Book review

Differential equations arise in connection with mathematical models in diverse setting in mathematics, engineering, physics, biology, astronomy and even in the social sciences. Since solutions of ordinary differential equations (ODEs) define curves, much can be learned about the behavior of solutions by graphing them. The main focus of this workbook is on computer experiments that support and amplify the topics usually found in introductory ODEs texts. The workbook is intended as a supplement, not as a textbook.

Before the computer age, modelers were forced to keep their models simple enough to allow solutions by the analytic techniques of the day. Modern computers and software have liberated modelers from this constraint. Computers can numerically solve complicated systems of ODEs and, together with striking graphical displays, allow modelers an insightful look at complex systems.The approach in the workbook closely parallels what goes on in science and engineering laboratories. Each computer problem set is a combination of pencil-and-paper and computer work selected from the tasks given in an experiment. The experiments generally follow the order of presentation of topics in a traditional first course in ODEs, but no references are made to standard textbooks. Al1 the experiments require the use of computers at certain stages.

The material in the workbook presumes a knowledge of single and multivariable calculus and some linear algebra. It is expected that the reader is concurrently enrolled in a course involving ODEs and that he (or she) has available a software package that can numerically solve systems of differential equations and present the solutions in graphical form on suitable hardware platforms.

This workbook provides an excellent guide to the study of the ODEs and can be recommended to all researchers, teachers and especially to students interested in this fundamental aspect of mathematics.