We shall describe the diffusion of heat energy through a long thin rod G with uniform cross section S. As before, we identify G with the open interval (a, b), and we assume the rod is perfectly insulated along its length. Let u(x, t) denote the temperature within the rod at a point x ∈ G and at time t > 0. Our previous experience shows that the heat flux q(x, t) at the point x, i.e., the flow r...