Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 32/Table of General Properties of Laplace Transforms

Table of General Properties of Laplace Transforms
In the following, $s$ and $t$ are the independent variables of the real functions $f$ and $F$ respectively.

$f$ denotes results of the Laplace transform on functions denoted with $F$.

$a$ and $b$ are constants.


 * $32.3$: Laplace Transform of $a \map {F_1} t + b \map {F_2} t$


 * $32.4$: Laplace Transform of $a \, \map F {a t}$


 * $32.5$: Laplace Transform of $e^{a t} \, \map F t$


 * $32.6$: Laplace Transform of $\map F {t - a}$


 * $32.7$: Laplace Transform of $\map {F'} t$


 * $32.8$: Laplace Transform of $\map {F''} t$


 * $32.9$: Laplace Transform of $\map {F^{\paren n} } t$


 * $32.10$: Laplace Transform of $-t \, \map F t$