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Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering [Anglais] [Relié]

Steven H. Strogatz

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Amazon.com: 4.7 étoiles sur 5  67 commentaires
114 internautes sur 116 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 Excellent introduction and reference text 7 mars 2003
Par Reviewer - Publié sur Amazon.com
Format:Broché|Achat vérifié
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.
72 internautes sur 72 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 Template for a Math book! 29 mars 2005
Par A reader - Publié sur Amazon.com
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!
31 internautes sur 32 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 Great intro to nonlinear dynamics with excellent examples 28 juillet 1998
Par Un client - Publié sur Amazon.com
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.
25 internautes sur 26 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 Nice intuitive introduction to chaos and nonlinear phenomena 24 novembre 2003
Par Josh Isralowitz - Publié sur Amazon.com
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.
12 internautes sur 12 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 Perfect introduction to Nonlinear Dynamics and Chaos 8 août 2002
Par "capitalistnihilist" - Publié sur Amazon.com
If you have read about Chaos and Nonlinear Dynamics and you wish to delve deeper into the mathematics behind the theories then this is the book for you. Strogatz is an excellent writer with an uncanny ability to make advanced concepts seem amazingly simple. The exercises and examples make this book perfect for the motivated self-learner. I must warn you however that you had better be at least somewhat familiar with ODE before you dive into this text. I strongly recommend this book!
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