Fourier Series (Clarification of Concept)

[galaxy_twirl]

Hi everyone. I ran into a problem while attempting my Fourier Series tutorial. I don't really understand the "L" in the general formula for a Fourier Series (integration form). I shall post my question and doubts as images. Thank you for any assistance rendered.

<I am solving Q3 in the image.>

 

[Simon Bridge]

Its the region that you want the series to be accurate for - that you are looking at.
If f(x) is periodic, then you want to choose L: 2L=wavelength ...

http://tutorial.math.lamar.edu/Classes/DE/FourierSeries.aspx

 

[galaxy_twirl]

Hi Simon. Thank you for your reply. The limits of the integral sign denotes which part of a graph you want to integrate. However, I am confused by the L outside the integral. From what I observe, it seems that L (outside the integral sign) is different from [-L, L] (which is your domain over which you want to integrate). Am I right to say this?

Thank you.

 

[LCKurtz]

Hi Simon. Thank you for your reply. The limits of the integral sign denotes which part of a graph you want to integrate. However, I am confused by the L outside the integral. From what I observe, it seems that L (outside the integral sign) is different from [-L, L] (which is your domain over which you want to integrate). Am I right to say this?

Thank you.

They are the same $L$. By the way, posting images instead of typing your work is frowned on in these forums. That goes double for images that are posted sideways.

 

[Simon Bridge]

The same rules apply to that L as for any letter used as a name for a constant or a variable in algebra.
That L is just a number. Where you see it, it's the same number.

 

[epenguin]

They are the same $L$. By the way, posting images instead of typing your work is frowned on in these forums. That goes double for images that are posted sideways.

But if you do do that, there are apps, at least one I know called DocScan HD which if you are taking these with I-pad or similar cleans them up from the hard-to-read grey-yellow.

 

[galaxy_twirl]

They are the same $L$. By the way, posting images instead of typing your work is frowned on in these forums. That goes double for images that are posted sideways.

Hi LCKurtz. Thank you for your help. I will take note about this and type instead of posting my questions as picture. Sorry.

 

[galaxy_twirl]

The same rules apply to that L as for any letter used as a name for a constant or a variable in algebra.
That L is just a number. Where you see it, it's the same number.

I see. Thank you. I think I know where my mistake was. I failed to see that f(x) was 0 over a certain range, so I could have just changed the limits to (-pi/2) to (pi/2). :)

 

[galaxy_twirl]

But if you do do that, there are apps, at least one I know called DocScan HD which if you are taking these with I-pad or similar cleans them up from the hard-to-read grey-yellow.

Hi epenguin. Thank you for your suggestion. The reason why I posted my question as a picture was because I am not familiar with LaTeX and I found that it can be quite hard to read if I typed it in purely character form. I will take note of your suggestion and try to type my questions out in the future. Thanks again.