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Asymptotic Expansions

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Asymptotic Expansions Cover

 

Synopses & Reviews

Publisher Comments:

Originally prepared for the Office of Naval Research, this important monograph introduces various methods for the asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. Author's preface. Bibliography.

Synopsis:

Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.

Table of Contents

  Introduction; References

Chapter I. Asymptotic Series

  1.1 O-symbols

  1.2 Asymptotic sequences

  1.3 Asymptotic expansions

  1.4 Linear operations with asymptotic expansions

  1.5 Other operations with asymptotic expansions

  1.6 Asymptotic power series

  1.7 Summation of asymptotic series

  References

Chapter II. Integrals

  2.1 Integration by parts

  2.2 Laplace integrals

  2.3 Critical points

  2.4 Laplace's method

  2.5 The method of steepest descents

  2.6 Airy's integral

  2.7 Further examples

  2.8 Fourier integrals

  2.9 The method of stationary phase

  References

Chapter III. Singularities of Differential Equations

  3.1 Classification of singularities

  3.2 Normal solutions

  3.3 The integral equation and its solution

  3.4 Asymptotic expansions of the solutions

  3.5 Complex variable. Stokes' phenomenon

  3.6 Bessel functions of order zero

  References

Chapter IV. Differential Equations with a Large Parameter

  4.1 Liouville's problem

  4.2 Formal solutions

  4.3 Asymptotic solutions

  4.4 Application to Bessel functions

  4.5 Transition points

  4.6 Airy functions

  4.7 Asymptotic solutions valid in the transition region

  4.8 Uniform asymptotic representations of Bessel functions

  References

Product Details

ISBN:
9780486603186
Author:
Erdelyi, Arthur
Author:
Erdbelyi, Arthur
Author:
lyi
Author:
Erdelyi, A.
Author:
lyi, A.
Author:
Mathematics
Author:
A. Erd
Author:
Erd
Author:
&
Author:
eacute
Publisher:
Dover Publications
Subject:
General
Subject:
Asymptotic expansions
Subject:
General Mathematics
Subject:
Mathematics - General
Subject:
Infinity
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20101131
Binding:
TRADE PAPER
Language:
English
Pages:
128
Dimensions:
8 x 5.38 in 0.33 lb

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Related Subjects

» History and Social Science » World History » General
» Science and Mathematics » Mathematics » Advanced
» Science and Mathematics » Mathematics » Analysis General
» Science and Mathematics » Mathematics » General
» Science and Mathematics » Mathematics » Numeric Analysis
» Young Adult » General

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Product details 128 pages Dover Publications - English 9780486603186 Reviews:
"Synopsis" by ,
Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.
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