2
votes
0answers
20 views

Laplace transform on a finite interval $f(t)= \int_0^1 e^{-xt} f(x) \, dx$

What is the name of this transform? It's basically the Laplace transform where we integrate over a finite interval. $$ F(t)= \int_0^1 e^{-xt} f(x) \, dx$$ Is it still just the Laplace transform? ...
0
votes
0answers
35 views

reference text for all transforms

I want to learn Fourier and laplace transform by myself.I have learnt 'calculus-one variable' and beginning to enter 'calculus-multiple variables'.can anybody tell any good books for begin studying ...
5
votes
2answers
185 views

What kind of book would show where the inspiration for the Laplace transform came from?

I'm trying to find out where to learn about integral transforms and inversions like the Laplace transform and the Bromwich integral. I'm looking for a book that describes how you can find (derive) ...
3
votes
2answers
277 views

Two-sided Laplace transform

I want to study more formally the properties of the two sided Laplace transform $$ \hat f(z)=\int_{-\infty}^{\infty} f(t)e^{zt}dt $$ as a kind of generalization of the Fourier transform. I found some ...