# Math Help - Laplace Transforms

1. ## 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

2. 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:

$L\left\{e^{t}H(t-3)\right\}=e^{-3s}L\left\{e^{t+a}\right\}$

3. Thanks, that helps.