Finding the inverse laplace transform of $s$

Question

How do I find the inverse laplace transform of $s$, i.e. $$L^{-1}\{s\}=\ ?$$

score 10 · Answer 1 · edited Nov 23 '14 at 13:30

10

$\mathcal{L}^{-1}\{s\}=\delta'(t)$. More generally:

$\forall n\in\mathbb{Z},~\mathcal{L}^{-1}\{s^n\}=\delta^{(n)}(t)$.

edited Nov 23 '14 at 13:30

Géry Ogam

251

answered Jun 10 '13 at 21:22

paul2357paul

304

Sorry this might be a stupid question, but what is this function $\delta (t)$? This inverse transform doesn't seem to appear on tables? – JackReacher Oct 07 '14 at 09:18

score 2 · Answer 2 · answered Jun 08 '13 at 11:05

2

One would have a hard time finding such a function since Laplace transforms of functions go to zero at infinity and Laplace transforms of measures are bounded.

answered Jun 08 '13 at 11:05

Did

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Finding the inverse laplace transform of $s$

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