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anonymous

  • 5 years ago

Fourier Series Help!

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  1. anonymous
    • 5 years ago
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    \[f(x)= 0 -3\le x<-1, 3 -1\le x < 1, 0 1 \le x < 3\]

  2. anonymous
    • 5 years ago
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    what's the question?

  3. anonymous
    • 5 years ago
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    Solve for 3 non zero terms

  4. anonymous
    • 5 years ago
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    remind me, we have to integrate between these points, right?

  5. anonymous
    • 5 years ago
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    Yes with formulas for ao, an, bn

  6. anonymous
    • 5 years ago
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    \[ f(x) = a0 + \sum_{n=1}^{\infty}(an \cos nx +bn \sin nx)\]

  7. anonymous
    • 5 years ago
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    Not familiar with it in that form but it looks similar yeah

  8. anonymous
    • 5 years ago
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    so the question is : 0 + \[\int\limits_{-3}^{-1} (an \cos n x + bn \sin nx) dx \] for the first term right?

  9. anonymous
    • 5 years ago
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    let me look

  10. anonymous
    • 5 years ago
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    then 3 - (the integral between -1 and 1) , right?

  11. anonymous
    • 5 years ago
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    for the second term.

  12. anonymous
    • 5 years ago
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    \[ao= 1/2L \int\limits_{-L}^{L} f(x) dx\]

  13. anonymous
    • 5 years ago
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    \[an= 1/L \int\limits_{-L}^{L} f(x)\cos* n \pi x/L dx\]

  14. anonymous
    • 5 years ago
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    lol, yes! For the first one the interval is between [-3,-1) so you'll integrate and get the following form:\[= \int\limits_{-3}^{-1}a0 dx + \int\limits_{-3}^{-1}\sum_{n=1}^{\infty}(an \cos nx + bn \sin nx)dx\]

  15. anonymous
    • 5 years ago
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    That is for solving a0 right? I'm not used to seeing sigma or it done with all the integrals combined.

  16. anonymous
    • 5 years ago
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    \[=2 a0 +\sum_{n=1}^ {\infty} an \int\limits_{-3}^{-1} \cos nx dx + \sum_{n=1}^{\infty}bn \int\limits_{-3}^{-1}\sin nx dx\]

  17. anonymous
    • 5 years ago
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    lol, that's the general form of fourier's series ^_^

  18. anonymous
    • 5 years ago
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    then you can integrate cos nx and sin nx and treat n as csts :), then you'll get the answer

  19. anonymous
    • 5 years ago
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    Hmm alright. Thanks

  20. anonymous
    • 5 years ago
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    separate them and solve each one alone then combine them and you'll get: \[\int\limits_{-3}^{-1}\cos nx dx\] and then integrate : \[\int\limits_{-3}^{-1}\sin nx dx\] find the answer and combine it with : = 2ao + _____ + _____ ( the answers you'll get after integrating)

  21. anonymous
    • 5 years ago
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    same thing goes with the other zeros ^_^ good luck! hope I made it easier for you :)

  22. anonymous
    • 5 years ago
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    A little :) Thanks

  23. anonymous
    • 5 years ago
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    lol, np ^_^ good luck.

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