Laplace Transform

Let f(t) be a function of t defined all for all t > 0 then the laplace transforms of f(t) denoted by L{f(t)} is defined by L{f(t)}=∫_0^∞▒e^(-st) f(t)dt This integral exists (i.e ., has some finite value ) It is a function of s , say F(s) or¯f(s) i.e ., L{f(t)}= L(f) = F(s) = f ̅(s) ∴f(t) = L^(-1) (f) =L^(-1) {¯f(s)} Thenf(t) is called inverse Laplace Transform off ̅(s) The symbolL, which transforms f(t) into ¯f(s) is called the Laplace Transformation operator .