Some Observations For Teaching Mathematics/Physics/Mechanics

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 Engineering 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.