Hello,

Can anyone please help me with the attached file. Questions (iv) to (vi). Its related to Fourier Series.

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- Aug 17th 2007, 12:56 AMatwinixFourier Series
Hello,

Can anyone please help me with the attached file. Questions (iv) to (vi). Its related to Fourier Series. - Aug 17th 2007, 11:02 AMCaptainBlack
What is the problem with these? The third line in each tells you that the function is periodic with period

$\displaystyle 2 \pi$ so any interval of that length is what you use in the integrations and the basis functions are

$\displaystyle \sin(nx)$ and $\displaystyle \cos(nx)$.

RonL - Aug 17th 2007, 08:29 PMatwinix
Yes, I know how the Fourier series expansion work.

I am having problem with the integration between the limits for question 6 (iv) as you get something like:

∫ (π+t) cos (nt) dt + ∫ (π-t) cos (nt) dt - Aug 17th 2007, 09:20 PMCaptainBlack
Using integration by parts with $\displaystyle u=(\pi-t)$ and $\displaystyle dv=\cos(nt)$:

$\displaystyle \int_0^\pi (\pi-t) \cos(nt)~dt = \left[ \frac{(\pi-t)}{n} \sin(nt) \right]_0^{\pi}+\int_0^{\pi}\frac{1}{n^2} \sin(nt)~dt$$\displaystyle =\frac{1}{n^2}(1-(-1)^n)$

which is $\displaystyle 2/n^2,\ n=1, 3, 5, ..$ and $\displaystyle 0,\ n=2,4,.. $

RonL - Aug 18th 2007, 01:13 AMatwinix
Oh!!! So that's the catch! I shall try it.

Thanks loads.