Delivering lectures in introductory graduate-level continuum mechanics courses using mathematica

In the authors' experience, having been on both the giving and receiving ends of the "lecturing process," some of the topics covered in introductory (as well as advanced) continuum mechanics courses turn out to be particularly hard to communicate and to grasp. Representative examples might involve subjects such as the polar and the spectral decompositions of a tensor and their physical significance. In this paper we discuss how the authors make use of the software package Mathematica to create lectures allowing one to expose key concepts by taking advantage of the programming, manipulation, visualization, and animation capabilities of the computer program Mathematica, developed by Wolfram Research. The emphasis of this paper is as much on the way a lecture can be delivered using Mathematica as it is on the specific examples presented. In other words, we want to illustrate that software such as Mathematica, by combining symbolic manipulation, computation, and visualization, allows one to turn "a laptop and a projector" into an "electronic color-board" which makes for effective and dynamic presentations of even the most sophisticated topic.