Chapter 7.8, Problem 14P

In Problems 11 to 14, parts (a) and (b), you are given in each case one period of a function. Sketch several periods of the function and expand it in a sine-cosine Fourier series, and in a complex exponential Fourier series.

(a) $f(x)=\sin \pi x,-\frac{1}{2}<x<\frac{1}{2}$;

(b) $f(x)=\sin \pi x,0<x<1$.