Chapter I. Introduction
1.1 Preliminary Notation
1.2 The Ordinary Differential Equation
1.3 An Existence and Uniqueness Theorem
1.4 The Maximum Interval of Existence
Problems
Chapter 2. The Linear Equation: General Discussion
2.1 Introduction
2.2 Fundamental Solutions
2.3 The Wronskian
2.4 The Nonhomogeneous Linear Equation
2.5 The nth-Order Linear Equation
2.6 The Nonhomogeneous nth-Order Linear Equation
Problems
Chapter 3. The Linear Equation with Constant Coefficients
3.1 The nth-Order Linear Equation
3.2 The Nonhomogeneous nth-Order Linear Equation
3.3 The Behavior of Solutions
3.4 The First-Order Linear System
Problems
Chapter 4. Autonomous Systems and Phase Space
4.1 Introduction
4.2 Linear Systems--Constant Coefficients
4.3 A General Discussion
4.4 Nonlinear Systems
Problems
Chapter 5. Stability for Nonautonomous Equations
5.1 Introduction
5.2 Stability for Linear Systems
5.3 Two Results for Nonlinear Systems
5.4 Liapunov's Direct Method
5.5 Some Results for the Second-Order Linear Equation
Problems
Chapter 6. Existence, Uniqueness, and Related Topics
6.1 Proof of the Existence and Uniqueness of Solutions
6.2 Continuation of Solutions and the Maximum Interval of Existence
6.3 The Dependence of Solutions on Parameters and Approximate Solutions
Problems
Appendix A. Series Solutions of Second-Order Linear Equations
Appendix B. Linear Systems with Periodic Coefficients
References; Index

David A. Sanchez received his PhD in Mathematics from the University of Michigan in 1964. He taught at several universities, including UCLA, the University of Wisconsin, and the University of New Mexico, and he held various administrative positions in academia and elsewhere, including with the National Science Foundation and the Los Alamos National Laboratory. Dr. Sanchez is the author of several books on aspects of ordinary differential equations.