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Math Help - Convolution of Laplace Transformation?

  1. #1
    lpd
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    Convolution of Laplace Transformation?

    Hi.

    I am stuck on this question and not quite sure how to start it off.

    Use convolution to find the Laplace transforms of

    a. f(t) = \int_0^t sin(t - \tau) e^{3 \tau}d\tau
    and b. f(t) = \int_0^t \sigma(\tau) (t - \tau) d\tau

    .

    Maybe I don't understand the whole concept of convolution. Any help would be great.

    Thanks!
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  2. #2
    Flow Master
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    Quote Originally Posted by lpd View Post
    Hi.

    I am stuck on this question and not quite sure how to start it off.

    Use convolution to find the Laplace transforms of

    a. f(t) = \int_0^t sin(t - \tau) e^{3 \tau}d\tau
    and b. f(t) = \int_0^t \sigma(\tau) (t - \tau) d\tau

    .

    Maybe I don't understand the whole concept of convolution. Any help would be great.

    Thanks!
    You should know that LT[g(t) * h(t)] = LT[g(t)] \cdot LT[h(t)].

    a. By definition, f(t) = e^{3t} * \sin t.

    b. is left for you to think about.
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