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I know that the heaviside distribition is a piecewise function that deals with a discontinuous forcing functions but does the dirac delta function deal with the same type of situations? If so, what is the difference between them?

Zach
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  • You may want to check: http://math.stackexchange.com/q/479810/137035 –  Mar 26 '15 at 16:30

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The Heaviside function is usually defined to be an antiderivative of the Dirac distribution:

$$ H'(x) = \delta(x) $$

For some $a < 0$ one gets:

$$ \int\limits_a^x \delta(\xi) \, d\xi = \left\{ \begin{array}{rc} 0 & x < 0 \\ 1 & x > 0 \end{array} \right. = H(x) $$

mvw
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  • So if I am given one Heaviside Distribution (just the general form) and the general form of a dirac distribution, the difference is that the heaviside is just the antiderviative of the dirac? – Zach Mar 26 '15 at 16:30
  • No I mean what makes them different from one another. Is there a physical example that would pertian to each to help me better understand? – Zach Mar 26 '15 at 16:35
  • They are not different distributions. One could say the Dirac delta function is the density function and the Heaviside function is the cumulative distribution function, but of course the Dirac delta function isn't even really a function in the sense in which mathematicians usually define that term. – Michael Hardy Mar 26 '15 at 17:00
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    The Heaviside function is interpreted as a step, some value changes to a new value suddenly and stays that value, like turning on the light.The Dirac distribution is interpreted as an impulse, some value changing suddenly and then taking the old value, like the impact of a hammer on a nail. I am looking for a nice example where both show up, but fail to find one. – mvw Mar 26 '15 at 17:27