Laplace Inverse of 1: Dirac(t) Explained

[momen salah]

hi I'm new here and i wanted to ask a question

what is the laplace inverse of 1 ?

i have been told that it's laplace transform of dirac(t).

but what is dirac(t) please i have looked every where in the web for it it's two marks bonus for me if i get it and it's due today.

 

[Defennder]

Did you try Wikipedia?
http://en.wikipedia.org/wiki/Dirac_delta_function

L(\delta(t-a)) = e^{-as}
Let a=0. And there you have it.

 

[HallsofIvy]

The "Dirac delta function" is more commonly called just "the delta function". It is not, in fact, a "function" but rather a "generalized function" or "distribution". Roughly speaking that's a that's a functional: an operator that assigns a number to every function. The delta function assigns the number f(0) to every function f (so \delta(t- a) that Defennnder show assigns the number f(a) to every function f).

 

[momen salah]

thanks guys