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The fundamental theorem of calculus, \(f(x) = \frac{d}{dx}\int_{a}^{x}f(s)ds\), expresses the essential inverse relationship between the derivative and integral operators.

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

In Einstein's special relativity, the rest energy of a mass \(m\) is \(E = mc^2\), where \(c\) is the speed of light in a vacuum.