Stephen Lynch

Dynamical Systems with Applications using Mathematica® (eBook, PDF)

• Format: PDF

Produktbeschreibung

Dynamical Systems with Applications using Mathematica^® provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks.

Mathematica's symbolic, numerical, and graphical capabilities make it ideal for the study of nonlinear dynamical systems. An introductory chapter provides complete tutorials on how to use Mathematica's text-based input commands and palettes, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at http://library.wolfram.com/infocenter/Books/AppliedMathematics/.

Throughout the book, the author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum. The first part of the book deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Some of the material presented is at the postgraduate level and has been influenced by the author's own research interests. Exercises are included at the end of every chapter. A comprehensive bibliography including textbooks and research papers rounds out the work.

The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work.

Also by the author:

Dynamical Systems with Applications usingMATLAB^®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Maple, ISBN 978-0-8176-4150-4

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 484
• Erscheinungstermin: 20. September 2007
• Englisch
• ISBN-13: 9780817645861
• Artikelnr.: 43730029

Autorenporträt

Stephen Lynch is Senior Lecturer in the Department of Computing and Mathematics at Manchester Metropolitan University. Also by the author: Dynamical Systems with Applications using Maple(TM), ISBN 978-0-8176-4389-8 Dynamical Systems with Applications using MATLAB®, ISBN 978-3-319-06819-0

Inhaltsangabe

A Tutorial Introduction to Mathematica.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincaré Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of 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.- Examination-Type Questions.- Solutions to Exercises.

Rezensionen

"Lynch's book provides a through and very readable introduction to the dynamical systems. It addresses all the topics that one would expect, including both continuous-time and discrete-time models and at a level appropriate for experienced undergraduates and early postgraduates." (J.M Christian, Mathematics Today, Vol. 54 (04), August, 2018)