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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.
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
The Taylor series
The Taylor series for an infinitely differentiable \(f\) at point \(a\), given by \(f(x) = \sum_{k=0} ^ {\infty} \frac {f^{(k)}(a)}{k!} \, (x-a)^{k}\), allows \(f\) to be expressed in terms of its derivatives.