Advanced Mathematical Methods for Scientists and Engineers: Asymptotic by Carl M. Bender

Product Description

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader 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.
Product Details
Amazon Sales Rank: #220333 in Books
Published on: 1999-10-29
Number of items: 1
Binding: Hardcover
593 pages
Editorial Reviews

Review

"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)

Book Info
Provides, a clear practical, and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. DLC: Differential equations--Numerical solutions.
Customer Reviews

Excellent !!!!!!!!
This is one of the finest books ever written on classical asymptotic analysis, one of the most useful areas in mathematics for engineering applications. The material is quite outdated now since the present research is almost completely computational.

Nevertheless, one of the finest applied mathematics texts.

very good
It's a very good book for students and engineers of science and technology. It's worth reading Orszag's book.

Deeply insightful and utterly fascinating
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!