The purpose of this exercise is to give a slightly different argument for the property (8.7) than in the text above. Recall that the starting point of our analysis leading to this inequality was to...

The purpose of this exercise is to give a slightly different argument for the property (8.7) than in the text above. Recall that the starting point of our analysis leading to this inequality was to multiply the left- and right-hand sides of the diffusion equation by u. In this exercise we ask you to start off by differentiating the function E1.t /, defined in (8.4), with respect to t and apply the differential equation (8.1), integration by parts, the boundary condition (8.2), and so on, in order to derive (8.7).