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Price: $60.95

Format:
Paperback 448 pp.
306 b/w line drawings, 31 b/w halftones, 189 mm x 246 mm

ISBN-10:
0199566445

ISBN-13:
9780199566440

Publication date:
September 2012

Imprint: OUP UK

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Chaos and Fractals

An Elementary Introduction

David P. Feldman

This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.

The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.

Readership : Undergraduate students and lecturers on specialist and non-specialist courses in physics and mathematics.

Reviews

  • "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

  • "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

I. Introducing Discrete Dynamical Systems
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

There are no Instructor/Student Resources available at this time.

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. He has recently begun a research project looking at trends in extreme precipitation events in Maine.

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Special Features

  • 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..