# Math Help - Fourier Series, Sketch and Compute

1. ## Fourier Series, Sketch and Compute

See figure attached for problem statement as well as my attempt.

I'm not entirely sure if I've done the sketch in part a) correctly, can someone verify this for me?

Also, when solving for $a_{n}$ I noticed that all even values of n will give me 0. I tried to rewrite this so that only odd n's are valid.

Can I do this, and am I correct in doing so?

Can anyone else spot any other problems?

Thanks again!

2. Originally Posted by jegues
See figure attached for problem statement as well as my attempt.

I'm not entirely sure if I've done the sketch in part a) correctly, can someone verify this for me?

Also, when solving for $a_{n}$ I noticed that all even values of n will give me 0. I tried to rewrite this so that only odd n's are valid.

Can I do this, and am I correct in doing so?

Can anyone else spot any other problems?

Thanks again!

Assuming you evaluated correctly the corresponding integrals (and it looks like you did it correctly, indeed. It's

only that I didn't check them), your result looks fine.

Just do not write in the last line "f(x)=..." since you still have to calculate the coefficients of the sines...

Tonio

3. Originally Posted by tonio
Assuming you evaluated correctly the corresponding integrals (and it looks like you did it correctly, indeed. It's

only that I didn't check them), your result looks fine.

Just do not write in the last line "f(x)=..." since you still have to calculate the coefficients of the sines...

Tonio
The only reason I stated the last line was because the question stated NOT to calculate the coefficients of the sine series. Is it still unacceptable to write f(x) = ... ?

4. Originally Posted by jegues
The only reason I stated the last line was because the question stated NOT to calculate the coefficients of the sine series. Is it still unacceptable to write f(x) = ... ?

Of course, since the equality (within the limits of the theorem about Fourieri series) follows whn you have the whole

Fourier series on the right. That you didin't calculate the sines' coefficients doesn't necessarily mean they equal zero,

Tonio

5. Originally Posted by tonio
Of course, since the equality (within the limits of the theorem about Fourieri series) follows whn you have the whole

Fourier series on the right. That you didin't calculate the sines' coefficients doesn't necessarily mean they equal zero,