Asymptotic analysis of differential equations

著者

• White, R. B.

書誌事項

Asymptotic analysis of differential equations

Roscoe B. White

Imperial college press, c2010

Rev. ed

• : pbk

注記

Includes bibliographical references (p. 397-400) and index

内容説明・目次

内容説明

The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.

目次

• Dominant Balance
• Exact Solutions
• Complex Variables
• Local Approximate Solutions
• Phase Integral Methods I
• Perturbation Theory
• Asymptotic Evaluation of Integrals
• The Euler Gamma Function
• Integral Solutions
• Expansion in Basis Functions
• Airy
• Phase Integral Methods II
• Bessel
• Weber-Hermite
• Whittaker and Watson
• Inhomogeneous Differential Equations
• The Riemann Zeta Function
• Boundary Layer Problems.

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詳細情報

• NII書誌ID(NCID): BB03242787
• ISBN:
  • 9781848166073
  • 9781848166080
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: London
• ページ数/冊数: xxiii, 405 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA372
  • DC22 : 515.35
• 件名:
  • LCSH : Differential equations -- Asymptotic theory