Customer Reviews

Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers (Oxford Texts in Applied and Engineering Mathematics)

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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)

(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.

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.

I am in an introductory graduate level math course using this textbook. I agree with the other reviewer who criticizes its lack of rigor, numerous typos, and overabundance of examples. The text is not well-written, so the authors wander among seemingly related topics within each chapter without giving much explanation of their background or intuitive insight into the physical phenomena they describe. Moreover, the examples have not been very instructive for me. They often leave out several steps (for example, many assume that you already have an analytic solution for a differential equation, thus I sometimes find myself needing to use Mathematica to derive one). The problems are loosely related to the examples, but there is enough of a disconnect between the two so that I have trouble doing the homework assignments. I find myself referring to other (more elementary) texts on differential equations for better insight into the problems.

I strongly discourage the use of this book and am looking forward to when the class ends.

Certainly worth the price. Very approachable. I haven't reviewed many similar books -- this text is good enough that I haven't felt the need.

Covers: solution, characterization, and stability analysis, including bifurcation and chaos.

The new 3rd edition is much better and significantly longer than the earlier editions.