Let f(r, 0, ) be a harmonic function (written in spherical coordinates). we define sr to be the the sphere of radius r centered at the origin. we denote the average of f interesting observation regarding f for harmonic functions f. we assume that f is a function of r and over this sphere by f. our goal is to make an f(r) write it as (a) write down the divergence theorem (gauss's theorem) for the vector field vf integrated surface sr over the 1 s vf da in terms of the function f (r) and its derivatives (b) use spherical coordinates to express (c) use what you learned in part (a) from gauss's theorem to show that f(r) is independent of r. deduce that the average of a harmonic function over a function at the center of the sphere. sphere is equal to the value of the