 --> 00:06:28,030
+(x) polynomial يبقى شكل ال particular solution 
+
+82
+00:06:28,030 --> 00:06:32,070
+polynomial في x<sup>s</sup> من نفس الدرجة إذا والله 
+
+83
+00:06:32,070 --> 00:06:34,610
+polynomial في exponential يبقى كمان 
+
+84
+00:06:34,610 --> 00:06:38,150
+polynomial في exponential في x<sup>s</sup> إذا
+
+85
+00:06:38,150 --> 00:06:41,190
+polynomial في exponential في sin أو cos أو 
+
+86
+00:06:41,190 --> 00:06:44,730
+مجموحمة أو الفرق فيما بينهما يبقى x<sup>s</sup> 
+
+87
+00:06:44,730 --> 00:06:47,950
+polynomial في ال cos زائد polynomial من نفس
+
+88
+00:06:47,950 --> 00:06:50,990
+الدرجة في ال sin وكله مضروب في مين؟ في ال
+
+89
+00:06:50,990 --> 00:06:54,980
+exponential نيجي لقصة ال x<sup>s</sup> الشي هذه
+
+90
+00:06:54,980 --> 00:07:00,360
+شايفين هذا الحل يا بنات ال complementary solution 
+
+91
+00:07:00,360 --> 00:07:05,670
+هذا لو حل ال homogeneous من حد ما اتطلع له بتحط ليه في
+
+92
+00:07:05,670 --> 00:07:11,330
+برواز وهنجي نرجع له ايش نرجع له؟ انا كتبت شكل ال 
+
+93
+00:07:11,330 --> 00:07:15,570
+particular solution وغطيت هنا كأنّهـا مش موجودة و
+
+94
+00:07:15,570 --> 00:07:22,210
+جيت طلعت في الحل هل أي جزء هنا يشبه أي جزء هنا ولا
+
+95
+00:07:22,210 --> 00:07:28,150
+لا إذا فيش تشابه يبقى S = 0 يبقى بيصير x<sup>0</sup> 
+
+96
+00:07:28,150 --> 00:07:32,550
+بقداش؟ يبقى اللي كتبته هو وبلا x<sup>s</sup> 
+
+97
+00:07:32,550 --> 00:07:40,970
+إذا في term واحد يشابه أي term من هذول بحط S = 1
+
+98
+00:07:40,970 --> 00:07:47,230
+بيصير هذه مضروبة كلها في x باجي بطلع بعد هيك اختلف
+
+99
+00:07:47,230 --> 00:07:52,820
+كل term عن ال term هنا يبقى شغلي تمام 100% خلصت إذا 
+
+100
+00:07:52,820 --> 00:07:58,060
+لاجيت لا يزال أي term من ال particular solution 
+
+101
+00:07:58,060 --> 00:08:03,800
+يشبه أي term من ال complementary solution بحط S =
+
+102
+00:08:03,800 --> 00:08:08,540
+2 يعني إذا واحد ما جابتش النتيجة بحط ب 2 تمام؟ و
+
+103
+00:08:08,540 --> 00:08:13,460
+باجي بضرب فيها بيصير عندي x<sup>2</sup> مضروبة في الجثة و
+
+104
+00:08:13,460 --> 00:08:17,730
+x<sup>2</sup> في الجثة و x<sup>2</sup> في الجثة و باجي بطلع هل
+
+105
+00:08:17,730 --> 00:08:22,170
+أي term من هنا يشبه أي term إذا مافيش شبه خلاص
+
+106
+00:08:22,170 --> 00:08:27,450
+يبقى ال S بقداش؟ ب 2، في شبه بحط ال S ب 3 و
+
+107
+00:08:27,450 --> 00:08:32,130
+هكذا واضحة الصورة اللي هنا؟ يبقاش بقول here ال S
+
+108
+00:08:32,130 --> 00:08:35,510
+ممكن تأخذ 0 وممكن 1 وممكن 2 وممكن 
+
+109
+00:08:35,510 --> 00:08:38,550
+3 وممكن إلى ما شاء الله حصل طبيعة المعادلة 
+
+110
+00:08:38,940 --> 00:08:45,180
+بحيث no term of the solution y<sub>p</sub> وليه جزء في الحل
+
+111
+00:08:45,180 --> 00:08:51,040
+y<sub>p</sub> اللي طلعنا هذا is a term in the solution y<sub>c</sub> هو
+
+112
+00:08:51,040 --> 00:08:55,240
+عبارة عن term موجود هنا فيش وبحيث ما يكونش عندي
+
+113
+00:08:55,240 --> 00:09:01,040
+term بالمعنى وبالتالي لما بأجيخ بخلصك بجمع ال y<sub>p</sub>
+
+114
+00:09:01,040 --> 00:09:05,580
+مع ال y<sub>c</sub> بيعطيني ال general solution تبع المعادلة
+
+115
+00:09:05,580 --> 00:09:12,050
+star أظن واضحة الصورة؟ ها بدنا نطبقها على أرض
+
+116
+00:09:12,050 --> 00:09:16,970
+الواقع يبقى جاب اللاب توب يبدأ تطلع لشغل تيم هل
+
+117
+00:09:16,970 --> 00:09:22,110
+المعادلة معاملتها ثوابت ولا لا؟ اثنين هل ال f(x)
+
+118
+00:09:22,110 --> 00:09:25,870
+على أي شكل من الأشكال اللي عندي هذول ولا لا؟ إذا
+
+119
+00:09:25,870 --> 00:09:29,210
+والله تحقق الشرطان automatic بروح ال undetermined
+
+120
+00:09:29,210 --> 00:09:32,790
+coefficients ما تحقق يبقى روح دور على ال variation 
+
+121
+00:09:32,790 --> 00:09:35,690
+of parameters أو ال reduction of order أو ما إلى
+
+122
+00:09:35,690 --> 00:09:39,860
+ذلك بناخد أمثلة بقول هات لي ال general solution
+
+123
+00:09:39,860 --> 00:09:44,040
+للمعادلة اللي قدامي بقوله كويس يبقى أنا بدي أبدأ
+
+124
+00:09:44,040 --> 00:09:47,860
+بمين؟ بال homogeneous differential equation يبقى 
+
+125
+00:09:47,860 --> 00:09:55,040
+الحل كتير بدي أقوله let y = e<sup>rx</sup> be a
+
+126
+00:09:55,040 --> 00:10:05,800
+solution of the homogeneous differential equation
+
+127
+00:10:06,110 --> 00:10:12,970
+equation للمعادلة y'' + 3y
+
+128
+00:10:12,970 --> 00:10:20,990
+' + 2y = 0 then
+
+129
+00:10:20,990 --> 00:10:25,710
+the characteristic 
+
+130
+00:10:27,280 --> 00:10:35,640
+equation is r<sup>2</sup> + 3r + 2 =
+
+131
+00:10:35,640 --> 00:10:41,900
+0 بدي احل المعادلة هذه يبقى هذه r + 1 في 
+
+132
+00:10:41,900 --> 00:10:49,560
+r + 2 = 0 ومنها r<sub>1</sub> = -1
+
+133
+00:10:49,560 --> 00:10:55,040
+و r<sub>2</sub> = -2 يبقى بناء عليه أصبح ال
+
+134
+00:10:55,040 --> 00:11:01,760
+complementary solution y<sub>c</sub> = c<sub>1</sub>e<sup>-x</sup> 
+
+135
+00:11:01,760 --> 00:11:09,040
++ c<sub>2</sub>e<sup>-2x</sup> وببرزه وبروحه بخليه
+
+136
+00:11:09,560 --> 00:11:16,760
+خلصنا ال homogeneous بدنا نروح ندور على ال
+
+137
+00:11:16,760 --> 00:11:21,000
+particular solution تبع ال non homogeneous 
+
+138
+00:11:21,000 --> 00:11:25,940
+differential equation مشان هيك بدي اروح افحص الشرطين
+
+139
+00:11:25,940 --> 00:11:29,940
+اللي عندنا بجيب اطلع على المعادلة اللي عندي هذه
+
+140
+00:11:31,200 --> 00:11:36,060
+فالعولي هنا المعاملات كلهم ثوابت يبقى تحقق الشرط
+
+141
+00:11:36,060 --> 00:11:40,940
+الأول هنا ال f(x) = 36xe<sup>6x</sup> يبقى 
+
+142
+00:11:40,940 --> 00:11:45,420
+polynomial من الدرجة الأولى مضروبة في ال
+
+143
+00:11:45,420 --> 00:11:49,200
+exponential اللي هو e<sup>6x</sup> الحالة الثانية اللي عندنا
+
+144
+00:11:49,200 --> 00:11:58,800
+إذا باجي بقوله the particular solution
+
+145
+00:12:00,390 --> 00:12:11,590
+of the differential equation is in the form على
+
+146
+00:12:11,590 --> 00:12:19,620
+الشكل التالي y<sub>p</sub> = x<sup>s</sup> الآن بدي 
+
+147
+00:12:19,620 --> 00:12:22,680
+اجي لل polynomial ال polynomial عندي من مين؟ من
+
+148
+00:12:22,680 --> 00:12:30,100
+الدرجة الأولى يبقى باجي بقوله a<sub>0</sub>x + a<sub>1</sub> في 
+
+149
+00:12:30,100 --> 00:12:36,240
+e<sup>-2x</sup> مظبوط؟ e<sup>-2x</sup> بالشكل اللي عندنا
+
+150
+00:12:36,240 --> 00:12:43,360
+وباجي بقول استنى شوية الآن بدي أشوف قد ايش قيمة S 
+
+151
+00:12:43,360 --> 00:12:48,560
+تمام؟ هذول لما غطي هذا من هنا كم term بيكونوا؟ 
+
+152
+00:12:50,830 --> 00:12:59,390
+هل a<sub>1</sub>e<sup>-2x</sup> لها term شبيه في y<sub>c</sub> ولا لا؟ وهل a<sub>0</sub>x في 
+
+153
+00:12:59,390 --> 00:13:03,590
+e<sup>-2x</sup> لها term شبيه في y<sub>c</sub> ولا لا؟
+
+154
+00:13:06,660 --> 00:13:13,920
+اي والسالب x هذه مفيش زيها هذي c<sub>2</sub>e<sup>-2x</sup> وهذه
+
+155
+00:13:13,920 --> 00:13:19,760
+constant في e<sup>-2x</sup> هذه مع هذه مافيش تشابه
+
+156
+00:13:19,760 --> 00:13:25,020
+تمام؟ إذا التشابه constant في مين؟ في e<sup>-2x</sup>
+
+157
+00:13:25,020 --> 00:13:30,940
+إذا من شان أشيل هذا التشابه بحط S بقد ايش؟ لو حطيت S
+
+158
+00:13:30,940 --> 00:13:36,160
+ب 1 بيصير
+
+159
+00:13:36,160 --> 00:13:39,880
+عندي x<sup>2</sup> ما عنديش x<sup>2</sup> في ال exponential
+
+160
+00:13:39,880 --> 00:13:46,580
+بيصير عندي x في a<sub>1</sub> في ال exponential فيه زيها يبقى
+
+161
+00:13:46,580 --> 00:13:52,040
+ما عنديش إلا S بقد ايش؟ فقط لا غير يبقى باجي بقوله 
+
+162
+00:13:52,040 --> 00:13:58,610
+here ال S = 1 اللي بتغلق في هذه البنات
+
+163
+00:13:58,610 --> 00:14:03,310
+بيكون ضايع المسألة لأن هذا عمود فقري عندي في 
+
+164
+00:14:03,310 --> 00:14:10,470
+المسألة إذا بناء عليه بدي يصير ال y<sub>p</sub> كتالي x في a
+
+165
+00:14:10,470 --> 00:14:17,440
+<sub>0</sub>x + a<sub>1</sub>x في e<sup>-2x</sup> يعني كأنه بدي
+
+166
+00:14:17,440 --> 00:14:24,620
+يصير a<sub>0</sub>x<sup>2</sup> + a<sub>1</sub>x في e<sup>-2x</sup> 
+
+167
+00:14:35,120 --> 00:14:44,100
+أنا مش سارق واحد x أنا مش سارق واحد x أنا مش
+
+168
+00:14:44,100 --> 00:14:50,480
+سارق واحد x أنا مش سارق واحد x هذه يا بنات هي e
+
+169
+00:14:50,480 --> 00:14:56,780
+<sup>6x</sup> وليس e<sup>-2x</sup> يعني أنا بطلع للي عندنا هذه
+
+170
+00:14:56,780 --> 00:15:01,960
+طبعا polynomial فيه 6 إذا بناء على كل الكلام اللي
+
+171
+00:15:01,960 --> 00:15:06,960
+قلته هذا ماله؟ ماهو صح يبقى ماهو الصحيح إنّهـ S
+
+172
+00:15:06,960 --> 00:15:12,200
+بقد ايش؟ بصفر لأن مفيش e<sup>6x</sup> عندي بالمرة طبعا يبقى
+
+173
+00:15:12,200 --> 00:15:18,390
+باجي بقوله here ال S = 0 يبقى بناء عليه أصبح 
+
+174
+00:15:18,390 --> 00:15:27,850
+y<sub>p</sub> بدي أساوي a<sub>0</sub>x + a<sub>1</sub> في ال e<sup>6x</sup> هل 
+
+175
+00:15:27,850 --> 00:15:32,690
+احنا جبنا شكل ال particle solution؟ مجهولين بدي 
+
+176
+00:15:32,690 --> 00:15:37,410
+أعرفهم هذول هم ال undetermined coefficients a<sub>0</sub> 
+
+177
+00:15:37,410 --> 00:15:43,59
+
+201
+00:18:18,970 --> 00:18:26,570
+بصير عندي اتنين A node زائد A node X زائد الـ A1
+
+202
+00:18:26,570 --> 00:18:35,010
+زائد تلاتة A node زائد تلاتة A node X زائد تلاتة 
+
+203
+00:18:35,010 --> 00:18:43,610
+A1 زائد اتنين A node X زائد اتنين أو اتنين أو اتنين
+
+204
+00:18:43,610 --> 00:18:44,950
+أو اتنين أو اتنين أو اتنين أو اتنين أو اتنين أو
+
+205
+00:18:44,950 --> 00:18:47,610
+اتنين أو اتنين أو اتنين أو اتنين أو اتنين أو اتنين
+
+206
+00:18:47,610 --> 00:18:51,090
+أو اتنين أو اتنين أو اتنين أو اتنين أو اتنين أو
+
+207
+00:18:51,090 --> 00:18:53,370
+اتنين أو اتنين أو اتنين أو اتنين أو اتنين أو اتنين
+
+208
+00:18:53,370 --> 00:18:54,090
+أو اتنين أو اتنين أو اتنين أو اتنين أو اتنين أو
+
+209
+00:18:54,090 --> 00:18:54,870
+اتنين أو اتنين أو اتنين أو اتنين أو اتنين أو اتنين
+
+210
+00:18:54,870 --> 00:19:02,180
+أو اتنين، هذه المعادلة فيها X وهذه المعادلة فيها X
+
+211
+00:19:02,180 --> 00:19:06,560
+إيش غير و سالب؟ ما عنديش بالمرة في المعادلة، مش مشكلة.
+
+212
+00:19:06,560 --> 00:19:12,160
+يبقى عندي هنا يا بنات كده إيش A node X و تلاتة A node X
+
+213
+00:19:12,160 --> 00:19:19,060
+يبقى أربعة A node X و اتنين A node X يبقى ستة A 
+
+214
+00:19:19,060 --> 00:19:26,670
+node X، الآن عندنا مين؟ عندنا اتنين a نوت و اتنين a 
+
+215
+00:19:26,670 --> 00:19:33,230
+one و تلاتة a note و تلاتة a one و اتنين a one، نجي 
+
+216
+00:19:33,230 --> 00:19:38,890
+نجمع، عندنا تلاتة a note و اتنين a note يبقى خمسة a
+
+217
+00:19:38,890 --> 00:19:45,000
+note، نجمع A1 و A1 و A1 و A1 و A1 و A1 و A1 و A1 و
+
+218
+00:19:45,000 --> 00:19:57,620
+A1 و A1 و A1 و A1 و A1 و A1 و A1 و A1 و A1 و A1
+
+219
+00:19:58,110 --> 00:20:02,270
+الآن بعد ما وصلنا هكذا، بروح بقارن المعاملات في 
+
+220
+00:20:02,270 --> 00:20:06,710
+الطرفين، إذا لو روحنا قارننا المعاملات في الطرفين
+
+221
+00:20:06,710 --> 00:20:14,790
+بصير 6A نود بده يساوي 36، يبقى A نود يبقى 6 يا بنات
+
+222
+00:20:15,660 --> 00:20:23,420
+بستة تمام، and المعادلة الثانية خمسة a node زائد
+
+223
+00:20:23,420 --> 00:20:28,780
+ستة a one بده يساوي قداش؟ zero، هالحين a node عندي
+
+224
+00:20:28,780 --> 00:20:37,400
+بستة يبقى بصير عندي هنا بصير خمسة في ستة زائد اللي 
+
+225
+00:20:37,400 --> 00:20:46,210
+هو ستة a one بده يساوي zero، خمسة في ستة سالب تلاتين
+
+226
+00:20:46,210 --> 00:20:55,650
+على ستة، بصير الـ A1 سالب خمسة، يبقى بناء عليه أصبح
+
+227
+00:20:55,650 --> 00:21:01,990
+الـ particular solution YP يساوي، هذا شكل الـ
+
+228
+00:21:01,990 --> 00:21:06,510
+particular solution، هشيل الـ A node و احط مكانها 
+
+229
+00:21:06,510 --> 00:21:15,050
+ستة يبقى هي 6 X ناقص خمسة، كله في من؟ في الـ E<sup>-6</sup>
+
+230
+00:21:15,050 --> 00:21:21,070
+بدنا شكل الـ general solution، يبقى باجي بقوله شكل 
+
+231
+00:21:21,070 --> 00:21:25,950
+الـ general solution على الشكل التالي ده
+
+232
+00:21:40,470 --> 00:21:43,270
+general solution
+
+233
+00:21:46,420 --> 00:21:56,140
+Y تساوي YC زائد YP، يبقى Y تساوي، نجي YC، وين YC هيو؟
+
+234
+00:21:56,140 --> 00:22:07,700
+يبقى C1 E<sup>-X</sup> زائد C2 E<sup>-2X</sup> زائد الحل اللي طلعناه YP
+
+235
+00:22:07,700 --> 00:22:16,910
+زائد 6X-5 كله في E<sup>-X</sup>، يبقى هذا الجنرال سوليوشين للامام 
+
+236
+00:22:16,910 --> 00:22:23,510
+للمعادلة التفاضلية اللي عندنا، نجي ناخد مثال ثاني
+
+237
+00:22:23,510 --> 00:22:27,490
+example
+
+238
+00:22:27,490 --> 00:22:32,190
+two solve
+
+239
+00:22:32,190 --> 00:22:39,930
+the differential equation
+
+240
+00:22:39,930 --> 00:22:46,550
+حل المعادلة التفاضلية، أصل الـ initial value problem
+
+241
+00:22:46,550 --> 00:23:01,850
+يبقى الـ initial value problem، يبقى
+
+242
+00:23:01,850 --> 00:23:02,790
+الـ initial value problem، يبقى الـ initial value
+
+243
+00:23:02,790 --> 00:23:04,550
+problem، يبقى الـ initial value problem، يبقى الـ
+
+244
+00:23:04,550 --> 00:23:04,590
+initial value problem، يبقى الـ initial value
+
+245
+00:23:04,590 --> 00:23:04,730
+initial value problem، يبقى الـ initial value
+
+246
+00:23:04,730 --> 00:23:08,010
+initial value problem، يبقى الـ initial value
+
+247
+00:23:08,010 --> 00:23:09,990
+problem، يبقى الـ initial value problem، يبقى الـ
+
+248
+00:23:09,990 --> 00:23:10,550
+initial value problem، يبقى الـ initial value
+
+249
+00:23:10,550 --> 00:23:15,400
+problem، يو الـ y عند الـ zero بده يساوي سالب واحد و
+
+250
+00:23:15,400 --> 00:23:21,400
+الـ y prime عند الـ zero بده يساوي واحد، و هذا يسميها
+
+251
+00:23:21,400 --> 00:23:24,140
+لهمين المعادلة star
+
+252
+00:23:46,020 --> 00:23:55,040
+هذا خلصنا منه، نرجع
+
+253
+00:23:55,040 --> 00:23:56,220
+لسؤال مرة ثانية
+
+254
+00:24:01,960 --> 00:24:08,220
+بنقول بسيطة، يبقى احنا بدنا نيجي للحل على الشكل 
+
+255
+00:24:08,220 --> 00:24:14,900
+التالي، بدنا ناخد الـ homogeneous ونفرض اللي حل يبقى 
+
+256
+00:24:14,900 --> 00:24:23,600
+let Y تساوي E<sup>RX</sup> بيه solution of the
+
+257
+00:24:23,920 --> 00:24:29,780
+Differential equation اللى ع الشكل التالي زى prime 
+
+258
+00:24:29,780 --> 00:24:33,700
+ناقص اتنين Y يساوي زيرو، اللي هي الـ homogeneous
+
+259
+00:24:33,700 --> 00:24:38,200
+بعد هيك باجي بقوله the characteristic 
+
+260
+00:24:41,660 --> 00:24:49,880
+Equation is R تربيع زائد الـ R ناقص اتنين يساوي
+
+261
+00:24:49,880 --> 00:24:55,460
+زيرو، هذه لو جيت حللتها، بحللها إلى قوسين كله بده
+
+262
+00:24:55,460 --> 00:25:01,180
+يساوي زيرو، يبقى هنا R وهنا R، هنا واحد هنا اتنين 
+
+263
+00:25:01,180 --> 00:25:07,570
+هنا زائد ناقص، يبقى بالنسبة عليه صارت الـ R تساوي
+
+264
+00:25:07,570 --> 00:25:13,890
+واحد والـ R تساوي سالب اتنين، يبقى بالنسبة عليه بجيب
+
+265
+00:25:13,890 --> 00:25:21,190
+حل المعادلة المتجانسة وبسميه YC، يبقى C واحد E<sup>0S X</sup> 
+
+266
+00:25:21,190 --> 00:25:27,310
+زائد C اتنين E<sup>OS ناقص اتنين X</sup>، الشكل اللي عندنا هذا
+
+267
+00:25:28,160 --> 00:25:32,960
+الآن بروح ادور على شكل الـ particular solution، باجي 
+
+268
+00:25:32,960 --> 00:25:37,920
+بطلع في المعادلة اللي عندي الشرط اللي هو المتحقق
+
+269
+00:25:37,920 --> 00:25:44,680
+كله ثوابت، الشرط الثاني two exponential تنتين
+
+270
+00:25:44,680 --> 00:25:50,160
+مختلفات عن بعض تماماً، إذا سأذهب لحفظ المعادلة التي 
+
+271
+00:25:50,160 --> 00:25:54,460
+لدي إلى معادلتين، يعني بدل ما كنت أريد حل مثلاً أريد
+
+272
+00:25:54,460 --> 00:25:59,480
+حل مان تنتين معاكم، المرة التي فاتت أخر نقطة في 
+
+273
+00:25:59,480 --> 00:26:04,580
+محاضرة المرة الماضية قلنا لو L of Y يساوي F of X و
+
+274
+00:26:04,580 --> 00:26:08,900
+L of Y يساوي G of X هذه لـ particular solution وهذه 
+
+275
+00:26:08,900 --> 00:26:11,240
+لـ particular solution، يبقى الـ particular solution
+
+276
+00:26:11,240 --> 00:26:15,440
+للمعادلة الأصلية هو مجموع للاثنين تمام، يبقى الآن 
+
+277
+00:26:15,440 --> 00:26:21,830
+بدنا نذهب نستخدمه، يبقى باجي بقوله the differential
+
+278
+00:26:21,830 --> 00:26:30,910
+equation a star is written as، بروح بكتب على الشكل 
+
+279
+00:26:30,910 --> 00:26:38,510
+التالي Y W prime زائد Y prime ناقص اتنين Y يساوي 
+
+280
+00:26:38,510 --> 00:26:45,110
+ستة E<sup>-X</sup>، المعادلة الثانية Y W prime زائد Y 
+
+281
+00:26:45,110 --> 00:26:51,670
+prime ناقص اتنين Y يساوي أربعة E<sup>أس ناقص تلاتة X</sup>
+
+282
+00:26:51,670 --> 00:26:55,110
+واضحة
+
+283
+00:26:56,200 --> 00:27:01,000
+نظرة لأن F of X مجموعة دلتين وكل واحدة منفصلة عن 
+
+284
+00:27:01,000 --> 00:27:05,300
+الثانية، فجسمت المعادلة إلى معادلتين، يعني لو روحت
+
+285
+00:27:05,300 --> 00:27:10,300
+رجعتهم لأصلهم، بصير هذا هو المعادلة الأصلية اللي
+
+286
+00:27:10,300 --> 00:27:15,240
+عندي بس مضروبة في نص، بيأثر على شكل الحل؟ لا بيأثرش،
+
+287
+00:27:15,240 --> 00:27:19,080
+النص بيجي مع الـ constants، وكان الله بالسر عليم.
+
+288
+00:27:19,080 --> 00:27:27,930
+نجي لهذه، بدنا الـ YP1، يبقى باجي بقول X to the power 
+
+289
+00:27:27,930 --> 00:27:33,910
+S في Ion بقول 
+
+290
+00:27:33,910 --> 00:27:37,510
+المعادلة اللي عندنا هذه نظراً لإن الـ exponential
+
+291
+00:27:37,510 --> 00:27:41,630
+هذه تختلف عن الـ exponential هذه، بجزء المعادلة إلى
+
+292
+00:27:41,630 --> 00:27:46,150
+معادلتين تمام، بجيب الحل الخاص للمعادلة الأولى و
+
+293
+00:27:46,150 --> 00:27:50,050
+بجيب الحل الخاص لمعادلة ثانية، يبقى الحل الخاص الكل
+
+294
+00:27:50,050 --> 00:27:55,230
+هو مجموع ليمين، مجموع للاثنين، طبعاً قد تستغربوا إنه
+
+295
+00:27:55,230 --> 00:27:59,390
+أنا لو جمعت المعادلة الاتنين هدول بيعطيهم
+
+296
+00:27:59,390 --> 00:28:03,070
+المعادلة الأصلية هذه زمان هي بس الطرف هذا مضروب في 
+
+297
+00:28:03,070 --> 00:28:06,730
+نص لإنه بيصير اتنين المعادلة ع الشمال يساوي المجموع
+
+298
+00:28:06,730 --> 00:28:11,090
+للاثنين، نصها اللي بيؤثر على شكل الحل لأن نصها عند
+
+299
+00:28:11,090 --> 00:28:14,530
+مناسب الحل بيكون داخل مع مين؟ مع الـ constants وكان 
+
+300
+00:28:14,530 --> 00:28:18,290
+الله بالسر عليم تمام، يبقى باجي للمعادلة الأولى
+
+301
+00:28:18,290 --> 00:28:22,620
+بقول X to the power S و باجي بطلع، في عندي هنا
+
+302
+00:28:22,620 --> 00:28:27,320
+polynomial يا بنات؟ اه، في بس polynomial من الدرجة
+
+303
+00:28:27,320 --> 00:28:36,560
+الصفرية، بقى بقوله إيه؟ A E<sup>-X</sup> بس مش أكتر، بدي 
+
+304
+00:28:36,560 --> 00:28:41,300
+أروح أدور على الـ S، باجي باطلع هل اللي بين قوسين
+
+305
+00:28:41,300 --> 00:28:44,020
+يشبه أي term عندنا؟
+
+306
+00:28:51,250 --> 00:29:03,920
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى، نجي 
+
+307
+00:29:03,920 --> 00:29:13,660
+للمعادلة الثانية، الـ YP2، YP2 بده يساوي هذا الـ X to
+
+308
+00:29:13,660 --> 00:29:18,920
+the power S فيه كمان نفس القصة بس بغير الـ
+
+309
+00:29:18,920 --> 00:29:25,040
+polynomial اللي هناك، بروح بقوله هذه P في E<sup>أس ناقص</sup>
+
+310
+00:29:25,040 --> 00:29:34,940
+تلاتة X، تلاتة X، في زيها، يبقى الـ S يساوي 0 تمام؟ من 
+
+311
+00:29:34,940 --> 00:29:40,400
+أين جاءت التلاتة هذه؟ آه، الحيها فوق، لا لا لا، 
+
+312
+00:29:40,400 --> 00:29:46,220
+استنى شوية، هي E<sup>أس تلاتة X</sup> في المسألة، مظبوط؟ آه،
+
+313
+00:29:46,220 --> 00:29:52,200
+يبقى هي E<sup>أس تلاتة X</sup> في المسألة الموجودة، يبقى فيش
+
+314
+00:29:52,200 --> 00:29:57,140
+تشابه ما بينها وبين أي term هنا، يبقى كمان هنا،
+
+315
+00:29:57,140 --> 00:30:04,970
+here S is equal to zero، يبقى أصبح الـ YP2 بيساوي B
+
+316
+00:30:04,970 --> 00:30:10,010
+في E<sup>أس ناقص تلاتة X</sup>، إذا صار شكل الـ particular
+
+317
+00:30:10,010 --> 00:30:18,590
+solution YP يساوي YP1 زائد YP2، يبقى A في E<sup>أس ناقص</sup>
+
+318
+00:30:18,590 --> 00:30:25,050
+X زائد B في E<sup>أس ناقص تلاتة X</sup>، يبقى صار شكل الـ
+
+319
+00:30:25,050 --> 00:30:26,530
+general solution
+
+320
+00:30:33,070 --> 00:30:44,770
+Y تساوي YC زائد YP، وين الـ Y؟ يبقى هذه الـ Y تساوي YC
+
+321
+00:30:52,230 --> 00:30:59,650
+بنطلع شكل A قد قيمة A و B، يبقى بدي ارجع وين بدي
+
+322
+00:30:59,650 --> 00:31:04,490
+ارجع، اه اه اه، استنى استنى شوية هذا شكله بس بدي 
+
+323
+00:31:04,490 --> 00:31:11,390
+اطلع قد قيمة A و B، يبقى بداجي هنا Y P one prime
+
+324
+00:31:11,390 --> 00:31:15,310
+ناقص A في E<sup>-X</sup> تمام
+
+325
+00:31:19,020 --> 00:31:25,340
+و YP1W' يساوي A في E<sup>أس ناقص X</sup>، نرجع نعوض، ناخد
+
+326
+00:31:25,340 --> 00:31:29,840
+المعلومات هذه ونعوض في المعادلة اللي فوق، يبقى الـ
+
+327
+00:31:29,840 --> 00:31:39,340
+YW' صارت A في E<sup>أس ناقص X</sup> زائد Y' اللي هي ناقص A
+
+328
+00:31:39,340 --> 00:31:46,860
+في E<sup>أس ناقص X</sup>، وهنا ناقص اتنين A في الـ E<sup>أس ناقص X</sup>
+
+329
+00:31:46,860 --> 00:31:52,840
+كله بدي يساوي الستة E<sup>أس ناقص X</sup>، أظن هدول اتنين مع 
+
+330
+00:31:52,840 --> 00:31:57,860
+بعض، الله سهل عليهم، وبناء عليه بصير سالب اتنين
+
+331
+00:31:57,860 --> 00:32:05,460
+A يساوي ستة، يبقى الـ A تساوي قداش؟ سالب تلاتة، نجي
+
+332
+00:32:05,460 --> 00:32:10,380
+بالمثل هنا يساوي 
+
+333
+00:32:10,380 --> 00:32:18,080
+ناقص تلاتة B E<sup>-3X</sup>، والـ YPW prime 
+
+334
+00:32:18,080 --> 00:32:24,440
+يساوي تسعة B E<sup>-3X</sup>، بدنا ناخد المعلومة 
+
+335
+00:32:24,440 --> 00:32:28,960
+اللي حصلنا عليها و نرجع نعوض في المعادلة اللي فوق
+
+336
+00:33:00,010 --> 00:33:06,460
+يبقى إيش بيصير عندنا؟ الش معي ليه؟ هدول قداش؟ خمسة، 
+
+337
+00:33:06,460 --> 00:33:11,700
+مظبوط؟ خمسة هو، هذه واحدة، تسعة، يبقى بصير عندك 
+
+338
+00:33:11,700 --> 00:33:18,200
+قداش؟ أربعة B تساوي، هذا بدي يعطيني أربعة B
+
+339
+00:33:18,200 --> 00:33:24,380
+تساوي قداش؟ أربعة، يبقى B تساوي واحد، يبقى أصبح
+
+340
+00:33:24,380 --> 00:33:31,280
+YP2 يساوي E<sup>أس ناقص تلاتة X</sup> بالشكل اللي عندنا
+
+341
+00:33:31,280 --> 00:33:41,490
+هذا، يبقى الآن أصبح YP يساوي YP1 زائد YP2، يساوي الآن
+
+342
+00:33:41,490 --> 00:33:44,630
+YP1
+
+343
+00:33:44,630 --> 00:33:50,330
+يساوي
+
+344
+00:33:50,330 --> 00:33:58,350
+YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1
+
+345
+00:33:58,350 --> 00:33:58,810
+يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي
+
+346
+00:33:58,810 --> 00:34:00,170
+YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1
+
+347
+00:34:00,170 --> 00:34:00,570
+يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي
+
+348
+00:34:00,570 --> 00:34:01,730
+YP1 يساوي YP1 يساوي YP1 يساوي YP1 يساوي YP1 يسو، هذا الـ
+
+349
+00:34:01,730 --> 00:34:10,930
+P1 بالزائد زائد E<sup>أس ناقص تلاتة X</sup> بالضبط، تمام طيب
+
+350
+00:34:10,930 --> 00:34:15,290
+الآن بدي الـ general solution، باجي بقول له that 
+
+351
+00:34:15,290 --> 00:34:19,110
+general solution
+
+352
+00:34:25,570 --> 00:34:31,490
+Y C  Y P Y C  Y P Y C  Y P
+
+353
+00:34:31,490 --> 00:34:32,730
+Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P 
+
+354
+00:34:32,730 --> 00:34:33,470
+Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P 
+
+355
+00:34:33,470 --> 00:34:37,870
+Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P
+
+356
+00:34:37,870 --> 00:34:40,570
+Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P Y C  Y P
+
+357
+00:34:40,570 --> 00:34:41,730
+Y C  Y P Y C  Y P
+
+358
+00:34:49,970 --> 00:34:54,770
+الآن مديني initial conditions اثنين، يبقى بقدر أنا
+
+359
+00:34:54,770 --> 00:34:59,520
+أجيب له Y عندي الـ zero، Y prime بعد ما نشتق هذه، يبقى 
+
+360
+00:34:59,520 --> 00:35:07,840
+لو جيت كلفة Y' يبقى C1 E<sup>OS X</sup> ناقص اتنين C2 E<sup>OS ناقص</sup>
+
+361
+00:35:07,840 --> 00:35:15,760
+اتنين X، وهنا زائد تلاتة E<sup>OS ناقص X</sup>، وهنا ناقص تلاتة 
+
+362
+00:35:15,760 --> 00:35:23,230
+E<sup>OS ناقص تلاتة X</sup>، الآن نجي يقول Y عند الـ zero تساوي
+
+363
+00:35:23,230 --> 00:35:27,790
+قيمة سالب واحد، و Y عند الـ zero تساوي سالب واحد
+
+36
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOFH4XnuduE_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOFH4XnuduE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..27d29765e1680ef51b226937d2de7f23103b278b
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOFH4XnuduE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3459, "start": 19.49, "end": 34.59, "text": "بسم الله الرحمن الرحيم في حديثنا السابق في ال sections الماضي من خمسة واحد لغاية خمسة خمسة كنا بنتكلم على ال homogenous differential equation", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 11331, 16254, 12984, 8315, 21136, 16758, 4587, 8978, 2423, 10863, 9673, 46958, 1829, 9154, 16490, 2304, 3794, 3660, 36764, 24401, 5296, 17082, 995, 10632, 16490, 2304, 3794, 3660, 16490, 2304, 3794, 3660, 9122, 8315, 4724, 29399, 4117, 19528, 15844, 2423, 3655, 45519, 15756, 5367], "avg_logprob": -0.14616477110169152, "compression_ratio": 1.4635761589403973, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 19.49, "end": 19.79, "word": "بسم", "probability": 0.756591796875}, {"start": 19.79, "end": 20.03, "word": " الله", "probability": 0.9638671875}, {"start": 20.03, "end": 20.49, "word": " الرحمن", "probability": 0.9611002604166666}, {"start": 20.49, "end": 21.07, "word": " الرحيم", "probability": 0.9908854166666666}, {"start": 21.07, "end": 23.17, "word": " في", "probability": 0.72802734375}, {"start": 23.17, "end": 23.83, "word": " حديثنا", "probability": 0.980224609375}, {"start": 23.83, "end": 24.45, "word": " السابق", "probability": 0.9967447916666666}, {"start": 24.45, "end": 24.57, "word": " في", "probability": 0.9091796875}, {"start": 24.57, "end": 24.69, "word": " ال", "probability": 0.8115234375}, {"start": 24.69, "end": 25.11, "word": " sections", "probability": 0.80029296875}, {"start": 25.11, "end": 25.69, "word": " الماضي", "probability": 0.8225911458333334}, {"start": 25.69, "end": 25.85, "word": " من", "probability": 0.59130859375}, {"start": 25.85, "end": 26.31, "word": " خمسة", "probability": 0.8277587890625}, {"start": 26.31, "end": 26.61, "word": " واحد", "probability": 0.934814453125}, {"start": 26.61, "end": 27.15, "word": " لغاية", "probability": 0.9754638671875}, {"start": 27.15, "end": 27.65, "word": " خمسة", "probability": 0.987060546875}, {"start": 27.65, "end": 28.29, "word": " خمسة", "probability": 0.986083984375}, {"start": 28.29, "end": 28.85, "word": " كنا", "probability": 0.95654296875}, {"start": 28.85, "end": 29.55, "word": " بنتكلم", "probability": 0.85400390625}, {"start": 29.55, "end": 29.87, "word": " على", "probability": 0.68212890625}, {"start": 29.87, "end": 30.13, "word": " ال", "probability": 0.94384765625}, {"start": 30.13, "end": 33.13, "word": " homogenous", "probability": 0.422119140625}, {"start": 33.13, "end": 33.99, "word": " differential", "probability": 0.88916015625}, {"start": 33.99, "end": 34.59, "word": " equation", "probability": 0.939453125}], "temperature": 1.0}, {"id": 2, "seek": 5898, "start": 35.7, "end": 58.98, "text": "في خمسة ستة اعطينا مقدمة بسيطة انه انا لو بده اجيب حل ال non homogeneous equation star هذا بده اقسم المسألة الى جزئين ال homogeneous و ال non homogeneous ال homogeneous بحلها زى ما كنت حل في ال sections الماضية و بده اسميه ال complementary solution 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37.04, "word": " ستة", "probability": 0.7220865885416666}, {"start": 37.04, "end": 37.38, "word": " اعطينا", "probability": 0.79921875}, {"start": 37.38, "end": 38.0, "word": " مقدمة", "probability": 0.9729817708333334}, {"start": 38.0, "end": 38.86, "word": " بسيطة", "probability": 0.990234375}, {"start": 38.86, "end": 39.56, "word": " انه", "probability": 0.527099609375}, {"start": 39.56, "end": 39.8, "word": " انا", "probability": 0.942626953125}, {"start": 39.8, "end": 40.0, "word": " لو", "probability": 0.9697265625}, {"start": 40.0, "end": 40.28, "word": " بده", "probability": 0.567626953125}, {"start": 40.28, "end": 40.52, "word": " اجيب", "probability": 0.9271240234375}, {"start": 40.52, "end": 40.96, "word": " حل", "probability": 0.971435546875}, {"start": 40.96, "end": 41.1, "word": " ال", "probability": 0.60400390625}, {"start": 41.1, "end": 41.32, "word": " non", "probability": 0.72265625}, {"start": 41.32, "end": 41.86, "word": " homogeneous", "probability": 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بتقسيم الهموجينياس بالأول اللي هي المعادلة اللي عندنا هدى بدون f of x لو كانت تساوي زيرو يبقى الحل تبعها هيكون على الشكل اللي أننا كنا بنطلعه", "tokens": [3224, 24192, 9673, 3615, 18513, 37977, 8608, 10721, 4587, 20498, 39894, 4587, 3794, 32640, 11296, 46740, 2304, 29245, 9957, 25528, 3794, 4032, 1863, 11536, 8032, 2304, 29245, 9957, 25528, 3794, 8608, 10721, 4587, 20498, 39894, 4587, 3794, 32640, 2423, 3224, 2304, 29245, 9957, 25528, 3794, 20666, 10721, 12610, 13672, 1829, 39896, 9673, 3615, 18513, 37977, 13672, 1829, 43242, 8315, 8032, 3215, 7578, 47525, 11536, 283, 295, 2031, 45164, 25961, 2655, 6055, 3794, 995, 45865, 30767, 13546, 2407, 7251, 3555, 4587, 7578, 21542, 1211, 6055, 3555, 3615, 11296, 39896, 30544, 15844, 25124, 28820, 13672, 1829, 14739, 8315, 9122, 8315, 44945, 9566, 1211, 3615, 3224], "avg_logprob": -0.4179687448419057, "compression_ratio": 1.989071038251366, "no_speech_prob": 0.0, "words": [{"start": 127.71, "end": 128.73, "word": "هذه", "probability": 0.207275390625}, {"start": 128.73, "end": 129.57, "word": " المعادلة", "probability": 0.953369140625}, {"start": 129.57, "end": 130.31, "word": " سأقوم", "probability": 0.5089263916015625}, {"start": 130.31, "end": 130.75, "word": " بتقسيمها", "probability": 0.597607421875}, {"start": 130.75, "end": 131.67, "word": " لهموجينياس", "probability": 0.627197265625}, {"start": 131.67, "end": 132.21, "word": " ونون", "probability": 0.5369466145833334}, {"start": 132.21, "end": 133.05, "word": " هموجينياس", "probability": 0.9048665364583334}, {"start": 133.05, "end": 133.97, "word": " سأقوم", "probability": 0.5816192626953125}, {"start": 133.97, "end": 133.97, "word": " بتقسيم", "probability": 0.716552734375}, {"start": 133.97, "end": 134.77, "word": " الهموجينياس", "probability": 0.8153948102678571}, {"start": 134.77, "end": 135.41, "word": " بالأول", "probability": 0.7005208333333334}, {"start": 135.41, "end": 135.71, "word": " اللي", "probability": 0.431854248046875}, {"start": 135.71, "end": 135.83, "word": " هي", "probability": 0.69580078125}, {"start": 135.83, "end": 136.53, "word": " المعادلة", "probability": 0.9573974609375}, {"start": 136.53, "end": 136.71, "word": " اللي", "probability": 0.614990234375}, {"start": 136.71, "end": 137.27, "word": " عندنا", "probability": 0.873291015625}, {"start": 137.27, "end": 138.01, "word": " هدى", "probability": 0.5928548177083334}, {"start": 138.01, "end": 138.47, "word": " بدون", "probability": 0.96533203125}, {"start": 138.47, "end": 138.71, "word": " f", "probability": 0.4853515625}, {"start": 138.71, "end": 138.91, "word": " of", "probability": 0.56396484375}, {"start": 138.91, "end": 139.15, "word": " x", "probability": 0.88037109375}, {"start": 139.15, "end": 139.41, "word": " لو", "probability": 0.90087890625}, {"start": 139.41, "end": 139.91, "word": " كانت", "probability": 0.951904296875}, {"start": 139.91, "end": 140.51, "word": " تساوي", "probability": 0.897705078125}, {"start": 140.51, "end": 141.07, "word": " زيرو", "probability": 0.5872395833333334}, {"start": 141.07, "end": 141.93, "word": " يبقى", "probability": 0.911865234375}, {"start": 141.93, "end": 142.37, "word": " الحل", "probability": 0.926513671875}, {"start": 142.37, "end": 142.89, "word": " تبعها", "probability": 0.823486328125}, {"start": 142.89, "end": 143.29, "word": " هيكون", "probability": 0.721435546875}, {"start": 143.29, "end": 143.45, "word": " على", "probability": 0.908203125}, {"start": 143.45, "end": 143.85, "word": " الشكل", "probability": 0.955810546875}, {"start": 143.85, "end": 143.97, "word": " اللي", "probability": 0.664306640625}, {"start": 143.97, "end": 144.19, "word": " أننا", "probability": 0.3759765625}, {"start": 144.19, "end": 144.75, "word": " كنا", "probability": 0.84619140625}, {"start": 144.75, "end": 145.41, "word": " بنطلعه", "probability": 0.88701171875}], "temperature": 1.0}, {"id": 7, "seek": 16297, "start": 145.59, "end": 162.97, "text": "في ال sections الماضية سواء كان ال complex roots or repeated roots ال roots are all different يبقى بالطرق التلاتة السابقة اللي كنا بيعملها وقلعنا هذا الحل تمام؟ الآن بدأ افترض ان هذا الحل هو لميلا المعادلة هذه", "tokens": [41185, 2423, 10863, 9673, 46958, 10632, 8608, 2407, 16606, 25961, 2423, 3997, 10669, 420, 10477, 10669, 2423, 10669, 366, 439, 819, 7251, 3555, 4587, 7578, 20666, 9566, 2288, 4587, 16712, 1211, 9307, 3660, 21136, 16758, 28671, 13672, 1829, 9122, 8315, 4724, 1829, 25957, 1211, 11296, 4032, 4587, 1211, 3615, 8315, 23758, 21542, 1211, 46811, 10943, 22807, 6024, 48506, 47525, 10721, 1975, 5172, 2655, 43042, 16472, 23758, 21542, 1211, 31439, 32767, 1829, 15040, 9673, 3615, 18513, 37977, 29538], "avg_logprob": -0.3026842983105244, "compression_ratio": 1.5598086124401913, "no_speech_prob": 0.0, "words": [{"start": 145.59, "end": 145.79, "word": "في", "probability": 0.55322265625}, {"start": 145.79, "end": 145.93, "word": " ال", "probability": 0.5283203125}, {"start": 145.93, "end": 146.37, "word": " sections", "probability": 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ونجيب ال characteristic كواشي ونذهب للحل هنا ونجيبها خلصنا حل ال homogeneous بداجي للحل الخاص تبع ال non homogeneous اللي انها دي فباجي بقول we use the method of undetermined coefficients بدنا نستخدم طريقة المعاملات المجهولة والحين هنقولك لسه منها معادلات مجهولة", "tokens": [1863, 5172, 43042, 398, 6055, 3794, 995, 45865, 7251, 9381, 2288, 1783, 4032, 1863, 7435, 1829, 3555, 2423, 2517, 468, 299, 9122, 2407, 33599, 1829, 4032, 1863, 24192, 3555, 24976, 5016, 1211, 34105, 4032, 1863, 7435, 1829, 3555, 11296, 16490, 1211, 9381, 8315, 11331, 1211, 2423, 42632, 47525, 26108, 1829, 24976, 5016, 1211, 33962, 33546, 6055, 3555, 3615, 2423, 2107, 42632, 13672, 1829, 16472, 11296, 11778, 1829, 6156, 3555, 26108, 1829, 4724, 39648, 321, 764, 264, 3170, 295, 674, 35344, 2001, 31994, 47525, 8315, 8717, 14851, 9778, 40448, 23032, 16572, 28671, 9673, 3615, 10943, 1211, 9307, 9673, 7435, 3224, 12610, 3660, 16070, 5016, 9957, 8032, 1863, 39648, 4117, 5296, 3794, 3224, 9154, 11296, 20449, 18513, 1211, 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"end": 167.73, "word": " للحل", "probability": 0.734375}, {"start": 167.73, "end": 167.99, "word": " هنا", "probability": 0.81884765625}, {"start": 167.99, "end": 169.03, "word": " ونجيبها", "probability": 0.6775716145833334}, {"start": 169.03, "end": 170.05, "word": " خلصنا", "probability": 0.74444580078125}, {"start": 170.05, "end": 170.29, "word": " حل", "probability": 0.894287109375}, {"start": 170.29, "end": 170.41, "word": " ال", "probability": 0.98681640625}, {"start": 170.41, "end": 170.89, "word": " homogeneous", "probability": 0.6513671875}, {"start": 170.89, "end": 172.03, "word": " بداجي", "probability": 0.401123046875}, {"start": 172.03, "end": 172.75, "word": " للحل", "probability": 0.9020182291666666}, {"start": 172.75, "end": 173.51, "word": " الخاص", "probability": 0.989990234375}, {"start": 173.51, "end": 174.21, "word": " تبع", "probability": 0.7565104166666666}, {"start": 174.21, "end": 174.37, "word": " ال", "probability": 0.9541015625}, {"start": 174.37, "end": 174.53, "word": " non", "probability": 0.8818359375}, {"start": 174.53, "end": 175.11, "word": " homogeneous", "probability": 0.66552734375}, {"start": 175.11, "end": 175.45, "word": " اللي", "probability": 0.675048828125}, {"start": 175.45, "end": 175.75, "word": " انها", "probability": 0.33721923828125}, {"start": 175.75, "end": 176.05, "word": " دي", "probability": 0.61865234375}, {"start": 176.05, "end": 176.75, "word": " فباجي", "probability": 0.729888916015625}, {"start": 176.75, "end": 177.05, "word": " بقول", "probability": 0.864501953125}, {"start": 177.05, "end": 177.25, "word": " we", "probability": 0.5107421875}, {"start": 177.25, "end": 177.51, "word": " use", "probability": 0.86767578125}, {"start": 177.51, "end": 177.67, "word": " the", "probability": 0.6962890625}, {"start": 177.67, "end": 177.95, "word": " method", "probability": 0.9619140625}, {"start": 177.95, "end": 178.19, "word": " of", "probability": 0.97216796875}, {"start": 178.19, "end": 178.97, "word": " 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"end": 186.93, "word": " مجهولة", "probability": 0.9919921875}], "temperature": 1.0}, {"id": 9, "seek": 20562, "start": 187.28, "end": 205.62, "text": "عن طريق البحث عن حل لإيجاد حل خاص للنهوموجينيس الـ differential equation من الـ start اللي فوق اللي هي الـ non homogenous احنا هذا جيبنا له ال homogenous بدنا ال non homogenous يعطيه رمز YP", "tokens": [3615, 1863, 23032, 16572, 4587, 29739, 5016, 12984, 18871, 11331, 1211, 5296, 28814, 1829, 7435, 18513, 11331, 1211, 16490, 33546, 24976, 1863, 3224, 20498, 29245, 9957, 1829, 3794, 2423, 39184, 15756, 5367, 9154, 2423, 39184, 722, 13672, 1829, 6156, 30543, 13672, 1829, 39896, 2423, 39184, 2107, 3655, 45519, 1975, 5016, 8315, 23758, 10874, 1829, 3555, 8315, 46740, 2423, 3655, 45519, 47525, 8315, 2423, 2107, 3655, 45519, 7251, 3615, 9566, 1829, 3224, 12602, 2304, 11622, 398, 47], "avg_logprob": -0.5162337383666595, "compression_ratio": 1.543956043956044, "no_speech_prob": 0.0, "words": [{"start": 187.28, "end": 187.7, "word": "عن", 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"probability": 0.56298828125}, {"start": 196.42, "end": 197.16, "word": " الـ", "probability": 0.3494873046875}, {"start": 197.16, "end": 197.54, "word": " start", "probability": 0.5283203125}, {"start": 197.54, "end": 198.08, "word": " اللي", "probability": 0.5262451171875}, {"start": 198.08, "end": 198.42, "word": " فوق", "probability": 0.9833984375}, {"start": 198.42, "end": 198.6, "word": " اللي", "probability": 0.60614013671875}, {"start": 198.6, "end": 198.76, "word": " هي", "probability": 0.48583984375}, {"start": 198.76, "end": 198.86, "word": " الـ", "probability": 0.642578125}, {"start": 198.86, "end": 199.12, "word": " non", "probability": 0.7353515625}, {"start": 199.12, "end": 199.88, "word": " homogenous", "probability": 0.50732421875}, {"start": 199.88, "end": 200.54, "word": " احنا", "probability": 0.8046061197916666}, {"start": 200.54, "end": 200.72, "word": " هذا", "probability": 0.76416015625}, {"start": 200.72, "end": 201.04, "word": " جيبنا", "probability": 0.9095458984375}, {"start": 201.04, "end": 201.18, "word": " له", "probability": 0.6845703125}, {"start": 201.18, "end": 201.28, "word": " ال", "probability": 0.95166015625}, {"start": 201.28, "end": 201.9, "word": " homogenous", "probability": 0.5635986328125}, {"start": 201.9, "end": 202.94, "word": " بدنا", "probability": 0.945556640625}, {"start": 202.94, "end": 203.42, "word": " ال", "probability": 0.69970703125}, {"start": 203.42, "end": 203.62, "word": " non", "probability": 0.744140625}, {"start": 203.62, "end": 204.1, "word": " homogenous", "probability": 0.860595703125}, {"start": 204.1, "end": 204.64, "word": " يعطيه", "probability": 0.7791015625}, {"start": 204.64, "end": 205.0, "word": " رمز", "probability": 0.9781901041666666}, {"start": 205.0, "end": 205.62, "word": " YP", "probability": 0.57958984375}], "temperature": 1.0}, {"id": 10, "seek": 22086, "start": 206.5, "end": 220.86, "text": "كيف بنجيبه؟ بنستخدم طريقة الـ Undetermined coefficients إذا تحقق في المعادلة أمران ما هم الأمران هذه؟ الأمر الأول ذكرناه إن المعاملات هذول كلهم ثوابت", "tokens": [4117, 33911, 44945, 7435, 1829, 3555, 3224, 22807, 44945, 14851, 9778, 40448, 23032, 16572, 28671, 2423, 39184, 2719, 35344, 2001, 31994, 11933, 15730, 6055, 5016, 4587, 4587, 8978, 9673, 3615, 18513, 37977, 5551, 29973, 7649, 19446, 8032, 2304, 16247, 29973, 7649, 29538, 22807, 16247, 29973, 16247, 12610, 29910, 37983, 8315, 3224, 36145, 9673, 3615, 10943, 1211, 9307, 8032, 8848, 12610, 28242, 16095, 38637, 14407, 3555, 2655], "avg_logprob": -0.1854011260751468, "compression_ratio": 1.5029940119760479, "no_speech_prob": 0.0, "words": [{"start": 206.5, "end": 206.82, "word": "كيف", "probability": 0.58367919921875}, {"start": 206.82, "end": 207.88, "word": " بنجيبه؟", "probability": 0.8157958984375}, {"start": 207.88, "end": 208.76, "word": " بنستخدم", "probability": 0.93017578125}, {"start": 208.76, "end": 209.32, "word": " طريقة", "probability": 0.99169921875}, {"start": 209.32, "end": 209.56, "word": " الـ", "probability": 0.771240234375}, {"start": 209.56, "end": 210.4, "word": " Undetermined", "probability": 0.7469889322916666}, {"start": 210.4, "end": 211.02, "word": " coefficients", "probability": 0.8740234375}, {"start": 211.02, "end": 211.4, "word": " إذا", "probability": 0.8935546875}, {"start": 211.4, "end": 212.12, "word": " تحقق", "probability": 0.977783203125}, {"start": 212.12, "end": 212.32, "word": " في", "probability": 0.9716796875}, {"start": 212.32, "end": 213.06, "word": " المعادلة", "probability": 0.985107421875}, {"start": 213.06, "end": 213.84, "word": " أمران", "probability": 0.9090169270833334}, {"start": 213.84, "end": 214.58, "word": " ما", "probability": 0.35986328125}, {"start": 214.58, "end": 214.84, "word": " هم", "probability": 0.71826171875}, {"start": 214.84, "end": 215.42, "word": " الأمران", "probability": 0.9873046875}, {"start": 215.42, "end": 215.92, "word": " هذه؟", "probability": 0.64111328125}, {"start": 215.92, "end": 216.26, "word": " الأمر", "probability": 0.942138671875}, {"start": 216.26, "end": 216.7, "word": " الأول", "probability": 0.992919921875}, {"start": 216.7, "end": 217.7, "word": " ذكرناه", "probability": 0.960693359375}, {"start": 217.7, "end": 218.04, "word": " إن", "probability": 0.41162109375}, {"start": 218.04, "end": 218.86, "word": " المعاملات", "probability": 0.9759765625}, {"start": 218.86, "end": 219.18, "word": " هذول", "probability": 0.6171875}, {"start": 219.18, "end": 220.04, "word": " كلهم", "probability": 0.907470703125}, {"start": 220.04, "end": 220.86, "word": " ثوابت", "probability": 0.92578125}], "temperature": 1.0}, {"id": 11, "seek": 23830, "start": 221.6, "end": 238.3, "text": "الأمر الثاني يجب أن يكون ال f of x على شكل معين ماهو هذا الشكل المعين اللي لو تحقق في ال f of x بقدر استخدم ال undetermined coefficients دون غيرها بقول بسيطة جدا", "tokens": [6027, 10721, 29973, 6024, 104, 7649, 1829, 7251, 7435, 3555, 14739, 7251, 30544, 2423, 283, 295, 2031, 15844, 13412, 28820, 20449, 9957, 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223.74, "end": 224.0, "word": " of", "probability": 0.458251953125}, {"start": 224.0, "end": 224.24, "word": " x", "probability": 0.9560546875}, {"start": 224.24, "end": 224.84, "word": " على", "probability": 0.88720703125}, {"start": 224.84, "end": 225.58, "word": " شكل", "probability": 0.97021484375}, {"start": 225.58, "end": 226.52, "word": " معين", "probability": 0.970703125}, {"start": 226.52, "end": 227.64, "word": " ماهو", "probability": 0.599609375}, {"start": 227.64, "end": 227.92, "word": " هذا", "probability": 0.9248046875}, {"start": 227.92, "end": 228.42, "word": " الشكل", "probability": 0.97119140625}, {"start": 228.42, "end": 228.98, "word": " المعين", "probability": 0.9733072916666666}, {"start": 228.98, "end": 229.42, "word": " اللي", "probability": 0.65771484375}, {"start": 229.42, "end": 229.64, "word": " لو", "probability": 0.9306640625}, {"start": 229.64, "end": 230.34, "word": " تحقق", "probability": 0.8370361328125}, {"start": 230.34, "end": 230.48, "word": " في", "probability": 0.869140625}, {"start": 230.48, "end": 230.58, "word": " ال", "probability": 0.828125}, {"start": 230.58, "end": 230.76, "word": " f", "probability": 0.7763671875}, {"start": 230.76, "end": 230.96, "word": " of", "probability": 0.97216796875}, {"start": 230.96, "end": 231.22, "word": " x", "probability": 0.98828125}, {"start": 231.22, "end": 231.96, "word": " بقدر", "probability": 0.87158203125}, {"start": 231.96, "end": 232.48, "word": " استخدم", "probability": 0.8933919270833334}, {"start": 232.48, "end": 232.62, "word": " ال", "probability": 0.75439453125}, {"start": 232.62, "end": 233.7, "word": " undetermined", "probability": 0.7677408854166666}, {"start": 233.7, "end": 234.64, "word": " coefficients", "probability": 0.9267578125}, {"start": 234.64, "end": 235.54, "word": " دون", "probability": 0.950439453125}, {"start": 235.54, "end": 236.64, "word": " غيرها", "probability": 0.8702799479166666}, {"start": 236.64, "end": 237.42, "word": " بقول", "probability": 0.795166015625}, {"start": 237.42, "end": 238.04, "word": " بسيطة", "probability": 0.9658203125}, {"start": 238.04, "end": 238.3, "word": " جدا", "probability": 0.976318359375}], "temperature": 1.0}, {"id": 12, "seek": 26008, "start": 239.13, "end": 260.09, "text": "لو جيت على الفوفيكس لاجيتها polynomial بدي اكتب شكل ال particular solution على polynomial زيها من نفس الدرجة بس المعاملات مش هم يبقى هدول هم ال undetermined coefficients تبعت طريقتنا هذه مضروبة كلها", "tokens": [1211, 2407, 10874, 36081, 15844, 27188, 38688, 1829, 4117, 3794, 5296, 26108, 36081, 11296, 26110, 4724, 16254, 1975, 4117, 2655, 3555, 13412, 28820, 2423, 1729, 3827, 15844, 26110, 30767, 1829, 11296, 9154, 8717, 36178, 32748, 47341, 3660, 4724, 3794, 9673, 3615, 10943, 1211, 9307, 37893, 8032, 2304, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 8032, 2304, 2423, 674, 35344, 2001, 31994, 6055, 3555, 34268, 23032, 16572, 38149, 8315, 29538, 3714, 11242, 32887, 49401, 28242, 11296], "avg_logprob": -0.24095395285832255, 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"end": 247.01, "word": " solution", "probability": 0.9345703125}, {"start": 247.01, "end": 247.41, "word": " على", "probability": 0.74853515625}, {"start": 247.41, "end": 248.29, "word": " polynomial", "probability": 0.92822265625}, {"start": 248.29, "end": 249.13, "word": " زيها", "probability": 0.8723958333333334}, {"start": 249.13, "end": 249.33, "word": " من", "probability": 0.9228515625}, {"start": 249.33, "end": 249.69, "word": " نفس", "probability": 0.99658203125}, {"start": 249.69, "end": 250.69, "word": " الدرجة", "probability": 0.8919270833333334}, {"start": 250.69, "end": 251.61, "word": " بس", "probability": 0.904052734375}, {"start": 251.61, "end": 252.33, "word": " المعاملات", "probability": 0.98828125}, {"start": 252.33, "end": 252.59, "word": " مش", "probability": 0.97412109375}, {"start": 252.59, "end": 253.05, "word": " هم", "probability": 0.857177734375}, {"start": 253.05, "end": 253.97, "word": " يبقى", "probability": 0.746337890625}, {"start": 253.97, "end": 254.39, "word": " هدول", "probability": 0.9549153645833334}, {"start": 254.39, "end": 254.85, "word": " هم", "probability": 0.843505859375}, {"start": 254.85, "end": 255.05, "word": " ال", "probability": 0.90283203125}, {"start": 255.05, "end": 256.45, "word": " undetermined", "probability": 0.8264973958333334}, {"start": 256.45, "end": 257.27, "word": " coefficients", "probability": 0.91455078125}, {"start": 257.27, "end": 257.95, "word": " تبعت", "probability": 0.8273111979166666}, {"start": 257.95, "end": 258.67, "word": " طريقتنا", "probability": 0.9140625}, {"start": 258.67, "end": 258.89, "word": " هذه", "probability": 0.52734375}, {"start": 258.89, "end": 259.45, "word": " مضروبة", "probability": 0.9078369140625}, {"start": 259.45, "end": 260.09, "word": " كلها", "probability": 0.95703125}], "temperature": 1.0}, {"id": 13, "seek": 27947, "start": 260.63, "end": 279.47, "text": "فى x to the power s مين ال x to the power s هذا ما سنجيب عليه بعد قليل يبقى خلّيكم صحين معانا لأن هذا very important مين هي ال x أس s هذا very important وهي عمود في قريف الحل والإجابة", "tokens": [5172, 7578, 2031, 281, 264, 1347, 262, 3714, 9957, 2423, 2031, 281, 264, 1347, 262, 23758, 19446, 8608, 1863, 7435, 1829, 3555, 47356, 39182, 12174, 20292, 1211, 7251, 3555, 4587, 7578, 16490, 1211, 11703, 1829, 24793, 20328, 5016, 9957, 20449, 7649, 995, 5296, 33456, 23758, 588, 1021, 3714, 9957, 39896, 2423, 2031, 5551, 3794, 262, 23758, 588, 1021, 37037, 1829, 6225, 2304, 23328, 8978, 12174, 16572, 5172, 21542, 1211, 16070, 28814, 7435, 16758, 3660], "avg_logprob": -0.34645833174387614, "compression_ratio": 1.56, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 260.63, "end": 260.91, "word": "فى", "probability": 0.4429779052734375}, {"start": 260.91, "end": 261.17, "word": " x", "probability": 0.36865234375}, {"start": 261.17, "end": 261.41, "word": " to", "probability": 0.1983642578125}, {"start": 261.41, "end": 261.61, "word": " the", "probability": 0.9228515625}, {"start": 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"probability": 0.98095703125}, {"start": 265.37, "end": 266.27, "word": " بعد", "probability": 0.96630859375}, {"start": 266.27, "end": 267.21, "word": " قليل", "probability": 0.99267578125}, {"start": 267.21, "end": 267.95, "word": " يبقى", "probability": 0.8277587890625}, {"start": 267.95, "end": 268.37, "word": " خلّيكم", "probability": 0.674267578125}, {"start": 268.37, "end": 268.77, "word": " صحين", "probability": 0.9371744791666666}, {"start": 268.77, "end": 269.25, "word": " معانا", "probability": 0.7635904947916666}, {"start": 269.25, "end": 269.79, "word": " لأن", "probability": 0.77783203125}, {"start": 269.79, "end": 270.05, "word": " هذا", "probability": 0.58251953125}, {"start": 270.05, "end": 270.41, "word": " very", "probability": 0.7822265625}, {"start": 270.41, "end": 271.51, "word": " important", "probability": 0.9619140625}, {"start": 271.51, "end": 271.89, "word": " مين", "probability": 0.8408203125}, {"start": 271.89, "end": 272.05, "word": " هي", "probability": 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"text": "نجي لقصة ال X to the powers الشي هذه شايفين هذا الحل يا بنات ال complementary solution هذا", "tokens": [1863, 7435, 1829, 5296, 4587, 9381, 3660, 2423, 1783, 281, 264, 8674, 25124, 1829, 29538, 13412, 995, 33911, 9957, 23758, 21542, 1211, 35186, 4724, 8315, 2655, 2423, 40705, 3827, 23758], "avg_logprob": -0.43019154379444735, "compression_ratio": 1.1504424778761062, "no_speech_prob": 0.0, "words": [{"start": 411.88, "end": 412.46, "word": "نجي", "probability": 0.3777262369791667}, {"start": 412.46, "end": 413.1, "word": " لقصة", "probability": 0.9373779296875}, {"start": 413.1, "end": 413.24, "word": " ال", "probability": 0.40673828125}, {"start": 413.24, "end": 413.48, "word": " X", "probability": 0.4208984375}, {"start": 413.48, "end": 413.68, "word": " to", "probability": 0.880859375}, {"start": 413.68, "end": 413.86, "word": " the", "probability": 0.90185546875}, {"start": 413.86, "end": 414.16, "word": " powers", "probability": 0.402587890625}, {"start": 414.16, "end": 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0.91796875}, {"start": 2238.05, "end": 2238.97, "word": " يبقى", "probability": 0.9901123046875}, {"start": 2238.97, "end": 2239.35, "word": " بناء", "probability": 0.83154296875}, {"start": 2239.35, "end": 2239.91, "word": " عليه", "probability": 0.367919921875}, {"start": 2239.91, "end": 2240.69, "word": " أصبح", "probability": 0.9469401041666666}, {"start": 2240.69, "end": 2241.23, "word": " ذا", "probability": 0.6513671875}], "temperature": 1.0}, {"id": 99, "seek": 227076, "start": 2241.4, "end": 2270.76, "text": "Solution of the initial value problem is Y تساوي هاي بده اشيل C1 و اكتب مكان واحد يبقى وضلت EOS X C2 ب Zero يبقى طاري ال term اللي عندنا هذا يبقى ناقص تلاتة EOS ناقص X زائد EOS ناقص تلاتة X", "tokens": [50, 3386, 295, 264, 5883, 2158, 1154, 307, 398, 6055, 3794, 995, 45865, 8032, 47302, 47525, 3224, 1975, 8592, 26895, 383, 16, 4032, 1975, 4117, 2655, 3555, 3714, 41361, 36764, 24401, 7251, 3555, 4587, 7578, 4032, 11242, 1211, 2655, 462, 4367, 1783, 383, 17, 4724, 17182, 7251, 3555, 4587, 7578, 23032, 9640, 1829, 2423, 1433, 13672, 1829, 43242, 8315, 23758, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 462, 4367, 8717, 995, 4587, 9381, 1783, 30767, 16373, 3215, 462, 4367, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 1783], "avg_logprob": -0.2544880398410432, "compression_ratio": 1.4256410256410257, "no_speech_prob": 0.0, "words": [{"start": 2241.4, "end": 2242.72, "word": "Solution", "probability": 0.55535888671875}, {"start": 2242.72, "end": 2244.58, "word": " of", "probability": 0.7919921875}, {"start": 2244.58, "end": 2245.8, "word": " the", "probability": 0.7177734375}, {"start": 2245.8, "end": 2247.04, "word": " initial", "probability": 0.705078125}, {"start": 2247.04, "end": 2248.2, "word": " value", "probability": 0.95849609375}, {"start": 2248.2, "end": 2249.08, "word": " problem", "probability": 0.8642578125}, {"start": 2249.08, "end": 2249.92, "word": " is", "probability": 0.8671875}, {"start": 2249.92, "end": 2251.62, "word": " Y", "probability": 0.425048828125}, {"start": 2251.62, "end": 2252.58, "word": " تساوي", "probability": 0.72784423828125}, {"start": 2252.58, "end": 2253.42, "word": " هاي", "probability": 0.47308349609375}, {"start": 2253.42, "end": 2254.48, "word": " بده", "probability": 0.5062255859375}, {"start": 2254.48, "end": 2254.68, "word": " اشيل", "probability": 0.86572265625}, {"start": 2254.68, "end": 2255.36, "word": " C1", "probability": 0.8408203125}, {"start": 2255.36, "end": 2255.62, "word": " و", "probability": 0.7138671875}, {"start": 2255.62, "end": 2255.86, "word": " اكتب", "probability": 0.966064453125}, {"start": 2255.86, "end": 2256.26, "word": " مكان", "probability": 0.981201171875}, {"start": 2256.26, "end": 2256.74, "word": " واحد", "probability": 0.814697265625}, {"start": 2256.74, "end": 2256.98, "word": " يبقى", "probability": 0.9439697265625}, {"start": 2256.98, "end": 2257.7, "word": " وضلت", "probability": 0.54345703125}, {"start": 2257.7, "end": 2258.22, "word": " EOS", "probability": 0.422027587890625}, {"start": 2258.22, "end": 2258.52, "word": " X", "probability": 0.515625}, {"start": 2258.52, "end": 2259.66, "word": " C2", "probability": 0.84521484375}, {"start": 2259.66, "end": 2259.82, "word": " ب", "probability": 0.888671875}, {"start": 2259.82, "end": 2260.2, "word": " Zero", "probability": 0.2001953125}, {"start": 2260.2, "end": 2260.66, "word": " يبقى", "probability": 0.988525390625}, {"start": 2260.66, "end": 2261.28, "word": " طاري", "probability": 0.6608072916666666}, {"start": 2261.28, "end": 2261.44, "word": " ال", "probability": 0.73828125}, {"start": 2261.44, "end": 2261.72, "word": " term", "probability": 0.92529296875}, {"start": 2261.72, "end": 2262.02, "word": " اللي", "probability": 0.9296875}, {"start": 2262.02, "end": 2262.42, "word": " عندنا", "probability": 0.836181640625}, {"start": 2262.42, "end": 2262.72, "word": " هذا", "probability": 0.89013671875}, {"start": 2262.72, "end": 2263.74, "word": " يبقى", "probability": 0.9822998046875}, {"start": 2263.74, "end": 2264.42, "word": " ناقص", "probability": 0.7930908203125}, {"start": 2264.42, "end": 2265.1, "word": " تلاتة", "probability": 0.8719482421875}, {"start": 2265.1, "end": 2265.6, "word": " EOS", "probability": 0.764404296875}, {"start": 2265.6, "end": 2266.12, "word": " ناقص", "probability": 0.9893798828125}, {"start": 2266.12, "end": 2266.44, "word": " X", "probability": 0.966796875}, {"start": 2266.44, "end": 2267.46, "word": " زائد", "probability": 0.91015625}, {"start": 2267.46, "end": 2268.52, "word": " EOS", "probability": 0.932861328125}, {"start": 2268.52, "end": 2269.42, "word": " ناقص", "probability": 0.990234375}, {"start": 2269.42, "end": 2270.44, "word": " تلاتة", "probability": 0.8985595703125}, {"start": 2270.44, "end": 2270.76, "word": " X", "probability": 0.98486328125}], "temperature": 1.0}, {"id": 100, "seek": 228059, "start": 2271.19, "end": 2280.59, "text": "بالشكل اللي عندنا هذا لا يزال هناك المزيد من الأمثلة إلى المحاضرة القادمة ان شاء الله تعالى", "tokens": [3555, 6027, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 20193, 7251, 11622, 6027, 34105, 4117, 9673, 11622, 25708, 9154, 16247, 2304, 12984, 37977, 30731, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.1076722786976741, "compression_ratio": 1.5229357798165137, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2271.19, "end": 2271.67, "word": "بالشكل", "probability": 0.861572265625}, {"start": 2271.67, "end": 2271.83, "word": " اللي", "probability": 0.860595703125}, {"start": 2271.83, "end": 2272.17, "word": " عندنا", "probability": 0.798828125}, {"start": 2272.17, "end": 2272.47, "word": " هذا", "probability": 0.857421875}, {"start": 2272.47, "end": 2273.31, "word": " لا", "probability": 0.395263671875}, {"start": 2273.31, "end": 2273.77, "word": " يزال", "probability": 0.9788411458333334}, {"start": 2273.77, "end": 2274.23, "word": " هناك", "probability": 0.9736328125}, {"start": 2274.23, "end": 2275.15, "word": " المزيد", "probability": 0.9952799479166666}, {"start": 2275.15, "end": 2275.71, "word": " من", "probability": 0.89794921875}, {"start": 2275.71, "end": 2276.47, "word": " الأمثلة", "probability": 0.979736328125}, {"start": 2276.47, "end": 2276.77, "word": " إلى", "probability": 0.826171875}, {"start": 2276.77, "end": 2277.57, "word": " المحاضرة", "probability": 0.9876708984375}, {"start": 2277.57, "end": 2278.31, "word": " القادمة", "probability": 0.9951171875}, {"start": 2278.31, "end": 2278.89, "word": " ان", "probability": 0.48583984375}, {"start": 2278.89, "end": 2279.27, "word": " شاء", "probability": 0.958740234375}, {"start": 2279.27, "end": 2279.71, "word": " الله", "probability": 0.9365234375}, {"start": 2279.71, "end": 2280.59, "word": " تعالى", "probability": 0.9938151041666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2281.22125, "duration_after_vad": 2204.204374999997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/E3_JyQeSPp8_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/E3_JyQeSPp8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..72096557fb8077378638b68b383ddc14722c7344
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/E3_JyQeSPp8_raw.srt
@@ -0,0 +1,1852 @@
+1
+00:00:20,740 --> 00:00:25,580
+بسم الله الرحمن الرحيم عودا على بدأ بجينا نتحدث
+
+2
+00:00:25,580 --> 00:00:29,820
+المرة اللى فاتت عن ال diagonalization ل matrix
+
+3
+00:00:29,820 --> 00:00:34,300
+واخدنا مجموعة من الأمثلة بدل المثال تلاتة بجينا
+
+4
+00:00:34,300 --> 00:00:38,400
+نجيب ال eigen values و ال eigen vectors و نثبت هل
+
+5
+00:00:38,400 --> 00:00:42,040
+المصفوفة اللى عندى diagonalizable ولا لأ طبعا
+
+6
+00:00:42,040 --> 00:00:46,280
+عرفنا انه معناه ايه similar to B معناته انه في
+
+7
+00:00:46,280 --> 00:00:51,970
+diagonalization لمن للمصفوفة Aالمثال الرابع بيقول
+
+8
+00:00:51,970 --> 00:00:56,110
+افترض المصفوفة a هي على الشكل اللي قدامنا هذا
+
+9
+00:00:56,110 --> 00:01:00,090
+بطالب تلت مطاليب المطلوب الأول قال لي هاتل ال
+
+10
+00:01:00,090 --> 00:01:05,850
+eigenvectors شغلة روتينية يا ما أوجدناها في
+
+11
+00:01:05,850 --> 00:01:09,370
+السيكشن هذا أو السيكشن اللي جابله أربعة واحد
+
+12
+00:01:09,370 --> 00:01:13,230
+المطلوب التاني بيقول find a the dimension of the
+
+13
+00:01:13,230 --> 00:01:18,070
+eigenvector space وبرضه أوجدناها قبل ذلكالأمر
+
+14
+00:01:18,070 --> 00:01:21,230
+الثالث بيقول لي هل ال matrix is similar to a
+
+15
+00:01:21,230 --> 00:01:25,390
+diagonal matrix ولا لأ؟ يعني ايش قصد يقول ليه؟ قال
+
+16
+00:01:25,390 --> 00:01:29,750
+لي هل المحصوفة is diagonalizable ولا لأ؟ هي السؤال
+
+17
+00:01:29,750 --> 00:01:35,710
+السؤال اللي قال لي شوف لي هل ال a is similar to a
+
+18
+00:01:35,710 --> 00:01:39,430
+diagonal matrix يعني كانوا بيسأل ليه هل المحصوفة
+
+19
+00:01:39,430 --> 00:01:44,620
+is diagonalizable ولا لأ؟بقول يفسه إن كان الأمر
+
+20
+00:01:44,620 --> 00:01:49,760
+كذلك find a matrix K من ال matrix K and diagonal
+
+21
+00:01:49,760 --> 00:01:54,040
+ال matrix D بحيث أن ال K inverse A K بده يساوي من؟
+
+22
+00:01:54,040 --> 00:01:58,340
+بده يساوي دي مش هتعريف ال similar يبقى similar
+
+23
+00:01:58,340 --> 00:02:01,380
+والله ديagonalizeهم الإتنين are the same نفس
+
+24
+00:02:01,380 --> 00:02:05,660
+المفهوم بالضبط تماماطيب نجي نحل هذا السؤال يبقى
+
+25
+00:02:05,660 --> 00:02:09,940
+أول نقطة بدي أروح أجيب main ال eigen ال eigen
+
+26
+00:02:09,940 --> 00:02:13,740
+values لمين للمصوفة اللي عندنا ايه يبقى بدي أبدأ
+
+27
+00:02:13,740 --> 00:02:19,680
+بمين بالمعادلة الأساسية اللي هي lambda I ناقص A
+
+28
+00:02:19,680 --> 00:02:27,580
+تساوي I lambda 00 lambda 00 lambda بالشكل اللي
+
+29
+00:02:27,580 --> 00:02:34,270
+عندنا هذا تمام؟في ناقص المصفوفة ايه بنزل المصفوفة
+
+30
+00:02:34,270 --> 00:02:41,370
+كما هي واحد اتنين تلاتة سالب واحد اربعة تلاتة واحد
+
+31
+00:02:41,370 --> 00:02:48,050
+سالب اتنين سالب واحد بالشكل اللي عندنا هذا الكلام
+
+32
+00:02:48,050 --> 00:02:54,910
+بده يساوي لندن ناقص واحدلاندا ناقص واحد ناقص اتنين
+
+33
+00:02:54,910 --> 00:03:03,070
+ناقص تلاتة هنا واحد هنا لاندا ناقص اربع وهنا ناقص
+
+34
+00:03:03,070 --> 00:03:10,790
+تلاتة وهنا ناقص واحد وهنا اتنين وهنا لاندا زائد
+
+35
+00:03:10,790 --> 00:03:15,290
+واحد بالشكل اللي عندنا هذابعد ذلك لكي احصل على الـ
+
+36
+00:03:15,290 --> 00:03:20,930
+eigenvalues انا باخد المحدد لهذه المصفوفة اذا انا
+
+37
+00:03:20,930 --> 00:03:28,550
+باخد ال determinant لمين للاندا I ناقص ال A وهو
+
+38
+00:03:28,550 --> 00:03:35,530
+المحدد لاندا minus one سالب اتنين سالب ثلاث وهنا
+
+39
+00:03:35,530 --> 00:03:40,650
+one وهنا لاندا minus four وهنا minus three minus
+
+40
+00:03:40,650 --> 00:03:49,350
+oneto lambda plus one هذا المحدد بدي احسب قيمة هذا
+
+41
+00:03:49,350 --> 00:03:53,950
+المحدد يبقى بدي افك المحدد اللي عندنا باستخدام
+
+42
+00:03:53,950 --> 00:03:59,890
+مثلا عناصر الصف الأول يبقى باجي بقول هذا الكلام
+
+43
+00:03:59,890 --> 00:04:07,040
+بدي يسوى lambda minus oneيبقى لاندا minus one في
+
+44
+00:04:07,040 --> 00:04:14,200
+المحدد الأصغر المناظر له اللاندا minus four مضروبة
+
+45
+00:04:14,200 --> 00:04:20,400
+في لاندا plus one minus مع minus بصير زائد ستة
+
+46
+00:04:21,170 --> 00:04:25,650
+العنصر اللي بعده حسب قطع الإشارات شرطه موجبة يبقى
+
+47
+00:04:25,650 --> 00:04:32,590
+زائد اتنين في نشطه بصفه و عموده يبقى لاندا plus
+
+48
+00:04:32,590 --> 00:04:38,910
+one minus three يبقى لاندا plus one minus three
+
+49
+00:04:38,910 --> 00:04:44,830
+اللي بعده minus three فيه نشطه بصفه و عموده يبقى
+
+50
+00:04:44,830 --> 00:04:50,590
+اتنين minus مع minus بصير زائد لاندا minus four
+
+51
+00:04:50,920 --> 00:04:56,460
+بالشكل اللي عندنا هذا يبقى هذا لو جيته اختصرته بده
+
+52
+00:04:56,460 --> 00:05:01,520
+يصير كتالي لاندا minus one هذا بده يفكه يا بناتي
+
+53
+00:05:01,520 --> 00:05:09,300
+يبقى لاندا تربيع ناقص تلاتة لاندا وهنا زائد اتنين
+
+54
+00:05:09,940 --> 00:05:15,480
+اللي بعده زائد اتنين في لاندا ماينوس اتنين اللي
+
+55
+00:05:15,480 --> 00:05:20,360
+بعده ناقص ثلاثة في لاندا ماينوس اتنين كل هذا
+
+56
+00:05:20,360 --> 00:05:25,460
+الكلام بدى يساوي جداش بدى يساوي Zero او ممكن اقول
+
+57
+00:05:25,460 --> 00:05:30,410
+هذا الكلام لاندا ماينوس ال oneهذه المناطق بقدر
+
+58
+00:05:30,410 --> 00:05:37,330
+أحللها، اللي هو مين؟ لاندا جوز و جوز تاني لاندا
+
+59
+00:05:37,330 --> 00:05:42,570
+وهي الجوز، هنا بقدر أقول واحد و هنا بقدر أقول
+
+60
+00:05:42,570 --> 00:05:49,530
+اتنينيبقى هذه بالناقص وهذه بالنقص هذا ال term
+
+61
+00:05:49,530 --> 00:05:54,370
+الأول طلعيلي لل term هذا هذا ال term اتنين بالموجب
+
+62
+00:05:54,370 --> 00:05:58,910
+و تلاتة بالسلب لنفس المقدار يبقى وفضل term واحد
+
+63
+00:05:58,910 --> 00:06:06,150
+بمين بالموجب يبقى هذا الكلام زائد lambda minus
+
+64
+00:06:06,150 --> 00:06:12,210
+اتنين فقط لا غير ناقص lambda ناقص اتنين وين هنا؟
+
+65
+00:06:13,530 --> 00:06:23,490
+هذه نقص
+
+66
+00:06:23,490 --> 00:06:29,830
+واحد يعني واحد اه حاطين سالب اه هذه بالسالب الصحية
+
+67
+00:06:30,540 --> 00:06:36,220
+100% أصابة امرأة وأختها عمر هذا الكلام يبدو يساوي
+
+68
+00:06:36,220 --> 00:06:43,160
+اللي هو لاندا minus two عامل مشترك من الكل بيظل
+
+69
+00:06:43,160 --> 00:06:50,900
+مين هنا هنا بيظل لاندا ناقص واحد الكل تاربيعنقص
+
+70
+00:06:50,900 --> 00:06:55,860
+واحد بالشكل لأن هذا بدي ساوي 100 بدي ساوي 0 او
+
+71
+00:06:55,860 --> 00:07:01,140
+بقدر اقول لاندا ماينوس تو فيه بدي افك الجثة دايما
+
+72
+00:07:01,140 --> 00:07:07,420
+بصير لاندا تربيع نقص اتنين لاندا وزايد واحد ونقص
+
+73
+00:07:07,420 --> 00:07:13,280
+واحد مع السلامةإذا ممكن أخد لاندا عامل مشترك من
+
+74
+00:07:13,280 --> 00:07:20,540
+هذا الجوس الثاني يبقى لاندا minus two في لاندا في
+
+75
+00:07:20,540 --> 00:07:26,080
+لاندا minus two بده يساوي zero يبقى لاندا في لاندا
+
+76
+00:07:26,080 --> 00:07:30,780
+minus two لكل تربية بده يساوي جداش بده يساوي zero
+
+77
+00:07:31,450 --> 00:07:37,290
+إذا طلع عندي قيمتين فقط للاندا وليس ثلاث قيم وطلع
+
+78
+00:07:37,290 --> 00:07:44,110
+القيمتين والقيمتين متساويات أو اللاندا طلعت مكررة
+
+79
+00:07:44,110 --> 00:07:52,010
+يبقى بناء ان علي بروح بقوله هنا the eigenvalues
+
+80
+00:07:52,010 --> 00:07:59,880
+areاللي هو lambda تساوي zero و lambda تساوي اتنين
+
+81
+00:07:59,880 --> 00:08:06,300
+فقط لا غير و هذه ال lambda مكررة كدهش مرتين يبقى و
+
+82
+00:08:06,300 --> 00:08:11,980
+بقول of multiplicity two يعني مكررة مرتين او بقدر
+
+83
+00:08:11,980 --> 00:08:16,220
+اقول lambda اتنين تساوي اتنين و lambda تلاتة تساوي
+
+84
+00:08:16,220 --> 00:08:23,140
+اتنين يبقى هذه lambda تساوي اتنين is of multi
+
+85
+00:08:28,120 --> 00:08:32,700
+Lambda تساوي اتنين مكررة مرتين إذا انتهينا من
+
+86
+00:08:32,700 --> 00:08:36,480
+المطلوب الأول اللي قال لي عنه من عند ما بدأنا هنا
+
+87
+00:08:36,480 --> 00:08:40,140
+و كل و احنا بنحاول نحصل على المطلوب الأول اللي هو
+
+88
+00:08:40,140 --> 00:08:44,320
+ال eigen values قال لي بعد هيك اتهتلي ال dimension
+
+89
+00:08:44,320 --> 00:08:49,900
+لمن؟ ل ال eigen vector spaces يبقى بدأ أخد lambda
+
+90
+00:08:49,900 --> 00:08:52,660
+تساوي زيرو بعد هيك lambda تساوي اتنين و أشوف إيش
+
+91
+00:08:52,660 --> 00:08:59,700
+اللي بيحصل معانايبقى باجي بقوله هنا if لاندا تساوي
+
+92
+00:08:59,700 --> 00:09:05,160
+zero then بدي أخد لاندا الأولى بدي أرجع لمين
+
+93
+00:09:05,160 --> 00:09:10,440
+للمعادلة الأصلية اللي عندنا هذه تمام و بدي أخد
+
+94
+00:09:10,440 --> 00:09:17,120
+المعادلة كثيرة then لاندا I نقص ال A في ال X يساوي
+
+95
+00:09:17,120 --> 00:09:22,020
+Zero implies هي المصممة بدي أشيل لاندا و أحط
+
+96
+00:09:22,020 --> 00:09:28,070
+مكانها Zeroبظلنا ناقص واحد ناقص اتنين ناقص ثلاثة
+
+97
+00:09:28,070 --> 00:09:34,850
+واحد ناقص اربعة وهنا ناقص ثلاثة وهنا ناقص واحد
+
+98
+00:09:34,850 --> 00:09:40,730
+اتنين وهنا واحد بالشكل اللي عندنا هذا X واحد X
+
+99
+00:09:40,730 --> 00:09:46,610
+اتنين X تلاتة هذا الكلام بده يساوي Zero و Zero و
+
+100
+00:09:46,610 --> 00:09:52,780
+Zeroإذا ترجمتي المعادلة اللي عندنا هذه عامليا
+
+101
+00:09:52,780 --> 00:09:58,140
+بالقيم اللي موجودة عندنا نحاول نجيب قيم كلها من X1
+
+102
+00:09:58,140 --> 00:10:04,980
+و X2 و X3 لإن هذه ال X بتجيب لمين ال Eigen vectors
+
+103
+00:10:05,520 --> 00:10:10,720
+إذا بدي أجهزي و أقول بدي أعطي المعادلة دُغري يبقاش
+
+104
+00:10:10,720 --> 00:10:19,060
+بصير انا لابنت هنا ناقص X1 ناقص 2 X2 ناقص 3 X3 بده
+
+105
+00:10:19,060 --> 00:10:29,280
+يساوي 0 وهنا X1 ناقص 4 X2 ناقص 3 X3 بده يساوي كمان
+
+106
+00:10:29,280 --> 00:10:37,590
+100 بده يساوي 0 ناقص X1وهنا زائد اتنين X2 وهنا
+
+107
+00:10:37,590 --> 00:10:42,830
+زائد X3 يسوى Zero يبقى حصلنا على ال homogenous
+
+108
+00:10:42,830 --> 00:10:46,870
+system اللي عندنا بنحاول نحل ال homogenous system
+
+109
+00:10:46,870 --> 00:10:52,870
+بأي طريقة من الطرق التي سبقت دراستهافمثلًا لو جيت
+
+110
+00:10:52,870 --> 00:10:57,370
+أخدت المعادلة الأولى والتانية هذه يا بنات وجيت
+
+111
+00:10:57,370 --> 00:11:02,750
+جماعة طبعًا هتروح هذه مع هذه مظبوط؟ بضع أننا ناقص
+
+112
+00:11:02,750 --> 00:11:11,540
+6x2 وناقص 6x3 بدل سوى قداش؟ Zeroأو لو جسمت على
+
+113
+00:11:11,540 --> 00:11:18,080
+سالب ستة بصير X2 زائد X3 يساوي Zero أو بقدر أقول
+
+114
+00:11:18,080 --> 00:11:25,540
+ان X2 يساوي سالب X3 هذا لما أخد الأولى مع مين؟ مع
+
+115
+00:11:25,540 --> 00:11:32,230
+الثانية طب لو أخدت التانية مع مين؟ مع التالتةهذه
+
+116
+00:11:32,230 --> 00:11:37,830
+خد مع هذه أو أخد الأولى مع التالتة مثلا لو أخدت
+
+117
+00:11:37,830 --> 00:11:43,170
+الأولى مع التالتة يبقى الأولى ناقص x واحد ناقص
+
+118
+00:11:43,170 --> 00:11:48,470
+اتنين x اتنين ناقص تلاتة x تلاتة بدى يساوي zero
+
+119
+00:11:48,470 --> 00:11:55,370
+وهنا سالب x واحد اتنين x اتنين زائد x تلاتة بدى
+
+120
+00:11:55,370 --> 00:12:00,490
+يساوي zero طبعا هذه هتروح مع هذه بظل هنا mainاللي
+
+121
+00:12:00,490 --> 00:12:08,410
+هو من سالب اتنين X1 و هنا سالب اتنين X3 بده يسوي
+
+122
+00:12:08,410 --> 00:12:15,650
+Zero يبقى X1 زائد X3 بده يسوي Zero يبقى X1 يسوي
+
+123
+00:12:15,650 --> 00:12:23,510
+سالب X3 يبقى بناء عليه أصبح عندي X1 بده يسوي X2
+
+124
+00:12:23,510 --> 00:12:34,890
+بده يسوي X3 إذا لو أخدتإن ال X3 بدها تساوي .. لو
+
+125
+00:12:34,890 --> 00:12:46,170
+أخدت ال X3 مثلا تساوي A أو أخدت X1 تساوي X2 تساوي
+
+126
+00:12:46,170 --> 00:12:46,670
+A
+
+127
+00:12:50,670 --> 00:12:56,790
+ثم سالب اكس ثري تساوي ايه؟ هذا يعطيك ان اكس ثري
+
+128
+00:12:56,790 --> 00:13:03,570
+يساوي قداش سالب ايه؟ يبقى باجي بقوله the eigen
+
+129
+00:13:03,570 --> 00:13:14,010
+vectors corresponding to
+
+130
+00:13:14,010 --> 00:13:22,650
+the lambda تساوي zero are inThe form على الشكل
+
+131
+00:13:22,650 --> 00:13:28,490
+التالي X1
+
+132
+00:13:28,490 --> 00:13:38,950
+X2 X3 X1
+
+133
+00:13:38,950 --> 00:13:41,850
+X2 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 X3
+
+134
+00:13:41,850 --> 00:13:45,530
+X3 X3 X3 X3 X3 X3 X3طب ايش بيقوللي قاللي هتلت
+
+135
+00:13:45,530 --> 00:13:51,890
+dimension لل eigen vector space يبقى هذا ال vector
+
+136
+00:13:51,890 --> 00:13:54,990
+اللي
+
+137
+00:13:54,990 --> 00:14:05,670
+هو من واحد واحد سالب واحد is a basis for the eigen
+
+138
+00:14:05,670 --> 00:14:10,310
+vector space
+
+139
+00:14:11,660 --> 00:14:19,860
+يبقى هذا بدّي يعطينا مين؟ انه its dimension اللي
+
+140
+00:14:19,860 --> 00:14:23,020
+بدّويا كده؟ واحدة
+
+141
+00:14:26,410 --> 00:14:31,950
+يبقى أنا جبت له ال A و ال B مرة واحدة تمام طيب قال
+
+142
+00:14:31,950 --> 00:14:35,850
+لي is the matrix A similar يبقى استنى شوية لبسها
+
+143
+00:14:35,850 --> 00:14:39,330
+سيه فيها كلام تاني بعد هيك بدى أروح أجيب لاندا
+
+144
+00:14:39,330 --> 00:14:49,070
+تساوي اتنين يبقى F لاندا تساوي اتنين then لاندا I
+
+145
+00:14:49,070 --> 00:14:56,540
+ناقص A في ال X بدها تساوي Zero impliesعن طريق
+
+146
+00:14:56,540 --> 00:15:00,260
+المصوفة اللي عندنا هذه بدي اشيل كلان ده و احط مكان
+
+147
+00:15:00,260 --> 00:15:05,940
+اقدر اش اتنين اتنين ناقص واحد بدل ان اقدر اش واحد
+
+148
+00:15:05,940 --> 00:15:12,880
+وعندنا هنا ناقص اتنين ناقص تلاتة الصف التاني واحد
+
+149
+00:15:12,880 --> 00:15:19,620
+و هنا ناقص اتنين و هنا ناقص تلاتةصفة تالت ناقص
+
+150
+00:15:19,620 --> 00:15:26,460
+واحد اتنين وهنا بدنا نحط اتنين بيصير تلاتة في X
+
+151
+00:15:26,460 --> 00:15:33,640
+واحد X اتنين X تلاتة بده يساوي Zero و Zero و Zero
+
+152
+00:15:35,940 --> 00:15:41,500
+هذه المعادلة تجيب لي ثلاث معادلات لكن في الحقيقة
+
+153
+00:15:41,500 --> 00:15:47,620
+هما ثلاث معادلات ولا تنتين ولا معادلة واحدة يبقى
+
+154
+00:15:47,620 --> 00:15:53,240
+هذه المعادلة واحدة فقط لا غيرالصف هذا لو ضربت في
+
+155
+00:15:53,240 --> 00:15:57,980
+سالب واحد بيطلع الصفين اللي فوق تمام يبقى هذه مش
+
+156
+00:15:57,980 --> 00:16:02,280
+معادلة واحدة وانما او الثلاث معادلات عبارة عن
+
+157
+00:16:02,280 --> 00:16:07,680
+معادلة واحدة فقط لا غير يبقى معناه هذا الكلام ان X
+
+158
+00:16:07,680 --> 00:16:14,000
+واحد ناقص اتنين X اتنين ناقص تلاتة X تلاتة بيساوي
+
+159
+00:16:14,000 --> 00:16:22,030
+قدر Zero او ان شئتم فقولوا ان X واحديساوي 2 X2
+
+160
+00:16:22,030 --> 00:16:29,970
+زائد 3 X3 يبقى هذه المعادلة مجهولة بثلاثة مجهول
+
+161
+00:16:29,970 --> 00:16:35,710
+إذا لا يمكن حل هذه المعادلة إلا إذا أعطينا قيمتين
+
+162
+00:16:35,710 --> 00:16:45,690
+لمجهولين يبقى ممكن أحط مثلا X2 بA و X3 بB وبالتالي
+
+163
+00:16:45,690 --> 00:16:53,400
+بجيب X1بتلات X2 و X3 يبقى if ال X2 بده يساوي ال A
+
+164
+00:16:53,400 --> 00:17:03,580
+and X3 بده يساوي ال B then ال X1 بده يساوي 2A زائد
+
+165
+00:17:03,580 --> 00:17:09,080
+3B أظن هذا كله مالش لزومة الحين
+
+166
+00:17:25,020 --> 00:17:34,100
+طيب بنواصل الحلل، الآن باجي بقول the eigenvectors
+
+167
+00:17:34,100 --> 00:17:40,500
+corresponding to
+
+168
+00:17:40,500 --> 00:17:51,440
+land تساوي اتنين are in the form في الشكل التالي
+
+169
+00:17:55,340 --> 00:18:04,820
+X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
+
+170
+00:18:04,820 --> 00:18:05,960
+X11 X12 X13 X12 X13 X12 X12 X12 X12 X12 X12 X12
+
+171
+00:18:05,960 --> 00:18:06,060
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+172
+00:18:06,060 --> 00:18:06,100
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+173
+00:18:06,100 --> 00:18:06,140
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+174
+00:18:06,140 --> 00:18:06,160
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+175
+00:18:06,160 --> 00:18:06,160
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+176
+00:18:06,160 --> 00:18:06,160
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+177
+00:18:06,160 --> 00:18:06,180
+X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12 X12
+
+178
+00:18:06,180 --> 00:18:07,880
+X12 X12 X12 X12 X12 X12
+
+179
+00:18:11,270 --> 00:18:16,110
+بقدر هذه المصوفة يا بنات اقسمها الى مجموعة مصففين
+
+180
+00:18:16,110 --> 00:18:23,190
+يبقى بقدر اقول هذا الكلام يساوي اتنين A A Zero
+
+181
+00:18:23,190 --> 00:18:31,910
+زائد تلاتة B Zero B او ان شئتم فقولوا هي ال A برا
+
+182
+00:18:31,910 --> 00:18:40,510
+و هنا اتنين واحد Zero زائد B في تلاتة Zero واحد
+
+183
+00:18:43,330 --> 00:18:48,050
+أريد أن أرى قيمة الـBases للـVector Space المولد
+
+184
+00:18:48,050 --> 00:18:51,850
+بالـTwo Vectors بإذن الله أخرج في الاتنين هل هما
+
+185
+00:18:51,850 --> 00:18:56,470
+Linearly Dependent و لا Linearly Independent إذا
+
+186
+00:18:56,470 --> 00:19:00,910
+كانوا Linearly Dependent يكفي واحد منهم وإذا كانوا
+
+187
+00:19:00,910 --> 00:19:05,770
+اتنين Linearly Independent يبقى بصير الـBases في
+
+188
+00:19:05,770 --> 00:19:11,230
+عنصرين وبالتالي الـDimension يساوي اتنين أخرجني في
+
+189
+00:19:11,230 --> 00:19:16,500
+الاتنين هؤلاءعمر واحد فيهم بيصير مضاعفات الآخر
+
+190
+00:19:16,500 --> 00:19:24,280
+مافيش إمكانية على الإطلاق يبقى باجي بقول since the
+
+191
+00:19:24,280 --> 00:19:36,660
+two vectors اللي هم اتنين واحد زيرو وتلاتة
+
+192
+00:19:36,660 --> 00:19:46,740
+زيرو واحد are linearly independentbecause anyone
+
+193
+00:19:46,740 --> 00:20:06,640
+is not multiple of the other we have انه ده set
+
+194
+00:20:06,640 --> 00:20:16,380
+اللي هي mainاتنين واحد وزيرو والعنصر التاني تلاتة
+
+195
+00:20:16,380 --> 00:20:35,940
+زيرو واحد is a basis for the eigen vector space
+
+196
+00:20:35,940 --> 00:20:38,360
+corresponding
+
+197
+00:20:43,870 --> 00:20:53,750
+تو لاندا تو ساوة اتنين اذا انتهينا من نمر بي و لا
+
+198
+00:20:53,750 --> 00:21:01,290
+مانتهيناش بدنا ال dimension يبقى هنا هدول يبقى as
+
+199
+00:21:01,290 --> 00:21:07,450
+a basis for the corresponding to لاندا تو and its
+
+200
+00:21:07,450 --> 00:21:09,390
+dimension
+
+201
+00:21:13,670 --> 00:21:20,990
+is two يبقى ال dimension يساوي كده؟ يساوي اتنين
+
+202
+00:21:20,990 --> 00:21:26,410
+يبقى انتهينا من المطلوب A وB ضايل عندنا مين؟ ضايل
+
+203
+00:21:26,410 --> 00:21:31,910
+عندنا C C بيقول مانو؟ بيقول هل ال matrix A similar
+
+204
+00:21:31,910 --> 00:21:37,350
+to A diagonal matrix ام لا؟ بمعنى اخر هل ال A
+
+205
+00:21:37,350 --> 00:21:43,570
+دياجونالي Z بالو ولا لا؟ شفوي بمجرد النظرالحين
+
+206
+00:21:43,570 --> 00:21:48,090
+طلعنا مين؟ قداش الـ linearly independent element
+
+207
+00:21:48,090 --> 00:21:54,490
+طيب اه استنى شوية طلعيلي الاتنين هدول واطلعيلي
+
+208
+00:21:54,490 --> 00:22:00,650
+لمين؟ للتالت اللي هو عندنا هذا هل التلاتة هدول are
+
+209
+00:22:00,650 --> 00:22:03,590
+linearly dependent ولا linearly independent؟
+
+210
+00:22:03,590 --> 00:22:09,010
+بتعمليلهم ال check يبقى هنا بدك تقوليلي ما يأتي
+
+211
+00:22:09,010 --> 00:22:12,570
+بدك تعمليلي ال check التالي
+
+212
+00:22:23,900 --> 00:22:31,240
+check that vectors
+
+213
+00:22:31,240 --> 00:22:39,170
+اللي هم مين ال vector الأول يعنيالتي هو واحد واحد
+
+214
+00:22:39,170 --> 00:22:44,630
+سالب واحد والتاني اللي طالع عندنا اللي هو اتنين
+
+215
+00:22:44,630 --> 00:22:54,190
+واحد زيرو والتالت اللي هو من تلاتة زيرو واحد are
+
+216
+00:22:54,190 --> 00:23:00,150
+linearly independent كيف
+
+217
+00:23:00,150 --> 00:23:04,940
+بدي أسويهم linearly independentكيف بدي أعملهم بقى؟
+
+218
+00:23:04,940 --> 00:23:10,480
+وكيف بدي أثبت انهم linearly independent؟ نفرض C1
+
+219
+00:23:10,480 --> 00:23:15,900
+وC2 وC3 تكون أصلاً C في الأول زي C في التاني زي C
+
+220
+00:23:15,900 --> 00:23:20,520
+في التالي يساوي Zero وأثبت ان C1 يساوي C2 يساوي C3
+
+221
+00:23:20,520 --> 00:23:25,700
+يساوي Zero هذه إحدى الطرق الطويلة في أكثر منها ايش
+
+222
+00:23:25,700 --> 00:23:32,810
+اللي أكثر منها؟نعمل محدد وليست مصفورة نعمل محدد
+
+223
+00:23:32,810 --> 00:23:38,970
+ونثبت أن المحدد لا يساوي zero انطلع ذلك يبقى بيصير
+
+224
+00:23:38,970 --> 00:23:42,790
+عندي linearly independent يبقى تبعت المحدد أسهل من
+
+225
+00:23:42,790 --> 00:23:46,290
+الأولين الأولين بدها شغل شوية لإن بدي أعمل system
+
+226
+00:23:46,290 --> 00:23:49,610
+و ال system بتروح علّه بس ال determinant ده سهل
+
+227
+00:23:49,610 --> 00:23:54,130
+جدا يعني في خطوة واحدة بكون جيبينجبت الحلقة و
+
+228
+00:23:54,130 --> 00:23:59,010
+أثبتت إن هدول linearly independent طيب معناته
+
+229
+00:23:59,010 --> 00:24:04,710
+التلاتة هدول بيكملولي من the complete set of
+
+230
+00:24:04,710 --> 00:24:08,690
+linearly independent elements صحيح ولا لأ؟ يعني في
+
+231
+00:24:08,690 --> 00:24:14,810
+غيرهم؟ مافيش عندي غيرهم، قداش عددهم؟ قداش نظام
+
+232
+00:24:14,810 --> 00:24:20,800
+الوصوفة؟يبقى ياش المصحوفة diagonalizable اصلا عن
+
+233
+00:24:20,800 --> 00:24:25,780
+اللي مرضى او similar to a diagonal matrix الصيغة
+
+234
+00:24:25,780 --> 00:24:29,540
+هذه والصيغة هذه الاتنين are the same يبقى باجي
+
+235
+00:24:29,540 --> 00:24:34,860
+بقول هدول كولوني linearly independent element this
+
+236
+00:24:34,860 --> 00:24:46,690
+means that the setالي هي مين؟ واحد واحد سالب واحد
+
+237
+00:24:46,690 --> 00:24:57,570
+اتنين واحد زيرو تلاتة زيرو واحد is the complete
+
+238
+00:24:57,570 --> 00:25:05,050
+set of eigen vectors
+
+239
+00:25:11,120 --> 00:25:18,700
+يبقى sense بما ان number of
+
+240
+00:25:18,700 --> 00:25:37,640
+these vectors is three and the degree of the
+
+241
+00:25:38,390 --> 00:25:52,170
+ماتريكس a is a3 ال a is diagonalizable
+
+242
+00:25:52,170 --> 00:25:58,430
+ايش يعني diagonalizable يعني ال a is similar to a
+
+243
+00:25:58,430 --> 00:26:04,190
+diagonal هذا معناته ان ال a is similar
+
+244
+00:26:27,350 --> 00:26:35,370
+مش هذا معناه يا بنات؟طيب، بدنا نجي نشوف هالكلام
+
+245
+00:26:35,370 --> 00:26:41,480
+هذا اللي احنا بنقوله هذاماذا قاله؟ قال يفسه إن كان
+
+246
+00:26:41,480 --> 00:26:45,420
+الأمر كذا لك هاتل ال matrix K and إذا يجون ال
+
+247
+00:26:45,420 --> 00:26:50,620
+matrix دي فهي تبقى العلاقة هذه مالها صحيحة يبقى
+
+248
+00:26:50,620 --> 00:26:54,760
+احنا بدنا نجيبله K ونجيب ال K and بس الحين
+
+249
+00:26:54,760 --> 00:27:01,020
+الكيابانات هي من؟ هي المصفوفة العناصرها من؟ عناصر
+
+250
+00:27:01,020 --> 00:27:08,470
+ال eigenvectors يبقى واحد واحد سالب واحداتنين واحد
+
+251
+00:27:08,470 --> 00:27:16,030
+زيرو تلاتة زيرو واحد بدنا نجيب المعكوس تبعها مشان
+
+252
+00:27:16,030 --> 00:27:21,630
+نجيب المعكوس بدنا نروح نجيب مين المحدد يبقى هذا
+
+253
+00:27:21,630 --> 00:27:29,360
+بده يعطينا المحدد تبع المصوفة كذا بده يساوياللي هو
+
+254
+00:27:29,360 --> 00:27:35,380
+main المحدد تبع واحد اتنين تلاتة واحد واحد زيرو
+
+255
+00:27:35,380 --> 00:27:40,380
+سالب واحد زير واحد ويساوي
+
+256
+00:27:42,730 --> 00:27:47,770
+بتفكر ايش رأيكوا بالاستخدام عناصر الصف الثاني او
+
+257
+00:27:47,770 --> 00:27:51,550
+العمود التالت او العمود التاني سياد ناخد العمود
+
+258
+00:27:51,550 --> 00:27:58,930
+التالت يبقى هاي تلاتة فيه نشطة بصفه و عموده تمام
+
+259
+00:27:58,930 --> 00:28:04,950
+بصير واحد ناقص اتنين اللي بعده حسب قاعة الإشارات
+
+260
+00:28:04,950 --> 00:28:09,370
+بزيره في قد ما يكون يكون مش مشكلة زائد واحد في
+
+261
+00:28:09,370 --> 00:28:18,160
+قشطة بصفهلأ استنى شوية سطبنا صفه و عمضه صفه و عمضه
+
+262
+00:28:18,160 --> 00:28:20,460
+يجيه بجهة zero زياد واحد
+
+263
+00:28:22,770 --> 00:28:28,250
+زائد واحد اللي بعد واحد نشطب صف وعمود لواحد ناقص
+
+264
+00:28:28,250 --> 00:28:36,110
+اتنين واحد ناقص اتنين يبقى النتيجة تلاتة وهنا ناقص
+
+265
+00:28:36,110 --> 00:28:43,810
+واحد ويساوي كده؟ ويساوي اتنين تمامبدي أجيب له الـK
+
+266
+00:28:43,810 --> 00:28:50,450
+inverse يبقى الـK inverse ويو ساوي اللي هو واحد
+
+267
+00:28:50,450 --> 00:28:58,630
+على المحدد فاهمين؟ فيه بدي أستبدل هذه المصفوفة كل
+
+268
+00:28:58,630 --> 00:29:04,650
+عنصر فيها بال cofactor تبعه مظبوط؟ يبقى بدي أجيب
+
+269
+00:29:04,650 --> 00:29:09,810
+للواحدبدي أشيل صفه و عموده، بيظل واحد نخزنه كله
+
+270
+00:29:09,810 --> 00:29:16,310
+بواحد و حسب قاعة الإشارات شرطه بالموجة نجي لبعده،
+
+271
+00:29:16,310 --> 00:29:21,370
+لإتنين حسب قاعة الإشارات شرطه بمين؟ بالسالف نشطب
+
+272
+00:29:21,370 --> 00:29:29,780
+صفه و عموده، بيصير واحد فقط كذلكنجي للي بعده حسب
+
+273
+00:29:29,780 --> 00:29:35,800
+قاعدة شرعتي شرطه بالموجة نشطه بصفه و عموده بيصير
+
+274
+00:29:35,800 --> 00:29:42,380
+zero زيد واحد اللي هو بواحد بعد هيك نجي لصفه
+
+275
+00:29:42,380 --> 00:29:49,040
+الثاني بدي أشيل اللي صفه و عموده بيصير اتنين ناقص
+
+276
+00:29:49,040 --> 00:29:55,720
+تلاتة بقدرش باتنين بدي أجي لعنصر اللي بعدهطبعا هذا
+
+277
+00:29:55,720 --> 00:30:00,160
+حسب قاعدة الإشارة الشرط السالي بيبنى تمام اللي بقى
+
+278
+00:30:00,160 --> 00:30:04,820
+ده الشرط موجبه يبقى ده شيل صفه و عموده بصير واحد
+
+279
+00:30:04,820 --> 00:30:12,370
+ناقص ثلاثة يعني زائد تلاتة اللي بقى كدهش قلناعشان
+
+280
+00:30:12,370 --> 00:30:17,670
+نشيل هذا يبقى اشيلنا هذا يبقى واحد زائد تلاتة اللي
+
+281
+00:30:17,670 --> 00:30:22,130
+هو بقداش اربعة هذا حسب قاعد الإشارات شرط بين
+
+282
+00:30:22,130 --> 00:30:28,810
+بالسالم نشط بصفه و عموده يبقى zero زائدي اتنين
+
+283
+00:30:28,810 --> 00:30:32,950
+اللي هو بقداش بناقص اتنين نجي لبعده حسب قاعد
+
+284
+00:30:32,950 --> 00:30:38,050
+الإشارات شرط بالموجة اشط بصفه و عموده zero ناقص
+
+285
+00:30:38,050 --> 00:30:45,400
+تلاتة نجي للي بعدهاللي بعده حسب قاعدة الإشارات
+
+286
+00:30:45,400 --> 00:30:51,680
+شرطه سالب يبقى يسالب نشط بصفه و عموده يبقى zero
+
+287
+00:30:51,680 --> 00:30:57,420
+ناقص تلاتة بالصير زائد تلاتة اللي بعده حسب قاعدة
+
+288
+00:30:57,420 --> 00:31:01,840
+الإشارات شرطه موجبة نشط بصفه و عموده بصير واحد
+
+289
+00:31:01,840 --> 00:31:06,300
+ناقص اتنين اللي هو قداشر بناقص واحد بالشكل اللي
+
+290
+00:31:06,300 --> 00:31:15,580
+عندنا أنا بدي أجيب له D يبقى Dبدا تساوي K inverse
+
+291
+00:31:15,580 --> 00:31:22,780
+اي K تمام؟ يبقى هذا الكلام بده يساوي النص و هنا
+
+292
+00:31:22,780 --> 00:31:28,040
+واحد سالب واحد واحد سالب اتنين اربعة سالب اتنين
+
+293
+00:31:28,040 --> 00:31:33,480
+سالب تلاتة تلاتة سالب واحد في مين؟ في ايه؟ راس
+
+294
+00:31:33,480 --> 00:31:39,440
+المسألة واحد اتنين تلاتة و هنا سالب واحد اربعة
+
+295
+00:31:39,700 --> 00:31:47,760
+تلاتة و هنا واحد سالب اتنين سالب واحد في مين في ال
+
+296
+00:31:47,760 --> 00:31:54,820
+K ال K اللي هي واحد اتنين تلاتة واحد واحد زيرو
+
+297
+00:31:54,820 --> 00:32:01,570
+سالب واحد زيرو واحد بالشكل اللي عندنا هناكداش
+
+298
+00:32:01,570 --> 00:32:09,730
+تتوقع يكون النتيجة؟ Zero اتنين اتنين و الباقي يبقى
+
+299
+00:32:09,730 --> 00:32:16,050
+أسفل يبقى هذا يكون المصوفة القطرية التالية Zero و
+
+300
+00:32:16,050 --> 00:32:24,330
+هنا Zero Zero Zero اتنين Zero Zero اتنينليس لاندا
+
+301
+00:32:24,330 --> 00:32:27,670
+طلعت هندم Zero و لاندا طلعت هندم اتنين و اتنين
+
+302
+00:32:27,670 --> 00:32:32,350
+يبقى هاي عناصر قط رئيسي ال diagonal matrix اللي
+
+303
+00:32:32,350 --> 00:32:36,310
+يقولنا عليها ال diagonal دي يبقى براحتك تروح تضرب
+
+304
+00:32:36,310 --> 00:32:40,730
+هدول مصففات في بعض في بيتك و الناتج هي ماعطينك
+
+305
+00:32:40,730 --> 00:32:44,410
+إياه إذا طلع غلط يبقى غلط علينا مش عليك أو عليك
+
+306
+00:32:44,410 --> 00:32:48,630
+إذا بتضرب غلط لكن عندنا احنا ماعطينك الجواب بدك
+
+307
+00:32:48,630 --> 00:32:52,270
+تضربه و الناتج هيه عندك في واحدة أبناء ماسجلتش
+
+308
+00:32:52,270 --> 00:32:52,930
+اسمها هنا
+
+309
+00:32:56,050 --> 00:33:04,170
+طيب ننتقل إلى مثال يختلف عن هذا نوعا ما لكنه مرتبط
+
+310
+00:33:04,170 --> 00:33:11,030
+معه ارتباطا هذا المثال جبته نظري من خلال أسئلة
+
+311
+00:33:11,030 --> 00:33:18,830
+التمرين وهو سؤال 16 في التمرين تبع ال section 4-3
+
+312
+00:33:18,830 --> 00:33:21,310
+السؤال بيقول ما يأتي
+
+313
+00:33:30,400 --> 00:33:39,760
+يبقى example خمسة له سؤال ستة عشر من الكتاب بيقول
+
+314
+00:33:39,760 --> 00:33:53,260
+if ال A and ال B are similar matrices
+
+315
+00:33:53,260 --> 00:34:11,520
+matrices so thatبحيث ان ال B تساوي ال K inverse اك
+
+316
+00:34:11,520 --> 00:34:16,420
+show
+
+317
+00:34:16,420 --> 00:34:20,720
+that بيّلي
+
+318
+00:34:20,720 --> 00:34:35,330
+ان ال X is Ais an eigen vector
+
+319
+00:34:35,330 --> 00:34:51,530
+of a if and only if ال K inverse X is an eigen
+
+320
+00:34:51,530 --> 00:34:54,730
+vector
+
+321
+00:34:56,190 --> 00:35:02,050
+هو ايجن فيكتر بي
+
+322
+00:35:41,120 --> 00:35:47,340
+سؤال مرة ثانية السؤال بيقول لو كانت ال A و ال B
+
+323
+00:35:47,340 --> 00:35:52,440
+are similar matrices طبعا احنا أخدنا علاقة المرة
+
+324
+00:35:52,440 --> 00:35:57,020
+قبل الماضي لو كان A similar to B يبقى B similar to
+
+325
+00:35:57,020 --> 00:36:00,980
+A و أثبتناها مظبوط يبقى الأن جلدتين هدول are
+
+326
+00:36:00,980 --> 00:36:08,170
+similarيعني ايه؟ يعني ان الـP بدى يسوي K inverse
+
+327
+00:36:08,170 --> 00:36:14,750
+AK طيب أصبحت هذه معلومة عندنا بيقول شوية بيه لإن
+
+328
+00:36:14,750 --> 00:36:19,790
+ال X is an eigen value ل A إيه فندقول إذا K
+
+329
+00:36:19,790 --> 00:36:25,730
+inverse X is an eigen vector ل A إيه فندقول إذا K
+
+330
+00:36:25,730 --> 00:36:30,450
+inverse X is an eigen vector لمين لبين يبقى هذا
+
+331
+00:36:30,450 --> 00:36:34,960
+سؤال والله سؤالينسؤالين بدى امشك واحد واصله لمين
+
+332
+00:36:34,960 --> 00:36:39,240
+للثانى و بعدين امشك الثانى واصله لمين للأول السبب
+
+333
+00:36:39,240 --> 00:36:44,560
+كلمة if and only if ده يبقى الآن بداجي بالخطوة
+
+334
+00:36:44,560 --> 00:36:58,390
+الأولى let ال a be similar to b thenThere exists a
+
+335
+00:36:58,390 --> 00:37:11,750
+non-zero matrix K such that بحيث أن الـ B بده
+
+336
+00:37:11,750 --> 00:37:20,410
+يساوي الـ K inverse AK المعطىيبقى حتى لان انا بس
+
+337
+00:37:20,410 --> 00:37:27,450
+اتجمد الشي المقطع عندي خطوة تانية بدي افترض ان X
+
+338
+00:37:27,450 --> 00:37:33,910
+عبارة عن مين عن Eigen vector لمن للمصفوف A يبقى ا
+
+339
+00:37:33,910 --> 00:37:43,590
+assume that ان X is an Eigen vector
+
+340
+00:37:47,640 --> 00:38:00,920
+for the matrix for the matrix A then ايش فرضنا ان
+
+341
+00:38:00,920 --> 00:38:08,220
+ال X هي eigen vector لمين لهذه ايش يعني معناها ايش
+
+342
+00:38:08,220 --> 00:38:12,800
+يعني معناها ان ال X هي eigen vector ل A يعني لو
+
+343
+00:38:12,800 --> 00:38:15,240
+ضربت ال A في ال X ايش بدي يطلع ليه
+
+344
+00:38:19,660 --> 00:38:24,580
+تعريف الـ eigen vector و ال eigen value شبتر
+
+345
+00:38:24,580 --> 00:38:32,700
+section 4-1 أول تعريف أخدناه إيش يعني؟ يعني هلاجي
+
+346
+00:38:32,700 --> 00:38:38,360
+عدد الـ scalar لأن ده مضروف x بدي يسوي x الشركة
+
+347
+00:38:38,360 --> 00:38:43,690
+أخدنا التعريف؟يبقى هذا معناه x is an eigen value
+
+348
+00:38:43,690 --> 00:38:56,190
+then ال ax بده ساوي lambda x for some real lambda
+
+349
+00:38:56,190 --> 00:38:58,770
+اللي موجودة في ال 6 real number
+
+350
+00:39:01,740 --> 00:39:05,920
+يبقى هلاقي مادام هذا eigenvector هو بيجيش ال
+
+351
+00:39:05,920 --> 00:39:09,340
+eigenvector إلا إذا كان عندي eigenvalue صحيح ولا
+
+352
+00:39:09,340 --> 00:39:12,800
+لأ طيب مادام عندي eigenvalue مادام عندي
+
+353
+00:39:12,800 --> 00:39:15,380
+eigenvector إيه اللي هو اصلي اللي هو ال eigenvalue
+
+354
+00:39:15,380 --> 00:39:22,120
+اللي هو lambda X مش lambda I lambda X بالشكل اللي
+
+355
+00:39:22,120 --> 00:39:26,460
+عندنايبقى ال AX بديه يسوي مين؟ بديه يسوي لاندا X
+
+356
+00:39:26,460 --> 00:39:32,880
+for some real اللي هو لاندا أو for some بلاش كلمة
+
+357
+00:39:32,880 --> 00:39:38,540
+real لأنهم كرروا مرتين بالصريحة X for some لاندا
+
+358
+00:39:38,540 --> 00:39:44,280
+اللي موجودة في ال set of real numbersيبقى هذه
+
+359
+00:39:44,280 --> 00:39:49,460
+المعلومة أخدتها من الفرض طب بدي أشوف إيش اللي بدي
+
+360
+00:39:49,460 --> 00:39:54,140
+إياه إيش بيقوللي بيقوللي أثبتلي إن هذا هو
+
+361
+00:39:54,140 --> 00:40:00,760
+eigenvector لمام ل B يعني بدي أثبت إن حصل ضرب هذا
+
+362
+00:40:00,760 --> 00:40:07,540
+في B بدي أساوي scalar في ال X صحيح ولا لأ طيب
+
+363
+00:40:07,540 --> 00:40:09,880
+بداجي أقوله الآن consider
+
+364
+00:40:13,970 --> 00:40:19,370
+خُد لي بدي أثبت إن هذا is an eigenvector يبقى بدي
+
+365
+00:40:19,370 --> 00:40:25,110
+أخد لمين لي بيه يبقى بدي أخد بيه في مين في ال K
+
+366
+00:40:25,110 --> 00:40:26,670
+inverse X
+
+367
+00:40:30,270 --> 00:40:36,190
+هه مش هذه هنا ax بدي اثبت ان ال b في ال k inverse
+
+368
+00:40:36,190 --> 00:40:42,510
+x بده يساوي الرقم مضروب في x انطلع هذا الرقم بصير
+
+369
+00:40:42,510 --> 00:40:47,750
+هذا هو eigen vector صحيح ولا لأ طيب ماشي الحال
+
+370
+00:40:47,750 --> 00:40:53,970
+يبقى باجي اقول هذا الكلام بده يساوي طلعيلي هنا هذه
+
+371
+00:40:55,360 --> 00:41:01,500
+أنا عند مين؟ عند بي بده تساوي K inverse AK إذا
+
+372
+00:41:01,500 --> 00:41:08,500
+بقدر أشيل ال B و أكتب بدلها K inverse AK يبقى بقدر
+
+373
+00:41:08,500 --> 00:41:17,360
+أقول هذا الكلام بده يساوي K inverse AK الشكل اللي
+
+374
+00:41:17,360 --> 00:41:22,480
+عندنا هنا كله مضروب في مين؟ في ال K inverse X
+
+375
+00:41:22,480 --> 00:41:28,940
+الشكل اللي عندنا هناخاصية ال associative صحيحة على
+
+376
+00:41:28,940 --> 00:41:35,300
+من؟ على المصفوفات و دول كلهم مصفوفات ال X و ال A و
+
+377
+00:41:35,300 --> 00:41:39,980
+ال K و ال K inverse كلهم مصفوفات اذا بقدر اقول هذا
+
+378
+00:41:39,980 --> 00:41:49,460
+الكلام K inverse A و هنا K في ال K inverse في مين؟
+
+379
+00:41:49,460 --> 00:41:57,970
+في ال Xكيف الكي انفرس بمين؟ بال identity ال
+
+380
+00:41:57,970 --> 00:42:05,330
+identity matrix نفس ال matrix يبقى هذا بده يعطينا
+
+381
+00:42:05,330 --> 00:42:14,090
+ان ك انفرس اكس كيف؟
+
+382
+00:42:15,500 --> 00:42:20,800
+هالحين بده اجيل ال AX ال AX هي هم اعطاها بقدر
+
+383
+00:42:20,800 --> 00:42:25,700
+اشيلها و احط مكانها مالها لاندا X يبقى هذا الكلام
+
+384
+00:42:25,700 --> 00:42:31,000
+بده يساوي AX
+
+385
+00:42:31,000 --> 00:42:36,640
+بده يساوي K inverse زي ما هي وهذه بده اشيلها و
+
+386
+00:42:36,640 --> 00:42:44,400
+اكتب بدالها لاندا X لاندا scalar والله matrixيبقى
+
+387
+00:42:44,400 --> 00:42:48,220
+بقدر أطلعه برا، مالهوش دعوة، صحيح ولا لأ؟ إذا هذا
+
+388
+00:42:48,220 --> 00:42:56,190
+الكلام بده يساوي lambda برا في K inverse Xطلعلي
+
+389
+00:42:56,190 --> 00:43:01,730
+بيش بدأت بدأت بمصفوفة في مصفوفة تانية لجيتها
+
+390
+00:43:01,730 --> 00:43:06,330
+scalar في نفس المصفوفة اللي عندنا هذا ايش معناه مش
+
+391
+00:43:06,330 --> 00:43:11,190
+هي هذه المعادلة اللي عندنا زي هذه بالضبط تماما
+
+392
+00:43:11,190 --> 00:43:16,790
+يبقى هذا معناته ايه ايش انه k inverse x is an
+
+393
+00:43:16,790 --> 00:43:22,280
+eigen vector ايش هو قال اللي هناهذا هو eigenvector
+
+394
+00:43:22,280 --> 00:43:32,220
+لمن؟ ل B يبقى هذا معناه ان ال K inverse X is an
+
+395
+00:43:32,220 --> 00:43:37,480
+eigenvector
+
+396
+00:43:37,480 --> 00:43:50,210
+for the matrix Bخلصنا لاتجاه الأول لاتجاه
+
+397
+00:43:50,210 --> 00:43:55,730
+الثاني المعاكس conversely
+
+398
+00:43:55,730 --> 00:44:02,590
+ايش يعني conversely assume that
+
+399
+00:44:02,590 --> 00:44:13,490
+افرض ان ال K inverse X is an eigen value
+
+400
+00:44:14,320 --> 00:44:23,160
+for the matrix B
+
+401
+00:44:23,160 --> 00:44:39,120
+بدا اترجم هذا عمليا then there exist a number سميه
+
+402
+00:44:39,120 --> 00:44:45,140
+لندن وان علشان نميزه على الاول لندن وان مثلاالرقم
+
+403
+00:44:45,140 --> 00:44:48,780
+اللي بدكيه يسمى alpha أي رقم اللي بدكيه يسمى
+
+404
+00:44:48,780 --> 00:44:51,780
+النامبر الواحد في الست الواحد في الست الواحد في
+
+405
+00:44:51,780 --> 00:44:52,760
+الست الواحد في الست الواحد في الست الواحد في الست
+
+406
+00:44:52,760 --> 00:44:53,860
+الواحد في الست الواحد في الست الواحد في الست
+
+407
+00:44:53,860 --> 00:44:57,280
+الواحد في الست الواحد في الست الواحد في الست
+
+408
+00:44:57,280 --> 00:44:58,160
+الواحد في الست الواحد في الست الواحد في الست
+
+409
+00:44:58,160 --> 00:44:58,180
+الواحد في الست الواحد في الست الواحد في الست
+
+410
+00:44:58,180 --> 00:44:58,180
+الواحد في الست الواحد في الست الواحد في الست
+
+411
+00:44:58,180 --> 00:44:58,180
+الواحد في الست الواحد في الست الواحد في الست
+
+412
+00:44:58,180 --> 00:44:58,600
+الواحد في الست الواحد في الست الواحد في الست
+
+413
+00:44:58,600 --> 00:45:01,940
+الواحد في الست الواحد في الست الواحد في الست
+
+414
+00:45:01,940 --> 00:45:13,000
+الواحد في الست الواحد في الستفي ال K inverse X بده
+
+415
+00:45:13,000 --> 00:45:21,490
+يساوي Lambda 1 بال X هاي طبقت التعريفاللي أنا إيش
+
+416
+00:45:21,490 --> 00:45:27,710
+بقوله هو بقولي أثبت إنه X هو Eigen vector لمن؟
+
+417
+00:45:27,710 --> 00:45:34,330
+للمصوفة A يعني بده أروح أثبت إنه AX بده يساوي
+
+418
+00:45:34,330 --> 00:45:41,390
+scalar في من؟ في X إذا مداجي أقوله consider خدلي
+
+419
+00:45:41,390 --> 00:45:47,250
+ال A في ال X طيب
+
+420
+00:45:48,040 --> 00:45:52,180
+بدأ أجي لمن؟ لي معلومة عندي، هي المعلومة عندي هي
+
+421
+00:45:52,180 --> 00:45:59,620
+هذه أو هذه بقدر أجيب ال a بدلالة ال b و ال k و ال
+
+422
+00:45:59,620 --> 00:46:11,240
+k inverse بقوله خليلي هذه since بما أن ال b بده
+
+423
+00:46:11,240 --> 00:46:20,220
+تساوي ال k inverse a k we haveبتخلّي A لحالها يا
+
+424
+00:46:20,220 --> 00:46:26,100
+بنات يبقى بدي أضرم من جهة الشمال في مين؟ في K وهنا
+
+425
+00:46:26,100 --> 00:46:31,720
+بيه ومن جهة اليمين في مين؟ في ال K inverse بدي
+
+426
+00:46:31,720 --> 00:46:39,880
+أساوي مين؟ بدي أساوي المصفوفة A كويس then بدي أخد
+
+427
+00:46:39,880 --> 00:46:49,800
+ال X يساوي ال A بدي أشيلها و أكتب بدالها Kبك انفرس
+
+428
+00:46:49,800 --> 00:46:58,230
+وهنا هي ال Xهي اخدته شيلت ال a و حطيت قيمتها تمام
+
+429
+00:46:58,230 --> 00:47:05,390
+طيب انا عندي بي كي انفرس اكس هذه موجودة بقدر
+
+430
+00:47:05,390 --> 00:47:09,870
+اشيلها و اكتبها لقداش لاندا وان اكس يبقى هذا
+
+431
+00:47:09,870 --> 00:47:17,870
+الكلام بده يساوي كي لحالها و هنا بي كي انفرس اكس و
+
+432
+00:47:17,870 --> 00:47:25,270
+يساوي كي فيالـ BK inverse X بدي اشيل و اكتب بدالها
+
+433
+00:47:25,270 --> 00:47:27,510
+Landau 1 X
+
+434
+00:47:30,890 --> 00:47:37,090
+طيب لن دا ون هذا بقدر اطلع وين؟ اطلع برا إذا هذا
+
+435
+00:47:37,090 --> 00:47:43,410
+الكلام لأ بي اه لن دا ون اكس بي ك انفرستكس كتب لها
+
+436
+00:47:43,410 --> 00:47:51,630
+لن دا ون اكس طيب هذا الكلام بده يساوي طيب انا فارض
+
+437
+00:47:52,970 --> 00:48:00,990
+استنى شوية هى ax شيلت ال a حاطبها ك بك inverse x
+
+438
+00:48:00,990 --> 00:48:11,130
+مظبوط وجيت على هذه كتبت ك برا و بك inverse x مظبوط
+
+439
+00:48:11,130 --> 00:48:18,170
+بك inverse x هي lambda one x يبقى هذا الكلام بده
+
+440
+00:48:18,170 --> 00:48:33,230
+يساويلن دا ون برا في مين؟ في كي اكس تمام؟ ايوة علي
+
+441
+00:48:33,230 --> 00:48:37,450
+صوتك شوية هادي
+
+442
+00:48:37,450 --> 00:48:38,230
+بيبقى ساوي
+
+443
+00:48:44,890 --> 00:48:52,330
+لأ اه بده تساوي الرقم في K اه بده تساوي الرقم في K
+
+444
+00:48:52,330 --> 00:48:57,410
+inverse X صحيح هذه الخطأ هنا صحيح هذه يا بنات
+
+445
+00:48:57,410 --> 00:49:07,420
+اليولاندة في K inverse X مظبوط شو اسمك انت؟سمح
+
+446
+00:49:07,420 --> 00:49:12,380
+أصابة امرأة وأختها عمر على طول الخط يبقى هذه لاندا
+
+447
+00:49:12,380 --> 00:49:19,240
+in verse 6 إذا بدي أشيل هذه يا بنات كالتالي و أكتب
+
+448
+00:49:19,240 --> 00:49:24,840
+بدالها ما ياتي يبقى هاي عملت ال associativity تبع
+
+449
+00:49:24,840 --> 00:49:32,720
+المصففات هذا الكلام بدي أساوي كافيبك انفرست اكس
+
+450
+00:49:32,720 --> 00:49:42,030
+بدي اشيله و اكتب بداله لانداون ك انفرست اكسلأن
+
+451
+00:49:42,030 --> 00:49:46,970
+لاندا وان كونستانت بقدر أقوله شرفنا برا يبقى هاي
+
+452
+00:49:46,970 --> 00:49:54,070
+لاندا وان برا صار ك في ك inverse في من؟ في ال X
+
+453
+00:49:54,070 --> 00:50:00,690
+يبقى هذا لاندا وان هذه مصفوفة من؟ الوحدة في أي
+
+454
+00:50:00,690 --> 00:50:06,980
+مصفوفة تعطيني نفس المصفوفةيبقى صار عند هنا مين
+
+455
+00:50:06,980 --> 00:50:13,420
+ابنت ان ال ax يسوى لاندا وان x ايش معنى هذا الكلام
+
+456
+00:50:13,420 --> 00:50:20,500
+معناه ان ال x عبارة عن eigen vector لمن للمصفوفة a
+
+457
+00:50:20,500 --> 00:50:32,760
+يبقى هنا ال x is an eigen vector for the
+
+458
+00:50:39,610 --> 00:50:45,990
+لحد هنا stop انتهى هذا ال section وإلى يكون أرقام
+
+459
+00:50:45,990 --> 00:50:53,090
+المسائل يبقى exercises أربعة تلاتة المسائل التالية
+
+460
+00:50:53,090 --> 00:51:02,570
+من واحد إلى عشرةومن تلتاش لغاية ستاش الشكل اللي
+
+461
+00:51:02,570 --> 00:51:05,810
+عندنا هذا المرة جاء ان شاء الله بنبدأ في المعادلات
+
+462
+00:51:05,810 --> 00:51:10,470
+التفاضلية خلصنا الجبر الخط الآن بنرجع ضايل علينا
+
+463
+00:51:10,470 --> 00:51:13,630
+two chapters في ال ordinary differential
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..627a43e6ceac7c4c541629e11ad0e935f251dad0
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc.srt
@@ -0,0 +1,1536 @@
+1
+00:00:20,700 --> 00:00:24,640
+بسم الله الرحمن الرحيم عود على بدء، نعود لما 
+
+2
+00:00:24,640 --> 00:00:31,620
+ابتدأنا به قبل ساعتين من الآن وهو introduction to
+
+3
+00:00:31,620 --> 00:00:35,160
+a differential equation، أخذنا بعض الـ definitions و
+
+4
+00:00:35,160 --> 00:00:40,100
+أعطينا بعض الأمثلة، ونحن نواصل الأمثلة على ما
+
+5
+00:00:40,100 --> 00:00:45,240
+شرحناه في الفترة الصباحية، أعطينا مثال، وهذا المثال رقم
+
+6
+00:00:45,240 --> 00:00:50,680
+اثنين، بيقول if the function g is a solution of the
+
+7
+00:00:50,680 --> 00:00:54,860
+initial value problem، يبقى g هي عبارة عن دالة، هذه
+
+8
+00:00:54,860 --> 00:00:58,620
+الدالة هي حل الـ initial value problem اللي بيملكه 
+
+9
+00:00:58,620 --> 00:01:02,540
+اللي عندنا، هذه بناء عليه بدنا نجيب له قداش قيمة g 
+
+10
+00:01:02,540 --> 00:01:08,320
+double prime of سالب واحد، وقداش g triple prime of
+
+11
+00:01:08,320 --> 00:01:14,940
+سالب واحد، لذلك الآن جي هي حل، يبقى باجي بقول له 
+
+12
+00:01:14,940 --> 00:01:27,280
+solution since، يعني بما أن الـ جي is a solution of
+
+13
+00:01:27,280 --> 00:01:35,420
+the initial value problem we have، شو اللي بده يحصل؟
+
+14
+00:01:35,420 --> 00:01:42,930
+يبقى بدي أشيل كل y وأحط مكانها جي، يبقى g w prime
+
+15
+00:01:42,930 --> 00:01:51,930
+زائد أو g w prime of x، g of x في الـ g prime of x 
+
+16
+00:01:51,930 --> 00:02:01,450
+ناقص x تكعيب، يساوي zero، أو إنشاءتهم، بدي أعيد كتابة 
+
+17
+00:02:01,450 --> 00:02:08,170
+المعادلة على الشكل التالي، الشكل التالي هي g of x
+
+18
+00:02:08,170 --> 00:02:15,970
+double prime، يساوي x تكعيب ناقص الـ g of x في الـ
+
+19
+00:02:15,970 --> 00:02:21,870
+g prime of x، ليش كتبتها على الشكل هذا؟ لأنه مطلوب
+
+20
+00:02:21,870 --> 00:02:26,050
+من عندي g double prime of سالب واحد، و g triple
+
+21
+00:02:26,050 --> 00:02:32,270
+prime of سالب واحد، هذا المعادلة سأسميها المعادلة
+
+22
+00:02:32,270 --> 00:02:38,060
+رقم واحد، يبقى أنا الآن لو شيلت كل X وحطيت، طبعاً في
+
+23
+00:02:38,060 --> 00:02:43,140
+عليها initial conditions، شو الـ initial conditions
+
+24
+00:02:43,140 --> 00:02:50,260
+اللي هي G prime of سالب واحد، G of سالب واحد بدي
+
+25
+00:02:50,260 --> 00:02:55,080
+أساوي واحد، والـ G prime of سالب واحد بدي أساوي مين؟
+
+26
+00:02:55,080 --> 00:03:00,790
+بدي أساوي اثنين، يبقى بناء عليه لو شيلت كل X وحطيت
+
+27
+00:03:00,790 --> 00:03:06,550
+مكانها سالب واحد، هذه بتأخذ الشكل التالي، G double
+
+28
+00:03:06,550 --> 00:03:12,850
+prime of سالب واحد، بتساوي السالب واحد لكل تكعيب
+
+29
+00:03:12,850 --> 00:03:21,760
+سالب G of سالب واحد في G prime of سالب واحد، يبقى
+
+30
+00:03:21,760 --> 00:03:27,560
+بناء عليه g w prime of سالب واحد، ساوي سالب واحد
+
+31
+00:03:27,560 --> 00:03:33,460
+تكعيب سالب واحد، هاي السالب اللي عندنا، g of سالب
+
+32
+00:03:33,460 --> 00:03:38,900
+واحد اللي قداش؟ واحد صحيح، يبقى هاي الواحد الصحيح، g
+
+33
+00:03:38,900 --> 00:03:43,920
+prime of سالب واحد اللي قداش؟ اثنين، يبقى الواحد
+
+34
+00:03:43,920 --> 00:03:48,560
+مضروب اثنين، يبقى الجواب قداش؟ سالب ثلاثة، يبقى بناء
+
+35
+00:03:48,560 --> 00:03:53,740
+عليه المطلوب الأول اللي وصلنا له، جي دابل برايم اف
+
+36
+00:03:53,740 --> 00:03:59,080
+سالب واحد يساوي قداش؟ سالب ثلاثة، هذا المطلوب الأول.
+
+37
+00:03:59,610 --> 00:04:05,110
+المطلوب الثاني، قال لي هات لي g triple prime of سالب
+
+38
+00:04:05,110 --> 00:04:09,750
+واحد، يبقى بناء عليها هروح على المعادلة هادي، وروح
+
+39
+00:04:09,750 --> 00:04:14,970
+اشتقها، لو اشتقتها بحصل على g triple prime of x
+
+40
+00:04:14,970 --> 00:04:21,050
+وبعدها بروح بأكمل، إذا لو جيت على المعادلة واحد
+
+41
+00:04:21,050 --> 00:04:26,770
+يبقى باجي بقول له from واحد we have، بدنا نيجي نشتق يا
+
+42
+00:04:26,770 --> 00:04:33,350
+بناتي، يبقى الـ g triple prime of x بدو يساوي ثلاثة 
+
+43
+00:04:33,350 --> 00:04:41,670
+x تربيع، اه هذه مشتقة حاصل ضرب دالتين، يبقى الدالة
+
+44
+00:04:41,670 --> 00:04:48,090
+الأولى في مشتقة الدالة الثانية، الـ g prime المشتقة
+
+45
+00:04:48,090 --> 00:04:55,730
+الثانية الـ gw prime، الآن ناقص g prime of x مشتقة
+
+46
+00:04:55,730 --> 00:05:02,510
+الأولى في الثانية اللي هي g prime of x، يبقى هاي
+
+47
+00:05:02,510 --> 00:05:07,090
+اشتقينا المعادلة رقم واحد، الآن لو عوضت بسالب واحد
+
+48
+00:05:07,090 --> 00:05:12,010
+بكون وصلت للنتيجة اللي أنا بدي إياها، يبقى أنا بدي g
+
+49
+00:05:12,010 --> 00:05:16,770
+triple prime of سالب واحد، بدو يصير ثلاثة في سالب
+
+50
+00:05:16,770 --> 00:05:22,010
+واحد لكل تربيع ناقص g of سالب واحد في الـ g double
+
+51
+00:05:22,010 --> 00:05:34,450
+prime of سالب واحد، ناقص g prime of سالب واحد طبعاً
+
+52
+00:05:34,450 --> 00:05:41,100
+هي في نفسها، يعني لكل تربيع، G prime of X في G prime
+
+53
+00:05:41,100 --> 00:05:46,040
+يعني G prime of X لكل تربيع، طيب اللي مطلوب عندي 
+
+54
+00:05:46,040 --> 00:05:51,460
+mean G triple prime of سالب واحد يساوي سالب واحد
+
+55
+00:05:51,460 --> 00:05:57,820
+تربيع اللي هو بواحد، في ثلاثة بتلاتة ناقص G of سالب
+
+56
+00:05:57,820 --> 00:06:03,660
+واحد اللي هي بقداش؟ بواحد، يبقى ناقص واحد، G double
+
+57
+00:06:03,660 --> 00:06:08,200
+prime of سالب واحد، هي حصلنا عليها اللي بسالب ثلاثة
+
+58
+00:06:08,480 --> 00:06:14,840
+يبقى هذه مضروبة في سالب ثلاثة، خلصنا من الـ term لأن
+
+59
+00:06:14,840 --> 00:06:21,080
+هذا، يبقى ناقص هذا، غوث، بدي g prime of سالب واحد، g
+
+60
+00:06:21,080 --> 00:06:26,280
+prime of سالب واحد، يبقى قداش؟ باثنين، يبقى اثنين لكل
+
+61
+00:06:26,280 --> 00:06:34,400
+تربيع، ويساوي ثلاثة زائد ثلاثة ناقص أربعة، ويساوي
+
+62
+00:06:34,400 --> 00:06:39,960
+قداش؟ اثنين، يبقى بناء عليه الـ G triple prime of
+
+63
+00:06:39,960 --> 00:06:45,240
+سالب واحد يساوي اثنين، وانتهينا من المسألة اللي
+
+64
+00:06:45,240 --> 00:06:48,780
+عندنا، على هيك stop، يكون انتهينا من الـ section
+
+65
+00:06:48,780 --> 00:06:54,640
+الأول، والآن بدنا نعطيكم شوية exercises، اتمرنوا
+
+66
+00:06:54,640 --> 00:07:00,260
+إيديكم فيهم، ولا يصعب عليكم، الآن بعطيكم ساعاتي
+
+67
+00:07:00,260 --> 00:07:06,000
+المكتبية، وقتاش بدك تيجي؟ اهلاً وسهلاً، طيب نيجي ل
+
+68
+00:07:06,000 --> 00:07:11,820
+exercises، واحد واحد، يبقى exercises واحد واحد، بد
+
+69
+00:07:11,820 --> 00:07:21,900
+المسائل التالية، السؤال الأول بدي منه نقطة B وC وE
+
+70
+00:07:21,900 --> 00:07:37,040
+وF وH، السؤال الثاني بدي منه نقاط B وC وE وF، سؤال
+
+71
+00:07:37,040 --> 00:07:48,560
+التالت بدي منه C وF وH، السؤال الرابع كاملاً، السؤال
+
+72
+00:07:48,560 --> 00:08:00,000
+الخامس بدي منه A وC، السؤال السادس بدي A وE، السؤال
+
+73
+00:08:00,000 --> 00:08:12,350
+السابع والتاسع والعاشر بدنا إياهم كلهم، حدا
+
+74
+00:08:12,350 --> 00:08:16,110
+فيكم إله أي تسأل، الآن في هذا الـ section سواء
+
+75
+00:08:16,110 --> 00:08:21,470
+الذي درسه في الفترة الصباحية، أو المثال اللي عندنا
+
+76
+00:08:21,470 --> 00:08:27,130
+هذا، حدا بتحب تسأل أي سؤال؟ none
+
+77
+00:08:28,360 --> 00:08:35,200
+إذا، سأدخل في الـ section الذي يليه، يبقى الخانة
+
+78
+00:08:35,200 --> 00:08:41,000
+هادية، حد بده أي نقطة منها؟ ها فيه
+
+79
+00:09:00,220 --> 00:09:08,220
+الآن بنجي يا بنات لـ section 1-2 اللي هو separable
+
+80
+00:09:08,220 --> 00:09:11,320
+equations.
+
+81
+00:09:18,680 --> 00:09:23,160
+يعني separable differential equations، أو شهدتوا أن
+
+82
+00:09:23,160 --> 00:09:27,780
+إذا قلنا separable first order differential
+
+83
+00:09:27,780 --> 00:09:33,100
+equation، يعني معادلة تفاضلية من الرتبة الأولى، شو
+
+84
+00:09:33,100 --> 00:09:38,030
+يعني separate؟ separate معناته منفصل، فلما أقول
+
+85
+00:09:38,030 --> 00:09:43,530
+separation أو separable equations أو separation of
+
+86
+00:09:43,530 --> 00:09:48,170
+variables، فصل المتغيرات، يعني بالعامية على المعادلة
+
+87
+00:09:48,170 --> 00:09:53,090
+أن دي واخل الـ x كلهم في شغلة، واخل الـ y في شغلة، و
+
+88
+00:09:53,090 --> 00:09:59,310
+بعدين اكملوا اشتغلوا شغلي تمام؟ إذا هاروح هحط تعريف
+
+89
+00:09:59,310 --> 00:10:03,250
+للـ separable equation، طبعاً هذا المحاضرة كلها أمثلة 
+
+90
+00:10:03,250 --> 00:10:06,350
+بس كلمتين صغيرات، التعريف تبع الـ separable equation
+
+91
+00:10:06,350 --> 00:10:11,150
+وبعدين كلّه ايه؟ كلّه أمثلة، ما عندنا نظر كتير زي الـ
+
+92
+00:10:11,150 --> 00:10:15,150
+section اللي فات، يبقى هنعطي تعريف للـ separable
+
+93
+00:10:15,150 --> 00:10:21,030
+equation، التعريف بيقول ما يأتي، definition a first
+
+94
+00:10:21,030 --> 00:10:21,710
+order 
+
+95
+00:10:40,740 --> 00:10:51,600
+الشكل التالي، دي واي باي دي اكس بدو يساوي P of X a
+
+96
+00:10:51,600 --> 00:11:05,170
+Q of Yu of y، هو قادر يسميها المعادلة star، معادلة
+
+97
+00:11:05,170 --> 00:11:15,050
+star is said to be، is said to be separable
+
+98
+00:11:15,050 --> 00:11:18,310
+differential
+
+99
+00:11:18,310 --> 00:11:19,270
+equation
+
+100
+00:11:26,470 --> 00:11:30,870
+to solve the 
+
+101
+00:11:30,870 --> 00:11:43,330
+differential equation star، we write it، we write it
+
+102
+00:11:43,330 --> 00:11:51,850
+بروح نكتبها in the form، in the form، بروح بكتبها 
+
+103
+00:11:51,850 --> 00:12:01,630
+على الشكل التالي، واحد على q of y في الـ dy بدو
+
+104
+00:12:01,630 --> 00:12:14,130
+يساوي p of x في ال dx، by integration، بالتكامل
+
+105
+00:12:14,130 --> 00:12:19,110
+by integration we get its solution.
+
+106
+00:12:25,740 --> 00:12:34,320
+بنحصل على الحل تبعها، examples، أول
+
+107
+00:12:34,320 --> 00:12:46,740
+مثال، solve the initial value problem، اللي هي x
+
+108
+00:12:46,740 --> 00:12:54,920
+تربيع زائد أربعة، x تربيع زائد أربعة في الـ y prime
+
+109
+00:12:55,760 --> 00:13:04,000
+بدو يساوي XY، وY عند الـ Zero بدو يساوي كده؟ بدو
+
+110
+00:13:04,000 --> 00:13:04,960
+يساوي ستة.
+
+111
+00:13:34,440 --> 00:13:40,480
+نرجع للتعريف اللي احنا كاتبينه، نقرأه مرة ثانية، ومن
+
+112
+00:13:40,480 --> 00:13:46,700
+ثم نذهب إلى حل المثال، يبقى separable equations
+
+113
+00:13:46,700 --> 00:13:53,300
+المعادلات التي يمكن فيها فصل المتغيرات، نعطي تعريف
+
+114
+00:13:53,300 --> 00:13:57,120
+لها، فباجي بقول a first order differential equation
+
+115
+00:13:57,120 --> 00:14:01,670
+يبقى المعادلة التفاضلية من الرتبة الأولى، اللي بتبقى
+
+116
+00:14:01,670 --> 00:14:06,450
+على الشكل التالي «dy» على «dx» يساوي حاصل ضرب
+
+117
+00:14:06,450 --> 00:14:11,010
+دالتين، واحدة دالة في «x» والثانية دالة في «y»، كأنه
+
+118
+00:14:11,010 --> 00:14:17,230
+فصلنا الـ «x» في دالة، وفصلنا الـ «y» في دالة لحالها،
+
+119
+00:14:17,230 --> 00:14:21,690
+يبقى إن حدث ذلك، بقول عن هذه المعادلة هي معادلة
+
+120
+00:14:21,690 --> 00:14:28,670
+تفاضلية separable، يمكن فيها فصل المتغيرات، يبقى هذه
+
+121
+00:14:28,670 --> 00:14:32,050
+الـ 6 بيه separable differential equation، مشان
+
+122
+00:14:32,050 --> 00:14:36,870
+أنحل المعادلة هذه اللي الـ star، بدي أحاول أكتبها
+
+123
+00:14:36,870 --> 00:14:42,300
+بشكل آخر، يبقى يا بنات لو ضربت كلّه في DX بيصير DY
+
+124
+00:14:42,300 --> 00:14:49,100
+يساوي P of X في Q of Y في DX، طيب لو جسمت على الـ QY
+
+125
+00:14:49,100 --> 00:14:56,060
+بيصير DY على الـ QY، بيصير P of X DX، يبقى فصلت الـ Y
+
+126
+00:14:56,060 --> 00:15:00,900
+في شغلة، والـ X في شغلة، من هنا سميناها separable
+
+127
+00:15:00,900 --> 00:15:05,180
+equation، طب بدو حلها، كامل هذا الطرف وكامل هذا 
+
+128
+00:15:05,180 --> 00:15:10,240
+الطرف، بتحصل لحالها زائد constant C، إلا إذا كان عندك 
+
+129
+00:15:10,240 --> 00:15:13,640
+initial value problem، تقدر تجيب قيمة مين؟ الـC
+
+130
+00:15:13,640 --> 00:15:19,420
+ما عندكش، يبقى بتضلي المثلة بدلالة مين؟ بدلالة هذا الـ
+
+131
+00:15:19,420 --> 00:15:23,980
+constant، واضح الفكرة؟ يبقى من حد بشوف المعذرة إذا 
+
+132
+00:15:23,980 --> 00:15:30,060
+بقدر أفصل المتغيرات X لحالها، و Y لحالها، كل واحد
+
+133
+00:15:30,060 --> 00:15:35,400
+باللي معاه، يعني نقسم العرب عربين، وكلّهم بحيث يكون
+
+134
+00:15:35,400 --> 00:15:39,780
+هذول متجانسين، وهذول يكون متجانسين، يبقى خلاص، سرد
+
+135
+00:15:39,780 --> 00:15:43,660
+separable differential equation، بكامل هذه بالنسبة
+
+136
+00:15:43,660 --> 00:15:47,920
+لـ X، بكامل هذه الطرف الثانية بالنسبة لـ Y، بكون حصلت
+
+137
+00:15:47,920 --> 00:15:54,740
+على مين؟ على الحل، نيجي لسؤالنا، كمثال تطبيق على ذلك
+
+138
+00:15:54,740 --> 00:15:58,380
+نقول let's solve the differential equation، وشايف
+
+139
+00:15:58,380 --> 00:16:04,420
+دالة في X في Y'، وهنا X وY التنين مع بعض، بدي أحاول
+
+140
+00:16:04,420 --> 00:16:08,920
+أفصل المتغيرة، طبعاً هذا شرط عليهم، من هنا سميناها 
+
+141
+00:16:08,920 --> 00:16:12,950
+initial value problem، بدي أحاول أفصل الـ X في شغلة، و
+
+142
+00:16:12,950 --> 00:16:18,790
+الـ Y في شغلة، بس قبل اللي تبدأ تكتبها بشكل آخر، يبقى 
+
+143
+00:16:18,790 --> 00:16:24,270
+باجي بقول X تربيع زائد أربعة، الـ Y prime اللي هي
+
+144
+00:16:24,270 --> 00:16:29,010
+عبارة عن DY على DX، يساوي X في Y
+
+145
+00:16:31,810 --> 00:16:39,050
+لو رحنا ضربنا كلّه في DX، بصير X تربيع زائد أربعة DY
+
+146
+00:16:39,050 --> 00:16:43,250
+يساوي XY DX
+
+147
+00:16:45,310 --> 00:16:51,090
+أظن ليزال عندي مشكلتين، المشكلة دي y مضروبة في dx
+
+148
+00:16:51,090 --> 00:16:57,810
+والمشكلة دي x مضروبة في من؟ في dy، إذا شو رأيك أجسم 
+
+149
+00:16:57,810 --> 00:17:06,290
+الطرفين على y ضرب x تربيع زائد 4، يبقى هذي إيش 
+
+150
+00:17:06,290 --> 00:17:15,560
+بيصير عندي، بيصير عندي dy على y، يساوي x على x تربيع
+
+151
+00:17:15,560 --> 00:17:22,420
+زائد أربعة في dx، مظبوط هكذا؟ يبقى لو جسمنا على هذه
+
+152
+00:17:22,420 --> 00:17:25,900
+بتجيني في المقام، ولو جسمنا على هذه بتجي في المقام
+
+153
+00:17:25,900 --> 00:17:31,570
+يبقى هاي كل واحدة في شغلة، طبعاً أظن هذا الـ bus تفاضل
+
+154
+00:17:31,570 --> 00:17:36,950
+المقام، يبقى in absolute value للمقام، هذا الـ bus
+
+155
+00:17:36,950 --> 00:17:42,010
+تفاضل المقام، بس بدو قداش؟ يبقى بضرب في اثنين وبجسم
+
+156
+00:17:42,010 --> 00:17:47,710
+على اثنين، بدون مشاكل، يبقى بناء عليه هذي عبارة عن dy
+
+157
+00:17:47,710 --> 00:17:56,110
+على y، يساوي 2x على x تربيع زائد أربعة، وبرة بدرب في 
+
+158
+00:17:56,110 --> 00:18:07,330
+قداش؟ بدرب في نص، يبقى هذا نص وهذا dx، نكمل يا بنات.
+
+159
+00:18:08,270 --> 00:18:14,550
+طيب لو كملنا الطرف الأول، يبقى لن absolute value ل
+
+160
+00:18:14,550 --> 00:18:23,750
+Y، كمان هذه نص لن absolute value ل X تربيع زائد 4
+
+161
+00:18:24,110 --> 00:18:28,830
+هذه كمية مربعة، ضروري أكتب لها absolute value، يعني
+
+162
+00:18:28,830 --> 00:18:33,450
+قيمة موجبة، لإن X تربيع مضافة إليها أربعة، حتى لو 
+
+163
+00:18:33,450 --> 00:18:38,190
+كانت X المربعة، تربيع بيصير موجبة زائد أربعة، كمية
+
+164
+00:18:38,190 --> 00:18:43,190
+موجبة، كتبت الـ absolute، والله ما كتبته C، يعني كتبت
+
+165
+00:18:43,190 --> 00:18:49,030
+زيادة كلّها في الكتابة لا قيمة لها، زائد constant
+
+166
+00:18:49,030 --> 00:18:55,190
+main، زائد constant C، طب النُص هذا يا بنات مش يعني 
+
+167
+00:18:55,190 --> 00:19:02,710
+اللي هو len X تربيع زائد أربعة أُص نص، زائد كون 
+
+168
+00:19:02,710 --> 00:19:09,630
+أُص، تنسى؟ مش هيك الخواص؟ صح ولا لأ؟ طيب مادام هيك
+
+169
+00:19:09,630 --> 00:19:18,680
+طيب إيش رأيك هذه؟ لو جيت قلت أنا بدي Y، مدى ما بدي 
+
+170
+00:19:18,680 --> 00:19:25,780
+أتخ
+
+201
+00:22:39,610 --> 00:22:47,810
+حد بتحب تسألي سؤال هنا في خطوات الحل واضح يعني نخش
+
+202
+00:22:47,810 --> 00:22:52,530
+على مثال تاني؟ اه تفضلي. أكتر نقطة وهي ليش ستننا
+
+203
+00:22:52,530 --> 00:22:58,050
+السالب بس خلينا نقصمهم ده جدا شايفة ال condition
+
+204
+00:22:58,050 --> 00:23:03,610
+هذا؟ ايش بيقول؟ y عند ال zero يساوي 6 يعني احنا
+
+205
+00:23:03,610 --> 00:23:08,450
+بدنا نجيب الحل عند نقطة محددة مين هي النقطة؟ zero
+
+206
+00:23:08,450 --> 00:23:14,310
+و 6 يعني y ب 6 هل هي سالبة؟ لأ يبقى y موجبة من هنا
+
+207
+00:23:14,310 --> 00:23:20,170
+عملنا الإشارة السالبة في تساؤل تاني؟ خلاص؟ طيب
+
+208
+00:23:20,170 --> 00:23:25,430
+نروح للمثال رقم اتنين يبقى example two
+
+209
+00:23:35,600 --> 00:23:43,060
+Solve the differential equation حل المعادلة
+
+210
+00:23:43,060 --> 00:23:51,100
+التفاضلية cos تربيع الـ X كله في الـ Y' بده يساوي
+
+211
+00:23:51,100 --> 00:23:59,320
+Y تربيع في Y ناقص الواحد كله في sin X
+
+212
+00:24:27,450 --> 00:24:31,890
+نرجع لسؤالنا جالي يحل المعادلة وما جاليش initial
+
+213
+00:24:31,890 --> 00:24:35,950
+value problem يقول ماعنديش initial condition بيبقى
+
+214
+00:24:35,950 --> 00:24:39,890
+بضل الحل بدلالة ال c بدلالة ال constant اللي 
+
+215
+00:24:39,890 --> 00:24:46,860
+بطلع بس قبل هيك اه هذه هنا cosine تربيع وهذه مكتوبة
+
+216
+00:24:46,860 --> 00:24:51,140
+y prime إذا ما بقدر أشيل y prime مكتوب بدالها dy
+
+217
+00:24:51,140 --> 00:24:58,020
+by dx يبقى باجي بقول هنا cosine تربيع ال x هذه
+
+218
+00:24:58,020 --> 00:25:05,040
+كلها في dy by dx يساوي y تربيع في y ناقص واحد في
+
+219
+00:25:05,040 --> 00:25:14,090
+sin x تمام بدأ أحاول أفصل المتغيرات يبقى بدي أضرب
+
+220
+00:25:14,090 --> 00:25:20,650
+في DX وأقسم على cosine تربيع ال X وY تربيع في Y
+
+221
+00:25:20,650 --> 00:25:28,450
+ناقص واحد يبقى لو قسمتها بصير ال dy على Y تربيع
+
+222
+00:25:28,450 --> 00:25:37,650
+في Y ناقص واحد يساوي sin X على cosine تربيع ال X
+
+223
+00:25:37,650 --> 00:25:50,650
+في DX أو بقدر اقول هذه يا بنات هي sin x على cos x
+
+224
+00:25:50,650 --> 00:26:00,330
+في cos x في dx أو بقدر اكتب المثل على الشكل واحد
+
+225
+00:26:00,330 --> 00:26:07,630
+على Y تربيع في Y ناقص واحد dy بدي يساوي واحد على
+
+226
+00:26:07,630 --> 00:26:17,800
+cosine تربيع؟ sec ال X sec ال X في tan ال X في ال DX
+
+227
+00:26:17,800 --> 00:26:24,400
+فصلنا المتغيرات؟ خلصنا؟ من حد ما نفصل المتغيرات
+
+228
+00:26:24,400 --> 00:26:30,900
+بيظل علينا بس كامل أظن الطرف اليمين سهل تكامله sec
+
+229
+00:26:30,900 --> 00:26:36,710
+ال X في tan ال X تكامله؟ sec x يبقى ضال الطرف
+
+230
+00:26:36,710 --> 00:26:41,490
+الشمال حد بتقدر فيكوا تقولي أوي اذكرني كيف بدي
+
+231
+00:26:41,490 --> 00:26:47,330
+أكامل الطرف الشمال اللي بدي واحد ارفعي يدك واتحكي
+
+232
+00:26:47,330 --> 00:26:51,270
+حتى لو كان غلط اتعودي تحكي احكي غلط اليوم واحكي
+
+233
+00:26:51,270 --> 00:26:55,130
+غلط بكرا بعد بكرا بتحكي صح وكده دلكيش اللي ابدا
+
+234
+00:26:55,130 --> 00:26:59,210
+ارفعي يدك واحكي مين بتحب اذكر ان انا كهمدا كامل
+
+235
+00:26:59,210 --> 00:27:06,520
+الدالة هذه يعني يا بنات كأنما نكامل دالة البسط مقدار
+
+236
+00:27:06,520 --> 00:27:11,880
+ثابت أو polynomial درجتها أقل من درجة المقام
+
+237
+00:27:11,880 --> 00:27:20,260
+المقام من درجة التالتة قسمتي ايش؟ مش سامع قسمتي ايش؟
+
+238
+00:27:20,260 --> 00:27:27,890
+و الله قسمة و نصيب قسمتي ايش و بدنا نقسم بنقسم البسط
+
+239
+00:27:27,890 --> 00:27:32,730
+على المقام لو كانت درجة البسط أكبر من درجة المقام
+
+240
+00:27:32,730 --> 00:27:38,470
+أو تساويها لكن إذا درجة البسط أقل من درجة المقام
+
+241
+00:27:38,470 --> 00:27:45,640
+بنروح إلى الكسور الجزئية للـ Partial Fractions يبقى
+
+242
+00:27:45,640 --> 00:27:53,280
+بدنا نروح نشوف الكسور الجزئية للمقدار واحد على Y
+
+243
+00:27:53,280 --> 00:28:01,240
+ناقص واحد في الـ Y تربيع أيوا يبقى هذا بناقص Y
+
+244
+00:28:01,240 --> 00:28:09,380
+ناقص واحد زائد Y تربيع أيوا يبقى هذه المقام من
+
+245
+00:28:09,380 --> 00:28:15,780
+الدرجة الأولى إذا بنحط في ال بسط ده الأقل منه في
+
+246
+00:28:15,780 --> 00:28:20,640
+الدرجة يبقى ما عنديش إلا constant يبقى بقوله هنا a
+
+247
+00:28:20,640 --> 00:28:25,940
+طيب هذه من الدرجة الثانية أو من الدرجة الأولى مكرر
+
+248
+00:28:25,940 --> 00:28:30,520
+بنعمل الشغلتين يعني من الدرجة الأولى أو من الدرجة
+
+249
+00:28:30,520 --> 00:28:38,920
+الثانية يبقى بقدر أقول له ب y زائد c تمام؟
+
+250
+00:28:38,920 --> 00:28:45,800
+الآن بدرح أدور على المجاهيل A وB وC مشان هيك صح
+
+251
+00:28:45,800 --> 00:28:48,620
+أصفّر معايا شو بدنا نعمل؟ أنا بذكر التذكير اللي أنا
+
+252
+00:28:48,620 --> 00:28:53,240
+خدت فيك الكلاس بهذي يبقى بدرح على الطرفين و أضرب
+
+253
+00:28:53,240 --> 00:28:58,230
+في المقام اللي عندنا لو ضربت في هذا المقام ايش بيظل
+
+254
+00:28:58,230 --> 00:29:09,130
+هنا؟ هنا بيظل a y تربيع هنا بيظل by زائد c في ال y
+
+255
+00:29:09,130 --> 00:29:13,690
+ناقص واحد، مظبوط ايه؟ يعني معنى هذا الكلام باطل
+
+256
+00:29:13,690 --> 00:29:18,570
+يصير عندنا كسور يبقى هذه وسيلة عملية ان اتخلص من
+
+257
+00:29:18,570 --> 00:29:25,330
+الكسور حتى اقدر اجيب قيمة ال a و ال b و ال c تمام؟
+
+258
+00:29:26,120 --> 00:29:32,000
+طيب عندنا أكثر من طريقة لإيجاد قيمة الـA والـB
+
+259
+00:29:32,000 --> 00:29:39,040
+والـC إما طريقة المقارنة في الطرفين أو أحط قيم من
+
+260
+00:29:39,040 --> 00:29:45,700
+عندي وبالتالي أشوف قيم المجاهيل و أحل الشغلات هذه
+
+261
+00:29:45,700 --> 00:29:54,470
+مع بعض لو جيت قلت هذه يا بنات a y تربيع زائد b y تربيع
+
+262
+00:29:54,470 --> 00:30:05,090
+ناقص by زائد c y ناقص c، مظبوط هيك؟ يبقى هذا واحد
+
+263
+00:30:05,090 --> 00:30:15,510
+يساوي a زائد b في y تربيع زائد c ناقص b كله في y
+
+264
+00:30:15,510 --> 00:30:24,100
+ناقص c الآن بنقول بمقارنة المعاملات في الطرفين
+
+265
+00:30:24,100 --> 00:30:29,280
+comparing the coefficients in both sides we get
+
+266
+00:30:29,280 --> 00:30:34,140
+بدنا نقارن المعاملات في الطرفين هذه y تربيع هنا في
+
+267
+00:30:34,140 --> 00:30:39,100
+y تربيع إذا في الأصل موجودة بس معاملها بقداش؟ zero
+
+268
+00:30:39,100 --> 00:30:46,770
+يبقى ال a زائد ال b بده يساوي zero في هنا y يبقى
+
+269
+00:30:46,770 --> 00:30:52,550
+الـ C ناقص الـ B كمان يساوي Zero اللي بعدها اللي
+
+270
+00:30:52,550 --> 00:30:59,610
+هو اللي عندك هنا ناقص C يساوي كم؟ يساوي واحد ومنها
+
+271
+00:30:59,610 --> 00:31:07,600
+C تساوي سالب واحد طب لما C تساوي سالب واحد هدول
+
+272
+00:31:07,600 --> 00:31:13,080
+المعادلتين شو بده يصير فيهم؟ بده يصير سالب واحد
+
+273
+00:31:13,080 --> 00:31:21,380
+ناقص B تساوي Zero يبقى B تساوي قداش؟ سالب واحد لما
+
+274
+00:31:21,380 --> 00:31:27,600
+B تساوي سالب واحد تصير A ناقص واحد يساوي Zero يبقى
+
+275
+00:31:27,600 --> 00:31:34,170
+هذا معناته ان A تساوي واحد يبقى بيب واحد بيب سالب
+
+276
+00:31:34,170 --> 00:31:41,350
+واحد اب واحد و سيب سالب واحد يبقى مسألة هذه ستصبح
+
+277
+00:31:41,350 --> 00:31:46,670
+على الشكل التالي إذا بدي اشيل هذا و اعوض بدله
+
+278
+00:31:46,670 --> 00:31:53,640
+بالمقدار هذا A عندي بواحد يبقى واحد على Y ناقص واحد
+
+279
+00:31:53,640 --> 00:32:01,680
+زائد B عندي بقداش؟ بسالب واحد يبقى سالب Y C بسالب
+
+280
+00:32:01,680 --> 00:32:10,100
+واحد يبقى كمان سالب واحد كله على Y تربيع هذا في DY
+
+281
+00:32:10,100 --> 00:32:20,060
+يساوي شو رأيك أبسطه؟ يبقى هذا واحد على Y ناقص واحد
+
+282
+00:32:20,060 --> 00:32:27,880
+هذه على هذه بيظل ناقص واحد على Y وهذه ناقص واحد
+
+283
+00:32:27,880 --> 00:32:34,520
+على Y تربيع كله في دي Y يساوي الطرف اليمين الطرف
+
+284
+00:32:34,520 --> 00:32:40,160
+اليمين اللي همين سك ال X في تان ال X في دي X يبقى
+
+285
+00:32:40,160 --> 00:32:47,600
+سك ال X في تان ال X في الـ dx أظن لو كملت بحصل على
+
+286
+00:32:47,600 --> 00:32:52,740
+الحل مظبوط يبقى بعد ما عملت ال partial fraction
+
+287
+00:32:52,740 --> 00:32:57,980
+هذه السهل تكاملها هذه السهل تكاملها هذه السهل
+
+288
+00:32:57,980 --> 00:33:04,280
+تكاملها هذه السهل تكاملها يبقى كل هذا سهل خالص
+
+289
+00:33:04,280 --> 00:33:10,380
+يبقى مش ضايل عليه إلا عملية التكامل يبقى بدنا نجي
+
+290
+00:33:10,380 --> 00:33:13,060
+نكامل هذه المسألة
+
+291
+00:33:15,030 --> 00:33:21,930
+طيب تكامل هذه بقداش يا بنات دي Y على Y ناقص واحد
+
+292
+00:33:21,930 --> 00:33:30,350
+بـ ln المقام يبقى هذا ln absolute value لـY ناقص
+
+293
+00:33:30,350 --> 00:33:39,130
+واحد هذه زيها اظن كمان ناقص ln absolute value لـY
+
+294
+00:33:39,130 --> 00:34:02,790
+هذه y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²
+
+295
+00:34:03,070 --> 00:34:12,210
+بس sec X يبقى sec X زائد constant C أظن ممكن أنبسط
+
+296
+00:34:12,210 --> 00:34:21,000
+شوية طيب هذه عبارة عن ln ناقص ln يعني ln خارج
+
+297
+00:34:21,000 --> 00:34:27,760
+القسمة يبقى هذه ln absolute value Y ناقص واحد كله
+
+298
+00:34:27,760 --> 00:34:36,680
+على Y زائد 1 على Y يساوي sec X زائد constant C
+
+299
+00:34:36,680 --> 00:34:42,950
+يبقى هذا هو حل ضمني ايش يعني حل ضمني؟ يعني مش
+
+300
+00:34:42,950 --> 00:34:48,370
+قادرين نطلع ال Y في شغلة و ال X في شغلة تانية يعني
+
+301
+00:34:48,370 --> 00:34:53,090
+مش قادر أقول Y تساوي دالة في X وإنما ال Y و ال X
+
+302
+00:34:53,090 --> 00:34:58,150
+لو ضربت كله في Y و جيته سلك يبقى بتضلها مشربكة مع
+
+303
+00:34:58,150 --> 00:35:01,890
+بعضها ماقدرش أفصل Y في ناحية و الباقي كله في ناحية
+
+304
+00:35:01,890 --> 00:35:06,970
+تانية يبقى هذا هو الحل ضمني لهذه المعادلة
+
+305
+00:35:06,970 --> 00:35:14,770
+التفاضلية حد فيكم بتحب تسأل أي سؤال هنا؟ أي سؤال
+
+306
+00:35:14,770 --> 00:35:20,190
+على التكامل على التفاضل على اللي بدك إياه مافيهش
+
+307
+00:35:20,190 --> 00:35:28,910
+طيب نروح للمثال اللي بعده
+
+308
+00:35:28,910 --> 00:35:36,670
+يبقى نيجي للمثال الذي يليه وهو مثال رقم 3 يبقى
+
+309
+00:35:36,670 --> 00:35:47,220
+example 3 يقول لي y prime 10 inverse y بده يساوي x
+
+310
+00:35:47,220 --> 00:35:57,440
+في 1 زائد y تربيع شو 
+
+311
+00:35:57,440 --> 00:36:04,000
+رأيكوا؟ يبقى بدنا نحل يبقى ما ليش إلا أحط y prime
+
+312
+00:36:04,000 --> 00:36:13,240
+على الصيغة dy على dx يبقى ال solution هي عندي tan
+
+313
+00:36:13,240 --> 00:36:22,760
+inverse y في dy على dx يساوي x في 1 زائد y تربيع
+
+314
+00:36:22,760 --> 00:36:28,140
+بنقدر نخلي المتغيرات يا بنات نخلي ال y في شغلة و ال
+
+315
+00:36:28,140 --> 00:36:35,660
+x في شغلة بنقدر؟ اه بنقدر يبقى بقدر اقول له هذه 10
+
+316
+00:36:35,660 --> 00:36:43,240
+inverse y 1 زائد y تربيع كله في dy بده يساوي ال x
+
+317
+00:36:43,240 --> 00:36:52,040
+في dx فصلنا المتغيرات؟ صارت c parabola equation؟
+
+318
+00:36:52,040 --> 00:36:59,020
+طيب السؤال هو كيف بدي أكامل الطرف الشمال علما انه
+
+319
+00:36:59,020 --> 00:37:03,600
+very easy ما هو
+
+320
+00:37:03,600 --> 00:37:09,840
+مشتقة البسط هو المقاس مشتقة ال 10 inverse هي X 1
+
+321
+00:37:09,840 --> 00:37:16,100
+على 1 زائد X تربيع إذا مشتقة 10 inverse Y هي 1 على
+
+322
+00:37:16,560 --> 00:37:23,700
+واحد زائد واي تربيع إذا بإمكاني أعيد صياغة هذه
+
+323
+00:37:23,700 --> 00:37:29,460
+المسألة كالتالي هذه بقدر أقول بقدر أكتبها على
+
+324
+00:37:29,460 --> 00:37:39,160
+الشكل التالي ten inverse y دي ل ten inverse y هي
+
+325
+00:37:39,160 --> 00:37:46,490
+الشغلة الشمالي مش دي إشارة تفاضل صح؟ يبقى مشتقة tan
+
+326
+00:37:46,490 --> 00:37:52,210
+inverse Y هي واحد على واحد زائد Y تربيع DY يبقى أنا
+
+327
+00:37:52,210 --> 00:37:57,150
+حتى لما كملتش كل اللي عملته شلت واحد على واحد زائد
+
+328
+00:37:57,150 --> 00:38:01,670
+Y تربيع DY وحطيت درجة d tan inverse اصلا في calculus
+
+329
+00:38:01,670 --> 00:38:06,210
+P عملت لكم شغلات كتير زي هيك تمام يا ما عملناها
+
+330
+00:38:06,210 --> 00:38:11,960
+وحتى في ايه عملتها كمان طبعا يبقى ما هو جديد طيب
+
+331
+00:38:11,960 --> 00:38:15,040
+هذا الطرف الشمالي الطرف اليمين مسكين مافيه عنده
+
+332
+00:38:15,040 --> 00:38:21,960
+حاجة يبقى هذا X في DX الآن بقدر أكامل بسهولة هذي
+
+333
+00:38:21,960 --> 00:38:29,300
+كإن ايش؟ كإنّي بكامل ZDZ صح ولا لا؟ يبقى تكامل ZDZ
+
+334
+00:38:29,300 --> 00:38:37,160
+بقداش؟ Z تربيع على اتنين صحيح؟ يبقى هذه ه كإنها tan
+
+335
+00:38:37,160 --> 00:38:43,540
+inverse y الكل تربيع على اتنين ال X كمان ال X
+
+336
+00:38:43,540 --> 00:38:50,560
+تربيع على اتنين زائد constant C أظن لو ضربنا
+
+337
+00:38:50,560 --> 00:38:57,480
+الطرفين في اتنين مافي مشكلة يبقى هذا يا بنات بالصير
+
+338
+00:38:57,480 --> 00:39:06,220
+10 inverse y لكل تربيع يساوي x تربيع زائد 2c
+
+339
+00:39:06,220 --> 00:39:13,820
+ناخد الجذر التربيعي على الطرفين طب لما ناخد الجذر
+
+340
+00:39:13,820 --> 00:39:17,080
+التربيعي على الطرفين بيطلع عندي absolute value ولا
+
+341
+00:39:17,080 --> 00:39:22,350
+لا؟ الجذر التربيعي لـ X تربيع مش هو absolute value
+
+342
+00:39:22,350 --> 00:39:28,330
+لـ X إذاً هذا absolute value يبقى بقدر أقول لو
+
+343
+00:39:28,330 --> 00:39:33,230
+أخدت الجذر التربيعي للطرفين يبقى absolute value ل
+
+344
+00:39:33,230 --> 00:39:39,590
+10 inverse Y بدي يساوي الجذر التربيعي للـ X تربيع
+
+345
+00:39:39,590 --> 00:39:46,770
+زائد 2C أخدت الجذر التربيعي للطرفين طيب باجي
+
+346
+00:39:46,770 --> 00:39:51,730
+بسهل هو هذه ال absolute value يعني ضروري أن اكتبها
+
+347
+00:39:51,730 --> 00:39:57,110
+بقول لك اه ضروري لأن tan inverse بتاخد قيم موجبة و
+
+348
+00:39:57,110 --> 00:40:00,910
+بتاخد قيم سالبة بعد ال zero قيمها موجبة و قبل ال
+
+349
+00:40:00,910 --> 00:40:05,130
+zero من الذاكرين منحنى ten inverse x و الله كله
+
+350
+00:40:05,130 --> 00:40:11,750
+كلام ten inverse x طب ال range تبعه من وين لوين
+
+351
+00:40:11,750 --> 00:40:18,110
+يالا مين تتذكر من سالب واحد لواحد حرام عليك و تاجه
+
+352
+00:40:18,110 --> 00:40:24,810
+الله من سالب باي على اتنين لباي على اتنين يعني منحنى ال ten
+
+353
+00:40:24,810 --> 00:40:29,470
+inverse لو حبيت أذكرك فيه كان على الشكل التالي
+
+354
+00:40:29,470 --> 00:40:35,690
+هذا محور x هذا محور Y وهذا نقطة وهذا خط وهمي بباي
+
+355
+00:40:35,690 --> 00:40:40,530
+على اتنين وهذا خط وهمي زيه بسالب بي على اتنين
+
+356
+00:40:40,530 --> 00:40:46,510
+ومنحنا ال 10 inverse بجي لك هيك بالشكل هذا يبقى هذا
+
+357
+00:40:46,510 --> 00:40:51,710
+اللي هو 10 inverse X يعني ال 10 inverse بعد ال
+
+358
+00:40:51,710 --> 00:40:55,520
+zero بتاخد positive values وقبل ال zero بتاخد
+
+359
+00:40:55,520 --> 00:41:00,080
+negative values من هنا ال absolute value ضرورية
+
+360
+00:41:00,080 --> 00:41:04,420
+ولا يمكن التنازل عنها زي الثوابط الفلسطينية يا
+
+361
+00:41:04,420 --> 00:41:09,840
+بنات حد فيكم بتعرف شو الثوابط الفلسطينية يعني حق
+
+362
+00:41:09,840 --> 00:41:18,620
+العودة واللاجئين وفلسطين من البحر إلى النهر ولا لا
+
+363
+00:41:19,070 --> 00:41:23,290
+طيب ماشي يالا مكفّي يا بناشي ناطمع عليكم كتير طيب
+
+364
+00:41:23,290 --> 00:41:28,050
+ال absolute value بده تخلص منها يبقى بسيطة جدا حط
+
+365
+00:41:28,050 --> 00:41:34,410
+زائد أو ناقص و بمشي الحالة يبقى هذه ههه بصير ten
+
+366
+00:41:34,410 --> 00:41:41,650
+inverse y يساوي زائد أو ناقص الجذر التربيعي ال x
+
+367
+00:41:41,650 --> 00:41:49,600
+تربيع زائد اتنين سي سؤالي هو بنقدر نوجد y لحالها
+
+
+401
+00:45:35,520 --> 00:45:46,360
+هذه  V في dV على dx على dx اللي هي dV على 
+
+402
+00:45:46,360 --> 00:45:53,460
+dx زائد 2 هذا الطرف من؟ الطرف الشمال الطرف اليمين
+
+403
+00:45:53,460 --> 00:46:03,800
+3V زائد 1 ببدأ أفك هذا بيصير V في الـdV على dx زائد
+
+404
+00:46:03,800 --> 00:46:11,500
+2V يساوي 3V زائد 1 لو جيبنا 2V على الجهة الثانية
+
+405
+00:46:11,500 --> 00:46:21,680
+بيصير V في dV على dx بدي أساوي V زائد 1 أظن بقدر
+
+406
+00:46:21,680 --> 00:46:31,920
+أفصل المتغيرات يبقى V على V زائد واحد كله في dV بده
+
+407
+00:46:31,920 --> 00:46:36,840
+يساوي dx لحالها مسكينة ما عنده دوال ما عنده متغيرات
+
+408
+00:46:36,840 --> 00:46:45,080
+تمام؟ طب بدنا نكمل هذه درجة البسط قد درجة المقام
+
+409
+00:46:45,080 --> 00:46:49,760
+يبقى قسمة طويلة واحدة مفتوحة أكثر من أشواق الليلة
+
+410
+00:46:49,760 --> 00:46:53,700
+ولا قسمة طويلة ولا حاجة نضيف واحد ونطرح واحد كان
+
+411
+00:46:53,700 --> 00:47:01,940
+ناضيف قداش؟ صفر يبقى هذه بقدر أقول V زائد واحد ناقص
+
+412
+00:47:01,940 --> 00:47:07,720
+واحد على V زائد واحد في ال dV بده يساوي dx قولنا
+
+413
+00:47:07,720 --> 00:47:11,780
+والله كلامك مظبوط قالت الحين بده نوزع ال بسط على 
+
+414
+00:47:11,780 --> 00:47:16,400
+المقام V زائد واحد على V زائد واحد بقداش؟ بواحد
+
+415
+00:47:16,400 --> 00:47:23,980
+يبقى الناتج عندي واحد ناقص واحد على V زائد واحد كله 
+
+416
+00:47:23,980 --> 00:47:31,810
+في dV بده يساوي قداش؟ dx بقدر أكامل؟ بقدر أظن هذه
+
+417
+00:47:31,810 --> 00:47:38,490
+تكاملها V وهذا ln absolute value ل V زائد الواحد
+
+418
+00:47:38,490 --> 00:47:46,190
+وهذا يبدو يساوي X زائد constant C بعد ذلك بشيل ال V
+
+419
+00:47:46,720 --> 00:47:52,880
+وبرجعها بدلالة الـ y والـ x يبقى بيصير هنا الـ y
+
+420
+00:47:52,880 --> 00:48:04,280
+ناقص 2x ناقص 2x ناقص ln absolute value y ناقص 2x
+
+421
+00:48:04,280 --> 00:48:13,950
+زائد 1 يساوي x زائد constant c أو إن شريت فيقولي Y
+
+422
+00:48:13,950 --> 00:48:22,690
+ناقص ln absolute value Y ناقص 2X زائد 1 ك
+
+423
+00:48:22,690 --> 00:48:31,710
+absolute value بده يساوي 3X زائد constant C يبقى
+
+424
+00:48:31,710 --> 00:48:37,160
+هذا الحل وهو حل ضمني ما أنت شايفها بقدرش أفصل ال
+
+425
+00:48:37,160 --> 00:48:42,980
+X في جهة وال Y في جهة لحد هنا stop انتهى ال
+
+426
+00:48:42,980 --> 00:48:50,900
+section إلى يكون أرقام المسائل يبقى exercises واحد
+
+427
+00:48:50,900 --> 00:48:59,820
+اثنين السؤال الأول والخامس والسبع أيوة اسم
+
+428
+00:49:04,780 --> 00:49:13,120
+كاتب section واحد اثنين طبع طبع طبع طبع طبع طبع
+
+429
+00:49:13,120 --> 00:49:18,800
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+430
+00:49:18,800 --> 00:49:21,000
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+431
+00:49:21,000 --> 00:49:21,040
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+432
+00:49:21,040 --> 00:49:27,940
+طبع طبع طبع طبع طبع
+
+433
+00:49:27,940 --> 00:49:32,850
+طبع هذا هو يبقى كتابة الطابعة الرابعة وهذه أرقام
+
+434
+00:49:32,850 --> 00:49:36,630
+المسائل من الطابعة الرابعة حد فيكم يلاقي سؤال؟
+
+435
+00:49:36,630 --> 00:49:41,510
+المرة الجاية شيل لكم بعد، أدرى بكم الساعات المكتبية
+
+436
+00:49:41,510 --> 00:49:46,090
+اثنين
+
+437
+00:49:46,090 --> 00:49:54,070
+أربعاء من العشرة للاحد عشر ومن الثانية عشر للواحدة بتكون
+
+438
+00:49:54,070 --> 00:50:00,130
+شيلكم يوم السبت أما يوم الأحد فمن ال 11 و نص
+
+439
+00:50:00,130 --> 00:50:05,610
+للواحدة بتبقى لكم هذه يعني نص ساعة مش لكم ساعة
+
+440
+00:50:05,610 --> 00:50:15,650
+لكم وكذلك يوم الثلاثاء من الساعة 11 و نص للواحدة
+
+441
+00:50:15,650 --> 00:50:23,990
+ويوم الأربعاء يوم الأربعاء من 12 للواحدة هذه
+
+442
+00:50:23,990 --> 00:50:27,560
+لكم .. لأ مش لكم يوم الأربعاء لأ مش .. يبقى
+
+443
+00:50:27,560 --> 00:50:31,340
+أنتم لكم سبت اثنين أربعاء من عشرة الليلة الى
+
+444
+00:50:31,340 --> 00:50:36,680
+الاحد عشر ونص ساعة يوم الأحد ونص ساعة يوم اثنين .. كيف
+
+445
+00:50:36,680 --> 00:50:41,900
+نص ساعة؟ لأ لأ لكم ساعتين كمان اللي هو من الثانية عشر
+
+446
+00:50:41,900 --> 00:50:45,660
+لواحدة أحد وثلاثة يبقى هذه بدل الساعة كمان ساعتين
+
+447
+00:50:45,660 --> 00:50:47,440
+وكّل على الله 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c856b570cd2d400675f61d8f5cfc50d4a9e062b6
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc_postprocess.srt
@@ -0,0 +1,1788 @@
+1
+00:00:20,700 --> 00:00:24,640
+بسم الله الرحمن الرحيم عود على بدء نعود لما
+
+2
+00:00:24,640 --> 00:00:31,620
+ابتدأنا به قبل ساعتين من الآن وهو introduction to
+
+3
+00:00:31,620 --> 00:00:35,160
+a differential equation أخدنا بعض ال definitions و
+
+4
+00:00:35,160 --> 00:00:40,100
+أعطينا بعض الأمثلة و نحن نواصل الأمثلة على ما
+
+5
+00:00:40,100 --> 00:00:45,240
+شرحناه في الفترة الصبعيةعطينا مثال وهذا المثال رقم
+
+6
+00:00:45,240 --> 00:00:50,680
+اتنين بيقول if the function g is a solution of the
+
+7
+00:00:50,680 --> 00:00:54,860
+initial value problem يبقى g هي عبارة عن دالة هذه
+
+8
+00:00:54,860 --> 00:00:58,620
+الدالة هي حل ال initial value problem اللي بيلمل
+
+9
+00:00:58,620 --> 00:01:02,540
+اللي عندنا هذه بناء عليه بدنا نجيبله قداش قيمة g
+
+10
+00:01:02,540 --> 00:01:08,320
+double prime of سالب واحد وقداش g triple prime of
+
+11
+00:01:08,320 --> 00:01:14,940
+سالب واحد لذلكالان جي هي حل يبقى باجي بقوله
+
+12
+00:01:14,940 --> 00:01:27,280
+solution since يعني بما أن ال جي is a solution of
+
+13
+00:01:27,280 --> 00:01:35,420
+the initial value problem we have شو اللي بده يحصل
+
+14
+00:01:35,420 --> 00:01:42,930
+يبقى بدي أشيل كل y و أحط مكانها جييبقى g w prime
+
+15
+00:01:42,930 --> 00:01:51,930
+زائد أو g w prime of x g of x في الـ g prime of x
+
+16
+00:01:51,930 --> 00:02:01,450
+ناقص x تكييب يسوى zero أو انشئتهم بدي اعيد كتابة
+
+17
+00:02:01,450 --> 00:02:08,170
+المعادلة على الشكل التاليالشكل التالي هي g of x
+
+18
+00:02:08,170 --> 00:02:15,970
+double prime يساوي x تكييب ناقص الـ g of x في الـ
+
+19
+00:02:15,970 --> 00:02:21,870
+g prime of x ليش كتبتها على الشكل هذا لأنه مطلوب
+
+20
+00:02:21,870 --> 00:02:26,050
+من عندي g double prime of سالب واحد و g triple
+
+21
+00:02:26,050 --> 00:02:32,270
+prime of سالب واحد هذا المعادلة سأسميها المعادلة
+
+22
+00:02:32,270 --> 00:02:38,060
+رقم واحديبقى انا الان لو شيلت كل X وحطي طبعا في
+
+23
+00:02:38,060 --> 00:02:43,140
+عليها initial conditions شو ال initial conditions
+
+24
+00:02:43,140 --> 00:02:50,260
+اللي هي G prime of سالب واحد G of سالب واحد بدي
+
+25
+00:02:50,260 --> 00:02:55,080
+ساوي واحد وال G prime of سالب واحد بدي ساوي مين
+
+26
+00:02:55,080 --> 00:03:00,790
+بدي ساوي اتنينيبقى بناء عليه لو شيلت كل X وحطيت
+
+27
+00:03:00,790 --> 00:03:06,550
+مكانها سالب واحد هذه بتاخد الشكل التالي G double
+
+28
+00:03:06,550 --> 00:03:12,850
+prime of سالب واحد بتساوي السالب واحد لكل تكييب
+
+29
+00:03:12,850 --> 00:03:21,760
+سالب G of سالب واحد في G prime of سالب واحديبقى
+
+30
+00:03:21,760 --> 00:03:27,560
+بناء عليه g w prime of سالب واحد ساوي سالب واحد
+
+31
+00:03:27,560 --> 00:03:33,460
+تكيب سالب واحد هاي السالب اللى عندنا g of سالب
+
+32
+00:03:33,460 --> 00:03:38,900
+واحد اللى قداش واحد صحيح يبقى هاي الواحد الصحيح g
+
+33
+00:03:38,900 --> 00:03:43,920
+prime of سالب واحد اللى قداش اتنينيبقى الواحد
+
+34
+00:03:43,920 --> 00:03:48,560
+مضروف اتنين يبقى الجواب قداش سالب تلاتة يبقى بناء
+
+35
+00:03:48,560 --> 00:03:53,740
+عليه المطلوب الاول اللى وصلناله جي دابل ا برايم اف
+
+36
+00:03:53,740 --> 00:03:59,080
+سالب واحد يساوي قداش سالب تلاتة هذا المطلوب الاول
+
+37
+00:03:59,610 --> 00:04:05,110
+المطلوب الثاني قال لي هاتلي g triple prime of سالب
+
+38
+00:04:05,110 --> 00:04:09,750
+واحد يبقى بناء عليها هروح على المعادلة هادى وروح
+
+39
+00:04:09,750 --> 00:04:14,970
+اشتقها لو اشتقتها بحصل على g triple prime of x
+
+40
+00:04:14,970 --> 00:04:21,050
+وبعدها بروح باه بكمل إذا لو جيت على المعادلة واحد
+
+41
+00:04:21,050 --> 00:04:26,770
+يبقى باجي بقوله from واحد we haveبدنا نجي نشتق يا
+
+42
+00:04:26,770 --> 00:04:33,350
+بناتي يبقى الـ g triple prime of x بد يساوي تلاتة
+
+43
+00:04:33,350 --> 00:04:41,670
+x تربيع اه هذه مشتقة حاصل ضرب دالتين يبقى الدالة
+
+44
+00:04:41,670 --> 00:04:48,090
+الأولى في مشتقة الدالة الثانيةالـ g prime المشتقة
+
+45
+00:04:48,090 --> 00:04:55,730
+التانية الـ gw prime الان ناقص g prime of x مشتقة
+
+46
+00:04:55,730 --> 00:05:02,510
+الأولى في التانية اللي هي g prime of xيبقى هاي
+
+47
+00:05:02,510 --> 00:05:07,090
+اشتقين المعادلة رقم واحد الان لو عوضت بسالب واحد
+
+48
+00:05:07,090 --> 00:05:12,010
+بكون وصلت للنتيجة اللي انا بديها يبقى انا بدي g
+
+49
+00:05:12,010 --> 00:05:16,770
+triple prime of سالب واحد بديصير تلاتة في سالب
+
+50
+00:05:16,770 --> 00:05:22,010
+واحد لكل تربية ناقص g of سالب واحد في ال g double
+
+51
+00:05:22,010 --> 00:05:34,450
+prime of سالب واحدناقص g prime of سالب واحد طبعا
+
+52
+00:05:34,450 --> 00:05:41,100
+هي في نفسها يعني لكل تربيعG prime of X في G prime
+
+53
+00:05:41,100 --> 00:05:46,040
+يعني G prime of X لكل تربيع طيب اللي مطلوب عندي
+
+54
+00:05:46,040 --> 00:05:51,460
+mean G triple prime of سالب واحد يساوي سالب واحد
+
+55
+00:05:51,460 --> 00:05:57,820
+تربيع اللي هو بواحد في تلاتة بتلاتة ناقص G of سالب
+
+56
+00:05:57,820 --> 00:06:03,660
+واحد اللي هي بقداش بواحد يبقى ناقص واحد G double
+
+57
+00:06:03,660 --> 00:06:08,200
+prime of سالب واحد هي حصلنا عليها اللي بسالب تلاتة
+
+58
+00:06:08,480 --> 00:06:14,840
+يبقى هذه مضروبة في سالب ثلاثة خلصنا من ال term لأن
+
+59
+00:06:14,840 --> 00:06:21,080
+هذا يبقى ناقص هذا غوث بدي g prime of سالب واحد g
+
+60
+00:06:21,080 --> 00:06:26,280
+prime of سالب واحد يبقى داشت باتنينيبقى اتنين لكل
+
+61
+00:06:26,280 --> 00:06:34,400
+تربيع ويساوي تلاتة زائد تلاتة ناقص اربعة ويساوي
+
+62
+00:06:34,400 --> 00:06:39,960
+قداش اتنين يبقى بناء عليه الـ G triple prime of
+
+63
+00:06:39,960 --> 00:06:45,240
+سالب واحد يساوي اتنين وانتهينا من المسألة اللي
+
+64
+00:06:45,240 --> 00:06:48,780
+عندنا على هيك stop يكون انتهينا من ال section
+
+65
+00:06:48,780 --> 00:06:54,640
+الأولوالان بدنا نعطيكوا شوية exercises اتمرنوا
+
+66
+00:06:54,640 --> 00:07:00,260
+إيديكوا فيهم ولا يصعب عليكي الآن بعطيكي ساعاتي
+
+67
+00:07:00,260 --> 00:07:06,000
+المكتبية وقتاش بدك تيجي أهلا وسهلا طيب نيجي ل
+
+68
+00:07:06,000 --> 00:07:11,820
+exercises واحد واحديبقى exercises واحد واحد بد
+
+69
+00:07:11,820 --> 00:07:21,900
+المسائل التالية السؤال الأول بد منه نقطة B وC وE
+
+70
+00:07:21,900 --> 00:07:37,040
+وF وH السؤال الثاني بد منه نقاط B وC وE وFسؤال
+
+71
+00:07:37,040 --> 00:07:48,560
+التالت بدي منه C وF وH السؤال الرابع كاملا السؤال
+
+72
+00:07:48,560 --> 00:08:00,000
+الخامس بدي منه A وC السؤال السادس بدي A وE السؤال
+
+73
+00:08:00,000 --> 00:08:12,350
+السابعو التاسع والعاشر بدنا ياهم كلهم حدا
+
+74
+00:08:12,350 --> 00:08:16,110
+فيكوا إلها أي تسأل الآن في هذا ال section سواء
+
+75
+00:08:16,110 --> 00:08:21,470
+الذي درسه في الفترة الصباحية أو المثال اللي عندنا
+
+76
+00:08:21,470 --> 00:08:27,130
+هذا حدا بتحب تسأل أي سؤال none
+
+77
+00:08:28,360 --> 00:08:35,200
+إذا سأدخل في ال section اللذي يليه يبقى الخانة
+
+78
+00:08:35,200 --> 00:08:41,000
+هادية حد بده اي نقطة منها ها فيه
+
+79
+00:09:00,220 --> 00:09:08,220
+الان بنجه يا بنات ل section 1-2 اللي هو separable
+
+80
+00:09:08,220 --> 00:09:11,320
+equations
+
+81
+00:09:18,680 --> 00:09:23,160
+يعني separable differential equations او شهدتوا ان
+
+82
+00:09:23,160 --> 00:09:27,780
+اذا قلنا separable first order differential
+
+83
+00:09:27,780 --> 00:09:33,100
+equation يعني معادلة تفاضلية من الرتبة الأولى شو
+
+84
+00:09:33,100 --> 00:09:38,030
+يعني separate؟separate معناته منفصل فلما اقول
+
+85
+00:09:38,030 --> 00:09:43,530
+separation او separable equations او separation of
+
+86
+00:09:43,530 --> 00:09:48,170
+variables فصل المتغيرات يعني بالداجة على المعادلة
+
+87
+00:09:48,170 --> 00:09:53,090
+ان دي واخل ال x كلهم في شجة واخل ال y في شجة و
+
+88
+00:09:53,090 --> 00:09:59,310
+بعدين اكملو أشتغل شغلي تمام؟ اذا هاروح هحط تعريف
+
+89
+00:09:59,310 --> 00:10:03,250
+لل separable equation طبعا هذا المحاضرة كلها أمثلة
+
+90
+00:10:03,250 --> 00:10:06,350
+بس كلمتين صغارة التعريف تبع ال separable equation
+
+91
+00:10:06,350 --> 00:10:11,150
+و بعدين كله ايه؟ كله أمثلة ماعنداش نظر كتير زي ال
+
+92
+00:10:11,150 --> 00:10:15,150
+section اللي فات يبجى هنعطي تعريف لل separable
+
+93
+00:10:15,150 --> 00:10:21,030
+equation التعريف بيقول ما يأتي definition a first
+
+94
+00:10:21,030 --> 00:10:21,710
+order
+
+95
+00:10:40,740 --> 00:10:51,600
+الشكل التالي دي واي باي دي اكس بده يساوي P of X a
+
+96
+00:10:51,600 --> 00:11:05,170
+Q of Yu of y هو قادر يسميها المعادلة star معادلة
+
+97
+00:11:05,170 --> 00:11:15,050
+star is said to be is said to be separable
+
+98
+00:11:15,050 --> 00:11:18,310
+differential
+
+99
+00:11:18,310 --> 00:11:19,270
+equation
+
+100
+00:11:26,470 --> 00:11:30,870
+to solve the
+
+101
+00:11:30,870 --> 00:11:43,330
+differential equation star we write it we write it
+
+102
+00:11:43,330 --> 00:11:51,850
+بروح نكتبها in the form in the form بروح بكتبها
+
+103
+00:11:51,850 --> 00:12:01,630
+على الشكل التالي واحدعلى q of y في الـ dy بده
+
+104
+00:12:01,630 --> 00:12:14,130
+يساوي p of x في ال dx by integration بالتكامل
+
+105
+00:12:14,130 --> 00:12:19,110
+by integration we get its solution
+
+106
+00:12:25,740 --> 00:12:34,320
+بنحصل على الحل تبعها examples أول
+
+107
+00:12:34,320 --> 00:12:46,740
+مثال solve the initial value problem اللي هي x
+
+108
+00:12:46,740 --> 00:12:54,920
+تربيع زائد أربعة x تربيع زائد أربعة في ال y prime
+
+109
+00:12:55,760 --> 00:13:04,000
+بدو يساوي XY وY عند الـ Zero بدو يساوي كده؟ بدو
+
+110
+00:13:04,000 --> 00:13:04,960
+يساوي ستة
+
+111
+00:13:34,440 --> 00:13:40,480
+نرجع للتعريف اللي احنا كاتبينه نقرأه مرة ثانية ومن
+
+112
+00:13:40,480 --> 00:13:46,700
+ثم نذهب إلى حل المثال يبقى separable equations
+
+113
+00:13:46,700 --> 00:13:53,300
+المعادلات التي يمكن فيها فصل المتغيرات نعطي تعريف
+
+114
+00:13:53,300 --> 00:13:57,120
+لها فباجي بقول a first order differential equation
+
+115
+00:13:57,120 --> 00:14:01,670
+يبقى المعادلة التفاضلية من الرتبة الأولىاللي بتبقى
+
+116
+00:14:01,670 --> 00:14:06,450
+على الشكل التالي «dy» على «dx» يساوي حصل ضرب
+
+117
+00:14:06,450 --> 00:14:11,010
+دالتين واحدة دالة في «x» والتانية دالة في «y» كأنه
+
+118
+00:14:11,010 --> 00:14:17,230
+فصلنا ال «x» في دالة وفصلنا ال «y» في دالة لحالة
+
+119
+00:14:17,230 --> 00:14:21,690
+يبقى إن حدث ذلك بقول عن هذه المعادلة هي معادلة
+
+120
+00:14:21,690 --> 00:14:28,670
+تفاضلية separable يمكن فيها فصل المتغيراتيبقى هذه
+
+121
+00:14:28,670 --> 00:14:32,050
+الـ 6 بيه separable differential equation مشان
+
+122
+00:14:32,050 --> 00:14:36,870
+انحل المعادلة هذه اللي ال star بدي احاول اكتبها
+
+123
+00:14:36,870 --> 00:14:42,300
+بشكل اخريبقى يا بنات لو ضربت كله في DX بيصير DY
+
+124
+00:14:42,300 --> 00:14:49,100
+يسوي P of X في Q of Y في DX طيب لو جسمت على ال QY
+
+125
+00:14:49,100 --> 00:14:56,060
+بيصير DY على ال QY بيصير P of X DX يبقى فاصلت ال Y
+
+126
+00:14:56,060 --> 00:15:00,900
+في شجة و ال X في شجة من هنا سمنها separable
+
+127
+00:15:00,900 --> 00:15:05,180
+equation طب بده حلهاكامل هذا الطرف و كامل هذا
+
+128
+00:15:05,180 --> 00:15:10,240
+الطرف بتحصل لحالة زائد constant C إلا إذا كان عندك
+
+129
+00:15:10,240 --> 00:15:13,640
+initial value problem تقدر تجيب قيمة مين الـC
+
+130
+00:15:13,640 --> 00:15:19,420
+ماعندكش يبقى بتضلي المثلة بدلالة مين بدلالة هذا ال
+
+131
+00:15:19,420 --> 00:15:23,980
+constant واضح الفكرة يبقى من حد بشوف المعذرة إذا
+
+132
+00:15:23,980 --> 00:15:30,060
+بقدر أفصل المتغيرات X لحالة و Y لحالة كل واحد
+
+133
+00:15:30,060 --> 00:15:35,400
+باللي معاهيعني نقسم العرب عربين و كلهم بحيث يكون
+
+134
+00:15:35,400 --> 00:15:39,780
+هذول متجانسين و هذول يكون متجانسين يبقى خلاص سرد
+
+135
+00:15:39,780 --> 00:15:43,660
+separable differential equation بكامل هذه بالنسبة
+
+136
+00:15:43,660 --> 00:15:47,920
+ل X بكامل هذه الطرف تانية بالنسبة ل Y بكون حصلت
+
+137
+00:15:47,920 --> 00:15:54,740
+على مين على الحلنجي لسؤالنا كمثال تطبيق على ذلك
+
+138
+00:15:54,740 --> 00:15:58,380
+نقول let's solve the differential equation وشايف
+
+139
+00:15:58,380 --> 00:16:04,420
+دالة في X في Y' وهنا X وY التنين مع بعض بدي أحاول
+
+140
+00:16:04,420 --> 00:16:08,920
+أفصل المتغيرة طبعا هذا شرط عليهم من هنا سمناها
+
+141
+00:16:08,920 --> 00:16:12,950
+initial value problemبدي احاول افصل ال X في شجة و
+
+142
+00:16:12,950 --> 00:16:18,790
+ال Y في شجة بس قبل اللي تبدأ اكتبها بشكل اخر يبقى
+
+143
+00:16:18,790 --> 00:16:24,270
+باجي بقول X تربية زائد اربعة ال Y prime اللي هي
+
+144
+00:16:24,270 --> 00:16:29,010
+عبارة عن DY على DX يساوي X في Y
+
+145
+00:16:31,810 --> 00:16:39,050
+لو رحنا ضربنا كله في DX بصير X تربيع زائد أربعة DY
+
+146
+00:16:39,050 --> 00:16:43,250
+يساوي XY DX
+
+147
+00:16:45,310 --> 00:16:51,090
+أظن ليزال عندي مشكلتين المشكلة دي y مضروبة في dx
+
+148
+00:16:51,090 --> 00:16:57,810
+والمشكلة دي x مضروبة في من؟ في dy إذا شو رايك أجسم
+
+149
+00:16:57,810 --> 00:17:06,290
+الطرفين على y ضرب x تربيع زائد 4 يبقى هذي إيش
+
+150
+00:17:06,290 --> 00:17:15,560
+بيصير عندي بيصير عندي dy على yيساوي x على x تربيع
+
+151
+00:17:15,560 --> 00:17:22,420
+زائد أربعة في dx مظبوط هكذا يبقى لو جسمنا على هذه
+
+152
+00:17:22,420 --> 00:17:25,900
+بتجيني في المقام و لو جسمنا على هذه بتجي في المقام
+
+153
+00:17:25,900 --> 00:17:31,570
+يبقى هاي كل واحدة في شجةطبعا أظن هذا ال bus تفاضل
+
+154
+00:17:31,570 --> 00:17:36,950
+المقام يبقى in absolute value للمقام هذا ال bus
+
+155
+00:17:36,950 --> 00:17:42,010
+تفاضل المقام بس بده قداش يبقى بضرب في اتنين و بجسم
+
+156
+00:17:42,010 --> 00:17:47,710
+على اتنين بدون مشاكليبقى بناء عليه هذي عبارة عن dy
+
+157
+00:17:47,710 --> 00:17:56,110
+على y يسوى 2x على x تربية زائد أربعة و برة بدرب في
+
+158
+00:17:56,110 --> 00:18:07,330
+قداش بدرب في نص يبقى هذا نص وهذا dx نكمل يا بنادر
+
+159
+00:18:08,270 --> 00:18:14,550
+طيب لو كملنا الطرف الأول يبقى لن absolute value ل
+
+160
+00:18:14,550 --> 00:18:23,750
+Y كمان هذه نص لن absolute value ل X تربية زائد 4
+
+161
+00:18:24,110 --> 00:18:28,830
+هذه كمية مربعة ضروري اكتب لها absolute value يعني
+
+162
+00:18:28,830 --> 00:18:33,450
+قيمة موجبة لإن X تربية مضافة إليها أربعة حتى لو
+
+163
+00:18:33,450 --> 00:18:38,190
+كانت X المربعة مربعة بيصير موجبة زائد أربعة كمية
+
+164
+00:18:38,190 --> 00:18:43,190
+موجبة كتبت ال absolute والله ما كتبته C يعني كتبت
+
+165
+00:18:43,190 --> 00:18:49,030
+زيادة كلكة في الكتابة لا قيمة لها زائد constant
+
+166
+00:18:49,030 --> 00:18:55,190
+main زائد constant Cطب النُص هذا يا بنات مش يعني
+
+167
+00:18:55,190 --> 00:19:02,710
+اللي هو len x تربية زائد أربعة أُص نُص زائد كون
+
+168
+00:19:02,710 --> 00:19:09,630
+أُص تنسى؟ مش هيك الخواص؟ صح ولا لأ؟ طيب مادام هيك
+
+169
+00:19:09,630 --> 00:19:18,680
+طيب إيش رأيك هذه؟ لو جيت قلتأنا بدي Y مدى ما بدي
+
+170
+00:19:18,680 --> 00:19:25,780
+اتخلي هذي C1 يا بنات لسه لو هذي C1يبقى انا بدي ال
+
+171
+00:19:25,780 --> 00:19:33,440
+Y يبقى انا بدي ارفع كله كأسل العدد E يبقى E أسلن
+
+172
+00:19:33,440 --> 00:19:40,480
+absolute value ل Y يساوي E أسلن الجذر التربيع إلى
+
+173
+00:19:40,480 --> 00:19:50,550
+X تربية زائد 4 زائد constant C مظبوط هك؟من خواص
+
+174
+00:19:50,550 --> 00:19:56,730
+الـ LIN هذا E أُس LIN الجذر التربية إلى X تربية
+
+175
+00:19:56,730 --> 00:20:05,830
+زائد أربعة في E أُس C1وزعت اللي هو الأُس اللي
+
+176
+00:20:05,830 --> 00:20:11,110
+عندنا هادى تمام تمام طب إيه إيش رأيك هادى؟ مش هادى
+
+177
+00:20:11,110 --> 00:20:16,490
+مقدار ثابت و لا متغير ثابت لإن ال E ب 2 و 7 من 10
+
+178
+00:20:16,490 --> 00:20:21,410
+أُس مقدار ثابت يبقى مقدار ثابتيبقى هذا كله لو
+
+179
+00:20:21,410 --> 00:20:26,430
+شيلته و حطيت بداله C مش أسهللي في الكلكعة شوية
+
+180
+00:20:26,430 --> 00:20:31,830
+يبقى بده أشيله و أحط بداله C طيب يا بنات هنا E أس
+
+181
+00:20:31,830 --> 00:20:37,530
+لن ال E و لن عكس بعض يبقى بصير عندي absolute value
+
+182
+00:20:37,530 --> 00:20:48,110
+ل Yيساوي C في الـ E والـ N برضه بلغوا بعض بصير X
+
+183
+00:20:48,110 --> 00:20:56,770
+تربيع زائد كداش زائد أربعة تمامبدي أحاول أجيب قيمة
+
+184
+00:20:56,770 --> 00:21:00,710
+الـ C هذه برجع من ال initial condition اللي عندي
+
+185
+00:21:00,710 --> 00:21:06,410
+انا عندي Y عند Zero يساوي ستة absolute value لست
+
+186
+00:21:06,410 --> 00:21:14,230
+بقداش بستة يساوي C في الجذر التربيعي لكس تربيعي ب
+
+187
+00:21:14,230 --> 00:21:21,930
+Zero زائد قداشزائد أربعة يعني هذا يساوي اتنين C
+
+188
+00:21:21,930 --> 00:21:28,570
+إذا ومنها C تساوي قداش تلاتة يبقى صار عندي
+
+189
+00:21:28,570 --> 00:21:34,690
+absolute value ل Y يساوي تلاتة الجذر التربيع إلى X
+
+190
+00:21:34,690 --> 00:21:40,150
+تربيع زائد أربعة يبقى هذا الحل النهائي لان او
+
+191
+00:21:40,150 --> 00:21:45,050
+بتقولي Y تساوي زائد او نقص الجذر تفرقش عندنا تمام
+
+192
+00:21:48,220 --> 00:21:54,080
+لكن كونوا كلام محدد انا عندي Y ال initial
+
+193
+00:21:54,080 --> 00:21:58,500
+condition بيقولي Y عند Zero تساوي ستة يعني قيمة
+
+194
+00:21:58,500 --> 00:22:03,670
+موجبةما دام قيمة موجبة يبقى Y لن تأخذ عندي قيمة
+
+195
+00:22:03,670 --> 00:22:09,030
+سالبة لأن أنا جبت الحل عند النقطة عند النقطة اللي
+
+196
+00:22:09,030 --> 00:22:14,930
+هي الـ 0 و 6 لما تبقى X بـ 0 و Y ب6 يعني موجبة
+
+197
+00:22:14,930 --> 00:22:22,250
+بناء عليه بقول الحل Y تساوي 3 الجذر التربية ل X
+
+198
+00:22:22,250 --> 00:22:28,170
+تربية زائد 4 هذا هو الحل النهائيلكن لو كان C هذا
+
+199
+00:22:28,170 --> 00:22:33,810
+ماقدرتش اجيبه يا بنات بكتب زائد او نقص او بخليها
+
+200
+00:22:33,810 --> 00:22:39,610
+absolute value ل Y يساوي كذا هذا هو المثال الأول
+
+201
+00:22:39,610 --> 00:22:47,810
+حد بتحب تسألي سؤال هنا في خطوات الحل واضح يعني نخش
+
+202
+00:22:47,810 --> 00:22:52,530
+على مثال تاني اه تفضلي اكتر نقطة و هي ليش ستننا
+
+203
+00:22:52,530 --> 00:22:58,050
+السالد بس خلينا نقصمهم ده جدا شايفة ال condition
+
+204
+00:22:58,050 --> 00:23:03,610
+هذا؟ ايش بيقول؟ y عند ال zero يساوي 6 يعني احنا
+
+205
+00:23:03,610 --> 00:23:08,450
+بدنا نجيب الحل عند نقطة محددة مين هي النقطة؟ zero
+
+206
+00:23:08,450 --> 00:23:14,310
+و 6 يعني y ب 6 هل هي مسالبة؟ لأ يبقى y موجة من هنا
+
+207
+00:23:14,310 --> 00:23:20,170
+أعملنا الإشارة السالبة في تساول تاني؟ خلاص؟ طيب
+
+208
+00:23:20,170 --> 00:23:25,430
+نروح للمثال رقم اتنين يبقى example two
+
+209
+00:23:35,600 --> 00:23:43,060
+Solve the differential equation حل المعادلة
+
+210
+00:23:43,060 --> 00:23:51,100
+التفاضلية cos تربيع الـ X كله في الـ Y' بده يساوي
+
+211
+00:23:51,100 --> 00:23:59,320
+Y تربيع في Y ناقص الواحد كله في sin X
+
+212
+00:24:27,450 --> 00:24:31,890
+نرجع لسؤالنا جالي يحل المعادلة وما جاليش initial
+
+213
+00:24:31,890 --> 00:24:35,950
+value problem يقول ماعنديش initial condition بيبقى
+
+214
+00:24:35,950 --> 00:24:39,890
+بضل الحل بدلالة ال man بدلالة ال constant اللي
+
+215
+00:24:39,890 --> 00:24:46,860
+بطلع بس قبل هيكأه هذه هنا cosine تربيع وهذه مكتوبة
+
+216
+00:24:46,860 --> 00:24:51,140
+y prime إذا ما بقدر أشيل y prime مكتوب بدالها dy
+
+217
+00:24:51,140 --> 00:24:58,020
+by dx يبقى باجي بقول هنا cosine تربيع ال x هذه
+
+218
+00:24:58,020 --> 00:25:05,040
+كلها في dy by dx يساوي y تربيع في y ناقص واحد في
+
+219
+00:25:05,040 --> 00:25:14,090
+sin x تمام بدأ أحاول أفصل المتغيراتيبقى بدي أضرب
+
+220
+00:25:14,090 --> 00:25:20,650
+في DX وأجسم على cosine تربيع ال X وY تربيع في Y
+
+221
+00:25:20,650 --> 00:25:28,450
+ناقص واحد يبقى لو قسمتها بصير ال DIY على Y تربيع
+
+222
+00:25:28,450 --> 00:25:37,650
+في Y ناقص واحد يساوي sin X على cosine تربيع ال X
+
+223
+00:25:37,650 --> 00:25:50,650
+في DX أوبقدر اقول هذه يا بنات هي sin x على cos x
+
+224
+00:25:50,650 --> 00:26:00,330
+في cos x في dx او بقدر اكتب المثل على الشكل واحد
+
+225
+00:26:00,330 --> 00:26:07,630
+على y تربيع في y ناقص واحد dy بدي يساوي واحد على
+
+226
+00:26:07,630 --> 00:26:17,800
+cosineجداش؟ سك ال X سك ال X في تان ال X في ال DX
+
+227
+00:26:17,800 --> 00:26:24,400
+فصلنا المتغيرات؟ خلصنا؟ من حد ما نفصل المتغيرات
+
+228
+00:26:24,400 --> 00:26:30,900
+بيظل علينا بس كامل أظن الطرف اليمين سهل تكامله سك
+
+229
+00:26:30,900 --> 00:26:36,710
+ال X في تان ال X تكامله؟psychics يبقى ضال الطرف
+
+230
+00:26:36,710 --> 00:26:41,490
+الشمال حد بتقدر فيكوا تقولي أوي اذكرني كيف بدي
+
+231
+00:26:41,490 --> 00:26:47,330
+أكامل الطرف الشمال اللي بدي واحد ارفع عيدك واتحكي
+
+232
+00:26:47,330 --> 00:26:51,270
+حتى لو كان غلط اتعودي تحكي احكي غلط اليوم واحكي
+
+233
+00:26:51,270 --> 00:26:55,130
+غلط بكرا بعد بكرا بتحكي صح وكده دلكيش اللي ابدا
+
+234
+00:26:55,130 --> 00:26:59,210
+ارفع عيدك واحكي مين بتحب اذكر ان انا كهمدا كامل
+
+235
+00:26:59,210 --> 00:27:06,520
+الدالة هذهيعني يا بنات كهب نكمل دالة البسط مقدار
+
+236
+00:27:06,520 --> 00:27:11,880
+ثابت أو polynomial درجتها أقل من درجة المقام
+
+237
+00:27:11,880 --> 00:27:20,260
+المقام من درجة التالتة قسمت ايش؟ مش سامع قسمت ايش؟
+
+238
+00:27:20,260 --> 00:27:27,890
+و الله قسمة و نصيب قسمت ايش و بدنا نقسمبنقسم البصد
+
+239
+00:27:27,890 --> 00:27:32,730
+على المقام لو كانت درجة البصد أكبر من درجة المقام
+
+240
+00:27:32,730 --> 00:27:38,470
+أو تساويها لكن إذا درجة البصد أقل من درجة المقام
+
+241
+00:27:38,470 --> 00:27:45,640
+بنروح إلىالكسور الجزئية للـ Partial Fractions يبقى
+
+242
+00:27:45,640 --> 00:27:53,280
+بدنا نروح نشوف الكسور الجزئية للمقدار واحد على Y
+
+243
+00:27:53,280 --> 00:28:01,240
+ناقص واحد في الـ Y تربيع أيوا يبقى هذا بناقص Y
+
+244
+00:28:01,240 --> 00:28:09,380
+ناقص واحد زائد Y تربيعايوة يبقى هذه المقام من
+
+245
+00:28:09,380 --> 00:28:15,780
+الدرجة الأولى إذا بنحط في ال bus ده الأقل منه في
+
+246
+00:28:15,780 --> 00:28:20,640
+الدرجة يبقى ماعنديش إلا constant يبقى بقوله هنا a
+
+247
+00:28:20,640 --> 00:28:25,940
+طيب هذه من الدرجة الثانية أو من الدرجة الأولى مكرر
+
+248
+00:28:25,940 --> 00:28:30,520
+بنفع الشجتينيعني من الدرجة الأولى أو من الدرجة
+
+249
+00:28:30,520 --> 00:28:38,920
+الثانية يبقى بقدر أقول له بي واي زائد سي تمام؟
+
+250
+00:28:38,920 --> 00:28:45,800
+الآن بدرح أدور على المجاهيل A وB وC مشان هيك صح
+
+251
+00:28:45,800 --> 00:28:48,620
+أصفر معايا شو بدنا نعمل أنا بذكر التذكير اللي أنا
+
+252
+00:28:48,620 --> 00:28:53,240
+خدت فيك الكلاص بي هذي يبقى بدرح على الطرفين و أضرب
+
+253
+00:28:53,240 --> 00:28:58,230
+في المقام اللي عندنالو ضربت في هذا المقام ايش بيظل
+
+254
+00:28:58,230 --> 00:29:09,130
+هنا؟ هنا بيظل a y تربيع هنا بيظل by زائد c في ال y
+
+255
+00:29:09,130 --> 00:29:13,690
+ناقص واحد، مظبوط ايه؟ يعني معنى هذا الكلام باطل
+
+256
+00:29:13,690 --> 00:29:18,570
+يصير عندنا كسور يبقى هذه وسيلة عملية ان اتخلص من
+
+257
+00:29:18,570 --> 00:29:25,330
+الكسور حتى اقدر اجيب قيمة ال a و ال b و ال c تمام؟
+
+258
+00:29:26,120 --> 00:29:32,000
+طيب عندنا أكثر من طريقة لإيجاد قيمة الـA والـB
+
+259
+00:29:32,000 --> 00:29:39,040
+والـC إما طريقة المقارنة في الطرفين أو أحط قيم من
+
+260
+00:29:39,040 --> 00:29:45,700
+عندي وبالتالي أشوف قيم المجاهيل و أحل الشغلات هذه
+
+261
+00:29:45,700 --> 00:29:54,470
+مع بعضلو جيت قلت هذه بنات a y تربية زائد b y تربية
+
+262
+00:29:54,470 --> 00:30:05,090
+ناقص by زائد c y ناقص c، مظبوط هيك؟ يبقى هذا واحد
+
+263
+00:30:05,090 --> 00:30:15,510
+يساوي a زائد b في y تربية زائد c ناقص b كله في y
+
+264
+00:30:15,510 --> 00:30:24,100
+ناقص cالان بنقول بمقارنة المعاملات في الطرفين
+
+265
+00:30:24,100 --> 00:30:29,280
+comparing the coefficients in both sides we get
+
+266
+00:30:29,280 --> 00:30:34,140
+بدنا نقارن المعاملات في الطرفين هذه y تربيع هنا في
+
+267
+00:30:34,140 --> 00:30:39,100
+y تربيع إذا في الأصل موجودة بس معاملها بقداش zero
+
+268
+00:30:39,100 --> 00:30:46,770
+يبقى ال a زائد ال b بده يساوي zero في هنا yيبقى
+
+269
+00:30:46,770 --> 00:30:52,550
+الـ C ناقص الـ B كمان يساوي Zero اللي بعدها اللي
+
+270
+00:30:52,550 --> 00:30:59,610
+هو اللي عندك هنا ناقص C يساوي كم؟ يساوي واحد ومنها
+
+271
+00:30:59,610 --> 00:31:07,600
+C تساوي سالب واحدطب لما C تساوي سالب واحد هدول
+
+272
+00:31:07,600 --> 00:31:13,080
+المعادلتين شو بده يصير فيهم؟ بده يصير سالب واحد
+
+273
+00:31:13,080 --> 00:31:21,380
+سالب B تساوي Zero يبقى B تساوي قداش؟ سالب واحد لما
+
+274
+00:31:21,380 --> 00:31:27,600
+B تساوي سالب واحد تصير A سالب واحد يساوي Zero يبقى
+
+275
+00:31:27,600 --> 00:31:34,170
+هذا معناته ان A تساوي واحديبقى بيب واحد بيب سالب
+
+276
+00:31:34,170 --> 00:31:41,350
+واحد اب واحد و سيب سالب واحد يبقى مسألة هذه ستصبح
+
+277
+00:31:41,350 --> 00:31:46,670
+على الشكل التالي اذا بدي اشيل هذا و اعوض بدله
+
+278
+00:31:46,670 --> 00:31:53,640
+بالمقدار هذاA عندي بواحد يبقى واحد على Y ناقص واحد
+
+279
+00:31:53,640 --> 00:32:01,680
+زائد B عندي بقداشي بسالب واحد يبقى سالب Y C بسالب
+
+280
+00:32:01,680 --> 00:32:10,100
+واحد يبقى كمان سالب واحد كله على Y تربيع هذا في DY
+
+281
+00:32:10,100 --> 00:32:20,060
+يساوي شو رأيك ابسطه؟يبقى هذا واحد على Y ناقص واحد
+
+282
+00:32:20,060 --> 00:32:27,880
+هذه على هذه بيظل ناقص واحد على Y وهذه ناقص واحد
+
+283
+00:32:27,880 --> 00:32:34,520
+على Y تربيع كله في دي Y يساوي الطرف اليمين الطرف
+
+284
+00:32:34,520 --> 00:32:40,160
+اليمين اللي همين سك ال X في تان ال X في دي X يبقى
+
+285
+00:32:40,160 --> 00:32:47,600
+سك ال X في تان ال Xفي الـ dx أظن لو كملت بحصل على
+
+286
+00:32:47,600 --> 00:32:52,740
+الحل مظبوط يبقى بعد ما عملت ال partial fraction
+
+287
+00:32:52,740 --> 00:32:57,980
+هذه السهل تكاملها هذه السهل تكاملها هذه السهل
+
+288
+00:32:57,980 --> 00:33:04,280
+تكاملها هذه السهل تكاملها يبقى كل هذا سهل خالص
+
+289
+00:33:04,280 --> 00:33:10,380
+يبقى مش ضايل عليه إلا عملية التكامل يبقى بدنا نجي
+
+290
+00:33:10,380 --> 00:33:13,060
+نكامل هذه المسألة
+
+291
+00:33:15,030 --> 00:33:21,930
+طيب تكامل هذه بقداش يا بنات دي Y على Y ناقص واحد
+
+292
+00:33:21,930 --> 00:33:30,350
+بـLin المقام يبقى هذا Lin absolute value لـY ناقص
+
+293
+00:33:30,350 --> 00:33:39,130
+واحد هذه زيها اظن كمان ناقص Lin absolute value لـY
+
+294
+00:33:39,130 --> 00:34:02,790
+هذهy²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²
+
+295
+00:34:03,070 --> 00:34:12,210
+بسكل X يبقى سكل X زائد constant C أظن ممكن أنبسط
+
+296
+00:34:12,210 --> 00:34:21,000
+شويةطيب هذه عبارة عن لن ناقص لن يعني لن خارج
+
+297
+00:34:21,000 --> 00:34:27,760
+القسمة يبقى هذه لن absolute value Y ناقص واحد كله
+
+298
+00:34:27,760 --> 00:34:36,680
+على Y زائد واحد على Y يساوي سك X زائد constant C
+
+299
+00:34:36,680 --> 00:34:42,950
+يبقى هذا هو حل ضمنين ايش يعني حل ضمنين؟يعني مش
+
+300
+00:34:42,950 --> 00:34:48,370
+قادرين نطلع ال Y في شجة و ال X في شجة تانية يعني
+
+301
+00:34:48,370 --> 00:34:53,090
+مش قادر أقول Y تساوي دلّة في X وإنما ال Y و ال X
+
+302
+00:34:53,090 --> 00:34:58,150
+لو ضربت كله في Y و جيته سلك يبقى بتضلها مشربكة مع
+
+303
+00:34:58,150 --> 00:35:01,890
+بعضها ماقدرش أفصل Y في ناحية و الباقي كله في ناحية
+
+304
+00:35:01,890 --> 00:35:06,970
+تانية يبقى هذا هو الحل ضمني لهذه المعادلة
+
+305
+00:35:06,970 --> 00:35:14,770
+التفاضلية حد فيكم بتحب تسأل أي سؤال هنا؟أي سؤال
+
+306
+00:35:14,770 --> 00:35:20,190
+على التكامل على التفاضل على اللي بدك هيه مافيهش
+
+307
+00:35:20,190 --> 00:35:28,910
+طيب نروح للمثال اللي بعده
+
+308
+00:35:28,910 --> 00:35:36,670
+يبقى نيجي للمثال الذي يليه وهو مثال رقم 3 يبقى
+
+309
+00:35:36,670 --> 00:35:47,220
+example 3يقول لي y prime 10 inverse y بده يساوي x
+
+310
+00:35:47,220 --> 00:35:57,440
+في 1 زائد y تربيع شو
+
+311
+00:35:57,440 --> 00:36:04,000
+ورايكوا؟يبقى بدنا نحل يبقى ماليش إلا أحط y prime
+
+312
+00:36:04,000 --> 00:36:13,240
+على الصيغة dy على dx يبقى ال solution هي عندي tan
+
+313
+00:36:13,240 --> 00:36:22,760
+inverse y في dy على dx يسوى x في 1 زائد y تربية
+
+314
+00:36:22,760 --> 00:36:28,140
+بنقدر نخصل المتغيرات يا بنات نخل ال y في شجة و ال
+
+315
+00:36:28,140 --> 00:36:35,660
+x في شجةبنقدر؟ اه بنقدر يبقى بقدر اقول له هذه 10
+
+316
+00:36:35,660 --> 00:36:43,240
+inverse y 1 زائد y تربيع كله في dy بده يساوي ال x
+
+317
+00:36:43,240 --> 00:36:52,040
+في dx فصلنا المتغيرات؟ صارت c parabola equation؟
+
+318
+00:36:52,040 --> 00:36:59,020
+طيب السؤال هوكيف بدي أكامل الطرف الشمال علما انه
+
+319
+00:36:59,020 --> 00:37:03,600
+very easy ماهو
+
+320
+00:37:03,600 --> 00:37:09,840
+مشتقة البسط هو المقاس مشتقة ال 10 inverse هي X 1
+
+321
+00:37:09,840 --> 00:37:16,100
+على 1 زي X تربيع اذا مشتقة 10 inverse Y هي 1 على
+
+322
+00:37:16,560 --> 00:37:23,700
+واحد زائد واي تربية إذا بإمكاني أعيد صياغة هذه
+
+323
+00:37:23,700 --> 00:37:29,460
+المسألة كالتالي هذه بقدر أقول بقدر أكتبها على
+
+324
+00:37:29,460 --> 00:37:39,160
+الشكل التالي ten inverse y دي ل ten inverse y هي
+
+325
+00:37:39,160 --> 00:37:46,490
+الشجة الشمالي مش دي إشارة تفاضل صح؟يبقى مشتقة تان
+
+326
+00:37:46,490 --> 00:37:52,210
+انفرس Y هي واحد على واحد زاد Y تربية DY يبقى انا
+
+327
+00:37:52,210 --> 00:37:57,150
+حتى لما كملتش كل اللي عملته شلت واحد على واحد زاد
+
+328
+00:37:57,150 --> 00:38:01,670
+Y تربية DY وحطيت درجة D تان انفرس اصلا في calculus
+
+329
+00:38:01,670 --> 00:38:06,210
+P عملتكوا شغلات كتير زي هيك تمام يا ما عملناها
+
+330
+00:38:06,210 --> 00:38:11,960
+وحتى في ايه عملتها كمانطبعا يبقى ما هوش جديد طيب
+
+331
+00:38:11,960 --> 00:38:15,040
+هذا الطرف الشمالي الطرف اليمين مسكين مافي عنده
+
+332
+00:38:15,040 --> 00:38:21,960
+حاجة يبقى هذا X في DX الآن بقدر أكمل بسهولة هذي
+
+333
+00:38:21,960 --> 00:38:29,300
+كإن ايش كإني بكمل ZDZ صح ولا لا يبقى تكامل ZDZ
+
+334
+00:38:29,300 --> 00:38:37,160
+بقدراش Z تربية على اتنين صحيح؟يبقى هذه ه كإنها tan
+
+335
+00:38:37,160 --> 00:38:43,540
+inverse y الكل تربيع على اتنين ال X كمان ال X
+
+336
+00:38:43,540 --> 00:38:50,560
+تربيع على اتنين زاد constant C أظن لو ضربنا
+
+337
+00:38:50,560 --> 00:38:57,480
+الطرفين في اتنين مافي مشكلةيبقى هذا يا بنات بالصير
+
+338
+00:38:57,480 --> 00:39:06,220
+10 inverse y لكل تربيع يساوي x تربية الزائدة 2c
+
+339
+00:39:06,220 --> 00:39:13,820
+ناخد الجدر التربية على الطرفين طب لما ناخد الجدر
+
+340
+00:39:13,820 --> 00:39:17,080
+التربية على الطرفين بيطلع عندي absolute value ولا
+
+341
+00:39:17,080 --> 00:39:22,350
+لا؟الجذر التربيع لـ X تربيع مش هو absolute value
+
+342
+00:39:22,350 --> 00:39:28,330
+لـ X إذاً هذا absolute value يبقى بقدر أقول لو
+
+343
+00:39:28,330 --> 00:39:33,230
+أخدت الجذر التربيع للطرفين يبقى absolute value ل
+
+344
+00:39:33,230 --> 00:39:39,590
+10 inverse Yبدي أساوي الجذر التربيعي للـ X تربيع
+
+345
+00:39:39,590 --> 00:39:46,770
+زائدي اتنين C أخدت الجذر التربيعي للطرفين طيب باجي
+
+346
+00:39:46,770 --> 00:39:51,730
+بسهل هو هذه ال absolute value يعني ضروري ان اكتبها
+
+347
+00:39:51,730 --> 00:39:57,110
+بقولك اه ضروري لان تان inverse بتاخد قيم موجبة و
+
+348
+00:39:57,110 --> 00:40:00,910
+بتاخد قيم سالبة بعد ال zero قيمها موجبة و قبل ال
+
+349
+00:40:00,910 --> 00:40:05,130
+zeroمن الذاكرين منحنى ten inverse x و الله كله
+
+350
+00:40:05,130 --> 00:40:11,750
+كلام ten inverse x طب ال range تبعه من وين لوين
+
+351
+00:40:11,750 --> 00:40:18,110
+يالا مين تتذكر من سالب واحد لواحد حرام عليك و تاجه
+
+352
+00:40:18,110 --> 00:40:24,810
+الله من سالب بايع اتنين لبياني يعني منحنى ال ten
+
+353
+00:40:24,810 --> 00:40:29,470
+inverse لو حبيت اذاكرك فيه كان على الشكل التالي
+
+354
+00:40:29,470 --> 00:40:35,690
+هذا محور xهذا محور Y وهذا نقطة وهذا خط وهمي ببي
+
+355
+00:40:35,690 --> 00:40:40,530
+على اتنين وهذا خط وهمي زيه بسالف بي على اتنين
+
+356
+00:40:40,530 --> 00:40:46,510
+ومنحنا ال 10 inverse بجيكي هيك بالشكل هذا يبقى هذا
+
+357
+00:40:46,510 --> 00:40:51,710
+اللي هو 10 inverse X يعني ال 10 inverse بعد ال
+
+358
+00:40:51,710 --> 00:40:55,520
+zero بتاخدpositive values وقبل ال zero بتاخد
+
+359
+00:40:55,520 --> 00:41:00,080
+negative values من هنا ال absolute value ضرورية
+
+360
+00:41:00,080 --> 00:41:04,420
+ولا يمكن التنازل عنها زي الثوابط الفلسطينية يا
+
+361
+00:41:04,420 --> 00:41:09,840
+بنات حد فيكم بتعرف شو الثوابط الفلسطينية يعني حق
+
+362
+00:41:09,840 --> 00:41:18,620
+العودة واللاجئين وفلسطين من البحر إلى النهر ولا لا
+
+363
+00:41:19,070 --> 00:41:23,290
+طيب ماشي يالا مكفف يابناشي ناطمع عليكوا كتير طيب
+
+364
+00:41:23,290 --> 00:41:28,050
+ال absolute value بده تخلص منها يبقى بسيطة جدا حط
+
+365
+00:41:28,050 --> 00:41:34,410
+زائد او ناقص و بمشي الحالة يبقى هذه ههه بصير ten
+
+366
+00:41:34,410 --> 00:41:41,650
+inverse y يساوي زائد او ناقص الجدرى التربيعى الاكس
+
+367
+00:41:41,650 --> 00:41:49,600
+تربيه زائد اتنين سي سؤالي هوبنقدر نوجد y لحالها
+
+368
+00:41:49,600 --> 00:41:56,960
+بدون tan inverse؟ نقدر؟ ما هو domain التان من سالب
+
+369
+00:41:56,960 --> 00:42:00,720
+infinity إلى infinity إذا ماعندي مشكلة أخد tan
+
+370
+00:42:00,720 --> 00:42:05,800
+للطرفين يبقى لو أخدنا tan للطرف الشمال بتطير tan
+
+371
+00:42:05,800 --> 00:42:10,590
+inverse وبتصير tan للطرف اليمينفتان القيمة الموجبة
+
+372
+00:42:10,590 --> 00:42:15,330
+بالقيمة الموجبة وتان القيمة السالبة لأن تان odd
+
+373
+00:42:15,330 --> 00:42:19,190
+سالب بيطلع برا يبقى الزائد و النقص مضى المكان جوه
+
+374
+00:42:19,190 --> 00:42:25,450
+و بيسيروا برا لأن تان is an odd function يبقى بناء
+
+375
+00:42:25,450 --> 00:42:32,570
+عليه الحل هنا Y يساوي الزائد أو ناقص تان الجذر
+
+376
+00:42:32,570 --> 00:42:38,510
+التربيع إلى X تربيع زائد 2Cكفى الله المؤمنين
+
+377
+00:42:38,510 --> 00:42:45,810
+القتال يبقى هذا حل مين؟ حل المسألة اللى عندنا آخر
+
+378
+00:42:45,810 --> 00:42:54,190
+مثال في هذا ال section آه آه بضل قيمتين يحقق هذه
+
+379
+00:42:54,190 --> 00:43:01,730
+المعادلة آخر
+
+380
+00:43:01,730 --> 00:43:09,660
+مثال بيقول لي مثال أربعةsolve the differential
+
+381
+00:43:09,660 --> 00:43:18,280
+equation اللي هو y ناقص اتنين x في الـ y prime
+
+382
+00:43:18,280 --> 00:43:27,500
+يساوي تلاتة y ناقص ستة x زائد واحد هذا آخر تمرين
+
+383
+00:43:27,500 --> 00:43:33,460
+في الكتاب حاطط تلت مسائل او اربع مسائل هذا أحدهم
+
+384
+00:43:34,160 --> 00:43:40,620
+وانا جبته متعمد مثال لإنه في فكرة جديدة مش موجودة
+
+385
+00:43:40,620 --> 00:43:47,340
+في كل الأمثلة اللي قبل شو هذه الفكرة؟ بقدرش أفصل
+
+386
+00:43:47,340 --> 00:43:52,620
+ال X في شجة و ال Y في شجة مش قادرلكن بقدر اعمل
+
+387
+00:43:52,620 --> 00:44:01,360
+عملية التحايل عملية التحايل كتالة هي y ناقص اتنين
+
+388
+00:44:01,360 --> 00:44:08,500
+x كله في dy على dx يساوي شو رايك اخد هنا تلاتة
+
+389
+00:44:08,500 --> 00:44:15,240
+عامل مشترك يبقى y ناقص اتنين x زائد واحد عملية
+
+390
+00:44:15,240 --> 00:44:20,420
+التحايلبدي أشيل المقدار بين القوسين و أضعه بـ
+
+391
+00:44:20,420 --> 00:44:27,980
+variable جديدإذا باجي بقول له pot حط لي v يساوي y
+
+392
+00:44:27,980 --> 00:44:34,400
+ناقص 2x بعدين روح اشتقيها بالنسبة إلى x يبقى باجي
+
+393
+00:44:34,400 --> 00:44:43,280
+بقول له dv على dx بده يساوي dy على dx ناقص 2 إذا
+
+394
+00:44:43,280 --> 00:44:50,380
+بقدر أجيب ال dy على dx بدلالةdv على dx يبقى بيصير
+
+395
+00:44:50,380 --> 00:44:58,360
+dv على dx زائد اتنين بده يساوي dy على dx صحيح ولا
+
+396
+00:44:58,360 --> 00:45:03,720
+لا؟ إذا برجع للمعادلة الأصلية اللي هسميها star
+
+397
+00:45:03,720 --> 00:45:10,880
+المعادلة star واجي أعوض فيها يبقى المعادلة star
+
+398
+00:45:10,880 --> 00:45:16,790
+بدنا نجي نعوض فيها ونشوف كيف شكل الحل بده يكونفي
+
+399
+00:45:16,790 --> 00:45:23,430
+مثل هذه الحالة طيب
+
+400
+00:45:23,430 --> 00:45:34,210
+الان باجي بقوله substitute in equation star we get
+
+401
+00:45:35,520 --> 00:45:46,360
+هذه بنصار V في Dy على DX Dy على DX اللي هي DV على
+
+402
+00:45:46,360 --> 00:45:53,460
+DX زائد 2 هذا الطرف من؟ الطرف الشمال الطرف اليمين
+
+403
+00:45:53,460 --> 00:46:03,800
+3V زائد 1بدا افك هذا بيصير V في الـDV على DX زائد
+
+404
+00:46:03,800 --> 00:46:11,500
+2V يساوي 3V زائد 1 لو جيبنا 2V على الشجة التانية
+
+405
+00:46:11,500 --> 00:46:21,680
+بيصير V في DV على DX بدي ساوي V زائد 1 اظن بقدر
+
+406
+00:46:21,680 --> 00:46:31,920
+افصل المتغيراتيبقى V على V زائد واحد كله في DV بده
+
+407
+00:46:31,920 --> 00:46:36,840
+يساوي DX لحالها مسكينة ماعهاش دوال ماعهاش متغيرات
+
+408
+00:46:36,840 --> 00:46:45,080
+تمام؟ طب بدنا نكمل هذه درجة ال bus قد درجة المقام
+
+409
+00:46:45,080 --> 00:46:49,760
+يبقى قسم مطولة واحدة مفتحة اكتر من اشواقات الليلة
+
+410
+00:46:49,760 --> 00:46:53,700
+ولا قسم مطولة ولا حاجة نضيف واحد ونطرح واحدكان
+
+411
+00:46:53,700 --> 00:47:01,940
+نظيف قداش؟ zero يبقى هذه بقدر اقولv زائد واحد ناقص
+
+412
+00:47:01,940 --> 00:47:07,720
+واحد على v زائد واحد في ال dv بده يساوي dx قولنا
+
+413
+00:47:07,720 --> 00:47:11,780
+والله كلامك مظهر قالت الحين بده اوزع ال bus على
+
+414
+00:47:11,780 --> 00:47:16,400
+المقام v زائد واحد على v زائد واحد بقداش بواحد
+
+415
+00:47:16,400 --> 00:47:23,980
+يبقى السعر عندي واحد ناقص واحد على v زائد واحد كله
+
+416
+00:47:23,980 --> 00:47:31,810
+في dv بده يساوي قداش dx بقدر أكاملنقدر أظن هذه
+
+417
+00:47:31,810 --> 00:47:38,490
+تكاملها V وهذا لين absolute value ل V زائد الواحد
+
+418
+00:47:38,490 --> 00:47:46,190
+وهذا يبدو يسوى X زائد constant C بعد ذلك بشيل ال V
+
+419
+00:47:46,720 --> 00:47:52,880
+وبرجعها بدلالة الـ y و الـ x يبقى بيصير هنا الـ y
+
+420
+00:47:52,880 --> 00:48:04,280
+ناقص 2x ناقص 2x ناقص لـ absolute value y ناقص 2x
+
+421
+00:48:04,280 --> 00:48:13,950
+زائد 1 يساوي x زائد constant cأو انشريت فيقولي Y
+
+422
+00:48:13,950 --> 00:48:22,690
+ناقص لأن absolute value Y ناقص 2X زائد 1 ك
+
+423
+00:48:22,690 --> 00:48:31,710
+absolute value بده يساوي 3X زائد constant C يبقى
+
+424
+00:48:31,710 --> 00:48:37,160
+هذا الحل وهو حل ضمنيزي ما انت شايفها بقدرش أفصل ال
+
+425
+00:48:37,160 --> 00:48:42,980
+X في شجة وال Y في شجة لحد هنا stop انتهى ال
+
+426
+00:48:42,980 --> 00:48:50,900
+section إلى يكون أرقام المسائل يبقى exercises واحد
+
+427
+00:48:50,900 --> 00:48:59,820
+اتنين السؤال الأول والخامس والسبع ايوة اسم
+
+428
+00:49:04,780 --> 00:49:13,120
+كاتب section واحد اتنين طبع طبع طبع طبع طبع طبع
+
+429
+00:49:13,120 --> 00:49:18,800
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+430
+00:49:18,800 --> 00:49:21,000
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+431
+00:49:21,000 --> 00:49:21,040
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+432
+00:49:21,040 --> 00:49:27,940
+طبع طبع طبع طبع طبع
+
+433
+00:49:27,940 --> 00:49:32,850
+طهذا هو يبقى كتابة الطابعة الرابعة وهذه أرقام
+
+434
+00:49:32,850 --> 00:49:36,630
+المسائل من الطابعة الرابعة حد فيكوا يلاقي سؤال؟
+
+435
+00:49:36,630 --> 00:49:41,510
+المرة جايسك شيل لبعد، ادري بالكوا الساعات المكتبية
+
+436
+00:49:41,510 --> 00:49:46,090
+اثنين
+
+437
+00:49:46,090 --> 00:49:54,070
+أربعاء من العشرة للاحداشر ومن اتناشر للواحدة بتكون
+
+438
+00:49:54,070 --> 00:50:00,130
+شيلكوا يوم السبتأما يوم الأحد فمن ال 11 و نص
+
+439
+00:50:00,130 --> 00:50:05,610
+للواحدة بتبقى إلكوا هذه يعني نص ساعة مش إلكوا ساعة
+
+440
+00:50:05,610 --> 00:50:15,650
+إلكوا و كذلك يوم الثلاثة من الساعة 11 و نص للواحدة
+
+441
+00:50:15,650 --> 00:50:23,990
+و يوم الأربعاء يوم الأربعاء من 12 للواحدة هذه
+
+442
+00:50:23,990 --> 00:50:27,560
+إلكوا .. لأ مش إلكوا يوم الأربعاءلأ مش .. يبقى
+
+443
+00:50:27,560 --> 00:50:31,340
+أنتوا إلكوا سبت اتنين اربعة من عشرة الليلة الى
+
+444
+00:50:31,340 --> 00:50:36,680
+احداشر ونص ساعة يوم الأحد ونص ساعة يوم اثن .. كيف
+
+445
+00:50:36,680 --> 00:50:41,900
+نص ساعة؟ لأ لأ إلكوا ساعتين كمان اللي هو من اتناشر
+
+446
+00:50:41,900 --> 00:50:45,660
+لواحدة أحد وثلاثة يبقى هاي بدل الساعة كمان ساعات
+
+447
+00:50:45,660 --> 00:50:47,440
+وكّر على الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8e462e1a85d8b679fe92c949ee735e7764f7c09c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/FstSt1JOblc_raw.srt
@@ -0,0 +1,1796 @@
+1
+00:00:20,700 --> 00:00:24,640
+بسم الله الرحمن الرحيم عود على بدء نعود لما
+
+2
+00:00:24,640 --> 00:00:31,620
+ابتدأنا به قبل ساعتين من الآن وهو introduction to
+
+3
+00:00:31,620 --> 00:00:35,160
+a differential equation أخدنا بعض ال definitions و
+
+4
+00:00:35,160 --> 00:00:40,100
+أعطينا بعض الأمثلة و نحن نواصل الأمثلة على ما
+
+5
+00:00:40,100 --> 00:00:45,240
+شرحناه في الفترة الصبعيةعطينا مثال وهذا المثال رقم
+
+6
+00:00:45,240 --> 00:00:50,680
+اتنين بيقول if the function g is a solution of the
+
+7
+00:00:50,680 --> 00:00:54,860
+initial value problem يبقى g هي عبارة عن دالة هذه
+
+8
+00:00:54,860 --> 00:00:58,620
+الدالة هي حل ال initial value problem اللي بيلمل
+
+9
+00:00:58,620 --> 00:01:02,540
+اللي عندنا هذه بناء عليه بدنا نجيبله قداش قيمة g
+
+10
+00:01:02,540 --> 00:01:08,320
+double prime of سالب واحد وقداش g triple prime of
+
+11
+00:01:08,320 --> 00:01:14,940
+سالب واحد لذلكالان جي هي حل يبقى باجي بقوله
+
+12
+00:01:14,940 --> 00:01:27,280
+solution since يعني بما أن ال جي is a solution of
+
+13
+00:01:27,280 --> 00:01:35,420
+the initial value problem we have شو اللي بده يحصل
+
+14
+00:01:35,420 --> 00:01:42,930
+يبقى بدي أشيل كل y و أحط مكانها جييبقى g w prime
+
+15
+00:01:42,930 --> 00:01:51,930
+زائد أو g w prime of x g of x في الـ g prime of x
+
+16
+00:01:51,930 --> 00:02:01,450
+ناقص x تكييب يسوى zero أو انشئتهم بدي اعيد كتابة
+
+17
+00:02:01,450 --> 00:02:08,170
+المعادلة على الشكل التاليالشكل التالي هي g of x
+
+18
+00:02:08,170 --> 00:02:15,970
+double prime يساوي x تكييب ناقص الـ g of x في الـ
+
+19
+00:02:15,970 --> 00:02:21,870
+g prime of x ليش كتبتها على الشكل هذا لأنه مطلوب
+
+20
+00:02:21,870 --> 00:02:26,050
+من عندي g double prime of سالب واحد و g triple
+
+21
+00:02:26,050 --> 00:02:32,270
+prime of سالب واحد هذا المعادلة سأسميها المعادلة
+
+22
+00:02:32,270 --> 00:02:38,060
+رقم واحديبقى انا الان لو شيلت كل X وحطي طبعا في
+
+23
+00:02:38,060 --> 00:02:43,140
+عليها initial conditions شو ال initial conditions
+
+24
+00:02:43,140 --> 00:02:50,260
+اللي هي G prime of سالب واحد G of سالب واحد بدي
+
+25
+00:02:50,260 --> 00:02:55,080
+ساوي واحد وال G prime of سالب واحد بدي ساوي مين
+
+26
+00:02:55,080 --> 00:03:00,790
+بدي ساوي اتنينيبقى بناء عليه لو شيلت كل X وحطيت
+
+27
+00:03:00,790 --> 00:03:06,550
+مكانها سالب واحد هذه بتاخد الشكل التالي G double
+
+28
+00:03:06,550 --> 00:03:12,850
+prime of سالب واحد بتساوي السالب واحد لكل تكييب
+
+29
+00:03:12,850 --> 00:03:21,760
+سالب G of سالب واحد في G prime of سالب واحديبقى
+
+30
+00:03:21,760 --> 00:03:27,560
+بناء عليه g w prime of سالب واحد ساوي سالب واحد
+
+31
+00:03:27,560 --> 00:03:33,460
+تكيب سالب واحد هاي السالب اللى عندنا g of سالب
+
+32
+00:03:33,460 --> 00:03:38,900
+واحد اللى قداش واحد صحيح يبقى هاي الواحد الصحيح g
+
+33
+00:03:38,900 --> 00:03:43,920
+prime of سالب واحد اللى قداش اتنينيبقى الواحد
+
+34
+00:03:43,920 --> 00:03:48,560
+مضروف اتنين يبقى الجواب قداش سالب تلاتة يبقى بناء
+
+35
+00:03:48,560 --> 00:03:53,740
+عليه المطلوب الاول اللى وصلناله جي دابل ا برايم اف
+
+36
+00:03:53,740 --> 00:03:59,080
+سالب واحد يساوي قداش سالب تلاتة هذا المطلوب الاول
+
+37
+00:03:59,610 --> 00:04:05,110
+المطلوب الثاني قال لي هاتلي g triple prime of سالب
+
+38
+00:04:05,110 --> 00:04:09,750
+واحد يبقى بناء عليها هروح على المعادلة هادى وروح
+
+39
+00:04:09,750 --> 00:04:14,970
+اشتقها لو اشتقتها بحصل على g triple prime of x
+
+40
+00:04:14,970 --> 00:04:21,050
+وبعدها بروح باه بكمل إذا لو جيت على المعادلة واحد
+
+41
+00:04:21,050 --> 00:04:26,770
+يبقى باجي بقوله from واحد we haveبدنا نجي نشتق يا
+
+42
+00:04:26,770 --> 00:04:33,350
+بناتي يبقى الـ g triple prime of x بد يساوي تلاتة
+
+43
+00:04:33,350 --> 00:04:41,670
+x تربيع اه هذه مشتقة حاصل ضرب دالتين يبقى الدالة
+
+44
+00:04:41,670 --> 00:04:48,090
+الأولى في مشتقة الدالة الثانيةالـ g prime المشتقة
+
+45
+00:04:48,090 --> 00:04:55,730
+التانية الـ gw prime الان ناقص g prime of x مشتقة
+
+46
+00:04:55,730 --> 00:05:02,510
+الأولى في التانية اللي هي g prime of xيبقى هاي
+
+47
+00:05:02,510 --> 00:05:07,090
+اشتقين المعادلة رقم واحد الان لو عوضت بسالب واحد
+
+48
+00:05:07,090 --> 00:05:12,010
+بكون وصلت للنتيجة اللي انا بديها يبقى انا بدي g
+
+49
+00:05:12,010 --> 00:05:16,770
+triple prime of سالب واحد بديصير تلاتة في سالب
+
+50
+00:05:16,770 --> 00:05:22,010
+واحد لكل تربية ناقص g of سالب واحد في ال g double
+
+51
+00:05:22,010 --> 00:05:34,450
+prime of سالب واحدناقص g prime of سالب واحد طبعا
+
+52
+00:05:34,450 --> 00:05:41,100
+هي في نفسها يعني لكل تربيعG prime of X في G prime
+
+53
+00:05:41,100 --> 00:05:46,040
+يعني G prime of X لكل تربيع طيب اللي مطلوب عندي
+
+54
+00:05:46,040 --> 00:05:51,460
+mean G triple prime of سالب واحد يساوي سالب واحد
+
+55
+00:05:51,460 --> 00:05:57,820
+تربيع اللي هو بواحد في تلاتة بتلاتة ناقص G of سالب
+
+56
+00:05:57,820 --> 00:06:03,660
+واحد اللي هي بقداش بواحد يبقى ناقص واحد G double
+
+57
+00:06:03,660 --> 00:06:08,200
+prime of سالب واحد هي حصلنا عليها اللي بسالب تلاتة
+
+58
+00:06:08,480 --> 00:06:14,840
+يبقى هذه مضروبة في سالب ثلاثة خلصنا من ال term لأن
+
+59
+00:06:14,840 --> 00:06:21,080
+هذا يبقى ناقص هذا غوث بدي g prime of سالب واحد g
+
+60
+00:06:21,080 --> 00:06:26,280
+prime of سالب واحد يبقى داشت باتنينيبقى اتنين لكل
+
+61
+00:06:26,280 --> 00:06:34,400
+تربيع ويساوي تلاتة زائد تلاتة ناقص اربعة ويساوي
+
+62
+00:06:34,400 --> 00:06:39,960
+قداش اتنين يبقى بناء عليه الـ G triple prime of
+
+63
+00:06:39,960 --> 00:06:45,240
+سالب واحد يساوي اتنين وانتهينا من المسألة اللي
+
+64
+00:06:45,240 --> 00:06:48,780
+عندنا على هيك stop يكون انتهينا من ال section
+
+65
+00:06:48,780 --> 00:06:54,640
+الأولوالان بدنا نعطيكوا شوية exercises اتمرنوا
+
+66
+00:06:54,640 --> 00:07:00,260
+إيديكوا فيهم ولا يصعب عليكي الآن بعطيكي ساعاتي
+
+67
+00:07:00,260 --> 00:07:06,000
+المكتبية وقتاش بدك تيجي أهلا وسهلا طيب نيجي ل
+
+68
+00:07:06,000 --> 00:07:11,820
+exercises واحد واحديبقى exercises واحد واحد بد
+
+69
+00:07:11,820 --> 00:07:21,900
+المسائل التالية السؤال الأول بد منه نقطة B وC وE
+
+70
+00:07:21,900 --> 00:07:37,040
+وF وH السؤال الثاني بد منه نقاط B وC وE وFسؤال
+
+71
+00:07:37,040 --> 00:07:48,560
+التالت بدي منه C وF وH السؤال الرابع كاملا السؤال
+
+72
+00:07:48,560 --> 00:08:00,000
+الخامس بدي منه A وC السؤال السادس بدي A وE السؤال
+
+73
+00:08:00,000 --> 00:08:12,350
+السابعو التاسع والعاشر بدنا ياهم كلهم حدا
+
+74
+00:08:12,350 --> 00:08:16,110
+فيكوا إلها أي تسأل الآن في هذا ال section سواء
+
+75
+00:08:16,110 --> 00:08:21,470
+الذي درسه في الفترة الصباحية أو المثال اللي عندنا
+
+76
+00:08:21,470 --> 00:08:27,130
+هذا حدا بتحب تسأل أي سؤال none
+
+77
+00:08:28,360 --> 00:08:35,200
+إذا سأدخل في ال section اللذي يليه يبقى الخانة
+
+78
+00:08:35,200 --> 00:08:41,000
+هادية حد بده اي نقطة منها ها فيه
+
+79
+00:09:00,220 --> 00:09:08,220
+الان بنجه يا بنات ل section 1-2 اللي هو separable
+
+80
+00:09:08,220 --> 00:09:11,320
+equations
+
+81
+00:09:18,680 --> 00:09:23,160
+يعني separable differential equations او شهدتوا ان
+
+82
+00:09:23,160 --> 00:09:27,780
+اذا قلنا separable first order differential
+
+83
+00:09:27,780 --> 00:09:33,100
+equation يعني معادلة تفاضلية من الرتبة الأولى شو
+
+84
+00:09:33,100 --> 00:09:38,030
+يعني separate؟separate معناته منفصل فلما اقول
+
+85
+00:09:38,030 --> 00:09:43,530
+separation او separable equations او separation of
+
+86
+00:09:43,530 --> 00:09:48,170
+variables فصل المتغيرات يعني بالداجة على المعادلة
+
+87
+00:09:48,170 --> 00:09:53,090
+ان دي واخل ال x كلهم في شجة واخل ال y في شجة و
+
+88
+00:09:53,090 --> 00:09:59,310
+بعدين اكملو أشتغل شغلي تمام؟ اذا هاروح هحط تعريف
+
+89
+00:09:59,310 --> 00:10:03,250
+لل separable equation طبعا هذا المحاضرة كلها أمثلة
+
+90
+00:10:03,250 --> 00:10:06,350
+بس كلمتين صغارة التعريف تبع ال separable equation
+
+91
+00:10:06,350 --> 00:10:11,150
+و بعدين كله ايه؟ كله أمثلة ماعنداش نظر كتير زي ال
+
+92
+00:10:11,150 --> 00:10:15,150
+section اللي فات يبجى هنعطي تعريف لل separable
+
+93
+00:10:15,150 --> 00:10:21,030
+equation التعريف بيقول ما يأتي definition a first
+
+94
+00:10:21,030 --> 00:10:21,710
+order
+
+95
+00:10:40,740 --> 00:10:51,600
+الشكل التالي دي واي باي دي اكس بده يساوي P of X a
+
+96
+00:10:51,600 --> 00:11:05,170
+Q of Yu of y هو قادر يسميها المعادلة star معادلة
+
+97
+00:11:05,170 --> 00:11:15,050
+star is said to be is said to be separable
+
+98
+00:11:15,050 --> 00:11:18,310
+differential
+
+99
+00:11:18,310 --> 00:11:19,270
+equation
+
+100
+00:11:26,470 --> 00:11:30,870
+to solve the
+
+101
+00:11:30,870 --> 00:11:43,330
+differential equation star we write it we write it
+
+102
+00:11:43,330 --> 00:11:51,850
+بروح نكتبها in the form in the form بروح بكتبها
+
+103
+00:11:51,850 --> 00:12:01,630
+على الشكل التالي واحدعلى q of y في الـ dy بده
+
+104
+00:12:01,630 --> 00:12:14,130
+يساوي p of x في ال dx by integration بالتكامل
+
+105
+00:12:14,130 --> 00:12:19,110
+by integration we get its solution
+
+106
+00:12:25,740 --> 00:12:34,320
+بنحصل على الحل تبعها examples أول
+
+107
+00:12:34,320 --> 00:12:46,740
+مثال solve the initial value problem اللي هي x
+
+108
+00:12:46,740 --> 00:12:54,920
+تربيع زائد أربعة x تربيع زائد أربعة في ال y prime
+
+109
+00:12:55,760 --> 00:13:04,000
+بدو يساوي XY وY عند الـ Zero بدو يساوي كده؟ بدو
+
+110
+00:13:04,000 --> 00:13:04,960
+يساوي ستة
+
+111
+00:13:34,440 --> 00:13:40,480
+نرجع للتعريف اللي احنا كاتبينه نقرأه مرة ثانية ومن
+
+112
+00:13:40,480 --> 00:13:46,700
+ثم نذهب إلى حل المثال يبقى separable equations
+
+113
+00:13:46,700 --> 00:13:53,300
+المعادلات التي يمكن فيها فصل المتغيرات نعطي تعريف
+
+114
+00:13:53,300 --> 00:13:57,120
+لها فباجي بقول a first order differential equation
+
+115
+00:13:57,120 --> 00:14:01,670
+يبقى المعادلة التفاضلية من الرتبة الأولىاللي بتبقى
+
+116
+00:14:01,670 --> 00:14:06,450
+على الشكل التالي «dy» على «dx» يساوي حصل ضرب
+
+117
+00:14:06,450 --> 00:14:11,010
+دالتين واحدة دالة في «x» والتانية دالة في «y» كأنه
+
+118
+00:14:11,010 --> 00:14:17,230
+فصلنا ال «x» في دالة وفصلنا ال «y» في دالة لحالة
+
+119
+00:14:17,230 --> 00:14:21,690
+يبقى إن حدث ذلك بقول عن هذه المعادلة هي معادلة
+
+120
+00:14:21,690 --> 00:14:28,670
+تفاضلية separable يمكن فيها فصل المتغيراتيبقى هذه
+
+121
+00:14:28,670 --> 00:14:32,050
+الـ 6 بيه separable differential equation مشان
+
+122
+00:14:32,050 --> 00:14:36,870
+انحل المعادلة هذه اللي ال star بدي احاول اكتبها
+
+123
+00:14:36,870 --> 00:14:42,300
+بشكل اخريبقى يا بنات لو ضربت كله في DX بيصير DY
+
+124
+00:14:42,300 --> 00:14:49,100
+يسوي P of X في Q of Y في DX طيب لو جسمت على ال QY
+
+125
+00:14:49,100 --> 00:14:56,060
+بيصير DY على ال QY بيصير P of X DX يبقى فاصلت ال Y
+
+126
+00:14:56,060 --> 00:15:00,900
+في شجة و ال X في شجة من هنا سمنها separable
+
+127
+00:15:00,900 --> 00:15:05,180
+equation طب بده حلهاكامل هذا الطرف و كامل هذا
+
+128
+00:15:05,180 --> 00:15:10,240
+الطرف بتحصل لحالة زائد constant C إلا إذا كان عندك
+
+129
+00:15:10,240 --> 00:15:13,640
+initial value problem تقدر تجيب قيمة مين الـC
+
+130
+00:15:13,640 --> 00:15:19,420
+ماعندكش يبقى بتضلي المثلة بدلالة مين بدلالة هذا ال
+
+131
+00:15:19,420 --> 00:15:23,980
+constant واضح الفكرة يبقى من حد بشوف المعذرة إذا
+
+132
+00:15:23,980 --> 00:15:30,060
+بقدر أفصل المتغيرات X لحالة و Y لحالة كل واحد
+
+133
+00:15:30,060 --> 00:15:35,400
+باللي معاهيعني نقسم العرب عربين و كلهم بحيث يكون
+
+134
+00:15:35,400 --> 00:15:39,780
+هذول متجانسين و هذول يكون متجانسين يبقى خلاص سرد
+
+135
+00:15:39,780 --> 00:15:43,660
+separable differential equation بكامل هذه بالنسبة
+
+136
+00:15:43,660 --> 00:15:47,920
+ل X بكامل هذه الطرف تانية بالنسبة ل Y بكون حصلت
+
+137
+00:15:47,920 --> 00:15:54,740
+على مين على الحلنجي لسؤالنا كمثال تطبيق على ذلك
+
+138
+00:15:54,740 --> 00:15:58,380
+نقول let's solve the differential equation وشايف
+
+139
+00:15:58,380 --> 00:16:04,420
+دالة في X في Y' وهنا X وY التنين مع بعض بدي أحاول
+
+140
+00:16:04,420 --> 00:16:08,920
+أفصل المتغيرة طبعا هذا شرط عليهم من هنا سمناها
+
+141
+00:16:08,920 --> 00:16:12,950
+initial value problemبدي احاول افصل ال X في شجة و
+
+142
+00:16:12,950 --> 00:16:18,790
+ال Y في شجة بس قبل اللي تبدأ اكتبها بشكل اخر يبقى
+
+143
+00:16:18,790 --> 00:16:24,270
+باجي بقول X تربية زائد اربعة ال Y prime اللي هي
+
+144
+00:16:24,270 --> 00:16:29,010
+عبارة عن DY على DX يساوي X في Y
+
+145
+00:16:31,810 --> 00:16:39,050
+لو رحنا ضربنا كله في DX بصير X تربيع زائد أربعة DY
+
+146
+00:16:39,050 --> 00:16:43,250
+يساوي XY DX
+
+147
+00:16:45,310 --> 00:16:51,090
+أظن ليزال عندي مشكلتين المشكلة دي y مضروبة في dx
+
+148
+00:16:51,090 --> 00:16:57,810
+والمشكلة دي x مضروبة في من؟ في dy إذا شو رايك أجسم
+
+149
+00:16:57,810 --> 00:17:06,290
+الطرفين على y ضرب x تربيع زائد 4 يبقى هذي إيش
+
+150
+00:17:06,290 --> 00:17:15,560
+بيصير عندي بيصير عندي dy على yيساوي x على x تربيع
+
+151
+00:17:15,560 --> 00:17:22,420
+زائد أربعة في dx مظبوط هكذا يبقى لو جسمنا على هذه
+
+152
+00:17:22,420 --> 00:17:25,900
+بتجيني في المقام و لو جسمنا على هذه بتجي في المقام
+
+153
+00:17:25,900 --> 00:17:31,570
+يبقى هاي كل واحدة في شجةطبعا أظن هذا ال bus تفاضل
+
+154
+00:17:31,570 --> 00:17:36,950
+المقام يبقى in absolute value للمقام هذا ال bus
+
+155
+00:17:36,950 --> 00:17:42,010
+تفاضل المقام بس بده قداش يبقى بضرب في اتنين و بجسم
+
+156
+00:17:42,010 --> 00:17:47,710
+على اتنين بدون مشاكليبقى بناء عليه هذي عبارة عن dy
+
+157
+00:17:47,710 --> 00:17:56,110
+على y يسوى 2x على x تربية زائد أربعة و برة بدرب في
+
+158
+00:17:56,110 --> 00:18:07,330
+قداش بدرب في نص يبقى هذا نص وهذا dx نكمل يا بنادر
+
+159
+00:18:08,270 --> 00:18:14,550
+طيب لو كملنا الطرف الأول يبقى لن absolute value ل
+
+160
+00:18:14,550 --> 00:18:23,750
+Y كمان هذه نص لن absolute value ل X تربية زائد 4
+
+161
+00:18:24,110 --> 00:18:28,830
+هذه كمية مربعة ضروري اكتب لها absolute value يعني
+
+162
+00:18:28,830 --> 00:18:33,450
+قيمة موجبة لإن X تربية مضافة إليها أربعة حتى لو
+
+163
+00:18:33,450 --> 00:18:38,190
+كانت X المربعة مربعة بيصير موجبة زائد أربعة كمية
+
+164
+00:18:38,190 --> 00:18:43,190
+موجبة كتبت ال absolute والله ما كتبته C يعني كتبت
+
+165
+00:18:43,190 --> 00:18:49,030
+زيادة كلكة في الكتابة لا قيمة لها زائد constant
+
+166
+00:18:49,030 --> 00:18:55,190
+main زائد constant Cطب النُص هذا يا بنات مش يعني
+
+167
+00:18:55,190 --> 00:19:02,710
+اللي هو len x تربية زائد أربعة أُص نُص زائد كون
+
+168
+00:19:02,710 --> 00:19:09,630
+أُص تنسى؟ مش هيك الخواص؟ صح ولا لأ؟ طيب مادام هيك
+
+169
+00:19:09,630 --> 00:19:18,680
+طيب إيش رأيك هذه؟ لو جيت قلتأنا بدي Y مدى ما بدي
+
+170
+00:19:18,680 --> 00:19:25,780
+اتخلي هذي C1 يا بنات لسه لو هذي C1يبقى انا بدي ال
+
+171
+00:19:25,780 --> 00:19:33,440
+Y يبقى انا بدي ارفع كله كأسل العدد E يبقى E أسلن
+
+172
+00:19:33,440 --> 00:19:40,480
+absolute value ل Y يساوي E أسلن الجذر التربيع إلى
+
+173
+00:19:40,480 --> 00:19:50,550
+X تربية زائد 4 زائد constant C مظبوط هك؟من خواص
+
+174
+00:19:50,550 --> 00:19:56,730
+الـ LIN هذا E أُس LIN الجذر التربية إلى X تربية
+
+175
+00:19:56,730 --> 00:20:05,830
+زائد أربعة في E أُس C1وزعت اللي هو الأُس اللي
+
+176
+00:20:05,830 --> 00:20:11,110
+عندنا هادى تمام تمام طب إيه إيش رأيك هادى؟ مش هادى
+
+177
+00:20:11,110 --> 00:20:16,490
+مقدار ثابت و لا متغير ثابت لإن ال E ب 2 و 7 من 10
+
+178
+00:20:16,490 --> 00:20:21,410
+أُس مقدار ثابت يبقى مقدار ثابتيبقى هذا كله لو
+
+179
+00:20:21,410 --> 00:20:26,430
+شيلته و حطيت بداله C مش أسهللي في الكلكعة شوية
+
+180
+00:20:26,430 --> 00:20:31,830
+يبقى بده أشيله و أحط بداله C طيب يا بنات هنا E أس
+
+181
+00:20:31,830 --> 00:20:37,530
+لن ال E و لن عكس بعض يبقى بصير عندي absolute value
+
+182
+00:20:37,530 --> 00:20:48,110
+ل Yيساوي C في الـ E والـ N برضه بلغوا بعض بصير X
+
+183
+00:20:48,110 --> 00:20:56,770
+تربيع زائد كداش زائد أربعة تمامبدي أحاول أجيب قيمة
+
+184
+00:20:56,770 --> 00:21:00,710
+الـ C هذه برجع من ال initial condition اللي عندي
+
+185
+00:21:00,710 --> 00:21:06,410
+انا عندي Y عند Zero يساوي ستة absolute value لست
+
+186
+00:21:06,410 --> 00:21:14,230
+بقداش بستة يساوي C في الجذر التربيعي لكس تربيعي ب
+
+187
+00:21:14,230 --> 00:21:21,930
+Zero زائد قداشزائد أربعة يعني هذا يساوي اتنين C
+
+188
+00:21:21,930 --> 00:21:28,570
+إذا ومنها C تساوي قداش تلاتة يبقى صار عندي
+
+189
+00:21:28,570 --> 00:21:34,690
+absolute value ل Y يساوي تلاتة الجذر التربيع إلى X
+
+190
+00:21:34,690 --> 00:21:40,150
+تربيع زائد أربعة يبقى هذا الحل النهائي لان او
+
+191
+00:21:40,150 --> 00:21:45,050
+بتقولي Y تساوي زائد او نقص الجذر تفرقش عندنا تمام
+
+192
+00:21:48,220 --> 00:21:54,080
+لكن كونوا كلام محدد انا عندي Y ال initial
+
+193
+00:21:54,080 --> 00:21:58,500
+condition بيقولي Y عند Zero تساوي ستة يعني قيمة
+
+194
+00:21:58,500 --> 00:22:03,670
+موجبةما دام قيمة موجبة يبقى Y لن تأخذ عندي قيمة
+
+195
+00:22:03,670 --> 00:22:09,030
+سالبة لأن أنا جبت الحل عند النقطة عند النقطة اللي
+
+196
+00:22:09,030 --> 00:22:14,930
+هي الـ 0 و 6 لما تبقى X بـ 0 و Y ب6 يعني موجبة
+
+197
+00:22:14,930 --> 00:22:22,250
+بناء عليه بقول الحل Y تساوي 3 الجذر التربية ل X
+
+198
+00:22:22,250 --> 00:22:28,170
+تربية زائد 4 هذا هو الحل النهائيلكن لو كان C هذا
+
+199
+00:22:28,170 --> 00:22:33,810
+ماقدرتش اجيبه يا بنات بكتب زائد او نقص او بخليها
+
+200
+00:22:33,810 --> 00:22:39,610
+absolute value ل Y يساوي كذا هذا هو المثال الأول
+
+201
+00:22:39,610 --> 00:22:47,810
+حد بتحب تسألي سؤال هنا في خطوات الحل واضح يعني نخش
+
+202
+00:22:47,810 --> 00:22:52,530
+على مثال تاني اه تفضلي اكتر نقطة و هي ليش ستننا
+
+203
+00:22:52,530 --> 00:22:58,050
+السالد بس خلينا نقصمهم ده جدا شايفة ال condition
+
+204
+00:22:58,050 --> 00:23:03,610
+هذا؟ ايش بيقول؟ y عند ال zero يساوي 6 يعني احنا
+
+205
+00:23:03,610 --> 00:23:08,450
+بدنا نجيب الحل عند نقطة محددة مين هي النقطة؟ zero
+
+206
+00:23:08,450 --> 00:23:14,310
+و 6 يعني y ب 6 هل هي مسالبة؟ لأ يبقى y موجة من هنا
+
+207
+00:23:14,310 --> 00:23:20,170
+أعملنا الإشارة السالبة في تساول تاني؟ خلاص؟ طيب
+
+208
+00:23:20,170 --> 00:23:25,430
+نروح للمثال رقم اتنين يبقى example two
+
+209
+00:23:35,600 --> 00:23:43,060
+Solve the differential equation حل المعادلة
+
+210
+00:23:43,060 --> 00:23:51,100
+التفاضلية cos تربيع الـ X كله في الـ Y' بده يساوي
+
+211
+00:23:51,100 --> 00:23:59,320
+Y تربيع في Y ناقص الواحد كله في sin X
+
+212
+00:24:27,450 --> 00:24:31,890
+نرجع لسؤالنا جالي يحل المعادلة وما جاليش initial
+
+213
+00:24:31,890 --> 00:24:35,950
+value problem يقول ماعنديش initial condition بيبقى
+
+214
+00:24:35,950 --> 00:24:39,890
+بضل الحل بدلالة ال man بدلالة ال constant اللي
+
+215
+00:24:39,890 --> 00:24:46,860
+بطلع بس قبل هيكأه هذه هنا cosine تربيع وهذه مكتوبة
+
+216
+00:24:46,860 --> 00:24:51,140
+y prime إذا ما بقدر أشيل y prime مكتوب بدالها dy
+
+217
+00:24:51,140 --> 00:24:58,020
+by dx يبقى باجي بقول هنا cosine تربيع ال x هذه
+
+218
+00:24:58,020 --> 00:25:05,040
+كلها في dy by dx يساوي y تربيع في y ناقص واحد في
+
+219
+00:25:05,040 --> 00:25:14,090
+sin x تمام بدأ أحاول أفصل المتغيراتيبقى بدي أضرب
+
+220
+00:25:14,090 --> 00:25:20,650
+في DX وأجسم على cosine تربيع ال X وY تربيع في Y
+
+221
+00:25:20,650 --> 00:25:28,450
+ناقص واحد يبقى لو قسمتها بصير ال DIY على Y تربيع
+
+222
+00:25:28,450 --> 00:25:37,650
+في Y ناقص واحد يساوي sin X على cosine تربيع ال X
+
+223
+00:25:37,650 --> 00:25:50,650
+في DX أوبقدر اقول هذه يا بنات هي sin x على cos x
+
+224
+00:25:50,650 --> 00:26:00,330
+في cos x في dx او بقدر اكتب المثل على الشكل واحد
+
+225
+00:26:00,330 --> 00:26:07,630
+على y تربيع في y ناقص واحد dy بدي يساوي واحد على
+
+226
+00:26:07,630 --> 00:26:17,800
+cosineجداش؟ سك ال X سك ال X في تان ال X في ال DX
+
+227
+00:26:17,800 --> 00:26:24,400
+فصلنا المتغيرات؟ خلصنا؟ من حد ما نفصل المتغيرات
+
+228
+00:26:24,400 --> 00:26:30,900
+بيظل علينا بس كامل أظن الطرف اليمين سهل تكامله سك
+
+229
+00:26:30,900 --> 00:26:36,710
+ال X في تان ال X تكامله؟psychics يبقى ضال الطرف
+
+230
+00:26:36,710 --> 00:26:41,490
+الشمال حد بتقدر فيكوا تقولي أوي اذكرني كيف بدي
+
+231
+00:26:41,490 --> 00:26:47,330
+أكامل الطرف الشمال اللي بدي واحد ارفع عيدك واتحكي
+
+232
+00:26:47,330 --> 00:26:51,270
+حتى لو كان غلط اتعودي تحكي احكي غلط اليوم واحكي
+
+233
+00:26:51,270 --> 00:26:55,130
+غلط بكرا بعد بكرا بتحكي صح وكده دلكيش اللي ابدا
+
+234
+00:26:55,130 --> 00:26:59,210
+ارفع عيدك واحكي مين بتحب اذكر ان انا كهمدا كامل
+
+235
+00:26:59,210 --> 00:27:06,520
+الدالة هذهيعني يا بنات كهب نكمل دالة البسط مقدار
+
+236
+00:27:06,520 --> 00:27:11,880
+ثابت أو polynomial درجتها أقل من درجة المقام
+
+237
+00:27:11,880 --> 00:27:20,260
+المقام من درجة التالتة قسمت ايش؟ مش سامع قسمت ايش؟
+
+238
+00:27:20,260 --> 00:27:27,890
+و الله قسمة و نصيب قسمت ايش و بدنا نقسمبنقسم البصد
+
+239
+00:27:27,890 --> 00:27:32,730
+على المقام لو كانت درجة البصد أكبر من درجة المقام
+
+240
+00:27:32,730 --> 00:27:38,470
+أو تساويها لكن إذا درجة البصد أقل من درجة المقام
+
+241
+00:27:38,470 --> 00:27:45,640
+بنروح إلىالكسور الجزئية للـ Partial Fractions يبقى
+
+242
+00:27:45,640 --> 00:27:53,280
+بدنا نروح نشوف الكسور الجزئية للمقدار واحد على Y
+
+243
+00:27:53,280 --> 00:28:01,240
+ناقص واحد في الـ Y تربيع أيوا يبقى هذا بناقص Y
+
+244
+00:28:01,240 --> 00:28:09,380
+ناقص واحد زائد Y تربيعايوة يبقى هذه المقام من
+
+245
+00:28:09,380 --> 00:28:15,780
+الدرجة الأولى إذا بنحط في ال bus ده الأقل منه في
+
+246
+00:28:15,780 --> 00:28:20,640
+الدرجة يبقى ماعنديش إلا constant يبقى بقوله هنا a
+
+247
+00:28:20,640 --> 00:28:25,940
+طيب هذه من الدرجة الثانية أو من الدرجة الأولى مكرر
+
+248
+00:28:25,940 --> 00:28:30,520
+بنفع الشجتينيعني من الدرجة الأولى أو من الدرجة
+
+249
+00:28:30,520 --> 00:28:38,920
+الثانية يبقى بقدر أقول له بي واي زائد سي تمام؟
+
+250
+00:28:38,920 --> 00:28:45,800
+الآن بدرح أدور على المجاهيل A وB وC مشان هيك صح
+
+251
+00:28:45,800 --> 00:28:48,620
+أصفر معايا شو بدنا نعمل أنا بذكر التذكير اللي أنا
+
+252
+00:28:48,620 --> 00:28:53,240
+خدت فيك الكلاص بي هذي يبقى بدرح على الطرفين و أضرب
+
+253
+00:28:53,240 --> 00:28:58,230
+في المقام اللي عندنالو ضربت في هذا المقام ايش بيظل
+
+254
+00:28:58,230 --> 00:29:09,130
+هنا؟ هنا بيظل a y تربيع هنا بيظل by زائد c في ال y
+
+255
+00:29:09,130 --> 00:29:13,690
+ناقص واحد، مظبوط ايه؟ يعني معنى هذا الكلام باطل
+
+256
+00:29:13,690 --> 00:29:18,570
+يصير عندنا كسور يبقى هذه وسيلة عملية ان اتخلص من
+
+257
+00:29:18,570 --> 00:29:25,330
+الكسور حتى اقدر اجيب قيمة ال a و ال b و ال c تمام؟
+
+258
+00:29:26,120 --> 00:29:32,000
+طيب عندنا أكثر من طريقة لإيجاد قيمة الـA والـB
+
+259
+00:29:32,000 --> 00:29:39,040
+والـC إما طريقة المقارنة في الطرفين أو أحط قيم من
+
+260
+00:29:39,040 --> 00:29:45,700
+عندي وبالتالي أشوف قيم المجاهيل و أحل الشغلات هذه
+
+261
+00:29:45,700 --> 00:29:54,470
+مع بعضلو جيت قلت هذه بنات a y تربية زائد b y تربية
+
+262
+00:29:54,470 --> 00:30:05,090
+ناقص by زائد c y ناقص c، مظبوط هيك؟ يبقى هذا واحد
+
+263
+00:30:05,090 --> 00:30:15,510
+يساوي a زائد b في y تربية زائد c ناقص b كله في y
+
+264
+00:30:15,510 --> 00:30:24,100
+ناقص cالان بنقول بمقارنة المعاملات في الطرفين
+
+265
+00:30:24,100 --> 00:30:29,280
+comparing the coefficients in both sides we get
+
+266
+00:30:29,280 --> 00:30:34,140
+بدنا نقارن المعاملات في الطرفين هذه y تربيع هنا في
+
+267
+00:30:34,140 --> 00:30:39,100
+y تربيع إذا في الأصل موجودة بس معاملها بقداش zero
+
+268
+00:30:39,100 --> 00:30:46,770
+يبقى ال a زائد ال b بده يساوي zero في هنا yيبقى
+
+269
+00:30:46,770 --> 00:30:52,550
+الـ C ناقص الـ B كمان يساوي Zero اللي بعدها اللي
+
+270
+00:30:52,550 --> 00:30:59,610
+هو اللي عندك هنا ناقص C يساوي كم؟ يساوي واحد ومنها
+
+271
+00:30:59,610 --> 00:31:07,600
+C تساوي سالب واحدطب لما C تساوي سالب واحد هدول
+
+272
+00:31:07,600 --> 00:31:13,080
+المعادلتين شو بده يصير فيهم؟ بده يصير سالب واحد
+
+273
+00:31:13,080 --> 00:31:21,380
+سالب B تساوي Zero يبقى B تساوي قداش؟ سالب واحد لما
+
+274
+00:31:21,380 --> 00:31:27,600
+B تساوي سالب واحد تصير A سالب واحد يساوي Zero يبقى
+
+275
+00:31:27,600 --> 00:31:34,170
+هذا معناته ان A تساوي واحديبقى بيب واحد بيب سالب
+
+276
+00:31:34,170 --> 00:31:41,350
+واحد اب واحد و سيب سالب واحد يبقى مسألة هذه ستصبح
+
+277
+00:31:41,350 --> 00:31:46,670
+على الشكل التالي اذا بدي اشيل هذا و اعوض بدله
+
+278
+00:31:46,670 --> 00:31:53,640
+بالمقدار هذاA عندي بواحد يبقى واحد على Y ناقص واحد
+
+279
+00:31:53,640 --> 00:32:01,680
+زائد B عندي بقداشي بسالب واحد يبقى سالب Y C بسالب
+
+280
+00:32:01,680 --> 00:32:10,100
+واحد يبقى كمان سالب واحد كله على Y تربيع هذا في DY
+
+281
+00:32:10,100 --> 00:32:20,060
+يساوي شو رأيك ابسطه؟يبقى هذا واحد على Y ناقص واحد
+
+282
+00:32:20,060 --> 00:32:27,880
+هذه على هذه بيظل ناقص واحد على Y وهذه ناقص واحد
+
+283
+00:32:27,880 --> 00:32:34,520
+على Y تربيع كله في دي Y يساوي الطرف اليمين الطرف
+
+284
+00:32:34,520 --> 00:32:40,160
+اليمين اللي همين سك ال X في تان ال X في دي X يبقى
+
+285
+00:32:40,160 --> 00:32:47,600
+سك ال X في تان ال Xفي الـ dx أظن لو كملت بحصل على
+
+286
+00:32:47,600 --> 00:32:52,740
+الحل مظبوط يبقى بعد ما عملت ال partial fraction
+
+287
+00:32:52,740 --> 00:32:57,980
+هذه السهل تكاملها هذه السهل تكاملها هذه السهل
+
+288
+00:32:57,980 --> 00:33:04,280
+تكاملها هذه السهل تكاملها يبقى كل هذا سهل خالص
+
+289
+00:33:04,280 --> 00:33:10,380
+يبقى مش ضايل عليه إلا عملية التكامل يبقى بدنا نجي
+
+290
+00:33:10,380 --> 00:33:13,060
+نكامل هذه المسألة
+
+291
+00:33:15,030 --> 00:33:21,930
+طيب تكامل هذه بقداش يا بنات دي Y على Y ناقص واحد
+
+292
+00:33:21,930 --> 00:33:30,350
+بـLin المقام يبقى هذا Lin absolute value لـY ناقص
+
+293
+00:33:30,350 --> 00:33:39,130
+واحد هذه زيها اظن كمان ناقص Lin absolute value لـY
+
+294
+00:33:39,130 --> 00:34:02,790
+هذهy²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²-y²
+
+295
+00:34:03,070 --> 00:34:12,210
+بسكل X يبقى سكل X زائد constant C أظن ممكن أنبسط
+
+296
+00:34:12,210 --> 00:34:21,000
+شويةطيب هذه عبارة عن لن ناقص لن يعني لن خارج
+
+297
+00:34:21,000 --> 00:34:27,760
+القسمة يبقى هذه لن absolute value Y ناقص واحد كله
+
+298
+00:34:27,760 --> 00:34:36,680
+على Y زائد واحد على Y يساوي سك X زائد constant C
+
+299
+00:34:36,680 --> 00:34:42,950
+يبقى هذا هو حل ضمنين ايش يعني حل ضمنين؟يعني مش
+
+300
+00:34:42,950 --> 00:34:48,370
+قادرين نطلع ال Y في شجة و ال X في شجة تانية يعني
+
+301
+00:34:48,370 --> 00:34:53,090
+مش قادر أقول Y تساوي دلّة في X وإنما ال Y و ال X
+
+302
+00:34:53,090 --> 00:34:58,150
+لو ضربت كله في Y و جيته سلك يبقى بتضلها مشربكة مع
+
+303
+00:34:58,150 --> 00:35:01,890
+بعضها ماقدرش أفصل Y في ناحية و الباقي كله في ناحية
+
+304
+00:35:01,890 --> 00:35:06,970
+تانية يبقى هذا هو الحل ضمني لهذه المعادلة
+
+305
+00:35:06,970 --> 00:35:14,770
+التفاضلية حد فيكم بتحب تسأل أي سؤال هنا؟أي سؤال
+
+306
+00:35:14,770 --> 00:35:20,190
+على التكامل على التفاضل على اللي بدك هيه مافيهش
+
+307
+00:35:20,190 --> 00:35:28,910
+طيب نروح للمثال اللي بعده
+
+308
+00:35:28,910 --> 00:35:36,670
+يبقى نيجي للمثال الذي يليه وهو مثال رقم 3 يبقى
+
+309
+00:35:36,670 --> 00:35:47,220
+example 3يقول لي y prime 10 inverse y بده يساوي x
+
+310
+00:35:47,220 --> 00:35:57,440
+في 1 زائد y تربيع شو
+
+311
+00:35:57,440 --> 00:36:04,000
+ورايكوا؟يبقى بدنا نحل يبقى ماليش إلا أحط y prime
+
+312
+00:36:04,000 --> 00:36:13,240
+على الصيغة dy على dx يبقى ال solution هي عندي tan
+
+313
+00:36:13,240 --> 00:36:22,760
+inverse y في dy على dx يسوى x في 1 زائد y تربية
+
+314
+00:36:22,760 --> 00:36:28,140
+بنقدر نخصل المتغيرات يا بنات نخل ال y في شجة و ال
+
+315
+00:36:28,140 --> 00:36:35,660
+x في شجةبنقدر؟ اه بنقدر يبقى بقدر اقول له هذه 10
+
+316
+00:36:35,660 --> 00:36:43,240
+inverse y 1 زائد y تربيع كله في dy بده يساوي ال x
+
+317
+00:36:43,240 --> 00:36:52,040
+في dx فصلنا المتغيرات؟ صارت c parabola equation؟
+
+318
+00:36:52,040 --> 00:36:59,020
+طيب السؤال هوكيف بدي أكامل الطرف الشمال علما انه
+
+319
+00:36:59,020 --> 00:37:03,600
+very easy ماهو
+
+320
+00:37:03,600 --> 00:37:09,840
+مشتقة البسط هو المقاس مشتقة ال 10 inverse هي X 1
+
+321
+00:37:09,840 --> 00:37:16,100
+على 1 زي X تربيع اذا مشتقة 10 inverse Y هي 1 على
+
+322
+00:37:16,560 --> 00:37:23,700
+واحد زائد واي تربية إذا بإمكاني أعيد صياغة هذه
+
+323
+00:37:23,700 --> 00:37:29,460
+المسألة كالتالي هذه بقدر أقول بقدر أكتبها على
+
+324
+00:37:29,460 --> 00:37:39,160
+الشكل التالي ten inverse y دي ل ten inverse y هي
+
+325
+00:37:39,160 --> 00:37:46,490
+الشجة الشمالي مش دي إشارة تفاضل صح؟يبقى مشتقة تان
+
+326
+00:37:46,490 --> 00:37:52,210
+انفرس Y هي واحد على واحد زاد Y تربية DY يبقى انا
+
+327
+00:37:52,210 --> 00:37:57,150
+حتى لما كملتش كل اللي عملته شلت واحد على واحد زاد
+
+328
+00:37:57,150 --> 00:38:01,670
+Y تربية DY وحطيت درجة D تان انفرس اصلا في calculus
+
+329
+00:38:01,670 --> 00:38:06,210
+P عملتكوا شغلات كتير زي هيك تمام يا ما عملناها
+
+330
+00:38:06,210 --> 00:38:11,960
+وحتى في ايه عملتها كمانطبعا يبقى ما هوش جديد طيب
+
+331
+00:38:11,960 --> 00:38:15,040
+هذا الطرف الشمالي الطرف اليمين مسكين مافي عنده
+
+332
+00:38:15,040 --> 00:38:21,960
+حاجة يبقى هذا X في DX الآن بقدر أكمل بسهولة هذي
+
+333
+00:38:21,960 --> 00:38:29,300
+كإن ايش كإني بكمل ZDZ صح ولا لا يبقى تكامل ZDZ
+
+334
+00:38:29,300 --> 00:38:37,160
+بقدراش Z تربية على اتنين صحيح؟يبقى هذه ه كإنها tan
+
+335
+00:38:37,160 --> 00:38:43,540
+inverse y الكل تربيع على اتنين ال X كمان ال X
+
+336
+00:38:43,540 --> 00:38:50,560
+تربيع على اتنين زاد constant C أظن لو ضربنا
+
+337
+00:38:50,560 --> 00:38:57,480
+الطرفين في اتنين مافي مشكلةيبقى هذا يا بنات بالصير
+
+338
+00:38:57,480 --> 00:39:06,220
+10 inverse y لكل تربيع يساوي x تربية الزائدة 2c
+
+339
+00:39:06,220 --> 00:39:13,820
+ناخد الجدر التربية على الطرفين طب لما ناخد الجدر
+
+340
+00:39:13,820 --> 00:39:17,080
+التربية على الطرفين بيطلع عندي absolute value ولا
+
+341
+00:39:17,080 --> 00:39:22,350
+لا؟الجذر التربيع لـ X تربيع مش هو absolute value
+
+342
+00:39:22,350 --> 00:39:28,330
+لـ X إذاً هذا absolute value يبقى بقدر أقول لو
+
+343
+00:39:28,330 --> 00:39:33,230
+أخدت الجذر التربيع للطرفين يبقى absolute value ل
+
+344
+00:39:33,230 --> 00:39:39,590
+10 inverse Yبدي أساوي الجذر التربيعي للـ X تربيع
+
+345
+00:39:39,590 --> 00:39:46,770
+زائدي اتنين C أخدت الجذر التربيعي للطرفين طيب باجي
+
+346
+00:39:46,770 --> 00:39:51,730
+بسهل هو هذه ال absolute value يعني ضروري ان اكتبها
+
+347
+00:39:51,730 --> 00:39:57,110
+بقولك اه ضروري لان تان inverse بتاخد قيم موجبة و
+
+348
+00:39:57,110 --> 00:40:00,910
+بتاخد قيم سالبة بعد ال zero قيمها موجبة و قبل ال
+
+349
+00:40:00,910 --> 00:40:05,130
+zeroمن الذاكرين منحنى ten inverse x و الله كله
+
+350
+00:40:05,130 --> 00:40:11,750
+كلام ten inverse x طب ال range تبعه من وين لوين
+
+351
+00:40:11,750 --> 00:40:18,110
+يالا مين تتذكر من سالب واحد لواحد حرام عليك و تاجه
+
+352
+00:40:18,110 --> 00:40:24,810
+الله من سالب بايع اتنين لبياني يعني منحنى ال ten
+
+353
+00:40:24,810 --> 00:40:29,470
+inverse لو حبيت اذاكرك فيه كان على الشكل التالي
+
+354
+00:40:29,470 --> 00:40:35,690
+هذا محور xهذا محور Y وهذا نقطة وهذا خط وهمي ببي
+
+355
+00:40:35,690 --> 00:40:40,530
+على اتنين وهذا خط وهمي زيه بسالف بي على اتنين
+
+356
+00:40:40,530 --> 00:40:46,510
+ومنحنا ال 10 inverse بجيكي هيك بالشكل هذا يبقى هذا
+
+357
+00:40:46,510 --> 00:40:51,710
+اللي هو 10 inverse X يعني ال 10 inverse بعد ال
+
+358
+00:40:51,710 --> 00:40:55,520
+zero بتاخدpositive values وقبل ال zero بتاخد
+
+359
+00:40:55,520 --> 00:41:00,080
+negative values من هنا ال absolute value ضرورية
+
+360
+00:41:00,080 --> 00:41:04,420
+ولا يمكن التنازل عنها زي الثوابط الفلسطينية يا
+
+361
+00:41:04,420 --> 00:41:09,840
+بنات حد فيكم بتعرف شو الثوابط الفلسطينية يعني حق
+
+362
+00:41:09,840 --> 00:41:18,620
+العودة واللاجئين وفلسطين من البحر إلى النهر ولا لا
+
+363
+00:41:19,070 --> 00:41:23,290
+طيب ماشي يالا مكفف يابناشي ناطمع عليكوا كتير طيب
+
+364
+00:41:23,290 --> 00:41:28,050
+ال absolute value بده تخلص منها يبقى بسيطة جدا حط
+
+365
+00:41:28,050 --> 00:41:34,410
+زائد او ناقص و بمشي الحالة يبقى هذه ههه بصير ten
+
+366
+00:41:34,410 --> 00:41:41,650
+inverse y يساوي زائد او ناقص الجدرى التربيعى الاكس
+
+367
+00:41:41,650 --> 00:41:49,600
+تربيه زائد اتنين سي سؤالي هوبنقدر نوجد y لحالها
+
+368
+00:41:49,600 --> 00:41:56,960
+بدون tan inverse؟ نقدر؟ ما هو domain التان من سالب
+
+369
+00:41:56,960 --> 00:42:00,720
+infinity إلى infinity إذا ماعندي مشكلة أخد tan
+
+370
+00:42:00,720 --> 00:42:05,800
+للطرفين يبقى لو أخدنا tan للطرف الشمال بتطير tan
+
+371
+00:42:05,800 --> 00:42:10,590
+inverse وبتصير tan للطرف اليمينفتان القيمة الموجبة
+
+372
+00:42:10,590 --> 00:42:15,330
+بالقيمة الموجبة وتان القيمة السالبة لأن تان odd
+
+373
+00:42:15,330 --> 00:42:19,190
+سالب بيطلع برا يبقى الزائد و النقص مضى المكان جوه
+
+374
+00:42:19,190 --> 00:42:25,450
+و بيسيروا برا لأن تان is an odd function يبقى بناء
+
+375
+00:42:25,450 --> 00:42:32,570
+عليه الحل هنا Y يساوي الزائد أو ناقص تان الجذر
+
+376
+00:42:32,570 --> 00:42:38,510
+التربيع إلى X تربيع زائد 2Cكفى الله المؤمنين
+
+377
+00:42:38,510 --> 00:42:45,810
+القتال يبقى هذا حل مين؟ حل المسألة اللى عندنا آخر
+
+378
+00:42:45,810 --> 00:42:54,190
+مثال في هذا ال section آه آه بضل قيمتين يحقق هذه
+
+379
+00:42:54,190 --> 00:43:01,730
+المعادلة آخر
+
+380
+00:43:01,730 --> 00:43:09,660
+مثال بيقول لي مثال أربعةsolve the differential
+
+381
+00:43:09,660 --> 00:43:18,280
+equation اللي هو y ناقص اتنين x في الـ y prime
+
+382
+00:43:18,280 --> 00:43:27,500
+يساوي تلاتة y ناقص ستة x زائد واحد هذا آخر تمرين
+
+383
+00:43:27,500 --> 00:43:33,460
+في الكتاب حاطط تلت مسائل او اربع مسائل هذا أحدهم
+
+384
+00:43:34,160 --> 00:43:40,620
+وانا جبته متعمد مثال لإنه في فكرة جديدة مش موجودة
+
+385
+00:43:40,620 --> 00:43:47,340
+في كل الأمثلة اللي قبل شو هذه الفكرة؟ بقدرش أفصل
+
+386
+00:43:47,340 --> 00:43:52,620
+ال X في شجة و ال Y في شجة مش قادرلكن بقدر اعمل
+
+387
+00:43:52,620 --> 00:44:01,360
+عملية التحايل عملية التحايل كتالة هي y ناقص اتنين
+
+388
+00:44:01,360 --> 00:44:08,500
+x كله في dy على dx يساوي شو رايك اخد هنا تلاتة
+
+389
+00:44:08,500 --> 00:44:15,240
+عامل مشترك يبقى y ناقص اتنين x زائد واحد عملية
+
+390
+00:44:15,240 --> 00:44:20,420
+التحايلبدي أشيل المقدار بين القوسين و أضعه بـ
+
+391
+00:44:20,420 --> 00:44:27,980
+variable جديدإذا باجي بقول له pot حط لي v يساوي y
+
+392
+00:44:27,980 --> 00:44:34,400
+ناقص 2x بعدين روح اشتقيها بالنسبة إلى x يبقى باجي
+
+393
+00:44:34,400 --> 00:44:43,280
+بقول له dv على dx بده يساوي dy على dx ناقص 2 إذا
+
+394
+00:44:43,280 --> 00:44:50,380
+بقدر أجيب ال dy على dx بدلالةdv على dx يبقى بيصير
+
+395
+00:44:50,380 --> 00:44:58,360
+dv على dx زائد اتنين بده يساوي dy على dx صحيح ولا
+
+396
+00:44:58,360 --> 00:45:03,720
+لا؟ إذا برجع للمعادلة الأصلية اللي هسميها star
+
+397
+00:45:03,720 --> 00:45:10,880
+المعادلة star واجي أعوض فيها يبقى المعادلة star
+
+398
+00:45:10,880 --> 00:45:16,790
+بدنا نجي نعوض فيها ونشوف كيف شكل الحل بده يكونفي
+
+399
+00:45:16,790 --> 00:45:23,430
+مثل هذه الحالة طيب
+
+400
+00:45:23,430 --> 00:45:34,210
+الان باجي بقوله substitute in equation star we get
+
+401
+00:45:35,520 --> 00:45:46,360
+هذه بنصار V في Dy على DX Dy على DX اللي هي DV على
+
+402
+00:45:46,360 --> 00:45:53,460
+DX زائد 2 هذا الطرف من؟ الطرف الشمال الطرف اليمين
+
+403
+00:45:53,460 --> 00:46:03,800
+3V زائد 1بدا افك هذا بيصير V في الـDV على DX زائد
+
+404
+00:46:03,800 --> 00:46:11,500
+2V يساوي 3V زائد 1 لو جيبنا 2V على الشجة التانية
+
+405
+00:46:11,500 --> 00:46:21,680
+بيصير V في DV على DX بدي ساوي V زائد 1 اظن بقدر
+
+406
+00:46:21,680 --> 00:46:31,920
+افصل المتغيراتيبقى V على V زائد واحد كله في DV بده
+
+407
+00:46:31,920 --> 00:46:36,840
+يساوي DX لحالها مسكينة ماعهاش دوال ماعهاش متغيرات
+
+408
+00:46:36,840 --> 00:46:45,080
+تمام؟ طب بدنا نكمل هذه درجة ال bus قد درجة المقام
+
+409
+00:46:45,080 --> 00:46:49,760
+يبقى قسم مطولة واحدة مفتحة اكتر من اشواقات الليلة
+
+410
+00:46:49,760 --> 00:46:53,700
+ولا قسم مطولة ولا حاجة نضيف واحد ونطرح واحدكان
+
+411
+00:46:53,700 --> 00:47:01,940
+نظيف قداش؟ zero يبقى هذه بقدر اقولv زائد واحد ناقص
+
+412
+00:47:01,940 --> 00:47:07,720
+واحد على v زائد واحد في ال dv بده يساوي dx قولنا
+
+413
+00:47:07,720 --> 00:47:11,780
+والله كلامك مظهر قالت الحين بده اوزع ال bus على
+
+414
+00:47:11,780 --> 00:47:16,400
+المقام v زائد واحد على v زائد واحد بقداش بواحد
+
+415
+00:47:16,400 --> 00:47:23,980
+يبقى السعر عندي واحد ناقص واحد على v زائد واحد كله
+
+416
+00:47:23,980 --> 00:47:31,810
+في dv بده يساوي قداش dx بقدر أكاملنقدر أظن هذه
+
+417
+00:47:31,810 --> 00:47:38,490
+تكاملها V وهذا لين absolute value ل V زائد الواحد
+
+418
+00:47:38,490 --> 00:47:46,190
+وهذا يبدو يسوى X زائد constant C بعد ذلك بشيل ال V
+
+419
+00:47:46,720 --> 00:47:52,880
+وبرجعها بدلالة الـ y و الـ x يبقى بيصير هنا الـ y
+
+420
+00:47:52,880 --> 00:48:04,280
+ناقص 2x ناقص 2x ناقص لـ absolute value y ناقص 2x
+
+421
+00:48:04,280 --> 00:48:13,950
+زائد 1 يساوي x زائد constant cأو انشريت فيقولي Y
+
+422
+00:48:13,950 --> 00:48:22,690
+ناقص لأن absolute value Y ناقص 2X زائد 1 ك
+
+423
+00:48:22,690 --> 00:48:31,710
+absolute value بده يساوي 3X زائد constant C يبقى
+
+424
+00:48:31,710 --> 00:48:37,160
+هذا الحل وهو حل ضمنيزي ما انت شايفها بقدرش أفصل ال
+
+425
+00:48:37,160 --> 00:48:42,980
+X في شجة وال Y في شجة لحد هنا stop انتهى ال
+
+426
+00:48:42,980 --> 00:48:50,900
+section إلى يكون أرقام المسائل يبقى exercises واحد
+
+427
+00:48:50,900 --> 00:48:59,820
+اتنين السؤال الأول والخامس والسبع ايوة اسم
+
+428
+00:49:04,780 --> 00:49:13,120
+كاتب section واحد اتنين طبع طبع طبع طبع طبع طبع
+
+429
+00:49:13,120 --> 00:49:18,800
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+430
+00:49:18,800 --> 00:49:21,000
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+431
+00:49:21,000 --> 00:49:21,000
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+432
+00:49:21,000 --> 00:49:21,000
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+433
+00:49:21,000 --> 00:49:21,040
+طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع طبع
+
+434
+00:49:21,040 --> 00:49:27,940
+طبع طبع طبع طبع طبع
+
+435
+00:49:27,940 --> 00:49:32,850
+طهذا هو يبقى كتابة الطابعة الرابعة وهذه أرقام
+
+436
+00:49:32,850 --> 00:49:36,630
+المسائل من الطابعة الرابعة حد فيكوا يلاقي سؤال؟
+
+437
+00:49:36,630 --> 00:49:41,510
+المرة جايسك شيل لبعد، ادري بالكوا الساعات المكتبية
+
+438
+00:49:41,510 --> 00:49:46,090
+اثنين
+
+439
+00:49:46,090 --> 00:49:54,070
+أربعاء من العشرة للاحداشر ومن اتناشر للواحدة بتكون
+
+440
+00:49:54,070 --> 00:50:00,130
+شيلكوا يوم السبتأما يوم الأحد فمن ال 11 و نص
+
+441
+00:50:00,130 --> 00:50:05,610
+للواحدة بتبقى إلكوا هذه يعني نص ساعة مش إلكوا ساعة
+
+442
+00:50:05,610 --> 00:50:15,650
+إلكوا و كذلك يوم الثلاثة من الساعة 11 و نص للواحدة
+
+443
+00:50:15,650 --> 00:50:23,990
+و يوم الأربعاء يوم الأربعاء من 12 للواحدة هذه
+
+444
+00:50:23,990 --> 00:50:27,560
+إلكوا .. لأ مش إلكوا يوم الأربعاءلأ مش .. يبقى
+
+445
+00:50:27,560 --> 00:50:31,340
+أنتوا إلكوا سبت اتنين اربعة من عشرة الليلة الى
+
+446
+00:50:31,340 --> 00:50:36,680
+احداشر ونص ساعة يوم الأحد ونص ساعة يوم اثن .. كيف
+
+447
+00:50:36,680 --> 00:50:41,900
+نص ساعة؟ لأ لأ إلكوا ساعتين كمان اللي هو من اتناشر
+
+448
+00:50:41,900 --> 00:50:45,660
+لواحدة أحد وثلاثة يبقى هاي بدل الساعة كمان ساعات
+
+449
+00:50:45,660 --> 00:50:47,440
+وكّر على الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HSZXZRH7pd0_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HSZXZRH7pd0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..44a55b3383f90e2e575a6768b7110d1ff1135f4e
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HSZXZRH7pd0_raw.srt
@@ -0,0 +1,1620 @@
+1
+00:00:19,290 --> 00:00:23,430
+بسم الله الرحمن الرحيم في نهاية المحاضرة الماضية
+
+2
+00:00:23,430 --> 00:00:27,850
+ابتدأنا في section واحد خمسة وهو ال linear first
+
+3
+00:00:27,850 --> 00:00:32,050
+order differential equation وعرفنا ان شكل ال first
+
+4
+00:00:32,050 --> 00:00:35,990
+order linear differential equation على الشكل a
+
+5
+00:00:35,990 --> 00:00:40,310
+node of x في ال y prime زائد a one of x في ال y
+
+6
+00:00:40,310 --> 00:00:44,610
+بدل سوى ال f of x وبعد ذلك رحنا لمعامل y prime
+
+7
+00:00:44,610 --> 00:00:51,550
+خلنا الواحد الصحيح واشترطناعند تطبيق الحل لهذه
+
+8
+00:00:51,550 --> 00:00:56,570
+المعادلة لازم يكون المعامل هو واحد صحيح فأصبحت
+
+9
+00:00:56,570 --> 00:00:59,190
+الصورة الجديدة لل first order differential
+
+10
+00:00:59,190 --> 00:01:05,670
+equation على صيغة y prime زائد P of x Vy بده يسوى
+
+11
+00:01:05,670 --> 00:01:11,210
+مين ال Q of x حيث ال P و ال X ال P و ال Q دوا
+
+12
+00:01:11,210 --> 00:01:16,750
+المتصلة على فترة ماوقلنا إن الحل هذه المعادلة على
+
+13
+00:01:16,750 --> 00:01:24,770
+صيغة الـ Mu of X في Y بتشوي تكامل Mu of X في Q of
+
+14
+00:01:24,770 --> 00:01:30,310
+X في DX حيث الـ Mu of X اللي هو عامل التكامل هو
+
+15
+00:01:30,310 --> 00:01:37,150
+عبارة عن E فُس تكامل P of X DX واخدنا على ذلك
+
+16
+00:01:37,150 --> 00:01:43,460
+مثالين وهذا اللي بين أيدنا هو المثال رقم 3يبقى
+
+17
+00:01:43,460 --> 00:01:46,400
+المثال رقم تلاتة بيقول solve the differential
+
+18
+00:01:46,400 --> 00:01:53,080
+equation xy prime زائد y وسوى x sin x علما بأن x
+
+19
+00:01:53,080 --> 00:01:59,180
+دائما و أبدا أكبر من 0 يبقى مثلا مشان انحل
+
+20
+00:01:59,180 --> 00:02:02,760
+المعادلة التفاضلية اللي قدامنا هذه بدي اكتبها على
+
+21
+00:02:02,760 --> 00:02:08,370
+ال standard form تبعهااللي بدي أخلّي معامل y' هو
+
+22
+00:02:08,370 --> 00:02:14,270
+main واحد، إذا بروح نقسم الطرفين على x وهذا ممكن
+
+23
+00:02:14,270 --> 00:02:18,490
+لأن x greater than zero ولا تساوي zero إذا
+
+24
+00:02:18,490 --> 00:02:25,930
+المعادلة العادية هتأخد الصيغة الجديدة هي y' زائد
+
+25
+00:02:25,930 --> 00:02:32,130
+واحد على x في y يساوي main يساوي sign xيبقى هاي
+
+26
+00:02:32,130 --> 00:02:37,390
+حطيناها على صيغة y prime زي p of x في y بده ساوي ل
+
+27
+00:02:37,390 --> 00:02:42,990
+q of x يبقى بناء انا عليه بقدر اجيب عامل التكامل
+
+28
+00:02:42,990 --> 00:02:49,430
+لهذه المعادلة فبروح بقول ل mu of x يساوي E of
+
+29
+00:02:49,430 --> 00:02:57,830
+تكامل واحد على x dx يبقى E أصل ان ال x يبقى ال x
+
+30
+00:02:57,830 --> 00:03:03,900
+اتصليبقى عامل التكامل هو X إذا لو روحت سميت
+
+31
+00:03:03,900 --> 00:03:12,620
+المعادلة الأصلية star بقول له solution of the
+
+32
+00:03:12,620 --> 00:03:23,080
+differential equation star isاللي هو الـ x في الـ
+
+33
+00:03:23,080 --> 00:03:30,120
+y يسوى تكامل x في sign الـ x كله بالنسبة لهذه الـ
+
+34
+00:03:30,120 --> 00:03:35,320
+x يبقى ضايل علينا تكامل هذه تابنا نكامل هذه الدالة
+
+35
+00:03:35,320 --> 00:03:40,380
+يا بنات تكامل integration by parts وهذه أخدناها
+
+36
+00:03:40,380 --> 00:03:49,180
+صيغة محددة وقلنا بروح ناخد الدالة ومشتقتها يبقى
+
+37
+00:03:49,180 --> 00:03:58,490
+باجي باخداللي هو مين ال .. ال U و هذه ال D V ال U
+
+38
+00:03:58,490 --> 00:04:04,410
+اللي هي عبارة عن X و ال D V اللي هي صين ال X بروح
+
+39
+00:04:04,410 --> 00:04:09,270
+بفاضل هذه بقى تفاضلها بواحد وبجي او بقول هذه
+
+40
+00:04:09,270 --> 00:04:13,090
+derivatives وهذه integrals in general يعني هذه
+
+41
+00:04:13,090 --> 00:04:17,530
+بقول عليها derivatives وهذه بروح بقول عليها
+
+42
+00:04:17,530 --> 00:04:19,610
+integrals
+
+43
+00:04:25,340 --> 00:04:32,500
+بعد ذلك اشتغل كمان مرة يبقى مشتقة هذه بـ0 تكمل هذه
+
+44
+00:04:32,500 --> 00:04:39,920
+بـSin X بعدين بقول الدالة هذه في الدالة هذهوالدالة
+
+45
+00:04:39,920 --> 00:04:44,400
+اللي عندنا هذه في الدالة هذه و بروح باستخدم قاعدة
+
+46
+00:04:44,400 --> 00:04:49,660
+الإشارات يبقى ببدأ بالموجب اللي بعده سالب موجب
+
+47
+00:04:49,660 --> 00:04:54,840
+سالب إلى ما شاء الله يبقى بناء عليها أصبح عند ال X
+
+48
+00:04:54,840 --> 00:05:02,580
+Y يساوي ناقص X في cosine X حصل ضرب الاتنين زائد
+
+49
+00:05:02,580 --> 00:05:09,780
+sine X زائد constant Cأنا بدي y as a function of x
+
+50
+00:05:09,780 --> 00:05:15,280
+إذا بروح بجسم كله على مين؟ على x يبقى بيصير حل
+
+51
+00:05:15,280 --> 00:05:21,680
+المعادلة التفاضرية الى star هو y تساوي سالب cosine
+
+52
+00:05:21,680 --> 00:05:28,760
+ال x زائد sine ال x على x زائد c على x هذا ال
+
+53
+00:05:28,760 --> 00:05:33,740
+general solution لمين؟ للمعادلة التفاضرية اللى هي
+
+54
+00:05:33,740 --> 00:05:39,670
+ال starيبقى بناء عليه أخدنا على هذه المعادلة ثلاثة
+
+55
+00:05:39,670 --> 00:05:43,010
+أمثلة أو على ال first order linear differential
+
+56
+00:05:43,010 --> 00:05:47,610
+equation ثلاثة أمثلة مثلين المرة الماضية وهذا هو
+
+57
+00:05:47,610 --> 00:05:52,750
+المثال الثالث مش دائما المعادلة بمجرد ما أطلع لها
+
+58
+00:05:52,750 --> 00:05:58,390
+تكون linear أحيان بدي أضطر أحولها إلى linear first
+
+59
+00:05:58,390 --> 00:06:03,770
+order differential equationيعني المعادلة بمجرد
+
+60
+00:06:03,770 --> 00:06:08,410
+النظر لا تكون Linear لكن بقدر أحولها إلى Linear زي
+
+61
+00:06:08,410 --> 00:06:10,970
+ما في ال Homogeneous حولناها إلى Homogeneous وال
+
+62
+00:06:10,970 --> 00:06:14,630
+Exact كانت ماهياش Exact حولناها إلى Exact وال
+
+63
+00:06:14,630 --> 00:06:18,290
+Superb كان ماهياش Superb وحولناها إلى Superb لا
+
+64
+00:06:18,290 --> 00:06:22,850
+Superb يعني ماحدش أحسن من حد طيب بدنا نيجي نشوف
+
+65
+00:06:22,990 --> 00:06:29,010
+النوع من المعادلات ليست Linear لكن يمكن تحويلها
+
+66
+00:06:29,010 --> 00:06:33,830
+إلى Linear وهذا ما يسمى معادلة Bernoulli يبقى
+
+67
+00:06:33,830 --> 00:06:38,270
+Bernoulli equation بدنا نعطيها Definition وبعدها
+
+68
+00:06:38,270 --> 00:06:44,750
+نحل معادلة Bernoulli يبقى باجي بقول Definition
+
+69
+00:06:44,750 --> 00:06:48,230
+differential equation
+
+70
+00:06:50,280 --> 00:06:56,980
+differential equation المعادلة التفاضلية y prime
+
+71
+00:06:56,980 --> 00:07:05,820
+زايد p of x في ال y بدو يساوي ل q of x في ميم في
+
+72
+00:07:05,820 --> 00:07:15,340
+ال y to the power n و ال n لا تساوي zero and و
+
+73
+00:07:15,340 --> 00:07:25,200
+كذلكالـ N لا تساوي واحد is called بنروح نسميها
+
+74
+00:07:25,200 --> 00:07:31,380
+Bernoulli equation Bernoulli
+
+75
+00:07:31,380 --> 00:07:35,540
+Bernoulli
+
+76
+00:07:35,540 --> 00:07:39,500
+equation يبقى معادلة Bernoulli
+
+77
+00:07:49,170 --> 00:07:55,790
+طيب الآن ظهرت عندنا معادلة جديدة هذه المعادلة ليست
+
+78
+00:07:55,790 --> 00:08:00,470
+linear first order differential equation السبب في
+
+79
+00:08:00,470 --> 00:08:04,870
+ذلك أنها ماهياش linear لو طلعت للطرف الشمال اللى
+
+80
+00:08:04,870 --> 00:08:09,310
+عندنا يبقى هو ال linear first order differential
+
+81
+00:08:09,310 --> 00:08:13,160
+equation اللى احنا عارفينهالـ Q of X هي يبقى
+
+82
+00:08:13,160 --> 00:08:19,560
+الجديد من Y to the power N يبقى بسبب وجود الـ Y to
+
+83
+00:08:19,560 --> 00:08:24,060
+the power N بطلت تصير هذه first order differential
+
+84
+00:08:24,060 --> 00:08:28,960
+equation طيب حطلي شرط هنا قال الـ N ممنوع تساوي
+
+85
+00:08:28,960 --> 00:08:34,640
+Zero وكذلك الـ N ممنوع تساوي واحد السؤال هو ليش
+
+86
+00:08:34,640 --> 00:08:37,260
+الـ N ممنوع تساوي Zero يعني لو تساوي Zero إيش
+
+87
+00:08:37,260 --> 00:08:42,440
+بيصير؟بصير هادي واحد وبتالي بصير linear طبيعي يعني
+
+88
+00:08:42,440 --> 00:08:48,460
+وبتالي احنا ماسووناش اشي طيب؟لو كانت الـ N بواحد
+
+89
+00:08:48,460 --> 00:08:53,020
+يبدو يصير هنا Y إذا بجيبها على الشجة التانية و
+
+90
+00:08:53,020 --> 00:08:57,680
+باخد Y عامل مشترك و بصير P of X زايد لQ of X و
+
+91
+00:08:57,680 --> 00:09:02,360
+بتساوي Zero وبالتالي صارت Linear كذلك إذا مشان
+
+92
+00:09:02,360 --> 00:09:06,740
+أضمن إنها ماهياش Linear لازم الـ N ممنوع تساوي
+
+93
+00:09:06,740 --> 00:09:13,000
+Zero و الـ N ممنوع تساوي واحد تمام السؤال هو كيف
+
+94
+00:09:13,000 --> 00:09:19,740
+يمكن حل هذه المعادلةبنقولك بنقدر نحلها كالتالي بدي
+
+95
+00:09:19,740 --> 00:09:24,740
+أحولها إلى linear كيف بدي أحولها إلى linear هذا ما
+
+96
+00:09:24,740 --> 00:09:32,400
+سنشير إليه يبقى باجي بقوله هنا to solve Bernoulli
+
+97
+00:09:32,400 --> 00:09:38,280
+equation Bernoulli
+
+98
+00:09:38,280 --> 00:09:41,320
+equation multiply
+
+99
+00:09:46,660 --> 00:09:54,180
+both sides كلا الطرفين هذا ما نسميه ال equation
+
+100
+00:09:54,180 --> 00:10:06,620
+star نضربها
+
+101
+00:10:06,620 --> 00:10:14,660
+بواي أس ناقص into gainبنحصل على بدأ اضغط في Y تدا
+
+102
+00:10:14,660 --> 00:10:22,380
+power سالب N يبقى بيصير سالب N في ال Y prime زائد
+
+103
+00:10:22,380 --> 00:10:33,080
+P of X في Y أس واحد سالب N تمام بدأ أساوي من AQ of
+
+104
+00:10:33,080 --> 00:10:33,480
+X
+
+105
+00:10:36,350 --> 00:10:41,670
+بعملية الضرب البسيطة اللي عملته هذه يبقى طارة y to
+
+106
+00:10:41,670 --> 00:10:47,310
+the power n من الطرف اليمين في المعادلة و أصبحت
+
+107
+00:10:47,310 --> 00:10:51,470
+المعادلة على الشكل الجديد اللي عندنا هل هذه linear
+
+108
+00:10:51,470 --> 00:10:59,470
+لأ يبقى مش أنا أحولها إلى linear بجي بقوله pot حط
+
+109
+00:10:59,470 --> 00:11:07,690
+ليالـ U يسوي Y أس واحد ناقص N اشتقوا يا بنات بيصير
+
+110
+00:11:07,690 --> 00:11:17,390
+U' واحد ناقص N في ال Y أس ناقص N في ال Y' مظبوط
+
+111
+00:11:17,390 --> 00:11:23,310
+هيك؟ طيب كويس لو جسمت الطرفين على المقدار اللي
+
+112
+00:11:23,310 --> 00:11:27,970
+عندنا هذا بيصير واحد على واحد ناقص N
+
+113
+00:11:41,030 --> 00:11:46,350
+الترم اللي عندنا هذا في المعادلةأذا بقدر أحول
+
+114
+00:11:46,350 --> 00:11:51,170
+المعادلة تبعتي إلى الشكل التالي يبقى المعادلة
+
+115
+00:11:51,170 --> 00:11:57,970
+ستصبح على الشكل التالي يبقى باجي بقول المعادلة
+
+116
+00:11:57,970 --> 00:12:05,130
+بدها تصير واحد على واحد ناقص N في ال U prime زائد
+
+117
+00:12:05,130 --> 00:12:15,040
+P of X في ال U بدها تساوي Q of Xهذا متغير ولا رقم؟
+
+118
+00:12:15,040 --> 00:12:22,880
+رقم لأن هو الـS7 الـY1-N إذا بدي أضغط في هذا الرقم
+
+119
+00:12:22,880 --> 00:12:29,980
+يبقى بيصير المعادلة U prime زائد واحد ناقص N في P
+
+120
+00:12:29,980 --> 00:12:38,400
+of X في U يساوي واحد ناقص N في Q of X إذا هذا بنيت
+
+121
+00:12:38,400 --> 00:12:44,160
+رقم وهذا رقملا يغير من شكل المعادلة السؤال هو
+
+122
+00:12:44,160 --> 00:12:50,820
+المعادلة دي شو أصبح شكلها linear مظبوط هي y prime
+
+123
+00:12:50,820 --> 00:12:57,100
+function في x في ال y ال y أجابتها ل u يسوى ل q of
+
+124
+00:12:57,100 --> 00:13:06,720
+x فقط لغير يبقى هذه linear first order
+
+125
+00:13:06,720 --> 00:13:08,860
+differential
+
+126
+00:13:09,820 --> 00:13:23,700
+equation that can be solved as before يبقى هذه
+
+127
+00:13:23,700 --> 00:13:28,820
+بروح بحلها زي ما كنت بحل ال linear اللي هو قبل
+
+128
+00:13:28,820 --> 00:13:35,360
+قليل واضحة اظن هذه طيب نبدأ نعطي امثلة على ال
+
+129
+00:13:35,360 --> 00:13:38,920
+Bernoulli equation يبقى example one
+
+130
+00:13:51,100 --> 00:13:59,880
+Solve the differential equation المعادلة التفاضلية
+
+131
+00:13:59,880 --> 00:14:05,140
+Y'-2Sin
+
+132
+00:14:05,140 --> 00:14:20,280
+X كل هذا في Y سيكون ناقص 2Sin XY أس ثلاثة على
+
+133
+00:14:20,280 --> 00:14:21,460
+اتنين
+
+134
+00:14:52,430 --> 00:14:56,350
+نعود إلى أسئلة قبل أن نعود إلى أسئلة سأعود إلى
+
+135
+00:14:56,350 --> 00:15:00,470
+التعريف جالي بيرنولي كوشن هي معادلة بالشكل هذا
+
+136
+00:15:00,470 --> 00:15:05,290
+استبعت أن الان تساوي زيرو واستبعت أن الان تساوي
+
+137
+00:15:05,290 --> 00:15:10,770
+واحد لكن هل جولت الان لازم يكون عدد صحيح موجه لم
+
+138
+00:15:10,770 --> 00:15:16,410
+أقول ذلكقد يكون الان عدد موجب وقد يكون عدد سالب
+
+139
+00:15:16,410 --> 00:15:21,050
+وقد يكون كثري موجب وقد يكون كثري سالب كل
+
+140
+00:15:21,050 --> 00:15:25,450
+الاحتمالات واردة يعني ليس بالضرورة ان يكون عددا
+
+141
+00:15:25,450 --> 00:15:30,650
+صحيحا وهذا مثال بين ادينا على ان الأس تبع الواي
+
+142
+00:15:30,650 --> 00:15:36,790
+هناك ليس عددا صحيحاطب الطرف الشمال جاهز على شكل ال
+
+143
+00:15:36,790 --> 00:15:41,930
+linear الطرف اليمين لأ لإن Y أس 3 على 2 هذي إيه
+
+144
+00:15:41,930 --> 00:15:45,530
+اللي جديدة في المثلة اللي خلتني المثلة ماهياش
+
+145
+00:15:45,530 --> 00:15:51,230
+linear لذلك بتروح أحولها إلى linear ثم أحلها
+
+146
+00:15:51,230 --> 00:15:55,290
+بطريقة main ال linear first order differential
+
+147
+00:15:55,290 --> 00:16:00,620
+equation يبقى شو نعمل يا بنات؟بنذهب نضرب في Y
+
+148
+00:16:00,620 --> 00:16:07,380
+مرفوعة لهذا الأسبوع بإشارة سالب يبقى ساميه لمعادلة
+
+149
+00:16:07,380 --> 00:16:12,360
+هذه الـ main التي هي star يبقى باجي بقول هنا
+
+150
+00:16:12,360 --> 00:16:17,600
+multiply equation
+
+151
+00:16:17,600 --> 00:16:28,030
+star byواي أس سالب تلاتة على اتنين together نحصل
+
+152
+00:16:28,030 --> 00:16:36,410
+على واي أس سالب تلاتة على اتنين في الـ y' ناقص
+
+153
+00:16:36,410 --> 00:16:45,450
+اتنين sin x واي أس عندك واي أس واحد وواي أس سالب
+
+154
+00:16:45,450 --> 00:17:01,910
+واحد ونص بيظل واي أس سالب نصبدي أعمل
+
+155
+00:17:01,910 --> 00:17:07,270
+تعويضة في المثلة هذه التعويضة بتحولها إلى linear
+
+156
+00:17:07,270 --> 00:17:11,770
+first order differential equation شو هذه التعويضة
+
+157
+00:17:11,770 --> 00:17:18,820
+بروح بقول له potعن طريق الوصول لـ U يساوي Y أسالب
+
+158
+00:17:18,820 --> 00:17:29,920
+نص Y أسالب نص يبقى نشتاق
+
+159
+00:17:29,920 --> 00:17:38,840
+يبقى الـ U' يساوي سالب نص Y أسالب تلاتة على اتنين
+
+160
+00:17:38,840 --> 00:17:44,960
+في من؟ في الـ Y' هنا ماعنديش انصاريبقى بروح بضرب
+
+161
+00:17:44,960 --> 00:17:50,840
+كله في مين؟ في سالب اتنين لو ضربت في سالب اتنين
+
+162
+00:17:50,840 --> 00:17:57,580
+بصير سالب اتنين U prime يساوي Y السالب تلاتة على
+
+163
+00:17:57,580 --> 00:18:02,500
+اتنين في ال Y prime الان الطرف اليمين في التعويضة
+
+164
+00:18:02,500 --> 00:18:08,250
+هو هذا ال term مظبوط؟أذا بقدر أشيل وقته بدل سالي
+
+165
+00:18:08,250 --> 00:18:15,550
+باتنين U' يبقى هذا بالصيرة سالي باتنين U' سالي
+
+166
+00:18:15,550 --> 00:18:23,660
+باتنين في صين ال X هذه مين يا بنات؟الـ U يبقى
+
+167
+00:18:23,660 --> 00:18:30,480
+بشيلها و بحط بدالها U يساوي سالب اتنين في Sine X
+
+168
+00:18:30,480 --> 00:18:36,000
+شو رأيك اجسم المعادلة كلها على سالب اتنين اذا لو
+
+169
+00:18:36,000 --> 00:18:42,880
+جسمنا على سالب اتنين تصبح المعادلة U Prime ناقظ
+
+170
+00:18:42,880 --> 00:18:52,880
+زائد Sine X في الـ U بده يساوي له Sine Xوهذه عبارة
+
+171
+00:18:52,880 --> 00:19:02,060
+عن first order linear differential
+
+172
+00:19:02,060 --> 00:19:03,920
+equation
+
+173
+00:19:06,230 --> 00:19:11,110
+يبقى بالعملية اللي عملت هذه استطاعت تحويل المعادلة
+
+174
+00:19:11,110 --> 00:19:14,990
+هذه اللي هي non-linear differential equation إلى
+
+175
+00:19:14,990 --> 00:19:20,170
+first order linear differential equation إذا بدنا
+
+176
+00:19:20,170 --> 00:19:26,470
+نحلها زي ما كنا بنحل من قبل يبقى بدروح أجيب عامل
+
+177
+00:19:26,470 --> 00:19:33,430
+التكمل لهذه المعادلةيبقى الـ Mu of X بيساوي E أس
+
+178
+00:19:33,430 --> 00:19:43,230
+تكامل قداش Sine X في DX قداش تكامل الـ Sine أبعد؟
+
+179
+00:19:43,230 --> 00:19:52,230
+سالب Cos يبقى E أس سالب Cos X
+
+180
+00:19:56,980 --> 00:20:02,540
+يبقى هذا عامل التكامل بناء عليه بقدر أجيب الحل
+
+181
+00:20:02,540 --> 00:20:08,200
+اللي هو you يبقى هنا هذا بنات مشان ميزها عن اللي
+
+182
+00:20:08,200 --> 00:20:15,480
+فوق سميها للمعادلة double star فبجي بقوله هنا that
+
+183
+00:20:15,480 --> 00:20:27,590
+solution of thatdifferential equation double star
+
+184
+00:20:27,590 --> 00:20:37,760
+is الـ U تزاويةبشيل ال U و بحط قمة او بقول له ال E
+
+185
+00:20:37,760 --> 00:20:48,080
+الحال تبعها E أث ناقص Cos X في ال U يساوي تكامل E
+
+186
+00:20:48,080 --> 00:20:55,580
+أث ناقص Cos X في ال Q of X اللي هي Sin X كله
+
+187
+00:20:55,580 --> 00:21:02,770
+بالنسبة إلى DXيبقى بصيرة أن E أسالب Cos X في الـ U
+
+188
+00:21:02,770 --> 00:21:10,550
+يساوي بدنا نكمل هذه الدالة يبقى المصعب المثال مين؟
+
+189
+00:21:10,550 --> 00:21:18,490
+الـ E أسالب أو الـ Sine؟ الـ Sine؟
+
+190
+00:21:18,490 --> 00:21:25,680
+الأس تبع الـ X و لا الدالة اللي برا؟مين اللي وضحه
+
+191
+00:21:25,680 --> 00:21:30,400
+مش طبيعي الاص الاص احنا بقول ايه و ال six دايما
+
+192
+00:21:30,400 --> 00:21:34,900
+مقولش ايه اص ناقص قصارى ناقص اذا بدي اشيل كل الاص
+
+193
+00:21:34,900 --> 00:21:38,640
+هذا و احط بدله و اتغير جديد و اشوف الدنيا و ان
+
+194
+00:21:38,640 --> 00:21:45,980
+بدها توجهإذاً هذه لو جيت قلت حطي لي مثلا T تساوي
+
+195
+00:21:45,980 --> 00:21:53,440
+ناقص cosine X يبقى ال DT تفاضل cosine بسالب sin X
+
+196
+00:21:53,440 --> 00:22:00,000
+DX إذاً بقدر أشيل هذا كل وقت و بدلا منه DT يبقى
+
+197
+00:22:00,000 --> 00:22:10,750
+تكامل ل E أس T DTيبقى بيصير E Os ناقص Cos X في الـ
+
+198
+00:22:10,750 --> 00:22:19,270
+U بE Os T زائد Constant C يعني هذا معناه ان ال E
+
+199
+00:22:19,270 --> 00:22:26,530
+Os ناقص Cos X في الـ U بده يساوي E Os بده يشيل ال
+
+200
+00:22:26,530 --> 00:22:34,120
+T ويرجعها إلى أصلة ناقص Cos X زائد Constant Cأنا
+
+201
+00:22:34,120 --> 00:22:37,320
+أريد أن أشهد أن يجب أن يكون الـ U لوحدها يبقى
+
+202
+00:22:37,320 --> 00:22:44,700
+بادرب الطرفين في E أس موجة بكوصين X يبقى بناء على
+
+203
+00:22:44,700 --> 00:22:53,470
+الـ U ده سوى 1 زائد C في E أس كوصين Xبرجع مرة
+
+204
+00:22:53,470 --> 00:23:01,350
+تانية انا ال U حاططها كدهش؟ Y أس ناقص نص يبقى بصير
+
+205
+00:23:01,350 --> 00:23:10,110
+عندنا هنا ميم Y أس ناقص نص يسوى واحد زائد C في E
+
+206
+00:23:10,110 --> 00:23:15,310
+أس Cos X هنشكلب
+
+207
+00:23:15,310 --> 00:23:24,840
+هذهيعني 1 على y أُص نُص بيكون 1 زائد c في e أُص
+
+208
+00:23:24,840 --> 00:23:32,100
+cos x مش هاجلب؟ يبقى لو هاجلبنا المثل بصير y أُص
+
+209
+00:23:32,100 --> 00:23:43,120
+نُص يسوى 1 على 1 زائد c في e أُص cos x خلص الحل؟
+
+210
+00:23:44,810 --> 00:23:50,750
+بقدر أجيب Y شو نعمل؟ ربع الطرفين يبقى لو ربعنا
+
+211
+00:23:50,750 --> 00:23:55,890
+الطرفين بنحصل على الحل اللي هو Y مربع الواحد بواحد
+
+212
+00:23:55,890 --> 00:24:05,210
+واحد زائد C في E أس Cos X لكل تربيع يبقى هذا هو حل
+
+213
+00:24:05,210 --> 00:24:10,730
+ال differential equation الأصلية حدا فيكم بتحب
+
+214
+00:24:10,730 --> 00:24:16,770
+تسأل أي نقطة هنا؟أي خطوة أو نقطة مافهمتهاش تحب
+
+215
+00:24:16,770 --> 00:24:22,310
+تسأل أي سؤال في الموضوع عندما نجيب المنواصة اه في
+
+216
+00:24:22,310 --> 00:24:34,010
+عرفت تسأل؟ differential equation y' ناقص واحد على
+
+217
+00:24:34,010 --> 00:24:43,980
+x زائد واحد في ال Y في لن ال Yبتساوي X زي الواحد
+
+218
+00:24:43,980 --> 00:24:57,460
+في Y والـ X greater than Zero باجي
+
+219
+00:24:57,460 --> 00:25:04,300
+بتطلع في مثلتي هذه ليست Linear لسببينالسبب الأول
+
+220
+00:25:04,300 --> 00:25:09,000
+عندي Y في الناحية التانية والسبب الثاني في عندي
+
+221
+00:25:09,000 --> 00:25:15,160
+هنا ال Y إذا شغلتي أحاول أحول المعادلة هذه إلى
+
+222
+00:25:15,160 --> 00:25:20,480
+linear مشان أقدر أحلها و أحصل على حل هذه المثلة
+
+223
+00:25:20,480 --> 00:25:26,040
+بيقولوا تمام هذه المعادلة بدي أسميها استعار يبقى
+
+224
+00:25:26,040 --> 00:25:34,970
+هذه بدي أسميها اللي عندنا استعار طيبمشان هيك بدي
+
+225
+00:25:34,970 --> 00:25:40,770
+اقول له هذه جاهزة صح و الله ايش رأيكوا اضرب كله في
+
+226
+00:25:40,770 --> 00:25:46,890
+y أسالي بواحد عشان اتخلص من y اللي على اليمين بدي
+
+227
+00:25:46,890 --> 00:25:52,870
+بقوله هنا multiply او solution بالأول solution
+
+228
+00:25:52,870 --> 00:25:57,350
+multiply
+
+229
+00:25:57,350 --> 00:26:01,250
+both
+
+230
+00:26:01,250 --> 00:26:02,030
+sides
+
+231
+00:26:04,680 --> 00:26:16,720
+of equation star by y السلب واحد we get بصير عند
+
+232
+00:26:16,720 --> 00:26:26,860
+هنا y السلب واحد y prime ناقص واحد على x زائد واحد
+
+233
+00:26:26,860 --> 00:26:32,520
+في لن ال y يساوي x زائد واحد
+
+234
+00:26:35,780 --> 00:26:42,220
+يبقى كتبنا المعادلة بشكل جديد لكن هذه شكلها مش زي
+
+235
+00:26:42,220 --> 00:26:47,040
+مين مش زي السؤال اللي قبله ليش انه عندي هنا لين
+
+236
+00:26:47,040 --> 00:26:53,020
+واي ماعنديش واي to the power ان واي لين مش لين بدك
+
+237
+00:26:53,020 --> 00:26:59,660
+تحول هالي إلى مين إلىلينا يعني الشكل اللي قلناه
+
+238
+00:26:59,660 --> 00:27:05,820
+لبرنولي قبل قليل ليس قرآنا نزل من السماوة لكن هو
+
+239
+00:27:05,820 --> 00:27:09,720
+ال general form يعني ممكن ألاقي حالة و الله تنتهي
+
+240
+00:27:09,720 --> 00:27:15,060
+الشكل لكن تبقى كذلك بيرنولي إذا أنا مشكلتي مع مين
+
+241
+00:27:15,060 --> 00:27:20,720
+هنا؟ مع لين الواي يفضل أروح أقوله هنا بالهامش أقعد
+
+242
+00:27:25,640 --> 00:27:32,100
+يبقى الـ U' بواحد على Y في الـ Y' يعني Y أسالب
+
+243
+00:27:32,100 --> 00:27:37,400
+واحد في الـ Y' هي هذه يعني يا بنات لما نشتاق لازم
+
+244
+00:27:37,400 --> 00:27:42,300
+تطلع المقدار هذا أو مقدار مضروب فيه رقام فيه عدد
+
+245
+00:27:42,300 --> 00:27:51,000
+تمامأذا هذه باكتب بدالها U' ناقص واحد على X زائد
+
+246
+00:27:51,000 --> 00:27:57,740
+واحد في الـ U بده ساول X زائد واحد ايش رايك وصلت
+
+247
+00:27:57,740 --> 00:28:02,540
+Linear؟ يبقى اللي كانت non-linear ليه سببه اللي
+
+248
+00:28:02,540 --> 00:28:10,500
+قدرنا نحولها إلى Linear؟ يبقى هذه هنا Linear first
+
+249
+00:28:10,500 --> 00:28:12,480
+order
+
+250
+00:28:16,380 --> 00:28:22,800
+مشان هيك بده أروح عجيب عامل التكامل لميو as a
+
+251
+00:28:22,800 --> 00:28:29,140
+function of X يبقى E أص ناقص تكامل واحد على X زائد
+
+252
+00:28:29,140 --> 00:28:39,020
+واحد DX أو إن شئتم فقولوا E أص ناقص ل X زائد واحد
+
+253
+00:28:39,530 --> 00:28:47,910
+يعني هذه E أس ل X ناقص واحد أس ناقص واحد يعني X
+
+254
+00:28:47,910 --> 00:28:53,770
+ناقص واحد أس ناقص واحد أو واحد على X ناقص واحد
+
+255
+00:28:53,770 --> 00:28:59,950
+يبقى هذا الآن عامل التكامل يبقى بناء عليه حل
+
+256
+00:28:59,950 --> 00:29:05,270
+المعادلة هذه اللي هي double star سموها ليا بناتحل
+
+257
+00:29:05,270 --> 00:29:10,550
+المعادلة double star سيكون على الشكل التالي يبقى
+
+258
+00:29:10,550 --> 00:29:28,050
+هنا solution of
+
+259
+00:29:28,050 --> 00:29:39,990
+the differentialEquation W star S A
+
+260
+00:29:39,990 --> 00:29:48,490
+لـ Mu هو واحد عالى X زائد واحد في الـ U بده يسوي
+
+261
+00:29:48,490 --> 00:29:56,090
+تكامل واحد عالى X زائد واحد في الـ Q قداش الـ Q هو
+
+262
+00:29:56,090 --> 00:30:05,540
+Xزائد واحد كله بالنسبة الى DX طيب هذا بده يسوي
+
+263
+00:30:05,540 --> 00:30:13,640
+تكامل ل DX واللي بده يسوي X زائد كونستان C إذن الـ
+
+264
+00:30:13,640 --> 00:30:23,080
+U يا بناتي يسوي X زائد واحد X زائد كونستان Cبرجع
+
+265
+00:30:23,080 --> 00:30:29,120
+لمن؟ لل U ال U اللي عندي كده؟ لإن ال Y إذا بدي
+
+266
+00:30:29,120 --> 00:30:35,780
+أشيل ال U هذه و أكتب بدلها من؟ لإن ال Y يبقى باجي
+
+267
+00:30:35,780 --> 00:30:43,720
+هنا لإن ال Y بدي يساوي X زائد واحد في X زائد كنص
+
+268
+00:30:43,720 --> 00:30:49,760
+تن C هذا لا يزال حل ضمني أنا ماجبتش ال Y جبت له
+
+269
+00:30:49,760 --> 00:30:56,430
+لغارتما ال Yبقدر أجيب له ال Y يبقى برفع اتنين كأس
+
+270
+00:30:56,430 --> 00:31:03,450
+للعدد E يبقى بناء عليه هذا بدي يعطيني انه solution
+
+271
+00:31:03,450 --> 00:31:13,210
+أو بقدر أقول له هنا دوري the solution of the
+
+272
+00:31:13,850 --> 00:31:23,150
+Differential equation أسطار الأصلية is Y تساوي E
+
+273
+00:31:23,150 --> 00:31:31,490
+أس X زائد واحد في X زائد constant C يعني رفعت
+
+274
+00:31:31,490 --> 00:31:38,870
+الطرفين كأس للعدد D وبالتالي حصلنا على هذا الحللحد
+
+275
+00:31:38,870 --> 00:31:47,310
+هنا stop في عندنا مجموعة من المسائل exercises واحد
+
+276
+00:31:47,310 --> 00:31:57,770
+خمسة المسائل التالية واحد اتنين تلاتة خمسة ستة
+
+277
+00:31:57,770 --> 00:32:12,610
+سبعةعشرة احداش خمستاش ستاش تمانتاش تسعتاش واحد
+
+278
+00:32:12,610 --> 00:32:18,150
+وعشرين اتنين وعشرين تلاتة وعشرين
+
+279
+00:32:37,860 --> 00:32:44,940
+طيب، حد بتحب تسأل أي سؤال هنا يا بنات؟ خلاص؟ ايوة
+
+280
+00:32:44,940 --> 00:32:52,420
+لو ايش؟
+
+281
+00:32:52,420 --> 00:32:58,620
+ممنوع السوى Zero، ممنوع السوى واحدهذا لمن تبقى جيش
+
+282
+00:32:58,620 --> 00:33:06,180
+لمن تبقى هادى هنا واحد لحالهاصح فإن ما صرتش يصر Y
+
+283
+00:33:06,180 --> 00:33:11,560
+في الـny إذا اختلف الشكل العام اللي عندنا مظبوط
+
+284
+00:33:11,560 --> 00:33:16,080
+يبقى من هنا صرتك لو سوى واحد والله غيره ماعنديش
+
+285
+00:33:16,080 --> 00:33:20,320
+مشكلة في هذه العالم كويس ان افكرت وقالت انت قلت
+
+286
+00:33:20,320 --> 00:33:25,340
+كلامه هذا خلفه السؤال هذا خلف المسألة كلها ليش؟
+
+287
+00:33:25,340 --> 00:33:29,060
+انه صرت المخالف على اليمين وصرت المخالف على الشمال
+
+288
+00:33:29,060 --> 00:33:34,740
+لكن باقية المعادلة هي معادلة Bernoulliطيب حدا فيكم
+
+289
+00:33:34,740 --> 00:33:38,700
+بتسأل اي سؤال بالنسبة لهذا ال section اللي هو
+
+290
+00:33:38,700 --> 00:33:43,560
+linear first order differential equation طيب حدا
+
+291
+00:33:43,560 --> 00:33:48,740
+فيكم بتسأل اي سؤال بالنسبة للخمسة sections اللي
+
+292
+00:33:48,740 --> 00:33:58,260
+درسناهم اول خمسة sections من هذا الشبطر اقرأ
+
+293
+00:33:58,260 --> 00:34:05,770
+الامتحان وصل اقل من شهر باقي للامتحانzero point اه
+
+294
+00:34:05,770 --> 00:34:12,990
+اه هاليومين هينزلولكم موعد لامتحان اه اه هينزل في
+
+295
+00:34:12,990 --> 00:34:18,050
+الجدول رسميا لان هاي شبه عند الطلاب و شبه عند
+
+296
+00:34:18,050 --> 00:34:22,170
+الطلبات اذا العدد كبير لازم ينزلولكوا يهدف الجدول
+
+297
+00:34:22,170 --> 00:34:26,870
+فانت ماتنميش على روحك مش discussion يبغى انك تروح
+
+298
+00:34:26,870 --> 00:34:31,050
+تحلي و تجي تسألي حتى الان ولا واحدة اجت فيكوا
+
+299
+00:34:31,050 --> 00:34:38,010
+تسألي سؤالهذا إما انكم كلكوا علماء و فاهمين تماما
+
+300
+00:34:38,010 --> 00:34:47,150
+لكني لا أظن ذلك أو انكم كلكوا سالة و تبقى بالك هذا
+
+301
+00:34:47,150 --> 00:34:50,910
+بينعكس سلبا عليك بعد هيك و انا قلتك من اول يوم
+
+302
+00:34:50,910 --> 00:34:56,190
+دخلت المحاضرة بتروح تجري المحاضرة تاخديها مباشرة و
+
+303
+00:34:56,190 --> 00:35:00,050
+تحلي الأسئلة اللي عليها و اللي بيصبح ان موجودين و
+
+304
+00:35:00,050 --> 00:35:07,670
+اعطيتك ساعات مكتبيةيبقى بعد ذنبك على جنبك لذنب
+
+305
+00:35:07,670 --> 00:35:13,970
+لخيرلازلنا في نفس ال chapter لكن في مسائل اللي
+
+306
+00:35:13,970 --> 00:35:19,950
+عندي second order differential equation بدي أنزلها
+
+307
+00:35:19,950 --> 00:35:24,290
+إلى first order differential equation ويمكن تطلع
+
+308
+00:35:24,290 --> 00:35:29,610
+separable ويمكن تطلع homogeneous ويمكن تطلع exact
+
+309
+00:35:29,610 --> 00:35:34,270
+ويمكن تطلع linear ويمكن تطلع Bernoulli ونحولها إلى
+
+310
+00:35:34,270 --> 00:35:39,750
+linear يبقى كل الاحتمالات واردةهذا الكلام اللي هو
+
+311
+00:35:39,750 --> 00:35:45,110
+سيكشن واحد احداش يبقى من واحد خمسة بدنا نقفز لمين
+
+312
+00:35:45,110 --> 00:35:50,410
+الى واحد احداش يبقى نتوجه الان الى سيكشن واحد
+
+313
+00:35:50,410 --> 00:36:00,110
+احداش مباشرة اذا سيكشن واحد احداش بيقول two
+
+314
+00:36:00,110 --> 00:36:06,390
+special two special types
+
+315
+00:36:09,820 --> 00:36:15,680
+of second order
+
+316
+00:36:15,680 --> 00:36:19,000
+differential
+
+317
+00:36:19,000 --> 00:36:22,560
+equations
+
+318
+00:36:22,560 --> 00:36:25,620
+شكلنا
+
+319
+00:36:25,620 --> 00:36:31,980
+نعطيها definition a
+
+320
+00:36:31,980 --> 00:36:35,920
+second order
+
+321
+00:36:39,130 --> 00:36:51,250
+Differential equation is an equation inفورا في
+
+322
+00:36:51,250 --> 00:37:05,570
+الشكل التالي F of F T و X و DX على DT و D² X على
+
+323
+00:37:05,570 --> 00:37:16,620
+DT² بده ساوي من؟ بده ساوي Zero نرجع مرة تانيةأنا
+
+324
+00:37:16,620 --> 00:37:20,560
+عندي معادلة من الرتبة الثانية وبتنزل رتبتها إلى
+
+325
+00:37:20,560 --> 00:37:26,360
+الرتبة الأولى ومن ثم أروح أحل هذه المعادلة فجال لي
+
+326
+00:37:26,360 --> 00:37:31,260
+two special types نوعين من الأنواع الخاصة ل second
+
+327
+00:37:31,260 --> 00:37:34,420
+order differential equation يعني second order
+
+328
+00:37:34,420 --> 00:37:41,140
+كثيرة جدا أنا بدي أخد بس نوعين والباقي بنخليه فيما
+
+329
+00:37:41,140 --> 00:37:44,950
+بعدبقول الـ second order differential equation هي
+
+330
+00:37:44,950 --> 00:37:50,250
+عبارة عن معادلة في الشكل التالي هي function تحتوي
+
+331
+00:37:50,250 --> 00:37:55,450
+على المتغير T والمتغير X ومشتقة X بالنسبة إلى T
+
+332
+00:37:55,450 --> 00:38:01,890
+والمشتقة الثانية X بالنسبة إلى T وكل هذا بده يساوي
+
+333
+00:38:01,890 --> 00:38:06,860
+مين؟ بده يساوي Zeroيعني أنا عندي دالة هذه الدالة
+
+334
+00:38:06,860 --> 00:38:12,100
+تحتوي على المتغير المستقل X ال independent
+
+335
+00:38:12,100 --> 00:38:16,260
+variable والمتغير التابع اللي هو dependent
+
+336
+00:38:16,260 --> 00:38:22,020
+variable X ومشتقة ال X بالنسبة إلى T والمشتقة
+
+337
+00:38:22,020 --> 00:38:26,080
+الثانية بالنسبة إلى X بالنسبة إلى Tكون المشتقة
+
+338
+00:38:26,080 --> 00:38:31,540
+التانية موجودة يبقى من هنا سمنها second order
+
+339
+00:38:31,540 --> 00:38:35,660
+differential equation لسه ما اتكلمناش في ال two
+
+340
+00:38:35,660 --> 00:38:41,480
+types لسه احنا اعطينا صورة عامة ل second order
+
+341
+00:38:41,480 --> 00:38:45,820
+differential equation بده يجي لأول نوع من هذه
+
+342
+00:38:45,820 --> 00:38:52,090
+الأنواع اللي بنسميها equations withx missing يعني
+
+343
+00:38:52,090 --> 00:38:57,490
+معادلة المتغيرة التي تبقى الهو y مش موجود مفقود من
+
+344
+00:38:57,490 --> 00:39:02,790
+المعادلة كيف بدنا نحل هذا النوع من المعادلات you
+
+345
+00:39:02,790 --> 00:39:07,810
+can بالدرجة لأول نوع من هذه المعادلات اللي هو
+
+346
+00:39:07,810 --> 00:39:15,210
+differential equations المعادلات التفاضلية with
+
+347
+00:39:15,210 --> 00:39:19,330
+the dependent
+
+348
+00:39:22,130 --> 00:39:28,090
+with a dependent variable X
+
+349
+00:39:28,090 --> 00:39:36,950
+missing يبقى الـ SLX مفقودةIt is an equation in
+
+350
+00:39:36,950 --> 00:39:45,630
+the form يبقى It is an equation in the form هي
+
+351
+00:39:45,630 --> 00:39:54,790
+عبارة عن معادلة على الشكل التالي G وT وDX على DT
+
+352
+00:39:54,790 --> 00:40:02,910
+وD²X على DT² كله بده يساوي Zero وبده يسمي هذه
+
+353
+00:40:02,910 --> 00:40:05,090
+المعادلة رقم واحد
+
+354
+00:40:07,670 --> 00:40:12,010
+يبقى المعادلة اللي فوق يا بنات هي نفس المعادلة
+
+355
+00:40:12,010 --> 00:40:17,450
+التحت بس ال X هذا ماله لا يظهر في المعادلة بتظهر
+
+356
+00:40:17,450 --> 00:40:23,410
+مين؟ بس مشتقته الأولى والثانية لكن هو بسلامته بظهر
+
+357
+00:40:23,410 --> 00:40:26,750
+ليش يعني مش موجود حد ما يشوف المعادلة بيقول مافيش
+
+358
+00:40:26,750 --> 00:40:32,940
+فيها Xكيف بدي احل هذه المعادلة يبقى باجي بقوله to
+
+359
+00:40:32,940 --> 00:40:41,620
+solve the differential equation one شو بدي اعمل
+
+360
+00:40:41,620 --> 00:40:53,330
+put حطلي V تساوي DX على DT تماميبقى هذا يعطينا ان
+
+361
+00:40:53,330 --> 00:41:05,710
+الـ dv على dt هو d²x على dt² يبقى هنا سة equation
+
+362
+00:41:05,710 --> 00:41:17,510
+one becomes تصبح على الشكل التالي g ofT موجودة و V
+
+363
+00:41:17,510 --> 00:41:25,230
+موجودة و DV على DT يبدو يسوى 0 ايش رأيك في هذه
+
+364
+00:41:25,230 --> 00:41:34,210
+second ولا first first order يبقى هذه first order
+
+365
+00:41:34,210 --> 00:41:47,670
+differential equation that canbe solved as before
+
+366
+00:41:47,670 --> 00:41:53,730
+يبقى بروح انحلها زي ما كنا نحل من قبل اللي هو ال
+
+367
+00:41:53,730 --> 00:41:56,570
+first order ده الحلقة اللي يمكن تطلع exactly يمكن
+
+368
+00:41:56,570 --> 00:42:00,950
+linear يمكن homogeneous يمكن separable كل الأمور
+
+369
+00:42:00,950 --> 00:42:05,490
+اللي مرت علينا بصير واردة عندنا يبقى هذه اللي هي
+
+370
+00:42:05,490 --> 00:42:12,450
+النقطة الأولى بنجي للنقطة الثانية يبقى نمر اتنين
+
+371
+00:42:12,870 --> 00:42:18,710
+بدنا نيجي الى differential equations with the
+
+372
+00:42:18,710 --> 00:42:26,370
+independent variable with the independent
+
+373
+00:42:26,370 --> 00:42:29,830
+variable
+
+374
+00:42:29,830 --> 00:42:37,310
+T
+
+375
+00:42:37,310 --> 00:42:37,830
+missing
+
+376
+00:42:41,050 --> 00:42:48,990
+يبقى الـ T قد تكون مفقودة يبقى في هذه الحالة تصبح
+
+377
+00:42:48,990 --> 00:42:51,350
+المعادلة للشكل التالي
+
+378
+00:43:18,630 --> 00:43:24,950
+يبقى في هذه الحالة المعادلة المتغير المستقل هو
+
+379
+00:43:24,950 --> 00:43:30,550
+الغائبايوة شو نعمل يبقى هذه السمهالة اللي هي
+
+380
+00:43:30,550 --> 00:43:38,950
+المعادلة رقم واحد يبقى بجي بقول two solve equation
+
+381
+00:43:38,950 --> 00:43:49,250
+one pot حطيلي V بده يسوى DX على DT تمام يعني زي
+
+382
+00:43:49,250 --> 00:43:55,030
+اللي قبلبس في خلاف شويه شو الخلاف يبقى هذا بدي
+
+383
+00:43:55,030 --> 00:44:03,390
+اعطيك انه DV على DT ايش بده يساوي؟ بده يساوي ما
+
+384
+00:44:03,390 --> 00:44:09,010
+يأتي يعني بدنا نشتق كمان مرة بديش اجيب هك بدي اقول
+
+385
+00:44:09,010 --> 00:44:18,560
+D² X على DT² معناته بدي اشتق بالنسبة لمن؟الى T
+
+386
+00:44:18,560 --> 00:44:28,980
+يبقى باجي بقول هي DV على DT تمام اللي بقدر اقول هي
+
+387
+00:44:28,980 --> 00:44:39,820
+عبارة عن DV على DX في DX على DT مظبوط طيب ال DX
+
+388
+00:44:39,820 --> 00:44:48,300
+على DT انا اش كاتبهاV يبقى هذه بدها ساوي V في الـD
+
+389
+00:44:48,300 --> 00:44:55,780
+V على DX لأيش؟ لأن T مش موجودة يبقى بدي أحولها
+
+390
+00:44:55,780 --> 00:45:02,580
+بدلالة V و X وكأن X هي المتغير المستقل و V هو
+
+391
+00:45:02,580 --> 00:45:08,180
+المتغير التابع T ملاش وجود في هذه الحالة يبقى باجي
+
+392
+00:45:08,180 --> 00:45:15,760
+بقول الساعةEquation one becomes تصبح على الشكل
+
+393
+00:45:15,760 --> 00:45:22,040
+التالي H X موجودة هذه حطيت بدالها V هذه حطيت
+
+394
+00:45:22,040 --> 00:45:29,240
+بدالها V في ال D V على DXوكأن X هنا هو المتغير
+
+395
+00:45:29,240 --> 00:45:35,540
+المستقل وV هو المتغير التابع وهذه كلها بدها تساوي
+
+396
+00:45:35,540 --> 00:45:44,200
+مين؟ بدها تساوي Zero يبقى هذه This is a first
+
+397
+00:45:44,200 --> 00:45:58,690
+order differential equation thatcan be solved as
+
+398
+00:45:58,690 --> 00:46:06,290
+beforeيعني هذه المعادلة ممكن تطلع exact وممكن تطلع
+
+399
+00:46:06,290 --> 00:46:10,190
+linear وممكن تطلع homogeneous وممكن تطلع separable
+
+400
+00:46:10,190 --> 00:46:15,010
+او ممكن تطلع تولل homogeneous او تولل linear او
+
+401
+00:46:15,010 --> 00:46:19,170
+تولل exact او تولل separable يبقى اي واحدة فيهم
+
+402
+00:46:19,170 --> 00:46:23,010
+بيكون اتعلمنا الحل في الخمسة sections الماضية
+
+403
+00:46:23,010 --> 00:46:27,330
+بنروح انحلها كما كنا بنحل في الخمسة sections
+
+404
+00:46:27,330 --> 00:46:34,180
+الماضيةبقيت الآن مجموعة من الأمثلة على هذا ال
+
+405
+00:46:34,180 --> 00:46:38,880
+section للمرة القادمة إن شاء الله تبارك وتعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/JYkoCgwSRmw_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/JYkoCgwSRmw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7e499b02e1178fbff74757dfef2832d95458c968
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/JYkoCgwSRmw_raw.srt
@@ -0,0 +1,1684 @@
+1
+00:00:19,510 --> 00:00:24,150
+بسم الله الرحمن الرحيم بنتابع الحديث في الموضوع
+
+2
+00:00:24,150 --> 00:00:27,510
+اللي ابتدينا ابوه وهو إيجاد معكوس المصفوفة
+
+3
+00:00:27,510 --> 00:00:31,310
+بطريقتين شرحنا الطريقة الأولى والآن بدنا نروح
+
+4
+00:00:31,310 --> 00:00:35,730
+لطريقة الثانية الطريقة الثانية قولنا تتكون من ثلاث
+
+5
+00:00:35,730 --> 00:00:40,370
+نقاط النقطة الأولى بده اشيل كل عنصر في المصفوفة A
+
+6
+00:00:40,370 --> 00:00:45,530
+I J وحط بدل ال cofactor المناظر له
+
+7
+00:00:49,180 --> 00:00:55,200
+الخطوة الثانية بده يجيب مدور هذه المصفوفة الناتجة
+
+8
+00:00:55,200 --> 00:01:02,080
+الخطوة التالتة بده يجيب محدد المصفوفة الأصلية
+
+9
+00:01:02,080 --> 00:01:07,060
+ويقول معكوس المصفوفة يساوي واحد على محدد المصفوفة
+
+10
+00:01:07,060 --> 00:01:11,940
+في ال Transpose اللي جيبناه في الخطوة الثانيةبيها
+
+11
+00:01:11,940 --> 00:01:17,160
+هذا بيكون جيبنا ميه؟ جيبنا معكوس المصفوفة، واضح
+
+12
+00:01:17,160 --> 00:01:19,920
+كلامي؟ يبقى هاي الخطوات التلاتة اللي كتبتيها في
+
+13
+00:01:19,920 --> 00:01:24,500
+المحاضرة السابقة قبل ساعة وشوية، تمام؟ لما بدنا
+
+14
+00:01:24,500 --> 00:01:27,500
+نطبقها عمليا، المصفوفة اللي قدامنا هادي يا بنات
+
+15
+00:01:27,500 --> 00:01:32,970
+أوجدنا المعكوس سبعها بالطريقة الأولىاللي هي طريقة
+
+16
+00:01:32,970 --> 00:01:37,610
+انه المصوفة الموسعة و احولها الى مصوفة واحدة الطرف
+
+17
+00:01:37,610 --> 00:01:40,450
+اليمين والطرف الشمال والطرف اليمين بيكون هي
+
+18
+00:01:40,450 --> 00:01:45,190
+المعكوزة الان هحل نفس السؤال لكن بمهم بالطريقة
+
+19
+00:01:45,190 --> 00:01:48,830
+الجديدة و نثبت ان إيجابتين الإتنين ما لهم نفس
+
+20
+00:01:48,830 --> 00:01:54,500
+الشيءإذا أنا بداجي للحل بداجي للمصفوفة اللي عندى
+
+21
+00:01:54,500 --> 00:02:01,380
+يبقى في هذه المصفوفة بدى أروح أشيل كل عنصر من
+
+22
+00:02:01,380 --> 00:02:06,340
+عناصر المصفوفة و أكتب بداله مين و أكتب بداله ال
+
+23
+00:02:06,340 --> 00:02:11,060
+cofactor تبعه أو العامل المرافق لهم يبقى لو جيت
+
+24
+00:02:11,060 --> 00:02:16,300
+للمصفوفة الأولى بداجي أقول هذه المصفوفة الأولى بدى
+
+25
+00:02:16,300 --> 00:02:20,770
+أشيل الواحد يا منامحسب قاعدة الإشارات شرطه بالموجة
+
+26
+00:02:20,770 --> 00:02:25,370
+يبقى اشطب صفه و عموده يبقى تمانية ناقص اتنين يبقى
+
+27
+00:02:25,370 --> 00:02:31,770
+كم؟ تمانية يبقى عنصر تلاتة حسب قاعدة الإشارات
+
+28
+00:02:31,770 --> 00:02:37,530
+الشرط هي سالبة يبقى هذه السالبة يبقى اشطب صفه و
+
+29
+00:02:37,530 --> 00:02:44,130
+عموده صفه و عموده يبقى Zero زائد اتنين يبقى ناقص
+
+30
+00:02:44,130 --> 00:02:49,710
+اتنينبالدالي للعنصر التالت سالب واحد قشط بصفه و
+
+31
+00:02:49,710 --> 00:02:56,450
+عموده بيظل zero زائد واحد يبقى بواحد حسب قاعدة
+
+32
+00:02:56,450 --> 00:02:57,570
+الإشارات
+
+33
+00:03:00,950 --> 00:03:05,930
+بتجي للصف الثاني الصف الثاني بتجي لزيرو حسب قاعدة
+
+34
+00:03:05,930 --> 00:03:10,910
+الإشارات شرط مالها سالبة يبقى بدنا نشطب صفه و
+
+35
+00:03:10,910 --> 00:03:16,450
+عموده تلاتة في تمانية باربع و عشرين ناقص زيرو يبقى
+
+36
+00:03:16,450 --> 00:03:22,090
+باربع و عشرينالعنصر اللي بعده حسب قاعة الإشارات
+
+37
+00:03:22,090 --> 00:03:27,870
+شرطه موجبه يبقى بالنشط بصفه عمودي يبقى تمانية ناقص
+
+38
+00:03:27,870 --> 00:03:32,710
+واحد اللي هو بيطلع بقداش بسبعة حسب قاعة الإشارات
+
+39
+00:03:32,710 --> 00:03:36,990
+اللي بعده اللي شرطه السالب يبقى بالروح نشط بصفه
+
+40
+00:03:36,990 --> 00:03:43,750
+وعموده يبقى zero زائد تلاتة يبقى بصير ناقص تلاتة
+
+41
+00:03:44,270 --> 00:03:48,630
+بالدالي للصف التالت حسب قاعد الإشارات شرطه بالموجة
+
+42
+00:03:48,630 --> 00:03:54,950
+يبقى بالداشطه بصفه عموده ستة زائد واحد واللي هي
+
+43
+00:03:54,950 --> 00:03:59,890
+جداش سبعة بالدالي للعنصر بعده حسب قاعد الإشارات
+
+44
+00:03:59,890 --> 00:04:06,490
+شرطه السالبنشطه بصفه وعموده يبقى اتنين واللي بعده
+
+45
+00:04:06,490 --> 00:04:10,890
+zero يبقى ماعنديش الا اتنين نيجي العنصر التالت حسب
+
+46
+00:04:10,890 --> 00:04:14,950
+قرص الشرط شرطه موجهه من نشطه بصفه وعموده يبقى واحد
+
+47
+00:04:14,950 --> 00:04:19,110
+ناقص تلاتة اللي يبقى داشت بواحد بالشكل اللي عندنا
+
+48
+00:04:19,110 --> 00:04:26,170
+هذا يبقى هذه الخطوة الأولى الخطوة الثانية بدي أجيب
+
+49
+00:04:26,170 --> 00:04:28,030
+له المصوف بيه
+
+50
+00:04:40,960 --> 00:04:45,680
+بببببببببببببببيبقى بدي أجيب لـ Transpose بالنسبة
+
+51
+00:04:45,680 --> 00:04:50,300
+إليها يبقى هذا الكلام بدي يساوي المصوفة على الشكل
+
+52
+00:04:50,300 --> 00:04:55,340
+التالي الصف الأول بدي يصير العمود الأول الصف
+
+53
+00:04:55,340 --> 00:05:02,040
+الثاني بدي يصير العمود الثاني الصف التالت بدي يصير
+
+54
+00:05:02,040 --> 00:05:07,220
+العمود التالت نقص اتنين واحد بالشكل اللي عندنا هنا
+
+55
+00:05:07,880 --> 00:05:12,380
+يبقى هذه المصوفة بيحصلنا عليها من خطواتين الخطوة
+
+56
+00:05:12,380 --> 00:05:16,920
+الأولى استبدلنا كل عنصر بالـ cofactor تبعه خطوة
+
+57
+00:05:16,920 --> 00:05:21,220
+ثانية جيبنا ل Transpose ل المصوفة الناتجة بقيت
+
+58
+00:05:21,220 --> 00:05:26,640
+علينا الخطوةمش هجيب الخطوة الأخيرة بلزمني محدد
+
+59
+00:05:26,640 --> 00:05:31,920
+المصوفة إيه، إذا بروح بقوله بدي أجيبله determinant
+
+60
+00:05:31,920 --> 00:05:36,740
+للمصوفة إيه، يبقى هذه الخطوة الأولى و هذه الخطوة
+
+61
+00:05:36,740 --> 00:05:40,740
+التانية يا بناتبتجي للخطوة التالتة determinant
+
+62
+00:05:40,740 --> 00:05:49,560
+لإيه؟ بتسوي المحدد بتجي لإيه الأصلية؟ 1 3-1 0 1 2
+
+63
+00:05:49,560 --> 00:05:58,260
+-1 0 8 بالشكل اللي عندنابدا فك المصوفة باستخدام
+
+64
+00:05:58,260 --> 00:06:04,320
+عناصر العمود الأول مثلا يبقى هذا الكلام واحد فيه
+
+65
+00:06:04,320 --> 00:06:10,140
+نشطب صفه عموده يبقى تمانية ناقص Zero اللي بعده
+
+66
+00:06:10,140 --> 00:06:16,520
+ناقص Zero زائد ناقص واحد فيهأشط بيصفوا عمود بيصير
+
+67
+00:06:16,520 --> 00:06:24,800
+ستة زائد واحد يبقى ستة زائد واحد الشكل عن هنا يبقى
+
+68
+00:06:24,800 --> 00:06:30,760
+هنا تمانية و هنا نقص سبعة يبقى الجواب كدهش؟واحد
+
+69
+00:06:30,760 --> 00:06:37,140
+صحيح يبقى الـ A inverse يبقى واحد على ال
+
+70
+00:06:37,140 --> 00:06:43,760
+determinant للـ A في المصوفة B يبقى واحد على واحد
+
+71
+00:06:43,760 --> 00:06:48,840
+في المصوفة B اللي طلعت اللي هي تمانية سالب اربعة
+
+72
+00:06:48,840 --> 00:06:57,020
+وعشرين سبعة ناقص اتنين سبعة ناقص اتنين واحد ناقص
+
+73
+00:06:57,020 --> 00:07:04,230
+تلاتة واحد بالشكل اللي عندناطبعا هذه هي نفسها
+
+74
+00:07:04,230 --> 00:07:12,210
+الهمين تمانية سالب اربعة وعشرين سابعة سالب اتنين
+
+75
+00:07:12,210 --> 00:07:19,210
+سابعة سالب اتنين واحد لبتلاتة واحدةالطلاعيل في
+
+76
+00:07:19,210 --> 00:07:22,170
+النتيجة هذه والنتيجة اللى أوجدناها في المحاضرة
+
+77
+00:07:22,170 --> 00:07:26,210
+السابقة الاتنين are the same يبقى نفس النتيجة
+
+78
+00:07:26,210 --> 00:07:30,970
+بالحرف الوعيد إذا سواء استخدمت الطريقة الأولى في
+
+79
+00:07:30,970 --> 00:07:34,870
+إيجاد معكوس المصوفة أو استخدمت الطريقة الثانية في
+
+80
+00:07:34,870 --> 00:07:41,840
+إيجاد معكوس المصوفة الاتنين are the same تمام؟طيب
+
+81
+00:07:41,840 --> 00:07:47,940
+بدنا نيجي الآن بعد ما انتهينا من ذلك نعطيكي كمان
+
+82
+00:07:47,940 --> 00:07:56,920
+مثال المثال بيقول ما يأتي example find
+
+83
+00:07:56,920 --> 00:08:09,550
+the inverse ofالـ A تساوي اللي هو مين الـ A تساوي
+
+84
+00:08:09,550 --> 00:08:14,810
+اتنين تلاتة واحد اربعة بالشكل اللي عندنا هذا
+
+85
+00:08:14,810 --> 00:08:18,210
+solution
+
+86
+00:08:18,210 --> 00:08:31,970
+طلبتي
+
+87
+00:08:31,970 --> 00:08:42,480
+ايش؟هادي واحد على ال determinant في ال B واحدة
+
+88
+00:08:42,480 --> 00:08:45,860
+واحدة بس ناس ماعيش بتقول تاني عيدي تاني هيقولنا
+
+89
+00:08:45,860 --> 00:08:49,920
+واحد على ال determinant في بي بي اللي هي هادي لإن
+
+90
+00:08:49,920 --> 00:08:54,580
+كاتب عليها Transpose لسه بدي أحولي فبكتب هادي
+
+91
+00:08:54,580 --> 00:09:02,110
+تمام؟طيب نجي يالا كل واحد يتعلمك بالاسمة وإياك
+
+92
+00:09:02,110 --> 00:09:05,650
+واحدة تعلم قدام اسمة واحدة تانية دي يا ربالكم، فضل
+
+93
+00:09:05,650 --> 00:09:08,290
+يالا، تعلم اسمك باسم المحاضرة هادي
+
+94
+00:09:12,560 --> 00:09:16,100
+طيب، بدنا نيجي للمصوفة اللي قدامنا يا بنات، هذه
+
+95
+00:09:16,100 --> 00:09:22,160
+المصوفة 2×2 وليست 3×3 كما كانت المصوفة قبل قليل،
+
+96
+00:09:22,160 --> 00:09:26,580
+تمام؟ لكن أنا بدي أحاول أحل بنفس الطريقة اللي
+
+97
+00:09:26,580 --> 00:09:31,700
+اتبعت هنا قبل قليل، فباجي أول خطة، بدي أجيب الـ
+
+98
+00:09:31,700 --> 00:09:33,020
+Determinant
+
+99
+00:09:34,840 --> 00:09:40,620
+يبقى المحدد اتنين تلاتة واحد اربعة تمانية ناقص
+
+100
+00:09:40,620 --> 00:09:46,980
+تلاتة ويساوي كم؟ خمسة يبقى هذا قيمة المحدد يساوي
+
+101
+00:09:46,980 --> 00:09:53,520
+خمسة بعد هيك بدي اجي لالمصوف اللي عندي واستبدل كل
+
+102
+00:09:53,520 --> 00:10:01,000
+عنصر بال cofactor المناظر لهيبقى باجي بقوله الان
+
+103
+00:10:01,000 --> 00:10:04,420
+بدي اجيل المصعوفة اللي عندنا هذه و بدي اجيب ال
+
+104
+00:10:04,420 --> 00:10:10,460
+cofactor يبقى بدي اشيل اتنين و اشطب صف و عمود و
+
+105
+00:10:10,460 --> 00:10:15,580
+بضل قداش عندنا اربعة بس يبقى جاهز بحط اربعة زي مين
+
+106
+00:10:15,580 --> 00:10:20,000
+و حسب قاعدة الإشارات العنصر هذا إشارته بالمين
+
+107
+00:10:20,000 --> 00:10:24,560
+بالموجةالان بدى اروح للعنصر بعده اللى هو التلاتة
+
+108
+00:10:24,560 --> 00:10:29,440
+يبقى بدي اشطب صفه و عموده بضال قداش واحد بس حسب
+
+109
+00:10:29,440 --> 00:10:38,060
+قاعدة الإشارات الإشارة مالها بالثاني بدي اشطب صفه
+
+110
+00:10:38,060 --> 00:10:42,900
+و عموده بضال قداش تلاتة بس حسب قاعدة الإشارات
+
+111
+00:10:42,900 --> 00:10:50,060
+الإشارةبالسالب تمام بالداجل العنصر أربعة رشد بصفه
+
+112
+00:10:50,060 --> 00:10:57,320
+و عموده بضاله كده اتنين و حسب قاعدة الإشاراتموجة
+
+113
+00:10:57,320 --> 00:11:03,560
+تمام طيب انا بدي اشهد بدي لترانسبوز تبعها يبقى
+
+114
+00:11:03,560 --> 00:11:10,220
+بكتب عليها ترانسبوز و بروح بسميها المصوفة بي تمام
+
+115
+00:11:10,220 --> 00:11:18,020
+مين لترانسبوز تبعها يساوي اللي هو الصف الأول بده
+
+116
+00:11:18,020 --> 00:11:23,020
+يصير العمود الأول الصف الثاني بده يصير العمود
+
+117
+00:11:23,020 --> 00:11:28,220
+الثاني بالشكل اللي عندنا هذابعد ذلك بدي أروح أجيب
+
+118
+00:11:28,220 --> 00:11:35,360
+معكوس المصفوفة A من الصيغة 1 على محدد ال A في
+
+119
+00:11:35,360 --> 00:11:50,140
+المصفوفة B يبقى 1 على 5 في المصفوفة B 4-3-1 2 يا
+
+120
+00:11:50,140 --> 00:11:55,400
+بتخليها زي ما هييا إما بتدخليها عليها وتقوليلي هذه
+
+121
+00:11:55,400 --> 00:12:02,400
+أربع أخماس ناقص ثلاث أخماس وهنا ناقص خمس وهنا
+
+122
+00:12:02,400 --> 00:12:08,820
+خمسين بالشكل اللي عندنا هذا طيب
+
+123
+00:12:10,080 --> 00:12:14,680
+بصوا صبر شوية لسه مخلصتش يعني احنا هيك جيبنا
+
+124
+00:12:14,680 --> 00:12:19,800
+المعكوس تماما مائة بالمائة بدون اي مشاكل السؤال
+
+125
+00:12:19,800 --> 00:12:25,900
+اللي بده اطرحه طب خليني ندقيق النظر في المصفوفة B
+
+126
+00:12:25,900 --> 00:12:31,960
+هذه و نشوف نقارنها بالمصفوفة الأصلية لو جيتلى
+
+127
+00:12:31,960 --> 00:12:37,590
+المصفوفة الأصلية بلاحظبدلت عناصر القطر الرئيسي
+
+128
+00:12:37,590 --> 00:12:43,550
+مكان بعض وغيرت إشارات عناصر القطري الثانوي، مظبوط
+
+129
+00:12:43,550 --> 00:12:48,730
+ولا لأ؟ إذا من الآن فساعدا يا بنات، إذا بدي أجيب
+
+130
+00:12:48,730 --> 00:12:53,910
+المصفوف بيهاديلا داعي أن أذهب و أبدأ أحسب من أول و
+
+131
+00:12:53,910 --> 00:12:58,050
+جديد يبقى بس بدلي عناصر القطر الرئيسي مكان بعض
+
+132
+00:12:58,050 --> 00:13:01,990
+مليون متشين عناصر القطر الثانوي خليهم زي ما هم
+
+133
+00:13:01,990 --> 00:13:05,790
+بسحطنهم شهر السالم بكون جيبتي المصوفة بياش ضايل
+
+134
+00:13:05,790 --> 00:13:10,490
+عليه ضايل عليه أجيب جدش محدد المصوفة ايه و أضرب
+
+135
+00:13:10,490 --> 00:13:13,630
+واحد على قيمة المحدد في هذه المصوفة بكون جيبتي
+
+136
+00:13:13,630 --> 00:13:19,870
+المعكوس بس هذه للمصوفة اللي نضامها اتنين في اتنين
+
+137
+00:13:20,110 --> 00:13:26,330
+واللي ال inverse تبعها exist مش لاي مصبوفة يبقى
+
+138
+00:13:26,330 --> 00:13:32,270
+شرطين المعكوس هذا ماله موجود اتنين ويكون نظامها
+
+139
+00:13:32,270 --> 00:13:38,990
+اتنين في اتنين ماشي في اي تساؤل؟ خلاصنا عظمنا
+
+140
+00:13:38,990 --> 00:13:47,050
+جابنا تساؤلك؟كما أنت سؤالة اتفضلي اذا
+
+141
+00:13:47,050 --> 00:13:50,910
+ال determinant سالب و الله موجب و الله كسر ايش ما
+
+142
+00:13:50,910 --> 00:13:54,750
+يكون يكون لا دخلة له في الموضوع واحد على المحدد
+
+143
+00:13:54,750 --> 00:14:00,330
+ماجي و اللي جوا جوا المصوفة زي ما هي لحد هيك يكون
+
+144
+00:14:00,330 --> 00:14:06,230
+انتهى هذا ال section و لا يكون ارقام المسائلاللي
+
+145
+00:14:06,230 --> 00:14:13,810
+هي exercises اللي هو اتنين اتناشر المسائل التالية
+
+146
+00:14:13,810 --> 00:14:22,110
+اللي هي واحد و تلاتة و خمسة و سبعة و من عشرة لغاية
+
+147
+00:14:22,110 --> 00:14:29,650
+خمستاشر و بنروح ال additional exercises additional
+
+148
+00:14:29,650 --> 00:14:37,490
+exercises و بدنا المسائل من واحد لغاية تمانىلكن في
+
+149
+00:14:37,490 --> 00:14:41,870
+المقابل في بعض الأسئلة النظرية في الـ Additional
+
+150
+00:14:41,870 --> 00:14:49,670
+Exercises بدي أروح أحل هذه الأسئلة حالها كالتالي
+
+151
+00:15:05,220 --> 00:15:11,500
+مين اللي بتسأل السؤال؟ كيف؟ وين مابدك؟ لو كان ال
+
+152
+00:15:11,500 --> 00:15:14,120
+system معين، عدد ال unknowns فيه بيساوي عدد
+
+153
+00:15:14,120 --> 00:15:18,040
+المعادلات، بقدر أقول مية بالمية إنه خلّاها؟ لأ
+
+154
+00:15:18,040 --> 00:15:21,180
+طيب،
+
+155
+00:15:21,180 --> 00:15:23,840
+على أي حال، بدنا نيجي ل exercises
+
+156
+00:15:30,340 --> 00:15:41,080
+اتنين اتناشر page صفحة مية وخمسة واربعين لغاية مية
+
+157
+00:15:41,080 --> 00:15:49,940
+وستة واربعين السؤال اتناشر بيقول ما يأتي if ال a
+
+158
+00:15:49,940 --> 00:15:54,500
+is non singular
+
+159
+00:15:56,270 --> 00:16:08,370
+non-singular matrix show that بيّن إن الـ A
+
+160
+00:16:08,370 --> 00:16:09,470
+transpose
+
+161
+00:16:15,830 --> 00:16:25,890
+الكل inverse يساوي a inverse transpose بالشكل
+
+162
+00:16:25,890 --> 00:16:30,670
+اللي عندنا هنا solution
+
+163
+00:16:39,690 --> 00:16:45,290
+الان بدي أحلك مجموعة من الأسئلة عن نظرية على هذا
+
+164
+00:16:45,290 --> 00:16:49,510
+ال section الأسئلة
+
+165
+00:16:49,510 --> 00:17:03,870
+هذه موجودة كلها في الكتابهو نفسه
+
+166
+00:17:03,870 --> 00:17:09,850
+بالضبط تماما كما لو جبت المعكوس أولا ثم جبت المدور
+
+167
+00:17:09,850 --> 00:17:15,730
+من المصوفة الناتجة يبقى A inverse transpose هو A
+
+168
+00:17:15,730 --> 00:17:21,170
+transpose inverse تمام؟ بنقوله بسيطة احنا عندنا ال
+
+169
+00:17:21,170 --> 00:17:29,310
+Ais non-singular يبقى هذا أيش معناه يا بنات؟ ان ال
+
+170
+00:17:29,310 --> 00:17:35,390
+a inverse existأو الـ determinant للـ A اللي لا
+
+171
+00:17:35,390 --> 00:17:40,790
+يساوي 0 يقبل A inverse exist مدام A inverse exist
+
+172
+00:17:40,790 --> 00:17:48,330
+هذا معناه ايش ان ال A في ال A inverse بده يساوي ال
+
+173
+00:17:48,330 --> 00:17:54,770
+identity matrix and ال A inverse في ال A كمان بده
+
+174
+00:17:54,770 --> 00:18:00,210
+يساوي ال identity matrix مظبوط؟طب احنا موضوعنا
+
+175
+00:18:00,210 --> 00:18:05,790
+موضوعش اللي مطلوب الـ Transpose إذا بدي أروح أدخل
+
+176
+00:18:05,790 --> 00:18:08,230
+ال Transpose في الموضوع معناه أنني بدي أخد ال
+
+177
+00:18:08,230 --> 00:18:13,970
+Transpose للطرفين يقول لو أخدت ال Transpose عندنا
+
+178
+00:18:13,970 --> 00:18:19,190
+هنا إيش بصير؟هذا بدّي يعطيكي أن الـ A في الـ A
+
+179
+00:18:19,190 --> 00:18:25,330
+inverse transpose بده يساوي الآية transpose and
+
+180
+00:18:25,330 --> 00:18:31,110
+الـ A inverse A transpose بده يساوي الآية
+
+181
+00:18:31,110 --> 00:18:38,350
+transposeطيب هذا معناهم أظن أخدنا لو كان عندي حاصل
+
+182
+00:18:38,350 --> 00:18:43,190
+ضرب A في B Transpose بيصير B Transpose A Transpose
+
+183
+00:18:43,190 --> 00:18:47,910
+نجلبها يبقى بناء عليه بدهاجي هادي و أجلبهاش بيصير
+
+184
+00:18:47,910 --> 00:18:55,070
+عندنا A Inverse Transpose في ال A Transpose بده
+
+185
+00:18:55,070 --> 00:18:58,450
+يساوي مصفوفتي اللي واحدة اللي همجيبها ال Transpose
+
+186
+00:18:58,450 --> 00:19:05,130
+ده بقىنفسها تمام يبقى هذا بده يعطينا مصوفة الوحدة
+
+187
+00:19:05,130 --> 00:19:12,930
+and اللي هو ال a transpose a inverse a transpose
+
+188
+00:19:12,930 --> 00:19:22,020
+كله بده يساوي مصوفة الوحدة طيب هذا معناه ايه؟هذه
+
+189
+00:19:22,020 --> 00:19:25,280
+مصفوفة الوحدة وهذه مصفوفة الوحدة المعناهة وحصل ضرب
+
+190
+00:19:25,280 --> 00:19:31,320
+الاتنين هدول are equal يبقى هذا معناه ان ال A
+
+191
+00:19:31,320 --> 00:19:36,780
+inverse transpose في ال A transpose بده يسوى A
+
+192
+00:19:36,780 --> 00:19:41,880
+transpose في ال A inverse transpose بده يسوى مين؟
+
+193
+00:19:41,880 --> 00:19:47,940
+بده يسوى مصفوفة الوحدةما هو معنى هذا الكلام؟ إن
+
+194
+00:19:47,940 --> 00:19:53,740
+هؤلاء المصففين هو معكوسات لبعضهم، صح ولا لأ؟ يبقى
+
+195
+00:19:53,740 --> 00:20:00,960
+هذا معناه إن الـ A inverse A transpose is the
+
+196
+00:20:00,960 --> 00:20:06,060
+inverse of A transpose
+
+197
+00:20:13,080 --> 00:20:19,680
+معكوس المصفوفة ثانية يعني كأن هذه هي a transpose
+
+198
+00:20:19,680 --> 00:20:20,680
+inverse
+
+199
+00:20:22,710 --> 00:20:31,270
+يبقى هذا معناه ان ال a inverse transpose بالضبط ال
+
+200
+00:20:31,270 --> 00:20:36,530
+inverse تبع a transpose يبقى هي a transpose
+
+201
+00:20:36,530 --> 00:20:40,490
+inverse أظن
+
+202
+00:20:40,490 --> 00:20:46,870
+هو المطلوب مش هي اللي بدنا نتبته؟ خلصنا أيضا، صعب؟
+
+203
+00:20:47,520 --> 00:20:52,020
+والهجر أخذنا تاريف non-singular يبقى المعكوس موجود
+
+204
+00:20:52,020 --> 00:20:58,160
+عرفنا المعكوس أخذنا ال Transpose وعملنا المساوية
+
+205
+00:20:58,160 --> 00:21:02,980
+ليس إلا لو طلعت معانا على طول القاطع ماعنداش مشكلة
+
+206
+00:21:02,980 --> 00:21:09,700
+يبقى هذا كان سؤال 12 عندك من الكتاب نجلس سؤال 13
+
+207
+00:21:09,700 --> 00:21:18,770
+اللي ورا مباشرة هذا سؤال 13ثلاثاش بيقول افترض ان
+
+208
+00:21:18,770 --> 00:21:25,550
+ال A and ال B بيكون بيكون بيكون بيكون بيكون بيكون
+
+209
+00:21:25,550 --> 00:21:26,290
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+210
+00:21:26,290 --> 00:21:27,250
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+211
+00:21:27,250 --> 00:21:28,650
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+212
+00:21:28,650 --> 00:21:28,890
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+213
+00:21:28,890 --> 00:21:28,890
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+214
+00:21:28,890 --> 00:21:28,890
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+215
+00:21:28,890 --> 00:21:28,890
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+216
+00:21:28,890 --> 00:21:37,850
+بيكون بيكون بيكون بيكون بيكون بيكون بي
+
+217
+00:21:37,990 --> 00:21:44,850
+the same order اتن تان من نفس الرثبه او نفس النظام
+
+218
+00:21:44,850 --> 00:21:54,370
+بيقول ل F إذا كان ال C إذا كان المصوفة C بدها
+
+219
+00:21:54,370 --> 00:22:04,540
+السوى حصل الضرب F بي show thatShow that بيّلي ان
+
+220
+00:22:04,540 --> 00:22:11,920
+الـ C inverse بده يساوي B inverse في ال A inverse
+
+221
+00:22:11,920 --> 00:22:24,480
+نرجع
+
+222
+00:22:24,480 --> 00:22:30,110
+لسؤالنا مرة تانيةالسؤال بيقول لو كان كل من a و b
+
+223
+00:22:30,110 --> 00:22:34,490
+non singular matrices يبقى محدد كل واحدة فيهم ماله
+
+224
+00:22:34,490 --> 00:22:40,950
+لا يساوي zero وتنتهي من نفس الورقة قال لو كان ال c
+
+225
+00:22:40,950 --> 00:22:48,030
+حصل لضرب a في b بدي أثبت أن المعكوس تبع المصوفة c
+
+226
+00:22:48,030 --> 00:22:53,730
+هو ال b inverse في ال a inverse طب هو قال هل ال a
+
+227
+00:22:53,730 --> 00:23:01,550
+b لها معكوسماجاليش انا بدي اثبت ان الها معكوس
+
+228
+00:23:01,550 --> 00:23:05,670
+وبعدين اروح اثبت ان المعكوس هذا بيساوي بعضه صح ولا
+
+229
+00:23:05,670 --> 00:23:12,650
+لا بقوله بسيطة جدا اذا انا بدي اجي لل solution بدي
+
+230
+00:23:12,650 --> 00:23:22,710
+اجي للمعطيات ال a and ال b are non singular هذا
+
+231
+00:23:22,710 --> 00:23:28,580
+ايش معناه يا بناتnon singular هذا معناته أن ال
+
+232
+00:23:28,580 --> 00:23:34,780
+determinant لل A لا يساوي zero and ال determinant
+
+233
+00:23:34,780 --> 00:23:40,640
+لل B لا يساوي zero صح؟
+
+234
+00:23:41,180 --> 00:23:47,260
+طب لو ضربت اتنين في بعض يبقى هذا بده يعطينا ان ال
+
+235
+00:23:47,260 --> 00:23:53,400
+determinant لل A في ال determinant لل B ماله لا
+
+236
+00:23:53,400 --> 00:24:01,170
+يساوي Zero هذا معناه انه حصل الضربهذا الـ
+
+237
+00:24:01,170 --> 00:24:05,170
+determinant للـ A فالـ determinant للـ B اللي بده
+
+238
+00:24:05,170 --> 00:24:10,550
+يساوي الـ determinant للـ A في B لا يساوي Zero
+
+239
+00:24:10,550 --> 00:24:18,090
+تمام؟ هذا معناته إيش؟ معناته إن الـ A في B is non
+
+240
+00:24:18,090 --> 00:24:28,870
+singularهذا معناته أن الـ A B إنفرس exist
+
+241
+00:24:31,040 --> 00:24:37,780
+يبقى المعكوس هذا ماله موجود طيب هو بيقول لو كان ال
+
+242
+00:24:37,780 --> 00:24:43,040
+C يساوي ال A في ال B بدك تثبت لي أن هذا المعكوس
+
+243
+00:24:43,040 --> 00:24:47,820
+يساوي B inverse A inverse يعني كأنه أنا بدأ أثبت
+
+244
+00:24:47,820 --> 00:24:52,640
+أن ال A بي الكل inverse يساوي B inverse يعني كأنه
+
+245
+00:24:52,640 --> 00:24:57,620
+بنغلب و أضعهم زي ال transpose بالظبطمش حصل ضرب a
+
+246
+00:24:57,620 --> 00:25:00,880
+بي لكل transpose بجينا نقول بي transpose في ال a
+
+247
+00:25:00,880 --> 00:25:05,080
+transpose يبقى هنا نفس الجثة كل واحد علمت على اسم
+
+248
+00:25:05,080 --> 00:25:13,600
+هنا بنادر كله تمام طيبنرجع الان نجي نشوف صحة هذا
+
+249
+00:25:13,600 --> 00:25:23,840
+الكلام لو انا جيت اخدت ال a,b في ال a,b او a في ده
+
+250
+00:25:23,840 --> 00:25:30,800
+في اخده في مين في ال b inverse a inverse اللي قايل
+
+251
+00:25:30,800 --> 00:25:38,250
+عليه هذا طيب هذا الكلام بده يساويبدي اجي لخاصية ال
+
+252
+00:25:38,250 --> 00:25:43,110
+associativity على المصففات خاصية الدمج اذا هذه
+
+253
+00:25:43,110 --> 00:25:50,450
+تساوي A في الـ B بي انفرس A انفرس، مظبوط؟ هذه اللي
+
+254
+00:25:50,450 --> 00:25:56,050
+بين قوسين مين هي ال identity matrix يبقى ال A في
+
+255
+00:25:56,050 --> 00:26:00,830
+ال identity matrix في ال A انفرس ال identity
+
+256
+00:26:00,830 --> 00:26:04,990
+matrix لما تضربيها في اي مصففة شو بيطلع؟نفس
+
+257
+00:26:04,990 --> 00:26:08,870
+المصوفة the same matrix يبقى الـA في الـA inverse
+
+258
+00:26:08,870 --> 00:26:16,150
+اللي هي الـmain المصوفة A طيب and لو أخدت الـB
+
+259
+00:26:16,150 --> 00:26:21,770
+inverse A inverse ضربت في الـAB يا مانا شو بدي
+
+260
+00:26:21,770 --> 00:26:26,750
+يعطيني؟ بدي أستخدم خاصية ال associativity يبقى B
+
+261
+00:26:26,750 --> 00:26:36,240
+inverse A inverse ABمعكوس المصوفة في المصوفة الـ
+
+262
+00:26:36,240 --> 00:26:43,480
+Identity Matrix يبقى B inverse IB يعني B inverse B
+
+263
+00:26:43,480 --> 00:26:49,180
+يعني الـ Identity Matrixإذا من الاتنين هدول، إيش
+
+264
