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  • 常微分方程 英文版 W. 沃尔特 Ordinary Differential Equations 研究生及相关专业数学
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    • 作者: 无著
    • 出版社:世界图书出版公司
    • ISBN:9783731943501
    • 版权提供:世界图书出版公司

     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

    基本信息

    图书名称:
     常微分方程 
    作者:
     W. 沃尔特
    定价:
     99
    ISBN号:
     9787519255831
    出版社:
     SJ图书出版公司
    开本:
     
    装帧:
     
    内容介绍
    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. 
    本书是在1996年出版的《常微分方程》(德文)一书的基础上编写而成的,书中主要介绍常微分方程的基础理论。内容包括:可积一阶微分方程,微分方程解的存在性和*一性,微分方程的初极值问题,边值问题和特征值问题,稳定性与渐进稳定性理论。阅读本书需要具备一定的计算代数、线性代数及泛函分析的基础知识。适用于高校数学专业、牧业专业和计算机科学等相关专业的本科生和研究生。

    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

    1230089811
    1
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