Let f(t) be a function of t defined all for all t > 0 then the laplace transforms of f(t) denoted byL{{f(t)}} is defined byL{{f(t)}}=∫_0^∞▒e^(-st) f(t)dtThis 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 Transformoff ̅(s)The symbolL, which transforms f(t) into ¯f(s) is calledthe Laplace Transformation operator .
Let f(t) be a function of t defined all for all t > 0 then the laplace transforms of f(t) denoted byL{{f(t)}} is defined byL{{f(t)}}=∫_0^∞▒e^(-st) f(t)dtThis 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 Transformoff ̅(s)The symbolL, which transforms f(t) into ¯f(s) is calledthe Laplace Transformation operator .