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
Hey that's the shifting theorem with u being the unit step function or the Heaviside function H. So:
$\displaystyle L\left\{f(t-a)H(t-a)\right\}=e^{-at}L\left\{f(t)\right\}$
So how about if we let $\displaystyle f(x)=e^{x+a}$ so that $\displaystyle f(t-a)=e^{t-a+a}=e^{t}$ then:
$\displaystyle L\left\{e^{t}H(t-3)\right\}=e^{-3s}L\left\{e^{t+a}\right\}$