Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics (Academic Press), 60.)

Book Description

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.

* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon

NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems

Customer Reviews:

A new version of a classic book.......2007-02-21

I bought a copy of this new book and I have its old version with Hirsch and Smale as its only authors. Main differences between these books are some new chapters covering chaos and the exercises. Old version has better chapters dealing with linear algebra. I find this new version hard to read and it leaves many details to be filled by the reader. I would say that the new version is still a good choice for a second course in ODE or supplementary text for a graduate course. I gave it four stars.

Excellent Book.......2006-05-05

This is a great introduction to the next stage of differential equations after a first course. Devaney is a master of presenation, and makes everything seem easy. It is not as encyclopedic as some other books on this material, such as Arnold and Perko, but it is easier to read and still covers the most important advanced material.

good, not ideal.......2005-12-08

the two books by hirsch smale, one with devaney, seem like good books, but I am not crazy about either, at least from the few pages one can search online here.

the latter book with devaney just seems a dumbed down version of the earlier book by the two more famous authors. i expected that earlier book to be far better, but found to my regret that the two books actually share almost the same first page, and the main difference noticeable in the early going is that the 2 author work is poorly written, and the 3 author one is not written much better.

it is clearer but seems to be talking down to the reader in an annoying way. so neither is the absolute pleasure to read that the wonderfully written text of arnol'd is, or the classic of hurewicz. i would skip these books and get arnold and hurewicz instead.

New Edition.......2004-02-26

You should be aware that there are two similar books with similar titles by the same authors. The old edition is a hardcover all green book by Hirsch and Smale called:

"Differential Equations, Dynamical Systems and Linear Algebra"

The second with the lorenz attractors in yellow on the cover is by Hirsch, Smale and Devaney and is called:

"Differential Equations, Dynamical Systems and an Introduction to Chaos"

Now, that may be obvious to you, but it is important to note that because those are VERY different books (which I have both of right here). The 'old' one is a more theoretical text that mainly addresses linear systems and is organized more like a math monograph than a contemporary (i.e. with pictures and examples) textbook. It is difficult for most people. The newer version is COMPLETELY different and is written for a more diverse audience. It starts with linear systems but then goes into nonlinear systems and discrete systems. It is somewhat similar in character to Strogatz's Nonlinear Dynamics and Chaos. If you do not have a very strong abstract theoretical type of math background I would not recommend you start learning about differential equations from the "old" edition. You will find it very difficult. If you are used to a general abstract presentation of results you should be fine. For the NEW edition the level is very different. I would guess that courses in multi-variable calc, elementary diff eq, and linear algebra (if you understood them) would be sufficient preparation. Both books are excellent, just be clear on what you are looking for.

Global Lorentzian Geometry (Pure and Applied Mathematics)

Average customer rating:

Essential for an advanced student of relativity

Global Lorentzian Geometry (Pure and Applied Mathematics)
John K. Beem , Paul Ehrlich , and Kevin Easley
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824793242

Book Description

Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.

Customer Reviews:

Essential for an advanced student of relativity.......2005-11-16

My review is based on a previous edition of this text. I have seen the new (2nd) edition and it appears that several chapters have been added but the old chapters are essentially the same.

As of the time of this writing, I have only made it to the 2nd chapter (again, of the 1st edition). Nevertheless, I've read the introductory material in the introductory (1st) chapter several times, because it is so rich.

This text is perhaps most useful to a student who knows a few things about differential, to be more precise, Riemannian geometry (and is interested in general relativity). There are many differences between a Riemannian manifold and a Lorentzian manifold, where the latter metric is not positive definite in that the metric gives one negative eigenvalue. This text is quick to point out the differences, which is a great aid in understanding the new material.

I have some background in general relativity and from my experience in the subject there were many questions I had unanswered. This book is a blessing to me in that it has uncovered for me some of the mystery of Lorentzian manifolds, in particular space-times. There are still many things I do not understand but I am confident this text will aid me in getting a clearer picture.

I highly recommend this text to student of relativity theory who has an understanding of mathematical reasoning, and yearns for a stronger mathematical understanding of the Lorentzian manifold. The current edition is a bit expensive but even if you do not think it is worth it there are still some 1st editions floating around (#67 in the Dekker Pure & Applied Math Series) which are much cheaper. I may eventually buy the 2nd edition if I find the additional chapters make the book worth the price.

Advanced Calculus (Pure and Applied Mathematics)

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Advanced Calculus (Pure and Applied Mathematics)
Voxman
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 082476949X

Thermodynamics of Chaos and Order (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)

Average customer rating:

Great on many new insights... but where's chaos?
Great on many new insights... but where's chaos?
Great book!

Thermodynamics of Chaos and Order (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)
V Berdichevsky
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0582087341

Book Description

The discovery of chaotic motion in low-dimensional systems raised the question: What kind of thermodynamics describes a system if it is neither ergodic nor Hamiltonian or possesses a finite number of degrees of freedom? This Monographs is the first to discuss this question.

Customer Reviews:

Great on many new insights... but where's chaos?.......2002-04-10

Let me start out by saying that the previous reviewer was not
refering to this book at all. If there's something this book
does NOT cover is "quantum level events in liquid forms". It
is true that the author, in the last two chapters, covers the
statistical mechanics of turbulent flow, but quantum mechanics
is "barely" mentioned (at least *I* couldn't find it).

