stumbled upon it years ago but I’m terrible at math so kinda forgot about it for years, recently stumbled upon it again so out of pure curiosity, what is it? does it have real world use or is it something purely theoretical?
In: Mathematics
Do you know how if you wanted to add a large number of the same number, you could multiply once? And how instead of multiplying a number multiple times, you could find the exponent?
Differentiation is an operation we do to break up a continuous function into an infinite number of tiny tiny pieces.
Integration is the reverse operation and it builds the function back from the differentiated pieces. Now, this operation is easy for simple functions. But it can get hairy for difficult ones. And physics is full of very difficult integrals.
Laplace transform converts any function from real space into a complex space. In this complex space, differentiation and integration becomes multiplication and division.
So all of a sudden, you can complete your operations without having to figure out and solve complex differentials by transforming to the Fourier domain, complete the operations and transform back.
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