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 .
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