Harmonic Functions: why they are cool!

Here we introduce harmonic functions and some multivariable calculus used to understand them. Most of the video is about showing the "mean value thoerem" of harmonic functions, that the average value of a harmonic function in any disk is equal to the value of the function at the center. This tells us that harmonic functions vary in a nice way in any disk (a lot of variation in the function in one direction is certain to be offset).