Fourier Sine Series of f(x)=x: Solution & Explanation

Click For Summary

Homework Help Overview

The discussion revolves around finding the Fourier Sine Series (F.S.S.) of the function f(x) = x defined on the interval 0 ≤ x ≤ 1, with an indicated period of 2. Participants are examining the implications of the period and the function's behavior in relation to Fourier series expansion.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the validity of the problem statement regarding the specified period and its implications on the function's expansion. There is a discussion about whether the function can be considered periodic with the given conditions and what that means for the Fourier series representation.

Discussion Status

The discussion is ongoing, with participants exploring the correctness of the problem statement and its implications. Some guidance has been offered regarding the need for clarity on the function's periodicity and the potential need to disregard the specified period of 2.

Contextual Notes

There is uncertainty regarding the completeness of the problem statement as it was presented in class, with suggestions that the professor may have made an error. The implications of this uncertainty on the Fourier series expansion are being examined.

DreamSanchez
Messages
3
Reaction score
0

Homework Statement



Find the F.S.S. of f(x)=x
0≤x≤1
of period 2

Homework Equations



(uploading photo with equations shown)

The Attempt at a Solution



(uploaded photo)

I have completely worked this problem out in the provided photo but I am unsure as to whether or not I went about it in the correct manner. If anyone could take a look at it and let me know how I did, I would truly appreciate it!
 

Attachments

  • IMG_0708.jpg
    IMG_0708.jpg
    26.4 KB · Views: 455
Physics news on Phys.org
DreamSanchez said:

Homework Statement



Find the F.S.S. of f(x)=x
0≤x≤1
of period 2

Homework Equations



(uploading photo with equations shown)

The Attempt at a Solution



(uploaded photo)

I have completely worked this problem out in the provided photo but I am unsure as to whether or not I went about it in the correct manner. If anyone could take a look at it and let me know how I did, I would truly appreciate it!

There is something wrong with your problem statement. If f(x) really does have period 2, you either have to specify it also on the interval (-1,0) or else on the interval (1,2). If all you have is f(x) on (0,1), its Fourier series will have period 1, not 2; and in that case it will not be an odd function, and so will not be expandable only in sines---you will also need cosines.
 
The way I wrote the problem is how it was given to me in class. The professor is known for making mistakes though when writing the homework on the board. Perhaps neglect the "period of 2" portion. Would my work make sense in that case?
 
DreamSanchez said:
The way I wrote the problem is how it was given to me in class. The professor is known for making mistakes though when writing the homework on the board. Perhaps neglect the "period of 2" portion. Would my work make sense in that case?

Yes, but it is giving the series for the function g(x) = x, -1 < x < 1, with period 2. (To convince yourself of this, try plotting sums of, say, 20 or 30 terms on the interval -1 < x < 1.)
 

Similar threads

Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
12
Views
7K
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K