Q3 Analyse the corresponding waveform in Figure Q3 in term of: f() A -2 2 3 Figure Q3 (i) The function f(t) of the waveform. (4 marks) (ii) Find the Fourier series solution, f(1) (10 marks) (iii) Consider the positive period of the function in (i), sketch graph of even and odd expansion over -60 (a) u (0, t) = u (5, t) = 0, (b) u (x, 0) = 0, (c) us (x, 0) = 6. (10 marks) (b ) Find a formal solution to the heat diffusion problem by the given initial-boundary value problem. Solve the final answer for each of the given different initial conditions. (10 marks) Uxx = U. 00 u (0, t) = u (it, t) = 0, (a) u (x, 0) = 3sin 2x - 6sin 5x + 10 sin 7x, 0