Assignment:
Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer.
Expand the function
f(x) = {x^4, 0 <= x < 2
{0, 2 <= x <= pi
in terms of the eigenfunctions of the given eigenvalue problem. Use computer software, such as the Maple int command, to evaluate the expansion coefficient an as a function of n.
(a) y" + λy = 0, y'(0) = 0, y'(Π) = 0
(b) y" + λy = 0, y'(0) = 0, y(Π) = 0
(c) y" + λy = 0, y(0) = 0, y'(Π) = 0