noun
Meaning 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.
Definition source: English Wiktionary via Wiktextract
Usage: sometimes
Qualifier: differential geometry
Examples
- The notion of differential form combines the concepts of multilinear form (itself an extension of linear form) and smooth function.
- The choice of a Riemannian manifold - roughly speaking, a differentiable manifold whose every point has a tangent space with a defined metric - means it is possible to define a differential form over it.
- Differential forms provide a unified approach to defining integrands over curves, surfaces and higher-dimensional manifolds, as well as providing an approach to multivariable calculus that is independent of coordinates.
- 2004, Ismo V. Lindell, Differential Forms in Electromagnetics, IEEE Press, 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided