A First Course in Discrete Dynamical Systems

  • Richard A. Holmgren

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Richard A. Holmgren
    Pages 1-7
  3. Richard A. Holmgren
    Pages 9-19
  4. Richard A. Holmgren
    Pages 21-29
  5. Richard A. Holmgren
    Pages 31-39
  6. Richard A. Holmgren
    Pages 41-46
  7. Richard A. Holmgren
    Pages 47-56
  8. Richard A. Holmgren
    Pages 57-66
  9. Richard A. Holmgren
    Pages 67-77
  10. Richard A. Holmgren
    Pages 79-93
  11. Richard A. Holmgren
    Pages 105-114
  12. Richard A. Holmgren
    Pages 115-139
  13. Richard A. Holmgren
    Pages 141-153
  14. Richard A. Holmgren
    Pages 155-180
  15. Richard A. Holmgren
    Pages 181-189
  16. Back Matter
    Pages 191-215

About this book

Introduction

An increasing number of colleges and universities are offering undergradu­ ate courses in discrete dynamical systems. This growth is due in part to the proliferation of inexpensive and powerful computers, which have provided access to the interesting and complex phenomena that are at the heart of dynamics. A second reason for introducing dynamics into the undergradu­ ate curriculum is that it serves as a bridge from concrete, often algorithmic calculus courses, to the more abstract concepts of analysis and topology. Discrete dynamical systems are essentially iterated functions, and if there is one thing computers do well, it is iteration. It is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Every effort has been made to exploit this opportunity to illustrate the beauty and power of mathematics in an interesting and engaging way. This work is first and foremost a mathematics book. Individuals who read it and do the exercises will gain not only an understanding of dynamical systems, but an increased understanding of the related areas in analysis as well.

Keywords

Calc Mathematica Microsoft Access bifurcation calculus chaos development dynamical systems function functions mathematical analysis mathematics proof sets system

Authors and affiliations

  • Richard A. Holmgren
    • 1
  1. 1.Department of MathematicsAllegheny CollegeMeadvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0222-3
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94208-7
  • Online ISBN 978-1-4684-0222-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book