Linear Algebra and Differential Equation
Matrices and their operations. Types of matrices. Elementary transformations. Linear systems of equations. Determinants, elementary properties. Inverse of a matrix. Vector spaces, linear independence,
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Introduction
- Introduction 02:16
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CHAPTER 1 System of Linear Equation and Matrices
- 1.1 Linear Equation 11:41
- 1.1 Solution of System of Linear Equations 13:56
- 1.1 Introduction to Matrices 06:31
- 1.1 Type of Matrices 10:32
- 1.1 Augmented Matrix 07:40
- 1.1 Elementary Row Operation 08:05
- 1.1 Extra Example 02:41
- 1.1 Solving Linear system (with unique solution) 13:52
- 1.1 Example 1 08:42
- 1.1 Example 2 06:17
- 1.1 Example 3 06:31
- 1.1 Some Notes 04:48
- 1.1 Solving Many Systems 09:22
- 1.2 Reduced Echelon Form 07:00
- 1.2 Examples of Reduced Echelon Form 05:49
- 1.2 Finding Reduced Echelon Form 13:01
- 1.2 Example 1 07:57
- 1.2 Example 2 12:21
- 1.2 Example 3 10:09
- 1.2 Example 4 08:03
- 1.2 Example 5 05:56
- 1.2 Homogeneous Linear System 08:47
- 1.3 Gauss Elimination 33:26
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CHAPTER 2 Matrices
- 2.1 Equal Matrices 05:55
- 2.1 Adding Two Matrices 04:15
- 2.1 Scalar Multiplication of Matrices 05:00
- 2.1 Multiplication of Two Matrices 12:10
- 2.1 Examples of Multiplying Two Matrices 09:00
- 2.1 More Examples of Multiplying Matrices 03:01
- 2.1 Special Matrices 04:52
- 2.1 Properties of Identity Matrix and Zero Matrix 05:08
- 2.1 Partitioning of Matrices 12:18
- 2.2 Algebraic Properties of Matrix Operation 11:34
- 2.2 Number of Multiplications 14:49
- 2.2 Cancellation Law 05:42
- 2.2 Powers of Matrices 08:27
- 2.2 Idempotent and Nilpotent 06:05
- 2.3 Transpose 08:36
- 2.3 Symmetric Matrices 07:03
- 2.3 If and Only If 08:06
- 2.3 Trace of a Matrix 07:48
- 2.3 Matrices With Complex Elements 13:58
- 2.3 Conjugate , Conjugate Transpose, Hermitian 05:48
- 2.4 Inverse of Matrices 08:46
- 2.4 Finding The Inverse 11:35
- 2.4 Properties of Matrix Inverse 10:41
- 2.4 Solving Linear System Using Inverse Matrix 13:13
- 2.4 Elementary Matrix 04:35
- 2.4 Row Operations Using Elementary Matrices 10:10
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CHAPTER 3 Determinants
- 3.1 The Determinant of 2x2 Matrices 06:04
- 3.1 Minor and Cofactor of Elements 09:11
- 3.1 Finding Determinant of Any Square Matrix 10:21
- 3.1 Theorem 3.1 14:48
- 3.1 The Determinant of 3x3 Matrices 04:51
- 3.2 Properties of Determinants Part 1 09:44
- 3.2 Properties of Determinants Part 2 11:20
- 3.2 Properties of Determinants Part 3 11:10
- 3.2 Properties of Determinants Part 4 13:20
- 3.3 Upper and Lower Triangular Matrix 07:21
- 3.3 Evaluating Determinant by Row Operations 12:56
- 3.4 Adjoint Matrix 08:25
- 3.4 Finding Inverse by Adjoint Matrix 09:16
- 3.4 Example of Finding Inverse by Adjoint Matrix 09:58
