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Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) [Paperback]

Steven H. Strogatz
4.7 out of 5 stars  See all reviews (63 customer reviews)

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Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity)
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Book Description

January 19, 2001 0738204536 978-0738204536 1
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.

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Editorial Reviews

About the Author

Steven H. Strogatz is professor of applied mathematics at Cornell University. He received his Ph.D. from Harvard University in 1986. Professor Strogatz has been honored with several awards including MIT's highest teaching prize, the E.M. Baker Award for Excellence in Undergraduate Teaching, as well as a Presidential Young Investigator Award from the National Science Foundation. His research on a wide variety of nonlinear systems-from synchronized fireflies to small-world networks-has been featured in the pages of Scientific American, Nature, Discover, Business Week, and The New York Times . 

Product Details

  • Series: Studies in Nonlinearity
  • Paperback: 512 pages
  • Publisher: Westview Press; 1 edition (January 19, 2001)
  • Language: English
  • ISBN-10: 0738204536
  • ISBN-13: 978-0738204536
  • Product Dimensions: 9.2 x 6 x 1 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (63 customer reviews)
  • Amazon Best Sellers Rank: #11,953 in Books (See Top 100 in Books)

More About the Author

Steven Strogatz is the Schurman Professor of applied mathematics at Cornell University. A renowned teacher and one of the world's most highly cited mathematicians, he has been a frequent guest on National Public Radio's Radiolab. Among his honors are MIT's highest teaching prize, membership in the American Academy of Arts and Sciences, and a lifetime achievement award for communication of math to the general public, awarded by the four major American mathematical societies. He also wrote a popular New York Times online column, "The Elements of Math," which formed the basis for his new book, The Joy of x. He lives in Ithaca, New York with his wife and two daughters.

Customer Reviews

Most Helpful Customer Reviews
114 of 116 people found the following review helpful
5.0 out of 5 stars Excellent introduction and reference text March 7, 2003
Format:Paperback|Verified Purchase
It is rare that books of this type are both comprehensive and readable. Strogatz has managed to cover a wide range of concepts in significant detail while providing examples to illustrate his major points.

The beginning of the text starts of with one dimensional nonlinear systems of first order (like the logistic equation), and Strogatz outlines the typical framework that one uses to analyze such systems. He defines fixed points, illustrates and defines bifurcations, and solidifies every claim with good examples.

The text eventually moves to higher order systems with coupled or non-coupled sets of differential equations. For the most part, exercises for the student involve sets of two differential equations that can be linearized using Jacobian methods.

Later, Strogatz provides a nicely executed description of fractals and fractal dimension, using examples from the Cantor set and the von Koch curve.

The beauty of the book is that it is well written and complete. It even provides some limited solutions to selected exercises in the back. The examples in the book cover a wide range of areas. Mechanical oscillating systems like a mass on a spring, electrical circuits that follow the same equations, laser models that follow a modified logistic equation, and many variations of the Lotka-Volterra model are outlined through examples in the text.

The book is a stand-alone text, equally useful as a textbook for an intorductory course or as a reference for someone merely surveying the subject. It deserves the highest rating possible.

Edit: 2/28/07

Now with a few years of hindsight, I would say this might have been the best stand alone textbook I had in grad school. This was one of the few books I had where I could teach myself the subject matter by just reading it. It is a great book that takes the mysticism out of a new and growing field.
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72 of 72 people found the following review helpful
5.0 out of 5 stars Template for a Math book! March 28, 2005
Were all Math books written like this, the number of students majoring in Math, Physics, etc. would rise considerably. The presentation is clear, lucid and comprehensive. Each concept is introduced with its motivating phenomena and the mathematical treatment is logical and elegant with many worked examples. This is one of those rare Math books that "begin at the beginning", yet go on to develop the concepts to a point useful even to grad students who want a review of basics before plunging into more advanced material. (If you are looking for more detailed mathematical stuff, I'd suggest Kevorkian's "Multiple Scale and Singular Perturbation Methods" or "Perturbation Methods" by Hinch.)

For the benefit of those reviewers who have complained that the mathematics is not rigorous enough, may I point out that the author clearly states the book is an introduction to the topic. I have come across other introductory books using basic differential equations, on similar topics where the material is presented in a disjointed way. Strogatz, however, shows us the inter-relatedness of the broad range of concepts and applications that fall within the title. Therein lies a major strength of this book.

Another big plus is that Strogatz presents those intermediate diagrams and results that take us to the final conclusion. Also he interprets the Math en route to the finale. He does not employ the usual "it is apparent that ..." strategy to pole-vault to miracle steps. This approach makes the book a breezy read; a remark not commonly made about advanced Math books!
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31 of 32 people found the following review helpful
By A Customer
This book is an excellent introductory graduate level text on nonlinear dynamics for those who wish to understand the basic concepts before seeing the mathematical rigor at the heart of the subject. Strogatz avoids getting caught up in mathematical nuances which often cloud the big picture for non-math students, and thereby clearly impresses upon the reader the essence of nonlinear dynamics, eventually building up to chaos. The examples and problems are truly unique and inspiring. This book is an excellent starting place for someone who knows little or nothing about nonlinear dynamics but has done some basic work with linear differential equations and linear algebra.
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25 of 26 people found the following review helpful
Basically, if you have a solid foundation in elementary multivariable calculus (calc III) and some aspects of ODEs, and want to know just what's going on with this new 'chaos trend,' and more importantly want to know why 'chaos' is actually useful, then read this book. As one reviewer noted, this book is not mathematically rigorous, and there's a simple reason for this: one can't explain nonlinear phenomena rigorously with just an elementary multivariable calculus backround. To rigorously treat the material in this book, you must have at least some point-set topological backround and have a decently strong real analysis backround (even Strogatz uses concepts from analysis and topology in an elementary way, such as compactness and measure) and even more advanced books that assume such a backround are sometimes less than rigorous (i.e. 'Perko' often says 'it can be shown' rather than showing it himself.) However, the lack of rigor I think is a good thing. Strogatz always nicely indicates 'why something should be true,' which for a beginner will give them a intuition about the subject so that if they gain the backround mentioned above, they can dive farther into this subject by using other advanced books. Finally, this book should be used as a third year undergraduate text. It should not be used as an advanced undergraduate/first year graduate text, since such courses should be more in depth and rigorous.
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Most Recent Customer Reviews
5.0 out of 5 stars Strogatz always keeps it interesting
Strogatz is very applications-oriented in his writing. Every chapter builds a framework of analyzing nonlinear systems that is immediately applied to tumor growth, lasing... Read more
Published 2 months ago by Matthew Murphy
4.0 out of 5 stars Just about the right amount of math
I bought this book to get a little more of the math than what was in Gleick's Chaos book from years ago. Read more
Published 3 months ago by Greg Steele
5.0 out of 5 stars An exciting work
Clear exposition of the qualitative and mathematically descriptive aspects of nonlinear dynamics. Lucid in most spots, but requiring an alert, intelligent reader in others. Read more
Published 4 months ago by Thomas J. Martino
5.0 out of 5 stars Superb Textbook
This is an incredible book, I must say. It's definitely a bit technical at times, but it's all presented so well. Read more
Published 5 months ago by C. Kemp
5.0 out of 5 stars Probably the best-written math book I ever encountered
The subject was very interesting to me and the qualitative and highly descriptive approach coupled with Strogatz's casual style made this book a page-turner in my case.
Published 6 months ago by falcor84
5.0 out of 5 stars Indispensable textbook for your advanced undergraduate library
Classic textbook. The exposition is rather elementary, but it was a wealth of examples that are interesting, engaging and accessible to the students. Read more
Published 7 months ago by RH
5.0 out of 5 stars Necessary for all in dynamical systems
The book meets the expectations built upon the numerous references it has in scientific publications. Straightforward and very clearly written, tackling complex notions.
Published 8 months ago by Athanasia Nikolaou
5.0 out of 5 stars Great Text
I used this book for a class last fall. I did not buy this book at the time but instead made use of a copy from our library. Read more
Published 10 months ago by RAR
4.0 out of 5 stars very good
If only my college math textbooks had been written this way. This is a nice, lucid approach. It gives a good foundation and introduction, with basic concepts explained without... Read more
Published 13 months ago by John Gardener
4.0 out of 5 stars Good read
He makes studying dynamics thousand times more fun, what a total recommendation for any graduate Math or Engineering class.. cool
Published 14 months ago by Mochamad Adrian Prananda
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