Web Reference: Nov 16, 2022 · In this section we giver a brief introduction to the convolution integral and how it can be used to take inverse Laplace transforms. We also illustrate its use in solving a differential equation in which the forcing function (i.e. the term without an y’s in it) is not known. On the next slide we give an example that shows that this equality does not hold, and hence the Laplace transform cannot in general be commuted with ordinary multiplication. To find the inverse Laplace transform, partial fraction decomposition is very useful, but sometimes it can be very difficult to find the partial fraction decomposition, so there are cases where the inverse Laplace transform can be found with the help of the convolution integral.
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