- 3.4 The Relation Between Determinant and Inverse 04:56
- 3.4 Example of The Relation Between Determinant and Inverse 08:56
- 3.4 The Relation Between Solution of a System and Determinant of Coffeciant Matrix 05:57
- 3.4 Example of The Relation Between Solution of a System and Determinant of Coffeciant Matrix 04:05
- 3.4 Cramer's Rule 07:50
- 3.4 Proof of Cramer's Rule 03:57
- 3.4 Example of Cramer's Rule 04:39
- 3.4 Example 6 07:34
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CHAPTER 4 Vector Spaces
- 4.1 Introduction to Vectors 04:20
- 4.1 Operation on Vectors 05:10
- 4.1 Examples of Addition and Scalar Multiplication in Vector 07:20
- 4.1 Properties of Rn 06:13
- 4.2 Dot Product 06:56
- 4.2 Norm Vector 04:24
- 4.2 Unit Vector 06:37
- 4.2 The Angle Between Vectors in Rn 05:05
- 4.2 Orthogonal Vectors 09:18
- 4.2 Distance Between Vectors 06:54
- 4.3 Vector Space 20:58
- 4.3 Matrices of Size 2X2 is a Vector Space 08:19
- 4.3 Vector Space of Function 07:26
- 4.3 Useful Properties 04:02
- 4.4 Subspaces 08:30
- 4.4 Examples of Subspace and not Subspace Set 07:08
- 4.4 Vector Space of Polynomial 08:43
- 4.5 Linear Combination 06:58
- 4.5 Is the Vector Linear Combination of Other Vectors ? 06:52
- 4.5 Express Vector as Linear Combination ofSome Vectors 05:10
- 4.5 Liner Combination in Matrices 08:42
- 4.5 Linear Combination in Function 04:33
- 4.5 Spaning Set 11:14
- 4.5 Spanning Set is a Subspace of V 08:37
- 4.5 Equal Spanning Set 09:57
- 4.5 Example 11 04:01
- 4.6 Linearly Dependent and Independent 11:21
- 4.6 More in Linearly Dependent and Independent 07:59
- 4.6 Some Theorems 06:19
- 4.7 Basis 22:19
- 4.7 Some Theorems about Basis 12:11
- 4.7 Dimension 09:16
- 4.7 Some Theorems about Dimension 08:57
- 4.7 True or False 06:49
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CHAPTER 5 Eigenvalues and Eigenvectors
- 5.1 The Meaning of Eigenvalue and Eigenvector 06:23
- 5.1 Computing Eigenvalues and Eigenvectors 16:40
- 5.1 Example 1 (Finding Eigenvalue and Eigenvector for 2x2 Matrix) 11:58
- 5.1 Eigenspace 03:44
- 5.1 Example 1 (Finding Eigenvalue and Eigenvector for 3x3 Matrix) 20:31
- 5.3 Similar Matrices 03:09
- 5.3 The Eigenvalues of Similar Matrices 04:21
- 5.3 Diagonalization 03:55
- 5.3 Diagonalizable Matrix 05:27
- 5.3 Example 4 07:56
- 5.3 Computing Powers of a Matrix by Diagonalization 08:46
- 5.3 Example of a Matrix that it is not Diagonalizable 03:42
- 5.3 Symmetric Matrices 02:59
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CHAPTER 4 Vector Spaces (from the book) فقط للترم الصيفي
- 4.1 vectors in a plane 16:34
- 4.1 Vectors in Rn 19:59
- 4.1 Theorem 4.3 29:23
- 4.1 Linear Combination 16:20
- 4.2 The Meaning of Vector Space 11:04
- 4.2 Some Example about Vector Spaces 08:28
- 4.2 Showing That a Polynomial of Degree 2 or Less Is a Vector Space 15:24
- 4.2 More About Vector Space 13:15
- 4.2 Example of Sets That Is Not a Vector Space 15:01
- 4.3 Subspaces 14:30
- 4.3 Theorem 4.5 10:20
