Derivation of the divergence theorem from the "microscopic version" we had done last time.
Discussion of the physics value of this theorem - sometimes you need to learn about what's going on in the volume but can't look there (e.g, learning about sources of heat inside the earth, by looking at the flux of heat out of the surface. Or, my dog figuring out the strength of the "source of smell" in a barbeque by integrating the flow of smell past her nose as she walks all around it, and assuming some symmetries....)
Sometimes you need to learn about what's going on out at the surface but can't look there (e.g, learning about the flux of electric field out of surface, just by knowing about the charges distributed inside!)
Examples - doing both sides of the divergence theorem (surface integral, or volume integral) for some fairly simple fields.
Started proof of Gauss' law, by assuming Coulomb's law and superposition.
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