This is an applied math book which is highly usable, and also very good for building intuitive understanding. I have recommended this book highly for many years, and I am delighted to see it back in print.

This is the best applied mathematics book I have ever read, bar none. It is primarily a text on asymptotic methods for integrals, sums, differential equations, and difference equations (recurrence relations). Major topics are Laplace's method, steepest descents, stationary phase, WKB theory, boundary layer theory, and regular and singular perturbation theory. The exposition shows an understanding of the needs and tastes of physicists and engineers far beyond the usual dry theorems. It is full of lore and insight, plus the best analytic and numerical examples extant. There are hundreds of good problems as well. If you need to use asymptotic methods in your work, or just want a good read in applied math, this is your book

Very useful, in contrast with the cookbooks on 'mathematical physics' otherwise available. Systematic, with good examples and workable but challenging homework problems (I used this book for years while teaching advanced 'math methods in physics')Where else do you learn about Fuch's theorem? Good, systematic approach to asmptotic expansions, especially evaluation of integrals. Provided examples of deterministic chaotic systems before that subject was in vogue. Best description (as motion in phase space) of torque-free rigid body in free fall. Also good on boundary layer theory. Excellent text!

I have the fortune of having Professor Bender teach the content of this book to me. His dynamic lecturing style, sense of humor, and astounding cleverness are all visible through the text of this book.

If you can't get to Washington University to take a class with him, at least buy the book. His writing style and frequent examples make the most elusive and suble concepts quite clear. I can't wait for his and Orzag's second book to be released!

I learned more mathematics from Bender & Orszag than from any other math book I own. I'm an applied physicist, and as any physicist knows, a sleazy approximation that provides good physical insight into what's going on in some system is far more useful than an unintelligible exact result.

This book covers approximate methods for solving differential and difference equations, asymptotic methods for integrals, and asymptotic and extrapolation methods for sums. There are a great many beautiful plots, and lots of discussion of the actual lore of doing--alternative ways of attacking the same problem, things to watch out for, what sorts of problems a given method is best at.

I think the most valuable parts of this book are the examples and problems, both of which are the best anywhere.

It's really great to see this old friend (first published in 1978) back in print. If you have ugly differential equations or integrals to solve, buy it!