- 4.3 Examples of Subspace and not Subspace Set 17:50
- 4.3 More Examples about Subspaces 22:40
- 4.4 Linear Combination 06:31
- 4.4 Finding Linear Combination 15:43
- 4.4 Spanning Vector Space 25:42
- 4.4 Testing for Spanning 17:24
- 4.4 Span of a Set 12:57
- 4.4 Linearly Independent and Linearly Dependent 17:03
- 4.4 Testing for Linear Independence 10:45
- 4.4 More Examples in Linearly Independent and Linearly Dependent 17:25
- 4.4 Linearly Dependent 20:20
- 4.5 Basis 17:34
- 4.5 More Examples about Basis 11:30
- 4.5 Basis and Linear Dependence 19:54
- 4.5 Number of Vectors in a Basis 07:56
- 4.5 Dimension 17:47
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CHAPTER 7 Eigenvalue and Eigenvector (from the book) فقط للترم الصيفي
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Exercises of linear algebra
- 1.1 Matrices and System of Linear Equations part 1 (Q1,Q2,Q4,Q5) 09:33
- 1.1 Matrices and System of Linear Equations part 2 (Q6,Q7) 10:20
- 1.1 Matrices and System of Linear Equations part 3 ( Q10(a,b) ) 10:54
- 1.1 Matrices and System of Linear Equations part 4 ( Q10(c) ) 10:21
- 1.1 Matrices and System of Linear Equations part 5 ( Q10(d,e) ) 15:00
- 1.1 Matrices and System of Linear Equations part 6 (Q10(f), Q13) 12:36
- 1.1 Matrices and System of Linear Equations part 7 ( Q11(e) ) 07:04
- 1.1 Matrices and Systems of Linear Equations (Q11(d), !2(a)) 17:10
- 1.2 Gauss Jordan Elimination part 1 ( Q2, Q5(a) ) 14:33
- 1.2 Gauss Jordan Elimination part 2 (Q5(b,c)) 14:28
- 1.2 Gauss Jordan Elimination part 3 (Q5(d,e,f)) 09:19
- 1.2 Gauss Jordan Elimination part 4 (Q8(a)) 11:56
- 1.2 Gauss Jordan Elimination part 5(Q8(b,c,d,e)) 08:34
- 1.2 Gauss Jordan Elimination part 6 (Q8(g,f), Q14(a,b)) 13:46
- 1.2 Gauss Jordan Elimination part 7 (Q1, Q3(a,c,d,e),Q6(f),Q7(d)) 21:20
- 1.2 Gauss-Jordan Elimination (Q6(a,c,e), Q7(c,e)) 39:19
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 1 (Q5) 16:41
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 2 (Q8,Q11,Q17) 15:14
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 3 (Q2, Q4, Q12, Q16) 30:44
- 2.1 Addition, Scalar Multiplication, and Multiplication of Matrices ( Q1(a,b,e,f), Q3(a,b,c,d,h) Q9(b,c,e,g) Q10(a)) 26:22
- 2.2 Properties of Matrix Operations Part 1 (Q6,Q8) 08:46
- 2.2 Properties of Matrix Operations Part 2 (Q19, Q27) 09:54
- 2.2 Properties of Matrix Operations Part 3 (Q31, Q11) 10:13
- 2.2 Properties of Matrix Operations Part 4 (Q3, Q4(a,c), Q5(a), Q12(b,c), Q17, Q24, Q29(a)) 21:41
- 2.2 Properties of Matrix Operations (Q1(a), Q5(c,d), Q30, Q32(c)) 19:18
- 2.3 Symmetric Matrices Part 1 ( Q1(a,d), Q2(a,b,c), Q3(a,b) ) 07:32
- 2.3 Symmetric Matrices Part 2 ( Q5(a,b), Q11, Q23 ) 15:52
- 2.3 Symmetric Matrices Part 3 ( Q1(e,f), Q3(c,e), Q15 ) 09:33
- 2.3 Symmetric Matrices (Q1(i), Q3(d), Q6, Q7, Q14) 17:58
- 2.4 The Inverse of a Matrix Part 1 (Q3(a), Q4(a), 6(a)) 10:10
- 2.4 The Inverse of a Matrix Part 2 (Q6(b,c), Q7(a,b), Q8(a,b)) 14:28
