Synopses & Reviews
Review
From the reviews: "Stephen Lynch's book offers a comprehensive introduction to the theory and application of differential equations and dynamical systems methods. Its focus on applications and avoidance of overly technical arguments makes it a an equally good choice for teaching an undergraduate course in dynamical systems, as self-study for graduate students interested in dynamical systems, or as an introductory text for researchers seeking an overview of some current developments in applied dynamical systems. Most importantly, its content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the first place.--Dynamical Systems Magazine "This accessible university text shows how a wide range of differential equations work and begin to fail to work over a very wide range of solved and unsolvable applications. Mathematica is used throughout, from its tutorial introduction in Chapter 0 to the minimally chaotic neuromodule of the final section. This is the first work I have seen in which genuine self-education by computer is expected of the reader. The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.--Datafile, The Journal of the HPCC "The book is a good introduction to dynamical systems theory. ... This book presents an original, cheap and powerful solution to the problem of analysis of large data sets. ... The text is aimed at graduate students and working scientists in various branches of applied mathematics, natural sciences and engineering. ... recommend 'Dynamical Systems with Applications using MATHEMATICA®' as a good handbook for a diverse readership, for graduates and professionals in mathematics, physics, science and engineering." (Damian Trif, Studia Universitatis Babeş-Bolyai. Mathematica, Vol. LIV (4), December, 2009)
Synopsis
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. 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. Exercises are included at the end of every chapter. Both textbooks and research papers are presented in the list of references. Working Mathematica notebooks will be available at http: //library.wolfram.com/infocenter/Books/AppliedMathematics/. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. The material is also accessible to readers with a general mathematical background. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work.
Synopsis
This book provides an introduction to the theory of dynamical systems with the (R) aid of the Mathematica computer algebra system. It is written for both senior undergraduates and graduate students. The ?rst part of the book deals with c- tinuous systems using ordinary differential equations (Chapters 1-10), the second part is devoted to the study of discrete dynamical systems (Chapters 11-15), and Chapters 16 and 17 deal with both continuous and discrete systems. It should be pointedoutthatdynamicalsystemstheoryisnotlimitedtothesetopicsbutalso- compassespartialdifferentialequations, integralandintegrodifferentialequations, stochastic systems, and time-delay systems, for instance. References 1]- 4] given at the end of the Preface provide more information for the interested reader. The author has gone for breadth of coverage rather than ?ne detail and theorems with proofs are kept at a minimum. The material is not clouded by functional analytic and group theoretical de?nitions, and so is intelligible to readers with a general mathematical background. Some of the topics covered are scarcely covered el- where. Most of the material in Chapters 9, 10, 14, 16, and 17 is at a postgraduate levelandhasbeenin?uencedbytheauthor'sownresearchinterests. Thereismore theory in these chapters than in the rest of the book since it is not easily accessed anywhere else. It has been found that these chapters are especially useful as ref- ence material for senior undergraduate project work. The theory in other chapters of the book is dealt with more comprehensively in other texts, some of which may be found in the references section of the corresponding chapter.
Synopsis
This book 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.
Table of Contents
Preface 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 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 Examination-Type Questions Solutions to Exercises References Mathematica Program Index Index