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Saturday, May 9, 2020 | History

2 edition of Asymptotic expansions for ordinary differential equations found in the catalog.

Asymptotic expansions for ordinary differential equations

Wolfgang Richard Wasow

Asymptotic expansions for ordinary differential equations

by Wolfgang Richard Wasow

  • 275 Want to read
  • 5 Currently reading

Published by Interscience in New York .
Written in English


Edition Notes

Statement Wolfgang Richard Wasow.
SeriesPure and applied mathematics : a series of texts and monographs -- v.14, Pure and applied mathematics -- v.14.
The Physical Object
Pagination362p.
Number of Pages362
ID Numbers
Open LibraryOL18401437M

  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. : Jack K. Hale. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow.

  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. :   My book "Asymptotic Expansions for Ordinary Differential Equations" published in is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing.5/5(1).

  Rachana marked it as to-read Originally prepared for the Office of Naval Research, this important monograph introduces various methods for expansins asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. The book Asymptotic Expansions for Ordinary Differential Equations can give more knowledge and also the precise product information about everything you want. Why must we leave the good thing like a book Asymptotic Expansions for Ordinary Differential Equations? Wide variety you have a different opinion about e-book.


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Asymptotic expansions for ordinary differential equations by Wolfgang Richard Wasow Download PDF EPUB FB2

"A book Asymptotic expansions for ordinary differential equations book 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 Cited by:   "A book of great value it should have a profound influence upon future research." — Mathematical Reviews In this outstanding text, author Wolfgang Wasow concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite : Wolfgang Wasow.

"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.

Generally speaking, the Poincaré asymptotics is too general for the study of ordinary differential equations. A motivation of the Gevrey asymptotics is also given by the Maillet Theorem (cf. Theorem V). In §XI-1, we summarize the basic properties of asymptotic expansions of functions in the sense of Poincaré.

“This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations.

This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go.

Series Expansions for Periodic Solutions of Singular Perturbation Problems Chapter XI. Integration of Differential Equations by Factorial Series Factorial Series and Laplace Integrals Solution of Differential Equations of Rank One by Factorial Series Remarks on the Solution of Differential Equations of Higher Rank by Factorial Series.

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. Partial Differential Equations 11 Asymptotic Methods: Basic Ideas Asymptotic Expansions The Asymptotic Evaluation of Integrals 12 Asymptotic Methods: Differential Equations An Instructive Analogy: Algebraic Equations Ordinary Differential Equations Partial Differential Equations.

Differential Equations with a Large Parameter 4. Originally prepared for the Office erselyi 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.

The asymptotic analysis of nonlinear differential equations is a very difficult problem in general. Perhaps the most useful result in this area is the Cauchy–Kovalevskaya theorem, which guarantees the existence of Taylor series solutions for initial value problems related to analytic differential equations.

AsymptoticDSolveValue computes such a solution for the .Asymptotic Expansions (Cambridge Tracts in Mathematics) Book Title:Asymptotic Expansions (Cambridge Tracts in Mathematics) 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.