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Yes. The course includes 141 lessons across 1 modules.

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

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Yes. This CourseHive course is available to learn online for free.

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 Example 03:25

Chap 1 Review || Systems of Eqns and Linear Independence || Linear Algebra 13:02

Chap 1 Review || Linear Transformations || Linear Algebra 22:19

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 Algebra 06:24

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 Algebra 14:55

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? R 29:27

4.6 Change of Basis || Algorithm for Change of Basis Matrix 10:31

4.6 Change of Basis || Polynomials Example 08:06

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 Algebra 13:19

Determinants Cofactor Expansion Practice Problem || Linear Algebra 07:35

Subspaces Practice Problems || Linear Algebra 31:37

Chap 4 Review || Finding Bases for Subspaces || Spanning Set Theorem || Linear Algebra 19:48

Chap 4 Review || Bases for Kernel and Range || Linear Algebra 16:49

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

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

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