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(10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, alum x) = zaiuo, x), t e (0, 00), x 5 (0,3); with initial condition u(0, x) = f(x), where f (0) = 0 and f '(3) = 0, and with boundary conditions u(t,0) = 0, 6xu(t, 3) = 0. Using separation of variables, the solution of this problem is 00 u(t, 9:) = 2 c" vn(t) w,.(X), n=1 with the normalization conditions 11,,(0): 1, w() :1 a. (5/10) Find the functions w,\" with index n 2 1. w,.(x) = 2 b. (5/10) Find the functions U", with index n 2 1. Una) = z