Text: Differential Equations and Linear Algebra, by Stephen W. Goode and Scott A. Annin, Fourth Edition, 2017.

**Chapter 1: First-Order Differential Equations**

1.2 Basic Ideas and terminology

1.4 Separable Differential Equations

1.6 First Order Linear Differential Equations

1.9 Exact Differential Equations

**Chapter 2: Matrices and Systems of Linear Equations**

2.1 Matrices: Definitions and Notations

2.2 Matrix Algebra

2.4 Elementary Row Operations and Row-Echelon Matrices

2.5 Gaussian Elimination

2.6 Inverse of a Square Matrix

**Chapter 3: Determinants**

3.1 The definition of the Determinant

3.2 Properties of the Determinant

3.3 Cofactor Expansions

**Chapter 4: Vector Spaces**

4.2 Definition of a Vector Space

4.3 Subspaces

4.4 Spanning Sets

4.5 Linear Dependence and Linear Independence

4.6 Bases and Dimension

**Chapter 6: Linear Transformations**

6.1 Definition of a Linear Transformation

6.3 The Kernel and Range of a Linear Transformation

**Chapter 7: Eigenvalues and Eigenvectors**

7.1 The Eigenvalue/Eigenvector Problem

7.2 General Results for Eigenvalues and Eigenvectors

**Chapter 8: Linear Differential Equations of Order n**

8.1 General Theory for Linear Differential Equations

8.2 Constant-Coefficient Homogeneous Linear Differential Equations

8.3 The Method of Undetermined Coefficients. Annihilators

8.7 The Variation of Parameters

**Chapter 9: Systems of Differential Equations**

9.1 First-Order Linear Systems

9.2 Vector Formulation

9.3 General Results for First-Order Linear Differential Systems

9.4 Vector Differential Equations: Non-defective Coefficient Matrix

9.6 Variation of Parameters for Linear Systems

**Chapter 10: The Laplace Transform and Some Elementary Applications**

10.1 Definition of Laplace Transform

10.2 Existence of the Laplace Transform and Inverse Transform

10.4 The Transform of Derivatives and Solution of Initial-Value Problems

10.5 The First Shifting Theorem

10.6 The Unit Step Function

10.7 The Second Shifting Theorem

**Optional topics** that could be taught at the discretion of the instructor include:

1.8 Change of Variables, Homogeneous Equations, Bernoulli's Equation

1.11 Some Higher-Order Differential Equations

7.3 Diagonalization

7.4 An introduction to the Matrix Exponential Function.

8.9 Reduction of Order

Determined by the 2011 Math 2090 Committee: Michael M. Tom, Pat Gilmer, Paul Britt, Charles Egedy,

Boris Rubin; updated by Moscatello on November 2017 for fourth edition.