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Springer, 2010. - 382 pages.Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations.After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations. No prior knowledge of Maple is assumed, and all Maple examples are included on a CD.The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.
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Wiley, 2010. — 318 pages.
The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an...
Springer, 2011. — xvi;313 p. — ISBN 978-1-4419-6869-2 (Print) 978-1-4419-6870-8 (Online).
Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices...
Название: Hirsch M. ,Smale S. , Devaney R. , Differential Equations, Dynamical Systems, and an Introduction to Chaos.
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical...
Wiley, 1995. - 720 pages.
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems...
2-е изд., испр. - М.: ФИЗМАТЛИТ, 2003. - 296 с.
Обобщаются известные и предлагаются новые методы математического моделирования нелинейных динамических систем. На простых примерах пояснены механизмы возникновения динамического хаоса, самоорганизации и др. Предложен принципиально новый подход к моделированию динамических систем, основанный на теории возможностей и нечеткой...