Exterior Derivative -- from Wolfram MathWorld
https://mathworld.wolfram.com/ExteriorDerivative.html
WEB2 days ago · The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a zero-form, the exterior derivative extends linearly to all differential k-forms using the formula d(alpha ^ beta)=dalpha ^ beta+(-1)^kalpha ^ dbeta, (2) when alpha is a …
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