Student Research Projects for Multivariate Calculus

Michael M. Neumann

Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762

Grant Number: DUE: 9551248

Our student research projects are extended mathematical and scientific projects, which invite the student to relate a variety of ideas, skills, and techniques, make essential use of computer capabilities, and require a final written report. They are effective means of integrating technology in larger classes. As part of this NSF-ILI grant, the Department of Mathematics and Statistics at Mississippi State University has now implemented student research projects in all multivariate calculus classes.

A classroom laboratory has been constructed with twenty-five workstations and audio-visual capability. It is equipped with a Novell network of Pentium based machines, each with 16 MB of RAM, and with the computer algebra system Mathematica as the primary software. The computer laboratory serves about two hundred sophomore calculus students each semester. In the morning, the computer lab is mainly used for in-class instruction of multivariate calculus, an introduction to the Mathematica language, and a preliminary discussion of the student projects. During the rest of the day, the computer lab is reserved for the students to work on their projects. It is open about fifty hours per week and monitored by graduate assistants who provide help with the software whenever needed. In most cases, the students work in groups of two to four and have about two weeks to complete their assignments. The final written report of the group is discussed in detail in an exit interview with the instructor. A collection of typical student projects has recently been published in Mathematica Projects for Vector Calculus by Michael M. Neumann and T. Len Miller, Kendall/Hunt Publishing Company, ISBN 0-7872-2858-3.

In the poster presentation and handouts, we shall provide details about our computer lab, illustrate our experience with in-depth student projects, describe our specific procedures, and display some of our projects and their solutions by our students. It seems that powerful computer algebra systems like Mathematica or Maple should be particularly useful in an area like vector calculus, where the traditional tools of computation and visualization are poor and cumbersome. We shall present a number of concrete examples to show how such computer algebra systems and our student research projects may be used to enhance the traditional teaching of multivariate calculus.

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