Chapter 7.9, Problem 17P

In Problems 17 to 22 you are given $f(x)$ on an interval, say $0<x<b$.

Sketch several periods of the even function $f_c$ of period 2b, the odd function $f_c$ of period 2b, and the function $f_p$ of periodb, each of which equals $f(x)$ on $0<x<b.$ Expand each of the three functions in an appropriate Fourier series.

$f(x)=$ { $1,0<x<\frac{1}{2}$, $-1,\frac{1}{2}<x<1$.