A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4.  The bar’s initial temperature is given by the function f(x) = 200 - 30x degrees Celsius.  The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C.  Let u(x,t)   be the temperature in the bar at x at time t, with t measured in seconds. Find u(x,t) and then u5(2, 0.1).

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