Dynamical Systems with Applications Using MAPLE
Seiten
2001
Birkhauser Boston (Verlag)
9780817641504 (ISBN)
Birkhauser Boston (Verlag)
9780817641504 (ISBN)
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Suitable for many kinds of dynamical systems courses, this book shows the power of using a computer algebra program to study dynamical systems. It provides an introduction to the theory of dynamical systems with the aid of the Maple algebraic manipulation package.
This work covers material for an introductory course in the theory of dynamical systems. There is a short tutorial in MAPLE to facilitate the understanding of the theory. The text is divided into two parts: continuous systems using differential equations and discrete dynamical systems. Differential equations are used to model examples taken from various topics such as mechanical systems, interacting species, electronic circuits, chemical reactions, and meterology. The second part of the text deals with real and complex dynamical systems. Examples are taken from population modelling, nonlinear optics, and materials science. Linear algebra and real and complex analysis are prerequisites.
This work covers material for an introductory course in the theory of dynamical systems. There is a short tutorial in MAPLE to facilitate the understanding of the theory. The text is divided into two parts: continuous systems using differential equations and discrete dynamical systems. Differential equations are used to model examples taken from various topics such as mechanical systems, interacting species, electronic circuits, chemical reactions, and meterology. The second part of the text deals with real and complex dynamical systems. Examples are taken from population modelling, nonlinear optics, and materials science. Linear algebra and real and complex analysis are prerequisites.
Preface.- A Tutorial Introduction to Maple Toolbox.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincare Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of David Hilbert's Sixteenth Problem.- Linear Discrete Dynamical Systems.- Nonlinear Discrete Dynamical Systems.- Complex Iterative Maps.- Electromagnetic Waves and Optical Resonators.- Fractals and Multifractals.- Chaos Control and Synchronization.- Neural Networks.- Simulation.- Examination-Type Questions.- Solutions to Exercises.- References.- Maple Program Index.- Index.
| Erscheint lt. Verlag | 1.4.2001 |
|---|---|
| Reihe/Serie | Progress in Mathematics ; No. 183 |
| Zusatzinfo | 200 black & white illustrations, 200 black & white line drawings |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 585 g |
| Einbandart | Paperback |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-13 | 9780817641504 / 9780817641504 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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