Math 2.0

concept

Closed and exact forms

Summary

A differential form is closed if its exterior derivative is zero, and exact if it is the exterior derivative of another form. Each exact form is closed. Whether each closed form is exact depends on the shape of the domain, so these notions detect holes in the domain.

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Differential form, concept, no evidence levelDifferential formconceptExterior derivative, concept, no evidence levelExterior derivativeconceptClosed and exact forms, concept, no evidence levelClosed and exact formsconcept
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.
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  1. Differential form concept
  2. Exterior derivative concept
  3. Closed and exact forms concept

Sources

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

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