( Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° Cso that half of it is in the air at 20°C. At t=Q, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t) , where x is the distance from the left end of the rod, x=0. The U(x,t) is a solution of the initial boundary value problem: ww = « Uxx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 Initial condition : U(x,0) = 30, 0

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