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Chaos and Fractals

David P Feldman

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.
Chaos and Fractals
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Expected delivery Sep 29 – Oct 05

Publisher Description

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.

Author Biography

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; II. CHAOS; III. FRACTALS; IV. JULIA SETS AND THE MANDELBROT SET; V. HIGHER-DIMENSIONAL SYSTEMS; VI. CONCLUSION; VII. APPENDICES

Review

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

Long Description

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.

Review Text

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 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

Feature

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.

Product Details

Author
David P Feldman
Year
2012
ISBN-10
0199566445
ISBN-13
9780199566440
Media
Book
Short Title
CHAOS & FRACTALS
Language
English
Publication Date
2012-08-09
Subtitle
An Elementary Introduction
Country of Publication
United Kingdom
Illustrations
306 b/w line drawings, 31 b/w halftones
Pages
408
Audience
College/Higher Education
Publisher
Oxford University Press, USA