UID:
almahu_9949199326402882
Umfang:
XIII, 399 p. 83 illus.
,
online resource.
Ausgabe:
1st ed. 2001.
ISBN:
9781489928498
Inhalt:
"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple." -UK Nonlinear News (Review of First Edition) "The book will be useful for all kinds of dynamical systems courses.... [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. ... [It] is well written and a pleasure to read, which is helped by its attention to historical background." -Mathematical Reviews (Review of First Edition) Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gröbner bases, and chaos synchronization. The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author's website. Additional applications and further links of interest may be found at Maplesoft's Application Center. Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering. ISBN 978-0-8176-4389-8 § Also by the author: Dynamical Systems with Applications using MATLAB®, ISBN 978-0-8176-4321-8 Dynamical Systems with Applications using Mathematica®, ISBN 978-0-8176-4482-6.
Anmerkung:
0 A Tutorial Introduction to Maple -- 1 Differential Equations -- 2 Linear Systems in the Plane -- 3 Nonlinear Systems in the Plane -- 4 Interacting Species -- 5 Limit Cycles -- 6 Hamiltonian Systems, Lyapunov Functions, and Stability -- 7 Bifurcation Theory -- 8 Three-Dimensional Autonomous Systems and Chaos -- 9 Poincaré Maps and Nonautonomous Systems in the Plane -- 10 Local and Global Bifurcations -- 11 The Second Part of David Hilbert's Sixteenth Problem -- 12 Limit Cycles of Liénard Systems -- 13 Linear Discrete Dynamical Systems -- 14 Nonlinear Discrete Dynamical Systems -- 15 Complex Iterative Maps -- 16 Electromagnetic Waves and Optical Resonators -- 17 Analysis of Nonlinear Optical Resonators -- 18 Fractals -- 19 Multifractals -- 20 Controlling Chaos -- 21 Examination-Type Questions -- 22 Solutions to Exercises -- References -- Textbooks -- Research Papers.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9780817641504
Weitere Ausg.:
Printed edition: ISBN 9781489928504
Sprache:
Englisch
DOI:
10.1007/978-1-4899-2849-8
URL:
https://doi.org/10.1007/978-1-4899-2849-8
