The Content and Novel
Features of the Book

Below you will find generous (and downloadable!) PDF previews of material from the book. However, if you want to study the book in a serious way we strongly recommend that you...

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Also available at Amazon or Barnes & Noble.

The book was reviewed here by William Satzer for the MAA. And here is the MathSciNet review.

Published by The American Mathematical Society.
ISBN-10: 0-8218-2138-5
ISBN-13: 978-0-8218-2138-1

We encourage visitors to download 3D-XplorMath, a free mathematical visualization program available in both a Mac only and a cross-platform Java version. It is very useful for visualizing differential equations and their solutions, such as those studied in the book. We have also collected a Gallery of ODE applets created using the Java version. This can serve as your online playground for experimenting with ODE of many types. To use it please visit: http://virtualmathmuseum.org/ODE/index.html.

• Preface
• Table of Contents
• Introduction
• Index

1. Differential Equations and Their Solutions

first 35 pages; Online Supplement

2. Linear Differential Equations

first 5 pages; Online Supplement

3. Second-Order ODE and the Calculus of Variations

first 5 pages

4. Newtonian Mechanics

first 5 pages; Online Supplement

5. Numerical Methods

first 38 pages; Online Supplement

Appendices (76 pages)

• Appendix A. Linear Algebra and Analysis
• Appendix B. The Magic of Iteration
• Appendix C. Vector Fields as Differential Operators
• Appendix D. Coordinate Systems and Canonical Forms
• Appendix E. Parametrized Curves and Arclength
• Appendix F. Smoothness with Respect to Initial Conditions
• Appendix G. Canonical Form for Linear Operators
• Appendix H. Runge-Kutta Methods
• Appendix I. Multistep Methods
• Appendix J. Iterative Interpolation and Its Error

Supplemental

Appendix K. Fast Fourier Transform.

Appendix L. Introduction to Fourier Methods.

Bibliography (Further Reading in ODE, Mechanics, and Numerical Methods)

Other ODE Resources