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Mathematics
The Laplace transform
Complicated convolution operations become simple multiplications via the Laplace transform \(F(s) = \int_{-\infty}^{\infty}f(x)e^{-s x}dx\) for function \(f\).
Mathematics
Euler's Formula for polyhedra
Euler's formula for convex polyhedra is a function of their number of faces (\(F\)), edges (\(E\)), and vertices (\(V\)), stating that \(F-E+V=2\).
Mathematics
The fundamental theorem of calculus
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.