Introductory Differential Equations

Differential equations are the subject of many introductory textbooks, so the task of the reviewer is to identify the place of the book under review on this very large spectrum.

This is a book for a one-semester course, in which the topics follow each other in the usual order, and in which there are plenty of exercises. The first unusual decision that the authors made is that they cover the method of power series in two sections only. In the experience of this reviewer, that is the technique that students find the most difficult. Three times as much space would not be too much.

Based on that decision, we might be tempted to think that the book is targeted at easier courses on the subject, but we would be wrong to think so. When systems of differential equations are discussed, the author go into notions from linear algebra, such as eigenvectors and eigenvalues, even though in many mathematics programs, linear algebra is offerred after differential equations. So perhaps the best use of the book is in a course where most students will not subsequently take a separate course in linear algebra.

Miklós Bóna is Professor of Mathematics at the University of Florida.