Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry And Engineering (Studies in Nonlinearity) 1st Edition

by Steven H. Strogatz (Author)

65 customer reviews

ISBN-13: 978-0201543445

ISBN-10: 0201543443

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Nonlinear Dynamics and Chaos with Student Solutions Manual: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and ... Edition (Studies in Nonlinearity) (Volume 1)
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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.

Product details

Series: Studies in Nonlinearity
Hardcover: 512 pages
Publisher: CRC Press; 1 edition (April 20, 1994)
Language: English
ISBN-10: 0201543443
ISBN-13: 978-0201543445
Product Dimensions: 6.4 x 1.2 x 9.5 inches
Shipping Weight: 1.3 pounds
Average Customer Review: 65 customer reviews
Amazon Best Sellers Rank: #355,555 in Books (See Top 100 in Books)
- #1121 in General Chemistry
- #1017 in Physics (Books)
- #22 in Biomathematics

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Best Math Textbook I've Read to Date

January 27, 2016

Format: PaperbackVerified Purchase

Preface: I'm a physicist first and a mathematician second, so rigor is less my focus than ideas. That said, this is the best math textbook I've ever read. I decided to start reading it the day before my class started, but by the time I walked into the class I was already to chapter 4 - the book was that easy to read. (I jumped into a higher level class because I knew I would be done the book in a week anyway.) If there was ever a math textbook I would recommend to people from outside of math, this would be it.

16 people found this helpful

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Cheesenerd

Exceptionally well written

December 8, 2010

Format: PaperbackVerified Purchase

This book was the textbook in a course on nonlinear dynamics that I took. The course covered most of chapters 2-8 (chapter 1 is an introduction and is very short), so please consider my comments from that context. Speaking personally as an individual student- I tend to rely very heavily on my textbooks for learning and generally read them deeply. This book was no exception.

Overwhelmingly, the great strength of this book is the quality of the writing style. This is a very rare math book in that it is actually fun to read. The examples are for the most part very good- easy to follow and understand. The author focuses a lot on the big picture perspective of the techniques involved and does a superb job of developing a very good intuition and feel for nonlinear systems. In fact, the prose is so readable, I would not have any hesitation recommending this book for someone wanting to teach them self the topic (assuming the necessary background of course). I feel that this book could easily accommodate such a student.

Another great strength of this book is the way that ideas build upon one another. The author has masterfully written a book in which your intuition about early concepts pave the way for understanding later concepts even though missing some ideas in the beginning will not cripple you in later chapters. (IE, in many books if you do not understand chapter 1, you will fail in chapter 2, etc...)

The problems are very doable, but yet seem to capture the essence of ideas in the chapters well. This is in contrast to many books in which the easy problems are practically busy work, and the problems that teach you something require you to saw off your left foot. The author strikes a nice balance here. Another nice feature is that the author draws actual models from a broad range of disciplines to build the practice problem sets and worked examples.

The only real complaint I have about this book (as a pure math guy), is that this book is VERY skimpy on the theory(as in proofs and connection with deeper ideas)- but I think this book is targeted to a non-mathematics or an applied math audience. Personally, I found this frustrating and somewhat unsatisfying, but consider the nature of the class/audience. The author does sprinkle some theory around, such as the occasional reference to Topology and a section on index theory- but don't blink, you might miss it. The author rarely provides proof for theorems, those that he does provide are generally very simple and seem to be provided for their intuitive value rather than rigorous completeness. I considered giving it 4 stars instead of 5 due to the lack of rigor, but both considering its intended audience and its effectiveness at building intuition dismissed that consideration quickly. If you are looking for a book that digs into the theory, this is definitely not the book for you- at least not as a primary reference.

Another minor shortcoming (not so much a short coming as quality which is lacking which could make this book better) is that the book provides practice problems for use on a computer(appropriately) but does not provide any example code at all. This is not a big deal, a quick google search could easily provide you with a basic demonstration of the syntax necessary to plot a system using the language of your choice, but still. Personally, I would not let such a thing be a deal breaker for this book. (At least the author has not taken the other extreme and written the book entirely around one particular proprietary language!)

Despite these shortcomings, I strongly recommend this book either as a primary text for a course in nonlinear dynamics targeted to a non-pure-math audience, or as a secondary reference for anyone. I think this is a great book that will serve you well!

Oh, if the author is reading this post-
ADD MORE COLOR PICTURES OF CHAOTIC SYSTEMS PLEASE!! I love looking at those!

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Average Consumer

Superb book.

June 15, 2007

Format: PaperbackVerified Purchase

This book provides an exceptional introduction to nonlinear dynamics. Math books are often trapped in equating rigor with formalisms and in compromising intuition to generalities. Strogatz book provides an exemplary guideline how both intuition and rigor may be served to transform a difficult topic into fun reading and highly applicable set of ideas. Here are the key elements of what you will find in this book.

A. The book builds up intuitive understanding of the key ideas of the field
from simple one dimensional dynamics to complex multi-dimensional behaviors.
B. Each chapter contains fascinating applications -- from fireflies synchronization and josephson junction to population dynamics and chaotic laser behaviors-- which are
fun to read and useful if you need to apply dynamics to solve research problems.
C. There are ample exercises and solutions to render this ideal book for self-learners. It provides a relatively broad coverage of the key ideas of the field, without taxing the reader with far corners of little interest.

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User

The book teaches how to approach problems and which techniques work best for which situations

May 7, 2015

Format: Kindle EditionVerified Purchase

An outstanding textbook that avoids the usual mathematics pitfall of being painfully dry. The book teaches how to approach problems and which techniques work best for which situations, instead of just the techniques themselves. Also, the Kindle edition of this book is likely the best Kindle edition of any textbook I've seen.

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Reviewer

Excellent introduction and reference text

March 7, 2003

Format: PaperbackVerified 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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Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry And Engineering (Studies in Nonlinearity) 1st Edition

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