Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition (Pure and Applied Mathematics) [Hardcover]

Stephen Smale (Author), Morris W. Hirsch (Author), Robert L. Devaney (Author)

Book Description

ISBN-10: 0123497035 | ISBN-13: 978-0123497031 | Publication Date: November 5, 2003 | Edition: 2

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

Editorial Reviews

Review

"The exposition is excellent. I particularly liked how the proofs are fairly easy to follow... There are several instances where 'What if...?' questions come up naturally and the authors explore these as though they were reading your mind." - Gareth Roberts, Holy Cross

"This text contains exactly what a student entering graduate school in Dynamical Systems needs to know; it is Dynamical Systems from three mathematicians who are not only among the world's most prominent experts in dynamical systems, but who are also among the world's best mathematical expositors. The book contains the benchmark models of chaos to which much of current research is compared"
- Bruce Peckham, University of Minnesota

"The presentation is very clear and often supported by carefully selected key-examples. The book meets very high pedagogical standards and certainly is a worthy successor of the original version."
-R. Steinbauer, Wien, in MONATSHEFTE FUR MATHEMATIC, VOL 147

Book Description

Rigorous yet accessible introduction to differential equations and dynamical systems

See all Editorial Reviews

Product Details

• Hardcover: 425 pages
• Publisher: Academic Press; 2 edition (November 5, 2003)
• Language: English
• ISBN-10: 0123497035
• ISBN-13: 978-0123497031
• Product Dimensions: 9.4 x 6.2 x 1.1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #60,842 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

106 of 106 people found the following review helpful:

4.0 out of 5 stars New Edition, February 25, 2004

By 

ken "kenhall" - See all my reviews

This review is from: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition (Pure and Applied Mathematics) (Hardcover)

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.

14 of 15 people found the following review helpful:

5.0 out of 5 stars Excellent Book, May 4, 2006

By 

W. Basener - See all my reviews
(REAL NAME)   

This review is from: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition (Pure and Applied Mathematics) (Hardcover)

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.

10 of 12 people found the following review helpful:

4.0 out of 5 stars A new version of a classic book, February 20, 2007

By 

areader "jguevara7" (Caracas, D.F. Venezuela) - See all my reviews

This review is from: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition (Pure and Applied Mathematics) (Hardcover)

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.