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Math Help - Laplace Transforms

  1. #1
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    Laplace Transforms

    Determine the Laplace Transform of the following function:

    u(t - 3)e^t


    I didn't really understand this part of my professors lecture, so if someone could explain to me what to do, that would be very helpful. Thanks
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  2. #2
    Super Member
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    Hey that's the shifting theorem with u being the unit step function or the Heaviside function H. So:

    L\left\{f(t-a)H(t-a)\right\}=e^{-at}L\left\{f(t)\right\}

    So how about if we let f(x)=e^{x+a} so that f(t-a)=e^{t-a+a}=e^{t} then:

    L\left\{e^{t}H(t-3)\right\}=e^{-3s}L\left\{e^{t+a}\right\}
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  3. #3
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    Thanks, that helps.
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