Advanced Mathematical Methods for Scientists and Engineers I
Subtitle: Asymptotic Methods and Perturbation Theory
By: by Carl M. Bender, Steven A. Orszag
Contributors: Orszag, Steven A.
Publisher: Springer New York
Published: 1999
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 593
ISBN-13: 9781441931870; 9781475730692
Subjects: Mathematics; Global analysis (Mathematics); Engineering mathematics; Mathematical physics
Description: 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 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 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 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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Table of contents: title: Preface; title: Ordinary Differential Equations; title: Difference Equations; title: Approximate Solution of Linear Differential Equations; title: Approximate Solution of Nonlinear Equations; title: Approximate Solution of Difference Equations; title: Asymptotic Expansion of Integrals; title: Perturbation Series; title: Summation of Series; title: Boundary Layer Theory; title: WKB Theory; title: Multiple Scales Analysis; title: Appendix; title: References; title: Index.