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25 Remote Warehouse Mathematics- Differential Equations

Asymptotic Expansions

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Asymptotic Expansions Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

The theory of 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.

Synopsis:

Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.

Table of Contents

Preface; 1. Introduction; 2. Preliminaries; 3. Integration by parts; 4. The method of stationary phase; 5. The method of Laplace; 6. Watson's lemma; 7. The method of steepest descents; 8. The saddle-point method; 9. Airy's integral; 10. Uniform asymptotic expansions; Bibliography; Index.

Product Details

ISBN:
9780521604826
Editor:
Bollobas, Bela
Editor:
Fulton, W.
Editor:
Bollobas, Bela
Editor:
Fulton, W.
Author:
Kirwan, F.
Author:
Katok, A.
Author:
E. T., Copson
Author:
Bollobas, B.
Author:
Copson, E. T.
Author:
Fulton, W.
Author:
Sarnak, P.
Publisher:
Cambridge University Press
Location:
Cambridge
Subject:
General
Subject:
Differential Equations
Subject:
General Mathematics
Subject:
Mathematics-Differential Equations
Subject:
Algebra - Abstract
Edition Description:
Trade paper
Series:
Cambridge Tracts in Mathematics
Series Volume:
55
Publication Date:
20040431
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Pages:
132
Dimensions:
8.48x5.58x.36 in. .39 lbs.

Related Subjects

Science and Mathematics » Materials Science » General
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry

Asymptotic Expansions New Trade Paper
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Product details 132 pages Cambridge University Press - English 9780521604826 Reviews:
"Synopsis" by , The theory of 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.
"Synopsis" by , Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
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