Evaluating Total Differentials: "Zapping with d"

Highlights of the activity

1. This small group activity is designed to help students practice finding total differentials of non-trivial functions.
2. Students work together to find the total differential of internal energy, and the Helmholtz Free energy of an ideal gas and three-state system.
3. The wrap-up discussion summarizes group findings and places of difficulty, emphasizing the best approach to computing total differentials.

Reasons to spend class time on the activity

We would like our students to have both a practical and mathematical understanding of a total differential. In particular, with this activity students learn what the consequences of “zapping” a function with the operator “d” are. This activity also opens up a conversation on infinitesimals, and their relation to total differentials. The use of variables not associated with the Partial Derivative Machine in this activity allows students to apply the mathematical techniques they have been practicing during the course to a less familiar physical system.

Reflections

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Instructor's Guide

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