- 2.4 The Inverse of a Matrix Part 3 (Q9(a), Q14, Q15) 10:36
- 2.4 The Inverse of a Matrix Part 4 (Q16, Q19) 07:04
- 2.4 The Inverse of a Matrix Part 5 (Q21) 06:00
- 2.4 The Inverse of a Matrix Part 6 (Q1(b), Q2(b), Q3(b,e), Q4(d), Q5(b), Q7(c), Q9(b), Q18) 52:10
- 2.4 The Inverse of a Matrix (Q1(a,c), Q3(c), Q5(c), Q7(d), Q13, Q17) 30:20
- 3.1 Introduction to Determinants Part 1 (Q1,Q3,Q5) 14:14
- 3.1 Introduction to Determinants Part 2 (Q7) 08:20
- 3.1 Introduction to Determinants Part 3 (Q9) 06:13
- 3.1 Introduction to Determinants Part 4 (Q11, Q13) 15:29
- 3.1 Introduction to Determinant Part 5 (Q6(b), Q8(b), Q14) 22:45
- 3.2 Properties of Determinants Part 1 (Q1) 11:25
- 3.2 Properties of Determinants Part 2 (Q3, Q5, Q7) 12:59
- 3.2 Properties of Determinants Part 3 (Q9, Q13) 10:04
- 3.2 Properties of Determinant ( Q4, Q6(a,b), Q8, Q12(c) ) 17:01
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part1 (Q1, Q5) 11:59
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part 2 (Q7) 09:55
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part 3 ( Q9, Q11(a) ) 14:13
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part 4 (Q11(b,c), Q13, Q15) 10:27
- 3.3 Determinant, Inverse Matrix, Linear System part 5( Q3(b), Q4(b), Q6(c), Q8(b), Q10(a) ) 20:46
- 3.3 Determinant, Inverse Matrix, Linear System part 5( Q3(a,d) ) 05:01
- 1.3 The Vector Space Rn (Q3(a,c), Q5(a,b,c,h), Q7, Q9, Q10(a,c)) 13:00
- 1.3 The Vector Space Rn (Q5(a,g), Q6(b,d)) 03:36
- 1,6 Dot Product, Norm, Angle and Distance (Q3, Q7, Q8, Q9, Q11, Q13, Q16(a,c), Q17(a,c), Q26(a,c,e), Q36) 19:54
- 1.6 Dot Product, Norm, Angle and Distance (Q2(a,b), Q4(a,c), Q6(a,e), Q10(a,c), 12(a,b), Q26(d), Q16(e), Q33, Q35) 08:57
- 4.1 General Vector Spaces and Subspaces Part 1 (Q5, Q7, Q11) 06:26
- 4.1 General Vector Spaces and Subspaces Part 2 (Q13, Q15, Q19, Q21, Q23, Q25, Q27, Q29, Q33) 27:20
- 4.1 General Vector Space and Subspace (Q14, Q18(c), 22(c), 28(a)) 10:49
- 4.2 Linear Combination of Vectors Part 1 (Q1, Q3) 13:19
- 4.2 Linear Combination of Vectors Part 2 (Q5, Q7) 09:53
- 4.2 Linear Combination of Vectors Part 3 (Q9, Q11, Q15, Q17) 19:48
- 4.2 Linear Combinations of Vectors (Q2(a), Q4(c), Q8(a)) 10:57
- 4.3 Linear Independence of Vectors Part 1 (Q1, Q3) 12:39
- 4.3 Linear Independence of Vectors Part 2 (Q7, Q9) 07:43
- 4.3 Linear Independence of Vectors Part 3 (Q11, Q15, Q16) 09:30
- 4.3 Linear Independence of Victors Part 4 (Q2(b), Q6(d), Q8(c)) 09:47
- 4.4 Properties of Basis (Q1, Q5, Q11, Q13, Q15, Q17) 18:47
- 4.4 Properties of Basis (Q2(a), Q3(b), Q4(a), Q6(a,c), Q10, Q16(b), Q20(a,d)) 08:55
- 3.4 Eigenvalue and Eigenvectors Part 1 (Q1) 08:09
- 3.4 Eigenvalue and Eigenvectors Part 2 (Q9) 09:49
- 3.4 Eigenvalue and Eigenvectors Part 3 (Q10) 09:44
- 3.4 Eigenvalue and Eigenvectors Part 4 (Q13) 06:58
- 3.4 Eigenvalue and Eigenvectors Part 5 (Q15) 07:52
- 3.4 Eigenvalue and Eigenvectors Par6 (Q24, Q26, Q32) 09:26
