# Differential Equations and Their Applications

## An Introduction to Applied Mathematics

• Martin Braun
Textbook

Part of the Applied Mathematical Sciences book series (AMS, volume 15)

1. Front Matter
Pages i-xiii
2. Martin Braun
Pages 1-124
3. Martin Braun
Pages 125-261
4. Martin Braun
Pages 262-369
5. Martin Braun
Pages 370-473
6. Martin Braun
Pages 474-511
7. Back Matter
Pages 512-546

### Introduction

There are three major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is the addition of a new section, 4.9, dealing with bifurcation theory, a subject of much current interest. We felt it desirable to give the reader a brief but nontrivial introduction to this important topic. Our third major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. New York City Martin Braun Nooember, 1982 Preface to the First Edition This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained.

### Keywords

Fourier series applied mathematics bifurcation calculus differential equation ordinary differential equation

#### Authors and affiliations

• Martin Braun
• 1
1. 1.Department of Mathematics, Queens CollegeCity University of New YorkFlushingUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-9229-3
• Copyright Information Springer-Verlag New York 1983
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-97938-0
• Online ISBN 978-1-4684-9229-3
• Series Print ISSN 0066-5452
• Buy this book on publisher's site