Mathematics

University of Nebraska
Real-world problem solving in Mathematica lab

Reproduced with permission from NeXT Computer, Inc.
A Reference Guide to NeXT in Higher Education, Fall 1992
ยช 1992 NeXT Computer, Inc


Steve Dunbar, associate professor of mathematics at the University of Nebraska, Lincoln, never felt teaching differential equations was easy-until he started using NeXT computers in the course.

"One of the interesting things we discovered after we started using the computers was the ease of teaching," he says. "In our orientation, we show students everything from how to log in to running Mathematica. We show them how to make a quick graph, paste it into WriteNow, and print the results. All this takes an hour. That's pretty remarkable for students who've never used computers before."

In 1990, when Nebraska's Mathematics Department purchased a 14-station NeXT lab with a grant from the Instrumentation and Laboratory Initiative of the National Science Foundation, Dunbar immediately bid adieu to his traditional method of teaching differential equations. Gone are his daily chalkboard-based lectures and homework assignments completed on paper.

"We chose NeXT," he says, " because we needed a workstation with a windowing environment, a graphical user interface, UNIX underneath, and networking capabilities to allow us to grow beyond the confines of the room we're in. The bundled Mathematica saved us hundreds of dollars on each machine; plus, we didn't see MS-DOS or Macintosh growing into the future."

Dunbar has three uses for NeXT machines in the course. He has prepared a series of Mathematica Notebooks for students to review outside the classroom. The Notebooks explore various topics in differential equations-from finding orthogonal trajectories of a given family of curves to using the variation-of-parameters formula to solve nonhomogeneous linear differential equations.
Students also use Mathematica and WriteNow to derive, solve, and graph differential equations Dunbar gives as homework assignments.

"I really like the idea of NeXT's multitasking environment. When they're writing reports, students typically work with one window open with Mathematica and another with WriteNow. The assignments emphasize writing because when you get a job, employers don't want a page with a lot of calculations. They expect explanations."

Throughout the semester-long course, Dunbar also assigns five teamprojects. Typically, the projects involve investigating a particular differential equation. Students are asked to discuss the physical derivation, linearization, special small- amplitude solutions, and final solution of the equation. These projects require the use of WriteNow, CharFind, Draw, and Mathematica.

"Mathematical analysis and presentation are the core of the course," says Dunbar, "so I want students to be exposed to multiple applications-just like professionals are. Students are not tied to one particular application for solving problems. For example, they can use Mathematica, a programming language, or some other application."

When he returns from his six-month sabbatical in fal 1992, Dunbar says he "plans to use NeXT for everything I teach from here on out. We've had overwhelming student approval for using NeXT in the Differential Equations course. Students love the power, ease of use, speed, and hands-on feel when solving mathematical equations on the NeXT platform."

For more information, please contact:

Steve Dunbar
Associate Professor of Mathematics
University of Nebraska
Lincoln, Nebraska 68588-0323
(402) 472-7236
srd@mathcml.unl.edu