Advertisement

It's a Nonlinear World

  • Richard H.¬†Enns

Table of contents

  1. Front Matter
    Pages 1-1
  2. WORLD OF MATHEMATICS

    1. Front Matter
      Pages 1-1
    2. Richard H. Enns
      Pages 3-28
    3. Richard H. Enns
      Pages 29-69
    4. Richard H. Enns
      Pages 71-98
    5. Richard H. Enns
      Pages 99-128
  3. OUR NONLINEAR WORLD

    1. Front Matter
      Pages 129-129
    2. Richard H. Enns
      Pages 131-171
    3. Richard H. Enns
      Pages 173-192
    4. Richard H. Enns
      Pages 193-233
    5. Richard H. Enns
      Pages 235-253
    6. Richard H. Enns
      Pages 255-279
    7. Richard H. Enns
      Pages 281-310
    8. Richard H. Enns
      Pages 311-344
  4. Back Matter
    Pages 339-339

About this book

Introduction

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the remainder of Part I covers nonlinear mathematical concepts such as fixed points, limit cycles, fractals, chaos, bifurcations, and solitons, and nonlinear diagnostic tools such as fixed point analysis, bifurcation diagrams, and Lyapunov exponents, to name a few. Part II of the text presents illustrative examples of nonlinear dynamics that are highly relevant to the contemporary world. At the end of each chapter, a wide variety of problems are presented which extend the ideas developed in the chapter as well as allow the reader to explore other aspects of our nonlinear world. The mathematical level of the text assumes good working knowledge of basic calculus and prior exposure to ordinary differential equations and the wave and diffusion equations. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world" or for self-study by practicing scientists and engineers. The more casual reader can simply read the book for intellectual enjoyment.

Keywords

Differential Equations Mathematical Modeling Nonlinear Systems

Authors and affiliations

  • Richard H.¬†Enns
    • 1
  1. 1., Department of PhysicsSimon Fraser UniversityBurnabyCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-75340-9
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-75338-6
  • Online ISBN 978-0-387-75340-9
  • Series Print ISSN 1867-5506
  • Series Online ISSN 1867-5514
  • Buy this book on publisher's site
Industry Sectors
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences