Short Fourier series question

  • #1

Homework Statement



ynms7.jpg


Homework Equations



Usual equations for calculating fourier series coefficients

The Attempt at a Solution



Well essentially I don't know what to let f(x) equal to for calculating the coefficients a0, an and bn. Should I use 1 + x/pi or 1 - x/pi? And what about the limits? I was thinking maybe between -pi and pi.

Anyway here's my progress thus far, I think the graph is ok anyways.

519dnb.jpg


Thanks dudes. I would use latex but I suck at it :yuck:
 

Answers and Replies

  • #2
I like Serena
Homework Helper
6,577
176
Looks fine.
Just start with the generic formula for a0.
The integral can be calculated by splitting it into the sum of 2 integrals.
 
  • #3
1,796
53
Take for example:

[tex]a_1=\frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(x)dx[/tex]

now, I want to integrate that function between -pi and pi but it's defined differently in two intervals. Why not just split up the intervals and write:

[tex]a_1=\frac{1}{\pi}\left(\int_{-\pi}^{0} (1+x\pi)\cos(x)dx+\int_{0}^{\pi} (1-x\pi)\cos(x)dx\right)[/tex]

However it is an even function so there are short-cuts for computing them. But for now, you may want to just do it this way.
 
  • #4
Take for example:

[tex]a_1=\frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(x)dx[/tex]

now, I want to integrate that function between -pi and pi but it's defined differently in two intervals. Why not just split up the intervals and write:

[tex]a_1=\frac{1}{\pi}\left(\int_{-\pi}^{0} (1+x\pi)\cos(x)dx+\int_{0}^{\pi} (1-x\pi)\cos(x)dx\right)[/tex]

However it is an even function so there are short-cuts for computing them. But for now, you may want to just do it this way.

Looks fine.
Just start with the generic formula for a0.
The integral can be calculated by splitting it into the sum of 2 integrals.

Great I understand completely now, thanks everyone. :smile:
 

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