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Linear Algebra & Differential Equations (Full Course) || Math 54 || UC Berkeley

5.0 (0)
13 learners

What you'll learn

This course includes

  • 31.5 hours of video
  • Certificate of completion
  • Access on mobile and TV

Course content

1 modules • 141 lessons • 31.5 hours of video

Linear Algebra & Differential Equations (Full Course) || Math 54 || UC Berkeley

141 lessons • 31.5 hours
  • 1.1 Linear Equations--Overview (Video 1)00:49
  • 1.1 Linear Equations--Review of Linear Equations (Video 2)20:29
  • 1.1 Linear Equations--Augmented Matrices (Video 3)13:10
  • 1.2 Echelon Forms--Overview (Video 1)01:44
  • 1.2 Echelon Forms--Echelon Form and Reduced Echelon Form (Video 2)29:08
  • 1.2 Echelon Forms--Consistent and Inconsistent (Video 3)10:50
  • 1.3 Vector Equations--Overview (Video 1)00:50
  • 1.3 Vector Equations--Vectors in R^n (Video 2)14:51
  • 1.3 Vector Equations--Linear Combination and Span (Video 3)11:58
  • 1.3 Vector Equations--Vectors and Existence of Solutions (Video 4)28:09
  • 1.4 Matrix Equation--Overview (Video 1)00:51
  • 1.4 Matrix Equation--Defining Ax (Video 2)18:18
  • 1.5 Parametric Vector Form--Overview (Video 1)00:54
  • 1.5 Parametric Vector Form--Solving Ax=b in Parametric Vector Form (Video 2)17:44
  • 1.7 Linear Independence--Overview (Video 1)00:38
  • 1.7 Linear Independence--What is Linear Independence? (Video 2)09:07
  • 1.7 Linear Independence--Testing for Independence (Video 3)11:39
  • 1.7 Linear Independence--Conceptual Examples (Video 4)11:36
  • 1.8-1.9 Linear Transformations--Overview (Video 1)00:54
  • 1.8-1.9 Linear Transformations--Matrices as Transformations (Video 2)23:28
  • 1.8-1.9 Linear Transformations--Standard Matrix (Video 3)26:44
  • 1.8-1.9 Linear Transformations--Onto and One-to-One (Video 4)14:59
  • 1.8-1.9 Linear Transformations || One-to-one Example03:25
  • Chap 1 Review || Systems of Eqns and Linear Independence || Linear Algebra13:02
  • Chap 1 Review || Linear Transformations || Linear Algebra22:19
  • 2.1 Matrix Operations--Overview (Video 1)01:12
  • 2.1 Matrix Operations--Adding and Scaling Matrices (Video 2)08:13
  • 2.1 Matrix Operations--Defining Matrix Multiplication (Video 3)15:32
  • 2.1 Matrix Operations--Row Column Rule for Matrix Multiplication (Video 4)09:16
  • 2.1 Matrix Operations--Properties of Matrix Operations (Video 5)12:57
  • 2.2-2.3 Inverse Matrices--Overview (Video 1)00:54
  • 2.2-2.3 Inverse Matrices--What is an Invertible Matrix? (Video 2)15:04
  • 2.2-2.3 Inverse Matrices--Computing the Inverse (Video 3)20:28
  • 2.2-2.3 Inverse Matrices--Proof Example (Video 4)19:45
  • 2.2-2.3 Inverse Matrices--Another Proof Example (Video 5)11:48
  • 3.1-3.2 Determinants--Overview (Video 1)00:57
  • 3.1-3.2 Determinants--Cofactor Expansion for Determinants (Video 2)21:01
  • 3.1-3.2 Determinants--Using Row Operations to Compute Determinants (Video 3)27:06
  • 3.1-3.2 Determinants--Other Determinant Properties (Video 4)04:24
  • 3.2 Determinant Proof || Linear Algebra06:24
  • 4.1 Vector Spaces--Overview (Video 1)00:58
  • 4.1 Vector Spaces--Vector Spaces (Video 2)23:22
  • 4.1 Vector Spaces--Subspaces (Video 3)17:41
  • 4.1 More Subspace Examples || Linear Algebra14:55
  • 4.2 Null Space, Column Space, Kernel, and Range--Overview (Overview)01:56
  • 4.2 Null Space, Column Space, Kernel, and Range--Null Space (Video 2)20:48
