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Unit Step Function or Series?

  1. Mar 24, 2007 #1
    1. The problem statement, all variables and given/known data
    I have an equation that has the following values at different intervals:

    It is:

    r when 0<x<2Pi
    r - (1)d when 2Pi<x<4Pi
    r - (2)d when 4Pi<x<6Pi

    And so on. I want to find a function that encompasses this whole function. Unit functions / discontinuity functions are fine; as long as I can take derivatives in the future.

    2. The attempt at a solution

    The furthest I could get is to define a series as follows:

    r - n*d when 2nPi < x < 2(n+1)*Pi

    At this point, my mind thinks discontinuity functions, but those would only work if 'n' was always a constant value, and didn't increase by 1 each iteration.

    Thank you!
  2. jcsd
  3. Mar 25, 2007 #2
    cough, cough...the floor function.
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