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Chaos and Fractals
An Elementary Introduction
David P. Feldman
432 pages
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306 b/w line drawings, 31 b/w halftones
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246x189mm
978-0-19-956644-0
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Paperback
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09 August 2012
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- 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.
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.
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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. Author page
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"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
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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
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The specification in this catalogue, including without limitation price, format, extent, number of illustrations, and month of publication, was as accurate as possible at the time the catalogue was compiled. Occasionally, due to the nature of some contractual restrictions, we are unable to ship a specific product to a particular territory. Jacket images are provisional and liable to change before publication.
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