Mathematics
University of NebraskaReal-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