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Total Differentials on a Surface

Keywords: Differentials, Zapping with d, Surfaces, Thermodynamics, Variables, Derivatives


Highlights of the activity

  1. This small group activity is designed to help students understand differentials in multivariable functions.
  2. Students work in small groups to generalize symbolic and graphical representations of differentials for a single variable function to a multivariable case using a plastic surface as a test case.
  3. The whole class wrap-up discussion emphasizes that differentials are a way of linearizing the relationship between variables by expressing how small changes in those variables are related.

Reasons to spend class time on the activity

This activity helps set the stage for the extensive use of differentials in thermodynamics. In particular, students are guided to think about differentials in multiple representations so that they can build stronger connections between aspects of functions and derivatives that they already understand.


Instructor's Guide

Authors: Paul Emigh
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