+00:26:49,180 --> 00:26:56,520
+بنستنتج يا بنات؟ بنستنتج إن الـAB في الـB inverse
+
+265
+00:26:56,520 --> 00:27:03,020
+A inverse بدو يساوي الـB inverse A inverse في
+
+266
+00:27:03,020 --> 00:27:10,890
+الـAB في الـAB بدو يساوي 100يبقى معناته كل واحدة
+
+267
+00:27:10,890 --> 00:27:17,950
+فيهم معكس للتانية هذا معناه ان ال b inverse a
+
+268
+00:27:17,950 --> 00:27:31,150
+inverse is the inverse of a في b صح ولا لأ but the
+
+269
+00:27:31,150 --> 00:27:35,010
+inverse of
+
+270
+00:27:37,100 --> 00:27:48,620
+A B is denoted by A B الكل انفر
+
+271
+00:27:51,920 --> 00:27:55,860
+و قبل شوية في المحاضرة الصحيفة أثبتنا نظرية أن ال
+
+272
+00:27:55,860 --> 00:28:02,500
+inverse يكون واحدا إذا هذا هو التاني يبقى but the
+
+273
+00:28:02,500 --> 00:28:09,360
+inverse of a b is denoted by كذا and the inverse
+
+274
+00:28:09,360 --> 00:28:12,740
+of
+
+275
+00:28:12,740 --> 00:28:17,180
+a matrix is
+
+276
+00:28:18,080 --> 00:28:23,940
+يكون هناك يكون وحيداً هذا بدي يعطينا ان ال a b
+
+277
+00:28:23,940 --> 00:28:29,720
+الكل inverse بدي يسوى b inverse a inverse
+
+278
+00:28:33,320 --> 00:28:38,080
+هتحين لما تكون هذه الـC بده يساوي الـAB قال لي
+
+279
+00:28:38,080 --> 00:28:42,660
+اثبتلي ان الـC inverse يساوي كذا، مظبوط؟ الحين
+
+280
+00:28:42,660 --> 00:28:47,440
+الـC inverse بده يساوي مين؟ AB inverse يبقى هذا
+
+281
+00:28:47,440 --> 00:28:53,960
+بده يعطينا ان الـC inverse بده يساوي B inverse A
+
+282
+00:28:53,960 --> 00:28:59,350
+inverse عظم ما هو المطلوبإذا من الآن فصاعدا هذا
+
+283
+00:28:59,350 --> 00:29:03,650
+السؤال ليش بيقول ليه؟ بيقول لو عندي حاصل ضرب
+
+284
+00:29:03,650 --> 00:29:09,370
+مفصوفين A وB واختلهم الكل inverse تساوي inverse
+
+285
+00:29:09,370 --> 00:29:13,490
+التانية في inverse الأميرة الأولى بدنا نجلبها زي
+
+286
+00:29:13,490 --> 00:29:16,330
+ال transpose بالضبط تماما
+
+287
+00:29:31,740 --> 00:29:37,780
+هذا كان سؤال 13 من الكتاب نجي لسؤال 14 برضه نظري
+
+288
+00:29:37,780 --> 00:29:50,280
+سؤال 14 بيقول مياتي let ال a be a non singular
+
+289
+00:29:50,280 --> 00:30:00,470
+matrix non singular matrix show thatShow that أن
+
+290
+00:30:00,470 --> 00:30:07,910
+الـ A Inverse Inverse بدي يعطيني الـ A
+
+291
+00:30:19,610 --> 00:30:23,630
+نفس التكتيك اللي اتبع في السؤالين السابقين بمسك
+
+292
+00:30:23,630 --> 00:30:27,590
+المعلومة بحاول أستفيد منها مش بيعطينا المعلومة
+
+293
+00:30:27,590 --> 00:30:31,270
+بلاش بس نتفرج عليها لأ لأ لأ بحاول نستفيد منها إذا
+
+294
+00:30:31,270 --> 00:30:39,890
+احنا بدنا نيجي هنا الان let ال a be a non singular
+
+295
+00:30:39,890 --> 00:30:47,000
+matrix يبقى هذا معناه يا جماعةأن الـ determinant
+
+296
+00:30:47,000 --> 00:30:54,740
+للـ A لا يسوي 0 هذا معناه أن الـ A inverse exists
+
+297
+00:30:54,740 --> 00:31:01,120
+يعني هذا معناه أن الـ A في الـ A inverse سيكون مهم
+
+298
+00:31:01,120 --> 00:31:08,420
+مصفوفة الوحدة تمام؟ حتى لأن كلام اللي بقوله كأنه
+
+299
+00:31:08,420 --> 00:31:12,720
+ليس له علاقة بالمطلوب المطلوب دي أثبت أن معكوس
+
+300
+00:31:12,720 --> 00:31:18,910
+المعكوس يعطينا الأصلصح؟ يعني لو جيبت معكوس مصوفة و
+
+301
+00:31:18,910 --> 00:31:23,030
+روحت جيبت لها كمان معكوس للمعكوس بديه يطلع المصوفة
+
+302
+00:31:23,030 --> 00:31:27,570
+الأصلي، مظبوط؟هو اللي بيقول لي اثبت ان a inverse
+
+303
+00:31:27,570 --> 00:31:32,610
+inverse بدي ساوي من ال a اذا انا مشان اجيب له ال
+
+304
+00:31:32,610 --> 00:31:36,110
+inverse بدي اروح اخد inverse لمين للنتيجة اللي انا
+
+305
+00:31:36,110 --> 00:31:44,390
+توصلت لها تمام فبجي بقول له هذا معناه ان ال a في
+
+306
+00:31:44,390 --> 00:31:50,510
+ال a inverse الكل inverse بدي ساوي ال I inverse
+
+307
+00:31:53,570 --> 00:32:00,070
+سؤال كمان مرة، معكوس مصفوفة الوحدة مين هي؟ نفس
+
+308
+00:32:00,070 --> 00:32:05,870
+الوحدة itself، مظبوط؟ يبقى باجي بقول هنا هذا بده
+
+309
+00:32:05,870 --> 00:32:11,330
+يعطيك بدرجة على الخواص تبعت من؟ تبعت ال inverse
+
+310
+00:32:11,330 --> 00:32:14,970
+اللي أثبتناها هنا، يبقى هذا ال inverse ليش بدنا
+
+311
+00:32:14,970 --> 00:32:19,850
+نسويه؟ بدنا نجلب وضعهايبقى هذا بيعطيك a inverse
+
+312
+00:32:19,850 --> 00:32:25,050
+inverse في ال a inverse بده يسوى ال identity
+
+313
+00:32:25,050 --> 00:32:30,190
+matrix هذا جيبته من وين؟ من السؤال وين؟ من السؤال
+
+314
+00:32:30,190 --> 00:32:40,390
+13 يبقى هذا from exercises 13 طيب كويس ايش رأيك؟
+
+315
+00:32:40,390 --> 00:32:48,290
+انا بدي هذه صح؟طب خليني اضرب من جهة اليمين في
+
+316
+00:32:48,290 --> 00:32:53,850
+المصفوفة A مش انا اخليها دي لوحدها اذا لو جهة ضربت
+
+317
+00:32:53,850 --> 00:33:00,070
+من جهة اليمين في المصفوفة A بصير A inverse inverse
+
+318
+00:33:00,070 --> 00:33:06,290
+A inverse في مين في المصفوفة A بدو سوى ال identity
+
+319
+00:33:06,290 --> 00:33:12,740
+matrix في المصفوفة Aهذا معناه ان ال a inverse
+
+320
+00:33:12,740 --> 00:33:19,740
+inverse هدف هدف من بال identity matrix بده يساوي
+
+321
+00:33:19,740 --> 00:33:25,220
+المصوفة a طيب المصوفة الوحدة لما نضربها في أي
+
+322
+00:33:25,220 --> 00:33:30,800
+مصوفة بتعطيني مين نفس المصوفة يبقى ال a inverse
+
+323
+00:33:30,800 --> 00:33:38,940
+inverse بده يساوي المصوفة a itselfمظبوط هكذا؟ يبقى
+
+324
+00:33:38,940 --> 00:33:44,420
+ماسوّناش اشي خلاصنا يبقى أثبتنا أن معكوس لمعكوس
+
+325
+00:33:44,420 --> 00:33:50,620
+المصفوفة بيعطينا المصفوفة itsel ناخد كمان سؤال
+
+326
+00:33:50,620 --> 00:33:59,640
+السؤال الخامس عشر بيقول لي the matrix the matrix
+
+327
+00:33:59,640 --> 00:34:03,160
+IN
+
+328
+00:34:03,160 --> 00:34:14,280
+لل identity matrix isits is its own inverse يعني
+
+329
+00:34:14,280 --> 00:34:23,060
+هي معكوس لنفسها since ليش؟ لأن ال identity matrix
+
+330
+00:34:23,060 --> 00:34:28,520
+لما نضربها في ال identity matrix بيطلع من عندنا ال
+
+331
+00:34:28,520 --> 00:34:33,660
+identity matrix المطلوب الأول من السؤال find
+
+332
+00:34:35,470 --> 00:34:45,290
+at least على الأقل to second
+
+333
+00:34:45,290 --> 00:34:48,830
+order
+
+334
+00:34:48,830 --> 00:34:57,030
+to second order matrices matrices
+
+335
+00:34:57,030 --> 00:35:04,050
+other than I N
+
+336
+00:35:07,740 --> 00:35:18,800
+that have this property إلا
+
+337
+00:35:18,800 --> 00:35:27,080
+دي الخاصية نمر بيه if ال a بده يساوي ال a inverse
+
+338
+00:35:27,080 --> 00:35:28,800
+show that
+
+339
+00:35:32,000 --> 00:35:39,460
+show that بيّلي أن الـ determinant للإيه بده يساوي
+
+340
+00:35:39,460 --> 00:35:41,860
+زائد أو ناقص واحد
+
+341
+00:36:10,490 --> 00:36:16,950
+نرجع لسؤالنا مرة ثانية السؤال ذو شقين نقرأ السؤال
+
+342
+00:36:16,950 --> 00:36:21,370
+كويس و بعد هي كده تعالي يا بنت، يا بنت تعالي تعالي
+
+343
+00:36:21,370 --> 00:36:27,510
+تعالي بقول طلعت
+
+344
+00:36:27,510 --> 00:36:30,990
+كلمة جوال، مش هيك؟ بتاخدي كتبك وصلي تعودي على
+
+345
+00:36:30,990 --> 00:36:35,750
+المحاضرة أبدا، يا بتقعدي وانسي حكاية الجوال أنا من
+
+346
+00:36:35,750 --> 00:36:37,630
+أول محاضرة قلتك يا جوال يا محاضرة
+
+347
+00:36:48,030 --> 00:36:52,030
+قلتك المحاضرة مثل صلاة الجمعة فاش الإيمان بالمخطب
+
+348
+00:36:52,030 --> 00:36:55,410
+واحد يطلع يرد على الجوال ويعود لخطبة مسخرة هذه مش
+
+349
+00:36:55,410 --> 00:37:00,510
+صلاة واحنا هنا مكان المحاضرة مكان عبادة تماما مثل
+
+350
+00:37:00,510 --> 00:37:07,150
+الصلاة عندي يبقى يا دي دراسة يا إما جوال نرجع
+
+351
+00:37:07,150 --> 00:37:08,190
+لسؤالنا مرة تانية
+
+352
+00:37:13,170 --> 00:37:18,390
+مثوفة الوحدة هي مصوفة معكوس لنفسها
+
+353
+00:37:29,590 --> 00:37:37,050
+هاتلي at least على الأقل مصفوفتين من ال second
+
+354
+00:37:37,050 --> 00:37:42,530
+order يعني النظام هتنين في اتنين من غير ال I انت
+
+355
+00:37:42,530 --> 00:37:45,910
+مش هتروح تقولي المصفوف I too صفين و عاملين تقولي
+
+356
+00:37:45,910 --> 00:37:51,650
+أي واحد لأ ده هتجيب مصفوفتين غيرهمبحيث لهم هذه
+
+357
+00:37:51,650 --> 00:37:55,770
+الخاصية يعني لو ضرب المصوفة في نفسها بدي أطيني
+
+358
+00:37:55,770 --> 00:38:01,290
+مصوفة الوحدة بس بشرط ما تكونش مصوفة الوحدة تمام؟
+
+359
+00:38:01,290 --> 00:38:05,490
+ايوة هذا المطلوب الأول مطلوب التاني بقول لو كان ال
+
+360
+00:38:05,490 --> 00:38:09,030
+a بدو يساوي ال inverse show that أن ال determinant
+
+361
+00:38:09,030 --> 00:38:14,670
+لل a بدو يساوي زائد أو ناقص واحد بسيطة جدا خلينا
+
+362
+00:38:14,670 --> 00:38:20,460
+مع المطلوب الأول بدي أحاول أدور على مصوفةلو ضربت
+
+363
+00:38:20,460 --> 00:38:25,940
+في نفسي يطلع مين عندي مصفوفة الوحدة حد فيكم بتقدر
+
+364
+00:38:25,940 --> 00:38:28,480
+تجيبلي مصفوفة نظامها اتنين في اتنين مابتداش كتير
+
+365
+00:38:28,480 --> 00:38:36,140
+يعني اغششك اكتر القطر الرئيسي أسفارا يلا ضل عليكي
+
+366
+00:38:36,140 --> 00:38:41,020
+عددين بس مصفوفة نظامها اتنين في اتنين و القطر
+
+367
+00:38:41,020 --> 00:38:46,620
+الرئيسي أسفارا بدي لو ضربت تطلع مصفوفة الوحدة
+
+368
+00:39:14,950 --> 00:39:16,550
+تلاتة و تلت تلاتة و تلت تلت تلت تلت تلت تلت تلت
+
+369
+00:39:18,130 --> 00:39:23,410
+بنفع أربعة و رابعة بنفع خمسة و خمس يبجى هاي مش
+
+370
+00:39:23,410 --> 00:39:28,410
+مصفف تينهاد صار ملاي .. إيجاداش ملايين عدد لانهاء
+
+371
+00:39:28,410 --> 00:39:32,270
+من المصففات و ليس .. بس من ده اتكد ان كلامنا هذا
+
+372
+00:39:32,270 --> 00:39:37,450
+صح ولا لأ يبجى انا الاول اقتراح كان عند الطلبات
+
+373
+00:39:37,450 --> 00:39:45,750
+اللي هم يأتي بيداخد المصففة Zero اتنين نص Zeroمش
+
+374
+00:39:45,750 --> 00:39:47,970
+شايف لما اعطاك القدرة ياسي واحد يقعد تلات اتنين و
+
+375
+00:39:47,970 --> 00:39:54,050
+نص الان بدي اضربها في نفسها يبقى zero اتنين نص
+
+376
+00:39:54,050 --> 00:40:01,270
+zero النتج يساوي الصف الأول في العمود الأول بواحد
+
+377
+00:40:01,270 --> 00:40:07,350
+الصف الأول في العمود التاني بزيرو الصف التاني في
+
+378
+00:40:07,350 --> 00:40:11,910
+العمود الأول بزيرو الصف التاني في العمود الثاني
+
+379
+00:40:11,910 --> 00:40:19,250
+بواحداللي هي الـ identity matrix اللي عندنا يبقى
+
+380
+00:40:19,250 --> 00:40:23,950
+هيجيبنا لهياش مصفوفة اتنين هذا بنفعله التلاتة اه
+
+381
+00:40:23,950 --> 00:40:29,930
+بنفعله الأربعة الخمسة اذا بقوله in general يبقى
+
+382
+00:40:29,930 --> 00:40:40,050
+باجي بقوله in general for any real number
+
+383
+00:40:41,660 --> 00:40:46,500
+مثلًا K for
+
+384
+00:40:46,500 --> 00:40:54,920
+any real number K we have يبقى لو جيت قلت Zero K
+
+385
+00:40:54,920 --> 00:41:05,300
+واحد على K Zero في Zero K واحد على K Zero يبقى
+
+386
+00:41:05,300 --> 00:41:11,010
+الناتج واحد زيرو زيرو واحديبقى جبتله مش مصففتين،
+
+387
+00:41:11,010 --> 00:41:16,050
+جبتله مليارات المصففات، شيل كده و حط أي رقم عدى
+
+388
+00:41:16,050 --> 00:41:19,870
+الـ0، يبقى ايش قولت ان انا ساوي الـ0 for any real
+
+389
+00:41:19,870 --> 00:41:24,890
+number كده، لا يساوي الـ0، ضروري مايساويش ان انا
+
+390
+00:41:24,890 --> 00:41:29,360
+ساوي الـ0، بصي كلامنا مش صحيحيبقى بالناشي يساوي
+
+391
+00:41:29,360 --> 00:41:34,060
+zero يبقى بصير كلامنا يعني استبعد السفر وحطي موجة
+
+392
+00:41:34,060 --> 00:41:37,360
+بسالب اللي بدك إياه يبقى بصير كلامنا هذا ما قاله
+
+393
+00:41:37,360 --> 00:41:41,540
+صح على طول اللي هو المطلوب الأول من المسألة
+
+394
+00:41:41,540 --> 00:41:46,220
+المطلوب الثاني بيقول لو كان ال A في ال A بده يساوي
+
+395
+00:41:46,220 --> 00:41:51,300
+ال A inverse بيبين لي أن ال determinant لل A بده
+
+396
+00:41:51,300 --> 00:41:57,390
+يساوي واحد وكأنه بيقولاستبعدني اللي هو من ال
+
+397
+00:41:57,390 --> 00:42:03,070
+determinant لل A inverse صحيح ولا لأ بقوله بسيطة
+
+398
+00:42:03,070 --> 00:42:07,670
+احنا عندنا نمر بيه انا عند ال A بده يساوي ال A
+
+399
+00:42:07,670 --> 00:42:11,670
+inverse مش
+
+400
+00:42:11,670 --> 00:42:18,990
+رأيك تخلص من المعكوس هذامظرف في ايش؟ في ايه؟ يبقى
+
+401
+00:42:18,990 --> 00:42:27,370
+هدف يعطيني ان ايه في ايه يبقى ايه في ايه يبقى درفة
+
+402
+00:42:27,370 --> 00:42:33,430
+من جهة الشمال في ايه يبقى معناته ايه في ايه يبقى
+
+403
+00:42:33,430 --> 00:42:39,870
+ايهالـ Identity Matrix يبقى
+
+404
+00:42:39,870 --> 00:42:45,310
+بيصير عندي الـ determinant للـ A في الـ A بده
+
+405
+00:42:45,310 --> 00:42:51,390
+يساوي ال determinant لمصفوفة الوحدة I حسب خواص ال
+
+406
+00:42:51,390 --> 00:42:56,490
+determinant يبقى هذا determinant للـ Aفي الـ
+
+407
+00:42:56,490 --> 00:43:01,990
+determinant للـ a بده يساوي ال determinant لمصوفة
+
+408
+00:43:01,990 --> 00:43:08,590
+الواحدة هذا معناه ان ال determinant لل a لكل تربيع
+
+409
+00:43:08,590 --> 00:43:13,010
+بده يساوي قداش ال determinant لمصوفة الواحدة واحدة
+
+410
+00:43:13,010 --> 00:43:17,030
+لو أخدنا الجدر التربيع إلى الطرفين يبقى بيصير ال
+
+411
+00:43:17,030 --> 00:43:22,510
+determinant لل a يساوي ازايد او ناقص واحدة اظن وهو
+
+412
+00:43:22,510 --> 00:43:28,560
+المطلوبيبقى هذول أربع أسئلة متوالية و كلهم أسئلة
+
+413
+00:43:28,560 --> 00:43:33,740
+نظرية موجودة عندك في الكتاب 12 و 13 و 14 و 15 وهي
+
+414
+00:43:33,740 --> 00:43:40,380
+حللنا لك الأربع أسئلة النظرية ولا عذر لك بعد ذلك
+
+415
+00:43:40,380 --> 00:43:45,200
+طبعا احنا قولنا ال exercises اتنين اتناشطة ناكل
+
+416
+00:43:45,200 --> 00:43:49,140
+مسائل عليهم اللي هو واحد تلاتة خمسة سبعة و من عشر
+
+417
+00:43:49,140 --> 00:43:54,300
+لخمستاشروالـ exercise من واحد لتمانية مش هيك تمام
+
+418
+00:43:54,300 --> 00:44:00,940
+تمام يبقى على هيك يكون انتهى هذا ال section اللي
+
+419
+00:44:00,940 --> 00:44:08,700
+هو section اتنين اتناش وبنتهيه ينتهي chapter اتنين
+
+420
+00:44:08,700 --> 00:44:14,520
+والمرة الجاية بدنا نتيجي مفتحين ومخكوا صاحي ونظيف
+
+421
+00:44:14,520 --> 00:44:20,680
+مشان نبدأ chapter تلاتةاللي بتكلم عن vector spaces
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2347aa84c8211a0ad77bbb0816ff37cbb1ccf1b3
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg.srt
@@ -0,0 +1,1490 @@
+1
+00:00:19,340 --> 00:00:23,660
+بالله الرحمن الرحيم لازلنا في نفس الـ section تبع
+
+2
+00:00:23,660 --> 00:00:28,740
+المرة الماضية وهو Kramer's rule في نهاية هذا الـ
+
+3
+00:00:28,740 --> 00:00:33,940
+section حضرتنا نظرية النظرية بتتحدث عن الـ
+
+4
+00:00:33,940 --> 00:00:38,540
+homogeneous system فبتقول لي معاياتي لو كان عند الـ
+
+5
+00:00:38,540 --> 00:00:44,580
+homogeneous system Ax يساوي 0 في N من المعادلات و
+
+6
+00:00:44,580 --> 00:00:50,020
+N من المجاهيل يبقى في هذه الحالة هذا الـ system له 
+
+7
+00:00:50,020 --> 00:00:53,920
+non-trivial solution إذا كان الـ determinant لـ A
+
+8
+00:00:53,920 --> 00:00:57,700
+بده يساوي zero طبعا احنا بالنسبة للهوموجينيوس
+
+9
+00:00:57,700 --> 00:01:01,460
+السابقة نقول إن ماعنديش إلا أحد أمرين، يا إما في
+
+10
+00:01:01,460 --> 00:01:06,360
+الحل الصفري فقط، يا إما في عدد لا نهائي من
+
+11
+00:01:06,360 --> 00:01:12,400
+الحلول الممكنة عالميا على الحل الصفري لأن عندما لا
+
+12
+00:01:12,400 --> 00:01:16,520
+يوجد لدي إلا الحل الصفري ولا يوجد لدي عدد لا نهائي
+
+13
+00:01:16,520 --> 00:01:20,660
+من الحلول بقول والله إذا كان الـ determinant للـ A
+
+14
+00:01:20,660 --> 00:01:25,100
+محدد الـ A يساوي Zero معناته عندي عدد لا نهائي من
+
+15
+00:01:25,100 --> 00:01:30,280
+الحلول الـ determinant لا يساوي Zero يبقى ماعنديش
+
+16
+00:01:30,280 --> 00:01:34,990
+إلا الحل الصفري يبقى بالنسبة للـ Homogeneous System
+
+17
+00:01:34,990 --> 00:01:39,830
+يا بنات إذا المحدد لا يساوي Zero تبع مصفوفة
+
+18
+00:01:39,830 --> 00:01:44,470
+المعاملات، لا يوجد عندي إلا الحل الصفري أما إذا
+
+19
+00:01:44,470 --> 00:01:50,930
+كان المحدد يساوي Zero لمصفوفة المعاملات فعندي عدد
+
+20
+00:01:50,930 --> 00:01:57,000
+لا نهائي من الحلول بناخد مثال على ذلك بيقول determine
+
+21
+00:01:57,000 --> 00:02:03,180
+all values هتلي كل القيم تبع المقدار الثابت C بحيث
+
+22
+00:02:03,180 --> 00:02:09,100
+أن الـ system التالي has none trivial solution and
+
+23
+00:02:09,100 --> 00:02:13,380
+then find all such solution يعني بعد ما تجيبلي
+
+24
+00:02:13,380 --> 00:02:19,210
+قيمة C بدك تروح تجيبلي حل هذا الـ system طبعا إيش
+
+25
+00:02:19,210 --> 00:02:23,870
+بقول هنا جالي non-trivial solution يعني بدي قد إيش
+
+26
+00:02:23,870 --> 00:02:30,970
+قيمة C اللي بتخليه non-trivial يعني بدي الـ determinant
+
+27
+00:02:30,970 --> 00:02:35,370
+لـ A هسويه بالـ Zero وروح نحل هذا
+
+28
+00:02:35,370 --> 00:02:41,210
+الكلام إذا احنا هنجي على الـ system of linear
+
+29
+00:02:41,210 --> 00:02:46,450
+equations هذا ونجي نحل هذا الـ system بعد ما نتقل
+
+30
+00:02:46,450 --> 00:02:50,890
+... لكن هذا بنا نحله بعد ما نجيب قيمة C تمام؟ يبقى
+
+31
+00:02:50,890 --> 00:02:55,850
+باجي بقوله الحل كتالة الـ System has non-trivial
+
+32
+00:02:55,850 --> 00:03:00,970
+solution يبقى
+
+33
+00:03:00,970 --> 00:03:13,550
+هنا since بما أن الـ System star has non-trivial
+
+34
+00:03:13,550 --> 00:03:15,450
+solution
+
+35
+00:03:23,670 --> 00:03:26,430
+Determinant لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم 
+
+36
+00:03:26,430 --> 00:03:27,670
+بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero لـ A
+
+37
+00:03:27,670 --> 00:03:28,590
+بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero
+
+38
+00:03:28,590 --> 00:03:30,010
+لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ
+
+39
+00:03:30,010 --> 00:03:31,310
+Zero لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء
+
+40
+00:03:31,310 --> 00:03:32,910
+الـ Zero لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم
+
+41
+00:03:32,910 --> 00:03:35,590
+بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero لـ A
+
+42
+00:03:35,590 --> 00:03:43,870
+بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero
+
+43
+00:03:43,870 --> 00:03:48,170
+لـ A بيقوم
+
+44
+00:03:48,170 --> 00:03:54,160
+بإعطاء هذا لازم يساوي قد إيش؟ بده يساوي zero هذا بده
+
+45
+00:03:54,160 --> 00:03:59,220
+يعطينا بنروح نفك المحدد هذا بنات باستخدام عناصر أي
+
+46
+00:03:59,220 --> 00:04:04,140
+صف أو أي عمود فلو رحت فاكرته باستخدام العمود
+
+47
+00:04:04,140 --> 00:04:08,720
+الثالث لإنه في الصفر نتالب نشتغل طولتين الشغل مش 
+
+48
+00:04:08,720 --> 00:04:15,100
+الشغل كامل يبقى بروح بقول له هذا عندنا C في مين في
+
+49
+00:04:15,100 --> 00:04:20,100
+المحدد أصغر منظر اللي بدأشته بصفه عموده بصير تلاتة
+
+50
+00:04:20,100 --> 00:04:26,960
+ناقص اثنين يبقى في تلاتة ناقص اثنين ناقص Zero في
+
+51
+00:04:26,960 --> 00:04:33,760
+محدده Zero نجي اللي بعده زائد واحد في نشطة بصفه
+
+52
+00:04:33,760 --> 00:04:40,920
+وعموده يبقى سالب واحد سالب ستة يبقى سالب واحد سالب
+
+53
+00:04:40,920 --> 00:04:45,420
+ستة كل هذا الكلام بدو يساوي مين بدو يساوي Zero إذا
+
+54
+00:04:45,420 --> 00:04:51,700
+صار أن هذا C ناقص سبعة بده يساوي Zero هذا معناته
+
+55
+00:04:51,700 --> 00:04:57,460
+أن C قد إيش تساوي سبعة إذا لو كان عندنا C تساوي سبعة
+
+56
+00:04:57,460 --> 00:05:04,760
+بيكون عندنا Non-trivial solution قال هنا ههه بجيت
+
+57
+00:05:04,760 --> 00:05:09,980
+السؤال and then find all such solutions ولما تجيب
+
+58
+00:05:09,980 --> 00:05:13,900
+قيمة C هاتلي ما هو الشكل الحالي اللي هو بيجيبلي
+
+59
+00:05:13,900 --> 00:05:19,100
+عدد لا نهائي من الحلول يبقى بدنا نروح نحل الـ system
+
+60
+00:05:19,100 --> 00:05:25,140
+هذا بأي طريقة من الطرق التي سبقت دراستها اتعودنا
+
+61
+00:05:25,140 --> 00:05:29,580
+هذا أن نحله الـ homogeneous system بواسطة المصوفة
+
+62
+00:05:29,580 --> 00:05:35,600
+الموسعة أو echelon form يبقى بداجي اقوله هنا هذه
+
+63
+00:05:35,600 --> 00:05:46,830
+المصفوفة اللي عندي العناصر تبعها 1 2 c 3 -1 0 إلى
+
+64
+00:05:46,830 --> 00:05:55,750
+أقصى 2 1 1 بنجيب ونضيف الـ constants اللي هم
+
+65
+00:05:55,750 --> 00:05:59,590
+الثلاثة اللي عندنا يبقى في هذه الحالة بقول هذه
+
+66
+00:05:59,590 --> 00:06:06,990
+بدنا نعمل الهمياتي سالب ثلاثة R واحد بنضيفها ل
+
+67
+00:06:06,990 --> 00:06:14,690
+R اثنين وبعدين اثنين ار واحد اثنين ار ثلاثة بنحصل
+
+68
+00:06:14,690 --> 00:06:19,450
+على الشكل التالي الصف الأول زي ما هو واحد اثنين C
+
+69
+00:06:19,450 --> 00:06:24,730
+الصف الثاني بيصير Zero سالب تلاتة في اثنين بسالب
+
+70
+00:06:24,730 --> 00:06:31,010
+ستة وسالب واحد بيصير سالب سبعة سالب تلاتة C هنا
+
+71
+00:06:31,010 --> 00:06:36,920
+سالب تلاتة C هنا بده يصير عندنا Zero اثنين في اثنين
+
+72
+00:06:36,920 --> 00:06:45,020
+بأربعة واحد خمسة وهنا اثنين ضربنا اثنين C باثنين C
+
+73
+00:06:45,020 --> 00:06:55,240
+زائد واحد وهذا كله Zero Zero Zero تمام؟ الآن بقدر
+
+74
+00:06:55,240 --> 00:07:00,200
+أخلي هذا الرقم اللي عندي كده ... نخليه واحد صحيح
+
+75
+00:07:00,200 --> 00:07:04,780
+لما نخليه واحد صحيح يبقى بدي أضرب كله في سالب سبعة
+
+76
+00:07:04,780 --> 00:07:12,220
+يبقى ... في حكم ... إيش فيه؟ مش سامع مين اللي بتحكي،
+
+77
+00:07:12,220 --> 00:07:16,300
+اتوريني ... اه اتفضلي اه
+
+78
+00:07:18,230 --> 00:07:24,170
+لازم نعوض عنها سبعة يا بنات هذه هنا سبعة صحيح بنا
+
+79
+00:07:24,170 --> 00:07:30,730
+نستخدمها وهذه هنا سبعة إذا بدنا نعدل الكلام اللي
+
+80
+00:07:30,730 --> 00:07:38,190
+احنا جايليه هذا كت ليه طبعا احنا ضربنا الصف الأول
+
+81
+00:07:38,190 --> 00:07:43,150
+في سالب تلاتة وبنضيفه للصف التالي يبقى سالب تلاتة
+
+82
+00:07:43,150 --> 00:07:48,950
+في سبعة بسالب واحد وعشرين يبقى سالب واحد وعشرين
+
+83
+00:07:48,950 --> 00:07:54,400
+هضربنا في اثنين أربعة عشر واحد اللي هي خمسة عشر يبقى
+
+84
+00:07:54,400 --> 00:08:01,980
+الآن بيجي ناخد من سالب سبعة قارئ اثنين يبقى هذا
+
+85
+00:08:01,980 --> 00:08:08,000
+بتصير المصوفة على الشكل التالي واحد اثنين سبعة
+
+86
+00:08:08,000 --> 00:08:16,680
+زيرو هنا زيرو وهنا واحد وهنا تلاتة وهنا زيرو و
+
+87
+00:08:16,680 --> 00:08:25,460
+بالمرة ناخد كمان خمسة R تلاتة وهذا كمان خمسة R
+
+88
+00:08:25,460 --> 00:08:31,580
+تلاتة يبقى هذا بده يعطينا كمان Zero واحد وهنا
+
+89
+00:08:31,580 --> 00:08:37,210
+تلاتة وهنا Zero الشكل اللي عندنا هذا تمام؟ يبقى
+
+90
+00:08:37,210 --> 00:08:43,370
+هذا المصير تاخد الشكل التالي بدي أضرب الصف الثاني
+
+91
+00:08:43,370 --> 00:08:50,450
+في سالب وأضيفه فوق وتحت يبقى السالب R أو سالب
+
+92
+00:08:50,450 --> 00:09:01,120
+اثنين سالب اثنين R اثنين to R one وبعد ذلك سالب R2
+
+93
+00:09:01,120 --> 00:09:08,240
+to R3 نحصل على ما يأتي الآن هذه واحدة زي ما هي و
+
+94
+00:09:08,240 --> 00:09:16,040
+هنا سالب اثنين مع اثنين بـ 0 سالب اثنين في تلاتة سالب ستة وسبعة ليه
+
+95
+00:09:16,040 --> 00:09:21,620
+يبقى الواحد وهنا Zero وهنا Zero واحد تلاتة Zero
+
+96
+00:09:21,990 --> 00:09:28,430
+وهنا 00000 مش هيك لأننا ضربنا فيه سالب وضفناه كله
+
+97
+00:09:28,430 --> 00:09:33,150
+بيصير Zero يبقى الـ system بالشكل هذا يبقى الـ system
+
+98
+00:09:33,150 --> 00:09:37,090
+اللي عندنا الـ star الأصلي يبقى بدي بقوله the
+
+99
+00:09:37,090 --> 00:09:43,250
+system star is equivalent
+
+100
+00:10:00,320 --> 00:10:07,320
+ماعنديش إلا معادلتين في ثلاثة مجاهيل إذا لا يمكن حل
+
+101
+00:10:07,320 --> 00:10:12,020
+هذا الـ system إلا بإعطاء قيمة لأحد المجاهيل
+
+102
+00:10:12,020 --> 00:10:19,600
+الثلاثة ونأتي بقيمة المجهولين الآخرين إذا لو جيت
+
+103
+00:10:19,600 --> 00:10:30,320
+هنا قلت مثلا if x3 يساوي مثلا سالب a حطيت x3 يساوي
+
+104
+00:10:30,320 --> 00:10:38,700
+سالب a الـ X1 بيصير كده يا جماعة؟ A والـ X2 بيصير
+
+105
+00:10:38,700 --> 00:10:44,560
+ثلاثة A لما أضع هذه بالسالب A بيصير X1 بيصير A وإذا
+
+106
+00:10:44,560 --> 00:10:47,620
+أضع هذه بالسالب A بيصير سالب تلاتة A وإذا أضعها على
+
+107
+00:10:47,620 --> 00:10:54,280
+الشجرة الثانية بيصير تلاتة A يبقى سار The solution
+
+108
+00:10:56,960 --> 00:11:11,120
+The system A star is X1 و X2 و X3 بده يساوي X1
+
+109
+00:11:11,120 --> 00:11:20,650
+طلعناها بـ A و X2 بـ 3A و X3 بـ -A بهذا الشكل ما عنديش
+
+110
+00:11:20,650 --> 00:11:26,210
+قيود على A إذا هذا يعتبر عدد لا نهائي من الحلول
+
+111
+00:11:26,210 --> 00:11:30,070
+الجادمة تكون قيمة A تكون مع أنها مشكلة في هذه
+
+112
+00:11:30,070 --> 00:11:36,730
+الحالة يبقى بدنا نيجي لـ exercises اثنين أحد عشر
+
+113
+00:11:36,730 --> 00:11:44,250
+المسائل واحد وثلاثة ومن سبعة لغاية اثنا عشر
+
+114
+00:11:46,540 --> 00:11:51,620
+على هيك بكون انتهى هذا الـ section ولم يبقى أمامنا
+
+115
+00:11:51,620 --> 00:11:56,420
+إلا الـ section الأخير اللي هو الـ section 212
+
+116
+00:12:09,590 --> 00:12:15,030
+يبقى بالذات يليه section اثنين اثنا عشر اللي هو the
+
+117
+00:12:15,030 --> 00:12:19,190
+inverse of a matrix
+
+118
+00:12:26,460 --> 00:12:32,280
+Inverse of a matrix يعني معكوس المصوفة طبعا هنعطي
+
+119
+00:12:32,280 --> 00:12:37,860
+تعريف لمعكوس المصوفة وبعد ما نعطي التعريف بنتسأل
+
+120
+00:12:37,860 --> 00:12:43,260
+هل المعكوس هذا موجود لأي مصفوفة والله موجود لبعض
+
+121
+00:12:43,260 --> 00:12:51,150
+المصوفات ولبعض الآخر لأ طبعا مش كل مصفوفة لها معكوس
+
+122
+00:12:51,150 --> 00:12:56,050
+وإنما المصوفة اللي لها معكوس فقط هي المصوفة
+
+123
+00:12:56,050 --> 00:13:03,230
+المحددها لا يساوي Zero لذا المصوفة المحددها لا
+
+124
+00:13:03,230 --> 00:13:07,590
+يساوي Zero يبقى المعكوس existence ليش؟ هذا ما
+
+125
+00:13:07,590 --> 00:13:13,320
+سنعرفه بعد قليل إن شاء الله تعالى يبقى بدنا نضع
+
+126
+00:13:13,320 --> 00:13:20,140
+تعريف لمعكوس المصفوفة definition بيقول
+
+127
+00:13:20,140 --> 00:13:29,400
+لذا N by N matrix A المصفوفة لنظام N في N has an
+
+128
+00:13:29,400 --> 00:13:36,540
+inverse matrix has an inverse matrix
+
+129
+00:13:40,240 --> 00:13:49,000
+فإذا كان الـ A في الـ B يساوي الـ B في الـ A يساوي الـ
+
+130
+00:13:49,000 --> 00:13:58,720
+identity matrix IN remark الـ
+
+131
+00:13:58,720 --> 00:14:10,870
+matrix A الـ matrix A has an inverse has an Inverse
+
+132
+00:14:10,870 --> 00:14:18,290
+هديله الرمز A وفوقها سالب واحد if and only if الـ
+
+133
+00:14:18,290 --> 00:14:26,210
+determinant للـ A لا يساوي Zero نأخذ
+
+134
+00:14:26,210 --> 00:14:33,670
+أول نظرية على هذا الموضوع theorem بتقول let الـ A بـ
+
+135
+00:14:38,070 --> 00:14:56,890
+an n by n matrix if there exists a matrix B such
+
+136
+00:14:56,890 --> 00:15:01,450
+that الـ
+
+137
+00:15:01,450 --> 00:15:08,650
+A في الـ B بده يساوي الـ identity matrix I N بعد ذلك
+
+138
+00:15:08,650 --> 00:15:15,530
+الـ B في الـ A بيكون يساوي الـ Identity Matrix I N
+
+139
+00:15:15,530 --> 00:15:23,410
+وبعد ذلك الـ B بيكون يساوي A inverse
+
+140
+00:15:35,480 --> 00:15:57,820
+أظن أن هذا الشجة انتهى هنا منها خلاص وين
+
+141
+00:15:57,820 --> 00:16:02,860
+وصلت الورقة اللي بتلف؟ كل واحدة علمت من اللي قعدت
+
+142
+00:16:02,860 --> 00:16:16,860
+علي اسمها كل واحدة أشرة تجب على اسمها هنا طيب
+
+143
+00:16:16,860 --> 00:16:20,800
+نرجع لـ section 212 وهو آخر section موجود في هذا الـ
+
+144
+00:16:20,800 --> 00:16:25,700
+chapter بتحدث عن معكوس المصوفة بدأ نعطي تعريف
+
+145
+00:16:25,700 --> 00:16:31,120
+لمعكوس المصوفة ومن ثم نروح نلاقي وقت إيش المعكوس
+
+146
+00:16:31,120 --> 00:16:36,310
+هذا يكون موجود دائما وأبدا بعدين بقول لو كان عندي
+
+147
+00:16:36,310 --> 00:16:43,130
+n by n matrix A هذه لها معكوس B إذا تحقق ما يأتي
+
+148
+00:16:43,130 --> 00:16:47,950
+جيت على المصوفة A ضربت من اليمين طلعت مصوفة الواحدة
+
+149
+00:16:47,950 --> 00:16:52,010
+ضربت من الشمال في هذا المعكوس طلعت main مصوفة
+
+150
+00:16:52,010 --> 00:16:56,760
+الواحدة يعني أن لو ادعيت إنه B هذه معكوس لازم
+
+151
+00:16:56,760 --> 00:16:59,720
+إذا ضربت في A من اليمين أو ضربت في A من
+
+152
+00:16:59,720 --> 00:17:04,880
+الشمال بدو يعطيني مصفوفة الوحدة إن ما طلعش ... بدو
+
+153
+00:17:04,880 --> 00:17:08,060
+يعطيني مصفوفة الوحدة إن ما طلعش هذا الكلام يبقى
+
+154
+00:17:08,060 --> 00:17:12,960
+المصفوفة B هذه ماهياش معكوس المصوفة طبعا طرحنا سؤال
+
+155
+00:17:12,960 --> 00:17:17,780
+قبل قليل قلنا كل مصفوفة لها معكوس الإجابة كانت مش
+
+156
+00:17:17,780 --> 00:17:22,390
+كل المصوفات لها معكوس المعكوس الريمارك هذا بتقول الـ
+
+157
+00:17:22,390 --> 00:17:28,990
+matrix A لها المعكوس A وفوقها سالب واحد مش اه وسالب
+
+158
+00:17:28,990 --> 00:17:34,650
+واحد هذا رمز يدل على معكوس المصوفة وليس يساوي واحد
+
+159
+00:17:34,650 --> 00:17:39,990
+على A لأن ماعندناش حاجة اسمها قسمة مصوفات مش
+
+160
+00:17:39,990 --> 00:17:45,760
+عندنا في علم المصوفات حاجة اسمها قسمة مصوفات يبقى
+
+161
+00:17:45,760 --> 00:17:51,720
+الـ A أس سالب واحد يدل على معكوس المصوفة
+
+162
+00:17:51,720 --> 00:17:56,920
+وليس A أس سالب واحد تمام؟ يبقى هذا رمز يدل على
+
+163
+00:17:56,920 --> 00:18:02,160
+معكوس المصوفة يبقى المعكوس هذا موجود إذا كان
+
+164
+00:18:02,160 --> 00:18:07,920
+المحدد لا يساوي Zero والعكس لو كان المحدد لا يساوي
+
+165
+00:18:07,920 --> 00:18:12,710
+Zero يبقى المعكوس ماله؟ موجود طبعا ليش هذا الكلام
+
+166
+00:18:12,710 --> 00:18:17,690
+لا يساوي Zero بعد قليل هنقول لك ليش إن شاء الله طيب
+
+167
+00:18:17,690 --> 00:18:21,650
+بقول let a,b,n,n by n matrix نظرية جالي إذا
+
+168
+00:18:21,650 --> 00:18:26,430
+وجدنا نلاقي matrix B بحيث أن الـ A في الـ B بدو
+
+169
+00:18:26,430 --> 00:18:31,630
+يساوي الـ identity matrix يبقى automatic لازم يكون
+
+170
+00:18:31,630 --> 00:18:36,250
+B في A بدو يساوي الـ identity matrix وبالتالي B
+
+171
+00:18:36,250 --> 00:18:43,430
+تبعنا هذه هي مين؟ هي معكوس المصفوفة A يبقى B هي
+
+172
+00:18:43,430 --> 00:18:48,870
+عبارة عن inverse بدنا
+
+201
+00:21:47,550 --> 00:21:54,200
+أنا قلت له خذ لي هنا الـ a في الـ c شوف اللي بالله كده
+
+202
+00:21:54,200 --> 00:22:00,720
+بتطلع هذه بقول له اه هذه بدها تساوي a في الـ c main
+
+203
+00:22:00,720 --> 00:22:07,700
+عندي لـ b في الـ a صحيح ولا لأ السؤال هو خاصية الـ
+
+204
+00:22:07,700 --> 00:22:12,260
+associative صحيحة على المصفوفات ولا لأ خاصية الدمج
+
+205
+00:22:12,260 --> 00:22:18,620
+صحيحة يبقى هذا الكلام بده يساوي a b في الـ main في الـ
+
+206
+00:22:18,620 --> 00:22:24,670
+a طبعا أنا عندي معطيات أن الـ A B قد ايش ساوي الـ
+
+207
+00:22:24,670 --> 00:22:33,470
+identity هذا معناه ان الـ identity matrix في الـ A A
+
+208
+00:22:33,470 --> 00:22:38,330
+B احنا قلنا A C بده يساوي كذا هذا بده يعطينا مين؟
+
+209
+00:22:38,640 --> 00:22:42,540
+هذا الكلام
+
+210
+00:22:42,540 --> 00:22:47,420
+بده يساوي الـ identity matrix في الـ A طب الـ
+
+211
+00:22:47,420 --> 00:22:51,080
+identity matrix لو ضربتها في أي مصفوفة ايش الناتج؟
+
+212
+00:22:51,080 --> 00:22:58,340
+نفس المصفوفة يبقى هذا بده يعطيني الـ A يبقى يا بنات
+
+213
+00:22:58,340 --> 00:23:04,070
+ايش صار عندي؟ إن الـ A في الـ C بده يساوي الـ A هي
+
+214
+00:23:04,070 --> 00:23:11,750
+اللي طلعت منه مظبوط هذا معناه ان الـ a في الـ c ناقص
+
+215
+00:23:11,750 --> 00:23:16,790
+الـ a بده يساوي كده؟ Zero طبعا هذه المصفوفة الصفرية
+
+216
+00:23:16,790 --> 00:23:21,550
+مش العنصر الصفري يعني هذه الـ zero اللي مطاولة
+
+217
+00:23:21,550 --> 00:23:27,250
+بالشكل هذا هذه المصفوفة الصفرية سؤال بنقدر نأخذ
+
+218
+00:23:27,250 --> 00:23:32,590
+عامل مشترك من هذه المعادلة يبقى ايش بيصير عندنا؟
+
+219
+00:23:32,590 --> 00:23:38,490
+أي عامل مشترك بيظل C ناقص كده؟ ناقص واحد
+
+220
+00:23:41,650 --> 00:23:46,990
+ناقص الـ identity matrix مش واحد يبقى ناقص الـ
+
+221
+00:23:46,990 --> 00:23:52,110
+identity matrix ولا ايه و هذا الكلام بده يساوي مين؟
+
+222
+00:23:52,110 --> 00:23:58,190
+بده يساوي زي ما ولا ايه لو كان واحد هل بقدر أضيف
+
+223
+00:23:58,190 --> 00:24:03,380
+الواحد لأي مصفوفة؟ ولو كان واحد كان قلنا هذه يبقى
+
+224
+00:24:03,380 --> 00:24:07,160
+هذه بدها تساوي Zero أو هذه بدها تساوي Zero صحيح
+
+225
+00:24:07,160 --> 00:24:11,800
+ولا لا؟ إذا بصير الـ C ناقص للواحد تساوي Zero يبقى
+
+226
+00:24:11,800 --> 00:24:15,880
+المصفوفة C تساوي Zero صحيح هذا الكلام؟ أو تساوي
+
+227
+00:24:15,880 --> 00:24:20,700
+واحد واحد number رقم مش مصفوفة يبقى ليس صحيح يبقى
+
+228
+00:24:20,700 --> 00:24:25,280
+لما نأخذ عامل مشترك في حالة المصفوفة بدل الواحد في
+
+229
+00:24:25,280 --> 00:24:30,250
+العملية الشغل العادي بيصير الـ identity matrix تمام
+
+230
+00:24:30,250 --> 00:24:35,390
+تمام يبقى توصلنا إلى أن الكلام اللي عندنا طيب
+
+231
+00:24:35,390 --> 00:24:40,410
+احنا عندنا يا بنات ان الـ a inverse exist و الـ
+
+232
+00:24:40,410 --> 00:24:47,170
+determinant لا يمكن أن يساوي zero تمام يبقى معنى
+
+233
+00:24:47,170 --> 00:24:52,330
+هذا الكلام ان المصفوفة لا يمكن أن تساوي zero يبقى
+
+234
+00:24:52,330 --> 00:24:57,370
+مين اللي بده يساوي zero الـ C ناقص الـ I أو بمعنى
+
+235
+00:24:57,370 --> 00:25:02,830
+آخر من معنى آخر بدي أجيب لك بطريقة أخرى لو ضربت
+
+236
+00:25:02,830 --> 00:25:08,370
+الطرفين في الـ a inverse من جهة اليمين يبقى بيصير
+
+237
+00:25:08,370 --> 00:25:17,150
+عندي الـ a inverse a في الـ c ناقص الـ I كله بده يساوي
+
+238
+00:25:17,150 --> 00:25:24,890
+الـ a inverse في الـ zero مظبوط؟ طيب الـ a في الـ a
+
+239
+00:25:24,890 --> 00:25:29,760
+inverse شو بتعطينا هذه؟ مصفوفة الوحدة الـ identity
+
+240
+00:25:29,760 --> 00:25:33,280
+الـ identity matrix لما نضربها في أي مصفوفة ايش
+
+241
+00:25:33,280 --> 00:25:38,300
+بيعطينا نفس المصفوفة مظبوط طبعا يا بنات لما أقول I
+
+242
+00:25:38,300 --> 00:25:44,200
+كله I in هذه كله I in زي ما هي ماشي معانا I in
+
+243
+00:25:44,200 --> 00:25:51,800
+يبقى هذا معناه الـ identity matrix I in في C ناقص
+
+244
+00:25:51,800 --> 00:25:58,010
+الـ I in كله بده يساوي مين؟ المصفوفة الصفرية هذا
+
+245
+00:25:58,010 --> 00:26:05,370
+معناه ان الـ C ناقص I N بده يساوي قدر؟ له Zero يبقى
+
+246
+00:26:05,370 --> 00:26:13,650
+الـ C بدها تساوي المصفوفة I M من هي الـ C؟ B في A
+
+247
+00:26:13,650 --> 00:26:19,430
+يبقى هذا معناه ان B في A بده يساوي الـ identity
+
+248
+00:26:19,430 --> 00:26:24,580
+matrix as in و هو المطلوب؟ بيبدوا يساووا الـ
+
+249
+00:26:24,580 --> 00:26:28,720
+identity بيبدوا
+
+250
+00:26:28,720 --> 00:26:31,920
+يساوي الـ identity بيبدوا يساووا الـ identity بيبدوا
+
+251
+00:26:31,920 --> 00:26:34,120
+يساوي الـ identity بيبدوا يساووا الـ identity بيبدوا
+
+252
+00:26:34,120 --> 00:26:37,840
+يساووا الـ identity بيبدوا يساووا الـ identity بيبدوا
+
+253
+00:26:37,840 --> 00:26:37,900
+يساووا الـ identity بيبدوا يساووا الـ identity بيبدوا
+
+254
+00:26:37,900 --> 00:26:40,600
+يساووا الـ identity بيالـ A في B بديه يساوي الـ
+
+255
+00:26:40,600 --> 00:26:45,880
+Identity and الـ B في الـ A بديه يساوي الـ
+
+256
+00:26:45,880 --> 00:26:51,440
+Identity Matrix اللي هو I N حسب الـ Definition هذا
+
+257
+00:26:51,440 --> 00:26:58,440
+بدي يعطينا أنه بيبدأ يساوي الـ A inverse يعني هي
+
+258
+00:26:58,440 --> 00:27:05,070
+معكوس المصفوفة A طب خليني أسأل السؤال التالي هل يمكن
+
+259
+00:27:05,070 --> 00:27:12,450
+المصفوفة أن يكون لها أكثر من معكوس؟ يعني كل المصفوف
+
+260
+00:27:12,450 --> 00:27:18,470
+معكوسين، تلاتة، أربعة، خمسة؟ يعني معكوسا محيدا، بس
+
+261
+00:27:18,470 --> 00:27:22,850
+بدنا نثبت صحة هذا الكلام، يبقى هدف أن نحطه على
+
+262
+00:27:22,850 --> 00:27:25,510
+صيغة النظرية التالية
+
+263
+00:27:56,110 --> 00:27:59,970
+لو كانت A معكوسة
+
+264
+00:28:02,270 --> 00:28:14,630
+الـ B هذه is the unique inverse of A نظرية مرة
+
+265
+00:28:14,630 --> 00:28:21,550
+ثانية بقول ليش؟ لو كان الـ A مصفوفة مربعة نظامها N
+
+266
+00:28:21,550 --> 00:28:27,150
+في N وكان B هو معكوس الـ A then B is the unique
+
+267
+00:28:27,150 --> 00:28:33,170
+inverse of A يبقى B هي المعكوس الوحيد لإيه؟ unique
+
+268
+00:28:33,170 --> 00:28:39,390
+inverse يبقى المعكوس الوحيد للمصفوفة A يعني المصفوفة
+
+269
+00:28:39,390 --> 00:28:45,190
+A لا يوجد لها إلا معكوس وحيد واحد فقط لا غير طب
+
+270
+00:28:45,190 --> 00:28:50,950
+نثبت هذا الكلام نثبته كيف؟ بروح بفرض ان في عندي
+
+271
+00:28:50,950 --> 00:28:57,470
+معكوسين للمصفوفة A و بروح بثبت ان هذان المعكوسين
+
+272
+00:28:57,470 --> 00:29:04,990
+متساويان والله ان هذين المعكوسين متساويان مظبوط
+
+273
+00:29:04,990 --> 00:29:09,670
+طبعا انها بتنصب اسم و بترفع خبرها مش هيك وان هذين
+
+274
+00:29:09,670 --> 00:29:15,690
+المعكوسين متساويان يبقى بنرجع ايه هنا تاني يبقى أنا
+
+275
+00:29:15,690 --> 00:29:19,550
+بدي أفرض انه عندي معكسين هو قال لي مين قال لي B
+
+276
+00:29:19,550 --> 00:29:23,430
+يبقى أنا بدي اقوله بدي افترض انه B و C معكسين
+
+277
+00:29:23,430 --> 00:29:34,650
+للمصفوفة من A يبقى هنا assume that ان الـ B and
+
+278
+00:29:34,650 --> 00:29:38,810
+الـ C are two
+
+279
+00:29:41,570 --> 00:29:52,570
+inverses of the matrix A then
+
+280
+00:29:52,570 --> 00:29:58,390
+مدالها دول معكوسين طبقا لهذا التعريف يبقى بيصير
+
+281
+00:29:58,390 --> 00:30:05,610
+عنها A في B بده يساوي B في A بده يساوي
+
+282
+00:30:05,610 --> 00:30:12,970
+identity matrix وطبعا كون النظام N في N يبقى الـ I
+
+283
+00:30:12,970 --> 00:30:23,030
+N وفي نفس الوقت الـ A C بده يساوي C في A بده يساوي
+
+284
+00:30:23,030 --> 00:30:25,970
+الـ identity matrix I N
+
+285
+00:30:29,230 --> 00:30:34,270
+بدي اثبت ايه يا بنات؟ بدي اثبت ان المصفوفة A بدي
+
+286
+00:30:34,270 --> 00:30:40,130
+اثبت ان المصفوفة B هي نفس المصفوفة من C يبقى بدجي
+
+287
+00:30:40,130 --> 00:30:49,330
+اقول له consider خذ لي المصفوفة B ايش رأيك الـ B
+
+288
+00:30:49,330 --> 00:30:56,650
+هذه؟ مش هي عبارة عن B في الـ identity صح ولا لأ؟
+
+289
+00:30:56,650 --> 00:31:04,090
+صح؟ طيب هذه بدها تساوي الـ identity بقدر اشيلها و
+
+290
+00:31:04,090 --> 00:31:09,350
+اكتب بدالها اي واحدة من هدول صح يبقى هذه الـ
+
+291
+00:31:09,350 --> 00:31:13,510
+identity بدها احط مثلا الـ AC
+
+292
+00:31:15,520 --> 00:31:20,180
+طب ليش ما أخذتش ولا واحدة من هدول؟ بقول اه لأنه أنا
+
+293
+00:31:20,180 --> 00:31:25,780
+بدي اثبت انه B تساوي C، اذا بدي ادخل C معانا، مشان
+
+294
+00:31:25,780 --> 00:31:31,940
+نقدر نوصل لها، يبقى انا شيلت الـ identity matrix I N
+
+295
+00:31:31,940 --> 00:31:38,570
+و حطيت بدلها I Cالامن خاصية الـ associative على
+
+296
+00:31:38,570 --> 00:31:47,580
+المصفوفات يبقى هادي عبارة عن B في المصفوفة C بترجع
+
+297
+00:31:47,580 --> 00:31:53,480
+هنا الـ B في A بقد ايش بالـ identity matrix I N في
+
+298
+00:31:53,480 --> 00:31:58,700
+المصفوفة C الـ identity matrix لما نضربها في أي
+
+299
+00:31:58,700 --> 00:32:03,840
+مصفوفة بيطلع مين؟ نفس المصفوفة يبقى بناء عليه
+
+300
+00:32:03,840 --> 00:32:09,500
+صارت B تساوي مين؟ تساوي C يبقى معنى هذا الكلام انه
+
+301
+00:32:09,500 --> 00:32:16,110
+ماعنديش اللي A معكوس واحد فقط لا غير يبقى So B is
+
+302
+00:32:16,110 --> 00:32:24,230
+the unique inverse of the matrix A يبقى هنا So B
+
+303
+00:32:24,230 --> 00:32:31,330
+is the unique inverse
+
+304
+00:32:31,330 --> 00:32:36,550
+of
+
+305
+00:32:39,910 --> 00:32:48,730
+The Matrix A هو المعكوس الوحيد الذي لا يوجد غيره
+
+306
+00:32:52,370 --> 00:33:00,030
+طيب السؤال هو كيف يمكن إيجاد المعكوس لمصفوفة ما؟
+
+307
+00:33:00,030 --> 00:33:04,770
+احنا تكلمنا و حطينا العنوان معكوس المصفوفة حتى الآن
+
+308
+00:33:04,770 --> 00:33:09,050
+قلنا بس وجود المعكوس موجود والله مش موجود و
+
+309
+00:33:09,050 --> 00:33:13,310
+واحد ايش و موحيد والله مش واحد هذا الكلام لكن كيف
+
+310
+00:33:13,310 --> 00:33:18,310
+نجد هذا المعكوس لسه مش عارفين لذلك هروح نحط السؤال
+
+311
+00:33:18,310 --> 00:33:21,330
+التالي السؤال هو
+
+312
+00:33:24,770 --> 00:33:40,670
+to find the inverse for the n by n matrix A الشكل
+
+313
+00:33:40,670 --> 00:33:47,170
+لأن أنا الاجابة في أكثر من طريقة بالداخل الـ first
+
+314
+00:33:47,170 --> 00:33:55,140
+method الطريقة الأولى لإيجاد المعكوس خطوتين لثالث
+
+315
+00:33:55,140 --> 00:34:06,380
+لهم الخطوة الأولى write the augmented matrix
+
+316
+00:34:06,380 --> 00:34:18,740
+اكتب المصفوفة الموسعة a ومعها مين؟ مصفوفة الوحدة نمر
+
+317
+00:34:18,740 --> 00:34:22,380
+ة اتنين use
+
+318
+00:34:25,130 --> 00:34:32,910
+row echelon form use
+
+319
+00:34:32,910 --> 00:34:40,050
+row echelon form to write to
+
+320
+00:34:40,050 --> 00:34:45,710
+write the
+
+321
+00:34:45,710 --> 00:34:51,270
+matrix ايه
+
+322
+00:34:51,270 --> 00:35:10,070
+مع الـ I N A مع الـ I N in the form في الشكل I N و
+
+323
+00:35:10,070 --> 00:35:19,850
+بعدين B then B اللي بتطلع بتكون هي معكوس المصفوفة
+
+324
+00:35:19,850 --> 00:35:23,190
+A نعطي مثال
+
+325
+00:35:38,720 --> 00:35:41,220
+معكوس المصفوفة
+
+326
+00:35:44,950 --> 00:35:57,290
+1 3 -1 0 1 2 -1 0 8 بالشكل اللي عندنا
+
+327
+00:36:00,630 --> 00:36:07,630
+أنا عندي مصفوفة مربعة A عدد صفوفها N و عدد أعمدتها
+
+328
+00:36:07,630 --> 00:36:12,850
+N بقول كيف بدك تجيب المعكوس لهذه المصفوفة بقول له
+
+329
+00:36:12,850 --> 00:36:19,410
+خطوتان لثالث لهما الخطوة الأولى write the
+
+330
+00:36:19,410 --> 00:36:23,950
+augmented matrix A و I in يعني بده احط المصفوفة A
+
+331
+00:36:23,950 --> 00:36:29,770
+وجانبها مصفوفة الـ واحدة اعتبرهم كلهم مصفوفة موسعة
+
+332
+00:36:29,770 --> 00:36:33,910
+مصفوفة واحدة الخط هذا بس مشان يحد فاصل ما بين
+
+333
+00:36:33,910 --> 00:36:38,240
+الاثنين لكن كلها مصفوفة واحدة الخطوة الثانية هي
+
+334
+00:36:38,240 --> 00:36:44,220
+استخدام الـ row echelon form لحوّل الـ A على اليمين
+
+335
+00:36:44,220 --> 00:36:48,240
+والـ I on الشمال يعني أنا بدي أخلي الـ identity
+
+336
+00:36:48,240 --> 00:36:53,200
+matrix في جهة الشمال وهذه A بس ماتضلش A هتتلخبط
+
+337
+00:36:53,200 --> 00:36:58,740
+هذه لما تتلخبط هسميها B دي بدي اكتبها على شكل I N
+
+338
+00:36:58,740 --> 00:37:04,050
+و B كمصفوفة موسعة B اللي بتطلع هذي بتكون هي مين هي
+
+339
+00:37:04,050 --> 00:37:09,870
+معكوس المصفوفة واذا مش مصدقة فبنضرب الاثنين في بعض
+
+340
+00:37:09,870 --> 00:37:19,230
+ولا بزم النتيج يطلع identity matrix المعكوس
+
+341
+00:37:19,230 --> 00:37:22,990
+المصفوفة اللي قدامنا هذه إذا أنا بدي أطبق له
+
+342
+00:37:22,990 --> 00:37:27,010
+الخطوتين اللي قلنا عليهم يبقى بدجي أخذ له الـ
+
+343
+00:37:27,010 --> 00:37:33,930
+augmented matrix اللي هي الـ A مع مين؟ مع المصفوفة
+
+344
+00:37:33,930 --> 00:37:39,310
+I يبقى هذا الكلام بده يساوي هذه المصفوفة هاي واحد
+
+345
+00:37:39,310 --> 00:37:45,170
+هاي تلاتة هاي سالب واحد Zero واحد اتنين سالب واحد
+
+346
+00:37:45,170 --> 00:37:49,590
+Zero تمانية هو Y خاطر المصفوفة الواحدة واحد من
+
+347
+00:37:49,590 --> 00:37:56,480
+نفس نظامها Zero واحد Zero Zero Zero واحد اعمل
+
+348
+00:37:56,480 --> 00:38:00,840
+اللي بدك اياه هي رياضيا بحيث اخلي مصفوفة الوحدة في هذا
+
+349
+00:38:00,840 --> 00:38:06,400
+المكان وهذه تنتقل بأرقام جديدة لوين؟ الى اليمين
+
+350
+00:38:06,400 --> 00:38:12,570
+كويس يبقى مشان هيك أنا بدي هذا يكون قد ايش بدي Zero
+
+351
+00:38:12,570 --> 00:38:17,770
+اذا حضر بالصف الاول او اضيف الصف الاول للصف الثالث
+
+352
+00:38:17,770 --> 00:38:26,070
+يبقى باجي بقوله هذا مباشرة R1 to R3 ليش؟ لإن R2
+
+353
+00:38:26,070 --> 00:38:32,730
+جاهز مش محتاج حاجة يبقى هاي واحد تلاتة سالب واحد و
+
+354
+00:38:32,730 --> 00:38:38,780
+واحد Zero Zero هيقفلنا نجي لبعده زي ما هو Zero واحد
+
+355
+00:38:38,780 --> 00:38:44,500
+اتنين Zero واحد Zero اضفنا إضافة يبقى هنا Zero
+
+356
+00:38:44,500 --> 00:38:51,600
+وهنا تلاتة تمام؟ و اضفنا يبقى هنا سبعة و اضفنا يبقى
+
+357
+00:38:51,600 --> 00:38:57,060
+هنا واحد وهنا Zero وهنا واحد لانه إضافة ما سويتش
+
+358
+00:38:57,060 --> 00:39:06,260
+اشياء واضحة زين؟ في أي تسويلة؟ طيب نكمل الحين ان
+
+359
+00:39:06,260 --> 00:39:11,900
+هذا الشخص يأتي للـ leading اللي عندنا هنا بتخلي
+
+360
+00:39:11,900 --> 00:39:15,880
+اللي تحته Zero واللي فوقه Zero يبقى بده اضربه بسالب
+
+361
+00:39:15,880 --> 00:39:21,180
+تلاتة و اضيفه للصف الاول و للصف الثالث يبقى هنا
+
+362
+00:39:21,180 --> 00:39:34,100
+سالب تلاتة R2 سالب تلاتة R2 to R1 and to R3 بيصير
+
+363
+00:39:34,100 --> 00:39:39,650
+بالشكل التالي طبعا هنا واحد وهنا Zero و لما ضربت في
+
+364
+00:39:39,650 --> 00:39:45,610
+سالب تلاتة بيصير سالب ستة وسالب واحد سالب سبعة
+
+365
+00:39:45,610 --> 00:39:51,910
+سالب تلاتة بيصير هنا واحد زي ما هي وهنا سالب
+
+366
+00:39:51,910 --> 00:39:58,580
+تلاتة مظبوط يا بنات؟ وهذا Zero زي ما هو نجي هذا
+
+367
+00:39:58,580 --> 00:40:05,400
+Zero واحد اتنين Zero واحد Zero الان بدي اضيفه للصف
+
+368
+00:40:05,400 --> 00:40:11,720
+اللي بعده يبقى Zero Zero سالب ستة بيضل هنا واحد و
+
+369
+00:40:11,720 --> 00:40:17,660
+بعد هيك هنا بيضل واحد زي ما هو وهنا ضربنا في سالب
+
+370
+00:40:17,660 --> 00:40:24,080
+تلاتة بيصير هنا سالب تلاتة وهنا واحد زي ما هو
+
+371
+00:
+
+401
+00:43:48,530 --> 00:43:54,570
+في الماتريكس A في الماتريكس
+
+402
+00:43:54,570 --> 00:44:07,710
+A من الـ Cofactor من الـ Cofactor من الـ Cofactor
+
+403
+00:44:07,710 --> 00:44:11,890
+من A i j
+
+404
+00:44:11,890 --> 00:44:16,090
+وهو IN
+
+405
+00:44:17,540 --> 00:44:32,360
+replace استبدل a i j by a i j بدي أسوي السلب
+
+406
+00:44:32,360 --> 00:44:39,860
+واحد مرفوع للأس واحد زائد j في ال minor اللي هو m
+
+407
+00:44:39,860 --> 00:44:40,900
+i j
+
+408
+00:44:45,820 --> 00:44:52,680
+هذه الخطوة الأولى الخطوة الثانية take the
+
+409
+00:44:52,680 --> 00:45:00,120
+transpose of
+
+410
+00:45:00,120 --> 00:45:07,200
+the resulting matrix 
+
+411
+00:45:07,200 --> 00:45:13,620
+resulting matrix in part one
+
+412
+00:45:16,180 --> 00:45:24,620
+part one and denoted
+
+413
+00:45:24,620 --> 00:45:28,080
+it
+
+414
+00:45:28,080 --> 00:45:41,840
+by B and denoted it by B أعطيها الرمز B خطوة
+
+415
+00:45:41,840 --> 00:45:54,750
+التالتة والأخيرة find A inverse from the formula من
+
+416
+00:45:54,750 --> 00:46:04,730
+الصيغة A inverse يساوي واحد على ال determinant لل A
+
+417
+00:46:04,730 --> 00:46:08,790
+هذا كله في المصوفة B
+
+418
+00:46:18,720 --> 00:46:19,280
+ماذا نحتاج؟
+
+419
+00:46:28,860 --> 00:46:32,620
+يبقى باختصار بدنا نعمل ثلاث خطوات الخطوة الأولى
+
+420
+00:46:32,620 --> 00:46:38,420
+بدي أشيل كل a ij و أضع كوفكتور تبعه ناقص واحد من
+
+421
+00:46:38,420 --> 00:46:44,360
+a ij في ال m ij الخطوة الثانية بدي أجيب مدور هذه
+
+422
+00:46:44,360 --> 00:46:50,300
+المصوفة التي نتجت في الخطوة الأولى خطوة تالتة
+
+423
+00:46:50,300 --> 00:46:53,240
+المصوفة التي حصلت عليها بدي أضربها في واحد على 
+
+424
+00:46:53,240 --> 00:46:59,320
+محدد المصوفة وهذا يتفق مع الكلام الذي قبل قليل ليش
+
+425
+00:46:59,320 --> 00:47:05,680
+محدد المصوفة لا يساوي zero لأن لو كان المحدد يساوي
+
+426
+00:47:05,680 --> 00:47:09,470
+zero هل أقدر أجيب هذا المعكوس؟ يبقى فيش مكان يبقى
+
+427
+00:47:09,470 --> 00:47:14,650
+هذا الكلام الذي ادعيناه قبل قليل الآن السبب في أن
+
+428
+00:47:14,650 --> 00:47:19,930
+المحدد لا يساوي zero يبقى بدي أخل المعكوس exist
+
+429
+00:47:19,930 --> 00:47:25,490
+وإلا لو كان المحدد يساوي zero لأصبح المعكوس غير
+
+430
+00:47:25,490 --> 00:47:27,310
+موجود أعطيكم العافية 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..771cfe44000959a24ae5ed55e699b6c67c891372
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg_postprocess.srt
@@ -0,0 +1,1720 @@
+1
+00:00:19,340 --> 00:00:23,660
+بالله الرحمن الرحيم لازلنا في نفس ال section تبع
+
+2
+00:00:23,660 --> 00:00:28,740
+المرة الماضية وهو kramer's rule في نهاية هذا ال
+
+3
+00:00:28,740 --> 00:00:33,940
+section حضرتنا نظرية النظرية بتتحدث عن ال
+
+4
+00:00:33,940 --> 00:00:38,540
+homogeneous system فبتقول لي معاياتي لو كان عند ال
+
+5
+00:00:38,540 --> 00:00:44,580
+homogeneous system Ax يساوي 0 في N من المعادلات و
+
+6
+00:00:44,580 --> 00:00:50,020
+N من المجاهينيبقى في هذه الحالة هذا الـ system له
+
+7
+00:00:50,020 --> 00:00:53,920
+non-trivial solution إذا كان الـ determinant لإيه
+
+8
+00:00:53,920 --> 00:00:57,700
+بده ساوي zero طبعا أحنا بالنسبة للهومولينيا
+
+9
+00:00:57,700 --> 00:01:01,460
+السابقة نقول إن ماعنديش إلا أحد أمرين، يا إما في
+
+10
+00:01:01,460 --> 00:01:06,360
+الحل الصفري فقط لغير، يا إما في عدد لنهائي من
+
+11
+00:01:06,360 --> 00:01:12,400
+الحلول المجتملة عالمياعلى الحل الصفري لان عندما لا
+
+12
+00:01:12,400 --> 00:01:16,520
+يوجد لدي إلا الحل الصفري و لا يوجد لدي عدد لنهائي
+
+13
+00:01:16,520 --> 00:01:20,660
+من الحلول بقول و الله إذا كان ال determinant لل A
+
+14
+00:01:20,660 --> 00:01:25,100
+محدد ال A يساوي Zero معناته عندي عدد لنهائي من
+
+15
+00:01:25,100 --> 00:01:30,280
+الحلول ال determinant لا يساوي Zero يبقى ماعنديش
+
+16
+00:01:30,280 --> 00:01:34,990
+إلا الحل الصفرييبقى بالنسبة للـ Homogeneous System
+
+17
+00:01:34,990 --> 00:01:39,830
+يا بنات إذا المحدد لا يساوي Zero تبع مصفوفة
+
+18
+00:01:39,830 --> 00:01:44,470
+المعاملات، لا يوجد عندى إلا الحل الصفري أما إذا
+
+19
+00:01:44,470 --> 00:01:50,930
+كان المحدد يساوي Zero لمصفوفة المعاملات فعندي عدد
+
+20
+00:01:50,930 --> 00:01:57,000
+لنهائي من الحلولبناخد مثال على ذلك بيقول determine
+
+21
+00:01:57,000 --> 00:02:03,180
+all values هتلي كل القيم تبع المقدار الثابت C بحيث
+
+22
+00:02:03,180 --> 00:02:09,100
+ان ال system التالي has none trivial solution and
+
+23
+00:02:09,100 --> 00:02:13,380
+then find all such solution يعني بعد ما تجيبلي
+
+24
+00:02:13,380 --> 00:02:19,210
+قيمة C بدك تروح تجيبلي حل هذا ال systemطبعا اش
+
+25
+00:02:19,210 --> 00:02:23,870
+بقول هنا جالي non-trivial solution يعني بدي قداش
+
+26
+00:02:23,870 --> 00:02:30,970
+قيمة C اللي بتخليه non-trivialيعني بدي determinant
+
+27
+00:02:30,970 --> 00:02:35,370
+ايه هسويه بالـ main هسويه بالـ zero و روح نحل هذا
+
+28
+00:02:35,370 --> 00:02:41,210
+الكلام اذا احنا هنجي على ال system of linear
+
+29
+00:02:41,210 --> 00:02:46,450
+equations هذا و نجي نحل هذا ال system بعد ما نتقل
+
+30
+00:02:46,450 --> 00:02:50,890
+.. لكن هذا بنا نحله بعد ما نجيب قيمة C تمام؟ يبقى
+
+31
+00:02:50,890 --> 00:02:55,850
+باجي بقوله الحل كتالةالـ System has non-trivial
+
+32
+00:02:55,850 --> 00:03:00,970
+solution يبقى
+
+33
+00:03:00,970 --> 00:03:13,550
+هنا since بما أن الـ System star has non-trivial
+
+34
+00:03:13,550 --> 00:03:15,450
+solution
+
+35
+00:03:23,670 --> 00:03:26,430
+Determinant لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم
+
+36
+00:03:26,430 --> 00:03:27,670
+بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero لـ A
+
+37
+00:03:27,670 --> 00:03:28,590
+بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero
+
+38
+00:03:28,590 --> 00:03:30,010
+لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ
+
+39
+00:03:30,010 --> 00:03:31,310
+Zero لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء
+
+40
+00:03:31,310 --> 00:03:32,910
+الـ Zero لـ A بيقوم بإعطاء الـ Zero لـ A بيقوم
+
+41
+00:03:32,910 --> 00:03:35,590
+بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero لـ A
+
+42
+00:03:35,590 --> 00:03:43,870
+بيقوم بإعطاء الـ Zero لـ A بيقوم بإعطاء الـ Zero
+
+43
+00:03:43,870 --> 00:03:48,170
+لـ A بيقوم
+
+44
+00:03:48,170 --> 00:03:54,160
+بإعهذا لازم يساوي قداش؟ بده يساوي zero هذا بده
+
+45
+00:03:54,160 --> 00:03:59,220
+يعطينا بنروح نفك المحدد هذا بنات باستخدام عناصر أي
+
+46
+00:03:59,220 --> 00:04:04,140
+صف أو أي عمود فلو رحت فاكرته باستخدام العمودي
+
+47
+00:04:04,140 --> 00:04:08,720
+الثالث لإنه في الصفر نتالب نشتغل طولتين الشغل مش
+
+48
+00:04:08,720 --> 00:04:15,100
+الشغل كاملايبقى بروح بقول له هذا عندنا C في مين في
+
+49
+00:04:15,100 --> 00:04:20,100
+المحدد أصغر منظر اللي بدأشته بصفه عموده بصير تلاتة
+
+50
+00:04:20,100 --> 00:04:26,960
+ناقص اتنين يبقى في تلاتة ناقص اتنين ناقص Zero في
+
+51
+00:04:26,960 --> 00:04:33,760
+محدده Zero نجي اللي بعده زائد واحدفى نشطة بصفه
+
+52
+00:04:33,760 --> 00:04:40,920
+وعموده يبقى سالب واحد سالب ستة يبقى سالب واحد سالب
+
+53
+00:04:40,920 --> 00:04:45,420
+ستة كل هذا الكلام بدى يساوي مين بدى يساوي Zero اذا
+
+54
+00:04:45,420 --> 00:04:51,700
+صار ان هذا C ناقص سبعة بدى يساوي Zero هذا معناته
+
+55
+00:04:51,700 --> 00:04:57,460
+ان C جداش تساوي سبعةإذا لو كان عندنا C تساوي سبعة
+
+56
+00:04:57,460 --> 00:05:04,760
+بيكون عندنا Non-trivial solution قال هنا ههه بجيت
+
+57
+00:05:04,760 --> 00:05:09,980
+السؤال and then find all such solutions ولمّا تجيب
+
+58
+00:05:09,980 --> 00:05:13,900
+قيمة C هاتلي ما هو الشكل الحالي اللي هو بيجيبلي
+
+59
+00:05:13,900 --> 00:05:19,100
+عدد لنهائي منالحلول يبقى بدنا نروح نحل ال system
+
+60
+00:05:19,100 --> 00:05:25,140
+هذا بأي طريقة من الطرق التي سبقت دراستها اتعودنا
+
+61
+00:05:25,140 --> 00:05:29,580
+هذا انحله ال homogeneous system بواسطة المصوفة
+
+62
+00:05:29,580 --> 00:05:35,600
+المواسعة او echelon four يبقى بداجي اقوله هنا هذه
+
+63
+00:05:35,600 --> 00:05:46,830
+المصوفة اللي عنديالعناصر تبعتها 1 2 c 3-1 0 إلى
+
+64
+00:05:46,830 --> 00:05:55,750
+نقص 2 1 1بنجيب ونضيف الـ consonants اللي هم
+
+65
+00:05:55,750 --> 00:05:59,590
+التلاتة اللي عندنا يبقى في هذه الحالة بقول هذه
+
+66
+00:05:59,590 --> 00:06:06,990
+بدنا نعمل الهمياتي سالب تلاتة R واحد بضيف فلامين ل
+
+67
+00:06:06,990 --> 00:06:14,690
+R اتنينو بعدين اتنين ار واحد اتنين ار ثلاثة بنحصل
+
+68
+00:06:14,690 --> 00:06:19,450
+على الشكل التالف الصف الأول زي ما هو واحد اتنين C
+
+69
+00:06:19,450 --> 00:06:24,730
+الصف التاني بيصير Zero سالب تلاتة في اتنين بسالب
+
+70
+00:06:24,730 --> 00:06:31,010
+ستة و سالب واحد بيصير سالب سبعة سالب تلاتة C هنا
+
+71
+00:06:31,010 --> 00:06:36,920
+سالب تلاتة Cهنا بده يصير عندنا zero اتنين في اتنين
+
+72
+00:06:36,920 --> 00:06:45,020
+باربع واحد خمسة وهنا اتنين ضربنا اتنين C باتنين C
+
+73
+00:06:45,020 --> 00:06:55,240
+زائد واحد وهذا كله Zero Zero Zeroتمام؟ الآن بقدر
+
+74
+00:06:55,240 --> 00:07:00,200
+أخلي هذا الرقم اللي عندي كده .. نخليه واحد صحيح
+
+75
+00:07:00,200 --> 00:07:04,780
+لما نخليه واحد صحيح يبقى بدي أضرب كله في سالب سبع
+
+76
+00:07:04,780 --> 00:07:12,220
+يبقى .. في حكم .. إيش فيه؟ مش سامع مين اللي بتحكي،
+
+77
+00:07:12,220 --> 00:07:16,300
+اتوريني .. اه اتفضلي اه
+
+78
+00:07:18,230 --> 00:07:24,170
+لازم نعوض عنها سبعة يا بنات هذه هنا سبعة صحيح بنا
+
+79
+00:07:24,170 --> 00:07:30,730
+نستخدمها وهذه هنا سبعة اذا بدنا نعدل الكلام اللي
+
+80
+00:07:30,730 --> 00:07:38,190
+احنا جايليه هذا كت ليهطبعا احنا ضربنا الصف الأول
+
+81
+00:07:38,190 --> 00:07:43,150
+في سالب تلاتة و بنضيف ولا التالي يبقى سالب تلاتة
+
+82
+00:07:43,150 --> 00:07:48,950
+في سبعة بسالب واحد وعشرين يبقى سالب واحد وعشرين
+
+83
+00:07:48,950 --> 00:07:54,400
+هضربنا في اتنين اربعتاشر واحد اللي هي خمستاشريبقى
+
+84
+00:07:54,400 --> 00:08:01,980
+الأن بيجي ناخد من سالب سبع قاري اتنين يبقى هذا
+
+85
+00:08:01,980 --> 00:08:08,000
+بتصير المصوفة على الشكل التالي واحد اتنين سبعة
+
+86
+00:08:08,000 --> 00:08:16,680
+زيرو هنا زيرو وهنا واحد وهنا تلاتة وهنا زيروو
+
+87
+00:08:16,680 --> 00:08:25,460
+بالمرة ناخد كمان خمس R تلاتة و هذا كمان خمس R
+
+88
+00:08:25,460 --> 00:08:31,580
+تلاتة يبقى هذا بده يعطينا كمان Zero واحد و هنا
+
+89
+00:08:31,580 --> 00:08:37,210
+تلاتة و هنا Zero الشكل اللي عندنا هذاتمام؟ يبقى
+
+90
+00:08:37,210 --> 00:08:43,370
+هذا المصير تاخد الشكل التالي بدي أضرب الصف الثاني
+
+91
+00:08:43,370 --> 00:08:50,450
+في سالب و أضيفه فوق و تحت يبقى السالب R او سالب
+
+92
+00:08:50,450 --> 00:09:01,120
+اتنين سالب اتنين R اتنين to R oneو بعد ذلك سالب R2
+
+93
+00:09:01,120 --> 00:09:08,240
+to R3 نحصل على ما يأتي الآن هذه واحدة زي ما هي و
+
+94
+00:09:08,240 --> 00:09:16,040
+هنا سالب 2 مع 2 بـ 0 سالب 2 في 3 سالب 6 و 7 ليه
+
+95
+00:09:16,040 --> 00:09:21,620
+يبقى الواحد و هنا Zero و هنا Zero واحد تلاتة Zero
+
+96
+00:09:21,990 --> 00:09:28,430
+وهنا 00000 مش هيك لإننا ضربنا فيه سالب وضفناه كله
+
+97
+00:09:28,430 --> 00:09:33,150
+بصير zero يبقى ال system بالشكل هذا يبقى ال system
+
+98
+00:09:33,150 --> 00:09:37,090
+اللي عندنا ال star الأصلي يبقى بدي بقوله the
+
+99
+00:09:37,090 --> 00:09:43,250
+system star is equivalent
+
+100
+00:10:00,320 --> 00:10:07,320
+ماعنديش إلا معادلتين في ثلاثة مجاهيلإذا لا يمكن حل
+
+101
+00:10:07,320 --> 00:10:12,020
+هذا الـ system إلا بإعطاء قيمة لأحد المجاهيل
+
+102
+00:10:12,020 --> 00:10:19,600
+الثلاثة و نأتي بقيمة المجهولين الآخرين إذا لو جيت
+
+103
+00:10:19,600 --> 00:10:30,320
+هنا قلت مثلا if x3 يساوي مثلا سالب a حطيت x3 يساوي
+
+104
+00:10:30,320 --> 00:10:38,700
+سالب aالـ X1 بيصير كده يا جماعة؟ A والـ X2 بيصير
+
+105
+00:10:38,700 --> 00:10:44,560
+ثلاثة A لما أضع هذه بالسلب A بيصير X1 بيصير A وإذا
+
+106
+00:10:44,560 --> 00:10:47,620
+أضع هذه بالسلب A بيصير سلب ثلاثة A وإذا أضعها على
+
+107
+00:10:47,620 --> 00:10:54,280
+الشجرة التانية بيصير ثلاثة A يبقى سار The solution
+
+108
+00:10:56,960 --> 00:11:11,120
+The system A star is X1 و X2 و X3 بده يساوي X1
+
+109
+00:11:11,120 --> 00:11:20,650
+طلعناها بـA و X2 بـ3A و X3 بـ-A بهذا الشكلماعنديش
+
+110
+00:11:20,650 --> 00:11:26,210
+قيود على إيه إذا هذا يعتبر عدد لانهائي من الحلول
+
+111
+00:11:26,210 --> 00:11:30,070
+الجادمة تكون قيمة إيه تكون مع أنها مشكلة في هذه
+
+112
+00:11:30,070 --> 00:11:36,730
+الحالة يبقى بدنا نيجي ل exercises اتنين احداشر
+
+113
+00:11:36,730 --> 00:11:44,250
+المسائل واحد و تلاتة ومن سبعة لغاية اتناشر
+
+114
+00:11:46,540 --> 00:11:51,620
+على هيك بكون انتهى هذا ال section ولم يبقى أمامنا
+
+115
+00:11:51,620 --> 00:11:56,420
+إلا ال section الأخير اللي هو ال section 212
+
+116
+00:12:09,590 --> 00:12:15,030
+يبقى بالذات يليه section اتنين اتناش اللي هو the
+
+117
+00:12:15,030 --> 00:12:19,190
+inverse of A matrix
+
+118
+00:12:26,460 --> 00:12:32,280
+Inverse of a matrix يعني معكوس المصوفة طبعاً هنعطي
+
+119
+00:12:32,280 --> 00:12:37,860
+تعريف لمعكوس المصوفة وبعد ما نعطي التعريف بنتسأل
+
+120
+00:12:37,860 --> 00:12:43,260
+هل المعكوس هذا موجود لأي مصوفة و الله موجود لبعض
+
+121
+00:12:43,260 --> 00:12:51,150
+المصوفات و لبعض الآخر لأطبعا مش كل مصوفة لها معكوس
+
+122
+00:12:51,150 --> 00:12:56,050
+وإنما المصوفة اللي لها معكوس فقط هي المصوفة
+
+123
+00:12:56,050 --> 00:13:03,230
+المحددها لا يساوي zero لذا المصوفة المحددها لا
+
+124
+00:13:03,230 --> 00:13:07,590
+يساوي zero يبقى المعكوس existence ليش؟ هذا ما
+
+125
+00:13:07,590 --> 00:13:13,320
+سنعرفه بعد قليل ان شاء الله تعالىيبقى بدنا نضع
+
+126
+00:13:13,320 --> 00:13:20,140
+تعريف لمعكوس المصفوفة definition بيقول
+
+127
+00:13:20,140 --> 00:13:29,400
+لذا N by N matrix A المصفوفة لنظام N في N has an
+
+128
+00:13:29,400 --> 00:13:36,540
+inverse matrix has an inverse matrix
+
+129
+00:13:40,240 --> 00:13:49,000
+فإذا كان ال A في ال B سوى ال B في ال A سوى ال
+
+130
+00:13:49,000 --> 00:13:58,720
+identity matrix IN remark ال
+
+131
+00:13:58,720 --> 00:14:10,870
+matrix A ال matrix A has an inverse has anInverse
+
+132
+00:14:10,870 --> 00:14:18,290
+هدّيله الرمز A و فوقها سالب واحد if and only if ال
+
+133
+00:14:18,290 --> 00:14:26,210
+determinant للـ A لا يساوي zero نأخد
+
+134
+00:14:26,210 --> 00:14:33,670
+أول نظرية على هذا الموضوع theorem بتقول let ال A ب
+
+135
+00:14:38,070 --> 00:14:56,890
+an n by n matrix if there exists a matrix B such
+
+136
+00:14:56,890 --> 00:15:01,450
+that ال
+
+137
+00:15:01,450 --> 00:15:08,650
+A في ال B بده يساوي ال identity matrix I Nبعد ذلك
+
+138
+00:15:08,650 --> 00:15:15,530
+الـ B في الـ A بيكون ساوية الـ Identity Matrix I N
+
+139
+00:15:15,530 --> 00:15:23,410
+وبعد ذلك الـ B بيكون ساوية A انفرز
+
+140
+00:15:35,480 --> 00:15:57,820
+أظن أن هذا الشجة انتهي هنا منها خلاص وين
+
+141
+00:15:57,820 --> 00:16:02,860
+وصلت الورقة اللي بتلف؟ كل واحدة علمت من اللي قعدت
+
+142
+00:16:02,860 --> 00:16:16,860
+علي اسمهاكل واحدة أشرة تجب علي اسمها هنا طيب
+
+143
+00:16:16,860 --> 00:16:20,800
+نرجع ل section 212 وهو آخر section موجود في هذا ال
+
+144
+00:16:20,800 --> 00:16:25,700
+chapter بتحدث عن معكوث المصوفة بدأ نعطي تعريف
+
+145
+00:16:25,700 --> 00:16:31,120
+لمعكوث المصوفة ومن ثم نروح نلاقي وقت إيش المعكوث
+
+146
+00:16:31,120 --> 00:16:36,310
+هذا يكون موجود دائما و أبدافبعدين بقول لو كان عندي
+
+147
+00:16:36,310 --> 00:16:43,130
+n by n matrix A هذي لها معكوس B إذا تحقق ما يأتي
+
+148
+00:16:43,130 --> 00:16:47,950
+جيت على المصوف A ضربت من اليمين طلعت مصوف الواحدة
+
+149
+00:16:47,950 --> 00:16:52,010
+ضربت من الشمال في هذا المعكوس طلعت main مصوف
+
+150
+00:16:52,010 --> 00:16:56,760
+الواحدة يعني أنالو إدعيت إنه بيه هذه معكوس لازم
+
+151
+00:16:56,760 --> 00:16:59,720
+إذا ضربت في إيه من اليمين أو ضربت في إيه من
+
+152
+00:16:59,720 --> 00:17:04,880
+الشمال، بدي يعطيني مصوفة الوحدة إن ما طلعش .. بدي
+
+153
+00:17:04,880 --> 00:17:08,060
+يعطيني مصوفة الوحدة إن ما طلعش هذا الكلام يبقى
+
+154
+00:17:08,060 --> 00:17:12,960
+المصوفة بيه ماهياش معكوس المصوفة طبعا طرحنا سؤال
+
+155
+00:17:12,960 --> 00:17:17,780
+قبل قليل قلنا كل مصوفة لها معكوس الإجابة كانت مش
+
+156
+00:17:17,780 --> 00:17:22,390
+كل المصوفات لها معكوسالمعكوس الريمارك هذا بتقول ال
+
+157
+00:17:22,390 --> 00:17:28,990
+matrix A لها المعكوس A وفوقه سالب واحد مش اه وسالب
+
+158
+00:17:28,990 --> 00:17:34,650
+واحد هذا رمز يدل على معكوس المصوفة ولا يسوي واحد
+
+159
+00:17:34,650 --> 00:17:39,990
+على ايه لان ماعندناش حاجة اسمها قسمة مصوفات مش
+
+160
+00:17:39,990 --> 00:17:45,760
+عندنا في علم المصوفات حاجة اسمها قسمة مصوفاتيبقى
+
+161
+00:17:45,760 --> 00:17:51,720
+الـ A أفاجأو أس سالب واحد يدل على معكوس المصوفة
+
+162
+00:17:51,720 --> 00:17:56,920
+وليس A أس سالب واحد تمام؟ يبقى هذا رمز يدل على
+
+163
+00:17:56,920 --> 00:18:02,160
+معكوس المصوفة يبقى المعكوس هذا موجود إذا كان
+
+164
+00:18:02,160 --> 00:18:07,920
+المحدد لا يساوي Zero والعكس لو كان المحدد لا يساوي
+
+165
+00:18:07,920 --> 00:18:12,710
+Zero يبقى المعكوس ماله؟موجود طبعاً ليش هذا الكلام
+
+166
+00:18:12,710 --> 00:18:17,690
+لا يساوي زرع بعد قليل هنقول لك ليش ان شاء الله طيب
+
+167
+00:18:17,690 --> 00:18:21,650
+بقول little a,b,n,n by n matrix نظرية جالي إذا
+
+168
+00:18:21,650 --> 00:18:26,430
+جدرنا نلاقي matrix B بحيث أن ال A في ال B بدو
+
+169
+00:18:26,430 --> 00:18:31,630
+يساوي ال identity matrix يبقى automatic لازم يكون
+
+170
+00:18:31,630 --> 00:18:36,250
+B في A بدو يساوي ال identity matrix وبالتالي B
+
+171
+00:18:36,250 --> 00:18:43,430
+تبعتنا هذههي مين؟ هي معكوس المصفوفة A يبقى B هي
+
+172
+00:18:43,430 --> 00:18:48,870
+عبارة عن inverse بدنا نروح نثبت صحة هذه النظرية
+
+173
+00:18:48,870 --> 00:18:55,210
+يبقى أنا عندي الشغلة الأولى أنا عندي نظامها N في M
+
+174
+00:18:55,480 --> 00:19:01,800
+لو وجدت مصفوفة بي ضربتها في إيه من جهة اليمين طلع
+
+175
+00:19:01,800 --> 00:19:05,560
+ال identity؟ بدي أثبت إيه؟ إنه لو ضربتها من جهة
+
+176
+00:19:05,560 --> 00:19:10,520
+الشمال بدي أعطيني ال identity وبالتالي تحققت اللي
+
+177
+00:19:10,520 --> 00:19:17,420
+فوق وبالتالي ال بي هي معكس من إيه؟ صحيح ولا لأ؟
+
+178
+00:19:17,420 --> 00:19:18,860
+طيب نيجي لل proof
+
+179
+00:19:33,380 --> 00:19:40,890
+هل قلنا ان المعكوس موجود؟ما قلناش يبقى انا بدي
+
+180
+00:19:40,890 --> 00:19:45,550
+اثبتله ان المعكوس موجود قبل ما ابدأ اشتغل الشغل
+
+181
+00:19:45,550 --> 00:19:49,490
+اللي هو طالبه هذا بقولك اذا مشان اثبت المعكوس
+
+182
+00:19:49,490 --> 00:19:55,190
+موجود بدي اخد ال determinant للطرفين يبقى هذا بدي
+
+183
+00:19:55,190 --> 00:20:00,550
+يعطينا ان ال determinant لل A في ال B يساوي ال
+
+184
+00:20:00,550 --> 00:20:06,840
+determinant لمصفوفة الواحدة هذا بدي يعطيناهذا
+
+185
+00:20:06,840 --> 00:20:10,160
+معناه مين؟ الـ determinant لـ A في الـ determinant
+
+186
+00:20:10,160 --> 00:20:15,860
+لـ B يبقى هذا معناته الـ determinant لـ A في الـ
+
+187
+00:20:15,860 --> 00:20:20,320
+determinant لـ B بده يساوي جداش ال determinant
+
+188
+00:20:20,320 --> 00:20:21,840
+لمصوفة الوحدة؟
+
+189
+00:20:28,940 --> 00:20:35,180
+ممتاز جدا يبقى انا طلعت حصل ضرب كميتين يساوي واحد
+
+190
+00:20:35,180 --> 00:20:41,050
+صحيح واتنين are real numberهل يمكن لأحدهما أن تكون
+
+191
+00:20:41,050 --> 00:20:45,070
+zero في يوم من الأيام، ولو مرة واحدة في التاريخ،
+
+192
+00:20:45,070 --> 00:20:50,650
+ليس إمكانية يبقى هذا معناه أن ال determinant للايه
+
+193
+00:20:50,650 --> 00:20:55,530
+لا يمكن أن يساوي zero مادام حصل ضرب الأتنين بسوعة
+
+194
+00:20:55,530 --> 00:21:00,100
+صحيح يبقى أحدهم لايمكن أن يكون zeroولو كان Zero
+
+195
+00:21:00,100 --> 00:21:04,240
+لأصبح الناتج يساوي Zero طيب إذا ال determinant
+
+196
+00:21:04,240 --> 00:21:11,200
+لإيه لأ يساوي Zero معناته المعكوس ماله exist يبقى
+
+197
+00:21:11,200 --> 00:21:20,560
+هذا بدي أعطيه لك the inverse matrix لإيه inverse
+
+198
+00:21:20,560 --> 00:21:25,140
+exist exist
+
+199
+00:21:25,140 --> 00:21:35,090
+كويسأحنا بنثبت ان b في a يسوى ال identity لو رحت
+
+200
+00:21:35,090 --> 00:21:47,550
+وقلت افترضي ان عندي مصفوفة c تساوي b في a جيت
+
+201
+00:21:47,550 --> 00:21:54,200
+انا قلت له خدلي هنا ال a في cشوف اللي بالله كده
+
+202
+00:21:54,200 --> 00:22:00,720
+بتطلع هذه بقول له اه هذه بدها تساوي a في c main
+
+203
+00:22:00,720 --> 00:22:07,700
+عندي ل b في ال a صحيح ولا لأ السؤال هو خاصية ال
+
+204
+00:22:07,700 --> 00:22:12,260
+associative صحيحة على المصبوحات ولا لأ خاصية الدمج
+
+205
+00:22:12,260 --> 00:22:18,620
+صحيحة يبقى هذا الكلام بده يساوي a b في main في ال
+
+206
+00:22:18,620 --> 00:22:24,670
+aطبعا انا عندي معطيات ان الـ A B قد شو ساوي ال
+
+207
+00:22:24,670 --> 00:22:33,470
+identity هذا معناه ان ال identity matrix في ال A A
+
+208
+00:22:33,470 --> 00:22:38,330
+B احنا قولنا A C بده يساوي كذا هذا بده يعطينا مين؟
+
+209
+00:22:38,640 --> 00:22:42,540
+هذا الكلام
+
+210
+00:22:42,540 --> 00:22:47,420
+بده يساوي ال identity matrix في ال A طب ال
+
+211
+00:22:47,420 --> 00:22:51,080
+identity matrix لو ضربتها في أي مصفوفة إيش الناتج؟
+
+212
+00:22:51,080 --> 00:22:58,340
+نفس المصفوفة يبقى هذا بده يعطيني ال A يبقى يا بنات
+
+213
+00:22:58,340 --> 00:23:04,070
+إيش صار عندي؟ إن ال A في ال C بده يساوي ال Aهي
+
+214
+00:23:04,070 --> 00:23:11,750
+اللي طلعت منه مظبوط هذا معناه ان ال a في ال c ناقص
+
+215
+00:23:11,750 --> 00:23:16,790
+ال a بده يساوي كده؟ Zero طبعا هذه المصفوفة الصفرية
+
+216
+00:23:16,790 --> 00:23:21,550
+مش العنصر الصفري يعني هذه ال zero اللي مطاولة
+
+217
+00:23:21,550 --> 00:23:27,250
+بالشكل هذا هذه المصفوفة الصفرية سؤالبنقدر ناخد
+
+218
+00:23:27,250 --> 00:23:32,590
+عامل مشترك من هذه المعادلة يبقى ايش بيصير عندنا؟
+
+219
+00:23:32,590 --> 00:23:38,490
+اي عامل مشترك بيظل C نقص كده؟ نقص واحد
+
+220
+00:23:41,650 --> 00:23:46,990
+نقص ال identity matrix مش واحد يبقى ناقص ال
+
+221
+00:23:46,990 --> 00:23:52,110
+identity matrix و إلا و هذا الكلام بده يساوي مين؟
+
+222
+00:23:52,110 --> 00:23:58,190
+بده يساوي زي ما و إلا لو كان واحد هل بقدر أضيف
+
+223
+00:23:58,190 --> 00:24:03,380
+الواحد لأي مصفوفة؟ولو كان واحد كان قولنا هذه يبقى
+
+224
+00:24:03,380 --> 00:24:07,160
+هذه بدها تساوي Zero أو هذه بدها تساوي Zero صحيح
+
+225
+00:24:07,160 --> 00:24:11,800
+ولا لا؟ إذا بصير ال C نقص للواحد تساوي Zero يبقى
+
+226
+00:24:11,800 --> 00:24:15,880
+المصفوفة C تساوي Zero صحيح هذا الكلام؟ أو تساوي
+
+227
+00:24:15,880 --> 00:24:20,700
+واحد واحد number رقم مش مصفوفة يبقى ليس صحيح يبقى
+
+228
+00:24:20,700 --> 00:24:25,280
+لما ناخد عامل مشترك في حالة المصفوفة بدل الواحد في
+
+229
+00:24:25,280 --> 00:24:30,250
+العملية الشغل العادى بيصير ال identity matrixتمام
+
+230
+00:24:30,250 --> 00:24:35,390
+تمام يبقى توصلنا الى انه الكلام اللى عندنا طيب
+
+231
+00:24:35,390 --> 00:24:40,410
+احنا عندنا يا بنات ان ال a inverse exist و ال
+
+232
+00:24:40,410 --> 00:24:47,170
+determinant لا يمكن ان يساوي zero تمام يبقى معنى
+
+233
+00:24:47,170 --> 00:24:52,330
+هذا الكلام ان المصوفة لا يمكن ان تساوي zero يبقى
+
+234
+00:24:52,330 --> 00:24:57,370
+مين اللى بده يساوي zero ال C ناقص الله او بمعنى
+
+235
+00:24:57,370 --> 00:25:02,830
+اخرمن معنى آخر بدي أجيبلك بطريقة أخرى لو ضربت
+
+236
+00:25:02,830 --> 00:25:08,370
+الطرفين في a inverse من جهة الشمال يبقاش بيصير
+
+237
+00:25:08,370 --> 00:25:17,150
+عندي ال a inverse a في c minus ال I كله بده يساوي
+
+238
+00:25:17,150 --> 00:25:24,890
+ال a inverse في ال zero مظبوط؟ طيب ال a في ال a
+
+239
+00:25:24,890 --> 00:25:29,760
+inverse شو بتعطينا هذه؟مصفوفة الوحدة ال identity
+
+240
+00:25:29,760 --> 00:25:33,280
+ال identity matrix لما نضربها في أي مصفوفة ايش
+
+241
+00:25:33,280 --> 00:25:38,300
+بيعطينا نفس المصفوفة مظبوط طبعا يا بنات لما اقول I
+
+242
+00:25:38,300 --> 00:25:44,200
+كله I in هذه كله I in زي ما هي ماشي معانا I in
+
+243
+00:25:44,200 --> 00:25:51,800
+يبقى هذا معناه ال identity matrix I in في C minus
+
+244
+00:25:51,800 --> 00:25:58,010
+ال I inكله بده يساوي مين؟ المصفوفة الصفرية هذا
+
+245
+00:25:58,010 --> 00:26:05,370
+معناه ان الـC minus IN بده يساوي قدر؟ له Zero يبقى
+
+246
+00:26:05,370 --> 00:26:13,650
+الـC بدها تساوي المصفوفة IM من هي الـC؟ بي في A
+
+247
+00:26:13,650 --> 00:26:19,430
+يبقى هذا معناه ان بي في A بده يساوي ال identity
+
+248
+00:26:19,430 --> 00:26:24,580
+magical as in و هو المطلوب؟بيبدوا يسووا ال
+
+249
+00:26:24,580 --> 00:26:28,720
+identity بيبدوا
+
+250
+00:26:28,720 --> 00:26:31,920
+يسووا ال identity بيبدوا يسووا ال identity بيبدوا
+
+251
+00:26:31,920 --> 00:26:34,120
+يسووا ال identity بيبدوا يسووا ال identity بيبدوا
+
+252
+00:26:34,120 --> 00:26:37,840
+يسووا ال identity بيبدوا يسووا ال identity بيبدوا
+
+253
+00:26:37,840 --> 00:26:37,900
+يسووا ال identity بيبدوا يسووا ال identity بيبدوا
+
+254
+00:26:37,900 --> 00:26:40,600
+يسووا ال identity بيالـ A في B بديه يساوي الـ
+
+255
+00:26:40,600 --> 00:26:45,880
+Identity and الـ B في الـ A بديه يساوي الـ
+
+256
+00:26:45,880 --> 00:26:51,440
+Identity Matrix اللي هو IN حسب الـ Definition هذا
+
+257
+00:26:51,440 --> 00:26:58,440
+بدي يعطينا أنه بيبدأ يساوي الـ A inverse يعني هي
+
+258
+00:26:58,440 --> 00:27:05,070
+معكوس المصوفة Aطب خليني أسأل السؤال التالي هل يمكن
+
+259
+00:27:05,070 --> 00:27:12,450
+المصوفة أن يكون لها أكثر من معكوس؟ يعني كل المصوف
+
+260
+00:27:12,450 --> 00:27:18,470
+معكوسين، تلاتة، أربعة، خمسة؟ يعني معكوسا محيدا، بس
+
+261
+00:27:18,470 --> 00:27:22,850
+بدنا نثبت صحة هذا الكلام، يبقى هدف أن نحطه على
+
+262
+00:27:22,850 --> 00:27:25,510
+صيغة النظرية التالية
+
+263
+00:27:56,110 --> 00:27:59,970
+لو كانت A معكوسة
+
+264
+00:28:02,270 --> 00:28:14,630
+الـ B هذه is the unique inverse of A نظرية مرة
+
+265
+00:28:14,630 --> 00:28:21,550
+تانيةبقول ليش؟ لو كان الـ A مصحوفة مربعة نظامها N
+
+266
+00:28:21,550 --> 00:28:27,150
+في N وكان B هو معكوس الـ A then B is the unique
+
+267
+00:28:27,150 --> 00:28:33,170
+inverse of A يبقى B هي المعكوس الوحيد لإيه؟ unique
+
+268
+00:28:33,170 --> 00:28:39,390
+inverse يبقى المعكوس الوحيد للمصحوف A يعني المصحوف
+
+269
+00:28:39,390 --> 00:28:45,190
+A لا يوجد لها إلا معكوس وحيد واحد فقطده غير طب
+
+270
+00:28:45,190 --> 00:28:50,950
+نثبت هذا الكلام نثبته كيف بروح بفرض ان في عندي
+
+271
+00:28:50,950 --> 00:28:57,470
+معكوسين للمصوفة A و بروح بثبت ان هذان المعكوسين
+
+272
+00:28:57,470 --> 00:29:04,990
+متساويان والله ان هذين المعكوسين متساويان مظبوط
+
+273
+00:29:04,990 --> 00:29:09,670
+طبعا انها بتنصب اسم و بترفع خبرها مش هيك و ان هذين
+
+274
+00:29:09,670 --> 00:29:15,690
+المعكوسين متساويةيبقى بنرجع آية هنا تاني يبقى أنا
+
+275
+00:29:15,690 --> 00:29:19,550
+بدي أفرض أنه عندي معكسين هو قال لي مين قال لي بي
+
+276
+00:29:19,550 --> 00:29:23,430
+يبقى أنا بدي أقوله بدي أفترض أنه بي و سي معكسين
+
+277
+00:29:23,430 --> 00:29:34,650
+للمصوفة من ايه يبقى هنا assume that أن ال بي and
+
+278
+00:29:34,650 --> 00:29:38,810
+ال سي are two
+
+279
+00:29:41,570 --> 00:29:52,570
+inverses of the matrix A then
+
+280
+00:29:52,570 --> 00:29:58,390
+مدالها دول معكوسين طبقا لهذا التعريف يبقاش بده
+
+281
+00:29:58,390 --> 00:30:05,610
+يصير عنها A في B بده يساوي B في A بده يساوي
+
+282
+00:30:05,610 --> 00:30:12,970
+identity matrixوطبعاً كون النظام N في N يبقى ال I
+
+283
+00:30:12,970 --> 00:30:23,030
+N وفي نفس الوقت ال A C بده يساوي C في A بده يساوي
+
+284
+00:30:23,030 --> 00:30:25,970
+ال identity matrix I N
+
+285
+00:30:29,230 --> 00:30:34,270
+بدي أثبت إيه يا بنات؟ بدي أثبت إن المصوفة A بدي
+
+286
+00:30:34,270 --> 00:30:40,130
+أثبت إن المصوفة B هي نفس المصوفة من C يبقى بداجي
+
+287
+00:30:40,130 --> 00:30:49,330
+أقول له consider خدلي المصوفة B إيش رأيك الـ B
+
+288
+00:30:49,330 --> 00:30:56,650
+هذه؟ مش هي عبارة عن B في ال identity صح ولا لأ؟
+
+289
+00:30:56,650 --> 00:31:04,090
+صح؟طيب هذه بدها تساوي ال identity بقدر اشيلها و
+
+290
+00:31:04,090 --> 00:31:09,350
+اكتب بدالها اي واحدة من هدول صح يبقى هذه ال
+
+291
+00:31:09,350 --> 00:31:13,510
+identity بدها احط مثلا ال AC
+
+292
+00:31:15,520 --> 00:31:20,180
+طب ليش مااخدتش ولا واحدة من هدول؟ بقول اه لأنه انا
+
+293
+00:31:20,180 --> 00:31:25,780
+بدي اثبت انه B تساوي C، اذا بدي ادخل C معانا، مشان
+
+294
+00:31:25,780 --> 00:31:31,940
+نقدر نوصل لها، يبقى انا شيلت ال identity matrix IN
+
+295
+00:31:31,940 --> 00:31:38,570
+وحطيت بدلها ICالامن خاصية ال associative على
+
+296
+00:31:38,570 --> 00:31:47,580
+المصوفات يبقى هادي عبارة عن بي في المصوفة Cبترجع
+
+297
+00:31:47,580 --> 00:31:53,480
+هنا ال B في A بقداش بال identity matrix I N في
+
+298
+00:31:53,480 --> 00:31:58,700
+المصهوفة C ال identity matrix لما نضربها في أي
+
+299
+00:31:58,700 --> 00:32:03,840
+مصهوفة بيطلع مين؟ نفس المصهوفة يبقى بناءً عليه
+
+300
+00:32:03,840 --> 00:32:09,500
+صارت B تساوي مين؟ تساوي C يبقى معنى هذا الكلام انه
+
+301
+00:32:09,500 --> 00:32:16,110
+ماعنديش اللي Aمعكوس واحد فقط لا غير يبقى So P is
+
+302
+00:32:16,110 --> 00:32:24,230
+the unique inverse of the matrix A يبقى هنا So P
+
+303
+00:32:24,230 --> 00:32:31,330
+is the unique inverse
+
+304
+00:32:31,330 --> 00:32:36,550
+of
+
+305
+00:32:39,910 --> 00:32:48,730
+The Matrix A هو المعكوس الوحيد الذي لا يوجد غيره
+
+306
+00:32:52,370 --> 00:33:00,030
+طيب السؤال هو كيف يمكن إيجاد المعكوس لمصوفة ما؟
+
+307
+00:33:00,030 --> 00:33:04,770
+احنا اتكلمنا وحطينا العنوان معكوس المصوفة حتى الآن
+
+308
+00:33:04,770 --> 00:33:09,050
+قلنا بس وجود المعكوس موجود و الله مش موجود و
+
+309
+00:33:09,050 --> 00:33:13,310
+واجداش و موحيد و الله مش واحد هذا الكلام لكن كيف
+
+310
+00:33:13,310 --> 00:33:18,310
+نجد هذا المعكوس لسه مش عارفين لذلك هروح نحط السؤال
+
+311
+00:33:18,310 --> 00:33:21,330
+التالي السؤال هو
+
+312
+00:33:24,770 --> 00:33:40,670
+to find a inverse for the n by n matrix A الشكل
+
+313
+00:33:40,670 --> 00:33:47,170
+لأن أنا الاجابة في أكثر من طريقة بالداخل ال first
+
+314
+00:33:47,170 --> 00:33:55,140
+method الطريقة الأولى لإيجاد المعكوسخطوتين لثالث
+
+315
+00:33:55,140 --> 00:34:06,380
+لهم الخطوة الأولى write the argumented matrix
+
+316
+00:34:06,380 --> 00:34:18,740
+اكتب المصوفة الموسعة a ومعها مين مصوفة الوحدة نمر
+
+317
+00:34:18,740 --> 00:34:22,380
+اتنين use
+
+318
+00:34:25,130 --> 00:34:32,910
+Echelon form use
+
+319
+00:34:32,910 --> 00:34:40,050
+echelon form to write to
+
+320
+00:34:40,050 --> 00:34:45,710
+write the
+
+321
+00:34:45,710 --> 00:34:51,270
+matrix ايه
+
+322
+00:34:51,270 --> 00:35:10,070
+معالـ I N A مع ال I N in the form في الشكل I N و
+
+323
+00:35:10,070 --> 00:35:19,850
+بعدين B then B اللي بتطلع بتكون هي معكوس المصفوفة
+
+324
+00:35:19,850 --> 00:35:23,190
+A نعطي مثال
+
+325
+00:35:38,720 --> 00:35:41,220
+معكس المصفوفة
+
+326
+00:35:44,950 --> 00:35:57,290
+1 3-1 0 1 2-1 0 8 بالشكل اللي عندنا
+
+327
+00:36:00,630 --> 00:36:07,630
+أنا عندي مصوفة مربعة A عدد صفوفها N و عدد أعملاتها
+
+328
+00:36:07,630 --> 00:36:12,850
+N بقول كيف بدك تجيب المعكوس لهذه المصوفة بقوله
+
+329
+00:36:12,850 --> 00:36:19,410
+خطوتان لثالث لهماالخطوة الأولى write the
+
+330
+00:36:19,410 --> 00:36:23,950
+geometrical matrix A و I in يعني بده احط المصوفة A
+
+331
+00:36:23,950 --> 00:36:29,770
+وجانبها مصوفة ال واحدة اعتبرهم كلهم مصوفة موسعة
+
+332
+00:36:29,770 --> 00:36:33,910
+مصوفة واحدة الخط هذا بس مشان يحد فاصل ما بين
+
+333
+00:36:33,910 --> 00:36:38,240
+الاتنين لكن كلها مصوفة واحدةالخطوة التانية هي
+
+334
+00:36:38,240 --> 00:36:44,220
+استخدام الـ ocean floor لحوّل الـ A على اليمين
+
+335
+00:36:44,220 --> 00:36:48,240
+والـ I on الشمال يعني انا بدي اخلّي ال identity
+
+336
+00:36:48,240 --> 00:36:53,200
+matrix في الشجة الشمال وهذه A بس ماتضلش A هتتلخبط
+
+337
+00:36:53,200 --> 00:36:58,740
+هذه لما تتلخبط هسميها B دي بدي اكتبها على شكل I N
+
+338
+00:36:58,740 --> 00:37:04,050
+وB كمصوفة موسعةب اللي بتطلع هذي بتكون هي مين هي
+
+339
+00:37:04,050 --> 00:37:09,870
+معكوس المصوفة و اذا مش مصدقة فبنضرب التنتين في بعض
+
+340
+00:37:09,870 --> 00:37:19,230
+و لازم النتيج يطلعidentity matrix المعكوس
+
+341
+00:37:19,230 --> 00:37:22,990
+المصفوفة اللي قدامنا هذه إذا أنا بدي أطبقله
+
+342
+00:37:22,990 --> 00:37:27,010
+الخطوطين اللي قلنا عليهم يبقى بدايجي أخدله ال
+
+343
+00:37:27,010 --> 00:37:33,930
+argumentive matrix اللي هي ال A مع مين مع المصفوفة
+
+344
+00:37:33,930 --> 00:37:39,310
+I يبقى هذا الكلام بده يساويهذه المصوفة هاي واحد
+
+345
+00:37:39,310 --> 00:37:45,170
+هاي تلاتة هاي سالب واحد Zero واحد اتنين سالب واحد
+
+346
+00:37:45,170 --> 00:37:49,590
+Zero تمانية هو Y الخاطر المصوفة الواحدة واحد من
+
+347
+00:37:49,590 --> 00:37:56,480
+نفس النظامها Zero واحد Zero Zero Zero واحدأعمل
+
+348
+00:37:56,480 --> 00:38:00,840
+اللي بدك هي رياضيا بحيث أخلي مصوفة الوحدة في هذا
+
+349
+00:38:00,840 --> 00:38:06,400
+المكان وهذه تنتقل بأرقام جديدة لوين إلى اليامين
+
+350
+00:38:06,400 --> 00:38:12,570
+كويس يبقى مشان هيك أنا بدي هذا يكون جداشبدي zero
+
+351
+00:38:12,570 --> 00:38:17,770
+إذا حضر بالصف الأول أو أضيف الصف الأول للصف التالت
+
+352
+00:38:17,770 --> 00:38:26,070
+يبقى باجي بقوله هذا مباشرة R1 to R3 ليش؟ لإن R2
+
+353
+00:38:26,070 --> 00:38:32,730
+جاهز مش محتاج حاجة يبقى هاي واحد تلاتة سالب واحد و
+
+354
+00:38:32,730 --> 00:38:38,780
+واحد Zero Zero هيقفلنانجي لبعده زي ما هو Zero واحد
+
+355
+00:38:38,780 --> 00:38:44,500
+اتنين Zero واحد Zero اضفنا إضافة يبقى هنا Zero
+
+356
+00:38:44,500 --> 00:38:51,600
+وهنا تلاتة تمام؟ واضفنا يبقى هنا سبعة واضفنا يبقى
+
+357
+00:38:51,600 --> 00:38:57,060
+هنا واحد وهنا Zero وهنا واحد لأنه إضافة ماسويتش
+
+358
+00:38:57,060 --> 00:39:06,260
+أشياء واضحة زين؟ في أي تسويل؟ طيب، نكملالحين ان
+
+359
+00:39:06,260 --> 00:39:11,900
+هذا الشخص يأتي للـ leading اللي عندنا هنابتخلّي
+
+360
+00:39:11,900 --> 00:39:15,880
+اللي تحته Zero و اللي فوقه Zero يبقى بده أضربه سلب
+
+361
+00:39:15,880 --> 00:39:21,180
+تلاتة و أضيفه للصف الأول و الصف الثالث يبقى هنا
+
+362
+00:39:21,180 --> 00:39:34,100
+سالب تلاتة R2 سالب تلاتة R2 to R1 and to R3 بيصير
+
+363
+00:39:34,100 --> 00:39:39,650
+بالشكل التالي طبعا هنا واحد وهنا Zeroو لما ضربت في
+
+364
+00:39:39,650 --> 00:39:45,610
+سالب تلاتة بيصير سالب ستة و سالب واحد سالب سبعة
+
+365
+00:39:45,610 --> 00:39:51,910
+سالب تلاتة بيصير هنا واحد زي ما هي و هنا سالب
+
+366
+00:39:51,910 --> 00:39:58,580
+تلاتة مظبوط يا بنات؟وهذا zero زي ما هو نجي هذا
+
+367
+00:39:58,580 --> 00:40:05,400
+zero واحد اتنين zero واحد zero الان بده اضيفه للصف
+
+368
+00:40:05,400 --> 00:40:11,720
+اللي بعد يبقى zero zero سالب ستة بيضل هنا واحد و
+
+369
+00:40:11,720 --> 00:40:17,660
+بعد هيك هنا بيضل واحد زي ما هو و هنا ضربنا في سالب
+
+370
+00:40:17,660 --> 00:40:24,080
+تلاتة بيصير هنا سالب تلاتة و هنا واحد زي ما هو
+
+371
+00:40:26,750 --> 00:40:34,190
+الحين احنا جاهزين بدي اخلي هذا Zero واخلي هذا Zero
+
+372
+00:40:34,190 --> 00:40:40,830
+يبقى سبعة R تلاتة to R one يبقى انا بدي اعمل ما
+
+373
+00:40:40,830 --> 00:40:48,510
+ياتي سبعة R تلاتة to R one وفي نفس الوقت سالي
+
+374
+00:40:48,510 --> 00:40:55,280
+باتنين R تلاتة to R twoيبقى بيصبح هذا المصوفة على
+
+375
+00:40:55,280 --> 00:41:01,260
+الشكل التالي هذا واحد زي ما هو وماعناش مشكلة تمام؟
+
+376
+00:41:01,260 --> 00:41:08,120
+وهذا زيرو زي ما هو وهذا بيصير زيرو هلها مضربين هذا
+
+377
+00:41:08,120 --> 00:41:14,580
+في جداش قلنا؟في سبعة سبعة في واحد سبعة وواحد
+
+378
+00:41:14,580 --> 00:41:20,580
+تمانية سبعة في تلاتة سالب واحد وعشرين يبقى سالب
+
+379
+00:41:20,580 --> 00:41:26,410
+اربعة وعشرين سبعة في واحد في سبعة يبقى سبعةخلصنا
+
+380
+00:41:26,410 --> 00:41:32,650
+الصفة الأولة الان بدي اضربه في سالب اتنين واضيفه
+
+381
+00:41:32,650 --> 00:41:38,370
+فوق بصير zero و بصير هنا سالب اتنين و بصير هنا
+
+382
+00:41:38,370 --> 00:41:44,310
+سبعة لان اضربه في سالب اتنين بصير ستة واحد سبعة
+
+383
+00:41:44,310 --> 00:41:52,370
+الان سالب اتنين يبقى سالب اتنين هنا zero zero واحد
+
+384
+00:41:52,370 --> 00:42:00,020
+واحد سالب تلاتةواحد بالشكل اللي عناهأيوة يبقى ايش
+
+385
+00:42:00,020 --> 00:42:04,760
+بيقوللي الخطوة التانية استخدم الاشيلون form مشان
+
+386
+00:42:04,760 --> 00:42:09,640
+تكتب ال matrix a في ال identity المصفوفة الموسعة
+
+387
+00:42:09,640 --> 00:42:14,460
+مشان نكتب ال identity مع بي كمصفوفة موسعة اظن
+
+388
+00:42:14,460 --> 00:42:21,160
+كتبناها يبقى بي مين هي المصفوفة هذه يبقى هذا بده
+
+389
+00:42:21,160 --> 00:42:26,320
+يعطيكي the inverse matrix
+
+390
+00:42:27,970 --> 00:42:39,130
+of a is بيتساوي بيتساوي تمانية سالب اربعة وعشرين
+
+391
+00:42:39,130 --> 00:42:47,530
+وسبعة وسالب اتنين وسبعة وسالب اتنين وواحد وسالب
+
+392
+00:42:47,530 --> 00:42:56,760
+تلاتة وكمان جداش وكمان واحد تمام؟ طيبالان هذه هي
+
+393
+00:42:56,760 --> 00:43:01,120
+الطريقة الأولى يا بنات للحصول على معكوس المصوفة
+
+394
+00:43:01,120 --> 00:43:06,420
+الان عندك فراغ بعد نمطها ان شاء الله جربي أضرب
+
+395
+00:43:06,420 --> 00:43:10,800
+المصوفة هذه في المصوفة هذه وشوف يطلع معاك مصوفة
+
+396
+00:43:10,800 --> 00:43:15,920
+الواحدة ولا لا بس بدي أعطيكي الطريقة الثانية كنظري
+
+397
+00:43:15,920 --> 00:43:20,720
+و بنحل المثال نفسه في المحاضرة القادمة بعد الظهر
+
+398
+00:43:20,720 --> 00:43:25,550
+ان شاء الله بالطريقة الجديدةيبقى بدأتي لـ second
+
+399
+00:43:25,550 --> 00:43:34,670
+method second method الطريقة الثانية نمر واحد
+
+400
+00:43:34,670 --> 00:43:47,050
+بنعمل تلت خطوات replace استبدل each element a i j
+
+401
+00:43:48,530 --> 00:43:54,570
+في الماتريكس A في الماتريكس
+
+402
+00:43:54,570 --> 00:44:07,710
+A من الـ Cofactor من الـ Cofactor من الـ Cofactor
+
+403
+00:44:07,710 --> 00:44:11,890
+من AIG
+
+404
+00:44:11,890 --> 00:44:16,090
+وهو IN
+
+405
+00:44:17,540 --> 00:44:32,360
+replace استبدل a i j by by a i j بدي اسوي السلب
+
+406
+00:44:32,360 --> 00:44:39,860
+واحد مرفوع للأس واحد زائد j في ال minor اللي هو m
+
+407
+00:44:39,860 --> 00:44:40,900
+i j
+
+408
+00:44:45,820 --> 00:44:52,680
+هذه الخطوة الأولى الخطوة الثانية take the
+
+409
+00:44:52,680 --> 00:45:00,120
+transpose of
+
+410
+00:45:00,120 --> 00:45:07,200
+the resulting matrix
+
+411
+00:45:07,200 --> 00:45:13,620
+resulting matrix in part one
+
+412
+00:45:16,180 --> 00:45:24,620
+part one and denoted
+
+413
+00:45:24,620 --> 00:45:28,080
+it
+
+414
+00:45:28,080 --> 00:45:41,840
+by B and denoted it by B أعطيها الرمز B خطوة
+
+415
+00:45:41,840 --> 00:45:54,750
+التالتة والأخيرة findA inverse from the formula من
+
+416
+00:45:54,750 --> 00:46:04,730
+الصيغة A inverse يسوى واحد على ال determinant لل A
+
+417
+00:46:04,730 --> 00:46:08,790
+هذا كله في المصوفة B
+
+418
+00:46:18,720 --> 00:46:19,280
+ماذا بحاجة؟
+
+419
+00:46:28,860 --> 00:46:32,620
+يبقى باختصار بدنا نعمل ثلاث خطوات الخطوة الأولى
+
+420
+00:46:32,620 --> 00:46:38,420
+بدي أشيل كل a ij و أضع كوفكتور تبعه ناقص واحد من
+
+421
+00:46:38,420 --> 00:46:44,360
+aij في ال m ij الخطوة الثانية بدي أجيب مدور هذه
+
+422
+00:46:44,360 --> 00:46:50,300
+المصوفة اللى نتجت في الخطوة الأولىخطوة تالتة
+
+423
+00:46:50,300 --> 00:46:53,240
+المصوفة اللى حصلت عليها بدي أضربها في واحد على
+
+424
+00:46:53,240 --> 00:46:59,320
+محدد المصوفة وهذا يتفق مع الكلام اللى قبل قليل ليش
+
+425
+00:46:59,320 --> 00:47:05,680
+محدد المصوفة لا يساوي zero لأن لو كان المحدد يساوي
+
+426
+00:47:05,680 --> 00:47:09,470
+zero هل بقدر أجيب هذا المعكوس؟يبقى فيش مكان يبقى
+
+427
+00:47:09,470 --> 00:47:14,650
+هذا الكلام الذي ادعيناه قبل قليل الآن السبب في أن
+
+428
+00:47:14,650 --> 00:47:19,930
+المحدد لا يساوي zero يبقى بدي أخل المعكوس exist
+
+429
+00:47:19,930 --> 00:47:25,490
+وإلا لو كان المحدد يساوي zero لأصبح المعكوس غير
+
+430
+00:47:25,490 --> 00:47:27,310
+موجود أعطيكم العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc1e1a5fd618de98ce0119604743fad65543fc83
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/LnjjOsm63Sg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4666, "start": 19.34, "end": 46.66, "text": "بالله الرحمن الرحيم لازلنا في نفس ال section تبع المرة الماضية وهو kramer's rule في نهاية هذا ال section حضرتنا نظرية النظرية بتتحدث عن ال homogeneous system فبتقول لي معاياتي لو كان عند ال homogeneous system Ax يساوي 0 في N من المعادلات و N من المجاهين", "tokens": [3555, 6027, 43761, 34892, 5016, 27842, 34892, 5016, 32640, 5296, 31377, 1211, 8315, 8978, 8717, 36178, 2423, 3541, 6055, 3555, 3615, 9673, 25720, 9673, 46958, 10632, 37037, 2407, 350, 44772, 311, 4978, 8978, 8717, 11296, 10632, 23758, 2423, 3541, 11331, 11242, 43500, 8315, 8717, 19913, 2288, 10632, 28239, 19913, 2288, 10632, 39894, 2655, 24401, 12984, 18871, 2423, 42632, 1185, 6156, 3555, 2655, 39648, 32239, 20449, 47302, 9307, 1829, 45164, 25961, 43242, 2423, 42632, 1185, 20118, 7251, 3794, 995, 45865, 1958, 8978, 426, 9154, 9673, 3615, 18513, 1211, 9307, 4032, 426, 9154, 9673, 7435, 40294, 9957], "avg_logprob": -0.24397787172347307, 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{"start": 101.49, "end": 101.99, "word": " يوجد", "probability": 0.9571940104166666}, {"start": 101.99, "end": 102.41, "word": " عندى", "probability": 0.675537109375}, {"start": 102.41, "end": 102.71, "word": " إلا", "probability": 0.9345703125}, {"start": 102.71, "end": 103.19, "word": " الحل", "probability": 0.953369140625}, {"start": 103.19, "end": 103.71, "word": " الصفري", "probability": 0.8603515625}, {"start": 103.71, "end": 104.15, "word": " أما", "probability": 0.74560546875}, {"start": 104.15, "end": 104.47, "word": " إذا", "probability": 0.976806640625}, {"start": 104.47, "end": 104.87, "word": " كان", "probability": 0.9931640625}, {"start": 104.87, "end": 105.73, "word": " المحدد", "probability": 0.9957682291666666}, {"start": 105.73, "end": 106.59, "word": " يساوي", "probability": 0.9716796875}, {"start": 106.59, "end": 107.09, "word": " Zero", "probability": 0.397216796875}, {"start": 107.09, "end": 109.07, "word": " لمصفوفة", "probability": 0.89716796875}, {"start": 109.07, "end": 109.87, "word": " المعاملات", "probability": 0.9951171875}, {"start": 109.87, "end": 110.53, "word": " فعندي", "probability": 0.74365234375}, {"start": 110.53, "end": 110.93, "word": " عدد", "probability": 0.98828125}, {"start": 110.93, "end": 111.71, "word": " لنهائي", "probability": 0.89189453125}, {"start": 111.71, "end": 112.03, "word": " من", "probability": 0.99072265625}, {"start": 112.03, "end": 112.99, "word": " الحلول", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 5, "seek": 13810, "start": 113.3, "end": 138.1, "text": "بناخد مثال على ذلك بيقول determine all values هتلي كل القيم تبع المقدار الثابت C بحيث ان ال system التالي has none trivial solution and then find all such solution يعني بعد ما تجيبلي قيمة C بدك تروح تجيبلي حل هذا ال system", "tokens": [3555, 1863, 47283, 3215, 50113, 6027, 15844, 29910, 23275, 4724, 1829, 39648, 6997, 439, 4190, 8032, 2655, 20292, 28242, 25062, 32640, 6055, 3555, 3615, 9673, 28543, 9640, 6024, 104, 16758, 2655, 383, 4724, 5016, 1829, 12984, 16472, 2423, 1185, 16712, 6027, 1829, 575, 6022, 26703, 3827, 293, 550, 915, 439, 1270, 3827, 37495, 22653, 39182, 19446, 6055, 7435, 1829, 3555, 20292, 12174, 32640, 3660, 383, 47525, 4117, 6055, 32887, 5016, 6055, 7435, 1829, 3555, 20292, 11331, 1211, 23758, 2423, 1185], "avg_logprob": -0.22202931804421508, "compression_ratio": 1.5188679245283019, "no_speech_prob": 0.0, "words": [{"start": 113.3, "end": 114.42, "word": "بناخد", "probability": 0.447998046875}, {"start": 114.42, "end": 114.88, "word": " مثال", "probability": 0.961669921875}, {"start": 114.88, "end": 115.1, "word": " على", "probability": 0.7294921875}, {"start": 115.1, "end": 115.62, "word": " ذلك", "probability": 0.975830078125}, {"start": 115.62, "end": 116.3, "word": " بيقول", "probability": 0.7159016927083334}, {"start": 116.3, "end": 117.0, "word": " determine", "probability": 0.11334228515625}, {"start": 117.0, "end": 117.52, "word": " all", "probability": 0.93017578125}, {"start": 117.52, "end": 118.2, "word": " values", "probability": 0.9375}, {"start": 118.2, "end": 118.66, "word": " هتلي", "probability": 0.6571451822916666}, {"start": 118.66, "end": 119.18, "word": " كل", "probability": 0.94189453125}, {"start": 119.18, "end": 119.86, "word": " القيم", "probability": 0.93603515625}, {"start": 119.86, "end": 120.26, "word": " تبع", "probability": 0.7978515625}, {"start": 120.26, "end": 120.98, "word": " المقدار", "probability": 0.9044596354166666}, {"start": 120.98, "end": 121.62, "word": " الثابت", "probability": 0.87646484375}, {"start": 121.62, "end": 122.0, "word": " C", "probability": 0.57177734375}, {"start": 122.0, "end": 123.18, "word": " بحيث", "probability": 0.979248046875}, {"start": 123.18, "end": 123.62, "word": " ان", "probability": 0.5146484375}, {"start": 123.62, "end": 124.54, "word": " ال", "probability": 0.9462890625}, {"start": 124.54, "end": 125.14, "word": " system", "probability": 0.86181640625}, {"start": 125.14, "end": 126.2, "word": " التالي", "probability": 0.9425455729166666}, {"start": 126.2, "end": 126.84, "word": " has", "probability": 0.7744140625}, {"start": 126.84, "end": 127.28, "word": " none", "probability": 0.433837890625}, {"start": 127.28, "end": 127.98, "word": " trivial", "probability": 0.9091796875}, {"start": 127.98, "end": 128.8, "word": " solution", "probability": 0.822265625}, {"start": 128.8, "end": 129.1, "word": " and", "probability": 0.89404296875}, {"start": 129.1, "end": 129.32, "word": " then", "probability": 0.5703125}, {"start": 129.32, "end": 129.84, "word": " find", "probability": 0.88525390625}, {"start": 129.84, "end": 130.38, "word": " all", "probability": 0.9404296875}, {"start": 130.38, "end": 130.88, "word": " such", "probability": 0.92236328125}, {"start": 130.88, "end": 131.62, "word": " solution", "probability": 0.65087890625}, {"start": 131.62, "end": 132.42, "word": " يعني", "probability": 0.928955078125}, {"start": 132.42, "end": 132.7, "word": " بعد", "probability": 0.962890625}, {"start": 132.7, "end": 132.86, "word": " ما", "probability": 0.79052734375}, {"start": 132.86, "end": 133.38, "word": " تجيبلي", "probability": 0.9427734375}, {"start": 133.38, "end": 134.02, "word": " قيمة", "probability": 0.9943033854166666}, {"start": 134.02, "end": 134.46, "word": " C", "probability": 0.9033203125}, {"start": 134.46, "end": 135.26, "word": " بدك", "probability": 0.828125}, {"start": 135.26, "end": 135.72, "word": " تروح", "probability": 0.98291015625}, {"start": 135.72, "end": 136.24, "word": " تجيبلي", "probability": 0.89130859375}, {"start": 136.24, "end": 136.76, "word": " حل", "probability": 0.984130859375}, {"start": 136.76, "end": 137.34, "word": " هذا", "probability": 0.94970703125}, {"start": 137.34, "end": 137.74, "word": " ال", "probability": 0.8896484375}, {"start": 137.74, "end": 138.1, "word": " system", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 6, "seek": 14744, "start": 138.69, "end": 147.45, "text": "طبعا اش بقول هنا جالي non-trivial solution يعني بدي قداش قيمة C اللي بتخليه non-trivial", "tokens": [9566, 3555, 3615, 995, 1975, 8592, 4724, 39648, 34105, 10874, 6027, 1829, 2107, 12, 83, 470, 22640, 3827, 37495, 22653, 4724, 16254, 12174, 3215, 33599, 12174, 32640, 3660, 383, 13672, 1829, 39894, 9778, 20292, 3224, 2107, 12, 83, 470, 22640], "avg_logprob": -0.4096798780487805, "compression_ratio": 1.1944444444444444, "no_speech_prob": 0.0, "words": [{"start": 138.69, "end": 139.09, "word": "طبعا", "probability": 0.7383880615234375}, {"start": 139.09, "end": 139.21, "word": " اش", "probability": 0.25115966796875}, {"start": 139.21, "end": 139.55, "word": " بقول", "probability": 0.892578125}, {"start": 139.55, "end": 140.01, "word": " هنا", "probability": 0.916015625}, {"start": 140.01, "end": 140.57, "word": " جالي", "probability": 0.4972330729166667}, {"start": 140.57, "end": 140.89, "word": " non", "probability": 0.296142578125}, {"start": 140.89, "end": 141.77, "word": "-trivial", "probability": 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هذا الكلام اذا احنا هنجي على ال system of linear equations هذا و نجي نحل هذا ال system بعد ما نتقل .. لكن هذا بنا نحله بعد ما نجيب قيمة C تمام؟ يبقى باجي بقوله الحل كتالة", "tokens": [40228, 22653, 4724, 16254, 41296, 1975, 1829, 3224, 8032, 3794, 45865, 3224, 20666, 39184, 2135, 8032, 3794, 45865, 3224, 20666, 39184, 4018, 4032, 12602, 2407, 5016, 8717, 5016, 1211, 23758, 2423, 28820, 10943, 1975, 15730, 1975, 5016, 8315, 8032, 1863, 7435, 1829, 15844, 2423, 1185, 295, 8213, 11787, 23758, 4032, 8717, 7435, 1829, 8717, 5016, 1211, 23758, 2423, 1185, 39182, 19446, 8717, 2655, 4587, 1211, 4386, 44381, 23758, 4724, 8315, 8717, 5016, 43761, 39182, 19446, 8717, 7435, 1829, 3555, 12174, 32640, 3660, 383, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 21542, 1211, 9122, 2655, 6027, 3660], "avg_logprob": -0.3261529236163908, "compression_ratio": 1.7077625570776256, "no_speech_prob": 0.0, "words": [{"start": 149.41, "end": 149.89, "word": "يعني", 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"probability": 0.8204345703125}], "temperature": 1.0}, {"id": 8, "seek": 19545, "start": 173.13, "end": 195.45, "text": "الـ System has non-trivial solution يبقى هنا since بما أن الـ System star has non-trivial solution", "tokens": [6027, 39184, 8910, 575, 2107, 12, 83, 470, 22640, 3827, 7251, 3555, 4587, 7578, 34105, 1670, 4724, 15042, 14739, 2423, 39184, 8910, 3543, 575, 2107, 12, 83, 470, 22640, 3827], "avg_logprob": -0.5655242166211528, "compression_ratio": 1.288888888888889, "no_speech_prob": 0.0, "words": [{"start": 173.13, "end": 173.75, "word": "الـ", "probability": 0.3271331787109375}, {"start": 173.75, "end": 174.31, "word": " System", "probability": 0.4638671875}, {"start": 174.31, "end": 174.69, "word": " has", "probability": 0.70166015625}, {"start": 174.69, "end": 175.13, "word": " non", "probability": 0.69921875}, {"start": 175.13, "end": 175.85, "word": "-trivial", "probability": 0.73876953125}, {"start": 175.85, "end": 176.47, "word": " solution", "probability": 0.654296875}, {"start": 176.47, "end": 180.97, "word": " يبقى", "probability": 0.712066650390625}, {"start": 180.97, "end": 181.17, "word": " هنا", "probability": 0.60498046875}, {"start": 181.17, "end": 181.89, "word": " since", "probability": 0.1651611328125}, {"start": 181.89, "end": 182.65, "word": " بما", "probability": 0.947509765625}, {"start": 182.65, "end": 183.37, "word": " أن", "probability": 0.7080078125}, {"start": 183.37, "end": 183.89, "word": " الـ", "probability": 0.5718994140625}, {"start": 183.89, "end": 185.51, "word": " System", "probability": 0.83740234375}, {"start": 185.51, "end": 187.91, "word": " star", "probability": 0.0989990234375}, {"start": 187.91, "end": 189.77, "word": " has", "probability": 0.56689453125}, {"start": 189.77, "end": 191.31, "word": " non", "probability": 0.89111328125}, {"start": 191.31, "end": 193.55, "word": "-trivial", "probability": 0.9000244140625}, {"start": 193.55, "end": 195.45, "word": " solution", "probability": 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الصف", "probability": 0.782958984375}, {"start": 457.41, "end": 458.19, "word": " الأول", "probability": 0.815185546875}, {"start": 458.19, "end": 458.81, "word": " في", "probability": 0.83935546875}, {"start": 458.81, "end": 459.41, "word": " سالب", "probability": 0.7850748697916666}, {"start": 459.41, "end": 459.93, "word": " تلاتة", "probability": 0.8458251953125}, {"start": 459.93, "end": 460.01, "word": " و", "probability": 0.568359375}, {"start": 460.01, "end": 460.59, "word": " بنضيف", "probability": 0.6338297526041666}, {"start": 460.59, "end": 460.85, "word": " ولا", "probability": 0.693359375}, {"start": 460.85, "end": 461.51, "word": " التالي", "probability": 0.6927490234375}, {"start": 461.51, "end": 462.23, "word": " يبقى", "probability": 0.9317626953125}, {"start": 462.23, "end": 462.63, "word": " سالب", "probability": 0.91845703125}, {"start": 462.63, "end": 463.15, "word": " تلاتة", "probability": 0.9320068359375}, {"start": 463.15, "end": 463.27, "word": " في", "probability": 0.953125}, {"start": 463.27, "end": 463.65, "word": " سبعة", "probability": 0.9290364583333334}, {"start": 463.65, "end": 464.39, "word": " بسالب", "probability": 0.8525390625}, {"start": 464.39, "end": 465.55, "word": " واحد", "probability": 0.885498046875}, {"start": 465.55, "end": 466.37, "word": " وعشرين", "probability": 0.8677978515625}, {"start": 466.37, "end": 466.93, "word": " يبقى", "probability": 0.87109375}, {"start": 466.93, "end": 467.61, "word": " سالب", "probability": 0.9767252604166666}, {"start": 467.61, "end": 468.27, "word": " واحد", "probability": 0.942138671875}, {"start": 468.27, "end": 468.95, "word": " وعشرين", "probability": 0.949951171875}, {"start": 468.95, "end": 470.01, "word": " هضربنا", "probability": 0.809326171875}, {"start": 470.01, "end": 470.17, "word": " في", "probability": 0.931640625}, {"start": 470.17, "end": 470.47, "word": " اتنين", "probability": 0.946533203125}, {"start": 470.47, "end": 471.21, "word": " اربعتاشر", "probability": 0.79833984375}, {"start": 471.21, "end": 471.77, "word": " واحد", "probability": 0.918701171875}, {"start": 471.77, "end": 472.15, "word": " اللي", "probability": 0.91748046875}, {"start": 472.15, "end": 472.37, "word": " هي", "probability": 0.77880859375}, {"start": 472.37, "end": 473.39, "word": " خمستاشر", "probability": 0.863427734375}], "temperature": 1.0}, {"id": 22, "seek": 49592, "start": 473.68, "end": 495.92, "text": "يبقى الأن بيجي ناخد من سالب سبع قاري اتنين يبقى هذا بتصير المصوفة على الشكل التالي واحد اتنين سبعة زيرو هنا زيرو وهنا واحد وهنا تلاتة وهنا زيرو", "tokens": [1829, 3555, 4587, 7578, 16247, 1863, 4724, 1829, 7435, 1829, 8717, 47283, 3215, 9154, 8608, 6027, 3555, 8608, 3555, 3615, 12174, 9640, 1829, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 23758, 39894, 9381, 13546, 9673, 9381, 38688, 3660, 15844, 25124, 28820, 16712, 6027, 1829, 36764, 24401, 1975, 2655, 1863, 9957, 8608, 3555, 27884, 30767, 13546, 2407, 34105, 30767, 13546, 2407, 37037, 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0.9359130859375}, {"start": 481.7, "end": 481.98, "word": " هذا", "probability": 0.65087890625}, {"start": 481.98, "end": 482.58, "word": " بتصير", "probability": 0.6541341145833334}, {"start": 482.58, "end": 483.48, "word": " المصوفة", "probability": 0.84478759765625}, {"start": 483.48, "end": 483.72, "word": " على", "probability": 0.8349609375}, {"start": 483.72, "end": 484.36, "word": " الشكل", "probability": 0.84033203125}, {"start": 484.36, "end": 485.06, "word": " التالي", "probability": 0.9768880208333334}, {"start": 485.06, "end": 486.02, "word": " واحد", "probability": 0.829345703125}, {"start": 486.02, "end": 486.98, "word": " اتنين", "probability": 0.968505859375}, {"start": 486.98, "end": 488.0, "word": " سبعة", "probability": 0.9609375}, {"start": 488.0, "end": 489.1, "word": " زيرو", "probability": 0.7498372395833334}, {"start": 489.1, "end": 490.0, "word": " هنا", "probability": 0.908203125}, {"start": 490.0, "end": 491.04, "word": " زيرو", "probability": 0.85400390625}, {"start": 491.04, "end": 491.7, "word": " وهنا", "probability": 0.75927734375}, {"start": 491.7, "end": 492.42, "word": " واحد", "probability": 0.975830078125}, {"start": 492.42, "end": 493.4, "word": " وهنا", "probability": 0.826904296875}, {"start": 493.4, "end": 494.5, "word": " تلاتة", "probability": 0.952392578125}, {"start": 494.5, "end": 495.26, "word": " وهنا", "probability": 0.84326171875}, {"start": 495.26, "end": 495.92, "word": " زيرو", "probability": 0.9646809895833334}], "temperature": 1.0}, {"id": 23, "seek": 51479, "start": 496.32, "end": 514.8, "text": "و بالمرة ناخد كمان خمس R تلاتة و هذا كمان خمس R تلاتة يبقى هذا بده يعطينا كمان Zero واحد و هنا تلاتة و هنا Zero الشكل اللي عندنا هذا", "tokens": [2407, 20666, 2304, 25720, 8717, 47283, 3215, 9122, 2304, 7649, 16490, 2304, 3794, 497, 6055, 1211, 9307, 3660, 4032, 23758, 9122, 2304, 7649, 16490, 2304, 3794, 497, 6055, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 9122, 2304, 7649, 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"word": " كمان", "probability": 0.9658203125}, {"start": 503.02, "end": 504.36, "word": " خمس", "probability": 0.9855143229166666}, {"start": 504.36, "end": 505.46, "word": " R", "probability": 0.97900390625}, {"start": 505.46, "end": 506.3, "word": " تلاتة", "probability": 0.984375}, {"start": 506.3, "end": 507.6, "word": " يبقى", "probability": 0.9439697265625}, {"start": 507.6, "end": 507.86, "word": " هذا", "probability": 0.92724609375}, {"start": 507.86, "end": 508.28, "word": " بده", "probability": 0.5350341796875}, {"start": 508.28, "end": 508.9, "word": " يعطينا", "probability": 0.9193115234375}, {"start": 508.9, "end": 509.46, "word": " كمان", "probability": 0.9759114583333334}, {"start": 509.46, "end": 509.98, "word": " Zero", "probability": 0.45068359375}, {"start": 509.98, "end": 511.08, "word": " واحد", "probability": 0.8017578125}, {"start": 511.08, "end": 511.34, "word": " و", "probability": 0.64501953125}, {"start": 511.34, "end": 511.58, "word": " هنا", "probability": 0.93505859375}, {"start": 511.58, "end": 512.26, "word": " تلاتة", "probability": 0.9771728515625}, {"start": 512.26, "end": 512.38, "word": " و", "probability": 0.8798828125}, {"start": 512.38, "end": 512.68, "word": " هنا", "probability": 0.97412109375}, {"start": 512.68, "end": 513.18, "word": " Zero", "probability": 0.8974609375}, {"start": 513.18, "end": 514.04, "word": " الشكل", "probability": 0.865478515625}, {"start": 514.04, "end": 514.22, "word": " اللي", "probability": 0.948974609375}, {"start": 514.22, "end": 514.58, "word": " عندنا", "probability": 0.942138671875}, {"start": 514.58, "end": 514.8, "word": " هذا", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 24, "seek": 53777, "start": 515.41, "end": 537.77, "text": "تمام؟ يبقى هذا المصير تاخد الشكل التالي بدي أضرب الصف الثاني في سالب و أضيفه فوق و تحت يبقى السالب R او سالب اتنين سالب اتنين R اتنين to R one", "tokens": [2655, 15042, 2304, 22807, 7251, 3555, 4587, 7578, 23758, 9673, 9381, 13546, 6055, 47283, 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519.29, "end": 520.17, "word": " التالي", "probability": 0.96142578125}, {"start": 520.17, "end": 521.21, "word": " بدي", "probability": 0.591064453125}, {"start": 521.21, "end": 521.79, "word": " أضرب", "probability": 0.8650716145833334}, {"start": 521.79, "end": 522.63, "word": " الصف", "probability": 0.95751953125}, {"start": 522.63, "end": 523.37, "word": " الثاني", "probability": 0.83050537109375}, {"start": 523.37, "end": 523.63, "word": " في", "probability": 0.884765625}, {"start": 523.63, "end": 524.01, "word": " سالب", "probability": 0.7799479166666666}, {"start": 524.01, "end": 524.17, "word": " و", "probability": 0.9931640625}, {"start": 524.17, "end": 524.65, "word": " أضيفه", "probability": 0.8333740234375}, {"start": 524.65, "end": 525.23, "word": " فوق", "probability": 0.975830078125}, {"start": 525.23, "end": 525.37, "word": " و", "probability": 0.654296875}, {"start": 525.37, "end": 525.65, "word": " تحت", "probability": 0.4385986328125}, {"start": 525.65, "end": 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{"start": 807.78, "end": 808.06, "word": " N", "probability": 0.2822265625}, {"start": 808.06, "end": 808.28, "word": " في", "probability": 0.8798828125}, {"start": 808.28, "end": 808.58, "word": " N", "probability": 0.8046875}, {"start": 808.58, "end": 808.96, "word": " has", "probability": 0.58349609375}, {"start": 808.96, "end": 809.4, "word": " an", "probability": 0.849609375}, {"start": 809.4, "end": 809.88, "word": " inverse", "probability": 0.8828125}, {"start": 809.88, "end": 810.66, "word": " matrix", "probability": 0.966796875}, {"start": 810.66, "end": 811.3, "word": " has", "probability": 0.29150390625}, {"start": 811.3, "end": 812.46, "word": " an", "probability": 0.9287109375}, {"start": 812.46, "end": 814.18, "word": " inverse", "probability": 0.783203125}, {"start": 814.18, "end": 816.54, "word": " matrix", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 37, "seek": 84884, "start": 820.24, "end": 848.84, "text": "فإذا كان ال A في ال B سوى ال B في ال A سوى ال identity matrix IN remark ال matrix A ال matrix A has an inverse has an", "tokens": [5172, 28814, 15730, 25961, 2423, 316, 8978, 2423, 363, 8608, 2407, 7578, 2423, 363, 8978, 2423, 316, 8608, 2407, 7578, 2423, 6575, 8141, 6892, 7942, 2423, 8141, 316, 2423, 8141, 316, 575, 364, 17340, 575, 364], "avg_logprob": -0.32538008045505834, "compression_ratio": 1.494949494949495, "no_speech_prob": 0.0, "words": [{"start": 820.24, "end": 821.62, "word": "فإذا", "probability": 0.6643880208333334}, {"start": 821.62, "end": 822.28, "word": " كان", "probability": 0.9892578125}, {"start": 822.28, "end": 823.62, "word": " ال", "probability": 0.91064453125}, {"start": 823.62, "end": 824.08, "word": " A", "probability": 0.30126953125}, {"start": 824.08, "end": 824.76, "word": " في", "probability": 0.5546875}, {"start": 824.76, "end": 825.02, "word": " ال", "probability": 0.78125}, {"start": 825.02, "end": 825.36, "word": " B", "probability": 0.95166015625}, {"start": 825.36, "end": 826.44, "word": " سوى", "probability": 0.69921875}, {"start": 826.44, "end": 826.6, "word": " ال", "probability": 0.93798828125}, {"start": 826.6, "end": 826.86, "word": " B", "probability": 0.9052734375}, {"start": 826.86, "end": 827.26, "word": " في", "probability": 0.97265625}, {"start": 827.26, "end": 827.54, "word": " ال", "probability": 0.93701171875}, {"start": 827.54, "end": 827.88, "word": " A", "probability": 0.9912109375}, {"start": 827.88, "end": 828.88, "word": " سوى", "probability": 0.8683268229166666}, {"start": 828.88, "end": 829.0, "word": " ال", "probability": 0.91796875}, {"start": 829.0, "end": 829.68, "word": " identity", "probability": 0.77490234375}, {"start": 829.68, "end": 830.72, "word": " matrix", "probability": 0.95751953125}, {"start": 830.72, "end": 831.96, "word": " IN", "probability": 0.413330078125}, {"start": 831.96, "end": 834.26, "word": " remark", "probability": 0.7080078125}, {"start": 834.26, "end": 838.72, "word": " ال", "probability": 0.306396484375}, {"start": 838.72, "end": 839.26, "word": " matrix", "probability": 0.90625}, {"start": 839.26, "end": 839.96, "word": " A", "probability": 0.9814453125}, {"start": 839.96, "end": 842.7, "word": " ال", "probability": 0.402099609375}, {"start": 842.7, "end": 843.4, "word": " matrix", "probability": 0.9677734375}, {"start": 843.4, "end": 844.1, "word": " A", "probability": 0.9853515625}, {"start": 844.1, "end": 845.36, "word": " has", "probability": 0.242431640625}, {"start": 845.36, "end": 845.84, "word": " an", "probability": 0.91455078125}, {"start": 845.84, "end": 846.52, "word": " inverse", "probability": 0.87744140625}, {"start": 846.52, "end": 847.78, "word": " has", "probability": 0.79345703125}, {"start": 847.78, "end": 848.84, "word": " an", "probability": 0.775390625}], "temperature": 1.0}, {"id": 38, "seek": 87367, "start": 849.91, "end": 873.67, "text": "Inverse هدّيله الرمز A و فوقها سالب واحد if and only if ال determinant للـ A لا يساوي zero نأخد أول نظرية على هذا الموضوع theorem بتقول let ال A ب", "tokens": [4575, 4308, 8032, 3215, 11703, 26895, 3224, 34892, 2304, 11622, 316, 4032, 6156, 30543, 11296, 8608, 6027, 3555, 36764, 24401, 498, 293, 787, 498, 2423, 41296, 24976, 39184, 316, 20193, 7251, 3794, 995, 45865, 4018, 8717, 10721, 9778, 3215, 5551, 12610, 8717, 19913, 2288, 10632, 15844, 23758, 9673, 2407, 11242, 45367, 20904, 39894, 39648, 718, 2423, 316, 4724], "avg_logprob": -0.4242584705352783, "compression_ratio": 1.2485549132947977, "no_speech_prob": 0.0, "words": [{"start": 849.91, "end": 850.87, "word": "Inverse", "probability": 0.4666748046875}, {"start": 850.87, "end": 851.97, "word": " هدّيله", "probability": 0.5246337890625}, {"start": 851.97, "end": 852.59, "word": " الرمز", "probability": 0.970703125}, {"start": 852.59, "end": 852.89, "word": " A", "probability": 0.34814453125}, {"start": 852.89, "end": 853.07, "word": " و", "probability": 0.740234375}, {"start": 853.07, "end": 853.51, "word": " فوقها", "probability": 0.6637369791666666}, {"start": 853.51, "end": 854.05, "word": " سالب", "probability": 0.8824869791666666}, {"start": 854.05, "end": 854.77, "word": " واحد", "probability": 0.945068359375}, {"start": 854.77, "end": 855.81, "word": " if", "probability": 0.234375}, {"start": 855.81, "end": 856.35, "word": " and", "probability": 0.78466796875}, {"start": 856.35, "end": 856.81, "word": " only", "probability": 0.84716796875}, {"start": 856.81, "end": 857.41, "word": " if", "probability": 0.9794921875}, {"start": 857.41, "end": 858.29, "word": " ال", "probability": 0.6494140625}, {"start": 858.29, "end": 859.13, "word": " determinant", "probability": 0.5205078125}, {"start": 859.13, "end": 860.03, "word": " للـ", "probability": 0.518310546875}, {"start": 860.03, "end": 860.37, "word": " A", "probability": 0.60302734375}, {"start": 860.37, "end": 861.25, "word": " لا", "probability": 0.3837890625}, {"start": 861.25, "end": 862.19, "word": " يساوي", "probability": 0.9571533203125}, {"start": 862.19, "end": 862.85, 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"probability": 0.7470703125}], "temperature": 1.0}, {"id": 39, "seek": 90677, "start": 878.07, "end": 906.77, "text": "an n by n matrix if there exists a matrix B such that ال A في ال B بده يساوي ال identity matrix I N", "tokens": [282, 297, 538, 297, 8141, 498, 456, 8198, 257, 8141, 363, 1270, 300, 2423, 316, 8978, 2423, 363, 47525, 3224, 7251, 3794, 995, 45865, 2423, 6575, 8141, 286, 426], "avg_logprob": -0.3776041666666667, "compression_ratio": 1.1734693877551021, "no_speech_prob": 0.0, "words": [{"start": 878.07, "end": 878.73, "word": "an", "probability": 0.10089111328125}, {"start": 878.73, "end": 879.43, "word": " n", "probability": 0.61962890625}, {"start": 879.43, "end": 879.79, "word": " by", "probability": 0.5439453125}, {"start": 879.79, "end": 880.81, "word": " n", "probability": 0.9736328125}, {"start": 880.81, "end": 882.51, "word": " matrix", "probability": 0.919921875}, {"start": 882.51, "end": 885.51, "word": " if", "probability": 0.6748046875}, {"start": 885.51, "end": 887.25, "word": " there", "probability": 0.85302734375}, {"start": 887.25, "end": 888.11, "word": " exists", "probability": 0.693359375}, {"start": 888.11, "end": 889.89, "word": " a", "probability": 0.974609375}, {"start": 889.89, "end": 890.51, "word": " matrix", "probability": 0.9443359375}, {"start": 890.51, "end": 891.09, "word": " B", "probability": 0.63720703125}, {"start": 891.09, "end": 896.89, "word": " such", "probability": 0.7080078125}, {"start": 896.89, "end": 897.71, "word": " that", "probability": 0.95458984375}, {"start": 897.71, "end": 901.45, "word": " ال", "probability": 0.767578125}, {"start": 901.45, "end": 901.81, "word": " A", "probability": 0.323486328125}, {"start": 901.81, "end": 902.09, "word": " في", "probability": 0.7158203125}, {"start": 902.09, "end": 902.29, "word": " ال", "probability": 0.75439453125}, {"start": 902.29, "end": 902.47, "word": " B", "probability": 0.9501953125}, {"start": 902.47, "end": 902.97, "word": " بده", "probability": 0.3330078125}, {"start": 902.97, "end": 903.39, "word": " يساوي", "probability": 0.843994140625}, {"start": 903.39, "end": 903.63, "word": " ال", "probability": 0.77783203125}, {"start": 903.63, "end": 904.39, "word": " identity", "probability": 0.8310546875}, {"start": 904.39, "end": 905.39, "word": " matrix", "probability": 0.97900390625}, {"start": 905.39, "end": 906.19, "word": " I", "probability": 0.64404296875}, {"start": 906.19, "end": 906.77, "word": " N", "probability": 0.6787109375}], "temperature": 1.0}, {"id": 40, "seek": 92341, "start": 907.97, "end": 923.41, "text": "بعد ذلك الـ B في الـ A بيكون ساوية الـ Identity Matrix I N وبعد ذلك الـ B بيكون ساوية A انفرز", "tokens": [3555, 22488, 29910, 23275, 2423, 39184, 363, 8978, 2423, 39184, 316, 4724, 1829, 30544, 8608, 995, 2407, 10632, 2423, 39184, 25905, 507, 36274, 286, 426, 46599, 22488, 29910, 23275, 2423, 39184, 363, 4724, 1829, 30544, 8608, 995, 2407, 10632, 316, 16472, 5172, 2288, 11622], "avg_logprob": -0.5375000264909532, "compression_ratio": 1.4356435643564356, "no_speech_prob": 0.0, "words": [{"start": 907.97, "end": 908.65, "word": "بعد", "probability": 0.3341064453125}, {"start": 908.65, "end": 908.65, "word": " ذلك", "probability": 0.752685546875}, {"start": 908.65, "end": 910.47, "word": " الـ", "probability": 0.3985595703125}, {"start": 910.47, "end": 910.77, "word": " B", "probability": 0.388916015625}, {"start": 910.77, "end": 911.11, "word": " في", "probability": 0.6181640625}, {"start": 911.11, "end": 911.43, "word": " الـ", "probability": 0.630859375}, {"start": 911.43, "end": 911.79, "word": " A", "probability": 0.9169921875}, {"start": 911.79, "end": 912.61, "word": " بيكون", "probability": 0.3683675130208333}, {"start": 912.61, "end": 913.17, "word": " ساوية", "probability": 0.5582275390625}, {"start": 913.17, "end": 913.35, "word": " الـ", "probability": 0.5335693359375}, {"start": 913.35, "end": 914.15, "word": " Identity", "probability": 0.7178955078125}, {"start": 914.15, "end": 914.71, "word": " Matrix", "probability": 0.90380859375}, {"start": 914.71, "end": 915.13, "word": " I", "probability": 0.2117919921875}, {"start": 915.13, "end": 915.53, "word": " N", "probability": 0.486572265625}, {"start": 915.53, "end": 917.65, "word": " وبعد", "probability": 0.456298828125}, {"start": 917.65, "end": 917.65, "word": " ذلك", "probability": 0.96533203125}, {"start": 917.65, "end": 919.95, "word": " الـ", "probability": 0.853271484375}, {"start": 919.95, "end": 920.29, "word": " B", "probability": 0.91650390625}, {"start": 920.29, "end": 921.33, "word": " بيكون", "probability": 0.7439778645833334}, {"start": 921.33, "end": 922.03, "word": " ساوية", "probability": 0.96630859375}, {"start": 922.03, "end": 922.55, "word": " A", "probability": 0.56494140625}, {"start": 922.55, "end": 923.41, "word": " انفرز", "probability": 0.66363525390625}], "temperature": 1.0}, {"id": 41, "seek": 96348, "start": 935.48, "end": 963.48, "text": "أظن أن هذا الشجة انتهي هنا منها خلاص وين وصلت الورقة اللي بتلف؟ كل واحدة علمت من اللي قعدت علي اسمها", "tokens": [10721, 19913, 1863, 14739, 23758, 25124, 7435, 3660, 16472, 47395, 1829, 34105, 9154, 11296, 16490, 1211, 33546, 4032, 9957, 4032, 36520, 2655, 2423, 13063, 28671, 13672, 1829, 39894, 46538, 22807, 28242, 36764, 24401, 3660, 11203, 2304, 2655, 9154, 13672, 1829, 12174, 22488, 2655, 25894, 24525, 2304, 11296], "avg_logprob": -0.24479166666666666, "compression_ratio": 1.4516129032258065, "no_speech_prob": 0.0, "words": [{"start": 935.48, "end": 935.88, "word": "أظن", "probability": 0.78662109375}, {"start": 935.88, "end": 936.0, "word": " أن", "probability": 0.59326171875}, {"start": 936.0, "end": 936.12, "word": " هذا", "probability": 0.2154541015625}, {"start": 936.12, "end": 936.48, "word": " الشجة", "probability": 0.8147786458333334}, {"start": 936.48, "end": 936.68, "word": " انتهي", "probability": 0.699951171875}, {"start": 936.68, "end": 936.88, "word": " هنا", "probability": 0.76611328125}, {"start": 936.88, "end": 937.14, "word": " منها", "probability": 0.67138671875}, {"start": 937.14, "end": 938.6, "word": " خلاص", "probability": 0.9178059895833334}, {"start": 938.6, "end": 957.82, "word": " وين", "probability": 0.772705078125}, {"start": 957.82, "end": 958.3, "word": " وصلت", "probability": 0.9578450520833334}, {"start": 958.3, "end": 958.68, "word": " الورقة", "probability": 0.9059244791666666}, {"start": 958.68, "end": 958.82, "word": " اللي", "probability": 0.9345703125}, {"start": 958.82, "end": 960.92, "word": " بتلف؟", "probability": 0.7744954427083334}, {"start": 960.92, "end": 961.38, "word": " كل", "probability": 0.95361328125}, {"start": 961.38, "end": 961.9, "word": " واحدة", "probability": 0.83056640625}, {"start": 961.9, "end": 962.36, "word": " علمت", "probability": 0.9137369791666666}, {"start": 962.36, "end": 962.46, "word": " من", "probability": 0.90283203125}, {"start": 962.46, "end": 962.58, "word": " اللي", "probability": 0.9423828125}, {"start": 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"ممتاز جدا يبقى انا طلعت حصل ضرب كميتين يساوي واحد صحيح واتنين are real number", "tokens": [2304, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 1975, 8315, 23032, 1211, 34268, 11331, 36520, 48812, 25513, 9122, 2304, 36081, 9957, 7251, 3794, 995, 45865, 36764, 24401, 20328, 5016, 1829, 5016, 4032, 9307, 1863, 9957, 366, 957, 1230], "avg_logprob": -0.22541921313216046, "compression_ratio": 1.165137614678899, "no_speech_prob": 0.0, "words": [{"start": 1228.94, "end": 1229.94, "word": "ممتاز", "probability": 0.7061538696289062}, {"start": 1229.94, "end": 1230.32, "word": " جدا", "probability": 0.947021484375}, {"start": 1230.32, "end": 1231.22, "word": " يبقى", "probability": 0.81500244140625}, {"start": 1231.22, "end": 1231.52, "word": " انا", "probability": 0.76708984375}, {"start": 1231.52, "end": 1232.2, "word": " طلعت", "probability": 0.96240234375}, {"start": 1232.2, "end": 1232.78, "word": " حصل", "probability": 0.73876953125}, {"start": 1232.78, "end": 1233.12, "word": " 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zero", "tokens": [3224, 1211, 7251, 43020, 5296, 10721, 24401, 3224, 15042, 14739, 6055, 30544, 4018, 8978, 7251, 20498, 9154, 16247, 1829, 10943, 12399, 35525, 2407, 3714, 25720, 36764, 24401, 3660, 8978, 16712, 9640, 1829, 9778, 12399, 32239, 3794, 11933, 2304, 41361, 10632, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 14739, 2423, 41296, 5296, 15040, 1829, 3224, 20193, 7251, 43020, 14739, 7251, 3794, 995, 45865, 4018, 3714, 18513, 10943, 11331, 36520, 48812, 25513, 16247, 2655, 1863, 9957, 4724, 3794, 2407, 27884, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 5551, 24401, 16095, 20193, 32640, 19452, 14739, 7251, 30544, 4018], "avg_logprob": -0.26849489552634104, "compression_ratio": 1.6824644549763033, "no_speech_prob": 0.0, "words": [{"start": 1237.63, "end": 1238.17, "word": "هل", "probability": 0.966552734375}, {"start": 1238.17, "end": 1238.71, "word": " يمكن", "probability": 0.94091796875}, {"start": 1238.71, "end": 1240.29, "word": " لأحدهما", "probability": 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عامل مشترك بيظل C نقص كده؟ نقص واحد", "tokens": [3555, 1863, 28543, 2288, 8717, 47283, 3215, 6225, 10943, 1211, 37893, 2655, 31747, 9154, 29538, 9673, 3615, 18513, 37977, 7251, 3555, 4587, 7578, 1975, 1829, 8592, 4724, 1829, 9381, 13546, 43242, 8315, 22807, 1975, 1829, 6225, 10943, 1211, 37893, 2655, 31747, 4724, 1829, 19913, 1211, 383, 8717, 4587, 9381, 9122, 3215, 3224, 22807, 8717, 4587, 9381, 36764, 24401], "avg_logprob": -0.21040783443693387, "compression_ratio": 1.4915254237288136, "no_speech_prob": 0.0, "words": [{"start": 1405.91, "end": 1406.77, "word": "بنقدر", "probability": 0.78125}, {"start": 1406.77, "end": 1407.25, "word": " ناخد", "probability": 0.9794921875}, {"start": 1407.25, "end": 1407.65, "word": " عامل", "probability": 0.95654296875}, {"start": 1407.65, "end": 1408.17, "word": " مشترك", "probability": 0.9718424479166666}, {"start": 1408.17, "end": 1408.37, "word": " من", "probability": 0.95654296875}, {"start": 1408.37, "end": 1408.69, "word": " هذه", 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"word": " كده؟", "probability": 0.746337890625}, {"start": 1416.71, "end": 1417.91, "word": " نقص", "probability": 0.9485677083333334}, {"start": 1417.91, "end": 1418.49, "word": " واحد", "probability": 0.920166015625}], "temperature": 1.0}, {"id": 62, "seek": 144019, "start": 1421.65, "end": 1440.19, "text": "نقص ال identity matrix مش واحد يبقى ناقص ال identity matrix و إلا و هذا الكلام بده يساوي مين؟ بده يساوي زي ما و إلا لو كان واحد هل بقدر أضيف الواحد لأي مصفوفة؟", "tokens": [1863, 4587, 9381, 2423, 6575, 8141, 37893, 36764, 24401, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 2423, 6575, 8141, 4032, 11933, 15040, 4032, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 3714, 9957, 22807, 47525, 3224, 7251, 3794, 995, 45865, 30767, 1829, 19446, 4032, 11933, 15040, 45164, 25961, 36764, 24401, 8032, 1211, 4724, 28543, 2288, 5551, 11242, 33911, 2423, 14407, 24401, 5296, 10721, 1829, 3714, 9381, 5172, 38688, 3660, 22807], "avg_logprob": -0.1906672226818832, 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{"start": 1428.67, "end": 1428.85, "word": " و", "probability": 0.8017578125}, {"start": 1428.85, "end": 1429.23, "word": " إلا", "probability": 0.6248779296875}, {"start": 1429.23, "end": 1430.01, "word": " و", "probability": 0.56298828125}, {"start": 1430.01, "end": 1430.27, "word": " هذا", "probability": 0.9140625}, {"start": 1430.27, "end": 1430.71, "word": " الكلام", "probability": 0.9480794270833334}, {"start": 1430.71, "end": 1431.09, "word": " بده", "probability": 0.690185546875}, {"start": 1431.09, "end": 1431.43, "word": " يساوي", "probability": 0.9796142578125}, {"start": 1431.43, "end": 1432.11, "word": " مين؟", "probability": 0.7584635416666666}, {"start": 1432.11, "end": 1432.63, "word": " بده", "probability": 0.8984375}, {"start": 1432.63, "end": 1433.15, "word": " يساوي", "probability": 0.99169921875}, {"start": 1433.15, "end": 1433.51, "word": " زي", "probability": 0.5108642578125}, {"start": 1433.51, "end": 1433.63, "word": " ما", "probability": 0.215576171875}, 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1469.24, "text": "ولو كان واحد كان قولنا هذه يبقى هذه بدها تساوي Zero أو هذه بدها تساوي Zero صحيح ولا لا؟ إذا بصير ال C نقص للواحد تساوي Zero يبقى المصفوفة C تساوي Zero صحيح هذا الكلام؟ أو تساوي واحد واحد number رقم مش مصفوفة يبقى ليس صحيح يبقى لما ناخد عامل مشترك في حالة المصفوفة بدل الواحد في العملية الشغل العادى بيصير ال identity matrix", "tokens": [12610, 2407, 25961, 36764, 24401, 25961, 12174, 12610, 8315, 29538, 7251, 3555, 4587, 7578, 29538, 47525, 11296, 6055, 3794, 995, 45865, 17182, 34051, 29538, 47525, 11296, 6055, 3794, 995, 45865, 17182, 20328, 5016, 1829, 5016, 49429, 20193, 22807, 11933, 15730, 4724, 9381, 13546, 2423, 383, 8717, 4587, 9381, 24976, 14407, 24401, 6055, 3794, 995, 45865, 17182, 7251, 3555, 4587, 7578, 9673, 9381, 5172, 38688, 3660, 383, 6055, 3794, 995, 45865, 17182, 20328, 5016, 1829, 5016, 23758, 2423, 28820, 10943, 22807, 34051, 6055, 3794, 995, 45865, 36764, 24401, 36764, 24401, 1230, 12602, 4587, 2304, 37893, 3714, 9381, 5172, 38688, 3660, 7251, 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يبقى", "probability": 0.81182861328125}, {"start": 1443.38, "end": 1443.62, "word": " هذه", "probability": 0.81494140625}, {"start": 1443.62, "end": 1443.96, "word": " بدها", "probability": 0.5382080078125}, {"start": 1443.96, "end": 1444.34, "word": " تساوي", "probability": 0.9520263671875}, {"start": 1444.34, "end": 1444.68, "word": " Zero", "probability": 0.201171875}, {"start": 1444.68, "end": 1444.94, "word": " أو", "probability": 0.58056640625}, {"start": 1444.94, "end": 1445.22, "word": " هذه", "probability": 0.8779296875}, {"start": 1445.22, "end": 1445.5, "word": " بدها", "probability": 0.85791015625}, {"start": 1445.5, "end": 1445.94, "word": " تساوي", "probability": 0.98974609375}, {"start": 1445.94, "end": 1446.34, "word": " Zero", "probability": 0.943359375}, {"start": 1446.34, "end": 1447.16, "word": " صحيح", "probability": 0.9671630859375}, {"start": 1447.16, "end": 1447.32, "word": " ولا", "probability": 0.93310546875}, {"start": 1447.32, "end": 1447.94, "word": " لا؟", "probability": 0.5184326171875}, {"start": 1447.94, "end": 1448.22, "word": " إذا", "probability": 0.697509765625}, {"start": 1448.22, "end": 1448.74, "word": " بصير", "probability": 0.8479817708333334}, {"start": 1448.74, "end": 1448.94, "word": " ال", "probability": 0.87646484375}, {"start": 1448.94, "end": 1449.1, "word": " C", "probability": 0.393798828125}, {"start": 1449.1, "end": 1449.58, "word": " نقص", "probability": 0.9427083333333334}, {"start": 1449.58, "end": 1450.28, "word": " للواحد", "probability": 0.8121744791666666}, {"start": 1450.28, "end": 1450.78, "word": " تساوي", "probability": 0.9793701171875}, {"start": 1450.78, "end": 1451.14, "word": " Zero", "probability": 0.955078125}, {"start": 1451.14, "end": 1451.8, "word": " يبقى", "probability": 0.9476318359375}, {"start": 1451.8, "end": 1452.56, "word": " المصفوفة", "probability": 0.8501953125}, {"start": 1452.56, "end": 1452.8, "word": " C", "probability": 0.78759765625}, {"start": 1452.8, "end": 1453.46, "word": " تساوي", "probability": 0.9644775390625}, {"start": 1453.46, "end": 1453.78, "word": " Zero", "probability": 0.97021484375}, {"start": 1453.78, "end": 1454.26, "word": " صحيح", "probability": 0.9654541015625}, {"start": 1454.26, "end": 1454.46, "word": " هذا", "probability": 0.951171875}, {"start": 1454.46, "end": 1455.18, "word": " الكلام؟", "probability": 0.9185791015625}, {"start": 1455.18, "end": 1455.4, "word": " أو", "probability": 0.66748046875}, {"start": 1455.4, "end": 1455.88, "word": " تساوي", "probability": 0.9864501953125}, {"start": 1455.88, "end": 1456.28, "word": " واحد", "probability": 0.979736328125}, {"start": 1456.28, "end": 1456.98, "word": " واحد", "probability": 0.7283935546875}, {"start": 1456.98, "end": 1457.28, "word": " number", "probability": 0.376708984375}, {"start": 1457.28, "end": 1458.32, "word": " رقم", "probability": 0.8085123697916666}, {"start": 1458.32, "end": 1458.52, "word": " مش", "probability": 0.66552734375}, {"start": 1458.52, "end": 1459.22, "word": " مصفوفة", "probability": 0.97861328125}, {"start": 1459.22, "end": 1459.78, "word": " يبقى", "probability": 0.947265625}, {"start": 1459.78, "end": 1460.14, "word": " ليس", "probability": 0.978759765625}, {"start": 1460.14, "end": 1460.46, "word": " صحيح", "probability": 0.9822998046875}, {"start": 1460.46, "end": 1460.7, "word": " يبقى", "probability": 0.98486328125}, {"start": 1460.7, "end": 1460.92, "word": " لما", "probability": 0.88427734375}, {"start": 1460.92, "end": 1461.46, "word": " ناخد", "probability": 0.68603515625}, {"start": 1461.46, "end": 1461.74, "word": " عامل", "probability": 0.8650716145833334}, {"start": 1461.74, "end": 1462.16, "word": " مشترك", "probability": 0.8797200520833334}, {"start": 1462.16, "end": 1462.64, "word": " في", "probability": 0.64697265625}, {"start": 1462.64, "end": 1463.08, "word": " حالة", "probability": 0.9954427083333334}, {"start": 1463.08, "end": 1463.7, "word": " المصفوفة", "probability": 0.9443359375}, {"start": 1463.7, "end": 1464.18, "word": " بدل", "probability": 0.98193359375}, {"start": 1464.18, "end": 1464.8, "word": " الواحد", "probability": 0.98095703125}, {"start": 1464.8, "end": 1465.28, "word": " في", "probability": 0.9736328125}, {"start": 1465.28, "end": 1466.0, "word": " العملية", "probability": 0.9246419270833334}, {"start": 1466.0, "end": 1466.68, "word": " الشغل", "probability": 0.94580078125}, {"start": 1466.68, "end": 1467.18, "word": " العادى", "probability": 0.9078776041666666}, {"start": 1467.18, "end": 1467.62, "word": " بيصير", "probability": 0.71160888671875}, {"start": 1467.62, "end": 1467.8, "word": " ال", "probability": 0.8544921875}, {"start": 1467.8, "end": 1468.54, "word": " identity", "probability": 0.64990234375}, {"start": 1468.54, "end": 1469.24, "word": " matrix", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 64, "seek": 149777, "start": 1469.79, "end": 1497.77, "text": "تمام تمام يبقى توصلنا الى انه الكلام اللى عندنا طيب احنا عندنا يا بنات ان ال a inverse exist و ال determinant لا يمكن ان يساوي zero تمام يبقى معنى هذا الكلام ان المصوفة لا يمكن ان تساوي zero يبقى مين اللى بده يساوي zero ال C ناقص الله او بمعنى اخر", "tokens": [39237, 10943, 46811, 10943, 7251, 3555, 4587, 7578, 33427, 36520, 8315, 2423, 7578, 16472, 3224, 2423, 28820, 10943, 13672, 7578, 43242, 8315, 23032, 1829, 3555, 1975, 5016, 8315, 43242, 8315, 35186, 4724, 8315, 2655, 16472, 2423, 257, 17340, 2514, 4032, 2423, 41296, 20193, 7251, 43020, 16472, 7251, 3794, 995, 45865, 4018, 46811, 10943, 7251, 3555, 4587, 7578, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 9673, 9381, 38688, 3660, 20193, 7251, 43020, 16472, 6055, 3794, 995, 45865, 4018, 7251, 3555, 4587, 7578, 3714, 9957, 13672, 7578, 47525, 3224, 7251, 3794, 995, 45865, 4018, 2423, 383, 8717, 995, 4587, 9381, 21984, 1975, 2407, 4724, 2304, 3615, 1863, 7578, 1975, 34740], "avg_logprob": -0.17201705195687034, "compression_ratio": 2.00990099009901, "no_speech_prob": 0.0, "words": [{"start": 1469.79, "end": 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"probability": 0.5927734375}, {"start": 1772.59, "end": 1772.87, "word": " ال", "probability": 0.794921875}, {"start": 1772.87, "end": 1774.21, "word": " بي", "probability": 0.690185546875}, {"start": 1774.21, "end": 1774.65, "word": " and", "probability": 0.75341796875}, {"start": 1774.65, "end": 1775.03, "word": " ال", "probability": 0.57763671875}, {"start": 1775.03, "end": 1775.77, "word": " سي", "probability": 0.86474609375}, {"start": 1775.77, "end": 1777.31, "word": " are", "probability": 0.93896484375}, {"start": 1777.31, "end": 1778.81, "word": " two", "probability": 0.81005859375}], "temperature": 1.0}, {"id": 76, "seek": 180719, "start": 1781.57, "end": 1807.19, "text": "inverses of the matrix A then مدالها دول معكوسين طبقا لهذا التعريف يبقاش بده يصير عنها A في B بده يساوي B في A بده يساوي identity matrix", "tokens": [259, 840, 279, 295, 264, 8141, 316, 550, 3714, 3215, 6027, 11296, 11778, 12610, 20449, 4117, 41779, 9957, 23032, 3555, 4587, 995, 46740, 15730, 16712, 3615, 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يمكن", "probability": 0.99267578125}, {"start": 1976.63, "end": 1977.35, "word": " إيجاد", "probability": 0.9306640625}, {"start": 1977.35, "end": 1978.11, "word": " المعكوس", "probability": 0.9356689453125}, {"start": 1978.11, "end": 1979.07, "word": " لمصوفة", "probability": 0.91259765625}, {"start": 1979.07, "end": 1980.03, "word": " ما؟", "probability": 0.706298828125}, {"start": 1980.03, "end": 1980.53, "word": " احنا", "probability": 0.8738606770833334}, {"start": 1980.53, "end": 1981.15, "word": " اتكلمنا", "probability": 0.90986328125}, {"start": 1981.15, "end": 1981.63, "word": " وحطينا", "probability": 0.76328125}, {"start": 1981.63, "end": 1982.17, "word": " العنوان", "probability": 0.9422607421875}, {"start": 1982.17, "end": 1983.05, "word": " معكوس", "probability": 0.72369384765625}, {"start": 1983.05, "end": 1983.63, "word": " المصوفة", "probability": 0.979248046875}, {"start": 1983.63, "end": 1984.19, "word": " حتى", "probability": 0.502471923828125}, {"start": 1984.19, 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"text": "to find a inverse for the n by n matrix A الشكل لأن أنا الاجابة في أكثر من طريقة بالداخل ال first method الطريقة الأولى لإيجاد المعكوس", "tokens": [1353, 915, 257, 17340, 337, 264, 297, 538, 297, 8141, 316, 25124, 28820, 5296, 33456, 41850, 2423, 26108, 16758, 3660, 8978, 5551, 4117, 49115, 9154, 23032, 16572, 28671, 20666, 3215, 47283, 1211, 2423, 700, 3170, 41950, 16572, 28671, 16247, 12610, 7578, 5296, 28814, 1829, 7435, 18513, 9673, 3615, 4117, 41779], "avg_logprob": -0.291666680691289, "compression_ratio": 1.2987012987012987, "no_speech_prob": 0.0, "words": [{"start": 2004.77, "end": 2005.41, "word": "to", "probability": 0.384765625}, {"start": 2005.41, "end": 2006.31, "word": " find", "probability": 0.91650390625}, {"start": 2006.31, "end": 2008.81, "word": " a", "probability": 0.53515625}, {"start": 2008.81, "end": 2009.73, "word": " inverse", "probability": 0.8359375}, {"start": 2009.73, "end": 2011.97, "word": " for", "probability": 0.857421875}, {"start": 2011.97, "end": 2013.57, "word": " the", "probability": 0.80126953125}, {"start": 2013.57, "end": 2014.71, "word": " n", "probability": 0.67822265625}, {"start": 2014.71, "end": 2015.77, "word": " by", "probability": 0.69775390625}, {"start": 2015.77, "end": 2016.45, "word": " n", "probability": 0.93408203125}, {"start": 2016.45, "end": 2018.23, "word": " matrix", "probability": 0.943359375}, {"start": 2018.23, "end": 2019.03, "word": " A", "probability": 0.62109375}, {"start": 2019.03, "end": 2020.67, "word": " الشكل", "probability": 0.639404296875}, {"start": 2020.67, "end": 2020.99, "word": " لأن", "probability": 0.5709228515625}, {"start": 2020.99, "end": 2021.23, "word": " أنا", "probability": 0.2252197265625}, {"start": 2021.23, "end": 2023.25, "word": " الاجابة", "probability": 0.74261474609375}, {"start": 2023.25, "end": 2023.69, "word": " في", "probability": 0.8349609375}, {"start": 2023.69, "end": 2024.17, "word": " أكثر", "probability": 0.884765625}, {"start": 2024.17, "end": 2024.47, "word": " من", "probability": 0.99658203125}, {"start": 2024.47, "end": 2025.05, "word": " طريقة", "probability": 0.9923502604166666}, {"start": 2025.05, "end": 2026.19, "word": " بالداخل", "probability": 0.478851318359375}, {"start": 2026.19, "end": 2026.45, "word": " ال", "probability": 0.7353515625}, {"start": 2026.45, "end": 2027.17, "word": " first", "probability": 0.358154296875}, {"start": 2027.17, "end": 2028.23, "word": " method", "probability": 0.974609375}, {"start": 2028.23, "end": 2030.33, "word": " الطريقة", "probability": 0.9632161458333334}, {"start": 2030.33, "end": 2030.89, "word": " الأولى", "probability": 0.9915364583333334}, {"start": 2030.89, "end": 2031.57, "word": " لإيجاد", "probability": 0.9748046875}, {"start": 2031.57, "end": 2032.45, "word": " المعكوس", "probability": 0.9061279296875}], "temperature": 1.0}, {"id": 87, "seek": 206238, "start": 2033.3, "end": 2062.38, "text": "خطوتين لثالث لهم الخطوة الأولى write the argumented matrix اكتب المصوفة الموسعة a ومعها مين مصوفة الوحدة نمر اتنين use", "tokens": [9778, 9566, 35473, 9957, 5296, 12984, 6027, 12984, 5296, 16095, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 2464, 264, 6770, 292, 8141, 1975, 4117, 2655, 3555, 9673, 9381, 38688, 3660, 9673, 41779, 27884, 257, 4032, 2304, 3615, 11296, 3714, 9957, 3714, 9381, 38688, 3660, 2423, 2407, 24401, 3660, 8717, 29973, 1975, 2655, 1863, 9957, 764], "avg_logprob": -0.20340401413185255, "compression_ratio": 1.3795620437956204, "no_speech_prob": 0.0, "words": [{"start": 2033.3, "end": 2034.34, "word": "خطوتين", "probability": 0.83782958984375}, {"start": 2034.34, "end": 2035.14, "word": " لثالث", "probability": 0.9493408203125}, {"start": 2035.14, "end": 2035.48, "word": " لهم", "probability": 0.75537109375}, {"start": 2035.48, "end": 2036.04, "word": " الخطوة", "probability": 0.9134521484375}, {"start": 2036.04, "end": 2036.84, "word": " الأولى", "probability": 0.9581705729166666}, {"start": 2036.84, "end": 2038.04, "word": " write", 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نمر", "probability": 0.64990234375}, {"start": 2058.74, "end": 2059.38, "word": " اتنين", "probability": 0.965576171875}, {"start": 2059.38, "end": 2062.38, "word": " use", "probability": 0.87841796875}], "temperature": 1.0}, {"id": 88, "seek": 209321, "start": 2065.13, "end": 2093.21, "text": "Echelon form use echelon form to write to write the matrix ايه مع", "tokens": [36, 339, 338, 266, 1254, 764, 36803, 338, 266, 1254, 281, 2464, 281, 2464, 264, 8141, 1975, 1829, 3224, 20449], "avg_logprob": -0.3415178684961228, "compression_ratio": 1.1864406779661016, "no_speech_prob": 0.0, "words": [{"start": 2065.13, "end": 2066.11, "word": "Echelon", "probability": 0.6912841796875}, {"start": 2066.11, "end": 2066.95, "word": " form", "probability": 0.5087890625}, {"start": 2066.95, "end": 2072.91, "word": " use", "probability": 0.2274169921875}, {"start": 2072.91, "end": 2073.43, "word": " echelon", "probability": 0.8546549479166666}, {"start": 2073.43, "end": 2074.01, "word": " form", "probability": 0.94970703125}, {"start": 2074.01, "end": 2074.75, "word": " to", "probability": 0.912109375}, {"start": 2074.75, "end": 2075.41, "word": " write", "probability": 0.935546875}, {"start": 2075.41, "end": 2080.05, "word": " to", "probability": 0.66552734375}, {"start": 2080.05, "end": 2080.73, "word": " write", "probability": 0.943359375}, {"start": 2080.73, "end": 2085.71, "word": " the", "probability": 0.64404296875}, {"start": 2085.71, "end": 2086.61, "word": " matrix", "probability": 0.93896484375}, {"start": 2086.61, "end": 2091.27, "word": " ايه", "probability": 0.7556966145833334}, {"start": 2091.27, "end": 2093.21, "word": " مع", "probability": 0.6826171875}], "temperature": 1.0}, {"id": 89, "seek": 212319, "start": 2093.73, "end": 2123.19, "text": "الـ I N A مع ال I N in the form في الشكل I N و بعدين B then B اللي بتطلع بتكون هي معكوس المصفوفة A نعطي مثال", "tokens": [6027, 39184, 286, 426, 316, 20449, 2423, 286, 426, 294, 264, 1254, 8978, 25124, 28820, 286, 426, 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matrix المعكوس المصفوفة اللي قدامنا هذه إذا أنا بدي أطبقله الخطوطين اللي قلنا عليهم يبقى بدايجي أخدله ال argumentive matrix اللي هي ال A مع مين مع المصفوفة I يبقى هذا الكلام بده يساوي", "tokens": [1078, 507, 8141, 9673, 3615, 4117, 41779, 9673, 9381, 5172, 38688, 3660, 13672, 1829, 12174, 3215, 10943, 8315, 29538, 11933, 15730, 41850, 4724, 16254, 5551, 9566, 3555, 4587, 43761, 33962, 9566, 2407, 9566, 9957, 13672, 1829, 12174, 1211, 8315, 25894, 16095, 7251, 3555, 4587, 7578, 4724, 28259, 1829, 7435, 1829, 5551, 9778, 3215, 43761, 2423, 6770, 488, 8141, 13672, 1829, 39896, 2423, 316, 20449, 3714, 9957, 20449, 9673, 9381, 5172, 38688, 3660, 286, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865], "avg_logprob": -0.29332387244159525, "compression_ratio": 1.6772486772486772, "no_speech_prob": 0.0, "words": [{"start": 2232.83, "end": 2233.81, "word": "identity", "probability": 0.5712890625}, {"start": 2233.81, "end": 2234.29, "word": " matrix", 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2251.51, "word": " مع", "probability": 0.99365234375}, {"start": 2251.51, "end": 2252.01, "word": " مين", "probability": 0.7161865234375}, {"start": 2252.01, "end": 2252.67, "word": " مع", "probability": 0.88232421875}, {"start": 2252.67, "end": 2253.93, "word": " المصفوفة", "probability": 0.973828125}, {"start": 2253.93, "end": 2254.27, "word": " I", "probability": 0.96484375}, {"start": 2254.27, "end": 2255.17, "word": " يبقى", "probability": 0.9617919921875}, {"start": 2255.17, "end": 2255.41, "word": " هذا", "probability": 0.96875}, {"start": 2255.41, "end": 2255.93, "word": " الكلام", "probability": 0.9703776041666666}, {"start": 2255.93, "end": 2256.31, "word": " بده", "probability": 0.61669921875}, {"start": 2256.31, "end": 2256.79, "word": " يساوي", "probability": 0.941650390625}], "temperature": 1.0}, {"id": 97, "seek": 227455, "start": 2257.35, "end": 2274.55, "text": "هذه المصوفة هاي واحد هاي تلاتة هاي سالب واحد Zero واحد اتنين سالب واحد Zero تمانية هو Y الخاطر المصوفة الواحدة واحد من نفس النظامها Zero واحد Zero Zero Zero واحد", "tokens": [3224, 24192, 9673, 9381, 38688, 3660, 8032, 47302, 36764, 24401, 8032, 47302, 6055, 1211, 9307, 3660, 8032, 47302, 8608, 6027, 3555, 36764, 24401, 17182, 36764, 24401, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 36764, 24401, 17182, 46811, 7649, 10632, 31439, 398, 33962, 41193, 2288, 9673, 9381, 38688, 3660, 2423, 14407, 24401, 3660, 36764, 24401, 9154, 8717, 36178, 28239, 19913, 10943, 11296, 17182, 36764, 24401, 17182, 17182, 17182, 36764, 24401], "avg_logprob": -0.2810267737933568, "compression_ratio": 2.0381679389312977, "no_speech_prob": 0.0, "words": [{"start": 2257.35, "end": 2257.83, "word": "هذه", "probability": 0.47705078125}, {"start": 2257.83, "end": 2258.55, "word": " المصوفة", "probability": 0.73760986328125}, {"start": 2258.55, "end": 2258.91, "word": " هاي", "probability": 0.3931884765625}, {"start": 2258.91, "end": 2259.31, "word": " واحد", "probability": 0.937744140625}, {"start": 2259.31, "end": 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{"start": 2272.51, "end": 2273.03, "word": " Zero", "probability": 0.88134765625}, {"start": 2273.03, "end": 2273.77, "word": " Zero", "probability": 0.970703125}, {"start": 2273.77, "end": 2274.55, "word": " واحد", "probability": 0.905517578125}], "temperature": 1.0}, {"id": 98, "seek": 229086, "start": 2275.88, "end": 2290.86, "text": "أعمل اللي بدك هي رياضيا بحيث أخلي مصوفة الوحدة في هذا المكان وهذه تنتقل بأرقام جديدة لوين إلى اليامين كويس يبقى مشان هيك أنا بدي هذا يكون جداش", "tokens": [10721, 25957, 1211, 13672, 1829, 47525, 4117, 39896, 12602, 1829, 46958, 25528, 4724, 5016, 1829, 12984, 5551, 9778, 20292, 3714, 9381, 38688, 3660, 2423, 2407, 24401, 3660, 8978, 23758, 9673, 41361, 37037, 24192, 6055, 29399, 4587, 1211, 4724, 10721, 2288, 4587, 10943, 10874, 16254, 41891, 5296, 2407, 9957, 30731, 45595, 10943, 9957, 9122, 45865, 3794, 7251, 3555, 4587, 7578, 37893, 7649, 39896, 4117, 41850, 4724, 16254, 23758, 7251, 30544, 10874, 3215, 33599], "avg_logprob": -0.3035102772386107, "compression_ratio": 1.6474358974358974, "no_speech_prob": 0.0, "words": [{"start": 2275.88, "end": 2276.48, "word": "أعمل", "probability": 0.63092041015625}, {"start": 2276.48, "end": 2276.56, "word": " اللي", "probability": 0.46795654296875}, {"start": 2276.56, "end": 2276.9, "word": " بدك", "probability": 0.880615234375}, {"start": 2276.9, "end": 2277.12, "word": " هي", "probability": 0.90869140625}, {"start": 2277.12, "end": 2278.0, "word": " رياضيا", "probability": 0.916748046875}, {"start": 2278.0, "end": 2278.8, "word": " بحيث", "probability": 0.847412109375}, {"start": 2278.8, "end": 2279.36, "word": " أخلي", "probability": 0.6470540364583334}, {"start": 2279.36, "end": 2280.02, "word": " مصوفة", "probability": 0.645050048828125}, {"start": 2280.02, "end": 2280.44, "word": " الوحدة", "probability": 0.943603515625}, {"start": 2280.44, "end": 2280.6, "word": " في", "probability": 0.95458984375}, {"start": 2280.6, "end": 2280.84, "word": " هذا", "probability": 0.9560546875}, {"start": 2280.84, "end": 2281.4, "word": " المكان", "probability": 0.992919921875}, {"start": 2281.4, "end": 2282.46, "word": " وهذه", "probability": 0.774169921875}, {"start": 2282.46, "end": 2283.18, "word": " تنتقل", "probability": 0.9705810546875}, {"start": 2283.18, "end": 2283.78, "word": " بأرقام", "probability": 0.97529296875}, {"start": 2283.78, "end": 2284.32, "word": " جديدة", "probability": 0.9895833333333334}, {"start": 2284.32, "end": 2284.92, "word": " لوين", "probability": 0.5349527994791666}, {"start": 2284.92, "end": 2285.6, "word": " إلى", "probability": 0.349609375}, {"start": 2285.6, "end": 2286.4, "word": " اليامين", "probability": 0.620361328125}, {"start": 2286.4, "end": 2287.32, "word": " كويس", "probability": 0.7710774739583334}, {"start": 2287.32, "end": 2288.04, "word": " يبقى", "probability": 0.8800048828125}, {"start": 2288.04, "end": 2288.44, "word": " مشان", "probability": 0.73193359375}, {"start": 2288.44, "end": 2288.82, "word": " هيك", "probability": 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"probability": 0.8291015625}, {"start": 2310.95, "end": 2311.59, "word": " سالب", "probability": 0.9435221354166666}, {"start": 2311.59, "end": 2312.23, "word": " واحد", "probability": 0.982177734375}, {"start": 2312.23, "end": 2312.73, "word": " و", "probability": 0.76025390625}, {"start": 2312.73, "end": 2313.29, "word": " واحد", "probability": 0.6929931640625}, {"start": 2313.29, "end": 2313.77, "word": " Zero", "probability": 0.19580078125}, {"start": 2313.77, "end": 2314.49, "word": " Zero", "probability": 0.60693359375}, {"start": 2314.49, "end": 2315.47, "word": " هيقفلنا", "probability": 0.840576171875}], "temperature": 1.0}, {"id": 100, "seek": 234317, "start": 2316.02, "end": 2343.18, "text": "نجي لبعده زي ما هو Zero واحد اتنين Zero واحد Zero اضفنا إضافة يبقى هنا Zero وهنا تلاتة تمام؟ واضفنا يبقى هنا سبعة واضفنا يبقى هنا واحد وهنا Zero وهنا واحد لأنه إضافة ماسويتش أشياء واضحة زين؟ في أي تسويل؟ طيب، نكمل", "tokens": [1863, 7435, 1829, 5296, 3555, 22488, 3224, 30767, 1829, 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1.0}, {"id": 103, "seek": 239421, "start": 2378.41, "end": 2394.21, "text": "و لما ضربت في سالب تلاتة بيصير سالب ستة و سالب واحد سالب سبعة سالب تلاتة بيصير هنا واحد زي ما هي و هنا سالب تلاتة مظبوط يا بنات؟", "tokens": [2407, 5296, 15042, 48812, 25513, 2655, 8978, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 4724, 1829, 9381, 13546, 8608, 6027, 3555, 8608, 2655, 3660, 4032, 8608, 6027, 3555, 36764, 24401, 8608, 6027, 3555, 8608, 3555, 27884, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 4724, 1829, 9381, 13546, 34105, 36764, 24401, 30767, 1829, 19446, 39896, 4032, 34105, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 3714, 19913, 3555, 2407, 9566, 35186, 4724, 8315, 2655, 22807], "avg_logprob": -0.20217482423460162, "compression_ratio": 1.9322033898305084, "no_speech_prob": 0.0, "words": [{"start": 2378.41, "end": 2378.55, "word": "و", "probability": 0.2274169921875}, {"start": 2378.55, "end": 2378.83, "word": " لما", "probability": 0.56024169921875}, {"start": 2378.83, "end": 2379.47, "word": " 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2631.05, "word": " في", "probability": 0.17822265625}, {"start": 2631.05, "end": 2634.57, "word": " الماتريكس", "probability": 0.95625}, {"start": 2634.57, "end": 2635.33, "word": " A", "probability": 0.95166015625}, {"start": 2635.33, "end": 2637.17, "word": " من", "probability": 0.5126953125}, {"start": 2637.17, "end": 2637.33, "word": " الـ", "probability": 0.149688720703125}, {"start": 2637.33, "end": 2638.35, "word": " Cofactor", "probability": 0.6946614583333334}, {"start": 2638.35, "end": 2639.83, "word": " من", "probability": 0.89013671875}, {"start": 2639.83, "end": 2641.25, "word": " الـ", "probability": 0.4571533203125}, {"start": 2641.25, "end": 2643.49, "word": " Cofactor", "probability": 0.888671875}, {"start": 2643.49, "end": 2646.45, "word": " من", "probability": 0.912109375}, {"start": 2646.45, "end": 2646.65, "word": " الـ", "probability": 0.642822265625}, {"start": 2646.65, "end": 2647.71, "word": " Cofactor", "probability": 0.8883463541666666}, {"start": 2647.71, "end": 2648.67, "word": " من", "probability": 0.650390625}, {"start": 2648.67, "end": 2651.89, "word": " AIG", "probability": 0.623291015625}, {"start": 2651.89, "end": 2653.89, "word": " وهو", "probability": 0.55145263671875}, {"start": 2653.89, "end": 2656.09, "word": " IN", "probability": 0.24072265625}], "temperature": 1.0}, {"id": 115, "seek": 268090, "start": 2657.54, "end": 2680.9, "text": "replace استبدل a i j by by a i j بدي اسوي السلب واحد مرفوع للأس واحد زائد j في ال minor اللي هو m i j", "tokens": [265, 6742, 44713, 44510, 1211, 257, 741, 361, 538, 538, 257, 741, 361, 4724, 16254, 24525, 45865, 21136, 46152, 36764, 24401, 3714, 28480, 45367, 24976, 10721, 3794, 36764, 24401, 30767, 16373, 3215, 361, 8978, 2423, 6696, 13672, 1829, 31439, 275, 741, 361], "avg_logprob": -0.3895348823347757, "compression_ratio": 1.2820512820512822, "no_speech_prob": 0.0, "words": [{"start": 2657.54, "end": 2658.72, "word": "replace", "probability": 0.64990234375}, {"start": 2658.72, "end": 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"probability": 0.9072265625}, {"start": 2680.52, "end": 2680.9, "word": " j", "probability": 0.69873046875}], "temperature": 1.0}, {"id": 116, "seek": 271362, "start": 2685.82, "end": 2713.62, "text": "هذه الخطوة الأولى الخطوة الثانية take the transpose of the resulting matrix resulting matrix in part one", "tokens": [3224, 24192, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 33962, 9566, 2407, 3660, 6024, 104, 7649, 10632, 747, 264, 25167, 295, 264, 16505, 8141, 16505, 8141, 294, 644, 472], "avg_logprob": -0.24674478471279143, "compression_ratio": 1.346938775510204, "no_speech_prob": 0.0, "words": [{"start": 2685.82, "end": 2686.14, "word": "هذه", "probability": 0.572021484375}, {"start": 2686.14, "end": 2686.52, "word": " الخطوة", "probability": 0.899658203125}, {"start": 2686.52, "end": 2686.82, "word": " الأولى", "probability": 0.8185221354166666}, {"start": 2686.82, "end": 2687.38, "word": " الخطوة", "probability": 0.81195068359375}, {"start": 2687.38, "end": 2688.14, "word": " الثانية", "probability": 0.9520263671875}, {"start": 2688.14, "end": 2690.5, "word": " take", "probability": 0.28076171875}, {"start": 2690.5, "end": 2692.68, "word": " the", "probability": 0.8271484375}, {"start": 2692.68, "end": 2695.22, "word": " transpose", "probability": 0.740234375}, {"start": 2695.22, "end": 2700.12, "word": " of", "probability": 0.6572265625}, {"start": 2700.12, "end": 2701.88, "word": " the", "probability": 0.744140625}, {"start": 2701.88, "end": 2703.78, "word": " resulting", "probability": 0.96923828125}, {"start": 2703.78, "end": 2707.2, "word": " matrix", "probability": 0.94140625}, {"start": 2707.2, "end": 2709.8, "word": " resulting", "probability": 0.70361328125}, {"start": 2709.8, "end": 2710.66, "word": " matrix", "probability": 0.9677734375}, {"start": 2710.66, "end": 2711.34, "word": " in", "probability": 0.80712890625}, {"start": 2711.34, "end": 2713.08, "word": " part", "probability": 0.89013671875}, {"start": 2713.08, "end": 2713.62, "word": " one", "probability": 0.6728515625}], "temperature": 1.0}, {"id": 117, "seek": 274456, "start": 2716.18, "end": 2744.56, "text": "part one and denoted it by B and denoted it by B أعطيها الرمز B خطوة التالتة والأخيرة find", "tokens": [6971, 472, 293, 1441, 23325, 309, 538, 363, 293, 1441, 23325, 309, 538, 363, 5551, 3615, 9566, 1829, 11296, 34892, 2304, 11622, 363, 16490, 9566, 2407, 3660, 16712, 6027, 2655, 3660, 16070, 10721, 9778, 48923, 915], "avg_logprob": -0.22677365348145767, "compression_ratio": 1.263157894736842, "no_speech_prob": 0.0, "words": [{"start": 2716.18, "end": 2716.64, "word": "part", "probability": 0.256103515625}, {"start": 2716.64, "end": 2717.18, "word": " one", "probability": 0.68359375}, {"start": 2717.18, "end": 2719.54, "word": " and", "probability": 0.87548828125}, {"start": 2719.54, "end": 2724.62, "word": " denoted", "probability": 0.862548828125}, {"start": 2724.62, "end": 2728.08, "word": " it", "probability": 0.89453125}, {"start": 2728.08, "end": 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"word": " والأخيرة", "probability": 0.875}, {"start": 2743.22, "end": 2744.56, "word": " find", "probability": 0.79541015625}], "temperature": 1.0}, {"id": 118, "seek": 276879, "start": 2746.07, "end": 2768.79, "text": "A inverse from the formula من الصيغة A inverse يسوى واحد على ال determinant لل A هذا كله في المصوفة B", "tokens": [32, 17340, 490, 264, 8513, 9154, 31767, 1829, 17082, 3660, 316, 17340, 7251, 3794, 2407, 7578, 36764, 24401, 15844, 2423, 41296, 24976, 316, 23758, 28242, 3224, 8978, 9673, 9381, 38688, 3660, 363], "avg_logprob": -0.28929924242424243, "compression_ratio": 1.139344262295082, "no_speech_prob": 0.0, "words": [{"start": 2746.07, "end": 2746.53, "word": "A", "probability": 0.465087890625}, {"start": 2746.53, "end": 2747.39, "word": " inverse", "probability": 0.309326171875}, {"start": 2747.39, "end": 2749.05, "word": " from", "probability": 0.70654296875}, {"start": 2749.05, "end": 2751.15, "word": " the", "probability": 0.56884765625}, {"start": 2751.15, "end": 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2765.93, "word": " هذا", "probability": 0.64404296875}, {"start": 2765.93, "end": 2767.09, "word": " كله", "probability": 0.985107421875}, {"start": 2767.09, "end": 2767.37, "word": " في", "probability": 0.57958984375}, {"start": 2767.37, "end": 2768.65, "word": " المصوفة", "probability": 0.7403564453125}, {"start": 2768.65, "end": 2768.79, "word": " B", "probability": 0.74951171875}], "temperature": 1.0}, {"id": 119, "seek": 277928, "start": 2778.72, "end": 2779.28, "text": "ماذا بحاجة؟", "tokens": [2304, 45636, 995, 4724, 5016, 26108, 3660, 22807], "avg_logprob": -1.1336805555555556, "compression_ratio": 0.7241379310344828, "no_speech_prob": 0.0184783935546875, "words": [{"start": 2778.72, "end": 2778.96, "word": "ماذا", "probability": 0.4702860514322917}, {"start": 2778.96, "end": 2779.28, "word": " بحاجة؟", "probability": 0.41163330078125}], "temperature": 1.0}, {"id": 120, "seek": 280886, "start": 2788.86, "end": 2808.86, "text": "يبقى باختصار بدنا نعمل ثلاث خطوات الخطوة الأولى بدي أشيل كل a ij و أضع كوفكتور تبعه ناقص واحد من aij في ال m ij الخطوة الثانية بدي أجيب مدور هذه المصوفة اللى نتجت في الخطوة الأولى", "tokens": [1829, 3555, 4587, 7578, 4724, 47283, 2655, 9381, 9640, 47525, 8315, 8717, 25957, 1211, 38637, 1211, 5718, 104, 16490, 9566, 2407, 9307, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 4724, 16254, 5551, 8592, 26895, 28242, 257, 741, 73, 4032, 5551, 11242, 3615, 9122, 38688, 4117, 2655, 13063, 6055, 3555, 3615, 3224, 8717, 995, 4587, 9381, 36764, 24401, 9154, 257, 1718, 8978, 2423, 275, 741, 73, 33962, 9566, 2407, 3660, 6024, 104, 7649, 10632, 4724, 16254, 5551, 7435, 1829, 3555, 3714, 3215, 13063, 29538, 9673, 9381, 38688, 3660, 13672, 7578, 8717, 2655, 7435, 2655, 8978, 33962, 9566, 2407, 3660, 16247, 12610, 7578], "avg_logprob": -0.24678308385259964, "compression_ratio": 1.7784090909090908, "no_speech_prob": 0.0, "words": [{"start": 2788.86, "end": 2789.22, "word": "يبقى", "probability": 0.83538818359375}, {"start": 2789.22, "end": 2789.78, "word": " باختصار", "probability": 0.971875}, {"start": 2789.78, "end": 2790.02, "word": " بدنا", "probability": 0.506103515625}, {"start": 2790.02, "end": 2790.22, "word": " نعمل", "probability": 0.9586588541666666}, {"start": 2790.22, "end": 2790.56, "word": " ثلاث", "probability": 0.9410400390625}, {"start": 2790.56, "end": 2791.12, "word": " خطوات", "probability": 0.9676513671875}, {"start": 2791.12, "end": 2792.14, "word": " الخطوة", "probability": 0.9158935546875}, {"start": 2792.14, "end": 2792.62, "word": " الأولى", "probability": 0.9759114583333334}, {"start": 2792.62, "end": 2792.94, "word": " بدي", "probability": 0.610107421875}, {"start": 2792.94, "end": 2793.42, "word": " أشيل", "probability": 0.8689778645833334}, {"start": 2793.42, "end": 2793.84, "word": " كل", "probability": 0.87451171875}, {"start": 2793.84, "end": 2794.22, "word": " a", "probability": 0.364501953125}, {"start": 2794.22, "end": 2794.88, "word": " ij", "probability": 0.423828125}, {"start": 2794.88, "end": 2795.36, "word": " و", "probability": 0.91796875}, {"start": 2795.36, "end": 2795.62, "word": " أضع", "probability": 0.6110026041666666}, {"start": 2795.62, "end": 2796.66, "word": " كوفكتور", "probability": 0.6266845703125}, {"start": 2796.66, "end": 2797.32, "word": " تبعه", "probability": 0.744140625}, {"start": 2797.32, "end": 2798.04, "word": " ناقص", "probability": 0.682464599609375}, {"start": 2798.04, "end": 2798.26, "word": " واحد", "probability": 0.906982421875}, {"start": 2798.26, "end": 2798.42, "word": " من", "probability": 0.490966796875}, {"start": 2798.42, "end": 2798.84, "word": " aij", "probability": 0.632080078125}, {"start": 2798.84, "end": 2799.06, "word": " في", "probability": 0.7060546875}, {"start": 2799.06, "end": 2799.46, "word": " ال", "probability": 0.406982421875}, {"start": 2799.46, "end": 2799.82, "word": " m", "probability": 0.1951904296875}, {"start": 2799.82, "end": 2800.54, "word": " ij", "probability": 0.791015625}, {"start": 2800.54, "end": 2801.58, "word": " الخطوة", "probability": 0.83343505859375}, {"start": 2801.58, "end": 2802.06, "word": " الثانية", "probability": 0.9720458984375}, {"start": 2802.06, "end": 2802.62, "word": " بدي", "probability": 0.866455078125}, {"start": 2802.62, "end": 2803.02, "word": " أجيب", "probability": 0.9610595703125}, {"start": 2803.02, "end": 2803.78, "word": " مدور", "probability": 0.9762369791666666}, {"start": 2803.78, "end": 2804.36, "word": " هذه", "probability": 0.97705078125}, {"start": 2804.36, "end": 2805.44, "word": " المصوفة", "probability": 0.9425048828125}, {"start": 2805.44, "end": 2806.24, "word": " اللى", "probability": 0.7861328125}, {"start": 2806.24, "end": 2807.04, "word": " نتجت", "probability": 0.9808349609375}, {"start": 2807.04, "end": 2807.44, "word": " في", "probability": 0.8837890625}, {"start": 2807.44, "end": 2808.16, "word": " الخطوة", "probability": 0.97900390625}, {"start": 2808.16, "end": 2808.86, "word": " الأولى", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 121, "seek": 282796, "start": 2809.18, "end": 2827.96, "text": "خطوة تالتة المصوفة اللى حصلت عليها بدي أضربها في واحد على محدد المصوفة وهذا يتفق مع الكلام اللى قبل قليل ليش محدد المصوفة لا يساوي zero لأن لو كان المحدد يساوي zero هل بقدر أجيب هذا المعكوس؟", "tokens": [9778, 9566, 2407, 3660, 6055, 6027, 2655, 3660, 9673, 9381, 38688, 3660, 13672, 7578, 11331, 36520, 2655, 25894, 11296, 4724, 16254, 5551, 11242, 25513, 11296, 8978, 36764, 24401, 15844, 3714, 24401, 3215, 9673, 9381, 38688, 3660, 37037, 15730, 7251, 2655, 5172, 4587, 20449, 2423, 28820, 10943, 13672, 7578, 12174, 36150, 12174, 20292, 1211, 32239, 8592, 3714, 24401, 3215, 9673, 9381, 38688, 3660, 20193, 7251, 3794, 995, 45865, 4018, 5296, 33456, 45164, 25961, 9673, 24401, 3215, 7251, 3794, 995, 45865, 4018, 8032, 1211, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 23758, 9673, 3615, 4117, 41779, 22807], "avg_logprob": -0.11612955519619088, "compression_ratio": 1.8876404494382022, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2809.18, "end": 2809.78, "word": "خطوة", "probability": 0.9180908203125}, {"start": 2809.78, "end": 2810.3, "word": " تالتة", "probability": 0.9390869140625}, {"start": 2810.3, "end": 2810.82, "word": " المصوفة", "probability": 0.847412109375}, {"start": 2810.82, "end": 2810.96, "word": " اللى", "probability": 0.757568359375}, {"start": 2810.96, "end": 2811.46, "word": " حصلت", "probability": 0.97509765625}, {"start": 2811.46, "end": 2811.78, "word": " عليها", "probability": 0.98974609375}, {"start": 2811.78, "end": 2812.04, "word": " بدي", "probability": 0.5362548828125}, {"start": 2812.04, "end": 2812.48, "word": " أضربها", "probability": 0.816650390625}, {"start": 2812.48, "end": 2812.62, "word": " في", "probability": 0.892578125}, {"start": 2812.62, "end": 2813.0, "word": " واحد", "probability": 0.990478515625}, {"start": 2813.0, "end": 2813.24, "word": " على", "probability": 0.84716796875}, {"start": 2813.24, "end": 2814.04, "word": " محدد", "probability": 0.9915364583333334}, {"start": 2814.04, "end": 2815.28, "word": " المصوفة", "probability": 0.9871826171875}, {"start": 2815.28, "end": 2815.64, "word": " وهذا", "probability": 0.840087890625}, {"start": 2815.64, "end": 2816.38, "word": " يتفق", "probability": 0.96826171875}, {"start": 2816.38, "end": 2816.88, "word": " مع", "probability": 0.9853515625}, {"start": 2816.88, "end": 2817.28, "word": " الكلام", "probability": 0.9505208333333334}, {"start": 2817.28, "end": 2817.42, "word": " اللى", "probability": 0.96875}, {"start": 2817.42, "end": 2818.18, "word": " قبل", "probability": 0.931640625}, {"start": 2818.18, "end": 2818.74, "word": " قليل", "probability": 0.9822591145833334}, {"start": 2818.74, "end": 2819.32, "word": " ليش", "probability": 0.80078125}, {"start": 2819.32, "end": 2820.3, "word": " محدد", "probability": 0.98779296875}, {"start": 2820.3, "end": 2821.36, "word": " المصوفة", "probability": 0.9896240234375}, {"start": 2821.36, "end": 2821.92, "word": " لا", "probability": 0.5654296875}, {"start": 2821.92, "end": 2822.76, "word": " يساوي", "probability": 0.9539794921875}, {"start": 2822.76, "end": 2823.4, "word": " zero", "probability": 0.450927734375}, {"start": 2823.4, "end": 2824.16, "word": " لأن", "probability": 0.70166015625}, {"start": 2824.16, "end": 2824.38, "word": " لو", "probability": 0.84765625}, {"start": 2824.38, "end": 2824.66, "word": " كان", "probability": 0.978515625}, {"start": 2824.66, "end": 2825.28, "word": " المحدد", "probability": 0.98583984375}, {"start": 2825.28, "end": 2825.68, "word": " يساوي", "probability": 0.981201171875}, {"start": 2825.68, "end": 2825.96, "word": " zero", "probability": 0.84765625}, {"start": 2825.96, "end": 2826.28, "word": " هل", "probability": 0.967529296875}, {"start": 2826.28, "end": 2826.7, "word": " بقدر", "probability": 0.9423828125}, {"start": 2826.7, "end": 2826.98, "word": " أجيب", "probability": 0.920654296875}, {"start": 2826.98, "end": 2827.18, "word": " هذا", "probability": 0.935546875}, {"start": 2827.18, "end": 2827.96, "word": " المعكوس؟", "probability": 0.8673828125}], "temperature": 1.0}, {"id": 122, "seek": 284731, "start": 2828.15, "end": 2847.31, "text": "يبقى فيش مكان يبقى هذا الكلام الذي ادعيناه قبل قليل الآن السبب في أن المحدد لا يساوي zero يبقى بدي أخل المعكوس exist وإلا لو كان المحدد يساوي zero لأصبح المعكوس غير موجود أعطيكم العافية", "tokens": [1829, 3555, 4587, 7578, 8978, 8592, 3714, 41361, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 43527, 1975, 3215, 3615, 9957, 40294, 12174, 36150, 12174, 20292, 1211, 6024, 48506, 21136, 3555, 3555, 8978, 14739, 9673, 24401, 3215, 20193, 7251, 3794, 995, 45865, 4018, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 9778, 1211, 9673, 3615, 4117, 41779, 2514, 4032, 28814, 15040, 45164, 25961, 9673, 24401, 3215, 7251, 3794, 995, 45865, 4018, 5296, 10721, 9381, 49628, 9673, 3615, 4117, 41779, 32771, 13546, 3714, 29245, 23328, 5551, 3615, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.21841032965027768, "compression_ratio": 1.7459459459459459, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2828.15, "end": 2828.53, "word": "يبقى", "probability": 0.7762451171875}, {"start": 2828.53, "end": 2828.81, "word": " فيش", "probability": 0.39013671875}, {"start": 2828.81, "end": 2829.17, "word": " مكان", "probability": 0.704833984375}, {"start": 2829.17, "end": 2829.47, "word": " يبقى", "probability": 0.967529296875}, {"start": 2829.47, "end": 2829.67, "word": " هذا", "probability": 0.88330078125}, {"start": 2829.67, "end": 2830.29, "word": " الكلام", "probability": 0.9471028645833334}, {"start": 2830.29, "end": 2831.05, "word": " الذي", "probability": 0.5859375}, {"start": 2831.05, "end": 2831.71, "word": " ادعيناه", "probability": 0.736865234375}, {"start": 2831.71, "end": 2832.09, "word": " قبل", "probability": 0.99365234375}, {"start": 2832.09, "end": 2832.73, "word": " قليل", "probability": 0.9884440104166666}, {"start": 2832.73, "end": 2833.59, "word": " الآن", "probability": 0.6944580078125}, {"start": 2833.59, "end": 2834.37, "word": " السبب", "probability": 0.9723307291666666}, {"start": 2834.37, "end": 2834.51, "word": " في", "probability": 0.87158203125}, {"start": 2834.51, "end": 2834.65, "word": " أن", "probability": 0.363525390625}, {"start": 2834.65, "end": 2835.19, "word": " المحدد", "probability": 0.9833984375}, {"start": 2835.19, "end": 2835.33, "word": " لا", "probability": 0.65185546875}, {"start": 2835.33, "end": 2835.93, "word": " يساوي", "probability": 0.8720703125}, {"start": 2835.93, "end": 2836.33, "word": " zero", "probability": 0.429931640625}, {"start": 2836.33, "end": 2837.51, "word": " يبقى", "probability": 0.969970703125}, {"start": 2837.51, "end": 2838.17, "word": " بدي", "probability": 0.546142578125}, {"start": 2838.17, "end": 2838.41, "word": " أخل", "probability": 0.5352376302083334}, {"start": 2838.41, "end": 2839.13, "word": " المعكوس", "probability": 0.78472900390625}, {"start": 2839.13, "end": 2839.93, "word": " exist", "probability": 0.87646484375}, {"start": 2839.93, "end": 2840.71, "word": " وإلا", "probability": 0.8810221354166666}, {"start": 2840.71, "end": 2840.95, "word": " لو", "probability": 0.97119140625}, {"start": 2840.95, "end": 2841.19, "word": " كان", "probability": 0.98779296875}, {"start": 2841.19, "end": 2841.73, "word": " المحدد", "probability": 0.9951171875}, {"start": 2841.73, "end": 2842.17, "word": " يساوي", "probability": 0.981689453125}, {"start": 2842.17, "end": 2842.55, "word": " zero", "probability": 0.83056640625}, {"start": 2842.55, "end": 2843.45, "word": " لأصبح", "probability": 0.81732177734375}, {"start": 2843.45, "end": 2844.29, "word": " المعكوس", "probability": 0.981689453125}, {"start": 2844.29, "end": 2845.49, "word": " غير", "probability": 0.994873046875}, {"start": 2845.49, "end": 2846.43, "word": " موجود", "probability": 0.9925130208333334}, {"start": 2846.43, "end": 2846.89, "word": " أعطيكم", "probability": 0.78984375}, {"start": 2846.89, "end": 2847.31, "word": " العافية", "probability": 0.8580729166666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2848.3455, "duration_after_vad": 2718.3999999999946}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Mrn4yfKCaMs_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Mrn4yfKCaMs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..379e7f13a8048b7eb746326e1187b22c1b118133
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Mrn4yfKCaMs_postprocess.srt
@@ -0,0 +1,1968 @@
+1
+00:00:20,700 --> 00:00:24,540
+بسم الله الرحمن الرحيم لازلنا في section تلاتة
+
+2
+00:00:24,540 --> 00:00:29,360
+سبعة اللي بتحدث عن ال linear transformations وما
+
+3
+00:00:29,360 --> 00:00:33,880
+درسناه سابقا تعريف ال linear transformation وعرفنا
+
+4
+00:00:33,880 --> 00:00:36,920
+انه function من vector space إلى vector space تاني
+
+5
+00:00:36,920 --> 00:00:42,050
+وتعقق خاصيتينوبعد ذلك رحنا جيبنا الـKernel
+
+6
+00:00:42,050 --> 00:00:45,890
+للـLinear Transformation و أثبتنا إنه الـSubspace
+
+7
+00:00:45,890 --> 00:00:51,110
+من الـSpace الأساسي و رحنا جيبنا الـRange كذلك
+
+8
+00:00:51,110 --> 00:00:55,110
+للـT أو للـLinear Transformation و أثبتنا إنه
+
+9
+00:00:55,110 --> 00:00:58,850
+Subspace من الـVector Space الثاني و ابتدأنا نأخذ
+
+10
+00:00:58,850 --> 00:01:03,870
+على ذلك أمثلة و أخدنا ثلاثة أمثلة و هذا هو المثال
+
+11
+00:01:03,870 --> 00:01:09,040
+الرابعإذا المثال الرابع بيقول افترض ان T من R2 الى
+
+12
+00:01:09,040 --> 00:01:14,840
+R2 بيه linear transformation defined by T of X بدي
+
+13
+00:01:14,840 --> 00:01:19,960
+سوى X طبعا احنا اخدنا مثال المرة الماضية انه اي
+
+14
+00:01:19,960 --> 00:01:25,120
+linear transformation من ال Rn الى ال Rm بتكون على
+
+15
+00:01:25,120 --> 00:01:31,940
+الشكل T of X بدي سوى Min Xأذا من R2 إلى R2 الـ
+
+16
+00:01:31,940 --> 00:01:36,680
+Linear Transformation هي T of X بدي ساوي AX و بحيث
+
+17
+00:01:36,680 --> 00:01:41,600
+الـ A هي المصفوفة 3 سلب 2 سلب 6 سلب .. اللي هو 4
+
+18
+00:01:41,600 --> 00:01:46,560
+طلب عدة شغلات ال kernel التي بدي أعرف شو شكله
+
+19
+00:01:46,560 --> 00:01:52,380
+اتنين بدي أعرف ال bases لل kernel تلاتة بدي أسأل
+
+20
+00:01:52,380 --> 00:01:57,700
+هل ال element هذا موجود في ال kernel لاللإجابة علي
+
+21
+00:01:57,700 --> 00:02:03,080
+هذا السؤال بدنا نروح نحط ال T of X ال X هذا
+
+22
+00:02:03,080 --> 00:02:09,700
+element وين بناطى؟ في R2 يبقى عبارة عن مركبتين X1
+
+23
+00:02:09,700 --> 00:02:18,580
+و X2 إذا بقدر أقول نمرا إيه هنا احنا عندنا T of X
+
+24
+00:02:18,580 --> 00:02:26,410
+يعني T of X1 و X2شكل ان هنا بدك تحطيها على شكل
+
+25
+00:02:26,410 --> 00:02:32,690
+مصففة مع أنها مشكلة بقول T of هذا X واحد وهذا X
+
+26
+00:02:32,690 --> 00:02:39,590
+اتنين على شكل مصففة بصفين و عمودين واحد بده يسوي A
+
+27
+00:02:39,590 --> 00:02:46,330
+X ال A هي عبارة عن مين تلاتة سلب اتنين سلب ستة
+
+28
+00:02:46,330 --> 00:02:54,400
+اربعة في ال X ال E X واحد و X اتنينإذا أصبح ال T
+
+29
+00:02:54,400 --> 00:03:01,920
+of X على الشكل التالي يبقى
+
+30
+00:03:01,920 --> 00:03:06,620
+الصف الأول في العمود الأول ثلاثة X واحد minus
+
+31
+00:03:06,620 --> 00:03:12,940
+اتنين X اتنين الصف الثاني في العمود الأول ناقص ستة
+
+32
+00:03:12,940 --> 00:03:20,960
+X واحد زائد اربعة X اتنينيبقى هي اعطيت شكل مين؟
+
+33
+00:03:20,960 --> 00:03:25,860
+شكل ال function بعد ما اعطيت شكل ال function بدي
+
+34
+00:03:25,860 --> 00:03:29,800
+اروح ادور على مين؟ على اللي انا طالبه ال kernel ل
+
+35
+00:03:29,800 --> 00:03:36,540
+T برجع لتعريف ال kernel ال kernel ل ال function T
+
+36
+00:03:36,540 --> 00:03:44,580
+قولنا كل ال X اللي موجودة في ال R2 بحيث T of X بده
+
+37
+00:03:44,580 --> 00:03:50,230
+يسوى 100 بده يسوى 0 مش شك تعريف ال kernelمظبوط زي
+
+38
+00:03:50,230 --> 00:03:56,310
+ما عرفنا هيك؟ طيب يعني كأنه هذا كل ال elements x1
+
+39
+00:03:56,310 --> 00:04:06,070
+و x2 اللي موجودة في ال R2 such that T of x1 و x2
+
+40
+00:04:06,070 --> 00:04:11,330
+بالشكل اللي عندنا هذا بده يساوي مين؟ بده يساوي ال
+
+41
+00:04:11,330 --> 00:04:18,490
+zero بالشكل اللي عندناطيب ال antivx1 x2 هي الشكل
+
+42
+00:04:18,490 --> 00:04:22,670
+اللي عندنا هذا يبقى هذا الكلام بده يساوي كل
+
+43
+00:04:22,670 --> 00:04:31,270
+العناصر x1 و x2 اللي موجودة في R2 بحيث ان تلاتة x1
+
+44
+00:04:31,270 --> 00:04:38,650
+ناقص اتنين x2 بده يساوي zero وناقص ستة x1 زائد
+
+45
+00:04:38,650 --> 00:04:45,740
+اربعة x2 بده يساوي zero بالشكل اللي عندنا هذايبقى
+
+46
+00:04:45,740 --> 00:04:54,980
+هذا يعطينا المعادلة الأولى 3x1-2x2 يساوي 0 ايش
+
+47
+00:04:54,980 --> 00:04:59,240
+رايك المعادلة التانية لو ضربتها في سالب نص
+
+48
+00:05:05,670 --> 00:05:09,570
+معادلة اللي فوق يبقى هدول في الحقيقة مش معادلتين
+
+49
+00:05:09,570 --> 00:05:14,330
+وانما مين معادلة واحدة فقط لغيره يبقى انا عندي
+
+50
+00:05:14,330 --> 00:05:20,730
+المعادلة دي تمثل اتنين هدول على طول الخط يبقى بناء
+
+51
+00:05:20,730 --> 00:05:27,510
+عليه ال X واحد بده يساوي اتنين X اتنين على كده اش
+
+52
+00:05:27,510 --> 00:05:38,320
+على تلاتة يبقى بناء عليه بقدر اقول لو كانالـ X1
+
+53
+00:05:38,320 --> 00:05:47,360
+بدر يساوي الـ A ثم X2 بدر يساوي 3 على 2A
+
+54
+00:05:50,560 --> 00:05:54,700
+يبقى لو كان هذا ايه بيصير هذا تلاتة على اتنين اللي
+
+55
+00:05:54,700 --> 00:05:58,920
+همان اكس اتنين اذا انا جابت اكس واحد و اكس اتنين
+
+56
+00:05:58,920 --> 00:06:04,920
+بدلالة real number و هذا ال a موجود في ال set of
+
+57
+00:06:04,920 --> 00:06:09,400
+real number ماعليش قيود ممكن zero ممكن واحد ممكن
+
+58
+00:06:09,400 --> 00:06:14,500
+اتنين ممكن سلب نص ممكن تلت اربع اي قيمة صفرية موجة
+
+59
+00:06:14,500 --> 00:06:17,840
+بسلب عدد صحي عدد كتر ماعناها مشكلة ايش ما يكون
+
+60
+00:06:17,840 --> 00:06:23,950
+يكونبناء ان انا عليها بعرف شكل ال kernel يبقى أصبح
+
+61
+00:06:23,950 --> 00:06:31,670
+شكل ال kernel لل function T بده يساوي ال X1 يبقى
+
+62
+00:06:31,670 --> 00:06:40,450
+اتقداش A وال X2 تلاتة على اتنين A بحيث ال A موجودة
+
+63
+00:06:40,450 --> 00:06:48,290
+في set of real numbers بالشكل اللي عندنايبقى كل ال
+
+64
+00:06:48,290 --> 00:06:52,470
+order pair اللي بالشكل هذا بحيث ال a موجودة في set
+
+65
+00:06:52,470 --> 00:06:59,650
+of real number او ان شئتم فقولوا لو أخدت ال a عامل
+
+66
+00:06:59,650 --> 00:07:06,410
+مشترك ايش بضع اللي عندى؟ واحد و تلاتة على اتنين
+
+67
+00:07:08,980 --> 00:07:14,060
+بالشكل اللي عندنا هنا تحب تحطيها على شكل برضه
+
+68
+00:07:14,060 --> 00:07:18,860
+مصحوفة مع أنها مشكلة يعني بقدر أقول هذه اللي هي اه
+
+69
+00:07:18,860 --> 00:07:24,440
+في المصحوفة واحد و تلاتة على اتنين بالشكل اللي
+
+70
+00:07:24,440 --> 00:07:30,180
+عندنا هنا بهذا و بهذا سيان يبقى أكم انصر موجود
+
+71
+00:07:30,180 --> 00:07:31,680
+عندى في الكيار نالي
+
+72
+00:07:35,900 --> 00:07:40,960
+واحد عدد لانهائي من العناصر حط ايه الرقم اللي هي
+
+73
+00:07:40,960 --> 00:07:46,340
+عجبك تمام وضربه في الجوس ولا ضربه في المصوفة بيطلع
+
+74
+00:07:46,340 --> 00:07:51,240
+عندنا كل عنصر بيطلع بيكون موجود في ال kernel هذا
+
+75
+00:07:51,240 --> 00:07:56,080
+اللي هو جبناله شكل ال kernel يبقى شكل ال kernel كل
+
+76
+00:07:56,080 --> 00:07:59,140
+العناصر اللي بالشكل اللي عندنا هذا خلصنا المطلوب
+
+77
+00:07:59,140 --> 00:08:04,320
+الأول المطلوب التالي جالي هاتلي basis لل kernelطيب
+
+78
+00:08:04,320 --> 00:08:08,320
+العنصر هذا مش بيولد جميع عناصر ال kernel بلا
+
+79
+00:08:08,320 --> 00:08:13,640
+إستثناء، مظبوط؟ ها جميع عناصر ال kernel بلا
+
+80
+00:08:13,640 --> 00:08:18,340
+إستثناء بيجيبهم مدعوم، يبقى دهش يمثل، basis يبقى
+
+81
+00:08:18,340 --> 00:08:20,660
+هنا باجي بقوله نمرق بيه
+
+82
+00:08:24,010 --> 00:08:36,670
+العنصر 1 و 3 على 2 لحاله يكن is a basis for الكيرن
+
+83
+00:08:36,670 --> 00:08:43,370
+لمن لتي لإن أي عنصر في الكيرن هو linear
+
+84
+00:08:43,370 --> 00:08:49,550
+combination من هذا الرقم يبقى هذا يمثل basis له
+
+85
+00:08:49,550 --> 00:08:53,800
+خلصنا المطلوب التاني المطلوب التالفلو نمرسيه بيقول
+
+86
+00:08:53,800 --> 00:08:58,840
+لي هل العنصر اتنين و تلاتة موجود في ال kernel ولا
+
+87
+00:08:58,840 --> 00:09:03,100
+لأ؟ بقول والله اتنين و تلاتة إذا جدرنا نحط على
+
+88
+00:09:03,100 --> 00:09:07,840
+صيغة رقم مضروب في هذا العنصر بيكون موجود في ال
+
+89
+00:09:07,840 --> 00:09:12,600
+kernel صحيح ولا لأ؟ يبقى باجي بقوله الآن اتنين و
+
+90
+00:09:12,600 --> 00:09:18,340
+تلاتة يساوي بقدر أخد اتنين عامل مشترك صحيح ولا لأ؟
+
+91
+00:09:18,340 --> 00:09:24,160
+طيب قداش بظل عند هنا؟واحد و تلاتة على اتنين مين
+
+92
+00:09:24,160 --> 00:09:28,720
+هذا؟ مش هو ال basis تبع ال kernel يبقى موجود في ال
+
+93
+00:09:28,720 --> 00:09:34,320
+kernel ولا لا؟ يبقى هذا موجود في ال kernel تبع
+
+94
+00:09:34,320 --> 00:09:39,900
+مين؟ تبع ال T وهو المطلوب يبقى انتهينا من المثلة
+
+95
+00:09:39,900 --> 00:09:50,160
+ننتقل إلى سؤال آخر مثال خمسة أو example خمسة
+
+96
+00:09:52,460 --> 00:10:02,960
+السؤال بيقول let T من R3 إلى R2 be a linear
+
+97
+00:10:02,960 --> 00:10:08,300
+transformation
+
+98
+00:10:08,300 --> 00:10:13,900
+such that بحيث
+
+99
+00:10:13,900 --> 00:10:27,120
+انT of E1 بدر ساوي واحد وسالي باتنين وT of E2 بدر
+
+100
+00:10:27,120 --> 00:10:41,380
+ساوي Zero وتلاتة وT of E3 بدر ساوي واحد وواحد نمرأ
+
+101
+00:10:41,380 --> 00:10:52,700
+Aبقول find a matrix A اعطينا
+
+102
+00:10:52,700 --> 00:11:02,820
+مصفوفة A such that بحيث ان T of X يساوي ال A في ال
+
+103
+00:11:02,820 --> 00:11:07,800
+X نمرى ب find
+
+104
+00:11:09,850 --> 00:11:13,590
+T of واحد و اتنين و تلاتة
+
+105
+00:11:44,770 --> 00:11:50,770
+يبقى في عنا مثال آخر المثال الآخر كالتالي بيقول
+
+106
+00:11:50,770 --> 00:11:55,190
+افترض في من R3 الى R2 عبارة عن Linear
+
+107
+00:11:55,190 --> 00:11:59,570
+Transformation إذا شكل Linear Transformation هو
+
+108
+00:11:59,570 --> 00:12:06,290
+دائما و أبدا T of X بده سواء من X هذا شكله بيقول
+
+109
+00:12:06,290 --> 00:12:11,930
+هنا بحيث T of E1 يسوى واحد وسلم اتنين مين E1 يا
+
+110
+00:12:11,930 --> 00:12:12,510
+مانات هذه؟
+
+111
+00:12:15,250 --> 00:12:21,950
+مين؟ انصر في R تلاتة اللي هو مين؟ واحد و Zero و
+
+112
+00:12:21,950 --> 00:12:25,650
+Zero واحدة A واحد و E اتنين و E تلاتة عناصر مين؟
+
+113
+00:12:25,650 --> 00:12:32,350
+ال standard basis ل R تلاتة اذا ال A واحد هي واحد
+
+114
+00:12:32,350 --> 00:12:36,270
+و Zero و Zero و ال E اتنين هي Zero و واحد و Zero و
+
+115
+00:12:36,270 --> 00:12:42,390
+ال E تلاتة Zero Zero واحدطيب صورة T E2 هي 0 و 3
+
+116
+00:12:42,390 --> 00:12:50,210
+صورة E3 هي 1 و 1 يعني كل من E1 و E2 و E3 عبارة عن
+
+117
+00:12:50,210 --> 00:12:55,250
+vector ب 3 components بده تبقى صورته في أرضه
+
+118
+00:12:55,250 --> 00:13:01,370
+element ب 2 component فقط زي ما انت شايفه 1 و 2 0
+
+119
+00:13:01,370 --> 00:13:06,750
+3 1 و 1 بيقول find a matrix A such that T of X بده
+
+120
+00:13:06,750 --> 00:13:12,450
+يسوى من Xيبقى السؤال اللى جابله اعطانى المصوفة ايه
+
+121
+00:13:12,450 --> 00:13:15,930
+مظبوط سؤالها دى جالى لأ انت اللى بدك تجيب لمام
+
+122
+00:13:15,930 --> 00:13:21,590
+المصوفة ايه بدي اعرف ماهو شكل المصوفة ايه في هذه
+
+123
+00:13:21,590 --> 00:13:26,090
+الحالة بنقوله بسيطة جدا خليكم معانا كويس بدنا
+
+124
+00:13:26,090 --> 00:13:30,890
+نحاول نجيب شكل المصوفة ايه من خلال ايه من خلال
+
+125
+00:13:30,890 --> 00:13:35,030
+المعلومات بتبعتنا الحين يا بنات لما انا اجى اقول
+
+126
+00:13:35,030 --> 00:13:44,070
+انا T of X بده يساوي A Xيعني معنى هذا الكلام أن T
+
+127
+00:13:44,070 --> 00:13:48,350
+of E1 ساوي A في E1
+
+128
+00:13:50,750 --> 00:13:56,990
+يعني هذا الكلام بده يساوي .. بده يساوي مين؟ ال A
+
+129
+00:13:56,990 --> 00:14:02,730
+في ال E1، هذه ال A، و ال E1 اللي هو واحد، Zero،
+
+130
+00:14:02,730 --> 00:14:09,390
+Zero، قداش بده يساوي واحد وسائق، والراحة الأولى
+
+131
+00:14:09,390 --> 00:14:11,030
+واحد وسائق اتنين، صحيح
+
+132
+00:14:13,860 --> 00:14:22,060
+الان لو جيت لل T of E2 يبقى ال A في ال E2 يبقى ال
+
+133
+00:14:22,060 --> 00:14:28,180
+A في ال E2 اللي هو Zero واحد و Zero والان لو جيت
+
+134
+00:14:28,180 --> 00:14:36,820
+لل T في ال E3 يبقى A E3 اللي هو ال A في Zero Zero
+
+135
+00:14:36,820 --> 00:14:43,420
+واحدوهذا الكلام بده يساوي كم؟ بده يساوي التالتة
+
+136
+00:14:43,420 --> 00:14:49,420
+اللي هي واحد واحد وهذه كم تساوي يا بنات؟ هذه تساوي
+
+137
+00:14:49,420 --> 00:14:51,440
+اللي هي zero وتلتة
+
+138
+00:14:53,450 --> 00:14:57,230
+هذا T لما يؤثر على عنصر واحد طب بده أجيب التلت
+
+139
+00:14:57,230 --> 00:15:01,750
+عناصر مع بعض فبروح بقول مياتي بده أكتبهم على شكل
+
+140
+00:15:01,750 --> 00:15:12,270
+مصمومة يبقى T of X بده يساوي A X implies that ال A
+
+141
+00:15:12,270 --> 00:15:13,290
+عندي هيها
+
+142
+00:15:15,800 --> 00:15:22,640
+الان عناصر الاولى تبعت ا واحد واحد زيرو زيرو زيرو
+
+143
+00:15:22,640 --> 00:15:28,300
+واحد زيرو زيرو واحد هاي جبت اكس واحد و اكس اتنين و
+
+144
+00:15:28,300 --> 00:15:35,100
+اكس اتنين يعني ا واحد و اتنين و اتلاتةحصل ضرب ال a
+
+145
+00:15:35,100 --> 00:15:39,820
+في الأول هي ال a في الأول اللي بده يساوي كده؟ واحد
+
+146
+00:15:39,820 --> 00:15:45,480
+وسالي باتنين إذا هذا واحد وسالي باتنين ال a في
+
+147
+00:15:45,480 --> 00:15:51,760
+الثاني بده يساوي كده؟ Zero وتلاتة ال a في التالت
+
+148
+00:15:51,760 --> 00:15:57,800
+بده يساوي واحد واحد بالشكل اللي عندنا هذا طيب كويس
+
+149
+00:15:57,800 --> 00:16:02,620
+هذا الكلام بده يساوي هذه مين هي ابنات المصوفة؟
+
+150
+00:16:03,730 --> 00:16:07,910
+مصوفة الوحدة اضربها في اي مصوفة بيطلع نفس المصوفة
+
+151
+00:16:07,910 --> 00:16:14,770
+اذا بناء عليه ال a بدأت ساوي واحد zero واحد ناقص
+
+152
+00:16:14,770 --> 00:16:22,070
+اتنين تلاتة واحدأيوة هذا من أبسط أنواع الأسئلة لإن
+
+153
+00:16:22,070 --> 00:16:27,030
+استخدمنا له standard basis وبالتالي المصروفة A في
+
+154
+00:16:27,030 --> 00:16:30,550
+مصروفة الوحدة أعطتني مصروفة الوحدة مباشرة ايه
+
+155
+00:16:30,550 --> 00:16:35,830
+أعطتني المصروفة A مباشرة تمام سوة مين سوة الطرف
+
+156
+00:16:35,830 --> 00:16:41,070
+اللي على اليمين يبقى سوة المصروفة اللي هي 101 سالب
+
+157
+00:16:41,070 --> 00:16:46,580
+2 3 1 بالشكل العنانييبقى انت هنا من ميم من المطلوب
+
+158
+00:16:46,580 --> 00:16:52,320
+لو القليل find a matrix A على T of X يساوي A X هاي
+
+159
+00:16:52,320 --> 00:16:56,200
+استخدمناها و طبقنا و جيبنا له ميم المصموم فائل
+
+160
+00:16:57,320 --> 00:17:04,620
+بعدها قال لي هاتلي T of واحد و اتنين و تلاتة بقول
+
+161
+00:17:04,620 --> 00:17:07,640
+انا مش بعرفني T واحد و اتنين و تلاتة ايش يعني كيف
+
+162
+00:17:07,640 --> 00:17:13,160
+بده اجيبها لكن بقول انا اذا جدرت احط الواحد و
+
+163
+00:17:13,160 --> 00:17:18,960
+اتنين و تلاتة على صيغة linear combination من ال
+
+164
+00:17:18,960 --> 00:17:26,250
+basis بكون دستنصرة سهلة كاف كتالةالان انا لو جيت
+
+165
+00:17:26,250 --> 00:17:31,570
+لل 1 و 2 و 3 اللي قاللي عنه هذا element موجود وين؟
+
+166
+00:17:31,570 --> 00:17:39,610
+ب R3 R3 هو ال standard basis ال E1 و E2 و E3 مظبوط
+
+167
+00:17:39,610 --> 00:17:43,450
+اذا هذا ال element بقدر اكتبه على صيغة linear
+
+168
+00:17:43,450 --> 00:17:49,110
+combination من ال E1 و E2 و E3 مظبوط يبقى بقدر
+
+169
+00:17:49,110 --> 00:17:52,130
+اقوله but ولكن
+
+170
+00:17:59,390 --> 00:18:05,410
+C1E1 C2E2 C3E3
+
+171
+00:18:07,200 --> 00:18:14,200
+أظن هذا الكلام سيسوى C1 E1 C1 E1 E1 E1 E1 E1 E1 E1
+
+172
+00:18:14,200 --> 00:18:18,300
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+173
+00:18:18,300 --> 00:18:18,940
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+174
+00:18:18,940 --> 00:18:19,640
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+175
+00:18:19,640 --> 00:18:19,680
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+176
+00:18:19,680 --> 00:18:20,320
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+177
+00:18:20,320 --> 00:18:23,800
+E1 E1 E1 E1 E1 E1 E1 E1
+
+178
+00:18:23,800 --> 00:18:24,500
+E1 E1 E1
+
+179
+00:18:43,050 --> 00:18:47,710
+بناء عليه بقدر اكتب هذا ال element على الشكل
+
+180
+00:18:47,710 --> 00:18:48,730
+التالي
+
+181
+00:19:01,250 --> 00:19:07,790
+إذا ال element واحد و اتنين و تلاتة يبدو يساوي ال
+
+182
+00:19:07,790 --> 00:19:12,210
+E ال C واحد بواحد يبقى هنا يبدو يعطيني E واحد فقط
+
+183
+00:19:12,210 --> 00:19:16,930
+ال C اتنين باتنين يبقى اتنين E اتنين ال C تلاتة
+
+184
+00:19:16,930 --> 00:19:22,330
+بتلاتة E تلاتة بالشكل اللي عندنا هذاإذا قدرت أكتب
+
+185
+00:19:22,330 --> 00:19:26,210
+ال element اللي انا بدي أجيب صوته على صيغة linear
+
+186
+00:19:26,210 --> 00:19:31,470
+combination من عناصر من ال mases طب ليش عملت هيك؟
+
+187
+00:19:31,470 --> 00:19:36,770
+اه عملت هيك لإن هو يعطيني ToV واحد و ToV اتنين و
+
+188
+00:19:36,770 --> 00:19:41,480
+ToV تلاتة عشان أستخدمها في الحلإذا بناء عليه بدي
+
+189
+00:19:41,480 --> 00:19:47,840
+أثر على الطرفين بـT يبقى باجي بقوله إذا صارت T of
+
+190
+00:19:47,840 --> 00:19:54,180
+واحد واتنين وتلاتة بديه سوى T of E واحد E اتنين E
+
+191
+00:19:54,180 --> 00:20:02,740
+اتنين تلاتة E تلاتة مظبوط الحين T شو اسمها؟من
+
+192
+00:20:02,740 --> 00:20:08,160
+خلاصة ان T of A زي W سوى T of A زي T of B يعني ت
+
+193
+00:20:08,160 --> 00:20:12,740
+بتقدر تدخل على مهم على كل واحدة من ال three terms
+
+194
+00:20:12,740 --> 00:20:18,920
+اللي موجودة بين القوسين يبقى هذا كأن T of A واحد
+
+195
+00:20:19,030 --> 00:20:27,570
+زاية T of 2 E2 زاية T of 3 E3 هذا الكلام يساوي
+
+196
+00:20:27,570 --> 00:20:32,410
+الان T of E1 كما هي من خواص ال linear
+
+197
+00:20:32,410 --> 00:20:35,850
+transformation لو عندنا scalar فيه vector بقول يا
+
+198
+00:20:35,850 --> 00:20:40,090
+scalar تعال إيه تعال برا وهي أول خاصية من خواص ال
+
+199
+00:20:40,090 --> 00:20:46,240
+linear transformationيبقى زائد اتنين في T of E
+
+200
+00:20:46,240 --> 00:20:53,020
+اتنين زائد تلاتة في T of E تلاتة و يسابق T of E
+
+201
+00:20:53,020 --> 00:20:59,620
+واحد جاهزة اللي هي كداش واحد و سالب اتنين T of E
+
+202
+00:20:59,620 --> 00:21:05,060
+اتنين هي Zero و تلاتة تلاتة T of E تلاتة اللي هي
+
+203
+00:21:05,060 --> 00:21:12,230
+واحد و واحديبقى النتيجة واحد وسالي باتنين زائد
+
+204
+00:21:12,230 --> 00:21:19,330
+زيرو وستة زائد تلاتة وتلاتة ويساوي نجمع ال face
+
+205
+00:21:19,330 --> 00:21:23,830
+component واحد وزيرو وتلاتة ليه بقداش يا بنات اربع
+
+206
+00:21:23,830 --> 00:21:30,150
+نقص اتنين وستة بضل قداش اربعة وتلاتة قداش سبعة إذا
+
+207
+00:21:30,150 --> 00:21:35,260
+صورة العنصرو احد و اتنين و تلاتة هي عبارة عن مين
+
+208
+00:21:35,260 --> 00:21:40,040
+اربعة و سبعة يبقى بناء عليه لو في يوم من الأيام
+
+209
+00:21:40,040 --> 00:21:44,740
+جالي هتلي جديش صورة عنصر زي هذا بدي احاول اكتب هذا
+
+210
+00:21:44,740 --> 00:21:48,600
+العنصر على صورة linear ال combination من مين من
+
+211
+00:21:48,600 --> 00:21:55,180
+عناصر ال bases و من ثم باخد T للطرفين بكون حصلت
+
+212
+00:21:55,180 --> 00:22:00,700
+على المطبخ او وصلت الى المطبخلاحظي أن هذين
+
+213
+00:22:00,700 --> 00:22:06,900
+المثالين يختلفان عن ما سبقهم من الأمثلة، مظبوط؟
+
+214
+00:22:06,900 --> 00:22:12,640
+طيب نتجل شوية، نعطي كمان مثال ثاني، يبقى هذا كان
+
+215
+00:22:12,640 --> 00:22:20,040
+مثال خمس، هنيجي example ستة، example ستة
+
+216
+00:22:27,110 --> 00:22:39,490
+بقول تي من R2 الى R3 بيه a linear transformation
+
+217
+00:22:39,490 --> 00:22:52,010
+if إذا كان T of واحد واثنين يساوي واحد وسالب واحد
+
+218
+00:22:52,010 --> 00:22:54,410
+وزيرو وT
+
+219
+00:22:56,420 --> 00:23:04,340
+of واحد و واحد بده يساوي واحد و اتنين و سالب واحد
+
+220
+00:23:04,340 --> 00:23:14,640
+المطلوب الاول find بدنا T of واحد و اربع نمره V
+
+221
+00:23:14,640 --> 00:23:17,940
+find
+
+222
+00:23:17,940 --> 00:23:25,460
+a matrix A such that
+
+223
+00:23:28,620 --> 00:23:44,840
+T of X هدي ساوي A في ال X نمر C find a formula for
+
+224
+00:23:44,840 --> 00:23:46,400
+T
+
+225
+00:24:14,910 --> 00:24:22,140
+يبقى السؤال مرة تانيةالـ T من R2 إلى R3 Linear
+
+226
+00:24:22,140 --> 00:24:26,320
+Transformation ومعطيني T of واحد واثنين بدي أساوي
+
+227
+00:24:26,320 --> 00:24:30,380
+واحد و سالب واحد و Zero و T of واحد و واحد يا واحد
+
+228
+00:24:30,380 --> 00:24:34,900
+و اتنين و سالب واحد بيجيلي هاتلي T of واحد و أربعة
+
+229
+00:24:34,900 --> 00:24:40,200
+و هاتلي Matrix A بحيث T of X يساوي A of X و هاتلي
+
+230
+00:24:40,200 --> 00:24:44,600
+صيغة لشكل ال Linear Transformation بدي أعرف شو شكل
+
+231
+00:24:44,600 --> 00:24:49,970
+هذهطبعا معلومات في غالبها جديدة كلها ما ده بعض
+
+232
+00:24:49,970 --> 00:24:54,890
+الأشياء البسيطة تعالي ننشي مرة تانية لو اطلعتي
+
+233
+00:24:54,890 --> 00:25:01,900
+السؤال اللي قبله كان T من R3 إلى R2 صح؟غير هي كانت
+
+234
+00:25:01,900 --> 00:25:07,960
+ال T بتأثر على ال standard basis مظبوط هنا لأ
+
+235
+00:25:07,960 --> 00:25:12,060
+بتأثر على عناصر غير ال standard basis إذا من هنا
+
+236
+00:25:12,060 --> 00:25:16,500
+أجى هذا الخلاف الأول بين السؤال الأول والسؤال
+
+237
+00:25:16,500 --> 00:25:23,880
+الثاني هداك من R3 إلى R2 هذا لأ من R2 إلى R32 كان
+
+238
+00:25:23,880 --> 00:25:27,560
+هناك هم عناصر ال basis اللي بتأثر عليهم T هنا
+
+239
+00:25:27,560 --> 00:25:33,890
+عناصر أخرى غير عناصرلستاندر بيزز طيب ماعنداش مشكلة
+
+240
+00:25:33,890 --> 00:25:38,870
+تعالى نشوف تفكر شوية ايه قال لي المطلوب الاول هتل
+
+241
+00:25:38,870 --> 00:25:44,010
+ال T of واحد واربعة يبقى انا لو جدرت اكتب الواحد
+
+242
+00:25:44,010 --> 00:25:48,750
+واربعة على صيغة linear combination من عناصر ال
+
+243
+00:25:48,750 --> 00:25:54,390
+bases اللى عندنا بتم المطلوبصح؟ طيب من وين بدك
+
+244
+00:25:54,390 --> 00:25:58,170
+تجيب عناصر ال basis؟ بقول ما هو ال standard basis
+
+245
+00:25:58,170 --> 00:26:04,230
+معروف E1 و E2 1 و 0 و 0 و 1 صحيح ولا لا؟ مش هدول
+
+246
+00:26:04,230 --> 00:26:10,590
+ال basis تبعات R2 بس ماعنديش لا T of 1 و 0 ولا T
+
+247
+00:26:10,590 --> 00:26:15,050
+of 0 و 1 مظبوط؟ ماعنديش لا هدى ولا هدى زي السؤال
+
+248
+00:26:15,050 --> 00:26:19,100
+اللي جابله أبدأ و أمشي و أتوكل اللهيبقى كيف بدي
+
+249
+00:26:19,100 --> 00:26:23,820
+أعمل؟ بقولك دبر حالك كيف أدبر حالي؟ تعالى تشوف
+
+250
+00:26:23,820 --> 00:26:31,800
+يبقى أنا بدي أجي للمطموب الأول يبقى solution بدي
+
+251
+00:26:31,800 --> 00:26:38,660
+أجي لنمرق ايه الآن ال dimension لل R2 كده شو ساوي؟
+
+252
+00:26:40,270 --> 00:26:45,110
+كداش؟ اتنين لإيش ان ال standard basis واحد و Zero
+
+253
+00:26:45,110 --> 00:26:50,610
+و Zero و واحد يعني عنصرين يبجى اي basis اخر بدى
+
+254
+00:26:50,610 --> 00:26:56,170
+يكون فيه كداش عنصرين two vectors only الان باجى
+
+255
+00:26:56,170 --> 00:27:05,770
+بقول since بما ان ال dimension ل ال R2 بدى يساوي
+
+256
+00:27:05,770 --> 00:27:16,320
+اتنين يبجى we haveأي مؤسسة
+
+257
+00:27:16,320 --> 00:27:24,180
+يكون لـ R لديها
+
+258
+00:27:24,180 --> 00:27:26,960
+فقط اتجاربين
+
+259
+00:27:30,540 --> 00:27:35,760
+يبقى اي بيزاز مش هلاجه فيه الا عنصرين فقط طيب
+
+260
+00:27:35,760 --> 00:27:41,080
+تعالى نحاول نستخدم المعلومات اللى عندنا اطلعيلى
+
+261
+00:27:41,080 --> 00:27:45,120
+هنا بناتي يبقى T of واحد و اتنين يبقى واحد و اتنين
+
+262
+00:27:45,120 --> 00:27:52,800
+منهم موجداد في R2 واحد و واحد في R2 هل هدول
+
+263
+00:27:53,370 --> 00:27:58,050
+linearly dependent ولا linearly independent؟
+
+264
+00:27:58,050 --> 00:28:03,230
+linearly independent إذا بنفعه basis ولا لا؟ لأن
+
+265
+00:28:03,230 --> 00:28:08,280
+عددهم كده؟ اتنينيبقى هدول linear لإنه ولا واحد
+
+266
+00:28:08,280 --> 00:28:12,960
+فيهم مضعفات الآخر أو لو أخدتلهم المحدد بلاقي ماله
+
+267
+00:28:12,960 --> 00:28:19,280
+لا يساوي zero صحيح ولا لأ يبقى باجي بقول بقولت هنا
+
+268
+00:28:19,280 --> 00:28:24,840
+any basis لل R2 has two elements فقط باجي بقوله
+
+269
+00:28:24,840 --> 00:28:33,300
+but ولكنالـ vector الأولاني اللي هو واحد اتنين
+
+270
+00:28:33,300 --> 00:28:38,260
+بالشكل اللي عندنا هذا and التاني اللي هو واحد و
+
+271
+00:28:38,260 --> 00:28:43,580
+واحد are linearly independent because
+
+272
+00:28:46,730 --> 00:28:54,550
+المحدد تبع واحد اتنين واحد واحد يساوي واحد ناقص
+
+273
+00:28:54,550 --> 00:29:00,830
+اتنين ويساوي ناقص واحد لا يساوي مين لا يساوي ال
+
+274
+00:29:00,830 --> 00:29:06,090
+zero يبقى هدول linearly independent وعددهم يساوي
+
+275
+00:29:06,090 --> 00:29:12,750
+اتنين اذا هدول يشكلوا لمينباسيز لمن؟ لل R2 احنا
+
+276
+00:29:12,750 --> 00:29:16,830
+بنعرف ال vectors بس في باسيز كتيرة ليس بضرورة يكون
+
+277
+00:29:16,830 --> 00:29:20,150
+ال standard basis بل ال standard basis وزيادة على
+
+278
+00:29:20,150 --> 00:29:23,910
+ذلك باسيز اخرى اذا بنفع اتنين يكونوا هدول باسيز
+
+279
+00:29:23,910 --> 00:29:36,040
+لمن؟ لل R2 يبقى so the vectorsاللي هو واحد اتنين
+
+280
+00:29:36,040 --> 00:29:48,660
+and اللي هو واحد وواحد أيوة form a basis for R2
+
+281
+00:29:50,710 --> 00:29:53,990
+إذا الفرق ما بين السؤال هذا والسؤال اللي هو أجيب
+
+282
+00:29:53,990 --> 00:29:57,690
+له ذاك استخدمت main ل standard basis، هنا جبت
+
+283
+00:29:57,690 --> 00:30:01,610
+main، جبت basis جديد من خلال main، من خلال
+
+284
+00:30:01,610 --> 00:30:05,350
+المعطيات تبع المثلة اللي عندي، يعني أنا الرقم ال
+
+285
+00:30:05,350 --> 00:30:08,590
+.. ال two vectors هدوة اللي ما جبته مش عشوائي من
+
+286
+00:30:08,590 --> 00:30:12,740
+عنديلأ هى موجودة عندى في المثلة اجبتهم من خلال ال
+
+287
+00:30:12,740 --> 00:30:16,920
+main من خلال المثلة طب انت ايش بتسوي؟ هو ايش يقلل
+
+288
+00:30:16,920 --> 00:30:21,080
+المطاولة؟ بده T لواحد واربعة بقوله اه الان بدي
+
+289
+00:30:21,080 --> 00:30:26,400
+احاول اكتم الواحد واربعة بدلالة ال business اللى
+
+290
+00:30:26,400 --> 00:30:31,700
+عندى هذه واشوف ايش يسوي يبقى باجي بقول الان since
+
+291
+00:30:32,400 --> 00:30:38,320
+واحد واربعة موجودة
+
+292
+00:30:38,320 --> 00:30:45,000
+في R2 we have الواحد واربعة بقدر اقول constant
+
+293
+00:30:45,000 --> 00:30:52,700
+مثلا C1 في الاول اللي هو واحد واتنين زي C2 في
+
+294
+00:30:52,700 --> 00:30:59,090
+الواحد واحديبقى بناء ان عليه الواحد والاربعة بده
+
+295
+00:30:59,090 --> 00:31:07,170
+يساوي بدي اضرب واجمع دغري يبقى C1 زائد C2 وهنا 2C1
+
+296
+00:31:07,170 --> 00:31:14,660
+زائد C2نعمل منهم اللي هو ال linear system يبقى c1
+
+297
+00:31:14,660 --> 00:31:22,560
+زائد c2 يساوي واحد اتنين c1 زائد c2 بده يساوي كده
+
+298
+00:31:22,560 --> 00:31:26,540
+اش؟ بده يساوي اربعة اذا يا بنات لو روحت ضربت
+
+299
+00:31:26,540 --> 00:31:31,980
+المعادلة الأولى فيه سالب بصير سالب c1 سالب c2
+
+300
+00:31:31,980 --> 00:31:37,420
+يساوي سالب c1المعادلة التانية اتنين C واحد زائد C
+
+301
+00:31:37,420 --> 00:31:41,760
+اتنين يساوي جداش اربع وجه الجماعة يبقى هدول مع
+
+302
+00:31:41,760 --> 00:31:47,540
+السلامة بظل C واحد يساوي جداش تلاتة طب لما C واحد
+
+303
+00:31:47,540 --> 00:31:54,700
+يساوي تلاتة C اتنين جداش سالب اتنين يبقى بناء عليه
+
+304
+00:31:54,700 --> 00:32:00,360
+أصبح ال vector واحد واربعة بدي اكتب على شكل ال
+
+305
+00:32:00,360 --> 00:32:05,140
+linear combination التانية تلاتة في واحدو اتنين
+
+306
+00:32:05,140 --> 00:32:11,460
+ناقص اتنين في واحد و واحد بالشكل اللي عندنا هنا
+
+307
+00:32:11,460 --> 00:32:17,420
+يعني صحيح لو ضربت هدول هنا وجماعة بتطلع هذا
+
+308
+00:32:17,420 --> 00:32:24,000
+الإجابة نعم هي تلاتة و ناقص اتنين واحد هي الان هي
+
+309
+00:32:24,000 --> 00:32:30,310
+ستة و ناقص اتنين و اربع يبقى ميرة مية الميةعن طريق
+
+310
+00:32:30,310 --> 00:32:34,230
+السؤال اللي قبله، جبت ال element اللي عندي وحطيته
+
+311
+00:32:34,230 --> 00:32:38,210
+على صيغة linear combination من عناصر ال basis في
+
+312
+00:32:38,210 --> 00:32:41,250
+السؤال اللي قبله جبت ال element عنه وحطيته على
+
+313
+00:32:41,250 --> 00:32:45,290
+صيغة linear combination من عناصر ال standard basis
+
+314
+00:32:45,290 --> 00:32:48,470
+لكن هنا حطيته من عناصر ال basis اللي ما هوش
+
+315
+00:32:48,470 --> 00:32:55,170
+standard ليش؟ لإن في معطع بدلالتهمطيب اذا انا جالي
+
+316
+00:32:55,170 --> 00:33:00,990
+هاتلي T of واحد واربعة معناته بتأثر على اتنين ب T
+
+317
+00:33:00,990 --> 00:33:06,190
+of واحد واربعة يبقى T للطرف هذا كله من خواص ال
+
+318
+00:33:06,190 --> 00:33:11,010
+linear transformation يبقى هذا بده يسوى تلاتة في T
+
+319
+00:33:11,010 --> 00:33:17,900
+واحد واثنين ناقص اتنين في T واحد وواحديبقى بناء
+
+320
+00:33:17,900 --> 00:33:24,460
+عليه أصبح T of واحد و أربعة بده يساوي تلاتة فيه
+
+321
+00:33:24,460 --> 00:33:29,760
+برجع لراس المثلة T of واحد و اتنين يبقى باجي بقول
+
+322
+00:33:29,760 --> 00:33:34,220
+T of واحد و اتنين اللي هو واحد سالب واحد زيرو يبقى
+
+323
+00:33:34,220 --> 00:33:41,160
+هذا واحد و سالب واحد و زيرو ماقص اتنين في T of
+
+324
+00:33:41,160 --> 00:33:46,300
+واحد و واحد له واحد و اتنين و سالب واحد و يساوي
+
+325
+00:33:47,770 --> 00:33:53,730
+الجوز الأول تلاتة و سالب تلاتة و zero الجوز التاني
+
+326
+00:33:53,730 --> 00:33:59,910
+سالب اتنين سالب اربعة و اتنين و اللي هو بده يساوي
+
+327
+00:33:59,910 --> 00:34:05,110
+تلاتة و ناقص اتنين اللي هو بواحد سالب تلاتة و سالب
+
+328
+00:34:05,110 --> 00:34:10,000
+اربعة اللي هو بسالب سبعةزيرو اتنين باتنين بالشكل
+
+329
+00:34:10,000 --> 00:34:14,260
+اللي عندنا يبقى أصبحت صورة العنصر واحد واربع اللي
+
+330
+00:34:14,260 --> 00:34:18,900
+موجود في R2 هو عبارة عن واحد سلب سبعة واتنين اللي
+
+331
+00:34:18,900 --> 00:34:24,840
+موجود في R3 يبقى شايفين كيف أنا نفسي الفكرة تبع
+
+332
+00:34:24,840 --> 00:34:28,380
+السؤال السابق بس هنا كان الشغل على ال standard
+
+333
+00:34:28,380 --> 00:34:33,160
+basis هنا لأ على basis عادي وليس ال standard basis
+
+334
+00:34:33,660 --> 00:34:37,080
+هذا المطلوب الأول من المأسالة المطلوب التاني قال
+
+335
+00:34:37,080 --> 00:34:44,200
+find a matrix A such that T of X بدي سوى قداش X
+
+336
+00:34:44,200 --> 00:34:49,120
+يبقى بدي أجيب نفسي الفكرة السابقة تبع المثال
+
+337
+00:34:49,120 --> 00:34:55,840
+السابق يبقى نمر بيه احنا نابنا T of X بدي سوى قداش
+
+338
+00:34:55,840 --> 00:35:06,290
+Xطيب بقوله كويس هذا الكلام بده يساوي إيه في ال X
+
+339
+00:35:06,290 --> 00:35:10,370
+قداشي ال element اللي عندي اللي هو واحد و اتنين ال
+
+340
+00:35:10,370 --> 00:35:16,970
+element التاري اللي همين واحد و واحديبقى هذا الـ X
+
+341
+00:35:16,970 --> 00:35:22,570
+يبدأ تعطيني مين؟ الصورة تبعتهم يبقى A X 1 يبقى
+
+342
+00:35:22,570 --> 00:35:27,530
+تعطيني مين؟ واحد سالب واحد زيرو واحد سالب واحد
+
+343
+00:35:27,530 --> 00:35:32,790
+زيرو التانية بدأ تعطيني واحد اتنين سالب واحد
+
+344
+00:35:32,790 --> 00:35:40,480
+بالشكل اللي عندنا هنايبقى هذه معادلة مصفوفية حاصل
+
+345
+00:35:40,480 --> 00:35:45,120
+ضرب two matrices يساوي main matrix بدي أعرف قداش
+
+346
+00:35:45,120 --> 00:35:51,640
+من المصفوفة A كيف بدي أجيب المصفوفة A؟بقول بسيط،
+
+347
+00:35:51,640 --> 00:35:56,700
+أنا مش عارف، لكن أنا بقول بكل بساطة لو ضربت
+
+348
+00:35:56,700 --> 00:36:02,660
+الطرفين في معكوس المصوفة هذه، مين بيضل ع الشمال؟
+
+349
+00:36:02,660 --> 00:36:06,720
+المصوفة ايه فقط وبالتالي بيصير هادي في معكوس
+
+350
+00:36:06,720 --> 00:36:10,620
+المصوفة ايه طيب هي المصوفة ايه اللي هي معكوس؟
+
+351
+00:36:10,620 --> 00:36:17,630
+معكوس واحدما هي المعكوس؟ لأنها تطلعت المحدد جدّاش؟
+
+352
+00:36:17,630 --> 00:36:21,990
+لأ يا سويد يعني هذه non singular matrix يعني ما هي
+
+353
+00:36:21,990 --> 00:36:25,530
+المعكوس؟ يعني هذا ال determinant أفدني شغلتين
+
+354
+00:36:25,530 --> 00:36:28,530
+أفدني أثبت أن ال two vectors are linearly
+
+355
+00:36:28,530 --> 00:36:33,550
+independent اتنين بيجيلي أن ال A inverse exist لأن
+
+356
+00:36:33,550 --> 00:36:37,930
+المصحوفة non singular تمام؟ يبقى مدام المعكوس
+
+357
+00:36:37,930 --> 00:36:43,790
+موجود إذا بقدر أضرب الطرفين في معكوس المصحوفة اللي
+
+358
+00:36:43,790 --> 00:36:48,760
+عندنا هنايبقى لو ضربت الطرفين بدي أحصل على ما يأتي
+
+359
+00:36:48,760 --> 00:36:56,860
+ال a في واحد اتنين واحد واحد في واحد واحد اتنين
+
+360
+00:36:56,860 --> 00:37:03,140
+واحد inverse بدي ساوي واحد سالب واحد zero واحد
+
+361
+00:37:03,140 --> 00:37:10,380
+اتنين سالب واحد في واحد واحد اتنين واحد inverse
+
+362
+00:37:10,380 --> 00:37:11,240
+بالشكل العام
+
+363
+00:37:15,110 --> 00:37:21,430
+طيب هذه المصوفة في معكوس ايش بيعطينا؟ مصوفة الوحدة
+
+364
+00:37:21,430 --> 00:37:25,930
+مصوفة الوحدة في اي مصوفة بيعطينا نفس المصوفة يبقى
+
+365
+00:37:25,930 --> 00:37:31,390
+ال a تساوي بالداجل المصوفة هذه اكتبها كما هي واحد
+
+366
+00:37:31,390 --> 00:37:37,970
+سالب واحد zero واحد اتنين سالب واحد بالداجل معكوس
+
+367
+00:37:37,970 --> 00:37:39,130
+المصوفة هذه
+
+368
+00:37:42,560 --> 00:37:46,380
+المصوفة اللى نضامها اتنين فى اتنين كيف قولنا بنجيب
+
+369
+00:37:46,380 --> 00:37:53,080
+معكوسة من ال chapter اللى فات نجيب قيمة المحدد و
+
+370
+00:37:53,080 --> 00:37:57,320
+بنبدل عناصر القطر الرئيسى مع بعض و بنغير اشارات
+
+371
+00:37:57,320 --> 00:38:01,500
+عناصر القطر الثانوي صحى ولا لأ واحد على المحدد فى
+
+372
+00:38:01,500 --> 00:38:06,780
+المصوفة اللى ناتجة بناء ان عليه المعكوسة ده تبع
+
+373
+00:38:06,780 --> 00:38:14,110
+هذهبدي يكون مضروب في واحد على سالب واحد، واحد على
+
+374
+00:38:14,110 --> 00:38:20,710
+المحدد، في مين؟ في هذه العناص القطر الرئيسي زي ما
+
+375
+00:38:20,710 --> 00:38:25,850
+هما، يبقى لو بدلتهم بطلع هما هما، العناص القطر
+
+376
+00:38:25,850 --> 00:38:31,520
+الثانوي بدي أغير باس إشاراتهم بالشكل العنانييبقى
+
+377
+00:38:31,520 --> 00:38:37,600
+اصبحت المصوفة ايه؟ بده يساوي حصل ضرب المصوفة واحد
+
+378
+00:38:37,600 --> 00:38:43,440
+سالب واحد زيرو واحد اتنين سالب واحد السالب بده
+
+379
+00:38:43,440 --> 00:38:47,300
+يدخل على المصوفة التانية بنتش بيصير عندى هنا سالب
+
+380
+00:38:47,300 --> 00:38:55,720
+واحد وهنا واحد وهنا اتنين وهنا سالب واحد ويساوي
+
+381
+00:38:56,390 --> 00:39:00,610
+يبقى بالدرجة هذه المصوفة نظامها تلاتة في اتنين
+
+382
+00:39:00,610 --> 00:39:04,570
+وهذه اتنين في اتنين يبقى نتيجة تلاتة في اتنين يبقى
+
+383
+00:39:04,570 --> 00:39:09,430
+بالدرجة الصف الأول في العمودي الأول يبقى سالب واحد
+
+384
+00:39:09,430 --> 00:39:16,770
+واتنين واحد صف الأول في العمودي الثاني يبقى سالب
+
+385
+00:39:16,770 --> 00:39:23,880
+واحد وسالب اتنينسالب تلاتة الصف التالت في العمود
+
+386
+00:39:23,880 --> 00:39:28,760
+الصف الأول في العمود الأول قلنا الصف الأول في
+
+387
+00:39:28,760 --> 00:39:32,840
+العمود التاني انتهينا منه بعد هي الصف الثاني في
+
+388
+00:39:32,840 --> 00:39:37,900
+العمود الأول يبقى واحد وهنا أربع جدش بيكون تمام
+
+389
+00:39:41,030 --> 00:39:46,010
+صف الأول في العمود الأول هي سالب وهذا اتنين بيظل
+
+390
+00:39:46,010 --> 00:39:51,810
+واحد صف الأول في العمود الثاني هي واحد وهي سالب
+
+391
+00:39:51,810 --> 00:39:57,410
+واحد بيصير zero صحيح بيصير هنا zero الصف الثاني في
+
+392
+00:39:57,410 --> 00:40:02,150
+العمود الأول بيكون واحد واربعة خمسة الصف الثاني في
+
+393
+00:40:02,150 --> 00:40:07,470
+العمود هي سالب واحد وسالب اتنين اللي هو سالب تلاتة
+
+394
+00:40:07,890 --> 00:40:12,210
+الصفة الثالثة في العمودي الأولى الـ Zero و سالب
+
+395
+00:40:12,210 --> 00:40:18,210
+اتنين هنا Zero وهنا واحد بالشكل اللي عندنا يبقى
+
+396
+00:40:18,210 --> 00:40:22,290
+هاي جيبت الشكل ال main شكل المصموم فإيه اللي عندنا
+
+397
+00:40:33,640 --> 00:40:39,680
+حتى الآن احنا جيبنا مطلبين من المثلة جيبت صورة
+
+398
+00:40:39,680 --> 00:40:43,500
+الواحد واربع جدش تساوي زي ما انتوا شايفين و بعد
+
+399
+00:40:43,500 --> 00:40:48,120
+هيك جيبت T of X تساوي A X مش جيبت شكل المصوفة A
+
+400
+00:40:48,120 --> 00:40:50,600
+اللي هي المصوفة اللي طالعة عندنا بس المرة اللي
+
+401
+00:40:50,600 --> 00:40:54,100
+فاتت كانت المصوفة أسئلة ليش ان كان A في مصوفة
+
+402
+00:40:54,100 --> 00:40:58,460
+الواحدة وبالتالي ماتغلبتش زي هذه هذي لأ لو جبت مين
+
+403
+00:40:58,460 --> 00:41:04,840
+جبت المعكوس هذه المصوفةطيب نجي لمطلوبة اللي بيقولي
+
+404
+00:41:04,840 --> 00:41:10,600
+find a formula for T بدك تجيبلي صيغة لـT هذي إيش
+
+405
+00:41:10,600 --> 00:41:15,860
+شكلها T of ال element اللي موجود في R22 بدي صوتها
+
+406
+00:41:15,860 --> 00:41:20,060
+تبقى وين في R3 يعني بدي أخلي T تأثر على two
+
+407
+00:41:20,060 --> 00:41:24,320
+components بدي أطلع عندي جداش three components
+
+408
+00:41:24,320 --> 00:41:30,820
+مظبوط؟ بسيطة جدا يبقى أنا بدي أروح أخد عنصر عشوائي
+
+409
+00:41:30,820 --> 00:41:43,510
+وين؟بارتو تو بارتو
+
+410
+00:41:43,510 --> 00:41:55,370
+تو بارتو
+
+411
+00:41:55,370 --> 00:41:57,710
+تو بارتو تو بارتو تو بارتو تو بارتو تو بارتو تو
+
+412
+00:41:57,710 --> 00:41:57,890
+بارتو تو بارتو تو بارتو تو بارتو تو بارتو تو بارتو
+
+413
+00:41:57,890 --> 00:41:57,970
+بارتو تو بارتو تو بارتو تو بارتو تو بارتو تو بارتو
+
+414
+00:41:57,970 --> 00:42:04,920
+تو بارتو تو بارالان عناصر ال basis ل R2 هو عبارة
+
+415
+00:42:04,920 --> 00:42:10,760
+عن مين؟عن اتنين عنصرين صحيح ولا لأ اللي هم مين
+
+416
+00:42:10,760 --> 00:42:15,880
+اللي هم واحد و اتنين و واحد و واحد يبقى بادر اكتب
+
+417
+00:42:15,880 --> 00:42:18,580
+هذا c واحد فاهمين
+
+418
+00:42:37,130 --> 00:42:42,810
+زائد C2 اتنين C واحد زائد C اتنين بشكل كله هذا
+
+419
+00:42:42,810 --> 00:42:48,750
+يساوي مين A وB اذا اصلا عندي كام معادلة معادلتين
+
+420
+00:42:48,750 --> 00:42:54,910
+يبقى C واحد زائد C اتنين يساوي A اتنين C واحد زائد
+
+421
+00:42:54,910 --> 00:43:00,730
+C اتنين يساوي مين يساوي B بدنا نحل هدول و نجيب C
+
+422
+00:43:00,730 --> 00:43:07,630
+واحد و C اتنين بدلالة A وBيبقى هذا معناه ان سالب
+
+423
+00:43:07,630 --> 00:43:15,390
+C1 سالب C2 يساوي سالب A اتنين C1 زائد C2 يساوي
+
+424
+00:43:15,390 --> 00:43:22,230
+كده؟ يساوي B لو جمعنا هدول مع بعض هدول مع السلامة
+
+425
+00:43:22,230 --> 00:43:29,610
+يبقى بناء عليه بصير عندي C1بدو يساوي ال B ناقص ال
+
+426
+00:43:29,610 --> 00:43:38,010
+A طيب بدنا نجيب C2 يبقى احنا عندنا C2 يساوي ال A
+
+427
+00:43:38,010 --> 00:43:47,410
+ناقص C1 يبقى يساوي ال A ناقص B زائد ال A دخلت
+
+428
+00:43:47,410 --> 00:43:54,140
+الناقص على من؟ على اللي فوق يساوي 2A ناقص Bيبقى
+
+429
+00:43:54,140 --> 00:44:00,540
+أنا جبتله c1 و جبتله c2 بناء عليه أصبح ال element
+
+430
+00:44:00,540 --> 00:44:10,440
+a و b على الشكل التالي c1 بيناقص ال a في 8 في 1 و
+
+431
+00:44:10,440 --> 00:44:21,470
+2 زائد 2a ناقص ال b في 1 و 1السؤال قال لي هاتلي
+
+432
+00:44:21,470 --> 00:44:28,990
+الشكل اللينيري لمان اللي موجود عندنا يبقى بناء ان
+
+433
+00:44:28,990 --> 00:44:33,750
+انا عليه بدي أثر على الطرفين بـT يبقى لو أثرت على
+
+434
+00:44:33,750 --> 00:44:40,550
+الطرفين بـT بصير مين عندي؟ T of A وBبدو يسوى T
+
+435
+00:44:40,550 --> 00:44:45,310
+هتدخل على المقدار كل ابناء يبقى بدي اوزعها إلى
+
+436
+00:44:45,310 --> 00:44:51,630
+جزين و بعمل دي هيك بعمل خطوة تانية يبقى بصير TR B
+
+437
+00:44:51,630 --> 00:45:05,020
+ناقص ال A في واحد و اتنين زائد TR2a-b8x1
+
+438
+00:45:05,020 --> 00:45:09,700
+1 بالشكل اللي عندنا هنا هذي linear transformation
+
+439
+00:45:09,700 --> 00:45:16,620
+يبقى ال constant برا يبقى b ناقص ال a في t 1 2
+
+440
+00:45:16,620 --> 00:45:28,010
+زائد 2a ناقص ال b في t of 1 1طب نفك هذه يبقى P
+
+441
+00:45:28,010 --> 00:45:33,850
+ناقص ال A في T of واحد و واحد موطاع عندي في المثلة
+
+442
+00:45:33,850 --> 00:45:40,870
+قداش كانت T of واحد و اتنين لواحد سالب واحد Zero
+
+443
+00:45:40,870 --> 00:45:48,930
+واحد سالب واحد و Zero زيدي اتنين A ناقص P في T of
+
+444
+00:45:48,930 --> 00:45:55,580
+واحد و واحد لواحد و اتنين و سالب واحدبدا افك
+
+445
+00:45:55,580 --> 00:45:59,220
+الأقواص هذه يبقى لو فكيت الأقواص هذه ماشي بيحصل
+
+446
+00:45:59,220 --> 00:46:07,880
+عندنا مانعة بيناقص ال a و ناقص بي زائد ال a وهذا
+
+447
+00:46:07,880 --> 00:46:15,050
+zero زي ما هو زائدبدا افك الجثة هدا اتنين a ناقص
+
+448
+00:46:15,050 --> 00:46:25,250
+ال b اربعة a ناقص اتنين b وبعدها بيه ناقص اتنين a
+
+449
+00:46:31,980 --> 00:46:39,640
+بدي أجمع يبقى أصبح ال T of A وB بدها تساوي القوس
+
+450
+00:46:39,640 --> 00:46:46,360
+الأول طلعي لهنا هي B وناقص B هيروحوا مع بعض هادي
+
+451
+00:46:46,360 --> 00:46:53,860
+وهادي مع السلامة بظل فقط A فاصلة نيجي للي بعده
+
+452
+00:46:53,860 --> 00:47:01,600
+ناقص B وناقص B ناقص تلاتة يبقى خمسة A ناقص تلاتة B
+
+453
+00:47:02,070 --> 00:47:11,340
+اللي بعده Zero بتروح بضل بيه ناقص 2Aإذا طلعت صورة
+
+454
+00:47:11,340 --> 00:47:17,140
+ولصيغة الـ linear transformation تبع T of A وB
+
+455
+00:47:17,140 --> 00:47:22,980
+اللي هو بده يسوي A وخمسة A ناقص تلاتة B والـ B
+
+456
+00:47:22,980 --> 00:47:30,840
+ناقص اتنين A وانتهى السؤال طيب سؤاللكم تقدروا
+
+457
+00:47:30,840 --> 00:47:36,560
+تحسبوا ال kernel اللي لها ال kernel لل linear
+
+458
+00:47:36,560 --> 00:47:43,640
+transformationT of the element هو Zero يعني هذا
+
+459
+00:47:43,640 --> 00:47:51,320
+الكلام كله هو Zero Zero Zero يبقى A ب Zero فعرة
+
+460
+00:47:51,320 --> 00:47:56,010
+هذه سلب تلاتة B تسلب تلاتة B يبقى B ب Zeroهنا
+
+461
+00:47:56,010 --> 00:48:00,310
+بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو
+
+462
+00:48:00,310 --> 00:48:00,910
+بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو
+
+463
+00:48:00,910 --> 00:48:01,230
+بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو
+
+464
+00:48:01,230 --> 00:48:05,710
+بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو
+
+465
+00:48:05,710 --> 00:48:19,930
+بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو بيبزيرو
+
+466
+00:48:19,930 --> 00:48:22,750
+بيبزيرو
+
+467
+00:48:23,480 --> 00:48:28,560
+يبقى هذا هو مين هذا هو ال kernel يعني ايه ب zero
+
+468
+00:48:28,560 --> 00:48:33,840
+بتطلعوا بيه ايه ب zero يبقى فقط هو ال zero قلبي
+
+469
+00:48:33,840 --> 00:48:38,120
+يبقى لغاية هنا stop انتهى هذا section طبعا هذا
+
+470
+00:48:38,120 --> 00:48:43,280
+المثال very important لأنه بيجيب البدري و الواخري
+
+471
+00:48:43,280 --> 00:48:48,500
+بيجيب الحاضر و الغاية و هو السؤال موجود بالكتاب
+
+472
+00:48:48,500 --> 00:48:54,100
+موجود أكتر من السؤال هذا هو أحدهمطيب إذا بناء عليه
+
+473
+00:48:54,100 --> 00:49:04,000
+بنوصل ل exercises تلاتة سبعة المسائل التالية من
+
+474
+00:49:04,000 --> 00:49:13,690
+واحد لغاية أربعةوبعد هيك بدنا سؤال سبعة A وD وبعد
+
+475
+00:49:13,690 --> 00:49:24,930
+سؤال سبعة بدنا عشرة وحداش واطماش A وC وبنروح ال
+
+476
+00:49:24,930 --> 00:49:31,870
+additional exercisesadditional exercises بدنا
+
+477
+00:49:31,870 --> 00:49:40,550
+المسائل من واحد لغاية سبعة وسؤال تسعة وسؤال اتمار
+
+478
+00:49:43,110 --> 00:49:48,250
+عليك توقف انتهى هذا section و بانتهي هذا section
+
+479
+00:49:48,250 --> 00:49:53,750
+ينتهي المطلوب من هذا ال chapter وبالتالي انتهينا
+
+480
+00:49:53,750 --> 00:49:58,750
+من ال chapter الثاني من الجبر الخطي و لسه ضايل
+
+481
+00:49:58,750 --> 00:50:03,270
+علينا كمان chapter ب two sections اللي هو ال eigen
+
+482
+00:50:03,270 --> 00:50:06,150
+values و ال eigen vectors اللي هنبدأها اليوم ان
+
+483
+00:50:06,150 --> 00:50:12,120
+شاء الله الساعة اتناشرو كذلك بيظل عليها كمصفوفة و
+
+484
+00:50:12,120 --> 00:50:17,900
+diagonalizable يعني كيف نخلي مصفوفة على شكل ايه؟
+
+485
+00:50:17,900 --> 00:50:25,200
+على شكل قطري ان شاء الله الامتحان لغاية هذه النقطة
+
+486
+00:50:25,200 --> 00:50:29,260
+بس يبقى الامتحان و chapter تلاتة كله لشان هو
+
+487
+00:50:29,260 --> 00:50:34,980
+chapter تقيله مليان و كذلك ال two sections اللي
+
+488
+00:50:34,980 --> 00:50:39,720
+ضال عندنا من chapter المحددات و المصفوفاتاللي هو
+
+489
+00:50:39,720 --> 00:50:47,240
+chapter 11,2,11 اللي بتكلم عن كرامر ذرول و chapter
+
+490
+00:50:47,240 --> 00:50:52,780
+12 اللي بتكلم عن ال inverse function تمام ال
+
+491
+00:50:52,780 --> 00:50:58,480
+inverse matrix قصدي معكوس المصممة جاب جاب لغاية
+
+492
+00:50:58,480 --> 00:50:59,520
+تانية أعطيكم العزيزي
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Mrn4yfKCaMs_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Mrn4yfKCaMs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..37ffc30db749ba67d7eea7f723c407425d14cab9
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/Mrn4yfKCaMs_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3915, "start": 20.7, "end": 39.16, "text": "بسم الله الرحمن الرحيم لازلنا في section تلاتة سبعة اللي بتحدث عن ال linear transformations وما درسناه سابقا تعريف ال linear transformation وعرفنا انه function من vector space إلى vector space تاني وتعقق خاصيتين", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 5296, 31377, 1211, 8315, 8978, 3541, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 13672, 1829, 39894, 24401, 12984, 18871, 2423, 8213, 34852, 4032, 15042, 11778, 2288, 3794, 8315, 3224, 8608, 16758, 4587, 995, 37279, 16572, 5172, 2423, 8213, 9887, 4032, 3615, 28480, 8315, 16472, 3224, 2445, 9154, 8062, 1901, 30731, 8062, 1901, 6055, 7649, 1829, 4032, 2655, 3615, 4587, 4587, 16490, 33546, 36081, 9957], "avg_logprob": -0.13703547941671834, "compression_ratio": 1.6282722513089005, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 20.7, "end": 21.04, "word": "بسم", "probability": 0.86767578125}, {"start": 21.04, "end": 21.28, 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"tokens": [6027, 3794, 33604, 6027, 4724, 1829, 39648, 718, 314, 9154, 497, 18, 30731, 497, 17, 312, 257, 8213, 9887, 1270, 300, 4724, 5016, 1829, 12984, 16472], "avg_logprob": -0.30497683860637526, "compression_ratio": 0.9423076923076923, "no_speech_prob": 0.0, "words": [{"start": 592.46, "end": 593.02, "word": "السؤال", "probability": 0.85064697265625}, {"start": 593.02, "end": 593.66, "word": " بيقول", "probability": 0.8307291666666666}, {"start": 593.66, "end": 594.7, "word": " let", "probability": 0.2489013671875}, {"start": 594.7, "end": 596.82, "word": " T", "probability": 0.72802734375}, {"start": 596.82, "end": 597.82, "word": " من", "probability": 0.974609375}, {"start": 597.82, "end": 598.84, "word": " R3", "probability": 0.67724609375}, {"start": 598.84, "end": 599.88, "word": " إلى", "probability": 0.63525390625}, {"start": 599.88, "end": 601.08, "word": " R2", "probability": 0.9931640625}, {"start": 601.08, "end": 602.32, "word": " be", "probability": 0.1826171875}, 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0.392822265625}, {"start": 661.92, "end": 662.36, "word": " A", "probability": 0.81005859375}, {"start": 662.36, "end": 662.66, "word": " في", "probability": 0.8876953125}, {"start": 662.66, "end": 662.82, "word": " ال", "probability": 0.58837890625}, {"start": 662.82, "end": 663.24, "word": " X", "probability": 0.970703125}, {"start": 663.24, "end": 664.9, "word": " نمرى", "probability": 0.7420247395833334}, {"start": 664.9, "end": 665.16, "word": " ب", "probability": 0.91552734375}, {"start": 665.16, "end": 667.8, "word": " find", "probability": 0.1849365234375}], "temperature": 1.0}, {"id": 26, "seek": 67359, "start": 669.85, "end": 673.59, "text": "T of واحد و اتنين و تلاتة", "tokens": [51, 295, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 4032, 6055, 1211, 9307, 3660], "avg_logprob": -0.3455729126930237, "compression_ratio": 0.9534883720930233, "no_speech_prob": 0.0, "words": [{"start": 669.85, "end": 670.39, "word": "T", "probability": 0.2320556640625}, {"start": 670.39, "end": 671.09, "word": " of", "probability": 0.359619140625}, {"start": 671.09, "end": 671.77, "word": " واحد", "probability": 0.871337890625}, {"start": 671.77, "end": 671.97, "word": " و", "probability": 0.865234375}, {"start": 671.97, "end": 672.59, "word": " اتنين", "probability": 0.78759765625}, {"start": 672.59, "end": 672.93, "word": " و", "probability": 0.8271484375}, {"start": 672.93, "end": 673.59, "word": " تلاتة", "probability": 0.9185791015625}], "temperature": 1.0}, {"id": 27, "seek": 73251, "start": 704.77, "end": 732.51, "text": "يبقى في عنا مثال آخر المثال الآخر كالتالي بيقول افترض في من R3 الى R2 عبارة عن Linear Transformation إذا شكل Linear Transformation هو دائما و أبدا T of X بده سواء من X هذا شكله بيقول هنا بحيث T of E1 يسوى واحد وسلم اتنين مين E1 يا مانات هذه؟", "tokens": [1829, 3555, 4587, 7578, 8978, 6225, 8315, 50113, 6027, 19753, 34740, 9673, 12984, 6027, 6024, 95, 34740, 9122, 6027, 2655, 6027, 1829, 4724, 1829, 39648, 1975, 5172, 2655, 43042, 8978, 9154, 497, 18, 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"end": 715.19, "word": " Linear", "probability": 0.6781005859375}, {"start": 715.19, "end": 716.25, "word": " Transformation", "probability": 0.88916015625}, {"start": 716.25, "end": 717.09, "word": " إذا", "probability": 0.686279296875}, {"start": 717.09, "end": 717.59, "word": " شكل", "probability": 0.947509765625}, {"start": 717.59, "end": 718.13, "word": " Linear", "probability": 0.8017578125}, {"start": 718.13, "end": 719.09, "word": " Transformation", "probability": 0.975830078125}, {"start": 719.09, "end": 719.57, "word": " هو", "probability": 0.9755859375}, {"start": 719.57, "end": 720.11, "word": " دائما", "probability": 0.8981119791666666}, {"start": 720.11, "end": 720.27, "word": " و", "probability": 0.8251953125}, {"start": 720.27, "end": 720.75, "word": " أبدا", "probability": 0.8662109375}, {"start": 720.75, "end": 721.35, "word": " T", "probability": 0.6796875}, {"start": 721.35, "end": 721.67, "word": " of", "probability": 0.63427734375}, {"start": 721.67, "end": 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و", "probability": 0.81982421875}, {"start": 1576.93, "end": 1577.29, "word": " أتوكل", "probability": 0.7222900390625}, {"start": 1577.29, "end": 1577.65, "word": " الله", "probability": 0.75146484375}], "temperature": 1.0}, {"id": 64, "seek": 159866, "start": 1578.0, "end": 1598.66, "text": "يبقى كيف بدي أعمل؟ بقولك دبر حالك كيف أدبر حالي؟ تعالى تشوف يبقى أنا بدي أجي للمطموب الأول يبقى solution بدي أجي لنمرق ايه الآن ال dimension لل R2 كده شو ساوي؟", "tokens": [1829, 3555, 4587, 7578, 9122, 33911, 4724, 16254, 5551, 25957, 1211, 22807, 4724, 39648, 4117, 11778, 26890, 11331, 6027, 4117, 9122, 33911, 5551, 3215, 26890, 11331, 6027, 1829, 22807, 37279, 6027, 7578, 6055, 8592, 38688, 7251, 3555, 4587, 7578, 41850, 4724, 16254, 5551, 7435, 1829, 5296, 19528, 9566, 2304, 2407, 3555, 16247, 12610, 7251, 3555, 4587, 7578, 3827, 4724, 16254, 5551, 7435, 1829, 5296, 1863, 29973, 4587, 1975, 1829, 3224, 6024, 48506, 2423, 10139, 24976, 497, 17, 9122, 3215, 3224, 13412, 2407, 8608, 995, 45865, 22807], "avg_logprob": -0.2819683853237108, "compression_ratio": 1.6242424242424243, "no_speech_prob": 0.0, "words": [{"start": 1578.0, "end": 1578.54, "word": "يبقى", "probability": 0.675689697265625}, {"start": 1578.54, "end": 1578.84, "word": " كيف", "probability": 0.947021484375}, {"start": 1578.84, "end": 1579.1, "word": " بدي", "probability": 0.6630859375}, {"start": 1579.1, "end": 1579.84, "word": " أعمل؟", "probability": 0.8160400390625}, {"start": 1579.84, "end": 1580.46, "word": " بقولك", "probability": 0.8465169270833334}, {"start": 1580.46, "end": 1581.1, "word": " دبر", "probability": 0.4990234375}, {"start": 1581.1, "end": 1581.68, "word": " حالك", "probability": 0.9599609375}, {"start": 1581.68, "end": 1582.36, "word": " كيف", "probability": 0.882080078125}, {"start": 1582.36, "end": 1582.74, "word": " أدبر", "probability": 0.8663736979166666}, {"start": 1582.74, "end": 1583.2, "word": " حالي؟", "probability": 0.883056640625}, {"start": 1583.2, "end": 1583.56, "word": " تعالى", "probability": 0.888671875}, {"start": 1583.56, "end": 1583.82, "word": " تشوف", "probability": 0.7682291666666666}, {"start": 1583.82, "end": 1585.0, "word": " يبقى", "probability": 0.8824462890625}, {"start": 1585.0, "end": 1585.28, "word": " أنا", "probability": 0.6669921875}, {"start": 1585.28, "end": 1585.54, "word": " بدي", "probability": 0.4373779296875}, {"start": 1585.54, "end": 1585.84, "word": " أجي", "probability": 0.6876627604166666}, {"start": 1585.84, "end": 1586.62, "word": " للمطموب", "probability": 0.7816569010416666}, {"start": 1586.62, "end": 1587.04, "word": " الأول", "probability": 0.989990234375}, {"start": 1587.04, "end": 1587.42, "word": " يبقى", "probability": 0.847412109375}, {"start": 1587.42, "end": 1588.22, "word": " solution", "probability": 0.9248046875}, {"start": 1588.22, "end": 1591.8, "word": " بدي", "probability": 0.87158203125}, {"start": 1591.8, "end": 1591.98, "word": " أجي", "probability": 0.9602864583333334}, {"start": 1591.98, "end": 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بدى يكون فيه كداش عنصرين two vectors only الان باجى بقول since بما ان ال dimension ل ال R2 بدى يساوي اتنين يبجى we have", "tokens": [4117, 3215, 33599, 22807, 1975, 2655, 1863, 9957, 5296, 28814, 1829, 8592, 16472, 2423, 3832, 5143, 36764, 24401, 4032, 17182, 4032, 17182, 4032, 36764, 24401, 37495, 22653, 18871, 9381, 2288, 9957, 7251, 3555, 7435, 7578, 1975, 1829, 5143, 1975, 34740, 47525, 7578, 7251, 30544, 8978, 3224, 9122, 3215, 33599, 18871, 9381, 2288, 9957, 732, 18875, 787, 2423, 7649, 4724, 26108, 7578, 4724, 39648, 1670, 4724, 15042, 16472, 2423, 10139, 5296, 2423, 497, 17, 47525, 7578, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 7251, 3555, 7435, 7578, 321, 362], "avg_logprob": -0.2946180479394065, "compression_ratio": 1.6080402010050252, "no_speech_prob": 0.0, "words": [{"start": 1600.27, "end": 1601.33, "word": "كداش؟", "probability": 0.5961532592773438}, {"start": 1601.33, "end": 1601.71, "word": " اتنين", "probability": 0.6511993408203125}, {"start": 1601.71, "end": 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2131.53, "word": " اتنين", "probability": 0.9825439453125}, {"start": 2131.53, "end": 2132.17, "word": " سالب", "probability": 0.9886067708333334}, {"start": 2132.17, "end": 2132.79, "word": " واحد", "probability": 0.99462890625}, {"start": 2132.79, "end": 2133.65, "word": " بالشكل", "probability": 0.9524739583333334}, {"start": 2133.65, "end": 2133.83, "word": " اللي", "probability": 0.89404296875}, {"start": 2133.83, "end": 2134.43, "word": " عندنا", "probability": 0.838134765625}, {"start": 2134.43, "end": 2134.81, "word": " هنا", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 89, "seek": 215036, "start": 2135.44, "end": 2150.36, "text": "يبقى هذه معادلة مصفوفية حاصل ضرب two matrices يساوي main matrix بدي أعرف قداش من المصفوفة A كيف بدي أجيب المصفوفة A؟", "tokens": [1829, 3555, 4587, 7578, 29538, 20449, 18513, 37977, 3714, 9381, 5172, 38688, 10632, 11331, 33546, 1211, 48812, 25513, 732, 32284, 7251, 3794, 995, 45865, 2135, 8141, 4724, 16254, 5551, 3615, 28480, 12174, 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2994.69, "end": 2995.49, "word": " الثاني", "probability": 0.9085693359375}, {"start": 2995.49, "end": 2996.17, "word": " من", "probability": 0.9091796875}, {"start": 2996.17, "end": 2996.81, "word": " الجبر", "probability": 0.70361328125}, {"start": 2996.81, "end": 2997.59, "word": " الخطي", "probability": 0.7574869791666666}, {"start": 2997.59, "end": 2998.03, "word": " و", "probability": 0.70751953125}, {"start": 2998.03, "end": 2998.43, "word": " لسه", "probability": 0.92578125}, {"start": 2998.43, "end": 2998.75, "word": " ضايل", "probability": 0.5492757161458334}, {"start": 2998.75, "end": 2999.13, "word": " علينا", "probability": 0.941162109375}, {"start": 2999.13, "end": 2999.47, "word": " كمان", "probability": 0.7549641927083334}, {"start": 2999.47, "end": 3000.05, "word": " chapter", "probability": 0.91796875}, {"start": 3000.05, "end": 3000.33, "word": " ب", "probability": 0.59521484375}, {"start": 3000.33, "end": 3001.05, "word": " two", "probability": 0.654296875}, {"start": 3001.05, "end": 3001.99, "word": " sections", "probability": 0.90771484375}, {"start": 3001.99, "end": 3002.69, "word": " اللي", "probability": 0.799072265625}, {"start": 3002.69, "end": 3002.83, "word": " هو", "probability": 0.78564453125}, {"start": 3002.83, "end": 3002.95, "word": " ال", "probability": 0.6630859375}, {"start": 3002.95, "end": 3003.27, "word": " eigen", "probability": 0.71826171875}, {"start": 3003.27, "end": 3003.83, "word": " values", "probability": 0.66650390625}, {"start": 3003.83, "end": 3003.99, "word": " و", "probability": 0.8662109375}, {"start": 3003.99, "end": 3004.09, "word": " ال", "probability": 0.80224609375}, {"start": 3004.09, "end": 3004.41, "word": " eigen", "probability": 0.9384765625}, {"start": 3004.41, "end": 3004.97, "word": " vectors", "probability": 0.85986328125}, {"start": 3004.97, "end": 3005.19, "word": " اللي", "probability": 0.85546875}, {"start": 3005.19, "end": 3005.73, "word": " هنبدأها", "probability": 0.9029296875}, {"start": 3005.73, "end": 3005.99, "word": " اليوم", "probability": 0.912841796875}, {"start": 3005.99, "end": 3006.15, "word": " ان", "probability": 0.70703125}, {"start": 3006.15, "end": 3006.43, "word": " شاء", "probability": 0.97119140625}, {"start": 3006.43, "end": 3006.63, "word": " الله", "probability": 0.95654296875}, {"start": 3006.63, "end": 3007.89, "word": " الساعة", "probability": 0.8050944010416666}, {"start": 3007.89, "end": 3008.49, "word": " اتناشر", "probability": 0.820263671875}], "temperature": 1.0}, {"id": 126, "seek": 303836, "start": 3008.78, "end": 3038.36, "text": "و كذلك بيظل عليها كمصفوفة و diagonalizable يعني كيف نخلي مصفوفة على شكل ايه؟ على شكل قطري ان شاء الله الامتحان لغاية هذه النقطة بس يبقى الامتحان و chapter تلاتة كله لشان هو chapter تقيله مليان و كذلك ال two sections اللي ضال عندنا من chapter المحددات و المصفوفات", "tokens": [2407, 9122, 8848, 23275, 4724, 1829, 19913, 1211, 25894, 11296, 9122, 2304, 9381, 5172, 38688, 3660, 4032, 21539, 22395, 37495, 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"end": 3011.38, "word": " عليها", "probability": 0.86962890625}, {"start": 3011.38, "end": 3011.96, "word": " كمصفوفة", "probability": 0.4914957682291667}, {"start": 3011.96, "end": 3012.12, "word": " و", "probability": 0.7177734375}, {"start": 3012.12, "end": 3013.42, "word": " diagonalizable", "probability": 0.703125}, {"start": 3013.42, "end": 3014.18, "word": " يعني", "probability": 0.876953125}, {"start": 3014.18, "end": 3014.5, "word": " كيف", "probability": 0.970947265625}, {"start": 3014.5, "end": 3015.1, "word": " نخلي", "probability": 0.7903645833333334}, {"start": 3015.1, "end": 3016.18, "word": " مصفوفة", "probability": 0.9357421875}, {"start": 3016.18, "end": 3016.72, "word": " على", "probability": 0.8984375}, {"start": 3016.72, "end": 3017.26, "word": " شكل", "probability": 0.9794921875}, {"start": 3017.26, "end": 3017.9, "word": " ايه؟", "probability": 0.76336669921875}, {"start": 3017.9, "end": 3018.16, "word": " على", "probability": 0.84375}, {"start": 3018.16, "end": 3018.82, "word": " شكل", "probability": 0.98095703125}, {"start": 3018.82, "end": 3019.74, "word": " قطري", "probability": 0.8458658854166666}, {"start": 3019.74, "end": 3020.18, "word": " ان", "probability": 0.7021484375}, {"start": 3020.18, "end": 3020.42, "word": " شاء", "probability": 0.9873046875}, {"start": 3020.42, "end": 3020.7, "word": " الله", "probability": 0.9501953125}, {"start": 3020.7, "end": 3023.14, "word": " الامتحان", "probability": 0.91181640625}, {"start": 3023.14, "end": 3024.12, "word": " لغاية", "probability": 0.9912109375}, {"start": 3024.12, "end": 3024.56, "word": " هذه", "probability": 0.97705078125}, {"start": 3024.56, "end": 3025.2, "word": " النقطة", "probability": 0.9864908854166666}, {"start": 3025.2, "end": 3025.6, "word": " بس", "probability": 0.98828125}, {"start": 3025.6, "end": 3026.38, "word": " يبقى", "probability": 0.8720703125}, {"start": 3026.38, "end": 3027.26, "word": " الامتحان", "probability": 0.92451171875}, {"start": 3027.26, "end": 3027.5, "word": " و", "probability": 0.603515625}, {"start": 3027.5, "end": 3027.88, "word": " chapter", "probability": 0.537109375}, {"start": 3027.88, "end": 3028.52, "word": " تلاتة", "probability": 0.9378662109375}, {"start": 3028.52, "end": 3028.78, "word": " كله", "probability": 0.977294921875}, {"start": 3028.78, "end": 3029.14, "word": " لشان", "probability": 0.5155436197916666}, {"start": 3029.14, "end": 3029.26, "word": " هو", "probability": 0.44873046875}, {"start": 3029.26, "end": 3029.6, "word": " chapter", "probability": 0.89404296875}, {"start": 3029.6, "end": 3030.16, "word": " تقيله", "probability": 0.841064453125}, {"start": 3030.16, "end": 3030.78, "word": " مليان", "probability": 0.9695638020833334}, {"start": 3030.78, "end": 3031.54, "word": " و", "probability": 0.9716796875}, {"start": 3031.54, "end": 3032.34, "word": " كذلك", "probability": 0.92724609375}, {"start": 3032.34, "end": 3032.7, "word": " ال", "probability": 0.958984375}, {"start": 3032.7, "end": 3032.9, "word": " two", "probability": 0.92822265625}, {"start": 3032.9, "end": 3033.76, "word": " sections", "probability": 0.88330078125}, {"start": 3033.76, "end": 3034.98, "word": " اللي", "probability": 0.9560546875}, {"start": 3034.98, "end": 3035.34, "word": " ضال", "probability": 0.71533203125}, {"start": 3035.34, "end": 3035.8, "word": " عندنا", "probability": 0.82421875}, {"start": 3035.8, "end": 3036.08, "word": " من", "probability": 0.94287109375}, {"start": 3036.08, "end": 3036.5, "word": " chapter", "probability": 0.8251953125}, {"start": 3036.5, "end": 3037.4, "word": " المحددات", "probability": 0.9835205078125}, {"start": 3037.4, "end": 3037.54, "word": " و", "probability": 0.6396484375}, {"start": 3037.54, "end": 3038.36, "word": " المصفوفات", "probability": 0.87021484375}], "temperature": 1.0}, {"id": 127, "seek": 305952, "start": 3038.76, "end": 3059.52, "text": "اللي هو chapter 11,2,11 اللي بتكلم عن كرامر ذرول و chapter 12 اللي بتكلم عن ال inverse function تمام ال inverse matrix قصدي معكوس المصممة جاب جاب لغاية تانية أعطيكم العزيزي", "tokens": [6027, 20292, 31439, 7187, 2975, 11, 17, 11, 5348, 13672, 1829, 39894, 4117, 19528, 18871, 9122, 2288, 10943, 2288, 29910, 2288, 12610, 4032, 7187, 2272, 13672, 1829, 39894, 4117, 19528, 18871, 2423, 17340, 2445, 46811, 10943, 2423, 17340, 8141, 12174, 9381, 16254, 20449, 4117, 41779, 9673, 9381, 2304, 46007, 10874, 16758, 10874, 16758, 5296, 17082, 995, 10632, 6055, 7649, 10632, 5551, 3615, 9566, 1829, 24793, 18863, 11622, 1829, 11622, 1829], "avg_logprob": -0.2935739344274494, "compression_ratio": 1.5470588235294118, "no_speech_prob": 0.0, "words": [{"start": 3038.76, "end": 3039.44, "word": "اللي", "probability": 0.738037109375}, {"start": 3039.44, "end": 3039.72, "word": " هو", "probability": 0.75}, {"start": 3039.72, "end": 3040.16, "word": " chapter", "probability": 0.63671875}, {"start": 3040.16, "end": 3040.86, "word": " 11", "probability": 0.7958984375}, {"start": 3040.86, "end": 3041.36, "word": 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"probability": 0.99755859375}, {"start": 3049.12, "end": 3049.3, "word": " ال", "probability": 0.7294921875}, {"start": 3049.3, "end": 3049.82, "word": " inverse", "probability": 0.95166015625}, {"start": 3049.82, "end": 3050.84, "word": " function", "probability": 0.87939453125}, {"start": 3050.84, "end": 3052.26, "word": " تمام", "probability": 0.8173828125}, {"start": 3052.26, "end": 3052.78, "word": " ال", "probability": 0.58447265625}, {"start": 3052.78, "end": 3053.22, "word": " inverse", "probability": 0.95068359375}, {"start": 3053.22, "end": 3053.96, "word": " matrix", "probability": 0.91064453125}, {"start": 3053.96, "end": 3054.42, "word": " قصدي", "probability": 0.73681640625}, {"start": 3054.42, "end": 3055.46, "word": " معكوس", "probability": 0.7172037760416666}, {"start": 3055.46, "end": 3056.72, "word": " المصممة", "probability": 0.79229736328125}, {"start": 3056.72, "end": 3057.24, "word": " جاب", "probability": 0.3211669921875}, {"start": 3057.24, "end": 3057.72, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5d379610f34565ba284805aeebbb76935f579736
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw_postprocess.srt
@@ -0,0 +1,1792 @@
+1
+00:00:19,980 --> 00:00:23,680
+بسم الله الرحمن الرحيم آخر حاجة أخدناها في
+
+2
+00:00:23,680 --> 00:00:29,300
+المحاضرة الماضية وهو Laplace transform لمين
+
+3
+00:00:29,300 --> 00:00:34,540
+للمشتقة فقولنا أخدنا Laplace transform للمشتقة
+
+4
+00:00:34,540 --> 00:00:39,220
+الأورا عبارة عن S الدلة بين اشتقاق ناقص ال
+
+5
+00:00:39,220 --> 00:00:43,820
+function and when and zeroو بعد ذلك رحنا اخدنا
+
+6
+00:00:43,820 --> 00:00:49,180
+لبلاس للمشتقة الثانية قولنا هو عبارة عن S2 في
+
+7
+00:00:49,180 --> 00:00:55,620
+لبلاس لل F of T بدون اشتقاق ناقص S في F of Zero
+
+8
+00:00:55,620 --> 00:01:02,440
+ناقص F prime of Zero بعد ذلك عمّمناها لو كانت
+
+9
+00:01:02,440 --> 00:01:07,810
+مشتقة نونيةالمدني ناخد بعض الأمثلة على ذلك بيقول
+
+10
+00:01:07,810 --> 00:01:11,090
+استخدم Laplace transform عشان نحل المعادلات
+
+11
+00:01:11,090 --> 00:01:16,370
+التفاضلية الآتية واخدنا المعادلة الأولى من الرتبة
+
+12
+00:01:16,370 --> 00:01:22,200
+الأولى والمعادلة الثانية من الرتبة الثانيةيبقى
+
+13
+00:01:22,200 --> 00:01:27,180
+بالنسبة للحل المعادلة الأولى نأخد لبلاس ترانسفورم
+
+14
+00:01:27,180 --> 00:01:35,060
+للطرفين يبقى لبلاس ترانسفورم لل X' of T زائد تلاتة
+
+15
+00:01:35,060 --> 00:01:42,900
+X of T كله بده يسوى لبلاس ترانسفورم لل E أس اتنين
+
+16
+00:01:42,900 --> 00:01:47,680
+T بالشكل اللي عنهايبقى Laplace للطرف الشمال من
+
+17
+00:01:47,680 --> 00:01:52,980
+المعادلة هو Laplace الطرف اليمين من المعادلة المرة
+
+18
+00:01:52,980 --> 00:01:57,560
+الماضية أخدنا Laplace هذا مؤثر خاطي إذا بروح
+
+19
+00:01:57,560 --> 00:02:01,720
+أستخدم هذه الخاصية إذا بصير Laplace الأول زائد
+
+20
+00:02:01,720 --> 00:02:07,800
+تلاتة Laplace للثانييبقى لبلاس ترانسفورم لمن؟ لل
+
+21
+00:02:07,800 --> 00:02:16,600
+X' of T زائد تلاتة لبلاس ترانسفورم لل X of T
+
+22
+00:02:16,600 --> 00:02:22,040
+بالشكل ان هذا بدي يسوي لبلاس ترانسفورم لل E أس
+
+23
+00:02:22,040 --> 00:02:28,360
+اتنين Tالان بدي اجي لبلاس ترانسفورم لل X' بدي بقول
+
+24
+00:02:28,360 --> 00:02:36,900
+هذا عبارة عن مين؟ عبارة عن S في X of S X of S هو
+
+25
+00:02:36,900 --> 00:02:41,620
+لبلاس ترانسفورم لدى X of T
+
+26
+00:02:50,710 --> 00:02:55,630
+خلصنا الترم الأول والترم التاني زي التلاتة ل plus
+
+27
+00:02:55,630 --> 00:03:02,910
+لل X of T بدي أسميه X of S يساوي هذه حسبناها المرة
+
+28
+00:03:02,910 --> 00:03:10,270
+الماضية وقلنا هذه عبارة عن ايش عبارة عن واحدعلى اس
+
+29
+00:03:10,270 --> 00:03:16,230
+ناقص اتنين يبقى واحد على اس ناقص اتنين يبقى واحد
+
+30
+00:03:16,230 --> 00:03:18,410
+على اس ناقص اتنين يبقى واحد على اس ناقص اتنين يبقى
+
+31
+00:03:18,410 --> 00:03:18,470
+واحد على اس ناقص اتنين يبقى واحد على اس ناقص اتنين
+
+32
+00:03:18,470 --> 00:03:20,430
+يبقى واحد على اس ناقص اتنين يبقى واحد على اس ناقص
+
+33
+00:03:20,430 --> 00:03:21,630
+اتنين يبقى واحد على اس ناقص اتنين يبقى واحد على اس
+
+34
+00:03:21,630 --> 00:03:23,730
+ناقص اتنين يبقى واحد على اس ناقص اتنين يبقى واحد
+
+35
+00:03:23,730 --> 00:03:27,250
+على اس ناقص اتنين يبقى واحد على اس ناقص اتنين يبقى
+
+36
+00:03:27,250 --> 00:03:34,840
+واحد على اس ناقص اتنين يبقى وازائد تلاتة في ال X
+
+37
+00:03:34,840 --> 00:03:41,040
+to the power S ناقص ال X Zero بواحد يبقى ناقص ناقص
+
+38
+00:03:41,040 --> 00:03:48,060
+بصير زائد واحد بدي يسوي واحد على S ناقص اتنين
+
+39
+00:03:48,060 --> 00:03:53,090
+بالشكل اللي انا اناطيب الآن بدي أجيب الواحد على
+
+40
+00:03:53,090 --> 00:03:59,470
+الشجة التانية يبقاش بصير عندي بصير ال S زائد تلاتة
+
+41
+00:03:59,470 --> 00:04:06,870
+في ال X of S بدي أساوي واحد على S ناقص اتنين ناقص
+
+42
+00:04:06,870 --> 00:04:13,630
+الواحد ان وحد المقامات للطرفين بيظل S ناقص اتنين
+
+43
+00:04:13,630 --> 00:04:22,070
+لمين لا واحد لا ناقص Sزائد اتنين يبقى تلاتة ناقص S
+
+44
+00:04:22,070 --> 00:04:28,890
+على S ناقص اتنين يبقى بناء انا عليه بقدر اجيبله ال
+
+45
+00:04:28,890 --> 00:04:37,410
+X of S يبقى ال X of S يساوي اللي هو من تلاتة ناقص
+
+46
+00:04:37,410 --> 00:04:46,270
+S على من على S ناقص اتنين مقسومة على S زائد تلاتة
+
+47
+00:04:48,450 --> 00:04:55,330
+أنا جبت له لبلاسي ترانسفورم الألميم للحل تبعت ده
+
+48
+00:04:55,330 --> 00:04:59,510
+اللي هو بدوش لبلاسي ترانسفورم للحل بده الحل itself
+
+49
+00:04:59,510 --> 00:05:03,030
+لإنه يشرح جالي يستخدم لبلاسي ترانسفورم لتحل
+
+50
+00:05:03,030 --> 00:05:06,810
+المعادلة
+
+51
+00:05:06,810 --> 00:05:13,110
+التفاضليةبقول له كويس اذا انا بروح ادور على الدالة
+
+52
+00:05:13,110 --> 00:05:17,010
+اللى Laplace transform اللى هي يساوي مين؟ يساوي
+
+53
+00:05:17,010 --> 00:05:20,090
+الجزر اللى قدامنا هذا، باجي بقول يا ورادي هو ايش
+
+54
+00:05:20,090 --> 00:05:22,830
+بدي .. ايش بدي جيبني Laplace مين؟ هي الدالة
+
+55
+00:05:22,830 --> 00:05:26,150
+Laplace اللى هي يساوي اللى هو الجزر اللى عندنا
+
+56
+00:05:26,650 --> 00:05:30,910
+بالشكل هذا صعب مش عارفها، لكن ربنا سبحانه وتعالى
+
+57
+00:05:30,910 --> 00:05:37,250
+أعطانا عقل نفكر به و نستنبط و نستنتج الأشياء أو
+
+58
+00:05:37,250 --> 00:05:41,770
+نخرج من المشكلة اللي احنا فيها إلى مشكلة بسيطة جدا
+
+59
+00:05:41,770 --> 00:05:49,270
+وسهل الحل تبعها، إذا البسط عندي معادلة من الدرجة
+
+60
+00:05:51,450 --> 00:05:57,730
+البصف معادلة من الدرجة والمقام من الدرجة ومحللة
+
+61
+00:05:57,730 --> 00:06:03,750
+إلى two factors و ال two factors are different
+
+62
+00:06:03,750 --> 00:06:08,410
+أخدنا partial fractions صحيح ولا لأ؟ إذا بندروح
+
+63
+00:06:08,410 --> 00:06:13,900
+أعمل لهذه partial fractionsيبقى لما أقعد أعمل لهدي
+
+64
+00:06:13,900 --> 00:06:20,140
+partial fractions بقدر أقول هدي a على s ناقص اتنين
+
+65
+00:06:20,140 --> 00:06:26,980
+زائد b على s زائد تلاتة بالشكل اللي عندناطيب بدا
+
+66
+00:06:26,980 --> 00:06:30,800
+اجي على ال term هذا كله واستخدم خاصية ال partial
+
+67
+00:06:30,800 --> 00:06:35,120
+fraction نبدأ نروح اضرب في مين؟ في المقام اللي
+
+68
+00:06:35,120 --> 00:06:40,580
+عندنا هذا اضرب الطرفين بنحصل على ما يأتي تلاتة
+
+69
+00:06:40,580 --> 00:06:48,900
+ناقص S يساوي A في S زائد تلاتة زائد B في S ناقص
+
+70
+00:06:48,900 --> 00:06:54,020
+اتنينالان بدي اجيب له قيمة a وb فبجيب اقول لو
+
+71
+00:06:54,020 --> 00:07:02,040
+حطينا ال s تساوي 2 them بصير هنا تلاتة نقص اتنين
+
+72
+00:07:02,040 --> 00:07:07,500
+هنا بدي نحطها اتنين بدي يساوي a في اتنين زائد
+
+73
+00:07:07,500 --> 00:07:15,480
+تلاتة زائد zeroومنها الـ A تساوي خمس، تلاتة نقص،
+
+74
+00:07:15,480 --> 00:07:18,880
+اتنين قطع الواحد، اتنين و تلاتة خمسة يبقى الـ A
+
+75
+00:07:18,880 --> 00:07:24,820
+تساوي خمس الان لو جمنا حاطينا ال S تساوي سالب
+
+76
+00:07:24,820 --> 00:07:33,500
+تلاتة thenهذا بيروح بيظل أن تلاتة زائد تلاتة يساوي
+
+77
+00:07:33,500 --> 00:07:39,420
+Zero زائد اللي هو P تلاتة نقص اتنين اللي هو واحد
+
+78
+00:07:39,420 --> 00:07:49,890
+وبالتالي فال P أنها تساوي قداش تساوي ستةيبقى مرة
+
+79
+00:07:49,890 --> 00:07:54,610
+تانية بقول لو حطينا S بسالب تلاتة في المعادلة اللى
+
+80
+00:07:54,610 --> 00:07:59,530
+فوق بصير تلاتة زي التلاتة حطيها هنا سالب تلاتة
+
+81
+00:07:59,530 --> 00:08:06,310
+بالطير هنا سالب تلاتة سالب تلاتة بصير
+
+82
+00:08:13,290 --> 00:08:18,590
+إذا لو حطينا هذه بسلب تلاتة بصير هذه zero وهذه
+
+83
+00:08:18,590 --> 00:08:25,590
+زائد بي في سلب تلاتة سلب اتنين وبالتالي بي تساوي
+
+84
+00:08:25,590 --> 00:08:32,660
+سلب اللي هو ستة على خمسةسالب ست أخمس يبقى بناء
+
+85
+00:08:32,660 --> 00:08:39,460
+عليه أصبح ال X as a function of S هو عبارة عن ال A
+
+86
+00:08:39,460 --> 00:08:45,320
+بدهش لو حط مكانها خمس يبقى صارت خمس في واحد على S
+
+87
+00:08:45,320 --> 00:08:53,260
+ناقص اتنين وال B هذي بسالب ست أخمس في واحد على S
+
+88
+00:08:53,260 --> 00:09:00,160
+زائد تلتةإذا انجزت اللي هو Laplace transform للدلة
+
+89
+00:09:00,160 --> 00:09:06,120
+اللي فوق هذه إلى جزئين الجزئين كل واحد فيهم بعرف
+
+90
+00:09:06,120 --> 00:09:10,220
+Laplace transform الأصلي اللي هو وبالتالي قضيتنا
+
+91
+00:09:10,220 --> 00:09:17,680
+بصير سهلة فبروح بقوله solution of
+
+92
+00:09:17,680 --> 00:09:26,270
+theDifferential equation one is سميها للمعادلة هذه
+
+93
+00:09:26,270 --> 00:09:32,190
+اللي هي المعادلة رقم واحد is x of t يبقى انا
+
+94
+00:09:32,190 --> 00:09:36,490
+مابديش لابلاس ترانسفورم بدي ارجعها للاصل ابتباعها
+
+95
+00:09:36,490 --> 00:09:42,890
+يبقى ال x of t يساوي خمس مين هي الدالة اللي لابلاس
+
+96
+00:09:42,890 --> 00:09:45,050
+يساوي واحدة وليس ناقص اتنين
+
+97
+00:10:03,220 --> 00:10:06,900
+طيب لو جربت أحلها بأي طريقة من الطرق السابقة يعني
+
+98
+00:10:06,900 --> 00:10:11,390
+الطرق اللي بدي أطلع هذا الجواب ولا غيره؟نفس الجواب
+
+99
+00:10:11,390 --> 00:10:16,750
+وهذه بلغتنا لزمان initial value problem ما علينا
+
+100
+00:10:16,750 --> 00:10:23,330
+نجي لنمر بيهنمنع بيه برضه بنفس الطريقة بدي أخد
+
+101
+00:10:23,330 --> 00:10:27,110
+لبلاس ترانسفورم للطرفين و بدي أدخل حسب ال
+
+102
+00:10:27,110 --> 00:10:31,010
+linearity تبع لبلاس على كل term من ال termات اللي
+
+103
+00:10:31,010 --> 00:10:37,330
+عنها اذا بدي أجي أقول لبلاس ترانسفورم لل x w prime
+
+104
+00:10:37,330 --> 00:10:48,240
+of t زائد اتنين لبلاس لل x prime of tزائد لبلاس لل
+
+105
+00:10:48,240 --> 00:10:53,480
+X of T بالشكل اللي عندنا هذا كله بده يساوي لبلاس
+
+106
+00:10:53,480 --> 00:11:27,150
+لمين ل Tإذا بدنا نجيب لبلاس لهذه الدلاله همين
+
+107
+00:11:29,150 --> 00:11:36,550
+أتنين فيهم لبلاس ال X prime اللي هو S في X of S
+
+108
+00:11:36,550 --> 00:11:44,590
+ناقص ال X عند ال zero فقط لغير ووصلنا للي بعدها
+
+109
+00:11:44,590 --> 00:11:51,430
+زائد X as a function of S بدنا لبلاس transform لل
+
+110
+00:11:51,430 --> 00:11:56,420
+Tوتلك المرة اللي فات كل واحد اجيب كتابة معاها
+
+111
+00:11:56,420 --> 00:12:05,120
+مظبوط يابجي افتحلي على الجدول اللي هو في section
+
+112
+00:12:05,120 --> 00:12:09,760
+تسعة تلاتة ال section اللي بعد هيك يلا افتحلي
+
+113
+00:12:09,760 --> 00:12:18,120
+بسرعة في section تسعة تلاتة بعدي اللي هو عنوانه
+
+114
+00:12:18,120 --> 00:12:23,100
+properties of Laplace transformProperties of
+
+115
+00:12:23,100 --> 00:12:28,740
+Laplace Transform كاتب شوية Properties و تحتها مات
+
+116
+00:12:28,740 --> 00:12:33,840
+بعض Laplace Transform لبعض الدول و بدأ بأول دليل T
+
+117
+00:12:33,840 --> 00:12:41,080
+to the power N Laplace ل T to the power N مكتوب
+
+118
+00:12:41,080 --> 00:12:47,860
+عندك جنبها F of S ل N factorial على S أس N زائد
+
+119
+00:12:47,860 --> 00:12:55,060
+واحديبقى N factorial يعني ال plus ل T أوس N هو N
+
+120
+00:12:55,060 --> 00:13:00,180
+factorial على S أوس N زي الواحد يبقى بناء عليه ال
+
+121
+00:13:00,180 --> 00:13:05,140
+plus transform ل T عبارة عن ايه؟ واحد factorial
+
+122
+00:13:05,140 --> 00:13:12,820
+على S أوس واحد زي الواحد يعني واحد على S تربيع،
+
+123
+00:13:12,820 --> 00:13:20,040
+مظبوط؟وأحد على السربيع، إذا بشيل هذه كلها و بكتب
+
+124
+00:13:20,040 --> 00:13:23,100
+بدلها واحد على السربيع
+
+125
+00:13:26,700 --> 00:13:32,640
+هذه المناطق بالصير وهذه فيها x of s وهذه لو جيت
+
+126
+00:13:32,640 --> 00:13:39,260
+فكتها بx of s وهذه بx of s يبقى هذه لو جيت أخدت ال
+
+127
+00:13:39,260 --> 00:13:45,500
+x of s عامل مشترك مضل عندي s تربيع زائدي اتنين s
+
+128
+00:13:45,500 --> 00:13:57,110
+زائد واحد كله في ال x of sبعد ذلك ناقص S X of 0 X
+
+129
+00:13:57,110 --> 00:14:05,330
+of 0 بقدهش بواحد يبقى في واحد اللي بعدها ناقص X
+
+130
+00:14:05,330 --> 00:14:14,210
+prime of 0 ناقص اتنينخلصنا هذه دلنا ناقص اتنين في
+
+131
+00:14:14,210 --> 00:14:19,710
+ال X of Zero اللي هو قداش أبواحد كله بده يساوي
+
+132
+00:14:19,710 --> 00:14:24,930
+واحد على اس تربيع إذا شيلنا X of Zero وحطنا بدلها
+
+133
+00:14:24,930 --> 00:14:28,930
+واحد شيلنا X prime of Zero وحطنا مكانها اتنين
+
+134
+00:14:28,930 --> 00:14:35,530
+واخدنا من اللي تحتهم خط هدول X of S عامل مشترك
+
+135
+00:14:35,530 --> 00:14:40,990
+تمام؟ يبقاش اللي حصل عندناحصل عندما يأتي اللي هو
+
+136
+00:14:40,990 --> 00:14:52,470
+الـ S² زائد 2S زائد 1 في ال X of S بده يساوي 1 على
+
+137
+00:14:52,470 --> 00:14:57,210
+S تربيع هذه يا بنات ناقص S لما نوديها على الشجة
+
+138
+00:14:57,210 --> 00:15:01,810
+التانية إيش بيصير؟ زائد S هذه ناقص 4 لما نوديها
+
+139
+00:15:01,810 --> 00:15:08,530
+على الشجة التانية بيصير كده إيش؟ زائد 4بمعنى أخر
+
+140
+00:15:08,530 --> 00:15:15,250
+لو جيت وحة المقامات للكل هدول كله على استربيع بصير
+
+141
+00:15:15,250 --> 00:15:24,490
+واحد زائد استكيب زائد أربعة استربيعالشكل اللي
+
+142
+00:15:24,490 --> 00:15:30,010
+عندنا هنا يبقى بناء عليه بدي يصبح عند ال X of S
+
+143
+00:15:30,010 --> 00:15:38,010
+يساوي اللي هو S تكيب زائد أربعة S تربيع زائد واحد
+
+144
+00:15:38,010 --> 00:15:44,210
+كله مقسوما على S تربيع هذا S تربيع زائد اتنين S
+
+145
+00:15:44,210 --> 00:15:49,470
+زائد واحد اللي هو S زائد واحد لكل تربيع
+
+146
+00:16:03,410 --> 00:16:09,950
+إذا توصلت إلى Laplace transform للحل تبع المعادلة
+
+147
+00:16:09,950 --> 00:16:15,130
+شو Laplace transform؟ معادلة من الدرجة التالتة على
+
+148
+00:16:15,130 --> 00:16:20,230
+معادلة من الدرجة الرابعةيبقى بقدر أقوم بعمل
+
+149
+00:16:20,230 --> 00:16:25,050
+partial fractions لأن درجة البسط أقل من درجة
+
+150
+00:16:25,050 --> 00:16:30,370
+المقام يبقى جاهزين اتنين محللة إلى أبسط العوامل
+
+151
+00:16:30,370 --> 00:16:35,770
+الأولية يبقى بدي أرجع لل partial fractions و أعمل
+
+152
+00:16:35,770 --> 00:16:41,270
+partial fractions لهذا المقدارالـ S تكيب زائد
+
+153
+00:16:41,270 --> 00:16:48,330
+أربعة S تربيع زائد أربعة S تربيع زائد واحد كله
+
+154
+00:16:48,330 --> 00:16:56,090
+مقسوما على مين على S تربيع في مين في S زائد واحد
+
+155
+00:16:56,090 --> 00:17:03,580
+لكل تربيع بدنا نيجي للـ Gauss الأولالمقدار الأول
+
+156
+00:17:03,580 --> 00:17:08,580
+هو معادلة من الدرجة الثانية لما تحط ال bus بمعادلة
+
+157
+00:17:08,580 --> 00:17:16,940
+من الدرجة الأولى يبقى هذا الكلام بده يساوي AS زائد
+
+158
+00:17:16,940 --> 00:17:28,230
+B على S تربيعهذا قسم مكرر مرتين يبقى زائد C على S
+
+159
+00:17:28,230 --> 00:17:35,310
+زائد واحد زائد D على S زائد واحد لكل ترمية يبقى
+
+160
+00:17:35,310 --> 00:17:38,430
+عملنا ال partial fraction انا بده احاول اجيب قيمة
+
+161
+00:17:38,430 --> 00:17:44,070
+ثوابتالـA والـB والـC والـD لذلك هروح أضرب في
+
+162
+00:17:44,070 --> 00:17:48,730
+المقام اللي عندنا هذا فبتصبح المعادلة على الشكل
+
+163
+00:17:48,730 --> 00:17:55,810
+التالي استكيب زياد أربع استربيع زياد واحد يساوي AS
+
+164
+00:17:55,810 --> 00:18:07,010
+زياد B في S زياد واحد لكل تربيعزائد C S تربيع في S
+
+165
+00:18:07,010 --> 00:18:17,670
+زائد 1 زائد D في S تربيع مرة تانية اضرب هنابطير
+
+166
+00:18:17,670 --> 00:18:22,250
+المقام بظل ال bus زي ما هو اضرب هنا بطير ال S
+
+167
+00:18:22,250 --> 00:18:27,970
+تربيع بظل ال S زائد واحد لكل تربيع نضرب هنا بظل ال
+
+168
+00:18:27,970 --> 00:18:33,170
+S تربيع و ال S زائد واحد نضرب هنا بس بظل دي S
+
+169
+00:18:33,170 --> 00:18:34,150
+تربيع
+
+170
+00:18:36,670 --> 00:18:41,970
+يبقى بدل من معادلة كانت معادلة كسرية عملتها معادلة
+
+171
+00:18:41,970 --> 00:18:49,810
+عادية يبقى هذا الكلام بدي أس زائد بي في من في أس
+
+172
+00:18:49,810 --> 00:18:59,450
+تربيع زائد اتنين أس زائد واحد زائد س تكيب زائد س
+
+173
+00:18:59,450 --> 00:19:07,720
+أس تربيع زائد دي أس تربيعهذا لو روحت فكته بصير AS
+
+174
+00:19:07,720 --> 00:19:18,880
+تكريم زائدي اتنين AS ثربية زائد AS زائدBS تربيع
+
+175
+00:19:18,880 --> 00:19:31,900
+زائدي اتنين BS زائد B زائد C استكيب زائد C استربيع
+
+176
+00:19:31,900 --> 00:19:39,940
+زائد D استربيعنجمع اللي فيهم S تكييب مع بعض والـ S
+
+177
+00:19:39,940 --> 00:19:45,200
+تربيع مع بعض والـ S مع بعض والسوابط مع بعض يبقى
+
+178
+00:19:45,200 --> 00:19:52,560
+هذه A استكيب وهذه C استكيب يبقى A زائد C في
+
+179
+00:19:52,560 --> 00:20:00,820
+الاستكيب اللي فيهم تربيع اتنين A زائد B زائد C
+
+180
+00:20:00,820 --> 00:20:10,200
+زائد D في الاستربيعاللي فيهم S يبقى زائد A زائدي
+
+181
+00:20:10,200 --> 00:20:18,120
+اتنين B كله في من؟ في ال S خلصنا ال S و اتنين B
+
+182
+00:20:18,120 --> 00:20:24,560
+ضال السوابط السوابط ماعنديش إلا من؟ ماعنديش إلا B
+
+183
+00:20:24,560 --> 00:20:32,560
+كله بده يساوي من؟ S تكيب زائد أربعة S تربيع زائد
+
+184
+00:20:32,560 --> 00:20:38,430
+واحدصار عندنا معادلة المعادلة بدنا نروح نقارن
+
+185
+00:20:38,430 --> 00:20:43,510
+المعاملات في الطرفين يبقى لو روحنا نقارن المعاملات
+
+186
+00:20:43,510 --> 00:20:47,590
+في الطرفين بنحصل على المعادلات التالية او ال
+
+187
+00:20:47,590 --> 00:20:50,670
+system of linear equations as follows
+
+188
+00:20:55,630 --> 00:21:01,650
+الـ A زائد الـ C كله بده يساوي معامل S تكيبه بواحد
+
+189
+00:21:01,650 --> 00:21:10,190
+بعد هيك اتنين A زائد B زائد C زائد D معامل ال S
+
+190
+00:21:10,190 --> 00:21:16,510
+تربيهه يساوي جدد اربع بعد هيك ال A زائد اتنين B
+
+191
+00:21:16,510 --> 00:21:22,590
+بده يساوي معامل ال S ب Zero ماعنديش S اخر حاجة عند
+
+192
+00:21:22,590 --> 00:21:30,530
+B تساوي واحدطيب لما B تساوي واحد ال A بقداش؟ سالي
+
+193
+00:21:30,530 --> 00:21:37,310
+باتنين يبقى ال A تساوي سالي باتنين طيب لما ال A
+
+194
+00:21:37,310 --> 00:21:44,760
+بسالي باتنين C بقداش؟ثالث ثلاثة ثلاثة ثلاثة ثلاثة
+
+195
+00:21:44,760 --> 00:21:46,500
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+196
+00:21:46,500 --> 00:21:49,780
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+197
+00:21:49,780 --> 00:21:52,860
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+198
+00:21:52,860 --> 00:21:57,440
+ثلاثة ثلاثة
+
+199
+00:21:57,440 --> 00:22:07,430
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثةوالـ C عندنا بتلاتة
+
+200
+00:22:07,430 --> 00:22:15,070
+زائد تلاتة زائد D كله بده يساوي أربعة عندك هنا
+
+201
+00:22:15,070 --> 00:22:23,610
+سالب أربعة وزائد أربعة بروحه بصفر يبقى D تساوي
+
+202
+00:22:23,610 --> 00:22:30,230
+أربعة الشكل اللي عندنايبقى بناء عليه أصبح عندنا ال
+
+203
+00:22:30,230 --> 00:22:36,230
+S تكييب أو ال X of S كله بدرساه
+
+204
+00:22:38,840 --> 00:22:44,340
+أصبح الـ X of S يعني لأ بلاس ترانسفورم لده لا بد
+
+205
+00:22:44,340 --> 00:22:51,960
+يسوي بدي أشيل الـ A و أحط مكانها ناقص 2S و أشيل
+
+206
+00:22:51,960 --> 00:22:58,840
+الـ B و أحط مكانها واحد و كل هذا على S تربيع زائد
+
+207
+00:22:58,840 --> 00:23:08,900
+الـ C عندي بتلاتة على S زائد واحدو بعد ذلك اضيف 4
+
+208
+00:23:08,900 --> 00:23:15,920
+على S زائد 2 لكل تربيع لو على الترتيب يا بناتي
+
+209
+00:23:15,920 --> 00:23:26,340
+بجادي الناقص 2 في 1 على S زائد 1 على S تربيع زائد
+
+210
+00:23:26,340 --> 00:23:38,380
+1 على S تربيع زائد 3 في 1 على S زائد 1زائد اربع في
+
+211
+00:23:38,380 --> 00:23:47,180
+واحد على اس زائد اتنين لكل تربية اه
+
+212
+00:23:47,180 --> 00:23:57,260
+اس زائد واحد اس زائد واحد لكل تربيةطيب هذا لا بلاس
+
+213
+00:23:57,260 --> 00:24:02,900
+ترانسفورم للدالة إذا أنا بديش لا بلاس ترانسفورم
+
+214
+00:24:02,900 --> 00:24:06,620
+للدالة يعني للحل تبع ال differential equation
+
+215
+00:24:06,620 --> 00:24:12,580
+وإنما بدي الحل itself يبقى بروح بقول هنا the
+
+216
+00:24:12,580 --> 00:24:28,330
+solution of the givendifferential equation is
+
+217
+00:24:28,330 --> 00:24:39,940
+ال X of T بدرساه ناقص اتنين واحد على اس هذه مين؟لـ
+
+218
+00:24:39,940 --> 00:24:43,980
+Blessed Transfer لمن؟ للواحد الصحيح اخدناه المرة
+
+219
+00:24:43,980 --> 00:24:50,660
+الماضية يبقى هذا ناقص اتنين في واحد الآن زائد واحد
+
+220
+00:24:50,660 --> 00:25:01,190
+على استربيعيمين T بس كويس يبقى هذه T بدنا زائد
+
+221
+00:25:01,190 --> 00:25:09,210
+تلاتة واحد عليه زائد واحد يمين E أس ناقص T مظبوط
+
+222
+00:25:09,210 --> 00:25:15,830
+ايه؟بس هكذا الشعب مش EOS ES 1 على S ناقص ال A لو
+
+223
+00:25:15,830 --> 00:25:22,710
+حطيه ناقص بال T لزاد يبقى تلاتة EOS ناقص T زائد
+
+224
+00:25:22,710 --> 00:25:29,390
+أربعة نيجي لهذه واحد على S زائد واحد لكل تربية
+
+225
+00:25:29,390 --> 00:25:33,930
+يالا شوفوا هالي من الجدول اللي قلتلكوا عليه برضه
+
+226
+00:25:40,530 --> 00:25:46,390
+يا ضنيات منهم؟ كيف؟
+
+227
+00:25:46,390 --> 00:25:49,430
+أه طبعا، هجيبلك ال .. الجدول، هاي اللي بتاعك،
+
+228
+00:25:49,430 --> 00:25:53,230
+صورتها، مانجتش اللي راح هتصور كل امتحان بيجيك
+
+229
+00:25:53,230 --> 00:25:57,850
+الجدول، مش هذا، كله أكتر منه كمان، مصور من أوله
+
+230
+00:25:57,850 --> 00:26:05,110
+إلى آخرهطبعا .. طبعا مشان تكون في الصورة رقم تسعة
+
+231
+00:26:05,110 --> 00:26:10,330
+في هذا الجدول عندك في الكتاب في section تسعة تلاتة
+
+232
+00:26:10,330 --> 00:26:15,930
+رقم تسعة بيقولك لو كانت الدالة او Laplace
+
+233
+00:26:15,930 --> 00:26:19,550
+transform ل T to the power N
+
+234
+00:26:35,780 --> 00:26:42,570
+هذا الموضوع لانهذا ما أقدر أقوله ياشي واحد يبقى لو
+
+235
+00:26:42,570 --> 00:26:48,150
+كانت واحد بيصير هنا ياشي واحد factorial اللي هو
+
+236
+00:26:48,150 --> 00:26:54,890
+بواحد و هنا S ناقص واحد أس واحد زائد واحد بيصير S
+
+237
+00:26:54,890 --> 00:27:02,470
+ناقص واحد لكل تربيع احنا عنا ياشي عنا من عنا S
+
+238
+00:27:02,470 --> 00:27:06,750
+زائد واحد يبقى E أس
+
+239
+00:27:23,570 --> 00:27:31,080
+لحد هنا انتهى هذا السؤاليبقى حلينا المعادلة
+
+240
+00:27:31,080 --> 00:27:36,280
+التفاضلية من الرتبة الثانية زي ما حلينا المعادلة
+
+241
+00:27:36,280 --> 00:27:40,800
+التفاضلية من الرتبة الأولى بطريقة Laplace
+
+242
+00:27:40,800 --> 00:27:56,620
+transform بقى هناك مثال أخر المثال
+
+243
+00:27:56,620 --> 00:27:57,940
+بيقول ما يأتي
+
+244
+00:28:01,390 --> 00:28:11,970
+مثال فاين لابلاس ترانسفورم فاين لابلاس ترانسفورم
+
+245
+00:28:20,140 --> 00:28:28,540
+لذالك F of T تساوي أحد أمرين، يا إما واحد لما T
+
+246
+00:28:28,540 --> 00:28:34,540
+محصورة بين Zero و واحد، يا إما Zero لما T greater
+
+247
+00:28:34,540 --> 00:28:41,360
+than one خلّي
+
+248
+00:28:41,360 --> 00:28:46,060
+بالك بالكجليهات لابلاس ترانسفورم للدالة اللى عندنا
+
+249
+00:28:46,060 --> 00:28:50,220
+طبعا من يوم ما بدأنا نشتغل في لابلاس ترانسفورم أول
+
+250
+00:28:50,220 --> 00:28:54,340
+مرة بنشوف function من هذا القبيل لكن هذه ال
+
+251
+00:28:54,340 --> 00:29:00,080
+function هتمر معانا كتير جدا في خلال دراستنا لميل
+
+252
+00:29:00,080 --> 00:29:04,340
+لابلاس ترانسفورم في ال sections القادمة وسنمر
+
+253
+00:29:04,340 --> 00:29:09,560
+عليها بعد قليل ان شاء اللهلكن باجي بقول انا
+
+254
+00:29:09,560 --> 00:29:14,340
+مااخدتش الا التعريف يبقى لما نقول ل plus transform
+
+255
+00:29:14,340 --> 00:29:22,580
+بقول له solution احنا بدنا ال plus transform لمين؟
+
+256
+00:29:22,610 --> 00:29:29,510
+لأ ده ل F of T برجع للتعريف المرة اللي فاتت قلنا
+
+257
+00:29:29,510 --> 00:29:37,730
+من Zero إلى Infinity لل E أث ناقص ST في F of T في
+
+258
+00:29:37,730 --> 00:29:41,050
+ال DTمش هاي التعريف اللي قلناه المرة اللي فاتت
+
+259
+00:29:41,050 --> 00:29:47,510
+الان بدنا نطبق هذا التعريف لكن هذه كونها دالة مجزة
+
+260
+00:29:47,510 --> 00:29:53,950
+إلى جزئين يبقى بدي أجزء هذا التكامل إلى تكاملين كل
+
+261
+00:29:53,950 --> 00:29:59,630
+بما يناسموا من zero لواحد قيمة الدالة واحد اذا
+
+262
+00:29:59,630 --> 00:30:07,290
+بداك اقوله تكامل من zero لواحد لل E أس ناقص ST ضرب
+
+263
+00:30:07,290 --> 00:30:15,550
+واحد DTزاد تكامل من واحد إلى infinity لل E أُس
+
+264
+00:30:15,550 --> 00:30:24,520
+ناقص ST ال F of T هي Zero في DTيبقى آلة المثالة
+
+265
+00:30:24,520 --> 00:30:29,940
+طبعاً zero في أي term هو zero يبقى بدرجين مين؟
+
+266
+00:30:29,940 --> 00:30:38,440
+بدرجين تكامل فقط من zero إلى T لل E أس ناقص S T DT
+
+267
+00:30:38,440 --> 00:30:45,600
+فقط لغيره يبقى هذا الكلام يساوي E أس ناقص S T على
+
+268
+00:30:45,600 --> 00:30:52,440
+تفاضل الأس اللي هو ناقص S والحكي هذا من zero لواحد
+
+269
+00:30:56,760 --> 00:31:02,920
+بنعوض بالقيمة اللي فوق ناقص اللي تحت يبقى E أس
+
+270
+00:31:02,920 --> 00:31:16,890
+ناقص S على ناقص S ناقص E أس ناقص S على ناقص Sيبقى
+
+271
+00:31:16,890 --> 00:31:25,190
+هذا الكلام بده يساوي 1 على S تربيع ناقص EOS ناقص S
+
+272
+00:31:25,190 --> 00:31:33,090
+على main على S هذا main ل plus transform لدالة
+
+273
+00:31:33,090 --> 00:31:43,630
+المعطاعة حد بتسأل أي سؤال هنا بنات؟ كيف؟
+
+274
+00:31:47,820 --> 00:31:52,840
+ما لها؟ ناقص
+
+275
+00:31:52,840 --> 00:31:58,120
+لا لا زائد واحد على اس واحد على اس فقط ناقص ناقص
+
+276
+00:31:58,120 --> 00:32:03,000
+زائد واحد على اس وهادي ناقص يعني بتقدر تقول كل
+
+277
+00:32:03,000 --> 00:32:09,700
+واحد على اس عامل مشترك واحد ناقص ايه اص ناقص اس
+
+278
+00:32:09,700 --> 00:32:15,840
+بالشكل هذاطب ننتقل الان الى ال section اللى يليه
+
+279
+00:32:15,840 --> 00:32:23,740
+بعد ان نعطيه الاكثر sizes اللى هى تسعة واحد تسعة
+
+280
+00:32:23,740 --> 00:32:32,260
+واحد المسائل التالية السؤال الاول بدنا منه A وC وF
+
+281
+00:32:32,260 --> 00:32:45,500
+وG وIوالسؤال التاني بدنا منه A وD وE وF والسؤال
+
+282
+00:32:45,500 --> 00:32:54,300
+التالت بدنا منه A وD وE وبعد هيك بدنا السؤال
+
+283
+00:32:54,300 --> 00:32:59,180
+التامن بدنا
+
+284
+00:32:59,180 --> 00:33:04,820
+نروح الأن ل section تسعة تلاتةتسعة اتنين نشطبه
+
+285
+00:33:04,820 --> 00:33:12,340
+ونروح لتسعة تلاتة اللي هي ال properties of Laplace
+
+286
+00:33:12,340 --> 00:33:19,260
+transforms Laplace transforms
+
+287
+00:33:19,260 --> 00:33:27,220
+يبقى خاص تحويلات Laplace بقول
+
+288
+00:33:27,220 --> 00:33:30,720
+if Laplace
+
+289
+00:33:36,950 --> 00:33:43,730
+transfer exist for
+
+290
+00:33:43,730 --> 00:33:46,950
+a
+
+291
+00:33:46,950 --> 00:34:01,110
+given function لدالة ماطعة then نقطة
+
+292
+00:34:01,110 --> 00:34:10,300
+الأولىبدنا Laplace transform ل C1 في F of T زائد
+
+293
+00:34:10,300 --> 00:34:19,320
+C2 في G of T اللي هي بده تساوي C1 Laplace
+
+294
+00:34:19,320 --> 00:34:28,960
+transform لل F of T زائد C2 Laplace transform لل G
+
+295
+00:34:28,960 --> 00:34:30,140
+of T
+
+296
+00:34:35,100 --> 00:34:47,980
+اللي هي بقدر أقول C1 F of S زائد C2 G of S هذه
+
+297
+00:34:47,980 --> 00:34:52,020
+خاصية لينيراتي خاصية طبيعية أخدناها المرة اللي
+
+298
+00:34:52,020 --> 00:35:04,440
+فاتت الجديد هو ما يأتي F H of T بدي يساوي E of C T
+
+299
+00:35:05,020 --> 00:35:16,880
+CT في ال F of T في ال F of T then H of S لولا plus
+
+300
+00:35:16,880 --> 00:35:25,700
+transform لها بده يساوي capital F في S ناقص ال C
+
+301
+00:35:25,700 --> 00:35:38,480
+نمري تلاتة F ال K of Tبدي يساوي تكامل من zero
+
+302
+00:35:38,480 --> 00:35:49,920
+تكامل من zero إلى T لل F of U دي U then capital K
+
+303
+00:35:49,920 --> 00:35:59,800
+of S بدي يساوي واحد على S في مين؟ في capital F of
+
+304
+00:35:59,800 --> 00:36:00,420
+S
+
+305
+00:36:02,830 --> 00:36:14,210
+نمرة أربعة if ال PN as a function of T هو عبارة عن
+
+306
+00:36:14,210 --> 00:36:22,290
+T to the power N فاهمين؟ في ال F of T في ال F of T
+
+307
+00:36:22,290 --> 00:36:31,270
+then ال PN of S ال PN of S
+
+308
+00:36:49,230 --> 00:37:00,240
+نمر الخمسة بيقول Fالـ Q of T بده يساوي أحد أمرين
+
+309
+00:37:00,240 --> 00:37:08,440
+يا إما zero لما T أكبر من ال zero و أقل من C يا
+
+310
+00:37:08,440 --> 00:37:16,100
+إما ال F of T ناقص ال C لما T أكبر من ال C
+
+311
+00:37:19,130 --> 00:37:35,140
+الـ Q of S بده يساوي E أُس ناقص CS في F of Sأخر
+
+312
+00:37:35,140 --> 00:37:39,640
+حاجة كتبناها قبل هيك المرة في نهاية المحاضرة
+
+313
+00:37:39,640 --> 00:37:47,620
+الماضية بدي ل plus transform لتفاضل رقم N عند T
+
+314
+00:37:47,620 --> 00:37:56,080
+بدي ساوي S to the power N capital F of S ناقص
+
+315
+00:37:56,080 --> 00:38:02,880
+افتحي جوس اللي هو ال S أس N ولا بلغ الجوس خليها
+
+316
+00:38:02,880 --> 00:38:13,500
+دغرييبقى ناقص SN-1F0
+
+317
+00:38:13,500 --> 00:38:20,460
+-SN-2F'0
+
+318
+00:38:23,450 --> 00:38:31,770
+نظل ناقص لغاية ما نوصل في التفضل رقم N ناقص واحد
+
+319
+00:38:31,770 --> 00:38:34,510
+عند مين؟ عند الـ Zero
+
+320
+00:38:55,110 --> 00:38:58,650
+الان بدنا نجمل بعض الشغلات اللي أخدناها في Laplace
+
+321
+00:38:58,650 --> 00:39:03,670
+transform و اللي موجودة في الكتاب سواء أخدناها أو
+
+322
+00:39:03,670 --> 00:39:08,710
+ما أخدناها قبل ذلك هنعطيك جمال مثلها وهي some
+
+323
+00:39:08,710 --> 00:39:15,190
+basic Laplace
+
+324
+00:39:15,190 --> 00:39:18,210
+transforms
+
+325
+00:39:23,680 --> 00:39:34,200
+النقطة الأولى if ال F of T تساوي T to the power N
+
+326
+00:39:34,200 --> 00:39:43,660
+then اللي هو capital F of S بده يساوي N factorial
+
+327
+00:39:43,660 --> 00:39:52,060
+على S أثنى plus one نمر اتنين if
+
+328
+00:39:53,410 --> 00:40:07,810
+الـ F of T يبدو يسوى E أس AT ثم F of S يبدو
+
+329
+00:40:07,810 --> 00:40:12,570
+يسوى واحد على S ناقص الـ A
+
+330
+00:40:16,480 --> 00:40:26,080
+ال F of T بدي ساوي cosine AT then capital F of S
+
+331
+00:40:26,080 --> 00:40:35,260
+بدي ساوي ال S على استربيع زائد A تربيع نمرة أربعة
+
+332
+00:40:35,260 --> 00:40:46,050
+F ال F of T بدي ساوي ال sine AT thenاللي هو
+
+333
+00:40:46,050 --> 00:40:53,410
+capital F of S بده يساوي من؟ بده يساوي ال A على S
+
+334
+00:40:53,410 --> 00:41:02,070
+تربيع زائد A تربيع خمسة F ال F of T بده يساوي
+
+335
+00:41:02,070 --> 00:41:14,820
+since AT then capital F of S بده يساويA على S
+
+336
+00:41:14,820 --> 00:41:24,340
+تربيع ناقص A تربيع نمرأ ستة لو كان ال F of T والله
+
+337
+00:41:24,340 --> 00:41:29,840
+F ال F of T بدي ساوي جوش
+
+338
+00:41:32,360 --> 00:41:44,520
+F of S بيساوي S على S تربيع نقص A تربيع نمرا سبعة
+
+339
+00:41:44,520 --> 00:41:57,980
+F F of T بيساوي E أس AT في صين ET
+
+340
+00:42:02,120 --> 00:42:19,040
+بعد ذلك F of S بيساوي B علىS ناقص A كل تربيع زائد
+
+341
+00:42:19,040 --> 00:42:30,700
+B تربيع تمانية F ال F of T بده يساوي E أس A T فيه
+
+342
+00:42:30,700 --> 00:42:38,760
+cosine BT then capital F of S بده يساوي اللي هو ال
+
+343
+00:42:38,760 --> 00:42:50,030
+Sناقص ال A على S ناقص ال A لكل تربيع زائد بيه
+
+344
+00:42:50,030 --> 00:43:01,370
+تربيع أخر حاجة نمرة تسعة بيقول F ال F of T بده
+
+345
+00:43:01,370 --> 00:43:14,020
+يساوي T أس N E أس ATT was in A was in AT then the
+
+346
+00:43:14,020 --> 00:43:25,420
+capital F of S بده يساوي N factorial مقسوما على S
+
+347
+00:43:25,420 --> 00:43:35,480
+ناقص ال A to the power N plus one و ال N is a
+
+348
+00:43:35,480 --> 00:43:38,940
+positiveانتجار
+
+349
+00:43:54,030 --> 00:43:58,770
+ألا من أن أتعرض لكل نقطة بالتفصيل، شو مفهوم هذه
+
+350
+00:43:58,770 --> 00:44:03,830
+بنات، بيجيكوا مش 9 ولا 15 واحدة في الامتحان،
+
+351
+00:44:03,830 --> 00:44:09,290
+بيجيبونكوا في جدول مشان تستخدميها متى أم كان ذلك،
+
+352
+00:44:09,290 --> 00:44:12,330
+مش مشكلة موجودة عندك في الكتاب نفسا، ضايقش وقت
+
+353
+00:44:12,330 --> 00:44:16,450
+فيها، خلينا ما نفهم بس، لإن فهمنا هدول، بصير
+
+354
+00:44:16,450 --> 00:44:22,320
+قضيتنا بعد ذلك قضية سهلةيبقى ابنات الآن في خمسة
+
+355
+00:44:22,320 --> 00:44:27,180
+نماذج امتحانات موجودة في مكتبة الطالب كل واحدة
+
+356
+00:44:27,180 --> 00:44:31,280
+بدأت نسخة بتروح تاخد نسخة طبعا امتحانات سابقة
+
+357
+00:44:31,280 --> 00:44:37,300
+وغالبا امتحانات حديثة الخواصلة class transform
+
+358
+00:44:37,870 --> 00:44:42,870
+بيقول لو كان Laplace transform لدالة ما exist يبقى
+
+359
+00:44:42,870 --> 00:44:48,790
+عندنا ست خواص أو ست خواص نتعرض لهذه الخواص الست
+
+360
+00:44:48,790 --> 00:44:54,530
+خاصية الأولى خاصية ال linearity يعني اللي لما تدخل
+
+361
+00:44:54,530 --> 00:44:59,950
+على مجموعة من الدوال مضروبة في ثوابت بقول الثابت
+
+362
+00:44:59,950 --> 00:45:03,730
+في Laplace transform للدالة الثابت التاني في
+
+363
+00:45:03,730 --> 00:45:08,630
+Laplace transform للدالة الثانيةأو لبلاس ترانسفورم
+
+364
+00:45:08,630 --> 00:45:14,910
+الدلالة بتعطي الرمز capital F of S وهذا قلناه
+
+365
+00:45:14,910 --> 00:45:17,710
+المرة اللي فاترة أول ما عرفنا لبلاس ترانسفورم
+
+366
+00:45:17,710 --> 00:45:22,150
+للدلالة F of T قلنا يا ابنك تب لبلاس لل F of T هم
+
+367
+00:45:22,150 --> 00:45:25,770
+يقولوا capital F of S وليش capital F of S؟ لأن
+
+368
+00:45:25,770 --> 00:45:30,310
+الدلالة بتطلع بتطلع بدلالة S يعني بتطلع as a
+
+369
+00:45:30,310 --> 00:45:39,550
+function of Sيبقى هنا بقول C1 F of S زي C2 G of S
+
+370
+00:45:39,550 --> 00:45:45,190
+هذا الخاصية الأولى خاصية تانية لو كان شكل الدلة
+
+371
+00:45:45,190 --> 00:45:50,810
+اللى بدي أوجد لها لأبلاس على شكل E و CT في F of T
+
+372
+00:45:50,810 --> 00:45:56,590
+و بدي لأبلاس أترانسفورم لهاأذا لبلاس ترانسفورم
+
+373
+00:45:56,590 --> 00:46:02,110
+لهذه الدالة بتديله H capital of S يساوي F of S
+
+374
+00:46:02,110 --> 00:46:08,270
+ناقصة C ايش يعني نسوي بالضغط بقول R بتنسى ال F بال
+
+375
+00:46:08,270 --> 00:46:13,370
+E و ال CT وبجي على الدالة F of T وبجيبلها لبلاس
+
+376
+00:46:13,370 --> 00:46:20,080
+ترانسفورم وبعد هيكبشيل كل S و بحط مكانة S ناقص ال
+
+377
+00:46:20,080 --> 00:46:25,060
+S بكون جبت Laplace transform هذه لمين للدولة طبعا
+
+378
+00:46:25,060 --> 00:46:29,600
+المرة الجاية هعطيك بدل المثال ثمانية أمثلة كيف
+
+379
+00:46:29,600 --> 00:46:35,180
+بدنا نحسب Laplace للدوال المختلفة وسيكون مثلة أو
+
+380
+00:46:35,180 --> 00:46:41,080
+مسائل من هذا القبيل يبقى مرة تانيةعندي exponential
+
+381
+00:46:41,080 --> 00:46:44,760
+في F of T بدي أجيب لبلاس ترانسفورم لها بروح بجيب
+
+382
+00:46:44,760 --> 00:46:49,880
+لبلاس ترانسفورم لدلة F of T تطلع بدلالة S بشيل كل
+
+383
+00:46:49,880 --> 00:46:56,460
+S و بحط مكانة S ناقص C F of S ناقص C طب لو كانت
+
+384
+00:46:56,460 --> 00:47:03,570
+هذه سلبة بناتبصير هذه F of S زائد C تمام واضحة
+
+385
+00:47:03,570 --> 00:47:07,950
+يعني نجي للنقطة التالتة لو كانت K معطية على شكل
+
+386
+00:47:07,950 --> 00:47:13,730
+تكامل من Zero إلى T لل F of U دي U و بدي لبلاس
+
+387
+00:47:13,730 --> 00:47:19,580
+ترانسوني بقوله capital K of Sهو لبلاس ترانسوميل
+
+388
+00:47:19,580 --> 00:47:24,140
+كيه اف تين ميه لبلاس لهذه بقوله واحد على اس في
+
+389
+00:47:24,140 --> 00:47:29,200
+capital F of S يعني ايش يعني باجي على الدالة F of
+
+390
+00:47:29,200 --> 00:47:33,720
+U هذه وبنسى ان عندي تكمل وبكذا باخدها لوحديها F of
+
+391
+00:47:33,720 --> 00:47:39,350
+Uو بروح بجيبلها لـ plus transform تبعها و بضربه في
+
+392
+00:47:39,350 --> 00:47:44,410
+1 على S بيكون هو ال plus اللي التكامل اللي موجود
+
+393
+00:47:44,410 --> 00:47:51,390
+بس بشرط يكون من 0 إلى T طيب، الآن بدا جيل الحالة
+
+394
+00:47:51,390 --> 00:47:57,660
+التالتة لو P N of T هي حاصل ضرب T to the power Nفى
+
+395
+00:47:57,660 --> 00:48:02,460
+ال F of D بدي لبلاس ترانسفورم لها ايش بدي اعمل؟
+
+396
+00:48:02,460 --> 00:48:07,280
+بدي اقول لبلاس ترانسفورم لها هو عبارة عن سالب واحد
+
+397
+00:48:07,280 --> 00:48:12,400
+أس ان يعني لو هذه المشتقة الثانية بقول سالب واحد
+
+398
+00:48:12,400 --> 00:48:16,620
+تربية مشتقة التالتة سالب واحد تكييف مشتقة العشرة
+
+399
+00:48:16,620 --> 00:48:22,460
+سالب واحد أس عشرة فمين؟ فى المشتقة النونية بالنسبة
+
+400
+00:48:22,460 --> 00:48:26,960
+للأس لل F of S يعني ايش بدي اقصه بالظبط؟أقول لك
+
+401
+00:48:26,960 --> 00:48:32,900
+بانسى ان في عندك T والسن باخد ميم F of T و بروح
+
+402
+00:48:32,900 --> 00:48:37,660
+بجيبلها لبلاس الترانسوري لما حصلت على ميم على F of
+
+403
+00:48:37,660 --> 00:48:45,120
+S بروح بفاضلها N من المراتيعني لو كان انها ت تربيه
+
+404
+00:48:45,120 --> 00:48:50,800
+بتفاضل هنا مرتين، لو كان ت وصوحى بتفاضل مرة واحدة،
+
+405
+00:48:50,800 --> 00:48:55,300
+لو كان ت تكعيب بتفاضل ثلاث مرات، وفي كل مرة بدي
+
+406
+00:48:55,300 --> 00:48:59,440
+اضغط نتيجة التفاضل في سالب واحد او سالب واحد تربيه
+
+407
+00:48:59,440 --> 00:49:04,700
+او سالب واحد تكعيب، حسب طبيعة المثلة، لا تنسيح مرة
+
+408
+00:49:04,700 --> 00:49:09,930
+تانيةT أوس N في F of T بجيب لبلاس ل F of T و بروح
+
+409
+00:49:09,930 --> 00:49:14,830
+بشتقة T من المرات و بضرب فيه سلب واحد أوس N بكون
+
+410
+00:49:14,830 --> 00:49:19,770
+حصلت على لبلاس transform لهذه الدالة قبل قليل كان
+
+411
+00:49:19,770 --> 00:49:24,710
+عندنا دالة مكونة من جزءين من هذا القبيل بدي ابحث
+
+412
+00:49:24,710 --> 00:49:29,690
+على لبلاس transform لدالة من هذا القبيل الدالة هذه
+
+413
+00:49:29,690 --> 00:49:34,430
+تسوي Zero من Zero إلى C لما ال T تتغير من Zero إلى
+
+414
+00:49:34,430 --> 00:49:41,540
+C أوF of T ناقص C لما T أكبر من C يعني كانوا
+
+415
+00:49:41,540 --> 00:49:47,920
+الدالة معمولة لها shift إزاحة جهة اليمين بمقدار C
+
+416
+00:49:47,920 --> 00:49:52,940
+بدي لها plus transform لها ل plus transform ل Q of
+
+417
+00:49:52,940 --> 00:49:58,420
+T بدي أقول كابتة ل Q of S إيش بدي أسوي؟ بدي أجي
+
+418
+00:49:58,420 --> 00:50:04,430
+على الدالة هذهوشيل ال C بيظل مين عندي؟ F of D
+
+419
+00:50:04,430 --> 00:50:10,030
+بيظلوح أجيب لبلاس Transform لل F of D مين بيطلع؟ F
+
+420
+00:50:10,030 --> 00:50:17,870
+of S بضربه في E أس ناقص CS اللي عندنا يعني لو كانت
+
+421
+00:50:17,870 --> 00:50:23,590
+هدى زائد بيصير هدى زائد هدى ناقص هدى ناقص مرة
+
+422
+00:50:23,590 --> 00:50:28,710
+تانية الخاصية ده جيه كويس very importantأنا بدي
+
+423
+00:50:28,710 --> 00:50:33,670
+لابلاس لهذه الدالة بقول لابلاس ل باجي على ال F of
+
+424
+00:50:33,670 --> 00:50:40,590
+T و بجيب لابلاس ل بعدين هذه اللي جبتها بضربها في
+
+425
+00:50:40,590 --> 00:50:45,730
+ال E أُس ناخص ال shift اللي عندنا هذا مضروب في مين
+
+426
+00:50:45,730 --> 00:50:50,570
+في S هذه ماهياش جديدة كتبناها معاك المرة اللي فاتت
+
+427
+00:50:50,570 --> 00:50:55,080
+هذه الأيه يوجد فيها أي حرف جديداللي هو الـ in
+
+428
+00:50:55,080 --> 00:50:59,900
+general عاممنا نظرية ناخدناها المرة الماضية، هذا
+
+429
+00:50:59,900 --> 00:51:03,920
+الجدول لو كانت الدلة الشكلها إيش، بيقولها place،
+
+430
+00:51:03,920 --> 00:51:07,100
+إيه هي transfer؟ هذه و هذه حسبناها المرة اللي
+
+431
+00:51:07,100 --> 00:51:11,920
+فاتت، مظبوط؟ ال exponential كمان حسبناها المرة
+
+432
+00:51:11,920 --> 00:51:16,740
+اللي فاتت، هذه ماحسبناش صحيح، هي قيمتهاهذه الباقية
+
+433
+00:51:16,740 --> 00:51:21,500
+جوش وسنش حسبنا ضربنا في نص و جيبنا في حالة ال
+
+434
+00:51:21,500 --> 00:51:25,300
+linearity و جيبنا ما بعرف هذه او هذه واحدة منهم و
+
+435
+00:51:25,300 --> 00:51:29,740
+التانية زيها هذول ماجيبنهمش صحيح لكن هي لابلاس
+
+436
+00:51:29,740 --> 00:51:35,440
+ترانسفورم اللهم هذول و هذه و بعض الشغلات هذه كلها
+
+437
+00:51:35,440 --> 00:51:40,130
+هتلاقيها موجودة وينفي الجدول اللي بجيكي في نهاية
+
+438
+00:51:40,130 --> 00:51:45,390
+ورقية الامتحان نكتفي بهذا القدر ان شاء الله ولان
+
+439
+00:51:45,390 --> 00:51:52,010
+إليه عوضة في المحاضرة القادمة وسنبدأ بحل أمثلة على
+
+440
+00:51:52,010 --> 00:51:57,190
+كيفية استخدام هذه الخواص وهو very important لذلك
+
+441
+00:51:57,190 --> 00:52:00,930
+المرة الجاية كل واحدة بتجيب كتابة معاها بأكد على
+
+442
+00:52:00,930 --> 00:52:05,210
+وجود الكتاب بلاش تخلوني أطردكوا برا كل واحدة بتجيب
+
+443
+00:52:05,210 --> 00:52:09,680
+كتابة معاهاو تيجي مطالع عالي على الخواص لإنه تضطيق
+
+444
+00:52:09,680 --> 00:52:13,680
+عامة اللي بيقولك افتح الكتاب و اي سؤال و نية خاصية
+
+445
+00:52:13,680 --> 00:52:18,340
+بتناسب و نروح نستخدم الخاصية لإن في الامتحان
+
+446
+00:52:18,340 --> 00:52:21,940
+بيجيكوا سؤال زي ايه دايما هو بيجيب زي ايه بيبقى
+
+447
+00:52:21,940 --> 00:52:25,300
+challenge و بتعرف انت تستخدمه الجدل اللي عندك و
+
+448
+00:52:25,300 --> 00:52:28,360
+اكتشف يلزم ام لا برك الله فيك
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d508193f08fdb93ccb82c679eadd74670521d7fc
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8.srt
@@ -0,0 +1,1405 @@
+1
+00:00:20,500 --> 00:00:25,220
+بسم الله الرحمن الرحيم آخر حاجة أخذناها المرة
+
+2
+00:00:25,220 --> 00:00:30,220
+اللي فيها كانت نظرية ونتيجة عليها وكانت النتيجة لو
+
+3
+00:00:30,220 --> 00:00:35,140
+عندي diagonal matrix وهذه الـ diagonal كانت scalar
+
+4
+00:00:35,140 --> 00:00:39,880
+matrix وضربت الـ scalar matrix من جهة الشمال في
+
+5
+00:00:39,880 --> 00:00:44,640
+المصفوفة A إيه يساوي تماما الرقم اللي موجود في الـ
+
+6
+00:00:44,640 --> 00:00:49,560
+scalar matrix كما لو ضربته في مين؟ في المصفوفة A
+
+7
+00:00:49,950 --> 00:00:53,930
+فقلنا diagonal matrix أو الـ scalar diagonal matrix
+
+8
+00:00:53,930 --> 00:01:00,050
+C ضربناها في A؟ بدنا نساوي الرقم C مضروب في A؟
+
+9
+00:01:00,050 --> 00:01:04,490
+اللي هو الموجود في A؟ هذا آخر ما كتبناه المرة
+
+10
+00:01:04,490 --> 00:01:10,280
+الماضية. بنعطي مثال على ذلك بقول لو كان المصفوفة A
+
+11
+00:01:10,280 --> 00:01:15,800
+هي المصفوفة اللي قدامنا هذه، والمصفوفة C هي الـ
+
+12
+00:01:15,800 --> 00:01:21,240
+scalar matrix 3 0 0 , 0 3 0 , 0 0 3
+
+13
+00:01:21,720 --> 00:01:27,760
+جاء لي هات لي حاصل ضرب المصفوفتين C مضروبة في A وكذلك 
+
+14
+00:01:27,760 --> 00:01:33,280
+حاصل ضرب الرقم 3 في المصفوفة A. What can you say
+
+15
+00:01:33,280 --> 00:01:38,680
+وإيش ممكن تقول عن النتائج اللي بنحصل عليها في كلا
+
+16
+00:01:38,680 --> 00:01:44,020
+الأمرين؟ الآن المصفوفة اللي عندي هذه 3 في 4 
+
+17
+00:01:44,230 --> 00:01:49,430
+تمام. هذه المصفوفة عبارة عن إيش؟ 3 في 3. إذًا 
+
+18
+00:01:49,430 --> 00:01:59,770
+لا يمكن ضرب هذه المصفوفة. تمام. لا إحنا بنضرب إذًا C
+
+19
+00:01:59,770 --> 00:02:06,950
+في A وليس A في C. إذًا اللي مطلوب هنا CA وليست AC.
+
+20
+00:02:06,950 --> 00:02:09,570
+فبعدين بقوله هنا solution.
+
+21
+00:02:13,030 --> 00:02:20,570
+بناخد C في الـ A، يبقى C اللي هي 3 0 0 , 0 3 0 , 0 0 3 
+
+22
+00:02:20,570 --> 00:02:28,230
+مضروبة في 2 3 1 , -1 -2 1, 0 0 1
+
+23
+00:02:28,230 --> 00:02:34,070
+, -1 1 2 , 0 1 3 يبقى هذه المصفوفة 3 في 3 وهذه
+
+24
+00:02:34,070 --> 00:02:39,570
+3 في 4. إذًا يمكن ضرب هاتين المصفوفتين.
+
+25
+00:02:39,570 --> 00:02:44,230
+والنتج هو 3 في 4. يبقى لو جيت ضربت هذه
+
+26
+00:02:44,230 --> 00:02:49,330
+المصفوفات هيكون حاصل الضرب على الشكل التالي: الصف
+
+27
+00:02:49,330 --> 00:02:53,650
+الأول في العمود الأول 3 في 2 بـ 6
+
+28
+00:02:53,650 --> 00:02:57,550
+والباقي صفرًا. الصف الأول في العمود الثاني يبقى
+
+29
+00:02:57,550 --> 00:03:03,560
+بالنظر بـ 3 في 3 والباقي صفرًا. 3 في 
+
+30
+00:03:03,560 --> 00:03:08,560
+1 بـ 3 والباقي صفرًا. 3 في
+
+31
+00:03:08,560 --> 00:03:14,080
+3 بقد إيش؟ بـ 9. اللي بعده 3 في 1 بـ 3
+
+32
+00:03:14,080 --> 00:03:20,040
+وهذا -3 يبقى هذا الصف الأول بدأجي للصف
+
+33
+00:03:20,040 --> 00:03:25,640
+الثاني في العمود الأول 0. 3 في 1 بـ 3
+
+34
+00:03:25,640 --> 00:03:26,900
+والباقي 0.
+
+35
+00:03:34,200 --> 00:03:42,540
+الصف الثاني في العمود الثالث يبقى الصف الثاني في
+
+36
+00:03:42,540 --> 00:03:50,630
+العمود الرابع بـ -6. هذا -6. الصف هذا في العمود
+
+37
+00:03:50,630 --> 00:03:56,030
+الثالث هذه اللي هي بـ 3. الصف هذا في العمود هذا
+
+38
+00:03:56,030 --> 00:04:02,590
+يبقى 0 0 0 يبقى كله بـ 0. نيجي الصف
+
+39
+00:04:02,590 --> 00:04:07,870
+الثالث في العمود اللي هو 0 0 0 كذلك زي ما
+
+40
+00:04:07,870 --> 00:04:18,390
+هو بـ 0. بعد ذلك 0 0 3، اللي بعده 0 0 3×2=6
+
+41
+00:04:18,390 --> 00:04:23,410
+اللي بعده 0 0 3×3=9
+
+42
+00:04:23,410 --> 00:04:28,170
+بالشكل اللي عندنا هذا. يبقى هذا حاصل ضرب الـ scalar
+
+43
+00:04:28,170 --> 00:04:32,830
+diagonal matrix اللي عندنا هذا في مين؟ في A. الآن
+
+44
+00:04:32,830 --> 00:04:38,570
+بالدرجة أشوف C في A. C هي اليومين الرقم 3، يبقى
+
+45
+00:04:38,570 --> 00:04:44,450
+بالداجي، إيه 3 في المصفوفة A؟ يبقى 3 في
+
+46
+00:04:44,450 --> 00:04:50,550
+المصفوفة A: 2 3 1, -1 -2 1, 0 0 1 
+
+47
+00:04:50,550 --> 00:04:58,290
+, 2 3 يساوي الـ 3 عندما
+
+48
+00:04:58,290 --> 00:05:03,090
+أضربها في المصفوفة أضربها في جميع عناصر المصفوفة
+
+49
+00:05:03,090 --> 00:05:08,250
+بالاستثناء. يبقى 3 في 2 بـ 6، 3 في 3
+
+50
+00:05:08,250 --> 00:05:15,070
+بـ 9، 3 في -1 بـ -3 وهنا 3 وهنا -6 
+
+51
+00:05:15,070 --> 00:05:20,070
+وهنا 3 في 1 بـ 3 وهنا 0 وهنا كمان 0
+
+52
+00:05:20,070 --> 00:05:25,930
+وهنا 3 6 9 بالشكل اللي عندنا هذا. تعالوا 
+
+53
+00:05:25,930 --> 00:05:30,990
+قارنوا بين النتيجتين. الأول ضربنا مصفوفتين في بعض، هنا
+
+54
+00:05:30,990 --> 00:05:36,370
+ضربنا الرقم في مصفوفة وبتلاحظوا إن النتيجتين اثنتين
+
+55
+00:05:36,370 --> 00:05:42,710
+are equal. يبقى هذا معناه على طول الخط إن C
+
+56
+00:05:42,710 --> 00:05:49,810
+في A بده يساوي مين؟ بده يساوي اللي هو 3 A 
+
+57
+00:05:49,810 --> 00:05:55,130
+مباشرة. لأنه قال لي إيش بتقدر تقول عن النتيجة فبقول
+
+58
+00:05:55,130 --> 00:06:00,250
+له حصل ضرب الـ scalar matrix C في الـ A بده يساوي
+
+59
+00:06:00,250 --> 00:06:04,870
+حاصل ضرب 3 في A وهذا تطبيق مباشر على الـ Corollary تبع
+
+60
+00:06:04,870 --> 00:06:12,230
+الماضية. ننتقل الآن إلى تعريف جديد أو ثلاث
+
+61
+00:06:12,230 --> 00:06:17,890
+تعريفات وهي very important لأنها بتجيب لي معلومات
+
+62
+00:06:17,890 --> 00:06:24,330
+جديدة يعني مش درجة عندنا قبل ذلك، معلومات جديدة
+
+63
+00:06:24,330 --> 00:06:30,250
+يبقى بدنا نيجي إلى definitions. التعريف الأول بيقول
+
+64
+00:06:30,250 --> 00:06:44,840
+If الـ A is a m في n matrix. m في n matrix, we
+
+65
+00:06:44,840 --> 00:06:58,160
+define. We define the transpose, A transpose of A
+
+66
+00:06:58,160 --> 00:07:01,460
+written
+
+67
+00:07:07,860 --> 00:07:23,020
+ويُكتب as A transpose to be the n by m matrix
+
+68
+00:07:23,020 --> 00:07:33,060
+whose
+
+69
+00:07:33,060 --> 00:07:33,880
+elements
+
+70
+00:07:39,760 --> 00:07:49,300
+الأشياء التي تسميها aij transpose تسمى aji، 
+
+71
+00:07:49,300 --> 00:07:53,640
+أو
+
+72
+00:07:53,640 --> 00:07:53,740
+اي اي اي اي اي اي اي اي اي اي اي اي
+
+73
+00:08:07,470 --> 00:08:14,970
+اللي هو 2 3 1 5 0 0 , -1 1 1 
+
+74
+00:08:14,970 --> 00:08:26,290
+2 3 4, then A transpose تساوي 
+
+75
+00:08:26,290 --> 00:08:28,790
+اللي هو main
+
+76
+00:08:47,710 --> 00:08:56,930
+تعريف الأول، تعريف الثاني، تعريف
+
+77
+00:08:56,930 --> 00:09:08,380
+الثاني. A matrix A. A matrix A is called symmetric is
+
+78
+00:09:08,380 --> 00:09:17,380
+called symmetric if
+
+79
+00:09:17,380 --> 00:09:33,110
+A transpose تساوي A. المرة الثالثة A matrix A
+
+80
+00:09:33,110 --> 00:09:46,790
+is called skew symmetric skew
+
+81
+00:09:46,790 --> 00:09:54,490
+symmetric if A transpose تساوي سالب A.
+
+82
+00:10:06,490 --> 00:10:15,050
+Example. Determine whether
+
+83
+00:10:15,050 --> 00:10:23,110
+the following matrices
+
+84
+00:10:23,110 --> 00:10:26,550
+are
+
+85
+00:10:26,550 --> 00:10:29,270
+symmetric
+
+86
+00:10:32,520 --> 00:10:43,280
+or skew symmetric. مصفوفة 
+
+87
+00:10:43,280 --> 00:10:47,660
+A تساوي
+
+88
+00:10:47,660 --> 00:10:58,000
+1 2 3, 1 2 3 4 -2
+
+89
+00:10:58,000 --> 00:11:11,730
+5 1 بتساوي 0 -3 2, 0 -3
+
+90
+00:11:11,730 --> 00:11:19,190
+3 3, 0 -1 -1 1 0
+
+91
+00:11:19,190 --> 00:11:20,170
+بالشكل إن
+
+92
+00:12:02,920 --> 00:12:07,800
+يبقى بيجي الآن للمصفوفة A. ده إيه؟ ده لم نتعامل معها
+
+93
+00:12:07,800 --> 00:12:16,540
+من قبل. هذه المصفوفة كالتالي: يبقى فيها m 
+
+94
+00:12:16,540 --> 00:12:22,220
+من الصفوف و n من الأعمدة. بنعرف the transpose of A
+
+95
+00:12:22,220 --> 00:12:28,180
+يعني مدور المصفوفة A أو بيسموه منقول المصفوفة A.
+
+96
+00:12:28,180 --> 00:12:33,710
+أعتقد في الثانوية كنت بيسموه مدور المصفوفة A. يبقى 
+
+97
+00:12:33,710 --> 00:12:37,950
+الـ transpose of A هو مضاورة المصفوفة A، written as A و
+
+98
+00:12:37,950 --> 00:12:43,650
+بحط فجهة T وتقرأ A transpose يعني transpose of
+
+99
+00:12:43,650 --> 00:12:49,090
+matrix A to be the n by m matrix. يبقى الصف بيصير
+
+100
+00:12:49,090 --> 00:12:56,070
+عمود والعمود بيصير صف. يبقى الـ n في m, n في m 
+
+101
+00:12:56,070 --> 00:13:03,790
+matrix whose elements aij transpose هو aji. يبقى مش
+
+102
+00:13:03,790 --> 00:13:06,730
+عادي أجيب ليه الـ transpose تبع الـ element، ببدل
+
+103
+00:13:06,730 --> 00:13:10,330
+الصف عمود والعمود صف، يعني الـ answer كان في الصف
+
+104
+00:13:10,330 --> 00:13:14,390
+الثاني والعمود الأول بصير في الصف الأول والعمود
+
+105
+00:13:14,390 --> 00:13:19,030
+الثاني وهكذا. نعطي مثال for example لو كانت
+
+106
+00:13:19,030 --> 00:13:23,110
+المصفوفة اللي عندنا هذه بدي أجيب الـ A transpose 
+
+107
+00:13:23,110 --> 00:13:28,470
+تبعها، يبقى الصف الأول بدي أخليه العمود الأول، الصف
+
+108
+00:13:28,470 --> 00:13:31,730
+الثاني بدي أخليه العمود الثاني، الصف الثالث بدي
+
+109
+00:13:31,730 --> 00:13:36,790
+أخليه العمود الثالث. يبقى 2 3 1 5 هو العمود الأول
+
+110
+00:13:36,790 --> 00:13:42,230
+طلع 2 3 1 5. الصف الثاني بدي أخليه العمود الثاني
+
+111
+00:13:42,230 --> 00:13:50,420
+يبقى 0 0 -1 1. 0 0 -1 1 لأن الصف الثالث بدنا نخليه العمود الثالث 1 
+
+112
+00:13:50,420 --> 00:13:56,420
+2 3 4 يكون 1 2 3 4. يبقى إذا خلت الصفوف أعمدة والأعمدة صفوف. نظام المصفوفة الأصلي كان m في n، يبقى
+
+114
+00:14:01,060 --> 00:14:07,900
+نظام المصفوفة الجديدة هو n في m. بنقلب الوضع. يبقى هذا 
+
+115
+00:14:07,900 --> 00:14:12,060
+بالنسبة للتعريف الأول. التعريف الثاني symmetric 
+
+116
+00:14:12,060 --> 00:14:17,360
+matrix يعني مصفوفة متماثلة. بقول عنها وقت إيش؟ لو 
+
+117
+00:14:17,360 --> 00:14:23,870
+جبت لها transpose طلعت main نفس المصفوفة تمامًا. إذًا
+
+118
+00:14:23,870 --> 00:14:27,950
+لو جبت لترانسبوز للمصفوفة وطلع نفس المصفوفة بقول
+
+119
+00:14:27,950 --> 00:14:32,410
+هذه اللي هو symmetric matrix اللي هو التعريف الأول.
+
+120
+00:14:32,410 --> 00:14:37,170
+بدأجي للتعريف الثاني: لو جبت لترانسبوز لـ matrix A
+
+121
+00:14:37,170 --> 00:14:46,540
+طلع نفس المصفوفة A بإشارة سالبة. يبقى متمثل
+
+122
+00:14:46,540 --> 00:14:56,700
+متخلف متمثل متخلف متمثل متخلف متمثل
+
+123
+00:14:56,700 --> 00:15:03,240
+متخلف يبقى matrix is called skew symmetric لو تمثل
+
+124
+00:15:03,240 --> 00:15:09,160
+متخلف F الـ A في الـ A transpose مش الـ A ناقص 
+
+125
+00:15:09,160 --> 00:15:16,760
+واحد. صلحيها بالله! A transpose بده يساوي سالب A.
+
+126
+00:15:16,760 --> 00:15:22,630
+يبقى إذا كان الـ A transpose يساوي سالب A. الآن مثال
+
+127
+00:15:22,630 --> 00:15:25,390
+بيقول دي: determine whether the following matrices
+
+128
+00:15:25,390 --> 00:15:29,570
+are symmetric or skew symmetric. أكملوا على كل
+
+129
+00:15:29,570 --> 00:15:34,130
+مصفوفة من هذه المصفوفات: هل هي symmetric ولا skew symmetric؟
+
+130
+00:15:34,130 --> 00:15:41,560
+نمسك المصفوفة الأولى يبقى بدنا نأخذ الـ A
+
+131
+00:15:41,560 --> 00:15:48,840
+transpose. بيزود الصف الأول بيصير العمود الأول يبقى
+
+132
+00:15:48,840 --> 00:15:53,560
+أي 1 2 3. الصف الثاني بيصير العمود
+
+133
+00:15:53,560 --> 00:16:06,310
+الثاني يبقى 2 4 -2. يبقى 3
+
+134
+00:16:06,310 --> 00:16:10,870
+-2 5 بالشكل اللي عندنا هذا. إيش رأيك؟ وهي 
+
+135
+00:16:10,870 --> 00:16:17,250
+المصفوفة الأصلية؟ صح ولا لأ؟ يبقى هذا معناه إن A
+
+136
+00:16:17,250 --> 00:16:22,230
+transpose بده يساوي A. يبقى A عبارة عن إيش؟
+
+137
+00:16:22,230 --> 00:16:30,310
+Symmetric matrix. يبقى هنا الـ A is a symmetric
+
+138
+00:16:30,310 --> 00:16:33,530
+matrix.
+
+139
+00:16:33,530 --> 00:16:42,570
+يبقى مصفوفة متماثلة. And بالدالي للمصفوفة B transpose.
+
+140
+00:16:42,570 --> 00:16:49,010
+بدي أخلي الصف الأول هو العمود الأول يبقى 0 -3 2.
+
+141
+00:16:49,010 --> 00:16:54,470
+الصف الثاني هو العمود الثاني 3 0 -1.
+
+142
+00:16:54,470 --> 00:16:58,890
+الصف الثالث هو العمود الثالث يبقى
+
+143
+00:16:58,890 --> 00:17:04,270
+-1 1 0 بالشكل اللي عنها. هل هذا هو
+
+144
+00:17:04,270 --> 00:17:11,130
+المصفوفة B؟ لأ. طب خليني أجرب آخذ سالب 1 عامل مشترك.
+
+145
+00:17:11,130 --> 00:17:16,950
+يبقى لو جيت أخذت سالب 1 بيصير سالب هذا 0 زي
+
+146
+00:17:16,950 --> 00:17:23,370
+ما هو هذا، -3 هذا 1 هذا 3 هذا 0
+
+147
+00:17:23,370 --> 00:17:30,830
+هذا -1 هذا -2 هذا 1 هذا 0. هذه 
+
+148
+00:17:30,830 --> 00:17:32,730
+هي المصفوفة B ولا لأ؟
+
+149
+00:17:53,240 --> 00:17:59,260
+بترانسبوز هي الصف الأول 0 -3 2.
+
+150
+00:17:59,260 --> 00:18:03,360
+3 0 -1, -1 1 
+
+151
+00:18:06,280 --> 00:18:13,860
+استنى استنى شوية استنى شوية براجع كتابتها المصفوفة
+
+152
+00:18:13,860 --> 00:18:21,140
+B عندنا 0 -3 2, 3 0 -1
+
+153
+00:18:21,140 --> 00:18:27,020
+-1 -2, هذه من عندك، هذه -2 0 
+
+154
+00:18:27,020 --> 00:18:32,710
+1 بس خطأ في الكتابة. إذا الصف الأول هو الـ A يبقى
+
+155
+00:18:32,710 --> 00:18:40,090
+هذه transpose يبقى الصف الأول هو العمود الأول، الصف 
+
+156
+00:18:40,090 --> 00:18:47,170
+الثاني يبقى هذه بدها تصير -2، يبقى الصف من 
+
+157
+00:18:47,170 --> 00:18:52,930
+-2 1 0. الآن بدنا نأخذ سالب عامل مشترك 
+
+158
+00:18:52,930 --> 00:19:00,770
+بيصير هذه 2 تمام، هذه 2 وهذه 3 0 
+
+159
+00:19:00,770 --> 00:19:05,130
+-1 وهذه -2 1 0. اطلع لي
+
+160
+00:19:05,130 --> 00:19:09,100
+المصفوفة هذه هي اللي هي المصفوفة اللي فوق، يبقى هي
+
+161
+00:19:09,100 --> 00:19:13,320
+المصفوفة اللي فوق بالضبط تمامًا. يبقى هذه بدها تساوي
+
+162
+00:19:13,320 --> 00:19:19,740
+مين؟ سالب B. إذا B transpose تساوي سالب B يبقى هنا
+
+163
+00:19:19,740 --> 00:19:24,960
+B سكيو
+
+164
+00:19:24,960 --> 00:19:29,940
+symmetric matrix.
+
+165
+00:19:37,920 --> 00:19:43,380
+طيب، مجرد ملاحظة على هذه المصفوفة. لو طلعنا للمصفوفة A
+
+166
+00:19:43,380 --> 00:19:48,640
+ثم لمصفوفة B. ها، لو بدنا نستنتج هالشيء قبل ما أبدأ
+
+167
+00:19:48,640 --> 00:19:53,340
+أشتغل، باجي باطلع في المصفوفة A لاحظ الصف الأول هو
+
+168
+00:19:53,340 --> 00:19:58,520
+العمود الأول، العنصر هذا هو العنصر هذا والقطر
+
+169
+00:19:58,520 --> 00:20:03,110
+الرئيسي مش مشكلة مين ما يكون يكون. تمام؟ لماذا؟ لأن
+
+170
+00:20:03,110 --> 00:20:08,050
+under transpose كل العناصر القطرية تبقى كما هي. هذا
+
+171
+00:20:08,050 --> 00:20:12,190
+إيه؟ ده كانت مصفوفة مربعة يبقى بتبقى العناصر كما هي.
+
+172
+00:20:12,190 --> 00:20:15,970
+معناها مش مشكلة. تعالوا لأن المصفوفة B إيش بتلاحظ على
+
+173
+00:20:15,970 --> 00:20:21,990
+القطر الرئيسي كله أصفار. يبقى في حالة الـ skew الـ
+
+174
+00:20:21,990 --> 00:20:27,030
+symmetric والمصفوفة مربعة لازم يكونوا عناصر القطر
+
+175
+00:20:27,030 --> 00:20:33,590
+الرئيسي أصفار. اثنين مشان اللي المصفوفة تطلع اللي هو
+
+176
+00:20:33,590 --> 0
+
+201
+00:23:36,850 --> 00:23:44,390
+main diagonal القطر الرئيسي
+
+202
+00:23:44,390 --> 00:23:54,360
+عناصر القطر الرئيسي the main diagonal elements are
+
+203
+00:23:54,360 --> 00:24:12,320
+zero يبقى دائما وأبدا بتكون أصفارا that is that
+
+204
+00:24:12,320 --> 00:24:26,040
+اللي هو الـ Aii بده يساوي 0 for all i بنجي  is
+
+205
+00:24:26,040 --> 00:24:33,540
+ليه some properties of
+
+206
+00:24:33,540 --> 00:24:39,980
+a transpose matrix
+
+207
+00:24:41,720 --> 00:24:54,900
+بعد خواص مدور المصفوفة four square matrices
+
+208
+00:24:54,900 --> 00:24:59,140
+matrices
+
+209
+00:24:59,140 --> 00:25:05,140
+a and b we have
+
+210
+00:25:10,340 --> 00:25:16,300
+النقطة الأولى A Transpose زي ال Transpose بده
+
+211
+00:25:16,300 --> 00:25:24,480
+يساوي A نفسها نمرة اثنين A زي B Transpose بده
+
+212
+00:25:24,480 --> 00:25:34,940
+يساوي A Transpose زي B Transpose تلاتة A
+
+213
+00:25:34,940 --> 00:25:42,600
+B transpose بدي يساوي B transpose في ال A transpose
+
+214
+00:25:42,600 --> 00:25:58,900
+نمرة أربعة four any scalar c c a كله transpose
+
+215
+00:25:58,900 --> 00:26:02,960
+بيسوي c في ال A transpose
+
+216
+00:26:13,180 --> 00:26:26,560
+example example one show that show
+
+217
+00:26:26,560 --> 00:26:34,100
+that if ال A is
+
+218
+00:26:38,460 --> 00:26:45,100
+square matrix then
+
+219
+00:27:11,840 --> 00:27:17,280
+نمرة A الـ
+
+220
+00:27:17,280 --> 00:27:25,060
+A في الـ A Transpose و الـ A زائد الـ A
+
+221
+00:27:25,060 --> 00:27:33,400
+Transpose are symmetric نمرة
+
+222
+00:27:33,400 --> 00:27:44,930
+اثنين  الـ A ناقص الـ A transpose as a skew
+
+223
+00:27:44,930 --> 00:27:46,610
+symmetric
+
+224
+00:28:26,180 --> 00:28:29,100
+نرجع للكلام اللي احنا كاتبينه هذا مرة ثانية
+
+225
+00:28:29,100 --> 00:28:35,140
+نتعرض له تفصيليا ثم نذهب إلى حل المثال الأول على
+
+226
+00:28:35,140 --> 00:28:36,320
+هذا الموضوع
+
+227
+00:28:42,630 --> 00:28:49,450
+المصفوفة المتماثلة أو شبه المتماثلة أو المتماثلة
+
+228
+00:28:49,450 --> 00:28:54,370
+المتخالفة اثنين مصفوفتين مربعيتين ليش إن عدد
+
+229
+00:28:54,370 --> 00:28:58,530
+الصفوف يساوي عدد الأعمدة فإن جلبتها تصبح عدد الصفوف
+
+230
+00:28:58,530 --> 00:29:04,740
+يساوي عدد الأعمدة يجب أن تكون مصفوفة مربعة النقطة
+
+231
+00:29:04,740 --> 00:29:07,580
+الثانية الـ diagonal matrix في ال square matrix A
+
+232
+00:29:07,580 --> 00:29:12,240
+و الـ A transpose are the same نفس الشيء يبقى مسحنا
+
+233
+00:29:12,240 --> 00:29:18,100
+شوية تول مصفوفة لما نعملها عناصر قطر الرئيسي A11,
+
+234
+00:29:18,440 --> 00:29:23,760
+A22, A33 وإن نزل كله بتظل العنصر لأن العنصر موقع
+
+235
+00:29:23,760 --> 00:29:28,380
+في الصف ونفس موقع في العمود يبقى هذا لا يتغير
+
+236
+00:29:28,380 --> 00:29:32,540
+بتغيره من العناصر الأخرى لكن عناصر القطر الرئيسي
+
+237
+00:29:32,540 --> 00:29:33,780
+تبقى كما هي
+
+238
+00:29:38,310 --> 00:29:49,210
+العنصر الذي يقع في الصف i والعمود رقم i يبقى
+
+239
+00:29:49,210 --> 00:29:54,800
+العنصر نفسه لا يتغير النقطة الثالثة في الـ SQL
+
+240
+00:29:54,800 --> 00:29:57,140
+Symmetric Matrix of the mean ده يجب أن العناصر
+
+241
+00:29:57,140 --> 00:30:03,900
+كله مالها أصفارا يعني ال Aii بده يساوي zero لكل
+
+242
+00:30:03,900 --> 00:30:08,300
+اللي هو العناصر i لما تجيب ال transpose برضه
+
+243
+00:30:08,300 --> 00:30:14,940
+بظلّن برضه zero zero يعني بتقدر تقول ال Aii بده
+
+244
+00:30:14,940 --> 00:30:20,520
+يساوي zero بده يساوي ال Aii transpose هذا والله هذا
+
+245
+00:30:20,520 --> 00:30:28,560
+كله أصفارا طيب في لـ .. ليه transpose هذا للمصفوفة
+
+246
+00:30:28,560 --> 00:30:33,600
+اللي Transpose Matrix لها بعض الخصائص فبقول لو كان
+
+247
+00:30:33,600 --> 00:30:39,680
+عندي A و B مصفوفة ثاني مربعيتان ف A transpose
+
+248
+00:30:39,680 --> 00:30:42,740
+Transpose Transpose Transpose Transpose Transpose
+
+249
+00:30:42,740 --> 00:30:43,280
+Transpose Transpose Transpose Transpose Transpose
+
+250
+00:30:43,280 --> 00:30:43,520
+Transpose Transpose Transpose Transpose Transpose
+
+251
+00:30:43,520 --> 00:30:43,760
+Transpose Transpose Transpose Transpose Transpose
+
+252
+00:30:43,760 --> 00:30:50,040
+Transpose Transpose Transpose Transpose Transpose
+
+253
+00:30:50,040 --> 00:30:50,560
+Transpose Transpose Transpose Transpose Transpose
+
+254
+00:30:50,560 --> 00:30:50,720
+Transpose Transpose Transpose Transpose Transpose
+
+255
+00:30:50,720 --> 00:30:50,780
+Transpose Transpose Transpose Transpose Transpose
+
+256
+00:30:50,780 --> 00:30:51,950
+Transpose Transpose Transpose Transpose يبقى بيصير A
+
+257
+00:30:51,950 --> 00:30:56,710
+Transpose و Transpose هي مصفوفة A لو كان A
+
+258
+00:30:56,710 --> 00:31:02,530
+زائد B Transpose جمعتهم ثم جبت لي Transpose تبعهم
+
+259
+00:31:02,530 --> 00:31:06,450
+تمامًا كما لو جبت لي Transpose للأولى و Transpose
+
+260
+00:31:06,450 --> 00:31:11,850
+للثانية ومن ثم روحنا جمعنا هيعطيني نفس النتيجة
+
+261
+00:31:11,850 --> 00:31:15,810
+خاصية الثالثة هذه بتختلف شوية هذه الأولانية
+
+262
+00:31:15,810 --> 00:31:19,870
+بالنسبة لعملية الجمع لكن الثانية بالنسبة لعملية
+
+263
+00:31:19,870 --> 00:31:20,370
+الضرب
+
+264
+00:31:23,540 --> 00:31:32,500
+بنجلب وضع الـ A ووضع الـ B ونجلب
+
+265
+00:31:32,500 --> 00:31:33,260
+وضع الـ A ونجلب وضع الـ A ونجلب وضع الـ B ونجلب
+
+266
+00:31:33,260 --> 00:31:34,920
+وضع الـ A ونجلب وضع الـ A ونجلب وضع الـ A ونجلب
+
+267
+00:31:34,920 --> 00:31:37,080
+وضع الـ A ونجلب وضع الـ A ونجلب وضع الـ A ونجلب
+
+268
+00:31:37,080 --> 00:31:37,480
+وضع الـ A ونجلب وضع الـ A ونجلب وضع الـ A ونجلب
+
+269
+00:31:37,480 --> 00:31:44,310
+وضع الـ A ونجلب وضع الـ A ونطيب for any scalar C
+
+270
+00:31:44,310 --> 00:31:49,590
+يعني لأي عدد حقيقي الـC لو ضربت الـC في المصفوفة
+
+271
+00:31:49,590 --> 00:31:55,570
+الـA وبعد ذلك جبت لها الترانسبوز تمامًا كما لو جبت
+
+272
+00:31:55,570 --> 00:31:58,970
+الترانسبوز لـA وضربت في ميهن الـC يعني الـconstant
+
+273
+00:31:58,970 --> 00:32:02,710
+ضربته قبل الترانسبوز والله بعد الترانسبوز على كل
+
+274
+00:32:02,710 --> 00:32:07,930
+الأمرين بيعطيني ميهن بيعطيني نفس النتيجة نعطي بعض
+
+275
+00:32:07,930 --> 00:32:12,830
+الأمثلة على كيفية تطبيق هذه الخاصة بيقول المثال هو
+
+276
+00:32:12,830 --> 00:32:17,550
+البيان إنه لو كانت اسمها مصفوفة مربعة يبقى المطلوب
+
+277
+00:32:17,550 --> 00:32:22,810
+الأول أثبت له إن الـA مضروبة في الـA transpose هي
+
+278
+00:32:22,810 --> 00:32:28,310
+symmetric وكذلك الـA زي الـA transpose هي man هي
+
+279
+00:32:28,310 --> 00:32:32,510
+symmetric هذا المطلوب الأول المطلوب الثاني أثبت له
+
+280
+00:32:32,510 --> 00:32:35,990
+أن الـ A ناقص الـ A Transpose هو Q اسم متغير
+
+281
+00:32:47,080 --> 00:32:51,720
+Symmetric يبقى بدي آخذ لها الترانسبوز لما آخذ لها
+
+282
+00:32:51,720 --> 00:32:57,240
+الترانسبوز بدي الناتج يطلع مين؟ المصفوفة الأصلية ليه؟
+
+283
+00:32:57,240 --> 00:33:03,140
+A في A ترانسبوز بقول له كويس هذا ترانسبوز لمين؟
+
+284
+00:33:03,140 --> 00:33:07,160
+لحاصل الضرب بيقول الـ A transpose اللي حصل الضرب
+
+285
+00:33:07,160 --> 00:33:12,400
+بدك تفكه وتقلب وضع كل واحدة فيهم يبقى هذه شو بدها
+
+286
+00:33:12,400 --> 00:33:18,240
+تصير A transpose في A transpose في A transpose
+
+287
+00:33:18,240 --> 00:33:23,640
+يبقى هاي قلبنا الوضع تمام هذا الكلام جبته من وين؟
+
+288
+00:33:23,640 --> 00:33:30,620
+من ال property تلاتة من هذا جبته من ال property
+
+289
+00:33:30,620 --> 00:33:36,690
+تلاتة طيب هذا الآن بدي يساوي A ترانسبوز ترانسبوز
+
+290
+00:33:36,690 --> 00:33:42,910
+بمين؟ ب A في ال A ترانسبوز يبقى هذا property مين؟
+
+291
+00:33:42,910 --> 00:33:48,410
+one أول خاصية طيب إيش تفسيرك لهذه؟ هاي اللي بين
+
+292
+00:33:48,410 --> 00:33:52,110
+قوسين هي اللي طلعت عندها يبقى هذه مالها؟ symmetric
+
+293
+00:33:52,110 --> 00:33:58,390
+يبقى سواء اللي هو ال A في ال A ترانسبوز is
+
+294
+00:33:58,390 --> 00:34:00,770
+symmetric
+
+295
+00:34:04,440 --> 00:34:12,620
+ماتريكس تمام بدنا نيجي و ال A زي ال A ترانسبوز
+
+296
+00:34:12,620 --> 00:34:18,180
+الكل ترانسبوز إذا
+
+297
+00:34:18,180 --> 00:34:21,400
+غيرت أثبت أنها تساوي اللي بينجو السين A زي A
+
+298
+00:34:21,400 --> 00:34:28,360
+ترانسبوز هيبقى بيصير هاد A symmetric بقول له تمام باجي
+
+299
+00:34:28,360 --> 00:34:33,420
+برجع على الخاصية اللي عندنا هذه خاصية بيقول A زائد
+
+300
+00:34:33,420 --> 00:34:38,540
+B ترانسبوز يساوي A ترانسبوز زائد B ترانسبوز يبقى
+
+301
+00:34:38,540 --> 00:34:43,220
+بناء على أن أنا بقدر أقول له هذه A ترانسبوز زائد A
+
+302
+00:34:43,220 --> 00:34:46,620
+ترانسبوز ترانسبوز هذه property
+
+303
+00:34:49,830 --> 00:34:55,630
+property two تمام هذا الكلام يساوي A transpose
+
+304
+00:34:55,630 --> 00:35:00,150
+زائد A transpose الترانسبوز اللي you mean أو هذه
+
+305
+00:35:00,150 --> 00:35:04,250
+property one الحين لما أقول يا بنات A transpose
+
+306
+00:35:04,250 --> 00:35:08,610
+زائد A والله A زائد transpose مش هي نفسها مش أخذنا
+
+307
+00:35:08,610 --> 00:35:13,460
+عملية إن جمع المصفوفات is commutative يبقى بناء عليها
+
+308
+00:35:13,460 --> 00:35:20,440
+دي بدها تساوي A زائد A Transpose يبقى هنا سائل A
+
+309
+00:35:20,440 --> 00:35:34,220
+زائد الـ A زائد A Transpose is symmetric كويس
+
+310
+00:35:35,120 --> 00:35:41,240
+بعد ذلك قال أثبت لي إن ال A ناقص A ترانسبوز is SQ
+
+311
+00:35:41,240 --> 00:35:47,080
+symmetric بقول له كويس يبقى بدي آجي الـ A لنمرة B نمرة B
+
+312
+00:35:47,080 --> 00:35:53,120
+بدي آجي آخذ له ال A ماينوس A ترانسبوز كله ترانسبوز
+
+313
+00:35:56,760 --> 00:36:06,280
+هذه بقدر أقول وتساوي A زائد ناقص واحد في A
+
+314
+00:36:06,280 --> 00:36:15,350
+transpose كله transpose صح ولا لا؟ طلع لي هنا
+
+315
+00:36:15,350 --> 00:36:22,530
+لما يكون الرقم مضروب في ال A ناقص A transpose وهذه
+
+316
+00:36:22,530 --> 00:36:25,670
+ال transpose اللي برّا هذا الكلام جبته من أين يا
+
+317
+00:36:25,670 --> 00:36:30,450
+بنات؟ الخاصية أربعة يبقى هذا اللي هي property
+
+318
+00:36:30,450 --> 00:36:38,130
+أربعة بعد هيك بقدر أدخل Transpose على كل واحدة فيهم
+
+319
+00:36:38,130 --> 00:36:46,130
+يبقى هذا الكلام بده يساوي A Transpose زائد ناقص A
+
+320
+00:36:46,130 --> 00:36:54,850
+Transpose كله Transpose هذه الخاصية من؟ الخاصية
+
+321
+00:36:54,850 --> 00:37:00,330
+الثانية كيف نقولها؟ يبقى هذه property
+
+322
+00:37:06,420 --> 00:37:13,060
+two هذا الآن يبدو يساوي A ل Transpose زي ما هي
+
+323
+00:37:13,060 --> 00:37:18,380
+زائد الحين هذه ناقص A Transpose Transpose حسب
+
+324
+00:37:18,380 --> 00:37:25,520
+الخاصية الأولى يبقى هذا يبدو يساوي ناقص A فقط لا
+
+325
+00:37:25,520 --> 00:37:32,320
+غير يبقى هذا الكلام
+
+326
+00:37:32,320 --> 00:37:38,640
+يساوي ممكن آخذ ناقص برّا عامل مشترك من الكل يبقى لو
+
+327
+00:37:38,640 --> 00:37:44,320
+أخذت ناقص برّا عامل مشترك من الكل بيظل A ناقص A
+
+328
+00:37:44,320 --> 00:37:49,280
+transpose يبقى معناه دي عبارة عن ايه skew
+
+329
+00:37:49,280 --> 00:37:57,100
+symmetric يبقى هنا السؤال ال A ناقص ال A transpose
+
+330
+00:38:11,590 --> 00:38:13,930
+بنعطي مثال
+
+331
+00:38:35,280 --> 00:38:43,180
+show that if ال
+
+332
+00:38:43,180 --> 00:38:53,060
+A و ال B are symmetric matrices
+
+333
+00:38:53,060 --> 00:38:53,780
+then
+
+334
+00:39:02,270 --> 00:39:14,510
+الـ A في B is symmetric if and only if ال
+
+335
+00:39:14,510 --> 00:39:17,470
+A في ال B بدها تساوي ال B في ال A
+
+336
+00:39:31,610 --> 00:39:48,910
+علي بالكم السؤال
+
+337
+00:39:48,910 --> 00:39:53,520
+مرة ثانية بقول يبين إن لو كانت الـA والـB الاثنتين
+
+338
+00:39:53,520 --> 00:39:59,460
+symmetric يبقى حاصل ضربهم بيكون symmetric إذا كان
+
+339
+00:39:59,460 --> 00:40:03,000
+الـA في B بدها تساوي الـB في A إذا كانوا commutative
+
+340
+00:40:03,000 --> 00:40:07,240
+والعكس بالعكس لأن هذه if and only if تعني إن البرهان
+
+341
+00:40:07,240 --> 00:40:14,440
+بدي يحصل في اتجاهين يبقى if and only if معناته لو كان
+
+342
+00:40:14,440 --> 00:40:18,340
+ال A في ال B بدها تساوي ال B في ال A يبقى بدنا نحاول
+
+343
+00:40:18,340 --> 00:40:23,920
+نثبته إن ال A و ال B are symmetric يبقى مشان أبرهن
+
+344
+00:40:23,920 --> 00:40:31,480
+يبقى assume يبقى بدي آجي أقول له assume افترض that إن
+
+345
+00:40:31,480 --> 00:40:36,680
+ال A و ال B are symmetric
+
+346
+00:40:43,590 --> 00:40:50,170
+بعد ذلك هذه معناها إن ال A Transpose بدها تساوي ال A
+
+347
+00:40:50,170 --> 00:40:57,570
+و ال B Transpose بدها تساوي ال B هذه المعلومة أنا بدي
+
+348
+00:40:57,570 --> 00:41:03,010
+أستخدمها متى لازم ألقاها بيقول لي ايش ذنب A بيه
+
+349
+00:41:03,010 --> 00:41:08,910
+symmetric اف عندها الف يبقى أنا بدي آجي أقول له assume
+
+350
+00:41:08,910 --> 00:41:19,310
+افترض that إن ال A,B is symmetric ايش
+
+351
+00:41:19,310 --> 00:41:26,070
+بدي أثبت بدي أثبت إن A في B بدها تساوي ال B في A يبقى
+
+352
+00:41:26,070 --> 00:41:34,530
+then ال A B transpose بدها تساوي اللي هو ال A في ال B
+
+353
+00:41:35,740 --> 00:41:39,920
+مش هذا معنى الترانسبوز؟ أنا فارض إنه هذه symmetric
+
+354
+00:41:39,920 --> 00:41:44,640
+يبقى مناطق ال A B ترانسبوز بدها تساوي AB بدي أرجع
+
+355
+00:41:44,640 --> 00:41:52,300
+مرة ثانية لمين لخواص ال A B ترانسبوز يبقى ال A B
+
+356
+00:41:52,300 --> 00:41:59,740
+ترانسبوز هي عبارة عن B ترانسبوز في ال A ترانسبوز و
+
+357
+00:41:59,740 --> 00:42:03,800
+هذه بدها تساوي مين؟ بدها تساوي A في ال B اللي عندنا
+
+358
+00:42:03,800 --> 00:42:09,420
+صحيح ولا لا؟ يبقى هذا معناه ال B transpose اللي هي
+
+359
+00:42:09,420 --> 00:42:13,880
+عبارة عن مين يا بنات؟ B، بدي أشيلها وأحط مكانها
+
+360
+00:42:13,880 --> 00:42:19,560
+B ال A transpose هي عبارة عن مين؟ ال A، بدها تساوي
+
+361
+00:42:19,560 --> 00:42:25,930
+مين؟ وأظنها هو المطلوب خلصنا يبقى أخذت ال A B ال
+
+362
+00:42:25,930 --> 00:42:30,890
+symmetric أثبت أن ال A B تساوي ال B في ال A الآن
+
+363
+00:42:30,890 --> 00:42:35,910
+بدي أعمل عملية عكسية يبقى بدي أقول له conversely
+
+364
+00:42:35,910 --> 00:42:45,790
+وعلى العكس assume that إن ال A في B بدها تساوي ال B في
+
+365
+00:42:45,790 --> 00:42:48,110
+A ايش بدها تثبت؟
+
+366
+00:42:50,990 --> 00:42:56,590
+بدي أثبت إن ال A في B is symmetric صح ولا لأ يبقى
+
+367
+00:42:56,590 --> 00:43:05,570
+بدي آخذ لها ال A B Transpose بدي أثبت له إن هذه
+
+368
+00:43:05,570 --> 00:43:10,470
+تساوي A في B إذا أثبت له إنها A في B بتنتهي
+
+369
+00:43:10,470 --> 00:43:21,000
+قصتنا بقول له كويس هذا الكلام يساوي الآن كيف؟ هذا ال
+
+370
+00:43:21,000 --> 00:43:29,000
+A B Transpose بقدر أكتب بدالها B A Transpose يبقى
+
+371
+00:43:29,000 --> 00:43:35,240
+هذا B A Transpose ليش؟ لأن ال B في ال A هي ال A
+
+372
+00:43:35,240 --> 00:43:41,280
+في ال B صح ولا لا؟ طيب هذا الكلام حسب الخصائص بدي
+
+373
+00:43:41,280 --> 00:43:48,850
+يساوي A Transpose B Transpose مظبوط؟ طيب هذا الكلام
+
+374
+00:43:48,850 --> 00:43:53,910
+بدي يساوي A Transpose هي مين؟ ب A و B Transpose هي
+
+375
+00:43:53,910 --> 00:43:58,490
+مين؟ ب B يبقى بناء على أخذنا A B Transpose طلعت
+
+376
+00:43:58,490 --> 00:44:02,670
+مين؟ ب A يبقى ال A في B is symmetric يبقى هذا
+
+377
+00:44:02,670 --> 00:44:12,330
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ed34295559e2462847707f5415085388c4094789
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8_postprocess.srt
@@ -0,0 +1,1536 @@
+1
+00:00:20,500 --> 00:00:25,220
+بسم الله الرحمن الرحيم الأخر حاجة أخدناها المرة
+
+2
+00:00:25,220 --> 00:00:30,220
+اللي فيها كانت نظرية ونتيجة عليها وكانت النتيجة لو
+
+3
+00:00:30,220 --> 00:00:35,140
+عندي diagonal matrix وهذه ال diagonal كانت scalar
+
+4
+00:00:35,140 --> 00:00:39,880
+matrix وضربت ال scalar matrix من جهة الشمال في
+
+5
+00:00:39,880 --> 00:00:44,640
+المصحوف أيه يسوى تماما الرقم اللي موجود في ال
+
+6
+00:00:44,640 --> 00:00:49,560
+scalar matrix كما لو ضربته في مين في المصحوف أيه
+
+7
+00:00:49,950 --> 00:00:53,930
+فقلنا دياجونال متريكس أو ال scalar دياجونال متريكس
+
+8
+00:00:53,930 --> 00:01:00,050
+C ضربناها في أيه؟ بدي نسوي الرقم C مضروب في أيه؟
+
+9
+00:01:00,050 --> 00:01:04,490
+اللي هو المصموم في أيه؟ هذا آخر ما كتبتيه المرة
+
+10
+00:01:04,490 --> 00:01:10,280
+الماضيةبنعطي مثال على ذلك بقول لو كان المصروفة A
+
+11
+00:01:10,280 --> 00:01:15,800
+هي المصروفة اللي قدامنا هذه والمصروفة C هي ال
+
+12
+00:01:15,800 --> 00:01:21,240
+scalar matrix 30000030003
+
+13
+00:01:21,720 --> 00:01:27,760
+جالي هاتلي حصل ضرب المفتوحتين C كبتن في A و كذلك
+
+14
+00:01:27,760 --> 00:01:33,280
+حصل ضرب الرقم تلاتة في المصفوفة A what can you say
+
+15
+00:01:33,280 --> 00:01:38,680
+و إيش ممكن تقول عن النتائج اللي بنحصل عليها في كلا
+
+16
+00:01:38,680 --> 00:01:44,020
+الأمرين الآن المصفوفة اللي عندي هذه تلاتة في أربع
+
+17
+00:01:44,230 --> 00:01:49,430
+تمام هذه المصفوفة عبارة عن ايش تلاتة في تلاتة اذا
+
+18
+00:01:49,430 --> 00:01:59,770
+لا يمكن ضرب هذه المصفوفة تمام لا احنا بنضرب اذا C
+
+19
+00:01:59,770 --> 00:02:06,950
+في A وليس A في C اذا اللي مطلوب هنا CA وليست AC
+
+20
+00:02:06,950 --> 00:02:09,570
+فبعدين بقوله هنا solution
+
+21
+00:02:13,030 --> 00:02:20,570
+بناخد C في الـ A يبقى C اللي هي تلاتة Zero Zero
+
+22
+00:02:20,570 --> 00:02:28,230
+Zero تلاتة Zero Zero تلاتة مضروبة في اتنين تلاتة
+
+23
+00:02:28,230 --> 00:02:34,070
+واحد سالب واحد واحد سالب اتنين واحد Zero Zero واحد
+
+24
+00:02:34,070 --> 00:02:39,570
+اتنين تلاتةيبقى هذه النظامة تلاتة في تلاتة وهذه
+
+25
+00:02:39,570 --> 00:02:44,230
+تلاتة في أربع إذا يمكن ضرب هتين المصفوف هتين
+
+26
+00:02:44,230 --> 00:02:49,330
+والنتج هو تلاتة في أربع يبقى لو جيت ضربت هذه
+
+27
+00:02:49,330 --> 00:02:53,650
+المصفوف هيكون حاصل الضرب على الشكل التالي الصف
+
+28
+00:02:53,650 --> 00:02:57,550
+الأول في العمود الأول تلاتة في اتنين في ستة
+
+29
+00:02:57,550 --> 00:03:03,560
+والباقيأصفرًا صفر الأول في العمود الثاني يبقى
+
+30
+00:03:03,560 --> 00:03:08,560
+بالنظر بالتلاتة في تلاتة والباقي أصفرًا تلاتة في
+
+31
+00:03:08,560 --> 00:03:14,080
+تلاتة بقداش بتسعة اللي بعده تلاتة في واحد بتلاتة
+
+32
+00:03:14,080 --> 00:03:20,040
+وهذا سالب تلاتة يبقى هذا الصفر الأول بدأجي للصفر
+
+33
+00:03:20,040 --> 00:03:25,640
+الثاني في العمود الأول Zero تلاتة في واحد بتلاتة
+
+34
+00:03:25,640 --> 00:03:26,900
+والباقي Zero
+
+35
+00:03:34,200 --> 00:03:42,540
+الصف الثاني في العمود التالت يبقى الصف الثاني في
+
+36
+00:03:42,540 --> 00:03:50,630
+العمود الـ 0 سلب 6هذا سالب ستة الصف هذا في العمود
+
+37
+00:03:50,630 --> 00:03:56,030
+التالت هذه اللي هي بتلاتة الصف هذا في العمود هذا
+
+38
+00:03:56,030 --> 00:04:02,590
+يبقى Zero Zero Zero يبقى كله ب Zero نيجي الصف
+
+39
+00:04:02,590 --> 00:04:07,870
+التالت في العمود اللي هو Zero Zero Zero كذلك زي ما
+
+40
+00:04:07,870 --> 00:04:18,390
+هو ب Zero بعد ذلك Zero Zero تلاتةاللي بعده 003×2×6
+
+41
+00:04:18,390 --> 00:04:23,410
+اللي بعده 003×3×9
+
+42
+00:04:23,410 --> 00:04:28,170
+بالشكل اللي عندنا هذا يبقى هذا حاصل ضرب ال scholar
+
+43
+00:04:28,170 --> 00:04:32,830
+diagonal matrix اللي عندنا هذا في مين في ايه الآن
+
+44
+00:04:32,830 --> 00:04:38,570
+بالدرجة اشوف C في ايه C اليومين الرقم 3يبقى
+
+45
+00:04:38,570 --> 00:04:44,450
+بالداجي الا تلاتة في المصوفة ايه؟ يبقى تلاتة في
+
+46
+00:04:44,450 --> 00:04:50,550
+المصوفة ايه؟ اتنين تلاتة واحد ناقص واحد ناقص اتنين
+
+47
+00:04:50,550 --> 00:04:58,290
+واحد زير واحد اتنين تلاتة يساويالتلاتة عندما
+
+48
+00:04:58,290 --> 00:05:03,090
+أضربها في المصوفة أضربها في جميع أناصر المصوفة
+
+49
+00:05:03,090 --> 00:05:08,250
+بالاستثناء يبقى تلاتة في اتنين بستة تلاتة في تلاتة
+
+50
+00:05:08,250 --> 00:05:15,070
+بتسعة تلاتة سالب تلاتة وهنا تلاتة وهنا سالب ستة
+
+51
+00:05:15,070 --> 00:05:20,070
+وهنا تلاتة في واحد بتلاتة وهنا Zero وهنا كمان Zero
+
+52
+00:05:20,070 --> 00:05:25,930
+وهنا تلاتة ستة تسعة بالشكل اللي عندنا هذاتعالى
+
+53
+00:05:25,930 --> 00:05:30,990
+قارنى بين النتجتين الاول ضربنا مصوفتين في بعض هنا
+
+54
+00:05:30,990 --> 00:05:36,370
+ضربنا الرقم في مصوشه و بتلاحظوا انها نتجتين اتنتين
+
+55
+00:05:36,370 --> 00:05:42,710
+are equal يبقى هذا معناه على طول الخط انه capital
+
+56
+00:05:42,710 --> 00:05:49,810
+C في ال A بده يساوي مين بده يساوي اللى هو تلاتة ا
+
+57
+00:05:49,810 --> 00:05:55,130
+مباشرةلأنه قال لي ايش بتقدر تقول عن النتيجة فبقول
+
+58
+00:05:55,130 --> 00:06:00,250
+له حصل ضرب ال scalar matrix A في ال A بدي يساوي
+
+59
+00:06:00,250 --> 00:06:04,870
+حصل ضرب 3 في A وهذا تطبيق مباشر على الكرولري تبع
+
+60
+00:06:04,870 --> 00:06:12,230
+المرة الماضيةننتقل الآن إلى تعريف جديد أو ثلاث
+
+61
+00:06:12,230 --> 00:06:17,890
+تعريفات وهي very important لأنها بتجيبلي معلومات
+
+62
+00:06:17,890 --> 00:06:24,330
+جديدة يعني مش درجة عندنا قبل ذلك معلومات جديدة
+
+63
+00:06:24,330 --> 00:06:30,250
+يبقى بدنا نيجي إلى definitions التعريف الأول بيقول
+
+64
+00:06:30,250 --> 00:06:44,840
+if ال a is aم في ان matrix م في ان matrix we
+
+65
+00:06:44,840 --> 00:06:58,160
+define we define the transpose a transpose of a
+
+66
+00:06:58,160 --> 00:07:01,460
+written
+
+67
+00:07:07,860 --> 00:07:23,020
+و يُكتب as a transpose to be the n by m matrix
+
+68
+00:07:23,020 --> 00:07:33,060
+whose
+
+69
+00:07:33,060 --> 00:07:33,880
+elements
+
+70
+00:07:39,760 --> 00:07:49,300
+الأشياء التي تسميها a i j ترانسبوز تسمي اي جي اي
+
+71
+00:07:49,300 --> 00:07:53,640
+او
+
+72
+00:07:53,640 --> 00:07:53,740
+اي اي اي اي اي اي اي اي اي اي اي اي
+
+73
+00:08:07,470 --> 00:08:14,970
+اللي هو اتنين تلاتة واحد خمسة zero zero سالب واحد
+
+74
+00:08:14,970 --> 00:08:26,290
+واحد واحد اتنين تلاتة اربعة then a transpose تساوي
+
+75
+00:08:26,290 --> 00:08:28,790
+اللي هو main
+
+76
+00:08:47,710 --> 00:08:56,930
+تعريف الأول تعريف الثاني تعريف
+
+77
+00:08:56,930 --> 00:09:08,380
+الثانيA matrix A A matrix A is called symmetric is
+
+78
+00:09:08,380 --> 00:09:17,380
+called symmetric if
+
+79
+00:09:17,380 --> 00:09:33,110
+A transpose تساوي ال A المرة تلاتةA matrix A
+
+80
+00:09:33,110 --> 00:09:46,790
+is called skew symmetric skew
+
+81
+00:09:46,790 --> 00:09:54,490
+symmetric if A transpose تساوي سلب A
+
+82
+00:10:06,490 --> 00:10:15,050
+example determine whether
+
+83
+00:10:15,050 --> 00:10:23,110
+the following matrices
+
+84
+00:10:23,110 --> 00:10:26,550
+are
+
+85
+00:10:26,550 --> 00:10:29,270
+symmetric
+
+86
+00:10:32,520 --> 00:10:43,280
+or skew symmetric أصوفة
+
+87
+00:10:43,280 --> 00:10:47,660
+A تساوي
+
+88
+00:10:47,660 --> 00:10:58,000
+واحد اتنين تلاتة واحد اتنين تلاتة اربع سالب اتنين
+
+89
+00:10:58,000 --> 00:11:11,730
+خمسة واحدبتساوي Zero سالب تلاتة اتنين Zero سالب
+
+90
+00:11:11,730 --> 00:11:19,190
+تلاتة تلاتة Zero سالب واحد ناقص واحد واحد Zero
+
+91
+00:11:19,190 --> 00:11:20,170
+بالشكل ان
+
+92
+00:12:02,920 --> 00:12:07,800
+يبقى بيجي الان لمصحوفة J ده ايه ده لم نتعامل معها
+
+93
+00:12:07,800 --> 00:12:16,540
+من قبل هذه المصحوفة كالتالية يبقى فيها M
+
+94
+00:12:16,540 --> 00:12:22,220
+من الصفوف و N من الأعمدة بنعرف the transpose of A
+
+95
+00:12:22,220 --> 00:12:28,180
+يعني مدور المصحوفة A او بيسموه منقول المصحوفة A
+
+96
+00:12:28,180 --> 00:12:33,710
+اعتقد في الثانوية كنت بيسموه مدور المصحوفة Aيبقى
+
+97
+00:12:33,710 --> 00:12:37,950
+الـ Transpose of A هو مضاور مصحوفة written as A و
+
+98
+00:12:37,950 --> 00:12:43,650
+بحط فجهة T و تقرأ A Transpose يعني Transpose of
+
+99
+00:12:43,650 --> 00:12:49,090
+Matrix A to be the N by M Matrix يبقى الصف بيصير
+
+100
+00:12:49,090 --> 00:12:56,070
+عمود و العمود مش بيصير صف يبقى ال N في Mن في m
+
+101
+00:12:56,070 --> 00:13:03,790
+matrix whose elements aij transpose هو aji يبقى مش
+
+102
+00:13:03,790 --> 00:13:06,730
+عادي أجيب ليه ال transpose تبع ال element ببدل
+
+103
+00:13:06,730 --> 00:13:10,330
+الصف عمود و العمود صف يعني ال answer كان في الصف
+
+104
+00:13:10,330 --> 00:13:14,390
+الثاني و العمود الأول بصير في الصف الأول و العمود
+
+105
+00:13:14,390 --> 00:13:19,030
+الثاني و هكذا نعطي مثال for example لو كانت
+
+106
+00:13:19,030 --> 00:13:23,110
+المصوفة اللي عندنا هذهبدي أجيب الـ A transpose
+
+107
+00:13:23,110 --> 00:13:28,470
+تبعها يبقى الصف الأول بدي أخليه العمود الأول الصف
+
+108
+00:13:28,470 --> 00:13:31,730
+الثاني بدي أخليه العمود التاني الصف التالت بدي
+
+109
+00:13:31,730 --> 00:13:36,790
+أخليه العمود التالت يبقى 2 3 1 5 هو العمود الأول
+
+110
+00:13:36,790 --> 00:13:42,230
+طلع 2 3 1 5 الصف الثاني بدي أخليه العمود التاني
+
+111
+00:13:42,230 --> 00:13:50,420
+يبقى 00-1 1 00-1 1لأن صفة تالت بتخلي العمود تلو 1
+
+112
+00:13:50,420 --> 00:13:56,420
+2 3 4 يكون 1 2 3 4 يبقى إذا خلت الصفوف أعمدة و
+
+113
+00:13:56,420 --> 00:14:01,060
+الأعمدة صفوف نظام المصوفة الأصلي كان M في N يبقى
+
+114
+00:14:01,060 --> 00:14:07,900
+نظام المصوفة الجديدة هو Nبنقلب الوضع يبقى هذا
+
+115
+00:14:07,900 --> 00:14:12,060
+بالنسبة للتعريف الأول التعريف الثاني symmetric
+
+116
+00:14:12,060 --> 00:14:17,360
+matrix يعني مصفوفة متماثلة بقول عنها وقت أشهر لو
+
+117
+00:14:17,360 --> 00:14:23,870
+جبت لها transpose طلعت main نفس المصفوفة تمامأذا
+
+118
+00:14:23,870 --> 00:14:27,950
+لو جبت لترانسبوز للمصروفة وطلع نفس المصروفة بقول
+
+119
+00:14:27,950 --> 00:14:32,410
+هذي اللي هو symmetric matrix اللي هو التعريف الأول
+
+120
+00:14:32,410 --> 00:14:37,170
+بدأجي للتعريف الثاني لو جبت لترانسبوز ل matrix A
+
+121
+00:14:37,170 --> 00:14:46,540
+طلع نفس المصروفة A بإشارةسالة يبقى متمثل
+
+122
+00:14:46,540 --> 00:14:56,700
+متخلف متمثل متخلف متمثل متخلف متمثل
+
+123
+00:14:56,700 --> 00:15:03,240
+متخلفيبقى matrix is called skew symmetric لو تمثل
+
+124
+00:15:03,240 --> 00:15:09,160
+متخلف F الـ A في الـ A transpose مش الـ A ناقص
+
+125
+00:15:09,160 --> 00:15:16,760
+واحد صلحيها بالله A transpose بده يساوي سالب A
+
+126
+00:15:16,760 --> 00:15:22,630
+يبقى إذا كان الـ A transpose يساوي سالب Aالان مثال
+
+127
+00:15:22,630 --> 00:15:25,390
+بيقول دي determine whether the following matrices
+
+128
+00:15:25,390 --> 00:15:29,570
+are symmetric or skew symmetric اكملي على كل
+
+129
+00:15:29,570 --> 00:15:34,130
+مصفوفة من هذه المصفوفات هل هي سيمتريك ولا سكيوي
+
+130
+00:15:34,130 --> 00:15:41,560
+سيمتريك نمسك المصفوفة الأولىيبقى بضاجي اخد ال a
+
+131
+00:15:41,560 --> 00:15:48,840
+transpose يزاود الصف الأول بيصير العمود الأول يبقى
+
+132
+00:15:48,840 --> 00:15:53,560
+اي واحد اتنين تلاتة الصف الثاني بيصير العمود
+
+133
+00:15:53,560 --> 00:16:06,310
+التاني يبقى اتنين اربعة سالب اتنينيبقى تلاتة
+
+134
+00:16:06,310 --> 00:16:10,870
+نقص اتنين خمسة بالشكل اللي عندنا هذا ايش رايك؟ وهي
+
+135
+00:16:10,870 --> 00:16:17,250
+المصوفة الأصلية؟صح ولا لأ؟ يبقى هذا معناه ان A
+
+136
+00:16:17,250 --> 00:16:22,230
+Transpose بده يساوي A يبقى A عبارة عن ايه؟
+
+137
+00:16:22,230 --> 00:16:30,310
+Symmetric Matrix يبقى هنا الـ A is a Symmetric
+
+138
+00:16:30,310 --> 00:16:33,530
+Matrix
+
+139
+00:16:33,530 --> 00:16:42,570
+يبقى مصوفا متمثلا andبالدالي للمصوفة B transpose
+
+140
+00:16:42,570 --> 00:16:49,010
+بدي اخل الصف الأول هو العمود الأول يبقى Zero سالب
+
+141
+00:16:49,010 --> 00:16:54,470
+تلاتة اتنين الصف التاني هو العمود التاني تلاتة
+
+142
+00:16:54,470 --> 00:16:58,890
+Zero سالب واحد الصف التالت هو العمود التالت يبقى
+
+143
+00:16:58,890 --> 00:17:04,270
+سالب واحد واحد Zero بالشكل اللي عنها هل هذا هو
+
+144
+00:17:04,270 --> 00:17:11,130
+المصوفة Bلأ طب خليني أجرب أخد سالب واحد عامل مشترك
+
+145
+00:17:11,130 --> 00:17:16,950
+يبقى لو جيت أخدت سالب واحد بيصير سالب هذا Zero زي
+
+146
+00:17:16,950 --> 00:17:23,370
+ما هو هذا سالب تلاتة هذا واحد هذا تلاتة هذا Zero
+
+147
+00:17:23,370 --> 00:17:30,830
+هذا سالب واحد هذا سالب اتنين هذا واحد هذا Zero هذه
+
+148
+00:17:30,830 --> 00:17:32,730
+هي المصوفة بيه ولا لأ؟
+
+149
+00:17:53,240 --> 00:17:59,260
+بترانسبوز هي الصف الأول Zero سالب تلاتة اتنين
+
+150
+00:17:59,260 --> 00:18:03,360
+تلاتة Zero سالب واحد سالب واحد واحد
+
+151
+00:18:06,280 --> 00:18:13,860
+استنى استنى شوية استنى شوية براجع كتابتها المصفوف
+
+152
+00:18:13,860 --> 00:18:21,140
+بيه عندنا Zero سالب تلاتة اتنين تلاتة Zero سالب
+
+153
+00:18:21,140 --> 00:18:27,020
+واحد سالب اتنين هذه من عندك هذه سالب اتنين Zero
+
+154
+00:18:27,020 --> 00:18:32,710
+واحد بس خطأ في الكتابةإذا الصف الأول هو الـ A يبقى
+
+155
+00:18:32,710 --> 00:18:40,090
+هذه transpose يبقى الصف الأول هو العمود الأول الصف
+
+156
+00:18:40,090 --> 00:18:47,170
+الثاني يبقى هذه بدها تصير سالب اتنينيبقى الصفت من
+
+157
+00:18:47,170 --> 00:18:52,930
+سلب اتنين واحد زيرو الان بداش ياخد سلب عمل مشترك
+
+158
+00:18:52,930 --> 00:19:00,770
+بيصير هادي اتنين تمام هادي اتنين و هادي تلاتة زيرو
+
+159
+00:19:00,770 --> 00:19:05,130
+سلب واحد و هادي سلب اتنين واحد زيرو اطلعيلي
+
+160
+00:19:05,130 --> 00:19:09,100
+المصوفة هذه هي اللي هي المصوفة اللي فوقيبقى هى
+
+161
+00:19:09,100 --> 00:19:13,320
+المصيفة اللى فوق بالضبط تماما يبقى هدى بدى يسوى
+
+162
+00:19:13,320 --> 00:19:19,740
+مين سالب بى إذا بيترانسبوز سوى تسالب بى يبقى هنا
+
+163
+00:19:19,740 --> 00:19:24,960
+بيساسكيوي
+
+164
+00:19:24,960 --> 00:19:29,940
+symmetric matrix
+
+165
+00:19:37,920 --> 00:19:43,380
+طيب مجرد ملاحظة على هذه المصوفة لو طلعنا للمصوفة A
+
+166
+00:19:43,380 --> 00:19:48,640
+ثم لمصوفة B ها لو بدى أستنتج السنتين قبل ما أبدأ
+
+167
+00:19:48,640 --> 00:19:53,340
+أشتغل باجي باطلع في المصوفة A لاحظ الصف الأول هو
+
+168
+00:19:53,340 --> 00:19:58,520
+العمود الأول العنصر هذا هو العنصر هذا و القطة
+
+169
+00:19:58,520 --> 00:20:03,110
+الرئيسية مش مشكلة مينما يكون يكونتمام؟ لماذا؟ لأن
+
+170
+00:20:03,110 --> 00:20:08,050
+under transpose كل العناصر القطرية تبقى كما هي هذا
+
+171
+00:20:08,050 --> 00:20:12,190
+ايه ده كانت مصوفة مربعة يبقى بتبقى العناصر كما هي
+
+172
+00:20:12,190 --> 00:20:15,970
+ماعناها مشكلة تعالى لأن المصوفة بيه ايش بتلاحظ على
+
+173
+00:20:15,970 --> 00:20:21,990
+القطر الرئيسي كله أصفرا يبقى في حالة ال skew ال
+
+174
+00:20:21,990 --> 00:20:27,030
+symmetric والمصوفة مربعة لازم يكونوا عناصر القطر
+
+175
+00:20:27,030 --> 00:20:33,590
+الرئيسي أصفراإتنان مشان اللي المصحوفة تطلع اللي هو
+
+176
+00:20:33,590 --> 00:20:37,950
+ال transpose هو نفسها لازم تكون المصحوفة عندى
+
+177
+00:20:37,950 --> 00:20:44,730
+مصحوفة مربعة تمام يبقى symmetric و skew symmetric
+
+178
+00:20:44,730 --> 00:20:49,280
+لازم الأصل تبقى مصحوفة مربعةالكلام اللى بقوله
+
+179
+00:20:49,280 --> 00:20:55,460
+هضطرك في صيغة الملاحظات التالية يعني لو جيبنالك
+
+180
+00:20:55,460 --> 00:20:59,020
+مصفوفة مستطيلة و قولنا لك هذه symmetric و الله
+
+181
+00:20:59,020 --> 00:21:03,000
+ماهياش symmetric من دون ما تشتغلي بدك تقول هذه
+
+182
+00:21:03,000 --> 00:21:08,360
+ماهياش symmetric لأن عدد الصفوف إذا ماسواش عدد
+
+183
+00:21:08,360 --> 00:21:13,480
+الأعمدة لما جيبلي transpose لايمكن تطلع المصفوفة
+
+184
+00:21:13,480 --> 00:21:20,830
+الأصلية بأي حال من الأحواليبقى الملاحظة كتالة
+
+185
+00:21:20,830 --> 00:21:28,890
+remark هجسمها
+
+186
+00:21:28,890 --> 00:21:40,090
+إلى ثلاث نقاط النقطة الأولى the symmetric and
+
+187
+00:21:40,090 --> 00:21:44,310
+skew symmetric
+
+188
+00:21:58,170 --> 00:22:04,870
+must be يجب
+
+189
+00:22:04,870 --> 00:22:14,290
+أن تكون a² matrix الملاحظة
+
+190
+00:22:14,290 --> 00:22:20,020
+الثانية دا دا يقول ال matrixof the diagonal
+
+191
+00:22:20,020 --> 00:22:30,200
+elements of
+
+192
+00:22:30,200 --> 00:22:34,040
+a
+
+193
+00:22:34,040 --> 00:22:45,820
+square matrix A and A transpose
+
+194
+00:22:48,290 --> 00:22:57,350
+are the same that
+
+195
+00:22:57,350 --> 00:23:04,890
+is أي أن الـ
+
+196
+00:23:04,890 --> 00:23:14,950
+AII transpose هو عبارة عن الـ AII for all I النقطة
+
+197
+00:23:14,950 --> 00:23:22,950
+الثالثةand askew symmetric and askew
+
+198
+00:23:22,950 --> 00:23:28,170
+symmetric and
+
+199
+00:23:28,170 --> 00:23:32,850
+askew symmetric matrix
+
+200
+00:23:32,850 --> 00:23:36,850
+the
+
+201
+00:23:36,850 --> 00:23:44,390
+main diagonal القطر
+
+202
+00:23:44,390 --> 00:23:54,360
+الرئيسيالـ main diagonal elements are
+
+203
+00:23:54,360 --> 00:24:12,320
+zero يبقى دائما وابدا بتكون أصفرا that is that
+
+204
+00:24:12,320 --> 00:24:26,040
+isاللي هو الـ AII بده يساوي 0 for all I بنجي
+
+205
+00:24:26,040 --> 00:24:33,540
+ليه some properties of
+
+206
+00:24:33,540 --> 00:24:39,980
+a transpose matrix
+
+207
+00:24:41,720 --> 00:24:54,900
+بعد خواص مدور المصفوفة four a square matrices
+
+208
+00:24:54,900 --> 00:24:59,140
+matrices
+
+209
+00:24:59,140 --> 00:25:05,140
+a and b we have
+
+210
+00:25:10,340 --> 00:25:16,300
+النقطة الأولى A Transpose زي ال Transpose بده
+
+211
+00:25:16,300 --> 00:25:24,480
+يساوي A itself نمرة اتنين A زي B Transpose بده
+
+212
+00:25:24,480 --> 00:25:34,940
+يساوي A Transpose زي B Transpose تلاتة A
+
+213
+00:25:34,940 --> 00:25:42,600
+Btranspose بدي يسوي بي ترانسبوز في ال a transpose
+
+214
+00:25:42,600 --> 00:25:58,900
+نمرة أربع four any scalar c c a كله transpose
+
+215
+00:25:58,900 --> 00:26:02,960
+بيسوي c في ال a transpose
+
+216
+00:26:13,180 --> 00:26:26,560
+example example one show that show
+
+217
+00:26:26,560 --> 00:26:34,100
+that if ال a is
+
+218
+00:26:38,460 --> 00:26:45,100
+square matrix then
+
+219
+00:27:11,840 --> 00:27:17,280
+نمرة A الـ
+
+220
+00:27:17,280 --> 00:27:25,060
+A في الـ A Transpose and الـ A زائد الـ A
+
+221
+00:27:25,060 --> 00:27:33,400
+Transpose are symmetric نمرة
+
+222
+00:27:33,400 --> 00:27:44,930
+Vنمر بي ال a ناقص ال a transpose as a skew
+
+223
+00:27:44,930 --> 00:27:46,610
+symmetric
+
+224
+00:28:26,180 --> 00:28:29,100
+نرجع الكلام اللى احنا كاتبينه هذا مرة تانية
+
+225
+00:28:29,100 --> 00:28:35,140
+نتعرضله تفصيليا ثم نذهب الى حل المثال الأول على
+
+226
+00:28:35,140 --> 00:28:36,320
+هذا الموضوع
+
+227
+00:28:42,630 --> 00:28:49,450
+مثوفة المتماثلة أو شبه المتماثلة أو المتماثلة
+
+228
+00:28:49,450 --> 00:28:54,370
+تماثلة المتخالف اتنين مصوفتين مربعتين ليش ان عدد
+
+229
+00:28:54,370 --> 00:28:58,530
+الصفوف يسوى عدد الأعمدة فإن جلبتها تصبح عدد الصفوف
+
+230
+00:28:58,530 --> 00:29:04,740
+يسوى عدد الأعمدة يجب أن تكون مصوفة مربعةالنقطة
+
+231
+00:29:04,740 --> 00:29:07,580
+التانية الـ diagonal matrix في ال square matrix A
+
+232
+00:29:07,580 --> 00:29:12,240
+والـ A transpose are the same نفس الشيء يبقى مسحنا
+
+233
+00:29:12,240 --> 00:29:18,100
+شوية تول مصفوفة لما نعملنا عناصر قطر الرئيسي A11,
+
+234
+00:29:18,440 --> 00:29:23,760
+A22, A33 وإن نزل كله بتظل العنصر لأن العنصر موقع
+
+235
+00:29:23,760 --> 00:29:28,380
+في الصف ونفس موقع في العمود يبقى هذا لايتغير
+
+236
+00:29:28,380 --> 00:29:32,540
+بتغيره من العناصر الأخرى لكن عناصر القطر الرئيسي
+
+237
+00:29:32,540 --> 00:29:33,780
+تبقى كما هي
+
+238
+00:29:38,310 --> 00:29:49,210
+العنصر الذي يقع في الصف I و العمود رقم I يبقى
+
+239
+00:29:49,210 --> 00:29:54,800
+العنصر نفسه لايتغيرالنقطة التالتة في الـ SQL
+
+240
+00:29:54,800 --> 00:29:57,140
+Symmetric Matrix of the mean ده يجب ان ال elements
+
+241
+00:29:57,140 --> 00:30:03,900
+كله ماله أسفارا يعني ال aii بده يساوي zero لكل
+
+242
+00:30:03,900 --> 00:30:08,300
+اللي هو العناصر i لما تجيب ال transpose برضه
+
+243
+00:30:08,300 --> 00:30:14,940
+بظلمين برضه zero zero يعني بتقدر تقول ال aii بده
+
+244
+00:30:14,940 --> 00:30:20,520
+يساوي zero بده يساوي ال ai transpose هذا والله هذا
+
+245
+00:30:20,520 --> 00:30:28,560
+كله أسفاراطيب فى ل .. ليه transpose هذا للمصفوفة
+
+246
+00:30:28,560 --> 00:30:33,600
+اللى Transpose Matrix لها بعض الخواصة فبقول لو كان
+
+247
+00:30:33,600 --> 00:30:39,680
+عندى a و b مصفوفة تانى مربعتان ف m a transpose
+
+248
+00:30:39,680 --> 00:30:42,740
+Transpose Transpose Transpose Transpose Transpose
+
+249
+00:30:42,740 --> 00:30:43,280
+Transpose Transpose Transpose Transpose Transpose
+
+250
+00:30:43,280 --> 00:30:43,520
+Transpose Transpose Transpose Transpose Transpose
+
+251
+00:30:43,520 --> 00:30:43,760
+Transpose Transpose Transpose Transpose Transpose
+
+252
+00:30:43,760 --> 00:30:50,040
+Transose Transose Transose Transose Transose
+
+253
+00:30:50,040 --> 00:30:50,560
+Transose Transose Transose Transose Transose
+
+254
+00:30:50,560 --> 00:30:50,720
+Transose Transose Transose Transose Transose
+
+255
+00:30:50,720 --> 00:30:50,780
+Transose Transose Transose Transose Transose
+
+256
+00:30:50,780 --> 00:30:51,950
+Transose Transose Transose Transoseيبقى بصير A
+
+257
+00:30:51,950 --> 00:30:56,710
+Transpose و Transpose هي مهم المصحوفة A لو كان A
+
+258
+00:30:56,710 --> 00:31:02,530
+زائد B Transpose جمعتهم ثم جبتلي Transpose تبعهم
+
+259
+00:31:02,530 --> 00:31:06,450
+تماما كما لو جبتلي Transpose للأولى و Transpose
+
+260
+00:31:06,450 --> 00:31:11,850
+للثانية و من ثم روحنا جمعنا هيعطيني نفس الناتجة
+
+261
+00:31:11,850 --> 00:31:15,810
+خاصية التالتة هذه بتختلف شوية هذه الأولانية
+
+262
+00:31:15,810 --> 00:31:19,870
+بالنسبة لعملية الجمع لكن التانية بالنسبة لعملية
+
+263
+00:31:19,870 --> 00:31:20,370
+الضرب
+
+264
+00:31:23,540 --> 00:31:32,500
+بنجلب وضع ال A و وضع ال B و نجلب
+
+265
+00:31:32,500 --> 00:31:33,260
+وضع ال A و نجلب وضع ال A و نجلب وضع ال B و نجلب
+
+266
+00:31:33,260 --> 00:31:34,920
+وضع ال A و نجلب وضع ال A و نجلب وضع ال A و نجلب
+
+267
+00:31:34,920 --> 00:31:37,080
+وضع ال A و نجلب وضع ال A و نجلب وضع ال A و نجلب
+
+268
+00:31:37,080 --> 00:31:37,480
+وضع ال A و نجلب وضع ال A و نجلب وضع ال A و نجلب
+
+269
+00:31:37,480 --> 00:31:44,310
+وضع ال A و نجلب وضع ال A و نطيب for any scalar C
+
+270
+00:31:44,310 --> 00:31:49,590
+يعني لأي عدد حقيقي الـC لو ضربت الـC في المصوفة
+
+271
+00:31:49,590 --> 00:31:55,570
+الـA و بعد ذلك جبتلها لترانسبوز تماما كما لو جبت
+
+272
+00:31:55,570 --> 00:31:58,970
+لترانسبوز لA و ضربت في ميهن الـC يعني الـconstant
+
+273
+00:31:58,970 --> 00:32:02,710
+ضربته قبل الترانسبوز والله بعد الترانسبوز على كل
+
+274
+00:32:02,710 --> 00:32:07,930
+الأمرين بيعطيني ميهن بيعطيني نفس النتيجةنعطي بعض
+
+275
+00:32:07,930 --> 00:32:12,830
+الأمثلة على كيفية تطبيق هذه الخاصة بيقول المثال هو
+
+276
+00:32:12,830 --> 00:32:17,550
+البيان إنه لو كانت اسمها صوفة مربعة يبقى المطلوب
+
+277
+00:32:17,550 --> 00:32:22,810
+الأول أثبتله إن الـA مضروبة في الـA transpose هي
+
+278
+00:32:22,810 --> 00:32:28,310
+symmetric وكذلك الـA زي الـA transpose هي man هي
+
+279
+00:32:28,310 --> 00:32:32,510
+symmetric هذا المطلوب الأول المطلوب التانيأثبت له
+
+280
+00:32:32,510 --> 00:32:35,990
+أن الـ A نقص الـ A Transpose هو Q أسم مترك
+
+281
+00:32:47,080 --> 00:32:51,720
+Symmetric يبقى بدي أخدلها لترانسبوز لما أخدلها
+
+282
+00:32:51,720 --> 00:32:57,240
+لترانسبوز بدي الناتج يطلع مين؟ المصفوف الأصلي ليه؟
+
+283
+00:32:57,240 --> 00:33:03,140
+A في A ترانسبوز بقوله كويس هذا ترانسبوز لمين؟
+
+284
+00:33:03,140 --> 00:33:07,160
+لحاصل الضرببيقول الـ A transpose اللي حصل الدرب
+
+285
+00:33:07,160 --> 00:33:12,400
+بدك تفكه و تقلب وضع كل واحدة فيهم يبقى هذه شو بدها
+
+286
+00:33:12,400 --> 00:33:18,240
+تصير A transpose A transpose في ال A transpose
+
+287
+00:33:18,240 --> 00:33:23,640
+يبقى هاي قلبنا الوضع تمام هذا الكلام جبته من وين؟
+
+288
+00:33:23,640 --> 00:33:30,620
+من ال property تلاتة من هذا جبته من ال property
+
+289
+00:33:30,620 --> 00:33:36,690
+تلاتةطيب هذا الان بدى يساوي A ترانسبوز ترانسبوز
+
+290
+00:33:36,690 --> 00:33:42,910
+بمين؟ بA في ال A ترانسبوز يبقى هذا property مين؟
+
+291
+00:33:42,910 --> 00:33:48,410
+one أول خاصية طيب إيش تفسيرك لهذه؟ هاي اللي بين
+
+292
+00:33:48,410 --> 00:33:52,110
+قوسين هي اللي طلعت عندها يبقى هذه معلها؟ symmetric
+
+293
+00:33:52,110 --> 00:33:58,390
+يبقى سواء اللي هو ال A في ال A ترانسبوز is
+
+294
+00:33:58,390 --> 00:34:00,770
+asymmetric
+
+295
+00:34:04,440 --> 00:34:12,620
+ماتريكس تمام بدنا نيجي and ال a زي ال a ترانسبوز
+
+296
+00:34:12,620 --> 00:34:18,180
+الكل ترانسبوز إذا
+
+297
+00:34:18,180 --> 00:34:21,400
+غيرت أثبت أنها تساوي اللي بينجو السين a زي a
+
+298
+00:34:21,400 --> 00:34:28,360
+ترانسبوز هيبقى بصير هاد a سيماتريك بقوله تمام باجي
+
+299
+00:34:28,360 --> 00:34:33,420
+برجع على الخاصية اللي عندنا هادىخاصية بيقول ا زائد
+
+300
+00:34:33,420 --> 00:34:38,540
+بي ترانسبوز يساوي ا ترانسبوز زائد بي ترانسبوز يبقى
+
+301
+00:34:38,540 --> 00:34:43,220
+بناء ان انا بقدر اقول له هذه ا ترانسبوز زائد ا
+
+302
+00:34:43,220 --> 00:34:46,620
+ترانسبوز ترانسبوز هذه property
+
+303
+00:34:49,830 --> 00:34:55,630
+property two تمام هذا الكلام يساوي a transpose
+
+304
+00:34:55,630 --> 00:35:00,150
+زائد a transpose ال transpose اللي you mean او هذه
+
+305
+00:35:00,150 --> 00:35:04,250
+property one الحين لما اقول يا بنات a transpose
+
+306
+00:35:04,250 --> 00:35:08,610
+زائد a والله a زائد transpose مش هي نفسها مش خدنا
+
+307
+00:35:08,610 --> 00:35:13,460
+عملية انجمع المصفات is commutativeيبقى بناء عليها
+
+308
+00:35:13,460 --> 00:35:20,440
+دي بدها تساوي A زائد A Transpose يبقى هنا سائل A
+
+309
+00:35:20,440 --> 00:35:34,220
+أقل زائد ال A زائد A Transpose is symmetric كويس
+
+310
+00:35:35,120 --> 00:35:41,240
+بعد ذلك قال اثبت لي ان ال A ناقص A ترانسبوز is S Q
+
+311
+00:35:41,240 --> 00:35:47,080
+سيماترك بقوله كويس يبقى بداجي ال A لنمرة B نمرة B
+
+312
+00:35:47,080 --> 00:35:53,120
+بداجي اخد له ال A ماينوس A ترانسبوز لكل ترانسبوز
+
+313
+00:35:56,760 --> 00:36:06,280
+هذه بقدر اقول وتساوي ا زائد ناقص واحد في ال a ا
+
+314
+00:36:06,280 --> 00:36:15,350
+transpose كله transpose صح ولا لا؟طب اطلعيلي هنا
+
+315
+00:36:15,350 --> 00:36:22,530
+لما يكون الرقم مضوب في ال a ناقص a transpose و هذه
+
+316
+00:36:22,530 --> 00:36:25,670
+ال transpose اللي برا هذا الكلام جيبته من أين يا
+
+317
+00:36:25,670 --> 00:36:30,450
+بنات؟ الخاصية أربعة يبقى هذا اللي هي property
+
+318
+00:36:30,450 --> 00:36:38,130
+أربعةبعد هيك بقدر ادخل Transpose على كل واحدة فيهم
+
+319
+00:36:38,130 --> 00:36:46,130
+يبقى هذا الكلام بده يساوي A Transpose زائد ناقص A
+
+320
+00:36:46,130 --> 00:36:54,850
+Transpose لكل Transpose هذه الخاصية من؟ الخاصية
+
+321
+00:36:54,850 --> 00:37:00,330
+التانية كيف نقولها؟ يبقى هذه property
+
+322
+00:37:06,420 --> 00:37:13,060
+two هذا الأن يبدو يساوي a ل Transpose زي ما هي
+
+323
+00:37:13,060 --> 00:37:18,380
+زائد الحين هذه ناقص a Transpose Transpose حسب
+
+324
+00:37:18,380 --> 00:37:25,520
+الخاصية الأولى يبقى هذا يبدو يساوي ناقص a فقط لا
+
+325
+00:37:25,520 --> 00:37:32,320
+غيريبقى هذا الكلام
+
+326
+00:37:32,320 --> 00:37:38,640
+يساويممكن اخد ناقص برا عامل مشترك من الكل يبقى لو
+
+327
+00:37:38,640 --> 00:37:44,320
+اخدت ناقص برا عامل مشترك من الكل بيظل a ناقص a
+
+328
+00:37:44,320 --> 00:37:49,280
+transpose يبقى معناته دي عبارة عن ايه اسكيوي
+
+329
+00:37:49,280 --> 00:37:57,100
+سيماتريك يبقى هنا السا ال a ناقص ال a transpose
+
+330
+00:38:11,590 --> 00:38:13,930
+بنعطي مثال
+
+331
+00:38:35,280 --> 00:38:43,180
+show that if ال
+
+332
+00:38:43,180 --> 00:38:53,060
+A and ال B are symmetric matrices
+
+333
+00:38:53,060 --> 00:38:53,780
+then
+
+334
+00:39:02,270 --> 00:39:14,510
+الـ A في B is symmetric if and only if ال
+
+335
+00:39:14,510 --> 00:39:17,470
+A في ال B بدي سوى ال B في ال A
+
+336
+00:39:31,610 --> 00:39:48,910
+علي بالكم السؤال
+
+337
+00:39:48,910 --> 00:39:53,520
+مرة تانيةبقول يبين إن لو كانت الـA والـB التنتين
+
+338
+00:39:53,520 --> 00:39:59,460
+symmetric يبقى حاصل ضربهم بيكون symmetric إذا كان
+
+339
+00:39:59,460 --> 00:40:03,000
+الـA في B بدي سوى الـB في A إذا كانوا commutative
+
+340
+00:40:03,000 --> 00:40:07,240
+والعكس بالعكس لأن هذه F and all F تعني إن البرهان
+
+341
+00:40:07,240 --> 00:40:14,440
+بدي يحصل في اتجاهينيبقى f and only f معناته لو كان
+
+342
+00:40:14,440 --> 00:40:18,340
+ال a في ال b بدي اسوي ال b في ال a يبقى بدنا نحاول
+
+343
+00:40:18,340 --> 00:40:23,920
+نثبته ان ال a و ال b are symmetric يبقى مشان ابرهن
+
+344
+00:40:23,920 --> 00:40:31,480
+يبقى assume يبقى بداجي اقوله assume افترض that ان
+
+345
+00:40:31,480 --> 00:40:36,680
+ال a and ال b are symmetric
+
+346
+00:40:43,590 --> 00:40:50,170
+بعد ذلك هذي معناها ان ال A Transpose بدي ساوي ال A
+
+347
+00:40:50,170 --> 00:40:57,570
+و ال B Transpose بدي ساوي ال Bهذه المعلومة انا بدي
+
+348
+00:40:57,570 --> 00:41:03,010
+استخدمها متى لازم ألقامها بيقول لي ايش ذنب ايه بيه
+
+349
+00:41:03,010 --> 00:41:08,910
+سيماتريك اف عنده الف يبقى انا بداجي اقول له اسيوم
+
+350
+00:41:08,910 --> 00:41:19,310
+افترض ذات ان ال a,b is symmetric ايش
+
+351
+00:41:19,310 --> 00:41:26,070
+بدي اثبتبدي اثبت انه a في b بدي سوى ال b في a يبقى
+
+352
+00:41:26,070 --> 00:41:34,530
+then ال a b transpose بدي سوى اللي هو ال a في ال b
+
+353
+00:41:35,740 --> 00:41:39,920
+مش هذا معنى لترانسبوز؟ انا فارض انه هذي symmetric
+
+354
+00:41:39,920 --> 00:41:44,640
+يبقى مناطق ال A B ترانسبوز بدي تسوى AB بدي ارجع
+
+355
+00:41:44,640 --> 00:41:52,300
+مرة تانية لمين لخواص ال A B ترانسبوز يبقى ال A B
+
+356
+00:41:52,300 --> 00:41:59,740
+ترانسبوز هي عبارة عن B ترانسبوز في ال A ترانسبوزو
+
+357
+00:41:59,740 --> 00:42:03,800
+هذي بده تساوي مين؟ بده تساوي A في الـB اللي عندنا
+
+358
+00:42:03,800 --> 00:42:09,420
+صحيح ولا لا؟ يبقى هذا معناه الـB transpose اللي هي
+
+359
+00:42:09,420 --> 00:42:13,880
+عبارة عن مين يا بناتي؟ B، بده اشيلها و احط مكانها
+
+360
+00:42:13,880 --> 00:42:19,560
+B الـA transpose هي عبارة عن مين؟ الـA، بده يساوي
+
+361
+00:42:19,560 --> 00:42:25,930
+مين؟وأظنها هو المطلوب خلصنا يبقى أخدت ال A بي ال
+
+362
+00:42:25,930 --> 00:42:30,890
+symmetric أثبت أن ال A بي يسوى ال B في ال A الآن
+
+363
+00:42:30,890 --> 00:42:35,910
+بدأي أعمل عملية عكسية يبقى بدأي أقول له conversely
+
+364
+00:42:35,910 --> 00:42:45,790
+و بالعكس assume that أن ال A في B بده يسوى ال B في
+
+365
+00:42:45,790 --> 00:42:48,110
+A إيش بده يثبت؟
+
+366
+00:42:50,990 --> 00:42:56,590
+بدي أثبت إن الـ A في B is symmetric صح ولا لأ يبقى
+
+367
+00:42:56,590 --> 00:43:05,570
+بداجي أخدله الـ A بي Transpose بدي أثبت له إن هذه
+
+368
+00:43:05,570 --> 00:43:10,470
+تساوي 100 في B إذا أثبت له إنها A في B بتنتهي
+
+369
+00:43:10,470 --> 00:43:21,000
+قصتنا بقوله كويس هذا الكلام يساوي الان كيف؟هذا الـ
+
+370
+00:43:21,000 --> 00:43:29,000
+A B Transpose بقدر أكتب بدالها B A Transpose يبقى
+
+371
+00:43:29,000 --> 00:43:35,240
+هذا B A Transpose ليش؟ لأن الـ B في الـ A هي الـ A
+
+372
+00:43:35,240 --> 00:43:41,280
+في الـ B صح ولا لا؟ طيب هذا الكلام حسب الخواص بدي
+
+373
+00:43:41,280 --> 00:43:48,850
+يسوي A Transpose B Transposeمظبوط؟ طيب هذا الكلام
+
+374
+00:43:48,850 --> 00:43:53,910
+بده يسوي A Transpose هي مين؟ ب A و B Transpose هي
+
+375
+00:43:53,910 --> 00:43:58,490
+مين؟ ب B يبجى بناء علي أخدنا A B Transpose طلعت
+
+376
+00:43:58,490 --> 00:44:02,670
+مين؟ ب A يبجى ال A في B is symmetric يبجى هذا
+
+377
+00:44:02,670 --> 00:44:12,330
+معناه أن ال A B is symmetric وهو المطلوبطيب لحد
+
+378
+00:44:12,330 --> 00:44:16,490
+هنا stop انتهى هذا ال section وإلى يكون أرقام
+
+379
+00:44:16,490 --> 00:44:24,070
+المسائل من exercises اتنين سبعة المسائل التالية
+
+380
+00:44:24,070 --> 00:44:29,030
+اتنين
+
+381
+00:44:29,030 --> 00:44:35,930
+سبعة المسائل من واحد لغاية تمانية و احداشر و
+
+382
+00:44:35,930 --> 00:44:46,520
+اتناشرواربعتاش ب وسي ب وسي
+
+383
+00:44:46,520 --> 00:44:53,080
+المرة
+
+384
+00:44:53,080 --> 00:44:56,900
+جاى بنبدأ ال section اللى بعده ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..15553d97e3f89883ac7a433fa40d0b0d56e0bf92
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/OshDqhIzcK8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4956, "start": 20.5, "end": 49.56, "text": "بسم الله الرحمن الرحيم الأخر حاجة أخدناها المرة اللي فيها كانت نظرية ونتيجة عليها وكانت النتيجة لو عندي diagonal matrix وهذه ال diagonal كانت scalar matrix وضربت ال scalar matrix من جهة الشمال في المصحوف أيه يسوى تماما الرقم اللي موجود في ال scalar matrix كما لو ضربته في مين في المصحوف أيه", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16247, 34740, 11331, 26108, 3660, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 13672, 1829, 8978, 11296, 25961, 2655, 8717, 19913, 2288, 10632, 4032, 29399, 1829, 7435, 3660, 25894, 11296, 4032, 41361, 2655, 28239, 31371, 7435, 3660, 45164, 18871, 16254, 21539, 8141, 37037, 24192, 2423, 21539, 25961, 2655, 39684, 8141, 4032, 11242, 25513, 2655, 2423, 39684, 8141, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 8978, 9673, 9381, 5016, 38688, 36632, 3224, 7251, 3794, 2407, 7578, 46811, 10943, 995, 34892, 4587, 2304, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 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"probability": 0.81280517578125}, {"start": 40.6, "end": 41.36, "word": " أيه", "probability": 0.6343994140625}, {"start": 41.36, "end": 42.22, "word": " يسوى", "probability": 0.7440185546875}, {"start": 42.22, "end": 42.8, "word": " تماما", "probability": 0.986328125}, {"start": 42.8, "end": 43.48, "word": " الرقم", "probability": 0.8943684895833334}, {"start": 43.48, "end": 43.78, "word": " اللي", "probability": 0.927001953125}, {"start": 43.78, "end": 44.34, "word": " موجود", "probability": 0.9871419270833334}, {"start": 44.34, "end": 44.52, "word": " في", "probability": 0.951171875}, {"start": 44.52, "end": 44.64, "word": " ال", "probability": 0.9619140625}, {"start": 44.64, "end": 45.04, "word": " scalar", "probability": 0.95849609375}, {"start": 45.04, "end": 45.62, "word": " matrix", "probability": 0.9677734375}, {"start": 45.62, "end": 46.04, "word": " كما", "probability": 0.88623046875}, {"start": 46.04, "end": 46.32, "word": " لو", "probability": 0.99609375}, {"start": 46.32, "end": 47.1, "word": " ضربته", "probability": 0.9694010416666666}, {"start": 47.1, "end": 47.68, "word": " في", "probability": 0.94677734375}, {"start": 47.68, "end": 47.98, "word": " مين", "probability": 0.59991455078125}, {"start": 47.98, "end": 48.16, "word": " في", "probability": 0.9013671875}, {"start": 48.16, "end": 48.92, "word": " المصحوف", "probability": 0.957275390625}, {"start": 48.92, "end": 49.56, "word": " أيه", "probability": 0.91796875}], "temperature": 1.0}, {"id": 2, "seek": 6577, "start": 49.95, "end": 65.77, "text": "فقلنا دياجونال متريكس أو ال scalar دياجونال متريكس C ضربناها في أيه؟ بدي نسوي الرقم C مضروب في أيه؟ اللي هو المصموم في أيه؟ هذا آخر ما كتبتيه المرة الماضية", "tokens": [5172, 4587, 1211, 8315, 11778, 1829, 26108, 11536, 6027, 44650, 16572, 4117, 3794, 34051, 2423, 39684, 11778, 1829, 26108, 11536, 6027, 44650, 16572, 4117, 3794, 383, 48812, 25513, 8315, 11296, 8978, 36632, 3224, 22807, 4724, 16254, 8717, 3794, 45865, 34892, 4587, 2304, 383, 3714, 11242, 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"probability": 0.60302734375}, {"start": 54.29, "end": 55.61, "word": " ضربناها", "probability": 0.938232421875}, {"start": 55.61, "end": 55.77, "word": " في", "probability": 0.89892578125}, {"start": 55.77, "end": 55.99, "word": " أيه؟", "probability": 0.6656087239583334}, {"start": 55.99, "end": 56.17, "word": " بدي", "probability": 0.57269287109375}, {"start": 56.17, "end": 56.59, "word": " نسوي", "probability": 0.5636393229166666}, {"start": 56.59, "end": 57.53, "word": " الرقم", "probability": 0.9568684895833334}, {"start": 57.53, "end": 58.09, "word": " C", "probability": 0.951171875}, {"start": 58.09, "end": 59.17, "word": " مضروب", "probability": 0.8603515625}, {"start": 59.17, "end": 59.47, "word": " في", "probability": 0.990234375}, {"start": 59.47, "end": 60.05, "word": " أيه؟", "probability": 0.7833658854166666}, {"start": 60.05, "end": 60.31, "word": " اللي", "probability": 0.9609375}, {"start": 60.31, "end": 60.65, "word": " هو", "probability": 0.98876953125}, {"start": 60.65, "end": 61.81, "word": " المصموم", "probability": 0.7198486328125}, {"start": 61.81, "end": 61.95, "word": " في", "probability": 0.9677734375}, {"start": 61.95, "end": 62.51, "word": " أيه؟", "probability": 0.8572591145833334}, {"start": 62.51, "end": 62.79, "word": " هذا", "probability": 0.9052734375}, {"start": 62.79, "end": 63.21, "word": " آخر", "probability": 0.84619140625}, {"start": 63.21, "end": 63.37, "word": " ما", "probability": 0.96142578125}, {"start": 63.37, "end": 63.95, "word": " كتبتيه", "probability": 0.97978515625}, {"start": 63.95, "end": 64.49, "word": " المرة", "probability": 0.951416015625}, {"start": 64.49, "end": 65.77, "word": " الماضية", "probability": 0.990234375}], "temperature": 1.0}, {"id": 3, "seek": 8123, "start": 65.98, "end": 81.24, "text": "بنعطي مثال على ذلك بقول لو كان المصروفة A هي المصروفة اللي قدامنا هذه والمصروفة C هي ال scalar matrix 30000030003", "tokens": [3555, 1863, 3615, 9566, 1829, 50113, 6027, 15844, 29910, 23275, 4724, 39648, 45164, 25961, 9673, 9381, 32887, 5172, 3660, 316, 39896, 9673, 9381, 32887, 5172, 3660, 13672, 1829, 12174, 3215, 10943, 8315, 29538, 16070, 2304, 9381, 32887, 5172, 3660, 383, 39896, 2423, 39684, 8141, 6641, 1360, 43160, 18], "avg_logprob": -0.3778698979591837, "compression_ratio": 1.4031007751937985, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 65.98, "end": 66.82, "word": "بنعطي", "probability": 0.601953125}, {"start": 66.82, "end": 67.34, "word": " مثال", "probability": 0.964599609375}, {"start": 67.34, "end": 67.72, "word": " على", "probability": 0.7021484375}, {"start": 67.72, "end": 68.16, "word": " ذلك", "probability": 0.947021484375}, {"start": 68.16, "end": 68.56, "word": " بقول", "probability": 0.4176025390625}, {"start": 68.56, "end": 68.82, "word": " لو", "probability": 0.7900390625}, {"start": 68.82, "end": 69.18, "word": " كان", "probability": 0.8955078125}, {"start": 69.18, "end": 70.02, "word": " المصروفة", "probability": 0.6865966796875}, {"start": 70.02, "end": 70.28, "word": " A", "probability": 0.49365234375}, {"start": 70.28, "end": 70.9, "word": " هي", "probability": 0.7822265625}, {"start": 70.9, "end": 71.6, "word": " المصروفة", "probability": 0.936328125}, {"start": 71.6, "end": 71.72, "word": " اللي", "probability": 0.83447265625}, {"start": 71.72, "end": 72.38, "word": " قدامنا", "probability": 0.9674072265625}, {"start": 72.38, "end": 72.68, "word": " هذه", "probability": 0.48046875}, {"start": 72.68, "end": 74.34, "word": " والمصروفة", "probability": 0.8680419921875}, {"start": 74.34, "end": 74.8, "word": " C", "probability": 0.80908203125}, {"start": 74.8, "end": 75.6, "word": " هي", "probability": 0.94482421875}, {"start": 75.6, "end": 75.8, "word": " ال", "probability": 0.705078125}, {"start": 75.8, "end": 76.34, "word": " scalar", "probability": 0.1917724609375}, {"start": 76.34, "end": 77.28, "word": " matrix", "probability": 0.96337890625}, {"start": 77.28, "end": 81.24, "word": " 30000030003", "probability": 0.40789794921875}], "temperature": 1.0}, {"id": 4, "seek": 10402, "start": 81.72, "end": 104.02, "text": "جالي هاتلي حصل ضرب المفتوحتين C كبتن في A و كذلك حصل ضرب الرقم تلاتة في المصفوفة A what can you say و إيش ممكن تقول عن النتائج اللي بنحصل عليها في كلا الأمرين الآن المصفوفة اللي عندي هذه تلاتة في أربع", "tokens": [7435, 6027, 1829, 8032, 9307, 20292, 11331, 36520, 48812, 25513, 9673, 5172, 2655, 2407, 33753, 9957, 383, 9122, 3555, 2655, 1863, 8978, 316, 4032, 9122, 8848, 23275, 11331, 36520, 48812, 25513, 34892, 4587, 2304, 6055, 1211, 9307, 3660, 8978, 9673, 9381, 5172, 38688, 3660, 316, 437, 393, 291, 584, 4032, 11933, 1829, 8592, 3714, 43020, 6055, 39648, 18871, 28239, 2655, 16373, 7435, 13672, 1829, 44945, 5016, 36520, 25894, 11296, 8978, 9122, 15040, 16247, 29973, 9957, 6024, 48506, 9673, 9381, 5172, 38688, 3660, 13672, 1829, 18871, 16254, 29538, 6055, 1211, 9307, 3660, 8978, 5551, 25513, 3615], "avg_logprob": -0.24446613931407532, "compression_ratio": 1.758974358974359, 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{"start": 94.34, "end": 94.88, "word": " تقول", "probability": 0.979736328125}, {"start": 94.88, "end": 95.38, "word": " عن", "probability": 0.99609375}, {"start": 95.38, "end": 96.44, "word": " النتائج", "probability": 0.9512939453125}, {"start": 96.44, "end": 96.6, "word": " اللي", "probability": 0.898193359375}, {"start": 96.6, "end": 97.16, "word": " بنحصل", "probability": 0.94970703125}, {"start": 97.16, "end": 97.74, "word": " عليها", "probability": 0.993896484375}, {"start": 97.74, "end": 98.28, "word": " في", "probability": 0.6318359375}, {"start": 98.28, "end": 98.68, "word": " كلا", "probability": 0.732666015625}, {"start": 98.68, "end": 99.38, "word": " الأمرين", "probability": 0.8875325520833334}, {"start": 99.38, "end": 100.18, "word": " الآن", "probability": 0.57794189453125}, {"start": 100.18, "end": 100.9, "word": " المصفوفة", "probability": 0.96201171875}, {"start": 100.9, "end": 101.04, "word": " اللي", "probability": 0.954833984375}, {"start": 101.04, "end": 101.44, "word": " عندي", "probability": 0.843994140625}, {"start": 101.44, "end": 101.88, "word": " هذه", "probability": 0.3447265625}, {"start": 101.88, "end": 103.1, "word": " تلاتة", "probability": 0.9647216796875}, {"start": 103.1, "end": 103.4, "word": " في", "probability": 0.9873046875}, {"start": 103.4, "end": 104.02, "word": " أربع", "probability": 0.8435872395833334}], "temperature": 1.0}, {"id": 5, "seek": 12957, "start": 104.23, "end": 129.57, "text": "تمام هذه المصفوفة عبارة عن ايش تلاتة في تلاتة اذا لا يمكن ضرب هذه المصفوفة تمام لا احنا بنضرب اذا C في A وليس A في C اذا اللي مطلوب هنا CA وليست AC فبعدين بقوله هنا solution", "tokens": [39237, 10943, 29538, 9673, 9381, 5172, 38688, 3660, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 1975, 15730, 20193, 7251, 43020, 48812, 25513, 29538, 9673, 9381, 5172, 38688, 3660, 46811, 10943, 20193, 1975, 5016, 8315, 44945, 11242, 25513, 1975, 15730, 383, 8978, 316, 4032, 20292, 3794, 316, 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"probability": 0.98486328125}, {"start": 109.11, "end": 109.43, "word": " اذا", "probability": 0.7108154296875}, {"start": 109.43, "end": 109.65, "word": " لا", "probability": 0.7236328125}, {"start": 109.65, "end": 110.21, "word": " يمكن", "probability": 0.8818359375}, {"start": 110.21, "end": 110.69, "word": " ضرب", "probability": 0.9912109375}, {"start": 110.69, "end": 111.29, "word": " هذه", "probability": 0.9716796875}, {"start": 111.29, "end": 113.37, "word": " المصفوفة", "probability": 0.98671875}, {"start": 113.37, "end": 114.55, "word": " تمام", "probability": 0.887939453125}, {"start": 114.55, "end": 117.07, "word": " لا", "probability": 0.214111328125}, {"start": 117.07, "end": 117.49, "word": " احنا", "probability": 0.9549153645833334}, {"start": 117.49, "end": 118.97, "word": " بنضرب", "probability": 0.77734375}, {"start": 118.97, "end": 119.33, "word": " اذا", "probability": 0.7353515625}, {"start": 119.33, "end": 119.77, "word": " C", "probability": 0.57275390625}, {"start": 119.77, "end": 120.09, "word": " في", "probability": 0.95166015625}, {"start": 120.09, "end": 120.27, "word": " A", "probability": 0.927734375}, {"start": 120.27, "end": 121.05, "word": " وليس", "probability": 0.9142252604166666}, {"start": 121.05, "end": 121.59, "word": " A", "probability": 0.884765625}, {"start": 121.59, "end": 121.77, "word": " في", "probability": 0.96875}, {"start": 121.77, "end": 122.13, "word": " C", "probability": 0.98095703125}, {"start": 122.13, "end": 123.03, "word": " اذا", "probability": 0.85888671875}, {"start": 123.03, "end": 123.61, "word": " اللي", "probability": 0.92724609375}, {"start": 123.61, "end": 124.07, "word": " مطلوب", "probability": 0.945068359375}, {"start": 124.07, "end": 124.35, "word": " هنا", "probability": 0.978515625}, {"start": 124.35, "end": 124.95, "word": " CA", "probability": 0.27880859375}, {"start": 124.95, "end": 126.27, "word": " وليست", "probability": 0.93359375}, {"start": 126.27, "end": 126.95, "word": " AC", "probability": 0.94287109375}, {"start": 126.95, "end": 127.95, "word": " فبعدين", "probability": 0.75213623046875}, {"start": 127.95, "end": 128.45, "word": " بقوله", "probability": 0.91845703125}, {"start": 128.45, "end": 128.73, "word": " هنا", "probability": 0.97314453125}, {"start": 128.73, "end": 129.57, "word": " solution", "probability": 0.931640625}], "temperature": 1.0}, {"id": 6, "seek": 15597, "start": 133.03, "end": 155.97, "text": "بناخد C في الـ A يبقى C اللي هي تلاتة Zero Zero Zero تلاتة Zero Zero تلاتة مضروبة في اتنين تلاتة واحد سالب واحد واحد سالب اتنين واحد Zero Zero واحد اتنين تلاتة", "tokens": [3555, 1863, 47283, 3215, 383, 8978, 2423, 39184, 316, 7251, 3555, 4587, 7578, 383, 13672, 1829, 39896, 6055, 1211, 9307, 3660, 17182, 17182, 17182, 6055, 1211, 9307, 3660, 17182, 17182, 6055, 1211, 9307, 3660, 3714, 11242, 32887, 49401, 8978, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 8608, 6027, 3555, 1975, 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"probability": 0.82745361328125}, {"start": 139.45, "end": 139.93, "word": " Zero", "probability": 0.203125}, {"start": 139.93, "end": 140.57, "word": " Zero", "probability": 0.81884765625}, {"start": 140.57, "end": 141.17, "word": " Zero", "probability": 0.94140625}, {"start": 141.17, "end": 141.97, "word": " تلاتة", "probability": 0.9580078125}, {"start": 141.97, "end": 142.59, "word": " Zero", "probability": 0.95361328125}, {"start": 142.59, "end": 143.67, "word": " Zero", "probability": 0.95849609375}, {"start": 143.67, "end": 144.75, "word": " تلاتة", "probability": 0.963623046875}, {"start": 144.75, "end": 145.55, "word": " مضروبة", "probability": 0.9307861328125}, {"start": 145.55, "end": 146.05, "word": " في", "probability": 0.94970703125}, {"start": 146.05, "end": 147.37, "word": " اتنين", "probability": 0.925537109375}, {"start": 147.37, "end": 148.23, "word": " تلاتة", "probability": 0.964599609375}, {"start": 148.23, "end": 148.71, "word": " واحد", "probability": 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"text": "يبقى هذه النظامة تلاتة في تلاتة وهذه تلاتة في أربع إذا يمكن ضرب هتين المصفوف هتين والنتج هو تلاتة في أربع يبقى لو جيت ضربت هذه المصفوف هيكون حاصل الضرب على الشكل التالي الصف الأول في العمود الأول تلاتة في اتنين في ستة والباقي", "tokens": [1829, 3555, 4587, 7578, 29538, 28239, 19913, 10943, 3660, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 37037, 24192, 6055, 1211, 9307, 3660, 8978, 5551, 25513, 3615, 11933, 15730, 7251, 43020, 48812, 25513, 8032, 2655, 9957, 9673, 9381, 5172, 38688, 8032, 2655, 9957, 16070, 29399, 7435, 31439, 6055, 1211, 9307, 3660, 8978, 5551, 25513, 3615, 7251, 3555, 4587, 7578, 45164, 10874, 36081, 48812, 25513, 2655, 29538, 9673, 9381, 5172, 38688, 39896, 30544, 11331, 33546, 1211, 6024, 114, 25513, 15844, 25124, 28820, 16712, 6027, 1829, 31767, 5172, 16247, 12610, 8978, 18863, 2304, 23328, 16247, 12610, 6055, 1211, 9307, 3660, 8978, 1975, 2655, 1863, 9957, 8978, 8608, 2655, 3660, 16070, 3555, 995, 38436], "avg_logprob": -0.16496128529573964, "compression_ratio": 2.248618784530387, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 156.45, "end": 157.09, "word": "يبقى", "probability": 0.82220458984375}, {"start": 157.09, "end": 157.31, "word": " هذه", "probability": 0.61328125}, {"start": 157.31, "end": 157.95, "word": " النظامة", "probability": 0.74951171875}, {"start": 157.95, "end": 158.45, "word": " تلاتة", "probability": 0.812744140625}, {"start": 158.45, "end": 158.57, "word": " في", "probability": 0.82470703125}, {"start": 158.57, "end": 159.17, "word": " تلاتة", "probability": 0.982421875}, {"start": 159.17, "end": 159.57, "word": " وهذه", "probability": 0.6971435546875}, {"start": 159.57, "end": 160.21, "word": " تلاتة", "probability": 0.9659423828125}, {"start": 160.21, "end": 160.37, "word": " في", "probability": 0.95556640625}, {"start": 160.37, "end": 160.85, "word": " أربع", "probability": 0.6814778645833334}, {"start": 160.85, "end": 161.45, "word": " إذا", "probability": 0.5775146484375}, {"start": 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"probability": 0.9697265625}, {"start": 174.37, "end": 174.81, "word": " العمود", "probability": 0.96923828125}, {"start": 174.81, "end": 175.21, "word": " الأول", "probability": 0.974609375}, {"start": 175.21, "end": 175.79, "word": " تلاتة", "probability": 0.9569091796875}, {"start": 175.79, "end": 175.95, "word": " في", "probability": 0.96337890625}, {"start": 175.95, "end": 176.47, "word": " اتنين", "probability": 0.953125}, {"start": 176.47, "end": 177.13, "word": " في", "probability": 0.25537109375}, {"start": 177.13, "end": 177.55, "word": " ستة", "probability": 0.9733072916666666}, {"start": 177.55, "end": 178.31, "word": " والباقي", "probability": 0.87158203125}], "temperature": 1.0}, {"id": 8, "seek": 20690, "start": 179.06, "end": 206.9, "text": "أصفرًا صفر الأول في العمود الثاني يبقى بالنظر بالتلاتة في تلاتة والباقي أصفرًا تلاتة في تلاتة بقداش بتسعة اللي بعده تلاتة في واحد بتلاتة وهذا سالب تلاتة يبقى هذا الصفر الأول بدأجي للصفر الثاني في العمود الأول Zero تلاتة في واحد بتلاتة والباقي Zero", "tokens": [10721, 9381, 5172, 2288, 14111, 995, 20328, 5172, 2288, 16247, 12610, 8978, 18863, 2304, 23328, 6024, 104, 7649, 1829, 7251, 3555, 4587, 7578, 20666, 1863, 19913, 2288, 20666, 2655, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 16070, 3555, 995, 38436, 5551, 9381, 5172, 2288, 14111, 995, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 4724, 28543, 33599, 39894, 3794, 27884, 13672, 1829, 39182, 3224, 6055, 1211, 9307, 3660, 8978, 36764, 24401, 39894, 1211, 9307, 3660, 37037, 15730, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 23758, 31767, 5172, 2288, 16247, 12610, 47525, 10721, 7435, 1829, 24976, 9381, 5172, 2288, 6024, 104, 7649, 1829, 8978, 18863, 2304, 23328, 16247, 12610, 17182, 6055, 1211, 9307, 3660, 8978, 36764, 24401, 39894, 1211, 9307, 3660, 16070, 3555, 995, 38436, 17182], "avg_logprob": -0.1513967848185337, "compression_ratio": 2.5314285714285716, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 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202.1, "word": " الأول", "probability": 0.970458984375}, {"start": 202.1, "end": 202.86, "word": " Zero", "probability": 0.369140625}, {"start": 202.86, "end": 203.88, "word": " تلاتة", "probability": 0.970947265625}, {"start": 203.88, "end": 204.02, "word": " في", "probability": 0.99365234375}, {"start": 204.02, "end": 204.54, "word": " واحد", "probability": 0.990966796875}, {"start": 204.54, "end": 205.64, "word": " بتلاتة", "probability": 0.9522705078125}, {"start": 205.64, "end": 206.44, "word": " والباقي", "probability": 0.9642333984375}, {"start": 206.44, "end": 206.9, "word": " Zero", "probability": 0.82470703125}], "temperature": 1.0}, {"id": 9, "seek": 22508, "start": 214.2, "end": 225.08, "text": "الصف الثاني في العمود التالت يبقى الصف الثاني في العمود الـ 0 سلب 6", "tokens": [6027, 9381, 5172, 6024, 104, 7649, 1829, 8978, 18863, 2304, 23328, 16712, 6027, 2655, 7251, 3555, 4587, 7578, 2423, 9381, 5172, 6024, 104, 7649, 1829, 8978, 18863, 2304, 23328, 2423, 39184, 1958, 8608, 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"probability": 0.98828125}, {"start": 267.53, "end": 267.77, "word": " ال", "probability": 0.76953125}, {"start": 267.77, "end": 268.17, "word": " scholar", "probability": 0.1201171875}, {"start": 268.17, "end": 268.81, "word": " diagonal", "probability": 0.66162109375}, {"start": 268.81, "end": 269.67, "word": " matrix", "probability": 0.955078125}, {"start": 269.67, "end": 270.37, "word": " اللي", "probability": 0.910400390625}, {"start": 270.37, "end": 270.75, "word": " عندنا", "probability": 0.972900390625}, {"start": 270.75, "end": 270.99, "word": " هذا", "probability": 0.467041015625}, {"start": 270.99, "end": 271.23, "word": " في", "probability": 0.908203125}, {"start": 271.23, "end": 271.51, "word": " مين", "probability": 0.781494140625}, {"start": 271.51, "end": 271.75, "word": " في", "probability": 0.89794921875}, {"start": 271.75, "end": 272.09, "word": " ايه", "probability": 0.7359212239583334}, {"start": 272.09, "end": 272.83, "word": " الآن", "probability": 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تلاتة ستة تسعة بالشكل اللي عندنا هذا", "tokens": [6027, 2655, 1211, 9307, 3660, 43242, 15042, 5551, 11242, 25513, 11296, 8978, 9673, 9381, 38688, 3660, 5551, 11242, 25513, 11296, 8978, 10874, 2304, 40228, 14739, 33546, 2288, 9673, 9381, 38688, 3660, 20666, 995, 14851, 12984, 1863, 16606, 7251, 3555, 4587, 7578, 6055, 1211, 9307, 3660, 8978, 1975, 2655, 1863, 9957, 4724, 14851, 3660, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 39894, 3794, 27884, 6055, 1211, 9307, 3660, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 37037, 8315, 6055, 1211, 9307, 3660, 37037, 8315, 8608, 6027, 3555, 8608, 2655, 3660, 37037, 8315, 6055, 1211, 9307, 3660, 8978, 36764, 24401, 39894, 1211, 9307, 3660, 37037, 8315, 17182, 37037, 8315, 9122, 2304, 7649, 17182, 37037, 8315, 6055, 1211, 9307, 3660, 8608, 2655, 3660, 6055, 3794, 27884, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758], "avg_logprob": -0.20054041084490323, "compression_ratio": 2.386243386243386, "no_speech_prob": 0.0, "words": [{"start": 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347.53, "end": 348.13, "word": " اللى", "probability": 0.684814453125}, {"start": 348.13, "end": 348.37, "word": " هو", "probability": 0.591796875}, {"start": 348.37, "end": 349.63, "word": " تلاتة", "probability": 0.91162109375}, {"start": 349.63, "end": 349.81, "word": " ا", "probability": 0.417724609375}, {"start": 349.81, "end": 350.89, "word": " مباشرة", "probability": 0.9822998046875}], "temperature": 1.0}, {"id": 15, "seek": 36735, "start": 351.27, "end": 367.35, "text": "لأنه قال لي ايش بتقدر تقول عن النتيجة فبقول له حصل ضرب ال scalar matrix A في ال A بدي يساوي حصل ضرب 3 في A وهذا تطبيق مباشر على الكرولري تبع المرة الماضية", "tokens": [1211, 33456, 3224, 50239, 32239, 1975, 1829, 8592, 39894, 28543, 2288, 6055, 39648, 18871, 28239, 31371, 7435, 3660, 6156, 3555, 39648, 46740, 11331, 36520, 48812, 25513, 2423, 39684, 8141, 316, 8978, 2423, 316, 4724, 16254, 7251, 3794, 995, 45865, 11331, 36520, 48812, 25513, 805, 8978, 316, 37037, 15730, 6055, 9566, 21292, 4587, 3714, 3555, 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{"start": 385.13, "end": 385.45, "word": " نيجي", "probability": 0.958251953125}, {"start": 385.45, "end": 385.67, "word": " إلى", "probability": 0.354248046875}, {"start": 385.67, "end": 386.41, "word": " definitions", "probability": 0.88330078125}, {"start": 386.41, "end": 388.85, "word": " التعريف", "probability": 0.9903564453125}, {"start": 388.85, "end": 389.59, "word": " الأول", "probability": 0.98779296875}, {"start": 389.59, "end": 390.25, "word": " بيقول", "probability": 0.9708658854166666}, {"start": 390.25, "end": 391.05, "word": " if", "probability": 0.251953125}, {"start": 391.05, "end": 392.91, "word": " ال", "probability": 0.79736328125}, {"start": 392.91, "end": 393.29, "word": " a", "probability": 0.290771484375}, {"start": 393.29, "end": 394.57, "word": " is", "probability": 0.94482421875}, {"start": 394.57, "end": 395.55, "word": " a", "probability": 0.767578125}], "temperature": 1.0}, {"id": 17, "seek": 42146, "start": 397.0, "end": 421.46, "text": "م في ان matrix م في ان matrix we define we define the transpose a transpose of a written", "tokens": [2304, 8978, 16472, 8141, 3714, 8978, 16472, 8141, 321, 6964, 321, 6964, 264, 25167, 257, 25167, 295, 257, 3720], "avg_logprob": -0.48437502086162565, "compression_ratio": 1.4202898550724639, "no_speech_prob": 0.0, "words": [{"start": 397.0, "end": 397.7, "word": "م", "probability": 0.57275390625}, {"start": 397.7, "end": 399.04, "word": " في", "probability": 0.71630859375}, {"start": 399.04, "end": 399.72, "word": " ان", "probability": 0.31591796875}, {"start": 399.72, "end": 402.04, "word": " matrix", "probability": 0.353271484375}, {"start": 402.04, "end": 402.6, "word": " م", "probability": 0.55908203125}, {"start": 402.6, "end": 402.92, "word": " في", "probability": 0.9150390625}, {"start": 402.92, "end": 403.34, "word": " ان", "probability": 0.85302734375}, {"start": 403.34, "end": 404.06, "word": " matrix", "probability": 0.89111328125}, {"start": 404.06, "end": 404.84, "word": " we", 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zero zero سالب واحد واحد واحد اتنين تلاتة اربعة then a transpose تساوي اللي هو main", "tokens": [6027, 20292, 31439, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 36764, 24401, 16490, 2304, 3794, 3660, 4018, 4018, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 550, 257, 25167, 6055, 3794, 995, 45865, 13672, 1829, 31439, 2135], "avg_logprob": -0.21338848506703095, "compression_ratio": 1.584070796460177, "no_speech_prob": 0.0, "words": [{"start": 487.47, "end": 487.91, "word": "اللي", "probability": 0.2952880859375}, {"start": 487.91, "end": 488.13, "word": " هو", "probability": 0.92236328125}, {"start": 488.13, "end": 488.75, "word": " اتنين", "probability": 0.902587890625}, {"start": 488.75, "end": 489.85, "word": " تلاتة", "probability": 0.8995361328125}, {"start": 489.85, "end": 490.53, "word": " واحد", "probability": 0.845458984375}, {"start": 490.53, "end": 491.93, "word": " خمسة", "probability": 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0.54833984375}, {"start": 504.53, "end": 506.29, "word": " تساوي", "probability": 0.9095458984375}, {"start": 506.29, "end": 508.35, "word": " اللي", "probability": 0.930908203125}, {"start": 508.35, "end": 508.39, "word": " هو", "probability": 0.98388671875}, {"start": 508.39, "end": 508.79, "word": " main", "probability": 0.5908203125}], "temperature": 1.0}, {"id": 21, "seek": 53759, "start": 527.71, "end": 537.59, "text": "تعريف الأول تعريف الثاني تعريف الثاني", "tokens": [2655, 3615, 16572, 5172, 16247, 12610, 37279, 16572, 5172, 6024, 104, 7649, 1829, 37279, 16572, 5172, 6024, 104, 7649, 1829], "avg_logprob": -0.14090401785714285, "compression_ratio": 1.6046511627906976, "no_speech_prob": 0.0, "words": [{"start": 527.71, "end": 529.11, "word": "تعريف", "probability": 0.8272705078125}, {"start": 529.11, "end": 529.51, "word": " الأول", "probability": 0.824462890625}, {"start": 529.51, "end": 530.67, "word": " تعريف", "probability": 0.8074544270833334}, {"start": 530.67, "end": 531.75, "word": " الثاني", "probability": 0.962158203125}, {"start": 531.75, "end": 536.93, "word": " تعريف", "probability": 0.96826171875}, {"start": 536.93, "end": 537.59, "word": " الثاني", "probability": 0.9058837890625}], "temperature": 1.0}, {"id": 22, "seek": 56605, "start": 538.94, "end": 566.06, "text": "A matrix A A matrix A is called symmetric is called symmetric if A transpose تساوي ال A المرة تلاتة", "tokens": [32, 8141, 316, 316, 8141, 316, 307, 1219, 32330, 307, 1219, 32330, 498, 316, 25167, 6055, 3794, 995, 45865, 2423, 316, 9673, 25720, 6055, 1211, 9307, 3660], "avg_logprob": -0.35797992455107824, "compression_ratio": 1.3181818181818181, "no_speech_prob": 0.0, "words": [{"start": 538.94, "end": 539.26, "word": "A", "probability": 0.410888671875}, {"start": 539.26, "end": 539.76, "word": " matrix", "probability": 0.666015625}, {"start": 539.76, "end": 540.34, "word": " A", "probability": 0.6865234375}, {"start": 540.34, "end": 541.28, "word": " A", "probability": 0.2239990234375}, {"start": 541.28, "end": 543.4, "word": " matrix", "probability": 0.8017578125}, {"start": 543.4, "end": 544.54, "word": " A", "probability": 0.85546875}, {"start": 544.54, "end": 545.94, "word": " is", "probability": 0.671875}, {"start": 545.94, "end": 546.26, "word": " called", "probability": 0.91796875}, {"start": 546.26, "end": 547.08, "word": " symmetric", "probability": 0.82763671875}, {"start": 547.08, "end": 548.38, "word": " is", "probability": 0.320556640625}, {"start": 548.38, "end": 550.8, "word": " called", "probability": 0.9169921875}, {"start": 550.8, "end": 553.26, "word": " symmetric", "probability": 0.8251953125}, {"start": 553.26, "end": 557.38, "word": " if", "probability": 0.81298828125}, {"start": 557.38, "end": 559.06, "word": " A", "probability": 0.89892578125}, {"start": 559.06, "end": 560.38, "word": " transpose", "probability": 0.64453125}, {"start": 560.38, "end": 562.02, "word": " تساوي", "probability": 0.7833251953125}, {"start": 562.02, "end": 562.62, "word": " ال", "probability": 0.791015625}, {"start": 562.62, "end": 563.06, "word": " A", "probability": 0.66552734375}, {"start": 563.06, "end": 565.32, "word": " المرة", "probability": 0.51702880859375}, {"start": 565.32, "end": 566.06, "word": " تلاتة", "probability": 0.909423828125}], "temperature": 1.0}, {"id": 23, "seek": 59449, "start": 567.57, "end": 594.49, "text": "A matrix A is called skew symmetric skew symmetric if A transpose تساوي سلب A", "tokens": [32, 8141, 316, 307, 1219, 8756, 86, 32330, 8756, 86, 32330, 498, 316, 25167, 6055, 3794, 995, 45865, 8608, 46152, 316], "avg_logprob": -0.30681817775422876, "compression_ratio": 1.0897435897435896, "no_speech_prob": 0.0, "words": [{"start": 567.57, "end": 567.97, "word": "A", "probability": 0.51513671875}, {"start": 567.97, "end": 568.83, "word": " matrix", "probability": 0.470458984375}, {"start": 568.83, "end": 573.11, "word": " A", "probability": 0.70947265625}, {"start": 573.11, "end": 574.09, "word": " is", "probability": 0.64794921875}, {"start": 574.09, "end": 575.85, "word": " called", "probability": 0.9248046875}, {"start": 575.85, "end": 576.89, "word": " skew", "probability": 0.72509765625}, {"start": 576.89, "end": 577.61, "word": " symmetric", "probability": 0.845703125}, {"start": 577.61, "end": 586.79, "word": " skew", "probability": 0.65869140625}, {"start": 586.79, "end": 587.61, "word": " symmetric", "probability": 0.8203125}, {"start": 587.61, "end": 588.29, "word": " if", "probability": 0.56201171875}, {"start": 588.29, "end": 589.51, "word": " A", "probability": 0.8984375}, {"start": 589.51, "end": 591.07, "word": " transpose", "probability": 0.81103515625}, {"start": 591.07, "end": 593.11, "word": " تساوي", "probability": 0.72802734375}, {"start": 593.11, "end": 593.99, "word": " سلب", "probability": 0.729736328125}, {"start": 593.99, "end": 594.49, "word": " A", "probability": 0.86376953125}], "temperature": 1.0}, {"id": 24, "seek": 62927, "start": 606.49, "end": 629.27, "text": "example determine whether the following matrices are symmetric", "tokens": [3121, 335, 781, 6997, 1968, 264, 3480, 32284, 366, 32330], "avg_logprob": -0.16912286931818182, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 606.49, "end": 607.89, "word": "example", "probability": 0.752197265625}, {"start": 607.89, "end": 609.29, "word": " determine", "probability": 0.90673828125}, {"start": 609.29, "end": 615.05, "word": " whether", "probability": 0.82958984375}, {"start": 615.05, "end": 617.41, "word": " the", "probability": 0.90966796875}, {"start": 617.41, "end": 619.57, "word": " following", "probability": 0.85693359375}, {"start": 619.57, "end": 623.11, "word": " matrices", "probability": 0.96044921875}, {"start": 623.11, "end": 626.55, "word": " are", "probability": 0.96826171875}, {"start": 626.55, "end": 629.27, "word": " symmetric", "probability": 0.86572265625}], "temperature": 1.0}, {"id": 25, "seek": 66108, "start": 632.52, "end": 661.08, "text": "or skew symmetric أصوفة A تساوي واحد اتنين تلاتة واحد اتنين تلاتة اربع سالب اتنين خمسة واحد", "tokens": [284, 8756, 86, 32330, 5551, 9381, 38688, 3660, 316, 6055, 3794, 995, 45865, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 3615, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 16490, 2304, 3794, 3660, 36764, 24401], "avg_logprob": -0.2137500002980232, "compression_ratio": 1.4705882352941178, "no_speech_prob": 0.0, "words": [{"start": 632.52, "end": 633.2, "word": "or", "probability": 0.2476806640625}, {"start": 633.2, "end": 635.28, "word": " skew", "probability": 0.67822265625}, {"start": 635.28, "end": 636.2, "word": " symmetric", "probability": 0.427001953125}, {"start": 636.2, "end": 643.28, "word": " أصوفة", "probability": 0.69769287109375}, {"start": 643.28, "end": 643.72, "word": " A", "probability": 0.5380859375}, {"start": 643.72, "end": 647.66, "word": " تساوي", "probability": 0.945068359375}, {"start": 647.66, "end": 650.4, "word": " واحد", "probability": 0.73291015625}, {"start": 650.4, "end": 650.96, "word": " اتنين", "probability": 0.945068359375}, {"start": 650.96, "end": 652.12, "word": " تلاتة", "probability": 0.9521484375}, {"start": 652.12, "end": 653.16, "word": " واحد", "probability": 0.617919921875}, {"start": 653.16, "end": 653.92, "word": " اتنين", "probability": 0.9710693359375}, {"start": 653.92, "end": 655.0, "word": " تلاتة", "probability": 0.994384765625}, {"start": 655.0, "end": 656.1, "word": " اربع", "probability": 0.7298177083333334}, {"start": 656.1, "end": 656.88, "word": " سالب", "probability": 0.7980143229166666}, {"start": 656.88, "end": 658.0, "word": " اتنين", "probability": 0.9759521484375}, {"start": 658.0, "end": 660.4, "word": " خمسة", "probability": 0.9615478515625}, {"start": 660.4, "end": 661.08, "word": " واحد", "probability": 0.8701171875}], "temperature": 1.0}, {"id": 26, "seek": 68017, "start": 661.99, "end": 680.17, "text": "بتساوي Zero سالب تلاتة اتنين Zero سالب تلاتة تلاتة Zero سالب واحد ناقص واحد واحد Zero بالشكل ان", "tokens": [3555, 2655, 3794, 995, 45865, 17182, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 17182, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 17182, 8608, 6027, 3555, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 36764, 24401, 17182, 20666, 8592, 28820, 16472], "avg_logprob": -0.23740434160037915, "compression_ratio": 1.7444444444444445, "no_speech_prob": 0.0, "words": [{"start": 661.99, "end": 663.53, "word": "بتساوي", "probability": 0.758642578125}, {"start": 663.53, "end": 666.49, "word": " Zero", "probability": 0.1231689453125}, {"start": 666.49, "end": 667.35, "word": " سالب", "probability": 0.661865234375}, {"start": 667.35, "end": 668.05, "word": " تلاتة", "probability": 0.8668212890625}, {"start": 668.05, "end": 668.63, "word": " اتنين", "probability": 0.8895263671875}, {"start": 668.63, "end": 671.29, "word": " Zero", "probability": 0.80615234375}, {"start": 671.29, "end": 671.73, "word": " سالب", "probability": 0.9405924479166666}, {"start": 671.73, "end": 671.99, "word": " تلاتة", "probability": 0.9366455078125}, {"start": 671.99, "end": 672.97, "word": " تلاتة", "probability": 0.7999267578125}, {"start": 672.97, "end": 673.99, "word": " Zero", "probability": 0.9189453125}, {"start": 673.99, "end": 674.67, "word": " سالب", "probability": 0.9874674479166666}, {"start": 674.67, "end": 675.27, "word": " واحد", "probability": 0.994140625}, {"start": 675.27, "end": 676.57, "word": " ناقص", "probability": 0.877685546875}, {"start": 676.57, "end": 677.17, "word": " واحد", "probability": 0.984130859375}, {"start": 677.17, "end": 677.99, "word": " واحد", "probability": 0.94677734375}, {"start": 677.99, "end": 679.19, "word": " Zero", "probability": 0.89697265625}, {"start": 679.19, "end": 679.87, "word": " بالشكل", "probability": 0.96484375}, {"start": 679.87, "end": 680.17, "word": " ان", "probability": 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16490, 1211, 2655, 31767, 5172, 38688, 5551, 25957, 41891, 4032, 16247, 25957, 41891, 20328, 5172, 38688, 8717, 19913, 10943, 9673, 9381, 38688, 3660, 16247, 9381, 20292, 25961, 376, 8978, 426, 7251, 3555, 4587, 7578, 8717, 19913, 10943, 9673, 9381, 38688, 3660, 25724, 16254, 41891, 31439, 426], "avg_logprob": -0.2234374951571226, "compression_ratio": 1.7808219178082192, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 827.18, "end": 827.8, "word": "لأن", "probability": 0.546142578125}, {"start": 827.8, "end": 828.48, "word": " صفة", "probability": 0.6338704427083334}, {"start": 828.48, "end": 828.96, "word": " تالت", "probability": 0.8289388020833334}, {"start": 828.96, "end": 829.44, "word": " بتخلي", "probability": 0.5564778645833334}, {"start": 829.44, "end": 829.88, "word": " العمود", "probability": 0.9152018229166666}, {"start": 829.88, "end": 830.22, "word": " تلو", "probability": 0.5205891927083334}, {"start": 830.22, "end": 830.42, "word": " 1", "probability": 0.2198486328125}, {"start": 830.42, "end": 830.7, "word": " 2", "probability": 0.556640625}, {"start": 830.7, "end": 831.08, "word": " 3", "probability": 0.9853515625}, {"start": 831.08, "end": 831.4, "word": " 4", "probability": 0.98974609375}, {"start": 831.4, "end": 831.62, "word": " يكون", "probability": 0.5667724609375}, {"start": 831.62, "end": 831.8, "word": " 1", "probability": 0.70166015625}, {"start": 831.8, "end": 832.14, "word": " 2", "probability": 0.97705078125}, {"start": 832.14, "end": 832.52, "word": " 3", "probability": 0.990234375}, {"start": 832.52, "end": 833.42, "word": " 4", "probability": 0.994140625}, {"start": 833.42, "end": 834.52, "word": " يبقى", "probability": 0.928466796875}, {"start": 834.52, "end": 834.76, "word": " إذا", "probability": 0.787841796875}, {"start": 834.76, "end": 835.28, "word": " خلت", "probability": 0.892578125}, {"start": 835.28, "end": 835.82, "word": " الصفوف", "probability": 0.9773763020833334}, {"start": 835.82, "end": 836.28, "word": " أعمدة", "probability": 0.8712565104166666}, {"start": 836.28, "end": 836.42, "word": " و", "probability": 0.62158203125}, {"start": 836.42, "end": 836.96, "word": " الأعمدة", "probability": 0.8702799479166666}, {"start": 836.96, "end": 837.56, "word": " صفوف", "probability": 0.9869791666666666}, {"start": 837.56, "end": 838.3, "word": " نظام", "probability": 0.9602864583333334}, {"start": 838.3, "end": 838.86, "word": " المصوفة", "probability": 0.9063720703125}, {"start": 838.86, "end": 839.36, "word": " الأصلي", "probability": 0.8180338541666666}, {"start": 839.36, "end": 839.78, "word": " كان", "probability": 0.974609375}, {"start": 839.78, "end": 840.14, "word": " M", "probability": 0.54150390625}, {"start": 840.14, "end": 840.36, "word": " في", "probability": 0.72119140625}, {"start": 840.36, "end": 840.68, "word": " N", "probability": 0.97314453125}, {"start": 840.68, "end": 841.06, "word": " يبقى", "probability": 0.941162109375}, {"start": 841.06, "end": 841.42, "word": " نظام", "probability": 0.9798177083333334}, {"start": 841.42, "end": 842.02, "word": " المصوفة", "probability": 0.9754638671875}, {"start": 842.02, "end": 842.48, "word": " الجديدة", "probability": 0.9002278645833334}, {"start": 842.48, "end": 842.74, "word": " هو", "probability": 0.826171875}, {"start": 842.74, "end": 843.36, "word": " N", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 32, "seek": 86256, "start": 843.66, "end": 862.56, "text": "بنقلب الوضع يبقى هذا بالنسبة للتعريف الأول التعريف الثاني symmetric matrix يعني مصفوفة متماثلة بقول عنها وقت أشهر لو جبت لها transpose طلعت main نفس المصفوفة تمام", "tokens": [3555, 1863, 4587, 46152, 2423, 2407, 11242, 3615, 7251, 3555, 4587, 7578, 23758, 20666, 1863, 35457, 3660, 24976, 2655, 3615, 16572, 5172, 16247, 12610, 16712, 3615, 16572, 5172, 6024, 104, 7649, 1829, 32330, 8141, 37495, 22653, 3714, 9381, 5172, 38688, 3660, 44650, 2304, 5718, 104, 37977, 4724, 39648, 18871, 11296, 4032, 38149, 5551, 8592, 3224, 2288, 45164, 10874, 3555, 2655, 5296, 11296, 25167, 23032, 1211, 34268, 2135, 8717, 36178, 9673, 9381, 5172, 38688, 3660, 46811, 10943], "avg_logprob": -0.26116070344850617, "compression_ratio": 1.5083798882681565, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 843.66, "end": 845.0, "word": "بنقلب", "probability": 0.60443115234375}, {"start": 845.0, "end": 846.98, "word": " الوضع", "probability": 0.803466796875}, {"start": 846.98, "end": 847.66, "word": " يبقى", "probability": 0.732086181640625}, {"start": 847.66, "end": 847.9, "word": " هذا", "probability": 0.88134765625}, {"start": 847.9, "end": 848.38, "word": " بالنسبة", "probability": 0.97607421875}, {"start": 848.38, "end": 849.22, "word": " للتعريف", "probability": 0.97587890625}, {"start": 849.22, "end": 849.68, "word": " الأول", "probability": 0.5894775390625}, {"start": 849.68, "end": 850.28, "word": " التعريف", "probability": 0.98681640625}, {"start": 850.28, "end": 850.9, "word": " الثاني", "probability": 0.9647216796875}, {"start": 850.9, "end": 852.06, "word": " symmetric", "probability": 0.38330078125}, {"start": 852.06, "end": 852.92, "word": " matrix", "probability": 0.9404296875}, {"start": 852.92, "end": 853.28, "word": " يعني", "probability": 0.822265625}, {"start": 853.28, "end": 853.96, "word": " مصفوفة", "probability": 0.94345703125}, {"start": 853.96, "end": 855.62, "word": " متماثلة", "probability": 0.8046875}, {"start": 855.62, "end": 856.36, "word": " بقول", "probability": 0.828857421875}, {"start": 856.36, "end": 856.66, "word": " عنها", "probability": 0.90869140625}, {"start": 856.66, "end": 856.94, "word": " وقت", "probability": 0.916015625}, {"start": 856.94, "end": 857.2, "word": " أشهر", "probability": 0.548126220703125}, {"start": 857.2, "end": 857.36, "word": " لو", "probability": 0.83837890625}, {"start": 857.36, "end": 857.7, "word": " جبت", "probability": 0.9749348958333334}, {"start": 857.7, "end": 857.96, "word": " لها", "probability": 0.480224609375}, {"start": 857.96, "end": 858.54, "word": " transpose", "probability": 0.70654296875}, {"start": 858.54, "end": 859.0, "word": " طلعت", "probability": 0.78369140625}, {"start": 859.0, "end": 859.38, "word": " main", "probability": 0.256103515625}, {"start": 859.38, "end": 860.58, "word": " نفس", "probability": 0.951171875}, {"start": 860.58, "end": 861.88, "word": " المصفوفة", "probability": 0.990625}, {"start": 861.88, "end": 862.56, "word": " تمام", "probability": 0.8828125}], "temperature": 1.0}, {"id": 33, "seek": 88033, "start": 863.39, "end": 880.33, "text": "أذا لو جبت لترانسبوز للمصروفة وطلع نفس المصروفة بقول هذي اللي هو symmetric matrix اللي هو التعريف الأول بدأجي للتعريف الثاني لو جبت لترانسبوز ل matrix A طلع نفس المصروفة A بإشارة", "tokens": [10721, 15730, 45164, 10874, 3555, 2655, 5296, 2655, 2288, 7649, 3794, 3555, 2407, 11622, 5296, 19528, 9381, 32887, 5172, 3660, 4032, 9566, 1211, 3615, 8717, 36178, 9673, 9381, 32887, 5172, 3660, 4724, 39648, 8032, 8848, 1829, 13672, 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"word": " نفس", "probability": 0.94091796875}, {"start": 867.09, "end": 867.61, "word": " المصروفة", "probability": 0.98349609375}, {"start": 867.61, "end": 867.95, "word": " بقول", "probability": 0.718505859375}, {"start": 867.95, "end": 868.77, "word": " هذي", "probability": 0.4593912760416667}, {"start": 868.77, "end": 869.07, "word": " اللي", "probability": 0.81591796875}, {"start": 869.07, "end": 869.31, "word": " هو", "probability": 0.9111328125}, {"start": 869.31, "end": 870.11, "word": " symmetric", "probability": 0.28076171875}, {"start": 870.11, "end": 870.97, "word": " matrix", "probability": 0.966796875}, {"start": 870.97, "end": 871.21, "word": " اللي", "probability": 0.9130859375}, {"start": 871.21, "end": 871.33, "word": " هو", "probability": 0.97412109375}, {"start": 871.33, "end": 871.91, "word": " التعريف", "probability": 0.9898681640625}, {"start": 871.91, "end": 872.41, "word": " الأول", "probability": 0.977783203125}, {"start": 872.41, "end": 873.45, "word": " بدأجي", "probability": 0.546844482421875}, {"start": 873.45, "end": 873.99, "word": " للتعريف", "probability": 0.9716796875}, {"start": 873.99, "end": 874.41, "word": " الثاني", "probability": 0.97314453125}, {"start": 874.41, "end": 874.63, "word": " لو", "probability": 0.94189453125}, {"start": 874.63, "end": 874.97, "word": " جبت", "probability": 0.99365234375}, {"start": 874.97, "end": 875.93, "word": " لترانسبوز", "probability": 0.897216796875}, {"start": 875.93, "end": 876.11, "word": " ل", "probability": 0.75146484375}, {"start": 876.11, "end": 876.75, "word": " matrix", "probability": 0.69091796875}, {"start": 876.75, "end": 877.17, "word": " A", "probability": 0.7548828125}, {"start": 877.17, "end": 878.05, "word": " طلع", "probability": 0.8502604166666666}, {"start": 878.05, "end": 878.41, "word": " نفس", "probability": 0.991943359375}, {"start": 878.41, "end": 879.09, "word": " المصروفة", "probability": 0.9869140625}, {"start": 879.09, "end": 879.25, "word": " A", "probability": 0.607421875}, {"start": 879.25, "end": 880.33, "word": " بإشارة", "probability": 0.857666015625}], "temperature": 1.0}, {"id": 34, "seek": 89790, "start": 880.8, "end": 897.9, "text": "سالة يبقى متمثل متخلف متمثل متخلف متمثل متخلف متمثل متخلف", "tokens": [3794, 6027, 3660, 7251, 3555, 4587, 7578, 44650, 2304, 12984, 1211, 44650, 9778, 46538, 44650, 2304, 12984, 1211, 44650, 9778, 46538, 44650, 2304, 12984, 1211, 44650, 9778, 46538, 44650, 2304, 12984, 1211, 44650, 9778, 46538], "avg_logprob": -0.3634982680281003, "compression_ratio": 2.234042553191489, "no_speech_prob": 0.0, "words": [{"start": 880.8, "end": 881.32, "word": "سالة", "probability": 0.4169921875}, {"start": 881.32, "end": 881.44, "word": " يبقى", "probability": 0.72747802734375}, {"start": 881.44, "end": 886.54, "word": " متمثل", "probability": 0.6461181640625}, {"start": 886.54, "end": 888.0, "word": " متخلف", "probability": 0.8937174479166666}, {"start": 888.0, "end": 889.42, "word": " متمثل", "probability": 0.6085662841796875}, {"start": 889.42, "end": 891.02, "word": " متخلف", "probability": 0.9635416666666666}, {"start": 891.02, "end": 893.52, "word": " متمثل", "probability": 0.845947265625}, {"start": 893.52, "end": 893.54, "word": " متخلف", "probability": 0.96875}, {"start": 893.54, "end": 896.7, "word": " متمثل", "probability": 0.90771484375}, {"start": 896.7, "end": 897.9, "word": " متخلف", "probability": 0.9685872395833334}], "temperature": 1.0}, {"id": 35, "seek": 92092, "start": 899.06, "end": 920.92, "text": "يبقى matrix is called skew symmetric لو تمثل متخلف F الـ A في الـ A transpose مش الـ A ناقص واحد صلحيها بالله A transpose بده يساوي سالب A يبقى إذا كان الـ A transpose يساوي سالب A", "tokens": [1829, 3555, 4587, 7578, 8141, 307, 1219, 8756, 86, 32330, 45164, 46811, 12984, 1211, 44650, 9778, 46538, 479, 2423, 39184, 316, 8978, 2423, 39184, 316, 25167, 37893, 2423, 39184, 316, 8717, 995, 4587, 9381, 36764, 24401, 20328, 1211, 5016, 1829, 11296, 20666, 43761, 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"probability": 0.9013671875}, {"start": 904.16, "end": 904.58, "word": " F", "probability": 0.30615234375}, {"start": 904.58, "end": 905.36, "word": " الـ", "probability": 0.425537109375}, {"start": 905.36, "end": 905.82, "word": " A", "probability": 0.47509765625}, {"start": 905.82, "end": 906.74, "word": " في", "probability": 0.595703125}, {"start": 906.74, "end": 907.08, "word": " الـ", "probability": 0.670654296875}, {"start": 907.08, "end": 907.26, "word": " A", "probability": 0.79736328125}, {"start": 907.26, "end": 907.9, "word": " transpose", "probability": 0.48095703125}, {"start": 907.9, "end": 908.24, "word": " مش", "probability": 0.68115234375}, {"start": 908.24, "end": 908.52, "word": " الـ", "probability": 0.844970703125}, {"start": 908.52, "end": 908.68, "word": " A", "probability": 0.78759765625}, {"start": 908.68, "end": 909.16, "word": " ناقص", "probability": 0.916748046875}, {"start": 909.16, "end": 909.62, "word": " واحد", "probability": 0.97705078125}, {"start": 909.62, "end": 911.26, "word": " صلحيها", "probability": 0.69588623046875}, {"start": 911.26, "end": 911.82, "word": " بالله", "probability": 0.880126953125}, {"start": 911.82, "end": 912.84, "word": " A", "probability": 0.56884765625}, {"start": 912.84, "end": 914.16, "word": " transpose", "probability": 0.703125}, {"start": 914.16, "end": 914.62, "word": " بده", "probability": 0.4429931640625}, {"start": 914.62, "end": 915.24, "word": " يساوي", "probability": 0.963134765625}, {"start": 915.24, "end": 916.34, "word": " سالب", "probability": 0.8580729166666666}, {"start": 916.34, "end": 916.76, "word": " A", "probability": 0.9287109375}, {"start": 916.76, "end": 917.76, "word": " يبقى", "probability": 0.927734375}, {"start": 917.76, "end": 917.96, "word": " إذا", "probability": 0.8017578125}, {"start": 917.96, "end": 918.3, "word": " كان", "probability": 0.986328125}, {"start": 918.3, "end": 918.52, "word": " الـ", "probability": 0.78662109375}, {"start": 918.52, "end": 918.72, "word": " A", "probability": 0.84765625}, {"start": 918.72, "end": 919.3, "word": " transpose", "probability": 0.8369140625}, {"start": 919.3, "end": 920.12, "word": " يساوي", "probability": 0.967529296875}, {"start": 920.12, "end": 920.78, "word": " سالب", "probability": 0.9724934895833334}, {"start": 920.78, "end": 920.92, "word": " A", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 36, "seek": 93815, "start": 921.49, "end": 938.15, "text": "الان مثال بيقول دي determine whether the following matrices are symmetric or skew symmetric اكملي على كل مصفوفة من هذه المصفوفات هل هي سيمتريك ولا سكيوي سيمتريك نمسك المصفوفة الأولى", "tokens": [6027, 7649, 50113, 6027, 4724, 1829, 39648, 11778, 1829, 6997, 1968, 264, 3480, 32284, 366, 32330, 420, 8756, 86, 32330, 1975, 24793, 20292, 15844, 28242, 3714, 9381, 5172, 38688, 3660, 9154, 29538, 9673, 9381, 5172, 38688, 9307, 8032, 1211, 39896, 8608, 32640, 2655, 16572, 4117, 49429, 8608, 4117, 1829, 45865, 8608, 32640, 2655, 16572, 4117, 8717, 2304, 3794, 4117, 9673, 9381, 5172, 38688, 3660, 16247, 12610, 7578], "avg_logprob": -0.25275734023136254, "compression_ratio": 1.5517241379310345, "no_speech_prob": 0.0, "words": [{"start": 921.49, "end": 922.01, "word": "الان", "probability": 0.6837158203125}, {"start": 922.01, "end": 922.63, "word": " مثال", "probability": 0.8515625}, {"start": 922.63, "end": 923.07, "word": " بيقول", "probability": 0.83056640625}, {"start": 923.07, "end": 923.37, "word": " دي", "probability": 0.502044677734375}, {"start": 923.37, "end": 923.79, "word": " determine", "probability": 0.64697265625}, {"start": 923.79, "end": 924.17, "word": " whether", "probability": 0.8505859375}, {"start": 924.17, "end": 924.47, "word": " the", "probability": 0.8759765625}, {"start": 924.47, "end": 924.83, "word": " following", "probability": 0.7451171875}, {"start": 924.83, "end": 925.39, "word": " matrices", "probability": 0.9716796875}, {"start": 925.39, "end": 925.99, "word": " are", "probability": 0.95947265625}, {"start": 925.99, "end": 926.43, "word": " symmetric", "probability": 0.85546875}, {"start": 926.43, "end": 926.91, "word": " or", "probability": 0.9482421875}, {"start": 926.91, "end": 927.39, "word": " skew", "probability": 0.801513671875}, {"start": 927.39, "end": 927.89, "word": " symmetric", "probability": 0.79443359375}, {"start": 927.89, "end": 929.05, "word": " اكملي", "probability": 0.624267578125}, {"start": 929.05, "end": 929.25, "word": " على", "probability": 0.8974609375}, {"start": 929.25, "end": 929.57, "word": " كل", "probability": 0.986328125}, {"start": 929.57, "end": 930.13, "word": " مصفوفة", "probability": 0.805029296875}, {"start": 930.13, "end": 930.29, "word": " من", "probability": 0.98046875}, {"start": 930.29, "end": 930.57, "word": " هذه", "probability": 0.9296875}, {"start": 930.57, "end": 931.21, "word": " المصفوفات", "probability": 0.8935546875}, {"start": 931.21, "end": 931.51, "word": " هل", "probability": 0.927734375}, {"start": 931.51, "end": 931.75, "word": " هي", "probability": 0.8974609375}, {"start": 931.75, "end": 932.73, "word": " سيمتريك", "probability": 0.6269775390625}, {"start": 932.73, "end": 933.29, "word": " ولا", "probability": 0.587890625}, {"start": 933.29, "end": 934.13, "word": " سكيوي", "probability": 0.768310546875}, {"start": 934.13, "end": 935.19, "word": " سيمتريك", "probability": 0.9099609375}, {"start": 935.19, "end": 936.01, "word": " نمسك", "probability": 0.9525146484375}, {"start": 936.01, "end": 937.03, "word": " المصفوفة", "probability": 0.9798828125}, {"start": 937.03, "end": 938.15, "word": " الأولى", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 37, "seek": 95618, "start": 938.58, "end": 956.18, "text": "يبقى بضاجي اخد ال a transpose يزاود الصف الأول بيصير العمود الأول يبقى اي واحد اتنين تلاتة الصف الثاني بيصير العمود التاني يبقى اتنين اربعة سالب اتنين", "tokens": [1829, 3555, 4587, 7578, 4724, 11242, 26108, 1829, 1975, 9778, 3215, 2423, 257, 25167, 7251, 11622, 995, 23328, 31767, 5172, 16247, 12610, 4724, 1829, 9381, 13546, 18863, 2304, 23328, 16247, 12610, 7251, 3555, 4587, 7578, 1975, 1829, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 31767, 5172, 6024, 104, 7649, 1829, 4724, 1829, 9381, 13546, 18863, 2304, 23328, 16712, 7649, 1829, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 8608, 6027, 3555, 1975, 2655, 1863, 9957], "avg_logprob": -0.2261813982594304, "compression_ratio": 1.8461538461538463, "no_speech_prob": 0.0, "words": [{"start": 938.58, "end": 939.3, "word": "يبقى", "probability": 0.79754638671875}, {"start": 939.3, "end": 940.02, "word": " بضاجي", "probability": 0.45892333984375}, {"start": 940.02, "end": 940.66, "word": " اخد", "probability": 0.7185872395833334}, {"start": 940.66, "end": 940.86, "word": " ال", "probability": 0.80029296875}, {"start": 940.86, "end": 941.56, "word": " a", "probability": 0.2529296875}, {"start": 941.56, "end": 942.64, "word": " transpose", "probability": 0.413818359375}, {"start": 942.64, "end": 944.08, "word": " يزاود", "probability": 0.69598388671875}, {"start": 944.08, "end": 945.14, "word": " الصف", "probability": 0.953857421875}, {"start": 945.14, "end": 946.02, "word": " الأول", "probability": 0.955322265625}, {"start": 946.02, "end": 946.86, "word": " بيصير", "probability": 0.75164794921875}, {"start": 946.86, "end": 947.44, "word": " العمود", "probability": 0.9402669270833334}, {"start": 947.44, "end": 948.04, "word": " الأول", "probability": 0.966064453125}, {"start": 948.04, "end": 948.84, "word": " يبقى", "probability": 0.945556640625}, {"start": 948.84, "end": 949.02, "word": " اي", "probability": 0.6541748046875}, {"start": 949.02, "end": 949.54, "word": " واحد", "probability": 0.945556640625}, {"start": 949.54, "end": 950.18, "word": " اتنين", "probability": 0.96630859375}, {"start": 950.18, "end": 950.9, "word": " تلاتة", "probability": 0.92919921875}, {"start": 950.9, "end": 951.9, "word": " الصف", "probability": 0.979736328125}, {"start": 951.9, "end": 952.56, "word": " الثاني", "probability": 0.95751953125}, {"start": 952.56, "end": 953.12, "word": " بيصير", "probability": 0.9312744140625}, {"start": 953.12, "end": 953.56, "word": " العمود", "probability": 0.9798177083333334}, {"start": 953.56, "end": 953.76, "word": " التاني", "probability": 0.5960286458333334}, {"start": 953.76, "end": 954.06, "word": " يبقى", "probability": 0.955810546875}, {"start": 954.06, "end": 954.58, "word": " اتنين", "probability": 0.9815673828125}, {"start": 954.58, "end": 955.2, "word": " اربعة", "probability": 0.83154296875}, {"start": 955.2, "end": 955.72, "word": " سالب", "probability": 0.59765625}, {"start": 955.72, "end": 956.18, "word": " اتنين", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 38, "seek": 97227, "start": 956.37, "end": 972.27, "text": "يبقى تلاتة نقص اتنين خمسة بالشكل اللي عندنا هذا ايش رايك؟ وهي المصوفة الأصلية؟", "tokens": [1829, 3555, 4587, 7578, 6055, 1211, 9307, 3660, 8717, 4587, 9381, 1975, 2655, 1863, 9957, 16490, 2304, 3794, 3660, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 1975, 1829, 8592, 12602, 47302, 4117, 22807, 37037, 1829, 9673, 9381, 38688, 3660, 16247, 36520, 10632, 22807], "avg_logprob": -0.26510415607028537, "compression_ratio": 1.3364485981308412, "no_speech_prob": 0.0, "words": [{"start": 956.37, "end": 957.15, "word": "يبقى", "probability": 0.8831787109375}, {"start": 957.15, "end": 966.31, "word": " تلاتة", "probability": 0.722625732421875}, {"start": 966.31, "end": 967.01, "word": " نقص", "probability": 0.716064453125}, {"start": 967.01, "end": 967.67, "word": " اتنين", "probability": 0.919189453125}, {"start": 967.67, "end": 968.33, "word": " خمسة", "probability": 0.8885498046875}, {"start": 968.33, "end": 968.83, "word": " بالشكل", "probability": 0.8235677083333334}, {"start": 968.83, "end": 968.99, "word": " اللي", "probability": 0.869873046875}, {"start": 968.99, "end": 969.31, "word": " عندنا", "probability": 0.8466796875}, {"start": 969.31, "end": 969.63, "word": " هذا", "probability": 0.689453125}, {"start": 969.63, "end": 970.39, "word": " ايش", "probability": 0.7119140625}, {"start": 970.39, "end": 970.67, "word": " رايك؟", "probability": 0.77337646484375}, {"start": 970.67, "end": 970.87, "word": " وهي", "probability": 0.783447265625}, {"start": 970.87, "end": 971.47, "word": " المصوفة", "probability": 0.9007568359375}, {"start": 971.47, "end": 972.27, "word": " الأصلية؟", "probability": 0.7821044921875}], "temperature": 1.0}, {"id": 39, "seek": 99775, "start": 972.83, "end": 997.75, "text": "صح ولا لأ؟ يبقى هذا معناه ان A Transpose بده يساوي A يبقى A عبارة عن ايه؟ Symmetric Matrix يبقى هنا الـ A is a Symmetric Matrix يبقى مصوفا متمثلا and", "tokens": [9381, 5016, 49429, 5296, 10721, 22807, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 316, 6531, 43501, 47525, 3224, 7251, 3794, 995, 45865, 316, 7251, 3555, 4587, 7578, 316, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 3224, 22807, 3902, 2174, 17475, 36274, 7251, 3555, 4587, 7578, 34105, 2423, 39184, 316, 307, 257, 3902, 2174, 17475, 36274, 7251, 3555, 4587, 7578, 3714, 9381, 38688, 995, 44650, 2304, 12984, 15040, 293], "avg_logprob": -0.30545774479986915, "compression_ratio": 1.4038461538461537, "no_speech_prob": 0.0, "words": [{"start": 972.83, "end": 973.19, "word": "صح", "probability": 0.70751953125}, {"start": 973.19, "end": 973.43, "word": " ولا", "probability": 0.72509765625}, {"start": 973.43, "end": 974.17, "word": " لأ؟", "probability": 0.6942545572916666}, {"start": 974.17, "end": 974.55, "word": " يبقى", "probability": 0.81451416015625}, {"start": 974.55, "end": 974.97, "word": " هذا", "probability": 0.93359375}, {"start": 974.97, "end": 975.77, "word": " معناه", "probability": 0.97412109375}, {"start": 975.77, "end": 976.63, "word": " ان", "probability": 0.564453125}, {"start": 976.63, "end": 977.25, "word": " A", "probability": 0.21533203125}, {"start": 977.25, "end": 978.51, "word": " Transpose", "probability": 0.6827392578125}, {"start": 978.51, "end": 979.01, "word": " بده", "probability": 0.32244873046875}, {"start": 979.01, "end": 979.91, "word": " يساوي", "probability": 0.9700927734375}, {"start": 979.91, "end": 980.31, "word": " A", "probability": 0.39306640625}, {"start": 980.31, "end": 981.15, "word": " يبقى", "probability": 0.8482666015625}, {"start": 981.15, "end": 981.33, "word": " A", "probability": 0.83251953125}, {"start": 981.33, "end": 981.71, "word": " عبارة", "probability": 0.956298828125}, {"start": 981.71, "end": 981.89, "word": " عن", "probability": 0.94921875}, {"start": 981.89, "end": 982.23, "word": " ايه؟", "probability": 0.6630859375}, {"start": 982.23, "end": 983.59, "word": " Symmetric", "probability": 0.773681640625}, {"start": 983.59, "end": 984.29, "word": " Matrix", "probability": 0.96142578125}, {"start": 984.29, "end": 985.35, "word": " يبقى", "probability": 0.9609375}, {"start": 985.35, "end": 985.73, "word": " هنا", "probability": 0.9521484375}, {"start": 985.73, "end": 987.41, "word": " الـ", "probability": 0.452392578125}, {"start": 987.41, "end": 987.53, "word": " A", "probability": 0.6875}, {"start": 987.53, "end": 988.31, "word": " is", "probability": 0.41259765625}, {"start": 988.31, "end": 988.93, "word": " a", "probability": 0.8291015625}, {"start": 988.93, "end": 990.31, "word": " Symmetric", "probability": 0.7645670572916666}, {"start": 990.31, "end": 993.53, "word": " Matrix", "probability": 0.98046875}, {"start": 993.53, "end": 995.37, "word": " يبقى", "probability": 0.9293212890625}, {"start": 995.37, "end": 995.93, "word": " مصوفا", "probability": 0.89404296875}, {"start": 995.93, "end": 996.71, "word": " متمثلا", "probability": 0.73468017578125}, {"start": 996.71, "end": 997.75, "word": " and", "probability": 0.5771484375}], "temperature": 1.0}, {"id": 40, "seek": 102560, "start": 999.25, "end": 1025.61, "text": "بالدالي للمصوفة B transpose بدي اخل الصف الأول هو العمود الأول يبقى Zero سالب تلاتة اتنين الصف التاني هو العمود التاني تلاتة Zero سالب واحد الصف التالت هو العمود التالت يبقى سالب واحد واحد Zero بالشكل اللي عنها هل هذا هو المصوفة B", "tokens": [3555, 6027, 3215, 6027, 1829, 5296, 19528, 9381, 38688, 3660, 363, 25167, 4724, 16254, 1975, 9778, 1211, 31767, 5172, 16247, 12610, 31439, 18863, 2304, 23328, 16247, 12610, 7251, 3555, 4587, 7578, 17182, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 31767, 5172, 16712, 7649, 1829, 31439, 18863, 2304, 23328, 16712, 7649, 1829, 6055, 1211, 9307, 3660, 17182, 8608, 6027, 3555, 36764, 24401, 31767, 5172, 16712, 6027, 2655, 31439, 18863, 2304, 23328, 16712, 6027, 2655, 7251, 3555, 4587, 7578, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 17182, 20666, 8592, 28820, 13672, 1829, 18871, 11296, 8032, 1211, 23758, 31439, 9673, 9381, 38688, 3660, 363], "avg_logprob": -0.20179835271160557, "compression_ratio": 2.2191011235955056, "no_speech_prob": 0.0, "words": [{"start": 999.25, "end": 999.97, "word": "بالدالي", "probability": 0.43916015625}, {"start": 999.97, "end": 1001.09, "word": " للمصوفة", "probability": 0.86748046875}, {"start": 1001.09, "end": 1001.47, "word": " B", "probability": 0.307861328125}, {"start": 1001.47, "end": 1002.57, "word": " transpose", "probability": 0.3974609375}, {"start": 1002.57, "end": 1003.47, "word": " بدي", "probability": 0.31396484375}, {"start": 1003.47, "end": 1003.83, "word": " اخل", "probability": 0.5550130208333334}, {"start": 1003.83, "end": 1004.45, "word": " الصف", "probability": 0.85009765625}, {"start": 1004.45, "end": 1005.09, "word": " الأول", "probability": 0.9111328125}, {"start": 1005.09, "end": 1005.33, "word": " هو", "probability": 0.91748046875}, {"start": 1005.33, "end": 1005.89, "word": " العمود", "probability": 0.94873046875}, {"start": 1005.89, "end": 1006.61, "word": " الأول", "probability": 0.9521484375}, {"start": 1006.61, "end": 1007.85, "word": " يبقى", "probability": 0.9246826171875}, {"start": 1007.85, "end": 1008.25, "word": " 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0.587646484375}, {"start": 1397.91, "end": 1398.77, "word": " symmetric", "probability": 0.69775390625}, {"start": 1398.77, "end": 1399.77, "word": " and", "probability": 0.398681640625}, {"start": 1399.77, "end": 1402.95, "word": " askew", "probability": 0.9371744791666666}, {"start": 1402.95, "end": 1404.95, "word": " symmetric", "probability": 0.7197265625}, {"start": 1404.95, "end": 1408.17, "word": " and", "probability": 0.67822265625}, {"start": 1408.17, "end": 1408.95, "word": " askew", "probability": 0.990234375}, {"start": 1408.95, "end": 1409.83, "word": " symmetric", "probability": 0.810546875}, {"start": 1409.83, "end": 1412.85, "word": " matrix", "probability": 0.93896484375}, {"start": 1412.85, "end": 1416.85, "word": " the", "probability": 0.716796875}, {"start": 1416.85, "end": 1418.43, "word": " main", "probability": 0.5888671875}, {"start": 1418.43, "end": 1420.63, "word": " diagonal", "probability": 0.9140625}, {"start": 1420.63, "end": 1424.39, "word": " القطر", "probability": 0.78759765625}, {"start": 1424.39, "end": 1425.31, "word": " الرئيسي", "probability": 0.97490234375}], "temperature": 1.0}, {"id": 56, "seek": 145292, "start": 1427.08, "end": 1452.92, "text": "الـ main diagonal elements are zero يبقى دائما وابدا بتكون أصفرا that is that is", "tokens": [6027, 39184, 2135, 21539, 4959, 366, 4018, 7251, 3555, 4587, 7578, 11778, 16373, 15042, 4032, 16758, 28259, 39894, 30544, 5551, 9381, 5172, 23557, 300, 307, 300, 307], "avg_logprob": -0.3546316942998341, "compression_ratio": 1.0388349514563107, "no_speech_prob": 0.0, "words": [{"start": 1427.08, "end": 1427.42, "word": "الـ", "probability": 0.76025390625}, {"start": 1427.42, "end": 1427.7, "word": " main", "probability": 0.189208984375}, {"start": 1427.7, "end": 1428.32, "word": " diagonal", "probability": 0.81494140625}, {"start": 1428.32, "end": 1430.46, "word": " elements", "probability": 0.72021484375}, {"start": 1430.46, "end": 1434.36, "word": " are", "probability": 0.859375}, {"start": 1434.36, "end": 1435.72, "word": " zero", "probability": 0.44677734375}, {"start": 1435.72, "end": 1437.46, "word": " يبقى", "probability": 0.8878173828125}, {"start": 1437.46, "end": 1437.88, "word": " دائما", "probability": 0.94921875}, {"start": 1437.88, "end": 1438.38, "word": " وابدا", "probability": 0.5048014322916666}, {"start": 1438.38, "end": 1439.04, "word": " بتكون", "probability": 0.84375}, {"start": 1439.04, "end": 1439.9, "word": " أصفرا", "probability": 0.810302734375}, {"start": 1439.9, "end": 1441.04, "word": " that", "probability": 0.3134765625}, {"start": 1441.04, "end": 1442.12, "word": " is", "probability": 0.95751953125}, {"start": 1442.12, "end": 1452.32, "word": " that", "probability": 0.75830078125}, {"start": 1452.32, "end": 1452.92, "word": " is", "probability": 0.970703125}], "temperature": 1.0}, {"id": 57, "seek": 147998, "start": 1454.4, "end": 1479.98, "text": "اللي هو الـ AII بده يساوي 0 for all I بنجي ليه some properties of a transpose matrix", "tokens": [6027, 20292, 31439, 2423, 39184, 7318, 40, 47525, 3224, 7251, 3794, 995, 45865, 1958, 337, 439, 286, 44945, 7435, 1829, 32239, 3224, 512, 7221, 295, 257, 25167, 8141], "avg_logprob": -0.4216055993376107, "compression_ratio": 1.0384615384615385, "no_speech_prob": 0.0, "words": [{"start": 1454.4, "end": 1454.92, "word": "اللي", "probability": 0.662353515625}, {"start": 1454.92, "end": 1455.3, "word": " هو", "probability": 0.89453125}, {"start": 1455.3, "end": 1455.96, "word": " الـ", "probability": 0.525146484375}, {"start": 1455.96, "end": 1457.72, "word": " AII", "probability": 0.6331787109375}, {"start": 1457.72, "end": 1458.6, "word": " بده", "probability": 0.252960205078125}, {"start": 1458.6, "end": 1459.18, "word": " يساوي", "probability": 0.91845703125}, {"start": 1459.18, "end": 1459.84, "word": " 0", "probability": 0.2239990234375}, {"start": 1459.84, "end": 1461.2, "word": " for", "probability": 0.796875}, {"start": 1461.2, "end": 1462.06, "word": " all", "probability": 0.92041015625}, {"start": 1462.06, "end": 1463.0, "word": " I", "probability": 0.763671875}, {"start": 1463.0, "end": 1466.04, "word": " بنجي", "probability": 0.6791178385416666}, {"start": 1466.04, "end": 1466.34, "word": " ليه", "probability": 0.629638671875}, {"start": 1466.34, "end": 1466.74, "word": " some", "probability": 0.69970703125}, {"start": 1466.74, "end": 1468.38, "word": " properties", "probability": 0.90234375}, {"start": 1468.38, "end": 1473.54, "word": " of", "probability": 0.54541015625}, {"start": 1473.54, "end": 1475.7, "word": " a", "probability": 0.92529296875}, {"start": 1475.7, "end": 1477.42, "word": " transpose", "probability": 0.67626953125}, {"start": 1477.42, "end": 1479.98, "word": " matrix", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 58, "seek": 150514, "start": 1481.72, "end": 1505.14, "text": "بعد خواص مدور المصفوفة four a square matrices matrices a and b we have", "tokens": [3555, 22488, 16490, 2407, 33546, 3714, 3215, 13063, 9673, 9381, 5172, 38688, 3660, 1451, 257, 3732, 32284, 32284, 257, 293, 272, 321, 362], "avg_logprob": -0.20589192708333334, "compression_ratio": 1.0348837209302326, "no_speech_prob": 0.0, "words": [{"start": 1481.72, "end": 1482.28, "word": "بعد", "probability": 0.878173828125}, {"start": 1482.28, "end": 1483.14, "word": " خواص", "probability": 0.8430989583333334}, {"start": 1483.14, "end": 1483.9, "word": " مدور", "probability": 0.9537760416666666}, {"start": 1483.9, "end": 1485.24, "word": " المصفوفة", "probability": 0.96845703125}, {"start": 1485.24, "end": 1487.58, "word": " four", "probability": 0.59326171875}, {"start": 1487.58, "end": 1489.62, "word": " a", "probability": 0.5048828125}, {"start": 1489.62, "end": 1491.7, "word": " square", "probability": 0.72802734375}, {"start": 1491.7, "end": 1494.9, "word": " matrices", "probability": 0.92724609375}, {"start": 1494.9, "end": 1499.14, "word": " matrices", "probability": 0.546875}, {"start": 1499.14, "end": 1500.46, "word": " a", "probability": 0.7236328125}, {"start": 1500.46, "end": 1502.4, "word": " and", "probability": 0.955078125}, {"start": 1502.4, "end": 1503.0, "word": " b", "probability": 0.42041015625}, {"start": 1503.0, "end": 1504.7, "word": " we", "probability": 0.8173828125}, {"start": 1504.7, "end": 1505.14, "word": " have", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 59, "seek": 153540, "start": 1510.34, "end": 1535.4, "text": "النقطة الأولى A Transpose زي ال Transpose بده يساوي A itself نمرة اتنين A زي B Transpose بده يساوي A Transpose زي B Transpose تلاتة A B", "tokens": [6027, 1863, 47432, 3660, 16247, 12610, 7578, 316, 6531, 43501, 30767, 1829, 2423, 6531, 43501, 47525, 3224, 7251, 3794, 995, 45865, 316, 2564, 8717, 2304, 25720, 1975, 2655, 1863, 9957, 316, 30767, 1829, 363, 6531, 43501, 47525, 3224, 7251, 3794, 995, 45865, 316, 6531, 43501, 30767, 1829, 363, 6531, 43501, 6055, 1211, 9307, 3660, 316, 363], "avg_logprob": -0.32976974520766944, "compression_ratio": 1.608695652173913, "no_speech_prob": 0.0, "words": [{"start": 1510.34, "end": 1511.02, "word": "النقطة", "probability": 0.781005859375}, {"start": 1511.02, "end": 1511.96, "word": " الأولى", "probability": 0.9705403645833334}, {"start": 1511.96, "end": 1513.12, "word": " A", "probability": 0.39892578125}, {"start": 1513.12, "end": 1514.08, "word": " Transpose", "probability": 0.6331787109375}, {"start": 1514.08, "end": 1514.26, "word": " زي", "probability": 0.41339111328125}, {"start": 1514.26, "end": 1514.34, "word": " ال", "probability": 0.447509765625}, {"start": 1514.34, "end": 1515.36, "word": " Transpose", "probability": 0.7666015625}, {"start": 1515.36, "end": 1516.3, "word": " بده", "probability": 0.28948974609375}, {"start": 1516.3, "end": 1516.76, "word": " يساوي", "probability": 0.82452392578125}, {"start": 1516.76, "end": 1517.12, "word": " A", "probability": 0.8212890625}, {"start": 1517.12, "end": 1517.78, "word": " itself", "probability": 0.346923828125}, {"start": 1517.78, "end": 1519.12, "word": " نمرة", "probability": 0.4289957682291667}, {"start": 1519.12, "end": 1519.76, "word": " اتنين", "probability": 0.9544677734375}, {"start": 1519.76, "end": 1520.94, "word": " A", "probability": 0.8486328125}, {"start": 1520.94, "end": 1521.44, "word": " زي", "probability": 0.6650390625}, {"start": 1521.44, "end": 1522.06, "word": " B", "probability": 0.483154296875}, {"start": 1522.06, "end": 1523.8, "word": " Transpose", "probability": 0.954833984375}, {"start": 1523.8, "end": 1524.48, "word": " بده", "probability": 0.747314453125}, {"start": 1524.48, "end": 1524.88, "word": " يساوي", "probability": 0.98779296875}, {"start": 1524.88, "end": 1525.26, "word": " A", "probability": 0.9462890625}, {"start": 1525.26, "end": 1526.32, "word": " Transpose", "probability": 0.93603515625}, {"start": 1526.32, "end": 1527.2, "word": " زي", "probability": 0.950439453125}, {"start": 1527.2, "end": 1527.72, "word": " B", "probability": 0.8017578125}, {"start": 1527.72, "end": 1529.0, "word": " Transpose", "probability": 0.94140625}, {"start": 1529.0, "end": 1531.9, "word": " تلاتة", "probability": 0.9400634765625}, {"start": 1531.9, "end": 1534.94, "word": " A", "probability": 0.354736328125}, {"start": 1534.94, "end": 1535.4, "word": " B", "probability": 0.6962890625}], "temperature": 1.0}, {"id": 60, "seek": 156296, "start": 1536.86, "end": 1562.96, "text": "transpose بدي يسوي بي ترانسبوز في ال a transpose نمرة أربع four any scalar c c a كله transpose بيسوي c في ال a transpose", "tokens": [24999, 43501, 4724, 16254, 7251, 3794, 45865, 4724, 1829, 6055, 2288, 7649, 3794, 3555, 2407, 11622, 8978, 2423, 257, 1145, 43501, 8717, 2304, 25720, 5551, 25513, 3615, 1451, 604, 39684, 269, 269, 257, 28242, 3224, 1145, 43501, 4724, 1829, 3794, 45865, 269, 8978, 2423, 257, 1145, 43501], "avg_logprob": -0.4680989645421505, "compression_ratio": 1.3644067796610169, "no_speech_prob": 0.0, "words": [{"start": 1536.86, "end": 1537.86, "word": "transpose", "probability": 0.613037109375}, {"start": 1537.86, "end": 1538.2, "word": " بدي", "probability": 0.249267578125}, {"start": 1538.2, "end": 1538.7, "word": " يسوي", "probability": 0.7610677083333334}, {"start": 1538.7, "end": 1539.16, "word": " بي", "probability": 0.5784912109375}, {"start": 1539.16, "end": 1540.24, "word": " ترانسبوز", "probability": 0.779296875}, {"start": 1540.24, "end": 1541.02, "word": " في", "probability": 0.53515625}, {"start": 1541.02, "end": 1541.28, "word": " ال", "probability": 0.87890625}, {"start": 1541.28, "end": 1541.54, "word": " a", "probability": 0.448974609375}, {"start": 1541.54, "end": 1542.6, "word": " transpose", "probability": 0.4761962890625}, {"start": 1542.6, "end": 1545.08, "word": " نمرة", "probability": 0.60205078125}, {"start": 1545.08, "end": 1546.32, "word": " أربع", "probability": 0.7742513020833334}, {"start": 1546.32, "end": 1547.64, "word": " four", "probability": 0.6455078125}, {"start": 1547.64, "end": 1549.04, "word": " any", "probability": 0.3935546875}, {"start": 1549.04, "end": 1550.58, "word": " scalar", "probability": 0.84033203125}, {"start": 1550.58, "end": 1552.64, "word": " c", "probability": 0.35986328125}, {"start": 1552.64, "end": 1555.64, "word": " c", "probability": 0.1307373046875}, {"start": 1555.64, "end": 1556.84, "word": " a", "probability": 0.8232421875}, {"start": 1556.84, "end": 1558.0, "word": " كله", "probability": 0.88818359375}, {"start": 1558.0, "end": 1558.9, "word": " transpose", "probability": 0.5838623046875}, {"start": 1558.9, "end": 1559.92, "word": " بيسوي", "probability": 0.7574462890625}, {"start": 1559.92, "end": 1560.46, "word": " c", "probability": 0.84326171875}, {"start": 1560.46, "end": 1561.12, "word": " في", "probability": 0.96142578125}, {"start": 1561.12, "end": 1561.36, "word": " ال", "probability": 0.92626953125}, {"start": 1561.36, "end": 1561.78, "word": " a", "probability": 0.9658203125}, {"start": 1561.78, "end": 1562.96, "word": " transpose", "probability": 0.709228515625}], "temperature": 1.0}, {"id": 61, "seek": 159410, "start": 1573.18, "end": 1594.1, "text": "example example one show that show that if ال a is", "tokens": [3121, 335, 781, 1365, 472, 855, 300, 855, 300, 498, 2423, 257, 307], "avg_logprob": -0.42578124148505075, "compression_ratio": 1.1304347826086956, "no_speech_prob": 0.0, "words": [{"start": 1573.1799999999998, "end": 1574.58, "word": "example", "probability": 0.6558024088541666}, {"start": 1574.58, "end": 1575.98, "word": " example", "probability": 0.35986328125}, {"start": 1575.98, "end": 1576.6, "word": " one", "probability": 0.75}, {"start": 1576.6, "end": 1579.38, "word": " show", "probability": 0.85400390625}, {"start": 1579.38, "end": 1580.88, "word": " that", "probability": 0.9404296875}, {"start": 1580.88, "end": 1586.56, "word": " show", "probability": 0.51904296875}, {"start": 1586.56, "end": 1587.4, "word": " that", "probability": 0.955078125}, {"start": 1587.4, "end": 1588.46, "word": " if", "probability": 0.73974609375}, {"start": 1588.46, "end": 1590.66, "word": " ال", "probability": 0.8466796875}, {"start": 1590.66, "end": 1591.14, "word": " a", "probability": 0.6689453125}, {"start": 1591.14, "end": 1594.1, "word": " is", "probability": 0.94140625}], "temperature": 1.0}, {"id": 62, "seek": 160510, "start": 1598.46, "end": 1605.1, "text": "square matrix then", "tokens": [33292, 543, 8141, 550], "avg_logprob": -0.683984375, "compression_ratio": 0.6923076923076923, "no_speech_prob": 0.0, "words": [{"start": 1598.4599999999998, "end": 1599.86, "word": "square", "probability": 0.5361328125}, {"start": 1599.86, "end": 1601.04, "word": " matrix", "probability": 0.9267578125}, {"start": 1601.04, "end": 1605.1, "word": " then", "probability": 0.60205078125}], "temperature": 1.0}, {"id": 63, "seek": 165372, "start": 1631.84, "end": 1653.72, "text": "نمرة A الـ A في الـ A Transpose and الـ A زائد الـ A Transpose are symmetric نمرة V", "tokens": [1863, 2304, 25720, 316, 2423, 39184, 316, 8978, 2423, 39184, 316, 6531, 43501, 293, 2423, 39184, 316, 30767, 16373, 3215, 2423, 39184, 316, 6531, 43501, 366, 32330, 8717, 2304, 25720, 691], "avg_logprob": -0.32397459633648396, "compression_ratio": 1.4155844155844155, "no_speech_prob": 0.0, "words": [{"start": 1631.84, "end": 1632.36, "word": "نمرة", "probability": 0.5110677083333334}, {"start": 1632.36, "end": 1632.82, "word": " A", "probability": 0.5458984375}, {"start": 1632.82, "end": 1637.28, "word": " الـ", "probability": 0.45574951171875}, {"start": 1637.28, "end": 1637.66, "word": " A", "probability": 0.83203125}, {"start": 1637.66, "end": 1638.64, "word": " في", "probability": 0.689453125}, {"start": 1638.64, "end": 1638.96, "word": " الـ", "probability": 0.890869140625}, {"start": 1638.96, "end": 1639.2, "word": " A", "probability": 0.91064453125}, {"start": 1639.2, "end": 1640.44, "word": " Transpose", "probability": 0.57672119140625}, {"start": 1640.44, "end": 1641.98, "word": " and", "probability": 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الأن يبدو يساوي a ل Transpose زي ما هي زائد الحين هذه ناقص a Transpose Transpose حسب الخاصية الأولى يبقى هذا يبدو يساوي ناقص a فقط لا غير", "tokens": [20534, 23758, 16247, 1863, 7251, 44510, 2407, 7251, 3794, 995, 45865, 257, 5296, 6531, 43501, 30767, 1829, 19446, 39896, 30767, 16373, 3215, 21542, 9957, 29538, 8717, 995, 4587, 9381, 257, 6531, 43501, 6531, 43501, 11331, 35457, 33962, 33546, 10632, 16247, 12610, 7578, 7251, 3555, 4587, 7578, 23758, 7251, 44510, 2407, 7251, 3794, 995, 45865, 8717, 995, 4587, 9381, 257, 6156, 47432, 20193, 32771, 13546], "avg_logprob": -0.3213942307692308, "compression_ratio": 1.5616438356164384, "no_speech_prob": 0.0, "words": [{"start": 2226.42, "end": 2227.48, "word": "two", "probability": 0.0771484375}, {"start": 2227.48, "end": 2228.54, "word": " هذا", "probability": 0.70458984375}, {"start": 2228.54, "end": 2229.0, "word": " الأن", "probability": 0.6746826171875}, {"start": 2229.0, "end": 2229.34, "word": " يبدو", "probability": 0.446044921875}, 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if ال A في ال B بدي سوى ال B في ال A", "tokens": [6027, 39184, 316, 8978, 363, 307, 32330, 498, 293, 787, 498, 2423, 316, 8978, 2423, 363, 4724, 16254, 8608, 2407, 7578, 2423, 363, 8978, 2423, 316], "avg_logprob": -0.26388889109646835, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 2342.27, "end": 2342.77, "word": "الـ", "probability": 0.781005859375}, {"start": 2342.77, "end": 2343.23, "word": " A", "probability": 0.55517578125}, {"start": 2343.23, "end": 2343.59, "word": " في", "probability": 0.71630859375}, {"start": 2343.59, "end": 2343.97, "word": " B", "probability": 0.845703125}, {"start": 2343.97, "end": 2345.07, "word": " is", "probability": 0.4404296875}, {"start": 2345.07, "end": 2347.21, "word": " symmetric", "probability": 0.744140625}, {"start": 2347.21, "end": 2349.97, "word": " if", "probability": 0.81884765625}, {"start": 2349.97, "end": 2350.27, "word": " and", "probability": 0.94189453125}, {"start": 2350.27, "end": 2350.61, "word": " only", "probability": 0.91748046875}, {"start": 2350.61, "end": 2351.17, "word": " if", "probability": 0.98291015625}, {"start": 2351.17, "end": 2354.51, "word": " ال", "probability": 0.583984375}, {"start": 2354.51, "end": 2354.93, "word": " A", "probability": 0.69140625}, {"start": 2354.93, "end": 2355.23, "word": " في", "probability": 0.96337890625}, {"start": 2355.23, "end": 2355.43, "word": " ال", "probability": 0.74755859375}, {"start": 2355.43, "end": 2355.65, "word": " B", "probability": 0.9716796875}, {"start": 2355.65, "end": 2356.01, "word": " بدي", "probability": 0.5205078125}, {"start": 2356.01, "end": 2356.43, "word": " سوى", "probability": 0.7097981770833334}, {"start": 2356.43, "end": 2356.57, "word": " ال", "probability": 0.86474609375}, {"start": 2356.57, "end": 2356.77, "word": " B", "probability": 0.96484375}, {"start": 2356.77, "end": 2356.97, "word": " في", "probability": 0.98046875}, {"start": 2356.97, "end": 2357.19, "word": " ال", "probability": 0.90869140625}, {"start": 2357.19, "end": 2357.47, "word": " A", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 93, "seek": 238955, "start": 2371.61, "end": 2389.55, "text": "علي بالكم السؤال مرة تانية", "tokens": [3615, 20292, 20666, 24793, 21136, 33604, 6027, 3714, 25720, 6055, 7649, 10632], "avg_logprob": -0.1887019184919504, "compression_ratio": 0.9411764705882353, "no_speech_prob": 0.0, "words": [{"start": 2371.61, "end": 2371.91, "word": "علي", "probability": 0.647216796875}, {"start": 2371.91, "end": 2372.29, "word": " بالكم", "probability": 0.809814453125}, {"start": 2372.29, "end": 2388.91, "word": " السؤال", "probability": 0.8505859375}, {"start": 2388.91, "end": 2389.17, "word": " مرة", "probability": 0.88720703125}, {"start": 2389.17, "end": 2389.55, "word": " تانية", "probability": 0.9401041666666666}], "temperature": 1.0}, {"id": 94, "seek": 240902, "start": 2390.44, "end": 2409.02, "text": "بقول يبين إن لو كانت الـA والـB التنتين symmetric يبقى حاصل ضربهم بيكون symmetric إذا كان الـA في B بدي سوى الـB في A إذا كانوا commutative والعكس بالعكس لأن هذه F and all F تعني إن البرهان بدي يحصل في اتجاهين", "tokens": [3555, 39648, 7251, 3555, 9957, 36145, 45164, 25961, 2655, 2423, 39184, 32, 16070, 39184, 33, 16712, 29399, 9957, 32330, 7251, 3555, 4587, 7578, 11331, 33546, 1211, 48812, 25513, 16095, 4724, 1829, 30544, 32330, 11933, 15730, 25961, 2423, 39184, 32, 8978, 363, 4724, 16254, 8608, 2407, 7578, 2423, 39184, 33, 8978, 316, 11933, 15730, 25961, 14407, 800, 325, 1166, 16070, 3615, 4117, 3794, 20666, 3615, 4117, 3794, 5296, 33456, 29538, 479, 293, 439, 479, 37279, 22653, 36145, 2423, 26890, 3224, 7649, 4724, 16254, 7251, 5016, 36520, 8978, 1975, 2655, 7435, 40294, 9957], "avg_logprob": -0.3055366711772006, "compression_ratio": 1.6372549019607843, "no_speech_prob": 0.0, "words": [{"start": 2390.44, "end": 2390.76, "word": "بقول", "probability": 0.296875}, {"start": 2390.76, "end": 2391.18, "word": " يبين", "probability": 0.5477701822916666}, {"start": 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{"start": 2402.36, "end": 2403.0, "word": " commutative", "probability": 0.7889811197916666}, {"start": 2403.0, "end": 2403.58, "word": " والعكس", "probability": 0.837646484375}, {"start": 2403.58, "end": 2404.2, "word": " بالعكس", "probability": 0.9234619140625}, {"start": 2404.2, "end": 2404.76, "word": " لأن", "probability": 0.765869140625}, {"start": 2404.76, "end": 2404.98, "word": " هذه", "probability": 0.280029296875}, {"start": 2404.98, "end": 2405.24, "word": " F", "probability": 0.63671875}, {"start": 2405.24, "end": 2405.52, "word": " and", "probability": 0.91845703125}, {"start": 2405.52, "end": 2405.72, "word": " all", "probability": 0.560546875}, {"start": 2405.72, "end": 2405.96, "word": " F", "probability": 0.83349609375}, {"start": 2405.96, "end": 2406.52, "word": " تعني", "probability": 0.76171875}, {"start": 2406.52, "end": 2406.78, "word": " إن", "probability": 0.48095703125}, {"start": 2406.78, "end": 2407.24, "word": " البرهان", "probability": 0.763916015625}, {"start": 2407.24, "end": 2407.52, "word": " بدي", "probability": 0.909423828125}, {"start": 2407.52, "end": 2407.86, "word": " يحصل", "probability": 0.72119140625}, {"start": 2407.86, "end": 2408.08, "word": " في", "probability": 0.96875}, {"start": 2408.08, "end": 2409.02, "word": " اتجاهين", "probability": 0.9478515625}], "temperature": 1.0}, {"id": 95, "seek": 243667, "start": 2409.54, "end": 2436.68, "text": "يبقى f and only f معناته لو كان ال a في ال b بدي اسوي ال b في ال a يبقى بدنا نحاول نثبته ان ال a و ال b are symmetric يبقى مشان ابرهن يبقى assume يبقى بداجي اقوله assume افترض that ان ال a and ال b are symmetric", "tokens": [1829, 3555, 4587, 7578, 283, 293, 787, 283, 20449, 8315, 47395, 45164, 25961, 2423, 257, 8978, 2423, 272, 4724, 16254, 24525, 45865, 2423, 272, 8978, 2423, 257, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 5016, 995, 12610, 8717, 12984, 3555, 47395, 16472, 2423, 257, 4032, 2423, 272, 366, 32330, 7251, 3555, 4587, 7578, 37893, 7649, 1975, 26890, 3224, 1863, 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"end": 2423.32, "word": " مشان", "probability": 0.7431640625}, {"start": 2423.32, "end": 2423.92, "word": " ابرهن", "probability": 0.7447509765625}, {"start": 2423.92, "end": 2424.56, "word": " يبقى", "probability": 0.9554443359375}, {"start": 2424.56, "end": 2425.48, "word": " assume", "probability": 0.818359375}, {"start": 2425.48, "end": 2425.88, "word": " يبقى", "probability": 0.9681396484375}, {"start": 2425.88, "end": 2426.42, "word": " بداجي", "probability": 0.581298828125}, {"start": 2426.42, "end": 2427.0, "word": " اقوله", "probability": 0.8614908854166666}, {"start": 2427.0, "end": 2428.0, "word": " assume", "probability": 0.89794921875}, {"start": 2428.0, "end": 2429.42, "word": " افترض", "probability": 0.9658203125}, {"start": 2429.42, "end": 2430.66, "word": " that", "probability": 0.8564453125}, {"start": 2430.66, "end": 2431.48, "word": " ان", "probability": 0.779296875}, {"start": 2431.48, "end": 2431.86, "word": " ال", "probability": 0.97216796875}, {"start": 2431.86, "end": 2432.28, "word": " a", "probability": 0.96728515625}, {"start": 2432.28, "end": 2433.18, "word": " and", "probability": 0.9462890625}, {"start": 2433.18, "end": 2434.22, "word": " ال", "probability": 0.97705078125}, {"start": 2434.22, "end": 2434.6, "word": " b", "probability": 0.97314453125}, {"start": 2434.6, "end": 2435.7, "word": " are", "probability": 0.9541015625}, {"start": 2435.7, "end": 2436.68, "word": " symmetric", "probability": 0.8291015625}], "temperature": 1.0}, {"id": 96, "seek": 245471, "start": 2443.59, "end": 2454.71, "text": "بعد ذلك هذي معناها ان ال A Transpose بدي ساوي ال A و ال B Transpose بدي ساوي ال B", "tokens": [3555, 22488, 29910, 23275, 8032, 8848, 1829, 20449, 8315, 11296, 16472, 2423, 316, 6531, 43501, 4724, 16254, 8608, 995, 45865, 2423, 316, 4032, 2423, 363, 6531, 43501, 4724, 16254, 8608, 995, 45865, 2423, 363], "avg_logprob": -0.5316964217594692, "compression_ratio": 1.4578313253012047, "no_speech_prob": 0.0, "words": [{"start": 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2499.3, "word": " هذي", "probability": 0.4981282552083333}, {"start": 2499.3, "end": 2499.92, "word": " symmetric", "probability": 0.338134765625}, {"start": 2499.92, "end": 2500.66, "word": " يبقى", "probability": 0.92236328125}, {"start": 2500.66, "end": 2501.08, "word": " مناطق", "probability": 0.5330810546875}, {"start": 2501.08, "end": 2501.26, "word": " ال", "probability": 0.7841796875}, {"start": 2501.26, "end": 2501.5, "word": " A", "probability": 0.26904296875}, {"start": 2501.5, "end": 2501.8, "word": " B", "probability": 0.64892578125}, {"start": 2501.8, "end": 2502.52, "word": " ترانسبوز", "probability": 0.88232421875}, {"start": 2502.52, "end": 2502.78, "word": " بدي", "probability": 0.3663330078125}, {"start": 2502.78, "end": 2503.2, "word": " تسوى", "probability": 0.5916748046875}, {"start": 2503.2, "end": 2503.6, "word": " AB", "probability": 0.64990234375}, {"start": 2503.6, "end": 2504.14, "word": " بدي", "probability": 0.6937255859375}, {"start": 2504.14, "end": 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"probability": 0.71484375}, {"start": 2641.41, "end": 2642.27, "word": " يبجى", "probability": 0.96533203125}, {"start": 2642.27, "end": 2642.67, "word": " هذا", "probability": 0.9814453125}, {"start": 2642.67, "end": 2643.47, "word": " معناه", "probability": 0.9806315104166666}, {"start": 2643.47, "end": 2644.23, "word": " أن", "probability": 0.677734375}, {"start": 2644.23, "end": 2644.59, "word": " ال", "probability": 0.8818359375}, {"start": 2644.59, "end": 2644.93, "word": " A", "probability": 0.93701171875}, {"start": 2644.93, "end": 2645.47, "word": " B", "probability": 0.255615234375}, {"start": 2645.47, "end": 2646.45, "word": " is", "probability": 0.87744140625}, {"start": 2646.45, "end": 2647.77, "word": " symmetric", "probability": 0.810546875}, {"start": 2647.77, "end": 2649.91, "word": " وهو", "probability": 0.80419921875}, {"start": 2649.91, "end": 2650.43, "word": " المطلوب", "probability": 0.9512939453125}], "temperature": 1.0}, {"id": 105, "seek": 267695, "start": 2651.65, "end": 2676.95, "text": "طيب لحد هنا stop انتهى هذا ال section وإلى يكون أرقام المسائل من exercises اتنين سبعة المسائل التالية اتنين سبعة المسائل من واحد لغاية تمانية و احداشر و اتناشر", "tokens": [9566, 1829, 3555, 5296, 24401, 34105, 1590, 16472, 47395, 7578, 23758, 2423, 3541, 4032, 28814, 23942, 7251, 30544, 5551, 2288, 4587, 10943, 9673, 3794, 16373, 1211, 9154, 11900, 1975, 2655, 1863, 9957, 8608, 3555, 27884, 9673, 3794, 16373, 1211, 16712, 6027, 10632, 1975, 2655, 1863, 9957, 8608, 3555, 27884, 9673, 3794, 16373, 1211, 9154, 36764, 24401, 5296, 17082, 995, 10632, 46811, 7649, 10632, 4032, 1975, 24401, 33599, 2288, 4032, 1975, 2655, 1863, 33599, 2288], "avg_logprob": -0.18479166587193807, "compression_ratio": 1.6770186335403727, "no_speech_prob": 0.0, "words": [{"start": 2651.65, "end": 2651.93, "word": "طيب", "probability": 0.5823567708333334}, {"start": 2651.93, "end": 2652.33, "word": " لحد", "probability": 0.816162109375}, {"start": 2652.33, "end": 2652.59, "word": 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"word": " اتنين", "probability": 0.82830810546875}, {"start": 2660.89, "end": 2661.45, "word": " سبعة", "probability": 0.83740234375}, {"start": 2661.45, "end": 2662.59, "word": " المسائل", "probability": 0.9671630859375}, {"start": 2662.59, "end": 2664.07, "word": " التالية", "probability": 0.9744466145833334}, {"start": 2664.07, "end": 2669.03, "word": " اتنين", "probability": 0.9521484375}, {"start": 2669.03, "end": 2669.49, "word": " سبعة", "probability": 0.9679361979166666}, {"start": 2669.49, "end": 2670.15, "word": " المسائل", "probability": 0.984375}, {"start": 2670.15, "end": 2670.33, "word": " من", "probability": 0.95556640625}, {"start": 2670.33, "end": 2670.91, "word": " واحد", "probability": 0.954833984375}, {"start": 2670.91, "end": 2671.57, "word": " لغاية", "probability": 0.9879150390625}, {"start": 2671.57, "end": 2672.49, "word": " تمانية", "probability": 0.9581705729166666}, {"start": 2672.49, "end": 2673.93, "word": " و", "probability": 0.77880859375}, {"start": 2673.93, "end": 2675.77, "word": " احداشر", "probability": 0.71380615234375}, {"start": 2675.77, "end": 2675.93, "word": " و", "probability": 0.90234375}, {"start": 2675.93, "end": 2676.95, "word": " اتناشر", "probability": 0.797607421875}], "temperature": 1.0}, {"id": 106, "seek": 269690, "start": 2678.92, "end": 2696.9, "text": "واربعتاش ب وسي ب وسي المرة جاى بنبدأ ال section اللى بعده ان شاء الله تعالى", "tokens": [2407, 9640, 3555, 34268, 33599, 4724, 46952, 1829, 4724, 46952, 1829, 9673, 25720, 10874, 995, 7578, 44945, 44510, 10721, 2423, 3541, 13672, 7578, 39182, 3224, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.3134469696969697, "compression_ratio": 1.292929292929293, "no_speech_prob": 0.0, "words": [{"start": 2678.92, "end": 2680.0, "word": "واربعتاش", "probability": 0.7138671875}, {"start": 2680.0, "end": 2680.96, "word": " ب", "probability": 0.60986328125}, {"start": 2680.96, "end": 2681.7, "word": " وسي", "probability": 0.5277099609375}, {"start": 2681.7, "end": 2683.44, "word": " ب", "probability": 0.74365234375}, {"start": 2683.44, "end": 2686.52, "word": " وسي", "probability": 0.890869140625}, {"start": 2686.52, "end": 2693.08, "word": " المرة", "probability": 0.74658203125}, {"start": 2693.08, "end": 2693.46, "word": " جاى", "probability": 0.5421549479166666}, {"start": 2693.46, "end": 2693.76, "word": " بنبدأ", "probability": 0.8328450520833334}, {"start": 2693.76, "end": 2693.88, "word": " ال", "probability": 0.544921875}, {"start": 2693.88, "end": 2694.22, "word": " section", "probability": 0.8642578125}, {"start": 2694.22, "end": 2695.0, "word": " اللى", "probability": 0.8466796875}, {"start": 2695.0, "end": 2695.5, "word": " بعده", "probability": 0.9404296875}, {"start": 2695.5, "end": 2695.78, "word": " ان", "probability": 0.84033203125}, {"start": 2695.78, "end": 2696.12, "word": " شاء", "probability": 0.96240234375}, {"start": 2696.12, "end": 2696.32, "word": " الله", "probability": 0.94482421875}, {"start": 2696.32, "end": 2696.9, "word": " تعالى", "probability": 0.8740234375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2697.69425, "duration_after_vad": 2455.4724999999894}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5f14c084ba293490406a60795d755911b216e272
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_postprocess.srt
@@ -0,0 +1,1416 @@
+1
+00:00:19,170 --> 00:00:24,010
+بسم الله الرحمن الرحيم نرجع لبداية ال section اللي
+
+2
+00:00:24,010 --> 00:00:28,950
+هو ال subspaces هذا اللي هو الفضاءات الاتجاهية
+
+3
+00:00:28,950 --> 00:00:34,010
+الجزئية المرة اللي فاتت أعطينا تعريف للفضاء
+
+4
+00:00:34,010 --> 00:00:39,590
+الاتجاهي الجزئي وابتدأنا ناخد عليه أمثلةأخذنا
+
+5
+00:00:39,590 --> 00:00:44,870
+أربعة أمثلة وهذا هو المثال الخامس بتذكر بالتعريف
+
+6
+00:00:44,870 --> 00:00:51,090
+لإننا بنحاول نستخدمه في الحكم على ال sets المختلفة
+
+7
+00:00:51,090 --> 00:00:57,670
+هل هي subspaces أم لا بجينا نقول أنه لو أخدت
+
+8
+00:00:57,670 --> 00:01:03,330
+subset U من vector space V هذا ال subset بقول عنه
+
+9
+00:01:03,330 --> 00:01:08,870
+vector space إذا حقق ليهثلاثة شروط الشرط الأول إن
+
+10
+00:01:08,870 --> 00:01:13,410
+هذا الـ subset اللي أخدته is non-empty على الأقل
+
+11
+00:01:13,410 --> 00:01:17,850
+بدي أثبت ولو عنصر واحد موجود في هذا ال subset
+
+12
+00:01:17,850 --> 00:01:23,850
+اتنين لو أخدت scalar من R مع vector من U ضربت
+
+13
+00:01:23,850 --> 00:01:28,050
+اتنين في بعض بدي أطلع ناتج vector جديد موجود في
+
+14
+00:01:28,050 --> 00:01:33,250
+الـ U itself الأمر الثالث لو أخدت vectors من U
+
+15
+00:01:33,250 --> 00:01:38,530
+وجمعت الاتنينالجامعه دي بدى اثبت ان هذا المجموع
+
+16
+00:01:38,530 --> 00:01:44,070
+موجود في U كذلك ان تحقق الشروط التلاته يبقى ال
+
+17
+00:01:44,070 --> 00:01:49,470
+subset اللى اخدتها من V بتكون subspace اختل اي شرط
+
+18
+00:01:49,470 --> 00:01:54,210
+من الشروط التلاته يبقى ماهياش subspace واخدنا على
+
+19
+00:01:54,210 --> 00:01:59,870
+ذلك اربعة امثلة وهذا هو المثال الخامسيبقى المثال
+
+20
+00:01:59,870 --> 00:02:05,990
+الخامس بقول let P بيبدأ تسوى PN مين هي ال PN؟ يبقى
+
+21
+00:02:05,990 --> 00:02:11,470
+هي كثيرات الحدود اللي درجتها أقصى ما يكون هو N
+
+22
+00:02:11,470 --> 00:02:17,650
+يعني يا إما N يا إما أقل من N وال N عدد صحيح موجب
+
+23
+00:02:17,650 --> 00:02:23,670
+ال N is a positive integer تمام؟يبقى الـ P of X هي
+
+24
+00:02:23,670 --> 00:02:27,670
+الـ polynomial of degree at most M كل كثيرات
+
+25
+00:02:27,670 --> 00:02:33,250
+الحدود اللي أقصى درجة فيها N يعني N أو أقل منها
+
+26
+00:02:33,250 --> 00:02:40,370
+حيث ان عدد صحيح موجب، that isأي أن الـ P in الـ
+
+27
+00:02:40,370 --> 00:02:45,750
+set of all polynomials P X such that P of X يعني
+
+28
+00:02:45,750 --> 00:02:50,610
+أنا بدي أترجم الكلام اللي فوق رياضيا مشان نستعمله
+
+29
+00:02:50,610 --> 00:02:58,870
+ال P of X هي A0 زي A1X زي A2X³ زي A3X³ وظل ماشي
+
+30
+00:02:58,870 --> 00:03:03,450
+لغاية ما وصل إلى An X to the power n اللي أنا قلت
+
+31
+00:03:03,450 --> 00:03:08,960
+at most ال degree تبعتها بتكون Mيبقى هذا من هذا ال
+
+32
+00:03:08,960 --> 00:03:14,080
+vector space V أخدت منه subspace أخدت مجموعة من ال
+
+33
+00:03:14,080 --> 00:03:19,040
+polynomial من هذه ال polynomial تعالى نشوف قال
+
+34
+00:03:19,040 --> 00:03:23,740
+يفترض أن ال U اللي هي ال subset من V the set of
+
+35
+00:03:23,740 --> 00:03:28,720
+all elements P of X such that P of X سوى Ax² زي Bx
+
+36
+00:03:28,720 --> 00:03:33,040
+زي C والA والB والC موجودة في R يعنياللي همين
+
+37
+00:03:33,040 --> 00:03:38,280
+كثيرات الحدود من الدرجة ثانية أخدتهم كلهم و روحت
+
+38
+00:03:38,280 --> 00:03:44,220
+حاطيتهم في ال set و سميت ال set هذه U بدي أحاول
+
+39
+00:03:44,220 --> 00:03:48,870
+أثبت أنه U subspace و يمكن ما اقدرش الله أعلملما
+
+40
+00:03:48,870 --> 00:03:53,190
+يقول prove or disapprove ان ال USA subspace وفيه
+
+41
+00:03:53,190 --> 00:03:57,550
+مش إجباري أثبت أنها subspace يمكن تطلع subspace
+
+42
+00:03:57,550 --> 00:04:01,150
+ويمكن ماتطلعش يعني prove أثبت this prove ماتثبتش
+
+43
+00:04:01,150 --> 00:04:05,390
+اللي بدك هي اللي تقدر عليه اشتغله تمام يبقى باجي
+
+44
+00:04:05,390 --> 00:04:11,810
+بقول بدي أحاول أثبت أن هذه هي subspace إن قدرت كان
+
+45
+00:04:11,810 --> 00:04:15,250
+بها ماقدرت كان بها طيب يبقى مشان أثبت أنها
+
+46
+00:04:15,250 --> 00:04:20,100
+subspace أنا بتروح أحقق الشروطالتالاتة السؤال هو
+
+47
+00:04:20,100 --> 00:04:27,000
+حد فيكم تقدر تثبتلي انه هذه ال non-empty يعني على
+
+48
+00:04:27,000 --> 00:04:33,540
+الأقل فيها عنصر و لو كان صفر موجود الصفر فيها ولا
+
+49
+00:04:33,540 --> 00:04:39,170
+لا؟موجود موجود ليش؟ لأنه جالس اللي هتبجى على الشكل
+
+50
+00:04:39,170 --> 00:04:43,870
+اللي عندها ده وال A والB والC موجودة وين حطلي قيود
+
+51
+00:04:43,870 --> 00:04:48,750
+على A وB وC ماحطش قيود تاخدهم أسفار تاخدهم أعداد
+
+52
+00:04:48,750 --> 00:04:52,810
+تاخد اللي بدكياه يبجى ماعنديش مشكلة في هذه الحالة
+
+53
+00:04:52,810 --> 00:04:56,790
+يبجى بروح بقول الخطوة الأولى أو ال condition الأول
+
+54
+00:04:56,790 --> 00:05:00,810
+ال U is non-empty
+
+55
+00:05:02,620 --> 00:05:10,640
+ليش؟ because الـ zero ههه بقدر اكتبه zero X ثربية
+
+56
+00:05:10,640 --> 00:05:16,460
+زائد zero X زائد zero منفع لا منفعش يبقى هذه ال
+
+57
+00:05:16,460 --> 00:05:22,490
+polynomial الصفرية هذا موجود وين؟ موجود في Uإذا
+
+58
+00:05:22,490 --> 00:05:26,950
+الـ U non-empty يبقى ال condition الأول تحقق يبقى
+
+59
+00:05:26,950 --> 00:05:39,710
+ال condition
+
+60
+00:05:39,710 --> 00:05:45,270
+الأول تحقق يبقى
+
+61
+00:05:45,270 --> 00:05:49,290
+ال condition الأول تحقق يبقى ال condition الأول
+
+62
+00:05:49,290 --> 00:05:50,170
+تحقق يبقى ال condition الأول تحقق يبقى ال
+
+63
+00:05:50,170 --> 00:05:50,890
+condition الأول تحقق يبقى ال condition الأول تحقق
+
+64
+00:05:50,890 --> 00:05:51,250
+الأول تحقق يبقى ال condition الأول تحقق يبقى ال
+
+65
+00:05:51,810 --> 00:06:00,640
+موجودة في اليوم thenبدأ انا اخد C1 في P of X اللي
+
+66
+00:06:00,640 --> 00:06:06,300
+عندنا هذه اشوف هل هي موجودة في ال U ام لا يبقى هذا
+
+67
+00:06:06,300 --> 00:06:14,100
+بدي يعطينا C1 بدي اضربها في AX تربية زائد BX زائد
+
+68
+00:06:14,100 --> 00:06:23,990
+C طبعا يبقى بدي افك الجثة ده يبقى هذا بصير C1AX³
+
+69
+00:06:23,990 --> 00:06:36,770
+AX³
+
+70
+00:06:36,770 --> 00:06:41,810
+AX³ AX³ AX³
+
+71
+00:06:41,810 --> 00:06:51,530
+AX³ AX³مظبوط؟ لأن هذا رقمه هذا رقم و هذا رقم real
+
+72
+00:06:51,530 --> 00:06:56,890
+numbers إذا هذا كله موجود وين؟ في الـ set U إذا
+
+73
+00:06:56,890 --> 00:07:00,750
+انتحقق منين؟ انتحقق ال condition الثاني أخد
+
+74
+00:07:00,750 --> 00:07:05,510
+element من R و أخد element من U لكي تحصل الضرب هذا
+
+75
+00:07:05,510 --> 00:07:09,970
+موجود فيه يبقى باقيا عندي بس ال condition التالت
+
+76
+00:07:09,970 --> 00:07:16,050
+condition التالت بذلك أقول FLP
+
+77
+00:07:28,610 --> 00:07:36,750
+على الشكل A1 X سربية زائد B1 X زائد C1 موجودة في U
+
+78
+00:07:39,100 --> 00:07:45,640
+يبقى بدي أخد مجموعهم بدي أخد ال P of X زائد ل Q of
+
+79
+00:07:45,640 --> 00:07:51,280
+X يبقى هذا الكلام يساوي الجمع component-wise يبقى
+
+80
+00:07:51,280 --> 00:07:57,380
+بدي أجمع هذه مع هذه منهايبقاش بلاقي بلاقي ال ax
+
+81
+00:07:57,380 --> 00:08:09,000
+تربيع زائد a1x تربيع زائد bx زائد b1x زائد c زائد
+
+82
+00:08:09,000 --> 00:08:14,790
+c1 هذا الكلام يساويما رأيك لو هنا في عامل مشترك
+
+83
+00:08:14,790 --> 00:08:19,770
+اللي هو X تربيع وهنا في عامل مشترك اللي هو X وهنا
+
+84
+00:08:19,770 --> 00:08:27,430
+مافيش عامل مشترك يبقى بقدر اقول هذا A زائد A1 كله
+
+85
+00:08:27,430 --> 00:08:35,350
+في X زائد B زائد B1 كله في X هذا X تربيع وهذا X
+
+86
+00:08:35,350 --> 00:08:45,410
+زائد C زائد C1real number في ال X تربيها موجود
+
+87
+00:08:45,410 --> 00:08:50,850
+في ال U أم لا يبقى هدف belongs to main to you إذا
+
+88
+00:08:50,850 --> 00:08:55,310
+انت حققت الشروط التلاتة أم لا يبقى باجي بقوله so
+
+89
+00:08:55,310 --> 00:08:59,770
+ال U is a subspace
+
+90
+00:09:01,690 --> 00:09:09,590
+R V يبقى هذا subspace من V نكمل الأمثلة على نفس
+
+91
+00:09:09,590 --> 00:09:14,130
+الموضوع يبقى
+
+92
+00:09:14,130 --> 00:09:19,630
+هذا المثال رقم خمسة بدنا نروح للمثال رقم ستة يبقى
+
+93
+00:09:19,630 --> 00:09:30,600
+example 6 بقول let V تساوي P تكيب letالـ V تساوي R
+
+94
+00:09:30,600 --> 00:09:39,420
+تكييب و اللي هي بدل ساوي The set of all طبعا
+
+95
+00:09:39,420 --> 00:09:43,900
+اللي هي the set of all X واحد و X اتنين و X ثلاثة
+
+96
+00:09:43,900 --> 00:09:49,280
+و X واحد و X اتنين و X ثلاثة موجودة في ال set of
+
+97
+00:09:49,280 --> 00:09:58,160
+real numbers Little u و دي لنا ال U تساوياللي هو
+
+98
+00:09:58,160 --> 00:10:05,860
+the set of all elements x1 وx2 وx3 such that بحيث
+
+99
+00:10:05,860 --> 00:10:18,160
+ان x3 يساوي x1 زائد x2 السؤال هو show that
+
+100
+00:10:21,470 --> 00:10:35,830
+Show that U is a subspace of V هذا المثال رقم ستة
+
+101
+00:10:35,830 --> 00:10:41,510
+بيقول ما ياتي بدأ أخد ال vector space V هو ال R3
+
+102
+00:10:41,510 --> 00:10:46,490
+تحت عملية الضرب والجمع العاديةاليوزر ستة و برنامج
+
+103
+00:10:46,490 --> 00:10:50,050
+X واحد و X اتنين و X تلاتة بحيث X واحد و X اتنين و
+
+104
+00:10:50,050 --> 00:10:55,830
+X تلاتة are real number بداخل اليوزر تتكون من تلت
+
+105
+00:10:55,830 --> 00:11:01,510
+مراكبات لكن المراكبة الثالثة هي مجموع ال two
+
+106
+00:11:01,510 --> 00:11:06,740
+components الأولى والثانىطلعيني هنا x1 و x2 و x3
+
+107
+00:11:06,740 --> 00:11:12,360
+such that x3 اللي هي تساوي x1 زائد x2 يعني هذا يا
+
+108
+00:11:12,360 --> 00:11:18,440
+بنات لو بدي أصيغة بقول هي كل العناصر على صيغة x1 و
+
+109
+00:11:18,440 --> 00:11:24,680
+x2 و x1 زائد x2 يعني بالشكل اللي عندنا هذا و x1 و
+
+110
+00:11:24,680 --> 00:11:29,540
+x2 موجودة في R تمام يبقى هاي المقصود بالشكل اللي
+
+111
+00:11:29,540 --> 00:11:34,870
+عندنا هذاقال لي بيظهر لي أن هذا is a subspace يبقى
+
+112
+00:11:34,870 --> 00:11:40,290
+أنا بتروح لمين للشروط الثلاثة بدي أثبت أن هذه الـU
+
+113
+00:11:40,290 --> 00:11:45,470
+على الأقل فيها مام فيها element واحد وبعد هيك بروح
+
+114
+00:11:45,470 --> 00:11:50,290
+بكمل إذا بدي أجي للنقطة الأولى حد فيكم بتقدر
+
+115
+00:11:50,290 --> 00:11:54,050
+تجيبلي answer واحد موجود في الـU
+
+116
+00:11:59,950 --> 00:12:11,230
+يبقى باجي بقوله هنا ال U is non-empty ليش؟ because
+
+117
+00:12:13,230 --> 00:12:19,290
+أن الـ zero و ال zero و ال zero موجودة في ال use
+
+118
+00:12:19,290 --> 00:12:26,510
+sentence ليش؟ لأن ال zero بده يساوي zero زائد zero
+
+119
+00:12:26,510 --> 00:12:30,470
+اللي هي المراكبة التالتة تساوي المراكبة الأولى
+
+120
+00:12:30,470 --> 00:12:36,510
+زائد المراكبة آت ثانية النقطة الثانية بداجي أخد
+
+121
+00:12:36,510 --> 00:12:43,490
+element a موجود في set of real numbers andالـ V
+
+122
+00:12:43,490 --> 00:12:49,110
+مثلا موجود في الـ U و الـ V بدي أكتبه على الشكل
+
+123
+00:12:49,110 --> 00:12:57,530
+التالي الـ V تساوي الـ X واحد و X اتنين و X واحد
+
+124
+00:12:57,530 --> 00:13:04,330
+زائد X اتنين موجود في الـ U دامن بدي أخد حصة للضرب
+
+125
+00:13:04,330 --> 00:13:12,520
+يبقى بدي أخد A في Vيبقى هذا بيصير A في X1 و X2 و
+
+126
+00:13:12,520 --> 00:13:22,020
+X1 زائد X2 انطلع هذا موجود في ال U بكون انت هنا من
+
+127
+00:13:22,020 --> 00:13:25,000
+ال condition التاني و بروح بدور عالميا على ال
+
+128
+00:13:25,000 --> 00:13:30,220
+condition الثالث يبقى بيدفك هذا القصة بجي بقوله A
+
+129
+00:13:30,220 --> 00:13:50,600
+X1ax2 a x1 a x2 a x2 a x1 a x2 a x2 a x2 a x2 a x2
+
+130
+00:13:50,600 --> 00:13:56,850
+a x2 a x2 a x2 a x2 a x2 a x2 a x2 a x2 a x2هل هو
+
+131
+00:13:56,850 --> 00:14:01,130
+مجموع الـ two terms اللي هنا؟ يعني المركبة التالتة
+
+132
+00:14:01,130 --> 00:14:04,210
+مجموع المركبة الأولى والمركبة الثانية في الـ a
+
+133
+00:14:04,210 --> 00:14:09,150
+three useful نعم بالضبط إذا هذه موجودة وين؟ موجودة
+
+134
+00:14:09,150 --> 00:14:13,850
+في U يبقى تحقق ال condition الثاني بدأ أروح لل
+
+135
+00:14:13,850 --> 00:14:22,110
+condition الثالث يبقى باجي بقوله F اللي هو من؟ F
+
+136
+00:14:22,360 --> 00:14:29,720
+الـ U بـ small بدها تساوي X واحد و X اتنين و X
+
+137
+00:14:29,720 --> 00:14:37,140
+واحد زائد X اتنين و ال V بدها تساوي Y واحد و Y
+
+138
+00:14:37,140 --> 00:14:43,000
+اتنين و Y واحد زائد Y اتنين هذا الكلام موجود في U
+
+139
+00:14:43,000 --> 00:14:48,550
+thenيبقى أخد عنصرين موجودة في U بالـD أشوف هل
+
+140
+00:14:48,550 --> 00:14:54,410
+جامعهم موجود في U أم لا يبقى بروح باخد له الـU
+
+141
+00:14:54,410 --> 00:15:01,660
+زائد الـVيبقى لجمع component twice يبقى x واحد
+
+142
+00:15:01,660 --> 00:15:10,980
+زائد y واحد x اتنين زائد y اتنين نجمع x واحد زائد
+
+143
+00:15:10,980 --> 00:15:17,660
+x اتنين زائد y واحد زائد y اتنين وهذه المركبة اللي
+
+144
+00:15:17,660 --> 00:15:23,490
+عندناطيب انا بدي اياها مجموع الاولى زي دى التانية
+
+145
+00:15:23,490 --> 00:15:34,420
+بقدر اعيد الترتيب و اقول X1 زي Y1 X2 زي Y2ممكن
+
+146
+00:15:34,420 --> 00:15:42,640
+اجمع هذه مع هذه يبقى مين؟ x واحد زائد y واحد زائد
+
+147
+00:15:42,640 --> 00:15:48,700
+x اتنين زائد y اتنين بالشكل اللي عندنا هذا طلعيلي
+
+148
+00:15:48,700 --> 00:15:52,440
+في ال term اللي عندنا هذا هو مجموع ال components
+
+149
+00:15:52,440 --> 00:15:56,970
+الاتنين هدولنعم هو مجموعة .. إذا هذا موجود وين؟
+
+150
+00:15:56,970 --> 00:16:02,610
+موجود في الـ U إذا تحققت الشروط التلاتة فباجي بقول
+
+151
+00:16:02,610 --> 00:16:11,830
+له الـ U is a subspace of
+
+152
+00:16:11,830 --> 00:16:14,950
+V وانتهينا منها
+
+153
+00:16:42,900 --> 00:16:57,320
+يبقى هذا المثال السادس مثال السابع مثال سبعة بقول
+
+154
+00:16:57,320 --> 00:17:01,940
+الات ال V بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+155
+00:17:01,940 --> 00:17:04,100
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+156
+00:17:09,670 --> 00:17:22,270
+Define لف معرفة on an interval I معرفة على فترة ما
+
+157
+00:17:22,270 --> 00:17:31,670
+نأخد الـ U لت الـ U تساويthe set of all element f
+
+158
+00:17:31,670 --> 00:17:40,910
+such that ال F W prime of X زائد اتنين في ال F of
+
+159
+00:17:40,910 --> 00:17:47,750
+X بده يساوي Zero وهذا الكلام لكل ال X اللي موجودة
+
+160
+00:17:47,750 --> 00:17:57,350
+في ال interval I السؤال هو بيقول prove or disprove
+
+161
+00:17:58,880 --> 00:18:11,160
+prove or disprove that ال U is a subspace of V
+
+162
+00:18:11,160 --> 00:18:26,380
+خانة
+
+163
+00:18:26,380 --> 00:18:32,490
+هذه انتهينا منهاطيب انتوا ملاحظين الأمثلة بالنوعها
+
+164
+00:18:32,490 --> 00:18:37,630
+كل مرة بنجيب مثال شكل يختلف في مضمونه عن المثال
+
+165
+00:18:37,630 --> 00:18:42,030
+القبل لكن بالنسبة للبرهين كله نفس الفكرة تبعة
+
+166
+00:18:42,030 --> 00:18:47,710
+البرهان بس نقدر نطبق له تطبيق صحيح نرجع لسؤالنا
+
+167
+00:18:47,710 --> 00:18:51,710
+هذا مرة ثانية قال ياخد ال V the set of all
+
+168
+00:18:51,710 --> 00:18:56,420
+functions المعرفة على فترة مايعني أنا جيت على ال
+
+169
+00:18:56,420 --> 00:19:00,720
+real line و أخدت فترة محددة و جبت كل ال functions
+
+170
+00:19:00,720 --> 00:19:05,240
+اللي خلقها ربنا و اللي احنا بنعرفه المعرفة على هذه
+
+171
+00:19:05,240 --> 00:19:11,280
+الفترة و قلت هدول vector space اللي هو Vروحت من
+
+172
+00:19:11,280 --> 00:19:14,840
+هذا الـ vector space أخدت مجموعة من ال functions
+
+173
+00:19:14,840 --> 00:19:18,700
+مين هي المجموعة من ال functions؟ هي المجموعة التي
+
+174
+00:19:18,700 --> 00:19:23,240
+تحقق المعادلة اللي بين أدينا هذه يعني لو اشتقت
+
+175
+00:19:23,240 --> 00:19:29,640
+المعادلة مرتين وضفت لها اتنين ضعف الدالة بدي
+
+176
+00:19:29,640 --> 00:19:34,400
+يعطيني الناتج من zero لأي element x موجود في ال
+
+177
+00:19:34,400 --> 00:19:40,780
+interval I مرة تانيةأنا جيت كل ال functions
+
+178
+00:19:40,780 --> 00:19:43,580
+المعرفة على ال interval اللي بدي اعتبره البنات
+
+179
+00:19:43,580 --> 00:19:46,780
+اللي قاعدة قدامي في القاعة هدول كلهم functions
+
+180
+00:19:46,780 --> 00:19:53,000
+معرفة على ال interval تبع القاعة ماشي طيب الان من
+
+181
+00:19:53,000 --> 00:19:58,700
+هدول بدي اختار البنات اللي مشتقتها الثانية زائد
+
+182
+00:19:58,700 --> 00:20:04,750
+اتنين ضرب نفسها بيعطيني zero دائما و أبدايعني كل
+
+183
+00:20:04,750 --> 00:20:09,130
+البنات اللي لا E يحققنا هذه المعادلة كنت اطلع
+
+184
+00:20:09,130 --> 00:20:14,570
+اشكها روحت سميتهم مين؟ سميتهم ال U بدي اثبت ان ال
+
+185
+00:20:14,570 --> 00:20:20,570
+U هذا ال sub space من مين؟ من V او من ال set
+
+186
+00:20:20,570 --> 00:20:23,690
+الأصلي هذا الفكرة في الموضوع دي روايالكوا هذا
+
+187
+00:20:23,690 --> 00:20:28,850
+جيبناه في الامتحانات قبل ذلك يعني هذا سؤال امتحان
+
+188
+00:20:28,850 --> 00:20:35,590
+طيب تعالى نشوفأحاول أن أثبت له أن هذا الـ subspace
+
+189
+00:20:35,590 --> 00:20:40,010
+من الـ 6 اللي فوق يبقى أنا بروح أحقق الشروط
+
+190
+00:20:40,010 --> 00:20:45,810
+التلاتة بداجة للشرط الأول السؤال هو هل بتعرفولي
+
+191
+00:20:45,810 --> 00:20:51,590
+دالة مشتقتها الثانية زائدي اتنين في نفسها بيعطيني
+
+192
+00:20:51,590 --> 00:20:52,010
+zero
+
+193
+00:20:55,610 --> 00:21:00,670
+في كتير في كتير لكن أبسط واحدة منهم ليه ليه
+
+194
+00:21:00,670 --> 00:21:05,810
+trivial function لف وف اكس ساوي قداش Zero مشتقتها
+
+195
+00:21:05,810 --> 00:21:08,630
+مرتين ب Zero و اتنين ب Zero ب Zero يبقى مجموعهم
+
+196
+00:21:08,630 --> 00:21:13,930
+Zero صحيح ولا لأ يبقى هذا أبسط أنواع الدوال مما
+
+197
+00:21:13,930 --> 00:21:20,010
+يثبت ان ال U is non empty يبقى باجي بقوله takeخذ
+
+198
+00:21:20,010 --> 00:21:24,010
+الفرصة f of x يساوي 0
+
+199
+00:21:28,300 --> 00:21:34,420
+الـ F prime of X يساوي Zero والـ F W prime of X
+
+200
+00:21:34,420 --> 00:21:44,280
+يساوي Zero يبقى أصبح لدي الـ F W prime of X زائدي
+
+201
+00:21:44,280 --> 00:21:48,920
+اتنين F of X يساوي Zero الـ F W prime of Zero
+
+202
+00:21:48,920 --> 00:21:55,820
+زائدي اتنين في Zero يساوي Zero هذا معناه ان الـ F
+
+203
+00:21:55,820 --> 00:22:00,710
+اللي عندها موجودة وينفي الـ U هذا معناه ان الـ U
+
+204
+00:22:00,710 --> 00:22:07,850
+is non-empty يبقى هذه ما هياش الفئة الخاوية يبقى
+
+205
+00:22:07,850 --> 00:22:13,350
+هذه الفئة وفيها من وفيها عناصر يبقى هذه أثبتنا ان
+
+206
+00:22:13,350 --> 00:22:19,410
+هذه ال set على الأقل فيها و لو عنصر واحد نجي رقم
+
+207
+00:22:19,410 --> 00:22:26,770
+اتنين بدي اخد ال C موجود في set of real numbers
+
+208
+00:22:29,320 --> 00:22:36,160
+والـ F موجودة في الـ U فالـ F موجودة في الـ U
+
+209
+00:22:36,160 --> 00:22:41,400
+معناته الـ F double prime of X زائدي اتنين F of X
+
+210
+00:22:41,400 --> 00:22:49,460
+بده يساوي Zeroأنا مين بدي أثبت؟ بدي أثبت إن الـCF
+
+211
+00:22:49,460 --> 00:22:55,520
+كلها double prime زائد اتنين CF بده يساوي Zero إن
+
+212
+00:22:55,520 --> 00:23:01,240
+أثبت ذلك بصير الـCF موجودة في الـU وبالتالي بكون
+
+213
+00:23:01,240 --> 00:23:06,540
+تحقق ال condition هالثاني يبقى الآن بداجي أقول
+
+214
+00:23:06,540 --> 00:23:07,420
+consider
+
+215
+00:23:10,510 --> 00:23:17,550
+كده لي كده
+
+216
+00:23:17,550 --> 00:23:23,150
+كده كده كده
+
+217
+00:23:23,150 --> 00:23:32,350
+كده
+
+218
+00:23:32,350 --> 00:23:36,930
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+219
+00:23:36,930 --> 00:23:37,610
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+220
+00:23:37,610 --> 00:23:41,070
+كده كده كده كده كده كدهأظن المقدار الثابت لو فضل
+
+221
+00:23:41,070 --> 00:23:45,790
+مرة ولا مرتين ولا تلاتة ولا عشرة بيظل .. بيظل زي
+
+222
+00:23:45,790 --> 00:23:49,930
+ما هو كل ال function موجودة F لكن لو ال function
+
+223
+00:23:49,930 --> 00:23:54,430
+انتهت بيصير مشتق لبعضها ب Zero مظبوط طب احنا عندنا
+
+224
+00:23:54,430 --> 00:24:00,310
+مشتقتين فبجي بقول له هذا معناه C في ال F double
+
+225
+00:24:00,310 --> 00:24:05,650
+prime of X زاد
+
+226
+00:24:06,250 --> 00:24:14,350
+هذه لو جيت فكتها بيصير اتنين C في ال F of X هذه لو
+
+227
+00:24:14,350 --> 00:24:19,810
+روحت اخدت ال C عام المشترك بيظل F double prime of
+
+228
+00:24:19,810 --> 00:24:26,410
+X زائد اتنين F of X يبقى ده بتسوى كده شبه انا
+
+229
+00:24:26,410 --> 00:24:31,910
+هتهيأ ال C لبرا ل بين جثين هايهأنا فرضه من قبل
+
+230
+00:24:31,910 --> 00:24:38,970
+بقداش؟ بزيرو يبقى الـC في زيرو بقداش ايش تفسير كل
+
+231
+00:24:38,970 --> 00:24:43,730
+هذا الكلام؟ يبقى الـCF موجودة في الـU يبقى هنا
+
+232
+00:24:43,730 --> 00:24:49,290
+بروح بقول له الساعة الـCF موجودة في الـU بده اروح
+
+233
+00:24:49,290 --> 00:24:54,430
+لل condition التالدبدي اخد two functions موجودات
+
+234
+00:24:54,430 --> 00:25:00,450
+في الـ U بمعنى ان الـ f double prime of x زي دي
+
+235
+00:25:00,450 --> 00:25:05,230
+اتنين f of x بدي سوى zero ودالة تانية g of x بحيث
+
+236
+00:25:05,230 --> 00:25:09,270
+الـ g double prime of x زي دي اتنين g of x بدي سوى
+
+237
+00:25:09,270 --> 00:25:16,060
+مين؟ Zero يبقى بداجي اقوله هنا افترضيإن الـ F و
+
+238
+00:25:16,060 --> 00:25:22,200
+الـ G موجودة في الـ U ثم الـ F double prime of X
+
+239
+00:25:22,200 --> 00:25:29,880
+زائد اتنين F of X بدي ساوي Zero و في نفس الوقت G
+
+240
+00:25:29,880 --> 00:25:35,180
+double prime of X زائد اتنين G of X كل هذا بدي
+
+241
+00:25:35,180 --> 00:25:40,510
+ساوي مين؟ بدي ساوي Zeroأنا بدي أثبت إن مجموعهم
+
+242
+00:25:40,510 --> 00:25:45,950
+موجود في الـ U يعني بدي أثبت إن ال F of X زائد ال
+
+243
+00:25:45,950 --> 00:25:51,210
+G of X كله موجود وين؟ بدي موجود في الـ U ليش هكذا؟
+
+244
+00:25:51,210 --> 00:25:58,530
+بدي أروح أقول ما يأتي خوديلي اللي هو F of X زائد
+
+245
+00:25:58,530 --> 00:26:02,150
+ال G of X W prime
+
+246
+00:26:05,020 --> 00:26:16,460
+زائد اتنين F of X زائد G of X اذا طلع هذا يساوي
+
+247
+00:26:16,460 --> 00:26:22,420
+Zero بصير المجموع هذا موجود في اليوم التالي يكون
+
+248
+00:26:22,420 --> 00:26:27,660
+انتهينا من القصة هذا الكلام يساوي نرجع لل calculus
+
+249
+00:26:30,100 --> 00:26:35,200
+مشتقت المجموع الجبري لدالتين يسوى مين؟ المجموع
+
+250
+00:26:35,200 --> 00:26:43,300
+الجبري للمشتقتين ولو اشتقت كمان مرة يبقى
+
+251
+00:26:43,300 --> 00:26:49,960
+المجموع الجبري للمشتقتين يبقى هذا معناه ال F W
+
+252
+00:26:49,960 --> 00:26:58,150
+prime of X زائد ال G W prime of Xمظبوط؟ طيب هذا
+
+253
+00:26:58,150 --> 00:27:03,530
+الكلام بدي أضيفله بدي أفك الـ Goal السادة يبقى 2 F
+
+254
+00:27:03,530 --> 00:27:12,500
+of X زائدي 2 G of X Y الساويبدي اخلهم مجموعتين بدي
+
+255
+00:27:12,500 --> 00:27:17,840
+احط ال f مع بعض و ال g مع بعض يبقى هذا بده يعطينا
+
+256
+00:27:17,840 --> 00:27:24,640
+مين بده يعطينا fw prime of x زي دي اتنين f of x
+
+257
+00:27:24,640 --> 00:27:25,900
+بدي اخدهم مع بعض
+
+258
+00:27:29,230 --> 00:27:37,490
+GW'XGW'XGW
+
+259
+00:27:37,490 --> 00:27:46,250
+'XGW'XGW
+
+260
+00:27:46,250 --> 00:27:51,170
+'XGW
+
+261
+00:27:51,170 --> 00:27:52,930
+'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW
+
+262
+00:27:52,930 --> 00:27:53,370
+'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW
+
+263
+00:27:53,370 --> 00:28:00,970
+'XGW'XGW'Xزائد ال جي موجودة في ال U يبقى ال U is a
+
+264
+00:28:00,970 --> 00:28:02,090
+subspace
+
+265
+00:28:17,170 --> 00:28:27,670
+الـ U is a subspace of Z
+
+266
+00:28:30,300 --> 00:28:36,120
+طيب أخدنا حتى الآن بدل المثال سبعة أمثلة أعتقد أن
+
+267
+00:28:36,120 --> 00:28:41,260
+هذه الأمثلة السابعة ثبتت مفهوم ال subspace عندنا
+
+268
+00:28:41,260 --> 00:28:46,700
+بدرجة كبيرة يبقى ندخل شوية كمان في نفس ال section
+
+269
+00:28:46,700 --> 00:28:52,380
+فإننا نعطي تعريف جديد التعريف بيقول ما يأتي
+
+270
+00:28:52,380 --> 00:28:54,900
+definition let
+
+271
+00:29:01,360 --> 00:29:12,560
+الـ V بإيه؟ Vector Space Vector Space and let
+
+272
+00:29:12,560 --> 00:29:22,560
+وافترضوا كذلك أن V1 و V2 و لغاية VM موجودة في
+
+273
+00:29:22,560 --> 00:29:34,310
+capital V We say that We say thatإن الـ V هذه الـ
+
+274
+00:29:34,310 --> 00:29:43,350
+V الصغير is a linear combination linear
+
+275
+00:29:43,350 --> 00:29:47,490
+combination
+
+276
+00:29:47,490 --> 00:29:57,930
+linear combination of V1 و V2 و لغاية الـ VM
+
+277
+00:30:00,530 --> 00:30:13,850
+there exist c1 و c2 و cm in are such that
+
+278
+00:30:13,850 --> 00:30:27,170
+بحيث ان ال V بده ساوي c1 v1 c2 v2 cm vm
+
+279
+00:30:29,300 --> 00:30:39,640
+كمان definition تاني if
+
+280
+00:30:39,640 --> 00:30:47,100
+every element
+
+281
+00:30:47,100 --> 00:31:00,720
+of a vector a spaceof a vector space V if every
+
+282
+00:31:00,720 --> 00:31:07,700
+element of a vector space V is a linear
+
+283
+00:31:07,700 --> 00:31:18,280
+combination of
+
+284
+00:31:18,280 --> 00:31:32,320
+V1و V2 و V M We say that .. We say that .. بروح
+
+285
+00:31:32,320 --> 00:31:45,940
+نقول We say that capital V هذا is Spannid .. is
+
+286
+00:31:45,940 --> 00:31:57,570
+Spannid by ..this elements by this elements also
+
+287
+00:31:57,570 --> 00:32:01,170
+وكذلك
+
+288
+00:32:01,170 --> 00:32:15,170
+we say that we say that the elements اللي
+
+289
+00:32:15,170 --> 00:32:25,020
+هو V واحد و V اتنينو VM Span V
+
+290
+00:33:35,580 --> 00:33:41,880
+طيب نجي لل two definitions اللي احنا معرفينهم و
+
+291
+00:33:41,880 --> 00:33:46,100
+بدأنا في الجد شوية اهدروا بالكم الآنمع بداية
+
+292
+00:33:46,100 --> 00:33:49,820
+التعريفات الاتنين دول بدأنا ندخش في صميم الموضوع
+
+293
+00:33:49,820 --> 00:33:53,960
+كل الكلام اللى فات كله كلام بسيط يعتبر اللى هم
+
+294
+00:33:53,960 --> 00:33:58,420
+بيقولوا يفترض ال V هو عبارة عن vector space أخدت
+
+295
+00:33:58,420 --> 00:34:03,100
+مجموعة من ال vectors موجودة وين في V يعني أخدت
+
+296
+00:34:03,100 --> 00:34:08,260
+خمسة ستة سبعة جد ما يكون عددهم V1 وV2 لغاية VM
+
+297
+00:34:08,260 --> 00:34:12,950
+موجودة في capital Vيبقى الفيات هدول كلهم إيش؟ كلهم
+
+298
+00:34:12,950 --> 00:34:17,290
+vectors داخل ال vector space يعني لو جيت قولت
+
+299
+00:34:17,290 --> 00:34:21,190
+البنات هدول ال vector space أخدت من؟ أخدت أول خمسة
+
+300
+00:34:21,190 --> 00:34:24,630
+يبقى أول خمسة يعتبروا vectors في من؟ في ال vector
+
+301
+00:34:24,630 --> 00:34:30,650
+space مالهم الخمسة هدول؟ we say that منقول ال V is
+
+302
+00:34:30,650 --> 00:34:36,270
+a linear combination ofأنا لو روحت و أخدت vector
+
+303
+00:34:36,270 --> 00:34:42,070
+تاني و لاجئت ان ال vector التاني قدرت اكتبه بدلالة
+
+304
+00:34:42,070 --> 00:34:45,990
+الخمسة هدول يعني اخدت اي vector من ال vector اسمه
+
+305
+00:34:45,990 --> 00:34:49,550
+اذا قدرت اكتبه بدلالة الخمسة هدول
+
+306
+00:35:04,700 --> 00:35:11,400
+ماشي يعني يعني لو جيت أخدت أخدت مجموعة من ال
+
+307
+00:35:11,400 --> 00:35:16,860
+vector قولي خمسة زي ما قلنا هنا و الخمسة هدول روحت
+
+308
+00:35:16,860 --> 00:35:21,920
+أخدت vector تاني لجيت ال vector هذا بقدر أكتب
+
+309
+00:35:21,920 --> 00:35:27,040
+بدلالة الخمسة constant في ال vector الأول زاد
+
+310
+00:35:27,040 --> 00:35:29,640
+constant في ال vector التاني زاد constant في ال
+
+311
+00:35:29,640 --> 00:35:34,310
+vector التاني زاد constant في ال vector الخامسإن
+
+312
+00:35:34,310 --> 00:35:39,750
+حدث ذلك يبقى بقول الـ vector V الـ vector الـ
+
+313
+00:35:39,750 --> 00:35:44,790
+element الواحد V هو linear combination مجموعة خطية
+
+314
+00:35:44,790 --> 00:35:52,110
+أو تجميع خطي من ال vectors V1 و V2 و لغاية V5 يبقى
+
+315
+00:35:52,110 --> 00:35:56,450
+هذا معنى linear linear خطي combination تجميعيبقى
+
+316
+00:35:56,450 --> 00:36:02,690
+تجميع خطي تمام لكن هل كل vector of space بقدر
+
+317
+00:36:02,690 --> 00:36:07,690
+أكتبه بدلالة الخمسة هدول الإجابة قد يكون و قد لا
+
+318
+00:36:07,690 --> 00:36:13,310
+يكون طبعا حيكون إذا حدث ذلك في كلام تاني سنتحدث به
+
+319
+00:36:13,310 --> 00:36:18,770
+اليوم ان شاء الله تعالى أو المرة القادمة خليني
+
+320
+00:36:18,770 --> 00:36:24,600
+أسمع هذا مرة تانية بقولأنا عندى .. انا عندى .. اه
+
+321
+00:36:24,600 --> 00:36:29,900
+vector space أخدت منه مجموعة المجموعة هذه قلتلهم
+
+322
+00:36:29,900 --> 00:36:35,140
+صفع شجة صفع شجة جيت ضربت كل صنف الأول كل صنف
+
+323
+00:36:35,140 --> 00:36:39,920
+التاني كل صنف التالت مرة أبقى وجمعتهمأعطانى هذا
+
+324
+00:36:39,920 --> 00:36:43,860
+المجموع vector من ال vector space اللى موجود
+
+325
+00:36:43,860 --> 00:36:48,300
+vector جديد من عناصر ال vector space اللى كبيرة
+
+326
+00:36:48,300 --> 00:36:52,680
+يبقى هذا العنصر بقول هو linear combination من
+
+327
+00:36:52,680 --> 00:36:57,120
+مجموعة العناصر اللى خدتها واضح اظن مش فيه مشكلة
+
+328
+00:36:57,120 --> 00:37:02,270
+واضح على التعريف طيب نجلةالتعريف التاني بيقول لو
+
+329
+00:37:02,270 --> 00:37:07,030
+كان كل عنصر في ال vector space هو linear
+
+330
+00:37:07,030 --> 00:37:12,030
+combination من ال vectors هدول بنروح نقول ال V
+
+331
+00:37:12,030 --> 00:37:16,170
+spanned by this vector بنقول ال vector space V
+
+332
+00:37:16,170 --> 00:37:25,030
+يولد بهذه العناصر أو هذه العناصر تولد من؟ تولد ال
+
+333
+00:37:25,030 --> 00:37:30,140
+vector V تولد V والله هم بولدوا V كله نفس الشيءمرة
+
+334
+00:37:30,140 --> 00:37:39,320
+تانية مرة تانية التعريف التاني إذا بالبلد هيك إذا
+
+335
+00:37:39,320 --> 00:37:44,480
+أخدت أي vector موجود في ال space اللي جيته هو
+
+336
+00:37:44,480 --> 00:37:49,180
+linear combination من مجموعة من ال vectors بقول إن
+
+337
+00:37:49,180 --> 00:37:53,860
+هذه المجموعة ال vectors تولد ال vector space أو ال
+
+338
+00:37:53,860 --> 00:37:59,180
+vector space يولد بهذه المجموعة الموضوع أكترعصير
+
+339
+00:37:59,180 --> 00:38:03,980
+البنات اللي في الشجة دي ستة بس شايفينهم؟ into كل
+
+340
+00:38:03,980 --> 00:38:07,360
+co-vector space من اللي أخدت الستة اللي قلتلهم
+
+341
+00:38:07,360 --> 00:38:13,760
+تعالوا على الشجة جيت مسكت أي واحدة فيكم لجيتها هي
+
+342
+00:38:13,760 --> 00:38:17,220
+كل صفر الأول كل صفر التاني كل صفر التالتة كل صفر
+
+343
+00:38:17,220 --> 00:38:20,160
+الرابعة كل صفر الخمسة كل صفر السادسة طلع بالضبط
+
+344
+00:38:20,160 --> 00:38:25,210
+تمامابعد ذلك جيت لها تانى بنى كنستان تانى جديد مش
+
+345
+00:38:25,210 --> 00:38:29,890
+الكنستان الأولانى تمام و لجيتها بالشكل هذا لما
+
+346
+00:38:29,890 --> 00:38:33,650
+نمسكت من عند أول واحدة لأخر لغاية أخر واحدة من
+
+347
+00:38:33,650 --> 00:38:38,550
+هناك لجيت كل واحدة فيكوا هي عبارة عن حاصل ضرب
+
+348
+00:38:38,550 --> 00:38:41,530
+كنستان في الأولى زي كنستان في التانية زي كنستان في
+
+349
+00:38:41,530 --> 00:38:47,200
+السادسة ان حدث ذلك بقول البنات الستة هدولبوالده كل
+
+350
+00:38:47,200 --> 00:38:52,760
+البنات اللى موجودة فى القاعة او او ال vector space
+
+351
+00:38:52,760 --> 00:38:58,620
+هذا كله يولد بواسطة ده ست بنات صعبة؟ لأبدا، هيبقى
+
+352
+00:38:58,620 --> 00:39:03,040
+هذا معناه اللى ال span تبع اللى طبعا نخش عمق شوية
+
+353
+00:39:03,040 --> 00:39:06,120
+فى المحاضرة بعد الظهر اللى انا منها اتوقف مشان
+
+354
+00:39:06,120 --> 00:39:07,700
+نوزع أوراق
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0d0fb8a4a7dc3a2b8b3271a00b52fd50607b803a
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_raw.srt
@@ -0,0 +1,1444 @@
+1
+00:00:19,170 --> 00:00:24,010
+بسم الله الرحمن الرحيم نرجع لبداية ال section اللي
+
+2
+00:00:24,010 --> 00:00:28,950
+هو ال subspaces هذا اللي هو الفضاءات الاتجاهية
+
+3
+00:00:28,950 --> 00:00:34,010
+الجزئية المرة اللي فاتت أعطينا تعريف للفضاء
+
+4
+00:00:34,010 --> 00:00:39,590
+الاتجاهي الجزئي وابتدأنا ناخد عليه أمثلةأخذنا
+
+5
+00:00:39,590 --> 00:00:44,870
+أربعة أمثلة وهذا هو المثال الخامس بتذكر بالتعريف
+
+6
+00:00:44,870 --> 00:00:51,090
+لإننا بنحاول نستخدمه في الحكم على ال sets المختلفة
+
+7
+00:00:51,090 --> 00:00:57,670
+هل هي subspaces أم لا بجينا نقول أنه لو أخدت
+
+8
+00:00:57,670 --> 00:01:03,330
+subset U من vector space V هذا ال subset بقول عنه
+
+9
+00:01:03,330 --> 00:01:08,870
+vector space إذا حقق ليهثلاثة شروط الشرط الأول إن
+
+10
+00:01:08,870 --> 00:01:13,410
+هذا الـ subset اللي أخدته is non-empty على الأقل
+
+11
+00:01:13,410 --> 00:01:17,850
+بدي أثبت ولو عنصر واحد موجود في هذا ال subset
+
+12
+00:01:17,850 --> 00:01:23,850
+اتنين لو أخدت scalar من R مع vector من U ضربت
+
+13
+00:01:23,850 --> 00:01:28,050
+اتنين في بعض بدي أطلع ناتج vector جديد موجود في
+
+14
+00:01:28,050 --> 00:01:33,250
+الـ U itself الأمر الثالث لو أخدت vectors من U
+
+15
+00:01:33,250 --> 00:01:38,530
+وجمعت الاتنينالجامعه دي بدى اثبت ان هذا المجموع
+
+16
+00:01:38,530 --> 00:01:44,070
+موجود في U كذلك ان تحقق الشروط التلاته يبقى ال
+
+17
+00:01:44,070 --> 00:01:49,470
+subset اللى اخدتها من V بتكون subspace اختل اي شرط
+
+18
+00:01:49,470 --> 00:01:54,210
+من الشروط التلاته يبقى ماهياش subspace واخدنا على
+
+19
+00:01:54,210 --> 00:01:59,870
+ذلك اربعة امثلة وهذا هو المثال الخامسيبقى المثال
+
+20
+00:01:59,870 --> 00:02:05,990
+الخامس بقول let P بيبدأ تسوى PN مين هي ال PN؟ يبقى
+
+21
+00:02:05,990 --> 00:02:11,470
+هي كثيرات الحدود اللي درجتها أقصى ما يكون هو N
+
+22
+00:02:11,470 --> 00:02:17,650
+يعني يا إما N يا إما أقل من N وال N عدد صحيح موجب
+
+23
+00:02:17,650 --> 00:02:23,670
+ال N is a positive integer تمام؟يبقى الـ P of X هي
+
+24
+00:02:23,670 --> 00:02:27,670
+الـ polynomial of degree at most M كل كثيرات
+
+25
+00:02:27,670 --> 00:02:33,250
+الحدود اللي أقصى درجة فيها N يعني N أو أقل منها
+
+26
+00:02:33,250 --> 00:02:40,370
+حيث ان عدد صحيح موجب، that isأي أن الـ P in الـ
+
+27
+00:02:40,370 --> 00:02:45,750
+set of all polynomials P X such that P of X يعني
+
+28
+00:02:45,750 --> 00:02:50,610
+أنا بدي أترجم الكلام اللي فوق رياضيا مشان نستعمله
+
+29
+00:02:50,610 --> 00:02:58,870
+ال P of X هي A0 زي A1X زي A2X³ زي A3X³ وظل ماشي
+
+30
+00:02:58,870 --> 00:03:03,450
+لغاية ما وصل إلى An X to the power n اللي أنا قلت
+
+31
+00:03:03,450 --> 00:03:08,960
+at most ال degree تبعتها بتكون Mيبقى هذا من هذا ال
+
+32
+00:03:08,960 --> 00:03:14,080
+vector space V أخدت منه subspace أخدت مجموعة من ال
+
+33
+00:03:14,080 --> 00:03:19,040
+polynomial من هذه ال polynomial تعالى نشوف قال
+
+34
+00:03:19,040 --> 00:03:23,740
+يفترض أن ال U اللي هي ال subset من V the set of
+
+35
+00:03:23,740 --> 00:03:28,720
+all elements P of X such that P of X سوى Ax² زي Bx
+
+36
+00:03:28,720 --> 00:03:33,040
+زي C والA والB والC موجودة في R يعنياللي همين
+
+37
+00:03:33,040 --> 00:03:38,280
+كثيرات الحدود من الدرجة ثانية أخدتهم كلهم و روحت
+
+38
+00:03:38,280 --> 00:03:44,220
+حاطيتهم في ال set و سميت ال set هذه U بدي أحاول
+
+39
+00:03:44,220 --> 00:03:48,870
+أثبت أنه U subspace و يمكن ما اقدرش الله أعلملما
+
+40
+00:03:48,870 --> 00:03:53,190
+يقول prove or disapprove ان ال USA subspace وفيه
+
+41
+00:03:53,190 --> 00:03:57,550
+مش إجباري أثبت أنها subspace يمكن تطلع subspace
+
+42
+00:03:57,550 --> 00:04:01,150
+ويمكن ماتطلعش يعني prove أثبت this prove ماتثبتش
+
+43
+00:04:01,150 --> 00:04:05,390
+اللي بدك هي اللي تقدر عليه اشتغله تمام يبقى باجي
+
+44
+00:04:05,390 --> 00:04:11,810
+بقول بدي أحاول أثبت أن هذه هي subspace إن قدرت كان
+
+45
+00:04:11,810 --> 00:04:15,250
+بها ماقدرت كان بها طيب يبقى مشان أثبت أنها
+
+46
+00:04:15,250 --> 00:04:20,100
+subspace أنا بتروح أحقق الشروطالتالاتة السؤال هو
+
+47
+00:04:20,100 --> 00:04:27,000
+حد فيكم تقدر تثبتلي انه هذه ال non-empty يعني على
+
+48
+00:04:27,000 --> 00:04:33,540
+الأقل فيها عنصر و لو كان صفر موجود الصفر فيها ولا
+
+49
+00:04:33,540 --> 00:04:39,170
+لا؟موجود موجود ليش؟ لأنه جالس اللي هتبجى على الشكل
+
+50
+00:04:39,170 --> 00:04:43,870
+اللي عندها ده وال A والB والC موجودة وين حطلي قيود
+
+51
+00:04:43,870 --> 00:04:48,750
+على A وB وC ماحطش قيود تاخدهم أسفار تاخدهم أعداد
+
+52
+00:04:48,750 --> 00:04:52,810
+تاخد اللي بدكياه يبجى ماعنديش مشكلة في هذه الحالة
+
+53
+00:04:52,810 --> 00:04:56,790
+يبجى بروح بقول الخطوة الأولى أو ال condition الأول
+
+54
+00:04:56,790 --> 00:05:00,810
+ال U is non-empty
+
+55
+00:05:02,620 --> 00:05:10,640
+ليش؟ because الـ zero ههه بقدر اكتبه zero X ثربية
+
+56
+00:05:10,640 --> 00:05:16,460
+زائد zero X زائد zero منفع لا منفعش يبقى هذه ال
+
+57
+00:05:16,460 --> 00:05:22,490
+polynomial الصفرية هذا موجود وين؟ موجود في Uإذا
+
+58
+00:05:22,490 --> 00:05:26,950
+الـ U non-empty يبقى ال condition الأول تحقق يبقى
+
+59
+00:05:26,950 --> 00:05:39,710
+ال condition
+
+60
+00:05:39,710 --> 00:05:45,270
+الأول تحقق يبقى
+
+61
+00:05:45,270 --> 00:05:49,290
+ال condition الأول تحقق يبقى ال condition الأول
+
+62
+00:05:49,290 --> 00:05:50,170
+تحقق يبقى ال condition الأول تحقق يبقى ال
+
+63
+00:05:50,170 --> 00:05:50,890
+condition الأول تحقق يبقى ال condition الأول تحقق
+
+64
+00:05:50,890 --> 00:05:50,890
+يبقى ال condition الأول تحقق يبقى ال condition
+
+65
+00:05:50,890 --> 00:05:51,250
+الأول تحقق يبقى ال condition الأول تحقق يبقى ال
+
+66
+00:05:51,250 --> 00:05:51,250
+condition الأول تحقق يبقى ال condition الأول تحقق
+
+67
+00:05:51,250 --> 00:05:51,250
+يبقى ال condition الأول تحقق يبقى ال condition
+
+68
+00:05:51,250 --> 00:05:51,250
+الأول تحقق يبقى ال condition الأول تحقق يبقى ال
+
+69
+00:05:51,250 --> 00:05:51,250
+condition الأول تحقق يبقى ال condition الأول تحق
+
+70
+00:05:51,810 --> 00:06:00,640
+موجودة في اليوم thenبدأ انا اخد C1 في P of X اللي
+
+71
+00:06:00,640 --> 00:06:06,300
+عندنا هذه اشوف هل هي موجودة في ال U ام لا يبقى هذا
+
+72
+00:06:06,300 --> 00:06:14,100
+بدي يعطينا C1 بدي اضربها في AX تربية زائد BX زائد
+
+73
+00:06:14,100 --> 00:06:23,990
+C طبعا يبقى بدي افك الجثة ده يبقى هذا بصير C1AX³
+
+74
+00:06:23,990 --> 00:06:36,770
+AX³
+
+75
+00:06:36,770 --> 00:06:41,810
+AX³ AX³ AX³
+
+76
+00:06:41,810 --> 00:06:51,530
+AX³ AX³مظبوط؟ لأن هذا رقمه هذا رقم و هذا رقم real
+
+77
+00:06:51,530 --> 00:06:56,890
+numbers إذا هذا كله موجود وين؟ في الـ set U إذا
+
+78
+00:06:56,890 --> 00:07:00,750
+انتحقق منين؟ انتحقق ال condition الثاني أخد
+
+79
+00:07:00,750 --> 00:07:05,510
+element من R و أخد element من U لكي تحصل الضرب هذا
+
+80
+00:07:05,510 --> 00:07:09,970
+موجود فيه يبقى باقيا عندي بس ال condition التالت
+
+81
+00:07:09,970 --> 00:07:16,050
+condition التالت بذلك أقول FLP
+
+82
+00:07:28,610 --> 00:07:36,750
+على الشكل A1 X سربية زائد B1 X زائد C1 موجودة في U
+
+83
+00:07:39,100 --> 00:07:45,640
+يبقى بدي أخد مجموعهم بدي أخد ال P of X زائد ل Q of
+
+84
+00:07:45,640 --> 00:07:51,280
+X يبقى هذا الكلام يساوي الجمع component-wise يبقى
+
+85
+00:07:51,280 --> 00:07:57,380
+بدي أجمع هذه مع هذه منهايبقاش بلاقي بلاقي ال ax
+
+86
+00:07:57,380 --> 00:08:09,000
+تربيع زائد a1x تربيع زائد bx زائد b1x زائد c زائد
+
+87
+00:08:09,000 --> 00:08:14,790
+c1 هذا الكلام يساويما رأيك لو هنا في عامل مشترك
+
+88
+00:08:14,790 --> 00:08:19,770
+اللي هو X تربيع وهنا في عامل مشترك اللي هو X وهنا
+
+89
+00:08:19,770 --> 00:08:27,430
+مافيش عامل مشترك يبقى بقدر اقول هذا A زائد A1 كله
+
+90
+00:08:27,430 --> 00:08:35,350
+في X زائد B زائد B1 كله في X هذا X تربيع وهذا X
+
+91
+00:08:35,350 --> 00:08:45,410
+زائد C زائد C1real number في ال X تربيها موجود
+
+92
+00:08:45,410 --> 00:08:50,850
+في ال U أم لا يبقى هدف belongs to main to you إذا
+
+93
+00:08:50,850 --> 00:08:55,310
+انت حققت الشروط التلاتة أم لا يبقى باجي بقوله so
+
+94
+00:08:55,310 --> 00:08:59,770
+ال U is a subspace
+
+95
+00:09:01,690 --> 00:09:09,590
+R V يبقى هذا subspace من V نكمل الأمثلة على نفس
+
+96
+00:09:09,590 --> 00:09:14,130
+الموضوع يبقى
+
+97
+00:09:14,130 --> 00:09:19,630
+هذا المثال رقم خمسة بدنا نروح للمثال رقم ستة يبقى
+
+98
+00:09:19,630 --> 00:09:30,600
+example 6 بقول let V تساوي P تكيب letالـ V تساوي R
+
+99
+00:09:30,600 --> 00:09:39,420
+تكييب و اللي هي بدل ساوي The set of all طبعا
+
+100
+00:09:39,420 --> 00:09:43,900
+اللي هي the set of all X واحد و X اتنين و X ثلاثة
+
+101
+00:09:43,900 --> 00:09:49,280
+و X واحد و X اتنين و X ثلاثة موجودة في ال set of
+
+102
+00:09:49,280 --> 00:09:58,160
+real numbers Little u و دي لنا ال U تساوياللي هو
+
+103
+00:09:58,160 --> 00:10:05,860
+the set of all elements x1 وx2 وx3 such that بحيث
+
+104
+00:10:05,860 --> 00:10:18,160
+ان x3 يساوي x1 زائد x2 السؤال هو show that
+
+105
+00:10:21,470 --> 00:10:35,830
+Show that U is a subspace of V هذا المثال رقم ستة
+
+106
+00:10:35,830 --> 00:10:41,510
+بيقول ما ياتي بدأ أخد ال vector space V هو ال R3
+
+107
+00:10:41,510 --> 00:10:46,490
+تحت عملية الضرب والجمع العاديةاليوزر ستة و برنامج
+
+108
+00:10:46,490 --> 00:10:50,050
+X واحد و X اتنين و X تلاتة بحيث X واحد و X اتنين و
+
+109
+00:10:50,050 --> 00:10:55,830
+X تلاتة are real number بداخل اليوزر تتكون من تلت
+
+110
+00:10:55,830 --> 00:11:01,510
+مراكبات لكن المراكبة الثالثة هي مجموع ال two
+
+111
+00:11:01,510 --> 00:11:06,740
+components الأولى والثانىطلعيني هنا x1 و x2 و x3
+
+112
+00:11:06,740 --> 00:11:12,360
+such that x3 اللي هي تساوي x1 زائد x2 يعني هذا يا
+
+113
+00:11:12,360 --> 00:11:18,440
+بنات لو بدي أصيغة بقول هي كل العناصر على صيغة x1 و
+
+114
+00:11:18,440 --> 00:11:24,680
+x2 و x1 زائد x2 يعني بالشكل اللي عندنا هذا و x1 و
+
+115
+00:11:24,680 --> 00:11:29,540
+x2 موجودة في R تمام يبقى هاي المقصود بالشكل اللي
+
+116
+00:11:29,540 --> 00:11:34,870
+عندنا هذاقال لي بيظهر لي أن هذا is a subspace يبقى
+
+117
+00:11:34,870 --> 00:11:40,290
+أنا بتروح لمين للشروط الثلاثة بدي أثبت أن هذه الـU
+
+118
+00:11:40,290 --> 00:11:45,470
+على الأقل فيها مام فيها element واحد وبعد هيك بروح
+
+119
+00:11:45,470 --> 00:11:50,290
+بكمل إذا بدي أجي للنقطة الأولى حد فيكم بتقدر
+
+120
+00:11:50,290 --> 00:11:54,050
+تجيبلي answer واحد موجود في الـU
+
+121
+00:11:59,950 --> 00:12:11,230
+يبقى باجي بقوله هنا ال U is non-empty ليش؟ because
+
+122
+00:12:13,230 --> 00:12:19,290
+أن الـ zero و ال zero و ال zero موجودة في ال use
+
+123
+00:12:19,290 --> 00:12:26,510
+sentence ليش؟ لأن ال zero بده يساوي zero زائد zero
+
+124
+00:12:26,510 --> 00:12:30,470
+اللي هي المراكبة التالتة تساوي المراكبة الأولى
+
+125
+00:12:30,470 --> 00:12:36,510
+زائد المراكبة آت ثانية النقطة الثانية بداجي أخد
+
+126
+00:12:36,510 --> 00:12:43,490
+element a موجود في set of real numbers andالـ V
+
+127
+00:12:43,490 --> 00:12:49,110
+مثلا موجود في الـ U و الـ V بدي أكتبه على الشكل
+
+128
+00:12:49,110 --> 00:12:57,530
+التالي الـ V تساوي الـ X واحد و X اتنين و X واحد
+
+129
+00:12:57,530 --> 00:13:04,330
+زائد X اتنين موجود في الـ U دامن بدي أخد حصة للضرب
+
+130
+00:13:04,330 --> 00:13:12,520
+يبقى بدي أخد A في Vيبقى هذا بيصير A في X1 و X2 و
+
+131
+00:13:12,520 --> 00:13:22,020
+X1 زائد X2 انطلع هذا موجود في ال U بكون انت هنا من
+
+132
+00:13:22,020 --> 00:13:25,000
+ال condition التاني و بروح بدور عالميا على ال
+
+133
+00:13:25,000 --> 00:13:30,220
+condition الثالث يبقى بيدفك هذا القصة بجي بقوله A
+
+134
+00:13:30,220 --> 00:13:50,600
+X1ax2 a x1 a x2 a x2 a x1 a x2 a x2 a x2 a x2 a x2
+
+135
+00:13:50,600 --> 00:13:56,850
+a x2 a x2 a x2 a x2 a x2 a x2 a x2 a x2 a x2هل هو
+
+136
+00:13:56,850 --> 00:14:01,130
+مجموع الـ two terms اللي هنا؟ يعني المركبة التالتة
+
+137
+00:14:01,130 --> 00:14:04,210
+مجموع المركبة الأولى والمركبة الثانية في الـ a
+
+138
+00:14:04,210 --> 00:14:09,150
+three useful نعم بالضبط إذا هذه موجودة وين؟ موجودة
+
+139
+00:14:09,150 --> 00:14:13,850
+في U يبقى تحقق ال condition الثاني بدأ أروح لل
+
+140
+00:14:13,850 --> 00:14:22,110
+condition الثالث يبقى باجي بقوله F اللي هو من؟ F
+
+141
+00:14:22,360 --> 00:14:29,720
+الـ U بـ small بدها تساوي X واحد و X اتنين و X
+
+142
+00:14:29,720 --> 00:14:37,140
+واحد زائد X اتنين و ال V بدها تساوي Y واحد و Y
+
+143
+00:14:37,140 --> 00:14:43,000
+اتنين و Y واحد زائد Y اتنين هذا الكلام موجود في U
+
+144
+00:14:43,000 --> 00:14:48,550
+thenيبقى أخد عنصرين موجودة في U بالـD أشوف هل
+
+145
+00:14:48,550 --> 00:14:54,410
+جامعهم موجود في U أم لا يبقى بروح باخد له الـU
+
+146
+00:14:54,410 --> 00:15:01,660
+زائد الـVيبقى لجمع component twice يبقى x واحد
+
+147
+00:15:01,660 --> 00:15:10,980
+زائد y واحد x اتنين زائد y اتنين نجمع x واحد زائد
+
+148
+00:15:10,980 --> 00:15:17,660
+x اتنين زائد y واحد زائد y اتنين وهذه المركبة اللي
+
+149
+00:15:17,660 --> 00:15:23,490
+عندناطيب انا بدي اياها مجموع الاولى زي دى التانية
+
+150
+00:15:23,490 --> 00:15:34,420
+بقدر اعيد الترتيب و اقول X1 زي Y1 X2 زي Y2ممكن
+
+151
+00:15:34,420 --> 00:15:42,640
+اجمع هذه مع هذه يبقى مين؟ x واحد زائد y واحد زائد
+
+152
+00:15:42,640 --> 00:15:48,700
+x اتنين زائد y اتنين بالشكل اللي عندنا هذا طلعيلي
+
+153
+00:15:48,700 --> 00:15:52,440
+في ال term اللي عندنا هذا هو مجموع ال components
+
+154
+00:15:52,440 --> 00:15:56,970
+الاتنين هدولنعم هو مجموعة .. إذا هذا موجود وين؟
+
+155
+00:15:56,970 --> 00:16:02,610
+موجود في الـ U إذا تحققت الشروط التلاتة فباجي بقول
+
+156
+00:16:02,610 --> 00:16:11,830
+له الـ U is a subspace of
+
+157
+00:16:11,830 --> 00:16:14,950
+V وانتهينا منها
+
+158
+00:16:42,900 --> 00:16:57,320
+يبقى هذا المثال السادس مثال السابع مثال سبعة بقول
+
+159
+00:16:57,320 --> 00:17:01,940
+الات ال V بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+160
+00:17:01,940 --> 00:17:04,100
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+161
+00:17:09,670 --> 00:17:22,270
+Define لف معرفة on an interval I معرفة على فترة ما
+
+162
+00:17:22,270 --> 00:17:31,670
+نأخد الـ U لت الـ U تساويthe set of all element f
+
+163
+00:17:31,670 --> 00:17:40,910
+such that ال F W prime of X زائد اتنين في ال F of
+
+164
+00:17:40,910 --> 00:17:47,750
+X بده يساوي Zero وهذا الكلام لكل ال X اللي موجودة
+
+165
+00:17:47,750 --> 00:17:57,350
+في ال interval I السؤال هو بيقول prove or disprove
+
+166
+00:17:58,880 --> 00:18:11,160
+prove or disprove that ال U is a subspace of V
+
+167
+00:18:11,160 --> 00:18:26,380
+خانة
+
+168
+00:18:26,380 --> 00:18:32,490
+هذه انتهينا منهاطيب انتوا ملاحظين الأمثلة بالنوعها
+
+169
+00:18:32,490 --> 00:18:37,630
+كل مرة بنجيب مثال شكل يختلف في مضمونه عن المثال
+
+170
+00:18:37,630 --> 00:18:42,030
+القبل لكن بالنسبة للبرهين كله نفس الفكرة تبعة
+
+171
+00:18:42,030 --> 00:18:47,710
+البرهان بس نقدر نطبق له تطبيق صحيح نرجع لسؤالنا
+
+172
+00:18:47,710 --> 00:18:51,710
+هذا مرة ثانية قال ياخد ال V the set of all
+
+173
+00:18:51,710 --> 00:18:56,420
+functions المعرفة على فترة مايعني أنا جيت على ال
+
+174
+00:18:56,420 --> 00:19:00,720
+real line و أخدت فترة محددة و جبت كل ال functions
+
+175
+00:19:00,720 --> 00:19:05,240
+اللي خلقها ربنا و اللي احنا بنعرفه المعرفة على هذه
+
+176
+00:19:05,240 --> 00:19:11,280
+الفترة و قلت هدول vector space اللي هو Vروحت من
+
+177
+00:19:11,280 --> 00:19:14,840
+هذا الـ vector space أخدت مجموعة من ال functions
+
+178
+00:19:14,840 --> 00:19:18,700
+مين هي المجموعة من ال functions؟ هي المجموعة التي
+
+179
+00:19:18,700 --> 00:19:23,240
+تحقق المعادلة اللي بين أدينا هذه يعني لو اشتقت
+
+180
+00:19:23,240 --> 00:19:29,640
+المعادلة مرتين وضفت لها اتنين ضعف الدالة بدي
+
+181
+00:19:29,640 --> 00:19:34,400
+يعطيني الناتج من zero لأي element x موجود في ال
+
+182
+00:19:34,400 --> 00:19:40,780
+interval I مرة تانيةأنا جيت كل ال functions
+
+183
+00:19:40,780 --> 00:19:43,580
+المعرفة على ال interval اللي بدي اعتبره البنات
+
+184
+00:19:43,580 --> 00:19:46,780
+اللي قاعدة قدامي في القاعة هدول كلهم functions
+
+185
+00:19:46,780 --> 00:19:53,000
+معرفة على ال interval تبع القاعة ماشي طيب الان من
+
+186
+00:19:53,000 --> 00:19:58,700
+هدول بدي اختار البنات اللي مشتقتها الثانية زائد
+
+187
+00:19:58,700 --> 00:20:04,750
+اتنين ضرب نفسها بيعطيني zero دائما و أبدايعني كل
+
+188
+00:20:04,750 --> 00:20:09,130
+البنات اللي لا E يحققنا هذه المعادلة كنت اطلع
+
+189
+00:20:09,130 --> 00:20:14,570
+اشكها روحت سميتهم مين؟ سميتهم ال U بدي اثبت ان ال
+
+190
+00:20:14,570 --> 00:20:20,570
+U هذا ال sub space من مين؟ من V او من ال set
+
+191
+00:20:20,570 --> 00:20:23,690
+الأصلي هذا الفكرة في الموضوع دي روايالكوا هذا
+
+192
+00:20:23,690 --> 00:20:28,850
+جيبناه في الامتحانات قبل ذلك يعني هذا سؤال امتحان
+
+193
+00:20:28,850 --> 00:20:35,590
+طيب تعالى نشوفأحاول أن أثبت له أن هذا الـ subspace
+
+194
+00:20:35,590 --> 00:20:40,010
+من الـ 6 اللي فوق يبقى أنا بروح أحقق الشروط
+
+195
+00:20:40,010 --> 00:20:45,810
+التلاتة بداجة للشرط الأول السؤال هو هل بتعرفولي
+
+196
+00:20:45,810 --> 00:20:51,590
+دالة مشتقتها الثانية زائدي اتنين في نفسها بيعطيني
+
+197
+00:20:51,590 --> 00:20:52,010
+zero
+
+198
+00:20:55,610 --> 00:21:00,670
+في كتير في كتير لكن أبسط واحدة منهم ليه ليه
+
+199
+00:21:00,670 --> 00:21:05,810
+trivial function لف وف اكس ساوي قداش Zero مشتقتها
+
+200
+00:21:05,810 --> 00:21:08,630
+مرتين ب Zero و اتنين ب Zero ب Zero يبقى مجموعهم
+
+201
+00:21:08,630 --> 00:21:13,930
+Zero صحيح ولا لأ يبقى هذا أبسط أنواع الدوال مما
+
+202
+00:21:13,930 --> 00:21:20,010
+يثبت ان ال U is non empty يبقى باجي بقوله takeخذ
+
+203
+00:21:20,010 --> 00:21:24,010
+الفرصة f of x يساوي 0
+
+204
+00:21:28,300 --> 00:21:34,420
+الـ F prime of X يساوي Zero والـ F W prime of X
+
+205
+00:21:34,420 --> 00:21:44,280
+يساوي Zero يبقى أصبح لدي الـ F W prime of X زائدي
+
+206
+00:21:44,280 --> 00:21:48,920
+اتنين F of X يساوي Zero الـ F W prime of Zero
+
+207
+00:21:48,920 --> 00:21:55,820
+زائدي اتنين في Zero يساوي Zero هذا معناه ان الـ F
+
+208
+00:21:55,820 --> 00:22:00,710
+اللي عندها موجودة وينفي الـ U هذا معناه ان الـ U
+
+209
+00:22:00,710 --> 00:22:07,850
+is non-empty يبقى هذه ما هياش الفئة الخاوية يبقى
+
+210
+00:22:07,850 --> 00:22:13,350
+هذه الفئة وفيها من وفيها عناصر يبقى هذه أثبتنا ان
+
+211
+00:22:13,350 --> 00:22:19,410
+هذه ال set على الأقل فيها و لو عنصر واحد نجي رقم
+
+212
+00:22:19,410 --> 00:22:26,770
+اتنين بدي اخد ال C موجود في set of real numbers
+
+213
+00:22:29,320 --> 00:22:36,160
+والـ F موجودة في الـ U فالـ F موجودة في الـ U
+
+214
+00:22:36,160 --> 00:22:41,400
+معناته الـ F double prime of X زائدي اتنين F of X
+
+215
+00:22:41,400 --> 00:22:49,460
+بده يساوي Zeroأنا مين بدي أثبت؟ بدي أثبت إن الـCF
+
+216
+00:22:49,460 --> 00:22:55,520
+كلها double prime زائد اتنين CF بده يساوي Zero إن
+
+217
+00:22:55,520 --> 00:23:01,240
+أثبت ذلك بصير الـCF موجودة في الـU وبالتالي بكون
+
+218
+00:23:01,240 --> 00:23:06,540
+تحقق ال condition هالثاني يبقى الآن بداجي أقول
+
+219
+00:23:06,540 --> 00:23:07,420
+consider
+
+220
+00:23:10,510 --> 00:23:17,550
+كده لي كده
+
+221
+00:23:17,550 --> 00:23:23,150
+كده كده كده
+
+222
+00:23:23,150 --> 00:23:32,350
+كده
+
+223
+00:23:32,350 --> 00:23:36,930
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+224
+00:23:36,930 --> 00:23:37,610
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+225
+00:23:37,610 --> 00:23:41,070
+كده كده كده كده كده كدهأظن المقدار الثابت لو فضل
+
+226
+00:23:41,070 --> 00:23:45,790
+مرة ولا مرتين ولا تلاتة ولا عشرة بيظل .. بيظل زي
+
+227
+00:23:45,790 --> 00:23:49,930
+ما هو كل ال function موجودة F لكن لو ال function
+
+228
+00:23:49,930 --> 00:23:54,430
+انتهت بيصير مشتق لبعضها ب Zero مظبوط طب احنا عندنا
+
+229
+00:23:54,430 --> 00:24:00,310
+مشتقتين فبجي بقول له هذا معناه C في ال F double
+
+230
+00:24:00,310 --> 00:24:05,650
+prime of X زاد
+
+231
+00:24:06,250 --> 00:24:14,350
+هذه لو جيت فكتها بيصير اتنين C في ال F of X هذه لو
+
+232
+00:24:14,350 --> 00:24:19,810
+روحت اخدت ال C عام المشترك بيظل F double prime of
+
+233
+00:24:19,810 --> 00:24:26,410
+X زائد اتنين F of X يبقى ده بتسوى كده شبه انا
+
+234
+00:24:26,410 --> 00:24:31,910
+هتهيأ ال C لبرا ل بين جثين هايهأنا فرضه من قبل
+
+235
+00:24:31,910 --> 00:24:38,970
+بقداش؟ بزيرو يبقى الـC في زيرو بقداش ايش تفسير كل
+
+236
+00:24:38,970 --> 00:24:43,730
+هذا الكلام؟ يبقى الـCF موجودة في الـU يبقى هنا
+
+237
+00:24:43,730 --> 00:24:49,290
+بروح بقول له الساعة الـCF موجودة في الـU بده اروح
+
+238
+00:24:49,290 --> 00:24:54,430
+لل condition التالدبدي اخد two functions موجودات
+
+239
+00:24:54,430 --> 00:25:00,450
+في الـ U بمعنى ان الـ f double prime of x زي دي
+
+240
+00:25:00,450 --> 00:25:05,230
+اتنين f of x بدي سوى zero ودالة تانية g of x بحيث
+
+241
+00:25:05,230 --> 00:25:09,270
+الـ g double prime of x زي دي اتنين g of x بدي سوى
+
+242
+00:25:09,270 --> 00:25:16,060
+مين؟ Zero يبقى بداجي اقوله هنا افترضيإن الـ F و
+
+243
+00:25:16,060 --> 00:25:22,200
+الـ G موجودة في الـ U ثم الـ F double prime of X
+
+244
+00:25:22,200 --> 00:25:29,880
+زائد اتنين F of X بدي ساوي Zero و في نفس الوقت G
+
+245
+00:25:29,880 --> 00:25:35,180
+double prime of X زائد اتنين G of X كل هذا بدي
+
+246
+00:25:35,180 --> 00:25:40,510
+ساوي مين؟ بدي ساوي Zeroأنا بدي أثبت إن مجموعهم
+
+247
+00:25:40,510 --> 00:25:45,950
+موجود في الـ U يعني بدي أثبت إن ال F of X زائد ال
+
+248
+00:25:45,950 --> 00:25:51,210
+G of X كله موجود وين؟ بدي موجود في الـ U ليش هكذا؟
+
+249
+00:25:51,210 --> 00:25:58,530
+بدي أروح أقول ما يأتي خوديلي اللي هو F of X زائد
+
+250
+00:25:58,530 --> 00:26:02,150
+ال G of X W prime
+
+251
+00:26:05,020 --> 00:26:16,460
+زائد اتنين F of X زائد G of X اذا طلع هذا يساوي
+
+252
+00:26:16,460 --> 00:26:22,420
+Zero بصير المجموع هذا موجود في اليوم التالي يكون
+
+253
+00:26:22,420 --> 00:26:27,660
+انتهينا من القصة هذا الكلام يساوي نرجع لل calculus
+
+254
+00:26:30,100 --> 00:26:35,200
+مشتقت المجموع الجبري لدالتين يسوى مين؟ المجموع
+
+255
+00:26:35,200 --> 00:26:43,300
+الجبري للمشتقتين ولو اشتقت كمان مرة يبقى
+
+256
+00:26:43,300 --> 00:26:49,960
+المجموع الجبري للمشتقتين يبقى هذا معناه ال F W
+
+257
+00:26:49,960 --> 00:26:58,150
+prime of X زائد ال G W prime of Xمظبوط؟ طيب هذا
+
+258
+00:26:58,150 --> 00:27:03,530
+الكلام بدي أضيفله بدي أفك الـ Goal السادة يبقى 2 F
+
+259
+00:27:03,530 --> 00:27:12,500
+of X زائدي 2 G of X Y الساويبدي اخلهم مجموعتين بدي
+
+260
+00:27:12,500 --> 00:27:17,840
+احط ال f مع بعض و ال g مع بعض يبقى هذا بده يعطينا
+
+261
+00:27:17,840 --> 00:27:24,640
+مين بده يعطينا fw prime of x زي دي اتنين f of x
+
+262
+00:27:24,640 --> 00:27:25,900
+بدي اخدهم مع بعض
+
+263
+00:27:29,230 --> 00:27:37,490
+GW'XGW'XGW
+
+264
+00:27:37,490 --> 00:27:46,250
+'XGW'XGW
+
+265
+00:27:46,250 --> 00:27:51,170
+'XGW
+
+266
+00:27:51,170 --> 00:27:52,930
+'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW
+
+267
+00:27:52,930 --> 00:27:53,370
+'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW
+
+268
+00:27:53,370 --> 00:27:53,370
+'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW
+
+269
+00:27:53,370 --> 00:27:53,370
+'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW'XGW
+
+270
+00:27:53,370 --> 00:28:00,970
+'XGW'XGW'Xزائد ال جي موجودة في ال U يبقى ال U is a
+
+271
+00:28:00,970 --> 00:28:02,090
+subspace
+
+272
+00:28:17,170 --> 00:28:27,670
+الـ U is a subspace of Z
+
+273
+00:28:30,300 --> 00:28:36,120
+طيب أخدنا حتى الآن بدل المثال سبعة أمثلة أعتقد أن
+
+274
+00:28:36,120 --> 00:28:41,260
+هذه الأمثلة السابعة ثبتت مفهوم ال subspace عندنا
+
+275
+00:28:41,260 --> 00:28:46,700
+بدرجة كبيرة يبقى ندخل شوية كمان في نفس ال section
+
+276
+00:28:46,700 --> 00:28:52,380
+فإننا نعطي تعريف جديد التعريف بيقول ما يأتي
+
+277
+00:28:52,380 --> 00:28:54,900
+definition let
+
+278
+00:29:01,360 --> 00:29:12,560
+الـ V بإيه؟ Vector Space Vector Space and let
+
+279
+00:29:12,560 --> 00:29:22,560
+وافترضوا كذلك أن V1 و V2 و لغاية VM موجودة في
+
+280
+00:29:22,560 --> 00:29:34,310
+capital V We say that We say thatإن الـ V هذه الـ
+
+281
+00:29:34,310 --> 00:29:43,350
+V الصغير is a linear combination linear
+
+282
+00:29:43,350 --> 00:29:47,490
+combination
+
+283
+00:29:47,490 --> 00:29:57,930
+linear combination of V1 و V2 و لغاية الـ VM
+
+284
+00:30:00,530 --> 00:30:13,850
+there exist c1 و c2 و cm in are such that
+
+285
+00:30:13,850 --> 00:30:27,170
+بحيث ان ال V بده ساوي c1 v1 c2 v2 cm vm
+
+286
+00:30:29,300 --> 00:30:39,640
+كمان definition تاني if
+
+287
+00:30:39,640 --> 00:30:47,100
+every element
+
+288
+00:30:47,100 --> 00:31:00,720
+of a vector a spaceof a vector space V if every
+
+289
+00:31:00,720 --> 00:31:07,700
+element of a vector space V is a linear
+
+290
+00:31:07,700 --> 00:31:18,280
+combination of
+
+291
+00:31:18,280 --> 00:31:32,320
+V1و V2 و V M We say that .. We say that .. بروح
+
+292
+00:31:32,320 --> 00:31:45,940
+نقول We say that capital V هذا is Spannid .. is
+
+293
+00:31:45,940 --> 00:31:57,570
+Spannid by ..this elements by this elements also
+
+294
+00:31:57,570 --> 00:32:01,170
+وكذلك
+
+295
+00:32:01,170 --> 00:32:15,170
+we say that we say that the elements اللي
+
+296
+00:32:15,170 --> 00:32:25,020
+هو V واحد و V اتنينو VM Span V
+
+297
+00:33:35,580 --> 00:33:41,880
+طيب نجي لل two definitions اللي احنا معرفينهم و
+
+298
+00:33:41,880 --> 00:33:46,100
+بدأنا في الجد شوية اهدروا بالكم الآنمع بداية
+
+299
+00:33:46,100 --> 00:33:49,820
+التعريفات الاتنين دول بدأنا ندخش في صميم الموضوع
+
+300
+00:33:49,820 --> 00:33:53,960
+كل الكلام اللى فات كله كلام بسيط يعتبر اللى هم
+
+301
+00:33:53,960 --> 00:33:58,420
+بيقولوا يفترض ال V هو عبارة عن vector space أخدت
+
+302
+00:33:58,420 --> 00:34:03,100
+مجموعة من ال vectors موجودة وين في V يعني أخدت
+
+303
+00:34:03,100 --> 00:34:08,260
+خمسة ستة سبعة جد ما يكون عددهم V1 وV2 لغاية VM
+
+304
+00:34:08,260 --> 00:34:12,950
+موجودة في capital Vيبقى الفيات هدول كلهم إيش؟ كلهم
+
+305
+00:34:12,950 --> 00:34:17,290
+vectors داخل ال vector space يعني لو جيت قولت
+
+306
+00:34:17,290 --> 00:34:21,190
+البنات هدول ال vector space أخدت من؟ أخدت أول خمسة
+
+307
+00:34:21,190 --> 00:34:24,630
+يبقى أول خمسة يعتبروا vectors في من؟ في ال vector
+
+308
+00:34:24,630 --> 00:34:30,650
+space مالهم الخمسة هدول؟ we say that منقول ال V is
+
+309
+00:34:30,650 --> 00:34:36,270
+a linear combination ofأنا لو روحت و أخدت vector
+
+310
+00:34:36,270 --> 00:34:42,070
+تاني و لاجئت ان ال vector التاني قدرت اكتبه بدلالة
+
+311
+00:34:42,070 --> 00:34:45,990
+الخمسة هدول يعني اخدت اي vector من ال vector اسمه
+
+312
+00:34:45,990 --> 00:34:49,550
+اذا قدرت اكتبه بدلالة الخمسة هدول
+
+313
+00:35:04,700 --> 00:35:11,400
+ماشي يعني يعني لو جيت أخدت أخدت مجموعة من ال
+
+314
+00:35:11,400 --> 00:35:16,860
+vector قولي خمسة زي ما قلنا هنا و الخمسة هدول روحت
+
+315
+00:35:16,860 --> 00:35:21,920
+أخدت vector تاني لجيت ال vector هذا بقدر أكتب
+
+316
+00:35:21,920 --> 00:35:27,040
+بدلالة الخمسة constant في ال vector الأول زاد
+
+317
+00:35:27,040 --> 00:35:29,640
+constant في ال vector التاني زاد constant في ال
+
+318
+00:35:29,640 --> 00:35:34,310
+vector التاني زاد constant في ال vector الخامسإن
+
+319
+00:35:34,310 --> 00:35:39,750
+حدث ذلك يبقى بقول الـ vector V الـ vector الـ
+
+320
+00:35:39,750 --> 00:35:44,790
+element الواحد V هو linear combination مجموعة خطية
+
+321
+00:35:44,790 --> 00:35:52,110
+أو تجميع خطي من ال vectors V1 و V2 و لغاية V5 يبقى
+
+322
+00:35:52,110 --> 00:35:56,450
+هذا معنى linear linear خطي combination تجميعيبقى
+
+323
+00:35:56,450 --> 00:36:02,690
+تجميع خطي تمام لكن هل كل vector of space بقدر
+
+324
+00:36:02,690 --> 00:36:07,690
+أكتبه بدلالة الخمسة هدول الإجابة قد يكون و قد لا
+
+325
+00:36:07,690 --> 00:36:13,310
+يكون طبعا حيكون إذا حدث ذلك في كلام تاني سنتحدث به
+
+326
+00:36:13,310 --> 00:36:18,770
+اليوم ان شاء الله تعالى أو المرة القادمة خليني
+
+327
+00:36:18,770 --> 00:36:24,600
+أسمع هذا مرة تانية بقولأنا عندى .. انا عندى .. اه
+
+328
+00:36:24,600 --> 00:36:29,900
+vector space أخدت منه مجموعة المجموعة هذه قلتلهم
+
+329
+00:36:29,900 --> 00:36:35,140
+صفع شجة صفع شجة جيت ضربت كل صنف الأول كل صنف
+
+330
+00:36:35,140 --> 00:36:39,920
+التاني كل صنف التالت مرة أبقى وجمعتهمأعطانى هذا
+
+331
+00:36:39,920 --> 00:36:43,860
+المجموع vector من ال vector space اللى موجود
+
+332
+00:36:43,860 --> 00:36:48,300
+vector جديد من عناصر ال vector space اللى كبيرة
+
+333
+00:36:48,300 --> 00:36:52,680
+يبقى هذا العنصر بقول هو linear combination من
+
+334
+00:36:52,680 --> 00:36:57,120
+مجموعة العناصر اللى خدتها واضح اظن مش فيه مشكلة
+
+335
+00:36:57,120 --> 00:37:02,270
+واضح على التعريف طيب نجلةالتعريف التاني بيقول لو
+
+336
+00:37:02,270 --> 00:37:07,030
+كان كل عنصر في ال vector space هو linear
+
+337
+00:37:07,030 --> 00:37:12,030
+combination من ال vectors هدول بنروح نقول ال V
+
+338
+00:37:12,030 --> 00:37:16,170
+spanned by this vector بنقول ال vector space V
+
+339
+00:37:16,170 --> 00:37:25,030
+يولد بهذه العناصر أو هذه العناصر تولد من؟ تولد ال
+
+340
+00:37:25,030 --> 00:37:30,140
+vector V تولد V والله هم بولدوا V كله نفس الشيءمرة
+
+341
+00:37:30,140 --> 00:37:39,320
+تانية مرة تانية التعريف التاني إذا بالبلد هيك إذا
+
+342
+00:37:39,320 --> 00:37:44,480
+أخدت أي vector موجود في ال space اللي جيته هو
+
+343
+00:37:44,480 --> 00:37:49,180
+linear combination من مجموعة من ال vectors بقول إن
+
+344
+00:37:49,180 --> 00:37:53,860
+هذه المجموعة ال vectors تولد ال vector space أو ال
+
+345
+00:37:53,860 --> 00:37:59,180
+vector space يولد بهذه المجموعة الموضوع أكترعصير
+
+346
+00:37:59,180 --> 00:38:03,980
+البنات اللي في الشجة دي ستة بس شايفينهم؟ into كل
+
+347
+00:38:03,980 --> 00:38:07,360
+co-vector space من اللي أخدت الستة اللي قلتلهم
+
+348
+00:38:07,360 --> 00:38:13,760
+تعالوا على الشجة جيت مسكت أي واحدة فيكم لجيتها هي
+
+349
+00:38:13,760 --> 00:38:17,220
+كل صفر الأول كل صفر التاني كل صفر التالتة كل صفر
+
+350
+00:38:17,220 --> 00:38:20,160
+الرابعة كل صفر الخمسة كل صفر السادسة طلع بالضبط
+
+351
+00:38:20,160 --> 00:38:25,210
+تمامابعد ذلك جيت لها تانى بنى كنستان تانى جديد مش
+
+352
+00:38:25,210 --> 00:38:29,890
+الكنستان الأولانى تمام و لجيتها بالشكل هذا لما
+
+353
+00:38:29,890 --> 00:38:33,650
+نمسكت من عند أول واحدة لأخر لغاية أخر واحدة من
+
+354
+00:38:33,650 --> 00:38:38,550
+هناك لجيت كل واحدة فيكوا هي عبارة عن حاصل ضرب
+
+355
+00:38:38,550 --> 00:38:41,530
+كنستان في الأولى زي كنستان في التانية زي كنستان في
+
+356
+00:38:41,530 --> 00:38:47,200
+السادسة ان حدث ذلك بقول البنات الستة هدولبوالده كل
+
+357
+00:38:47,200 --> 00:38:52,760
+البنات اللى موجودة فى القاعة او او ال vector space
+
+358
+00:38:52,760 --> 00:38:58,620
+هذا كله يولد بواسطة ده ست بنات صعبة؟ لأبدا، هيبقى
+
+359
+00:38:58,620 --> 00:39:03,040
+هذا معناه اللى ال span تبع اللى طبعا نخش عمق شوية
+
+360
+00:39:03,040 --> 00:39:06,120
+فى المحاضرة بعد الظهر اللى انا منها اتوقف مشان
+
+361
+00:39:06,120 --> 00:39:07,700
+نوزع أوراق
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/TyJEG3dRJH8.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/TyJEG3dRJH8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d45071060645d4eec9de6595e95ef07ee8407a19
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/TyJEG3dRJH8.srt
