# 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 1-120
3. Martin Braun
Pages 121-239
4. Martin Braun
Pages 240-347
5. Martin Braun
Pages 348-445
6. Martin Braun
Pages 446-483
7. Back Matter
Pages 484-520

### Introduction

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 un­ derstood 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. First, the problem to be solved is outlined clearly, and one or more differential equa­ tions are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text. I. In Section 1.3 we prove that the beautiful painting "Disciples of Emmaus" which was bought by the Rembrandt Society of Belgium for \$170,000 was a modem forgery. 2. In Section 1.5 we derive differential equations which govern the population growth of various species, and compare the results predicted by our models with the known values of the populations. 3. In Section 1.6 we derive differential equations which govern the rate at which farmers adopt new innovations. Surprisingly, these same differen­ tial equations govern the rate at which technological innovations are adopted in such diverse industries as coal, iron and steel, brewing, and railroads.

### Keywords

Dirac delta function Equations Fourier series calculus convolution difference equation differential equation eigenvalue equilibrium linear differential equation ordinary differential equation partial differential equation society solution wave equation

#### Authors and affiliations

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

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-9360-3
• Copyright Information Springer-Verlag New York 1978
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-90266-1
• Online ISBN 978-1-4684-9360-3
• Series Print ISSN 0066-5452
• Buy this book on publisher's site