Question

find the fourier series of this

Answer 1

of this

Answer 2

Is there any general form for a Fourier series of a function f(x)? I'm not particularly well-versed in the subject, although I'll try to help... :)

Answer 3

My first observation of the problem is that f(x) goes through three cycles over the interval (-3pi, 3pi)...

Answer 4

yeah i know

Answer 5

the first thing I have to find is the fourier coefficient. I think it is 1/4?

Answer 6

\[1/(2\pi)(\int\limits_{-\pi}^{0}0 dx + \int\limits_{0}^{\pi}(1/\pi)x dx\]

Answer 7

which is 1/4

Answer 8

Yep, that appears correct to me.

Answer 9

\[a _{n}=1/\pi \int\limits_{-\pi}^{0}0 dx + \int\limits_{0}^{\pi}(1/\pi)x dx\]

Answer 10

I am not sure if I am doing it right on the last one

Answer 11

The resource I am checking indicate that the formula for a_n would be 1/pi * integral from -pi to pi of f(x) cos(nx) dx

Answer 12

So...
\( \displaystyle a_n = \frac{1}{\pi} \left( \int_{-\pi}^{0} 0 \; \textrm{d}x + \int_{0}^{\pi} \frac{1}{\pi} x \cos nx \; \textrm{d}x \right) \)

Answer 13

yeah so then it is correct

Answer 14

so then it is 1/pi?

Answer 15

sin (1/pi)

Answer 16

So I am finding:
\( \displaystyle a_n = \frac{\pi n \sin n \pi + \cos \pi n - 1}{\pi^2 n^2} \)

Answer 17

and then I must do a \[b _{n}\]

Answer 18

\[b _{n}=1/\pi(\int\limits_{-\pi}^{0}0dx + \int\limits_{0}^{\pi}(1/\pi)x dx\]

Answer 19

My resource shows an additional sin(nx) there
\( \displaystyle \frac{1}{\pi} \int_{0}^{\pi} \frac{1}{\pi} x \sin nx \; \textrm{d}x \)

Answer 20

oh it's the same I just forgot to write the nx

Answer 21

and that -cos (pi/pi)

Answer 22

Sorry, I gotta go for school. I take the calculation of this integral to wolfram...
Wolfram evaluates it out as:
\( \displaystyle b_n = \frac{\sin \pi n - \pi n \cos \pi n}{\pi^2 n^2} \)
http://www.wolframalpha.com/input/?i=integral+from+0+to+pi+of+1%2Fpi%5E2+x+sin%28n+x%29+dx

Answer 23

okey. thank you

Answer 24

You're welcome! :)

Answer 25

and good luck, I think you're on the right track. :)

I was using this as my resource: http://mathworld.wolfram.com/GeneralizedFourierSeries.html
Just the end bit with the formula.

Answer 26

thank you :)