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Cambridge Tracts in Mathematics : Asymptotic Expansions Series Number 55 - E. T. Copson

Cambridge Tracts in Mathematics

Asymptotic Expansions Series Number 55

Paperback

Published: 2nd August 2004
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Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions.

Preface
Introduction
Preliminaries
Integration by parts
The method of stationary phase
The method of Laplace
Watson's lemma
The method of steepest descents
The saddle-point method
Airy's integral
Uniform asymptotic expansions
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521604826
ISBN-10: 0521604826
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 132
Published: 2nd August 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 21.5 x 14.2  x 0.9
Weight (kg): 0.18