Differential and Difference Equations through Computer Experiments

With Diskettes Containing PHASER: An Animator/Simulator for Dynamical Systems for IBM Personal Computers

  • Hüseyin Koçak

Table of contents

  1. Front Matter
    Pages i-xv
  2. Mathematical Synopsis

    1. Front Matter
      Pages 1-1
    2. Hüseyin Koçak
      Pages 3-11
    3. Hüseyin Koçak
      Pages 13-18
    4. Hüseyin Koçak
      Pages 19-30
  3. Handbook of PHASER

    1. Front Matter
      Pages 31-31
    2. Hüseyin Koçak
      Pages 35-40
    3. Hüseyin Koçak
      Pages 41-86
    4. Hüseyin Koçak
      Pages 87-111
  4. Library of Equations

    1. Front Matter
      Pages 113-113
    2. Hüseyin Koçak
      Pages 115-169
    3. Hüseyin Koçak
      Pages 171-201
  5. Back Matter
    Pages 203-224

About this book

Introduction

This is a somewhat unusual book with a dual purpose. First, it is a manual to help readers learn how to use PRASER, the program on the accompanying diskette for mM personal computers. Second, it is an illustrated guide to the wonderful world of experimental and theoretical dynamics, one which presents dozens of concrete examples ranging from the most rudimentary, appropriate for the beginning student, to the highly complex, suitable for the research mathematician. Before indicating what PRASER does and how it works, let me describe how it came a.bout. During the past decade the field of differential and difference equations has witnessed a remarkable explo­ sion of knowledge, not only in theory but also in applications to discip­ lines as diverse as biology and fluid mechanics. Computers have played a crucial role in this process by making possible detailed analyses of specific systems. In this regard, one need only mention the work of Lorenz on strange attractors and the discoveries of Feigenbaum on the bifurcations of interval maps.

Keywords

Equations bifurcation biology boundary element method computer difference equation differential equation equation field knowledge mechanics numerical method numerics personal computer

Authors and affiliations

  • Hüseyin Koçak
    • 1
  1. 1.Lefschetz Center for Dynamical Systems Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0271-1
  • Copyright Information Springer-Verlag New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0273-5
  • Online ISBN 978-1-4684-0271-1
  • About this book