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Vektorkalkül Definition
Vector calculus or vector analysis is the use of calculus (limits, derivatives, and integrals) with two or more independent variables, or two or more dependent variables. This can be thought of as the calculus of three dimensional figures. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space R3. The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. Common elements of multivariable calculus include parametric equations, vectors, partial derivatives, multiple integrals, line integrals, and surface integrals. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields and fluid flow.
Überblick
Vector Calculus wurde von der Quatern-Analyse von J. Willard Gibbs und Oliver Heaviside am Ende des 19. Jahrhunderts entwickelt, und die meiste Notation und Terminologie wurde von Gibbs und Edwin Bidwell Wilson in ihrem 1901-Buch-Vektoranalyse gegründet. In der herkömmlichen Form mit Kreuzprodukten verallt der Vektorkalculus nicht zu höheren Abmessungen, während der alternative Ansatz der geometrischen Algebra, der Außenkörper verwendet, verallgemeinert.
Verwandte Definitionen
Quellen
“Vector Calculus.” Wikipedia, Wikimedia Foundation, 19 Apr. 2020, en.wikipedia.org/wiki/Vector_calculus.