@@ -0,0 +1,1018 @@
+1
+00:00:19,620 --> 00:00:24,920
+بسم الله الرحمن الرحيم المرة اللي فاتت قلنا بدنا 
+
+2
+00:00:24,920 --> 00:00:29,680
+نيجي لل complex solutions للمعادلة التفاضلية ذات 
+
+3
+00:00:29,680 --> 00:00:35,990
+المعاملات الثابتة من الدرجة النونية وبدأنا بأول 
+
+4
+00:00:35,990 --> 00:00:40,310
+حالة إن هذه المعادلة لو جبنا لها الجذور جبنا 
+
+5
+00:00:40,310 --> 00:00:44,730
+المعادلة المساعدة ومن ثم جيبنا لها الجذور الجذور 
+
+6
+00:00:44,730 --> 00:00:48,870
+هذه قلنا قد تكون حقيقية ومختلفة قد تكون حقيقية 
+
+7
+00:00:48,870 --> 00:00:54,930
+ومكررة قد تكون تخيولية أخذنا الحالة الأولى لو كانت 
+
+8
+00:00:54,930 --> 00:01:00,490
+الجذور حقيقية ومختلفة والآن ننتقل إذا كانت الجذور 
+
+9
+00:01:00,490 --> 00:01:08,070
+ايش كانت؟ التخيلية ممتاز جداً يبقى موضوعنا اليوم 
+
+10
+00:01:08,070 --> 00:01:11,850
+موضوع ال complex rules يبقى حاطين العنوان complex 
+
+11
+00:01:11,850 --> 00:01:15,270
+solutions of the differential equation of y يساوي 
+
+12
+00:01:15,270 --> 00:01:20,490
+مين يساوي zero إذا بدنا نجي نجيب الحلول التخيلية 
+
+13
+00:01:20,490 --> 00:01:24,870
+للمعادلة اللي بالشكل عنها هنا كيف بدها يكون شكلها 
+
+14
+00:01:25,420 --> 00:01:29,380
+جال يعتبر المعادلة الأصلية اللي عندنا هذه اللي 
+
+15
+00:01:29,380 --> 00:01:34,220
+بتدخل دراستنا فيها في ال section الماضي تمام ده 
+
+16
+00:01:34,220 --> 00:01:37,260
+أنا بدي حل هذه المعادلة طبعاً ال a naught و ال a 
+
+17
+00:01:37,260 --> 00:01:41,140
+one و ال a n minus one و ال a n كلهم ثوابت 
+
+18
+00:01:52,970 --> 00:01:59,620
+الرقم هذا قد يكون حقيقي وقد يكون تخيّلي طيب فرضنا 
+
+19
+00:01:59,620 --> 00:02:04,300
+أنه هذا حل لما جينا هذا الحل اشتقتنا مرة و اثنين و 
+
+20
+00:02:04,300 --> 00:02:08,220
+ثلاثة و أربع و اثنتا و كل الحلول هذه are linearly 
+
+21
+00:02:08,220 --> 00:02:14,740
+independent و من ثم حصلنا على المعادلة المساعدة 
+
+22
+00:02:14,740 --> 00:02:19,880
+هذه من خلال تعويض BY ومشتقتها في هذه المعادلة 
+
+23
+00:02:19,880 --> 00:02:23,480
+حصلنا على المعادلة هذه بجهد بسميها المعادلة 
+
+24
+00:02:23,480 --> 00:02:29,590
+المساعدة للمعادلة السهر وبديها الرقم Double star 
+
+25
+00:02:29,590 --> 00:02:34,970
+أو بسميها المعادلة المميزة للمعادلة رقم star 
+
+26
+00:02:34,970 --> 00:02:39,290
+المعادلة هذه هي اللي جذورها قد تكون حقيقية مختلفة 
+
+27
+00:02:39,290 --> 00:02:43,210
+وقد تكون حقيقية مكررة وقد تكون complex موضوعنا 
+
+28
+00:02:43,210 --> 00:02:46,570
+اليوم if the roots of equation double star are 
+
+29
+00:02:46,570 --> 00:02:51,430
+complex يبقى then every pair of solutions are 
+
+30
+00:02:51,430 --> 00:02:58,110
+conjugated كل زوج من هذه الحلول بيكون مترافق هذا 
+
+31
+00:02:58,110 --> 00:03:02,610
+يعني لو كان الحل الأول هو a زائد ib اللي هي R1 
+
+32
+00:03:02,610 --> 00:03:09,050
+يبقى R2 يكون a ناقص ib يبقى the two solutions of 
+
+33
+00:03:09,050 --> 00:03:12,250
+the differential equation هذي R يعني لو كانت 
+
+34
+00:03:12,250 --> 00:03:16,650
+المعادلة من الرتبة الثانية يبقى الحلول هتكون على 
+
+35
+00:03:16,650 --> 00:03:25,820
+الشكل التالي الحل الأول يكون Y1 يساوي E أُس R1 X 
+
+36
+00:03:25,820 --> 00:03:31,980
+يبقى E أُس R1 هو عبارة عن مين عن الجدر يطلع أنه A 
+
+37
+00:03:31,980 --> 00:03:40,980
+زائد IB يبقى A زائد IB في ال X أو إن شئتم فقولوا E 
+
+38
+00:03:40,980 --> 00:03:46,560
+في ال A X مضروبة في ال E أُس IBX 
+
+39
+00:03:48,760 --> 00:03:54,140
+إذا وزعت ال X على القوس فصلت اثنين إلى حاصل ضرب 
+
+40
+00:03:54,140 --> 00:04:00,840
+لأنه عند الضرب إذا تساوت الأساسات تجمع الأسس هذا 
+
+41
+00:04:00,840 --> 00:04:05,400
+الجزء الأول واضح أن هذا real ماليش دعوة إذا هذا 
+
+42
+00:04:05,400 --> 00:04:13,890
+بروح بكتب زي ما هو X بنجي ل E أُس I BX خدنا صيغة 
+
+43
+00:04:13,890 --> 00:04:17,630
+Euler المرة اللي فاتت فقلنا للشغلات اللي من ال 
+
+44
+00:04:17,630 --> 00:04:21,170
+complex number اللي بتلزمنا فكانت عندنا صيغة Euler 
+
+45
+00:04:21,170 --> 00:04:26,230
+E أُس I ثيتا يساوي cosine theta زائد I sine theta 
+
+46
+00:04:26,230 --> 00:04:34,730
+إذا هذه بدها تصير cosine BX زائد I sine BX 
+
+47
+00:04:48,380 --> 00:04:58,730
+الحل الثاني اللي هو and يبقى Y2 بيساوي E أُس R2 X E 
+
+48
+00:04:58,730 --> 00:05:02,510
+أُس A ناقص I B X 
+
+49
+00:05:10,510 --> 00:05:16,490
+يبقى هذا الكلام E أس AX زي ما هو وهذه بصيغة Euler 
+
+50
+00:05:16,490 --> 00:05:25,490
+كذلك اللي هي mean cosine BX ناقص I sine BX أو إن 
+
+51
+00:05:25,490 --> 00:05:35,790
+شئتم فقولوا يبقى E أس AX cosine BX ناقص I E أس AX 
+
+52
+00:05:35,790 --> 00:05:37,990
+sine BX 
+
+53
+00:05:40,030 --> 00:05:48,050
+طلع لي في الحلول اثنين هذول عشان نلاحظ عليهم اثنين 
+
+54
+00:05:48,050 --> 00:05:53,370
+نفس الشيء بس مفرقين عن بعض مين بإشارة سالب يبقى 
+
+55
+00:05:53,370 --> 00:05:59,050
+سالب I والله زائد I عند هذول ثوابت مظبوط ولا لا؟ 
+
+56
+00:05:59,050 --> 00:06:03,010
+آه لو رجعنا للخواص اللي أخذناها المرة اللي فاتت 
+
+57
+00:06:03,010 --> 00:06:10,500
+الخاصية رقم خمسة فيهم خاصية رقم خمسة بتقول لو كان 
+
+58
+00:06:10,500 --> 00:06:16,060
+ال W of X يساوي U of X زائد I of X عبارة عن 
+
+59
+00:06:16,060 --> 00:06:20,720
+solution يبقى كل من المركبة الحقيقية والتخيلية 
+
+60
+00:06:20,720 --> 00:06:26,080
+عبارة عن حل يبقى ال U of X عبارة عن حل وكذلك ال V 
+
+61
+00:06:26,080 --> 00:06:32,700
+of X عبارة عن حل مظبوط مكتوب معكم صح؟ ساكتين إن 
+
+62
+00:06:32,700 --> 00:06:39,210
+.. افتح دفترك وشوف الخاصية رقم 5 خاصية رقم خمسة في 
+
+63
+00:06:39,210 --> 00:06:42,310
+المرة الماضية في نهاية المحاضرة الماضية لما 
+
+64
+00:06:42,310 --> 00:06:47,210
+ابتدأنا هذا section أخذنا ست خواص خاصية رقم خمسة 
+
+65
+00:06:47,210 --> 00:06:52,270
+فيهم مرة ثانية بتقول لو كان W of X بدي أساوي U of 
+
+66
+00:06:52,270 --> 00:06:57,010
+X زائد I V of X عبارة عن solution للمعادلة 
+
+67
+00:06:57,010 --> 00:07:01,630
+التفاضلية يبقى كلهم من U of X وV of X عبارة عن 
+
+68
+00:07:01,630 --> 00:07:06,370
+solution مظبوط ولا لأ يبقى معنا هذا الكلام from 
+
+69
+00:07:11,410 --> 00:07:23,570
+property five we have أنه E أس X E أس X cosine BX 
+
+70
+00:07:23,570 --> 00:07:35,590
+and ال E أس X sin BX are two solutions 
+
+71
+00:07:52,310 --> 00:07:55,890
+هل هم linearly independent ولا linearly 
+
+72
+00:07:55,890 --> 00:08:00,790
+dependent الله أعلم إذا طلع linearly independent 
+
+73
+00:08:00,790 --> 00:08:07,010
+يبقى دول بيجيبوا لي شكل ال general solution طيب يبقى 
+
+74
+00:08:07,010 --> 00:08:11,410
+هنا باجي بقول له الرونسكين as a function of x يساوي 
+
+75
+00:08:11,410 --> 00:08:22,860
+المحدد E أس AX Cos BX و E أس AX Sin BX بدنا نشتق 
+
+76
+00:08:22,860 --> 00:08:31,260
+هذه مشتقة حاصل ضرب دالتين يبقى a في e أس a x في 
+
+77
+00:08:31,260 --> 00:08:41,120
+cosine bx ناقص b في e أس a x في sin bx أفضل cosine 
+
+78
+00:08:41,120 --> 00:08:46,980
+بسالب sin ضرب مشتقة الزاوية هذا بنفس الطريقة a في e 
+
+79
+00:08:46,980 --> 00:08:57,120
+أس a x في sin bx زائد اللي هو B في E أس AX في Cos 
+
+80
+00:08:57,120 --> 00:09:08,660
+BX شكلها النانو يبقى هذا المحدد كالتالي الرئيس 
+
+81
+00:09:08,660 --> 00:09:17,950
+الناقص الثانوي يبقى A E أس اثنين AX في مين؟ في sin 
+
+82
+00:09:17,950 --> 00:09:28,430
+بي إكس كسين بي إكس زائد ب في الـ E أسي اثنين AX 
+
+83
+00:09:28,430 --> 00:09:38,150
+كوصين تربيع للـ BX هذا الرئيسي ناقصي الثانوي ناقص 
+
+84
+00:09:38,150 --> 00:09:48,570
+A في الـ E أسي اثنين AX في الـ sine بيكس كوصين بيكس 
+
+85
+00:09:48,570 --> 00:09:59,490
+ناقص مع ناقص بصير زائد بي أس اثنين اكس صين تربيع 
+
+86
+00:09:59,490 --> 00:10:01,570
+بكس 
+
+87
+00:10:03,720 --> 00:10:09,580
+أظن هذه بالسالب وهذه بالموجب بنفس الشيء مع السلامة 
+
+88
+00:10:09,580 --> 00:10:16,840
+يساوي بي في e أس اثنين ax في cosine تربيع بي اكس 
+
+89
+00:10:16,840 --> 00:10:21,200
+زائد sin تربيع بي اكس اللي هو القداش اللي بين قوسين 
+
+90
+00:10:21,200 --> 00:10:32,440
+يساوي بي في e أس اثنين ax طبيب 
+
+91
+00:10:32,440 --> 00:10:40,880
+كويس السؤال هو هل يمكن ل B أن تبقى ب Zero؟ B تبقى ب 
+
+92
+00:10:40,880 --> 00:10:48,850
+Zero؟ من وين جتني B؟ هي جتني من هنا هذا واحد وهذا 
+
+93
+00:10:48,850 --> 00:10:53,150
+واحد، لو كانت هدف Zero أو هدف Zero، بيظل الحل 
+
+94
+00:10:53,150 --> 00:10:56,230
+Complex لو بيصير Real، بيصير Real، يبقى احنا 
+
+95
+00:10:56,230 --> 00:11:00,450
+طالعنا برا الكلام ده، إذا لا يمكن الـ B أن تساوي 
+
+96
+00:11:00,450 --> 00:11:04,690
+Zero، هذا واحد. الثانية، هل ال exponential في يوم 
+
+97
+00:11:04,690 --> 00:11:09,210
+من الأيام بتساوي Zero؟ طبعاً لأ، يبقى بناء عليه 
+
+98
+00:11:09,210 --> 00:11:13,450
+المحدد هذا لا يساوي Zero إذن اثنين هذول are 
+
+99
+00:11:13,450 --> 00:11:17,410
+linearly independent solution يبقى هذول بيجيبوا لي 
+
+100
+00:11:17,410 --> 00:11:20,750
+main الحل العام يبقى هنا 
+
+101
+00:11:27,130 --> 00:11:35,070
+And الـ E أُس X في side بي X are linearly 
+
+102
+00:11:35,070 --> 00:11:45,010
+independent يبقى بناء عليه The general solution of 
+
+103
+00:11:45,010 --> 00:11:46,830
+equation 
+
+104
+00:11:50,280 --> 00:11:57,780
+ما رأيكم بأخذ E أس A X عامل مشترك بيظل C1 في 
+
+105
+00:11:57,780 --> 00:12:04,860
+cosine بيكس زي C2 في sin بيكس بالشكل اللي عندنا 
+
+106
+00:12:04,860 --> 00:12:12,440
+مرة 
+
+107
+00:12:12,440 --> 00:12:13,060
+ثانية بقول 
+
+108
+00:12:17,870 --> 00:12:23,910
+جلبنا كل من R واحد و R اثنين يبقى صار عندي الحل 
+
+109
+00:12:23,910 --> 00:12:28,690
+لأن الحل الأول Y one E أس R one X حطينا ال R one و 
+
+110
+00:12:28,690 --> 00:12:34,630
+حطينا بدالها A زائد I B X فكيت الجزء وصار two 
+
+111
+00:12:34,630 --> 00:12:38,650
+exponentials هذه الريا اللي بخليها زي ما هي هذه 
+
+112
+00:12:38,650 --> 00:12:43,110
+complex مكتوبة بصيغة Euler كتبناها بالشكل اللي 
+
+113
+00:12:43,110 --> 00:12:50,460
+عندنا ده بالمِثل Y2E2R2A-IBX زي كتبناها بالشكل اللي 
+
+114
+00:12:50,460 --> 00:12:53,920
+عندنا هذا الدالة اللي هنا هي الدالة اللي هنا و 
+
+115
+00:12:53,920 --> 00:12:57,680
+اللي هنا اللي هنا الباقية تكون ثوابت يبقى طبقة 
+
+116
+00:12:57,680 --> 00:13:04,810
+للخاصية كومنكس نموذج السابق رقم خمسة EOSX Cos BX 
+
+117
+00:13:04,810 --> 00:13:10,770
+وكذلك EOSX Sin BX are solutions لكن هل هدول هم 
+
+118
+00:13:10,770 --> 00:13:15,390
+اللي بيجيبوا لي ال general solution ولا لأ أو هم ال 
+
+119
+00:13:15,390 --> 00:13:19,710
+bases للـ vector space of all solutions ولا لأ 
+
+120
+00:13:19,710 --> 00:13:24,090
+الله أعلم إذا لو رحت أخذت اللي هم الرونسكين حسبنا 
+
+121
+00:13:24,090 --> 00:13:28,290
+الرونسكين اللي جيت له ما له لا يساوي 0 يقل اثنين هذول are 
+
+122
+00:13:28,290 --> 00:13:32,810
+linearly independent مدام linearly independent 
+
+123
+00:13:32,810 --> 00:13:37,170
+يبقى بناء عليه شكل ال general solution constant في 
+
+124
+00:13:37,170 --> 00:13:43,680
+الأول زائد constant في الثاني الـ E Os X عامل 
+
+125
+00:13:43,680 --> 00:13:47,740
+المشترك ما بين الاثنين أخذناهم يبقى شكل الحل في 
+
+126
+00:13:47,740 --> 00:13:54,280
+حالة ال complex root هو E Os X في C1 Cos BX زي C2 
+
+127
+00:13:54,280 --> 00:14:00,730
+Sin BX يبقى يا بنات لو احنا بنحل شغل رسمي الآن من 
+
+128
+00:14:00,730 --> 00:14:04,830
+حد ملاقي ال roots هدول complex ما فيش داعي لكل 
+
+129
+00:14:04,830 --> 00:14:10,410
+الكلام هذا أنا أعطيته لكم نظري ووصلتكم لمين للإجابة من 
+
+130
+00:14:10,410 --> 00:14:13,550
+حد ما جيب لي ال roots قولوا لي الحل على الشكل التالي 
+
+131
+00:14:13,550 --> 00:14:19,570
+مين هي ال a هو الرقم الأول اللي عندنا هذا طب افرض 
+
+132
+00:14:19,570 --> 00:14:24,340
+ما طلعش عندي a لما جبته طلعت بس ib منها دي بتشيل 
+
+133
+00:14:24,340 --> 00:14:27,900
+بيطلع E و ال zero اللي هو ال main إيه بواحد؟ طب و 
+
+134
+00:14:27,900 --> 00:14:31,360
+ال B main هو المعامل تبع ال I اللي عندنا ده 
+
+135
+00:14:31,360 --> 00:14:35,420
+وبالتالي صارت قصتنا بسيطة حد فيكم بتسأل أسئلة لإنه 
+
+136
+00:14:35,420 --> 00:14:40,460
+خلصنا النظر تبع ال section بدنا نبدأ ناخذ أمثلة حد 
+
+137
+00:14:40,460 --> 00:14:47,380
+فيكم ليه تسأل هنا؟ آه فيش؟ إذا ما فيش أنا بسألك كل 
+
+138
+00:14:47,380 --> 00:14:50,280
+وقت اكتب اسم و رقم الجامعة هنا تفضل 
+
+139
+00:14:54,150 --> 00:14:58,650
+طيب يبقى بدنا نجي الأول مثال على هذا الموضوع 
+
+140
+00:14:58,650 --> 00:15:07,370
+المثال بيقول يبقى example one يقول 
+
+141
+00:15:07,370 --> 00:15:09,110
+find the general solution 
+
+142
+00:15:21,630 --> 00:15:27,350
+of the differential equation of the differential 
+
+143
+00:15:27,350 --> 00:15:39,890
+equation للمعادلة التفاضلية D² زائد أربعة D زائد 
+
+144
+00:15:39,890 --> 00:15:45,890
+خمسة كله في ال Y بده يساوي مين بده يساوي Zero 
+
+145
+00:16:14,340 --> 00:16:19,500
+قبل نبدأ حل أنا هسأل لأن قلت لكم حد بتسأل أي سؤال 
+
+146
+00:16:19,500 --> 00:16:24,400
+ولو حد حكى اطلقته ساكتي يبقى أنا بدي أسأل احنا 
+
+147
+00:16:24,400 --> 00:16:28,780
+حكينا اللي طلعنا الحل هذا لو كانت المعادلة من 
+
+148
+00:16:28,780 --> 00:16:36,800
+الرتبة الثانية فبفرض طلعت من الرتبة الثالثة بدي 
+
+149
+00:16:36,800 --> 00:16:41,240
+أبدأ نفس القصة USRX هو عبارة عن حل نجيب ال 
+
+150
+00:16:41,240 --> 00:16:44,480
+characteristic equation بس ال characteristic لها 
+
+151
+00:16:44,480 --> 00:16:51,620
+ثلاثة حلول ممكن يطلعوا الثلاثة complex؟ ممكن؟ مش 
+
+152
+00:16:51,620 --> 00:16:55,460
+ممكنية ممكن يطلعوا اثنين complex إن الواحد هو 
+
+153
+00:16:55,460 --> 00:17:00,380
+المرافق تبعه إذا لا يمكن يكونوا الثلاثة complex 
+
+154
+00:17:00,380 --> 00:17:05,280
+اثنين complex واحد real طب افرض من الرتبة الرابعة 
+
+155
+00:17:06,130 --> 00:17:12,350
+وطلع أربعة complex يبقى كل اثنين بيكونوا conjugate 
+
+156
+00:17:12,350 --> 00:17:20,890
+يعني احنا هدول حلين بيجي كمان زائد C ثلاثة في E أس 
+
+157
+00:17:20,890 --> 00:17:26,170
+الرقم غير الرقم هذا هيكون و ال B هذه كمان رقم ثاني 
+
+158
+00:17:26,170 --> 00:17:31,250
+يبقى زيها بس بنكررها للرقمين الآخرين و هكذا يعني 
+
+159
+00:17:31,250 --> 00:17:35,370
+كل اثنين بيكونوا conjugate يبقى ال exponential 
+
+160
+00:17:35,370 --> 00:17:39,790
+بيكون L أُس انتقلت لرقم ثلاثة بلاي ال exponential 
+
+161
+00:17:39,790 --> 00:17:43,750
+ل L أُس ثاني والزاوية تابعة ال cosine والsin كمان 
+
+162
+00:17:43,750 --> 00:17:48,490
+زاوية ثانية و هكذا واضح كلامي؟ لأن أول ما بدأنا هو 
+
+163
+00:17:48,490 --> 00:17:52,890
+معادلة من الرتبة النونية، بسطنا وقلنا معادلة من 
+
+164
+00:17:52,890 --> 00:17:57,470
+الرتبة الثانية وليه سميناها المعادلة رقم واحد، لكن 
+
+165
+00:17:57,470 --> 00:18:00,090
+لو صارت من الرتبة الثالثة أو الرابعة أو الخامسة، 
+
+166
+00:18:00,090 --> 00:18:04,960
+شوفوا إذا رتبة فردية لا يمكن يطلعوا كلهم complex 
+
+167
+00:18:04,960 --> 00:18:08,780
+ممكن يكونوا complex وإذا real لكن إذا رتبة زوجية 
+
+168
+00:18:08,780 --> 00:18:13,860
+ممكن كلهم يكونوا complex عادي جداً ليش؟ لأن كل حل 
+
+169
+00:18:13,860 --> 00:18:20,340
+المرافق طبعه على طول الخطوط طب نجي لسؤالنا أنت كاتب 
+
+170
+00:18:20,340 --> 00:18:23,580
+D هنا بقول لك آدم هم نار و نار اللي فاتت قلنا D 
+
+171
+00:18:23,580 --> 00:18:27,620
+هي المشتقة الأولى بالنسبة ل X D² هي المشتقة 
+
+172
+00:18:27,620 --> 00:18:32
+
+201
+00:21:32,490 --> 00:21:42,680
+star isY to 7 E أُس A X الـ A عندي بقدرش بسالي
+
+202
+00:21:42,680 --> 00:21:51,840
+باتنين X فى C واحد كوصين الـ B بقدرش بواحد كوصين X
+
+203
+00:21:51,840 --> 00:21:58,700
+زائد C اتنين صين الـ X كفى الله المؤمنين القتالى
+
+204
+00:21:58,700 --> 00:22:01,980
+يبقى هذا حل المعادلة التفاضلية
+
+205
+00:22:04,640 --> 00:22:13,960
+المثال الثاني example 2 solve
+
+206
+00:22:13,960 --> 00:22:22,680
+the initial value problem اللي هي y double prime
+
+207
+00:22:22,680 --> 00:22:30,200
+زائد ستاشر y بده يساوي zero والـ y عند الـ zero بده
+
+208
+00:22:30,200 --> 00:22:35,320
+يساوي لإتنين والـ y prime عند الـ zero بده يساوي
+
+209
+00:22:35,320 --> 00:22:36,360
+سالب اتنين
+
+210
+00:22:44,390 --> 00:22:50,990
+يبقى بنفس الطريقة افترض ان الـ Y تساوي E أُص R X
+
+211
+00:22:50,990 --> 00:23:02,310
+بيه solution of the initial value problem وسموها
+
+212
+00:23:02,310 --> 00:23:11,290
+لي Star then the characteristic equation
+
+213
+00:23:15,620 --> 00:23:25,200
+R تربيع زائد ستاشر يساوي زيرو هذا بدى يعطينا يا
+
+214
+00:23:25,200 --> 00:23:32,120
+بنات اللي هو قداش اللي هو R تساوي زائد او ناقص
+
+215
+00:23:32,120 --> 00:23:41,040
+الجذر التربيع الى ناقص ستاشر اللي هو قداش زائد او
+
+216
+00:23:41,040 --> 00:23:48,900
+ناقص اربعة I يبقى الـ A عندي بقدرش؟ Zero و الـ B
+
+217
+00:23:48,900 --> 00:23:54,860
+باربع يعني هذا معناته ان الـ A تساوي Zero و الـ B
+
+218
+00:23:54,860 --> 00:23:59,720
+تساوي أربع يبقى بناء عليه أصبح the solution
+
+219
+00:24:14,300 --> 00:24:18,840
+يبقى C1cos4xC2sin4x وماعنديش exponential
+
+220
+00:24:21,930 --> 00:24:29,930
+ما رايكوا بالمرة نجيب y' يساوي اللي هو سالب 4 c1
+
+221
+00:24:29,930 --> 00:24:40,600
+sin 4x زائد 4 c2 cos 4x بنجي لان نقش ال condition
+
+222
+00:24:40,600 --> 00:24:47,720
+الأول جالي y عند الـ zero بده يتساوي قداش اتنين هذا
+
+223
+00:24:47,720 --> 00:24:56,500
+معناته انه اتنين بده يساوي c واحد قصين الـ zero اظن
+
+224
+00:24:56,500 --> 00:25:02,580
+صين الـ zero ب zero يبقى طارت يبقى زائد زيرو هذا
+
+225
+00:25:02,580 --> 00:25:07,980
+معناته انه C1 يساوي 2 لان الـ cosine صفر بواحد الآن
+
+226
+00:25:07,980 --> 00:25:12,900
+نيجي للـ Y prime عند الـ zero Y prime عند الـ zero
+
+227
+00:25:12,900 --> 00:25:18,580
+بده ساوي سالي ب 2 هذا implies انه سالي ب 2 بدنا
+
+228
+00:25:18,580 --> 00:25:27,130
+نيجي للـ Y prime يبقى zero وهنا زائد اربع c اتنين
+
+229
+00:25:27,130 --> 00:25:33,790
+cosine صفر cosine صفر بواحد يبقى معناته انه c
+
+230
+00:25:33,790 --> 00:25:39,490
+اتنين بده يساوي سالب نص يبقى باجي بقوله هنا
+
+231
+00:25:39,490 --> 00:25:43,890
+solution of
+
+232
+00:25:44,620 --> 00:25:57,820
+The initial value problem is Y تساوي C1-B2 Cos 4X
+
+233
+00:25:57,820 --> 00:26:04,380
+C2-1.5 Sin 4X
+
+234
+00:26:24,020 --> 00:26:34,960
+الأمثلة الثالثة Solve
+
+235
+00:26:34,960 --> 00:26:44,720
+the differential equation Y
+
+236
+00:26:44,720 --> 00:26:51,240
+to the derivative of 5 V
+
+237
+00:26:55,090 --> 00:27:02,990
+ناقص 16Y' يساوي 0 هذه
+
+238
+00:27:02,990 --> 00:27:04,210
+معدلة من أي رتبة
+
+239
+00:27:06,830 --> 00:27:11,790
+الخامسة معناته عندي خمسة حلول معناته في إشي
+
+240
+00:27:11,790 --> 00:27:17,410
+complex و إشي real تمام؟ لإنه فردي الرقم فردي يمكن
+
+241
+00:27:17,410 --> 00:27:23,370
+يكون عندي أربع complex و واحد real أو تلاتة real و
+
+242
+00:27:23,370 --> 00:27:28,590
+اتنين complex مظبوط؟ هاي الخمسة تعالوا نشوف يبقى
+
+243
+00:27:28,590 --> 00:27:32,510
+بدي أبدأ بنفس التكتيك المتبعة عند حل المثالين
+
+244
+00:27:32,510 --> 00:27:35,050
+السابقين
+
+245
+00:27:35,740 --> 00:27:45,940
+بدا اقول له let Y تساوي E بصر X بيه solution of
+
+246
+00:27:45,940 --> 00:27:53,640
+the differential equation star وسميلي هذه المعادلة
+
+247
+00:27:53,640 --> 00:28:00,430
+اللي هي رقم star يبقى بناءً عليه بقوله دي
+
+248
+00:28:00,430 --> 00:28:10,190
+characteristic equation is R أس خمسة ناقص ست عشر R
+
+249
+00:28:10,190 --> 00:28:18,240
+بدي ساوي قداش Zero أو ممكن اخد R عامل مشترك بظل R
+
+250
+00:28:18,240 --> 00:28:24,880
+أربعة ناقص ستة عشر يسوى جداش Zero هذا فرق بين
+
+251
+00:28:24,880 --> 00:28:33,070
+المربعين يبقى R فى R تربيع ناقص أربعة فى R تربيع
+
+252
+00:28:33,070 --> 00:28:37,970
+زائد أربعة يساوي Zero هذا الجوز كمان فرق بين
+
+253
+00:28:37,970 --> 00:28:46,010
+المربعين يبقى R فى R ناقص اتنين فى R زائد اتنين فى
+
+254
+00:28:46,010 --> 00:28:52,070
+R تربيع زائد أربعة يساوي Zero هذا لا يمكن تحليله
+
+255
+00:28:52,070 --> 00:28:59,160
+تمام؟ إذا بقدر أقول هنا يا إما R تساوي Zero ياما R
+
+256
+00:28:59,160 --> 00:29:06,600
+تساوي اتنين، ياما R تساوي سالب اتنين، ياما R تربيه
+
+257
+00:29:06,600 --> 00:29:12,060
+تساوي سالب اربعة، هذا بتعطيك ان R تساوي زائد او
+
+258
+00:29:12,060 --> 00:29:23,380
+ناقص جداش اتنين I إذا أصلا عندي كام حل خمسة حلول
+
+259
+00:29:23,380 --> 00:29:28,880
+اتنين complex و تلاتة real تمام؟ اذا بتروح اجيب
+
+260
+00:29:28,880 --> 00:29:33,940
+شكل الحل العام بس الـ real زي ما انت شايفها هذا
+
+261
+00:29:33,940 --> 00:29:40,520
+عنده الـ a بقداش؟ Zero و الـ b؟ باتنين يبقى هذا الحل
+
+262
+00:29:40,520 --> 00:29:47,460
+بالذات يعني ان a تساوي zero و b تساوي اتنين يبقى
+
+263
+00:29:47,460 --> 00:29:54,900
+بناء عليه أصبح هذه هي حلقة
+
+264
+00:29:54,900 --> 00:30:02,080
+عامة لإيقاع
+
+265
+00:30:08,760 --> 00:30:16,100
+سي واحد في E أس زيرو E أس زيرو بجداش مع السلامة
+
+266
+00:30:16,100 --> 00:30:24,360
+زائد C اتنين E أس اتنين X زائد C تلاتة E أس ناقص
+
+267
+00:30:24,540 --> 00:30:29,820
+أتنين أكس خلصنا الـ real وزي ما انت شايف وقال هدول
+
+268
+00:30:29,820 --> 00:30:34,360
+التلاتة real and different ولا واحد يوم زي التاني
+
+269
+00:30:34,360 --> 00:30:39,380
+يعني كأن هذا السؤال أصبح مزيجا ما بين الـ section
+
+270
+00:30:39,380 --> 00:30:44,480
+اللي بين إيدنا و الـ section الجذور الماضي كانوا
+
+271
+00:30:44,480 --> 00:30:50,040
+حقيقية ومختلفة يبقى انا عندي ثلاثة جذور وهذه
+
+272
+00:30:50,040 --> 00:30:54,500
+الثلاثة حقيقية ومختلفة هذول اتنين complex و الـ
+
+273
+00:30:54,500 --> 00:30:58,920
+complex are conjugated يبقى تبعين الحقيقه بده اطبق
+
+274
+00:30:58,920 --> 00:31:02,440
+عليهم الحقيقه و الـ complex بده اطبق عليهم الـ
+
+275
+00:31:02,440 --> 00:31:11,210
+complex زادكو صين اتنين اكس زائد C خمسة صين اتنين
+
+276
+00:31:11,210 --> 00:31:17,290
+اكس لإن E of Zero يبقى داشر بواحد يبقى هذا الشكل
+
+277
+00:31:17,290 --> 00:31:22,830
+الـ general solution لمين للمعادلة اللي عندنا فهم
+
+278
+00:31:22,830 --> 00:31:27,250
+اللي هو المعادلة رقم start حد فيكم بتسأل أي سؤال
+
+279
+00:31:27,250 --> 00:31:31,190
+انا
+
+280
+00:31:31,190 --> 00:31:39,780
+بسأل بعدين اه طيب انا بسأل بسألكوا كلكوا حل المسائل
+
+281
+00:31:39,780 --> 00:31:47,540
+التالية exercises خمسة تلاتة المسائل السؤال التالت
+
+282
+00:31:47,540 --> 00:31:56,300
+بدنا a و b و c و السؤال السابع و السؤال التام
+
+283
+00:32:00,350 --> 00:32:05,690
+هذا الرقم D أول مثال فيهم هو رقم D 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/W-gk0MowpAY_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/W-gk0MowpAY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..93e859cb467fbda6ffd400289ce4d733a8e8cdd8
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/W-gk0MowpAY_postprocess.srt
@@ -0,0 +1,1668 @@
+1
+00:00:20,700 --> 00:00:25,610
+بسم الله الرحمن الرحيمأنت هنا في section 2-4 من
+
+2
+00:00:25,610 --> 00:00:31,490
+ضرب المصوفة مقدار ثامت أو جامع مصوفتين أو ال raw
+
+3
+00:00:31,490 --> 00:00:35,570
+vectors و ال cone vectors ننتقل هنا في section 2-5
+
+4
+00:00:35,570 --> 00:00:40,270
+ل matrix multiplication يعني عملية ضرب المصوفات
+
+5
+00:00:40,270 --> 00:00:44,210
+يعني بدنا نضرب مصوفتين في بعض ال section السابق
+
+6
+00:00:44,210 --> 00:00:48,010
+كان ضرب كونستان في مصوفة لأ هنا بدنا نضرب two
+
+7
+00:00:48,010 --> 00:00:53,950
+matrices مع بعضهم البعضبقول لو كان عندنا ال system
+
+8
+00:00:53,950 --> 00:00:57,890
+of linear equation بالشكل اللي عندنا هذا كويس هذا
+
+9
+00:00:57,890 --> 00:01:02,810
+ال system بدي أحاول أصيغه بصياغة أخرى باستخدام
+
+10
+00:01:02,810 --> 00:01:07,870
+عملية ضرب المصفوفات إذا بدي أجمع الثوابط الإيهات
+
+11
+00:01:07,870 --> 00:01:13,850
+كلهم في مصفوفة والمجاهيل ال X في مصفوفة والثوابط
+
+12
+00:01:13,850 --> 00:01:17,770
+في مصفوفة زي ما انتوا شايفين الشكل اللي عندنا هذا
+
+13
+00:01:18,060 --> 00:01:22,200
+يبقى هذا ال system قدرت اكتب على شكل حاصل ضرب
+
+14
+00:01:22,200 --> 00:01:27,560
+مصففتين بده يساوي مان بده يساوي مصففة المصففة هذا
+
+15
+00:01:27,560 --> 00:01:32,500
+ايش كنا نسميها بنات؟مصوفة المعاملات الـ
+
+16
+00:01:32,500 --> 00:01:38,440
+coefficient matrix هذه المصوفة مصوفة المجاهيل الـ
+
+17
+00:01:38,440 --> 00:01:43,620
+unknown matrix هذه مصوفة الثوابت الـ constant
+
+18
+00:01:43,620 --> 00:01:47,920
+matrix يبقى هذه مصوفة الثوابت هذه مصوفة المجاهيل
+
+19
+00:01:47,920 --> 00:01:54,420
+هذه مصوفة المعاملات لو ضربنا هدول في بعض بيطلع
+
+20
+00:01:54,420 --> 00:01:58,020
+عندنا من؟ بيطلع عندنا اللي فوق كيف عملية الضرب؟
+
+21
+00:01:58,040 --> 00:02:09,500
+بدرب الصف الأول في العمودي الأول A11x1 A12x2 A13x3
+
+22
+00:02:09,500 --> 00:02:13,060
+A14x4 A1nxn
+
+23
+00:02:18,190 --> 00:02:23,950
+وهكذا الان الصف الثاني في نفس العمود اللى عندنا
+
+24
+00:02:23,950 --> 00:02:28,790
+هذا بطلع المعادلة رقم اتنين الصف التالت في نفس
+
+25
+00:02:28,790 --> 00:02:33,150
+العمود بطلع المعادلة اتنين الصف رقم M في العمود
+
+26
+00:02:33,150 --> 00:02:39,170
+بيعطينا المعادلة رقم M اللى عندنا طيب هذا بدي يخلي
+
+27
+00:02:39,170 --> 00:02:47,130
+عندنا شرط متى يمكن ضرب مصوفتين تماميمكن ضربها تاني
+
+28
+00:02:47,130 --> 00:02:53,370
+المصفوف تاني إذا كان عدد أعمدة المصفوف الأولى يسوى
+
+29
+00:02:53,370 --> 00:02:59,290
+عدد صفوف المصفوف الثاني اطلع هدول الأعمدة كم واحد؟
+
+30
+00:02:59,290 --> 00:03:05,470
+واحد اتنين تلاتة أربعة ان عدد صفوف التانية واحد
+
+31
+00:03:05,470 --> 00:03:11,730
+اتنين تلاتة أربعة ان يبقى تساوى عدد أعمدة الأولى
+
+32
+00:03:11,730 --> 00:03:18,180
+مع عدد صفوفالثانية إذا يمكن أن تتم عملية الضرب
+
+33
+00:03:18,180 --> 00:03:25,660
+والناتج هو مصفوفة عبارة عن عدد صفوف المصفوفة
+
+34
+00:03:25,660 --> 00:03:33,050
+الأولى وأعمدة من المصفوفة الثانية وهكذاهذا الكلام
+
+35
+00:03:33,050 --> 00:03:36,130
+اللي أنا بقوله بدنا نحطه في صيغة الـ definition
+
+36
+00:03:36,130 --> 00:03:40,590
+التالي اللي موجود عندنا ال definition بيقول ما
+
+37
+00:03:40,590 --> 00:03:48,290
+ياتي F ال A is an اللي هو مين M في N matrix يبقى
+
+38
+00:03:48,290 --> 00:03:54,030
+مصفوفة ال size تبعها M في N عدد الصفوف M عدد
+
+39
+00:03:54,030 --> 00:04:01,250
+الأعمدة Nو B كانت عبارة عن matrix ل N في K يبقى
+
+40
+00:04:01,250 --> 00:04:06,170
+عدد الصفوف يساوي N وعدد الأعمدة يساوي K يبقى عدد
+
+41
+00:04:06,170 --> 00:04:11,410
+الصفوف هنا يساوي عدد الأعمدة هنا بالضبط تماما إذا
+
+42
+00:04:11,410 --> 00:04:17,150
+يمكن أن تتم عملية الضربthen we define the
+
+43
+00:04:17,150 --> 00:04:20,730
+multiplication matrix المصفوفة الناتجة من عملية
+
+44
+00:04:20,730 --> 00:04:26,390
+ضرب بدي اعطيها الرمز capital C وهي تساوي A في B
+
+45
+00:04:26,390 --> 00:04:33,070
+with size M في K يعني يا بنات المصفوفة الأولى M في
+
+46
+00:04:33,070 --> 00:04:42,400
+N والتانية N في K البشطة بهذه وهذه بيظل M في Kيبقى
+
+47
+00:04:42,400 --> 00:04:48,420
+المصحوفة الناتجة بد يكون فيها M من الصفوف و K من
+
+48
+00:04:48,420 --> 00:04:53,300
+الأعمل واضح كلامنا كم؟ مرة تانية بقول يبقى أنا عند
+
+49
+00:04:53,300 --> 00:04:58,760
+المصحوفة الأولى نظامها M في Nالمصوفة التانية
+
+50
+00:04:58,760 --> 00:05:04,080
+نظامها N في K عدد الأعمدة في الأولى يسوى عدد
+
+51
+00:05:04,080 --> 00:05:09,380
+الصفوف في الثانية إذا يمكن أن نقوم بعملية الضغط طب
+
+52
+00:05:09,380 --> 00:05:14,560
+ضربنا شو شكل المصوفة الناتجة شكلها ومصوفها فيها M
+
+53
+00:05:14,560 --> 00:05:20,500
+من الصفوف وK من الأعمدة هذا يجعلني أطرح السؤال
+
+54
+00:05:20,500 --> 00:05:28,850
+التالي أنا هنا ضربت A في B هل هذه هي B في A؟إتنين
+
+55
+00:05:28,850 --> 00:05:33,350
+هل يمكن أن تتم عملية الـ B في A؟ بقول والله ماهنا
+
+56
+00:05:33,350 --> 00:05:38,810
+عارفين إذا لو جيت ال B في A يبقى بدي أكتب ال B في
+
+57
+00:05:38,810 --> 00:05:46,910
+الأول ال B اللي هي N في K الآن A ل M في N يبقى M
+
+58
+00:05:46,910 --> 00:05:53,110
+في N عدد الأعمدة هنا لا يسوى عدد الصفوف إذا لا
+
+59
+00:05:53,110 --> 00:05:58,790
+يمكن أن تتم عملية الضرب هذهإذا بناء أن علي بقدر
+
+60
+00:05:58,790 --> 00:06:05,450
+استنتج أن ال A في ال B ليه تسوى B في A؟ يبقى عملية
+
+61
+00:06:05,450 --> 00:06:10,530
+ضرب المصوفات ليست عملية إبدالية، بعكس الجامعة
+
+62
+00:06:11,180 --> 00:06:16,000
+الجامعة المصوفة عملية إبدالية لكن الضرب عملية ليست
+
+63
+00:06:16,000 --> 00:06:20,440
+إبدالية يبقى ضرب الابتكاشن matrix is not
+
+64
+00:06:20,440 --> 00:06:26,280
+commutative ليست عملية إبدالية تعالوا نشوف هذا
+
+65
+00:06:26,280 --> 00:06:29,960
+الكلام على أرض الواقع بأمثلة مختلفة
+
+66
+00:06:41,170 --> 00:06:46,570
+يعني إذا معرف بدك تضرب مش معرف خلاص مافيش داعي لها
+
+67
+00:06:46,570 --> 00:06:51,210
+يشغل نقدرش نعملها شغلها دي for each of the full or
+
+68
+00:06:51,210 --> 00:06:53,770
+for the following matrices لكل من المصفوفات
+
+69
+00:06:53,770 --> 00:06:58,570
+التالية وطاني نمرة A ونمرة B نمرة A سؤال في الكتاب
+
+70
+00:06:58,570 --> 00:07:02,970
+ونمرة B سؤال أخر أعتقد ستة و تمانية أو ستة وتسعة
+
+71
+00:07:02,970 --> 00:07:08,310
+الأول ستة والتاني تسعة أعتقد تمام؟إذاً بتدجل
+
+72
+00:07:08,310 --> 00:07:14,170
+المصحوفة إيه؟ المصحوفة فيها صفين و كم عمود يا
+
+73
+00:07:14,170 --> 00:07:20,850
+بنات؟ تلاتة المصحوفة دي فيها تلت صفوف و عمودين،
+
+74
+00:07:20,850 --> 00:07:27,210
+مظبوط؟إذاً عدد الأعمدة هنا يسوى عدد الصفوف هنا،
+
+75
+00:07:27,210 --> 00:07:33,490
+إذاً هذا الضرب ممكن أن يحدث والنتج هو مصوفة نظامها
+
+76
+00:07:33,490 --> 00:07:41,190
+2×2 بس صفين وعمدين كيف بدي تم كتالة؟ طلعي لي هنا
+
+77
+00:07:41,190 --> 00:07:48,040
+نمرة Aبجي بقوله بكتب المصفوفة a في b زي ما هو قال
+
+78
+00:07:48,040 --> 00:07:54,140
+هنا a في b هذا الكلام بده يساوي a الهي اتنين واحد
+
+79
+00:07:54,140 --> 00:08:00,800
+زيرو سالب واحد سالبي اتنين اتنين في b الهي اتنين
+
+80
+00:08:00,800 --> 00:08:07,600
+اربع واحد سالب واحد تلاتة واحد النتج بديها تطلع
+
+81
+00:08:07,600 --> 00:08:15,600
+مصفوفة اتنين في اتنين كما زعمنامظبوطيبقى انا بقدر
+
+82
+00:08:15,600 --> 00:08:19,620
+اعرف جديش هذا الصفوف و هذا العملية قبل ان اقوم
+
+83
+00:08:19,620 --> 00:08:24,620
+بعملية الضرب كيف بروح في الهامش بقول الاولة اتنين
+
+84
+00:08:24,620 --> 00:08:30,420
+في تلاتة و التانية تلاتة في اتنين اذا ممكن ان تتم
+
+85
+00:08:30,420 --> 00:08:34,320
+العملية و بظهر جديش اتنين في اتنين يبقى المصوفة
+
+86
+00:08:34,320 --> 00:08:38,440
+النتيجة انا عارف فيها صفين و عمودين قبل ان ابدأ
+
+87
+00:08:38,440 --> 00:08:44,390
+الان عمليا كيف ستتم عملية الضرب شوف يا منامبدي
+
+88
+00:08:44,390 --> 00:08:50,830
+بضرب الصف الأول في العمود الأول كل عنصر مع نظيره
+
+89
+00:08:50,830 --> 00:08:57,930
+وبجمع الناتج عنصر أول في المصفوفة الجديدة طلع هنا
+
+90
+00:08:57,930 --> 00:09:04,690
+اتنين في اتنين اربعة واحد في واحد واحد واربعة خمسة
+
+91
+00:09:04,690 --> 00:09:12,190
+zero يبقى العنصر الأول خمسةاللي عملت للعمودي الأول
+
+92
+00:09:12,190 --> 00:09:18,230
+بدروح أعمل للعمودي التاني يبقى 2×4 تمانية و سالب
+
+93
+00:09:18,230 --> 00:09:25,960
+واحد بدل سبعة و هنا zero يبقى سبعةخلصنا الصف الأول
+
+94
+00:09:25,960 --> 00:09:32,760
+بيجي للصف الثاني يبقى باجي للصف الثاني في العمود
+
+95
+00:09:32,760 --> 00:09:38,340
+الأول كل عنصر مع نظيره هنا سالب اتنين و هنا سالب
+
+96
+00:09:38,340 --> 00:09:47,310
+اتنين سالب اربعة سالب اربعة و ستة بيضل اتنينالان
+
+97
+00:09:47,310 --> 00:09:52,430
+الصف الثاني في العمود التالت سالب أربعة أموجة
+
+98
+00:09:52,430 --> 00:09:58,650
+باتنين بيظل سالب اتنين سالب اتنين أموجة باتنين
+
+99
+00:09:58,650 --> 00:10:05,270
+Zero تمام؟ أظن نفس الشي اللي اتعلمنا في الثانوية
+
+100
+00:10:05,930 --> 00:10:10,950
+بغيرنا شوية لكلمة عادي جدا باجي العناصر الصف الأول
+
+101
+00:10:10,950 --> 00:10:14,230
+في العمود الأول بضرب كل عنصر في نظيره وبجمع بتطلع
+
+102
+00:10:14,230 --> 00:10:19,790
+العنصر الأول اللي هو خمسة نفس الصف العمود الثاني
+
+103
+00:10:19,790 --> 00:10:24,350
+بجيب للعنصر التاني خلصت الصف الأول ضربته في كل
+
+104
+00:10:24,350 --> 00:10:28,580
+عناصر المصوفةبعد ذلك بروح بالصف الثاني و بضربه في
+
+105
+00:10:28,580 --> 00:10:32,960
+كل عناصر و بضربه في العمود الأول و بطلع ليه العنصر
+
+106
+00:10:32,960 --> 00:10:35,780
+الأول من الصف الثاني و بضربه في العمود الثاني و
+
+107
+00:10:35,780 --> 00:10:39,740
+بطلعه للعنصر الثاني من الصف الثاني و بكون خلصت
+
+108
+00:10:39,740 --> 00:10:44,340
+يبقى هي طلعت جداش نظامها اتنين في اتنين كما ازعمنا
+
+109
+00:10:44,340 --> 00:10:50,960
+احنا قبل قليل تمام؟ طيب بدي اجي الان ل B في A
+
+110
+00:10:50,960 --> 00:10:59,060
+تطلعيلي هنا بدي اجي لل B في Aand فى ايه؟ قداش نظام
+
+111
+00:10:59,060 --> 00:11:06,660
+ال B؟ تلاتة فى اتنين اذا هادي تلاتة فى اتنين قداش
+
+112
+00:11:06,660 --> 00:11:14,240
+نظام ال A؟ اتنين فى تلاتة اتنين فى تلاتة اذا يمكن
+
+113
+00:11:14,240 --> 00:11:21,490
+ان تتم عملية الضرب والناتج تلات صفوفوثلاثة أعمدة،
+
+114
+00:11:21,490 --> 00:11:26,850
+مظبوط؟ يبقى ثلاثة صفوف وثلاثة أعمدة يبقى بدي أجي
+
+115
+00:11:26,850 --> 00:11:31,570
+أقوله هيك مشان ماتوش يا بنات بروح بصفطهم جانب بعض
+
+116
+00:11:31,570 --> 00:11:36,590
+و بعد ذلك بقوم بعملية ضرب مش عن غيرهم يبقى بجي ل B
+
+117
+00:11:36,590 --> 00:11:43,530
+و بكتبها كما هي اتنين اربعة واحد سالب واحد تلاتة
+
+118
+00:11:43,530 --> 00:11:56,060
+واحد بدي أجي ل A2 1 0 1 2 1 0 سالب واحد سالب اتنين
+
+119
+00:11:56,060 --> 00:12:01,200
+اتنين بالشكل اللي عندنا هنا النتج بدي يكون تلاتة
+
+120
+00:12:01,200 --> 00:12:06,520
+في تلاتة يبقى هذه المصوفة اللي بعدها بنفس الطريقة
+
+121
+00:12:06,520 --> 00:12:12,040
+بدي ابدأ الصف الأول في العمود الأول يبقى اتنين في
+
+122
+00:12:12,040 --> 00:12:15,240
+اتنين اربعة اربعة في سالب واحد
+
+123
+00:12:18,720 --> 00:12:24,140
+الصف الأول في العمود الثاني اتنين و سالب تمانية
+
+124
+00:12:24,140 --> 00:12:29,760
+بصير سالب ستة الصف الأول في العمود التالت زيرو
+
+125
+00:12:29,760 --> 00:12:34,880
+وأربعة في اتنين بتمانية اللحظة الصف الأول مكوّن من
+
+126
+00:12:34,880 --> 00:12:39,400
+تلات عناصر خلصت الصف الأول الآن بدي أجي للصف
+
+127
+00:12:39,400 --> 00:12:45,210
+التاني و أضره فيه جميع عناصر المصوفة بالترتيبالصف
+
+128
+00:12:45,210 --> 00:12:52,890
+الثاني في العمود الأول يبقى اتنين وواحد تلاتة يبقى
+
+129
+00:12:52,890 --> 00:12:57,110
+هاي تلاتة الصف الثاني في العمود الثاني هاي واحد
+
+130
+00:12:57,110 --> 00:13:03,750
+واتنين كمان تلاتة الصف الأول يبقى zero وهنا سالي
+
+131
+00:13:03,750 --> 00:13:08,710
+باتنين الآن الصف التالت في العمود الأول تلاتة في
+
+132
+00:13:08,710 --> 00:13:16,100
+اتنين ستة وناقص واحد يظل خمسةالان بالدالي للصف
+
+133
+00:13:16,100 --> 00:13:21,680
+التالت في العمود التاني تلاتة و ناقص اتنين بضال
+
+134
+00:13:21,680 --> 00:13:28,040
+قداش واحد الصف التالت في العمود التالت zero و هنا
+
+135
+00:13:28,040 --> 00:13:33,120
+اتنين بالشكل انه زي ما انت شايفه هذه طلعت تلاتة في
+
+136
+00:13:33,120 --> 00:13:39,290
+تلاتة زي ما احنا قلنا هنا قبل قليلإذاً عملية الضرب
+
+137
+00:13:39,290 --> 00:13:45,890
+ممكن أن تتم خلصنا نمرة A بداجي لنمرة B من المثلة
+
+138
+00:13:45,890 --> 00:13:52,410
+برضه بيمنعطيني مصفوفة الأولى هذه نظامها صف واحد
+
+139
+00:13:52,410 --> 00:14:01,810
+وثلاثة أعمدةهذه ثلاثة صفوف و قداش و عمودين عدد
+
+140
+00:14:01,810 --> 00:14:07,650
+الأعمدة يسوى عدد الصفوف إذا ممكن والنتج هو مصفوفة
+
+141
+00:14:07,650 --> 00:14:12,370
+واحد في اتنين يعني في الصف واحد و عمودين يعني بس
+
+142
+00:14:12,370 --> 00:14:16,030
+عنصرين فيها شايف من الكتار اللي بيطلع بس عنصرين
+
+143
+00:14:16,030 --> 00:14:27,250
+كيف كان التاني يبقى بداشي أخد هنا FB يسوىFB 2 3-1
+
+144
+00:14:27,250 --> 00:14:34,330
+FB 2 0 1 4-2 1
+
+145
+00:14:37,410 --> 00:14:42,450
+بدو يطلع عندي مصفوفة قولنا اللي هي واحد في اتنين
+
+146
+00:14:42,450 --> 00:14:52,270
+مافيش غيرها ليش؟ لأن هذه واحد في تلاتة وهذه تلاتة
+
+147
+00:14:52,270 --> 00:14:57,170
+في اتنين اذا تلاتة مع تلاتة بيظل واحد واتنين صف
+
+148
+00:14:57,170 --> 00:15:03,610
+واحد وعمودين فقط لا غير تعالى نضرب الصف الأول طبعا
+
+149
+00:15:03,610 --> 00:15:09,780
+مافيش غيره في العمود الأولها طلع الصف الأول في
+
+150
+00:15:09,780 --> 00:15:18,500
+العمود الأول يبقى 2 في 2 أربعة و 3 7 و 2 9 يبقى
+
+151
+00:15:18,500 --> 00:15:25,140
+العنصر الأول 9 فش غيره الصف نفسه في العمودي الثاني
+
+152
+00:15:25,140 --> 00:15:32,680
+يبقى zero وهنا 12 وهنا ناقص واحد يبقى 11 في غير
+
+153
+00:15:32,680 --> 00:15:38,860
+هيك؟زي ما انت شايفها صف واحد و عمودين فقط هذا a في
+
+154
+00:15:38,860 --> 00:15:46,720
+b طب بتجي ل b في a تعالى b في a لو جيت قلت ال b هي
+
+155
+00:15:46,720 --> 00:15:51,700
+عبارة عن تلاتة في اتنين في الهعم مش هيك هي تلاتة
+
+156
+00:15:51,700 --> 00:15:59,470
+في اتنينو جيت ل a اللي هي واحد في تلاتة عدد
+
+157
+00:15:59,470 --> 00:16:05,610
+الأعمدة لا يساوي عدد الصفوف بالتالي لا يمكن أن
+
+158
+00:16:05,610 --> 00:16:18,070
+يحدث ذلك يبقى بالداجي and ال b في a does not exist
+
+159
+00:16:19,440 --> 00:16:29,440
+هذا الكلام مش ممكن نقوله ليش؟ because the
+
+160
+00:16:29,440 --> 00:16:34,340
+number of
+
+161
+00:16:34,340 --> 00:16:46,440
+columns in المصهوفة a عدد الأعمدة في المصهوفة a is
+
+162
+00:16:46,440 --> 00:16:48,680
+three and
+
+163
+00:16:51,910 --> 00:17:05,530
+the number of rows in B is عدد الصفوف في المصفوف
+
+164
+00:17:05,530 --> 00:17:08,850
+بي
+
+165
+00:17:08,850 --> 00:17:15,410
+.. إيش احنا بدنا بي في إيه؟ لأ بدنا في بي، الأولى
+
+166
+00:17:15,410 --> 00:17:25,130
+عدد من بيفي بي is three وهنا عدد الصفوف is one
+
+167
+00:17:25,130 --> 00:17:33,790
+الأولى عدد الأعمدة فيها اتنين والتانية واحد ودول
+
+168
+00:17:33,790 --> 00:17:39,650
+اتنين are not equal من هنا لا يمكن ان تتم عملية
+
+169
+00:17:39,650 --> 00:17:40,370
+الضرب
+
+170
+00:17:59,400 --> 00:18:09,360
+مثال اتنين example two write
+
+171
+00:18:09,360 --> 00:18:14,860
+the system write the system
+
+172
+00:18:16,500 --> 00:18:23,840
+كتبولنا الـ system اللي هو اتنين X one زائد خمسة X
+
+173
+00:18:23,840 --> 00:18:33,000
+two بده يساوي سالب واحد و تلاتة X one ناقص اتنين X
+
+174
+00:18:33,000 --> 00:18:40,520
+two بده يساوي Zero و X one زائد X two بده يساوي
+
+175
+00:18:40,520 --> 00:19:00,770
+تلاتة in the formin the form ax بدي شاوي b يبقى
+
+176
+00:19:00,770 --> 00:19:06,560
+بيقولي اكتبنظام المعادلات الخطية اللى عندك على
+
+177
+00:19:06,560 --> 00:19:11,980
+الشكل ax يساوي b على شكل مصروفة معاملات في مصروفة
+
+178
+00:19:11,980 --> 00:19:16,940
+مجاهيل بده يساوي مصروفة الثوارث بقول له كويس فتدهي
+
+179
+00:19:16,940 --> 00:19:25,460
+لمصروفة المعاملات يبقى اتنين خمسة تلاتة نقص اتنين
+
+180
+00:19:25,460 --> 00:19:34,810
+واحد واحدالمجاهيل كم واحد؟ اتنين فش غيرهم يبقى X
+
+181
+00:19:34,810 --> 00:19:41,950
+واحد وهنا X اتنين بيسوي مصفوفة الثوابت سالب واحد
+
+182
+00:19:41,950 --> 00:19:48,770
+زيرو تلتة السؤال هو هل تتم هذه العملية ام لا تعالى
+
+183
+00:19:48,770 --> 00:19:56,000
+نشوف هذه المصفوفة نظامها تلت صفوف و عمودينتمام تلت
+
+184
+00:19:56,000 --> 00:20:01,660
+صفوف و عمودين هذه المصروفة نضعها صفين و عمود واحد
+
+185
+00:20:01,660 --> 00:20:07,840
+تمام إذا عدد الأعمدة يسوى عدد الصفوف وضع المصروفة
+
+186
+00:20:07,840 --> 00:20:13,760
+تلت صفوف و عمود واحد هي تلاتة في واحد يبقى تلت
+
+187
+00:20:13,760 --> 00:20:18,560
+صفوف و عمود واحد إذا كلامي صحيح عملنا الضرب هذه
+
+188
+00:20:18,560 --> 00:20:23,690
+بتتمو لو ضربت بيطلع عند مين المعادلة اللي فوق يبقى
+
+189
+00:20:23,690 --> 00:20:32,030
+كتابتي سليمة مائة بالمائة example three بقول
+
+190
+00:20:32,030 --> 00:20:39,830
+find the system of equations find the system of
+
+191
+00:20:39,830 --> 00:20:48,370
+equations that corresponding that corresponding
+
+192
+00:20:52,110 --> 00:21:03,410
+that corresponding to the vector equation ax بدي
+
+193
+00:21:03,410 --> 00:21:09,750
+ساوي b where حيث
+
+194
+00:21:11,950 --> 00:21:25,810
+where ال A تساوي اللي هو السالي ب 2 1 3 و 3 0 1
+
+195
+00:21:25,810 --> 00:21:32,690
+and ال B تساوي 0 0
+
+196
+00:21:48,030 --> 00:21:51,810
+بنرجع لسؤالنا مرة تانية بيقول هات ال system of
+
+197
+00:21:51,810 --> 00:21:53,990
+equations that corresponding to the vector
+
+198
+00:21:53,990 --> 00:21:58,490
+equation x بالساوية بيه حيث ال a و ال b معطيات
+
+199
+00:21:58,490 --> 00:22:03,010
+بالشكل اللي عنها يعني كأنه بيقول امشي عملية عكسية
+
+200
+00:22:03,010 --> 00:22:08,530
+لمن لسؤال اللي جابله باجي بقوله كويس انا عندي a في
+
+201
+00:22:08,530 --> 00:22:15,350
+x بده يساوي بيه ال a هي موجودةيبقى باجي بقوله ال a
+
+202
+00:22:15,350 --> 00:22:21,310
+موجودة هذا ال a في ال x يبقى هذا الكلام بده يساوي
+
+203
+00:22:21,310 --> 00:22:30,530
+ال a اللي هيبقى رعنين سلب 2 1 3 ودي 3 0 1 في
+
+204
+00:22:30,530 --> 00:22:36,990
+مصفوفة هنا مين هي الله أعلم بدها تساوي 0 و 0
+
+205
+00:22:38,870 --> 00:22:45,670
+المصوفة هذه نظامها كم؟ اتنين في تلاتة كويس المصوفة
+
+206
+00:22:45,670 --> 00:22:51,930
+هذه نظامها اتنين في واحد صفين و عمود هذه مشان
+
+207
+00:22:51,930 --> 00:22:58,600
+تنضرب بدى يكون عندى هنا كم؟تلاتة صفوف و عمود واحد
+
+208
+00:22:58,600 --> 00:23:03,800
+يبقى هذا يريد تلاتة صفوف و عمود واحد تلاتة صفوف
+
+209
+00:23:03,800 --> 00:23:09,300
+اذا انا بادر اقول اكس واحد و اكس اتنين و اكس تلاتة
+
+210
+00:23:09,300 --> 00:23:12,720
+مظبوط اذا هو اللي يقول find the system of
+
+211
+00:23:12,720 --> 00:23:18,440
+equations هاتلي نظام المعادلة او المعادلة المكونة
+
+212
+00:23:18,440 --> 00:23:24,720
+لنظام المنظر لهذه المعادلة اذا انا حتى الآن كتبت
+
+213
+00:23:25,030 --> 00:23:29,330
+هذه المعادلة المصرفية كتبتها بشكل أعظم لهذا ال
+
+214
+00:23:29,330 --> 00:23:34,310
+system يبقى بدي أضرب الصف الأول في العمود الأول
+
+215
+00:23:34,310 --> 00:23:38,930
+بيعطيني المعادلة الأولى من هذا ال system يبقى
+
+216
+00:23:38,930 --> 00:23:42,370
+المعادلة الأولى الصف الأول في العمود الأول يبقى
+
+217
+00:23:42,370 --> 00:23:50,270
+ناقص اتنين x one زائد x two زائد تلاتة x three
+
+218
+00:23:50,270 --> 00:23:59,640
+بدون سوينالمعادلة التانية تلاتة اكس وان زائد اكس
+
+219
+00:23:59,640 --> 00:24:00,860
+ثري زائد اكس ثري زائد اكس ثري زائد اكس ثري زائد
+
+220
+00:24:00,860 --> 00:24:01,040
+زائد اكس ثري زائد اكس ثري زائد اكس ثري زائد اكس
+
+221
+00:24:01,040 --> 00:24:01,740
+ثري زائد اكس ثري زائد اكس ثري زائد اكس ثري زائد
+
+222
+00:24:01,740 --> 00:24:02,580
+اكس ثري زائد اكس ثري زائد اكس ثري زائد اكس ثري
+
+223
+00:24:02,580 --> 00:24:05,280
+زائد اكس ثري زائد اكس ثري زائد اكس ثري زائد اكس
+
+224
+00:24:05,280 --> 00:24:13,100
+ثري زائد اكس ثري زائد اكس ثري زائد اكس ثري
+
+225
+00:24:19,640 --> 00:24:25,080
+الو حل على الأقل الحل الصفري مش شغلتنا هذه المهم
+
+226
+00:24:25,080 --> 00:24:30,060
+احنا بدنا نعرف هالشغل هذا طيب بدنا نيجي لملاحظة ما
+
+227
+00:24:30,060 --> 00:24:36,420
+نكتب هذه الملاحظة ونحاول نستخدمها او نعمم ما سبق
+
+228
+00:24:36,420 --> 00:24:46,580
+الحديث عنه يبقى remark in general على
+
+229
+00:24:46,580 --> 00:24:56,480
+وجه العمومthe product product
+
+230
+00:24:56,480 --> 00:25:03,380
+of matrices of
+
+231
+00:25:03,380 --> 00:25:13,820
+matrices is not commutative is not يعني
+
+232
+00:25:13,820 --> 00:25:18,280
+عملية ضرب المصوفات ليست إبدالية
+
+233
+00:25:20,320 --> 00:25:27,560
+that is if الـ
+
+234
+00:25:27,560 --> 00:25:39,560
+A and ال B are matrices such
+
+235
+00:25:39,560 --> 00:25:52,360
+that بحيث أن ال A في ال B andالـ B في ال A are
+
+236
+00:25:52,360 --> 00:26:06,400
+both defined كلاهما معرف then it is not
+
+237
+00:26:06,400 --> 00:26:07,460
+necessarily
+
+238
+00:26:19,130 --> 00:26:28,790
+necessary that أن ال A في ال B بدي ساوي ال B في ال
+
+239
+00:26:28,790 --> 00:26:37,150
+A example نمرة
+
+240
+00:26:37,150 --> 00:26:56,740
+A show that بينيلي F ال A تساوي-2 5 1 4 and B
+
+241
+00:26:56,740 --> 00:27:11,620
+تساوي اللي هو تلاتة اتنين ناقص تلاتة أربعة then ال
+
+242
+00:27:11,620 --> 00:27:25,380
+A في B لا يساوي ال B في ال ANimra B Show that if
+
+243
+00:27:25,380 --> 00:27:31,160
+ال A تساوي واحد
+
+244
+00:27:31,160 --> 00:27:40,080
+اتنين سالب واحد Zero and ال B تساوي سالب واحد
+
+245
+00:27:40,080 --> 00:27:46,560
+اتنين سالب واحد سالب اتنين then
+
+246
+00:27:48,780 --> 00:27:53,120
+الـ A في الـ B يساوي الـ B في الـ A
+
+247
+00:28:24,260 --> 00:28:28,440
+بنجي لل remark اللي احنا كاتبينه هذا بقول in
+
+248
+00:28:28,440 --> 00:28:33,760
+general على وجه العموم the product of matrices is
+
+249
+00:28:33,760 --> 00:28:38,960
+not commutative عملية ضرب المصحفات ليست عملية
+
+250
+00:28:38,960 --> 00:28:43,400
+إبدالية that is لو كان ال a و ال e are matrices
+
+251
+00:28:43,400 --> 00:28:47,200
+بحيث أن ال a و ال a في b و ال b في a are both
+
+252
+00:28:47,200 --> 00:28:50,580
+defined لو كانت عملية الضرب من اليمين و من الي
+
+253
+00:28:50,580 --> 00:28:56,470
+أسار معرفةthen it is not necessary ليس بالضرورة أن
+
+254
+00:28:56,470 --> 00:29:00,170
+ال A في ال B بدوا يسووا مين، B في ال A يعني عملية
+
+255
+00:29:00,170 --> 00:29:04,110
+ضرب المصرفات ليست عملية .. لما أقول in general يا
+
+256
+00:29:04,110 --> 00:29:09,030
+بنات يعني على وجه العوم يعني قد شوذ حالة أو حالتين
+
+257
+00:29:09,030 --> 00:29:13,000
+أو تلاتة عن مين عن هذا النظاملكن in general بقول
+
+258
+00:29:13,000 --> 00:29:17,780
+غير ما ان طلعت مرة و الله مرتين و الله تلاتة يحدث
+
+259
+00:29:17,780 --> 00:29:23,140
+تسوي هذا معناه انه مش دايما هو بيحدث تسوي لكن بقدر
+
+260
+00:29:23,140 --> 00:29:28,390
+الله طلعت مرتين او مرة او تلاتةالآن سأعطيك مثال
+
+261
+00:29:28,390 --> 00:29:32,790
+أبيّلك أن ضرب المصوفات ليست commutative وضرب
+
+262
+00:29:32,790 --> 00:29:35,790
+الاكتنترون واطلعهم commutative يبقى يعطينا النتج
+
+263
+00:29:35,790 --> 00:29:41,330
+في كلامنا وبالتالي عملية التساوي غير صحيحة بيقول
+
+264
+00:29:41,330 --> 00:29:46,290
+مثال show that أنه لو كانت المصوفة A بالشكل اللي
+
+265
+00:29:46,290 --> 00:29:51,810
+عندنا هو B يبقى ال A في B لا يساوي ال B في A إذا
+
+266
+00:29:51,810 --> 00:29:55,750
+أنا بروح أخد ال A في ال B solution
+
+267
+00:29:58,690 --> 00:30:03,490
+وبدأ أخذ الجزء الأول ان هو المرأةبدأ أخد الـ a في
+
+268
+00:30:03,490 --> 00:30:09,710
+الـ b بدأ تساوي اللي هو سالب اتنين خمسة واحد اربع
+
+269
+00:30:09,710 --> 00:30:15,130
+في b اللي هو تلاتة اتنين سالب تلاتة اربع يبقى
+
+270
+00:30:15,130 --> 00:30:19,430
+المصفوفة الناتج كالتالي طبعا اتنين في اتنين وهذا
+
+271
+00:30:19,430 --> 00:30:22,410
+اتنين في اتنين يبقى الناتج اتنين في اتنين كذلك
+
+272
+00:30:22,410 --> 00:30:27,890
+الصف الأول في العمود الأول يبقى ناقص ستة وناقص
+
+273
+00:30:27,890 --> 00:30:33,200
+خمستاشر بناقص واحد وعشرينيبقى هاي ناقص واحد عشرين
+
+274
+00:30:33,200 --> 00:30:38,640
+الصف الأول في العمودي الثاني يبقى ناقص أربعة وعندك
+
+275
+00:30:38,640 --> 00:30:45,200
+هنا عشرين بيظل قداش ستة عشر الصف الثاني في العمودي
+
+276
+00:30:45,200 --> 00:30:51,720
+الأول تلاتة و هنا ناقص اتناشر بيظل قداش ناقص تسعة
+
+277
+00:30:51,720 --> 00:30:56,480
+الصف الثاني في العمودي التاني يبقى اتنين وستاش
+
+278
+00:30:56,480 --> 00:31:03,400
+بعدين امينتمنتاش يبقى ثمانية عشر بالشكل اللي عندنا
+
+279
+00:31:03,400 --> 00:31:12,700
+طيب بدنا نيجي B في A and ال B في ال A بده يساوي هي
+
+280
+00:31:12,700 --> 00:31:19,580
+تلاتة اتنين ناقص تلاتة اربعة في سالب اتنين خمسة
+
+281
+00:31:19,580 --> 00:31:25,290
+واحد اربعةبيده يساوي طبعا هيعطيني كمان مصوفة نظام
+
+282
+00:31:25,290 --> 00:31:29,370
+اتنين في اتنين يبقى الصف الأول في العمود الأول
+
+283
+00:31:29,370 --> 00:31:35,970
+سالب ستة وموجة باتنين يظل سالب أربع اللحظة اختلف
+
+284
+00:31:35,970 --> 00:31:40,030
+من البداية من أول عنصر قبل ما تكمل يبقى تساوي غير
+
+285
+00:31:40,030 --> 00:31:46,850
+حاصل طيب نكمل يبقى تلاتة في خمسة بخمستاشر وتمانية
+
+286
+00:31:46,850 --> 00:31:54,050
+تلاتة وعشرينالان الصف الثاني في العمود الأول ستة و
+
+287
+00:31:54,050 --> 00:31:59,570
+أربعة عشرة الصف الثاني في العمود الثاني سالب
+
+288
+00:31:59,570 --> 00:32:05,470
+خمستاش و عندك ستاش بيبقى القداش واحد يبقى من
+
+289
+00:32:05,470 --> 00:32:12,810
+الاتنين هدول بقدر استنتج ان ال A B لا يساوي ال B
+
+290
+00:32:12,810 --> 00:32:13,570
+في ال A
+
+291
+00:32:20,340 --> 00:32:28,320
+طيب بدي اخد ال a في ال b ويساوي يبقى واحد اتنين
+
+292
+00:32:28,320 --> 00:32:34,540
+سلب واحد زيرو واحد اتنين سلب واحد زيرو في b اللي
+
+293
+00:32:34,540 --> 00:32:39,820
+هو من سلب واحد اتنين سلب واحد سلب اتنين سلب واحد
+
+294
+00:32:39,820 --> 00:32:45,840
+اتنين سلب واحد سلب اتنين ويساويالصف الأول في
+
+295
+00:32:45,840 --> 00:32:50,640
+العمود الأول يبقى سالب واحد وسالب اتنين في الجدار
+
+296
+00:32:50,640 --> 00:32:55,280
+بسالب تلاتة الصف الأول في العمود التاني اتنين
+
+297
+00:32:55,280 --> 00:33:00,840
+وسالب اربعة بسالب اتنين الصف الثاني في العمود
+
+298
+00:33:00,840 --> 00:33:06,520
+الأول بواحد الصف الثاني في العمود التاني بسالب
+
+299
+00:33:06,520 --> 00:33:12,970
+اتنينالان بداجي للـ B في الـ A الـ B في الـ A يبقى
+
+300
+00:33:12,970 --> 00:33:17,890
+سالب واحد اتنين سالب واحد سالب اتنين في واحد اتنين
+
+301
+00:33:17,890 --> 00:33:23,250
+سالب واحد Zero ويساوي الصف الأول في العمود الأول
+
+302
+00:33:23,250 --> 00:33:29,250
+يبقى سالب واحد وسالب اتنين بسالب تلاتة الصف الأول
+
+303
+00:33:29,250 --> 00:33:34,510
+في العمود التاني سالب اتنين وذاك ب Zero الصف
+
+304
+00:33:34,510 --> 00:33:40,520
+الثاني في العمود الأوليبقى هاي عندى الوامين بسالب
+
+305
+00:33:40,520 --> 00:33:47,480
+واحد بسالب واحد وموجة باتنين يبقى بواحد الصف
+
+306
+00:33:47,480 --> 00:33:52,180
+الثاني في العمود الثاني بسالب اتنين والاخر بزيرو
+
+307
+00:33:52,340 --> 00:33:57,380
+أطلع النتيجة طلع a المصففين بيساووا بعض يبقى باجي
+
+308
+00:33:57,380 --> 00:34:03,300
+بقول الساعة ال a في ال b بده يساوي ال b في ال a
+
+309
+00:34:03,300 --> 00:34:07,960
+يعني يا بنات قد يحدث التساوي و قد لا يحدث لكن في
+
+310
+00:34:07,960 --> 00:34:14,490
+الغالبلن يحدث هذا التساوي يبقى in general على وجه
+
+311
+00:34:14,490 --> 00:34:20,130
+العموم عملية ضرب المصوفات ليست عملية إبدالية بمعنى
+
+312
+00:34:20,130 --> 00:34:25,450
+أن a في b لا يساوي ال b في a الآن زي ما أخدنا
+
+313
+00:34:25,450 --> 00:34:30,390
+نظرية على عملية جمع المصوفات بناخد نظرية على عملية
+
+314
+00:34:30,390 --> 00:34:35,890
+ضرب المصوفات النظرية بتقول ما يأتي theorem
+
+315
+00:34:43,300 --> 00:34:58,080
+بقول if c is a number كان هذا عدد حقيقي and if ال
+
+316
+00:34:58,080 --> 00:35:11,140
+a will be and c and capital c والله if a و b و c
+
+317
+00:35:13,350 --> 00:35:22,350
+and D are matrices
+
+318
+00:35:22,350 --> 00:35:29,050
+مصفوفات such that
+
+319
+00:35:29,050 --> 00:35:33,550
+the indicated
+
+320
+00:35:33,550 --> 00:35:37,130
+sums
+
+321
+00:35:37,130 --> 00:35:41,970
+and products
+
+322
+00:35:43,980 --> 00:35:54,760
+عملية الجمع هو الضرب are defined then النقطة
+
+323
+00:35:54,760 --> 00:36:06,880
+الأولى C في A في B بده يساوي A في CB يساوي
+
+324
+00:36:06,880 --> 00:36:10,020
+C في B
+
+325
+00:36:14,240 --> 00:36:31,380
+النقطة الثانية النقطة
+
+326
+00:36:31,380 --> 00:36:40,240
+التالتة اللي هو B زائد C كلها في D تساوي
+
+327
+00:36:42,440 --> 00:36:52,360
+BD زائد C في D زائد
+
+328
+00:36:52,360 --> 00:37:02,700
+C في D النقطة الرابعة ال A في ال B في ال D يساوي
+
+329
+00:37:02,700 --> 00:37:06,780
+ال A في ال B في ال D
+
+330
+00:37:09,610 --> 00:37:14,970
+طيب نيجي لنظرية هذه بيقول if c is a number لو كان
+
+331
+00:37:14,970 --> 00:37:19,390
+c عدد حقيقي و كان ال a و ال b و ال c و d عبارة عن
+
+332
+00:37:19,390 --> 00:37:24,890
+مصرفات بحيث أن indicated sums and products عاملين
+
+333
+00:37:24,890 --> 00:37:30,030
+الجمع والضرب الموضحة are defined يبقى كل عملية
+
+334
+00:37:30,030 --> 00:37:35,680
+الضرب و عملية الجمع هنا معرفةيبقى them لو ضربت
+
+335
+00:37:35,680 --> 00:37:40,020
+constant في a تطلع مصهوفة جديدة لإن ال c بدربه في
+
+336
+00:37:40,020 --> 00:37:46,180
+جميع عناصر a وضربت النتج في المصهوف b تماما كما لو
+
+337
+00:37:46,180 --> 00:37:50,020
+ضربت ال constant في b و اللي نتج ضربت في main
+
+338
+00:37:50,020 --> 00:37:54,720
+المصهوف a أو ضربت المصهوفين a و b في بعض و اللي
+
+339
+00:37:54,720 --> 00:37:59,800
+نتج ضربته في main في c الثلاث قيم are the sameيبقى
+
+340
+00:37:59,800 --> 00:38:02,880
+بتفرجش عندي لإني بضرب constant في مصفوفة مش
+
+341
+00:38:02,880 --> 00:38:06,600
+مصفوفتين في بعض يبقى constant مصفوفة تضرب يمين أو
+
+342
+00:38:06,600 --> 00:38:11,160
+تضرب شمال كنا بأثرش عنها سابقا ناخدناها طيب النقطة
+
+343
+00:38:11,160 --> 00:38:15,880
+الثانية بدي أضرب a في b زائد c يبقى هذي كلها
+
+344
+00:38:15,880 --> 00:38:21,860
+مصفوفات يبقى كأنه بدى وزع عملية الضرب على عملية من
+
+345
+00:38:21,860 --> 00:38:28,040
+الجامع يبقى يساوي a في b زائد a في c لحظة الضرب من
+
+346
+00:38:28,040 --> 00:38:35,620
+وين؟من جهتي الشمال يبقى a في b ثم a في c الترتيب
+
+347
+00:38:35,620 --> 00:38:40,440
+ضروري جدا مش هتقولي لي a في b زائد c في a لأ غلط
+
+348
+00:38:40,440 --> 00:38:44,300
+يبقى ضربتي من جهتي الشمال يبقى ضلك مش هتضرب من
+
+349
+00:38:44,300 --> 00:38:49,940
+جهتي الشمال ضربتي من جهتي اليمين b زائد c في d
+
+350
+00:38:49,940 --> 00:38:56,820
+يبقى b في d زائد c في dيبقى هدول اتنين اللي هم الـ
+
+351
+00:38:56,820 --> 00:39:02,700
+distributive law عملية التوزيع وهنا الخاصية رابعة
+
+352
+00:39:02,700 --> 00:39:10,160
+عملية الدمج A في B في C يسوى A في B في D يسوى A في
+
+353
+00:39:10,160 --> 00:39:16,080
+B في D يعني ايه؟يعني لو ضربت B في D أولا نتجة
+
+354
+00:39:16,080 --> 00:39:20,920
+مصروفة ضربتها من جهة الشمال في A تماما كما لو ضربت
+
+355
+00:39:20,920 --> 00:39:24,660
+A في B في بعض والنتجة ضربتها في D و هذه الخاصية
+
+356
+00:39:24,660 --> 00:39:30,920
+بجينا نسميها خاصيةالدمج ال associative law اللي هو
+
+357
+00:39:30,920 --> 00:39:35,100
+قانون الدمج اللي جابله ال distributive law اللي هو
+
+358
+00:39:35,100 --> 00:39:40,480
+قانون التوزيع تمام؟ بقت عندنا في هذا section
+
+359
+00:39:40,480 --> 00:39:46,140
+ملاحظة أخرى remark يبقى
+
+360
+00:39:46,140 --> 00:39:57,630
+remark بتقول ما تقفل AFالـ a is an n by n matrix
+
+361
+00:39:57,630 --> 00:40:06,930
+يبقى لو كانت مصوفة مربعة is an m في n matrix m في
+
+362
+00:40:06,930 --> 00:40:24,360
+n matrix and ال b and ال b is aninvp matrix مصفوفة
+
+363
+00:40:24,360 --> 00:40:31,680
+نظام invp then is
+
+364
+00:40:31,680 --> 00:40:49,200
+written as is written as call vectors as followas
+
+365
+00:40:49,200 --> 00:40:56,900
+follow كالتالي بي
+
+366
+00:40:56,900 --> 00:41:11,600
+بدها تساوي مثلا بي ون بي تو بي بي بي and
+
+367
+00:41:11,600 --> 00:41:24,280
+hence ومن ثمthe product a
+
+368
+00:41:24,280 --> 00:41:43,880
+في b is اللي هو a b مدرساوي اللي هو a b1 a b2 a bp
+
+369
+00:41:43,880 --> 00:41:50,640
+الشكل عن هذاعوادة بتدعيها الرمز main والرمز star
+
+370
+00:41:50,640 --> 00:41:56,860
+example
+
+371
+00:41:56,860 --> 00:42:02,360
+if
+
+372
+00:42:02,360 --> 00:42:12,290
+ال a تساوياتنين واحد سالب واحد Zero اتنين تلاتة
+
+373
+00:42:12,290 --> 00:42:26,050
+واحد نقص اتنين Zero and ال B تساوي واحد واحد سالب
+
+374
+00:42:26,050 --> 00:42:33,810
+واحد تلاتة اتنين واحد right then
+
+375
+00:42:38,590 --> 00:42:52,510
+product AB as in the formula star أكتب هالي زي ما
+
+376
+00:42:52,510 --> 00:42:54,510
+هي في ال formula star
+
+377
+00:43:09,210 --> 00:43:11,890
+بنرجع الـ remarkable اللي عندنا ونطبق عليه هذا
+
+378
+00:43:11,890 --> 00:43:17,630
+المثال تطبيقا مباشرة ebf اللي is an m by n matrix
+
+379
+00:43:17,630 --> 00:43:23,150
+و ال b عبارة عن np matrix إذا يمكن أن يكون هناك
+
+380
+00:43:23,150 --> 00:43:29,070
+حصلة ضرب a في b then ال b is written as convictors
+
+381
+00:43:29,070 --> 00:43:33,870
+as follows ال b بقدر أكتبها حسب عدد الأعمد اللي
+
+382
+00:43:33,870 --> 00:43:39,600
+فيها v1,v1,v2 لغاية vpهنا نسميها باسم ال بي بي وان
+
+383
+00:43:39,600 --> 00:43:42,040
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+384
+00:43:42,040 --> 00:43:44,260
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+385
+00:43:44,260 --> 00:43:45,480
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+386
+00:43:45,480 --> 00:43:51,800
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+387
+00:43:51,800 --> 00:43:52,920
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+388
+00:43:52,920 --> 00:43:52,980
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+389
+00:43:52,980 --> 00:43:53,380
+بي وان بي وان بي وان بي وان بي وان بي وان بي وان
+
+390
+00:43:53,380 --> 00:44:05,240
+بي وان بي وان
+
+391
+00:44:05,240 --> 00:44:15,060
+بي وانبدأجي أقوله a في b يساوي a في بي بدها اكتبها
+
+392
+00:44:15,060 --> 00:44:21,080
+ب b1 و b2 العمود الأول و العمود التاني زي ما احنا
+
+393
+00:44:21,080 --> 00:44:27,880
+كاتبينه هنا تماما يبقى هذه البنات بدها تساوي a في
+
+394
+00:44:27,880 --> 00:44:38,780
+b1 و a في b2كويس يعني هذه بدها تساوي هي هنا ال a
+
+395
+00:44:38,780 --> 00:44:45,080
+بدها حطها زي ما هي اتنين واحد سالب واحد zero اتنين
+
+396
+00:44:45,080 --> 00:44:51,720
+تلاتة واحد ناقص اتنين zero في مين في ال b one ال b
+
+397
+00:44:51,720 --> 00:44:57,900
+one اللي هو واحد ناقص واحد اتنين واحد المصوفة a
+
+398
+00:44:57,900 --> 00:45:01,480
+نفسها ليه اتنين واحد سالب واحد
+
+399
+00:45:14,130 --> 00:45:24,710
+يبقى الكلام يساوي تطلع المصفوفة التالية يبقى الصف
+
+400
+00:45:24,710 --> 00:45:31,570
+الأول في العمود الأول يطلع العنصر الأوليبقى اتنين
+
+401
+00:45:31,570 --> 00:45:37,030
+و سالب واحد و سالب اتنين اتنين و سالب اتنين مع
+
+402
+00:45:37,030 --> 00:45:43,220
+السلمة بيطلع كده؟ سالب واحد خلصنا منهالان بالدالي
+
+403
+00:45:43,220 --> 00:45:49,700
+للصف الأول في العمود نفسه يبقى zero سالي باتنين
+
+404
+00:45:49,700 --> 00:45:54,620
+وزائد ستة بضال قداش أربعة بالشكل اللي عندنا هذا
+
+405
+00:45:54,620 --> 00:45:58,680
+بكتبش في الصف لإن ماعنديش بكتب بالشكل اللي عندنا
+
+406
+00:45:58,680 --> 00:46:05,010
+هذا يبقى هنا واحدو سالب اتنين يعني بصير اتنين
+
+407
+00:46:05,010 --> 00:46:10,850
+تلاتة و zero يبقى هنا ياش تلاتة لحظة المصفوفة
+
+408
+00:46:10,850 --> 00:46:14,810
+تلاتة في تلاتة وهذه تلاتة في واحد بيصير تلاتة في
+
+409
+00:46:14,810 --> 00:46:19,570
+واحد هذه تلتة صفوف و واحد خلصنا هنا بدأجي لهذه
+
+410
+00:46:19,570 --> 00:46:26,150
+بنفس الطريقة اتنين و تلاتة خمسة و سالب واحد يبقى
+
+411
+00:46:26,150 --> 00:46:36,230
+اربعةاللي بعده Zero ستة وتلاتة يبقى تسعة اللي بعده
+
+412
+00:46:36,230 --> 00:46:43,430
+واحد و سالب ستة يبقى سالب خمسة و Zero يبقى سالب
+
+413
+00:46:43,430 --> 00:46:49,640
+خمسةيبقى هذه المصوفة الناتجة من حاصل الضرب وصلنا ل
+
+414
+00:46:49,640 --> 00:46:57,440
+exercises 2-5 يبقى exercises 2-5 المسائل التالية
+
+415
+00:46:57,440 --> 00:47:09,330
+اللي همين اتنين تلاتةخمسة، سبعة، تسعة، عشرة،
+
+416
+00:47:09,330 --> 00:47:17,530
+أحداشر، أتناشر، ستاشر، سبعتاشر، تسعتاشر، يعطيكوا
+
+417
+00:47:17,530 --> 00:47:17,850
+العجب
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/XTSVi7CEhGg_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/XTSVi7CEhGg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f820faa7c3df5fac0c2d47b68b2e904af18b2f4d
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/XTSVi7CEhGg_postprocess.srt
@@ -0,0 +1,1776 @@
+1
+00:00:21,650 --> 00:00:26,270
+بسم الله الرحمن الرحيم يبقى نعود الان الى اكمال
+
+2
+00:00:26,270 --> 00:00:30,790
+المحاضرة فى الفترة الصباحية حيث واخدنا ثلاث نظريات
+
+3
+00:00:30,790 --> 00:00:34,830
+وذكرنا بالتعريفين التعريف الاول كان تعريف ال
+
+4
+00:00:34,830 --> 00:00:38,090
+finite dimensional vector space او لو vector space
+
+5
+00:00:38,090 --> 00:00:42,250
+عنده dimension ايه له يسوئن شو معناه معناه شغلتين
+
+6
+00:00:42,250 --> 00:00:46,710
+وبعد ذلك روحنا لتعريف ال basis وقلنا ان مجموعا ال
+
+7
+00:00:46,710 --> 00:00:50,470
+vector بسميهم basis اذا تحقق شرطانالأول كانوا
+
+8
+00:00:50,470 --> 00:00:55,410
+linearly independent والثاني كانوا بيودولي جميع
+
+9
+00:00:55,410 --> 00:00:58,630
+أناصر ال vector space أو أي عنصر في ال vector
+
+10
+00:00:58,630 --> 00:01:02,970
+space بقدر أكتب علاصية linear combination من هذه
+
+11
+00:01:02,970 --> 00:01:07,870
+ال linearly independent vector ثم بعد ذلك دخلني
+
+12
+00:01:07,870 --> 00:01:13,750
+على ثلاث نظريات مجملهمإن لو أنا عندي basis في هذا
+
+13
+00:01:13,750 --> 00:01:17,290
+ال basis ليس واحدا يعني ممكن ال vector space يكون
+
+14
+00:01:17,290 --> 00:01:22,670
+أكتر من basis و أعطينا مثال اللي لجناته لا يزال في
+
+15
+00:01:22,670 --> 00:01:28,210
+R2 اعطونك بدل ال basis خمسة لل vector space اللي
+
+16
+00:01:28,210 --> 00:01:34,010
+هو ال standard basis 1 و 0 و 0 و 1 اللي يسمونه A1
+
+17
+00:01:34,010 --> 00:01:37,770
+و A2و بعدين اخدنا واحد و تلاتة و واحد و سالف واحد
+
+18
+00:01:37,770 --> 00:01:42,170
+و باقيتهم كمان فكل هما دول بيشكلوا basis يعني أصبح
+
+19
+00:01:42,170 --> 00:01:48,070
+ال basis ليس وحيدا لل vector space الواحد اثنان اي
+
+20
+00:01:48,070 --> 00:01:53,510
+عناصر لل basis بيجيبولي كل عناصر ال vector space
+
+21
+00:01:53,510 --> 00:02:00,610
+الأخرى طبعا يبقى هذا باختصار المجموعالعناصر في أي
+
+22
+00:02:00,610 --> 00:02:04,910
+basis كله متساوي و يسووا ال dimension تبع ال
+
+23
+00:02:04,910 --> 00:02:08,430
+vector space اعطينا مثال و ندخل الان الى المثال
+
+24
+00:02:08,430 --> 00:02:13,050
+الثاني يبقى بيقول بيالي ان مجموعة المصفوفات اللي
+
+25
+00:02:13,050 --> 00:02:15,870
+على الشكل اللي عندها دبيهات ال a والb والc والd
+
+26
+00:02:15,870 --> 00:02:20,190
+are real numbers is a finite dimensional vector
+
+27
+00:02:20,190 --> 00:02:24,890
+spaceأثنين and find its dimension بدي أعرف قداش ال
+
+28
+00:02:24,890 --> 00:02:29,150
+dimension لل vector space هذا و بدك تجيلي find a
+
+29
+00:02:29,150 --> 00:02:33,670
+basis ماقلتش find the basis لو قلت find the basis
+
+30
+00:02:33,670 --> 00:02:37,650
+يبقى ماعنديش إلا basis محدد بديها اذا find a basis
+
+31
+00:02:37,650 --> 00:02:41,530
+هاتي ال basis اللي تقدر عليه لمين لل vector space
+
+32
+00:02:41,530 --> 00:02:46,930
+اللي عندها كانبقول له كويس يبقى انا ها ها بدي اجي
+
+33
+00:02:46,930 --> 00:02:51,590
+اخد بعض ال vectors و اشوف هل هدول بنفع يكونوا
+
+34
+00:02:51,590 --> 00:02:55,150
+bases و لا بنفعش يكونوا bases و من خلالها بجيب ال
+
+35
+00:02:55,150 --> 00:02:59,770
+dimension و بأثبت ان هذا finite dimensional vector
+
+36
+00:02:59,770 --> 00:03:03,910
+space اللي عندنا فاهمه كويس يبقى انا بروح اخد
+
+37
+00:03:03,910 --> 00:03:10,730
+مجموعة من المصوفات موجودة وين في ال M22 كتالة يبقى
+
+38
+00:03:10,730 --> 00:03:12,330
+لو جيكي قول solution
+
+39
+00:03:14,990 --> 00:03:22,130
+أو روح تقول ثلاث E1 بده يساوي واحد وزير وزير وE2
+
+40
+00:03:22,130 --> 00:03:29,270
+بده يساوي زير وواحد وزير وزير وE3 بده يساوي زير
+
+41
+00:03:29,270 --> 00:03:36,170
+وزير وواحد وزير وE4 بده يساوي زير وزير وواحد
+
+42
+00:03:36,170 --> 00:03:42,710
+موجودة في ال M22أخذت الـ vectors هذه الموجودة في
+
+43
+00:03:42,710 --> 00:03:45,430
+الـ M22 بالشكل اللي عندنا
+
+44
+00:03:54,830 --> 00:04:07,030
+أفترض أن هناك أسكالر كواحد و كاتنين و كتلتا و
+
+45
+00:04:07,030 --> 00:04:11,110
+كاربا in R such that
+
+46
+00:04:14,340 --> 00:04:21,420
+كواحد اواحد زائد كاتنين اتنين زائد كتلاتة اتلاتة
+
+47
+00:04:21,420 --> 00:04:26,740
+زائد كاربعة اي اربعة بده يساوي مان بده يساوي زيرو
+
+48
+00:04:26,740 --> 00:04:30,780
+معناه يا بنات شو بده يصير عندنا بده يصير كواحد
+
+49
+00:04:30,780 --> 00:04:40,250
+زيرو زيرو زائدزيرو كتنين زيرو زيرو زائد زيرو زيرو
+
+50
+00:04:40,250 --> 00:04:49,030
+كتلاتة زيرو زائد زيرو زيرو كاربعة بدي يساوي زيرو
+
+51
+00:04:49,030 --> 00:04:55,850
+زيرو زيرو المصفوفة من الصفريةيبقى هذا معناه إيش؟
+
+52
+00:04:55,850 --> 00:04:59,930
+بدي أجمع الأربع مصفوفات مع بعضهم، لو روحت جماعة
+
+53
+00:04:59,930 --> 00:05:06,190
+الأربع مصفوفات مع بعضهم، يبقى بيصير عند مين؟ يبقى
+
+54
+00:05:06,190 --> 00:05:10,310
+بدي أجمع هذه المصفوفات الأربع، يبقى بيصير كواحد،
+
+55
+00:05:10,310 --> 00:05:18,010
+كتنين، كتلاتة، كاربعة، بدي سوى Zero Zero Zeroأنا
+
+56
+00:05:18,010 --> 00:05:22,730
+عندي مصفتين متساويات يبقى العناصر المتناضرة في
+
+57
+00:05:22,730 --> 00:05:27,790
+الأولى تساوي العناصر المتناضرة من الثانية يبقى هذا
+
+58
+00:05:27,790 --> 00:05:31,210
+معناه ان K واحد يساوي K اتنين
+
+59
+00:05:40,960 --> 00:05:50,700
+يبقى هذا معناه ان ال E1 والE2 والE3 والE4 هم
+
+60
+00:05:50,700 --> 00:05:52,500
+linearly independent
+
+61
+00:05:55,280 --> 00:06:01,520
+طب كويس يبقى تحقق الشرط الأول من شروط ال basis
+
+62
+00:06:01,520 --> 00:06:08,140
+تمام؟ إذا بروح أخد element موجود في ال M22 و أشوف
+
+63
+00:06:08,140 --> 00:06:12,500
+هل بقدر أكتب علاصية linear combination من الآخرين
+
+64
+00:06:12,500 --> 00:06:20,100
+أم لا يبقى باجي بقوله الآن خطوة ثانية let x, y, z,
+
+65
+00:06:20,620 --> 00:06:28,020
+w موجودة في ال M22تمام؟ يبقى هذا ال element موجود
+
+66
+00:06:28,020 --> 00:06:28,420
+هنا
+
+67
+00:06:31,630 --> 00:06:36,810
+هل بقدر اكتب الـ element هذا بدلالة المصحوفات
+
+68
+00:06:36,810 --> 00:06:41,610
+الأخرى او بدلالة الإيهات اللي عندي ولا لا؟ يبقى
+
+69
+00:06:41,610 --> 00:06:48,750
+المصحوفة هذه بقدر اكتبها للـ X Y Z W بدها تساوي X
+
+70
+00:06:48,750 --> 00:06:56,690
+Zero Zero زائد Zero Y Zero Zero زائد Zero Zero Z
+
+71
+00:06:56,690 --> 00:07:04,540
+Zero زائد Zero Zeroالشكل اللي قلنا هذا يبقى كتبت
+
+72
+00:07:04,540 --> 00:07:08,660
+هذا ال element العشوائي اللي أخدته من المكان يكون
+
+73
+00:07:08,660 --> 00:07:13,260
+من ال M22 على شكل linear combination من من من
+
+74
+00:07:13,260 --> 00:07:21,410
+الأخرين يبقى هذا الكلام يساوي Xبارا واحد زيرو زيرو
+
+75
+00:07:21,410 --> 00:07:28,170
+زائد Y عامل مشترك زيرو واحد زيرو زيرو Z عامل مشترك
+
+76
+00:07:28,170 --> 00:07:34,790
+زيرو زيرو واحد زيرو W عامل مشترك زيرو زيرو واحد
+
+77
+00:07:34,790 --> 00:07:39,150
+بالشكل اللي عندنا هذا فبالمصوفة الأولى مش هي اي
+
+78
+00:07:39,150 --> 00:07:45,220
+واحدوالتانية E2 والتالتة E3 إذا بقدر أقول هذا
+
+79
+00:07:45,220 --> 00:07:55,700
+الكلام بده يساوي XE1 زائد YE2 زائد ZE3 زائد WE4
+
+80
+00:07:55,700 --> 00:07:59,410
+بالشكل اللي عندنا هذايبقى ال element اللي أنا
+
+81
+00:07:59,410 --> 00:08:04,270
+كتبته على شكل linear combination من من ال linearly
+
+82
+00:08:04,270 --> 00:08:12,470
+independent elements يبقى هنا سواء ال X Y Z W اللي
+
+83
+00:08:12,470 --> 00:08:21,750
+موجود اللي موجود في M 2 2 is a linear combination
+
+84
+00:08:21,750 --> 00:08:26,610
+combination of
+
+85
+00:08:27,110 --> 00:08:33,550
+E1 وE2 وE3 وE4
+
+86
+00:08:37,810 --> 00:08:41,970
+Linearly independent و أي element في M22 هو Linear
+
+87
+00:08:41,970 --> 00:08:45,310
+combination يعني اتحقق الشرطين يبقى دول شكله ال
+
+88
+00:08:45,310 --> 00:08:56,590
+main basis يبقى هنا thus وهكذا اللي هو the set E1
+
+89
+00:08:56,590 --> 00:09:08,780
+E2 E3 E4 formأيه بيزيز بتشكل ليه بيزيز four m two
+
+90
+00:09:08,780 --> 00:09:13,240
+two جيب
+
+91
+00:09:13,240 --> 00:09:18,000
+جيبتله بيزيز ولا لا لل vector space اللي عندنا هنا
+
+92
+00:09:19,910 --> 00:09:24,710
+الان هدول يمثلولي basis لل vector space اللي عندنا
+
+93
+00:09:24,710 --> 00:09:28,970
+شوفوا رأيكم ان هذا في كل الكتب تابعة الرياضيات
+
+94
+00:09:28,970 --> 00:09:33,730
+بنسميه standard basis يعني هذا ال basis اللي مشهور
+
+95
+00:09:33,730 --> 00:09:38,950
+للكل لكن هناك basis أخرى يفجأة باجي بقول this
+
+96
+00:09:38,950 --> 00:09:40,930
+basis
+
+97
+00:10:01,540 --> 00:10:05,940
+طيب قاللي هاتله ال dimension لل vector space و
+
+98
+00:10:05,940 --> 00:10:09,920
+اثبتله انه finite dimensional قديش ال dimension
+
+99
+00:10:09,920 --> 00:10:15,040
+هنا؟أربعة عدد العناصر في ال business أخدناها نظرا
+
+100
+00:10:15,040 --> 00:10:23,460
+هي الصعبة يبقى باجي بقوله the dimension of
+
+101
+00:10:23,460 --> 00:10:36,460
+the vector space M22 is أربعةطب مادام اربعة يبقى
+
+102
+00:10:36,460 --> 00:10:39,320
+ده finite dimensional ولا ماهواش finite؟ finite
+
+103
+00:10:39,320 --> 00:10:49,900
+أيوة يبقى this برضه means that هذا يعني ان ال M22
+
+104
+00:10:49,900 --> 00:10:59,760
+is a finite dimensional vector
+
+105
+00:10:59,760 --> 00:11:00,380
+space
+
+106
+00:11:11,940 --> 00:11:18,880
+نغير هذه الأنواع بنوع جديد أو vector space جديد
+
+107
+00:11:18,880 --> 00:11:20,580
+غير هذا ال vector space
+
+108
+00:11:28,610 --> 00:11:32,410
+هذه الـ vector spaces و ال dimension تبعهم و ال
+
+109
+00:11:32,410 --> 00:11:37,410
+bases very important لما بعد ذلك يعني ال standard
+
+110
+00:11:37,410 --> 00:11:40,030
+bases بتعرف ان حد ما يقولك ال vector space كذا
+
+111
+00:11:40,030 --> 00:11:43,130
+بيقولي ال standard space تبعه كذا بيكون عارفها
+
+112
+00:11:43,130 --> 00:11:46,770
+تماما لإن هي عندما بجيبه أقولك هذا هو ال standard
+
+113
+00:11:46,770 --> 00:11:51,750
+bases و منه بقدر أعرف قداشة ال dimension اللي هو
+
+114
+00:11:51,750 --> 00:11:55,770
+عدد العناصر في ال bases لهذا ال vector space يبقى
+
+115
+00:11:55,770 --> 00:12:02,440
+بداجة ل example تلاتةمثال ثلاثة
+
+116
+00:12:05,690 --> 00:12:12,410
+الـ V اللي هي PN مين ال PN يبقى the set of all
+
+117
+00:12:12,410 --> 00:12:19,950
+polynomials PX بحيث أن ال PX بدها تساوي ال A نعد
+
+118
+00:12:19,950 --> 00:12:29,350
+زائد A عن X زائد A to X تربية زائد زائد A N X to
+
+119
+00:12:29,350 --> 00:12:33,170
+the power N Find
+
+120
+00:12:36,100 --> 00:12:44,520
+او او او
+
+121
+00:13:07,920 --> 00:13:12,780
+طيب، لأن أخدنا vector space جديد غير اللي اتعودنا
+
+122
+00:13:12,780 --> 00:13:16,060
+عليهم في المثالين السابقين، مين ال vector space
+
+123
+00:13:16,060 --> 00:13:20,180
+هذا؟ طبعا شفناها قبل هيك، بس احنا هنا لقى انا
+
+124
+00:13:20,180 --> 00:13:23,280
+أخدناها مش لتنين ولا لتلاتة ولا احد، وإنما لغاية
+
+125
+00:13:23,280 --> 00:13:29,480
+N، وهي كل ال polynomials اللي درجتها N أو أقل من N
+
+126
+00:13:30,080 --> 00:13:33,960
+يبقى كل ال polynoms اللي على الشكل انه كثيرات ال
+
+127
+00:13:33,960 --> 00:13:41,260
+a0 و a1 و a2 و an are constants جالي هاتلي bases
+
+128
+00:13:41,260 --> 00:13:46,140
+لمن ل ال vector space هذا و هاتلي ال dimension
+
+129
+00:13:46,140 --> 00:13:50,200
+يبقى انا بتدور على bases و بدى ادور على من على
+
+130
+00:13:50,200 --> 00:13:56,450
+dimension الان لو جيت قولتلك the functions مثلالي
+
+131
+00:13:56,450 --> 00:14:05,830
+واحد و X و X تربية و X تكييب و لغاية XN ما رأيك
+
+132
+00:14:05,830 --> 00:14:10,730
+دول linearly dependent ولا linearly independent؟
+
+133
+00:14:11,530 --> 00:14:16,350
+الله قال احنا ندعي انهم linearly independent لكن
+
+134
+00:14:16,350 --> 00:14:21,430
+مطلوب نثبت هذا الكلام يبقى هدول linearly
+
+135
+00:14:21,430 --> 00:14:23,030
+independent
+
+136
+00:14:32,620 --> 00:14:43,620
+اللي هو if الـ A0 والـ A1 والـ A2 والـ AN موجودة
+
+137
+00:14:43,620 --> 00:14:52,120
+في set of real numbers then اللي هو A0 زائد A1X
+
+138
+00:14:52,120 --> 00:14:59,580
+زائد A2X تربية زائد ANXN كل هذا الكلام بيساوي كده؟
+
+139
+00:14:59,580 --> 00:15:05,620
+بيساوي Zeroالان بدى اقارن المعاملات فى الطرفين
+
+140
+00:15:05,620 --> 00:15:09,440
+يبقى ال constant هنا بدى يقابله ال constant
+
+141
+00:15:09,440 --> 00:15:12,800
+المعامل X1 بدى يقابله المعامل X1 المعامل X2 بدى
+
+142
+00:15:12,800 --> 00:15:17,130
+يقابله المعامل X2 طب الشجة الشمال مالها؟معناة كل
+
+143
+00:15:17,130 --> 00:15:21,950
+المعاملات بأسفار صحيح ولا لأ؟ يبقى هنا لو قررنا
+
+144
+00:15:21,950 --> 00:15:27,370
+المعاملات في الطرفين يبقى يصير a0 بدري يسوى a1
+
+145
+00:15:27,370 --> 00:15:33,770
+بدري يسوى a2 بدري يسوى an بدري يسوى مين ال zero
+
+146
+00:15:33,770 --> 00:15:39,150
+لما قررنا المعاملات يبقى لأن ادعيته ان اتنين هدول
+
+147
+00:15:39,150 --> 00:15:44,930
+are linearly independent كلام صحيح مظبوط طيب يبقى
+
+148
+00:15:44,930 --> 00:15:51,340
+خلصنا مين؟المطلوب الأول من ال basis اتنين بتاخد أي
+
+149
+00:15:51,340 --> 00:15:57,320
+polynomial موجودة في ال PN و أثبت أنه بقدر أكتبها
+
+150
+00:15:57,320 --> 00:16:01,360
+على صيغة linear combination من ال function اللي
+
+151
+00:16:01,360 --> 00:16:09,420
+عندنا يعني يبقى باجي بقوله let P of X موجودة في ال
+
+152
+00:16:09,420 --> 00:16:10,200
+PN
+
+153
+00:16:12,960 --> 00:16:23,000
+الـ P of X ممكن اكتبها P0 زائد P1X زائد P2X ترابيع
+
+154
+00:16:23,000 --> 00:16:32,620
+زائد زائد PNXN اللي هي تساوي بقدر اكتبها بمناط P0
+
+155
+00:16:32,620 --> 00:16:44,040
+في واحد زائد P1 في Xزائد P2 في X ترابيع زائد PN في
+
+156
+00:16:44,040 --> 00:16:50,440
+X to the power N يعني
+
+157
+00:16:50,440 --> 00:16:56,080
+أصبحت ال PX اللي موجودة في PN اللي أخدت هذه
+
+158
+00:16:56,080 --> 00:17:02,160
+عشوائيا من PN هي عبارة عن من؟ linear combination
+
+159
+00:17:02,160 --> 00:17:08,040
+من من؟ من ال linearly independent vectors هدولصح؟
+
+160
+00:17:08,040 --> 00:17:14,460
+يعني معناته ان هدول ال vectors بيولدولي مين؟ اللي
+
+161
+00:17:14,460 --> 00:17:27,120
+هو ال P in يبقى هنا this means that ان ال
+
+162
+00:17:27,120 --> 00:17:33,800
+P of X is a linear combination
+
+163
+00:17:44,900 --> 00:17:48,760
+يبقى هدول linearly independent وكل element في
+
+164
+00:17:48,760 --> 00:17:51,480
+البرنامج اللي هو linear combination يبقى هدول
+
+165
+00:17:51,480 --> 00:17:52,480
+عبارة عن ايه؟
+
+166
+00:18:00,130 --> 00:18:08,250
+لي واحد و X و X تربية و X to the power N is a
+
+167
+00:18:08,250 --> 00:18:22,070
+basis for PN this basis is called the
+
+168
+00:18:22,070 --> 00:18:27,170
+standard basis
+
+169
+00:18:29,930 --> 00:18:39,370
+for PN طب هو في السؤال قال لي هاتلي بيزز و هاتلي
+
+170
+00:18:39,370 --> 00:18:45,870
+ال dimension لل vector space PN مش هيك سؤال يبقى
+
+171
+00:18:45,870 --> 00:18:50,570
+احنا أجبنا حتى الآن على نصف السؤال و بقى النصف
+
+172
+00:18:50,570 --> 00:18:54,470
+الآخر find a basis او جدنا له basis وطوله هو ال
+
+173
+00:18:54,470 --> 00:19:01,120
+standard basisجالي هكذا ال dimension ل PN يبقى عدد
+
+174
+00:19:01,120 --> 00:19:04,560
+اللي انا صرفيه ال biases هو ال dimension اكم واحد
+
+175
+00:19:04,560 --> 00:19:11,560
+هدول جديد؟ متكده؟ بتقول نور هدول عددهم N زي واحد
+
+176
+00:19:11,560 --> 00:19:18,710
+طلعوا فيهم كويس موافقين؟ و الله بس Nن زاد واحد،
+
+177
+00:19:18,710 --> 00:19:26,450
+لماذا؟ لأن هذا الواحد كلهم عددهم N وفيه كمان واحد
+
+178
+00:19:26,450 --> 00:19:32,090
+بدون X يعني كأنه X أوز Zero يعني يفجر هذول ال
+
+179
+00:19:32,090 --> 00:19:35,210
+dimension اللي يساوي N زاد واحد اللي هو عدد
+
+180
+00:19:35,210 --> 00:19:40,390
+العناصر في ال Basel باجي بقوله دي dimension
+
+181
+00:19:42,480 --> 00:19:50,600
+R PN is N plus one هذا السؤال جبناه مرة في
+
+182
+00:19:50,600 --> 00:19:54,480
+الخيارات المتعددة يبقى يقول the dimension of the
+
+183
+00:19:54,480 --> 00:20:02,420
+vector space PN is N N زياد واحد Zero Infinity
+
+184
+00:20:02,420 --> 00:20:07,990
+حطيلي خط تحت الإجابة الصحيحة يبقى المفهومكثير
+
+185
+00:20:07,990 --> 00:20:12,070
+بيحطوله انه N لان قبل قدومها لغاية N يبقى هذا N
+
+186
+00:20:12,070 --> 00:20:16,450
+وبينسى انه في واحد جاب المبدأ A بال X يبقى هو N
+
+187
+00:20:16,450 --> 00:20:24,610
+زائد واحد وليس M لخاطر اخد special cases من هذه ال
+
+188
+00:20:24,610 --> 00:20:31,770
+polynomial يبقى بالدرجة اخد special cases حالات
+
+189
+00:20:31,770 --> 00:20:39,890
+خاصة لهذه ال polynomial نمرة واحدالأساس اليمين
+
+190
+00:20:39,890 --> 00:20:56,890
+واحد و X و X تربيع هو الأساس الواضح لـ
+
+191
+00:20:56,890 --> 00:21:01,490
+P3 ولا P2 يا فنات؟ P2
+
+192
+00:21:03,140 --> 00:21:15,360
+and the dimension of P2 is اتنين تلاتة يبقى اكتر
+
+193
+00:21:15,360 --> 00:21:29,480
+من ال N دائما وابدا بمقدار واحد صحيح طيب
+
+194
+00:21:29,480 --> 00:21:35,880
+نمر اتنينبدأ أخليه على شكل كأنه مثال صغير show
+
+195
+00:21:35,880 --> 00:21:43,120
+that the set اللي
+
+196
+00:21:43,120 --> 00:21:52,580
+هو main x تربيع زائد x x ناقص واحد x زائد واحد is
+
+197
+00:21:52,580 --> 00:21:58,400
+a basis for P2
+
+198
+00:22:02,730 --> 00:22:14,490
+بدي اثبت ان هدول basis على مين على شكل ال P2 يا
+
+199
+00:22:14,490 --> 00:22:20,030
+بنات احنا هنا جبنا هدول standard basis لمين لل P2
+
+200
+00:22:20,030 --> 00:22:25,250
+اللي هو ال dimension له يسوى كده؟ يسوى تلاتة الان
+
+201
+00:22:25,250 --> 00:22:31,670
+ميعطيني تلاتة vectors اخرى وهي موجودة وين؟فى P2
+
+202
+00:22:31,670 --> 00:22:37,790
+صح؟ فش درجة اكتر من اتنين كله X تربية وانزل يبقى
+
+203
+00:22:37,790 --> 00:22:42,290
+بييل لي ان هدول is a basis for P2 اول شي هدول
+
+204
+00:22:42,290 --> 00:22:47,170
+موجودة فى P2 بدي اثبت له انهم linearly independent
+
+205
+00:22:47,170 --> 00:22:53,830
+و بدي اثبت انه اي element موجود فى P2 هو linear
+
+206
+00:22:53,830 --> 00:23:00,430
+combination من هدول او بمعنى اخر هدول عددهم تلاتةو
+
+207
+00:23:00,430 --> 00:23:05,550
+linearly independent و ال dimension ل P2 هو تلاتة
+
+208
+00:23:05,550 --> 00:23:10,250
+إذا لا داعي الخطوة الأخيرة صح ولا لا لأن عدد
+
+209
+00:23:10,250 --> 00:23:15,210
+العناصر في ال bases في أي bases are equal مظبوط
+
+210
+00:23:15,210 --> 00:23:18,270
+يبقى بس ضايل عليه أثبت إن هدول linearly
+
+211
+00:23:18,270 --> 00:23:22,750
+independent طيب تعالوا نشوف ندفتهم linearly
+
+212
+00:23:22,750 --> 00:23:26,270
+independent يبقى باجي بقوله solution
+
+213
+00:23:30,510 --> 00:23:40,910
+that there exist A وB وC in R such that بحيث أن
+
+214
+00:23:40,910 --> 00:23:49,270
+الـ A في الـ X تربيع زياد X زائد B الـ X ناقص واحد
+
+215
+00:23:49,270 --> 00:23:55,370
+زياد C في الـ X زياد واحد كله يساوي Zeroإذا طلع
+
+216
+00:23:55,370 --> 00:23:59,290
+عندى أن a يساوي b يساوي 0 يبقى دول linearly
+
+217
+00:23:59,290 --> 00:24:04,330
+independent تمام تمام يبقى بدى أفك هذه الأقواس
+
+218
+00:24:04,330 --> 00:24:09,210
+يبقى ax²axbx
+
+219
+00:24:09,210 --> 00:24:18,590
+-b plus cx plus c كله بدى ساوي 0هذه AX² مافيش
+
+220
+00:24:18,590 --> 00:24:23,370
+غيرها من الدرجة التانية هذه و هذه و هذه كلهم من
+
+221
+00:24:23,370 --> 00:24:29,150
+الدرجة الأولى يبقى بدي أخد X عامل مشترك بيظل A
+
+222
+00:24:29,150 --> 00:24:37,650
+زائد B زائد C في ال X الثوابط كتالي يبقى زائد عندك
+
+223
+00:24:37,650 --> 00:24:44,310
+هنا C و سالب B كله بده يسوي قداش Zero
+
+224
+00:24:47,160 --> 00:24:53,360
+اذا لو جينا قارننا المعاملات في الطرفين يبقى لو
+
+225
+00:24:53,360 --> 00:24:57,160
+قارننا المعاملات في الطرفين بيصير ال a يساوي كم يا
+
+226
+00:24:57,160 --> 00:25:03,720
+بنات؟ Zero و ال a زيدي ال b زيدي ال c يبقى يساوي
+
+227
+00:25:03,720 --> 00:25:09,440
+Zero و ال c ناقص ال b يساوي Zero الحين هذه ال a
+
+228
+00:25:09,440 --> 00:25:14,940
+يساوي Zero يبقى هذا معناته ان ال b زيدي ال c يساوي
+
+229
+00:25:14,940 --> 00:25:22,000
+كم؟ Zeroوهذا الـ C نقص الـ B يبقى يساوي زيرو. اجمع
+
+230
+00:25:22,000 --> 00:25:27,900
+هدول مع هدول، بيروحوا، بظل اتنين، C يساوي زيرو،
+
+231
+00:25:27,900 --> 00:25:34,160
+يبقى C تساوي زيرو. لما C تساوي زيرو، يبقى B قداش؟
+
+232
+00:25:34,580 --> 00:25:42,640
+يبقى and ال B تساوي 0 يبقى هنا S ال A تساوي ال B
+
+233
+00:25:42,640 --> 00:25:49,040
+تساوي ال C تساوي ال 0 معناته هدول مالهم هذا معناه
+
+234
+00:25:49,040 --> 00:25:56,580
+ان ال X تربيع زائد X وال X minus ال one وال X plus
+
+235
+00:25:56,580 --> 00:26:02,720
+one is linearly independent vectors
+
+236
+00:26:08,410 --> 00:26:13,190
+يبقى هؤلاء صاروا nearly independent vectors in P2
+
+237
+00:26:17,900 --> 00:26:21,340
+بس اسمع شوية، لو أنا ماعيش خبر هيك ونايم على روحي
+
+238
+00:26:21,340 --> 00:26:25,260
+وكذا، يمكن بروح أثبت أن أي element في الـP2 هو
+
+239
+00:26:25,260 --> 00:26:29,680
+linear combination من هدول، بس هذه قصة بتطول شوية،
+
+240
+00:26:29,680 --> 00:26:32,880
+يعني بالدرجة على معلوماتي في النظريات تبعت الصبح،
+
+241
+00:26:32,880 --> 00:26:38,380
+أي basis في نفس العدد منالعناصر. إذا هؤلاء ينفعوا
+
+242
+00:26:38,380 --> 00:26:43,800
+الـ Bases ولا لا؟ لأن عددهم يسوى كم؟ تلاتة و هم
+
+243
+00:26:43,800 --> 00:26:55,540
+نوعيا مستقلين. يبقى باجي بقولهم بما أن هؤلاء هم
+
+244
+00:26:55,540 --> 00:26:59,680
+ثلاثة عناصر
+
+245
+00:27:06,560 --> 00:27:20,060
+of P2 is A3 we have ان ال X تربيع زائد ال X وال X
+
+246
+00:27:20,060 --> 00:27:30,900
+ناقص واحد وال X زائد واحد هذه form A بيزز فور من
+
+247
+00:27:30,900 --> 00:27:37,870
+P2يبقى يا بنات طلعنا الان ال standard basis هو
+
+248
+00:27:37,870 --> 00:27:43,370
+واحد و X و X تربيع و جيبنا basis أخر اللي هو اللي
+
+249
+00:27:43,370 --> 00:27:48,310
+قدامنا هذا طبعا ممكن نجيب basis أخرين و هكذا مثل
+
+250
+00:27:48,310 --> 00:27:52,610
+اللي هو المثال في محاضرة الصبح أخر مثال لما جيبنا
+
+251
+00:27:52,950 --> 00:27:57,130
+للـ R2 أربعة basis غير ال standard يبقى طلعنا له
+
+252
+00:27:57,130 --> 00:28:01,710
+خمسة كل basis اللي عدد فيه كده بده يساوي بده يساوي
+
+253
+00:28:01,710 --> 00:28:07,890
+ال dimension تبع ال vector space R2 طلعنا كل basis
+
+254
+00:28:07,890 --> 00:28:13,210
+فيه بس two elements جينا على P2 طلعنا ان ال
+
+255
+00:28:13,210 --> 00:28:17,890
+dimension اللي هيساوي تلاتة و أي تلاتة مش أي تلاتة
+
+256
+00:28:17,890 --> 00:28:22,010
+بعض ال vectorsالموادات في P2 are linearly
+
+257
+00:28:22,010 --> 00:28:27,550
+independent اللي بنفع يكونوا basis لهذا ال vector
+
+258
+00:28:27,550 --> 00:28:34,150
+space نعطي كمان مثال بس عادى بيختلف شوية عن ما سبق
+
+259
+00:28:34,150 --> 00:28:38,390
+من الأمثلة لذلك بده تفكير شوية
+
+260
+00:28:48,830 --> 00:29:00,030
+يبقى example four بيقول
+
+261
+00:29:00,030 --> 00:29:08,650
+let ال V تساوي R3 طبعا من هذا مناطق احنا عارفين هي
+
+262
+00:29:08,650 --> 00:29:11,470
+دي مشهورة عندنا let
+
+263
+00:29:12,920 --> 00:29:18,580
+الـ U تساوي اللي هي the set of all elements X واحد
+
+264
+00:29:18,580 --> 00:29:27,080
+و X اتنين و X تلاتة such that X تلاتة بده ساوي
+
+265
+00:29:27,080 --> 00:29:32,560
+اتنين X واحد زائد X اتنين بالشكل اللي عندنا هنا
+
+266
+00:29:32,560 --> 00:29:37,520
+find a
+
+267
+00:29:37,520 --> 00:29:38,460
+basis
+
+268
+00:29:52,950 --> 00:30:02,530
+والدمينشن لـ subspace U
+
+269
+00:30:19,880 --> 00:30:25,440
+سؤال مرة تانية احنا عندنا ال vector space R3 اللي
+
+270
+00:30:25,440 --> 00:30:31,160
+كل element فيه عبارة عن عنصر مكون من ثلاث مركبات
+
+271
+00:30:31,160 --> 00:30:35,720
+X1 و X2 و X3 اللي موجودة في R3 هذا ال vector space
+
+272
+00:30:35,720 --> 00:30:42,220
+R3 ال X1 و X2 و X3 عارية ال number روحنا أخدنا منه
+
+273
+00:30:42,220 --> 00:30:46,820
+مجموعة من العناصر أو ال elements أو ال vector مين
+
+274
+00:30:46,820 --> 00:30:51,640
+هم هدول؟اللي بتكون من ثلاث مراكبات المراكبة الاولى
+
+275
+00:30:51,640 --> 00:30:56,140
+X واحد المراكبة التانية X التانية المراكبة التالتة
+
+276
+00:30:56,140 --> 00:31:01,700
+اتنين المراكبة الاولى زائد المراكبة التالتة كويس
+
+277
+00:31:01,700 --> 00:31:06,130
+هذا بلغتنا قبل هيك اثبتنا انه الصعب ال spaceما هو
+
+278
+00:31:06,130 --> 00:31:09,330
+ال subspace هو ال vector space الجديد صحيح ولا لا
+
+279
+00:31:09,330 --> 00:31:14,250
+ال vector space الجديد أو ال subspace بدي ابحث عن
+
+280
+00:31:14,250 --> 00:31:20,970
+bases له أعرف قداشة و dimension طب هو subspace من
+
+281
+00:31:20,970 --> 00:31:24,930
+R3 تتوقع ال bases يكونوا له تلاتة و ال dimension
+
+282
+00:31:24,930 --> 00:31:32,570
+يسوى تلاتة؟قد يكون وقد لا يكون، لا احتمالين وردات،
+
+283
+00:31:32,570 --> 00:31:37,090
+ليش؟ لإن انا إذا لجيت له أي basis، عدد عناصره أجل
+
+284
+00:31:37,090 --> 00:31:39,610
+من تلاتة، خلاص، بمشي الحال، ماعنديش مشكلة
+
+285
+00:31:42,290 --> 00:31:46,750
+يبقى مرة تانية انا عند ال U بالشكل اللي عندها ده
+
+286
+00:31:46,750 --> 00:31:53,610
+يعني ايش يعني ال U هذا يمنعطل وعلى الشكل التالي كل
+
+287
+00:31:53,610 --> 00:32:00,890
+العناصر X واحد و X اتنين و اتنين X واحد زاد X
+
+288
+00:32:00,890 --> 00:32:06,460
+اتنينبحيث ان ال X واحد وال X اتنين موجودة في ال
+
+289
+00:32:06,460 --> 00:32:10,480
+set of real number يبقى هذا ال subspace اللي عندي
+
+290
+00:32:10,480 --> 00:32:16,420
+ال subspace بتروح ادورله على bases و اذا دورتله
+
+291
+00:32:16,420 --> 00:32:20,340
+على bases بكون حلت باقى المشاكل لان هو هاتله bases
+
+292
+00:32:20,340 --> 00:32:24,140
+و هاتله ال dimension ما هو ال dimension بسيطة على
+
+293
+00:32:24,140 --> 00:32:27,040
+العناصر في ال bases يبقى انا لو جبت bases بكون
+
+294
+00:32:27,040 --> 00:32:36,200
+خلصتتعالى نشوف أي element موجود هنا يبقى لو أخدت
+
+295
+00:32:36,200 --> 00:32:46,680
+العنصر x1 وx2 و2x1 زائد x2 هل بقدر أكتبه على صيغة
+
+296
+00:32:46,680 --> 00:32:54,160
+مجموعة two vectors أو تلاتة مثلا؟ نقدر؟طيب لو جيت
+
+297
+00:32:54,160 --> 00:33:03,040
+كتبته بقول X واحد و Zero و اتنين X واحد زائد Zero
+
+298
+00:33:03,040 --> 00:33:10,000
+و X اتنين و X اتنين مش بنفعك؟ لو جماعة تبعطيني هنا
+
+299
+00:33:10,000 --> 00:33:16,540
+طيب هدول فيهم عامل مشترك؟ بيبقوا واحد و Zero و
+
+300
+00:33:16,540 --> 00:33:24,820
+اتنين زائد X اتنين Zero و واحد و واحديبقى أي
+
+301
+00:33:24,820 --> 00:33:29,600
+element في ال vector space كتبته على صيغة linear
+
+302
+00:33:29,600 --> 00:33:37,840
+combination وين؟ بدلالة ال vectors هدول صح ولا لا؟
+
+303
+00:33:37,840 --> 00:33:52,040
+يبقى هذا any element of U is a linear combination
+
+304
+00:34:08,020 --> 00:34:14,220
+أي عنصر في U هو linear combination من اتنين هدول
+
+305
+00:34:14,220 --> 00:34:19,960
+السؤال هو هل اتنين هدول linearly dependent ولا
+
+306
+00:34:19,960 --> 00:34:22,560
+linearly independent؟
+
+307
+00:34:24,420 --> 00:34:28,840
+اندمنت لماذا؟ لأول واحد فيهم مضاعفات الأخرى، يعني
+
+308
+00:34:28,840 --> 00:34:32,840
+بقدرش أقول إن أحدهم يسوي constant في الثاني، مين
+
+309
+00:34:32,840 --> 00:34:36,400
+ما يكون ال constant هذا، يبقى هدول اتنين linearly،
+
+310
+00:34:36,400 --> 00:34:38,860
+يبقى بصيروا bases ولا لا؟
+
+311
+00:34:53,260 --> 00:35:04,240
+لكن ال V1 و V2 هم مستقلين لأن
+
+312
+00:35:04,240 --> 00:35:07,340
+اي شخص
+
+313
+00:35:23,250 --> 00:35:29,950
+ما هوش مضاعفات الآخر مادام ما هوش مضاعفات الآخر
+
+314
+00:35:29,950 --> 00:35:38,630
+يبقى هدول بتكونول ايه بيزز يبقى هنا the setاللي هي
+
+315
+00:35:38,630 --> 00:35:46,870
+مين؟ اللي هي واحد وزيرو واتنين وزيرو واحد وواحد
+
+316
+00:35:46,870 --> 00:36:01,670
+form a basis for the subspace U خلصت المطلب الأول؟
+
+317
+00:36:01,670 --> 00:36:09,070
+إيش قال ليه؟ كداش ال dimensionأتنين لإن الوزرافش
+
+318
+00:36:09,070 --> 00:36:16,070
+فيه إلا عنصرين، هم في واحد و بيتنين يبقى هنا ال
+
+319
+00:36:16,070 --> 00:36:27,090
+dimension of you is اتنين اللي هو يبدو يساوي
+
+320
+00:36:27,090 --> 00:36:31,210
+number of
+
+321
+00:36:31,210 --> 00:36:33,050
+elements
+
+322
+00:36:35,560 --> 00:36:44,540
+in the given bases يبقى
+
+323
+00:36:44,540 --> 00:36:53,140
+عدد العناصر في ال bases المقطع أعظم
+
+324
+00:36:53,140 --> 00:36:54,980
+ولا مرة أخدنا مثال زي هذا
+
+325
+00:37:04,510 --> 00:37:10,290
+طيب، لغاية هنا انتهى هذا section، لكن سنرجعله
+
+326
+00:37:10,290 --> 00:37:14,550
+ثانية خلال ال chapter هذا و ال chapter القادم
+
+327
+00:37:14,550 --> 00:37:20,430
+لازلنا .. ها في شغل معتمد عليه، يبقى باجي بقول
+
+328
+00:37:20,430 --> 00:37:29,650
+exercisesتلاتة خمسة المسائل التالية أربعة وخمسة
+
+329
+00:37:29,650 --> 00:37:40,710
+وسبعة وتسعة وعشرة وتلتاش تلتاش مكف منكوا ايه راسي؟
+
+330
+00:37:46,820 --> 00:37:52,640
+الان بدنا نشتغل شغل تانى، لكن بيعتمد على مين؟ على
+
+331
+00:37:52,640 --> 00:37:57,120
+ال vector space، بنشتغل functions، بس ال functions
+
+332
+00:37:57,120 --> 00:38:00,620
+مش على ال sets عادية، وإنما من vector space إلى
+
+333
+00:38:00,620 --> 00:38:06,220
+vector space ثانى، وهى الجزء الثانى من هذا ال
+
+334
+00:38:06,220 --> 00:38:08,740
+chapter، ال chapter هذا حاطين عنوان
+
+335
+00:38:14,150 --> 00:38:20,610
+أول خمسة سيكشن من هذا الشبطة يبقى احنا بنروح
+
+336
+00:38:20,610 --> 00:38:25,750
+الألمان لسيكشن اللي بعده اللي هو linear
+
+337
+00:38:25,750 --> 00:38:27,110
+transformations
+
+338
+00:38:42,840 --> 00:38:48,020
+بعد تلاتة خمسة بروح لتلاتة ستة وبن cancel تلاتة
+
+339
+00:38:48,020 --> 00:38:52,780
+ستة وبن cancel تمام نشط وبروح لتلاتة سبعة يبقى
+
+340
+00:38:52,780 --> 00:39:01,080
+تلاتة سبعة هو ال linear transformations
+
+341
+00:39:10,520 --> 00:39:18,680
+لينا transformations يعني التحويلات الخطية نعطي
+
+342
+00:39:18,680 --> 00:39:25,260
+definition للتحويل الخطية ثم بعد ذلك ناخد بعض
+
+343
+00:39:25,260 --> 00:39:31,360
+الأمثلة على هذا ال definition يبقى definition let
+
+344
+00:39:31,360 --> 00:39:36,400
+ال V and ال W
+
+345
+00:39:45,050 --> 00:39:59,930
+توا فكتر خطوات توا فكتر خطوات توا فكتر خطوات توا
+
+346
+00:39:59,930 --> 00:40:03,710
+فكتر خطوات توا فكتر
+
+347
+00:40:03,710 --> 00:40:06,120
+خطوات توا فكتر خطوات توا فكتر خطوات توا فكتربـ
+
+348
+00:40:06,120 --> 00:40:12,660
+Mapping Mapping او Functions يام تفريقش عندنا Then
+
+349
+00:40:12,660 --> 00:40:21,440
+a T is called T is called a linear transformation
+
+350
+00:40:21,440 --> 00:40:26,880
+A linear transformation
+
+351
+00:40:32,450 --> 00:40:39,170
+أو بعض الكتب تكتبها linear mapping linear mapping
+
+352
+00:40:39,170 --> 00:40:45,090
+لو لقيتها في أي مرجع linear mapping تستغربيش if
+
+353
+00:40:45,090 --> 00:40:55,670
+the following if
+
+354
+00:40:55,670 --> 00:40:59,690
+the following properties
+
+355
+00:41:09,960 --> 00:41:20,080
+أول خاصية من هذه الخواص هي T of C في U بده يساوي C
+
+356
+00:41:20,080 --> 00:41:29,880
+في T of U for any scalar C
+
+357
+00:41:42,630 --> 00:41:53,400
+Condition التانيT of U زائد ال V يساوي T of U زائد
+
+358
+00:41:53,400 --> 00:42:00,820
+T of V لكل ال U و ال V اللي موجودة في ال vector
+
+359
+00:42:00,820 --> 00:42:08,080
+space V Note V
+
+360
+00:42:08,080 --> 00:42:14,020
+above two properties
+
+361
+00:42:15,910 --> 00:42:22,050
+the above two properties can be
+
+362
+00:42:22,050 --> 00:42:30,810
+written as one
+
+363
+00:42:30,810 --> 00:42:38,810
+property as
+
+364
+00:42:38,810 --> 00:42:39,470
+follows
+
+365
+00:42:42,770 --> 00:42:55,950
+إن الـ T of CU زائد V بده يساوي C في T of U زائد T
+
+366
+00:42:55,950 --> 00:43:07,450
+of V والـ C موجودة في R and الـ U والـ V موجودة في
+
+367
+00:43:07,450 --> 00:43:11,550
+الـ V كابتن example one
+
+368
+00:43:16,590 --> 00:43:34,470
+لت الـ T من الـ M M في N إلى الـ M N في M بـ a
+
+369
+00:43:34,470 --> 00:43:39,330
+mapping بـ
+
+370
+00:43:39,330 --> 00:43:42,650
+a mapping defined by
+
+371
+00:43:46,270 --> 00:43:53,770
+معرّفة كالتالي T of A بديو يساوي ال A transpose
+
+372
+00:43:53,770 --> 00:44:06,910
+for all A اللي موجودة في M M N السؤال
+
+373
+00:44:06,910 --> 00:44:15,410
+هو is T a linear transformation؟
+
+374
+00:44:24,270 --> 00:44:27,770
+هل التليانات تتغير أو لا؟
+
+375
+00:45:12,150 --> 00:45:15,690
+خلّيني أركب معايا العلماء البناتفي هذه الدقيقات
+
+376
+00:45:15,690 --> 00:45:20,050
+المتبقيات الأخيرات من هذه المحاضرة نعطي تعريف
+
+377
+00:45:20,050 --> 00:45:23,390
+الـLinear Transformation وتعطي مثال واحد والمرة
+
+378
+00:45:23,390 --> 00:45:28,610
+الجاية ان شاء الله بنكمل بقية هذه الأمثلة بيقولي
+
+379
+00:45:28,610 --> 00:45:34,690
+انا عندي two vector spaces V وW أخدنا T من V لW
+
+380
+00:45:34,690 --> 00:45:43,810
+يبقى function او mapping من V لWيبقى تحويل
+
+381
+00:45:43,810 --> 00:45:52,830
+خطيئة أو Linear Mapping دالة خطيئة كويس إذا تحقق
+
+382
+00:45:52,830 --> 00:45:59,310
+عندما يكون الخاصيتينالخاصية الأولى T لما تأثر على
+
+383
+00:45:59,310 --> 00:46:02,970
+C في U الـ C scalar موجود في الستة والولى ال
+
+384
+00:46:02,970 --> 00:46:07,650
+number ال U هو vector من ال vector space V يبقى T
+
+385
+00:46:07,650 --> 00:46:13,050
+of C في U بده يسوى C في T of U for any scalar C in
+
+386
+00:46:13,050 --> 00:46:19,170
+R and U in V الخاصية الأولى يعني لو T أثرت على C
+
+387
+00:46:19,170 --> 00:46:25,610
+في ال U بقول يا C قليك برا و T بده يصير of Uخاصية
+
+388
+00:46:25,610 --> 00:46:30,250
+تانية لو T أثرت على مجموعة و vectors يساوي تأثير T
+
+389
+00:46:30,250 --> 00:46:33,790
+على ال vector الأول زي تأثير T على ال vector
+
+390
+00:46:33,790 --> 00:46:39,650
+الثاني و U و V موجددات في main Vملاحظة بقول الـ
+
+391
+00:46:39,650 --> 00:46:42,810
+above two properties can be written as one
+
+392
+00:46:42,810 --> 00:46:46,990
+property بدل ما هما خاصيتين ممكن أجمعهم و أخليهم
+
+393
+00:46:46,990 --> 00:46:53,290
+خاصية واحدة كيف؟ كالتالت بقول T of C في U زائد V U
+
+394
+00:46:53,290 --> 00:46:57,810
+ساوي C في T of U زائد T of E يعني بدل ما أعمل
+
+395
+00:46:57,810 --> 00:47:02,480
+خطواتين هنا بمكان يعمل manلكنني لأ افضلها، لأ
+
+396
+00:47:02,480 --> 00:47:07,140
+افضلها ليش؟ لإن في احتمال تغلط هنا، لكن هنا دايسة،
+
+397
+00:47:07,140 --> 00:47:10,940
+لو غلطت، لو مشيت معاك الخطوة الأولى، بتبقى الخطوة
+
+398
+00:47:10,940 --> 00:47:14,060
+التانية، يعني بتجيب نص العلامة بدون مشاكل، ابقى
+
+399
+00:47:14,060 --> 00:47:19,090
+أنا بفضل نمشي الخطواتين وليست الخطوة الواحدةبنعطي
+
+400
+00:47:19,090 --> 00:47:24,450
+مثال قال افترض ان T عندك من مجموعة المصفوفات اللي
+
+401
+00:47:24,450 --> 00:47:29,630
+نضامها M في N الى مجموعة المصفوفات اللي نضامها N
+
+402
+00:47:29,630 --> 00:47:36,290
+في M يعني جلبناها تمام ب M I can define by T of M
+
+403
+00:47:36,290 --> 00:47:41,010
+لساوي A transpose صحيح الكلام هذا؟ يعني لو كانت
+
+404
+00:47:41,010 --> 00:47:45,890
+هذه المصفوفة نظامها M في N وجبت A transpose ايش
+
+405
+00:47:45,890 --> 00:47:51,800
+بصيها؟ن في م يبقى تعريف هذا صحيح ولا لا صحيح مائة
+
+406
+00:47:51,800 --> 00:47:56,900
+بالمائة يبقى هذا لكل ال ال موجودة في مجموعة
+
+407
+00:47:56,900 --> 00:48:01,820
+المصممات اللي هو ال domain بتابع من؟ بتابع ال T بس
+
+408
+00:48:01,820 --> 00:48:06,240
+هل ال T هذي linear transformation؟ والله ماهياش
+
+409
+00:48:06,240 --> 00:48:10,360
+linear transformationبقول والله كويس، إذا اتحققوا
+
+410
+00:48:10,360 --> 00:48:14,140
+الشرطين يبقى هي Linear اترافية، ما يتحققوا الشرطين
+
+411
+00:48:14,140 --> 00:48:20,000
+يبقى معناها مشكلة يبقى أنا بدا أجي ل solution بدا
+
+412
+00:48:20,000 --> 00:48:27,160
+أجي لمن أبنات للشرط الأول أشوف هل T في C في U
+
+413
+00:48:27,160 --> 00:48:32,060
+بتسوي C في T of U ولا لأ؟ الله أعلم، فباجي بقول
+
+414
+00:48:32,060 --> 00:48:39,960
+هنا Fالـ C موجودة في الـ set of real numbers والـ
+
+415
+00:48:39,960 --> 00:48:45,660
+A موجودة في الـ M الأولى
+
+416
+00:49:00,430 --> 00:49:06,350
+طبقا للتعريف T لما تأثر على الوضع تسوى مين؟
+
+417
+00:49:06,350 --> 00:49:15,650
+لترانسبوز هذا الوضع يبقى هذا C A كله ترانسبوزسي
+
+418
+00:49:15,650 --> 00:49:21,090
+كونستانت رقم ماخو جود فيه R يبقى ال C هذا بقوله
+
+419
+00:49:21,090 --> 00:49:25,930
+خليك برا من خواص اللي أخدناها ل Transpose يبقى هذا
+
+420
+00:49:25,930 --> 00:49:31,930
+C في A Transpose من خواص ل Transpose خليكم معايا
+
+421
+00:49:31,930 --> 00:49:37,530
+سيبقوا من الفشريبقى هنا هذا C في A transpose يبقى
+
+422
+00:49:37,530 --> 00:49:41,550
+هذا الكلام بده يساوي C ال A transpose هي عبارة عن
+
+423
+00:49:41,550 --> 00:49:50,130
+ماذا؟ T of A يبقى C في T of A يبقى اثبات ان T في C
+
+424
+00:49:50,130 --> 00:49:54,070
+of A بده يساوي C في T of A يبقى خلصت من ال
+
+425
+00:49:54,070 --> 00:49:57,250
+condition الأول ولا لا؟بدا اذهب للـcondition
+
+426
+00:49:57,250 --> 00:50:02,230
+التاني يبقى النقطة الثانية بدا اقول little mass of
+
+427
+00:50:02,230 --> 00:50:11,710
+two a و b موجودة في مين؟ في ال M M في N ثم بدي اخد
+
+428
+00:50:11,710 --> 00:50:17,570
+ال T of ال A زي ال B اذا كنت اثبت ان هذا الكلام
+
+429
+00:50:17,570 --> 00:50:21,790
+يسوى T of A بصراحة انا كنت اتكلم على اسمها بسرعة
+
+430
+00:50:23,590 --> 00:50:28,950
+يبقى T في A زائد الـB بده يساوي حسب التعريف يبقى
+
+431
+00:50:28,950 --> 00:50:36,890
+هذا الكلام بده يساوي A زائد B كله Transpose طبعا؟
+
+432
+00:50:36,890 --> 00:50:42,410
+طيب، نرجع لخاص للـTranspose A زائد B Transpose
+
+433
+00:50:42,410 --> 00:50:47,110
+يساوي A Transpose زائد B Transpose يبقى هذا بده
+
+434
+00:50:47,110 --> 00:50:53,770
+يعطينا A Transpose زائد B Transposeالـ A Transpose
+
+435
+00:50:53,770 --> 00:51:00,330
+أليس T of A يبقى طبق للـ Definition T of A، B
+
+436
+00:51:00,330 --> 00:51:06,390
+Transpose طبق للـ Definition يبقى T of B، يبقى
+
+437
+00:51:06,390 --> 00:51:10,010
+تحقق الـ A عن ال condition التاني ولا لا، يبقى
+
+438
+00:51:10,010 --> 00:51:15,960
+معناه يتكلم ان الـ T ما لهالينير ترانسفورماشن يبقى
+
+439
+00:51:15,960 --> 00:51:25,440
+سا تي از اي لينير ترانسفورماشن
+
+440
+00:51:25,440 --> 00:51:32,960
+حد فيكم لايه تساول هنا؟ رب يا الله جهزولي خلصولي
+
+441
+00:51:32,960 --> 00:51:33,780
+الورقة يا الله
+
+442
+00:51:38,050 --> 00:51:41,950
+احنا عليكي بكون انتهينا ولسه لازلنا في بداية هذا
+
+443
+00:51:41,950 --> 00:51:46,210
+section اللي هو مليان زي ال dimension وال bases
+
+444
+00:51:46,210 --> 00:51:50,850
+وهو أساسي لن يخلو أي امتحان ينسوان عليه
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6583b6ba6ef141dd029fcb5d82897fa5b056fb26
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY.srt
@@ -0,0 +1,1218 @@
+1
+00:00:27,790 --> 00:00:33,170
+الشطر أشبه بالمراجعة لمدرس في الثانوية العامة
+
+2
+00:00:33,170 --> 00:00:38,450
+بنضيف عليه بعض الإضافات الشطر هو عبارة عن
+
+3
+00:00:38,450 --> 00:00:43,710
+matrices and determinants المصفوفات والمحددات
+
+4
+00:00:43,710 --> 00:00:47,150
+matrices يا بنات هذه هي جمع matrix
+
+5
+00:00:50,130 --> 00:00:55,770
+يبقى مفردها matrix جمعها matrices بنجي لأول section
+
+6
+00:00:55,770 --> 00:00:58,790
+في هذا الـ chapter هو systems of linear equations
+
+7
+00:00:58,790 --> 00:01:05,550
+أنظمة المعادلات الخطية معادلات عادية، مش تفاضلية
+
+8
+00:01:05,550 --> 00:01:10,880
+يبقى أنظمة المعادلات الخطية هي نقطة مجموعة من الـ
+
+9
+00:01:10,880 --> 00:01:15,680
+definitions أول تعريف من هذه الـ definitions هو a
+
+10
+00:01:15,680 --> 00:01:19,420
+non homogeneous system هذا اختصار non homogeneous
+
+11
+00:01:19,420 --> 00:01:23,900
+system of linear equations من المعادلات الخطية، of
+
+12
+00:01:23,900 --> 00:01:30,480
+M equations في M من المعادلات و N من المجاهيل is a
+
+13
+00:01:30,480 --> 00:01:33,940
+system in the form يبقى أنا عندي مجموعة من
+
+14
+00:01:33,940 --> 00:01:41,190
+المعادلات عددها M وعدد المجاهيل فيها N ممكن يتساوى
+
+15
+00:01:41,190 --> 00:01:49,150
+وممكن لا يتساوى، ال system بيقول a11x1 زائد a12x2
+
+16
+00:01:49,150 --> 00:01:55,170
+زائد a13x3 زائد ... لغاية ما نوصل لـ a1nxn=b1
+
+17
+00:01:56,300 --> 00:02:09,480
+الثانية a21x1 a22x2 a23x3 ... a2nb2 a31x1
+
+18
+00:02:09,480 --> 00:02:18,540
+a32x2 a33x3 a23x2 a33x3 a31x1 a32x2 a33x3 a31x1
+
+19
+00:02:18,540 --> 00:02:20,320
+a32x2 a33x3 a31x1 a32x2 a33x3 a31x1 a32x2 a33x3
+
+20
+00:02:20,320 --> 00:02:21,660
+a31x1 a32x2 a32x2 a33x3 a31x1 a32x2 a32x2 a32x2
+
+21
+00:02:21,660 --> 00:02:22,240
+a32x2 a32x2 a32x2 a32x2 a32x2 a32x2 a32x2 a32x2
+
+22
+00:02:22,240 --> 00:02:22,260
+a32x2 a32x2 a32x2 a32x2 a32x2 a32x2 a32x2 a32x2
+
+23
+00:02:22,260 --> 00:02:27,490
+a32x2 a32x...ويمكن خمس أو يمكن ست أو يمكن عشر أو يمكن
+
+24
+00:02:27,490 --> 00:02:32,250
+عشرين، جد ما يكونوا يكونوا يبقى لما حطيت فراغ حطي
+
+25
+00:02:32,250 --> 00:02:37,810
+جد ما بدك معادلات على هذا الشكل بيقول لي حيث M في
+
+26
+00:02:37,810 --> 00:02:43,410
+N numbers a<sub>ij</sub> هدول يا بنات M في N يعني مضروبات في
+
+27
+00:02:43,410 --> 00:02:48,450
+بعض، ضرب اللي هو main a<sub>ij</sub> تطلع هدول كم واحدة واحدة
+
+28
+00:02:48,450 --> 00:02:55,310
+اثنتين ثلاثة أربعة خمسة N هنا واحدة اثنتين ثلاثة أربعة
+
+29
+00:02:55,310 --> 00:03:01,290
+M إذا لو ضربت M في N بيجيب لي كل الـ a هات هدول كل
+
+30
+00:03:01,290 --> 00:03:07,330
+الـ a<sub>11</sub> و الـ a<sub>12</sub> و الـ ... ثلاثة آخرين يبقى هدول عددهم M
+
+31
+00:03:07,330 --> 00:03:15,370
+في N وهو a<sub>ij</sub> والـ i تتغير من 1 إلى M 1 2 3 4 ... M
+
+32
+00:03:15,370 --> 00:03:21,710
+اللي هو الرمز الأول، الرمز الثاني j يتغير من 1
+
+33
+00:03:21,710 --> 00:03:32,520
+لغاية N 1 2 3 4 ... لغاية N، المعاملات هم
+
+34
+00:03:32,520 --> 00:03:45,200
+ثوابت هذا النظام، x<sub>1</sub>
+
+35
+00:03:45,200 --> 00:03:50,180
+و x<sub>2</sub> و x<sub>3</sub> و x<sub>n</sub> هم المجاهيل
+
+36
+00:03:51,980 --> 00:03:56,220
+طب والباقي؟ b<sub>1</sub> و b<sub>2</sub> و b<sub>m</sub> بسميهم
+
+37
+00:03:56,220 --> 00:04:00,820
+الثوابت يبقى أنا في عندي المعاملات وفي عندي
+
+38
+00:04:00,820 --> 00:04:06,580
+المجاهيل وفي عندي من الثوابت، هذول القيم كلهم
+
+39
+00:04:06,580 --> 00:04:11,600
+بسميهم الثوابت، الـ x's اللي عندنا هدول كلهم بسميهم
+
+40
+00:04:11,600 --> 00:04:17,680
+المجاهيل unknowns، هاي هجيلك عليها الـ unknowns اللي
+
+41
+00:04:17,680 --> 00:04:22,500
+هو الـ x<sub>i</sub> و i من 1 إلى N، ضالوا البيهات اللي عندنا
+
+42
+00:04:22,500 --> 00:04:27,220
+ليه بسميهم مين؟ المعاملات لهذا ال system يبقى عندي
+
+43
+00:04:27,220 --> 00:04:33,620
+معاملات، عندي مجاهيل، عندي ثوابت لل system *، طيب
+
+44
+00:04:33,620 --> 00:04:38,260
+نأخذ بعض أنواع من هذا ال system، بعض أنواع من هذا
+
+45
+00:04:38,260 --> 00:04:43,220
+ال system ممكن يكون عندي معادلتين في مجهولين
+
+46
+00:04:43,220 --> 00:04:49,360
+المجهول x<sub>1</sub> و x<sub>2</sub> وماعنديش إلا معادلتين، ممكن يكون
+
+47
+00:04:49,360 --> 00:04:54,880
+عندي ثلاث معادلات ومجهولين بس، ممكن أربع معادلات
+
+48
+00:04:54,880 --> 00:05:00,420
+ومجهولين قد ما بدك ماعنديش مشكلة، النقطة الثانية الـ
+
+49
+00:05:00,420 --> 00:05:04,480
+linear system of the three unknowns يبقى هذا عندي
+
+50
+00:05:04,480 --> 00:05:08,800
+مجهولين، هذا ال system فيه ثلاثة مجاهيل يمكن أن
+
+51
+00:05:08,800 --> 00:05:15,920
+يكون ثلاث معادلات في ثلاثة مجاهيل، ممكن يكون M من
+
+52
+00:05:15,920 --> 00:05:22,920
+المعادلات في ثلاثة مجاهيل فقط وهكذا، يعني هذه بعض
+
+53
+00:05:22,920 --> 00:05:28,500
+أنواع من ال system *، ممكن يكون أربع معادلات في
+
+54
+00:05:28,500 --> 00:05:32,940
+أربع مجاهيل، ممكن يكون أربع معادلات في عشر مجاهيل و
+
+55
+00:05:32,940 --> 00:05:37,200
+وإلى آخره، يعني هذه بس أمثلة عملية على ال system
+
+56
+00:05:37,200 --> 00:05:42,780
+هذا كيف ممكن يكون شكله في حالات مختلفة، طيب الـ
+
+57
+00:05:42,780 --> 00:05:47,400
+system هذا ممكن نسميه homogeneous وممكن نسميه non
+
+58
+00:05:47,400 --> 00:05:53,080
+homogeneous، non homogeneous، إذا هدول ماكانوش أصفار
+
+59
+00:05:53,080 --> 00:05:58,860
+طيب افترضي هدول عشرة، تسعة منهم أصفار وواحدة لأ
+
+60
+00:05:58,860 --> 00:06:02,200
+أسميه homogeneous ولا non homogeneous؟ non
+
+61
+00:06:02,200 --> 00:06:07,260
+homogeneous، لكن لو كانوا كلهم أصفار بسميه
+
+62
+00:06:07,260 --> 00:06:12,020
+homogeneous system، يبقى system متجانس يبقى أنا
+
+63
+00:06:12,020 --> 00:06:19,320
+عندي two systems أحدهما متجانس والآخر غير متجانس
+
+64
+00:06:19,320 --> 00:06:24,120
+يبقى non homogeneous system هذا homogeneous if the
+
+65
+00:06:24,120 --> 00:06:28,400
+above constants دول are all zero the above systems
+
+66
+00:06:28,400 --> 00:06:34,270
+are called homogeneous إذا كان كل البيهات هذول اللي
+
+67
+00:06:34,270 --> 00:06:39,750
+عندنا أصفار، لكن لو كان واحدة بس على الأقل منهم
+
+68
+00:06:39,750 --> 00:06:44,670
+ليس صفر والباقي كله أصفار يبقى هذا non-homogeneous
+
+69
+00:06:44,670 --> 00:06:49,810
+النقطة الرابعة، ال system إذا كان ال system is not
+
+70
+00:06:49,810 --> 00:06:54,550
+of the form، أستعار يعني ليس على هذا الشكل كافي
+
+71
+00:06:54,550 --> 00:06:58,190
+يعني ليس على هذا الشكل يعني مش هلاقي x واحد دي
+
+72
+00:06:58,190 --> 00:07:03,420
+ممكن هلاقي x واحد تربيع، يمكن أن ألاقي x ثلاثة تكعيب
+
+73
+00:07:03,420 --> 00:07:10,160
+مثلاً ممكن ألاقي x اثنين في x ثلاثة، ممكن ألاقي sin
+
+74
+00:07:10,160 --> 00:07:14,900
+x أربعة مثلاً، من حد ما ألاقي شغلات من هذا القبيل
+
+75
+00:07:14,900 --> 00:07:21,080
+يبقى هذا ليس linear system تمام؟ بعدين بقول if the
+
+76
+00:07:21,080 --> 00:07:25,160
+system is not in the above form، أسطر إنه ماكانش
+
+77
+00:07:25,160 --> 00:07:29,920
+على الشكل هذه يعني الإكسات هذه تغير وضعها then it
+
+78
+00:07:29,920 --> 00:07:36,090
+is nonlinear يمكن بسميه system غير خطي، فمثلاً لو
+
+79
+00:07:36,090 --> 00:07:40,890
+قلت x<sub>1</sub> تربيع زائد خمسة x<sub>2</sub> يساوي ثلاثة، 2x<sub>1</sub>
+
+80
+00:07:40,890 --> 00:07:44,990
+زائد 2x<sub>2</sub> يساوي اثنين، طلع لي في المعادلة
+
+81
+00:07:44,990 --> 00:07:49,390
+x<sub>1</sub> تربيع، لكن ال system هنا ماعنديش x<sub>1</sub>
+
+82
+00:07:49,390 --> 00:07:55,050
+تربيع بالمرة نهائي ولا في أي معادلة، إذا حتى لو كانت
+
+83
+00:07:55,050 --> 00:07:59,410
+الثانية linear يبقى ال system على بعضه nonlinear
+
+84
+00:07:59,410 --> 00:08:04,470
+يعني لو جيت معادلة واحدة شذت عن حكاية ال linear
+
+85
+00:08:04,470 --> 00:08:08,750
+هدول يبقى ال system على بعضه كله بقول nonlinear
+
+86
+00:08:08,750 --> 00:08:13,500
+system تمام؟ هذا ليس خطي بس بسبب x<sub>1</sub> تربيع، لأ كمان
+
+87
+00:08:13,500 --> 00:08:19,380
+عندي لين x<sub>2</sub> يبقى هذا ليس linear system، لو جيت هنا
+
+88
+00:08:19,380 --> 00:08:24,780
+x<sub>1</sub> في x<sub>2</sub> اللي جت مضروبات في بعض ضرب وليس بتربيع
+
+89
+00:08:24,780 --> 00:08:29,280
+يبقى كمان هذا non linear system، لو اللي جت e<sup>x<sub>1</sub></sup>
+
+90
+00:08:29,280 --> 00:08:34,640
+exponential ليست linear يبقى هذه كمان non
+
+91
+00:08:34,640 --> 00:08:38,690
+linear، cos x<sub>2</sub> وهكذا، طلع المعادلة الثالثة Linear
+
+92
+00:08:38,690 --> 00:08:43,430
+عادي جداً، x<sub>1</sub> - x<sub>2</sub> يساوي صفر، عادي جداً المعادلة هذه
+
+93
+00:08:43,430 --> 00:08:47,590
+Linear لكن الاثنتين هذول Non-Linear يبقى ال system
+
+94
+00:08:47,590 --> 00:08:54,370
+على بعض بيقول عنه ماله Non-Linear System، حد بتسأل
+
+95
+00:08:54,370 --> 00:08:57,950
+أي سؤال في هذه التعريفات؟
+
+96
+00:08:59,320 --> 00:09:04,340
+أصل هذه الساعة أو هذه المحاضرة أقرب إلى النظر منها
+
+97
+00:09:04,340 --> 00:09:11,800
+إلى الشغل العملي، نأخذ
+
+98
+00:09:11,800 --> 00:09:16,620
+الآن تعريف آخر، ال system اللي توه * يا بنات لو
+
+99
+00:09:16,620 --> 00:09:23,500
+حطيت البيهات في مصفوفة بسميها مصوفة المعاملات، أضفت
+
+100
+00:09:23,500 --> 00:09:28,460
+عليها عمود ثوابت بسميها المصوفة الموسعة، زي الثانوية
+
+101
+00:09:28,460 --> 00:09:32,500
+بالضبط تماماً، فبعدين بحطيها الـ definition التالي
+
+102
+00:09:32,500 --> 00:09:36,260
+definition for
+
+103
+00:09:36,260 --> 00:09:42,740
+the above system * for the above system
+
+104
+00:09:45,000 --> 00:09:54,860
+استعار اللي كان قبل قليل، الـ matrix المصفوفة اللي
+
+105
+00:09:54,860 --> 00:10:11,700
+هي من a<sub>11</sub>, a<sub>12</sub>, a<sub>13</sub>, a<sub>1n</sub>, a<sub>21</sub>, a<sub>22</sub>, a<sub>23</sub>, a<sub>2n</sub>، نفض
+
+106
+00:10:11,700 --> 00:10:24,380
+الماشيل لغاية a<sub>m1</sub>a<sub>m1</sub> a<sub>m2</sub> a<sub>m3</sub> a<sub>mn</sub>، يبقى هذه بسميها
+
+107
+00:10:24,380 --> 00:10:34,500
+مصوفة المعاملات، يبقى هذه is called the coefficient
+
+108
+00:10:34,500 --> 00:10:39,540
+matrix، the
+
+109
+00:10:39,540 --> 00:10:41,980
+coefficient
+
+110
+00:10:45,550 --> 00:10:57,730
+a coefficients matrix يبقى مصوفة المعاملات، and الـ
+
+111
+00:10:57,730 --> 00:11:03,770
+matrix والمصفوفة
+
+112
+00:11:03,770 --> 00:11:12,750
+اللي هي من a<sub>11</sub> a<sub>12</sub> a<sub>1n</sub>
+
+113
+00:11:12,750 --> 00:11:25,270
+a<sub>1n</sub>أو جيت ماشي a<sub>21</sub> a<sub>22</sub> a<sub>2n</sub> أو ضليت ماشي لغاية
+
+114
+00:11:25,270 --> 00:11:34,550
+a<sub>m1</sub> a<sub>m2</sub> a<sub>mn</sub> ورحت أضفت لها عمود زيادة اللي هو
+
+115
+00:11:34,550 --> 00:11:42,110
+عمود ثوابت b<sub>1</sub> و b<sub>2</sub> وضلت ماشية لغاية b<sub>m</sub>
+
+116
+00:11:42,110 --> 00:11:50,910
+هذه بسميها المصوفة الموسعة is called the
+
+117
+00:11:50,910 --> 00:11:52,290
+augmented matrix
+
+118
+00:12:01,730 --> 00:12:09,890
+بعدها بسميها المصفوفة الموسعة، definition آخر، the
+
+119
+00:12:09,890 --> 00:12:15,650
+solution of
+
+120
+00:12:15,650 --> 00:12:21,370
+the system * is an n-tuple
+
+121
+00:12:21,370 --> 00:12:29,390
+n-tuple of numbers من الأعداد x<sub>1</sub> و x<sub>2</sub> و لغاية x<sub>n</sub>
+
+122
+00:12:30,850 --> 00:12:45,390
+and satisfies the
+
+123
+00:12:45,390 --> 00:12:54,670
+and satisfies the
+
+124
+00:12:54,670 --> 00:12:55,350
+system
+
+125
+00:13:05,180 --> 00:13:14,640
+remark for the solution of
+
+126
+00:13:14,640 --> 00:13:25,620
+the above system * there are three
+
+127
+00:13:25,620 --> 00:13:29,720
+possibilities، there are
+
+128
+00:13:33,240 --> 00:13:40,800
+three possibilities يوجد
+
+129
+00:13:40,800 --> 00:13:51,120
+ثلاثة احتمالات، نمر واحد ال system has
+
+130
+00:13:51,120 --> 00:13:56,580
+no solution، الـ
+
+131
+00:13:56,580 --> 00:14:01,180
+system ممكن مايكونش له حل يعني
+
+132
+00:14:01,790 --> 00:14:06,690
+No intersection
+
+133
+00:14:06,690 --> 00:14:11,290
+of
+
+134
+00:14:11,290 --> 00:14:22,490
+lines or planes، نمر
+
+135
+00:14:22,490 --> 00:14:30,010
+اثنين The system has one solution
+
+136
+00:14:32,590 --> 00:14:38,510
+الواحد فقط يبقى
+
+137
+00:14:38,510 --> 00:14:49,850
+all linear lines
+
+138
+00:14:49,850 --> 00:14:54,590
+intersect
+
+139
+00:14:54,590 --> 00:14:59,330
+in
+
+140
+00:14:59,330 --> 00:15:10,470
+one point في نقطة واحدة، الاحتمال الثالث والاخير الـ
+
+141
+00:15:10,470 --> 00:15:17,730
+system has infinite number
+
+142
+00:15:17,730 --> 00:15:22,090
+of
+
+143
+00:15:22,090 --> 00:15:27,750
+solutions، infinite
+
+144
+00:15:27,750 --> 00:15:31,090
+number of solutions يعني
+
+145
+00:15:34,630 --> 00:15:38,170
+lines، lines go inside
+
+146
+00:16:10,480 --> 00:16:20,560
+coincide or all the planes جميع المستويات
+
+147
+00:16:20,560 --> 00:16:25,920
+intersect in
+
+148
+00:16:25,920 --> 00:16:35,900
+a line تتقطع في خط مستقيم واحد or coincide
+
+149
+00:16:42,960 --> 00:16:50,240
+كوانصيف نوت for
+
+150
+00:16:50,240 --> 00:17:00,980
+the system * for the system *
+
+151
+00:17:00,980 --> 00:17:13,790
+there is no two solutions there is no two solutions
+
+152
+00:17:13,790 --> 00:17:19,610
+or three
+
+153
+00:17:19,610 --> 00:17:22,730
+solutions
+
+154
+00:17:22,730 --> 00:17:26,870
+or
+
+155
+00:17:26,870 --> 00:17:32,330
+but
+
+156
+00:17:32,330 --> 00:17:35,670
+one
+
+157
+00:17:36,760 --> 00:17:46,840
+solution or infinite number
+
+158
+00:17:46,840 --> 00:17:57,120
+of solutions division
+
+159
+00:17:57,120 --> 00:18:04,900
+the above system *
+
+160
+00:18:06,800 --> 00:18:16,540
+is called consistent if
+
+161
+00:18:16,540 --> 00:18:22,780
+it
+
+162
+00:18:22,780 --> 00:18:26,860
+has consistent
+
+163
+00:18:26,860 --> 00:18:31,480
+if
+
+164
+00:18:31,480 --> 00:18:32,240
+it has
+
+165
+00:18:36,720 --> 00:18:42,720
+one solution or
+
+166
+00:18:42,720 --> 00:18:54,160
+infinite number of solutions
+
+167
+00:18:54,160 --> 00:18:58,200
+نمرأ
+
+168
+00:18:58,200 --> 00:19:03,000
+نان دوا first semester
+
+169
+00:19:10,010 --> 00:19:18,470
+الشركة السابقة * اسمها ان
+
+170
+00:19:18,470 --> 00:19:35,210
+consistent inconsistent إذا كان لديه، إذا
+
+171
+00:19:35,210 --> 00:19:38,630
+كان لديه لا حلول
+
+172
+00:19:41,490 --> 00:19:53,310
+ثلاثة a set of all solutions a
+
+173
+00:19:53,310 --> 00:20:04,510
+set of all solutions of the system * is
+
+174
+00:20:04,510 --> 00:20:06,450
+called
+
+175
+00:20:07,880 --> 00:20:15,000
+the general أو
+
+176
+00:20:15,000 --> 00:20:23,380
+complete solution
+
+177
+00:20:23,380 --> 00:20:27,840
+of
+
+178
+00:20:27,840 --> 00:20:34,700
+the system، تعريف
+
+179
+00:20:34,700 --> 00:20:35,320
+الرابع
+
+180
+00:20:38,220 --> 00:20:44,800
+two system أو
+
+181
+00:20:44,800 --> 00:20:56,460
+equations هم قادرين يكونوا equivalent
+
+182
+00:20:56,460 --> 00:21:01,960
+هم
+
+183
+00:21:01,960 --> 00:21:04,740
+قادرين يكونوا equivalent إذا كانوا
+
+184
+00:21:10,620 --> 00:21:17,480
+if they have exactly exactly
+
+185
+00:21:17,480 --> 00:21:23,060
+the same solutions
+
+186
+00:
+
+201
+00:22:37,020 --> 00:22:40,860
+مرتم X واحد هي القيمة الأولى و X اثنين هي من
+
+202
+00:22:40,860 --> 00:22:44,820
+القيمة الثانية و بقول هذا الحل طب لكن لو صارت ثلاث
+
+203
+00:22:44,820 --> 00:22:51,370
+مجهولات بقول عليها three tuple يعني كأنه ثلاث مركبات
+
+204
+00:22:51,370 --> 00:22:54,350
+موجودة يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1
+
+205
+00:22:54,350 --> 00:22:54,690
+و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى
+
+206
+00:22:54,690 --> 00:22:55,830
+X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3
+
+207
+00:22:55,830 --> 00:22:59,630
+يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و
+
+208
+00:22:59,630 --> 00:23:03,910
+X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و
+
+209
+00:23:03,910 --> 00:23:05,490
+X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى
+
+210
+00:23:05,490 --> 00:23:09,200
+X1 و X2 التي طلعت عندي Unsatisfy the system وهذه
+
+211
+00:23:09,200 --> 00:23:14,260
+القيم تحقق الـ system يبقى حل هذا الـ system هو
+
+212
+00:23:14,260 --> 00:23:20,920
+عبارة عن قيم X1 و X2 و X3 بحطها على شكل قوس و
+
+213
+00:23:20,920 --> 00:23:25,460
+فواصل بين هذه القيم X1 هي القيمة الأولى X2 هي القيمة
+
+214
+00:23:25,460 --> 00:23:32,030
+الثانية X3 هي القيمة الثالثة Xn هي القيم الرقمية وهذه
+
+215
+00:23:32,030 --> 00:23:37,330
+يجب أن تحقق هذا الـ system طيب السؤال هو هل الـ
+
+216
+00:23:37,330 --> 00:23:43,010
+system هذا دائماً و أبداً له حل؟ الإجابة قد يكون و
+
+217
+00:23:43,010 --> 00:23:47,590
+قد لا يكون طب إن كان هناك حل لهذا الـ system حل
+
+218
+00:23:47,590 --> 00:23:51,330
+واحد أو اثنين أو ثلاثة أو أربعة أو ما لا
+
+219
+00:23:51,330 --> 00:23:57,330
+نهاية من الحلول هذا ما سنجيب عليه يبقى أي system من
+
+220
+00:23:57,330 --> 00:24:02,970
+المعادلات الخطية له أحد ثلاثة احتمالات الاحتمال
+
+221
+00:24:02,970 --> 00:24:08,310
+الأول أن لا يكون هناك حل لا حل يحقق المعادلات مع
+
+222
+00:24:08,310 --> 00:24:13,990
+بعضها الـ system has no solution no solution يعني
+
+223
+00:24:13,990 --> 00:24:19,390
+المعادلات إذا كانت خطوط مستقيمات لا يمكن للخطوط
+
+224
+00:24:19,390 --> 00:24:24,250
+المستقيمات كلها أن تتقاطع في نقطة واحدة وإن كانت
+
+225
+00:24:24,250 --> 00:24:29,360
+مستويات برضه المستويات هذه لا تتقاطع زي المستوى هذا
+
+226
+00:24:29,360 --> 00:24:34,220
+والمستوى هذا مافيش تقاطع تمام؟ ممكن يكونوا مستقيمات
+
+227
+00:24:34,220 --> 00:24:39,200
+و كل اثنين يتقاطعوا مع بعض لكن ما يتقاطعوش كلهم في
+
+228
+00:24:39,200 --> 00:24:42,280
+نفس النقطة هذا و هذا يتقاطعوا في نقطة هذا و هذا في
+
+229
+00:24:42,280 --> 00:24:45,420
+نقطة هذا و هذا في نقطة ثانية و اللي بعد إيه؟ يبقى
+
+230
+00:24:45,420 --> 00:24:49,140
+هذا الذي لا يوجد حل في هذه الحالة يبقى في هذه
+
+231
+00:24:49,140 --> 00:24:52,720
+الحالة يبقى there is no solution كيف هذا مثلاً
+
+232
+00:24:52,720 --> 00:24:57,420
+نعرفه بعد قليل من خلال الأمثلة طيب الأمر الثاني
+
+233
+00:24:57,420 --> 00:25:03,380
+ممكن يكون عندي حل وحيد فقط وهذا يحصل إذا كانت
+
+234
+00:25:03,380 --> 00:25:07,700
+المعادلات هذه معادلات مستقيمات إذا أنت تقاطع في
+
+235
+00:25:07,700 --> 00:25:13,580
+نقطة واحدة فقط لغيرها لأن المستويات إذا تقاطعت في
+
+236
+00:25:13,580 --> 00:25:17,020
+نقطة .. في .. إذا تقاطعت هذه المستقيمات فإن
+
+237
+00:25:17,020 --> 00:25:23,200
+تقاطعها يكون في خط مستقيم زي مستوى السقف ومستوى
+
+238
+00:25:23,200 --> 00:25:27,820
+الحائط اللي عندنا التقاطع في خط مستقيم والخط
+
+239
+00:25:27,820 --> 00:25:32,380
+المستقيم عبارة عن مهلة نهاية من النقاط وليست نقطة
+
+240
+00:25:32,380 --> 00:25:38,070
+واحدة يبقى هنا ليس عندي إلا حل واحد يبقى الـ Linear
+
+241
+00:25:38,070 --> 00:25:42,770
+Loss تتقاطع في نقطة واحدة وبالتالي لا يظهر إلا حل
+
+242
+00:25:42,770 --> 00:25:47,870
+واحد لهذا الـ system أو لمجموعة هذه المعادلات
+
+243
+00:25:47,870 --> 00:25:51,690
+الاحتمال الثالث يكون عندي infinite number of solutions
+
+244
+00:25:51,690 --> 00:25:57,790
+يبقى عندي عدد لا نهائي من الحلول في هذه الحالة
+
+245
+00:25:57,790 --> 00:26:03,030
+المستويات كلها ممكن أنت تقاطع في نقطة واحدة زي ما
+
+246
+00:26:03,030 --> 00:26:07,410
+أقول هذا المجلد اللي بينك كلها مستويات و تقاطعت في
+
+247
+00:26:07,410 --> 00:26:11,160
+الظهر زي الدفتر اللي عندك كلها تقاطعت في الحرف
+
+248
+00:26:11,160 --> 00:26:15,240
+الجانبي يبقى الحرف الجانبي هو خط التقاطع كم نقطة
+
+249
+00:26:15,240 --> 00:26:19,740
+فيه يبقى مالها نهاية من النقاط ممكن مستويات تنطبق
+
+250
+00:26:19,740 --> 00:26:23,600
+زي ما تلاقي في الدفتر و كل ورقة بذاصير كانت مستوية
+
+251
+00:26:23,600 --> 00:26:27,500
+يبقى كلهم انطبقوا على بعض تمام الانطباق يبقى كلهم
+
+252
+00:26:27,500 --> 00:26:31,900
+اشتركوا في نفس النقاط يبقى في هذه الحالة كم حل
+
+253
+00:26:31,900 --> 00:26:36,720
+عندي، عندي مالها نهاية من الحلول فبنقول في هذه
+
+254
+00:26:36,720 --> 00:26:42,060
+الحالة the lines coincide الخطوط هذه تنطبق أو الـ
+
+255
+00:26:42,060 --> 00:26:46,580
+planes تتقاطع في خط أو تنطبق مع بعضها في هذه
+
+256
+00:26:46,580 --> 00:26:52,090
+الحالة يبقى أي system يبقى نتكلم أحد ثلاثة احتمالات
+
+257
+00:26:52,090 --> 00:26:57,790
+يا إما مافيش حل يا إما حل واحد unique solution
+
+258
+00:26:57,790 --> 00:27:03,010
+مافيش غيره exactly one solution بالضبط يا إما عدد
+
+259
+00:27:03,010 --> 00:27:08,980
+لا نهائي من الحلول وبالتالي مافيش system له حلين أو
+
+260
+00:27:08,980 --> 00:27:12,620
+الـ system له ثلاث حلول أو الـ system له أربعة
+
+261
+00:27:12,620 --> 00:27:16,960
+حلول، لا يمكن أن يكون هناك نتيجتان أو لا يوجد نتيجة
+
+262
+00:27:16,960 --> 00:27:18,360
+أو هناك نتيجة أو هناك نتيجة أو هناك نتيجة أو هناك
+
+263
+00:27:18,360 --> 00:27:23,650
+نتيجة أو هناك نتيجة كتبنا لك هذه الملاحظة كتبنا لك
+
+264
+00:27:23,650 --> 00:27:26,650
+هذه الملاحظة في الملاحظة التالية في الملاحظة
+
+265
+00:27:26,650 --> 00:27:27,290
+التالية في الملاحظة التالية في الملاحظة
+
+266
+00:27:27,290 --> 00:27:28,010
+التالية في الملاحظة التالية في الملاحظة
+
+267
+00:27:28,010 --> 00:27:33,110
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+268
+00:27:33,110 --> 00:27:36,230
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+269
+00:27:36,230 --> 00:27:36,810
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+270
+00:27:36,810 --> 00:27:40,090
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+271
+00:27:40,090 --> 00:27:40,790
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+272
+00:27:40,790 --> 00:27:47,350
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+273
+00:27:47,350 --> 00:27:52,010
+التالية في المفي عندي الآن أربعة تعريفات ضروري أن
+
+274
+00:27:52,010 --> 00:27:57,350
+نكون ملمين بها و بتيجي أحياناً منها في الخيارات
+
+275
+00:27:57,350 --> 00:28:02,470
+المتعددة في الامتحانات يبقى صح صح كويس the above
+
+276
+00:28:02,470 --> 00:28:07,290
+system star is called consistent يعني consistent
+
+277
+00:28:07,290 --> 00:28:15,350
+متطابق تمام if it has أو متين يعني بالعربي if it
+
+278
+00:28:15,350 --> 00:28:19,390
+has one solution or infinite number of solutions
+
+279
+00:28:19,390 --> 00:28:24,990
+يعني الـ system الذي له حل وحيد أو عدد لا نهائي
+
+280
+00:28:24,990 --> 00:28:32,070
+من الحلول نسميه consistent طب وإذا ما لوش حلول ولا
+
+281
+00:28:32,070 --> 00:28:38,550
+حل نسميه inconsistent يعني نفيها تمام فبتجيب وقلت
+
+282
+00:28:38,550 --> 00:28:41,250
+لكني that the above system is called inconsistent
+
+283
+00:28:41,250 --> 00:28:46,150
+if it has no solution ما فيش ولا حل نسميه
+
+284
+00:28:46,150 --> 00:28:54,720
+inconsistent زي إيه إيش نقول العدد الرشيد number و
+
+285
+00:28:54,720 --> 00:29:00,600
+بقول irrational يعني ليس عدداً نسبياً rational نسبي
+
+286
+00:29:00,600 --> 00:29:05,240
+rational rational rational rational rational rational
+
+287
+00:29:05,240 --> 00:29:10,400
+rational rational rational
+
+288
+00:29:11,170 --> 00:29:17,030
+الأمر الثالث مجموعة الحلول هذه يابا نسميها الـ
+
+289
+00:29:17,030 --> 00:29:20,990
+general solution الحل العام لهذا الـ system يابا
+
+290
+00:29:20,990 --> 00:29:25,590
+نسميها الـ complete solution الحل الكامل لهذا
+
+291
+00:29:25,590 --> 00:29:29,810
+النظام يابا نسميها الـ general أو الـ complete
+
+292
+00:29:29,810 --> 00:29:37,410
+solution لهذا الـ system في كمان باقية عندنا ممكن
+
+293
+00:29:37,410 --> 00:29:42,630
+توصيف وهذا very important هنستخدمه في حل الـ system
+
+294
+00:29:42,630 --> 00:29:47,510
+إيش هو هذا بيقول لي two systems of equations
+
+295
+00:29:47,510 --> 00:29:55,110
+مجموعة من الـ system و System هذا فيه equations وهذا
+
+296
+00:29:55,110 --> 00:29:59,090
+فيه equations لكن يختلفوا عن بعض المعادلتين غير
+
+297
+00:29:59,090 --> 00:30:03,370
+المعادلتين لكن نفس المجاهيل ونفس المعادلتين
+
+298
+00:30:03,370 --> 00:30:07,950
+معادلتين ثلاثة ثلاثة عشرة عشرة وهكذا بيقول لي two
+
+299
+00:30:07,950 --> 00:30:12,630
+systems of equations are said to be equivalent بقول
+
+300
+00:30:12,630 --> 00:30:17,910
+هدول اثنين متكافئين if they have exactly the same
+
+301
+00:30:17,910 --> 00:30:22,590
+solutions إذا كان لهما نفس الحل يعني أنا عنده
+
+302
+00:30:22,590 --> 00:30:26,510
+system وعنده system إذا جئت على الـ system الأول
+
+303
+00:30:26,510 --> 00:30:30,510
+اللي جيت عليه طلعت الحل تبعه وجئت على الـ system
+
+304
+00:30:30,510 --> 00:30:34,690
+الثاني وطلعت الحل تبعه اللي جيت عليه اثنين زي بعض بقول
+
+305
+00:30:34,690 --> 00:30:40,310
+two systems are equivalent اثنين متكافئين إذا هذا
+
+306
+00:30:40,310 --> 00:30:43,670
+عنده عدد لا نهائي من الحلول وهذا عنده عدد لا نهائي
+
+307
+00:30:43,670 --> 00:30:44,030
+من الحلول وهذا عنده عدد لا نهائي من الحلول وهذا
+
+308
+00:30:44,030 --> 00:30:45,190
+عنده عدد لا نهائي من الحلول وهذا عنده عدد لا نهائي
+
+309
+00:30:45,190 --> 00:30:46,470
+من الحلول وهذا عنده عدد لا نهائي من الحلول وهذا
+
+310
+00:30:46,470 --> 00:30:47,050
+عنده عدد لا نهائي من الحلول وهذا عنده عدد لا نهائي
+
+311
+00:30:47,050 --> 00:30:49,090
+من الحلول وهذا عنده عدد لا نهائي من الحلول وهذا
+
+312
+00:30:49,090 --> 00:30:55,150
+عنده عدد لا نهائي من الحلول وهذا عنده عدد لا نهائي
+
+313
+00:30:55,150 --> 00:30:57,830
+من الحلول وهذا عنده عدد لا نهائي من الحلول وهذا
+
+314
+00:30:57,830 --> 00:31:03,150
+عنده عدد لا نهائي من الحلول وهذا عنده عدد الحلول
+
+315
+00:31:03,150 --> 00:31:06,330
+متساوية في الـ two systems بقول هدول are equivalent
+
+316
+00:31:06,330 --> 00:31:10,650
+ماشي شايف فرق شايف ما بين إيه؟ ما بين الاثنين
+
+317
+00:31:10,650 --> 00:31:14,530
+المعلومات التي أعطانا إياها هذه بدنا نبدأ نأخذ أمثلة
+
+318
+00:31:14,530 --> 00:31:22,970
+تطبيقية عليها مرة جاية؟ قصد إيه بعد الظهر؟ طيب
+
+319
+00:31:22,970 --> 00:31:25,150
+يبقى وصلنا إلى الأمثلة
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8583a3f5db5803131ae188f888e269afddd8fceb
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY_raw.srt
@@ -0,0 +1,1280 @@
+1
+00:00:27,790 --> 00:00:33,170
+الشبطر أشبه بالمراجعة لمدرس في الثانوية العامة
+
+2
+00:00:33,170 --> 00:00:38,450
+بنضيف عليه بعض الإضافات الشبطر هو عبارة عن
+
+3
+00:00:38,450 --> 00:00:43,710
+matrices and determinants المصفوفات والمحددات
+
+4
+00:00:43,710 --> 00:00:47,150
+matrices يا بنات هذه هي جامع matrix
+
+5
+00:00:50,130 --> 00:00:55,770
+يبقى مفردها matrix جمعها matrices بنجي أول section
+
+6
+00:00:55,770 --> 00:00:58,790
+في هذا ال chapter هو systems of linear equations
+
+7
+00:00:58,790 --> 00:01:05,550
+أنظمة المعادلات الخطية معادلات عادية مش تفاضلية
+
+8
+00:01:05,550 --> 00:01:10,880
+يبقى أنظمة المعادلات الخطيةهنقط مجموعة من الـ
+
+9
+00:01:10,880 --> 00:01:15,680
+definitions أول تعريف من هذه الـ definition هو a
+
+10
+00:01:15,680 --> 00:01:19,420
+non homogeneous system هذا اختصار non homogeneous
+
+11
+00:01:19,420 --> 00:01:23,900
+system of linear equations من المعادلات الخطية of
+
+12
+00:01:23,900 --> 00:01:30,480
+M equations في M من المعادلات و N من المجاهيل is a
+
+13
+00:01:30,480 --> 00:01:33,940
+system in the form يبقى أنا عندي مجموعة من
+
+14
+00:01:33,940 --> 00:01:41,190
+المعادلات عددها Mوعدد المجاهيل فيها N ممكن يتساوى
+
+15
+00:01:41,190 --> 00:01:49,150
+وممكن لا يتساوى ال system بيقول a11x1 زائد a12x2
+
+16
+00:01:49,150 --> 00:01:55,170
+زائد a13x3 زائد زايد بغير ما نوصل ل a1nxnb1
+
+17
+00:01:56,300 --> 00:02:09,480
+التانية A21X1 A22X2 A23X3 A2N B2 A31X1
+
+18
+00:02:09,480 --> 00:02:18,540
+A32X2 A33X3 A23X2 A33X3 A31X1 A32X2 A33X3 A31X1
+
+19
+00:02:18,540 --> 00:02:20,320
+A32X2 A33X3 A31X1 A32X2 A33X3 A31X1 A32X2 A33X3
+
+20
+00:02:20,320 --> 00:02:21,660
+A31X1 A32X2 A32X2 A33X3 A31X1 A32X2 A32X2 A32X2
+
+21
+00:02:21,660 --> 00:02:22,240
+A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2
+
+22
+00:02:22,240 --> 00:02:22,260
+A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2
+
+23
+00:02:22,260 --> 00:02:22,260
+A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2
+
+24
+00:02:22,260 --> 00:02:27,490
+A32X2 A32Xويمكن خمس أو يمكن ست أو يمكن عشر أو يمكن
+
+25
+00:02:27,490 --> 00:02:32,250
+عشرين جد ما يكونوا يكونوا يبقى لما حطيت فراغ حطي
+
+26
+00:02:32,250 --> 00:02:37,810
+جد ما بدك معادلات على هذا الشكل بيقول لي حيث M في
+
+27
+00:02:37,810 --> 00:02:43,410
+N numbers AI هدول يا بنات M في N يعني مضربات في
+
+28
+00:02:43,410 --> 00:02:48,450
+بعض ضرباللي هو main AI اتطلع هدول كم واحدة واحدة
+
+29
+00:02:48,450 --> 00:02:55,310
+تنتين تلتة اربعة خمسة N هنا واحدة تنتين تلتة اربعة
+
+30
+00:02:55,310 --> 00:03:01,290
+M إذا لو ضربت M في N بيجيب لي كل ال A هات هدول كل
+
+31
+00:03:01,290 --> 00:03:07,330
+ال A11 و ال A12 و ال Aثلاث آخرينيبقى هدول عددهم M
+
+32
+00:03:07,330 --> 00:03:15,370
+في N وهو A I J والـ I تتغير من 1 إلى M 1 2 3 4 M
+
+33
+00:03:15,370 --> 00:03:21,710
+اللي هو الرمز الأول الرمز التاني J يتغير من 1
+
+34
+00:03:21,710 --> 00:03:32,520
+لغاية N 1 2 3 4 لغاية Mالمعاملات هم
+
+35
+00:03:32,520 --> 00:03:45,200
+ثوابت هذا النظام X1
+
+36
+00:03:45,200 --> 00:03:50,180
+و X2 و X3 و XN هم المجاهيل
+
+37
+00:03:51,980 --> 00:03:56,220
+طب والبهات بي واحد و بي اتنين و بي ام بسميهم
+
+38
+00:03:56,220 --> 00:04:00,820
+الثوابت يبقى انا في عند المعاملات و في عند
+
+39
+00:04:00,820 --> 00:04:06,580
+المجاهيل و في عند من الثوابت هذول القيم كلهم
+
+40
+00:04:06,580 --> 00:04:11,600
+بسميهم الثوابتالـ X's اللي عندنا هدول كلهم بسميهم
+
+41
+00:04:11,600 --> 00:04:17,680
+المجاهيل unknowns هاي هجيلك عليها ال unknowns اللي
+
+42
+00:04:17,680 --> 00:04:22,500
+هو ال X I و I من 1 إلى N ضالوا الإيهات اللي عندنا
+
+43
+00:04:22,500 --> 00:04:27,220
+ليه بسميهم مين المعاملات لهذا ال system يبقى عندي
+
+44
+00:04:27,220 --> 00:04:33,620
+معاملات عندي مجاهيل عندي ثوابت لل system starطيب
+
+45
+00:04:33,620 --> 00:04:38,260
+نأخد بعض أنواع من هذا ال system بعض أنواع من هذا
+
+46
+00:04:38,260 --> 00:04:43,220
+ال system ممكن يكون عندي معادلتين في مجهولين
+
+47
+00:04:43,220 --> 00:04:49,360
+المجهول x1 و x2 وماعنديش إلا معادلتين ممكن يكون
+
+48
+00:04:49,360 --> 00:04:54,880
+عندي تلت معادلات ومجهولين بس ممكن أربع معادلات
+
+49
+00:04:54,880 --> 00:05:00,420
+ومجهولين قد ما بدك ماعنديش مشكلةالنقطة الثانية الـ
+
+50
+00:05:00,420 --> 00:05:04,480
+linear system of the three unknowns يبقى هذا عندي
+
+51
+00:05:04,480 --> 00:05:08,800
+مجهولين هذا ال system فيه ثلاثة مجاهيل يمكن أن
+
+52
+00:05:08,800 --> 00:05:15,920
+يكون ثلاث معادلات في ثلاثة مجاهيلممكن يكون M من
+
+53
+00:05:15,920 --> 00:05:22,920
+المعادلات في ثلاثة مجاهيل فقط وهكذا يعني هذه بعض
+
+54
+00:05:22,920 --> 00:05:28,500
+أنواع من ال system start ممكن يكون أربع معادلات في
+
+55
+00:05:28,500 --> 00:05:32,940
+أربع مجاهيل ممكن يكون أربع معادلات في عشر مجاهيل و
+
+56
+00:05:32,940 --> 00:05:37,200
+و إلى آخرى يعني هذه بس أمثلة عملية على ال system
+
+57
+00:05:37,200 --> 00:05:42,780
+هذا كيف ممكن يكون شكله في حالات مختلفةطيب ال
+
+58
+00:05:42,780 --> 00:05:47,400
+system هذا ممكن نسميه homogeneous و ممكن نسميه non
+
+59
+00:05:47,400 --> 00:05:53,080
+homogeneous non homogeneous إذا هدول ماكانوش أسفار
+
+60
+00:05:53,080 --> 00:05:58,860
+طيب افترضي هدول عشرة تسعة منهم أسفار و واحدة لأ
+
+61
+00:05:58,860 --> 00:06:02,200
+أسميه homogeneous ولا non homogeneousnon
+
+62
+00:06:02,200 --> 00:06:07,260
+homogeneous لكن لو كانوا كلهم أصفر بسميه
+
+63
+00:06:07,260 --> 00:06:12,020
+homogeneous system يبقى system متجانس يبقى أنا
+
+64
+00:06:12,020 --> 00:06:19,320
+عندي two systems أحدهما متجانس والآخر غير متجانس
+
+65
+00:06:19,320 --> 00:06:24,120
+يبقى non homogeneous system هذا homogeneous if the
+
+66
+00:06:24,120 --> 00:06:28,400
+above constants دول are all zero the above systems
+
+67
+00:06:28,400 --> 00:06:34,270
+are called homogeneousإذا كان كل البيهات هذول اللي
+
+68
+00:06:34,270 --> 00:06:39,750
+عند مالها أصفر لكن لو كان واحدة بس على الأقل منهم
+
+69
+00:06:39,750 --> 00:06:44,670
+ليس صفر و الباقي كله أصفر يبقى هذا non-homogeneous
+
+70
+00:06:44,670 --> 00:06:49,810
+النقطة الرابعة ال system إذا كان ال system is not
+
+71
+00:06:49,810 --> 00:06:54,550
+of the form أستعارف يعني ليس على هذا الشكل كافي
+
+72
+00:06:54,550 --> 00:06:58,190
+يعني ليس على هذا الشكل يعني مش هلاجي x واحد دي
+
+73
+00:06:58,190 --> 00:07:03,420
+ممكن هلاجي x واحد تربيةيمكن أن ألاقي X تلاتة تكعيب
+
+74
+00:07:03,420 --> 00:07:10,160
+مثلا ممكن ألاقي X اتنين في X تلاتة ممكن ألاقي sign
+
+75
+00:07:10,160 --> 00:07:14,900
+X أربعة مثلا من حد ما ألاقي شغلات من هذا القبيل
+
+76
+00:07:14,900 --> 00:07:21,080
+يبقى هذا ليس linear system تمامفبعدين بقول if the
+
+77
+00:07:21,080 --> 00:07:25,160
+system is not in the above form أسطر إنه ماكانش
+
+78
+00:07:25,160 --> 00:07:29,920
+على الشكل هذه يعني الإكسات هذه تغير وضعها then it
+
+79
+00:07:29,920 --> 00:07:36,090
+is nonlinear يمكن بسميه system غير خاطي فمثلالو
+
+80
+00:07:36,090 --> 00:07:40,890
+قلت X1 تربية زياد خمسة X اتنين يساوي تلاتة اتنين X
+
+81
+00:07:40,890 --> 00:07:44,990
+واحد زيادين X اتنين يساوي اتنين طلعيلي في المعادلة
+
+82
+00:07:44,990 --> 00:07:49,390
+X واحد تربية لكن ال system هنا ماعنديش X واحد
+
+83
+00:07:49,390 --> 00:07:55,050
+تربية بالمرة نهائي ولا في اي معادلةإذا حتى لو كانت
+
+84
+00:07:55,050 --> 00:07:59,410
+التانية linear يبقى ال system على بعضه nonlinear
+
+85
+00:07:59,410 --> 00:08:04,470
+يعني لو لجيت معادلة واحدة شذت عن حكاية ال linear
+
+86
+00:08:04,470 --> 00:08:08,750
+هدول يبقى ال system على بعضه كله بقول nonlinear
+
+87
+00:08:08,750 --> 00:08:13,500
+system تمام؟هذا ليس شد بس بسبب X1 تربية لأ كمان
+
+88
+00:08:13,500 --> 00:08:19,380
+عندي لين X2 يبقى هذا ليس linear system لو جيت هنا
+
+89
+00:08:19,380 --> 00:08:24,780
+X1 في X2 اللي جت مضربات في بعض ضرب وليس بتربية
+
+90
+00:08:24,780 --> 00:08:29,280
+يبقى كمان هذا non linear system لو اللي جت E أوس
+
+91
+00:08:29,280 --> 00:08:34,640
+X1 exponential ليست linear يبقى هذه كمان non
+
+92
+00:08:34,640 --> 00:08:38,690
+linear cosine X2 و هكذاطلع المعادلة تالتة Linear
+
+93
+00:08:38,690 --> 00:08:43,430
+عادي جدا X1-X2 يساوي Zero عادي جدا المعادلة هذه
+
+94
+00:08:43,430 --> 00:08:47,590
+Linear لكن التنتين هذول Non-Linear يبقى ال system
+
+95
+00:08:47,590 --> 00:08:54,370
+على بعض بيقول عنه ماله Non-Linear System حد بتسأل
+
+96
+00:08:54,370 --> 00:08:57,950
+أي سؤال في هذه التعريفات؟
+
+97
+00:08:59,320 --> 00:09:04,340
+أصل هذه الساعة أو هذه المحاضرة أقرب إلى النظر منها
+
+98
+00:09:04,340 --> 00:09:11,800
+إلى الشغل العملي ناخد
+
+99
+00:09:11,800 --> 00:09:16,620
+الآن تعريف آخرالـ System اللي توستار يا بنات لو
+
+100
+00:09:16,620 --> 00:09:23,500
+حطيت الإيهات في مصوفة بسميها مصوفة المعاملات أضفت
+
+101
+00:09:23,500 --> 00:09:28,460
+عليها عمود ثواب بسميها المصوفة الموسعة زي الثانوية
+
+102
+00:09:28,460 --> 00:09:32,500
+بالضبط تماما فبعدين بحطيها ال definition التالي
+
+103
+00:09:32,500 --> 00:09:36,260
+definition for
+
+104
+00:09:36,260 --> 00:09:42,740
+the above system star for the above system
+
+105
+00:09:45,000 --> 00:09:54,860
+استعار اللي كان قبل قليل الـ matrix المصفوفة اللي
+
+106
+00:09:54,860 --> 00:10:11,700
+هي من a11, a12, a13, a1n, a21, a22, a23, a2n نفض
+
+107
+00:10:11,700 --> 00:10:24,380
+الماشيل لغاية am1am1 am2 am3 amn يبجى هذه بسميها
+
+108
+00:10:24,380 --> 00:10:34,500
+مصوفة المعاملات يبجى هذه is called the coefficient
+
+109
+00:10:34,500 --> 00:10:39,540
+matrix the
+
+110
+00:10:39,540 --> 00:10:41,980
+coefficient
+
+111
+00:10:45,550 --> 00:10:57,730
+a coefficients matrix يبقى مصوفة المعاملات and ال
+
+112
+00:10:57,730 --> 00:11:03,770
+matrix والمصوفة
+
+113
+00:11:03,770 --> 00:11:12,750
+اللي هي من a11 a12 a1n
+
+114
+00:11:12,750 --> 00:11:25,270
+a1nأو جيت ماشي اتون اتوتون اتون او ضليت ماشي لغاية
+
+115
+00:11:25,270 --> 00:11:34,550
+امون امتونامن و رحت اضفت لها عمود زيادة اللي هو
+
+116
+00:11:34,550 --> 00:11:42,110
+عمود ثوابت بي وان و بيتو وضلت ماشية لغاية بي ام
+
+117
+00:11:42,110 --> 00:11:50,910
+هذي بسميها المصوفة الموسعة is called the
+
+118
+00:11:50,910 --> 00:11:52,290
+augmented matrix
+
+119
+00:12:01,730 --> 00:12:09,890
+بعدها بسميها المصفوفة الموسعة definition آخر the
+
+120
+00:12:09,890 --> 00:12:15,650
+solution of
+
+121
+00:12:15,650 --> 00:12:21,370
+the system a
+
+122
+00:12:21,370 --> 00:12:29,390
+star is an entupel
+
+123
+00:12:30,850 --> 00:12:45,390
+نتيوفل of numbers من الأعداد X1 و X2 و لغاية XN
+
+124
+00:12:45,390 --> 00:12:54,670
+and satisfies the
+
+125
+00:12:54,670 --> 00:12:55,350
+system
+
+126
+00:13:05,180 --> 00:13:14,640
+remark for the solution of
+
+127
+00:13:14,640 --> 00:13:25,620
+the above system star there are three
+
+128
+00:13:25,620 --> 00:13:29,720
+possibilities there are
+
+129
+00:13:33,240 --> 00:13:40,800
+three possibilities يحد
+
+130
+00:13:40,800 --> 00:13:51,120
+ثلاثة احتمالات نمر واحد ال system has
+
+131
+00:13:51,120 --> 00:13:56,580
+no solution ال
+
+132
+00:13:56,580 --> 00:14:01,180
+system ممكن مايكونش له حل يعني
+
+133
+00:14:01,790 --> 00:14:06,690
+No intersection
+
+134
+00:14:06,690 --> 00:14:11,290
+of
+
+135
+00:14:11,290 --> 00:14:22,490
+lines or planes نمري
+
+136
+00:14:22,490 --> 00:14:30,010
+اتنين The system has one solution
+
+137
+00:14:32,590 --> 00:14:38,510
+الواحد فقط يبقى
+
+138
+00:14:38,510 --> 00:14:49,850
+all linear lines
+
+139
+00:14:49,850 --> 00:14:54,590
+intersect
+
+140
+00:14:54,590 --> 00:14:59,330
+in
+
+141
+00:14:59,330 --> 00:15:10,470
+one pointفي نقطة واحدة الاحتمال الثالث والاخير ال
+
+142
+00:15:10,470 --> 00:15:17,730
+system has infinite number
+
+143
+00:15:17,730 --> 00:15:22,090
+of
+
+144
+00:15:22,090 --> 00:15:27,750
+solutions infinite
+
+145
+00:15:27,750 --> 00:15:31,090
+number of solutions يعني
+
+146
+00:15:34,630 --> 00:15:38,170
+lines lines go inside
+
+147
+00:16:10,480 --> 00:16:20,560
+coincide or all the planes جميع المستويات
+
+148
+00:16:20,560 --> 00:16:25,920
+intersect in
+
+149
+00:16:25,920 --> 00:16:35,900
+a line تتقطع في خط مستقيم واحد or coincide
+
+150
+00:16:42,960 --> 00:16:50,240
+كوانصيف نوت for
+
+151
+00:16:50,240 --> 00:17:00,980
+the system star for the system star
+
+152
+00:17:00,980 --> 00:17:13,790
+there is no two solutions there isno two solutions
+
+153
+00:17:13,790 --> 00:17:19,610
+or three
+
+154
+00:17:19,610 --> 00:17:22,730
+solutions
+
+155
+00:17:22,730 --> 00:17:26,870
+or
+
+156
+00:17:26,870 --> 00:17:32,330
+but
+
+157
+00:17:32,330 --> 00:17:35,670
+one
+
+158
+00:17:36,760 --> 00:17:46,840
+solution or infinite number
+
+159
+00:17:46,840 --> 00:17:57,120
+of solutions division
+
+160
+00:17:57,120 --> 00:18:04,900
+the above system star
+
+161
+00:18:06,800 --> 00:18:16,540
+is called consistent if
+
+162
+00:18:16,540 --> 00:18:22,780
+it
+
+163
+00:18:22,780 --> 00:18:26,860
+has consistent
+
+164
+00:18:26,860 --> 00:18:31,480
+if
+
+165
+00:18:31,480 --> 00:18:32,240
+it has
+
+166
+00:18:36,720 --> 00:18:42,720
+one solution or
+
+167
+00:18:42,720 --> 00:18:54,160
+infinite number of solutions
+
+168
+00:18:54,160 --> 00:18:58,200
+نمرأ
+
+169
+00:18:58,200 --> 00:19:03,000
+نان دوا first semester
+
+170
+00:19:10,010 --> 00:19:18,470
+الشركة السابقة استارة اسمها ان
+
+171
+00:19:18,470 --> 00:19:35,210
+كون سيستانت ان كون سيستانت اذا كان لديه اذا
+
+172
+00:19:35,210 --> 00:19:38,630
+كان لديه لا حلول
+
+173
+00:19:41,490 --> 00:19:53,310
+تلاتة a set of all solutions a
+
+174
+00:19:53,310 --> 00:20:04,510
+set of all solutions of the system a star is
+
+175
+00:20:04,510 --> 00:20:06,450
+called
+
+176
+00:20:07,880 --> 00:20:15,000
+the general أو
+
+177
+00:20:15,000 --> 00:20:23,380
+complete solution
+
+178
+00:20:23,380 --> 00:20:27,840
+of
+
+179
+00:20:27,840 --> 00:20:34,700
+the system تعريف
+
+180
+00:20:34,700 --> 00:20:35,320
+الرابع
+
+181
+00:20:38,220 --> 00:20:44,800
+تو سيستام او
+
+182
+00:20:44,800 --> 00:20:56,460
+اكوايشن هم قادرين يكونوا اكوالينت
+
+183
+00:20:56,460 --> 00:21:01,960
+هم
+
+184
+00:21:01,960 --> 00:21:04,740
+قادرين يكونوا اكوالينت اذا كانوا
+
+185
+00:21:10,620 --> 00:21:17,480
+if they have exactly exactly
+
+186
+00:21:17,480 --> 00:21:23,060
+the same solutions
+
+187
+00:21:23,060 --> 00:21:26,980
+درجع لكلام اللي احنا كاتبينه هذا مرة تانية يا بنات
+
+188
+00:21:26,980 --> 00:21:31,740
+يبقى شوية تعريف وبها ننهي الجزء النظري وبعدين نبدأ
+
+189
+00:21:31,740 --> 00:21:36,120
+ناخد أمثلة التعريف يقول ال system المجموعة
+
+190
+00:21:36,120 --> 00:21:40,310
+المعادلة اللي كنا كاتبينها قبل قليللو أخدت
+
+191
+00:21:40,310 --> 00:21:45,370
+المعاملات بس و حطيتهم في مصوفة بجهد المصوفة بسميها
+
+192
+00:21:45,370 --> 00:21:50,370
+coefficient matrix of the system يعني اللي هم
+
+193
+00:21:50,370 --> 00:21:56,920
+مصوفة المعاملات لهذا النظاملو جيت مصوفة المعاملة
+
+194
+00:21:56,920 --> 00:22:02,200
+أضفت لها عمود واحد فقط هو عمود الثوابت يبقى بسميها
+
+195
+00:22:02,200 --> 00:22:06,680
+الـ Augmented Matrix يعني المصوفة الموسعة يعني
+
+196
+00:22:06,680 --> 00:22:11,460
+أضفناها عمود فوسعناها شوية من هما سميت المصوفة
+
+197
+00:22:11,460 --> 00:22:17,900
+الموسعة تمام؟ دي التعريف الثانيالحل تبع ال system
+
+198
+00:22:17,900 --> 00:22:22,820
+is star يبقى احنا بندور على حل هذا ال system هو
+
+199
+00:22:22,820 --> 00:22:26,880
+عبارة عن in a tuple لما اقول يا بنات انا عندي
+
+200
+00:22:26,880 --> 00:22:32,260
+معادلتين في مجهولين يبقى بطلع ليه قيم ال X واحد
+
+201
+00:22:32,260 --> 00:22:37,020
+وقيم ال X اتنين يبقى بقول هذا ordered pair زوج
+
+202
+00:22:37,020 --> 00:22:40,860
+مرتم X واحد هي القيمة الأولى و X اتنين هي من
+
+203
+00:22:40,860 --> 00:22:44,820
+القيمة الثانية و بقول هذا الحل طب لكن لو صارت تلت
+
+204
+00:22:44,820 --> 00:22:51,370
+مجهيلبقول عليها three tuple يعني كأنه تلت مركبات
+
+205
+00:22:51,370 --> 00:22:54,350
+موجودة يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1
+
+206
+00:22:54,350 --> 00:22:54,690
+و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى
+
+207
+00:22:54,690 --> 00:22:55,830
+X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3
+
+208
+00:22:55,830 --> 00:22:59,630
+يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و
+
+209
+00:22:59,630 --> 00:23:03,910
+X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و
+
+210
+00:23:03,910 --> 00:23:05,490
+X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى
+
+211
+00:23:05,490 --> 00:23:09,200
+X1 و X2اللي طلعت عندي Unsatisfy the system وهذه
+
+212
+00:23:09,200 --> 00:23:14,260
+القيم تحقق ال system يبقى حل هذا ال system هو
+
+213
+00:23:14,260 --> 00:23:20,920
+عبارة عن قيم X1 و X2 و X3 بحطها على شكل قوس و
+
+214
+00:23:20,920 --> 00:23:25,460
+فواصل بين هذه القيم X1 هي القيم الأولى X2 هي القيم
+
+215
+00:23:25,460 --> 00:23:32,030
+التالتة X3 هي القيم التالتة Xn هي القيم الرقموهذه
+
+216
+00:23:32,030 --> 00:23:37,330
+يجب أن تحقق هذا ال system طيب السؤال هو هل ال
+
+217
+00:23:37,330 --> 00:23:43,010
+system هذا دائما و أبدا إله حل؟ الإجابة قد يكون و
+
+218
+00:23:43,010 --> 00:23:47,590
+قد لا يكون طب إن كان هناك حل لهذا ال system حل
+
+219
+00:23:47,590 --> 00:23:51,330
+واحد و لا اتنين و لا تلاتة و لا اربع و لا ما لا
+
+220
+00:23:51,330 --> 00:23:57,330
+نهاية من الحلول هذا ما سنجيب عليهيبقى اي system من
+
+221
+00:23:57,330 --> 00:24:02,970
+المعادلة الخاطية له احد ثلاثة احتمالاتالاحتمال
+
+222
+00:24:02,970 --> 00:24:08,310
+الاول ان لا يكون هناك حل لا حل يحقق المعادلات مع
+
+223
+00:24:08,310 --> 00:24:13,990
+بعضها ال system has no solution no solution يعني
+
+224
+00:24:13,990 --> 00:24:19,390
+المعادلة إذا تعت خط مستقيمات لا يمكن للخطوط
+
+225
+00:24:19,390 --> 00:24:24,250
+المستقيمات كلها أن تتقاطع في نقطة واحدة وإن كانت
+
+226
+00:24:24,250 --> 00:24:29,360
+مستويات برضه المستويات هذه لا تتقاطعزي المستوى هذا
+
+227
+00:24:29,360 --> 00:24:34,220
+والمستوى هذا مافيش تقاطع تمام؟ ممكن يكونوا مستقيمة
+
+228
+00:24:34,220 --> 00:24:39,200
+و كل اتنين يتقاطعوا مع بعض لكن مايتقاطعوش كلهم في
+
+229
+00:24:39,200 --> 00:24:42,280
+نفس النقطة هذا و هذا يتقاطعوا في نقطة هذا و هذا في
+
+230
+00:24:42,280 --> 00:24:45,420
+نقطة هذا و هذا في نقطة تانية و اللي بعد ايه؟يبقى
+
+231
+00:24:45,420 --> 00:24:49,140
+هذا اللي لا يوجد حل في هذه الحالة يبقى في هذه
+
+232
+00:24:49,140 --> 00:24:52,720
+الحالة يبقى there is no solution كيف هذا مثلا
+
+233
+00:24:52,720 --> 00:24:57,420
+نعرفه بعد قليل من خلال الأمثلة طيب الأمر الثاني
+
+234
+00:24:57,420 --> 00:25:03,380
+ممكن يكون عندي حل وحيد فقطوهذا بيحصل إذا كانت
+
+235
+00:25:03,380 --> 00:25:07,700
+المعادلات هذه معادلات مستقيمات إذا انت تقاطع في
+
+236
+00:25:07,700 --> 00:25:13,580
+نقطة واحدة فقط لغيرها لأن المستويات إذا تقاطعت في
+
+237
+00:25:13,580 --> 00:25:17,020
+نقطة .. في .. إذا تقاطعت هذه المستقيمات فإن
+
+238
+00:25:17,020 --> 00:25:23,200
+تقاطعها يكون في خط مستقيم زي مستوى السقفو مستوى
+
+239
+00:25:23,200 --> 00:25:27,820
+الحقيقة اللي عندنا التقاطة في خط مستقيم والخط
+
+240
+00:25:27,820 --> 00:25:32,380
+مستقيم عبارة عن مهلة نهاية من النقط وليست نقطة
+
+241
+00:25:32,380 --> 00:25:38,070
+واحدةيبقى هنا ليس عندى إلا حل واحد يبقى الـ Linear
+
+242
+00:25:38,070 --> 00:25:42,770
+Loss تتخطى في نقطة واحدة وبالتالي لا يظهر إلا حل
+
+243
+00:25:42,770 --> 00:25:47,870
+واحد لهذا الـ system أو لمجموعة هذه المعادلات
+
+244
+00:25:47,870 --> 00:25:51,690
+الاحتمال يكون عندى infinite number of solutions
+
+245
+00:25:51,690 --> 00:25:57,790
+يبقى عندى عددلنهائي من الحلول في هذه الحلقة
+
+246
+00:25:57,790 --> 00:26:03,030
+المستويات كلها ممكن أنت تقاطع في نقطة واحدة زي ما
+
+247
+00:26:03,030 --> 00:26:07,410
+اقول هذا الملزم اللي بينك كلها مستويات و تقاطعة في
+
+248
+00:26:07,410 --> 00:26:11,160
+الحرارة زي الدفتر اللي عندككلها تقطعت في الحرف
+
+249
+00:26:11,160 --> 00:26:15,240
+الجانبي يبقى الحرف الجانبي هو خط التقطع كام نقطة
+
+250
+00:26:15,240 --> 00:26:19,740
+فيه يبقى مالة نهاية من النقاط ممكن مستويات تنطبق
+
+251
+00:26:19,740 --> 00:26:23,600
+زي ما تجه في الدفتر و كل ورقة بذاصير كانت مستوية
+
+252
+00:26:23,600 --> 00:26:27,500
+يبقى كلهم انطبقوا على بعض تمام الانطباق يبقى كلهم
+
+253
+00:26:27,500 --> 00:26:31,900
+اشتركوا في نفس النقاطيبقى في هذه الحلقة كام حل
+
+254
+00:26:31,900 --> 00:26:36,720
+عندي، عندي مالة نهاية من الحلول فبنقول في هذه
+
+255
+00:26:36,720 --> 00:26:42,060
+الحلقة the lines coincide الخطوط هذه بتنطبق أو ال
+
+256
+00:26:42,060 --> 00:26:46,580
+planes تتقاطع في خط أو تنطبق مع بعضها في هذه
+
+257
+00:26:46,580 --> 00:26:52,090
+الحلقةيبقى اي system يبقى نتقله احد ثلاثة احتمالات
+
+258
+00:26:52,090 --> 00:26:57,790
+يا اما مافيش حل يا اما حل واحد unique solution
+
+259
+00:26:57,790 --> 00:27:03,010
+مافيش غيره exactly one solution بالضبط يا اما عدد
+
+260
+00:27:03,010 --> 00:27:08,980
+لا نهائي من الحلول وبالتالي مافيش system له حلينأو
+
+261
+00:27:08,980 --> 00:27:12,620
+الـ system له ثلاث حلول أو الـ system له أربعة
+
+262
+00:27:12,620 --> 00:27:16,960
+حلول، لا يمكن أن يكون هناك نتيجة أو لا يوجد نتيجة
+
+263
+00:27:16,960 --> 00:27:18,360
+أو هناك نتيجة أو هناك نتيجة أو هناك نتيجة أو هناك
+
+264
+00:27:18,360 --> 00:27:23,650
+نتيجة أو هناك نتيجةكتبنا لك هذه الملاحظة كتبنا لك
+
+265
+00:27:23,650 --> 00:27:26,650
+هذه الملاحظة في الملاحظة التالية في الملاحظة
+
+266
+00:27:26,650 --> 00:27:27,290
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+267
+00:27:27,290 --> 00:27:28,010
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+268
+00:27:28,010 --> 00:27:33,110
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+269
+00:27:33,110 --> 00:27:36,230
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+270
+00:27:36,230 --> 00:27:36,810
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+271
+00:27:36,810 --> 00:27:40,090
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+272
+00:27:40,090 --> 00:27:40,790
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+273
+00:27:40,790 --> 00:27:47,350
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+274
+00:27:47,350 --> 00:27:52,010
+التالية في المفي عندي الأن أربع تعريفات ضروري أن
+
+275
+00:27:52,010 --> 00:27:57,350
+نكون ملمين بها و بتيجي أحيانا منها في الخيارات
+
+276
+00:27:57,350 --> 00:28:02,470
+المتعددة في الامتحانات يبقى صح صح كويسthe above
+
+277
+00:28:02,470 --> 00:28:07,290
+system star is called consistent يعني consistent
+
+278
+00:28:07,290 --> 00:28:15,350
+متطابق تمام if it has او متين يعني بالعربي if it
+
+279
+00:28:15,350 --> 00:28:19,390
+has one solution or infinite number of solutions
+
+280
+00:28:19,390 --> 00:28:24,990
+يعني ال system اللي بلاجئله حل وحيد او عدد لانهائي
+
+281
+00:28:24,990 --> 00:28:32,070
+من الحلول بسميه consistent طب وإذا مالوش حلولولا
+
+282
+00:28:32,070 --> 00:28:38,550
+حل بسمي inconsistent يعني نفيها تمام فبتجيب وقلت
+
+283
+00:28:38,550 --> 00:28:41,250
+لني that the above system is called inconsistent
+
+284
+00:28:41,250 --> 00:28:46,150
+if it has no solution مافيش ولا حل بسميه
+
+285
+00:28:46,150 --> 00:28:54,720
+inconsistent زي ايه ايش مقولالعدد الراشونال نمبر و
+
+286
+00:28:54,720 --> 00:29:00,600
+بقول irrational يعني ليس عددا نسبي راشونال نسبي
+
+287
+00:29:00,600 --> 00:29:05,240
+راشونال راشونال راشونال راشونال راشونال راشونال
+
+288
+00:29:05,240 --> 00:29:10,400
+راشونال راشونال راشونال
+
+289
+00:29:11,170 --> 00:29:17,030
+الأمر الثالث مجموعة الحلول هذه يابا ساميها ال
+
+290
+00:29:17,030 --> 00:29:20,990
+general solution الحل العام لهذا ال system يابا
+
+291
+00:29:20,990 --> 00:29:25,590
+ساميها ال complete solution الحل الكامل لهذا
+
+292
+00:29:25,590 --> 00:29:29,810
+النظام يابا ساميها ال general أو ال complete
+
+293
+00:29:29,810 --> 00:29:37,410
+solution لهذا ال systemفي كمان ضايلة عندنا ممكن
+
+294
+00:29:37,410 --> 00:29:42,630
+توصيه وهذا very important هنستخدمه في حل ال system
+
+295
+00:29:42,630 --> 00:29:47,510
+ايش هو هذا بيقول لي two systems of equations
+
+296
+00:29:47,510 --> 00:29:55,110
+مجموعة من systemو System هذا فيه equations وهذا
+
+297
+00:29:55,110 --> 00:29:59,090
+فيه equations لكن بيختلفوا عن بعض المعادلتين غير
+
+298
+00:29:59,090 --> 00:30:03,370
+المعادلتين لكن نفسي المجاهيل و نفسي المعادلتين
+
+299
+00:30:03,370 --> 00:30:07,950
+معادلتين تلاتة تلاتة عشرة عشرة و هكذا بيقول لي two
+
+300
+00:30:07,950 --> 00:30:12,630
+systems of equations are said to be equivalentبقول
+
+301
+00:30:12,630 --> 00:30:17,910
+هدول اتنين متكافئين if they have exactly the same
+
+302
+00:30:17,910 --> 00:30:22,590
+solutions اذا كان اللهم نفس الحل يعني انا عنده
+
+303
+00:30:22,590 --> 00:30:26,510
+system و عنده system اذا جيت على ال system الأول
+
+304
+00:30:26,510 --> 00:30:30,510
+اللي جيته طلعت الحل تبعه و جيت على ال system
+
+305
+00:30:30,510 --> 00:30:34,690
+التاني و طلعت الحل تبعه اللي جيت اتنين زي بعض بقول
+
+306
+00:30:34,690 --> 00:30:40,310
+two systems are equivalentاتنين متكافئين إذا هذا
+
+307
+00:30:40,310 --> 00:30:43,670
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+308
+00:30:43,670 --> 00:30:44,030
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+309
+00:30:44,030 --> 00:30:45,190
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+310
+00:30:45,190 --> 00:30:46,470
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+311
+00:30:46,470 --> 00:30:47,050
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+312
+00:30:47,050 --> 00:30:49,090
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+313
+00:30:49,090 --> 00:30:55,150
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+314
+00:30:55,150 --> 00:30:57,830
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+315
+00:30:57,830 --> 00:31:03,150
+عنده عدد لانهائي من الحلول و هذا عنده عددالحلول
+
+316
+00:31:03,150 --> 00:31:06,330
+متساوية في ال two systems بقول هدول are equivalent
+
+317
+00:31:06,330 --> 00:31:10,650
+ماشي شافة فرق شاسف ما بين ايه؟ ما بين الاتنين
+
+318
+00:31:10,650 --> 00:31:14,530
+المعلومات اللي اعطاناها هذه بدنا نبدأ ناخد أمثلة
+
+319
+00:31:14,530 --> 00:31:22,970
+تطبيقية عليها مرة جاية؟ قصد ايه بعد الظهر؟ طيب
+
+320
+00:31:22,970 --> 00:31:25,150
+يبقى وصلنا إلى الأمثلة
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_O3Qrzgzn80_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_O3Qrzgzn80_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eeee583592e1faa4c0fb17c0f949ad31a803b1d4
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_O3Qrzgzn80_raw.srt
@@ -0,0 +1,1480 @@
+1
+00:00:19,470 --> 00:00:23,070
+بسم الله الرحمن الرحيم المرة اللى فات انت يا انا
+
+2
+00:00:23,070 --> 00:00:26,350
+من section تلاته اتنين اللى كان بتحدث عن ال
+
+3
+00:00:26,350 --> 00:00:32,550
+subspaces الفضاءات الجزئية الاتجاهية والان بننتقل
+
+4
+00:00:32,870 --> 00:00:38,350
+الموضوع الجديد اللي هو linear dependence الاستقلال
+
+5
+00:00:38,350 --> 00:00:42,790
+الخطي وفيه كمان linear independence اللي هو
+
+6
+00:00:42,790 --> 00:00:46,870
+الاستقلال الخطي وlinear dependence الاعتماد الخطي
+
+7
+00:00:46,870 --> 00:00:49,750
+يبقى العنوان اللي احنا كاتبينه فوق linear
+
+8
+00:00:49,750 --> 00:00:54,870
+dependence الاعتماد الخطي والجزء الثاني اللي هو
+
+9
+00:00:54,870 --> 00:00:56,370
+linear independence
+
+10
+00:01:02,960 --> 00:01:08,080
+هنعطي تعريف لكل من الاعتماد الخطي والاستقلال الخطي
+
+11
+00:01:08,080 --> 00:01:14,360
+ثم بعد ذلك ناخد أمثلة على ذلك التعريف الأول بقول
+
+12
+00:01:14,360 --> 00:01:21,220
+let VBA vector space يبقى احنا في عيننا وضائع
+
+13
+00:01:21,220 --> 00:01:26,040
+اتجاه VThe finite vectors، العدد المحدود من
+
+14
+00:01:26,040 --> 00:01:32,020
+المتجهات V1 وV2 ولغاية VM الموجودة في VR6 بيكون
+
+15
+00:01:32,020 --> 00:01:37,160
+linearly dependent، بيقول معتمدات على بعضهم اعتمدا
+
+16
+00:01:37,160 --> 00:01:44,890
+قطياإذا جدرت لاجي ثواب C1 وC2 وCM أو أعداد حقيقية
+
+17
+00:01:44,890 --> 00:01:48,650
+موجودة في الـ set of real numbers not all zeros
+
+18
+00:01:48,650 --> 00:01:55,110
+such that بحيث ان C1 V1 زي C2 V2 زي زي CM VM بديوا
+
+19
+00:01:55,110 --> 00:02:00,630
+يساوي مهم بديوا يساوي Zero يبقى أنا جيت على ال
+
+20
+00:02:00,630 --> 00:02:05,790
+vector space أخدت منه مجموعة من ال vectorsهذه الـ
+
+21
+00:02:05,790 --> 00:02:11,490
+vectors بقول عنها معتمدة على بعض اعتمادا قطية إذا
+
+22
+00:02:11,490 --> 00:02:17,030
+جدرت ألاقي ثوابت مش كلها zero على الأقل بدي و لو
+
+23
+00:02:17,030 --> 00:02:22,990
+مقدار ثابت واحد يكون لا يساوي zero بحيث C1V1 زي
+
+24
+00:02:22,990 --> 00:02:29,430
+C2V2 زي CMVM كله بدي ساوي مين؟ بدي ساوي zeroطبعا
+
+25
+00:02:29,430 --> 00:02:32,670
+هرجع لهذا التعريف مرة ثانية بس خلينا ناخد التعريف
+
+26
+00:02:32,670 --> 00:02:37,530
+التاني حتى نلاحظ الفرق ما بين الاتنين التعريف
+
+27
+00:02:37,530 --> 00:02:41,290
+الثاني بيقول the finite vectors من V1 لغاية VM
+
+28
+00:02:41,290 --> 00:02:45,530
+اللي موجودة في ال vector space V بقول عنهم
+
+29
+00:02:45,530 --> 00:02:51,190
+linearly independent يبقى مستقلة عن بعضهم استقلالا
+
+30
+00:02:51,190 --> 00:02:58,300
+خاطياإذا كان عندي C1 V1 زي C2 V2 زي Cm Vm بده
+
+31
+00:02:58,300 --> 00:03:03,280
+يساوي Zero We must have لازم ألاقي انه C1 يساوي C2
+
+32
+00:03:03,280 --> 00:03:08,920
+يساوي يساوي Cm بده يساوي Zero خليني أتسأل التساؤل
+
+33
+00:03:08,920 --> 00:03:16,360
+التالي هل هناك فرق بين التعريفين المكتوب قدامي
+
+34
+00:03:16,360 --> 00:03:19,800
+علوة في فرق بين الاتنين واللحظة من كرر تكرار
+
+35
+00:03:23,050 --> 00:03:29,250
+في الحالة الأولى لاعتماد الخط إلى المتجات بقول
+
+36
+00:03:29,250 --> 00:03:35,660
+يعتمدوا على بعض خطيا لو قدرت ألاقي ثوابتممكن يكون
+
+37
+00:03:35,660 --> 00:03:40,280
+بعضهم أسفار وممكن يكون بعض مش أسفار وممكن يكون فيش
+
+38
+00:03:40,280 --> 00:03:44,440
+فيهم ولا zero بحيث أضرب constant في الأول زاد
+
+39
+00:03:44,440 --> 00:03:46,460
+constant في التانية زاد constant في التانية يطلع
+
+40
+00:03:46,460 --> 00:03:51,160
+النتج يساوي صفر إن حدث ذلك بقول هذه ال vectors من
+
+41
+00:03:51,160 --> 00:03:56,520
+v1 لغاية vm are linearly dependent يعني معتمدات
+
+42
+00:03:56,520 --> 00:04:01,220
+على بعض خطيئةهذه تعريف الأول التعريف التاني لو جئت
+
+43
+00:04:01,220 --> 00:04:05,900
+على ال vectors و جبت ثوابت و ضربتهم فيهم و جمعت
+
+44
+00:04:05,900 --> 00:04:11,560
+لجيت النتج يساوي zero ان قدرت أثبت ان c1 يساوي c2
+
+45
+00:04:11,560 --> 00:04:16,060
+يساوي cm يساوي zero إذا بيكون هذول مستقلات عن بعض
+
+46
+00:04:16,060 --> 00:04:21,200
+خطيئة linearly independent لكن إذا لجيت ولا واحد
+
+47
+00:04:21,200 --> 00:04:27,020
+فيهم يساوي zero إذا هذول معتمدات و ليست مستقلات عن
+
+48
+00:04:27,020 --> 00:04:31,400
+بعضهمواضح كلامي؟ يبقى انا لو اعطاني مجموعة من ال
+
+49
+00:04:31,400 --> 00:04:34,440
+vectors وقال لي شوف لي هدول are linearly dependent
+
+50
+00:04:34,440 --> 00:04:38,840
+ولا linearly independent بدي اضرب كل صندوق في
+
+51
+00:04:38,840 --> 00:04:41,600
+الأول وكل صندوق في التاني و .. و .. و .. كل صندوق
+
+52
+00:04:41,600 --> 00:04:47,600
+في الأخير و أجمع و أروح أجيب قيم هذه الثوابتانطلع
+
+53
+00:04:47,600 --> 00:04:53,760
+قيم هذه ثوابت ليست اسفارا يعني مش كلها اسفارا يبقى
+
+54
+00:04:53,760 --> 00:04:56,500
+بيصيروا ال vectors هذه linearly independent
+
+55
+00:04:56,500 --> 00:05:00,720
+وانطلعوا الثوابت كلهم اسفارا يبقى بيقول linearly
+
+56
+00:05:00,720 --> 00:05:05,750
+independent طيب تعالى نشوفDetermine whether the
+
+57
+00:05:05,750 --> 00:05:08,810
+following vectors are linearly-dependent or
+
+58
+00:05:08,810 --> 00:05:13,390
+linearly-independent Ld اختصار لـ linearly
+
+59
+00:05:13,390 --> 00:05:18,390
+-dependent وLi اختصار لـ linearly-independent
+
+60
+00:05:18,390 --> 00:05:22,710
+ومعطيني مجموعة من ال vectors الأولى موجودة في R3
+
+61
+00:05:22,710 --> 00:05:28,150
+ومجموعة ثانية موجودة في R4 يبقى هذول كانوا مسؤالين
+
+62
+00:05:28,150 --> 00:05:34,420
+مستقلين عن بعض خاطئينهل المجموعة الأولى مستقلة عن
+
+63
+00:05:34,420 --> 00:05:40,060
+بعض خطيا؟ و الله معتمدة على بعض خطيا فبقى اقول له
+
+64
+00:05:40,060 --> 00:05:44,720
+assume that
+
+65
+00:05:44,720 --> 00:05:56,110
+there exist c1 و c2 و c3 in R such thatبحيث ان الـ
+
+66
+00:05:56,110 --> 00:06:04,930
+C1 V1 زائد C2 V2 زائد C3 V3 بده يساوي 0 والان بعد
+
+67
+00:06:04,930 --> 00:06:11,830
+هيك بتروح ابحث قيم C1 وC2 وC3 اللي و الله يطلع
+
+68
+00:06:11,830 --> 00:06:17,400
+كلهم أسفار بقول هدول linearly independentبطلع بقيم
+
+69
+00:06:17,400 --> 00:06:20,820
+عددية بقول linearly dependent وبالتالي بكون
+
+70
+00:06:20,820 --> 00:06:25,660
+انتهينا من السؤال يبقى انا بدي اضرب C في V واحد
+
+71
+00:06:25,660 --> 00:06:30,300
+يبقى C واحد V واحد زائد C اتنين V اتنين زائد C
+
+72
+00:06:30,300 --> 00:06:35,020
+تلاتة V تلاتة يساوي بدي اضرب C واحد في الجوس الأول
+
+73
+00:06:35,020 --> 00:06:42,020
+يبقاش بصير انا بنقطع اتنين C واحد و C واحد و سالب
+
+74
+00:06:42,020 --> 00:06:52,460
+C واحد زائدالتاني بدي أضرب فيه C2 يبقى 2C2 و-3C2 و
+
+75
+00:06:52,460 --> 00:07:02,180
+-2C2 زائد القوس التالت اللي هو 2C3
+
+76
+00:07:02,180 --> 00:07:05,260
+و3C3
+
+77
+00:07:06,040 --> 00:07:12,020
+تلاتة C تلاتة وسبعة C تلاتة كل هذا الكلام يجب أن
+
+78
+00:07:12,020 --> 00:07:17,440
+يساوي كم؟ يجب أن يساوي Zero هؤلاء المجموع تلات
+
+79
+00:07:17,440 --> 00:07:22,360
+عناصر يجب أن أجمعهم و أجعلهم عنصرا واحدا يبقى لو
+
+80
+00:07:22,360 --> 00:07:27,600
+أجعلهم عنصرا واحدا يصير هذا الكلام يساوي اتنين C
+
+81
+00:07:27,600 --> 00:07:32,700
+واحد المركبة الأولى مع المركبة الأولى مع المركبة
+
+82
+00:07:32,700 --> 00:07:40,570
+الأولى هناكبعد ذلك المركبة التانية C1-3C2
+
+83
+00:07:40,570 --> 00:07:52,490
+وزائد 3C3 المركبة التالتة ناقص C1 و ناقص C1 ناقص
+
+84
+00:07:52,490 --> 00:08:02,780
+2C2 زائد 7C3 جفلنا كله بده يساوي 000الان نعمل
+
+85
+00:08:02,780 --> 00:08:07,120
+مقارنة ما بين الطرفين يبقى بناء عليه بصير اتنين C
+
+86
+00:08:07,120 --> 00:08:11,400
+واحد اتنين C اتنين اتنين C تلاتة يساوي Zero
+
+87
+00:08:11,400 --> 00:08:16,860
+المعادلة الأولى المعادلة التانية C واحد نقص تلاتة
+
+88
+00:08:16,860 --> 00:08:21,880
+C اتنين زائد تلاتة C تلاتة يساوي Zero المعادلة
+
+89
+00:08:21,880 --> 00:08:28,860
+التالتة سالب C واحد سالب اتنين C اتنين زائد سبعة C
+
+90
+00:08:28,860 --> 00:08:35,700
+تلاتة كله يساوي 100يساوي 0 هذا ال system مش بنسميه
+
+91
+00:08:35,700 --> 00:08:40,860
+homogeneous system يمكن انتقل تلان من vectors إلى
+
+92
+00:08:40,860 --> 00:08:44,360
+homogeneous system بدنا نروح ندور على حل ال
+
+93
+00:08:44,360 --> 00:08:47,860
+homogeneous system هذا بأي طريقة من الطرق التي
+
+94
+00:08:47,860 --> 00:08:52,700
+سبقت دراستها باجي بقول هذا ال system بقدر أكتبه
+
+95
+00:08:52,700 --> 00:08:57,500
+على الشكل التالي في مشكلة لو جسمت المعادلة الأولى
+
+96
+00:08:57,500 --> 00:09:05,520
+على اتنينالأولى جسمت كلها في حاجة مافيش مشكلة إذا
+
+97
+00:09:05,520 --> 00:09:10,600
+بقدر أكتب ال system هذا مرة أخرى على الشكل التالي
+
+98
+00:09:10,600 --> 00:09:20,660
+C1 زائد C2 زائد C3 يساوي Zero C1 نقص 3 C2 زائد 3
+
+99
+00:09:20,660 --> 00:09:30,000
+C3 يساوي Zero نقص C1 نقص 2 C2 زائد 7 C3 يساوي Zero
+
+100
+00:09:31,520 --> 00:09:36,280
+أريد أن أحل هذا الـ system بالـ row echelon form
+
+101
+00:09:36,280 --> 00:09:40,620
+مثلاً تمام؟ إذا أذهب وأحصل على الـ augmented
+
+102
+00:09:40,620 --> 00:09:45,840
+matrix إذا جئت إلى الـ augmented matrix واحد واحد
+
+103
+00:09:45,840 --> 00:09:53,040
+واحد وهنا Zero اللي بعده واحد ناقص تلاتة تلاتة
+
+104
+00:09:53,040 --> 00:10:00,260
+Zero سالب واحد سالب اتنين سبعة Zero بالشكل اللي
+
+105
+00:10:00,260 --> 00:10:07,850
+عندنا هناإذا أنا ممكن أعمل ما يأتي ناقص R1 to R2
+
+106
+00:10:07,850 --> 00:10:10,950
+وR1
+
+107
+00:10:10,950 --> 00:10:19,670
+to R3 نحصل على ما يأتي هاي واحد واحد واحد Zero صف
+
+108
+00:10:19,670 --> 00:10:27,410
+اللي بعده Zero سالب أربعة هنا ضربنا في سالب واحد
+
+109
+00:10:27,410 --> 00:10:35,060
+بضال جدوش اتنينهنا Zero كما هو إضافة يبقى Zero
+
+110
+00:10:35,060 --> 00:10:41,560
+وهنا سالب واحد وهنا تمانية وهنا Zero بالشكل اللي
+
+111
+00:10:41,560 --> 00:10:45,460
+عندنا ده الآن
+
+112
+00:10:45,460 --> 00:10:51,560
+مضاجي الى المعادلة اللي عندنا هذه هنا تلاتة وهنا
+
+113
+00:10:51,560 --> 00:11:02,140
+مظبوط صحيح يبقى أنا هنا ممكن ارتلت الأرواحطيب تيجي
+
+114
+00:11:02,140 --> 00:11:10,700
+بتنفع تنفع ليش لا؟ ولا هم هاي R تلاتة ل R واحد طب
+
+115
+00:11:10,700 --> 00:11:16,940
+انا ممكن اخد نص هذه او اخد ناقص نص في الأول يعني
+
+116
+00:11:16,940 --> 00:11:23,180
+ممكن اقول بدي اخد ناقص نص عارية اتنين الشكل اللي
+
+117
+00:11:23,180 --> 00:11:29,850
+عندنا هنا يبقى حصير على الشكل التالفرابع ناقص رابع
+
+118
+00:11:29,850 --> 00:11:33,990
+اقاري اتنين يبقى لو اخدت ناقص رابع اقاري اتنين
+
+119
+00:11:33,990 --> 00:11:41,330
+بصير واحد واحد زيرو وهنا زيرو وهنا واحد وهنا ناقص
+
+120
+00:11:41,330 --> 00:11:48,370
+نص وهنا زيرو وهنا زيرو وهنا سالب واحد تمانية وهي
+
+121
+00:11:48,370 --> 00:11:54,630
+زيرو الآن بعمل ما يأتيبقول هذا السهم اللي عندنا
+
+122
+00:11:54,630 --> 00:12:05,550
+إذا بدي أخد ناقص R2 to R1 و بدي أخد R2 to R3 مرة
+
+123
+00:12:05,550 --> 00:12:13,170
+واحدة لـ R3 يبقى بدي أحصل ما ياتي هذا واحد و هنا
+
+124
+00:12:13,170 --> 00:12:20,590
+zeroوهنا بيصير ذات بيصير هذا تلاتة على اتنين وهنا
+
+125
+00:12:20,590 --> 00:12:28,890
+Zero وهنا واحد وهنا ناقص نص وهنا Zero وهنا Zero
+
+126
+00:12:28,890 --> 00:12:34,070
+وهنا سبعة على اتنين يعني خمستاشر على اتنين سبعة و
+
+127
+00:12:34,070 --> 00:12:40,970
+نص يعني خمستاشر على اتنين وهنا Zero Zero Zero
+
+128
+00:12:40,970 --> 00:12:49,830
+بالشكل اللي عندنابناء عليه بقدر اقول ما يأتي من
+
+129
+00:12:49,830 --> 00:12:58,580
+هذهخلاص يعني بقدر اقول هنا اللي هو خمس طعشة على
+
+130
+00:12:58,580 --> 00:13:04,060
+اتنين C تلاتة بده يساوي Zero يبقى C تلاتة بده
+
+131
+00:13:04,060 --> 00:13:11,440
+يساوي Zero الان C تنين ناقص نص C تلاتة بده يساوي
+
+132
+00:13:11,440 --> 00:13:16,960
+مين؟ بده يساوي Zero C تلاتة ب Zero هذا معناته انه
+
+133
+00:13:16,960 --> 00:13:23,300
+C تنين بده يساوي Zero الان C واحدزائد تلاتة على
+
+134
+00:13:23,300 --> 00:13:28,500
+اتنين C تلاتة بده يساوي Zero هذا بدي اخبرك ان C
+
+135
+00:13:28,500 --> 00:13:36,240
+واحد بده يساوي Zero يبدو
+
+136
+00:13:36,240 --> 00:13:41,740
+في خطأ عندنا يا بنات استنى شوية هنا هذا واحد سالب
+
+137
+00:13:41,740 --> 00:13:48,520
+هنا واحد من وين جتني النقص هذه؟ هذه
+
+138
+00:13:50,060 --> 00:14:02,380
+هذه ناقص C1 هذه ناقص C1 هذه ناقص C1 هذه ناقص C1
+
+139
+00:14:02,380 --> 00:14:11,800
+هذه ناقص C1 هذه ناقص
+
+140
+00:14:11,800 --> 00:14:17,880
+C1 هذه ناقص C1 هذه ناقص C1والله يصلحوه يا بنات
+
+141
+00:14:17,880 --> 00:14:25,180
+اتنين ناقص واحد واحد واللي بعده اتنين هو ناقص
+
+142
+00:14:25,180 --> 00:14:31,500
+تلاتة ناقص اتنين اتنين تلاتة سبعة بناء عليه يصير
+
+143
+00:14:31,500 --> 00:14:41,920
+هذي بما يأتي اتنين وهذه ناقص C واحديبقى ناقص C1
+
+144
+00:14:41,920 --> 00:14:48,000
+وزائد C1 والباقي كله سليم لما جينا جمعنا صار اتنين
+
+145
+00:14:48,000 --> 00:14:58,360
+C1 يبقى صار هذه التانية اللي هو سالب C1 و سالب
+
+146
+00:14:58,360 --> 00:15:08,520
+تلاتة C2 زائد تلاتة C3 مظبوط واللي بعده موجب C1
+
+147
+00:15:08,520 --> 00:15:14,300
+والباقي سليمخلّي بالكوا هنا صارت هذه المعادلة 2 2
+
+148
+00:15:14,300 --> 00:15:21,980
+2 مظبوطة هذه ناقص C1 وهذه ناقص 3 وهذه زائد 3 واللي
+
+149
+00:15:21,980 --> 00:15:31,520
+بعدها زائد C1 ناقص 2 C2 زائد 7 C3 إذا صارت هذه زي
+
+150
+00:15:31,520 --> 00:15:39,320
+ما هي هذه ناقصهذه ناقص وهذه ناقص وهذه تلاتة وهذه
+
+151
+00:15:39,320 --> 00:15:46,340
+زائد C واحد وهذه زي ما هي تمام طيب إذا بدنا نيجي
+
+152
+00:15:46,340 --> 00:15:51,820
+المعادلة واحد واحد واحد مظبوطة هذه ناقص ناقص زائد
+
+153
+00:15:51,820 --> 00:15:59,970
+هذه زائد واللي بعدها كما هيبناء عليه بدي أقول هنا
+
+154
+00:15:59,970 --> 00:16:08,790
+R1 to R2 و سالب R1 to R3 بدي أصبح أن هذا مظبوط
+
+155
+00:16:08,790 --> 00:16:14,570
+يبقى هذا بدي أضيفه بدي أصبح هذا سالب 2لما أضيف
+
+156
+00:16:14,570 --> 00:16:22,270
+إضافة وهذا سيصبح اربعة وهذا زيرو هذا سيصبح سالب او
+
+157
+00:16:22,270 --> 00:16:27,030
+اربعة او اتوار ثلاثة زيرو سالب سيصبح هذا سالب
+
+158
+00:16:27,030 --> 00:16:36,970
+تلاتة وهذا سيصبح ستة هذه ستة والباقي زيرو هذا بدل
+
+159
+00:16:36,970 --> 00:16:44,920
+الربع ناقص نصناقص نص يبقى هذا زي ما هو وهذا يصبح
+
+160
+00:16:44,920 --> 00:16:52,660
+واحد وهذا ناقص اتنين لان انا اخدنا ناقص نص يبقى
+
+161
+00:16:52,660 --> 00:16:57,920
+هذا ناقص اتنين وهذا زيرو والباقي كما هو ما عدا هذا
+
+162
+00:16:57,920 --> 00:17:04,960
+يصبح سالب تلاتة وهذا يصبح ستةيبقى ايش بده يصير
+
+163
+00:17:04,960 --> 00:17:12,600
+عندنا الان؟ بده اضيف سالب R2 to R1 مظبوط و تلاتة
+
+164
+00:17:12,600 --> 00:17:19,280
+R2 to R3 ماشي الحال يبقى ايش بده يصير عندنا؟ بده
+
+165
+00:17:19,280 --> 00:17:26,350
+يصير كالتاليالعمود الأول زي ما هو و العمود الثاني
+
+166
+00:17:26,350 --> 00:17:32,250
+سالب سيصبح فوق 0 و اللي تحت 3 سيصبح 0 العمود
+
+167
+00:17:32,250 --> 00:17:42,560
+التالد الان سالب R2 to R1 سيصبح هنا 3وهنا سالب
+
+168
+00:17:42,560 --> 00:17:48,120
+اتنين زي ما هي وهنا بدي اضيف تلاتة في اتنين سالب
+
+169
+00:17:48,120 --> 00:17:55,540
+ستة بيصير zero وهذه كمان zero مظبوط100% إذا تغير
+
+170
+00:17:55,540 --> 00:18:02,980
+وضع المعادلات كالتالي يبقى بصير انه ايش C1 زائد 3
+
+171
+00:18:02,980 --> 00:18:13,260
+C3 بده يسوي 0 وC2 ناقص 2 C3 بده يسوي 0 إذا ننقلب
+
+172
+00:18:13,260 --> 00:18:16,740
+وضع المعادلة شوفي من linearly independent بده يصير
+
+173
+00:18:16,740 --> 00:18:21,080
+linearly independent مشان غلطنا بس في إشارة واحدة
+
+174
+00:18:21,360 --> 00:18:26,720
+يبقى بناء عليه بقدر أقول ما يأتي هدول معادلتين في
+
+175
+00:18:26,720 --> 00:18:31,920
+ثلاثة مجاهيل لا يمكن حلهم إلا إذا فرطت أحد
+
+176
+00:18:31,920 --> 00:18:39,890
+المجاهيل من عندي إذا لو جيت قلت مثلا FC3 تساوي A
+
+177
+00:18:39,890 --> 00:18:51,650
+ثم C1 تساوي نقص 3A ثم C2 تساوي 2A يبقى أصبح
+
+178
+00:18:51,650 --> 00:19:00,450
+solution is C1 وC2 وC3
+
+179
+00:19:10,180 --> 00:19:14,400
+يبقى هذا كله لا يساوي
+
+180
+00:19:31,850 --> 00:19:32,030
+السلام عليكم
+
+181
+00:19:50,970 --> 00:19:56,590
+يبقى أمنات أنا فرط c1 و c2 و c3 من عندى مجاهل
+
+182
+00:19:56,590 --> 00:20:01,350
+ضربتهم فى ال vectors طلعوا هدول ثوابت و ليسوا
+
+183
+00:20:01,350 --> 00:20:05,730
+أسفارا طبعا يعنى طلعوا أرقام و ليسوا أسفارا
+
+184
+00:20:05,730 --> 00:20:08,470
+وبالتالي صار ال three vectors are linearly
+
+185
+00:20:08,470 --> 00:20:12,730
+dependent الآن بنفس الفكرة بإن أنا اجى للمطموب
+
+186
+00:20:12,730 --> 00:20:18,110
+الثانى Nimra Vيمكننا نمر بيه بداية اقول له assume
+
+187
+00:20:18,110 --> 00:20:29,830
+افترض assume that there exist c1 و c2 و c3 in a
+
+188
+00:20:29,830 --> 00:20:37,690
+set of real numbers such that بحيث ان c1, v1, c2,
+
+189
+00:20:37,910 --> 00:20:47,790
+v2زائد C تلاتة V تلاتة زائد C تلاتة V تلاتة زائد C
+
+190
+00:20:47,790 --> 00:20:53,690
+تلاتة V تلاتة زائد C تلاتة V تلاتةتلاتة vector
+
+191
+00:20:53,690 --> 00:20:58,330
+يبقى بدّاه دي اضرب في ال vector أولاني بده يصير
+
+192
+00:20:58,330 --> 00:21:08,070
+الجثه الأول C1 و 0 و C1 و 2 C1 اللي بعده ضربته في
+
+193
+00:21:08,070 --> 00:21:19,010
+C2 بده يصير 0 و C2 و C2و2C2 زائد اللي بعده ضربته
+
+194
+00:21:19,010 --> 00:21:32,010
+في C3 C3 وC3 وC3 و3C3 ساوية 0بتجمعهم مع بعض يبقى
+
+195
+00:21:32,010 --> 00:21:42,910
+C1 زائد C3 اللي بعده C2 زائد C3 يبقى C1 راح هذا
+
+196
+00:21:42,910 --> 00:21:48,550
+راح هذا بظل C3 اللي بعده Zero بروح بظل C2 زائد C3
+
+197
+00:21:49,090 --> 00:22:00,590
+اللي بعده بيصير c1 زائد c2 زائد c3 اللي بعده اتنين
+
+198
+00:22:00,590 --> 00:22:09,590
+c1 زائد اتنين c2 زائد تلاتة c3 بده ساوي zero يبقى
+
+199
+00:22:09,590 --> 00:22:15,370
+هذا ككل جوز بده ساوي zero و zero و zero بالشكل
+
+200
+00:22:15,370 --> 00:22:20,350
+اللي عندنا هذانعمل مقارنة ما بين الطرفين يبقى C1
+
+201
+00:22:20,350 --> 00:22:25,770
+زائد C3 زائد
+
+202
+00:22:25,770 --> 00:22:34,410
+C3 زائد
+
+203
+00:22:34,410 --> 00:22:44,280
+C3 زائدالثاني اللي هو C2 زائد C3 بده يساوي 0
+
+204
+00:22:44,280 --> 00:22:53,420
+التالت C1 زائد C2 زائد C3 بده يساوي 0 التالت 2C1
+
+205
+00:22:53,420 --> 00:23:01,220
+2C2 3C3 بده يساوي كده؟ بده يساوي 0
+
+206
+00:23:03,560 --> 00:23:09,920
+طيب لو جينا ضربنا يا بنات هذول المعادلتين في سالي
+
+207
+00:23:09,920 --> 00:23:16,660
+بإتنين يبقاش بصير سالي بإتنين C واحد سالب سالب
+
+208
+00:23:16,660 --> 00:23:21,900
+اللي هو اتنين C اتنين سالي بإتنين C تلاتة بده يسوي
+
+209
+00:23:21,900 --> 00:23:27,480
+Zero هنا اتنين C واحد زيدي اتنين C اتنين زي
+
+210
+00:23:27,480 --> 00:23:32,180
+التلاتة C تلاتة بده يسوي Zero وجمعنا هدول مع
+
+211
+00:23:32,180 --> 00:23:38,680
+السلامةيبقى هذا بيظل عندى C3 لحاله بده يساوي Zero
+
+212
+00:23:38,680 --> 00:23:45,020
+لما C3 يساوي Zero C2 بقداش ب Zero هذا بده يعطينا
+
+213
+00:23:45,020 --> 00:23:53,580
+انه C2 يساوي Zero لما C3 يساوي Zero وكذلك C1 بده
+
+214
+00:23:53,580 --> 00:23:57,080
+يساوي Zero يبقى أصبح C1
+
+215
+00:24:13,010 --> 00:24:16,730
+يبقى هذا مثال على الـ linearly dependent و ال
+
+216
+00:24:16,730 --> 00:24:19,610
+linearly independent vectors
+
+217
+00:24:53,500 --> 00:24:57,140
+بنجي الآن لنظرية على هذا الموضوع نظرية بتقول ما
+
+218
+00:24:57,140 --> 00:25:03,400
+يأتي theorem the
+
+219
+00:25:03,400 --> 00:25:07,620
+set اللي
+
+220
+00:25:07,620 --> 00:25:20,980
+هي V1 و V2 و VM islinearly dependent if and only
+
+221
+00:25:20,980 --> 00:25:28,400
+if at least one
+
+222
+00:25:28,400 --> 00:25:35,100
+element of
+
+223
+00:25:35,100 --> 00:25:44,760
+the set is a linear combination
+
+224
+00:25:48,820 --> 00:25:51,460
+معظم الاخرين
+
+225
+00:26:10,130 --> 00:26:14,770
+نرجع لنص النظرية تانية نقرأ النص نحاول نفهم هذا
+
+226
+00:26:14,770 --> 00:26:20,410
+النص فاهما صحيحا ثم نذهب إلى برهنة هذه النظرية
+
+227
+00:26:20,410 --> 00:26:25,710
+النظرية بتقول the set of vectors V1 و V2 و لغاية
+
+228
+00:26:25,710 --> 00:26:29,790
+VM اللي موجودة في vector space V linearly
+
+229
+00:26:29,790 --> 00:26:34,990
+dependent if and only if at least one element of
+
+230
+00:26:34,990 --> 00:26:39,370
+the set is a linear combination of the otherيبقى
+
+231
+00:26:39,370 --> 00:26:43,150
+احنا جينا على vector space أخدنا منه مجموعة من ال
+
+232
+00:26:43,150 --> 00:26:47,870
+vectors هيها قدامي البرهان بدي يصير في اتجاهين لإن
+
+233
+00:26:47,870 --> 00:26:52,510
+في موجود عنده إيش if and only if يعني لو كان هذا
+
+234
+00:26:52,510 --> 00:26:56,570
+معطيات هذا مطلوب والعكس لو كان هذا مطلوب بدي يكون
+
+235
+00:26:56,570 --> 00:27:00,550
+هذا إيه معطيات إيه ده البرهان بدي يصير في اتجاهين
+
+236
+00:27:00,550 --> 00:27:05,700
+يبقى بدي أفترض أولا إن هدول ما لهمLinearly
+
+237
+00:27:05,700 --> 00:27:10,760
+Dependent ومن خلالهم اروح اثبت انه اي vector من
+
+238
+00:27:10,760 --> 00:27:15,600
+هدول Linear Combination للاخرين يعني اي vector من
+
+239
+00:27:15,600 --> 00:27:19,780
+هدول بقدر اكتبه على صيغة Linear Combination من
+
+240
+00:27:19,780 --> 00:27:25,640
+باقية من ال vectors الأخرى تبعات هذه الست يبقى بدأ
+
+241
+00:27:25,640 --> 00:27:32,740
+امشي الاتجاه الأول بداجي اقول اسيومالذات اللي هو
+
+242
+00:27:32,740 --> 00:27:40,660
+V1 و V2 و لغاية ال VM are linearly dependent
+
+243
+00:27:42,680 --> 00:27:46,080
+بالدرجة على تعريف linearly dependent معناته there
+
+244
+00:27:46,080 --> 00:27:54,100
+exist scholars C1 وC2 وCM موجودات يار not all zero
+
+245
+00:27:54,100 --> 00:27:59,420
+مش كلهم zero بحيث يكون مجموعهم يسوي قداش zero يبقى
+
+246
+00:27:59,420 --> 00:28:09,010
+هذا معناته there exist scholarsاللي هم مين؟ C1 وC2
+
+247
+00:28:09,010 --> 00:28:23,050
+وCm ان ار not all zero مش كلهم زيرو such that بحيث
+
+248
+00:28:23,050 --> 00:28:33,130
+ان C1 V1 زائد C2 V2 زائد زائد Cm Vm دي ساوي جداش؟
+
+249
+00:28:33,130 --> 00:28:39,150
+دي ساوي زيرويعني السلسلات يا بنات ممكن يكون بعضهم
+
+250
+00:28:39,150 --> 00:28:44,230
+أسفار وممكن يكون بعضهم مواشي أسفار لكن كلهم أسفار
+
+251
+00:28:44,230 --> 00:28:50,550
+ممنوع على الأقل عندي ولا واحد فقط بيكون هنا لا
+
+252
+00:28:50,550 --> 00:28:57,690
+يساوي الزير تمام؟ إذا بروح أخد واحد منهم و أثبت
+
+253
+00:28:57,690 --> 00:29:03,970
+أني بقدر أكتبه بدلالة من؟ بدلالة الآخرين فباجي
+
+254
+00:29:03,970 --> 00:29:14,960
+بقول هنا FCI موجود في R and CI not equal to zero
+
+255
+00:29:14,960 --> 00:29:30,000
+then the vector اللي هو CI VI بده يساوي is ده
+
+256
+00:29:30,000 --> 00:29:38,670
+ياخد CI VIكيف يعني؟ يعني افترض انه CIV اياجاني هنا
+
+257
+00:29:38,670 --> 00:29:44,230
+في هذا المكان يبقى بده يخليه في مكانه والباقية كله
+
+258
+00:29:44,230 --> 00:29:47,950
+بده يوديه وين؟ على الشجرة التانية يبقى ايش بده
+
+259
+00:29:47,950 --> 00:29:58,270
+يصير هنا؟ بده يساويسالب C1 V1 سالب C2 V2 سالب ونظل
+
+260
+00:29:58,270 --> 00:30:05,890
+ماشيين لغاية ما نوصل لسالب C I minus ال one V I
+
+261
+00:30:05,890 --> 00:30:11,050
+minus ال one من اللي بيجي بعده C I V I هيوا برا
+
+262
+00:30:11,550 --> 00:30:18,750
+يبقى اللي بده يجي بعده ناقص c i plus one v i plus
+
+263
+00:30:18,750 --> 00:30:25,770
+one زائد زائد لغاية ماوصل آخر واحد اللي هو c m v m
+
+264
+00:30:27,070 --> 00:30:30,570
+يعني اللي في النص هذا ما بين الاتنين خلّيته
+
+265
+00:30:30,570 --> 00:30:34,830
+والباقي نجلته وين؟ على الشجة التانية الان أنا جاي
+
+266
+00:30:34,830 --> 00:30:39,590
+لهذا اللي لا يساوي zero إذا بقدر أجسم عليه صحيح
+
+267
+00:30:39,590 --> 00:30:45,870
+ولا لأ؟ إذا لو جسمت عليه بحصل على VI دي ساوي سالب
+
+268
+00:30:45,870 --> 00:30:55,520
+C1 على CI في V1سالب C2 على CI في V2 سالب سالب اللي
+
+269
+00:30:55,520 --> 00:31:04,740
+هو CI minus 1 على CI في VI minus 1 سالب CI plus 1
+
+270
+00:31:04,740 --> 00:31:12,060
+على CI في VI plus 1 طبعا هنا مش زاد ناقص يا بنات
+
+271
+00:31:12,060 --> 00:31:20,570
+كلهوهنا ناقص يبقى هنا ناقص ونظل ماشيين ناقص cm على
+
+272
+00:31:20,570 --> 00:31:28,030
+ci في ال VM طب ايش رايكوا هذا مقدار ثابت يا بنات و
+
+273
+00:31:28,030 --> 00:31:35,150
+هذا مقدار ثابت يعني بقدر اقول هذا a1v1 زائد a2v2
+
+274
+00:31:35,150 --> 00:31:49,600
+زائدAI-1VI-1 زائد اللي هو AI plus one VI plus one
+
+275
+00:31:49,600 --> 00:31:55,900
+زائد زائد اللي هو AMVM
+
+276
+00:31:55,900 --> 00:32:02,780
+ايش تفسيرك لهذا انه VI linear combination من
+
+277
+00:32:02,780 --> 00:32:11,460
+الآخرين اظن هو المضطب الأوليبقى هنا this means
+
+278
+00:32:11,460 --> 00:32:24,260
+that هذا يعني ان ال vi is a linear combination of
+
+279
+00:32:24,260 --> 00:32:34,300
+the others طيب
+
+280
+00:32:34,950 --> 00:32:39,990
+بنعمل العملية العكسية بناخد واحد فيهم linear
+
+281
+00:32:39,990 --> 00:32:44,490
+combination من الآخرين ونثبت أن هذه المجموعة
+
+282
+00:32:44,490 --> 00:32:49,390
+linearly dependent تمام يبقى بالداجي أقول له
+
+283
+00:32:49,390 --> 00:32:59,830
+conversely conversely يعني بالعكس assume that
+
+284
+00:33:00,820 --> 00:33:13,440
+VK is a linear combination of
+
+285
+00:33:13,440 --> 00:33:27,220
+the vectors V1 و V2 و لغاية VK-L1 و VK plus one
+
+286
+00:33:27,820 --> 00:33:34,900
+وانظر لمشي لغاية ال VM هذا
+
+287
+00:33:34,900 --> 00:33:41,740
+Linear Combination من من؟ من هذول تمامالان انا
+
+288
+00:33:41,740 --> 00:33:46,940
+فرضت ان ال vector رقم K من المجموع اللي عندى هذا
+
+289
+00:33:46,940 --> 00:33:51,700
+ماله هو vector رقم K هو linear combination من
+
+290
+00:33:51,700 --> 00:33:57,320
+الأخرين هو النظرية هى is a linear combination of
+
+291
+00:33:57,320 --> 00:34:01,940
+the other بدي اثبت ان هذه ال vector كلها بما فيها
+
+292
+00:34:01,940 --> 00:34:07,520
+ال V وK are linearly dependent تمام يبقى assume
+
+293
+00:34:07,520 --> 00:34:11,180
+that linear combination of the vectorsيبقى هذا
+
+294
+00:34:11,180 --> 00:34:21,880
+معناته ان there exist c1 و c2 و لغاية cm in R such
+
+295
+00:34:21,880 --> 00:34:22,500
+that
+
+296
+00:34:25,350 --> 00:34:40,530
+بحيث ان ال VK بده ساوي C1 V1 زاد C2 V2 زاد CK-1 في
+
+297
+00:34:40,530 --> 00:34:53,590
+VK-1 زاد CK plus 1 في VK plus 1 زاد زاد CMVM
+
+298
+00:34:58,080 --> 00:35:04,220
+السؤال هو هل أنا حطيت قيود على السيهات هذه؟ قولت
+
+299
+00:35:04,220 --> 00:35:07,840
+أسفار ولا غير أسفار؟ أبدا، linear cum أسفار ولا
+
+300
+00:35:07,840 --> 00:35:11,360
+غير أسفار؟ بهلنير، إنما دول scholars موجودات في
+
+301
+00:35:11,360 --> 00:35:15,280
+أرض وحققوا لمين المعادلة اللي عندنا، طب شو رأيكوا
+
+302
+00:35:15,280 --> 00:35:20,290
+أعملها معادلة سفرية بنفع؟بنفع طيب يبقى لو روحت
+
+303
+00:35:20,290 --> 00:35:28,330
+عملتها معادلة صفرية بصير كيف C1 C1 زاد C2 V2 زاد
+
+304
+00:35:28,330 --> 00:35:36,110
+زاد CK-1 VK-1 هذا اللي بدي أجيبه على الشك التاني
+
+305
+00:35:36,110 --> 00:35:42,530
+يا بنات بدي يجي بشرة جدية سالب واحد في ال VK يبقى
+
+306
+00:35:42,530 --> 00:35:52,660
+هذا سالب واحد في ال VKزائد ck plus one vk plus one
+
+307
+00:35:52,660 --> 00:36:02,900
+زائد زائد cm vm كله بده يساوي zeroطيب الحين لجيت
+
+308
+00:36:02,900 --> 00:36:07,920
+ايش لجيت constants not all zero مش عارف انه not
+
+309
+00:36:07,920 --> 00:36:13,540
+all zero بقولك اه هاي واحد فيهم بجداش بسالب واحد
+
+310
+00:36:13,540 --> 00:36:23,840
+يبقى هنا so there exist constants in
+
+311
+00:36:23,840 --> 00:36:29,380
+cnr not all zero
+
+312
+00:36:34,070 --> 00:36:42,530
+بالتالي CK-1 يبقى هناك إذا أصلا كانت نقطة او زيرو
+
+313
+00:36:42,530 --> 00:36:57,200
+لأن هذا such thatبحيث ان c1v1 زاد c2v2 زاد cmvm
+
+314
+00:36:57,200 --> 00:37:05,380
+بده يساوي zero هذا معناه ان v1 وv2 وvm are
+
+315
+00:37:05,380 --> 00:37:11,340
+linearly dependent وهو المطلوب حد فيكم بتحب تسأل
+
+316
+00:37:11,340 --> 00:37:13,240
+أي سؤال في برهان النظرية
+
+317
+00:37:16,490 --> 00:37:20,770
+برهاء النظرية، حد بتحب تسأل اي سؤال؟ اذا ماكنتش
+
+318
+00:37:20,770 --> 00:37:25,250
+تسأل وانا بدي اسأل، اه، ايوة
+
+319
+00:37:30,360 --> 00:37:34,180
+حطينا إيش؟ مش خلّينا واحد في ناحية و الباقي في
+
+320
+00:37:34,180 --> 00:37:39,980
+ناحية تانية كنا نجلناهم يعني بلغة لبتدائي أضافنا
+
+321
+00:37:39,980 --> 00:37:46,020
+المعكوس الجامعي لكل من ال vectors إلى الطرفين،
+
+322
+00:37:46,020 --> 00:37:49,620
+تمام؟ وعلى السريع بقولنا نجلناهم علشان جتنا بتجي
+
+323
+00:37:49,620 --> 00:37:56,020
+بشرقة مخالفة، مش هيك؟ في كمان تسأل؟ طيب، بدأ أسأل
+
+324
+00:37:56,020 --> 00:38:00,060
+السؤال اللي يتتلي أنالو عند فيه two vectors يامنات
+
+325
+00:38:00,060 --> 00:38:05,100
+واحد مضاعفات التاني واحد نص التاني جده مرتين جده
+
+326
+00:38:05,100 --> 00:38:13,240
+تلت مرات جده عشر مرات قلي بركوا كويس يعني C1 يساوي
+
+327
+00:38:13,240 --> 00:38:20,620
+مثلا خمسة C2 V1 يساوي خمسة V2 هل ال V1 و V2 are
+
+328
+00:38:20,620 --> 00:38:24,980
+linearly dependent ولا linearly independent؟
+
+329
+00:38:27,080 --> 00:38:29,620
+اللي بتعرف ترفع أيضا فوق بس مش هنتناقش انا و
+
+330
+00:38:29,620 --> 00:38:37,340
+الباقي يفهم انا عندي V1 بده ساوي خمسة V2 سؤالي هو
+
+331
+00:38:37,340 --> 00:38:41,840
+ال V1 و ال V2 هذا linearly dependent ولا linearly
+
+332
+00:38:41,840 --> 00:38:44,420
+independent ده اللي بتعرف ترفع أيضا فوق مش هنتناقش
+
+333
+00:38:44,420 --> 00:38:49,300
+احنا وياه ايوة linearly dependent ليش؟ لأن نقدر
+
+334
+00:38:49,300 --> 00:38:55,380
+ناخد خمسة V1 نقدر نخلد V1 نعمل تكتر ثاني خمسة V1
+
+335
+00:38:56,290 --> 00:39:01,550
+لأنه ممكن ننجلها على الشجة التانية ويصير V1 ناقص
+
+336
+00:39:01,550 --> 00:39:07,050
+خمسة V2 يساوي كم؟ Zero. بيصير معامل ال V1 هو V1
+
+337
+00:39:07,050 --> 00:39:12,450
+ومعامل ال V2 هو سالب خمسة واثنين not zero وبالتالي
+
+338
+00:39:12,450 --> 00:39:17,610
+هذول اتنين linearly dependentيبجى ابنات any two
+
+339
+00:39:17,610 --> 00:39:21,810
+vectors واحد مضاعفات النص و تلت و ربع و ناقص خمسة
+
+340
+00:39:21,810 --> 00:39:26,050
+جد و خمسين مرة كله are linearly dependent هكتبها
+
+341
+00:39:26,050 --> 00:39:30,910
+لك بصيغة ال remark التالية يبجى خليني امسح الشجة
+
+342
+00:39:30,910 --> 00:39:33,510
+هذه و نكتب هذه ال remark
+
+343
+00:39:58,520 --> 00:40:05,460
+remark let v
+
+344
+00:40:05,460 --> 00:40:19,020
+be a vector space then v1
+
+345
+00:40:19,020 --> 00:40:28,800
+وv2 اللي موجودة في vare linearly dependent if and
+
+346
+00:40:28,800 --> 00:40:41,400
+only if if and only if one is a multiple of
+
+347
+00:40:41,400 --> 00:40:49,900
+the other واحد فيهم كان مضعفات الثاني that is
+
+348
+00:40:53,870 --> 00:41:00,650
+V1 بيساوي CV2 والـ C هذه موجودة في set of real
+
+349
+00:41:00,650 --> 00:41:05,410
+numbers طبعا ليش؟ أقول لو نجلت هذه على الشجة هذه و
+
+350
+00:41:05,410 --> 00:41:10,970
+الله هذه على الشجة هذه بصير اللي هو أحد المعاملات
+
+351
+00:41:10,970 --> 00:41:15,510
+لا يساوي zero C أنا مش عارف منه قد يكون zero و قد
+
+352
+00:41:15,510 --> 00:41:19,670
+لا يكون zero بس معامل ال V هو جداش واحد صحيح
+
+353
+00:41:19,670 --> 00:41:22,810
+وبالتالي enough all zeroيبقى هدول linearly
+
+354
+00:41:22,810 --> 00:41:33,150
+dependent نعطي مثال examples example one لان بيقول
+
+355
+00:41:33,150 --> 00:41:36,930
+little v determine whether the vectors
+
+356
+00:41:50,760 --> 00:41:57,360
+these are the vectors اللي هو V1 بده يساوي اتنين
+
+357
+00:41:57,360 --> 00:42:09,340
+سالب واحد و Zero واحد and V2 بده يساوي V2 بده
+
+358
+00:42:09,340 --> 00:42:18,040
+يساوي ستة وناقص تلاتة و Zero تلاتة areLinearly
+
+359
+00:42:18,040 --> 00:42:27,440
+dependent or linearly independent solution يبقى
+
+360
+00:42:27,440 --> 00:42:31,520
+بنرجع لسؤال هذا مرة ثانية و بنقول determine
+
+361
+00:42:31,520 --> 00:42:34,800
+whether the two vectors هدول are linearly
+
+362
+00:42:34,800 --> 00:42:39,480
+dependent ولا linearly independent لو روحت دقيقة
+
+363
+00:42:39,480 --> 00:42:44,150
+النظر في ال two vectors يا مانت إيش بتلاحظني؟و أحد
+
+364
+00:42:44,150 --> 00:42:52,060
+ثلاثة أمثال الثاني يبقى هدول اتنين مالهم؟يبقى باجي
+
+365
+00:42:52,060 --> 00:42:59,740
+بقوله ال V2 يساوي ستة سالب تلاتة و Zero تلاتة لو
+
+366
+00:42:59,740 --> 00:43:04,740
+أخدنا تلاتة عامل مشترك بيصير عندنا هنا اتنين و
+
+367
+00:43:04,740 --> 00:43:11,160
+سالب واحد و Zero و واحد هذا من هو V1 يبقى هذا
+
+368
+00:43:11,160 --> 00:43:19,610
+يساوي تلاتة V1يبقى صارع هنا V2
+
+369
+00:43:19,610 --> 00:43:33,250
+is a multiple of V1 هذا معناته ان V1 و V2 are
+
+370
+00:43:33,250 --> 00:43:38,550
+linearly dependent وانتهينا من المثل
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/bP46PxbK2bE.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/bP46PxbK2bE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..976f06f85e79dbaa3f829ae6e0ae65e2bc2e34ff
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/bP46PxbK2bE.srt
@@ -0,0 +1,1594 @@
+1
+00:00:19,740 --> 00:00:24,020
+بسم الله الرحمن الرحيم نعود إلى الـ section ابتدأنا 
+
+2
+00:00:24,020 --> 00:00:29,360
+في الفترة الصباحية و نجي نكمل عليه يبقى فيها بعض
+
+3
+00:00:29,360 --> 00:00:34,020
+التعريفات الجديدة مثل الـ singular matrix و الـ non 
+
+4
+00:00:34,020 --> 00:00:38,440
+singular matrix المصروفة المربعة بقول عنها
+
+5
+00:00:38,440 --> 00:00:44,500
+singular لو جيت أخدت المحدد لها و لقيته يساوي
+
+6
+00:00:44,500 --> 00:00:50,760
+الصفر non singular لو أخدت المحدد له ووجدت القيمة لا
+
+7
+00:00:50,760 --> 00:00:54,280
+تساوي zero singular بقى singular بالعربي يعني
+
+8
+00:00:54,280 --> 00:00:59,800
+بترجموها مصفوفة شاذة مصفوفة منفردة مصفوفة منعزلة
+
+9
+00:00:59,800 --> 00:01:03,900
+الترجمة اللي بدكِ إياها باختلاف الترجمة من دولة
+
+10
+00:01:04,000 --> 00:01:08,500
+لأخرى لكن درجة أنها مصفوفة شاذة يبقى المصوفة اللي
+
+11
+00:01:08,500 --> 00:01:13,940
+محددها يساوي zero بسميها singular matrix و المصفوفة
+
+12
+00:01:13,940 --> 00:01:18,280
+اللي محددها لا يساوي zero بسميها non singular
+
+13
+00:01:18,280 --> 00:01:24,260
+matrix يعني مصفوفة غير شاذة أو غير منعزلة بنجي الآن
+
+14
+00:01:24,260 --> 00:01:30,300
+لمشتقة المحدد كيف بنحصل على المشتقة الأولى لمحدد
+
+15
+00:01:30,300 --> 00:01:34,360
+ما بنحط التعريف كالتالي لو كان الـ determinant لـ أيه
+
+16
+00:01:34,360 --> 00:01:38,280
+هو المحدد اللي عندنا هذا يبقى بدنا مشتقة الـ
+
+17
+00:01:38,280 --> 00:01:42,360
+determinant لـ أيه أو الـ determinant لـ أيه prime
+
+18
+00:01:42,360 --> 00:01:46,760
+شوفوا شو بنعمل بنجي على الصف الأول اللي بنشتقه و
+
+19
+00:01:46,760 --> 00:01:52,110
+بنثبت باقي الصفوف بنضيف له بنثبت الصف الأول و بشتق
+
+20
+00:01:52,110 --> 00:01:57,070
+الصف الثاني و بنثبت باقي الصفوف بروح زائد على الصف
+
+21
+00:01:57,070 --> 00:02:00,590
+التالت و بشتقه بنثبت الصفين اللي جابله و باقي
+
+22
+00:02:00,590 --> 00:02:05,030
+الصفوف اللي ... و بضل مستمر على الشغل هذه لغاية
+
+23
+00:02:05,030 --> 00:02:12,150
+ما أوصل للمحدد رقم N اللي بنثبت كل الصفوف من أعلى
+
+24
+00:02:12,150 --> 00:02:17,620
+عدا الصف الأخير بنجي بنشتقه بنجمع بفكر محددة و بجيب
+
+25
+00:02:17,620 --> 00:02:23,320
+النتج بكون حصلت على مشتقة هذا المحدد اطلع هنا
+
+26
+00:02:23,320 --> 00:02:28,300
+اشتقت الصف الأول و ثبت باقي الصف زائد اشتقت الصف
+
+27
+00:02:28,300 --> 00:02:33,080
+الثاني و ثبت اللي قبله و اللي بعده زائد زائد لغاية ما
+
+28
+00:02:33,080 --> 00:02:38,020
+وصل لمين لآخر محدد ثبت الصفوف الأولى كلها و اشتقت
+
+29
+00:02:38,020 --> 00:02:43,680
+الصف الأخيرة مجموع هذول كله مع بعض بيعطيني قيمة
+
+30
+00:02:43,680 --> 00:02:49,710
+مشتقة هذا المحدد جالي مثال لو كان عندنا محدد ثلاثي
+
+31
+00:02:49,710 --> 00:02:53,650
+بالشكل هذا و زي ما أنت شايفه دوال جالي هاتلي
+
+32
+00:02:53,650 --> 00:03:00,550
+determinant للـ A prime يعني مشتقة هذا المحدد بقوله
+
+33
+00:03:00,550 --> 00:03:06,290
+بسيطة الحل كان تاليباجي بقوله الـ determinant لـ أيه
+
+34
+00:03:06,290 --> 00:03:11,490
+لكل prime يساوي باجي بقوله هي المحدد باجي على الصف
+
+35
+00:03:11,490 --> 00:03:16,690
+الأول مشتقة الـ X تربيع بقداش باتنين X مشتقة
+
+36
+00:03:16,690 --> 00:03:21,010
+التانية بواحد مشتقة اللي بعدها سالب واحد على X
+
+37
+00:03:21,010 --> 00:03:21,470
+تربيع
+
+38
+00:03:34,440 --> 00:03:39,820
+المحدد اللي بعده بنثبت الصف الأول زي ما هو اللي هو X 
+
+39
+00:03:39,820 --> 00:03:44,960
+تربيع و X هو واحد على X الصف الثاني بدي أشتاقه
+
+40
+00:03:44,960 --> 00:03:49,100
+مشتقة الـ E و الـ six بالـ E و الـ six السلم مشتقة
+
+41
+00:03:49,100 --> 00:03:53,340
+الـ zero بالـ zero و مشتقة اتنين بالـ zero الصف
+
+42
+00:03:53,340 --> 00:04:03,140
+الثالث زي ما هو تان الـ X خمسة X سين الـ X  جفلنا زائد
+
+43
+00:04:03,140 --> 00:04:09,480
+اللي هو المحدد التالت الصف الأول زي ما هو بدون
+
+44
+00:04:09,480 --> 00:04:15,680
+تغيير الصف الثاني زي ما هو بدون تغيير الصف التالت
+
+45
+00:04:15,680 --> 00:04:21,840
+بدي أشتقهم مشتقة التان بالسكتر بها الـ X مشتقة
+
+46
+00:04:21,840 --> 00:04:28,240
+خمسة X بخمسة مشتقة الـ sine بها الـ cosine X روح
+
+47
+00:04:28,240 --> 00:04:31,680
+يفكر كل محدد من هذه المحادثة ويجمع يكون حصلنا
+
+48
+00:04:31,680 --> 00:04:36,500
+عليه على المشتقة يبقى هذا مثال عملي على كيفية
+
+49
+00:04:36,500 --> 00:04:41,320
+الحصول على مشتقة محددة ضايق لأن في هذه الـ section
+
+50
+00:04:41,320 --> 00:04:48,700
+هذه الملاحظة A التالية يبقى باجي إلى remark remark
+
+51
+00:04:48,700 --> 00:04:52,320
+بتقول
+
+52
+00:04:52,320 --> 00:04:59,540
+the value of a determinant the value of a
+
+53
+00:04:59,540 --> 00:05:13,690
+determinant determinant of an upper أو lower أعلى 
+
+54
+00:05:13,690 --> 00:05:14,590
+أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+55
+00:05:14,590 --> 00:05:16,650
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+56
+00:05:16,650 --> 00:05:22,830
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+57
+00:05:22,830 --> 00:05:23,190
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+58
+00:05:23,190 --> 00:05:23,290
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+59
+00:05:23,290 --> 00:05:23,850
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+60
+00:05:23,850 --> 00:05:24,770
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+61
+00:05:24,770 --> 00:05:26,610
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+62
+00:05:26,610 --> 00:05:34,730
+أعلى أو أعلى أو أعلى أو أعلى أو أعلى أو
+
+63
+00:05:34,730 --> 00:05:41,070
+أعلى أو أعلى أو أعلى أو
+
+64
+00:05:46,710 --> 00:05:54,890
+الـ triangular matrix  من الـ triangular matrix  من الـ
+
+65
+00:05:54,890 --> 00:05:57,450
+triangular matrix من الـ triangular matrix من الـ triangular
+
+66
+00:05:57,450 --> 00:05:58,170
+matrix من الـ triangular matrix من الـ triangular
+
+67
+00:05:58,170 --> 00:06:00,430
+matrix من الـ triangular matrix من الـ triangular
+
+68
+00:06:00,430 --> 00:06:00,510
+matrix من الـ triangular matrix من الـ
+
+69
+00:06:00,510 --> 00:06:09,830
+triangular matrix 
+
+70
+00:06:15,470 --> 00:06:21,010
+show that بيُثبت
+
+71
+00:06:21,010 --> 00:06:30,330
+أن المحدد تبع 2 1 -3 0 -1
+
+72
+00:06:30,330 --> 00:06:40,700
+3 0 0 -2 يساوي المحدد تبع 2
+
+73
+00:06:40,700 --> 00:06:49,520
+0 0 0 -1 0 0 0 -2
+
+74
+00:06:49,520 --> 00:06:56,980
+يساوي 2 0 0 1 -1 0 0
+
+75
+00:06:56,980 --> 00:07:02,770
+3 - نرجع للـ remark اللي احنا كاتبينه بيقول لي
+
+76
+00:07:02,770 --> 00:07:08,170
+قيمة محدد الـ Upper Triangle Matrix أو الـ Lower
+
+77
+00:07:08,170 --> 00:07:12,430
+Triangle Matrix Upper Triangle Matrix يبقى العناصر
+
+78
+00:07:12,430 --> 00:07:16,350
+تحت القطر الرئيسي أصفار Lower Triangle Matrix
+
+79
+00:07:16,350 --> 00:07:21,730
+يبقى العناصر أعلى القطر الرئيسي أصفار المصوفتين
+
+80
+00:07:21,730 --> 00:07:26,800
+الأثنين هذول أو الـ Diagonal Matrix المصفوفة القطرية
+
+81
+00:07:26,800 --> 00:07:30,460
+يعني اللي عناصرها أعلى القطر الرئيسي و أسفل القطر
+
+82
+00:07:30,460 --> 00:07:34,680
+الرئيسي كله أصفار شو بده يساوي هذا؟ is the
+
+83
+00:07:34,680 --> 00:07:37,080
+product of the interest of the mind بيقول إن هو
+
+84
+00:07:37,080 --> 00:07:43,160
+حاصل ضرب عناصر القطر الرئيسي يعني المصوفات التلاتة
+
+85
+00:07:43,160 --> 00:07:48,400
+بدل المجعد أحسب المحدد لكل واحدة فيهم أقول فك
+
+86
+00:07:48,400 --> 00:07:51,800
+باستخدام كذا و لا لأ بصدر بعناصر القطر الرئيسي وخل
+
+87
+00:07:51,800 --> 00:07:55,950
+عنك يعني اللي قال لو بدي أجي لمحدد المصورة دي بدي
+
+88
+00:07:55,950 --> 00:07:58,890
+أقول له 2 في -1 في -2 يبقى
+
+89
+00:07:58,890 --> 00:08:03,210
+الجواب قداش؟ 4 هنا بدي أقول له 2 في -
+
+90
+00:08:03,210 --> 00:08:06,610
+1 في -2 يبقى برضه 4 وهنا 2 في
+
+91
+00:08:06,610 --> 00:08:10,490
+-1 في -2 يبقى الجواب 4 هيك بدي
+
+92
+00:08:10,490 --> 00:08:16,110
+أقوله بس أنا بدي أبين صحة هذا الكلام قبل كل شيء
+
+93
+00:08:16,430 --> 00:08:22,170
+يبقى أنا لو جيت أحل هذا الكلام بقول الحل كالتالي
+
+94
+00:08:22,170 --> 00:08:28,150
+يبقى solution بدا أجي للمحدد الأول إني أتأكد أفكه
+
+95
+00:08:28,150 --> 00:08:34,230
+باستخدام عناصر الصف الأول و لا العمود الأول العمود
+
+96
+00:08:34,230 --> 00:08:38,070
+الأول ليش في النص صفرين بحتاج هجمع يبقى بقول زي
+
+97
+00:08:38,070 --> 00:08:43,550
+0 زي 0 خلاصنا يبقى باجي بقول هذا 2 و
+
+98
+00:08:43,550 --> 00:08:49,230
+باجي بشطب صفه و عموده بظل قداش اللي هو المحدد
+
+99
+00:08:49,230 --> 00:08:56,300
+اللي عندنا هذا صح؟ يبقى الرئيسي ناقصي ثانوي يبقى
+
+100
+00:08:56,300 --> 00:09:03,720
+الرئيسي ناقص 1 في مين في -2 ناقص 0
+
+101
+00:09:03,720 --> 00:09:08,900
+يبقى قداش بيطلع يحصل ضرب عناصر القطر الرئيسي و لا
+
+102
+00:09:08,900 --> 00:09:15,960
+لا مظبوط يبقى هذا قداش بده يساوي بده يساوي 4 طبعا
+
+103
+00:09:15,960 --> 00:09:20,520
+اللي بعده 0 في محدده 0 في محدده 0 يبقى
+
+104
+00:09:20,520 --> 00:09:25,520
+هنا بدي أقوله هذا جابله هيك يبقى هذا ناقص 0 اللي
+
+105
+00:09:25,520 --> 00:09:32,260
+بعده ناقص 0 زائد 0 يبقى النتيجة بتساوي قداش
+
+106
+00:09:32,260 --> 00:09:40,580
+4 بعد ذلك بالداجي للمحدد الثاني باستخدام الصف
+
+107
+00:09:40,580 --> 00:09:44,580
+الأول و الله العمود الأول سِيان مش كله نفس الشيء
+
+108
+00:09:44,580 --> 00:09:51,870
+يبقى بالداجي أقول له هذا 2 فري أوشطب بصفه و
+
+109
+00:09:51,870 --> 00:09:57,330
+عموده بظل عندنا الرئيسي -1 في -2
+
+110
+00:09:57,330 --> 00:10:05,300
+ناقص 0 واللي بعده ناقص 0 زائد 0 يبقى كده
+
+111
+00:10:05,300 --> 00:10:11,080
+أشهده بدي يعطيني؟ كذلك 4 اللي بعده التالت يبقى
+
+112
+00:10:11,080 --> 00:10:16,740
+بداجي أفكه باستخدام أصر الصف الأول يبقى هذا 2
+
+113
+00:10:16,740 --> 00:10:21,880
+فيه طال الليل لوشطب بصفه وعمدة بيظل -1 فـ -
+
+114
+00:10:21,880 --> 00:10:28,600
+2 ناقص 0 يبقى -1 فـ -2 ناقص
+
+115
+00:10:28,600 --> 00:10:32,950
+0 كل اللي بعدهنقل نقل نقل نقل نقل نقل نقل نقل
+
+116
+00:10:32,950 --> 00:10:34,550
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+117
+00:10:34,550 --> 00:10:43,550
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+118
+00:10:43,550 --> 00:10:49,330
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+119
+00:10:49,330 --> 00:10:54,270
+نقل نقل نقل
+
+120
+00:10:55,520 --> 00:11:00,220
+يبقى إذا كانت المصوفة diagonal matrix أو upper and
+
+121
+00:11:00,220 --> 00:11:04,680
+lower triangle matrix على طول الخط مش تقعد تكتب و
+
+122
+00:11:04,680 --> 00:11:08,560
+هتقولي قيمة المحدد يساوي حاصل ضرب عناصر القطر الرئيسي و
+
+123
+00:11:08,560 --> 00:11:11,680
+بتروح تضرب عناصر القطر الرئيسي في بعض و خلاص يعني
+
+124
+00:11:11,680 --> 00:11:14,720
+بيبقى تقولي لي هنا 2 في -1 -2 و
+
+125
+00:11:14,720 --> 00:11:17,860
+ما تكتبيش لا محددات ولا .. بتقولي قيمة المحدد يساوي
+
+126
+00:11:17,860 --> 00:11:24,160
+كذا هذا لو كانت upper triangle أو Lower Triangle أو
+
+127
+00:11:24,160 --> 00:11:30,740
+Diagonal Matrix فقط لغير ما خلت ذلك كلامنا غير صحيح
+
+128
+00:11:30,740 --> 00:11:37,380
+و هذا لا يكون إلا لمصفوفة مربعة تمام إلى هنا stop
+
+129
+00:11:37,380 --> 00:11:42,200
+exercises ليكن أرقام المسائل exercises 2 8
+
+130
+00:11:42,200 --> 00:11:49,570
+يبقى exercises 2 8 المسائل التالية السؤال
+
+131
+00:11:49,570 --> 00:11:58,500
+الأول و السؤال الثاني D و F و G و بعد ذلك إسرائيلي
+
+132
+00:11:58,500 --> 00:12:07,760
+التالت C و D و E بعد ذلك إسرائيلي السادس و إسرائيلي
+
+133
+00:12:07,760 --> 00:12:19,880
+السابع B و C و بعد ذلك إسرائيلي الثامن A و D و بعد ذلك
+
+134
+00:12:19,880 --> 00:12:26,620
+من 9 لغاية 13 يبقى هذه الأمثلة مطلوب تتدربي
+
+135
+00:12:26,620 --> 00:12:34,600
+عليها من الكتاب بنجي لـ section 2 9 اللي هو الـ
+
+136
+00:12:34,600 --> 00:12:39,860
+properties of 
+
+137
+00:12:39,860 --> 00:12:45,000
+determinants
+
+138
+00:12:47,900 --> 00:12:51,880
+يبقى خواص المحددات طبعا هذه الخواص خدتها في
+
+139
+00:12:51,880 --> 00:12:55,700
+الثانوية العامة بس بالعربي احنا بدنا نكرر هذه
+
+140
+00:12:55,700 --> 00:13:01,620
+الخواص ثماني مرات ثانية بس بدنا نكتبها بالانجليزي
+
+141
+00:13:01,620 --> 00:13:06,420
+طبعا بعض البنات استغربوا 8 خواص 8 خواص ويمكن
+
+142
+00:13:06,420 --> 00:13:09,580
+يكونوا يفرضوهم ويخلوهم 10 في الثانوية لكن احنا
+
+143
+00:13:09,580 --> 00:13:15,310
+بنختصرهم في 8 خواص الخاصية الأولى فبالي بيجي
+
+144
+00:13:15,310 --> 00:13:24,870
+بقول فالـ A is a square matrix مصفوفة مربعة  ذِين
+
+145
+00:13:24,870 --> 00:13:31,770
+الخاصية الأولى الـ determinant للـ A transpose
+
+146
+00:13:31,770 --> 00:13:40,510
+يساوي الـ determinant لمين للـ A for
+
+147
+00:13:40,510 --> 00:13:41,150
+example
+
+148
+00:13:45,320 --> 00:13:51,240
+المحدد لمصفوفة أيه؟ بدي أحط مثلا 3 في 3
+
+149
+00:13:51,240 --> 00:13:57,860
+يبقى البنات هناك يلا 2 3 1 0
+
+150
+00:13:57,860 --> 00:14:06,260
+1 2 4 0 0 تمام؟ هذا محدد بدي أجيب
+
+151
+00:14:06,260 --> 00:14:10,500
+له determined بدي أجيب له الـ transpose تبعه و أخد
+
+152
+00:14:10,500 --> 00:14:16,000
+له المحدد يبقى هذا الـ transpose الصف الأول بدي
+
+153
+00:14:16,000 --> 00:14:21,080
+يصير العمود الأول الصف الثاني بدي يصير العمود
+
+154
+00:14:21,080 --> 00:14:27,520
+الثاني الصف الثالث بدي يصير معه العمود الثالث
+
+155
+00:14:27,520 --> 00:14:33,680
+هذول المحددين الاثنين are equal بنقدر نستنتج بمجرد
+
+156
+00:14:33,680 --> 00:14:38,090
+النظر إن هذول المحددين ما زي كيف؟ لو بدأ فك هذا
+
+157
+00:14:38,090 --> 00:14:41,750
+باستخدام عناصر الصف في الثالث طبعا 0 في المحدد
+
+158
+00:14:41,750 --> 00:14:45,050
+و 0 بـ 0 بيضل 4 بس في المحدد واش بيضل
+
+159
+00:14:45,050 --> 00:14:50,990
+صف و عمود بيضل مين؟ بيضل المحدد هذا مظبوط؟ 4
+
+160
+00:14:50,990 --> 00:14:55,470
+في قيمة هذا نجي هذا لو روحت كتب باستخدام عناصر
+
+161
+00:14:55,470 --> 00:15:01,810
+العمودي الثالث يبقى 4 و نشطب بصف و عمود بيضل
+
+162
+00:15:01,810 --> 00:15:07,860
+هذا تمام؟ طيب هذا المحدد اللي هو 3 في 2
+
+163
+00:15:07,860 --> 00:15:13,780
+زائد 1 يبقى 7 في 4 وين 7 في 4
+
+164
+00:15:13,780 --> 00:15:19,400
+بـ 28 نجي لها دي هي 4 هي 6 زائد
+
+165
+00:15:19,400 --> 00:15:22,980
+1 7 في 4 بـ 28 يبقى على كل
+
+166
+00:15:22,980 --> 00:15:28,500
+الأمر كله 28 يبقى الـ A هو الـ
+
+167
+00:15:28,500 --> 00:15:31,560
+determinant للـ A transpose هو الـ determinant
+
+168
+00:15:31,560 --> 00:15:35,780
+لمين للـ A يعني لو جينا المصفوفة و جينا مدور
+
+169
+00:15:35,780 --> 00:15:40,940
+المصفوفة و أخذنا محدد المصفوفة A و محدد مدور
+
+170
+00:15:40,940 --> 00:15:46,060
+المصفوفة بلاج الاثنين are equal لا تتغير هذه
+
+171
+00:15:46,060 --> 00:15:56,180
+الخاصية الأولى الخاصية الثانية if every element إذا 
+
+172
+00:15:56,180 --> 00:16:11,180
+كان كل عنصر in a row في أي صف أو عمود في صف أو
+
+173
+00:16:11,180 --> 00:16:18,620
+عمود of a is zero then 
+
+174
+00:16:21,770 --> 00:16:27,650
+الـ determinant للـ A بده يساوي كده؟ بده يساوي 0
+
+175
+00:16:27,650 --> 00:16:37,730
+for example كمثال على ذلك لو أخدت بدي أخلي أحد
+
+176
+00:16:37,730 --> 00:16:44,290
+الصفوف أو أحد الأعمدة أصفار يبقى بدالي أقول 2
+
+177
+00:
+
+201
+00:19:35,360 --> 00:19:40,520
+is multiplied by a number C يعني ضربنا الـC في أحد 
+
+202
+00:19:40,520 --> 00:19:44,160
+الصفوف يعني في جميع العناصر اللي موجودة فيها
+
+203
+00:19:44,160 --> 00:19:48,760
+الصفوف أو أحد الأعمدة في جميع عناصر أحد الأعمدة
+
+204
+00:19:49,090 --> 00:19:53,850
+then the determinant of the resulting matrix محدد 
+
+205
+00:19:53,850 --> 00:19:58,230
+المصفوفة الناتجة equal to C في الـdeterminant لـA
+
+206
+00:19:58,230 --> 00:20:02,430
+كانوا بيقولوا يخلوا الـC برا ويجيبوا المحدد لحاله
+
+207
+00:20:02,430 --> 00:20:06,890
+ويضربوا في الـC اه ايش معنى هذا الكلام استنوا
+
+208
+00:20:06,890 --> 00:20:13,070
+شوية معنى هذا الكلام أنه لو ضربت رقم في محدد يبقى
+
+209
+00:20:13,070 --> 00:20:18,410
+هذا الرقم بدي أضربه في جميع عناصر المحدد ولا بس في 
+
+210
+00:20:18,410 --> 00:20:19,750
+صف أو عمود
+
+211
+00:20:23,270 --> 00:20:27,930
+في صف أو عمود بس في المصفوفة إذا ضربت رقم في 
+
+212
+00:20:27,930 --> 00:20:32,310
+مصفوفة بضربه في جميع عناصر المصفوفة بلا استثناء
+
+213
+00:20:32,310 --> 00:20:36,830
+لكن في حالة المحدد بتضرب رقم في محدد بتضربه فقط
+
+214
+00:20:36,830 --> 00:20:42,210
+في أحد الصفوف أو أحد الأعمدة اللي يعجبك فيهم
+
+215
+00:20:42,210 --> 00:20:46,890
+وبالتالي ما عندهاش مشكلة وبالتالي لو عندي مقدار
+
+216
+00:20:46,890 --> 00:20:51,470
+مشترك أو رقم مشترك بين عناصر أي صف أو عناصر أي
+
+217
+00:20:51,470 --> 00:20:55,690
+عمود فيجب نقول خده برا بصير كأنه مضروب في كل
+
+218
+00:20:55,690 --> 00:21:02,950
+المحدد اه يعني هذا بقدر اكتبه يساوي ايه المحدد؟
+
+219
+00:21:02,950 --> 00:21:07,690
+ايه رأيك نضربه في الصف التاني؟ تاني او العمود
+
+220
+00:21:07,690 --> 00:21:10,690
+التالت أو العمود الأول أو اصلا ايه اللي بديه كده و
+
+221
+00:21:10,690 --> 00:21:14,550
+ايه كل واحدة تضرب في شكلها هذا بيعتبر تلات اصول تلات
+
+222
+00:21:14,550 --> 00:21:18,350
+عمليات ستة كل واحدة تضرب بشكل وتطلع النتيجة هتلاقي
+
+223
+00:21:18,350 --> 00:21:23,050
+كلهم يسووا بعض تمام؟ إذا هذا الكلام بده يسوي لو 
+
+224
+00:21:23,050 --> 00:21:27,850
+ضربت في العمود الأول بيصير ستة سالب تلاتة سالب
+
+225
+00:21:27,850 --> 00:21:32,630
+تسعة وهنا تلاتة زيرو واحد واحد اتنين سالب اتنين
+
+226
+00:21:32,630 --> 00:21:41,060
+شكل اناه يبقى لو ضربت رقم في محدد هذا بضربه في أحد
+
+227
+00:21:41,060 --> 00:21:45,100
+الصفوف أو أحد الأعمدة اللي يجي في بالك ضربه فيه
+
+228
+00:21:45,100 --> 00:21:52,320
+وفي المقابل لو كان عندي عامل مشترك بين أحد الأعمدة
+
+229
+00:21:52,320 --> 00:21:57,120
+أو أحد الصفوف بقدر أعمل مشترك أطلعه برا المحدد
+
+230
+00:21:57,120 --> 00:22:01,340
+فمثلا لو أنا شايف هنا ما عيش خبر هذي وجهت هذي في
+
+231
+00:22:01,340 --> 00:22:07,080
+بينهم عامل مشترك في تلاتة وفي سالب تلاتة كمان يعني
+
+232
+00:22:07,080 --> 00:22:11,320
+أنا ممكن بدل تلاتة اخد سالب تلاتة وأروح اقولك هذا
+
+233
+00:22:11,320 --> 00:22:17,580
+يساوي سالب تلاتة في المحدد بيظل هنا كده هـ سالب
+
+234
+00:22:17,580 --> 00:22:23,340
+اتنين تلاتة واحد بيظل هنا واحد وبيظل هنا zero
+
+235
+00:22:23,340 --> 00:22:29,120
+اتنين وبيظل هنا تلاتة وهنا واحد وهنا سالب اتنين
+
+236
+00:22:29,680 --> 00:22:34,840
+هي عندك تلات محددات في الكهادة لحد في الكهادة لحد
+
+237
+00:22:34,840 --> 00:22:38,120
+وضربيه تلاتة في الكهادة وضربيه في سلب تلاتة كله
+
+238
+00:22:38,120 --> 00:22:43,480
+بدي أطلع نفسي الإجابة يبقى إذا ضربت عدد في محدد
+
+239
+00:22:43,480 --> 00:22:47,660
+بضرب بس في أحد الصفوف أو أحد الأعمدة إذا بدي أعمل
+
+240
+00:22:47,660 --> 00:22:52,500
+العملية العكسية لو في عمل مشترك من أحد الصفوف أو
+
+241
+00:22:52,500 --> 00:22:57,500
+أحد الأعمدة باخده برا ايه عشان برا المحدد دي .. دي 
+
+242
+00:22:57,500 --> 00:22:57,980
+اية
+
+243
+00:23:01,080 --> 00:23:05,440
+عامل مشترك وضربته في صف عمود يعني واحد تاني غير
+
+244
+00:23:05,440 --> 00:23:08,540
+إن أنا اخد منه راح يطلع نفس الشيء صحيح بتقول
+
+245
+00:23:08,540 --> 00:23:13,080
+زميلاتكم ما يأتي افترض اني اخدت انا عامل مشترك هنا
+
+246
+00:23:13,080 --> 00:23:17,860
+اخدته من مين اخدته من العمود الأول بدروح اضربه في 
+
+247
+00:23:17,860 --> 00:23:23,230
+الصف التاني تضرب في الصف الثاني، مظبوط ولا لا؟ هل 
+
+248
+00:23:23,230 --> 00:23:27,470
+ستتغير قيمة المحدد؟ لا، اضرب في أي صف يعمد اللي
+
+249
+00:23:27,470 --> 00:23:31,150
+بدك يا، كل واحدة تضرب بشكل وروح أحسب النتيجة زي ما
+
+250
+00:23:31,150 --> 00:23:38,170
+كنا بنحسبه قبل قليل، كله سيعطيني نفس النتيجة ننتقل
+
+251
+00:23:38,170 --> 00:23:46,370
+الآن إلى الخاصية الرابعة، الخاصية الرابعة بتقول 
+
+252
+00:23:46,370 --> 00:23:46,630
+F
+
+253
+00:23:50,880 --> 00:24:02,560
+two rows or columns إذا عندي صفين أو عمودين إذا
+
+254
+00:24:02,560 --> 00:24:08,280
+عندي صفين أو عمودين إذا عندي صفين أو عمودين إذا
+
+255
+00:24:08,280 --> 00:24:08,300
+عندي صفين او عمودين اذا عندي صفين او عمودين اذا
+
+256
+00:24:08,300 --> 00:24:08,540
+عندي صفين أو عمودين إذا عندي صفين أو عمودين اذا
+
+257
+00:24:08,540 --> 00:24:15,840
+عندي صفين أو عمودين إذا عندي صفين أو عم
+
+258
+00:24:21,140 --> 00:24:34,280
+determinant of the resulting matrix محدد المصوفة
+
+259
+00:24:34,280 --> 00:24:40,380
+النتيجة equals equals
+
+260
+00:24:40,380 --> 00:24:48,920
+to minus the determinant لل A for example
+
+261
+00:25:11,730 --> 00:25:17,970
+الخاصية دي يا بنات بتقول لو بدلت صف مكان صف أو عمود
+
+262
+00:25:17,970 --> 00:25:22,810
+مكان عمود يبقى في هذه الحالة بتتفضل قيمة المحدد كم
+
+263
+00:25:22,810 --> 00:25:28,530
+هي بس بتجيبها من اشارة سالب فقط لا غير طلعي لي هنا
+
+264
+00:25:28,530 --> 00:25:33,790
+هاي ناقص اتنين ستة خمسة هنبدل أي صف بدك يا أو أي
+
+265
+00:25:33,790 --> 00:25:39,150
+عمود حب نبدل أي صف ولا أي عمود صف ولا عمود صف صف
+
+266
+00:25:39,150 --> 00:25:40,490
+صف صف صف صف صف صف صف صف صف صف صف صف صف صف صف صف
+
+267
+00:25:40,490 --> 00:25:43,750
+صف صف صف صف صف صف صف صف صف صف صف صف صف صف صف صف
+
+268
+00:25:43,750 --> 00:25:44,640
+صف صف صف صف صف صف صف صف صف صف صف صف صفبتاني
+
+269
+00:25:44,640 --> 00:25:49,580
+ومين؟ والتالت .. الثاني والتالت يبقى هذا بالضبط
+
+270
+00:25:49,580 --> 00:25:55,040
+بدي يساوي سالب الأول زي ما هو هي ستة خمسة وهي اتنين
+
+271
+00:25:55,040 --> 00:26:01,060
+ناقص خمسة واحد وهي واحد زيرو وتلاتة المحدد هذا هو 
+
+272
+00:26:01,060 --> 00:26:05,600
+نفس القيمة اللي عندها دي بس بإشارة سالب طب كيف بدي
+
+273
+00:26:05,600 --> 00:26:12,850
+أتأكد؟ good exercise لك روح احسب للمحدد هذا والمحدد
+
+274
+00:26:12,850 --> 00:26:18,770
+الثاني هتلاقي نفس القيمة بس بإشارة مخالفة طيب
+
+275
+00:26:18,770 --> 00:26:28,090
+النقطة الخامسة النقطة الخامسة if two rows if two
+
+276
+00:26:28,090 --> 00:26:36,790
+rows or columns إذا كان عندي صفين أو عمودين of
+
+277
+00:27:01,180 --> 00:27:11,940
+المحدد تلاتة أربعة واحد زيرو أو هنا zero على هذا
+
+278
+00:27:11,940 --> 00:27:20,820
+التلاتة هنا zero هنا اتنين هنا zero واحد خمسة واحد
+
+279
+00:27:25,720 --> 00:27:31,400
+ماشي بقول ليه؟ بقول إذا تساوى صفاني أو عمودان فإن
+
+280
+00:27:31,400 --> 00:27:36,780
+قيمة المحدد تساوي zero في عندي صفين متساوين أو
+
+281
+00:27:36,780 --> 00:27:41,980
+عمودين متساوية؟ اه عندنا العمود الأول والعمود
+
+282
+00:27:41,980 --> 00:27:47,260
+الثالث هذا العمود وهذا العمود هذول اتنين مالهم
+
+283
+00:27:47,260 --> 00:27:57,780
+بساووا بعض إذا قيمة المحدد يساوي zero نتكدلأ مكفك
+
+284
+00:27:57,780 --> 00:28:03,360
+سنة قبل هذا دوري يبقى بدأ أفكه باستخدام عناصر
+
+285
+00:28:03,360 --> 00:28:08,840
+الصف الثاني ليش إن فيها صفار كتير يبقى بقوله هاي 
+
+286
+00:28:08,840 --> 00:28:15,560
+سالب zero الأولاني اللي بعده زائد اتنين في أشط
+
+287
+00:28:15,560 --> 00:28:23,690
+بصفه وأشط بعموده بيظل تلاتة ناقص تلاتة يبقى تلاتة
+
+288
+00:28:23,690 --> 00:28:28,330
+ناقص تلاتة واللي بعده ناقص زيرو في محدد بزيرو يبقى
+
+289
+00:28:28,330 --> 00:28:33,750
+الجواب كده؟ يساوي زيرو يبقى إذا تساوى صفاني أو
+
+290
+00:28:33,750 --> 00:28:39,310
+عموداني في محدد فإن قيمة هذا المحدد تساوي صفرا
+
+291
+00:28:39,310 --> 00:28:43,890
+الخاصية السادسة بقول any determinant
+
+292
+00:28:52,120 --> 00:28:59,480
+can be written as
+
+293
+00:28:59,480 --> 00:29:14,000
+some كمجموع of two determinants كمجموع
+
+294
+00:29:14,000 --> 00:29:17,100
+محددين for example
+
+295
+00:29:21,530 --> 00:29:35,450
+لو عندي المحدد a b زائد اتنين c x y ناقص واحد z l
+
+296
+00:29:35,450 --> 00:29:44,030
+m زائد تلاتة k يبقى دا يساوي
+
+297
+00:29:46,960 --> 00:29:51,980
+هذا محدد بقدر اكتب على شكل مجموع محددين كيف كان
+
+298
+00:29:51,980 --> 00:30:10,240
+التالي a b c x y z l l m k z العمودين هذول زي ما
+
+299
+00:30:10,240 --> 00:30:18,710
+هما ايش زي مهمة يعني axl العمودي التاني ينظل اتنين هو
+
+300
+00:30:18,710 --> 00:30:23,570
+سالب واحد وتلاتة يبقى اتنين وسالب واحد وتلاتة
+
+301
+00:30:23,570 --> 00:30:30,230
+للبعده czk ايش
+
+302
+00:30:30,230 --> 00:30:37,490
+قصدك تقول قصد أقول ما يأتي طالعلك كويس إن لو عندي
+
+303
+00:30:37,490 --> 00:30:45,050
+محدد بقدر اكتبه على شكل مجموع محددين بمسك أي عمود
+
+304
+00:30:45,050 --> 00:30:50,530
+منهم أو أي صف وبجزئه إلى جزئين والصفين التانيات
+
+305
+00:30:50,530 --> 00:30:55,730
+أو العمودين التانيين بظلوا ثابتين لا يتغيروا يعني
+
+306
+00:30:55,730 --> 00:30:58,730
+أنا مسكته وحاطط ايه بس يعني لو قلتلك مثلا أعطيته
+
+307
+00:30:58,730 --> 00:31:05,930
+أرقام أرقام وليس زي ما نكتب يعني مثلا لو جيت قلتلك
+
+308
+00:31:05,930 --> 00:31:12,010
+أنا عندي المحدد اتنين تلاتة Zero واحد ناقص واحد
+
+309
+00:31:12,010 --> 00:31:20,790
+خمسة تلاتة ناقص اتنين وهي Zero كويس؟ بدي اكتبه على
+
+310
+00:31:20,790 --> 00:31:27,990
+شكل مجموع محددين اه بقدر اكتبه يساوي تختار إن نفصل
+
+311
+00:31:27,990 --> 00:31:33,510
+مين؟ مين من الأعمدة هذه؟ الأول ما .. الثاني الثاني
+
+312
+00:31:33,510 --> 00:31:36,670
+يا عزيزي ما نبديش نقارن نخليه ازاي بالحرف الواحد
+
+313
+00:31:36,670 --> 00:31:39,750
+يعني القرآن لا أي واحد من الاعمال اخد اللي بدي اكتر
+
+314
+00:31:39,750 --> 00:31:45,310
+فترضي الأول يبقى الأول بدي اكتب واحد وتلاتة و
+
+315
+00:31:45,310 --> 00:31:52,470
+Zero وواحد وناقص واحد وخمسة وهذا واحد مثلا و
+
+316
+00:31:52,470 --> 00:31:57,890
+ناقص اتنين وZero يبقى العمودين التانية تثبتهم كما
+
+317
+00:31:57,890 --> 00:32:03,170
+هم يبقى زاد العمود الأول هذا اتنين خات من واحد جدش
+
+318
+00:32:03,170 --> 00:32:08,710
+بظال واحد الصفين العمودين التانية زي ما هما هذا
+
+319
+00:32:08,710 --> 00:32:13,200
+خات من واحد جدش بظال واحد واحد أخدت من واحد بيظل
+
+320
+00:32:13,200 --> 00:32:18,620
+كده؟ بيظل Zero تمام سالب واحد وخمسة زي ما هو
+
+321
+00:32:18,620 --> 00:32:24,160
+التلاتة أخدت من واحد كده؟ بيظل اتنين ناقص اتنين
+
+322
+00:32:24,160 --> 00:32:29,420
+Zero احس بقيمة المحدد هذا واحس بقيمة المحددين
+
+323
+00:32:29,420 --> 00:32:34,400
+اتنين التانيات بتلاقي الاتنين are the same أو كما
+
+324
+00:32:34,400 --> 00:32:38,260
+قالت إحدى كنا قبل قليل good exercise
+
+325
+00:32:41,750 --> 00:32:46,990
+أنا بهمن تعرف الخاصية وليس تعرف تجيب مثال عليها
+
+326
+00:32:46,990 --> 00:32:53,650
+أنا بهمن الخاصية in general يبقى دي كانت الخاصية
+
+327
+00:32:53,650 --> 00:32:59,230
+السادسة نيجي للخاصية السابعة الخاصية السابعة بتقول
+
+328
+00:32:59,230 --> 00:33:04,490
+ما يأتي بتقول if a multiple of
+
+329
+00:33:11,300 --> 00:33:19,440
+one row or column إذا كان مضاعفات أي صفر عمول of a
+
+330
+00:33:19,440 --> 00:33:37,320
+matrix A of a matrix A is added is added ضعافنا to
+
+331
+00:33:37,320 --> 00:33:37,880
+another
+
+332
+00:33:43,990 --> 00:33:48,770
+to produce مشان
+
+333
+00:33:48,770 --> 00:34:01,530
+ينتجوا عندنا a matrix B then determinant
+
+334
+00:34:01,530 --> 00:34:05,030
+للـA بدي يساوي determinant للـB
+
+335
+00:34:15,310 --> 00:34:21,410
+إجراء الخاصية كويس أظن كنا بنعمل هذه في عملية الصف
+
+336
+00:34:21,410 --> 00:34:26,870
+البسيطة بنقول لا يتغير حل الـsystem مظبوط؟ بجي
+
+337
+00:34:26,870 --> 00:34:31,250
+نضرب أي معادلة في رقم ونضيفه لصف ثاني وبالتالي
+
+338
+00:34:31,250 --> 00:34:36,590
+ما كانش بيحصل لنا أي تغير دي بجي نقول إذا ضربت أي
+
+339
+00:34:36,590 --> 00:34:41,850
+صف أو أي عمود في رقم وأضفته إلى صف ثاني أو عمود
+
+340
+00:34:41,850 --> 00:34:48,930
+ثاني فلا تتغير قيمة المحدد طلع لي هنا ش بقول if a
+
+341
+00:34:48,930 --> 00:34:54,270
+multiple of one row or كل إذا كان مضاعفات أي صف أو
+
+342
+00:34:54,270 --> 00:34:57,950
+عمود ضربنا في اتنين في تلاتة في عشرة في ناقص خمسة
+
+343
+00:34:57,950 --> 00:35:03,570
+زي ما بدك of a matrix is added to another يعني أنا
+
+344
+00:35:03,570 --> 00:35:07,250
+جيت على المصفوفة ومسكت أحد الصفوف وضربت في رقم
+
+345
+00:35:07,250 --> 00:35:12,370
+أو أحد الأعمدة وضربت في رقم وأضفته إلى صف آخر أو
+
+346
+00:35:12,370 --> 00:35:17,670
+عمود آخر يبقى قيمة المحدد تبع المصفوفة الأصلية
+
+347
+00:35:17,670 --> 00:35:22,750
+والمصفوفة الجديدة اتنين زي بعض ي added to another
+
+348
+00:35:22,750 --> 00:35:27,410
+يعني إذا ضربت في صف بضيفه لصف آخر ليس بضرورة
+
+349
+00:35:27,410 --> 00:35:30,470
+الصف اللي بعده واللي بعده يمكن اللي بعده بعده أو
+
+350
+00:35:30,470 --> 00:35:34,610
+ما بعده بعده حيفا تمام يبقى ليس اللي وراه مباشرة
+
+351
+00:35:34,610 --> 00:35:40,650
+ممكن تبعد شوية ما عندناش مشكلة Matrix A is added to
+
+352
+00:35:40,650 --> 00:35:45,110
+another to produce A number B then determinant ل A
+
+353
+00:35:45,110 --> 00:35:51,070
+بده يساوي determinant ل B يبقى محدد المصفوفة A يساوي 
+
+354
+00:35:51,070 --> 00:35:56,850
+محدد B يعني ضرب أي صف في رقم وإضافته إلى صف آخر أو
+
+355
+00:35:56,850 --> 00:36:01,580
+ضرب أي عمود في رقم وإضافته إلى عمود آخر لا يغير من 
+
+356
+00:36:01,580 --> 00:36:06,720
+قيمة محدد المصفوفة الناتجة هذه اللي بتقوله هذه
+
+357
+00:36:06,720 --> 00:36:13,140
+الخاصية الخاصية الثامنة والأخيرة بتقول ما يأتي
+
+358
+00:36:13,140 --> 00:36:26,320
+بتقول if الـA والـB are both matrices are both
+
+359
+00:36:27,020 --> 00:36:35,600
+matrices كانت تنتهي من صفوفات of order n اثنين
+
+360
+00:36:35,600 --> 00:36:45,440
+مرات بانونية then determinant للـA في الـB يساوي 
+
+361
+00:36:45,440 --> 00:36:53,880
+الـdeterminant للـA في الـdeterminant للـB for
+
+362
+00:36:53,880 --> 00:37:06,790
+example كمثال على ذلك if الـA تساوي واحد اتنين ناقص
+
+363
+00:37:06,790 --> 00:37:17,030
+اتنين تلاتة and الـB بدها تساوي zero تلاتة ناقص 
+
+364
+00:37:17,030 --> 00:37:20,430
+واحد ناقص واحد then
+
+365
+00:37:29,180 --> 00:37:33,840
+خلي بالكامل يبقى الخاصية بتقول ليش بتقول لو عندي 
+
+366
+00:37:33,840 --> 00:37:38,000
+مصوفتين A وB من نفس النظام أو من نفس الـsize الـ
+
+367
+00:37:38,000 --> 00:37:41,500
+order لهم يساوي n then determinant للـA في B
+
+368
+00:37:41,500 --> 00:37:45,700
+بيبقى يساوي determinant للـA في B يعني محدد حاصل
+
+369
+00:37:45,700 --> 00:37:52,520
+ضرب مصوفتين يساوي حاصل ضرب المحدد دايما تماما يبقى
+
+370
+00:37:52,520 --> 00:37:58,430
+لو أنا جيت أخدت الـA في الـB يبقى بالداجة اقول له 
+
+371
+00:37:58,430 --> 00:38:03,990
+واحد اتنين ناقص اتنين ت
+
+401
+00:42:17,050 --> 00:42:23,270
+example consider the
+
+402
+00:42:23,270 --> 00:42:28,070
+set لواحد 
+
+403
+00:42:28,070 --> 00:42:38,410
+واتنين تلاتة أربعة خمسة take the permutation take
+
+404
+00:42:38,410 --> 00:42:39,510
+the
+
+405
+00:42:42,670 --> 00:42:57,490
+Permutation خلي الpermutation علي 
+
+406
+00:42:57,490 --> 00:43:02,050
+بالك هنا احنا الآن ماخدين الpermutation اللي
+
+407
+00:43:02,050 --> 00:43:06,130
+عندنا بدي اخذ تبديلة منها اختار التبديلة اللي بدك 
+
+408
+00:43:06,130 --> 00:43:11,540
+اياها يلا واحد قولي التبديل اللي تعجبك يلا هي
+
+409
+00:43:11,540 --> 00:43:16,380
+الأرقام قدامك بدل زي ما بدك تلاتة ايوه تلاتة و
+
+410
+00:43:16,380 --> 00:43:24,120
+واحد واحد خمسة خمسة ايوه اربعة اربعة اربعة اربعة
+
+411
+00:43:24,120 --> 00:43:24,220
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+412
+00:43:24,220 --> 00:43:24,380
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+413
+00:43:24,380 --> 00:43:26,060
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+414
+00:43:26,060 --> 00:43:32,020
+اربعة اربعة اربعة
+
+415
+00:43:32,020 --> 00:43:40,040
+اربعة اربعة in a permutation are interchange يعني
+
+416
+00:43:40,040 --> 00:43:44,660
+بدلت اتنين هدول مكان بعض والباقي باقية كما هو
+
+417
+00:43:44,660 --> 00:43:48,680
+then the parity of the permutation even ولا odd
+
+418
+00:43:48,680 --> 00:43:52,040
+is exchanged يعني ايش؟ اذا كانت الpermutation
+
+419
+00:43:52,040 --> 00:43:56,200
+الأصلية even لجديدة، odd واذا كانت الأصلية odd
+
+420
+00:43:56,200 --> 00:44:00,260
+لجديدة، even دعونا نشوف الحين اخذنا ال
+
+421
+00:44:00,260 --> 00:44:03,800
+permutation، هبتدي اعرف هذي even ولا odd؟ يبقى
+
+422
+00:44:03,800 --> 00:44:10,600
+بتروح اخذله Alpha 1 يساوي كده؟ 2 يبقى اخذله Alpha 
+
+423
+00:44:10,600 --> 00:44:16,580
+2 بـ 0 يبقى اخذله Alpha 3 بـ 2 يبقى اخذله Alpha 4
+
+424
+00:44:16,580 --> 00:44:23,640
+بـ 1 مظبوط؟ يبقى هذا الآن Alpha 1 زي Alpha 2 زي
+
+425
+00:44:23,640 --> 00:44:31,780
+Alpha 3 زي Alpha 4 يساوي 2 زي 0 زي 2 زي 1 يساوي 5
+
+426
+00:44:32,590 --> 00:44:38,230
+يبقى الpermutation هذي ايش؟ odd يبقى هذي odd
+
+427
+00:44:38,230 --> 00:44:43,730
+permutation طيب
+
+428
+00:44:43,730 --> 00:44:48,990
+روح اخترلك اي رقمين منها بس اتنين بشرط يكونوا ورا
+
+429
+00:44:48,990 --> 00:44:53,290
+بعض مش هجيب واحد من الأول وواحد من الآخر مين؟
+
+430
+00:44:55,160 --> 00:44:59,420
+خمسة واربعه بتقول زميلتكم بتاخدوا الرقمين هدول
+
+431
+00:44:59,420 --> 00:45:04,700
+بقولها كويس يبقى باجي بقوله and الpermutation
+
+432
+00:45:04,700 --> 00:45:08,320
+تلاتة واحد اربعة خمس اتنين
+
+433
+00:45:12,700 --> 00:45:18,340
+بعد التلاتة يبقى واحد واتنين ما فيش غير اتنين Alpha 
+
+434
+00:45:18,340 --> 00:45:24,640
+2 تساوي Zero Alpha 3 تساوي واحد Alpha 4 تساوي واحد
+
+435
+00:45:25,980 --> 00:45:31,280
+يبقى الان بالداجي لهدول اللي عندنا يبقى بالداجي
+
+436
+00:45:31,280 --> 00:45:36,780
+اخذ الف واحد زاد الف اتنين زاد الف تلاتة زاد الف
+
+437
+00:45:36,780 --> 00:45:41,220
+اربعة اتنين زاد زيرو زاد واحد زاد واحد يسوي كده؟
+
+438
+00:45:41,220 --> 00:45:45,480
+أربعة يبقى أصبحت الpermutation هذه 
+
+439
+00:45:51,670 --> 00:45:57,790
+اللي هي تلاتة أو واحد أو أربعة أو خمس أو اتنين is
+
+440
+00:45:57,790 --> 00:46:03,870
+even يبقى يا بنات لو غيرتي بس عنصر يكونوا اتنين
+
+441
+00:46:03,870 --> 00:46:10,670
+ورا بعض غيرتيهم على طول الخط بصير ايش؟ بصير القدر
+
+442
+00:46:10,670 --> 00:46:15,130
+بتنقلب even ولو كانت even بتنقلب odd ضايل علينا
+
+443
+00:46:15,130 --> 00:46:22,080
+سطر واحد فقط لغير الملاحظة التالية بقول remember
+
+444
+00:46:22,080 --> 00:46:30,740
+that تذكر
+
+445
+00:46:30,740 --> 00:46:42,280
+أن if الـ A is an n by n matrix مصموم مربع نظامها 
+
+446
+00:46:42,280 --> 00:46:49,260
+n في m بس بشرط upper or lower
+
+447
+00:46:52,570 --> 00:47:03,210
+A triangle A triangle matrix then
+
+448
+00:47:03,210 --> 00:47:06,450
+determinant
+
+449
+00:47:06,450 --> 00:47:18,650
+لل A بده يساوي A11 A22 A3 A3 ANN
+
+450
+00:47:24,450 --> 00:47:29,590
+لا يزال عندنا مجموعة من الأمثلة للمرة القادمة نعطي 
+
+451
+00:47:29,590 --> 00:47:33,830
+هذه الأمثلة وننهي هذا ال section يعطيكم العافية 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6bd78216627c66e6ceaa4bdf0148616edb16e6e9
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA.srt
@@ -0,0 +1,1974 @@
+1
+00:00:20,670 --> 00:00:27,070
+بسم الله الرحمن الرحيم يسعدنا أن نرحب بكم في
+
+2
+00:00:27,070 --> 00:00:32,550
+بداية هذا الفصل الدراسي الجديد وهو الفصل الثاني من 
+
+3
+00:00:32,550 --> 00:00:40,040
+العام 2012-2013 هذه المادة التي هي مادة معدلات وجبر 
+
+4
+00:00:40,040 --> 00:00:47,920
+خطي هي عبارة عن أربع ساعات يعني تسجل في كشف درجاتك 
+
+5
+00:00:47,920 --> 00:00:52,140
+أربع ساعات طبعًا التي تجيب فوق التسعين بتضمن أن 
+
+6
+00:00:52,140 --> 00:00:56,720
+المعدل سيظل عاليًا دائمًا وأبدًا لأن هذه أربع ساعات
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+7
+00:00:56,720 --> 00:01:01,840
+مش ساعة ولا ساعتين فلما تجيب فيها فوق التسعين بتظل 
+
+8
+00:01:01,840 --> 00:01:05,470
+المعدلُها عاليًا دائمًا أو أبدًا وأنتم غالبكم بنات
+
+9
+00:01:05,470 --> 00:01:10,150
+كلية الهندسة يبقى حرصي على أن تكوني في هذا المستوى
+
+10
+00:01:10,150 --> 00:01:13,590
+لأن مستواكم في الثانوية العامة كان مستوى عاليًا 
+
+11
+00:01:13,590 --> 00:01:16,530
+والشغل في الجامعة يختلف عن الشغل في المرحلة 
+
+12
+00:01:16,530 --> 00:01:21,130
+الثانوية وأنتم درستم قبل هيك سنة عندنا وهذه هي 
+
+13
+00:01:21,130 --> 00:01:25,230
+السنة الثانية أو هذا هو الفصل الرابع الذي كنا في 
+
+14
+00:01:25,230 --> 00:01:30,600
+هذه الجامعة التي لم يكن لبعضنا أكثر من ذلك لكن
+
+15
+00:01:30,600 --> 00:01:35,300
+هذه التي هي الحالة المثالية لذلك أحرصنا على 
+
+16
+00:01:35,300 --> 00:01:41,280
+الدراسة بشكلٍ سليمٍ أنا أحب أن أذكر من باب قول الله
+
+17
+00:01:41,280 --> 00:01:47,080
+تعالى "واذكر فإن الذكرى تنفع المؤمنين" أحب أن أذكر
+
+18
+00:01:47,080 --> 00:01:54,740
+بكيفية الدراسة أولًا قبل أن نبدأ في الموضوعات ال...
