Fundamentals of Differential Equations

For one-semester sophomore- or junior-level courses in Differential Equations.

An introduction to the basic theory and applications of differential equations

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. For the first time, MyLab™ Math is available for this text, providing online homework with immediate feedback, the complete eText, and more.

Note that a longer version of this text, entitled Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition, contains enough material for a two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm–Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

Table of Contents

1. Introduction

2. First-Order Differential Equations

3. Mathematical Models and Numerical Methods Involving First-Order Equations

4. Linear Second-Order Equations

5. Introduction to Systems and Phase Plane Analysis

6. Theory of Higher-Order Linear Differential Equations

7. Laplace Transforms

8. Series Solutions of Differential Equations

9. Matrix Methods for Linear Systems

10. Partial Differential Equations

APPENDICES

ANSWERS to Odd-Numbered Problems