exterior derivative
A differential operator which acts on a differential k-form to yield a…A differential operator which acts on a differential k-form to yield a differential (k+1)-form, unless the k-form is a pseudoscalar, in which case it yields 0.
» The exterior derivative has various properties, some of which are obvious and some of which are not.
Die äußere Ableitung hat verschiedene Eigenschaften, von denen einige offensichtlich sind, andere hingegen nicht. — Waldelfe
Waldelfe · Tatoeba · CC BY 2.0 FRMeaning
1 sensesA differential operator which acts on a differential k-form to yield a differential (k+1)-form, unless the k-form is a pseudoscalar, in which case it yields 0.
The exterior derivative of a “scalar”, i.e., a function f=f(x¹,x²,...,xⁿ) where the xⁱ’s are coordinates of ℝⁿ, is df=∂f/∂x¹dx¹+∂f/∂x²dx²+...+∂f/∂xⁿdxⁿ.
The exterior derivative of a k-blade f,dx∧dx∧...∧dx is df∧dx∧dx∧...∧dx.
Examples
1 sentencesThe exterior derivative has various properties, some of which are obvious and some of which are not.
deDie äußere Ableitung hat verschiedene Eigenschaften, von denen einige offensichtlich sind, andere hingegen nicht. — Waldelfe
Translations
2 languagesForms
plural: exterior derivatives| Singular | exterior derivative |
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| Plural | exterior derivatives |
regular
See also
neighbours in the dictionaryDictionary text adapted from Wiktionary (Wiktionary contributors, CC BY-SA 4.0) and Open English WordNet / Princeton WordNet (CC BY 4.0, WordNet License); shared under CC BY-SA 4.0. Example sentences and recordings are credited where they appear.