This book was written, according to the author, with an
undergraduate level of engineering in mind, and therefore is
extremely accessible. Indeed, the first two chapters on the
ergodic foundations of statistical mechanics are extremely
easygoing (AND fairly rigorous). In chapter 3, particular
emphasis is put on low-dimensional systems, e.g. the
Henon-Heiles oscillators, and chains of oscillators, e.g. the
Fermi-Pasta-Ulam problem. Both are shown to present statistical
behavior. After also spending a whole chapter with damped
systems, the author dedicates a long discussion on the stat
mech of turbulent flow in both 2- and 3-dimensions, which is
precisely his main subject of research.

In summary, it is actually a pretty neat book on ergodic
techniques for both low-dimensional systems and fluid motion,
and I strongly encourage you to buy it if you are interested
in either of these two subjects. The only reason I gave it 4
stars is, as the title suggests, because one could expect at
least *some* systematic discussion concerning "chaos" itself
and its relation to thermodynamics/statistical mechanics.
However, even elementary concepts such as Lyapunov instability,
KAM theorem and Kolmogorov-Sinai entropy are barely mentioned.

Great on many new insights... but where's chaos?.......2002-04-10

Great book!.......1999-04-27

The world that we live in is full of unpredictable and predictable occurrances. This book provides full explanations regarding quantum level events in liquid forms. Thermodynamics has is a key topic tha has opened and paved the road to many unknown events and this book rules!!!

Mathematical and Physical Theory of Turbulence, Volume 250 (Lecture Notes in Pure and Applied Mathematics)

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Mathematical and Physical Theory of Turbulence, Volume 250 (Lecture Notes in Pure and Applied Mathematics)

Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824723236

Book Description

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities and inviscid dissipation energy; validity of the idealized model incorporating local isotropy, homogeneity, and universality of small scales of high Reynolds numbers, Lagrangian statistics, and measurements; and subrigid-scale modeling and hybrid methods involving a mix of Reynolds-averaged Navier-Stokes (RANS), large-eddy simulations (LES), and direct numerical simulations (DNS). By sharing their expertise and recent research results, the authoritative contributors in Mathematical and Physical Theory of Turbulence promote further advances in the field, benefiting applied mathematicians, physicists, and engineers involved in understanding the complex issues of the turbulence problem.

Topological Vector Spaces (Pure and Applied Mathematics)

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Topological Vector Spaces (Pure and Applied Mathematics)
Lawrence Narici , and Edward Beckenstein
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824773152

The Navier-Stokes Equations: Theory & Numerical Methods (Lecture Notes in Pure and Applied Mathematics)

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The Navier-Stokes Equations: Theory & Numerical Methods (Lecture Notes in Pure and Applied Mathematics)
Rodolfo Salvi
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824706722

Book Description

"Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."

Optimal Design of Control Systems: Stochastic and Deterministic Problems (Pure and Applied Mathematics: A Series of Monographs and Textbooks/221) (Pure and Applied Mathematics)

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Optimal Design of Control Systems: Stochastic and Deterministic Problems (Pure and Applied Mathematics: A Series of Monographs and Textbooks/221) (Pure and Applied Mathematics)
Gennadii E. Kolosov
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824775376

Book Description

"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."

Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

Average customer rating:

Good book
good backround
The most understandable treatment of waves I have read!

Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
G. B. Whitham
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 0471359424

Book Description

Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Customer Reviews:

Good book.......2007-09-20

I took some graduate level courses from Dr. Whitham at CalTech in 1973 while this book was still in draft form, and he was the head of the Applied Mathematics department. He was an excellent lecturer, and this book has long been an exemplar of that style as well as the pioneer book in the treatment of non linear waves. To my knowledege it was the first textbook to treat solitons. The book is very subtle in its treatment of physics, and the adept reader will note the bearing of dispersion relations on the foundations of quantum mechanics.

good backround.......2000-03-06

Most treatment of waves involves their role in electromagnetic spectra. The writer provides the historical account of the derivation of these algebraic (read numerical analysis) versions which implement in MathCad and Matlab well. The book's material on water waves is worth the price alone. However, only at the end,does the author venture into the world of non-linear dynamics which is so important to this area. Most of the book treats the wave phenomenology as most physicists will in the kinematical sense trying to linearize everything and avoiding the path if it can't be linearized. (In this sense most of the arguements and examples are structured in the conservation of mass and energy). This is great, however for the construction of first order linear diff. equations for implementation in Mathcad or Matlab. If one were not aware of bifurcations, limit-cycles or even total response waves from control theory, one would still be left feeling secure that water waves are standing waves. (They are not). Early research breaks them up into first part(Airy) long-standing(middle of the wave) and orgin to get around this problem. Book does not approach treatment as a diffusion problem.

The most understandable treatment of waves I have read!.......1998-06-30

Linear and Nonlinear Waves provides an excellent treatment of the wave phenomena. This is a very complex and mathematically intesive subject, which Whitham conveys in an understandable and followable manner. He takes the approach that the reader has some knowlege of the subject, but writes at an introductory graduate level. This book will give any mathematician or engineer interested in waves an excellent introduction and bring them to a superior understanding.

Stability by Liapunov's Matrix Function Method with Applications (Pure and Applied Mathematics) (Pure and Applied Mathematics)

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Stability by Liapunov's Matrix Function Method with Applications (Pure and Applied Mathematics) (Pure and Applied Mathematics)
A.A. Martynyuk
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824701917

Book Description

"Provides a systematic study of matrix Liapunov functions, incorporating new techniques for the qualitative analysis of nonlinear systems encountered in a wide variety of real-world situations."

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