Unit Step Function

f$\left(\vphantom{ t}\right.$t$\left.\vphantom{ t}\right)$ F$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$ = L$\left\{\vphantom{
f}\right.$f$\left.\vphantom{
f}\right\}$$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$
eatf$\left(\vphantom{ t}\right.$t$\left.\vphantom{ t}\right)$ F$\left(\vphantom{ s-a}\right.$s - a$\left.\vphantom{ s-a}\right)$


f$\left(\vphantom{ t-a}\right.$t - a$\left.\vphantom{ t-a}\right)$u$\left(\vphantom{ t-a}\right.$t - a$\left.\vphantom{ t-a}\right)$     e-asF$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$


u$\left(\vphantom{ t-a}\right.$t - a$\left.\vphantom{ t-a}\right)$ ${\dfrac{{e^{-as}}}{{s}}}$