Well, I'm just a boy who trying to understand Calculus better.

I realise that S is kind of change of variable. So it is really same x than before Laplace transformation. Is it true that S=X when:

$\displaystyle

\mathcal{L} [2x](s) = 2 \mathcal{L}[x](s)= 2 \cdot \frac 1{s^2} = \frac 2{s^2}

$

?

I have some fundamental hole in my understanding about Laplace. So questions are still very basic ones. Why to use Laplace transformation? What I can achieve with Laplace transformation? And last but not the least: Could you show me some practical example from real life how to use Laplace transform?

I'm enthusiastic hooked to learn more.