SearchOnMath

Maxwell's equations in a vacuum describe a wave propagating at speed \(c\) as the interaction of electric field \(E\) and magnetic field \(B\): \(\nabla \cdot E = 0\), \(\nabla \times E = -\frac{\partial B}{\partial t}\), \(\nabla \cdot B = 0\), \(\nabla \times B = \frac{1}{c^2} \frac{\partial E}{\partial t}\).

The normal density, \(p(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\), has become important in many applications because of its close relationship to the central limit theorem.

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