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    • 常微分方程(影印版)(英文版)
      • 作者:(德)W.沃尔特
      • 出版社:世界图书出版公司
      • ISBN:9787519255831
      • 出版日期:2019/03/01
      • 页数:380
    • 售价:39.6
  • 内容大纲

        本书是在1996年第六版《常微分方程》(德文)一书的基础上编写而成的。本书主要介绍了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唯一性,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。此外,本书还增加了在一般相关教材中很少涉及但具有一定难度的内容,并对一些复杂基本定理给出了新的证明。阅读本书须具备一定的计算代数、线性代数及泛函分析的基础知识。
  • 作者介绍

  • 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. Differential 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 Invariance
      Supplement II: Differential Equations in the Senseof Caratheodory
      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 Sohltions 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 Principles
      Supplement II: Nonlinear Boundary Value Problems
      27. The Sturm-Liouville Eigenvalue Problem

      Supplement: Rotation-Symmetric Elliptic 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. Functional Analysis
    Solutions and Hints for Selected Exercises
    Literature
    Index
    Notation

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