Applications of differential/integral calculus in crystallography (teaching undergraduates)?
This site may give you some ideas. In particular, look at the Petrology and Geochemistry section:


  Metamorphic phase diagrams show which minerals are stable under
  various temperatures and pressures. The slopes of the boundaries
  between the areas where different minerals are stable depend on the
  properties of the minerals (like the entropy and the molar volume).
  
  And... well, mineralogy, petrology, and geochemistry are full of ideas
  taken from chemical thermodynamics. And thermodynamics is full of
  multivariable calculus. (How does changing the pressure change the
  amount of calcium in garnet vs the amount of calcium in plagioclase?
  The question is a partial derivative.) From my own favorite,
  metamorphic petrology, there are all kinds of techniques for using
  metamorphic minerals to tell stories of heating and burial and cooling
  and exhumation. And none of the techniques would be possible without
  calculus. (Or, in many cases, differential equations.) I'm sure
  igneous rocks and ore deposits have similar uses of thermodynamics.


Here's an example of a metamorphic P-T Diagram with the source link with more examples:



Source:  https://serc.carleton.edu/research_education/equilibria/metamorphic_diagrams.html