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Session 2793

Delivering Lectures in Introductory Graduate-Level Continuum Mechanics Courses using Mathematica Andrew C. Arvin, Scott T. Miller, Francesco Costanzo The Pennsylvania State University

Abstract

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, visual- ization, 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 manipu- lation, 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.

Introduction

The third author of this paper has been actively teaching mechanics courses at the Penn- sylvania State University for the last seven years. During these years, he has made an effort to make the students excited about mechanics as a way to characterize the behavior of materials at various scales and for a variety of applications, including topics such as the descriptions of phase transitions and the derivation of nonlinear continuum properties for molecular dynamics simulations. Behind this effort there is a strong belief that the- oretical mechanics has much to offer to the solution of today’s technological challenges, which, with a strong emphasis on nano-scale phenomena, require a deep exploration of subjects such as nonlinear deformations, material inhomogeneity, evolving micro- and nano-structure. As nonlinearity and inhomogeneity are at the core of the authors’ research activities, they have struggled to acquire the necessary familiarity, intuition, and instincts that allow one to “think nonlinearly.” In turn, this struggle has made the authors meditate on how to transmit their experience to new generations of students. As a response to this need,

Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright c 2003, American Society for Engineering Education

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Miller, S. T., & Arvin, A. C., & Costanzo, F. (2003, June), Delivering Lectures In Introductory Graduate Level Continuum Mechanics Courses Using Mathematica Paper presented at 2003 Annual Conference, Nashville, Tennessee. 10.18260/1-2--11773