1. So far, we considered the heat transfer of a cylindrical rod with a cross sectional radius R for which the cylindrical surface was insulated. This time assume that the cylindrical surface is not insulated (so heat can ow through the two ends as well as through the cylindrical surface), and neglect any heat sources. Assume that the heat energy owing out of the cylindrical surface per unit surface area per unit time is p(x,t). Derive the partial differential equation for the temperature u(x,t), following similar steps as we did in class to derive the heat equation