Since the ?rst edition of this book was published in 2001, the algebraic computa- T tion package Maple has evolved from Maple V into Maple 13. Accordingly, the second edition has been thoroughly updated and new material has been added. In this edition, there are many more applications, examples, and exercises, all with solutions, and new chapters on neural networks and simulation have been added. Therearealsonewsectionsonperturbationmethods,normalforms,Gröbnerbases, and chaos synchronization. This book provides an introduction to the theory of dynamical systems with the aid of the Maple algebraic manipulation package. 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 16-18 deal with both continuous and discrete systems. Chapter 19 lists examination-type questions used by the author over many years, one set to be used in a computer laboratory with access to Maple, and the other set to be used without access to Maple. Chapter 20 lists answers to all of the exercises given in the book. It should be pointed out that dynamical systems theory is not l- ited to these topics but also encompasses partial differential equations, integral and integro-differential equations, stochastic systems, and time delay systems, for instance. References [1]-[5] given at the end of the Preface provide more inf- mation for the interested reader.
Rezensionen / Stimmen
From the reviews of the second edition:"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 (1st Edition)"This book covers standard material for an introduction to dynamical systems theory. Written for both advanced undergraduates and new postgraduate students, this book is split into two distinctive parts: continuous systems using ordinary differential equations and discrete dynamical systems. Lynch uses the Maple package as a tool throughout the text to help with the understanding of the subject. The book contains over 250 examples and exercises with solutions and takes a hands-on approach. There are over 300 individual figures including about 200 Maple plots, with simple commands and programs listed at the end of each chapter...This publication will provide a solid basis for both research and education in nonlinear dynamical systems." -The Maple Reporter (1st 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 (1st Edition)". a very nice tutorial on Maple in which quite a few mathematical and graphical commands are illustrated. A student could quickly work through this tutorial and then be ready to do quite a bit with Maple..[The second part of Hilbert's 16th problem] is not the topic encountered in most ODE texts, even if the question has been open for 100 years! .Lynch's book provides great references, as well as Maple code that could be easily modified by readers who have the tools to quickly engage in quite sophisticated numerical experimentation." -SIAM Review (1st Edition)"A student or scientist, who works through some chapters of the book, learns a good deal about the presented mathematical concepts and possibilities of the symbolic algebra package to assist the researcher in understanding his mathematical model." -Dynamical Systems Magazine (1st Edition)"This book, that provides an introduction to the study of dynamical systems with the aid of the algebraic package Maple, is the second edition of the well known classical book of Stephen Lynch . . a well written and highly readable introduction to the numerical study dynamical systems with Maple at an introductory level that covers many topics of this subject and can be used as a very valuable resource for many courses in applied mathematics and modelization in engineering and physical sciences." (Manuel Calvo, Zentralblatt MATH, Vol. 1193, 2010)
Auflage
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
216 s/w Abbildungen
XVIII, 500 p. 216 illus.
Dateigröße
ISBN-13
978-0-8176-4605-9 (9780817646059)
DOI
10.1007/978-0-8176-4605-9
Schweitzer Klassifikation
A Tutorial Introduction to Maple.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincar#x00E9; Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of Hilbert#x2019;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.
