A powerful search engine for mathematical formulas with LaTeX support
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Physics
The wave equation
The wave equation, \(\frac{\partial^2u}{\partial t^2}= c^2\nabla^2 u\), relates how \(u\) varies with time and with the spatial coordinates as a wave propagates with speed \(c\).
Physics
Einstein's field equations in general relativity
In Einstein's general relativity, the field equation \(\mathcal{G} = - \frac{8\pi G}{c^4} \mathcal{T}\) relates spacetime curvature (\(\mathcal{G}\)) to its mass-energy content (\(\mathcal{T}\)).
Mathematics
Sannon's entropy
Shannon's entropy, \(H(X) = -\sum_{x \in \mathbf{X}} p(x) \log p(x)\), measures how informative the mass function \(p\) is about the occurrence of the possible values of variable \(X\).