Recently the Academic Senate and Board of Trustees approved the Science and Mathematics Division's request to expand our differential equations course to include a three hour per week laboratory component. The ordinary differential equations course is being changed in this manner nation-wide, mainly due to the fact that it is a core requirement for every engineering, physics, and mathematics major. Of all the courses we teach in mathematics, differential equations is probably the one most heavily used by professional engineers, and they apply this knowledge through the use of computers on a daily basis. Instruction that includes a technology component this therefore essential.

This semester (Fall 1994) we enrolled our first class of students in the new course structure. I have begun to develop laboratory exercises for the course on a weekly basis utilizing the mathematical programming language Mathematica. (I feel that this choice is appropriate since the language itself is in widespread use by practicing scientists, engineers, and mathematicians.) I believe that my initial work has resulted in some very rough laboratories by the "wee hours of the morning" programming technique. The heavy workload of my teaching assignment precludes the level of professionalism I am capable of. It is essential that the development of the materials for this laboratory be given greater attention so that the students in the course receive the best possible instruction and laboratory experience. Simply put, my lack of development time has dictated that the labs be shorter, and less challenging than they should be.

The labs should also be streamlined in order to mesh with the course's lecture component, and be tied more heavily to actual physical, chemical, biological and economic applications taken from the "real world."

My sabbatical project is proposed to be: To develop and implement laboratory curriculum for the differential equations course. This goal is amplified in the following description of its components:

1. Further develop my existing labs, and develop new labs, using the Mathematica environment that synchronize the laboratory with the lecture component of the course. I will produce at least 12 of these labs, but will probably accomplish closer to 18 if time permits.

   This work will have to be original, since few laboratory exercises exist, and those that are available from publishers at the moment are either aimed at a one year/two semester audience taking senior level ordinary differential equations, or use generic materials not tailored to Delta's mathematics laboratory environment. I believe that in about three to five years we will start to see published materials that would fit our requirements, but since Delta is part of the first wave of schools nation-wide in reforming its differential equations course, we need the material now. Should this sabbatical proposal itself lead to publication, all royalties would, of course, go to the College.

2. Develop a set of "real world" experiments that tie in with both the theory presented in lecture and the computer solution methods learned in lab. I will produce at least six of these labs, but will probably accomplish closer to 12 if time permits.

   This work may be based to some extent on the work of Dr. Courtney Coleman, et al. at the Consortium for Ordinary Differential Equations Experiments (CODEE.) Dr. Coleman recently spoke at one of the Mathematics Colloquia held here at Delta, and enthusiastically encouraged us to try to integrate some of CODEE's material into our program. Unfortunately, for the materials to be usable they need to be rewritten in such a way as to address the sophomore level, as opposed to the senior level, audience.

3. Develop two Mathematica labs covering topics normally left out of the standard "lecture only" course. One of these labs would cover solving systems of differential equations, and the other would address the use of numerical algorithms in arriving at approximate solutions to differential equations which do not succumb to standard manipulative techniques. This numerical component will be the one our graduating engineers use the most once they enter the work-place.

4. I will run workshops following the completion of these laboratories for the Delta faculty, (and others interested) on the classroom use of my materials. I shall also present this work at a regional or national meeting of mathematics educators, such as CMC³, AMS, or MAA.

I believe that if and when these components are implemented our "new and improved" differential equations course could be one of the best offered anywhere. It would certainly produce a class of engineering student far more capable of addressing the work-place with a level of understanding that goes beyond the "theoretically brilliant, practically incompetent" criticism leveled at so many new graduates in this field..

In my opinion the project described above forms the basis for an excellent sabbatical. My ability to complete these tasks has been demonstrated by the work that I have already completed-cited above, and the fact that I hold degrees in both mathematics and computer science. Upon successful completion they will benefit all students taking Math 4, regardless of instructor, and be available for all instructors teaching Math 4. Thank you for your consideration.