- 5.3 Diagonalization of a Matrix Part 1 18:31
- 5.3 Diagonalization of a Matrix Part 2 05:04
- 1.4 Subspace of Rn 08:23
- 1.5 Basis and Dimension in Rn 17:40
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Exam of Linear algebra
- REVIEW MID 1 01:05:30
- REVIEW MID 2 19:07
- حل ميد 1 عام 2020 جزء 1 16:35
- حل ميد 1 عام 2020 جزء 2 09:59
- حل ميد 2 عام 2020 جزء 1 17:00
- حل ميد 2 عام 2020 جزء 2 31:34
- حل كويز 1 2020 15:01
- حل كويز 2 2020 21:44
- Quiz 1 (عام 2022) 16:14
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Homeworks of linear algebra
- Homework 1 part1 17:21
- Homework 1 part2 13:42
- Homework 1 part3 17:26
- Homework 1 part4 14:17
- Homework 2 part1 23:31
- Homework 2 part2 30:00
- Homework 3 part1 16:11
- Homework 3 part2 28:30
- Homework 4 27:23
- Homework 5 52:27
- Homework 6 (Solve Caramer's rule) 13:47
- Homework 7 (true or false about ch 4 ) 17:57
- مقاطع لأهم الأساسيات
- الكويز والميد الخاص بالمعادلات التفاضلية
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First Order Differential Equations
- Differential equations + Order + degree 18:50
- The Solution of Differential Equation 18:05
- Direct integration + Separation of variables 24:11
- Integration Factor 26:56
- Exact Equation - 1 34:45
- Exact Equation - 2 16:35
- Not Exact equation 12:43
- Exercise ( 1-35 ) 19:49
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Second-Order DE - Homogeneous
- Homogeneous - Part 1 20:48
- Homogeneous - Part 2 06:33
- Homogeneous - Part 3 11:02
- Exercises (تمارين إضافية ) 29:44
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Second-Order DE - Non Homogeneous
- Finding the Particular integral - 1 15:28
- Finding the Particular integral - 2 10:45
- Finding the Particular integral - 3 08:50
- Example 8 07:38
- Example 9 10:33
- The variation of parameters method 36:05
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Sec.4.4 Undetermined Coefficients- Superposition Approach
- Undetermined Coefficients 24:15
- Example 2 + 3 35:31
- Example 4 + 5 +6 16:02
- Example 7 + 8 17:37
- Example 9 12:53
- Exercises 38:17
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تمارين المعادلات التفاضلية
- تمارين 2.3 (2 -4- 6 -8 ) 35:34
- تمارين 2.4 23:04
- تمارين 4.1 11:33
- تمارين 4.3 10:05
- Exe 4.2 06:37
- Exe 4.3 14:16
- Exe 4.4 38:17
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Final Exam
- Final exam - female - 2021 37:07
- Q2 13:13
- Q3+Q4+Q5 21:01
- أسئلة فاينل جزئية الجبر مهمه جداً 53:02
- Final 13:01
- Final - جزء المعادلات 27:05
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Introduction
- Matrices and their operations. Types of matrices. Elementary transformations. Linear systems of equations. Determinants, elementary properties. Inverse of a matrix. Vector spaces, linear independence, finite dimensional spaces, linear subspaces. Eigenvalues and Eigenvectors of a matrix linear . Diagonalizable Matrix
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