Page 50 - LAPLACE TRANSFORM

3.0 INVERSE LAPLACE TRANSFORM

3.1 SIMPLE FUNCTIONS METHOD

3.1.1 Definition Of Inverse Laplace Transform :-

If the Laplace Transform of f(t) is F(s) , then we say that the Inverse Laplace Transform
1
−
of F(s) is f(t) where L is called the Inverse Laplace Transform Operator.We are going
to be given a transform, F(s), and ask what function (or functions) did we have
originally. As you will see this can be a more complicated and lengthy process than
taking transforms. In these situations, we use following notation and state that we
are determining the Inverse Laplace Transform of F(s).

f (t ) = L − 1 { (sF ) } (tf ) = L − 1 { (sF } )

As with Laplace transforms, we’ve got the following fact to help us take the inverse
transform. Given two Laplace transforms for F(s) and G(s) then,

) bL
}} aL
) bG
L − 1 {aF (s + (s } ) = aL − 1 { (sF } ) + bL − 1 { (sG } ) − L − 1 { { aF (s + (s ) = − 1 F (s + − 1 { (sG } )
) bG

for any constants a and b.

So, we take the inverse transform of the individual transforms, put any constants
back in and then add or subtract the result backup.

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