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Fourier Series (Half-range expansion)

  1. Nov 19, 2014 #1
    1. The problem statement, all variables and given/known data

    rbz30j.jpg

    2. Relevant equations

    11uvwc4.jpg

    3. The attempt at a solution

    I don't really understand why my solution is wrong as I think I have substituted everything in correctly..

    Is it okay if anyone can help me take a look at my solution? Thank you. :)

    My solution: (Only bn)

    k1wi1d.jpg

    My teacher's solution (not the whole solution):

    2hfnjbt.jpg

    The thing I don't understand is why is my teacher's sin portion "sin nx" and not "sin 2nx" like mine?

    Thanks. :)
     
  2. jcsd
  3. Nov 19, 2014 #2

    Orodruin

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    Your L should be pi. As it is now you are missing half of the interval and not using all of the basis functions.
     
  4. Nov 19, 2014 #3
    I see. Is this due to the half-range expansion, or is it because of the range from (0, π)?

    Thank you. :)
     
  5. Nov 19, 2014 #4

    Orodruin

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    Well, both. The half-range is 0 to pi so the length of the full range must be 2pi. In the end, you could just as well have considered it to be just an expansion on 0 to pi without making an extension, the basis functions are the same.
     
  6. Nov 19, 2014 #5
    I see. Just wondering, if this is just a normal Fourier series expansion of cos(x) from (0,π), will the L still be the same?
     
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