Assignment:
In this problem, you will devise a computer experiment to investigate Gibb's phenomenon, which is the presence of spurious oscillations in the graph of a truncated Fourier series near the places where the full Fourier series is discontinous.
Choose any function you like that demonstrates Gibb's phenomenon. Your goal is to answer these two questions:
(a) You should find that the amount of overshoot only depends on the height of the discontinuity of your function. Expressed as a ratio to the height of the discontinuity, what is the approximate amount of overshoot/undershoot?
(b) What happens to the amount of overshoot/undershoot as you increadse the number of terms in your truncated Fourier series?