+
+19
+00:01:54,740 --> 00:01:59,500
+بالنسبة للدراسة حتى تدرسي دراسةً سليمةً وتجيبي
+
+20
+00:01:59,500 --> 00:02:04,980
+علامات أنا بشرح المحاضرة تفصيليًا على اللوح وأفتح
+
+21
+00:02:04,980 --> 00:02:09,940
+المجال للأسئلة لمن أرادت أن تسأل بل بطلب منكنّ
+
+22
+00:02:09,940 --> 00:02:13,980
+أحيانًا أنكنّ تسألن بقول من عندها سؤال من بتحب 
+
+23
+00:02:13,980 --> 00:02:19,240
+تسأل ليه سؤال حتى نخرج وقد استفدنا أو فهمنا ما قيل 
+
+24
+00:02:19,240 --> 00:02:24,140
+أمامنا على السبورة هنا شرحنا الموضوع شرحًا كاملًا
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+25
+00:02:24,140 --> 00:02:31,990
+مطلوب منّا ندرس المحاضرة فور الذهاب إلى البيت إن
+
+26
+00:02:31,990 --> 00:02:36,530
+أجلناها لبكرة بصير بدها وقت ضعف وإن أجلناها لآخر 
+
+27
+00:02:36,530 --> 00:02:42,830
+الأسبوع بدنا وقت أضعاف الوقت الذي أخذناه أو الكلام
+
+28
+00:02:42,830 --> 00:02:46,410
+الذي نذاكره اليوم يعني الأربع ساعات ممكن تروح في
+
+29
+00:02:46,410 --> 00:02:49,730
+البيت تجريها في نصف ساعة أو في ساعة وربع وتكون 
+
+30
+00:02:49,730 --> 00:02:53,970
+قراءتك للمحاضرة كاملة واستوعبتيها لكن إذا بتخليها 
+
+31
+00:02:53,970 --> 00:02:58,230
+لنهاية الأسبوع من نصف ساعة أو ساعة وربع لعلها تحتاج 
+
+32
+00:02:58,230 --> 00:03:04,150
+إلى أربع ساعات يبقى لا تؤجلي عمل اليوم إلى الغد لأن
+
+33
+00:03:04,150 --> 00:03:08,910
+هذه الساعات ليست تراكمًا وأنا في الأسبوع أعطيكِ أربع 
+
+34
+00:03:08,910 --> 00:03:12,070
+ساعات في المادة فما بالك بغيرها لما يعطيكِ أستاذ 
+
+35
+00:03:12,070 --> 00:03:16,970
+ساعة وأستاذ ساعتين وأستاذ ثلاث ساعات وربما يكون عند
+
+36
+00:03:16,970 --> 00:03:22,070
+بعضكنّ أربع ساعات أخرى يبقى يتراكم الشيء علشان  و
+
+37
+00:03:22,070 --> 00:03:27,290
+إذا تراكم بصير من الصعب الدراسة يبقى يجب أن ندرس
+
+38
+00:03:27,290 --> 00:03:33,060
+أولًا بأول النقطة الثانية الدراسة ليست أن نقرأ
+
+39
+00:03:33,060 --> 00:03:36,560
+المحاضرة ونقرأ الأمثلة ونقول احنا تمام لا مش 
+
+40
+00:03:36,560 --> 00:03:42,000
+تمام يعني إذا اكتفيتِ بالمحاضرة والأمثلة ربما
+
+41
+00:03:42,000 --> 00:03:46,940
+تنجحي ربما لا أستطيع التأكيد لكن مشان تنجحي وتجيبي
+
+42
+00:03:46,940 --> 00:03:53,150
+درجات لازم تمسكي القلم وتحلي بيدكِ أنتنّ... وبعد
+
+43
+00:03:53,150 --> 00:03:56,470
+هيك هتصعب عليكِ بعض الأسئلة أن تصعب عليكِ بعض
+
+44
+00:03:56,470 --> 00:04:00,550
+الأسئلة تعالوا نقاشُنا بنجاوبكِ طبعًا عندي ساعات
+
+45
+00:04:00,550 --> 00:04:06,950
+مكتبية هقولكِ وهو ضرورةُ الذي هو دراسة المحاضرة فورًا
+
+46
+00:04:06,950 --> 00:04:11,610
+العودة إلى البيت ثم حلّ الأسئلة والتي يصعب عليكِ
+
+47
+00:04:11,610 --> 00:04:16,270
+إحنا موجودون تعالي بنناقشكِ فيه وبنتناقشُنا فيه حتى
+
+48
+00:04:16,270 --> 00:04:20,810
+إذا نقطة ما فهمتيهاش برضه تعالي اسألي فيها يعني
+
+49
+00:04:20,810 --> 00:04:24,450
+إذا ما قدرتيش تساوعي بها هنا أو في البيت تعالي
+
+50
+00:04:24,450 --> 00:04:28,330
+اسألينا فيها إحنا بنجاوبكِ إن شاء الله وتعالي و
+
+51
+00:04:28,330 --> 00:04:32,570
+لن نُبخل عليكِ بأي معلومة إن شاء الله وتباركي  و
+
+52
+00:04:32,570 --> 00:04:39,360
+تعالي بعد هيك وصلنا للامتحان فلما نصل للامتحان
+
+53
+00:04:39,360 --> 00:04:45,880
+علينا أن نأتي بنماذج من الامتحانات السابقة نطلع 
+
+54
+00:04:45,880 --> 00:04:50,880
+عليها بس مشان نعرف كيف نماذج الامتحانات أو كيف 
+
+55
+00:04:50,880 --> 00:04:55,020
+يُوضع نظام الامتحان وبالتالي ما نصير في صورة
+
+56
+00:04:55,020 --> 00:04:59,900
+الامتحان قبل أيّه قبل أن ندخل الامتحان مش نتفاجأ 
+
+57
+00:04:59,900 --> 00:05:04,540
+بشكلِه يوم الامتحان الذين يكونون مُتدربين ومأخذين 
+
+58
+00:05:04,540 --> 00:05:08,380
+احتياطاتنا الله سبحانه وتعالى بيعيدنا على النجاح
+
+59
+00:05:08,380 --> 00:05:14,880
+لأن الله تبارك وتعالى لا يضيع أجر من أحسن عمله
+
+60
+00:05:14,880 --> 00:05:19,560
+التي تحسن العمل الله سبحانه وتعالى بيعطيها الأجر 
+
+61
+00:05:19,560 --> 00:05:26,000
+ويرزقها النجاح بس بدك تعتمدي على الله أولًا وأخيرًا
+
+62
+00:05:26,000 --> 00:05:31,050
+مش على قراءتكِ الاجتهاد ضروري وهي من جانب الأخذ 
+
+63
+00:05:31,050 --> 00:05:35,630
+ بالأسباب ثم الاعتماد على الله يعني أنا بدلت كل 
+
+64
+00:05:35,630 --> 00:05:41,310
+جهدي وكل طاقتي في أني أستوعب أو أفهم أو أحل
+
+65
+00:05:41,310 --> 00:05:46,150
+المسائل وبعد ذلك برفع يدي إلى الله سبحانه وتعالى 
+
+66
+00:05:46,150 --> 00:05:51,010
+وخاصة في دُوري كل صلاة وأطلب من الله النجاح والله 
+
+67
+00:05:51,010 --> 00:05:56,260
+سبحانه وتعالى لن يخيب دعائكِ قوله تبارك ليس في مادة 
+
+68
+00:05:56,260 --> 00:06:01,680
+معدلات تفاضلية وجبر خطي وإنما في كل المساقات الأخرى
+
+69
+00:06:01,680 --> 00:06:07,120
+لأن هذا هو الأساس الصحيح للدراسة من خلال خبرتنا 
+
+70
+00:06:07,120 --> 00:06:13,170
+السابقة على مدى أكثر من عشرين عامًا في الجامعة
+
+71
+00:06:13,170 --> 00:06:18,010
+الإسلامية وعلى مدى أكثر من ثلاثين عامًا في حقل 
+
+72
+00:06:18,010 --> 00:06:23,370
+التدريس بنعطيكِ خبرتنا بسهولة بضيف شغلة بس لو قبل
+
+73
+00:06:23,370 --> 00:06:29,650
+تيجي حضرتِ الموضوع قرأته مثل قراءة الجريدة الواحد 
+
+74
+00:06:29,650 --> 00:06:32,610
+ما يجي جنرال بيطلع معه بس العناوين الرئيسية بس
+
+75
+00:06:32,610 --> 00:06:36,510
+التفاصيل ما يحفظهاش لكن العناوين الرئيسية بتضلها
+
+76
+00:06:36,510 --> 00:06:39,790
+راسخة يوم صار كذا كذا وكان الرد عليه كذا كذا 
+
+77
+00:06:39,790 --> 00:06:44,970
+يبقى احنا بنعطيها لكِ بس مشان تكوني... يعني يكون عندي 
+
+78
+00:06:44,970 --> 00:06:48,350
+خلفية شو احنا بنحكي فلو جيتي جاية اللي بتجي 
+
+79
+00:06:48,350 --> 00:06:53,780
+على المحاضرة وكنتِ يعني قرأتيها قراءة مرور الكرام
+
+80
+00:06:53,780 --> 00:06:57,820
+قراءة الجريدة بيكون شيء جاهز ما بديش هيك تجيني حافظة 
+
+81
+00:06:57,820 --> 00:07:02,320
+ولا حاجة بديكِ بس تعرفي شو الموضوع الذي نتحدث 
+
+82
+00:07:02,320 --> 00:07:09,500
+فيه المتابعة لها دور أساسي في تواصل المعلومات
+
+83
+00:07:09,500 --> 00:07:14,780
+والبناء زي ما أنتم شايفينه من خلال اسم المساق معادلة
+
+84
+00:07:14,780 --> 00:07:20,520
+تفاضلية وجبر خطي يبقى النص المقرر معادلة تفاضلية
+
+85
+00:07:20,520 --> 00:07:28,700
+والنص في الآخر جبر خطي هناخد six chapters تلاتة
+
+86
+00:07:28,700 --> 00:07:34,340
+معادلة تفاضلية وتلاتة جبر خطي سنبدأ أول شيء بـ
+
+87
+00:07:34,340 --> 00:07:38,220
+chapter واحد معادلة تفاضلية وهي المعادلة التفاضلية
+
+88
+00:07:38,390 --> 00:07:44,150
+من الرتبة الأولى بأنواعها المختلفة ثم بعد ذلك إلى
+
+89
+00:07:44,150 --> 00:07:49,350
+ثلاثة شابتر جبر خطي بصير أربعة وبعد ذلك بنرجع إلى 
+
+90
+00:07:49,350 --> 00:07:54,610
+شابترين معدلة تفاضلية بصير ستة وهذا هو المقرر في
+
+91
+00:07:54,610 --> 00:08:02,810
+هذا المساق نأتي الآن لاسم المساق اسم الكتاب المؤلف 
+
+92
+00:08:02,810 --> 00:08:07,750
+المساقات التي سندرسها في هذا الفصل إن شاء الله
+
+93
+00:08:07,750 --> 00:08:11,130
+تعالي الكتاب اسمه elementary differential
+
+94
+00:08:11,130 --> 00:08:17,390
+equations with linear algebra يبقى اسم الكتاب هو
+
+95
+00:08:17,390 --> 00:08:18,250
+elementary
+
+96
+00:08:27,420 --> 00:08:36,620
+Elementary Differential Equations
+
+97
+00:08:36,620 --> 00:08:42,740
+كلمة equations باختصرها إلى الأربع تعرف اللي عندنا 
+
+98
+00:08:42,740 --> 00:08:48,380
+يبقى elementary differential equations with linear
+
+99
+00:08:48,380 --> 00:08:49,040
+algebra
+
+100
+00:08:57,860 --> 00:09:05,440
+اسم المؤلف البرت البرت 
+
+101
+00:09:05,440 --> 00:09:07,140
+رامانستان 
+
+102
+00:09:27,120 --> 00:09:34,760
+الآن جايكي يبقى اسم الكتاب elementary differential
+
+103
+00:09:34,760 --> 00:09:40,200
+equations with linear algebra المؤلف اسمه البرت 
+
+104
+00:09:40,200 --> 00:09:45,260
+رابانستين الطبعة الرابعة يبقى باجي بقول هنا 
+
+105
+00:09:45,260 --> 00:09:51,880
+fourth edition يبقى
+
+106
+00:09:51,880 --> 00:09:58,510
+الطبعة الرابعة الكتاب موجود في مكتبة الطالب وهي 
+
+107
+00:09:58,510 --> 00:10:03,450
+الشكل تبعه طبعًا أنا مجلده hard cover لكن ماهو hard cover 
+
+108
+00:10:03,450 --> 00:10:07,730
+لأن hard cover بكلف أكثر فأنتم الكتاب
+
+109
+00:10:07,730 --> 00:10:11,850
+هي الجلدة الأساسية من برّا مش هالكلّ واحدة تشوفها بعد 
+
+110
+00:10:11,850 --> 00:10:15,970
+المحاضرة ممكنِ أنتِ تتوجهي إلى مكتبة الطالب وتشتري
+
+111
+00:10:15,970 --> 00:10:21,430
+هذا الكتاب لكن إن كان هناك أحد أقاربكِ أو واحدة من 
+
+112
+00:10:21,430 --> 00:10:25,830
+قريباتكِ كانت بتدرس المادة العام الماضي فالكتاب هو
+
+113
+00:10:25,830 --> 00:10:29,970
+هو لم يتغير لا العام الماضي ولا العام الذي قبله
+
+114
+00:10:29,970 --> 00:10:32,890
+يبقى نفس الكتاب بس الذي قبله كانت الطبعة التي
+
+115
+00:10:32,890 --> 00:10:36,510
+قبله لكن الطبعة الرابعة إن سنتين بندرس نفس 
+
+116
+00:10:36,510 --> 00:10:40,290
+الطبعة الرابعة يبقى هذا الشكل العام طبعًا أشكال
+
+117
+00:10:40,290 --> 00:10:44,590
+هندسية فرجار ومحايات وما بعرف إيه على الجلد هايم
+
+118
+00:10:44,590 --> 00:10:48,880
+تمام موجود في مكتبة الطالب بعد المحاضرة بإمكانكِ 
+
+119
+00:10:48,880 --> 00:10:53,260
+تروحي تشتري أو ما هي لذلك يبقى هذا بالنسبة لمن؟ 
+
+120
+00:10:53,260 --> 00:10:58,620
+بالنسبة للكتاب نيجي ندخل الآن في صميم الموضوعات
+
+121
+00:10:58,620 --> 00:11:03,880
+الخاصة بهذا الكتاب يبقى بدنا نيجي لأول chapter الذي
+
+122
+00:11:03,880 --> 00:11:06,940
+هو introduction to a differential equation يعني
+
+123
+00:11:06,940 --> 00:11:13,180
+مقدمة في المعادلات التفاضلية يبقى بعد ذلك بدنا
+
+124
+00:11:13,180 --> 00:11:18,420
+نيجي لأول chapter الذي هو chapter one بتكلم عن 
+
+125
+00:11:18,420 --> 00:11:23,560
+introduction مقدمة
+
+126
+00:11:23,560 --> 00:11:28,880
+to differential equations
+
+127
+00:11:31,050 --> 00:11:36,230
+يبقى مقدمة في المعادلات التفاضلية حنُعطي صورة 
+
+128
+00:11:36,230 --> 00:11:40,850
+عامة للمعادلات التفاضلية ونبدأ بأول نوع من هذه 
+
+129
+00:11:40,850 --> 00:11:45,090
+المعادلات التي هي المعادلات التفاضلية من الرتبة
+
+130
+00:11:45,090 --> 00:11:50,840
+الأولى first order differential equation من هذه
+
+131
+00:11:50,840 --> 00:11:55,580
+المعادلة أو تحت الرتبة الأولى هناخد عدة معادلات 
+
+132
+00:11:55,580 --> 00:12:00,200
+أول معادلة من هذه المعادلات التي هي الـ separable
+
+133
+00:12:00,200 --> 00:12:08,330
+equation separable equations يبقى المعادلات التي
+
+134
+00:12:08,330 --> 00:12:15,290
+يمكن فيها فصل المتغيرات إيش فصل المتغيرات يعني 
+
+135
+00:12:15,290 --> 00:12:20,690
+بنحاول نُخلي الـ X في ناحية والـ Y في ناحية أخرى
+
+136
+00:12:20,690 --> 00:12:25,930
+وبالتالي هذا نسميه فصل المتغيرات ثم نذهب إلى 
+
+137
+00:12:25,930 --> 00:12:32,890
+التكامل إذا موضوع المعادلات التفاضلية يعتمد فقط على
+
+138
+00:12:32,890 --> 00:12:38,910
+ما درسناه في Calculus A وB في موضوع التكامل مش
+
+139
+00:12:38,910 --> 00:12:43,310
+تكاملات صعبة ومعقدة لها تكاملات بسيطة وما إلى 
+
+140
+00:12:43,310 --> 00:12:47,670
+ذلك يعني التي نجحت بجدارة في Calculus A وB بتروح
+
+141
+00:12:47,670 --> 00:12:53,030
+تكامل A بسهولة يبقى الأساس تبع المادة هو موضوع 
+
+142
+00:12:53,030 --> 00:12:57,000
+التكامل لأن ما أقول differential equation معادلات 
+
+143
+00:12:57,000 --> 00:13:01,300
+تفاضلية يعني فيها أن معادلة ظهر فيها المشتقة 
+
+144
+00:13:01,300 --> 00:13:04,480
+الأولى أو المشتقة الثانية إذا التي ما بدها ترجعها إلى 
+
+145
+00:13:04,480 --> 00:13:09,460
+أصلها معناته بدها تكامل مرة أو مرتين أو نحو ذلك إذا
+
+146
+00:13:09,460 --> 00:13:15,700
+بالزمن موضوع التكامل مش على هذه بس في كل chapter
+
+147
+00:13:15,700 --> 00:13:19,860
+ساعات المعادلة التفاضلية بالزمن مين بالزمن موضوع 
+
+148
+00:13:19,860 --> 00:13:24,550
+التكامل بعد هيك بدنا نيجي للـ homogeneous equations
+
+149
+00:13:31,250 --> 00:13:37,210
+يبقى الـ homogeneous equations المعادلات المتجانسة
+
+150
+00:13:37,210 --> 00:13:42,670
+فيها صيغة من خلالها بنقدر نحكم على المعادلة هل هي 
+
+151
+00:13:42,670 --> 00:13:48,290
+separable وهل هي homogeneous طبعًا سنقول هذا الشرط
+
+152
+00:13:48,290 --> 00:13:52,550
+في حينه إن شاء الله بعد الـ homogeneous بدنا نيجي
+
+153
+00:13:52,550 --> 00:13:57,990
+للـ exact هذه exact equation طبعًا كمان فيها شرط
+
+154
+00:13:58,210 --> 00:14:01,890
+الشرط هذا لو تحقق بقول أن المعادلة هذه ما لها
+
+155
+00:14:01,890 --> 00:14:07,010
+exact equation بعد الـ exact equation بتداجي لمين
+
+156
+00:14:07,010 --> 00:14:15,270
+للـ linear equations المعادلات الخطية يبقى إليها 
+
+157
+00:14:15,270 --> 00:14:19,750
+شكل محدد بالشكل المحدد هذا لو شفتوا مجرد ما شوفوا
+
+158
+00:14:19,750 --> 00:14:23,270
+بقول هذه إيه معادلة خطية وبالتالي طريقة حل
+
+159
+00:14:23,270 --> 00:14:29,340
+المعادلة بالطريقة الفلانية بعد هيك بدنا نيجي لـ
+
+160
+00:14:29,340 --> 00:14:37,840
+two types of
+
+161
+00:14:37,840 --> 00:14:45,720
+second order differential
+
+162
+00:14:45,720 --> 00:14:48,400
+equations
+
+163
+00:14:52,970 --> 00:14:58,670
+هذا يا بنات إجمال ما سندرسه في الشابتر الأول يبقى
+
+164
+00:14:58,670 --> 00:15:02,770
+الشابتر الأول عبارة عن مجموعة من الـ sections طبعًا 
+
+165
+00:15:02,770 --> 00:15:07,270
+أكثر في الكتاب مش كلهم هندرسهم هندرس فقط الذي احنا
+
+166
+00:15:07,270 --> 00:15:11,770
+كاتبينه قدامنا على اللوح كل عنوان هنا يمثل section 
+
+167
+00:15:11,770 --> 00:15:15,290
+في الكتاب وفي نهاية الـ section فيه مجموعة من
+
+168
+00:15:15,290 --> 00:15:20,110
+الأسئلة هعطيكِ أمثلة إن شاء الله من خلال الأسئلة
+
+169
+00:15:20,110 --> 00:15:23,350
+تبع التمرين والأمثلة المحلولة في الكتاب هذه 
+
+170
+00:15:23,350 --> 00:15:27,570
+هدية إليك تقرأيها براحتك من الكتاب أنا بعطيكِ أمثلة
+
+171
+00:15:27,570 --> 00:15:31,750
+من خلال الأسئلة تبع التمرين وبالتالي قللت عدد 
+
+172
+00:15:31,750 --> 00:15:37,230
+الأسئلة المطلوب منكِ تحليها وبحاول أغطيلي كل الفكر 
+
+173
+00:15:37,230 --> 00:15:43,020
+الموجودة بحيثِ أنتِ ما تلاقيش صعوبة أثناء الحل يبقى 
+
+174
+00:15:43,020 --> 00:15:47,360
+أول section separable equations المعادلات التي 
+
+175
+00:15:47,360 --> 00:15:53,060
+يمكن فيها
+
+201
+00:17:55,380 --> 00:17:58,760
+الثانية إلى الرتبة الأولى وبالتالي بصير كانها
+
+202
+00:17:58,760 --> 00:18:03,540
+first order differential equation هذا كل ما يتعلق 
+
+203
+00:18:03,540 --> 00:18:07,760
+بالشابتر الأول اللي هو ال first order differential
+
+204
+00:18:07,760 --> 00:18:13,120
+equation بنجي الآن نخش في ال chapter الثاني وهو
+
+205
+00:18:13,120 --> 00:18:18,580
+بداية الجبر الخطي linear algebra يبقى بنجي لل
+
+206
+00:18:18,580 --> 00:18:23,300
+chapter الثاني ال chapter الثاني موضوعين أساسيين
+
+207
+00:18:23,300 --> 00:18:31,720
+matrices and determinants المصفوفات والمحددات يبقى 
+
+208
+00:18:31,720 --> 00:18:36,820
+matrices and
+
+209
+00:18:39,250 --> 00:18:46,070
+data منين أنت؟
+
+210
+00:18:46,070 --> 00:18:49,850
+يبقى
+
+211
+00:18:49,850 --> 00:18:58,400
+المصفوفات والمحددات طبعًا المصفوفات والمحددات لن يزيد
+
+212
+00:18:58,400 --> 00:19:02,360
+عما درستِ في الثانوية العامة مش في الثانوية أخذتِ
+
+213
+00:19:02,360 --> 00:19:07,940
+المصفوفات والمحددات أو بقى تسموه الجبر الإضافي غير 
+
+214
+00:19:07,940 --> 00:19:10,720
+الجبر العادي كان معكُم الجبر الإضافي أو الجبر
+
+215
+00:19:10,720 --> 00:19:14,960
+الخاص في الثانوية العامة ولا في تانية ثانوية؟ في
+
+216
+00:19:14,960 --> 00:19:19,570
+تانية؟ آه يعني درستِ فيها مرتين على أي حال في
+
+217
+00:19:19,570 --> 00:19:23,410
+التانية ولا في التالتة بتفرقش عنها المهم أنه سبق
+
+218
+00:19:23,410 --> 00:19:28,150
+الدراسة الثانية يبقى احنا بنذكرها من جديد وكأنك لم 
+
+219
+00:19:28,150 --> 00:19:33,830
+تدرسيها من قبل طب السؤال هو شو بدنا ندرس في موضوع
+
+220
+00:19:33,830 --> 00:19:40,550
+المصفوفات يبقى هذا هو الشابتر الثاني زي ما كان هذا 
+
+221
+00:19:40,550 --> 00:19:45,110
+هو الشابتر الأول يبقى أول موضوع سنأخذه في هذا 
+
+222
+00:19:45,110 --> 00:19:57,360
+الشابتر هو systems of linear equations
+
+223
+00:19:57,360 --> 00:20:00,460
+أنظمة
+
+224
+00:20:00,460 --> 00:20:05,640
+المعادلات الخطية إيش يعني أنظمة المعادلة الخطية
+
+225
+00:20:05,640 --> 00:20:11,960
+مثلًا قد تكون المعادلة فيها مجهولين وقد يكون بثلاثة 
+
+226
+00:20:11,960 --> 00:20:17,670
+مجاهيل وقد يكون بأربعة مجاهيل أو نحو ذلك زي إيش مثلًا
+
+227
+00:20:17,670 --> 00:20:26,650
+زي ما أجي أقول لك المعادلة هذه مثلًا a1x زائد a2y زائد 
+
+228
+00:20:26,650 --> 00:20:38,610
+a3z يساوي مثلًا ال oneA2X أو B1X
+
+229
+00:20:38,610 --> 00:20:51,650
+زائد B2Y زائد B3Z بده يساوي L2 مثلًا C1X زائد C2Y
+
+230
+00:20:51,650 --> 00:21:00,430
+زائد C3Z يساوي L3 هذا النظام المعادلات بسميه system
+
+231
+00:21:00,430 --> 00:21:05,470
+of linear equations يعني معادلة خطية شوية في ال X
+
+232
+00:21:05,470 --> 00:21:10,790
+و Y و Z اللي هو المجاهيل كلها من الدرجات الأولى
+
+233
+00:21:10,790 --> 00:21:15,470
+يبقى هذه بسميها معادلة خطية المعادلات مع بعض كل
+
+234
+00:21:15,470 --> 00:21:19,510
+ثلاثة مجموعة بسميها system of linear equations
+
+235
+00:21:19,510 --> 00:21:26,890
+يعني نظام مكون من مجموعة من المعادلات الخطية الـ A1
+
+236
+00:21:26,890 --> 00:21:30,370
+والـ A2 والـ A3 والـ B1 والـ B2 والـ B3 والـ C وكل 
+
+237
+00:21:30,370 --> 00:21:35,230
+هذه أرقام real numbers أرقام عادية لكن الـ X والـ
+
+238
+00:21:35,230 --> 00:21:39,850
+Y والـ Z هذه مجاهيل فلمّا بده أحل ال system يعني 
+
+239
+00:21:39,850 --> 00:21:44,670
+بده أجيب قيم هذه المجاهيل دير بالك ال system
+
+240
+00:21:44,670 --> 00:21:49,400
+المعادلات ليس بضرورة يكون ثلاث معادلات ويكون أربعة 
+
+241
+00:21:49,400 --> 00:21:53,980
+معادلات في ثلاثة مجاهيل ممكن يكون أربعة معادلات في 
+
+242
+00:21:53,980 --> 00:21:59,040
+أربعة مجاهيل ممكن يكون معادلتين في مجهولين ممكن 
+
+243
+00:21:59,040 --> 00:22:06,480
+يكون معادلتين في مجهولين وهكذا يعني ليس بضرورة
+
+244
+00:22:06,480 --> 00:22:10,240
+ثلاث مجاهيل ممكن مجهولين ممكن ثلاث ممكن أربعة 
+
+245
+00:22:10,240 --> 00:22:15,200
+ممكن خمسة إلى آخره يبقى هذا كله system في عندي أحد
+
+246
+00:22:15,200 --> 00:22:21,170
+ثلاثة احتمالات الاحتمال الأول يكون عندي حل واحدة 
+
+247
+00:22:21,170 --> 00:22:26,510
+ما فيش غيره حل واحد للثلاث معادلات ممكن يكون عندي
+
+248
+00:22:26,510 --> 00:22:32,350
+عدد لا نهائي من الحلول مش حل واثنين وثلاثة أو
+
+249
+00:22:32,350 --> 00:22:37,530
+أربعة لأ عدد لا نهائي من الحلول الأمر الثالث no 
+
+250
+00:22:37,530 --> 00:22:42,230
+solution أو الحل does not exist يبقى ال system 
+
+251
+00:22:42,230 --> 00:22:47,810
+المعادلة قد يكون حلا واحدة وقد يكون عدد لا نهائي من
+
+252
+00:22:47,810 --> 00:22:53,070
+الحلول وقد لا يوجد حل يبقى هي الاحتمالات الثلاثة 
+
+253
+00:22:53,070 --> 00:22:56,870
+بالنسبة لل system of linear equations وهذا ما 
+
+254
+00:22:56,870 --> 00:23:02,310
+سنجده عند دراسة هذا النوع من المعادلات الخطية
+
+255
+00:23:02,310 --> 00:23:06,170
+النقطة الثانية اللي سندرسها هي ال homogeneous
+
+256
+00:23:06,170 --> 00:23:13,830
+systems بعد هيك بدنا نيجي لحاجة اسمها Homo Genius
+
+257
+00:23:13,830 --> 00:23:16,090
+Systems
+
+258
+00:23:18,410 --> 00:23:21,650
+إيش يعني homogeneous system؟ طب ماهي homogeneous
+
+259
+00:23:21,650 --> 00:23:25,210
+system ماهي اللي فوق هذا system of linear
+
+260
+00:23:25,210 --> 00:23:28,470
+equations إيش يعني homogeneous system؟ باجي بقول
+
+261
+00:23:28,470 --> 00:23:34,530
+لو كانت الواحد والاثنين والثلاثة بيقى صفر
+
+262
+00:23:34,530 --> 00:23:38,890
+المعادلة الثلاثة أو الثنتين أو الأربع كلها معادلة
+
+263
+00:23:38,890 --> 00:23:45,060
+صفرية بسمي هذا homogeneous system يبقى لو كانت هذه 
+
+264
+00:23:45,060 --> 00:23:51,420
+كلها بأصفار يبقى هذا بسميه اللي هو ال homogenous
+
+265
+00:23:51,420 --> 00:23:59,220
+system ال system المتجانس تمام؟ يبقى هذه النقطة
+
+266
+00:23:59,220 --> 00:24:03,220
+الثانية اللي سندرسها وبعد هيك بدنا نيجي لحاجة 
+
+267
+00:24:03,220 --> 00:24:08,580
+اسمها matrices and
+
+268
+00:24:08,580 --> 00:24:10,320
+vectors
+
+269
+00:24:14,590 --> 00:24:22,560
+matrices يا بنات بنات مصفوفات هي جامعة matrix Matrix
+
+270
+00:24:22,560 --> 00:24:30,080
+هي مصفوفة جمعها matrices بشيل ال X وبحط CES يبقى
+
+271
+00:24:30,080 --> 00:24:35,320
+matrices مصفوفات Matrix عبارة عن مصفوفة vectors
+
+272
+00:24:35,320 --> 00:24:42,420
+يعني متجهات الصف الأول أو الصف الواحد أو العمود
+
+273
+00:24:42,420 --> 00:24:47,420
+الواحد من عناصر مصفوفة بسميه vector يبقى ال vector
+
+274
+00:24:47,420 --> 00:24:53,660
+هو عبارة عن مصفوفة عمودية أو مصفوفة أفقية تمام؟
+
+275
+00:24:53,660 --> 00:24:58,880
+يبقى هذه بسميها .. بسميها اللي هو ال vector مش 
+
+276
+00:24:58,880 --> 00:25:02,520
+vector اثنين I زي ثلاث جيه زي أربعة كيه سوى مثلًا
+
+277
+00:25:02,520 --> 00:25:07,420
+رقم زي ما أخذنا في ال calculus C لأ لأ لأ هذه ال
+
+278
+00:25:07,420 --> 00:25:10,580
+vector بيختلف عن ال vector هناك وليها دراستها 
+
+279
+00:25:10,580 --> 00:25:16,970
+متعلقة بموضوع المصوفات والمحددات بعد هيك بدنا نيجي 
+
+280
+00:25:16,970 --> 00:25:22,670
+لحاجة اسمها matrix multiplication
+
+281
+00:25:22,670 --> 00:25:28,530
+يبقى
+
+282
+00:25:28,530 --> 00:25:33,410
+عملية ضرب المصوفات طبعًا أخذنا ضرب المصوفات في 
+
+283
+00:25:33,410 --> 00:25:38,770
+الثانوية بدأينا نذكره ثاني ومشان أضرب مصوفتين في
+
+284
+00:25:38,770 --> 00:25:43,330
+بعض لازم أتحقق عندي شرط يعني مش أي مصوفتين بقوم
+
+285
+00:25:43,330 --> 00:25:48,370
+بضربهم في بعض لأ لابد يكون عدد الأعمدة في المصوفة
+
+286
+00:25:48,370 --> 00:25:54,270
+الأولى يساوي عدد الصفوف في المصوفة الثانية إن تحقق
+
+287
+00:25:54,270 --> 00:25:59,620
+ذلك بيكون بقدر أضرب المصوفتين ما هذول في بعض
+
+288
+00:25:59,620 --> 00:26:03,860
+وبالتالي المصوفتين ممكن ال system تبع الأولى يختلف
+
+289
+00:26:03,860 --> 00:26:07,620
+عن ال system تبع المصوفة لما أقول system بالنسبة 
+
+290
+00:26:07,620 --> 00:26:12,600
+للمصفوفة يعني عدد الصفوف في عدد الأعمدة يعني نوعية
+
+291
+00:26:12,600 --> 00:26:17,220
+المصفوفة ثلاث صفوف وعمودين عمودين وأربعة صفوف 
+
+292
+00:26:17,220 --> 00:26:23,700
+صفين وثلاثة أعمدة صفين وأربعة أعمدة يبقى هذا هو 
+
+293
+00:26:23,700 --> 00:26:29,500
+النظام تبع مين؟ تبع المصوفة أو بيبقى نقول نوعها M في 
+
+294
+00:26:29,500 --> 00:26:37,280
+N M رقم لعدد الصفوف N عدد الأعمدة وهكذا يبقى في 
+
+295
+00:26:37,280 --> 00:26:41,600
+شرط لازم أتحقق مشان أقدر أضرب المصوفتين هذول في 
+
+296
+00:26:41,600 --> 00:26:47,820
+بعض وبعد هيك some special matrices يبقى هنا some
+
+297
+00:26:47,820 --> 00:26:49,720
+special
+
+298
+00:26:52,090 --> 00:26:56,450
+بعض المصوفات الخاصة 
+
+299
+00:26:58,850 --> 00:27:01,930
+ماذا عن بعض المصفوفات الخاصة؟ هذه في الثانوية
+
+300
+00:27:01,930 --> 00:27:07,630
+وكنتُم مذكرين بجينا نقول أنواع المصفوفات types of
+
+301
+00:27:07,630 --> 00:27:13,430
+matrices بجينا نقول المصفوفة الصفرية مصفوفة الوحدة 
+
+302
+00:27:13,430 --> 00:27:19,170
+المصفوفة القياسية المصفوفة القطرية المصفوفة
+
+303
+00:27:19,170 --> 00:27:25,090
+المثلثة العليا المصفوفة المثلثة السفلى كل هذول
+
+304
+00:27:25,090 --> 00:27:29,000
+اللي بتسمعهم هذه هي أنواع المصفوفات يبقى نحن لم
+
+305
+00:27:29,000 --> 00:27:33,000
+نأتي بجديد هو الكلام اللي بتيجي بس بنذكره وبدل ما 
+
+306
+00:27:33,000 --> 00:27:37,340
+كنت تكتبيه بالعربي بنكتب هناك بالإنكليزي عادية يبقى 
+
+307
+00:27:37,340 --> 00:27:43,160
+لا توجد أي صعوبة أثناء الدراسة وخاصة اللي بتابع
+
+308
+00:27:43,160 --> 00:27:47,720
+الأول بأول يبقى للمُدرّس some special matrices بعض 
+
+309
+00:27:47,720 --> 00:27:52,740
+المصفوفات الخاصة يعني المصفوفات اللي لها اسم محدد 
+
+310
+00:27:52,740 --> 00:27:58,280
+مصفوفة صفرية مصفوفة قطرية مصفوفة قياسية مصفوفة
+
+311
+00:27:58,280 --> 00:28:03,140
+مربعة مصفوفة مستطيلة مصفوفة الوحدة مصفوفة مثلثة
+
+312
+00:28:03,140 --> 00:28:06,970
+عليا مصفوفة مثلثة ..so كله هنذكره ونعطي عليه
+
+313
+00:28:06,970 --> 00:28:12,410
+أمثلة إن شاء الله تعالى بعد ذلك بنجي ل
+
+314
+00:28:12,410 --> 00:28:15,370
+determinants المحددات 
+
+315
+00:28:22,890 --> 00:28:28,550
+الفرق بين الاثنين الكتابة متشابهة قريبة من بعض إلى 
+
+316
+00:28:28,550 --> 00:28:34,570
+حد بعيد لكن المصوفة لو ضربتيها في رقم أو ضربتِ
+
+317
+00:28:34,570 --> 00:28:39,970
+مصوفتين في بعض فالنتج هو مصفوفة لكن المحدد له
+
+318
+00:28:39,970 --> 00:28:45,440
+قيمة عددية واحدة one real number يعني المحدد له
+
+319
+00:28:45,440 --> 00:28:50,380
+قيمة حقيقية ما فيش غيرها يعني بقدر أفك المحدد وأ
+
+320
+00:28:50,380 --> 00:28:53,700
+أطلع قد إيش قيمته العددية ومن هنا هذا الفرق 
+
+321
+00:28:53,700 --> 00:28:58,020
+الأساسي بينه وبين المصوفة المصوفات لها خواص
+
+322
+00:28:58,020 --> 00:29:04,420
+المحددات لها خواص تختلف كذلك عن خواص من المصوفات
+
+323
+00:29:04,700 --> 00:29:09,400
+يبقى المصفوفات والمحددات كل واحدة فيهم لها خواص خاص
+
+324
+00:29:09,400 --> 00:29:15,060
+ة بها تختلف فيها عن الخواص الأخرى وفي الثانوية أخذتم
+
+325
+00:29:15,060 --> 00:29:20,380
+خواص المحددات وهنرجع نعطي خواص المحددات لـ
+
+326
+00:29:20,380 --> 00:29:25,220
+properties of determinants بعد هيك هنجي في
+
+327
+00:29:25,220 --> 00:29:29,300
+المحددات نأخذ حاجة اسمها cofactors
+
+328
+00:29:32,500 --> 00:29:39,000
+يعني العوامل المرافقة شو العوامل المرافقة؟ نذكركم
+
+329
+00:29:39,000 --> 00:29:43,820
+لما جينا نفك المحدد مثلًا نفكه باستخدام عناصر الصف 
+
+330
+00:29:43,820 --> 00:29:47,600
+اللي أول اللي بمسك هو العنصر نشطه بصفه وعموده
+
+331
+00:29:47,600 --> 00:29:54,320
+المحدد اللي بيظل بسميه المحدد الأصغر المناظر لهذا 
+
+332
+00:29:54,320 --> 00:29:58,700
+العنصر يبقى هذا هو ال cofactor اللي هو العامل
+
+333
+00:29:58,700 --> 00:30:03,420
+المرافق لمين؟ للعنصر اللي موجود في المحدد أنا بس
+
+334
+00:30:03,420 --> 00:30:07,740
+مجرد تذكير ليس إلا لكن عندما نوصله هنعطيه نشتغل
+
+335
+00:30:07,740 --> 00:30:12,800
+شغل تفصيلي وحسابات دقيقة إن شاء الله تبارك وتعالى
+
+336
+00:30:13,890 --> 00:30:20,230
+بعد هيك بدنا نيجي نتناول Cramer's rule قاعدة كرامر لحل 
+
+337
+00:30:20,230 --> 00:30:25,890
+المعادلات وكذلك طريقة معكوس المصفوفة نستخدمها في 
+
+338
+00:30:25,890 --> 00:30:29,710
+حل ال system of linear equations يبقى بدنا نيجي 
+
+339
+00:30:29,710 --> 00:30:40,410
+نأخذ حاجة اسمها Cramer's rule يبقى كرامر كرامر
+
+340
+00:30:40,410 --> 00:30:48,060
+رولقاعدة كرامر لحل المعادلات وبعد هيك بدنا نأخذ
+
+341
+00:30:48,060 --> 00:30:59,420
+the inverse of a matrix يبقى معكوس المصفوفة
+
+342
+00:30:59,420 --> 00:31:04,860
+واستخدام معكوس المصفوفة في حل المعادلات التفاضلية
+
+343
+00:31:05,610 --> 00:31:10,710
+هذا بالنسبة لمين؟ للشبتر الثاني يبقى كل اللي سمعته 
+
+344
+00:31:10,710 --> 00:31:16,270
+هو ملخص الشابتر الثاني الشابتر الثاني أكثر من عشر
+
+345
+00:31:16,270 --> 00:31:21,770
+سكاشن يعني طويل شوية مش زي الأول الأولاني الشابتر
+
+346
+00:31:21,770 --> 00:31:27,150
+الأول قصير هذا أطول منه كثيرًا بعد هيك كده بنجي
+
+347
+00:31:27,150 --> 00:31:33,830
+للشابتر الثالث يبقى بدنا نجي لحاجة اسمها vector
+
+348
+00:31:34,910 --> 00:31:43,510
+spaces and linear transformations
+
+349
+00:32:05,280 --> 00:32:11,780
+الفضاءات الاتجاهية والتحويلات الخطية يبقى vector
+
+350
+00:32:11,780 --> 00:32:15,700
+spaces الفضاءات الاتجاهية linear transformations
+
+351
+00:32:15,700 --> 00:32:22,460
+التحويلات الخطية موضوع يا أم كل واحد مستقل عن الثاني 
+
+352
+00:32:22,460 --> 00:32:27,980
+وهذا يعتبر ethical chapter موجود في المقرر يعني 
+
+353
+00:32:27,980 --> 00:32:33,940
+مليان شوية وبده متابعة أول بأول هنعطي تعريف ال
+
+354
+00:32:33,940 --> 00:32:38,520
+vector space في هذا ال chapter هنبدأ أول حاجة بال
+
+355
+00:32:38,520 --> 00:32:48,000
+vector spaces الفضاءات الاتجاهية بعدين نأخذ مجموعات
+
+356
+00:32:48,000 --> 00:32:53,120
+جزئية من هذه الفضاءات اسمها ال sub-spaces يبقى
+
+357
+00:32:53,120 --> 00:32:58,340
+بدنا نيجي لحاجة اسمها sub-spaces الفضاءات 
+
+358
+00:32:58,340 --> 00:33:02,640
+الاتجاهية يعني وقتش لما أخذ مجموعة جزئية من ال
+
+359
+00:33:02,640 --> 00:33:07,520
+vector space بقدر أقول عنها ال subspace وما كنتش 
+
+360
+00:33:07,520 --> 00:33:11,200
+بقدر أقول عنها ما هي ال subspace يعني نفترض لو 
+
+361
+00:33:11,200 --> 00:33:14,800
+قلنا البنات اللي قاعدتها دول كلهم عبارة عن vector
+
+362
+00:33:14,800 --> 00:33:19,020
+space لو أخذتِ الشجة هذه هل هذه subspace ولا لا 
+
+363
+00:33:19,020 --> 00:33:23,960
+الله أعلم يبقى في شروط إن تحققت هذه الشروط بقول 
+
+364
+00:33:23,960 --> 00:33:27,870
+هذه subspace إن اختل أي شرط من هذه الشروط يبقى ما
+
+365
+00:33:27,870 --> 00:33:31,150
+أقدرش أقول عن هذه subspace كل اللي بقدر أقول إنها
+
+366
+00:33:31,150 --> 00:33:36,250
+مجموعة جزئية subset مجموعة جزئية لكنها ليست
+
+367
+00:33:36,250 --> 00:33:47,070
+subspace طيب بعد هيك بنجي لحاجة اسمها linear بنجي
+
+368
+00:33:47,070 --> 00:33:51,450
+لحاجة اسمها linear dependence
+
+369
+00:33:56,360 --> 00:34:01,980
+and linear independence الاستقلال الخطي والاعتماد
+
+370
+00:34:01,980 --> 00:34:02,980
+الخطي
+
+371
+00:34:05,350 --> 00:34:11,590
+واجتِش مستقلات عن بعض خطيًا أو واجتِش معتمدات على
+
+372
+00:34:11,590 --> 00:34:17,810
+بعض خطيًا يبقى هذا بالنسبالك كله متعلق بمين؟ متعلق
+
+373
+00:34:17,810 --> 00:34:23,470
+بال vector spaces الاثنين على حد سواء بدنا نيجي 
+
+374
+00:34:23,470 --> 00:34:31,790
+لحاجة اسمها ال wronskian ال
+
+375
+00:34:31,790 --> 00:34:37,130
+wronskian دي بنت عبارة عن محدد determinant بس 
+
+376
+0
+
+401
+00:36:48,220 --> 00:36:51,160
+function من ال vector space الأول إلى ال vector 
+
+402
+00:36:51,160 --> 00:36:56,180
+space الثاني ولها شروط أن تحقق أو لها شرطين مش 
+
+403
+00:36:56,180 --> 00:37:00,920
+أكثر أن تحقق هذان الشرطان بقول عن هذه هي linear
+
+404
+00:37:00,920 --> 00:37:05,490
+transformation وهاد ال linear transformation لها 
+
+405
+00:37:05,490 --> 00:37:11,030
+خواص وشغل اللي هيكون منصب كله على الخواص يبقى 
+
+406
+00:37:11,030 --> 00:37:14,930
+بدنا نيجي لآخر نقطة موجودة في هاد ال section وهي 
+
+407
+00:37:14,930 --> 00:37:20,730
+properties of linear transformations
+
+408
+00:37:30,790 --> 00:37:41,430
+يبقى هذا كل ما سندرسه في ال chapter الثالث برضه
+
+409
+00:37:41,430 --> 00:37:44,650
+ال chapter هذا طويل بنات يعني chapter اثنين و
+
+410
+00:37:44,650 --> 00:37:50,190
+ثلاثة هما أطول two chapters في المقرر يبقى أخذنا 
+
+411
+00:37:50,190 --> 00:37:54,470
+chapterين جبر خطي chapter اثنين و chapter ثلاثة
+
+412
+00:37:54,470 --> 00:37:58,450
+ابنجي ل chapter أربعة اللي هو ال diagonalization
+
+413
+00:38:07,780 --> 00:38:11,960
+ال chapter هذا مش هنكتر عليكم بس two sections مش 
+
+414
+00:38:11,960 --> 00:38:17,140
+أكثر two sections طبعا هذا مرتبط بموضوع مين بموضوع 
+
+415
+00:38:17,140 --> 00:38:22,200
+ال vector spaces اللي قبله يبقى two sections أول
+
+416
+00:38:22,200 --> 00:38:25,020
+حاجة بدنا نيجي للحاجة اسمها ال characteristic 
+
+417
+00:38:25,020 --> 00:38:25,820
+values
+
+418
+00:38:34,130 --> 00:38:38,530
+القيم المميزة وبعد ذلك بنجي اليوميا لل
+
+419
+00:38:38,530 --> 00:38:46,670
+diagonalization أيه 
+
+420
+00:38:46,670 --> 00:38:49,910
+ال two sections ما فيش غيرهم أيش معناه diagonalization
+
+421
+00:38:49,910 --> 00:38:56,350
+الليمانات قطر ممتاز جدا يبقى diagonalization كيف 
+
+422
+00:38:56,350 --> 00:39:01,870
+بدي أعمل مصفوفة قطرية قطرية يعني أيه؟ أي شيء يعني 
+
+423
+00:39:01,870 --> 00:39:06,070
+مصفوفة مثلثة عليا أو سفلى يعني اللي فوق القطر 
+
+424
+00:39:06,070 --> 00:39:11,290
+الرئيسي صفر أو اللي تحت القطر الرئيسي صفر أو 
+
+425
+00:39:11,290 --> 00:39:14,610
+اللي فوق صفر واللي تحت صفر وما يضلش إلا من؟ 
+
+426
+00:39:14,610 --> 00:39:20,550
+عناصر القطر الرئيسي هذا كلمة دا هذا المعنى البلدي 
+
+427
+00:39:20,550 --> 00:39:23,970
+القريب إلى الفهم لمعنى ال diagonalization لكن 
+
+428
+00:39:23,970 --> 00:39:29,530
+تحتها بنشر خطوات رياضية كأني بدي أحول المصفوفة اللي 
+
+429
+00:39:29,530 --> 00:39:34,430
+عندنا إلى ال diagonal matrix في شغل بدنا نشتغله 
+
+430
+00:39:34,430 --> 00:39:39,330
+هذا ومن خلاله بكون جيب ال diagonalization لمام 
+
+431
+00:39:39,330 --> 00:39:43,700
+لهذه المصفوفة مش كل مصفوفة اللي هي diagonalization مش 
+
+432
+00:39:43,700 --> 00:39:48,160
+كل واحدة بنفعلها تمام يبقى في شروط لازم تتحقق مشان 
+
+433
+00:39:48,160 --> 00:39:53,180
+أقدر أعمل ال diagonalization لمصفوفة قبل هذه بدي 
+
+434
+00:39:53,180 --> 00:39:58,000
+أخد ال characteristic values اللي هي القيم و ال
+
+435
+00:39:58,000 --> 00:40:03,740
+characteristic vectors يعني المتجهات المميزة والقيم 
+
+436
+00:40:03,740 --> 00:40:08,500
+المميزة لهذه المصفوفة يبقى نقطتين فقط في هذا ال
+
+437
+00:40:08,500 --> 00:40:13,700
+chapter أو two sections فقط في هذا ال chapter على 
+
+438
+00:40:13,700 --> 00:40:18,280
+هيك بيكون انتهينا من الجبر الخطي يبقى أخذنا 
+
+439
+00:40:18,280 --> 00:40:24,060
+chapter معادلة تفاضلية و three chapters اللي هو 
+
+440
+00:40:24,060 --> 00:40:29,400
+جبر خطي يبقى هي قد إيش أربعة ظل قد إيش ضايل اثنين
+
+441
+00:40:29,400 --> 00:40:33,040
+اللي هم عبارة عن معادلات تفاضلية في ال chapter 
+
+442
+00:40:33,040 --> 00:40:37,940
+الأول بدأنا بالرتبة الأولى هنا بدنا ندرس الرتبة
+
+443
+00:40:37,940 --> 00:40:43,100
+الثانية الثالثة الرابعة إلى آخرها يبقى لو جينا ل
+
+444
+00:40:43,100 --> 00:40:50,660
+chapter خمسة chapter خمسة اسمه linear differential
+
+445
+00:40:50,660 --> 00:40:57,660
+equations linear differential equations طبعا يمكن 
+
+446
+00:40:57,660 --> 00:41:01,180
+واحدة تقولي متوسعة كتبنا linear equations هذه ال 
+
+447
+00:41:01,180 --> 00:41:04,900
+linear equations من ال first order هذه ال second 
+
+448
+00:41:04,900 --> 00:41:09,300
+order، third order، fourth order، nth order دي 
+
+449
+00:41:09,300 --> 00:41:11,840
+بيجمع الرتبة الثانية، الثالثة، الرابعة، الرتبة 
+
+450
+00:41:11,840 --> 00:41:15,400
+النونية لكن ال linear اللي أخذناها قبل شوية هذه هي 
+
+451
+00:41:15,400 --> 00:41:21,040
+من؟ من ال first order فقط لغير تحت هذا العنوان
+
+452
+00:41:21,040 --> 00:41:26,850
+بدنا ندرس عدة شغلات أول شيء بدنا نأخذ هو الـ
+
+453
+00:41:26,850 --> 00:41:33,290
+Homogeneous Equations هذه اختصار لكلمة homogeneous
+
+454
+00:41:33,290 --> 00:41:38,470
+بدا المكتوبة بالشكل الطويل هذا بقول هنا homogeneous
+
+455
+00:41:38,470 --> 00:41:45,630
+equations يبقى المعادلات المتجانسة المعادلات
+
+456
+00:41:45,630 --> 00:41:49,790
+المتجانسة مش المعادلات المتجانسة الأولية لأ من
+
+457
+00:41:49,790 --> 00:41:53,570
+الرتبة الثانية أو الثالثة الطرف اليميني يساوي صفرة
+
+458
+00:41:53,570 --> 00:41:58,850
+بقول المعادلة تساوي صفر من حد ما أشوف هيك بسميها
+
+459
+00:41:58,850 --> 00:42:03,700
+homogeneous طب لو ما كناش صفر كانت رقم بسميها الـ
+
+460
+00:42:03,700 --> 00:42:07,640
+Non-homogeneous differential equation يبقى الـ
+
+461
+00:42:07,640 --> 00:42:11,540
+homogeneous لها طريقة للحل والـ non-homogeneous
+
+462
+00:42:11,540 --> 00:42:17,080
+لها طريقة للحل الطريقة بتعتمد على حل ال
+
+463
+00:42:17,080 --> 00:42:23,750
+homogeneous طيب هنا هذه ال homogenous equations هذه 
+
+464
+00:42:23,750 --> 00:42:31,090
+ممكن أكثر من طريقة لمعرفة حل هذه المعادلة من ذلك
+
+465
+00:42:31,090 --> 00:42:37,850
+طريقة ال complex root الجذور التخيلية يبقى بداجي
+
+466
+00:42:37,850 --> 00:42:44,710
+لحاجة اسمها complex solutions complex solutions
+
+467
+00:42:46,330 --> 00:42:52,310
+الحلول المركبة وممكن
+
+468
+00:42:52,310 --> 00:43:03,010
+المعادلة تبقى equations with constant coefficients
+
+469
+00:43:03,010 --> 00:43:07,570
+يعني
+
+470
+00:43:07,570 --> 00:43:13,550
+المعادلة التفاضلية مثلا الـ A1 والـ A2 والـ A3
+
+471
+00:43:13,550 --> 00:43:19,510
+هدول ثوابت ممكن يكونوا ثوابت وممكن ما يكونوش ثوابت
+
+472
+00:43:19,510 --> 00:43:25,330
+إن كانوا ثوابت يبقى بسميها equations with constant 
+
+473
+00:43:25,330 --> 00:43:29,770
+coefficients بمعاملات ثابتة وبستخدمها ال complex 
+
+474
+00:43:29,770 --> 00:43:36,380
+solutions بالإضافة إلى بعض الطرق الأخرى لكن لو كانت
+
+475
+00:43:36,380 --> 00:43:41,320
+هذه المعادلة homogeneous equation لكن المعادلات ما
+
+476
+00:43:41,320 --> 00:43:47,420
+هيش ثوابت يبقى ممكن تحوير المعادلة إن كانت بصيغة 
+
+477
+00:43:47,420 --> 00:43:52,960
+محددة بحيث أضيع هذه المتغيرات وأقلبها إلى معادلة 
+
+478
+00:43:52,960 --> 00:43:58,260
+بمعاملات ثابتة وهذه اسمها Cauchy-Euler equations
+
+479
+00:43:58,260 --> 00:44:02,960
+يبقى بدنا نيجي لحاجة اسمها Cauchy-Euler equations
+
+480
+00:44:03,670 --> 00:44:11,290
+كوشي كوشي 
+
+481
+00:44:11,290 --> 00:44:13,810
+أويلر equations
+
+482
+00:44:19,450 --> 00:44:25,130
+معادلة مشهورة باسم الاتنين هذه المعادلة بيكون
+
+483
+00:44:25,130 --> 00:44:30,570
+مسبوقة المعامل تبعها بدلالة ال X الأس تبعه جد
+
+484
+00:44:30,570 --> 00:44:35,610
+الرتبة تبعت ال Y فنقول X تربيع Y Double Prime زائد
+
+485
+00:44:35,610 --> 00:44:40,230
+XY Prime زائد Constant يساوي مين؟ Constant في Y
+
+486
+00:44:40,230 --> 00:44:44,250
+يساوي Zero يبقى هذه اللي بيسمي الكوشيه Euler
+
+487
+00:44:44,250 --> 00:44:48,750
+Equation وحناخد طريقة كيف أحولها من معادلة 
+
+488
+00:44:48,990 --> 00:44:53,610
+بالمعاملات تبعتها متغيرة إلى معادلة بمعاملات ثابتة
+
+489
+00:44:53,610 --> 00:44:59,710
+وبعدين كيف أنحل هذا النوع من المعادلات بعد ذلك بدا
+
+490
+00:44:59,710 --> 00:45:03,130
+نيجي لـ Non-homogeneous يبقى أخذنا أول حاجة الـ
+
+491
+00:45:03,130 --> 00:45:08,750
+homogeneous بدا أجي لـ Non-homogeneous
+
+492
+00:45:08,750 --> 00:45:12,310
+differential equations
+
+493
+00:45:15,460 --> 00:45:17,800
+هنا الـ Non-homogeneous differential اللي كنا 
+
+494
+00:45:17,800 --> 00:45:24,400
+بياخد ثلاث طرق للحل ثلاث طرق لحل هذا النوع من
+
+495
+00:45:24,400 --> 00:45:30,320
+المعادلات الطريقة الأولى والطريقة الثانية والطريقة
+
+496
+00:45:30,320 --> 00:45:34,520
+الثالثة الطريقة الأولى اللي بناخدها طريقة 
+
+497
+00:45:34,520 --> 00:45:40,700
+المعاملات الثابتة فأول طريقة من هذه الطرق اللي هي
+
+498
+00:45:40,700 --> 00:45:44,300
+الـ Undetermined 
+
+499
+00:45:51,060 --> 00:45:56,620
+coefficients طريقة المعاملات المجهولة طريقة
+
+500
+00:45:56,620 --> 00:46:02,720
+الثانية variation of
+
+501
+00:46:02,720 --> 00:46:10,960
+parameters يعني 
+
+502
+00:46:10,960 --> 00:46:18,080
+طريقة تغيير المتغيرات طريقة الثالثة reduction of 
+
+503
+00:46:18,080 --> 00:46:28,440
+order reduction of order طريقة اختزال الرتبة يعني
+
+504
+00:46:28,440 --> 00:46:33,340
+كيف أنزل الرتبة من الرتبة الثانية إلى الرتبة الأولى
+
+505
+00:46:33,340 --> 00:46:39,420
+مثلا وبالتالي هي الطرق الثلاث في هذه الحالة يبقى 
+
+506
+00:46:39,420 --> 00:46:42,780
+في هذا الشبط راح نأخذ نوعين من المعادلات النوع 
+
+507
+00:46:42,780 --> 00:46:47,660
+الأول المعادلات المعاملات ثوابت النوع الثاني 
+
+508
+00:46:47,660 --> 00:46:52,780
+المعاملات متغيرة المعاملات المتغيرة يمكن تحويلها 
+
+509
+00:46:52,780 --> 00:46:58,120
+إلى معادلة homogeneous بمعاملات ثابتة وهذا لها
+
+510
+00:46:58,120 --> 00:47:02,740
+أكثر من طريقة للحل ال complex هو أحد العلوم بعد
+
+511
+00:47:02,740 --> 00:47:05,480
+ذلك يجب أن نصل إلى non homogeneous يعني الطرف اللي 
+
+512
+00:47:05,480 --> 00:47:10,520
+بين المعادلة يجب أن يكون دالة وليس zero يبقى هذا 
+
+513
+00:47:10,520 --> 00:47:15,040
+النوع من المعادلات له ثلاث طرق للحل الطريقة الأولى
+
+514
+00:47:15,040 --> 00:47:18,420
+طريقة ال undetermined coefficients المعاملات
+
+515
+00:47:18,420 --> 00:47:22,870
+المجهولة وطريقة الثانية طريقة ال variation of
+
+516
+00:47:22,870 --> 00:47:27,570
+parameters تغيير المتغيرات والحصول على هذه
+
+517
+00:47:27,570 --> 00:47:31,430
+المتغيرات في قد إيش قيمتها الطريقة الثالثة طريقة 
+
+518
+00:47:31,430 --> 00:47:35,490
+اختزال الرتبة أو تنزيل الرتبة من الرتبة الثانية 
+
+519
+00:47:35,490 --> 00:47:42,410
+إلى الرتبة الأولى يبقى هذا باختصار كل ما هو موجود 
+
+520
+00:47:42,410 --> 00:47:48,950
+في chapter 5 بنجي ل chapter 6 اللي هو Laplace 
+
+521
+00:47:51,030 --> 00:47:55,510
+هذا ليس chapter ستة هذه الواحدة خمسة هذا بنفط لبعض و
+
+522
+00:47:55,510 --> 00:48:00,690
+بروح ل chapter تسعة يبقى ال chapter السادس هو chapter تسعة 
+
+523
+00:48:00,690 --> 00:48:07,770
+يبقى ال chapter تسعة اللي هو Laplace transforms 
+
+524
+00:48:08,410 --> 00:48:15,950
+تحويلات لابلاس وما يتعلق بها وكيفية استخدامها في 
+
+525
+00:48:15,950 --> 00:48:23,450
+حل المعادلات التفاضلية وبعد هيك using Laplace 
+
+526
+00:48:23,450 --> 00:48:32,850
+transform to 
+
+527
+00:48:32,850 --> 00:48:42,100
+solve second order differential
+
+528
+00:48:42,100 --> 00:48:48,350
+equations يعني كيف بنستخدم ال Laplace transform في حل 
+
+529
+00:48:48,350 --> 00:48:52,310
+المعادلة التفاضلية من الرتبة الثانية أو حتى من
+
+530
+00:48:52,310 --> 00:48:57,450
+الرتبة الثالثة أو الرابعة حسب طبيعة المثال لكن
+
+531
+00:48:57,450 --> 00:49:01,730
+الرتبة الثانية هي الأكثر يبقى هذا باختصار
+
+532
+00:49:01,730 --> 00:49:05,110
+مثلا يبقى هذا الشيء الجديد Laplace transform
+
+533
+00:49:05,110 --> 00:49:09,630
+بيكون عندنا معادلة بنات قصدي function هذه ال
+
+534
+00:49:09,630 --> 00:49:14,710
+function صعبة التعامل معها فبنجيب معادلة مكافئة
+
+535
+00:49:14,710 --> 00:49:20,550
+لها تقريبا وبنحاول نستخدمها في إيه في الحل طبعا و
+
+536
+00:49:20,550 --> 00:49:24,330
+في عندنا جدول كل معادلة سهولة Laplace transform لها 
+
+537
+00:49:24,330 --> 00:49:30,050
+وهذا يعتمد على التكامل اللي درسناه في Calculus B
+
+538
+00:49:30,500 --> 00:49:36,400
+infinite integration تكامل من 0 إلى infinity أو من 
+
+539
+00:49:36,400 --> 00:49:37,440
+رقم إلى infinity
+
+540
+00:49:46,480 --> 00:49:51,840
+يعتمد عليها Laplace transform بهذا القدر أكتفي و
+
+541
+00:49:51,840 --> 00:49:56,320
+أظن أننا قد وصلنا إلى نهاية المحاضرة فالمرة الجاية
+
+542
+00:49:56,320 --> 00:50:00,860
+إن شاء الله هندخل في صميم الموضوع من أول و جديد
+
+543
+00:50:00,860 --> 00:50:05,480
+هذا كلام عام حول المنهج بارك الله
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..becf3d01d416ed65c03ce32d8312ccf735235f40
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ_postprocess.srt
@@ -0,0 +1,1784 @@
+1
+00:00:20,700 --> 00:00:24,720
+بسم الله الرحمن الرحيم بنرجع لان ل section تلاتة
+
+2
+00:00:24,720 --> 00:00:29,240
+سبعة اللي ابتدأنا المرة الماضية وهو يتحدث عن ال
+
+3
+00:00:29,240 --> 00:00:35,700
+linear transformations التحويلات الخطية طبعا
+
+4
+00:00:35,700 --> 00:00:40,840
+أعطينا تعريف لتحويلة خطية ثم أعطينا مثلا واحد فقط
+
+5
+00:00:40,840 --> 00:00:45,360
+في المرة الماضية و اليوم بنكمل الأمثلة و بنكمل نفس
+
+6
+00:00:45,360 --> 00:00:49,700
+الموضوع ان شاء الله و تعالىطبعا حابب أذكر قبل أن
+
+7
+00:00:49,700 --> 00:00:54,820
+نبدأ بـlinear transformation هي عبارة عن function
+
+8
+00:00:54,820 --> 00:00:59,960
+أو mapping من vector space V إلى vector space W
+
+9
+00:00:59,960 --> 00:01:06,420
+بحيث هذه ال function تحقق خاصيتين الخاصية الأولى T
+
+10
+00:01:06,420 --> 00:01:13,360
+of C في V يسوى C في T of V حيث C is color يعني عدد
+
+11
+00:01:13,360 --> 00:01:18,810
+حقيقيوالـ V هو فيكتور موجود في الـ vector space V
+
+12
+00:01:18,810 --> 00:01:23,070
+هذه الخاصية الأولى الخاصية التانية T لما اتأثر على
+
+13
+00:01:23,070 --> 00:01:30,170
+مجموعته vectors V1 زي V2 بيكون T of V1 زي T of V2
+
+14
+00:01:30,450 --> 00:01:34,390
+يبقى هاي الخاصية ان لو تحققوا بقول عن ال mapping
+
+15
+00:01:34,390 --> 00:01:37,730
+اللي عندنا او ال function هي عبارة عن linear
+
+16
+00:01:37,730 --> 00:01:41,870
+transformation يبقى هذا اللي اتكلمنا المرة الماضية
+
+17
+00:01:41,870 --> 00:01:47,530
+وعطينا على ذلك مثالا واحدا وهذا هو المثال الرقم 2
+
+18
+00:01:48,270 --> 00:01:52,790
+يبقى المثال رقم 2 بيقول افترض انه عندي mapping او
+
+19
+00:01:52,790 --> 00:01:57,430
+function T من ال vector space R3 الى ال vector
+
+20
+00:01:57,430 --> 00:02:03,810
+space R2 هذه ال function معرفة على الشكل التالي T
+
+21
+00:02:03,810 --> 00:02:08,650
+لما تأثر على الأنصار الموجودة في R3 الو X1 و X2 و
+
+22
+00:02:08,650 --> 00:02:15,460
+X3 صورته بيبقى موجودة في R2 وهي على الشكلاللي هو
+
+23
+00:02:15,460 --> 00:02:20,740
+element of two components مركبتين وليس تلاتة تلاتة
+
+24
+00:02:20,740 --> 00:02:26,640
+لأن هذا ال R3 مركبتين لمين لأن هذا R2 طيب ما هو
+
+25
+00:02:26,640 --> 00:02:31,260
+شكل الأنصار؟ شكله هو المركبة التالتة اللي عندنا
+
+26
+00:02:31,260 --> 00:02:34,600
+بتخليه هنا المركبة الأولى في ال vector space اللي
+
+27
+00:02:34,600 --> 00:02:39,940
+جديد وهنا واحد صحيحهو يسأل هل هذه T لينا
+
+28
+00:02:39,940 --> 00:02:44,900
+transformation ام لا؟ يعني الجواب ليس نقول نعم او
+
+29
+00:02:44,900 --> 00:02:49,140
+لا، نعم او لا مبني على المعلومات التي سأتحدث عنها
+
+30
+00:02:49,140 --> 00:02:53,140
+و why؟ إذا قلت لينا transformation ستقولين ليش؟
+
+31
+00:02:53,140 --> 00:02:55,640
+وإذا قلت لي تينا ماهياش لينا transformation
+
+32
+00:02:55,640 --> 00:03:02,230
+ستقولين ليه؟إذا احنا بنروح ندور على الخاصيتين هل
+
+33
+00:03:02,230 --> 00:03:06,590
+الخاصيتين محققتين ولا لأ بدي أمسك الخاصية الأولى
+
+34
+00:03:06,590 --> 00:03:11,590
+لو تحققت الخاصية الأولى بروح لمين للخاصية الثانية
+
+35
+00:03:11,590 --> 00:03:16,290
+لو ماتحققتش مافيش داعي أروح لمين للتانية حتى لو
+
+36
+00:03:16,290 --> 00:03:20,310
+بدأت بالتانية ثم بالأولى مافيش مشكلة المهم أنا بدي
+
+37
+00:03:20,310 --> 00:03:29,650
+الخاصيتين أن يتحققوا في آن واحد فبدي أقوله هنا ifC
+
+38
+00:03:29,650 --> 00:03:36,070
+موجود في ال set of real number and ال V بده يساوي
+
+39
+00:03:36,070 --> 00:03:43,170
+X واحد و X اتنين و X تلاتة X واحد و X اتنين و X
+
+40
+00:03:43,170 --> 00:03:52,770
+تلاتة هذا كله موجود في R3 thenبدي اخد T of C في ال
+
+41
+00:03:52,770 --> 00:04:00,030
+V يبقى هذا بدي يسوي T of C ال V اللي عبارة عن X
+
+42
+00:04:00,030 --> 00:04:07,710
+واحد و X اتنين و X ثلاثة بهذا الشكل هذا
+
+43
+00:04:07,710 --> 00:04:13,340
+بدي يعطيني T ofحاضروا الكون الصندوق هذا في كل
+
+44
+00:04:13,340 --> 00:04:21,240
+component من المراكبات التلاتة يبقى CX1 CX2 CX3
+
+45
+00:04:21,240 --> 00:04:26,960
+بالشكل اللي عندنا هذا طبقا للتعريف اللي ماتيني
+
+46
+00:04:26,960 --> 00:04:31,240
+يعني يبقى هذا الكلام بدي يسوي المراكبة الأخيرة
+
+47
+00:04:31,240 --> 00:04:38,500
+وقدرش واحد صحيحطيب بدي أخد C برا و أشوف شو بيصير
+
+48
+00:04:38,500 --> 00:04:44,160
+معايا يمكن لو أخدت C برا بيصير عندي هذا C في X
+
+49
+00:04:44,160 --> 00:04:51,570
+تلاتة و واحد على Zهل ال element هذا موجود في R2؟
+
+50
+00:04:51,570 --> 00:04:55,750
+موجود في R2 الصحيح لكن هل هو على الشكل اللي عندنا
+
+51
+00:04:55,750 --> 00:05:00,290
+هذا؟ لأ ماهواش على الشكل اللي عندنا هذا يبقى هذا
+
+52
+00:05:00,290 --> 00:05:08,550
+لا يساوي C في TRV
+
+53
+00:05:10,600 --> 00:05:14,960
+بساويش الكلام هذا طبعا مادام بساويش يبقى T هادى
+
+54
+00:05:14,960 --> 00:05:17,180
+linear transformation ولا ماهياش linear
+
+55
+00:05:17,180 --> 00:05:25,560
+transformation يعني يبقى هنا بقوله C so it is not
+
+56
+00:05:25,560 --> 00:05:28,200
+a linear transformation
+
+57
+00:05:31,980 --> 00:05:35,800
+طب كان بإمكان أي واحدة فيكوا تبدأ من مين؟ من ال
+
+58
+00:05:35,800 --> 00:05:40,380
+condition التاني وليس من ال condition الأول ونشوف
+
+59
+00:05:40,380 --> 00:05:44,940
+هل يتحقق والله لا يتحقق أما حتي هيك انتهينا من
+
+60
+00:05:44,940 --> 00:05:48,540
+الحل خلصنا يعني لو أجينا حل تاني واحدة ابتدت
+
+61
+00:05:48,540 --> 00:05:53,520
+بالخطوة الثانية وليست بالخطوة الأولىو راحت قالتلي
+
+62
+00:05:53,520 --> 00:06:00,940
+انا بدي اخد v واحد بده يساوي x واحد و x اتنين و x
+
+63
+00:06:00,940 --> 00:06:08,560
+تلاتة و ال v اتنين بده يساوي y واحد و y اتنين و y
+
+64
+00:06:08,560 --> 00:06:12,660
+تلاتة اللي موجودة في R3
+
+65
+00:06:32,220 --> 00:06:35,020
+النتيجة تساوي
+
+66
+00:06:44,260 --> 00:06:48,260
+التعريف بيقول ال component الأخيرة والأخر واحد
+
+67
+00:06:48,260 --> 00:06:52,880
+يبقى ال component الأخيرة ليه؟ X ثلاثة زائد Y
+
+68
+00:06:52,880 --> 00:06:58,760
+تلاتة ومين وواحد بدي أشوف هل هذا بيسوي T of V واحد
+
+69
+00:06:58,760 --> 00:07:04,180
+زائد T of V اتنين ولا لأبقوله كويس إذا بدي أحط هذا
+
+70
+00:07:04,180 --> 00:07:09,200
+على شكل مجموع اللي هو two vectors يبقى بقدر أقول
+
+71
+00:07:09,200 --> 00:07:16,500
+هذا X ثلاثة واحد زائد Y تلاتة وقداش و Zero هذا من
+
+72
+00:07:16,500 --> 00:07:23,480
+الأول T of V واحد وهذا زي ما هو يبقى هذا الكلام
+
+73
+00:07:23,480 --> 00:07:30,220
+بدي أساوي T of V واحد زائد هل هذا T of V اتنينلا
+
+74
+00:07:30,220 --> 00:07:35,880
+يبقى بحطه زي ما هو يبقى هذا زائد Y تلاتة و Zero
+
+75
+00:07:35,880 --> 00:07:43,200
+وهذا الكلام لا يساوي T of V واحد زائد T of V اتنين
+
+76
+00:07:44,620 --> 00:07:50,580
+لأن T of V2 عبارة عن Y3 و 1 و ليس Y3 و 0 يبقى كمان
+
+77
+00:07:50,580 --> 00:07:55,580
+ال condition التاني مش متحقق is not satisfied يبقى
+
+78
+00:07:55,580 --> 00:08:00,140
+بناء عليه برضه T not linear transformation يبقى
+
+79
+00:08:00,140 --> 00:08:08,390
+بروح بقوله CT is not a linear transformationيبقى
+
+80
+00:08:08,390 --> 00:08:14,190
+معناها كلام اللي أخدت الخاصية الأولى ولاجتها غير
+
+81
+00:08:14,190 --> 00:08:18,490
+متحققة وقالت 120 transformations صحيح اللي راحت
+
+82
+00:08:18,490 --> 00:08:23,090
+على الخاصية التانية مباشرة ولاجتها غير متحققة برضه
+
+83
+00:08:23,090 --> 00:08:28,890
+كلامها صحيح يبقى هدول حلين وليس حلا واحدا يعني
+
+84
+00:08:28,890 --> 00:08:35,990
+يكفيني أحدهما طب نيجي لالمثال اللي بعده example 3
+
+85
+00:08:41,890 --> 00:08:52,810
+تقول define a mapping define a mapping a mapping T
+
+86
+00:08:52,810 --> 00:09:02,290
+من R2 إلى R2 by T
+
+87
+00:09:02,290 --> 00:09:11,880
+of X1 و X2 بده يساويالأول اتنين x واحد ناقص x
+
+88
+00:09:11,880 --> 00:09:21,300
+اتنين وx واحد زائد x اتنين السؤال هو prove or
+
+89
+00:09:21,300 --> 00:09:31,840
+disprove prove or disprove that T is a linear
+
+90
+00:09:31,840 --> 00:09:33,200
+transformation
+
+91
+00:09:59,840 --> 00:10:03,840
+بنرجع لسؤالنا تاني يبقى انا في عندي mapping او
+
+92
+00:10:03,840 --> 00:10:08,980
+function معرفة من R2 ل R2 itself نفسها بالضبط
+
+93
+00:10:08,980 --> 00:10:16,460
+تماما معرفة كيف؟ T of X1 و X2 يساوي اتنين المركبة
+
+94
+00:10:16,460 --> 00:10:19,620
+الأولى ناقص المركبة الثانية هذه بيعطيني ال
+
+95
+00:10:19,620 --> 00:10:24,660
+component الأولىالكمبوننت الثانية هي مجموع من
+
+96
+00:10:24,660 --> 00:10:28,960
+المراكبات اللي اتنين هدول يبقى عرفنا function بهذا
+
+97
+00:10:28,960 --> 00:10:34,300
+الشكل سؤالنا هو هل هذه ال function ممكن تكون لنا
+
+98
+00:10:34,300 --> 00:10:38,740
+transformation ام لا بنقوله الله أعلم تعالى نشوف
+
+99
+00:10:38,740 --> 00:10:42,840
+نتأكد جالي probe or disprobe يعني اذا بتقدر تبره
+
+100
+00:10:42,840 --> 00:10:46,020
+انها كان بها ماجدرتش خلاص نعفى الله عنك
+
+101
+00:10:49,350 --> 00:10:55,770
+النقطة الأولى بدي أخد C موجودة في ال set of real
+
+102
+00:10:55,770 --> 00:11:01,690
+numbers and ال V اللي يتساوي X واحد و X اتنين
+
+103
+00:11:01,690 --> 00:11:11,150
+موجودة في ال R اتنين then بدي أخد T of C في ال V
+
+104
+00:11:11,830 --> 00:11:20,690
+يبقى هذه T في C of V ل X واحد و X اتنين يبقى هذا
+
+105
+00:11:20,690 --> 00:11:27,470
+الكلام T of ده فك الجثة ده يبقى C X واحد و C X
+
+106
+00:11:27,470 --> 00:11:33,130
+اتنين بهذا الشكل Y سوىالان بدأجي اطبق التعريف اللى
+
+107
+00:11:33,130 --> 00:11:36,730
+عندنا اللى احنا قايلينه يبقى هذا الكلام بده يساوي
+
+108
+00:11:36,730 --> 00:11:46,950
+اتنين CX1 ناقص CX2 هيا تمام يبقى اتنين المركبة
+
+109
+00:11:46,950 --> 00:11:52,770
+الأولى ناقص المركبة التانية المركبة الأولى زائد
+
+110
+00:11:52,770 --> 00:11:58,160
+المركبة التانية اللى عندناطيب اجبصرت بالشكل اللي
+
+111
+00:11:58,160 --> 00:12:03,590
+عندنا هذا لحظة يا بنات ان ال C موجودة وين؟موجودة
+
+112
+00:12:03,590 --> 00:12:07,850
+في كل مركبة يبقى بقدر اخدها برا عامل مشترك من
+
+113
+00:12:07,850 --> 00:12:14,990
+الكون يبقى بقدر اقول هذا الكلام يساوي C2 X1 ناقص
+
+114
+00:12:14,990 --> 00:12:22,830
+X2 و X1 زائد X2 بهذا الشكل طب اللي بينجو سين هذا
+
+115
+00:12:22,830 --> 00:12:30,310
+مش هو عبارة عن T of X1 و X2يعني كأن هذا الكلام
+
+116
+00:12:30,310 --> 00:12:35,750
+يساوي C في T أو V اللي بدأنا فيها إذا ال condition
+
+117
+00:12:35,750 --> 00:12:41,150
+الأول ماله متحقق بدي أجي لل condition التاني ال
+
+118
+00:12:41,150 --> 00:12:45,230
+condition التاني بدي أخد two vectors موجودات وين
+
+119
+00:12:45,230 --> 00:12:51,920
+في الارض ويبقى باشي بجولةاللي هو ال V1 بده يساوي
+
+120
+00:12:51,920 --> 00:13:02,300
+X1 و X2 و V2 بده يساوي Y1 و Y2، الإتنين هدول
+
+121
+00:13:02,300 --> 00:13:04,940
+موجودات في R2
+
+122
+00:13:08,310 --> 00:13:17,070
+بدي اخد T of ال V1 زائد V2 يبقى T of بدي اجمع ال
+
+123
+00:13:17,070 --> 00:13:26,830
+two vectors هدول يبقى X1 زائد Y1 و X2 زائد Y2 يبقى
+
+124
+00:13:26,830 --> 00:13:34,110
+ايه جمعة اتنين مرة واحدة طب الان هذا كلهكله
+
+125
+00:13:34,110 --> 00:13:58,890
+element موجود في الارتو كله
+
+126
+00:13:58,890 --> 00:14:00,550
+element موجود في الارتو كله element موجود في
+
+127
+00:14:00,550 --> 00:14:00,770
+الارتو كله element موجود في الارتو كله element
+
+128
+00:14:00,770 --> 00:14:00,850
+element موجود في الارتو كله element موجود في
+
+129
+00:14:00,850 --> 00:14:04,270
+الارتوبتداجي لمين؟ بتداجي للمراكبة الثانية
+
+130
+00:14:04,270 --> 00:14:09,390
+المراكبة الثانية اللي هي الأولى زائد التانية يبقى
+
+131
+00:14:09,390 --> 00:14:18,430
+x واحد زائد y واحد زائد x اتنين زائد y اتنين بهذا
+
+132
+00:14:18,430 --> 00:14:24,320
+الشكلطبعا يبقى هاي كتابة العنصر اللي عندنا بدالي
+
+133
+00:14:24,320 --> 00:14:28,940
+افك الجوس هذا يبقى لو جيت فكيت الجوس هذا بيصير على
+
+134
+00:14:28,940 --> 00:14:34,200
+الشكل التالي اتنين اكس واحد زائد اتنين واي واحد
+
+135
+00:14:34,200 --> 00:14:39,040
+ناقص اكس اتنين ناقص واي اتنين هذه المراكبة الأولى
+
+136
+00:14:39,040 --> 00:14:43,700
+المراكبة الثانية كما هي اكس واحد زائد واي واحد
+
+137
+00:14:43,700 --> 00:14:50,460
+زائد اكس اتنين زائد واي اتنين هذا الكلام يساويهذا
+
+138
+00:14:50,460 --> 00:14:55,780
+كله يعتبر عنصر واحد بدي أحاول أكتبه على شكل عنصرين
+
+139
+00:14:55,780 --> 00:15:02,200
+و أشوف هل ممكن ولا لأ بدي أخد 2X1 مع ال X يعني بدي
+
+140
+00:15:02,200 --> 00:15:09,920
+أخد ال X مع بعضها و ال Y مع بعضها يبقى هذا 2X1 نقص
+
+141
+00:15:09,920 --> 00:15:17,630
+X2 وهنا X1 زائد X2 زائدبقى اللي عندى هنا مين؟
+
+142
+00:15:17,630 --> 00:15:24,990
+اتنين y واحد ناقص y اتنين و y واحد زائد y اتنين
+
+143
+00:15:24,990 --> 00:15:29,690
+بالشكل اللى عندنا لو جمعت اللى هو ال two vectors
+
+144
+00:15:29,690 --> 00:15:33,350
+هدول بطلع مين؟ بطلع ال vector اللى فوق بالضبط
+
+145
+00:15:33,350 --> 00:15:39,430
+تماما طيب هذا مين؟مش T of X واحد و X اتنين يبقى
+
+146
+00:15:39,430 --> 00:15:46,910
+هذا الكلام يساوي T of X واحد و X اتنين زائد التاني
+
+147
+00:15:46,910 --> 00:15:55,890
+T of Y واحد و Y اتنين يعني هذا كأنه T of V1 زائد T
+
+148
+00:15:55,890 --> 00:16:01,290
+of V2 بالضبط تماما إذا انتحقت الخاصية ثانية ولا
+
+149
+00:16:01,290 --> 00:16:11,100
+لا؟يبقى هنا TSA Linear Transformation يبقى هنا TSA
+
+150
+00:16:11,100 --> 00:16:13,340
+Linear Transformation
+
+151
+00:16:35,780 --> 00:16:41,440
+نأخد ملاحظة if
+
+152
+00:16:41,440 --> 00:16:49,480
+ال
+
+153
+00:16:49,480 --> 00:16:57,020
+V and ال W are two vector spaces
+
+154
+00:17:10,000 --> 00:17:21,060
+وT من V إلى W هو
+
+155
+00:17:21,060 --> 00:17:24,400
+تغيير
+
+156
+00:17:24,400 --> 00:17:29,960
+عسل من T
+
+157
+00:17:29,960 --> 00:17:39,190
+من V إلى Wالـ Zero بتبع ال V سوى ال Zero بتبع ال W
+
+158
+00:17:39,190 --> 00:17:48,010
+لأخطر
+
+159
+00:17:48,010 --> 00:17:53,410
+نثبتها بس
+
+160
+00:17:53,410 --> 00:18:00,260
+لأخطر نفهمها قبل أن نثبتها مين تقول أيش معناها؟T
+
+161
+00:18:00,260 --> 00:18:03,500
+of Zero تبع الـ B يبدو يسوي الـ Zero التبع دوله شو
+
+162
+00:18:03,500 --> 00:18:08,400
+يعني المعنى هذا تبعه واحد
+
+163
+00:18:08,400 --> 00:18:13,000
+يحكي و لو غلط بس يحكوا تعودوا تفهموش الكلام اللي
+
+164
+00:18:13,000 --> 00:18:17,860
+مكتوب T
+
+165
+00:18:17,860 --> 00:18:23,180
+function ده اللي عادي أثرت على العنصر هذا خلّى صوت
+
+166
+00:18:23,180 --> 00:18:26,380
+العنصر ايش يعني يا دي ايش معناها
+
+167
+00:18:29,110 --> 00:18:31,330
+بدي واحد قللي بس اللي بتحكي بس اللي رفع أيديها، دي
+
+168
+00:18:31,330 --> 00:18:36,650
+ناس ماعرفش بتقول ولا واحدة بطلوا خلاص someone بقوا
+
+169
+00:18:36,650 --> 00:18:42,470
+نعمل انفهم لا يعقلون؟ ها أيوة، قولي ممكن يعني انه
+
+170
+00:18:42,470 --> 00:18:45,030
+على أساس ان ال people اللي قدامي يقولي متولد او
+
+171
+00:18:45,030 --> 00:18:48,530
+ماتش من الدين تأثر عليا، فهنا بيقولكي انه
+
+172
+00:19:04,680 --> 00:19:09,320
+بالبلد هي كلمتين صغيرة يعني صورة zero تبع ال
+
+173
+00:19:09,320 --> 00:19:14,600
+vector space V صورة Zero تبع ال W بس هي كلمتين
+
+174
+00:19:14,600 --> 00:19:18,370
+صغيرة مافيش غيرهاT لما تأثر على الـ Zero تبع ال V
+
+175
+00:19:18,370 --> 00:19:23,010
+بيروحش لأي عنصر أخر وإنما صوته هو ال Zero تبعد،
+
+176
+00:19:23,010 --> 00:19:25,950
+يعني ال Zero هنا بيروح لـ Zero تحت أثير ال Linear
+
+177
+00:19:25,950 --> 00:19:29,210
+Transformation T، صعبة ما هي قدامك مكتوبة على
+
+178
+00:19:29,210 --> 00:19:33,690
+اللغةأنا جاي اللي هي team ال vector space V لل
+
+179
+00:19:33,690 --> 00:19:38,590
+vector space W هذه linear transformation إن حدث
+
+180
+00:19:38,590 --> 00:19:45,730
+ذلك يبقى صورة ال zero تبع ال vector space V هي ال
+
+181
+00:19:45,730 --> 00:19:49,710
+zero تبع ال W صورة ال zero هنا هي ال zero هنا لكن
+
+182
+00:19:49,710 --> 00:19:53,250
+هل ال zero في ال vector space الأول هو ال zero تبع
+
+183
+00:19:53,250 --> 00:19:56,580
+ال vector space التاني؟لأ لأن كل واحد عليها عملية
+
+184
+00:19:56,580 --> 00:20:01,260
+مختلفة تمام وبالتالي و بالتالي ال zero هنا غير
+
+185
+00:20:01,260 --> 00:20:04,920
+zero قد يكون هو و قد لا يكون لأنه قد يكون ال
+
+186
+00:20:04,920 --> 00:20:09,040
+vector space إلى نفسه وارد ولا لا يبقى ممكن يكون
+
+187
+00:20:09,040 --> 00:20:12,780
+هو و ممكن ما يكون شهو طيب بدنا نروح نثبت صحة هذا
+
+188
+00:20:12,780 --> 00:20:19,940
+الكلام بسيطة جدا يبقى انا بدي اخدي T of zero سبع
+
+189
+00:20:19,940 --> 00:20:24,080
+ال V كويس؟
+
+190
+00:20:24,600 --> 00:20:29,960
+يبقى مقدر اقول هذا ت اف بدا اكتبه بصورة تانية يا
+
+191
+00:20:29,960 --> 00:20:37,560
+بنات بنفع اقول ال zero is scalar كمضروب في اي
+
+192
+00:20:37,560 --> 00:20:38,520
+vector V
+
+193
+00:20:42,010 --> 00:20:45,570
+أي vector من ال vector space V أضربه في ال scalar
+
+194
+00:20:45,570 --> 00:20:50,830
+0 بيعطينا ال zero تبع ال V إذا أنا شيلت ال zero
+
+195
+00:20:50,830 --> 00:20:56,310
+تبع ال V و كتبت بداله scalar هه مش همتوهيش هي كانت
+
+196
+00:20:56,310 --> 00:21:02,950
+انا راح عملت و ال zero مضوره هي scalar مش همتوهيش
+
+197
+00:21:02,950 --> 00:21:06,990
+فيه و ال V هو vector موجود وين في ال vector space
+
+198
+00:21:06,990 --> 00:21:11,080
+Vطيب الان هذا الكلام بده يساوي
+
+199
+00:21:15,560 --> 00:21:20,120
+أول خاصية من خاصية الـ Linear Transformation إذا
+
+200
+00:21:20,120 --> 00:21:23,900
+عندك T بتأثر على S color في الـ vector يبقى الـ S
+
+201
+00:21:23,900 --> 00:21:31,800
+color برا التأثير، مظبوط؟ إذا هذا بده يساوي 0 أو
+
+202
+00:21:31,800 --> 00:21:39,420
+هذا بده يساوي 0 scalar في T of V، الشكل اللي عندنا
+
+203
+00:21:39,420 --> 00:21:46,890
+هناطب T of V موجود وين؟ في ال V ولا في ال W؟ في ال
+
+204
+00:21:46,890 --> 00:21:53,070
+W يبقى لما أضربه في Zero بيطلع من؟الـ zero تبع من؟
+
+205
+00:21:53,070 --> 00:21:58,930
+تبع ال W يبقى هذا يقدر يعطينا ال zero تبع ال W
+
+206
+00:21:58,930 --> 00:22:05,190
+والكلام صحيح لكل ال V الموجود في ال vector space V
+
+207
+00:22:05,190 --> 00:22:10,170
+يعني مااخدتش vector بعينيه وإنما أي vector موجود،
+
+208
+00:22:10,170 --> 00:22:16,270
+إذا بناء عليهبتكون T of 0 V بتسوى من الـ 0 W من
+
+209
+00:22:16,270 --> 00:22:20,490
+الارفة ساعدا بديك تعرفيه لإنه source العنصر الصفري
+
+210
+00:22:20,490 --> 00:22:24,090
+في ال vector space V هو العنصر الصفري في ال vector
+
+211
+00:22:24,090 --> 00:22:31,470
+space W نأخد تعريفين مهمين very important يبقى
+
+212
+00:22:31,470 --> 00:22:41,130
+التعريف الأول بيقول ما يأتي let ال T من V إلى ال W
+
+213
+00:22:50,560 --> 00:23:03,240
+كبتل K كمجلد من جميع الأشياء كمجلد من جميع الأشياء
+
+214
+00:23:03,240 --> 00:23:08,340
+كمجلد
+
+215
+00:23:08,340 --> 00:23:09,080
+من جميع الأشياء
+
+216
+00:23:12,920 --> 00:23:32,370
+ذات مابس تو الـ Zero W Zero W ذات is I N كبتل Kبدي
+
+217
+00:23:32,370 --> 00:23:39,350
+يساوي كل العناصر V اللي موجودة في capital V such
+
+218
+00:23:39,350 --> 00:23:46,730
+that T of V بدي يساوي ال zero تبع ال W بالشكل اللي
+
+219
+00:23:46,730 --> 00:23:56,550
+عندنا هنا then K then K is called
+
+220
+00:24:00,670 --> 00:24:06,050
+Kernel of T
+
+221
+00:24:06,050 --> 00:24:15,170
+يبقى بنسميه كيرنل تي كمان Definition بيقول
+
+222
+00:24:15,170 --> 00:24:24,510
+الات ال T من ال V إلى ال W بإي لينير ترانسفورماشن
+
+223
+00:24:24,510 --> 00:24:29,590
+بإي لينير ترانسفورماشن
+
+224
+00:24:30,920 --> 00:24:34,540
+then the
+
+225
+00:24:34,540 --> 00:24:49,600
+range of T is defined by بروح
+
+226
+00:24:49,600 --> 00:24:56,430
+بنعرفهعلى ان ال R of T أو ال range تبع ال T بد
+
+227
+00:24:56,430 --> 00:25:02,090
+يساوي كل ال W اللي موجودة في ال vector space W
+
+228
+00:25:02,090 --> 00:25:14,030
+كابتل such that ال W بد يساوي T of V for some V
+
+229
+00:25:14,030 --> 00:25:17,550
+اللي موجودة في كابتل V
+
+230
+00:25:42,630 --> 00:25:55,830
+بنجي لأول نظرية على هذا الموضوع F T
+
+231
+00:25:55,830 --> 00:26:06,390
+من V ل W is a linear transformation is a linear
+
+232
+00:26:06,390 --> 00:26:09,310
+transformation
+
+233
+00:26:20,680 --> 00:26:30,440
+النقطة الأولى is the kernel of
+
+234
+00:26:30,440 --> 00:26:34,520
+T is a subspace of V
+
+235
+00:26:45,000 --> 00:26:54,960
+النقطة الثانية the range of T is
+
+236
+00:26:54,960 --> 00:27:02,240
+a subspace of
+
+237
+00:27:02,240 --> 00:27:04,020
+W
+
+238
+00:27:25,500 --> 00:27:31,700
+أحنا عندنا هنا تعريفين وعندنا نظرية بدنا نقرأ هذين
+
+239
+00:27:31,700 --> 00:27:38,260
+التعريفين قراءة رياضية سليمة ومن ثم نذهب للنظرية
+
+240
+00:27:38,260 --> 00:27:44,340
+بشقيها ونحاول نثبت هذه النظرية نجي للتعريف الأول
+
+241
+00:27:44,340 --> 00:27:48,360
+اللي هو متحدث عن حاجة اسمها ال kernel of T يعني
+
+242
+00:27:48,360 --> 00:27:53,080
+النواة تبع من؟ تبع ال kernel الترجمة العرفية لها
+
+243
+00:27:53,080 --> 00:27:59,520
+نواةبعدها بقول التعريف الأول بقول خلّي T من V ل W
+
+244
+00:27:59,520 --> 00:28:06,920
+Linear Transformation خلّي 6K مين هذه؟ كل العناصر
+
+245
+00:28:06,920 --> 00:28:13,440
+LV اللي ذات maps domain to 0W يعني كل العناصر اللي
+
+246
+00:28:13,440 --> 00:28:18,060
+في ال vector space V اللي صورتها هي من؟ هي الصفر
+
+247
+00:28:18,060 --> 00:28:22,990
+كل اللي بتروحله ال that isالـ Kernel K هو كل الـ V
+
+248
+00:28:22,990 --> 00:28:27,730
+اللي موجود فيه capital V such that T of V بده يسوي
+
+249
+00:28:27,730 --> 00:28:34,510
+0 W يبقى ذنب الـ K is called the kernel of T طب
+
+250
+00:28:34,510 --> 00:28:38,250
+بناءً على هذا التاريخ بده أسهل السؤال التالي هل ال
+
+251
+00:28:38,250 --> 00:28:44,910
+kernel هذا subset من V ولا من ال W subset من مين
+
+252
+00:28:44,910 --> 00:28:52,820
+يا بنات؟كل ال V الموجودة في V يبقى subset من V
+
+253
+00:28:52,820 --> 00:28:58,860
+بصرتها مش بتكون ال zero تبع ال W نجي أي function
+
+254
+00:28:58,860 --> 00:29:04,200
+إلها domain و إلها range يبقى ال kernel هو جزء من
+
+255
+00:29:04,200 --> 00:29:08,800
+ال domain و لا جزء من ال rangeجزء من ال domain
+
+256
+00:29:08,800 --> 00:29:14,100
+كلام كويس إذا بدنا نروح لل range جالي ال range تبع
+
+257
+00:29:14,100 --> 00:29:18,520
+ال Lena transformation T اللي من فيه W ال range
+
+258
+00:29:18,520 --> 00:29:23,320
+تبعها هديله رمز R of T يبقى R of T هو ال range
+
+259
+00:29:23,320 --> 00:29:28,540
+لLena transformation V هو مهم كل ال W اللي موجودة
+
+260
+00:29:28,540 --> 00:29:35,770
+وين في ال Wواللي إلها أصل وين في V يعني أنا لما
+
+261
+00:29:35,770 --> 00:29:39,930
+أجي على ال code domain يا بنات ليس بالضرورة أن ال
+
+262
+00:29:39,930 --> 00:29:43,890
+function تغطي كل عناصر ال code domain بس لازم تغطي
+
+263
+00:29:43,890 --> 00:29:46,610
+جميع عناصر ال domain يعني تأثر على جميع عناصر ال
+
+264
+00:29:46,610 --> 00:29:51,590
+domain لكن صورهم ليس بالضرورة كل ال code domainبعض
+
+265
+00:29:51,590 --> 00:29:56,330
+العناصر و يمكن يطلعوا كلهم أحيانا مش دايما تمام
+
+266
+00:29:56,330 --> 00:29:59,870
+يبقى الصورة اللي طلعت هذي بسميها ال range بدي أخد
+
+267
+00:29:59,870 --> 00:30:04,830
+الصورة اللي طلعت هذول اللي هو mean R of T كل ال W
+
+268
+00:30:04,830 --> 00:30:11,640
+اللي موجودة في ال W و اللي إلها أصلفي الـ domain
+
+269
+00:30:11,640 --> 00:30:16,060
+يبقى كل الـ W اللي موجودة في الـ W يعني الـ W هذه
+
+270
+00:30:16,060 --> 00:30:22,400
+تساوي T of V for some V اللي موجودة في V يعني V
+
+271
+00:30:22,400 --> 00:30:28,240
+هذا element موجود في V صورة الـ V هي من؟ هي الـ W
+
+272
+00:30:28,240 --> 00:30:32,980
+يبقى كل الصور اللي ظهرت في من؟ في الـ W إذا الـ W
+
+273
+00:30:32,980 --> 00:30:39,910
+هذهالـ range تبع ال T هو جزء من ال vector space V
+
+274
+00:30:39,910 --> 00:30:44,630
+والله جزء من ال vector space W من ال W اللي بيهدف
+
+275
+00:30:44,630 --> 00:30:50,750
+ال range لإن ال W هو ال code domain المجال المصاحب
+
+276
+00:30:50,750 --> 00:30:56,470
+تمام ال range هذا قد يسوى ال W كلها وقد يكون جزء
+
+277
+00:30:56,470 --> 00:31:02,110
+منها لو كانت الدالة on to يعني دالة فوقيا بصير ال
+
+278
+00:31:02,110 --> 00:31:06,440
+domain هو ال ال code domain هو ال rangeماكنتش on
+
+279
+00:31:06,440 --> 00:31:09,920
+two يبقى ليه؟ يمكن لل code main انه يساوي من؟
+
+280
+00:31:09,920 --> 00:31:15,500
+يساوي ال range طيب يبقى احنا لان صار عندنا K
+
+281
+00:31:15,500 --> 00:31:25,700
+subset من ال vector space V وR of T subset من ال W
+
+282
+00:31:27,030 --> 00:31:32,630
+الحين انا ادعي ان ال K هذي ال subspace و ال R of T
+
+283
+00:31:32,630 --> 00:31:36,590
+subspace،يعني النظرية بتقول لو كان T من V إلى
+
+284
+00:31:36,590 --> 00:31:40,390
+W،linear transformation يبقى ال kernel of T اللي
+
+285
+00:31:40,390 --> 00:31:45,250
+هو ال data الرمز capital K subspace من V وكذلك ال
+
+286
+00:31:45,250 --> 00:31:48,370
+range تبع ال T اللي Data الرمز R of T هو subspace
+
+287
+00:31:48,370 --> 00:31:53,910
+من من ال W،إذا بدي أثبت ان كل واحد فيهم subspace
+
+288
+00:31:53,910 --> 00:32:02,710
+من ال Wنرجع بالذاكرة الى section 3-1 اللى كان ال
+
+289
+00:32:02,710 --> 00:32:07,050
+vector space والتلاتة اتنين كانت ال subspace صحيح
+
+290
+00:32:07,050 --> 00:32:10,350
+ولا لأ يبقى انا بدي اثبت هدول subspace قولنا مش
+
+291
+00:32:10,350 --> 00:32:13,970
+هناخد ال subset من ال vector space وانه اثبت ان ال
+
+292
+00:32:13,970 --> 00:32:20,030
+subspace بدي اثبت كام شغلة تلاتة الشغلة الأولىعلى
+
+293
+00:32:20,030 --> 00:32:24,310
+الأقل بدي أثبت أنه في عنصر واحد لعمر الثاني لو
+
+294
+00:32:24,310 --> 00:32:27,950
+أخدت element من R و element من ال vector من ال
+
+295
+00:32:27,950 --> 00:32:32,620
+subset هذا و ضربتهم في بعض بدي أجيه داخللو أخدت
+
+296
+00:32:32,620 --> 00:32:35,960
+مجموع two elements من ال subset هذا بدي أجيب
+
+297
+00:32:35,960 --> 00:32:39,420
+موجودة في ال subset ان حدث ذلك يظهر ال subset بقول
+
+298
+00:32:39,420 --> 00:32:44,520
+هذه عبارة عن name subspace تمام؟ اذا انا بدي أروح
+
+299
+00:32:44,520 --> 00:32:49,480
+أحقق لكل من k و r of t لي three conditions هدول
+
+300
+00:32:49,480 --> 00:32:53,020
+اذا بدي اجي لمن؟ للنقطة الأولة و بدي اجي لل
+
+301
+00:32:53,020 --> 00:32:56,980
+condition الأول ال condition الأول او قبل ما بدي
+
+302
+00:32:56,980 --> 00:33:03,020
+اجي أقول ال kernelهو كل ال V اللي موجودة في
+
+303
+00:33:03,020 --> 00:33:09,020
+capital V بحيث ان T of V بده يساوي Zero مش هذا
+
+304
+00:33:09,020 --> 00:33:17,700
+تعريف ال kernel يبقى هذا is the kernel of T هذا هو
+
+305
+00:33:17,700 --> 00:33:21,860
+ال kernel اللي عندي ال zero هذا هو ال zero تبع ال
+
+306
+00:33:21,860 --> 00:33:27,120
+W معناه مش ال zero scalar يبقى ال zero تبع من تبع
+
+307
+00:33:27,120 --> 00:33:34,820
+ال W طيب كويسالان بدي أبينه هذا على الأقل في ولو
+
+308
+00:33:34,820 --> 00:33:41,340
+عنصر واحد تمام؟ الان عشان احنا عندنا في عندي
+
+309
+00:33:41,340 --> 00:33:50,820
+element هنا ال kernel is non-empty ايش السبب؟
+
+310
+00:33:50,820 --> 00:34:01,050
+because هي موجودة عندى، مظبوط؟ because ال T0V بدي
+
+311
+00:34:01,050 --> 00:34:08,130
+يساوي الـ0 تبع الـW هذا يعني ان الـ0 تبع الـV
+
+312
+00:34:08,130 --> 00:34:14,530
+موجود في الكيرن الـK يبقى هذا non-empty يبقى هذه
+
+313
+00:34:14,530 --> 00:34:20,150
+هي main الخاصية الأولى الخاصية التانيةبدي أخد
+
+314
+00:34:20,150 --> 00:34:25,610
+element من R و element من ال vector S P أو من ال
+
+315
+00:34:25,610 --> 00:34:30,790
+kernel يبقى let C belongs to set of real numbers
+
+316
+00:34:30,790 --> 00:34:37,430
+and ال V موجود في ال kernel مدام ال move V موجود
+
+317
+00:34:37,430 --> 00:34:42,750
+في ال kernel يبقى فنتي لو أثرت على V قدش بتعطينا؟
+
+318
+00:34:42,750 --> 00:34:51,040
+Zero W يبقى Zero W تمام تماميبقى انا بدي اثبت انه
+
+319
+00:34:51,040 --> 00:34:58,040
+C في V موجودة يعني بدي اثبت ان الصورة T او T لما
+
+320
+00:34:58,040 --> 00:35:02,420
+تأثر على CV بدي تعطينا الـ Zero التبادل ان حدث ذلك
+
+321
+00:35:02,420 --> 00:35:06,120
+يبقى بقول الـC في الـV موجودة وين؟ في ال kernel
+
+322
+00:35:06,120 --> 00:35:15,620
+يبقى بدي اخد T of C في الـV هذا الكلام يساوي انا
+
+323
+00:35:15,620 --> 00:35:20,360
+فرض انه T عبارة عن ايش؟هذا من خواصة لينا
+
+324
+00:35:20,360 --> 00:35:26,260
+Transformation بصير C في T of V يبقى هذا الكلام
+
+325
+00:35:26,260 --> 00:35:33,980
+بده يساوي C في T of V اليمين Zero W ايش بيعطينا؟
+
+326
+00:35:33,980 --> 00:35:39,820
+ايش تفسيرك لهذا الكلام؟ ان ال C في ال V موجودة
+
+327
+00:35:39,820 --> 00:35:45,380
+وين؟ في ال kernelيبقى اخدت element من ال kernel
+
+328
+00:35:45,380 --> 00:35:49,320
+واخدت real number ضربت اتنين في بعض لجيتهم موجودة
+
+329
+00:35:49,320 --> 00:35:53,040
+في ال kernel يعني لجيتهم صورتهم متساومهم ال zero
+
+330
+00:35:53,040 --> 00:36:01,260
+تبع ال W بداجي للخطوة التالتة بداجي اقولت V1 و V2
+
+331
+00:36:01,260 --> 00:36:09,760
+موجودة في ال kernelطب هذا إيش معناها؟ لما تكون في
+
+332
+00:36:09,760 --> 00:36:18,080
+الكيرن المعناته T of V1 جداش بده يساوي Zero W يبقى
+
+333
+00:36:18,080 --> 00:36:27,160
+Zero تبع ال W and T of V2 بده يساوي مين كمان؟ Zero
+
+334
+00:36:27,160 --> 00:36:33,300
+تبع ال W بالشكل اللي عندناطيب انا بدي اشوف T لما
+
+335
+00:36:33,300 --> 00:36:41,120
+اتأثر على V1 زائد V2 ان اعطتنا Zero تبع ال W و تم
+
+336
+00:36:41,120 --> 00:36:49,040
+المطلوب يبقى باجي بقوله هذا الكلام بده يساوي T
+
+337
+00:36:49,040 --> 00:36:54,960
+of V1 زائد T of V2 ليش؟ لأنه T Linear
+
+338
+00:36:54,960 --> 00:37:02,390
+Transformation T of V1 هي Zero تبع ال Wالـ T of V2
+
+339
+00:37:02,390 --> 00:37:07,990
+هي الـ Zero تبع الـ W Zero زائد Zero بيعطيني Zero
+
+340
+00:37:07,990 --> 00:37:16,070
+تبع الـ W يبقى هنا معنى هذا الكلام ان V1 زائد V2في
+
+341
+00:37:16,070 --> 00:37:20,310
+الـKernel لأن صيرتها تساوي الـ0 التابعة الـW إذا
+
+342
+00:37:20,310 --> 00:37:24,410
+انتحقت الشروط التلاتة للـ subspace ولا لا يبقى
+
+343
+00:37:24,410 --> 00:37:30,650
+بناءنا عليه من الآن فصاعدا بقوله يبقى الـKernel K
+
+344
+00:37:30,650 --> 00:37:39,850
+is a subspace of ال vector space اللي هو main V
+
+345
+00:37:44,760 --> 00:37:49,700
+الان بدنا نجي للشطر الثاني من النظرية بدنا نثبت ان
+
+346
+00:37:49,700 --> 00:37:57,400
+ال range التي هو عبارة عن subspace كذلكباجي بقوله
+
+347
+00:37:57,400 --> 00:38:05,120
+النقطة التانية احنا عندنا ال R of T بده ساوي كل W
+
+348
+00:38:05,120 --> 00:38:11,740
+اللي موجودة في ال vector space W بحيث ان ال W هذه
+
+349
+00:38:11,740 --> 00:38:20,400
+بدها تساوي T of V for some V اللي موجودة في ال
+
+350
+00:38:20,400 --> 00:38:24,590
+vector space V بالشكل اللي عندنا هنابدي أثبت إن
+
+351
+00:38:24,590 --> 00:38:31,210
+هذا كمان sub space بدي أثبت إن هذا non-empty كذلك
+
+352
+00:38:31,210 --> 00:38:38,830
+يبقى النقطة الأولى ال R of T is non-empty شو السبب
+
+353
+00:38:38,830 --> 00:38:46,360
+في ذلك؟ because ال zero تبع ال Wمش ال zero هذا
+
+354
+00:38:46,360 --> 00:38:50,700
+الموجود في ال vector space W بقدر اكتبه بال remark
+
+355
+00:38:50,700 --> 00:38:59,480
+اللي قبل قليل T of zero V، مظبوط؟ طيب هاي ال zero
+
+356
+00:38:59,480 --> 00:39:04,990
+V وين موجود؟في ال V يبقى انطباق التعريف ولا لا
+
+357
+00:39:04,990 --> 00:39:11,710
+يبقى هذا بده يستوي اللي هو موجود وين؟ موجود في ال
+
+358
+00:39:11,710 --> 00:39:18,230
+W أو هذا موجود في ال R of T هذا موجود في ال range
+
+359
+00:39:18,230 --> 00:39:24,790
+تبع ال T يبقى ال R of T is non-emptyبدي اجي للخطوة
+
+360
+00:39:24,790 --> 00:39:33,890
+الثانية if ال C موجود في ال R and ال W موجود في ال
+
+361
+00:39:33,890 --> 00:39:40,930
+R of T then ال
+
+362
+00:39:40,930 --> 00:39:50,710
+W بده يساوي ال T of V for some V اللي موجودة في V
+
+363
+00:39:50,710 --> 00:39:56,730
+capitalيبقى انا بدي اثبت ان ال CW موجودة في ال
+
+364
+00:39:56,730 --> 00:40:04,270
+range يبقى بالدرجة اقوله CW تساوي ال C في ال W
+
+365
+00:40:04,270 --> 00:40:13,370
+اليمين TAV التي اشجعين عليهالينيرا ترانسفورماشن،
+
+366
+00:40:13,370 --> 00:40:19,290
+إذا الـC تدخل وين؟ تدخل جوا، يبقى هذا بصير T of
+
+367
+00:40:19,290 --> 00:40:24,790
+CV، صار هذا element موجود في ال range ولا لا؟يبقى
+
+368
+00:40:24,790 --> 00:40:30,870
+هذا موجود كله في ال R of T يعني صار ال C في ال W
+
+369
+00:40:30,870 --> 00:40:35,190
+موجودة في ال R of T إذا انتحقق ال condition التاني
+
+370
+00:40:35,190 --> 00:40:40,090
+بده يروح لوين؟ لل condition التالت بده يقوله let
+
+371
+00:40:40,090 --> 00:40:52,350
+W1 و W2 موجود في ال R of T thenthere exist V1 و V2
+
+372
+00:40:52,350 --> 00:41:00,590
+موجودات في ال V such that يبقى لازم أجد V1 و V2
+
+373
+00:41:00,590 --> 00:41:12,370
+بحيث ال W1 بدر سوى T of V1 و ال W2 بدر سوى T of V2
+
+374
+00:41:12,370 --> 00:41:21,460
+بالداخل ال W1 زائد W2بدي اثبت ان هذا موجود وين في
+
+375
+00:41:21,460 --> 00:41:27,160
+ال range يعني بدي اثبت ان هذا صورة لعمصر موجود وين
+
+376
+00:41:27,160 --> 00:41:33,620
+في ال domain بقوله بسيطة هذا عبارة عن T of V1 وهذا
+
+377
+00:41:33,620 --> 00:41:41,100
+T of V2 طيب ال T Linear Transformation الخاصية
+
+378
+00:41:41,100 --> 00:41:48,510
+التالتة منها بتقول هذا سوى T of V1 زي V2هذا مجموع
+
+379
+00:41:48,510 --> 00:41:52,270
+two vectors في V يبقى هذا عبارة عن vector واحد في
+
+380
+00:41:52,270 --> 00:41:59,890
+V بقدر أقول هذا T of V تلاتة و ال V تلاتة هو V
+
+381
+00:41:59,890 --> 00:42:02,530
+واحد زائد V اتنين يبقى موجود في ال range ولا لا
+
+382
+00:42:02,530 --> 00:42:10,810
+يبقى هذا موجود في R of T و V تلاتة بده يسوى V واحد
+
+383
+00:42:10,810 --> 00:42:15,790
+زائد V اتنين إذا صار مجموح موجود في R of T إذا R
+
+384
+00:42:15,790 --> 00:42:23,990
+of T عبارة عن عاشرعبارة عن ايش؟ يبقى دص وهكذا ال R
+
+385
+00:42:23,990 --> 00:42:36,830
+of T is a subspace of ال vector space W طب
+
+386
+00:42:36,830 --> 00:42:43,450
+نعطي مثال يبقى example one
+
+387
+00:42:50,630 --> 00:43:00,330
+بقول define a mapping define a mapping T
+
+388
+00:43:00,330 --> 00:43:18,190
+من ال M two two ل ال M two two by ال T of Aبدي
+
+389
+00:43:18,190 --> 00:43:24,730
+اساوي ال a زائد a transpose المطلوب
+
+390
+00:43:24,730 --> 00:43:34,170
+الأول show that بيينيلي ان T is a linear
+
+391
+00:43:34,170 --> 00:43:41,850
+transformation نمرا بيه find the kernel of T find
+
+392
+00:43:41,850 --> 00:43:58,510
+the kernel of Tمطلوب التالت find the range of T
+
+393
+00:44:24,650 --> 00:44:29,810
+خلّى بركةجلب ان انا اعرف ده اللي هي فيه من مجموعة
+
+394
+00:44:29,810 --> 00:44:34,330
+المصففات اللي نضامها 2 ل 2 إلى نفسها إلى مجموعة
+
+395
+00:44:34,330 --> 00:44:38,550
+المصففات اللي نضامها 2 في 2 باقي فيه لما تأثر على
+
+396
+00:44:38,550 --> 00:44:43,650
+المصففة اللي نضامها 2 في 2 بتعطيني A نفسها زائد A
+
+397
+00:44:43,650 --> 00:44:47,930
+transpose هيعرفنا ال function بالضبط ده لو جمعت
+
+398
+00:44:47,930 --> 00:44:52,310
+ليه 2 هدول مش بيطلع مصففها برضه نظامها 2 في 2 اذا
+
+399
+00:44:52,310 --> 00:45:02,290
+التعريف صحيح 100% ولا غضار عليايبقى الخطوة
+
+400
+00:45:02,290 --> 00:45:07,490
+الأولى بدي أثبت انها Linear Transformation يعني
+
+401
+00:45:07,490 --> 00:45:10,090
+بدي أثبت ال two properties تبع Linear
+
+402
+00:45:10,090 --> 00:45:16,390
+Transformation يبقى بداجي للخاصية الأولى بداجي
+
+403
+00:45:16,390 --> 00:45:25,000
+أقوله لو كانت ال C موجودة في ال R andالـ A موجودة
+
+404
+00:45:25,000 --> 00:45:31,980
+في ال M to to them بدأ
+
+405
+00:45:31,980 --> 00:45:39,480
+أخد اللي هو T of C في ال A حسب ال definition
+
+406
+00:45:39,480 --> 00:45:47,620
+المناشي بده ساوي ال A بده ساوي اللي هو CA زائد CA
+
+407
+00:45:47,620 --> 00:45:48,800
+transpose
+
+408
+00:45:52,090 --> 00:45:59,150
+التعريف يبقى كويس هذي بيضهر ساوي CA زائد لما نيجي
+
+409
+00:45:59,150 --> 00:46:04,130
+لهذا لو رجعنا لخواصل Transpose مش هذا بيضهر ساوي C
+
+410
+00:46:04,130 --> 00:46:09,270
+itself في A Transpose كذلك يعني هذا بقدر اخد C
+
+411
+00:46:09,270 --> 00:46:15,270
+عامل مشترك مضال A زائد A Transpose طيب نكمل سؤالنا
+
+412
+00:46:16,110 --> 00:46:20,630
+يبقى أثبتنا النقطة الأولى بدنا نروح للنقطة الثانية
+
+413
+00:46:20,630 --> 00:46:24,370
+جالي افترض ان ال A و ال B موجودة في ال M two to
+
+414
+00:46:24,370 --> 00:46:31,680
+then بدى اخد T of ال A زائد ال Bحسب ال definition
+
+415
+00:46:31,680 --> 00:46:37,660
+هدا بدي يعطينا مين؟ بدي يعطينا a زائد ال b زائد ال
+
+416
+00:46:37,660 --> 00:46:41,900
+a زائد ال b transpose تعريف ال linear
+
+417
+00:46:41,900 --> 00:46:46,280
+transformation تمام؟ يبقى هذا الكلام بديه يسوى
+
+418
+00:46:46,280 --> 00:46:52,020
+مين؟ بديه يسوى ال a زائد ال b زائد هذه من خواصة ال
+
+419
+00:46:52,020 --> 00:46:57,920
+transpose a transpose زائد b transposeممكن اجزيها
+
+420
+00:46:57,920 --> 00:47:04,860
+لجزين اخد a زائد a transpose زائد b زائد b
+
+421
+00:47:04,860 --> 00:47:11,040
+transpose يبقى هذا يعطيني الأول T of A و التاني من
+
+422
+00:47:11,040 --> 00:47:21,220
+T of B يبقى هنا Sir T is a linear transformation
+
+423
+00:47:22,390 --> 00:47:26,530
+بدي اجي للمطلوب التاني Nimra B، Nimra B قالي هاتلي
+
+424
+00:47:26,530 --> 00:47:35,190
+ال kernel بقوله اه يبقى ال kernel تبع ال T اللي هو
+
+425
+00:47:35,190 --> 00:47:42,580
+بده يساوي ال kernel لل T، بده يساويكل المصفوفات A
+
+426
+00:47:42,580 --> 00:47:50,920
+اللى موجودة فى ال M22 بحيث أن T of A بده ساوى
+
+427
+00:47:50,920 --> 00:47:56,500
+المصفوفة الصفرية مش شايف تعريف ال kernel؟كل
+
+428
+00:47:56,500 --> 00:48:00,460
+المصففات اللى موجودة في ال vector space و اللى
+
+429
+00:48:00,460 --> 00:48:05,600
+صورتها بدها تساوي مين بدها تساوي zero بقوله كويس
+
+430
+00:48:05,600 --> 00:48:11,740
+يبقى هذا الكلام بده يساوي كل المصففات اللى موجودة
+
+431
+00:48:11,740 --> 00:48:16,960
+في ال M to to such that ال T of A حسب ال
+
+432
+00:48:16,960 --> 00:48:23,470
+definition اللى هو ال Aزائد ال a transpose
+
+433
+00:48:23,470 --> 00:48:31,590
+بده يساوي من؟ بده يساوي ال zero مظبوط هيك؟ طيب شو
+
+434
+00:48:31,590 --> 00:48:37,470
+رأيك هذا؟ هو كل المصففات a اللي موجودة في ال M22
+
+435
+00:48:37,470 --> 00:48:45,930
+such that ال a transpose بده يساوي سالب a مظبوط؟
+
+436
+00:48:45,930 --> 00:48:52,440
+يعني ايش؟يعني ايش؟ مين هم المصطفات هدول؟ شو اسمها؟
+
+437
+00:48:52,440 --> 00:48:58,580
+ادري بتحقق من الخاصية هدى؟ مين؟ الـ skew symmetric
+
+438
+00:48:58,580 --> 00:49:04,040
+يبقى كل skew symmetric matrices يبقى هذا الكلام
+
+439
+00:49:04,040 --> 00:49:16,100
+بدي يسوي the set of all skew symmetric matrices
+
+440
+00:49:18,830 --> 00:49:27,390
+N M 2 2 يبقى كل المصففات اللي بتكون main بتكون
+
+441
+00:49:27,390 --> 00:49:33,150
+skew symmetric يبقى ضايل علينا إيش؟ C good
+
+442
+00:49:33,150 --> 00:49:37,670
+exercise لك فكر فيه و حاولي تجيبي ليه و ان شاء
+
+443
+00:49:37,670 --> 00:49:42,030
+الله يوم السبت بنشوفكوا جيبتوا ولا لأ ماشي؟
+
+444
+00:49:42,030 --> 00:49:45,410
+يرفعلكوا هذا جيبتوا سؤال في إحدى الامتحانات
+
+445
+00:49:45,410 --> 00:49:46,830
+النصفية
+
+446
+00:49:48,590 --> 00:49:51,470
+هذا السؤال مثل اللي قدامك هذا
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/czq6xxZJyIg.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/czq6xxZJyIg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c12ac587335e6aca8d4f98e1793414b813a5b5fc
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/czq6xxZJyIg.srt
@@ -0,0 +1,1592 @@
+1
+00:00:21,800 --> 00:00:27,080
+بسم الله الرحمن الرحيم نبدأ اليوم بأول محاضرة
+
+2
+00:00:27,080 --> 00:00:33,120
+فعلية في صميم المنهج المقرر لهذا الفصل وهو مادة 
+
+3
+00:00:33,120 --> 00:00:39,930
+معادلات .. مادة مساق معادلات تفاضلية وجبر خطي هذا
+
+4
+00:00:39,930 --> 00:00:43,570
+المساق كما قلنا في المرة الماضية تكون من جزء يعني
+
+5
+00:00:43,570 --> 00:00:47,750
+جزء معادلات تفاضلية وجزء اللي هو جبر خطي three
+
+6
+00:00:47,750 --> 00:00:51,090
+chapters في المعادلات التفاضلية و three chapters
+
+7
+00:00:51,090 --> 00:00:55,950
+في الجبر الخطي أو ال linear algebra نبدأ بأول
+
+8
+00:00:55,950 --> 00:00:59,450
+section اللي كله بيتحدث عن المعادلات التفاضلية
+
+9
+00:00:59,450 --> 00:01:03,050
+العنوان introduction to differential equations
+
+10
+00:01:03,050 --> 00:01:08,690
+يعني مقدمة للمعادلات التفاضلية نعطي بعض ال
+
+11
+00:01:08,690 --> 00:01:13,850
+definitions الأساسية اللي لازم نعرفها حتى ندخل في
+
+12
+00:01:13,850 --> 00:01:19,310
+صميم هذا المساق في عندي نوعين من المعادلات
+
+13
+00:01:19,310 --> 00:01:23,150
+التفاضلية معادلة تفاضلية نسميها ordinary
+
+14
+00:01:23,150 --> 00:01:27,750
+differential equation معادلة تفاضلية عادية وفي
+
+15
+00:01:27,750 --> 00:01:32,290
+partial differential equation معادلة تفاضلية جزئية
+
+16
+00:01:32,830 --> 00:01:36,530
+المعادلة التفاضلية الجزئية تعتمد على ما دُرس في
+
+17
+00:01:36,530 --> 00:01:40,430
+Calculus C وهي دراسة الـ function of several
+
+18
+00:01:40,430 --> 00:01:45,570
+variables طبعا هذه خارج نطاق دراستنا في هذا المساق
+
+19
+00:01:45,570 --> 00:01:49,910
+و فقط ستقتصر دراستنا على ال ordinary differential
+
+20
+00:01:49,910 --> 00:01:55,400
+equations اللي هي المعادلات التفاضلية العادية بنبدأ
+
+21
+00:01:55,400 --> 00:01:59,120
+بتعريف المعادلة التفاضلية فبجي بقول the ordinary
+
+22
+00:01:59,120 --> 00:02:03,960
+differential equation is an equation هي عبارة عن
+
+23
+00:02:03,960 --> 00:02:09,080
+معادلة that involves تشتمل أو تحتوي على single
+
+24
+00:02:09,080 --> 00:02:14,920
+unknown function دالة واحدة مجهولة فيها مجهول واحد
+
+25
+00:02:14,920 --> 00:02:20,500
+of a single variable في متغير واحد يعني ايه؟ عندها
+
+26
+00:02:20,500 --> 00:02:27,060
+متغير دالة في متغيرة Y تساوي F of X يبقى Y هو
+
+27
+00:02:27,060 --> 00:02:32,340
+المتغير التابع و X هو المتغير المستقل يبقى Y
+
+28
+00:02:32,340 --> 00:02:37,560
+function في X هذه لما أقول دالة في متغيرين واحد
+
+29
+00:02:38,010 --> 00:02:43,410
+يبقى هنا المعادلة اللي عندي تحتوي على متغير واحد
+
+30
+00:02:43,410 --> 00:02:49,790
+في متغير واحد آخر and some finite number of its
+
+31
+00:02:49,790 --> 00:02:50,410
+derivatives
+
+32
+00:02:53,660 --> 00:02:57,900
+فيها أو تحتوي أو المعادلة تحتوي على مجموعة من
+
+33
+00:02:57,900 --> 00:03:02,320
+المشتقات المشتقة الأولى أو المشتقة الأولى والثانية
+
+34
+00:03:02,320 --> 00:03:06,240
+أو المشتقة الأولى والثانية والثالثة أو الثالثة
+
+35
+00:03:06,240 --> 00:03:10,980
+والثانية فقط أو غير ذلك يبقى احنا عندنا y
+
+36
+00:03:10,980 --> 00:03:15,580
+function في x اشتقناها مرة واتنين وتلاتة كونا منها
+
+37
+00:03:15,580 --> 00:03:20,800
+أربعة خمسة جد ما يكون كونا منها معادلة هذه المعادلة
+
+38
+00:03:20,800 --> 00:03:26,020
+بُسميها معادلة تفاضلية نعطي بعض الأمثلة لأنواع
+
+39
+00:03:26,020 --> 00:03:31,880
+المعادلات التفاضلية فمثلا المتغير الواحد اللي هو y
+
+40
+00:03:31,880 --> 00:03:35,780
+function في x لكن المعادلة احتوت على what do you mean
+
+41
+00:03:35,780 --> 00:03:41,020
+مشتقتها لأن قلنا هنا finite number of its
+
+42
+00:03:41,020 --> 00:03:44,680
+derivatives يبقى هي عند المشتقة الأولى موجودة لو
+
+43
+00:03:44,680 --> 00:03:48,140
+جينا للمعادلة الثانية تحتوي على المشتقة الأولى
+
+44
+00:03:48,140 --> 00:03:52,980
+والثانية هو الدالة بدون اشتقاق تمام؟ إذا المعادلة
+
+45
+00:03:52,980 --> 00:03:56,940
+تحتوي على المشتقة الأولى والثانية لو جيت للمعادلة
+
+46
+00:03:56,940 --> 00:04:01,900
+الثالثة تحتوي على المشتقة الثالثة والثانية والأولى
+
+47
+00:04:01,900 --> 00:04:06,300
+مش موجودة ما عنديش مشكلة المعادلة موجودة with بعض
+
+48
+00:04:06,300 --> 00:04:09,900
+ال derivatives ما قلت كل ال derivatives قلت some
+
+49
+00:04:09,900 --> 00:04:14,520
+يبقى بعض ال derivatives موجودة يبقى كل مثل هذه
+
+50
+00:04:14,520 --> 00:04:20,540
+الأنواع بقول عنها معادلة تفاضلية عادية طيب في عندنا
+
+51
+00:04:20,540 --> 00:04:24,060
+بنات لما كنا ندرسنا في المرحلة الإعدادية والثانوية بقى
+
+52
+00:04:24,060 --> 00:04:30,220
+نقول درجة المعادلة العادية لكن احنا هنا في فرق بين
+
+53
+00:04:30,220 --> 00:04:36,260
+الرتبة والدرجة الدرجة بنحطها للأسس تبع المعادلة
+
+54
+00:04:36,260 --> 00:04:41,540
+اللي موجودة عندي لكن إذا معادلة تفاضلية وفيها
+
+55
+00:04:41,540 --> 00:04:48,820
+مشتقة فبقول رتبة المعادلة التفاضلية هي أعلى مشتقة
+
+56
+00:04:48,820 --> 00:04:53,760
+موجودة عندنا هذا أنا مكتوب قدامي بيقولي the order
+
+57
+00:04:53,760 --> 00:04:58,820
+of a differential equation يعني رتبة المعادلة
+
+58
+00:04:58,820 --> 00:05:03,240
+التفاضلية is the order of the highest derivative
+
+59
+00:05:03,240 --> 00:05:10,220
+يبقى هي رتبة أعلى معامل
+
+60
+00:05:10,220 --> 00:05:17,320
+تفاضلي موجود في هذه المعادلة فمثلا هنا أعلى معامل
+
+61
+00:05:17,320 --> 00:05:22,340
+تفاضلي كده؟ واحد مشتقة الأولى يبقى هذه معادلة من
+
+62
+00:05:22,340 --> 00:05:27,880
+الرتبة الأولى المعادلة الثانية أعلى معامل تفاضل
+
+63
+00:05:27,880 --> 00:05:33,960
+ثاني يبقى هذه معادلة من الرتبة الثانية هذه أعلى
+
+64
+00:05:33,960 --> 00:05:39,640
+مشتقة ثالث يبقى المعادلة هذه من الرتبة الثالثة
+
+65
+00:05:39,640 --> 00:05:43,640
+يبقى بنفرق بين الدرجة و الرتبة الدرجة هي الأسس
+
+66
+00:05:43,640 --> 00:05:46,860
+اللي بتكون مرفوعة إليها المعادلة سواء كانت تفاضلية
+
+67
+00:05:46,860 --> 00:05:50,050
+ولا غير تفاضلية ما عليش علاقة فيها يبقى أنا بتكلم
+
+68
+00:05:50,050 --> 00:05:58,360
+بالرتبة وليس على الدرجة طيب فمثلا الـ order for
+
+69
+00:05:58,360 --> 00:06:02,720
+example the differential equation خمسة y triple
+
+70
+00:06:02,720 --> 00:06:06,800
+prime زائد تلاتة x y double prime ناقص اتنين y
+
+71
+00:06:06,800 --> 00:06:13,180
+prime أس خمسة زائد y يساوي x أس أربعة يا ترى رتبة
+
+72
+00:06:13,180 --> 00:06:18,960
+المعادلة هل هي أربعة ولا خمسة ولا اتنين ولا تلاتة
+
+73
+00:06:18,960 --> 00:06:25,160
+ثلاثة لأن أعلى رتبة معامل تفاضل هي ثالث المعادلة
+
+74
+00:06:25,160 --> 00:06:30,740
+فيها المشتقة الثالثة يبقى هذه is of order three
+
+75
+00:06:30,740 --> 00:06:36,020
+يبقى هنا الرتبة ثلاثة لا خمسة ولا أربعة ولا اتنين
+
+76
+00:06:36,020 --> 00:06:43,710
+وإنما هي من ثلاثة بنجي كمان معلومة جديدة اللي هو حل
+
+77
+00:06:43,710 --> 00:06:46,910
+المعادلة التفاضلية شو يعني حل المعادلة التفاضلية
+
+78
+00:06:46,910 --> 00:06:51,450
+لما أقول المعادلة هذه موجودة فيها عند المشتقة
+
+79
+00:06:51,450 --> 00:06:56,710
+الأولى يبقى أنا بدي الأصل قبل الاشتقاق يعني بدي y
+
+80
+00:06:56,710 --> 00:07:02,710
+as a function of x هذا اللي بسميه حل المعادلة
+
+81
+00:07:02,710 --> 00:07:07,870
+التفاضلية هذه ههه لو بدي أحلها معناته بدي أكامل
+
+82
+00:07:07,870 --> 00:07:12,020
+مرتين لو كمان مرتين ينتهي الـ derivative وبالتالي
+
+83
+00:07:12,020 --> 00:07:16,300
+يُحصل على حل المعادلة التفاضلية هذه نفس القصة
+
+84
+00:07:16,300 --> 00:07:21,140
+وهكذا إذا بدنا نيجي إلى تعريف حل المعادلة
+
+85
+00:07:21,140 --> 00:07:24,820
+التفاضلية the solution of a differential equation
+
+86
+00:07:24,820 --> 00:07:30,300
+هو عبارة عن function هذه ال function نظريا بقول هي
+
+87
+00:07:30,300 --> 00:07:35,560
+Phi of X يبقى الحل هو Y تساوي Phi of X ما له هذا
+
+88
+00:07:35,560 --> 00:07:41,160
+الحل؟ معرف على فترة ما that is defined on an
+
+89
+00:07:41,160 --> 00:07:46,040
+interval هذا الحل لازم يكون معرف على فترة يعني صحيح
+
+90
+00:07:46,040 --> 00:07:49,580
+على فترة and satisfying the given differential
+
+91
+00:07:49,580 --> 00:07:54,640
+equation وفي نفس الوقت يحقق المعادلة التفاضلية
+
+92
+00:07:54,640 --> 00:08:00,020
+الموجودة مشان يكون حل بدي يكون معرف على فترة تمام
+
+93
+00:08:00,020 --> 00:08:05,080
+اثنين لو جيت على وطب في المعادلة التفاضلية بدي يحقق
+
+94
+00:08:05,080 --> 00:08:11,300
+هذه المعادلة نعطي مثال عملي لما نقول باجي بقول for
+
+95
+00:08:11,300 --> 00:08:14,440
+example the solution of the differential equation
+
+96
+00:08:14,440 --> 00:08:21,780
+هذه واحد is y يساوي E أس ناقص اتنين X هذا حل باجي
+
+97
+00:08:21,780 --> 00:08:26,540
+بشوف والله إذا حقق المعادلة التفاضلية اللي عند رقم
+
+98
+00:08:26,540 --> 00:08:30,900
+واحد بيكون حل ما حققش يبقى كلامنا ماله غير صحيح
+
+99
+00:08:30,900 --> 00:08:36,000
+يبقى هذا حل because لو بدي أجي أخد y prime يا بنات
+
+100
+00:08:36,630 --> 00:08:41,310
+يبقى الـ exponential مشتقتها كما هي زي ما أخذنا في
+
+101
+00:08:41,310 --> 00:08:48,790
+كل قاعد بيضرب مشتقة الأس يبقى هاي ناقص اتنين بدنا
+
+102
+00:08:48,790 --> 00:08:56,370
+مين كمان؟ YW prime يبقى هذا يعطيك Y'' يبقى اشتق
+
+103
+00:08:56,370 --> 00:09:00,910
+كمان مرة يبقى ال X وهذا مقدار ثابت ما لهوش دعوة وهذا
+
+104
+00:09:00,910 --> 00:09:05,310
+نشتقه كمان مرة بيجينا ناقص اتنين فناقص اتنين بقداش
+
+105
+00:09:05,310 --> 00:09:12,510
+أربعة E أس ناقص اتنين X الآن بدي أعوض في المعادلة
+
+106
+00:09:12,510 --> 00:09:19,090
+عن ال Y وY' وY'' في المعادلة رقم واحد نشوف هنحصل
+
+107
+00:09:19,090 --> 00:09:27,970
+على ايه يبقى لو جيت للـ YW' زائد Y' ناقص 2Y لو جيت
+
+108
+00:09:27,970 --> 00:09:32,650
+عوضت بهذه الحلول إن طلع الناتج يساوي الصفر يبقى
+
+109
+00:09:32,650 --> 00:09:37,930
+كلامنا صحيح ما طلع يساوي الصفر يبقى كلامنا ماله غير
+
+110
+00:09:37,930 --> 00:09:45,920
+صحيح يبقى نعوض YW' هي أربعة E أس ناقص اتنين X يبقى
+
+111
+00:09:45,920 --> 00:09:48,420
+نعوض YW' هي أربعة E أس ناقص اتنين X يبقى نعوض YW'
+
+112
+00:09:48,760 --> 00:09:51,100
+هي أربعة E أس ناقص اتنين X يبقى نعوض YW' هي أربعة
+
+113
+00:09:51,100 --> 00:09:58,000
+E أس ناقص اتنين X يبقى نعوض
+
+114
+00:09:58,000 --> 00:10:05,340
+YW' هي أربعة E أس ناقص اتنين X طلع لي أربعة بالموجب
+
+115
+00:10:05,340 --> 00:10:10,680
+يا أبو هدول قداش؟ أربعة سالب يبقى الناتج يساوي Zero
+
+116
+00:10:10,680 --> 00:10:17,000
+يبقى الناتج يساوي Zero معناته دا فعلا هو عبارة عن
+
+117
+00:10:17,000 --> 00:10:22,540
+حل لهذه المعادلة بدي أخليك تمرني يدك check
+
+118
+00:10:22,540 --> 00:10:23,420
+that
+
+119
+00:10:27,380 --> 00:10:38,120
+إن Y تساوي constant C E أس ناقص 2X is a solution
+
+120
+00:10:38,120 --> 00:10:49,160
+of the differential equation 1 اتحققيلي أو اتأكدي
+
+121
+00:10:49,160 --> 00:10:56,120
+إن هذا كمان عبارة عن حل آخر للمعادلة التفاضلية شو
+
+122
+00:10:56,120 --> 00:11:03,490
+يعني معناه؟ معناته إن المعادلة التفاضلية ممكن
+
+123
+00:11:03,490 --> 00:11:08,750
+لجيلها عدة حلول وليس حلا واحدا
+
+124
+00:11:10,320 --> 00:11:15,340
+من هنا بعد قليل هروح أقول لك في إن حاجة اسمها ال
+
+125
+00:11:15,340 --> 00:11:20,720
+general solution للمعادلة التفاضلية يبقى هذا أنتِ
+
+126
+00:11:20,720 --> 00:11:25,160
+بتمرني يدك فيه في البيت تتأكدي إن هذا عبارة عن حل
+
+127
+00:11:25,160 --> 00:11:31,700
+المعادلة التفاضلية كذلك نعطي ال definition الكلام
+
+128
+00:11:31,700 --> 00:11:37,580
+اللي قلته شفويا بدنا نحطه على شكل تعريف the set
+
+129
+00:11:37,580 --> 00:11:39,840
+of
+
+130
+00:11:40,610 --> 00:11:51,330
+all solutions مجموعة كل الحلول of a differential
+
+131
+00:11:51,330 --> 00:12:00,010
+equation للمعادلة التفاضلية is called بنروح نسميه
+
+132
+00:12:00,010 --> 00:12:07,270
+the general solution الحل
+
+133
+00:12:07,270 --> 00:12:12,480
+العام of the differential equation of the
+
+134
+00:12:12,480 --> 00:12:18,380
+differential equation الحل العام للمعادلة
+
+135
+00:12:18,380 --> 00:12:25,740
+التفاضلية نعطي مثال example find
+
+136
+00:12:25,740 --> 00:12:30,080
+the general solution of the
+
+137
+00:12:41,300 --> 00:12:50,920
+Differential equations التالية نمرا واحد f w prime
+
+138
+00:12:50,920 --> 00:13:01,200
+of x يساوي اثنا عشر x تربيع زائد ستة x ناقص ثمانية
+
+139
+00:13:01,200 --> 00:13:03,660
+solution
+
+140
+00:13:23,180 --> 00:13:30,580
+مرة ثانية أقول لو جت للمعادلة التفاضلية أو جت
+
+141
+00:13:30,580 --> 00:13:35,600
+الحل الأول والثاني والثالث فمثلا اللي كتبناه قبل 
+
+142
+00:13:35,600 --> 00:13:39,720
+قليل ما كنا نشيك that see هذا كنا نكتب ثاني اثنين ثلاثة
+
+143
+00:13:39,720 --> 00:13:44,140
+أربعة خمسة ستة جد اثنين زي ما بدك كويسيك بقى كم حل
+
+144
+00:13:44,140 --> 00:13:49,170
+بيصير عندي ما لا نهاية من الحلول إذا هذا الحل اللي
+
+145
+00:13:49,170 --> 00:13:55,030
+بيطلع هو صيغة الحل العام الذي يستمل على بقية
+
+146
+00:13:55,030 --> 00:14:01,290
+الحلول تمام؟ إذا في عندي حاجة اسمها الحل العام يبقى
+
+147
+00:14:01,290 --> 00:14:05,550
+مجموعة الحلول كلها بيسميها مين؟ الحل العام فمثلا
+
+148
+00:14:05,550 --> 00:14:09,930
+بدنا نروح نجيب الحل العام لهذه المعادلة المعادلة
+
+149
+00:14:09,930 --> 00:14:11,790
+تحتوي على المشتقة الثانية
+
+150
+00:14:17,920 --> 00:14:23,390
+يبقى مشان أحصل على ال F of X شكليش بدي أعمل له؟ وضروحه
+
+151
+00:14:23,390 --> 00:14:30,630
+كامل مرتين صحيح ولا لأ؟ إذا لو جيت كاملت f double
+
+152
+00:14:30,630 --> 00:14:39,390
+prime of x dx بدي يساوي تكامل للـ 12x تربيع زائد 6x
+
+153
+00:14:39,390 --> 00:14:45,130
+ناقص ثمانية كله بالنسبة لمن؟ الـ dx تكامل مرة
+
+154
+00:14:45,130 --> 00:14:51,970
+واحدة بيعطينا ماذا؟ f prime of x يساوي أربعة x
+
+155
+00:14:51,970 --> 00:14:58,890
+تكعيب زائد ثلاثة x تربيع ناقص ثمانية x التكامل هذا
+
+156
+00:14:58,890 --> 00:15:04,330
+تكامل غير محدود مشاناك ايش بعمل؟ بقول زائد
+
+157
+00:15:04,330 --> 00:15:12,140
+constant c زائد constant C طيب كويس الآن لكي أجيب
+
+158
+00:15:12,140 --> 00:15:17,660
+شكل ال F of X بدي أروح أكامل كمان مرة إذا لو كاملت
+
+159
+00:15:17,660 --> 00:15:26,280
+كمان مرة بيصير عندي مين؟ F of X يساوي X أس أربعة زائد
+
+160
+00:15:26,280 --> 00:15:35,280
+X تكعيب ناقص أربعة X تربيع زائد CX زائد C1
+
+161
+00:15:37,220 --> 00:15:41,640
+إذاً هذا البنات اللي حصلت عليه بيكون هو ال general
+
+162
+00:15:41,640 --> 00:15:48,080
+solution للمعادلة اللي عندنا هذه وبالتالي قدرت
+
+163
+00:15:48,080 --> 00:15:55,320
+أجيب اللي هو شكل الحل العام لهذه المعادلة نعطيكي
+
+164
+00:15:55,320 --> 00:16:04,410
+معادلة ثانية نمرا اثنين لو جيت قلت لك why w prime بدو
+
+165
+00:16:04,410 --> 00:16:14,330
+يساوي sec ال X في tan ال X زائد sec تربيع ال X و
+
+166
+00:16:14,330 --> 00:16:18,890
+بدنا نروح نحل هذه المعادلة هذه معادلة مشتملة
+
+167
+00:16:18,890 --> 00:16:25,090
+على المشتقة الثانية إذا مشان أروح أحلها
+
+168
+00:16:25,090 --> 00:16:31,680
+بدي أروح أكامل كم مرة؟ مرتين كل تكامل بيجيب لي كنستانت
+
+169
+00:16:31,680 --> 00:16:35,340
+الكنستانت اللي أنا بحطه من عندي ممكن يكون أي قيمة
+
+170
+00:16:35,340 --> 00:16:39,180
+تيجي في بالنا ومن هنا صار اللي اللي في المستطيل
+
+171
+00:16:39,180 --> 00:16:43,200
+هذا هو ال general solution لماذا؟ للمعادلة الأولى
+
+172
+00:16:43,200 --> 00:16:46,880
+بنفس الطريقة بنحاول نجيب ال general solution
+
+173
+00:16:46,880 --> 00:16:51,620
+للمعادلة الثانية إذا لو كاملت مرة بيصير عندنا هنا
+
+174
+00:16:51,620 --> 00:17:01,560
+كده؟ وايه؟ تكامل sec tan مقداش؟ sec مهم دا زي دا لأن
+
+175
+00:17:01,560 --> 00:17:08,340
+مشتقة ال sec هي sec ال X tan ال X يبقى sec ال X زائد
+
+176
+00:17:08,340 --> 00:17:15,900
+مشتقة ال tan sec تربيع إذا أنت كاملت sec تربيع بتان
+
+177
+00:17:15,900 --> 00:17:25,360
+ال X يبقى هذه tan ال X زائد constant C نكامل كمان
+
+178
+
+201
+00:19:38,050 --> 00:19:41,330
+اسمها الـ initial value problem شو هو الـ initial value 
+
+202
+00:19:41,330 --> 00:19:45,840
+problem؟ يعني أنا عندي معادلة تفاضلية مثل هذه
+
+203
+00:19:45,840 --> 00:19:50,780
+المعادلة بروح بحط عليها شرط أو شرطين أو ثلاثة أو
+
+204
+00:19:50,780 --> 00:19:56,440
+غيره حسب طبيعة المثلة من خلال هذه الشروط يمكن
+
+205
+00:19:56,440 --> 00:20:01,220
+الحصول على الثوابت اللي عندنا هذه فلما أحصل على ثوابت
+
+206
+00:20:01,220 --> 00:20:06,060
+ببطل يصير عندي ثوابت وبالتالي بجيب شكل الحل
+
+207
+00:20:06,060 --> 00:20:11,000
+الفعلي لمين؟ للمعادلة هذه ومن هنا بسميه الـ initial 
+
+208
+00:20:11,000 --> 00:20:16,980
+value problem يعني نظرية القيمة الأساسية أو السؤال
+
+209
+00:20:16,980 --> 00:20:21,840
+اللي يعتمد على القيم الأساسية نعطيكي definition
+
+210
+00:20:21,840 --> 00:20:31,230
+ومثال يبقى definition The initial 
+
+211
+00:20:31,230 --> 00:20:37,170
+value 
+
+212
+00:20:37,170 --> 00:20:41,990
+problem اللي
+
+213
+00:20:41,990 --> 00:20:55,250
+حديها الرمز IVP is a differential equation يبقى هي
+
+214
+00:20:55,250 --> 00:21:05,870
+عبارة عن معادلة تفاضلية with initial conditions مع
+
+215
+00:21:05,870 --> 00:21:14,870
+شروط ابتدائية موجودة على المثلة example solve
+
+216
+00:21:14,870 --> 00:21:25,400
+the initial value problem Y triple prime يساوي
+
+217
+00:21:25,400 --> 00:21:32,980
+تسعة E أس ناقص ثلاثة X والـ Y عند الـ Zero بدها 
+
+218
+00:21:32,980 --> 00:21:37,740
+تساوي الواحد والـ Y prime عند الـ Zero بدها تساوي
+
+219
+00:21:37,740 --> 00:21:40,980
+اثنين
+
+220
+00:21:48,470 --> 00:21:53,950
+بنرجع للتعريف اللي إحنا كتبناه نقرأ هذا التعريف
+
+221
+00:21:53,950 --> 00:22:00,070
+نحاول أن نفهم كل كلمة في هذا التعريف ثم بعد ذلك
+
+222
+00:22:00,070 --> 00:22:07,610
+ناخد مثال كتطبيق مباشر على هذا التعريف التعريف
+
+223
+00:22:07,610 --> 00:22:14,990
+بيقول الـ initial value problem هأختصرها إلى IVP مش
+
+224
+00:22:14,990 --> 00:22:19,110
+زي التصريح اللي باخده الناس اللي كان حالهم عمره
+
+225
+00:22:19,110 --> 00:22:26,130
+أي يوم Vip لأ IVP هديك very important person يعني 
+
+226
+00:22:26,130 --> 00:22:32,570
+شخص مهم جدا سهل مروره عن الحواجز لأ لأ هدا IVP بقى
+
+227
+00:22:32,570 --> 00:22:37,070
+مثلة وعليها شروط The initial value problem is a
+
+228
+00:22:37,070 --> 00:22:41,350
+differential equation يبقى هي معادلة تفاضلية with
+
+229
+00:22:41,350 --> 00:22:45,790
+initial conditions عليها شروط بسمي هذه الشروط هي
+
+230
+00:22:45,790 --> 00:22:51,510
+الشروط الإبتدائية نعطي مثال على ذلك بقول solve the
+
+231
+00:22:51,510 --> 00:22:55,230
+initial value problem y double prime يساوي تسعة e وأص
+
+232
+00:22:55,230 --> 00:23:00,750
+ناقص ثلاثة x وروحنا حاطين عليها شروط ابتدائية هذه
+
+233
+00:23:00,750 --> 00:23:05,750
+بسميها الـ initial condition وهدول اثنين هم السبب
+
+234
+00:23:05,750 --> 00:23:10,210
+في أن اسميت المعادلة اللي عندنا هذه initial value 
+
+235
+00:23:10,210 --> 00:23:15,110
+problem طيب بنشوف كيف بنحلها يبقى نفس التكتيك اللي 
+
+236
+00:23:15,110 --> 00:23:20,190
+اتبعناه عند حل السؤالين قبل قليل مع الفارق أن
+
+237
+00:23:20,190 --> 00:23:26,350
+ثوابت هدول هجيب قدرش القيم العددية عندهم طبقا لهذه
+
+238
+00:23:26,350 --> 00:23:34,150
+الشروط يبقى لما أقول أنا عندي y'' يساوي تسعة اي أس
+
+239
+00:23:34,150 --> 00:23:42,340
+ناقص ثلاثة اكس لو كملت مرة واحدة يا بنات يبقى أحد
+
+240
+00:23:42,340 --> 00:23:47,920
+المشتقات تبقى مشتقة واحدة هذه تسعة زي ما هي وهي E 
+
+241
+00:23:47,920 --> 00:23:55,760
+أس ناقص ثلاثة X مقسوما على مشتقة الأس إن كان الأس
+
+242
+00:23:55,760 --> 00:24:01,030
+من الدرجة الأولى طبعاً ثلاثة X من الدرجة الأولى
+
+243
+00:24:01,030 --> 00:24:08,390
+يبقى مقسم على سالب ثلاثة زائد constant C1 يبقى 
+
+244
+00:24:08,390 --> 00:24:16,970
+الجواب سالب ثلاثة E وسالب ثلاثة X زائد C1 الآن أنا
+
+245
+00:24:16,970 --> 00:24:20,890
+عندي initial condition هي و بدي أستخدمه ايش
+
+246
+00:24:20,890 --> 00:24:25,170
+بيقول لي في الـ initial condition بيقول لي y prime
+
+247
+00:24:25,170 --> 00:24:29,450
+عند الـ zero بدها تساوي اثنين إذا بدي آجي على 
+
+248
+00:24:29,450 --> 00:24:33,190
+المعادلة اللي عندها دي y prime عند الـ zero بدها
+
+249
+00:24:33,190 --> 00:24:39,850
+تساوي قداش؟ اثنين إذا بدي أشيل كل x وأحط مكانه
+
+250
+00:24:39,850 --> 00:24:49,200
+قداش؟ zero زائد constant c one E0 بقداش يا بنات يعني 
+
+251
+00:24:49,200 --> 00:24:55,960
+معناها كلام أن الـ C1 بدها تساوي قداش؟ خمسة E0 بواحدة
+
+252
+00:24:55,960 --> 00:25:01,640
+سالب ثلاثة ثلاثة واثنين خمسة يبقى صارت المعادلة
+
+253
+00:25:01,640 --> 00:25:07,860
+اللي عندي Y prime يساوي ناقص ثلاثة E أص ناقص ثلاثة 
+
+254
+00:25:07,860 --> 00:25:14,860
+X زائد خمسة أنا ما بدي Y prime بدي Y يبقى ما بعمل بروح 
+
+255
+00:25:14,860 --> 00:25:20,200
+كامل كمان مرة إذا لو روحنا كمان كاملنا كمان مرة
+
+256
+00:25:20,200 --> 00:25:26,720
+بنحصل على y يساوي ناقص ثلاثة ايص ناقص ثلاثة اكس على
+
+257
+00:25:26,720 --> 00:25:35,360
+قداش؟ على سالب ثلاثة زائد خمسة زائد خمسة X زائد c
+
+258
+00:25:35,360 --> 00:25:43,200
+two constant جديد يعني هذا هذا بيعطيك أن الـ y اللي 
+
+259
+00:25:43,200 --> 00:25:50,500
+بندهور عليها بيبقى اي أص ناقص ثلاثة x زائد خمسة x 
+
+260
+00:25:50,500 --> 00:25:55,780
+زائد c2 في عندنا لا يزال initial condition ما 
+
+261
+00:25:55,780 --> 00:26:01,210
+استخدمناهوش اللي هو y عند الـ zero تساوي واحد
+
+262
+00:26:01,210 --> 00:26:07,950
+الآن y عند الـ zero تساوي واحد implies يعني هشيل كل
+
+263
+00:26:07,950 --> 00:26:12,250
+y وأحط مكانها واحد وأشيل كل x وأعوض عنها بـ zero
+
+264
+00:26:12,250 --> 00:26:16,750
+يبقى بصير عندنا واحد يساوي ايه والـ zero بقداش يا 
+
+265
+00:26:16,750 --> 00:26:25,540
+بنات؟ بواحد زائد خمسة في zero بـ zero زائد C2 هذا
+
+266
+00:26:25,540 --> 00:26:30,620
+معناته أن C2 بدها تساوي قداش؟ يبقى بناء أنا عليه
+
+267
+00:26:30,620 --> 00:26:39,240
+بروح بقول له the solution of the given
+
+268
+00:26:40,460 --> 00:26:50,760
+initial value problem is y تساوي e أس ناقص ثلاثة x 
+
+269
+00:26:50,760 --> 00:26:58,860
+زائد خمسة x فقط لغير لإيش؟ لأن c2 عندنا راح بـ zero
+
+270
+00:26:58,860 --> 00:27:06,880
+وبالتالي انتهينا من مشكلته هذه طيب نيجي لآخر تعريف
+
+271
+00:27:06,880 --> 00:27:13,700
+في محاضرة اليوم تعريف definition وهذا التعريف 
+
+272
+00:27:13,700 --> 00:27:17,920
+أساسي للدراسة المستفيدة في الـ differential
+
+273
+00:27:17,920 --> 00:27:22,280
+equations بعد ذلك بيقول لي the linear differential
+
+274
+00:27:22,280 --> 00:27:30,220
+equation الـ معادلة
+
+275
+00:27:30,220 --> 00:27:37,500
+التفاضلية الخطية is an equation هي عبارة عن معادلة
+
+276
+00:27:37,500 --> 00:27:47,320
+in the form في الشكل التالي اللي هي a0 as a 
+
+277
+00:27:47,320 --> 00:27:53,600
+function of x في الـ y to the derivative n الشكل
+
+278
+00:27:53,600 --> 00:28:01,320
+اللي عندنا هذا to the derivative n زائد a1 as a
+
+279
+00:28:01,320 --> 00:28:07,680
+function of x to the derivative n minus الـ 1 زائد
+
+280
+00:28:07,820 --> 00:28:12,420
+اكتشف الـ a2 as a function of x في الـ y to the
+
+281
+00:28:12,420 --> 00:28:18,990
+derivative of n minus 2 زائد زائد نضل ماشيين لغاية
+
+282
+00:28:18,990 --> 00:28:25,830
+ما نوصل للـ a n minus الـ one as a function of x في 
+
+283
+00:28:25,830 --> 00:28:33,950
+الـ y prime زائد a n as a function of x في الـ y بدها
+
+284
+00:28:33,950 --> 00:28:41,230
+تساوي الـ f of x وهذه سامحالي المعادلة star where
+
+285
+00:28:41,230 --> 00:28:50,490
+حيث الـ a0 of x والـ a1 of x والـ a2 of x ونظل
+
+286
+00:28:50,490 --> 00:28:57,710
+ماشيين والـ a n minus one as a function of x والـ
+
+287
+00:28:57,710 --> 00:29:08,410
+a n and الـ f of x كلهم هدول are functions are
+
+288
+00:29:08,410 --> 00:29:20,140
+functions of x only يبقى هدول دوال في x فقط if the 
+
+289
+00:29:20,140 --> 00:29:28,000
+differential equation is not in the form star is
+
+290
+00:29:28,000 --> 00:29:36,680
+not in the form star لو ماكنتش على الشكل star it
+
+291
+00:29:36,680 --> 00:29:49,480
+is called it is called بنروح نسميها a nonlinear 
+
+292
+00:29:49,480 --> 00:29:52,960
+differential
+
+293
+00:29:52,960 --> 00:29:56,040
+equation
+
+294
+00:29:56,040 --> 00:29:59,580
+example
+
+295
+00:29:59,580 --> 00:30:06,320
+equations
+
+296
+00:30:06,320 --> 00:30:09,300
+المعادلات
+
+297
+00:30:10,210 --> 00:30:20,030
+نمرة 1 يساوي
+
+298
+00:30:20,030 --> 00:30:28,490
+ثلاثة X تربيع أو نمرة اثنين
+
+299
+00:30:28,490 --> 00:30:34,530
+Y to the derivative of five زائد ثلاثة y triple
+
+300
+00:30:34,530 --> 00:30:42,330
+prime زائد y prime بدها تساوي zero كلهم هدول are
+
+301
+00:30:42,330 --> 00:30:55,610
+linear differential equations but the equations
+
+302
+00:30:55,610 --> 00:31:08,790
+ولكن المعادلات نمرة 2 y prime زائد 3 لإن الـ واي لإن 
+
+303
+00:31:08,790 --> 00:31:19,620
+الـ واي بدها تساوي x ونمرة 3 y double prime زائد Y في
+
+304
+00:31:19,620 --> 00:31:28,340
+الـ Y prime زائد X في الـ Y يساوي واحد نمرة C Y
+
+305
+00:31:28,340 --> 00:31:39,320
+triple prime زائد X تربيع Y prime الكل تكعيب زائد Y
+
+306
+00:31:39,320 --> 00:31:50,170
+يساوي Zero هدول كلهم are nonlinear differential
+
+307
+00:31:50,170 --> 00:31:52,390
+equations
+
+308
+00:32:21,620 --> 00:32:27,640
+نرجع لتعريفنا هذا مرة ثانية هذا التعريف بنات بيفرق
+
+309
+00:32:27,640 --> 00:32:31,780
+فقط ما بين الـ linear differential equations وما
+
+310
+00:32:31,780 --> 00:32:35,000
+بين الـ nonlinear differential equations يعني
+
+311
+00:32:35,000 --> 00:32:38,720
+وقتاش لو شفت المعادلة بقول عليها الـ linear
+
+312
+00:32:38,720 --> 00:32:42,290
+differential equations ووقتاش لو شفتها بقول ماهياش
+
+313
+00:32:42,290 --> 00:32:47,310
+linear equation يعني ليست معادلة تفاضلية خطية بغض
+
+314
+00:32:47,310 --> 00:32:49,850
+النظر عن الرتبة الأولى أو الثانية أو الثالثة أو
+
+315
+00:32:49,850 --> 00:32:54,730
+الرابعة أو حتى رتبة نونية التعريف بيقولاش the linear
+
+316
+00:32:54,730 --> 00:32:59,730
+differential equation المعادلة التفاضلية الخطية هي
+
+317
+00:32:59,730 --> 00:33:06,180
+عبارة عن equation في الشكل التالي a node of x في y 
+
+318
+00:33:06,180 --> 00:33:11,260
+to the derivative n من حد ما نشوف y بنات فوقه عدد
+
+319
+00:33:11,260 --> 00:33:16,920
+إذا بين قوسين معناته مشتقة بدون أقواس معناته أس
+
+320
+00:33:16,920 --> 00:33:23,880
+تمام اطلع كل رمز من هذه الرموز حتى تقول لك ايه بين 
+
+321
+00:33:23,880 --> 00:33:29,470
+قوسين عشان نعرف أن هذا معناه اشتقاق يبقى هذا a node
+
+322
+00:33:29,470 --> 00:33:34,150
+of x y to the derivative n يعني المشتقة النونية لـ
+
+323
+00:33:34,150 --> 00:33:43,530
+y زائد a1x في y to the derivative n-1 زائد a2 of x
+
+324
+00:33:43,530 --> 00:33:47,930
+y to the derivative n-2 زائد زائد الله باللحظة 
+
+325
+00:33:47,930 --> 00:33:51,790
+المشتقة قاعدة بتنزل نونية نونية ناقص واحد نونية 
+
+326
+00:33:51,790 --> 00:33:56,610
+ناقص اثنين وكذا لغاية ما أوصل للمشتقة الأولى
+
+327
+00:33:57,050 --> 00:34:02,770
+وهنا an of x y بدون اشتقاق يساوي f of x كل 
+
+328
+00:34:02,770 --> 00:34:07,750
+المعاملات اللي عندنا a node of x a1 of x a2 of x 
+
+329
+00:34:07,750 --> 00:34:14,330
+an-1 of x an of x f of x كلها دوال في المتغير x لا
+
+330
+00:34:14,330 --> 00:34:21,710
+تحتوي على y يبقى y للمشتقات وآخر term بدون مهم بدون
+
+331
+00:34:21,710 --> 00:34:26,990
+اشتقاق تمام واللي هدول الباقي كلهم دوال هدول are
+
+332
+00:34:26,990 --> 00:34:32,170
+functions of x only يبقى هذا شكل الدالة الخطية
+
+333
+00:34:32,170 --> 00:34:36,710
+بدي أطرح السؤال التالي ضروري كل المشتقات يكونوا 
+
+334
+00:34:36,710 --> 00:34:41,600
+موجودات ولا ممكن بعضهم يكون مش موجود زي ايش مثلا زي
+
+335
+00:34:41,600 --> 00:34:45,420
+بدأت أنا من المشتقة العاشرة مثلا وإحنا ماشيين في 
+
+336
+00:34:45,420 --> 00:34:49,860
+الطريق المشتقة السادسة والخامسة والرابعة مش
+
+337
+00:34:49,860 --> 00:34:53,520
+موجودة لكن الباقي موجود different linear ولا لا
+
+338
+00:34:53,520 --> 00:34:58,380
+linear على طول الخط لإن المشتقة قاعدة بتنزل اثنين
+
+339
+00:34:58,380 --> 00:35:02,340
+المعاملة دوال في X يعني ما عندناش مش مشكلة طب لو
+
+340
+00:35:02,340 --> 00:35:06,900
+كانت هذه طارت الأخيرة بضل linear ولا ماهياش
+
+341
+00:35:06,900 --> 00:35:10,970
+linear Linear لأن طبقا للشرط كل المعاملات دوال
+
+342
+00:35:10,970 --> 00:35:14,650
+fixed والمشتقات قاعدة بتنزل تغيب واحدة تغيب 
+
+343
+00:35:14,650 --> 00:35:18,170
+اثنتين تغيب .. يعني بتكون إحدى المشتقات بـ zero هذا
+
+344
+00:35:18,170 --> 00:35:23,530
+اللي خلها تغيب يبقى لو غاب بعضها لا بظل في ذلك 
+
+345
+00:35:23,530 --> 00:35:31,290
+تمام؟ طب لو كل هدول كانوا غايبات مرة واحدة وهاد
+
+346
+00:35:31,290 --> 00:35:38,790
+اللي موجودة كيف لأ عاد؟ ليه معادلة تفاضلية خطية من
+
+347
+00:35:38,790 --> 00:35:43,450
+الرتب النونية كمان؟ ليش مش نونية موجودة وهكذا؟
+
+348
+00:35:43,450 --> 00:35:47,590
+طب الآن بدنا نعرف وقت ايش بتبطل تصير Linear يبقى 
+
+349
+00:35:47,590 --> 00:35:50,530
+نعطي بعض الأمثلة if the differential equation
+
+350
+00:35:50,530 --> 00:35:54,010
+ما كانتش في الشكل الستاري يبقى بقول عنها nonlinear
+
+351
+00:35:54,010 --> 00:36:01,780
+فمثلا طلع لي هنا في Y' ما عنديش راحت تمام؟ لكن هذه
+
+352
+00:36:01,780 --> 00:36:05,400
+دالة في X وهذا كونوسنت اللي بعتبره دالة في X وهذا 
+
+353
+00:36:05,400 --> 00:36:11,560
+دالة في X وY'' يبقى هذه دالة خطية طلع هنا كلهم
+
+354
+00:36:11,560 --> 00:36:16,280
+ثوابت والثوابت بعتبره دالة في X ليه؟ لأن ثلاثة في 
+
+355
+00:36:16,280 --> 00:36:21,610
+X أس Zero هي اللي خلتها ثلاثة تمام؟ يبقى كلها
+
+356
+00:36:21,610 --> 00:36:25,850
+دوال fixed الـأسس خمسة وثلاثة واحد المشتقات مش
+
+357
+00:36:25,850 --> 00:36:29,810
+الأسس المشتقات يبقى خمسة وثلاثة واحد قاعدة بتنزل
+
+358
+00:36:29,810 --> 00:36:34,270
+ها والـ Y مش موجودة المشتقة الثانية مش موجودة وY
+
+359
+00:36:34,270 --> 00:36:37,830
+بدون اشتقاق مش موجودة والـ Y للمشتقة الرابعة مش
+
+360
+00:36:37,830 --> 00:36:41,810
+موجودة برضه معادلة خطية ما عندناش مشكلة إن شاء الله
+
+361
+00:36:41,810 --> 00:36:47,270
+يغيبوا كلهم معدة واحدة واحدة من المشتقات لكن لو
+
+362
+00:36:47,270 --> 00:36:52,960
+غابوا هدول كلهم ظل هذا بقول هذه معادلة تفاضلية؟ لأ
+
+363
+00:36:52,960 --> 00:36:57,140
+لأن ما فيش مشتقة يبقى أقل حاجة اللي لازم يكون عندي 
+
+364
+00:36:57,140 --> 00:37:01,860
+ولو المشتقة الأولى مشان أقول عليها معادلة تفاضلية
+
+365
+00:37:01,860 --> 00:37:07,420
+فعلاً طيب هدول كلهم إذا هي معادلة تفاضلية لكن
+
+366
+00:37:07,420 --> 00:37:11,540
+المعادلة الثانية معادلة تفاضلية خطية لكن المعادلة
+
+367
+00:37:11,540 --> 00:37:16,380
+التالية ليست معادلة تفاضلية خطية ليش؟ ايه 
+
+368
+00:37:16,380 --> 00:37:23,310
+المشكلة؟ دالة في X ماشي شرط الأول تحقق هذه Y' هنا
+
+369
+00:37:23,310 --> 00:37:30,170
+ما عنديش Y عندي لن Y يبقى فيها عندي لن هنا يبقى
+
+370
+00:37:30,170 --> 00:37:35,470
+ليست معادلة خطية تمام أعطيكي مثال آخر عندما أقول لك
+
+371
+00:37:35,470 --> 00:37:40,290
+y double prime زائد y y prime زائد x y يساوي واحد
+
+372
+00:37:40,290 --> 00:37:43,990
+الواحد ده اللي في x وهذا x وهذا كل الصندوق .. بس
+
+373
+00:37:43,990 --> 00:37:49,770
+هذا ايش؟ y هو قال لي كل هدول بدهم يكونوا دوال في x
+
+374
+00:37:49,770 --> 00:37:53,450
+لقيت واحدة ماهياش ده اللي في x يبقى هذه الـ non
+
+375
+00:
+
+401
+00:41:07,150 --> 00:41:08,750
+solution
+
+402
+00:41:25,650 --> 00:41:29,930
+السؤال مرة ثانية مقول يتأكد لي أن y يساوي u أس 
+
+403
+00:41:29,930 --> 00:41:34,190
+ناقص x  و y تساوي u أس تلاتة x هي عبارة عن حل
+
+404
+00:41:34,190 --> 00:41:38,530
+المعادلة التفاضلية الأولى على أي فترة من الفترات
+
+405
+00:41:38,530 --> 00:41:46,520
+بدّك فيها إثنين ثم يظهر أنه يتساوي constant في الحل
+
+406
+00:41:46,520 --> 00:41:50,200
+الأول زائد constant ثاني في الحل الثاني هو عبارة عن
+
+407
+00:41:50,200 --> 00:41:56,080
+حل المعادلة اللي بعدها لأي قيم لل constant C1 وC2
+
+408
+00:41:56,080 --> 00:42:00,010
+ما عنديش قيود عليهم يعني ما  يكونوا يكونوا بنقوله
+
+409
+00:42:00,010 --> 00:42:06,050
+بسيطة جدا الآن بدنا نجي نتأكد أن y تساوي e أس ناقص
+
+410
+00:42:06,050 --> 00:42:10,610
+الـ x هي عبارة عن حل للمعادلة التفاضلية فانا عندي
+
+411
+00:42:10,610 --> 00:42:17,230
+y يساوي e أس ناقص الـ x لو اشتقيناها y prime بصير
+
+412
+00:42:17,230 --> 00:42:23,050
+ناقص e أس ناقص x لو جبنا المشتقة الثانية يبقى y'' 
+
+413
+00:42:23,530 --> 00:42:29,370
+بصير ناقص e أس ناقص x في ناقص يبقى بصير e أس ناقص x 
+
+414
+00:42:29,370 --> 00:42:33,930
+نمسك المعلومات هذه ونعوض في المعادلة  إن طلع مجموعهم
+
+415
+00:42:33,930 --> 00:42:39,280
+يساوي صفر بصير خلاص يبقى كلامنا صحيح يبقى بالداخل
+
+416
+00:42:39,280 --> 00:42:46,540
+إلى الـ y'' ناقص اثنين y' ناقص ثلاثة y يساوي الـ
+
+417
+00:42:46,540 --> 00:42:54,800
+y'' هي e أس ناقص x وهي ناقص اثنين الـ y' اللي هي 
+
+418
+00:42:54,800 --> 00:43:02,440
+ناقص e أس ناقص x وهنا ناقص ثلاثة في الـ y الـ y هي
+
+419
+00:43:02,440 --> 00:43:12,010
+e أس ناقص x  y  ساوي عندكم هنا بنات e أس ناقص x تمام
+
+420
+00:43:12,010 --> 00:43:19,490
+وعندك ناقص في ناقص بيزيد اثنين e أس ناقص x وعندك 
+
+421
+00:43:19,490 --> 00:43:24,510
+ناقص ثلاثة e أس ناقص x وe  ساوي هذول قداش
+
+422
+00:43:24,510 --> 00:43:30,050
+مجموعهم ثلاثة  و هذه ثلاثة بالسالب بالنتيجة يساوي
+
+423
+00:43:30,050 --> 00:43:37,550
+كذا؟ صفر يبقى بناء عليه اللي هو y تساوي e أس
+
+424
+00:43:37,550 --> 00:43:48,890
+ناقص x is a solution of the differential equation
+
+425
+00:43:48,890 --> 00:43:53,890
+one سمّي لي هذه المعادلة اللي فوق رقم واحد هي
+
+426
+00:43:53,890 --> 00:43:54,930
+الأساسية
+
+427
+00:44:01,100 --> 00:44:10,880
+بنفس الطريقة عندك y تساوي e أس ثلاثة x اللي هو
+
+428
+00:44:10,880 --> 00:44:12,540
+الحل الثاني اللي جاي لي عليه
+
+429
+00:44:16,170 --> 00:44:24,270
+يبقى y' يساوي ثلاثة e أس ثلاثة x بدي أشتق كمان مرة
+
+430
+00:44:24,270 --> 00:44:32,390
+يبقى تسعة e أس ثلاثة x بدي امسك المعلومات اللي 
+
+431
+00:44:32,390 --> 00:44:36,770
+وصلت لها هذه وإيه ونجي نعوض وبفهمين في هذه
+
+432
+00:44:36,770 --> 00:44:42,410
+المعادلة يبقى لما نجي نعوض في هذه المعادلة بصير y''
+
+433
+00:44:42,410 --> 00:44:48,550
+ناقص اثنين y' ناقص ثلاثة y يساوي بدي
+
+434
+00:44:48,550 --> 00:44:53,730
+أشوفها بدي تساوي صفر ولا بدهاش تساوي صفر يبقى
+
+435
+00:44:53,730 --> 00:44:59,770
+باجي بقوله الـ y'' اللي هي تسعة e أس ثلاثة x
+
+436
+00:45:00,560 --> 00:45:08,380
+ناقص اثنين الـ y' يا بنات اللي هي ثلاثة e أس ثلاثة 
+
+437
+00:45:08,380 --> 00:45:16,140
+x  الـ y'' أو المعادلة بعدها ناقص ثلاثة في e أس
+
+438
+00:45:16,140 --> 00:45:24,720
+ثلاثة x يساوي يساوي تسعة e أس ثلاثة x ناقص ستة e 
+
+439
+00:45:24,720 --> 00:45:31,530
+أس ثلاثة x ناقص e أس ثلاثة x يساوي قداش؟ صفر يبقى
+
+440
+00:45:31,530 --> 00:45:40,610
+بناء عليه y تساوي e أس 3x is a solution إيش ضال
+
+441
+00:45:40,610 --> 00:45:47,850
+عليه كنتوا نتأكد أن هذا هو حل يبقى تشيك
+
+442
+00:45:50,130 --> 00:45:58,270
+y يساوي C1E-X زائد C2E-3X
+
+443
+00:46:06,860 --> 00:46:11,520
+طبعا عندكم محاضرة اليوم من 12 للواحدة مظبوط يلا في
+
+444
+00:46:11,520 --> 00:46:15,100
+الوقت اللي شوفي حالك عندك فرق شيكي شوفي لي هذا حل
+
+445
+00:46:15,100 --> 00:46:20,320
+ولا لأ وإذا حد طلعته ما هو حل بنحله احنا إن شاء
+
+446
+00:46:20,320 --> 00:46:23,180
+الله في المحاضرة القادمة
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..487cba4c1e0dcfe857ed6ce945e79140c69f956f
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ.srt
@@ -0,0 +1,1393 @@
+1
+00:00:19,640 --> 00:00:25,380
+بسم الله الرحمن الرحيم بنرجع نكمل الموضوع الذي كنا
+
+2
+00:00:25,380 --> 00:00:31,040
+بنتحدث فيه قبل ساعتين طبعا أعطينا الـ three
+
+3
+00:00:31,040 --> 00:00:34,800
+integrating factors الـ integrating factor الأول
+
+4
+00:00:34,800 --> 00:00:39,860
+كان μ of Y بده يساوي E أس تكامل ∂N by
+
+5
+00:00:39,860 --> 00:00:41,840
+∂X ناقص ∂M
+
+6
+00:00:56,840 --> 00:01:04,230
+أو مقدار ثابت، ودرَسنا واخدنا مثالًا على كل منهما، باقي
+
+7
+00:01:04,230 --> 00:01:08,170
+الـ integrating factor الأخير أنه لو ما حصلش لا
+
+8
+00:01:08,170 --> 00:01:12,830
+هذا ولا ذاك، شو نعمل؟ قلنا بنروح نفرض أن الـ
+
+9
+00:01:12,830 --> 00:01:17,290
+integrating factor عليه الشكل μ of X و Y يساوي X
+
+10
+00:01:17,290 --> 00:01:23,570
+to the power M في Y to the power N، و بنحاول نوجد
+
+11
+00:01:23,570 --> 00:01:29,090
+قيمة M و N، وإذا وجدناهم بيكون جبنا شكل الـ
+
+12
+00:01:29,090 --> 00:01:33,700
+integrating factor وبالتالي بنضرب فيه وبتنحل
+
+13
+00:01:33,700 --> 00:01:37,800
+مشكلتنا تمام، يبقى هذا هو الـ integration factor
+
+14
+00:01:37,800 --> 00:01:43,140
+الجديد، يبقى بدنا نيجي هنا ونبحث هذه المعادلة
+
+15
+00:01:43,140 --> 00:01:48,320
+الأصلية اللي هي مين؟ اللي سميناها star، يبقى بدنا نيجي
+
+16
+00:01:48,320 --> 00:01:55,580
+ناخد تفاضل الـ M بالنسبة إلى Y، اه بس يا بنات بفضل 
+
+17
+00:01:55,580 --> 00:02:01,940
+قبل ذلك أن نحاول نرتب المعادلة اللي عندنا بشكل جديد
+
+18
+00:02:01,940 --> 00:02:05,980
+بحيث تبقى في وضعها الطبيعي، يبقى هذه بدي أجيبها في
+
+19
+00:02:05,980 --> 00:02:13,860
+الأول 2Y تكعيب ناقص 3XY زائد اللي هو مين؟
+
+20
+00:02:13,860 --> 00:02:19,960
+اللي هو الـ X تربيع زائد XY تربيع، كله في الـ Y
+
+21
+00:02:19,960 --> 00:02:25,000
+prime يساوي صفر، هذه الـ equation هي star في وضعها
+
+22
+00:02:25,000 --> 00:02:31,910
+الطبيعي، يبقى بتروح تاخد تفاضل الـ M بالنسبة إلى Y
+
+23
+00:02:31,910 --> 00:02:40,250
+يبقى بنشتق الأولى بالنسبة إلى Y، يبقى 6Y تربيع ناقص
+
+24
+00:02:40,250 --> 00:02:47,370
+3X، الآن بدنا نيجي تفاضل الـ N بالنسبة إلى X
+
+25
+00:02:47,370 --> 00:02:54,950
+المعادلة الثانية، يبقى 2X زائد Y تربيع، تمام التمام.
+
+26
+00:02:56,390 --> 00:03:02,030
+من اللي اتنين هدول بنستنتج انه تفاضل الـ M بالنسبة
+
+27
+00:03:02,030 --> 00:03:11,350
+إلى Y لا يساوي تفاضل الـ N بالنسبة إلى X، يعني معنى
+
+28
+00:03:11,350 --> 00:03:18,930
+هذا الكلام انه The differential equation star is
+
+29
+00:03:18,930 --> 00:03:25,900
+not exact، Madam، not exactly، بدأ أروح أدور على الـ
+
+30
+00:03:25,900 --> 00:03:30,460
+two integrating factors الأساسيات الاتنين بتاعتنا
+
+31
+00:03:30,460 --> 00:03:34,700
+يبقى أنا مش عارف أبدأ .. يبقى بدي أغمض وأتوكل على
+
+32
+00:03:34,700 --> 00:03:40,480
+الله وأشوف تيجي ولا بتجيش لإن شكلهم مكلكع يعني مش
+
+33
+00:03:40,480 --> 00:03:45,990
+.. مش عند بعض ليش؟ لإن لو طرحتممكن انتهيش أو
+
+34
+00:03:45,990 --> 00:03:49,990
+ما أوصلش لـ function of y أو function of x، إذا لو
+
+35
+00:03:49,990 --> 00:03:55,430
+جيت أخد ∂N by ∂x ناقص ∂m by
+
+36
+00:03:55,430 --> 00:04:00,710
+∂y بدي أقسم على m، ∂N by ∂x له 
+
+37
+00:04:00,710 --> 00:04:09,410
+2X زائد Y تربيع ناقص 6Y تربيع زائد 3X
+
+38
+00:04:09,410 --> 00:04:20,220
+كله على مين؟ على m، يبقى M بـ 2Y تكعيب ناقص 3XY، و
+
+39
+00:04:20,220 --> 00:04:27,760
+يساوي هذه لو جمعتها مع بعض بيصير 5X، وعندك Y تربيع
+
+40
+00:04:27,760 --> 00:04:35,160
+و ناقص 6Y تربيع بيظل ناقص 5Y تربيع على مين؟ على ليه
+
+41
+00:04:35,160 --> 00:04:41,520
+2Y تكعيب ناقص 3XY
+
+42
+00:04:42,450 --> 00:04:48,590
+طيب في عامل مشترك فوق اللي هو فيه خمسة فقط لغير
+
+43
+00:04:48,590 --> 00:04:57,390
+بيضل X ناقص Y تربيع، تحت في عندنا Y عامل مشترك فقط
+
+44
+00:04:57,390 --> 00:05:04,490
+لغير مصبوط بيضل عندنا 2Y تربيع 2Y تربيع
+
+45
+00:05:04,490 --> 00:05:13,900
+ناقص 3X، هل هذه function of y في اختصارات؟
+
+46
+00:05:13,900 --> 00:05:24,060
+ماعنديش، يبقى هذه not function of y only، ما هيش
+
+47
+00:05:24,060 --> 00:05:30,660
+function في Y فقط، يبقى بنفعش، شو نعمل؟ نبدل النص في
+
+48
+00:05:30,660 --> 00:05:37,200
+الثاني، يبقى بدي أخد تفاضل الـ M بالنسبة إلى Y ناقص
+
+49
+00:05:37,200 --> 00:05:43,720
+تفاضل الـ N بالنسبة إلى X، كله مقسومًا على N، يبقى بدنا
+
+50
+00:05:43,720 --> 00:05:52,340
+نقلب الوضع ∂M by ∂Y، 6Y تربيع ناقص 3X
+
+51
+00:05:52,340 --> 00:05:59,300
+ناقص 2X
+
+52
+00:05:59,300 --> 00:06:07,760
+ناقص Y تربيع، كل هذا مقسومًا على N، وين الـ N؟ هيها X
+
+53
+00:06:07,760 --> 00:06:14,880
+تربيع زائد XY تربيع، تمام، يبقى هذه بدها تساوي
+
+54
+00:06:14,880 --> 00:06:21,140
+طلع لي هنا 6Y تربيع وناقص Y تربيع بيظل 5Y
+
+55
+00:06:21,140 --> 00:06:31,240
+تربيع ناقص 5X كله مقسومًا على X تربيع زائد XY
+
+56
+00:06:31,240 --> 00:06:39,550
+تربيع، يبقى بناء عليه أصبح عندي ∂M by ∂
+
+57
+00:06:39,550 --> 00:06:47,830
+Y ناقص ∂N by ∂X كله مقسومًا على N، بده
+
+58
+00:06:47,830 --> 00:06:53,510
+يساوي، في عندي هنا خمسة عامل مشترك وبظل عندي Y
+
+59
+00:06:53,510 --> 00:07:02,090
+تربيع ناقص X، على هنا في X عامل مشترك وبظل عندي X
+
+60
+00:07:02,090 --> 00:07:09,000
+زائد Y، تعرفيها في اختصارات؟ لأ لأ، يبقى اختصارات
+
+61
+00:07:09,000 --> 00:07:16,800
+ماعنديش، اتنين ليست function في X تمام، يبقى not
+
+62
+00:07:16,800 --> 00:07:22,420
+يبقى
+
+63
+00:07:22,420 --> 00:07:31,770
+الـ not a function of X only، يبقى ما نفعش لا هادي ولا
+
+64
+00:07:31,770 --> 00:07:36,150
+هادي بتجيب لي integrative factors، يبقى ما ضلش قدام
+
+65
+00:07:36,150 --> 00:07:39,490
+التالت
+
+66
+00:07:39,490 --> 00:07:42,270
+يبقى بالعامية أقول suppose that
+
+67
+00:07:46,510 --> 00:07:53,830
+الـ μ of x و y يساوي X to the power M في Y to the
+
+68
+00:07:53,830 --> 00:08:01,910
+power N، suppose that هذا يساوي هذا is an
+
+69
+00:08:01,910 --> 00:08:13,810
+integrating factor for the differential
+
+70
+00:08:16,920 --> 00:08:25,080
+equation star، مدام هذا هو عامل تكامل، إذا هضرب
+
+71
+00:08:25,080 --> 00:08:30,840
+الطرفين في X أس M في Y أس N
+
+72
+00:08:34,700 --> 00:08:40,280
+بدي أضربها كلها من أولها إلى آخرها في الـ X أس M
+
+73
+00:08:40,280 --> 00:08:47,680
+Y أس N، شوف أيش اللي بدي يصير، ها 2 زي ما هي X
+
+74
+00:08:47,680 --> 00:08:56,540
+أس M ماعنديش X أس M، عندك Y أس N زائد 3
+
+75
+00:08:56,540 --> 00:09:06,350
+انتهينا منه، ناقص هاي 3X أس M زائد 1 Y
+
+76
+00:09:06,350 --> 00:09:15,270
+أس N زائد 1 ضربناها، زائد هاي قصة، وعندك هنا X
+
+77
+00:09:15,270 --> 00:09:26,130
+أس M زائد 2 في الـ Y أس N زائد X أس M زائد
+
+78
+00:09:26,130 --> 00:09:35,390
+1 Y أس N زائد 2، كل هذا في الـ Y prime بده
+
+79
+00:09:35,390 --> 00:09:42,910
+يساوي قداش؟ صفر، هو هذي اللي هي الـ main double star، مدام
+
+80
+00:09:42,910 --> 00:09:48,610
+فرضنا هذي integrative، وهذي إيش بدتكون؟ exact، لإنه
+
+81
+00:09:48,610 --> 00:09:55,590
+جالها integrative vector، يبقى هنا we get بنحصل على
+
+82
+00:09:55,590 --> 00:09:59,030
+من الـ differential هذي is exact
+
+83
+00:10:01,250 --> 00:10:06,790
+ما دام exact يبقى بدي أخد تفاضل الـ M by ∂Y
+
+84
+00:10:06,790 --> 00:10:13,010
+و تفاضل N بالنسبة لـ X، و زي أساسًا يساوي بعض، يبقى بدي
+
+85
+00:10:13,010 --> 00:10:22,270
+أخد هنا تفاضل هذا كله، تفاضل الـ M بالنسبة إلى Y
+
+86
+00:10:22,270 --> 00:10:25,490
+تفاضل
+
+87
+00:10:25,490 --> 00:10:31,230
+الـ M بالنسبة إلى Y، تفاضل الـ M بالنسبة إلى Y، تفاضل
+
+88
+00:10:31,230 --> 00:10:36,610
+الـ M بالنسبة إلى Y، تفاضل الـ M بالنسبة إلى Y، تفاضل
+
+89
+00:10:36,610 --> 00:10:38,710
+الـ M بالنسبة إلى Y، تفاضل الـ M بالنسبة إلى Y، تفاضل
+
+90
+00:10:38,710 --> 00:10:40,710
+الـ M بالنسبة إلى Y، تفاضل الـ M بالنسبة إلى Y، تفاضل
+
+91
+00:10:40,710 --> 00:10:41,590
+الـ M بالنسبة إلى Y، تفاضل الـ M بالنسبة إلى Y، تفاضل
+
+92
+00:10:41,590 --> 00:10:42,050
+الـ M بالنسبة إلى Y، تفاضل الـ M بالنسبة إلى Y، تفاضل
+
+93
+00:10:42,050 --> 00:10:45,320
+الـ M بالنسبة إلى Y، تفاضل الـ M بالن...لأنه بيفضل الـ Y
+
+94
+00:10:45,320 --> 00:10:52,360
+نيجي هذه بيفضل لها كمان، يبقى ناقص 3 في M زائد
+
+95
+00:10:52,360 --> 00:11:03,990
+1 في X أس M زائد 1 في الـ Y أس N، واضحة ظنطب
+
+96
+00:11:03,990 --> 00:11:08,370
+ايش رأيك؟ وبده أخد منهم عامل مشترك، يبقى لو جيت
+
+97
+00:11:08,370 --> 00:11:15,170
+أخدت الـ X أس M في الـ Y أس N عامل مشترك بظل عندنا
+
+98
+00:11:15,170 --> 00:11:22,830
+مين؟ 2N زائد 6، هذا ما له دعوة، هذه طارت بظل
+
+99
+00:11:22,830 --> 00:11:31,870
+Y تربيع شكل عندنا هذا اللي بعد...ناقص وهذه 3N
+
+100
+00:11:31,870 --> 00:11:39,450
+زائد 3 وهنا X، والـ X أس طلعت والـ Y أس N
+
+101
+00:11:39,450 --> 00:11:47,530
+طلعت مع السلامة، طيب بدي آخد تفاضل الـ N بالنسبة
+
+102
+00:11:47,530 --> 00:11:54,570
+إلى X، يبقى بضرورة أفضّل هذه بالنسبة إلى X، بصير M
+
+103
+00:11:54,570 --> 00:12:01,850
+زائد 2 X أس M زائد 1 الـ Y أس N، مقدار
+
+104
+00:12:01,850 --> 00:12:10,810
+ثابت ما له دعوة، اللي بعده زائد M زائد 1 في الـ X
+
+105
+00:12:10,810 --> 00:12:19,330
+أس M في الـ Y أس N زائد 2، خلّصنا منها، يساوي
+
+106
+00:12:19,330 --> 00:12:27,020
+بدي أخد X أس M في Y أس N عامل مشترك، يبقى بيظل هنا
+
+107
+00:12:27,020 --> 00:12:34,720
+مين؟ بيظل M زائد 2 في الـ X، يبقى M زائد 2
+
+108
+00:12:34,720 --> 00:12:40,240
+كله في الـ X والـ X والاسم والـ Y والسن هيبرة ليه
+
+109
+00:12:40,240 --> 00:12:47,920
+جلال اللي بعده؟ زائد M زائد 1 الـ X والاسم يجه Y
+
+110
+00:12:47,920 --> 00:12:53,860
+تربيع، الآن يا بنات احنا عندنا هذه exact، ما دام
+
+111
+00:12:53,860 --> 00:13:00,340
+exact، هدول لازم يساووا بعض مظبوط، يبقى sense
+
+112
+00:13:00,340 --> 00:13:09,720
+equation double star is exact
+
+113
+00:13:13,220 --> 00:13:20,340
+أن تفاضل الـ M بالنسبة الى Y بيساوي تفاضل الـ N
+
+114
+00:13:20,340 --> 00:13:27,940
+بالنسبة إلى X، هذا معناه ان هدول بيساوي بعض، أظن هذا
+
+115
+00:13:27,940 --> 00:13:32,360
+لو شطبتهم بيروح ما عندناش مشكلة، بيظل الـ term هذا
+
+116
+00:13:32,360 --> 00:13:40,430
+بيساوي الـ term هذا، يبقى بصير عندنا 2N زائد 6 في الـ
+
+117
+00:13:40,430 --> 00:13:51,630
+Y تربيع ناقص 3N زائد 3 في الـ X بده يساوي الـ M
+
+118
+00:13:51,630 --> 00:13:59,030
+زائد 2 كله في الـ X زائد الـ M زائد 1 في الـ Y
+
+119
+00:13:59,030 --> 00:14:04,000
+تربيع، هذه بدي أكتبها هنا وأكتبها هنا، بيكون جسمت
+
+120
+00:14:04,000 --> 00:14:10,460
+عليهم بيظلوا بيساووا بعض، إذا يا بنات معامل Y تربيع
+
+121
+00:14:10,460 --> 00:14:16,180
+هنا هو معامل Y تربيع هنا، ومعامل X هنا هو معامل X
+
+122
+00:14:16,180 --> 00:14:20,970
+هنا، تعالوا نسوي هذه المعاملات ببعض، يبقى أنا عندي
+
+123
+00:14:20,970 --> 00:14:30,690
+هنا M زائد 2 تبعت الـ X بدها تساوي ناقص 3N ناقص
+
+124
+00:14:30,690 --> 00:14:36,190
+3، ناقص بتخش على الاتنين، المعادلة الثانية، معامل
+
+125
+00:14:36,190 --> 00:14:46,550
+Y تربيع يبقى M زائد 1 بدها تساوي 2N زائد 6
+
+126
+00:14:47,100 --> 00:14:53,900
+معادلتين في مجهولين بقدر أحلهم مع بعض بدون مشاكل
+
+127
+00:14:53,900 --> 00:15:01,370
+تمام، باجي بقول هذا بده يعطينا، أظن هذه لو كانت M
+
+128
+00:15:01,370 --> 00:15:07,070
+زائد 1 كانت انتهت مشكلتنا، يبقى خلّيني أطرح 1
+
+129
+00:15:07,070 --> 00:15:12,810
+من الطرفين، يبقى لو طرحنا 1 من الطرفين بصير M
+
+130
+00:15:12,810 --> 00:15:22,920
+زائد 1 تساوي ناقص 3N ناقص 4، وهذي بدها
+
+131
+00:15:22,920 --> 00:15:30,680
+يخلّيها زي ما هي، M زائد 1 يساوي 2N زائد
+
+132
+00:15:30,680 --> 00:15:35,440
+6، مش الطرف الشمال هو الطرف الشمال، إذا الطرف
+
+133
+00:15:35,440 --> 00:15:40,820
+اليمين بدها تساوي الطرف اليمين، يبقى هذا معناه ان
+
+134
+00:15:40,820 --> 00:15:48,600
+2N زائد 6 بدها تساوي ناقص 3N ناقص
+
+135
+00:15:48,600 --> 00:15:55,330
+4، هذا معناه...بيدخل الـ N في شغلة والـ constant في
+
+136
+00:15:55,330 --> 00:16:03,050
+شغلة ثانية، يبقى هذا بيصير 5N يساوي ناقص 10
+
+137
+00:16:03,050 --> 00:16:11,170
+إذا الـ N بيبقى ناقص 2، طيب بدي أشيل الـ N وأحط
+
+138
+00:16:11,170 --> 00:16:17,150
+مكانها ناقص 2 وأشوف قداش الـ M، يبقى هذه
+
+139
+00:16:17,150 --> 00:16:23,790
+المعلومة الأولى، هذا بدي أعطيكي ان M زائد 1
+
+140
+00:16:23,790 --> 00:16:28,490
+يساوي أي واحدة من الاتنين سبين، يبقى هذه قداش
+
+141
+00:16:28,490 --> 00:16:36,850
+بـ ناقص 2، يبقى 2 في ناقص 2 زائد 6 يعني
+
+142
+00:16:36,850 --> 00:16:43,990
+M زائد 1 بدها تساوي كده يا بنات؟ تساوي 2 لإنه
+
+143
+00:16:43,990 --> 00:16:50,010
+ناقص 4 وزائد 6 بيظل 2، هذا معناه إن الـ M
+
+144
+00:16:50,010 --> 00:16:56,890
+يساوي كده؟ يساوي 1، إذا أصبح شكل الـ integrating
+
+145
+00:16:56,890 --> 00:17:00,910
+factor على الشكل التالي
+
+146
+00:17:08,060 --> 00:17:13,960
+يبقى الآن the integrating
+
+147
+00:17:13,960 --> 00:17:25,060
+factor is
+
+148
+00:17:26,210 --> 00:17:36,290
+الـ μ X Y يساوي X أس M ما بجيبش 1، يبقى X فقط، و
+
+149
+00:17:36,290 --> 00:17:43,550
+Y أس N، ما بجيبش ناقص 2، هل حين بدي أشوف هذا
+
+150
+00:17:43,550 --> 00:17:49,850
+بيحوّل لي الـ equation الـ star الى exact equation ولا
+
+151
+00:17:49,850 --> 00:17:55,150
+لأ، يبقى بدي أروح أضرب المعادلة star في XY أس -2، يبقى بدي امسك كده
+
+152
+00:17:55,150 --> 00:17:59,610
+integrating factor
+
+153
+00:17:59,610 --> 00:18:04,450
+و أضربه في المعادلة هذه، يبقى هذه بيصير 2 يا
+
+154
+00:18:04,450 --> 00:18:12,540
+بنات، وهنا X زي ما هي وهنا Y فقط لا غير، هنا ناقص
+
+155
+00:18:12,540 --> 00:18:25,740
+3X تربيع Y أس -1، زائد هنا يصير X تكعيب Y أس
+
+156
+00:18:25,740 --> 00:18:33,680
+ناقص 2 زائد X تربيع والـ Y مع السلامة، Y prime
+
+157
+00:18:33,680 --> 00:18:40,540
+يساوي صفر، وهذه المعادلة هي double star لإن بدي
+
+158
+00:18:40,540 --> 00:18:47,720
+أشوف double star exact ولا لا، يبقى هذه كلها أصبحت
+
+159
+00:18:47,720 --> 00:18:55,760
+بـ M وهذه كلها أصبحت بالـ N، يبقى بدي أخد تفاضل M
+
+160
+00:18:55,760 --> 00:19:04,210
+بالنسبة إلى Y، بقدرش يا بنات هنا 2X وهنا زائد
+
+161
+00:19:04,210 --> 00:19:12,490
+3X تربيع Y أس -2، بدي أخد تفاضل الـ N
+
+162
+00:19:12,490 --> 00:19:20,610
+بالنسبة إلى X تمام؟ بالنسبة إلى X، وY، يساوي 3
+
+163
+00:19:33,840 --> 00:19:41,320
+يبقى شغلنا الأولاني كله سليم 100%، يبقى من هدول
+
+164
+00:19:41,320 --> 00:19:46,660
+اتنين مع بعض بس ننتج انه ∂m by ∂y
+
+165
+00:19:46,660 --> 00:19:53,240
+يساوي ∂n by ∂x، يبقى هذا بيعطيني انه
+
+166
+00:19:53,240 --> 00:20:00,700
+the differential equation double star is exact
+
+167
+00:20:00,700 --> 00:20:09,
+
+201
+00:24:06,210 --> 00:24:10,290
+يتفتح هي الكتاب هيك طبعًا السؤال في الكتاب ما تلاقيهش 
+
+202
+00:24:10,290 --> 00:24:14,910
+هذا الجواب تقول هيك والله حالي غلط مظبوط لأ حالي
+
+203
+00:24:14,910 --> 00:24:18,630
+غلط لأ جد حال سليم مائة بالمائة طب إيش الجواب اللي
+
+204
+00:24:18,630 --> 00:24:20,870
+ممكن ألاقيه تعالي أوريكي إيش الجواب اللي ممكن
+
+205
+00:24:20,870 --> 00:24:27,560
+أتلاقيه الحين عندنا هذه هيك بده يساوي كونستانسيأنا
+
+206
+00:24:27,560 --> 00:24:32,480
+عندي Y بالموجب وهنا Y الأس تبعها السالب بقدر أخلي 
+
+207
+00:24:32,480 --> 00:24:38,420
+الأس تبعي معله موجب شو أعمل؟ أضرب الطرفين في Y إذا
+
+208
+00:24:38,420 --> 00:24:43,180
+المعادلة هذه بقدر أكتبها على الشكل التالي X تربيع
+
+209
+00:24:43,180 --> 00:24:52,310
+Y تربيع ناقص X تكعيب يساوي C في Y ضربت الطرفين في Y
+
+210
+00:24:52,310 --> 00:24:58,490
+فقط لا غير ممكن أعيد ترتيبها و أقول X تربيع Y
+
+211
+00:24:58,490 --> 00:25:08,210
+تربيع ناقص Cy ناقص X تكعيب يساوي Zero إيش رأيك؟ هذه 
+
+212
+00:25:08,210 --> 00:25:13,750
+معادلة من الدرجة الثانية في Y، مظبوط؟ إذا منحلك
+
+213
+00:25:14,980 --> 00:25:22,960
+بالقانون تمام يبقى بناء عليه y يساوي ناقص با يعني
+
+214
+00:25:22,960 --> 00:25:29,700
+ايش صارت ناقص ناقص بصير زائد c زائد أو ناقص الجذري
+
+215
+00:25:29,700 --> 00:25:35,260
+التربيع اللي هي c تربيع ناقص أربعة الف اللي هي x
+
+216
+00:25:35,260 --> 00:25:42,940
+تربيع جيم اللي هو ناقص x تكعيب كله على اتنين الف 
+
+217
+00:25:42,940 --> 00:25:50,860
+يبقى اتنين اكس تربيع أو إن شئت قولنا فقلنا هذه C
+
+218
+00:25:50,860 --> 00:25:59,780
+زائد أو ناقص الجذر التربيعي لمن؟ لـC تربيع زائد
+
+219
+00:25:59,780 --> 00:26:08,940
+أربعة اكس أس خمسة تمام؟ كل هذا الكلام على الاتنين
+
+220
+00:26:08,940 --> 00:26:16,530
+اكس تربيع طيب هذا الكلام بده يساوي يا بنات لو طلعت
+
+221
+00:26:16,530 --> 00:26:22,410
+فوق x وقلت أسالي باتنين بنفعلها بالفعلبظل في
+
+222
+00:26:22,410 --> 00:26:29,930
+المقام اتنين يعني C على اتنين زائد أو ناقص الجذري
+
+223
+00:26:29,930 --> 00:26:34,750
+التربيعي اتنين هذه لو دخلتها تحتها بتدخل بقداش
+
+224
+00:26:34,750 --> 00:26:41,370
+أربعة يعني كانها بصير C على اتنين لكل تربيع يبقى
+
+225
+00:26:41,370 --> 00:26:48,170
+هذه C على اتنين لكل تربيع زائد أربعة هتروح مع 
+
+226
+00:26:48,170 --> 00:26:56,980
+الاربعة فح يبقى بظل جداش X أُس خمسة تمام يبقى C على 
+
+227
+00:26:56,980 --> 00:27:01,380
+اتنين زائد أو ناقص الجدران لـC على اتنين لكل تربيع
+
+228
+00:27:01,380 --> 00:27:06,040
+زائد X أُس خمسة لو روحت في الكتاب ما تلاقيهش هذا
+
+229
+00:27:06,040 --> 00:27:12,170
+الجواب كمان عايش ما تلاقيهش مش هذا مقدار ثابت وهذا مقدر
+
+230
+00:27:12,170 --> 00:27:18,750
+أبدأ اسميه ثابت جديد يبقى هذا بقدر أقول Y يساوي X 
+
+231
+00:27:18,750 --> 00:27:26,210
+أسالي باتنين في C مثلا والله سميه بدل الـ C سميه
+
+232
+00:27:26,210 --> 00:27:36,230
+A زائد أو ناقص الجذري التربيعي لـ A تربيع زائد X أس
+
+233
+00:27:36,230 --> 00:27:41,080
+خمسة يبقى هذا الجواب اللي بتلاقيه في الكتاب بتلاقيه
+
+234
+00:27:41,080 --> 00:27:44,400
+بالشكل هذا طبعًا ليس بالضرورة ايه يمكن تلاقيه P
+
+235
+00:27:44,400 --> 00:27:49,020
+يمكن تلاقيه C يمكن يمكن آخره بس أنا مشان ما أخليش ال
+
+236
+00:27:49,020 --> 00:27:52,440
+C واحد و ال C اتنين اللي فوق هما هما أو اروح اجيب لك
+
+237
+00:27:52,440 --> 00:27:56,060
+عليك C تلاتة جولتك ايه وخلاصنا يبقى هتلاقي الحل
+
+238
+00:27:56,060 --> 00:27:59,220
+على الشكل اللي عندنا على أي حال ما تلاقيهش T على الشكل
+
+239
+00:27:59,220 --> 00:28:04,190
+هذا والله ما تلاقيهش T على الشكل هذا اللي عندنا الإتنين
+
+240
+00:28:04,190 --> 00:28:11,830
+أرضسين كله نفس الحل طيب وصلنا إلى نهاية هذا ال
+
+241
+00:28:11,830 --> 00:28:18,970
+section وبدنا نروح ناخد المسائل التالية يبقى
+
+242
+00:28:18,970 --> 00:28:25,470
+exercises واحد أربعة exercises واحد أربعة المسائل
+
+243
+00:28:25,470 --> 00:28:35,580
+التالية واحد و ثلاثة و خمسة و سبعة و عشرة و أحد عشر
+
+244
+00:28:35,580 --> 00:28:44,060
+و ستة عشر و سبعة عشر و تسعة عشر و عشرين و اثنين و
+
+245
+00:28:44,060 --> 00:28:51,450
+عشرين أيوة هذه الطريقة إني أعجب انتجريتياللي جبت
+
+246
+00:28:51,450 --> 00:28:54,930
+ايه؟ آخر واحدة التالتة فأستخدمها لو كانت من هنا
+
+247
+00:28:54,930 --> 00:28:58,610
+متحققين اللي بالأول ولا لازم يعني لازم يعني أنت
+
+248
+00:28:58,610 --> 00:29:02,650
+حابّة توجه على دماغك أكثر من اللازم لأ قصدي إن مثلا
+
+249
+00:29:02,650 --> 00:29:07,150
+واحد فكرها ما تصبّتش بالأول وكانت إنّها بتتصبّ وراح
+
+250
+00:29:07,150 --> 00:29:11,270
+انتجها للتالت طب أنا بقدر أسألك بمجرد النظر بتنفع 
+
+251
+00:29:11,270 --> 00:29:16,690
+ولا بتنفعش أنا بقوله بتنفعش لأن هناك X بولينشي
+
+252
+00:29:16,690 --> 00:29:21,230
+فانكشن وهذه دالة X مرفوعة لأس في Y مرفوعة لأس
+
+253
+00:29:21,230 --> 00:29:27,680
+فكيف ينفع في الشركة مظبوط؟ يبقى لا يمكنها نفع ده 
+
+254
+00:29:27,680 --> 00:29:31,320
+يعني إذا نفعت إذا نفعت أنا بروح أدور في اللي بعدها
+
+255
+00:29:31,320 --> 00:29:35,120
+وأنا قاعد بشتغل نفعت بقول الحمد لله وبأرتاح لسه
+
+256
+00:29:35,120 --> 00:29:38,560
+في مشاكل في مسائل ثانية بروح أحد السؤال ثاني و
+
+257
+00:29:38,560 --> 00:29:41,960
+هكذا ولا بروح أعكس ليش هو بينفع ولا بينفعش لأ جد
+
+258
+00:29:41,960 --> 00:29:45,620
+أنا بس إنّه لو واحد يعني الطالب من جرد مجلّة جهة
+
+259
+00:29:45,620 --> 00:29:49,280
+بتنفس السعادة بقول الحمد لله خلاص هذا ايه ما اروحش 
+
+260
+00:29:49,280 --> 00:29:54,260
+يدور على اللي أصعب مظبوط؟ هي اللي بيحصل طيب لحد هنا
+
+261
+00:29:54,260 --> 00:29:58,100
+انتهى هذا ال section منتقل الآن إلى ال section
+
+262
+00:29:58,100 --> 00:30:04,220
+الذي يليه وهو ال first order linear differential
+
+263
+00:30:04,220 --> 00:30:10,860
+equations يبقى بدنا نيجي ال section واحد خمسة
+
+264
+00:30:10,860 --> 00:30:21,900
+first order linear differential equations
+
+265
+00:30:22,600 --> 00:30:28,320
+يبقى المعادلة التفاضلية الخطية من الرتبة الأولى
+
+266
+00:30:28,320 --> 00:30:36,400
+نمسح هذا ولا لسه نعطي
+
+267
+00:30:36,400 --> 00:30:44,420
+تعريف وبعدين بنمسح ولا يمنع يبقى هذا definition the
+
+268
+00:30:44,420 --> 00:30:45,780
+first order
+
+269
+00:30:51,340 --> 00:30:57,540
+first order linear differential
+
+270
+00:30:57,540 --> 00:31:13,600
+equation is an equation in the form الشكل التالي A0
+
+271
+00:31:13,600 --> 00:31:21,020
+as a function of X في الـ Y' A1 of X في الـ Y بده 
+
+272
+00:31:21,020 --> 00:31:28,540
+يساوي ال F of X هذه ممكن أحطها على الشكل التالي Y'
+
+273
+00:31:29,340 --> 00:31:35,720
+زائد P of X في الـ Y بده يساوي Q of X واسميها
+
+274
+00:31:35,720 --> 00:31:44,510
+المعادلة رقم واحد where حيث ال P of X يساوي A1 of X
+
+275
+00:31:44,510 --> 00:31:54,090
+على A node of X and ال Q of X هي عبارة عن F of X
+
+276
+00:31:54,090 --> 00:32:07,520
+على A node of X and ال P of X andالـ q of x
+
+277
+00:32:07,520 --> 00:32:15,660
+دليليتين الاتنين هدول are continuous functions
+
+278
+00:32:15,660 --> 00:32:29,580
+دوال متصلة on an open interval ده
+
+279
+00:32:29,580 --> 00:32:30,020
+يا ريم
+
+280
+00:32:51,350 --> 00:33:03,290
+المعادلة رقم واحد is given from the formula
+
+281
+00:33:07,860 --> 00:33:15,900
+هذه هي الفورملة لـ Mu of X في الـ Y as a function
+
+282
+00:33:15,900 --> 00:33:25,860
+of X يساوي تكامل لـ Mu of X في الـ Q of X في الـ DX
+
+283
+00:33:32,800 --> 00:33:43,160
+where الـ mu of x بده يساوي E أس تكامل ال P of x
+
+284
+00:33:43,160 --> 00:33:51,760
+dx note كملاحظة بسيطة we must sure that
+
+285
+00:34:02,460 --> 00:34:08,560
+ويجب أن نتأكد أن
+
+286
+00:34:08,560 --> 00:34:16,560
+الـ coefficient .. الـ
+
+287
+00:34:16,560 --> 00:34:28,260
+coefficient of Y' هو 1 في الـ equation 1
+
+288
+00:35:52,210 --> 00:35:56,910
+نيجي إلى سكتشن واحد خمسة اللي بتكلم عن ال first
+
+289
+00:35:56,910 --> 00:36:03,050
+order linear differential equation اللي
+
+290
+00:36:03,050 --> 00:36:05,570
+هو ال first order linear differential equation
+
+291
+00:36:05,570 --> 00:36:12,160
+معادلة التفاضلية الخطية من الرتبة الأولى الـ First
+
+292
+00:36:12,160 --> 00:36:17,580
+Order Differential Equation بقول عنها Linear إذا
+
+293
+00:36:17,580 --> 00:36:19,280
+كانت على الشكل التالي
+
+294
+00:36:27,690 --> 00:36:33,870
+هذه المعادلة يمكن إعادة صياغتها وكتابتها على الشكل
+
+295
+00:36:33,870 --> 00:36:39,730
+التالي لو روحنا قسمنا الطرفين على a node of x يبقى 
+
+296
+00:36:39,730 --> 00:36:43,490
+المعامل هنا قداش بصير واحد صحيح في ال wire prime
+
+297
+00:36:43,490 --> 00:36:48,670
+هي ال wire prime A1 of X على A node of X بدي اسميها
+
+298
+00:36:48,670 --> 00:36:55,010
+P of X F of X على A node of X بدي اسميها Q of X
+
+299
+00:36:55,010 --> 00:36:58,790
+إذا المعادلة اللي فوق هذا كتبناها بالشكل الجديد
+
+300
+00:36:58,790 --> 00:37:04,250
+لهذين الشكل واحد إذا أصبح الشكل المتعارف عليه أو 
+
+301
+00:37:04,250 --> 00:37:08,010
+الدارج عندنا لل first order linear differential
+
+302
+00:37:08,010 --> 00:37:12,160
+equation هو الـ y prime زائد p of x في الـ y بيبقى
+
+303
+00:37:12,160 --> 00:37:18,000
+ساويًا ل q of x حيث هذه حصلنا عليها عن طريق إن
+
+304
+00:37:18,000 --> 00:37:22,680
+ال p of x صار a1 of x على a node و ال q of x هي f
+
+305
+00:37:22,680 --> 00:37:28,180
+of x على a node of x و ال p و ال q كانوا دوال
+
+306
+00:37:28,180 --> 00:37:35,440
+متصلة على فترة ما طيب يبقى الآن حتى الآن أنا بس 
+
+307
+00:37:35,440 --> 00:37:39,000
+اتعرفت على شكل ال first order linear differential
+
+308
+00:37:39,000 --> 00:37:42,640
+equation إحنا قبل هيك أعطيناكوا شكل ال linear 
+
+309
+00:37:42,640 --> 00:37:46,800
+differential equation in the general form إذا
+
+310
+00:37:46,800 --> 00:37:49,900
+كنتوا بتذكروا سواء كان من الرتبة الأولى ولا 
+
+311
+00:37:49,900 --> 00:37:53,130
+الثانية ولا الثالثة ولا الرابعة ولا النونية وكنا 
+
+312
+00:37:53,130 --> 00:37:57,990
+بنقول لك a node of x y to the derivative n زائد a
+
+313
+00:37:57,990 --> 00:38:02,410
+one of x y to the derivative n minus one زائد زائد
+
+314
+00:38:02,410 --> 00:38:09,610
+a n minus one of x في ال y prime زائد a n of x في
+
+315
+00:38:09,610 --> 00:38:14,110
+ال y بده يساوي f of x هذا ال general form إذا لو
+
+316
+00:38:14,110 --> 00:38:17,330
+أنا أخدت ال first order كل اللي جابله هذا بالغي 
+
+317
+00:38:17,330 --> 00:38:20,550
+تصبح المعادلة على الشكل اللي عندنا هذا اللي
+
+318
+00:38:20,550 --> 00:38:25,470
+روحت حطيتها في الشكل اللي عندنا هذا الآن بدنا نبحث
+
+319
+00:38:25,470 --> 00:38:29,350
+عن الحل طبعًا الكتب اللي إن الطلاب اللي بيدرسوا
+
+320
+00:38:29,350 --> 00:38:34,310
+differential equation فقط بروح بنثبت لهم كيف يكون
+
+321
+00:38:34,310 --> 00:38:38,320
+شكل الحل اللي إحنا بنتكلم عليه هنا أنتم هندسة بني
+
+322
+00:38:38,320 --> 00:38:41,660
+بأعطيكوا الحل على طول القرن يبقى النظرية بيقول ال
+
+323
+00:38:41,660 --> 00:38:45,360
+solution تبع ال differential equation هذه هو ال mu
+
+324
+00:38:45,360 --> 00:38:50,800
+of x في ال y اللي هي الحل بده يساوي تكامل ال mu of
+
+325
+00:38:50,800 --> 00:38:57,920
+x في ال q of x اللي عندنا هذا dx طب مين هي ال mu؟
+
+326
+00:38:58,050 --> 00:39:05,230
+ميو اف اكس يا ايه تكامل P of X DX إذا الميو
+
+327
+00:39:05,230 --> 00:39:11,570
+كأنها عامل التكامل جبتها من وين؟ من تكامل المعامل
+
+328
+00:39:11,570 --> 00:39:17,670
+تبع ال Y والطرف اليمين حاصل ضرب الميو اللي طلعت
+
+329
+00:39:17,670 --> 00:39:22,470
+عندي في ال Q بكامل إثنين بعض وبالتالي بجيب شكل
+
+330
+00:39:22,470 --> 00:39:28,630
+الحل تبع هذه المعادلة التفاضلية إذا لما بدي أجيب
+
+331
+00:39:28,630 --> 00:39:33,550
+هذا الحل اللي عندي مشان يجيب كلامي الصحيح لازم
+
+332
+00:39:33,550 --> 00:39:40,750
+أخلي المعامل تبع y' هو واحد صحيح دري بالك كتبت لك
+
+333
+00:39:40,750 --> 00:39:45,490
+ملاحظة مشان ما تنسهاش we must sure that لازم أتأكد
+
+334
+00:39:45,490 --> 00:39:51,190
+أنّه المعامل تبع y' هو واحد صحيح في ال equation one
+
+335
+00:39:51,190 --> 00:39:56,240
+حد فيكم بيحب يسأل أي سؤال هنا خلصنا النظرية بدنا
+
+336
+00:39:56,240 --> 00:40:00,240
+ندخل في الأعمال يعني ندخل أمثلة على ال first order
+
+337
+00:40:00,240 --> 00:40:03,980
+linear differential equation حد بيحب يسأل أي سؤال 
+
+338
+00:40:03,980 --> 00:40:10,120
+طيب نبدأ في الأمثلة بنأخذ أول مثال يبقى example
+
+339
+00:40:10,120 --> 00:40:18,240
+one بيقول
+
+340
+00:40:18,240 --> 00:40:23,780
+solve the initial value problem solve the initial
+
+341
+00:40:24,310 --> 00:40:29,310
+Value Problem XY'
+
+342
+00:40:31,970 --> 00:40:35,270
+-3Y
+
+343
+00:40:35,270 --> 00:40:38,550
+X تكعيب
+
+344
+00:40:51,130 --> 00:40:56,310
+هذه المثلة محفوظة على الشكل الأصلي لإنّها تمام لكن
+
+345
+00:40:56,310 --> 00:41:00,390
+إحنا لإيش فرضنا ده؟ بدنا نخلي المعامل تبع واي فاي
+
+346
+00:41:00,390 --> 00:41:06,470
+هو جذر وإلا بدنا نضطر X في الطرفين على الـP على X
+
+347
+00:41:06,470 --> 00:41:12,390
+للجابان يبقى جمال أصلاً للإنسان المعادلة هذه بحطها 
+
+348
+00:41:12,390 --> 00:41:18,770
+بالشكل التام واي برايم نقص ثلاثة على XP1 يساوي
+
+349
+00:41:18,770 --> 00:41:24,630
+كده؟ يساوي X تربيع يساوي على X الأشياء ال
+
+350
+00:41:24,630 --> 00:41:29,490
+condition بيظل زي ما هو يساوي Zero وهذه المعادلة
+
+351
+00:41:29,490 --> 00:41:34,770
+بتسميها Minimum معادلة واحدة زي ما أنت شايف هذه 
+
+352
+00:41:34,770 --> 00:41:40,150
+First Father Minimum
+
+353
+00:41:47,490 --> 00:41:52,210
+ماذا بصراحة كده بتروح تدور على ال integrating
+
+354
+00:41:52,210 --> 00:42:02,050
+factor يبدأ ال U of X هو E of Z تكامل، تكامل مين؟
+
+355
+00:42:02,050 --> 00:42:07,250
+بأخذها بإشارتها، مش هتروح تصيب الإشارة إلى موجة بقى،
+
+356
+00:42:07,250 --> 00:42:11,810
+مش هتروح تقرأ ال E ده السنة، بأخذها بإشارتها يبقى
+
+357
+00:42:11,810 --> 00:42:19,230
+أنا ناقص ثلاثة على X بالديكس يبقى E أس ناقص ثلاثة من
+
+358
+00:42:19,230 --> 00:42:28,070
+X يبقى E من X أس ناقص ثلاثة يبقى X أس ناقص ثلاثة
+
+359
+00:42:28,070 --> 00:42:33,170
+يبقى هذا ال integrating factor يبقى بعدين بقوله ذا
+
+360
+00:42:33,170 --> 00:42:46,360
+solution of equation one is Given from الميو
+
+361
+00:42:46,360 --> 00:42:55,300
+of X في ال Y as a function of X تكامل الميو of X في 
+
+362
+00:42:55,300 --> 00:43:03,080
+ال Q of X من DX الميو of X هي X أس ناقص ثلاثة وهذا
+
+363
+00:43:03,080 --> 00:43:09,720
+ال Y يساوي وهي تكامل الميو X أس ناقص ثلاثة ال Q هذا
+
+364
+00:43:09,720 --> 00:43:18,120
+جمعناها يبقى X تربيع يبقى X تربيع وهذا مين يكون dx
+
+365
+00:43:18,120 --> 00:43:26,620
+يبقى صارع ب X أساليب تلاتة يسمي تكامل X أساليب واحد
+
+366
+00:43:26,620 --> 00:43:38,200
+dx يعني مين؟ يعني تكامل واحد على X dx شكل أنا تمام؟
+
+367
+00:43:38,200 --> 00:43:47,820
+طيب هذا ما هو عبارة عن إن ال X ذات المنصة C طب ليش 
+
+368
+00:43:47,820 --> 00:43:51,900
+أنا ما كنتش اشتغل أبسل و زجل X؟
+
+369
+00:44:07,160 --> 00:44:15,120
+بعد أن أقول Y يستخدم X تكعيب
+
+370
+00:44:20,070 --> 00:44:24,850
+زائد قد سي X تقريبًا الآن أنا بروح لل condition
+
+371
+00:44:24,850 --> 00:44:32,690
+conditions but ولكن عندك ال Y عند ال واحد يساوي 
+
+372
+00:44:32,690 --> 00:44:43,670
+زيرو it implies Y بالزيرو ولن الواحد تربيع زيرو زائد 
+
+373
+00:44:43,6
+
+401
+00:48:37,290 --> 00:48:45,980
+تلاتة يبقى صارت Sin تكامل X زائد constant c لو
+
+402
+00:48:45,980 --> 00:48:53,140
+جسمنا كله على sin بصير الحل يساوي sin تربيع ال x
+
+403
+00:48:53,140 --> 00:49:01,680
+زائد c على sin ال x أو الحل بديّش اخلي فيه كسور
+
+404
+00:49:01,680 --> 00:49:09,160
+ماعناش مشكلة يبقى y تساوي sin تربيع ال x زائد c
+
+405
+00:49:09,160 --> 00:49:17,890
+واحد على sin المقلوب من مقلوب الـ sin مين؟
+
+406
+00:49:17,890 --> 00:49:24,990
+cosecant x يبقى الـ C في cosecant X يبقى هذا حل 
+
+407
+00:49:24,990 --> 00:49:31,070
+المعادلة التفاضلية لا يزال عندنا المزيد من الأمثلة
+
+408
+00:49:31,070 --> 00:49:36,850
+للمحاضرة القادمة إن شاء الله تبارك وتعالى يعطيكم 
+
+409
+00:49:36,850 --> 00:49:37,510
+العافية
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ac14422b878ee9310f03d97c471ca3a6d7665577
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_raw.srt
@@ -0,0 +1,1644 @@
+1
+00:00:19,640 --> 00:00:25,380
+بسم الله الرحمن الرحيم بنرجع نكمل الموضوع اللى كنا
+
+2
+00:00:25,380 --> 00:00:31,040
+بنتحدث فيه قبل ساعتين طبعا اعطينا ال three
+
+3
+00:00:31,040 --> 00:00:34,800
+integrating factors ال integrating factor الاول
+
+4
+00:00:34,800 --> 00:00:39,860
+كان mu of Y بده يساوي E أُس تكامل partial N by
+
+5
+00:00:39,860 --> 00:00:41,840
+partial X ناقص partial M
+
+6
+00:00:56,840 --> 00:01:04,230
+أو مقدار ثابت درجتنا واخدنا مثال على كل منهمباقي
+
+7
+00:01:04,230 --> 00:01:08,170
+الـ integrating factor الأخير أنه لو ما حصلش لا
+
+8
+00:01:08,170 --> 00:01:12,830
+هذا ولا ذاك، شو نعمل؟ قلنا بنروح نفرض أن ال
+
+9
+00:01:12,830 --> 00:01:17,290
+integrating factor عليه الشكل M U of X و Y يسوى X
+
+10
+00:01:17,290 --> 00:01:23,570
+to the power M في Y to the power N و بنحاول نوجد
+
+11
+00:01:23,570 --> 00:01:29,090
+قيمة M و N و إذا وجدناهم بيكون جيبنا شكل ال
+
+12
+00:01:29,090 --> 00:01:33,700
+integrating factorوبالتالي بنضرب فيه وبتنحل
+
+13
+00:01:33,700 --> 00:01:37,800
+مشكلتنا تمام يبقى هذا هو ال integration factor
+
+14
+00:01:37,800 --> 00:01:43,140
+الجديد يبقى بدنا نيجي هنا ونبحث هذه المعادلة
+
+15
+00:01:43,140 --> 00:01:48,320
+الأصلية اللي هي مين اللي سمناها star يبقى بداجي
+
+16
+00:01:48,320 --> 00:01:55,580
+أخد تفاضل ال M بالنسبة إلى Y أه بس يا بنات بفضل
+
+17
+00:01:55,580 --> 00:02:01,940
+قبل ذلك أن نحاول نرتبالمعادلة اللي عندنا بشكل جديد
+
+18
+00:02:01,940 --> 00:02:05,980
+بحيث تبقى في وضعها الطبيعي يبقى هذه بدي أجيبها في
+
+19
+00:02:05,980 --> 00:02:13,860
+الأول اتنين y تكيب ناقص ثلاثة x y زائد اللي هو مين
+
+20
+00:02:13,860 --> 00:02:19,960
+اللي هو ال x تربية زائد x y تربية كله في ال y
+
+21
+00:02:19,960 --> 00:02:25,000
+prime يساوي zero هذه ال equation هي star في وضعها
+
+22
+00:02:25,000 --> 00:02:31,910
+الطبيعييبقى بتروح اخد تفاضل ال M بالنسبة الى Y
+
+23
+00:02:31,910 --> 00:02:40,250
+يبقى بنشتق الأولى بالنسبة الى Y يبقى 6Y تربيع ناقص
+
+24
+00:02:40,250 --> 00:02:47,370
+3X الان بدنا نيجي تفاضل ال N بالنسبة الى X
+
+25
+00:02:47,370 --> 00:02:54,950
+المعادلة التانية يبقى 2X زائد Y تربيع تمام التمام
+
+26
+00:02:56,390 --> 00:03:02,030
+من اللي اتنين هدول بنستنتج انه تفاضل ال M بالنسبة
+
+27
+00:03:02,030 --> 00:03:11,350
+الى Y لا يساوي تفاضل ال N بالنسبة الى X يعني معنى
+
+28
+00:03:11,350 --> 00:03:18,930
+هذا الكلام انه The differential equation A star is
+
+29
+00:03:18,930 --> 00:03:25,900
+not exactMadam not exactly بدأ أروح أدور على ال
+
+30
+00:03:25,900 --> 00:03:30,460
+two integrating factors الأساسيات الأثنين بتاعتنا
+
+31
+00:03:30,460 --> 00:03:34,700
+يبقى أنا مش عارف أبدأ .. يبقى بدي أغمض و أتوكل على
+
+32
+00:03:34,700 --> 00:03:40,480
+الله و أشوف تيجي ولا بتجيش لإن شكلهم مكلكع يعني مش
+
+33
+00:03:40,480 --> 00:03:45,990
+.. مش عند بعض ليش؟ لإن لو طرحتممكن انتهيش او
+
+34
+00:03:45,990 --> 00:03:49,990
+ماوصلش لـ function of y او function of x اذا لو
+
+35
+00:03:49,990 --> 00:03:55,430
+جيت اخد partial n by partial x ناقص partial m by
+
+36
+00:03:55,430 --> 00:04:00,710
+partial y بدي اقسم على m partial n by partial x له
+
+37
+00:04:00,710 --> 00:04:09,410
+اتنين x زائد y تربيع ناقص ستة y تربيع زائد تلاتة x
+
+38
+00:04:09,410 --> 00:04:20,220
+كله على مين؟ على mيبقى M بـ 2Y تكييب ناقص 3XY و
+
+39
+00:04:20,220 --> 00:04:27,760
+يساوي هذه لو جمعتها مع بعض بيصير 5X و عندك Y تربيع
+
+40
+00:04:27,760 --> 00:04:35,160
+و ناقص 6Y تربيع بيظل ناقص 5Y تربيع على مين على ليه
+
+41
+00:04:35,160 --> 00:04:41,520
+2Y تكييب ناقص 3XY
+
+42
+00:04:42,450 --> 00:04:48,590
+طيب في عامل مشترك فوق اللي هو فيه خمسة فقط لغير
+
+43
+00:04:48,590 --> 00:04:57,390
+بيضل x ناقص y تربية تحت في عندنا y عامل مشترك فقط
+
+44
+00:04:57,390 --> 00:05:04,490
+لغير مصبوط بيضل عندنا اتنين y تربية اتنين y تربية
+
+45
+00:05:04,490 --> 00:05:13,900
+ناقص تلاتة xهل هذه function of y في اختصارات؟
+
+46
+00:05:13,900 --> 00:05:24,060
+ماعنديش، يبقى هذه not function of y onlyما هيش
+
+47
+00:05:24,060 --> 00:05:30,660
+function في Y فقط يبقى بنفعش شو نعمل نبدل النص في
+
+48
+00:05:30,660 --> 00:05:37,200
+الثاني يبقى بدي أخد تفاضل ال M بالنسبة إلى Y نقص
+
+49
+00:05:37,200 --> 00:05:43,720
+تفاضل ال N بالنسبة إلى X كله مقسوما على Nيبقى بدنا
+
+50
+00:05:43,720 --> 00:05:52,340
+نقلب الوضع PARTIAL M BY PARTIAL Y 6Y تربية ناقص 3X
+
+51
+00:05:52,340 --> 00:05:59,300
+ناقص 2X
+
+52
+00:05:59,300 --> 00:06:07,760
+ناقص Y تربية كل هذا مقسوما على Nوين ال N هيها؟ X
+
+53
+00:06:07,760 --> 00:06:14,880
+تربيع زائد XY تربيع تمام يبقى هذه بدها تساوي
+
+54
+00:06:14,880 --> 00:06:21,140
+طلعيلي هنا ستة Y تربيع وناقص Y تربيع بيظل خمسة Y
+
+55
+00:06:21,140 --> 00:06:31,240
+تربيع ناقص خمسة X كله مقسوما على X تربيع زائد XY
+
+56
+00:06:31,240 --> 00:06:39,550
+تربيعيبقى بناء عليه أصبح عندي partial M by partial
+
+57
+00:06:39,550 --> 00:06:47,830
+Y ناقص partial N by partial X كله مقسوما على N بده
+
+58
+00:06:47,830 --> 00:06:53,510
+يساوي في عندي هنا خمسة عامل مشترك وبظل عندي Y
+
+59
+00:06:53,510 --> 00:07:02,090
+تربيع ناقص X على هنا في X عامل مشترك وبظل عندي X
+
+60
+00:07:02,090 --> 00:07:09,000
+زائدY تعرفيها في اختصارات؟ لأ لأ يبقى اختصارات
+
+61
+00:07:09,000 --> 00:07:16,800
+ماعنديش اتنين ليست function في X تمام يبقى not
+
+62
+00:07:16,800 --> 00:07:22,420
+يبقى
+
+63
+00:07:22,420 --> 00:07:31,770
+ال not a function of X onlyيبقى مانفعش لا هادي ولا
+
+64
+00:07:31,770 --> 00:07:36,150
+هادي بتجيبلي integrative factors يبقى ماضلش قدام
+
+65
+00:07:36,150 --> 00:07:39,490
+التالت
+
+66
+00:07:39,490 --> 00:07:42,270
+يبقى بالداجة اقول suppose that
+
+67
+00:07:46,510 --> 00:07:53,830
+الميو of x و y يسوي x to the power m في y to the
+
+68
+00:07:53,830 --> 00:08:01,910
+power n suppose that هذا يسوي هذا is an
+
+69
+00:08:01,910 --> 00:08:13,810
+integrating factor for the differential
+
+70
+00:08:16,920 --> 00:08:25,080
+Equation star مدام هذا هو عامل تكمل إذا هضرب
+
+71
+00:08:25,080 --> 00:08:30,840
+الطرفين في X أس M في Y أس N
+
+72
+00:08:34,700 --> 00:08:40,280
+بدي أضربها كلها من أولها إلى آخرها في الـ X أُس M
+
+73
+00:08:40,280 --> 00:08:47,680
+Y أُس N شوف أيش اللي بدي يصير ها اتنين زي ما هي X
+
+74
+00:08:47,680 --> 00:08:56,540
+أُس M ماعنديش X أُس M عندك Y أُس N زائد تلاتة
+
+75
+00:08:56,540 --> 00:09:06,350
+انتهينا منهانقص هاي تلاتة اكس اس ام زائد واحد واي
+
+76
+00:09:06,350 --> 00:09:15,270
+اس ان زائد واحد ضربناهازائد هاي قصة وعندك هنا X
+
+77
+00:09:15,270 --> 00:09:26,130
+أُس M زائدي اتنين في ال Y أُس N زائد X أُس M زائد
+
+78
+00:09:26,130 --> 00:09:35,390
+واحد Y أُس N زائدي اتنين كل هذا في ال Y prime بده
+
+79
+00:09:35,390 --> 00:09:42,910
+سوى قداش0 هو هذي اللي هي الـ main double star مدام
+
+80
+00:09:42,910 --> 00:09:48,610
+فرضنا هذي integrative و هذي إيش بدتكون exact لإنه
+
+81
+00:09:48,610 --> 00:09:55,590
+جالها integrative vector يبقى هنا we get بنحصل على
+
+82
+00:09:55,590 --> 00:09:59,030
+من ال differential هذي is exact
+
+83
+00:10:01,250 --> 00:10:06,790
+ما دام exact يبقى بدي اخد تفاضل ال M by partial Y
+
+84
+00:10:06,790 --> 00:10:13,010
+و تفاضل N بالنسبة ل X وزي أساوي اتنين بعض يبقى بدي
+
+85
+00:10:13,010 --> 00:10:22,270
+اخد هنا تفاضل هذا كلهتفاضل ال M بالنسبة إلى Y
+
+86
+00:10:22,270 --> 00:10:25,490
+تفاضل
+
+87
+00:10:25,490 --> 00:10:31,230
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+88
+00:10:31,230 --> 00:10:36,610
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+89
+00:10:36,610 --> 00:10:38,710
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+90
+00:10:38,710 --> 00:10:40,710
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+91
+00:10:40,710 --> 00:10:41,590
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+92
+00:10:41,590 --> 00:10:42,050
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+93
+00:10:42,050 --> 00:10:42,050
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+94
+00:10:42,050 --> 00:10:42,050
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+95
+00:10:42,050 --> 00:10:45,320
+ال M بالنسبة إلى Y تفاضل ال M بالنلأنه بيفضل ال Y
+
+96
+00:10:45,320 --> 00:10:52,360
+نيجي هذه بيدفضلها كمان يبقى ناقص تلاتة في M زائد
+
+97
+00:10:52,360 --> 00:11:03,990
+واحد في X أس M زائد واحد في ال Y أس N واضحة ظنطب
+
+98
+00:11:03,990 --> 00:11:08,370
+ايش رايك؟ و بده اخد منهم عامل مشترك يبقى لو جيت
+
+99
+00:11:08,370 --> 00:11:15,170
+اخدت ال X أُس M في ال Y أُس N عامل مشترك بظل عندنا
+
+100
+00:11:15,170 --> 00:11:22,830
+مين؟ اتنين N زائد ستة هذا مالوش دعوة هذه طارت بظل
+
+101
+00:11:22,830 --> 00:11:31,870
+Y تربيع شكل عندنا هذا اللي بعدناقص وهذه ثلاثة N
+
+102
+00:11:31,870 --> 00:11:39,450
+زائد ثلاثة وهنا X والـ X أُسم طلعت والـ Y أُسم N
+
+103
+00:11:39,450 --> 00:11:47,530
+طلعت مع السلامة طيب بدالي أخد تفاضل الـ N بالنسبة
+
+104
+00:11:47,530 --> 00:11:54,570
+إلى X يبقى بضروحة فاضل هذه بالنسبة إلى Xبصير M
+
+105
+00:11:54,570 --> 00:12:01,850
+زائدي اتنين X أُس M زائد واحد ال Y أُس N مقدار
+
+106
+00:12:01,850 --> 00:12:10,810
+ثابت مالوش دعوة اللي بعده زائد M زائد واحد في ال X
+
+107
+00:12:10,810 --> 00:12:19,330
+أُس M في ال Y أُس N زائدي اتنينخلّصنا منها يساوي
+
+108
+00:12:19,330 --> 00:12:27,020
+بدي أخد X أُس M في Y أُس N عامل مشتركيبقى بيظل هنا
+
+109
+00:12:27,020 --> 00:12:34,720
+مين؟ بيظل M زائد اتنين في ال X يبقى M زائد اتنين
+
+110
+00:12:34,720 --> 00:12:40,240
+كله في ال X و ال X و السم و ال Y و السن هيبرة ليه
+
+111
+00:12:40,240 --> 00:12:47,920
+جلال اللي بعده؟ زائد M زائد واحد ال X و السم يجه Y
+
+112
+00:12:47,920 --> 00:12:53,860
+تربيع الآن يا بنات احنا عندنا هذه exactما دام
+
+113
+00:12:53,860 --> 00:13:00,340
+exact هدول لازم يساويوا بعض مظبوط يبقى sense
+
+114
+00:13:00,340 --> 00:13:09,720
+equation double star is exact
+
+115
+00:13:13,220 --> 00:13:20,340
+ان تفاضل ال M بالنسبة الى Y بيساوي تفاضل ال N
+
+116
+00:13:20,340 --> 00:13:27,940
+بالنسبة الى X هذا معناه ان هذول بيساوي بعض اظن هذا
+
+117
+00:13:27,940 --> 00:13:32,360
+لو شطبتهم بيروح ماعناش مشكلة بيظل ال term هذا
+
+118
+00:13:32,360 --> 00:13:40,430
+بيساوي ال term هذا يبقى بصير عندنا2N زائد 6 في الـ
+
+119
+00:13:40,430 --> 00:13:51,630
+Y تربيع ناقص 3N زائد 3 في الـ X بده يساوي الـ M
+
+120
+00:13:51,630 --> 00:13:59,030
+زائد 2 كله في الـ X زائد الـ M زائد 1 في الـ Y
+
+121
+00:13:59,030 --> 00:14:04,000
+تربيعهذه بدي اكتبها هنا و اكتبها هنا بيكون جسمت
+
+122
+00:14:04,000 --> 00:14:10,460
+عليهم بيظلوا بيساووا بعض اذا يا بنات معامل Y تربيع
+
+123
+00:14:10,460 --> 00:14:16,180
+هنا هو معامل Y تربيع هنا و معامل X هنا هو معامل X
+
+124
+00:14:16,180 --> 00:14:20,970
+هنا تعالوا نسوي هذه المعاملات ببعضيبقى انا عندى
+
+125
+00:14:20,970 --> 00:14:30,690
+هنا M زائد 2 تبعت ال X بدى تساوي ناقص تلاتة N ناقص
+
+126
+00:14:30,690 --> 00:14:36,190
+تلاتة ناقص بتخش على الاتنين المعادلة التانية معامل
+
+127
+00:14:36,190 --> 00:14:46,550
+Y تربية يبقى M زائد 1 بدى يساوي اتنين N زائد ستة
+
+128
+00:14:47,100 --> 00:14:53,900
+معادلتين في مجهولين بقدر أحلهم مع بعض بدون مشاكل
+
+129
+00:14:53,900 --> 00:15:01,370
+تمام باجي بقول هذا بده يعطيناأظن هذه لو كانت M
+
+130
+00:15:01,370 --> 00:15:07,070
+زائد واحد كانت انتهت مشكلتنا يبقى خلّيني أطرح واحد
+
+131
+00:15:07,070 --> 00:15:12,810
+من الطرفين يبقى لو طرحنا واحد من الطرفين بصير M
+
+132
+00:15:12,810 --> 00:15:22,920
+زائد واحد تساوي ناقص ثلاثة N ناقص أربعةو هذي بده
+
+133
+00:15:22,920 --> 00:15:30,680
+يخلّيها زي ما هي M زائد واحد يساوي اتنين N زائد
+
+134
+00:15:30,680 --> 00:15:35,440
+ستة مش الطرف الشمال هو الطرف الشمال اذا الطرف
+
+135
+00:15:35,440 --> 00:15:40,820
+اليمين بده يساوي الطرف اليمين يبقى هذا معناه ان
+
+136
+00:15:40,820 --> 00:15:48,600
+اتنين N زائد ستة بده يساوي ناقص تلاتة N ناقص
+
+137
+00:15:48,600 --> 00:15:55,330
+الاربع هذا معناهبيدخل ال N في شجة و ال constant في
+
+138
+00:15:55,330 --> 00:16:03,050
+شجة تانية يبقى هذا بيصير خمسة N يساوي ناقص عشرة
+
+139
+00:16:03,050 --> 00:16:11,170
+إذا ال N بيبقى ناقص اتنينطيب بدي أشيل ال N و أحط
+
+140
+00:16:11,170 --> 00:16:17,150
+مكانها ناقص اتنين و أشوف قداش ال M يبقى هذه
+
+141
+00:16:17,150 --> 00:16:23,790
+المعلومة الأولى هذا بدي أعطيكي ان M زائد واحد
+
+142
+00:16:23,790 --> 00:16:28,490
+يساوي اي واحدة من التنتين سبيان يبقى هذه قداش
+
+143
+00:16:28,490 --> 00:16:36,850
+بناقص اتنين يبقى اتنين في ناقص اتنين زائد ستة يعني
+
+144
+00:16:36,850 --> 00:16:43,990
+Mزائد واحد بده يساوي كده يا بنات؟ يساوي اتنين لإنه
+
+145
+00:16:43,990 --> 00:16:50,010
+ناقص اربعة وزايد ستة بيظل اتنين هذا معناه إن ال M
+
+146
+00:16:50,010 --> 00:16:56,890
+يساوي كده؟ يساوي واحد إذا أصبح شكل ال integrating
+
+147
+00:16:56,890 --> 00:17:00,910
+factor على الشكل التالي
+
+148
+00:17:08,060 --> 00:17:13,960
+يبقى الان the integrating
+
+149
+00:17:13,960 --> 00:17:25,060
+factor is
+
+150
+00:17:26,210 --> 00:17:36,290
+الميو X Y يساوي X أُس M مابجداش واحد يبجى X فقط و
+
+151
+00:17:36,290 --> 00:17:43,550
+Y أُس N مابجداش ناقص اتنينهل حين بدى اشوف هذا
+
+152
+00:17:43,550 --> 00:17:49,850
+بيحولى ال equation ال star الى exact equation ولا
+
+153
+00:17:49,850 --> 00:17:55,150
+لأ يبقى بدى اروح اضرب المعادلة star في x y اصلا
+
+154
+00:17:55,150 --> 00:17:59,610
+قصة اتنين يبقى بدى امسك كده ال integrating factor
+
+155
+00:17:59,610 --> 00:18:04,450
+و اضربه في المعادلة هذه يبقى هذه بيصير اتنين يا
+
+156
+00:18:04,450 --> 00:18:12,540
+بنات و هنا x زي ما هي و هنا y فقط لا غيروهنا ناقص
+
+157
+00:18:12,540 --> 00:18:25,740
+تلاتة X تربيع Y ناقص واحد زائدهنا يصير x تكيب y اص
+
+158
+00:18:25,740 --> 00:18:33,680
+ناقص اتنين زائد x تربيع و ال y مع السلامة y prime
+
+159
+00:18:33,680 --> 00:18:40,540
+يساوي zero وهذه المعادلة هي double star لان بدى
+
+160
+00:18:40,540 --> 00:18:47,720
+اشوف double star exact ولا لايبقى هذه كلها أصبحت
+
+161
+00:18:47,720 --> 00:18:55,760
+بـ M وهذه كلها أصبحت بالـ N يبقى بدي أخد تفاضل M
+
+162
+00:18:55,760 --> 00:19:04,210
+بالنسبة إلى Yبقدرش يا بنات هنا اتنين X وهنا زائد
+
+163
+00:19:04,210 --> 00:19:12,490
+تلاتة X تربيع Y أثناء قصي اتنين بدي اخد تفاضل ال N
+
+164
+00:19:12,490 --> 00:19:20,610
+بالنسبة إلى X تمام؟ بالنسبة إلى X وY وساوي تلاتة
+
+165
+00:19:33,840 --> 00:19:41,320
+يبقى شغلنا الأولاني كله سليم 100%يبقى من هدول
+
+166
+00:19:41,320 --> 00:19:46,660
+اتنين مع بعض بس تنتج انه partial m by partial y
+
+167
+00:19:46,660 --> 00:19:53,240
+يسوى partial n by partial x يبقى هذا بيعطيني انه
+
+168
+00:19:53,240 --> 00:20:00,700
+the differential equation double star is exact
+
+169
+00:20:00,700 --> 00:20:09,770
+مدام exact يبقى there exists a functionفاي of x و
+
+170
+00:20:09,770 --> 00:20:20,170
+y يكون سنسيوان such that بحيث ان اظن الشغل هذا كله
+
+171
+00:20:20,170 --> 00:20:25,030
+مالوش لزومة الحين حد ضايق بده اي كلمة من العمود
+
+172
+00:20:25,030 --> 00:20:31,610
+اللي هناك نصفة ثانية من الصبورة لازم طيب خلاص نمسح
+
+173
+00:20:31,610 --> 00:20:34,830
+هذا عشان نكمل حل السؤال
+
+174
+00:20:41,210 --> 00:20:49,240
+بحيث انPartial FI by partial X يساوي الـ M هذه لـ
+
+175
+00:20:49,240 --> 00:20:58,280
+2XY ناقص 3X تربيع Y أساليب واحد وتفاضل الـ FI
+
+176
+00:20:58,280 --> 00:21:06,520
+بالنسبة إلى Y يساوي الـ M لـ X تكييب Y أساليب 2
+
+177
+00:21:06,520 --> 00:21:14,220
+زائد X تربيع بالشكل اللي عندنا هناالان بدي اكمل
+
+178
+00:21:14,220 --> 00:21:19,200
+هذه بالنسبة ل X سهلة و بدي اكمل هذه او هذه بالنسبة
+
+179
+00:21:19,200 --> 00:21:24,380
+ل Y على كل الأمرين التنتين سهلات ماعناش مشكلة يبقى
+
+180
+00:21:24,380 --> 00:21:29,480
+اتنين تنتين بنفس السهولة يبقى لو جيت قلت لك في of
+
+181
+00:21:29,480 --> 00:21:35,190
+XY يساويبدي أكمل بالنسبة لـ x يبقى دي x تربيع على
+
+182
+00:21:35,190 --> 00:21:42,450
+2 بصير x تربيع y و 2 مع 2 هذه الناقص x تكيب على 3
+
+183
+00:21:42,450 --> 00:21:50,590
+مع 3 وهذه y أسالب 1 كملة بالنسبة ل x يبقى زائد f
+
+184
+00:21:50,590 --> 00:21:59,050
+of yبدي أشتق هذه الدالة بالنسبة إلى Y يساوي هنا
+
+185
+00:21:59,050 --> 00:22:09,150
+عندك X تربيع وهنا ناقص يصير زائد X تكييب Y ناقص
+
+186
+00:22:09,150 --> 00:22:16,650
+اتنين زائد F prime of Yهذه اللي هي نفس المشتقة
+
+187
+00:22:16,650 --> 00:22:21,490
+أيضًا بدي أسوأ المقدارين اللي اتنين هدول ببعض يبقى
+
+188
+00:22:21,490 --> 00:22:28,810
+هذا بدي يعطيلك انه X تربيع زائد X تكييب Y أس ناقص
+
+189
+00:22:28,810 --> 00:22:35,730
+اتنين زائد F prime of Y يسوى X تكييب Y أس ناقص
+
+190
+00:22:35,730 --> 00:22:41,870
+اتنين زائد X تربيع أظن هذه هي هذه وهذه هي هذه
+
+191
+00:22:41,870 --> 00:22:48,600
+بالضبطيبقى بناء عليه ال f prime of y بده يسوي zero
+
+192
+00:22:48,600 --> 00:22:55,560
+يبقى ال f of y بده يسوي constant c2 يبقى حل
+
+193
+00:22:55,560 --> 00:23:01,960
+المعادلة الأصلية هو يبقى باجي بقوله the solution
+
+194
+00:23:01,960 --> 00:23:13,930
+of theDifferential equation star is phi of x,y
+
+195
+00:23:13,930 --> 00:23:14,710
+يساوي
+
+196
+00:23:29,670 --> 00:23:32,790
+أه هذا بياخد واجس مش زي اللي جابله اللي جابله
+
+197
+00:23:32,790 --> 00:23:36,870
+بسيطات لأن هذا عبارة عن حل مجموعة من الأسلة مش
+
+198
+00:23:36,870 --> 00:23:40,970
+عاجزة سؤال واحد طيب وصلنا
+
+199
+00:23:43,840 --> 00:23:50,920
+إلى نهاية هذا المثال لكن بإمكاني أن أحط هذا الحل
+
+200
+00:23:50,920 --> 00:23:57,620
+بصيغة أخرى غير هذه الصيغة يعني بقدر أجيب الحل مش
+
+201
+00:23:57,620 --> 00:24:02,060
+ضمني زي هيك بقدر أجيب الحل why as a function of g
+
+202
+00:24:02,060 --> 00:24:06,210
+انت هيك خلصتيلكن يمكن واحدة يطرح عبالة أوي تروح
+
+203
+00:24:06,210 --> 00:24:10,290
+يتفتح هي الكتاب هيك طبعا السؤال في الكتاب ماتلاقيش
+
+204
+00:24:10,290 --> 00:24:14,910
+هذا الجواب تقول هيك والله حالي غلط مظبوط لأ حالي
+
+205
+00:24:14,910 --> 00:24:18,630
+غلط لأ جد حال سليم مائة بالمائة طب إيش الجواب اللي
+
+206
+00:24:18,630 --> 00:24:20,870
+ممكن ألاقيه تعالى أوريكي إيش الجواب اللي ممكن
+
+207
+00:24:20,870 --> 00:24:27,560
+أتلاقيه الحين عندنا هذه هيك بده يساوي كونستانسيأنا
+
+208
+00:24:27,560 --> 00:24:32,480
+عندي Y بالموجب وهنا Y الأس تبعها السالد بقدر أخلي
+
+209
+00:24:32,480 --> 00:24:38,420
+الأس تبعي معله موجب شو أعمل؟ أضرب الطرفين في Y إذا
+
+210
+00:24:38,420 --> 00:24:43,180
+المعادلة هذه بقدر أكتبها على الشكل التالي X تربيع
+
+211
+00:24:43,180 --> 00:24:52,310
+Y تربيع ناقص X تكعيب يساوي C في Yضربت الطرفين في Y
+
+212
+00:24:52,310 --> 00:24:58,490
+فقط لا غير ممكن أعيد ترتيبها و أقول X تربيع Y
+
+213
+00:24:58,490 --> 00:25:08,210
+تربيع ناقص Cy ناقص X تكيب يساوي Zero إيش رأيك؟ هذه
+
+214
+00:25:08,210 --> 00:25:13,750
+معادلة من الدرجة الثانية في Y، مظبوط؟ إذا منحلك
+
+215
+00:25:14,980 --> 00:25:22,960
+بالقانون تمام يبقى بناء عليه y يسوى ناقص با يعني
+
+216
+00:25:22,960 --> 00:25:29,700
+ايش صارت ناقص ناقص بصير زائد c زائد او ناقص الجذري
+
+217
+00:25:29,700 --> 00:25:35,260
+التربية اللي هي c تربية ناقص أربعة الف اللي هي x
+
+218
+00:25:35,260 --> 00:25:42,940
+تربية جيم اللي هو ناقص x تكيبكله على اتنين الف
+
+219
+00:25:42,940 --> 00:25:50,860
+يبقى اتنين اكس تربيع او ان شئتولنا فقلنا هذه C
+
+220
+00:25:50,860 --> 00:25:59,780
+زائدة او ناقص الجذر التربيعي لمن؟ لـC تربيع زائد
+
+221
+00:25:59,780 --> 00:26:08,940
+اربعة اكس أس خمسة تمام؟ كل هذا الكلام على الاتنين
+
+222
+00:26:08,940 --> 00:26:16,530
+اكس تربيعطيب هذا الكلام بده يساوي يا بنات لو طلعت
+
+223
+00:26:16,530 --> 00:26:22,410
+فوق x وقلت أسالي باتنين بنفعلها بالفعلبظل في
+
+224
+00:26:22,410 --> 00:26:29,930
+المقام اتنين يعني C على اتنين زادة أو ناقص الجذري
+
+225
+00:26:29,930 --> 00:26:34,750
+التربيعي اتنين هذه لو دخلتها تحتها بتدخل بقداش
+
+226
+00:26:34,750 --> 00:26:41,370
+اربعة يعني كانها بصير C على اتنين لكل تربية يبقى
+
+227
+00:26:41,370 --> 00:26:48,170
+هذه C على اتنين لكل تربية زاد اربعة هتروح مع
+
+228
+00:26:48,170 --> 00:26:56,980
+الاربعة فح يبقى بظل جداشX أُس خمسة تمام يبقى C على
+
+229
+00:26:56,980 --> 00:27:01,380
+اتنين زائد او ناقص الجدران لـC على اتنين لكل تربية
+
+230
+00:27:01,380 --> 00:27:06,040
+زائد X أُس خمسة لو روحت في الكتاب بلاجيش هذا
+
+231
+00:27:06,040 --> 00:27:12,170
+الجواب كمان عايش بلاجي مش هذا مقدار ثابتوهذا مقدر
+
+232
+00:27:12,170 --> 00:27:18,750
+ابدأ اسميه ثابت جديد يبقى هذا بقدر اقول Y يسوى X
+
+233
+00:27:18,750 --> 00:27:26,210
+أسالي باتنين في C مثلا و الله سميه بدل الـ C سميه
+
+234
+00:27:26,210 --> 00:27:36,230
+A زائد أو ناقص الجدري التربيعي ل A تربيع زائد X أس
+
+235
+00:27:36,230 --> 00:27:41,080
+خمسةيبقى هذا الجواب اللي بتلاقيه في الكتاب بتلاقيه
+
+236
+00:27:41,080 --> 00:27:44,400
+بالشكل هذا طبعا ليس بالضرورة ايه يمكن تلاقيه P
+
+237
+00:27:44,400 --> 00:27:49,020
+يمكن تلاقيه C يمكن يمكن اخره بس انا مشان ماخليش ال
+
+238
+00:27:49,020 --> 00:27:52,440
+C واحد و ال C اتنين اللي فوق هما هما او اروح اجالك
+
+239
+00:27:52,440 --> 00:27:56,060
+عليك C تلاتة جولتك ايه و خلاصنا يبقى هتلاقي الحل
+
+240
+00:27:56,060 --> 00:27:59,220
+على الشكل اللي عندنا على اي حال لاجي T على الشكل
+
+241
+00:27:59,220 --> 00:28:04,190
+هذا و الله لاجي T على الشكل هذا اللي عندنالإتنين
+
+242
+00:28:04,190 --> 00:28:11,830
+أرضسين كله نفس الحل طيب وصلنا إلى نهاية هذا ال
+
+243
+00:28:11,830 --> 00:28:18,970
+section و بدنا نروح ناخد المسائل التالية يبقى
+
+244
+00:28:18,970 --> 00:28:25,470
+exercises واحد أربعة exercises واحد أربعة المسائل
+
+245
+00:28:25,470 --> 00:28:35,580
+التاليةواحد و تلاتة و خمسة و سبعة و عشرة و أحداشر
+
+246
+00:28:35,580 --> 00:28:44,060
+و ستاشر و سبعتاشر و تسعتاشر و عشرين و اتنين و
+
+247
+00:28:44,060 --> 00:28:51,450
+عشرين ايوة هذه الطريقة اني عجيب انتجريتياللي جبت
+
+248
+00:28:51,450 --> 00:28:54,930
+ايه؟ اخر واحدة التالتة فأستخدمها لو كانت من هنا
+
+249
+00:28:54,930 --> 00:28:58,610
+متحققين اللي بالاول و لا لازم يعني لازم يعني انت
+
+250
+00:28:58,610 --> 00:29:02,650
+حابة توجه ع دماغك اكتر من اللازم لأ جصدي ان مثلا
+
+251
+00:29:02,650 --> 00:29:07,150
+واحد فكرها ماتصبتش بالاول و كانت انها بتصبط و راح
+
+252
+00:29:07,150 --> 00:29:11,270
+انتجها للتالت طب انا بقدر اسألك بمجرد النظر بتنفع
+
+253
+00:29:11,270 --> 00:29:16,690
+ولا بتنفعش انا بقوله بتنفعشلأن هناك اكس بولينشي
+
+254
+00:29:16,690 --> 00:29:21,230
+فانكشن وهذه دالة X مرفوعة لأس في Y مرفوعة على أس
+
+255
+00:29:21,230 --> 00:29:27,680
+فكيف ينفع في الشركةمظبوط؟ يبقى لا يمكنها نفعة ده
+
+256
+00:29:27,680 --> 00:29:31,320
+يعني إذا نفعت إذا نفعت أنا بروح أدور في اللي بعدها
+
+257
+00:29:31,320 --> 00:29:35,120
+و أنا قاعد بشتغل نفعت بقول الحمد لله و بتريح لسه
+
+258
+00:29:35,120 --> 00:29:38,560
+في مشاكل في مسائل تانية بروح أحد السؤال تاني و
+
+259
+00:29:38,560 --> 00:29:41,960
+هكذا و لا بروح أعكس ليش هو بنفع ولا بنفعش لأ جد
+
+260
+00:29:41,960 --> 00:29:45,620
+أنا بس إنه لو واحد يعني الطالب من جرد مجلة جهة
+
+261
+00:29:45,620 --> 00:29:49,280
+بتنفس السعادة بقول الحمد لله خلاص هذا ايه ماروحش
+
+262
+00:29:49,280 --> 00:29:54,260
+يدور على اللي أصعب مظبوط؟ هي اللي بيحصلطيب لحد هنا
+
+263
+00:29:54,260 --> 00:29:58,100
+انتهى هذا ال section منتقل الان الى ال section
+
+264
+00:29:58,100 --> 00:30:04,220
+اللذي يليه وهو ال first order linear differential
+
+265
+00:30:04,220 --> 00:30:10,860
+equations يبقى بدنا نيجي ال section واحد خمسة
+
+266
+00:30:10,860 --> 00:30:21,900
+first order linear differential equations
+
+267
+00:30:22,600 --> 00:30:28,320
+يبقى المعادلة التفاضلية الخطية من الرتبة الأولى
+
+268
+00:30:28,320 --> 00:30:36,400
+نمسح هذا ولا لسه نعطي
+
+269
+00:30:36,400 --> 00:30:44,420
+تعريف وبعدين بنمسح ولا يمن يبقى هذا definition the
+
+270
+00:30:44,420 --> 00:30:45,780
+first order
+
+271
+00:30:51,340 --> 00:30:57,540
+first order linear differential
+
+272
+00:30:57,540 --> 00:31:13,600
+equation is an equation in the form الشكل التاليA0
+
+273
+00:31:13,600 --> 00:31:21,020
+as a function of X في الـ Y' A1 of X في الـ Y بده
+
+274
+00:31:21,020 --> 00:31:28,540
+يساوي ال F of X هذه ممكن أحطها على الشكل التالي Y'
+
+275
+00:31:29,340 --> 00:31:35,720
+زائد P of X في ال Y بده يساوي Q of X واسميها
+
+276
+00:31:35,720 --> 00:31:44,510
+المعادلة رقم واحد whereحيث ال P of X يسوى A1 of X
+
+277
+00:31:44,510 --> 00:31:54,090
+على A node of X and ال Q of X هي عبارة عن F of X
+
+278
+00:31:54,090 --> 00:32:07,520
+على A node of X and ال P of X andالـ q of x
+
+279
+00:32:07,520 --> 00:32:15,660
+دليليتين الأتنين هدول are continuous functions
+
+280
+00:32:15,660 --> 00:32:29,580
+دوال متصلة on an open interval ده
+
+281
+00:32:29,580 --> 00:32:30,020
+يا ريم
+
+282
+00:32:51,350 --> 00:33:03,290
+المعادلة الرقم واحد is given from the formula
+
+283
+00:33:07,860 --> 00:33:15,900
+هذه هي الفورملة لـ Mu of X في الـ Y as a function
+
+284
+00:33:15,900 --> 00:33:25,860
+of X يسوى تكامل لـ Mu of X في الـ Q of X في الـ DX
+
+285
+00:33:32,800 --> 00:33:43,160
+where الـ mu of x بده يساوي E أس تكامل ال P of x
+
+286
+00:33:43,160 --> 00:33:51,760
+dx note كملاحظة بسيطة we must sure that
+
+287
+00:34:02,460 --> 00:34:08,560
+و يجب أن نتأكد أن
+
+288
+00:34:08,560 --> 00:34:16,560
+الـ coefficient .. الـ
+
+289
+00:34:16,560 --> 00:34:28,260
+coefficient of Y' هو 1 في الـ equation 1
+
+290
+00:35:52,210 --> 00:35:56,910
+يجي الى سكتشن واحد خمسة اللى بتكلم عن ال first
+
+291
+00:35:56,910 --> 00:36:03,050
+order linear differential equation اللى
+
+292
+00:36:03,050 --> 00:36:05,570
+هو ال first order linear differential equation
+
+293
+00:36:05,570 --> 00:36:12,160
+معادلة التفاضلية الخطية من الرتبة الأولىالـ First
+
+294
+00:36:12,160 --> 00:36:17,580
+Order Differential Equation بقول عنها Linear إذا
+
+295
+00:36:17,580 --> 00:36:19,280
+كانت على الشكل التالي
+
+296
+00:36:27,690 --> 00:36:33,870
+هذه المعادلة يمكن إعادة صياغتها وكتابتها على الشكل
+
+297
+00:36:33,870 --> 00:36:39,730
+التالي لو روحنا جسمنا الطرفين على a node of x يبقى
+
+298
+00:36:39,730 --> 00:36:43,490
+المعامل هنا قداش بصير واحد صحيح في ال wire prime
+
+299
+00:36:43,490 --> 00:36:48,670
+هي ال wire primeA1 of X على A node of X بدي اسميها
+
+300
+00:36:48,670 --> 00:36:55,010
+P of X F of X على A node of X بدي اسميها Q of X
+
+301
+00:36:55,010 --> 00:36:58,790
+إذا المعادلة اللي فوق هذا كتبناها بالشكل الجديد
+
+302
+00:36:58,790 --> 00:37:04,250
+لهمين الشكل واحد إذا أصبح الشكل المتعرف عليه أو
+
+303
+00:37:04,250 --> 00:37:08,010
+الدارج عندنا لل first order linear differential
+
+304
+00:37:08,010 --> 00:37:12,160
+equationهو الـ y prime زاد p of x في الـ y بيبقى
+
+305
+00:37:12,160 --> 00:37:18,000
+ساوية مان ل q of x حيث هذي حصلنا عليها عن طريق ان
+
+306
+00:37:18,000 --> 00:37:22,680
+ال p of x صار a1 of x على a node و ال q of x هي f
+
+307
+00:37:22,680 --> 00:37:28,180
+of x على a node of x و ال p و ال q كانوا دوال
+
+308
+00:37:28,180 --> 00:37:35,440
+متصلة على فترة ماطيب يبقى الآن حتى الآن أنا بس
+
+309
+00:37:35,440 --> 00:37:39,000
+اتعرفت على شكل ال first order linear differential
+
+310
+00:37:39,000 --> 00:37:42,640
+equation احنا قبل هيك اعطيناكوا شكل ال linear
+
+311
+00:37:42,640 --> 00:37:46,800
+differential equation in the general form اذا
+
+312
+00:37:46,800 --> 00:37:49,900
+كنتوا بتذكروا سواء كان من الرتبة الأولى ولا
+
+313
+00:37:49,900 --> 00:37:53,130
+التانية ولا التالتة ولا الرابعة ولا النونيةوكنا
+
+314
+00:37:53,130 --> 00:37:57,990
+بنقول لك a node of x y to the derivative n زائد a
+
+315
+00:37:57,990 --> 00:38:02,410
+one of x y to the derivative n minus one زائد زائد
+
+316
+00:38:02,410 --> 00:38:09,610
+a n minus one of x في ال y prime زائد a n of x في
+
+317
+00:38:09,610 --> 00:38:14,110
+ال y بده يساوي f of x هذا ال general form إذا لو
+
+318
+00:38:14,110 --> 00:38:17,330
+أنا أخدت ال first order كل اللي جابله هذا بالغيوب
+
+319
+00:38:17,330 --> 00:38:20,550
+تصبح المعادل عالمينعلى الشكل اللي عندنا هذا اللي
+
+320
+00:38:20,550 --> 00:38:25,470
+روحت حطيتها في الشكل اللي عندنا هذا الان بدنا نبحث
+
+321
+00:38:25,470 --> 00:38:29,350
+عن الحل طبعا الكتب اللي ان الطلاب اللي بدرسوا
+
+322
+00:38:29,350 --> 00:38:34,310
+differential equation فقط بروح نثبت لهم كيف يكون
+
+323
+00:38:34,310 --> 00:38:38,320
+شكل الحل اللي احنا بنتكلم عليه هناإنتوا هندسة بني
+
+324
+00:38:38,320 --> 00:38:41,660
+أعطيكوا الحل على طول القرن يبقى النظرية بيقول ال
+
+325
+00:38:41,660 --> 00:38:45,360
+solution تبع ال differential equation هذي هو ال mu
+
+326
+00:38:45,360 --> 00:38:50,800
+of x في ال y اللي هي الحل بدو يساوي تكمن ال mu of
+
+327
+00:38:50,800 --> 00:38:57,920
+x في ال q of x اللي عندنا هذا dx طب مين هي ال mu؟
+
+328
+00:38:58,050 --> 00:39:05,230
+ميو اف اكس يا ايه استكامل P of X DX اذا الميو
+
+329
+00:39:05,230 --> 00:39:11,570
+كأنها عامل التكامل جبتها من وين؟ من تكامل المعامل
+
+330
+00:39:11,570 --> 00:39:17,670
+تبع ال Y والطرف اليمين حاصل ضرب الميو اللي طلعت
+
+331
+00:39:17,670 --> 00:39:22,470
+عندي في ال Q بكمل اتنين مبعض وبالتالي بجيب شكل
+
+332
+00:39:22,470 --> 00:39:28,630
+الحل تبع هذه المعادلة التفاضليةإذا لما بدي أجيب
+
+333
+00:39:28,630 --> 00:39:33,550
+هذا الحل اللي عندى مشان يجيب كلامي الصحيح لازم
+
+334
+00:39:33,550 --> 00:39:40,750
+أخلي المعامل تبع y' هو واحد صحيح ديري بالك كتبتلك
+
+335
+00:39:40,750 --> 00:39:45,490
+ملاحظة مشان ماتنسهاش we must sure that لازم أتأكد
+
+336
+00:39:45,490 --> 00:39:51,190
+أنه المعامل تبع y' هو واحد صحيح في ال equation one
+
+337
+00:39:51,190 --> 00:39:56,240
+حد فيكم بتحب تسأل أي سؤال هناخلصنا النظرية بدنا
+
+338
+00:39:56,240 --> 00:40:00,240
+ندخل في الأعمل يعني ندخل أمثلة على ال first order
+
+339
+00:40:00,240 --> 00:40:03,980
+linear differential equation حد بتحب تسأل أي سؤال
+
+340
+00:40:03,980 --> 00:40:10,120
+طيب نبدأ في الأمثلة بنأخد أول مثال يبقى example
+
+341
+00:40:10,120 --> 00:40:18,240
+one بيقول
+
+342
+00:40:18,240 --> 00:40:23,780
+solve the initial value problem solve the initial
+
+343
+00:40:24,310 --> 00:40:29,310
+Value Problem XY'
+
+344
+00:40:31,970 --> 00:40:35,270
+-3Y
+
+345
+00:40:35,270 --> 00:40:38,550
+X تكيب
+
+346
+00:40:51,130 --> 00:40:56,310
+هذه المثلة محفوظة على الشكل الأصلي لإنها تمام لكن
+
+347
+00:40:56,310 --> 00:41:00,390
+إحنا لإيش تفرضه ده بدنا نخلي المعامل تبع واي فاي
+
+348
+00:41:00,390 --> 00:41:06,470
+هو جدرس وإلا بدنا نضطر X في الطرفين على الـP على X
+
+349
+00:41:06,470 --> 00:41:12,390
+للجابان يبقى جمال أصلاً للإنسانالمعادلة هذي بحطها
+
+350
+00:41:12,390 --> 00:41:18,770
+بالشكل التام و أي prime نقص ثلاثة على XP1 يساوي
+
+351
+00:41:18,770 --> 00:41:24,630
+كده؟ يساوي X ترمية يساوية على X الاشياء ال
+
+352
+00:41:24,630 --> 00:41:29,490
+condition بيظل زي ما يساوي Zero وهذه المعادلة
+
+353
+00:41:29,490 --> 00:41:34,770
+بتسميها Minimum معادلة واحدة زي ما انت شايف هذه
+
+354
+00:41:34,770 --> 00:41:40,150
+First Father Minimum
+
+355
+00:41:47,490 --> 00:41:52,210
+ماذا بصراحة كده بتروح أدور على ال integrating
+
+356
+00:41:52,210 --> 00:42:02,050
+factor يبدأ ال U of X هو E of Z تكامل، تكامل مين؟
+
+357
+00:42:02,050 --> 00:42:07,250
+بأخدها بإشارة، مش هتروح أصيب الإشارة إلى موجة بقى،
+
+358
+00:42:07,250 --> 00:42:11,810
+مش هتروح تقرأ ال E ده السنة، بأخدها بإشارتهايبقى
+
+359
+00:42:11,810 --> 00:42:19,230
+اناقس ثلاثة على X بالديكس يبقى E أس ناقس ثلاثة من
+
+360
+00:42:19,230 --> 00:42:28,070
+X يبقى E من X أس ناقس ثلاثة يبقى X أس ناقس ثلاثة
+
+361
+00:42:28,070 --> 00:42:33,170
+يبقى هذا ال integrating factor يبقى بعدين بقوله ذا
+
+362
+00:42:33,170 --> 00:42:46,360
+solution of equation one isGiven from الميو
+
+363
+00:42:46,360 --> 00:42:55,300
+of X في ال Y as a function of X تكمن الميو of X في
+
+364
+00:42:55,300 --> 00:43:03,080
+ال Q of X من DX الميو of X هي X والثالث ثلاثة وهذا
+
+365
+00:43:03,080 --> 00:43:09,720
+ال Y يساوي وهي تكمن الميو X والثالث ثلاثة ال Q هذا
+
+366
+00:43:09,720 --> 00:43:18,120
+جمعناهايبقى x تربيع يبقى x تربيع وهذا مين يكون dx
+
+367
+00:43:18,120 --> 00:43:26,620
+يبقى صارع بx أساليب تلاتة يسمي تكامل x أساليب واحد
+
+368
+00:43:26,620 --> 00:43:38,200
+dx يعني مين يعني تكامل واحد على x dxشكل انا تمام؟
+
+369
+00:43:38,200 --> 00:43:47,820
+طيب هذا ما هو عبارة عن ان ال X ذات المنصة C طب ليش
+
+370
+00:43:47,820 --> 00:43:51,900
+انا ماكنتش اشتغل أبسل و زجل X؟
+
+371
+00:44:07,160 --> 00:44:15,120
+بعد ان اقول Y يستخدم اكس تكعيد
+
+372
+00:44:20,070 --> 00:44:24,850
+زا قد سي X تقريبا الان انا بروح لل condition
+
+373
+00:44:24,850 --> 00:44:32,690
+conditions but ولكن عندك ال Y عند ال واحد يسوي
+
+374
+00:44:32,690 --> 00:44:43,670
+زيرو it implies Y بالزيرو ولن الواحد جدرس زيرو زا
+
+375
+00:44:43,670 --> 00:44:51,250
+قد سي في الواحد تقريبا يبقى سي جدرس تشغلان0 يبقى
+
+376
+00:44:51,250 --> 00:44:59,010
+بالإنها ليه أصبح الحل هو Y يسوى X تقريب من X فقط
+
+377
+00:44:59,010 --> 00:45:14,470
+هذا is the solution of the initial value of Y أخد
+
+378
+00:45:14,470 --> 00:45:16,330
+كمان مثلها بسيطة زي ذلك
+
+379
+00:45:28,690 --> 00:45:38,170
+يبقى example two provenance
+
+380
+00:45:38,170 --> 00:45:47,470
+of the differential equation المعادلة التفاغرية
+
+381
+00:45:47,470 --> 00:45:59,330
+الـ y' سنة و ثانية x في الواقع جسم تلاتةصين ال X
+
+382
+00:45:59,330 --> 00:46:07,470
+فيكو صين ال X وال X هذه موجودة في الفقرة المفتوحة
+
+383
+00:46:07,470 --> 00:46:20,810
+من Zero لوا يطول فطول
+
+384
+00:46:20,810 --> 00:46:26,090
+ال question انا منك اظن المعادلة جاهزة؟لا بدأ أقسم
+
+385
+00:46:26,090 --> 00:46:30,130
+ولا أقرأ، المعاملة تبع واي القرآن هي واحد صحيح،
+
+386
+00:46:30,130 --> 00:46:36,430
+كذا بدأ أروح أجيب له الـ Mu of X مباشرة، يبقى E
+
+387
+00:46:36,430 --> 00:46:42,970
+أُس تكامل الـP of X DX يبقى E أُس تكامل P of X
+
+388
+00:46:42,970 --> 00:46:50,290
+اللي هو كتان الـX بالنسبة إلى DX، يبقى E أس، كدهش
+
+389
+00:46:50,290 --> 00:46:58,760
+الكتانتكمل .. لن لل sign .. لن لل sign مظبوط يعني
+
+390
+00:46:58,760 --> 00:47:03,360
+ال cosine على ال science على البسطى فاض مقام يبقى
+
+391
+00:47:03,360 --> 00:47:11,840
+لن للمقام يبقى لن لصين ال X ولا داعي نفسي نفرق من
+
+392
+00:47:11,840 --> 00:47:16,360
+الصين خلال الفترة هذه دايما أو أبدا و جمال من صفر
+
+393
+00:47:16,360 --> 00:47:23,260
+لغاية 180 يمكن أن تجمع مدار صين ال Xيبقى هذه
+
+394
+00:47:23,260 --> 00:47:28,020
+المعالجة لو راح تسميتها معالجة رقم واحد فأنا راح
+
+395
+00:47:28,020 --> 00:47:37,120
+بقول لها solution of the differential equation
+
+396
+00:47:37,120 --> 00:47:45,600
+when this الـ mu of x هو sin of x dy يسوى تكامل
+
+397
+00:47:45,600 --> 00:47:50,720
+الـ mu of x هو sin of x في الـ q of x اللي هي
+
+398
+00:47:50,720 --> 00:47:51,800
+تلاتة
+
+399
+00:48:08,450 --> 00:48:18,170
+مش تقت ال sign ولا لا صح يبقى بقدر اقول دي لصين ال
+
+400
+00:48:18,170 --> 00:48:26,310
+Xيبقى هذه التلاتة اللي برا وهذه تكاملها بالـSin
+
+401
+00:48:26,310 --> 00:48:33,490
+تكييب X على ثلاثة زائد كنصان لأن هذه كانت تكامل
+
+402
+00:48:33,490 --> 00:48:37,290
+اللي همين زي التربية دي زي دي وزي التكييب على
+
+403
+00:48:37,290 --> 00:48:45,980
+تلاتة يبقى صارت Sin تكييب Xزائد constant c لو
+
+404
+00:48:45,980 --> 00:48:53,140
+جسمنا كله على sign بصير الحل يساوي sign تربيع ال x
+
+405
+00:48:53,140 --> 00:49:01,680
+زائد c على sign ال x او الحل بديش اخلي فيه كسور
+
+406
+00:49:01,680 --> 00:49:09,160
+ماعناش مشكلة يبقى y تساوي sign تربيع ال x زائد c
+
+407
+00:49:09,160 --> 00:49:17,890
+واحد على sign المقلوب منمقلب الصين مين؟ ال
+
+408
+00:49:17,890 --> 00:49:24,990
+cosecant x يبقى ال C في cosecant X يبقى هذا حل
+
+409
+00:49:24,990 --> 00:49:31,070
+المعادلة التفاضلية لا يزال عندنا المزيد من الأمثلة
+
+410
+00:49:31,070 --> 00:49:36,850
+للمحاضرة القادمة ان شاء الله تبارك وتعالى يعطيكم
+
+411
+00:49:36,850 --> 00:49:37,510
+العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1db2230bed8118f2e36a28d443f8f43b36733bbf
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc.srt
@@ -0,0 +1,1603 @@
+1
+00:00:18,070 --> 00:00:22,870
+بسم الله الرحمن الرحيم عودنا على بدأ نعود إلى
+
+2
+00:00:22,870 --> 00:00:28,390
+محاضرة الصباح والحمد لله لازال نظريتين مش مسحينهم
+
+3
+00:00:28,390 --> 00:00:31,830
+الناس اللي بعدنا أو ما لزموش لهم أو ما كانش في
+
+4
+00:00:31,830 --> 00:00:38,320
+محاضرة الله أعلم طبعا احنا أعطينا بدل المثال ثلاثة
+
+5
+00:00:38,320 --> 00:00:43,900
+أمثلة A وB وC في الفترة الصباحية والثلاثة أمثلة
+
+6
+00:00:43,900 --> 00:00:48,540
+كانت على النقطة اللي فوق وعلى مين وعلى الملاحظة
+
+7
+00:00:48,540 --> 00:00:53,320
+اللي عندنا لكن هذه النظرية لم نعطي عليها مثالا
+
+8
+00:00:53,320 --> 00:00:59,200
+أذكرها ثم أتي إلى هذا المثال بقول أنا عندي
+
+9
+00:00:59,200 --> 00:01:03,100
+مجموعة من ال vectors موجودة في ال vector space V
+
+10
+00:01:03,100 --> 00:01:07,940
+عندي مجموعة ثانية من ال vectors هذه موجودة في V
+
+11
+00:01:07,940 --> 00:01:15,700
+بقول لو كان ال M أقل من ال N بس بشرط كل واحد من
+
+12
+00:01:15,700 --> 00:01:20,040
+هدول من الفيهات يكتب على linear combination من هدول
+
+13
+00:01:20,240 --> 00:01:27,680
+يبقى الأصليات هدول لو كان عددهم أكبر من عدد الفيهات
+
+14
+00:01:27,680 --> 00:01:32,840
+أو عدد الفيهات أقل من عدد ال vectors اللي فوق هدول
+
+15
+00:01:32,840 --> 00:01:36,000
+automatic ال vectors اللي فوق بيكونوا linearly 
+
+16
+00:01:36,000 --> 00:01:41,200
+dependent تمام؟ الآن نعطي مثالا على هذه النظرية
+
+17
+00:01:41,200 --> 00:01:46,720
+لأننا لم نعطي عليها مثالا في الفترة الصباحية فبقول
+
+18
+00:01:46,720 --> 00:01:52,280
+يأخذ ال V ال vector space كل المصفوفة لنظامها
+
+19
+00:01:52,280 --> 00:01:57,120
+2 في 2 تحت عملية ضرب المصفوفات وعملية ضرب
+
+20
+00:01:57,120 --> 00:02:01,800
+المصفوفة بمقدار scalar اللي هي العملية ال usual
+
+21
+00:02:01,800 --> 00:02:07,360
+addition and usual multiplication ب scalar يبقى
+
+22
+00:02:07,360 --> 00:02:11,540
+هذا  vector space V بتروح تأخذ منه مجموعة من ال
+
+23
+00:02:11,540 --> 00:02:18,400
+vectors أخذ V1 و V2 و V3 و V4 يبقى أخذت قداش أربع
+
+24
+00:02:18,400 --> 00:02:23,910
+vectors موجودة في V وكذلك أخذت three vectors
+
+25
+00:02:23,910 --> 00:02:30,370
+موجودة كمان في V كل vector هنا 1 هنا 1
+
+26
+00:02:30,370 --> 00:02:34,850
+هنا 1 والباقي كله بمين بأصفار طبعا خذ بالك
+
+27
+00:02:34,850 --> 00:02:38,910
+هدول E واحد و E اثنين إن شاء الله بالسلامة و E ثلاثة 
+
+28
+00:02:38,910 --> 00:02:43,770
+أو أربعة هت لعب معانا دوري كبير جدا في ال section
+
+29
+00:02:43,770 --> 00:02:49,270
+بعد القادم في حجم نسميها اللي هو ال standard basis
+
+30
+00:02:49,270 --> 00:02:53,410
+لمين ال vector space اللي موجود ما علينا الكلام
+
+31
+00:02:53,410 --> 00:02:59,090
+هذا سابق لأوانه يبقى احنا نلتزم بس بما عندنا بقول
+
+32
+00:02:59,090 --> 00:03:02,730
+يبين لي أن ال vectors هدول الأربعة are linearly
+
+33
+00:03:02,730 --> 00:03:09,100
+dependent بقوله والله كويس مين الكتار لفوق أربعة و
+
+34
+00:03:09,100 --> 00:03:16,720
+لتحت أقل منهم ثلاثة يبقى N أكبر من M هدول عددهم هاي
+
+35
+00:03:16,720 --> 00:03:22,840
+N أربعة هدول عددهم مين ثلاثة يبقى أنا إذا قدرت
+
+36
+00:03:22,840 --> 00:03:28,420
+أكتب كل واحد من الأربعة ك linear combination من
+
+37
+00:03:28,420 --> 00:03:31,420
+الثلاثة automatically الأربعة بيكونوا مالهم
+
+38
+00:03:31,780 --> 00:03:36,960
+linearly independent تمام وما عنديش قيود على ال
+
+39
+00:03:36,960 --> 00:03:40,960
+vector space مش زي النظرية الأولى قلنا الشغل كله
+
+40
+00:03:40,960 --> 00:03:46,140
+على ال RM يبقى هنا RM ولا غير ال RM بيهمنيش مين
+
+41
+00:03:46,140 --> 00:03:50,050
+ما كان ال vectors يكونوا هدول واضح يا بنا يبقى بدنا 
+
+42
+00:03:50,050 --> 00:03:55,290
+نطبق هذه النظرية فبدأ أمسك كل vector من ال vectors
+
+43
+00:03:55,290 --> 00:03:59,330
+الأربعة أشوف بقدر أكتبه على صيغة linear
+
+44
+00:03:59,330 --> 00:04:02,130
+combination من ال vectors الثلاثة هدول و لا لأ
+
+45
+00:04:02,130 --> 00:04:07,030
+تعالوا نشوف الآن لو جيت لل V1 لما نهت الفي واحد
+
+46
+00:04:07,030 --> 00:04:14,640
+اللي هو عبارة عن 2 Zero 1 Zero بقدر اكتبه 
+
+47
+00:04:14,640 --> 00:04:23,460
+على شكل مجموع مصفوفتين شو المصفوفتين هدول 2000 زائد
+
+48
+00:04:23,460 --> 00:04:32,740
+0010 مظبوط هيك؟ صح؟ لو جيت جامعة التنتين برجع للأصل
+
+49
+00:04:32,740 --> 00:04:36,860
+اللي عندنا هنا طيب هذه فيها 2 عامل مشترك ما قدر
+
+50
+00:04:36,860 --> 00:04:42,160
+أخده برا إذا لو أخذت هذا برا بدي يصير مين بدي 
+
+51
+00:04:42,160 --> 00:04:49,000
+يصيري 2 في 1 Zero Zero زائد Zero Zero 1
+
+52
+00:04:49,000 --> 00:04:51,240
+Zero يساوي
+
+53
+00:04:52,710 --> 00:04:59,310
+ال V1 صار يساوي هذه مين يا بنات E1 يبقى هذا 2 
+
+54
+00:04:59,310 --> 00:05:10,410
+E1 هذه مين E3 يبقى زائد E3 طيب لو أضفت عليهم Zero
+
+55
+00:05:10,410 --> 00:05:17,530
+في E4 بيأثر ولا بيعمل حاجة، مظبوط؟ يبقى هذه بقدر 
+
+56
+00:05:17,530 --> 00:05:27,410
+أقول هو 2E1 زائد E3 زائد 0 في E4 إذا صارت V1
+
+57
+00:05:27,410 --> 00:05:34,110
+linear combination من ال E1 وال E3 وال E4 مظبوط إذا
+
+58
+00:05:34,110 --> 00:05:37,890
+خلصنا هذا منه ال vector بدنا نشوف اللي بعده و اللي
+
+59
+00:05:37,890 --> 00:05:41,310
+بعده اللي وقت نكمل ال 4 vectors اللي عندنا إذا
+
+60
+00:05:41,310 --> 00:05:47,720
+بندي لل vector الثاني V2 يبقى V2 هو عبارة عن سالب
+
+61
+00:05:47,720 --> 00:05:54,380
+2 زيرو سالب 1 1 بدي اكتبه على شكل مجموعة ثلاث
+
+62
+00:05:54,380 --> 00:06:02,880
+مصفوفات يبقى إيه سالب 2 زيرو زيرو زائد زيرو زيرو
+
+63
+00:06:02,880 --> 00:06:12,100
+سالب 1 زيرو زائد زيرو زيرو زيرو 1 يعني لو روحت
+
+64
+00:06:12,100 --> 00:06:17,940
+جمعت الثلاث مصفوفات هدول بيعطون المصفوفة هذه طلع
+
+65
+00:06:17,940 --> 00:06:22,480
+سالب 2 زائد Zero زائد Zero بسالب 2 زيرو زيرو
+
+66
+00:06:22,480 --> 00:06:26,640
+زيرو يبقى بزيرو زيرو سالب 1 زيرو يبقى بسالب 1
+
+67
+00:06:26,640 --> 00:06:31,020
+زيرو زيرو 1 يبقى ب 1 يبقى مظبوط مية المية
+
+68
+00:06:31,020 --> 00:06:36,490
+تمام إذا باجي بقدر أقول هذا الكلام بده يساوي بدي
+
+69
+00:06:36,490 --> 00:06:41,750
+أخذ سالب 2 برا بصير 1 Zero Zero و هنا بدي
+
+70
+00:06:41,750 --> 00:06:48,350
+أخذ ناقص 1 برا بصير Zero Zero 1 Zero و هذا
+
+71
+00:06:48,350 --> 00:06:55,350
+كما هو Zero Zero 1 و يساوي أظن الأول 2 في
+
+72
+00:06:55,350 --> 00:07:05,980
+E1 اللي بعده ناقص E3 اللي بعده زائد E4 يبقى معناته
+
+73
+00:07:05,980 --> 00:07:11,560
+قدرت أكتب V2 على صيغة Linear Combination من E1 و E3
+
+74
+00:07:11,560 --> 00:07:20,200
+و E4 بالمثل لو روحت ل V3 V3 عندي اللي هي مين Zero
+
+75
+00:07:20,200 --> 00:07:26,940
+Zero 4 5 بدأنا نكتبها على شكل مجموع مصفوفتين
+
+76
+00:07:27,420 --> 00:07:34,340
+زائد Zero Zero Zero 5 بتأخذ عوامل مشتركة يبقى
+
+77
+00:07:34,340 --> 00:07:41,740
+4 Zero Zero 1 Zero زائد 5 Zero Zero Zero
+
+78
+00:07:41,740 --> 00:07:49,240
+1 و يساوي 4 برا يبقى هذه 4 في مين يا 
+
+79
+00:07:49,240 --> 00:07:57,640
+بنات في E ثلاثة وهذه زائد 5 في E أربعة طب لو
+
+80
+00:07:57,640 --> 00:08:02,540
+أضفت لها Zero في E1 بيبقى third يبقى هذا الكلام
+
+81
+00:08:02,540 --> 00:08:10,680
+بده يساوي Zero في E1 زائد 4 في E3 زائد 5 في
+
+82
+00:08:10,680 --> 00:08:16,240
+E4 يبقى معناته أن V3 هي linear combination من E1
+
+83
+00:08:16,240 --> 00:08:22,320
+و E3 و E4 بالمثل بده نيجي لل vector الأخير
+
+84
+00:08:28,730 --> 00:08:34,190
+إذا لو جيت لل vector الأخير اللي هو V4 V4 عندي
+
+85
+00:08:34,190 --> 00:08:42,030
+اللي هو عبارة عن 3 0 0 اللي هو يساوي 3 في 1 0 0
+
+86
+00:08:42,030 --> 00:08:51,590
+اللي هو مين 3 E1 اللي بقدر اكتبه 3 E1 زائد 0 E3
+
+87
+00:08:51,590 --> 00:08:58,260
+زائد 0 E4 يبقى الآن قدرت أكتب كل واحد من الذئاب
+
+88
+00:08:58,260 --> 00:09:03,040
+الأربعة على صيغة linear combination من من من 
+
+89
+00:09:03,040 --> 00:09:10,280
+الأخرين بنص النظرية هذه ال M أجل من N يبقى هذا
+
+90
+00:09:10,280 --> 00:09:19,300
+linear combination يبقى هنا by the أو هنا the اللي 
+
+91
+00:09:19,300 --> 00:09:30,420
+هو each of V1 و V2 و V3 و V4 is a linear 
+
+92
+00:09:30,420 --> 00:09:34,120
+combination
+
+93
+00:09:34,120 --> 00:09:47,040
+linear combination of the vectors ال E1 و E3 و E4
+
+94
+00:09:47,040 --> 00:09:50,680
+by the
+
+95
+00:09:51,600 --> 00:09:59,640
+by the second theorem النظرية الثانية by the
+
+96
+00:09:59,640 --> 00:10:10,100
+second theorem ال V1 و V2 
+
+97
+00:10:10,100 --> 00:10:17,480
+و V3 و V4 are linearly dependent وانتهينا من هذه
+
+98
+00:10:17,480 --> 00:10:23,650
+المسألة لحد دي لما لا تنتهي ال section وإلى يكون
+
+99
+00:10:23,650 --> 00:10:29,770
+أرقام المسائل اللي مطلوب تتمرن عليهم يبقى
+
+100
+00:10:29,770 --> 00:10:36,470
+exercises ثلاثة ثلاثة المسائل التالية 1 2
+
+101
+00:10:36,470 --> 00:10:43,790
+4 5 6 7 11 12
+
+102
+00:10:48,030 --> 00:10:53,490
+حاجة فيكم تحب تسأل أي سؤال هنا؟ أي سؤال؟
+
+103
+00:11:34,080 --> 00:11:39,540
+طيب نجي لقى ال section اللي يليه اللي هو ال
+
+104
+00:11:39,540 --> 00:11:45,780
+Wronskian ال Wronskian اللي هو المحدد سواء كان محدد
+
+105
+00:11:45,780 --> 00:11:50,620
+ثنائي، ثلاثي، رباعي، قد ما يكون يكون يبقى بيننا نجي
+
+106
+00:11:50,620 --> 00:11:57,380
+ل section ثلاثة أربعة اللي هو ال Wronskian
+
+107
+00:12:01,930 --> 00:12:22,990
+تعريف definition let ال I be a fixed interval let
+
+108
+00:12:22,990 --> 00:12:35,400
+ال N be a nonzero positive integer
+
+109
+00:12:35,400 --> 00:12:50,000
+عدد صحيح موجب then ال FN is the vector space is
+
+110
+00:12:50,000 --> 00:12:55,480
+the vector space
+
+111
+00:12:57,010 --> 00:13:05,050
+of all functions of all functions that are defined
+
+112
+00:13:05,050 --> 00:13:21,730
+that are defined on interval I and has at least
+
+113
+00:13:21,730 --> 00:13:32,870
+على الأقل N derivatives in derivatives على الفترة 
+
+114
+00:13:32,870 --> 00:13:43,310
+اللي عندناها definition ثاني let ال F واحد و ال F
+
+115
+00:13:43,310 --> 00:13:53,000
+اثنين و لغاية ال FM موجودات في ال vector space FM
+
+116
+00:13:53,000 --> 00:14:01,900
+الـ Wronskian الـ 
+
+117
+00:14:01,900 --> 00:14:12,340
+Wronskian of these functions is
+
+118
+00:14:12,340 --> 00:14:16,940
+the determinant
+
+119
+00:14:18,400 --> 00:14:30,180
+من هنا أنت المحدد اللي هو من F1 of X F2 of X ونظل
+
+120
+00:14:30,180 --> 00:14:40,080
+ماشيين لغاية ال FM of X بعدها F1 prime of X F2 
+
+121
+00:14:40,080 --> 00:15:02,740
+prime of X F2 F M F' X F1 W' X F2 W' X F M W' X F1
+
+122
+00:15:02,740 --> 00:15:10,100
+W' X F2 W' X F M W' X F2 W' X F2 W' X F M W' X F2
+
+123
+00:15:10,100 --> 00:15:14,550
+F2 W' X F2 W' X F2 وهنا F2 ل derivative M minus
+
+124
+00:15:14,550 --> 00:15:24,130
+one of X ونظل ماشيين تمام لغاية من التفاضل ورقم M
+
+125
+00:15:24,130 --> 00:15:36,170
+minus one as a function of X this
+
+126
+00:15:40,460 --> 00:15:50,300
+this determinant is
+
+127
+00:15:50,300 --> 00:15:53,380
+denoted
+
+128
+00:15:53,380 --> 00:16:06,350
+by .. بنعرفه بالشكل التالي ال Wronskian of X و F1 و F2
+
+129
+00:16:06,350 --> 00:16:14,070
+و لغاية ال FM أو اختصارا بقول ال Wronskian as a
+
+130
+00:16:14,070 --> 00:16:16,230
+function of X
+
+131
+00:17:12,140 --> 00:17:17,880
+كلمة ال Wronskian ال W هذه silent لا تنطق زي ما 
+
+132
+00:17:17,880 --> 00:17:23,300
+تقول يوم الأربع نقول Wednesday ال W مابننطقاش ال W
+
+133
+00:17:23,300 --> 00:17:31,500
+silent و هنا عندنا ال W silent غير هيك هذا يعني 
+
+134
+00:17:31,500 --> 00:17:37,760
+اسم لوحد اكتشف هذا المحدد فسميه باسمه طبعا هذا ممر 
+
+135
+00:17:37,760 --> 00:17:42,070
+في الرياضيات كثير وكذلك في الفيزياء اللي هو قيمة
+
+136
+00:17:42,070 --> 00:17:45,890
+هذا المحدد هو إن كان محدد من الرتبة الثانية أو
+
+137
+00:17:45,890 --> 00:17:50,850
+الثالثة أو الرابعة أو النونية أو الميمية اللي
+
+138
+00:17:50,850 --> 00:17:55,970
+عندنا هذه سيية طيب في عن التعريفين التعريفين هدول
+
+139
+00:17:55,970 --> 00:18:00,970
+مهمات جدا نعرفهم اللي بيجالي little I بي fix the
+
+140
+00:18:00,970 --> 00:18:06,010
+interval اللي بيجالي أنا أخذت فترة ثابتة let n be a
+
+141
+00:18:06,010 --> 00:18:10,290
+non-zero positive integer إن عدد صحيح موجب لا
+
+142
+00:18:10,290 --> 00:18:17,350
+يساوي الـ zero then ال F وفوقها N مش المقصود F أس
+
+143
+00:18:17,350 --> 00:18:22,970
+N لأ هذا ما هو اس وإنما رمز الرمز يدل على مين 
+
+144
+00:18:22,970 --> 00:18:27,890
+قال لي is the vector space of all functions يبقى
+
+145
+00:18:27,890 --> 00:18:34,570
+هذا vector space لكل دوال اللي إلها خاصيتين الخاصية
+
+146
+00:18:34,570 --> 00:18:41,430
+الأولى إنها معرفة على نفس الفترة I الخاصية الثانية
+
+147
+00:18:41,430 --> 00:18:48,790
+إنها إلها N من المشتقات على الفترة I يبقى ال N هذا
+
+148
+00:18:48,790 --> 00:18:56,690
+يدل على عدد المشتقات التي تخضع لها هذه الدول يعني
+
+149
+00:18:56,690 --> 00:19:00,230
+إيش مقصود؟ المقصود يا بنت يعني المشتقة الأولى
+
+150
+00:19:00,230 --> 00:19:03,570
+exist والمشتقة الثانية exist والثالثة exist
+
+151
+00:19:03,570 --> 00:19:09,010
+والنونية exist طب ال N زاد واحد ليس بالضرورة، المهم
+
+152
+00:19:09,010 --> 00:19:14,430
+أنا بدي N من المشتقات للدوال اللي موجودة أو لأي
+
+153
+00:19:14,430 --> 00:19:18,510
+دالة موجودة داخل هذا ال vector space تبقى إلها ..
+
+154
+00:19:18,510 --> 00:19:22,310
+يعني كله مشتقة الأولى والثانية والثالثة و
+
+155
+00:19:22,310 --> 00:19:27,520
+الرابعة والنونية كل هذه المشتقات موجودة هذا
+
+156
+00:19:27,520 --> 00:19:31,700
+التعريف الأول التعريف الثاني بيقول خد لي هدول
+
+157
+00:19:31,700 --> 00:19:35,960
+الدوال موجودة في ال vector space هذا يبقى ال
+
+158
+00:19:35,960 --> 00:19:40,980
+vector space هذا الدوال اللي فيه كم مشتقة متحققة
+
+159
+00:19:40,980 --> 00:19:46,680
+فيه الأولى والثانية والثالثة ورا وال M ناقص الواحد 
+
+160
+00:19:46,680 --> 00:19:52,800
+لكن المشتقة ال M ليس بالضرورة طيب ماشي يبقى
+
+161
+00:19:52,800 --> 00:19:57,400
+أنا في عندي vectors موجودة في ال vector
+
+162
+00:19:57,400 --> 00:20:01,560
+space هنا بالدلالة على الأنواع اللي أنا كاتبه يبقى the
+
+163
+00:20:01,560 --> 00:20:06,320
+Wronskian of this function is the determinant مين
+
+164
+00:20:06,320 --> 00:20:10,860
+هو ال Wronskian لهذه الدوال هو قيمة هذا المحدد من
+
+165
+00:20:10,860 --> 00:20:15,340
+المحدد هذه باجي بحط الدوال هذه كلها في الصف الأول
+
+166
+00:20:15,340 --> 00:20:19,080
+الصف الثاني المشتقة الأولى الصف الثالث المشتقة
+
+167
+00:20:19,080 --> 00:20:24,520
+الثانية الصف الثالث المشتقة رقم 2 يعني أقل من
+
+168
+00:20:24,520 --> 00:20:31,320
+رتبة الصف بالمقدار إذا لما أظل ماشي للصف رقم M تبقى
+
+169
+00:20:31,320 --> 00:20:37,500
+المشتقة أقل بواحد يبقى المشتقة رقم M ناقص 1 وهي
+
+170
+00:20:37,500 --> 00:20:43,900
+حطيت لك بين قوسين مشان أقول لك هدول مشتقات وليس أسس
+
+171
+00:20:43,900 --> 00:20:48,120
+يبقى طلع هنا الدالة بدون اشتقاق مشتقة الأولى
+
+172
+00:20:48,120 --> 00:20:53,000
+الثانية الثالثة الرابعة المشتقة رقم M ناقص 1
+
+173
+00:20:53,150 --> 00:20:58,650
+تمام واضح يبقى عرفنا ليش قلت هدول موجودات في ال
+
+174
+00:20:58,650 --> 00:21:03,130
+vector space هذا لأن ال vector space هذا فيه مشتقات
+
+175
+00:21:03,130 --> 00:21:08,410
+لدوال لغاية M ناقص 1 اللي هو اللي بلزمه لمين 
+
+176
+00:21:08,410 --> 00:21:15,410
+للمحدد هذا يبقى هذا المحدد هو ال Wronskian لمين لدوال F1
+
+177
+00:21:15,410 --> 00:21:22,450
+و F2 و لغاية مين و لغاية
+
+201
+00:23:36,990 --> 00:23:42,510
+باجي بحط الدالة الأولى، الدالة الثانية، والدالة 
+
+202
+00:23:42,510 --> 00:23:49,070
+الثالثة يبقى F1، F2 لغاية F3، الصف الثاني بحط
+
+203
+00:23:49,070 --> 00:23:51,890
+المشتقة الأولى، مشتقة الـ X
+
+204
+00:23:55,230 --> 00:24:02,930
+مشتقة حاصل ضرب دالتين يبقى هذه E<sup>2X</sup> زائد X في الـ
+
+205
+00:24:02,930 --> 00:24:11,810
+E<sup>2X</sup>، هذه Zero هذه كما هي، هذه E<sup>2X</sup> كما هي، وهذه زائد
+
+206
+00:24:11,810 --> 00:24:18,930
+تجيها كمان هنا كده بيصير اثنين E<sup>2X</sup> زائد X E<sup>2X</sup>
+
+207
+00:24:18,930 --> 00:24:26,290
+مرتين أنا خلي بالكوا يا بنات يبقى بدي أشتق هذه، مشتقة هذا
+
+208
+00:24:26,290 --> 00:24:30,650
+بـ U<sup>6</sup> بدي أشتق هذه، إيه اللي هي هذه يعني هذا بدي 
+
+209
+00:24:30,650 --> 00:24:36,650
+أتكرر كمان مرة وعندي U<sup>6</sup> يبقى وصلي اثنين U<sup>6</sup> زي X
+
+210
+00:24:36,650 --> 00:24:43,430
+U<sup>6</sup>، هاي جفلنا مين؟ جفلنا المحدد، بدي أعرف قداش قيمة
+
+211
+00:24:43,430 --> 00:24:49,190
+هذا المحدد يبقى بضرورة أفكه إن حبيت باستخدام عناصر
+
+212
+00:24:49,190 --> 00:24:54,790
+الصف الثالث أو عناصر العمود الأول، سيان تفرقش عندنا
+
+213
+00:24:54,790 --> 00:25:01,170
+يبقى باجي بقول هذا الكلام بده يساوي X فيه أشرطة بصفه
+
+214
+00:25:01,170 --> 00:25:10,990
+و عمود بصير عندك هنا 2E<sup>2X</sup> زائد X E<sup>2X</sup>، هذا
+
+215
+00:25:10,990 --> 00:25:15,490
+حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب عناصر 
+
+216
+00:25:15,490 --> 00:25:24,530
+القطر الثانوي ناقص E<sup>2X</sup> ناقص X E<sup>2X</sup>، هذا الـ
+
+217
+00:25:24,530 --> 00:25:30,410
+term الأول الآن حسب قاعدة الإشارات الإشارة هذه مالها
+
+218
+00:25:30,410 --> 00:25:39,470
+بالسالب، وهذا قصه أشرطة بصفه وعموده يبقى بدأ تجيه
+
+219
+00:25:39,470 --> 00:25:44,070
+لمين؟ للترم اللي عندنا هذا يبقى E<sup>X</sup> بدي أضربه 
+
+220
+00:25:44,070 --> 00:25:51,010
+هنا يبقى إيش بصير عندي؟ اثنين E<sup>2X</sup> زائد X 
+
+221
+00:25:51,010 --> 00:25:58,390
+E<sup>2X</sup> هيخلصنا مين؟ خلصنا الرئيسي ناقص 
+
+222
+00:25:58,390 --> 00:26:06,050
+ثانوي يبقى ناقص X E<sup>2X</sup>، اللي بعده زائد 
+
+223
+00:26:06,050 --> 00:26:12,230
+Zero هذا الكلام يساوي، تعال نجي ل هذول يا بنات أظن 
+
+224
+00:26:12,230 --> 00:26:16,970
+هذي بالموجب و هذي بالسالب، مع السلامة بيظل عندنا
+
+225
+00:26:16,970 --> 00:26:21,450
+مين؟ هاي واحدة سالبة و تنتهي بالموجب بتروح واحدة
+
+226
+00:26:21,450 --> 00:26:28,250
+بيظل عندك X E<sup>2X</sup>، هاي دل عندي جوا E<sup> </sup>
+
+227
+00:26:28,250 --> 00:26:33,250
+2X ضربتها في الـ X اللي عندنا، نجي ل بعدها هذي
+
+228
+00:26:34,650 --> 00:26:39,490
+هي هذا بالضبط تماما، مظبوط يا بنات؟ إذا بصير عند
+
+229
+00:26:39,490 --> 00:26:46,930
+مين؟ ناقص اثنين E<sup>2X</sup>، هذا الكلام يساوي E<sup> </sup>
+
+230
+00:26:46,930 --> 00:26:54,400
+2X في X ناقص اثنين يبقى هذا قيمة الـ Wronskian، قيمة 
+
+231
+00:26:54,400 --> 00:26:59,080
+الـ Wronskian، وزي ما أنتو شايفين طلع الـ Wronskian طلع دالة في
+
+232
+00:26:59,080 --> 00:27:02,720
+X زي ما احنا قلنا هنا في الجزء النظري بيطلع
+
+233
+00:27:02,720 --> 00:27:07,760
+Function في X يبقى أنا بفضل أنه اكتبه اختصارا بهذا
+
+234
+00:27:07,760 --> 00:27:12,600
+الشكل وليس بهذا الشكل، لكن إن دعته ضرورة كتبته بهذا
+
+235
+00:27:12,600 --> 00:27:18,340
+الشكل، بدي اكتبه بهذا الشكل، هذا هو المثال الأول
+
+236
+00:27:18,340 --> 00:27:25,610
+المثال الثاني، Example two، بيقولي show that
+
+237
+00:27:29,140 --> 00:27:38,540
+بيّلي أن الـ Wronskian تبع الـ X والـ G F1 والـ G F2
+
+238
+00:27:38,540 --> 00:27:44,400
+كل واحد فيهم as a function of X بده يساوي G of X
+
+239
+00:27:44,400 --> 00:27:50,980
+الكل تربيع في الـ Wronskian بتبع الـ X والـ F1
+
+240
+00:27:50,980 --> 00:27:52,520
+والـ F2
+
+241
+00:28:25,120 --> 00:28:34,480
+الـ Wronskian X و G F1 و G F2 يتساوي مربع G مضروب في
+
+242
+00:28:34,480 --> 00:28:40,950
+Wronskian F1 و F2 فقط لا غير، طب احنا خلينا نجيب الـ
+
+243
+00:28:40,950 --> 00:28:44,910
+Wronskian تبع الـ F1 و الـ F2 ونشوف ما هو شكله بعد
+
+244
+00:28:44,910 --> 00:28:49,110
+هيك، أروح أدور عالمين على الـ Wronskian الثاني و أعرف
+
+245
+00:28:49,110 --> 00:28:54,570
+شو بيساوي، يبقى باجي بقوله أنا بده الـ Wronskian تبع
+
+246
+00:28:54,570 --> 00:29:02,650
+الـ X و الـ F1 و الـ F2 يساوي المحدد بدي أحطله الـ F1
+
+247
+00:29:02,650 --> 00:29:12,150
+و الـ F2، مشتقة الـ F1، مشتقة الـ F2، طبعا يبقى هذا
+
+248
+00:29:12,150 --> 00:29:17,970
+المحدد الثنائي لمصفوفة نظامها اثنين في اثنين بدي 
+
+249
+00:29:17,970 --> 00:29:23,090
+أفك هذا المحدد وأشوف كده يساوي، إذا هذا يا بنات بده 
+
+250
+00:29:23,090 --> 00:29:29,390
+يساوي F1 F2' ناقص
+
+251
+00:29:29,390 --> 00:29:35,530
+الرئيسي ناقص الثانوي ناقص F1' F2
+
+252
+00:29:37,830 --> 00:29:43,110
+عندما أقول هذا، أعود على الشجرة لما نشوف إيش علاقتك 
+
+253
+00:29:43,110 --> 00:29:47,370
+بالـ Wronskian الثاني، بالدادي للـ Wronskian الثاني
+
+254
+00:29:47,370 --> 00:29:59,070
+الـ Wronskian تبع الـ X و الـ F1 أو الـ GF1، GF1 و GF2
+
+255
+00:29:59,070 --> 00:30:10,390
+يبقى المحدد GF1، GF2' كويسبدي أشتق الآن هذا 
+
+256
+00:30:10,390 --> 00:30:15,450
+مشتقتاش حاصل ضرب دالتين، مش هتروح تقولي f prime g
+
+257
+00:30:15,450 --> 00:30:19,830
+prime لأ، بدي أستخدم قواعد الاشتقاق اللي درسناها في 
+
+258
+00:30:19,830 --> 00:30:24,930
+Calculus a و b، إذا هذه مشتقة حاصل ضرب دالتين بدي 
+
+259
+00:30:24,930 --> 00:30:28,670
+أقول الأولى في مشتقة الثانية زائد الثانية في مشتقة
+
+260
+00:30:28,670 --> 00:30:36,300
+الأولى وهكذا، إذا بدي أجي أقوله هذه الأولى في مشتقة 
+
+261
+00:30:36,300 --> 00:30:42,420
+الدالة الثانية زائد مشتقة الأولى في الدالة الثانية
+
+262
+00:30:42,420 --> 00:30:45,680
+اللي عملته لهذا الـ Function بتعمله الـ Function
+
+263
+00:30:45,680 --> 00:30:53,640
+الثانية يبقى G F2' زائد G' F2، ي جفلنا
+
+264
+00:30:53,640 --> 00:31:04,580
+منهم المحدد هذا المحدد يجب أن يكون G تربيع في الـ
+
+265
+00:31:04,580 --> 00:31:17,790
+F1 F2' زائد الـ G G' في الـ F1 F2، هذا حاصل ضرب 
+
+266
+00:31:17,790 --> 00:31:22,190
+عناصر القطر الرئيسي بداجي ناقص حاصل ضرب عناصر 
+
+267
+00:31:22,190 --> 00:31:32,990
+القطر الثانوي ناقص G تربيع في الـ F1 F2 ناقص الـ G
+
+268
+00:31:32,990 --> 00:31:41,950
+G' في الـ F1 F2 بالشكل هذا يبقى أي فكرة المحدد
+
+269
+00:31:41,950 --> 00:31:47,110
+حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب عناصر 
+
+270
+00:31:47,110 --> 00:31:53,730
+القطر الثانوي، يبقى بدأيش أطلعيلي للترم اللي 
+
+271
+00:31:53,730 --> 00:31:58,390
+عندنا هذا والترم اللي عندنا ده هو نفسه اللي بخلف 
+
+272
+00:31:58,390 --> 00:32:04,910
+عنه إذا واحد موجب وواحد سالب معاهم مع السلامة إذا 
+
+273
+00:32:04,910 --> 00:32:11,930
+نتيجة الـ Wronskian كانت تساوي G تربيع F1 F2' ناقص G
+
+274
+00:32:11,930 --> 00:32:21,130
+تربيع F1' F2، أظن في عامل مشترك اللي هو الـ G تربيع
+
+275
+00:32:21,130 --> 00:32:32,170
+بظال عندي F1 F2' ناقص F1' F2 ويساوي طلعيلي 
+
+276
+00:32:32,170 --> 00:32:37,830
+الـ Wronskian هذا وطلعيلي للنتيجة هذه، الـ Wronskian هناك
+
+277
+00:32:37,830 --> 00:32:41,470
+هي هذه النتيجة ولا لا؟ إذا بقدر أشيلها و أكتب 
+
+278
+00:32:41,470 --> 00:32:47,830
+بلـ Wronskian تبعها يبقى هذا الكلام يعطيني الـ G تربيع 
+
+279
+00:32:47,830 --> 00:32:54,790
+في الـ Wronskian تبع الـ X و الـ F1 و الـ F2، أظن هو هو 
+
+280
+00:32:54,790 --> 00:33:02,410
+المطلوب؟ 100% طيب، ننتقل الآن لأول نظرية في هذا الـ
+
+281
+00:33:02,410 --> 00:33:10,410
+Section، Theorem بيقول
+
+282
+00:33:10,410 --> 00:33:21,970
+لتف1 وف2 ولغاية الـ Fm موجودة في الـ Fm-1
+
+283
+00:33:21,970 --> 00:33:28,990
+relative relative
+
+284
+00:33:28,990 --> 00:33:35,050
+to an interval I
+
+285
+00:33:37,960 --> 00:33:50,380
+إذا الـ F1 و الـ F2 و الـ FM هم مستقلين
+
+286
+00:33:50,380 --> 00:33:56,960
+على الـ Interval I فالـ Wronskian
+
+287
+00:33:56,960 --> 00:34:10,670
+تبع الـ X و الـ F1 و الـ F2 و الـ FM بده يساوي Zero
+
+288
+00:34:10,670 --> 00:34:24,190
+at h x موجودة في الـ Interval I alternatively
+
+289
+00:34:24,190 --> 00:34:27,870
+if
+
+290
+00:34:27,870 --> 00:34:42,810
+there exists a point x0 في الـ Interval I such that
+
+291
+00:34:42,810 --> 00:35:00,090
+بحيث أن الـ Wronskian عند الـ x0 للـ F1 و F2 و FM FM
+
+292
+00:35:00,090 --> 00:35:13,240
+كل هذا الكلام لا يساوي Zero then اللي هو الـ F1 و F2
+
+293
+00:35:13,240 --> 00:35:30,900
+و FM are linearly independent remark the
+
+294
+00:35:30,900 --> 00:35:31,740
+converse
+
+295
+00:35:35,330 --> 00:35:46,690
+of the theorem، the converse of the theorem is not
+
+296
+00:35:46,690 --> 00:35:55,790
+true that is if
+
+297
+00:35:55,790 --> 00:35:59,570
+الـ Wronskian
+
+298
+00:35:59,570 --> 00:36:10,060
+بتبع الـ X و الـ F1 و الـ F2 و لغاية الـ FM بده
+
+299
+00:36:10,060 --> 00:36:15,880
+يساوي Zero then it
+
+300
+00:36:15,880 --> 00:36:25,580
+is not true that الـ
+
+301
+00:36:25,580 --> 00:36:36,320
+F1 و الـ F2 و الـ FM are linearly dependent
+
+302
+00:37:04,160 --> 00:37:10,320
+كل هذا كشف جاهز وحضور غياب كلها أشرتك بالاسم هاه؟
+
+303
+00:38:07,350 --> 00:38:12,150
+نرجع للنظرية اللي بين إيدينا هذه النظرية بتقول ما
+
+304
+00:38:12,150 --> 00:38:17,370
+يأتي بتقول افترض عندي Elements في واحد أو في اثنين 
+
+305
+00:38:17,370 --> 00:38:23,190
+لغة الـ FM موجودة في الـ Vector space FM minus الـ
+
+306
+00:38:23,190 --> 00:38:28,570
+one يعني الدالة المعرفة على fixed interval اثنين 
+
+307
+00:38:28,570 --> 00:38:34,930
+كل المشتقات من الدرجة M أو من الرتبة M ناقص واحد
+
+308
+00:38:34,930 --> 00:38:40,140
+موجودة في هذا الـ Vector space relative to an
+
+309
+00:38:40,140 --> 00:38:44,040
+interval I يعني على Interval I بقول لو كان الـ 
+
+310
+00:38:44,040 --> 00:38:48,580
+Functions هدول linearly dependent يبقى الـ Wronskian 
+
+311
+00:38:48,580 --> 00:38:53,860
+بده يساوي Zero عند كل نقطة موجودة داخل الـ Interval
+
+312
+00:38:53,860 --> 00:38:59,020
+I مش عند بعض النقط Zero، عند بعض النقط لأ بقول اه 
+
+313
+00:38:59,020 --> 00:39:03,940
+دججي قال لهدول كلهم Linearly dependent على الـ
+
+314
+00:39:03,940 --> 00:39:08,900
+interval I إن حدث ذلك يبقى الـ Wronskian تبع هذه الـ
+
+315
+00:39:08,900 --> 00:39:13,760
+Function دائما وأبدا بده يساوي Zero at each x 
+
+316
+00:39:13,760 --> 00:39:20,240
+موجودة في I، يبقى عندك كل نقطة موجودة داخل هذه الـ 
+
+317
+00:39:20,240 --> 00:39:24,300
+interval تعالوا نمشي لاتجاه المعاكس Alternatively
+
+318
+00:39:24,300 --> 00:39:30,660
+يعني من جهة أخرى أو من ناحية أخرى ها بدي أنفي هذه 
+
+319
+00:39:31,610 --> 00:39:38,650
+هذا يعني كل نقطة في البرنامج
+
+320
+00:39:38,650 --> 00:39:45,810
+إذا كان هناك نقطة X نوت عند I بحيث أن الـ Wronskian
+
+321
+00:39:45,810 --> 00:39:51,870
+تبع الـ Functions عند X نوت كان لا يساوي Zero يبقى 
+
+322
+00:39:51,870 --> 00:39:55,990
+هدول Linearly لايهاش independent إذا يا بنات لما
+
+323
+00:39:55,990 --> 00:39:59,930
+يعطيني مجموع من الـ Functions ويقول شوف لي هدول 
+
+324
+00:39:59,930 --> 00:40:04,470
+Linearly dependent ولا Linearly independent تمام
+
+325
+00:40:04,470 --> 00:40:08,690
+بأروح آخذ الـ Wronskian تبعهم إذا لجيت الـ Wronskian 
+
+326
+00:40:08,690 --> 00:40:13,690
+هذا أو أو إذا كانوا هدول Linearly dependent
+
+327
+00:40:13,690 --> 00:40:18,350
+لازم الـ Wronskian تبعهم بده يساوي Zero عند كل الـ x
+
+328
+00:40:18,350 --> 00:40:19,510
+بلا استثناء
+
+329
+00:40:21,960 --> 00:40:26,780
+العملية العكسية بس لو لجيت نقطة واحدة الـ 
+
+330
+00:40:26,780 --> 00:40:30,840
+Functions هدول عند هذه النقطة أخدت Wronskian تبعهم
+
+331
+00:40:30,840 --> 00:40:35,060
+لجيته لا يساوي Zero إذا هدول ما لهم Linearly
+
+332
+00:40:35,060 --> 00:40:39,590
+independent طب أنا بدأ أقولكوا إيش فهمت من هالكلام
+
+333
+00:40:39,590 --> 00:40:44,930
+ده وشوفوا فاهمي الصح و الله غلط، أعطاني Functions و
+
+334
+00:40:44,930 --> 00:40:49,370
+الـ Functions معرفات على Vector space و قاللي شوفلي
+
+335
+00:40:49,370 --> 00:40:52,050
+هدولي Linearly dependent و الله Linearly
+
+336
+00:40:52,050 --> 00:40:57,370
+independent تمام بقوله باخذ الـ Wronskian تبعهم إذا
+
+337
+00:40:57,370 --> 00:41:00,510
+الـ Wronskian تبعهم يساوي Zero يبقى هدول Linearly
+
+338
+00:41:00,510 --> 00:41:03,590
+dependent وإذا لا يساوي Zero يبقى Linearly
+
+339
+00:41:03,590 --> 00:41:07,410
+independent إيش رأيكم في هذا الفهم؟ مظبوط؟ هك؟ 
+
+340
+00:41:07,410 --> 00:41:10,910
+والله أنا غلطان، نص الأول .. نقل .. بدي واحدة تحكي 
+
+341
+00:41:10,910 --> 00:41:15,390
+مشان نتناقش احنا وياها، أيوة وصف صح ووصف غلط يعني 
+
+342
+00:41:15,390 --> 00:41:23,350
+كلامي غلط إذا إذا بدنا نبحث أين الخطأ مشان ما توجعيش
+
+343
+00:41:23,350 --> 00:41:27,810
+فيه الكلام اللي أنا قلته هذا بتقول زميلتكوا نصه صح
+
+344
+00:41:27,810 --> 00:41:32,750
+ونصه غلط، بدنا ندور وين الصح وين الخطأ حتى لا
+
+345
+00:41:32,750 --> 00:41:38,590
+نقع فيه، أنا زعمت قبل قليل أن أنا بدأ أخر و آخذ
+
+346
+00:41:38,590 --> 00:41:42,730
+Wronskian هذا إذا والله Zero يبقى هدول Linearly
+
+347
+00:41:42,730 --> 00:41:48,780
+dependent، صح ولا غلط؟ غلط هذا الكلام غلط، ليش؟ لأنه
+
+348
+00:41:48,780 --> 00:41:52,720
+ما قالليش F هتقولي F، ما قالليش اتجاه .. أعطاني اتجاه
+
+349
+00:41:52,720 --> 00:41:56,680
+واحد قاللي لو كانوا Linearly dependent إيه ده أنا
+
+350
+00:41:56,680 --> 00:42:00,520
+ما قلتش كم؟ بده يساوي Zero لكل الـ x، تمام؟ يبقى هذا 
+
+351
+00:42:00,520 --> 00:42:06,000
+هو الخطأ بعينيه، طب وده اللي مش خطأ قاللي هنا لو
+
+352
+00:42:06,000 --> 00:42:10,520
+روحت حسبت الـ Wronskian عنده نقطة والله عند كل النقطة
+
+353
+00:42:10,620 --> 00:42:14,540
+أنا ما حددتش والـ Wronskian هذا اللي جيت له لا يساوي
+
+354
+00:42:14,540 --> 00:42:17,500
+Zero إذا الـ Functions هذي اللي بيكونوا معاهم
+
+355
+00:42:17,500 --> 00:42:21,500
+Linearly independent، دي بالكلام صح، يبقى أنا لو 
+
+356
+00:42:21,500 --> 00:42:28,120
+بدأت بالـ Wronskian وطلع يساوي Zero بقدرش أحكم .. 
+
+357
+00:42:28,120 --> 00:42:32,280
+بقدرش أقول Linearly dependent ولا Linearly .. يعني 
+
+358
+00:42:32,280 --> 00:42:36,260
+قد يكون Linearly dependent صح وقد يكون Linearly
+
+359
+00:42:36,260 --> 00:42:40,460
+independent الله أعلم .. بقدرش أحكم .. يجب أن نفهم
+
+360
+00:42:40,460 --> 00:42:45,580
+الكلام هذا فهما صحيحا ولذلك روحت أعطيتك التحذير
+
+361
+00:42:45,580 --> 00:42:47,080
+هذا الـ Remark التالي
+
+362
+00:42:52,410 --> 00:43:00,210
+معكوس النظرية ليس صحيحا أو عكس النظرية
+
+363
+00:43:00,210 --> 00:43:05,510
+ليس
+
+364
+00:43:05,510 --> 00:43:12,070
+صحيحا غلط وقد طرحته من خلال السؤال قبل قليل يبقى
+
+365
+00:43:12,070 --> 00:43:16,390
+هذه is not true that is لو كان الـ Wronskian يساوي Zero
+
+366
+00:43:16,390 --> 00:43:20,630
+then it is not true that ليس بالضرورة هدول يكونوا
+
+367
+00:43:20,630 --> 00:43:25,530
+Linearly dependent، يبقى كل اللي بقدر أعمل و أنا 
+
+368
+00:43:25,530 --> 00:43:31,460
+مط
+
+401
+00:47:04,300 --> 00:47:11,080
+يحصل then بدي اخذ الـWronskian as a function of X
+
+402
+00:47:11,080 --> 00:47:15,920
+يساوي إذا أكبر من الـ 0 يبقى الدالة الأولى قداش
+
+403
+00:47:16,910 --> 00:47:24,990
+والدالة الثانية كده؟ مجتق تاني كده؟ مجتق تاني كده؟
+
+404
+00:47:24,990 --> 00:47:30,510
+يبقى 2x تكعيب ناقص 2x تكعيب يساوي كده؟
+
+405
+00:47:30,510 --> 00:47:40,470
+يساوي زي إذا كان الـ x أقل من الـ 0، فالـWronskian
+
+406
+00:47:40,470 --> 00:47:45,410
+كمشكلة x، الدالة الأولى x تربيع مافيش عليها مشكلة،
+
+407
+00:47:45,410 --> 00:47:51,730
+الدالة الثانية قداش سالب x تربيع، مشتقتها -2x وهذه
+
+408
+00:47:51,730 --> 00:47:59,200
+سالبة -2x بدي أفكها يبقى ناقص 2X تكعيب ناقص مع
+
+409
+00:47:59,200 --> 00:48:05,240
+ناقص بصير زائد 2X تكعيب هو سوى قداش إذا على
+
+410
+00:48:05,240 --> 00:48:11,440
+كل الأمر يعني الـWronskian قداش يبقى هنا الـ
+
+411
+00:48:11,440 --> 00:48:18,720
+Wronskian تبع الـ G1 والـ G2 بده يساوي Zero لكل الـ
+
+412
+00:48:18,720 --> 00:48:25,860
+X اللي موجودة من سالب Infinity إلى Infinity يبقى
+
+413
+00:48:25,860 --> 00:48:29,580
+الـWronskian هذا ماله بده يساوي Zero يبقى احنا
+
+414
+00:48:29,580 --> 00:48:34,130
+خلصنا من مين؟ من المطلب الأول بدي آجي للمطلوب
+
+415
+00:48:34,130 --> 00:48:37,970
+الثاني المطلوب الثاني بيقول لي ايش اثبت لي ان الـ two
+
+416
+00:48:37,970 --> 00:48:44,770
+functions هدول are linearly تقول لي كويس قال لي لو
+
+417
+00:48:44,770 --> 00:48:50,490
+قدرت ولو عند نقطة واحدة تثبت لي ان الـWronskian هذا
+
+418
+00:48:50,490 --> 00:48:55,950
+لا يساوي zero بيطلع كلامك مظبوط صحيح ولا لا يبقى
+
+419
+00:48:55,950 --> 00:48:59,270
+بآجي بقول له هنا اسم
+
+420
+00:49:01,430 --> 00:49:15,410
+that there exist c1 و c2 in R such that c1 g1 زي
+
+421
+00:49:15,410 --> 00:49:20,030
+c2 g2 بده يساوي من؟ بده يساوي 0
+
+422
+00:49:23,290 --> 00:49:28,730
+كويس؟ طيب أنا بروح أدور على c1 و c2 إذا طلع c1
+
+423
+00:49:28,730 --> 00:49:32,690
+يساوي c2 يساوي zero معناته هدول linearly
+
+424
+00:49:32,690 --> 00:49:38,590
+independent بيكون هو المطلوب مظبوط؟ اه لكن لما
+
+425
+00:49:38,590 --> 00:49:42,590
+جاء لي alternatively جاء لي وين الـ alternatively؟ جاء لي
+
+426
+00:49:42,590 --> 00:49:47,550
+لو قدرت لآجي ولو نقطة واحدة بقول له ماشي الحال أنا
+
+427
+00:49:47,550 --> 00:49:51,930
+بتدّرجي على الدوال اللي عندي هذه مرة أكبر من الـ zero
+
+428
+00:49:51,930 --> 00:49:56,550
+ومرة أقل من الـ zero إذا بدي آخذ مرة أكبر من الـ
+
+429
+00:49:56,550 --> 00:50:02,030
+zero ومرة أقل من الـ zero تمام فبآجي بقول هنا at
+
+430
+00:50:02,030 --> 00:50:08,760
+مثلا x تساوي 1 لما الـx ساوي 1 بده يصير c
+
+431
+00:50:08,760 --> 00:50:17,180
+واحد g واحد of 1 زائد c اثنين g اثنين of 1
+
+432
+00:50:17,180 --> 00:50:23,560
+بده يساوي زيرو هذا معناه g واحد يا بنات من هاية
+
+433
+00:50:24,690 --> 00:50:33,490
+يبقى C1 في الـ 1 تربيع زائد C2 في الـ g واحد
+
+434
+00:50:33,490 --> 00:50:38,350
+تربيع كمان قداش اللي هو 1 لكل تربيع بده يساوي
+
+435
+00:50:38,350 --> 00:50:46,730
+Zero يبقى C1 زائد C2 بده يساوي Zero الآن لو جيت
+
+436
+00:50:46,730 --> 00:50:52,710
+قلت at x يساوي سالب 1 مش هأجيب الدالة كلها مش
+
+437
+00:50:52,710 --> 00:50:57,650
+هأجيب جزء وجزء ثاني لا يبقى عند x يساوي سالب 1
+
+438
+00:50:57,650 --> 00:51:04,650
+بصير c واحد g واحد of سالب 1 زائد c اثنين g
+
+439
+00:51:04,650 --> 00:51:11,190
+اثنين of سالب 1 بده يساوي zero هذا معناه c of
+
+440
+00:51:11,190 --> 00:51:21,190
+واحد في سالب واحد لكل تربيع زائد c2 في g2 اللي هو
+
+441
+00:51:21,190 --> 00:51:29,970
+g2 اللي هو سالب لسالب واحد لكل تربيع سالب x تربيع
+
+442
+00:51:29,970 --> 00:51:33,950
+يبقى هي السالب برا واخذنا الـx بسالب 1 تربيع
+
+443
+00:51:33,950 --> 00:51:42,950
+هذا الكلام بده يساوي zero هذا معناه ان c1 ناقص c2
+
+444
+00:51:42,950 --> 00:51:49,180
+بده يساوي zero مظبوط هيك؟ طيب تعال نجمع لو جمعنا
+
+445
+00:51:49,180 --> 00:51:54,020
+هدول بيروحوا هدول بيصير قداش يا بنات 2 C واحد
+
+446
+00:51:54,020 --> 00:51:58,060
+بده يساوي Zero هذا معناه انه C واحد بده يساوي Zero
+
+447
+00:51:58,060 --> 00:52:03,220
+لما C واحد بده يساوي Zero هذا معناه انه C اثنين
+
+448
+00:52:03,220 --> 00:52:08,140
+بده يساوي Zero يبقى بعض انه C واحد يساوي C اثنين
+
+449
+00:52:08,140 --> 00:52:13,360
+يساوي Zero يبقى أنا لما عندي linear combination
+
+450
+00:52:13,360 --> 00:52:17,880
+بيساوي zero و أثبت ان الثوابت هدول بده يساوي zero
+
+451
+00:52:17,880 --> 00:52:21,960
+يبقى الـ two functions are linearly independent
+
+452
+00:52:21,960 --> 00:52:31,620
+يبقى هنا الـ g1 and الـ g2 are linearly independent
+
+453
+00:52:31,620 --> 00:52:34,680
+وهو المطلوب
+
+454
+00:52:38,150 --> 00:52:42,810
+المخرج يؤشر لي ان انتهى الوقت واحنا بنقول خلاص
+
+455
+00:52:42,810 --> 00:52:47,170
+نكتفي اليوم بهذا القدر لكن لا يزال عندي بعض
+
+456
+00:52:47,170 --> 00:52:49,290
+الأمثلة في هذا الـ situation 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a6e7f43d7f974fc1b30496b76967149b862ee5ac
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc_raw.json
@@ -0,0 +1 @@
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87.2, "end": 87.68, "word": " اليهود", "probability": 0.7244466145833334}, {"start": 87.68, "end": 88.0, "word": " أو", "probability": 0.71630859375}, {"start": 88.0, "end": 88.46, "word": " عدد", "probability": 0.97119140625}, {"start": 88.46, "end": 88.88, "word": " اليهود", "probability": 0.99072265625}, {"start": 88.88, "end": 89.86, "word": " أقل", "probability": 0.9720052083333334}, {"start": 89.86, "end": 90.56, "word": " من", "probability": 0.9921875}, {"start": 90.56, "end": 91.16, "word": " عدد", "probability": 0.9954427083333334}, {"start": 91.16, "end": 91.3, "word": " ال", "probability": 0.91259765625}, {"start": 91.3, "end": 91.62, "word": " vectors", "probability": 0.728515625}, {"start": 91.62, "end": 92.0, "word": " اللي", "probability": 0.9033203125}, {"start": 92.0, "end": 92.4, "word": " فوق", "probability": 0.984619140625}, {"start": 92.4, "end": 92.84, "word": " هدول", "probability": 0.9786783854166666}, {"start": 92.84, "end": 93.72, "word": " automatic", "probability": 0.4912109375}, {"start": 93.72, "end": 94.0, "word": " ال", "probability": 0.865234375}, {"start": 94.0, "end": 94.36, "word": " vectors", "probability": 0.9423828125}, {"start": 94.36, "end": 94.62, "word": " اللي", "probability": 0.989990234375}, {"start": 94.62, "end": 94.86, "word": " فوق", "probability": 0.989013671875}, {"start": 94.86, "end": 95.34, "word": " بيكونوا", "probability": 0.9283447265625}, {"start": 95.34, "end": 96.0, "word": " linearly", "probability": 0.8994140625}, {"start": 96.0, "end": 97.3, "word": " dependent", "probability": 0.77587890625}, {"start": 97.3, "end": 98.7, "word": " تمام؟", "probability": 0.74462890625}, {"start": 98.7, "end": 99.16, "word": " الأبدأ", "probability": 0.7189127604166666}, {"start": 99.16, "end": 99.6, "word": " نعطي", "probability": 0.982421875}, {"start": 99.6, "end": 100.12, "word": " مثال", "probability": 0.994384765625}, {"start": 100.12, "end": 100.4, "word": " على", "probability": 0.89697265625}, {"start": 100.4, "end": 100.72, "word": " هذه", "probability": 0.98583984375}, {"start": 100.72, "end": 101.2, "word": " النظرية", "probability": 0.9490966796875}, {"start": 101.2, "end": 101.72, "word": " لأننا", "probability": 0.8232421875}, {"start": 101.72, "end": 101.92, "word": " لم", "probability": 0.9677734375}, {"start": 101.92, "end": 102.32, "word": " نعطي", "probability": 0.9930419921875}, {"start": 102.32, "end": 102.7, "word": " عليها", "probability": 0.982177734375}, {"start": 102.7, "end": 103.24, "word": " مثلا", "probability": 0.80615234375}, {"start": 103.24, "end": 103.82, "word": " في", "probability": 0.8291015625}, {"start": 103.82, "end": 104.32, "word": " الفترة", "probability": 0.9905598958333334}, {"start": 104.32, "end": 105.5, "word": " الصباحية", "probability": 0.91796875}], "temperature": 1.0}, {"id": 5, "seek": 12466, "start": 106.06, "end": 124.66, "text": "فبقول ياخد ال V ال vector space كل المصفوفة لنظامها اتنين في اتنين تحت عملية ضرب المصفوفات وعملية ضرب المصفوفة بمقدار scalar اللي هي العملية ال usual addition and usual multiplication", "tokens": [5172, 3555, 39648, 7251, 47283, 3215, 2423, 691, 2423, 8062, 1901, 28242, 9673, 9381, 5172, 38688, 3660, 5296, 1863, 19913, 10943, 11296, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 6055, 33753, 6225, 42213, 10632, 48812, 25513, 9673, 9381, 5172, 38688, 9307, 4032, 25957, 1211, 10632, 48812, 25513, 9673, 9381, 5172, 38688, 3660, 4724, 2304, 28543, 9640, 39684, 13672, 1829, 39896, 18863, 42213, 10632, 2423, 7713, 4500, 293, 7713, 27290], "avg_logprob": -0.22721354415019354, "compression_ratio": 1.6453488372093024, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 106.06, "end": 106.72, "word": "فبقول", "probability": 0.4501546223958333}, {"start": 106.72, "end": 107.28, "word": " ياخد", "probability": 0.6358235677083334}, {"start": 107.28, "end": 107.5, "word": " ال", "probability": 0.65234375}, {"start": 107.5, "end": 107.8, "word": " V", "probability": 0.61083984375}, {"start": 107.8, "end": 108.3, "word": " ال", "probability": 0.448974609375}, {"start": 108.3, "end": 108.7, "word": " vector", "probability": 0.58056640625}, {"start": 108.7, "end": 109.32, "word": " space", "probability": 0.931640625}, {"start": 109.32, "end": 109.9, "word": " كل", "probability": 0.8388671875}, {"start": 109.9, "end": 111.3, "word": " المصفوفة", "probability": 0.8318359375}, {"start": 111.3, "end": 112.28, "word": " لنظامها", "probability": 0.9}, {"start": 112.28, "end": 112.72, "word": " اتنين", "probability": 0.830810546875}, {"start": 112.72, "end": 112.86, "word": " في", "probability": 0.370849609375}, {"start": 112.86, "end": 113.38, "word": " اتنين", "probability": 0.9827880859375}, {"start": 113.38, "end": 114.14, "word": " تحت", "probability": 0.968017578125}, {"start": 114.14, "end": 114.8, "word": " عملية", "probability": 0.9798177083333334}, {"start": 114.8, "end": 115.18, "word": " ضرب", "probability": 0.991943359375}, {"start": 115.18, "end": 116.12, "word": " المصفوفات", "probability": 0.90751953125}, {"start": 116.12, "end": 116.8, "word": " وعملية", "probability": 0.81085205078125}, {"start": 116.8, "end": 117.12, "word": " ضرب", "probability": 0.992431640625}, {"start": 117.12, "end": 117.88, "word": " المصفوفة", "probability": 0.93525390625}, {"start": 117.88, "end": 118.76, "word": " بمقدار", "probability": 0.9080810546875}, {"start": 118.76, "end": 119.64, "word": " scalar", "probability": 0.5537109375}, {"start": 119.64, "end": 120.3, "word": " اللي", "probability": 0.71484375}, {"start": 120.3, "end": 120.42, "word": " هي", "probability": 0.72900390625}, {"start": 120.42, "end": 120.98, "word": " العملية", "probability": 0.81982421875}, {"start": 120.98, "end": 121.16, "word": " ال", "probability": 0.87939453125}, {"start": 121.16, "end": 121.8, "word": " usual", "probability": 0.90673828125}, {"start": 121.8, "end": 122.98, "word": " addition", "probability": 0.91357421875}, {"start": 122.98, "end": 123.52, "word": " and", "probability": 0.8349609375}, {"start": 123.52, "end": 123.94, "word": " usual", "probability": 0.84521484375}, {"start": 123.94, "end": 124.66, "word": " multiplication", "probability": 0.85595703125}], "temperature": 1.0}, {"id": 6, "seek": 14002, "start": 125.26, "end": 140.02, "text": "بياس كيلار يبقى هذا mid vector space V بتروح أخد منه مجموعة من ال vectors أخد V1 و V2 و V3 و V4 يبقى أخدت قداش أربع vectors موجودات في V", "tokens": [21292, 32277, 9122, 26895, 9640, 7251, 3555, 4587, 7578, 23758, 2062, 8062, 1901, 691, 39894, 32887, 5016, 5551, 9778, 3215, 9154, 3224, 3714, 7435, 2304, 2407, 27884, 9154, 2423, 18875, 5551, 9778, 3215, 691, 16, 4032, 691, 17, 4032, 691, 18, 4032, 691, 19, 7251, 3555, 4587, 7578, 5551, 9778, 3215, 2655, 12174, 3215, 33599, 5551, 25513, 3615, 18875, 3714, 29245, 23328, 9307, 8978, 691], "avg_logprob": -0.27201705584020325, "compression_ratio": 1.3972602739726028, "no_speech_prob": 0.0, "words": [{"start": 125.26, "end": 126.26, "word": "بياس", "probability": 0.252197265625}, {"start": 126.26, "end": 126.64, "word": " كيلار", "probability": 0.523681640625}, {"start": 126.64, "end": 127.36, "word": " يبقى", "probability": 0.8310546875}, {"start": 127.36, "end": 127.6, "word": " هذا", "probability": 0.86962890625}, {"start": 127.6, "end": 127.88, "word": " mid", "probability": 0.09466552734375}, {"start": 127.88, "end": 128.28, "word": " vector", "probability": 0.87451171875}, {"start": 128.28, "end": 128.8, "word": " space", "probability": 0.814453125}, {"start": 128.8, "end": 129.14, "word": " V", "probability": 0.68017578125}, {"start": 129.14, "end": 129.88, "word": " بتروح", "probability": 0.8406575520833334}, {"start": 129.88, "end": 130.3, "word": " أخد", "probability": 0.759521484375}, {"start": 130.3, "end": 130.6, "word": " منه", "probability": 0.97998046875}, {"start": 130.6, "end": 131.22, "word": " مجموعة", "probability": 0.9244140625}, {"start": 131.22, "end": 131.4, "word": " من", "probability": 0.986328125}, {"start": 131.4, "end": 131.54, "word": " ال", "probability": 0.974609375}, {"start": 131.54, "end": 131.98, "word": " vectors", "probability": 0.8681640625}, {"start": 131.98, "end": 132.44, "word": " أخد", "probability": 0.9187825520833334}, {"start": 132.44, "end": 132.9, "word": " V1", "probability": 0.751220703125}, {"start": 132.9, "end": 133.12, "word": " و", "probability": 0.70263671875}, {"start": 133.12, "end": 133.58, "word": " V2", "probability": 0.81103515625}, {"start": 133.58, "end": 133.72, "word": " و", "probability": 0.9892578125}, {"start": 133.72, "end": 134.3, "word": " V3", "probability": 0.945068359375}, {"start": 134.3, "end": 134.5, "word": " و", "probability": 0.99560546875}, {"start": 134.5, "end": 135.18, "word": " V4", "probability": 0.969482421875}, {"start": 135.18, "end": 135.82, "word": " يبقى", "probability": 0.9527587890625}, {"start": 135.82, "end": 136.16, "word": " أخدت", "probability": 0.8656005859375}, {"start": 136.16, "end": 136.76, "word": " قداش", "probability": 0.7665201822916666}, {"start": 136.76, "end": 138.4, "word": " أربع", "probability": 0.6311442057291666}, {"start": 138.4, "end": 138.98, "word": " vectors", "probability": 0.9443359375}, {"start": 138.98, "end": 139.62, "word": " موجودات", "probability": 0.813232421875}, {"start": 139.62, "end": 139.78, "word": " في", "probability": 0.98583984375}, {"start": 139.78, "end": 140.02, "word": " V", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 7, "seek": 15799, "start": 140.43, "end": 157.99, "text": "و كذلك اخدت three vectors موجودة كمان في V كل vector هنا هنا واحد هنا واحد هنا واحد و الباقي كله بمين باصفار طبعا خد بالك هدول E واحد و E اتنين ان شاء الله بالسلامة", "tokens": [2407, 9122, 8848, 23275, 1975, 9778, 3215, 2655, 1045, 18875, 3714, 29245, 23328, 3660, 9122, 2304, 7649, 8978, 691, 28242, 8062, 34105, 34105, 36764, 24401, 34105, 36764, 24401, 34105, 36764, 24401, 4032, 29739, 995, 38436, 28242, 3224, 4724, 2304, 9957, 4724, 33546, 5172, 9640, 23032, 3555, 3615, 995, 16490, 3215, 20666, 4117, 8032, 3215, 12610, 462, 36764, 24401, 4032, 462, 1975, 2655, 1863, 9957, 16472, 13412, 16606, 21984, 20666, 3794, 37440, 3660], "avg_logprob": -0.1946703799783367, "compression_ratio": 1.6385542168674698, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 140.43, "end": 140.87, "word": "و", "probability": 0.81396484375}, {"start": 140.87, "end": 141.67, "word": " كذلك", "probability": 0.80224609375}, {"start": 141.67, "end": 142.47, "word": " اخدت", "probability": 0.7591552734375}, {"start": 142.47, "end": 142.89, "word": " three", "probability": 0.6103515625}, {"start": 142.89, "end": 143.91, "word": " vectors", "probability": 0.93994140625}, {"start": 143.91, "end": 145.57, "word": " موجودة", "probability": 0.964599609375}, {"start": 145.57, "end": 146.11, "word": " كمان", "probability": 0.825439453125}, {"start": 146.11, "end": 146.37, "word": " في", "probability": 0.96337890625}, {"start": 146.37, "end": 146.73, "word": " V", "probability": 0.7451171875}, {"start": 146.73, "end": 147.59, "word": " كل", "probability": 0.72900390625}, {"start": 147.59, "end": 148.19, "word": " vector", "probability": 0.95751953125}, {"start": 148.19, "end": 148.61, "word": " هنا", "probability": 0.97802734375}, {"start": 148.61, "end": 148.97, "word": " هنا", "probability": 0.5595703125}, {"start": 148.97, "end": 149.59, "word": " واحد", "probability": 0.967041015625}, {"start": 149.59, "end": 149.85, "word": " هنا", "probability": 0.87646484375}, {"start": 149.85, "end": 150.37, "word": " واحد", "probability": 0.9873046875}, {"start": 150.37, "end": 150.61, "word": " هنا", "probability": 0.95361328125}, {"start": 150.61, "end": 151.03, "word": " واحد", "probability": 0.98779296875}, {"start": 151.03, "end": 151.15, "word": " و", "probability": 0.52978515625}, {"start": 151.15, "end": 151.45, "word": " الباقي", "probability": 0.8209635416666666}, {"start": 151.45, "end": 151.97, "word": " كله", "probability": 0.90771484375}, {"start": 151.97, "end": 152.43, "word": " بمين", "probability": 0.73681640625}, {"start": 152.43, "end": 153.57, "word": " باصفار", "probability": 0.7034912109375}, {"start": 153.57, "end": 154.19, "word": " طبعا", "probability": 0.924072265625}, {"start": 154.19, "end": 154.43, "word": " خد", "probability": 0.635498046875}, {"start": 154.43, "end": 154.85, "word": " بالك", "probability": 0.92578125}, {"start": 154.85, "end": 155.25, "word": " هدول", "probability": 0.927734375}, {"start": 155.25, "end": 155.45, "word": " E", "probability": 0.728515625}, {"start": 155.45, "end": 155.91, "word": " واحد", "probability": 0.811279296875}, {"start": 155.91, "end": 156.09, "word": " و", "probability": 0.8896484375}, {"start": 156.09, "end": 156.43, "word": " E", "probability": 0.8232421875}, {"start": 156.43, "end": 156.81, "word": " اتنين", "probability": 0.921875}, {"start": 156.81, "end": 156.99, "word": " ان", "probability": 0.81494140625}, {"start": 156.99, "end": 157.23, "word": " شاء", "probability": 0.7587890625}, {"start": 157.23, "end": 157.25, "word": " الله", "probability": 0.95654296875}, {"start": 157.25, "end": 157.99, "word": " بالسلامة", "probability": 0.93212890625}], "temperature": 1.0}, {"id": 8, "seek": 18645, "start": 158.15, "end": 186.45, "text": "وي تلاتة او اربعة هتلعب معانا دوري كبير جدا في ال section بعد القادم في حجم نسميها اللي هو ال standard basis لمين ال vector space اللي موجود ما علينا الكلام هذا سابق لأوانه يبقى احنا بنلتزم بس بما عندنا بقول يبينلي ان ال vectors هدول الأربعة are linearly dependent بقوله والله كويس مين الكتار", "tokens": [45865, 6055, 1211, 9307, 3660, 1975, 2407, 1975, 25513, 27884, 8032, 2655, 1211, 3615, 3555, 20449, 7649, 995, 11778, 13063, 1829, 9122, 3555, 13546, 10874, 28259, 8978, 2423, 3541, 39182, 25062, 18513, 2304, 8978, 11331, 7435, 2304, 8717, 38251, 1829, 11296, 13672, 1829, 31439, 2423, 3832, 5143, 32767, 9957, 2423, 8062, 1901, 13672, 1829, 3714, 29245, 23328, 19446, 25894, 8315, 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" بعده", "probability": 0.936767578125}, {"start": 418.32, "end": 419.56, "word": " ناقص", "probability": 0.8154296875}, {"start": 419.56, "end": 420.64, "word": " E3", "probability": 0.843017578125}, {"start": 420.64, "end": 421.6, "word": " اللي", "probability": 0.67138671875}, {"start": 421.6, "end": 422.2, "word": " بعده", "probability": 0.951171875}, {"start": 422.2, "end": 423.16, "word": " زائد", "probability": 0.7750651041666666}, {"start": 423.16, "end": 424.2, "word": " E4", "probability": 0.994140625}], "temperature": 1.0}, {"id": 20, "seek": 44694, "start": 425.1, "end": 446.94, "text": "يبقى معناته قدرت اكتب V2 على صيغة Linear Combination من E1 وE3 وE4 بالمثل لو روحت ل V3 V3 عند اللي هي مين Zero Zero أربعة خمسة بدا اكتبها على شكل مجموع مصفوفتين", "tokens": [1829, 3555, 4587, 7578, 20449, 8315, 47395, 12174, 3215, 43500, 1975, 4117, 2655, 3555, 691, 17, 15844, 20328, 1829, 17082, 3660, 14670, 289, 25939, 2486, 9154, 462, 16, 4032, 36, 18, 4032, 36, 19, 20666, 2304, 12984, 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0.93017578125}, {"start": 455.4, "end": 456.18, "word": " Zero", "probability": 0.96826171875}, {"start": 456.18, "end": 457.16, "word": " واحد", "probability": 0.950439453125}, {"start": 457.16, "end": 457.72, "word": " Zero", "probability": 0.94384765625}, {"start": 457.72, "end": 458.7, "word": " زائد", "probability": 0.9680989583333334}, {"start": 458.7, "end": 459.58, "word": " خمسة", "probability": 0.9921875}, {"start": 459.58, "end": 460.32, "word": " Zero", "probability": 0.97314453125}, {"start": 460.32, "end": 461.0, "word": " Zero", "probability": 0.9638671875}, {"start": 461.0, "end": 461.74, "word": " Zero", "probability": 0.97314453125}, {"start": 461.74, "end": 462.68, "word": " واحد", "probability": 0.9775390625}, {"start": 462.68, "end": 464.58, "word": " ويساوي", "probability": 0.890625}, {"start": 464.58, "end": 466.02, "word": " أربعة", "probability": 0.9069010416666666}, {"start": 466.02, "end": 466.54, "word": " برا", "probability": 0.775390625}, {"start": 466.54, "end": 467.12, "word": " يبقى", "probability": 0.9674072265625}, {"start": 467.12, "end": 467.42, "word": " هذه", "probability": 0.66552734375}, {"start": 467.42, "end": 468.34, "word": " أربعة", "probability": 0.9588216145833334}, {"start": 468.34, "end": 468.84, "word": " في", "probability": 0.94873046875}, {"start": 468.84, "end": 469.1, "word": " مين", "probability": 0.853515625}, {"start": 469.1, "end": 469.24, "word": " يا", "probability": 0.95361328125}, {"start": 469.24, "end": 469.7, "word": " بنات", "probability": 0.8821614583333334}, {"start": 469.7, "end": 470.6, "word": " في", "probability": 0.44580078125}, {"start": 470.6, "end": 470.98, "word": " E", "probability": 0.63427734375}, {"start": 470.98, "end": 471.88, "word": " تلاتة", "probability": 0.8720703125}, {"start": 471.88, "end": 472.8, "word": " وهذه", "probability": 0.7724609375}, {"start": 472.8, "end": 473.66, "word": " زائد", "probability": 0.955078125}, {"start": 473.66, "end": 474.7, "word": " خمسة", "probability": 0.9903564453125}, {"start": 474.7, "end": 474.9, "word": " في", "probability": 0.98388671875}, {"start": 474.9, "end": 475.24, "word": " E", "probability": 0.99169921875}, {"start": 475.24, "end": 475.74, "word": " أربعة", "probability": 0.9256184895833334}], "temperature": 1.0}, {"id": 22, "seek": 50232, "start": 477.14, "end": 502.32, "text": "طب لو ضافت لها zero في E1 بيبقى third يبقى هذا الكلام بده يساوي zero في E1 زائد اربعة في E3 زائد خمسة في E4 يبقى معناته ان V3 هي linear combination من E1 وE3 وE4 بالمثل بده نيجي لل vector الأخير", "tokens": [9566, 3555, 45164, 48812, 31845, 2655, 5296, 11296, 4018, 8978, 462, 16, 4724, 1829, 3555, 4587, 7578, 2636, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 4018, 8978, 462, 16, 30767, 16373, 3215, 1975, 25513, 27884, 8978, 462, 18, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 8978, 462, 19, 7251, 3555, 4587, 7578, 20449, 8315, 47395, 16472, 691, 18, 39896, 8213, 6562, 9154, 462, 16, 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"probability": 0.9232177734375}, {"start": 481.58, "end": 481.92, "word": " هذا", "probability": 0.95654296875}, {"start": 481.92, "end": 482.54, "word": " الكلام", "probability": 0.95849609375}, {"start": 482.54, "end": 482.96, "word": " بده", "probability": 0.40643310546875}, {"start": 482.96, "end": 483.62, "word": " يساوي", "probability": 0.96337890625}, {"start": 483.62, "end": 484.38, "word": " zero", "probability": 0.403564453125}, {"start": 484.38, "end": 484.98, "word": " في", "probability": 0.94873046875}, {"start": 484.98, "end": 485.92, "word": " E1", "probability": 0.972412109375}, {"start": 485.92, "end": 487.06, "word": " زائد", "probability": 0.85888671875}, {"start": 487.06, "end": 487.74, "word": " اربعة", "probability": 0.7256673177083334}, {"start": 487.74, "end": 488.06, "word": " في", "probability": 0.9794921875}, {"start": 488.06, "end": 489.12, "word": " E3", "probability": 0.98193359375}, {"start": 489.12, "end": 489.56, "word": " زائد", "probability": 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"end": 497.04, "word": " وE3", "probability": 0.8206380208333334}, {"start": 497.04, "end": 498.28, "word": " وE4", "probability": 0.9602864583333334}, {"start": 498.28, "end": 499.8, "word": " بالمثل", "probability": 0.95751953125}, {"start": 499.8, "end": 500.18, "word": " بده", "probability": 0.5770263671875}, {"start": 500.18, "end": 500.52, "word": " نيجي", "probability": 0.9669189453125}, {"start": 500.52, "end": 500.78, "word": " لل", "probability": 0.666015625}, {"start": 500.78, "end": 501.32, "word": " vector", "probability": 0.896484375}, {"start": 501.32, "end": 502.32, "word": " الأخير", "probability": 0.876953125}], "temperature": 1.0}, {"id": 23, "seek": 53399, "start": 508.73, "end": 533.99, "text": "إذا لو جيت لل vector الأخير اللي هو V4 V4 عندي اللي هو عبارة عن 3 0 0 اللي هو يساوي 3 في 1 0 0 اللي هو مين 3 E1 اللي بقدر أكتمه 3 E1 زائد 0 E3 زائد 0 E4", "tokens": [28814, 15730, 45164, 10874, 36081, 24976, 8062, 16247, 9778, 13546, 13672, 1829, 31439, 691, 19, 691, 19, 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"probability": 0.872802734375}, {"start": 511.05, "end": 511.19, "word": " هو", "probability": 0.93408203125}, {"start": 511.19, "end": 512.29, "word": " V4", "probability": 0.74365234375}, {"start": 512.29, "end": 513.75, "word": " V4", "probability": 0.7958984375}, {"start": 513.75, "end": 514.19, "word": " عندي", "probability": 0.760009765625}, {"start": 514.19, "end": 514.35, "word": " اللي", "probability": 0.9208984375}, {"start": 514.35, "end": 514.47, "word": " هو", "probability": 0.7705078125}, {"start": 514.47, "end": 515.05, "word": " عبارة", "probability": 0.9774169921875}, {"start": 515.05, "end": 515.37, "word": " عن", "probability": 0.9951171875}, {"start": 515.37, "end": 515.99, "word": " 3", "probability": 0.403076171875}, {"start": 515.99, "end": 516.75, "word": " 0", "probability": 0.70703125}, {"start": 516.75, "end": 517.47, "word": " 0", "probability": 0.9794921875}, {"start": 517.47, "end": 518.15, "word": " اللي", "probability": 0.8603515625}, {"start": 518.15, "end": 518.31, "word": " هو", "probability": 0.9091796875}, {"start": 518.31, "end": 518.99, "word": " يساوي", "probability": 0.777099609375}, {"start": 518.99, "end": 519.65, "word": " 3", "probability": 0.8056640625}, {"start": 519.65, "end": 519.95, "word": " في", "probability": 0.6005859375}, {"start": 519.95, "end": 520.37, "word": " 1", "probability": 0.79638671875}, {"start": 520.37, "end": 521.09, "word": " 0", "probability": 0.67236328125}, {"start": 521.09, "end": 522.03, "word": " 0", "probability": 0.931640625}, {"start": 522.03, "end": 522.71, "word": " اللي", "probability": 0.970458984375}, {"start": 522.71, "end": 522.87, "word": " هو", "probability": 0.87646484375}, {"start": 522.87, "end": 523.29, "word": " مين", "probability": 0.784912109375}, {"start": 523.29, "end": 524.55, "word": " 3", "probability": 0.3984375}, {"start": 524.55, "end": 525.63, "word": " E1", "probability": 0.61865234375}, {"start": 525.63, "end": 526.07, "word": " اللي", "probability": 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بنص النظرية هذه ال M أجل من N يبقى هذا linear combination يبقى هنا by the أو هنا the اللي هو each of", "tokens": [1829, 3555, 4587, 7578, 16247, 1863, 12174, 3215, 43500, 5551, 4117, 2655, 3555, 28242, 36764, 24401, 9154, 32545, 19986, 16758, 16247, 25513, 3615, 15844, 20328, 1829, 17082, 3660, 8213, 6562, 9154, 9154, 9154, 16247, 34740, 9957, 44945, 9381, 28239, 19913, 2288, 10632, 29538, 2423, 376, 5551, 7435, 1211, 9154, 426, 7251, 3555, 4587, 7578, 23758, 8213, 6562, 7251, 3555, 4587, 7578, 34105, 538, 264, 34051, 34105, 264, 13672, 1829, 31439, 1184, 295], "avg_logprob": -0.20473030985218205, "compression_ratio": 1.598901098901099, "no_speech_prob": 0.0, "words": [{"start": 534.6, "end": 535.16, "word": "يبقى", "probability": 0.8970947265625}, {"start": 535.16, "end": 535.62, "word": " الأن", "probability": 0.646484375}, {"start": 535.62, "end": 536.18, "word": " قدرت", "probability": 0.7776692708333334}, {"start": 536.18, "end": 536.7, "word": " أكتب", "probability": 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المشتقات على الفترة I", "tokens": [6027, 20292, 11933, 1211, 11296, 16490, 33546, 36081, 9957, 33962, 33546, 10632, 16247, 12610, 7578, 36145, 11296, 20449, 28480, 3660, 15844, 8717, 36178, 27188, 2655, 25720, 286, 33962, 33546, 10632, 6024, 104, 7649, 10632, 36145, 11296, 11933, 1211, 11296, 426, 9154, 9673, 8592, 2655, 4587, 9307, 15844, 27188, 2655, 25720, 286], "avg_logprob": -0.10757211810694291, "compression_ratio": 1.780701754385965, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1110.91, "end": 1111.65, "word": "اللي", "probability": 0.7005615234375}, {"start": 1111.65, "end": 1112.01, "word": " إلها", "probability": 0.7377115885416666}, {"start": 1112.01, "end": 1113.27, "word": " خاصيتين", "probability": 0.991943359375}, {"start": 1113.27, "end": 1114.57, "word": " الخاصية", "probability": 0.9423828125}, {"start": 1114.57, "end": 1115.11, "word": " الأولى", "probability": 0.9806315104166666}, {"start": 1115.11, "end": 1115.61, "word": " إنها", "probability": 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"word": " عليها", "probability": 0.975830078125}, {"start": 1340.01, "end": 1340.43, "word": " مش", "probability": 0.94091796875}, {"start": 1340.43, "end": 1340.87, "word": " ناخدها", "probability": 0.9569091796875}, {"start": 1340.87, "end": 1340.99, "word": " و", "probability": 0.998046875}, {"start": 1340.99, "end": 1341.69, "word": " نسيبها", "probability": 0.97890625}, {"start": 1341.69, "end": 1342.45, "word": " طيب", "probability": 0.8605143229166666}, {"start": 1342.45, "end": 1342.91, "word": " بنيجي", "probability": 0.78692626953125}, {"start": 1342.91, "end": 1343.37, "word": " لأول", "probability": 0.9168294270833334}, {"start": 1343.37, "end": 1343.97, "word": " مثال", "probability": 0.966552734375}, {"start": 1343.97, "end": 1344.23, "word": " على", "probability": 0.91357421875}, {"start": 1344.23, "end": 1344.85, "word": " هذا", "probability": 0.98193359375}, {"start": 1344.85, "end": 1345.73, "word": " الموضوع", "probability": 0.9974365234375}, {"start": 1345.73, 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linearly dependent يبقى الورس كان بده يساوي Zero عند كل نقطة موجودة داخل ال interval I مش عند بعض النقط Zero عند بعض النقط لأ بقول اه دججي قال لي", "tokens": [4419, 1166, 281, 364, 15035, 286, 37495, 22653, 15844, 15035, 286, 4724, 39648, 45164, 25961, 2423, 6828, 8032, 3215, 12610, 43586, 12334, 7251, 3555, 4587, 7578, 2423, 13063, 3794, 25961, 47525, 3224, 7251, 3794, 995, 45865, 17182, 43242, 28242, 8717, 47432, 3660, 3714, 29245, 23328, 3660, 11778, 47283, 1211, 2423, 15035, 286, 37893, 43242, 45030, 11242, 28239, 47432, 17182, 43242, 45030, 11242, 28239, 47432, 5296, 10721, 4724, 39648, 1975, 3224, 11778, 7435, 7435, 1829, 50239, 32239], "avg_logprob": -0.19713880411990278, "compression_ratio": 1.625, "no_speech_prob": 0.0, "words": [{"start": 2318.12, "end": 2319.46, "word": "relative", "probability": 0.7578125}, {"start": 2319.46, "end": 2319.84, "word": " to", "probability": 0.8759765625}, {"start": 2319.84, "end": 2320.14, "word": " an", "probability": 0.67333984375}, 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{"id": 103, "seek": 258703, "start": 2572.41, "end": 2587.03, "text": "معكوس النظرية ليس صحيحا او عكس النظرية ليس صحيحا", "tokens": [2304, 3615, 4117, 41779, 28239, 19913, 2288, 10632, 32239, 3794, 20328, 5016, 1829, 5016, 995, 1975, 2407, 6225, 4117, 3794, 28239, 19913, 2288, 10632, 32239, 3794, 20328, 5016, 1829, 5016, 995], "avg_logprob": -0.20581054547801614, "compression_ratio": 1.543859649122807, "no_speech_prob": 0.0, "words": [{"start": 2572.41, "end": 2573.81, "word": "معكوس", "probability": 0.65435791015625}, {"start": 2573.81, "end": 2574.55, "word": " النظرية", "probability": 0.9703369140625}, {"start": 2574.55, "end": 2574.99, "word": " ليس", "probability": 0.910888671875}, {"start": 2574.99, "end": 2575.71, "word": " صحيحا", "probability": 0.86201171875}, {"start": 2575.71, "end": 2576.15, "word": " او", "probability": 0.6854248046875}, {"start": 2576.15, "end": 2576.55, "word": " عكس", "probability": 0.9892578125}, {"start": 2576.55, "end": 2580.21, "word": " النظرية", "probability": 0.983154296875}, {"start": 2580.21, "end": 2585.51, "word": " ليس", "probability": 0.919677734375}, {"start": 2585.51, "end": 2587.03, "word": " صحيحا", "probability": 0.95869140625}], "temperature": 1.0}, {"id": 104, "seek": 260663, "start": 2587.07, "end": 2606.63, "text": "غلط وقد طرحته من خلال السؤال قبل قليل يبقى هذه is not true that is لو كان ال risk يساوي zero then it is not true that ليس بالضرورة هدول يكونوا linearly dependent يبقى كل اللي بقدر أعمل و أنا مطمئن", "tokens": [17082, 1211, 9566, 4032, 28543, 23032, 2288, 33753, 3224, 9154, 16490, 1211, 6027, 21136, 33604, 6027, 12174, 36150, 12174, 20292, 1211, 7251, 3555, 4587, 7578, 29538, 307, 406, 2074, 300, 307, 45164, 25961, 2423, 3148, 7251, 3794, 995, 45865, 4018, 550, 309, 307, 406, 2074, 300, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 8032, 3215, 12610, 7251, 30544, 14407, 43586, 12334, 7251, 3555, 4587, 7578, 28242, 13672, 1829, 4724, 28543, 2288, 5551, 25957, 1211, 4032, 41850, 3714, 9566, 2304, 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is", "probability": 0.212158203125}, {"start": 2592.79, "end": 2593.03, "word": " not", "probability": 0.953125}, {"start": 2593.03, "end": 2593.37, "word": " true", "probability": 0.8642578125}, {"start": 2593.37, "end": 2593.87, "word": " that", "probability": 0.52001953125}, {"start": 2593.87, "end": 2594.19, "word": " is", "probability": 0.79443359375}, {"start": 2594.19, "end": 2594.75, "word": " لو", "probability": 0.84423828125}, {"start": 2594.75, "end": 2595.03, "word": " كان", "probability": 0.98779296875}, {"start": 2595.03, "end": 2595.15, "word": " ال", "probability": 0.54345703125}, {"start": 2595.15, "end": 2595.37, "word": " risk", "probability": 0.85791015625}, {"start": 2595.37, "end": 2595.93, "word": " يساوي", "probability": 0.7681884765625}, {"start": 2595.93, "end": 2596.39, "word": " zero", "probability": 0.560546875}, {"start": 2596.39, "end": 2596.89, "word": " then", "probability": 0.7001953125}, {"start": 2596.89, "end": 2597.07, "word": " it", "probability": 0.962890625}, {"start": 2597.07, "end": 2597.27, "word": " is", "probability": 0.9443359375}, {"start": 2597.27, "end": 2597.61, "word": " not", "probability": 0.96044921875}, {"start": 2597.61, "end": 2598.07, "word": " true", "probability": 0.9755859375}, {"start": 2598.07, "end": 2598.53, "word": " that", "probability": 0.8740234375}, {"start": 2598.53, "end": 2599.27, "word": " ليس", "probability": 0.96923828125}, {"start": 2599.27, "end": 2599.89, "word": " بالضرورة", "probability": 0.9611328125}, {"start": 2599.89, "end": 2600.17, "word": " هدول", "probability": 0.7220052083333334}, {"start": 2600.17, "end": 2600.63, "word": " يكونوا", "probability": 0.9620768229166666}, {"start": 2600.63, "end": 2601.21, "word": " linearly", "probability": 0.96240234375}, {"start": 2601.21, "end": 2602.45, "word": " dependent", "probability": 0.8994140625}, {"start": 2602.45, "end": 2603.25, "word": " يبقى", "probability": 0.97119140625}, {"start": 2603.25, "end": 2603.71, "word": " كل", "probability": 0.97509765625}, {"start": 2603.71, "end": 2603.95, "word": " اللي", "probability": 0.97607421875}, {"start": 2603.95, "end": 2604.55, "word": " بقدر", "probability": 0.986328125}, {"start": 2604.55, "end": 2605.07, "word": " أعمل", "probability": 0.8271484375}, {"start": 2605.07, "end": 2605.25, "word": " و", "probability": 0.52880859375}, {"start": 2605.25, "end": 2605.53, "word": " أنا", "probability": 0.57080078125}, {"start": 2605.53, "end": 2606.63, "word": " مطمئن", "probability": 0.9509765625}], "temperature": 1.0}, {"id": 105, "seek": 262672, "start": 2607.78, "end": 2626.72, "text": "إذا كانوا الـ vectors دول linearly dependent، إذا الـ Runnerskin يساوي 0 على كل الـ Interval، تمام؟ الحالة الثانية، لو لجيت بس نقطة واحدة في الـ Interval، الـ Runnerskin عندها لا يساوي 0، يبقى هذه الـ functions تبقى linearly", "tokens": [28814, 15730, 25961, 14407, 2423, 39184, 18875, 11778, 12610, 43586, 12334, 12399, 11933, 15730, 2423, 39184, 8950, 2999, 5843, 7251, 3794, 995, 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"probability": 0.71142578125}, {"start": 2610.38, "end": 2611.46, "word": " dependent،", "probability": 0.5389404296875}, {"start": 2611.46, "end": 2611.7, "word": " إذا", "probability": 0.90234375}, {"start": 2611.7, "end": 2611.84, "word": " الـ", "probability": 0.881103515625}, {"start": 2611.84, "end": 2612.34, "word": " Runnerskin", "probability": 0.256103515625}, {"start": 2612.34, "end": 2612.84, "word": " يساوي", "probability": 0.8443603515625}, {"start": 2612.84, "end": 2613.14, "word": " 0", "probability": 0.37255859375}, {"start": 2613.14, "end": 2613.48, "word": " على", "probability": 0.77880859375}, {"start": 2613.48, "end": 2614.52, "word": " كل", "probability": 0.97509765625}, {"start": 2614.52, "end": 2614.84, "word": " الـ", "probability": 0.816650390625}, {"start": 2614.84, "end": 2615.9, "word": " Interval،", "probability": 0.5649007161458334}, {"start": 2615.9, "end": 2616.78, "word": " تمام؟", "probability": 0.9046223958333334}, {"start": 2616.78, "end": 2617.48, "word": " الحالة", "probability": 0.96630859375}, {"start": 2617.48, "end": 2618.28, "word": " الثانية،", "probability": 0.93603515625}, {"start": 2618.28, "end": 2618.44, "word": " لو", "probability": 0.9638671875}, {"start": 2618.44, "end": 2618.8, "word": " لجيت", "probability": 0.6310221354166666}, {"start": 2618.8, "end": 2619.16, "word": " بس", "probability": 0.865478515625}, {"start": 2619.16, "end": 2619.72, "word": " نقطة", "probability": 0.9861653645833334}, {"start": 2619.72, "end": 2620.2, "word": " واحدة", "probability": 0.99365234375}, {"start": 2620.2, "end": 2620.34, "word": " في", "probability": 0.962890625}, {"start": 2620.34, "end": 2620.6, "word": " الـ", "probability": 0.805419921875}, {"start": 2620.6, "end": 2621.58, "word": " Interval،", "probability": 0.88916015625}, {"start": 2621.58, "end": 2621.84, "word": " الـ", "probability": 0.820556640625}, {"start": 2621.84, "end": 2622.3, "word": " Runnerskin", "probability": 0.88427734375}, {"start": 2622.3, "end": 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النظرية نجي لأول مثال في هذا الموضوع المثال بيقول ما ياتي example let", "tokens": [9566, 3555, 45164, 34892, 1863, 3794, 25961, 8608, 14407, 4018, 4724, 39648, 21984, 5551, 3615, 19528, 12174, 3215, 7251, 30544, 4032, 12174, 3215, 20193, 7251, 30544, 46952, 10721, 3615, 9566, 1829, 50113, 15040, 7251, 2407, 11242, 5016, 19446, 5551, 39648, 3224, 8978, 29538, 28239, 19913, 2288, 10632, 8717, 7435, 1829, 5296, 10721, 12610, 50113, 6027, 8978, 23758, 9673, 2407, 11242, 45367, 9673, 12984, 6027, 4724, 1829, 39648, 19446, 7251, 9307, 1829, 1365, 718], "avg_logprob": -0.1581503372337367, "compression_ratio": 1.606936416184971, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2627.42, "end": 2628.2, "word": "طب", "probability": 0.476318359375}, {"start": 2628.2, "end": 2628.38, "word": " لو", "probability": 0.9697265625}, {"start": 2628.38, "end": 2628.84, "word": " الرنس", "probability": 0.7102864583333334}, {"start": 2628.84, "end": 2629.08, "word": " كان", "probability": 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" Zero", "probability": 0.5029296875}, {"start": 3115.12, "end": 3115.8, "word": " هذا", "probability": 0.67333984375}, {"start": 3115.8, "end": 3116.3, "word": " معناه", "probability": 0.9773763020833334}, {"start": 3116.3, "end": 3116.62, "word": " انه", "probability": 0.693603515625}, {"start": 3116.62, "end": 3116.74, "word": " C", "probability": 0.9130859375}, {"start": 3116.74, "end": 3117.06, "word": " واحد", "probability": 0.987548828125}, {"start": 3117.06, "end": 3117.32, "word": " بده", "probability": 0.97021484375}, {"start": 3117.32, "end": 3117.7, "word": " يساوي", "probability": 0.994873046875}, {"start": 3117.7, "end": 3118.06, "word": " Zero", "probability": 0.9462890625}, {"start": 3118.06, "end": 3118.84, "word": " لما", "probability": 0.91748046875}, {"start": 3118.84, "end": 3119.12, "word": " C", "probability": 0.95263671875}, {"start": 3119.12, "end": 3119.5, "word": " واحد", "probability": 0.99267578125}, {"start": 3119.5, "end": 3119.86, "word": " بده", "probability": 0.99169921875}, {"start": 3119.86, "end": 3120.36, "word": " يساوي", "probability": 0.9945068359375}, {"start": 3120.36, "end": 3120.92, "word": " Zero", "probability": 0.9736328125}, {"start": 3120.92, "end": 3121.6, "word": " هذا", "probability": 0.8955078125}, {"start": 3121.6, "end": 3122.02, "word": " معناه", "probability": 0.9002278645833334}, {"start": 3122.02, "end": 3122.36, "word": " انه", "probability": 0.9619140625}, {"start": 3122.36, "end": 3122.56, "word": " C", "probability": 0.9658203125}, {"start": 3122.56, "end": 3123.22, "word": " اتنين", "probability": 0.9495849609375}, {"start": 3123.22, "end": 3123.86, "word": " بده", "probability": 0.98681640625}, {"start": 3123.86, "end": 3124.28, "word": " يساوي", "probability": 0.9910888671875}, {"start": 3124.28, "end": 3124.74, "word": " Zero", "probability": 0.97509765625}, {"start": 3124.74, "end": 3125.24, "word": " يبقى", "probability": 0.8336181640625}, {"start": 3125.24, "end": 3125.58, "word": " بعض", "probability": 0.6898193359375}, {"start": 3125.58, "end": 3125.84, "word": " انه", "probability": 0.511962890625}, {"start": 3125.84, "end": 3126.0, "word": " C", "probability": 0.93603515625}, {"start": 3126.0, "end": 3126.6, "word": " واحد", "probability": 0.982666015625}, {"start": 3126.6, "end": 3127.36, "word": " يساوي", "probability": 0.9825439453125}, {"start": 3127.36, "end": 3127.58, "word": " C", "probability": 0.876953125}, {"start": 3127.58, "end": 3128.14, "word": " اتنين", "probability": 0.9757080078125}, {"start": 3128.14, "end": 3129.3, "word": " يساوي", "probability": 0.9820556640625}, {"start": 3129.3, "end": 3130.06, "word": " Zero", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 128, "seek": 315468, "start": 3130.48, "end": 3154.68, "text": "يبقى انا لما عندي linear combination بيساوي zero و اثبت ان الثوابت هدول بده يساوي zero يبقى ال two functions are linearly independent يبقى هنا ال g1 and ال g2 are linearly independent وهو المطلوب", "tokens": [1829, 3555, 4587, 7578, 1975, 8315, 5296, 15042, 18871, 16254, 8213, 6562, 4724, 1829, 3794, 995, 45865, 4018, 4032, 1975, 12984, 3555, 2655, 16472, 6024, 104, 14407, 3555, 2655, 8032, 3215, 12610, 47525, 3224, 7251, 3794, 995, 45865, 4018, 7251, 3555, 4587, 7578, 2423, 732, 6828, 366, 43586, 6695, 7251, 3555, 4587, 7578, 34105, 2423, 290, 16, 293, 2423, 290, 17, 366, 43586, 6695, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.2975352045515893, "compression_ratio": 1.5952380952380953, "no_speech_prob": 0.0, "words": [{"start": 3130.48, "end": 3131.04, "word": "يبقى", "probability": 0.81060791015625}, {"start": 3131.04, "end": 3131.34, "word": " انا", "probability": 0.634521484375}, {"start": 3131.34, "end": 3131.64, "word": " لما", "probability": 0.7257080078125}, {"start": 3131.64, "end": 3132.04, "word": " عندي", "probability": 0.7042236328125}, {"start": 3132.04, "end": 3132.4, "word": " linear", "probability": 0.68115234375}, {"start": 3132.4, "end": 3133.36, "word": " combination", "probability": 0.95361328125}, {"start": 3133.36, "end": 3134.1, "word": " بيساوي", "probability": 0.850390625}, {"start": 3134.1, "end": 3134.5, "word": " zero", "probability": 0.309814453125}, {"start": 3134.5, "end": 3135.04, "word": " و", "probability": 0.64501953125}, {"start": 3135.04, "end": 3135.5, "word": " اثبت", "probability": 0.82012939453125}, {"start": 3135.5, "end": 3135.74, "word": " ان", "probability": 0.92236328125}, {"start": 3135.74, "end": 3136.46, "word": " الثوابت", "probability": 0.86357421875}, {"start": 3136.46, "end": 3136.78, "word": " هدول", "probability": 0.7574869791666666}, {"start": 3136.78, "end": 3137.08, "word": " بده", "probability": 0.46484375}, {"start": 3137.08, "end": 3137.5, "word": " يساوي", "probability": 0.872802734375}, {"start": 3137.5, "end": 3137.88, "word": " zero", "probability": 0.73486328125}, {"start": 3137.88, "end": 3138.56, "word": " يبقى", "probability": 0.9688720703125}, {"start": 3138.56, "end": 3138.66, "word": " ال", "probability": 0.89404296875}, {"start": 3138.66, "end": 3138.78, "word": " two", "probability": 0.7900390625}, {"start": 3138.78, "end": 3139.38, "word": " functions", "probability": 0.8466796875}, {"start": 3139.38, "end": 3139.78, "word": " are", "probability": 0.8447265625}, {"start": 3139.78, "end": 3140.54, "word": " linearly", "probability": 0.89990234375}, {"start": 3140.54, "end": 3141.96, "word": " independent", "probability": 0.9423828125}, {"start": 3141.96, "end": 3143.2, "word": " يبقى", "probability": 0.931396484375}, {"start": 3143.2, "end": 3143.6, "word": " هنا", "probability": 0.9609375}, {"start": 3143.6, "end": 3144.22, "word": " ال", "probability": 0.26708984375}, {"start": 3144.22, "end": 3145.56, "word": " g1", "probability": 0.5797119140625}, {"start": 3145.56, "end": 3146.56, "word": " and", "probability": 0.411865234375}, {"start": 3146.56, "end": 3147.38, "word": " ال", "probability": 0.66357421875}, {"start": 3147.38, "end": 3148.18, "word": " g2", "probability": 0.98388671875}, {"start": 3148.18, "end": 3149.2, "word": " are", "probability": 0.79833984375}, {"start": 3149.2, "end": 3150.38, "word": " linearly", "probability": 0.9404296875}, {"start": 3150.38, "end": 3151.62, "word": " independent", "probability": 0.9501953125}, {"start": 3151.62, "end": 3152.72, "word": " وهو", "probability": 0.87353515625}, {"start": 3152.72, "end": 3154.68, "word": " المطلوب", "probability": 0.944580078125}], "temperature": 1.0}, {"id": 129, "seek": 316929, "start": 3158.15, "end": 3169.29, "text": "المخرج يؤشر لي ان انتهى الوقت و احنا بنقول خلاص نكتفي اليوم بهذا القدر لكن لا يزال عندي بعض الأمثلة في هذا ال situation", "tokens": [45340, 34740, 7435, 7251, 33604, 46309, 32239, 16472, 16472, 47395, 7578, 2423, 30543, 2655, 4032, 1975, 5016, 8315, 44945, 39648, 16490, 1211, 33546, 8717, 4117, 2655, 41185, 45595, 20498, 39627, 15730, 25062, 3215, 2288, 44381, 20193, 7251, 11622, 6027, 18871, 16254, 45030, 11242, 16247, 2304, 12984, 37977, 8978, 23758, 2423, 2590], "avg_logprob": -0.1912560142003573, "compression_ratio": 1.4206896551724137, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3158.15, "end": 3158.91, "word": "المخرج", "probability": 0.9456380208333334}, {"start": 3158.91, "end": 3159.47, "word": " يؤشر", "probability": 0.8391927083333334}, {"start": 3159.47, "end": 3159.73, "word": " لي", "probability": 0.7744140625}, {"start": 3159.73, "end": 3159.91, "word": " ان", "probability": 0.29248046875}, {"start": 3159.91, "end": 3160.35, "word": " انتهى", "probability": 0.9542643229166666}, {"start": 3160.35, "end": 3161.15, "word": " الوقت", "probability": 0.9899088541666666}, {"start": 3161.15, "end": 3161.65, "word": " و", "probability": 0.46728515625}, {"start": 3161.65, "end": 3161.91, "word": " احنا", "probability": 0.7840983072916666}, {"start": 3161.91, "end": 3162.39, "word": " بنقول", "probability": 0.797119140625}, {"start": 3162.39, "end": 3162.81, "word": " خلاص", "probability": 0.8919270833333334}, {"start": 3162.81, "end": 3163.29, "word": " نكتفي", "probability": 0.8355712890625}, {"start": 3163.29, "end": 3163.51, "word": " اليوم", "probability": 0.947509765625}, {"start": 3163.51, "end": 3163.79, "word": " بهذا", "probability": 0.641357421875}, {"start": 3163.79, "end": 3164.37, "word": " القدر", "probability": 0.9925130208333334}, {"start": 3164.37, "end": 3164.95, "word": " لكن", "probability": 0.7587890625}, {"start": 3164.95, "end": 3165.23, "word": " لا", "probability": 0.74853515625}, {"start": 3165.23, "end": 3166.09, "word": " يزال", "probability": 0.9817708333333334}, {"start": 3166.09, "end": 3166.81, "word": " عندي", "probability": 0.83740234375}, {"start": 3166.81, "end": 3167.17, "word": " بعض", "probability": 0.943603515625}, {"start": 3167.17, "end": 3167.81, "word": " الأمثلة", "probability": 0.9649658203125}, {"start": 3167.81, "end": 3168.09, "word": " في", "probability": 0.96875}, {"start": 3168.09, "end": 3168.57, "word": " هذا", "probability": 0.85546875}, {"start": 3168.57, "end": 3168.99, "word": " ال", "probability": 0.7939453125}, {"start": 3168.99, "end": 3169.29, "word": " situation", "probability": 0.49365234375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3171.242, "duration_after_vad": 2859.8081249999914}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..313a42c25f7e879fdd92cc293122658e656ab7b9
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ftnFGaIbyMc_raw.srt
@@ -0,0 +1,1844 @@
+1
+00:00:18,070 --> 00:00:22,870
+بسم الله الرحمن الرحيم عودنا على بدأ نعود إلى
+
+2
+00:00:22,870 --> 00:00:28,390
+محاضرة الصباح والحمد لله لازال نضريتين مش مسحينهم
+
+3
+00:00:28,390 --> 00:00:31,830
+الناس اللي بعدنا أو ما لزموش لهم أو ماكانش في
+
+4
+00:00:31,830 --> 00:00:38,320
+محاضرة الله أعلاطبعا احنا أعطينا بدل المثال ثلاثة
+
+5
+00:00:38,320 --> 00:00:43,900
+أمثلة A وB وC في الفترة الصباحية والثلاثة أمثلة
+
+6
+00:00:43,900 --> 00:00:48,540
+كانوا على النقطة اللي فوق وعلى مين وعلى الملاحظة
+
+7
+00:00:48,540 --> 00:00:53,320
+اللي عندنا لكن هذه النظرية لم نعطي عليها مثالة
+
+8
+00:00:53,320 --> 00:00:59,200
+أذكر ابها ثم أتي إلى هذا المثالبقول انا عندي
+
+9
+00:00:59,200 --> 00:01:03,100
+مجموعة من ال vectors موجودة في ال vector space V
+
+10
+00:01:03,100 --> 00:01:07,940
+عندي مجموعة تانية من ال vectors هذه موجودة في V
+
+11
+00:01:07,940 --> 00:01:15,700
+بقول لو كان ال M أقل من ال N بس بشرط كل واحد من
+
+12
+00:01:15,700 --> 00:01:20,040
+هدول من الفيهات كتبته ع linear combination من هدول
+
+13
+00:01:20,240 --> 00:01:27,680
+يبقى الأصليات هدول لو كان عددهم أكبر من عدد اليهود
+
+14
+00:01:27,680 --> 00:01:32,840
+أو عدد اليهود أقل من عدد ال vectors اللي فوق هدول
+
+15
+00:01:32,840 --> 00:01:36,000
+automatic ال vectors اللي فوق بيكونوا linearly
+
+16
+00:01:36,000 --> 00:01:41,200
+dependent تمام؟ الأبدأ نعطي مثال على هذه النظرية
+
+17
+00:01:41,200 --> 00:01:46,720
+لأننا لم نعطي عليها مثلا في الفترة الصباحيةفبقول
+
+18
+00:01:46,720 --> 00:01:52,280
+ياخد ال V ال vector space كل المصفوفة لنظامها
+
+19
+00:01:52,280 --> 00:01:57,120
+اتنين في اتنين تحت عملية ضرب المصفوفات وعملية ضرب
+
+20
+00:01:57,120 --> 00:02:01,800
+المصفوفة بمقدار scalar اللي هي العملية ال usual
+
+21
+00:02:01,800 --> 00:02:07,360
+addition and usual multiplicationبياس كيلار يبقى
+
+22
+00:02:07,360 --> 00:02:11,540
+هذا mid vector space V بتروح أخد منه مجموعة من ال
+
+23
+00:02:11,540 --> 00:02:18,400
+vectors أخد V1 و V2 و V3 و V4 يبقى أخدت قداش أربع
+
+24
+00:02:18,400 --> 00:02:23,910
+vectors موجودات في Vو كذلك اخدت three vectors
+
+25
+00:02:23,910 --> 00:02:30,370
+موجودة كمان في V كل vector هنا هنا واحد هنا واحد
+
+26
+00:02:30,370 --> 00:02:34,850
+هنا واحد و الباقي كله بمين باصفار طبعا خد بالك
+
+27
+00:02:34,850 --> 00:02:38,910
+هدول E واحد و E اتنين ان شاء الله بالسلامةوي تلاتة
+
+28
+00:02:38,910 --> 00:02:43,770
+او اربعة هتلعب معانا دوري كبير جدا في ال section
+
+29
+00:02:43,770 --> 00:02:49,270
+بعد القادم في حجم نسميها اللي هو ال standard basis
+
+30
+00:02:49,270 --> 00:02:53,410
+لمين ال vector space اللي موجود ما علينا الكلام
+
+31
+00:02:53,410 --> 00:02:59,090
+هذا سابق لأوانه يبقى احنا بنلتزم بس بما عندنا بقول
+
+32
+00:02:59,090 --> 00:03:02,730
+يبينلي ان ال vectors هدول الأربعة are linearly
+
+33
+00:03:02,730 --> 00:03:09,100
+dependent بقوله والله كويس مين الكتارلفوق أربعة و
+
+34
+00:03:09,100 --> 00:03:16,720
+لتع أقل منهم تلاتة يبقى N أكبر من M هدول عددهم هاي
+
+35
+00:03:16,720 --> 00:03:22,840
+ن أربعة هدول عددهم مين تلاتة يبقى أنا إذا جدرت
+
+36
+00:03:22,840 --> 00:03:28,420
+أكتب كل واحد من الأربعة ك linear combination من
+
+37
+00:03:28,420 --> 00:03:31,420
+التلاتة automatically الأربعة بيكونوا مالهم
+
+38
+00:03:31,780 --> 00:03:36,960
+Linearly independent تمام وماعنديش قيود على ال
+
+39
+00:03:36,960 --> 00:03:40,960
+vector space مش زي النظرية الأولى قلنا الشغل كله
+
+40
+00:03:40,960 --> 00:03:46,140
+على ال RM يبقى هنا RM ولا غير ال RM بهمنيش مين
+
+41
+00:03:46,140 --> 00:03:50,050
+ماكان ال vectors يكونوا هدول واضح يا بنايبقى بدنا
+
+42
+00:03:50,050 --> 00:03:55,290
+نطبق هذه النظرية فبدأ أمسك كل vector من ال vectors
+
+43
+00:03:55,290 --> 00:03:59,330
+الأربعة أشوف بقدر أكتبه على صيغة linear
+
+44
+00:03:59,330 --> 00:04:02,130
+combination من ال vectors التلاتة هدول و لا لأ
+
+45
+00:04:02,130 --> 00:04:07,030
+تعالوا نشوف الان لو جيت لل V1 لما نهت الفي واحد
+
+46
+00:04:07,030 --> 00:04:14,640
+اللي هو عبارة عن اتنين Zero واحد Zeroبقدر اكتبه
+
+47
+00:04:14,640 --> 00:04:23,460
+على شكل مجموع مصرفتين شو المصرفتين هدول 2000 زائد
+
+48
+00:04:23,460 --> 00:04:32,740
+0010 مظبوط هيك؟ صح؟لو جيت جامعة التنتين برجع للأصل
+
+49
+00:04:32,740 --> 00:04:36,860
+اللي عندنا هنا طيب هذه فيها اتنين عامل مشرك ماقدر
+
+50
+00:04:36,860 --> 00:04:42,160
+أخده برا إذا لو أخدت هذا برا بدي يصير مين بدي
+
+51
+00:04:42,160 --> 00:04:49,000
+يصيري اتنين في واحد Zero Zero زائد Zero Zero واحد
+
+52
+00:04:49,000 --> 00:04:51,240
+Zero يساوي
+
+53
+00:04:52,710 --> 00:04:59,310
+ال V1 صار يساوي هذه مين يا بنات E1 يبقى هذا اتنين
+
+54
+00:04:59,310 --> 00:05:10,410
+E1 هذه مين E3 يبقى زائد E3 طيب لو أضفت عليهم zero
+
+55
+00:05:10,410 --> 00:05:17,530
+في E4 بيأثر ولا بيعمل حاجة، مظبوط؟يبقى هذي بقدر
+
+56
+00:05:17,530 --> 00:05:27,410
+اقول الهو 2E1 زائد E3 زائد 0 في E4 إذا صارت V1
+
+57
+00:05:27,410 --> 00:05:34,110
+linear combination من ال E1 والE3 والE4 مظبوط إذا
+
+58
+00:05:34,110 --> 00:05:37,890
+خلصنا هذا منه ال vector بدنا نشوف اللي بعد و اللي
+
+59
+00:05:37,890 --> 00:05:41,310
+بعد اللي وقت نكمل ال 4 vectors اللي عندنا إذا
+
+60
+00:05:41,310 --> 00:05:47,720
+بيداجي لل vector التاني V2يبقى V2 هو عبارة عن سلب
+
+61
+00:05:47,720 --> 00:05:54,380
+2 زيرو سلب واحد واحد بدي اكتفه على شكل مجموعة ثلاث
+
+62
+00:05:54,380 --> 00:06:02,880
+مصفوفات يبقى ايه سلب 2 زيرو زيرو زائد زيرو زيرو
+
+63
+00:06:02,880 --> 00:06:12,100
+سلب واحد زيرو زائد زيرو زيرو زيرو واحديعني لو روحت
+
+64
+00:06:12,100 --> 00:06:17,940
+جماعة الثلاث مصفوفات هدول بيعطون المصفوفة هذه طلع
+
+65
+00:06:17,940 --> 00:06:22,480
+سلب اتنين زائد زيرو زائد زيرو بسلب اتنين زيرو زيرو
+
+66
+00:06:22,480 --> 00:06:26,640
+زيرو يبقى بزيرو زيرو سلب واحد زيرو يبقى بسلب واحد
+
+67
+00:06:26,640 --> 00:06:31,020
+زيرو زيرو واحد يبقى بواحد يبقى مظبوط مية المية
+
+68
+00:06:31,020 --> 00:06:36,490
+تمامإذا باجي بقدر أقول هذا الكلام بده يساوي بدي
+
+69
+00:06:36,490 --> 00:06:41,750
+أخد سالي باتنين برا بصير واحد Zero Zero و هنا بدي
+
+70
+00:06:41,750 --> 00:06:48,350
+أخد ناقص واحد برا بصير Zero Zero واحد Zero و هذا
+
+71
+00:06:48,350 --> 00:06:55,350
+كما هو Zero Zero واحد و يساوي أظن الأول اتنين في
+
+72
+00:06:55,350 --> 00:07:05,980
+E1اللي بعده ناقص E3 اللي بعده زائد E4يبقى معناته
+
+73
+00:07:05,980 --> 00:07:11,560
+قدرت اكتب V2 على صيغة Linear Combination من E1 وE3
+
+74
+00:07:11,560 --> 00:07:20,200
+وE4 بالمثل لو روحت ل V3 V3 عند اللي هي مين Zero
+
+75
+00:07:20,200 --> 00:07:26,940
+Zero أربعة خمسة بدا اكتبها على شكل مجموع مصفوفتين
+
+76
+00:07:27,420 --> 00:07:34,340
+زائد Zero Zero Zero خمسة بتاخد عوامل مشتركة يبقى
+
+77
+00:07:34,340 --> 00:07:41,740
+أربعة Zero Zero واحد Zero زائد خمسة Zero Zero Zero
+
+78
+00:07:41,740 --> 00:07:49,240
+واحد ويساوي أربعة برا يبقى هذه أربعة في مين يا
+
+79
+00:07:49,240 --> 00:07:57,640
+بنات في E تلاتة وهذه زائد خمسة في E أربعةطب لو
+
+80
+00:07:57,640 --> 00:08:02,540
+ضافت لها zero في E1 بيبقى third يبقى هذا الكلام
+
+81
+00:08:02,540 --> 00:08:10,680
+بده يساوي zero في E1 زائد اربعة في E3 زائد خمسة في
+
+82
+00:08:10,680 --> 00:08:16,240
+E4 يبقى معناته ان V3 هي linear combination من E1
+
+83
+00:08:16,240 --> 00:08:22,320
+وE3 وE4 بالمثل بده نيجي لل vector الأخير
+
+84
+00:08:28,730 --> 00:08:34,190
+إذا لو جيت لل vector الأخير اللي هو V4 V4 عندي
+
+85
+00:08:34,190 --> 00:08:42,030
+اللي هو عبارة عن 3 0 0 اللي هو يساوي 3 في 1 0 0
+
+86
+00:08:42,030 --> 00:08:51,590
+اللي هو مين 3 E1 اللي بقدر أكتمه 3 E1 زائد 0 E3
+
+87
+00:08:51,590 --> 00:08:58,260
+زائد 0 E4يبقى الأن قدرت أكتب كل واحد من الذئاب
+
+88
+00:08:58,260 --> 00:09:03,040
+الأربع على صيغة linear combination من من من
+
+89
+00:09:03,040 --> 00:09:10,280
+الأخرين بنص النظرية هذه ال M أجل من N يبقى هذا
+
+90
+00:09:10,280 --> 00:09:19,300
+linear combination يبقى هنا by the أو هنا the اللي
+
+91
+00:09:19,300 --> 00:09:30,420
+هو each ofV1 و V2 و V3 و V4 is a linear
+
+92
+00:09:30,420 --> 00:09:34,120
+combination
+
+93
+00:09:34,120 --> 00:09:47,040
+linear combination of the vectors اله E1 و E3 و E4
+
+94
+00:09:47,040 --> 00:09:50,680
+by they
+
+95
+00:09:51,600 --> 00:09:59,640
+by the second theorem النظرية التانية by the
+
+96
+00:09:59,640 --> 00:10:10,100
+second theorem ال V1 و V2
+
+97
+00:10:10,100 --> 00:10:17,480
+و V3 و V4 are linearly dependent وانتهينا من هذه
+
+98
+00:10:17,480 --> 00:10:23,650
+المسألةلحد دي لما لا تنتهي ال section وإلى يكون
+
+99
+00:10:23,650 --> 00:10:29,770
+أرقام المسائل اللي مطلوب تتمرن عليهم يبقى
+
+100
+00:10:29,770 --> 00:10:36,470
+exercises تلاتة تلاتة المسائل التالية واحد اتنين
+
+101
+00:10:36,470 --> 00:10:43,790
+اربع خمسة ستة سبعة احداش اتناش
+
+102
+00:10:48,030 --> 00:10:53,490
+حاجة فيكم تحب تسأل أي سؤال هنا؟ أي سؤال؟
+
+103
+00:11:34,080 --> 00:11:39,540
+طيب نجي لقى ل ال section اللي يليه اللي هو ال
+
+104
+00:11:39,540 --> 00:11:45,780
+runescan ال runescan اللي هو المحدد سواء كان محدد
+
+105
+00:11:45,780 --> 00:11:50,620
+ثنائي، ثلاثي، ربعي، قد ما يكون يكون يبقى بيننا نجي
+
+106
+00:11:50,620 --> 00:11:57,380
+ل section تلاتة أربعة اللي هو ال runescan
+
+107
+00:12:01,930 --> 00:12:22,990
+تعريف definition let ال I be a fixed interval let
+
+108
+00:12:22,990 --> 00:12:35,400
+ال N be a nonzero positive integer
+
+109
+00:12:35,400 --> 00:12:50,000
+عدد صحيح موجب then ال FN is the vector space is
+
+110
+00:12:50,000 --> 00:12:55,480
+the vector space
+
+111
+00:12:57,010 --> 00:13:05,050
+of all functions of all functions that are defined
+
+112
+00:13:05,050 --> 00:13:21,730
+that are defined on interval I and has at least
+
+113
+00:13:21,730 --> 00:13:32,870
+على الأقلin derivatives in derivatives على الفترة
+
+114
+00:13:32,870 --> 00:13:43,310
+اللي عندناها دفينيشن تاني let ال F واحد و ال F
+
+115
+00:13:43,310 --> 00:13:53,000
+اتنين و لغاية ال FMموجودات في الـ vector space FM
+
+116
+00:13:53,000 --> 00:14:01,900
+-L1 الـ Runnigan الـ
+
+117
+00:14:01,900 --> 00:14:12,340
+Runnigan of these functions is
+
+118
+00:14:12,340 --> 00:14:16,940
+the data
+
+119
+00:14:18,400 --> 00:14:30,180
+من هنا انت المحدد اللي هو من F1 of X F2 of X وانضل
+
+120
+00:14:30,180 --> 00:14:40,080
+مغاشين لغاية ال FM of X بعدها F1 prime of X F2
+
+121
+00:14:40,080 --> 00:15:02,740
+prime of XF2 F M F' X F1 W' X F2 W' X F M W' X F1
+
+122
+00:15:02,740 --> 00:15:10,100
+W' X F2 W' X F M W' X F2 W' X F2 W' X F M W' X F2
+
+123
+00:15:10,100 --> 00:15:10,100
+W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W'
+
+124
+00:15:10,100 --> 00:15:10,100
+X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X
+
+125
+00:15:10,100 --> 00:15:10,100
+F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X F2
+
+126
+00:15:10,100 --> 00:15:10,100
+W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W'
+
+127
+00:15:10,100 --> 00:15:10,100
+X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X F2 W' X
+
+128
+00:15:10,100 --> 00:15:14,550
+F2 W' X F2 W' X F2وهنا F2 لـ derivative M minus
+
+129
+00:15:14,550 --> 00:15:24,130
+one of X ونظل ماشيين تمام لغاية من التفاضل ورقم M
+
+130
+00:15:24,130 --> 00:15:36,170
+minus one as a function of X this
+
+131
+00:15:40,460 --> 00:15:50,300
+this determinant is
+
+132
+00:15:50,300 --> 00:15:53,380
+denoted
+
+133
+00:15:53,380 --> 00:16:06,350
+by .. بنعرفه بالشكل التاليالرونسكين of X و F1 و F2
+
+134
+00:16:06,350 --> 00:16:14,070
+و لغاية ال FM أو اختصارا بقول الرونسكين as a
+
+135
+00:16:14,070 --> 00:16:16,230
+function of X
+
+136
+00:17:12,140 --> 00:17:17,880
+كلمة الرونس كانت ال W هذه silent لا تنطق زي ما
+
+137
+00:17:17,880 --> 00:17:23,300
+تقول يوم الأربع نقول Wednesday ال W مابننطقاش ال W
+
+138
+00:17:23,300 --> 00:17:31,500
+silent و هنا عندنا ال W silent غير هيك هذا يعني
+
+139
+00:17:31,500 --> 00:17:37,760
+اسم لوحد اكتشف هذا المحدد فسميه باسمه طبعا هذا ممر
+
+140
+00:17:37,760 --> 00:17:42,070
+في الرياضيات كتير و كذلك في الفيزيااللي هو قيمة
+
+141
+00:17:42,070 --> 00:17:45,890
+هذا المحدث هو إن كان محدد من الرتبة الثانية أو
+
+142
+00:17:45,890 --> 00:17:50,850
+التالتة أو الرابعة أو النونية أو الميمية اللي
+
+143
+00:17:50,850 --> 00:17:55,970
+عندنا هذه سيية طيب في عن التعريفين التعريفين هدول
+
+144
+00:17:55,970 --> 00:18:00,970
+مهمات جدا نعرفهم اللي بيجالي little I بي fix the
+
+145
+00:18:00,970 --> 00:18:06,010
+interval اللي بيجالي أنا أخدت فترة ثابتةlet n be a
+
+146
+00:18:06,010 --> 00:18:10,290
+non-zero positive integer إن عدد صحيح موجب لا
+
+147
+00:18:10,290 --> 00:18:17,350
+يساوي الـ zero then ال F وفوقها N مش المقصود F أُس
+
+148
+00:18:17,350 --> 00:18:22,970
+N لأ هذا ما هواش أُس وإنما رمز الرمز يدل على مين
+
+149
+00:18:22,970 --> 00:18:27,890
+قال لي is the vector space of all functions يبقى
+
+150
+00:18:27,890 --> 00:18:34,570
+هذا vector space لكل دوالاللي إلها خاصيتين الخاصية
+
+151
+00:18:34,570 --> 00:18:41,430
+الأولى إنها معرفة على نفس الفترة I الخاصية الثانية
+
+152
+00:18:41,430 --> 00:18:48,790
+إنها إلها N من المشتقات على الفترة Iيبقى ال N هذا
+
+153
+00:18:48,790 --> 00:18:56,690
+يدل على عدد المشتقات التي تخضع لها هذه الدول يعني
+
+154
+00:18:56,690 --> 00:19:00,230
+إيش مقصود؟ المقصود يا بنت يعني المشتقة الأولى
+
+155
+00:19:00,230 --> 00:19:03,570
+exist والمشتقة التانية exist والتالتة exist
+
+156
+00:19:03,570 --> 00:19:09,010
+والنونية exist طب ال N زاد واحدليس بالضرورة، المهم
+
+157
+00:19:09,010 --> 00:19:14,430
+أنا بدي in من المشتقات للدوال اللي موجودة أو لأي
+
+158
+00:19:14,430 --> 00:19:18,510
+دالة موجودة داخل هذا ال vector space تبقى بالها ..
