A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
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Editorial Reviews
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"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews)
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Most Helpful Customer Reviews
28 of 29 people found the following review helpful
By Glenn Ledder
Format:Hardcover
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.
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.
27 of 32 people found the following review helpful
By Philip Hobbs
Format:Hardcover
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!
8 of 9 people found the following review helpful
By A Customer
Format:Hardcover
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
Most Recent Customer Reviews
4.0 out of 5 stars
Thank you
Every thing in the book and delivery was perfect exept that it has no hard cover, I thought its price for hard cover.
Published 4 months ago by Dhuha Shareef
5.0 out of 5 stars
A must own book but very challenging....
I was introduced to this book when I first took a course on Perturbation and Asymptotic Methods. The chapters on Boundary Layer theory, and WKB theory are well written and fun to... Read more
Published 5 months ago by Bessel
5.0 out of 5 stars
Singularity is almost invariably a clue
This is, perhaps, one of the best textbooks I have ever read. I have a habit of reading books that are far above my education and skills. Read more
Published 9 months ago by ubpdqn
5.0 out of 5 stars
Classic, fun to read
This is one of those books that you can read for fun. I'd rate it as my best book along with Carrier's ODE book. It says it's meant for advanced undergrads and grad students. Read more
Published on April 19, 2011 by Praveen Narayanan
5.0 out of 5 stars
Very good book
I used this book for a Graduate level course. I liked it a lot, is very good but a little bit dense. I still used it after the course, it is absolutely worth the price.
Published on March 16, 2011 by Manu
4.0 out of 5 stars
useful book
The book is good and the methods seem effective. It assumes a very serious mathematical background, however, and the problems are quite challenging.
Published on February 19, 2011 by kgj
5.0 out of 5 stars
Every home should have one
I have learned a lot of asymptotic methods from this book, having spent several previous years wondering what that stationary phase method that the physicsts were on about was (by... Read more
Published on April 21, 2010 by Narada
1.0 out of 5 stars
Very disappointed.
I had seen this book in a bookstore over 15 years ago and regretted that I did not buy it at that time. Now that I have it, I am very disappointed. Read more
Published on February 9, 2010 by A. I. Haque
5.0 out of 5 stars
outstanding!
I was looking for a long time for a textbook to use for a graduate course in advanced mathematics for engineers and this book is exactly what I need! Read more
Published on December 30, 2009 by CSD
5.0 out of 5 stars
Still the Best
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. Read more
Published on May 15, 2008 by T.I.
Citations (learn more)
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- A Study in Scarlet (Oxford World's Classics) by Arthur Conan Doyle on page 3, page 36, and page 205
- A Study in Scarlet by Arthur Conan Sir Doyle on page 3, page 36, and page 205
- A Study in Scarlet (Penguin Popular Classics) by Sir Arthur Conan Doyle on page 3, page 36, and page 205
- Study in Scarlet on page 3, page 36, and page 205
- A Study in Scarlet by Arthur Conan Sir Doyle on page 3, page 36, and page 205
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- Mathematical Methods for Scientists and Engineers: Linear and Nonlinear Systems (Wiley Science Paperback Series) by Peter B. Kahn on 4 pages
- Mathematical Methods for the Natural and Engineering Sciences (Series on Advances in Mathematics for Applied Sciences, Vol. 65) by Ronald E. Mickens on page 193, page 304, and page 435
- Essential Mathematical Methods for Physicists: and Engineers by Hans J. Weber on page 318, page 904, and Back Matter
- Mathematical Methods for Physicists, Fourth Edition by George B. Arfken on page 361, page 1004, and Back Matter
- Mathematical Methods for Physicists, Sixth Edition: A Comprehensive Guide by George B. Arfken on page 401, page 1107, and page 1151
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