laplace transform

The laplace transform is the continuous analog of the summation of a power series,

${\sum }_{i=0}^{n}a(n)x^n=A(x)$
${\int }_0^{\infty }a(t)x^{t}dt=A(x)$
After cosmetic changes like $x=e^{-s}$, we get the laplace transform:
${\int }_0^{\infty }f(t)e^{-st}dt=F(s)$

The laplace transform is a generalization of the fourier transform.

Todo

finish playlist on fourier analysis, then…: