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On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described in its current form by Élie Cartan; it allows for a natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a -form is thought of as measuring the flux through an infinitesimal -parallelepiped, then its exterior derivative can be thought of as measuring the net flux through the boundary of a -parallelepiped. == Definition == The exterior derivative of a differential form of degree is a differential form of degree If is a smooth function (a -form), then the exterior derivative of is the differential of . That is, is the unique such that for every smooth vector field , , where is the directional derivative of in the direction of . There are a variety of equivalent definitions of the exterior derivative of a general -form. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「exterior derivative」の詳細全文を読む スポンサード リンク
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