6.46 Inverse Laplace transforms

Observe that in the table on slide 6.44, the Laplace transforms on the right-hand side are different for different $f(x)$ on the left-hand side.

If $F(s)$ is a rational function of the form $g(s)/h(s)$ where $\deg g<\deg h$, then the inverse Laplace transform of $F$ exists (and is indeed unique), and can be found using partial fractions and the table on slide 6.44. We denote the inverse Laplace transform by ${\mathcal{L}}^{-1}(F)$.