Ordinary differential equations

Abstract

Differential equations are among the mathematical instruments most widely used in applications to other fields. The book’s final chapter presents in a self-contained way the main notions, theorems and techniques of so-called ordinary differential equations. After explaining the basic principles underlying the theory we review the essential methods for solving several types of equations. We tackle existence and uniqueness issues for a solution to the initial value problem of a vectorial equation, then describe the structure of solutions of linear systems, for which algebraic methods play a central role, and equations of order higher than one. In the end the reader will find a concise introduction to asymptotic stability, with applications to pendulum motion, with and without damping.