Results 1 to 12 of 12

Math Help - question about answer to fourier series question

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    103

    question about answer to fourier series question

    I have worked through the following question

    f(t)=\begin{cases} -1, -2 < t < -1 \\ t, -1 < t < 1 \\ 1, 1 < t < 2 \\<br />
 \end{cases}

    with a period of 4

    and got

    4/n^2*pi^2 sin (n*pi/2) - 2/n*pi cos (n*pi)

    Can someone tell me why the cos part of the answer is n*pi and not (-1)^n?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Well,

    \cos(n\pi)=(-1)^{n}.

    You can convince yourself of this by looking at the graph of the cosine function.

    Does that answer your question?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    103
    so why would this be (-1)^2 and not the another?
    Attached Thumbnails Attached Thumbnails question about answer to fourier series question-unit-2-2010-11-fourierbooklet31.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I don't understand your question. Can you please rephrase?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2009
    Posts
    103
    The step before I got the answer of (-1)^2 was cos(n*pi) for post 3. The step before post 1 was cos(n*pi) and stayed cos(n*pi) and I dont know why.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Where did the (-1)^2 come from? I thought we were talking about (-1)^n. Did you mean (-1)^n in all your posts?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2009
    Posts
    103
    yeah sorry I do
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Ah. So the answer to your question is post # 5 is that I have no clue. Post # 2 still stands. It could be a preference of the author, though I find the exponential expression to be simpler than the trig expression.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Nov 2009
    Posts
    103
    so the answer can be both in post #2
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    They're entirely equivalent. It's a preference thing.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Nov 2009
    Posts
    103
    or right, we were never told that in class. Thats helped me, thanks for that.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're very welcome. Have a good one!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on fourier series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2011, 07:39 AM
  2. Question about Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 21st 2011, 04:33 AM
  3. Question about Fourier Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 5th 2011, 08:00 PM
  4. Fourier series question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 24th 2008, 08:35 AM
  5. A question on Fourier series
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 1st 2008, 11:54 PM

Search Tags


/mathhelpforum @mathhelpforum