Results 1 to 14 of 14

Math Help - Fourier Series Question

  1. #1
    Super Member
    Joined
    Dec 2008
    Posts
    509

    Fourier Series Question

    Hi
    The following two question i am having trouble finding the fourier series.
    Can someone tell me what i have done wrong in question 1?

    In Question 2 i am stuck after subbing t = 0 and 1 into the intergral. How should this be simplified?

    P.S
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Paymemoney View Post
    Hi
    The following two question i am having trouble finding the fourier series.
    Can someone tell me what i have done wrong in question 1?

    In Question 2 i am stuck after subbing t = 0 and 1 into the intergral. How should this be simplified?

    P.S
    Cos of an odd multiple of \pi is $$-1 and cos of $$0 is $$1

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2008
    Posts
    509
    Quote Originally Posted by CaptainBlack View Post
    Cos of an odd multiple of \pi is $$-1 and cos of $$0 is $$1

    CB
    is that reply to question 1 or 2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Paymemoney View Post
    Hi
    The following two question i am having trouble finding the fourier series.
    Can someone tell me what i have done wrong in question 1?

    In Question 2 i am stuck after subbing t = 0 and 1 into the intergral. How should this be simplified?

    P.S

    Why do you do what you do with a_0?? Do you hate yourself? Much easier to split the integral into a sum:

    \displaystyle{\int\limits^1_{-1}(1-|t|)dt=\int\limits^0_{-1} (1+t)dt+\int\limits^1_0(1-t)dt=1} , and then do the same for a_n\,,\,b_n

    If this exercise is what I think it is then it's a very nice and beautiful one. You'll get both

    the sums of \displaystyle{\sum\limits^\infty_{n=1}\frac{1}{(2n-1)^2}\,\,and\,\,\sum\limits^\infty_{n=1}\frac{1}{n  ^2}}

    Tonio
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Paymemoney View Post
    is that reply to question 1 or 2?
    2

    cb
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Dec 2008
    Posts
    509
    quick question how would i simplify the following line:

    a_n = \frac{1}{\pi}[\frac{-cos(1-n)\pi}{2(1-n)} - \frac{cos(1+n)\pi}{2(1+n)} - 0]
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Paymemoney View Post
    quick question how would i simplify the following line:

    a_n = \frac{1}{\pi}[\frac{-cos(1-n)\pi}{2(1-n)} - \frac{cos(1+n)\pi}{2(1+n)} - 0]

    Since \cos m\pi =(-1)^m we have that

    \displaystyle{a_n=\frac{1}{\pi}\left[\frac{(-1)^n}{2(1-n)}+\frac{(-1)^n}{2(1+n)}\right]=\frac{(-1)^n}{\pi}\cdot\frac{2}{1-n^2}}

    Tonio
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Dec 2008
    Posts
    509
    in this case would i need to determine when n-> even and n-> odd. Because i checked the answers and has it like \frac{2}{\pi}\sum\limits^\infty_{n=1} \frac{1}{4n^2-1}
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Dec 2008
    Posts
    509
    if  cos(m\pi) = (-1)^{m}

    then what would

    sin(m\pi) = ???
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Paymemoney View Post
    if  cos(m\pi) = (-1)^{m}

    then what would

    sin(m\pi) = ???
    Sketch a sine curve and observe its behaviour, if you actually try it is not difficult to answer your own question.

    Also if you do not know the value of the sine and cosine at interger multiples of pi you are not ready to study Fourier series and need to repeat trig.

    CB
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Paymemoney View Post
    if  cos(m\pi) = (-1)^{m}

    then what would

    sin(m\pi) = ???


    It is a little weird, imho, to make this kind of trivial questions in very basic trigonometry

    if you're dealing with Fourier series...even if you don't remember. and this is already weird,

    why don't you check your high school books or, at least, google it?

    The sine of any multiple of pi is zero...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Super Member
    Joined
    Dec 2008
    Posts
    509
    i think my question was not clear, my question was based on what does sin(1-n) equal to.

    We know that if cos(1-n)\pi = (-1)^{1-n} so would this apply to sin(1-n)\pi as well.
    Last edited by Paymemoney; March 13th 2011 at 12:45 AM.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Paymemoney View Post
    i think my question was not clear, my question was based on what does sin(1-n) equal to.
    No such term appears in this problem or its solution.

    CB
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Paymemoney View Post
    i think my question was not clear, my question was based on what does sin(1-n) equal to.

    We know that if cos(1-n)\pi = (-1)^{1-n} so would this apply to sin(1-n)\pi as well.

    This continues to be weird: first, as CB already pointed out, \sin (1-n) has nothing to do with do with your problem,

    and if you meant \sin (1-n)\pi this again is the sine of an integer multiple of pi

    and thus equals zero...

    Tonio
    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 sum of fourier series
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: April 5th 2011, 07:56 AM
  3. Question about Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 21st 2011, 04:33 AM
  4. Question about Fourier Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 5th 2011, 08:00 PM
  5. Fourier Series Question
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 24th 2010, 12:30 AM

Search Tags


/mathhelpforum @mathhelpforum