+
+159
+00:19:18,510 --> 00:19:22,310
+يعني كله مشتقة الأولى و التانية و التالتة و
+
+160
+00:19:22,310 --> 00:19:27,520
+الرابعة و النونيةكل هذه المشتقات موجودة هذا
+
+161
+00:19:27,520 --> 00:19:31,700
+التعريف الأول التعريف الثاني بيقول خدلي هدول
+
+162
+00:19:31,700 --> 00:19:35,960
+الدوال موجودة في ال vector space هذا يبقى ال
+
+163
+00:19:35,960 --> 00:19:40,980
+vector space هذا الدوال اللي فيه كام مشتقة متحققة
+
+164
+00:19:40,980 --> 00:19:46,680
+فيهاالأولى والتانية والتالتة ورا وال M ناقص الواحد
+
+165
+00:19:46,680 --> 00:19:52,800
+لكن المشتقة المي مية ليس بالضرورة طيب ماشي يبقى
+
+166
+00:19:52,800 --> 00:19:57,400
+انا في عندي vectors موجات موجودة في ال vector
+
+167
+00:19:57,400 --> 00:20:01,560
+space هنا بالدجلة للانواع اللي انا كاتبه يبقى the
+
+168
+00:20:01,560 --> 00:20:06,320
+Wronskian of this function is the determinant مين
+
+169
+00:20:06,320 --> 00:20:10,860
+هو ال Wronskian لهذه الدوال هو قيمة هذا المحددمن
+
+170
+00:20:10,860 --> 00:20:15,340
+المحدد هذه باجي بحط الدول هذه كلها في الصف الأول
+
+171
+00:20:15,340 --> 00:20:19,080
+الصف الثاني المشتقة الأولى الصف التالت المشتقة
+
+172
+00:20:19,080 --> 00:20:24,520
+التانية الصف التالت المشتقة رقم اتنين يعني أقل من
+
+173
+00:20:24,520 --> 00:20:31,320
+رتبة الصف بالمقدارإذا لما أظل ماشي للصف رقم M تبقى
+
+174
+00:20:31,320 --> 00:20:37,500
+المشتقة أقل بواحد يبقى المشتقة رقم M ناقص واحد وهي
+
+175
+00:20:37,500 --> 00:20:43,900
+حطيتلك بينجوسين مشان أقولك هدول مشتقات وليس أسس
+
+176
+00:20:43,900 --> 00:20:48,120
+يبقى طلع هنا الدلة بدون اشتقاق مشتقة الأولى
+
+177
+00:20:48,120 --> 00:20:53,000
+التانية التالتة الرابعة المشتقة رقم M ناقص واحد
+
+178
+00:20:53,150 --> 00:20:58,650
+تمام واضح يبقى عرفنا ليش قلت هذول موجودات في ال
+
+179
+00:20:58,650 --> 00:21:03,130
+vector space هذا لأن ال vector space هذا في مشتقات
+
+180
+00:21:03,130 --> 00:21:08,410
+لدول لغاية M ناقص واحد اللي هو اللي بلزمه لمين
+
+181
+00:21:08,410 --> 00:21:15,410
+للمحدد هذا يبقى هذا المحدد هو الرنسك لمين لدول F1
+
+182
+00:21:15,410 --> 00:21:22,450
+و F2 و لغاية مين و لغاية ال FMبقولي هذا المحدد is
+
+183
+00:21:22,450 --> 00:21:29,130
+denoted by بعطيله الرمز w المتغير تبع الدوال هو x
+
+184
+00:21:29,130 --> 00:21:35,330
+و بعد ذلك بحط ال functions f1 و f2 لغاية fm تمام
+
+185
+00:21:35,330 --> 00:21:43,170
+او اختصارا بقول هذا w of x يعني كدالة في main في x
+
+186
+00:21:43,170 --> 00:21:47,850
+يبقى يا بنت اذا لو اعطاني مجموعة من الدوالوقال لي
+
+187
+00:21:47,850 --> 00:21:51,850
+هاتلر رونسكين تبعها بالدرجة أشوف المحدد قد إيش
+
+188
+00:21:51,850 --> 00:21:57,590
+قيمته بس قيمته بتطلع بدلالة مين بدلالة X يبقى
+
+189
+00:21:57,590 --> 00:22:00,850
+القيمة هذا اللي بتطلع بتكون هي قيمة ال رونسكين
+
+190
+00:22:00,850 --> 00:22:05,850
+المطلوبة حد بتسأل ليه سؤال قبل أن نبدأ فيه أخد
+
+191
+00:22:05,850 --> 00:22:13,190
+الأمثلةأه طبعا هذا له ما بعده هنستخدمه في ال
+
+192
+00:22:13,190 --> 00:22:16,230
+section اللي بعده و اللي بعده دي ربالكم يعني very
+
+193
+00:22:16,230 --> 00:22:20,990
+important كل شغل بناخدها هنبني عليها مش ناخدها و
+
+194
+00:22:20,990 --> 00:22:26,150
+نسيبها طيب بنيجي لأول مثال على هذا الموضوع example
+
+195
+00:22:26,150 --> 00:22:31,830
+one example one
+
+196
+00:22:33,360 --> 00:22:39,460
+بيقول لي find the
+
+197
+00:22:39,460 --> 00:22:53,400
+run skin of the functions للدوال اللي هي x و e أس
+
+198
+00:22:53,400 --> 00:22:57,720
+x و x في e أس x
+
+199
+00:23:01,280 --> 00:23:06,640
+أظن الدالة الأولى بعد مرتين بيصير zero بس هدولك ما
+
+200
+00:23:06,640 --> 00:23:10,960
+شاء الله عليهم زي قد ما بدك لمالانهم موجودات تمام
+
+201
+00:23:11,210 --> 00:23:15,710
+زي ما عندنا مشكلة في هذه الحالة طيب جال يهاتف
+
+202
+00:23:15,710 --> 00:23:21,710
+رونسكين فباجي بقول له رونسكين as a function of x
+
+203
+00:23:21,710 --> 00:23:28,790
+او رونسكين of x مباشرة اللي هو الاختصار تبعه يعني
+
+204
+00:23:28,790 --> 00:23:32,550
+لازم نتيجة المحدد تطلع function في x او حتى ثابت
+
+205
+00:23:32,550 --> 00:23:36,990
+حتى لو كان ثابت باعتبره function في 100 في x يبقى
+
+206
+00:23:36,990 --> 00:23:42,510
+باجي بحط الدالة الأولىالدالة الثانية والدالة
+
+207
+00:23:42,510 --> 00:23:49,070
+التالتة يبقى F1 F2 لغاية F3 الصف التاني بحط
+
+208
+00:23:49,070 --> 00:23:51,890
+المشتقة الأولى مشتقة ال X
+
+209
+00:23:55,230 --> 00:24:02,930
+مشتقت حاصل ضارب دلتين يبقى هذه EO6 زائد X في ال
+
+210
+00:24:02,930 --> 00:24:11,810
+EO6 هذه Zero هذه كما هي هذه EO6 كما هي وهذه زايد
+
+211
+00:24:11,810 --> 00:24:18,930
+تجيها كمان هنا كده بيصير اتنين EO6 زائد X EO6
+
+212
+00:24:18,930 --> 00:24:26,290
+مرتين انا خلي بالكواينةيبقى بدي اشتق هذه مشتقة هذا
+
+213
+00:24:26,290 --> 00:24:30,650
+ب U6 بدي اشتق هذه ايه اللي هي هذه يعني هذا بدي
+
+214
+00:24:30,650 --> 00:24:36,650
+اتكرر كمان مرة وعندي U6 يبقى وصيلي اتنين U6 زي X
+
+215
+00:24:36,650 --> 00:24:43,430
+U6 هاي جفلنا مين جفلنا المحدد بدي اعرف قداش قيمة
+
+216
+00:24:43,430 --> 00:24:49,190
+هذا المحدديبقى بضرورة افكه ان حبيته باستخدام عناصر
+
+217
+00:24:49,190 --> 00:24:54,790
+الصف التالد او عناصر العمود الاول سيان تفرجش عندنا
+
+218
+00:24:54,790 --> 00:25:01,170
+يبقى باجي بقول هذا الكلام بده يساوي X فيه اشط بصفه
+
+219
+00:25:01,170 --> 00:25:10,990
+و عمودهبصير عندك هنا 2E أس 2X زائد X E أس 2X هذا
+
+220
+00:25:10,990 --> 00:25:15,490
+حصل ضرب عناصر القطر الرئيسي ناقص حصل ضرب عناصر
+
+221
+00:25:15,490 --> 00:25:24,530
+القطر الثانوي ناقص E أس 2X ناقص X E أس 2X هذا ال
+
+222
+00:25:24,530 --> 00:25:30,410
+term الأولالان حسب قاعة الإشارات الإشارة هذه مالها
+
+223
+00:25:30,410 --> 00:25:39,470
+بالسالم وهذا قصه أشق بصفه وعمودهيبقى بدأ تجيه
+
+224
+00:25:39,470 --> 00:25:44,070
+لمين؟ الترم اللي عندنا هذا يبقى E أوس X بدي أضربه
+
+225
+00:25:44,070 --> 00:25:51,010
+هنا يبقى إيش بصير عندي؟ اتنين E أوس اتنين X زائد X
+
+226
+00:25:51,010 --> 00:25:58,390
+E أوس اتنين X هيخلصنا مين؟ خلصنا الرئيسي ناقص
+
+227
+00:25:58,390 --> 00:26:06,050
+ثانوي يبقى ناقص X E أوس اتنين X اللي بعده زائد
+
+228
+00:26:06,050 --> 00:26:12,230
+Zeroهذا الكلام يساوي تعال نجي ل هذول يا بنات أظن
+
+229
+00:26:12,230 --> 00:26:16,970
+هذي بالموجب و هذي بالسالب مع السلامة بيظل عندنا
+
+230
+00:26:16,970 --> 00:26:21,450
+مين؟ هاي واحدة سالبة و تنتهي بالموجب بتروح واحدة
+
+231
+00:26:21,450 --> 00:26:28,250
+بيظل عندك X E أس اتنين X هاي دل عندي جوا E أس
+
+232
+00:26:28,250 --> 00:26:33,250
+اتنين X ضربتها في ال X اللي عندنا نجي ل بعدها هذي
+
+233
+00:26:34,650 --> 00:26:39,490
+هي هذا بالضبط تماما، مظبوط يا بنات؟ إذا بصير عند
+
+234
+00:26:39,490 --> 00:26:46,930
+مين؟ ناقص اتنين E أس اتنين X هذا الكلام يسوى E أس
+
+235
+00:26:46,930 --> 00:26:54,400
+اتنين X في X ناقص اتنينيبقى هذا قيمة main قيمة
+
+236
+00:26:54,400 --> 00:26:59,080
+الرونسكين وزي ما انتوا شايفين طلع main طلع دالة في
+
+237
+00:26:59,080 --> 00:27:02,720
+X زي ما احنا قلنا هنا في الجزء النظري بطلع
+
+238
+00:27:02,720 --> 00:27:07,760
+function في X يبقى انا بفضل انه كتبه اختصارا بهذا
+
+239
+00:27:07,760 --> 00:27:12,600
+الشكل وليس بهذا الشكل لكن ان دعته ضرورة كتبته بهذا
+
+240
+00:27:12,600 --> 00:27:18,340
+الشكل بدي اكتبه بهذا الشكل هذا هو المثال الأول
+
+241
+00:27:18,340 --> 00:27:25,610
+المثال الثانيexample two بيقولي show that
+
+242
+00:27:29,140 --> 00:27:38,540
+بيّلّي أن الـrunnerskin تبع الـX والـG F1 والـG F2
+
+243
+00:27:38,540 --> 00:27:44,400
+كل واحد فيهم as a function of X بده يساوي G of X
+
+244
+00:27:44,400 --> 00:27:50,980
+الكل تربيع في الـrunnerskin بتبع الـX والـF1
+
+245
+00:27:50,980 --> 00:27:52,520
+والـF2
+
+246
+00:28:25,120 --> 00:28:34,480
+الرونسكين X و G F1 و G F2 يتساوي مربع G مضروب في
+
+247
+00:28:34,480 --> 00:28:40,950
+رونسكين F1 و F2 فقط لا غيرطب احنا خلينا نجيب ال
+
+248
+00:28:40,950 --> 00:28:44,910
+run skin تبع ال F1 و ال F2 و نشوف ما هو شكله بعد
+
+249
+00:28:44,910 --> 00:28:49,110
+هيك اروح ادور عالمين على ال run skin التاني و اعرف
+
+250
+00:28:49,110 --> 00:28:54,570
+شو بيساوي يبقى باجي بقوله انا بده ال run skin تبع
+
+251
+00:28:54,570 --> 00:29:02,650
+ال X و ال F1 و ال F2 يساوي المحدد بدي احطله ال F1
+
+252
+00:29:02,650 --> 00:29:12,150
+و ال F2 مشتقة ال F1 مشتقة ال F2طبعا يبقى هذا
+
+253
+00:29:12,150 --> 00:29:17,970
+المحدد الثنائي لمصفوفة نظامها اتنين في اتنين بدى
+
+254
+00:29:17,970 --> 00:29:23,090
+افك هذا المحدد واشوف كده يساوي اذا هذا يا بنات بده
+
+255
+00:29:23,090 --> 00:29:29,390
+يساوي F1 F2 ناقص
+
+256
+00:29:29,390 --> 00:29:35,530
+الرئيس ناقص الثانوي ناقص F1 F2
+
+257
+00:29:37,830 --> 00:29:43,110
+عندما أقول هذا أجود على الشجرة لما نشوف إيش علاقتك
+
+258
+00:29:43,110 --> 00:29:47,370
+بالرونسكين التاني بالدادي للرونسكين الثاني
+
+259
+00:29:47,370 --> 00:29:59,070
+الرونسكين تبع ال X و ال F1 أو ال GF1 GF1 و GF2
+
+260
+00:29:59,070 --> 00:30:10,390
+يبقى المحدد ال GF1 GF2 كويسبدي أشتق الآن هذا
+
+261
+00:30:10,390 --> 00:30:15,450
+مشتقتاش حاصل ضرب دالتين مش هتروح تقولي f prime g
+
+262
+00:30:15,450 --> 00:30:19,830
+prime لأ بدي أستخدم قواعد الشتقاق اللي دراسناها في
+
+263
+00:30:19,830 --> 00:30:24,930
+calculus a و b إذا هذه مشتقة حاصل ضرب دالتين بدي
+
+264
+00:30:24,930 --> 00:30:28,670
+أقول الأولى في مشتقة التانية زائد التانية في مشتقة
+
+265
+00:30:28,670 --> 00:30:36,300
+الأولى و هكذا إذا بدي أجي أقوله هذهالأولى في مشتقة
+
+266
+00:30:36,300 --> 00:30:42,420
+الدالة الثانية زائد مشتقة الأولى في الدالة الثانية
+
+267
+00:30:42,420 --> 00:30:45,680
+اللى عملته لهذا ال function بتعمله ال function
+
+268
+00:30:45,680 --> 00:30:53,640
+التانية يبقى g f2 prime زائد g prime f2 y جفلنا
+
+269
+00:30:53,640 --> 00:31:04,580
+منهم المحددهذا المحدد يجب أن يكون ج تربيع في الـ
+
+270
+00:31:04,580 --> 00:31:17,790
+F1 F2'زائد الـ G G Prime في ال F1 F2 هذا حاصل ضرب
+
+271
+00:31:17,790 --> 00:31:22,190
+عناصر القطر الرئيسي بداجي ناقص حاصل ضرب عناصر
+
+272
+00:31:22,190 --> 00:31:32,990
+القطر الثانوي ناقص G تربية في ال F1 F2ناقص الـ G
+
+273
+00:31:32,990 --> 00:31:41,950
+G' في الـ F1 F2 بالشكل هذا يبقى اي فكرة المحدد
+
+274
+00:31:41,950 --> 00:31:47,110
+حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب عناصر
+
+275
+00:31:47,110 --> 00:31:53,730
+القطر الثانوي يبقى بدأيش اتطلعيلي لل term اللي
+
+276
+00:31:53,730 --> 00:31:58,390
+عندنا هذاوالـ term اللى عندنا ده هو نفسه اللى بخلف
+
+277
+00:31:58,390 --> 00:32:04,910
+عنه إذا واحد موجب وواحد سالب معاهم مع السلامة إذا
+
+278
+00:32:04,910 --> 00:32:11,930
+نتيجة الوانوس كانت تساوي G تربية F1 F2 ناقص G
+
+279
+00:32:11,930 --> 00:32:21,130
+تربية F1 F2 أظن فى عامل مشترك اللى هو mainG تربيع
+
+280
+00:32:21,130 --> 00:32:32,170
+بظالمين F1 F2 prime ناقص F1 prime F2 ويساوي طلعيلي
+
+281
+00:32:32,170 --> 00:32:37,830
+البنجوسين هذا وطلعيلي للنتيجة هذه البنجوسين هناك
+
+282
+00:32:37,830 --> 00:32:41,470
+هي هذه النتيجة ولا لا إذا بقدر أشيلها و أكتب
+
+283
+00:32:41,470 --> 00:32:47,830
+بلورنسكين تبعهايبقى هذا الكلام يعطيني الـG تربيه
+
+284
+00:32:47,830 --> 00:32:54,790
+في الـRanskin تبع الـX و الـF1 و الـF2 أظن هو هو
+
+285
+00:32:54,790 --> 00:33:02,410
+المطلوب؟ 100% طيب، ننتقل الآن لأول نظرية في هذا ال
+
+286
+00:33:02,410 --> 00:33:10,410
+section Theorem بيقول
+
+287
+00:33:10,410 --> 00:33:21,970
+لتف1 وف2 و لغاية الـ Fm موجودة في الـ Fm-1
+
+288
+00:33:21,970 --> 00:33:28,990
+relative relative
+
+289
+00:33:28,990 --> 00:33:35,050
+to an interval I
+
+290
+00:33:37,960 --> 00:33:50,380
+إذا الـ F1 و الـ F2 و الـ FM هم مستقلين
+
+291
+00:33:50,380 --> 00:33:56,960
+على الانترال I فالرونسكين
+
+292
+00:33:56,960 --> 00:34:10,670
+تبع الـ X و الـ F1 و الـ F2 و الـ FMبدو يساوي zero
+
+293
+00:34:10,670 --> 00:34:24,190
+at h x موجودة في ال interval I alternatively
+
+294
+00:34:24,190 --> 00:34:27,870
+if
+
+295
+00:34:27,870 --> 00:34:42,810
+there exists a pointx0 في الـ interval I such that
+
+296
+00:34:42,810 --> 00:35:00,090
+بحيث ان الرنسكين عند ال x0 لل F1 و F2 و FM FM
+
+297
+00:35:00,090 --> 00:35:13,240
+كل هذا الكلام لا يساوي Zerothen اللي هو ال F1 و F2
+
+298
+00:35:13,240 --> 00:35:30,900
+و FM are linearly independent remark the
+
+299
+00:35:30,900 --> 00:35:31,740
+converse
+
+300
+00:35:35,330 --> 00:35:46,690
+of the theorem the converse of the theorem is not
+
+301
+00:35:46,690 --> 00:35:55,790
+true that is if
+
+302
+00:35:55,790 --> 00:35:59,570
+الرنسكين
+
+303
+00:35:59,570 --> 00:36:10,060
+بتبع ال X و ال F واحدو ال F2 و لغاية ال FM بده
+
+304
+00:36:10,060 --> 00:36:15,880
+يساوي Zero then it
+
+305
+00:36:15,880 --> 00:36:25,580
+is not true that ال
+
+306
+00:36:25,580 --> 00:36:36,320
+F1 و ال F2 و ال FM arelinearly dependent
+
+307
+00:37:04,160 --> 00:37:10,320
+كل هذا كشف جاهز وحضور غياب كلها أشرتك بالاسم هاه؟
+
+308
+00:38:07,350 --> 00:38:12,150
+نرجع للنظرية اللي بين إيدينا هذهالنظرية بتقول ما
+
+309
+00:38:12,150 --> 00:38:17,370
+يأتي بتقول افترض عندي elements في واحد أو في اتنين
+
+310
+00:38:17,370 --> 00:38:23,190
+لغة ال FM موجودة في ال vector space FM minus ال
+
+311
+00:38:23,190 --> 00:38:28,570
+one يعني الدالة المعرفة على fixed interval اتنين
+
+312
+00:38:28,570 --> 00:38:34,930
+كل المشتاقات من الدرجة M أو من الرتبة M ناقص واحد
+
+313
+00:38:34,930 --> 00:38:40,140
+موجودة في هذا ال vector spacerelative to an
+
+314
+00:38:40,140 --> 00:38:44,040
+interval I يعني على interval I بقول لو كان ال
+
+315
+00:38:44,040 --> 00:38:48,580
+functions هدول linearly dependent يبقى الورس كان
+
+316
+00:38:48,580 --> 00:38:53,860
+بده يساوي Zero عند كل نقطة موجودة داخل ال interval
+
+317
+00:38:53,860 --> 00:38:59,020
+I مش عند بعض النقط Zero عند بعض النقط لأ بقول اه
+
+318
+00:38:59,020 --> 00:39:03,940
+دججي قال ليهذول كلهم لينيار dependent على الـ
+
+319
+00:39:03,940 --> 00:39:08,900
+interval I إن حدث ذلك يبقى الرنسكين تبع هذه الـ
+
+320
+00:39:08,900 --> 00:39:13,760
+function دائما و أبدا بده يساوي zero at each x
+
+321
+00:39:13,760 --> 00:39:20,240
+موجودة في I يبقى عندك كل نقطة موجودة داخل هذه الـ
+
+322
+00:39:20,240 --> 00:39:24,300
+interval تعالوا نمشي لاتجاه المعاكس Alternatively
+
+323
+00:39:24,300 --> 00:39:30,660
+يعني من جهة أخرى أو من ناحية أخرى ها بدي أنفي هذه
+
+324
+00:39:31,610 --> 00:39:38,650
+هذا يعني كل نقطة في البرنامج
+
+325
+00:39:38,650 --> 00:39:45,810
+إذا كان هناك نقطة X نوت عند I بحيث أن الوارنس كان
+
+326
+00:39:45,810 --> 00:39:51,870
+تبع ال functions عند X نوت كان لا يساوي زيرو يبقى
+
+327
+00:39:51,870 --> 00:39:55,990
+هدول لينيار لايهاش independentإذا يا بنات لما
+
+328
+00:39:55,990 --> 00:39:59,930
+يعطيني مجموع من ال functions ويقولشوف لي هدول
+
+329
+00:39:59,930 --> 00:40:04,470
+linearly dependent ولا linearly independent تمام
+
+330
+00:40:04,470 --> 00:40:08,690
+بادروح أاخد ال worn skin تبعهم إذا لجيت ال worn
+
+331
+00:40:08,690 --> 00:40:13,690
+skin هذا أو او إذا كانوا هدول linearly dependent
+
+332
+00:40:13,690 --> 00:40:18,350
+لازم ال worn skin تبعهم بدل سوى zero عند كل ال x
+
+333
+00:40:18,350 --> 00:40:19,510
+بلا استثناء
+
+334
+00:40:21,960 --> 00:40:26,780
+العملية العكسية بس لو لجيت نقطة واحدة الـ
+
+335
+00:40:26,780 --> 00:40:30,840
+functions هدول عند هذه النقطة أخدت رونسكين تبعهم
+
+336
+00:40:30,840 --> 00:40:35,060
+لجيته لا يساوي زيرو إذا هدول ما لهم linearly
+
+337
+00:40:35,060 --> 00:40:39,590
+independentطب انا بدأ اقولكوا ايش فهمت من هالكلام
+
+338
+00:40:39,590 --> 00:40:44,930
+ده وشوفوا فاهمي الصح و الله غلط اعطاني functions و
+
+339
+00:40:44,930 --> 00:40:49,370
+ال functions معرفات على vector space و قاللي شوفلي
+
+340
+00:40:49,370 --> 00:40:52,050
+هدولي linearly dependent و الله linearly
+
+341
+00:40:52,050 --> 00:40:57,370
+independent تمامبقوله باخد الرنسكين تبعهم إذا
+
+342
+00:40:57,370 --> 00:41:00,510
+الرنسكين تبعهم يساوي zero يبقى هدول linearly
+
+343
+00:41:00,510 --> 00:41:03,590
+dependent وإذا لا يساوي zero يبقى linearly
+
+344
+00:41:03,590 --> 00:41:07,410
+independent إيش رأيكم في هذا الفهم؟ مظبوط؟ هك؟
+
+345
+00:41:07,410 --> 00:41:10,910
+والله أنا غلطان نص الأول .. نقل .. بدي واحدة تحكي
+
+346
+00:41:10,910 --> 00:41:15,390
+مشان نتناقش احنا وياها ايوة وصف صح ووصف غلط يعني
+
+347
+00:41:15,390 --> 00:41:23,350
+كلامي غلط إذاإذا بدنا نبحث أين الخطأ مشان متوجعيش
+
+348
+00:41:23,350 --> 00:41:27,810
+فيه الكلام اللي أنا قلته هذا بتقول زملتكوا نصه صح
+
+349
+00:41:27,810 --> 00:41:32,750
+و نصه غلط بدنا ندور وين الصح و وين الخطأ حتى لا
+
+350
+00:41:32,750 --> 00:41:38,590
+نقع فيه انا زعمت قبل قليل ان انا بدأ أخر و اخد
+
+351
+00:41:38,590 --> 00:41:42,730
+رونسكين هذا إذا والله zero يبقى هدول linearly
+
+352
+00:41:42,730 --> 00:41:48,780
+dependent صح ولا غلط؟ غلطهذا الكلام غلط ليش انه
+
+353
+00:41:48,780 --> 00:41:52,720
+ماقالليش F هتقولي F ماقالليش اتجاه .. اعطاني اتجاه
+
+354
+00:41:52,720 --> 00:41:56,680
+واحد قاللي لو كانوا linearly dependent ايه ده انا
+
+355
+00:41:56,680 --> 00:42:00,520
+ماقلش كم؟ بده يساوي Zero لكل ال axis تمام يبقى هذا
+
+356
+00:42:00,520 --> 00:42:06,000
+هو الخطأ بعينيه طب وده اللي مش خطأ قاللي هنا لو
+
+357
+00:42:06,000 --> 00:42:10,520
+روحت حسب تيرونيس كان عنده نقطة والله عند كل النقطة
+
+358
+00:42:10,620 --> 00:42:14,540
+أنا ماحددتش و ال run skill هذا اللي جيته لا يساوي
+
+359
+00:42:14,540 --> 00:42:17,500
+zero إذا ال functions هذي اللي يكونوا معاهم
+
+360
+00:42:17,500 --> 00:42:21,500
+linearly independent دي بالكلام صح يبقى أنا لو
+
+361
+00:42:21,500 --> 00:42:28,120
+بدأت بال run skill و طلع يساوي zeroبقدرش أحكم ..
+
+362
+00:42:28,120 --> 00:42:32,280
+بقدرش أقول linearly dependent ولا linearly .. يعني
+
+363
+00:42:32,280 --> 00:42:36,260
+قد يكون linearly dependent صح و قد يكون linearly
+
+364
+00:42:36,260 --> 00:42:40,460
+independent الله أعلم .. بقدرش أحكم .. يجب أن نفهم
+
+365
+00:42:40,460 --> 00:42:45,580
+الكلام هذا فهما صحيحا و لذلك روحت أعطيتك التحذير
+
+366
+00:42:45,580 --> 00:42:47,080
+هذا ال remark التالي
+
+367
+00:42:52,410 --> 00:43:00,210
+معكوس النظرية ليس صحيحا او عكس النظرية
+
+368
+00:43:00,210 --> 00:43:05,510
+ليس
+
+369
+00:43:05,510 --> 00:43:12,070
+صحيحاغلط وقد طرحته من خلال السؤال قبل قليل يبقى
+
+370
+00:43:12,070 --> 00:43:16,390
+هذه is not true that is لو كان ال risk يساوي zero
+
+371
+00:43:16,390 --> 00:43:20,630
+then it is not true that ليس بالضرورة هدول يكونوا
+
+372
+00:43:20,630 --> 00:43:25,530
+linearly dependent يبقى كل اللي بقدر أعمل و أنا
+
+373
+00:43:25,530 --> 00:43:31,460
+مطمئنإذا كانوا الـ vectors دول linearly dependent،
+
+374
+00:43:31,460 --> 00:43:35,900
+إذا الـ Runnerskin يساوي 0 على كل الـ Interval،
+
+375
+00:43:35,900 --> 00:43:40,600
+تمام؟ الحالة الثانية، لو لجيت بس نقطة واحدة في الـ
+
+376
+00:43:40,600 --> 00:43:44,640
+Interval، الـ Runnerskin عندها لا يساوي 0، يبقى
+
+377
+00:43:44,640 --> 00:43:49,460
+هذه الـ functions تبقى linearlyطب لو الرنس كان سوا
+
+378
+00:43:49,460 --> 00:43:55,760
+zero بقول الله أعلم قد يكون و قد لا يكون وسأعطي
+
+379
+00:43:55,760 --> 00:44:02,680
+مثلا يوضح ما أقوله في هذه النظرية نجي لأول مثال في
+
+380
+00:44:02,680 --> 00:44:11,140
+هذا الموضوع المثال بيقول ما ياتي example let
+
+381
+00:44:18,220 --> 00:44:26,840
+الـ G1 يساوي كده؟ X تربيع الـ G2 يساوي X في الـ
+
+382
+00:44:26,840 --> 00:44:35,560
+absolute value لـ X بيقول هنا شا ذات بيّلي ال
+
+383
+00:44:35,560 --> 00:44:42,080
+neuron skin تبع الـ G1والـ G2 بده يساوي zero but
+
+384
+00:44:42,080 --> 00:44:52,620
+ولكن الـ G1 and الـ G2 are linearly independent
+
+385
+00:44:52,620 --> 00:44:57,820
+يعني
+
+386
+00:44:57,820 --> 00:45:02,620
+هذا المثال كأنه بده يؤكد ما قلناه في النظرية أو
+
+387
+00:45:02,620 --> 00:45:07,360
+بده يعطي مثال عملي على ما قلناه في هذه النظرية مرة
+
+388
+00:45:07,360 --> 00:45:14,810
+تانية بقولبقول انا ميعطيني دالتين G1 و G2 طلب
+
+389
+00:45:14,810 --> 00:45:18,670
+اثبتله ان الرنسكين تبعهم بدي ساوي جداش بدي ساوي
+
+390
+00:45:18,670 --> 00:45:22,770
+زيرو لما القاتل بدي ساوي زيرو بيقولي بدك تثبتلي ان
+
+391
+00:45:22,770 --> 00:45:30,450
+ال G1 و G2 arelinearly independent وليست linearly
+
+392
+00:45:30,450 --> 00:45:35,710
+dependent تمام بقوله كويس يبقى بروح أدور على
+
+393
+00:45:35,710 --> 00:45:42,390
+الرونسكين تبعه لكن هذه ههه عشان أشتق صعب التعامل
+
+394
+00:45:42,390 --> 00:45:47,160
+معاها بالشكل هذا لكنلو روحت كتبتها على الشكل
+
+395
+00:45:47,160 --> 00:45:53,700
+التالي هذه هي x في x إذا كانت ال x greater than or
+
+396
+00:45:53,700 --> 00:45:59,200
+equal to zero و سالب x إذا كانت ال x less than
+
+397
+00:45:59,200 --> 00:46:04,060
+zero مش شك تعريف ال absolute valueأو بمعنى آخر لو
+
+398
+00:46:04,060 --> 00:46:09,340
+جيت قلت هذه على الشكل التالي X تربية إذا ال X أكبر
+
+399
+00:46:09,340 --> 00:46:14,980
+من أو تساوي Zero و سالب X تربية إذا ال X أقل من
+
+400
+00:46:14,980 --> 00:46:18,220
+Zero
+
+401
+00:46:30,380 --> 00:46:37,820
+إذا كان الـ x أقل من الـ zero, but g1 and g2 are
+
+402
+00:46:37,820 --> 00:46:47,480
+linearly independent تمام؟ إذا أنا عندي فترتينبدي
+
+403
+00:46:47,480 --> 00:46:52,000
+أشوف الرونسكين في كل الفترتين دائما و أبدا بده
+
+404
+00:46:52,000 --> 00:46:56,140
+يساوي 100 بده يساوي 0 إذا بدي أبدأ في الحالة
+
+405
+00:46:56,140 --> 00:47:04,300
+الأولى لو كانت ال X أكبر من أو تساوي 0 مش اللي بده
+
+406
+00:47:04,300 --> 00:47:11,080
+يحصل then بدي أخد الرونسكين as a function of X
+
+407
+00:47:11,080 --> 00:47:15,920
+يساوي إذا أكبر من ال 0 يبقى الدالة الأولى قداش
+
+408
+00:47:16,910 --> 00:47:24,990
+والدالة التانية كده؟ مجتق تاني كده؟ مجتق تاني كده؟
+
+409
+00:47:24,990 --> 00:47:30,510
+يبقى اتنين اكس تكيب ناقص اتنين اكس تكيب يساوي كده؟
+
+410
+00:47:30,510 --> 00:47:40,470
+يساوي زيكأذا كان الـ x أقل من الـ 0، فالرونسكين
+
+411
+00:47:40,470 --> 00:47:45,410
+كمشكلة x، الدالة لولا x ترمية مافيش عليها مشكلة،
+
+412
+00:47:45,410 --> 00:47:51,730
+الدالة التانية جداش سالب x ترمية، مشتقتها 2x وهذه
+
+413
+00:47:51,730 --> 00:47:59,200
+سالبة 2xبدي افكها يبقى ناقص اتنين X تكييب ناقص مع
+
+414
+00:47:59,200 --> 00:48:05,240
+ناقص بصير زائد اتنين X تكييب هو سوى قداش اذا على
+
+415
+00:48:05,240 --> 00:48:11,440
+كل الأمر يعني الرورس كان قداشيبقى هنا الـ
+
+416
+00:48:11,440 --> 00:48:18,720
+Runiscant تبع الـ G1 والـ G2 بده يساوي Zero لكل ال
+
+417
+00:48:18,720 --> 00:48:25,860
+X اللي موجودة من سالب Infinity إلى Infinity يبقى
+
+418
+00:48:25,860 --> 00:48:29,580
+الـ Runiscant هذا ماله بده يساوي Zero يبقى احنا
+
+419
+00:48:29,580 --> 00:48:34,130
+خلصنا من مين؟ من المطلب الأولبدي اجي للمطلوب
+
+420
+00:48:34,130 --> 00:48:37,970
+التاني المطلوب التاني بيقوللي ايش اثبتلي ان ال two
+
+421
+00:48:37,970 --> 00:48:44,770
+functions هدول are linearly تقوللي كويس قاللي لو
+
+422
+00:48:44,770 --> 00:48:50,490
+جدرت و لو عنده نقطة واحدة تثبتلي ان الرنس كان هذا
+
+423
+00:48:50,490 --> 00:48:55,950
+لا يساوي zero بيطلع كلبك مظبوط صحيح ولا لا يبقى
+
+424
+00:48:55,950 --> 00:48:59,270
+باجي بقوله هنا اسم
+
+425
+00:49:01,430 --> 00:49:15,410
+that there exist c1 و c2 in R such that c1 g1 زي
+
+426
+00:49:15,410 --> 00:49:20,030
+c2 g2 بده يساوي من؟ بده يساوي 0
+
+427
+00:49:23,290 --> 00:49:28,730
+كويس؟ طيب انا روح ادور على c1 و c2 اذا طلع c1
+
+428
+00:49:28,730 --> 00:49:32,690
+يساوي c2 يساوي zero معناته هدول linearly
+
+429
+00:49:32,690 --> 00:49:38,590
+independent بيكون هو المطلوب مظبوط؟ اه لكن لما
+
+430
+00:49:38,590 --> 00:49:42,590
+جالي alternatively جالي وين ال alternatively؟ جالي
+
+431
+00:49:42,590 --> 00:49:47,550
+لو قدرت لاجي ولو نقطة واحدة بقوله ماشي الحال انا
+
+432
+00:49:47,550 --> 00:49:51,930
+بتداجي على الدال اللي عندىهذه مرة أكبر من الـ zero
+
+433
+00:49:51,930 --> 00:49:56,550
+و مرة أقل من الـ zero إذا بدي أخد مرة أكبر من الـ
+
+434
+00:49:56,550 --> 00:50:02,030
+zero و مرة أقل من الـ zero تمام فبجي بقول هنا at
+
+435
+00:50:02,030 --> 00:50:08,760
+مثلا x تساوي واحدلما الاكسه ساوي واحد بده يصير c
+
+436
+00:50:08,760 --> 00:50:17,180
+واحد g واحد of واحد زائد c اتنين g اتنين of واحد
+
+437
+00:50:17,180 --> 00:50:23,560
+بده يساوي زيرو هذا معناه جي واحد يا بنات من هاية
+
+438
+00:50:24,690 --> 00:50:33,490
+يبقى C1 في الواحد تربيع زائد C2 في ال جي واحد
+
+439
+00:50:33,490 --> 00:50:38,350
+تربيع كمان جداش اللي هو واحد لكل تربيع بده يساوي
+
+440
+00:50:38,350 --> 00:50:46,730
+Zero يبقى C1 زائد C2 بده يساوي Zeroالان لو جيت
+
+441
+00:50:46,730 --> 00:50:52,710
+قولت at x يساوي سالب واحد مش هجيب الدالة كلها مش
+
+442
+00:50:52,710 --> 00:50:57,650
+هجيب جزء و جزء تاني لأ يبقى عند x يساوي سالب واحد
+
+443
+00:50:57,650 --> 00:51:04,650
+بصير c واحد g واحد of سالب واحد زايد c اتنين g
+
+444
+00:51:04,650 --> 00:51:11,190
+اتنين of سالب واحد بده يساوي zero هذا معناه c of
+
+445
+00:51:11,190 --> 00:51:21,190
+واحد في سالب واحد لكل تربيةزائد c2 في g2 اللي هو
+
+446
+00:51:21,190 --> 00:51:29,970
+g2 اللي هو سالب لسالب واحد لكل تربيع سالب x تربيع
+
+447
+00:51:29,970 --> 00:51:33,950
+يبقى هي السالب برا واخدنا ال x بسالب واحد تربيع
+
+448
+00:51:33,950 --> 00:51:42,950
+هذا الكلام بده يساوي zero هذا معناه ان c1 ناقص c2
+
+449
+00:51:42,950 --> 00:51:49,180
+بده يساوي zeroمظبوط هيك؟ طيب تعالى نجمع لو جمعنا
+
+450
+00:51:49,180 --> 00:51:54,020
+هدول بروحوا هدول بيصير قداش يا بنات اتنين C واحد
+
+451
+00:51:54,020 --> 00:51:58,060
+بده يساوي Zero هذا معناه انه C واحد بده يساوي Zero
+
+452
+00:51:58,060 --> 00:52:03,220
+لما C واحد بده يساوي Zero هذا معناه انه C اتنين
+
+453
+00:52:03,220 --> 00:52:08,140
+بده يساوي Zero يبقى بعض انه C واحد يساوي C اتنين
+
+454
+00:52:08,140 --> 00:52:13,360
+يساوي Zeroيبقى انا لما عندي linear combination
+
+455
+00:52:13,360 --> 00:52:17,880
+بيساوي zero و اثبت ان الثوابت هدول بده يساوي zero
+
+456
+00:52:17,880 --> 00:52:21,960
+يبقى ال two functions are linearly independent
+
+457
+00:52:21,960 --> 00:52:31,620
+يبقى هنا ال g1 and ال g2 are linearly independent
+
+458
+00:52:31,620 --> 00:52:34,680
+وهو المطلوب
+
+459
+00:52:38,150 --> 00:52:42,810
+المخرج يؤشر لي ان انتهى الوقت و احنا بنقول خلاص
+
+460
+00:52:42,810 --> 00:52:47,170
+نكتفي اليوم بهذا القدر لكن لا يزال عندي بعض
+
+461
+00:52:47,170 --> 00:52:49,290
+الأمثلة في هذا ال situation
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/gL3eIuaC1P8_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/gL3eIuaC1P8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..52135c8db1f4668ec93b058eb6e7944e33ae21b3
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/gL3eIuaC1P8_postprocess.srt
@@ -0,0 +1,1364 @@
+1
+00:00:20,750 --> 00:00:25,830
+بسم الله الرحمن الرحيم لان بنجي لهذا ال section
+
+2
+00:00:25,830 --> 00:00:30,810
+طبعا section 2-6 ابن الغيمة اللي مش داخل المقارة
+
+3
+00:00:30,810 --> 00:00:35,330
+بنجي ل section 2-7 اللي هو some special matrices
+
+4
+00:00:35,330 --> 00:00:41,860
+بعض المصوفات الخاصةنبدأ في أول مصوفة هي المصوفة
+
+5
+00:00:41,860 --> 00:00:46,260
+الصفرية ثم مصوفة الواحدة وبعد ذلك ننتقل إلى
+
+6
+00:00:46,260 --> 00:00:51,640
+المصوفات الأخرى يبقى the M في N matrix whose
+
+7
+00:00:51,640 --> 00:00:55,120
+elements are all zero is called the zero matrix of
+
+8
+00:00:55,120 --> 00:01:00,850
+size M في NAnd denoted by zero M N يعني بنكتب الـ
+
+9
+00:01:00,850 --> 00:01:05,470
+Zero لم طاول هذا شوية على شكل بيضاوي وبنحط تحته M
+
+10
+00:01:05,470 --> 00:01:09,890
+في N دليل على أنه نظامها أو ال size M في M يبقى
+
+11
+00:01:09,890 --> 00:01:13,650
+المصوفة الصفرية لو كانت مصوفة مربعة والله مصوفة
+
+12
+00:01:13,650 --> 00:01:19,860
+مستطيلة المهم جميع أنصرها بيكونوا أصفراًThe
+
+13
+00:01:19,860 --> 00:01:26,000
+Identity Matrix المصفوفة الوحدة المصفوفة الوحدة
+
+14
+00:01:26,000 --> 00:01:31,980
+هاديها الرمز IN وهي مصفوفة مربعة عدد الصفوف يساوي
+
+15
+00:01:31,980 --> 00:01:39,080
+فيها عدد الأعمدة square matrix هاديها الرمز IN وهي
+
+16
+00:01:39,080 --> 00:01:48,680
+100110 كل 001جميع عناصرها أصفرًا ما عدا عناصر
+
+17
+00:01:48,680 --> 00:01:53,780
+القطر الرئيسي كل واحد واحد واحد تمام؟ يبقى في
+
+18
+00:01:53,780 --> 00:01:57,160
+عندنا مناطق اسم القطر الرئيسي في القطر الثانوي
+
+19
+00:01:57,160 --> 00:02:01,260
+القطر اللي جاي من الشمال لليمين بسميه الرئيسي
+
+20
+00:02:01,260 --> 00:02:05,040
+واللي جاي من اليمين للشمال بسميه الثانوي ثانوي
+
+21
+00:02:05,040 --> 00:02:10,120
+بلزمنيش بلزمنا الرئيسي يبقى ال mean diagonal القطر
+
+22
+00:02:10,120 --> 00:02:13,750
+الرئيسي هو اللي جاي من الشمال لليمينجميع العناصر
+
+23
+00:02:13,750 --> 00:02:19,230
+كل واحد صحيح وباقي العناصر أصفرا ممكن أدّيها رمز
+
+24
+00:02:19,230 --> 00:02:25,950
+آخر غير رمز IN ممكن أقول عليها Delta IJ بحيث Delta
+
+25
+00:02:25,950 --> 00:02:31,170
+IJ يبدأ تساوي Zero يبدأ تساوي واحد تساوي Zero كم؟
+
+26
+00:02:31,170 --> 00:02:37,090
+إذا I لا تساوي الـJ إذا I سوى الـJ تساوي كم؟ واحد
+
+27
+00:02:37,090 --> 00:02:40,980
+صحيح فمثلاعندما أقول العنصر اللي عندي هذا واحد
+
+28
+00:02:40,980 --> 00:02:45,920
+يبقى جاي في الصف الأول والعمود الأول يبقى دلتا
+
+29
+00:02:45,920 --> 00:02:52,980
+واحد واحد I تساوي J هذا العنصر جاي في الصف الثاني
+
+30
+00:02:52,980 --> 00:02:58,500
+والعمود الثاني يبقى دلتا اتنين اتنين I تساوي J
+
+31
+00:02:58,500 --> 00:03:03,360
+اللي بعده هنا كمان واحد يبقى دلتا تلاتة تلاتة دلتا
+
+32
+00:03:03,360 --> 00:03:09,790
+اربعة اربعة دلتا خمسة خمسةDelta N N يبقى هنا مقداش
+
+33
+00:03:09,790 --> 00:03:15,270
+بواحد صين ما خلال ذلك لو جيت لهذا يبقى هذا Delta
+
+34
+00:03:15,270 --> 00:03:20,250
+واحد تلاتة الواحد لا تساوي تلاتة يبقى القيمة تساوي
+
+35
+00:03:20,250 --> 00:03:25,920
+قداش تساوي Zeroيبقى سواء رمزنا بالرمز هذا أو الرمز
+
+36
+00:03:25,920 --> 00:03:31,580
+هذا لإتنية الرمز لمصوفية الوحدة راح جلد delta ig
+
+37
+00:03:31,580 --> 00:03:37,200
+دي sample يعني الرمز delta ig بسميه chronicle
+
+38
+00:03:37,200 --> 00:03:37,900
+delta
+
+39
+00:03:40,980 --> 00:03:45,280
+من حد ما تشوف المصوفة هذه بديك تعرف إن هذه مصوفة
+
+40
+00:03:45,280 --> 00:03:49,280
+لوحدها سواء بالصيغة هذه أو بالصيغة هذه وما بتهمنيش
+
+41
+00:03:49,280 --> 00:03:53,500
+التسميات كرونيكار ماكرونيكار والزمني بالزمني تعرف
+
+42
+00:03:53,500 --> 00:03:58,340
+الإسم الدارج وهو مصوفة الواحدة هذه اللي هو very
+
+43
+00:03:58,340 --> 00:04:03,860
+important لأنه ولا كتاب هايت في الجبر الخطي إلا
+
+44
+00:04:03,860 --> 00:04:16,160
+وفي هذه التسمية اللي هي مصوفة الواحدةبنشوف بعض
+
+45
+00:04:16,160 --> 00:04:20,940
+الخواص بالنسبة لهم الخاصية الأولى لو جيت جامعة
+
+46
+00:04:20,940 --> 00:04:27,640
+المصوفة N لنظام N في N إلى من المصوفة الصفرية لكي
+
+47
+00:04:27,640 --> 00:04:33,110
+أقدر أجمعها لازم تبقى المصوفة الصفرية نظامهامفي ان
+
+48
+00:04:33,110 --> 00:04:38,090
+لذلك ماخلتكي اشتريها و روحت كتب تحت مفي ان دليل
+
+49
+00:04:38,090 --> 00:04:42,630
+على ان الصفوف هنا زي الصفوف هنا و الأعمد هنا زي
+
+50
+00:04:42,630 --> 00:04:46,390
+الصفوف زي الأعمد هنا طبعا في الجامعة كل عنصر مع
+
+51
+00:04:46,390 --> 00:04:50,650
+نظيرة لما اضيف الصفر لأي عنصر بيظل نفس الانصر
+
+52
+00:04:50,650 --> 00:04:56,420
+وبالتالي هتطلع ان المصوفة ايه الأصليةطيب لو جمعت A
+
+53
+00:04:56,420 --> 00:05:00,440
+و سالب واحد في ايه؟ سالب واحد بيضرب في جميع
+
+54
+00:05:00,440 --> 00:05:04,840
+العناصر بلا استثناء لما نقضره في جميع العنصر يبقى
+
+55
+00:05:04,840 --> 00:05:08,920
+الموجب بيصير سالب وسالب بيصير الموجب إذا لما أجمع
+
+56
+00:05:08,920 --> 00:05:12,780
+كل عنصر مع نظيره النتج بيديهي أعطيني مين؟ Zero
+
+57
+00:05:12,780 --> 00:05:18,730
+بالتالة بتطلع المصحوفة الصفرية اللي هو Zero MMيعني
+
+58
+00:05:18,730 --> 00:05:23,010
+بالبلد هيك إذا أضافت المصوفة الصفرية للمصوفة بيطلع
+
+59
+00:05:23,010 --> 00:05:27,090
+نفس المصوفة إذا أضافت المصوفة لسالب المصوفة النتج
+
+60
+00:05:27,090 --> 00:05:30,950
+هو المصوفة الصفرية ومن نفس النظام على كل الأمرين
+
+61
+00:05:30,950 --> 00:05:34,970
+النقطة التالتة المرة اللي فاتة خدنا ال matrix
+
+62
+00:05:34,970 --> 00:05:40,510
+multiplication ضرب المصوفات الآن أنا عندي مصوفة
+
+63
+00:05:40,510 --> 00:05:45,830
+نظامها M في N بدي أضربها في Zero in P بتتم عملية
+
+64
+00:05:45,830 --> 00:05:50,780
+الضرببتتم لأن عدد الأعمدة في المصوفة الأولى يساوي
+
+65
+00:05:50,780 --> 00:05:55,240
+عدد الصفوف في المصوفة الثانية والناتج مصوفة نظامها
+
+66
+00:05:55,240 --> 00:06:01,760
+M في P يبقى Zero M في P يبقى هذه المصوفة الصفرية
+
+67
+00:06:01,760 --> 00:06:07,910
+يبقى لو ضربمصوفة A و 0 و 2 و 2 مش من نفس النظام
+
+68
+00:06:07,910 --> 00:06:12,370
+لكن فيهم شرط عدد أعمدة المصوفة الأولى يسوى عدد
+
+69
+00:06:12,370 --> 00:06:17,950
+صفوف المصوفة الثانية فالنتج هو مصوفة صفرية عددها
+
+70
+00:06:17,950 --> 00:06:21,730
+صفوفة هو عدد صفوف المصوفة الأولى وعدد أعمدتها هو
+
+71
+00:06:21,730 --> 00:06:29,780
+عدد أعمدت المصوفة الثانية0 المصوفة الصفرية نظامها
+
+72
+00:06:29,780 --> 00:06:36,600
+Q M ده ضربها في A M هي M في N إذاً عدد الأعمدة في
+
+73
+00:06:36,600 --> 00:06:41,060
+المصوفة الصفرية يساوي عدد الصفوف في المصوفة A إذا
+
+74
+00:06:41,060 --> 00:06:46,420
+يمكن أن تتم عملية الضرب والناتج مصوفة نظامها Q في
+
+75
+00:06:46,420 --> 00:06:52,580
+M يبقى Zero Q في N إذاً هل هذه المصوفة هي المصوفة
+
+76
+00:06:52,580 --> 00:06:57,910
+هذه؟لأ هذه صفرية صحية و هذه صفرية بس عدد الصفوف
+
+77
+00:06:57,910 --> 00:07:00,610
+اللي أعمدها في الأولى ليست كعدد الصفوف اللي أعمدها
+
+78
+00:07:00,610 --> 00:07:04,730
+في الثانية وبالتالي هما صحيح مصففين صفريات لكن هما
+
+79
+00:07:04,730 --> 00:07:12,230
+ليست متساويةنجي للنقطة الرابعة، لو ضربت المصوفة
+
+80
+00:07:12,230 --> 00:07:15,030
+ايه في مصوفة الوحدة؟ احنا قولنا ان مصوفة الوحدة
+
+81
+00:07:15,030 --> 00:07:21,530
+مصوفة مربعة يبقى لما اقول in المقصود في in في in
+
+82
+00:07:21,530 --> 00:07:26,330
+بس اختصارا بقول in وبسكتيبقى مصروفتي الواحدة هي
+
+83
+00:07:26,330 --> 00:07:31,210
+مصروف ومربع يبقى لأ ده لأن اقول N في N فاختصارا
+
+84
+00:07:31,210 --> 00:07:36,550
+بقول IM يبقى لما نقدر المصروفة ايه لنظامها M في N
+
+85
+00:07:36,550 --> 00:07:42,270
+N في N بدي يطلع اللي هو من المصروفة الاصلية
+
+86
+00:07:42,270 --> 00:07:47,770
+لنظامها M في M لأن هذه M في N وهذه N في N بيظل M
+
+87
+00:07:47,770 --> 00:07:52,630
+في N اللي هي المصروفة الاصلية بنفس الطريقةلو روحت
+
+88
+00:07:52,630 --> 00:07:57,970
+ضربت من الشمال في مصفوفة الوحدة I M هذه الوحدة غير
+
+89
+00:07:57,970 --> 00:08:02,810
+الوحدة هذه صحيح؟ لأن هذه فيها N من الصفوف و N من
+
+90
+00:08:02,810 --> 00:08:08,990
+الأعمدة هذه فيها M من الصفوف و M من الأعمدة إذا
+
+91
+00:08:08,990 --> 00:08:13,850
+هاتان المصففات مختلفتان وإن كانتكل واحدة فيهم هي
+
+92
+00:08:13,850 --> 00:08:17,990
+مصوفة الواحدة يبقى كل واحدة حسب ال size تبعها أو
+
+93
+00:08:17,990 --> 00:08:22,030
+النظام تبعها بتضربها من جهة الشمال في ال A طبعا
+
+94
+00:08:22,030 --> 00:08:27,830
+ممكن لأن هذه M في M وهذه M في N يبقى ناتج نفس
+
+95
+00:08:27,830 --> 00:08:33,320
+المصوفة اللي نظامها M في Nلحظة ان هدول اتنتين ضرب
+
+96
+00:08:33,320 --> 00:08:38,920
+من اليمين و هنا ضرب من الشمال و اعطاني نفس النتيجة
+
+97
+00:08:38,920 --> 00:08:43,960
+رغم ان المصففات اللي اتنين هدول ما لهم غير
+
+98
+00:08:43,960 --> 00:08:50,560
+متساويتينطيب نجي تعريف جديد لو أخدنا المصوفة
+
+99
+00:08:50,560 --> 00:08:56,920
+المربعة اللي عندنا طالع a11 لغاية a1n ضالية نزل
+
+100
+00:08:56,920 --> 00:09:03,200
+لغاية a n1 و هنا a nn يبجى هذه مصوفة مربعة فيها n
+
+101
+00:09:03,200 --> 00:09:08,480
+من الصفوف و n من الأعمدة يبجى هي ال n بال n matrix
+
+102
+00:09:08,480 --> 00:09:12,300
+ان ان كانت هذه المصوفة هيك يبجى فيها عندنا بعض
+
+103
+00:09:12,300 --> 00:09:16,360
+الشغلات بدنا نشير لهاالنقطة الأولى جالي the
+
+104
+00:09:16,360 --> 00:09:22,500
+elements بسميهم
+
+105
+00:09:22,500 --> 00:09:29,020
+العناصر القطرية في المصفوفة يمكن بسميهم اياش ال
+
+106
+00:09:29,020 --> 00:09:33,320
+elements are called the diagonal elements of A
+
+107
+00:09:33,320 --> 00:09:38,760
+العناصر القطرية للمصفوفة A هذه النقطة الأولى
+
+108
+00:09:38,760 --> 00:09:39,660
+النقطة الثانية
+
+109
+00:09:48,190 --> 00:09:55,910
+إذا كان كل عنصر خارج هذا القطر الرئيسي هو 0
+
+110
+00:10:00,460 --> 00:10:05,200
+يبقى لو جيت على المصوفة المربعة و جيت على القطر
+
+111
+00:10:05,200 --> 00:10:11,100
+الرئيسي في هذه المصوفة و لجيت كل العناصر خارج
+
+112
+00:10:11,100 --> 00:10:16,400
+القطر الرئيسي بأصفار ما عدا عناصر القطر الرئيسي
+
+113
+00:10:16,400 --> 00:10:21,870
+يبقى بقول هذه ما لهاdiagonal matrix طب بنفعش يكون
+
+114
+00:10:21,870 --> 00:10:26,630
+أحد العناصر أسفرا في القطرة الرئيسية؟ بنفع ان شاء
+
+115
+00:10:26,630 --> 00:10:31,510
+الله يكونوا كلهم أسفرا و لو بس أنصر واحد مايكون
+
+116
+00:10:31,510 --> 00:10:36,290
+صفر عشان أميزها عن المصموفة الصفرية صحيح ولا لأ؟
+
+117
+00:10:36,420 --> 00:10:42,680
+إذا الـ diagonal matrix هي مصفوفة جميع عناصرها
+
+118
+00:10:42,680 --> 00:10:47,880
+أسفارا عدا عناصر القطرة الرئيسية ويمكن أن تكون بعض
+
+119
+00:10:47,880 --> 00:10:54,200
+عناصر القطرة الرئيسية أسفارا المهم لو حطيت إيدي
+
+120
+00:10:54,200 --> 00:10:58,780
+على القطرة الرئيسية يبقى خارج هذا القطرة الرئيسية
+
+121
+00:10:58,780 --> 00:11:04,160
+جميع العناصر أسفارا بلا إستثناءإن حدث ذلك يبقى هذه
+
+122
+00:11:04,160 --> 00:11:08,540
+المصفوفة بسميها الـ diagonal matrix المصفوفة
+
+123
+00:11:08,540 --> 00:11:14,140
+القطرية بديها الرمز capital D وهو الحرف الأول من
+
+124
+00:11:14,140 --> 00:11:18,980
+كلمة diagonal واختصارا بقول diagonal اختصرت
+
+125
+00:11:18,980 --> 00:11:25,280
+diagonal وكتب D1 وD2 وDN مين هم الدهات هدول هم
+
+126
+00:11:25,280 --> 00:11:32,660
+عناصر القطر الرئيسييبقى الـD1 والـD2 ولغاية DN هي
+
+127
+00:11:32,660 --> 00:11:41,260
+الـdiagonal elements ورد DI بذات ساوي AII يعني D1
+
+128
+00:11:41,260 --> 00:11:49,050
+هذه اللي عندنا هي A11 اللي عندناD2 هي A22 D3 هي
+
+129
+00:11:49,050 --> 00:11:55,570
+A33 يقول I من 1 إلى N يبقى هي من اين هي عناصر
+
+130
+00:11:55,570 --> 00:12:01,950
+القطر الرئيسي مثلا لو اتلك D هي الدياجونال 3 2
+
+131
+00:12:01,950 --> 00:12:07,570
+سالب 1 مثلا يبقى معنى هذا الكلام ان هذه المصفوفة
+
+132
+00:12:07,570 --> 00:12:13,270
+مصفوفة نظامها تلاتة في تلاتةهذه العناصر القطر
+
+133
+00:12:13,270 --> 00:12:18,330
+الرئيسي وباقي العناصر أسفرها طلع هنا هذه عناصر
+
+134
+00:12:18,330 --> 00:12:21,970
+القطر الرئيسي تلاتة اتنين سالب واحد وباقي العناصر
+
+135
+00:12:21,970 --> 00:12:25,730
+اللي فوق و اللي تحت كلهم مالهم كلهم أسفار زي ما
+
+136
+00:12:25,730 --> 00:12:30,250
+انت شايفهانجي للنقطة التالتة بدنا حاجة اسمة scalar
+
+137
+00:12:30,250 --> 00:12:35,090
+matrix يعني يا بنات كأنه احنا حتى هذه اللحظة بناخد
+
+138
+00:12:35,090 --> 00:12:40,110
+حالات خاصة من المصوفة الصفرية ومن اللي هو مصوفة
+
+139
+00:12:40,110 --> 00:12:44,910
+الوحدة او قياسا على مصوفة الوحدة بطلع منها شغلات
+
+140
+00:12:44,910 --> 00:12:50,010
+جديدةيبقى اخدنا الان الـ diagonal matrix هي زي
+
+141
+00:12:50,010 --> 00:12:53,150
+مصفوفة الواحدة بس العناصر مش كل واحد واحد واحد
+
+142
+00:12:53,150 --> 00:12:57,870
+ارقام مختلفة طيب بعد ذلك بنتاجي الى ال scalar
+
+143
+00:12:57,870 --> 00:13:05,830
+matrix المصفوفة القياسية هي مصفوفة قطرية يعني جميع
+
+144
+00:13:05,830 --> 00:13:10,230
+عناصرها أصفرًا ما عدا عناصر قطر رئيسي بس عناصر قطر
+
+145
+00:13:10,230 --> 00:13:14,720
+رئيسي كلها أرقام متساويةواحد واحد واحد .. اتنين
+
+146
+00:13:14,720 --> 00:13:18,320
+اتنين اتنين .. تلاتة تلاتة تلاتة .. عشرة عشرة عشرة
+
+147
+00:13:18,320 --> 00:13:21,840
+.. ناقص خمسة ناقص خمسة ناقص خمسة .. عناصر القطة
+
+148
+00:13:21,840 --> 00:13:27,910
+الرئيسية كلها متساوية .. شلتكون كلها أصفاراصح ولا
+
+149
+00:13:27,910 --> 00:13:30,930
+لأ؟ يبقى ان شاء الله نكون عايش بقول ان الـ scalar
+
+150
+00:13:30,930 --> 00:13:36,330
+matrix is a diagonal matrix هي مصفوفة قطرية such
+
+151
+00:13:36,330 --> 00:13:40,950
+that the diagonal elements are equal كل عناصر
+
+152
+00:13:40,950 --> 00:13:45,830
+القطر الرئيسي كلها متساوية بناء عليه بدي أسألكوا
+
+153
+00:13:45,830 --> 00:13:52,070
+السؤال التالي هل المصفوفة الصفرية scalar matrix؟
+
+154
+00:13:52,070 --> 00:13:57,170
+نعمهل مصفوفة الوحدة scalar matrix؟ أه لأن عناصر
+
+155
+00:13:57,170 --> 00:14:01,550
+القطر الرئيسي أصفة أرقام متزاوية والباقية ليست
+
+156
+00:14:01,550 --> 00:14:05,550
+علاقة بها أنا أريد عناصر القطر الرئيسي يبقى
+
+157
+00:14:05,550 --> 00:14:11,860
+المصفوفة القياسية هي مصفوفة قطريةيعني جميع عناصرها
+
+158
+00:14:11,860 --> 00:14:15,700
+أصفرًا عادة عناصر القطر الرئيسي زيادة على ذلك
+
+159
+00:14:15,700 --> 00:14:21,400
+عناصر القطر الرئيسي كلها أرقام متساوية يبقى هذه
+
+160
+00:14:21,400 --> 00:14:25,580
+اللي هي ال scalar matrix for example لو بدأتي أخد
+
+161
+00:14:25,580 --> 00:14:31,210
+ال scalar matrix و أديتها الرمز دييبقى دي دي دي دي
+
+162
+00:14:31,210 --> 00:14:36,030
+مصوفة مربعة وباقي العناصر أصفرًا اللي ممكن أكتبها
+
+163
+00:14:36,030 --> 00:14:41,410
+ممكن أخد الدي برا عامل مشترك لأن الدي الرقم لو
+
+164
+00:14:41,410 --> 00:14:46,110
+ضربته في المصوفة بضربه في جميع عناصر المصوفة فدي
+
+165
+00:14:46,110 --> 00:14:51,530
+في zero ب zero دي في واحدبـ D و هكذا يبقى يا
+
+166
+00:14:51,530 --> 00:14:54,990
+بكتبها على الشكل هذه يا بكتبها على الشكل اللي أنا
+
+167
+00:14:54,990 --> 00:15:00,990
+كاينه هنا خاتة D عامل مشترك من جميع أناصر المصورة
+
+168
+00:15:00,990 --> 00:15:05,710
+طيب اللي بين جسين هذه المصورة دي من مصوفة الوحدة
+
+169
+00:15:05,710 --> 00:15:11,130
+إذا بقدر أقول دي لحاله رقم مضروبا في مصوفة الوحدة
+
+170
+00:15:11,130 --> 00:15:17,150
+I N يبقى هذه بسميها what scalar matrixالان يا بنات
+
+171
+00:15:17,150 --> 00:15:22,170
+بدنا نيجي لحاجة اسمة المصوفة المثلثة العليا او
+
+172
+00:15:22,170 --> 00:15:27,310
+المصوفة المثلثة السفلاء طيب ال upper triangle
+
+173
+00:15:27,310 --> 00:15:31,310
+matrix او ال lower triangle matrix المصوفة المثلثة
+
+174
+00:15:31,310 --> 00:15:35,850
+العليا او المثلثة السفلاء المصوفة المثلثة العليا
+
+175
+00:15:35,850 --> 00:15:42,450
+هي المصوفة اللي جمع عنصرها اسفل القطرة رئيسي أصفرا
+
+176
+00:15:43,280 --> 00:15:47,300
+المصوفة المثلثة السفلية هي المصوفة اللى جميع
+
+177
+00:15:47,300 --> 00:15:52,600
+عناصرها أعلى القطر الرئيسى بيكونوا أسفارة الكلام
+
+178
+00:15:52,600 --> 00:15:57,900
+اللى قلته بدنا نروح نكتبه هنا مشان نعتمده بعدها
+
+179
+00:15:57,900 --> 00:15:58,700
+جدر الشغل
+
+180
+00:16:13,580 --> 00:16:18,380
+يبقى بدأجي الآن للمصوفة المثلثة العليا والمصوفة
+
+181
+00:16:18,380 --> 00:16:27,160
+المثلثة السفلاء يبقى اضع رقم أربعة The Upper أو
+
+182
+00:16:27,160 --> 00:16:33,500
+Lower بين قسين Triangle Matrix
+
+183
+00:16:43,080 --> 00:16:54,680
+is a square matrix is a square matrix a
+
+184
+00:16:54,680 --> 00:17:08,300
+that has all elements that has all elements under
+
+185
+00:17:08,300 --> 00:17:19,470
+being seen overThe diagonal elements are
+
+186
+00:17:19,470 --> 00:17:35,870
+zero
+
+187
+00:17:43,070 --> 00:17:49,710
+for example الـ
+
+188
+00:17:49,710 --> 00:18:02,530
+A تساوي تلاتة واحد ناقص اتنين Zero Zero اتنين Zero
+
+189
+00:18:02,530 --> 00:18:11,210
+Zero سالب واحد is another triangle matrix is an
+
+190
+00:18:12,890 --> 00:18:25,950
+upper is an upper triangle matrix
+
+191
+00:18:25,950 --> 00:18:29,810
+but
+
+192
+00:18:29,810 --> 00:18:33,250
+ولكن
+
+193
+00:18:33,250 --> 00:18:35,430
+بيتساوي
+
+194
+00:18:36,580 --> 00:18:48,720
+1,0,0,2,1,0,1,3,2 is a lower triangle matrix
+
+195
+00:19:25,030 --> 00:19:29,690
+مرة أخرى يبقى بالداجل المصفوفة المثلثة العليا
+
+196
+00:19:29,690 --> 00:19:34,230
+والمصفوفة المثلثة السفلة يبقى upper triangle
+
+197
+00:19:34,230 --> 00:19:39,010
+matrix مصفوفة مثلثة عليا lower triangle matrix
+
+198
+00:19:39,010 --> 00:19:40,870
+مصفوفة مثلثة سفلة
+
+199
+00:19:43,630 --> 00:19:49,030
+هي عبارة عن المصفوفة المربعة a that has all
+
+200
+00:19:49,030 --> 00:19:54,430
+elements under يبقى كل العناصر تحت ال diagonal
+
+201
+00:19:54,430 --> 00:19:59,950
+elements تحت العناصر القطرية كلها أصفرا يبقى بداجي
+
+202
+00:19:59,950 --> 00:20:05,310
+على ال main diagonal بدي اللي تحته تكون كلها أصفر
+
+203
+00:20:05,310 --> 00:20:08,970
+و اللي فوق تكون أرقام طيب ال diagonal matrix نفسه
+
+204
+00:20:09,600 --> 00:20:12,860
+بهمنيش يكون أعداد ولا يكون أسفار ماعنديش ماعنديش
+
+205
+00:20:12,860 --> 00:20:16,880
+أي شرط على ال diagonal matrix اللي شرط فقط على
+
+206
+00:20:16,880 --> 00:20:21,060
+العناصر اللي منه فوق أو العناصر اللي منه أسفار طيب
+
+207
+00:20:21,060 --> 00:20:24,060
+ال lower triangle matrix هو عبارة عن المصوفة
+
+208
+00:20:24,060 --> 00:20:28,500
+المربعة إيه اللي كل عناصرها أعلى ال diagonal
+
+209
+00:20:28,500 --> 00:20:32,820
+elements كلها أسفار فلو جيتنا المصوفة إيه طلعيلي
+
+210
+00:20:32,820 --> 00:20:37,290
+هذا ال mean diagonalأيوة تلاتة و Zero سالب واحد
+
+211
+00:20:37,290 --> 00:20:42,110
+اللي منه تحت كلها أصفر يبقى هذه upper triangle
+
+212
+00:20:42,110 --> 00:20:47,390
+matrix نجي للمصوفة هذه هذا هو القط طبعا لحظة هنا
+
+213
+00:20:47,390 --> 00:20:51,770
+في Zero حتى لو كان كل مصفر ماعنديش مشكلة طيب هذا
+
+214
+00:20:51,770 --> 00:20:55,670
+القط رئيسي كل اللي منه فوق أصفر و اللي تحت أرقام
+
+215
+00:20:55,670 --> 00:20:59,390
+طب ممكن يكون هنا في رقم يعني هذا ليس بضرورة انه
+
+216
+00:20:59,390 --> 00:21:04,270
+ممكن يكون Zero كمانأنا بيهمني اللي فوق أصفر تمام
+
+217
+00:21:04,270 --> 00:21:09,330
+يبقى اللي تحت ماعنديش عليهم أي شرط يبقى كمان هذه
+
+218
+00:21:09,330 --> 00:21:14,290
+بسميها ال lower triangle matrix خليني أسفل السؤال
+
+219
+00:21:14,290 --> 00:21:19,440
+التالي هل ال zero matrix Upper Triangle Matrix
+
+220
+00:21:19,440 --> 00:21:23,240
+Upper
+
+221
+00:21:23,240 --> 00:21:31,220
+Triangle Matrix Lower Triangle Matrix Identity
+
+222
+00:21:31,220 --> 00:21:36,920
+Matrixبرضه Upper and Lower Matrix على كلا الأمرين
+
+223
+00:21:36,920 --> 00:21:42,840
+الـ Scalar Matrix المصوف القياسي برضه بتنفع Upper
+
+224
+00:21:42,840 --> 00:21:47,200
+and Lower على كلا الأمرين يبقى معنا مشكلة في هذه
+
+225
+00:21:47,200 --> 00:21:52,320
+الحل يبقى نكتب الملاحظة هذه اللي بنقولها يبقى Not
+
+226
+00:21:52,320 --> 00:21:58,280
+الملاحظة رقم واحد The Identity Matrix
+
+227
+00:22:04,550 --> 00:22:11,390
+مصفوفة الوحدة IN and
+
+228
+00:22:11,390 --> 00:22:21,430
+the n by n matrix zero and the n by n zero matrix
+
+229
+00:22:21,430 --> 00:22:31,010
+والمصفوفة الصفرية لنظامها N في N هذول are examples
+
+230
+00:22:33,660 --> 00:22:43,320
+of scalar matrices number
+
+231
+00:22:43,320 --> 00:22:48,000
+اتنين
+
+232
+00:22:48,000 --> 00:22:57,160
+the diagonal matrix
+
+233
+00:22:57,160 --> 00:23:01,040
+is
+
+234
+00:23:01,040 --> 00:23:13,590
+anUpper and Lower and
+
+235
+00:23:13,590 --> 00:23:30,250
+Lower Triangle Matrix نجي
+
+236
+00:23:30,250 --> 00:23:31,630
+لنظرية theorem
+
+237
+00:23:34,900 --> 00:23:37,240
+طبعا الكلام اللي قلناه هو واضح مظبوط اللي قلناه
+
+238
+00:23:37,240 --> 00:23:42,500
+شفو بس بعدها كتبناه عشان نثبت هذه المعلومات F
+
+239
+00:23:42,500 --> 00:23:59,680
+المصوف A تساوي ال A A11 A12 A1N A21 A22 A2N
+
+240
+00:24:01,950 --> 00:24:11,590
+وضلنا مشيين لغاية AM1 AM2 AMN الشكل اللي عندنا هذا
+
+241
+00:24:11,590 --> 00:24:16,830
+هو المصحوفة
+
+242
+00:24:16,830 --> 00:24:20,390
+C والمصحوفة
+
+243
+00:24:20,390 --> 00:24:31,860
+capital Cبدها تساوي الـ diagonal اللي هو C1 و C2 و
+
+244
+00:24:31,860 --> 00:24:33,320
+لغاية CM
+
+245
+00:24:35,720 --> 00:24:51,240
+اللي هي main بدها تساوي C10000C200000CM
+
+246
+00:24:51,240 --> 00:24:57,220
+بالشكل اللي عندنا هنا جالي
+
+247
+00:24:57,220 --> 00:25:09,040
+zeroوهذه ستبقى نزلة وهذه نزلة بشكل انه CM and ال
+
+248
+00:25:09,040 --> 00:25:19,460
+D بدها تساوي ال diagonal دي واحد و دي اتنين و
+
+249
+00:25:19,460 --> 00:25:24,280
+لغاية DN و اللي هي بدها تساوي
+
+250
+00:25:33,440 --> 00:25:39,760
+D1 D2 D3
+
+251
+00:25:39,760 --> 00:25:40,200
+D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17
+
+252
+00:25:40,200 --> 00:25:42,960
+D18 D19 D20 D21 D22 D23 D22 D23 D23 D23 D23 D23
+
+253
+00:25:42,960 --> 00:25:46,260
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+254
+00:25:46,260 --> 00:25:47,280
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+255
+00:25:47,280 --> 00:25:47,960
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 Dert Dert
+
+256
+00:25:47,960 --> 00:25:57,900
+Dert Dert Dert Dert Dert Dert Dertالـ C في A الـ C
+
+257
+00:25:57,900 --> 00:26:04,180
+في A يبدو يساوي C1A11
+
+258
+00:26:04,180 --> 00:26:09,240
+C1A12
+
+259
+00:26:09,240 --> 00:26:14,460
+C1A1N
+
+260
+00:26:15,870 --> 00:26:25,250
+C to A to 1 C to A to 2 C to A to N هنظل نزلين
+
+261
+00:26:25,250 --> 00:26:42,370
+لغاية CM AM1 CM AM2 هنظل نزلين لغاية CM AM1
+
+262
+00:26:42,370 --> 00:26:50,940
+CM AM2شكلها انها ده and
+
+263
+00:26:50,940 --> 00:26:54,340
+ال
+
+264
+00:26:54,340 --> 00:27:03,180
+a دي بدها تساوي ال
+
+265
+00:27:03,180 --> 00:27:12,070
+d one a one one دي two a one twoوانضل ماشيين لغاية
+
+266
+00:27:12,070 --> 00:27:27,310
+D N A N او هنا D 1 A 2 1 D 1 A 2 1 D 2 A 2 2 او
+
+267
+00:27:27,310 --> 00:27:42,560
+هنا D N A 2 M وانضل ماشيين يبقى D 1 A M 1D to A M
+
+268
+00:27:42,560 --> 00:27:59,020
+to D N A M N كروه
+
+269
+00:27:59,020 --> 00:27:59,380
+لري
+
+270
+00:28:06,180 --> 00:28:24,560
+Let الـ A بي M by N Matrix and capital C بدو يساوي
+
+271
+00:28:24,560 --> 00:28:33,620
+C000C000
+
+272
+00:28:36,000 --> 00:28:43,720
+ونظل ماشيين لغاية Zero Zero Zero Zero Zero Zero
+
+273
+00:28:43,720 --> 00:28:46,320
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+274
+00:28:46,320 --> 00:28:46,420
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+275
+00:28:46,420 --> 00:28:48,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+276
+00:28:48,720 --> 00:28:50,960
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+277
+00:28:50,960 --> 00:28:51,020
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+278
+00:28:51,020 --> 00:28:51,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+279
+00:28:51,720 --> 00:28:51,800
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+280
+00:28:51,800 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+281
+00:28:54,700 --> 00:28:54,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+282
+00:28:54,720 --> 00:29:01,480
+Zero Zero Zero Zero
+
+283
+00:29:01,480 --> 00:29:03,160
+Zero Zero Zero
+
+284
+00:29:06,290 --> 00:29:26,770
+D Zero Zero Zero D Zero Zero Zero Zero Zero D In
+
+285
+00:29:26,770 --> 00:29:34,070
+By In Scalar Matrix
+
+286
+00:29:36,400 --> 00:29:43,640
+ماتريكس ثم C
+
+287
+00:29:43,640 --> 00:29:54,820
+في A بيساوي C في A و A
+
+288
+00:29:54,820 --> 00:30:00,980
+في D بيساوي D في A
+
+289
+00:30:21,260 --> 00:30:23,000
+عشان احنا بقى باستخدام البرنامج اللي بيعمله
+
+290
+00:31:00,970 --> 00:31:06,650
+نرجع لكلام اللي كتبناه هذا بيقول
+
+291
+00:31:06,650 --> 00:31:14,990
+لو عند المصوفة A نظامها M في N الـ A زي ما تشايف M
+
+292
+00:31:14,990 --> 00:31:20,270
+من الصفوف و N من الأعمدةوكان عندى الـ diagonal
+
+293
+00:31:20,270 --> 00:31:29,510
+matrix سميتها C والـ C نظامها M في M لإن الـ C1 C2
+
+294
+00:31:29,510 --> 00:31:35,910
+لغاية مين لغاية CM يبقى مصفوفة مربع نظامها M في M
+
+295
+00:31:35,910 --> 00:31:43,990
+الأولانية M في N والتانية دي M في Mوهي كتبت عليك
+
+296
+00:31:43,990 --> 00:31:47,890
+على الشكل اللي عندنا هذا اتنين عندي كمان ده يقول
+
+297
+00:31:47,890 --> 00:31:53,430
+ال matrix اعطيتها الرمز اللي هو capital D بس عدد
+
+298
+00:31:53,430 --> 00:31:59,590
+عناصرها او نظامها N في Nيبقى هذه دياجونة بتختلف عن
+
+299
+00:31:59,590 --> 00:32:03,570
+مين؟ عن اللي فوق يبقى عدد الصفوف يساوي عدد الأعمدة
+
+300
+00:32:03,570 --> 00:32:06,230
+في الأولى والتاني عدد الصفوف يساوي عدد الأعمدة في
+
+301
+00:32:06,230 --> 00:32:09,730
+التاني لكن عدد الصفوف في الأولى ليس كعدد الصفوف في
+
+302
+00:32:09,730 --> 00:32:15,450
+الثانية ولا حتى مين الأعمدة then لو ضربت C في A
+
+303
+00:32:15,450 --> 00:32:19,410
+يبقى بدي أضرب المصوفة اللي عندنا هذه في A بدي أشوف
+
+304
+00:32:19,410 --> 00:32:24,760
+بنفع تم عملية الضرب ولا لأيبقى انا عندي هذا ميم
+
+305
+00:32:24,760 --> 00:32:32,560
+اللي هو ال a نظامها m في m و هذه نظامها m في m
+
+306
+00:32:32,560 --> 00:32:38,300
+فبقول لي ca بدي اضرب ال c في a و بدي اضرب الصف
+
+307
+00:32:38,300 --> 00:32:44,480
+الأول في العمود الأول طلعيل الصف الأول في العمود
+
+308
+00:32:44,480 --> 00:32:54,060
+الأوليبقى a11 في c11 بأصفر
+
+309
+00:32:54,060 --> 00:33:00,840
+c1 a11 الصف الأول في العمودي الثاني صف الأول في
+
+310
+00:33:00,840 --> 00:33:06,380
+العمودي الثاني يبقى الأولاني ب0 وهذا يصبح c1 a11
+
+311
+00:33:07,910 --> 00:33:13,990
+يبقى هنا a الصف الأول في العمودي الثاني a11 في
+
+312
+00:33:13,990 --> 00:33:18,750
+zero بتروح a12
+
+313
+00:33:18,750 --> 00:33:25,090
+في c2 بصير a12 في a12
+
+314
+00:33:27,630 --> 00:33:32,230
+خلّي بالك هنا تاني تاني تاني يبقى انا انا بدي اضرب
+
+315
+00:33:32,230 --> 00:33:37,870
+C في A مش ال A في ال C يبقى انا بدي اضرب C في A و
+
+316
+00:33:37,870 --> 00:33:41,710
+ليس A في C يبقى باجي بقول الصف الأول في العملي
+
+317
+00:33:41,710 --> 00:33:48,490
+بصير C1 A11 هايوالصف الأول في العمود الثاني يبقى
+
+318
+00:33:48,490 --> 00:33:55,250
+C1A12 يبقى C1 يبقى المقصود في هذه الحالة أن العنصر
+
+319
+00:33:55,250 --> 00:34:01,050
+C1 بدي أضرب في جميع عناصر الصف الأول C1 C1 C1
+
+320
+00:34:01,050 --> 00:34:07,170
+والباقي العناصر كما هي C2 بضربه في الصف C3 في الصف
+
+321
+00:34:07,170 --> 00:34:15,560
+CM في الصفبالمثل لو جيت لمن لل A في D اللحظة ان ال
+
+322
+00:34:15,560 --> 00:34:20,620
+diagonal ضربت من جهة الشمال في A هنا ال diagonal
+
+323
+00:34:20,620 --> 00:34:26,160
+ضربت من جهة اليمين في A ايش الفرق ما بين الاتنين
+
+324
+00:34:26,160 --> 00:34:32,440
+الفرق في الحالة لقول ان C1 ضربت في الصفهنا D1 ضربت
+
+325
+00:34:32,440 --> 00:34:36,280
+في من؟ في العمود يبقى هذا الفرق ما بين الأتنين
+
+326
+00:34:36,280 --> 00:34:40,340
+والباقي كما هو تمام يبقى هذا الفرق ما بين الأتنين
+
+327
+00:34:40,340 --> 00:34:44,360
+ناخد كرولر كرولر يعني نتيجة على مين على هذه
+
+328
+00:34:44,360 --> 00:34:48,840
+النظرية بقول افترض ال A اللي هي M by N matrix اللي
+
+329
+00:34:48,840 --> 00:34:54,640
+فوق and ال C ال diagonal matrix نظامها M في M يعني
+
+330
+00:34:54,640 --> 00:34:59,960
+مين هي اللي فوق M في M تماماعند دي ال diagonal
+
+331
+00:34:59,960 --> 00:35:04,260
+matrix نظامها N في N اللي اللي فوق بالضبط تماما
+
+332
+00:35:04,260 --> 00:35:11,440
+then لو ضربت C في A كإني ضرب ال constant C في main
+
+333
+00:35:11,440 --> 00:35:17,920
+في المصوف A يعني بدل ما كنت أقول C1 وC2 وCM بدي
+
+334
+00:35:17,920 --> 00:35:19,400
+أخليها scalar matrix
+
+335
+00:35:22,290 --> 00:35:26,830
+متساويات تمام يبقى ايش اللي بده يصير؟ بده يصير
+
+336
+00:35:26,830 --> 00:35:34,230
+كأنه ضربت ال C لككنستان في جميع عناصر المصر فليش؟
+
+337
+00:35:34,230 --> 00:35:40,830
+لأن هذا اللي بده يصير هذي C C C C C كله C تمام؟
+
+338
+00:35:40,830 --> 00:35:45,250
+يبقى كأنه هضربها C في ايه؟بالمثل في حالة تانية
+
+339
+00:35:45,250 --> 00:35:49,850
+كأنه ضارب D في مين في المصوف A وكأنه هذه حالة خاصة
+
+340
+00:35:49,850 --> 00:35:53,930
+من مين من الحالة اللي فوق المرة الجاية بناخد أمثلة
+
+341
+00:35:53,930 --> 00:35:57,690
+على النظرية والنتائج اللي عليها ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d79cd91d796ad1155aa041d80fa821dd637cedc6
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0.srt
@@ -0,0 +1,1749 @@
+1
+00:00:20,670 --> 00:00:24,430
+بسم الله الرحمن الرحيم نعود إلى الـ section اللي
+
+2
+00:00:24,430 --> 00:00:29,070
+بدأناها في الفترة الصباحية وهو حل المعادلة 
+
+3
+00:00:29,070 --> 00:00:34,510
+التفاضلية إذا كان المعادلة إذا كانت مجموعة الحلول
+
+4
+00:00:34,510 --> 00:00:39,030
+للمعادلة المميزة للمعادلة التفاضلية هي عبارة عن
+
+5
+00:00:39,030 --> 00:00:45,640
+جذور حقيقية ومختلفة إذا كان R1 لا يساوي R2 لا يساوي
+
+6
+00:00:45,640 --> 00:00:51,860
+R3 لا يساوي RN إذا مجموعة الحلول على شكل Y ستكون 
+
+7
+00:00:51,860 --> 00:00:55,740
+C1E 
+
+8
+00:00:55,740 --> 00:01:06,480
+أس R1X  زي C2E أس R2X زي CNE أس RNX يبقى ناخد أول
+
+9
+00:01:06,480 --> 00:01:10,680
+مثال على ذلك بيقول حل المعادلة التفاضلية y double
+
+10
+00:01:10,680 --> 00:01:16,300
+prime ناقص خمسة y prime زائد ستة y equal to zero
+
+11
+00:01:16,300 --> 00:01:20,420
+يبقى التكتيك اللي هتبقى عند حل السؤال هتبقى عند حل
+
+12
+00:01:20,420 --> 00:01:27,870
+أي سؤال آخر بعد ذلك بداجي أقول له let الـ Y تساوي E
+
+13
+00:01:27,870 --> 00:01:38,730
+أُس RX بـ A solution of the differential equation
+
+14
+00:01:38,730 --> 00:01:44,050
+star سميلي هذه المعادلة الأصلية اللي هي main star
+
+15
+00:01:46,480 --> 00:01:53,800
+بالزمن المشتقة الأولى Y' يساوي R في E أُس RX و
+
+16
+00:01:53,800 --> 00:02:00,840
+بالزمن الـ Y'' بدي أشتق هذه كمان مرة يبقى R تربيع 
+
+17
+00:02:00,840 --> 00:02:05,020
+في E أُس RX قلنا الصبح أن مشتقة الـ exponential
+
+18
+00:02:05,020 --> 00:02:11,080
+بالـ exponential itself مضروب في مشتقة الأُس طبعا
+
+19
+00:02:11,080 --> 00:02:15,460
+الـR عندنا هنا مقدار ثابت يبقى المشتقات كما تراها
+
+20
+00:02:15,640 --> 00:02:21,100
+الآن بروح أعوض في المعادلة A star يبقى باجي بقول
+
+21
+00:02:21,100 --> 00:02:27,000
+المعادلة A star يلي Y'' ناقص خمسة Y'
+
+22
+00:02:27,000 --> 00:02:33,680
+زائد ستة Y يساوي Y'' يلي الـ R تربيع في E أس
+
+23
+00:02:33,680 --> 00:02:42,550
+RX ناقص خمسة الـ Y' يلي هو R في E أس RX زائد 
+
+24
+00:02:42,550 --> 00:02:49,170
+ستة في الـ Y الـ Y اللي هي E أُس RX كل هذا الكلام
+
+25
+00:02:49,170 --> 00:02:58,310
+بيساوي Zero الآن اقسم الطرفين على E أُس RX طبعا هذا
+
+26
+00:02:58,310 --> 00:03:04,470
+الكلام ممكن لأن E أُس RX لا يمكن أن تساوي Zero في أي
+
+27
+00:03:04,470 --> 00:03:10,790
+يوم من الأيام إذا بقدر اقسم عليها بدون أي مشكلة لو 
+
+28
+00:03:10,790 --> 00:03:16,470
+قسمت على E أُس RX المعادلة هذه تأخذ الشكل التالي R
+
+29
+00:03:16,470 --> 00:03:23,250
+تربيع ناقص خمسة R زائد ستة بده يساوي مين Zero يبقى
+
+30
+00:03:23,250 --> 00:03:29,650
+هذه يا بنات اللي بسميها الـ characteristic equation
+
+31
+00:03:29,650 --> 00:03:37,850
+of the differential equation Star يبقى هذه
+
+32
+00:03:37,850 --> 00:03:43,130
+المعادلة المميزة أو المعادلة المساعدة للمعادلة مين 
+
+33
+00:03:43,130 --> 00:03:48,230
+Star هذه المقدار زي ما تشوفين من الدرجة الثانية
+
+34
+00:03:48,230 --> 00:03:53,450
+بتروح أحللها و أحسب قدر قيمة a يبقى لو روحنا
+
+35
+00:03:53,450 --> 00:04:00,450
+حللناها كأقواس يساوي zero هنا R هنا R الـ 6 عبارة
+
+36
+00:04:00,450 --> 00:04:07,410
+عن 2 في 3 والإشارتين بالناقص يبقى بناء عليه الـ R
+
+37
+00:04:07,410 --> 00:04:16,320
+هتساوي 2 أو R1 تساوي 2 وR2 تساوي 3 يبقى الجذور 
+
+38
+00:04:16,320 --> 00:04:24,700
+حقيقية ومختلفة مدام حقيقية ومختلفة إذا بدي أشيل R
+
+39
+00:04:24,700 --> 00:04:29,860
+هذه و أحط بدلها مرة اتنين و مرة ثلاث إذا أحط بدلها
+
+40
+00:04:29,860 --> 00:04:40,600
+ثلاثة إذا the solutions of the differential
+
+41
+00:04:40,600 --> 00:04:54,160
+equation star are اللي هو Y1 بدي أساوي E أُس 2X و Y2
+
+42
+00:04:54,160 --> 00:05:00,930
+بدي أساوي E أُس 3X هو لم يقل الحل الأول و الحل
+
+43
+00:05:00,930 --> 00:05:05,970
+الثاني قال هات لي مين الـ general solution يبقى و حل
+
+44
+00:05:05,970 --> 00:05:09,830
+المعادلة هذه فبروح بقوله طبعا اثنين هدول الـ
+
+45
+00:05:09,830 --> 00:05:13,990
+exponential are linearly independent مش عاجزة
+
+46
+00:05:13,990 --> 00:05:18,610
+اثنين ثلاثة أربعة إن جد ما يكون عددهم أثبتنا سابقا
+
+47
+00:05:18,610 --> 00:05:21,530
+في section ثلاثة أربعة أن هدول are linearly
+
+48
+00:05:21,530 --> 00:05:27,490
+independent إذا بروح على شكل الحل فبروح بقوله ذا
+
+49
+00:05:27,790 --> 00:05:39,410
+General solution of the differential equation when
+
+50
+00:05:39,410 --> 00:05:52,260
+is in the form على الشكل التالي Y يساوي C1 Y1 زي C2
+
+51
+00:05:52,260 --> 00:06:04,180
+Y2 هذا معناه أن Y يساوي C1 Y1 هي طلعناها E2X C2E3X
+
+52
+00:06:04,180 --> 00:06:09,760
+يبقى هذا حل المعادلة التفاضلية star اللي عندنا فوق
+
+53
+00:06:09,760 --> 00:06:11,380
+نعم
+
+54
+00:06:15,160 --> 00:06:22,380
+آه في أي تساؤل؟ طيب نزل الآن المثال رقم 2 يبقى
+
+55
+00:06:22,380 --> 00:06:29,960
+المثال رقم 1 خمسة من الكتاب example 2 السؤال رقم
+
+56
+00:06:29,960 --> 00:06:35,940
+عشرة من الكتاب بقول find the general solution find
+
+57
+00:06:35,940 --> 00:06:45,700
+the general solution find the general solution of
+
+58
+00:06:45,700 --> 00:06:54,520
+the differential equation للمعادلة التفاضلية y
+
+59
+00:06:54,520 --> 00:07:01,140
+triple prime ناقص أربعة y prime بده يساوي zero
+
+60
+00:07:01,140 --> 00:07:05,260
+و هذا اللي يبدأ يسميها المعادلة رقم star
+
+61
+00:07:09,790 --> 00:07:15,310
+إذا تكتيك الحل نفس التكتيك اللي اتبعته هنا حرفيا
+
+62
+00:07:15,310 --> 00:07:21,950
+يبقى باجي بقوله افترض أن Y بيبقى يساوي E و أس RX
+
+63
+00:07:21,950 --> 00:07:32,610
+بيه solution of the differential equation a star
+
+64
+00:07:35,780 --> 00:07:39,180
+يستخدم المشتقة الأولى والثانية والثالثة يستخدم الـ
+
+65
+00:07:39,180 --> 00:07:44,380
+Y' يستخدم الـ R يستخدم الـ X يستخدم الـ X يستخدم
+
+66
+00:07:44,380 --> 00:07:46,580
+الـ Y'' يستخدم الـ Y يستخدم الـ Y'' يستخدم الـ X
+
+67
+00:07:46,580 --> 00:07:48,240
+يستخدم الـ Y يستخدم الـ Y'' يستخدم الـ X يستخدم الـ
+
+68
+00:07:48,240 --> 00:07:49,780
+Y يستخدم الـ Y'' يستخدم الـ X يستخدم الـ Y يستخدم
+
+69
+00:07:49,780 --> 00:07:50,400
+الـ Y'' يستخدم الـ X يستخدم الـ Y يستخدم الـ Y
+
+70
+00:07:50,400 --> 00:07:51,040
+يستخدم الـ Y يستخدم الـ Y يستخدم الـ Y يستخدم الـ
+
+71
+00:07:51,040 --> 00:07:51,840
+Y يستخدم الـ Y يستخدم الـ Y يستخدم الـ Y يستخدم
+
+72
+00:07:51,840 --> 00:07:52,400
+الـ Y يستخدم الـ Y يستخدم الـ Y
+
+73
+00:08:11,240 --> 00:08:12,640
+Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''Y'''
+
+74
+00:08:12,950 --> 00:08:16,770
+بتاخد المعلومات اللي عندها دي و روح اعوض وين في
+
+75
+00:08:16,770 --> 00:08:21,250
+المعادلة star يبقى لو روحت عوضت في المعادلة star
+
+76
+00:08:21,250 --> 00:08:28,170
+بتصير المعادلة على الشكل التالي اللي هي R تكعيب في
+
+77
+00:08:28,170 --> 00:08:36,450
+E أُس RX ناقص أربعة Y' لـ R في E أُس RX بدي 
+
+78
+00:08:36,450 --> 00:08:43,020
+أساوي كده؟ بدي أساوي زيرو لو رحنا قسمنا على E أُس R
+
+79
+00:08:43,020 --> 00:08:49,100
+X بصير R تكعيب ناقص أربعة R بديه يساوي مين؟ بديه 
+
+80
+00:08:49,100 --> 00:08:54,870
+يساوي Zero الآن هذه معادلة من الدرجة الثالثة لكن
+
+81
+00:08:54,870 --> 00:09:01,070
+الحمد لله سهلة حلها ما هو الصعب يبقى لو روحت أخدت
+
+82
+00:09:01,070 --> 00:09:05,970
+الـ R عامل مشترك بظل R تربيع ناقص أربعة بده يساوي
+
+83
+00:09:05,970 --> 00:09:10,990
+Zero المقدار بين القوسين هو عبارة عن فرق بين
+
+84
+00:09:10,990 --> 00:09:17,430
+المربعين بحلله R ناقص اثنين في R زائد اثنين يساوي
+
+85
+00:09:17,430 --> 00:09:23,610
+Zero هذا بيعطيني أن الـ R تساوي زيرو و R تساوي
+
+86
+00:09:23,610 --> 00:09:30,590
+اثنين والـ R تساوي سالب اثنين يبقى هدول هم الجذور
+
+87
+00:09:30,590 --> 00:09:35,290
+تابعة من الـ characteristic equation اللي هاد اللي
+
+88
+00:09:35,290 --> 00:09:41,210
+وصلنا لها ها هي من هي الـ characteristic 
+
+89
+00:09:41,210 --> 00:09:50,790
+equation of the Differential Equation Star يبقى هذه 
+
+90
+00:09:50,790 --> 00:09:55,210
+المعادلة المميزة للمعادلة Star رحنا حللناها و
+
+91
+00:09:55,210 --> 00:10:00,410
+طلعنا الجذور فالجذور كان R بـ Zero و R بـ اثنين و R
+
+92
+00:10:00,410 --> 00:10:07,170
+بـ سالب اثنين إذا في عندي ثلاثة حلول الأولاني Y
+
+93
+00:10:07,170 --> 00:10:15,530
+تساوي E أُس Zero X يبقى هذا واحد والثاني E أُس
+
+94
+00:10:15,530 --> 00:10:21,330
+اثنين X والثالث E أُس سالب اثنين X بدي أجيب الـ 
+
+95
+00:10:21,330 --> 00:10:24,230
+general solution يبقى constant في الأول و constant 
+
+96
+00:10:24,230 --> 00:10:27,230
+في الثاني يبقى بدل ما أقول إذا اللي حلو كله لأ بدي
+
+97
+00:10:27,230 --> 00:10:31,950
+أحط الـ general solution دوري تمام إذا بجيب أقول لكم
+
+98
+00:10:31,950 --> 00:10:37,870
+هنا the general solution
+
+99
+00:10:39,810 --> 00:10:53,670
+of the differential equation star is y تساوي c1 في
+
+100
+00:10:53,670 --> 00:11:01,990
+e أُس 0 نكتب بالكامل بالتفصيل e أُس 0 زائد c2 في e
+
+101
+00:11:01,990 --> 00:11:10,690
+أُس 2x زائد c3 في e أُس سالب 2x يبقى أصبح شكل الحل
+
+102
+00:11:10,690 --> 00:11:16,270
+Y تساوي C1 C2E2X
+
+103
+00:11:16,270 --> 00:11:20,670
+C3E2X
+
+104
+00:11:20,670 --> 00:11:26,830
+هذا الـ general solution لمن؟ للمعادلة رقم star
+
+105
+00:11:26,830 --> 00:11:35,710
+اللي عندنا أحد فيكم بتسأل أي سؤال هنا؟ آه أظن واضح
+
+106
+00:11:35,710 --> 00:11:41,230
+وضوح الشمس في ربيع النهار مش فيه مشكلة طب المثال 
+
+107
+00:11:41,230 --> 00:11:46,230
+الذي يليه مثال
+
+108
+00:11:46,230 --> 00:11:55,590
+ثلاثة find the general solution the general
+
+109
+00:11:55,590 --> 00:11:57,410
+solution
+
+110
+00:12:01,330 --> 00:12:11,710
+of the differential equation Y to
+
+111
+00:12:11,710 --> 00:12:13,810
+the derivative IV
+
+112
+00:12:16,630 --> 00:12:24,010
+y to the derivative of 3 ناقص 7 y double prime
+
+113
+00:12:24,010 --> 00:12:36,310
+ناقص y prime زائد 6y تساوي من؟ تساوي 0 و هذه اللي
+
+114
+00:12:36,310 --> 00:12:39,750
+هنسميها المعادلة رقم star
+
+115
+00:13:00,800 --> 00:13:06,520
+خلّيني أذكر بس بالرموز الـ I V و V وما إلى ذلك عندك 
+
+116
+00:13:06,520 --> 00:13:14,700
+I يعني رقم واحد double I رقم اثنين Triple I رقم 
+
+117
+00:13:14,700 --> 00:13:24,540
+ثلاثة IV رقم أربعة V خمسة VI ستة V double I ليه 
+
+118
+00:13:24,540 --> 00:13:28,140
+السبعة وما إلى ذلك إذا مر علينا أكثر من هيك 
+
+119
+00:13:28,140 --> 00:13:34,030
+بنقول لكم نخلينا على جد هيك اليوم طيب يبقى بقول هات 
+
+120
+00:13:34,030 --> 00:13:37,110
+للـ general solution لهذه المعادلة إذا بدي أبدأ 
+
+121
+00:13:37,110 --> 00:13:42,810
+بنفس التكتيك اللي اتبعته في المثالين السابقين يبقى 
+
+122
+00:13:42,810 --> 00:13:54,870
+بروح أقول هنا let Y تساوي E أُس RX بـ Solution of 
+
+123
+00:13:54,870 --> 00:14:01,390
+the Differential Equation Star
+
+124
+00:14:07,440 --> 00:14:17,060
+هي R E أُس R X Y' R تربيع E أُس R X Y'''
+
+125
+00:14:17,060 --> 00:14:23,360
+الـ Y to the derivative of 3 يبقى R تكعيب E أُس R 
+
+126
+00:14:23,360 --> 00:14:29,000
+X Y to the derivative of IV المشتقة الرابعة بيكون 
+
+127
+00:14:29,000 --> 00:14:33,500
+R أُس 4R X
+
+128
+00:14:36,100 --> 00:14:40,000
+لما تأخذ المعلومة اللي حصلت عليها و روح اعوض في 
+
+129
+00:14:40,000 --> 00:14:45,200
+المعادلة رقم star يبقى رقم star بتقول لي why to 
+
+130
+00:14:45,200 --> 00:14:54,130
+the derivative IV زائد y triple prime ناقص سبعة y
+
+131
+00:14:54,130 --> 00:15:02,630
+double prime ناقص y prime زائد ستة y يساوي بدا
+
+132
+00:15:02,630 --> 00:15:06,890
+أشيل كل term من الـ termات الخمسة اللي عندنا و أحط
+
+133
+00:15:06,890 --> 00:15:14,410
+القيمة بتاعتها يبقى المشتقة الأولى لـ R أس أربعة E
+
+134
+00:15:14,410 --> 00:15:24,070
+أس R X اللي بعده R تكعيب E أس R X اللي بعده ناقص
+
+135
+00:15:24,070 --> 00:15:32,970
+سبعة R تربيع E أُس RX - R E أُس RX 
+
+136
+00:15:32,970 --> 00:15:37,090
++6 E أُس RX
+
+137
+00:15:40,220 --> 00:15:45,080
+لو قسمنا طرفي المعادلة على E أس RX بنحصل على ما 
+
+138
+00:15:45,080 --> 00:15:53,460
+يأتي يبقى هي R أس أربعة زائد R تكعيب ناقص سبعة R 
+
+139
+00:15:53,460 --> 00:16:01,300
+تربيع ناقص R زائد ستة كله بده يساوي جداش؟ بده
+
+140
+00:16:01,300 --> 00:16:02,060
+يساوي زيرو
+
+141
+00:16:05,640 --> 00:16:10,180
+إذا بدنا نجي للمعادلة اللي عندنا هذا بدنا نحاول
+
+142
+00:16:10,180 --> 00:16:15,600
+نحلها آه ده مش زي المعادلتين اللي فاتوا تحلل وامشي 
+
+143
+00:16:15,600 --> 00:16:20,660
+بكل بساطة هنا بدنا نشغل عقلنا ممكن نشغل عقلنا 
+
+144
+00:16:20,660 --> 00:16:26,950
+بأكثر من طريقة طريقة أولى مثلا نشوف قواسم الستة
+
+145
+00:16:26,950 --> 00:16:31,970
+ونشوف الرقم من قواسم الستة الذي يحقق هذه المعادلة
+
+146
+00:16:31,970 --> 00:16:36,910
+وبالتالي نقسم على هذا الـ factor ونزل الدرجة من 
+
+147
+00:16:36,910 --> 00:16:41,510
+الدرجة الرابعة إلى الدرجة الثالثة وبعدين يمكن الله 
+
+148
+00:16:41,510 --> 00:16:46,530
+يحلها ويمكن نضطر نشوف كمان factor ثاني ينزل الدرجة
+
+149
+00:16:46,530 --> 00:16:51,750
+الثالثة إلى الدرجة الثانية وجهة نظر وجهة نظر أخرى
+
+150
+00:16:51,750 --> 00:16:56,370
+بيقول لأ خد بعض العناصر مع بعضهم يعني اعمل هذه 
+
+151
+00:16:56,370 --> 00:17:01,090
+المعادلة على شكل مجمعتهم وخد عوامل مشتركة وحلل
+
+152
+00:17:01,090 --> 00:17:06,970
+لعله يطلع عنصر مشترك ما بين الاثنين وبالتالي تنزل
+
+153
+00:17:06,970 --> 00:17:12,510
+الرتبة من الدرجة الرابعة إلى الدرجة الثالثة و
+
+154
+00:17:12,510 --> 00:17:16,790
+بعدين الله يحلها إن شاء الله بقول يبقى هي عندي
+
+155
+00:17:16,790 --> 00:17:22,030
+طريقتين للحل وشوف اللي أنسب بالنسبة لك واشتغل به
+
+156
+00:17:22,030 --> 00:17:25,270
+احنا أخذنا السؤال المرة اللي فاتت وروحنا شوفنا
+
+157
+00:17:25,270 --> 00:17:30,790
+القواسم تمام لما بدي أجرب طريقة ثانية بدي أخد بعض
+
+158
+00:17:30,790 --> 00:17:35,470
+العناصر مع بعضها و الباقي مع بعض الآخر يبقى يا 
+
+159
+00:17:35,470 --> 00:17:41,210
+بروح آخذ R أربعة و R تربيع و الـ constant مع بعض يا 
+
+160
+00:17:41,210 --> 00:17:48,390
+إما بروح باخد R تكعيب و R كمان مع بعض مجمعتين هذه
+
+161
+00:17:48,390 --> 00:17:53,950
+والله هذه سيان الاثنين are the same مرة ثانية بقول
+
+162
+00:17:53,950 --> 00:17:58,570
+R أس أربعة و R تربيع و كونها set up تعملي معادلة من
+
+163
+00:17:58,570 --> 00:18:02,030
+الدرجة الرابعة بس بقدر أحلها هلأ وسين يمكن نقدر
+
+164
+00:18:02,030 --> 00:18:05,710
+وممكن ما نقدرش الله أعلم وبعدها كده الـ R تكعيب و الـ 
+
+165
+00:18:05,710 --> 00:18:10,010
+R في بينهم عامل مشترك وبالتالي يمكن ألاقي العامل
+
+166
+00:18:10,010 --> 00:18:15,900
+مشترك مع الثانية يعني قدامي وبدأ للطريقة قداش أو
+
+167
+00:18:15,900 --> 00:18:20,660
+آخذ أول اثنين مع بعض وآخر ثلاثة مع بعض
+
+168
+00:18:44,710 --> 00:18:51,010
+بمجرد النظر لو أخذت R أربعة و سبعة R تربيع زائد 
+
+169
+00:18:51,01
+
+201
+00:21:41,660 --> 00:21:46,560
+المعادلة هذه اللي طلعتها هي مين هي المعادلة
+
+202
+00:21:46,560 --> 00:21:53,320
+المميزة يبقى هذه the characteristic equation of
+
+203
+00:21:53,320 --> 00:21:59,280
+the equation star الأصلية اللي عندنا هذه المعادلة راحت
+
+204
+00:21:59,280 --> 00:22:02,620
+حطيتها على الشكل هذا يبقى الـ characteristic
+
+205
+00:22:02,620 --> 00:22:06,680
+equation حطيتها على الشكل اللي عندنا هذا وبالتالي
+
+206
+00:22:06,680 --> 00:22:10,880
+صارت الحلول بالشكل اللي عندنا هذا يبقى من هنا ليه
+
+207
+00:22:10,880 --> 00:22:17,020
+بقدر أعرف شكل ال general solution بروح بقوله هنا
+
+208
+00:22:17,020 --> 00:22:29,010
+the general solution of the differential equation
+
+209
+00:22:29,010 --> 00:22:35,210
+star is y تساوي C1
+
+210
+00:22:51,850 --> 00:22:59,850
+يبقى هذا الشكل الحل العام للمعادلة طيب في مشكلة لو
+
+211
+00:22:59,850 --> 00:23:08,890
+جيت قلت C1 E أس 6 X زائد C2 E أس 2 X زائد C3 E أس سالب X
+
+212
+00:23:08,890 --> 00:23:14,610
+زائد C4 E أس سالب 3 X ولا حاجة يبقى الترتيب ليس
+
+213
+00:23:14,610 --> 00:23:19,470
+بالضرورة يكون مرتبات بالحرف الواحد المهم constant
+
+214
+00:23:19,470 --> 00:23:23,070
+في الحل الأول زائد constant في الحل الثاني زائد
+
+215
+00:23:23,070 --> 00:23:25,790
+constant في الحل الثالث زائد constant في الحل
+
+216
+00:23:25,790 --> 00:23:31,590
+الرابع إذا يا بنت من حد مجيب المعادلة المميزة بدي
+
+217
+00:23:31,590 --> 00:23:37,110
+أروح أحلها بأي طريقة إن كانت من طرق التحليل التي
+
+218
+00:23:37,110 --> 00:23:43,890
+تعلمناها ابتداءً من الصف السابع وحتى الصف التاسع مش
+
+219
+00:23:43,890 --> 00:23:48,610
+هذه الفترة اللي تعلمنا فيها تحليل المعادلات تمام
+
+220
+00:23:48,940 --> 00:23:54,820
+يبقى حللنا إذا حللنا بكون جبت اللي هو القيم التي
+
+221
+00:23:54,820 --> 00:23:59,200
+تحقق المعادلة اللي عندي من الدرجة الثانية أو
+
+222
+00:23:59,200 --> 00:24:03,500
+الثالثة أو الرابعة أو الخامسة أو الدرجة النونية
+
+223
+00:24:03,500 --> 00:24:08,620
+وبالتالي بكون جبت قيم r ومن ثم بكون عرفت شكل ال
+
+224
+00:24:08,620 --> 00:24:15,020
+general solution إذا كان these roots are real and
+
+225
+00:24:15,020 --> 00:24:18,200
+different ولا واحد زي الثاني
+
+226
+00:24:22,580 --> 00:24:29,000
+لحد هنا stop انتهى ال section وإلى يكون أرقام
+
+227
+00:24:29,000 --> 00:24:36,960
+المسائل يبقى exercises خمسة اثنين المسائل التالية
+
+228
+00:24:36,960 --> 00:24:42,260
+السؤال الأول والمسائل من خمسة لغاية عشرة
+
+229
+00:24:47,680 --> 00:25:10,200
+ننتقل الآن إلى الحالة الثانية الحالة
+
+230
+00:25:10,200 --> 00:25:13,440
+الثانية بتاخد لو كانت ال roots are complex
+
+231
+00:25:13,440 --> 00:25:21,460
+conjugate يبقى section خمسة ثلاثة بيقول ال complex
+
+232
+00:25:21,460 --> 00:25:24,820
+solutions
+
+233
+00:25:30,090 --> 00:25:34,810
+قبل ما ندخل في هذه ال solutions نسأل السؤال التالي
+
+234
+00:25:34,810 --> 00:25:41,910
+حد فيكم درس مساق complex analysis؟ طبعا ولا
+
+235
+00:25:41,910 --> 00:25:49,490
+واحدة تمام لذلك بدي أذكر ببعض المعلومات عن اللي هو
+
+236
+00:25:49,490 --> 00:25:54,310
+ال complex variable اللي طبعا أخذناها في الثانوية
+
+237
+00:25:54,760 --> 00:25:58,320
+لكن إحنا بدنا نذكره بالتذكير لإنه بدي أعتبرنا
+
+238
+00:25:58,320 --> 00:26:02,700
+الثانوية تناسينا أو ما أخذناش أو أو الآخرين بنحط
+
+239
+00:26:02,700 --> 00:26:06,580
+المعلومة الأساسية اللي بتلزمنا في هذا section قبل
+
+240
+00:26:06,580 --> 00:26:11,920
+أن نبدأ نشتغل معادلات تفاضلية إذا باقي محاضرتنا
+
+241
+00:26:11,920 --> 00:26:15,740
+هذه قبل ما نخش في الحلول لما يكونوا complex بدنا
+
+242
+00:26:15,740 --> 00:26:20,860
+نعطي بعض المعلومات عن ال complex numbers يبقى بدايتي
+
+243
+00:26:20,860 --> 00:26:25,220
+أكتب some properties about the complex numbers
+
+244
+00:26:25,220 --> 00:26:31,620
+يبقى بدايتي أقول هنا some basic
+
+245
+00:26:31,620 --> 00:26:35,200
+properties
+
+246
+00:26:35,200 --> 00:26:44,740
+بعض الخواص الأساسية of complex numbers
+
+247
+00:26:48,350 --> 00:26:52,470
+يبقى بعض الخواص للأعداد التخيولية ال imaginary
+
+248
+00:26:52,470 --> 00:26:57,450
+numbers أو اللي بنيجي نسميها الأعداد المركبة مركبة
+
+249
+00:26:57,450 --> 00:27:04,610
+ليه؟ لأن العدد التخيولي مكون من جزء حقيقي وجزء تخيولي يبقى أول
+
+250
+00:27:04,610 --> 00:27:10,690
+خاصية بتقول any complex
+
+251
+00:27:10,690 --> 00:27:24,810
+number أنت تديله رمز z is written as بكتبه
+
+252
+00:27:24,810 --> 00:27:36,410
+على الشكل التالي z يساوي a زائد i b where حيث ال a
+
+253
+00:27:36,410 --> 00:27:49,730
+is called the real part الجزء الحقيقي من العدد
+
+254
+00:27:49,730 --> 00:28:00,150
+التخيلي and b is called the imaginary part
+
+255
+00:28:00,150 --> 00:28:08,590
+الجزء
+
+256
+00:28:08,590 --> 00:28:12,930
+التخيلي and
+
+257
+00:28:13,880 --> 00:28:19,260
+وفي نفس الوقت الـ i تساوي الجذر التربيعي لسالب
+
+258
+00:28:19,260 --> 00:28:37,720
+واحد  Number two any real number a is a complex number
+
+259
+00:28:37,720 --> 00:28:38,580
+since
+
+260
+00:28:45,420 --> 00:28:54,860
+الـ a بقدر أكتب a زائد صفر في ال i  نمرة
+
+261
+00:28:54,860 --> 00:29:01,240
+ثلاثة Two
+
+262
+00:29:01,240 --> 00:29:10,800
+complex numbers Two
+
+263
+00:29:10,800 --> 00:29:19,690
+complex numbers a زائد ib and
+
+264
+00:29:19,690 --> 00:29:31,710
+c زائد id are equal if
+
+265
+00:29:31,710 --> 00:29:40,550
+and only if ال a تساوي ال c and ال b تساوي ال d
+
+266
+00:29:43,250 --> 00:29:52,750
+نمرة أربعة a complex function
+
+267
+00:29:52,750 --> 00:30:04,030
+حديها الرمز w as a function of x is written as
+
+268
+00:30:04,030 --> 00:30:12,000
+مكتوبة على الشكل التالي ال w prime of x يساوي u
+
+269
+00:30:12,000 --> 00:30:23,480
+prime of x زائد i في v prime of x and hence ومن ثم
+
+270
+00:30:23,480 --> 00:30:34,460
+ال w prime of x يساوي u prime of x زائد i في v
+
+271
+00:30:34,460 --> 00:30:35,900
+prime of x
+
+272
+00:30:38,750 --> 00:30:44,730
+for example f
+
+273
+00:30:44,730 --> 00:30:59,130
+w of x بده يساوي e أس 2x زائد i ln 2x
+
+274
+00:30:59,130 --> 00:31:05,970
+ln
+
+275
+00:31:05,970 --> 00:31:07,670
+3x مثلا
+
+276
+00:31:11,860 --> 00:31:34,340
+w prime of x بده يساوي نمر
+
+277
+00:31:34,340 --> 00:31:35,200
+الخامسة
+
+278
+00:31:42,400 --> 00:31:49,780
+ف ال w of x بدي
+
+279
+00:31:49,780 --> 00:31:57,680
+يساوي ال u of x زائد i v of x is a complex
+
+280
+00:31:57,680 --> 00:31:58,560
+solution
+
+281
+00:32:06,600 --> 00:32:10,180
+complex solution of the homogeneous differential
+
+282
+00:32:10,180 --> 00:32:18,740
+equation of the homogeneous differential
+
+283
+00:32:18,740 --> 00:32:27,600
+equation homogeneous differential equation L of y
+
+284
+00:32:27,600 --> 00:32:36,340
+بده يساوي صفر then both then both real
+
+285
+00:32:39,090 --> 00:32:45,350
+and imaginary and
+
+286
+00:32:45,350 --> 00:32:56,410
+imaginary parts اللي هم مين ال u of x and ال v of
+
+287
+00:32:56,410 --> 00:33:04,810
+x and v of x are real solutions
+
+288
+00:33:06,240 --> 00:33:14,080
+are real solutions of the same equation of the
+
+289
+00:33:14,080 --> 00:33:26,740
+same equation L of y بدها تساوي صفر نمرة ستة ال
+
+290
+00:33:26,740 --> 00:33:27,820
+Euler's formula
+
+291
+00:33:34,650 --> 00:33:44,730
+ال Euler's formula ال exponential function
+
+292
+00:33:44,730 --> 00:33:55,770
+e أس i θ is written as is
+
+293
+00:33:55,770 --> 00:34:06,090
+written as نمرة e أس i θ  كوس θ زائد i
+
+294
+00:34:06,090 --> 00:34:17,710
+جيب الزاوية θ  b e أس ناقص i θ يساوي c
+
+295
+00:34:17,710 --> 00:34:30,930
+e أس x زائد i yبدو يساوي e أس x في e أس i y
+
+296
+00:34:30,930 --> 00:34:44,150
+يساوي e أس x فيه نمرة d ال
+
+297
+00:34:44,150 --> 00:34:59,900
+e أس i π يساوي نمرة e ال a أس i bx زائد a أس
+
+298
+00:34:59,900 --> 00:35:04,620
+ناقص i bx بده يساوي
+
+299
+00:35:30,960 --> 00:35:35,240
+يبقى المكتوب قدامك على السبورة هنا هي المعلومات
+
+300
+00:35:35,240 --> 00:35:42,400
+الأساسية التي ستلزمنا عند دراسة هذا ال section وهو
+
+301
+00:35:42,400 --> 00:35:47,240
+إذا الحلول كانت أو ال roots ل ال auxiliary
+
+302
+00:35:47,240 --> 00:35:51,060
+equation أو ل ال characteristic equation كانت
+
+303
+00:35:51,060 --> 00:35:55,000
+complex numbers وكل اثنين في حالة ال complex
+
+304
+00:35:55,000 --> 00:36:00,180
+يكونوا دائما أو أبدا are conjugate complex numbers
+
+305
+00:36:00,180 --> 00:36:07,720
+يعني اثنين بيكونوا مترافقين كما سنشير بعد قليل أو
+
+306
+00:36:07,720 --> 00:36:13,820
+العمود هذا انتهينا منه ونصف العمود اللي هناك يالا
+
+307
+00:36:13,820 --> 00:36:18,310
+حاولوا تخلصوا اللي يفيدكم مش هنبدأ نعيد الحديث في
+
+308
+00:36:18,310 --> 00:36:23,670
+هذا لأن هذا أساسيات يجب أن نعرفها أنها هتمر علينا
+
+309
+00:36:23,670 --> 00:36:40,830
+كثير خلال دراستنا لهذا ال section كله
+
+310
+00:36:40,830 --> 00:36:44,550
+تمام هنا؟ خذي يلا
+
+311
+00:37:00,310 --> 00:37:04,090
+طيب نجي الآن ل section خمسة ثلاثة اللي هو بيقول
+
+312
+00:37:04,090 --> 00:37:08,910
+complex solutions وذكر ببعض الأشياء البسيطة اللي
+
+313
+00:37:08,910 --> 00:37:13,330
+قلناها في محاضرات الصبح محاضرة الصبح بدينا
+
+314
+00:37:13,330 --> 00:37:19,590
+بالمعادلة التفاضلية لمعاملات كلها ثوابت
+
+315
+00:37:19,590 --> 00:37:24,230
+وقلنا صارت على صيغة a n y to the derivative of n
+
+316
+00:37:24,230 --> 00:37:29,710
+زائد a one y to the derivative of n minus one زائد
+
+317
+00:37:29,710 --> 00:37:33,230
+a two y to the derivative of n minus one زائد زائد
+
+318
+00:37:33,230 --> 00:37:37,090
+a n minus one في ال y prime زائد a n y يبدو
+
+319
+00:37:37,090 --> 00:37:40,710
+يساوي مين؟ يساوي صفر قلنا هذه homogeneous
+
+320
+00:37:40,710 --> 00:37:44,950
+differential equation ويمكن اختصارها على صيغة l of
+
+321
+00:37:44,950 --> 00:37:50,830
+y يساوي مين؟ يساوي صفر فرضنا أن لهذه المعادلة حل
+
+322
+00:37:50,830 --> 00:37:56,190
+هو y تساوي e أس rx طلعنا ال Characteristic
+
+323
+00:37:56,190 --> 00:38:01,350
+Equation لها نتيجة اللي فرضنا لهذا الحل فصارت
+
+324
+00:38:01,350 --> 00:38:05,810
+المعادلة المميزة على الصيغة a naught r to the
+
+325
+00:38:05,810 --> 00:38:11,090
+power n زائد a1 r to the power n minus 1 زائد زائد
+
+326
+00:38:11,090 --> 00:38:16,150
+a n minus 1 في r زائد a n بده يساوي مين؟ بده يساوي
+
+327
+00:38:16,150 --> 00:38:22,080
+صفر وقلنا المعادلة هذه إلها أحد ثلاثة احتمالات هذه
+
+328
+00:38:22,080 --> 00:38:27,440
+معادلة من الدرجة النونية لاحتمال الأول أن تكون كل
+
+329
+00:38:27,440 --> 00:38:34,500
+الحلول حقيقية ومختلفة لاحتمال الثاني أن تكون كل
+
+330
+00:38:34,500 --> 00:38:41,430
+الحلول حقيقية ومتساوية مكررة repeated لاحتمال
+
+331
+00:38:41,430 --> 00:38:46,090
+الثالث والأخير كل الحلول تبقى complex conjugate
+
+332
+00:38:46,090 --> 00:38:51,390
+يعني كل اثنين بيكونوا complex واثنين مرافقين
+
+333
+00:38:51,390 --> 00:38:55,730
+لبعضهم تماما وقلنا معنى المرافق أنه لو كان الحل
+
+334
+00:38:55,730 --> 00:39:01,490
+الأول أو الجذر الأول هو a زائد ib فإن الجذر الثاني
+
+335
+00:39:01,490 --> 00:39:07,630
+هو a ناقص ib هذا ما ذكرناه في محاضرة الصبح وروحنا
+
+336
+00:39:07,630 --> 00:39:12,670
+أخذنا الحالة الأولى لو كانت الجذور حقيقية ومختلفة
+
+337
+00:39:12,670 --> 00:39:18,690
+الآن بدنا نيجي لو كانت الجذور حقيقية ومركبة إذا
+
+338
+00:39:18,690 --> 00:39:24,090
+بدنا بعض المعلومات عن الأعداد المركبة مشان نقدر
+
+339
+00:39:24,090 --> 00:39:30,050
+نستخدم أي من هذه المعلومات متى لازمة الأمر فيها
+
+340
+00:39:30,050 --> 00:39:33,190
+المعلومات اللي قدامنا على اللوحة دي اللي بتلزمنا خلال
+
+341
+00:39:33,190 --> 00:39:37,690
+دراستنا لهذا ال section بتيجي المعلومة الأولى يبقى
+
+342
+00:39:37,690 --> 00:39:41,330
+يقولنا some basic properties of complex numbers
+
+343
+00:39:41,330 --> 00:39:47,110
+بيقول لي any complex number z is written as بكتبه
+
+344
+00:39:47,110 --> 00:39:52,910
+على شكل عددين مركبين واحد a والثاني ib يعني جزء
+
+345
+00:39:52,910 --> 00:39:58,250
+حقيقي وجزء تخيلي قد يكون أحدهما بالصفر ما عنديش
+
+346
+00:39:58,250 --> 00:40:01,950
+مشكلة، ممكن يكون ال a بالصفر ويبقى ال ib
+
+347
+00:40:01,950 --> 00:40:07,170
+هو العدد المركب، ممكن يطلع b بالصفر ويبقى عندي a
+
+348
+00:40:07,170 --> 00:40:11,070
+فقط، وبعد قليل هأقول لك أن ال a هذا كمان complex
+
+349
+00:40:11,070 --> 00:40:15,650
+number يبقى in general على وجه العموم الشكل ال
+
+350
+00:40:15,650 --> 00:40:20,970
+complex number بكون a زائد ib ال a وال b أعداد
+
+351
+00:40:20,970 --> 00:40:26,490
+حقيقية لكن ال a بسميه ال real part وال b بسميه ال
+
+352
+00:40:26,490 --> 00:40:30,170
+imaginary part اللي هو الجزء الحقيقي والجزء
+
+353
+00:40:30,170 --> 00:40:33,890
+التخيلي وال i عندنا اللي هو الجذر التربيعي ل
+
+354
+00:40:33,890 --> 00:40:40,420
+لسالب واحد النقطة الثانية أي عدد حقيقي هو عبارة عن
+
+355
+00:40:40,420 --> 00:40:45,500
+عدد تخيلي كافي يعني فمثلا لو قلت العدد ثلاثة بقدر
+
+356
+00:40:45,500 --> 00:40:51,440
+أقول ثلاثة يساوي ثلاثة زائد صفر في i ال i اللي هي
+
+357
+00:40:51,440 --> 00:40:54,880
+الجذر التربيعي ل سالب واحد يبقى صار موجود في الست
+
+358
+00:40:54,880 --> 00:41:00,630
+complex number ولا لا يبقى بناء عليه مجموعة الأعداد
+
+359
+00:41:00,630 --> 00:41:07,050
+الحقيقية هي جزء من مجموعة الأعداد التخيلية لكن
+
+360
+00:41:07,050 --> 00:41:15,270
+العكس ليس صحيحا يبقى ال r subset من c ال r مجموعة
+
+361
+00:41:15,270 --> 00:41:21,090
+الأعداد الحقيقية c مجموعة ال complex numbers ال r
+
+362
+00:41:21,090 --> 00:41:26,870
+subset من c يبقى أي عدد حقيقي هو عدد تخيلي لكن
+
+363
+00:41:26,870 --> 00:41:29,330
+العكس ليس صحيحا
+
+364
+00:41:40,470 --> 00:41:48,620
+النقطة الثالثة متى يتساوى العددان المركبان يعني
+
+365
+00:41:48,620 --> 00:41:58,360
+لو عندي z1 يساوي a زائد ib وz2 يساوي c زائد id z1
+
+366
+00:41:58,360 --> 00:42:03,820
+يساوي z2 إذا تحقق شرطان الجزء الحقيقي للعدد الأول
+
+367
+00:42:03,820 --> 00:42:07,340
+بيساوي الجزء الحقيقي للعدد الثاني والجزء التخيلي
+
+368
+00:42:07,340 --> 00:42:11,180
+للعدد الأول بيساوي الجزء التخيلي لمن؟ للعدد الثاني
+
+369
+00:42:11,280 --> 00:42:15,840
+إن حدث ذلك بقول اثنين are equal يبقى هنا two
+
+370
+00:42:15,840 --> 00:42:19,780
+complex numbers a زي عيبي و c زي عيبي are equal if
+
+371
+00:42:19,780 --> 00:42:23,660
+and only if ال a بدي يساوي ال c وال b بدي يساوي
+
+372
+00:42:23,660 --> 00:42:28,650
+ال d بالضبط تماما اختلف ولا واحد فيهم معاني
+
+373
+00:42:28,650 --> 00:42:31,610
+الثانية يعني لو اختلف الجزء الحقيقي عن الجزء
+
+374
+00:42:31,610 --> 00:42:36,250
+الحقيقي فبتصيروا ايه اعداد تخيل مثل ذلك لو قلت لك
+
+375
+00:42:36,250 --> 00:42:42,550
+واحد زائد اثنين i وهنا قلت لك ثلاثة زائد اثنين i
+
+376
+00:42:42,550 --> 00:42:46,930
+اختلف ولا لا اختلفوا يبقى هدول not equal وهكذا
+
+377
+00:42:46,930 --> 00:42:50,150
+طيب نجي للنقطة الرابعة النقطة الرابعة بيقول
+
+378
+00:42:50,150 --> 00:42:52,110
+Complex function
+
+379
+00:42:54,460 --> 00:42:59,600
+الرمز w of x تُكتب
+
+380
+00:42:59,600 --> 00:43:04,200
+عليها شكل جزء حقيقي كذلك وجزء تخيلي بس مش عدد،
+
+381
+00:43:04,200 --> 00:43:09,450
+دالة في x والثانية دالة في x دالة في x زائد دالة في
+
+382
+00:43:09,450 --> 00:43:14,470
+x مضروبة في العدد التخيلي i وبالتالي صارت complex
+
+383
+00:43:14,470 --> 00:4
+
+401
+00:44:51,920 --> 00:44:57,780
+جداش رقم أربعة وهكذا إذا لزم نشتق في يوم من
+
+402
+00:44:57,780 --> 00:45:03,310
+الأيام لأي complex function نعود للنقطة الخامسة
+
+403
+00:45:03,310 --> 00:45:06,210
+النقطة الخامسة اللي بيقول لو في عندي complex
+
+404
+00:45:06,210 --> 00:45:10,770
+function على الشكل اللي قدامنا هذا يبقى لو كان هذا
+
+405
+00:45:10,770 --> 00:45:15,770
+complex solution لمن؟ للـ homogeneous linear
+
+406
+00:45:15,770 --> 00:45:19,030
+differential equation تبعت الصبح اللي ذكرناها أول 
+
+407
+00:45:19,030 --> 00:45:23,430
+مدينة تحدد الـ L of I يساوي Zero يبقى عبارة عن
+
+408
+00:45:23,430 --> 00:45:28,690
+مشتقة من الرتبة دالة معدلة تفاضلية من الرتبة النونية
+
+409
+00:45:28,940 --> 00:45:34,140
+لو كان هذا حل معناته الجزء الحقيقي هو حل والجزء 
+
+410
+00:45:34,140 --> 00:45:39,600
+التخيلي هو حل ليش ناخذنا إذا عندي حل وعندي حل يبقى
+
+411
+00:45:39,600 --> 00:45:42,720
+الحل العام كونصان في الأول زائد كونصان في الثاني
+
+412
+00:45:42,720 --> 00:45:46,440
+فبعتبر كونصان الأول هو واحد صحيح والكونصان الثاني
+
+413
+00:45:46,440 --> 00:45:51,040
+هو الجذر التربيعي للسالب واحد إذا مصير كل واحد فيهم 
+
+414
+00:45:51,040 --> 00:45:55,060
+عبارة عن حل وبالتالي هذا بيعطينا شكل الحل العام
+
+415
+00:45:55,060 --> 00:46:01,460
+للمعادلة التفاضلية then both كل من الـ real و الـ
+
+416
+00:46:01,460 --> 00:46:06,800
+imaginary parts اللي هو U of X و V of X are real
+
+417
+00:46:06,800 --> 00:46:12,200
+solutions يبقى هدول حلول حقيقية للمعادلة اللي
+
+418
+00:46:12,200 --> 00:46:17,070
+عندنا هذه تمام؟ إذا لو طلع عندي حل المعادلة
+
+419
+00:46:17,070 --> 00:46:22,210
+التفاضلية على الشكل Complex بيكون الجزء الحقيقي من
+
+420
+00:46:22,210 --> 00:46:26,390
+الدالة اللي طلع عبارة عن حل المعادلة الأصلية والجزء
+
+421
+00:46:26,390 --> 00:46:30,790
+التخيلي كمان بدون الـ I عبارة عن حل المعادلة 
+
+422
+00:46:30,790 --> 00:46:35,010
+التفاضلية اللي عندك الآن كنا في وادي وننتقل إلى
+
+423
+00:46:35,010 --> 00:46:40,410
+وادي آخر اللي مصيغة Euler لمن؟ للـ exponential
+
+424
+00:46:40,410 --> 00:46:44,570
+function يبقى formula الـ Euler بيقول الـ
+
+425
+00:46:44,570 --> 00:46:51,290
+exponential function E of I ثيتا is written as E
+
+426
+00:46:51,290 --> 00:46:56,590
+of I ثيتا تكتب كـ cos ثيتا زائد I sin ثيتا ضالت
+
+427
+00:46:56,590 --> 00:46:58,390
+complex و الله صارت real
+
+428
+00:47:01,310 --> 00:47:06,510
+يبقى هنا E أس I ثيتا complex تكتب على الصورة أس 
+
+429
+00:47:06,510 --> 00:47:13,430
+ثيتا زائد I sin ثيتا طيب لو E أس سالب I ثيتا هشوف كيف 
+
+430
+00:47:13,430 --> 00:47:19,790
+بالصير يبقى هذه المناطق بالصير E أس I سالب ثيتا 
+
+431
+00:47:19,790 --> 00:47:24,570
+مظبوط يعني معناته بيجي في اللي فوق شيل كل ثيتا وحط
+
+432
+00:47:24,570 --> 00:47:32,810
+مكانها سالب ثيتا يبقى هنا cos لسالب ثيتا زائد I
+
+433
+00:47:32,810 --> 00:47:39,250
+sin لسالب ثيتا ويساوي الـ cos even ولا odd يبقى 
+
+434
+00:47:39,250 --> 00:47:44,150
+أبداً cos سالب ثيتا هي بـ cos ثيتا والـ sin
+
+435
+00:47:45,020 --> 00:47:51,000
+يبقى السالب بيطلع برا يبقى ناقص I في الـSin الزاوية 
+
+436
+00:47:51,000 --> 00:47:57,720
+ثيتا طلع لي كويس نقارن ما بين اثنين يبقى E أس I 
+
+437
+00:47:57,720 --> 00:48:02,980
+ثيتا هي cos ثيتا زائد I sin ثيتا E أس سالب I ثيتا هي 
+
+438
+00:48:02,980 --> 00:48:08,320
+cos ثيتا سالب I sin ثيتا يبقى نفس اللي فوق بس غيرنا 
+
+439
+00:48:08,320 --> 00:48:15,760
+من الإشارة التي بينهما نجي لنقطة الثالثة E أس X 
+
+440
+00:48:15,760 --> 00:48:21,120
+زائد I ثيتا يبقى بقدر أقول E أس X في E أس I ثيتا 
+
+441
+00:48:21,120 --> 00:48:26,720
+لأنه إذا تساوت الأساسات عند الضرب تجمع الأسس مش 
+
+442
+00:48:26,720 --> 00:48:33,750
+هقول E أس X ضرب E أس I ثيتا يبقى مش قصدي او سكس 
+
+443
+00:48:33,750 --> 00:48:38,950
+زائد اوس اي ثيتا وإنما بقول ايش او سكس ضرب اوس اي
+
+444
+00:48:38,950 --> 00:48:43,490
+ثيتا لأن عند الضرب تجمع من الأساس الـ E او سكس زي ما 
+
+445
+00:48:43,490 --> 00:48:49,360
+هي هادي مش هي هاد اللي فوق بس بدل التاجان بين يبقى 
+
+446
+00:48:49,360 --> 00:48:57,980
+بقدر أقول هذه cos Y زائد I sin الـ Y بالشكل 
+
+447
+00:48:57,980 --> 00:49:04,740
+اللي عندها أو بقدر أقول cos X بقدر أقول E أس X 
+
+448
+00:49:04,740 --> 00:49:13,990
+cos الـ Y يبقى E او سكس Cos Y زائد I في E او سكس في 
+
+449
+00:49:13,990 --> 00:49:20,510
+sin Y بالشكل اللي لدينا هنا طيب بدنا نيجي لـ E او سكس
+
+450
+00:49:20,510 --> 00:49:25,670
+I باي يبقى نفس اللي فوق بس بدل الـ θ حطينا باي 
+
+451
+00:49:25,670 --> 00:49:33,270
+يبقى باجي بقوله هذه cos Pi زائد I sin Pi sin Pi 
+
+452
+00:49:33,270 --> 00:49:41,460
+يبقى درجة sin Pi بزيرو قصة مية و ثمانين يبقى 
+
+453
+00:49:41,460 --> 00:49:46,960
+السالب واحد بقدر أشيله دائماً أو أكتب دالة E أس I
+
+454
+00:49:46,960 --> 00:49:54,540
+باي نجي الآن لمجموع اثنين E أس I بي X زي E أس 
+
+455
+00:49:54,540 --> 00:49:59,560
+سالب I بي X أظن أنتو أخدتوا كل كلص بيمزاكن 
+
+456
+00:49:59,560 --> 00:50:03,540
+الجوش والسنش والشغل الثاني مش كنا نقول cos الـ X E
+
+457
+00:50:03,540 --> 00:50:10,820
+والسنش زائد E ناقص I X على اثنين تمام يبقى هنا 
+
+458
+00:50:10,820 --> 00:50:18,160
+باجي بقول هذه بيديها تساوي cos اللي هو BX زائد 
+
+459
+00:50:18,160 --> 00:50:25,700
+I sin BX زائد هذه الأولى الثانية اللي هو cos
+
+460
+00:50:26,410 --> 00:50:33,470
+BX ناقص I sin BX أظن إن هذه بالموجب وهذه بالسالب
+
+461
+00:50:33,470 --> 00:50:42,070
+مع السلامة يبقى هذا الكلام يساوي اثنين cos BX 
+
+462
+00:50:42,070 --> 00:50:47,550
+يبقى مجموع الاثنين بده يعطينا اثنين cos BX طب 
+
+463
+00:50:47,550 --> 00:50:48,930
+لو طرحتهم 
+
+464
+00:50:51,450 --> 00:51:01,210
+يبقى لو جت قلت and E-E-IBX يبقى ناقص E-E-IBX يبقى
+
+465
+00:51:01,210 --> 00:51:14,480
+ناقص E-E-IBX BX ناقص cos BX زائد I sin BX
+
+466
+00:51:14,480 --> 00:51:18,860
+سالب cos وموجب cos مع السلامة يبقى بصير
+
+467
+00:51:18,860 --> 00:51:28,380
+الناتج اللي هو اثنين I sin BX
+
+468
+00:51:33,790 --> 00:51:38,190
+يبقى هذا اللي هو الشكل العام لمين؟ للمعادلة اللي 
+
+469
+00:51:38,190 --> 00:51:38,510
+عندنا 
+
+470
+00:51:44,560 --> 00:51:50,860
+طيب جبت الآن الـ E او سكس بي X والـ E او سكس ناقص I بي X 
+
+471
+00:51:50,860 --> 00:51:57,260
+وطلعتهم يبقى بقدر أقول يا بنات من هذه المعادلة
+
+472
+00:51:57,260 --> 00:52:07,030
+بقدر أطلع شغلة كمان ايش الشغلة؟ لو cos BX يساوي
+
+473
+00:52:07,030 --> 00:52:18,250
+نص فيه لو جسمتها اثنين بيظل E أس I BX زائد E أس
+
+474
+00:52:18,250 --> 00:52:19,490
+ناقص I
+
+475
+00:52:22,350 --> 00:52:27,470
+بكتر بكتر بكتر 
+
+476
+00:52:27,470 --> 00:52:34,110
+بكتر 
+
+477
+00:52:34,110 --> 00:52:40,470
+بكتر
+
+478
+00:52:40,470 --> 00:52:45,370
+بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر
+
+479
+00:52:45,370 --> 00:52:46,340
+بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر هذا
+
+480
+00:52:46,340 --> 00:52:49,980
+اللي أعطينالكم المقدمات لهذا الـ section والمرة 
+
+481
+00:52:49,980 --> 00:52:55,660
+القادمة إن شاء الله بندخل في صميم الحل للمعادلة 
+
+482
+00:52:55,660 --> 00:53:01,260
+التفاضلية إذا الـ roots كانت مالها complex يبقى بدي
+
+483
+00:53:01,260 --> 00:53:05,500
+أكل مرة جاية قبل تيجي محاضرة تمر على هذه المعلومات 
+
+484
+00:53:05,500 --> 00:53:08,700
+مش لما نجي نشتغل نقول والله مش عارفين شو هذا و 
+
+485
+00:53:08,700 --> 00:53:14,880
+لا اسم وبتاخدش شي معاك كل منك عشر دقائق يعطيكم 
+
+486
+00:53:14,880 --> 00:53:15,280
+العافية
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c5efa7a0c4b2bbd43b199dadfb6b7da46af8a448
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0_postprocess.srt
@@ -0,0 +1,1944 @@
+1
+00:00:20,670 --> 00:00:24,430
+بسم الله الرحمن الرحيم نعودوا إلى ال section اللي
+
+2
+00:00:24,430 --> 00:00:29,070
+بدأناها في الفترة الصباحية وهو حل المعادلة
+
+3
+00:00:29,070 --> 00:00:34,510
+التفاضلية إذا كان المعادلة إذا كانت مجموعة الحلول
+
+4
+00:00:34,510 --> 00:00:39,030
+للمعادلة المميزة للمعادلة التفاضلية هي عبارة عن
+
+5
+00:00:39,030 --> 00:00:45,640
+جذورحقيقية ومختلفة اذا كان R1 لا يسوى R2 لا يسوى
+
+6
+00:00:45,640 --> 00:00:51,860
+R3 لا يسوى RN اذا مجموعة الحلول على شكل Y ستكون
+
+7
+00:00:51,860 --> 00:00:55,740
+C1E
+
+8
+00:00:55,740 --> 00:01:06,480
+أس R1X زي C2E أس R2X زي CNE أس RNXيبقى ناخد أول
+
+9
+00:01:06,480 --> 00:01:10,680
+مثال على ذلك بيقول حل المعادلة التفاظلية y double
+
+10
+00:01:10,680 --> 00:01:16,300
+prime ناقص خمسة y prime زائد ستة y equal to zero
+
+11
+00:01:16,300 --> 00:01:20,420
+يبقى التكتيك اللي هتبقى عند حل السؤال هتبقى عند حل
+
+12
+00:01:20,420 --> 00:01:27,870
+أي سؤال آخر بعد ذلك بداجي أقول له letالـ Y تساوي E
+
+13
+00:01:27,870 --> 00:01:38,730
+أُس RX بـ A solution of the differential equation
+
+14
+00:01:38,730 --> 00:01:44,050
+star سميلي هذه المعادلة الأصلية اللي هي main star
+
+15
+00:01:46,480 --> 00:01:53,800
+بالزمن المشتقة الأولى Y' يساوي R في E أُس RX و
+
+16
+00:01:53,800 --> 00:02:00,840
+بالزمن ال YW' بدي أشتق هذه كمان مرة يبقى R تربية
+
+17
+00:02:00,840 --> 00:02:05,020
+في E أُس RX قلنا الصبح أن مشتقة الـ exponential
+
+18
+00:02:05,020 --> 00:02:11,080
+بالـ exponential itself مضروب في مشتقة الأُس طبعا
+
+19
+00:02:11,080 --> 00:02:15,460
+الـR عندنا هنا مقدار ثابت يبقى المشتقات كما تراه
+
+20
+00:02:15,640 --> 00:02:21,100
+الان بروح اعوض في المعادلة A star يبقى باجي بقول
+
+21
+00:02:21,100 --> 00:02:27,000
+المعادلة A star يلي YW prime ناقص خمسة Y prime
+
+22
+00:02:27,000 --> 00:02:33,680
+زائد ستة Y يساوي YW prime يلي ال R تربية في E أس
+
+23
+00:02:33,680 --> 00:02:42,550
+RX ناقص خمسة ال Y prime يلي هو R في E أس RXزائد
+
+24
+00:02:42,550 --> 00:02:49,170
+ستة في ال Y ال Y اللي هي E أُس RX كل هذا الكلام
+
+25
+00:02:49,170 --> 00:02:58,310
+بيساوي Zeroالان اقسم الطرفين على E أص RX طبعا هذا
+
+26
+00:02:58,310 --> 00:03:04,470
+الكلام ممكن لأن E أص RX لايمكن أن تساوي Zero في أي
+
+27
+00:03:04,470 --> 00:03:10,790
+يوم من الأيام إذا بقدر اقسم عليها بدون أي مشكلة لو
+
+28
+00:03:10,790 --> 00:03:16,470
+قسمت على E أص RX المعادلة هذه تاخد الشكل التاليR
+
+29
+00:03:16,470 --> 00:03:23,250
+تربيه نقص خمسة R زائد ستة بده يسوي مين Zero يبقى
+
+30
+00:03:23,250 --> 00:03:29,650
+هذه يا بنات اللي بسميها ال characteristic equation
+
+31
+00:03:29,650 --> 00:03:37,850
+of the differential equation Star يبقى هذه
+
+32
+00:03:37,850 --> 00:03:43,130
+المعادلة المميزة أو المعادلة المساعدة للمعادلة مين
+
+33
+00:03:43,130 --> 00:03:48,230
+Starهذه المقادرة زي ما تشوفين من الدرجة الثانية
+
+34
+00:03:48,230 --> 00:03:53,450
+بتروح أحللها و أحسب قدر قيمة a يبقى لو روحنا
+
+35
+00:03:53,450 --> 00:04:00,450
+حللناها كأقواس يساوي zero هنا R هنا R ال 6 عبارة
+
+36
+00:04:00,450 --> 00:04:07,410
+عن 2 في 3 والإشارتين بالناقص يبقى بناء عليه ال R
+
+37
+00:04:07,410 --> 00:04:16,320
+هتساوي 2 او R1 تساوي 2 وR2 تساوي 3يبقى الجذور
+
+38
+00:04:16,320 --> 00:04:24,700
+حقيقية ومختلفة مدام حقيقية ومختلفة إذا بدي أشيل R
+
+39
+00:04:24,700 --> 00:04:29,860
+هذه و أحط بدلها مرة اتنين و مرة اذا أحط بدلها
+
+40
+00:04:29,860 --> 00:04:40,600
+تلاتة إذا the solutions of the differential
+
+41
+00:04:40,600 --> 00:04:54,160
+equation star areاللي هو Y1 بدي ساوي E أُس 2X و Y2
+
+42
+00:04:54,160 --> 00:05:00,930
+بدي ساوي E أُس 3Xهو لم يقل الحل الأول و الحل
+
+43
+00:05:00,930 --> 00:05:05,970
+الثاني قال هاتل مين ال general solution يبقى وحل
+
+44
+00:05:05,970 --> 00:05:09,830
+المعادلة هذه فبروح بقوله طبعا اتنين هدول ال
+
+45
+00:05:09,830 --> 00:05:13,990
+exponential are linearly independent مش عاجزة
+
+46
+00:05:13,990 --> 00:05:18,610
+انتين تلاتة اربعة ان جد ما يكون عددهم أثبتنا سابقا
+
+47
+00:05:18,610 --> 00:05:21,530
+في section تلاتة اربعة ان هدول are linearly
+
+48
+00:05:21,530 --> 00:05:27,490
+independent اذا بروح على شكل الحل فبروح بقوله ذا
+
+49
+00:05:27,790 --> 00:05:39,410
+General solution of the differential equation when
+
+50
+00:05:39,410 --> 00:05:52,260
+is in the formعلى الشكل التالي Y يسوى C1 Y1 زي C2
+
+51
+00:05:52,260 --> 00:06:04,180
+Y2 هذا معناه ان Y يسوى C1 Y1 هي طلعناها E2X C2E3X
+
+52
+00:06:04,180 --> 00:06:09,760
+يبقى هذا حل المعادلة تخف عضمية star اللي عندنا فوق
+
+53
+00:06:09,760 --> 00:06:11,380
+نعم
+
+54
+00:06:15,160 --> 00:06:22,380
+أه في أي تساؤل؟ طيب نزل الان المثال رقم 2 يبقى
+
+55
+00:06:22,380 --> 00:06:29,960
+المثال رقم 1 خمسة من الكتاب example 2 السؤال رقم
+
+56
+00:06:29,960 --> 00:06:35,940
+عشرة من الكتاب بقول find the general solution find
+
+57
+00:06:35,940 --> 00:06:45,700
+the general solution find the general solutionof
+
+58
+00:06:45,700 --> 00:06:54,520
+the differential equation للمعادلة التفاضلية y
+
+59
+00:06:54,520 --> 00:07:01,140
+triple prime ناقص أربعة y prime بده يساوي zero
+
+60
+00:07:01,140 --> 00:07:05,260
+وهذا اللي يبدأ يسميها المعادلة رقم star
+
+61
+00:07:09,790 --> 00:07:15,310
+أذا تكتيك الحل نفس التكتيك اللي اتبعته هنا حرفيا
+
+62
+00:07:15,310 --> 00:07:21,950
+يبقى باجي بقوله افترض ان Y بيبقى يساوي E و أس RX
+
+63
+00:07:21,950 --> 00:07:32,610
+بيه solution of the differential equation a star
+
+64
+00:07:35,780 --> 00:07:39,180
+يستخدم المشتقة الأولى والثانية والتالتة يستخدم الـ
+
+65
+00:07:39,180 --> 00:07:44,380
+Y' يستخدم الـ R يستخدم الـ X يستخدم الـ X يستخدم
+
+66
+00:07:44,380 --> 00:07:46,580
+الـ W يستخدم الـ Y يستخدم الـ W يستخدم الـ X
+
+67
+00:07:46,580 --> 00:07:48,240
+يستخدم الـ Y يستخدم الـ W يستخدم الـ X يستخدم الـ
+
+68
+00:07:48,240 --> 00:07:49,780
+Y يستخدم الـ W يستخدم الـ X يستخدم الـ Y يستخدم
+
+69
+00:07:49,780 --> 00:07:50,400
+الـ W يستخدم الـ X يستخدم الـ Y يستخدم الـ Y
+
+70
+00:07:50,400 --> 00:07:51,040
+يستخدم الـ Y يستخدم الـ Y يستخدم الـ Y يستخدم الـ
+
+71
+00:07:51,040 --> 00:07:51,840
+Y يستخدم الـ Y يستخدم الـ Y يستخدم الـ Y يستخدم
+
+72
+00:07:51,840 --> 00:07:52,400
+الـ Y يستخدم الـ Y يستخدم الـ Y
+
+73
+00:08:11,240 --> 00:08:12,640
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+74
+00:08:12,950 --> 00:08:16,770
+بتاخد المعلومات اللي عندها دي وروح اعوض وين في
+
+75
+00:08:16,770 --> 00:08:21,250
+المعادلة star يبقى لو روحت عوضت في المعادلة star
+
+76
+00:08:21,250 --> 00:08:28,170
+بتصير المعادلة على الشكل التالي اللي هي R تكيب في
+
+77
+00:08:28,170 --> 00:08:36,450
+E أُس RX ناقص أربعة Y prime لـR في E أُس RX بدي
+
+78
+00:08:36,450 --> 00:08:43,020
+ساوي كدهاش؟ بدي ساوي زيلةلو رحنا جسمنا على E أُس R
+
+79
+00:08:43,020 --> 00:08:49,100
+X بصير R تكييب ناقص أربعة R بديه يساوي مين؟ بديه
+
+80
+00:08:49,100 --> 00:08:54,870
+يساوي Zeroالان هذه معادلة من الدرجة التالتة لكن
+
+81
+00:08:54,870 --> 00:09:01,070
+الحمد لله سهل حلها ما هو الصعب يبقى لو روحت أخدت
+
+82
+00:09:01,070 --> 00:09:05,970
+ال R عام المشترك بظل R تربية ناقص أربعة بده يساوي
+
+83
+00:09:05,970 --> 00:09:10,990
+Zero المقدار بين القوسين هو عبارة عن فرق بين
+
+84
+00:09:10,990 --> 00:09:17,430
+المربعين بحلله R ناقص اتنين في R زائد اتنين يساوي
+
+85
+00:09:17,430 --> 00:09:23,610
+Zeroهذا بيعطيني ان الارتو ساوي زيرو وارتو ساوي
+
+86
+00:09:23,610 --> 00:09:30,590
+اتنين والارتو ساوي سالب اتنين يبقى هدول هم الجذور
+
+87
+00:09:30,590 --> 00:09:35,290
+تبعت من ال characteristic equation اللي هاد اللي
+
+88
+00:09:35,290 --> 00:09:41,210
+توصلنا لها هدها ها هي من هي ال characteristic
+
+89
+00:09:41,210 --> 00:09:50,790
+equation of theDifferential Equation Star يبقى هذه
+
+90
+00:09:50,790 --> 00:09:55,210
+المعادلة المميزة للمعادلة Star رحنا حللناها و
+
+91
+00:09:55,210 --> 00:10:00,410
+طلعنا الجذور فالجذور كان R ب Zero و R ب اتنين و R
+
+92
+00:10:00,410 --> 00:10:07,170
+ب سلب اتنين اذا في عندي ثلاثة حلول الاولاني Y
+
+93
+00:10:07,170 --> 00:10:15,530
+تساويE أُس Zero X يبقى الدياج واحد والتاني E أُس
+
+94
+00:10:15,530 --> 00:10:21,330
+اتنين X والتالت E أُس سالب تلاتة X بدي أجيب ال
+
+95
+00:10:21,330 --> 00:10:24,230
+general solution يبقى constant في الأول و constant
+
+96
+00:10:24,230 --> 00:10:27,230
+في التاني يبقى بدل ما أقول إذا اللي حلو كله لأ بدي
+
+97
+00:10:27,230 --> 00:10:31,950
+أحط ال general solution دوري تمام إذا بجيب أقولكوا
+
+98
+00:10:31,950 --> 00:10:37,870
+هنا the general solution
+
+99
+00:10:39,810 --> 00:10:53,670
+of the differential equation star is y تساوي c1 في
+
+100
+00:10:53,670 --> 00:11:01,990
+e أُس 0 نكتب بالك بالتفصيل e أُس 0 زائد c2 في e
+
+101
+00:11:01,990 --> 00:11:10,690
+أُس 2x زائد c3 في e أُس سالب 2xيبقى أصبح شكل الحل
+
+102
+00:11:10,690 --> 00:11:16,270
+Y تساوي C1C2E2X
+
+103
+00:11:16,270 --> 00:11:20,670
+C3E2X
+
+104
+00:11:20,670 --> 00:11:26,830
+هذا ال general solution لمن؟ للمعادلة رقم star
+
+105
+00:11:26,830 --> 00:11:35,710
+اللي عندنا حد فيكم بتسأل أي سؤال هنا؟ اهأظن واضح
+
+106
+00:11:35,710 --> 00:11:41,230
+وضوح الشمس في ربيعة النهار مش فيه مشكلة طب المثال
+
+107
+00:11:41,230 --> 00:11:46,230
+الذي يليه مثال
+
+108
+00:11:46,230 --> 00:11:55,590
+تلاتة find the general solution the general
+
+109
+00:11:55,590 --> 00:11:57,410
+solution
+
+110
+00:12:01,330 --> 00:12:11,710
+of the differential equation Y to
+
+111
+00:12:11,710 --> 00:12:13,810
+the derivative IV
+
+112
+00:12:16,630 --> 00:12:24,010
+y to the derivative of 3 ناقص 7 y double prime
+
+113
+00:12:24,010 --> 00:12:36,310
+ناقص y prime زائد 6y تساوي من؟ تساوي 0 وهذه اللي
+
+114
+00:12:36,310 --> 00:12:39,750
+هنسميها المعادلة رقم star
+
+115
+00:13:00,800 --> 00:13:06,520
+خلّيني أذكر بس بالرموز ال I V و V وما إلى ذلك عندك
+
+116
+00:13:06,520 --> 00:13:14,700
+I يعني رقم واحد double I رقم اتنينTriple I رقم
+
+117
+00:13:14,700 --> 00:13:24,540
+تلاتة IV رقم أربع V خمسة VI ستة V double I ليه
+
+118
+00:13:24,540 --> 00:13:28,140
+السبعة وما إلى ذلك إذا مر علينا أكتر من هيك
+
+119
+00:13:28,140 --> 00:13:34,030
+بنقولكوا نخلينا على جد هيك اليوم طيبيبقى بقول هات
+
+120
+00:13:34,030 --> 00:13:37,110
+لل general solution لهذه المعادلة إذا بدي أبدأ
+
+121
+00:13:37,110 --> 00:13:42,810
+بنفس التكتيك اللى اتبعته في المثالين السابقين يبقى
+
+122
+00:13:42,810 --> 00:13:54,870
+بروح اقول هنا letY تساوي E أُس RX بـ Solution of
+
+123
+00:13:54,870 --> 00:14:01,390
+the Differential Equation Star
+
+124
+00:14:07,440 --> 00:14:17,060
+هي R E أُس R X Y W Prime R تربيع E أُس R X Y تكييب
+
+125
+00:14:17,060 --> 00:14:23,360
+الـ Y to the derivative of 3 يبقى R تكييب E أُس R
+
+126
+00:14:23,360 --> 00:14:29,000
+X Y to the derivative of IV المشتقة الرابعة بيكون
+
+127
+00:14:29,000 --> 00:14:33,500
+R أُس 4R X
+
+128
+00:14:36,100 --> 00:14:40,000
+لما تأخذ المعلومة اللى حصلت عليها و روح اعوض في
+
+129
+00:14:40,000 --> 00:14:45,200
+المعادلة رقم star يبقى رقم star بتقول لي why to
+
+130
+00:14:45,200 --> 00:14:54,130
+the derivative IVزائد y triple prime ناقص سبعة y
+
+131
+00:14:54,130 --> 00:15:02,630
+double prime ناقص y prime زائد ستة y يساوي بدا
+
+132
+00:15:02,630 --> 00:15:06,890
+أشيل كل term من ال termات الخمسة اللي عندنا و أحط
+
+133
+00:15:06,890 --> 00:15:14,410
+القيمة بتبعدهايبقى المشتقة الأولى لـ R أس أربعة E
+
+134
+00:15:14,410 --> 00:15:24,070
+أس R X اللي بعده R تكييب E أس R X اللي بعده ناقص
+
+135
+00:15:24,070 --> 00:15:32,970
+سبعة R تربيعEOSRX-EOSRX
+
+136
+00:15:32,970 --> 00:15:37,090
+6EOSRX
+
+137
+00:15:40,220 --> 00:15:45,080
+لو جسمنا طرفيا المعادلة على E أس RX بنحصل على ما
+
+138
+00:15:45,080 --> 00:15:53,460
+يأتي يبقى هي R أس أربعة زائد R تكيب ناقص سبعة R
+
+139
+00:15:53,460 --> 00:16:01,300
+تربيع ناقص R زائد ستة كله بده يساوي جداش؟ بده
+
+140
+00:16:01,300 --> 00:16:02,060
+يساوي زيلة
+
+141
+00:16:05,640 --> 00:16:10,180
+إذا بدنا نجي للمعادلة اللى عندنا هذا بدنا نحاول
+
+142
+00:16:10,180 --> 00:16:15,600
+نحلها آه ده مش زي المعادلتين اللى فاتوا تحلل وامشي
+
+143
+00:16:15,600 --> 00:16:20,660
+بكل بساطة هنا بدنا نشغل عقلنا ممكن نشغل عقلنا
+
+144
+00:16:20,660 --> 00:16:26,950
+بأكثر من طريقةطريقة أولى مثلا نشوف قواسم الستة
+
+145
+00:16:26,950 --> 00:16:31,970
+ونشوف الرقم من قواسم الستة الذي يحقق هذه المعادلة
+
+146
+00:16:31,970 --> 00:16:36,910
+وبالتالي نقسم على هذا ال factor ونزل الدرجة من
+
+147
+00:16:36,910 --> 00:16:41,510
+الدرجة الرابعة إلى الدرجة التالتة وبعدين يمكن الله
+
+148
+00:16:41,510 --> 00:16:46,530
+يحلها ويمكن نضطر نشوف كمان factor تاني ينزل الدرجة
+
+149
+00:16:46,530 --> 00:16:51,750
+التالتة إلى الدرجة الثانية وجهة نظروجهة نظر أخرى
+
+150
+00:16:51,750 --> 00:16:56,370
+بيقول لأ خد بعض العناصر مع بعضهم يعني أعمل هذه
+
+151
+00:16:56,370 --> 00:17:01,090
+المعادلة على شكل مجمعتهم وخد عوامل مشتركة وحلل
+
+152
+00:17:01,090 --> 00:17:06,970
+لعله يطلع أنصر مشترك ما بين الإتنين وبالتالي تنزل
+
+153
+00:17:06,970 --> 00:17:12,510
+الرتبة من الدرجة الرابعة إلى الدرجة الثالثة و
+
+154
+00:17:12,510 --> 00:17:16,790
+بعدين الله بحلها ان شاء اللهبقول يبقى هي عندى
+
+155
+00:17:16,790 --> 00:17:22,030
+طريقتين للحل وشوف اللى أنسب بالنسبالك واشتغل بيه
+
+156
+00:17:22,030 --> 00:17:25,270
+احنا اخدنا السؤال المرة اللى فاتت وروحنا شوفنا
+
+157
+00:17:25,270 --> 00:17:30,790
+القواسم تمام لما بدى اجرب طريقة تانية بدى اخد بعض
+
+158
+00:17:30,790 --> 00:17:35,470
+العناصر مع بعضها و الباقى مع بعض الاخر يبقى يا
+
+159
+00:17:35,470 --> 00:17:41,210
+بروح اخد R أربعة و R تربيع و ال constant مع بعض يا
+
+160
+00:17:41,210 --> 00:17:48,390
+اما بروح باخد R تكيبو R كمان مع بعض مجمعتين هذه
+
+161
+00:17:48,390 --> 00:17:53,950
+والله هذه سيان لإتنين are the same مرة تانية بقول
+
+162
+00:17:53,950 --> 00:17:58,570
+R أس أربعة وR تربيع وكونه set up تعملي معادلة من
+
+163
+00:17:58,570 --> 00:18:02,030
+الدرجة الرابعة بس بقدر أحلي الهلق وسين يمكن نقدر
+
+164
+00:18:02,030 --> 00:18:05,710
+وممكن مانقدرش الله أعلم وبعدها كده ال R تكعيب و ال
+
+165
+00:18:05,710 --> 00:18:10,010
+R في بينهم عامل مشترك وبالتالي يمكن ألاقي العامل
+
+166
+00:18:10,010 --> 00:18:15,900
+مشترك مع التانية يعني قدامي وبدأ للطريقة قداشأو
+
+167
+00:18:15,900 --> 00:18:20,660
+اخذ اول اتنين مع بعض واخر تلاتة مع بعض
+
+168
+00:18:44,710 --> 00:18:51,010
+بمجرد النظر لو أخدت R و S أربعة و سبعة R تربيع زاد
+
+169
+00:18:51,010 --> 00:18:56,210
+ستة automatic بتحللوا و بظلمين عندي R تكيب و R
+
+170
+00:18:56,210 --> 00:19:01,950
+برضه بتحللوا إذا هذه طريقة ماشية بمجرد النظر لكن
+
+171
+00:19:01,950 --> 00:19:06,010
+لو أخدت الأول و التاني الصحيح بتحللوا و هدول
+
+172
+00:19:06,010 --> 00:19:10,660
+بتحللوا صحيح مظبوطوبرضه بلاقي عامل مشارك بني يعني
+
+173
+00:19:10,660 --> 00:19:16,100
+التندينت صح لتشتغلي صح إذا لو جيت اللي أسهلي بمجرد
+
+174
+00:19:16,100 --> 00:19:23,440
+النظر روحت أخد R أقص 4 ناقص 7 R تربيه زاد 6 هذا
+
+175
+00:19:23,440 --> 00:19:30,580
+جوز زاد ضال عندي ميم R تكيب وناقص R كله بده يساوي
+
+176
+00:19:30,580 --> 00:19:36,210
+من 0هذه بقدر احللها الى ايه؟ الى حصل ضرب قوسين
+
+177
+00:19:36,210 --> 00:19:43,930
+يبقى هذا القوس الأول هنا R هنا R هنا واحد هنا ستة
+
+178
+00:19:43,930 --> 00:19:50,770
+هنا ناخد هنا ناخد كيف؟ R تربية مظبوط وهنا R تربية
+
+179
+00:19:51,360 --> 00:19:55,980
+تمام يبقى هذا بيعطينا فعلا ناقص R تربيع و ناقص 6
+
+180
+00:19:55,980 --> 00:20:02,340
+ناقص 100% تمام زاد هنا بقدر اخد R عامل مشترك ايش
+
+181
+00:20:02,340 --> 00:20:08,800
+بيظل عندى R تربيع ناقص 1 و يسوى من 0 والله كويس
+
+182
+00:20:08,800 --> 00:20:14,180
+يعني ممكن اخد R تربيع ناقص 1 عامل مشترك من الشجتين
+
+183
+00:20:14,360 --> 00:20:19,860
+يبقى لو أخدت R تربيع ناقص واحد عامل مشترك من
+
+184
+00:20:19,860 --> 00:20:29,460
+الشكتين بيظل عندي R تربيع و هنا زائد R ناقص ستة
+
+185
+00:20:29,460 --> 00:20:30,860
+كله بده يساوي زير
+
+186
+00:20:34,410 --> 00:20:39,250
+هذا عامل مشترك، اذا كان هنا R تربية نقص 6، فهذه R
+
+187
+00:20:39,250 --> 00:20:42,890
+تربية نقص 6، اذا كان هنا R تربية نقص 6، فهذه R
+
+188
+00:20:42,890 --> 00:20:43,930
+تربية نقص 6، اذا كان هنا R تربية نقص 6، فهذه R
+
+189
+00:20:43,930 --> 00:20:45,830
+تربية نقص 6، اذا كان هنا R تربية نقص 6، اذا كان
+
+190
+00:20:45,830 --> 00:20:45,950
+هنا R تربية نقص 6، اذا كان هنا R تربية نقص 6، اذا
+
+191
+00:20:45,950 --> 00:20:48,310
+6، اذا كان هنا R تربية نقص 6، اذا كان هنا R تربية
+
+192
+00:20:48,310 --> 00:20:51,570
+نقص 6، اذا كان هنا R تربية نقص 6، اذا كان هنا R
+
+193
+00:20:51,570 --> 00:20:56,840
+تربية نقهذه تتحلل كمان كحاصل ضرب قوسين يساوي zero
+
+194
+00:20:56,840 --> 00:21:05,360
+هنا R وهنا R وهنا 2 وهنا 3 وهنا زائد وهنا ناقص هاي
+
+195
+00:21:05,360 --> 00:21:11,890
+ناقص 2R وزائد 3R بزائد R كلامنا سليم مئة بالمئةإذا
+
+196
+00:21:11,890 --> 00:21:16,790
+هذه جابت لي حلول مين؟ حلول المعادلة اللي عندنا
+
+197
+00:21:16,790 --> 00:21:24,630
+يبقى يا بقول R تساوي واحد وR تساوي سالب واحد طبعا
+
+198
+00:21:24,630 --> 00:21:30,870
+R واحد وهنا R اتنين وR تلاتة يساوي اتنين وR اربعة
+
+199
+00:21:30,870 --> 00:21:36,110
+يساوي سالب تلاتة بالشكل اللي عندنا هذا يبقى زي ما
+
+200
+00:21:36,110 --> 00:21:41,660
+انتوا شايفين هدول ال R real and differentيبقى بنات
+
+201
+00:21:41,660 --> 00:21:46,560
+المعادلة هذه اللي طلعتها هي مين هي المعادلة
+
+202
+00:21:46,560 --> 00:21:53,320
+المميزة يبقى هذه characteristic equation of
+
+203
+00:21:53,320 --> 00:21:59,280
+equation star الأصلية اللي عندنا هذه المعادلة روحت
+
+204
+00:21:59,280 --> 00:22:02,620
+حطيتها على الشكل هذايبقى الـ characteristic
+
+205
+00:22:02,620 --> 00:22:06,680
+equation حطيتها على الشكل اللي عندنا هذا وبالتالي
+
+206
+00:22:06,680 --> 00:22:10,880
+صارت الحلول بالشكل اللي عندنا هذا يبقى من هنا ليه
+
+207
+00:22:10,880 --> 00:22:17,020
+بقدر اعرف شكل ال general solution بروح بقوله هنا
+
+208
+00:22:17,020 --> 00:22:29,010
+the general solution of thedifferential equation
+
+209
+00:22:29,010 --> 00:22:35,210
+star is y تساوي C1
+
+210
+00:22:51,850 --> 00:22:59,850
+يبقى هذا الشكل الحل العام للمعادلةطيب في مشكلة لو
+
+211
+00:22:59,850 --> 00:23:08,890
+جيت قل C1 E أس 6 زيد C2 E أس 2 X زيد C3 E أس سلب X
+
+212
+00:23:08,890 --> 00:23:14,610
+زيد C4 E أس سلب 3 X ولا حاجة يبقى الترتيب ليس
+
+213
+00:23:14,610 --> 00:23:19,470
+بالضرورة يكون مرتبات بالحرف الواحد المهم constant
+
+214
+00:23:19,470 --> 00:23:23,070
+في الحل الأول زيد constant في الحل التاني زيد
+
+215
+00:23:23,070 --> 00:23:25,790
+constant في الحل التالت زيد constant في الحل
+
+216
+00:23:25,790 --> 00:23:31,590
+الرابعإذا يا بنت من حد مجيب المعادلة المميزة بدي
+
+217
+00:23:31,590 --> 00:23:37,110
+أروح أحلها بأي طريقة إن كانت من طرق التحليل التي
+
+218
+00:23:37,110 --> 00:23:43,890
+تعلمناها ابتدا من الصف السابع وحتى الصف التاسعة مش
+
+219
+00:23:43,890 --> 00:23:48,610
+هذه الفترة اللي تعلمنا فيها تحليل المعادلات تمام
+
+220
+00:23:48,940 --> 00:23:54,820
+يبقى حللنا إذا حللنا بكون جبت اللي هو القيم التي
+
+221
+00:23:54,820 --> 00:23:59,200
+تحقق المعادلة اللي عندي من الدرجة التانية أو
+
+222
+00:23:59,200 --> 00:24:03,500
+التالتة أو الرابعة أو الخمسة أو الدرجة النونية
+
+223
+00:24:03,500 --> 00:24:08,620
+وبالتالي بكون جبت قيم are ومن ثم بكون عرفت شكل ال
+
+224
+00:24:08,620 --> 00:24:15,020
+general solution إذا كان these roots are real and
+
+225
+00:24:15,020 --> 00:24:18,200
+different ولا واحد زي التاني
+
+226
+00:24:22,580 --> 00:24:29,000
+لحد هنا stop انتهى ال section وإلى يكون أرقام
+
+227
+00:24:29,000 --> 00:24:36,960
+المسائل يبقى exercises خمسة اتنين المسائل التالية
+
+228
+00:24:36,960 --> 00:24:42,260
+السؤال الأول والمسائل من خمسة لغاية عشرة
+
+229
+00:24:47,680 --> 00:25:10,200
+ننتقل الآن إلى الحالة الثانية الحالة
+
+230
+00:25:10,200 --> 00:25:13,440
+الثانية بتاخد لو كانت ال roots are complex
+
+231
+00:25:13,440 --> 00:25:21,460
+conjugateيبقى section خمسة تلاتة بيقول ال complex
+
+232
+00:25:21,460 --> 00:25:24,820
+solutions
+
+233
+00:25:30,090 --> 00:25:34,810
+قبل ما ندخل في هذه ال solution نسأل السؤال التالي
+
+234
+00:25:34,810 --> 00:25:41,910
+حد فيكوا درست مساق complex analysis؟ طبعا ولا
+
+235
+00:25:41,910 --> 00:25:49,490
+واحدة تمام لذلك بدي أذكر ببعض المعلومات عن اللي هو
+
+236
+00:25:49,490 --> 00:25:54,310
+ال complex variable اللي طبعا أخدناها في الثانوية
+
+237
+00:25:54,760 --> 00:25:58,320
+لكن احنا بدنا نذكره بالتذكير لإنه بدي اعتبرنا
+
+238
+00:25:58,320 --> 00:26:02,700
+الثانوية تناسية او ماخدتش او او الاخرين بنحط
+
+239
+00:26:02,700 --> 00:26:06,580
+المعلومة الأساسية اللي بتلزمنا في هذا section قبل
+
+240
+00:26:06,580 --> 00:26:11,920
+ان نبدأ نشتغل معادلات تفاضلية اذا باقى محاضرتنا
+
+241
+00:26:11,920 --> 00:26:15,740
+هذه قبل ما نخش في الحلول لما يكونوا complex بدنا
+
+242
+00:26:15,740 --> 00:26:20,860
+نعطي بعض المعلومات عن ال complex numbersيبقى بداجي
+
+243
+00:26:20,860 --> 00:26:25,220
+اكتب some properties about the complex numbers
+
+244
+00:26:25,220 --> 00:26:31,620
+يبقى بداجي اقول هنا some basic
+
+245
+00:26:31,620 --> 00:26:35,200
+properties
+
+246
+00:26:35,200 --> 00:26:44,740
+بعض الخواص الأساسية of complex numbers
+
+247
+00:26:48,350 --> 00:26:52,470
+يبقى بعض الخواص للأعداد التخيولية ال imaginary
+
+248
+00:26:52,470 --> 00:26:57,450
+number او اللي بجينا نسميها الأعداد المركبة مركبة
+
+249
+00:26:57,450 --> 00:27:04,610
+ليش؟ لإن العدد التخيولي مكون من جزء ايم يبقى أول
+
+250
+00:27:04,610 --> 00:27:10,690
+خاصية بتقول any complex
+
+251
+00:27:10,690 --> 00:27:24,810
+number انت تديله رمز zis written as بكتبه
+
+252
+00:27:24,810 --> 00:27:36,410
+على الشكل التالي z يساوي a زائد i b where حيث ال a
+
+253
+00:27:36,410 --> 00:27:49,730
+is called the real partالجزء الحقيقي من العدد
+
+254
+00:27:49,730 --> 00:28:00,150
+التخيّلي and will be is called the imaginary part
+
+255
+00:28:00,150 --> 00:28:08,590
+الجزء
+
+256
+00:28:08,590 --> 00:28:12,930
+التخيّلي and
+
+257
+00:28:13,880 --> 00:28:19,260
+وفي نفس الوقت الـ I تساوي الجدري التربيعي لسالب
+
+258
+00:28:19,260 --> 00:28:37,720
+واحد نين any real number a is a complex number
+
+259
+00:28:37,720 --> 00:28:38,580
+since
+
+260
+00:28:45,420 --> 00:28:54,860
+الـ A بقدر أكتب A زائد Zero في الـ I نمرأ
+
+261
+00:28:54,860 --> 00:29:01,240
+تلاتة Two
+
+262
+00:29:01,240 --> 00:29:10,800
+complex numbers Two
+
+263
+00:29:10,800 --> 00:29:19,690
+complex numbers Aزائد IB and
+
+264
+00:29:19,690 --> 00:29:31,710
+C زائد ID are equal if
+
+265
+00:29:31,710 --> 00:29:40,550
+and only if ال A تساوي ال C and ال B تساوي ال D
+
+266
+00:29:43,250 --> 00:29:52,750
+نمرة أربعة a complex function
+
+267
+00:29:52,750 --> 00:30:04,030
+حديها الرمز w as a function of x is written as
+
+268
+00:30:04,030 --> 00:30:12,000
+مكتوبة على الشكل التالي ال ww prime of x يساوي u
+
+269
+00:30:12,000 --> 00:30:23,480
+prime of x زائد i في v prime of x and hence ومن ثم
+
+270
+00:30:23,480 --> 00:30:34,460
+ال w prime of x يساوي u prime of x زائد i في v
+
+271
+00:30:34,460 --> 00:30:35,900
+prime of x
+
+272
+00:30:38,750 --> 00:30:44,730
+for example f
+
+273
+00:30:44,730 --> 00:30:59,130
+w of x بده يساوي e أس اتنين x زائد i لين اتنين x
+
+274
+00:30:59,130 --> 00:31:05,970
+لين
+
+275
+00:31:05,970 --> 00:31:07,670
+تلاتة x مثلا
+
+276
+00:31:11,860 --> 00:31:34,340
+w prime of x بده يساوي نمر
+
+277
+00:31:34,340 --> 00:31:35,200
+الخمسة
+
+278
+00:31:42,400 --> 00:31:49,780
+ف الـ w of x بدي
+
+279
+00:31:49,780 --> 00:31:57,680
+يساوي الـ u of x زائد i v of x is a complex
+
+280
+00:31:57,680 --> 00:31:58,560
+solution
+
+281
+00:32:06,600 --> 00:32:10,180
+complex solution of the homogeneous differential
+
+282
+00:32:10,180 --> 00:32:18,740
+equation of the homogeneous differential
+
+283
+00:32:18,740 --> 00:32:27,600
+equation homogeneous differential equation L of Y
+
+284
+00:32:27,600 --> 00:32:36,340
+بده سوى Zero then both then both real
+
+285
+00:32:39,090 --> 00:32:45,350
+and imaginary and
+
+286
+00:32:45,350 --> 00:32:56,410
+imaginary parts اللي هم مين ال U of X and ال V of
+
+287
+00:32:56,410 --> 00:33:04,810
+X and V of X are real solutions
+
+288
+00:33:06,240 --> 00:33:14,080
+are real solutions of the same equation of the
+
+289
+00:33:14,080 --> 00:33:26,740
+same equation L of Y بدها تساوي Zero نمرا ستة ال
+
+290
+00:33:26,740 --> 00:33:27,820
+Euler's formula
+
+291
+00:33:34,650 --> 00:33:44,730
+الـ Euler's formula الـ exponential function
+
+292
+00:33:44,730 --> 00:33:55,770
+E وصفة I ثيتا is written as is
+
+293
+00:33:55,770 --> 00:34:06,090
+written as نمره AE أُس I ثيتا كصين ثيتا زائد I
+
+294
+00:34:06,090 --> 00:34:17,710
+كصين الزاوية ثيتا B E أس ناقص I ثيتا يساوي C
+
+295
+00:34:17,710 --> 00:34:30,930
+E أس X زائد I Yبدو يساوي E أُس X في E أُس I Y
+
+296
+00:34:30,930 --> 00:34:44,150
+يساوي E أُس X فيه نمرة D ال
+
+297
+00:34:44,150 --> 00:34:59,900
+E أُس I باي يساوي نمرة Eالـ A أُس I BX زائد A أُس
+
+298
+00:34:59,900 --> 00:35:04,620
+ناقص I BX بده يساوي
+
+299
+00:35:30,960 --> 00:35:35,240
+يبقى المكتوب قدامك على الصبورة هنا هي المعلومات
+
+300
+00:35:35,240 --> 00:35:42,400
+الأساسية التي ستلزمنا عند دراسة هذا ال section وهو
+
+301
+00:35:42,400 --> 00:35:47,240
+إذا الحلول كانت أو ال roots ل ال accelerator
+
+302
+00:35:47,240 --> 00:35:51,060
+equation أو ل ال characteristic equation كانت
+
+303
+00:35:51,060 --> 00:35:55,000
+complex numbers وكل اتنين في حالة ال complex
+
+304
+00:35:55,000 --> 00:36:00,180
+يكونوا دائما أو أبداare conjugate complex numbers
+
+305
+00:36:00,180 --> 00:36:07,720
+يعني اتنين بيكونوا مترافقين كما سنشير بعد قليل او
+
+306
+00:36:07,720 --> 00:36:13,820
+العمود هذا انتهينا منه و نص العمود اللي هناك يالا
+
+307
+00:36:13,820 --> 00:36:18,310
+حاولوا تخلصوا اللي فيديكممش هنبدأ نعيد الحديث في
+
+308
+00:36:18,310 --> 00:36:23,670
+هذا لإن هذا أساسيات يجب أن نعرفها انها هتمر علينا
+
+309
+00:36:23,670 --> 00:36:40,830
+كتير خلال دراستنا لهذا ال section كله
+
+310
+00:36:40,830 --> 00:36:44,550
+تمام هنا؟ خدي يلا
+
+311
+00:37:00,310 --> 00:37:04,090
+طيب نجي الآن ل section خمسة تلاتة اللي هو بيقول
+
+312
+00:37:04,090 --> 00:37:08,910
+complex solutions وذكر ببعض الأشياء البسيطة اللي
+
+313
+00:37:08,910 --> 00:37:13,330
+قلناها في محاضرات الصبح محاضرة الصبح بدينا
+
+314
+00:37:13,330 --> 00:37:19,590
+بالمعادلة اللي خلينا التفاضلية لمعاملات كلها ثوابت
+
+315
+00:37:19,590 --> 00:37:24,230
+وقلنا صرت على صيغةا نود y to the derivative of n
+
+316
+00:37:24,230 --> 00:37:29,710
+زائد a one y to the derivative of n minus one زائد
+
+317
+00:37:29,710 --> 00:37:33,230
+a two y to the derivative of n minus one زائد زائد
+
+318
+00:37:33,230 --> 00:37:37,090
+a n minus one في ال y prime زائد a and y يبدو
+
+319
+00:37:37,090 --> 00:37:40,710
+يساوي مين؟ يساوي zero قلنا هذه homogeneous
+
+320
+00:37:40,710 --> 00:37:44,950
+differential equation ويمكن اختصارها على صيغة L of
+
+321
+00:37:44,950 --> 00:37:50,830
+y يساوي مين؟ يساوي zeroفرضنا إن لهذه المعادلة حل
+
+322
+00:37:50,830 --> 00:37:56,190
+هو Y تساوي E أُس R X طلعنا الـ Characteristic
+
+323
+00:37:56,190 --> 00:38:01,350
+Equation لها نتيجة اللي فرضنا لهذا الحل فصرت
+
+324
+00:38:01,350 --> 00:38:05,810
+المعادلة المميزة على الصينة A naught R to the
+
+325
+00:38:05,810 --> 00:38:11,090
+power N زائد A1 R to the power N minus 1 زائد زائد
+
+326
+00:38:11,090 --> 00:38:16,150
+A N minus 1 في R زائد A N بده ساوي مين؟ بده ساوي
+
+327
+00:38:16,150 --> 00:38:22,080
+Zeroوقلنا المعادلة هذه إلها أحد ثلاثة احتمالات هذه
+
+328
+00:38:22,080 --> 00:38:27,440
+معادلة من الدرجة النونية لاحتمال الأول أن تكون كل
+
+329
+00:38:27,440 --> 00:38:34,500
+الحلول حقيقية ومختلفة لاحتمال الثاني أن تكون كل
+
+330
+00:38:34,500 --> 00:38:41,430
+الحلول حقيقيةو متزاوية مكررة repeated لإحتمال
+
+331
+00:38:41,430 --> 00:38:46,090
+الثالث والأخير كل الحلول تبجيش complex conjugate
+
+332
+00:38:46,090 --> 00:38:51,390
+يعني كل اتنين بيكونوا complex و اتنين مرافقين
+
+333
+00:38:51,390 --> 00:38:55,730
+لبعضهم تماماوقولنا معنى المرافق أنه لو كان الحل
+
+334
+00:38:55,730 --> 00:39:01,490
+الأول أو الجدر الأول هو a زائد ib فإن الجدر التاني
+
+335
+00:39:01,490 --> 00:39:07,630
+هو a ناقص ib هذا ما ذكرناه في محاضرة الصبح وروحنا
+
+336
+00:39:07,630 --> 00:39:12,670
+أخدنا الحالة الأولى لو كانت الجذور حقيقية ومختلفة
+
+337
+00:39:12,670 --> 00:39:18,690
+الآن بدنا نيجي لو كانت الجذور حقيقيةومركبة إذا
+
+338
+00:39:18,690 --> 00:39:24,090
+بدنا بعض المعلومات عن الأعداد المركبة مشان نقدر
+
+339
+00:39:24,090 --> 00:39:30,050
+نستخدم أي من هذه المعلومات متى لازمة الأمرفيها
+
+340
+00:39:30,050 --> 00:39:33,190
+المعلومات اللي قدامنا اللوحة دي اللي بتلزمنا خلال
+
+341
+00:39:33,190 --> 00:39:37,690
+دراستنا لهذا ال section بتيجي المعلوم الأولى يبقى
+
+342
+00:39:37,690 --> 00:39:41,330
+يقولنا some basic properties of complex number
+
+343
+00:39:41,330 --> 00:39:47,110
+بيقول لي any complex number z is written as بكتبه
+
+344
+00:39:47,110 --> 00:39:52,910
+على شكل عددين مركبين واحد a والتاني ib يعني جزء
+
+345
+00:39:52,910 --> 00:39:58,250
+حقيقي وجزءتخيلي قد يكون أحدهم بالصفر ماعنديش
+
+346
+00:39:58,250 --> 00:40:01,950
+مشكلة، ممكن يكون الـA بالزرع و بالثالث يصبح الـIB
+
+347
+00:40:01,950 --> 00:40:07,170
+هو العدد المركب، ممكن يطلع B بالزرع و يظل عند A
+
+348
+00:40:07,170 --> 00:40:11,070
+فقط، و بعد قليل هقولك أن الـA هذا كمان complex
+
+349
+00:40:11,070 --> 00:40:15,650
+numberيبقى in general على وجه العموم الشكل ال
+
+350
+00:40:15,650 --> 00:40:20,970
+complex number بكون a زائد ib ال a و ال b أعداد
+
+351
+00:40:20,970 --> 00:40:26,490
+حقيقية لكن ال a بسميه ال real part و ال b بسميه ال
+
+352
+00:40:26,490 --> 00:40:30,170
+imaginary part اللي هو الجزء الحقيقي والجزء
+
+353
+00:40:30,170 --> 00:40:33,890
+التخيلي و ال i عندنا اللي هو الجدر التربية لمام
+
+354
+00:40:33,890 --> 00:40:40,420
+لسالب واحدالنقطة الثانية أي عدد حقيقي هو عبارة عن
+
+355
+00:40:40,420 --> 00:40:45,500
+عدد تخيل كافي يعني فمثلا لو قلت العدد تلاتة بقدر
+
+356
+00:40:45,500 --> 00:40:51,440
+أقول تلاتة يساوي تلاتة زائد zero في I I اللي هي
+
+357
+00:40:51,440 --> 00:40:54,880
+الجذر التربية لا سالب واحد يبقى صار موجود في الست
+
+358
+00:40:54,880 --> 00:41:00,630
+كومليكس number ولا لايبقى بناء عليه مجموعة الاعداد
+
+359
+00:41:00,630 --> 00:41:07,050
+الحقيقية هي جزء من مجموعة الاعداد التخيلية لكن
+
+360
+00:41:07,050 --> 00:41:15,270
+العكسليس صحيحا يبقى ال R subset من C R مجموعة
+
+361
+00:41:15,270 --> 00:41:21,090
+الأعداد الحقيقية C مجموعة ال complex number R
+
+362
+00:41:21,090 --> 00:41:26,870
+subset من C يبقى أي عدد حقيقي وهو عدد تخيلي لكن
+
+363
+00:41:26,870 --> 00:41:29,330
+العكس ليس صحيحا
+
+364
+00:41:40,470 --> 00:41:48,620
+النقطة التالتةوقتاش يتساوى العددان المُركّبان يعني
+
+365
+00:41:48,620 --> 00:41:58,360
+لو عندي Z1 يساوي A زائد IB و Z2 يساوي C زائد ID Z1
+
+366
+00:41:58,360 --> 00:42:03,820
+يساوي Z2 إذا تحقق شرطان الجزء الحقيقى للعدد الأول
+
+367
+00:42:03,820 --> 00:42:07,340
+بيساوي الجزء الحقيقى العدد الثاني والجزء التخيلي
+
+368
+00:42:07,340 --> 00:42:11,180
+للعدد الأول بيساوي الجزء التخيلي لمن؟ للعدد الثاني
+
+369
+00:42:11,280 --> 00:42:15,840
+إن حدث ذلك بقول اتنين are equal يبقى هنا two
+
+370
+00:42:15,840 --> 00:42:19,780
+complex number a زي عيبي وc زي عبيعي are equal if
+
+371
+00:42:19,780 --> 00:42:23,660
+and only if ال a بدى يسوى ال c و ال b بدى يسوى
+
+372
+00:42:23,660 --> 00:42:28,650
+main ال d بالضبط تمامااختلف ولا واحد فيهم معاني
+
+373
+00:42:28,650 --> 00:42:31,610
+التانية يعني لو اختلف الجزء الحقيقي عن الجزء
+
+374
+00:42:31,610 --> 00:42:36,250
+الحقيقي فبتصيروا ايه اعداد تخيل مثله ذلك لو قلتلك
+
+375
+00:42:36,250 --> 00:42:42,550
+واحد زائد اتنين I و هنا قلتلك تلاتة زائد اتنين I
+
+376
+00:42:42,550 --> 00:42:46,930
+اختلف ولا لا اختلفوا يبقى هدول not equal و هكذا
+
+377
+00:42:46,930 --> 00:42:50,150
+طيب نجي للنقطة الرابعة النقطة الرابعة بيقول
+
+378
+00:42:50,150 --> 00:42:52,110
+Complex function
+
+379
+00:42:54,460 --> 00:42:59,600
+الرمز W of X تُكتب
+
+380
+00:42:59,600 --> 00:43:04,200
+عليه شكل جزء حقيقي كذلك و جزء تخيله بس مش عدد،
+
+381
+00:43:04,200 --> 00:43:09,450
+دالة في X والتانية دالة في Xدالة في X زائد دالة في
+
+382
+00:43:09,450 --> 00:43:14,470
+X مضروبة في العدد التخيلي I وبالتالي صارت complex
+
+383
+00:43:14,470 --> 00:43:20,450
+function لأنها فيها الجزء التخيلي يبقى any complex
+
+384
+00:43:20,450 --> 00:43:25,890
+function بعد ذلك W of X بيكتبها U of X زائد I في V
+
+385
+00:43:25,890 --> 00:43:32,120
+of Xطبعا ال I ال U وال V هي ال functions بس لما
+
+386
+00:43:32,120 --> 00:43:35,600
+انضربت في I صار كلها على بعضها complex function
+
+387
+00:43:35,600 --> 00:43:39,900
+اللي انا لو بده أجي أشتقها يبقى مشتقة هذه مجموعة
+
+388
+00:43:39,900 --> 00:43:44,200
+دلتين مشتقة الأولى زائد مشتقة التانية مشتقة الأولى
+
+389
+00:43:44,200 --> 00:43:49,550
+U prime هذا ال I جادر سلب واحد مقدار ثابتبتغيرش
+
+390
+00:43:49,550 --> 00:43:53,850
+يبقى المقدار الثابت مضروب في مشتقة ال V of X اللي
+
+391
+00:43:53,850 --> 00:43:58,910
+هو من ال V prime of X مثال ذلك قال لو كان ال W of
+
+392
+00:43:58,910 --> 00:44:06,650
+X يساوي E أُس 2X زائد I لن 3X then بدي من ال W
+
+393
+00:44:06,650 --> 00:44:10,570
+prime المعنى هو بدي أشتق الدالة الأولى الدالة
+
+394
+00:44:10,570 --> 00:44:15,950
+الأولى ومشتقتها هي نفسها مضروب في مشتقة الأس اللي
+
+395
+00:44:15,950 --> 00:44:22,120
+هو بقدرش 2اللي بعدها زائد ال I مقدار ثابت مالوش
+
+396
+00:44:22,120 --> 00:44:28,720
+دعوة مشتقة لن تلاتة اكس بواحد على تلاتة اكس ضرب
+
+397
+00:44:28,720 --> 00:44:34,120
+مشتقة مداخل اللن اللي هو بقداش تلاتة اذا هذه بدها
+
+398
+00:44:34,120 --> 00:44:34,680
+تصير
+
+399
+00:44:41,900 --> 00:44:46,900
+تلاتة بتروح مع تلاتة وبالتالي صارت هذه هي مشتقة ال
+
+400
+00:44:46,900 --> 00:44:51,920
+function اللي هي w of x كمثال عاملي على القصية رقم
+
+401
+00:44:51,920 --> 00:44:57,780
+جداش رقم أربعة وهكذا إذا لازم نشتقق في يوم من
+
+402
+00:44:57,780 --> 00:45:03,310
+الأيام لأي complex functionنعود للنقطة الخامسة
+
+403
+00:45:03,310 --> 00:45:06,210
+النقطة الخامسة اللي بيقول لو في عندي complex
+
+404
+00:45:06,210 --> 00:45:10,770
+function على الشكل اللي قدامنا هذه يبقى لو كان هذا
+
+405
+00:45:10,770 --> 00:45:15,770
+complex solution لمن؟ لل homogeneous linear
+
+406
+00:45:15,770 --> 00:45:19,030
+differential equation تبعت الصبح اللي ذكرناها أول
+
+407
+00:45:19,030 --> 00:45:23,430
+مدينة تحدد ال L of I يساوي Zero يبقى عبارة عن
+
+408
+00:45:23,430 --> 00:45:28,690
+مشتقة من الرتب دالة معدلة تفاضلية من الرتب النونية
+
+409
+00:45:28,940 --> 00:45:34,140
+لو كان هذا حل معناته الجزء الحقيقي هو حل والجزء
+
+410
+00:45:34,140 --> 00:45:39,600
+التخيلي هو حل ليش ناخدنا إذا عندي حل وعندي حل يبقى
+
+411
+00:45:39,600 --> 00:45:42,720
+الحل العام كونصان في الأول زائد كونصان في التاني
+
+412
+00:45:42,720 --> 00:45:46,440
+فبعتبر كونصان الأول هو واحد صحيح والكونصان التاني
+
+413
+00:45:46,440 --> 00:45:51,040
+هو الجدر التربية للسالم واحد إذا مصير كل واحد فيهم
+
+414
+00:45:51,040 --> 00:45:55,060
+عبارة عن حل وبالتالي هذا بيعطينا شكل الحل العام
+
+415
+00:45:55,060 --> 00:46:01,460
+للمعادلة التفاضيةthen both كل من الـ real و ال
+
+416
+00:46:01,460 --> 00:46:06,800
+imaginary parts اللي هو U of X و V of X are real
+
+417
+00:46:06,800 --> 00:46:12,200
+solutions يبقى هدول حلول حقيقية للمعادلة اللي
+
+418
+00:46:12,200 --> 00:46:17,070
+عندنا هذهتمام؟ إذا لو طلع عندي حل المعادلة
+
+419
+00:46:17,070 --> 00:46:22,210
+التفاضلية على الشكل Complex بيكون الجزء الحقيقي من
+
+420
+00:46:22,210 --> 00:46:26,390
+الدل اللي طلع عبارة عن حل المعادلة الأصلية والجزء
+
+421
+00:46:26,390 --> 00:46:30,790
+التخيلي كمان بدون ال I عبارة عن حل المعادلة
+
+422
+00:46:30,790 --> 00:46:35,010
+التفاضلية اللي عندكالان كنا في وادي وننتقل الى
+
+423
+00:46:35,010 --> 00:46:40,410
+وادي آخر اللى مصيغة Euler لمن؟ للـ exponential
+
+424
+00:46:40,410 --> 00:46:44,570
+function يبقى formula الـ Euler بيقول الـ
+
+425
+00:46:44,570 --> 00:46:51,290
+exponential function E of I ثيتا is written as E
+
+426
+00:46:51,290 --> 00:46:56,590
+of I ثيتا تكتب كسين ثيتا زائد I ثين ثيتا ضالت
+
+427
+00:46:56,590 --> 00:46:58,390
+complex و الله صارت real
+
+428
+00:47:01,310 --> 00:47:06,510
+يبقى هنا E أس I ثيتا كومليكس تكتب على الصيرة أس
+
+429
+00:47:06,510 --> 00:47:13,430
+ثيتا زائد I ثيتا طيب لو E أس سالب I ثيتا هشوف كيف
+
+430
+00:47:13,430 --> 00:47:19,790
+بالصير يبقى هذه المناطق بالصير E أس I سالب ثيتا
+
+431
+00:47:19,790 --> 00:47:24,570
+مظبوطيعني معناته بيجي في اللي فوق شيل كل ثيتا وحط
+
+432
+00:47:24,570 --> 00:47:32,810
+مكانها سالب ثيتا يبقى هنا cosine لسالب ثيتا زائد I
+
+433
+00:47:32,810 --> 00:47:39,250
+sine لسالب ثيتا ويساوي ال cosine even ولا odd يبقى
+
+434
+00:47:39,250 --> 00:47:44,150
+أبدا cosine سالب ثيتا هي ب cosine ثيتا وال sign
+
+435
+00:47:45,020 --> 00:47:51,000
+يبقى السلب بيطلع برا يبقى ناقص I في الـSin الزاوية
+
+436
+00:47:51,000 --> 00:47:57,720
+ثيتا طلعيلي كويس انقار المابين اتنين يبقى I أس I
+
+437
+00:47:57,720 --> 00:48:02,980
+ثيتا هي Cos ثيتا زي I Sin ثيتا I أس سلب I ثيتا هي
+
+438
+00:48:02,980 --> 00:48:08,320
+Cos ثيتا سلب I Sin ثيتا يبقى نفس اللي فوق بس غيرنا
+
+439
+00:48:08,320 --> 00:48:15,760
+من الإشارة اللتي بينهمايجي لنقطة التالتة E أُس X
+
+440
+00:48:15,760 --> 00:48:21,120
+زائد I ثيتا يبقى بقدر أقول E أُس X في E أُس I ثيتا
+
+441
+00:48:21,120 --> 00:48:26,720
+لإنه إذا تساوت الأساسات عند ضرب تجمع الأساس مش
+
+442
+00:48:26,720 --> 00:48:33,750
+هقول E أُس X ضرب E أُس I ثيتايبقى مش جصدي او سكس
+
+443
+00:48:33,750 --> 00:48:38,950
+زائد اوس اي ثيتا وانما بقول ايش او سكس ضرب اوس اي
+
+444
+00:48:38,950 --> 00:48:43,490
+ثيتا لان عند الضرب تجمع من الاساس ال او سكس زي ما
+
+445
+00:48:43,490 --> 00:48:49,360
+هي هادي مش هي هاد اللي فوقبس بدل تتاجانبين يبقى
+
+446
+00:48:49,360 --> 00:48:57,980
+بقدر اقول هذه cosine y زائد I sine ال Y بالشكل
+
+447
+00:48:57,980 --> 00:49:04,740
+اللي عندها او بقدر اقول cosine X بقدر اقول E أس X
+
+448
+00:49:04,740 --> 00:49:13,990
+cosine ال Yيبقى EOS 6 Cos Y زائد I في EOS 6 في
+
+449
+00:49:13,990 --> 00:49:20,510
+Sine Y بالشكل اللي لدينا هنا طيب بدنا نيجي ل E EOS
+
+450
+00:49:20,510 --> 00:49:25,670
+I باي يبقى نفس اللي فوق بس بدل ال θ جانمين باي
+
+451
+00:49:25,670 --> 00:49:33,270
+يبقى باجي بقوله هذه Cos Pi زائد I Sine Pi Sine Pi
+
+452
+00:49:33,270 --> 00:49:41,460
+يبقى درجة Sine Piبزيرو قصة مية و تمانين يبقى
+
+453
+00:49:41,460 --> 00:49:46,960
+السالب واحد بقدر اشيله دائما او اكتب داله E اص I
+
+454
+00:49:46,960 --> 00:49:54,540
+باي نجي الان لمجموع لاتنين E اص I بي اكس زي E اص
+
+455
+00:49:54,540 --> 00:49:59,560
+سالب I بي اكس اظن انتوا أخدتوا كل كلص بيمزاكن
+
+456
+00:49:59,560 --> 00:50:03,540
+الجوش والسنش والشغل تاني مش كنا نقول جوش ال X E
+
+457
+00:50:03,540 --> 00:50:10,820
+والسنش زايد E ناقص I X على اتنين تمام يبقى هنا
+
+458
+00:50:10,820 --> 00:50:18,160
+باجي بقول هذه بيديها تساوي cosine اللي هو BX زايد
+
+459
+00:50:18,160 --> 00:50:25,700
+I سايد BX زايد هذه الأولى التانية اللي هو cosine
+
+460
+00:50:26,410 --> 00:50:33,470
+بكس ناقص I sin بكس اظن ان هذه بالموجب وهذه بالسلب
+
+461
+00:50:33,470 --> 00:50:42,070
+مع السلامة يبقى هذا الكلام يساوي اتنين cosine بكس
+
+462
+00:50:42,070 --> 00:50:47,550
+يبقى مجموعة الاتنين بده يعطينا اتنين cosine بكس طب
+
+463
+00:50:47,550 --> 00:50:48,930
+لو طرحتهم
+
+464
+00:50:51,450 --> 00:51:01,210
+يبقى لو جت قلت and E-E-IBX يبقى ناقص E-E-IBX يبقى
+
+465
+00:51:01,210 --> 00:51:14,480
+ناقص E-E-IBXبكس ناقص cosine بكس زائد I sine بكس
+
+466
+00:51:14,480 --> 00:51:18,860
+سالب cosine وموجب cosine مع السلامة يبقى بصير
+
+467
+00:51:18,860 --> 00:51:28,380
+الناتج اللي هو اتنين I sine بكس
+
+468
+00:51:33,790 --> 00:51:38,190
+يبقى هذا اللي هو الشكل العام لمين للمعادلة اللي
+
+469
+00:51:38,190 --> 00:51:38,510
+عندنا
+
+470
+00:51:44,560 --> 00:51:50,860
+طيب جبت الأن ال EOS بي إكس وال EOS ناقص I بي إكس
+
+471
+00:51:50,860 --> 00:51:57,260
+وطلعتهم يبقى بقدر أقول يا بنات من هذه المعادلة
+
+472
+00:51:57,260 --> 00:52:07,030
+بقدر أطلع شغلة كمان ايش الشغلة لوكو ساينبكس يساوي
+
+473
+00:52:07,030 --> 00:52:18,250
+نص فيه لو جسمتها اتنين بيظل E اص I بكس زائد E اص
+
+474
+00:52:18,250 --> 00:52:19,490
+ناقص I
+
+475
+00:52:22,350 --> 00:52:27,470
+بكتر بكتر بكتر
+
+476
+00:52:27,470 --> 00:52:34,110
+بكتر
+
+477
+00:52:34,110 --> 00:52:40,470
+بكتر
+
+478
+00:52:40,470 --> 00:52:45,370
+بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر
+
+479
+00:52:45,370 --> 00:52:46,340
+بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكتر بكترهذا
+
+480
+00:52:46,340 --> 00:52:49,980
+اللي أعطينالكم المقدمات لهذا ال section و المرة
+
+481
+00:52:49,980 --> 00:52:55,660
+القادمة ان شاء الله بندخل فيه صميم الحل للمعادلة
+
+482
+00:52:55,660 --> 00:53:01,260
+التفاضلية إذا ال roads كانت مالها complex يبقى بدي
+
+483
+00:53:01,260 --> 00:53:05,500
+أكل مرة جاية قبل تيجي محاضرة تمر على هذه المعلومات
+
+484
+00:53:05,500 --> 00:53:08,700
+مش لما نجي نشتغل نقول و الله مش عارفين شو هذا و
+
+485
+00:53:08,700 --> 00:53:14,880
+لاسم و بتاخدش شي معاك كل منك عشر دقايق يعطيكوا
+
+486
+00:53:14,880 --> 00:53:15,280
+العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i9JeLMWGd-k.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i9JeLMWGd-k.srt
new file mode 100644
index 0000000000000000000000000000000000000000..be0041d31f5a02a4b42e84c746ca95761424c72f
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i9JeLMWGd-k.srt
@@ -0,0 +1,1364 @@
+1
+00:00:20,690 --> 00:00:25,190
+بسم الله الرحمن الرحيم انتهينا من chapter 3 الذي 
+
+2
+00:00:25,190 --> 00:00:29,510
+يتحدث عن موضوعين، وهما الـ vector spaces والـ
+
+3
+00:00:29,510 --> 00:00:34,130
+linear transformations وانتقلنا الآن إلى chapter 4
+
+4
+00:00:34,130 --> 00:00:39,150
+وهو الـ chapter الثالث من الـ linear algebra لأن 
+
+5
+00:00:39,150 --> 00:00:43,670
+المادة التي معنا معادلات تفاضلية وجبر خطي، يبقى 
+
+6
+00:00:43,670 --> 00:00:49,110
+هذا هو الـ chapter الثالث والأخير من الجبر الخطي في 
+
+7
+00:00:49,110 --> 00:00:53,330
+هذا الشابتر بدنا نأخذ two sections، هذا أول section
+
+8
+00:00:53,330 --> 00:00:57,250
+بين أيدينا، الذي هو الـ characteristic values
+
+9
+00:00:57,250 --> 00:01:01,750
+والـ section الثاني الذي هو الـ diagonalization، خلينا 
+
+10
+00:01:01,750 --> 00:01:03,990
+الآن مع الـ section الأول 4.1 الذي هو الـ
+
+11
+00:01:03,990 --> 00:01:10,970
+characteristic values، يعني القيم المميزة أو القيم 
+
+12
+00:01:10,970 --> 00:01:16,730
+المميزة، ايش القيم المميزة؟ طبعاً القيم المميزة 
+
+13
+00:01:16,730 --> 00:01:22,670
+لمصفوفة ما، هي المقصود فيها، التعريف يقول ما يأتي
+
+14
+00:01:22,670 --> 00:01:31,410
+سأعطي تعريف لقيم المميزة والمتجهات المميزة لمصفوفة
+
+15
+00:01:32,200 --> 00:01:39,160
+التعريف الأول هو القيم المميزة لمصفوفة، يقول افترض 
+
+16
+00:01:39,160 --> 00:01:45,360
+الـ A هي مصفوفة مربعة نظامها N في N، number lambda
+
+17
+00:01:45,360 --> 00:01:50,920
+يبقى هذا العدد هو real number، العدد هذا قد يكون عدد 
+
+18
+00:01:50,920 --> 00:01:57,540
+حقيقي وقد يكون عدد تخيلي complex number، يبقى سواء 
+
+19
+00:01:57,540 --> 00:02:01,140
+كان عدد حقيقي، وطبعاً سنعطي أمثلة إن شاء الله على 
+
+20
+00:02:01,140 --> 00:02:06,520
+اللاندة تطلع مرة قيمة حقيقية ومرة قيمة تخيلية، يوجد 
+
+21
+00:02:06,520 --> 00:02:11,120
+رمّز للّامضة real or complex، يعني يا إما عدد حقيقي 
+
+22
+00:02:11,120 --> 00:02:15,800
+يا إما عدد مركب، is called an eigenvalue، أسمّيه 
+
+23
+00:02:15,800 --> 00:02:20,180
+الـ eigenvalue أو الـ characteristic value، القيمة 
+
+24
+00:02:20,180 --> 00:02:25,160
+المميزة لمن؟ للمصفوفة A؟ if there exists a non
+
+25
+00:02:25,160 --> 00:02:31,200
+-zero vector x موجود في الـ Rn، يبقى الـ X ده non
+
+26
+00:02:31,200 --> 00:02:34,560
+-zero، عمره ما هيساوي zero، دلوقت دوروا بالكم non
+
+27
+00:02:34,560 --> 00:02:41,160
+-zero vector X موجود في Rn بحيث أن الـ A في الـ X
+
+28
+00:02:41,160 --> 00:02:45,560
+يساوي الـ lambda ده في X، الـ lambda يا بنات، A مصفوفة 
+
+29
+00:02:45,560 --> 00:02:51,450
+نظامها N في N، والـ X هذي vector موجود وين؟ في Rn
+
+30
+00:02:51,450 --> 00:02:57,630
+يعني كأنه مصفوفة فيها N من الصفوف وعمود واحد، لو 
+
+31
+00:02:57,630 --> 00:03:03,870
+ضربت إثنين في بعض، يطلع مصفوفة، المصفوفة هذه يمكن 
+
+32
+00:03:03,870 --> 00:03:08,410
+إخراج بين جميع عناصرها عامل مشترك، آخذه برا، آخذه
+
+33
+00:03:08,410 --> 00:03:13,690
+برا، مين هو lambda؟ lambda بيضل في الـ vector X، إن حدث
+
+34
+00:03:13,690 --> 00:03:20,050
+ذلك، بقول، يبقى lambda هي قيمة مميزة للمصفوفة A، يبقى 
+
+35
+00:03:20,050 --> 00:03:24,650
+lambda التي عندي هذه عدد، لكن X هذا vector، يعني 
+
+36
+00:03:24,650 --> 00:03:31,730
+مصفوفة تتكون من N من الصفوف وعمود واحد، تمام، إذا 
+
+37
+00:03:31,730 --> 00:03:35,730
+قدرت أكتب هذه على الشكل الذي عندنا هذا، يبقى lambda
+
+38
+00:03:35,730 --> 00:03:43,640
+هذه مالها؟ شو اسمها؟ Eigenvalue أو characteristic 
+
+39
+00:03:43,640 --> 00:03:52,200
+value، بشرط الـ X non zero vector، نجي 
+
+40
+00:03:52,200 --> 00:03:57,330
+للتعريف الثاني، Every non-zero vector x الموجود في 
+
+41
+00:03:57,330 --> 00:04:02,450
+Rn satisfy the question، يحقق لهذا الهدف، is called
+
+42
+00:04:02,450 --> 00:04:05,890
+the eigenvector أو الـ characteristic vector
+
+43
+00:04:12,430 --> 00:04:16,970
+أيوه، يعني نفس المعادلة التي عندنا، هي نفس المعادلة 
+
+44
+00:04:16,970 --> 00:04:22,770
+هذه، يبقى الـ X الذي قلنا عليه non zero vector، الـ X 
+
+45
+00:04:22,770 --> 00:04:27,630
+الذي هو non zero vector الذي يحقق المعادلة هذه 
+
+46
+00:04:27,630 --> 00:04:34,670
+أسمّيه المتجه المميز، يبقى السؤال هو: هل ممكن للـ 
+
+47
+00:04:34,670 --> 00:04:37,890
+characteristic vector في يوم من الأيام يكون الـ 
+
+48
+00:04:37,890 --> 00:04:43,870
+zero vector؟ في الإمكانية قال non-zero vector، يبقى 
+
+49
+00:04:43,870 --> 00:04:49,430
+لا يمكن للمتجه الصفري أن يكون eigenvector، يبقى الـ 
+
+50
+00:04:49,430 --> 00:04:53,870
+eigenvalue يا بنات هو عدد حقيقي أو عدد تخيلي، لكن 
+
+51
+00:04:53,870 --> 00:04:58,750
+الـ eigenvector هو مصفوفة مكونة من N من الصفوف مثلاً
+
+52
+00:04:58,750 --> 00:05:04,720
+أو M من الصفوف وعمود واحد، وهو الذي يحقق، مين يحقق
+
+53
+00:05:04,720 --> 00:05:07,940
+المعادلة التي عندنا هذه، يبقى المعادلة هذه يابا 
+
+54
+00:05:07,940 --> 00:05:12,520
+أكتبها بالشكل هذا أو الشكل هذا أو الشكل هذا، الشكل
+
+55
+00:05:12,520 --> 00:05:16,140
+هذا من وين اجا؟ هذه البنات لو جبتها على الشجرة 
+
+56
+00:05:16,140 --> 00:05:23,120
+تنقّش بالصغير، lambda x ناقص ax يساوي صفر، يعني في 
+
+57
+00:05:23,120 --> 00:05:29,060
+الـ lambda مش هيك، لو جيت قلت lambda x ناقص ax بدي أساوي
+
+58
+00:05:29,060 --> 00:05:33,460
+مين؟ بدي أساوي صفر، في عامل مشترك ممكن نأخذه منهم 
+
+59
+00:05:33,460 --> 00:05:38,780
+الذي هو من الذي هو الـ X، طب آخذه برا ولا آخذه، يعني 
+
+60
+00:05:38,780 --> 00:05:44,420
+آخذه على اليمين ولا آخذه على اليسار؟ يسار، 
+
+61
+00:05:44,420 --> 00:05:49,210
+يعني آخذه هنا برا، نأخذه على اليمين، ليش؟ لأن عملية 
+
+62
+00:05:49,210 --> 00:05:55,550
+ضرب المصوفات ليست إبدالية، دي مش بمزاج يمين وشمال، 
+
+63
+00:05:55,550 --> 00:05:59,770
+إجباري هو على اليمين، جاي بيبقى بتخليه على اليمين،
+
+64
+00:05:59,770 --> 00:06:03,430
+إذا لو أخذتوا عامل مشترك، بيظل يمين هنا عندنا
+
+65
+00:06:03,430 --> 00:06:06,790
+lambda، lambda بس ولا lambda ..
+
+66
+00:06:13,110 --> 00:06:19,530
+هل يمكن للرقم أن أطرحه من المصفوفة؟ في الإمكانية 
+
+67
+00:06:19,530 --> 00:06:24,610
+يبقى بطرح مصفوفة من مصفوفة، يبقى lambda I ناقص الـ A
+
+68
+00:06:24,610 --> 00:06:29,190
+كله في X بده يساوي صفر، يبقى هذه المعادلة التي فوق
+
+69
+00:06:29,190 --> 00:06:35,070
+التي نحن جايلين عليها، طبعاً يا إما هنكتبها خلال شغلنا
+
+70
+00:06:35,070 --> 00:06:39,210
+في هذا الـ chapter بالطريقة التي عندنا هذه، تمام،
+
+71
+00:06:39,210 --> 00:06:43,470
+يبقى هي، عرفنا الـ eigen value والـ eigen vectors، 
+
+72
+00:06:43,470 --> 00:06:48,910
+بدنا نبدأ نأخذ أمثلة على ذلك، نبدأ بأول مثال، أول 
+
+73
+00:06:48,910 --> 00:06:56,290
+مثال، مثال بسيط، يبقى example one، example one يقول 
+
+74
+00:06:56,290 --> 00:07:05,110
+ما يأتي، F المصفوفة A؟ هي الـ identity matrix التي 
+
+75
+00:07:05,110 --> 00:07:13,950
+هي the identity matrix، لو كانت هذه مصفوفة الوحدة
+
+76
+00:07:13,950 --> 00:07:26,170
+then the only، the only eigen value، eigen
+
+77
+00:07:26,170 --> 00:07:36,000
+value is one، and 
+
+78
+00:07:36,000 --> 00:07:42,320
+hence every 
+
+79
+00:07:42,320 --> 00:07:54,700
+non zero vector، every non zero vector X الذي موجود 
+
+80
+00:07:54,700 --> 00:08:04,500
+في Rn is and eigen vector
+
+81
+00:08:04,500 --> 00:08:12,820
+السبب because أن
+
+82
+00:08:12,820 --> 00:08:19,020
+الـ I في الـ X يساوي
+
+83
+00:08:21,030 --> 00:08:26,090
+أحنا قلنا الـ X هذه وين موجودة؟ الـ Rn، يبقى X هذه 
+
+84
+00:08:26,090 --> 00:08:30,550
+vector، X1، X2 لغاية Xn مضروب في مصفوفة 
+
+85
+00:08:30,550 --> 00:08:35,090
+الواحدات، بيعطيني المصفوفة X بالشكل الذي عندنا هذه
+
+86
+00:08:35,090 --> 00:08:41,290
+التي أقدر أكتبها على الشكل واحد مضروب في مين؟ في X
+
+87
+00:08:41,290 --> 00:08:45,810
+ومن هنا الـ Eigen value الذي عندنا مين؟ الذي هي 
+
+88
+00:08:45,810 --> 00:08:52,200
+الواحد، يبقى هذه أتفه أنواع مين؟ الأمثلة، يبقى لو كانت 
+
+89
+00:08:52,200 --> 00:08:58,140
+الـ A هي مصفوفة الوحدة عندنا هنا، يبقى بناء عليه الـ 
+
+90
+00:08:58,140 --> 00:09:03,610
+eigen value هي الواحد الصحيح، ما فيش غيره، لكن الـ 
+
+91
+00:09:03,610 --> 00:09:08,690
+eigenvectors أكثر، كلهم eigenvectors مع عدم الـ 
+
+92
+00:09:08,690 --> 00:09:12,890
+zero vector، روح نقول أهنس every non zero vector
+
+93
+00:09:12,890 --> 00:09:17,490
+موجود في الـ Rn عبارة عن eigenvector، هذا الشغل 
+
+94
+00:09:17,490 --> 00:09:24,250
+البسيط، طيب، نشتغل شغل أحسن من هنا، يبقى example two
+
+95
+00:09:31,250 --> 00:09:37,990
+Let، المصفوفة A التي هي عبارة عن 1، 6، 5
+
+96
+00:09:37,990 --> 00:09:40,910
+2، بالشكل الذي عندنا هنا
+
+97
+00:09:43,790 --> 00:09:50,570
+الـ X بده يساوي الـ vector الذي هو مين؟ 6 وناقص 
+
+98
+00:09:50,570 --> 00:09:57,690
+5، والـ Y هو الـ vector الذي هو مين؟ 3 وسالب 
+
+99
+00:09:57,690 --> 00:10:04,110
+2، كل هذا الذي موجود وين؟ في R2، المطلوب الأول
+
+100
+00:10:04,110 --> 00:10:12,990
+يقول لي find the eigen value
+
+101
+00:10:37,730 --> 00:10:42,430
+هل هذول بيكونوا eigenvectors of a ولا لأ؟
+
+102
+00:10:53,800 --> 00:10:59,920
+سؤال مرة ثانية، سؤال يقول ما يأتي: عندي مصفوفة نظامها 
+
+103
+00:10:59,920 --> 00:11:05,320
+2 في 2، سمّيتها A، أخذت vector ما قلت عنه 
+
+104
+00:11:05,320 --> 00:11:09,760
+لا A كان ولا غيره، vector موجود في R2
+
+105
+00:11:09,760 --> 00:11:14,920
+الذي أقدر أقول 6 وسالب 5، أو مصفوفة عمودية
+
+106
+00:11:14,920 --> 00:11:19,100
+التي هي 6 وسالب 5، وvector ثاني موجود في 
+
+107
+00:11:19,100 --> 00:11:23,050
+R2 الذي هو 3 وسالب 2، مطلبين
+
+108
+00:11:23,050 --> 00:11:28,030
+جايليّن، للـ eigenvalue للمصفوفة من A، المطلب الأول، المطلب 
+
+109
+00:11:28,030 --> 00:11:32,070
+الثاني يقول: هل الـ X وY هذول بيكونوا eigenvectors
+
+110
+00:11:32,070 --> 00:11:36,710
+أم لا؟ طبعاً يمكن يطلعوا eigenvectors ويمكن ما 
+
+111
+00:11:36,710 --> 00:11:41,010
+يطلعوش، لما نشوف هل بنقدر نكتب على الصيغة التي 
+
+112
+00:11:41,010 --> 00:11:45,610
+عندنا هذه ولا لأ؟ وبعد هيك يمكن يجي في بالنا تساؤل
+
+113
+00:11:45,610 --> 00:11:50,160
+خليه لما نوصله يصير خير، يبقى النقطة الأولى قال لي
+
+114
+00:11:50,160 --> 00:11:54,000
+هات لي الـ eigen value لمين؟ للمصفوفة، باجي بقوله أنا 
+
+115
+00:11:54,000 --> 00:11:59,660
+بدي آخذ الـ A في الـ X، هشوف ايش بتعطينا، يبقى بداجي 
+
+116
+00:11:59,660 --> 00:12:05,640
+أقول له الـ A في الـ X يساوي، الـ A موجودة التي هي 1
+
+117
+00:12:05,640 --> 00:12:12,720
+6، 5، 2، الـ X عندنا قداش؟ 6 ناقص 5 
+
+118
+00:12:12,720 --> 00:12:13,740
+بالشكل الذي عندنا 
+
+119
+00:12:19,890 --> 00:12:25,610
+هل أقدر أكتب الرقم في الـ vector الذي عندنا هذا؟ و
+
+120
+00:12:25,610 --> 00:12:31,490
+لا، لأ حسب الـ definition، هل 
+
+121
+00:12:31,490 --> 00:12:34,950
+أقدر أكتب الرقم في الـ vector الذي عندنا هذا؟ ولا 
+
+122
+00:12:34,950 --> 00:12:39,150
+لأ، حسب الـ definition، تعالوا نضرب المصفتين هذول
+
+123
+00:12:39,150 --> 00:12:43,710
+ونشوف ايش الشغلاتين، يبقى الصف الأول في العمود الأول 
+
+124
+00:12:43,710 --> 00:12:50,550
+1 في 6 بـ 6، وهنا ناقص 30 بيظل قداش؟ ناقص 
+
+125
+00:12:50,550 --> 00:12:54,960
+24، يبقى هذا الصف الأول في العمود، الصف 
+
+126
+00:12:54,960 --> 00:12:59,900
+الثاني في العمود، 5 في 6 بـ 30 ناقص 10
+
+127
+00:12:59,900 --> 00:13:05,620
+بيظل قداش؟ 20، بالشكل الذي عندنا هذا، بنقدر نأخذ 
+
+128
+00:13:05,620 --> 00:13:09,760
+عامل مشترك، ايش العامل المشترك الذي ما بيُخليّنا ننام؟
+
+129
+00:13:11,370 --> 00:13:14,350
+4، لو أخذت 4 بيصير هنا سالب، بس أنا عندي 
+
+130
+00:13:14,350 --> 00:13:20,090
+سالب وين؟ تحت، يبقى آخذ سالب 4 من الكل، يبقى سالب 
+
+131
+00:13:20,090 --> 00:13:26,850
+4 بيظل عندنا قداش؟ 6 وهنا قداش؟ ناقص 5 
+
+132
+00:13:26,850 --> 00:13:31,660
+بالشكل الذي عندنا هنا، يبقى هذا X ولا لا؟ مش هو X
+
+133
+00:13:31,660 --> 00:13:37,440
+الذي عندنا؟ إذا حصل ضرب لإثنين، كتبته على صيغة رقم
+
+134
+00:13:37,440 --> 00:13:43,460
+مضروب في الـ X، يبقى Lambda بكم؟ سالب 4، يبقى 
+
+135
+00:13:43,460 --> 00:13:52,640
+هنا Lambda تساوي السالب 4، التي هي is the eigen 
+
+136
+00:13:52,640 --> 00:14:04,450
+value of the matrix المعطى، طب لو غيرنا المصفوفة 
+
+137
+00:14:04,450 --> 00:14:08,630
+هذه بمصفوفة ثانية، بضل الـ lambda هذه ولا بتتغير؟ 
+
+138
+00:14:10,080 --> 00:14:15,780
+بتتغير لأن هذه كل واحدة خاصة بمصفوفتها، إذا لو غيرت 
+
+139
+00:14:15,780 --> 00:14:19,940
+المصفوفة، بتتغير قيمة lambda، يعني بتبقى إشتاب، ده ليش 
+
+140
+00:14:19,940 --> 00:14:23,400
+أنا أقول the eigen value of the matrix A؟ غيرت 
+
+141
+00:14:23,400 --> 00:14:28,660
+الـ matrix، اتغير مين؟ بتتغير قيمة الـ lambda، يبقى هذا 
+
+142
+00:14:28,660 --> 00:14:34,780
+المطلوب الأول الذي هو نمرة a، نمرة b، نمرة b يقول هل
+
+143
+00:14:34,780 --> 00:14:39,120
+الـ X والـ Y Eigen Vectors ولا لا؟ ببدأ أسألكم 
+
+144
+00:14:39,120 --> 00:14:43,800
+السؤال التالي، هل الـ X Eigen Vector ولا لا؟ ليش؟ لأنه 
+
+145
+00:14:43,800 --> 00:14:49,320
+non-zero، إثنين حقق المعادلة التي عندنا هذه، صحيح 
+
+146
+00:14:49,320 --> 00:14:54,960
+ولا لا؟ يبقى باجي أقول is the Eigen Value، and الـ X 
+
+147
+00:14:54,960 --> 00:15:02,980
+بده يساوي 6 ناقص 5 is an Eigen Vector 
+
+148
+00:15:05,910 --> 00:15:10,650
+المصفوفة A؟ طب بدي آجي لنمرة b؟ بدي أشتغل نفسي 
+
+149
+00:15:10,650 --> 00:15:18,120
+الشغل فايش؟ بدي آجي أقوله؟ بدي آخذ الـ A في الـ Y، طبعاً 
+
+150
+00:15:18,120 --> 00:15:23,540
+إذا لما آخذ الـ A في الـ Y، بده يساوي المصفوفة 1، 6،
+
+151
+00:15:23,540 --> 00:15:29,620
+5، 2، فمين في الـ Y؟ عنده 3 وسالب 2، 
+
+152
+00:15:29,620 --> 00:15:34,260
+بالشكل الذي عندنا هذا، يبقى تعالوا نضرب الصف الأول في 
+
+153
+00:15:34,260 --> 00:15:39,820
+العمود، يبقى 3 وعندي ناقص 4، بيظل قداش؟ 
+
+154
+00:15:49,280 --> 00:15:55,740
+السؤال هو: هل تستطيع أن تأخذ عامل مشترك يطلع عندنا 
+
+155
+00:15:55,740 --> 00:15:57,100
+هذا الـ vector؟
+
+156
+00:15:59,630 --> 00:16:07,630
+يبقى هذا لا يساوي lambda في من؟ في 3، سالب 
+
+157
+00:16:07,630 --> 00:16:15,770
+2 for any number lambda، لأي number lambda، هذا الكلام 
+مش موجود عندي، معناته
+
+158
+00:16:21,210 --> 00:16:26,650
+هذا الـ vector Eigen vector، يبقى هذا لا يمكن أن يكون 
+
+159
+00:16:26,650 --> 00:16:34,390
+eigenvector في يوم من الأيام، يبقى هنا الـ Y تساوي 
+
+160
+00:16:34,390 --> 00:16:45,170
+3 وسالب 2 is not an eigenvector
+
+161
+00:16:46,610 --> 00:16:50,330
+يبقى معناته هذا الكلام، الـ Eigenvector يعتمد على 
+
+162
+00:16:50,330 --> 00:16:53,970
+مين؟ الـ Eigenvalue، إذا عندي ايش فيه Eigenvalue 
+
+163
+00:16:53,970 --> 00:16:57,010
+معناته فيه Eigenvector، ما فيش Eigenvalue، يبقى ما فيش 
+
+164
+00:16:57,010 --> 00:17:04,490
+Eigenvector، تمام؟ يبقى هذا مثال بسيط، واضح إنه معنى 
+
+165
+00:17:04,490 --> 00:17:07,930
+الـ Eigenvalue والـ Eigenvector الذي أعطينا 
+
+166
+00:17:07,930 --> 00:17:12,830
+تعريفاتهم أو تعريفاتهما قبل قليل
+
+167
+00:17:15,770 --> 00:17:21,710
+نأتي للنقطة الثانية، كيف بدنا نوجد الـ eigenvalues 
+
+168
+00:17:21,710 --> 00:17:29,170
+سنطرح حد على صيغة السؤال التالي، يبقى how to find 
+
+169
+00:17:29,170 --> 00:17:38,970
+كيف بدك توجد
+
+201
+00:22:09,510 --> 00:22:22,010
+A21 ناقص A21 وبعدين لامدا ناقص A22 وناقص A2N و
+
+202
+00:22:22,010 --> 00:22:31,530
+نضل ماشيين لغاية ناقص AN1 ناقص AN2 ونضل ماشيين 
+
+203
+00:22:31,530 --> 00:22:35,750
+لغاية لامدا ناقص ANN
+
+204
+00:23:08,940 --> 00:23:10,340
+اممم
+
+205
+00:23:17,590 --> 00:23:22,050
+الآن بنطرح السؤال الذي بين أيدينا هذا ونحاول نجاوب
+
+206
+00:23:22,050 --> 00:23:29,070
+على هذا السؤال بخطوتين لا ثالثة لهما، السؤال هو how
+
+207
+00:23:29,070 --> 00:23:33,690
+to find the eigenvalues of an n by n matrix  أيه 
+
+208
+00:23:33,690 --> 00:23:38,110
+ماهي الوسيلة العملية مشان نجيب ال eigenvalues
+
+209
+00:23:38,110 --> 00:23:44,140
+لمصفوفة مع نظامها n في n التي جابها في نقطتنا النقطة 
+
+210
+00:23:44,140 --> 00:23:49,020
+الأولى بيقول يا ليها write the equation AX بيساوي
+
+211
+00:23:49,020 --> 00:23:53,180
+Lambda X in the form قعدت كتابة المعادلة التي
+
+212
+00:23:53,180 --> 00:23:57,080
+عندنا تبع تعريف ال Eigen value على الشكل الذي 
+
+213
+00:23:57,080 --> 00:24:01,240
+عندنا هذا وهذا شفناها كيف قبل قليل كتبناها سميناها
+
+214
+00:24:01,240 --> 00:24:05,280
+المعادلة Star الآن المعادلة Star هذه homogeneous
+
+215
+00:24:05,280 --> 00:24:10,360
+system أم non homogeneous system؟ هوموجينيا ال
+
+216
+00:24:10,360 --> 00:24:13,880
+system مدام هوموجينيا ال system يا عندي ال trivial
+
+217
+00:24:13,880 --> 00:24:18,740
+solution يا إما عندي عدد لا نهائي من الحلول أنا بدي
+
+218
+00:24:18,740 --> 00:24:22,540
+أستبعد ال trivial solution لأن قلت الفكتور هذا non
+
+219
+00:24:22,540 --> 00:24:28,420
+zero vector معناته الحل الصفري مستبعد فإيش قال ليه؟
+
+220
+00:24:28,800 --> 00:24:32,860
+بما أن الـ X لا يمكن أن تساوي 0 يعني الحل الصفري
+
+221
+00:24:32,860 --> 00:24:39,580
+مستبعد يبقى ال system has a non-zero solution إذا
+
+222
+00:24:39,580 --> 00:24:43,540
+كان ال determinant هذا بيساوي قداش؟ Zero إذا 
+
+223
+00:24:43,540 --> 00:24:48,080
+المحدد تبع المصفوفة هذا بيساوي Zero بيكون عندي الذي 
+
+224
+00:24:48,080 --> 00:24:54,040
+هو حل غير صفري لمين؟ للس system الذي عندنا هذا
+
+225
+00:24:57,620 --> 00:25:05,030
+الحل تبع المحدد هذا بيعطيني قيم ال eigenvalues ليش؟
+
+226
+00:25:05,030 --> 00:25:10,350
+لأن هذه معادلة هذه أعداد هذه مصفوفة الوحدة المجهول
+
+227
+00:25:10,350 --> 00:25:14,710
+من عندي لامدا إذا بفكها دي وبجيب له قيم لامدا
+
+228
+00:25:14,710 --> 00:25:17,870
+يمكن تطلع معادلة من الدرجة الثانية يمكن من الدرجة 
+
+229
+00:25:17,870 --> 00:25:21,350
+الثالثة يمكن من الدرجة الرابعة حسب نوع المصفوفة
+
+230
+00:25:21,350 --> 00:25:26,120
+التي عندي فلو كانت المصفوفة من الدرجة الثانية يبقى
+
+231
+00:25:26,120 --> 00:25:29,840
+automatic لازم تطلع المعادلة من الدرجة الثانية إذا
+
+232
+00:25:29,840 --> 00:25:33,300
+المصفوفة نظامها ثلاثة في ثلاثة بتطلع من الدرجة 
+
+233
+00:25:33,300 --> 00:25:38,960
+الثالثة وهكذا تمام إلى آخره طيب ما علينا نجي
+
+234
+00:25:38,960 --> 00:25:42,940
+التعريف الثاني بقول المعادلة التي عندنا هذه التي
+
+235
+00:25:42,940 --> 00:25:46,860
+هو determinant لهذه بيساوي zero بسميها ال
+
+236
+00:25:46,860 --> 00:25:50,460
+characteristic equation أو ال polynomial equation
+
+237
+00:25:50,460 --> 00:25:56,020
+يبقى كثيرة الحدود أو معادلة كثيرة الحدود أو
+
+238
+00:25:56,020 --> 00:26:02,120
+المعادلة المميزة لمين؟ للمصفوفة أيه that is مين هي
+
+239
+00:26:02,120 --> 00:26:09,120
+لما أقول P of لامدا يعني دالة في لامدا بتطلع بدلالة 
+
+240
+00:26:09,120 --> 00:26:13,100
+لامدا من هي هي ال determinant للامدا أيه ناقص أيه
+
+241
+00:26:13,100 --> 00:26:17,480
+ناقص أيه وأن اللامدا أيه يبقى اللامدا مضروبة في مين
+
+242
+00:26:17,480 --> 00:26:24,610
+في مصفوفة الوحدة ناقص الـ A كتبتها بعناصرها يبقى بدي 
+
+243
+00:26:24,610 --> 00:26:29,370
+أطرح المصفوفتين من بعض بيصير كل عنصر بأطرحهم من
+
+244
+00:26:29,370 --> 00:26:34,590
+نظيره صفر ناقص يبقى البجر بيصير ناقص ما عدا عناصر
+
+245
+00:26:34,590 --> 00:26:37,270
+القطر الرئيسية القطر الرئيسي بيصير لامدا ناقص أيه 
+
+246
+00:26:37,270 --> 00:26:42,380
+one one لامدا ناقص a22 ناقص لامدا a33  الأخر حاجة
+
+247
+00:26:42,380 --> 00:26:47,440
+لامدا ناقص a nn والباقي عناصر المصفوفة هم هم بس
+
+248
+00:26:47,440 --> 00:26:53,380
+بغير مين إشارتهم؟ السبب بسبب سبق المصفوفة بمين 
+
+249
+00:26:53,380 --> 00:26:58,500
+بإشارة سالب يبقى الصورة العامة لهذه المصفوفة تصبح 
+
+250
+00:26:58,500 --> 00:27:03,280
+على الصورة التي عندها هي القطر الرئيسي كله لامدا
+
+251
+00:27:03,280 --> 00:27:07,690
+ناقص عناصر القطر الرئيسي والباقي هي المصفوفة A بس
+
+252
+00:27:07,690 --> 00:27:12,090
+بإشارة من؟ بإشارة سالب الآن الكلام الذي أقوله هذا
+
+253
+00:27:12,090 --> 00:27:16,970
+بدنا نروح نطبقه على أرض الواقع يبقى لما نيجي نحسب 
+
+254
+00:27:16,970 --> 00:27:22,010
+قيمة لامدا هنا يا بنات يمكن تطلع عدد حقيقي ويمكن
+
+255
+00:27:22,010 --> 00:27:27,990
+تطلع عدد تخيلي كما ذكرنا في التعريف قبل قليل تمام
+
+256
+00:27:27,990 --> 00:27:32,250
+إذا بدنا نروح نجرب نخلي مرة يطلع عدد حقيقي ومرة 
+
+257
+00:27:32,250 --> 00:27:36,390
+يطلع تخيلي ونشوف كيف بدنا نجيب ال eigenvalues وال
+
+258
+00:27:36,390 --> 00:27:40,690
+eigenvectors في هذه الحلقة هنبدأ بعدد حقيقي
+
+259
+00:27:40,690 --> 00:27:44,070
+لأنه أسهل شوية والمرة الجاية إن شاء الله بنجيب
+
+260
+00:27:44,070 --> 00:27:52,110
+اللعنة ده بعدد تخيلي يبقى example one example one
+
+261
+00:27:52,110 --> 00:27:59,610
+هذا سؤال واحد من الكتاب بقول find the eigenvalues
+
+262
+00:27:59,610 --> 00:28:05,450
+find the eigenvalues
+
+263
+00:28:05,450 --> 00:28:08,730
+and eigenvectors
+
+264
+00:28:16,270 --> 00:28:21,330
+والـ Eigenvectors of the
+
+265
+00:28:21,330 --> 00:28:26,730
+matrix للمصفوفة
+
+266
+00:28:26,730 --> 00:28:29,930
+التي تساوي 
+
+267
+00:28:41,860 --> 00:28:45,840
+يبقى بدل الـ Eigenvalues والـ Eigenvectors لمين؟
+
+268
+00:28:45,840 --> 00:28:47,740
+للمصفوفة التي عندنا هذه
+
+269
+00:28:53,790 --> 00:28:57,090
+كيف بدي أجيب الـ Eigenvalues؟ هذه المعادلة التي 
+
+270
+00:28:57,090 --> 00:29:02,510
+عندنا يبقى أنا بدي أذهب لمين؟ لـ lambda I ناقص A X
+
+271
+00:29:02,510 --> 00:29:07,210
+بده يساوي Zero وبعد هيك إذا قلت X non-zero يبقى 
+
+272
+00:29:07,210 --> 00:29:10,890
+بدي ال determinant لهذه وأخليه يساوي مين؟ ال Zero
+
+273
+00:29:10,890 --> 00:29:17,690
+إذا أنا بدي أبدأ بال determinant لمين؟ للامدا I
+
+274
+00:29:17,690 --> 00:29:23,070
+ناقص الـ A كله وأقول هذا الكلام بده يساوي قداش؟ 
+
+275
+00:29:23,070 --> 00:29:28,770
+بده يساوي Zero طيب مشان هيك تعال نشوف لامدا في I
+
+276
+00:29:28,770 --> 00:29:33,550
+ونشوف الـ A، اه الـ A موجود عندي إذا بقدر أعوض تعويض 
+
+277
+00:29:33,550 --> 00:29:37,470
+مباشر في الأخيرة التي تحت هذه ما انديش أقعد أكل
+
+278
+00:29:37,470 --> 00:29:42,270
+كثير يبقى بقدر أكتب على طول الخط يبقى هاي 
+
+279
+00:29:42,270 --> 00:29:47,910
+المصفوفة التي عندنا هاي التي عندنا ناقص a11 a11
+
+280
+00:29:47,910 --> 00:29:54,750
+بقداش سالف واحد يبقى بيصير زائد واحد هذا ناقص واحد
+
+281
+00:29:54,750 --> 00:30:00,450
+زي ما هو هذا ناقص أربعة زي ما هو هذه لامدا ناقص
+
+282
+00:30:00,450 --> 00:30:03,990
+اثنين هيجفلنا الجوز تمام؟
+
+283
+00:30:07,360 --> 00:30:13,640
+للامدا اي ناقص الاي له بده يساوي زيرو يعني معناه
+
+284
+00:30:13,640 --> 00:30:19,840
+هذا الكلام أنه عندي المحدد لامدا زائد واحد ناقص
+
+285
+00:30:19,840 --> 00:30:26,500
+واحد ناقص أربعة لامدا ناقص اثنين كل هذا الكلام بده
+
+286
+00:30:26,500 --> 00:30:32,060
+يساوي مين؟ بده يساوي زيرو إذا لو فكّت المحدد هذا حاصل 
+
+287
+00:30:32,060 --> 00:30:36,860
+ضرب عناصر القطر الرئيسي ناقص حاصل ضرب عناصر القطر
+
+288
+00:30:36,860 --> 00:30:43,680
+الثانوي هذا بيعطيك لامدا زائد واحد في لامدا ناقص
+
+289
+00:30:43,680 --> 00:30:49,580
+اثنين ناقص أربعة بيساوي مين؟ بيساوي Zero طبعا ناقص
+
+290
+00:30:49,580 --> 00:30:53,040
+واحد فناقص أربعة بيزيد أربعة الرئيسي ناقص الثانوي
+
+291
+00:30:53,040 --> 00:30:56,440
+بتيجي كمان إشارة ناقص فبيصير الناقص بالشكل الذي 
+
+292
+00:30:56,440 --> 00:31:01,360
+عندنا هذا يبقى أنا عندي معادلة من أي درجة ثانية 
+
+293
+00:31:01,360 --> 00:31:05,400
+يبقى أنا بدي أحل المعادلة هذه مشان أحل المعادلة
+
+294
+00:31:05,400 --> 00:31:11,300
+هذه بدي اروح أفكها يبقى هذه لامدا تربيع زائد لامدا 
+
+295
+00:31:11,300 --> 00:31:17,270
+وناقص اثنين لامدا بطلع قداش ناقص لامدا وعندك ناقص 
+
+296
+00:31:17,270 --> 00:31:23,190
+اثنين ناقص أربعة بده يساوي zero أو بمعنى آخر بده 
+
+297
+00:31:23,190 --> 00:31:29,790
+يصير لامدا تربيع ناقص لامدا ناقص ستة يساوي zero أو
+
+298
+00:31:29,790 --> 00:31:36,960
+لو حللتها كحاصل ضرب قوسين يساوي zero هنا لامدا وهنا
+
+299
+00:31:36,960 --> 00:31:43,380
+لامدا وهنا اثنين في ثلاثة بستة وواحدة ناقص وواحدة
+
+300
+00:31:43,380 --> 00:31:48,200
+زائد اثنين لامدا وناقص ثلاثة تحليل مية المية يبقى 
+
+301
+00:31:48,200 --> 00:31:54,560
+بناء عليه بقول له the eigen values
+
+302
+00:31:54,560 --> 00:31:58,320
+are
+
+303
+00:32:00,560 --> 00:32:06,900
+اللي هم مين؟ لامدا تساوي ناقص اثنين and لامدا تساوي 
+
+304
+00:32:06,900 --> 00:32:13,600
+كدهش ثلاثة يبقى جيبت ال eigen vectors التي عندنا
+
+305
+00:32:14,480 --> 00:32:19,200
+جيبت ال eigenvectors التي عندنا تمام يبقى جيبت ال
+
+306
+00:32:19,200 --> 00:32:23,840
+eigenvalues لسه ال eigenvectors ما جبتهمش اه تمام 
+
+307
+00:32:23,840 --> 00:32:29,120
+بدنا نروح ندور على مين؟ على ال eigenvectors لكل
+
+308
+00:32:29,120 --> 00:32:33,280
+لامدا من اللامدات الاثنين هدول اه يعني كانوا ضايل 
+
+309
+00:32:33,280 --> 00:32:38,040
+عليه لسه مسألتين مش مسألة واحدة كل لامدا لها
+
+310
+00:32:38,040 --> 00:32:43,040
+eigenvectors خاصة بها تمام يبقى أنا بدي أمسك أول
+
+311
+00:32:43,040 --> 00:32:48,300
+واحدة فيهم يبقى باجي بقول هنا إذا كانت ال لامدا 
+
+312
+00:32:48,300 --> 00:32:51,480
+تساوي الناقص اثنين then
+
+313
+00:32:54,310 --> 00:33:01,150
+آخذ الـ lambda في هذا كله من المصفوفة التي عندنا هذه
+
+314
+00:33:01,150 --> 00:33:07,710
+صحيح ولا لأ؟ والـ X موجود وين؟ موجود في R2 يبقى X1
+
+315
+00:33:07,710 --> 00:33:14,410
+وX2 أشعرفك R2 لأن المصفوفة نظامها 2 في 2 يبقى باجي
+
+316
+00:33:14,410 --> 00:33:18,670
+بقول بدّاجي على المصفوفة هذه هي يا بنات بالتفصيل 
+
+317
+00:33:18,670 --> 00:33:26,000
+المرة هذه يبقى هي ناقص 2 زائد 1 وهي ناقص واحد وهي
+
+318
+00:33:26,000 --> 00:33:34,660
+ناقص أربعة وهي ناقص اثنين ناقص اثنين في X واحد X
+
+319
+00:33:34,660 --> 00:33:41,340
+اثنين بده يساوي Zero و Zero يبقى أنا راجع أتعوض في 
+
+320
+00:33:41,340 --> 00:33:47,560
+مين؟ في المعادلة star عن مين؟ عن قيم lambda واخذ 
+
+321
+00:33:47,560 --> 00:33:52,360
+lambda الأولى أشوف هذه إيش بدها تجيب لي يبقى هذه
+
+322
+00:33:52,360 --> 00:33:58,900
+معناه يا بنت المصفوفة ناقص واحد ناقص واحد ناقص
+
+323
+00:33:58,900 --> 00:34:07,180
+أربعة ناقص أربعة X واحد X اثنين يساوي Zero و Zero
+
+324
+00:34:07,180 --> 00:34:11,710
+بالشكل الذي عندنا هذه العمود لو جيت فكيتها يبقيش 
+
+325
+00:34:11,710 --> 00:34:21,330
+بيصير ناقص x1 ناقص x2 والعمود الثاني ناقص 4x1
+
+326
+00:34:21,330 --> 00:34:29,550
+ناقص 4x2 هي هذه كلها بدها تساوي مين؟ Zero و Zero
+
+327
+00:34:29,550 --> 00:34:38,050
+هذا معناه أنه ناقص X1 ناقص X2 بده يساوي Zero وناقص 
+
+328
+00:34:38,050 --> 00:34:48,710
+4X1 ناقص 4X2 بده يساوي Zero هذه لو جيت ضربت الأولى 
+
+329
+00:34:48,710 --> 00:34:56,450
+في سالب واحد إيش بيصير؟ X1 زائد X2 يساوي Zero هذه لو
+
+330
+00:34:56,450 --> 00:35:03,640
+ضربتها في سالب أربعة بيصير نفس المعادلة هذه صح ولا لأ
+
+331
+00:35:03,640 --> 00:35:07,660
+يبقى الثانية صاروا مش معادلتين هذه مين؟ معادلة 
+
+332
+00:35:07,660 --> 00:35:14,900
+واحدة يبقى هذا معناه أن x واحد يساوي قداش؟ سالب x
+
+333
+00:35:14,900 --> 00:35:22,000
+اثنين إذا لو كانت x اثنين ب a x واحد قداش؟ سالب a
+
+334
+00:35:22,000 --> 00:35:32,360
+يبقى هنا بقول له fالـ X2 تساوي A ثم X1 يساوي سالب A
+
+335
+00:35:32,360 --> 00:35:43,060
+يبقى باجي بقول له The Eigen vectors are in the form
+
+336
+00:35:43,060 --> 00:35:46,880
+يبقى 
+
+337
+00:35:46,880 --> 00:35:56,420
+على الشكل التالي X1 بقدر أشوف عندي سالب A وX اثنين
+
+338
+00:35:56,420 --> 00:36:03,140
+تبقى A
+
+339
+00:36:03,140 --> 00:36:07,250
+X X X X X X X X X X يبقى هي جيب له
+
+340
+00:36:07,250 --> 00:36:12,370
+ال eigenvectors كل ال vectors التي بتبقى على الشكل
+
+341
+00:36:12,370 --> 00:36:16,030
+هذا يعني الرقم من ال set of real numbers الذي هو a
+
+342
+00:36:16,030 --> 00:36:20,610
+مضروب في سالب واحد واحد بيجيب لل eigenvectors
+
+343
+00:36:20,610 --> 00:36:27,170
+تبعات مين؟ تبعات lambda تساوي سالب اثنين فقط لأنه في
+
+344
+00:36:27,170 --> 00:36:30,030
+السؤال قال هي اتلقى كل ال eigenvalues وال
+
+345
+00:36:30,030 --> 00:36:34,370
+eigenvectors للمصفوفة هذه أنا جيبت لسه ل lambda 2 زي
+
+346
+00:36:34,370 --> 00:36:39,050
+ما جيبت ل lambda 2 بتروح أجيب لما ل lambda 3 يبقى
+
+347
+00:36:39,050 --> 00:36:46,590
+كله بالشكل الذي هنا كم واحد هدول بس المراكبة الأولى
+
+348
+00:36:46,590 --> 00:36:52,390
+هي سالب المراكبة الثانية كل العناصر التي بالشكل 
+
+349
+00:36:52,390 --> 00:36:55,150
+هذا بيكونوا eigenvectors واحنا شفنا في السؤال الذي
+
+350
+00:36:55,150 --> 00:36:59,690
+جاب له قبل قليل مش كل vector هو eigenvector يعني
+
+351
+00:36:59,690 --> 00:37:04,120
+بعضهم بنفع يكون eigenvectors وبعضهم بنفعل في السؤال
+
+352
+00:37:04,120 --> 00:37:07,280
+الذي جاب له الـ X طلع Eigen vector لكن الـ Y طلع
+
+353
+00:37:07,280 --> 00:37:11,980
+Eigen vector إذا يا بنات مش كل vector بنفع يكون
+
+354
+00:37:11,980 --> 00:37:15,760
+Eigen vector للمصفوفة التي موجودة البعض بنفع
+
+355
+00:37:15,760 --> 00:37:19,980
+والبعض بنفعش مين الذي بينفعه في السؤال هذا كل ال
+
+356
+00:37:19,980 --> 00:37:23,700
+vectors التي على الشكل area number مضروب في سالب
+
+357
+00:37:23,700 --> 00:37:28,320
+واحد وواحد طيب نجي للحالة الثانية
+
+358
+00:37:45,930 --> 00:37:51,970
+أخذنا لامدا تساوي سالب اثنين بدأت ياخد الان F
+
+359
+00:37:51,970 --> 00:37:57,370
+لامدا تساوي ثلاثة الذي هو القيمة الثانية التي 
+
+360
+00:37:57,370 --> 00:38:03,110
+طلعناها then لامدا
+
+361
+00:38:03,110 --> 00:38:11,610
+I ناقص الـ A في X بدها تساوي zero implies بتجي لنفس
+
+362
+00:38:11,610 --> 00:38:14,170
+المصفوفة التي عندنا هذي بدي أشيل اللامدا وأحط 
+
+363
+00:38:14,170 --> 00:38:21,050
+مكانها مالها ثلاثة يبقى ثلاثة زائد واحد وسالب
+
+364
+00:38:21,050 --> 00:38:29,290
+واحد وسالب أربعة وثلاثة ناقص اثنين هذه كلها في X
+
+365
+00:38:29,290 --> 00:38:36,650
+واحد X اثنين كله بدي يساوي مين؟ Zero و Zero ثلاثة
+
+366
+00:38:36,650 --> 00:38:42,480
+زائد واحد كدهش؟ أربعة وهنا سالب واحد وهنا سالب
+
+367
+00:38:42,480 --> 00:38:49,920
+أربعة وهنا واحد كله x واحد x اثنين بدي يسوى من 
+
+368
+00:38:49,920 --> 00:38:56,670
+Zero و Zero نضرب المصفوفتين هدول في بعض يبقى الصف 
+
+369
+00:38:56,670 --> 00:39:01,990
+الأول في العمود الأول أربعة X واحد ناقص X
+
+370
+00:39:01,990 --> 00:39:09,430
+اثنين صف الثاني ناقص أربعة X واحد زائد X اثنين
+
+371
+00:39:09,430 --> 00:39:15,760
+ك
+
+Please provide the Arabic/English lecture transcript that you would like me to review and correct. I will then provide the corrected transcript according to your specified guidelines. 
+
+I'm ready to help you polish your lecture transcript!  
