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Chaos and Fractals

An Elementary Introduction

David P. Feldman

09 August 2012

ISBN: 9780199566440

432 pages
Paperback
246x189mm

In Stock

Price: £35.99

For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.

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Description

For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.

  • Solutions manual available on request from the OUP website
  • The only textbook on chaos and fractals for non-science and mathematics majors.
  • Covers central phenomena and ideas of chaos and fractals in a careful, intellectually honest, but accessible way.
  • Covers current areas of physics and mathematics that are of wide interest
  • Richly illustrated.
  • Over 200 end-of-chapter exercises make it easy for instructors to assign homework problems.
  • A range of additional topics are covered from which instructors can chose as they put together their own courses.

About the Author(s)

David P. Feldman, Department od Physics and Mathematics, College of the Atlantic, Bar Harbor, Maine, USA

David Feldman joined the faculty at College of the Atlantic in 1998, having completed a PhD in Physics at the University of California. He served as Associate Dean for Academic Affairs from 2003 - 2007. At COA Feldman has taught over twenty different courses in physics, mathematics, and computer science. Feldman's research interests lie in the fields of statistical mechanics and nonlinear dynamics. In his research, he uses both analytic and computational techniques. Feldman has authored research papers in journals including Physical Review E, Chaos, and Advances in Complex Systems. In 2011-12 he was a U.S. Fulbright Lecturer in Kigali, Rwanda.

Table of Contents

    I. Introducing Discrete Dynamical Systems
    0:Opening Remarks
    1:Functions
    2:Iterating Functions
    3:Qualitative Dynamics
    4:Time Series Plots
    5:Graphical Iteration
    6:Iterating Linear Functions
    7:Population Models
    8:Newton, Laplace, and Determinism
    II. Chaos
    9:Chaos and the Logistic Equation
    10:The Buttery Effect
    11:The Bifurcation Diagram
    12:Universality
    13:Statistical Stability of Chaos
    14:Determinism, Randomness, and Nonlinearity
    III. Fractals
    15:Introducing Fractals
    16:Dimensions
    17:Random Fractals
    18:The Box-Counting Dimension
    19:When do Averages exist?
    20:Power Laws and Long Tails
    20:Introducing Julia Sets
    21:Infinities, Big and Small
    IV. Julia Sets and The Mandelbrot Set
    22:Introducing Julia Sets
    23:Complex Numbers
    24:Julia Sets for f(z) = z2 + c
    25:The Mandelbrot Set
    V. Higher-Dimensional Systems
    26:Two-Dimensional Discrete Dynamical Systems
    27:Cellular Automata
    28:Introduction to Differential Equations
    29:One-Dimensional Differential Equations
    30:Two-Dimensional Differential Equations
    31:Chaotic Differential Equations and Strange Attractors
    VI. Conclusion
    32:Conclusion
    VII. Appendices
    A:Review of Selected Topics from Algebra
    B:Histograms and Distributions
    C:Suggestions for Further Reading

Reviews

"... obtains top marks ... For any lecturer or teacher looking for a text on these subjects, this book is worthy of your consideration." - Gazette of the Australian Mathematical Society

"For the right audience and instructor, this is a wonderful book. With considerable effort on both sides it can take a wide audience with modest mathematics to a reasonable understanding of what is behind much of the complex phenomena seen in modern mathematical models of the physical universe." - Thomas B. Ward, Zentralblatt MATH

"This is an excellent book, and is highly recommended." - Mark Hunacek, Mathematical Association of America

"The only textbook on chaos and fractals for non-science and mathematics majors. Covers central phenomena and ideas of chaos and fractals in a careful, intellectually honest, but accessible way." - L'Enseignement Mathematique (2) 59

"Chaos and fractals are two intertwined concepts that have revolutionized many areas of science and renewed popular interest in mathematics over the past few decades. Feldman's book is a rich resource for anyone who wants a deeper understanding of these subjects without the need for advanced mathematics." - Julien Clinton Sprott, University of Wisconsin-Madison

"The style of writing is easy on the reader. The explanations are clear and illustrated with many diagrams and side notes....[Feldman] has produced an excellent book." - John Sykes, Mathematics in School

"David P. Feldman provides a delightful and thoughtful introduction to chaos and fractals requiring only a good background in algebra. The formal treatment of nonlinear dynamics, chaotic behavior, Lyapunov exponents, and fractal dimensions is leavened with creative analogies and many helpful and visually attractive figures and diagrams. Even more mathematically sophisticated readers will find this book a good starting point in exploring the complex and beguiling realms of chaos and fractals." - Robert C. Hilborn, Associate Executive Officer, American Association of Physics Teachers

"For the right audience and instructor, this is a wonderful book. With considerable effort on both sides it can take a wide audience with modest mathematics to a reasonable understanding of what is behind much of the complex phenomena seen in modern mathematical models of the physical universe." - Thomas B. Ward, Durham University

"The book is very well produced, with excellent diagrams and very informative notes provided beside the main text. It also provides an extensive list of references for further reading." - Scottish Mathematical Council Journal

"[haos and Fractals] offers at least the possibility of a radically different trajectory for school teaching, providing a motivated pathway to a lot of fascinating mathematics not normally considered accessible ..." - Danny Yee, Danny Reviews

Additional Resources

A solutions manual is available for this title. Please click here to order your copy.

A solutions manual is available for this title. Please click here to order your copy.

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