Differential Equations and Their Applications

Short Version

  • Martin Braun

Table of contents

  1. Front Matter
    Pages i-viii
  2. Martin Braun
    Pages 1-75
  3. Martin Braun
    Pages 76-193
  4. Martin Braun
    Pages 194-279
  5. Back Matter
    Pages 300-319

About this book

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 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. First, the problem to be solved is outlined clearly, and one or more differential equations 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 at Emmaus" which was bought by the Rembrandt Society of Belgium for $170,000 was a modern 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 try to determine whether tightly sealed drums filled with concentrated waste material will crack upon impact with the ocean floor. In this section we also describe several tricks for obtaining informa­ tion about solutions of a differential equation that cannot be solved explicitly.

Keywords

Applications Differentialgleichung Eigenvalue Equations Koordinatentransformation Rack calculus differential equation eigenvector equation form integral iteration model 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/10.1007/978-1-4684-0053-3
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0055-7
  • Online ISBN 978-1-4684-0053-3
  • About this book