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Session 1380

Some Observations for Teaching Mathematics/Physics/Mechanics Shirley Pomeranz The University of Tulsa

1 Introduction During the spring 1997 semester I was on sabbatical at the University of Texas-Austin (UT). There were three finite element method (FEM) courses offered that semester by the Texas Institute of Computational and Applied Mathematics (TICAM) at UT. I attended all three courses, which were cross-listed under TICAM and the Department of Aerospace Engineer- ing and Engineering Mechanics. The courses were an introductory course, Finite Element Methods, taught by a mathematician; an intermediate course, Computational Techniques in Finite Element Analysis, taught by a civil engineer (whose area of specialization was solid mechanics); and an advanced course, Advanced Theory of Finite Element Methods, taught by the institute director, whose degree was in engineering mechanics. Because I was observing all three courses during the same semester, instead of one course each semester, the interplay between the material in one course versus another was more evident. I noted some interesting connections between the material presented in the three courses. Some of the same topics were introduced in each course, but the approaches in the three courses were often different. Depending upon the course, material was introduced from a different perspective and with a different emphasis.

In Section 2, I select specific topics and show that by recognizing how the terminology and notation in one course related to that in another, I was able to gain new insights. For example, I was able to use the fact that I was familiar with some material in a mathematics context, in order to better understand the material presented from an engineering mechanics orientation (and with the accompanying engineering terminology).

I have become more aware of the opportunities for reinforcing material by presenting it in different contexts (and/or in different courses). This can be a powerful teaching tool, especially when the student clientele represent many diverse engineering disciplines [ 1, pages 1604-1612]. I h ave tried to apply these observations and experiences to the mathematics courses that I teach. Some specific examples are presented in Section 3, and the conclusion is given in Section 4.

2 Sample FEM topics from different perspectives Two representative topics that arose in all three FEM courses, the introductory course, the intermediate computational course, and the advanced theory course, will be considered.

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Pomeranz, S. B. (1998, June), Some Observations For Teaching Mathematics/Physics/Mechanics Paper presented at 1998 Annual Conference, Seattle, Washington. 10.18260/1-2--7417