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Advanced Mathematical Methods for Scientists and Engineers I : Asymptotic Methods and Perturbation Theory - 99 edition

Advanced Mathematical Methods for Scientists and Engineers I : Asymptotic Methods and Perturbation Theory (ISBN10: 0387989315; ISBN13: 9780387989310)
ISBN13: 978-0387989310
ISBN10: 0387989315

Summary: This book gives 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. These methods allow one to analyze problems that are encountered in physics and engineering that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The presentation is aimed at teaching the insig
hts that are most useful in approaching new problems; it avoids special methods and tricks that work only for particular problems, such as the traditional transcendental functions.

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 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.

...show more
Summary: This book gives 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. These methods allow one to analyze problems that are encountered in physics and engineering that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The presentation is aimed at teaching the insights that are most useful in approaching new problems; it avoids special methods and tricks that work only for particular problems, such as the traditional transcendental functions.

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 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.

...show less

Edition/Copyright: 99
Cover: Print On Demand
Publisher: Springer-Verlag New York
Year Published: 1999
International: No

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