Integrating Instructional Computing Into Differential Equations Courses

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The basis of this project is that differential equations present an excellent opportunity to learn how the real world works, that a good way to do this is by exploring specific real-world problems, and that this exploration can be fun. The project makes use of an enhanced version of the Harvard Consortium's `Rule of Three` (present things geometrically, numerically, and algebraically). The enhancement consistently provides real-world interpretations and applications. Traditionally, introductory differential equations courses concentrate on finding, by hand, closed form solutions to a few standard types of equation. This project focuses on helping students achieve a better understanding of the meanings of these equations. It emphasizes understanding key concepts such as linearity, equilibrium points, stability, and dependence on initial conditions or parameters. To make exploring and following up on curiosity a realistic goal throughout the course, the project supplies students with a powerful tool, the computer algebra system Maple. Maple plots the solutions and direction fields which are the keys to presenting things geometrically. There are other commands to do the same at the numeric level, and at the algebraic level. In addition, the project promotes a much greater involvement in the learning process on the part of the students. Cooperative learning is a significant aspect of the course. Material developed for the course will be available on the Department's web site.