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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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Top Customer Reviews
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.
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.
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!
Most Recent Customer Reviews
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. Read morePublished 6 months ago by Amazon Customer
This book is a fine way to gain a solid working introduction to non-linear dynamics. Written by an applied mathematician working in the area, the text is conceptually rich, while... Read morePublished 6 months ago by Critic at large
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... Read morePublished 14 months ago by User
No review can properly describe the value of this book. Simply the best!Published 15 months ago by mike kovy
Initially, I strongly disliked this book and the course I was taking it along side of. However, I found that Strogatz has his lectures on Youtube for this course and I started... Read morePublished 15 months ago by William F. Blake
Great introductory undergraduate book for dynamics.Published 23 months ago by Differential Manifold
It's the right book for both beginners and experts that want to keep a good reference.Published 23 months ago by fpnc