A community for students.
Here's the question you clicked on:
 0 viewing
nissn
 3 years ago
find the fourier series of this
nissn
 3 years ago
find the fourier series of this

This Question is Closed

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2Is there any general form for a Fourier series of a function f(x)? I'm not particularly wellversed in the subject, although I'll try to help... :)

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2My first observation of the problem is that f(x) goes through three cycles over the interval (3pi, 3pi)...

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0the first thing I have to find is the fourier coefficient. I think it is 1/4?

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0\[1/(2\pi)(\int\limits_{\pi}^{0}0 dx + \int\limits_{0}^{\pi}(1/\pi)x dx\]

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2Yep, that appears correct to me.

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0\[a _{n}=1/\pi \int\limits_{\pi}^{0}0 dx + \int\limits_{0}^{\pi}(1/\pi)x dx\]

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0I am not sure if I am doing it right on the last one

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2The 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

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2So... \( \displaystyle a_n = \frac{1}{\pi} \left( \int_{\pi}^{0} 0 \; \textrm{d}x + \int_{0}^{\pi} \frac{1}{\pi} x \cos nx \; \textrm{d}x \right) \)

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0yeah so then it is correct

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2So I am finding: \( \displaystyle a_n = \frac{\pi n \sin n \pi + \cos \pi n  1}{\pi^2 n^2} \)

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0and then I must do a \[b _{n}\]

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0\[b _{n}=1/\pi(\int\limits_{\pi}^{0}0dx + \int\limits_{0}^{\pi}(1/\pi)x dx\]

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2My resource shows an additional sin(nx) there \( \displaystyle \frac{1}{\pi} \int_{0}^{\pi} \frac{1}{\pi} x \sin nx \; \textrm{d}x \)

nissn
 3 years ago
Best ResponseYou've already chosen the best response.0oh it's the same I just forgot to write the nx

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2Sorry, 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

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2You're welcome! :)

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2and 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.