  • 4.2 Null Space, Column Space, Kernel, and Range--Column Space (Video 3)14:25
  • 4.2 Null Space, Column Space, Kernel, and Range--Kernel and Range (Video 4)19:26
  • 4.3 Bases--Overview (Video 1)01:20
  • 4.3 Bases--Linear Independence and Bases (Video 2)21:10
  • 4.3 Bases--Spanning Set Theorem (Video 3)12:42
  • 4.3 Bases--Bases for Nul(A) and Col(A) (Video 4)08:33
  • 4.4 Coordinate Systems--Overview (Video 1)00:33
  • 4.4 Coordinate Systems--Unique Representation Theorem and Coordinate Vectors (Video 2)16:29
  • 4.4 Coordinate Systems--Coordinate Mapping (Video 3)08:03
  • 4.5-4.6 Dimension & Rank--Overview (Video 1)01:55
  • 4.5-4.6 Dimension & Rank--Dimension (Video 2)19:40
  • 4.5-4.6 Dimension & Rank--Nullity and Rank (Video 3)13:51
  • 4.5-4.6 Dimension & Rank--Conceptual Examples (Video 4)12:12
  • 4.5-4.6 Dimension & Rank--Row Space (Video 5)10:08
  • 4.6 Change of Basis || What is the Change of Basis Matrix? R29:27
  • 4.6 Change of Basis || Algorithm for Change of Basis Matrix10:31
  • 4.6 Change of Basis || Polynomials Example08:06
  • 5.1 Eigenstuff--Overview (Video 1)01:01
  • 5.1 Eigenstuff--Eigenvectors and Eigenvalues (Video 2)24:33
  • 5.2 Characteristic Equation--Overview (Video 1)00:35
  • 5.2 Characteristic Equation--Characteristic Equation (Video 2)13:25
  • 5.2 Characteristic Equation--Eigenvalues of Triangular Matrices (Video 3)07:38
  • 5.1 Eigenstuff--Theorems About Eigenvectors and Eigenvalues (Video 3)16:07
  • 5.1 Eigenstuff--Conceptual Example (Video 4)04:13
  • 5.3 Diagonalization--Overview (Video 1)00:57
  • 5.3 Diagonalization--Diagonal and Diagonalizable Matrices (Video 2)08:13
  • 5.3 Diagonalization--Diagonalization Theorem (Video 3)09:59
  • 5.3 Diagonalization--Diagonalization Example (Video 4)10:57
  • 5.3 Diagonalization--Determining Whether a Matrix is Diagonalizable (Video 5)20:25
  • 5.3 Diagonalization--Diagonalization Example with Rational Roots Theorem (Video 6)25:26
  • 5.4 Eigenvectors and Linear Transformations--Overview (Video 1)01:30
  • 5.4 Eigenvectors and Linear Transformations--Matrix for T Relative to B and C (Video 2)27:21
  • 5.4 Eigenvectors and Linear Transformations--Diagonal Representation Theorem (Video 3)23:44
  • 6.1 Inner Product--Overview (Video 1)00:58
  • 6.1 Inner Product--What is an Inner Product? (Video 2)24:30
  • 6.1 Inner Product--Orthogonal Complement (Video 3)11:37
  • 6.1 Inner Product--Produce Vector Orthogonal to Given Vectors (Video 4)13:24
  • 6.2-6.3 Orthogonal Sets, Projections, Matrices--Overview (Video 1)01:16
  • 6.2-6.3 Orthogonal Sets, Projections, Matrices--Orthogonal Sets (Video 2)20:41
  • 6.2-6.3 Orthogonal Sets, Projections, Matrices--Orthogonal Projections (Video 3)24:19
  • 6.2-6.3 Orthogonal Sets, Projections, Matrices--Orthogonal Matrices (Video 4)28:46
  • 6.4 Gram-Schmidt--Overview (Video 1)00:28
  • 6.4 Gram-Schmidt--Gram-Schmidt Process (Video 2)24:37
  • 6.5 Least-Squares--Overview (Video 1)00:53
  • 6.5 Least-Squares--What is a Least-Squares Problem? (Video 2)18:40
  • 6.5 Least Squares--Least-Squares Examples (Video 3)15:59
  • 6.5 Least-Squares--Line of Best Fit (Video 4)17:34
  • 6.7 Inner Product Spaces --Overview (Video 1)00:48
  • 6.7 Inner Product Spaces--What is an Inner Product Space? (Video 2)13:55
  • 6.7 Inner Product Spaces--Length, Orthogonality, Projections (Video 3)16:56
  • 6.7 Inner Product Spaces--Gram-Schmidt with Inner Product (Video 4)21:18
  • 7.1 Diagonalization of Symmetric Matrices--Overview (Video 1)01:05
