You must have missed this: "In the end Laplace transforms, easier to use with a more rigorous structure and incorporating the powerful tool of convolution, overtook the operational calculus of Heaviside, and his methods largely fell victim to history."
Thanks. Agreed, that could have been a good point to mention that Laplace transforms are more or less the same as Heaviside’s method. As I read it, the article leaves the opposite impression instead.
They're closely related attempts to solve the same problem. The difference is - ironically - Laplace transforms are more rigorous, and don't leave as many loose ends.
Basically Laplace is a complete solution, while Heaviside's calculus wasn't.
It took about 100 years to work this out. Laplace's original work was early 19th century, but the transform didn't become widely used in engineering until after WWII.
