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Exterior
In mathematics, the exterior derivative operator of differential geometry extends the concept of the differential of a function to differential forms of higher degree. more...
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It is important in the theory of integration on manifolds, and is the differential (coboundary) used to define de Rham and Alexander-Spanier cohomology. Its current form was invented by Élie Cartan.
Definition
The exterior derivative of a differential form of degree k is a differential form of degree k + 1.
Given a multi-index over Rn is defined as
-
For general k-forms ω=ΣI fI dxI (where the components of the multi-index I run over all the values in {1, ..., n}), the definition of the exterior derivative is extended linearly. Note that whenever i is one of the components of the multi-index I, then
Examples
For a 1-form 
Properties
Exterior differentiation satisfies three important properties:
linearity;
the wedge product rule (see antiderivation);
-
and d2 = 0, a formula encoding the equality of mixed partial derivatives, so that always;
Read more at Wikipedia.org
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Air Dams, Exterior, Car & Truck Parts
Antennas, Exterior, Car & Truck Parts
Body Kits, Exterior, Car & Truck Parts
Bras, Exterior, Car & Truck Parts
Bug Shields, Exterior, Car & Truck Parts
Bumpers, Exterior, Car & Truck Parts
Car Cover, Exterior, Car & Truck Parts
Doors & Door Handles, Exterior, Car & Truck Parts
Fenders, Exterior, Car & Truck Parts
Grilles, Exterior, Car & Truck Parts
Hoods, Exterior, Car & Truck Parts
Locks & Hardware, Exterior, Car & Truck Parts
Mirrors, Exterior, Car & Truck Parts
Mouldings & Trim, Exterior, Car & Truck Parts
Nerf Bars & Running Boards, Exterior, Car & Truck Parts
Other, Exterior, Car & Truck Parts
Racks, Exterior, Car & Truck Parts
Snow Plows & Parts, Exterior, Car & Truck Parts
Splash Guards / Mud Flaps, Exterior, Car & Truck Parts
Spoilers & Wings, Exterior, Car & Truck Parts
Sunroof, Convertible & Hardtop, Exterior, Car & Truck Parts
Tailgates & Liftgates, Exterior, Car & Truck Parts
Towing & Hauling, Exterior, Car & Truck Parts
Truck Bed Accessories, Exterior, Car & Truck Parts
Trunk Lids & Parts, Exterior, Car & Truck Parts
Windshield Wiper System, Exterior, Car & Truck Parts
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