A function defined over an interval [-L, L] can be expanded in a Fourier series of the form, where f(x) = = 2 f(x) an + n=1 = bn = = 1 L 1 Find the Fourier series expansion L an COS L -L -L nax L f(x) cos f(x) sin + bn sin NAX L L -dx -dx for the function nat), L 0, if - L x -L/2 1/3, if L/2 x L/2 0 if L/2 x L (1) (2) (4) Plot the Fourier series expansion of this function for the first 1, 2, 5, 10, 100 and 1000 terms using Matlab, Wolfram Alpha, any other plotting package... or *shudder* Excel.