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Basic Theory of Ordinary Differential Equations : Universitext - P.F. Hsieh

Basic Theory of Ordinary Differential Equations

Universitext

Hardcover

Published: 22nd June 1999
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The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results that are applicable in a variety of different fields. The text is suitable for a one-year graduate course, as well as a reference book for research mathematicians. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history. The book has 114 illustrations and 206 exercises. Hints and comments for many problems are given.

"This book in pure mathematics will guide the reader on a newly marked path through classic and awesome terrain---first so well described by Coddington and Levinson---toward research in the important and useful areas of power series solutions and asymptotics. The path not taken would be marked by at least one explicit mention of a PoincarA (c) map, a resonance in celestial mechanics, an average, a traveling wave, or a transversal intersection of separatrices."--MATHEMATICAL REVIEWS

Fundamental Theorems of Ordinary Differential Equations
Dependenceof Data
Nonuniqueness
General Theory of Linear Systems
1= Singularities of the First Kind
Boundary-value Problems of LinearDifferential Equations of the Second Order
Asymptotic Behavior ofSolutions of Linear Systems
Stabiblity
Autonomous Systems
SecondOrder Differential Equations
Asymptotic Expansions
AsymptoticExpansions in a Parameter
Singularities of the Second Kind 1=
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387986999
ISBN-10: 0387986995
Series: Universitext
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 469
Published: 22nd June 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.77 x 16.51  x 3.18
Weight (kg): 0.84