ODEs—An Introduction

Abstract

Mathematical models in a vast range of disciplines, from science and technology to sociology and business, describe how quantities change. This leads naturally to the language of ordinary differential equations (ODEs). Typically, we first encounter ODEs in basic calculus courses, and we see examples that can be solved with pencil-and-paper techniques. This way, we learn about ODEs that are linear (constant or variable coefficient), homogeneous or inhomogeneous, separable, etc. Other ODEs not belonging to one of these classes may also be solvable by special one-off tricks. However, what motivates this book is the fact that the overwhelming majority of ODEs do not have solutions that can be expressed in terms of simple functions.