Math 320 Linear Algebra and Differential Equations

Textbook: 

• Differential Equations and Linear Algebra by Edwards, Penney, and Calvis, 4th Edition.

Software:

None

Topics:

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