Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

nissn Group Title

find the fourier series of this

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    of this

    • 2 years ago
  2. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 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... :)

    • 2 years ago
  3. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

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

    • 2 years ago
  4. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i know

    • 2 years ago
  5. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  6. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  7. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    which is 1/4

    • 2 years ago
  8. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yep, that appears correct to me.

    • 2 years ago
  9. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  10. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  11. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    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

    • 2 years ago
  12. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

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

    • 2 years ago
  13. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah so then it is correct

    • 2 years ago
  14. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so then it is 1/pi?

    • 2 years ago
  15. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sin (1/pi)

    • 2 years ago
  16. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

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

    • 2 years ago
  17. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  18. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  19. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

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

    • 2 years ago
  20. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • 2 years ago
  21. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and that -cos (pi/pi)

    • 2 years ago
  22. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    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

    • 2 years ago
  23. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okey. thank you

    • 2 years ago
  24. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You're welcome! :)

    • 2 years ago
  25. AccessDenied Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    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.

    • 2 years ago
  26. nissn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you :)

    • 2 years ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.