Homework Help: Fourier Series (Half-range expansion)

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1. Nov 19, 2014

galaxy_twirl

1. The problem statement, all variables and given/known data

2. Relevant equations

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)

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

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

Thanks. :)

2. Nov 19, 2014

Orodruin

Staff Emeritus
Your L should be pi. As it is now you are missing half of the interval and not using all of the basis functions.

3. Nov 19, 2014

galaxy_twirl

I see. Is this due to the half-range expansion, or is it because of the range from (0, π)?

Thank you. :)

4. Nov 19, 2014

Orodruin

Staff Emeritus
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.

5. Nov 19, 2014

galaxy_twirl

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?