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cc2d3f3cf80b72ea84b8d0f1cec0f7444f37204f
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo.srt
@@ -0,0 +1,1477 @@
+1
+00:00:20,160 --> 00:00:23,580
+بسم الله الرحمن الرحيم المرة اللي فاتت في نهاية
+
+2
+00:00:23,580 --> 00:00:27,880
+المحاضرة الماضية كتبنا ملاحظة، الملاحظة كانت على 
+
+3
+00:00:27,880 --> 00:00:31,980
+الشكل التالي، لو كانت المعادلة التفاضلية على شكل
+
+4
+00:00:31,980 --> 00:00:41,840
+a1x + b1y + c1 كلها في y' = a2x + b2y 
+
+5
+00:00:41,840 --> 00:00:48,040
++ c2 يبقى في هذه الحلقة نحاول نحل المعادلة
+
+6
+00:00:48,040 --> 00:00:52,680
+التفاضلية اللي عندنا. طبعا لو جسمنا الطرفين على X أو
+
+7
+00:00:52,680 --> 00:00:57,760
+على Y لا يمكن أن تظهر الـ Homogeneous Differential 
+
+8
+00:00:57,760 --> 00:01:06,040
+Equation. هل الـ A1 في B2 يساوي الـ A2 في B1 ولا 
+
+9
+00:01:06,040 --> 00:01:11,420
+لا؟ إن حدث ذلك يبقى من الحل هذه كما كنا نحل من قبل
+
+10
+00:01:11,420 --> 00:01:16,580
+بصير مسألتنا سهلة، لكن إن كانت الـ A1 B2 لا تساوي
+
+11
+00:01:16,580 --> 00:01:22,590
+B2 A1 يجب أن نكتب المعادلتين الاثنتين اللي عندنا 
+
+12
+00:01:22,590 --> 00:01:26,670
+و نسويهم بالصفر و نحل المعادلتين هدول مع بعضهم
+
+13
+00:01:26,670 --> 00:01:32,290
+نجيب قيمة كل من X وY أو نجيب قيمة P وQ لأن قلنا
+
+14
+00:01:32,290 --> 00:01:38,410
+نكتب معادلة على صيغة A1P + B1Q + C1 =
+
+15
+00:01:38,410 --> 00:01:45,390
+Zero و المعادلة الثانية A2P + B2Q + C2 
+
+16
+00:01:45,390 --> 00:01:51,930
+= Zero. بنروح ونقول إن نستبدل كل X بـ X كابتل + 
+
+17
+00:01:51,930 --> 00:01:57,250
+P اللي طلعت وكل Y بـ Y كابتل + Q اللي طلعت إن هو
+
+18
+00:01:57,250 --> 00:02:01,490
+في هذه الحالة automatically تتحول المعادلة اللي عندنا
+
+19
+00:02:01,490 --> 00:02:07,520
+إلى معادلة متجانسة. هذا آخر كلمتين نظري كتبناه المرة
+
+20
+00:02:07,520 --> 00:02:11,420
+الماضية، وهذا المثال اللي قدامي على اللوح مثال
+
+21
+00:02:11,420 --> 00:02:16,980
+مباشر على هذا النوع من المسائل. ممكن ما تظهر على
+
+22
+00:02:16,980 --> 00:02:20,580
+الكاميرات بالشكل هذا، ممكن تظهر y prime = y +
+
+23
+00:02:20,580 --> 00:02:25,500
+2 / x + y + 1. إن كان بالشكل هذا أو
+
+24
+00:02:25,500 --> 00:02:30,800
+بالشكل هذا سيان يبقى بدنا نعمل نفس الشغل، يعني ممكن 
+
+25
+00:02:30,800 --> 00:02:37,840
+تظهر y prime = y + 2 / x + y + 1
+
+26
+00:02:37,840 --> 00:02:42,080
+نظرت بالشكل هذا أو بالشكل هذا الاثنين لهم نفس
+
+27
+00:02:42,080 --> 00:02:49,920
+الشغل، يبقى ايش بدي اعمل؟ بدي اروح اشوف هل ال a1 في 
+
+28
+00:02:49,920 --> 00:02:56,320
+ال b2 يساوي ال a1 اللي هو معامل مين؟ معامل x بقدرش
+
+29
+00:02:56,320 --> 00:03:02,440
+يبقى a1 b2. b2 معامل y اللي هو بقدرش واحد، يبقى النتيجة
+
+30
+00:03:02,440 --> 00:03:09,390
+= 1.  بدأ اشوف a2b1 يبقى المعامل تبع x لأن
+
+31
+00:03:09,390 --> 00:03:14,550
+الوقت بدأ بالزيرو، معامل b1 معامل y هنا اللي هو
+
+32
+00:03:14,550 --> 00:03:22,090
+بواحد y = زيرو يبقى هذا معناه ان a1b2 لا يساوي 
+
+33
+00:03:22,090 --> 00:03:28,790
+a2 في ال b1. مدام هدول ما بيساويوش بعض، إذا بدنا
+
+34
+00:03:28,790 --> 00:03:33,470
+نروح نحل المعادلتين هدول مع بعض. يبقى بدي اكتب 
+
+35
+00:03:33,470 --> 00:03:39,950
+المعادلة هذه ل P + Q + 1 = Zero 
+
+36
+00:03:39,950 --> 00:03:46,990
+والمعادلة الثانية Q + 2 = Zero. من هذه
+
+37
+00:03:46,990 --> 00:03:51,790
+المعادلة بقدر اقول إذا ال Q = قداش؟ سالب ب
+
+38
+00:03:51,790 --> 00:03:56,920
+2. يبقى بناء عليه من الاثنين هدول مع بعض بصيرين
+
+39
+00:03:56,920 --> 00:04:02,940
+P - 2 + 1 = Zero ومنها P =
+
+40
+00:04:02,940 --> 00:04:10,680
+قداش؟ تساوي 1. إذا بدي اعمل التحويل اللي بدنا نضيع
+
+41
+00:04:10,680 --> 00:04:17,180
+الـ constant 1 و الـ constant 2 وهيبدنا نروح 
+
+42
+00:04:17,180 --> 00:04:25,860
+نحط x small = x capital + t. يعني مين؟ يعني
+
+43
+00:04:25,860 --> 00:04:33,160
+ال x small بدي يساوي x capital + 1 و ال y
+
+44
+00:04:33,160 --> 00:04:40,740
+بدي يساوي y capital + ل q يعني y small بدي
+
+45
+00:04:40,740 --> 00:04:46,910
+يساوي y capital - 2. قيمة q اللي عندنا
+
+46
+00:04:46,910 --> 00:04:52,410
+المعلومات هذه بروح اعوض فين؟ في المعادلة اللي فوق
+
+47
+00:04:52,410 --> 00:04:57,270
+اللي بدي اسميها المعادلة star. يبقى بدجي اقول هنا 
+
+48
+00:04:57,270 --> 00:05:02,830
+substitute in 
+
+49
+00:05:02,830 --> 00:05:12,070
+equation star we get بنحصل على المعادلة التالية
+
+50
+00:05:12,610 --> 00:05:17,730
+يبقى بده اشيل ال X Small واحط بدل X Capital +
+
+51
+00:05:17,730 --> 00:05:24,610
+1 يبقى هذا معناه اه بس استنى شوية لما نيجي لهذا
+
+52
+00:05:24,610 --> 00:05:29,990
+يا بنات ولما نيجي نشتقها، يبقى اشتقاقها دي بده يصير DX
+
+53
+00:05:29,990 --> 00:05:36,810
+Small = DX Capital. ولو نيجي نشتقها دي بصير
+
+54
+00:05:36,810 --> 00:05:47,650
+عندنا DY Small = dy capital. يبقى 
+
+55
+00:05:47,650 --> 00:05:51,070
+هذه المعادلة اللي بدها تصير على الشكل التالي. ال x
+
+56
+00:05:51,070 --> 00:05:56,590
+small بدي اشيلها و احط بدالها main x + 1
+
+57
+00:05:56,590 --> 00:06:04,750
++ y small اللي هي y - 2 وهذه + 1 
+
+58
+00:06:05,390 --> 00:06:11,010
+الآن الـ y prime يعني اللي هي dy / dx. dy اللي هي 
+
+59
+00:06:11,010 --> 00:06:19,630
+d capital y / dx capital. هذا الكلام بده يساوي y
+
+60
+00:06:19,630 --> 00:06:25,610
+small اللي هو capital y - 2 + 2 اللي 
+
+61
+00:06:25,610 --> 00:06:32,240
+عندنا. نختصر الاختصارات 1، 1. 2 وسالب 
+
+62
+00:06:32,240 --> 00:06:37,860
+بـ 2 مع السلامة. يبقى آلة المثال إلى x +
+
+63
+00:06:37,860 --> 00:06:47,270
+capital Y dy capital / dx = capital Y. يبقى 
+
+64
+00:06:47,270 --> 00:06:52,610
+العملية بناء التعويض اللي حطناها دي فائدتها إننا
+
+65
+00:06:52,610 --> 00:06:57,090
+نتخلص من الثوابت اللي موجودة عندنا في المعادلة 
+
+66
+00:06:57,090 --> 00:07:04,160
+اللي خلتني المعادلة اصلا non homogeneous. يبقى هاي 
+
+67
+00:07:04,160 --> 00:07:08,320
+النتيجة، لأن لو جيت عملت زي ما عملنا وما طلعتش
+
+68
+00:07:08,320 --> 00:07:13,040
+معادلة زيها دي يعني خالية من الثوابت، معناته شغلك 
+
+69
+00:07:13,040 --> 00:07:16,820
+في غلط، في غلطة، غلط من اللازم لما نعوض بهذه
+
+70
+00:07:16,820 --> 00:07:21,920
+التعويضة ما يضلش عندي ثوابت بالمرة، ديري بالك هذا
+
+71
+00:07:21,920 --> 00:07:22,640
+احنا بنبقى
+
+72
+00:07:28,660 --> 00:07:33,360
+يبقى في هذه الحالة لازم ثوابت تطول وبالتالي
+
+73
+00:07:33,360 --> 00:07:36,860
+تقول المعادلة الى homogeneous differential
+
+74
+00:07:36,860 --> 00:07:41,160
+equation. عرفنا إنها homogeneous بجي بقول لو جسمت 
+
+75
+00:07:41,160 --> 00:07:46,760
+كل المعادلة على الـ X. إذا لو جسمت كل المعادلة
+
+76
+00:07:46,760 --> 00:07:53,150
+على X بصير 1 + capital Y / capital X DY
+
+77
+00:07:53,150 --> 00:08:01,290
+capital / DX يبقى يساوي Y / X capital يبقى هاي 
+
+78
+00:08:01,290 --> 00:08:05,890
+المعادلة صارت بدلالة المتغير يبقى Y / X
+
+79
+00:08:08,990 --> 00:08:12,730
+يبقى هذه صارت homogeneous differential equation 
+
+80
+00:08:12,730 --> 00:08:16,890
+يبقى بروح بحل المعادلة هذه زي ما كنت بحل الـ
+
+81
+00:08:16,890 --> 00:08:20,490
+homogeneous differential equation في المرة الماضية
+
+82
+00:08:20,490 --> 00:08:26,710
+كيف؟ بجيب اقول let ال V بدي اساوي capital Y / 
+
+83
+00:08:26,710 --> 00:08:34,370
+capital X أو بمعنى آخر capital Y بدي أساوي X في V
+
+84
+00:08:35,870 --> 00:08:42,930
+نشتقها يبقى دي واي كابتل / دي اكس كابتل الطرف
+
+85
+00:08:42,930 --> 00:08:49,870
+اليمين حاصل ضرب دالتين يبقى V + X في دي V /
+
+86
+00:08:49,870 --> 00:08:56,490
+دي كابتل X. الآن نمسك المعلومات اللي حصلنا عليها
+
+87
+00:08:56,490 --> 00:09:02,530
+هذه ونعود في المعادلة اللي فوق يبقى بتصير المعادلة
+
+88
+00:09:02,530 --> 00:09:11,510
+1 + V. الـ dy / dx اللي هي v + capital X
+
+89
+00:09:11,510 --> 00:09:18,850
++ capital X في الـ dv / dx capital بالشكل
+
+90
+00:09:18,850 --> 00:09:23,110
+اللي عندنا. هذا هشيلنا هذه وضع للطرف اليمين اللي هو
+
+91
+00:09:23,110 --> 00:09:30,060
+main اللي هو كله بده يساوي v. بدأ افك القوس هذا يبقى
+
+92
+00:09:30,060 --> 00:09:34,820
+هضرب القوسين الاثنين هدول مع بعضهم. لو ضربت 1 
+
+93
+00:09:34,820 --> 00:09:40,480
+في القوس يبقى بيظل القوس كما هو، يبقى بيصير v + 
+
+94
+00:09:40,480 --> 00:09:49,920
+capital x في dv / dx capital + v تربيع + 
+
+95
+00:09:49,920 --> 00:09:54,880
+xv في dv / dx 
+
+96
+00:09:59,570 --> 00:10:05,670
+يبقى المعادلة هذه لو أضفت للطرفين سالب V بيبقى
+
+97
+00:10:05,670 --> 00:10:11,300
+بتروح هذه مع بعض. لو جيت على ال term هذا و ال term 
+
+98
+00:10:11,300 --> 00:10:16,580
+هذا في بينهم عوامل مشتركة، والـ v تربيع بدي اوديها
+
+99
+00:10:16,580 --> 00:10:22,840
+على شكل تاني بصير ايه؟ سالب v تربيع. اذا المعادلة 
+
+100
+00:10:22,840 --> 00:10:29,680
+هذه بصير على الشكل التالي. هذه X وهذا 1 + V 
+
+101
+00:10:29,680 --> 00:10:40,250
+وهذا DV / D X بدي يساوي سالب يبقى V تربيع يبقى
+
+102
+00:10:40,250 --> 00:10:46,190
+سالب V تربيع واضح أظن هذه وهذه أخدت X في دي V /
+
+103
+00:10:46,190 --> 00:10:51,270
+دي X عامل مشترك. هاي X وهي دي V / دي X بظل من
+
+104
+00:10:51,270 --> 00:10:57,050
+الأولى 1 صحيح وبظل من الثانية قداش؟ V أظن بقدر
+
+105
+00:10:57,050 --> 00:11:03,730
+أفصل المتغيرات الآن، يبقى لو جينا فاصلنا المتغيرات 
+
+106
+00:11:04,050 --> 00:11:11,210
+بصير على الشكل التالي 1 + V / V تربيع DV
+
+107
+00:11:11,210 --> 00:11:21,690
+= - D X / X أو إن شئتم فقولوا 1 / V
+
+108
+00:11:21,690 --> 00:11:31,950
+تربيع + 1 / V في الـ DV = DX / X 
+
+109
+00:11:31,950 --> 00:11:39,670
+الشكل اللي عملناها. طيب Integration كامل يبقى سالب 1
+
+110
+00:11:39,670 --> 00:11:49,670
+/ V + Ln absolute value لل V = - ل
+
+111
+00:11:49,670 --> 00:11:56,250
+n absolute value ل X + Constant وليكن الـ
+
+112
+00:11:56,250 --> 00:12:02,270
+constant ده C1. طب يا جماعة وكده يا بنات بدي أجيب ال V 
+
+113
+00:12:02,270 --> 00:12:07,030
+على الشجرة تاني وأجيب ال Ln على الشجرة هذه يبقى ايش 
+
+114
+00:12:07,030 --> 00:12:13,350
+بصير عندها؟ بصير Ln absolute value ل V + Ln
+
+115
+00:12:13,350 --> 00:12:21,550
+absolute value ل X = 1 / V + C1
+
+116
+00:12:21,550 --> 00:12:32,270
+طيب هذا الآن اللي هو كله، يبقى لن VX يبقى هذه بدها 
+
+117
+00:12:32,270 --> 00:12:40,190
+تقيمها لن absolute value ل VX بالشكل اللي عندنا
+
+118
+00:12:40,190 --> 00:12:49,210
+هذا يساوي اللي هو 1 / V + كل ثانوية من C1
+
+119
+00:12:49,210 --> 00:12:56,410
+تضيف قداش؟ جايلي عليها يعني هذه يبقى هذه y / x
+
+120
+00:12:56,410 --> 00:13:06,150
+وكأنها x / y مظبوط؟ طيب يبقى هذه كأنها تساوي x 
+
+121
+00:13:06,150 --> 00:13:14,490
+/ y + constant c1 طيب بترفع اثنين كأس للعدد 
+
+122
+00:13:14,490 --> 00:13:20,370
+e يبقى لو رفعنا كله كأس للعدد e بس قبل اللي ترفع
+
+123
+00:13:20,730 --> 00:13:27,290
+الـ X في الـ V هذه عبارة عن مين؟ Y كابتن، إذا هذه
+
+124
+00:13:27,290 --> 00:13:35,410
+بتصير mean لأن اللي هو Y كابتن بده يساوي اللي هو X
+
+125
+00:13:35,410 --> 00:13:44,930
+/ Y زائد كله سنة C1 طبعاً؟ طيب لو رفعت كله كوسل 
+
+126
+00:13:44,930 --> 00:13:49,920
+العدد وأشيلت ال X و ال Y وحطيت قيمة كل واحد 
+
+127
+00:13:49,920 --> 00:13:55,280
+بدلالة X small و Y small، يبقى لو شيلتهم بصير
+
+128
+00:13:55,280 --> 00:14:01,780
+الجواب لل absolute value. لو جيت لل Y capital ال Y
+
+129
+00:14:01,780 --> 00:14:09,480
+capital هو Y small + 2 يبقى Y small + 
+
+130
+00:14:09,480 --> 00:14:17,690
+2 = X capital ل X - 1 يبقى x small
+
+131
+00:14:17,690 --> 00:14:25,830
+- 1 / y + 2 + constant c1 طبعاً 
+
+132
+00:14:25,830 --> 00:14:30,910
+هذا الحل حل ضمني، بقدرش اطلع ال y في الشجرة والباقي 
+
+133
+00:14:30,910 --> 00:14:36,570
+في شجرة ثانية، يبقى بخلي الجواب كما هو بهذا الشكل و
+
+134
+00:14:36,570 --> 00:14:42,650
+بقول اعطيك العافية. تمام، ميرة، ميرة، ميرة، تمام، يعني 
+
+135
+00:14:42,650 --> 00:14:46,610
+بعد ما أجيب الحل بدلالة x capital و y capital
+
+136
+00:14:46,610 --> 00:14:51,810
+برجعه إلى أصله بدلالة x small و y small اللي هو
+
+137
+00:14:51,810 --> 00:15:03,510
+بداية مين؟ بداية المثال، نعطي مثال آخر example بقول
+
+138
+00:15:03,510 --> 00:15:10,150
+use the substitution use the substitution 
+
+139
+00:15:11,810 --> 00:15:21,990
+استخدم التعويضة y = v x تربيع to solve the 
+
+140
+00:15:21,990 --> 00:15:30,890
+differential equation x 
+
+141
+00:15:30,890 --> 00:15:43,030
+تربيع + y كله في dy / dx = - 2 X Y و
+
+142
+00:15:43,030 --> 00:15:46,930
+هذه بتسميها المعادلة الأصلية اللي يمين في الـ start
+
+143
+00:15:46,930 --> 00:15:54,250
+إذا أنا بدي أتقيت بالتعويض اللي اعطاه هالي وليست 
+
+144
+00:15:54,250 --> 00:15:58,430
+لا بال homogenous ولا غيره اللي احنا كنا بنحلها
+
+145
+00:15:58,430 --> 00:16:03,380
+قبلها، يبقى كانوا يقولوا التعويضة هذه ههه بتحل المسألة
+
+146
+00:16:03,380 --> 00:16:07,320
+اللي عندك، بقول له تمام إذا أنا بروح أستخدم هذه
+
+147
+00:16:07,320 --> 00:16:13,580
+التعويضة في حل المثال، بقول له solution التعويضة 
+
+148
+00:16:13,580 --> 00:16:19,340
+اللي اعطاها ليه جالي. حط ال Y = VX تربيعي 
+
+149
+00:16:19,340 --> 00:16:25,200
+بدي اشتق بالنسبة الى X عشان احصل على شكل DY / DX
+
+150
+00:16:25,870 --> 00:16:32,010
+إذا لو جيتش تقية إيمانات باللي بقول dy / dx =
+
+151
+00:16:32,010 --> 00:16:37,290
+مشتقة حاصل ضرب دالتين. الأولى في مشتقة الثانية
+
+152
+00:16:37,290 --> 00:16:47,690
+الثانية مشتقتها ب 2x يبقى 2xv + x تربيع في dv
+
+153
+00:16:47,690 --> 00:16:53,130
+/ dx. هذه قيمة من قيمة مشتقة الـ Y بالنسبة للـ X
+
+154
+00:16:53,130 --> 00:16:58,990
+ناخد المعلومات اللي حصلنا عليها هذه ونرجع نعوض في
+
+155
+00:16:58,990 --> 00:17:04,950
+المعادلة من الـ Star يبقى الآن بالنسبة للمعادلة ال
+
+156
+00:17:04,950 --> 00:17:11,390
+Star اللي عندنا، يبقى X تربيع كما هي الـ Y قال حط 
+
+157
+00:17:11,390 --> 00:17:19,290
+بدالها VX تربيع، حطينا بدالها VX تربيع. الـ dy / dx
+
+158
+00:17:19,290 --> 00:17:28,490
+ليه؟ 2xv + x تربيع في الـ dv / dx كله بده يساوي 
+
+159
+00:17:28,490 --> 00:17:37,670
+- 2x في الـ y ليه v x تربيع بدأت أفكر المعادلة
+
+160
+00:17:37,670 --> 00:17:43,290
+اللي عنها ليه و أبدأ أجمع طيب
+
+161
+00:17:43,930 --> 00:17:49,590
+بنفك المعادلة عنها، يبقى لو فكلها بصير 2x
+
+162
+00:17:49,590 --> 00:17:54,050
+تكعيب v. بدي اضرب x تربيع في ال two terms اللي 
+
+163
+00:17:54,050 --> 00:18:02,090
+عندنا، يبقى 2x تكعيب في ال v + x أس 4
+
+164
+00:18:02,090 --> 00:18:08,380
+في ال dv / ال x. بعدين بدي اضرب هذه يبقى هدف
+
+165
+00:18:08,380 --> 00:18:15,940
+تعطينا + 2 X تكعيب V تربيع. حصل ضرب الاثنين
+
+166
+00:18:15,940 --> 00:18:24,120
+هدول ببعض، زائد اللي هو هنا ما فيش الا V في X أس
+
+167
+00:18:24,120 --> 00:18:35,240
+4 في DV / DX = - 2 X تكعيب V طيب 
+
+168
+00:18:35,540 --> 00:18:41,760
+بالنسبة لهذا ال term وهذا ال term فيهم x أس 4 
+
+169
+00:18:41,760 --> 00:18:49,400
+عامل مشترك وفيه dv / dx يبقى هذا x أس 4 وهذا
+
+170
+00:18:49,400 --> 00:18:58,770
+1 + v في dv / dx مرة ثانية. لتحقيق الخط x أس
+
+171
+00:18
+
+201
+00:22:29,670 --> 00:22:36,790
+مش شامل اثنين she won لإنه ضربنا في اثنين مظبوط
+
+202
+00:22:36,790 --> 00:22:42,330
+أصابة امرأة وقفت عامة تمام ضربنا الطرف اليمين كله
+
+203
+00:22:42,330 --> 00:22:48,150
+في مين؟ في الاثنين يبقى لو جيت قلت لن V تربيع
+
+204
+00:22:48,150 --> 00:22:56,130
+زائدي اثنين Vزائد أربعة للـ absolute value لـ X
+
+205
+00:22:56,130 --> 00:23:02,730
+بتساوي اثنين C1 طيب هذه الأربعة لو جيت هنا إيش
+
+206
+00:23:02,730 --> 00:23:10,570
+بصير؟ X أُس أربعة طب و لن زائد لن لن حاصل الضرب
+
+207
+00:23:10,570 --> 00:23:18,150
+يبقى هذه بصير لن X أُس أربعة و هذا الـ absolute
+
+208
+00:23:18,150 --> 00:23:25,290
+value فاهمين؟ في الـ V تربيع زائد X أُس أربعة في
+
+209
+00:23:25,290 --> 00:23:35,110
+اثنين Vبدو يساوي 2C1 طيب رجعي شوية الـ VX تربيع
+
+210
+00:23:35,110 --> 00:23:42,610
+بقداش يا بنات إذا هشيل كل VX تربيع و أحط بدالة Y
+
+211
+00:23:42,610 --> 00:23:50,210
+يبقى هذي VX تربيع هذي بقداش؟ بـ Y تربيع تمام يبقى
+
+212
+00:23:50,210 --> 00:23:57,810
+هذي لان الـ absolute value لـ Y تربيعو هذه الزائد اثنين
+
+213
+00:23:57,810 --> 00:24:06,290
+وهذه اكس تربيع بظل في اكس تربي عليهمين ابو Y يبقى
+
+214
+00:24:06,290 --> 00:24:12,850
+هذه الـ Y يساوي اثنين C1 ايه ايش رايك اتخلص من الـ N
+
+215
+00:24:14,560 --> 00:24:21,260
+برفع اثنين كاصل العدد E يبقى بيصير الـ absolute value
+
+216
+00:24:21,260 --> 00:24:29,380
+للـ Y تربيع زائد اثنين X تربيع Y يسوى E أس اثنين C1
+
+217
+00:24:29,380 --> 00:24:35,200
+طب الاكس بولانش العمرها بتاخد قيمة سالبة إذا الـ
+
+218
+00:24:35,200 --> 00:24:41,480
+absolute هذا لا معناه لهيبقى هذا معناه ان y تربيع
+
+219
+00:24:41,480 --> 00:24:50,000
+زائدي اثنين x تربيع y بده يساوي c و c يساوي e اقصى
+
+220
+00:24:50,000 --> 00:24:57,460
+اثنين c one بده احطه ب c طيب بده اجيب من المعادلة
+
+221
+00:24:57,460 --> 00:25:01,640
+هذه y قداش تساوي؟
+
+222
+00:25:01,640 --> 00:25:08,890
+ليش؟ أليست معادلة من الدرجة الثانية في y؟إذا
+
+223
+00:25:08,890 --> 00:25:12,930
+بتتحلل بحلل .. لا بتتحللش بحلها بالقانون وبالتالي
+
+224
+00:25:12,930 --> 00:25:17,170
+بقدر أجيب y as a function of x وهو الـ general
+
+225
+00:25:17,170 --> 00:25:21,910
+solution للـ differential equation يعني بقدر أكتب y
+
+226
+00:25:21,910 --> 00:25:28,750
+تربية زيدي اثنين x تربيع y ناقص c يساوي zero
+
+227
+00:25:28,750 --> 00:25:38,050
+مظبوط؟ بدنا نحلها بالقانونيبقى Y يساوي ناقص با
+
+228
+00:25:38,050 --> 00:25:44,270
+يعني ناقص اثنين X تربيع زائد او ناقص الجدري
+
+229
+00:25:44,270 --> 00:25:51,230
+التربية يلي با تربيع يليه أربعة X أس أربعة ناقص
+
+230
+00:25:51,230 --> 00:25:59,190
+أربعة الف اللي هو بواحد جيم اللي هو قداش بناقص C
+
+231
+00:25:59,190 --> 00:26:09,310
+يبقى في ناقص C كل هذا الكلام على اثنين في واحد طيب
+
+232
+00:26:09,310 --> 00:26:14,610
+هذا الكلام بدي اعطيكي ان why you sowy اظن أربعة مع
+
+233
+00:26:14,610 --> 00:26:19,510
+أربعة تطلع برا باتنين و اثنين تطلع برا تروح مع مين
+
+234
+00:26:19,510 --> 00:26:26,550
+مع اثنين اللي تحت يبقى الجواب ناقص x تربيع زائد او
+
+235
+00:26:26,550 --> 00:26:36,320
+ناقص الجدر تربيعي لـ x أربعة زائد c يبقى ده شكل الحل
+
+236
+00:26:36,320 --> 00:26:42,220
+مين للمعادلة التفاضلية اللي علناها حد فيكم بتحب
+
+237
+00:26:42,220 --> 00:26:49,920
+تسأل أي سؤال هنا؟ خلاص؟ طيب لحد هنا انتهى هذا الـ
+
+238
+00:26:49,920 --> 00:26:56,640
+section لم يبقى إلا أن نعطيكم أرقام المسائل
+
+239
+00:26:56,640 --> 00:26:59,520
+المطلوب تمرنوا إيديكم فيها
+
+240
+00:27:11,610 --> 00:27:16,410
+يبقى exercises واحد
+
+241
+00:27:16,410 --> 00:27:25,770
+ثلاثة المسائل التالية ثلاثة، خمسة، ستة، عشرة،
+
+242
+00:27:25,770 --> 00:27:34,350
+أحد عشر، ثلاثة عشر، أربعة عشر، تسعة عشر، واحد وعشرين
+
+243
+00:27:42,890 --> 00:27:50,650
+بنجي الأن لـ section واحد أربعة اللي هو الـ exact
+
+244
+00:27:50,650 --> 00:27:54,170
+equations
+
+245
+00:27:54,170 --> 00:28:02,570
+المعادلة التامة نديلها تعريف definition the first
+
+246
+00:28:02,570 --> 00:28:05,650
+order
+
+247
+00:28:05,650 --> 00:28:08,870
+differential
+
+248
+00:28:08,870 --> 00:28:11,490
+equation
+
+249
+00:28:13,490 --> 00:28:22,150
+الـ M as a function of X وY زائد الـ N as a
+
+250
+00:28:22,150 --> 00:28:30,310
+function of X وY الـ GY على DX يساوي زيرو وهادي
+
+251
+00:28:30,310 --> 00:28:38,270
+بدي أسميها المعادلة star is called exact
+
+252
+00:28:38,270 --> 00:28:50,430
+معادلة تمة if there exists a function إذا قدرت
+
+253
+00:28:50,430 --> 00:29:01,190
+ألاقي دالة فاي of x و y such that بحيث أنه such
+
+254
+00:29:01,190 --> 00:29:08,490
+that اللي هو partial فاي على partial x بدي سوى الـ
+
+255
+00:29:08,490 --> 00:29:19,700
+M of x و yو Partial Phi على Partial Y يساوي N O X
+
+256
+00:29:19,700 --> 00:29:28,320
+Y. The solution of
+
+257
+00:29:28,320 --> 00:29:42,430
+the differential equation Star is فاي اكس واي يساوي
+
+258
+00:29:42,430 --> 00:29:53,250
+يكون مصطلح C اخر م الاختصار
+
+259
+00:29:53,250 --> 00:30:07,790
+الاختصار م اكس واي زائد م اكس واي dy على dx يساوي
+
+260
+00:30:09,150 --> 00:30:20,210
+is exact if and only if if and only if partial m
+
+261
+00:30:20,210 --> 00:30:26,450
+by partial y يسمي partial m by partial x
+
+262
+00:31:35,180 --> 00:31:40,220
+وحتى الآن احنا درسنا اول نوع من انواع المعادلات
+
+263
+00:31:40,220 --> 00:31:43,720
+اللي هو homogeneous differential equations افوا
+
+264
+00:31:43,720 --> 00:31:47,920
+نصي قلم ال equations و بعدين درسنا ال homogeneous
+
+265
+00:31:47,920 --> 00:31:51,780
+differential equations والان بنجي للنوع الثالث
+
+266
+00:31:51,780 --> 00:31:58,140
+اللي هو exact equations يعني المعادلات التامة نعطي
+
+267
+00:31:58,140 --> 00:32:03,700
+تاريخ لها و نشوف ايش بيقول هذا التاريخ بقول التعريف
+
+268
+00:32:03,700 --> 00:32:08,300
+the first order differential equation M of X Y زي
+
+269
+00:32:08,300 --> 00:32:13,500
+N of X Y دي Y على دي X بده يساوي زي 0 زي شكل
+
+270
+00:32:13,500 --> 00:32:18,990
+المثال قبل الأخير مش كان عندنا معادلة في dy على dx
+
+271
+00:32:18,990 --> 00:32:23,190
+يستوى معادلة تانية في الطرف اللي منها زيها طبعا بس
+
+272
+00:32:23,190 --> 00:32:28,650
+خلها كل إياش في طرف واحد وخلاها معادلة صفرية يبقى
+
+273
+00:32:28,650 --> 00:32:31,690
+أنا عندي معادلة من الرتبة الأولى لإن ماعنديش إلا
+
+274
+00:32:31,690 --> 00:32:35,530
+المشتقة الأولى زي ما أنتوا شايفين يبقى هذه
+
+275
+00:32:35,530 --> 00:32:41,050
+المعادلة بالشكلة بقول عنها exactly كيف؟ إذا جدرت
+
+276
+00:32:41,050 --> 00:32:48,420
+ألاقي دالة phi of x و y بحيث أن مشتقة هذه الدالة
+
+277
+00:32:48,420 --> 00:32:54,440
+بالنسبة إلى x يسوى الـ M ومشتقتها بالنسبة إلى y
+
+278
+00:32:54,440 --> 00:32:59,420
+يسوى main الـ M ويجيبها partial phi على partial x
+
+279
+00:32:59,420 --> 00:33:04,340
+يسوى M of x وy and partial y على partial y يساوي من
+
+280
+00:33:04,340 --> 00:33:09,500
+n of x y لما اقول partial يعني الاشتقاق الجزء
+
+281
+00:33:09,500 --> 00:33:14,840
+الاشتقاق الجزء ليش لإن الـ m و الـ n ده لتاني في
+
+282
+00:33:14,840 --> 00:33:21,770
+متغيرين و ليس ده لفي متغيرين واحد لو كانت فيه متغير
+
+283
+00:33:21,770 --> 00:33:27,970
+واحد لقول نتفاضل عادي dy by dx تمام لكن لا نظرا او
+
+284
+00:33:27,970 --> 00:33:33,970
+d phi على dx او d phi على dy لكن نظرا لان phi ده
+
+285
+00:33:33,970 --> 00:33:39,170
+اللي فيه متغيرين فبروح باشتق اشتقاقا جزئيا كما
+
+286
+00:33:39,170 --> 00:33:44,780
+سنرى بعد قليل يبقى باجي بقول الدالة اللى عندنا هذه
+
+287
+00:33:44,780 --> 00:33:49,240
+او المعادلة اللى عندنا star هي exact معادلة تامة
+
+288
+00:33:49,240 --> 00:33:54,820
+إذا قدرتى لاجي دالة five of x y بحيث أن المشتقة
+
+289
+00:33:54,820 --> 00:34:01,160
+الجزئية لها بالنسبة إلى x يساوي m of x y والمشتقة
+
+290
+00:34:01,160 --> 00:34:07,920
+الجزئية لها بالنسبة إلى y يساوي n of x y طيب تمام
+
+291
+00:34:08,170 --> 00:34:11,350
+السؤال هو طب وانك ايه بدي الاقي هذه الدالة بدي
+
+292
+00:34:11,350 --> 00:34:15,750
+اقعد ادور هدى تظبط و هدى ماتظبطش اقعد نص ساعة و لا
+
+293
+00:34:15,750 --> 00:34:18,610
+ساعة و لا ساعتين و لا تلت ساعات ادور هذه الشغله
+
+294
+00:34:18,610 --> 00:34:22,670
+يعني متعبه جدا و يمكن نجرب طول اليوم و مانقدرش
+
+295
+00:34:22,670 --> 00:34:28,130
+نجيب هذه ال function طبعا راح بحث العلماء لغاية ما
+
+296
+00:34:28,130 --> 00:34:35,480
+توصلوا الى نظرية تسهل هذه العملية شو النظرية هذه اه
+
+297
+00:34:35,480 --> 00:34:40,460
+طبعاً قبل النظرية الحل تبع المعادلة الى four مدى
+
+298
+00:34:40,460 --> 00:34:45,380
+ومشتقة هذه لهنا يساوي هذه ومشتقة هذه تساوي هذه
+
+299
+00:34:45,380 --> 00:34:50,580
+وطرف اليمين يساوي zero زير ومشتقة ال constant إذا
+
+300
+00:34:50,580 --> 00:34:55,220
+هذه phi of x y لازم تساوي مقدار ثاني حتى يبقى
+
+301
+00:34:55,220 --> 00:35:00,090
+مشتقته تساوي مين تساوي zero الان كيف تحكم على هذه
+
+302
+00:35:00,090 --> 00:35:04,850
+انها exact بدون ما اقعد ادور اوصل او ماوصلش فبقول
+
+303
+00:35:04,850 --> 00:35:08,690
+لأجزا differential equation هذه بقول عنها exact
+
+304
+00:35:08,690 --> 00:35:14,910
+اذا لقيت مشتقت هذا الكلام لو M بالنسبة الى Y سوى
+
+305
+00:35:14,910 --> 00:35:19,780
+مشتقت هذا بالنسبة لمن يعني الـ M مش بده أشتقها
+
+306
+00:35:19,780 --> 00:35:25,280
+بالنسبة ل X بده أشتقها بالنسبة إلى Y و الـ N بده
+
+307
+00:35:25,280 --> 00:35:30,580
+أشتقها كأن جلبت الوضع، طبعا يعني الدالة الأولى بده
+
+308
+00:35:30,580 --> 00:35:33,740
+أشتقها بالنسبة إلى Y و الدالة التانية بده أشتقها
+
+309
+00:35:33,740 --> 00:35:39,920
+بالنسبة ل X إن حدثت تساوي بقول هذه المعادلة exact
+
+310
+00:35:39,920 --> 00:35:44,700
+مدام exact إذا لازم ألاقي function phi of x y
+
+311
+00:35:44,700 --> 00:35:49,980
+تساوي كونستانت هي عبارة عن حل مين لهذه المعادلة
+
+312
+00:35:49,980 --> 00:35:55,000
+نعطيكم الأن أكثر من مثال على كيفية إيجاد هذه
+
+313
+00:35:55,000 --> 00:36:01,160
+الدالة وكيفية الحكم على إنها exact أو ماهياش exact
+
+314
+00:36:01,160 --> 00:36:04,440
+نبدأ بأول مثال هو example one
+
+315
+00:36:10,260 --> 00:36:13,240
+Example 1 بيقول سؤال الـ differential equation
+
+316
+00:36:13,240 --> 00:36:21,400
+سؤال الـ differential equation حل المعادلة التفاضلية
+
+317
+00:36:21,400 --> 00:36:31,260
+x في e to the power x في y في ال y prime زائد y في
+
+318
+00:36:31,260 --> 00:36:38,340
+e to the power xy ناقص أربعة x تكعيب يساوي مين؟
+
+319
+00:36:38,340 --> 00:36:38,960
+يساوي
+
+320
+00:36:46,740 --> 00:36:52,600
+أول خطوة يا عزيزي هي ارتب مسئلتي لتكون في الشكل
+
+321
+00:36:52,600 --> 00:36:58,340
+الـ star اللي فوق حتى أبدأ أشتغل شغل الطبيعي فبجي
+
+322
+00:36:58,340 --> 00:37:02,660
+بقول هنا y' بدأت الأول يجب أن أدخل هذه في الأول
+
+323
+00:37:02,660 --> 00:37:06,920
+وهذه في الآخر الجماعة لديها مشكلة إذا لو أعد
+
+324
+00:37:06,920 --> 00:37:14,580
+ترتيبها يجب أن أقول y بيقص xy ناقص 4x تقريبا
+
+325
+00:37:17,250 --> 00:37:26,770
+زائد X في E أُس XY في Y' يساوي 0 هاي الـ M في X و Y
+
+326
+00:37:26,770 --> 00:37:31,810
+بجهة دي تشكل مين الـ M زي ما انت شايفها دالة في X و
+
+327
+00:37:31,810 --> 00:37:38,890
+Y وهذه تشكل الـ N لأنها كذلك دالة في X و Y إذن هذه
+
+328
+00:37:38,890 --> 00:37:46,600
+هي الـ M تبعة الجزء النظري وهذه هي الـ N تبعت الجزء
+
+329
+00:37:46,600 --> 00:37:52,300
+النظري طب بدي احكم عليها exact و الله ماهياش exact
+
+330
+00:37:52,300 --> 00:37:58,660
+يبقى بدي اروح ادي ااخد تفاضل الـ M بالنسبة لـ X يبقى
+
+331
+00:37:58,660 --> 00:38:05,620
+بدي ااخد partial M by partial Y يزاوى اللي هو الـ
+
+332
+00:38:05,620 --> 00:38:10,910
+term اللي عندنا هذا يعني بدي أشتق هذا الجزء بالنسبة
+
+333
+00:38:10,910 --> 00:38:17,330
+ل why نظرا لإنه عندي أكثر من متغير فالمتغير اللي
+
+334
+00:38:17,330 --> 00:38:20,710
+بشتق بالنسبة له باعتبره هو المتغير و باقي
+
+335
+00:38:20,710 --> 00:38:26,050
+المتغيرات ثوابت زي واحد و اثنين و عشر و نص و تلت
+
+336
+00:38:26,050 --> 00:38:30,230
+تربع و اللي بدكي يعني يبقى أي متغير آخر باعتبره
+
+337
+00:38:30,230 --> 00:38:36,170
+مقدار ثابت وهذا معنى الاشتقاق الجزئي كما درسناه في
+
+338
+00:38:36,170 --> 00:38:40,670
+calculus C لكن لمّا ما درسوش calculus C أنا بذكرهم
+
+339
+00:38:40,670 --> 00:38:45,150
+لن يقابلنا حاجة نفيدنا من calculus C إلا هذا الـ
+
+340
+00:38:45,150 --> 00:38:50,670
+section فقط لا غير و هتلاقي الشغلات بسيطة جدا كما
+
+341
+00:38:50,670 --> 00:38:55,410
+ستراهم يبقى أنا بضروح أشتق هذا بالنسبة لمين يا
+
+342
+00:38:55,410 --> 00:39:00,000
+بنات نسبة لـ Y يبقى مشتقة هذا المقدار كله بيبقى داش
+
+343
+00:39:00,000 --> 00:39:05,160
+Zero مع السلامة لإن مافيش في Y في X تقعيه مشتقة
+
+344
+00:39:05,160 --> 00:39:09,420
+منه يبقى في Zero يبقى باجي لهذا الـ term هذي Y و
+
+345
+00:39:09,420 --> 00:39:13,960
+هذي E و ال 6Y تنتين فيهم Y يبقى هذا المشتقة حاصل
+
+346
+00:39:13,960 --> 00:39:19,340
+ضرب دالتين يبقى بدي أشتق الأولى بالنسبة ليه؟ لو
+
+347
+00:39:19,340 --> 00:39:26,670
+يبقى داش بواحد في E و ال 6Y يبقى E و ال 6Y زائد Y
+
+348
+00:39:26,670 --> 00:39:30,770
+بالـ Exponential
+
+349
+00:39:30,770 --> 00:39:39,090
+زي ما هي ضرب مشتقة الأس بالنسبة إلى Y يبقى كإن هذه
+
+350
+00:39:39,090 --> 00:39:44,430
+ثلاثة Y بداش تقها بالنسبة إلى Y إذا ثلاثة يبقى داش
+
+351
+00:39:44,430 --> 00:39:57,760
+يبقى X إذا هذه النتيجة هي E×XY زائد XY إيقص XY طيب
+
+352
+00:39:57,760 --> 00:40:05,000
+بدنا ناخد تفاضل الـ N بالنسبة الـ X وين الـ N هي الـ N
+
+353
+00:40:05,000 --> 00:40:11,100
+يبقى هذه فيها X وهذه فيها X إذا مشتقت حاصل ضرب
+
+354
+00:40:11,100 --> 00:40:16,800
+دلتين لما اشتق الأولى بالنسبة لـ X روحك وضلي تانية
+
+355
+00:40:16,800 --> 00:40:24,910
+يبقى إيقص XY زائد الـ X زي ما هي ومشتقة الـ X
+
+356
+00:40:24,910 --> 00:40:28,910
+exponential بالـ X exponential itself في مشتقة
+
+357
+00:40:28,910 --> 00:40:36,510
+الأس بالنسبة إلى X اللي هو قداش Y فقط لا غير لأن
+
+358
+00:40:36,510 --> 00:40:42,370
+الـ Y هنا يعتبر مقدارا ثابتا يبقى هذا الكلام بده
+
+359
+00:40:42,370 --> 00:40:50,680
+يساوي E أس XY زائد XY E أس XY ماذا تلاحظ على
+
+360
+00:40:50,680 --> 00:40:58,640
+المشتقتين؟ زي بعض يبقى هذا بده يعطينا ان تفاضل الـ
+
+361
+00:40:58,640 --> 00:41:04,760
+M بالنسبة إلى Y يسوى partial N by partial X هذا
+
+362
+00:41:04,760 --> 00:41:10,780
+ايش بده يعطينا؟ هذا بده يعطينا ما يأتي يبقى هذا يا
+
+363
+00:41:10,780 --> 00:41:16,620
+مناد اللي بده اسميها المعادلة Star يبقى هذا بده
+
+364
+00:41:16,620 --> 00:41:17,620
+يعطينا
+
+365
+00:41:19,870 --> 00:41:27,910
+differential equation a star is exact مدام exact
+
+366
+00:41:27,910 --> 00:41:33,590
+يبقى there exist هاد ال a المقلوبة there exist a
+
+367
+00:41:33,590 --> 00:41:43,110
+function phi of x y يساوي constant وليكن c1 such
+
+368
+00:41:43,110 --> 00:41:46,490
+that بحيث ان
+
+369
+00:41:57,320 --> 00:42:06,460
+Y في E أس X Y ناقص
+
+370
+00:42:06,460 --> 00:42:13,570
+أربع X تكعيب و partial phi على partial y بدي يسوى
+
+371
+00:42:13,570 --> 00:42:19,930
+من الـ n كل الـ n عندي x في e أُس xy يبقى x في e أُس
+
+372
+00:42:19,93
+
+401
+00:45:21,930 --> 00:45:28,410
+exponential كما هي مقسومة على تفاضل الأساس و قدر y
+
+402
+00:45:29,390 --> 00:45:34,270
+يبقى أنا بدي أكمل بالنسبة لـ X ناقص أربعة X أس 
+
+403
+00:45:34,270 --> 00:45:39,290
+أربعة على أربعة زائد مقدار ثابت، المقدار الثابت
+
+404
+00:45:39,290 --> 00:45:44,550
+باعتباره function في المتغير الثاني لأن المتغير
+
+405
+00:45:44,550 --> 00:45:48,870
+الثاني بالنسبة له يعتبر مقدارا ثابتا يبقى بروح
+
+406
+00:45:48,870 --> 00:45:55,740
+بقوله زائد F of Y، F of Y كله يعتبر مقدار ثابت
+
+407
+00:45:55,740 --> 00:46:00,820
+بالنسبة لمن؟ بالنسبة لـ X يعني يا بنات هذه بيصير E
+
+408
+00:46:00,820 --> 00:46:10,890
+of 6Y ناقص X أس أربعة زائد F of Y، هذا مين؟ F of x
+
+409
+00:46:10,890 --> 00:46:16,570
+و y، الحين مشكلتي بس بدي أعرف قداش F of y مشان أعرف
+
+410
+00:46:16,570 --> 00:46:23,470
+F of y، بدي أروح أكاملها، أفاضلها بالنسبة إلى y يبقى
+
+411
+00:46:23,470 --> 00:46:30,930
+partial phi على partial y، هذي قداش مشتقتها بالنسبة
+
+412
+00:46:30,930 --> 00:46:43,340
+إلى y يبقى x في e أس x y، ناقص هذه zero زائد f prime
+
+413
+00:46:43,340 --> 00:46:51,000
+of y، مش هي partial phi علي partial y فوق عندي وهي
+
+414
+00:46:51,000 --> 00:46:58,050
+أنا اشتقتها هنا، يبقى المقدارين هدول بدهم يساووا بعض
+
+415
+00:46:58,050 --> 00:47:04,990
+يبقى لما أساويهم بعض بيصير x e أس x y زائد f prime
+
+416
+00:47:04,990 --> 00:47:11,290
+of y بده يساوي x في e أس x y، هذا معناه أن f prime
+
+417
+00:47:11,290 --> 00:47:18,610
+of y بده يساوي كده؟ Zero، يبقى هذا معناه أن f of y
+
+418
+00:47:18,610 --> 00:47:25,290
+يساوي مقدار ثابت ثاني، يبقى بروح بقوله the solution
+
+419
+00:47:25,290 --> 00:47:35,010
+is phi of x y بده يساوي، وين phi of x y هي اللي
+
+420
+00:47:35,010 --> 00:47:36,410
+طلعناها هي
+
+421
+00:47:52,430 --> 00:47:59,930
+يبقى بيصير أن فاي of x و y يساوي e أس x y ناقص x
+
+422
+00:47:59,930 --> 00:48:00,870
+أس أربعة
+
+423
+00:48:06,820 --> 00:48:14,720
+هذا هو حل المعادلة، لا يزال لدينا مثال عن الـ exact
+
+424
+00:48:14,720 --> 00:48:19,380
+equation، وبعد ذلك الـ equation ممكن ما تطلعش exact
+
+425
+00:48:19,380 --> 00:48:24,740
+ونروح نحولها إلى exact زي ما قبل قليل كانت
+
+426
+00:48:24,740 --> 00:48:28,960
+homogeneous، وبنحولها إلى homogeneous وهكذا
+
+427
+00:48:28,960 --> 00:48:30,420
+يعطيكم العافية
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..93f9d231b0e828d0967bd0c20ccc3bc25ea32b4e
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo_postprocess.srt
@@ -0,0 +1,1708 @@
+1
+00:00:20,160 --> 00:00:23,580
+بسم الله الرحمن الرحيم المرة اللي فتت في نهاية
+
+2
+00:00:23,580 --> 00:00:27,880
+المحاضرة الماضية كتبنا ملاحظة الملاحظة كانت على
+
+3
+00:00:27,880 --> 00:00:31,980
+الشكل التالي لو كانت المعادلة التفاضلية على شكل
+
+4
+00:00:31,980 --> 00:00:41,840
+a1x زائد b1y زائد c1 كلها في y' يسوى a2x زائد b2y
+
+5
+00:00:41,840 --> 00:00:48,040
+زائد c2 يبقى في هذه الحلقة نحاول نحل المعادلة
+
+6
+00:00:48,040 --> 00:00:52,680
+التفاضلية اللي عندناطبعا لو جسمنا الطلبين على X أو
+
+7
+00:00:52,680 --> 00:00:57,760
+على Y لايمكن أن تظهر الـ Homogeneous Differential
+
+8
+00:00:57,760 --> 00:01:06,040
+Equation هل الـ A1 في B2 يساوي الـ A2 في B1 ولا
+
+9
+00:01:06,040 --> 00:01:11,420
+لأ؟ إن حدث ذلك يبقى من الحل هذه كما كنا نحل من قبل
+
+10
+00:01:11,420 --> 00:01:16,580
+بصير مسألتنا سهلة لكن إن كانت الـ A1 B2 لا تساوي
+
+11
+00:01:16,580 --> 00:01:22,590
+B2 A1يجب أن نكتب المعادلتين اللي اتنين اللي عندنا
+
+12
+00:01:22,590 --> 00:01:26,670
+و نسويهم بالصفر و نحل المعادلتين هدول مع بعضهم
+
+13
+00:01:26,670 --> 00:01:32,290
+نجيب قيمة كلها من X وY او نجيب قيمة P وQ لان قلنا
+
+14
+00:01:32,290 --> 00:01:38,410
+نكتب معادلة على صيغة A1P زائد B1Q زائد C1 يساوي
+
+15
+00:01:38,410 --> 00:01:45,390
+Zero و المعادلة التانية A2P زائد B2EQ زائد C2
+
+16
+00:01:45,390 --> 00:01:51,930
+يساوي Zeroبنروح ونقول ان استبدأ كل X بX كابتل زائد
+
+17
+00:01:51,930 --> 00:01:57,250
+P اللي طلعت وكل Y بY كابتل زائد Q اللي طلعت ان هو
+
+18
+00:01:57,250 --> 00:02:01,490
+في هذه الحالة automatic تتحول المعادلة اللي عندنا
+
+19
+00:02:01,490 --> 00:02:07,520
+إلى معادلة متجانسةهذا أخر كلمتين نظري كتبناه المرة
+
+20
+00:02:07,520 --> 00:02:11,420
+الماضية وهذا المثال اللي قدامي على اللوح مثال
+
+21
+00:02:11,420 --> 00:02:16,980
+مباشر على هذا النوع من المسائل ممكن ما تظهر شان
+
+22
+00:02:16,980 --> 00:02:20,580
+كاميرات بالشكل هذا ممكن تظهر y prime يساوي y زائد
+
+23
+00:02:20,580 --> 00:02:25,500
+2 مقسمة على x زائد y زائد 1 ان كان بالشكل هذا أو
+
+24
+00:02:25,500 --> 00:02:30,800
+بالشكل هذا سيان يبقى بدنا نعمل نفس الشغل يعني ممكن
+
+25
+00:02:30,800 --> 00:02:37,840
+تظهر y prime يساوي y زائد 2تقسيم x زائد y زائد 1
+
+26
+00:02:37,840 --> 00:02:42,080
+انظرت بالشكل هذا او بالشكل هذا الاتنين لهم نفس
+
+27
+00:02:42,080 --> 00:02:49,920
+الشغل يبقى ايش بدي اعمل بدي اروح اشوف هل ال a1 في
+
+28
+00:02:49,920 --> 00:02:56,320
+ال b2 يساوي ال a1 اللي هو معامل مين؟ معامل x بقدرش
+
+29
+00:02:56,320 --> 00:03:02,440
+يبغاها b2 معامل y اللي هو قدرش واحد يبقى النتيجة
+
+30
+00:03:02,440 --> 00:03:09,390
+يساوي واحدةبدأ اشوف a2b1 يبقى المعامل تبع اكس لان
+
+31
+00:03:09,390 --> 00:03:14,550
+الوقت بدأ بالزيرو معامل b1 معامل y هنا اللي هو
+
+32
+00:03:14,550 --> 00:03:22,090
+بواحد y يساوي زيرو يبقى هذا معناه ان a1b2 لا يساوي
+
+33
+00:03:22,090 --> 00:03:28,790
+a2 في ال b1 مدام هفتله هدول بيساووش بعض اذا بدنا
+
+34
+00:03:28,790 --> 00:03:33,470
+نروح نحل المعادلتين هدول مع بعضيبقى بدي اكتب
+
+35
+00:03:33,470 --> 00:03:39,950
+المعادلة هذه ل P زائد Q زائد واحد يساوي زيرو
+
+36
+00:03:39,950 --> 00:03:46,990
+والمعادلة التانية Q زائد اتنين يساوي زيرو من هذه
+
+37
+00:03:46,990 --> 00:03:51,790
+المعادلة بقدر اقول إذا ال Q يساوي قداش سالي ب
+
+38
+00:03:51,790 --> 00:03:56,920
+اتنينيبقى بناء عليه من الاتنين هدول مع بعض بصيرين
+
+39
+00:03:56,920 --> 00:04:02,940
+بي سالب اتنين زالد واحد يساوي زيرو ومنها بي تساوي
+
+40
+00:04:02,940 --> 00:04:10,680
+قداش تساوي واحد اذا بدي اعمل التحويل اللي بدها ضيع
+
+41
+00:04:10,680 --> 00:04:17,180
+ال constant واحد وال constant اتنين وهيبدنا نروح
+
+42
+00:04:17,180 --> 00:04:25,860
+نحط x small يساوي x capital زائد t يعني مين؟ يعني
+
+43
+00:04:25,860 --> 00:04:33,160
+ال x small بدي يساوي x capital زائد واحد و ال y
+
+44
+00:04:33,160 --> 00:04:40,740
+بدي يساوي y capital زائد ل q يعني y small بدي
+
+45
+00:04:40,740 --> 00:04:46,910
+يساوي y capitalناقص اتنين قيمة q اللي عندنا
+
+46
+00:04:46,910 --> 00:04:52,410
+المعلومات هذه بيروح عوض بوين في المعادلة اللي فوق
+
+47
+00:04:52,410 --> 00:04:57,270
+اللي بدي اسميها المعادلة star يبقى بداجي اقول هنا
+
+48
+00:04:57,270 --> 00:05:02,830
+substitute in
+
+49
+00:05:02,830 --> 00:05:12,070
+equation star we get بنحصل على المعادلة التالية
+
+50
+00:05:12,610 --> 00:05:17,730
+يبقى بده اشيل ال X Small وحط بدل X Capital زائد
+
+51
+00:05:17,730 --> 00:05:24,610
+واحد يبقى هذا معناه اه بس استنى شوية لما نيجي لهذا
+
+52
+00:05:24,610 --> 00:05:29,990
+يا بنات و نيجي نشتقها يبقى اشتقاقها دي بده يصير DX
+
+53
+00:05:29,990 --> 00:05:36,810
+Small يسوى DX Capital و لو نيجي نشتقها دي بصير
+
+54
+00:05:36,810 --> 00:05:47,650
+عندنا DY Smallيساوي dy كامتل يبقى
+
+55
+00:05:47,650 --> 00:05:51,070
+هذه المعادلة اللي بدها تصير على الشكل التالي ال x
+
+56
+00:05:51,070 --> 00:05:56,590
+small بده اشيلها و ده يحط بدالها main x زائد واحد
+
+57
+00:05:56,590 --> 00:06:04,750
+زائد y small اللي هي y ناقص اتنين وهذه زائد واحد
+
+58
+00:06:05,390 --> 00:06:11,010
+الان الـ y prime يعني اللي هي dy على dx dy اللي هي
+
+59
+00:06:11,010 --> 00:06:19,630
+d capital y على dx capital هذا الكلام بده يسوي y
+
+60
+00:06:19,630 --> 00:06:25,610
+small اللي هو capital y ناقص اتنين زائد اتنين اللي
+
+61
+00:06:25,610 --> 00:06:32,240
+عندنا نختصر الاختصارات واحد واحدإتنين و سالي
+
+62
+00:06:32,240 --> 00:06:37,860
+بإتنين مع السلامة يبقى آلة المثالة إلى x زائد
+
+63
+00:06:37,860 --> 00:06:47,270
+capital Y dy capital على dx يساوي capital Yيبقى
+
+64
+00:06:47,270 --> 00:06:52,610
+العملية بناء التعويض اللي حطناها دي فائدتها أننا
+
+65
+00:06:52,610 --> 00:06:57,090
+نتخلص من الثوابت اللي موجودة عندنا في المعادلة
+
+66
+00:06:57,090 --> 00:07:04,160
+اللي خلتني المعادلة أصلا non homogeneousيبقى هاي
+
+67
+00:07:04,160 --> 00:07:08,320
+النتيجة لأن لو جيت عملت زي ما عملنا و ما طلعتش
+
+68
+00:07:08,320 --> 00:07:13,040
+معادلة زيها دي يعني خالية من الثوابت معناته شغلك
+
+69
+00:07:13,040 --> 00:07:16,820
+في غلط في غلطة غلط من اللازم لما نعوض بهذه
+
+70
+00:07:16,820 --> 00:07:21,920
+التعويضة مايضلش عندي ثوابت بالمرة ديري بالك هذا
+
+71
+00:07:21,920 --> 00:07:22,640
+احنا بنبقى
+
+72
+00:07:28,660 --> 00:07:33,360
+يبقى في هذه الحالة لازمة ثوابت الطيلة وبالتالي
+
+73
+00:07:33,360 --> 00:07:36,860
+تقول المعادلة الى homogeneous differential
+
+74
+00:07:36,860 --> 00:07:41,160
+equation عرفنا انها homogeneous بجي بقول لو جسمت
+
+75
+00:07:41,160 --> 00:07:46,760
+كل المعادلة عالمهم على X إذا لو جسمت كل المعادلة
+
+76
+00:07:46,760 --> 00:07:53,150
+على X بصير واحد زائد capital Y على capital XDY
+
+77
+00:07:53,150 --> 00:08:01,290
+كابتل على DX يبقى يساوي Y على X كابتل يبقى هاي
+
+78
+00:08:01,290 --> 00:08:05,890
+المعادلة صارت بدلالة المتغير يبقى Y على X
+
+79
+00:08:08,990 --> 00:08:12,730
+يبقى هذه صارت homogeneous differential equation
+
+80
+00:08:12,730 --> 00:08:16,890
+يبقى بروح بحل المعادلة هذه زي ما كنت بحل ال
+
+81
+00:08:16,890 --> 00:08:20,490
+homogeneous differential equation في المرة الماضية
+
+82
+00:08:20,490 --> 00:08:26,710
+كيف؟ بجيب اقول quote ال V بدي سوى capital Y على
+
+83
+00:08:26,710 --> 00:08:34,370
+capital X او بمعنى اخر capital Y بدي سوى X في V
+
+84
+00:08:35,870 --> 00:08:42,930
+نشتقها يبقى دي واي كابتل على دي اكس كابتل الطرف
+
+85
+00:08:42,930 --> 00:08:49,870
+اليمين حاصل ضرب دالي تلف يبقى V زائد X في دي V على
+
+86
+00:08:49,870 --> 00:08:56,490
+دي كابتل X الآن نمسك المعلومات اللي حصلنا عليها
+
+87
+00:08:56,490 --> 00:09:02,530
+هذه ونعود في المعادلة اللي فوق يبقى بتصير المعادلة
+
+88
+00:09:02,530 --> 00:09:11,510
+واحد زائد Vالـ dy على dx اللي هي v زائد capital X
+
+89
+00:09:11,510 --> 00:09:18,850
+زائد capital X في الـ dv على dx capital بالشكل
+
+90
+00:09:18,850 --> 00:09:23,110
+اللي عندنا هذا هشيلنا هذه وضع للطرف اليمين اللي هو
+
+91
+00:09:23,110 --> 00:09:30,060
+main اللي هو كله بده ساوي vبدا افك القوس هذا يبقى
+
+92
+00:09:30,060 --> 00:09:34,820
+هضرب الجوسين اللي اتنين هدول مع بعضهم لو ضربت واحد
+
+93
+00:09:34,820 --> 00:09:40,480
+في الجوس يبقى بيظل الجوس كما هو يبقى بيصير v زائد
+
+94
+00:09:40,480 --> 00:09:49,920
+capital x في dv على dx capital زائد v تربيع زائد
+
+95
+00:09:49,920 --> 00:09:54,880
+xv في dv على dx
+
+96
+00:09:59,570 --> 00:10:05,670
+يبقى المعادلة هذه لو أضفت للطرفين سالف V بيبقى
+
+97
+00:10:05,670 --> 00:10:11,300
+بتروح هذه مع بعضهالو جيت على ال term هذا و ال term
+
+98
+00:10:11,300 --> 00:10:16,580
+هذا في بينهم عوامل مشتركة و ال V تربيع بدي اوديه
+
+99
+00:10:16,580 --> 00:10:22,840
+على شكل تاني بيصير ايه؟ سالب V تربيع اذا المعادلة
+
+100
+00:10:22,840 --> 00:10:29,680
+هذه بيصير على الشكل التالي هذه X وهذا واحد زائد V
+
+101
+00:10:29,680 --> 00:10:40,250
+وهذا DV على D X بدي ساوي سالبيبقى V تربيع يبقى
+
+102
+00:10:40,250 --> 00:10:46,190
+سالب V تربيع واضح أظن هذي و هذي أخدت X في دي V على
+
+103
+00:10:46,190 --> 00:10:51,270
+دي X عام المشترك هاي X وهي دي V على دي X بظل من
+
+104
+00:10:51,270 --> 00:10:57,050
+الأولى واحد صحيح و بظل من التانية قداش V أظن بقدر
+
+105
+00:10:57,050 --> 00:11:03,730
+أفصل المتغيرات الآن يبقى لو جينا فاصلنا المتغيرات
+
+106
+00:11:04,050 --> 00:11:11,210
+بصير على الشكل التالي واحد زائد V على V تربية DV
+
+107
+00:11:11,210 --> 00:11:21,690
+يساوي ناقص D X على X او ان شئتم فقولوا واحد على V
+
+108
+00:11:21,690 --> 00:11:31,950
+تربية زائد واحد على V في الـ DV يساوي D X على X
+
+109
+00:11:31,950 --> 00:11:39,670
+الشكل اللي عملناهاطيب Legion كامل يبقى سالب واحد
+
+110
+00:11:39,670 --> 00:11:49,670
+على V زائد Lin absolute value لل V يساوي الناقص ل
+
+111
+00:11:49,670 --> 00:11:56,250
+Lin absolute value ل X زائد Constant وليكن ال
+
+112
+00:11:56,250 --> 00:12:02,270
+constant ده C1طب يا جماعة و كده بنات بدي أجيب ال V
+
+113
+00:12:02,270 --> 00:12:07,030
+على الشجر تاني و أجيب ال Ln على الشجر هذي يبقى إيش
+
+114
+00:12:07,030 --> 00:12:13,350
+بصير عندها بصير Ln absolute value ل V زائد Ln
+
+115
+00:12:13,350 --> 00:12:21,550
+absolute value ل X بدي يساوي واحد على V زائد C1
+
+116
+00:12:21,550 --> 00:12:32,270
+طيب هذا الآناللي هو كلها يبقى لن VX يبقى هذه بدها
+
+117
+00:12:32,270 --> 00:12:40,190
+تقيمها لن absolute value لV X بالشكل اللي عندنا
+
+118
+00:12:40,190 --> 00:12:49,210
+هذا يساوي اللي هو واحد على V زائد كل ثانوية من C1
+
+119
+00:12:49,210 --> 00:12:56,410
+تضيف قداش جايلي عليها يعني هذهيبقى هذه y علي x
+
+120
+00:12:56,410 --> 00:13:06,150
+وكانها x علي y مظبوط طيب يبقى هذه كأنها تساوية x
+
+121
+00:13:06,150 --> 00:13:14,490
+علي y زائد constant c1 طيب بتارفع اتنين كأس للعدد
+
+122
+00:13:14,490 --> 00:13:20,370
+e يبقى لو رفعنا كله كأس للعدد e بس قبل اللي ترفع
+
+123
+00:13:20,730 --> 00:13:27,290
+الـ X في الـ V هذه عبارة عن مين؟ Y كابتن إذاً هذه
+
+124
+00:13:27,290 --> 00:13:35,410
+بتصير mean لان اللي هو Y كابتن بده يساوي اللي هو X
+
+125
+00:13:35,410 --> 00:13:44,930
+على Y زارت كله سنة C1 طبعاً؟ طيب لو رفعت كله كوسل
+
+126
+00:13:44,930 --> 00:13:49,920
+العدد أوشيلت ال X و ال Y و حطيت قيمة كل واحد
+
+127
+00:13:49,920 --> 00:13:55,280
+بدلالة X small و Y small يبقى لو شيلتهم بصير
+
+128
+00:13:55,280 --> 00:14:01,780
+الجواب لل absolute value لو جيت لل Y capital ال Y
+
+129
+00:14:01,780 --> 00:14:09,480
+capital هو Y small زائد اتنين يبقى Y small زائد
+
+130
+00:14:09,480 --> 00:14:17,690
+اتنين يساوي X capital ل X minus oneيبقى x small
+
+131
+00:14:17,690 --> 00:14:25,830
+minus one على y plus two زائد constant c one طبعا
+
+132
+00:14:25,830 --> 00:14:30,910
+هذا الحل حل ضمني بقدرش اطلع ال y في الشجة و الباقي
+
+133
+00:14:30,910 --> 00:14:36,570
+في شجة تانية يبقى بخل الجراب كما هو بهذا الشكل و
+
+134
+00:14:36,570 --> 00:14:42,650
+بقول اعطيك العافية تمام ميرة ميرة ميرة تماميعني
+
+135
+00:14:42,650 --> 00:14:46,610
+بعد ما أجيب الحل بدلالة x capital و y capital
+
+136
+00:14:46,610 --> 00:14:51,810
+برجعه إلى أصله بدلالة x small و y small اللي هو
+
+137
+00:14:51,810 --> 00:15:03,510
+بداية مين بداية المثلة نعطي مثال أخر example بقول
+
+138
+00:15:03,510 --> 00:15:10,150
+use the substitution use the substitution
+
+139
+00:15:11,810 --> 00:15:21,990
+استخدم التعويضة y تساوي v x تربيع to solve the
+
+140
+00:15:21,990 --> 00:15:30,890
+differential equation x
+
+141
+00:15:30,890 --> 00:15:43,030
+تربيع زائد y كله في dy by dxبتساوي نقص اتنين X Y و
+
+142
+00:15:43,030 --> 00:15:46,930
+هذي بتسميها المعاني الأصلي اللي يمين في ال start
+
+143
+00:15:46,930 --> 00:15:54,250
+اذا انا بدي اتقيت بالتعويض اللي اعطاه هالي و ليست
+
+144
+00:15:54,250 --> 00:15:58,430
+لا بال homogenous ولا غيره اللي احنا كنا بنحلبها
+
+145
+00:15:58,430 --> 00:16:03,380
+قبليبقى كانوا يقولوا التعويضة هذه ههه بتحل المسألة
+
+146
+00:16:03,380 --> 00:16:07,320
+اللي عندك بقول له تمام اذا انا بتروح استخدم هذه
+
+147
+00:16:07,320 --> 00:16:13,580
+التعويضة في حل المثل بقول له solution التعويضة
+
+148
+00:16:13,580 --> 00:16:19,340
+اللي يعطيها ليه جالي حط ال Y في ساوي VX ترابيعي
+
+149
+00:16:19,340 --> 00:16:25,200
+بدي اشتق بالنسبة الى X عشان احصل على شكل DY على DX
+
+150
+00:16:25,870 --> 00:16:32,010
+إذا لو جيتش تقية إيمانات بالي بقول dy على dx يسوي
+
+151
+00:16:32,010 --> 00:16:37,290
+مشتقة حاصل ضرب دالتين الأولى في مشتقة التانية
+
+152
+00:16:37,290 --> 00:16:47,690
+التانية مشتقتها ب2x يبقى 2xv زائد x تربيع في dv
+
+153
+00:16:47,690 --> 00:16:53,130
+على dxهذه قيمة من قيمة مشتقة الـ Y بالنسبة للـ X
+
+154
+00:16:53,130 --> 00:16:58,990
+ناخد المعلومات اللي حصلنا عليها هذه و نرجع نعوض في
+
+155
+00:16:58,990 --> 00:17:04,950
+المعادلة من الـ Star يبقى الآن بالنسبة للمعادلة ال
+
+156
+00:17:04,950 --> 00:17:11,390
+Star اللي عندنا يبقى X تربيع كما هي ال Y قال حط
+
+157
+00:17:11,390 --> 00:17:19,290
+بدالها VX تربيع حطينا بدالها VX تربيعالـ dy على dx
+
+158
+00:17:19,290 --> 00:17:28,490
+ليه 2xv زائد x تربيع في الـdv على dx كله بده يساوي
+
+159
+00:17:28,490 --> 00:17:37,670
+نقص 2x في الـy ليه v x تربيع بدأت أفكر المعادلة
+
+160
+00:17:37,670 --> 00:17:43,290
+اللي عنها ليه و أبدأ أجمع طيب
+
+161
+00:17:43,930 --> 00:17:49,590
+بنفك المعادلة عنها يبقى لو فكلها بصير اتنين x
+
+162
+00:17:49,590 --> 00:17:54,050
+تكييف v بدي اضرب x تربيع في ال two terms اللي
+
+163
+00:17:54,050 --> 00:18:02,090
+عندنا يبقى اتنين x تكييف في ال v زائد x أُص أربعة
+
+164
+00:18:02,090 --> 00:18:08,380
+في ال dv على ال x بعدين بدي اضرب هذهيبقى هدف
+
+165
+00:18:08,380 --> 00:18:15,940
+تعطينا زائد اتنين X تكييب V تربيع حصل ضرب الاتنين
+
+166
+00:18:15,940 --> 00:18:24,120
+هدول ببعض زائد اللي هو هنا مافيش الا V في X أس
+
+167
+00:18:24,120 --> 00:18:35,240
+أربعة في DV على DX يساوي نقص اتنين X تكييب V طيب
+
+168
+00:18:35,540 --> 00:18:41,760
+بالدالي لهذا ال term وهذا ال term فيهم x أُس 4
+
+169
+00:18:41,760 --> 00:18:49,400
+عامل مشترك وفيه dv على dx يبقى هذا x أُس 4 وهذا
+
+170
+00:18:49,400 --> 00:18:58,770
+واحد زائد v في dv على dx مرة تانيةلتحتيم الخط X أس
+
+171
+00:18:58,770 --> 00:19:04,130
+4 في DV على DX عامة مشترك بيبقى الواحد زائد V هاي
+
+172
+00:19:04,130 --> 00:19:08,670
+الواحد زائد V وهي ال DV على DX وهي ال X أس 4
+
+173
+00:19:08,670 --> 00:19:15,050
+الباقية هرحله جهتي اليمين يبقى هذا بده ساعة طلعيلي
+
+174
+00:19:15,050 --> 00:19:20,810
+في ال term اللي عندك هذا وهذا يبقى بيصير ناقص
+
+175
+00:19:20,810 --> 00:19:29,920
+أربعة X كعيب Vيبقى هذا ناقص اللي هو اربعة اكس
+
+176
+00:19:29,920 --> 00:19:36,480
+تكييب في ال V يبقى ناقص اربعة اكس تكييب في ال V
+
+177
+00:19:36,480 --> 00:19:40,880
+فلحظنا من هنا يبقى لنا ناقص اتنين اكس تكييب V
+
+178
+00:19:40,880 --> 00:19:49,580
+تربيع ناقص اتنين اكس تكييب V تربيع اول شئتم فقولوا
+
+179
+00:19:49,580 --> 00:19:57,410
+هاي الناقصو هنا هذا اتنين و بيظل عندنا مين بيظل
+
+180
+00:19:57,410 --> 00:20:04,150
+عندنا كمان x تكيب و بيظل عندنا v و هنا واحد زائد v
+
+181
+00:20:04,150 --> 00:20:11,250
+هصبط هيك هي ناقص برا و اتنين اه بيظل عندنا لا لا
+
+182
+00:20:11,250 --> 00:20:17,250
+لا استني شوية هي ناقص اتنين x تكيب v بيظل عندنا
+
+183
+00:20:17,250 --> 00:20:23,520
+هذه اتنين و ليست واحد بس هذه اتنينمظبوط؟ يبقى عادي
+
+184
+00:20:23,520 --> 00:20:29,360
+تماما طيب اننا نحاول نفسر المتغيرات بدي أخلي ال V
+
+185
+00:20:29,360 --> 00:20:35,440
+في شجة و ال X في شجة واحدة يبقى عادي يا ستة بصير
+
+186
+00:20:35,440 --> 00:20:46,240
+واحد زائد V على اتنين V زائد V تربيع كله في ال DV
+
+187
+00:20:46,240 --> 00:20:55,300
+بده يساوينقص اتنين x تكيب على x أس أربع في dx
+
+188
+00:20:55,300 --> 00:21:07,420
+واضحة اظن ؟ طيب هل ال bus تفاضل المقام بس
+
+189
+00:21:07,420 --> 00:21:10,880
+بده اتنين يبقى بدأ اضرف اتنين و اكسب مع اتنين مش
+
+190
+00:21:10,880 --> 00:21:19,080
+هنقدر اكملإذا هذه هي اتنين
+
+191
+00:21:19,080 --> 00:21:27,920
+زائد اتنين V عالى اتنين V زائد V ترابيع كله في DV
+
+192
+00:21:27,920 --> 00:21:36,640
+بده يساوي نقص اتنين على X كله بالنسبة الى DX X
+
+193
+00:21:36,640 --> 00:21:42,830
+تقيم X الصاربع بيبقى ال main X الكامليبقى هذا نص
+
+194
+00:21:42,830 --> 00:21:51,430
+لين absolute value لل V تربية زائد اتنين V بده
+
+195
+00:21:51,430 --> 00:21:57,950
+يساوي ناقص اتنين لين absolute value ل X زائد
+
+196
+00:21:57,950 --> 00:22:03,600
+constant C1بنقدر نتخلص من النص هذا و نضرب كله فى
+
+197
+00:22:03,600 --> 00:22:09,160
+قداش فى اتنين فلو ضربنا فى اتنين بيصير لن absolute
+
+198
+00:22:09,160 --> 00:22:16,740
+value ل V تربية زائد اتنين V يساوي ناقص اربعة ل
+
+199
+00:22:16,740 --> 00:22:24,200
+absolute value ل X زائد constant C1 شو رايك بدي
+
+200
+00:22:24,200 --> 00:22:29,670
+اجيب اللي نات عن بعض و اخلي ال constant لحالهكيف؟
+
+201
+00:22:29,670 --> 00:22:36,790
+مش شامل اتنين she won لإنه ضربنا في اتنين مظبوط
+
+202
+00:22:36,790 --> 00:22:42,330
+أصابة امرأة وقفت عامة تمام ضربنا الطرف اليمين كله
+
+203
+00:22:42,330 --> 00:22:48,150
+في مين؟ في الاتنين يبقى لو جيت قلت لن V تربيع
+
+204
+00:22:48,150 --> 00:22:56,130
+زائدي اتنين Vزائد أربعة لل absolute value ل X
+
+205
+00:22:56,130 --> 00:23:02,730
+بتساوي اتنين C1طيب هذه الأربعة لو جيت هنا إيش
+
+206
+00:23:02,730 --> 00:23:10,570
+بصير؟ X أُص أربعة طب و لن زائد لن لن حاصل الضرب
+
+207
+00:23:10,570 --> 00:23:18,150
+يبقى هذه بصير لن X أُص أربعة و هذا ال absolute
+
+208
+00:23:18,150 --> 00:23:25,290
+value فاهمين؟ في ال V تربيع زائد X أُص أربعة في
+
+209
+00:23:25,290 --> 00:23:35,110
+اتنين Vبدو يساوي 2C1 طيب رجعي شوية ال VX تربيع
+
+210
+00:23:35,110 --> 00:23:42,610
+بقداش يا بنات إذا هشيل كل VX تربيع و أحط بدالة Y
+
+211
+00:23:42,610 --> 00:23:50,210
+يبقى هذي VX تربيع هذي بقداش؟ بY تربيع تمام يبقى
+
+212
+00:23:50,210 --> 00:23:57,810
+هذي لان absolute value ل Y تربيعو هذه الزائد اتنين
+
+213
+00:23:57,810 --> 00:24:06,290
+وهذه اكس تربيع بظل في اكس تربي عليهمين ابو Y يبقى
+
+214
+00:24:06,290 --> 00:24:12,850
+هذه ال Y يساوي اتنين C1 ايه ايش رايك اتخلص من ال N
+
+215
+00:24:14,560 --> 00:24:21,260
+برفع اتنين كاصل العدد E يبقى بيصير absolute value
+
+216
+00:24:21,260 --> 00:24:29,380
+لل Y تربية زائد اتنين X تربية Y يسوى E أس اتنين C1
+
+217
+00:24:29,380 --> 00:24:35,200
+طب الاكس بولانش العمرها بتاخد قيمة سالبة إذا ال
+
+218
+00:24:35,200 --> 00:24:41,480
+absolute هذا لا معناه لهيبقى هذا معناه ان y تربية
+
+219
+00:24:41,480 --> 00:24:50,000
+زائدي اتنين x تربية y بده يساوي c و c يساوي e اقصى
+
+220
+00:24:50,000 --> 00:24:57,460
+اتنين c one بده احطه ب c طيب بده اجيب من المعادلة
+
+221
+00:24:57,460 --> 00:25:01,640
+هذه y قداش تساوي؟
+
+222
+00:25:01,640 --> 00:25:08,890
+ليش؟ أليست معادلة من الدرجة الثانية في y؟إذا
+
+223
+00:25:08,890 --> 00:25:12,930
+بتتحلل بحلل .. لا بتتحللش بحلها بالقانون وبالتالي
+
+224
+00:25:12,930 --> 00:25:17,170
+بقدر أجيب y as a function of x وهو ال general
+
+225
+00:25:17,170 --> 00:25:21,910
+solution لل differential equation يعني بقدر أكتب y
+
+226
+00:25:21,910 --> 00:25:28,750
+تربية زيدي اتنين x تربية y ناقص c يساوي zero
+
+227
+00:25:28,750 --> 00:25:38,050
+مظبوط؟ بدنا نحلها بالقانونيبقى Y يساوي ناقص با
+
+228
+00:25:38,050 --> 00:25:44,270
+يعني ناقص اتنين X تربية زائد او ناقص الجدري
+
+229
+00:25:44,270 --> 00:25:51,230
+التربية يلي با تربية يليه اربعة X أس اربعة ناقص
+
+230
+00:25:51,230 --> 00:25:59,190
+اربعة الف اللي هو بواحد جيم اللي هو قداش بناقص C
+
+231
+00:25:59,190 --> 00:26:09,310
+يبقى في ناقص Cكل هذا الكلام على اتنين في واحد طيب
+
+232
+00:26:09,310 --> 00:26:14,610
+هذا الكلام بدي اعطيكي ان why you sowy اظن اربعة مع
+
+233
+00:26:14,610 --> 00:26:19,510
+اربعة تطلع برا باتنين و اتنين تطلع برا تروح مع مين
+
+234
+00:26:19,510 --> 00:26:26,550
+مع اتنين اللي تحت يبقى الجواب ناقص x تربيع زائد او
+
+235
+00:26:26,550 --> 00:26:36,320
+ناقص الجدر تربيعي لx أربعة زائد cيبقى ده شكل الحل
+
+236
+00:26:36,320 --> 00:26:42,220
+مين للمعادلة التفاضلية اللي علناها حد فيكم بتحب
+
+237
+00:26:42,220 --> 00:26:49,920
+تسأل أي سؤال هنا؟ خلاص؟ طيب لحد هنا انتهى هذا ال
+
+238
+00:26:49,920 --> 00:26:56,640
+section لم يبقى إلا أن نعطيكم أرقام المسائل
+
+239
+00:26:56,640 --> 00:26:59,520
+المطلوب تمرنوا إيديكم فيها
+
+240
+00:27:11,610 --> 00:27:16,410
+يبقى exercises واحد
+
+241
+00:27:16,410 --> 00:27:25,770
+تلاتة المسائل التالية تلاتة، خمسة، ستة، عشرة،
+
+242
+00:27:25,770 --> 00:27:34,350
+احداشر، تلتاشر، اربعتاشر، تسعتاشر، واحد وعشرين
+
+243
+00:27:42,890 --> 00:27:50,650
+بنجي الأن ل section واحد أربعة اللي هو ال exact
+
+244
+00:27:50,650 --> 00:27:54,170
+equations
+
+245
+00:27:54,170 --> 00:28:02,570
+المعادلة التامة نديلها تعريف definition the first
+
+246
+00:28:02,570 --> 00:28:05,650
+order
+
+247
+00:28:05,650 --> 00:28:08,870
+differential
+
+248
+00:28:08,870 --> 00:28:11,490
+equation
+
+249
+00:28:13,490 --> 00:28:22,150
+الـ M as a function of X وY زائد الـ N as a
+
+250
+00:28:22,150 --> 00:28:30,310
+function of X وY الـ GY على DX يساوي زيرو وهادي
+
+251
+00:28:30,310 --> 00:28:38,270
+بدي أسميها المعادلة star is called exact
+
+252
+00:28:38,270 --> 00:28:50,430
+معادلة تمةif there exists a function إذا قدرت
+
+253
+00:28:50,430 --> 00:29:01,190
+ألاقي دلّا فاي of x و y such that بحيث أنه such
+
+254
+00:29:01,190 --> 00:29:08,490
+that اللي هو partial فاي على partial x بدي سوى ال
+
+255
+00:29:08,490 --> 00:29:19,700
+M of x و yو Partial Phi على Partial Y يساوي N O X
+
+256
+00:29:19,700 --> 00:29:28,320
+Y. The solution of
+
+257
+00:29:28,320 --> 00:29:42,430
+the differential equation Star isفاي اكس واي يساوي
+
+258
+00:29:42,430 --> 00:29:53,250
+يكون مصطلح C اخر م الاختصار
+
+259
+00:29:53,250 --> 00:30:07,790
+الاختصار م اكس واي زائد م اكس واي dy على dx يساوي
+
+260
+00:30:09,150 --> 00:30:20,210
+is exact if and only if if and only if partial m
+
+261
+00:30:20,210 --> 00:30:26,450
+by partial y يسمي partial m by partial x
+
+262
+00:31:35,180 --> 00:31:40,220
+وحتى الآن احنا درسنا اول نوع من انواع المعادلات
+
+263
+00:31:40,220 --> 00:31:43,720
+اللي هو homogeneous differential equations افوا
+
+264
+00:31:43,720 --> 00:31:47,920
+نصي قلم ال equations و بعدين درسنا ال homogeneous
+
+265
+00:31:47,920 --> 00:31:51,780
+differential equations والان بنجي للنوع التالت
+
+266
+00:31:51,780 --> 00:31:58,140
+اللي هو exact equations يعني المعادلات التامة نعطي
+
+267
+00:31:58,140 --> 00:32:03,700
+تاريخ لها و نشوف ايش بيقول هذا التاريخبقول التعريف
+
+268
+00:32:03,700 --> 00:32:08,300
+the first order differential equation M of X Y زي
+
+269
+00:32:08,300 --> 00:32:13,500
+N of X Y دي Y على دي X بده يساوي زي 0 زي شكل
+
+270
+00:32:13,500 --> 00:32:18,990
+المثال قبل الأخيرمش كان عندنا معادلة في dy على dx
+
+271
+00:32:18,990 --> 00:32:23,190
+يستوى معادلة تانية في الطرف اللي منها زيها طبعا بس
+
+272
+00:32:23,190 --> 00:32:28,650
+خلها كل إياش في طرف واحد وخلاها معادلة صفرية يبقى
+
+273
+00:32:28,650 --> 00:32:31,690
+أنا عندي معادلة من الرتبة الأولى لإن ماعنديش إلا
+
+274
+00:32:31,690 --> 00:32:35,530
+المشتقة الأولى زي ما أنتوا شايفين يبقى هذه
+
+275
+00:32:35,530 --> 00:32:41,050
+المعادلة بالشكلة بقول عنها exactly كيف؟ إذا جدرت
+
+276
+00:32:41,050 --> 00:32:48,420
+ألاقي دالة phi of x و yبحيث أن مشتقة هذه الدالة
+
+277
+00:32:48,420 --> 00:32:54,440
+بالنسبة إلى x يسوى ال M ومشتقتها بالنسبة إلى y
+
+278
+00:32:54,440 --> 00:32:59,420
+يسوى main ال M ويجيبها partial phi على partial x
+
+279
+00:32:59,420 --> 00:33:04,340
+يسوى M of x وyand partial y على partial y يساوي من
+
+280
+00:33:04,340 --> 00:33:09,500
+n of x y لما اقول partial يعني الاشتقاق الجزء
+
+281
+00:33:09,500 --> 00:33:14,840
+الاشتقاق الجزء ليش لإن ال m و ال n ده لتاني في
+
+282
+00:33:14,840 --> 00:33:21,770
+متغيرين و ليس ده لفي متغيرين واحدلو كانت فيه متغير
+
+283
+00:33:21,770 --> 00:33:27,970
+واحد لقول نتفاضل عادي dy by dx تمام لكن لا نظرا او
+
+284
+00:33:27,970 --> 00:33:33,970
+d phi على dx او d phi على dy لكن نظرا لان phi ده
+
+285
+00:33:33,970 --> 00:33:39,170
+اللي فيه متغيرين فبروح باشتق اشتقاقا جزئيا كما
+
+286
+00:33:39,170 --> 00:33:44,780
+سنرى بعد قليل يبقى باجي بقولالدالة اللى عندنا هذه
+
+287
+00:33:44,780 --> 00:33:49,240
+او المعادلة اللى عندنا star هي exact معادلة تامة
+
+288
+00:33:49,240 --> 00:33:54,820
+إذا قدرتى لاجي دالة five of x y بحيث أن المشتقة
+
+289
+00:33:54,820 --> 00:34:01,160
+الجزئية لها بالنسبة إلى x يساوي m of x y والمشتقة
+
+290
+00:34:01,160 --> 00:34:07,920
+الجزئية لها بالنسبة إلى y يساوي n of x y طيب تمام
+
+291
+00:34:08,170 --> 00:34:11,350
+السؤال هو طب وانك ايه بدي الاقي هذه الدالة بدي
+
+292
+00:34:11,350 --> 00:34:15,750
+اقعد ادور هدى تظبط و هدى ماتظبطش اقعد نص ساعة و لا
+
+293
+00:34:15,750 --> 00:34:18,610
+ساعة و لا ساعتين و لا تلت ساعات ادور هذه الشغله
+
+294
+00:34:18,610 --> 00:34:22,670
+يعني متعبه جدا و يمكن نجرب طول اليوم و مانقدرش
+
+295
+00:34:22,670 --> 00:34:28,130
+نجيب هذه ال function طبعا راح بحث العلماء لغاية ما
+
+296
+00:34:28,130 --> 00:34:35,480
+توصلوا الى نظرية تسهل هذه العملية شو النظرية هذهأه
+
+297
+00:34:35,480 --> 00:34:40,460
+طبعاً قبل النظرية الحل تبع المعادلة الى four مدى
+
+298
+00:34:40,460 --> 00:34:45,380
+ومشتقة هذه لهنا يساوي هذه ومشتقة هذه تساوي هذه
+
+299
+00:34:45,380 --> 00:34:50,580
+وطرف اليمين يساوي zero زير ومشتقة ال constant إذا
+
+300
+00:34:50,580 --> 00:34:55,220
+هذه phi of x y لازم تساوي مقدار ثاني حتى يبقى
+
+301
+00:34:55,220 --> 00:35:00,090
+مشتقته تساوي مين تساوي zeroالان كيف تحكم على هذه
+
+302
+00:35:00,090 --> 00:35:04,850
+انها exact بدون ما اقعد ادور اوصل او ماوصلش فبقول
+
+303
+00:35:04,850 --> 00:35:08,690
+لأجزا differential equation هذه بقول عنها exact
+
+304
+00:35:08,690 --> 00:35:14,910
+اذا لقيت مشتقت هذا الكلام لو M بالنسبة الى Y سوى
+
+305
+00:35:14,910 --> 00:35:19,780
+مشتقت هذا بالنسبة لمنيعني ال M مش بده أشتقها
+
+306
+00:35:19,780 --> 00:35:25,280
+بالنسبة ل X بده أشتقها بالنسبة إلى Y و ال N بده
+
+307
+00:35:25,280 --> 00:35:30,580
+أشتقها كأن جلبت الوضع، طبعا يعني الدالة الأولى بده
+
+308
+00:35:30,580 --> 00:35:33,740
+أشتقها بالنسبة إلى Y و الدالة التانية بده أشتقها
+
+309
+00:35:33,740 --> 00:35:39,920
+بالنسبة ل Xإن حدثت تساوي بقول هذه المعادلة exact
+
+310
+00:35:39,920 --> 00:35:44,700
+مدام exact إذا لازم ألاقي function phi of x y
+
+311
+00:35:44,700 --> 00:35:49,980
+تساوي كونستانت هي عبارة عن حل مين لهذه المعادلة
+
+312
+00:35:49,980 --> 00:35:55,000
+نعطيكم الأن أكثر من مثال على كيفية إيجاد هذه
+
+313
+00:35:55,000 --> 00:36:01,160
+الدالة وكيفية الحكم على إنها exact أو ماهياش exact
+
+314
+00:36:01,160 --> 00:36:04,440
+نبدأ بأول مثال هو example one
+
+315
+00:36:10,260 --> 00:36:13,240
+Example 1 بيقول سؤال الـ differential equation
+
+316
+00:36:13,240 --> 00:36:21,400
+سؤال الـ differential equation حل المعادلة تفاضرية
+
+317
+00:36:21,400 --> 00:36:31,260
+x في e to the power x في y في ال y prime زائد y في
+
+318
+00:36:31,260 --> 00:36:38,340
+e to the power xy ناقص أربعة x تكييب يساوي مين؟
+
+319
+00:36:38,340 --> 00:36:38,960
+يساوي
+
+320
+00:36:46,740 --> 00:36:52,600
+أول خطوة يا عزيزي هي ارتب مسئلتي لتكون في الشكل
+
+321
+00:36:52,600 --> 00:36:58,340
+الـ star اللي فوق حتى أبدأ أشتغل شغل الطبيعي فبجي
+
+322
+00:36:58,340 --> 00:37:02,660
+بقول هنا y' بدأت الأول يجب أن أدخل هذه في الأول
+
+323
+00:37:02,660 --> 00:37:06,920
+وهذه في الآخر الجماعة لديها مشكلة إذا لو أعد
+
+324
+00:37:06,920 --> 00:37:14,580
+ترتيبها يجب أن أقول y بيقص xy ناقص 4x تقريبا
+
+325
+00:37:17,250 --> 00:37:26,770
+زائد X في E أُس XY في Y' يساوي 0 هاي ال M في X و Y
+
+326
+00:37:26,770 --> 00:37:31,810
+بجهة دي تشكل مين ال M زي ما انت شايفها دالة في X و
+
+327
+00:37:31,810 --> 00:37:38,890
+Y وهذه تشكل ال N لأنها كذلك دالة في X و Y إذن هذه
+
+328
+00:37:38,890 --> 00:37:46,600
+هي ال M تبعة الجزء النظري وهذه هي ال Nتبعت الجزء
+
+329
+00:37:46,600 --> 00:37:52,300
+النظري طب بدي احكم عليها exact و الله ماهياش exact
+
+330
+00:37:52,300 --> 00:37:58,660
+يبقى بدي اروح ادي ااخد تفاضل ال M بالنسبة ل X يبقى
+
+331
+00:37:58,660 --> 00:38:05,620
+بدي ااخد partial M by partial Y يزاوى اللي هو ال
+
+332
+00:38:05,620 --> 00:38:10,910
+term اللي عندنا هذايعني بدي أشتق هذا الجزء بالنسبة
+
+333
+00:38:10,910 --> 00:38:17,330
+ل why نظرا لإنه عندي أكثر من متغير فالمتغير اللي
+
+334
+00:38:17,330 --> 00:38:20,710
+بشتق بالنسبة له باعتبره هو المتغير و باقي
+
+335
+00:38:20,710 --> 00:38:26,050
+المتغيرات ثوابت زي واحد و اتنين و عشر و نص و تلت
+
+336
+00:38:26,050 --> 00:38:30,230
+تربع و اللي بدكي يعنييبقى أي متغير آخر باعتبره
+
+337
+00:38:30,230 --> 00:38:36,170
+مقدار ثابت وهذا معنى الاشتقاق الجزئي كما درسناه في
+
+338
+00:38:36,170 --> 00:38:40,670
+calculus C لكن لمّا ما درسوش calculus C أنا بذكرهم
+
+339
+00:38:40,670 --> 00:38:45,150
+لن يقابلنا حاجة نفيدنا من calculus C إلا هذا ال
+
+340
+00:38:45,150 --> 00:38:50,670
+section فقط لا غير و هتلاقي الشغلات بسيطة جدا كما
+
+341
+00:38:50,670 --> 00:38:55,410
+ستراهم يبقى أنا بضروح أشتق هذا بالنسبة لمين يا
+
+342
+00:38:55,410 --> 00:39:00,000
+بناتنسبة ل Y يبقى مشتقة هذا المقدار كله بيبقى داش
+
+343
+00:39:00,000 --> 00:39:05,160
+Zero مع السلامة لإن مافيش في Y في X تقعيه مشتقة
+
+344
+00:39:05,160 --> 00:39:09,420
+منه يبقى في Zero يبقى باجي لهذا ال term هذي Y و
+
+345
+00:39:09,420 --> 00:39:13,960
+هذي E و ال 6Y تنتين فيهم Y يبقى هذا المشتقة حاصل
+
+346
+00:39:13,960 --> 00:39:19,340
+ضرب دالتين يبقى بدي أشتق الأولى بالنسبة ليه؟ لو
+
+347
+00:39:19,340 --> 00:39:26,670
+يبقى داش بواحد في E و ال 6Y يبقى E و ال 6Yزائد Y
+
+348
+00:39:26,670 --> 00:39:30,770
+بالـ Exponential
+
+349
+00:39:30,770 --> 00:39:39,090
+زي ما هي ضرب مشتقة الأس بالنسبة إلى Y يبقى كإن هذه
+
+350
+00:39:39,090 --> 00:39:44,430
+تلاتة Y بداش تقها بالنسبة إلى Y إذا تلاتة يبقى داش
+
+351
+00:39:44,430 --> 00:39:57,760
+يبقى X إذا هذه النتيجة هي E×XYزائد XY إيقص XY طيب
+
+352
+00:39:57,760 --> 00:40:05,000
+بدنا ناخد تفاضل ال N بالنسبة ال X وين ال N هي ال N
+
+353
+00:40:05,000 --> 00:40:11,100
+يبقى هذه فيها X وهذه فيها X إذا مشتقت حاصل ضرب
+
+354
+00:40:11,100 --> 00:40:16,800
+دلتين لما اشتق الأولى بالنسبة ل X روحك وضلي تانية
+
+355
+00:40:16,800 --> 00:40:24,910
+يبقى إيقص XY زائدالـ X زي ما هي ومشتقة الـ X
+
+356
+00:40:24,910 --> 00:40:28,910
+exponential بالـ X exponential itself في مشتقة
+
+357
+00:40:28,910 --> 00:40:36,510
+الأس بالنسبة إلى X اللي هو قداش Y فقط لا غير لأن
+
+358
+00:40:36,510 --> 00:40:42,370
+الـ Y هنا يعتبر مقدارا ثابتا يبقى هذا الكلام بده
+
+359
+00:40:42,370 --> 00:40:50,680
+يساوي E أس XY زائد XY E أس XYماذا تلاحظ على
+
+360
+00:40:50,680 --> 00:40:58,640
+المشتقتين؟ زي بعض يبقى هذا بده يعطينا ان تفاضل ال
+
+361
+00:40:58,640 --> 00:41:04,760
+M بالنسبة إلى Y يسوى partial N by partial X هذا
+
+362
+00:41:04,760 --> 00:41:10,780
+ايش بده يعطينا؟ هذا بده يعطينا ما يأتي يبقى هذا يا
+
+363
+00:41:10,780 --> 00:41:16,620
+مناد اللي بده اسميها المعادلة Star يبقى هذا بده
+
+364
+00:41:16,620 --> 00:41:17,620
+يعطينا
+
+365
+00:41:19,870 --> 00:41:27,910
+differential equation a star is exact مدام exact
+
+366
+00:41:27,910 --> 00:41:33,590
+يبقى there exist هاد ال a المقلوبة there exist a
+
+367
+00:41:33,590 --> 00:41:43,110
+function phi of x y يساوي constant وليكن c1 such
+
+368
+00:41:43,110 --> 00:41:46,490
+that بحيث ان
+
+369
+00:41:57,320 --> 00:42:06,460
+Y في E أس X Y ناقص
+
+370
+00:42:06,460 --> 00:42:13,570
+أربع X تكريمو partial phi على partial y بدي يسوى
+
+371
+00:42:13,570 --> 00:42:19,930
+من ال n كل ال n عندي x في e أُس xy يبقى x في e أُس
+
+372
+00:42:19,930 --> 00:42:26,730
+xy طب أنا بدي أعرف شكل ال phi عشان أعرف شكل ال phi
+
+373
+00:42:26,730 --> 00:42:30,430
+أيوة هذه؟
+
+374
+00:42:30,430 --> 00:42:37,710
+وين هذه؟ هاي شايفاها؟ مش تقتحاص الضرب ده اللي تاني
+
+375
+00:42:38,210 --> 00:42:45,770
+مشتقة الأولى كده؟ في التانية هي زائد الأولى هي
+
+376
+00:42:45,770 --> 00:42:50,890
+مشتقة ال exponential بال exponential زي ما هي ضرب
+
+377
+00:42:50,890 --> 00:42:57,230
+مشتقة الأس بالنسبة إلى X مشتقة بالنسبة إلى X يعني
+
+378
+00:42:57,230 --> 00:43:02,570
+Y اللي هي الكلسة يبقى هي ال Y واضحة؟ حد بتسأل أي
+
+379
+00:43:02,570 --> 00:43:12,130
+تساؤل ثاني؟ كده كده كده كدههي وين
+
+380
+00:43:12,130 --> 00:43:16,310
+يقول why prime تعالي ياريح تيجي هنا نشوف تعالي مش
+
+381
+00:43:16,310 --> 00:43:22,370
+فاش فيها حاجة تعالي نشوف بس إيش سؤالك بالضبط فضلي
+
+382
+00:43:22,370 --> 00:43:26,270
+لا
+
+383
+00:43:29,970 --> 00:43:34,790
+انت شايفه ايش مايقولك هذا ال course M و هذا N شايف
+
+384
+00:43:34,790 --> 00:43:40,330
+المثل هذا M و هذا N و المشتقة زي ما هي وصلها يعني
+
+385
+00:43:40,330 --> 00:43:46,070
+أنا بشتر على M و N بس يا بنات في حد بتسأل أي سؤال
+
+386
+00:43:46,070 --> 00:43:54,540
+تاني كمان؟ طيب نيجي .. نيجي مرة ثانيةيبقى انا حصلت
+
+387
+00:43:54,540 --> 00:43:58,480
+على تفاضل ال file اللي أنا بدياه اللي قاعد بدور
+
+388
+00:43:58,480 --> 00:44:04,740
+عليها هي شو شكلها الله أعلم قاعد بدور عليها بمجيب
+
+389
+00:44:04,740 --> 00:44:09,500
+مشتقتها بالنسبة ل X و بديم مشتقتها بالنسبة إلى Y
+
+390
+00:44:09,500 --> 00:44:16,920
+يبقى لو كملت الأولى بالنسبة ل X بحصل على Fi أو لو
+
+391
+00:44:16,920 --> 00:44:21,620
+كملت التانية بالنسبة إلى Y بحصل على Fi طب كامل مين
+
+392
+00:44:21,620 --> 00:44:27,280
+منهم؟باجي باططلع في شكل اللي أسهل روحي كاملي و
+
+393
+00:44:27,280 --> 00:44:32,220
+اصلا بلاش منه و اذا التنتين سهلاتي بأي واحدة بكمل
+
+394
+00:44:32,220 --> 00:44:37,080
+لو بكون حصل على النتيجة باجي باططلع لو بده كامل
+
+395
+00:44:37,080 --> 00:44:47,910
+هذه بالنسبة ل X Y مقدار ثابتوY مقدر ثابت يبقى
+
+396
+00:44:47,910 --> 00:44:52,210
+4X و 4 على 4 يعني سهل جدا
+
+397
+00:45:03,250 --> 00:45:07,010
+يبقى التنتين سواء كانت هذه والله هذه بدي أكملهم
+
+398
+00:45:07,010 --> 00:45:11,690
+اتنين صح تمام يبقى لو جيت كاملت الأولى يا بنات
+
+399
+00:45:11,690 --> 00:45:18,110
+يبقى لو كاملت الأولى بصير عندنا five of x و y يوسف
+
+400
+00:45:18,110 --> 00:45:21,930
+بدي أكملها بالاسم ال x ال y مقدار ثابت وال
+
+401
+00:45:21,930 --> 00:45:28,410
+exponential كما هي مقسومة على تفاضل الأسد وقدر y
+
+402
+00:45:29,390 --> 00:45:34,270
+يبقى انا بدي اكمل بالنسبة ل X ناقص أربعة X أص
+
+403
+00:45:34,270 --> 00:45:39,290
+أربعة على أربعة زائد مقدار ثابت المقدار الثابت
+
+404
+00:45:39,290 --> 00:45:44,550
+باعتبره function في المتغير الثاني لأن المتغير
+
+405
+00:45:44,550 --> 00:45:48,870
+الثاني بالنسبة ليه يعتبر مقدارا ثابتا يبقى بروح
+
+406
+00:45:48,870 --> 00:45:55,740
+بقوله زائد F of YF of Y كله يعتبر مقدار ثابت
+
+407
+00:45:55,740 --> 00:46:00,820
+بالنسبة لمن؟ بالنسبة ال X يعني يا بنات هذه بيصير E
+
+408
+00:46:00,820 --> 00:46:10,890
+of 6Y ناقص X أس أربعة زائد F of Yهذا مين فاي of x
+
+409
+00:46:10,890 --> 00:46:16,570
+و y الحين مشكلتي بس بدي اعرف قداش f of y مشان اعرف
+
+410
+00:46:16,570 --> 00:46:23,470
+f of y بدي اروح اكاملها افاضلها بالنسبة الى y يبقى
+
+411
+00:46:23,470 --> 00:46:30,930
+partial phi على partial y هذي قداش مستقتها بالنسبة
+
+412
+00:46:30,930 --> 00:46:43,340
+الى y يبقى x في i أس x yناقص هذه zero زاد f prime
+
+413
+00:46:43,340 --> 00:46:51,000
+of y مش هي partial phi علي partial y فوق عندي و هي
+
+414
+00:46:51,000 --> 00:46:58,050
+انا اشتقتها هنايبقى المقدارين هدول بدهم يساووا بعض
+
+415
+00:46:58,050 --> 00:47:04,990
+يبقى لما أساويهم بعض بصير x e أس x y زائد f prime
+
+416
+00:47:04,990 --> 00:47:11,290
+of y بده يساوي x في u أس x y هذا معناته أن f prime
+
+417
+00:47:11,290 --> 00:47:18,610
+of y بده يساوي كده؟ Zeroيبقى هذا معناه ان f of y
+
+418
+00:47:18,610 --> 00:47:25,290
+يساوي مقدار ثابت ثاني يبقى بروح بقوله the solution
+
+419
+00:47:25,290 --> 00:47:35,010
+is phi of x y بده يساوي وين phi of x y هي اللي
+
+420
+00:47:35,010 --> 00:47:36,410
+طلعناها هي
+
+421
+00:47:52,430 --> 00:47:59,930
+يبقى بيصير أن فاي of x و y يسوى e أوس x y ناقص x
+
+422
+00:47:59,930 --> 00:48:00,870
+أوس أربعة
+
+423
+00:48:06,820 --> 00:48:14,720
+هذا هو حل المعادلة لا يزال لدينا مثال عن الـ exact
+
+424
+00:48:14,720 --> 00:48:19,380
+equation و بعد ذلك ال equation ممكن ماتطلعش exact
+
+425
+00:48:19,380 --> 00:48:24,740
+و تروح نحولها إلى exact زي ما قبل قليل كانتش
+
+426
+00:48:24,740 --> 00:48:28,960
+homogeneous و بنحولها إلى homogeneous و هكذا
+
+427
+00:48:28,960 --> 00:48:30,420
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..93f9d231b0e828d0967bd0c20ccc3bc25ea32b4e
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ioT12D_ruOo_raw.srt
@@ -0,0 +1,1708 @@
+1
+00:00:20,160 --> 00:00:23,580
+بسم الله الرحمن الرحيم المرة اللي فتت في نهاية
+
+2
+00:00:23,580 --> 00:00:27,880
+المحاضرة الماضية كتبنا ملاحظة الملاحظة كانت على
+
+3
+00:00:27,880 --> 00:00:31,980
+الشكل التالي لو كانت المعادلة التفاضلية على شكل
+
+4
+00:00:31,980 --> 00:00:41,840
+a1x زائد b1y زائد c1 كلها في y' يسوى a2x زائد b2y
+
+5
+00:00:41,840 --> 00:00:48,040
+زائد c2 يبقى في هذه الحلقة نحاول نحل المعادلة
+
+6
+00:00:48,040 --> 00:00:52,680
+التفاضلية اللي عندناطبعا لو جسمنا الطلبين على X أو
+
+7
+00:00:52,680 --> 00:00:57,760
+على Y لايمكن أن تظهر الـ Homogeneous Differential
+
+8
+00:00:57,760 --> 00:01:06,040
+Equation هل الـ A1 في B2 يساوي الـ A2 في B1 ولا
+
+9
+00:01:06,040 --> 00:01:11,420
+لأ؟ إن حدث ذلك يبقى من الحل هذه كما كنا نحل من قبل
+
+10
+00:01:11,420 --> 00:01:16,580
+بصير مسألتنا سهلة لكن إن كانت الـ A1 B2 لا تساوي
+
+11
+00:01:16,580 --> 00:01:22,590
+B2 A1يجب أن نكتب المعادلتين اللي اتنين اللي عندنا
+
+12
+00:01:22,590 --> 00:01:26,670
+و نسويهم بالصفر و نحل المعادلتين هدول مع بعضهم
+
+13
+00:01:26,670 --> 00:01:32,290
+نجيب قيمة كلها من X وY او نجيب قيمة P وQ لان قلنا
+
+14
+00:01:32,290 --> 00:01:38,410
+نكتب معادلة على صيغة A1P زائد B1Q زائد C1 يساوي
+
+15
+00:01:38,410 --> 00:01:45,390
+Zero و المعادلة التانية A2P زائد B2EQ زائد C2
+
+16
+00:01:45,390 --> 00:01:51,930
+يساوي Zeroبنروح ونقول ان استبدأ كل X بX كابتل زائد
+
+17
+00:01:51,930 --> 00:01:57,250
+P اللي طلعت وكل Y بY كابتل زائد Q اللي طلعت ان هو
+
+18
+00:01:57,250 --> 00:02:01,490
+في هذه الحالة automatic تتحول المعادلة اللي عندنا
+
+19
+00:02:01,490 --> 00:02:07,520
+إلى معادلة متجانسةهذا أخر كلمتين نظري كتبناه المرة
+
+20
+00:02:07,520 --> 00:02:11,420
+الماضية وهذا المثال اللي قدامي على اللوح مثال
+
+21
+00:02:11,420 --> 00:02:16,980
+مباشر على هذا النوع من المسائل ممكن ما تظهر شان
+
+22
+00:02:16,980 --> 00:02:20,580
+كاميرات بالشكل هذا ممكن تظهر y prime يساوي y زائد
+
+23
+00:02:20,580 --> 00:02:25,500
+2 مقسمة على x زائد y زائد 1 ان كان بالشكل هذا أو
+
+24
+00:02:25,500 --> 00:02:30,800
+بالشكل هذا سيان يبقى بدنا نعمل نفس الشغل يعني ممكن
+
+25
+00:02:30,800 --> 00:02:37,840
+تظهر y prime يساوي y زائد 2تقسيم x زائد y زائد 1
+
+26
+00:02:37,840 --> 00:02:42,080
+انظرت بالشكل هذا او بالشكل هذا الاتنين لهم نفس
+
+27
+00:02:42,080 --> 00:02:49,920
+الشغل يبقى ايش بدي اعمل بدي اروح اشوف هل ال a1 في
+
+28
+00:02:49,920 --> 00:02:56,320
+ال b2 يساوي ال a1 اللي هو معامل مين؟ معامل x بقدرش
+
+29
+00:02:56,320 --> 00:03:02,440
+يبغاها b2 معامل y اللي هو قدرش واحد يبقى النتيجة
+
+30
+00:03:02,440 --> 00:03:09,390
+يساوي واحدةبدأ اشوف a2b1 يبقى المعامل تبع اكس لان
+
+31
+00:03:09,390 --> 00:03:14,550
+الوقت بدأ بالزيرو معامل b1 معامل y هنا اللي هو
+
+32
+00:03:14,550 --> 00:03:22,090
+بواحد y يساوي زيرو يبقى هذا معناه ان a1b2 لا يساوي
+
+33
+00:03:22,090 --> 00:03:28,790
+a2 في ال b1 مدام هفتله هدول بيساووش بعض اذا بدنا
+
+34
+00:03:28,790 --> 00:03:33,470
+نروح نحل المعادلتين هدول مع بعضيبقى بدي اكتب
+
+35
+00:03:33,470 --> 00:03:39,950
+المعادلة هذه ل P زائد Q زائد واحد يساوي زيرو
+
+36
+00:03:39,950 --> 00:03:46,990
+والمعادلة التانية Q زائد اتنين يساوي زيرو من هذه
+
+37
+00:03:46,990 --> 00:03:51,790
+المعادلة بقدر اقول إذا ال Q يساوي قداش سالي ب
+
+38
+00:03:51,790 --> 00:03:56,920
+اتنينيبقى بناء عليه من الاتنين هدول مع بعض بصيرين
+
+39
+00:03:56,920 --> 00:04:02,940
+بي سالب اتنين زالد واحد يساوي زيرو ومنها بي تساوي
+
+40
+00:04:02,940 --> 00:04:10,680
+قداش تساوي واحد اذا بدي اعمل التحويل اللي بدها ضيع
+
+41
+00:04:10,680 --> 00:04:17,180
+ال constant واحد وال constant اتنين وهيبدنا نروح
+
+42
+00:04:17,180 --> 00:04:25,860
+نحط x small يساوي x capital زائد t يعني مين؟ يعني
+
+43
+00:04:25,860 --> 00:04:33,160
+ال x small بدي يساوي x capital زائد واحد و ال y
+
+44
+00:04:33,160 --> 00:04:40,740
+بدي يساوي y capital زائد ل q يعني y small بدي
+
+45
+00:04:40,740 --> 00:04:46,910
+يساوي y capitalناقص اتنين قيمة q اللي عندنا
+
+46
+00:04:46,910 --> 00:04:52,410
+المعلومات هذه بيروح عوض بوين في المعادلة اللي فوق
+
+47
+00:04:52,410 --> 00:04:57,270
+اللي بدي اسميها المعادلة star يبقى بداجي اقول هنا
+
+48
+00:04:57,270 --> 00:05:02,830
+substitute in
+
+49
+00:05:02,830 --> 00:05:12,070
+equation star we get بنحصل على المعادلة التالية
+
+50
+00:05:12,610 --> 00:05:17,730
+يبقى بده اشيل ال X Small وحط بدل X Capital زائد
+
+51
+00:05:17,730 --> 00:05:24,610
+واحد يبقى هذا معناه اه بس استنى شوية لما نيجي لهذا
+
+52
+00:05:24,610 --> 00:05:29,990
+يا بنات و نيجي نشتقها يبقى اشتقاقها دي بده يصير DX
+
+53
+00:05:29,990 --> 00:05:36,810
+Small يسوى DX Capital و لو نيجي نشتقها دي بصير
+
+54
+00:05:36,810 --> 00:05:47,650
+عندنا DY Smallيساوي dy كامتل يبقى
+
+55
+00:05:47,650 --> 00:05:51,070
+هذه المعادلة اللي بدها تصير على الشكل التالي ال x
+
+56
+00:05:51,070 --> 00:05:56,590
+small بده اشيلها و ده يحط بدالها main x زائد واحد
+
+57
+00:05:56,590 --> 00:06:04,750
+زائد y small اللي هي y ناقص اتنين وهذه زائد واحد
+
+58
+00:06:05,390 --> 00:06:11,010
+الان الـ y prime يعني اللي هي dy على dx dy اللي هي
+
+59
+00:06:11,010 --> 00:06:19,630
+d capital y على dx capital هذا الكلام بده يسوي y
+
+60
+00:06:19,630 --> 00:06:25,610
+small اللي هو capital y ناقص اتنين زائد اتنين اللي
+
+61
+00:06:25,610 --> 00:06:32,240
+عندنا نختصر الاختصارات واحد واحدإتنين و سالي
+
+62
+00:06:32,240 --> 00:06:37,860
+بإتنين مع السلامة يبقى آلة المثالة إلى x زائد
+
+63
+00:06:37,860 --> 00:06:47,270
+capital Y dy capital على dx يساوي capital Yيبقى
+
+64
+00:06:47,270 --> 00:06:52,610
+العملية بناء التعويض اللي حطناها دي فائدتها أننا
+
+65
+00:06:52,610 --> 00:06:57,090
+نتخلص من الثوابت اللي موجودة عندنا في المعادلة
+
+66
+00:06:57,090 --> 00:07:04,160
+اللي خلتني المعادلة أصلا non homogeneousيبقى هاي
+
+67
+00:07:04,160 --> 00:07:08,320
+النتيجة لأن لو جيت عملت زي ما عملنا و ما طلعتش
+
+68
+00:07:08,320 --> 00:07:13,040
+معادلة زيها دي يعني خالية من الثوابت معناته شغلك
+
+69
+00:07:13,040 --> 00:07:16,820
+في غلط في غلطة غلط من اللازم لما نعوض بهذه
+
+70
+00:07:16,820 --> 00:07:21,920
+التعويضة مايضلش عندي ثوابت بالمرة ديري بالك هذا
+
+71
+00:07:21,920 --> 00:07:22,640
+احنا بنبقى
+
+72
+00:07:28,660 --> 00:07:33,360
+يبقى في هذه الحالة لازمة ثوابت الطيلة وبالتالي
+
+73
+00:07:33,360 --> 00:07:36,860
+تقول المعادلة الى homogeneous differential
+
+74
+00:07:36,860 --> 00:07:41,160
+equation عرفنا انها homogeneous بجي بقول لو جسمت
+
+75
+00:07:41,160 --> 00:07:46,760
+كل المعادلة عالمهم على X إذا لو جسمت كل المعادلة
+
+76
+00:07:46,760 --> 00:07:53,150
+على X بصير واحد زائد capital Y على capital XDY
+
+77
+00:07:53,150 --> 00:08:01,290
+كابتل على DX يبقى يساوي Y على X كابتل يبقى هاي
+
+78
+00:08:01,290 --> 00:08:05,890
+المعادلة صارت بدلالة المتغير يبقى Y على X
+
+79
+00:08:08,990 --> 00:08:12,730
+يبقى هذه صارت homogeneous differential equation
+
+80
+00:08:12,730 --> 00:08:16,890
+يبقى بروح بحل المعادلة هذه زي ما كنت بحل ال
+
+81
+00:08:16,890 --> 00:08:20,490
+homogeneous differential equation في المرة الماضية
+
+82
+00:08:20,490 --> 00:08:26,710
+كيف؟ بجيب اقول quote ال V بدي سوى capital Y على
+
+83
+00:08:26,710 --> 00:08:34,370
+capital X او بمعنى اخر capital Y بدي سوى X في V
+
+84
+00:08:35,870 --> 00:08:42,930
+نشتقها يبقى دي واي كابتل على دي اكس كابتل الطرف
+
+85
+00:08:42,930 --> 00:08:49,870
+اليمين حاصل ضرب دالي تلف يبقى V زائد X في دي V على
+
+86
+00:08:49,870 --> 00:08:56,490
+دي كابتل X الآن نمسك المعلومات اللي حصلنا عليها
+
+87
+00:08:56,490 --> 00:09:02,530
+هذه ونعود في المعادلة اللي فوق يبقى بتصير المعادلة
+
+88
+00:09:02,530 --> 00:09:11,510
+واحد زائد Vالـ dy على dx اللي هي v زائد capital X
+
+89
+00:09:11,510 --> 00:09:18,850
+زائد capital X في الـ dv على dx capital بالشكل
+
+90
+00:09:18,850 --> 00:09:23,110
+اللي عندنا هذا هشيلنا هذه وضع للطرف اليمين اللي هو
+
+91
+00:09:23,110 --> 00:09:30,060
+main اللي هو كله بده ساوي vبدا افك القوس هذا يبقى
+
+92
+00:09:30,060 --> 00:09:34,820
+هضرب الجوسين اللي اتنين هدول مع بعضهم لو ضربت واحد
+
+93
+00:09:34,820 --> 00:09:40,480
+في الجوس يبقى بيظل الجوس كما هو يبقى بيصير v زائد
+
+94
+00:09:40,480 --> 00:09:49,920
+capital x في dv على dx capital زائد v تربيع زائد
+
+95
+00:09:49,920 --> 00:09:54,880
+xv في dv على dx
+
+96
+00:09:59,570 --> 00:10:05,670
+يبقى المعادلة هذه لو أضفت للطرفين سالف V بيبقى
+
+97
+00:10:05,670 --> 00:10:11,300
+بتروح هذه مع بعضهالو جيت على ال term هذا و ال term
+
+98
+00:10:11,300 --> 00:10:16,580
+هذا في بينهم عوامل مشتركة و ال V تربيع بدي اوديه
+
+99
+00:10:16,580 --> 00:10:22,840
+على شكل تاني بيصير ايه؟ سالب V تربيع اذا المعادلة
+
+100
+00:10:22,840 --> 00:10:29,680
+هذه بيصير على الشكل التالي هذه X وهذا واحد زائد V
+
+101
+00:10:29,680 --> 00:10:40,250
+وهذا DV على D X بدي ساوي سالبيبقى V تربيع يبقى
+
+102
+00:10:40,250 --> 00:10:46,190
+سالب V تربيع واضح أظن هذي و هذي أخدت X في دي V على
+
+103
+00:10:46,190 --> 00:10:51,270
+دي X عام المشترك هاي X وهي دي V على دي X بظل من
+
+104
+00:10:51,270 --> 00:10:57,050
+الأولى واحد صحيح و بظل من التانية قداش V أظن بقدر
+
+105
+00:10:57,050 --> 00:11:03,730
+أفصل المتغيرات الآن يبقى لو جينا فاصلنا المتغيرات
+
+106
+00:11:04,050 --> 00:11:11,210
+بصير على الشكل التالي واحد زائد V على V تربية DV
+
+107
+00:11:11,210 --> 00:11:21,690
+يساوي ناقص D X على X او ان شئتم فقولوا واحد على V
+
+108
+00:11:21,690 --> 00:11:31,950
+تربية زائد واحد على V في الـ DV يساوي D X على X
+
+109
+00:11:31,950 --> 00:11:39,670
+الشكل اللي عملناهاطيب Legion كامل يبقى سالب واحد
+
+110
+00:11:39,670 --> 00:11:49,670
+على V زائد Lin absolute value لل V يساوي الناقص ل
+
+111
+00:11:49,670 --> 00:11:56,250
+Lin absolute value ل X زائد Constant وليكن ال
+
+112
+00:11:56,250 --> 00:12:02,270
+constant ده C1طب يا جماعة و كده بنات بدي أجيب ال V
+
+113
+00:12:02,270 --> 00:12:07,030
+على الشجر تاني و أجيب ال Ln على الشجر هذي يبقى إيش
+
+114
+00:12:07,030 --> 00:12:13,350
+بصير عندها بصير Ln absolute value ل V زائد Ln
+
+115
+00:12:13,350 --> 00:12:21,550
+absolute value ل X بدي يساوي واحد على V زائد C1
+
+116
+00:12:21,550 --> 00:12:32,270
+طيب هذا الآناللي هو كلها يبقى لن VX يبقى هذه بدها
+
+117
+00:12:32,270 --> 00:12:40,190
+تقيمها لن absolute value لV X بالشكل اللي عندنا
+
+118
+00:12:40,190 --> 00:12:49,210
+هذا يساوي اللي هو واحد على V زائد كل ثانوية من C1
+
+119
+00:12:49,210 --> 00:12:56,410
+تضيف قداش جايلي عليها يعني هذهيبقى هذه y علي x
+
+120
+00:12:56,410 --> 00:13:06,150
+وكانها x علي y مظبوط طيب يبقى هذه كأنها تساوية x
+
+121
+00:13:06,150 --> 00:13:14,490
+علي y زائد constant c1 طيب بتارفع اتنين كأس للعدد
+
+122
+00:13:14,490 --> 00:13:20,370
+e يبقى لو رفعنا كله كأس للعدد e بس قبل اللي ترفع
+
+123
+00:13:20,730 --> 00:13:27,290
+الـ X في الـ V هذه عبارة عن مين؟ Y كابتن إذاً هذه
+
+124
+00:13:27,290 --> 00:13:35,410
+بتصير mean لان اللي هو Y كابتن بده يساوي اللي هو X
+
+125
+00:13:35,410 --> 00:13:44,930
+على Y زارت كله سنة C1 طبعاً؟ طيب لو رفعت كله كوسل
+
+126
+00:13:44,930 --> 00:13:49,920
+العدد أوشيلت ال X و ال Y و حطيت قيمة كل واحد
+
+127
+00:13:49,920 --> 00:13:55,280
+بدلالة X small و Y small يبقى لو شيلتهم بصير
+
+128
+00:13:55,280 --> 00:14:01,780
+الجواب لل absolute value لو جيت لل Y capital ال Y
+
+129
+00:14:01,780 --> 00:14:09,480
+capital هو Y small زائد اتنين يبقى Y small زائد
+
+130
+00:14:09,480 --> 00:14:17,690
+اتنين يساوي X capital ل X minus oneيبقى x small
+
+131
+00:14:17,690 --> 00:14:25,830
+minus one على y plus two زائد constant c one طبعا
+
+132
+00:14:25,830 --> 00:14:30,910
+هذا الحل حل ضمني بقدرش اطلع ال y في الشجة و الباقي
+
+133
+00:14:30,910 --> 00:14:36,570
+في شجة تانية يبقى بخل الجراب كما هو بهذا الشكل و
+
+134
+00:14:36,570 --> 00:14:42,650
+بقول اعطيك العافية تمام ميرة ميرة ميرة تماميعني
+
+135
+00:14:42,650 --> 00:14:46,610
+بعد ما أجيب الحل بدلالة x capital و y capital
+
+136
+00:14:46,610 --> 00:14:51,810
+برجعه إلى أصله بدلالة x small و y small اللي هو
+
+137
+00:14:51,810 --> 00:15:03,510
+بداية مين بداية المثلة نعطي مثال أخر example بقول
+
+138
+00:15:03,510 --> 00:15:10,150
+use the substitution use the substitution
+
+139
+00:15:11,810 --> 00:15:21,990
+استخدم التعويضة y تساوي v x تربيع to solve the
+
+140
+00:15:21,990 --> 00:15:30,890
+differential equation x
+
+141
+00:15:30,890 --> 00:15:43,030
+تربيع زائد y كله في dy by dxبتساوي نقص اتنين X Y و
+
+142
+00:15:43,030 --> 00:15:46,930
+هذي بتسميها المعاني الأصلي اللي يمين في ال start
+
+143
+00:15:46,930 --> 00:15:54,250
+اذا انا بدي اتقيت بالتعويض اللي اعطاه هالي و ليست
+
+144
+00:15:54,250 --> 00:15:58,430
+لا بال homogenous ولا غيره اللي احنا كنا بنحلبها
+
+145
+00:15:58,430 --> 00:16:03,380
+قبليبقى كانوا يقولوا التعويضة هذه ههه بتحل المسألة
+
+146
+00:16:03,380 --> 00:16:07,320
+اللي عندك بقول له تمام اذا انا بتروح استخدم هذه
+
+147
+00:16:07,320 --> 00:16:13,580
+التعويضة في حل المثل بقول له solution التعويضة
+
+148
+00:16:13,580 --> 00:16:19,340
+اللي يعطيها ليه جالي حط ال Y في ساوي VX ترابيعي
+
+149
+00:16:19,340 --> 00:16:25,200
+بدي اشتق بالنسبة الى X عشان احصل على شكل DY على DX
+
+150
+00:16:25,870 --> 00:16:32,010
+إذا لو جيتش تقية إيمانات بالي بقول dy على dx يسوي
+
+151
+00:16:32,010 --> 00:16:37,290
+مشتقة حاصل ضرب دالتين الأولى في مشتقة التانية
+
+152
+00:16:37,290 --> 00:16:47,690
+التانية مشتقتها ب2x يبقى 2xv زائد x تربيع في dv
+
+153
+00:16:47,690 --> 00:16:53,130
+على dxهذه قيمة من قيمة مشتقة الـ Y بالنسبة للـ X
+
+154
+00:16:53,130 --> 00:16:58,990
+ناخد المعلومات اللي حصلنا عليها هذه و نرجع نعوض في
+
+155
+00:16:58,990 --> 00:17:04,950
+المعادلة من الـ Star يبقى الآن بالنسبة للمعادلة ال
+
+156
+00:17:04,950 --> 00:17:11,390
+Star اللي عندنا يبقى X تربيع كما هي ال Y قال حط
+
+157
+00:17:11,390 --> 00:17:19,290
+بدالها VX تربيع حطينا بدالها VX تربيعالـ dy على dx
+
+158
+00:17:19,290 --> 00:17:28,490
+ليه 2xv زائد x تربيع في الـdv على dx كله بده يساوي
+
+159
+00:17:28,490 --> 00:17:37,670
+نقص 2x في الـy ليه v x تربيع بدأت أفكر المعادلة
+
+160
+00:17:37,670 --> 00:17:43,290
+اللي عنها ليه و أبدأ أجمع طيب
+
+161
+00:17:43,930 --> 00:17:49,590
+بنفك المعادلة عنها يبقى لو فكلها بصير اتنين x
+
+162
+00:17:49,590 --> 00:17:54,050
+تكييف v بدي اضرب x تربيع في ال two terms اللي
+
+163
+00:17:54,050 --> 00:18:02,090
+عندنا يبقى اتنين x تكييف في ال v زائد x أُص أربعة
+
+164
+00:18:02,090 --> 00:18:08,380
+في ال dv على ال x بعدين بدي اضرب هذهيبقى هدف
+
+165
+00:18:08,380 --> 00:18:15,940
+تعطينا زائد اتنين X تكييب V تربيع حصل ضرب الاتنين
+
+166
+00:18:15,940 --> 00:18:24,120
+هدول ببعض زائد اللي هو هنا مافيش الا V في X أس
+
+167
+00:18:24,120 --> 00:18:35,240
+أربعة في DV على DX يساوي نقص اتنين X تكييب V طيب
+
+168
+00:18:35,540 --> 00:18:41,760
+بالدالي لهذا ال term وهذا ال term فيهم x أُس 4
+
+169
+00:18:41,760 --> 00:18:49,400
+عامل مشترك وفيه dv على dx يبقى هذا x أُس 4 وهذا
+
+170
+00:18:49,400 --> 00:18:58,770
+واحد زائد v في dv على dx مرة تانيةلتحتيم الخط X أس
+
+171
+00:18:58,770 --> 00:19:04,130
+4 في DV على DX عامة مشترك بيبقى الواحد زائد V هاي
+
+172
+00:19:04,130 --> 00:19:08,670
+الواحد زائد V وهي ال DV على DX وهي ال X أس 4
+
+173
+00:19:08,670 --> 00:19:15,050
+الباقية هرحله جهتي اليمين يبقى هذا بده ساعة طلعيلي
+
+174
+00:19:15,050 --> 00:19:20,810
+في ال term اللي عندك هذا وهذا يبقى بيصير ناقص
+
+175
+00:19:20,810 --> 00:19:29,920
+أربعة X كعيب Vيبقى هذا ناقص اللي هو اربعة اكس
+
+176
+00:19:29,920 --> 00:19:36,480
+تكييب في ال V يبقى ناقص اربعة اكس تكييب في ال V
+
+177
+00:19:36,480 --> 00:19:40,880
+فلحظنا من هنا يبقى لنا ناقص اتنين اكس تكييب V
+
+178
+00:19:40,880 --> 00:19:49,580
+تربيع ناقص اتنين اكس تكييب V تربيع اول شئتم فقولوا
+
+179
+00:19:49,580 --> 00:19:57,410
+هاي الناقصو هنا هذا اتنين و بيظل عندنا مين بيظل
+
+180
+00:19:57,410 --> 00:20:04,150
+عندنا كمان x تكيب و بيظل عندنا v و هنا واحد زائد v
+
+181
+00:20:04,150 --> 00:20:11,250
+هصبط هيك هي ناقص برا و اتنين اه بيظل عندنا لا لا
+
+182
+00:20:11,250 --> 00:20:17,250
+لا استني شوية هي ناقص اتنين x تكيب v بيظل عندنا
+
+183
+00:20:17,250 --> 00:20:23,520
+هذه اتنين و ليست واحد بس هذه اتنينمظبوط؟ يبقى عادي
+
+184
+00:20:23,520 --> 00:20:29,360
+تماما طيب اننا نحاول نفسر المتغيرات بدي أخلي ال V
+
+185
+00:20:29,360 --> 00:20:35,440
+في شجة و ال X في شجة واحدة يبقى عادي يا ستة بصير
+
+186
+00:20:35,440 --> 00:20:46,240
+واحد زائد V على اتنين V زائد V تربيع كله في ال DV
+
+187
+00:20:46,240 --> 00:20:55,300
+بده يساوينقص اتنين x تكيب على x أس أربع في dx
+
+188
+00:20:55,300 --> 00:21:07,420
+واضحة اظن ؟ طيب هل ال bus تفاضل المقام بس
+
+189
+00:21:07,420 --> 00:21:10,880
+بده اتنين يبقى بدأ اضرف اتنين و اكسب مع اتنين مش
+
+190
+00:21:10,880 --> 00:21:19,080
+هنقدر اكملإذا هذه هي اتنين
+
+191
+00:21:19,080 --> 00:21:27,920
+زائد اتنين V عالى اتنين V زائد V ترابيع كله في DV
+
+192
+00:21:27,920 --> 00:21:36,640
+بده يساوي نقص اتنين على X كله بالنسبة الى DX X
+
+193
+00:21:36,640 --> 00:21:42,830
+تقيم X الصاربع بيبقى ال main X الكامليبقى هذا نص
+
+194
+00:21:42,830 --> 00:21:51,430
+لين absolute value لل V تربية زائد اتنين V بده
+
+195
+00:21:51,430 --> 00:21:57,950
+يساوي ناقص اتنين لين absolute value ل X زائد
+
+196
+00:21:57,950 --> 00:22:03,600
+constant C1بنقدر نتخلص من النص هذا و نضرب كله فى
+
+197
+00:22:03,600 --> 00:22:09,160
+قداش فى اتنين فلو ضربنا فى اتنين بيصير لن absolute
+
+198
+00:22:09,160 --> 00:22:16,740
+value ل V تربية زائد اتنين V يساوي ناقص اربعة ل
+
+199
+00:22:16,740 --> 00:22:24,200
+absolute value ل X زائد constant C1 شو رايك بدي
+
+200
+00:22:24,200 --> 00:22:29,670
+اجيب اللي نات عن بعض و اخلي ال constant لحالهكيف؟
+
+201
+00:22:29,670 --> 00:22:36,790
+مش شامل اتنين she won لإنه ضربنا في اتنين مظبوط
+
+202
+00:22:36,790 --> 00:22:42,330
+أصابة امرأة وقفت عامة تمام ضربنا الطرف اليمين كله
+
+203
+00:22:42,330 --> 00:22:48,150
+في مين؟ في الاتنين يبقى لو جيت قلت لن V تربيع
+
+204
+00:22:48,150 --> 00:22:56,130
+زائدي اتنين Vزائد أربعة لل absolute value ل X
+
+205
+00:22:56,130 --> 00:23:02,730
+بتساوي اتنين C1طيب هذه الأربعة لو جيت هنا إيش
+
+206
+00:23:02,730 --> 00:23:10,570
+بصير؟ X أُص أربعة طب و لن زائد لن لن حاصل الضرب
+
+207
+00:23:10,570 --> 00:23:18,150
+يبقى هذه بصير لن X أُص أربعة و هذا ال absolute
+
+208
+00:23:18,150 --> 00:23:25,290
+value فاهمين؟ في ال V تربيع زائد X أُص أربعة في
+
+209
+00:23:25,290 --> 00:23:35,110
+اتنين Vبدو يساوي 2C1 طيب رجعي شوية ال VX تربيع
+
+210
+00:23:35,110 --> 00:23:42,610
+بقداش يا بنات إذا هشيل كل VX تربيع و أحط بدالة Y
+
+211
+00:23:42,610 --> 00:23:50,210
+يبقى هذي VX تربيع هذي بقداش؟ بY تربيع تمام يبقى
+
+212
+00:23:50,210 --> 00:23:57,810
+هذي لان absolute value ل Y تربيعو هذه الزائد اتنين
+
+213
+00:23:57,810 --> 00:24:06,290
+وهذه اكس تربيع بظل في اكس تربي عليهمين ابو Y يبقى
+
+214
+00:24:06,290 --> 00:24:12,850
+هذه ال Y يساوي اتنين C1 ايه ايش رايك اتخلص من ال N
+
+215
+00:24:14,560 --> 00:24:21,260
+برفع اتنين كاصل العدد E يبقى بيصير absolute value
+
+216
+00:24:21,260 --> 00:24:29,380
+لل Y تربية زائد اتنين X تربية Y يسوى E أس اتنين C1
+
+217
+00:24:29,380 --> 00:24:35,200
+طب الاكس بولانش العمرها بتاخد قيمة سالبة إذا ال
+
+218
+00:24:35,200 --> 00:24:41,480
+absolute هذا لا معناه لهيبقى هذا معناه ان y تربية
+
+219
+00:24:41,480 --> 00:24:50,000
+زائدي اتنين x تربية y بده يساوي c و c يساوي e اقصى
+
+220
+00:24:50,000 --> 00:24:57,460
+اتنين c one بده احطه ب c طيب بده اجيب من المعادلة
+
+221
+00:24:57,460 --> 00:25:01,640
+هذه y قداش تساوي؟
+
+222
+00:25:01,640 --> 00:25:08,890
+ليش؟ أليست معادلة من الدرجة الثانية في y؟إذا
+
+223
+00:25:08,890 --> 00:25:12,930
+بتتحلل بحلل .. لا بتتحللش بحلها بالقانون وبالتالي
+
+224
+00:25:12,930 --> 00:25:17,170
+بقدر أجيب y as a function of x وهو ال general
+
+225
+00:25:17,170 --> 00:25:21,910
+solution لل differential equation يعني بقدر أكتب y
+
+226
+00:25:21,910 --> 00:25:28,750
+تربية زيدي اتنين x تربية y ناقص c يساوي zero
+
+227
+00:25:28,750 --> 00:25:38,050
+مظبوط؟ بدنا نحلها بالقانونيبقى Y يساوي ناقص با
+
+228
+00:25:38,050 --> 00:25:44,270
+يعني ناقص اتنين X تربية زائد او ناقص الجدري
+
+229
+00:25:44,270 --> 00:25:51,230
+التربية يلي با تربية يليه اربعة X أس اربعة ناقص
+
+230
+00:25:51,230 --> 00:25:59,190
+اربعة الف اللي هو بواحد جيم اللي هو قداش بناقص C
+
+231
+00:25:59,190 --> 00:26:09,310
+يبقى في ناقص Cكل هذا الكلام على اتنين في واحد طيب
+
+232
+00:26:09,310 --> 00:26:14,610
+هذا الكلام بدي اعطيكي ان why you sowy اظن اربعة مع
+
+233
+00:26:14,610 --> 00:26:19,510
+اربعة تطلع برا باتنين و اتنين تطلع برا تروح مع مين
+
+234
+00:26:19,510 --> 00:26:26,550
+مع اتنين اللي تحت يبقى الجواب ناقص x تربيع زائد او
+
+235
+00:26:26,550 --> 00:26:36,320
+ناقص الجدر تربيعي لx أربعة زائد cيبقى ده شكل الحل
+
+236
+00:26:36,320 --> 00:26:42,220
+مين للمعادلة التفاضلية اللي علناها حد فيكم بتحب
+
+237
+00:26:42,220 --> 00:26:49,920
+تسأل أي سؤال هنا؟ خلاص؟ طيب لحد هنا انتهى هذا ال
+
+238
+00:26:49,920 --> 00:26:56,640
+section لم يبقى إلا أن نعطيكم أرقام المسائل
+
+239
+00:26:56,640 --> 00:26:59,520
+المطلوب تمرنوا إيديكم فيها
+
+240
+00:27:11,610 --> 00:27:16,410
+يبقى exercises واحد
+
+241
+00:27:16,410 --> 00:27:25,770
+تلاتة المسائل التالية تلاتة، خمسة، ستة، عشرة،
+
+242
+00:27:25,770 --> 00:27:34,350
+احداشر، تلتاشر، اربعتاشر، تسعتاشر، واحد وعشرين
+
+243
+00:27:42,890 --> 00:27:50,650
+بنجي الأن ل section واحد أربعة اللي هو ال exact
+
+244
+00:27:50,650 --> 00:27:54,170
+equations
+
+245
+00:27:54,170 --> 00:28:02,570
+المعادلة التامة نديلها تعريف definition the first
+
+246
+00:28:02,570 --> 00:28:05,650
+order
+
+247
+00:28:05,650 --> 00:28:08,870
+differential
+
+248
+00:28:08,870 --> 00:28:11,490
+equation
+
+249
+00:28:13,490 --> 00:28:22,150
+الـ M as a function of X وY زائد الـ N as a
+
+250
+00:28:22,150 --> 00:28:30,310
+function of X وY الـ GY على DX يساوي زيرو وهادي
+
+251
+00:28:30,310 --> 00:28:38,270
+بدي أسميها المعادلة star is called exact
+
+252
+00:28:38,270 --> 00:28:50,430
+معادلة تمةif there exists a function إذا قدرت
+
+253
+00:28:50,430 --> 00:29:01,190
+ألاقي دلّا فاي of x و y such that بحيث أنه such
+
+254
+00:29:01,190 --> 00:29:08,490
+that اللي هو partial فاي على partial x بدي سوى ال
+
+255
+00:29:08,490 --> 00:29:19,700
+M of x و yو Partial Phi على Partial Y يساوي N O X
+
+256
+00:29:19,700 --> 00:29:28,320
+Y. The solution of
+
+257
+00:29:28,320 --> 00:29:42,430
+the differential equation Star isفاي اكس واي يساوي
+
+258
+00:29:42,430 --> 00:29:53,250
+يكون مصطلح C اخر م الاختصار
+
+259
+00:29:53,250 --> 00:30:07,790
+الاختصار م اكس واي زائد م اكس واي dy على dx يساوي
+
+260
+00:30:09,150 --> 00:30:20,210
+is exact if and only if if and only if partial m
+
+261
+00:30:20,210 --> 00:30:26,450
+by partial y يسمي partial m by partial x
+
+262
+00:31:35,180 --> 00:31:40,220
+وحتى الآن احنا درسنا اول نوع من انواع المعادلات
+
+263
+00:31:40,220 --> 00:31:43,720
+اللي هو homogeneous differential equations افوا
+
+264
+00:31:43,720 --> 00:31:47,920
+نصي قلم ال equations و بعدين درسنا ال homogeneous
+
+265
+00:31:47,920 --> 00:31:51,780
+differential equations والان بنجي للنوع التالت
+
+266
+00:31:51,780 --> 00:31:58,140
+اللي هو exact equations يعني المعادلات التامة نعطي
+
+267
+00:31:58,140 --> 00:32:03,700
+تاريخ لها و نشوف ايش بيقول هذا التاريخبقول التعريف
+
+268
+00:32:03,700 --> 00:32:08,300
+the first order differential equation M of X Y زي
+
+269
+00:32:08,300 --> 00:32:13,500
+N of X Y دي Y على دي X بده يساوي زي 0 زي شكل
+
+270
+00:32:13,500 --> 00:32:18,990
+المثال قبل الأخيرمش كان عندنا معادلة في dy على dx
+
+271
+00:32:18,990 --> 00:32:23,190
+يستوى معادلة تانية في الطرف اللي منها زيها طبعا بس
+
+272
+00:32:23,190 --> 00:32:28,650
+خلها كل إياش في طرف واحد وخلاها معادلة صفرية يبقى
+
+273
+00:32:28,650 --> 00:32:31,690
+أنا عندي معادلة من الرتبة الأولى لإن ماعنديش إلا
+
+274
+00:32:31,690 --> 00:32:35,530
+المشتقة الأولى زي ما أنتوا شايفين يبقى هذه
+
+275
+00:32:35,530 --> 00:32:41,050
+المعادلة بالشكلة بقول عنها exactly كيف؟ إذا جدرت
+
+276
+00:32:41,050 --> 00:32:48,420
+ألاقي دالة phi of x و yبحيث أن مشتقة هذه الدالة
+
+277
+00:32:48,420 --> 00:32:54,440
+بالنسبة إلى x يسوى ال M ومشتقتها بالنسبة إلى y
+
+278
+00:32:54,440 --> 00:32:59,420
+يسوى main ال M ويجيبها partial phi على partial x
+
+279
+00:32:59,420 --> 00:33:04,340
+يسوى M of x وyand partial y على partial y يساوي من
+
+280
+00:33:04,340 --> 00:33:09,500
+n of x y لما اقول partial يعني الاشتقاق الجزء
+
+281
+00:33:09,500 --> 00:33:14,840
+الاشتقاق الجزء ليش لإن ال m و ال n ده لتاني في
+
+282
+00:33:14,840 --> 00:33:21,770
+متغيرين و ليس ده لفي متغيرين واحدلو كانت فيه متغير
+
+283
+00:33:21,770 --> 00:33:27,970
+واحد لقول نتفاضل عادي dy by dx تمام لكن لا نظرا او
+
+284
+00:33:27,970 --> 00:33:33,970
+d phi على dx او d phi على dy لكن نظرا لان phi ده
+
+285
+00:33:33,970 --> 00:33:39,170
+اللي فيه متغيرين فبروح باشتق اشتقاقا جزئيا كما
+
+286
+00:33:39,170 --> 00:33:44,780
+سنرى بعد قليل يبقى باجي بقولالدالة اللى عندنا هذه
+
+287
+00:33:44,780 --> 00:33:49,240
+او المعادلة اللى عندنا star هي exact معادلة تامة
+
+288
+00:33:49,240 --> 00:33:54,820
+إذا قدرتى لاجي دالة five of x y بحيث أن المشتقة
+
+289
+00:33:54,820 --> 00:34:01,160
+الجزئية لها بالنسبة إلى x يساوي m of x y والمشتقة
+
+290
+00:34:01,160 --> 00:34:07,920
+الجزئية لها بالنسبة إلى y يساوي n of x y طيب تمام
+
+291
+00:34:08,170 --> 00:34:11,350
+السؤال هو طب وانك ايه بدي الاقي هذه الدالة بدي
+
+292
+00:34:11,350 --> 00:34:15,750
+اقعد ادور هدى تظبط و هدى ماتظبطش اقعد نص ساعة و لا
+
+293
+00:34:15,750 --> 00:34:18,610
+ساعة و لا ساعتين و لا تلت ساعات ادور هذه الشغله
+
+294
+00:34:18,610 --> 00:34:22,670
+يعني متعبه جدا و يمكن نجرب طول اليوم و مانقدرش
+
+295
+00:34:22,670 --> 00:34:28,130
+نجيب هذه ال function طبعا راح بحث العلماء لغاية ما
+
+296
+00:34:28,130 --> 00:34:35,480
+توصلوا الى نظرية تسهل هذه العملية شو النظرية هذهأه
+
+297
+00:34:35,480 --> 00:34:40,460
+طبعاً قبل النظرية الحل تبع المعادلة الى four مدى
+
+298
+00:34:40,460 --> 00:34:45,380
+ومشتقة هذه لهنا يساوي هذه ومشتقة هذه تساوي هذه
+
+299
+00:34:45,380 --> 00:34:50,580
+وطرف اليمين يساوي zero زير ومشتقة ال constant إذا
+
+300
+00:34:50,580 --> 00:34:55,220
+هذه phi of x y لازم تساوي مقدار ثاني حتى يبقى
+
+301
+00:34:55,220 --> 00:35:00,090
+مشتقته تساوي مين تساوي zeroالان كيف تحكم على هذه
+
+302
+00:35:00,090 --> 00:35:04,850
+انها exact بدون ما اقعد ادور اوصل او ماوصلش فبقول
+
+303
+00:35:04,850 --> 00:35:08,690
+لأجزا differential equation هذه بقول عنها exact
+
+304
+00:35:08,690 --> 00:35:14,910
+اذا لقيت مشتقت هذا الكلام لو M بالنسبة الى Y سوى
+
+305
+00:35:14,910 --> 00:35:19,780
+مشتقت هذا بالنسبة لمنيعني ال M مش بده أشتقها
+
+306
+00:35:19,780 --> 00:35:25,280
+بالنسبة ل X بده أشتقها بالنسبة إلى Y و ال N بده
+
+307
+00:35:25,280 --> 00:35:30,580
+أشتقها كأن جلبت الوضع، طبعا يعني الدالة الأولى بده
+
+308
+00:35:30,580 --> 00:35:33,740
+أشتقها بالنسبة إلى Y و الدالة التانية بده أشتقها
+
+309
+00:35:33,740 --> 00:35:39,920
+بالنسبة ل Xإن حدثت تساوي بقول هذه المعادلة exact
+
+310
+00:35:39,920 --> 00:35:44,700
+مدام exact إذا لازم ألاقي function phi of x y
+
+311
+00:35:44,700 --> 00:35:49,980
+تساوي كونستانت هي عبارة عن حل مين لهذه المعادلة
+
+312
+00:35:49,980 --> 00:35:55,000
+نعطيكم الأن أكثر من مثال على كيفية إيجاد هذه
+
+313
+00:35:55,000 --> 00:36:01,160
+الدالة وكيفية الحكم على إنها exact أو ماهياش exact
+
+314
+00:36:01,160 --> 00:36:04,440
+نبدأ بأول مثال هو example one
+
+315
+00:36:10,260 --> 00:36:13,240
+Example 1 بيقول سؤال الـ differential equation
+
+316
+00:36:13,240 --> 00:36:21,400
+سؤال الـ differential equation حل المعادلة تفاضرية
+
+317
+00:36:21,400 --> 00:36:31,260
+x في e to the power x في y في ال y prime زائد y في
+
+318
+00:36:31,260 --> 00:36:38,340
+e to the power xy ناقص أربعة x تكييب يساوي مين؟
+
+319
+00:36:38,340 --> 00:36:38,960
+يساوي
+
+320
+00:36:46,740 --> 00:36:52,600
+أول خطوة يا عزيزي هي ارتب مسئلتي لتكون في الشكل
+
+321
+00:36:52,600 --> 00:36:58,340
+الـ star اللي فوق حتى أبدأ أشتغل شغل الطبيعي فبجي
+
+322
+00:36:58,340 --> 00:37:02,660
+بقول هنا y' بدأت الأول يجب أن أدخل هذه في الأول
+
+323
+00:37:02,660 --> 00:37:06,920
+وهذه في الآخر الجماعة لديها مشكلة إذا لو أعد
+
+324
+00:37:06,920 --> 00:37:14,580
+ترتيبها يجب أن أقول y بيقص xy ناقص 4x تقريبا
+
+325
+00:37:17,250 --> 00:37:26,770
+زائد X في E أُس XY في Y' يساوي 0 هاي ال M في X و Y
+
+326
+00:37:26,770 --> 00:37:31,810
+بجهة دي تشكل مين ال M زي ما انت شايفها دالة في X و
+
+327
+00:37:31,810 --> 00:37:38,890
+Y وهذه تشكل ال N لأنها كذلك دالة في X و Y إذن هذه
+
+328
+00:37:38,890 --> 00:37:46,600
+هي ال M تبعة الجزء النظري وهذه هي ال Nتبعت الجزء
+
+329
+00:37:46,600 --> 00:37:52,300
+النظري طب بدي احكم عليها exact و الله ماهياش exact
+
+330
+00:37:52,300 --> 00:37:58,660
+يبقى بدي اروح ادي ااخد تفاضل ال M بالنسبة ل X يبقى
+
+331
+00:37:58,660 --> 00:38:05,620
+بدي ااخد partial M by partial Y يزاوى اللي هو ال
+
+332
+00:38:05,620 --> 00:38:10,910
+term اللي عندنا هذايعني بدي أشتق هذا الجزء بالنسبة
+
+333
+00:38:10,910 --> 00:38:17,330
+ل why نظرا لإنه عندي أكثر من متغير فالمتغير اللي
+
+334
+00:38:17,330 --> 00:38:20,710
+بشتق بالنسبة له باعتبره هو المتغير و باقي
+
+335
+00:38:20,710 --> 00:38:26,050
+المتغيرات ثوابت زي واحد و اتنين و عشر و نص و تلت
+
+336
+00:38:26,050 --> 00:38:30,230
+تربع و اللي بدكي يعنييبقى أي متغير آخر باعتبره
+
+337
+00:38:30,230 --> 00:38:36,170
+مقدار ثابت وهذا معنى الاشتقاق الجزئي كما درسناه في
+
+338
+00:38:36,170 --> 00:38:40,670
+calculus C لكن لمّا ما درسوش calculus C أنا بذكرهم
+
+339
+00:38:40,670 --> 00:38:45,150
+لن يقابلنا حاجة نفيدنا من calculus C إلا هذا ال
+
+340
+00:38:45,150 --> 00:38:50,670
+section فقط لا غير و هتلاقي الشغلات بسيطة جدا كما
+
+341
+00:38:50,670 --> 00:38:55,410
+ستراهم يبقى أنا بضروح أشتق هذا بالنسبة لمين يا
+
+342
+00:38:55,410 --> 00:39:00,000
+بناتنسبة ل Y يبقى مشتقة هذا المقدار كله بيبقى داش
+
+343
+00:39:00,000 --> 00:39:05,160
+Zero مع السلامة لإن مافيش في Y في X تقعيه مشتقة
+
+344
+00:39:05,160 --> 00:39:09,420
+منه يبقى في Zero يبقى باجي لهذا ال term هذي Y و
+
+345
+00:39:09,420 --> 00:39:13,960
+هذي E و ال 6Y تنتين فيهم Y يبقى هذا المشتقة حاصل
+
+346
+00:39:13,960 --> 00:39:19,340
+ضرب دالتين يبقى بدي أشتق الأولى بالنسبة ليه؟ لو
+
+347
+00:39:19,340 --> 00:39:26,670
+يبقى داش بواحد في E و ال 6Y يبقى E و ال 6Yزائد Y
+
+348
+00:39:26,670 --> 00:39:30,770
+بالـ Exponential
+
+349
+00:39:30,770 --> 00:39:39,090
+زي ما هي ضرب مشتقة الأس بالنسبة إلى Y يبقى كإن هذه
+
+350
+00:39:39,090 --> 00:39:44,430
+تلاتة Y بداش تقها بالنسبة إلى Y إذا تلاتة يبقى داش
+
+351
+00:39:44,430 --> 00:39:57,760
+يبقى X إذا هذه النتيجة هي E×XYزائد XY إيقص XY طيب
+
+352
+00:39:57,760 --> 00:40:05,000
+بدنا ناخد تفاضل ال N بالنسبة ال X وين ال N هي ال N
+
+353
+00:40:05,000 --> 00:40:11,100
+يبقى هذه فيها X وهذه فيها X إذا مشتقت حاصل ضرب
+
+354
+00:40:11,100 --> 00:40:16,800
+دلتين لما اشتق الأولى بالنسبة ل X روحك وضلي تانية
+
+355
+00:40:16,800 --> 00:40:24,910
+يبقى إيقص XY زائدالـ X زي ما هي ومشتقة الـ X
+
+356
+00:40:24,910 --> 00:40:28,910
+exponential بالـ X exponential itself في مشتقة
+
+357
+00:40:28,910 --> 00:40:36,510
+الأس بالنسبة إلى X اللي هو قداش Y فقط لا غير لأن
+
+358
+00:40:36,510 --> 00:40:42,370
+الـ Y هنا يعتبر مقدارا ثابتا يبقى هذا الكلام بده
+
+359
+00:40:42,370 --> 00:40:50,680
+يساوي E أس XY زائد XY E أس XYماذا تلاحظ على
+
+360
+00:40:50,680 --> 00:40:58,640
+المشتقتين؟ زي بعض يبقى هذا بده يعطينا ان تفاضل ال
+
+361
+00:40:58,640 --> 00:41:04,760
+M بالنسبة إلى Y يسوى partial N by partial X هذا
+
+362
+00:41:04,760 --> 00:41:10,780
+ايش بده يعطينا؟ هذا بده يعطينا ما يأتي يبقى هذا يا
+
+363
+00:41:10,780 --> 00:41:16,620
+مناد اللي بده اسميها المعادلة Star يبقى هذا بده
+
+364
+00:41:16,620 --> 00:41:17,620
+يعطينا
+
+365
+00:41:19,870 --> 00:41:27,910
+differential equation a star is exact مدام exact
+
+366
+00:41:27,910 --> 00:41:33,590
+يبقى there exist هاد ال a المقلوبة there exist a
+
+367
+00:41:33,590 --> 00:41:43,110
+function phi of x y يساوي constant وليكن c1 such
+
+368
+00:41:43,110 --> 00:41:46,490
+that بحيث ان
+
+369
+00:41:57,320 --> 00:42:06,460
+Y في E أس X Y ناقص
+
+370
+00:42:06,460 --> 00:42:13,570
+أربع X تكريمو partial phi على partial y بدي يسوى
+
+371
+00:42:13,570 --> 00:42:19,930
+من ال n كل ال n عندي x في e أُس xy يبقى x في e أُس
+
+372
+00:42:19,930 --> 00:42:26,730
+xy طب أنا بدي أعرف شكل ال phi عشان أعرف شكل ال phi
+
+373
+00:42:26,730 --> 00:42:30,430
+أيوة هذه؟
+
+374
+00:42:30,430 --> 00:42:37,710
+وين هذه؟ هاي شايفاها؟ مش تقتحاص الضرب ده اللي تاني
+
+375
+00:42:38,210 --> 00:42:45,770
+مشتقة الأولى كده؟ في التانية هي زائد الأولى هي
+
+376
+00:42:45,770 --> 00:42:50,890
+مشتقة ال exponential بال exponential زي ما هي ضرب
+
+377
+00:42:50,890 --> 00:42:57,230
+مشتقة الأس بالنسبة إلى X مشتقة بالنسبة إلى X يعني
+
+378
+00:42:57,230 --> 00:43:02,570
+Y اللي هي الكلسة يبقى هي ال Y واضحة؟ حد بتسأل أي
+
+379
+00:43:02,570 --> 00:43:12,130
+تساؤل ثاني؟ كده كده كده كدههي وين
+
+380
+00:43:12,130 --> 00:43:16,310
+يقول why prime تعالي ياريح تيجي هنا نشوف تعالي مش
+
+381
+00:43:16,310 --> 00:43:22,370
+فاش فيها حاجة تعالي نشوف بس إيش سؤالك بالضبط فضلي
+
+382
+00:43:22,370 --> 00:43:26,270
+لا
+
+383
+00:43:29,970 --> 00:43:34,790
+انت شايفه ايش مايقولك هذا ال course M و هذا N شايف
+
+384
+00:43:34,790 --> 00:43:40,330
+المثل هذا M و هذا N و المشتقة زي ما هي وصلها يعني
+
+385
+00:43:40,330 --> 00:43:46,070
+أنا بشتر على M و N بس يا بنات في حد بتسأل أي سؤال
+
+386
+00:43:46,070 --> 00:43:54,540
+تاني كمان؟ طيب نيجي .. نيجي مرة ثانيةيبقى انا حصلت
+
+387
+00:43:54,540 --> 00:43:58,480
+على تفاضل ال file اللي أنا بدياه اللي قاعد بدور
+
+388
+00:43:58,480 --> 00:44:04,740
+عليها هي شو شكلها الله أعلم قاعد بدور عليها بمجيب
+
+389
+00:44:04,740 --> 00:44:09,500
+مشتقتها بالنسبة ل X و بديم مشتقتها بالنسبة إلى Y
+
+390
+00:44:09,500 --> 00:44:16,920
+يبقى لو كملت الأولى بالنسبة ل X بحصل على Fi أو لو
+
+391
+00:44:16,920 --> 00:44:21,620
+كملت التانية بالنسبة إلى Y بحصل على Fi طب كامل مين
+
+392
+00:44:21,620 --> 00:44:27,280
+منهم؟باجي باططلع في شكل اللي أسهل روحي كاملي و
+
+393
+00:44:27,280 --> 00:44:32,220
+اصلا بلاش منه و اذا التنتين سهلاتي بأي واحدة بكمل
+
+394
+00:44:32,220 --> 00:44:37,080
+لو بكون حصل على النتيجة باجي باططلع لو بده كامل
+
+395
+00:44:37,080 --> 00:44:47,910
+هذه بالنسبة ل X Y مقدار ثابتوY مقدر ثابت يبقى
+
+396
+00:44:47,910 --> 00:44:52,210
+4X و 4 على 4 يعني سهل جدا
+
+397
+00:45:03,250 --> 00:45:07,010
+يبقى التنتين سواء كانت هذه والله هذه بدي أكملهم
+
+398
+00:45:07,010 --> 00:45:11,690
+اتنين صح تمام يبقى لو جيت كاملت الأولى يا بنات
+
+399
+00:45:11,690 --> 00:45:18,110
+يبقى لو كاملت الأولى بصير عندنا five of x و y يوسف
+
+400
+00:45:18,110 --> 00:45:21,930
+بدي أكملها بالاسم ال x ال y مقدار ثابت وال
+
+401
+00:45:21,930 --> 00:45:28,410
+exponential كما هي مقسومة على تفاضل الأسد وقدر y
+
+402
+00:45:29,390 --> 00:45:34,270
+يبقى انا بدي اكمل بالنسبة ل X ناقص أربعة X أص
+
+403
+00:45:34,270 --> 00:45:39,290
+أربعة على أربعة زائد مقدار ثابت المقدار الثابت
+
+404
+00:45:39,290 --> 00:45:44,550
+باعتبره function في المتغير الثاني لأن المتغير
+
+405
+00:45:44,550 --> 00:45:48,870
+الثاني بالنسبة ليه يعتبر مقدارا ثابتا يبقى بروح
+
+406
+00:45:48,870 --> 00:45:55,740
+بقوله زائد F of YF of Y كله يعتبر مقدار ثابت
+
+407
+00:45:55,740 --> 00:46:00,820
+بالنسبة لمن؟ بالنسبة ال X يعني يا بنات هذه بيصير E
+
+408
+00:46:00,820 --> 00:46:10,890
+of 6Y ناقص X أس أربعة زائد F of Yهذا مين فاي of x
+
+409
+00:46:10,890 --> 00:46:16,570
+و y الحين مشكلتي بس بدي اعرف قداش f of y مشان اعرف
+
+410
+00:46:16,570 --> 00:46:23,470
+f of y بدي اروح اكاملها افاضلها بالنسبة الى y يبقى
+
+411
+00:46:23,470 --> 00:46:30,930
+partial phi على partial y هذي قداش مستقتها بالنسبة
+
+412
+00:46:30,930 --> 00:46:43,340
+الى y يبقى x في i أس x yناقص هذه zero زاد f prime
+
+413
+00:46:43,340 --> 00:46:51,000
+of y مش هي partial phi علي partial y فوق عندي و هي
+
+414
+00:46:51,000 --> 00:46:58,050
+انا اشتقتها هنايبقى المقدارين هدول بدهم يساووا بعض
+
+415
+00:46:58,050 --> 00:47:04,990
+يبقى لما أساويهم بعض بصير x e أس x y زائد f prime
+
+416
+00:47:04,990 --> 00:47:11,290
+of y بده يساوي x في u أس x y هذا معناته أن f prime
+
+417
+00:47:11,290 --> 00:47:18,610
+of y بده يساوي كده؟ Zeroيبقى هذا معناه ان f of y
+
+418
+00:47:18,610 --> 00:47:25,290
+يساوي مقدار ثابت ثاني يبقى بروح بقوله the solution
+
+419
+00:47:25,290 --> 00:47:35,010
+is phi of x y بده يساوي وين phi of x y هي اللي
+
+420
+00:47:35,010 --> 00:47:36,410
+طلعناها هي
+
+421
+00:47:52,430 --> 00:47:59,930
+يبقى بيصير أن فاي of x و y يسوى e أوس x y ناقص x
+
+422
+00:47:59,930 --> 00:48:00,870
+أوس أربعة
+
+423
+00:48:06,820 --> 00:48:14,720
+هذا هو حل المعادلة لا يزال لدينا مثال عن الـ exact
+
+424
+00:48:14,720 --> 00:48:19,380
+equation و بعد ذلك ال equation ممكن ماتطلعش exact
+
+425
+00:48:19,380 --> 00:48:24,740
+و تروح نحولها إلى exact زي ما قبل قليل كانتش
+
+426
+00:48:24,740 --> 00:48:28,960
+homogeneous و بنحولها إلى homogeneous و هكذا
+
+427
+00:48:28,960 --> 00:48:30,420
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/iuDuvfspJA8_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/iuDuvfspJA8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f34d6869f8d0fb4e7045a3079e2fe7c97350cc91
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/iuDuvfspJA8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2136, "start": 19.94, "end": 21.36, "text": "بسم الله الرحمن الرحيم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.05126953013241291, "compression_ratio": 1.0789473684210527, "no_speech_prob": 0.0, "words": [{"start": 19.94, "end": 20.22, "word": "بسم", "probability": 0.8896484375}, {"start": 20.22, "end": 20.46, "word": " الله", "probability": 0.98095703125}, {"start": 20.46, "end": 20.86, "word": " الرحمن", "probability": 0.9365234375}, {"start": 20.86, "end": 21.36, "word": " الرحيم", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 2, "seek": 5043, "start": 23.07, "end": 50.43, "text": "هذه المحاضرة نفضل ان تكون محاضرة مناقشة بسبب الامتحان اللى عندنا اليوم الساعتين دون فقبل ان نبدأ المناقشة انا بحب ان نشير الى رقم القاعة اللى سيكون فيها الامتحان لان اللى كان نزلكه في الأول N411 تغيرت وقسمته الى قاعتين القاعة الأولى اللى هى ال N", "tokens": [3224, 24192, 9673, 5016, 46958, 25720, 8717, 5172, 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المطلوب الأول من المثلة بدنا نيجي لمن؟ للمطلوب التاني نمربي", "tokens": [51, 307, 257, 8213, 9887, 4032, 7649, 47395, 1829, 8315, 9154, 9673, 9566, 1211, 37746, 16247, 12610, 9154, 9673, 12984, 37977, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 27842, 22807, 5296, 19528, 9566, 1211, 37746, 16712, 7649, 1829, 8717, 29973, 21292], "avg_logprob": -0.24162945931866056, "compression_ratio": 1.322314049586777, "no_speech_prob": 0.0, "words": [{"start": 560.45, "end": 560.77, "word": "T", "probability": 0.5322265625}, {"start": 560.77, "end": 562.09, "word": " is", "probability": 0.1748046875}, {"start": 562.09, "end": 563.23, "word": " a", "probability": 0.7880859375}, {"start": 563.23, "end": 564.29, "word": " linear", "probability": 0.8193359375}, {"start": 564.29, "end": 565.73, "word": " transformation", "probability": 0.75244140625}, {"start": 565.73, "end": 566.61, "word": " وانتهينا", "probability": 0.92373046875}, {"start": 566.61, "end": 567.17, "word": " من", "probability": 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624.96, "end": 649.46, "text": "طيب إذا بدنا نروح نعطي تعريف الكيرن لو نبدأ نطبق هذا التعريف يبقى انا لو جيت هنا و قولت الكيرن التي هي كل المصحفات A اللي موجودة في ال M22 such that T of A بده يساوي من؟ بده يساوي Z صحيح ولا لا؟", "tokens": [9566, 1829, 3555, 11933, 15730, 47525, 8315, 8717, 32887, 5016, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 33251, 13546, 1863, 45164, 8717, 44510, 10721, 8717, 9566, 3555, 4587, 23758, 16712, 3615, 16572, 5172, 7251, 3555, 4587, 7578, 1975, 8315, 45164, 10874, 36081, 34105, 4032, 12174, 12610, 2655, 33251, 13546, 1863, 38392, 39896, 28242, 9673, 9381, 5016, 5172, 9307, 316, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 376, 7490, 1270, 300, 314, 295, 316, 47525, 3224, 7251, 3794, 995, 45865, 9154, 22807, 47525, 3224, 7251, 3794, 995, 45865, 1176, 20328, 5016, 1829, 5016, 49429, 20193, 22807], "avg_logprob": -0.23550258223543463, "compression_ratio": 1.64, "no_speech_prob": 0.0, "words": [{"start": 624.96, "end": 625.38, "word": "طيب", 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{"start": 657.47, "end": 658.37, "word": " A12,", "probability": 0.810546875}, {"start": 658.67, "end": 659.49, "word": " A21,", "probability": 0.916748046875}, {"start": 659.77, "end": 660.65, "word": " A22", "probability": 0.95458984375}, {"start": 660.65, "end": 661.67, "word": " اللي", "probability": 0.9267578125}, {"start": 661.67, "end": 662.39, "word": " موجودة", "probability": 0.9912109375}, {"start": 662.39, "end": 662.59, "word": " في", "probability": 0.904296875}, {"start": 662.59, "end": 662.79, "word": " ال", "probability": 0.8408203125}, {"start": 662.79, "end": 663.71, "word": " M22", "probability": 0.73388671875}, {"start": 663.71, "end": 664.05, "word": " و", "probability": 0.65771484375}, {"start": 664.05, "end": 664.33, "word": " such", "probability": 0.284912109375}, {"start": 664.33, "end": 664.81, "word": " that", "probability": 0.93798828125}, {"start": 664.81, "end": 665.51, "word": " ال", "probability": 0.64697265625}, {"start": 665.51, "end": 665.75, "word": " T", "probability": 0.81884765625}, {"start": 665.75, "end": 666.07, "word": " of", "probability": 0.85595703125}, {"start": 666.07, "end": 666.27, "word": " A", "probability": 0.94970703125}, {"start": 666.27, "end": 666.55, "word": " هي", "probability": 0.830078125}, {"start": 666.55, "end": 667.35, "word": " صورتها", "probability": 0.9893798828125}], "temperature": 1.0}, {"id": 33, "seek": 68906, "start": 667.64, "end": 689.06, "text": "يبقى باجي بقوله ال T of A هي عبارة عن A11-A22 00 A12-A21 كله بده يساوي 0 يعني مين ال 0؟ هي المصفوفة الصفرية اللي عندنا بهذا الشكل", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 2423, 314, 295, 316, 39896, 6225, 3555, 9640, 3660, 18871, 316, 5348, 12, 32, 7490, 7143, 316, 4762, 12, 32, 4436, 28242, 3224, 47525, 3224, 7251, 3794, 995, 45865, 1958, 37495, 22653, 3714, 9957, 2423, 1958, 22807, 39896, 9673, 9381, 5172, 38688, 3660, 31767, 5172, 2288, 10632, 13672, 1829, 43242, 8315, 39627, 15730, 25124, 28820], "avg_logprob": 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كذلك", "probability": 0.8621419270833334}, {"start": 721.53, "end": 721.83, "word": " ال", "probability": 0.96044921875}, {"start": 721.83, "end": 722.77, "word": " a12", "probability": 0.994873046875}, {"start": 722.77, "end": 723.43, "word": " بده", "probability": 0.96484375}, {"start": 723.43, "end": 723.91, "word": " يساوي", "probability": 0.8695068359375}, {"start": 723.91, "end": 724.17, "word": " ال", "probability": 0.98193359375}, {"start": 724.17, "end": 725.63, "word": " a21", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 36, "seek": 75624, "start": 727.34, "end": 756.24, "text": "كويس إذا بقدر أحط الآن شكل العناصر اللي عندي هذه العناصر اللي موجودة وين في ال kernel يبقى أصبح عندي ال kernel اللتي بدي يكون على الشكل التالي كل العناصر اللي على الشكل التالي a11 تسوى a22 يعني لو قلت هنا a و قلت هنا a", "tokens": [4117, 45865, 3794, 11933, 15730, 4724, 28543, 2288, 5551, 5016, 9566, 6024, 48506, 13412, 28820, 18863, 1863, 33546, 2288, 13672, 1829, 18871, 16254, 29538, 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754.16, "end": 754.86, "word": " و", "probability": 0.87841796875}, {"start": 754.86, "end": 755.36, "word": " قلت", "probability": 0.810791015625}, {"start": 755.36, "end": 755.84, "word": " هنا", "probability": 0.99072265625}, {"start": 755.84, "end": 756.24, "word": " a", "probability": 0.921875}], "temperature": 1.0}, {"id": 37, "seek": 77595, "start": 756.69, "end": 775.95, "text": "و A to 1 لو قلت هذه بي و قلت هذه بي بالشكل اللي عندنا هذا ساتش ذات ال A و ال B موجودة في ال set of real numbers نمسح هذه خلاصنا يبقى كله عارف قاعات الامتحان اليوم", "tokens": [2407, 316, 281, 502, 45164, 12174, 1211, 2655, 29538, 4724, 1829, 4032, 12174, 1211, 2655, 29538, 4724, 1829, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 8608, 9307, 8592, 29910, 9307, 2423, 316, 4032, 2423, 363, 3714, 29245, 23328, 3660, 8978, 2423, 992, 295, 957, 3547, 8717, 2304, 3794, 5016, 29538, 16490, 1211, 33546, 8315, 7251, 3555, 4587, 7578, 28242, 3224, 6225, 9640, 5172, 12174, 45761, 9307, 2423, 10943, 2655, 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0.84033203125}, {"start": 760.45, "end": 760.75, "word": " بي", "probability": 0.979248046875}, {"start": 760.75, "end": 761.35, "word": " بالشكل", "probability": 0.9420572916666666}, {"start": 761.35, "end": 761.55, "word": " اللي", "probability": 0.92138671875}, {"start": 761.55, "end": 762.11, "word": " عندنا", "probability": 0.96337890625}, {"start": 762.11, "end": 762.59, "word": " هذا", "probability": 0.79248046875}, {"start": 762.59, "end": 763.57, "word": " ساتش", "probability": 0.5926920572916666}, {"start": 763.57, "end": 764.05, "word": " ذات", "probability": 0.9912109375}, {"start": 764.05, "end": 764.29, "word": " ال", "probability": 0.92333984375}, {"start": 764.29, "end": 764.57, "word": " A", "probability": 0.6767578125}, {"start": 764.57, "end": 764.77, "word": " و", "probability": 0.6328125}, {"start": 764.77, "end": 764.95, "word": " ال", "probability": 0.728515625}, {"start": 764.95, "end": 765.19, "word": " B", "probability": 0.91455078125}, {"start": 765.19, "end": 765.89, "word": " موجودة", "probability": 0.9835205078125}, {"start": 765.89, "end": 766.01, "word": " في", "probability": 0.9375}, {"start": 766.01, "end": 766.21, "word": " ال", "probability": 0.65380859375}, {"start": 766.21, "end": 766.55, "word": " set", "probability": 0.89990234375}, {"start": 766.55, "end": 766.93, "word": " of", "probability": 0.96875}, {"start": 766.93, "end": 767.41, "word": " real", "probability": 0.96484375}, {"start": 767.41, "end": 768.37, "word": " numbers", "probability": 0.69921875}, {"start": 768.37, "end": 771.77, "word": " نمسح", "probability": 0.9163818359375}, {"start": 771.77, "end": 772.03, "word": " هذه", "probability": 0.454833984375}, {"start": 772.03, "end": 772.71, "word": " خلاصنا", "probability": 0.9141845703125}, {"start": 772.71, "end": 773.77, "word": " يبقى", "probability": 0.852294921875}, {"start": 773.77, "end": 774.11, "word": " كله", "probability": 0.931884765625}, {"start": 774.11, "end": 774.37, "word": " عارف", "probability": 0.9454752604166666}, {"start": 774.37, "end": 774.89, "word": " قاعات", "probability": 0.8640950520833334}, {"start": 774.89, "end": 775.45, "word": " الامتحان", "probability": 0.94521484375}, {"start": 775.45, "end": 775.95, "word": " اليوم", "probability": 0.936279296875}], "temperature": 1.0}, {"id": 38, "seek": 80222, "start": 778.12, "end": 802.22, "text": "يبقى ما عليك الى تتوجهى الى احدتين القاعتين 202 و205 في مبنى المدينة المنورة نرجع لسؤالنا يبقى أصبح ال kernel كل المصففات اللى موجودة في ال M22 بحيث عناصر القطر الرئيسى are equal وعناصر القطر الثانوي are equal", "tokens": [1829, 3555, 4587, 7578, 19446, 25894, 4117, 2423, 7578, 6055, 2655, 29245, 3224, 7578, 2423, 7578, 1975, 24401, 2655, 9957, 25062, 45761, 2655, 9957, 945, 17, 4032, 2009, 20, 8978, 3714, 3555, 1863, 7578, 9673, 3215, 9957, 3660, 9673, 1863, 13063, 3660, 8717, 47341, 3615, 5296, 3794, 33604, 6027, 8315, 7251, 3555, 4587, 7578, 5551, 9381, 49628, 2423, 23434, 338, 28242, 9673, 9381, 5172, 5172, 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القاعتين", "probability": 0.8541259765625}, {"start": 781.8, "end": 782.86, "word": " 202", "probability": 0.55120849609375}, {"start": 782.86, "end": 784.6, "word": " و205", "probability": 0.8269856770833334}, {"start": 784.6, "end": 784.94, "word": " في", "probability": 0.84228515625}, {"start": 784.94, "end": 785.36, "word": " مبنى", "probability": 0.9239501953125}, {"start": 785.36, "end": 786.06, "word": " المدينة", "probability": 0.991455078125}, {"start": 786.06, "end": 787.22, "word": " المنورة", "probability": 0.982177734375}, {"start": 787.22, "end": 788.06, "word": " نرجع", "probability": 0.598388671875}, {"start": 788.06, "end": 788.9, "word": " لسؤالنا", "probability": 0.921484375}, {"start": 788.9, "end": 789.76, "word": " يبقى", "probability": 0.941650390625}, {"start": 789.76, "end": 790.38, "word": " أصبح", "probability": 0.8505859375}, {"start": 790.38, "end": 790.6, "word": " ال", "probability": 0.8359375}, {"start": 790.6, "end": 791.12, "word": " kernel", "probability": 0.26788330078125}, {"start": 791.12, "end": 791.54, "word": " كل", "probability": 0.9521484375}, {"start": 791.54, "end": 792.78, "word": " المصففات", "probability": 0.839453125}, {"start": 792.78, "end": 793.02, "word": " اللى", "probability": 0.69921875}, {"start": 793.02, "end": 793.86, "word": " موجودة", "probability": 0.9873046875}, {"start": 793.86, "end": 794.24, "word": " في", "probability": 0.71875}, {"start": 794.24, "end": 794.42, "word": " ال", "probability": 0.89208984375}, {"start": 794.42, "end": 795.12, "word": " M22", "probability": 0.5504150390625}, {"start": 795.12, "end": 796.08, "word": " بحيث", "probability": 0.9803466796875}, {"start": 796.08, "end": 796.68, "word": " عناصر", "probability": 0.9788411458333334}, {"start": 796.68, "end": 797.12, "word": " القطر", "probability": 0.98291015625}, {"start": 797.12, "end": 797.88, "word": " الرئيسى", "probability": 0.9326171875}, {"start": 797.88, "end": 798.18, "word": " are", "probability": 0.59326171875}, {"start": 798.18, "end": 798.82, "word": " equal", "probability": 0.873046875}, {"start": 798.82, "end": 800.04, "word": " وعناصر", "probability": 0.90166015625}, {"start": 800.04, "end": 800.56, "word": " القطر", "probability": 0.9944661458333334}, {"start": 800.56, "end": 801.24, "word": " الثانوي", "probability": 0.9573974609375}, {"start": 801.24, "end": 801.7, "word": " are", "probability": 0.91259765625}, {"start": 801.7, "end": 802.22, "word": " equal", "probability": 0.89794921875}], "temperature": 1.0}, {"id": 39, "seek": 81474, "start": 808.3, "end": 814.74, "text": "يبقى عناصر القطر الرئيسي ار اكول وعناصر القطر الثانوي اتنين ار اكول", "tokens": [1829, 3555, 4587, 7578, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 1975, 2288, 1975, 4117, 12610, 4032, 3615, 1863, 33546, 2288, 25062, 9566, 2288, 6024, 104, 7649, 45865, 1975, 2655, 1863, 9957, 1975, 2288, 1975, 4117, 12610], "avg_logprob": -0.31194196499529336, "compression_ratio": 1.5974025974025974, "no_speech_prob": 0.0, "words": [{"start": 808.3, "end": 809.42, "word": "يبقى", "probability": 0.7933349609375}, {"start": 809.42, "end": 809.92, "word": " عناصر", "probability": 0.69073486328125}, {"start": 809.92, "end": 810.16, "word": " القطر", "probability": 0.7412923177083334}, {"start": 810.16, "end": 810.74, "word": " الرئيسي", "probability": 0.9169921875}, {"start": 810.74, "end": 810.92, "word": " ار", "probability": 0.292724609375}, {"start": 810.92, "end": 811.24, "word": " اكول", "probability": 0.66064453125}, {"start": 811.24, "end": 811.78, "word": " وعناصر", "probability": 0.831689453125}, {"start": 811.78, "end": 812.1, "word": " القطر", "probability": 0.978515625}, {"start": 812.1, "end": 812.68, "word": " الثانوي", "probability": 0.7891845703125}, {"start": 812.68, "end": 813.32, "word": " اتنين", "probability": 0.9427490234375}, {"start": 813.32, "end": 814.06, "word": " ار", "probability": 0.893310546875}, {"start": 814.06, "end": 814.74, "word": " اكول", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 40, "seek": 84186, "start": 818.52, "end": 841.86, "text": "الان هذا هو الست اللي في ال kernels يبقى ال kernels التي كل المصوفات اللي من الدرجة من الرتبة الثانية والعناصر قطر الرئيس are equal وعناصر قطر الثانوي are equal بدنا ندور على bases لأ بدنا ندور بقول المرة الأخيرة بدنا ندور على bases وإلا ديروا بالكم", "tokens": [6027, 7649, 23758, 31439, 2423, 14851, 13672, 1829, 8978, 2423, 23434, 1625, 7251, 3555, 4587, 7578, 2423, 23434, 1625, 38392, 28242, 9673, 9381, 38688, 9307, 13672, 1829, 9154, 32748, 47341, 3660, 9154, 34892, 2655, 49401, 6024, 104, 7649, 10632, 16070, 3615, 8315, 9381, 2288, 12174, 9566, 2288, 34892, 19986, 1829, 3794, 366, 2681, 4032, 3615, 8315, 9381, 2288, 12174, 9566, 2288, 6024, 104, 7649, 45865, 366, 2681, 47525, 8315, 8717, 3215, 13063, 15844, 17949, 5296, 10721, 47525, 8315, 8717, 3215, 13063, 4724, 39648, 9673, 25720, 16247, 9778, 48923, 47525, 8315, 8717, 3215, 13063, 15844, 17949, 4032, 28814, 15040, 11778, 13546, 14407, 20666, 24793], "avg_logprob": -0.26592547131272465, "compression_ratio": 2.019607843137255, "no_speech_prob": 0.0, "words": [{"start": 818.52, "end": 819.1, "word": "الان", "probability": 0.69873046875}, {"start": 819.1, "end": 819.76, "word": " هذا", "probability": 0.4599609375}, {"start": 819.76, "end": 820.42, "word": " هو", "probability": 0.931640625}, {"start": 820.42, "end": 821.2, "word": " الست", "probability": 0.5211181640625}, {"start": 821.2, "end": 821.44, "word": " اللي", "probability": 0.80078125}, {"start": 821.44, "end": 821.62, "word": " في", "probability": 0.9189453125}, {"start": 821.62, "end": 821.82, "word": " ال", "probability": 0.83203125}, {"start": 821.82, "end": 822.62, "word": " kernels", "probability": 0.6732177734375}, {"start": 822.62, "end": 823.18, "word": " يبقى", "probability": 0.8975830078125}, {"start": 823.18, "end": 823.3, "word": " ال", "probability": 0.802734375}, {"start": 823.3, "end": 823.68, "word": " kernels", "probability": 0.905029296875}, {"start": 823.68, "end": 823.96, "word": " التي", "probability": 0.20849609375}, {"start": 823.96, "end": 824.4, "word": " كل", "probability": 0.9130859375}, {"start": 824.4, "end": 825.5, "word": " المصوفات", "probability": 0.862548828125}, {"start": 825.5, "end": 825.76, "word": " اللي", "probability": 0.717041015625}, {"start": 825.76, "end": 826.0, "word": " من", "probability": 0.95458984375}, {"start": 826.0, "end": 826.58, "word": " الدرجة", "probability": 0.88525390625}, {"start": 826.58, "end": 826.72, "word": " من", "probability": 0.724609375}, {"start": 826.72, "end": 827.2, "word": " الرتبة", "probability": 0.8772786458333334}, {"start": 827.2, "end": 827.82, "word": " الثانية", "probability": 0.966796875}, {"start": 827.82, "end": 828.94, "word": " والعناصر", "probability": 0.65263671875}, {"start": 828.94, "end": 829.16, "word": " قطر", "probability": 0.8191731770833334}, {"start": 829.16, "end": 829.54, "word": " الرئيس", "probability": 0.9576416015625}, {"start": 829.54, "end": 829.7, "word": " are", "probability": 0.244140625}, {"start": 829.7, "end": 830.0, "word": " equal", "probability": 0.837890625}, {"start": 830.0, "end": 830.52, "word": " وعناصر", "probability": 0.908203125}, {"start": 830.52, "end": 830.82, "word": " قطر", "probability": 0.86474609375}, {"start": 830.82, "end": 831.3, "word": " الثانوي", "probability": 0.84326171875}, {"start": 831.3, "end": 831.94, "word": " are", "probability": 0.91259765625}, {"start": 831.94, "end": 832.5, "word": " equal", "probability": 0.89111328125}, {"start": 832.5, "end": 833.28, "word": " بدنا", "probability": 0.6390380859375}, {"start": 833.28, "end": 833.7, "word": " ندور", "probability": 0.98291015625}, {"start": 833.7, "end": 834.16, "word": " على", "probability": 0.92578125}, {"start": 834.16, "end": 835.06, "word": " bases", "probability": 0.36328125}, {"start": 835.06, "end": 836.68, "word": " لأ", "probability": 0.502685546875}, {"start": 836.68, "end": 836.94, "word": " بدنا", "probability": 0.89013671875}, {"start": 836.94, "end": 837.16, "word": " ندور", "probability": 0.9685872395833334}, {"start": 837.16, "end": 837.5, "word": " بقول", "probability": 0.6011962890625}, {"start": 837.5, "end": 837.96, "word": " المرة", "probability": 0.768798828125}, {"start": 837.96, "end": 838.82, "word": " الأخيرة", "probability": 0.9274088541666666}, {"start": 838.82, "end": 839.28, "word": " بدنا", "probability": 0.638671875}, {"start": 839.28, "end": 839.74, "word": " ندور", "probability": 0.9890950520833334}, {"start": 839.74, "end": 840.02, "word": " على", "probability": 0.88818359375}, {"start": 840.02, "end": 840.28, "word": " bases", "probability": 0.5986328125}, {"start": 840.28, "end": 840.96, "word": " وإلا", "probability": 0.686767578125}, {"start": 840.96, "end": 841.4, "word": " ديروا", "probability": 0.7311197916666666}, {"start": 841.4, "end": 841.86, "word": " بالكم", "probability": 0.8408203125}], "temperature": 1.0}, {"id": 41, "seek": 86027, "start": 842.75, "end": 860.27, "text": "يبقى بقول هنا بدي اروح ادور على basis لهذا ال kernel بقول كويس مشان ادور على basis يبقى اي مصفوفة بده تبقى على الشكل اللي عندنا هذا لكن هذا الشكل بقدر اكتبه هنا كتالي", "tokens": [1829, 3555, 4587, 7578, 4724, 39648, 34105, 4724, 16254, 1975, 32887, 5016, 1975, 3215, 13063, 15844, 5143, 46740, 15730, 2423, 28256, 4724, 39648, 9122, 45865, 3794, 37893, 7649, 1975, 3215, 13063, 15844, 5143, 7251, 3555, 4587, 7578, 1975, 1829, 3714, 9381, 5172, 38688, 3660, 47525, 3224, 6055, 3555, 4587, 7578, 15844, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 44381, 23758, 25124, 28820, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 3224, 34105, 9122, 2655, 6027, 1829], "avg_logprob": -0.17979029369981667, "compression_ratio": 1.779874213836478, "no_speech_prob": 0.0, "words": [{"start": 842.75, "end": 843.21, "word": "يبقى", "probability": 0.74462890625}, {"start": 843.21, "end": 843.73, "word": " بقول", "probability": 0.859375}, 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1156.85, "end": 1157.55, "word": " مستاهل", "probability": 0.978271484375}], "temperature": 1.0}, {"id": 54, "seek": 118026, "start": 1158.18, "end": 1180.26, "text": "لما يكون ال A لها معكوس يبقى بدروح اقوله انه since بما ان ال A is invertable لها معكوس we have ان ال A انفرسمالها exist", "tokens": [1211, 15042, 7251, 30544, 2423, 316, 5296, 11296, 20449, 4117, 41779, 7251, 3555, 4587, 7578, 47525, 32887, 5016, 1975, 39648, 3224, 16472, 3224, 1670, 4724, 15042, 16472, 2423, 316, 307, 33966, 712, 5296, 11296, 20449, 4117, 41779, 321, 362, 16472, 2423, 316, 16472, 5172, 2288, 38251, 6027, 11296, 2514], "avg_logprob": -0.2781249988079071, "compression_ratio": 1.421875, "no_speech_prob": 0.0, "words": [{"start": 1158.18, "end": 1158.8, "word": "لما", "probability": 0.794921875}, {"start": 1158.8, "end": 1159.2, "word": " يكون", "probability": 0.951904296875}, {"start": 1159.2, "end": 1159.48, "word": " ال", "probability": 0.89501953125}, {"start": 1159.48, "end": 1159.78, "word": " A", "probability": 0.466552734375}, {"start": 1159.78, "end": 1160.36, "word": " لها", "probability": 0.6612548828125}, {"start": 1160.36, "end": 1161.24, "word": " معكوس", "probability": 0.9002278645833334}, {"start": 1161.24, "end": 1161.58, "word": " يبقى", "probability": 0.7244873046875}, {"start": 1161.58, "end": 1162.14, "word": " بدروح", "probability": 0.6969401041666666}, {"start": 1162.14, "end": 1162.96, "word": " اقوله", "probability": 0.6136881510416666}, {"start": 1162.96, "end": 1166.02, "word": " انه", "probability": 0.73828125}, {"start": 1166.02, "end": 1166.88, "word": " since", "probability": 0.3564453125}, {"start": 1166.88, "end": 1167.74, "word": " بما", "probability": 0.93310546875}, {"start": 1167.74, "end": 1168.2, "word": " ان", "probability": 0.68798828125}, {"start": 1168.2, "end": 1168.48, "word": " ال", "probability": 0.9794921875}, {"start": 1168.48, "end": 1168.98, "word": " A", "probability": 0.92138671875}, {"start": 1168.98, "end": 1170.2, "word": " is", "probability": 0.94140625}, {"start": 1170.2, "end": 1172.48, "word": " invertable", "probability": 0.69775390625}, {"start": 1172.48, "end": 1173.58, "word": " لها", "probability": 0.912841796875}, {"start": 1173.58, "end": 1174.48, "word": " معكوس", "probability": 0.9558919270833334}, {"start": 1174.48, "end": 1175.2, "word": " we", "probability": 0.46533203125}, {"start": 1175.2, "end": 1176.3, "word": " have", "probability": 0.97119140625}, {"start": 1176.3, "end": 1177.42, "word": " ان", "probability": 0.8564453125}, {"start": 1177.42, "end": 1177.72, "word": " ال", "probability": 0.94482421875}, {"start": 1177.72, "end": 1178.08, "word": " A", "probability": 0.9462890625}, {"start": 1178.08, "end": 1179.54, "word": " انفرسمالها", "probability": 0.7965494791666666}, {"start": 1179.54, "end": 1180.26, "word": " exist", "probability": 0.85693359375}], "temperature": 1.0}, {"id": 55, "seek": 119583, "start": 1182.08, "end": 1195.84, "text": "يبقى هذه موجودة مادام exist بقدر اقول يبقى ال a في ال a inverse بدي سوى مين ال a inverse في ال a بدي سوى مين ال identity element", "tokens": [1829, 3555, 4587, 7578, 29538, 3714, 29245, 23328, 3660, 3714, 18513, 10943, 2514, 4724, 28543, 2288, 1975, 39648, 7251, 3555, 4587, 7578, 2423, 257, 8978, 2423, 257, 17340, 4724, 16254, 8608, 2407, 7578, 3714, 9957, 2423, 257, 17340, 8978, 2423, 257, 4724, 16254, 8608, 2407, 7578, 3714, 9957, 2423, 6575, 4478], "avg_logprob": -0.23813101506003967, "compression_ratio": 1.5702479338842976, "no_speech_prob": 0.0, "words": [{"start": 1182.08, "end": 1182.6, "word": "يبقى", "probability": 0.81756591796875}, {"start": 1182.6, "end": 1182.9, "word": " هذه", "probability": 0.83154296875}, {"start": 1182.9, "end": 1183.5, "word": " موجودة", "probability": 0.976318359375}, {"start": 1183.5, "end": 1184.04, "word": " مادام", "probability": 0.5874837239583334}, {"start": 1184.04, "end": 1184.78, "word": " exist", "probability": 0.552734375}, {"start": 1184.78, "end": 1185.82, "word": " بقدر", "probability": 0.8955078125}, {"start": 1185.82, "end": 1186.1, "word": " اقول", "probability": 0.78759765625}, {"start": 1186.1, "end": 1186.58, "word": " يبقى", "probability": 0.966552734375}, {"start": 1186.58, "end": 1186.74, "word": " ال", "probability": 0.8466796875}, {"start": 1186.74, "end": 1187.1, "word": " a", "probability": 0.45947265625}, {"start": 1187.1, "end": 1187.4, "word": " في", "probability": 0.619140625}, {"start": 1187.4, "end": 1187.66, "word": " ال", "probability": 0.884765625}, {"start": 1187.66, "end": 1188.0, "word": " a", "probability": 0.802734375}, {"start": 1188.0, "end": 1188.74, "word": " inverse", "probability": 0.8623046875}, {"start": 1188.74, "end": 1189.16, "word": " بدي", "probability": 0.63916015625}, {"start": 1189.16, "end": 1189.6, "word": " سوى", "probability": 0.6416829427083334}, {"start": 1189.6, "end": 1189.94, "word": " مين", "probability": 0.64306640625}, {"start": 1189.94, "end": 1190.66, "word": " ال", "probability": 0.8955078125}, {"start": 1190.66, "end": 1191.04, "word": " a", "probability": 0.86865234375}, {"start": 1191.04, "end": 1191.84, "word": " inverse", "probability": 0.83056640625}, {"start": 1191.84, "end": 1192.08, "word": " في", "probability": 0.876953125}, {"start": 1192.08, "end": 1192.34, "word": " ال", "probability": 0.9296875}, {"start": 1192.34, "end": 1192.64, "word": " a", "probability": 0.951171875}, {"start": 1192.64, "end": 1193.08, "word": " بدي", "probability": 0.813720703125}, {"start": 1193.08, "end": 1193.44, "word": " سوى", "probability": 0.9524739583333334}, {"start": 1193.44, "end": 1193.82, "word": " مين", "probability": 0.868408203125}, {"start": 1193.82, "end": 1194.2, "word": " ال", "probability": 0.96826171875}, {"start": 1194.2, "end": 1195.04, "word": " identity", "probability": 0.90234375}, {"start": 1195.04, "end": 1195.84, "word": " element", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 56, "seek": 121419, "start": 1197.09, "end": 1214.19, "text": "خُد المحدد للطرفين يبقى هذا يعطينا ان ال determinant لمن ل A inverse A يساوي ال determinant لمصفوف من الواحدة", "tokens": [9778, 10859, 3215, 9673, 24401, 3215, 24976, 9566, 28480, 9957, 7251, 3555, 4587, 7578, 23758, 7251, 3615, 9566, 1829, 8315, 16472, 2423, 41296, 5296, 27842, 5296, 316, 17340, 316, 7251, 3794, 995, 45865, 2423, 41296, 32767, 9381, 5172, 38688, 9154, 2423, 14407, 24401, 3660], "avg_logprob": -0.3767360978656345, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1197.09, "end": 1197.75, "word": "خُد", "probability": 0.676513671875}, {"start": 1197.75, "end": 1198.61, "word": " المحدد", "probability": 0.9142252604166666}, {"start": 1198.61, "end": 1199.71, "word": " للطرفين", "probability": 0.9395751953125}, {"start": 1199.71, "end": 1200.63, "word": " يبقى", "probability": 0.8873291015625}, {"start": 1200.63, "end": 1200.97, "word": " هذا", "probability": 0.7724609375}, {"start": 1200.97, "end": 1202.09, "word": " يعطينا", "probability": 0.715185546875}, {"start": 1202.09, "end": 1202.39, "word": " ان", "probability": 0.2364501953125}, {"start": 1202.39, "end": 1202.61, "word": " ال", "probability": 0.71875}, {"start": 1202.61, "end": 1203.61, "word": " determinant", "probability": 0.6259765625}, {"start": 1203.61, "end": 1204.91, "word": " لمن", "probability": 0.7421875}, {"start": 1204.91, "end": 1205.69, "word": " ل", "probability": 0.353515625}, {"start": 1205.69, "end": 1206.99, "word": " A", "probability": 0.177490234375}, {"start": 1206.99, "end": 1208.09, "word": " inverse", "probability": 0.65380859375}, {"start": 1208.09, "end": 1208.69, "word": " A", "probability": 0.87353515625}, {"start": 1208.69, "end": 1209.61, "word": " يساوي", "probability": 0.499725341796875}, {"start": 1209.61, "end": 1209.75, "word": " ال", "probability": 0.69384765625}, {"start": 1209.75, "end": 1210.67, "word": " determinant", "probability": 0.86376953125}, {"start": 1210.67, "end": 1212.15, "word": " لمصفوف", "probability": 0.9161376953125}, {"start": 1212.15, "end": 1212.75, "word": " من", "probability": 0.38427734375}, {"start": 1212.75, "end": 1214.19, "word": " الواحدة", "probability": 0.8338623046875}], "temperature": 1.0}, {"id": 57, "seek": 124120, "start": 1214.22, "end": 1241.2, "text": "من خواص ال determinant ال determinant اللي حصل ضرب مصوفتين يساوي ال determinant للمصوفة الأولى في ال determinant للمصوفة الثانية ومحدد مصوفتي الواحدة بجداش بواحدة صحية طيب هدول عبارة عن real numbers مش مصوفات المحدد قيمة عددية إذا بقدر أقول أجسم على ال determinant لإيه؟ بنفع؟", "tokens": [27842, 16490, 14407, 9381, 2423, 41296, 2423, 41296, 13672, 1829, 11331, 36520, 48812, 25513, 3714, 9381, 38688, 2655, 9957, 7251, 3794, 995, 45865, 2423, 41296, 5296, 19528, 9381, 38688, 3660, 16247, 12610, 7578, 8978, 2423, 41296, 5296, 19528, 9381, 38688, 3660, 6024, 104, 7649, 10632, 4032, 2304, 24401, 3215, 3714, 9381, 38688, 31371, 2423, 14407, 24401, 3660, 4724, 7435, 3215, 33599, 4724, 14407, 24401, 3660, 20328, 5016, 10632, 23032, 1829, 3555, 8032, 3215, 12610, 6225, 3555, 9640, 3660, 18871, 957, 3547, 37893, 3714, 9381, 38688, 9307, 9673, 24401, 3215, 12174, 32640, 3660, 6225, 3215, 3215, 10632, 11933, 15730, 4724, 28543, 2288, 5551, 39648, 5551, 7435, 38251, 15844, 2423, 41296, 5296, 28814, 1829, 3224, 22807, 44945, 5172, 3615, 22807], "avg_logprob": -0.18802521308930983, "compression_ratio": 2.0045454545454544, "no_speech_prob": 0.0, "words": [{"start": 1214.22, "end": 1214.5, "word": "من", "probability": 0.72705078125}, {"start": 1214.5, "end": 1214.98, "word": " خواص", "probability": 0.705078125}, {"start": 1214.98, "end": 1215.12, "word": " ال", "probability": 0.5673828125}, {"start": 1215.12, "end": 1215.66, "word": " determinant", "probability": 0.53271484375}, {"start": 1215.66, "end": 1215.96, "word": " ال", "probability": 0.2099609375}, {"start": 1215.96, "end": 1216.22, "word": " determinant", "probability": 0.315185546875}, {"start": 1216.22, "end": 1216.48, "word": " اللي", "probability": 0.85986328125}, {"start": 1216.48, "end": 1216.84, "word": " حصل", "probability": 0.97265625}, {"start": 1216.84, "end": 1217.16, "word": " ضرب", "probability": 0.953369140625}, {"start": 1217.16, "end": 1218.08, "word": " مصوفتين", "probability": 0.85859375}, {"start": 1218.08, "end": 1218.98, "word": " يساوي", "probability": 0.82958984375}, {"start": 1218.98, "end": 1219.1, "word": " ال", "probability": 0.90234375}, {"start": 1219.1, "end": 1219.76, "word": " determinant", "probability": 0.97998046875}, {"start": 1219.76, "end": 1221.3, "word": " للمصوفة", "probability": 0.945703125}, {"start": 1221.3, "end": 1222.1, "word": " الأولى", "probability": 0.9733072916666666}, {"start": 1222.1, "end": 1222.52, "word": " في", "probability": 0.63818359375}, {"start": 1222.52, "end": 1222.66, "word": " ال", "probability": 0.9423828125}, {"start": 1222.66, "end": 1223.3, "word": " determinant", "probability": 0.9765625}, {"start": 1223.3, "end": 1224.44, "word": " للمصوفة", "probability": 0.97568359375}, {"start": 1224.44, "end": 1225.0, "word": " الثانية", "probability": 0.96240234375}, {"start": 1225.0, "end": 1226.12, "word": " ومحدد", "probability": 0.94384765625}, {"start": 1226.12, "end": 1226.68, "word": " مصوفتي", "probability": 0.9072265625}, {"start": 1226.68, "end": 1227.02, "word": " الواحدة", "probability": 0.7796630859375}, {"start": 1227.02, "end": 1227.86, "word": " بجداش", "probability": 0.5875244140625}, {"start": 1227.86, "end": 1229.02, "word": " بواحدة", "probability": 0.7520751953125}, {"start": 1229.02, "end": 1229.48, "word": " صحية", "probability": 0.97119140625}, {"start": 1229.48, "end": 1230.62, "word": " طيب", "probability": 0.9064127604166666}, {"start": 1230.62, "end": 1231.06, "word": " هدول", "probability": 0.8522135416666666}, {"start": 1231.06, "end": 1231.5, "word": " عبارة", "probability": 0.990234375}, {"start": 1231.5, "end": 1231.68, "word": " عن", "probability": 0.79052734375}, {"start": 1231.68, "end": 1232.0, "word": " real", "probability": 0.6787109375}, {"start": 1232.0, "end": 1232.82, "word": " numbers", "probability": 0.8525390625}, {"start": 1232.82, "end": 1233.14, "word": " مش", "probability": 0.95947265625}, {"start": 1233.14, "end": 1233.88, "word": " مصوفات", "probability": 0.985595703125}, {"start": 1233.88, "end": 1234.6, "word": " المحدد", "probability": 0.9202473958333334}, {"start": 1234.6, "end": 1235.0, "word": " قيمة", "probability": 0.9788411458333334}, {"start": 1235.0, "end": 1235.56, "word": " عددية", "probability": 0.84637451171875}, {"start": 1235.56, "end": 1236.14, "word": " إذا", "probability": 0.7099609375}, {"start": 1236.14, "end": 1236.66, "word": " بقدر", "probability": 0.8863932291666666}, {"start": 1236.66, "end": 1237.14, "word": " أقول", "probability": 0.861328125}, {"start": 1237.14, "end": 1237.82, "word": " أجسم", "probability": 0.8043619791666666}, {"start": 1237.82, "end": 1238.16, "word": " على", "probability": 0.90185546875}, {"start": 1238.16, "end": 1238.36, "word": " ال", "probability": 0.8837890625}, {"start": 1238.36, "end": 1239.2, "word": " determinant", "probability": 0.96826171875}, {"start": 1239.2, "end": 1239.96, "word": " لإيه؟", "probability": 0.812548828125}, {"start": 1239.96, "end": 1241.2, "word": " بنفع؟", "probability": 0.8701171875}], "temperature": 1.0}, {"id": 58, "seek": 126558, "start": 1241.24, "end": 1265.58, "text": "بنفع ليش؟ لأن invertible يعني محددها ليه يمكن أن يساوي zero مدام المحدد لا يمكن أن يساوي zero إذا بجسم عليه without problems يبقى هذا الكلام بده يعطينا أن ال determinant لل A inverse بده يساوي واحد على ال determinant ل A وانتهى الفرقان", "tokens": [3555, 1863, 5172, 3615, 32239, 8592, 22807, 5296, 33456, 33966, 964, 37495, 22653, 3714, 24401, 3215, 11296, 32239, 3224, 7251, 43020, 14739, 7251, 3794, 995, 45865, 4018, 3714, 3215, 10943, 9673, 24401, 3215, 20193, 7251, 43020, 14739, 7251, 3794, 995, 45865, 4018, 11933, 15730, 4724, 7435, 38251, 47356, 1553, 2740, 7251, 3555, 4587, 7578, 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"probability": 0.98974609375}, {"start": 1384.3, "end": 1384.5, "word": " basis", "probability": 0.9140625}, {"start": 1384.5, "end": 1384.94, "word": " كلهم", "probability": 0.94873046875}, {"start": 1384.94, "end": 1385.26, "word": " are", "probability": 0.84423828125}, {"start": 1385.26, "end": 1385.98, "word": " linearly", "probability": 0.9150390625}, {"start": 1385.98, "end": 1387.02, "word": " independent", "probability": 0.92041015625}, {"start": 1387.02, "end": 1388.0, "word": " فهل", "probability": 0.9895833333333334}, {"start": 1388.0, "end": 1388.2, "word": " ال", "probability": 0.9658203125}, {"start": 1388.2, "end": 1388.72, "word": " vectors", "probability": 0.93701171875}, {"start": 1388.72, "end": 1389.24, "word": " هدول", "probability": 0.6357421875}, {"start": 1389.24, "end": 1389.88, "word": " linearly", "probability": 0.95654296875}, {"start": 1389.88, "end": 1391.06, "word": " dependent", "probability": 0.8935546875}, {"start": 1391.06, "end": 1391.54, "word": " ولا", "probability": 0.473388671875}, {"start": 1391.54, "end": 1392.24, "word": " linearly", "probability": 0.947265625}, {"start": 1392.24, "end": 1393.1, "word": " independent", "probability": 0.9501953125}, {"start": 1393.1, "end": 1393.54, "word": " احنا", "probability": 0.8621419270833334}, {"start": 1393.54, "end": 1393.72, "word": " مش", "probability": 0.98193359375}, {"start": 1393.72, "end": 1394.22, "word": " عارفين", "probability": 0.9908447265625}], "temperature": 1.0}, {"id": 64, "seek": 141770, "start": 1394.8, "end": 1417.7, "text": "إذا بدى نتأكد هل هدول linearly dependent ولا linearly independent لأ انطلع linearly independent بيكون خلاصنا طب انطلع linearly dependent يبقى مانفعش بدي أخد مين؟ اتنين منهم هاتأكد في الأول هل هدول linearly dependent ولا linearly independent", "tokens": [28814, 15730, 47525, 7578, 8717, 2655, 10721, 4117, 3215, 8032, 1211, 8032, 3215, 12610, 43586, 12334, 49429, 43586, 6695, 5296, 10721, 16472, 9566, 1211, 3615, 43586, 6695, 4724, 1829, 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dependent", "probability": 0.58642578125}, {"start": 1398.06, "end": 1398.46, "word": " ولا", "probability": 0.75732421875}, {"start": 1398.46, "end": 1399.04, "word": " linearly", "probability": 0.98681640625}, {"start": 1399.04, "end": 1399.62, "word": " independent", "probability": 0.96142578125}, {"start": 1399.62, "end": 1399.94, "word": " لأ", "probability": 0.532958984375}, {"start": 1399.94, "end": 1400.46, "word": " انطلع", "probability": 0.81658935546875}, {"start": 1400.46, "end": 1401.22, "word": " linearly", "probability": 0.84912109375}, {"start": 1401.22, "end": 1402.52, "word": " independent", "probability": 0.97119140625}, {"start": 1402.52, "end": 1403.28, "word": " بيكون", "probability": 0.7228190104166666}, {"start": 1403.28, "end": 1405.06, "word": " خلاصنا", "probability": 0.9146728515625}, {"start": 1405.06, "end": 1405.52, "word": " طب", "probability": 0.902099609375}, {"start": 1405.52, "end": 1405.88, "word": " انطلع", "probability": 0.9801025390625}, {"start": 1405.88, "end": 1406.5, "word": " linearly", "probability": 0.96923828125}, {"start": 1406.5, "end": 1407.5, "word": " dependent", "probability": 0.95166015625}, {"start": 1407.5, "end": 1408.58, "word": " يبقى", "probability": 0.744140625}, {"start": 1408.58, "end": 1409.24, "word": " مانفعش", "probability": 0.863671875}, {"start": 1409.24, "end": 1409.5, "word": " بدي", "probability": 0.740478515625}, {"start": 1409.5, "end": 1409.88, "word": " أخد", "probability": 0.8497721354166666}, {"start": 1409.88, "end": 1410.42, "word": " مين؟", "probability": 0.643798828125}, {"start": 1410.42, "end": 1411.74, "word": " اتنين", "probability": 0.8807373046875}, {"start": 1411.74, "end": 1412.3, "word": " منهم", "probability": 0.989501953125}, {"start": 1412.3, "end": 1413.32, "word": " هاتأكد", "probability": 0.6603759765625}, {"start": 1413.32, "end": 1413.44, "word": " في", "probability": 0.546875}, {"start": 1413.44, "end": 1413.76, "word": " الأول", "probability": 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"end": 1437.66, "word": " دول", "probability": 0.774658203125}, {"start": 1437.66, "end": 1438.18, "word": " linearly", "probability": 0.97265625}, {"start": 1438.18, "end": 1439.12, "word": " independent", "probability": 0.95458984375}, {"start": 1439.12, "end": 1439.76, "word": " لكن", "probability": 0.87841796875}, {"start": 1439.76, "end": 1440.26, "word": " المحدد", "probability": 0.986328125}, {"start": 1440.26, "end": 1440.62, "word": " بطلع", "probability": 0.9615478515625}, {"start": 1440.62, "end": 1441.24, "word": " قداش", "probability": 0.759765625}, {"start": 1441.24, "end": 1442.4, "word": " قيمة", "probability": 0.9329427083333334}, {"start": 1442.4, "end": 1443.4, "word": " عددية", "probability": 0.9676513671875}, {"start": 1443.4, "end": 1444.56, "word": " تمام؟", "probability": 0.611328125}, {"start": 1444.56, "end": 1444.98, "word": " مدام", "probability": 0.794921875}, {"start": 1444.98, "end": 1445.4, "word": " قيمة", "probability": 0.9889322916666666}, {"start": 1445.4, "end": 1446.06, "word": " عددية", "probability": 0.984130859375}], "temperature": 1.0}, {"id": 66, "seek": 147550, "start": 1446.4, "end": 1475.5, "text": "يبقى هذا لا يؤكد انهم linearly dependent صح ولا لا؟ ليش؟ لأن الشرط انه لو كانوا linearly dependent إذا المحدد بدي ساوي zero لكن العكس ليس بالضرورة صحيحا يبقى حكاية هذه الطريقة بتنفعش يبقى بدول كونصان في الأول و كونصان في التاني و كونصان في التالت و اعمل system وحل و اثبت ان C1 وC2 وC3", "tokens": [1829, 3555, 4587, 7578, 23758, 20193, 7251, 33604, 4117, 3215, 16472, 16095, 43586, 12334, 20328, 5016, 49429, 20193, 22807, 32239, 8592, 22807, 5296, 33456, 25124, 2288, 9566, 16472, 3224, 45164, 25961, 14407, 43586, 12334, 11933, 15730, 9673, 24401, 3215, 4724, 16254, 8608, 995, 45865, 4018, 44381, 18863, 4117, 3794, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 20328, 5016, 1829, 5016, 995, 7251, 3555, 4587, 7578, 11331, 4117, 995, 10632, 29538, 41950, 16572, 28671, 39894, 1863, 5172, 3615, 8592, 7251, 3555, 4587, 7578, 47525, 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"end": 1451.86, "word": " صح", "probability": 0.96142578125}, {"start": 1451.86, "end": 1452.1, "word": " ولا", "probability": 0.9619140625}, {"start": 1452.1, "end": 1452.62, "word": " لا؟", "probability": 0.702880859375}, {"start": 1452.62, "end": 1453.64, "word": " ليش؟", "probability": 0.82861328125}, {"start": 1453.64, "end": 1454.0, "word": " لأن", "probability": 0.823486328125}, {"start": 1454.0, "end": 1454.9, "word": " الشرط", "probability": 0.8543294270833334}, {"start": 1454.9, "end": 1455.26, "word": " انه", "probability": 0.4913330078125}, {"start": 1455.26, "end": 1455.4, "word": " لو", "probability": 0.96630859375}, {"start": 1455.4, "end": 1456.04, "word": " كانوا", "probability": 0.98291015625}, {"start": 1456.04, "end": 1456.46, "word": " linearly", "probability": 0.96435546875}, {"start": 1456.46, "end": 1457.3, "word": " dependent", "probability": 0.93115234375}, {"start": 1457.3, "end": 1457.58, "word": " إذا", "probability": 0.705810546875}, {"start": 1457.58, 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1464.58, "end": 1465.06, "word": " الطريقة", "probability": 0.9934895833333334}, {"start": 1465.06, "end": 1465.78, "word": " بتنفعش", "probability": 0.877978515625}, {"start": 1465.78, "end": 1466.32, "word": " يبقى", "probability": 0.93408203125}, {"start": 1466.32, "end": 1466.62, "word": " بدول", "probability": 0.550537109375}, {"start": 1466.62, "end": 1467.14, "word": " كونصان", "probability": 0.6458740234375}, {"start": 1467.14, "end": 1467.28, "word": " في", "probability": 0.89453125}, {"start": 1467.28, "end": 1467.66, "word": " الأول", "probability": 0.9404296875}, {"start": 1467.66, "end": 1467.82, "word": " و", "probability": 0.97607421875}, {"start": 1467.82, "end": 1468.28, "word": " كونصان", "probability": 0.8756103515625}, {"start": 1468.28, "end": 1468.46, "word": " في", "probability": 0.92041015625}, {"start": 1468.46, "end": 1468.76, "word": " التاني", "probability": 0.9334309895833334}, {"start": 1468.76, "end": 1468.88, "word": " و", "probability": 0.9892578125}, {"start": 1468.88, "end": 1469.28, "word": " كونصان", "probability": 0.979248046875}, {"start": 1469.28, "end": 1469.42, "word": " في", "probability": 0.9609375}, {"start": 1469.42, "end": 1469.8, "word": " التالت", "probability": 0.8424479166666666}, {"start": 1469.8, "end": 1469.98, "word": " و", "probability": 0.83740234375}, {"start": 1469.98, "end": 1470.42, "word": " اعمل", "probability": 0.779296875}, {"start": 1470.42, "end": 1471.28, "word": " system", "probability": 0.91064453125}, {"start": 1471.28, "end": 1472.44, "word": " وحل", "probability": 0.8086751302083334}, {"start": 1472.44, "end": 1472.66, "word": " و", "probability": 0.8984375}, {"start": 1472.66, "end": 1473.18, "word": " اثبت", "probability": 0.876953125}, {"start": 1473.18, "end": 1473.38, "word": " ان", "probability": 0.888671875}, {"start": 1473.38, "end": 1474.12, "word": " C1", "probability": 0.54571533203125}, {"start": 1474.12, "end": 1474.78, "word": " وC2", "probability": 0.8341471354166666}, {"start": 1474.78, "end": 1475.5, "word": " وC3", "probability": 0.9720052083333334}], "temperature": 1.0}, {"id": 67, "seek": 150136, "start": 1475.88, "end": 1501.36, "text": "مش كلهم أصفر و يمكن و لا واحد فيهم صفر تمام يبقى هنا بنانيجي نقول لك تشيرك that these vectors are linearly dependent ارايحك شوية بدل من تاخده تلاتة؟", "tokens": [2304, 8592, 28242, 16095, 5551, 9381, 5172, 2288, 4032, 7251, 43020, 4032, 20193, 36764, 24401, 8978, 16095, 20328, 5172, 2288, 46811, 10943, 7251, 3555, 4587, 7578, 34105, 4724, 1863, 7649, 1829, 7435, 1829, 8717, 39648, 5296, 4117, 6055, 8592, 13546, 4117, 300, 613, 18875, 366, 43586, 12334, 1975, 23557, 1829, 5016, 4117, 13412, 2407, 10632, 47525, 1211, 9154, 6055, 47283, 3215, 3224, 6055, 1211, 9307, 3660, 22807], "avg_logprob": -0.44646139705882354, "compression_ratio": 1.3488372093023255, "no_speech_prob": 0.0, "words": [{"start": 1475.88, "end": 1476.44, "word": "مش", "probability": 0.5504150390625}, {"start": 1476.44, "end": 1477.1, "word": " كلهم", "probability": 0.903076171875}, {"start": 1477.1, "end": 1477.64, "word": " أصفر", "probability": 0.78558349609375}, {"start": 1477.64, "end": 1477.78, "word": " و", "probability": 0.3564453125}, {"start": 1477.78, "end": 1478.08, "word": " يمكن", "probability": 0.60760498046875}, {"start": 1478.08, "end": 1478.2, "word": " و", "probability": 0.237060546875}, {"start": 1478.2, "end": 1478.28, "word": " لا", "probability": 0.94580078125}, {"start": 1478.28, "end": 1478.58, "word": " واحد", "probability": 0.978759765625}, {"start": 1478.58, "end": 1478.82, "word": " فيهم", "probability": 0.878662109375}, {"start": 1478.82, "end": 1479.24, "word": " صفر", "probability": 0.7859700520833334}, {"start": 1479.24, "end": 1480.52, "word": " تمام", "probability": 0.8447265625}, {"start": 1480.52, "end": 1481.56, "word": " يبقى", "probability": 0.89013671875}, {"start": 1481.56, "end": 1481.82, "word": " هنا", "probability": 0.955078125}, {"start": 1481.82, "end": 1482.56, "word": " بنانيجي", "probability": 0.44952392578125}, {"start": 1482.56, "end": 1482.78, "word": " نقول", "probability": 0.8271484375}, {"start": 1482.78, "end": 1483.0, "word": " لك", "probability": 0.642578125}, {"start": 1483.0, "end": 1485.68, "word": " تشيرك", "probability": 0.61676025390625}, {"start": 1485.68, "end": 1486.5, "word": " that", "probability": 0.437744140625}, {"start": 1486.5, "end": 1488.22, "word": " these", "probability": 0.67822265625}, {"start": 1488.22, "end": 1490.52, "word": " vectors", "probability": 0.9462890625}, {"start": 1490.52, "end": 1492.9, "word": " are", "probability": 0.93359375}, {"start": 1492.9, "end": 1495.02, "word": " linearly", "probability": 0.927734375}, {"start": 1495.02, "end": 1496.48, "word": " dependent", "probability": 0.8525390625}, {"start": 1496.48, "end": 1499.7, "word": " ارايحك", "probability": 0.579248046875}, {"start": 1499.7, "end": 1500.04, "word": " شوية", "probability": 0.8531901041666666}, {"start": 1500.04, "end": 1500.24, "word": " بدل", "probability": 0.4666748046875}, {"start": 1500.24, "end": 1500.32, "word": " من", "probability": 0.80029296875}, {"start": 1500.32, "end": 1500.74, "word": " تاخده", "probability": 0.5372314453125}, {"start": 1500.74, "end": 1501.36, "word": " تلاتة؟", "probability": 0.89677734375}], "temperature": 1.0}, {"id": 68, "seek": 152015, "start": 1502.01, "end": 1520.15, "text": "خد اتنين منهم و قول كنصا في الأول و كنصا في التاني و سويهم بالتالت وبالتالي بصير عندي system of non homogeneous differential equation من معادلتين وبالتالي صار عندي معادلتين في ثلاثة", "tokens": [9778, 3215, 1975, 2655, 1863, 9957, 9154, 16095, 4032, 12174, 12610, 9122, 1863, 9381, 995, 8978, 16247, 12610, 4032, 9122, 1863, 9381, 995, 8978, 16712, 7649, 1829, 4032, 8608, 45865, 16095, 20666, 2655, 6027, 2655, 46599, 6027, 2655, 6027, 1829, 4724, 9381, 13546, 18871, 16254, 1185, 295, 2107, 42632, 15756, 5367, 9154, 20449, 18513, 1211, 2655, 9957, 46599, 6027, 2655, 6027, 1829, 20328, 9640, 18871, 16254, 20449, 18513, 1211, 2655, 9957, 8978, 38637, 1211, 5718, 104, 3660], "avg_logprob": -0.20733173688252768, "compression_ratio": 1.6900584795321638, "no_speech_prob": 0.0, "words": [{"start": 1502.01, "end": 1502.39, "word": "خد", "probability": 0.410888671875}, {"start": 1502.39, "end": 1502.91, "word": " اتنين", "probability": 0.9132080078125}, {"start": 1502.91, "end": 1503.53, "word": " منهم", "probability": 0.927734375}, {"start": 1503.53, "end": 1504.17, "word": " و", "probability": 0.86865234375}, {"start": 1504.17, "end": 1504.35, "word": " قول", "probability": 0.5484619140625}, {"start": 1504.35, "end": 1504.95, "word": " كنصا", "probability": 0.37432861328125}, {"start": 1504.95, "end": 1505.11, "word": " في", "probability": 0.828125}, {"start": 1505.11, "end": 1505.39, "word": " الأول", "probability": 0.796142578125}, {"start": 1505.39, "end": 1505.51, "word": " و", "probability": 0.97216796875}, {"start": 1505.51, "end": 1505.93, "word": " كنصا", "probability": 0.9833984375}, {"start": 1505.93, "end": 1506.05, "word": " في", "probability": 0.89404296875}, {"start": 1506.05, "end": 1506.37, "word": " التاني", "probability": 0.81103515625}, {"start": 1506.37, "end": 1506.45, "word": " و", "probability": 0.708984375}, {"start": 1506.45, "end": 1506.99, "word": " سويهم", "probability": 0.7902018229166666}, {"start": 1506.99, "end": 1507.93, "word": " بالتالت", "probability": 0.9422607421875}, {"start": 1507.93, "end": 1509.19, "word": " وبالتالي", "probability": 0.88974609375}, {"start": 1509.19, "end": 1509.59, "word": " بصير", "probability": 0.9189453125}, {"start": 1509.59, "end": 1510.03, "word": " عندي", "probability": 0.768310546875}, {"start": 1510.03, "end": 1510.65, "word": " system", "probability": 0.81591796875}, {"start": 1510.65, "end": 1511.03, "word": " of", "probability": 0.9580078125}, {"start": 1511.03, "end": 1511.45, "word": " non", "probability": 0.94482421875}, {"start": 1511.45, "end": 1512.19, "word": " homogeneous", "probability": 0.6455078125}, {"start": 1512.19, "end": 1512.85, "word": " differential", "probability": 0.904296875}, {"start": 1512.85, "end": 1513.75, "word": " equation", "probability": 0.80615234375}, {"start": 1513.75, "end": 1514.89, "word": " من", "probability": 0.9794921875}, {"start": 1514.89, "end": 1515.97, "word": " معادلتين", "probability": 0.92421875}, {"start": 1515.97, "end": 1517.31, "word": " وبالتالي", "probability": 0.9103515625}, {"start": 1517.31, "end": 1517.69, "word": " صار", "probability": 0.939453125}, {"start": 1517.69, "end": 1518.05, "word": " عندي", "probability": 0.889892578125}, {"start": 1518.05, "end": 1518.97, "word": " معادلتين", "probability": 0.975}, {"start": 1518.97, "end": 1519.17, "word": " في", "probability": 0.94970703125}, {"start": 1519.17, "end": 1520.15, "word": " ثلاثة", "probability": 0.966015625}], "temperature": 1.0}, {"id": 69, "seek": 154506, "start": 1521.8, "end": 1545.06, "text": "مجاهيل، مظبوط، إذا هذي linearly dependent على طول القطر ما علينا، طيب احنا بقول تشكي بجه أي وسيلة تنشأتي لأ يعني انهم linearly dependent قد يكون و قد لا يكون بس لكن في حالة ان M تساوي M", "tokens": [2304, 7435, 40294, 26895, 12399, 3714, 19913, 3555, 2407, 9566, 12399, 11933, 15730, 8032, 8848, 1829, 43586, 12334, 15844, 23032, 12610, 25062, 9566, 2288, 19446, 25894, 8315, 12399, 23032, 1829, 3555, 1975, 5016, 8315, 4724, 39648, 6055, 8592, 4117, 1829, 4724, 7435, 3224, 36632, 46952, 26895, 3660, 6055, 1863, 8592, 10721, 31371, 5296, 10721, 37495, 22653, 16472, 16095, 43586, 12334, 12174, 3215, 7251, 30544, 4032, 12174, 3215, 20193, 7251, 30544, 4724, 3794, 44381, 8978, 11331, 6027, 3660, 16472, 376, 6055, 3794, 995, 45865, 376], "avg_logprob": -0.2961397100897396, "compression_ratio": 1.5309278350515463, "no_speech_prob": 0.0, "words": [{"start": 1521.8000000000002, "end": 1522.6000000000001, "word": "مجاهيل،", "probability": 0.8115234375}, {"start": 1522.6000000000001, "end": 1523.4, "word": " مظبوط،", "probability": 0.860595703125}, {"start": 1523.4, "end": 1523.62, "word": " إذا", "probability": 0.664794921875}, {"start": 1523.62, "end": 1524.02, "word": " هذي", "probability": 0.4828287760416667}, {"start": 1524.02, "end": 1524.52, "word": " linearly", "probability": 0.8837890625}, {"start": 1524.52, "end": 1525.74, "word": " dependent", "probability": 0.49365234375}, {"start": 1525.74, "end": 1527.28, "word": " على", "probability": 0.60400390625}, {"start": 1527.28, "end": 1527.6, "word": " طول", "probability": 0.996826171875}, {"start": 1527.6, "end": 1528.24, "word": " القطر", "probability": 0.46044921875}, {"start": 1528.24, "end": 1528.66, "word": " ما", "probability": 0.72509765625}, {"start": 1528.66, "end": 1529.28, "word": " علينا،", "probability": 0.69775390625}, {"start": 1529.28, "end": 1529.62, "word": " طيب", "probability": 0.9622395833333334}, {"start": 1529.62, "end": 1530.12, "word": " احنا", "probability": 0.8343098958333334}, {"start": 1530.12, "end": 1530.36, "word": " بقول", "probability": 0.696533203125}, {"start": 1530.36, "end": 1530.96, "word": " تشكي", "probability": 0.8284912109375}, {"start": 1530.96, "end": 1531.28, "word": " بجه", "probability": 0.7117513020833334}, {"start": 1531.28, "end": 1531.5, "word": " أي", "probability": 0.52197265625}, {"start": 1531.5, "end": 1532.02, "word": " وسيلة", "probability": 0.9817708333333334}, {"start": 1532.02, "end": 1532.56, "word": " تنشأتي", "probability": 0.776220703125}, {"start": 1532.56, "end": 1538.88, "word": " لأ", "probability": 0.5126953125}, {"start": 1538.88, "end": 1539.28, "word": " يعني", "probability": 0.762939453125}, {"start": 1539.28, "end": 1539.54, "word": " انهم", "probability": 0.670166015625}, {"start": 1539.54, "end": 1539.94, "word": " linearly", "probability": 0.9580078125}, {"start": 1539.94, "end": 1540.66, "word": " dependent", "probability": 0.89794921875}, {"start": 1540.66, "end": 1541.08, "word": " قد", "probability": 0.91259765625}, {"start": 1541.08, "end": 1541.76, "word": " يكون", 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1918.28, "word": " a", "probability": 0.80029296875}, {"start": 1918.28, "end": 1918.94, "word": " linearly", "probability": 0.93603515625}, {"start": 1918.94, "end": 1920.26, "word": " independent", "probability": 0.93115234375}, {"start": 1920.26, "end": 1920.8, "word": " set", "probability": 0.96875}, {"start": 1920.8, "end": 1921.48, "word": " in", "probability": 0.6435546875}, {"start": 1921.48, "end": 1922.96, "word": " R2", "probability": 0.75146484375}], "temperature": 1.0}, {"id": 86, "seek": 194427, "start": 1924.19, "end": 1944.27, "text": "يبقى هذه false ليش؟ لأنه عدد العناصر اللي أخدها أكتر من عدد العناصر في ال basis تبع R2 ال R2 ال basis تبع يتكون من عنصرين هدول linearly independent لو أضفت عليهم كمان عنصر بصيروا linearly", "tokens": [1829, 3555, 4587, 7578, 29538, 7908, 32239, 8592, 22807, 5296, 33456, 3224, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 13672, 1829, 5551, 9778, 3215, 11296, 5551, 4117, 2655, 2288, 9154, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 8978, 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1928.05, "end": 1928.23, "word": " اللي", "probability": 0.837890625}, {"start": 1928.23, "end": 1928.83, "word": " أخدها", "probability": 0.83056640625}, {"start": 1928.83, "end": 1929.95, "word": " أكتر", "probability": 0.83197021484375}, {"start": 1929.95, "end": 1930.17, "word": " من", "probability": 0.9931640625}, {"start": 1930.17, "end": 1930.63, "word": " عدد", "probability": 0.9920247395833334}, {"start": 1930.63, "end": 1931.47, "word": " العناصر", "probability": 0.956787109375}, {"start": 1931.47, "end": 1931.63, "word": " في", "probability": 0.92919921875}, {"start": 1931.63, "end": 1931.77, "word": " ال", "probability": 0.97021484375}, {"start": 1931.77, "end": 1932.13, "word": " basis", "probability": 0.81396484375}, {"start": 1932.13, "end": 1932.57, "word": " تبع", "probability": 0.9278971354166666}, {"start": 1932.57, "end": 1933.27, "word": " R2", "probability": 0.86279296875}, {"start": 1933.27, "end": 1934.29, "word": " ال", "probability": 0.76953125}, {"start": 1934.29, "end": 1935.69, "word": " R2", "probability": 0.681640625}, {"start": 1935.69, "end": 1936.09, "word": " ال", "probability": 0.9365234375}, {"start": 1936.09, "end": 1936.35, "word": " basis", "probability": 0.6298828125}, {"start": 1936.35, "end": 1936.73, "word": " تبع", "probability": 0.8582356770833334}, {"start": 1936.73, "end": 1937.43, "word": " يتكون", "probability": 0.7644856770833334}, {"start": 1937.43, "end": 1937.77, "word": " من", "probability": 0.98095703125}, {"start": 1937.77, "end": 1938.79, "word": " عنصرين", "probability": 0.9383544921875}, {"start": 1938.79, "end": 1939.31, "word": " هدول", "probability": 0.8121744791666666}, {"start": 1939.31, "end": 1939.93, "word": " linearly", "probability": 0.93115234375}, {"start": 1939.93, "end": 1940.51, "word": " independent", "probability": 0.9287109375}, {"start": 1940.51, "end": 1940.81, "word": " لو", "probability": 0.767578125}, {"start": 1940.81, "end": 1941.51, "word": " أضفت", "probability": 0.95849609375}, {"start": 1941.51, "end": 1942.19, "word": " عليهم", "probability": 0.99169921875}, {"start": 1942.19, "end": 1942.95, "word": " كمان", "probability": 0.9422200520833334}, {"start": 1942.95, "end": 1943.33, "word": " عنصر", "probability": 0.9908854166666666}, {"start": 1943.33, "end": 1943.79, "word": " بصيروا", "probability": 0.8746337890625}, {"start": 1943.79, "end": 1944.27, "word": " linearly", "probability": 0.947265625}], "temperature": 1.0}, {"id": 87, "seek": 196426, "start": 1945.2, "end": 1964.26, "text": "يبقى أي مجموعة من العناصر أخدنا نظري عددها ان كانوا linearly independent لو أضفت عليهم كمان عنصر بصيروا ماله linearly dependent إذا هذه العبارة رقم أربعة wrong، false، مش صحيحة", "tokens": [1829, 3555, 4587, 7578, 36632, 3714, 7435, 2304, 2407, 27884, 9154, 18863, 1863, 33546, 2288, 5551, 9778, 3215, 8315, 8717, 19913, 16572, 6225, 3215, 3215, 11296, 16472, 25961, 14407, 43586, 6695, 45164, 5551, 11242, 5172, 2655, 25894, 16095, 9122, 2304, 7649, 18871, 9381, 2288, 4724, 9381, 13546, 14407, 3714, 6027, 3224, 43586, 12334, 11933, 15730, 29538, 18863, 3555, 9640, 3660, 12602, 4587, 2304, 5551, 25513, 27884, 2085, 12399, 7908, 12399, 37893, 20328, 5016, 1829, 5016, 3660], "avg_logprob": -0.20251624073301042, "compression_ratio": 1.4656084656084656, "no_speech_prob": 0.0, "words": [{"start": 1945.2, "end": 1945.72, "word": "يبقى", "probability": 0.84820556640625}, {"start": 1945.72, "end": 1946.06, "word": " أي", "probability": 0.57275390625}, {"start": 1946.06, "end": 1946.72, "word": " مجموعة", "probability": 0.951953125}, {"start": 1946.72, "end": 1946.88, "word": " من", "probability": 0.97802734375}, {"start": 1946.88, "end": 1947.46, "word": " العناصر", "probability": 0.9835205078125}, {"start": 1947.46, "end": 1948.06, "word": " أخدنا", "probability": 0.912353515625}, {"start": 1948.06, "end": 1948.68, "word": " نظري", "probability": 0.9265950520833334}, {"start": 1948.68, "end": 1949.58, "word": " عددها", "probability": 0.81756591796875}, {"start": 1949.58, "end": 1950.08, "word": " ان", "probability": 0.356689453125}, {"start": 1950.08, "end": 1950.9, "word": " كانوا", "probability": 0.94921875}, {"start": 1950.9, "end": 1951.48, "word": " linearly", "probability": 0.9365234375}, {"start": 1951.48, "end": 1952.8, "word": " independent", "probability": 0.9609375}, {"start": 1952.8, "end": 1953.6, "word": " لو", "probability": 0.61865234375}, {"start": 1953.6, "end": 1954.16, "word": " أضفت", "probability": 0.900390625}, {"start": 1954.16, "end": 1954.56, "word": " عليهم", "probability": 0.9873046875}, {"start": 1954.56, "end": 1954.92, "word": " كمان", "probability": 0.8346354166666666}, {"start": 1954.92, "end": 1955.26, "word": " عنصر", "probability": 0.9055989583333334}, {"start": 1955.26, "end": 1955.72, "word": " بصيروا", "probability": 0.8299560546875}, {"start": 1955.72, "end": 1956.1, "word": " ماله", "probability": 0.7762044270833334}, {"start": 1956.1, "end": 1956.88, "word": " linearly", "probability": 0.9150390625}, {"start": 1956.88, "end": 1958.16, "word": " dependent", "probability": 0.89306640625}, {"start": 1958.16, "end": 1958.6, "word": " إذا", "probability": 0.536865234375}, {"start": 1958.6, "end": 1959.08, "word": " هذه", "probability": 0.84716796875}, {"start": 1959.08, "end": 1959.62, "word": " العبارة", "probability": 0.85986328125}, {"start": 1959.62, "end": 1960.08, "word": " رقم", "probability": 0.9825846354166666}, {"start": 1960.08, "end": 1960.8, "word": " أربعة", "probability": 0.7107747395833334}, {"start": 1960.8, "end": 1961.96, "word": " wrong،", "probability": 0.3311767578125}, {"start": 1961.96, "end": 1963.44, "word": " false،", "probability": 0.66259765625}, {"start": 1963.44, "end": 1963.62, "word": " مش", "probability": 0.962890625}, {"start": 1963.62, "end": 1964.26, "word": " صحيحة", "probability": 0.959765625}], "temperature": 1.0}, {"id": 88, "seek": 199255, "start": 1965.51, "end": 1992.55, "text": "بنجي لنقطة رقم ستة بيقول if a is an n by n matrix and k is a non zero real number then ال determinant لكي في a بده يساوي الكي في determinant ل a ايش رايكوا في هذه؟ مش مظبوطة؟ كي و أس ان بيغيريها وليها ايش رايكوا بالعبارة هذه؟", "tokens": [3555, 1863, 7435, 1829, 5296, 1863, 47432, 3660, 12602, 4587, 2304, 8608, 2655, 3660, 4724, 1829, 39648, 498, 257, 307, 364, 297, 538, 297, 8141, 293, 350, 307, 257, 2107, 4018, 957, 1230, 550, 2423, 41296, 5296, 4117, 1829, 8978, 257, 47525, 3224, 7251, 3794, 995, 45865, 33251, 1829, 8978, 41296, 5296, 257, 1975, 1829, 8592, 12602, 47302, 4117, 14407, 8978, 29538, 22807, 37893, 3714, 19913, 3555, 2407, 9566, 3660, 22807, 9122, 1829, 4032, 5551, 3794, 16472, 4724, 1829, 17082, 13546, 1829, 11296, 4032, 20292, 11296, 1975, 1829, 8592, 12602, 47302, 4117, 14407, 20666, 3615, 3555, 9640, 3660, 29538, 22807], "avg_logprob": -0.3796411032723908, "compression_ratio": 1.5885167464114833, "no_speech_prob": 0.0, "words": [{"start": 1965.51, "end": 1966.05, "word": "بنجي", "probability": 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0.6180013020833334}, {"start": 1976.57, "end": 1976.89, "word": " في", "probability": 0.7578125}, {"start": 1976.89, "end": 1977.41, "word": " a", "probability": 0.440673828125}, {"start": 1977.41, "end": 1978.25, "word": " بده", "probability": 0.365234375}, {"start": 1978.25, "end": 1979.21, "word": " يساوي", "probability": 0.956787109375}, {"start": 1979.21, "end": 1980.13, "word": " الكي", "probability": 0.640380859375}, {"start": 1980.13, "end": 1980.23, "word": " في", "probability": 0.90478515625}, {"start": 1980.23, "end": 1981.07, "word": " determinant", "probability": 0.330078125}, {"start": 1981.07, "end": 1981.51, "word": " ل", "probability": 0.7734375}, {"start": 1981.51, "end": 1981.93, "word": " a", "probability": 0.489013671875}, {"start": 1981.93, "end": 1983.09, "word": " ايش", "probability": 0.6923828125}, {"start": 1983.09, "end": 1983.51, "word": " رايكوا", "probability": 0.805908203125}, {"start": 1983.51, "end": 1983.63, "word": " في", "probability": 0.90625}, {"start": 1983.63, "end": 1984.41, "word": " هذه؟", "probability": 0.51953125}, {"start": 1984.41, "end": 1984.77, "word": " مش", "probability": 0.5400390625}, {"start": 1984.77, "end": 1986.51, "word": " مظبوطة؟", "probability": 0.8859514508928571}, {"start": 1986.51, "end": 1986.81, "word": " كي", "probability": 0.6590576171875}, {"start": 1986.81, "end": 1986.89, "word": " و", "probability": 0.3984375}, {"start": 1986.89, "end": 1987.11, "word": " أس", "probability": 0.61376953125}, {"start": 1987.11, "end": 1987.37, "word": " ان", "probability": 0.28369140625}, {"start": 1987.37, "end": 1988.49, "word": " بيغيريها", "probability": 0.4980061848958333}, {"start": 1988.49, "end": 1989.01, "word": " وليها", "probability": 0.5380045572916666}, {"start": 1989.01, "end": 1991.31, "word": " ايش", "probability": 0.8694661458333334}, {"start": 1991.31, "end": 1991.59, "word": " رايكوا", "probability": 0.9613037109375}, {"start": 1991.59, "end": 1992.09, "word": " بالعبارة", "probability": 0.928515625}, {"start": 1992.09, "end": 1992.55, "word": " هذه؟", "probability": 0.8310546875}], "temperature": 1.0}, {"id": 89, "seek": 201822, "start": 1993.88, "end": 2018.22, "text": "خلّيني أذكركم لإجابة الصحية لما نضرب عنصر في مصفوفة خلّي بالك هنا لما نضرب عنصر في مصفوفة، فنضربه في جميع أناصر المصفوفة لكن لو ضربنا عنصر فيه محدد، فنضربه في الصف أو في عمود تمام؟ المصفوفة هذه نظامها N في N", "tokens": [9778, 1211, 11703, 9957, 1829, 5551, 8848, 37983, 24793, 5296, 28814, 7435, 16758, 3660, 31767, 5016, 10632, 5296, 15042, 8717, 11242, 25513, 18871, 9381, 2288, 8978, 3714, 9381, 5172, 38688, 3660, 16490, 1211, 11703, 1829, 20666, 4117, 34105, 5296, 15042, 8717, 11242, 25513, 18871, 9381, 2288, 8978, 3714, 9381, 5172, 38688, 3660, 12399, 6156, 1863, 11242, 25513, 3224, 8978, 10874, 2304, 40228, 14739, 33546, 2288, 9673, 9381, 5172, 38688, 3660, 44381, 45164, 48812, 25513, 8315, 18871, 9381, 2288, 8978, 3224, 3714, 24401, 3215, 12399, 6156, 1863, 11242, 25513, 3224, 8978, 31767, 5172, 34051, 8978, 6225, 2304, 23328, 46811, 10943, 22807, 9673, 9381, 5172, 38688, 3660, 29538, 8717, 19913, 10943, 11296, 426, 8978, 426], "avg_logprob": -0.18462170908848444, "compression_ratio": 2.043956043956044, "no_speech_prob": 0.0, "words": [{"start": 1993.88, "end": 1994.38, "word": "خلّيني", "probability": 0.801904296875}, {"start": 1994.38, "end": 1995.02, "word": " أذكركم", "probability": 0.909912109375}, {"start": 1995.02, "end": 1995.78, "word": " لإجابة", "probability": 0.63974609375}, {"start": 1995.78, "end": 1996.38, "word": " الصحية", "probability": 0.9051106770833334}, {"start": 1996.38, "end": 1998.02, "word": " لما", "probability": 0.575927734375}, {"start": 1998.02, "end": 1998.48, "word": " نضرب", "probability": 0.9474283854166666}, {"start": 1998.48, "end": 1999.14, "word": " عنصر", "probability": 0.94091796875}, {"start": 1999.14, "end": 1999.38, "word": " في", "probability": 0.94189453125}, {"start": 1999.38, "end": 2000.54, "word": " مصفوفة", "probability": 0.89404296875}, {"start": 2000.54, "end": 2001.06, "word": " خلّي", "probability": 0.67620849609375}, {"start": 2001.06, "end": 2001.4, "word": " بالك", "probability": 0.747802734375}, {"start": 2001.4, "end": 2001.7, "word": " هنا", "probability": 0.94384765625}, {"start": 2001.7, "end": 2002.38, "word": " لما", "probability": 0.871337890625}, {"start": 2002.38, "end": 2002.76, "word": " نضرب", "probability": 0.9910481770833334}, {"start": 2002.76, "end": 2003.24, "word": " عنصر", "probability": 0.9933268229166666}, {"start": 2003.24, "end": 2003.4, "word": " في", "probability": 0.98193359375}, {"start": 2003.4, "end": 2004.04, "word": " مصفوفة،", "probability": 0.8486735026041666}, {"start": 2004.04, "end": 2004.44, "word": " فنضربه", "probability": 0.776708984375}, {"start": 2004.44, "end": 2004.54, "word": " في", "probability": 0.96630859375}, {"start": 2004.54, "end": 2005.32, "word": " جميع", "probability": 0.9952799479166666}, {"start": 2005.32, "end": 2006.0, "word": " أناصر", "probability": 0.7390950520833334}, {"start": 2006.0, "end": 2006.82, "word": " المصفوفة", "probability": 0.98681640625}, {"start": 2006.82, "end": 2007.56, "word": " لكن", "probability": 0.796875}, {"start": 2007.56, "end": 2007.82, "word": " لو", "probability": 0.91796875}, {"start": 2007.82, "end": 2008.3, "word": " ضربنا", "probability": 0.982421875}, {"start": 2008.3, "end": 2008.76, "word": " عنصر", "probability": 0.9920247395833334}, {"start": 2008.76, "end": 2009.08, "word": " فيه", "probability": 0.86669921875}, {"start": 2009.08, "end": 2010.3, "word": " محدد،", "probability": 0.9639892578125}, {"start": 2010.3, "end": 2010.98, "word": " فنضربه", "probability": 0.88408203125}, {"start": 2010.98, "end": 2011.3, "word": " في", "probability": 0.63671875}, {"start": 2011.3, "end": 2012.18, "word": " الصف", "probability": 0.8076171875}, {"start": 2012.18, "end": 2012.48, "word": " أو", "probability": 0.6123046875}, {"start": 2012.48, "end": 2013.1, "word": " في", "probability": 0.92333984375}, {"start": 2013.1, "end": 2014.1, "word": " عمود", "probability": 0.9583333333333334}, {"start": 2014.1, "end": 2015.52, "word": " تمام؟", "probability": 0.6961263020833334}, {"start": 2015.52, "end": 2016.12, "word": " المصفوفة", "probability": 0.95849609375}, {"start": 2016.12, "end": 2016.32, "word": " هذه", "probability": 0.60107421875}, {"start": 2016.32, "end": 2016.96, "word": " نظامها", "probability": 0.9774169921875}, {"start": 2016.96, "end": 2017.3, "word": " N", "probability": 0.2802734375}, {"start": 2017.3, "end": 2017.68, "word": " في", "probability": 0.89501953125}, {"start": 2017.68, "end": 2018.22, "word": " N", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 90, "seek": 204550, "start": 2018.6, "end": 2045.5, "text": "يبقى الصحيح أن الـ determinant للـ K في A يكون K أس N في الـ determinant لمام إلى K يبقى هذا العبارة عبارة خاطئة فالس النقطة السابعة بيقول فالـ A is invertible matrix then ال determinant للـ A transpose يسوى ال determinant للـ A inverse transpose", "tokens": [1829, 3555, 4587, 7578, 31767, 5016, 1829, 5016, 14739, 2423, 39184, 41296, 24976, 39184, 591, 8978, 316, 7251, 30544, 591, 5551, 3794, 426, 8978, 2423, 39184, 41296, 32767, 10943, 30731, 591, 7251, 3555, 4587, 7578, 23758, 18863, 3555, 9640, 3660, 6225, 3555, 9640, 3660, 16490, 41193, 19986, 3660, 6156, 6027, 3794, 28239, 47432, 3660, 21136, 16758, 27884, 4724, 1829, 39648, 6156, 6027, 39184, 316, 307, 33966, 964, 8141, 550, 2423, 41296, 24976, 39184, 316, 25167, 7251, 3794, 2407, 7578, 2423, 41296, 24976, 39184, 316, 17340, 25167], "avg_logprob": -0.35811781746217575, "compression_ratio": 1.7313432835820894, "no_speech_prob": 0.0, "words": [{"start": 2018.6, "end": 2019.24, "word": "يبقى", "probability": 0.81884765625}, {"start": 2019.24, "end": 2019.88, "word": " الصحيح", "probability": 0.851318359375}, {"start": 2019.88, "end": 2020.02, "word": " أن", "probability": 0.3232421875}, {"start": 2020.02, "end": 2020.18, "word": " الـ", "probability": 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"probability": 0.7667236328125}, {"start": 2041.3, "end": 2041.4, "word": " ال", "probability": 0.7236328125}, {"start": 2041.4, "end": 2042.02, "word": " determinant", "probability": 0.79443359375}, {"start": 2042.02, "end": 2042.82, "word": " للـ", "probability": 0.812744140625}, {"start": 2042.82, "end": 2043.24, "word": " A", "probability": 0.9697265625}, {"start": 2043.24, "end": 2044.3, "word": " inverse", "probability": 0.84326171875}, {"start": 2044.3, "end": 2045.5, "word": " transpose", "probability": 0.8125}], "temperature": 1.0}, {"id": 91, "seek": 205112, "start": 2049.96, "end": 2051.12, "text": "بعد شوية المفروض غلط", "tokens": [3555, 22488, 13412, 2407, 10632, 9673, 5172, 32887, 11242, 32771, 1211, 9566], "avg_logprob": -0.3230168360930223, "compression_ratio": 0.7708333333333334, "no_speech_prob": 0.0, "words": [{"start": 2049.96, "end": 2050.08, "word": "بعد", "probability": 0.50885009765625}, {"start": 2050.08, "end": 2050.28, "word": " شوية", "probability": 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ال A inverse بدي ساوي مصوفة الواحدة", "tokens": [7435, 1211, 2423, 316, 33966, 964, 8141, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 2423, 316, 17340, 20449, 4117, 2407, 11622, 316, 3714, 10943, 2514, 37495, 22653, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 2423, 316, 8978, 2423, 316, 17340, 4724, 16254, 8608, 995, 45865, 3714, 9381, 38688, 3660, 2423, 14407, 24401, 3660], "avg_logprob": -0.341831131985313, "compression_ratio": 1.4326241134751774, "no_speech_prob": 0.0, "words": [{"start": 2081.49, "end": 2082.47, "word": "جل", "probability": 0.31494140625}, {"start": 2082.47, "end": 2082.69, "word": " ال", "probability": 0.64013671875}, {"start": 2082.69, "end": 2082.91, "word": " A", "probability": 0.52001953125}, {"start": 2082.91, "end": 2083.77, "word": " invertible", "probability": 0.5123291015625}, {"start": 2083.77, "end": 2084.55, "word": " matrix", "probability": 0.92431640625}, {"start": 2084.55, "end": 2085.41, "word": " مظبوط", "probability": 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"end": 2119.08, "text": "بدنا ندخل الـ Transpose لأن في السؤال جال الـ A determinant للـ A Transpose والـ determinant للـ A inverse Transpose إذا بناءً عليه لو روحت أنا أخدتلي ال Transpose للطرفين بصير ال A في ال A inverse Transpose يسوى مصفوفة الوحدة Transpose", "tokens": [3555, 3215, 8315, 8717, 3215, 9778, 1211, 2423, 39184, 6531, 43501, 5296, 33456, 8978, 21136, 33604, 6027, 10874, 6027, 2423, 39184, 316, 41296, 24976, 39184, 316, 6531, 43501, 16070, 39184, 41296, 24976, 39184, 316, 17340, 6531, 43501, 11933, 15730, 44945, 16606, 14111, 47356, 45164, 12602, 2407, 33753, 41850, 5551, 9778, 3215, 2655, 20292, 2423, 6531, 43501, 24976, 9566, 28480, 9957, 4724, 9381, 13546, 2423, 316, 8978, 2423, 316, 17340, 6531, 43501, 7251, 3794, 2407, 7578, 3714, 9381, 5172, 38688, 3660, 2423, 2407, 24401, 3660, 6531, 43501], "avg_logprob": -0.31932472497567366, "compression_ratio": 1.768421052631579, "no_speech_prob": 0.0, "words": [{"start": 2097.12, "end": 2097.58, "word": "بدنا", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a224f5f9efd756b616483366da98d91ae6c0a399
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_postprocess.srt
@@ -0,0 +1,1712 @@
+1
+00:00:19,670 --> 00:00:24,650
+بسم الله الرحمن الرحيم بنرجع لإكمال ال section
+
+2
+00:00:24,650 --> 00:00:30,670
+الماضي وهو ال cofactors وعرفنا المرة اللي فاتت ال
+
+3
+00:00:30,670 --> 00:00:34,670
+minor و ال cofactor قولنا ال minor هو المحدد
+
+4
+00:00:34,670 --> 00:00:41,930
+الأصغر المناظر لأنصر من عناصر مصحوفة ماوهو المحدد
+
+5
+00:00:41,930 --> 00:00:46,770
+الناتج من sub matrix بعد ما نشطب الصف اللى موجود
+
+6
+00:00:46,770 --> 00:00:51,970
+فيه هذا العنصر و العمود اللى موجود فيه هذا العنصر
+
+7
+00:00:51,970 --> 00:00:57,290
+الباقي بنسميه محدد الأصغر المناظر لهذا العنصر يبقى
+
+8
+00:00:57,290 --> 00:01:02,630
+هذا ال minor ال cofactor هو ال minor نفسه بس بنطبق
+
+9
+00:01:02,630 --> 00:01:08,580
+عليه قاعدة الإشاراتمنحط قبله سالب واحد ومنرفعها
+
+10
+00:01:08,580 --> 00:01:14,240
+للأس رقم الصف اللي موجود في هذا العنصر ورقم العمود
+
+11
+00:01:14,240 --> 00:01:18,660
+فإن كان هذا المجموع زوجي تبقى الإشارة موجب وإن كان
+
+12
+00:01:18,660 --> 00:01:23,360
+المجموع فردي بتكون الإشارة سالبة وهذا ما تحدثنا به
+
+13
+00:01:23,360 --> 00:01:29,840
+وعطينا عليه مثلا في المرة الماضيةالان بنكمل على ما
+
+14
+00:01:29,840 --> 00:01:33,760
+أخدناه في المرة الماضية و بنعطي النظرية التالية
+
+15
+00:01:33,760 --> 00:01:39,400
+النظرية هذه تتكون من نقطتهم النقطة الأولى كيف
+
+16
+00:01:39,400 --> 00:01:44,880
+بنحسب قيمة المحدد عدديا النقطة الثانية هو اكتشف
+
+17
+00:01:44,880 --> 00:01:50,340
+ممكن نطلع قيمة لمحدد ما هو هذه القيمة تساوي صفر
+
+18
+00:01:50,900 --> 00:01:54,160
+الأن لو جينا للنقطة الأولى بيقول if each element
+
+19
+00:01:54,160 --> 00:01:59,440
+in any row أو column of an n by n matrix A is
+
+20
+00:01:59,440 --> 00:02:04,040
+multiplied by X by its factor then their sum is
+
+21
+00:02:04,040 --> 00:02:09,790
+equal to determinant Aيعني لو بدنا نجيب محدد
+
+22
+00:02:09,790 --> 00:02:17,090
+المصفوف A المربع لنظام N في M بدنا نعمل ما يأتي
+
+23
+00:02:17,090 --> 00:02:24,830
+بدنا نمسك كل عنصر من عناصر أي صفرأو أي عمود ونضرب
+
+24
+00:02:24,830 --> 00:02:29,990
+كل عنصر من هذه العناصر في الـ cofactor المناظر لهو
+
+25
+00:02:29,990 --> 00:02:36,330
+نجمع المجموع هذا بيطلعني قيمة المحدد وهذا ليس
+
+26
+00:02:36,330 --> 00:02:40,150
+بجديد عليكم نفس الكلام اللي أخدناه في الثانوية
+
+27
+00:02:40,150 --> 00:02:45,850
+العامة طيب نجي للمرة اتنيننمر اتنين بيقول ليش؟ لو
+
+28
+00:02:45,850 --> 00:02:51,470
+كان كل عنصر في أي صفر I أو عمود J، أي عنصر من عنصر
+
+29
+00:02:51,470 --> 00:02:55,670
+أي صفر أو أي عمود، is multiplied by the factor of
+
+30
+00:02:55,670 --> 00:03:01,590
+another row K أو قلم L، بحيث الـK لا تساوي الـI
+
+31
+00:03:01,590 --> 00:03:05,850
+والـL لا تساوي الـJ، then the sum equals zero، إيش
+
+32
+00:03:05,850 --> 00:03:11,230
+يعني؟أحنا بنقول في النقطة الأولى لو جيت على صف
+
+33
+00:03:11,230 --> 00:03:15,910
+ضربت كل عنصر في الـ cofactor تبعه جمعة بيطلع لقيمة
+
+34
+00:03:15,910 --> 00:03:20,750
+المحدد هنا بقول لو جيت على عنصر صف أو أي عمود
+
+35
+00:03:20,750 --> 00:03:27,270
+وضربت في الـ cofactor المناظر لصف اخر او لعمود اخر
+
+36
+00:03:27,270 --> 00:03:32,630
+فالنتج يساوي Zero على طول الخط يعني هل قيمة المحدد
+
+37
+00:03:32,630 --> 00:03:37,880
+تساوي Zero؟لأ النقطة الأولى صحيح بتجيب لقيمة
+
+38
+00:03:37,880 --> 00:03:40,380
+المحدد بس النقطة التانية بتجيبش لقيمة المحدد
+
+39
+00:03:40,380 --> 00:03:44,660
+بتقولك كيف بتطلع القيمة zero بقولك مامسك أي صف
+
+40
+00:03:44,660 --> 00:03:48,580
+باجي الصف اللي جابله و الصف اللي بعده او اللي بعدي
+
+41
+00:03:48,580 --> 00:03:52,300
+بعده اللي بده هي المهم صف موازن له
+
+42
+00:04:01,360 --> 00:04:05,920
+الكلام اللى بنقوله بدنا نروح نبينه كعمليا فاخدنا
+
+43
+00:04:05,920 --> 00:04:11,260
+المثال التانيمعطيني المصوفة وقال هاتلي determinant
+
+44
+00:04:11,260 --> 00:04:17,460
+لإيه طبعا بدي أروح أفك هذه المصوفة باستخدام عناصر
+
+45
+00:04:17,460 --> 00:04:22,520
+أي صف أو أي عمود منها قال لي هنا that is for the I
+
+46
+00:04:22,520 --> 00:04:26,660
+throw يعني لو بدي أجيب قيمة المحدد باستخدام الصف
+
+47
+00:04:26,660 --> 00:04:34,220
+رقم I يبقى باجي بقول ايه I one في من؟ في المحدد في
+
+48
+00:04:34,220 --> 00:04:39,250
+ال my في ال cofactor تبعهزائد AI2 في الـ cofactor
+
+49
+00:04:39,250 --> 00:04:43,250
+تبعه زائد زائد لغاية مصر لغاية AIN في الـ cofactor
+
+50
+00:04:43,250 --> 00:04:47,990
+تبعه أجمع بتعطيني قيمة المحدد لكن لو بدأ فك
+
+51
+00:04:47,990 --> 00:04:52,830
+باستخدام العمود يبقى نفس النتيجة هتعطيني لأنت تغير
+
+52
+00:04:52,830 --> 00:04:59,140
+لأن المحدد له قيمة واحدة فقط لغيرأذا أردت أن أفكر
+
+53
+00:04:59,140 --> 00:05:01,300
+باستخدام العمود رقم ج
+
+54
+00:05:28,250 --> 00:05:33,450
+خلّينا مع النقطة الأولى اللى هى رقم ايه يبقى رقم
+
+55
+00:05:33,450 --> 00:05:39,070
+ايه انا بدى determined للمصفوفة
+
+56
+00:05:39,070 --> 00:05:43,210
+ايه بدى جداش قيمة محدد المصفوفة يعنى هي عندكوا
+
+57
+00:05:43,210 --> 00:05:47,750
+طالع صحوف اختارولى الصف انفك المحدد باستخدام هذا
+
+58
+00:05:47,750 --> 00:05:53,140
+الصف ايهتانى طبعا التانى لإنه فيه zero وبالتالي
+
+59
+00:05:53,140 --> 00:05:57,220
+بيبسط لعملية من عملية الشغل إذا بالدالي للصف
+
+60
+00:05:57,220 --> 00:06:02,800
+التانى الصف التانى لحد العنصر الأول قداش هاي ناقص
+
+61
+00:06:02,800 --> 00:06:08,080
+واحد جلبته ضروف مين في ال cofactor تبعه ال
+
+62
+00:06:08,080 --> 00:06:13,120
+cofactor تبعه بروح بقول هاي ناقص واحد هذا جاي في
+
+63
+00:06:13,120 --> 00:06:19,140
+أي صفرفي الصف الثاني والعمود الأول يبقى بقول أس
+
+64
+00:06:19,140 --> 00:06:25,000
+اتنين زائد واحد في المحدد الأصغر المناظر له نشطة
+
+65
+00:06:25,000 --> 00:06:30,380
+بصفه وعموده بضالة تلاتة ناقص اتنين تلاتة ناقص
+
+66
+00:06:30,380 --> 00:06:36,410
+اتنين و هنا ناقص واحد تلاتة بالشكل اللي عندهاالعدل
+
+67
+00:06:36,410 --> 00:06:42,190
+اللي بعده زائد اللي هو لإتنين في سالب واحد قصر هذا
+
+68
+00:06:42,190 --> 00:06:46,990
+جاي لإتنين في الصف الثاني و العمود الثاني إذا باجي
+
+69
+00:06:46,990 --> 00:06:52,130
+بقول هنا اتنين زائد اتنين في المحدد الأصغر المناظر
+
+70
+00:06:52,130 --> 00:06:57,110
+له بنشتغل صفه و عموده و بيظل اربعة سالب اتنين و
+
+71
+00:06:57,110 --> 00:07:04,020
+هنا واحد و هنا تلاتة زائداللي هو Zero في مين؟ في
+
+72
+00:07:04,020 --> 00:07:11,180
+سالب واحد مرفوع للأس اتنين زائد تلاتة في المحدد
+
+73
+00:07:11,180 --> 00:07:16,600
+الأصغر مضى نشطه بصفه و عموده بيصير أربع ثلاثة وهنا
+
+74
+00:07:16,600 --> 00:07:22,170
+واحد وهنا سالب واحدديجي نطلع النتيجة هذه جداش
+
+75
+00:07:22,170 --> 00:07:27,590
+وتساوي طبعا سالب واحد تكييب اللي هو جداش سالب واحد
+
+76
+00:07:27,590 --> 00:07:31,950
+في سالب واحد موجة بواحد مع السلمة تلاتة في تلاتة
+
+77
+00:07:31,950 --> 00:07:38,410
+بتسعة ناقص اتنين طبعا ناقص اتنين في ناقص واحد اللي
+
+78
+00:07:38,410 --> 00:07:46,490
+هو باتنين في ناقص بكمان اتنين اللي بعدها زائد
+
+79
+00:07:46,490 --> 00:07:53,590
+اتنين فيهتلاتة في اربعة باطن عشر زائد اتنين وهنا
+
+80
+00:07:53,590 --> 00:07:59,590
+زائد زيرو بهذا الشكل طبعا بيبقى اللي عند هنا سابعة
+
+81
+00:07:59,590 --> 00:08:05,830
+وهنا عندك اربعة اتاش في اتنين بتمانية وعشرين يبقى
+
+82
+00:08:05,830 --> 00:08:12,490
+هاي لأ زائد تمانية وعشرين سابعة زائد تمانية وعشرين
+
+83
+00:08:12,730 --> 00:08:17,790
+يبقى هاي زائد اربعتاش في اتنين ب تمانية و عشرين
+
+84
+00:08:17,790 --> 00:08:25,970
+يبقى النتيجة تساوي خمسة و تلاتين طيب نيجي الان بدي
+
+85
+00:08:25,970 --> 00:08:31,470
+افك المحدد باستخدام عمود اخر بطل عن الصفر الثاني
+
+86
+00:08:31,470 --> 00:08:39,030
+لو بداشي اقوله and يبقى بدنا determinant لل ايه
+
+87
+00:08:39,030 --> 00:08:45,390
+بده يساويالـ determinant للـ A بده يساوي تختاروا
+
+88
+00:08:45,390 --> 00:08:49,570
+مين من الأعمدة؟ برضه تلاتة يبقى بدي أبدأ بالعنصر
+
+89
+00:08:49,570 --> 00:08:55,050
+الأول ناقص اتنين في ناقص واحد مرفوع بالعمود التالت
+
+90
+00:08:55,050 --> 00:08:59,630
+يا بنات يبقى هذا موجود في الصف الأول والعمود
+
+91
+00:08:59,630 --> 00:09:05,770
+التالت يبقى واحد زائد تلاتة نشطة بصفه وعموده بيبقى
+
+92
+00:09:05,770 --> 00:09:14,210
+سالب واحد اتنين وهنا واحد وسالب واحداللي بعده زائد
+
+93
+00:09:14,210 --> 00:09:19,570
+زيرو زائد
+
+94
+00:09:19,570 --> 00:09:33,070
+زائد زائد زائد
+
+95
+00:09:33,070 --> 00:09:42,700
+زائد زائد زائد زائد زائد زائد زائديبقى هذا الكلام
+
+96
+00:09:42,700 --> 00:09:47,940
+يساوي هذا الأس أربع يبقى بواحد بيظل عندى سالب
+
+97
+00:09:47,940 --> 00:09:53,640
+اتنين فيه سالب واحد في سالب واحد بواحد ناقص اتنين
+
+98
+00:09:53,640 --> 00:10:00,700
+هنا زائد zero زائد سالب واحد أس ستة يبقى بواحد
+
+99
+00:10:00,700 --> 00:10:07,240
+بيظل عندى تلاتة في أربع في اتنين بتمانية زائد
+
+100
+00:10:07,240 --> 00:10:12,490
+تلاتةهذا الكلام يساوي طبعا واحد نقص اتنين بيظل نقص
+
+101
+00:10:12,490 --> 00:10:17,790
+واحد فنقص اتنين بزايد اتنين زايد تلاتة و تمانية
+
+102
+00:10:17,790 --> 00:10:24,270
+احداش احداش في تلاتة تلاتة و تلاتين و اتنين خمسة و
+
+103
+00:10:24,270 --> 00:10:29,610
+تلاتين وهي نفس الإجابة من اللي فوق يبقى فكّنها بصف
+
+104
+00:10:29,610 --> 00:10:36,360
+و لا فكّنها بعمل بيعطيني قيمة المحدد طيبنجي نمرا
+
+105
+00:10:36,360 --> 00:10:41,580
+بي نمرا بي من المثلة نمرا بي بقول applied part two
+
+106
+00:10:41,580 --> 00:10:44,640
+of the theorem ايش يعني applied part two of the
+
+107
+00:10:44,640 --> 00:10:49,700
+theorem يعني بنطبق للنقطة رقم اتنين وهي لو خات
+
+108
+00:10:49,700 --> 00:10:56,030
+صافرضربت في كوفة
+
+109
+00:10:56,030 --> 00:11:02,390
+المحدد الأصغر المناظر لهذا الصفر اختارونا صفر من
+
+110
+00:11:02,390 --> 00:11:05,770
+هذه الصفور او عمود من هذه الصفور اللي عجبكوا فيهم
+
+111
+00:11:05,770 --> 00:11:08,890
+التاني
+
+112
+00:11:08,890 --> 00:11:14,750
+العمودي التاني ماشي بدا اختار العمودي التاني يبقى
+
+113
+00:11:14,750 --> 00:11:19,710
+انا بادهاجي اقول ما يأتي بدا استخدم العمودي التاني
+
+114
+00:11:19,710 --> 00:11:27,260
+هذايبقى بداش اقول هاي تلاتة بديش اشطف صفه و عموده
+
+115
+00:11:27,260 --> 00:11:32,740
+لأ بدي اختار عمود موازن له يا بتاخد العمود اللي
+
+116
+00:11:32,740 --> 00:11:36,340
+بعضه يا العمود اللي جابله سيان اي واحد فيهم ها
+
+117
+00:11:36,340 --> 00:11:40,670
+تختاروا مين كمان؟اللي بعده .. اللي بعده ولا اهم
+
+118
+00:11:40,670 --> 00:11:44,530
+يبقى بدي اجعل اللي بعده اللي هو الموازي له بدي
+
+119
+00:11:44,530 --> 00:11:50,630
+اشطب صفه و عموده بيظل مين عندي؟ بيظل عندي هاي ناقص
+
+120
+00:11:50,630 --> 00:11:57,150
+واحد الان هذا جاي في الصف الأول و العمود التالت
+
+121
+00:11:57,150 --> 00:12:03,170
+يبقى واحد زائد تلاتة فيه شطبنا صفه و عموده بيصير
+
+122
+00:12:03,170 --> 00:12:11,690
+ناقص واحد اتنين واحد ناقص واحدزائد اتنين في ناقص
+
+123
+00:12:11,690 --> 00:12:16,630
+واحد في هل هيبقى نيجي في ال cofactor تبعه المناظر
+
+124
+00:12:16,630 --> 00:12:21,890
+له هي future and raw او كولم is multiplied by the
+
+125
+00:12:21,890 --> 00:12:27,670
+by the cofactor هذه ايضا هذه مش factor cofactor
+
+126
+00:12:27,670 --> 00:12:37,520
+صليها اللي عندي cofactor وليس factorتمام طيب يبقى
+
+127
+00:12:37,520 --> 00:12:44,620
+بصير اتنين في سالب واحد احنا اخدنا الآن اتنين اه
+
+128
+00:12:44,620 --> 00:12:48,560
+اخدنا العمود التالت احنا مش هيك اخدنا العمود
+
+129
+00:12:48,560 --> 00:12:54,740
+التالت يبقى بالدادي اشطف صفه و عموده بيظل اربعة
+
+130
+00:12:54,740 --> 00:13:01,980
+تلاتة واحد سالب واحدهي أربعة تلاتة واحد سالب واحد
+
+131
+00:13:01,980 --> 00:13:07,140
+وظلت الإشارة تبعته الإشارة تبعته هو واقع في الصف
+
+132
+00:13:07,140 --> 00:13:13,070
+التاني والعمود التالت يبقى اتنين زائد تلاتةبالداجي
+
+133
+00:13:13,070 --> 00:13:19,050
+اللي بعده يبقى ناقص واحد في ناقص واحد مرفوع للأس
+
+134
+00:13:19,050 --> 00:13:22,350
+بالداجي العنصر اللي بعده اللي هو التلاتة جاي في
+
+135
+00:13:22,350 --> 00:13:27,950
+الصف التالت والعمود التالت يبقى تلاتة زائد تلاتة
+
+136
+00:13:27,950 --> 00:13:32,730
+في المحدد الأصغر المناظر له يبقى بنروح نشطب صف
+
+137
+00:13:32,730 --> 00:13:37,110
+عموده بصير أربعة تلاتة ناقص واحد اتنين أربعة تلاتة
+
+138
+00:13:37,110 --> 00:13:42,290
+ناقص واحد اتنين بهذا الشكليبقى النتيجة هذه تساوي
+
+139
+00:13:42,290 --> 00:13:47,870
+هذا الأس زوجي يبقى بظل تلاتة و هنا عندنا واحد ناقص
+
+140
+00:13:47,870 --> 00:13:55,490
+اتنين هنا هذا الفردي بيصير ناقص اتنين في ناقص اربع
+
+141
+00:13:55,490 --> 00:14:01,690
+ناقص تلاتة هذا عندنا زوجي يبقى بظل ناقص واحد في
+
+142
+00:14:01,690 --> 00:14:09,410
+تمانية زائد تلاتةالنتيجة هنا تساوي واحد ناقص اتنين
+
+143
+00:14:09,410 --> 00:14:14,970
+بيبقى ناقص واحد يبقى هاي ناقص تلاتة هذا عندنا سبعة
+
+144
+00:14:14,970 --> 00:14:22,370
+بالثالث اتنين بموجب اربعتاش تمامهنا تلاتة وتمانية
+
+145
+00:14:22,370 --> 00:14:27,770
+احداش بالسالب يبقى السالب احداش سالب احداش وسالب
+
+146
+00:14:27,770 --> 00:14:32,790
+تلاتة سالب اربعتاش واربعتاش النتج يساوي كده؟ Zero
+
+147
+00:14:32,790 --> 00:14:40,230
+يبقى انا ضربت عناصر اي صف او اي عمود في ال main في
+
+148
+00:14:40,230 --> 00:14:45,610
+ال cofactor المناظر لعناصر صف او عمود موازي ال low
+
+149
+00:14:45,920 --> 00:14:49,840
+اللي قبله او اللي بعده كله بيعطيك ايه بيعطيك نفس
+
+150
+00:14:49,840 --> 00:14:54,460
+النتيجة لحد هنا stop انتهى هذا ال section الى يكون
+
+151
+00:14:54,460 --> 00:15:03,400
+اكسر سايزز اللي هو اتنين عشرة اللي هو السؤال الأول
+
+152
+00:15:03,400 --> 00:15:13,080
+بدنا منه A وC وD والسؤال التاني بدنا منه B والسؤال
+
+153
+00:15:13,080 --> 00:15:15,460
+التالت والسؤال السابع
+
+154
+00:15:39,790 --> 00:15:45,450
+ننتقل الان لـ Section الذي يليه وهو Section 2.11
+
+155
+00:15:45,450 --> 00:15:53,790
+يبقى Section 2.11 Kramers Rule
+
+156
+00:15:53,790 --> 00:16:07,320
+قاعدة Kramersبقول ي consider the system of linear
+
+157
+00:16:07,320 --> 00:16:08,180
+equations
+
+158
+00:16:14,090 --> 00:16:25,590
+اللي هو a11 x1 a12 x2 زائد a1n xn بده يساوي b1 a21
+
+159
+00:16:25,590 --> 00:16:33,770
+x1 a22 x2 زائد a2n xn بده يساوي b2
+
+160
+00:16:44,980 --> 00:16:50,740
+هذا كله اللي هو هنسميه system star
+
+161
+00:17:01,860 --> 00:17:10,700
+is written as بروح نكتب على الشكل التالي اللي هو
+
+162
+00:17:10,700 --> 00:17:23,340
+المصوفة a11, a12, a1n, a21, a22, a2n بظل ماشي
+
+163
+00:17:23,340 --> 00:17:37,030
+اللغات a n1, a n2A N N كل هذا في X1 X2 لغاية XN
+
+164
+00:17:37,030 --> 00:17:45,850
+بده يساوي اللي هو B1 B2 لغاية BN الشكل اللي عندنا
+
+165
+00:17:45,850 --> 00:17:56,050
+هنا or capital A في X بده يساوي B definition
+
+166
+00:18:00,340 --> 00:18:09,520
+the square matrix A is
+
+167
+00:18:09,520 --> 00:18:13,800
+called
+
+168
+00:18:13,800 --> 00:18:20,380
+singular if
+
+169
+00:18:20,380 --> 00:18:23,300
+determinant
+
+170
+00:18:26,440 --> 00:18:38,600
+للـ A بدو يساوي 0 and non singular if
+
+171
+00:18:38,600 --> 00:18:48,700
+determinant لل A does not equal to 0 theorem
+
+172
+00:18:48,700 --> 00:18:53,760
+if
+
+173
+00:18:55,600 --> 00:19:06,020
+الـ determinant للـ a لا يساوي zero if determinant
+
+174
+00:19:06,020 --> 00:19:20,200
+ل a لا يساوي zero then the system star has exactly
+
+175
+00:19:20,200 --> 00:19:24,900
+one solution
+
+176
+00:19:53,950 --> 00:20:03,830
+remark if the system star
+
+177
+00:20:03,830 --> 00:20:07,910
+has exactly one solution
+
+178
+00:20:22,510 --> 00:20:30,310
+we find it by
+
+179
+00:20:30,310 --> 00:20:36,670
+two methods
+
+180
+00:20:36,670 --> 00:20:47,330
+بطريقة تام طريقة الأولى ال raw echelon four
+
+181
+00:20:51,870 --> 00:20:58,390
+by the rational form on the
+
+182
+00:20:58,390 --> 00:21:08,710
+argumented matrix number
+
+183
+00:21:08,710 --> 00:21:15,870
+اتنين the
+
+184
+00:21:15,870 --> 00:21:16,830
+Gaussian elimination
+
+185
+00:21:31,410 --> 00:21:45,930
+Lawson elimination by exchange the matrix into
+
+186
+00:21:45,930 --> 00:21:50,370
+upper
+
+187
+00:21:50,370 --> 00:21:54,070
+triangle
+
+188
+00:21:54,070 --> 00:21:57,170
+matrix
+
+189
+00:22:05,240 --> 00:22:18,540
+Example Solve the system اتنين
+
+190
+00:22:18,540 --> 00:22:26,060
+اكس واحد زي اتنين اكس اتنين ناقص اكس تلاتة يساوي
+
+191
+00:22:26,060 --> 00:22:26,620
+اتنين
+
+192
+00:22:30,150 --> 00:22:36,850
+-3x1-x2 3x3
+
+193
+00:22:36,850 --> 00:22:46,410
+-2 4x1 2x2
+
+194
+00:22:46,410 --> 00:22:49,770
+-3x3
+
+195
+00:22:49,770 --> 00:22:51,530
+0
+
+196
+00:24:09,430 --> 00:24:14,030
+نرجع لكلام اللي احنا كتبينه هذا ال بيقول consider
+
+197
+00:24:14,030 --> 00:24:17,110
+the system of linear equations وعطاني n من
+
+198
+00:24:17,110 --> 00:24:22,230
+المعادلات في n من المجاهد طبعا سابقا ناخد هذا ال
+
+199
+00:24:22,230 --> 00:24:25,890
+system وكتبناه على شكل اللي هو حاصل ضرب مصوفات
+
+200
+00:24:25,890 --> 00:24:29,330
+بالطريقة هذه يعني ال system اصلا كتبناه على حاصل
+
+201
+00:24:29,330 --> 00:24:33,570
+ضرب على شكل حاصل ضرب مصوفتينبتساوي في مصوفة
+
+202
+00:24:33,570 --> 00:24:38,050
+الثوابت الأولانية سمناها مصوفة المعاملات هذه
+
+203
+00:24:38,050 --> 00:24:43,270
+سمناها مصوفة المجاهيل هذه سمناها مصوفة الثوابت
+
+204
+00:24:43,270 --> 00:24:47,390
+يبقى هذه سمناها coefficient matrix هذه unknown
+
+205
+00:24:47,390 --> 00:24:52,230
+matrix هذه constant matrix او اختصاراً حطيناها على
+
+206
+00:24:52,230 --> 00:24:57,330
+شكل ax يساوي b ax هي coefficient matrix والx هي
+
+207
+00:24:57,330 --> 00:25:02,240
+مصوفة المجاهيل والb هي مصوفة الثوابتالتعريف بيقول
+
+208
+00:25:02,240 --> 00:25:08,360
+لو أخدت المحدد للمصوفة المربعة اللي عندنا هذه يبقى
+
+209
+00:25:08,360 --> 00:25:13,120
+هذه بقول عليها singular إذا كان المحدد يساوي zero
+
+210
+00:25:13,120 --> 00:25:16,380
+حسبنا المحدد وجدنا يساوي zero يبقى المصوفة هذه
+
+211
+00:25:16,380 --> 00:25:20,220
+بقول عليها singular matrix يعني مصوفة شاذة أو
+
+212
+00:25:20,220 --> 00:25:25,210
+منعزلة أو منفردة أو التسمع اللي تعجبكبسميها non
+
+213
+00:25:25,210 --> 00:25:30,070
+singular إذا كان المحدد تبعها ماله لا يساوي zero
+
+214
+00:25:30,070 --> 00:25:34,110
+كويس النظرية هذه بتقول إذا المحدد لا يساوي zero
+
+215
+00:25:34,110 --> 00:25:38,430
+يبقى ال system ال star اللي فوق مضمون له main حل
+
+216
+00:25:38,430 --> 00:25:41,970
+واحد طبعا ال system اللي فوق ال star احنا سابقا
+
+217
+00:25:41,970 --> 00:25:47,230
+قلنا إله أحد ثلاثة احتمالات الاحتمال الأول أن يكون
+
+218
+00:25:47,230 --> 00:25:52,190
+له حلا واحدا الاحتمال الثانيان يكون له عدد ده
+
+219
+00:25:52,190 --> 00:25:56,870
+نهائي من الحلول الا احتمالية ان لا يكون حل هذا ال
+
+220
+00:25:56,870 --> 00:26:02,230
+system الان كإنه اللي بيعطيني ضمانة ما هي الضمانة
+
+221
+00:26:02,230 --> 00:26:07,310
+اللي ممكن تكون عندنا حتى يكون لل system حلا واحدة
+
+222
+00:26:07,600 --> 00:26:12,040
+هنقول له هروح نجيب المحدد تبع المعاملات إذا المحدد
+
+223
+00:26:12,040 --> 00:26:17,060
+لا يساوي zero يبقى مضمون مائة بالمائة يكون عندي حل
+
+224
+00:26:17,060 --> 00:26:21,880
+وحيد لهذا ال system وبروح نجيب له هذا الحل الوحيد
+
+225
+00:26:21,880 --> 00:26:27,480
+تمامهذا بالنسبة للنظرية الان نجي لل remark بيقول
+
+226
+00:26:27,480 --> 00:26:31,780
+ال system has exactly one solution لو كان له حل
+
+227
+00:26:31,780 --> 00:26:37,440
+واحد فقط يبقى ممكن الحصول عليه بطريقتين طريقة
+
+228
+00:26:37,440 --> 00:26:43,120
+أخدناها سابقا و طريقةاخدناها و احنا مش دارين تمام
+
+229
+00:26:43,120 --> 00:26:48,140
+ايش الطريقة الأولى اللي هو ال raw echelon form اني
+
+230
+00:26:48,140 --> 00:26:51,800
+اخل القدر الرئيسي واحد واحد و اللي منه فوق أصفر و
+
+231
+00:26:51,800 --> 00:26:55,860
+اللي منه تاح أصفر و بعد هي كده بجيب ال system
+
+232
+00:26:55,860 --> 00:27:01,460
+مكافئ لل system الأصليالطريقة الثانية هي طريقة
+
+233
+00:27:01,460 --> 00:27:06,340
+جاوس بيقول the gaussian elimination اللي هو محذفات
+
+234
+00:27:06,340 --> 00:27:10,240
+جاوس by changing the matrix into upper triangle
+
+235
+00:27:10,240 --> 00:27:14,380
+matrix يعني أنا بدي أحولها إلى مصغفة بحيث القطر
+
+236
+00:27:14,380 --> 00:27:19,040
+الرئيسي كله لتحتيثي روميان أسفار احنا بيقولك هي
+
+237
+00:27:19,040 --> 00:27:23,130
+الطريقتين يعني هل اختلفت الثانية عن الأولى؟بس
+
+238
+00:27:23,130 --> 00:27:26,470
+الأولى بدها شغل اكتر شغل اكتر ليش؟ انا بدي اللى
+
+239
+00:27:26,470 --> 00:27:30,530
+فوق كمان أسفار مش عقد اللى تحتى يبقى جاوسيا نسهى
+
+240
+00:27:30,530 --> 00:27:36,450
+أسهل من مين؟ من روشيلون 4 تمام طيب احنا بنعطي مثال
+
+241
+00:27:36,450 --> 00:27:42,890
+و من هذا المثال نحاول نستخدم الجاوسيا في حل هذا
+
+242
+00:27:42,890 --> 00:27:49,010
+المثال إذا كان بنحل ب solution واحد فقطأيش بيقول
+
+243
+00:27:49,010 --> 00:27:52,390
+Solve the system ومعطيني ال system هذا يبقى أنا
+
+244
+00:27:52,390 --> 00:27:56,910
+بدي أتأكد أنه له حل والله مالهوش حل والله عدد لا
+
+245
+00:27:56,910 --> 00:28:02,470
+نهاية من الحلول بروح باخد محدد مصوفة المعاملات
+
+246
+00:28:02,470 --> 00:28:10,070
+فباجي بقوله ال determinantللأي بدى يساوي يبقى بدى
+
+247
+00:28:10,070 --> 00:28:13,330
+اجه على ال system اللى عندنا واحط المعاملات على
+
+248
+00:28:13,330 --> 00:28:19,790
+شكل محدد هى اتنين وهى اتنين وهى سالب واحد وهنا
+
+249
+00:28:19,790 --> 00:28:25,370
+سالب تلاتة وهنا سالب واحد وهنا تلاتة وهنا اربعة
+
+250
+00:28:25,370 --> 00:28:32,550
+وهنا اتنين وهنا سالب تلاتة تمامسأفكر المحدد
+
+251
+00:28:32,550 --> 00:28:37,470
+باستخدام أي صفة أو عمود سيان لا يفرق عنها يبقى هذا
+
+252
+00:28:37,470 --> 00:28:40,830
+الكلام بيدرساه بدا أفكر على طول يا بنات مش هتقعد
+
+253
+00:28:40,830 --> 00:28:44,690
+كل حين هداك لأ بدي أفكر على طول الخط يبقى هذا
+
+254
+00:28:44,690 --> 00:28:50,210
+لإتنين فيه بدي أشطب صفه و عموده بصير عندك هنا
+
+255
+00:28:50,210 --> 00:28:55,970
+تلاتة ناقص ستةحسب قاعة الإشارات اللي بعده إشارته
+
+256
+00:28:55,970 --> 00:29:03,470
+سالب نشط بصفه و عموده بصير تسعة و هنا ناقص اتناش
+
+257
+00:29:03,470 --> 00:29:08,930
+هاي شطاب نصفه و عموده بصير تسعة ناقص اتناش اللي
+
+258
+00:29:08,930 --> 00:29:15,610
+بعده سالب واحد فيه أشط بصفه و عموده بصير سالب ستة
+
+259
+00:29:15,610 --> 00:29:21,830
+زائد أربعةسالب ستة زائد اربع يبقى هذا الكلام يساوي
+
+260
+00:29:21,830 --> 00:29:27,670
+تلاتة ناقص ستة بيظل ناقص تلاتة في اتنين بناقص ستة
+
+261
+00:29:27,670 --> 00:29:32,030
+تسعة ناقص اتناشر بيظل ناقص تلاتة في ناقص اتنين
+
+262
+00:29:32,030 --> 00:29:37,590
+بزائد ستة وعندك هنا سالب ستة وزائد اربع بيظل سالب
+
+263
+00:29:37,590 --> 00:29:42,610
+اتنين في سالب واحد بزائد اتنين يبقى النتيجة جداش
+
+264
+00:29:42,890 --> 00:29:48,090
+أتنين لا يساوي Zero معناته هذا ال system له حل
+
+265
+00:29:48,090 --> 00:29:55,230
+واحد يبقى باجي بقول since بما أن ال determinant لل
+
+266
+00:29:55,230 --> 00:30:04,590
+A يساوي اتنين ولا يساوي Zero ال system star has a
+
+267
+00:30:04,590 --> 00:30:09,170
+unique solution او has one solution has one
+
+268
+00:30:09,170 --> 00:30:10,830
+solution
+
+269
+00:30:12,680 --> 00:30:19,380
+طيب بدنا نروح نشوف كيف بدنا نجيب ال solution لهذا
+
+270
+00:30:19,380 --> 00:30:25,500
+ال system بطريقة جاوس لان اشيلون فورم اشتغلنا
+
+271
+00:30:25,500 --> 00:30:30,840
+عليها كتير لنشوف طريقة جاوس احنا تاول ساعة دعينا
+
+272
+00:30:30,840 --> 00:30:35,680
+او زعمنا انها أبسط شوية اذا انا هنا لو جيت على
+
+273
+00:30:35,680 --> 00:30:42,050
+الصف الأول وقلت المصوف عندنا كانت تالية هي اتنينو
+
+274
+00:30:42,050 --> 00:30:47,630
+بعدها اتنين و بعدها سالف واحد و هنا ناقص تلاتة و
+
+275
+00:30:47,630 --> 00:30:54,430
+هنا اربعة و هنا ناقص واحد اتنين و هنا ناقص تلاتة و
+
+276
+00:30:54,430 --> 00:30:58,750
+لا زائد تلاتة و هنا ناقص تلاتة بالشكل اللي عندنا
+
+277
+00:30:58,750 --> 00:31:05,450
+هذا بس بضروح اضيف ال االلي هو العمود تبع المعاملات
+
+278
+00:31:05,450 --> 00:31:08,950
+لإن احنا بناخد الـ Agumented Matrix الـ Agumented
+
+279
+00:31:08,950 --> 00:31:14,010
+Matrix اللي هم اتنين سلب اتنين زيرو اتنين سلب
+
+280
+00:31:14,010 --> 00:31:22,000
+اتنين زيرو pointيبقى انا بالنسبة للمصوفة لان ليس
+
+281
+00:31:22,000 --> 00:31:28,460
+بالضرورة اخل العنصر الأول واحد لكن لكي اجلب هذه
+
+282
+00:31:28,460 --> 00:31:34,100
+الصفر لازم اخلها دقيقاش واحد اذا بروح بدرب الصف
+
+283
+00:31:34,100 --> 00:31:42,100
+الأول في نص تمام يبقى باجي بقول بدي اخد هنا نص R1
+
+284
+00:31:42,620 --> 00:31:48,500
+بصير المصوفة على الشكل التالي هنا واحد وهنا واحد
+
+285
+00:31:48,500 --> 00:31:59,720
+وهنا ناقص نص وهنا ناقص نص تمام؟ وهنا واحدالصف
+
+286
+00:31:59,720 --> 00:32:04,560
+التاني زي ما هو ناقص تلاتة ناقص واحد تلاتة ناقص
+
+287
+00:32:04,560 --> 00:32:11,520
+اتنين اربعة اتنين ناقص تلاتة zero هاي جفلنا الان
+
+288
+00:32:11,520 --> 00:32:15,880
+بدي ادخلي مكان السلب تلاتة والاربعة اسفار يبقى بدي
+
+289
+00:32:15,880 --> 00:32:20,120
+اضرب الصف الأول في تلاتة واضيفه للصف الثاني واضربه
+
+290
+00:32:20,120 --> 00:32:24,660
+في السلب اربعة واضيفه للصف الثالث يبقى باجي بقول
+
+291
+00:32:24,660 --> 00:32:33,260
+كتالةتلاتة R1 بدي اضيفه to R2 و سالب اربعة R1 to
+
+292
+00:32:33,260 --> 00:32:48,280
+R3 بنحصل على المصفوفة التالية1 1 1 1 1 1 1 1 1 1 1
+
+293
+00:32:48,280 --> 00:32:48,500
+1 1 1 1 1
+
+294
+00:32:59,080 --> 00:33:05,080
+وهنا ضربنا في تلاتة بيظل كدهش هنا كمان واحد الان
+
+295
+00:33:05,080 --> 00:33:12,140
+هنا zero سالب اربع بيظل سالب اتنين وهنا ضربنا في
+
+296
+00:33:12,140 --> 00:33:18,340
+سالب اربع بيصير موجة باتنين بيظل ناقص واحد ضربنا
+
+297
+00:33:18,340 --> 00:33:27,260
+في سالب اربع بيصير عندك سالب اربع طيبالان انا بدي
+
+298
+00:33:27,260 --> 00:33:33,340
+ادخل هذا مكانه zero يبقى بدي اضيف الصف ثاني الى
+
+299
+00:33:33,340 --> 00:33:41,560
+الصف الثالث يبقى بدي ادخله R2 to R3 اضافة عادية
+
+300
+00:33:41,560 --> 00:33:46,880
+ماسوّناش اشي يبقى الصف الاول هي واحد واحد وهي سالب
+
+301
+00:33:46,880 --> 00:33:57,300
+نص وهذا واحد0 2 3 2 1 0 0
+
+302
+00:34:08,000 --> 00:34:13,860
+الان هذا ال system اللي عندنا او ال system الأصلي
+
+303
+00:34:13,860 --> 00:34:22,200
+is equivalent to يبقى باجي بقوله the system star
+
+304
+00:34:22,200 --> 00:34:32,300
+is equivalent to هذا يكافئ مين؟ يكافئ x واحد زي x
+
+305
+00:34:32,300 --> 00:34:39,190
+اتنين ناقص نص x تلاتة بده يساوي واحدهنا اكس اتنين
+
+306
+00:34:39,190 --> 00:34:44,810
+او اتنين اكس اتنين زائد تلاتة على اتنين اكس تلاتة
+
+307
+00:34:44,810 --> 00:34:51,490
+يساوي واحد وهنا المص اكس تلاتة بده يساوي قداش بده
+
+308
+00:34:51,490 --> 00:34:57,950
+يساوي ناقص تلاتةالان من هذا بقدر اقول له ال X3 كده
+
+309
+00:34:57,950 --> 00:35:05,010
+ساوي يا بنات؟ سالب ستة الان هاي جبنا له X3 بقدر
+
+310
+00:35:05,010 --> 00:35:10,450
+اجيب له X2 يبقى برجعود في المعادلة اللي من او فوق
+
+311
+00:35:10,450 --> 00:35:19,370
+يبقى 2X2 بدي اضرب في سالب ستة بصير عندى سالب تسعة
+
+312
+00:35:19,370 --> 00:35:27,070
+بده ساوي واحدمظبوط يبقى هذا معناه انه x2 بده يساوي
+
+313
+00:35:27,070 --> 00:35:34,850
+عشرة هذا معناه انه x2 بده يساوي خمسةالحين X2 و X3
+
+314
+00:35:34,850 --> 00:35:41,890
+موجودات برجع بعوض وين في المعادلة الأولى يبقى X1 و
+
+315
+00:35:41,890 --> 00:35:48,450
+هنا زائد خمسة و هنا ناقص مع ناقص بصير زائد ستة على
+
+316
+00:35:48,450 --> 00:35:54,990
+اتنين بصير تلاتة بده يسوى جداش واحد هذا معناه ان
+
+317
+00:35:54,990 --> 00:36:00,540
+X1 بده يسوى تلاتة و خمسةتمانية تجيبها على الشجة
+
+318
+00:36:00,540 --> 00:36:05,860
+التانية تصبح سالب تمانية واحد تصبح سالب سبعة يبقى
+
+319
+00:36:05,860 --> 00:36:19,260
+بروح بقوله solution of the system star is X واحد و
+
+320
+00:36:19,260 --> 00:36:25,680
+X اتنين و X تلاتة بده يساوي X واحد طلعناها بناقص
+
+321
+00:36:25,680 --> 00:36:35,180
+سبعةو X2 بخمسة و X3 بسالب ستة و زي ما تشايفين حلا
+
+322
+00:36:35,180 --> 00:36:41,980
+واحدا ليس اكثر و احنا اثبتنا انه حل واحد عن طريق
+
+323
+00:36:41,980 --> 00:36:45,040
+حساب قيمة المحدد
+
+324
+00:36:46,460 --> 00:36:51,620
+طيب، حتى الآن ما اتكلمناش في عنوان هذا ال section
+
+325
+00:36:51,620 --> 00:36:57,040
+اللي هو grammar rule اللي هي قاعدة ال grammar لحل
+
+326
+00:36:57,040 --> 00:37:02,460
+المعادلات، تمام؟ يبقى بدنا نيجي لقاعدة grammar
+
+327
+00:37:02,460 --> 00:37:11,760
+يبقى هذا grammar rule إيش بتقول grammar rules؟ we
+
+328
+00:37:11,760 --> 00:37:12,500
+use
+
+329
+00:37:15,860 --> 00:37:24,180
+أكرامر رول نستخدم قاعدة أكرامر إذا كان الـ
+
+330
+00:37:24,180 --> 00:37:28,920
+determinant للـ a لا يساوي zero يعني أيه الشبنات؟
+
+331
+00:37:30,570 --> 00:37:35,010
+يعني إذا كان عندي حل واحد فقط يبقى إذا أنا بدأ
+
+332
+00:37:35,010 --> 00:37:38,910
+أستخدم طريقة grammar بدي أجيب المحدد و أثبت إنه لا
+
+333
+00:37:38,910 --> 00:37:42,870
+يساوي zero إن حدث ذلك بقدر أستخدم طريقة grammar
+
+334
+00:37:42,870 --> 00:37:55,150
+غير هيك يبعتلك الله فبجي بقول the unknowns المجاهل
+
+335
+00:37:55,150 --> 00:37:57,050
+are found
+
+336
+00:37:59,680 --> 00:38:05,420
+بنوجدها من الصيغة from the formula from the
+
+337
+00:38:05,420 --> 00:38:11,040
+formula من الصيغة من الصيغة from the formula from
+
+338
+00:38:11,040 --> 00:38:11,960
+the formula from the formula من الصيغة من الصيغة
+
+339
+00:38:11,960 --> 00:38:12,120
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+340
+00:38:12,120 --> 00:38:12,640
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+341
+00:38:12,640 --> 00:38:14,720
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+342
+00:38:14,720 --> 00:38:17,280
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+343
+00:38:17,280 --> 00:38:17,300
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+344
+00:38:17,300 --> 00:38:21,140
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+345
+00:38:21,140 --> 00:38:24,520
+من
+
+346
+00:38:24,520 --> 00:38:28,400
+الصيغ
+
+347
+00:38:28,530 --> 00:38:42,890
+matrix where حيث the matrix بي كي is obtained
+
+348
+00:38:42,890 --> 00:38:54,630
+بنحصل عليها from the matrix a من المصوفة a after
+
+349
+00:38:54,630 --> 00:38:57,190
+replacing after
+
+350
+00:38:58,730 --> 00:39:10,810
+replacing بعد ما نستبدل the kiss calm العموض
+
+351
+00:39:10,810 --> 00:39:20,370
+رقم K by the constant calm
+
+352
+00:39:20,370 --> 00:39:22,950
+بعمودي ثوابت
+
+353
+00:39:32,450 --> 00:39:40,930
+Example use Kramer's
+
+354
+00:39:40,930 --> 00:39:52,250
+rule to solve the system
+
+355
+00:39:55,560 --> 00:40:10,540
+2x1 زائد 2x2 ناقص x3 يساوي 2 ناقص 3x1 ناقص x2 زائد
+
+356
+00:40:10,540 --> 00:40:17,620
+3x3 يساوي سالب 2 4x1
+
+357
+00:40:18,180 --> 00:40:27,540
+زائدي اتنين X2 ناقص تلاتة X3 بده يساوي Zero وهذا
+
+358
+00:40:27,540 --> 00:40:35,180
+هو ال system star اللي عندنا اظن
+
+359
+00:40:35,180 --> 00:40:39,380
+هو ال system السابق يا بنات في المثال السابق هو هو
+
+360
+00:40:39,380 --> 00:40:44,340
+ولا لا بس هناك حلناه بطريقة جاوس هنا بحله بطريقة
+
+361
+00:40:44,340 --> 00:40:47,820
+مين كرامر تمام تمام
+
+362
+00:40:53,170 --> 00:40:56,430
+يبقى على طريقة الـ Grammar شو بتقوله؟ بل جاي لهذا
+
+363
+00:40:56,430 --> 00:41:01,810
+المحدد كله يساوي Zero المجاهد X1 و X2 و X3 بدي
+
+364
+00:41:01,810 --> 00:41:06,590
+أجيبهم من القاعدة XK تساوي determinant لـPK على
+
+365
+00:41:06,590 --> 00:41:11,890
+determinant لـAهذا محدد مصوفة المعاملات هذا محدد
+
+366
+00:41:11,890 --> 00:41:16,510
+مصوفة المعاملات بس إذا بدي X1 بدي أقول determinant
+
+367
+00:41:16,510 --> 00:41:20,210
+بي وان مين بي وان هي محدد مصوفة المعاملات بس بدي
+
+368
+00:41:20,210 --> 00:41:23,530
+أجي على العمود الأول و أشيله و أحط بدله عمود
+
+369
+00:41:23,530 --> 00:41:28,170
+الثوابتبدي X2 باجي على العمود رقم اتنين بشيله و
+
+370
+00:41:28,170 --> 00:41:32,990
+بحط بدالي عمود ثوث في مصوفة المعاملة بدي X3 بنفس
+
+371
+00:41:32,990 --> 00:41:36,690
+الطريقة يبقى الكلام اللي بنقوله احنا لم نطبقه على
+
+372
+00:41:36,690 --> 00:41:41,530
+أرض الواقع الان بدي اجي ل determinant لإيه هنا
+
+373
+00:41:41,530 --> 00:41:42,390
+solution
+
+374
+00:41:47,030 --> 00:41:53,810
+الـ determinant للـ a اللي هو بده يساوي قداش اتنين
+
+375
+00:41:53,810 --> 00:42:00,550
+اتنين سالب واحد سالب تلاتة سالب واحد تلاتة اربع
+
+376
+00:42:00,550 --> 00:42:05,930
+اتنين سالب تلاتة اظن هذا طلعناه اتنين قبل قليل
+
+377
+00:42:05,930 --> 00:42:11,110
+اتنين يبقى طلعناه اتنين from above
+
+378
+00:42:13,090 --> 00:42:17,130
+قلناها قبل قليل بدا أروح أجيب determinant ل P1
+
+379
+00:42:17,130 --> 00:42:25,640
+يبقى بدي أجيب determinant ل P1 يا بناتهذا المحدد
+
+380
+00:42:25,640 --> 00:42:30,520
+يجب أن يشيل العمودي الأول وقته بدل عمودي الثوابت
+
+381
+00:42:30,520 --> 00:42:35,800
+يبقى اتنين سالب اتنين زيرو والعمودين اتنين اتنين
+
+382
+00:42:35,800 --> 00:42:40,300
+زي ما هم اتنين سالب واحد اتنين اتنين سالب واحد
+
+383
+00:42:40,300 --> 00:42:47,020
+اتنين وسالب واحد تلاتة سالب واحد تلاتة سالب تلاتة
+
+384
+00:42:47,020 --> 00:42:52,600
+بالشكل هنابتروح أفكه باستخدام العمود الأول يبقى
+
+385
+00:42:52,600 --> 00:42:59,440
+هذا اتنين فيه اشط بصفه عموده بصير تلاتة ناقص ستة
+
+386
+00:42:59,440 --> 00:43:03,940
+هاي تلاتة ناقص ستة نجي لبعده حسب قاعة الإشارات
+
+387
+00:43:03,940 --> 00:43:09,960
+إشارته سالب وهو سالب يبقى بصير زائد اتنين فيه نشط
+
+388
+00:43:09,960 --> 00:43:15,480
+بصفه عموده يبقى سالب ستة زائد اتنين سالب ستة زائد
+
+389
+00:43:15,480 --> 00:43:22,260
+اتنين زائد Zeroيبقى النتيجة هذه سالب تلاتة في
+
+390
+00:43:22,260 --> 00:43:28,880
+اتنين بسالب ستة هذي بيظل سالب اربعة في اتنين بسالب
+
+391
+00:43:28,880 --> 00:43:33,920
+تمانية ويسوى سالب اربعة اتاشر تمام؟ بدنا نجيب ال
+
+392
+00:43:33,920 --> 00:43:41,510
+determinant لل B2 يبقى المحددالعمود الثاني هو
+
+393
+00:43:41,510 --> 00:43:46,170
+اتنين هو سالب اتنين هو زيرو والعمود الأول زي ما هو
+
+394
+00:43:46,170 --> 00:43:50,970
+اتنين سالب تلاتة اربعة اتنين سالب تلاتة اربعة
+
+395
+00:43:50,970 --> 00:43:57,250
+والتالت زي ما هو سالب واحد تلاتة سالب تلاتةبدأ
+
+396
+00:43:57,250 --> 00:44:01,910
+أفكر مثلا باستخدام الصفر الصفي التالت يبقى هذا
+
+397
+00:44:01,910 --> 00:44:07,070
+الكلام بده يساوي أربعة قشط بصفه عموده يبقى بصير
+
+398
+00:44:07,070 --> 00:44:13,970
+هنا ستة ناقص اتنين اللي بعدها ناقص Zero اللي بعدها
+
+399
+00:44:13,970 --> 00:44:20,700
+زائد ناقص تلاتة فيهأشط بصفه عموده يبقى ناقص أربعة
+
+400
+00:44:20,700 --> 00:44:27,120
+زائد ستة ناقص أربعة زائد ستة ويساوي يبقى أربعة في
+
+401
+00:44:27,120 --> 00:44:33,360
+أربعة اللي هو ستاشر وهنا يبقى اتنين يبقى ناقص ستة
+
+402
+00:44:33,360 --> 00:44:42,720
+ويساوي عشرةالان بدأيجي لـ determinant للـ B3 يساوي
+
+403
+00:44:42,720 --> 00:44:47,640
+العمود الأول زي ما هو 2 سالب 3 أربعة العمودي
+
+404
+00:44:47,640 --> 00:44:53,320
+التاني زي ما هو 2 سالب 1 اتنين العمودي التالت بدأ
+
+405
+00:44:53,320 --> 00:44:57,540
+احط بداله عمود الثوابط اللي هو Zero بالشكل اللي
+
+406
+00:44:57,540 --> 00:45:03,940
+عندنابدي أفكر المحدد باستخدام عناصر الصف تالت يبقى
+
+407
+00:45:03,940 --> 00:45:10,300
+هذا أربعة فيه بدي أشطب صفه و عموده يبقى ناقص أربعة
+
+408
+00:45:10,300 --> 00:45:15,580
+زائد اتنين اللي بعده حسب قاعدة الإشارات بناقص
+
+409
+00:45:15,580 --> 00:45:21,520
+اتنين أشطب صفه و عموده يبقى ناقص أربعة زائد ستة
+
+410
+00:45:21,520 --> 00:45:27,500
+ناقص أربعة زائد ستة زائد زيرو هذا الكلام بدي أساوي
+
+411
+00:45:28,040 --> 00:45:33,500
+هنا بيظل ناقص اتنين يبقى بناقص تمانية هنا بيظل
+
+412
+00:45:33,500 --> 00:45:40,480
+اتنين يبقى ناقص اربعة ويسوى ناقص اتناش يبقى بدي
+
+413
+00:45:40,480 --> 00:45:46,280
+اكس واحد يا بنات يبقى determinant لل B1 على
+
+414
+00:45:46,280 --> 00:45:52,700
+determinant للـ A و يساوي determinant للـ B 1 طالع
+
+415
+00:45:52,700 --> 00:45:58,560
+عنده بناقص 14 و determinant لل A ب2 يساوي كده؟
+
+416
+00:45:58,560 --> 00:46:05,280
+سالب سبعة الان بDX 2 اللي هو determinant لل B 2
+
+417
+00:46:05,280 --> 00:46:11,240
+على determinant لل A و يساوي determinant لل B 2
+
+418
+00:46:11,240 --> 00:46:17,400
+طالع 10 على 2 و يساوي 5بدي الـ X3 اللي هي
+
+419
+00:46:17,400 --> 00:46:24,380
+determinant للـ B3 على ال determinant لل A ويساوي
+
+420
+00:46:24,380 --> 00:46:29,620
+determinant لـ B3 طالع عندنا ناقص اتناشر على اتنين
+
+421
+00:46:29,620 --> 00:46:35,860
+ناقص ستة يبقى هذا الحل ناقص سبعة وخمسة وسالب ستة
+
+422
+00:46:35,860 --> 00:46:40,290
+هو الحل اللي كان معانايبقى هو الحل لل system اللي
+
+423
+00:46:40,290 --> 00:46:45,910
+قبل قليل يبقى حلّين السؤال بطريقتين الطريقة الأولى
+
+424
+00:46:45,910 --> 00:46:50,110
+هي طريقة جوس والطريقة الثانية هي طريقة مين؟ طريقة
+
+425
+00:46:50,110 --> 00:46:55,590
+كرامر إذا لازلنا في نفس ال section هذا و بنكمل ان
+
+426
+00:46:55,590 --> 00:47:01,880
+شاء الله المرة القادمةدير باركو طريقة كتامر very
+
+427
+00:47:01,880 --> 00:47:06,820
+important بس لا ألجأ إليها إلا إذا كان المحدد لا
+
+428
+00:47:06,820 --> 00:47:08,480
+يساوي zero
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5a9251f3546507d3c4db7f1c693b1e6f35acdf06
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3972, "start": 19.67, "end": 39.73, "text": "بسم الله الرحمن الرحيم بنرجع لإكمال ال section الماضي وهو ال cofactors وعرفنا المرة اللي فاتت ال minor و ال cofactor قولنا ال minor هو المحدد الأصغر المناظر لأنصر من عناصر مصحوفة ما", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 44945, 47341, 3615, 5296, 28814, 24793, 6027, 2423, 3541, 9673, 46958, 1829, 37037, 2407, 2423, 598, 44919, 830, 4032, 3615, 28480, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 2423, 6696, 4032, 2423, 598, 69, 15104, 12174, 12610, 8315, 2423, 6696, 31439, 9673, 24401, 3215, 16247, 9381, 17082, 2288, 9673, 1863, 5718, 116, 2288, 5296, 33456, 9381, 2288, 9154, 18871, 33546, 2288, 3714, 9381, 5016, 38688, 3660, 19446], "avg_logprob": -0.13361377651110673, "compression_ratio": 1.7109826589595376, "no_speech_prob": 0.0, "words": [{"start": 19.67, "end": 19.99, "word": "بسم", "probability": 0.92333984375}, {"start": 19.99, "end": 20.21, "word": " الله", 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0.773193359375}, {"start": 29.83, "end": 30.01, "word": " اللي", "probability": 0.806640625}, {"start": 30.01, "end": 30.47, "word": " فاتت", "probability": 0.9871419270833334}, {"start": 30.47, "end": 30.67, "word": " ال", "probability": 0.62939453125}, {"start": 30.67, "end": 31.07, "word": " minor", "probability": 0.99072265625}, {"start": 31.07, "end": 31.29, "word": " و", "probability": 0.701171875}, {"start": 31.29, "end": 31.43, "word": " ال", "probability": 0.83642578125}, {"start": 31.43, "end": 32.13, "word": " cofactor", "probability": 0.87744140625}, {"start": 32.13, "end": 33.01, "word": " قولنا", "probability": 0.826171875}, {"start": 33.01, "end": 33.17, "word": " ال", "probability": 0.88623046875}, {"start": 33.17, "end": 33.43, "word": " minor", "probability": 0.98974609375}, {"start": 33.43, "end": 33.69, "word": " هو", "probability": 0.99169921875}, {"start": 33.69, "end": 34.67, "word": " المحدد", "probability": 0.9933268229166666}, {"start": 34.67, "end": 35.65, 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"probability": 0.95703125}, {"start": 57.29, "end": 57.63, "word": " هذا", "probability": 0.939453125}, {"start": 57.63, "end": 57.83, "word": " ال", "probability": 0.8134765625}, {"start": 57.83, "end": 58.17, "word": " minor", "probability": 0.94677734375}, {"start": 58.17, "end": 59.05, "word": " ال", "probability": 0.89208984375}, {"start": 59.05, "end": 59.93, "word": " cofactor", "probability": 0.7509765625}, {"start": 59.93, "end": 60.41, "word": " هو", "probability": 0.97412109375}, {"start": 60.41, "end": 60.65, "word": " ال", "probability": 0.8896484375}, {"start": 60.65, "end": 61.01, "word": " minor", "probability": 0.98388671875}, {"start": 61.01, "end": 61.61, "word": " نفسه", "probability": 0.9964192708333334}, {"start": 61.61, "end": 61.83, "word": " بس", "probability": 0.970458984375}, {"start": 61.83, "end": 62.63, "word": " بنطبق", "probability": 0.825439453125}, {"start": 62.63, "end": 62.99, "word": " عليه", "probability": 0.98681640625}, {"start": 62.99, "end": 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"end": 107.26, "word": " قيمة", "probability": 0.98681640625}, {"start": 107.26, "end": 107.94, "word": " لمحدد", "probability": 0.9781901041666666}, {"start": 107.94, "end": 108.1, "word": " ما", "probability": 0.73974609375}, {"start": 108.1, "end": 108.28, "word": " هو", "probability": 0.5615234375}, {"start": 108.28, "end": 108.56, "word": " هذه", "probability": 0.951171875}, {"start": 108.56, "end": 109.14, "word": " القيمة", "probability": 0.9622395833333334}, {"start": 109.14, "end": 109.8, "word": " تساوي", "probability": 0.868896484375}, {"start": 109.8, "end": 110.34, "word": " صفر", "probability": 0.8595377604166666}], "temperature": 1.0}, {"id": 5, "seek": 12594, "start": 110.9, "end": 125.94, "text": "الأن لو جينا للنقطة الأولى بيقول if each element in any row أو column of an n by n matrix A is multiplied by X by its factor then their sum is equal to determinant A", "tokens": [6027, 33456, 45164, 10874, 1829, 8315, 24976, 1863, 47432, 3660, 16247, 12610, 7578, 4724, 1829, 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أخدناه في الثانوية العامة طيب نجي للمرة اتنين", "tokens": [10721, 2407, 36632, 6225, 2304, 23328, 4032, 1863, 11242, 25513, 28242, 18871, 9381, 2288, 9154, 29538, 18863, 1863, 33546, 2288, 8978, 2423, 39184, 598, 69, 15104, 9673, 1863, 5718, 116, 2288, 46740, 2407, 8717, 7435, 2304, 3615, 9673, 7435, 2304, 45367, 23758, 4724, 1829, 9566, 1211, 3615, 22653, 12174, 32640, 3660, 9673, 24401, 3215, 37037, 15730, 32239, 3794, 4724, 7435, 16254, 3215, 25894, 24793, 8717, 36178, 2423, 28820, 10943, 13672, 1829, 5551, 9778, 3215, 8315, 3224, 8978, 6024, 104, 7649, 2407, 10632, 18863, 10943, 3660, 23032, 1829, 3555, 8717, 7435, 1829, 5296, 19528, 25720, 1975, 2655, 1863, 9957], "avg_logprob": -0.13083964676568002, "compression_ratio": 1.7025641025641025, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 142.35, "end": 142.83, "word": "أو", "probability": 0.924560546875}, {"start": 142.83, "end": 143.37, "word": " أي", "probability": 0.68212890625}, {"start": 143.37, "end": 144.09, 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square", "probability": 0.88916015625}, {"start": 1083.14, "end": 1085.9, "word": " matrix", "probability": 0.94775390625}, {"start": 1085.9, "end": 1086.38, "word": " A", "probability": 0.74658203125}, {"start": 1086.38, "end": 1089.52, "word": " is", "probability": 0.5732421875}, {"start": 1089.52, "end": 1093.8, "word": " called", "probability": 0.91552734375}, {"start": 1093.8, "end": 1095.72, "word": " singular", "probability": 0.97265625}, {"start": 1095.72, "end": 1100.38, "word": " if", "probability": 0.4541015625}, {"start": 1100.38, "end": 1103.3, "word": " determinant", "probability": 0.720703125}], "temperature": 1.0}, {"id": 46, "seek": 113376, "start": 1106.44, "end": 1133.76, "text": "للـ A بدو يساوي 0 and non singular if determinant لل A does not equal to 0 theorem if", "tokens": [1211, 1211, 39184, 316, 47525, 2407, 7251, 3794, 995, 45865, 1958, 293, 2107, 20010, 498, 41296, 24976, 316, 775, 406, 2681, 281, 1958, 20904, 498], "avg_logprob": -0.4738581868318411, 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{"id": 48, "seek": 120791, "start": 1193.95, "end": 1207.91, "text": "remark if the system star has exactly one solution", "tokens": [2579, 809, 498, 264, 1185, 3543, 575, 2293, 472, 3827], "avg_logprob": -0.2515980059450323, "compression_ratio": 0.9259259259259259, "no_speech_prob": 0.0, "words": [{"start": 1193.9499999999998, "end": 1195.35, "word": "remark", "probability": 0.689697265625}, {"start": 1195.35, "end": 1196.75, "word": " if", "probability": 0.7890625}, {"start": 1196.75, "end": 1198.51, "word": " the", "probability": 0.90283203125}, {"start": 1198.51, "end": 1200.49, "word": " system", "probability": 0.9765625}, {"start": 1200.49, "end": 1203.83, "word": " star", "probability": 0.450439453125}, {"start": 1203.83, "end": 1206.39, "word": " has", "probability": 0.9140625}, {"start": 1206.39, "end": 1206.77, "word": " exactly", "probability": 0.91796875}, {"start": 1206.77, "end": 1207.03, "word": " one", "probability": 0.9580078125}, {"start": 1207.03, "end": 1207.91, "word": " solution", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 49, "seek": 124733, "start": 1222.51, "end": 1247.33, "text": "we find it by two methods بطريقة تام طريقة الأولى ال raw echelon four", "tokens": [826, 915, 309, 538, 732, 7150, 4724, 9566, 16572, 28671, 6055, 10943, 23032, 16572, 28671, 16247, 12610, 7578, 2423, 8936, 36803, 338, 266, 1451], "avg_logprob": -0.3834375, "compression_ratio": 1.0340909090909092, "no_speech_prob": 0.0, "words": [{"start": 1222.51, "end": 1222.87, "word": "we", "probability": 0.10009765625}, {"start": 1222.87, "end": 1223.41, "word": " find", "probability": 0.9208984375}, {"start": 1223.41, "end": 1223.95, "word": " it", "probability": 0.9765625}, {"start": 1223.95, "end": 1230.31, "word": " by", "probability": 0.533203125}, {"start": 1230.31, "end": 1231.17, "word": " two", "probability": 0.90185546875}, {"start": 1231.17, "end": 1236.67, "word": " methods", "probability": 0.88818359375}, {"start": 1236.67, "end": 1239.19, "word": " بطريقة", "probability": 0.9476318359375}, {"start": 1239.19, "end": 1239.57, "word": " تام", "probability": 0.5269775390625}, {"start": 1239.57, "end": 1240.99, "word": " طريقة", "probability": 0.7793782552083334}, {"start": 1240.99, "end": 1241.93, "word": " الأولى", "probability": 0.97705078125}, {"start": 1241.93, "end": 1242.89, "word": " ال", "probability": 0.29833984375}, {"start": 1242.89, "end": 1244.73, "word": " raw", "probability": 0.34619140625}, {"start": 1244.73, "end": 1246.81, "word": " echelon", "probability": 0.89404296875}, {"start": 1246.81, "end": 1247.33, "word": " four", "probability": 0.4951171875}], "temperature": 1.0}, {"id": 50, "seek": 127683, "start": 1251.87, "end": 1276.83, "text": "by the rational form on the argumented matrix number اتنين the Gaussian elimination", "tokens": [2322, 264, 15090, 1254, 322, 264, 6770, 292, 8141, 1230, 1975, 2655, 1863, 9957, 264, 39148, 29224], "avg_logprob": -0.4804687367545234, "compression_ratio": 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1276.29, "word": " Gaussian", "probability": 0.66357421875}, {"start": 1276.29, "end": 1276.83, "word": " elimination", "probability": 0.95703125}], "temperature": 1.0}, {"id": 51, "seek": 131717, "start": 1291.41, "end": 1317.17, "text": "Lawson elimination by exchange the matrix into upper triangle matrix", "tokens": [43, 12282, 266, 29224, 538, 7742, 264, 8141, 666, 6597, 13369, 8141], "avg_logprob": -0.43058893313774693, "compression_ratio": 1.0303030303030303, "no_speech_prob": 0.0, "words": [{"start": 1291.41, "end": 1292.11, "word": "Lawson", "probability": 0.5185139973958334}, {"start": 1292.11, "end": 1292.89, "word": " elimination", "probability": 0.90673828125}, {"start": 1292.89, "end": 1294.77, "word": " by", "probability": 0.8515625}, {"start": 1294.77, "end": 1297.43, "word": " exchange", "probability": 0.65380859375}, {"start": 1297.43, "end": 1299.87, "word": " the", "probability": 0.5849609375}, {"start": 1299.87, "end": 1300.65, "word": " matrix", "probability": 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1344.5, "end": 1344.94, "word": " اكس", "probability": 0.9005533854166666}, {"start": 1344.94, "end": 1345.44, "word": " تلاتة", "probability": 0.8619384765625}, {"start": 1345.44, "end": 1346.06, "word": " يساوي", "probability": 0.85546875}, {"start": 1346.06, "end": 1346.62, "word": " اتنين", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 53, "seek": 137153, "start": 1350.15, "end": 1371.53, "text": "-3x1-x2 3x3-2 4x1 2x2-3x3 0", "tokens": [12, 18, 87, 16, 12, 87, 17, 805, 87, 18, 12, 17, 1017, 87, 16, 568, 87, 17, 12, 18, 87, 18, 1958], "avg_logprob": -0.2571614719927311, "compression_ratio": 0.8181818181818182, "no_speech_prob": 0.0, "words": [{"start": 1350.1499999999999, "end": 1351.55, "word": "-3x1", "probability": 0.6173095703125}, {"start": 1351.55, "end": 1352.95, "word": "-x2", "probability": 0.8357747395833334}, {"start": 1352.95, "end": 1356.85, "word": " 3x3", "probability": 0.62298583984375}, {"start": 1356.85, "end": 1359.57, "word": "-2", "probability": 0.615966796875}, {"start": 1359.57, "end": 1362.49, "word": " 4x1", "probability": 0.93212890625}, {"start": 1362.49, "end": 1366.41, "word": " 2x2", "probability": 0.7143961588541666}, {"start": 1366.41, "end": 1369.77, "word": "-3x3", "probability": 0.826904296875}, {"start": 1369.77, "end": 1371.53, "word": " 0", "probability": 0.0173797607421875}], "temperature": 1.0}, {"id": 54, "seek": 147199, "start": 1449.43, "end": 1471.99, "text": "نرجع لكلام اللي احنا كتبينه هذا ال بيقول consider the system of linear equations وعطاني n من المعادلات في n من المجاهد طبعا سابقا ناخد هذا ال system وكتبناه على شكل اللي هو حاصل ضرب مصوفات بالطريقة هذه يعني ال system اصلا كتبناه على حاصل ضرب على شكل حاصل ضرب مصوفتين", "tokens": [1863, 47341, 3615, 5296, 28820, 10943, 13672, 1829, 1975, 5016, 8315, 9122, 2655, 3555, 9957, 3224, 23758, 2423, 4724, 1829, 39648, 1949, 264, 1185, 295, 8213, 11787, 4032, 3615, 9566, 7649, 1829, 297, 9154, 9673, 3615, 18513, 1211, 9307, 8978, 297, 9154, 9673, 7435, 40294, 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{"start": 1451.03, "end": 1451.37, "word": " هذا", "probability": 0.76611328125}, {"start": 1451.37, "end": 1452.83, "word": " ال", "probability": 0.231689453125}, {"start": 1452.83, "end": 1453.55, "word": " بيقول", "probability": 0.7613932291666666}, {"start": 1453.55, "end": 1454.03, "word": " consider", "probability": 0.5498046875}, {"start": 1454.03, "end": 1454.25, "word": " the", "probability": 0.384033203125}, {"start": 1454.25, "end": 1454.67, "word": " system", "probability": 0.9580078125}, {"start": 1454.67, "end": 1454.83, "word": " of", "probability": 0.87890625}, {"start": 1454.83, "end": 1455.07, "word": " linear", "probability": 0.77734375}, {"start": 1455.07, "end": 1455.73, "word": " equations", "probability": 0.94970703125}, {"start": 1455.73, "end": 1456.47, "word": " وعطاني", "probability": 0.83876953125}, {"start": 1456.47, "end": 1456.77, "word": " n", "probability": 0.324462890625}, {"start": 1456.77, "end": 1457.11, "word": " من", "probability": 0.96630859375}, {"start": 1457.11, "end": 1458.27, "word": " المعادلات", "probability": 0.8994140625}, {"start": 1458.27, "end": 1458.59, "word": " في", "probability": 0.935546875}, {"start": 1458.59, "end": 1459.01, "word": " n", "probability": 0.87109375}, {"start": 1459.01, "end": 1459.37, "word": " من", "probability": 0.98095703125}, {"start": 1459.37, "end": 1460.15, "word": " المجاهد", "probability": 0.9063720703125}, {"start": 1460.15, "end": 1461.07, "word": " طبعا", "probability": 0.93603515625}, {"start": 1461.07, "end": 1461.57, "word": " سابقا", "probability": 0.859619140625}, {"start": 1461.57, "end": 1461.89, "word": " ناخد", "probability": 0.8063151041666666}, {"start": 1461.89, "end": 1462.11, "word": " هذا", "probability": 0.8671875}, {"start": 1462.11, "end": 1462.23, "word": " ال", "probability": 0.794921875}, {"start": 1462.23, "end": 1462.41, "word": " system", "probability": 0.95703125}, {"start": 1462.41, "end": 1463.09, "word": " وكتبناه", "probability": 0.8746744791666666}, {"start": 1463.09, "end": 1463.25, "word": " على", "probability": 0.9423828125}, {"start": 1463.25, "end": 1463.83, "word": " شكل", "probability": 0.966552734375}, {"start": 1463.83, "end": 1464.37, "word": " اللي", "probability": 0.68896484375}, {"start": 1464.37, "end": 1464.53, "word": " هو", "probability": 0.97705078125}, {"start": 1464.53, "end": 1464.93, "word": " حاصل", "probability": 0.7799479166666666}, {"start": 1464.93, "end": 1465.15, "word": " ضرب", "probability": 0.983154296875}, {"start": 1465.15, "end": 1465.89, "word": " مصوفات", "probability": 0.9002685546875}, {"start": 1465.89, "end": 1466.53, "word": " بالطريقة", "probability": 0.9774169921875}, {"start": 1466.53, "end": 1466.79, "word": " هذه", "probability": 0.720703125}, {"start": 1466.79, "end": 1467.43, "word": " يعني", "probability": 0.86328125}, {"start": 1467.43, "end": 1467.57, "word": " ال", "probability": 0.947265625}, {"start": 1467.57, "end": 1467.91, "word": " system", "probability": 0.97900390625}, {"start": 1467.91, "end": 1468.15, "word": " اصلا", "probability": 0.6297607421875}, {"start": 1468.15, "end": 1468.71, "word": " كتبناه", "probability": 0.9583984375}, {"start": 1468.71, "end": 1468.87, "word": " على", "probability": 0.9189453125}, {"start": 1468.87, "end": 1469.33, "word": " حاصل", "probability": 0.9873046875}, {"start": 1469.33, "end": 1469.71, "word": " ضرب", "probability": 0.99560546875}, {"start": 1469.71, "end": 1469.97, "word": " على", "probability": 0.8056640625}, {"start": 1469.97, "end": 1470.35, "word": " شكل", "probability": 0.954345703125}, {"start": 1470.35, "end": 1470.83, "word": " حاصل", "probability": 0.9876302083333334}, {"start": 1470.83, "end": 1471.09, "word": " ضرب", "probability": 0.9970703125}, {"start": 1471.09, "end": 1471.99, "word": " مصوفتين", "probability": 0.92275390625}], "temperature": 1.0}, {"id": 55, "seek": 150073, "start": 1472.19, "end": 1500.73, "text": "بتساوي في مصوفة الثوابت الأولانية سمناها مصوفة المعاملات هذه سمناها مصوفة المجاهيل هذه سمناها مصوفة الثوابت يبقى هذه سمناها coefficient matrix هذه unknown matrix هذه constant matrix او اختصاراً حطيناها على شكل ax يساوي b ax هي coefficient matrix والx هي مصوفة المجاهيل والb هي مصوفة الثوابت", "tokens": [3555, 2655, 3794, 995, 45865, 8978, 3714, 9381, 38688, 3660, 6024, 104, 14407, 3555, 2655, 16247, 12610, 7649, 10632, 8608, 2304, 8315, 11296, 3714, 9381, 38688, 3660, 9673, 3615, 10943, 1211, 9307, 29538, 8608, 2304, 8315, 11296, 3714, 9381, 38688, 3660, 9673, 7435, 40294, 26895, 29538, 8608, 2304, 8315, 11296, 3714, 9381, 38688, 3660, 6024, 104, 14407, 3555, 2655, 7251, 3555, 4587, 7578, 29538, 8608, 2304, 8315, 11296, 17619, 8141, 29538, 9841, 8141, 29538, 5754, 8141, 1975, 2407, 1975, 46456, 9381, 9640, 995, 14111, 11331, 9566, 1829, 8315, 11296, 15844, 13412, 28820, 6360, 7251, 3794, 995, 45865, 272, 6360, 39896, 17619, 8141, 16070, 87, 39896, 3714, 9381, 38688, 3660, 9673, 7435, 40294, 26895, 16070, 65, 39896, 3714, 9381, 38688, 3660, 6024, 104, 14407, 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ال system الان كإنه اللي بيعطيني ضمانة ما هي الضمانة اللي ممكن تكون عندنا حتى يكون لل system حلا واحدة", "tokens": [7649, 7251, 30544, 46740, 6225, 3215, 3215, 11778, 3224, 8717, 3224, 16373, 1829, 9154, 21542, 1211, 12610, 42963, 1975, 33753, 2304, 6027, 10632, 16472, 20193, 7251, 30544, 11331, 1211, 23758, 2423, 1185, 2423, 7649, 9122, 28814, 1863, 3224, 13672, 1829, 4724, 40228, 9566, 1829, 22653, 48812, 2304, 7649, 3660, 19446, 39896, 6024, 114, 2304, 7649, 3660, 13672, 1829, 3714, 43020, 6055, 30544, 43242, 8315, 11331, 49975, 7251, 30544, 24976, 1185, 11331, 15040, 36764, 24401, 3660], "avg_logprob": -0.33018092967961965, "compression_ratio": 1.7888198757763976, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1550.51, "end": 1550.89, "word": "ان", "probability": 0.102294921875}, {"start": 1550.89, "end": 1551.25, "word": " يكون", "probability": 0.930419921875}, {"start": 1551.25, "end": 1551.43, "word": " له", "probability": 0.87744140625}, {"start": 1551.43, "end": 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"end": 1590.52, "word": " solution", "probability": 0.96923828125}, {"start": 1590.52, "end": 1590.82, "word": " لو", "probability": 0.92138671875}, {"start": 1590.82, "end": 1591.1, "word": " كان", "probability": 0.98095703125}, {"start": 1591.1, "end": 1591.38, "word": " له", "probability": 0.2410888671875}, {"start": 1591.38, "end": 1591.78, "word": " حل", "probability": 0.980712890625}, {"start": 1591.78, "end": 1592.34, "word": " واحد", "probability": 0.9912109375}, {"start": 1592.34, "end": 1592.88, "word": " فقط", "probability": 0.99462890625}, {"start": 1592.88, "end": 1593.66, "word": " يبقى", "probability": 0.96728515625}, {"start": 1593.66, "end": 1594.0, "word": " ممكن", "probability": 0.97802734375}, {"start": 1594.0, "end": 1594.78, "word": " الحصول", "probability": 0.9930013020833334}, {"start": 1594.78, "end": 1595.28, "word": " عليه", "probability": 0.982421875}, {"start": 1595.28, "end": 1596.62, "word": " بطريقتين", "probability": 0.9880859375}, {"start": 1596.62, 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"probability": 0.97080078125}, {"start": 1609.58, "end": 1609.9, "word": " واحد", "probability": 0.9091796875}, {"start": 1609.9, "end": 1610.32, "word": " واحد", "probability": 0.90673828125}, {"start": 1610.32, "end": 1610.52, "word": " و", "probability": 0.814453125}, {"start": 1610.52, "end": 1610.64, "word": " اللي", "probability": 0.880615234375}, {"start": 1610.64, "end": 1611.02, "word": " منه", "probability": 0.865478515625}, {"start": 1611.02, "end": 1611.32, "word": " فوق", "probability": 0.89013671875}, {"start": 1611.32, "end": 1611.7, "word": " أصفر", "probability": 0.8280029296875}, {"start": 1611.7, "end": 1611.8, "word": " و", "probability": 0.97412109375}, {"start": 1611.8, "end": 1611.94, "word": " اللي", "probability": 0.97412109375}, {"start": 1611.94, "end": 1612.3, "word": " منه", "probability": 0.932373046875}, {"start": 1612.3, "end": 1612.74, "word": " تاح", "probability": 0.6016845703125}, {"start": 1612.74, "end": 1613.92, "word": " أصفر", "probability": 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1642.6, "text": "الطريقة الثانية هي طريقة جاوس بيقول the gaussian elimination اللي هو محذفات جاوس by changing the matrix into upper triangle matrix يعني أنا بدي أحولها إلى مصغفة بحيث القطر الرئيسي كله لتحتيثي روميان أسفار احنا بيقولك هي الطريقتين يعني هل اختلفت الثانية عن الأولى؟", "tokens": [6027, 9566, 16572, 28671, 6024, 104, 7649, 10632, 39896, 23032, 16572, 28671, 10874, 995, 41779, 4724, 1829, 39648, 264, 5959, 21948, 29224, 13672, 1829, 31439, 3714, 5016, 8848, 5172, 9307, 10874, 995, 41779, 538, 4473, 264, 8141, 666, 6597, 13369, 8141, 37495, 22653, 41850, 4724, 16254, 5551, 5016, 12610, 11296, 30731, 3714, 9381, 17082, 5172, 3660, 4724, 5016, 1829, 12984, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 28242, 3224, 5296, 2655, 33753, 1829, 12984, 1829, 12602, 20498, 1829, 7649, 5551, 3794, 5172, 9640, 1975, 5016, 8315, 4724, 1829, 39648, 4117, 39896, 41950, 16572, 38149, 9957, 37495, 22653, 8032, 1211, 1975, 46456, 46538, 2655, 6024, 104, 7649, 10632, 18871, 16247, 12610, 7578, 22807], "avg_logprob": -0.2678179926516717, "compression_ratio": 1.6827309236947792, "no_speech_prob": 0.0, "words": [{"start": 1619.46, "end": 1620.1, "word": "الطريقة", "probability": 0.863525390625}, {"start": 1620.1, "end": 1620.64, "word": " الثانية", "probability": 0.96240234375}, {"start": 1620.64, "end": 1621.0, "word": " هي", "probability": 0.79345703125}, {"start": 1621.0, "end": 1621.46, "word": " طريقة", "probability": 0.8987630208333334}, {"start": 1621.46, "end": 1621.86, "word": " جاوس", "probability": 0.5892333984375}, {"start": 1621.86, "end": 1622.14, "word": " بيقول", "probability": 0.597900390625}, {"start": 1622.14, "end": 1622.36, "word": " the", "probability": 0.1466064453125}, {"start": 1622.36, "end": 1623.88, "word": " gaussian", "probability": 0.535980224609375}, {"start": 1623.88, "end": 1624.62, "word": " elimination", "probability": 0.9462890625}, {"start": 1624.62, "end": 1625.38, "word": " اللي", "probability": 0.8046875}, {"start": 1625.38, "end": 1625.56, "word": " هو", "probability": 0.853515625}, {"start": 1625.56, "end": 1626.34, "word": " محذفات", "probability": 0.86416015625}, {"start": 1626.34, "end": 1626.7, "word": " جاوس", "probability": 0.93505859375}, {"start": 1626.7, "end": 1627.2, "word": " by", "probability": 0.058807373046875}, {"start": 1627.2, "end": 1628.14, "word": " changing", "probability": 0.833984375}, {"start": 1628.14, "end": 1628.3, "word": " the", "probability": 0.8125}, {"start": 1628.3, "end": 1628.64, "word": " matrix", "probability": 0.89453125}, {"start": 1628.64, "end": 1629.14, "word": " into", "probability": 0.81103515625}, {"start": 1629.14, "end": 1629.6, "word": " upper", "probability": 0.57470703125}, {"start": 1629.6, "end": 1630.24, "word": " triangle", "probability": 0.78564453125}, {"start": 1630.24, "end": 1631.0, "word": " matrix", "probability": 0.962890625}, {"start": 1631.0, "end": 1631.5, "word": " يعني", "probability": 0.901611328125}, {"start": 1631.5, "end": 1631.68, "word": " أنا", "probability": 0.697265625}, {"start": 1631.68, "end": 1631.86, "word": " بدي", "probability": 0.552001953125}, {"start": 1631.86, "end": 1632.4, "word": " أحولها", "probability": 0.86865234375}, {"start": 1632.4, "end": 1632.74, "word": " إلى", "probability": 0.875}, {"start": 1632.74, "end": 1633.34, "word": " مصغفة", "probability": 0.7291748046875}, {"start": 1633.34, "end": 1633.8, "word": " بحيث", "probability": 0.925537109375}, {"start": 1633.8, "end": 1634.38, "word": " القطر", "probability": 0.7640787760416666}, {"start": 1634.38, "end": 1634.86, "word": " الرئيسي", "probability": 0.93330078125}, {"start": 1634.86, "end": 1635.26, "word": " كله", "probability": 0.845458984375}, {"start": 1635.26, "end": 1635.94, "word": " لتحتيثي", "probability": 0.7243245442708334}, {"start": 1635.94, "end": 1636.4, "word": " روميان", "probability": 0.776123046875}, {"start": 1636.4, "end": 1637.7, "word": " أسفار", "probability": 0.84423828125}, {"start": 1637.7, "end": 1638.36, "word": " احنا", "probability": 0.7760416666666666}, {"start": 1638.36, "end": 1638.84, "word": " بيقولك", "probability": 0.69451904296875}, {"start": 1638.84, "end": 1639.04, "word": " هي", "probability": 0.85693359375}, {"start": 1639.04, "end": 1639.82, "word": " الطريقتين", "probability": 0.981689453125}, {"start": 1639.82, "end": 1640.32, "word": " يعني", "probability": 0.92138671875}, {"start": 1640.32, "end": 1640.6, "word": " هل", "probability": 0.95556640625}, {"start": 1640.6, "end": 1641.24, "word": " اختلفت", "probability": 0.9664306640625}, {"start": 1641.24, "end": 1641.64, "word": " الثانية", "probability": 0.9547119140625}, {"start": 1641.64, "end": 1641.84, "word": " عن", "probability": 0.94921875}, {"start": 1641.84, "end": 1642.6, "word": " الأولى؟", "probability": 0.944091796875}], "temperature": 1.0}, {"id": 63, "seek": 166781, "start": 1642.63, "end": 1667.81, "text": "بس الأولى بدها شغل اكتر شغل اكتر ليش؟ انا بدي اللى فوق كمان أسفار مش عقد اللى تحتى يبقى جاوسيا نسهى أسهل من مين؟ من روشيلون 4 تمام طيب احنا بنعطي مثال و من هذا المثال نحاول نستخدم الجاوسيا في حل هذا المثال إذا كان بنحل ب solution واحد فقط", "tokens": [3555, 3794, 16247, 12610, 7578, 47525, 11296, 13412, 17082, 1211, 1975, 4117, 2655, 2288, 13412, 17082, 1211, 1975, 4117, 2655, 2288, 32239, 8592, 22807, 1975, 8315, 4724, 16254, 13672, 7578, 6156, 30543, 9122, 2304, 7649, 5551, 3794, 5172, 9640, 37893, 6225, 28543, 13672, 7578, 6055, 33753, 7578, 7251, 3555, 4587, 7578, 10874, 995, 41779, 25528, 8717, 3794, 3224, 7578, 5551, 3794, 3224, 1211, 9154, 3714, 9957, 22807, 9154, 12602, 2407, 8592, 26895, 11536, 1017, 46811, 10943, 23032, 1829, 3555, 1975, 5016, 8315, 44945, 3615, 9566, 1829, 50113, 6027, 4032, 9154, 23758, 9673, 12984, 6027, 8717, 5016, 995, 12610, 8717, 14851, 9778, 40448, 25724, 995, 41779, 25528, 8978, 11331, 1211, 23758, 9673, 12984, 6027, 11933, 15730, 25961, 44945, 5016, 1211, 4724, 3827, 36764, 24401, 6156, 47432], "avg_logprob": -0.20907737965148593, 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"end": 2022.74, "word": " ماسوّناش", "probability": 0.5340169270833334}, {"start": 2022.74, "end": 2022.96, "word": " اشي", "probability": 0.7268880208333334}, {"start": 2022.96, "end": 2023.26, "word": " يبقى", "probability": 0.952880859375}, {"start": 2023.26, "end": 2023.64, "word": " الصف", "probability": 0.97509765625}, {"start": 2023.64, "end": 2024.06, "word": " الاول", "probability": 0.7156982421875}, {"start": 2024.06, "end": 2024.28, "word": " هي", "probability": 0.43603515625}, {"start": 2024.28, "end": 2024.74, "word": " واحد", "probability": 0.837646484375}, {"start": 2024.74, "end": 2025.32, "word": " واحد", "probability": 0.9365234375}, {"start": 2025.32, "end": 2026.28, "word": " وهي", "probability": 0.78125}, {"start": 2026.28, "end": 2026.88, "word": " سالب", "probability": 0.83984375}, {"start": 2026.88, "end": 2027.46, "word": " نص", "probability": 0.991943359375}, {"start": 2027.46, "end": 2028.28, "word": " وهذا", "probability": 0.854736328125}, {"start": 2028.28, "end": 2029.06, "word": " واحد", "probability": 0.985595703125}], "temperature": 1.0}, {"id": 80, "seek": 203730, "start": 2029.42, "end": 2037.3, "text": "0 2 3 2 1 0 0", "tokens": [15, 568, 805, 568, 502, 1958, 1958], "avg_logprob": -0.7294921949505806, "compression_ratio": 0.6842105263157895, "no_speech_prob": 0.0, "words": [{"start": 2029.42, "end": 2030.22, "word": "0", "probability": 0.0526123046875}, {"start": 2030.22, "end": 2031.24, "word": " 2", "probability": 0.3671875}, {"start": 2031.24, "end": 2032.06, "word": " 3", "probability": 0.86181640625}, {"start": 2032.06, "end": 2033.2, "word": " 2", "probability": 0.55126953125}, {"start": 2033.2, "end": 2034.72, "word": " 1", "probability": 0.716796875}, {"start": 2034.72, "end": 2036.26, "word": " 0", "probability": 0.95361328125}, {"start": 2036.26, "end": 2037.3, "word": " 0", "probability": 0.7861328125}], "temperature": 1.0}, {"id": 81, "seek": 207650, "start": 2048.0, "end": 2076.5, "text": "الان هذا ال system اللي عندنا او ال system الأصلي is equivalent to يبقى باجي بقوله the system star is equivalent to هذا يكافئ مين؟ يكافئ x واحد زي x اتنين ناقص نص x تلاتة بده يساوي واحد", "tokens": [6027, 7649, 23758, 2423, 1185, 13672, 1829, 43242, 8315, 1975, 2407, 2423, 1185, 16247, 9381, 20292, 307, 10344, 281, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 264, 1185, 3543, 307, 10344, 281, 23758, 7251, 4117, 31845, 19986, 3714, 9957, 22807, 7251, 4117, 31845, 19986, 2031, 36764, 24401, 30767, 1829, 2031, 1975, 2655, 1863, 9957, 8717, 995, 4587, 9381, 8717, 9381, 2031, 6055, 1211, 9307, 3660, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.25933442642162374, "compression_ratio": 1.5738636363636365, "no_speech_prob": 0.0, "words": [{"start": 2048.0, "end": 2048.96, "word": "الان", "probability": 0.63037109375}, {"start": 2048.96, "end": 2049.82, "word": " هذا", "probability": 0.4306640625}, {"start": 2049.82, "end": 2050.38, "word": " ال", "probability": 0.90625}, {"start": 2050.38, "end": 2050.74, "word": " system", "probability": 0.50341796875}, {"start": 2050.74, "end": 2051.08, "word": " اللي", "probability": 0.770263671875}, {"start": 2051.08, "end": 2052.02, "word": " عندنا", "probability": 0.753173828125}, {"start": 2052.02, "end": 2052.54, "word": " او", "probability": 0.6544189453125}, {"start": 2052.54, "end": 2052.72, "word": " ال", "probability": 0.94189453125}, {"start": 2052.72, "end": 2053.06, "word": " system", "probability": 0.9453125}, {"start": 2053.06, "end": 2053.86, "word": " الأصلي", "probability": 0.77587890625}, {"start": 2053.86, "end": 2054.44, "word": " is", "probability": 0.6904296875}, {"start": 2054.44, "end": 2055.46, "word": " equivalent", "probability": 0.92138671875}, {"start": 2055.46, "end": 2056.28, "word": " to", "probability": 0.9365234375}, {"start": 2056.28, "end": 2057.1, "word": " يبقى", "probability": 0.929443359375}, {"start": 2057.1, "end": 2057.52, "word": " باجي", "probability": 0.84716796875}, {"start": 2057.52, "end": 2058.22, "word": " بقوله", "probability": 0.710693359375}, {"start": 2058.22, "end": 2058.58, "word": " the", "probability": 0.277587890625}, {"start": 2058.58, "end": 2060.22, "word": " system", "probability": 0.9697265625}, {"start": 2060.22, "end": 2062.2, "word": " star", "probability": 0.3544921875}, {"start": 2062.2, "end": 2062.9, "word": " is", "probability": 0.9462890625}, {"start": 2062.9, "end": 2064.48, "word": " equivalent", "probability": 0.91162109375}, {"start": 2064.48, "end": 2066.62, "word": " to", "probability": 0.97314453125}, {"start": 2066.62, "end": 2067.62, "word": " هذا", "probability": 0.8662109375}, {"start": 2067.62, "end": 2068.26, "word": " يكافئ", "probability": 0.9503173828125}, {"start": 2068.26, "end": 2069.14, "word": " مين؟", "probability": 0.6512044270833334}, {"start": 2069.14, "end": 2070.02, "word": " يكافئ", "probability": 0.9765625}, {"start": 2070.02, "end": 2070.44, "word": " x", "probability": 0.74169921875}, {"start": 2070.44, "end": 2071.08, "word": " واحد", "probability": 0.6793212890625}, {"start": 2071.08, "end": 2071.82, "word": " زي", "probability": 0.807373046875}, {"start": 2071.82, "end": 2072.3, "word": " x", "probability": 0.5126953125}, {"start": 2072.3, "end": 2072.98, "word": " اتنين", "probability": 0.9222412109375}, {"start": 2072.98, "end": 2074.02, "word": " ناقص", "probability": 0.8814697265625}, {"start": 2074.02, "end": 2074.44, "word": " نص", "probability": 0.992431640625}, {"start": 2074.44, "end": 2074.84, "word": " x", "probability": 0.41455078125}, {"start": 2074.84, "end": 2075.46, "word": " تلاتة", "probability": 0.875732421875}, {"start": 2075.46, "end": 2075.72, "word": " بده", "probability": 0.4793701171875}, {"start": 2075.72, "end": 2076.16, "word": " يساوي", "probability": 0.8819580078125}, {"start": 2076.16, "end": 2076.5, "word": " واحد", "probability": 0.982177734375}], "temperature": 1.0}, {"id": 82, "seek": 209346, "start": 2077.13, "end": 2093.47, "text": "هنا اكس اتنين او اتنين اكس اتنين زائد تلاتة على اتنين اكس تلاتة يساوي واحد وهنا المص اكس تلاتة بده يساوي قداش بده يساوي ناقص تلاتة", "tokens": [3224, 8315, 1975, 4117, 3794, 1975, 2655, 1863, 9957, 1975, 2407, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 15844, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 6055, 1211, 9307, 3660, 7251, 3794, 995, 45865, 36764, 24401, 37037, 8315, 9673, 9381, 1975, 4117, 3794, 6055, 1211, 9307, 3660, 47525, 3224, 7251, 3794, 995, 45865, 12174, 3215, 33599, 47525, 3224, 7251, 3794, 995, 45865, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660], "avg_logprob": -0.17054116544200154, "compression_ratio": 2.2596153846153846, "no_speech_prob": 0.0, "words": [{"start": 2077.13, "end": 2077.75, "word": "هنا", "probability": 0.53369140625}, {"start": 2077.75, "end": 2078.51, "word": " اكس", "probability": 0.6211344401041666}, {"start": 2078.51, "end": 2079.19, "word": " اتنين", "probability": 0.931640625}, {"start": 2079.19, "end": 2079.55, "word": " او", "probability": 0.94482421875}, {"start": 2079.55, "end": 2080.23, "word": " اتنين", "probability": 0.97021484375}, {"start": 2080.23, "end": 2080.77, "word": " اكس", "probability": 0.9851888020833334}, {"start": 2080.77, "end": 2081.31, "word": " اتنين", "probability": 0.978515625}, {"start": 2081.31, "end": 2082.31, "word": " زائد", "probability": 0.7664388020833334}, {"start": 2082.31, "end": 2082.93, "word": " تلاتة", "probability": 0.9552001953125}, {"start": 2082.93, "end": 2083.19, "word": " على", "probability": 0.71240234375}, {"start": 2083.19, "end": 2083.77, "word": " اتنين", "probability": 0.9791259765625}, {"start": 2083.77, "end": 2084.31, "word": " اكس", "probability": 0.9306640625}, {"start": 2084.31, "end": 2084.81, "word": " تلاتة", "probability": 0.94873046875}, {"start": 2084.81, "end": 2085.39, "word": " يساوي", "probability": 0.8790283203125}, {"start": 2085.39, "end": 2085.91, "word": " واحد", "probability": 0.98779296875}, {"start": 2085.91, "end": 2086.91, "word": " وهنا", "probability": 0.791259765625}, {"start": 2086.91, "end": 2087.75, "word": " المص", "probability": 0.5865478515625}, {"start": 2087.75, "end": 2088.53, "word": " اكس", "probability": 0.95654296875}, {"start": 2088.53, "end": 2089.43, "word": " تلاتة", "probability": 0.9866943359375}, {"start": 2089.43, "end": 2090.11, "word": " بده", "probability": 0.60546875}, {"start": 2090.11, "end": 2090.45, "word": " يساوي", "probability": 0.948974609375}, {"start": 2090.45, "end": 2091.07, "word": " قداش", "probability": 0.6700032552083334}, {"start": 2091.07, "end": 2091.49, "word": " بده", "probability": 0.771484375}, {"start": 2091.49, "end": 2091.89, "word": " يساوي", "probability": 0.9771728515625}, {"start": 2091.89, "end": 2092.83, "word": " ناقص", "probability": 0.8779296875}, {"start": 2092.83, "end": 2093.47, "word": " تلاتة", "probability": 0.97265625}], "temperature": 1.0}, {"id": 83, "seek": 212092, "start": 2094.07, "end": 2120.93, "text": "الان من هذا بقدر اقول له ال X3 كده ساوي يا بنات؟ سالب ستة الان هاي جبنا له X3 بقدر اجيب له X2 يبقى برجعود في المعادلة اللي من او فوق يبقى 2X2 بدي اضرب في سالب ستة بصير عندى سالب تسعة بده ساوي واحد", "tokens": [6027, 7649, 9154, 23758, 4724, 28543, 2288, 1975, 39648, 46740, 2423, 1783, 18, 9122, 3215, 3224, 8608, 995, 45865, 35186, 4724, 8315, 2655, 22807, 8608, 6027, 3555, 8608, 2655, 3660, 2423, 7649, 8032, 47302, 10874, 3555, 8315, 46740, 1783, 18, 4724, 28543, 2288, 1975, 7435, 1829, 3555, 46740, 1783, 17, 7251, 3555, 4587, 7578, 4724, 47341, 3615, 23328, 8978, 9673, 3615, 18513, 37977, 13672, 1829, 9154, 1975, 2407, 6156, 30543, 7251, 3555, 4587, 7578, 568, 55, 17, 4724, 16254, 1975, 11242, 25513, 8978, 8608, 6027, 3555, 8608, 2655, 3660, 4724, 9381, 13546, 43242, 7578, 8608, 6027, 3555, 6055, 3794, 27884, 47525, 3224, 8608, 995, 45865, 36764, 24401], "avg_logprob": -0.27560762840288655, "compression_ratio": 1.87292817679558, "no_speech_prob": 0.0, "words": 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{"start": 2099.07, "end": 2100.31, "word": " سالب", "probability": 0.8167317708333334}, {"start": 2100.31, "end": 2100.93, "word": " ستة", "probability": 0.93603515625}, {"start": 2100.93, "end": 2102.13, "word": " الان", "probability": 0.6649169921875}, {"start": 2102.13, "end": 2102.65, "word": " هاي", "probability": 0.448486328125}, {"start": 2102.65, "end": 2103.03, "word": " جبنا", "probability": 0.7677408854166666}, {"start": 2103.03, "end": 2103.21, "word": " له", "probability": 0.4716796875}, {"start": 2103.21, "end": 2103.99, "word": " X3", "probability": 0.955078125}, {"start": 2103.99, "end": 2105.01, "word": " بقدر", "probability": 0.9593098958333334}, {"start": 2105.01, "end": 2105.41, "word": " اجيب", "probability": 0.826904296875}, {"start": 2105.41, "end": 2105.61, "word": " له", "probability": 0.73046875}, {"start": 2105.61, "end": 2106.53, "word": " X2", "probability": 0.984375}, {"start": 2106.53, "end": 2106.83, "word": " يبقى", "probability": 0.888671875}, {"start": 2106.83, "end": 2107.69, "word": " برجعود", "probability": 0.629486083984375}, {"start": 2107.69, "end": 2107.97, "word": " في", "probability": 0.529296875}, {"start": 2107.97, "end": 2109.31, "word": " المعادلة", "probability": 0.9384765625}, {"start": 2109.31, "end": 2109.65, "word": " اللي", "probability": 0.67431640625}, {"start": 2109.65, "end": 2109.87, "word": " من", "probability": 0.93212890625}, {"start": 2109.87, "end": 2110.13, "word": " او", "probability": 0.5946044921875}, {"start": 2110.13, "end": 2110.45, "word": " فوق", "probability": 0.92236328125}, {"start": 2110.45, "end": 2111.39, "word": " يبقى", "probability": 0.9639892578125}, {"start": 2111.39, "end": 2113.17, "word": " 2X2", "probability": 0.685546875}, {"start": 2113.17, "end": 2113.89, "word": " بدي", "probability": 0.665771484375}, {"start": 2113.89, "end": 2114.33, "word": " اضرب", "probability": 0.8904622395833334}, {"start": 2114.33, "end": 2114.53, "word": " في", "probability": 0.955078125}, {"start": 2114.53, "end": 2115.13, "word": " سالب", "probability": 0.8982747395833334}, {"start": 2115.13, "end": 2115.85, "word": " ستة", "probability": 0.9658203125}, {"start": 2115.85, "end": 2116.63, "word": " بصير", "probability": 0.8772786458333334}, {"start": 2116.63, "end": 2117.71, "word": " عندى", "probability": 0.6396484375}, {"start": 2117.71, "end": 2118.61, "word": " سالب", "probability": 0.96630859375}, {"start": 2118.61, "end": 2119.37, "word": " تسعة", "probability": 0.98046875}, {"start": 2119.37, "end": 2119.93, "word": " بده", "probability": 0.6116943359375}, {"start": 2119.93, "end": 2120.53, "word": " ساوي", "probability": 0.9303385416666666}, {"start": 2120.53, "end": 2120.93, "word": " واحد", "probability": 0.97607421875}], "temperature": 1.0}, {"id": 84, "seek": 213171, "start": 2121.41, "end": 2131.71, "text": "مظبوط يبقى هذا معناه انه x2 بده يساوي عشرة هذا معناه انه x2 بده يساوي خمسة", "tokens": [2304, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 23758, 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طلعناها", "probability": 0.9408203125}, {"start": 2185.0, "end": 2185.68, "word": " بناقص", "probability": 0.872802734375}, {"start": 2185.68, "end": 2186.3, "word": " سبعة", "probability": 0.9469401041666666}], "temperature": 1.0}, {"id": 87, "seek": 220504, "start": 2187.56, "end": 2205.04, "text": "و X2 بخمسة و X3 بسالب ستة و زي ما تشايفين حلا واحدا ليس اكثر و احنا اثبتنا انه حل واحد عن طريق حساب قيمة المحدد", "tokens": [2407, 1783, 17, 4724, 9778, 2304, 3794, 3660, 4032, 1783, 18, 4724, 3794, 6027, 3555, 8608, 2655, 3660, 4032, 30767, 1829, 19446, 6055, 8592, 995, 33911, 9957, 11331, 15040, 36764, 24401, 995, 32239, 3794, 1975, 4117, 49115, 4032, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 16472, 3224, 11331, 1211, 36764, 24401, 18871, 23032, 16572, 4587, 11331, 3794, 16758, 12174, 32640, 3660, 9673, 24401, 3215], "avg_logprob": -0.17104640828840662, "compression_ratio": 1.496124031007752, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2187.56, "end": 2187.86, 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قيمة", "probability": 0.9943033854166666}, {"start": 2203.38, "end": 2205.04, "word": " المحدد", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 88, "seek": 223250, "start": 2206.46, "end": 2232.5, "text": "طيب، حتى الآن ما اتكلمناش في عنوان هذا ال section اللي هو grammar rule اللي هي قاعدة ال grammar لحل المعادلات، تمام؟ يبقى بدنا نيجي لقاعدة grammar يبقى هذا grammar rule إيش بتقول grammar rules؟ we use", "tokens": [9566, 1829, 3555, 12399, 11331, 49975, 6024, 48506, 19446, 1975, 2655, 4117, 19528, 1863, 33599, 8978, 18871, 2407, 7649, 23758, 2423, 3541, 13672, 1829, 31439, 22317, 4978, 13672, 1829, 39896, 12174, 995, 22488, 3660, 2423, 22317, 5296, 5016, 1211, 9673, 3615, 18513, 1211, 9307, 12399, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 4587, 995, 22488, 3660, 22317, 7251, 3555, 4587, 7578, 23758, 22317, 4978, 11933, 1829, 8592, 39894, 39648, 22317, 4474, 22807, 321, 764], "avg_logprob": -0.16777819413237455, 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rules؟", "probability": 0.82763671875}, {"start": 2231.56, "end": 2231.76, "word": " we", "probability": 0.8515625}, {"start": 2231.76, "end": 2232.5, "word": " use", "probability": 0.90185546875}], "temperature": 1.0}, {"id": 89, "seek": 224892, "start": 2235.86, "end": 2248.92, "text": "أكرامر رول نستخدم قاعدة أكرامر إذا كان الـ determinant للـ a لا يساوي zero يعني أيه الشبنات؟", "tokens": [10721, 37983, 10943, 2288, 12602, 12610, 8717, 14851, 9778, 40448, 12174, 995, 22488, 3660, 5551, 37983, 10943, 2288, 11933, 15730, 25961, 2423, 39184, 41296, 24976, 39184, 257, 20193, 7251, 3794, 995, 45865, 4018, 37495, 22653, 36632, 3224, 25124, 3555, 8315, 2655, 22807], "avg_logprob": -0.4509447646695514, "compression_ratio": 1.216, "no_speech_prob": 0.0, "words": [{"start": 2235.8599999999997, "end": 2237.2599999999998, "word": "أكرامر", "probability": 0.6576995849609375}, {"start": 2237.2599999999998, "end": 2238.66, "word": " رول", "probability": 0.53350830078125}, {"start": 2238.66, "end": 2239.96, "word": " نستخدم", "probability": 0.773406982421875}, {"start": 2239.96, "end": 2240.58, "word": " قاعدة", "probability": 0.9576416015625}, {"start": 2240.58, "end": 2241.28, "word": " أكرامر", "probability": 0.80731201171875}, {"start": 2241.28, "end": 2241.84, "word": " إذا", "probability": 0.912109375}, {"start": 2241.84, "end": 2242.68, "word": " كان", "probability": 0.9921875}, {"start": 2242.68, "end": 2244.18, "word": " الـ", "probability": 0.5843505859375}, {"start": 2244.18, "end": 2245.08, "word": " determinant", "probability": 0.6904296875}, {"start": 2245.08, "end": 2245.98, "word": " للـ", "probability": 0.361328125}, {"start": 2245.98, "end": 2246.44, "word": " a", "probability": 0.2142333984375}, {"start": 2246.44, "end": 2246.56, "word": " لا", "probability": 0.442626953125}, {"start": 2246.56, "end": 2247.26, "word": " يساوي", "probability": 0.8525390625}, {"start": 2247.26, "end": 2247.64, "word": " zero", "probability": 0.348388671875}, {"start": 2247.64, 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2337.19, "text": "matrix where حيث the matrix بي كي is obtained بنحصل عليها from the matrix a من المصوفة a after replacing after", "tokens": [76, 267, 6579, 689, 11331, 1829, 12984, 264, 8141, 4724, 1829, 9122, 1829, 307, 14879, 44945, 5016, 36520, 25894, 11296, 490, 264, 8141, 257, 9154, 9673, 9381, 38688, 3660, 257, 934, 19139, 934], "avg_logprob": -0.4692095597000683, "compression_ratio": 1.1724137931034482, "no_speech_prob": 0.0, "words": [{"start": 2308.53, "end": 2310.27, "word": "matrix", "probability": 0.49920654296875}, {"start": 2310.27, "end": 2313.19, "word": " where", "probability": 0.1533203125}, {"start": 2313.19, "end": 2313.91, "word": " حيث", "probability": 0.7775065104166666}, {"start": 2313.91, "end": 2314.13, "word": " the", "probability": 0.201416015625}, {"start": 2314.13, "end": 2314.81, "word": " matrix", "probability": 0.94140625}, {"start": 2314.81, "end": 2316.15, "word": " بي", "probability": 0.3787841796875}, {"start": 2316.15, "end": 2317.25, "word": " كي", "probability": 0.8935546875}, {"start": 2317.25, "end": 2320.23, "word": " is", "probability": 0.51123046875}, {"start": 2320.23, "end": 2322.89, "word": " obtained", "probability": 0.88720703125}, {"start": 2322.89, "end": 2324.55, "word": " بنحصل", "probability": 0.738037109375}, {"start": 2324.55, "end": 2325.39, "word": " عليها", "probability": 0.983154296875}, {"start": 2325.39, "end": 2326.57, "word": " from", "probability": 0.88623046875}, {"start": 2326.57, "end": 2328.85, "word": " the", "probability": 0.79736328125}, {"start": 2328.85, "end": 2330.99, "word": " matrix", "probability": 0.94580078125}, {"start": 2330.99, "end": 2332.37, "word": " a", "probability": 0.346923828125}, {"start": 2332.37, "end": 2333.21, "word": " من", "probability": 0.935546875}, {"start": 2333.21, "end": 2334.05, "word": " المصوفة", "probability": 0.9185791015625}, {"start": 2334.05, "end": 2334.21, "word": " a", "probability": 0.293212890625}, {"start": 2334.21, "end": 2334.63, "word": " after", "probability": 0.8955078125}, {"start": 2334.63, "end": 2335.37, "word": " replacing", "probability": 0.93017578125}, {"start": 2335.37, "end": 2337.19, "word": " after", "probability": 0.85107421875}], "temperature": 1.0}, {"id": 93, "seek": 236294, "start": 2338.73, "end": 2362.95, "text": "replacing بعد ما نستبدل the kiss calm العموض رقم K by the constant calm بعمودي ثوابت", "tokens": [265, 564, 5615, 39182, 19446, 8717, 14851, 44510, 1211, 264, 7704, 7151, 2423, 25957, 2407, 11242, 12602, 4587, 2304, 591, 538, 264, 5754, 7151, 4724, 25957, 2407, 16254, 38637, 14407, 3555, 2655], "avg_logprob": -0.31202651515151514, "compression_ratio": 1.074766355140187, "no_speech_prob": 0.0, "words": [{"start": 2338.73, "end": 2340.13, "word": "replacing", "probability": 0.7513834635416666}, {"start": 2340.13, "end": 2341.15, "word": " بعد", "probability": 0.72216796875}, {"start": 2341.15, "end": 2341.37, "word": " ما", "probability": 0.8623046875}, {"start": 2341.37, "end": 2342.59, 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"word": " ثوابت", "probability": 0.8997802734375}], "temperature": 1.0}, {"id": 94, "seek": 239225, "start": 2372.45, "end": 2392.25, "text": "Example use Kramer's rule to solve the system", "tokens": [11149, 335, 781, 764, 591, 44772, 311, 4978, 281, 5039, 264, 1185], "avg_logprob": -0.49399038461538464, "compression_ratio": 0.9, "no_speech_prob": 0.0, "words": [{"start": 2372.45, "end": 2373.85, "word": "Example", "probability": 0.6530965169270834}, {"start": 2373.85, "end": 2375.25, "word": " use", "probability": 0.359130859375}, {"start": 2375.25, "end": 2380.93, "word": " Kramer's", "probability": 0.5946044921875}, {"start": 2380.93, "end": 2382.79, "word": " rule", "probability": 0.7724609375}, {"start": 2382.79, "end": 2385.21, "word": " to", "probability": 0.93701171875}, {"start": 2385.21, "end": 2385.59, "word": " solve", "probability": 0.95556640625}, {"start": 2385.59, "end": 2385.77, "word": " the", "probability": 0.88134765625}, {"start": 2385.77, "end": 2392.25, "word": " system", "probability": 0.953125}], "temperature": 1.0}, {"id": 95, "seek": 241762, "start": 2395.56, "end": 2417.62, "text": "2x1 زائد 2x2 ناقص x3 يساوي 2 ناقص 3x1 ناقص x2 زائد 3x3 يساوي سالب 2 4x1", "tokens": [17, 87, 16, 30767, 16373, 3215, 568, 87, 17, 8717, 995, 4587, 9381, 2031, 18, 7251, 3794, 995, 45865, 568, 8717, 995, 4587, 9381, 805, 87, 16, 8717, 995, 4587, 9381, 2031, 17, 30767, 16373, 3215, 805, 87, 18, 7251, 3794, 995, 45865, 8608, 6027, 3555, 568, 1017, 87, 16], "avg_logprob": -0.19607843429434532, "compression_ratio": 1.4583333333333333, "no_speech_prob": 0.0, "words": [{"start": 2395.56, "end": 2396.96, "word": "2x1", "probability": 0.5933024088541666}, {"start": 2396.96, "end": 2398.28, "word": " زائد", "probability": 0.5427068074544271}, {"start": 2398.28, "end": 2399.88, "word": " 2x2", "probability": 0.89453125}, {"start": 2399.88, "end": 2401.2, "word": " ناقص", "probability": 0.8436279296875}, {"start": 2401.2, "end": 2402.1, "word": " x3", "probability": 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هنا بيظل اتنين يبقى ناقص اربعة ويسوى ناقص اتناش يبقى بدي اكس واحد يا بنات يبقى determinant لل B", "tokens": [3224, 8315, 4724, 1829, 19913, 1211, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 44945, 995, 4587, 9381, 46811, 7649, 10632, 34105, 4724, 1829, 19913, 1211, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 1975, 25513, 27884, 4032, 1829, 3794, 2407, 7578, 8717, 995, 4587, 9381, 1975, 2655, 1863, 33599, 7251, 3555, 4587, 7578, 4724, 16254, 1975, 4117, 3794, 36764, 24401, 35186, 4724, 8315, 2655, 7251, 3555, 4587, 7578, 41296, 24976, 363], "avg_logprob": -0.25520833922021186, "compression_ratio": 1.7218045112781954, "no_speech_prob": 0.0, "words": [{"start": 2728.04, "end": 2728.38, "word": "هنا", "probability": 0.49664306640625}, {"start": 2728.38, "end": 2728.8, "word": " بيظل", "probability": 0.57220458984375}, {"start": 2728.8, "end": 2729.38, "word": " ناقص", "probability": 0.87109375}, {"start": 2729.38, "end": 2729.84, 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determinant للـ A و يساوي determinant للـ B 1 طالع عنده بناقص 14 و determinant لل A ب2 يساوي كده؟ سالب سبعة الان بDX 2 اللي هو determinant لل B 2 على determinant لل A و يساوي determinant لل B 2 طالع 10 على 2 و يساوي 5", "tokens": [16, 15844, 41296, 24976, 39184, 316, 4032, 7251, 3794, 995, 45865, 41296, 24976, 39184, 363, 502, 23032, 6027, 3615, 43242, 3224, 44945, 995, 4587, 9381, 3499, 4032, 41296, 24976, 316, 4724, 17, 7251, 3794, 995, 45865, 9122, 3215, 3224, 22807, 8608, 6027, 3555, 8608, 3555, 27884, 2423, 7649, 4724, 35, 55, 568, 13672, 1829, 31439, 41296, 24976, 363, 568, 15844, 41296, 24976, 316, 4032, 7251, 3794, 995, 45865, 41296, 24976, 363, 568, 23032, 6027, 3615, 1266, 15844, 568, 4032, 7251, 3794, 995, 45865, 1025], "avg_logprob": -0.328125, "compression_ratio": 1.9935897435897436, "no_speech_prob": 9.560585021972656e-05, "words": [{"start": 2745.04, "end": 2745.6, "word": "1", "probability": 0.161865234375}, {"start": 2745.6, "end": 2746.28, "word": " على", 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0.5913899739583334}, {"start": 2809.51, "end": 2810.11, "word": " طريقة", "probability": 0.9752604166666666}, {"start": 2810.11, "end": 2811.07, "word": " كرامر", "probability": 0.8223876953125}, {"start": 2811.07, "end": 2811.87, "word": " إذا", "probability": 0.594970703125}, {"start": 2811.87, "end": 2812.69, "word": " لازلنا", "probability": 0.9276123046875}, {"start": 2812.69, "end": 2812.91, "word": " في", "probability": 0.97265625}, {"start": 2812.91, "end": 2813.23, "word": " نفس", "probability": 0.9912109375}, {"start": 2813.23, "end": 2813.39, "word": " ال", "probability": 0.93310546875}, {"start": 2813.39, "end": 2813.75, "word": " section", "probability": 0.9228515625}, {"start": 2813.75, "end": 2814.25, "word": " هذا", "probability": 0.70166015625}, {"start": 2814.25, "end": 2814.85, "word": " و", "probability": 0.5849609375}, {"start": 2814.85, "end": 2815.41, "word": " بنكمل", "probability": 0.9269205729166666}, {"start": 2815.41, "end": 2815.59, "word": " ان", "probability": 0.56689453125}, {"start": 2815.59, "end": 2815.89, "word": " شاء", "probability": 0.98779296875}, {"start": 2815.89, "end": 2816.27, "word": " الله", "probability": 0.94873046875}, {"start": 2816.27, "end": 2817.31, "word": " المرة", "probability": 0.98291015625}, {"start": 2817.31, "end": 2819.13, "word": " القادمة", "probability": 0.9903971354166666}], "temperature": 1.0}, {"id": 114, "seek": 282848, "start": 2819.84, "end": 2828.48, "text": "دير باركو طريقة كتامر very important بس لا ألجأ إليها إلا إذا كان المحدد لا يساوي zero", "tokens": [3215, 13546, 4724, 9640, 4117, 2407, 23032, 16572, 28671, 9122, 2655, 10943, 2288, 588, 1021, 4724, 3794, 20193, 5551, 1211, 7435, 10721, 11933, 20292, 11296, 11933, 15040, 11933, 15730, 25961, 9673, 24401, 3215, 20193, 7251, 3794, 995, 45865, 4018], "avg_logprob": -0.26171875074505807, "compression_ratio": 1.1779661016949152, "no_speech_prob": 0.0, "words": [{"start": 2819.84, "end": 2820.14, "word": "دير", "probability": 0.28619384765625}, {"start": 2820.14, "end": 2820.46, "word": " باركو", "probability": 0.8018798828125}, {"start": 2820.46, "end": 2820.82, "word": " طريقة", "probability": 0.8870442708333334}, {"start": 2820.82, "end": 2821.58, "word": " كتامر", "probability": 0.59173583984375}, {"start": 2821.58, "end": 2821.88, "word": " very", "probability": 0.64892578125}, {"start": 2821.88, "end": 2822.96, "word": " important", "probability": 0.95361328125}, {"start": 2822.96, "end": 2823.36, "word": " بس", "probability": 0.916015625}, {"start": 2823.36, "end": 2823.62, "word": " لا", "probability": 0.76123046875}, {"start": 2823.62, "end": 2824.18, "word": " ألجأ", "probability": 0.9505615234375}, {"start": 2824.18, "end": 2824.76, "word": " إليها", "probability": 0.8707682291666666}, {"start": 2824.76, "end": 2825.4, "word": " إلا", "probability": 0.9765625}, {"start": 2825.4, "end": 2825.68, "word": " إذا", "probability": 0.980224609375}, {"start": 2825.68, "end": 2825.98, "word": " كان", "probability": 0.99169921875}, {"start": 2825.98, "end": 2826.66, "word": " المحدد", "probability": 0.9881184895833334}, {"start": 2826.66, "end": 2826.82, "word": " لا", "probability": 0.814453125}, {"start": 2826.82, "end": 2827.68, "word": " يساوي", "probability": 0.95703125}, {"start": 2827.68, "end": 2828.48, "word": " zero", "probability": 0.5576171875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2829.2585, "duration_after_vad": 2605.5006249999933}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..67badad0d598282fc9b1ed237e2046cf9271586e
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/j5jA0RPmugY_raw.srt
@@ -0,0 +1,1716 @@
+1
+00:00:19,670 --> 00:00:24,650
+بسم الله الرحمن الرحيم بنرجع لإكمال ال section
+
+2
+00:00:24,650 --> 00:00:30,670
+الماضي وهو ال cofactors وعرفنا المرة اللي فاتت ال
+
+3
+00:00:30,670 --> 00:00:34,670
+minor و ال cofactor قولنا ال minor هو المحدد
+
+4
+00:00:34,670 --> 00:00:41,930
+الأصغر المناظر لأنصر من عناصر مصحوفة ماوهو المحدد
+
+5
+00:00:41,930 --> 00:00:46,770
+الناتج من sub matrix بعد ما نشطب الصف اللى موجود
+
+6
+00:00:46,770 --> 00:00:51,970
+فيه هذا العنصر و العمود اللى موجود فيه هذا العنصر
+
+7
+00:00:51,970 --> 00:00:57,290
+الباقي بنسميه محدد الأصغر المناظر لهذا العنصر يبقى
+
+8
+00:00:57,290 --> 00:01:02,630
+هذا ال minor ال cofactor هو ال minor نفسه بس بنطبق
+
+9
+00:01:02,630 --> 00:01:08,580
+عليه قاعدة الإشاراتمنحط قبله سالب واحد ومنرفعها
+
+10
+00:01:08,580 --> 00:01:14,240
+للأس رقم الصف اللي موجود في هذا العنصر ورقم العمود
+
+11
+00:01:14,240 --> 00:01:18,660
+فإن كان هذا المجموع زوجي تبقى الإشارة موجب وإن كان
+
+12
+00:01:18,660 --> 00:01:23,360
+المجموع فردي بتكون الإشارة سالبة وهذا ما تحدثنا به
+
+13
+00:01:23,360 --> 00:01:29,840
+وعطينا عليه مثلا في المرة الماضيةالان بنكمل على ما
+
+14
+00:01:29,840 --> 00:01:33,760
+أخدناه في المرة الماضية و بنعطي النظرية التالية
+
+15
+00:01:33,760 --> 00:01:39,400
+النظرية هذه تتكون من نقطتهم النقطة الأولى كيف
+
+16
+00:01:39,400 --> 00:01:44,880
+بنحسب قيمة المحدد عدديا النقطة الثانية هو اكتشف
+
+17
+00:01:44,880 --> 00:01:50,340
+ممكن نطلع قيمة لمحدد ما هو هذه القيمة تساوي صفر
+
+18
+00:01:50,900 --> 00:01:54,160
+الأن لو جينا للنقطة الأولى بيقول if each element
+
+19
+00:01:54,160 --> 00:01:59,440
+in any row أو column of an n by n matrix A is
+
+20
+00:01:59,440 --> 00:02:04,040
+multiplied by X by its factor then their sum is
+
+21
+00:02:04,040 --> 00:02:09,790
+equal to determinant Aيعني لو بدنا نجيب محدد
+
+22
+00:02:09,790 --> 00:02:17,090
+المصفوف A المربع لنظام N في M بدنا نعمل ما يأتي
+
+23
+00:02:17,090 --> 00:02:24,830
+بدنا نمسك كل عنصر من عناصر أي صفرأو أي عمود ونضرب
+
+24
+00:02:24,830 --> 00:02:29,990
+كل عنصر من هذه العناصر في الـ cofactor المناظر لهو
+
+25
+00:02:29,990 --> 00:02:36,330
+نجمع المجموع هذا بيطلعني قيمة المحدد وهذا ليس
+
+26
+00:02:36,330 --> 00:02:40,150
+بجديد عليكم نفس الكلام اللي أخدناه في الثانوية
+
+27
+00:02:40,150 --> 00:02:45,850
+العامة طيب نجي للمرة اتنيننمر اتنين بيقول ليش؟ لو
+
+28
+00:02:45,850 --> 00:02:51,470
+كان كل عنصر في أي صفر I أو عمود J، أي عنصر من عنصر
+
+29
+00:02:51,470 --> 00:02:55,670
+أي صفر أو أي عمود، is multiplied by the factor of
+
+30
+00:02:55,670 --> 00:03:01,590
+another row K أو قلم L، بحيث الـK لا تساوي الـI
+
+31
+00:03:01,590 --> 00:03:05,850
+والـL لا تساوي الـJ، then the sum equals zero، إيش
+
+32
+00:03:05,850 --> 00:03:11,230
+يعني؟أحنا بنقول في النقطة الأولى لو جيت على صف
+
+33
+00:03:11,230 --> 00:03:15,910
+ضربت كل عنصر في الـ cofactor تبعه جمعة بيطلع لقيمة
+
+34
+00:03:15,910 --> 00:03:20,750
+المحدد هنا بقول لو جيت على عنصر صف أو أي عمود
+
+35
+00:03:20,750 --> 00:03:27,270
+وضربت في الـ cofactor المناظر لصف اخر او لعمود اخر
+
+36
+00:03:27,270 --> 00:03:32,630
+فالنتج يساوي Zero على طول الخط يعني هل قيمة المحدد
+
+37
+00:03:32,630 --> 00:03:37,880
+تساوي Zero؟لأ النقطة الأولى صحيح بتجيب لقيمة
+
+38
+00:03:37,880 --> 00:03:40,380
+المحدد بس النقطة التانية بتجيبش لقيمة المحدد
+
+39
+00:03:40,380 --> 00:03:44,660
+بتقولك كيف بتطلع القيمة zero بقولك مامسك أي صف
+
+40
+00:03:44,660 --> 00:03:48,580
+باجي الصف اللي جابله و الصف اللي بعده او اللي بعدي
+
+41
+00:03:48,580 --> 00:03:52,300
+بعده اللي بده هي المهم صف موازن له
+
+42
+00:04:01,360 --> 00:04:05,920
+الكلام اللى بنقوله بدنا نروح نبينه كعمليا فاخدنا
+
+43
+00:04:05,920 --> 00:04:11,260
+المثال التانيمعطيني المصوفة وقال هاتلي determinant
+
+44
+00:04:11,260 --> 00:04:17,460
+لإيه طبعا بدي أروح أفك هذه المصوفة باستخدام عناصر
+
+45
+00:04:17,460 --> 00:04:22,520
+أي صف أو أي عمود منها قال لي هنا that is for the I
+
+46
+00:04:22,520 --> 00:04:26,660
+throw يعني لو بدي أجيب قيمة المحدد باستخدام الصف
+
+47
+00:04:26,660 --> 00:04:34,220
+رقم I يبقى باجي بقول ايه I one في من؟ في المحدد في
+
+48
+00:04:34,220 --> 00:04:39,250
+ال my في ال cofactor تبعهزائد AI2 في الـ cofactor
+
+49
+00:04:39,250 --> 00:04:43,250
+تبعه زائد زائد لغاية مصر لغاية AIN في الـ cofactor
+
+50
+00:04:43,250 --> 00:04:47,990
+تبعه أجمع بتعطيني قيمة المحدد لكن لو بدأ فك
+
+51
+00:04:47,990 --> 00:04:52,830
+باستخدام العمود يبقى نفس النتيجة هتعطيني لأنت تغير
+
+52
+00:04:52,830 --> 00:04:59,140
+لأن المحدد له قيمة واحدة فقط لغيرأذا أردت أن أفكر
+
+53
+00:04:59,140 --> 00:05:01,300
+باستخدام العمود رقم ج
+
+54
+00:05:28,250 --> 00:05:33,450
+خلّينا مع النقطة الأولى اللى هى رقم ايه يبقى رقم
+
+55
+00:05:33,450 --> 00:05:39,070
+ايه انا بدى determined للمصفوفة
+
+56
+00:05:39,070 --> 00:05:43,210
+ايه بدى جداش قيمة محدد المصفوفة يعنى هي عندكوا
+
+57
+00:05:43,210 --> 00:05:47,750
+طالع صحوف اختارولى الصف انفك المحدد باستخدام هذا
+
+58
+00:05:47,750 --> 00:05:53,140
+الصف ايهتانى طبعا التانى لإنه فيه zero وبالتالي
+
+59
+00:05:53,140 --> 00:05:57,220
+بيبسط لعملية من عملية الشغل إذا بالدالي للصف
+
+60
+00:05:57,220 --> 00:06:02,800
+التانى الصف التانى لحد العنصر الأول قداش هاي ناقص
+
+61
+00:06:02,800 --> 00:06:08,080
+واحد جلبته ضروف مين في ال cofactor تبعه ال
+
+62
+00:06:08,080 --> 00:06:13,120
+cofactor تبعه بروح بقول هاي ناقص واحد هذا جاي في
+
+63
+00:06:13,120 --> 00:06:19,140
+أي صفرفي الصف الثاني والعمود الأول يبقى بقول أس
+
+64
+00:06:19,140 --> 00:06:25,000
+اتنين زائد واحد في المحدد الأصغر المناظر له نشطة
+
+65
+00:06:25,000 --> 00:06:30,380
+بصفه وعموده بضالة تلاتة ناقص اتنين تلاتة ناقص
+
+66
+00:06:30,380 --> 00:06:36,410
+اتنين و هنا ناقص واحد تلاتة بالشكل اللي عندهاالعدل
+
+67
+00:06:36,410 --> 00:06:42,190
+اللي بعده زائد اللي هو لإتنين في سالب واحد قصر هذا
+
+68
+00:06:42,190 --> 00:06:46,990
+جاي لإتنين في الصف الثاني و العمود الثاني إذا باجي
+
+69
+00:06:46,990 --> 00:06:52,130
+بقول هنا اتنين زائد اتنين في المحدد الأصغر المناظر
+
+70
+00:06:52,130 --> 00:06:57,110
+له بنشتغل صفه و عموده و بيظل اربعة سالب اتنين و
+
+71
+00:06:57,110 --> 00:07:04,020
+هنا واحد و هنا تلاتة زائداللي هو Zero في مين؟ في
+
+72
+00:07:04,020 --> 00:07:11,180
+سالب واحد مرفوع للأس اتنين زائد تلاتة في المحدد
+
+73
+00:07:11,180 --> 00:07:16,600
+الأصغر مضى نشطه بصفه و عموده بيصير أربع ثلاثة وهنا
+
+74
+00:07:16,600 --> 00:07:22,170
+واحد وهنا سالب واحدديجي نطلع النتيجة هذه جداش
+
+75
+00:07:22,170 --> 00:07:27,590
+وتساوي طبعا سالب واحد تكييب اللي هو جداش سالب واحد
+
+76
+00:07:27,590 --> 00:07:31,950
+في سالب واحد موجة بواحد مع السلمة تلاتة في تلاتة
+
+77
+00:07:31,950 --> 00:07:38,410
+بتسعة ناقص اتنين طبعا ناقص اتنين في ناقص واحد اللي
+
+78
+00:07:38,410 --> 00:07:46,490
+هو باتنين في ناقص بكمان اتنين اللي بعدها زائد
+
+79
+00:07:46,490 --> 00:07:53,590
