Scientific Computing

Book Description

Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.

Customer Reviews:

very nice conceptual overview.......2006-07-22

Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.

Not for the practitioner.......2005-11-17

If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.

Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.

He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.

I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.

Trash.......2005-10-14

If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.

Excellent Introduction, Sparse on Details.......2004-11-20

While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.

A Good Introductory Survey.......2002-11-05

This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.

Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications)

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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications)
V.L. Kocic , and G. Ladas
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 079232286X

Book Description

This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global asymptotic stability, periodicity, permanence and persistence, and also semicycles of solutions. As well as exposing the reader to the very frontiers of the subject, important open problems are also formulated.
The book has six chapters. Chapter 1 presents an introduction to the subject and deals with preliminaries. Chapter 2 considers global stability results. Chapter 3 is devoted to rational recursive structures. Chapter 4 describes various applications. The topic of Chapter 5 is periodic cycles, and Chapter 6 discusses a number of open problems and conjectures involving interesting types of difference equations. Each chapter includes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indices.
For graduate students and researchers whose work involves difference and differential equations.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences Vol. 42)

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Will never collect dust....
Background
Changed the Nature of Science As We Know It.
Basic and clasic

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences Vol. 42)
John Guckenheimer , and Philip Holmes
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0387908196

Book Description

From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2

Customer Reviews:

Will never collect dust...........2001-06-03

This book has been a continuing source of information and guidance for 18 years now. Students and researchers in many different fields have used this book due to its breadth and detail of coverage. The book does require a fairly advanced mathematical background, but the authors do include a glossary for the reader lacking this.

Chapter one is an overview of differential equations and dynamical systems. All the concepts needed for a study of such systems are discussed in great detail and also very informally, stressing instead the understanding of the concepts, and not merely their definition. Some of the proofs of the main results, such as the Hartman-Grobman and the stable manifold theorems, are omitted however.

This is followed in Chapter 2 by a very intuitive discussion of the van der Pols equation, Duffings equation, the Lorenz equations, and the bouncing ball. Numerical calculations are effectively employed to illustrate some of the main properties of the systems modeled by these equations.

A taste of bifurcation theory follows in Chapter 3. Center manifolds are defined and many examples are given, but the proof of the center manifold theorem is omitted unfortunately. Normal forms and Hopf bifurcations are treated in detail.

Averaging methods are discussed in Chapter 4, with part of the averaging theorem proved using a version of Gronwall's lemma. Several interesting examples of averaging are given, along with a discussion of to what extent the bifurcation properties of the averaged equations carry over to the original equations. Most importantly, this chapter discusses the Melnikov function, so very important in the study of small perturbations of dynamical systems with a hyperbolic fixed point. A full proof that simple zeros of the Melnikov function imply the transversal intersection of the stable and unstable manifolds is given.

Chapter 5 moves on to results of a more purely mathematical nature, where symbolic dynamics and the Smale horseshoe map are discussed. The proofs of the stable manifold theorem and the Palis lambda lemma are, however, omitted. Markov partitions and the shadowing lemma are discussed also but the latter is not proven. The authors do however give a proof of the Smale-Birkhoff homoclinic theorem. A purely mathematical overview of attractors is given along with measure-theoretic (ergodic) properties of dynamical systems.

The (local) bifurcation theory of Chapter 3 is extended to global bifurcations in the next chapter. A very detailed discussion of rotation numbers is given but the KAM theory is only briefly mentioned. The main emphasis is on 1-dimensional maps, the Lorentz system, and Silnikov theory. The authors give a very detailed treatment of wild hyperbolic sets.

The book ends with a discussion of bifurcations from equilibrium points that have multiple degeneracies. The discussion is more motivated from a physical standpont than the last few chapters. But some interesting mathematical constructions are employed, namely the role of k-jets, which have fascinating connections with algebraic goemetry, via the "blowing-up" techniques.

The concepts in the book have proven to have enduring value in the study of dynamical systems, and this book will no doubt continue to serve students and researchers in the years to come.

Background.......2001-01-11

Guckenheimer is one of my favourite book in nonlinear science. Another absolute reference. This books deserved to be milestone in nonlinear dynamics.

