Abstract
ABSTRACT This article presents a detailed description of an in-depth calculus project which is explored by the students from a variety of viewpoints. The problem under consideration is the determination of a relationship between the length of a pendulum and the period of its oscillatory motion. The students investigate this relationship in three different ways: a numerical solution of the initial value problem for pendulum motion, an analytic solution of the corresponding linearized initial value problem, and empirical measurements of actual pendulum motion. The combination of these three different approaches leads to far deeper understanding than would be achieved by any one of the methods alone. The basic project design was conceived by David Smith and Lawrence Moore of Duke University for use in their revised calculus program Project CALC. In this article we will consider the Mathematica version of the project, adapted for this platform by the current author. * Based on a presentation given at the Conf...
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