---
tag: 0ZHSTAG8ZY
kind: concept
name: Exterior derivative
msc: [58A10]
uses: [0E3G0GRPZ6]
sources:
  - url: https://en.wikipedia.org/wiki/Exterior_derivative
    locator: lead section
same_as:
  wikidata: Q1754547
  wikipedia: Exterior derivative
---

## Summary

The exterior derivative extends the differential of a function to [[differential forms|0E3G0GRPZ6]] of higher degree. It maps $k$-forms to $(k + 1)$-forms.
In $\mathbb{R}^3$ 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.