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

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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 $-t \map F t$