Customer Reviews

Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (v. 1)

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1 star:		(1)

 

 

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.

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!

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

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!

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 used this book in grad school about 15 years ago and got it out again yesterday to learn more about sophisticated path deformations in the complex plane. This style of going through interesting examples, pointing out possible trouble and explaining the main ideas is perfect for physicists who need advanced math tools but hate typical math papers of the proof-lemma-proof-type.
It's not outdated, symbolic math software can do a lot, but often can't handle the full problem and you have to simplify by hand before starting the computer.

This is an essential textbook for all applied mathematicians, physicists and research oriented engineers. It is very well written, and explains an enormous lot. It explains it all very well too. I've used chapter 3 and 6 in class, and they were full of insights and information that you cannot find in any other textbook.

Imagine a math text with quotations from Sherlock Holmes! This is without question the finest book in print and out of print in applied mathematics. An invaluable text, this book explains the hardest concepts clearly and with analytic grace. One can only hope that they will write a second book.

Great for anyone taking Partial differential equations, mathematical physics, and the related courses. Carl Bender is a master of the field as well as a great book writer, as well as Orszag. The only complaint is the type setting--a bit too small. But not a big problem