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Home > Exterior derivative

4.2 Curl

For a 1-form on R^3,

which restricted to the three- dimensional case is

Therefore, for vector field we have

the where denotes curl of ,

4.3 Divergence

For a 2-form

For three dimensions, with we get

where V is a vector field defined by

5 Examples

For a 1-form on R² we have

which is exactly the 2-form being integrated in Green's theorem.

6 See also

• Exterior covariant derivative
• Green's theorem
• Stoke's theorem

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Topics: Exterior Derivative Differential Vector Product Form Forms...

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Exterior derivativeIn mathematics, the exterior derivative operator of differential topology, extends the concept of the differential of a function to differential forms of higher degree. It is important in the theory of integration on manifolds, and is the differential use Exterior algebraIn mathematics, the exterior algebra (also known as the Grassmann algebra of a given vector space V is a certain unital associative algebra which contains V as a subspace. It is denoted by Λ V or Λ• V and its multiplication, known as the wed Exterior Gateway ProtocolThe Exterior Gateway Protocol EGP is a routing protocol for the Internet originally specified in 1982 by Eric C. Rosen of Bolt, Beranek and Newman. It was first described in and formally specified in ( 1984). EGP had limited scalability and was eventually Exterior (topology)Topology General topology In topology, the exterior of a subset S of a topological space X is the union of all open sets of X which do not meet S''. The exterior of S is denoted by ext ''S or S e''.