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Math Help - Laplace transformation and heaviside function

  1. #1
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    Laplace transformation and heaviside function

    If H is the Heaviside function with

    H(t-a)=0, t<a
    H(t-a)=1, t>a

    find the laplace transformation of H(t-a)g(t).

    I know how to find the transformation of H(t-a)g(t-a), but I can't do this one.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ricko View Post
    If H is the Heaviside function with

    H(t-a)=0, t<a
    H(t-a)=1, t>a

    find the laplace transformation of H(t-a)g(t).

    I know how to find the transformation of H(t-a)g(t-a), but I can't do this one.
     <br />
\mathfrak{L} \left[H(t-a)g(t)\right](s)=\int_0^{\infty} H(t-a)g(t)e^{-st}\;dt=\int_a^{\infty} g(t)e^{-st}\;dt= e^{-as}\int_0^{\infty} g(u+a)e^{-su}\;du=e^{-as}\mathfrak{L} \left[g(x+a)\right](s)<br />

    CB
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