what is convolution theorem in laplace transform and its uses?

Answer 1

Let f and g be two functions with convolution f * g and if T denotes the Laplace transform operator, then T[f] and T[g] are the Laplace transforms of the functions and the theorem states that T[f*g]=T[f]T[g].

It is used to solve integral equations .

Answer 2

The Laplace transform of a convolution is the product of the convolutions of the two functions. This is often used in reverse. If you know the inverse transforms of F(s) and G(s) and they are functions f(x) and g(x), then the inverse transform of F(s)G(s) is the convolution
f*g(x)=int_0^x f(t)g(x-t)dt.

Answer 3

The Laplace rework of a convolution is the made up of the convolutions of both purposes. that is used in opposite. in case you recognize the inverse transforms of F(s) and G(s) and they are purposes f(x) and g(x), then the inverse rework of F(s)G(s) is the convolution f*g(x)=int_0^x f(t)g(x-t)dt.