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===== Paramagnetism: Instructor's Guide =====



==== Main Ideas ====
  * Total differentials
  * Cyclic chain rule
  * Legendre transformations
    * Chain rule diagrams
    * Differential substitution



==== Students' Task ====
//Estimated Time: 35 minutes//
  * Students evaluate two given partial derivatives
  * Students must use a Legendre transformation for one of the given partial derivatives
  * Students may find it helpful to use a chain rule diagram




==== Prerequisite Knowledge ====

  * Familiarity with partial derivatives and their interpretations
  * Familiarity with total differentials
  * Familiarity with Legendre transformations
  * Familiarity with the cyclical chain rule

==== Props/Equipment ====

  * [[:Props:start#whiteboards|Tabletop Whiteboard]] with markers
  * A handout for each student

==== Activity: Introduction ====






==== Activity: Student Conversations ====

  * Students may recognize one of the equations as a hyperbolic tangent. Credit them for recognizing it.
  * Students may find the physical truth of the equations to be inspiring, so do not hesitate to state that the equations are valid physical relations.
  * Students may ask what magnetic susceptibility, $\chi_B$, is. Dr. Round provides an eloquent response of sufficient detail: "It's the thing that's defined to be that."
  * Students may be confused as to how to apply the cyclic chain rule.

==== Activity: Wrap-up ====
==== Extensions ====