True or False Explain your answer TrueFalse No explanation n

True or False? Explain your answer.

True/False No explanation needed for answers. Mark your answer clearly. (a) T F Let sigma be an unknown constant. Consider the initial value problem X\"(x) + 2X\'(x) - sigma X(x) = 0, X(0) = 0, and X(2) = 0. For this initial value problem, sigma = 0 is an eigenvalue. (b) T F If f(x) is an even function on the interval [-L, L] then the coefficients of the cosine terms in its Fourier Series are given by alpha_n = 2/L integral^L_0 f(x) cos (pi n x/2L) dx. (c) T F If S(x) is the Fourier Series expansion of f(x) = {x + 1: -1 lessthanorequalto x lessthanorequalto 1/2 x - 1: 1/2

Solution

a) True

b) False

c) True

d)   False

e) False