Chaos: An Introduction to Dynamical Systems (Textbooks in Mathematical Sciences)
|Rating||:||4.88 (541 Votes)|
|Number of Pages||:||603 Pages|
The only prerequisites are calculus, differential equations, and linear algebra. Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.
Add to this a discussion of $\omega$-limit sets, including periodic and strange attractors, as well as a chapter on fractals, and the result is one of the most comprehensive texts on the topic that has yet appeared." Mathematical Reviews . Also, while most other introductory texts concentrate almost exclusively upon discrete mappings, here at least three of the thirteen chapters are devoted to differential equations, including the Poincare-Bendixson theorem. This is an important feature since the dynamics for the two cases and methods employed for their analyses may differ significantly. From the reviews:"… Written by some prominent contributors to the development of the field … With regard to both style and content, the authors succeed in introducing junior/senior undergraduate students to the dynamics and analytical techniques associated with nonlinear systems, especially those related to chaos … There are several
For my Taste One of the Best Undegraduate Texts This book presents brilliantly the foundations to Dynamical Systems and Chaos. You need to have some Linear Algebra, Calculus and Multivariable Calculus and Differential Equations knowledge. Full of exercises, computer experiments and Challenges. I think that the text looses some substance due to the lack of presenting more or all the solutions to the Exercises. They should be solved detailed in a Solutions M. "Exciting and Lucid Introduction to Chaos Theory" according to E. Nichols. This book is a must-own for anyone interested in nonlinear dynamics and chaos -- I also highly recommend the "Nonlinear Dynamics and Chaos" text by Strogatz.I especially like the numerous diagrams that clarify everything so well in this book. In addition, the writing includes just the right amount of informal discussion to truly explain the material without retreating into jargon.A favorite moment in the book. great introduction to dynamical systems A Customer I was enrolled in a course at GMU in which the draft version of this text was used. The math was not as difficult as some of the graduate texts, therefore it serves as a good intoduction for someone with as little as 2 years of undergraduate math. The challenges at the end of each chapter are more difficult than the regular problems, but they are meant to be. Many of the systems can be modeled on a spreadshee