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Mathematics
The normal distribution
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.
Physics
The heat equation
The heat equation, \(\frac{\partial \varnothing}{\partial t} = D \nabla^2 \varnothing\), uses the Laplacian of \(\varnothing\) to express diffusion through a medium.
Mathematics
The definition of conditional probability
The conditional probability that an event \(A\) occurs given the occurrence of another event \(B\) is \(P(A|B) = \frac{P(A \cap B)}{P(B)}\).