Math 555: Differential Equations

Table of Contents

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Chapter 1 - Introduction

1.1 Direction Fields

1.2(a) Overview

1.2(b) Initial Value Problems

1.3 Classification

Chapter 2 - First Order Differential Equations

2.1 Integrating Factors

2.2 Separable Equations

2.3 Modeling with First Order Equations

2.4 Linear and Nonlinear Equations

2.5 Autonomous Equations

2.6 Exact Equations

2.7 Numerical Approximations

2.8 Existence and Uniqueness

Chapter 3 - Second Order Differential Equations

3.1 Homogeneous Equations

3.2 Linear Homogeneous Equations

3.3 Periodic Solutions

3.4 Damped Motion

3.5 Undetermined Coefficients

3.6 Variation of Parameters

3.7 Mechanical and Electrical Applications

3.8 Forced Periodic Motion

Chapter 5 - Series Solutions

5.1(a) Taylor Series

5.1(b) Analytic Functions

5.2 Series Solutions Near an Ordinary Point

5.3 Existence and Uniqueness of Analytic Solutions

5.4(a) Euler Equations and Singular Points

5.4(b) Frobenius Method

5.7 Bessels's Equation

Chapter 6 - Laplace Transform Methods

6.1 Laplace Transform

6.2 Solving Initial Value Problems

6.3 Step Functions

6.4 Discontinuous Forcing Functions

6.5 Impulse Functions

6.6 Convolution Methods

Laplace Transform Table

Additional Links and Resources

3Blue1Brown - The Essence of Linear Algebra

An excellent series of videos by Grant Sanderson that explore the fundamental concepts of linear algebra. Several ideas, such as vectors, linear transformations, dot products, and cross products, are presented in a highly visual way to aid students' intuition and ability to visualize the objects considered.

Houston Math Prep - Differential Equations

A video series covering many of the same topics we cover in this course. These can serve as a quick refresher or source of additional examples to materials in the above sections.

MIT Open CourseWare - 18.03

MIT provides many online resources through their Open Courseware program. Linked here is a full class, including video lectures, featuring MIT professor Arthur Mattuck. The authors of these notes take inspiration from his lectures on this subject for our own writing here and classroom presentations.

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