Text: Ordinary Differential Equations, by William A. Adkins and Mark G. Davidson, Springer, 2012.

**Chapter 1: First Order Differential Equations**

1.1 An introduction to Differential Equations

1.2 Direction Fields

1.3 Separable Differential Equations

1.4 Linear First Order Equations

1.5 Substitutions; Homogeneous and Bernoulli Equations

**Chapter 2: The Laplace Transform**

2.1 Laplace Transform Method: Introduction

2.2 Definitions, Basic Formulas, and Principles

2.3 Partial Fractions: A Recursive Method for Linear Terms

2.4 Partial Fractions: A Recursive Method for Irreducible Quadratics

2.5 Laplace Inversion

2.6 The Linear Spaces: Special Cases

2.7 The Linear Spaces: The General Case

2.8 Convolution

**Chapter 3: Second Order Constant Coefficient Linear Differential Equations**

3.1 Notation, Definitions, and some Basic Results

3.2 Linear Independence

3.3 Linear Homogeneous Differential Equations

3.4 The Method of Undetermined Coefficients

3.6 Spring Systems or 3.7 RCL Circuits

**Chapter 4: Linear Constant Coefficient Differential Equations**

4.1 Notation, Definitions, and Basic Results

4.2 Linear Homogeneous Differential Equations

4.3 Nonhomogeneous Differential Equations

**Chapter 5: Second Order Linear Differential Equations**

5.1 The Existence and Uniqueness Theorem

5.2 The Homogeneous Case

5.3 The Cauchy-Euler Equations

5.5 Reduction of Order

5.6 Variation of Parameters

**Chapter 8: Matrices** (no more than two lectures should be spent here)

8.1 Matrix Operations

8.2 Systems of Linear Equations

8.3 Invertible Matrices

8.4 Determinants

8.5 Eigenvectors and Eigenvalues

**Chapter 9: Linear Systems of Differential Equations**

9.1 Introduction

9.2 Linear Systems of Differential Equations

9.3 The Matrix Exponential Function and its Laplace Transform

9.4 Fulmer's Method

9.5 Constant Coefficient Linear Systems

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

3.5 The Incomplete Partial Fraction Method

6.3-6.5 Laplace Transform Method for a Heaviside Function, The Dirac Delta Function, etc.

The above topics were chosen by the 2011 Math 2065 Committee: Michael M. Tom, Mark Davidson, Charles Egedy, Jerome W Hoffman, Terrie White