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

ISBN-10: 0387989315
ISBN-13: 9780387989310
Edition: 1999
List price: $99.00 Buy it from $69.74
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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  More...

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Book details

List price: $99.00
Copyright year: 1999
Publisher: Springer
Publication date: 10/29/1999
Binding: Hardcover
Pages: 593
Size: 6.50" wide x 9.75" long x 1.25" tall
Weight: 2.090
Language: English

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.

Preface
Ordinary Differential Equations
Difference Equations
Approximate Solution of Linear Differential Equations
Approximate Solution of Nonlinear Equations
Approximate Solution of Difference Equations
Asymptotic Expansion of Integrals
Perturbation Series
Summation of Series
Boundary Layer Theory
WKB Theory
Multiple Scales Analysis
Appendix
References
Index

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