(a) Using the divergence theorem, determine an alternative expression for...

(a) Using the divergence theorem, determine an alternative expression for

(b) Using part (a), prove that the solution of Laplace’s equation ∇ ²u = 0 (with u given on the boundary) is unique.

(c) Modify part (b) if

(d) Modify part (b) if

on the boundary. Show that Newton’s law of cooling corresponds to h > 0.