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[size=120%]Advanced Mathematical Methods for Scientists and Engineers
(International Series in Pure and Applied Mathematics)
By Carl M. Bender, Steven A. Orszag
- Publisher: Mcgraw-Hill College
- Number Of Pages: 576
- Publication Date: 1978-06
- ISBN-10 / ASIN: 007004452X
- ISBN-13 / EAN: 9780070044524
Product Description:
This book gives a clear, practical and self-contained presentationof the methods of a symptotics and perturbation theory for obtainingapproximate analytical solutions to differential and differenceequations. These methods allow one to analyze physics and engineeringproblems that may not be solvable in closed form and for whichbrute-force numerical methods may not converge to useful solutions. Thepresentation is aimed at teaching the insights that are most useful inapproaching new problems; it avoids special methods and tricks thatwork only for particular problems, such as the traditionaltranscendental functions.
Intended for graduate students andadvanced undergraduates, the book assumes only a limited familiaritywith differential equations and complex variables.
Thepresentation begins with a review of differential and differenceequations; develops local asymptotic methods for differential anddifference equations; explains perturbation and summation theory; andconcludes with a an exposition of global asymptotic methods, includingboundary-layer theory, WKB theory, and multiple-scale analysis.Emphasizing applications, the discussion stresses care rather thanrigor and relies on many well-chosen examples to teach the reader howan applied mathematician tackles problems. There are 190computer-generated plots and tables comparing approximate and exactsolutions; over 600 problems, of varying levels of difficulty; and anappendix summarizing the properties of special functions.
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发表于 2009-7-10 16:58:33
发表于 2014-11-4 23:11:44