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.