Table of Contents

Preface

Chapter 1 A Brief Description
1. Linear Differential Equations
2. The Need for Qualitative Analysis
3. Description and Terminology

Chapter 2 Existence and Uniqueness
1. Introduction
2. Existence and Uniqueness
3. Dependence on Initial Data and Parameters
4. Maximal Interval of Existence
5. Fixed Point Method

Chapter 3 Linear Differential Equations
1. Introduction
2. General Nonhomogeneous Linear Equations
3. Linear Equations with Constant Coefficients
4. Periodic Coefficients and Floquet Theory

Chapter 4 Autonomous Differential Equations in R2
1. Introduction
2. Linear Autonomous Equations in R2
3. Perturbations on Linear Equations in R2
4. An Application： A Simple Pendulum

Chapter 5 Stability
1. Introduction
2. Linear Differential Equations
3. Perturbations on Linear Equations
4. Liapunovs Method for Autonomous Equations

Chapter 6 Periodic Solutions
1. Introduction
2. Linear Differential Equations
3. Nonlinear Differential Equations

Chapter 7 Dynamical Systems
1. Introduction
2. Poincare-Bendixson Theorem in R2
3. Limit Cycles
4. An Application： Lotka-Volterra Equation

Chapter 8 Some New Equations
1. Introduction
2. Finite Delay Differential Equations
3. Infinite Delay Differential Equations
4. Integrodifferential Equations
5. Impulsive Differential Equations
6. Equations with Nonlocal Conditions
7. Impulsive Equations with Nonlocal Conditions
8. Abstract Differential Equations
Appendix
References
Index