![]() ![]() New users will find the tutorials will enable them to become familiar with Mathematica within a few hours. The first chapter provides an efficient tutorial introduction to Mathematica. For this reason, SystemModeler is very popular in the field of engineering. It is as close as one can get to building apparatus and investigating the output for a given input without the need for an actual physical model. The Wolfram SystemModelerTM package is used for simulating dynamical processes. It is an ideal package to adopt for the study of nonlinear dynamical systems the numerical algorithms work very quickly, and complex pictures can be plotted within seconds. ![]() Mathematica is extremely popular with a wide range of researchers from all sorts of disciplines, it has a very user-friendly interface and has extensive visualization and numerical computation capabilities. The book has a very hands-on approach and takes the reader from the basic theory right through to recently published research material. 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. It has been found that these chapters are especially useful as reference material for senior undergraduate project work. There is more theory in these chapters than in the rest of the book since it is not easily accessedĪnywhere else. Most of the material in Chapters 9–12 and 16–22 is at postgraduate level and has been influenced by the author’s own research interests. Some of the topics covered are scarcely covered elsewhere. The material is not clouded by functional analytic and group theoretical definitions, and so is intelligible to readers with a general mathematical background. The author has gone for breadth of coverage rather than fine detail and theorems with proofs are kept at a minimum. References – given at the end of the Preface provide more information for the interested reader. It should be pointed out that dynamical systems theory is not limited to these topics but also encompasses partial differential equations, integral and integro-differential equations, and stochastic systems, for instance. Chapter 24 lists answers to all of the exercises given in the book. Chapter 23 gives examples of coursework and also lists three Mathematica-based examinations to be sat in a computer laboratory with access to Mathematica. The first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations (Chapters 2–12), the second part is devoted to the study of discrete systems (Chapters 13–17), and Chapters 18–22 deal with both continuous and discrete systems. Chapter 1 provides a tutorial introduction to Mathematica–new users should go through this chapter carefully whilst those moderately familiar and experienced users will find this chapter a useful source of reference. It is written for both senior undergraduates and graduate students. This book provides an introduction to the theory of dynamical systems with the aid of Mathematica. There are also new chapters on delay differential equations, image processing, binary oscillator computing, and simulation with Wolfram SystemModeler. In this edition, there are many more applications, examples and exercises, all with solutions, and new sections on series solutions of ordinary differential equations and Newton fractals, have been added. Accordingly, the second edition has been thoroughly updated and new material has been added. R Since the first printing of this book in 2007, Mathematica has evolved from Mathematica version 6.0 to Mathematica version 11.2 in 2017. Stephen Lynch School of Computing, Mathematics and Digital Technology Manchester Metropolitan University Manchester UK ISBN 978-4-7 ISBN 978-5-4 (eBook) DOI 10.1007/978-5-4 Library of Congress Control Number: 2017947473 c Birkh¨ 1st edition: auser Boston 2007 c Springer International Publishing AG 2017 2nd edition: This book is published under the trade name Birkhauser (The registered company is Springer International Publishing AG The registered company address is: GewerbestraCham, Switzerland Dynamical Systems with Applications using Mathematica Second Edition ![]()
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