find the possible fourier expansion that will respect the following non-periodic function. 1 , 0 < t < 1/2
f(t)={
0 , 1/2 < t < 1
What is the problem that you have with this? You need to evaluate the
integrals:
$\displaystyle
\int_0^1 f(x) \sin(2 \pi n x) dx=\int_0^{1/2} \sin(2 \pi n x) dx, \ \ n=1,2,..
$
and
$\displaystyle
\int_0^1 f(x) \cos(2 \pi n x) dx=\int_0^{1/2} \cos(2 \pi n x) dx, \ \ \ n=0,1,2,..
$
then plug these into the relevant buts of the expansion.
RonL