(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

trying to determine a general method for doing inverse-Laplace transforms of a product of two Laplace Transform (L.T.) functions f1(s) and f2(s) where f1(s) and f2(s) are the LTs of F1(t) and F2(t).

The scenario is for calculating the convolution integral for F1(t)*F2(t)

If I know the inverse-LT for f1(s) and f2(s), but the product f1(s)f2(s) is quite messy and does not lend itself to any easily identifiable inverse-LT (in what LT tables I have; but maybe I just need to look more carefully), is there a way to get the inverse-LT knowing the individual inverse-LTs?

2. Relevant equations

G(t)=F1(t)*F2(t) = f1(s)f2(s) = g(s)

G(t)=inverse-LT of g(s)

3. The attempt at a solution

I see a breif reference to a method, but there's no explanation.

in an old textbook "Mathematical Methods in Chemical Engineering Volume 3; Seinfeld and Lapidus, 1974" on page 62

Working with the notion of the convolution integral

below eqn 3.1.36

"Note that if the inverse of L.T.s of f1(s) and f2(s) are known, the inverse L.T. of the product can be obtained by integration."

here "the product" is f1(s)f2(s)

My only guess is I need to employ the "Residue Theorem" on the complex inversion integral of g(s) above.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Inverse Lapalce transform (inre convolution integral)

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