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\hline & $f(t)=\mathcal{L}^{-1}\{F(s)\}$ & $F(s)=\mathcal{L}\{f(t)\}$                                                                                                                        & Notes                   \\
\hline 1.                     1                                                                                                                                       & $\frac{1}{s},             \quad                            s>0$                          & Sec.     6.1;        Ex.        4                                       \\
2.     $e^{a                   t}$                                                                                                                                       & $\frac{1}{s-a},$,       & $s>a$                      & Sec.                        6.1;       Ex.         5 \\
3.     $t^{n},                 \quad                                                                                                                                         n=$                       positive                     integer                       & $\frac{n !}{s^{n+1}}, \quad          s>0$            & Sec. 6.1; Prob. 31   \\
4.     $t^{p},                 \quad                                                                                                                                         p>-1$                     & $\frac{\Gamma(p+1)}{s^{p+1}},$, & $s>0$                       & Sec.     6.1;        Prob.      31              \\
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