Preliminaries --
Introduction : linear equations of the first order --
Linear equations with constant coefficients --
Linear equations with variable coefficients --
Linear equations with regular singular points --
Existence and uniqueness of solutions to first order equations --
Existence and uniqueness of solutions to systems and [italic]n-th order equations.

This book is meant to be a text which can be used for a first course in ordinary differential equations. The student is assumed to have a knowledge of calculus but not what is usually called advanced calculus. The aim is to give an elementary, thorough systematic introduction to the subject. All significant results are stated as theorems, and careful proofs are given. The exercises in the book serve two purposes: to develop the student's technique in solving equations, or to help sharpen the student's understanding of the mathematical structure of the subject. The exercises also introduce the student to a variety of topics not treated in the text: stability, equations with periodic coefficients, and boundary value problems