Math 2.0

concept

Exterior derivative

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.

What this node needs for W2
  • edge instance_of in: at least two examples (0 of 2)
  • edge not_instance_of in: at least one non-example (0 of 1)
  • edge specializes both: the more general notions and the special cases (0 of 1)

The writing levels say how complete the text of a node is. They do not measure its truth.

What this needs

To read this node, read these 2 nodes in this order. The foundations come first, and the list ends with this node.

Differential form, concept, no evidence levelDifferential formconceptExterior derivative, concept, no evidence levelExterior derivativeconcept
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Differential form concept
  2. Exterior derivative concept

What depends on this

1 node uses this node, directly or through other nodes.

Sources

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

What links here

Definitions

Used by