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Cyclic Chain Rule

Keywords: Partial Derivative, Interlude, Total Differential, Small Group Activity, PDM


Highlights of the activity

  1. This small group activity is designed to help students practice measuring derivatives with the Partial Derivative Machine (PDM) and help them make connections between mathematical expressions and physical systems and measurement.
  2. Students are given a written representation of the Cyclic Chain Rule and are asked to assess whether the dimensions make sense and to use the PDM to verify the expression.
  3. The whole class discussion focuses on the results of the measurements and leads to the instructor introducing the concept of the “Cyclic Chain Rule”.

Reasons to spend class time on the activity

The cyclic chain rule is a common mathematical manipulation in thermodynamics. By exploring the rule with the Partial Derivative Machine, students can investigate the mathematical relationship through experimental measurements.


Instructor's Guide

Authors: David Roundy, Corinne Manogue
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