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====== Divergence ======

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  * Reading: GVC (ss) [[bb>book:math:divergence|Definition of Divergence]]--[[bb>book:math:divcoord|Divergence in Curvlinear Coordinates]],[[bb>book:physics:divact|Visualizing Divergence]]--[[bb>book:physics:divacthint|More Visualizing Divergence]]
  * Reading: GVC (ss) [[bb>book:math:divthm|Divergence Theorem]]
  * Reading: GVC (ss) [[bb>book:physics:maxwell1|Differential Form of Gauss's Law]]--[[bb>book:physics:lines|Electric Field Lines]]

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

  * Derivation of the Divergence Theorem (lecture - 15 min).  We follow "div, grad, curl and all that", by Schey.  The Divergence theorem is almost a lemma based on the definition of divergence.  Draw a diagram of an arbitrary volume divided into lots of little cubes.  Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary.
  * [[..:..:activities:vfact:vfdivergence|Visualizing Divergence]] (Maple Visualization - 30 min) Students practice estimating divergence from graphs of various vector fields.  We do this with printouts in dry-erasable sleeves now, with computer follow-up.
  * Differential Form of Gauss's Law: Maxwell's Eq 1 & 3:   $\Vec{\nabla} \cdot \Vec{E} = {\rho \over \epsilon_0}$, $\Vec{\nabla~} \cdot \Vec{B} = 0$ (lecture - 15 min)

===== Optional In-class Content =====
  * (//optional//) Divergence of a Coulomb field (//requires delta functions//) (lecture)
  * (//optional//) Electric field lines (lecture)


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