A (a) [10%) Define Haberman's Fourier transform pair. A(b) [30%] Assume /(x) = 2 on -1 :x 5 0 and f(x) = 0 otherwise. Compute the Fourier transform F(w) of f(). Graded Details: (1) Transform formula, (2) Integration details, (3) Answer. (c) [60%] The heat kernel g(x) and the error function erf(x) are defined by the equations g(x) = V kt e mi, erf(x) = edz. Solve the infinite rod heat conduction problem 14 ( I,t) 1 -00 0, u(I,0) = /(I), -DO 0, u(0, t) = 0. u(1, t) = 0, 120, L(I, 0) = f(I), 0