Changed the Nature of Science As We Know It........2000-01-26

This book has clearly withstood the test of time in over 15 years of continuous publication. On my bookcase, it stands among my most treasured and well-worn classics of fluid mechanics and differential equations--Hirsch and Smale, Birkhoff and Rota, Chandrasekhar, Bachelor, Lamb, Landau and Lifschitz... It changed many of the unquestioned assumptions of many fields besides my own. It redefined the terms of many scientific debates. And, it changed my life.

I obtained Guckenheimer and Holmes' classic when it first came out in 1983. It was so clear, concise and intellectually engaging that it inspired me to wonder whether the system of equations I was studying for my Ph.D. research at the time--the governing equations of thermal convection at infinite Prandtl number (which govern plate tectonics in the earth's mantle)--might have a chaotic solution. Guckenheimer and Holmes outlined a clear methodology to find out the answer.

My advisor at the University of Chicago thought not. Only steady solutions could be admitted in the absence of external forcing due to the lack of momentum transfer--this belief was widely held at the time, despite certain oscillatory solutions found by Fritz Busse (then at UCLA) and chaotic solutions found in certain limiting cases by Andrew Fowler at Oxford.

In despair, I left my studies at Chicago to work as a Unix sysadmin at my undergraduate alma mater --Cornell, where (unbeknownst to me when I took the job) John Guckenheimer had just relocated from UCSC. Delighted to find him there, I sat in on his courses. Later, with his help, I wrote a proposal to NASA to support the completion of my thesis--with him and Donald Turcotte serving as my advisors.

The 3-year fellowship was approved, and during this time I demonstrated and published that thermal convection at infinite Prandtl number--a condition that pervades many planetary interiors including our own--is indeed chaotic in the absence of external forcing.

Prior to this, planetary convection codes primarily looked for steady state solutions. Since, numerical analysts in the field have upgraded to time-dependent models. The source of chaos at infinite Prandtle number I identified--the heat advection term--is now widely accepted as the source of what is now called "Thermal Turbulence" in planetary interiors.

The defense at Chicago was quite an event. Since my new advisors were flown in from Ithaca, you might say my thesis--The Nonlinear Dynamics of Thermal Convection at Infinite Prandtl Number--passed with flying colors. Someone at Chicago might disagree, but his opinion is irrelevant.

Demonstrating the many possible solutions to a single set of equations and showing how the choice of solution depends very sensitively on the rather poorly-constrained initial conditions of the earth--does render mantle modeling itself rather superfluous and indeed, scientifically suspect. However, many important professors who stayed in the field nonetheless continue to run their time-dependent mantle convection codes, and never cease to wonder at the fact that they all get different results. It's rather amusing, really.

When all that too has passed away, the truths so beautifully put forth in Guckenheimer and Holmes will remain. Like I said, it's a classic. Furthermore, being number 42 in its series, it's got to be the answer to the ultimate question of life, the universe and everything. Was for me, anyway.

Basic and clasic.......1999-08-22

For the moment it is "the" book on Dynamical Systems, through the world. Its first chapter is a good introduction on the mathematics needed to aboard the subject. The second introduces chaos, and the rest is for a good understanding of the newest and prolific science.

Some Nonlinear Problems in Riemannian Geometry (Springer Monographs in Mathematics)

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Some Nonlinear Problems in Riemannian Geometry (Springer Monographs in Mathematics)
Thierry Aubin
Manufacturer: Springer
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Binding: Hardcover

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A Course in Differential Geometry (Graduate Studies in Mathematics)

ASIN: 3540607528

Book Description

During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber.

Iterative Methods for Linear and Nonlinear Equations (Frontiers in Applied Mathematics)

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Iterative Methods for Linear and Nonlinear Equations (Frontiers inApplied Mathematics, Vol. 16)

Iterative Methods for Linear and Nonlinear Equations (Frontiers in Applied Mathematics)
C. T. Kelley
Manufacturer: Society for Industrial Mathematics
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Binding: Paperback

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ASIN: 0898713528

Book Description

Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods.

Customer Reviews:

Iterative Methods for Linear and Nonlinear Equations (Frontiers inApplied Mathematics, Vol. 16).......2000-03-27

I recommend this book as a jump start to the arena. This is a comprehenshive book, that includes examples of the subjects discussed and script files in Matlab that are provided online.

