= Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 2 8u(t, x), te (0,0), TE (0,3); with Mixed boundary conditions du(t,0) = 0 and ut, 3) = 0 and with initial condition 5, ceo, [0, 3) u(0,r) = f(1) = 2 0, { The solution u of the problem above, with the conventions given in class, has the form ut, 2) = Un(t) wn(2), e ( 71 with the normalization conditions v. (0) = 1 and wn(0) =1 Find the functions on W, and the constants Cn Vr(t) = M