Find the Fourier series of each function \(f(x)\) of period \(2 \pi\). For each series, plot the Nth partial sum,

\[S_{N}=\frac{a_{0}}{2}+\sum_{n=1}^{N}\left[a_{n} \cos n x+b_{n} \sin n x\right]\]

for \(N=5,10,50\) and describe the convergence (Is it fast? What is it converging to?, etc.) [Some simple Maple code for computing partial sums is shown in the notes.]

a. \(f(x)=x,|x|<\pi\).

b. \(f(x)=|x|,|x|<\pi\).

c. \(f(x)=\left\{\begin{array}{lc}0, & -\pi