Advanced Mathematical Methods for Scientists and Engineers: Asymptotic

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!


A Classic Resource   October 7, 2005
Ed Borasky (Beaverton, Oregon USA)
6 out of 7 found this review helpful

I'll echo the sentiments of the other reviewers here. I have a well-worn and well-used copy of the first (1978) edition. Believe it or not, I actually had a chance to use these methods as recently as last month (September 2005). I would recommend, though, if you want to get the most out of this book, pick up a symbolic calculation program or calculator capable of doing symbolic math. I use the open-source programs Maxima and Axiom for this, but if you want to actually spend money, Amazon has some calculators that will handle this sort of thing.


The Classic Text on Asymptotics   December 9, 2005
Glenn Ledder (Lincoln, NE USA)
12 out of 12 found this review helpful

I am a mathematics professor, and asymptotic methods is my area of expertise. Bender and Orszag was the standard text on this topic in the early 1980s, and it remains by far the most thorough book on the subject. I had two courses from it in graduate school and have taught from it 3 times now. I have never found a mistake. The book is very well written; its only weakness is that its graphics reflect the technology of the 1970s. Nevertheless, I am teaching from it again next year, because it is in a class by itself.

There is one thing that individual readers and faculty users should be aware of. Some of the exercises, including a few marked as "intermediate," are incredibly difficult. My instructor made the mistake of assigning exercises without working them first. I am careful not to assign any exercises until after I have worked them.


Remarkably powerful and practical tools for analysis   December 1, 1996
6 out of 6 found this review helpful

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


Deeply insightful and utterly fascinating   December 20, 2006
Monishv158
2 out of 2 found this review helpful

I had the privilege to explore this guide to the universe of asymptotics under Prof. Bender. I used to think, and still do (about 2 decades on), that this book is like the Rosetta Stone, and enables us to solve anything in applied mathematics.

A must have for anyone looking to understand the incredible universe we find ourselves in!