SearchOnMath

Complicated convolution operations become simple multiplications via the Laplace transform \(F(s) = \int_{-\infty}^{\infty}f(x)e^{-s x}dx\) for function \(f\).

A famous irrational number, \(\pi = \frac{C}{d}\) is defined by the ratio of a circle's circumference (\(C\)) to its diameter (\(d\)).

The heat equation, \(\frac{\partial \varnothing}{\partial t} = D \nabla^2 \varnothing\), uses the Laplacian of \(\varnothing\) to express diffusion through a medium.