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(10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, alum x) = 2 (ne, 3:), t e (0, co), x 6 (0,3); with initial condition u(0, x) = f(x), where f (0) = O and f '(3) = 0, and with boundary conditions u(t,0) = 0, 6,4103, 3) = O. Using separation of variables, the solution of this problem is DO u(t, X) = 2 cu vn(t) wn(X), ":1 with the normalization conditions u,,(0)= 1, w() =1 a. (5/10) Find the functions 1/11", with index n 2 1. w,,(x) = 2 b. (5/10) Find the functions U", with index n 2 1. \"11\") = z