I recently encountered the term Laplace transform.
Since My background is mathematical, the definition itself is very easy for me. The thing which is less clear for me is the context. I assume, that there is a reason why this transform is so important. And this is what I lack off. I can't see why it is important and useful. For instance, suppose that I know that the Laplace transform of a function is converging. So, why is this important. What does it say about the function itself that makes this transform so important?
Thank you!
The "classical" use of Laplace transform is in solving linear differential equations (ordinary or partial). One reason why it is useful there is that it changes differentiation into multiplication.