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Math Help - Interval problem in Fourier series

  1. #1
    Member roshanhero's Avatar
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    Aug 2008
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    Unhappy Interval problem in Fourier series

    The functions are-
    (a) f(x)=\left | x \right |, -\pi\leq x\leq \pi
    (b) f(x)=\left | sin x \right |, -\pi\leq x\leq \pi
    Writing them individually
    a) f(x)=x and f(x)=-x
    b) f(x)=sin x and  f(x)=-sin x
    The problem is what should be the correct intervals for these functions. I am pretty messed up with this basic thing though I can easily compute the fourier series of these functions.
    Last edited by roshanhero; July 5th 2010 at 02:05 AM.
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    Basically you need to identify two things:
    1) What values of x make the expression inside the absolute value sign positive?
    2) What values of x make it negative?

    The first problem is simple, but we have to take into account that the domain is -\pi<x<\pi.

    f(x)=|x|=\begin{cases} x, & 0 \le x \le \pi \\ -x, & -\pi \le x < 0 \end{cases}

    Does this make sense? Can you figure out the second one like this?
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