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Math Help - Heaviside/Unit Step Function and other piecewise functions

  1. #1
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    Heaviside/Unit Step Function and other piecewise functions

    let f(t) be an elementary function defined for every real number t
    denote the unit step function as U(t-a), t >= 0, a real
    such that U(t-a) = {0 if 0<=t<a, and 1 if t>= a

    then

    f(t)U(t-a) = {0 if 0<=t<a, and f(t) if t >= a

    No problem.

    What happens when we compute the product U(t-a)p(t), where p(t) is itself a piecewise function? i.e. p(t) = { condition 1, 2, ..., n
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Noxide View Post
    let f(t) be an elementary function defined for every real number t
    denote the unit step function as U(t-a), t >= 0, a real
    such that U(t-a) = {0 if 0<=t<a, and 1 if t>= a

    then

    f(t)U(t-a) = {0 if 0<=t<a, and f(t) if t >= a

    No problem.

    What happens when we compute the product U(t-a)p(t), where p(t) is itself a piecewise function? i.e. p(t) = { condition 1, 2, ..., n
    Exactly as before:

    U(t-a)p(t) = {0 if 0<=t<a, and p(t) if t >= a

    CB
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  3. #3
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    lol, ty
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