Differential equations is a first semester sophomore course at
Stevens Institute of Technology. It covers such standard topics
as first order and second order ordinary differential equations,
undetermined coefficients, variation of parameters, LaPlace transforms,
and series solutions. Recently Stevens obtained a site license
for Scientific Workplace (SWP). SWP is a technical word processor
which produces .tex files. It also contains a Maple kernel which
allows the performance of a large number of mathematical procedures
such as algebraic manipulation and simplification, graphing, differentiation
and integration, solving algebraic and differential equations
both exactly and numerically, etc. SWP was used as an integral
part of this differential equations course. The World Wide Web
was used as both a vehicle for transmitting files as well as a
learning tool. Several projects were prepared in SWP which required
the student to use Maple. One project dealing with a mass-spring-damping
system is *interactive *and represents a rather striking
balance between analytic solution, use of Maple, and simulation.*
*A second project combines Web searching, software downloading
and installation and SWP to study some first order differential
equations.

*Software Distribution:* Every Stevens student is required
to have a computer. In addition, all dormitory rooms are connected
to the campus network. Thus the first issue to be dealt with was
the distribution of SWP to the students in the course. This was
done by compressing the program files which fill 17 diskettes
and putting the resulting .exe file on the network. A Web page
was then created which allows a student to simply click on a link
which then downloads SWP. Those students still running Win 3.11
instead of Win 95, had to download a win32.exe file also. Once
downloaded the files are unzipped by running them, and then the
student is lead through an installation procedure.

About 30% of the students live either in fraternity or sorority houses which are not networked or off-campus. These students were given CDs with SWP on them.

*Web Pages*: The instructor prepared several WEB pages to
go with the course. The starting page gives an overview of the
course which indicates office hours, grading policy, etc. It also
contains a number of links to pages which contain the homework
assignments, the syllabus, the students' grades, attendance records,
notes in SWP for the course material, exams given previously in
the course, and the Projects which were assigned.

*Classroom Demonstrations*: During most of the lectures the
instructor had an IBM Thinkpad CDV available for his use. This
Thinkpad is so constructed that the back of the screen can be
removed and placed on a high intensity overhead projector so that
whatever is on the screen can be projected for the entire class
to see. Students were shown how to access the Web pages, download
files, and use SWP. At appropriate times SWP was used in class
to solve differential equations, graph the solution to an equation,
evaluate an integral, find a derivative, find the first few terms
in the series solution of an equation, etc. Students were also
shown how to set up the Projects that were assigned.

*Projects:* Three projects were assigned: one on the Web
and differential equations, one on the mechanical vibrations of
a mass-spring-damping system, and one on Euler's method for solving
first order equations. These projects were written in SWP and
required the student to use SWP in specific ways as well as the
standard analytic tools taught in class. We discuss each in some
detail.

*WEBDE*: This project begins by directing the student to a Web site from which s/he has to download a .pdf file which requires Adobe Acrobat Reader 2.1 to be read. The student is then told to search the WEB, find Adobe Reader, download it, install it and then use SWP to solve two of the equations in the downloaded .pdf file. It turns out that close examination of the solution which SWP give to one of these equations shows that SWP misinterprets its own solution and reveals a "bug" in the Maple software which TCI Software, Inc. has acknowledged and hopes to fix. Thus students learn in a striking way that one cannot simply take what a computer returns at face value.*Vibrations:*A rather lengthy project dealing with a mass-spring-damping system was prepared as an application of the techniques taught to solve second order constant coefficient differential equations. This project deals with the standard topics of mechanical vibrations and simple harmonic motion, damped free vibrations, and forced vibrations. Students are required to use analytical techniques and the Maple kernel in SWP. Each is used to shed light on the other.- A unique feature of this project is that the .tex file describing
it is linked to a simulation program which vividly illustrates
the motion. Thus a student can select a certain combination of
mass, spring constant, and damping factor with certain initial
conditions, analyze the motion analytically by solving the resulting
initial value problem, check his/her solution using the Maple
in SWP, use SWP to graph the solution, and then view a simulation
of the motion for this combination by clicking on a link in the
SWP file which takes one to the simulation. Closing the simulation
returns one to the project file. Thus the project has the novel
feature of being
*interactive.*

The simulation program to which the vibrations project is linked was developed by Virginia Polytechnic Institute and State University as part of their SUCCESS Project.

*Euler's Method:*The third project is one which deals with Euler's Method for solving first order differential equations. The student is first introduced to the simple Euler Method and shown by comparing the numerical results to the exact solution of a simple equation that the numerical procedure in this method leads to error rather quickly. A more precise Improved Euler's Method based on a trapezoid scheme is then presented. This approach leads to a predictor-corrector method.

The Maple kernel in SWP does not allow for the option of writing routines. As a result, the simple and improved Euler Method routines had to be written in Maple Vr3 and then imported into SWP.

*Conclusions:* There is no question that the use of SWP in
the traditional differential equations course at Stevens has added
new and important dimensions to this course. Students were given
the experience of using a sophisticated piece of software as a
powerful tool in their study of this classical subject. In addition,
they gained experience on using the Web as a resource in their
study of differential equations. Student evaluations and discussions
indicate that many students feel that the experience was interesting
and valuable. There are some, however, who are not comfortable
with computers and thus found the project somewhat intimidating.
However, even these students felt that they gained much from doing
the projects.