Ordinary Differential Equations

1. Front Matter

   Pages i-xi

   PDF

2. Introduction

   • Wolfgang Walter

   Pages 1-7

3. First Order Equations: Some Integrable Cases

   • Wolfgang Walter

   Pages 9-52

4. Theory of First Order Differential Equations

   • Wolfgang Walter

   Pages 53-104

5. First Order Systems. Equations of Higher Order

   • Wolfgang Walter

   Pages 105-157

6. Linear Differential Equations

   • Wolfgang Walter

   Pages 159-212

7. Complex Linear Systems

   • Wolfgang Walter

   Pages 213-244

8. Boundary Value and Eigenvalue Problems

   • Wolfgang Walter

   Pages 245-303

9. Stability and Asymptotic Behavior

   • Wolfgang Walter

   Pages 305-331

10. Back Matter

    Pages 333-384

    PDF

Develops the theory of initial-, boundary-, and eigenvalue problems, real and complex linear systems, asymptotic behavior and stability. Using novel approaches to many subjects, the book emphasizes differential inequalities and treats more advanced topics such as Caratheodory theory, nonlinear boundary value problems and radially symmetric elliptic problems. New proofs are given which use concepts and methods from functional analysis. Applications from mechanics, physics, and biology are included, and exercises, which range from routine to demanding, are dispersed throughout the text. Solutions for selected exercises are included at the end of the book. All required material from functional analysis is developed in the book and is accessible to students with a sound knowledge of calculus and familiarity with notions from linear algebra. This text would be an excellent choice for a course for beginning graduate or advanced undergraduate students.

• Boundary value problem
• Eigenvalue
• Hilbert space
• calculus
• differential equation
• eigenvalue problem
• functional analysis
• maximum
• minimum
• ordinary differential equation

• Mathematisches Institut I, Universität Karlsruhe, Karlsruhe, Germany

  Wolfgang Walter

Policies and ethics