Synopses & Reviews
Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. 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, while 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, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.
Review
"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 PoincarÃ© map, a resonance in celestial mechanics, an average, a traveling wave, or a transversal intersection of separatrices."--MATHEMATICAL REVIEWS
Synopsis
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.
Table of Contents
* Fundamental Theorems of Ordinary Differential Equations * Dependence of Data * Nonuniqueness * General Theory of Linear Systems * 1= Singularities of the First Kind * Boundary-value Problems of Linear Differential Equations of the Second Order * Asymptotic Behavior of Solutions of Linear Systems * Stabiblity * Autonomous Systems * Second Order Differential Equations * Asymptotic Expansions * Asymptotic Expansions in a Parameter * Singularities of the Second Kind 1=