# Differential Equations: Theory and Applications

## with Maple®

• David Betounes
Textbook

1. Front Matter
Pages i-xiv
2. David Betounes
Pages 1-32
3. David Betounes
Pages 33-73
4. David Betounes
Pages 75-113
5. David Betounes
Pages 115-155
6. David Betounes
Pages 157-229
7. David Betounes
Pages 231-274
8. David Betounes
Pages 275-322
9. David Betounes
Pages 323-360
10. David Betounes
Pages 361-462
11. David Betounes
Pages 463-540
12. David Betounes
Pages 541-588
13. Back Matter
Pages 589-680

### Introduction

This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. His­ torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mathe­ matics, the material is organized so that the book can also be used in a wider setting within today's modern university and society (see "Ways to Use the Book" below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the in­ structor's or reader's preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend to­ gether the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab.

### Keywords

Elementary Analysis Implicit function calculus differential equation ordinary differential equation

#### Authors and affiliations

• David Betounes
• 1
1. 1.Mathematics DepartmentUniversity of Southern MississippiHattiesburgUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-4971-7
• Copyright Information Springer-Verlag New York 2001
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-4973-1
• Online ISBN 978-1-4757-4971-7
• Buy this book on publisher's site