differential form

Etymology
From early 20th century.

The concept was clarified chiefly by French mathematician (1869–1951). In his fundamental paper, 1899, Sur certaines expressions différentielles et le problème de Pfaff,  (3), tome 16, Cartan used the (French) term expression différentielle, and in his 1922, Leçons sur les invariants intégraux, Hermann, he used the terms exterior differential form and exterior derivative.

Noun

 * 1)  A completely antisymmetric tensor (of order p) that is defined on a Riemannian manifold; an expression, derived by applying a formalism to said tensor, that represents an integrand over the manifold.
 * 2) * 2004, Ismo V. Lindell, Differential Forms in Electromagnetics,, page xiii,
 * The present text attempts to serve as an introduction to the differential form formalism applicable to electromagnetic field theory. A glance at Figure 1.2 on page 18, presenting the Maxwell equations and the medium equation in terms of differential forms, gives the impression that there cannot exist a simpler way to express these equations, and so differential forms should serve as a natural language for electromagnetism.
 * 1) * 2004, Ismo V. Lindell, Differential Forms in Electromagnetics,, page xiii,
 * The present text attempts to serve as an introduction to the differential form formalism applicable to electromagnetic field theory. A glance at Figure 1.2 on page 18, presenting the Maxwell equations and the medium equation in terms of differential forms, gives the impression that there cannot exist a simpler way to express these equations, and so differential forms should serve as a natural language for electromagnetism.
 * 1) * 2004, Ismo V. Lindell, Differential Forms in Electromagnetics,, page xiii,
 * The present text attempts to serve as an introduction to the differential form formalism applicable to electromagnetic field theory. A glance at Figure 1.2 on page 18, presenting the Maxwell equations and the medium equation in terms of differential forms, gives the impression that there cannot exist a simpler way to express these equations, and so differential forms should serve as a natural language for electromagnetism.

Usage notes

 * The term often appears as differential $$p$$-form (or simply $$p$$-form), where $$p$$ is a variable representing a positive integer (the order of the tensor).

Hyponyms

 * p-form
 * p-form

Derived terms

 * differential p-form

Translations

 * Finnish: differentiaalimuoto