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====== Conservative Fields ======

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===== In-class Content =====

  * [[|Counting Paths]] (SGA - 30 min)
  * Lecture - 20 min
    * What is the difference between the line integral and the flux integral (given that both use the dot product)?
    * What does it mean for a field to be conservative?
      * Path independent
      * Corresponds to a surface (scalar field) that it is the gradient of
      * //Is curl free// **Note:** Curl is needed for 3 different ideas in this class: Conservative Work, Going from $\vec A$ to $\vec B$, and getting from $\vec B$ to $\vec J$. 
  * QUIZ
  * [[|Work]] (SGA - 30 min)
  * Lecture - 10 min

===== Optional In-class Content =====

  * [[..:..:activities:vfact:vfmurdermm|Murder Mystery Method]] (SGA - 50 min) (alternatively a homework problem - see below)
  * Conservative Fields (lecture) (//Math 3.5: Independence of Path//, //Math 3.6: Conservative Vector Fields//, //Math 3.7: Finding Potential Functions//)
  * Equivalent Statements (lecture)

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