**Math 2070 Syllabus**

Text: *Ordinary Differential Equations*, by William A. Adkins and Mark G. Davidson, Springer, 2012, plus a supplement on Fourier Series Methods available here. The student solutions manual for the text is available from the Springer website for the text. The student solutions manual for the Fourier Series Supplement is available here.

**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

1.6 Exact 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 *E _{q}*: Special Cases

2.7 The Linear Spaces

*E*: The General Case

_{q}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 6: Discontinuous Functions and the Laplace Transform **6.1 Calculus of Discontinuous Functions

6.2 The Heaviside Class

6.3 Laplace Transform Method for function in the Heaviside Class

6.4 The Dirac Delta Function

6.5 Convolution

**Chapter 8: Matrices**

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

**Supplement: Fourier Series Methods**

10.1 Periodic Functions and Orthogonality Relations

10.2 Fourier Series

10.3 Convergence of Fourier Series

10.4 Fourier Sine Series and Fourier Cosine Series

10.5 Operations on Fourier Series

10.6 Applications of Fourier Series

William A. Adkins, August 2013. Updated January 2016.