Asymptotic expansions for ordinary differential equations
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Asymptotic expansions for ordinary differential equations by Wolfgang Richard Wasow

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Published by Dover in New York .
Written in English

Subjects:

  • Asymptotic expansions.,
  • Differential equations -- Asymptotic theory.

Book details:

Edition Notes

Statementby Wolfgang Wasow.
Classifications
LC ClassificationsQA371 .W33 1987
The Physical Object
Paginationix, 374 p. :
Number of Pages374
ID Numbers
Open LibraryOL2380334M
ISBN 100486654567
LC Control Number87008906

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"A book of great value it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincaré in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to . Asymptotic expansions for ordinary differential equations. New York, Interscience Publishers [] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Wolfgang R Wasow. Additional Physical Format: Online version: Wasow, Wolfgang R. (Wolfgang Richard), Asymptotic expansions for ordinary differential equations. Similar expansions can be found for the other two solutions of (). This is a regular perturbation problem, since we have found asymptotic expansions for all three roots of the cubic equation using the simple expansion (). Figure showsthatthefunctionx3−x+ isqualitativelysimilarfor =0and0.

"A book of great value it should have a profound influence upon future research." — Mathematical Reviews. In this outstanding text, the first devoted exclusively to the subject, author Wolfgang Wasow concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. 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. unabridged republication of Technical Report 3, Office of Naval Research. 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. . This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure Mathematics.

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. This chapter discusses double asymptotic expansions for linear ordinary differential equations. The restrictive condition that the coefficient p(x) is a polynomial is not in itself necessary, particularly if the asymptotic study is limited to properly chosen sectors, provided that in this sectorp(x) shares with polynomials the properties of having a finitenumber of zeros, no poles, Cited by: 1. Ordinary differential equations an elementary text book with an introduction to Lie's theory of the group of one parameter. This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure . This chapter discusses double asymptotic expansions for linear ordinary differential equations. The restrictive condition that the coefficient p(x) is a polynomial is not in itself necessary, particularly if the asymptotic study is limited to properly chosen sectors, provided that in this sectorp(x) shares with polynomials the properties of.