Example 3.10 in the Textbook:  expand the function f(t)=exp(-t) for t\in[-1,1] into

a complex exponential series;

>	restart: A:=-1;B:=1;N:=5;

Function to be expanded on [-1,1]:  

>	f(t):=piecewise(t<A,0, t>A and t<B,exp(-t),t>B ,0); plot(f(t),t=-5..5);

Fourier Coefficients:

>	c[n]:=1/2*int(f(t)*exp(-n*Pi*t*I),t=-1..1);

nth Partial Sum of the Complex Exponential Series Expansion;

>

  E[N](t):=sum(c[n]*exp(n*Pi*t*I),n=-N..N);

>	plot({f(t),E[N](t)},t=-5..5,y=-2..3, color=[red,blue]);

>