Question

A question about even and odd functions in Fourier series.

Answer 1

when i tried to solve this question, i had a problem about finding (a)n

Answer 2

can't read it, and maybe can't even do it, but fourier series of even function will have only cosines for sure right?

Answer 3

cosn(pi)x/L is even, so the integration will not be zero, but...it is zero, right?

Answer 4

ok let me see if i recall

Answer 5

\[a_1=\frac{1}{\pi}\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}k\cos(x)dx\] in this case. does that look right?

Answer 6

L in this case is
\[\pi\]

Answer 7

and the function is even, so you will have only cosines in it

Answer 8

oh! i got it! know how to solve it suddenly with your hint, thank you very much!

Answer 9

really it has been a long time so i don't want to mislead you

Answer 10

but i get
\[a_1=\frac{2k}{\pi}\]

Answer 11

glad i helped even if i am a bit rusty

Answer 12

haha, sometimes rusty is the most clear answer