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Math Help - Question on fourier series

  1. #1
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    Question on fourier series

    Hi,

    Im trying to attempt a few questions for an exam in a couple of weeks, but am finding it hard, so was wondering if anyone on here is able to help. Below is the question:

    1. The function f(x) is periodic with period and is defined by

    f(x) = {-cos x when -pi <x<0
    {cos x when 0<x<pi

    a) Sketch f from x=-3pi to x=3pi .

    b) Decide if f is an even, odd function or neither.
    c) Find the Fourier series of f.
    d) By choosing a suitable value of x sum the series

    1/1.3 - 3/5.7 + 5/9.11 - 7/13.15 + .........
    Last edited by mr fantastic; December 8th 2011 at 12:54 PM. Reason: Title.
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  2. #2
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    Re: Help needed to answer question on fourier series

    Quote Originally Posted by NFS1 View Post
    Hi,

    Im trying to attempt a few questions for an exam in a couple of weeks, but am finding it hard, so was wondering if anyone on here is able to help. Below is the question:

    1. The function f(x) is periodic with period and is defined by

    f(x) = {-cos x when -pi <x<0
    {cos x when 0<x<pi

    a) Sketch f from x=-3pi to x=3pi .

    b) Decide if f is an even, odd function or neither.
    c) Find the Fourier series of f.
    d) By choosing a suitable value of x sum the series

    1/1.3 - 3/5.7 + 5/9.11 - 7/13.15 + .........
    for part a) just graph the piecewise function and shift it right and left using the fact that it is periodic.

    For b)

    look at two different cases

    Case 1 x > 0 then

    f(-x)=-\cos(-x)=-\cos(x)=-f(x) so it is odd so far....

    Now you try case 2

    x < 0

    From part b) you will find that the function is odd!

    So you only need to compute half of the fourier coefficents. Which ones? Use this to get started and post back with some work if you get stuck.
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