Laplace Transforms

**jkru** · November 25th 2008, 12:48 PM

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

**shawsend** · November 25th 2008, 01:07 PM

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:

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

**jkru** · November 25th 2008, 01:13 PM

Thanks, that helps.

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