Differential Dynamical Systems, Revised Edition by James D. Meiss (PDF)

Description

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems, Revised Edition begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts – flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Revisions include simplified and clarified proofs of a number of theorems, an expanded introduction to function spaces, additional exercises, and the correction of typographical errors. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.Audience: This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus.Contents: List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index

User’s Reviews

Editorial Reviews: About the Author James D. Meiss is a Professor in the Department of Applied Mathematics at the University of Colorado at Boulder. He is a fellow of the American Physical Society. His work in dynamical systems focuses on Hamiltonian dynamics, the transition to chaos, and the theory of transport.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I really like this book. It seems to be written for an engineer like myself. While I appreciate mathematical details and the finer points of many of the results, we always have the “yellow cover” math textbooks for providing those details. As a first technical entry into this hard subject, this is an excellent book.

⭐This is the worst written mathematical book I have ever read in my life. Author mentions functions without specifying what is the domain or codomain. What are the properties of a function? Is it smooth, continuous, neither? Definitions are so messy. For example: “Dynamical system is an evolution rule that defines a trajectory as a function of a single parameter (time) on a set of states (the phase space)” This won’t help me to determine what a dynamical system is and what is not. The notion of “evolution rule” is not given in a mathematically precise way anywhere. I apologise for being rude.

⭐I need it for my class, but It is definitely a reference that you should have. It covers all the topics it should cover.

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