Problem 2

[Peishan Wang]

Hi Professor,

I'm not sure if there's a typo but in Problem 2 I think we should be given a specific interval (say [-pi, pi]) in order to plot the graph. Thanks!

[Victor Ivrii]

You have $[-l,l]$ and you may plot for any value $l>0$ (say $l=1$)

[Aida Razi]

Part (c) solution is attached!

[Victor Ivrii]

Wher are calculatingly simpler  a), b)? And the sketch?

[Aida Razi]

Part (a) solution is attached!

[Aida Razi]

Part (b) solution is attached!

[Zarak Mahmud]

Since $f(x) = x^2$ was already computed in part c, to calculate part a (say $g(x) = x$), we could have also noted that $$g(x) = \frac{1}{2}\frac{d}{dx}f(x)$$ and applied this transformation term by term to the Fourier series of $f(x)$.