Math 2.0

Global analysis, analysis on manifolds Concept

Exterior derivative

Builds on Differential form

Summary

The exterior derivative extends the differential of a function to differential forms of higher degree. It maps kk-forms to (k+1)(k + 1)-forms. In ℝ3\mathbb{R}^3 it unifies the gradient, curl and divergence, and it gives a common form of the theorems of Green, Stokes and Gauss. Élie Cartan described it in its current form in 1899.

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Where this leads

33 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Exterior_derivative, lead section
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