Nonlinear Systems Analysis (Classics in Applied Mathematics)

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The best overview of nonlinear stability and control
A good book
Superb book for Nonlinear Systems

Nonlinear Systems Analysis (Classics in Applied Mathematics)
M. Vidyasagar
Manufacturer: SIAM: Society for Industrial and Applied Mathematics
ProductGroup: Book
Binding: Paperback

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ASIN: 0898715261

Book Description

When the first edition of this book was published, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques. The second edition provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. It contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Moreover, valuable reference material included in these chapters is unavailable elsewhere. The text also features a large number of problems that allow readers to test their understanding, and self-contained sections and chapters that make particular topics more accessible.

Customer Reviews:

The best overview of nonlinear stability and control.......2006-09-20

This is an elegant treatment of nonlinear systems concentrating on stability and controls. It includes all of the material in the textbooks only without the verbage. The treatment is deep and outstanding and parallels that of Khalil's and Isidori's books. The only caveat is that the book does assume a pretty good mathematical background from the reader and some experience reading very advanced mathematical tomes - some of the notation is never defined but those having the presumed background will not find this a problem. For the advanced student/practitioner.

A good book.......2003-11-24

Reviewer: NextNoName : )

The major portion of this book is on the conditions for stability of general nonlinear systems. The treatment is thorough. Stability is examined from both Lyapunov and I/O perspectives. Secondary portions are on quasi-linear approximation and differential geometry.

The commentaries of Dr. Vidyasagar at the beginning and end of each chapter are useful. This is because this book was written relatively recently by a master of this subject.

The thoughts flow well. I like the fact that the chapters are kept to only seven.

Superb book for Nonlinear Systems.......2003-01-07

Vid. is an excellent expositor. The material is presented rigourously, which might be standard for texts dealing with this subject, but also economically, which is not typical (read: Khalil). The most important distinction of this book however is that the author consistently explains the intuitions and motivation behind the theory (one example of many: what does a matrix norm mean "physically?"). This instead of you wading through mounds of mathematics never knowing why. The author is himself a practicing engineer, not an ivory tower researcher and this fortunate bias is evidenced in this book.

This text is unique in that it introduces the matrix measure (available elsewhere only in journal papers), a very useful technique that I personally have used in my own research. The final chapter on geometric methods distilled the essence of the very deep and daunting book by Van der Shaft, from which my course instructor culled his lecture notes. I was ahead of the curve in understanding the material thanks to this book.

In short, as an expositor nobody beat Vidyasagar.

Book Description

From the reviews:
"This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985
"Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985

Customer Reviews:

Excelent Reference .......2006-02-21

It is known among those people working in Elliptic Partial Differential Equations, that this book is one of the best references for the Most general results in the Theory. It is a Fantastic Book !!!! Furthermore, I was a little bit worried about the softcover since it is a big book, but the soft cover is completely fine. If you work in Elliptic PDE the book is a "must have"

Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists

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Not that good
Good Introduction To Chaos

Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists
J. M. T. Thompson , and Hugh B. Stewart
Manufacturer: John Wiley & Sons Ltd (Import)
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471909602

Book Description

Emphasizes the qualitative description of long-term recurrent motions of dissipative systems governed by genuinely nonlinear equations, with no assumptions of near-linearity. General concepts of the geometric theory are illustrated using computer simulations of specific ordinary differential and difference equations. The nonlinear phenomena discussed include the multiple attractors observable in a single system, chaotic long-term behaviour and its underlying order and structure, and discontinuous jump and hysteresis phenomena.

Customer Reviews:

Not that good.......2005-02-07

This book contains some standard topics treated on an elementary way. Unfortunatelly mathemathical formalism is almost left out.
The approach to the subject is pretty popular.
I think one is going to invest her/his own time in a better way by working first on V.I.Arnold's "Classical Mechanics" (symplectic formalism) then going on with E. Ott's "Chaos" (one of the best on the subject, but Lichtenberg-Liebermann is also a good one, in my opinion) and, finally, taking a look into some parts of Arnold's "Geometrical methods of ODE". More stuff is available on the Web (arxiv.org --> recent abstracts and new approaches on dynamical systems in Physics). This is a good way to gain a technical basis instead of a popular one.

Good Introduction To Chaos.......2004-03-27

The book is complex enough to provide good information on NLD, chaos, and the associated differential equations, but not so complex you can't get a firm working grasp of the subject. Lots of nice illustrations, clearly and concisely explained. Bifurcations, attractors and all that jazz is in there too if you want to make your own Poincare maps (also explained). I used the information from the book to generate visualizations of an externally excited system moving in and out of different modes of vibration. Such a techinique is not directly explaned in the text, but a good read of the first few chapters will provide the tools to do so. Recommended.

Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)

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Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)
Jan Chabrowski
Manufacturer: Walter de Gruyter
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ASIN: 311015269X

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

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A good book for introduction
An excellent introduction
A excellent introduction to chaos
fundamental, systematic
Good book!

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers
Robert Hilborn
Manufacturer: Oxford University Press, USA
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Binding: Paperback

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ASIN: 0198507232

Book Description

Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers). It is the only book at this level to include the increasingly important field of pattern formation and a survey of the controversial questions of quantum chaos. Important tools such as Lyapunov exponents and fractal dimensions are treated in detail. With over 200 figures and diagrams, and analytic and computer exercises for every chapter, the book can be used as a course-text or for self-instruction. This second edition has been restructured to make the book even more useful as a course text:many of the more complex examples and derivations have been moved to appendices. The extensive collection of annotated references has been updated through January 2000 and now includes listings of World Wide Web sites at many of the major nonlinear dynamics research centers. From reviews on the 1/e: 'What has been lacking is a single book that takes the reader with nothing but a knowledge of elementary calculus and physics all the way to the frontiers of research in chaos and nonlinear dynamics in all its facets. [...] a serious student, teacher, or researcher would be delighted to have this book on the shelf as a reference and as a window to the literature in this exciting and rapidly growing new field of chaos.' J.C. Sprott, American Journal of Physics, September 19944 'I congratulate the author on having managed to write an extremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self- explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner. [...] I strongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994

Customer Reviews:

A good book for introduction.......2007-05-22

I have recently bought this book. I have been studying on evolution of the test particles in a particular planewave spacetimes, and I have realized that the system admits a non-integrable structure. I should investigate whether the particle motion emerges chaos or not. But, my knowledge on chaos was almost zero, before buying this book. Now, I am going to complete the full analysis of the book, and I am much more familiar to the concept of chaos. However, this book can be used for just begining. To proceed to the advanced problems you should look for other materials, especially to the articles about chaos. I advise this book as a first book to start chaos.
Dr. Izzet Sakalli

An excellent introduction.......2007-03-09

Covers the basics in an in-depth manner, and exposes the reader to a wide range of exciting problems in dynamical systems theory. THE book to start with if one is interested in chaos.

A excellent introduction to chaos.......2003-11-25

This is an accessible and readable introductory textbook on chaos and nonlinear dynamics. It focuses on the ideas behind the theory of chaos, rather than on the details of the mathematics which can sometimes hinder rather than help the reader gain real insight into the mechanisms of nonlinear systems.

By this I do not mean that the author skips over the required mathematics. The text is intended for people with a solid background in differential equations, and some familiarity with classical dynamical systems is also helpful if not completely necessary. I would say it is targeted for advanced undergraduate or beginning graduate students in the mathematical sciences, as well as scientists/engineers with no background in chaos theory. However he does not get bogged down in mathematics at the expense of physical insight. I have been studying the book on my own and have run into few problems in understanding the explanations.

The first chapter goes over 3 chaotic systems as a practical way of introducing the reader to various features of such systems. This provides a basis of practical experience to draw upon for the rest of the book, where the principles of chaos are examined in greater detail. The extensive references given in the book are a valuable addition that can be used to further explore the scientific literature. The references include journal papers as well as books, articles, and software for dynamical systems.

If you have the requisite mathematical background and want to learn the basics of chaos and nonlinear dynamics, I highly recommend this book.

fundamental, systematic.......2001-11-07

If you are looking for a textbook or reference on chaos theory, I recommend you to buy this book.

If you read other books, you will eventually comment,'chaos is something related to mathematics, very abstract, has nothing to do with my messy bedroom...'

But if you read this book, you will scream,'Great! I have figured out the richness of the nonlinear world. I understand the different dynamical routes to chaos. I know different quantifying methods with their pros and cons. Most fascinating is that chaos is related to pattern formation and self organization, which I consider them as another field of knowledge before. Also chaos may provide a new approach to quantum mechanics, a good news for those including me who do not believe in the parallel universe interpretation. By the way, I learnt a lot from this book!'

Good book!.......2000-08-05

If you want to get on into chaos, just read this book. I especially like the very wide scope of the subjects considered and the insight provided by the author in pattern formation or quantum chaos.

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