If we have a simple RLC circuit like this one, we can say that $$V(t)=I(t)R+\frac{\int^t_0 I\space dt}{C}+L\frac{dI}{dt}(t).$$ If we apply the Laplace transform to both sides, we get $$V(s)=I(s)R+\frac{I(s)}{Cs}+LsI(s).$$ I understand that the first equation is a dynamic equation (all variables are a functions in time) but I really don't understand what the $s$ here represents.
