Textbook

Books Price Comparison (Including Amazon) - Guaranteed Lowest Prices on Books


 

Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

 
 
 
 
Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory
Author: Carl M. Bender - Steven A. Orszag
ISBN 13: 9780387989310
ISBN 10: 387989315
Edition: 1999
Publisher: Springer
Publication Date: 1999-10-29
Format: Hardcover
Pages: 593
List Price: $99.00
 
 

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.