Asymptotic Expansions for Ordinary Differential Equations

Wolfgang Wasow

Publisher:

Dover Publications

Publication Date:

2002

Number of Pages:

384

Format:

Hardcover

Series:

Dover Phoneix Editions

Price:

40.00

ISBN:

0486495183

Category:

Textbook

BLL Rating:

BLL

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

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Table of Contents

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Chapter I. Some Basic Properties of Linear Differential Equations in the Complex Domain
	1.	Preparatory Remarks
	2.	The Basic Existence Theorem and its Consequences
	3.	Circuit Relations About Singular Points
	Chapter II. Regular Singular Points
	4.	Method of Solution
	5.	Solutions at a Regular Singular Point
	Chapter III. Asymptotic Power Series
	6.	Introductory Remarks on Irregular Singular Points
	7.	Definition of Asymptotic Power Series
	8.	Elementary Properties of Asymptotic Series
	9.	The Existence of Asymptotic Series
	Chapter IV. Irregular Singular Points
	10.	Introduction
	11.	Formal Simplification
	12.	Analytic Symplification and Asymptotic Solution
	13.	Miscellaneous Remarks
	14.	Proof of the Main Asymptotic Existence Theorem when all Eigenvalues are Distinct
	15.	The Stokes Phenomenon
	Chapter V. Generalizations by Means of Jordan's Canonical Form
	16.	Jordan's Canonical Form
	17.	Solutions at Regular Singular Points: General Case
	18.	Proof of Theorem 12.1: General Case
	19.	Asymptotic Solution at an Irregular Singularity: General Case
	Chapter VI. Some Special Asymptotic Methods
	20.	Introduction
	21.	Calculating Asymptotic Expansions from Convergent Power Series
	22.	Solution by Laplace Contour Integrals
	23.	The Saddlepoint Method
	Chapter VII. Asymptotic Expansions with Respect to a Parameter
	24.	Introduction
	25.	Formal Theory
	26.	Analytic Symplification
	27.	Proof of Theorem 26.1
	28.	Shearing Transformations
	Chapter VIII. Turning Point Problems
	29.	Problems Reducible to Airy's Equation: Formal Theory
	30.	Problems Reducible to Airy's Equation: Analytic Theory
	31.	Short Report on Other Turning Point Problems
	Chapter IX. Nonlinear Equations
	32.	Introduction
	33.	Solution by Asymptotic Power Series
	34.	Transformation into a Linear Differential Equation
	35.	Solution by Exponential Series
	36.	Nonlinear Equations with a Parameter
	Chapter X. Singular Perturbations
	37.	Boundary Value Problems for Linear Equations
	38.	Boundary Value Problems for Linear Equations: The Method of Višik and Lyusternik
	37.	Initial Value Problems for Nonlinear Equations: Qualitative Theory
	40.	Series Expansions for the Initial Value Problem
	41.	Nonlinear Two-Point Boundary Value Problems
	42.	Decomposition of General Linear Systems of Singular Perturbation Type
	43.	Periodic Solutions of Singular Perturbation Problems: General Remarks
	44.	Periodic Solutions of Singular Perturbation Problems: Linear Theory
	45.	Series Expansions for Periodic Solutions of Singular Perturbation Problems
	Chapter XI. Integration of Differential Equations by Factorial Series
	46.	Factorial Series and Laplace Integrals
	47.	Solution of Differential Equations of Rank One by Factorial Series
	48.	Remarks on the Solution of Differential Equations of Higher Rank by Factorial Series
	Appendix: A Brief Summary of Some Recent Research
	Bibliography
	Subject Index