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Advanced Mathematical Methods for Scientists and Engineers I

Name: Advanced Mathematical Methods for Scientists and Engineers I
Brand: Springer, Berlin
SKU: 9781441931870
Price: 63.46 EUR
Availability: InStock

Asymptotic Methods and Perturbation Theory

Autor: Carl M. Bender, Steven A. Orszag

Jazyk:

Väzba: Brožovaná

Vydavateľ: Springer, Berlin

Dostupnosť: Skladom u dodávateľa

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63.46 €

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation th...

Informácie o knihe

Autor

Carl M. Bender, Steven A. Orszag

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2010

Stránok

593

EAN

9781441931870

ISBN

1441931872

Enbook ID

01421851

Vydavateľ

Springer, Berlin

Hmotnosť

910

Rozmery

155 x 235 x 32

Kompletný popis

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.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.

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Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

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