  • 7.1 Symmetric Matrices--Intro to Symmetric Matrices (Video 2)20:21
  • 7.1 Symmetric Matrices--Orthogonal Diagonalization Examples (Video 3)27:27
  • Diff Eq's 4.2-4.3 Second-Order ODEs--Overview (Video 1)01:18
  • Diff Eq's 4.2-4.3 Second-Order ODEs--Intro to Ordinary Differential Equations (Video 2)12:52
  • Diff Eq's 4.2-4.3 Second-Order ODEs--Solving Homogeneous Second-Order ODEs (Video 3)39:47
  • Diff Eq's 4.2-4.3 Second Order ODEs--Initial Value Problems (Video 4)13:57
  • Diff Eq's 4.2-4.3 Second Order ODEs--Boundary Value Problems (Video 5)08:30
  • Diff Eq's 4.2-4.3 Second Order ODEs--Linear Independence with Wronskian (Video 6)23:28
  • Diff Eq's 4.4-4.5 Undetermined Coefficients--Overview (Video 1)01:16
  • Diff Eq's 4.4-4.5 Undetermined Coefficients--Intro to Undetermined Coefficients (Video 2)24:54
  • Diff Eq's 4.4-4.5 Undetermined Coefficients--More Examples (Video 3)25:40
  • Diff Eq's 4.4-4.5 Undetermined Coefficients--Superposition Principle (Video 4)06:17
  • Diff Eq's 9.1, 9.4 Linear Systems--Overview (Video 1)01:14
  • Diff Eq's 9.1, 9.4 Linear Systems-- Intro to Systems of Differential Equations (Video 2)18:51
  • Diff Eq's 9.1, 9.4 Linear Systems--Normal Form (Video 3)15:15
  • Diff Eq's 9.1, 9.4 Linear Systems--Existence and Uniqueness of Solutions (Video 4)07:25
  • Diff Eq's 9.1, 9.4 Linear Systems--Linear Independence with Wronskian (Video 5)26:32
  • Diff Eq's 9.1, 9.4 Linear Systems--Fundamental Solution Set (Video 6)05:30
  • Diff Eq's 9.5-9.6 Solving Hom Lin Systems--Overview (Video 1)00:57
  • Diff Eq's 9.5-9.6 Solving Hom Lin Systems--Solving Linear Homogeneous Systems of ODEs (Video 2)16:36
  • Diff Eq's 9.5-9.6 Solving Hom Linear Systems--Initial Value Problems (Video 3)12:40
  • Diff Eq's 9.5-9.6 Solving Hom Linear Systems--Complex Eigenvalues (Video 4)27:08
  • Diff Eq's 10.3 Fourier Series--Overview (Video 1)00:43
  • Diff Eq's 10.3 Fourier Series--What is a Fourier Series?09:47
  • Diff Eq's 10.3 Fourier Series--Deriving Fourier Coefficients (Video 3)30:51
  • Diff Eq's 10.3 Fourier Series--Fourier Series Example (Video 4)17:09
  • Diff Eq's 10.3 Fourier Series--Piecewise Function Example (Video 5)32:32
  • Diff Eq's 10.3 Fourier Series--Convergence of Fourier Series (Video 6)19:39
  • Diff Eq's 10.4 Fourier Cosine and Sine Series--Overview (Video 1)00:45
  • Diff Eq's 10.4 Fourier Cosine and Sine Series--What are Fourier Cosine and Sine Series? (Video 2)28:06
  • Diff Eq's 10.4 Fourier Cosine and Sine Series--Example (Video 3)14:09
  • 7.4 Singular Value Decomposition--Overview (Video 1)00:56
  • 7.4 Singular Value Decomposition--What is a SVD? (Part 2)05:59
  • 7.4 Singular Value Decomposition--Deriving SVD Formula (Video 3)38:22
  • 7.4 Singular Value Decomposition--Example (Video 4)15:11
  • 7.4 Singular Value Decomposition--Visualization (Video 5)09:14
  • 7.4 Singular Value Decomposition--Bases in SVD and Computational Tools (Video 6)19:42
  • 7.4 Singular Value Decomposition--Harder Example (Video 7)19:33
  • Inverse Matrices Conceptual Problems || Linear Algebra13:19
  • Determinants Cofactor Expansion Practice Problem || Linear Algebra07:35
  • Subspaces Practice Problems || Linear Algebra31:37
  • Chap 4 Review || Finding Bases for Subspaces || Spanning Set Theorem || Linear Algebra19:48
  • Chap 4 Review || Bases for Kernel and Range || Linear Algebra16:49

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