+اتنين فيهتلاتة في اربعة باطن عشر زائد اتنين وهنا
+
+80
+00:07:53,590 --> 00:07:59,590
+زائد زيرو بهذا الشكل طبعا بيبقى اللي عند هنا سابعة
+
+81
+00:07:59,590 --> 00:08:05,830
+وهنا عندك اربعة اتاش في اتنين بتمانية وعشرين يبقى
+
+82
+00:08:05,830 --> 00:08:12,490
+هاي لأ زائد تمانية وعشرين سابعة زائد تمانية وعشرين
+
+83
+00:08:12,730 --> 00:08:17,790
+يبقى هاي زائد اربعتاش في اتنين ب تمانية و عشرين
+
+84
+00:08:17,790 --> 00:08:25,970
+يبقى النتيجة تساوي خمسة و تلاتين طيب نيجي الان بدي
+
+85
+00:08:25,970 --> 00:08:31,470
+افك المحدد باستخدام عمود اخر بطل عن الصفر الثاني
+
+86
+00:08:31,470 --> 00:08:39,030
+لو بداشي اقوله and يبقى بدنا determinant لل ايه
+
+87
+00:08:39,030 --> 00:08:45,390
+بده يساويالـ determinant للـ A بده يساوي تختاروا
+
+88
+00:08:45,390 --> 00:08:49,570
+مين من الأعمدة؟ برضه تلاتة يبقى بدي أبدأ بالعنصر
+
+89
+00:08:49,570 --> 00:08:55,050
+الأول ناقص اتنين في ناقص واحد مرفوع بالعمود التالت
+
+90
+00:08:55,050 --> 00:08:59,630
+يا بنات يبقى هذا موجود في الصف الأول والعمود
+
+91
+00:08:59,630 --> 00:09:05,770
+التالت يبقى واحد زائد تلاتة نشطة بصفه وعموده بيبقى
+
+92
+00:09:05,770 --> 00:09:14,210
+سالب واحد اتنين وهنا واحد وسالب واحداللي بعده زائد
+
+93
+00:09:14,210 --> 00:09:19,570
+زيرو زائد
+
+94
+00:09:19,570 --> 00:09:33,070
+زائد زائد زائد
+
+95
+00:09:33,070 --> 00:09:42,700
+زائد زائد زائد زائد زائد زائد زائديبقى هذا الكلام
+
+96
+00:09:42,700 --> 00:09:47,940
+يساوي هذا الأس أربع يبقى بواحد بيظل عندى سالب
+
+97
+00:09:47,940 --> 00:09:53,640
+اتنين فيه سالب واحد في سالب واحد بواحد ناقص اتنين
+
+98
+00:09:53,640 --> 00:10:00,700
+هنا زائد zero زائد سالب واحد أس ستة يبقى بواحد
+
+99
+00:10:00,700 --> 00:10:07,240
+بيظل عندى تلاتة في أربع في اتنين بتمانية زائد
+
+100
+00:10:07,240 --> 00:10:12,490
+تلاتةهذا الكلام يساوي طبعا واحد نقص اتنين بيظل نقص
+
+101
+00:10:12,490 --> 00:10:17,790
+واحد فنقص اتنين بزايد اتنين زايد تلاتة و تمانية
+
+102
+00:10:17,790 --> 00:10:24,270
+احداش احداش في تلاتة تلاتة و تلاتين و اتنين خمسة و
+
+103
+00:10:24,270 --> 00:10:29,610
+تلاتين وهي نفس الإجابة من اللي فوق يبقى فكّنها بصف
+
+104
+00:10:29,610 --> 00:10:36,360
+و لا فكّنها بعمل بيعطيني قيمة المحدد طيبنجي نمرا
+
+105
+00:10:36,360 --> 00:10:41,580
+بي نمرا بي من المثلة نمرا بي بقول applied part two
+
+106
+00:10:41,580 --> 00:10:44,640
+of the theorem ايش يعني applied part two of the
+
+107
+00:10:44,640 --> 00:10:49,700
+theorem يعني بنطبق للنقطة رقم اتنين وهي لو خات
+
+108
+00:10:49,700 --> 00:10:56,030
+صافرضربت في كوفة
+
+109
+00:10:56,030 --> 00:11:02,390
+المحدد الأصغر المناظر لهذا الصفر اختارونا صفر من
+
+110
+00:11:02,390 --> 00:11:05,770
+هذه الصفور او عمود من هذه الصفور اللي عجبكوا فيهم
+
+111
+00:11:05,770 --> 00:11:08,890
+التاني
+
+112
+00:11:08,890 --> 00:11:14,750
+العمودي التاني ماشي بدا اختار العمودي التاني يبقى
+
+113
+00:11:14,750 --> 00:11:19,710
+انا بادهاجي اقول ما يأتي بدا استخدم العمودي التاني
+
+114
+00:11:19,710 --> 00:11:27,260
+هذايبقى بداش اقول هاي تلاتة بديش اشطف صفه و عموده
+
+115
+00:11:27,260 --> 00:11:32,740
+لأ بدي اختار عمود موازن له يا بتاخد العمود اللي
+
+116
+00:11:32,740 --> 00:11:36,340
+بعضه يا العمود اللي جابله سيان اي واحد فيهم ها
+
+117
+00:11:36,340 --> 00:11:40,670
+تختاروا مين كمان؟اللي بعده .. اللي بعده ولا اهم
+
+118
+00:11:40,670 --> 00:11:44,530
+يبقى بدي اجعل اللي بعده اللي هو الموازي له بدي
+
+119
+00:11:44,530 --> 00:11:50,630
+اشطب صفه و عموده بيظل مين عندي؟ بيظل عندي هاي ناقص
+
+120
+00:11:50,630 --> 00:11:57,150
+واحد الان هذا جاي في الصف الأول و العمود التالت
+
+121
+00:11:57,150 --> 00:12:03,170
+يبقى واحد زائد تلاتة فيه شطبنا صفه و عموده بيصير
+
+122
+00:12:03,170 --> 00:12:11,690
+ناقص واحد اتنين واحد ناقص واحدزائد اتنين في ناقص
+
+123
+00:12:11,690 --> 00:12:16,630
+واحد في هل هيبقى نيجي في ال cofactor تبعه المناظر
+
+124
+00:12:16,630 --> 00:12:21,890
+له هي future and raw او كولم is multiplied by the
+
+125
+00:12:21,890 --> 00:12:27,670
+by the cofactor هذه ايضا هذه مش factor cofactor
+
+126
+00:12:27,670 --> 00:12:37,520
+صليها اللي عندي cofactor وليس factorتمام طيب يبقى
+
+127
+00:12:37,520 --> 00:12:44,620
+بصير اتنين في سالب واحد احنا اخدنا الآن اتنين اه
+
+128
+00:12:44,620 --> 00:12:48,560
+اخدنا العمود التالت احنا مش هيك اخدنا العمود
+
+129
+00:12:48,560 --> 00:12:54,740
+التالت يبقى بالدادي اشطف صفه و عموده بيظل اربعة
+
+130
+00:12:54,740 --> 00:13:01,980
+تلاتة واحد سالب واحدهي أربعة تلاتة واحد سالب واحد
+
+131
+00:13:01,980 --> 00:13:07,140
+وظلت الإشارة تبعته الإشارة تبعته هو واقع في الصف
+
+132
+00:13:07,140 --> 00:13:13,070
+التاني والعمود التالت يبقى اتنين زائد تلاتةبالداجي
+
+133
+00:13:13,070 --> 00:13:19,050
+اللي بعده يبقى ناقص واحد في ناقص واحد مرفوع للأس
+
+134
+00:13:19,050 --> 00:13:22,350
+بالداجي العنصر اللي بعده اللي هو التلاتة جاي في
+
+135
+00:13:22,350 --> 00:13:27,950
+الصف التالت والعمود التالت يبقى تلاتة زائد تلاتة
+
+136
+00:13:27,950 --> 00:13:32,730
+في المحدد الأصغر المناظر له يبقى بنروح نشطب صف
+
+137
+00:13:32,730 --> 00:13:37,110
+عموده بصير أربعة تلاتة ناقص واحد اتنين أربعة تلاتة
+
+138
+00:13:37,110 --> 00:13:42,290
+ناقص واحد اتنين بهذا الشكليبقى النتيجة هذه تساوي
+
+139
+00:13:42,290 --> 00:13:47,870
+هذا الأس زوجي يبقى بظل تلاتة و هنا عندنا واحد ناقص
+
+140
+00:13:47,870 --> 00:13:55,490
+اتنين هنا هذا الفردي بيصير ناقص اتنين في ناقص اربع
+
+141
+00:13:55,490 --> 00:14:01,690
+ناقص تلاتة هذا عندنا زوجي يبقى بظل ناقص واحد في
+
+142
+00:14:01,690 --> 00:14:09,410
+تمانية زائد تلاتةالنتيجة هنا تساوي واحد ناقص اتنين
+
+143
+00:14:09,410 --> 00:14:14,970
+بيبقى ناقص واحد يبقى هاي ناقص تلاتة هذا عندنا سبعة
+
+144
+00:14:14,970 --> 00:14:22,370
+بالثالث اتنين بموجب اربعتاش تمامهنا تلاتة وتمانية
+
+145
+00:14:22,370 --> 00:14:27,770
+احداش بالسالب يبقى السالب احداش سالب احداش وسالب
+
+146
+00:14:27,770 --> 00:14:32,790
+تلاتة سالب اربعتاش واربعتاش النتج يساوي كده؟ Zero
+
+147
+00:14:32,790 --> 00:14:40,230
+يبقى انا ضربت عناصر اي صف او اي عمود في ال main في
+
+148
+00:14:40,230 --> 00:14:45,610
+ال cofactor المناظر لعناصر صف او عمود موازي ال low
+
+149
+00:14:45,920 --> 00:14:49,840
+اللي قبله او اللي بعده كله بيعطيك ايه بيعطيك نفس
+
+150
+00:14:49,840 --> 00:14:54,460
+النتيجة لحد هنا stop انتهى هذا ال section الى يكون
+
+151
+00:14:54,460 --> 00:15:03,400
+اكسر سايزز اللي هو اتنين عشرة اللي هو السؤال الأول
+
+152
+00:15:03,400 --> 00:15:13,080
+بدنا منه A وC وD والسؤال التاني بدنا منه B والسؤال
+
+153
+00:15:13,080 --> 00:15:15,460
+التالت والسؤال السابع
+
+154
+00:15:39,790 --> 00:15:45,450
+ننتقل الان لـ Section الذي يليه وهو Section 2.11
+
+155
+00:15:45,450 --> 00:15:53,790
+يبقى Section 2.11 Kramers Rule
+
+156
+00:15:53,790 --> 00:16:07,320
+قاعدة Kramersبقول ي consider the system of linear
+
+157
+00:16:07,320 --> 00:16:08,180
+equations
+
+158
+00:16:14,090 --> 00:16:25,590
+اللي هو a11 x1 a12 x2 زائد a1n xn بده يساوي b1 a21
+
+159
+00:16:25,590 --> 00:16:33,770
+x1 a22 x2 زائد a2n xn بده يساوي b2
+
+160
+00:16:44,980 --> 00:16:50,740
+هذا كله اللي هو هنسميه system star
+
+161
+00:17:01,860 --> 00:17:10,700
+is written as بروح نكتب على الشكل التالي اللي هو
+
+162
+00:17:10,700 --> 00:17:23,340
+المصوفة a11, a12, a1n, a21, a22, a2n بظل ماشي
+
+163
+00:17:23,340 --> 00:17:37,030
+اللغات a n1, a n2A N N كل هذا في X1 X2 لغاية XN
+
+164
+00:17:37,030 --> 00:17:45,850
+بده يساوي اللي هو B1 B2 لغاية BN الشكل اللي عندنا
+
+165
+00:17:45,850 --> 00:17:56,050
+هنا or capital A في X بده يساوي B definition
+
+166
+00:18:00,340 --> 00:18:09,520
+the square matrix A is
+
+167
+00:18:09,520 --> 00:18:13,800
+called
+
+168
+00:18:13,800 --> 00:18:20,380
+singular if
+
+169
+00:18:20,380 --> 00:18:23,300
+determinant
+
+170
+00:18:26,440 --> 00:18:38,600
+للـ A بدو يساوي 0 and non singular if
+
+171
+00:18:38,600 --> 00:18:48,700
+determinant لل A does not equal to 0 theorem
+
+172
+00:18:48,700 --> 00:18:53,760
+if
+
+173
+00:18:55,600 --> 00:19:06,020
+الـ determinant للـ a لا يساوي zero if determinant
+
+174
+00:19:06,020 --> 00:19:20,200
+ل a لا يساوي zero then the system star has exactly
+
+175
+00:19:20,200 --> 00:19:24,900
+one solution
+
+176
+00:19:53,950 --> 00:20:03,830
+remark if the system star
+
+177
+00:20:03,830 --> 00:20:07,910
+has exactly one solution
+
+178
+00:20:22,510 --> 00:20:30,310
+we find it by
+
+179
+00:20:30,310 --> 00:20:36,670
+two methods
+
+180
+00:20:36,670 --> 00:20:47,330
+بطريقة تام طريقة الأولى ال raw echelon four
+
+181
+00:20:51,870 --> 00:20:58,390
+by the rational form on the
+
+182
+00:20:58,390 --> 00:21:08,710
+argumented matrix number
+
+183
+00:21:08,710 --> 00:21:15,870
+اتنين the
+
+184
+00:21:15,870 --> 00:21:16,830
+Gaussian elimination
+
+185
+00:21:31,410 --> 00:21:45,930
+Lawson elimination by exchange the matrix into
+
+186
+00:21:45,930 --> 00:21:50,370
+upper
+
+187
+00:21:50,370 --> 00:21:54,070
+triangle
+
+188
+00:21:54,070 --> 00:21:57,170
+matrix
+
+189
+00:22:05,240 --> 00:22:18,540
+Example Solve the system اتنين
+
+190
+00:22:18,540 --> 00:22:26,060
+اكس واحد زي اتنين اكس اتنين ناقص اكس تلاتة يساوي
+
+191
+00:22:26,060 --> 00:22:26,620
+اتنين
+
+192
+00:22:30,150 --> 00:22:36,850
+-3x1-x2 3x3
+
+193
+00:22:36,850 --> 00:22:46,410
+-2 4x1 2x2
+
+194
+00:22:46,410 --> 00:22:49,770
+-3x3
+
+195
+00:22:49,770 --> 00:22:51,530
+0
+
+196
+00:24:09,430 --> 00:24:14,030
+نرجع لكلام اللي احنا كتبينه هذا ال بيقول consider
+
+197
+00:24:14,030 --> 00:24:17,110
+the system of linear equations وعطاني n من
+
+198
+00:24:17,110 --> 00:24:22,230
+المعادلات في n من المجاهد طبعا سابقا ناخد هذا ال
+
+199
+00:24:22,230 --> 00:24:25,890
+system وكتبناه على شكل اللي هو حاصل ضرب مصوفات
+
+200
+00:24:25,890 --> 00:24:29,330
+بالطريقة هذه يعني ال system اصلا كتبناه على حاصل
+
+201
+00:24:29,330 --> 00:24:33,570
+ضرب على شكل حاصل ضرب مصوفتينبتساوي في مصوفة
+
+202
+00:24:33,570 --> 00:24:38,050
+الثوابت الأولانية سمناها مصوفة المعاملات هذه
+
+203
+00:24:38,050 --> 00:24:43,270
+سمناها مصوفة المجاهيل هذه سمناها مصوفة الثوابت
+
+204
+00:24:43,270 --> 00:24:47,390
+يبقى هذه سمناها coefficient matrix هذه unknown
+
+205
+00:24:47,390 --> 00:24:52,230
+matrix هذه constant matrix او اختصاراً حطيناها على
+
+206
+00:24:52,230 --> 00:24:57,330
+شكل ax يساوي b ax هي coefficient matrix والx هي
+
+207
+00:24:57,330 --> 00:25:02,240
+مصوفة المجاهيل والb هي مصوفة الثوابتالتعريف بيقول
+
+208
+00:25:02,240 --> 00:25:08,360
+لو أخدت المحدد للمصوفة المربعة اللي عندنا هذه يبقى
+
+209
+00:25:08,360 --> 00:25:13,120
+هذه بقول عليها singular إذا كان المحدد يساوي zero
+
+210
+00:25:13,120 --> 00:25:16,380
+حسبنا المحدد وجدنا يساوي zero يبقى المصوفة هذه
+
+211
+00:25:16,380 --> 00:25:20,220
+بقول عليها singular matrix يعني مصوفة شاذة أو
+
+212
+00:25:20,220 --> 00:25:25,210
+منعزلة أو منفردة أو التسمع اللي تعجبكبسميها non
+
+213
+00:25:25,210 --> 00:25:30,070
+singular إذا كان المحدد تبعها ماله لا يساوي zero
+
+214
+00:25:30,070 --> 00:25:34,110
+كويس النظرية هذه بتقول إذا المحدد لا يساوي zero
+
+215
+00:25:34,110 --> 00:25:38,430
+يبقى ال system ال star اللي فوق مضمون له main حل
+
+216
+00:25:38,430 --> 00:25:41,970
+واحد طبعا ال system اللي فوق ال star احنا سابقا
+
+217
+00:25:41,970 --> 00:25:47,230
+قلنا إله أحد ثلاثة احتمالات الاحتمال الأول أن يكون
+
+218
+00:25:47,230 --> 00:25:52,190
+له حلا واحدا الاحتمال الثانيان يكون له عدد ده
+
+219
+00:25:52,190 --> 00:25:56,870
+نهائي من الحلول الا احتمالية ان لا يكون حل هذا ال
+
+220
+00:25:56,870 --> 00:26:02,230
+system الان كإنه اللي بيعطيني ضمانة ما هي الضمانة
+
+221
+00:26:02,230 --> 00:26:07,310
+اللي ممكن تكون عندنا حتى يكون لل system حلا واحدة
+
+222
+00:26:07,600 --> 00:26:12,040
+هنقول له هروح نجيب المحدد تبع المعاملات إذا المحدد
+
+223
+00:26:12,040 --> 00:26:17,060
+لا يساوي zero يبقى مضمون مائة بالمائة يكون عندي حل
+
+224
+00:26:17,060 --> 00:26:21,880
+وحيد لهذا ال system وبروح نجيب له هذا الحل الوحيد
+
+225
+00:26:21,880 --> 00:26:27,480
+تمامهذا بالنسبة للنظرية الان نجي لل remark بيقول
+
+226
+00:26:27,480 --> 00:26:31,780
+ال system has exactly one solution لو كان له حل
+
+227
+00:26:31,780 --> 00:26:37,440
+واحد فقط يبقى ممكن الحصول عليه بطريقتين طريقة
+
+228
+00:26:37,440 --> 00:26:43,120
+أخدناها سابقا و طريقةاخدناها و احنا مش دارين تمام
+
+229
+00:26:43,120 --> 00:26:48,140
+ايش الطريقة الأولى اللي هو ال raw echelon form اني
+
+230
+00:26:48,140 --> 00:26:51,800
+اخل القدر الرئيسي واحد واحد و اللي منه فوق أصفر و
+
+231
+00:26:51,800 --> 00:26:55,860
+اللي منه تاح أصفر و بعد هي كده بجيب ال system
+
+232
+00:26:55,860 --> 00:27:01,460
+مكافئ لل system الأصليالطريقة الثانية هي طريقة
+
+233
+00:27:01,460 --> 00:27:06,340
+جاوس بيقول the gaussian elimination اللي هو محذفات
+
+234
+00:27:06,340 --> 00:27:10,240
+جاوس by changing the matrix into upper triangle
+
+235
+00:27:10,240 --> 00:27:14,380
+matrix يعني أنا بدي أحولها إلى مصغفة بحيث القطر
+
+236
+00:27:14,380 --> 00:27:19,040
+الرئيسي كله لتحتيثي روميان أسفار احنا بيقولك هي
+
+237
+00:27:19,040 --> 00:27:23,130
+الطريقتين يعني هل اختلفت الثانية عن الأولى؟بس
+
+238
+00:27:23,130 --> 00:27:26,470
+الأولى بدها شغل اكتر شغل اكتر ليش؟ انا بدي اللى
+
+239
+00:27:26,470 --> 00:27:30,530
+فوق كمان أسفار مش عقد اللى تحتى يبقى جاوسيا نسهى
+
+240
+00:27:30,530 --> 00:27:36,450
+أسهل من مين؟ من روشيلون 4 تمام طيب احنا بنعطي مثال
+
+241
+00:27:36,450 --> 00:27:42,890
+و من هذا المثال نحاول نستخدم الجاوسيا في حل هذا
+
+242
+00:27:42,890 --> 00:27:49,010
+المثال إذا كان بنحل ب solution واحد فقطأيش بيقول
+
+243
+00:27:49,010 --> 00:27:52,390
+Solve the system ومعطيني ال system هذا يبقى أنا
+
+244
+00:27:52,390 --> 00:27:56,910
+بدي أتأكد أنه له حل والله مالهوش حل والله عدد لا
+
+245
+00:27:56,910 --> 00:28:02,470
+نهاية من الحلول بروح باخد محدد مصوفة المعاملات
+
+246
+00:28:02,470 --> 00:28:10,070
+فباجي بقوله ال determinantللأي بدى يساوي يبقى بدى
+
+247
+00:28:10,070 --> 00:28:13,330
+اجه على ال system اللى عندنا واحط المعاملات على
+
+248
+00:28:13,330 --> 00:28:19,790
+شكل محدد هى اتنين وهى اتنين وهى سالب واحد وهنا
+
+249
+00:28:19,790 --> 00:28:25,370
+سالب تلاتة وهنا سالب واحد وهنا تلاتة وهنا اربعة
+
+250
+00:28:25,370 --> 00:28:32,550
+وهنا اتنين وهنا سالب تلاتة تمامسأفكر المحدد
+
+251
+00:28:32,550 --> 00:28:37,470
+باستخدام أي صفة أو عمود سيان لا يفرق عنها يبقى هذا
+
+252
+00:28:37,470 --> 00:28:40,830
+الكلام بيدرساه بدا أفكر على طول يا بنات مش هتقعد
+
+253
+00:28:40,830 --> 00:28:44,690
+كل حين هداك لأ بدي أفكر على طول الخط يبقى هذا
+
+254
+00:28:44,690 --> 00:28:50,210
+لإتنين فيه بدي أشطب صفه و عموده بصير عندك هنا
+
+255
+00:28:50,210 --> 00:28:55,970
+تلاتة ناقص ستةحسب قاعة الإشارات اللي بعده إشارته
+
+256
+00:28:55,970 --> 00:29:03,470
+سالب نشط بصفه و عموده بصير تسعة و هنا ناقص اتناش
+
+257
+00:29:03,470 --> 00:29:08,930
+هاي شطاب نصفه و عموده بصير تسعة ناقص اتناش اللي
+
+258
+00:29:08,930 --> 00:29:15,610
+بعده سالب واحد فيه أشط بصفه و عموده بصير سالب ستة
+
+259
+00:29:15,610 --> 00:29:21,830
+زائد أربعةسالب ستة زائد اربع يبقى هذا الكلام يساوي
+
+260
+00:29:21,830 --> 00:29:27,670
+تلاتة ناقص ستة بيظل ناقص تلاتة في اتنين بناقص ستة
+
+261
+00:29:27,670 --> 00:29:32,030
+تسعة ناقص اتناشر بيظل ناقص تلاتة في ناقص اتنين
+
+262
+00:29:32,030 --> 00:29:37,590
+بزائد ستة وعندك هنا سالب ستة وزائد اربع بيظل سالب
+
+263
+00:29:37,590 --> 00:29:42,610
+اتنين في سالب واحد بزائد اتنين يبقى النتيجة جداش
+
+264
+00:29:42,890 --> 00:29:48,090
+أتنين لا يساوي Zero معناته هذا ال system له حل
+
+265
+00:29:48,090 --> 00:29:55,230
+واحد يبقى باجي بقول since بما أن ال determinant لل
+
+266
+00:29:55,230 --> 00:30:04,590
+A يساوي اتنين ولا يساوي Zero ال system star has a
+
+267
+00:30:04,590 --> 00:30:09,170
+unique solution او has one solution has one
+
+268
+00:30:09,170 --> 00:30:10,830
+solution
+
+269
+00:30:12,680 --> 00:30:19,380
+طيب بدنا نروح نشوف كيف بدنا نجيب ال solution لهذا
+
+270
+00:30:19,380 --> 00:30:25,500
+ال system بطريقة جاوس لان اشيلون فورم اشتغلنا
+
+271
+00:30:25,500 --> 00:30:30,840
+عليها كتير لنشوف طريقة جاوس احنا تاول ساعة دعينا
+
+272
+00:30:30,840 --> 00:30:35,680
+او زعمنا انها أبسط شوية اذا انا هنا لو جيت على
+
+273
+00:30:35,680 --> 00:30:42,050
+الصف الأول وقلت المصوف عندنا كانت تالية هي اتنينو
+
+274
+00:30:42,050 --> 00:30:47,630
+بعدها اتنين و بعدها سالف واحد و هنا ناقص تلاتة و
+
+275
+00:30:47,630 --> 00:30:54,430
+هنا اربعة و هنا ناقص واحد اتنين و هنا ناقص تلاتة و
+
+276
+00:30:54,430 --> 00:30:58,750
+لا زائد تلاتة و هنا ناقص تلاتة بالشكل اللي عندنا
+
+277
+00:30:58,750 --> 00:31:05,450
+هذا بس بضروح اضيف ال االلي هو العمود تبع المعاملات
+
+278
+00:31:05,450 --> 00:31:08,950
+لإن احنا بناخد الـ Agumented Matrix الـ Agumented
+
+279
+00:31:08,950 --> 00:31:14,010
+Matrix اللي هم اتنين سلب اتنين زيرو اتنين سلب
+
+280
+00:31:14,010 --> 00:31:22,000
+اتنين زيرو pointيبقى انا بالنسبة للمصوفة لان ليس
+
+281
+00:31:22,000 --> 00:31:28,460
+بالضرورة اخل العنصر الأول واحد لكن لكي اجلب هذه
+
+282
+00:31:28,460 --> 00:31:34,100
+الصفر لازم اخلها دقيقاش واحد اذا بروح بدرب الصف
+
+283
+00:31:34,100 --> 00:31:42,100
+الأول في نص تمام يبقى باجي بقول بدي اخد هنا نص R1
+
+284
+00:31:42,620 --> 00:31:48,500
+بصير المصوفة على الشكل التالي هنا واحد وهنا واحد
+
+285
+00:31:48,500 --> 00:31:59,720
+وهنا ناقص نص وهنا ناقص نص تمام؟ وهنا واحدالصف
+
+286
+00:31:59,720 --> 00:32:04,560
+التاني زي ما هو ناقص تلاتة ناقص واحد تلاتة ناقص
+
+287
+00:32:04,560 --> 00:32:11,520
+اتنين اربعة اتنين ناقص تلاتة zero هاي جفلنا الان
+
+288
+00:32:11,520 --> 00:32:15,880
+بدي ادخلي مكان السلب تلاتة والاربعة اسفار يبقى بدي
+
+289
+00:32:15,880 --> 00:32:20,120
+اضرب الصف الأول في تلاتة واضيفه للصف الثاني واضربه
+
+290
+00:32:20,120 --> 00:32:24,660
+في السلب اربعة واضيفه للصف الثالث يبقى باجي بقول
+
+291
+00:32:24,660 --> 00:32:33,260
+كتالةتلاتة R1 بدي اضيفه to R2 و سالب اربعة R1 to
+
+292
+00:32:33,260 --> 00:32:48,280
+R3 بنحصل على المصفوفة التالية1 1 1 1 1 1 1 1 1 1 1
+
+293
+00:32:48,280 --> 00:32:48,500
+1 1 1 1 1
+
+294
+00:32:59,080 --> 00:33:05,080
+وهنا ضربنا في تلاتة بيظل كدهش هنا كمان واحد الان
+
+295
+00:33:05,080 --> 00:33:12,140
+هنا zero سالب اربع بيظل سالب اتنين وهنا ضربنا في
+
+296
+00:33:12,140 --> 00:33:18,340
+سالب اربع بيصير موجة باتنين بيظل ناقص واحد ضربنا
+
+297
+00:33:18,340 --> 00:33:27,260
+في سالب اربع بيصير عندك سالب اربع طيبالان انا بدي
+
+298
+00:33:27,260 --> 00:33:33,340
+ادخل هذا مكانه zero يبقى بدي اضيف الصف ثاني الى
+
+299
+00:33:33,340 --> 00:33:41,560
+الصف الثالث يبقى بدي ادخله R2 to R3 اضافة عادية
+
+300
+00:33:41,560 --> 00:33:46,880
+ماسوّناش اشي يبقى الصف الاول هي واحد واحد وهي سالب
+
+301
+00:33:46,880 --> 00:33:57,300
+نص وهذا واحد0 2 3 2 1 0 0
+
+302
+00:34:08,000 --> 00:34:13,860
+الان هذا ال system اللي عندنا او ال system الأصلي
+
+303
+00:34:13,860 --> 00:34:22,200
+is equivalent to يبقى باجي بقوله the system star
+
+304
+00:34:22,200 --> 00:34:32,300
+is equivalent to هذا يكافئ مين؟ يكافئ x واحد زي x
+
+305
+00:34:32,300 --> 00:34:39,190
+اتنين ناقص نص x تلاتة بده يساوي واحدهنا اكس اتنين
+
+306
+00:34:39,190 --> 00:34:44,810
+او اتنين اكس اتنين زائد تلاتة على اتنين اكس تلاتة
+
+307
+00:34:44,810 --> 00:34:51,490
+يساوي واحد وهنا المص اكس تلاتة بده يساوي قداش بده
+
+308
+00:34:51,490 --> 00:34:57,950
+يساوي ناقص تلاتةالان من هذا بقدر اقول له ال X3 كده
+
+309
+00:34:57,950 --> 00:35:05,010
+ساوي يا بنات؟ سالب ستة الان هاي جبنا له X3 بقدر
+
+310
+00:35:05,010 --> 00:35:10,450
+اجيب له X2 يبقى برجعود في المعادلة اللي من او فوق
+
+311
+00:35:10,450 --> 00:35:19,370
+يبقى 2X2 بدي اضرب في سالب ستة بصير عندى سالب تسعة
+
+312
+00:35:19,370 --> 00:35:27,070
+بده ساوي واحدمظبوط يبقى هذا معناه انه x2 بده يساوي
+
+313
+00:35:27,070 --> 00:35:34,850
+عشرة هذا معناه انه x2 بده يساوي خمسةالحين X2 و X3
+
+314
+00:35:34,850 --> 00:35:41,890
+موجودات برجع بعوض وين في المعادلة الأولى يبقى X1 و
+
+315
+00:35:41,890 --> 00:35:48,450
+هنا زائد خمسة و هنا ناقص مع ناقص بصير زائد ستة على
+
+316
+00:35:48,450 --> 00:35:54,990
+اتنين بصير تلاتة بده يسوى جداش واحد هذا معناه ان
+
+317
+00:35:54,990 --> 00:36:00,540
+X1 بده يسوى تلاتة و خمسةتمانية تجيبها على الشجة
+
+318
+00:36:00,540 --> 00:36:05,860
+التانية تصبح سالب تمانية واحد تصبح سالب سبعة يبقى
+
+319
+00:36:05,860 --> 00:36:19,260
+بروح بقوله solution of the system star is X واحد و
+
+320
+00:36:19,260 --> 00:36:25,680
+X اتنين و X تلاتة بده يساوي X واحد طلعناها بناقص
+
+321
+00:36:25,680 --> 00:36:35,180
+سبعةو X2 بخمسة و X3 بسالب ستة و زي ما تشايفين حلا
+
+322
+00:36:35,180 --> 00:36:41,980
+واحدا ليس اكثر و احنا اثبتنا انه حل واحد عن طريق
+
+323
+00:36:41,980 --> 00:36:45,040
+حساب قيمة المحدد
+
+324
+00:36:46,460 --> 00:36:51,620
+طيب، حتى الآن ما اتكلمناش في عنوان هذا ال section
+
+325
+00:36:51,620 --> 00:36:57,040
+اللي هو grammar rule اللي هي قاعدة ال grammar لحل
+
+326
+00:36:57,040 --> 00:37:02,460
+المعادلات، تمام؟ يبقى بدنا نيجي لقاعدة grammar
+
+327
+00:37:02,460 --> 00:37:11,760
+يبقى هذا grammar rule إيش بتقول grammar rules؟ we
+
+328
+00:37:11,760 --> 00:37:12,500
+use
+
+329
+00:37:15,860 --> 00:37:24,180
+أكرامر رول نستخدم قاعدة أكرامر إذا كان الـ
+
+330
+00:37:24,180 --> 00:37:28,920
+determinant للـ a لا يساوي zero يعني أيه الشبنات؟
+
+331
+00:37:30,570 --> 00:37:35,010
+يعني إذا كان عندي حل واحد فقط يبقى إذا أنا بدأ
+
+332
+00:37:35,010 --> 00:37:38,910
+أستخدم طريقة grammar بدي أجيب المحدد و أثبت إنه لا
+
+333
+00:37:38,910 --> 00:37:42,870
+يساوي zero إن حدث ذلك بقدر أستخدم طريقة grammar
+
+334
+00:37:42,870 --> 00:37:55,150
+غير هيك يبعتلك الله فبجي بقول the unknowns المجاهل
+
+335
+00:37:55,150 --> 00:37:57,050
+are found
+
+336
+00:37:59,680 --> 00:38:05,420
+بنوجدها من الصيغة from the formula from the
+
+337
+00:38:05,420 --> 00:38:11,040
+formula من الصيغة من الصيغة from the formula from
+
+338
+00:38:11,040 --> 00:38:11,960
+the formula from the formula من الصيغة من الصيغة
+
+339
+00:38:11,960 --> 00:38:11,960
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+340
+00:38:11,960 --> 00:38:12,120
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+341
+00:38:12,120 --> 00:38:12,640
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+342
+00:38:12,640 --> 00:38:14,720
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+343
+00:38:14,720 --> 00:38:17,280
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+344
+00:38:17,280 --> 00:38:17,300
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+345
+00:38:17,300 --> 00:38:21,140
+من الصيغة من الصيغة من الصيغة من الصيغة من الصيغة
+
+346
+00:38:21,140 --> 00:38:24,520
+من
+
+347
+00:38:24,520 --> 00:38:28,400
+الصيغ
+
+348
+00:38:28,530 --> 00:38:42,890
+matrix where حيث the matrix بي كي is obtained
+
+349
+00:38:42,890 --> 00:38:54,630
+بنحصل عليها from the matrix a من المصوفة a after
+
+350
+00:38:54,630 --> 00:38:57,190
+replacing after
+
+351
+00:38:58,730 --> 00:39:10,810
+replacing بعد ما نستبدل the kiss calm العموض
+
+352
+00:39:10,810 --> 00:39:20,370
+رقم K by the constant calm
+
+353
+00:39:20,370 --> 00:39:22,950
+بعمودي ثوابت
+
+354
+00:39:32,450 --> 00:39:40,930
+Example use Kramer's
+
+355
+00:39:40,930 --> 00:39:52,250
+rule to solve the system
+
+356
+00:39:55,560 --> 00:40:10,540
+2x1 زائد 2x2 ناقص x3 يساوي 2 ناقص 3x1 ناقص x2 زائد
+
+357
+00:40:10,540 --> 00:40:17,620
+3x3 يساوي سالب 2 4x1
+
+358
+00:40:18,180 --> 00:40:27,540
+زائدي اتنين X2 ناقص تلاتة X3 بده يساوي Zero وهذا
+
+359
+00:40:27,540 --> 00:40:35,180
+هو ال system star اللي عندنا اظن
+
+360
+00:40:35,180 --> 00:40:39,380
+هو ال system السابق يا بنات في المثال السابق هو هو
+
+361
+00:40:39,380 --> 00:40:44,340
+ولا لا بس هناك حلناه بطريقة جاوس هنا بحله بطريقة
+
+362
+00:40:44,340 --> 00:40:47,820
+مين كرامر تمام تمام
+
+363
+00:40:53,170 --> 00:40:56,430
+يبقى على طريقة الـ Grammar شو بتقوله؟ بل جاي لهذا
+
+364
+00:40:56,430 --> 00:41:01,810
+المحدد كله يساوي Zero المجاهد X1 و X2 و X3 بدي
+
+365
+00:41:01,810 --> 00:41:06,590
+أجيبهم من القاعدة XK تساوي determinant لـPK على
+
+366
+00:41:06,590 --> 00:41:11,890
+determinant لـAهذا محدد مصوفة المعاملات هذا محدد
+
+367
+00:41:11,890 --> 00:41:16,510
+مصوفة المعاملات بس إذا بدي X1 بدي أقول determinant
+
+368
+00:41:16,510 --> 00:41:20,210
+بي وان مين بي وان هي محدد مصوفة المعاملات بس بدي
+
+369
+00:41:20,210 --> 00:41:23,530
+أجي على العمود الأول و أشيله و أحط بدله عمود
+
+370
+00:41:23,530 --> 00:41:28,170
+الثوابتبدي X2 باجي على العمود رقم اتنين بشيله و
+
+371
+00:41:28,170 --> 00:41:32,990
+بحط بدالي عمود ثوث في مصوفة المعاملة بدي X3 بنفس
+
+372
+00:41:32,990 --> 00:41:36,690
+الطريقة يبقى الكلام اللي بنقوله احنا لم نطبقه على
+
+373
+00:41:36,690 --> 00:41:41,530
+أرض الواقع الان بدي اجي ل determinant لإيه هنا
+
+374
+00:41:41,530 --> 00:41:42,390
+solution
+
+375
+00:41:47,030 --> 00:41:53,810
+الـ determinant للـ a اللي هو بده يساوي قداش اتنين
+
+376
+00:41:53,810 --> 00:42:00,550
+اتنين سالب واحد سالب تلاتة سالب واحد تلاتة اربع
+
+377
+00:42:00,550 --> 00:42:05,930
+اتنين سالب تلاتة اظن هذا طلعناه اتنين قبل قليل
+
+378
+00:42:05,930 --> 00:42:11,110
+اتنين يبقى طلعناه اتنين from above
+
+379
+00:42:13,090 --> 00:42:17,130
+قلناها قبل قليل بدا أروح أجيب determinant ل P1
+
+380
+00:42:17,130 --> 00:42:25,640
+يبقى بدي أجيب determinant ل P1 يا بناتهذا المحدد
+
+381
+00:42:25,640 --> 00:42:30,520
+يجب أن يشيل العمودي الأول وقته بدل عمودي الثوابت
+
+382
+00:42:30,520 --> 00:42:35,800
+يبقى اتنين سالب اتنين زيرو والعمودين اتنين اتنين
+
+383
+00:42:35,800 --> 00:42:40,300
+زي ما هم اتنين سالب واحد اتنين اتنين سالب واحد
+
+384
+00:42:40,300 --> 00:42:47,020
+اتنين وسالب واحد تلاتة سالب واحد تلاتة سالب تلاتة
+
+385
+00:42:47,020 --> 00:42:52,600
+بالشكل هنابتروح أفكه باستخدام العمود الأول يبقى
+
+386
+00:42:52,600 --> 00:42:59,440
+هذا اتنين فيه اشط بصفه عموده بصير تلاتة ناقص ستة
+
+387
+00:42:59,440 --> 00:43:03,940
+هاي تلاتة ناقص ستة نجي لبعده حسب قاعة الإشارات
+
+388
+00:43:03,940 --> 00:43:09,960
+إشارته سالب وهو سالب يبقى بصير زائد اتنين فيه نشط
+
+389
+00:43:09,960 --> 00:43:15,480
+بصفه عموده يبقى سالب ستة زائد اتنين سالب ستة زائد
+
+390
+00:43:15,480 --> 00:43:22,260
+اتنين زائد Zeroيبقى النتيجة هذه سالب تلاتة في
+
+391
+00:43:22,260 --> 00:43:28,880
+اتنين بسالب ستة هذي بيظل سالب اربعة في اتنين بسالب
+
+392
+00:43:28,880 --> 00:43:33,920
+تمانية ويسوى سالب اربعة اتاشر تمام؟ بدنا نجيب ال
+
+393
+00:43:33,920 --> 00:43:41,510
+determinant لل B2 يبقى المحددالعمود الثاني هو
+
+394
+00:43:41,510 --> 00:43:46,170
+اتنين هو سالب اتنين هو زيرو والعمود الأول زي ما هو
+
+395
+00:43:46,170 --> 00:43:50,970
+اتنين سالب تلاتة اربعة اتنين سالب تلاتة اربعة
+
+396
+00:43:50,970 --> 00:43:57,250
+والتالت زي ما هو سالب واحد تلاتة سالب تلاتةبدأ
+
+397
+00:43:57,250 --> 00:44:01,910
+أفكر مثلا باستخدام الصفر الصفي التالت يبقى هذا
+
+398
+00:44:01,910 --> 00:44:07,070
+الكلام بده يساوي أربعة قشط بصفه عموده يبقى بصير
+
+399
+00:44:07,070 --> 00:44:13,970
+هنا ستة ناقص اتنين اللي بعدها ناقص Zero اللي بعدها
+
+400
+00:44:13,970 --> 00:44:20,700
+زائد ناقص تلاتة فيهأشط بصفه عموده يبقى ناقص أربعة
+
+401
+00:44:20,700 --> 00:44:27,120
+زائد ستة ناقص أربعة زائد ستة ويساوي يبقى أربعة في
+
+402
+00:44:27,120 --> 00:44:33,360
+أربعة اللي هو ستاشر وهنا يبقى اتنين يبقى ناقص ستة
+
+403
+00:44:33,360 --> 00:44:42,720
+ويساوي عشرةالان بدأيجي لـ determinant للـ B3 يساوي
+
+404
+00:44:42,720 --> 00:44:47,640
+العمود الأول زي ما هو 2 سالب 3 أربعة العمودي
+
+405
+00:44:47,640 --> 00:44:53,320
+التاني زي ما هو 2 سالب 1 اتنين العمودي التالت بدأ
+
+406
+00:44:53,320 --> 00:44:57,540
+احط بداله عمود الثوابط اللي هو Zero بالشكل اللي
+
+407
+00:44:57,540 --> 00:45:03,940
+عندنابدي أفكر المحدد باستخدام عناصر الصف تالت يبقى
+
+408
+00:45:03,940 --> 00:45:10,300
+هذا أربعة فيه بدي أشطب صفه و عموده يبقى ناقص أربعة
+
+409
+00:45:10,300 --> 00:45:15,580
+زائد اتنين اللي بعده حسب قاعدة الإشارات بناقص
+
+410
+00:45:15,580 --> 00:45:21,520
+اتنين أشطب صفه و عموده يبقى ناقص أربعة زائد ستة
+
+411
+00:45:21,520 --> 00:45:27,500
+ناقص أربعة زائد ستة زائد زيرو هذا الكلام بدي أساوي
+
+412
+00:45:28,040 --> 00:45:33,500
+هنا بيظل ناقص اتنين يبقى بناقص تمانية هنا بيظل
+
+413
+00:45:33,500 --> 00:45:40,480
+اتنين يبقى ناقص اربعة ويسوى ناقص اتناش يبقى بدي
+
+414
+00:45:40,480 --> 00:45:46,280
+اكس واحد يا بنات يبقى determinant لل B1 على
+
+415
+00:45:46,280 --> 00:45:52,700
+determinant للـ A و يساوي determinant للـ B 1 طالع
+
+416
+00:45:52,700 --> 00:45:58,560
+عنده بناقص 14 و determinant لل A ب2 يساوي كده؟
+
+417
+00:45:58,560 --> 00:46:05,280
+سالب سبعة الان بDX 2 اللي هو determinant لل B 2
+
+418
+00:46:05,280 --> 00:46:11,240
+على determinant لل A و يساوي determinant لل B 2
+
+419
+00:46:11,240 --> 00:46:17,400
+طالع 10 على 2 و يساوي 5بدي الـ X3 اللي هي
+
+420
+00:46:17,400 --> 00:46:24,380
+determinant للـ B3 على ال determinant لل A ويساوي
+
+421
+00:46:24,380 --> 00:46:29,620
+determinant لـ B3 طالع عندنا ناقص اتناشر على اتنين
+
+422
+00:46:29,620 --> 00:46:35,860
+ناقص ستة يبقى هذا الحل ناقص سبعة وخمسة وسالب ستة
+
+423
+00:46:35,860 --> 00:46:40,290
+هو الحل اللي كان معانايبقى هو الحل لل system اللي
+
+424
+00:46:40,290 --> 00:46:45,910
+قبل قليل يبقى حلّين السؤال بطريقتين الطريقة الأولى
+
+425
+00:46:45,910 --> 00:46:50,110
+هي طريقة جوس والطريقة الثانية هي طريقة مين؟ طريقة
+
+426
+00:46:50,110 --> 00:46:55,590
+كرامر إذا لازلنا في نفس ال section هذا و بنكمل ان
+
+427
+00:46:55,590 --> 00:47:01,880
+شاء الله المرة القادمةدير باركو طريقة كتامر very
+
+428
+00:47:01,880 --> 00:47:06,820
+important بس لا ألجأ إليها إلا إذا كان المحدد لا
+
+429
+00:47:06,820 --> 00:47:08,480
+يساوي zero
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nBcPdR84YtU.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nBcPdR84YtU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bac999c7653c61492e227dae6c0eba57bf705fdc
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nBcPdR84YtU.srt
@@ -0,0 +1,1725 @@
+1
+00:00:19,930 --> 00:00:24,750
+بسم الله الرحمن الرحيم بالعودة إلى موضوع الفترة
+
+2
+00:00:24,750 --> 00:00:28,830
+الصباحية ابتدأنا في آخر section من هذا ال chapter 
+
+3
+00:00:28,830 --> 00:00:34,990
+هو section خمسة تمانية الذي يتحدث عن حل المعادلة
+
+4
+00:00:34,990 --> 00:00:40,070
+الــتفاضلية بواسطة ال variation of parameters وتغيير 
+
+5
+00:00:40,070 --> 00:00:43,850
+الثوابت، قلنا بنروح نجيب حل ال homogenous
+
+6
+00:00:43,850 --> 00:00:48,090
+differential equation مشان اجيب ال particular
+
+7
+00:00:48,090 --> 00:00:51,910
+solution لل non homogenous differential equation
+
+8
+00:00:51,910 --> 00:00:55,230
+بس بتبدل الثوابت في حل ال homogenous differential
+
+9
+00:00:55,230 --> 00:00:59,950
+equation بدوال، وبدي اروح اجيب من هذه الدوال 
+
+10
+00:00:59,950 --> 00:01:04,690
+وعطينا على مثل مثلًا في المحاضرة الصبحية وهذا هو 
+
+11
+00:01:04,690 --> 00:01:09,650
+المثال رقم اثنين، مثال رقم 2 بيقول Solve the 
+
+12
+00:01:09,650 --> 00:01:13,410
+differential equation x تربيع y double prime ناقص 
+
+13
+00:01:13,410 --> 00:01:19,710
+2xy prime زائد 2y يساوي x تكعيب في ال E أس x طبعًا 
+
+14
+00:01:19,710 --> 00:01:23,350
+في حالة ال variational parameters اشتراك المعاملات 
+
+15
+00:01:23,350 --> 00:01:27,070
+ليس بالضرورة أن هذه المعاملات تكون ثابتة وهذه هي 
+
+16
+00:01:27,070 --> 00:01:31,660
+المعاملات المتغيرة، اثنين استراتيجيات  الـنو بيكس تكون على 
+
+17
+00:01:31,660 --> 00:01:36,540
+أي شكل يكون، يعني ماهيّاش على شكل محدد مش زي طريقة
+
+18
+00:01:36,540 --> 00:01:40,560
+ال undetermined coefficients، يبقى ممكن أستخدم أي
+
+19
+00:01:40,560 --> 00:01:43,680
+طريقة في ذلك ما علينا مشكلة في هذه الحالة
+
+20
+00:01:50,370 --> 00:01:57,550
+هذه معاملات متغيرة، إذا ماكنتش أقول أفرض الحل A و
+
+21
+00:01:57,550 --> 00:02:03,670
+B أو C أو D أو E أس X أو F أس X أو G أس X 
+
+22
+00:02:03,670 --> 00:02:05,650
+أس X أس X أس X أس X أس X أس X أس X أس X
+
+23
+00:02:05,650 --> 00:02:09,270
+أس X أس X أس X أس X أس X أس X أس X أس X أس X
+
+24
+00:02:09,270 --> 00:02:15,480
+أس X أس X أس X أس X أس X أس X أس X أس X، قلت 
+
+25
+00:02:15,480 --> 00:02:19,980
+هذه بـ zero هيك، هذه شو اسمها المعادلة؟ في section 
+
+26
+00:02:19,980 --> 00:02:27,700
+خمسة خمسة، ماشي شايفينها هذه؟ معادلة ايش؟ مش جارية
+
+27
+00:02:27,700 --> 00:02:34,040
+ولا كلمة؟ ايش اسمها؟ Cauchy-Euler equation طيب تمام
+
+28
+00:02:34,040 --> 00:02:37,860
+كويسة، في بعض الناس مش ذاكرين أو جارين يبقى هذه
+
+29
+00:02:37,860 --> 00:02:41,420
+اسمها Cauchy-Euler equation اللي كنا بنحلها
+
+30
+00:02:41,420 --> 00:02:47,020
+بطريقتين، إما بحولها إلى معادلة بمعاملات ثابتة عن
+
+31
+00:02:47,020 --> 00:02:52,340
+طريق استخدام التعويض X يساوي E أس T، وإما مباشر 
+
+32
+00:02:52,340 --> 00:02:57,540
+بفترض الحل على شكل Y يساوي X أس R، مش exponential 
+
+33
+00:02:57,540 --> 00:03:05,650
+function، تمام؟ إذا باجي بقول له هنا let Y تساوي X أس
+
+34
+00:03:05,650 --> 00:03:16,190
+R، بإيه؟ Solution of the differential equation اللي
+
+35
+00:03:16,190 --> 00:03:24,350
+هي من X تربيع Y double prime ناقص اثنين X Y prime زائد
+
+36
+00:03:24,350 --> 00:03:32,120
+اثنين Y تساوي زيرو، حل من ال homogenous، بدي اروح
+
+37
+00:03:32,120 --> 00:03:36,540
+أجيب شكل ال characteristic equation، يبقى هذه
+
+38
+00:03:36,540 --> 00:03:41,180
+سامحني، double star يبقى بدي بقول the
+
+39
+00:03:41,180 --> 00:03:47,880
+characteristic equation of the differential
+
+40
+00:03:47,880 --> 00:03:58,280
+equation double star is R في R ناقص واحد ناقص اثنين
+
+41
+00:03:58,280 --> 00:04:04,400
+R زائد اثنين يساوي كده؟ Zero، أو هذه لو كتبت على
+
+42
+00:04:04,400 --> 00:04:10,740
+الشكل التالي R تربيع ناقص R ناقص اثنين R زائد
+
+43
+00:04:10,740 --> 00:04:17,080
+اثنين يساوي Zero، أو R تربيع ناقص ثلاثة R زائد
+
+44
+00:04:17,080 --> 00:04:22,570
+اثنين يساوي Zero، هذه لو حللت إلى حاصل ضرب قوسين 
+
+45
+00:04:22,570 --> 00:04:29,570
+يساوي زيرو، يبقى هنا R ناقص واحد وهنا R ناقص اثنين
+
+46
+00:04:29,570 --> 00:04:35,070
+يكون تحليل يسلم مئة بالمئة وبالتالي يصير R واحد
+
+47
+00:04:35,070 --> 00:04:43,100
+تساوي واحد و R اثنين يساوي قد ايش؟ اثنين، بدي حل ال
+
+48
+00:04:43,100 --> 00:04:46,880
+homogenous differential equation، يبقى بدي بقوله
+
+49
+00:04:46,880 --> 00:04:55,440
+the solution of the homogenous differential
+
+50
+00:04:55,440 --> 00:05:05,000
+equation double star is على الشكل التالي Yc بده
+
+51
+00:05:05,000 --> 00:05:18,990
+يساوي C1 في قد ايش؟ في X أس 1 يبقى X زائد C2 X أس 2 و
+
+52
+00:05:18,990 --> 00:05:24,610
+بروح بأبرز هذا الحل اللي ممكن نرجع له وممكن
+
+53
+00:05:24,610 --> 00:05:31,520
+نرجعش له لكن إجباري سنرجع له، تمام؟ يبقى أنا عندي
+
+54
+00:05:31,520 --> 00:05:36,760
+حلّين، بنات، الحل الأول هو X والحل الثاني هو X تربيع
+
+55
+00:05:36,760 --> 00:05:42,520
+يبقى انتهينا من حل ال homogenous
+
+56
+00:05:42,520 --> 00:05:46,200
+differential equation، بدنا نروح ندور على
+
+57
+00:05:46,200 --> 00:05:53,120
+particular solution لمين؟ للمعادلة رقم star، هذا الآن
+
+58
+00:05:53,120 --> 00:05:58,840
+C1 و C2 ثوابت، بطريقة ال variation of parameters، بس
+
+59
+00:05:58,840 --> 00:06:03,520
+تتبدل الثوابت بدوال، fixed وبعد هيك بنروح نعين 
+
+60
+00:06:03,520 --> 00:06:10,400
+الدوال fixed، يبقى باجي بقوله هنا the particular
+
+61
+00:06:10,400 --> 00:06:13,500
+solution
+
+62
+00:06:13,500 --> 00:06:21,160
+of the differential equation
+
+63
+00:06:23,040 --> 00:06:28,860
+الحل الخاص بيستخدم
+
+64
+00:06:28,860 --> 00:06:36,340
+C1 as a function of x مضروب في x زائد C2 as a
+
+65
+00:06:36,340 --> 00:06:40,780
+function of x مضروب في x تربيع 
+
+66
+00:06:42,860 --> 00:06:49,560
+الآن بدي اروح ادور قد ايش قيمة C1 وقد ايش قيمة C2، كتبت
+
+67
+00:06:49,560 --> 00:06:53,520
+remark قبل المثال الأول، remark يعني لو كانت
+
+68
+00:06:53,520 --> 00:06:59,060
+المعادلة من الرتبة الثانية، يبقى بجيب ال Wronskian فقط
+
+69
+00:06:59,060 --> 00:07:02,180
+ولا داعي لإيجاد ال Wronskian one وال Wronskian two وال
+
+70
+00:07:02,180 --> 00:07:07,610
+Wronskian three، مش داعي له، يبقى على طول الخط بروح بجيب
+
+71
+00:07:07,610 --> 00:07:12,930
+ال Wronskian تبع مين؟ تبع الحلّين، يبقى ال Wronskian
+
+72
+00:07:12,930 --> 00:07:18,370
+as a function of x يساوي المحدد، الحل الأول كان X
+
+73
+00:07:18,370 --> 00:07:24,690
+والحل الثاني كان كم؟ X تربيع، مشتقته واحد، مشتقته
+
+74
+00:07:24,690 --> 00:07:31,910
+كم؟ 2X، الرئيسي 2X تربيع ناقص الثانوي X
+
+75
+00:07:31,910 --> 00:07:38,770
+تربيع، ويساوي كم؟ X تربيع، يبقى جبنا ال Wronskian، في
+
+76
+00:07:38,770 --> 00:07:43,050
+كتبنا ملاحظة ما استخدمناهاش في المثال السابق لأنه
+
+77
+00:07:43,050 --> 00:07:48,090
+ما احتجناهاش، أنه كان المعاملات ايش؟ ثابتة، ومعامل ال
+
+78
+00:07:48,090 --> 00:07:51,790
+Y triple prime كان واحد صحيح، بقى ما عندي مشكلة، ايش
+
+79
+00:07:51,790 --> 00:07:56,210
+الملاحظة اللي قلنا إذا عندنا معادلة من هالشكل هذا
+
+80
+00:07:56,210 --> 00:08:01,910
+يبقى عند الحل لازم يخلي المعامل هذا قد ايش؟ يبقى بدي 
+
+81
+00:08:01,910 --> 00:08:07,510
+أقسم كله على X تربيع، فبقى بقى بقوله the
+
+82
+00:08:07,510 --> 00:08:14,050
+differential equation star is written
+
+83
+00:08:17,020 --> 00:08:21,640
+written as، بكتبها على الشكل التالي، بدي أقسم على X 
+
+84
+00:08:21,640 --> 00:08:28,040
+تربيع يبقى بصير Y double prime ناقص اثنين على X في
+
+85
+00:08:28,040 --> 00:08:35,980
+ال Y prime زائد اثنين على X تربيع في ال Y بده يساوي 
+
+86
+00:08:35,980 --> 00:08:40,800
+لما أقسم على X تربيع عشان بصير X في ال E أس X 
+
+87
+00:08:40,800 --> 00:08:45,310
+يبقى هذه المنطقة ما كان اسمها سابقًا، في الجزء 
+
+88
+00:08:45,310 --> 00:08:52,010
+النظري F(X)، مظبوط، هذه ايش اسمها الآن؟ هذا
+
+89
+00:08:52,010 --> 00:08:58,750
+F1(X) تمام؟ أنه قلنا F1(X) عندك في الجزء النظري تساوي F(X) مطروحه على a
+
+90
+00:08:58,750 --> 00:09:02,850
+0(X)، حيث ال a0 معامل مين؟ معامل Y double prime 
+
+91
+00:09:02,850 --> 00:09:07,930
+هتنسى الخطوة دي، تنسىها، بتروح تحطها هناك وبتيجي
+
+92
+00:09:07,930 --> 00:09:12,490
+تكامل مطلع كل شغل غلط، ويمكن تبقى مسالتك ما تقدرش 
+
+93
+00:09:12,490 --> 00:09:17,650
+تكملها، إذا كتبت الشغل غلط، بس إذا شغلك صح 
+
+94
+00:09:17,650 --> 00:09:22,370
+بتكملها بسهولة بإذن الله، يبقى صار عندنا ال F1(X)
+
+95
+00:09:22,370 --> 00:09:27,950
+بالشكل هذا، إلا أن بدي أجيب له C1 as a function
+
+96
+00:09:27,950 --> 00:09:33,570
+of X، وقولنا تكامل لسالب Y2 في ال F1(X) على 
+
+97
+00:09:33,570 --> 00:09:41,150
+Wronskian(X) DX، Y، الآن هي التكامل وهي سالب Y2 كده 
+
+98
+00:09:41,150 --> 00:09:49,610
+كان بنات؟
+
+99
+00:09:49,610 --> 00:09:50,590
+X تربيع، هذا يعتبر X، هذا Y1 وهذا Y2، يبقى باجي بقوله
+
+100
+00:09:54,450 --> 00:09:59,550
+سالب X تربيع، ال F1(X) هي X في ال E أس X على 
+
+101
+00:09:59,550 --> 00:10:06,750
+ال Wronskian  قد ايش؟ X تربيع DX، يبقى صارت المسألة سالب
+
+102
+00:10:06,750 --> 00:10:13,450
+تكامل X في ال E أس X DX، بنعرف أن كامل هذه سهل
+
+103
+00:10:13,450 --> 00:10:22,170
+جدًا، أظن بالـ integration by parts، بالـ table
+
+104
+00:10:22,170 --> 00:10:26,720
+يبقى باجي بقول بدي أخذ جزء هنا derivatives وبدي 
+
+105
+00:10:26,720 --> 00:10:32,220
+أخذ جزء integrals، ليه derivative؟ اللي هي مين؟ ال
+
+106
+00:10:32,220 --> 00:10:37,840
+X وال integral E أس X نشتقها كمان مرة بصير واحد
+
+107
+00:10:37,840 --> 00:10:42,620
+نكامل كمان مرة نشتقها كمان مرة بصير Zero، نكامل كمان 
+
+108
+00:10:42,620 --> 00:10:47,300
+مرة بنفسها، هدف موجب وهدف سالب قد ايش؟ لو تنسوش 
+
+109
+00:10:47,300 --> 00:10:52,790
+السالب اللي برا، يبقى هذا الكلام بده يساوي الآن
+
+110
+00:10:52,790 --> 00:10:58,190
+السالب اللي برا بيخليه سالب X E أس X زائد E أس X 
+
+111
+00:11:03,790 --> 00:11:05,130
+والكونستانت مش لازمة
+
+112
+00:11:08,830 --> 00:11:15,370
+الآن بدنا نيجي لمين؟ ل C2 as a function of X، يبقى
+
+113
+00:11:15,370 --> 00:11:22,870
+تكامل ل Y1(X) في F1(X) على Wronskian(X) DX 
+
+114
+00:11:22,870 --> 00:11:26,310
+ويساوي تكامل Y1 هو بقد ايش؟
+
+115
+00:11:41,850 --> 00:11:51,000
+يبقى أصبح ال Yp بده يساوي C1(X) هيامشي هيّ يبقى
+
+116
+00:11:51,000 --> 00:11:57,020
+اللي هي E أس X ناقص X في ال E أس X كلها مضروبة في قد ايش؟
+
+117
+00:11:57,020 --> 00:12:04,240
+يا بنات؟ مضروبة في ال X زائد C2(X) اللي طلعناها بـ 
+
+118
+00:12:04,240 --> 00:12:10,340
+E أس X مضروبة في مين؟ مضروبة في ال X تربيع ويساوي
+
+119
+00:12:10,340 --> 00:12:20,100
+يبقى صارت X E أس X ناقص X تربيع E أس X زائد X تربيع E
+
+120
+00:12:20,100 --> 00:12:27,560
+أس X، يبقى طالع كده؟ X بس E أس X، هذا ال Yp، بدنا ال 
+
+121
+00:12:27,560 --> 00:12:34,220
+general solution of 
+
+122
+00:12:34,220 --> 00:12:35,760
+the
+
+123
+00:12:37,470 --> 00:12:51,190
+differential equation star is Y بيتساوي Yc زائد Yp
+
+124
+00:12:51,980 --> 00:12:59,400
+يبقى بيصير Y تساوي Yc اللي طلعناها في الأول، C1X
+
+125
+00:12:59,400 --> 00:13:08,320
+زائد C2X تربيع زائد ال Yp، زائد X في ال E أس X، يبقى هذا ال
+
+126
+00:13:08,320 --> 00:13:13,780
+general solution لمين؟ للمعادلة التفاضلية، ايش رأيك
+
+127
+00:13:13,780 --> 00:13:18,630
+بهذا المثال؟ احنا ضربنا على صفرين بحجر، كيف ضربنا على صفر
+
+128
+00:13:18,630 --> 00:13:25,770
+هنا بحجر؟ يعني جبنا السؤال هذا شمل section 558
+
+129
+00:13:25,770 --> 00:13:31,250
+بسؤال واحد، جبنا Cauchy Euler equation اللي روحنا ندرسها 
+
+130
+00:13:31,250 --> 00:13:35,890
+بالتفصيل في 55 مع section 58 اللي 
+
+131
+00:13:35,890 --> 00:13:39,370
+هو الحالة اللي تعتبر أصعب من المثال اللي جابله 
+
+132
+00:13:39,370 --> 00:13:44,670
+أصعب ليش؟ من المعاملات متغيرة، وكثير من الطلاب أثناء 
+
+133
+00:13:44,670 --> 00:13:50,830
+الحل بينسى يقسم على معامل Y double prime أو معامل
+
+134
+00:13:50,830 --> 00:13:54,310
+Y triple prime أو ما إلى ذلك، يبقى احط في دماغك 
+
+135
+00:13:54,310 --> 00:13:59,370
+إياكي ثم إياكي هذا، احنا بننبه وأنا متأكد أن جاب
+
+136
+00:13:59,370 --> 00:14:02,770
+سؤال على هذا الموضوع لازم نلاقي البعض ناسي، لكن 
+
+137
+00:14:02,770 --> 00:14:06,810
+هاني بنبه وبقول تنسي بصير على حسابك مش حسابي
+
+138
+00:14:06,810 --> 00:14:11,710
+تمام؟ يبقى بتتخلي هذا المعامل هذا واحد صحيح، ليش؟
+
+139
+00:14:11,710 --> 00:14:16,250
+لأن F1 هذه بتصير بتخليها هي هي زي ما قسمتيش
+
+140
+00:14:16,250 --> 00:14:21,070
+وبالتالي بصير شغلنا مش صحيح بصير خطأ بدرجة 
+
+141
+00:14:21,070 --> 00:14:27,560
+كبيرة، طيب حد عنده سؤال هنا؟ خلاص؟ طيب في هذا ال
+
+142
+00:14:27,560 --> 00:14:32,100
+section في نقطة، النقطة اللي هو حل المعادلة
+
+143
+00:14:32,100 --> 00:14:37,900
+التفاضلية المتجانسة الـ homogenous بطريقة جديدة
+
+144
+00:14:37,900 --> 00:14:44,680
+اسمها reduction of order، طريقة اختزال الرتبة وده
+
+145
+00:14:44,680 --> 00:14:50,040
+ما أخذناش قبل هيك، طبعًا كنا بنأخذها بنات في X
+
+146
+00:14:50,040 --> 00:14:53,600
+missing و Y missing، كنا بننزل رتبة المعادلة وكذا 
+
+147
+00:14:53,600 --> 00:14:58,080
+هذه نفس الفكرة بس مش بدها شغل مش زي ما كنا بناخدها
+
+148
+00:14:58,080 --> 00:15:02,820
+في حالة ال X missing وال Y missing، آخر نقطة في
+
+149
+00:15:02,820 --> 00:15:08,160
+هذا ال section اللي اسمها ال reduction of order
+
+150
+00:15:08,160 --> 00:15:16,300
+لحل المعادلة التفاضلية المتجانسة مش ال non homogenous للـ
+
+151
+00:15:16,300 --> 00:15:23,280
+homogeneous، يبقى بالذات لـ reduction of 
+
+152
+00:15:23,280 --> 00:15:24,020
+order
+
+153
+00:15:30,960 --> 00:15:34,980
+ربما تسأل إحدى كنت، طب وايه جابها دي ما دام
+
+154
+00:15:34,980 --> 00:15:37,940
+homogeneous؟ ليش ما أخذناش مع ال homogeneous هناك؟
+
+155
+00:15:37,940 --> 00:15:42,280
+ليش خلتها مع ال non homogenous؟ بقول لك اه، احنا لما
+
+156
+00:15:42,280 --> 00:15:45,200
+نيجي نحل ال non homogenous سواء بال undetermined
+
+157
+00:15:45,200 --> 00:15:48,980
+coefficients أو ال variation of parameters بدنا
+
+158
+00:15:48,980 --> 00:15:53,470
+نروح نأخذ حل ال homogeneous تمام؟ فإن كان بيعطيني
+
+159
+00:15:53,470 --> 00:15:57,610
+حل، يعني طريقة ال reduction أو فكرة تتلخص في أنه
+
+160
+00:15:57,610 --> 00:16:02,850
+بيعطيني أحد الحلول الغير صفرية للمعادلة وبطلب
+
+161
+00:16:02,850 --> 00:16:07,410
+الحل الثاني، يعني بقول اتفضل هي أحد الحلّين
+
+162
+00:16:07,410 --> 00:16:12,990
+للمعادلة وهات الحل الثاني، الحل الثاني فكرته زي 
+
+163
+00:16:12,990 --> 00:16:17,400
+فكرة man، زي فكرة السؤال تبعنا هذا زي فكرة اللي هو 
+
+164
+00:16:17,400 --> 00:16:21,400
+ال variational of parameters، ولذلك دي مع نفس
+
+165
+00:16:21,400 --> 00:16:26,000
+المبدأ، كيف يعني؟ لما أقول لك افترض أن هو Y1(X) هو
+
+166
+00:16:26,000 --> 00:16:31,960
+حل المعادلة التفاضلية، اطلب Y2 عندما يكون Y1 حل، يبقى
+
+167
+00:16:31,960 --> 00:16:37,040
+constant في Y1 عبارة عن حل آخر، هنا بدي أشيل ال
+
+168
+00:16:37,040 --> 00:16:42,120
+constant وأضع function في X وأسمّيها V(X)، وبدي 
+
+169
+00:16:42,120 --> 00:16:48,700
+أطلع شكل V(X)، أن طلعت شكل V(X) بكون في هذه
+
+170
+00:16:48,700 --> 00:16:53,000
+الحالة جبت الحل الثاني اللي نيجي مع بعض ويكونوا
+
+171
+00:16:53,000 --> 00:16:56,660
+linearly independent عشان أقدر أجيب ال General
+
+172
+00:16:56,660 --> 00:17:01,380
+solution للمعادلة التفاضلية اللي عندنا، إذا سنبدأ
+
+1
+
+201
+00:20:12,570 --> 00:20:16,030
+أعوم في المعادلة واحد وأشوف إيش بصير معايا يمكن
+
+202
+00:20:16,030 --> 00:20:24,460
+الله يفرجها يبقى باجي بقوله الـ Y' يساوي يبقى
+
+203
+00:20:24,460 --> 00:20:30,520
+الدالة الأولى في مشتقة الدالة الثانية زائد مشتقة 
+
+204
+00:20:30,520 --> 00:20:38,310
+الأولى في الثانية بعد هيك بقدر أجيب المشتقة الثانية
+
+205
+00:20:38,310 --> 00:20:43,930
+ضايدة بالـ prime كل واحدة من هدول مشتقة حاصل ضرب
+
+206
+00:20:43,930 --> 00:20:50,450
+دالتين يبقى الدالة الأولى في مشتقة الدالة الثانية
+
+207
+00:20:50,450 --> 00:20:57,180
+زائد مشتقة الأولى في الثانية بدي الثانية بنفس
+
+208
+00:20:57,180 --> 00:21:06,860
+الطريقة أظن
+
+209
+00:21:06,860 --> 00:21:10,900
+واضح إن الـ term هذا هو الـ term اللي عندنا هذا يبقى 
+
+210
+00:21:10,900 --> 00:21:12,560
+هذه بدها تساوي
+
+211
+00:21:23,630 --> 00:21:27,490
+المعلومات اللي حصلت عليها بدي أخدها وأعوض بها في 
+
+212
+00:21:27,490 --> 00:21:36,370
+المعادلة رقم واحد يبقى باجي بقوله substitute in 
+
+213
+00:21:36,790 --> 00:21:48,430
+Equation 1 We get المعادلة Y W' هي يبقى V في Y1 W'
+
+214
+00:21:48,910 --> 00:22:00,730
+زائد 2 V' Y1' زائد V W' Y1 اللي بعدها a1 x في الـ Y' وين 
+
+215
+00:22:00,730 --> 00:22:08,870
+الـ Y' هايها بدي أضربها في a of x يبقى زائد a of x 
+
+216
+00:22:08,870 --> 00:22:19,950
+في الـ V طبعا a1 a1 of x في الـ V في الـ Y1' زائد a1
+
+217
+00:22:19,950 --> 00:22:27,560
+of x في الـ V' في الـ Y1 خلاصة من الـ terminal زائد A2
+
+218
+00:22:27,560 --> 00:22:35,220
+في Y Y هيها يبقى زائد A2 as a function of X في الـ
+
+219
+00:22:35,220 --> 00:22:43,900
+V في الـ V في الـ Y كل هذا الكلام بده يساوي Zero بعد 
+
+220
+00:22:43,900 --> 00:22:50,800
+هيك بده أجي أبدأ أجمع اللي فيها V double prime مع
+
+221
+00:22:50,800 --> 00:22:56,780
+بعض واللي فيهم V prime مع بعض واللي فيهم V مع 
+
+222
+00:22:56,780 --> 00:23:01,760
+بعض وأشوف لوين بتوصل الدنيا أظن ما فيش غير هذه
+
+223
+00:23:01,760 --> 00:23:07,240
+فيها V double prime يبقى Y one في الـ V double
+
+224
+00:23:07,240 --> 00:23:13,360
+prime بالتاج اللي فيها V' يبقى هذه فيها V' وهذه
+
+225
+00:23:13,360 --> 00:23:25,540
+فيها V' ما فيش غيرهم يبقى زائد 2 Y1' زائد A1 of 
+
+226
+00:23:25,540 --> 00:23:34,460
+X في Y1 كل هذا في V' الباقي كله مضروب في V يبقى 
+
+227
+00:23:34,460 --> 00:23:42,120
+زائد Y1 W prime اللي هو أول term وهذا راح هذا إيه
+
+228
+00:23:42,120 --> 00:23:51,760
+زائد A1 of X في من؟ في الـ Y1 prime هذه راحت يبقى
+
+229
+00:23:51,760 --> 00:23:59,540
+زائد A2 of X Y1 كله في الـ V بده يساوي 0
+
+230
+00:24:03,220 --> 00:24:11,860
+طلعيني للـ ghost هذا هل هو هذا يا ترى؟ مش هو فرض
+
+231
+00:24:11,860 --> 00:24:17,420
+Y1 هو حل يعني بدي أحققها يعني Y1 حط الـ prime هي
+
+232
+00:24:17,420 --> 00:24:25,880
+A1 Y1 prime هي هنا A2 Y1 A2 اه والله هي موجودة 
+
+233
+00:24:25,880 --> 00:24:32,350
+تمام؟ إذا هذا كل الـ term مقدش يبقى هذا كله يبقى 
+
+234
+00:24:32,350 --> 00:24:38,730
+zero from one from one from one مدام zero يبقى هذا
+
+235
+00:24:38,730 --> 00:24:43,150
+الله سهل عليه تمام يبقى بتصير المعادلة اللي عندي
+
+236
+00:24:43,150 --> 00:24:50,530
+على الشكل التالي Y one V W prime زائد اللي هو
+
+237
+00:24:50,530 --> 00:24:59,750
+الـ 2 Y one prime زائد الـ a one of x في الـ Y1 كله
+
+238
+00:24:59,750 --> 00:25:05,190
+في الـ V' بده يساوي قداش Zero إيش رأيك نقسم على Y1 
+
+239
+00:25:05,190 --> 00:25:10,630
+بالمرة ما هو Y1 لا يساوي Zero من البداية صح؟ non
+
+240
+00:25:10,630 --> 00:25:15,170
+zero solution يبقى بقدر أقسم عليه يبقى لو قسمت 
+
+241
+00:25:15,170 --> 00:25:25,090
+عليه بصير المعادلة V W' زائد 2 Y1' على Y1 زائد الـ A1
+
+242
+00:25:25,090 --> 00:25:32,900
+of X كلها في الـ V' بده يساوي Zero إيش موضوع يا 
+
+243
+00:25:32,900 --> 00:25:37,680
+بنات الـ reduction of order يعني بدي أنزل الرتبة اللي
+
+244
+00:25:37,680 --> 00:25:43,420
+عندنا تمام إذا بدي أفترض الـ V' هذه بدالة U مثلا
+
+245
+00:25:43,420 --> 00:25:49,700
+يبقى الـ V'' بمين بـ U' وبتاني نزلت الرتبة من الرتبة
+
+246
+00:25:49,700 --> 00:25:56,000
+الثانية إلى الرتبة الأولى يبقى هنا بدي أقوله let 
+
+247
+00:25:56,550 --> 00:26:05,290
+الـ U تساوي V' يبقى الـ U' بده يساوي V W' يبقى هذا 
+
+248
+00:26:05,290 --> 00:26:14,250
+بده يقولك V W' بده أحط بدلها مين U' زائد 2 Y1' على
+
+249
+00:26:14,250 --> 00:26:23,610
+Y1 زائد A1 of X في الـ U بده يساوي 0 المعادلة هي دي
+
+250
+00:26:23,610 --> 00:26:29,090
+لو نقلت هد على الشجة التانية وجمعت عليه بصير U 
+
+251
+00:26:29,090 --> 00:26:36,070
+prime على U يساوي سالب 2 Y one prime على Y one
+
+252
+00:26:36,070 --> 00:26:48,860
+زائد A one of x مظبوط هيك؟ تمام؟ طيب هذه Y1 معروفة
+
+253
+00:26:48,860 --> 00:26:53,420
+وبالتالي مشتقته معروفة لو جمعتهم يبقى هذه ده اللي 
+
+254
+00:26:53,420 --> 00:26:57,820
+في X وهذه كمان ده اللي في X وبهذه كلها ده اللي في
+
+255
+00:26:57,820 --> 00:27:04,280
+X إذا لو كملت الطرفين بيطلع لأن الـ U يساوي تكامل
+
+256
+00:27:04,280 --> 00:27:08,720
+هذه الده لو بالتالي حصل على الـ U اللي هي تساوي V'
+
+257
+00:27:09,080 --> 00:27:14,950
+بكملها كمان مرة بكون حصل على شكل الـ V يبقى هذه
+
+258
+00:27:14,950 --> 00:27:25,190
+بالتكامل لين absolute value للـ U ناقص تكامل 2 Y1 
+
+259
+00:27:25,190 --> 00:27:35,270
+prime على Y1 زائد A1 of X DX هذه حصلت منها على U
+
+260
+00:27:35,270 --> 00:27:42,490
+بكملها كمان مرة بكون حصلت على شكل الـ V يبقى this
+
+261
+00:27:44,670 --> 00:27:56,010
+Equation gives أو give the function U أظن بقدر 
+
+262
+00:27:56,010 --> 00:27:59,750
+أرفع تنك أو exponential وبالتالي بيطلع النتيجة بحصول
+
+263
+00:27:59,750 --> 00:28:05,890
+نتيجة على U give the function U اللي بده يساوي V prime
+
+264
+00:28:05,890 --> 00:28:19,220
+If we integrate V prime we get V as a function of x
+
+265
+00:28:19,220 --> 00:28:25,320
+وبالتالي انتهت مسألتنا شايف التكتيك النظري اللي
+
+266
+00:28:25,320 --> 00:28:30,920
+اتبعناه هذا سنتابعه عند حل أي سؤال بطريقة reduction 
+
+267
+00:28:30,920 --> 00:28:35,420
+of order كل الخطوات هذه لو دلوقتي ما يضطرنا نحفظ
+
+268
+00:28:35,420 --> 00:28:36,320
+ولا كلمة
+
+269
+00:28:46,050 --> 00:28:55,750
+بعد ما أجيب له الـ V of X بكون جيبت له شكل الحل اللي
+
+270
+00:28:55,750 --> 00:29:00,450
+أنا جايب له هذا الحل الثاني الحل هذا والحل الأصلي
+
+271
+00:29:00,450 --> 00:29:05,430
+لازم يكون linearly independent حتى بواسطته نجيب شكل 
+
+272
+00:29:05,430 --> 00:29:11,650
+الـ general solution للمعادلة التفاضلية واضح كلامي؟
+
+273
+00:29:11,650 --> 00:29:18,470
+حد بتسأل قبل أن ندخل إلى المثال حد بتحب تسأل إذا
+
+274
+00:29:18,470 --> 00:29:20,450
+إلى المثال example
+
+275
+00:29:30,000 --> 00:29:40,220
+هذا سؤال 15 من الكتاب بيقول If Y تساوي 6 is a
+
+276
+00:29:40,220 --> 00:29:51,060
+solution of the homogeneous differential
+
+277
+00:29:51,060 --> 00:29:54,940
+equation corresponding
+
+278
+00:30:01,240 --> 00:30:08,560
+corresponding to the differential equation
+
+279
+00:30:08,560 --> 00:30:18,460
+للمعادلة التفاضلية 2 x Y W prime زائد 1 ناقص 4
+
+280
+00:30:18,460 --> 00:30:27,460
+x في الـ Y prime زائد 2 x ناقص 1 في الـ Y بده
+
+281
+00:30:27,460 --> 00:30:34,100
+يساوي e أس x بده يساوي e أس x وسمي المعادلة هذه
+
+282
+00:30:34,100 --> 00:30:38,360
+رقم كده؟ رقم واحد find
+
+283
+00:30:40,640 --> 00:30:51,580
+the other linearly independent solution solution
+
+284
+00:30:51,580 --> 00:31:07,320
+and then ومن ثم find the general solution of 
+
+285
+00:31:07,320 --> 00:31:09,880
+equation
+
+286
+00:31:10,470 --> 00:31:10,850
+one
+
+287
+00:31:37,880 --> 00:31:43,220
+أظن هذا السؤال جاب الـ reduction of order وجاب الـ
+
+288
+00:31:43,220 --> 00:31:46,060
+variation of parameter بسؤال واحد
+
+289
+00:31:48,590 --> 00:31:51,370
+لأن في الآخر طلب يبقى لهاتف الـ general solution
+
+290
+00:31:51,370 --> 00:31:54,370
+للمعادلة الأصلية اللي عندنا لهاتف اتنين هذه
+
+291
+00:31:54,370 --> 00:31:59,930
+المعادلة مش Euler يعني ماهي x تربيع في Y W هذه
+
+292
+00:31:59,930 --> 00:32:03,790
+اتنين x يبقى بـ Euler and C Euler يبقى دي اللي هي 
+
+293
+00:32:03,790 --> 00:32:07,370
+Euler ولا غيره لكن هذه بنحلها بالـ reduction of 
+
+294
+00:32:07,370 --> 00:32:12,080
+order ومن ثم بنروح نحل المعادلة الثانية بالـ 
+
+295
+00:32:12,080 --> 00:32:17,520
+variation of parameters طيب كويس بنا نيجي نحل قال
+
+296
+00:32:17,520 --> 00:32:21,820
+لو كان Y تساوي 6 هو solution للـ homogenous 
+
+297
+00:32:21,820 --> 00:32:25,920
+differential equation corresponding لهذه يعني إيش 
+
+298
+00:32:25,920 --> 00:32:30,060
+يعني كأنه بيقول هذا هو حل المعادلة لو ساوت zero
+
+299
+00:32:30,390 --> 00:32:45,110
+يبقى بدجي أقوله لأن Y1 يبقى Y1
+
+300
+00:32:45,110 --> 00:32:45,210
+يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1
+
+301
+00:32:45,210 --> 00:32:45,230
+يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1
+
+302
+00:32:45,230 --> 00:32:45,650
+يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1
+
+303
+00:32:45,650 --> 00:32:56,700
+يبقى Y1 يبقى Y1 يبقى Y1 يبقى Y1 هذه المعادلة
+
+304
+00:32:56,700 --> 00:33:02,060
+سأسميها رقم 2 وهو الـ homogeneous الآن سأبحث 
+
+305
+00:33:02,060 --> 00:33:07,540
+عن الحل الثاني لهذه المعادلة يبقى إيش بده أفرض
+
+306
+00:33:07,540 --> 00:33:17,240
+شكله إيه والـ 6 في دالة تانية V of X ونبحث عن
+
+307
+00:33:17,240 --> 00:33:25,000
+شكل V of X يبقى هنا بأجي بقوله assume افترض that
+
+308
+00:33:27,790 --> 00:33:36,250
+The other solution
+
+309
+00:33:36,250 --> 00:33:40,150
+of
+
+310
+00:33:40,150 --> 00:33:52,410
+equation 2 is Y تساوي اللي هي LV of X في الـ 6
+
+311
+00:33:54,750 --> 00:33:58,770
+بعد ذلك نشتغل
+
+312
+00:33:58,770 --> 00:34:02,370
+هذه المعادلة مرتين ونعود في المعادلة لرقم 2
+
+313
+00:34:02,370 --> 00:34:09,970
+يبقى باجي بقوله الـ Y prime يساوي الـ V كما هي والـ
+
+314
+00:34:09,970 --> 00:34:14,250
+exponential مشتقتها بالـ exponential itself زائد 
+
+315
+00:34:14,250 --> 00:34:19,510
+ولا نشتغل في الأول ناخد هذه V prime E 6 زائد V في 
+
+316
+00:34:19,510 --> 00:34:26,640
+الـ E 6 ناخد كمان من الـ Y W prime هذه مشتقة حاصل ضرب 
+
+317
+00:34:26,640 --> 00:34:34,360
+دالتين وهذه مشتقة حاصل ضرب دالتين هذه V W prime V W
+
+318
+00:34:34,360 --> 00:34:40,620
+prime في الـ E 6 زائد V prime مشتقة الـ E 6 بالـ E 6
+
+319
+00:34:40,620 --> 00:34:45,880
+خلصت الجزء الأول الجزء الثاني يبقى زائد اللي هو V
+
+320
+00:34:45,880 --> 00:34:53,020
+prime في الـ E 6 زائد V في الـ E 6 نجي نجمع هذا
+
+321
+00:34:53,020 --> 00:34:58,980
+الكلام يبدو يساوي V W' في الـ E OS 6 هذا وهذا باتنين 
+
+322
+00:34:58,980 --> 00:35:08,820
+يبقى زائدي 2 V' في الـ E OS X زائد V في الـ E OS 6
+
+323
+00:35:10,550 --> 00:35:15,450
+الآن نمسك المعلومات اللي حصلنا عليها ونعوضها في
+
+324
+00:35:15,450 --> 00:35:17,130
+المعادلة اللي عندنا
+
+325
+00:35:24,980 --> 00:35:32,080
+وها دي Y W prime قلت تساوي V W prime زائد 2 V
+
+326
+00:35:32,080 --> 00:35:37,080
+prime زائد V بالـ E 6 بدل الكلكة الاكتره تبع في الـ
+
+327
+00:35:37,080 --> 00:35:46,900
+E 6 يعني رحت اختصرتها الآن بدجي أقوله substitute in
+
+328
+00:35:46,900 --> 00:35:48,760
+equation
+
+329
+00:35:59,080 --> 00:36:05,620
+يبقى 2 X في الـ Y W prime الـ Y W prime اللي هي V W 
+
+330
+00:36:05,620 --> 00:36:13,520
+prime زائد 2 V prime زائد V في الـ E أس X اللي بعدها 
+
+331
+00:36:13,520 --> 00:36:15,980
+زائد
+
+332
+00:36:17,460 --> 00:36:23,160
+واحد ناقص 4 X في الـ Y prime Y prime هي V
+
+333
+00:36:23,160 --> 00:36:29,640
+prime زائد V في V prime زائد V كله في الـ E 6
+
+334
+00:36:29,640 --> 00:36:35,480
+خلصنا منها اللي بعده زائد 2 X ناقص 1 زائد 
+
+335
+00:36:35,480 --> 00:36:41,660
+2 X ناقص 1 في مين؟ في اللي هو الـ Y الـ Y
+
+336
+00:36:41,660 --> 00:36:51,650
+احنا فرضنا في جديد V في الـ E 6 الـ V في الـ E
+
+337
+00:36:51,650 --> 00:36:56,790
+أوس X كله بده يساوي Zero أظن لو جمعت الطرفين كله
+
+338
+00:36:56,790 --> 00:37:02,050
+على E أوس X هذه بتروح بدون مشكلة طب إيش اللي بيضل
+
+339
+00:37:02,050 --> 00:37:09,010
+عندنا؟ بيضل عندنا 2 X في الـ V W Prime زائد 4 X في
+
+340
+00:37:09,010 --> 00:37:15,600
+الـ V Prime زائد 2 X في الـ V الجوز الثاني يبدأ يفكه 
+
+341
+00:37:15,600 --> 00:37:22,000
+يبقى زائد V prime زائد V ناقص 4 X في الـ V
+
+342
+00:37:22,000 --> 00:37:30,160
+prime ناقص 4 X في الـ V هنا زائد 2 X في الـ
+
+343
+00:37:30,160 --> 00:37:37,250
+V وهنا ناقص الـ V كله بده يساوي zero أظن V'' ما عنديش 
+
+344
+00:37:37,250 --> 00:37:42,050
+إلا الدالة الأولى كما هي بادروح أدور علاميا على 
+
+345
+00:37:42,050 --> 00:37:48,630
+اللي فيهم V' هذه فيها V' وهذه كمان V' وهذه كمان V 
+
+346
+00:37:48,630 --> 00:37:54,730
+وما فيش غيرهم عندكوا هنا 4 X V' مُسّالِف 4 يبقى أجر 
+
+347
+00:37:54,730 --> 00:37:59,790
+الفاتحة على روحهم أمام؟ بضليش اللي عند مين؟ V'
+
+348
+00:38:00,370 --> 00:38:11,610
+يبقى زائد V' واحدة نجي هنا 2 X V و 2 X V وناقص 4 X V مع
+
+349
+00:38:11,610 --> 00:38:17,690
+السلامة طبعا طالعين DV وسالف V الحقوهم غير مأسوف
+
+350
+00:38:17,690 --> 00:38:23,930
+عليكم يساوي 0 يبقى زي جزء النظر اللي كان عندنا
+
+351
+00:38:23,930 --> 00:38:29,330
+بالضبط ما ضلش عندي إلا المعادلة فيها V double prime
+
+352
+00:38:29,330 --> 00:38:35,070
+و V prime فقط لا غيره مجسوم وجاهزين وكله طب
+
+353
+00:38:35,070 --> 00:38:40,390
+المعادلة هذه بدي أحاول أحلها مش إن أحلها بدي أقوله
+
+354
+00:38:40,390 --> 00:38:49,660
+افترض يبقى الـ U بيساوي V' يبقى U' بيساوي V W' يبقى 
+
+355
+00:38:49,660 --> 00:38:53,440
+هذه لو سميتها equation تلاتة هذا بيعطينا إن
+
+356
+00:38:53,440 --> 00:39:00,040
+equation تلاتة take the four يبقى بتصبح على الشكل
+
+357
+00:39:00,040 --> 00:39:05,980
+التالي 2 X في الـ U prime زائد الـ U بده يساوي
+
+358
+00:39:05,980 --> 00:39:14,720
+قداش Zero أو إن شاء الله فقولوا إن الـ U prime على U 
+
+359
+00:39:14,720 --> 00:39:21,640
+بده يساوي ناقص طلع لي كويسين هذه لو جبت هذه على
+
+360
+00:39:21,640 --> 00:39:26,040
+الشكل الثاني أظن بيصير سالب واحد على 2 X هي
+
+361
+00:39:26,040 --> 00:39:32,400
+كانت صح يا بنات تاكدن تمام؟ جيبنا هذه ناقص على 
+
+362
+00:39:32,400 --> 00:39:37,020
+الشجة الثانية وجمعنا عليها وجمعنا واحد على 2
+
+363
+00:39:37,020 --> 00:39:42,700
+اكتب كلام سليم مئة بالمائة طيب بدها تكامل يبقى لين 
+
+364
+00:39:42,700 --> 00:39:48,280
+absolute value لـ U هذا بده يعطينا لين absolute
+
+365
+00:39:48,280 --> 00:39:58,110
+value لـ U يساوي ناقص نصف لين absolute value لـ X بعد 
+
+366
+00:39:58,110 --> 00:40:08,250
+كمان constant كمان constant كمان
+
+367
+00:40:08,250 --> 00:40:08,890
+constant كمان constant كمان constant كمان constant
+
+368
+00:40:10,880 --> 00:40:17,600
+هذه اللي بقدر أكتبها لن اللي هو absolute value لـ X
+
+369
+00:40:17,600 --> 00:40:23,180
+ما قالش
+
+401
+00:44:05,220 --> 00:44:08,780
+بدي آخذه رقمي ضيالي الرقم اللي عندي و أحصل على
+
+402
+00:44:08,780 --> 00:44:13,240
+الدالة فقط لا غير الحين لما أقول هذا ب zero و هذا
+
+403
+00:44:13,240 --> 00:44:18,220
+أخدته بنص طلع الجواب جذر الـ X لو خلته زي ما هو
+
+404
+00:44:18,220 --> 00:44:22,600
+اتنين جذر الـ X هل المقدار الثابت يغير فيه شكل 
+
+405
+00:44:22,600 --> 00:44:26,950
+الحل؟ لأ يبقى بيبدأ تخلص منه ليش الكالكة أزاي ده؟
+
+406
+00:44:26,950 --> 00:44:30,850
+هذي واحدة اثنين هذا ليش شيلته بزيرو ليش ماخدتهش 
+
+407
+00:44:30,850 --> 00:44:36,330
+بواحد مثلا أو اتنين أو تلاتة أو أربعة بقول اه هذا
+
+408
+00:44:36,330 --> 00:44:39,790
+لو اخدته باتنين تلاتة أربعة الرقم اللي هي إن شاء
+
+409
+00:44:39,790 --> 00:44:45,250
+الله تاخديه بخمس دولار تمام هذا شكل الـ V of X الـ V
+
+410
+00:44:45,250 --> 00:44:50,730
+of X الحل هذا بدي أضربه في مين؟ بدي أضربه في الـ E
+
+411
+00:44:50,730 --> 00:44:55,510
+أُس X صح ولا؟ يبقى صار ثابت في الـ E أُس X يبقى 
+
+412
+00:44:55,510 --> 00:45:01,010
+كررت الحل اللي عندي ولا لا بس أنا عندي تكرار للحل
+
+413
+00:45:01,010 --> 00:45:04,610
+اللي عندي و هذا بدناشي يعني يبقى دائماً حتى لا يحدث
+
+414
+00:45:04,610 --> 00:45:08,950
+تكرار بأخد الثابت هذا ب Zero هذا بأخده بأي رقم
+
+415
+00:45:08,950 --> 00:45:12,550
+يضيع للثابت اللي هنا يعني لو كان سالب جدر الـ X
+
+416
+00:45:12,550 --> 00:45:17,260
+بأخد الـ K بسالب واحد عشان أتخلص من هذا يعرفنا ما هو 
+
+417
+00:45:17,260 --> 00:45:20,880
+السبب يبقى اللي عملته يبقى تعمل إزاي في حل كل 
+
+418
+00:45:20,880 --> 00:45:27,500
+سؤال من هذه المسائل طيب مدام هيك يبقى أنا جبته شكل
+
+419
+00:45:27,500 --> 00:45:32,060
+يبقى the other solution
+
+420
+00:45:40,050 --> 00:45:49,930
+يساوي V of X اللي هو جذر الـ X في الـ E<sup>X</sup> هذه
+
+421
+00:45:49,930 --> 00:45:53,430
+الاثنين هل لينيارلي اندبندنت أو لا لينيارلي 
+
+422
+00:45:53,430 --> 00:45:58,310
+اندبندنت إذا بتروح آخد الحل الأول اللي هو E<sup>X</sup>
+
+423
+00:45:58,310 --> 00:46:04,410
+والحل الثاني جذر الـ X يعني X<sup>نصف</sup> في الـ E<sup>X</sup>
+
+424
+00:46:04,410 --> 00:46:10,090
+مشتقة الـ exponential بالـ exponential هذه النص
+
+425
+00:46:19,790 --> 00:46:23,910
+يبدأ فك المحدد هذا يبقى لو فكينا هذا
+
+426
+00:46:30,580 --> 00:46:38,700
+زائد اللي هو مين X<sup>نصف</sup> في E<sup>2X</sup> هذا حاصل
+
+427
+00:46:38,700 --> 00:46:43,660
+ضرب عناصر القطر الرئيسي ناقص حاصل ضرب عناصر القطر
+
+428
+00:46:43,660 --> 00:46:49,680
+الثانوي اللي هو X<sup>نصف</sup> في E<sup>2X</sup> أظن هذا
+
+429
+00:46:49,680 --> 00:46:56,080
+وهذا مع السلامة يبقى آلة المسألة إلى واحد على
+
+430
+00:46:56,080 --> 00:47:02,260
+اتنين جذر الـ X في E<sup>2X</sup> الـ X أخدناها أكبر
+
+431
+00:47:02,260 --> 00:47:06,800
+من الـ zero يبقى هذا اللي يمكن في يوم من الأيام أنه
+
+432
+00:47:06,800 --> 00:47:10,180
+يساوي zero يبقى الحالين اللي عندي صاروا معاهم 
+
+433
+00:47:10,180 --> 00:47:18,820
+linearly independent يبقى هنا هذا ما لوش لزوم و
+
+434
+00:47:18,820 --> 00:47:22,120
+بعدين بقوله هنا ساعة
+
+435
+00:47:23,860 --> 00:47:31,220
+الـ E<sup>X</sup> and اللي هو التاني جذري الـ X في الـ E<sup>X</sup>
+
+436
+00:47:31,220 --> 00:47:40,180
+are linearly independent solutions of equation
+
+437
+00:47:40,180 --> 00:47:49,900
+المعادلة رقم 2 إذا صار الـ Y(x) يستوي الـ C1 في الـ E
+
+438
+00:47:49,900 --> 00:47:58,520
+والـ 6 زائد C2 جدر الـ X في الـ E والـ 6 وحتى الآن كل
+
+439
+00:47:58,520 --> 00:48:01,540
+اللخمة اللي عملناها جبنا الـ complementary
+
+440
+00:48:01,540 --> 00:48:08,460
+solution إيش بدنا نعمل الآن؟ بنجيب مين؟ اللي هو
+
+441
+00:48:08,460 --> 00:48:14,370
+مين؟ بنجيب حل الـ non homogeneous differential
+
+442
+00:48:14,370 --> 00:48:18,050
+equation بطريقة الـ variation of parameters يبقى
+
+443
+00:48:18,050 --> 00:48:23,830
+أول خطوة المعادلة واحدة هذه بد المعامل هذا يكون
+
+444
+00:48:23,830 --> 00:48:33,950
+كذا؟ أجسم المعادلة على جداش على اتنين اكس يبقى باجي
+
+445
+00:48:33,950 --> 00:48:35,330
+بقوله equation
+
+446
+00:48:40,390 --> 00:48:47,450
+أكتب على الشكل التالي y<sup>'</sup> زائد الهمين واحد
+
+447
+00:48:47,450 --> 00:48:55,050
+ناقص أربع x على اتنين x في الـ y<sup>'</sup> زائد اتنين x
+
+448
+00:48:55,050 --> 00:49:01,890
+ناقص واحد كله على اتنين x في الـ y يساوي E<sup>x</sup> على
+
+449
+00:49:01,890 --> 00:49:08,990
+اتنين x هذه يا بنات هي الـ F1 أظن أن الرونس كان هاي
+
+450
+00:49:10,070 --> 00:49:16,950
+جاهز يبقى مناش نقل نحسب هذا هنا هذا كتبيلي هي اللي 
+
+451
+00:49:16,950 --> 00:49:23,770
+هو الـ wronskian as a function of x إذا بدي أروح أجيب 
+
+452
+00:49:23,770 --> 00:49:33,070
+له main الـ C1(x) يساوي تكامل ناقص y2 في الـ F1 على
+
+453
+00:49:33,070 --> 00:49:44,320
+w(x) dx يبقى ناقص تكامل Y2 هو جذر X في الـ E<sup>X</sup>
+
+454
+00:49:44,320 --> 00:49:52,340
+X يبقى هذا X<sup>نصف</sup> في الـ E<sup>X</sup> في الـ F1 E<sup>X</sup>
+
+455
+00:49:52,340 --> 00:50:05,140
+على 2X على الـ wronskian يبقى E<sup>2X</sup> على 2X
+
+456
+00:50:05,140 --> 00:50:13,870
+<sup>نصف</sup> هذا إيش رأيك؟ سالي وهنا DX يساوي أظن أن 2X 
+
+457
+00:50:13,870 --> 00:50:20,770
+أو <sup>نصف</sup> بتطلع فوق يبقى 2 هذي لو طلعت فوق و X <sup>نصف</sup> مع
+
+458
+00:50:20,770 --> 00:50:31,250
+X <sup>نصف</sup> بصير 2X و E <sup>2X</sup> هذي 2X بتنزل تحت في E 
+
+459
+00:50:31,250 --> 00:50:39,620
+<sup>2X</sup> في DX يبقى صار ناقص تكامل والذي X يبقى ناقص X 
+
+460
+00:50:39,620 --> 00:50:48,160
+وثابت بالناشية تمام؟ الآن بدنا نروح ونجيب مين نجييب
+
+461
+00:50:48,160 --> 00:50:51,260
+اللي هو C2 
+
+462
+00:50:52,920 --> 00:51:00,140
+يبقى باجي بقوله C2(x) C1(x) يبقى
+
+463
+00:51:00,140 --> 00:51:06,640
+هذا الكلام تكامل y1 في الـ F1 على wronskian of x dx
+
+464
+00:51:06,640 --> 00:51:14,980
+يساوي تكامل y1 اللي هو E<sup>X</sup> الهدى E<sup>X</sup> على
+
+465
+00:51:14,980 --> 00:51:22,420
+اتنين X على الـ wronskian اللي هو من E<sup>2X</sup> على
+
+466
+00:51:22,420 --> 00:51:31,750
+اتنين X<sup>نصف</sup> DX هذا الكلام بدي يساوي تكامل E<sup>2X</sup>
+
+467
+00:51:31,750 --> 00:51:39,650
+على 2X ضرب 2X<sup>نصف</sup> على مين على E<sup>2X</sup> هذا مع
+
+468
+00:51:39,650 --> 00:51:48,140
+هذا و 2 مع 2 ضال تكامل 1 على X<sup>نصف</sup> DX يبقى هذا
+
+469
+00:51:48,140 --> 00:51:57,380
+الكلام تكامل X<sup>سالب نصف</sup> DX يبقى X<sup>نصف</sup> على نصف
+
+470
+00:51:57,380 --> 00:52:07,200
+يعني يساوي اتنين جذر الـ X طلعنا C1 و C2 يبقى بقدر 
+
+471
+00:52:07,200 --> 00:52:13,240
+اكتب له الـ particular solution تبع المعادلة اللي
+
+472
+00:52:13,240 --> 00:52:15,580
+عندنا فبجي بقوله 
+
+473
+00:52:19,480 --> 00:52:24,740
+particular solution of 
+
+474
+00:52:25,920 --> 00:52:37,280
+Equation 1 is Y<sub>P</sub> يساوي C1 هيو C1 يطلع كده ناقص X
+
+475
+00:52:37,280 --> 00:52:45,820
+في الحل اللي عندنا يسمى E<sup>X</sup> الآن C2 زائد 2 جذر الـ
+
+476
+00:52:45,820 --> 00:52:54,220
+X في الحل الثاني يسمى X<sup>نصف</sup> في الـ E<sup>X</sup> هذا اللي
+
+477
+00:52:54,220 --> 00:52:59,840
+هو الـ Y<sub>P</sub> C1(x) في الحل الأول C2(x) في الحل
+
+478
+00:52:59,840 --> 00:53:09,080
+الثاني يبقى النتيجة صارت ناقص X في الـ E<sup>X</sup> زائد 2 X 
+
+479
+00:53:09,080 --> 00:53:17,620
+في الـ E<sup>X</sup> يبقى النتيجة X E<sup>X</sup> فقط لا غير يبقى باجي
+
+480
+00:53:17,620 --> 00:53:22,920
+بقوله the general solution 
+
+481
+00:53:32,160 --> 00:53:37,720
+يبقى Y يبقى يساوي Y<sub>C</sub> + Y<sub>P</sub>
+
+482
+00:53:44,860 --> 00:53:55,320
+يبقى الـ C1 E<sup>X</sup> زائد C2 جذر الـ X E<sup>X</sup> زائد
+
+483
+00:53:55,320 --> 00:54:04,340
+Y<sub>P</sub> زائد X في الـ E<sup>X</sup> يبقى هاي الحل هنا لغاية
+
+484
+00:54:04,340 --> 00:54:09,480
+هنا انتهينا من هذا الـ section وإلى يكون أرقام
+
+485
+00:54:09,480 --> 00:54:19,840
+المسائليبقى exercises اللي هو خمسة تمانية المسائل
+
+486
+00:54:19,840 --> 00:54:29,160
+من واحد لغاية عشرة و من تلتاشر لغاية ستاشر و بروح 
+
+487
+00:54:29,160 --> 00:54:37,000
+على الـ additional exercises و بأخد المسائل من واحد
+
+488
+00:54:37,000 --> 00:54:44,490
+لغاية احداشر على هيك انتهى هذا الشبتر ويوم الأربعاء 
+
+489
+00:54:44,490 --> 00:54:49,710
+إن شاء الله بنبدأ شبتر تسعة اللي هو لابلاس
+
+490
+00:54:49,710 --> 00:54:54,810
+transform تحويلات لابلاس يعطيكم العافية
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nmLJemVXdy8_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nmLJemVXdy8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b5b1fedce086d1d3464611e63cd7e875f3662edd
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nmLJemVXdy8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2851, "start": 19.25, "end": 28.51, "text": "بسم الله الرحمن الرحيم المرة الماضية بدأنا في section ال exact equations المعادلات التامة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 9673, 46958, 10632, 47525, 10721, 8315, 8978, 3541, 2423, 1900, 11787, 9673, 3615, 18513, 1211, 9307, 16712, 10943, 3660], "avg_logprob": -0.13949093318754627, "compression_ratio": 1.3211009174311927, "no_speech_prob": 0.0, "words": [{"start": 19.25, "end": 19.37, "word": "بسم", "probability": 0.790771484375}, {"start": 19.37, "end": 19.57, "word": " الله", "probability": 0.9677734375}, {"start": 19.57, "end": 20.01, "word": " الرحمن", "probability": 0.9755859375}, {"start": 20.01, "end": 20.59, "word": " الرحيم", "probability": 0.99365234375}, {"start": 20.59, "end": 22.33, "word": " المرة", "probability": 0.9189453125}, {"start": 22.33, "end": 22.91, "word": " الماضية", "probability": 0.98974609375}, {"start": 22.91, "end": 23.63, 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1473.93, "end": 1502.17, "text": "وبنروح نحاول نوجد قيم M و N اللي بيخلولي هذه المعادلة exactly كيف بدنا نوجدهم طبعا هذا ما سنعرفه بعد قليل تفصيليا وإذا لم نلحق في محاضرة اليوم مرحبا بكم في محاضرة بعد الظهر بمثال توضيحي كيف بدنا نحسب ال M و ال N وإذا حسبناهم حلت مشكلتنا خارج بصير مسئلتنا بسيطة جدا", "tokens": [37746, 1863, 32887, 5016, 8717, 5016, 995, 12610, 8717, 2407, 7435, 3215, 12174, 32640, 376, 4032, 426, 13672, 1829, 4724, 1829, 9778, 1211, 12610, 1829, 29538, 9673, 3615, 18513, 37977, 2293, 9122, 33911, 47525, 8315, 8717, 2407, 7435, 3215, 16095, 23032, 3555, 3615, 995, 23758, 19446, 8608, 1863, 3615, 28480, 3224, 39182, 12174, 20292, 1211, 6055, 5172, 9381, 26895, 25528, 4032, 28814, 15730, 32767, 8717, 1211, 5016, 4587, 8978, 3714, 5016, 46958, 25720, 45595, 20498, 3714, 2288, 5016, 3555, 995, 4724, 24793, 8978, 3714, 5016, 46958, 25720, 39182, 6024, 116, 3224, 2288, 4724, 2304, 12984, 6027, 33427, 11242, 1829, 5016, 1829, 9122, 33911, 47525, 8315, 8717, 5016, 35457, 2423, 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0.912109375}, {"start": 1485.23, "end": 1485.93, "word": " قليل", "probability": 0.99462890625}, {"start": 1485.93, "end": 1487.15, "word": " تفصيليا", "probability": 0.87978515625}, {"start": 1487.15, "end": 1488.01, "word": " وإذا", "probability": 0.7657877604166666}, {"start": 1488.01, "end": 1488.15, "word": " لم", "probability": 0.83935546875}, {"start": 1488.15, "end": 1488.63, "word": " نلحق", "probability": 0.94091796875}, {"start": 1488.63, "end": 1488.77, "word": " في", "probability": 0.9375}, {"start": 1488.77, "end": 1489.43, "word": " محاضرة", "probability": 0.97705078125}, {"start": 1489.43, "end": 1489.93, "word": " اليوم", "probability": 0.9384765625}, {"start": 1489.93, "end": 1490.71, "word": " مرحبا", "probability": 0.88505859375}, {"start": 1490.71, "end": 1490.89, "word": " بكم", "probability": 0.762939453125}, {"start": 1490.89, "end": 1491.03, "word": " في", "probability": 0.444580078125}, {"start": 1491.03, "end": 1491.51, "word": " محاضرة", "probability": 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0.93505859375}, {"start": 1496.41, "end": 1497.15, "word": " وإذا", "probability": 0.9339192708333334}, {"start": 1497.15, "end": 1497.85, "word": " حسبناهم", "probability": 0.830322265625}, {"start": 1497.85, "end": 1498.37, "word": " حلت", "probability": 0.7677408854166666}, {"start": 1498.37, "end": 1499.09, "word": " مشكلتنا", "probability": 0.9864501953125}, {"start": 1499.09, "end": 1499.87, "word": " خارج", "probability": 0.8408203125}, {"start": 1499.87, "end": 1500.23, "word": " بصير", "probability": 0.7588704427083334}, {"start": 1500.23, "end": 1500.91, "word": " مسئلتنا", "probability": 0.742724609375}, {"start": 1500.91, "end": 1501.69, "word": " بسيطة", "probability": 0.9896484375}, {"start": 1501.69, "end": 1502.17, "word": " جدا", "probability": 0.992919921875}], "temperature": 1.0}, {"id": 59, "seek": 153066, "start": 1502.7, "end": 1530.66, "text": "طيب إذا الأن بدأ ناخد أمثلة على كل integrating factor من هذه ال .. من هذه ال .. من هذه ال differential equation يبقى example one solve the differential equation حل المعادلة التفاضلية", "tokens": [9566, 1829, 3555, 11933, 15730, 16247, 1863, 47525, 10721, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 15844, 28242, 26889, 5952, 9154, 29538, 2423, 4386, 9154, 29538, 2423, 4386, 9154, 29538, 2423, 15756, 5367, 7251, 3555, 4587, 7578, 1365, 472, 5039, 264, 15756, 5367, 11331, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632], "avg_logprob": -0.2903409134257923, "compression_ratio": 1.5240963855421688, "no_speech_prob": 0.0, "words": [{"start": 1502.7, "end": 1503.14, "word": "طيب", "probability": 0.7623697916666666}, {"start": 1503.14, "end": 1503.44, "word": " إذا", "probability": 0.779541015625}, {"start": 1503.44, "end": 1503.8, "word": " الأن", "probability": 0.6873779296875}, {"start": 1503.8, "end": 1504.14, "word": " بدأ", "probability": 0.550048828125}, {"start": 1504.14, "end": 1504.92, "word": " ناخد", "probability": 0.705078125}, {"start": 1504.92, "end": 1505.62, "word": " أمثلة", "probability": 0.934814453125}, {"start": 1505.62, "end": 1506.0, "word": " على", "probability": 0.73095703125}, {"start": 1506.0, "end": 1506.9, "word": " كل", "probability": 0.94775390625}, {"start": 1506.9, "end": 1509.14, "word": " integrating", "probability": 0.32958984375}, {"start": 1509.14, "end": 1509.96, "word": " factor", "probability": 0.828125}, {"start": 1509.96, "end": 1510.32, "word": " من", "probability": 0.947265625}, {"start": 1510.32, "end": 1510.92, "word": " هذه", "probability": 0.89208984375}, {"start": 1510.92, "end": 1511.36, "word": " ال", "probability": 0.9169921875}, {"start": 1511.36, "end": 1511.36, "word": " ..", "probability": 0.09423828125}, {"start": 1511.36, "end": 1513.28, "word": " من", "probability": 0.88671875}, {"start": 1513.28, "end": 1513.7, "word": " هذه", "probability": 0.9521484375}, {"start": 1513.7, "end": 1514.06, "word": " ال", "probability": 0.94921875}, {"start": 1514.06, "end": 1514.44, "word": " ..", "probability": 0.277099609375}, {"start": 1514.44, "end": 1514.94, "word": " من", "probability": 0.7861328125}, {"start": 1514.94, "end": 1515.2, "word": " هذه", "probability": 0.96875}, {"start": 1515.2, "end": 1515.32, "word": " ال", "probability": 0.95068359375}, {"start": 1515.32, "end": 1515.62, "word": " differential", "probability": 0.385009765625}, {"start": 1515.62, "end": 1516.38, "word": " equation", "probability": 0.81982421875}, {"start": 1516.38, "end": 1517.44, "word": " يبقى", "probability": 0.78326416015625}, {"start": 1517.44, "end": 1518.24, "word": " example", "probability": 0.94189453125}, {"start": 1518.24, "end": 1519.26, "word": " one", "probability": 0.66650390625}, {"start": 1519.26, "end": 1522.12, "word": " solve", "probability": 0.6572265625}, {"start": 1522.12, "end": 1523.76, "word": " the", "probability": 0.89990234375}, {"start": 1523.76, "end": 1525.34, "word": " differential", "probability": 0.86669921875}, {"start": 1525.34, "end": 1527.2, "word": " equation", "probability": 0.98486328125}, {"start": 1527.2, "end": 1528.06, "word": " حل", "probability": 0.91455078125}, {"start": 1528.06, "end": 1528.82, "word": " المعادلة", "probability": 0.97314453125}, {"start": 1528.82, "end": 1530.66, "word": " التفاضلية", "probability": 0.911328125}], "temperature": 1.0}, {"id": 60, "seek": 155481, "start": 1531.17, "end": 1554.81, "text": "اللي هي على الشكل التاني المعادلة بتقولي واحد ناقص xy في ال y prime في ال y prime زائد y ترابيع زائد تلاتة x", "tokens": [6027, 20292, 39896, 15844, 25124, 28820, 16712, 7649, 1829, 9673, 3615, 18513, 37977, 39894, 39648, 1829, 36764, 24401, 8717, 995, 4587, 9381, 2031, 88, 8978, 2423, 288, 5835, 8978, 2423, 288, 5835, 30767, 16373, 3215, 288, 6055, 2288, 16758, 40228, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 2031], "avg_logprob": -0.26705993924822125, "compression_ratio": 1.4390243902439024, "no_speech_prob": 0.0, "words": [{"start": 1531.17, "end": 1531.71, "word": "اللي", "probability": 0.541259765625}, {"start": 1531.71, "end": 1532.05, "word": " هي", "probability": 0.92333984375}, {"start": 1532.05, "end": 1532.43, "word": " على", "probability": 0.86474609375}, {"start": 1532.43, "end": 1533.23, "word": " الشكل", "probability": 0.94287109375}, {"start": 1533.23, "end": 1534.31, "word": " التاني", "probability": 0.83203125}, {"start": 1534.31, "end": 1537.39, "word": " المعادلة", "probability": 0.973876953125}, {"start": 1537.39, "end": 1538.33, "word": " بتقولي", "probability": 0.6998291015625}, {"start": 1538.33, "end": 1539.61, "word": " واحد", "probability": 0.885498046875}, {"start": 1539.61, "end": 1540.97, "word": " ناقص", "probability": 0.966796875}, {"start": 1540.97, "end": 1542.03, "word": " xy", "probability": 0.5040283203125}, {"start": 1542.03, "end": 1544.75, "word": " في", "probability": 0.82275390625}, {"start": 1544.75, "end": 1545.13, "word": " ال", "probability": 0.7109375}, {"start": 1545.13, "end": 1545.61, "word": " y", "probability": 0.2476806640625}, {"start": 1545.61, "end": 1546.49, "word": " prime", "probability": 0.40625}, {"start": 1546.49, "end": 1547.07, "word": " في", "probability": 0.2227783203125}, {"start": 1547.07, "end": 1547.21, "word": " ال", "probability": 0.92333984375}, {"start": 1547.21, "end": 1547.53, "word": " y", "probability": 0.93798828125}, {"start": 1547.53, "end": 1548.27, "word": " prime", "probability": 0.8349609375}, {"start": 1548.27, "end": 1550.15, "word": " زائد", "probability": 0.75537109375}, {"start": 1550.15, "end": 1550.75, "word": " y", "probability": 0.73681640625}, {"start": 1550.75, "end": 1551.85, "word": " ترابيع", "probability": 0.716064453125}, {"start": 1551.85, "end": 1553.21, "word": " زائد", "probability": 0.96240234375}, {"start": 1553.21, "end": 1554.35, "word": " تلاتة", "probability": 0.951904296875}, {"start": 1554.35, "end": 1554.81, "word": " x", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 61, "seek": 157935, "start": 1563.85, "end": 1579.35, "text": "يبقى باجب أقول الحل كالتالي بدي أعيد ترتيبي المثلة بهذا أخليها M زائد N في Dy بDX هذا كل ال term يعتبر ماذا؟", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 3555, 5551, 39648, 21542, 1211, 9122, 6027, 2655, 6027, 1829, 4724, 16254, 5551, 3615, 25708, 6055, 2288, 31371, 21292, 9673, 12984, 37977, 39627, 15730, 5551, 9778, 20292, 11296, 376, 30767, 16373, 3215, 426, 8978, 31193, 4724, 35, 55, 23758, 28242, 2423, 1433, 7251, 34268, 26890, 3714, 45636, 995, 22807], "avg_logprob": -0.49469864262001856, "compression_ratio": 1.3430656934306568, "no_speech_prob": 0.0, "words": [{"start": 1563.8500000000001, "end": 1565.17, "word": "يبقى", "probability": 0.600982666015625}, {"start": 1565.17, "end": 1565.53, "word": " باجب", "probability": 0.4613850911458333}, {"start": 1565.53, "end": 1565.81, "word": " أقول", "probability": 0.534423828125}, {"start": 1565.81, "end": 1566.55, "word": " الحل", "probability": 0.6385498046875}, {"start": 1566.55, "end": 1567.93, "word": " كالتالي", "probability": 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"probability": 0.75732421875}, {"start": 2924.84, "end": 2925.5, "word": " في", "probability": 0.3955078125}, {"start": 2925.5, "end": 2925.82, "word": " ال", "probability": 0.3759765625}, {"start": 2925.82, "end": 2925.84, "word": " E", "probability": 0.387451171875}, {"start": 2925.84, "end": 2926.62, "word": " والسكس", "probability": 0.6409912109375}, {"start": 2926.62, "end": 2927.14, "word": " Y", "probability": 0.76123046875}, {"start": 2927.14, "end": 2928.28, "word": " زائد", "probability": 0.7796223958333334}, {"start": 2928.28, "end": 2928.54, "word": " E", "probability": 0.95849609375}, {"start": 2928.54, "end": 2929.28, "word": " والسكس", "probability": 0.9813232421875}, {"start": 2929.28, "end": 2929.74, "word": " في", "probability": 0.6806640625}, {"start": 2929.74, "end": 2930.2, "word": " Y", "probability": 0.6611328125}, {"start": 2930.2, "end": 2930.96, "word": " تربيع", "probability": 0.7388916015625}, {"start": 2930.96, "end": 2931.64, "word": " وهذا", "probability": 0.6373291015625}, {"start": 2931.64, "end": 2932.04, "word": " كله", "probability": 0.94482421875}, {"start": 2932.04, "end": 2932.82, "word": " كونستان", "probability": 0.63665771484375}, {"start": 2932.82, "end": 2933.66, "word": " يبقى", "probability": 0.8236083984375}, {"start": 2933.66, "end": 2934.06, "word": " هذا", "probability": 0.87939453125}, {"start": 2934.06, "end": 2934.64, "word": " كله", "probability": 0.91064453125}, {"start": 2934.64, "end": 2935.52, "word": " ساوي", "probability": 0.671875}, {"start": 2935.52, "end": 2936.6, "word": " كونستان", "probability": 0.940673828125}, {"start": 2936.6, "end": 2937.08, "word": " C", "probability": 0.8515625}, {"start": 2937.08, "end": 2937.86, "word": " هذا", "probability": 0.6943359375}, {"start": 2937.86, "end": 2938.16, "word": " هو", "probability": 0.95849609375}, {"start": 2938.16, "end": 2938.76, "word": " الحل", "probability": 0.974609375}], "temperature": 1.0}, {"id": 115, "seek": 296233, "start": 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"end": 2939.49, "word": "تبع", "probability": 0.7535807291666666}, {"start": 2939.49, "end": 2940.33, "word": " المعادلة", "probability": 0.955322265625}, {"start": 2940.33, "end": 2942.57, "word": " التفاضلية", "probability": 0.95732421875}, {"start": 2942.57, "end": 2944.31, "word": " تمام", "probability": 0.6744384765625}, {"start": 2944.31, "end": 2944.83, "word": " لحد", "probability": 0.734619140625}, {"start": 2944.83, "end": 2945.05, "word": " هنا", "probability": 0.978515625}, {"start": 2945.05, "end": 2945.65, "word": " stop", "probability": 0.4619140625}, {"start": 2945.65, "end": 2946.51, "word": " لا", "probability": 0.4873046875}, {"start": 2946.51, "end": 2947.13, "word": " يزال", "probability": 0.98046875}, {"start": 2947.13, "end": 2947.59, "word": " عندنا", "probability": 0.94873046875}, {"start": 2947.59, "end": 2948.13, "word": " مثال", "probability": 0.974853515625}, {"start": 2948.13, "end": 2948.39, "word": " بس", "probability": 0.907470703125}, {"start": 2948.39, "end": 2948.83, "word": " المثال", "probability": 0.9261067708333334}, {"start": 2948.83, "end": 2949.27, "word": " طويل", "probability": 0.97119140625}, {"start": 2949.27, "end": 2949.77, "word": " شوية", "probability": 0.8663736979166666}, {"start": 2949.77, "end": 2950.41, "word": " عالمين", "probability": 0.651123046875}, {"start": 2950.41, "end": 2951.13, "word": " على", "probability": 0.64599609375}, {"start": 2951.13, "end": 2951.27, "word": " ال", "probability": 0.9775390625}, {"start": 2951.27, "end": 2951.83, "word": " integrating", "probability": 0.81787109375}, {"start": 2951.83, "end": 2952.53, "word": " factor", "probability": 0.60400390625}, {"start": 2952.53, "end": 2953.15, "word": " ثالث", "probability": 0.9397786458333334}, {"start": 2953.15, "end": 2954.09, "word": " بنخليه", "probability": 0.731201171875}, {"start": 2954.09, "end": 2955.03, "word": " للمحاضرة", "probability": 0.85498046875}, {"start": 2955.03, "end": 2956.53, "word": " الساعة", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nmLJemVXdy8_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nmLJemVXdy8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..72c83300a9514233ca33d1f707c30dbb70aa8cbd
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/nmLJemVXdy8_raw.srt
@@ -0,0 +1,1716 @@
+1
+00:00:19,250 --> 00:00:23,930
+بسم الله الرحمن الرحيم المرة الماضية بدأنا في
+
+2
+00:00:23,930 --> 00:00:29,500
+section ال exact equations المعادلات التامةوقلنا
+
+3
+00:00:29,500 --> 00:00:33,760
+إن المعادلة التفاضلية M of X و Y زائد N of X و Y
+
+4
+00:00:33,760 --> 00:00:38,060
+دي Y بقى دي X يساوي 0 بقول عنها exactly إذا جدت
+
+5
+00:00:38,060 --> 00:00:41,280
+تلاقي ال function Phi of X و Y بحيث مشتقتها
+
+6
+00:00:41,280 --> 00:00:46,740
+بالنسبة ل X يساوي M ومشتقتها بالنسبة ل Y يساوي L
+
+7
+00:00:46,740 --> 00:00:51,810
+فقولنا الصعب نوجد هذه الدلةفروحنا و حطينا نظرية
+
+8
+00:00:51,810 --> 00:00:57,130
+ثانية نظرية من خلالها بقدر احكم على اداء المعادلة
+
+9
+00:00:57,130 --> 00:01:02,010
+التفاضلية ل exactly ام لا وهي انه تفاضل M بالنسبة
+
+10
+00:01:02,010 --> 00:01:06,390
+الى Y اذا طلع يسوى تفاضل M بالنسبة ل X بنقول
+
+11
+00:01:06,390 --> 00:01:10,570
+المعادلة exact وبالتالي لازم الاقى ال function Phi
+
+12
+00:01:10,570 --> 00:01:15,970
+of X وY تساوي كونه صدية حد هذه المعادلة واخدنا على
+
+13
+00:01:15,970 --> 00:01:22,060
+ذلك نتائج واحدةواللي قدامنا هذا هو المثال رقم 2
+
+14
+00:01:22,060 --> 00:01:25,860
+فبقول الـ Solve the differential equation y تكيب
+
+15
+00:01:25,860 --> 00:01:31,620
+نقص y تربيع sin x نقص x زي التلاتة x y تربيع زي
+
+16
+00:01:31,620 --> 00:01:36,100
+الاثنين y cos x dy dy دي x بده يساوي من؟ بده يساوي
+
+17
+00:01:36,100 --> 00:01:40,420
+Zero بدني أحل المعادلة هذه اللي بتاعتوها طول إيه
+
+18
+00:01:40,420 --> 00:01:47,640
+فبدي أبحث أن هي exact أم مش exact تمام؟يبقى هذا
+
+19
+00:01:47,640 --> 00:01:52,420
+الجزء هو اللي أطلقنا عليه المرة اللي فات الاسم M و
+
+20
+00:01:52,420 --> 00:01:58,720
+هذا اللي هو أطلقنا عليه الاسم N طيب إذا بدي أخد
+
+21
+00:01:58,720 --> 00:02:03,160
+تفاضل ال Y ال M بالنسبة ال Y و تفاضل ال N بالنسبة
+
+22
+00:02:03,160 --> 00:02:07,860
+ال X و أشوف هل بيسووا بعض ولا بيسووش بعض فلما بدي
+
+23
+00:02:07,860 --> 00:02:14,440
+أخد partial M by partial Y يساويتفاضل Y تكيب لـ
+
+24
+00:02:14,440 --> 00:02:24,600
+3Y³ Sine X تعتبر مقدار ثابت أن تفاضل Y³ تنقص 2Y في
+
+25
+00:02:24,600 --> 00:02:29,640
+Sine X هذا كله يعتبر مقدار ثابت بالنسبة إلى Y ده
+
+26
+00:02:29,640 --> 00:02:35,940
+مشتغته بـ 0 بالمثل بدي أروح أخد تفاضل N بالنسبة
+
+27
+00:02:35,940 --> 00:02:42,330
+إلى Xيبقى تلاتة Y تربية تعتبر مقدرة ثابتة تفاضل X
+
+28
+00:02:42,330 --> 00:02:49,130
+بواحد يبقى تلاتة Y تربية الآن اتنين Y مقدر ثابت
+
+29
+00:02:49,130 --> 00:02:55,810
+تفاضل Cos X وسالب Sine X يبقى سالب اتنين Y في Sine
+
+30
+00:02:55,810 --> 00:03:01,510
+X بنلاحظ من هذا الكلام ان تفاضل M بالنسبة إلى Y
+
+31
+00:03:01,510 --> 00:03:09,980
+يسوى تفاضل M بالنسبة إلى Xهذا معناه ان ال
+
+32
+00:03:09,980 --> 00:03:13,740
+differential equation هذه لو سميتها star يا بنات
+
+33
+00:03:13,740 --> 00:03:21,460
+يبقى هذا معناه ان ال differential equation اللي هي
+
+34
+00:03:21,460 --> 00:03:29,460
+star is exact مدام exact هذا معناته there exists a
+
+35
+00:03:29,460 --> 00:03:39,730
+function فيof x,y يسوي constant c1 such that بحيث
+
+36
+00:03:39,730 --> 00:03:47,390
+أن تفاضل
+
+37
+00:03:47,390 --> 00:03:56,830
+الـ phi بالنسبة إلى x بدي يسوي M اللي عندناY تكيب
+
+38
+00:03:56,830 --> 00:04:05,130
+ناقص Y تربيع مضروبة في Sin X ناقص X وتفاضل الـ Phi
+
+39
+00:04:05,130 --> 00:04:11,390
+بالنسبة إلى Y يساوي الـ N اللي هي تلاتة X Y تربيع
+
+40
+00:04:11,390 --> 00:04:15,630
+زائد اتنين Y T Cos X
+
+41
+00:04:17,780 --> 00:04:22,740
+مرة تانية جبنا مشتقة ال N بالنسبة ال Y وجبنا مشتقة
+
+42
+00:04:22,740 --> 00:04:27,260
+ال N بالنسبة ال X وجدت القمتين متساويتين معناته
+
+43
+00:04:27,260 --> 00:04:31,500
+تفاضل N بالنسبة ال Y يسوى تفاضل N بالنسبة ال X طبق
+
+44
+00:04:31,500 --> 00:04:34,320
+النظرية في المرة الماضية يبقى differential
+
+45
+00:04:34,320 --> 00:04:39,670
+equation star is exactمدام exactly يبقى لازم ألاقي
+
+46
+00:04:39,670 --> 00:04:44,530
+function phi of x y يسوي مقدارا ثابتا بحيث أن
+
+47
+00:04:44,530 --> 00:04:48,930
+مشتقة ال phi بالنسبة ل x بدي سوى ال M ومشتقة ال
+
+48
+00:04:48,930 --> 00:04:54,820
+phi بالنسبة ل y بدي سوى مين ال Mالان بطلع .. بدي
+
+49
+00:04:54,820 --> 00:04:59,820
+احصل على phi of x و y بدون مقدار ثامن فباجي بقول
+
+50
+00:04:59,820 --> 00:05:03,460
+.. بطلع لاتنين .. انا عند المشتقة بالنسبة ل x و
+
+51
+00:05:03,460 --> 00:05:09,220
+المشتقة بالنسبة ل y بروح بكمل أسهل واحدة فيهم الان
+
+52
+00:05:09,220 --> 00:05:15,190
+لو بدي اكمل هذه بالنسبة ل y very easyو لو ده كامل
+
+53
+00:05:15,190 --> 00:05:19,730
+هادي بالنسبة إلى x كمان very easy يبقى ماعنداش
+
+54
+00:05:19,730 --> 00:05:23,610
+مشكلة في هذه الحالة لكن المثال السابق كمال هادي
+
+55
+00:05:23,610 --> 00:05:28,790
+مظبوط خلينا المثال هذا كامل هادي و نشوف لكن لو كان
+
+56
+00:05:28,790 --> 00:05:32,390
+فيهم واحدة صعبة و واحدة سهلة بسيب الصعبة و بروح
+
+57
+00:05:32,390 --> 00:05:37,740
+بكامل السهلة فيهميبقى هذه لو جيت كامل فبحصل على
+
+58
+00:05:37,740 --> 00:05:43,340
+فاي of x و y بدا كامل بالنسبة الى y يبقى تلاتة x و
+
+59
+00:05:43,340 --> 00:05:48,180
+اتبع المقدار ثابت و y تكييب على تلاتة تلاتة مع
+
+60
+00:05:48,180 --> 00:05:54,920
+تلاتة مع السلامة يبقى x y تكييب نجي الآن كامل هذه
+
+61
+00:05:54,920 --> 00:05:59,160
+بالنسبة الى y ال cosine مقدار ثابت و اتنين ثابت
+
+62
+00:05:59,160 --> 00:06:04,240
+يبقى تكامل ال y لو y تربيععلى الاتنين بتروح مع
+
+63
+00:06:04,240 --> 00:06:09,700
+اتنين يبقى y تربية في cosine ال X احنا كملنا
+
+64
+00:06:09,700 --> 00:06:14,820
+بالنسبة الى Y يبقى بدأ أقوله زائد مقدار ثابت
+
+65
+00:06:14,820 --> 00:06:21,920
+المقدار الثابت باعتبره function في X لأن X يعتبر
+
+66
+00:06:21,920 --> 00:06:28,770
+ثابت انا بكمله إلى Y زائد function of Xبعد ذلك
+
+67
+00:06:28,770 --> 00:06:34,710
+اشتق هذه الدالة بالنسبة إلى ما؟ بالنسبة إلى x و
+
+68
+00:06:34,710 --> 00:06:38,910
+أسويها بما؟ بالنسبة إلى x يبقى لو جيت اشتقت هذه
+
+69
+00:06:38,910 --> 00:06:43,370
+الدالة بالنسبة إلى x partial phi على partial x
+
+70
+00:06:43,370 --> 00:06:50,790
+يساوي هاي ال y تكيب و تفضل cosine بسالب sin يبقى
+
+71
+00:06:50,790 --> 00:07:02,630
+سالب y تربيع في sin xزائد الـ f prime of x طيب
+
+72
+00:07:02,630 --> 00:07:08,530
+الآن يبقى هذه هي هذه إذا من الإتنين هذول مع بعض ما
+
+73
+00:07:08,530 --> 00:07:14,310
+بستنتج أن إتنين هذول بيسووا بعض يعني معناه هذا
+
+74
+00:07:14,310 --> 00:07:21,590
+الكلام أن ال y تكعيد ناقص y تربيع في صين ال x زائد
+
+75
+00:07:21,590 --> 00:07:29,330
+ال f prime of xبتساوي y تكعيب ناقص y تربيع في sign
+
+76
+00:07:29,330 --> 00:07:35,410
+ال x ناقص من ال x اظن لو جيبنا هذه عند هذه بإشارة
+
+77
+00:07:35,410 --> 00:07:42,410
+مخالفة بتروح وهذه بنفس الطريقة يبقى يبقى عندي ان
+
+78
+00:07:42,410 --> 00:07:50,490
+ال f prime of xالـ f prime of x بدي يساوي سالب x
+
+79
+00:07:50,490 --> 00:07:57,990
+يبقى لو كاملتها بقول يبقى ال f of x يساوي ناقص x
+
+80
+00:07:57,990 --> 00:08:04,530
+تربيه على اتنين زائد كونستانت تاني c2إذا هذه الـ
+
+81
+00:08:04,530 --> 00:08:09,610
+file اللي عندنا اين راحت لما نكملها نهاية بس بدي
+
+82
+00:08:09,610 --> 00:08:14,850
+أشيل ال main ال F of X و أضع متة بكون حصلت على مين
+
+83
+00:08:14,850 --> 00:08:21,510
+على الحل اللي عندنا هذا يبقى باجي بقوله solution
+
+84
+00:08:21,510 --> 00:08:24,650
+of
+
+85
+00:08:24,650 --> 00:08:29,190
+the differential equation
+
+86
+00:08:31,990 --> 00:08:39,810
+فاي of x و y يساوي اللي طالع عندنا هنا x y تكيب
+
+87
+00:08:39,810 --> 00:08:48,130
+زائد y تربيع في cos x زائد f of x اللي هي ناقص x
+
+88
+00:08:48,130 --> 00:08:55,510
+تربيع على الاتنين زائد c2 كله سيساوي c1 إذا لو جبت
+
+89
+00:08:55,510 --> 00:09:00,510
+c2 عن c1 بتصبح فاي of x و y
+
+90
+00:09:21,540 --> 00:09:26,800
+طيب يا بنات مش تايم للمثال أفضل ال M بالنسبة للY
+
+91
+00:09:26,800 --> 00:09:33,520
+تسوي تفاضل X بالنسبة للXيمكن ماتصبعش exact لكن
+
+92
+00:09:33,520 --> 00:09:39,680
+بعملية بسيطة ب trick بسيط ممكن احول المعادلة الى
+
+93
+00:09:39,680 --> 00:09:44,360
+exact تمام و بالتالي لما احولها exact بحلها زي ما
+
+94
+00:09:44,360 --> 00:09:49,900
+حدثت مثالين لاثنين هدول في عندك شغلة توضح هذا
+
+95
+00:09:49,900 --> 00:09:55,260
+الكلام الإجابة نعم يعني انا لو طلع في المعادلة
+
+96
+00:09:55,260 --> 00:10:01,950
+ماهياش exactممكن أضرب المعادلة في دالة هذه الدالة
+
+97
+00:10:01,950 --> 00:10:06,810
+تحولها إلى مين إلى exact هذه الدالة اللي بضرب فيها
+
+98
+00:10:06,810 --> 00:10:13,630
+بسميها integrating factor عامل التكامل إذا بدنا
+
+99
+00:10:13,630 --> 00:10:20,030
+نحاول نعطي definition لعمل التكامل وبعد هيك روح
+
+100
+00:10:20,030 --> 00:10:27,140
+نشوف كيف بدنا نحسب هذا العامليبقى integrating
+
+101
+00:10:27,140 --> 00:10:32,120
+factor عامل
+
+102
+00:10:32,120 --> 00:10:43,440
+التكامل هعطيله التعريف التالي يبقى definition if
+
+103
+00:10:43,440 --> 00:10:50,700
+ال M as a function of x و y زائد ال N as a
+
+104
+00:10:50,700 --> 00:10:57,420
+function of x و y في dyby dx يستوي zero وهذه
+
+105
+00:10:57,420 --> 00:11:05,600
+المعادلة رقم واحد هذه كانت is not exact لو هذه
+
+106
+00:11:05,600 --> 00:11:14,160
+ماكنتش exact but ولكن ده differential equation
+
+107
+00:11:14,160 --> 00:11:24,390
+ولكن المعادلة التقاضنية ل mu of x y في mof x و y
+
+108
+00:11:24,390 --> 00:11:35,870
+زائد لميو of x و y في n of x و y في dy divide x
+
+109
+00:11:35,870 --> 00:11:43,650
+يساوي zero is exact لو
+
+110
+00:11:43,650 --> 00:11:53,070
+كانت هذه exact then لميو of x و yالـ mu of x y is
+
+111
+00:11:53,070 --> 00:12:03,430
+called .. هنروح نسميها an integrating factor
+
+112
+00:12:03,430 --> 00:12:13,590
+يفجر نسميها عامل تكامل for the differential
+
+113
+00:12:13,590 --> 00:12:17,830
+equation one
+
+114
+00:12:51,870 --> 00:12:57,180
+نرجع للتعريف اللي احنا كاتبونه هذايبقى باجي بقول
+
+115
+00:12:57,180 --> 00:13:01,600
+لو المعادلة التفاضلية هذه اللي اتعودنا عليها في
+
+116
+00:13:01,600 --> 00:13:05,380
+المثال قبل قليل ومثال المرة الماضية وجزء النظري
+
+117
+00:13:05,380 --> 00:13:09,440
+تبعه المعادلة هذه كانت ماهياش exact ايش يعني
+
+118
+00:13:09,440 --> 00:13:14,420
+ماهياش exact يعني تفاضل M بالنسبة الى Y لا يسوى
+
+119
+00:13:14,420 --> 00:13:20,460
+تفاضل M بالنسبة الى X ان حدث ذلك يبقى المعادلة هذه
+
+120
+00:13:20,460 --> 00:13:26,230
+ليست exact طيبلو قدرت أجيب دالة تانية دالة تانية
+
+121
+00:13:26,230 --> 00:13:32,530
+بسميها الـ mu of x y وروح أضرب فيها المعادلة واحد
+
+122
+00:13:32,530 --> 00:13:37,990
+يبقى صار الميو في ال M زائد الميو في ال N في ال dy
+
+123
+00:13:37,990 --> 00:13:42,850
+على dx يساوي zero صارت المعادلة بالشكل هذا ان طلعت
+
+124
+00:13:42,850 --> 00:13:48,730
+هذه المعادلة exact يبقى ال mu of x y بسميه عامل
+
+125
+00:13:48,730 --> 00:13:53,920
+التكامل للمعادلة منالأولانية ليش سميته عامل
+
+126
+00:13:53,920 --> 00:13:58,700
+التكامل لإن استطعت انه احول المعادلة هذه الى exact
+
+127
+00:13:58,700 --> 00:14:03,780
+وبالتالي بكملها بعد شوية وبحصل على شكل الحل لهذه
+
+128
+00:14:03,780 --> 00:14:09,020
+المعادلة التفاضلية يبقى الميوليوفيكس وايلة ضربت
+
+129
+00:14:09,020 --> 00:14:15,020
+فيها هذه هه بصير هي عامل التكامل طبعا كثير منكوا
+
+130
+00:14:15,020 --> 00:14:19,330
+هيسر يقول طب من وين بدنا نجيبالمعادلة هذه يعني
+
+131
+00:14:19,330 --> 00:14:26,250
+نقدر نحزر ولا نحزر ولا نفزر هنحط بعض القواعد اللي
+
+132
+00:14:26,250 --> 00:14:31,850
+يمكن استخدامها في كيفية إيجاد عامل التكمل عندك في
+
+133
+00:14:31,850 --> 00:14:36,210
+الكتاب ماتيك بعض المسائل و عامل التكمل لها وبعد
+
+134
+00:14:36,210 --> 00:14:41,470
+هيكد خلاك انت تحس بعوامل التكملإذا ما أعطيني عوامل
+
+135
+00:14:41,470 --> 00:14:45,290
+التكامل صار شغل روتيني عادي جدا المعادلة بضربها في
+
+136
+00:14:45,290 --> 00:14:49,350
+عامل التكامل بصير exact وبشتغل زي ما اشتغلت مثلين
+
+137
+00:14:49,350 --> 00:14:54,090
+السابقين لكن اللي أصعب من ذلك أنه أنا أوجد عامل
+
+138
+00:14:54,090 --> 00:14:58,970
+التكامل أولا ثم بعد ذلك أروح أحل المعادلات
+
+139
+00:14:58,970 --> 00:15:06,480
+التفاضلية لذلك بدي أعطيك بعض عوامل التكامللبعض
+
+140
+00:15:06,480 --> 00:15:11,580
+المعادلات التفاضلية مش كل عوامل التكامل يبقى بدأ
+
+141
+00:15:11,580 --> 00:15:17,060
+اكتب لقنوان جانبي some integrating factors يبقى
+
+142
+00:15:17,060 --> 00:15:22,760
+بدالي هنا some integrating
+
+143
+00:15:22,760 --> 00:15:26,440
+factors
+
+144
+00:15:26,440 --> 00:15:34,580
+بعض عوامل التكامل المشهورة في كل الكتبأول واحد من
+
+145
+00:15:34,580 --> 00:15:44,500
+هذه العوامل بيقول if the differential equation one
+
+146
+00:15:44,500 --> 00:15:54,900
+is not exact ماهياش exact and
+
+147
+00:15:54,900 --> 00:16:05,560
+if وإذا كان تفاضل ال Mبالنسبة ل X ناقص تفاضل M
+
+148
+00:16:05,560 --> 00:16:15,860
+بالنسبة ل Y بتساوي ال F of Y where حيث ال F of Y
+
+149
+00:16:15,860 --> 00:16:28,040
+is a function of Y only or constant او مقدارا
+
+150
+00:16:28,040 --> 00:16:39,940
+ثابتا thenthe integrating
+
+151
+00:16:39,940 --> 00:16:43,680
+and
+
+152
+00:16:43,680 --> 00:16:49,420
+the integrating factor as
+
+153
+00:16:49,420 --> 00:16:59,200
+the mu of y بدر ساوي E أُس تكامل F of y dy
+
+154
+00:17:04,680 --> 00:17:16,060
+if the differential equation one
+
+155
+00:17:16,060 --> 00:17:23,220
+is not exact
+
+156
+00:17:23,220 --> 00:17:34,760
+and if وإذا كان تفاضل ال M من نسبة إلى Yنقص تفاضل
+
+157
+00:17:34,760 --> 00:17:42,600
+ال N بالنسبة إلى X كله يا بنات هذا نسيت هذا كله
+
+158
+00:17:42,600 --> 00:17:51,000
+مقسوما على M وهذا كله مقسوما على N بده يساوي
+
+159
+00:17:51,000 --> 00:18:05,110
+function of X where ال F of X is a functionof x
+
+160
+00:18:05,110 --> 00:18:19,030
+only فقط or constant او مقدارا ثابتا then the
+
+161
+00:18:19,030 --> 00:18:22,090
+integrating
+
+162
+00:18:22,090 --> 00:18:35,810
+factor عامل التكلمل is the muof X يساوي E أُس
+
+163
+00:18:35,810 --> 00:18:46,650
+تكامل لل F of X DX رمضان تلاتة قد لا يكون لا هذا
+
+164
+00:18:46,650 --> 00:18:57,930
+ولا ذلك F the above to integrating
+
+165
+00:19:02,360 --> 00:19:10,420
+factors if the above two integrating factors does
+
+166
+00:19:10,420 --> 00:19:22,380
+not exist does not exist suppose
+
+167
+00:19:22,380 --> 00:19:26,600
+that the integrating factor suppose that
+
+168
+00:19:32,370 --> 00:19:42,390
+the integrating factor طرد أنه عامل التكامل in the
+
+169
+00:19:42,390 --> 00:19:54,450
+form in the form على الشكل الـ mu of x y يسوى x to
+
+170
+00:19:54,450 --> 00:20:05,220
+the power m y to the power nو .. نجد
+
+171
+00:20:05,220 --> 00:20:12,520
+.. و نجد القيم من
+
+172
+00:20:12,520 --> 00:20:26,460
+M و LN هذا يجعل المقارنة
+
+173
+00:20:26,460 --> 00:20:29,480
+واحدة
+
+174
+00:20:30,520 --> 00:20:48,840
+as exact يبقى
+
+175
+00:20:48,840 --> 00:20:56,460
+يا بنات في عندي ثلاثة من عوامل التكاملبنلجأ لهم
+
+176
+00:20:56,460 --> 00:21:00,740
+إذا كانت المعادلة تفاضلية لأن هذه معادلة ما هي
+
+177
+00:21:00,740 --> 00:21:04,300
+إجزاك إذا هذه معادلة ما هي إجزاك فانا بروح أدور
+
+178
+00:21:04,300 --> 00:21:09,700
+على عامل التكمشي بعمله بجيب تفاضل ال M بالنسبة إلى
+
+179
+00:21:09,700 --> 00:21:13,860
+Y وبجيب تفاضل ال N بالنسبة ل X اللي يخلون المعادلة
+
+180
+00:21:13,860 --> 00:21:18,320
+ما هي إجزاك تمام؟ بجبالي بقول if the differential
+
+181
+00:21:18,320 --> 00:21:24,050
+equation one is not exactAnd if تفاضل N بالنسبالي
+
+182
+00:21:24,050 --> 00:21:29,010
+X نقص تفاضل N بالنسبالي Y مقسم على M يسوى function
+
+183
+00:21:29,010 --> 00:21:31,710
+of Y فقط أو مقدار ثابت
+
+184
+00:21:38,040 --> 00:21:41,820
+و لما أقول دالة في Y ممكن تكون Y تربيع ممكن تجبه Y
+
+185
+00:21:41,820 --> 00:21:46,460
+تربيع زائد خمسة ممكن تبقى تلاتة فقط لا غير يبقى
+
+186
+00:21:46,460 --> 00:21:51,040
+مقدار ثامت يبقى دالة في Y أو مقدار ثامت ماعنا
+
+187
+00:21:51,040 --> 00:21:54,520
+مشكلة يبقى as a function of Y only or constant
+
+188
+00:21:54,520 --> 00:21:57,560
+then the integrated factor شكل ال integrating
+
+189
+00:21:57,560 --> 00:22:03,680
+factor و ال mu of Y يسوى E أست كأم لهذا المقدار
+
+190
+00:22:03,680 --> 00:22:11,500
+كله اللي وطال عنهاهو عامل التكامل لهذه المعادلة
+
+191
+00:22:11,500 --> 00:22:16,180
+يعني لو ضربت في هذه القمة تتحول المعادلة هذه إلى
+
+192
+00:22:16,180 --> 00:22:16,800
+مين؟
+
+193
+00:22:20,330 --> 00:22:24,550
+ممكن مايحصلش هذا يبقى باجي بقول لو خدت
+
+194
+00:22:24,550 --> 00:22:28,550
+differential equation is not exact روحت جالبت
+
+195
+00:22:28,550 --> 00:22:32,570
+وضعهم اخدت تفاضة ال N بالنسبة لو اناقص تفاضة ال N
+
+196
+00:22:32,570 --> 00:22:37,810
+بالنسبة ل X على X طلع function فاهمين؟فى x فقط لا
+
+197
+00:22:37,810 --> 00:22:42,470
+غير أو مقدار ثابت تمام يبقى ال f of x ده لا فى x
+
+198
+00:22:42,470 --> 00:22:46,430
+فقط أو مقدار ثابت يبقى ال integrating factor ميو
+
+199
+00:22:46,430 --> 00:22:50,750
+of x مابقولش ميو of x و y ليش لإن هنا صار function
+
+200
+00:22:50,750 --> 00:22:55,430
+في y فقط و هذا function في مين فى x فقط بديوا يسوي
+
+201
+00:22:55,430 --> 00:23:01,530
+ايه و يستكمل ال f of x dx تمام طب واحدة بيقول ليش
+
+202
+00:23:01,530 --> 00:23:05,110
+عرفني أن هذا و لا هذي يعني أنا كيف بدي أميز بينهم
+
+203
+00:23:05,590 --> 00:23:09,810
+مش هانا اميز بينهم very easy كده very easy خلّيه
+
+204
+00:23:09,810 --> 00:23:14,560
+ايه اللي هناهذه إشارة المقدار هو النقص المقداري
+
+205
+00:23:14,560 --> 00:23:18,720
+الثاني مقسوم على مين؟ على أبو الإشارة السالبة
+
+206
+00:23:18,720 --> 00:23:23,840
+مقسوم على M و الناتج بدي يكون function في مين في Y
+
+207
+00:23:23,840 --> 00:23:30,360
+هنا أبو الإشارة السالبة اللي هو N يسمت على N هذا
+
+208
+00:23:30,360 --> 00:23:35,280
+مشتغط بالنسبة لكي تعطيني function of X من هنا بقدر
+
+209
+00:23:35,280 --> 00:23:40,240
+أميز ما بين الأتنين على طول الخفقةمش تروح تطلع
+
+210
+00:23:40,240 --> 00:23:43,060
+هدول من بعض يطلع function في X يطلع function بيه
+
+211
+00:23:43,060 --> 00:23:46,740
+في X؟ مانفعش غير هذا يطلع function في X وهذا يطلع
+
+212
+00:23:46,740 --> 00:23:51,400
+function في مين؟ في Y يبقى بروح بكامل هذه الدالة
+
+213
+00:23:51,400 --> 00:23:56,440
+برفعها كاسل العدد E بكون هو عامل التكمل للمعادلة
+
+214
+00:23:56,440 --> 00:24:01,360
+التفاضلية اللي عندنا طيب لطلع function في X ولا
+
+215
+00:24:01,360 --> 00:24:06,440
+طلع function في Y كيف بنحل هالقضية؟ بقولك بسيطة
+
+216
+00:24:06,440 --> 00:24:11,260
+جدابفترض أن الـ Integrating factor اللي عندي على
+
+217
+00:24:11,260 --> 00:24:16,540
+الشكل X to the power of M في Y to the power of N و
+
+218
+00:24:16,540 --> 00:24:20,840
+الـ M و الـ N أنا مش عارف جداش أرقام جداش يطلعوا
+
+219
+00:24:20,840 --> 00:24:26,460
+الله أعلم يبقى لو الـ two integrative factors does
+
+220
+00:24:26,460 --> 00:24:30,640
+not exist يعني معيش للأول والثاني بروح بفترض أن ال
+
+221
+00:24:30,640 --> 00:24:34,910
+integrative factor على الشكل اللي عندنا هذاوبنروح
+
+222
+00:24:34,910 --> 00:24:39,850
+نحاول نوجد قيم M و N اللي بيخلولي هذه المعادلة
+
+223
+00:24:39,850 --> 00:24:45,230
+exactly كيف بدنا نوجدهم طبعا هذا ما سنعرفه بعد
+
+224
+00:24:45,230 --> 00:24:50,710
+قليل تفصيليا وإذا لم نلحق في محاضرة اليوم مرحبا
+
+225
+00:24:50,710 --> 00:24:55,230
+بكم في محاضرة بعد الظهر بمثال توضيحي كيف بدنا نحسب
+
+226
+00:24:55,230 --> 00:25:00,230
+ال M و ال N وإذا حسبناهم حلت مشكلتنا خارج بصير
+
+227
+00:25:00,230 --> 00:25:06,000
+مسئلتنا بسيطة جداطيب إذا الأن بدأ ناخد أمثلة على
+
+228
+00:25:06,000 --> 00:25:14,940
+كل integrating factor من هذه ال .. من هذه ال .. من
+
+229
+00:25:14,940 --> 00:25:19,260
+هذه ال differential equation يبقى example one
+
+230
+00:25:19,260 --> 00:25:28,820
+solve the differential equation حل المعادلة
+
+231
+00:25:28,820 --> 00:25:37,390
+التفاضليةاللي هي على الشكل التاني المعادلة
+
+232
+00:25:37,390 --> 00:25:48,270
+بتقولي واحد ناقص xy في ال y prime في ال y prime
+
+233
+00:25:48,270 --> 00:25:54,810
+زائد y ترابيع زائد تلاتة x
+
+234
+00:26:03,850 --> 00:26:11,210
+يبقى باجب أقول الحل كالتالي بدي أعيد ترتيبي المثلة
+
+235
+00:26:11,210 --> 00:26:18,010
+بهذا أخليها M زائد N في Dy بDX هذا كل ال term
+
+236
+00:26:18,010 --> 00:26:23,170
+يعتبر ماذا؟يبقى لو قعدت ترتيبة بس مشان ماغلطش و
+
+237
+00:26:23,170 --> 00:26:26,150
+الكلام اللي اخلتيه زميل و اشتغلتي ماعندهاش مشكلة
+
+238
+00:26:26,150 --> 00:26:33,030
+يبقى لو جيتك و قلت هذا y تربيه زائد تلاتة x y تكيب
+
+239
+00:26:33,030 --> 00:26:38,750
+لحاله زائد واحد ناقص x y في ال y prime يساوي zero
+
+240
+00:26:38,750 --> 00:26:45,890
+وروحت سميت المعادلة هذه معادلة start أخدت فضل ال m
+
+241
+00:26:45,890 --> 00:26:54,150
+بالنسبة إلى y يساوييبقى هذه كلها اللي تعتبر M وهذا
+
+242
+00:26:54,150 --> 00:27:00,410
+كلها اللي تعتبر مين؟ N بدي اشتق هذه بالنسبة الى Y
+
+243
+00:27:00,410 --> 00:27:11,350
+يبقى 2Y زائد 9 X Y تربيع بدي اشتق هذه بالنسبة الى
+
+244
+00:27:11,350 --> 00:27:12,130
+Y يبقى 2Y زائد 9 X Y تربيع بدي اشتق هذه بالنسبة
+
+245
+00:27:12,130 --> 00:27:13,030
+الى Y يبقى 2Y زائد 9 X Y تربيع بدي اشتق هذه
+
+246
+00:27:13,030 --> 00:27:13,450
+بالنسبة الى Y يبقى 2Y زائد 9 X Y تربيع بدي اشتق
+
+247
+00:27:13,450 --> 00:27:18,310
+هذه بالنسبة الى X تفاضل 1 ب Zero بقدرش بناقص Y
+
+248
+00:27:18,800 --> 00:27:23,320
+الطالعين اللي اتنين هدول هل بيسووا بعض يبقى هذا
+
+249
+00:27:23,320 --> 00:27:29,820
+بدي يعطيني انه تفاضل ال M بالنسبة ال Y لا يسوى
+
+250
+00:27:29,820 --> 00:27:35,280
+تفاضل ال N بالنسبة ال X هذا بدي يعطيني انه ال
+
+251
+00:27:35,280 --> 00:27:44,480
+differential equation star is not exact تمام تمام
+
+252
+00:27:44,870 --> 00:27:49,390
+مدى ما هيش exactly اذا بتروح ادور على مين على ال
+
+253
+00:27:49,390 --> 00:27:55,310
+integrating factor اذا عندك دقة نظر بتقدر تعرفي هل
+
+254
+00:27:55,310 --> 00:27:59,770
+بدي اخد تفاضل N بالنسبة ل Y نقص تفاضل N بالنسبة ل
+
+255
+00:27:59,770 --> 00:28:04,330
+X او العكس و اذا كان غالبا ماديكيش دقة نظر بروحه
+
+256
+00:28:04,330 --> 00:28:09,430
+غمضي واتوكل على الله وشوف ايش النتيجة بتطلع مازبطش
+
+257
+00:28:09,430 --> 00:28:13,470
+بجلب و بشوف التاني بس هدا هتاخد منك دقيقة دقيقتين
+
+258
+00:28:13,470 --> 00:28:21,350
+زيادةإذا أنا لو جيت أخدت تفاضل ال N بالنسبة إلى X
+
+259
+00:28:21,350 --> 00:28:28,110
+ناقص تفاضل ال M بالنسبة إلى Y كلها جيت جسمتها على
+
+260
+00:28:28,110 --> 00:28:35,950
+ال M تفاضل N بالنسبة ل X هي ناقص Y ناقص تفاضل
+
+261
+00:28:35,950 --> 00:28:40,390
+بالنسبة ل Y هي ناقص على كل term من ال two terms
+
+262
+00:28:40,390 --> 00:28:47,480
+اللي عندنايبقى بصير ناقص اتنين Y ناقص تسعة X Y
+
+263
+00:28:47,480 --> 00:28:53,380
+تربيع كله مقسوما على M وين ال M هذه يبقى مقسوما
+
+264
+00:28:53,380 --> 00:29:03,260
+على Y تربيع Y تربيع زائد تلاتة X Y تكيب ويساوي هذه
+
+265
+00:29:03,260 --> 00:29:11,480
+يا بنات بصير سالب تلاتة Y سالب تسعة X Y تربيععلى y
+
+266
+00:29:11,480 --> 00:29:19,820
+تربية زائد تلاتة x y تكييب y اش رايك في عامل مشترك
+
+267
+00:29:19,820 --> 00:29:27,900
+فوق اللي هو سالب تلاتة y عامل مشترك اذا بقدر اقول
+
+268
+00:29:27,900 --> 00:29:34,060
+هي سالب تلاتة y عامل مشترك بظل عندي واحد زائد
+
+269
+00:29:34,060 --> 00:29:42,530
+تلاتة x y علىفى عامل مشترك هنا عندنا y تربيع يبقى
+
+270
+00:29:42,530 --> 00:29:48,710
+لو أخدت y تربيع عامل مشترك بدون واحد زائد تلاتة xy
+
+271
+00:29:48,710 --> 00:29:55,130
+أظن بقدر اختصر جوس مع جوس و y مع y تربيع يبقى هذا
+
+272
+00:29:55,130 --> 00:30:01,990
+الكلام متساوى ناقص تلاتة على y ناقص تلاتة على y
+
+273
+00:30:01,990 --> 00:30:09,230
+ايش رأيك function في y onlyيبقى هذي function في
+
+274
+00:30:09,230 --> 00:30:16,450
+any only طب اطلعي هل الشغل الصح ولا غلط تعالى تشوف
+
+275
+00:30:16,450 --> 00:30:20,510
+فيه الأصل تكون function في y و الله function في x
+
+276
+00:30:20,510 --> 00:30:27,550
+الناقص لمن؟ لل M يبقى جسمت على ال M الناتج طلع
+
+277
+00:30:27,550 --> 00:30:33,310
+function في من؟ يبقى شغل سليم مائة بالمائةبدي اجي
+
+278
+00:30:33,310 --> 00:30:44,350
+اعرف ما هو شكل ال integrating factor يبقى
+
+279
+00:30:44,350 --> 00:30:51,430
+شكل ال integrating factor لميو of Y بده يسوي E أُس
+
+280
+00:30:51,430 --> 00:31:00,170
+تكامل F of Y Dy يعني E أُس تكاملالـ f of y عندنا
+
+281
+00:31:00,170 --> 00:31:05,570
+اللي يبقى dash ناقص ثلاثة على y يبقى ناقص ثلاثة
+
+282
+00:31:05,570 --> 00:31:14,130
+على y dy يبقى E أس ناقص ثلاثة لإن ال y و constant
+
+283
+00:31:14,130 --> 00:31:17,830
+تكتبهوش لإن بصير E أس constant بعد ذلك يعني
+
+284
+00:31:17,830 --> 00:31:22,930
+constant لا يغير ولا يبدل من شكل man من شكل الحل
+
+285
+00:31:23,380 --> 00:31:30,680
+يبقى النتيجة هادى E أس لن Y والسالب تلاتة ال E وال
+
+286
+00:31:30,680 --> 00:31:36,870
+لن عكس بعض يبقى النتيجة قداشy أسالب تلاتة إذا عامل
+
+287
+00:31:36,870 --> 00:31:43,030
+التكامل هو y أسالب تلاتة إذا بتاجي على المعادلة
+
+288
+00:31:43,030 --> 00:31:49,230
+star هذه وضربها في عامل التكامل بعد ما ضربها لازم
+
+289
+00:31:49,230 --> 00:31:54,990
+تطلع المعادلة عن مالها وإلا بصير شغلي في غلط بدي
+
+290
+00:31:54,990 --> 00:31:59,090
+أروح أدور وانا الغلطة و أرجعها إذا بدي أروح أضرب
+
+291
+00:31:59,090 --> 00:32:04,480
+المعادلة star في عامل التكامل y أسالب تلاتةيبقى
+
+292
+00:32:04,480 --> 00:32:15,800
+باجي بقوله multi if lie equation star by y السلب
+
+293
+00:32:15,800 --> 00:32:22,160
+ثلاث و جد نحصل على بدي أضرب y السلب تلاتة هنا بيضل
+
+294
+00:32:22,160 --> 00:32:32,260
+كده؟ y السلب واحد صح؟ يبقى هذا y السلب واحدبدي
+
+295
+00:32:32,260 --> 00:32:39,240
+اضرب y أساليب تلاتة هنا بظل بس تلاتة x يبقى زائد
+
+296
+00:32:39,240 --> 00:32:46,160
+تلاتة x زائد هنا y أساليب تلاتة في واحد في y
+
+297
+00:32:46,160 --> 00:32:55,870
+أساليب تلاتة وهنا سالب x y أساليب اتنين مظبوطضربت
+
+298
+00:32:55,870 --> 00:33:00,990
+في y السلب تلاتة و اتنين
+
+299
+00:33:00,990 --> 00:33:05,830
+و هاد ال y prime كلها تساوي zero و هاد المعادلة يا
+
+300
+00:33:05,830 --> 00:33:12,610
+بنات سميها y double starإذن كأنه الآن أنا سبت
+
+301
+00:33:12,610 --> 00:33:18,370
+المعادلة star و حولتها إلى شكل جديد إلى المعادلة y
+
+302
+00:33:18,370 --> 00:33:22,550
+double star الآن حسب المعلومات اللي عندي في الجزء
+
+303
+00:33:22,550 --> 00:33:26,330
+النظري اللي لازم غصب عن اللي مايرضح المعادلة ده
+
+304
+00:33:26,330 --> 00:33:30,910
+تطلع مالة exact لو ما طلعتش exact في أحد احتمالين
+
+305
+00:33:31,140 --> 00:33:35,240
+يا إما إشتقاطك خطأ يا إما حسابك في ال integrating
+
+306
+00:33:35,240 --> 00:33:40,180
+factor خطأ بديك تروح تراجع وين الغلطة و تكتش فيها
+
+307
+00:33:40,180 --> 00:33:45,180
+و تعدل المثال اللي قدري يبقى أنا بدي أخد تفاضل ال
+
+308
+00:33:45,180 --> 00:33:52,840
+M بالنسبة إلى Y يبقى ناقص Y أس ناقص 2 وهذه تبقى
+
+309
+00:33:52,840 --> 00:34:01,040
+ايه؟ Zero تمام؟بدي اخد تفاضل ال N بالنسبة ال X هذه
+
+310
+00:34:01,040 --> 00:34:08,240
+مش غتب جداش ب Zero ناقص تفاضل X بواحد بظل اص ناقص
+
+311
+00:34:08,240 --> 00:34:14,100
+اتنينماذا رأيك بالإجابتين؟ نفس الشيء يبقى هذا
+
+312
+00:34:14,100 --> 00:34:20,600
+معناه انه تفاضل ال M بالنسبة إلى Y يساوي تفاضل ال
+
+313
+00:34:20,600 --> 00:34:26,000
+M بالنسبة إلى X هذا معناه ان ال differential
+
+314
+00:34:26,000 --> 00:34:34,820
+equation W star is exact مدام exact هذا معناته
+
+315
+00:34:34,820 --> 00:34:41,440
+that there exists a functiony of x و y بده يساوي
+
+316
+00:34:41,440 --> 00:34:47,600
+constant c1 مثلا such that بحيث أن
+
+317
+00:34:53,930 --> 00:34:59,910
+تفاضل الـ Phi بالنسبة إلى X بدي يسوي M لجديدة مش
+
+318
+00:34:59,910 --> 00:35:04,370
+العتيقة لإن احنا المعادلة العتيقة حطناها بالشكل
+
+319
+00:35:04,370 --> 00:35:10,510
+الجديد هذا يبقى صار Y أس سالب واحد زائد تلاتة X
+
+320
+00:35:10,510 --> 00:35:18,270
+وتفاضل ال Phi بالنسبة إلى Y يسوي Y أس ناقص تلاتة
+
+321
+00:35:18,270 --> 00:35:25,610
+ناقص X وY أس ناقص اتنىأظن هذه أسهل في الحسابات
+
+322
+00:35:25,610 --> 00:35:29,570
+الآن لما لا يوجد فيها غير Y و لا يوجد فيها غير X
+
+323
+00:35:29,570 --> 00:35:34,290
+واحدة هذه فيها Y وهذه فيها يعني بدأت كاملة تنتين
+
+324
+00:35:34,290 --> 00:35:38,890
+وهذه بدأت كاملة تنتين بس هذه ليست فيها Y إذا الـ
+
+325
+00:35:38,890 --> 00:35:44,710
+Phi of X و Y لو كامل بالنسبة ل X بيصير Y أسالف
+
+326
+00:35:44,710 --> 00:35:53,550
+واحد X وهذه زائد تلاتة X تربية علىإتنين وزائد
+
+327
+00:35:53,550 --> 00:36:01,830
+function of y تمام بتروح اشتقها بالنسبة إلى y يبقى
+
+328
+00:36:01,830 --> 00:36:07,290
+لو اشتقتها إلى y بصير partial phi على partial y
+
+329
+00:36:07,290 --> 00:36:15,710
+يساوي هذه بصير سالف y و سالف اتنين في x
+
+330
+00:36:21,120 --> 00:36:26,960
+ما هو رأيك
+
+331
+00:36:26,960 --> 00:36:28,680
+في الاتنين؟
+
+332
+00:36:31,470 --> 00:36:37,070
+إذا بدروح أسويهم ببعض يبقى لو سويتهم ببعض بصينا
+
+333
+00:36:37,070 --> 00:36:45,150
+ناقص y أس ناقص اتنين x زائد f prime of y يبقى يسوي
+
+334
+00:36:45,150 --> 00:36:53,770
+y السالب تلاتة ناقص x y السالب اتنين أظن هذه هذه
+
+335
+00:36:53,770 --> 00:37:05,450
+صح يبقى هذا معناهإن ال F' of Y يسوي Y السلب تلاتة
+
+336
+00:37:05,660 --> 00:37:11,620
+هذا معناه ان F of Y بدي كامل بالنسبة ل Y يبقى
+
+337
+00:37:11,620 --> 00:37:17,540
+باضيف لل أس واحد وباقسم على الأس الجديد يبقى Y
+
+338
+00:37:17,540 --> 00:37:24,820
+السالب اتنين على سالب اتنين زائد constant to C2
+
+339
+00:37:24,820 --> 00:37:30,720
+إذن الحل تبع المعادلة الأصلية هو Phi اللي عندنا
+
+340
+00:37:30,720 --> 00:37:43,300
+يبقى باجي بقوله ذاSolution is Phi of XY يسوى Y
+
+341
+00:37:43,300 --> 00:37:51,100
+السلب واحد في ال X زائد تلاتة X تربيع على الإتنين
+
+342
+00:37:51,100 --> 00:38:00,200
+زائد F of Y هيها يبقى ناقص Y ناقص إتنينعلى اتنين
+
+343
+00:38:00,200 --> 00:38:07,400
+وكل هذا الكلام بيكون ساوي constant C يبقى هذا الحل
+
+344
+00:38:07,400 --> 00:38:11,980
+تبع المعادلة اللي عندنا يعني انا في الأول بدي احول
+
+345
+00:38:11,980 --> 00:38:17,560
+المعادلة الى exact ومن ثم بروح احل المعادلة اللي
+
+346
+00:38:17,560 --> 00:38:24,180
+عندنا هذه تمام نجي ناخد كمان مثال على هالشغل هذي
+
+347
+00:38:24,180 --> 00:38:26,040
+ونشوف كيف بدنا نحله
+
+348
+00:38:38,650 --> 00:38:52,930
+طيب example two solve
+
+349
+00:38:52,930 --> 00:38:54,350
+the differential equation
+
+350
+00:38:59,460 --> 00:39:11,040
+حل المعادلة التفاضلية xy زائد y ترابية زائد y كل
+
+351
+00:39:11,040 --> 00:39:21,140
+هذا مقدار واحد زائد x زائد اتنين y في dy by dx
+
+352
+00:39:21,140 --> 00:39:26,200
+يساوي zero وهذه المعادلة اليمين المعادلة
+
+353
+00:39:28,290 --> 00:39:34,930
+نعود لـ Solution ناخد
+
+354
+00:39:34,930 --> 00:39:43,410
+تفاضل M بالنسبة إلى Y Y يساوي تفاضل M بالنسبة إلى
+
+355
+00:39:43,410 --> 00:39:54,710
+Y هو X زائد 2Y زائد 1 وتفاضل M بالنسبة .. أولا
+
+356
+00:39:54,710 --> 00:40:03,360
+خليها السطر اللي بعدهوتفاضل ال M بالنسبة إلى X
+
+357
+00:40:03,360 --> 00:40:09,920
+يساوي واحد وانت مع السلامة بالزيرة من الأثنين هذول
+
+358
+00:40:09,920 --> 00:40:15,700
+بقدر أقول إذا تفاضل ال M بالنسبة إلى Y لا يساوي
+
+359
+00:40:15,700 --> 00:40:19,840
+تفاضل ال N بالنسبة إلى X إذا المعادلة أستخدمها
+
+360
+00:40:19,840 --> 00:40:26,860
+ديمانها not exact هذا يقدر يعطينا ذاتdifferential
+
+361
+00:40:26,860 --> 00:40:36,520
+equation is not exact مدام ما هياش exact تدبر حالك
+
+362
+00:40:36,520 --> 00:40:42,660
+اقوله بسيط اذا انا بدي اروح ادور على عامل التكامل
+
+363
+00:40:43,060 --> 00:40:49,860
+لذلك بروح اخد تفاضل ال N بالنسبة الى Y ناقص تفاضل
+
+364
+00:40:49,860 --> 00:41:03,740
+ال N بالنسبة ال X مقسوما على N يبجى
+
+365
+00:41:03,740 --> 00:41:07,760
+هذا الكلام بدى يسوي تفاضل ال N بالنسبة الى Y X
+
+366
+00:41:07,760 --> 00:41:15,260
+زائد 2Y زائد 1 ناقصطب فاضل ان بالنسبة إلى y بواحد
+
+367
+00:41:15,260 --> 00:41:24,040
+على n .. n اللي هو x زائد اتنين y يبجل x زائد
+
+368
+00:41:24,040 --> 00:41:30,180
+اتنين y على x زائد اتنين y وسبق الدرجة بعتبره
+
+369
+00:41:30,180 --> 00:41:37,000
+function في مين يا بنات في x يبجل هذا function of
+
+370
+00:41:37,000 --> 00:41:43,860
+x onlyما دام function في x only يبقى عامل التكامل
+
+371
+00:41:43,860 --> 00:41:50,960
+لميو of x وليس لميو of x و y يساوي E أُس تكامل
+
+372
+00:41:50,960 --> 00:41:58,520
+اللي هي f of x dx يبقى E أُس تكامل جداش واحد
+
+373
+00:41:58,520 --> 00:42:04,460
+بالنسبة إلى dx يبقى E أُس x بالدالي على المعادلة
+
+374
+00:42:04,460 --> 00:42:09,950
+الأصلية كلها و أضربها في مين؟ في E أُس xيبقى
+
+375
+00:42:09,950 --> 00:42:14,950
+multiply equation
+
+376
+00:42:14,950 --> 00:42:20,670
+star by
+
+377
+00:42:20,670 --> 00:42:27,890
+PO6 we get x
+
+378
+00:42:27,890 --> 00:42:38,210
+PO6 y زائد PO6 y تربية زائد PO6 y زائد
+
+379
+00:42:53,620 --> 00:43:01,500
+يجي ناخد تفاضل ال M بالنسبة الى Y لجديدة يبقى هذه
+
+380
+00:43:01,500 --> 00:43:09,710
+ال M صارت كلها M وهذه كلها مين ال Mتفاضلها بالنسبة
+
+381
+00:43:09,710 --> 00:43:19,890
+إلى Y يبقى X U6 زائد اتنين U6 في ال Y زائد ال U6
+
+382
+00:43:19,890 --> 00:43:28,310
+بدنا نيجي ناخد تفاضل ال N بالنسبة إلى X تانية هذه
+
+383
+00:43:28,310 --> 00:43:35,070
+تعتبر مستقبل حاصل ضرب دلتين يبقى ال U6
+
+384
+00:43:37,430 --> 00:43:46,530
+يو سكس زائد اتنين يو سكس وفي ال Y كما هي تمام
+
+385
+00:43:46,530 --> 00:43:51,850
+تعالى نشوف هل هذول بيسوا بعض و لا لا هذي هي هذي
+
+386
+00:43:51,850 --> 00:44:01,230
+تمام و هذي هي هذي او هذي هي هذي صح يبقى هذول اتنين
+
+387
+00:44:01,230 --> 00:44:08,360
+مالهم بيسوا بعض يبقى هذا معناهمإن تفاضل ال M
+
+388
+00:44:08,360 --> 00:44:14,820
+بالنسبة إلى Y يسوى تفاضل ال N بالنسبة إلى X يبقى
+
+389
+00:44:14,820 --> 00:44:22,160
+هذا بدي يعطينا ال differential equation W star is
+
+390
+00:44:22,160 --> 00:44:29,580
+exact مدام exact هذا شو بدي يعطينا يبقى there
+
+391
+00:44:29,580 --> 00:44:37,550
+exists a functionfive of x y متساوي constant c one
+
+392
+00:44:37,550 --> 00:44:41,290
+such that بحيث m
+
+393
+00:45:02,750 --> 00:45:10,670
+Partial Phi by Partial X يساوي M الجديدة الـ X في
+
+394
+00:45:10,670 --> 00:45:20,690
+E أس X في Y زائد E أس X في Y تربية E أس X في Y
+
+395
+00:45:20,690 --> 00:45:27,890
+تربية زائد E أس X في Y وتفاضل الـ Phi بالنسبة إلى
+
+396
+00:45:27,890 --> 00:45:30,490
+Y يساوي الterm التاني
+
+397
+00:45:41,480 --> 00:45:46,220
+مين أسهل يا بناتا كامل هذه بالنسبة ل X والله كامل
+
+398
+00:45:46,220 --> 00:45:52,500
+هذه بالنسبة ل Yتعني أسهل كتير مش كمان أسهل و بس
+
+399
+00:45:52,500 --> 00:45:57,820
+ليش؟ لأنها تحتاج ال integration by parts تكمل
+
+400
+00:45:57,820 --> 00:46:02,600
+بالتجزيه لسه بدي أجزه و أشهى القصة لها دي دوري
+
+401
+00:46:02,600 --> 00:46:11,300
+يبقى بروح بقوله five of x y يساوي x u6 في ال y
+
+402
+00:46:11,300 --> 00:46:17,460
+زائد u6 في ال y تربية على اتنين مع اتنين مع
+
+403
+00:46:17,460 --> 00:46:24,740
+السلامةزائد f of x كوني كاملت بالنسبة الى y يبقى
+
+404
+00:46:24,740 --> 00:46:31,200
+باعتبر هذا هي function of x طب الفاضلها partial
+
+405
+00:46:31,200 --> 00:46:39,200
+phi by partial x يساوي هذا يعتبر حصل ضرب داليتين
+
+406
+00:46:39,200 --> 00:46:46,820
+يبقى تفاضل x بواحد بصير EO6 في ال y تفاضل EO6 بال
+
+407
+00:46:46,820 --> 00:46:53,130
+EO6 itselfيبقى E أُس X في ال Y أي تفاضليزي الأول
+
+408
+00:46:53,130 --> 00:46:59,710
+تفاضلي الثاني E أُس X زي ما هي في ال Y تربية زائد
+
+409
+00:46:59,710 --> 00:47:08,400
+ال F Prime of X أليس تهادي هي هادي؟ صح؟مش هذه
+
+410
+00:47:08,400 --> 00:47:10,840
+تفاضل five بالنسبة لكتر او تفاضل five بالنسبة لكتر
+
+411
+00:47:10,840 --> 00:47:17,000
+اذا بسووا الطرفين البعض يبقى باجي بقوله اذا ال EO6
+
+412
+00:47:17,000 --> 00:47:26,520
+في ال Y زي ال X EO6 في ال Y زي
+
+413
+00:47:26,520 --> 00:47:31,520
+ال .. احنا .. اه بالفضل احنا مظبوط لا احنا بيجيب
+
+414
+00:47:31,520 --> 00:47:38,550
+.. هذه مظبوط ال EO6 في ال Yزاد X إيقص X في الـ Y
+
+415
+00:47:38,550 --> 00:47:47,650
+زاد إيقص X في الـ Y تربية زاد F prime of X يساوي
+
+416
+00:47:47,650 --> 00:47:54,770
+اللي عندنا X إيقص X في الـ Y زاد إيقص X في الـ Y
+
+417
+00:47:54,770 --> 00:48:01,390
+تربية زاد إيقص X في الـ Y أظن ال term هذا هو ال
+
+418
+00:48:01,390 --> 00:48:08,720
+term هذاو ال term هذا هو ال term هذا و ال term هذا
+
+419
+00:48:08,720 --> 00:48:13,080
+هو ال term هذا، مصبوح؟ يبقى بيننا يعني بيبقى لنا
+
+420
+00:48:13,080 --> 00:48:19,100
+five F prime of X يساوي كده؟ يساوي zero معناته ال
+
+421
+00:48:19,100 --> 00:48:26,680
+F of X بده يساوي كل مصطلح تاني و ليكن C2 إذا the
+
+422
+00:48:26,680 --> 00:48:38,160
+solution of theDifferential equation star S التي
+
+423
+00:48:38,160 --> 00:48:47,140
+حصلنا عليها في اكس و Y يساوي X في ال E والسكس Y
+
+424
+00:48:47,140 --> 00:48:54,060
+زائد E والسكس في Y تربيع وهذا كله كونستان يبقى هذا
+
+425
+00:48:54,060 --> 00:49:00,330
+كله ساوي كونستان C هذا هو الحلتبع المعادلة
+
+426
+00:49:00,330 --> 00:49:08,390
+التفاضلية تمام لحد هنا stop لا يزال عندنا مثال بس
+
+427
+00:49:08,390 --> 00:49:12,530
+المثال طويل شوية عالمين على ال integrating factor
+
+428
+00:49:12,530 --> 00:49:17,550
+ثالث بنخليه للمحاضرة الساعة اتناشر اللي هي بعد
+
+429
+00:49:17,550 --> 00:49:22,330
+الظهر ان شاء الله تبارك وتعالى يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/r9WgIkSN3M4_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/r9WgIkSN3M4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d757f899b43ba38505437642d1c660e97a2c6f24
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/r9WgIkSN3M4_postprocess.srt
@@ -0,0 +1,1740 @@
+1
+00:00:20,740 --> 00:00:25,060
+بسم الله الرحمن الرحيم نذكر باخر حاجة خدناها المرة
+
+2
+00:00:25,060 --> 00:00:28,800
+اللي فات في section تلاتة أربعة بدينا بالرونسكين
+
+3
+00:00:28,800 --> 00:00:33,680
+وعرفنا ان رونسكين هو عبارة عن محدد ثم انتقلنا إلى
+
+4
+00:00:33,680 --> 00:00:38,780
+نظرية نظرية دو شقين الشق الأول كان إذا كان عندي
+
+5
+00:00:38,780 --> 00:00:42,680
+مجموعة من ال vectors وكانوا linearly dependent
+
+6
+00:00:42,680 --> 00:00:48,580
+يبقى لازم الرونسكين يساوي zero عند كل X موجودة في
+
+7
+00:00:48,580 --> 00:00:53,670
+interval ماأخذنا العملية العكسية أنه لو كان ال
+
+8
+00:00:53,670 --> 00:00:58,710
+رونسكين لا يساوي 0 يبقى مجموعة هذه ال functions أو
+
+9
+00:00:58,710 --> 00:01:02,110
+مجموعة هذه ال vectors are linearly independent
+
+10
+00:01:02,110 --> 00:01:08,310
+وعطينا المرة اللي فاتت مثل على أنه ممكن يكون ال
+
+11
+00:01:08,310 --> 00:01:13,350
+رونسكين يساوي 0 لكن ال two functions are not
+
+12
+00:01:13,350 --> 00:01:18,440
+linearly dependentبالـ Linearly Independent لأنه
+
+13
+00:01:18,440 --> 00:01:24,120
+عكس النظرية ما هواش صحيح تمام يعطينا مثال كان G1
+
+14
+00:01:24,120 --> 00:01:28,240
+of X تساوي X تربيع و G2 of X هو X في absolute
+
+15
+00:01:28,240 --> 00:01:33,920
+value ل X ننتقل إلى مثال جديد يقول يشوف ليها ال
+
+16
+00:01:33,920 --> 00:01:37,280
+functions هذه الواحد و X السالب واحد و X السالب
+
+17
+00:01:37,280 --> 00:01:42,270
+اتنين علما من X دائما و أبدا تأخذ قيمة موجبةهل
+
+18
+00:01:42,270 --> 00:01:46,410
+هدول linearly dependent ولا linearly independent
+
+19
+00:01:46,410 --> 00:01:51,490
+فبجيب اقولك كويس اذا انا بدي اخد رونسكين as a
+
+20
+00:01:51,490 --> 00:01:56,830
+function of X هي الدالة الاولى هي الدالة التانية
+
+21
+00:01:56,830 --> 00:02:02,980
+هي الدالة التالتةمشان أكمل هذا المحدد بدي أشتق مرة
+
+22
+00:02:02,980 --> 00:02:08,660
+ثانية يبقى المشتق هذي بـ0 هذي ناقص X أس ناقص 2 هذي
+
+23
+00:02:08,660 --> 00:02:16,620
+ناقص 2 X أس ناقص 3 نشتق كمان مرة يبقى Zero اتنين X
+
+24
+00:02:16,620 --> 00:02:24,280
+أس ناقص تلاتة هذي ستة X أس ناقص أربعةيبقى هيشتغلنا
+
+25
+00:02:24,280 --> 00:02:29,900
+الدوال مرتين تمام الآن بدى قداش أحسب قيمة هذا
+
+26
+00:02:29,900 --> 00:02:34,680
+الرونسكين يبقى هفك المحدد باستخدام عناصر العمود
+
+27
+00:02:34,680 --> 00:02:42,250
+الأول يبقى هذا الكلام بده يساوي واحد فيهحاصل ضرب
+
+28
+00:02:42,250 --> 00:02:49,250
+عناصر القطرة الرئيسى يبقى ناقص 6 x أس ناقص 6 ناقص
+
+29
+00:02:49,250 --> 00:02:58,130
+مع ناقص زائد 4 x أس ناقص 6 ناقص 0 زائد 0يبقى بناء
+
+30
+00:02:58,130 --> 00:03:04,890
+ان عليه أصبح ناتج يساوي ناقص اتنين X أس ناقص ستة
+
+31
+00:03:04,890 --> 00:03:11,230
+طبعا هذا الكلام كله لا يساوي زيرو ليش؟ since لأن
+
+32
+00:03:11,230 --> 00:03:16,360
+ال X greater than zeroإذا هذا المقدار لا يمكن أن
+
+33
+00:03:16,360 --> 00:03:22,120
+يساوي zero في أي يوم من الأيام ولا عند نقطة ولا
+
+34
+00:03:22,120 --> 00:03:26,660
+عند كل النغاط لأن x greater than zero بناء عليه
+
+35
+00:03:26,660 --> 00:03:32,940
+هذا الكلام يعني أن هذه ال functions تلاتة are
+
+36
+00:03:32,940 --> 00:03:37,340
+linearly dependent ولا linearly independent
+
+37
+00:03:38,180 --> 00:03:44,400
+Linearly Independent يبقى هنا since بما أن
+
+38
+00:03:44,400 --> 00:03:48,940
+Erroneous can as a function of x لا يساوي zero
+
+39
+00:03:48,940 --> 00:03:56,420
+يبقى the functions اللي هي واحد و x السلب واحد و x
+
+40
+00:03:56,420 --> 00:04:02,620
+السلب اتنين are linearly independent functions
+
+41
+00:04:02,620 --> 00:04:14,460
+يبقى هذه دوال مساقلة عن بعض تمامانأخد مثال يبقى
+
+42
+00:04:14,460 --> 00:04:26,520
+مثال كذلك show
+
+43
+00:04:26,520 --> 00:04:30,660
+that مبينين
+
+44
+00:04:30,660 --> 00:04:32,740
+the functions
+
+45
+00:04:35,130 --> 00:04:46,210
+اللي هما F1 of X يساوي E أُس R1 X و F2 of X يساوي
+
+46
+00:04:46,210 --> 00:04:55,930
+E R2 أُس X ونظل ماشيين لغاية ال FN of X بده يساوي
+
+47
+00:04:55,930 --> 00:05:02,110
+E أُس RN of X و الRI
+
+48
+00:05:22,910 --> 00:05:29,240
+سؤال مرة ثانيةالسؤال بيقول عن ان من ال functions
+
+49
+00:05:29,240 --> 00:05:35,640
+f1 وf2 وf3 هذه ال functions كل واحدة فيهم كتبناها
+
+50
+00:05:35,640 --> 00:05:39,580
+بدلالة ال exponential يبقى عندنا الدالة الأولى E
+
+51
+00:05:39,580 --> 00:05:44,780
+أس R1 X الدالة التانية E أس R2 X الدالة التالتة E
+
+52
+00:05:44,780 --> 00:05:51,780
+أس R3 X وهكذا لغاية ما نكمل باقي الدوال لغاية E أس
+
+53
+00:05:51,780 --> 00:05:57,090
+R N X الدوال هدول ما لهم؟هؤلاء اللي بدنا نشوفه أو
+
+54
+00:05:57,090 --> 00:06:01,470
+بدنا نثبت انهم linearly independent بشرط ر واحدة
+
+55
+00:06:01,470 --> 00:06:05,410
+متساوي ر اتنين ولا ر تلاتة ولا ر ولا واحدة فيهم
+
+56
+00:06:05,410 --> 00:06:11,570
+متساوي التانية راح قال ليش ان ر اي لا تساوي ر جي
+
+57
+00:06:11,570 --> 00:06:16,230
+يبقى الارات هدول الأساس ولا واحدة زي التانية لكل
+
+58
+00:06:16,230 --> 00:06:21,290
+اي لا تساوي جي بدأ اثبت ان هذه ال functions هي ر
+
+59
+00:06:21,290 --> 00:06:27,330
+linearlyاندي من ده طيب نبدأ ب .. لو بدنا ناخدها
+
+60
+00:06:27,330 --> 00:06:31,530
+كلها مرة واحدة صعبة جدا و الصبورة تاعتنا مش هتكفي
+
+61
+00:06:31,530 --> 00:06:37,690
+للكتابة لكن لو جينا نسترسل فبجي بقول هنا solution
+
+62
+00:06:37,690 --> 00:06:45,950
+لو أخدت ال N تساوي 2 مثلا يبقى كام function بيكون
+
+63
+00:06:45,950 --> 00:06:52,540
+عندى؟ كدهش؟كم فانكشف يكون عندي تنتين يبقى مافيش
+
+64
+00:06:52,540 --> 00:06:56,960
+غيرهم خلي بالكم معانا هنا بقول خلي بالكم معانا هنا
+
+65
+00:06:58,160 --> 00:07:03,920
+يبقى لما ماعنديش فانكشن تنتين ان يساوي اتنين يبقى
+
+66
+00:07:03,920 --> 00:07:10,820
+بتروح اخد ال runner skin of X يبقى هذا E أس R1 X E
+
+67
+00:07:10,820 --> 00:07:21,660
+أس R2 X بدي اشتق يبقى R1 E أس R1 X R2 E أس R2 X
+
+68
+00:07:21,660 --> 00:07:28,260
+ويساويمن خواص المحددات إذا في عندي عامل مشارك بطلع
+
+69
+00:07:28,260 --> 00:07:34,660
+برا يبقى من العمودي الأول إيش عندي عمدات E أس R1 X
+
+70
+00:07:34,660 --> 00:07:42,460
+من العمودي التاني E أس R2 X بظل المحدد عندي 11 R1
+
+71
+00:07:42,460 --> 00:07:51,150
+R2 يبقى هذا لو فكته بدي يصير E أس R1 زائد R2هذا
+
+72
+00:07:51,150 --> 00:07:59,950
+كله في X و بدا فك هذا المحدد يبقى R2-R1 كله بالشكل
+
+73
+00:07:59,950 --> 00:08:04,470
+اللي عنا هذا السؤال هو هل ال X بننشل في أي يوم من
+
+74
+00:08:04,470 --> 00:08:06,950
+الأيام ممكن يأخذ القيمة الصفر؟
+
+75
+00:08:09,510 --> 00:08:14,670
+الـ R2 نقص R1 هل يمكن أن يأخذ صفر؟ اعطاني الشرط
+
+76
+00:08:14,670 --> 00:08:19,650
+أساسي أن الـRI لا تسوى RJ لكل I لا تسوى J
+
+77
+00:08:25,030 --> 00:08:32,510
+اختصارا يا بنات ممكن اكتب هذه E أس R1 زائد R2 X في
+
+78
+00:08:32,510 --> 00:08:41,170
+D2 وهذا الكلام لا يساوي 0 من D2 ل R2 ناقص R1 يبقى
+
+79
+00:08:41,170 --> 00:08:47,070
+لو كانت ال N بتنين لا يمكن لهذا المقدار أن يساوي 0
+
+80
+00:08:47,070 --> 00:08:55,510
+لو جيت أخد Fن تساوي تلاتة يبقى رونسكين of x يبقى
+
+81
+00:08:55,510 --> 00:09:04,930
+يساوي هذه E أس R1 X E أس R2 X E أس R3 X المشتقة
+
+82
+00:09:04,930 --> 00:09:15,220
+الأولى R1 E أس R1 X R2 E أس R2 X R3 E أس R3 Xاللي
+
+83
+00:09:15,220 --> 00:09:22,440
+هم بدنا نشتغل كمان مرة R1 تربيع E أس R1 X R2 تربيع
+
+84
+00:09:22,440 --> 00:09:28,620
+E أس R2 X R3 تربيع E أس R3 X
+
+85
+00:09:32,580 --> 00:09:36,020
+إذا انا ممكن اعمل زي اللي جابله بالضبط طلع عامله
+
+86
+00:09:36,020 --> 00:09:40,540
+مشتركة من العمود الأول والعمود الثاني والعمود
+
+87
+00:09:40,540 --> 00:09:47,380
+الثالث يبقى هذا الكلام بده يساوي E أس R 1 X E أس R
+
+88
+00:09:47,380 --> 00:09:56,380
+2 X E أس R 3 X يبقى عندنا المحدد واحد واحد واحدR1
+
+89
+00:09:56,380 --> 00:10:04,580
+R2 R3 R1 تربيع R2 تربيع R3 تربيع بالشكل اللي عندنا
+
+90
+00:10:04,580 --> 00:10:13,060
+هذا او بمعنى اخر هذا الكلام بده يساوي EUS R1 زائد
+
+91
+00:10:13,060 --> 00:10:19,760
+R2 زائد R3 كله fixed و بده روح افك المحدد هذا مثلا
+
+92
+00:10:19,760 --> 00:10:26,160
+باستخدام عناصر العمود الأوليبقى لو فكته باستخدام
+
+93
+00:10:26,160 --> 00:10:30,640
+عناصر العمود الأول بداجي هذا اللي أقوله هذا الكلام
+
+94
+00:10:30,640 --> 00:10:36,460
+مضروب فيه واحد في المحدد الأصغر المناظر له اللي هو
+
+95
+00:10:36,460 --> 00:10:46,240
+R2 R3 تربيع ناقص R2 تربيع R3 يبقى هذا ال term
+
+96
+00:10:46,240 --> 00:10:52,850
+الأول حسب قاعدة الإشارات ناقص R1وهنا نشطب الصف
+
+97
+00:10:52,850 --> 00:11:00,210
+تبعه والعمود بيصير R تلاتة تربيع ناقص R اتنين
+
+98
+00:11:00,210 --> 00:11:06,210
+تربيع جينا هنا زائد R one تربيع او square اشتت
+
+99
+00:11:06,210 --> 00:11:11,610
+بيصفوا عموده بيصير R تلاتة ناقص R اتنين جفلنا
+
+100
+00:11:11,610 --> 00:11:20,350
+الجوزهذا الكلام بدي يساوي E أس R1 زائد R2 زائد R3
+
+101
+00:11:20,350 --> 00:11:24,170
+كله في X هذا الكلام في
+
+102
+00:11:53,070 --> 00:11:57,440
+ممكن اخد من هذا عامل مشتركأنا ممكن أخد R ثلاثة
+
+103
+00:11:57,440 --> 00:12:03,060
+ناقص R اتنين عامل مشترك من كل ال three terms يبقى
+
+104
+00:12:03,060 --> 00:12:11,680
+هذا E أس R one زائد R two زائد R three كله في X في
+
+105
+00:12:11,680 --> 00:12:18,980
+R three ناقص R two مين بيضل عند هنا R two R three
+
+106
+00:12:19,660 --> 00:12:27,820
+وهنا بيظل ناقص R1 R3 ناقص
+
+107
+00:12:27,820 --> 00:12:35,460
+R1 R2 ناقص R1 في الجوس التاني يعني هداني فكته زائد
+
+108
+00:12:35,460 --> 00:12:43,140
+R1 تربيع مافيش غيرها بالشكل اللي عندنا هناطيب هذا
+
+109
+00:12:43,140 --> 00:12:51,100
+الكلام بده يساوي E أس R1 زائد R2 زائد R3 في X في
+
+110
+00:12:51,100 --> 00:12:58,780
+ال R3 ناقص R2 الشكل اللي عندنا هنا ناقص R2 لجوس
+
+111
+00:12:58,780 --> 00:13:04,020
+الأول شو رايكوا هدول ممكن اخد منهم ايه عشان R3
+
+112
+00:13:04,020 --> 00:13:12,330
+عامل مشتركيبقى لو أخدنا R3 عامل مشترك R3 بيظل من
+
+113
+00:13:12,330 --> 00:13:22,010
+عندي؟ بيظل عندي R2 ناقص R1 وهنا لو أخدنا ناقص R1
+
+114
+00:13:22,010 --> 00:13:26,890
+عامل مشترك بيظل R2 ناقص R1
+
+115
+00:13:29,040 --> 00:13:37,440
+طيب هنا انا انا انا انا
+
+116
+00:13:37,440 --> 00:13:53,920
+انا
+
+117
+00:13:53,920 --> 00:13:56,600
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+118
+00:13:56,600 --> 00:14:00,950
+انا انا انا انا اناهل يمكن لهذا المقدار أن يساوي
+
+119
+00:14:00,950 --> 00:14:05,430
+Zero في يوم من الأيام؟في الشمكانية ليش؟ لإن ال
+
+120
+00:14:05,430 --> 00:14:08,970
+exponential دائما و أبدا positive greater than
+
+121
+00:14:08,970 --> 00:14:15,910
+zero غير هيك ولا واحدة من R تسوى R التانية ر I لا
+
+122
+00:14:15,910 --> 00:14:22,570
+يسوى ر جي لكل ال I التي لا تسوى جي يبقى لا يمكن
+
+123
+00:14:22,570 --> 00:14:28,010
+لأي قوس من هذه الأقواس أن تسوى zero إذا بروح بقوله
+
+124
+00:14:28,010 --> 00:14:34,720
+هذا مالهلا يساوي 0 او ان شئتم فاقولوا هذا ايه؟ اصر
+
+125
+00:14:34,720 --> 00:14:43,440
+one زائد R2 زائد R3 كله في X في D تلاتة هذا كله
+
+126
+00:14:43,440 --> 00:14:49,770
+ماله؟لأ يساوي 0 إذا في الحالة الأولى كانت E أس R1
+
+127
+00:14:49,770 --> 00:14:54,750
+X و E أس R2 X are linearly independent في الحالة
+
+128
+00:14:54,750 --> 00:14:59,670
+التانية أصبح E أس R1 E أس R2 E أس R3 برضه are
+
+129
+00:14:59,670 --> 00:15:06,290
+linearly independent طيب الآن بداجي أقول لو كان
+
+130
+00:15:06,290 --> 00:15:11,870
+عند إيهاللي هو ال N من ال functions يعني احنا بدنا
+
+131
+00:15:11,870 --> 00:15:16,150
+نعمم بدل ما نمشي اتنين و تلاتة و اربعة بدنا نروح
+
+132
+00:15:16,150 --> 00:15:22,070
+الى M يبقى بداجي اخد هنا also
+
+133
+00:15:23,870 --> 00:15:28,890
+لو أخدت رونسكين as a function of x اللي هو بده
+
+134
+00:15:28,890 --> 00:15:39,410
+يساوي E أص R1X E أص R2X وظلت مستمر لغاية E أص RNX
+
+135
+00:15:40,000 --> 00:15:50,480
+بالدجاج أشتق يبقى R1 E أس R1 X R2 E أس R2 X RN E
+
+136
+00:15:50,480 --> 00:16:01,650
+أس RN X نشتق كمان مرة يبقى R1 تربية E أس R1 XR2
+
+137
+00:16:01,650 --> 00:16:11,070
+تربية E أُس R2 X ونظل ماشيين R N تربية E أُس R N X
+
+138
+00:16:11,070 --> 00:16:19,330
+لو ضلت مستمر يا بنات هوصل لوين لل R1 أُس N ناقص
+
+139
+00:16:19,330 --> 00:16:26,020
+واحد E أُس R1 Xيعني ما أقصدش للمشتاق قانونيا وإنما
+
+140
+00:16:26,020 --> 00:16:31,000
+أقل من المشتاق قانونيا بمقدار لإن الصف الأول مافيش
+
+141
+00:16:31,000 --> 00:16:36,920
+فيه اشتقاء طيب تمام التانية R2 to the power n
+
+142
+00:16:36,920 --> 00:16:45,760
+minus ال one E أس R to X نظل مستمرين لغاية RN أس N
+
+143
+00:16:45,760 --> 00:16:53,900
+ناقص واحد E أس RN X بالشكل اللي عندنا هذاطيب لو
+
+144
+00:16:53,900 --> 00:16:59,140
+جيتها ملت زي اللي قبل يبقى النتيجة حكت تالي بدي
+
+145
+00:16:59,140 --> 00:17:09,000
+يصير E أسرار 1 زائد R2 زائد R3 زائد RN كله في X في
+
+146
+00:17:09,000 --> 00:17:17,760
+مين يا بنات؟ في ال DN D2 D3 DN وهذا كله لا يساوي
+
+147
+00:17:17,760 --> 00:17:20,760
+zero where حيث
+
+148
+00:17:23,060 --> 00:17:30,820
+بنقلش نشوف مين هي DN هذه حيث ال DN هي عبارة عن
+
+149
+00:17:30,820 --> 00:17:43,210
+المحدد واحد واحد واحدهنا R1 R2 R3 RN هنا R1 تربيع
+
+150
+00:17:43,210 --> 00:17:52,090
+R2 تربيع R3 تربيع RN تربيع ونظل ماشيين لغاية R1
+
+151
+00:17:52,090 --> 00:17:59,020
+أسئل ناقص واحدR2 أُس N ناقص واحد R3 أُس N ناقص
+
+152
+00:17:59,020 --> 00:18:06,540
+واحد RN أُس N ناقص واحد وهي المحدد وهذا ما له لا
+
+153
+00:18:06,540 --> 00:18:13,810
+يساوي زيرو كذلكما دام لا يساوي زيرو يبقى صح اللي
+
+154
+00:18:13,810 --> 00:18:21,270
+هي ال E أس R one X وال E أس R two X ونظل ماشي لغة
+
+155
+00:18:21,270 --> 00:18:28,570
+E أس R in X are linearly independent ليش؟ لأن
+
+156
+00:18:28,570 --> 00:18:35,050
+المحدد تبعهم كله لا يساوي زيروland هنا stop انتهى
+
+157
+00:18:35,050 --> 00:18:42,830
+هذا section وإلى يكون أرقام المسائل من exercises
+
+158
+00:18:42,830 --> 00:18:50,210
+تلاتة أربعة يبقى exercises تلاتة أربعة واحد اتنين
+
+159
+00:18:50,210 --> 00:19:01,670
+أربعة وهنا سبعة وهنا تمانية بدنا
+
+160
+00:19:01,670 --> 00:19:09,520
+نيجي الآنلأهم section موجود في هذا الشبتر أو من
+
+161
+00:19:09,520 --> 00:19:25,620
+أهم ال sections اللي موجودة في هذا الشبتر هذا
+
+162
+00:19:25,620 --> 00:19:32,390
+الموضوع الآن اللي هو section 3-5تلاتة خمسة اللي هو
+
+163
+00:19:32,390 --> 00:19:38,550
+dimensions dimensions
+
+164
+00:19:38,550 --> 00:19:45,870
+مفرضها dimension يعني ابعاد dimensions يعني ابعاد
+
+165
+00:19:45,870 --> 00:19:52,230
+نعطي
+
+166
+00:19:52,230 --> 00:19:59,030
+تعريفين وبعد هيك نبدأ في طرح الأمثلة definition
+
+167
+00:20:01,970 --> 00:20:17,250
+لت كابتل V Be A Vector Space Vector Space Then V
+
+168
+00:20:17,250 --> 00:20:25,530
+Is Said To Be A Finite Dimensional Vector
+
+169
+00:20:39,370 --> 00:20:50,150
+finite dimensional vector space F النقطة الأولى
+
+170
+00:20:50,150 --> 00:20:52,330
+there exists a set
+
+171
+00:21:04,520 --> 00:21:18,660
+of linearly independent elements of V نقطة ثانية
+
+172
+00:21:18,660 --> 00:21:25,440
+every set
+
+173
+00:21:25,440 --> 00:21:30,740
+of more than
+
+174
+00:21:32,250 --> 00:21:38,710
+in elements as
+
+175
+00:21:38,710 --> 00:21:46,170
+linearly dependent ولحظة
+
+176
+00:21:46,170 --> 00:21:57,730
+بسيطة جدا in the above definition in the above
+
+177
+00:21:57,730 --> 00:22:00,890
+definition we say that
+
+178
+00:22:04,250 --> 00:22:18,330
+we say that ال V has dimension has dimension in يا
+
+179
+00:22:18,330 --> 00:22:31,170
+إما بنقول or V is n dimensional V is n dimensional
+
+180
+00:22:33,490 --> 00:22:49,930
+and dimensional vector space ملاحظة
+
+181
+00:22:49,930 --> 00:22:54,890
+ال vector space
+
+182
+00:23:02,280 --> 00:23:14,060
+V بده يساوي Zero فقط is finite dimensional
+
+183
+00:23:14,060 --> 00:23:17,740
+is
+
+184
+00:23:17,740 --> 00:23:28,620
+finite dimensional vector space
+
+185
+00:23:30,930 --> 00:23:40,190
+vector space and has and
+
+186
+00:23:40,190 --> 00:23:46,690
+has dimension zero
+
+187
+00:23:46,690 --> 00:23:53,610
+definition the
+
+188
+00:23:53,610 --> 00:23:59,810
+vectors V1
+
+189
+00:24:00,900 --> 00:24:19,860
+v2 و vk in a vector space in a vector space v are
+
+190
+00:24:19,860 --> 00:24:27,700
+set to form are
+
+191
+00:24:27,700 --> 00:24:35,670
+set to formA bases for
+
+192
+00:24:35,670 --> 00:24:47,290
+V F نمرة A نمرة
+
+193
+00:24:47,290 --> 00:24:55,790
+V واحد و V اتنين و V كاسبين
+
+194
+00:24:55,790 --> 00:24:58,050
+V
+
+195
+00:24:59,580 --> 00:25:11,300
+نمر بي V واحد و V اتنين و VK are linearly
+
+196
+00:25:11,300 --> 00:25:12,860
+independent
+
+197
+00:27:29,190 --> 00:27:35,270
+الان نبدأ بالتعريفين التعريفين الاثنين مركب عليهم
+
+198
+00:27:35,270 --> 00:27:41,190
+كل هذا ال section يعني بعد ذلك سناخد نظريات على ال
+
+199
+00:27:41,190 --> 00:27:45,150
+two definitions اللي عندنا لذلك ضروري نفهم كل
+
+200
+00:27:45,150 --> 00:27:50,410
+تعريف من هذين التعريفينالتعريف الأول بقول let V
+
+201
+00:27:50,410 --> 00:27:54,930
+بيه vector space then V is said to be a finite
+
+202
+00:27:54,930 --> 00:27:59,010
+dimensional vector space F إيش يعني finite
+
+203
+00:27:59,010 --> 00:28:04,150
+dimensional vector space؟ finite محدود و dimension
+
+204
+00:28:04,150 --> 00:28:09,060
+قعديبقى لما أقول finite dimensional vector space
+
+205
+00:28:09,060 --> 00:28:15,680
+يعني هذا ال vector space له أبعاد محدودة تمام إذا
+
+206
+00:28:15,680 --> 00:28:22,960
+تحقق شرطان ما هما هذان الشرطان الشرط الأولبقول if
+
+207
+00:28:22,960 --> 00:28:28,440
+there exists a set of n linearly independent of V
+
+208
+00:28:28,440 --> 00:28:33,860
+لقيت لي two vectors ثلاثة أربعة خمسة قد ما يكون
+
+209
+00:28:33,860 --> 00:28:38,900
+هدول المجموعة are linearly independent الشرط الأول
+
+210
+00:28:38,900 --> 00:28:44,820
+الشرط الثاني every set of more than n elements is
+
+211
+00:28:44,820 --> 00:28:51,840
+linearly dependent يبقى أنا لقيت عندين من الـ
+
+212
+00:28:51,840 --> 00:28:55,640
+linearly independent vectors لو حطيت عليهم كمان
+
+213
+00:28:55,640 --> 00:29:01,660
+واحد بصي العدد هم جديد ان زيد واحد اي ان زيد واحد
+
+214
+00:29:01,660 --> 00:29:07,680
+فما فوقه يعتبر linearly dependentممتاز جدا يبقى ال
+
+215
+00:29:07,680 --> 00:29:13,060
+vector اسمه CLV بقول عنه finite dimensional محدود
+
+216
+00:29:13,060 --> 00:29:18,800
+اذا جدرت الاجئين من ال linearly independent
+
+217
+00:29:18,800 --> 00:29:23,980
+elements اي عدد اخر سواء ان تبعتي هدول و ازيد
+
+218
+00:29:23,980 --> 00:29:28,560
+عليهم واحد او من غيرهم يجب ان يكونوا كلهم linearly
+
+219
+00:29:28,560 --> 00:29:33,320
+dependentإن حدث ذلك يبقى بقول هذا finite
+
+220
+00:29:33,320 --> 00:29:38,900
+dimensional vector space و ال dimension إله البعد
+
+221
+00:29:38,900 --> 00:29:43,100
+تبعه بدي يسوى جداش بدي يسوى M يبقى in the above
+
+222
+00:29:43,100 --> 00:29:46,320
+definition في التعريفة لو we say that بروح نقول
+
+223
+00:29:46,320 --> 00:29:52,020
+إنه في has dimension in أن البعد تبع هذا ال vector
+
+224
+00:29:52,020 --> 00:29:57,940
+space يسوى Nأو صياغة أخرى بقول ان ال V is N
+
+225
+00:29:57,940 --> 00:30:01,480
+dimensional vector space ان قلت ال dimension له
+
+226
+00:30:01,480 --> 00:30:06,920
+اللي عدد الأبعاد تبعه يساوي N أو قلت هو finite N
+
+227
+00:30:06,920 --> 00:30:10,140
+dimensional vector space الصياغة هذه أو الصياغة
+
+228
+00:30:10,140 --> 00:30:15,460
+هذه الاتنين are the same يبقاش متعبرة صح من ال two
+
+229
+00:30:15,460 --> 00:30:21,080
+definitions الاتنين هدولطب السؤال هو طب لو كان ال
+
+230
+00:30:21,080 --> 00:30:25,400
+vector space هو لتريفيا ال vector space شو لتريفيا
+
+231
+00:30:25,400 --> 00:30:28,200
+ال vector space؟ يعني ال vector space اللي لا
+
+232
+00:30:28,200 --> 00:30:34,240
+يحتوي إلا على عنصر واحد و عنصر صفرين يبقى هذا بقول
+
+233
+00:30:34,240 --> 00:30:38,920
+ال dimension له يساوي جداش؟ يساوي zero لأنه
+
+234
+00:30:38,920 --> 00:30:42,660
+ماعنديش غير main غير الواحد و هذا ماعش vectors
+
+235
+00:30:42,660 --> 00:30:50,340
+أخرى إذا هو مستقل و قائم بذاته يعني linearlyلو
+
+236
+00:30:50,340 --> 00:30:55,060
+وجدنا كلمة اخرى فيها اخرى مافيه اش لان هو zero
+
+237
+00:30:55,060 --> 00:30:59,420
+لحاله تمام يبقى كأنه هذا بيقولك لو فيه بدهم يكونوا
+
+238
+00:30:59,420 --> 00:31:03,960
+linearly dependent يبقى هذا محقق بالشرطين يبقى هذا
+
+239
+00:31:03,960 --> 00:31:09,740
+ال dimension له يساوي zero طيب كويس نجي للملاحظة
+
+240
+00:31:09,740 --> 00:31:14,270
+التانيةأو الـ Definition التانية بيقول إذا vectors
+
+241
+00:31:14,270 --> 00:31:20,470
+V1 و V2 لغاية V كإن Vector Space V are said to
+
+242
+00:31:20,470 --> 00:31:26,610
+form a basis for V باسيس يعني أساس يبقى هدول هم
+
+243
+00:31:26,610 --> 00:31:32,250
+الأساس بالنسبة ل V إذا تحقق شرطا الشرط الأول أن ال
+
+244
+00:31:32,250 --> 00:31:38,150
+V هدول Spain VSpan V يعني إيش؟ يعني بيولدولي جميع
+
+245
+00:31:38,150 --> 00:31:43,890
+أنصار ال vector space V بالاستثناء بالبلد هيك يعني
+
+246
+00:31:43,890 --> 00:31:49,530
+أي vector فيه V بديه يكون linear combination من ال
+
+247
+00:31:49,530 --> 00:31:54,410
+vectors من V1 لغاية VKيعني اي vector في ال vector
+
+248
+00:31:54,410 --> 00:31:59,850
+space V بقدر اكتبه على شكل linear combination من
+
+249
+00:31:59,850 --> 00:32:05,350
+V1 و V2 و V3 لغاية Vk لغاية Vk هذا الشرط الأول
+
+250
+00:32:05,350 --> 00:32:10,870
+الشرط التاني V1 و V2 و Vk are linearly independent
+
+251
+00:32:10,870 --> 00:32:15,950
+يبقى انا مشان اختبر ان هدول بنفع basis لل vector
+
+252
+00:32:15,950 --> 00:32:21,000
+space ولا لأ بدي امرين الأمر الأولأريد أن أثبت أن
+
+253
+00:32:21,000 --> 00:32:23,380
+هؤلاء الوكتورز مستقلين ومستقلين ومستقلين ومستقلين
+
+254
+00:32:23,380 --> 00:32:25,960
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+255
+00:32:25,960 --> 00:32:29,000
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+256
+00:32:29,000 --> 00:32:29,420
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+257
+00:32:29,420 --> 00:32:32,080
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+258
+00:32:32,080 --> 00:32:35,560
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+259
+00:32:35,560 --> 00:32:42,580
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين وم
+
+260
+00:32:43,930 --> 00:32:47,090
+بروح للشرط التاني في الأول أفضل ليش لأنه انطلع
+
+261
+00:32:47,090 --> 00:32:51,410
+linearly dependent بروح للشرط التاني لكن لو اذا
+
+262
+00:32:51,410 --> 00:32:55,010
+عملت الشرط الأول بدأ أروح أختبر من الشرط الثاني
+
+263
+00:32:55,010 --> 00:33:00,840
+إجباري يبقى الأفضل أن أروح لمين للشرط الثانييبقى
+
+264
+00:33:00,840 --> 00:33:07,620
+يا بنات مشان يكون عندى basis لل victory space بدى
+
+265
+00:33:07,620 --> 00:33:12,800
+هذه المجموعة من ال victories اللى تبقى basis يتحقق
+
+266
+00:33:12,800 --> 00:33:16,580
+فيها شرطا الشرط لو تبقى كلهم linearly independent
+
+267
+00:33:17,810 --> 00:33:21,650
+أي vector في ال vector space بقدر أكتبه على صيغة
+
+268
+00:33:21,650 --> 00:33:25,250
+linear combination من هذه ال vector يعني هذه ال
+
+269
+00:33:25,250 --> 00:33:30,250
+vector is PNV بتولد لل vector V نعطي مثال تونعي
+
+270
+00:33:30,250 --> 00:33:34,490
+مثال بيقول ما ياتي بيقول show the vectors ومعطيني
+
+271
+00:33:34,490 --> 00:33:40,890
+أربعة vectors موجودة وينهؤلاء يثبت لي ان هؤلاء
+
+272
+00:33:40,890 --> 00:33:46,310
+بيشكلوا بيزز ل ميم ل ال vector space اللي عندنا
+
+273
+00:33:46,310 --> 00:33:51,090
+بقوله والله كويس طيب تعالى نشوف هل هؤلاء بيشكلوا
+
+274
+00:33:51,090 --> 00:33:54,650
+بيزز ولا يبقى بأول خطة بدي أثبت ان هم يعيشين
+
+275
+00:33:55,660 --> 00:34:00,300
+Linearly Independent لكي أثبتهم اللي قبل الماضي
+
+276
+00:34:00,300 --> 00:34:04,900
+أخدنا شغلات
+
+277
+00:34:04,900 --> 00:34:08,960
+كثيرة بداك عن طريق المحدد ماشي بداك تقول ال
+
+278
+00:34:08,960 --> 00:34:12,620
+constant في الأول والثالث والرابع يتساوي زيرو
+
+279
+00:34:12,620 --> 00:34:16,640
+والروح نفسي بتانية دي ال constant بزيرو ماشي بسيان
+
+280
+00:34:16,640 --> 00:34:24,360
+اللي بدك إياه بأي وسيلة تنشأيبقى بالداجي اشوف اللي
+
+281
+00:34:24,360 --> 00:34:27,560
+هو لو قلت constant في الأول و constant في التاني و
+
+282
+00:34:27,560 --> 00:34:30,840
+constant في التالت يبقى بالداجي اقول له assume
+
+283
+00:34:30,840 --> 00:34:41,800
+that there exists c1 و c2 و c3 و c4 in R such that
+
+284
+00:34:42,190 --> 00:34:53,090
+بحيث ان C1 V1 زاد C2 V2 زاد C3 V3 زاد C4 V4 بده
+
+285
+00:34:53,090 --> 00:34:55,170
+يساوي كده؟ بده يساوي Zero
+
+286
+00:34:59,430 --> 00:35:11,530
+هذا C1 Zero C1 Zero زائد Zero C2 سلب C2 اتنين C2
+
+287
+00:35:11,530 --> 00:35:18,950
+زائدبدا يجي C3 يبقى Zero اتنين C تلاتة اتنين C
+
+288
+00:35:18,950 --> 00:35:25,750
+تلاتة C تلاتة ذات ال vector الرابع يبقاش بديكون
+
+289
+00:35:25,750 --> 00:35:34,450
+اللي همين C4 يبقى C4 و Zero و Zero و C4 كل هذا
+
+290
+00:35:34,450 --> 00:35:40,890
+الكلام بدي سوى قداش بدي سوى Zero تمام تمام
+
+291
+00:35:57,300 --> 00:36:03,380
+عن طريق الوصول
+
+292
+00:36:03,380 --> 00:36:12,340
+إلى الـ C1 مع السلامة زائد C4اللي بعده Zero C2
+
+293
+00:36:12,340 --> 00:36:23,460
+اللي بعده 2C3 2C3 Zero مع السلامة اللي بعده C1-C2
+
+294
+00:36:23,460 --> 00:36:26,720
+2C3
+
+295
+00:36:26,720 --> 00:36:35,180
+Zero مع السلامة العنصر الرابع الأول راح 2C2زائد C3
+
+296
+00:36:35,180 --> 00:36:42,120
+زائد C4 كله بده يساوي Zero و Zero و Zero شكل اللي
+
+297
+00:36:42,120 --> 00:36:47,820
+عندنا هنا نعمل مقارنة ما بين الطرفين يبقى بناء
+
+298
+00:36:47,820 --> 00:36:57,540
+عليه C1زائد C4 بده يساوي Zero اللي بعده C2 زائد 2
+
+299
+00:36:57,540 --> 00:37:07,820
+C3 بده يساوي Zero اللي بعده C1 ناقص C2 زائد 2 C3
+
+300
+00:37:07,820 --> 00:37:20,460
+بده يساوي Zero اللي بعده 2C2 زائد C3 زائد C4 كله
+
+301
+00:37:20,460 --> 00:37:27,600
+بده يساوي مين؟ بده يساوي Zeroطيب بدنا نجرب الان
+
+302
+00:37:27,600 --> 00:37:34,700
+نشوف شو بدنا نعمل في هذا ال system مشان نحل هذا ال
+
+303
+00:37:34,700 --> 00:37:41,520
+system له أربع معادلات في أربعة مجاهيل طيب لو
+
+304
+00:37:41,520 --> 00:37:51,420
+ضربنا هذا في سالب بيطير هذا بيظل C1 و C2 طيب لو
+
+305
+00:37:51,420 --> 00:38:00,630
+ضربنا الأولى في سالب بتروح هذهو .. او عن طريق
+
+306
+00:38:00,630 --> 00:38:05,130
+المصحفات يامان اتسيا المصحفات او اذا كانت بتيجي
+
+307
+00:38:05,130 --> 00:38:09,190
+عملية الدرب بكوني كويس يبقى هذه بدي اشوف بس بتيجي
+
+308
+00:38:09,190 --> 00:38:17,550
+و لا بتيجيش يبقى هذه بقدر اقول هذه لو جمعناهم بيظل
+
+309
+00:38:17,550 --> 00:38:25,480
+C تلاتة مافيش غيرهمو هدول سالب طب بتروح هدى طب لو
+
+310
+00:38:25,480 --> 00:38:36,420
+هدى السالب بتروح ا سالب انا C1 و C2 و C3 هدى طيب
+
+311
+00:38:36,420 --> 00:38:45,510
+هنا اتنين C2وها دي C4 يبقى واضح انه غير نشتغل
+
+312
+00:38:45,510 --> 00:38:57,410
+شغلتين مع بعض ومنهم نحاول اه تاني
+
+313
+00:38:57,410 --> 00:39:04,330
+تاني من أول جديد علي صوتك شوية صحيح
+
+314
+00:39:11,550 --> 00:39:13,830
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+315
+00:39:13,830 --> 00:39:14,690
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+316
+00:39:14,690 --> 00:39:18,270
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+317
+00:39:18,270 --> 00:39:19,890
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+318
+00:39:19,890 --> 00:39:20,410
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+319
+00:39:20,410 --> 00:39:20,850
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+320
+00:39:20,850 --> 00:39:21,570
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+321
+00:39:21,570 --> 00:39:23,510
+هذه اتنين و هذه اتنين و هذه اتنين و هذه اتنين و
+
+322
+00:39:23,510 --> 00:39:33,050
+هذه اتنين و هذه اتنين و هذه اتنين و
+
+323
+00:39:33,050 --> 00:39:41,580
+هذه اتنين و هذه اتنين و هذهو جيت جماعة و أشوف طب
+
+324
+00:39:41,580 --> 00:39:47,700
+هي C1 و C2 هذول بيجيبولي الأربعة هذول بيجيبولي
+
+325
+00:39:47,700 --> 00:39:54,680
+تلاتة و بجيب واحد بدلالته التاني وبالتالي هذا نفس
+
+326
+00:39:54,680 --> 00:39:59,520
+القصة على أي حال ماعناش مشكلة يبقى لو جيت قلت ما
+
+327
+00:39:59,520 --> 00:40:05,870
+ياتي شوف يا بناتأنا بدي أقول هذه بالشكل التالي بدي
+
+328
+00:40:05,870 --> 00:40:12,330
+أترك الأولى زي ما هي C1 و C4 و لو أنه لو ضربناها
+
+329
+00:40:12,330 --> 00:40:18,070
+أه بدي أضربها في سالب يبقى بدي أقول هذه السالب C1
+
+330
+00:40:18,070 --> 00:40:24,490
+و هنا السالب C4 بده يساوي Zero التانية لو خلتها زي
+
+331
+00:40:24,490 --> 00:40:33,250
+ما هي C2 زائد 2 C3 بده يساوي Zeroالتالتة لو ضربتها
+
+332
+00:40:33,250 --> 00:40:41,710
+في سالب يبقى التالتة لو روحت قول سالب C1 وزائد C2
+
+333
+00:40:41,710 --> 00:40:54,830
+ونقص 2 C3 بده يساوي 0 وهنا 2C2 زائد C3 زائد C4 بده
+
+334
+00:40:54,830 --> 00:40:58,960
+يساوي 0يبقى ضربت الأولى والتالتى في سالب والباقي
+
+335
+00:40:58,960 --> 00:41:04,950
+خليته زي ما هو اول شي هادى هتروح مع هادىتمام اتنين
+
+336
+00:41:04,950 --> 00:41:11,630
+C تلاتة بالسلب مع اتنين C تلاتة بالموجب تمام بضل
+
+337
+00:41:11,630 --> 00:41:19,490
+عند مين C واحد و C اتنين و C تلاتة كذلك مش مشكلة
+
+338
+00:41:19,490 --> 00:41:25,470
+يبقى بصير عندى سالب اتنين C واحد سالب اتنين C واحد
+
+339
+00:41:25,470 --> 00:41:31,110
+زائد C اتنين والله زائد تلاتة C اتنين
+
+340
+00:41:36,440 --> 00:41:46,500
+يبقى زائد 4C2 زائد 4C2 زائد C3 مافيش غيرها يبقى
+
+341
+00:41:46,500 --> 00:41:53,720
+زائد C3 بده يساوي مين؟ بده يساوي Zeroتمام تمام
+
+342
+00:41:53,720 --> 00:42:03,360
+يبقى هذه اتنين وهذه اربع طيب منها بقدر اشيل C3
+
+343
+00:42:03,360 --> 00:42:12,760
+واختيارها بدل ال C1 وC2 اذا هذه C3 تسوى 2C1 ناقص
+
+344
+00:42:12,760 --> 00:42:18,760
+4C2 تمام هذا بده يعطينا بده اجي اعوض في المعادلة
+
+345
+00:42:18,760 --> 00:42:28,680
+هذهالمعادلة هذه ايش بيصير عندنا بيصير عندنا c1-c2
+
+346
+00:42:28,680 --> 00:42:37,140
+زيدي 2c3 اتنين في اتنين باربعة c واحد ناقص تمانية
+
+347
+00:42:37,140 --> 00:42:42,380
+c2 بده يساوي كده؟ بده يساوي zero او ان شاتهم
+
+348
+00:42:42,380 --> 00:42:51,260
+فقولوا اربعة واحد خمسة c واحدوهنا ناقص عشرة C2
+
+349
+00:42:51,260 --> 00:42:59,000
+ناقص عشرة C2 سيكون Zero لو قسمت على واحد سيكون C1
+
+350
+00:42:59,000 --> 00:43:11,850
+يسوى 2C2 C1 يسوى 2C2 تمام هذا هو أول معلومةتمام
+
+351
+00:43:11,850 --> 00:43:21,710
+اذا لو جيت انا هي C3 عرفت C1 بدلالة C2 وعرفنا C3
+
+352
+00:43:21,710 --> 00:43:32,810
+بدلالة C1 وC2 بدنا نجيب C4 يبقى ايوة من اللي بتحكي
+
+353
+00:43:32,810 --> 00:43:35,850
+كيف؟ و سلب 9
+
+354
+00:43:38,670 --> 00:43:41,550
+خمسة C واحد ناقص عشرة C اتنين.
+
+355
+00:43:44,370 --> 00:43:50,170
+هى عندك ناقص .. هى اربعة C واحد واربع .. اه هدى
+
+356
+00:43:50,170 --> 00:43:56,420
+واحد وهدى تسعة صحيح. اه هدى تسعة معاك الحق.هذه
+
+357
+00:43:56,420 --> 00:44:04,960
+تسعة يبقى معنى هذا الكلام انه C1 بدي ساوي تسعة C2
+
+358
+00:44:04,960 --> 00:44:12,160
+على خمسة مظبوط يبقى ايه جيبنا C1 بدلالة الاخرين
+
+359
+00:44:12,160 --> 00:44:15,100
+بقدر اجيب C4 كذلك
+
+360
+00:44:18,620 --> 00:44:32,280
+C4 بدها تساوي سالب تسعة C2 على خمسة يبقى
+
+361
+00:44:32,280 --> 00:44:41,790
+انا عندي C1 بدلالة C2 وعندي C4 بدلالة C2وعندي C3
+
+362
+00:44:41,790 --> 00:44:48,890
+بدلالة A ممتاز ممتاز اتنى شوية الحين انا عندى لو
+
+363
+00:44:48,890 --> 00:44:55,550
+جيت اخدت المعادلة المعادلة الرابعة عندي C4 بدلالة
+
+364
+00:44:55,550 --> 00:45:08,110
+C2 وعندي C3 بدلالة C1 وC2 وعندي C3 وC3 تساوي
+
+365
+00:45:15,060 --> 00:45:22,340
+تسعة C اتنين على خمسة
+
+366
+00:45:22,340 --> 00:45:30,210
+ناقص اربعة C اتنينهذا كله عبارة عن مين؟ عبارة عن
+
+367
+00:45:30,210 --> 00:45:39,450
+كله على خمسة بيظل تمنتاشر C2 ناقص اربع في خمسة
+
+368
+00:45:39,450 --> 00:45:48,410
+بعشرين C2 ويساوي ناقص اتنين C2 على خمسة.الان بتعوض
+
+369
+00:45:48,410 --> 00:45:52,340
+يا بنات في المعادلة على الرابعةيبقى انا عندى اتنين
+
+370
+00:45:52,340 --> 00:45:59,460
+C اتنين زائد C تلاتة زائد C اربعة بده يساوي اتنين
+
+371
+00:45:59,460 --> 00:46:06,980
+C اتنين هاي اتنين C اتنين C تلاتة C تلاتة هاي اللي
+
+372
+00:46:06,980 --> 00:46:16,030
+طلعناها ناقص اتنين C اتنين على خمسةنقص اتنين C2
+
+373
+00:46:16,030 --> 00:46:23,590
+على خمسة وزايد C4 و هنا ناقص تسعة C2 على خمسة كل
+
+374
+00:46:23,590 --> 00:46:28,290
+هذا بده يساوي Zero إذا لو حتى لها المقامات كلها
+
+375
+00:46:28,290 --> 00:46:35,310
+على خمسة بصير عشرة C2 ناقص اتنين C2
+
+376
+00:46:38,130 --> 00:46:44,990
+-9C2==0 يبقى ناقص 11 وزاد عشرة يبقى ناقص C2 على
+
+377
+00:46:44,990 --> 00:46:52,550
+خمسة يساوي Zero هذا سيعطيك ان C2 يساوي Zero لما C2
+
+378
+00:46:52,550 --> 00:46:59,550
+يساوي Zero يبقى C4 يساوي Zero يبقى C1 يساوي Zero
+
+379
+00:46:59,550 --> 00:47:06,280
+يبقى C3 يساوي Zero هذا معناهان ال functions ان
+
+380
+00:47:06,280 --> 00:47:14,040
+هدول مالهم are linearly independent يبقى هنا V1 و
+
+381
+00:47:14,040 --> 00:47:23,080
+V2 و V3 و V4 are linearly independent يبقى انت هنا
+
+382
+00:47:23,080 --> 00:47:28,180
+من ال condition الثاني هذابعد ذلك نذهب إلى ال
+
+383
+00:47:28,180 --> 00:47:34,240
+condition الأول لكي نثبت أن أي element في ال
+
+384
+00:47:34,240 --> 00:47:39,400
+vector space V بدي أحاول أن أكتبه بدلالة من؟
+
+385
+00:47:39,400 --> 00:47:46,120
+بدلالة هذه ال vectors الأربعة يبقى هذه اللي حمّن
+
+386
+00:47:46,120 --> 00:47:51,620
+هنا اللي هي النقطة الأولى بداجة هنا النقطة الثانية
+
+387
+00:47:52,020 --> 00:47:58,980
+يبقى let اللي هو ال A والB والC والD هذا element
+
+388
+00:47:58,980 --> 00:48:11,620
+موجود في R بحيث ان C1V1 زي C2V2 زي C3V3 زي C4V4
+
+389
+00:48:12,030 --> 00:48:15,010
+يبقى هذا ال element يساوي لنا ال combination من
+
+390
+00:48:15,010 --> 00:48:19,270
+هذا الوضع يبقى
+
+391
+00:48:19,270 --> 00:48:28,550
+بناء عليه يبقى C1
+
+392
+00:48:29,330 --> 00:48:40,550
+زائد C4 بده يساوي A اللي بعده C2 زائد 2 C3 بده
+
+393
+00:48:40,550 --> 00:48:51,210
+يساوي B اللي بعده C1 ناقص C2 ناقص C2 زائد 2 C3 بده
+
+394
+00:48:51,210 --> 00:49:01,840
+يساوي C اللي بعده 2C2 زائد C3زائد C أربعة بده
+
+395
+00:49:01,840 --> 00:49:08,080
+يساوي قداش D هذا ال system اللي بدنا نحاول نحل هذا
+
+396
+00:49:08,080 --> 00:49:12,580
+ال system ان شاء الله و تعالى يبقى باجي بقول ال
+
+397
+00:49:12,580 --> 00:49:20,000
+system هذا بده أخدله اللي هو المصوفة الموسعة هذا
+
+398
+00:49:20,000 --> 00:49:27,240
+واحدZero Zero واحد و هنا Zero و هنا واحد و هنا
+
+399
+00:49:27,240 --> 00:49:36,020
+اتنين و هنا Zero و هنا واحد ناقص واحد اتنين Zero و
+
+400
+00:49:36,020 --> 00:49:46,940
+هنا Zero اتنين و هنا واحد و هنا واحد A B C D بشكل
+
+401
+00:49:46,940 --> 00:49:53,490
+عندناإذا أنا ممكن أضرب الصف الأول في سالب واحد و
+
+402
+00:49:53,490 --> 00:49:59,290
+أضيفه لمن؟ ل R ثلاثة يبقى باجي بقوله سالب R واحد
+
+403
+00:49:59,290 --> 00:50:07,410
+to R تلاتة يبقى بدنا أنحله ايه واحد؟ Zero Zero
+
+404
+00:50:07,410 --> 00:50:15,730
+واحد و هنا ايه زي ما هو؟هذا Zero وهنا واحد اتنين
+
+405
+00:50:15,730 --> 00:50:23,490
+Zero وهنا بي هنا Zero وهنا سالب واحد زي ما هو وهنا
+
+406
+00:50:23,490 --> 00:50:28,570
+اتنين زي ما هو وهذا سالب واحد بديجيلك هنا سالب
+
+407
+00:50:28,570 --> 00:50:37,840
+واحد وهنا سالب A اللي هو C سالب AC سالب A هذا زي
+
+408
+00:50:37,840 --> 00:50:43,880
+ما هو اللي هو Zero اتنين واحد واحد و هنا دي وهي
+
+409
+00:50:43,880 --> 00:50:48,940
+قفلنا الان بدنا نيجي لمين للرقم اللي عندنا يبقى
+
+410
+00:50:48,940 --> 00:50:53,540
+احنا هنا بدنا نيجي نقول هذا الكلام بده يعطينا
+
+411
+00:50:53,540 --> 00:51:03,440
+اتنين اتنين عارف اتنين اتنين عارف اتنين two are
+
+412
+00:51:03,440 --> 00:51:10,840
+تلاتةلأ اري اتنين تقار تلاتة دوري اري اتنين تقار
+
+413
+00:51:10,840 --> 00:51:18,340
+تلاتة و اتنين اري اتنين تقار اربع يبقى هنحصل على
+
+414
+00:51:18,340 --> 00:51:28,260
+ما ياتي واحد زيرو زيرو واحد و هنا aهذا Zero واحد
+
+415
+00:51:28,260 --> 00:51:37,740
+اتنين Zero بي هنا Zero وهنا Zero وهنا أربعة وهنا
+
+416
+00:51:37,740 --> 00:51:48,160
+سالب واحد وهنا بي زائد سي ناقص ايوهنا ضربنا في
+
+417
+00:51:48,160 --> 00:51:53,620
+اتنين سالب اتنين وضق السالب اتنين اللي بعد يا بنات
+
+418
+00:51:53,620 --> 00:52:01,520
+سالب اتنين R اتنين to R اربعة يبقى هذا Zero وهذا
+
+419
+00:52:01,520 --> 00:52:09,980
+Zero وهذه سالب سالب سيصبح سالب اربعة واحد يبقى
+
+420
+00:52:09,980 --> 00:52:17,540
+سالب تلاتةوهذا zero بيظل واحد زي ما هو وهنا سالب
+
+421
+00:52:17,540 --> 00:52:25,220
+اتنين بيبقى دي سالب اتنين بي بالشكل اللي عندنا هنا
+
+422
+00:52:25,220 --> 00:52:33,140
+الان وصلنا لهذا يبقى ما عليك إلا اتكملي وتثبتي ما
+
+423
+00:52:33,140 --> 00:52:40,500
+يأتي تثبتي عليك ما يأتيبطلع عندنا على الشكل التالي
+
+424
+00:52:40,500 --> 00:52:54,620
+و الله أعلم بده يطلع C1 يساوي 4A زائد 5B ناقص 3C
+
+425
+00:52:54,620 --> 00:53:10,130
+ناقص 4DوC2 بده يساوي اتنين A زائد تلاتة B نقص
+
+426
+00:53:10,130 --> 00:53:21,370
+اتنين C نقص اتنين D وC3 بده يساوي نقص
+
+427
+00:53:21,370 --> 00:53:37,460
+Aنقص B زائد C زائد D و C4 بده يساوي ناقص تلاتة A و
+
+428
+00:53:37,460 --> 00:53:48,260
+ناقص خمسة B ناقص خمسة B و زائد تلاتة C زائد 4D
+
+429
+00:53:53,550 --> 00:54:00,950
+يبقى بناء ان عليه أصبح V1 و V2 و V3 و V4 are bases
+
+430
+00:54:00,950 --> 00:54:11,210
+يعني بتقوليلي في الآخر هنا V1 و V2 و V3 و V4 are
+
+431
+00:54:11,210 --> 00:54:14,270
+bases
+
+432
+00:54:14,270 --> 00:54:22,990
+for the vector space R4
+
+433
+00:54:26,600 --> 00:54:30,460
+لأيش؟ لأن كل element في الحالة الأخيرة لقنا linear
+
+434
+00:54:30,460 --> 00:54:34,900
+combination من الأخرين و أثبتنا أن ال vectors هدور
+
+435
+00:54:34,900 --> 00:54:37,160
+are linearly independent
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/r9WgIkSN3M4_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/r9WgIkSN3M4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e7e2558ddcf225d5436a7890bb2645e516e3d8e2
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/r9WgIkSN3M4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4958, "start": 20.74, "end": 49.58, "text": "بسم الله الرحمن الرحيم نذكر باخر حاجة خدناها المرة اللي فات في section تلاتة أربعة بدينا بالرونسكين وعرفنا ان رونسكين هو عبارة عن محدد ثم انتقلنا إلى نظرية نظرية دو شقين الشق الأول كان إذا كان عندي مجموعة من ال vectors وكانوا linearly dependent يبقى لازم الرونسكين يساوي zero عند كل X موجودة في interval ما", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 8848, 37983, 4724, 47283, 2288, 11331, 26108, 3660, 16490, 3215, 8315, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 8978, 3541, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 47525, 1829, 8315, 20666, 2288, 11536, 3794, 4117, 9957, 4032, 3615, 28480, 8315, 16472, 12602, 11536, 3794, 4117, 9957, 31439, 6225, 3555, 9640, 3660, 18871, 3714, 24401, 3215, 38637, 2304, 16472, 2655, 4587, 1211, 8315, 30731, 8717, 19913, 2288, 10632, 8717, 19913, 2288, 10632, 11778, 2407, 13412, 4587, 9957, 25124, 4587, 16247, 12610, 25961, 11933, 15730, 25961, 18871, 16254, 3714, 7435, 2304, 2407, 27884, 9154, 2423, 18875, 4032, 41361, 14407, 43586, 12334, 7251, 3555, 4587, 7578, 5296, 31377, 2304, 34892, 11536, 3794, 4117, 9957, 7251, 3794, 995, 45865, 4018, 43242, 28242, 1783, 3714, 29245, 23328, 3660, 8978, 15035, 19446], "avg_logprob": -0.1738138642624347, "compression_ratio": 1.7750865051903115, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.74, "end": 21.06, "word": "بسم", "probability": 0.76123046875}, {"start": 21.06, "end": 21.24, "word": " الله", "probability": 0.9658203125}, {"start": 21.24, "end": 21.66, "word": " الرحمن", "probability": 0.9454752604166666}, {"start": 21.66, "end": 22.14, "word": " الرحيم", "probability": 0.9931640625}, {"start": 22.14, "end": 23.58, "word": " نذكر", "probability": 0.691162109375}, {"start": 23.58, "end": 24.04, "word": " باخر", "probability": 0.6494954427083334}, {"start": 24.04, "end": 24.28, "word": " حاجة", "probability": 0.9765625}, {"start": 24.28, "end": 24.74, "word": " خدناها", "probability": 0.8348388671875}, {"start": 24.74, "end": 25.06, "word": " المرة", "probability": 0.879150390625}, {"start": 25.06, "end": 25.22, "word": " اللي", "probability": 0.781982421875}, {"start": 25.22, "end": 25.4, "word": " فات", "probability": 0.93310546875}, {"start": 25.4, "end": 25.56, "word": " في", "probability": 0.80517578125}, {"start": 25.56, "end": 25.94, "word": " section", "probability": 0.70458984375}, {"start": 25.94, "end": 26.58, "word": " تلاتة", "probability": 0.760498046875}, {"start": 26.58, "end": 27.0, "word": " أربعة", "probability": 0.8158365885416666}, {"start": 27.0, "end": 28.02, "word": " بدينا", "probability": 0.7159830729166666}, {"start": 28.02, "end": 28.8, "word": " بالرونسكين", "probability": 0.6890869140625}, {"start": 28.8, "end": 29.26, "word": " وعرفنا", "probability": 0.913818359375}, {"start": 29.26, "end": 29.4, "word": " ان", "probability": 0.60302734375}, {"start": 29.4, "end": 29.92, "word": " رونسكين", "probability": 0.836376953125}, {"start": 29.92, "end": 30.1, "word": " هو", "probability": 0.55810546875}, {"start": 30.1, "end": 30.56, "word": " عبارة", "probability": 0.9931640625}, {"start": 30.56, "end": 30.92, "word": " عن", "probability": 0.99267578125}, {"start": 30.92, "end": 31.88, "word": " محدد", "probability": 0.9943033854166666}, {"start": 31.88, "end": 32.6, "word": " ثم", "probability": 0.980712890625}, {"start": 32.6, "end": 33.36, "word": " انتقلنا", "probability": 0.983984375}, {"start": 33.36, "end": 33.68, "word": " إلى", "probability": 0.4912109375}, {"start": 33.68, "end": 34.38, "word": " نظرية", "probability": 0.9842529296875}, {"start": 34.38, "end": 34.98, "word": " نظرية", "probability": 0.80999755859375}, {"start": 34.98, "end": 35.24, "word": " دو", "probability": 0.68359375}, {"start": 35.24, "end": 35.84, "word": " شقين", "probability": 0.9176432291666666}, {"start": 35.84, "end": 36.94, "word": " الشق", "probability": 0.94091796875}, {"start": 36.94, "end": 37.42, "word": " الأول", "probability": 0.96142578125}, {"start": 37.42, "end": 37.8, "word": " كان", "probability": 0.96484375}, {"start": 37.8, "end": 38.14, "word": " إذا", "probability": 0.815185546875}, {"start": 38.14, "end": 38.5, "word": " كان", "probability": 0.8310546875}, {"start": 38.5, "end": 38.78, "word": " عندي", "probability": 0.818603515625}, {"start": 38.78, "end": 39.24, "word": " مجموعة", "probability": 0.9322265625}, {"start": 39.24, "end": 39.38, "word": " من", "probability": 0.990234375}, {"start": 39.38, "end": 39.52, "word": " ال", "probability": 0.96826171875}, {"start": 39.52, "end": 39.88, "word": " vectors", "probability": 0.87939453125}, {"start": 39.88, "end": 40.56, "word": " وكانوا", "probability": 0.9220377604166666}, {"start": 40.56, "end": 41.26, "word": " linearly", "probability": 0.88232421875}, {"start": 41.26, "end": 42.68, "word": " dependent", "probability": 0.9306640625}, {"start": 42.68, "end": 43.16, "word": " يبقى", "probability": 0.9521484375}, {"start": 43.16, "end": 43.58, "word": " لازم", "probability": 0.97412109375}, {"start": 43.58, "end": 44.2, "word": " الرونسكين", "probability": 0.859912109375}, {"start": 44.2, "end": 44.82, "word": " يساوي", "probability": 0.9656982421875}, {"start": 44.82, "end": 45.7, "word": " zero", "probability": 0.453369140625}, {"start": 45.7, "end": 46.46, "word": " عند", "probability": 0.98486328125}, {"start": 46.46, "end": 46.98, "word": " كل", "probability": 0.98193359375}, {"start": 46.98, "end": 47.56, "word": " X", "probability": 0.60302734375}, {"start": 47.56, "end": 48.34, "word": " موجودة", "probability": 0.988525390625}, {"start": 48.34, "end": 48.58, "word": " في", "probability": 0.951171875}, {"start": 48.58, "end": 49.18, "word": " interval", "probability": 0.94677734375}, {"start": 49.18, "end": 49.58, "word": " ما", "probability": 0.72998046875}], "temperature": 1.0}, {"id": 2, "seek": 7495, "start": 50.37, "end": 74.95, "text": "أخذنا العملية العكسية أنه لو كان ال رونسكين لا يساوي 0 يبقى مجموعة هذه ال functions أو مجموعة هذه ال vectors are linearly independent وعطينا المرة اللي فاتت مثل على أنه ممكن يكون ال رونسكين يساوي 0 لكن ال two functions are not linearly dependent", "tokens": [10721, 9778, 8848, 8315, 18863, 42213, 10632, 18863, 4117, 3794, 10632, 14739, 3224, 45164, 25961, 2423, 12602, 11536, 3794, 4117, 9957, 20193, 7251, 3794, 995, 45865, 1958, 7251, 3555, 4587, 7578, 3714, 7435, 2304, 2407, 27884, 29538, 2423, 6828, 34051, 3714, 7435, 2304, 2407, 27884, 29538, 2423, 18875, 366, 43586, 6695, 4032, 3615, 9566, 1829, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 50113, 1211, 15844, 14739, 3224, 3714, 43020, 7251, 30544, 2423, 12602, 11536, 3794, 4117, 9957, 7251, 3794, 995, 45865, 1958, 44381, 2423, 732, 6828, 366, 406, 43586, 12334], "avg_logprob": -0.23980977936931278, "compression_ratio": 1.7751196172248804, "no_speech_prob": 0.0, "words": [{"start": 50.37, "end": 51.23, "word": "أخذنا", "probability": 0.57501220703125}, {"start": 51.23, "end": 51.67, "word": " العملية", "probability": 0.9337565104166666}, {"start": 51.67, "end": 52.35, "word": " العكسية", "probability": 0.9864501953125}, {"start": 52.35, "end": 52.85, "word": " أنه", "probability": 0.327789306640625}, {"start": 52.85, "end": 53.07, "word": " لو", "probability": 0.81494140625}, {"start": 53.07, "end": 53.51, "word": " كان", "probability": 0.884765625}, {"start": 53.51, "end": 53.67, "word": " ال", "probability": 0.69921875}, {"start": 53.67, "end": 54.39, "word": " رونسكين", "probability": 0.7159423828125}, {"start": 54.39, "end": 54.89, "word": " لا", "probability": 0.5849609375}, {"start": 54.89, "end": 55.61, "word": " يساوي", "probability": 0.927490234375}, {"start": 55.61, "end": 56.03, "word": " 0", "probability": 0.1922607421875}, {"start": 56.03, "end": 56.85, "word": " يبقى", "probability": 0.9296875}, {"start": 56.85, "end": 57.51, "word": " مجموعة", "probability": 0.9236328125}, {"start": 57.51, "end": 57.85, "word": " هذه", "probability": 0.87109375}, {"start": 57.85, "end": 58.03, "word": " ال", "probability": 0.861328125}, {"start": 58.03, "end": 58.43, "word": " functions", "probability": 0.343505859375}, {"start": 58.43, "end": 58.71, "word": " أو", "probability": 0.70654296875}, {"start": 58.71, "end": 59.17, "word": " مجموعة", "probability": 0.93095703125}, {"start": 59.17, "end": 59.43, "word": " هذه", "probability": 0.896484375}, {"start": 59.43, "end": 59.55, "word": " ال", "probability": 0.93017578125}, {"start": 59.55, "end": 59.83, "word": " vectors", "probability": 0.794921875}, {"start": 59.83, "end": 60.23, "word": " are", "probability": 0.309814453125}, {"start": 60.23, "end": 60.91, "word": " linearly", "probability": 0.892578125}, {"start": 60.91, "end": 62.11, "word": " independent", "probability": 0.93212890625}, {"start": 62.11, "end": 63.23, "word": " وعطينا", "probability": 0.8998046875}, {"start": 63.23, "end": 63.57, "word": " المرة", "probability": 0.971435546875}, {"start": 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2423, 7578, 376, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 9778, 3215, 34105, 611], "avg_logprob": -0.2094809296777693, "compression_ratio": 1.463768115942029, "no_speech_prob": 0.0, "words": [{"start": 907.47, "end": 907.93, "word": "اللي", "probability": 0.3402099609375}, {"start": 907.93, "end": 908.17, "word": " هو", "probability": 0.9287109375}, {"start": 908.17, "end": 908.37, "word": " ال", "probability": 0.80908203125}, {"start": 908.37, "end": 908.79, "word": " N", "probability": 0.57080078125}, {"start": 908.79, "end": 909.19, "word": " من", "probability": 0.98583984375}, {"start": 909.19, "end": 909.37, "word": " ال", "probability": 0.92236328125}, {"start": 909.37, "end": 910.33, "word": " functions", "probability": 0.78076171875}, {"start": 910.33, "end": 911.23, "word": " يعني", "probability": 0.853759765625}, {"start": 911.23, "end": 911.55, "word": " احنا", "probability": 0.8849283854166666}, {"start": 911.55, "end": 911.87, "word": " بدنا", "probability": 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"text": "R2 تربية E أُس R2 X ونظل ماشيين R N تربية E أُس R N X لو ضلت مستمر يا بنات هوصل لوين لل R1 أُس N ناقص واحد E أُس R1 X", "tokens": [49, 17, 6055, 25513, 10632, 462, 5551, 10859, 3794, 497, 17, 1783, 4032, 1863, 19913, 1211, 3714, 33599, 1829, 9957, 497, 426, 6055, 25513, 10632, 462, 5551, 10859, 3794, 497, 426, 1783, 45164, 48812, 1211, 2655, 3714, 14851, 29973, 35186, 4724, 8315, 2655, 8032, 2407, 36520, 45164, 9957, 24976, 497, 16, 5551, 10859, 3794, 426, 8717, 995, 4587, 9381, 36764, 24401, 462, 5551, 10859, 3794, 497, 16, 1783], "avg_logprob": -0.30072463077047595, "compression_ratio": 1.4076923076923078, "no_speech_prob": 0.0, "words": [{"start": 960.83, "end": 961.65, "word": "R2", "probability": 0.3839111328125}, {"start": 961.65, "end": 962.41, "word": " تربية", "probability": 0.6470540364583334}, {"start": 962.41, "end": 962.85, "word": " E", "probability": 0.67138671875}, {"start": 962.85, "end": 963.25, "word": " أُس", "probability": 0.567626953125}, {"start": 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عبارة عن المحدد واحد واحد واحد", "tokens": [3555, 1863, 4587, 1211, 8592, 8717, 8592, 38688, 3714, 9957, 39896, 21500, 29538, 11331, 1829, 12984, 2423, 21500, 39896, 6225, 3555, 9640, 3660, 18871, 9673, 24401, 3215, 36764, 24401, 36764, 24401, 36764, 24401], "avg_logprob": -0.2869944791583454, "compression_ratio": 1.3604651162790697, "no_speech_prob": 0.0, "words": [{"start": 1043.06, "end": 1043.72, "word": "بنقلش", "probability": 0.55556640625}, {"start": 1043.72, "end": 1044.14, "word": " نشوف", "probability": 0.943359375}, {"start": 1044.14, "end": 1044.46, "word": " مين", "probability": 0.86376953125}, {"start": 1044.46, "end": 1044.76, "word": " هي", "probability": 0.77001953125}, {"start": 1044.76, "end": 1045.34, "word": " DN", "probability": 0.27099609375}, {"start": 1045.34, "end": 1045.82, "word": " هذه", "probability": 0.5703125}, {"start": 1045.82, "end": 1047.26, "word": " حيث", "probability": 0.9215494791666666}, {"start": 1047.26, "end": 1047.44, "word": " ال", 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"probability": 0.886474609375}, {"start": 1141.93, "end": 1142.39, "word": " الآن", "probability": 0.7265625}], "temperature": 1.0}, {"id": 51, "seek": 116870, "start": 1143.18, "end": 1168.7, "text": "لأهم section موجود في هذا الشبتر أو من أهم ال sections اللي موجودة في هذا الشبتر هذا الموضوع الآن اللي هو section 3-5", "tokens": [1211, 10721, 16095, 3541, 3714, 29245, 23328, 8978, 23758, 25124, 3555, 2655, 2288, 34051, 9154, 5551, 16095, 2423, 10863, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 23758, 25124, 3555, 2655, 2288, 23758, 9673, 2407, 11242, 45367, 6024, 48506, 13672, 1829, 31439, 3541, 805, 12, 20], "avg_logprob": -0.2265624928733577, "compression_ratio": 1.6846846846846846, "no_speech_prob": 0.0, "words": [{"start": 1143.18, "end": 1144.1, "word": "لأهم", "probability": 0.72998046875}, {"start": 1144.1, "end": 1144.66, "word": " section", "probability": 0.326171875}, {"start": 1144.66, "end": 1145.42, "word": " موجود", "probability": 0.93408203125}, {"start": 1145.42, "end": 1145.72, "word": " في", "probability": 0.7392578125}, {"start": 1145.72, "end": 1146.52, "word": " هذا", "probability": 0.91015625}, {"start": 1146.52, "end": 1147.92, "word": " الشبتر", "probability": 0.70086669921875}, {"start": 1147.92, "end": 1149.28, "word": " أو", "probability": 0.47509765625}, {"start": 1149.28, "end": 1149.52, "word": " من", "probability": 0.955078125}, {"start": 1149.52, "end": 1150.04, "word": " أهم", "probability": 0.973388671875}, {"start": 1150.04, "end": 1150.6, "word": " ال", "probability": 0.73974609375}, {"start": 1150.6, "end": 1151.24, "word": " sections", "probability": 0.8349609375}, {"start": 1151.24, "end": 1152.24, "word": " اللي", "probability": 0.778076171875}, {"start": 1152.24, "end": 1152.92, "word": " موجودة", "probability": 0.9857177734375}, {"start": 1152.92, "end": 1153.18, "word": " في", "probability": 0.9619140625}, {"start": 1153.18, "end": 1153.86, "word": " هذا", "probability": 0.970703125}, {"start": 1153.86, "end": 1156.18, "word": " الشبتر", "probability": 0.97607421875}, {"start": 1156.18, "end": 1165.62, "word": " هذا", "probability": 0.72412109375}, {"start": 1165.62, "end": 1166.1, "word": " الموضوع", "probability": 0.9984130859375}, {"start": 1166.1, "end": 1166.6, "word": " الآن", "probability": 0.7017822265625}, {"start": 1166.6, "end": 1166.82, "word": " اللي", "probability": 0.927734375}, {"start": 1166.82, "end": 1167.0, "word": " هو", "probability": 0.978515625}, {"start": 1167.0, "end": 1167.54, "word": " section", "probability": 0.62255859375}, {"start": 1167.54, "end": 1168.12, "word": " 3", "probability": 0.4462890625}, {"start": 1168.12, "end": 1168.7, "word": "-5", "probability": 0.638916015625}], "temperature": 1.0}, {"id": 52, "seek": 119903, "start": 1169.79, "end": 1199.03, "text": "تلاتة خمسة اللي هو dimensions dimensions مفرضها dimension يعني ابعاد dimensions يعني ابعاد نعطي تعريفين وبعد هيك نبدأ في طرح الأمثلة definition", "tokens": [2655, 1211, 9307, 3660, 16490, 2304, 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"word": " في", "probability": 0.90478515625}, {"start": 1196.43, "end": 1196.99, "word": " طرح", "probability": 0.9908854166666666}, {"start": 1196.99, "end": 1197.85, "word": " الأمثلة", "probability": 0.9649658203125}, {"start": 1197.85, "end": 1199.03, "word": " definition", "probability": 0.83203125}], "temperature": 1.0}, {"id": 53, "seek": 122553, "start": 1201.97, "end": 1225.53, "text": "لت كابتل V Be A Vector Space Vector Space Then V Is Said To Be A Finite Dimensional Vector", "tokens": [1211, 2655, 9122, 16758, 2655, 1211, 691, 879, 316, 691, 20814, 8705, 691, 20814, 8705, 1396, 691, 1119, 26490, 1407, 879, 316, 3773, 642, 20975, 11075, 691, 20814], "avg_logprob": -0.5169719745372904, "compression_ratio": 1.1547619047619047, "no_speech_prob": 0.0, "words": [{"start": 1201.97, "end": 1202.75, "word": "لت", "probability": 0.37005615234375}, {"start": 1202.75, "end": 1204.41, "word": " كابتل", "probability": 0.5570068359375}, {"start": 1204.41, "end": 1204.81, "word": " V", 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0.935546875}, {"start": 1221.75, "end": 1222.05, "word": " A", "probability": 0.333984375}, {"start": 1222.05, "end": 1224.17, "word": " Finite", "probability": 0.830322265625}, {"start": 1224.17, "end": 1224.89, "word": " Dimensional", "probability": 0.8818359375}, {"start": 1224.89, "end": 1225.53, "word": " Vector", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 54, "seek": 125233, "start": 1239.37, "end": 1252.33, "text": "finite dimensional vector space F النقطة الأولى there exists a set", "tokens": [5194, 642, 18795, 8062, 1901, 479, 28239, 47432, 3660, 16247, 12610, 7578, 456, 8198, 257, 992], "avg_logprob": -0.46231617647058826, "compression_ratio": 0.9397590361445783, "no_speech_prob": 0.0, "words": [{"start": 1239.37, "end": 1240.77, "word": "finite", "probability": 0.5153350830078125}, {"start": 1240.77, "end": 1241.55, "word": " dimensional", "probability": 0.8544921875}, {"start": 1241.55, "end": 1242.61, "word": " vector", "probability": 0.93701171875}, {"start": 1242.61, "end": 1243.79, "word": " space", "probability": 0.30810546875}, {"start": 1243.79, "end": 1246.35, "word": " F", "probability": 0.317138671875}, {"start": 1246.35, "end": 1248.63, "word": " النقطة", "probability": 0.95458984375}, {"start": 1248.63, "end": 1250.15, "word": " الأولى", "probability": 0.9806315104166666}, {"start": 1250.15, "end": 1251.17, "word": " there", "probability": 0.51513671875}, {"start": 1251.17, "end": 1251.57, "word": " exists", "probability": 0.5595703125}, {"start": 1251.57, "end": 1251.83, "word": " a", "probability": 0.9736328125}, {"start": 1251.83, "end": 1252.33, "word": " set", "probability": 0.962890625}], "temperature": 1.0}, {"id": 55, "seek": 129074, "start": 1264.52, "end": 1290.74, "text": "of linearly independent elements of V نقطة ثانية every set of more than", "tokens": [2670, 43586, 6695, 4959, 295, 691, 8717, 47432, 3660, 38637, 7649, 10632, 633, 992, 295, 544, 813], "avg_logprob": -0.24544270667764875, "compression_ratio": 0.975609756097561, "no_speech_prob": 0.0, "words": [{"start": 1264.5199999999998, "end": 1265.9199999999998, "word": "of", "probability": 0.7802734375}, {"start": 1265.9199999999998, "end": 1267.32, "word": " linearly", "probability": 0.1910400390625}, {"start": 1267.32, "end": 1268.5, "word": " independent", "probability": 0.8857421875}, {"start": 1268.5, "end": 1270.84, "word": " elements", "probability": 0.8662109375}, {"start": 1270.84, "end": 1273.64, "word": " of", "probability": 0.943359375}, {"start": 1273.64, "end": 1275.16, "word": " V", "probability": 0.5859375}, {"start": 1275.16, "end": 1277.54, "word": " نقطة", "probability": 0.8181966145833334}, {"start": 1277.54, "end": 1278.66, "word": " ثانية", "probability": 0.984375}, {"start": 1278.66, "end": 1280.68, "word": " every", "probability": 0.72021484375}, {"start": 1280.68, "end": 1285.44, "word": " set", "probability": 0.96435546875}, {"start": 1285.44, "end": 1286.66, "word": " of", "probability": 0.9365234375}, {"start": 1286.66, "end": 1288.62, "word": " more", "probability": 0.9296875}, {"start": 1288.62, "end": 1290.74, "word": " than", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 56, "seek": 132089, "start": 1292.25, "end": 1320.89, "text": "in elements as linearly dependent ولحظة بسيطة جدا in the above definition in the above definition we say that", "tokens": [259, 4959, 382, 43586, 12334, 4032, 1211, 5016, 19913, 3660, 4724, 3794, 1829, 9566, 3660, 10874, 28259, 294, 264, 3673, 7123, 294, 264, 3673, 7123, 321, 584, 300], "avg_logprob": -0.23343211001363293, "compression_ratio": 1.196078431372549, "no_speech_prob": 0.0, "words": [{"start": 1292.25, "end": 1292.67, "word": "in", "probability": 0.22216796875}, {"start": 1292.67, "end": 1293.57, "word": " elements", "probability": 0.8583984375}, {"start": 1293.57, "end": 1298.71, "word": " as", "probability": 0.4873046875}, {"start": 1298.71, "end": 1300.13, "word": " linearly", "probability": 0.9345703125}, {"start": 1300.13, "end": 1301.11, "word": " dependent", "probability": 0.84423828125}, {"start": 1301.11, "end": 1306.17, "word": " ولحظة", "probability": 0.651513671875}, {"start": 1306.17, "end": 1306.77, "word": " بسيطة", "probability": 0.985546875}, {"start": 1306.77, "end": 1307.27, "word": " جدا", "probability": 0.98876953125}, {"start": 1307.27, "end": 1308.97, "word": " in", "probability": 0.88671875}, {"start": 1308.97, "end": 1310.39, "word": " the", "probability": 0.87353515625}, {"start": 1310.39, "end": 1312.15, "word": " above", "probability": 0.962890625}, {"start": 1312.15, "end": 1314.95, "word": " definition", "probability": 0.9462890625}, {"start": 1314.95, "end": 1317.19, "word": " in", "probability": 0.7255859375}, {"start": 1317.19, "end": 1317.41, "word": " the", "probability": 0.921875}, {"start": 1317.41, "end": 1317.73, "word": " above", "probability": 0.96337890625}, {"start": 1317.73, "end": 1318.57, "word": " definition", "probability": 0.93896484375}, 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{"start": 1343.51, "end": 1344.13, "word": " n", "probability": 0.5029296875}, {"start": 1344.13, "end": 1344.93, "word": " dimensional", "probability": 0.51171875}, {"start": 1344.93, "end": 1345.75, "word": " V", "probability": 0.8095703125}, {"start": 1345.75, "end": 1346.83, "word": " is", "probability": 0.9423828125}, {"start": 1346.83, "end": 1348.27, "word": " n", "probability": 0.7509765625}, {"start": 1348.27, "end": 1351.17, "word": " dimensional", "probability": 0.85791015625}], "temperature": 1.0}, {"id": 58, "seek": 137489, "start": 1353.49, "end": 1374.89, "text": "and dimensional vector space ملاحظة ال vector space", "tokens": [474, 18795, 8062, 1901, 3714, 15040, 5016, 19913, 3660, 2423, 8062, 1901], "avg_logprob": -0.7596154029552753, "compression_ratio": 1.0350877192982457, "no_speech_prob": 0.0, "words": [{"start": 1353.49, "end": 1353.95, "word": "and", "probability": 0.046630859375}, {"start": 1353.95, "end": 1355.03, "word": " dimensional", "probability": 0.5029296875}, {"start": 1355.03, "end": 1356.73, "word": " vector", "probability": 0.85302734375}, {"start": 1356.73, "end": 1359.67, "word": " space", "probability": 0.91943359375}, {"start": 1359.67, "end": 1369.93, "word": " ملاحظة", "probability": 0.8314697265625}, {"start": 1369.93, "end": 1371.59, "word": " ال", "probability": 0.1435546875}, {"start": 1371.59, "end": 1373.99, "word": " vector", "probability": 0.1739501953125}, {"start": 1373.99, "end": 1374.89, "word": " space", "probability": 0.873046875}], "temperature": 1.0}, {"id": 59, "seek": 140862, "start": 1382.28, "end": 1408.62, "text": "V بده يساوي Zero فقط is finite dimensional is finite dimensional vector space", "tokens": [53, 47525, 3224, 7251, 3794, 995, 45865, 17182, 6156, 47432, 307, 19362, 18795, 307, 19362, 18795, 8062, 1901], "avg_logprob": -0.5616776064822548, "compression_ratio": 1.1428571428571428, "no_speech_prob": 0.0, "words": [{"start": 1382.28, "end": 1382.92, "word": "V", "probability": 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"probability": 0.79345703125}], "temperature": 1.0}, {"id": 60, "seek": 143981, "start": 1410.93, "end": 1439.81, "text": "vector space and has and has dimension zero definition the vectors V1", "tokens": [303, 1672, 1901, 293, 575, 293, 575, 10139, 4018, 7123, 264, 18875, 691, 16], "avg_logprob": -0.504687507947286, "compression_ratio": 1.078125, "no_speech_prob": 0.0, "words": [{"start": 1410.93, "end": 1411.63, "word": "vector", "probability": 0.304534912109375}, {"start": 1411.63, "end": 1412.41, "word": " space", "probability": 0.8466796875}, {"start": 1412.41, "end": 1414.97, "word": " and", "probability": 0.74951171875}, {"start": 1414.97, "end": 1415.69, "word": " has", "probability": 0.8583984375}, {"start": 1415.69, "end": 1420.19, "word": " and", "probability": 0.300537109375}, {"start": 1420.19, "end": 1420.93, "word": " has", "probability": 0.89404296875}, {"start": 1420.93, "end": 1422.95, "word": " dimension", "probability": 0.92138671875}, {"start": 1422.95, "end": 1426.69, "word": " zero", "probability": 0.62353515625}, {"start": 1426.69, "end": 1429.37, "word": " definition", "probability": 0.78369140625}, {"start": 1429.37, "end": 1433.61, "word": " the", "probability": 0.5341796875}, {"start": 1433.61, "end": 1434.37, "word": " vectors", "probability": 0.87890625}, {"start": 1434.37, "end": 1439.81, "word": " V1", "probability": 0.6185302734375}], "temperature": 1.0}, {"id": 61, "seek": 146872, "start": 1440.9, "end": 1468.72, "text": "v2 و vk in a vector space in a vector space v are set to form are set to form", "tokens": [85, 17, 4032, 371, 74, 294, 257, 8062, 1901, 294, 257, 8062, 1901, 371, 366, 992, 281, 1254, 366, 992, 281, 1254], "avg_logprob": -0.3364470160525778, "compression_ratio": 1.4181818181818182, "no_speech_prob": 0.0, "words": [{"start": 1440.9, "end": 1441.92, "word": "v2", "probability": 0.47174072265625}, {"start": 1441.92, "end": 1443.1, "word": " و", "probability": 0.80810546875}, {"start": 1443.1, "end": 1444.14, "word": " vk", "probability": 0.6461181640625}, {"start": 1444.14, "end": 1446.2, "word": " in", "probability": 0.5673828125}, {"start": 1446.2, "end": 1448.32, "word": " a", "probability": 0.89111328125}, {"start": 1448.32, "end": 1449.16, "word": " vector", "probability": 0.9736328125}, {"start": 1449.16, "end": 1451.54, "word": " space", "probability": 0.75}, {"start": 1451.54, "end": 1453.82, "word": " in", "probability": 0.6982421875}, {"start": 1453.82, "end": 1454.36, "word": " a", "probability": 0.97607421875}, {"start": 1454.36, "end": 1454.84, "word": " vector", "probability": 0.97314453125}, {"start": 1454.84, "end": 1456.1, "word": " space", "probability": 0.93701171875}, {"start": 1456.1, "end": 1457.4, "word": " v", "probability": 0.609375}, {"start": 1457.4, "end": 1459.86, "word": " are", "probability": 0.21337890625}, {"start": 1459.86, "end": 1460.14, "word": " set", "probability": 0.57568359375}, {"start": 1460.14, "end": 1460.36, "word": " to", "probability": 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1492.21, "end": 1492.55, "word": " V", "probability": 0.9287109375}, {"start": 1492.55, "end": 1495.79, "word": " كاسبين", "probability": 0.6353759765625}, {"start": 1495.79, "end": 1498.05, "word": " V", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 63, "seek": 151286, "start": 1499.58, "end": 1512.86, "text": "نمر بي V واحد و V اتنين و VK are linearly independent", "tokens": [1863, 29973, 4724, 1829, 691, 36764, 24401, 4032, 691, 1975, 2655, 1863, 9957, 4032, 691, 42, 366, 43586, 6695], "avg_logprob": -0.45898437947034837, "compression_ratio": 0.971830985915493, "no_speech_prob": 0.0, "words": [{"start": 1499.58, "end": 1500.1, "word": "نمر", "probability": 0.4981689453125}, {"start": 1500.1, "end": 1501.56, "word": " بي", "probability": 0.6634521484375}, {"start": 1501.56, "end": 1502.92, "word": " V", "probability": 0.287841796875}, {"start": 1502.92, "end": 1503.62, "word": " واحد", "probability": 0.576904296875}, {"start": 1503.62, "end": 1504.6, "word": " و", 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يعتبر linearly dependent", "tokens": [1863, 9154, 2423, 39184, 43586, 6695, 18875, 45164, 11331, 9566, 36081, 25894, 16095, 9122, 2304, 7649, 36764, 24401, 4724, 9381, 1829, 18863, 3215, 3215, 8032, 2304, 10874, 16254, 3215, 16472, 30767, 1829, 3215, 36764, 24401, 1975, 1829, 16472, 30767, 25708, 36764, 24401, 6156, 15042, 6156, 30543, 3224, 7251, 34268, 26890, 43586, 12334], "avg_logprob": -0.3682193261272502, "compression_ratio": 1.5071428571428571, "no_speech_prob": 0.0, "words": [{"start": 1730.44, "end": 1731.08, "word": "ن", "probability": 0.341552734375}, {"start": 1731.08, "end": 1731.56, "word": " من", "probability": 0.6416015625}, {"start": 1731.56, "end": 1731.84, "word": " الـ", "probability": 0.449462890625}, {"start": 1731.84, "end": 1732.46, "word": " linearly", "probability": 0.796875}, {"start": 1732.46, "end": 1733.38, "word": " independent", "probability": 0.916015625}, {"start": 1733.38, "end": 1733.98, "word": " vectors", "probability": 0.89208984375}, {"start": 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"end": 1740.46, "word": " اي", "probability": 0.723388671875}, {"start": 1740.46, "end": 1740.88, "word": " ان", "probability": 0.83544921875}, {"start": 1740.88, "end": 1741.32, "word": " زيد", "probability": 0.728271484375}, {"start": 1741.32, "end": 1741.66, "word": " واحد", "probability": 0.98876953125}, {"start": 1741.66, "end": 1742.0, "word": " فما", "probability": 0.887939453125}, {"start": 1742.0, "end": 1742.48, "word": " فوقه", "probability": 0.9044596354166666}, {"start": 1742.48, "end": 1742.98, "word": " يعتبر", "probability": 0.84716796875}, {"start": 1742.98, "end": 1743.52, "word": " linearly", "probability": 0.90673828125}, {"start": 1743.52, "end": 1744.68, "word": " dependent", "probability": 0.89453125}], "temperature": 1.0}, {"id": 69, "seek": 177036, "start": 1745.46, "end": 1770.36, "text": "ممتاز جدا يبقى ال vector اسمه CLV بقول عنه finite dimensional محدود اذا جدرت الاجئين من ال linearly independent elements اي عدد اخر سواء ان تبعتي هدول و ازيد عليهم واحد او من غيرهم يجب ان يكونوا كلهم linearly dependent", "tokens": [2304, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 2423, 8062, 24525, 2304, 3224, 12855, 53, 4724, 39648, 18871, 3224, 19362, 18795, 3714, 24401, 23328, 1975, 15730, 10874, 3215, 43500, 2423, 26108, 19986, 9957, 9154, 2423, 43586, 6695, 4959, 1975, 1829, 6225, 3215, 3215, 1975, 34740, 8608, 2407, 16606, 16472, 6055, 3555, 3615, 31371, 8032, 3215, 12610, 4032, 1975, 11622, 25708, 25894, 16095, 36764, 24401, 1975, 2407, 9154, 32771, 13546, 16095, 7251, 7435, 3555, 16472, 7251, 30544, 14407, 28242, 16095, 43586, 12334], "avg_logprob": -0.24032738166196005, "compression_ratio": 1.5138888888888888, "no_speech_prob": 0.0, "words": [{"start": 1745.46, "end": 1746.34, "word": "ممتاز", "probability": 0.7451019287109375}, {"start": 1746.34, "end": 1746.74, "word": " جدا", "probability": 0.9345703125}, {"start": 1746.74, "end": 1747.58, "word": " يبقى", "probability": 0.848388671875}, {"start": 1747.58, "end": 1747.68, 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"end": 1837.78, "word": " يساوي", "probability": 0.962158203125}, {"start": 1837.78, "end": 1838.34, "word": " zero", "probability": 0.484130859375}, {"start": 1838.34, "end": 1838.92, "word": " لأنه", "probability": 0.6526692708333334}, {"start": 1838.92, "end": 1839.38, "word": " ماعنديش", "probability": 0.94951171875}, {"start": 1839.38, "end": 1839.62, "word": " غير", "probability": 0.98291015625}, {"start": 1839.62, "end": 1840.02, "word": " main", "probability": 0.74365234375}, {"start": 1840.02, "end": 1840.84, "word": " غير", "probability": 0.7021484375}, {"start": 1840.84, "end": 1841.12, "word": " الواحد", "probability": 0.5438232421875}, {"start": 1841.12, "end": 1841.24, "word": " و", "probability": 0.415771484375}, {"start": 1841.24, "end": 1841.52, "word": " هذا", "probability": 0.79833984375}, {"start": 1841.52, "end": 1842.12, "word": " ماعش", "probability": 0.8087565104166666}, {"start": 1842.12, "end": 1842.66, "word": " vectors", "probability": 0.35498046875}, 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1910.67, "word": " V1", "probability": 0.898681640625}, {"start": 1910.67, "end": 1911.29, "word": " لغاية", "probability": 0.96435546875}, {"start": 1911.29, "end": 1911.83, "word": " VK", "probability": 0.834228515625}], "temperature": 1.0}, {"id": 76, "seek": 193963, "start": 1912.15, "end": 1939.63, "text": "يعني اي vector في ال vector space V بقدر اكتبه على شكل linear combination من V1 و V2 و V3 لغاية Vk لغاية Vk هذا الشرط الأول الشرط التاني V1 و V2 و Vk are linearly independent يبقى انا مشان اختبر ان هدول بنفع basis لل vector space ولا لأ بدي امرين الأمر الأول", "tokens": [40228, 22653, 1975, 1829, 8062, 8978, 2423, 8062, 1901, 691, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 3224, 15844, 13412, 28820, 8213, 6562, 9154, 691, 16, 4032, 691, 17, 4032, 691, 18, 5296, 17082, 995, 10632, 691, 74, 5296, 17082, 995, 10632, 691, 74, 23758, 25124, 2288, 9566, 16247, 12610, 25124, 2288, 9566, 16712, 7649, 1829, 691, 16, 4032, 691, 17, 4032, 691, 74, 366, 43586, 6695, 7251, 3555, 4587, 7578, 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ل ال vector space اللي عندنا بقوله والله كويس طيب تعالى نشوف هل هؤلاء بيشكلوا بيزز ولا يبقى بأول خطة بدي أثبت ان هم يعيشين", "tokens": [3224, 33604, 1211, 16606, 7251, 12984, 3555, 2655, 32239, 16472, 8032, 33604, 1211, 16606, 4724, 1829, 8592, 28820, 14407, 4724, 1829, 11622, 11622, 5296, 3714, 32640, 5296, 2423, 8062, 1901, 13672, 1829, 43242, 8315, 4724, 39648, 3224, 16070, 43761, 9122, 45865, 3794, 23032, 1829, 3555, 37279, 6027, 7578, 8717, 8592, 38688, 8032, 1211, 8032, 33604, 1211, 16606, 4724, 1829, 8592, 28820, 14407, 4724, 1829, 11622, 11622, 49429, 7251, 3555, 4587, 7578, 4724, 10721, 12610, 16490, 9566, 3660, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 8032, 2304, 37495, 1829, 8592, 9957], "avg_logprob": -0.318337917982877, "compression_ratio": 1.7108433734939759, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2018.25, "end": 2019.13, "word": "هؤلاء", "probability": 0.607147216796875}, {"start": 2019.13, "end": 2019.59, "word": " يثبت", "probability": 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constant", "probability": 0.90625}, {"start": 2066.82, "end": 2067.12, "word": " في", "probability": 0.89453125}, {"start": 2067.12, "end": 2067.48, "word": " التاني", "probability": 0.8566080729166666}, {"start": 2067.48, "end": 2067.56, "word": " و", "probability": 0.93115234375}, {"start": 2067.56, "end": 2067.76, "word": " constant", "probability": 0.966796875}, {"start": 2067.76, "end": 2067.98, "word": " في", "probability": 0.9482421875}, {"start": 2067.98, "end": 2068.5, "word": " التالت", "probability": 0.9754231770833334}, {"start": 2068.5, "end": 2069.2, "word": " يبقى", "probability": 0.9415283203125}, {"start": 2069.2, "end": 2069.64, "word": " بالداجي", "probability": 0.974853515625}, {"start": 2069.64, "end": 2069.96, "word": " اقول", "probability": 0.897216796875}, {"start": 2069.96, "end": 2070.18, "word": " له", "probability": 0.5390625}, {"start": 2070.18, "end": 2070.84, "word": " assume", "probability": 0.5224609375}, {"start": 2070.84, "end": 2072.88, "word": " 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2081.1, "end": 2081.8, "word": " that", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 84, "seek": 209517, "start": 2082.19, "end": 2095.17, "text": "بحيث ان C1 V1 زاد C2 V2 زاد C3 V3 زاد C4 V4 بده يساوي كده؟ بده يساوي Zero", "tokens": [3555, 5016, 1829, 12984, 16472, 383, 16, 691, 16, 30767, 18513, 383, 17, 691, 17, 30767, 18513, 383, 18, 691, 18, 30767, 18513, 383, 19, 691, 19, 47525, 3224, 7251, 3794, 995, 45865, 9122, 3215, 3224, 22807, 47525, 3224, 7251, 3794, 995, 45865, 17182], "avg_logprob": -0.30156249470180935, "compression_ratio": 1.3012048192771084, "no_speech_prob": 0.0, "words": [{"start": 2082.19, "end": 2082.99, "word": "بحيث", "probability": 0.8590087890625}, {"start": 2082.99, "end": 2083.37, "word": " ان", "probability": 0.81494140625}, {"start": 2083.37, "end": 2084.71, "word": " C1", "probability": 0.54412841796875}, {"start": 2084.71, "end": 2085.77, "word": " V1", "probability": 0.64306640625}, {"start": 2085.77, "end": 2086.27, "word": " زاد", 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2871.62, "text": "بعد ذلك نذهب إلى ال condition الأول لكي نثبت أن أي element في ال vector space V بدي أحاول أن أكتبه بدلالة من؟ بدلالة هذه ال vectors الأربعة يبقى هذه اللي حمّن هنا اللي هي النقطة الأولى بداجة هنا النقطة الثانية", "tokens": [3555, 22488, 29910, 23275, 8717, 24192, 3555, 30731, 2423, 4188, 16247, 12610, 5296, 4117, 1829, 8717, 12984, 3555, 2655, 14739, 36632, 4478, 8978, 2423, 8062, 1901, 691, 4724, 16254, 5551, 5016, 995, 12610, 14739, 5551, 4117, 2655, 3555, 3224, 47525, 1211, 6027, 3660, 9154, 22807, 47525, 1211, 6027, 3660, 29538, 2423, 18875, 16247, 25513, 27884, 7251, 3555, 4587, 7578, 29538, 13672, 1829, 11331, 2304, 11703, 1863, 34105, 13672, 1829, 39896, 28239, 47432, 3660, 16247, 12610, 7578, 47525, 26108, 3660, 34105, 28239, 47432, 3660, 6024, 104, 7649, 10632], "avg_logprob": -0.4019886482168328, "compression_ratio": 1.715, "no_speech_prob": 0.0, "words": [{"start": 2846.86, "end": 2847.24, "word": "بعد", "probability": 0.17718505859375}, {"start": 2847.24, 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الأول في سالب واحد و أضيفه لمن؟ ل R ثلاثة يبقى باجي بقوله سالب R واحد to R تلاتة يبقى بدنا أنحله ايه واحد؟ Zero Zero واحد و هنا ايه زي ما هو؟", "tokens": [28814, 15730, 41850, 3714, 43020, 5551, 11242, 25513, 31767, 5172, 16247, 12610, 8978, 8608, 6027, 3555, 36764, 24401, 4032, 5551, 11242, 33911, 3224, 5296, 27842, 22807, 5296, 497, 38637, 1211, 5718, 104, 3660, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 8608, 6027, 3555, 497, 36764, 24401, 281, 497, 6055, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 47525, 8315, 14739, 5016, 43761, 1975, 1829, 3224, 36764, 24401, 22807, 17182, 17182, 36764, 24401, 4032, 34105, 1975, 1829, 3224, 30767, 1829, 19446, 31439, 22807], "avg_logprob": -0.23290440685608807, "compression_ratio": 1.6646706586826348, "no_speech_prob": 0.0, "words": [{"start": 2988.97, "end": 2989.31, "word": "إذا", "probability": 0.5946044921875}, {"start": 2989.31, "end": 2989.61, "word": " أنا", "probability": 0.6025390625}, {"start": 2989.61, "end": 2990.17, 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4D", "probability": 0.6094970703125}], "temperature": 1.0}, {"id": 133, "seek": 326299, "start": 3233.55, "end": 3262.99, "text": "يبقى بناء ان عليه أصبح V1 و V2 و V3 و V4 are bases يعني بتقوليلي في الآخر هنا V1 و V2 و V3 و V4 are bases for the vector space R4", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 16472, 47356, 5551, 9381, 49628, 691, 16, 4032, 691, 17, 4032, 691, 18, 4032, 691, 19, 366, 17949, 37495, 22653, 39894, 39648, 1829, 20292, 8978, 6024, 95, 34740, 34105, 691, 16, 4032, 691, 17, 4032, 691, 18, 4032, 691, 19, 366, 17949, 337, 264, 8062, 1901, 497, 19], "avg_logprob": -0.27102271751923995, "compression_ratio": 1.3257575757575757, "no_speech_prob": 0.0, "words": [{"start": 3233.55, "end": 3234.13, "word": "يبقى", "probability": 0.87939453125}, {"start": 3234.13, "end": 3234.51, "word": " بناء", "probability": 0.795654296875}, {"start": 3234.51, "end": 3234.67, "word": " ان", "probability": 0.34130859375}, {"start": 3234.67, "end": 3234.95, "word": " عليه", "probability": 0.3818359375}, {"start": 3234.95, "end": 3235.57, "word": " أصبح", "probability": 0.8623046875}, {"start": 3235.57, "end": 3236.47, "word": " V1", "probability": 0.725341796875}, {"start": 3236.47, "end": 3236.77, "word": " و", "probability": 0.68359375}, {"start": 3236.77, "end": 3237.35, "word": " V2", "probability": 0.819580078125}, {"start": 3237.35, "end": 3237.57, "word": " و", "probability": 0.9599609375}, {"start": 3237.57, "end": 3238.21, "word": " V3", "probability": 0.9404296875}, {"start": 3238.21, "end": 3238.41, "word": " و", "probability": 0.9541015625}, {"start": 3238.41, "end": 3239.07, "word": " V4", "probability": 0.9716796875}, {"start": 3239.07, "end": 3239.69, "word": " are", "probability": 0.430908203125}, {"start": 3239.69, "end": 3240.95, "word": " bases", "probability": 0.75244140625}, {"start": 3240.95, "end": 3241.65, "word": " يعني", "probability": 0.536376953125}, {"start": 3241.65, "end": 3242.41, "word": " بتقوليلي", "probability": 0.752685546875}, {"start": 3242.41, "end": 3242.53, "word": " في", "probability": 0.86181640625}, {"start": 3242.53, "end": 3242.99, "word": " الآخر", "probability": 0.8644205729166666}, {"start": 3242.99, "end": 3243.65, "word": " هنا", "probability": 0.8720703125}, {"start": 3243.65, "end": 3245.73, "word": " V1", "probability": 0.7103271484375}, {"start": 3245.73, "end": 3246.29, "word": " و", "probability": 0.407470703125}, {"start": 3246.29, "end": 3247.01, "word": " V2", "probability": 0.964599609375}, {"start": 3247.01, "end": 3247.49, "word": " و", "probability": 0.97216796875}, {"start": 3247.49, "end": 3248.33, "word": " V3", "probability": 0.944580078125}, {"start": 3248.33, "end": 3248.79, "word": " و", "probability": 0.90625}, {"start": 3248.79, "end": 3249.57, "word": " V4", "probability": 0.9755859375}, {"start": 3249.57, "end": 3251.21, "word": " are", "probability": 0.373291015625}, {"start": 3251.21, "end": 3254.27, "word": " bases", "probability": 0.669921875}, {"start": 3254.27, "end": 3256.17, "word": " for", "probability": 0.904296875}, {"start": 3256.17, "end": 3257.85, "word": " the", "probability": 0.7490234375}, {"start": 3257.85, "end": 3259.37, "word": " vector", "probability": 0.9521484375}, {"start": 3259.37, "end": 3261.41, "word": " space", "probability": 0.85595703125}, {"start": 3261.41, "end": 3262.99, "word": " R4", "probability": 0.913818359375}], "temperature": 1.0}, {"id": 134, "seek": 327716, "start": 3266.6, "end": 3277.16, "text": "لأيش؟ لأن كل element في الحالة الأخيرة لقنا linear combination من الأخرين و أثبتنا أن ال vectors هدور are linearly independent", "tokens": [1211, 10721, 1829, 8592, 22807, 5296, 33456, 28242, 4478, 8978, 21542, 6027, 3660, 16247, 9778, 48923, 5296, 4587, 8315, 8213, 6562, 9154, 16247, 34740, 9957, 4032, 5551, 12984, 3555, 2655, 8315, 14739, 2423, 18875, 8032, 3215, 13063, 366, 43586, 6695], "avg_logprob": -0.3151676712966547, "compression_ratio": 1.2695035460992907, "no_speech_prob": 0.0, "words": [{"start": 3266.6, "end": 3267.48, "word": "لأيش؟", "probability": 0.5826904296875}, {"start": 3267.48, "end": 3267.84, "word": " لأن", "probability": 0.84765625}, {"start": 3267.84, "end": 3268.28, "word": " كل", "probability": 0.89990234375}, {"start": 3268.28, "end": 3268.76, "word": " element", "probability": 0.54345703125}, {"start": 3268.76, "end": 3268.94, "word": " في", "probability": 0.859375}, {"start": 3268.94, "end": 3269.32, "word": " الحالة", "probability": 0.84375}, {"start": 3269.32, "end": 3269.7, "word": " الأخيرة", "probability": 0.927734375}, {"start": 3269.7, "end": 3270.06, "word": " لقنا", "probability": 0.5107421875}, {"start": 3270.06, "end": 3270.46, "word": " linear", "probability": 0.67431640625}, {"start": 3270.46, "end": 3271.24, "word": " combination", "probability": 0.97900390625}, {"start": 3271.24, "end": 3271.58, "word": " من", "probability": 0.95751953125}, {"start": 3271.58, "end": 3272.54, "word": " الأخرين", "probability": 0.85205078125}, {"start": 3272.54, "end": 3273.06, "word": " و", "probability": 0.72265625}, {"start": 3273.06, "end": 3273.62, "word": " أثبتنا", "probability": 0.8998046875}, {"start": 3273.62, "end": 3273.8, "word": " أن", "probability": 0.52880859375}, {"start": 3273.8, "end": 3273.96, "word": " ال", "probability": 0.73388671875}, {"start": 3273.96, "end": 3274.34, "word": " vectors", "probability": 0.80712890625}, {"start": 3274.34, "end": 3274.9, "word": " هدور", "probability": 0.711669921875}, {"start": 3274.9, "end": 3275.36, "word": " are", "probability": 0.78955078125}, {"start": 3275.36, "end": 3275.98, "word": " linearly", "probability": 0.96142578125}, {"start": 3275.98, "end": 3277.16, "word": " independent", "probability": 0.9658203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3279.40075, "duration_after_vad": 3030.718749999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/s69IfFzfWKg_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/s69IfFzfWKg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0fd9c2339cc69ea8b40e56c3b2f1cd8a7984905d
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/s69IfFzfWKg_raw.srt
@@ -0,0 +1,1820 @@
+1
+00:00:22,140 --> 00:00:27,940
+بسم الله الرحمن الرحيم يوم انا ابتدأنا هذا ال
+
+2
+00:00:27,940 --> 00:00:33,820
+chapter قولنا هذا اول chapter في الجبر الخطي و
+
+3
+00:00:33,820 --> 00:00:37,440
+ابتدأ من بداية هذا ال chapter و الى section اتنين
+
+4
+00:00:37,440 --> 00:00:42,160
+سبعة كنا بنتحدث فقط عن ال matrices و انواع ال
+
+5
+00:00:42,160 --> 00:00:47,040
+matrices و الجمع و الضرب بالنسبة لل matrices الان
+
+6
+00:00:47,040 --> 00:00:51,220
+بننتقل الى حاجة اسمها ال determinantsلأنه كان
+
+7
+00:00:51,220 --> 00:00:54,600
+العنوان الرئيسي لهذا الـ chapter هو matrices and
+
+8
+00:00:54,600 --> 00:01:00,080
+determinants يعني المصوفات والمحددات الان سكتشن
+
+9
+00:01:00,080 --> 00:01:06,220
+اتنين تمانية determinants المحددات بقول لو كان
+
+10
+00:01:06,220 --> 00:01:11,300
+المصوفة المربعة على الشكل ان هذا واضح ان عدد
+
+11
+00:01:11,300 --> 00:01:18,590
+الصفوف يساوي عدد الأعمدة ان رأسي وان أفقييبقى as a
+
+12
+00:01:18,590 --> 00:01:24,030
+matrix of order n هي مصوفة مربعة من الرتبة n يعني
+
+13
+00:01:24,030 --> 00:01:29,630
+نظامها n في n أو ال size تبعها n في m then the
+
+14
+00:01:29,630 --> 00:01:35,790
+determinant of a محدد المصوفة a حدي له الرمز data
+
+15
+00:01:38,590 --> 00:01:43,690
+DET اختصار لكلمة determinant لكن تقرأ determinant
+
+16
+00:01:43,690 --> 00:01:50,310
+of A او محدد المصوفة A هو نفس عناصر المصوفة بس بدل
+
+17
+00:01:50,310 --> 00:01:57,430
+قوسين كبار بحط خطين فقطالفرق بين المحدد والمصوفة
+
+18
+00:01:57,430 --> 00:02:02,530
+أن المصوفة إذا ضربت في رقم إذا ضربت في مصوفة أخرى
+
+19
+00:02:02,530 --> 00:02:08,070
+إذا جمعت لمصوفة أخرى يبقى الناتج مصوفة أما المحدد
+
+20
+00:02:08,070 --> 00:02:14,960
+فهو يفك ونحصل منه على قيمة عددية محددةيعني هذا كله
+
+21
+00:02:14,960 --> 00:02:18,420
+اللي شايفينه كبير بعد ما نفكه بطلع رقم و عدرية ال
+
+22
+00:02:18,420 --> 00:02:23,440
+number واحد فقط لغير this determinant is also of
+
+23
+00:02:23,440 --> 00:02:28,440
+order n هذا المحدد أيضا من الرتبة n لإن المصوفة
+
+24
+00:02:28,440 --> 00:02:33,680
+الأصلية كانت من الرتبة n فجداش في عندي عدد صفوف و
+
+25
+00:02:33,680 --> 00:02:37,860
+عدد أعمدة بقول المحدد من هذه الرتبةالمحدد اللي أنا
+
+26
+00:02:37,860 --> 00:02:41,820
+من الرتبة M لو كان صفين و عمودين بقول من الرتبة
+
+27
+00:02:41,820 --> 00:02:45,900
+الثانية لو كان تلت صفوف و تلت أعمدة بقول من الرتبة
+
+28
+00:02:45,900 --> 00:02:49,580
+التالتة أربع صفوف و أربع أعمدة بقول من الرتبة
+
+29
+00:02:49,580 --> 00:02:55,410
+الرابعة و هكذاالان من هذه المحددات بدي أخد محدد
+
+30
+00:02:55,410 --> 00:03:01,570
+2x2 و بعدين 3x3 و بعدين 4x4 وما إلى ذلك فلو جيت
+
+31
+00:03:01,570 --> 00:03:07,190
+مثلا على اللي هو لو كان ال determinant ليه is of
+
+32
+00:03:07,190 --> 00:03:13,170
+order two يعني صفين و عمودين يعني بدي أخد الصفين
+
+33
+00:03:13,170 --> 00:03:18,140
+الاتنين هدول و العمودين هدول فقطيبقى determinant ل
+
+34
+00:03:18,140 --> 00:03:26,000
+A11, A12, A21, A22الان بدي أعرف كيف بدي أجيب
+
+35
+00:03:26,000 --> 00:03:30,880
+القيمة العددية لهذا المحدد فبروح باخد حاصل ضرب
+
+36
+00:03:30,880 --> 00:03:36,280
+عناصر القطر الرئيسي ناقص حاصل ضرب عناصر القطر
+
+37
+00:03:36,280 --> 00:03:41,220
+الثانوي يبقى the product of the elements of the
+
+38
+00:03:41,220 --> 00:03:47,040
+main diagonal minus the product of the minor
+
+39
+00:03:47,040 --> 00:03:52,070
+elements أو product of the elementsof the minor
+
+40
+00:03:52,070 --> 00:03:58,770
+diagonal اللي هو القطر الثانوي يبقى حاصل ضرب عناصر
+
+41
+00:03:58,770 --> 00:04:01,990
+القطر الرئيسي ناقص حاصل ضرب عناصر القطر الثانوي
+
+42
+00:04:01,990 --> 00:04:11,210
+اطلع a11 a22 هيو minus a12 a21 بهذا الشكل يبقى فكل
+
+43
+00:04:11,210 --> 00:04:15,270
+محدد من الرتبة الثانية هو عبارة عن حاصل ضرب عناصر
+
+44
+00:04:15,270 --> 00:04:20,780
+القطر الرئيسي ناقص حاصل ضرب عناصر القطر الثانويإلا
+
+45
+00:04:20,780 --> 00:04:24,940
+أن نعطي مثال توضيح صغير فبقول لو كان عندنا المصوفة
+
+46
+00:04:24,940 --> 00:04:28,900
+من الرتبة الثانية نصفين و عمودين يبقى ال
+
+47
+00:04:28,900 --> 00:04:33,780
+determinant إلها بدي يساوي المحدد 2 3 سالب 1 أربعة
+
+48
+00:04:33,780 --> 00:04:40,400
+بدنا نفك حصل ضرب عناصر قوة رئيس 2 في 4 اللي هو
+
+49
+00:04:40,400 --> 00:04:46,600
+بقداش 8 ناقص حصل ضرب ده هدولة حصل ضرب مقداش سالب 3
+
+50
+00:04:46,600 --> 00:04:52,200
+مع سالبموجة بيصير موجة بتلاتة يبقى قيمة هذا المحدد
+
+51
+00:04:52,200 --> 00:04:57,060
+يساوي 11 زي ما قلنا و قبل قليل المحدد يساوي قيمة
+
+52
+00:04:57,060 --> 00:05:03,300
+عددية محددة فقيمة هذا المحدد عند بيقداش ب 11 طيب
+
+53
+00:05:03,300 --> 00:05:08,580
+ننتقل إلى تعريف جديد التعريف بيقول ايه permutation
+
+54
+00:05:08,580 --> 00:05:12,980
+of the set of positive integers permutation يعنيش
+
+55
+00:05:12,980 --> 00:05:19,570
+يا بناتبالعربي يعني تبديلة ممتازة يبقى بإننا نعطي
+
+56
+00:05:19,570 --> 00:05:26,290
+تعريف للتبديلة فبيقول التبديلة لمن؟ لمجموعة من
+
+57
+00:05:26,290 --> 00:05:30,470
+destinate positive integers لما أقول destinate إيش
+
+58
+00:05:30,470 --> 00:05:37,340
+يعني؟منفصل positive موجبة انتجر عدد صحية يبقى انا
+
+59
+00:05:37,340 --> 00:05:41,260
+عندي مجموعة من الاعداد الصحية ولا واحد بيساوي
+
+60
+00:05:41,260 --> 00:05:45,260
+التاني لان لو واحد ساوي التاني بطل يصير destinect
+
+61
+00:05:45,260 --> 00:05:50,680
+اتنين ولا واحد فيهم بيساوي كمية سالبة تلاتة ولا
+
+62
+00:05:50,680 --> 00:05:55,460
+واحد فيهم ب zerodestinate positive integers يبقى
+
+63
+00:05:55,460 --> 00:06:02,240
+كلها أعداد صحيحة موجبة غير مكررة ولا واحد زي تاني
+
+64
+00:06:02,240 --> 00:06:06,220
+يقول destinate كل واحد منفصل عن التاني لا يساوي
+
+65
+00:06:06,220 --> 00:06:12,240
+يبقى أعدادها دي أعطيتها الرمز J1 J2 J3 لغاية JN
+
+66
+00:06:12,240 --> 00:06:17,680
+يبقى هدول كام أعدادإن من العدد لكن لو في تقرار
+
+67
+00:06:17,680 --> 00:06:21,600
+بيبطل يصير عددهم in إذا لما يقول عددهم in معناته
+
+68
+00:06:21,600 --> 00:06:26,940
+ولا واحد زي التاني كلهم عناصر مختلفة هاي معناه
+
+69
+00:06:26,940 --> 00:06:31,730
+destiny يعني ولا عدد فيهم زي الثاني تمامايبقى is
+
+70
+00:06:31,730 --> 00:06:37,970
+an arrangement of this integer هو إعادة ترتيب لهذه
+
+71
+00:06:37,970 --> 00:06:42,430
+العناصر in some order without omission or
+
+72
+00:06:42,430 --> 00:06:47,950
+repetition يبقى بدي أعيد ترتيب هذا العناصر بشرط لا
+
+73
+00:06:47,950 --> 00:06:52,930
+يحذف واحد منهم ولا يكرر أي واحد يعني لما بدي أعمل
+
+74
+00:06:52,930 --> 00:06:57,030
+تبديل ما بديش ألاقي اتنين اتنينلا تجد مثلا خمسة
+
+75
+00:06:57,030 --> 00:07:03,190
+خمسة مكررها اتنان اذا عندي خمس اعداد موجودة في
+
+76
+00:07:03,190 --> 00:07:07,430
+التبديل دون تغيير اتنان اذا عندي خمس اعداد موجودة
+
+77
+00:07:07,430 --> 00:07:11,830
+في التبديل دون تغيير اتنان اذا عندي خمس اعداد
+
+78
+00:07:11,830 --> 00:07:12,470
+موجودة في التبديل دون تغيير اتنان اذا عندي خمس
+
+79
+00:07:12,470 --> 00:07:15,010
+اعداد موجودة في التبديل دون تغيير اتنان اتنان اذا
+
+80
+00:07:15,010 --> 00:07:16,690
+عندي خمس اعداد موجودة في التبديل دون تغيير اتنان
+
+81
+00:07:16,690 --> 00:07:16,750
+اتنان اتنان اتنان اتنان اتنان اتنان اتنان اتنان
+
+82
+00:07:16,750 --> 00:07:20,510
+اتنان اتنان اتنان اتنان اتنان ايعني لو كان عندها
+
+83
+00:07:20,510 --> 00:07:24,030
+خمسة أعداد بالديالاج ال permutation فيها خمسة
+
+84
+00:07:24,030 --> 00:07:28,390
+أعداد ولا واحد من الخمسة غايب اتنين ولا واحد من
+
+85
+00:07:28,390 --> 00:07:34,990
+هذه الأعداد بنكرره مرتين أو تلاباس بيظهرمرة واحدة
+
+86
+00:07:34,990 --> 00:07:37,510
+فقط لغير واضحة إيش معناه ال experimentation
+
+87
+00:07:37,510 --> 00:07:41,190
+التبديلة يعني يا بنات هدول قداش عددهم البنات في
+
+88
+00:07:41,190 --> 00:07:48,010
+الصف الأول أربع بنات بدي أبدل مواقعهم بشرط مانقولش
+
+89
+00:07:48,010 --> 00:07:53,270
+لو حد انتجل هناكيبقى ما نحذفهاش اتنين ماخليش
+
+90
+00:07:53,270 --> 00:07:56,930
+الواحدة مكررة مرتين طبعا ولا واحدة فيهم مكررة
+
+91
+00:07:56,930 --> 00:08:02,790
+مرتين يبقى هدول بدون حذف او تكرار مش هطلع اربعة
+
+92
+00:08:02,790 --> 00:08:06,690
+بدهم يضلوا اربعة زي ما هم لابد اضيف عليهم ولا بدي
+
+93
+00:08:06,690 --> 00:08:10,730
+اخد منهم بدوني ابقى كما هم بس بدي ابدل مواقع معين
+
+94
+00:08:10,730 --> 00:08:16,510
+في الجلوس تتوقعوا اكم عدد يكون او اكم تبديلة ينتج
+
+95
+00:08:16,510 --> 00:08:27,540
+من الاربع بنات هدوةكداش؟ ستة عشر لا أكتر
+
+96
+00:08:27,540 --> 00:08:33,400
+أربع وعشرين تبديلين تمام؟ خليني أجرب و أقولكوا
+
+97
+00:08:33,400 --> 00:08:37,560
+الفكرة بثلاثة و بعدين بنعمم للاربع و للخمسة و
+
+98
+00:08:37,560 --> 00:08:42,470
+للستة وما إلى ذلك يبقى بدنا نيجي ل exampleقال لو
+
+99
+00:08:42,470 --> 00:08:46,570
+كان ال a واحد و اتنين و تلاتة then all possible
+
+100
+00:08:46,570 --> 00:08:51,170
+permutations are يبقى بدنا نجيب التبديلات اللي
+
+101
+00:08:51,170 --> 00:08:56,190
+بقدر اعملهم من الاعداد التلاتة هذه طلعي معايا هاي
+
+102
+00:08:56,190 --> 00:09:00,130
+التبديلة الأولى واحد اتنين تلاتة بدنا نجيب
+
+103
+00:09:00,130 --> 00:09:03,810
+التبديلة التانيةأريد أن أثبت الواحد يا بنات و
+
+104
+00:09:03,810 --> 00:09:08,430
+أتحوذ منه اتنين والتلاتة ستصبح تلاتة اتنين هل هذه
+
+105
+00:09:08,430 --> 00:09:13,750
+مثل هذه حذفنا واحد فيهم و فيهم واحد مكرر يبقى
+
+106
+00:09:13,750 --> 00:09:18,250
+شغلنا سليم مائة بالمائة يبقى بعدك أبدأ اتنين كم
+
+107
+00:09:18,250 --> 00:09:23,350
+يبقى لدي واحد و تلاتة سابت لي اتنين و أتحوذ لي
+
+108
+00:09:23,350 --> 00:09:28,980
+التلاتة والواحد يبقى تلاتة واحد كم صار لديفيهم
+
+109
+00:09:28,980 --> 00:09:34,680
+واحدة زي التانية ولا تبديلة زي التانية زي ما بدأت
+
+110
+00:09:34,680 --> 00:09:39,260
+واحد واحد اتنين اتنين بدي ابدأ بتلاتة وهي واحد
+
+111
+00:09:39,260 --> 00:09:45,700
+اتنين وهي كمان تلاتة اتنين واحد هاي صاروا جداش
+
+112
+00:09:45,700 --> 00:09:52,280
+فيهم واحدة زي التانية الست هادول طيب فيهم عدد مكرر
+
+113
+00:09:52,280 --> 00:09:57,380
+في اي واحدة من الستةكل واحد اتنين تلاتة فيهم عدد
+
+114
+00:09:57,380 --> 00:10:03,520
+محذوف من التلاتة مافيش قداش عددهم دول يبقى لو كان
+
+115
+00:10:03,520 --> 00:10:09,940
+عندي تلت عناصر تلت عناصر يبقى في هذه الحالة ال
+
+116
+00:10:09,940 --> 00:10:14,140
+permutation اللي بقدر اتكونه منهم مضروب التلاتة in
+
+117
+00:10:14,140 --> 00:10:19,120
+factorial يبقى باجي بقوله هنا the number of
+
+118
+00:10:25,740 --> 00:10:32,360
+permutations are ستة اللي هو بده يساوي تلاتة
+
+119
+00:10:32,360 --> 00:10:41,060
+factorial تلاتة factorial similarly بنفس الطريقة
+
+120
+00:10:41,060 --> 00:10:51,480
+if ال a تساوي واحد و اتنين و تلاتة واربعة then the
+
+121
+00:10:52,150 --> 00:10:59,850
+number of permutations
+
+122
+00:10:59,850 --> 00:11:09,010
+عدد التبديلات is 4 factorial يعني كدهش 24 4 في 3 ب
+
+123
+00:11:09,010 --> 00:11:17,610
+12 في 2 ب 24 في 1 ب 24 طب شو رايكوا نعممها؟يبقى لو
+
+124
+00:11:17,610 --> 00:11:21,590
+كان عندي N من العناصر كم عدد التبديلات؟ N
+
+125
+00:11:21,590 --> 00:11:30,930
+factorial يبقى for أو in general نعممها أكتر يبقى
+
+126
+00:11:30,930 --> 00:11:39,930
+in general على وجه العموم for the distinct
+
+127
+00:11:39,930 --> 00:11:45,530
+elements اللي
+
+128
+00:11:45,530 --> 00:12:00,520
+هوj1 وj2 ولغاية jn number of permutations
+
+129
+00:12:00,520 --> 00:12:04,760
+is
+
+130
+00:12:04,760 --> 00:12:11,880
+n factorial يبقى أعدادهم بده يساوي n factorial
+
+131
+00:12:16,090 --> 00:12:24,610
+نجي لحاجة جديدة اسمها Inversions Inferiorly
+
+132
+00:12:24,610 --> 00:12:36,390
+التحويلات بيقول let J1 J2 و لغاية JN
+
+133
+00:12:39,050 --> 00:12:47,950
+جي ام بيرميتشن بيرميتشن
+
+134
+00:12:47,950 --> 00:13:02,570
+بيرميتشن of a set of n positive integers in
+
+135
+00:13:02,570 --> 00:13:11,440
+positive integers let alpha oneدع ألف واحد يكون
+
+136
+00:13:11,440 --> 00:13:17,060
+رقم .. يكون
+
+137
+00:13:17,060 --> 00:13:22,720
+رقم انتجارات
+
+138
+00:13:22,720 --> 00:13:26,780
+تتبع
+
+139
+00:13:26,780 --> 00:13:31,700
+جي
+
+140
+00:13:31,700 --> 00:13:35,800
+وان تتبع
+
+141
+00:13:37,100 --> 00:13:52,600
+are smaller than j1 let alpha to be the number of
+
+142
+00:13:52,600 --> 00:14:03,800
+integers following j2 that are smaller than j2 and
+
+143
+00:14:03,800 --> 00:14:14,540
+so onand ساقن و هكذا it
+
+144
+00:14:14,540 --> 00:14:18,820
+should
+
+145
+00:14:18,820 --> 00:14:32,300
+be noted that alpha n بدها تساوي جداش؟ بدها تساوي
+
+146
+00:14:32,300 --> 00:14:32,820
+زيرو
+
+147
+00:14:47,640 --> 00:14:52,580
+بنعطي definition لكيفية استخدام هذه ال parameters
+
+148
+00:14:52,580 --> 00:15:02,720
+يبقى definition تعريف the sum المجموع
+
+149
+00:15:02,720 --> 00:15:08,860
+اللي هو alpha واحد زائد alpha اتنين زائد زائد
+
+150
+00:15:08,860 --> 00:15:13,440
+alpha in minus ال one is called
+
+151
+00:15:18,520 --> 00:15:24,460
+the number of
+
+152
+00:15:24,460 --> 00:15:30,020
+inversion
+
+153
+00:15:30,020 --> 00:15:36,560
+in
+
+154
+00:15:36,560 --> 00:15:45,380
+the permutation in
+
+155
+00:15:45,380 --> 00:15:53,650
+the permutationاللي هي جي واحد فاصلة جي اتنين و
+
+156
+00:15:53,650 --> 00:15:58,950
+لغاية جي ام example
+
+157
+00:15:58,950 --> 00:16:04,550
+find
+
+158
+00:16:04,550 --> 00:16:12,510
+the number of inversions find the number of
+
+159
+00:16:12,510 --> 00:16:15,870
+inversions
+
+160
+00:16:17,090 --> 00:16:29,810
+inversions and the fermentation and
+
+161
+00:16:29,810 --> 00:16:30,550
+the fermentation
+
+162
+00:17:17,320 --> 00:17:21,600
+نرجع لنقطة جديدة في هذا الـ section وهي الـ
+
+163
+00:17:21,600 --> 00:17:28,340
+inversions التحويلاتفبجي بقول let j1 و j2 و jn بيه
+
+164
+00:17:28,340 --> 00:17:32,240
+ايه permutation يبقى هذه مجموعة من الاعداد و بدلنا
+
+165
+00:17:32,240 --> 00:17:38,540
+مواقعها فسميناها permutation دون حذف او تغيير of a
+
+166
+00:17:38,540 --> 00:17:44,020
+set of n positive integers بدي اسمي تسميات جديدة
+
+167
+00:17:44,020 --> 00:17:49,880
+let alpha 1 be the number of integers following j1
+
+168
+00:17:49,880 --> 00:17:55,800
+and smaller than j1 ايش يعني؟يعني انا هذه عندي
+
+169
+00:17:55,800 --> 00:18:02,000
+permutation Alpha 1 بدي امسك الرقم G1 بدي اعد كم
+
+170
+00:18:02,000 --> 00:18:07,460
+رقم يأتي بعده ويكون أصغر منه باخد الأرقام اللي
+
+171
+00:18:07,460 --> 00:18:10,900
+بتيجي بعده و اللي بتكون أصغر منه بدي أسميها Alpha
+
+172
+00:18:10,900 --> 00:18:16,420
+1خلص جي ون بدأ أجي ل جي تو بدأ أسمي الرقم اللي عند
+
+173
+00:18:16,420 --> 00:18:21,440
+مين Alpha 2 Alpha 2 هي مين؟ جميع الأرقام اللي جاية
+
+174
+00:18:21,440 --> 00:18:29,280
+بعد جي تو وتكون أصغر من جي توبدا اجي الـ α3 بدا
+
+175
+00:18:29,280 --> 00:18:34,040
+اروح على جي ثري يبقى بتشوف الأرقام اللي جاية بعد
+
+176
+00:18:34,040 --> 00:18:39,700
+جي ثري والتي تكون أصغر من جي ثري بدا أسميها α3 وضل
+
+177
+00:18:39,700 --> 00:18:44,080
+ماشي لغاية ما وصل للرقم اللي قبلها دي اللي هو جي
+
+178
+00:18:44,080 --> 00:18:49,050
+ان ماينوس الوانبدي أشوف الأرقام اللي جاية بعده و
+
+179
+00:18:49,050 --> 00:18:52,270
+اللي بتكون أصغر منه يمكن ألاقيه و يمكن مالاقيهش
+
+180
+00:18:52,270 --> 00:18:55,230
+يمكن اللي بعده يكون أصغر منه و يمكن يكون أكبر منه
+
+181
+00:18:55,230 --> 00:18:59,450
+إذا أصغر منه بقول في واحد إذا أكبر منه بقول صفر
+
+182
+00:18:59,450 --> 00:19:06,180
+مافيش طيب بدي أجي ل GNيجب ان انا اجهز الفا ان في
+
+183
+00:19:06,180 --> 00:19:10,800
+ارقام جاية بعده اذا اتوماتيك الفا ان قداش بده
+
+184
+00:19:10,800 --> 00:19:15,120
+تساوي زيرو يبقى هذا باجمعوش لان زيرو اللي تضفيه لا
+
+185
+00:19:15,120 --> 00:19:19,160
+ايه رقم بيعطينا نفس الرقم يبقى عارفنا الفا واحد و
+
+186
+00:19:19,160 --> 00:19:22,720
+الفا اتنين و الفا تلاتة كيف بسويابأجى على الرقم
+
+187
+00:19:22,720 --> 00:19:26,220
+بشوف الأعداد اللى بعده اللى بتبقى أقل منه كام واحد
+
+188
+00:19:26,220 --> 00:19:30,060
+واحد اتنين تلاتة مثلا بقول يبقى Alpha واحد تساوي
+
+189
+00:19:30,060 --> 00:19:34,420
+تلاتة رقمين بقول Alpha واحد تساوي رقمين رقم واحد
+
+190
+00:19:34,420 --> 00:19:38,480
+بقول Alpha واحد تساوي واحدحسب عدد الأرقام اللى
+
+191
+00:19:38,480 --> 00:19:43,360
+موجودة عندنا طيب من هذا بروح اكتب تعريف التعريف
+
+192
+00:19:43,360 --> 00:19:48,140
+بقولاش the sum جماعة الألفات هدول اللى جبتهم كلهم
+
+193
+00:19:48,140 --> 00:19:51,940
+Alpha 1 زيد Alpha 2 زيد Alpha 3 زيد Alpha N minus
+
+194
+00:19:51,940 --> 00:19:56,180
+ال 1 ماخدش Alpha N لأن Alpha N بزيرو يعني كتبتها
+
+195
+00:19:56,180 --> 00:19:59,920
+بس زيادة كلكعة زيادة كلكعة مش هجيبلي ولا معلومة
+
+196
+00:19:59,920 --> 00:20:07,480
+جديدةيبقى مجموعهم
+
+197
+00:20:07,480 --> 00:20:14,160
+هدول عبارة عن عدد التحويلات الموجودة في هذه ال
+
+198
+00:20:14,160 --> 00:20:18,330
+permutation نعطي مثالقولي find the number of
+
+199
+00:20:18,330 --> 00:20:23,450
+inversions in the permutation يبقى خديلي أعداد
+
+200
+00:20:23,450 --> 00:20:27,730
+بنعمل مثلا أعداد من واحد لخمسة من واحد لستة اللي
+
+201
+00:20:27,730 --> 00:20:31,330
+يعجبك بس بضل أخبطكم مع بعض مش بضرورة واحد اتنين
+
+202
+00:20:31,330 --> 00:20:36,270
+تلاتة أربعة يبقى ال permutation مثلا يالا فاتيلي
+
+203
+00:20:36,270 --> 00:20:40,310
+permutation من عندي قولي اللي تعجبك من واحد لستة
+
+204
+00:20:40,310 --> 00:20:49,820
+خمسة واحد واحدتلاتة اربعة اتنين ستة اربعة ستة
+
+205
+00:20:49,820 --> 00:20:55,600
+خلصنا في غيرهم لا تمام يبقى الان انا بداجي اجيب
+
+206
+00:20:55,600 --> 00:20:59,860
+هذه permutation بدليها زي ما بيطلع ستة factorial
+
+207
+00:20:59,860 --> 00:21:04,660
+يعني اعداد رهيبة مالي مالها انا بدي اتقيد بمين بس
+
+208
+00:21:04,660 --> 00:21:09,960
+بال permutation عندي فاصلة فاصلة فاصلة تمام بداجي
+
+209
+00:21:09,960 --> 00:21:33,370
+اجيب thenالفا ون يساوي الفا ون يساوي الفا
+
+210
+00:21:33,370 --> 00:21:33,770
+ون يساوي الفا ون يساوي الفا ون يساوي الفا ون يساوي
+
+211
+00:21:33,770 --> 00:21:33,770
+الفا ون يساوي الفا ون يساوي الفا ون يساوي الفا ون
+
+212
+00:21:33,770 --> 00:21:33,770
+يساوي الفا ون يساوي الفا ون يساوي الفا ون يساوي
+
+213
+00:21:33,770 --> 00:21:33,870
+الفا ون يساوي الفا ون يساوي الفا ون يساوي الفا ون
+
+214
+00:21:33,870 --> 00:21:33,870
+يساوي الفا ون يساوي الفا ون يساوي الفا ون يساوي
+
+215
+00:21:33,870 --> 00:21:33,870
+الفا ون يساوي الفا ون يساوي الفا ون يساوي الفا ون
+
+216
+00:21:33,870 --> 00:21:33,870
+يساوي الفا ون يساوي الفا ون يساوي الفا ون يساوي
+
+217
+00:21:33,870 --> 00:21:38,360
+الفا ون يسابأجي للعدد واحد مين أصغر منه بعده ولا
+
+218
+00:21:38,360 --> 00:21:44,880
+واحد يبقى النتج يساوي قداش Zero بدي Alpha 3 باجي
+
+219
+00:21:44,880 --> 00:21:48,420
+للعدد تلاته مافيش غير واحد أصغر منه تمام اللي هو
+
+220
+00:21:48,420 --> 00:21:55,430
+العدد قداش 2يبقى واحد يبقى واحد
+
+221
+00:21:55,430 --> 00:21:59,350
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+222
+00:21:59,350 --> 00:21:59,370
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+223
+00:21:59,370 --> 00:22:00,310
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+224
+00:22:00,310 --> 00:22:01,030
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+225
+00:22:01,030 --> 00:22:01,350
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+226
+00:22:01,350 --> 00:22:01,410
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+227
+00:22:01,410 --> 00:22:10,090
+يبقى واحد يبقى واحد يبقى واحد يبقى واحد يبقى واحد
+
+228
+00:22:10,090 --> 00:22:10,670
+يب
+
+229
+00:22:18,630 --> 00:22:26,790
+inversions is alpha 1 زيد alpha 2 زيد alpha 3 زيد
+
+230
+00:22:26,790 --> 00:22:34,850
+alpha 4 زيد alpha 5 ويساوي يساوي alpha 1 ب 4 زيد 0
+
+231
+00:22:34,850 --> 00:22:42,770
+زيد 1 زيد 1 زيد 0 يعني كده شبه انا ستةيبقى في عندي
+
+232
+00:22:42,770 --> 00:22:49,010
+ستة inversions لمين لهذه ال permutation طيب لو
+
+233
+00:22:49,010 --> 00:22:54,710
+غيرت وضع الأرقام يعني غيرت دي بدلت ومابعدت تبديلة
+
+234
+00:22:54,710 --> 00:22:58,820
+جديدة بطلع الرقم ستة ولا باخلف؟هيختلف على طول
+
+235
+00:22:58,820 --> 00:23:05,100
+الخطط يعني كل permutation لها inversion محددة تمام
+
+236
+00:23:05,100 --> 00:23:12,400
+طيب كويس ايش رأيك؟ بدنا نعطي تعريف نستخدم في ال
+
+237
+00:23:12,400 --> 00:23:16,340
+inversions هذايعني للـ inversion هذا بدنا نيجي
+
+238
+00:23:16,340 --> 00:23:22,180
+نقول هل التبديل هذه تبديلة زوجية ولا تبديلة فردية
+
+239
+00:23:22,180 --> 00:23:26,780
+يعتمد على النتيجة اللي وصلنا لها هذه إذا هذا الرقم
+
+240
+00:23:26,780 --> 00:23:31,860
+كان رقما زوجيا فهذه تبديلة زوجية إذا الرقم اللي
+
+241
+00:23:31,860 --> 00:23:38,380
+طالع انه رقم فردي بقول هذه تبديلة فردية تمام هنصيغ
+
+242
+00:23:38,380 --> 00:23:43,560
+هذا في ال definition التالي يبقى definitionA
+
+243
+00:23:43,560 --> 00:23:50,600
+permutation is
+
+244
+00:23:50,600 --> 00:23:56,380
+called even,
+
+245
+00:23:56,580 --> 00:24:08,800
+even or odd if the
+
+246
+00:24:08,800 --> 00:24:09,280
+number
+
+247
+00:24:13,800 --> 00:24:20,360
+إذا كتابة الـ number of inversions
+
+248
+00:24:20,360 --> 00:24:26,000
+كتابة الـ number of inversions كتابة الـ number of
+
+249
+00:24:26,000 --> 00:24:27,120
+inversions كتابة الـ number of inversions كتابة
+
+250
+00:24:27,120 --> 00:24:27,120
+الـ number of inversions كتابة الـ number of
+
+251
+00:24:27,120 --> 00:24:30,160
+inversions كتابة الـ number of inversions كتابة
+
+252
+00:24:30,160 --> 00:24:31,300
+الـ number of inversions كتابة الـ number of
+
+253
+00:24:31,300 --> 00:24:31,300
+inversions كتابة الـ number of inversions كتابة
+
+254
+00:24:31,300 --> 00:24:31,300
+الـ number of inversions كتابة الـ number of
+
+255
+00:24:31,300 --> 00:24:31,300
+inversions كتابة الـ number of inversions كتابة
+
+256
+00:24:31,300 --> 00:24:31,300
+الـ number of inversions كتابة الـ number of
+
+257
+00:24:31,300 --> 00:24:31,300
+inversions كتابة الـ number of inversions كتابة
+
+258
+00:24:31,300 --> 00:24:31,300
+الـ number of inversions كتابة الـ number of
+
+259
+00:24:31,300 --> 00:24:31,300
+inversions كتابة الـ number of inversions كتابة
+
+260
+00:24:31,300 --> 00:24:33,080
+الـ number of inversions كتابة الـ number of
+
+261
+00:24:33,080 --> 00:24:41,300
+inversions كتابة الـ
+
+262
+00:24:41,300 --> 00:24:43,580
+number of inversions كت
+
+263
+00:24:48,090 --> 00:24:54,450
+permutation the above permutation اللي خمسة واحد
+
+264
+00:24:54,450 --> 00:25:08,450
+تلاتة اربع اتنين ستة is even والله good even السبب
+
+265
+00:25:08,450 --> 00:25:13,950
+because the number
+
+266
+00:25:15,910 --> 00:25:19,890
+of inversions
+
+267
+00:25:19,890 --> 00:25:22,950
+is
+
+268
+00:25:22,950 --> 00:25:31,090
+even that is ستة
+
+269
+00:25:31,090 --> 00:25:39,470
+يبقى هذا العدد اللي هو ستة command
+
+270
+00:25:39,470 --> 00:25:40,090
+definition
+
+271
+00:25:43,070 --> 00:25:50,230
+برضه متعلق بالـ Inversions هذه يبقى F الجي واحد
+
+272
+00:25:50,230 --> 00:26:00,350
+والجي اتنين و لغاية الجي ان is a permutation is a
+
+273
+00:26:00,350 --> 00:26:07,890
+permutation we
+
+274
+00:26:07,890 --> 00:26:08,710
+define
+
+275
+00:26:14,150 --> 00:26:23,530
+Function Delta By Delta
+
+276
+00:26:23,530 --> 00:26:34,570
+Of J1 وJ2 وJN بدل يساوي أحد أمرين تبقى هذه بدأ
+
+277
+00:26:34,570 --> 00:26:40,730
+اكتب ال function على الشكل التالي يام واحد F
+
+278
+00:26:42,900 --> 00:26:56,380
+G1 و G2 و لغاية GN is even is even و سالب واحد F
+
+279
+00:26:56,380 --> 00:27:02,280
+G1 G2 و لغاية GN
+
+280
+00:27:08,870 --> 00:27:18,070
+جن is odd example
+
+281
+00:27:18,070 --> 00:27:25,630
+find
+
+282
+00:27:25,630 --> 00:27:33,950
+the value of
+
+283
+00:27:33,950 --> 00:27:36,770
+delta
+
+284
+00:27:38,340 --> 00:27:42,060
+واحد تلاتة خمسة اتنين اربع
+
+285
+00:28:06,620 --> 00:28:10,160
+اللي بيجي أعرفنا الآن عن ال permutation بقول إنها
+
+286
+00:28:10,160 --> 00:28:15,240
+alpha أو even حسب عدد ال inversions عدد ال
+
+287
+00:28:15,240 --> 00:28:19,360
+inversions زوجي بقول ال permutation زوجية عدد ال
+
+288
+00:28:19,360 --> 00:28:25,680
+inversions فردي بقول عدد بقول ال permutation هي
+
+289
+00:28:25,680 --> 00:28:29,800
+فردية فبجي بقول ال permutation is called even أو
+
+290
+00:28:29,800 --> 00:28:35,530
+او قد برتي برتي يعني نتيجة نديةيعني كأن ال even هو
+
+291
+00:28:35,530 --> 00:28:40,610
+ند لمين لل odd يبقى هذه الترجمة الحرفية لها ندية
+
+292
+00:28:41,150 --> 00:28:44,750
+ممكن تكتبيها وممكن ما تكتبيهاش يعني اختصارا تقولي
+
+293
+00:28:44,750 --> 00:28:47,890
+لي even و odd و تسكتي ماعش الهدف قولتيلي even
+
+294
+00:28:47,890 --> 00:28:52,370
+parity او ال odd parity سيام if the number of
+
+295
+00:28:52,370 --> 00:28:54,970
+inversions is even or odd يعني لو كانت ال
+
+296
+00:28:54,970 --> 00:28:58,410
+permutation بقول عنها even إذا كان عدد ال
+
+297
+00:28:58,410 --> 00:29:02,350
+inversions even بقول عنها odd إذا كان عدد ال
+
+298
+00:29:02,350 --> 00:29:06,150
+inversions odd مثلا the above permutation هذه اللي
+
+299
+00:29:06,150 --> 00:29:13,780
+فوق قدش طالع عددهم؟ستة عدد زوجي إذا هذه even لأن
+
+300
+00:29:13,780 --> 00:29:19,000
+العدد يساوي ستة نعطي تعريف جديد لو كان عندنا ال
+
+301
+00:29:19,000 --> 00:29:22,980
+permutation دي واحد جي اتنين لغاية جي ام نعرف
+
+302
+00:29:22,980 --> 00:29:29,280
+فانكشن Delta كتالي Delta لما اتأثر على هذا ال
+
+303
+00:29:29,280 --> 00:29:34,450
+element هو permutation بيعطيني أحد إيجابتينيا إما
+
+304
+00:29:34,450 --> 00:29:38,750
+واحد، يا إما سالب واحد بيعطيني واحد إذا كان ال
+
+305
+00:29:38,750 --> 00:29:42,690
+permutation هذه even بيعطيني سالب واحد إذا كان ال
+
+306
+00:29:42,690 --> 00:29:46,750
+permutation odd هيك عرفنا هذه ال function طيب
+
+307
+00:29:46,750 --> 00:29:51,190
+سؤالي هو مين domain هذه ال function يا مانا؟ ال
+
+308
+00:29:51,190 --> 00:29:57,890
+domain تبعها كل اللي هو العناصر تبع ال permutation
+
+309
+00:29:57,890 --> 00:30:04,850
+من واحد لغاية n مظبوط طيب مين ال range تبعها؟1-1
+
+310
+00:30:04,850 --> 00:30:08,710
+بس يبقى الـ range يحتوي على عنصرين وال domain
+
+311
+00:30:08,710 --> 00:30:14,330
+يحتوي على N من العناصر طبعاً لما نقول N يبقى N
+
+312
+00:30:14,330 --> 00:30:20,590
+factorial يعني عناصر كتير تبديلات خد زي ما بدك ما
+
+313
+00:30:20,590 --> 00:30:24,010
+علينا حطينا التعريف في هذه نعطي مثال عملي يجالي
+
+314
+00:30:24,010 --> 00:30:32,080
+هاتلي find the value of delta1 3 5 2 4 يبقى
+
+315
+00:30:32,080 --> 00:30:38,060
+الأعداد من واحد إلى خمسة بس إيه انبدالات مع بعضهم
+
+316
+00:30:38,060 --> 00:30:41,860
+عشان أجيب هذه الـ delta أول شيء بدي أعرف هذي even
+
+317
+00:30:41,860 --> 00:30:46,460
+ولا odd عشان أعرف هذي even ولا odd يبقى بدي أجيب
+
+318
+00:30:46,460 --> 00:30:49,940
+اللي هي الألفات الف واحد و الف اتنين و الف تلاتة
+
+319
+00:30:49,940 --> 00:30:54,660
+وما إلى ذلكأذا انا بداجي للحل بدروح اجيبله alpha
+
+320
+00:30:54,660 --> 00:30:59,600
+one وتساوي بد الأعداد اللي جاية بعد الواحد و اللي
+
+321
+00:30:59,600 --> 00:31:04,940
+بتكون أصغر من واحد كده؟ Zero فاش ولا رقم بداجي
+
+322
+00:31:04,940 --> 00:31:08,620
+alpha اتنين بد الأعداد اللي بعدي التلاتة و اللي
+
+323
+00:31:08,620 --> 00:31:14,960
+بتكون أقل من تلاتةعدد واحد اللي هو لعددي اتنين
+
+324
+00:31:14,960 --> 00:31:19,820
+نمرة تلاتة بدي alpha تلاتة الأعداد اللي جاء بعد
+
+325
+00:31:19,820 --> 00:31:24,200
+الخمسة و اللي أقل من خمسة جديش اللي هو اتنين
+
+326
+00:31:24,200 --> 00:31:28,880
+وأربعة بعد هيك بدي alpha أربعةبدي اللي عدد
+
+327
+00:31:28,880 --> 00:31:32,320
+الإيجابي عدد اتنين و اللي قل من اتنين ماعنديش و
+
+328
+00:31:32,320 --> 00:31:37,640
+الـ Alpha خمسة بزير تمام؟ إذا بدي أخد Alpha واحد
+
+329
+00:31:37,640 --> 00:31:41,740
+زائد Alpha اتنين زائد Alpha تلاتة زائد Alpha أربعة
+
+330
+00:31:41,740 --> 00:31:48,040
+Zero زائد واحد زائد اتنين زائد Zero يسوى كم؟ تلاتة
+
+331
+00:31:48,040 --> 00:31:56,130
+هذا ماله odd number يبقى هذا عدد فردييبقى الـ
+
+332
+00:31:56,130 --> 00:32:01,210
+permutation اللي عندنا هذه odd parity يبقى هنا الـ
+
+333
+00:32:01,210 --> 00:32:07,290
+permutation
+
+334
+00:32:07,290 --> 00:32:17,570
+اللي هي واحد، تلاتة، خمسة، اتنين، اربعة is odd
+
+335
+00:32:17,570 --> 00:32:18,710
+parity
+
+336
+00:32:20,690 --> 00:32:28,450
+ما دام odd يبقى بناء عليه delta لواحد تلاتة خمسة
+
+337
+00:32:28,450 --> 00:32:36,990
+اتنين اربعة سالب واحد لان هذه طلعت odd يبقى هذا
+
+338
+00:32:36,990 --> 00:32:44,610
+مثال عملي على ذلكالحكي الأول ما بدأنا كان على الـ
+
+339
+00:32:44,610 --> 00:32:48,610
+determinant اللي النظام تبعه اتنين في اتنين قلنا
+
+340
+00:32:48,610 --> 00:32:52,090
+بالفك وحصل ضرب عناصر القطر رئيسي ناقص حصل ضرب
+
+341
+00:32:52,090 --> 00:32:56,850
+عناصر القطر الثانوي ننتقل الى determinant النظام
+
+342
+00:32:56,850 --> 00:33:02,970
+تبعه او من الرتبة الثالثة يعني ثلاثة صفوف وثلاثة
+
+343
+00:33:02,970 --> 00:33:07,370
+أعمدة مين بتسأل؟ ايه؟
+
+344
+00:33:14,220 --> 00:33:19,740
+ممتاز جدا يبقى كل التبديلات لهذه العناصر يعتبر هو
+
+345
+00:33:19,740 --> 00:33:24,860
+ال domain تبع دلتها in factorial صحيح ايه نعم بس
+
+346
+00:33:24,860 --> 00:33:29,040
+ال permutation اللي واحدة فيها in من العناصر فقط
+
+347
+00:33:29,040 --> 00:33:36,000
+لا غير طيب يبقى الان بدنا نيجي لحاجة اسمها data
+
+348
+00:33:37,200 --> 00:33:46,020
+منين انت determinant of اللي هو تلاتة by تلاتة
+
+349
+00:33:46,020 --> 00:33:53,140
+matrix يبقى محدد المصوفة لنظامها تلاتة في تلاتة
+
+350
+00:33:53,140 --> 00:33:57,080
+definition if
+
+351
+00:33:57,080 --> 00:34:05,800
+a matrix if a matrix of order
+
+352
+00:34:06,900 --> 00:34:11,720
+تلاتة if
+
+353
+00:34:11,720 --> 00:34:25,400
+ال a is a matrix of order 3 if ال a is a matrix of
+
+354
+00:34:25,400 --> 00:34:36,340
+order 3 then the value then the value of
+
+355
+00:34:37,140 --> 00:34:48,240
+determinant لإيه is defined as
+
+356
+00:34:48,240 --> 00:34:53,320
+follow كالتالي
+
+357
+00:34:53,320 --> 00:34:59,420
+determinant
+
+358
+00:34:59,420 --> 00:35:11,210
+لإيه هو عبارة عن إيه واحد واحدE1 E2 E1 E3 E2 E1 E2
+
+359
+00:35:11,210 --> 00:35:18,730
+E2 E3 E3 E1 E32 E33
+
+360
+00:35:22,860 --> 00:35:28,220
+الان هذا شكل determinant ليه لكن انا بدى اعرف قداش
+
+361
+00:35:28,220 --> 00:35:33,640
+القيمة العددية لهذا المحدد مشان اعرف قداش القيمة
+
+362
+00:35:33,640 --> 00:35:38,140
+العددية هناك طريقتان هعطيكي الطريقة الأولى و
+
+363
+00:35:38,140 --> 00:35:42,840
+الطريقة الثانية لكيفى يتفك هذا المحدد و الوصول الى
+
+364
+00:35:42,840 --> 00:35:49,100
+الرقم المحدد اللى يسويه هذا المحدد فباجى بقول مات
+
+365
+00:35:49,100 --> 00:35:55,660
+يا ماناتباجي بقول هذا اي واحد واحد اي واحد اتنين
+
+366
+00:35:55,660 --> 00:36:03,980
+اي واحد تلاتة اتنين واحد اتنين اتنين اتنين تلاتة
+
+367
+00:36:03,980 --> 00:36:14,300
+اتلاتة واحد اتلاتة تلاتة اتلاتة اتنين اتلاتة تلاتة
+
+368
+00:36:16,370 --> 00:36:21,230
+اللي جوا هذا انا كتبتهم برا مش هقدّيكوا بس بضلوح
+
+369
+00:36:21,230 --> 00:36:26,230
+اضفلهم العمودي الأول والعمودي الثاني يبقى باجي
+
+370
+00:36:26,230 --> 00:36:32,910
+بقوله ايه واحد واحد ايه اتنين واحد ايه تلاتة واحد
+
+371
+00:36:32,910 --> 00:36:44,170
+ايه واحد اتنين ايه اتنين اتنين ايه تلاتة اتنينأظن
+
+372
+00:36:44,170 --> 00:36:49,410
+لو جيت أول قطر الرئيسي اللي هو هذا واللي بعده هو
+
+373
+00:36:49,410 --> 00:36:59,640
+هذا واللي بعده هو هذا صح؟يبقى هذا كله القطر
+
+374
+00:36:59,640 --> 00:37:04,260
+الرئيسي ماخل ذلك ماينفعش يكون قطر رئيسي كل واحد
+
+375
+00:37:04,260 --> 00:37:08,200
+فيه تلاتة الباقى فيه اتنين وواحد طب وين القطر
+
+376
+00:37:08,200 --> 00:37:14,480
+الثانوي بالداجي بالعكس يبقى هذا اول قطر ثانوي وهذا
+
+377
+00:37:14,480 --> 00:37:21,860
+تاني قطر ثانوي وهذا تالت قطر ثانوييبقى قيمة هذا
+
+378
+00:37:21,860 --> 00:37:29,380
+المحدد تساوي حق مجموح حواصل ضرب الأقطار الثانوية
+
+379
+00:37:29,380 --> 00:37:35,100
+القاطرة الرئيسية التلاتة ناقص حاصل ضرب اللي هو
+
+380
+00:37:35,100 --> 00:37:41,980
+عناصر الأقطار الثانوية التلاتة يبقى حاصل ضرب عناصر
+
+381
+00:37:41,980 --> 00:37:51,580
+الأقطار الرئيسية التلاتة يبقى A11a22 a33 زائد هي
+
+382
+00:37:51,580 --> 00:38:00,260
+القطر الأول زائد اللي بعده a12 a23
+
+383
+00:38:00,260 --> 00:38:15,240
+a23 a31 a31 زائد القطر التالت الرئيسي a13 في a21
+
+384
+00:38:15,960 --> 00:38:23,060
+A32 هاي جبنا حاصل ضرب عناصر الأقطار الرئيسية
+
+385
+00:38:23,060 --> 00:38:29,820
+الثلاثة ناقص حاصل ضرب الأقطار الثانوية الثلاثة
+
+386
+00:38:37,220 --> 00:38:56,280
+ناقص a11 a23 a32 ناقص a12 a21 a33 يبقى
+
+387
+00:38:56,280 --> 00:39:03,100
+هذا كله اجمع واطرح بنحصل عالميا على قيمة هذا
+
+388
+00:39:03,100 --> 00:39:06,380
+المحدد الثلاثين
+
+389
+00:39:08,150 --> 00:39:12,570
+طبعا هذا الطريقة ما علموكوش إياها في الثانوية لكن
+
+390
+00:39:12,570 --> 00:39:19,630
+علموكوا أنه يمكن فك المحدد باستخدام عناصر أي صف أو
+
+391
+00:39:19,630 --> 00:39:27,150
+عناصر أي عمود تمام يبقى الطريقة الثانية نفس المحدد
+
+392
+00:39:27,150 --> 00:39:33,430
+بدي determinant ل a يبقى هذا الكلام بدي أساوي
+
+393
+00:39:33,430 --> 00:39:50,640
+المحددA11,A12,A13,A21,A22,A23,A31,A32,A32,A33
+
+394
+00:39:54,240 --> 00:39:59,660
+يبقى يا بنات بدنا نفكه باستخدام عناصر أي صف أو أي
+
+395
+00:39:59,660 --> 00:40:04,620
+عمول كله بيعطيني نفس النتيجة كيف؟ باجي بقول افترض
+
+396
+00:40:04,620 --> 00:40:09,640
+بدي افكه باستخدام عناصر الصف الأول يبقى باجي بقول
+
+397
+00:40:09,640 --> 00:40:17,860
+العمصر a11 في المحدد الأصغر المناظر له أو بنسميه
+
+398
+00:40:17,860 --> 00:40:24,250
+المحدد تبعهما هو المحادثة التابعة له؟ اوشط بصفه
+
+399
+00:40:24,250 --> 00:40:29,750
+عموده بظهر مين؟ بظهر هذا المحادثة الأصغر المناظرة
+
+400
+00:40:29,750 --> 00:40:40,710
+اللي هو A22و a23 و a32 و a33 هذا بالزاد العنصر
+
+401
+00:40:40,710 --> 00:40:47,150
+اللي بعده هناخده بإشارة ناقص a12 في المحدد الأصغر
+
+402
+00:40:47,150 --> 00:40:57,360
+مناظره بعد ما تشتط بصفه و عموده بيظل a21 a23E3 1
+
+403
+00:40:57,360 --> 00:41:04,440
+E3 3 يبقى جينا على هذا العدد شطبنا صف و عموده يبقى
+
+404
+00:41:04,440 --> 00:41:11,640
+E2 1 E2 3 E3 1 E3 3 الناقص اللي بعدها بتيجي يزايد
+
+405
+00:41:11,640 --> 00:41:17,540
+العمصر اللي بعده هو E1 3 في المحدد الأصغر المناظر
+
+406
+00:41:17,540 --> 00:41:27,220
+له تشط بصفه و عموده يبقى E2 1 E2 2إيه تلاتة واحد؟
+
+407
+00:41:27,220 --> 00:41:33,120
+إيه تلاتة اثنين؟ أظن أن هذا بنعرف نفكه الرئيس
+
+408
+00:41:33,120 --> 00:41:37,540
+يناقص الثاني و الرئيس يناقص الثاني و الرئيس يناقص
+
+409
+00:41:37,540 --> 00:41:42,000
+الثاني و هكذا طيب مناد فيه أن قاعدة اسم قاعدة
+
+410
+00:41:42,000 --> 00:41:46,220
+الإشارات بدي أذكر بها تذكير قاعدة الإشارات بقيت
+
+411
+00:41:46,220 --> 00:41:51,440
+للمحدد الثلاثيةبأجي بقولها يا محب نبدأ من ينقب
+
+412
+00:41:51,440 --> 00:41:58,720
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+413
+00:41:58,720 --> 00:42:02,000
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+414
+00:42:02,000 --> 00:42:02,000
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+415
+00:42:02,000 --> 00:42:03,400
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+416
+00:42:03,400 --> 00:42:07,080
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+417
+00:42:07,080 --> 00:42:11,540
+زائد، ناقص، زائد، ناقص، زائد، ناقبدي اقول ناقص
+
+418
+00:42:11,540 --> 00:42:17,060
+زائد ناقص يعني بدي اقول ناقص اتنين واحد في محدده
+
+419
+00:42:17,060 --> 00:42:21,580
+زائد اتنين اتنين في محدده ناقص اتنين تلاتة في
+
+420
+00:42:21,580 --> 00:42:27,600
+محدده وهكذا يبقى هي عندك طريقتين لمين اللي فك هذا
+
+421
+00:42:27,600 --> 00:42:33,500
+المحدد نعطيكي مثال عمليا على ذلك example
+
+422
+00:42:39,490 --> 00:42:54,350
+Find the value of Determinant
+
+423
+00:42:54,350 --> 00:43:00,690
+للإيه بده يشاهد يلّا من هذه الشيء تعطيني أي محدد
+
+424
+00:43:00,690 --> 00:43:07,820
+ثلاثي يلّا قوليأه أه حط Zero وحط سالب وحط موجة
+
+425
+00:43:07,820 --> 00:43:15,320
+فقول أه تلاتة تلاتة اتنين اتنين Zero واحد ناقص
+
+426
+00:43:15,320 --> 00:43:23,700
+اتنين خمسة أيوة كام لأي حاجة سالب تلاتة Zero Zero
+
+427
+00:43:23,700 --> 00:43:28,180
+اتنين اتنينيبقى هذا محدد، نريد أن نعرف قيمة هذا
+
+428
+00:43:28,180 --> 00:43:32,660
+المحدد. يبقى أنا عندي طريقتين، بدي أجرب الطريقة
+
+429
+00:43:32,660 --> 00:43:35,100
+اللي أحنا مش متعودين عليه و اللي أنتم متعودين
+
+430
+00:43:35,100 --> 00:43:37,760
+عليه، تحسبواها لحالكم، تطلع نفس النتيجة و لك
+
+431
+00:43:37,760 --> 00:43:44,420
+الجواب.يبقى باجي بقوله determinant للإيه بدو يسوي
+
+432
+00:43:44,420 --> 00:43:48,720
+هبدوش اكتب المحدد بده اكتب العناصر دغري اللي هي
+
+433
+00:43:48,720 --> 00:43:55,580
+مين هاي تلاتة اتنين زيرو واحد ناقص اتنين خمسة ناقص
+
+434
+00:43:55,580 --> 00:43:59,540
+تلاتة زيرو اتنين بده اعيد العمود الأول والعمود
+
+435
+00:43:59,540 --> 00:44:06,890
+الثاني يبقى العمود الأول اللي هو تلاتةوأحد سالب
+
+436
+00:44:06,890 --> 00:44:12,850
+تلاتة العمودي التاني اتنين سالب اتنين زيرو هذا يا
+
+437
+00:44:12,850 --> 00:44:16,890
+بنات هو القطر الرئيسي الأول و هذا القطر الرئيسي
+
+438
+00:44:16,890 --> 00:44:20,930
+الثاني و هذا القطر الرئيسي الثالث يبقى بالداج
+
+439
+00:44:20,930 --> 00:44:27,590
+يقولوا حاصل ضربهم تلاتةفي سالب اتنين في اتنين زائد
+
+440
+00:44:27,590 --> 00:44:35,390
+اتنين في خمسة في سالب تلاتة زائد Zero في واحد في
+
+441
+00:44:35,390 --> 00:44:42,590
+Zero خلصنا الرئيسي ناقص الثانوي يبقى هذا الثانوي
+
+442
+00:44:42,590 --> 00:44:51,760
+Zeroفي سالب اتنين في سالب تلاتة ناقص هاي نجينا
+
+443
+00:44:51,760 --> 00:44:56,960
+اللي بعده تلاتة في خمسة في زيرو يبقى تلاتة في خمسة
+
+444
+00:44:56,960 --> 00:45:03,140
+في زيرو هذا اللي بعده اتنين واحد اتنين ناقص اتنين
+
+445
+00:45:03,140 --> 00:45:09,200
+في واحد في اتنين يبقى هذا الكلام بده يساوي ناقص
+
+446
+00:45:09,200 --> 00:45:16,860
+اتناشروهنا عشرة في ناقص تلاتة بناقص تلاتين واللي
+
+447
+00:45:16,860 --> 00:45:23,640
+بعده ب zero واللي بعده ب zero واللي بعده كمان ب
+
+448
+00:45:23,640 --> 00:45:31,400
+zero واللي بعده بناقص أربعة تمام يبقى المحدد سالب
+
+449
+00:45:31,400 --> 00:45:37,800
+اتنين واربعين وسالب أربعة يبقى سالب ستة واربعين
+
+450
+00:45:37,800 --> 00:45:43,630
+تماملو روحت تفك بالطريقة التانية بيقول جواب قداش
+
+451
+00:45:44,330 --> 00:45:50,710
+يبقى good exercise لك هذا السؤال وهذه الإجابة يلا
+
+452
+00:45:50,710 --> 00:45:55,590
+وشوف إنها الطريقة التانية بطلع 46 ولا لا يبقى
+
+453
+00:45:55,590 --> 00:46:00,630
+shake عليه للمحاضرة قبل أن تأكد فعلا إن أنت حسبتي
+
+454
+00:46:00,630 --> 00:46:08,730
+وطلع الناتج يساوي اللي هو 46 وسنكمل إن شاء الله في
+
+455
+00:46:08,730 --> 00:46:10,690
+بعض الظهر إن شاء الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..120457340de4bc632e8f46f5df75e71adaa79b1c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_postprocess.srt
@@ -0,0 +1,1756 @@
+1
+00:00:20,940 --> 00:00:25,680
+بسم الله الرحمن الرحيم نرجع الآن لل section
+
+2
+00:00:25,680 --> 00:00:30,820
+ابتدناه المرة الماضية وهو اول section من chapter 4
+
+3
+00:00:30,820 --> 00:00:36,040
+لاتحدث عن نقطتين فقط النقطة الأولى هي ال
+
+4
+00:00:36,040 --> 00:00:40,380
+eigenvalues والنقطة الثانية هي ال eigenvectors
+
+5
+00:00:40,380 --> 00:00:47,140
+وقولنا لو عندي matrix A تجب مصفوفة مربعة نضام n في
+
+6
+00:00:47,140 --> 00:00:51,040
+n اتنين في اتنينتلاتة في تلاتة اربعة في اربعة معنا
+
+7
+00:00:51,040 --> 00:00:58,040
+مشكلة يبقى باجي بقول المعادلة ل A X يساوي لاندا X
+
+8
+00:00:58,040 --> 00:01:02,420
+يعني اذا جدرنا نضرب المصفوفة A في المصفوفة X
+
+9
+00:01:02,420 --> 00:01:08,500
+لمصفوفة مجاهيل اعطاني لاندا وهو رقم real number او
+
+10
+00:01:08,500 --> 00:01:12,700
+complex number اعطاني لاندا X يبقى لاندا في هذه
+
+11
+00:01:12,700 --> 00:01:18,570
+الحالة بسميها هنا بسميها ال eigen valueالـ vector
+
+12
+00:01:18,570 --> 00:01:24,450
+x الذي يحقق هذه المعادلة بشرط أن لا يكون zero
+
+13
+00:01:24,450 --> 00:01:29,470
+vector بسميه الـ eigen vector واخدنا المرة الماضية
+
+14
+00:01:29,470 --> 00:01:33,450
+على ذلك مثال واحدة وهذا المثال طلعت أن ال land
+
+15
+00:01:33,450 --> 00:01:38,950
+مالها real number تمام؟ لما نأتي ناخد مثال رقم
+
+16
+00:01:38,950 --> 00:01:43,280
+اتنين ونشوف هل ال land هي complexوالله real وإذا
+
+17
+00:01:43,280 --> 00:01:46,660
+طلعت cumless كيف بدنا نشتغل في هذا الموضوع هل زي
+
+18
+00:01:46,660 --> 00:01:51,340
+ال real و الله بيختلف عنه تمام يبقى بنيجي لمثال
+
+19
+00:01:51,340 --> 00:01:54,920
+اتنين بيقول find the eigenvalues and eigenvectors
+
+20
+00:01:54,920 --> 00:01:59,680
+of the matrix A سالب واحد واتنين سالب واحد وواحد
+
+21
+00:01:59,680 --> 00:02:04,180
+يبقى احنا بدنا نروح للمعادلة اللي هو ابتدينا فيها
+
+22
+00:02:04,180 --> 00:02:10,350
+المرة الماضية وهي المعادلة lambda I ناقص Aطبعا
+
+23
+00:02:10,350 --> 00:02:16,130
+يبقى هذا الكلام بدها تساوي لاندا اي اللي هي الرقم
+
+24
+00:02:16,130 --> 00:02:20,590
+ال real او ال complex لاندا مضروب في مصوفة الوحدة
+
+25
+00:02:20,590 --> 00:02:27,390
+يبقى هذا عبارة عن لاندا زيرو زيرو لاندا ناقص
+
+26
+00:02:27,390 --> 00:02:33,230
+المصوفة ايه زي ما هي قدامنا هناك بالشكل اللي عندنا
+
+27
+00:02:33,230 --> 00:02:37,430
+هذا طيب هذا النتج بده يساوي بده يساوي المصوفة
+
+28
+00:02:37,430 --> 00:02:43,600
+التاليةلاندا ناقص ناقص واحد يبقى باللاندا ا زايد
+
+29
+00:02:43,600 --> 00:02:49,780
+واحد زيرو ناقص اتنين بناقص اتنين زيرو ناقص ناقص
+
+30
+00:02:49,780 --> 00:02:55,820
+واحد بواحد لاندا ناقص واحد باللاندا ناقص واحد
+
+31
+00:02:55,820 --> 00:03:00,340
+بالشكل اللي عندنا هذا بعد هيك بنروح ناخد ال
+
+32
+00:03:00,340 --> 00:03:06,020
+determinant لهذه المعادلة لو نسوي بالزيرو يبقى
+
+33
+00:03:06,020 --> 00:03:13,160
+باجي بقول ال determinantالمين للاندا اي ناقص ال a
+
+34
+00:03:13,160 --> 00:03:19,460
+بدل سوى المحدد لاندا plus one minus two one لاندا
+
+35
+00:03:19,460 --> 00:03:26,340
+minus one بدل نفك المحدد هذا حاصل ضرب عناصر القطر
+
+36
+00:03:26,340 --> 00:03:35,060
+الرئيسيناقص حاصل ضرب عناصر القطر الثانوي هذه لو
+
+37
+00:03:35,060 --> 00:03:39,920
+جيت فاكدت بتعطيني لاندا تربية ناقص واحد ليه؟ لأن
+
+38
+00:03:39,920 --> 00:03:44,640
+تحليل فرق بين المربعين رجعتها إلى أصلها قبل
+
+39
+00:03:44,640 --> 00:03:50,380
+التحليل زائد اتنين يبقى تساوي لاندا تربية زائد
+
+40
+00:03:50,380 --> 00:03:55,750
+واحد اللي بتروح أسويها من؟ بالزيرويبقى بناء عليه
+
+41
+00:03:55,750 --> 00:04:02,970
+بصير لاندا تربيع يسوى قدر؟ سالب واحد هل يُعقل إن
+
+42
+00:04:02,970 --> 00:04:07,770
+مجموعة كمية مربع يعطيني قيمة سالبة؟ إذا هذه لا
+
+43
+00:04:07,770 --> 00:04:13,690
+يمكن أن تكون real number وإنما complex number يبقى
+
+44
+00:04:13,690 --> 00:04:20,190
+هذا معناه إن لاندا تسوى الجدر التربيع إلى مين؟
+
+45
+00:04:20,190 --> 00:04:24,950
+لسالب واحدالجدر التربية إلى سالب واحد اللي هو زائد
+
+46
+00:04:24,950 --> 00:04:30,930
+او ناقص I حيث I اللي هو الجدر التربية إلى سالب
+
+47
+00:04:30,930 --> 00:04:37,350
+واحد I الحرف الأول من كلمة imaginary تخيّلي يبقى
+
+48
+00:04:37,350 --> 00:04:42,190
+قيمة لاندا يا اما واحد يا اما سالب واحد ودائما
+
+49
+00:04:42,190 --> 00:04:47,040
+وابدا بيطلع عندى حلين تخيليينبتلاقيهم اتنين مالهم
+
+50
+00:04:47,040 --> 00:04:54,040
+مترافقين يعني العدد التخيلي دائما هو بقول a زائد
+
+51
+00:04:54,040 --> 00:04:59,780
+bi حيث ال i له الجذر الترميه لسالب واحد الحل
+
+52
+00:04:59,780 --> 00:05:06,180
+التاني بكون a ناقص bi السالب للجزء التخيلي وليس
+
+53
+00:05:06,180 --> 00:05:13,060
+للجزء الحقيقيطبعا في سؤالنا هذا بي بي زيرو بيضل ا
+
+54
+00:05:13,060 --> 00:05:16,700
+ا بي زيرو بيضلش عندنا إلا مين إلا بي لي زيد أو
+
+55
+00:05:16,700 --> 00:05:23,280
+ناقص واحد في اي يبقى صار عندى قيمتين للامدة وكل
+
+56
+00:05:23,280 --> 00:05:29,260
+واحدة فيهم عبارة عن قيمة تخيلية يبقى الآن بدى أبدأ
+
+57
+00:05:29,260 --> 00:05:34,700
+أروح أدور على مين على ال eigenvectors فبنقول ما
+
+58
+00:05:34,700 --> 00:05:39,070
+ياتىأحنا الآن طلعنا الـ eigen values اللي لاندا
+
+59
+00:05:39,070 --> 00:05:42,650
+بزايد أو ناقص I و بنروح ندور على مين على ال eigen
+
+60
+00:05:42,650 --> 00:05:46,290
+vectors فبرجع للمعادلة الأصلية اللي عندي هي لاندا
+
+61
+00:05:46,290 --> 00:05:49,970
+I ناقص A فكس بده ساوي مين بده ساوي Zero اللي من
+
+62
+00:05:49,970 --> 00:05:54,770
+خلالها بدنا نجيب مين ال eigen vectors يبقى بده
+
+63
+00:05:54,770 --> 00:06:00,390
+أروح أصيغ هذه صياغة عملية لاندا I ناقص A هي جاهزة
+
+64
+00:06:00,390 --> 00:06:05,160
+عندي صح؟يبقى انا بدى احطها كما هي يبقى هذا بدى
+
+65
+00:06:05,160 --> 00:06:12,440
+يعطينا lambda plus one ناقص اتنين واحد lambda ناقص
+
+66
+00:06:12,440 --> 00:06:19,700
+واحد في x لي x واحد و x اتنين بدى يساوي مين؟ Zero
+
+67
+00:06:19,700 --> 00:06:25,970
+و Zeroالان بدنا ناخد النقطة الأولى لو كانت ال land
+
+68
+00:06:25,970 --> 00:06:31,590
+هذه تساوي I ايش اللي بد يحصل في هذه المعادلة اذا
+
+69
+00:06:31,590 --> 00:06:36,490
+بد اشيل كل land او احط مكانها مين I زي ما عملنا
+
+70
+00:06:36,490 --> 00:06:40,570
+المرة اللي فاتت في حالة ال real لما ال land كانت
+
+71
+00:06:40,570 --> 00:06:48,860
+real numberيبقى بناء عليه ستصبح هذه كتالة I plus
+
+72
+00:06:48,860 --> 00:06:57,300
+one سالب اتنين واحد I minus one I minus one في X
+
+73
+00:06:57,300 --> 00:07:04,710
+واحد X اتنين كله بده يساوي من؟ Zero و Zeroبنروح
+
+74
+00:07:04,710 --> 00:07:08,830
+اضرب المصفتين الاتنين هدول في بعض يبقى لو ضربت
+
+75
+00:07:08,830 --> 00:07:12,410
+المصفتين هدول بيصير الصف الأول في العمود الأول
+
+76
+00:07:12,410 --> 00:07:20,490
+يبقى I plus one في main في X one ناقص اتنين X two
+
+77
+00:07:20,490 --> 00:07:28,290
+صف الثاني في العمود الأول يبقى X one زائداللي هو I
+
+78
+00:07:28,290 --> 00:07:34,970
+minus ال 1 في ال X2 كله بده يساوي من؟ Zero و Zero
+
+79
+00:07:34,970 --> 00:07:40,870
+من هذا الكلام بده اطلع بالمعادلتين التاليتين ل I
+
+80
+00:07:40,870 --> 00:07:46,730
+زائد واحد في X واحد ناقص اتنين X اتنين يساوي Zero
+
+81
+00:07:46,730 --> 00:07:53,350
+المعادلة التانية X واحد زائد I ناقص واحد
+
+82
+00:08:00,610 --> 00:08:05,190
+شرايك المعادلات ان هذول زي بعض مختلفات تماما
+
+83
+00:08:10,930 --> 00:08:16,310
+بختلف عن بعض شكلا لكن في الحقيقة الاتنين are the
+
+84
+00:08:16,310 --> 00:08:21,190
+same كيف are the same يعني لو جيت ضربت المعادلة
+
+85
+00:08:21,190 --> 00:08:26,190
+هذه في مقدار ثابت و طلعت اللي فوق مش التان تان
+
+86
+00:08:26,190 --> 00:08:30,390
+بيكونوا نفس الشيء يبقى هدول اتنين نفس الشيء تعالى
+
+87
+00:08:30,390 --> 00:08:34,590
+نضرب المعادلة التانية في I plus one و نشوف تطلع
+
+88
+00:08:34,590 --> 00:08:39,290
+المعادلة اللي فوق ولا لأ يبقى هنا فاجب اقوله ما
+
+89
+00:08:39,290 --> 00:08:39,970
+يأتي
+
+90
+00:08:50,090 --> 00:08:54,790
+يبقى دول اتنين نفس الشيء ليش؟
+
+91
+00:08:55,660 --> 00:08:59,840
+بدا اجعل معادلة ثانية واضربها في I زائد واحد يبقى
+
+92
+00:08:59,840 --> 00:09:09,120
+I زائد واحد في X واحد زائد I زائد واحد في I ناقص
+
+93
+00:09:09,120 --> 00:09:15,460
+واحد في X اتنين بده يساوي Zero هذه بده تعطينا I
+
+94
+00:09:15,460 --> 00:09:24,300
+plus one في X oneهذا الفرق بين المربعين يبقى كذلك
+
+95
+00:09:24,300 --> 00:09:32,460
+بالصير زائد I تربيع ناقص واحد في ال X اتنين بده
+
+96
+00:09:32,460 --> 00:09:40,000
+يساوي Zero هذا بده يعطينا I زائد واحد في ال X واحد
+
+97
+00:09:40,000 --> 00:09:46,930
+قداش ال I تربيع يا بنات من هنا لو ربعت الطرفينسالب
+
+98
+00:09:46,930 --> 00:09:54,970
+واحد ستصبح سالب اتنين يبقى هذه I تربية عندى من هنا
+
+99
+00:09:54,970 --> 00:09:59,950
+بسالب واحد سالب واحد و سالب واحد بسالب اتنين يبقى
+
+100
+00:09:59,950 --> 00:10:05,250
+هذه سالب اتنين X اتنين تساوي Zero أليست هي
+
+101
+00:10:05,250 --> 00:10:10,690
+المعادلة الأولى؟يبقى دول معادلة شكل مش زي بعض لكن
+
+102
+00:10:10,690 --> 00:10:15,810
+في الحقيقة لما انضربت في العدد اللي عنده I plus
+
+103
+00:10:15,810 --> 00:10:20,150
+one طلعت نفس المعادلة الثانية كويس يبقى دول مش
+
+104
+00:10:20,150 --> 00:10:25,100
+معادلة وانما في الحقيقةمعادلة واحدة مافيش غيرها
+
+105
+00:10:25,100 --> 00:10:30,220
+طيب هذه المعادلة الواحدة بقدر اجيب منها x واحد
+
+106
+00:10:30,220 --> 00:10:35,680
+بدلالة x اتنين او x اتنين بدلالة اتنين بدلالة x
+
+107
+00:10:35,680 --> 00:10:40,960
+واحد يبقى بناء عليه هذه صارت معادلة واحدة يبقى
+
+108
+00:10:40,960 --> 00:10:45,100
+سواء قلت المعادلة الأولى والله المعادلة الثانية
+
+109
+00:10:45,100 --> 00:10:50,780
+الاتنين are the sameفبناء عليه لو روحت مشان ماخليش
+
+110
+00:10:50,780 --> 00:10:54,540
+عندي كسور بدل ما اخد المعادلة الأولى بدي اخد
+
+111
+00:10:54,540 --> 00:11:01,220
+المعادلة الثانية لو اخدنا المعادلة الثانية يبقى x
+
+112
+00:11:01,220 --> 00:11:10,340
+واحد تساوي اللي هو مين؟يبقى هذه المعادلة
+
+113
+00:11:10,340 --> 00:11:16,040
+الآن بناء على الكلام اللي قلته تكفي المعادلة X1
+
+114
+00:11:16,040 --> 00:11:23,580
+زائد I ناقص واحد في X2 بيساوي Zero او ان شئتم
+
+115
+00:11:23,580 --> 00:11:32,560
+فقولوا ان X1 يساوي ناقص I ناقص واحد في X2 بهذا
+
+116
+00:11:32,560 --> 00:11:41,130
+الشكلأو يساوي واحد ناقص I في من في ال X2 يبقى بناء
+
+117
+00:11:41,130 --> 00:11:50,670
+عليه لو كان ال X2 يساوي A مثلا then ال X1 بيساوي
+
+118
+00:11:50,670 --> 00:11:59,370
+واحد ناقص I في ال Aيبقى جبت من قيمة كل من x1 و x2
+
+119
+00:11:59,370 --> 00:12:07,330
+بواسطة ال number الهمان a a0 a1 a2 ما بعرف المهم a
+
+120
+00:12:07,330 --> 00:12:12,910
+any real number ماحطيتش عليه قيود يبقى بناء عليه
+
+121
+00:12:12,910 --> 00:12:27,010
+so the eigen vectors are in the formهذا اكس واحد
+
+122
+00:12:27,010 --> 00:12:32,130
+وهذا اكس اتنين بده يساوي اكس واحد كده اش قولنا
+
+123
+00:12:32,130 --> 00:12:39,470
+واحد ناقص I في ال A اكس اتنين اللي هي بمين ب A لو
+
+124
+00:12:39,470 --> 00:12:45,770
+أخدت ال A عامل مشترك يبقى بصير عندي واحد ناقص I
+
+125
+00:12:45,770 --> 00:12:53,080
+واحد ناقص I وهنا واحديبقى هذا ال call vector اللي
+
+126
+00:12:53,080 --> 00:12:59,680
+هو يعتبر من ال eigen vector طيب هذا واحد ولا اتنين
+
+127
+00:12:59,680 --> 00:13:03,460
+ولا تلاتة ولا عشرة ولا مية؟ كدهش؟
+
+128
+00:13:05,220 --> 00:13:10,280
+infinite number of eigenvectors يبقى هذا عدد
+
+129
+00:13:10,280 --> 00:13:15,560
+لانهائي من 100 من ال eigenvectors اللي عندنا ليش
+
+130
+00:13:15,560 --> 00:13:18,800
+هو السؤال قال هات ال eigenvalues و ال eigenvectors
+
+131
+00:13:18,800 --> 00:13:23,960
+يعني ال eigenvectors بتبقى في الشكل هذا هذا ال
+
+132
+00:13:23,960 --> 00:13:30,560
+eigenvectors المناظرة لمين المناظرة للامدة تساوي I
+
+133
+00:13:31,040 --> 00:13:36,040
+لسة كمان في Eigen vectors أخرى مناظرة لـ lambda
+
+134
+00:13:36,040 --> 00:13:41,840
+تساوي من يعني احنا كأنه بدنا نبدأ مسألة جديدة زي
+
+135
+00:13:41,840 --> 00:13:47,300
+المسألة هذه بالضبط تماما وقت اش لما lambda تساوي I
+
+136
+00:13:47,300 --> 00:13:53,720
+بدنا نروح نجيب ال Eigen vectors المناظرة لها بدنا
+
+137
+00:13:53,720 --> 00:13:58,560
+نيجي الآن if lambda تساوي ناقص I
+
+138
+00:14:01,230 --> 00:14:06,010
+بدي اعيد هذا الكلام من جديد بدي احط مباشرة دغري
+
+139
+00:14:06,010 --> 00:14:09,810
+يعني بدي اكتب هذا و لسه اعيد لا بدي احط لاندا دغري
+
+140
+00:14:09,810 --> 00:14:17,530
+لاندا بناقص I يبقى بصير عندنا هنا ناقص I زائد واحد
+
+141
+00:14:17,530 --> 00:14:25,290
+و هنا ناقص اتنين و هنا واحد و هنا ناقص I ناقص واحد
+
+142
+00:14:25,290 --> 00:14:34,940
+كله في X واحد X اتنين بدي ساويZero و Zeroبنفك
+
+143
+00:14:34,940 --> 00:14:40,620
+المعادلة هذه امانات يبقى هذه واحد ناقص I في من في
+
+144
+00:14:40,620 --> 00:14:46,840
+ال X واحد ناقص اتنين X اتنين بده يساوي Zero صف
+
+145
+00:14:46,840 --> 00:14:52,420
+الأول في العمول الأول بعدها X واحد كمان وهذه
+
+146
+00:14:52,420 --> 00:14:59,160
+يخليها ناقص يبقى ناقص I زائد واحد في ال X اتنين
+
+147
+00:14:59,160 --> 00:15:08,220
+بده يساوي من بده يساوي Zeroمعادلتين شكلا مختلفات
+
+148
+00:15:08,220 --> 00:15:14,340
+عن بعض تماما لكن انا بعتقد ان الاتنين نفس الشيء
+
+149
+00:15:17,140 --> 00:15:21,360
+بدي أضرب هنا في مين؟ واحد ناقص I يبقى بيصير واحد
+
+150
+00:15:21,360 --> 00:15:27,000
+ناقص I في I واحد هيو بدي أجينا هنا واحد ناقص I
+
+151
+00:15:27,000 --> 00:15:33,020
+وعندي ناقص بيصير I ناقص واحد صح؟ وبيطير السالي بعد
+
+152
+00:15:33,020 --> 00:15:36,560
+راحة ويصير I ناقص واحد في I زايد واحد اللي هو
+
+153
+00:15:36,560 --> 00:15:41,640
+الفرق بين المربعين يعني I تربية ناقص واحد طب I
+
+154
+00:15:41,640 --> 00:15:45,580
+تربية بناقص واحد وناقص واحد يبقى بناقص اتنين هي
+
+155
+00:15:46,030 --> 00:15:51,810
+يبقى هدول اتنين كمان نفس الشيء يبقى بعدي بقوله
+
+156
+00:15:51,810 --> 00:16:01,840
+these two equations are the sameيبقى هدول التنتين
+
+157
+00:16:01,840 --> 00:16:09,620
+نفس الشيء يبقى هذا معناه ان ال X واحد بدها تساوي I
+
+158
+00:16:09,620 --> 00:16:15,200
+زائد واحد في مين في ال X اتنين يبقى باجي بقوله لو
+
+159
+00:16:15,200 --> 00:16:24,940
+كانتالـ X2 بده يساوي ايه ثم X1 بده يساوي I زائد
+
+160
+00:16:24,940 --> 00:16:31,280
+واحد في مين في ايه يبقى هنا الشهر The Eigen
+
+161
+00:16:31,280 --> 00:16:37,360
+vectors Corresponding
+
+162
+00:16:44,790 --> 00:16:56,630
+cross bonding to the land يساوي السلب I are in the
+
+163
+00:16:56,630 --> 00:17:05,670
+formيبقى في الشكل التالي اللي هو X1 X2 بده يساوي
+
+164
+00:17:05,670 --> 00:17:14,630
+الآن ال X1 طلعت هنا ب I زائد واحد في ال A و X2 A ب
+
+165
+00:17:14,630 --> 00:17:22,210
+A اللي بقدر اقول A في I plus one وهنا واحد بالشكل
+
+166
+00:17:22,210 --> 00:17:23,390
+اللي عندنا هذا
+
+167
+00:17:29,220 --> 00:17:35,390
+نذهب الآن لمثال آخريبقى هذا مثال عمل يابانات على
+
+168
+00:17:35,390 --> 00:17:39,930
+ال eigenvectors اللي هو ممكن يطلعوا complex
+
+169
+00:17:39,930 --> 00:17:44,290
+numbers إذا أخدنا الآن مثالين مثال المرة الماضية
+
+170
+00:17:44,290 --> 00:17:49,030
+ومثال هذه المرة المثال الماضي كانت land a real
+
+171
+00:17:49,030 --> 00:17:53,830
+numbers والمرة هذه land كانت complex numbers لكن
+
+172
+00:17:53,830 --> 00:17:57,850
+كلا المثالين كانوا عندها مصوفة مربع نظام هاتنين في
+
+173
+00:17:57,850 --> 00:18:03,910
+اتنين أو مصوفة من الدرجة الثانيةنأخد مثال ثالث بس
+
+174
+00:18:03,910 --> 00:18:13,690
+نخل المصوفة من الدرجة الثالثة يبقى example 3 سؤال
+
+175
+00:18:13,690 --> 00:18:24,120
+عشرة من الكتاب بيقول خدلي المصوفة إيه تساوي؟1 2 3
+
+176
+00:18:24,120 --> 00:18:39,820
+-1 4 3 1-2-1 المطلوب الأول لمرة A find the
+
+177
+00:18:39,820 --> 00:18:46,020
+eigenvalues of
+
+178
+00:18:46,020 --> 00:19:00,800
+the matrix Aنمر بي find the eigen vectors of the
+
+179
+00:19:00,800 --> 00:19:14,420
+matrix A نمر سي بيقول find a basis for
+
+180
+00:19:14,420 --> 00:19:15,340
+the corresponding
+
+181
+00:19:29,990 --> 00:19:36,470
+Eigenspace of the
+
+182
+00:19:36,470 --> 00:19:40,070
+eigenvectors
+
+183
+00:19:40,070 --> 00:19:44,090
+يعني
+
+184
+00:19:44,090 --> 00:19:49,010
+لو قلناإن الـ eigenvectors كوّنولي vector space
+
+185
+00:19:49,010 --> 00:19:54,290
+بدي أعرف قداش ال basis لل vector space عظيم شافة
+
+186
+00:19:54,290 --> 00:19:59,610
+يا بنات لو جيت للحالة الأولى بنقدر نقول إن عندي
+
+187
+00:19:59,610 --> 00:20:03,960
+basis لل vector space الأول مين هوالو ال vector
+
+188
+00:20:03,960 --> 00:20:09,080
+واحد ناقص I وهنا واحد وبالتالي طبعا هذا linearly
+
+189
+00:20:09,080 --> 00:20:13,960
+independent لانه لحاله مافيش غيره مستقل تمام غير
+
+190
+00:20:13,960 --> 00:20:18,980
+ثابع لأي أحد يبقى بناء انا عليه بقول في هذه الحالة
+
+191
+00:20:18,980 --> 00:20:24,160
+ال basis في element واحد وبالتالي ال dimension إيه
+
+192
+00:20:24,160 --> 00:20:31,040
+جداش؟تمام في الحالة التانية نفس القصة ال basis هو
+
+193
+00:20:31,040 --> 00:20:34,180
+عبارة عن ال vector اللي عندنا هذا وبالتالي ال
+
+194
+00:20:34,180 --> 00:20:38,720
+dimension له يسوى جداش يسوى واحد صحيح طيب ماعلينا
+
+195
+00:20:38,720 --> 00:20:42,620
+نيجي للسؤال اللي عندنا عشان اجيب ال eigen value و
+
+196
+00:20:42,620 --> 00:20:46,740
+ال eigen vector بدي مباشرة اروح على النقطة الأولى
+
+197
+00:20:46,740 --> 00:20:52,420
+وهي حساب المصوفة lambda I ناقص ال A يبقى باجي
+
+198
+00:20:52,420 --> 00:21:00,760
+بقوله solutionبتدرج لاندا اي ناقص ال a وتساوي
+
+199
+00:21:00,760 --> 00:21:09,980
+لاندا اي اللي هي لاندا زيرو زيرو لاندا زيرو زيرو
+
+200
+00:21:09,980 --> 00:21:16,240
+لاندا اي لاندا اي ناقص المصفوفة a بده نزلها كما هي
+
+201
+00:21:16,240 --> 00:21:23,690
+واحد اتنين تلاتةنقص واحد اربعة تلاتة واحد ناقص
+
+202
+00:21:23,690 --> 00:21:30,930
+اتنين ناقص واحد ويساوي المصوف التالي لاندا ناقص
+
+203
+00:21:30,930 --> 00:21:37,610
+واحد ناقص اتنين ناقص تلاتة اللي بعدها ناقص ناقص
+
+204
+00:21:37,610 --> 00:21:43,850
+واحد اللي هي ابواحد بعدها لاندا ناقص اربعةبعدها
+
+205
+00:21:43,850 --> 00:21:50,290
+Zero ناقص ثلاثة يبقى بناقص ثلاثة اللي بعدها ناقص
+
+206
+00:21:50,290 --> 00:21:56,230
+واحد وهنا اتنين وهنا Lambda زائد واحد بالشكل اللي
+
+207
+00:21:56,230 --> 00:21:57,270
+عندنا هنا
+
+208
+00:22:14,290 --> 00:22:22,450
+طيب نحسب قيمة لاندا عن طريق المعادلة اللى عندنا
+
+209
+00:22:22,450 --> 00:22:29,190
+هذه يبقى بدي اجي اخد ال determinant للاندا I ناقص
+
+210
+00:22:29,190 --> 00:22:36,040
+ال A يبقى هي المحددlanda plus one ناقص اتنين ناقص
+
+211
+00:22:36,040 --> 00:22:42,940
+تلاتة واحد landa ناقص اربعة و هنا ناقص تلاتة ناقص
+
+212
+00:22:42,940 --> 00:22:49,600
+واحد اتنين landa plus one بهذا الشكل يبقى بدي اروح
+
+213
+00:22:49,600 --> 00:22:54,460
+افكر المحدد هذا باستخدام عناصر الصفر
+
+214
+00:23:00,730 --> 00:23:07,390
+أول لندن ناقص واحد اه هذه لندن ناقص واحد صحيح هذه
+
+215
+00:23:07,390 --> 00:23:12,030
+لندن ناقص اه هي كتبناها لندن ناقص واحد يبقى هنا
+
+216
+00:23:12,030 --> 00:23:16,330
+واحد لندن ناقص اربعة ناقص ثلاث مية المية تمام يبقى
+
+217
+00:23:16,330 --> 00:23:21,610
+بدي افكر المحدد هذا باستخدام عناصر الصف الأول مثلا
+
+218
+00:23:21,610 --> 00:23:27,250
+يبقى هذا المحدد بده يساوي هاي لندن ناقص واحد
+
+219
+00:23:27,640 --> 00:23:31,900
+فاهمين؟ في المحدد الأصغر موضوع اللي قشط بالصف هذا
+
+220
+00:23:31,900 --> 00:23:37,660
+وهذا بيصير lambda minus four في lambda plus one
+
+221
+00:23:37,660 --> 00:23:43,980
+هذا الرئيسي ناقص مع ناقص بيصير زائد ستة هذا ال
+
+222
+00:23:43,980 --> 00:23:47,920
+term الأول ال term التاني حسب قاعدة الإشارات شرطه
+
+223
+00:23:47,920 --> 00:23:54,010
+سلب وهو سلب بيصير موجةوشطبي برضه الصف تبعه و
+
+224
+00:23:54,010 --> 00:24:02,110
+العمود بصير lambda زائد واحد ناقص تلاتة يبقى هنا
+
+225
+00:24:02,110 --> 00:24:07,550
+ناقص تلاتة اللي بعده حسب قادة الشرط الشرط موجبة
+
+226
+00:24:07,550 --> 00:24:14,110
+وهو سالب فبظل سالببنجي نشطة بصفه وعموده بصير اتنين
+
+227
+00:24:14,110 --> 00:24:22,350
+ناقص مع ناقص بصير زائد يبقى لندن ناقص اربعة بالشكل
+
+228
+00:24:22,350 --> 00:24:27,350
+هذا وهذا كله اللي هو بيساوي مين؟ بيساوي ال zero
+
+229
+00:24:27,350 --> 00:24:31,490
+يبقى ال determinant بده يساوي zero طيب تعالى نشوف
+
+230
+00:24:31,490 --> 00:24:36,950
+هذه اللي وين بدها توصلنا يبقى هذا الكلام لندن ناقص
+
+231
+00:24:36,950 --> 00:24:42,720
+واحدهذه المناطق بتدفكها يبقى لاندا تربيع عندك ناقص
+
+232
+00:24:42,720 --> 00:24:48,740
+أربع لاندا وزائد لاندا بيظل ناقص تلاتة لاندا وهنا
+
+233
+00:24:48,740 --> 00:24:57,560
+عندنا قداش ناقص أربعةوعندك هنا اللي هو زائد ستة
+
+234
+00:24:57,560 --> 00:25:03,500
+الشكل لأن هذا هو هذا زائد اتنين فلاندا ناقص اتنين
+
+235
+00:25:03,500 --> 00:25:08,540
+وانا ناقص تلاندا فلاندا ناقص اتنين كله بده يساوي
+
+236
+00:25:08,540 --> 00:25:14,330
+zeroيبقى فكّت التربيع هذا هايقوا قدامك بالكامل هذا
+
+237
+00:25:14,330 --> 00:25:18,310
+واحد و سالب تلاتة بسالب اتنين هنا اتنين و سالب
+
+238
+00:25:18,310 --> 00:25:24,090
+اربعة بسالب اتنين يبقى هذا الكلام بده يساوي اللي
+
+239
+00:25:24,090 --> 00:25:31,110
+هو مين لاندا ناقص واحد في لاندا تربيع ناقص تلاتة
+
+240
+00:25:31,110 --> 00:25:39,180
+لاندا زائد اتنين هذه مش هي هذه يا بناتهذا المقدار
+
+241
+00:25:39,180 --> 00:25:42,880
+مش هو نفس المقدار هذا لاندا ناقص اتنين يبقى هنا
+
+242
+00:25:42,880 --> 00:25:47,440
+اتنين وهنا سالب تلاتة بيظل القداش سالب لاندا ناقص
+
+243
+00:25:47,440 --> 00:25:54,720
+اتنين يبقى هذا سالب لاندا ناقص اتنين كل هذا الكلام
+
+244
+00:25:54,720 --> 00:25:57,720
+بيساوي مين؟ بيساوي زر
+
+245
+00:26:00,680 --> 00:26:06,980
+وصلت إلى الـ determinant لـ lambda I ناقص الـ A
+
+246
+00:26:06,980 --> 00:26:07,960
+بده يساوي
+
+247
+00:26:11,430 --> 00:26:15,190
+هذه بنقدر نحللها اللي هي لاندا ناقص واحد في لاندا
+
+248
+00:26:15,190 --> 00:26:22,030
+ناقص اتنين يبقى هذه لاندا ناقص واحد في لاندا ناقص
+
+249
+00:26:22,030 --> 00:26:28,390
+اتنين وعنا هنا ناقص لاندا ناقص اتنين كله بده يستوي
+
+250
+00:26:28,390 --> 00:26:34,790
+zero بقدر اخد اعمال لاندا ناقص اتنين عامل مشترك من
+
+251
+00:26:34,790 --> 00:26:42,100
+الطرفينبظل كده؟ بظل land ناقص واحد لكل تربيع ناقص
+
+252
+00:26:42,100 --> 00:26:46,900
+واحد بده يساوي من zero يبقى من الاتنين هدولة خط
+
+253
+00:26:46,900 --> 00:26:51,660
+land ناقص اتنين بظل الجثة ده هو نفسه تربيع وهنا
+
+254
+00:26:51,660 --> 00:26:58,640
+بظل كده؟ ناقص واحديبقى هذا الكلام لاندا ناقص اتنين
+
+255
+00:26:58,640 --> 00:27:05,680
+هذا لو جيت فكته بيصير لاندا تربيع ناقص اتنين لاندا
+
+256
+00:27:05,680 --> 00:27:11,970
+زائد واحد وناقص واحد كله بده يساوي زيرونقص واحد
+
+257
+00:27:11,970 --> 00:27:16,770
+وزايد واحد مع السلامة يبقى آلة المسألة إلى لاندا
+
+258
+00:27:16,770 --> 00:27:22,530
+ناقص اتنين في لاندا تربية ناقص اتنين لاندا يسوى
+
+259
+00:27:22,530 --> 00:27:29,730
+كده؟ Zero اظن هذا بقدر اقول كتالي لاندا ناقص اتنين
+
+260
+00:27:30,050 --> 00:27:34,670
+وهذا بقدر اخد لاندا عامل مشترك بضال قداش لاندا
+
+261
+00:27:34,670 --> 00:27:41,150
+ناقص اتنين بده يساوي zero ومنها لاندا في لاندا
+
+262
+00:27:41,150 --> 00:27:48,170
+ناقص اتنين يساوي من يساوي zero يبقى هذا نتيجة من
+
+263
+00:27:48,170 --> 00:27:56,520
+فكل محدد بناء عليه لاندا complex ولا realهي قدامك
+
+264
+00:27:56,520 --> 00:28:02,600
+قداش real numbers يبقى بناء عليا اما lambda او
+
+265
+00:28:02,600 --> 00:28:10,240
+باجي بقوله هنا the eigen vectors the eigen values
+
+266
+00:28:10,240 --> 00:28:18,520
+are lambda تساوي zero او lambda تساوي قداش اتنين
+
+267
+00:28:18,520 --> 00:28:22,700
+يبقى في عندي قيمتين هنا لمين ل lambda
+
+268
+00:28:25,840 --> 00:28:30,060
+لاندا في لاندا تربيع هذه تربيعة منها لأن هذا الجثة
+
+269
+00:28:30,060 --> 00:28:34,360
+مضروف في بعض يبقى لاندا تربيع يبقى معناته الجثة
+
+270
+00:28:34,360 --> 00:28:38,080
+الأولى يساوي zero والجثة التانية يساوي zero يبقى
+
+271
+00:28:38,080 --> 00:28:43,080
+هذا لايعطني إلا قيمتين فقط للاندا ماهياش تلاتة
+
+272
+00:28:43,080 --> 00:28:46,440
+طبعا الجثة التانية لما أقول تربيع معناته في قيمتين
+
+273
+00:28:46,440 --> 00:28:50,560
+والقيمتين ماعنهم مكررات كل واحدة فيهم تساوي كده
+
+274
+00:28:50,560 --> 00:28:55,120
+إتنين يعني في الحقيقة ماعنديش إلا قيمتين وليست
+
+275
+00:29:00,210 --> 00:29:05,830
+أحنا فكرنا أن الضرر ناقصلأ ضرب هذه كلها عام
+
+276
+00:29:05,830 --> 00:29:12,210
+المشترك هي هذا نقطة لماذا؟ لأن تحليل أخذت لاندا من
+
+277
+00:29:12,210 --> 00:29:15,790
+القوس هذا عام المشترك يبقى لدي لاندا ناقص اتنين
+
+278
+00:29:15,790 --> 00:29:19,230
+لما أخد لاندا برا يبقى سار القوس لاندا في لاندا
+
+279
+00:29:19,230 --> 00:29:24,190
+ناقص اتنين لكل square يبقى كم؟ Zero يبقى لدي لاندا
+
+280
+00:29:24,190 --> 00:29:28,070
+تسوى Zero لاندا minus two لكل square يسوى Zeroلو
+
+281
+00:29:28,070 --> 00:29:32,310
+اختلها الجدر بيصير لاندا ناقص اتنين يساوي زيرو إذا
+
+282
+00:29:32,310 --> 00:29:36,950
+لاندا يساوي اتنين صحيح إن هذه معادلة من الدرجة
+
+283
+00:29:36,950 --> 00:29:42,130
+الثانية بس بتعطيني قيمتين مكررات يعني نفس القيمة
+
+284
+00:29:42,130 --> 00:29:46,030
+اللي هيقداش اتنين والتانية كمان اتنين يبقى في
+
+285
+00:29:46,030 --> 00:29:50,950
+الحقيقة ماعنديش إلا قيمتين وليست ثلاثيبقى باجي
+
+286
+00:29:50,950 --> 00:29:53,930
+بقول صاروا ال eigen values هو لاندا تساوي زيرو
+
+287
+00:29:53,930 --> 00:29:59,710
+لاندا تساوي اتنين إذا بدي أجي أخد الحالة الأولى لو
+
+288
+00:29:59,710 --> 00:30:04,630
+كانت لاندا تساوي زيرو then يبقى بدي أرجع على
+
+289
+00:30:04,630 --> 00:30:10,030
+المعادلة الأساسية اللي عندنا هنا و أجي أحط بدالها
+
+290
+00:30:10,030 --> 00:30:16,670
+لاندا بقداش بزيرو يبقى بدي أصير المعادلة لاندا I
+
+291
+00:30:16,790 --> 00:30:23,030
+ناقص ال a في ال x بدها تساوي zero has the form
+
+292
+00:30:23,030 --> 00:30:28,610
+يبقى بدها تاخد الشكل التالي هذا lambda I ناقص ال a
+
+293
+00:30:28,610 --> 00:30:32,890
+يبقى بده أشيل lambda و أحط مكانها جداش zero بصير
+
+294
+00:30:32,890 --> 00:30:38,250
+عند هنا مين ناقص واحد ناقص اتنين ناقص تلاتة واحد
+
+295
+00:30:38,250 --> 00:30:46,320
+ناقص اربعة ناقص تلاتة ناقص واحد اتنين واحدبالشكل
+
+296
+00:30:46,320 --> 00:30:50,420
+اللي عندنا ده يبقى شيلت لاندا وحطيت مكانها zero
+
+297
+00:30:50,420 --> 00:30:57,760
+وهنا X واحد X اتنين X تلاتة بده يساوي zero zero
+
+298
+00:30:57,760 --> 00:31:04,510
+zeroإذاً هذا بدي يقودني إلى الشكل التالي بدي أضرب
+
+299
+00:31:04,510 --> 00:31:14,070
+المصففين هدول في بعض يبقى ناقص X1 ناقص 2 X2 ناقص 3
+
+300
+00:31:14,070 --> 00:31:26,430
+X3 الصفر الثاني يبقى X1 ناقص 4 X2 ناقص 4 X2 ناقص 3
+
+301
+00:31:26,430 --> 00:31:37,150
+X3الصف التالت يبقى ناقص X1 زائد 2 X2 زائد X3 كل
+
+302
+00:31:37,150 --> 00:31:43,270
+هذا الكلام بده يساوي Zero و Zero و Zero إذا أصبحت
+
+303
+00:31:43,270 --> 00:31:48,310
+المعادلات التلاتة عندي على الشكل التالي سالب X1
+
+304
+00:31:48,310 --> 00:31:56,600
+سالب 2 X2 سالب 3 X3 بده تساوي Zeroالمعادلة التانية
+
+305
+00:31:56,600 --> 00:32:00,720
+x1-4x2
+
+306
+00:32:00,720 --> 00:32:14,180
+-3x3 بده يساوي 0-x1 زيدي 2x2 زيدي x3 بده يساوي 0
+
+307
+00:32:14,770 --> 00:32:19,570
+خلّينا نتأكد ان ال system هذا سليم 100% حتى نواصل
+
+308
+00:32:19,570 --> 00:32:26,110
+يبقى جيبنا ال lambda و راحنا عوضنا بال zero لما
+
+309
+00:32:26,110 --> 00:32:31,850
+عوضنا بال zero طلعت عندنا المعادلة ناقص x1 ناقص 2
+
+310
+00:32:31,850 --> 00:32:38,730
+x2 ناقص 3 x3 بده يسوي zero و x1 ناقص 4 x2 ناقص 3
+
+311
+00:32:38,730 --> 00:32:46,030
+x3 بده يسوي zero و هذه ناقص x1 زائد 2 x2زائد X
+
+312
+00:32:46,030 --> 00:32:52,770
+ثلاثة كله بيساوي Zero مطبوط مية المية طيب ايش رايك
+
+313
+00:32:52,770 --> 00:32:58,490
+لو جينا على المعادلات اللي عندنا هذه بدي احاول
+
+314
+00:32:58,490 --> 00:33:03,950
+اشوف ايش علاقتها مع بعضها لو جيت للمعادلات اللي
+
+315
+00:33:03,950 --> 00:33:10,030
+عندى الأولى و الثالثة المعادلات اللي اتنين هدوة
+
+316
+00:33:10,030 --> 00:33:17,740
+يعني هذه ههه وهذهجيت جمعت الاتنين مع بعض يبقى هذه
+
+317
+00:33:17,740 --> 00:33:24,100
+هتروح مع من؟ مع هذه بظل عندي قداش ناقص اتنين X
+
+318
+00:33:24,100 --> 00:33:31,200
+واحد ناقص اتنين X واحد ناقص اتنين X تلاتة يسوي
+
+319
+00:33:31,200 --> 00:33:38,860
+قداش Zero يعني هذا بده يعطينا ان X واحد زي X تلاتة
+
+320
+00:33:38,860 --> 00:33:44,880
+بده يسوي Zero هذا بده يعطينا ان X واحديساوي سالب
+
+321
+00:33:44,880 --> 00:33:55,660
+X3 طيب لو جينا جمعنا المعادلة هذه والمعادلة هذه
+
+322
+00:33:55,660 --> 00:34:00,460
+تين تين مع بعض ايش بده يعطينا هدول بيروحوا مع بعض
+
+323
+00:34:01,350 --> 00:34:05,950
+مظبوط بيظل ناقص
+
+324
+00:34:05,950 --> 00:34:12,890
+اتنين اكس اتنين او ناقص اتنين اكس تلاتة بده يساوي
+
+325
+00:34:12,890 --> 00:34:18,030
+زيرو يبقى هذا بده يعطينا انه اكس اتنين زايد اكس
+
+326
+00:34:18,030 --> 00:34:22,370
+تلاتة بده يساوي زيرو هذا بده يعطينا انه اكس اتنين
+
+327
+00:34:22,370 --> 00:34:31,050
+يساوي سالب اكس تلاتة اذا لو كانتالـ X ثلاثة بدها
+
+328
+00:34:31,050 --> 00:34:34,190
+تساوي من؟ بدها تساوي الـ A
+
+329
+00:34:46,100 --> 00:34:51,600
+بناء عليه بقدر أجيب له من المطلوب التاني جليهات
+
+330
+00:34:51,600 --> 00:34:55,620
+للـEigenvectors المطلوب الأول جيبناله
+
+331
+00:34:55,620 --> 00:35:00,840
+الـEigenvalues يبقى من هنا بدأ المطلوب الأول اللي
+
+332
+00:35:00,840 --> 00:35:07,960
+هو A وانتهى هنالما جيبنا اللانت من هنا بدنا نبدأ
+
+333
+00:35:07,960 --> 00:35:17,860
+نمرى بيه يبقى الآن بناء عليه بقوله the eigenvalues
+
+334
+00:35:17,860 --> 00:35:26,620
+the eigenvectors the eigenvectors corresponding
+
+335
+00:35:31,160 --> 00:35:42,280
+corresponding to لاندا بده يساوي zero are in the
+
+336
+00:35:42,280 --> 00:35:45,720
+form على الشكل التالي
+
+337
+00:35:48,930 --> 00:35:58,490
+اكس اتنين اكس تلاتة بده يساوي اكس واحد بناقص
+
+338
+00:35:58,490 --> 00:36:07,770
+a و اكس اتنين بناقص a و اكس تلاتة بناقص a و اكس
+
+339
+00:36:07,770 --> 00:36:12,110
+تلاتة بناقص
+
+340
+00:36:12,110 --> 00:36:18,270
+aإذا خلصنا من المطلوب نمر بي تبع من؟ تبع
+
+341
+00:36:18,270 --> 00:36:25,610
+الـEigenvectors المناظرة اللي لديها تساوي 0 لم يلأ
+
+342
+00:36:25,610 --> 00:36:31,030
+نقطة من نقطة C جاليهات ليه؟ اللي هو الـBases for
+
+343
+00:36:31,030 --> 00:36:37,830
+the corresponding Eigen spaceالان مش هذه تمثلي ال
+
+344
+00:36:37,830 --> 00:36:42,830
+space او ال vector space تبع ال eigen vectors يبقى
+
+345
+00:36:42,830 --> 00:36:48,390
+هذا شو يعتبر basis اللي هو طلبه يبقى هذا بده
+
+346
+00:36:48,390 --> 00:36:53,110
+يعطينا مين يبقى هذا النقطة بي و سي يا بنات مع بعض
+
+347
+00:36:53,110 --> 00:36:57,430
+اتنين مع بعض في اي نوع يبقى باجي بيقول هذا بده
+
+348
+00:36:57,430 --> 00:37:03,710
+يعطينا the basis of the
+
+349
+00:37:15,300 --> 00:37:20,160
+السطر اللي عندنا هذه اللي هو على شكل سالب واحد
+
+350
+00:37:20,160 --> 00:37:27,580
+سالب واحد واحد بالشكل اللي عندنا هنا كيف
+
+351
+00:37:27,580 --> 00:37:29,320
+مش سانة
+
+352
+00:37:33,000 --> 00:37:37,240
+Eigenvectors لاندا خلصناها من الأول يبقى هذه الان
+
+353
+00:37:37,240 --> 00:37:41,380
+اللي جيبناه لمين للنقطة الأولى لاندا تساوي Zero
+
+354
+00:37:41,380 --> 00:37:45,380
+اللي عملناه للاندا تساوي Zero بدنا نروح نكرره من
+
+355
+00:37:45,380 --> 00:37:51,040
+جديد للاندا تساوي اتنين طبعا الشطرة الأولى من
+
+356
+00:37:51,040 --> 00:37:57,460
+السؤال هذا انتهينا منه يبقى بدي اروح اجيب له بي و
+
+357
+00:37:57,460 --> 00:38:00,440
+سي لمين للاندا التانية
+
+358
+00:38:07,460 --> 00:38:16,300
+يبقى باجي بقوله لو كانت لاندا تساوي اتنين then
+
+359
+00:38:16,300 --> 00:38:26,120
+اللاندا I ناقص ال A في ال X بدي يساوي zero has the
+
+360
+00:38:26,120 --> 00:38:29,600
+form تبقى على الشكل التالي
+
+361
+00:38:35,100 --> 00:38:40,320
+ماذا كانت المعادلة؟ كانت أنها مناطق احنا مسحناها
+
+362
+00:38:40,320 --> 00:38:45,960
+بس خلينا نذكر بها كانت المعادلة اللي عندنا على
+
+363
+00:38:45,960 --> 00:38:52,180
+الشكل التالي اللي هي مين؟ المصوفة كانت اللي هو
+
+364
+00:38:52,180 --> 00:38:58,550
+بلندن أقص واحدوهنا ناقص اتنين ناقص تلاتة واحد
+
+365
+00:38:58,550 --> 00:39:06,190
+لاندا ناقص اربعة ناقص تلاتة هنا ناقص واحد اتنين
+
+366
+00:39:06,190 --> 00:39:11,310
+لاندا plus one يبقى هذه المصروفة اللي كانت عندنا
+
+367
+00:39:11,310 --> 00:39:16,410
+قبل قليل مكتوبة معاكي تمام؟ الآن بدي اعوض فيها على
+
+368
+00:39:16,410 --> 00:39:21,930
+لاندا بجداش باتنينبصير اتنين ناقص واحد يبقى هذا
+
+369
+00:39:21,930 --> 00:39:27,370
+اتنين ناقص واحد و عندك هنا ناقص اتنين ناقص تلاتة و
+
+370
+00:39:27,370 --> 00:39:34,470
+هنا واحد و هنا اتنين ناقص اربع و هنا ناقص تلاتة و
+
+371
+00:39:34,470 --> 00:39:42,890
+هنا ناقص واحد اتنين و هنا اتنين زائد واحد كله في X
+
+372
+00:39:42,890 --> 00:39:52,910
+واحد X اتنين X تلاتةبتساوي 000 هذا معناه ما يأتي
+
+373
+00:39:52,910 --> 00:39:58,210
+هذا بيصير المصفوف اتنين ناقص واحد يلو بواحد ناقص
+
+374
+00:39:58,210 --> 00:40:03,250
+اتنين ناقص تلاتة وهنا واحد وهنا ناقص اتنين وهنا
+
+375
+00:40:03,250 --> 00:40:10,750
+ناقص تلاتة وهنا سالب واحدهنا اتنين وهنا تلاتة اكس
+
+376
+00:40:10,750 --> 00:40:18,230
+واحد اكس اتنين اكس تلاتة بده يساوي زيرو زيرو زيرو
+
+377
+00:40:22,460 --> 00:40:27,600
+أنا جيت على المعادلة الأصلية لان دا اي ناقص ا كله
+
+378
+00:40:27,600 --> 00:40:32,400
+في اكس بده يسوى زيرو و كتبتها في شكل المصوفات ا
+
+379
+00:40:32,400 --> 00:40:35,780
+التالية اللي عندنا هنا يبقى بده اروح اضرب
+
+380
+00:40:35,780 --> 00:40:40,290
+المصوفتين هدول في بعضلو ضربت المصففين الاتنين هذا
+
+381
+00:40:40,290 --> 00:40:48,050
+الفواعد ياخدوني الشكل التالي يبقى هذا x1-2x2
+
+382
+00:40:48,050 --> 00:41:00,610
+-3x3 الصف التاني اللي هو x1-2x2-3x3 الصف الثالث
+
+383
+00:41:00,610 --> 00:41:10,120
+ناقص x1زائد اتنين X2 زائد تلاتة X3 كل هذا الكلام
+
+384
+00:41:10,120 --> 00:41:17,620
+بده يساوي Zero Zero Zero يبقى هذا بده يساوي من
+
+385
+00:41:17,620 --> 00:41:25,410
+Zero Zero Zeroلو قررنا العناصر المتنظرة في كل من
+
+386
+00:41:25,410 --> 00:41:36,790
+المصففاتين نحصل على ما يأتي x1-2x2-3x3 يساوي 0 x1
+
+387
+00:41:36,790 --> 00:41:47,810
+-2x2-x3 يساوي 0 x1-x2-x3
+
+388
+00:41:47,810 --> 00:41:57,800
+يساوي 0هذا الكم معادلة؟ كده؟ معادلتين؟ انا بقول
+
+389
+00:41:57,800 --> 00:42:02,820
+واحدة اضرب الصف التالت او المعادلة التالتة في سالب
+
+390
+00:42:02,820 --> 00:42:07,620
+واحد تطلع لمنا و فوق يبقى هدول مش تلت معادلات
+
+391
+00:42:07,620 --> 00:42:15,660
+وانما في الحقيقة معادلة واحدة يبقى هذه بقوله this
+
+392
+00:42:15,660 --> 00:42:17,680
+system
+
+393
+00:42:19,620 --> 00:42:22,080
+هذا الـ system is
+
+394
+00:42:25,210 --> 00:42:32,270
+one question only يبقى هذا معادلة واحدة فقط ل X
+
+395
+00:42:32,270 --> 00:42:37,890
+واحد ناقص اتنين X اتنين ناقص تلاتة X تلاتة يساوي
+
+396
+00:42:37,890 --> 00:42:42,190
+Zero ليش؟ لأن المعادلة التالتة لو ضربتها في سالب
+
+397
+00:42:42,190 --> 00:42:46,550
+واحد بتطلع المعادلة التانية او المعادلة الأولى
+
+398
+00:42:46,550 --> 00:42:50,630
+لاتنين are the same يبقى انا عندي معادلة واحدة في
+
+399
+00:42:50,630 --> 00:42:57,050
+كام مجهولةفي ثلاثة مجاهيل فيش إمكانية للحل اللي
+
+400
+00:42:57,050 --> 00:43:01,070
+أحط مجهولين من عندي و أروح أجيب قيمة المجهول
+
+401
+00:43:01,070 --> 00:43:07,590
+التالت بدلالة الاتنين هذول يبقى مثلا لو جيت قولتله
+
+402
+00:43:07,590 --> 00:43:20,250
+if ال X2 بدر ساوي A andالـ X تلاتة بده يساوي B ثم
+
+403
+00:43:20,250 --> 00:43:27,690
+X واحد جداش بده يساوي 2A زي التلاتة B يعني انا
+
+404
+00:43:27,690 --> 00:43:33,190
+بقوله مع الشجة التانية بصي X واحد يساوي 2A زي
+
+405
+00:43:33,190 --> 00:43:39,010
+التلاتة B إذن بقدر أجيب شكل الـEigenvectors يبقى
+
+406
+00:43:39,010 --> 00:43:43,710
+باجي بقوله هنا The Eigen
+
+407
+00:43:47,230 --> 00:43:53,370
+Vectors Corresponding المناظرة
+
+408
+00:43:53,370 --> 00:43:59,510
+to land يبقى في
+
+409
+00:43:59,510 --> 00:44:03,750
+الشكل
+
+410
+00:44:03,750 --> 00:44:06,930
+التالي X1
+
+411
+00:44:07,910 --> 00:44:22,610
+و X2 و X3 بده يساوي X1 ب 2A زي 3B X2 ب A و X3 ب B
+
+412
+00:44:27,060 --> 00:44:33,440
+طب ايش رأيك احط هادول على شكل مجموع مصوفتين يبقى
+
+413
+00:44:33,440 --> 00:44:43,360
+بقدر اقول هذا الكلام بده يساوي 2A و A و 0 زائد 3B
+
+414
+00:44:43,360 --> 00:44:55,000
+و 0 و B بنفعبنفع اقول ايه كذلك عامل مشترك بيضل 2 1
+
+415
+00:44:55,000 --> 00:45:03,280
+0 زائد بيعمل مشترك بيضل 3 0 1
+
+416
+00:45:05,790 --> 00:45:09,910
+يبقى هاي اللي جيبته الـEigenvectors تمام؟ كل
+
+417
+00:45:09,910 --> 00:45:13,850
+الـVectors اللي على الشكل اللي عندنا هذا او مجموعة
+
+418
+00:45:13,850 --> 00:45:17,410
+الـTwo Vectors هدول المطلوب التالت جاليهات
+
+419
+00:45:17,410 --> 00:45:23,450
+للـBases للـEigenspace بقوله كويس هدول
+
+420
+00:45:23,450 --> 00:45:27,470
+الـEigenvectors يبقى اي اي Eigenvector في
+
+421
+00:45:27,470 --> 00:45:31,190
+الـVector Space في الـEigenspace بدي اقدر اكتب
+
+422
+00:45:31,190 --> 00:45:36,090
+الشكل هذا إذا كانالاتنين هدول are linearly
+
+423
+00:45:36,090 --> 00:45:40,530
+independent
+
+424
+00:45:40,530 --> 00:45:44,630
+ممتاز جدا يبقى السؤال هو هل هدول linearly
+
+425
+00:45:44,630 --> 00:45:51,170
+dependent ولا linearly independent independent لأن
+
+426
+00:45:51,170 --> 00:46:01,830
+ولا واحد فيهم مضاعفات الآخر يبقى the two vectors
+
+427
+00:46:03,410 --> 00:46:12,890
+منهم اتنين واحد زيرو and اللي هو تلاتة زيرو واحد
+
+428
+00:46:12,890 --> 00:46:24,470
+are linearly independent because any one of them
+
+429
+00:46:24,470 --> 00:46:27,930
+is
+
+430
+00:46:27,930 --> 00:46:32,310
+not a multiple
+
+431
+00:46:35,060 --> 00:46:44,520
+of multiple of the other هذا
+
+432
+00:46:44,520 --> 00:46:47,880
+بدي اعطيك ان ال basis المطلوب
+
+433
+00:46:49,640 --> 00:46:57,560
+is the set يبقى هو عبارة عن المجموعة بحط فيها ال
+
+434
+00:46:57,560 --> 00:47:03,120
+vector الأول اتنين واحد زيرو و بروح بحط ال vector
+
+435
+00:47:03,120 --> 00:47:08,700
+التاني تلاتة زيرو واحد الشكل اللي عندنا هنا
+
+436
+00:47:14,930 --> 00:47:20,530
+حد فيكوا لايه تساؤل هنا؟ يعني كل أندعها بيقابلها
+
+437
+00:47:20,530 --> 00:47:26,450
+vector space خاص بها، يبقى كأنه فيها two vector أو
+
+438
+00:47:26,450 --> 00:47:31,490
+two eigenspaces، حد فيكوا لايه تساؤل؟ طيب أعطيكوا
+
+439
+00:47:31,490 --> 00:47:31,890
+العافية
+