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內容:本書為純數細及應數系研究所的教科書.研讀本書需具備的預備知識有線性代數.多變數微積分.多複變函數論內容廣,證明簡明.清晰,深入淺出,是難得的好書,唯不適用大學部學生.
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.
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.
目次
* Fundamental Theorems of Ordinary Differential Equations * Dependence of Data * Nonuniqueness * General Theory of Linear Systems * 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
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