Math 320 Linear Algebra and Differential Equations
University of Wisconsin-Madison, Fall 2019
University of Wisconsin-Madison, Fall 2019
Differential Equations and Linear Algebra by Edwards, Penney, and Calvis, 4th Edition.
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Chapter 1 First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations
Chapter 3 Linear Systems and Matrices
3.1 Introduction to Linear Systems
3.2 Matrices and Gaussian Elimination
3.3 Reduced Rwo-Echelon Matrices
3.4 Matrix Operations
3.5 Inverses of Matrices
3.6 Determinants
Chapter 4 Vector Spaces
4.1 The Vector Space R^3
4.2 The Vector Space R^n and Subspaces
4.3 Linear Combinations and Independence of Vectors
4.4 Bases and Dimension for Vector Spaces
4.5 Row and Column Spaces
4.7 General Vector Spaces
Chapter 5 Higher-Order Linear Differential Equations
5.1 Introduction: Second-Order Linear Equations
5.2 General Solutions of Linear Equations
5.3 Homogeneous Equations with Constant Coefficients
Chapter 6 Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalization of Matrices
Additional Topic: Cayley--Hamilton Theorem
Chapter 7 Linear Systems of Differential Equations
7.1 First-Order Systems and Applications
7.2 Matrices and Linear Systems
7.3 The Eigenvalue Method for Linear Systems
Chapter 8 Matrix Exponential Methods
8.1 Matrix Exponentials and Linear Systems
8.3 Spectral Decomposition Methods