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Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.

Price: $57.95

Format:
Paperback 384 pp.
168 b/w line and halftone illustrations, 189 mm x 246 mm

ISBN-10:
0199594589

ISBN-13:
9780199594580

Publication date:
December 2010

Imprint: OUP UK

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Chaos

The Science of Predictable Random Motion

Richard Kautz

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.

Readership : General readers, high-school and undergraduate students, and practising scientists who want a quick and easily accessible introduction to chaos theory.

Reviews

  • "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

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

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

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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Special Features

  • Elucidates the paradox of chaotic motion.
  • Discusses chaotic systems without the use of calculus.
  • Companion CD, with point-and-click animated experiments.
  • Uniquely comprehensive discussion at this level.
  • Includes historical perspective on chaos theory.