The adjoint operator of the exterior differential d.
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One can express any partial differential equation system as an exterior differential system with independence condition.
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The graded exterior algebra O ^ * ( Z ) is a graded differential algebra with respect to the graded exterior differential
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For instance, we can apply Cartan's method on partial differential equation systems by writing down the exterior differential system associated with it.
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Offhand I can think of things like partial derivative, exterior differential, covariant derivative, never mind the boundary operator looking like a partial derivative.
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In the calculus of exterior differential forms on a pseudo-Riemannian manifold of dimension, the normalised-form is called the volume form and can be written as
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Barr?de Saint-Venant developed a version of vector calculus similar to that of Grassmann ( now understood as exterior differential forms ) which he published in 1845.
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