Overview

Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.

Full Product Details

Author:   Richard Kautz (Formerly of the National Institute of Standards and Technology, Boulder, USA)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 19.00cm , Height: 2.00cm , Length: 24.70cm
Weight:   0.858kg
ISBN:  

9780199594580

ISBN 10:   0199594589
Pages:   384
Publication Date:   04 November 2010
Audience:   General/trade ,  Young adult ,  General ,  Teenage / Young adult
Format:   Paperback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

1: Chaos Everywhere 2: Galileo Galilei --- Birth of a New Science 3: Isaac Newton --- Dynamics Perfected 4: Celestial Mechanics --- Clockwork Universe 5: Pendulum --- Linear and Nonlinear 6: Josephson Effect --- Synchronization 7: Chaos Forgets the Past 8: Chaos Takes a Random Walk 9: Chaos Makes Noise 10: Edward Lorenz --- Butterfly Effect 11: Chaos Comes of Age 12: Tilt-A-Whirl --- Chaos at the Amusement Park 13: Billiard-Ball Chaos --- Atomic Disorder 14: Iterated Maps --- Chaos Made Simple 15: State Space --- Going with the Flow 16: Strange Attractor 17: Fractal Geometry 18: Stephen Smale --- Horseshoe Map 19: Henri Poincaré --- Topological Tangle 20: Chaos Goes to Work

Reviews

`This is altogether a brilliantly written book that reflects the huge dedication and passion of the author to explaining the phenomenon of chaos. I can highly recommend this work to any reader who wishes to understand fundamental concepts and ideas of chaos without the need to employ any advanced mathematical formalism.' Rainer Klages, Journal of Statistical Physics `Dr. Kautz has written a book that captures the essentials of chaos in a quantitative way but without advanced mathematics. It is highly recommended for students and others with a good background in algebra and trigonometry and with a desire for a better understanding of the concepts of chaos.' Julien Clinton Sprott, University of Wisconsin - Madison `The writing style is engaging and readable... while there is a great deal of mathematical detail in the book, it is introduced carefully and thoroughly. Having a 'Dynamics Lab' of computational examples is an excellent notion, and will complement the book ideally.' Rob Sturman, University of Leeds `Kautz's Chaos provides a lively and clear introduction to many aspects of nonlinear dynamics, weaving together tales about the pendulum, Josephson junctions, the quincunx, the first four notes of Beethoven's 5th Symphony, the tilt-a-whirl and homoclinic tangles, using just algebra, geometry and trigonometry.' Robert Hilborn, University of Texas at Dallas `[Chaos] could serve as the basis for a college-level general science course as well as a resource for curious nonscientists. Kautz writes well, provides easy-to-follow explanations, and includes historical context through biographical sketches.' Eric Kincanon, Choice Reviews `Richard Kautz has written an excellent text that is suitable for undergraduates and provides the mathematical detail necessary to give a thorough introduction to chaos ... a superb book that presents chaos and chaotic systems so that readers will understand the concepts and understand what is so fascinating about this phenomenon ... I highly recommend this book.' David Mazel, MAA Reviews

The book is a famous introduction into the wide field of chaos and provides a very good basis for further studies. It is very useful for many persons: students in engineering, natural sciences, and mathematics or people interested in a better understanding of the nature of chaos. It is highly recommended. ZAMM - Journal of Applied Mathematics and Mechanics

Author Information

Richard Kautz is an engineer and physicist who holds a doctorate from the Massachusetts Institute of Technology. During his career at the National Institute of Standards and Technology, he helped develop fundamental quantum standards for both voltage and capacitance. Kautz is a Fellow of the American Physical Society and a recipient of the Samuel Stratton Award for measurement science and the Edward Condon Award for scientific writing.

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