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.
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!
Product Details :
Paperback: 512 pages
Publisher: Westview Press; 1 edition (January 19, 2001)
Language: English
ISBN-10: 0738204536
ISBN-13: 978-0738204536
Product Dimensions: 6.1 x 1 x 9.3 inches
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