L{f″}=s2L{f}−sf(0−)−f′(0−){\displaystyle {\mathcal {L}}\{f''\}=s^{2}{\mathcal {L}}\{f\}-sf(0^{-})-f'(0^{-})} L{f(n)}=snL{f}−sn−1f(0−)−⋯−f(n−1)(0−){\displaystyle {\mathcal {L}}\left\{f^{(n)}\right\}=s^{n}{\mathcal {L}}\{f\}-s^{n-1}f(0^{-})-\cdots -f^{(n-1)}(0^{-})}
L{tnf(t)}=(−1)nF(n)(s){\displaystyle {\mathcal {L}}\{t^{n}f(t)\}=(-1)^{n}F^{(n)}(s)}
L−1{F(s−a)}=eatf(t){\displaystyle {\mathcal {L}}^{-1}\left\{F(s-a)\right\}=e^{at}f(t)}
L−1{e−asF(s)}=f(t−a)u(t−a){\displaystyle {\mathcal {L}}^{-1}\left\{e^{-as}F(s)\right\}=f(t-a)u(t-a)}
Where: