常微分方程

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作　者：	（）Wolfgang Walter著
出版社：	世界图书出版公司北京公司
丛编项：	Graduate Texts in Mathematics
标　签：	微积分

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ISBN：	9787506259286	出版时间：	2003-01-01	包装：	胶版纸
开本：	23cm	页数：	380页	字数：

内容简介

　　The author＇s book on GewShnliche Differentialgleichungen （Ordinary Differential Equations） was published in 1972. The present book is based on a translation of the latest， 6th， edition， which appeared in 1996， but it also treats some important subjects that are not found there. The German book is widely used as a textbook for a first course in ordinary differential equations. This is a rigorous course， and it contains some material that is more difficult than that usually found in a first course textbook; such as， for example， Peano＇s existence theorem. It is addressed to students of mathematics， physics， and computer science and is usually taken in the third semester. Let me remark here that in the German system the student learns calculus of one variable at the gymnasium1 and begins at the university with a two-semester course on real analysis which is usually followed by ordinary differential equations.

作者简介

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图书目录

Preface
Note to the Reader
Introduction
Chapter I. First Order Equations: Some Integrable Cases
　1. Explicit First Order Equations
　2. The Linear Differential Equation. Related Equations
　　　Supplement: The Generalized Logistic Equation
　3. Dif　ferential Equations for Families of Curves. Exact Equations
　4. Implicit First Order Differential Equations
Chapter II: Theory of First Order Differential Equations
　5. Tools from Functional Analysis
　6. An Existence and Uniqueness Theorem
　　Supplement: Singular Initial Value Problems
　7. The Peano Existence Theorem
　　Supplement: Methods of Functional Analysis
　8. Complex Differential Equations. Power Series Expansions
　9. Upper and Lower Solutions. Maximal and Minimal Integrals
　　Supplement: The Separatrix
Chapter III: First Order Systems. Equations of Higher Order
　10. The Initial Value Problem for a System of First Order
　　Supplement I: Differential Inequalities and Invarian e
　　Supplement II: Differential Equations in the Sense
of aratheodory
　11. Initial Value Problems for Equations of Higher Order
　　Supplement: Second Order Differential Inequalities
　12. Continuous Dependence of Solutions
　　Supplement: General Uniqueness and Dependence Theorems
　13. Dependence of Solutions on Initial Values and Parameters
Chapter IV: Linear Differential Equations
　14. Linear Systems
　15. Homogeneous Linear Systems
　16. Inhomogeneous Systems
　　Supplement: L1-Estimation of C-Solutions
　17. Systems with Constant Coefficients
　18. Matrix Functions. Inhomogeneous Systems
　　Supplement: Floquet Theory
　19. Linear Differential Equations of Order n
　20. Linear Equations of Order n with Constant Coefficients
　　Supplement: Linear Differential Equations with　Periodic Coefficients
Chapter V: Complex Linear Systems
　21. Homogeneous Linear Systems in the Regular Case
　22. Isolated Singularities
　23. Weakly Singular Points. Equations of Fuchsian Type
　24. Series Expansion of Solutions
　25. Second Order Linear Equations
Chapter VI: Boundary Value and Eigenvalue Problems
　26. Boundary Value Problems
　　Supplement I: Maximum and Minimum Prin iples
　　Supplement II: Nonlinear Boundary Value Problems
　27. The Sturm-Liouville Eigenvalue Problem
　　Supplement: Rotation-Symmetri Ellipti Problems
　28. Compact Self-Adjoint Operators in Hilbert Space
Chapter VII: Stability and Asymptotic Behavior
　29. Stability
　30. The Method of Lyapunov
Appendix
　A. Topology
　B. Real Analysis
　C. Complex Analysis
　D. Fun tional Analysis
Solutions and Hints for Selected Exercises
Literature
Index
Notation