On Transforms
September 08, 2026
September 30, 2026
this is a laplace transform!!
$$ F(s) = \int_0^{\infty} f(t)\, e^{-st}\, dt $$
and… this is a fourier transform
$$ F(\omega) = \int_{-\infty}^{\infty} f(t)\, e^{-i\omega t}\, dt $$
here’s a wee matrix too
$$ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} $$
and even a little table
$$ \begin{array}{l|cc} & \text{time} & \text{frequency} \\ \hline \text{laplace} & f(t) & F(s) \\ \text{fourier} & f(t) & F(\omega) \end{array} $$
this is a blog template for future reference :)