Summary

In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations.

Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems. The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions.

Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software. A solutions manual is available for qualifying instructors.

Choice Review

Roberts (Indiana State Univ., Terre Haute) gives a clear, detailed introduction to ordinary differential equations for students who have completed the full calculus sequence. The author states in the preface that his book "... is designed for instructors who wish to bring the computer into the classroom...." Thus, the book's exercises and examples require the use of software, but they are independent of any particular software--a very nice feature. Roberts provides a good balance between theoretical and applied material. Chapters include "The Initial Value Problem," "Applications of the Initial Value Problem," "Nth Order Linear Differential Equations," "The Laplace Transform Method," "Applications of Linear Systems with Constant Coefficients," and "Applications of Systems of Equations." Numerous examples and problems (with answers to selected problems) throughout enhance the material. The work is very readable and offers instructors much material to work with in their courses. Summing Up: Recommended. Mathematics collections serving upper-division undergraduates and faculty. S. L. Sullivan Catawba College