Consider the temperature distribution u(x, t) at time t at each point x of a bar of unit length sub- merged in ice at 0°C, with radiating heat at both ends. a. We assume that the thermal diffusivity and the heat convection coefficient are all equal to 1 and the initial temperature at each point x is given by the function f (x). Write down the initial boundary value problem that describes the temperature distribution u(x, t) in the bar. b. Determine the temperature in the bar at each point x and at time t, by solving the initial problem obtained in part a).