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Dynamical Systems with Applications using Maple(TM) [Paperback]

Stephen Lynch
4.6 out of 5 stars  See all reviews (8 customer reviews)
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Book Description

Nov. 27 2009 0817643893 978-0817643898 2nd ed. 2010

Excellent reviews of the first edition (Mathematical Reviews, SIAM, Reviews, UK Nonlinear News, The Maple Reporter)

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

Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science

Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering

A hands-on approach is used with 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 with additional applications and further links of interest at Maplesoft’s Application Center


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Review

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)

From the Back Cover

"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


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Customer Reviews

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Most helpful customer reviews
5.0 out of 5 stars More information Sept. 30 2003
Format:Paperback
Thought I'd give a more in depth review than the others here.
Most advanced math textbooks contain one or two chapters that turn me off. I must say that every chapter in this book had useful information or very good applications.
The opening chapter is a brief introduction to Maple V (some Maple 8 commands are posted on the books website). Note that Maple 9 is now out and no doubt Maple X will soon follow.
Chapters 1-7 cover planar systems in some detail, vectorfield in DEplot is a real winner here. Chapters 8 and 9 cover 3D and nonautonomous systems - the poincare command in Maple is a real time saver.
Chapters 10-12 cover a lot of research results on limit cycles - the most lucid I have seen in any textbook.
The remaining half of the book concentrates on both real and complex discrete systems. There are the usual cobweb diagrams, bifurcation diagrams and Mandelbrot set. Where this book comes into its own, however, is in Chapters 16-20.
Lasers and nonlinear optics are investigated using complex iterative maps. Fractals and even multifractals are discussed in some detail. The book ends with a chapter dedicated to chaos control.
Overall, the book is concise with pertinent examples and applications. It is not dogged down with math notation, theorems and proofs.
Strogatz, Perko and Allgood are good books to practice more Maple programing techniques.
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5.0 out of 5 stars This is great book Aug. 5 2003
By Woo
Format:Paperback
This is only book I find with program files that work right away. Graphics in Maple is excelent for chaotic system and algebra very powerful. I like to rotate figures in 3D and use animation. I learn more about optics, it nice to see complex numbers used in applications. Lots of other applications also.
Book is best for students who want to get programs working quickly. There is a website with working programs. You should also look at Maple Application website for many many examples.
I recomend book to everyone.
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2.0 out of 5 stars Not ready for print June 3 2003
Format:Paperback
This book is rife with errors, omissions, grammatical and programming mistakes, hand-waving and is generally misleading about theorems. Only if you know very little about linear algebra and diff eq. will you not notice this -- this book only skims the surface of topics (breaking down easy cases in R^2 so poorly that when the same topic comes up in R^3 it's "a whole new thing") and theorem statements are often confusing compared to better sources at best. In all fairness, the book is very ambitous, but there is not enough content in the book to tackle actual problems not couched in its own terms. Many of the graphs and examples are nice, but they do not make up for the lack of editing, organization, and rigor (of even the usual "applied math" variety -- no one is expecting pure math here) in this book. The first two chapters are deceptively nice -- things begin to drop off quickly. Update: The ever dropping price of a new edition does not lie -- if you can, pick up Perko instead.
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5.0 out of 5 stars very nice introduction to dynamical systems Feb. 7 2002
By A Customer
Format:Paperback
This book is a very nice introduction to the theory of dynamical
systems. It covers all aspects and even more than usually thaught
in a class on dynamical systems. Especially, I like to see
many examples for various applications. These examples and the
Maple programs make it well suitable for students to learn
on dynamical systems by themself.
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