Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford Applied and Engineering Mathematics) [Hardcover]

D. W. Jordan (Author), P. Smith (Author)

Book Description

ISBN-10: 0198565631 | ISBN-13: 978-0198565635 | Publication Date: October 21, 1999 | Edition: 3

Nonlinear ordinary differential equations was first published in 1977 and has since become a standard text in the teaching of the subject. It takes a qualitative approach, and is designed for advanced undergraduate and graduate students of dynamical systems in mathematics or mathematics-related subjects. The text of this third edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. The book is directed towards practical applications of the theory, with several hundred examples and problems covering a wide variety of applications. Prerequisites are kept to a minimum, with appendices containing the necessary mathematical theory new to this edition. From reviews of the first edition: "The book can profitably be used in a senior undergraduate course. It is well written, well motivated and contains some recent developments of interest which have not been readily accessible before at this level." V. Lakshmikantham in Mathematical Reviews From reviews of the second edition: "The subject has wide applications in physical, biological, and social sciences which continuously supply new problems of practical and theoretical importance. The book does a good job in motivating the reader in such pursuits, and presents the subject in a simple but elegant style."--P. K. Kythe in Applied Mechanics Reviews

Editorial Reviews

Review

On the second edition: "The subject has wide applications in physical, biological, and social sciences which continuously supply new problems of practical and theoretical importance. The book does a good job in motivating the reader in such pursuits, and presents the subject in a simple but elegant style." --P. K. Kythe in Applied Mechanics Reviews

On the first edition: "The book can profitably be used in a senior undergraduate course. It is well written, well motivated and contains some recent developments of interest which have not been readily accessible before at this level." --V. Lakshmikantham in Mathematical Reviews

About the Author

Dominic Jordan is at University of Keele. Peter Smith is at University of Keele.

Product Details

• Hardcover: 560 pages
• Publisher: Oxford University Press, USA; 3 edition (October 21, 1999)
• Language: English
• ISBN-10: 0198565631
• ISBN-13: 978-0198565635
• Product Dimensions: 9.3 x 6.1 x 1.5 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 3.6 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #3,951,689 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

5.0 out of 5 stars An Unique Resource, April 28, 2009

By 

Glenn E. Spangler "Chemical Physicist" (Baltimore, MD USA) - See all my reviews
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This review is from: Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers (Oxford Texts in Applied and Engineering Mathematics) (Paperback)

Jordan and Smith have done an excellent job in describing and providing techniques to solve non-linear differential equations. Non-linear ordinary differential equations are stiff and can be solved numerically, but numerical solutions do not provide physical parametric insight. Consequently, it is often necessary to find a closed analytical solution. When faced with this challenge in my personal research, I looked around for books that would help me solve the non-linear forced differential equation that science had presented to me. Even in a good research university library, I could not find any that beat Jordan and Smith's work. I did find summary presentations in the specialized literature of physics, but those works referenced Jordan and Smith for futher details. Together, Jordan and Smith's textbook and sourcbook provide a wealth of practical information for solving non-linear equations along with lots of good examples. I feel fortunate that I found their work and have successfully solved my equations following their advice. Their work even helped me to visualize and interpret my results. I heartily recommend the two books to anyone faced with the need to solve nonlinear ordinary differential equations using techniques (for example, averaging methods, perturbation methods, Fourier expansion methods, liapunov methods, chaos, etc.# that lie beyond those studied in college for solving linear differential equations.Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers #Oxford Texts in Applied and Engineering Mathematics#Nonlinear Ordinary Differential Equations: Problems and Solutions: A Sourcebook for Scientists and Engineers #Oxford Texts in Applied & Engineering Mathematics)

11 of 14 people found the following review helpful:

2.0 out of 5 stars very non-rigorous approach with a sizeable number of typos, February 23, 2006

By 

Stephen Becker - See all my reviews
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This review is from: Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford Applied and Engineering Mathematics) (Paperback)

(I am referring to the paperpack 3rd edition)

The text serves as an ok introduction to nonlinear ODEs. I would not recommend it for any kind of rigorous course, since the approach is very nonrigorous. There are no theorems, and no attempt at analysis, so you must take everything at the author's word. The book is mainly a large collection of examples. The difficulty of the problems depends on how rigorous you want the answers to be, and there are a lot of answers in the appendix (but without any comments about how they were derived).

Personally, the book irritates me, but I can see its usefulness. One of the main causes of irritation was the unusually high number of typos, at the rate of one per page in some chapters (and in the problems and their solutions too). I find this quite significant. This is the third edition, and there is no excuse for so many errors. I have never encountered a published book with this kind of error rate.

I do not have much experience with similar books, so I can't rate this text in context very well. It is similar to, say, Marion and Thornton's Classical Dynamics, except with less physics (of course) and more on difficult nonlinear ODEs, and with more typos.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Great book!, March 21, 2010

By 

Guerau B. Cabrera (Morgantown, WV) - See all my reviews
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Amazon Verified Purchase

This review is from: Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford Applied and Engineering Mathematics) (Hardcover)

I am taking a Nonlinear Dynamics course in grad school and this is the text book. Although it is very hard for any text book to be absolutely complete (without being extremely large) I think J&S do a good job at covering many aspects. There are several examples for each concept and good explanations. It will earn a place in my shelf of references.