About: Calculus on Euclidean space

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In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean space as well as a finite-dimensional real vector space. This calculus is also known as advanced calculus, especially in the United States. It is similar to multivariable calculus but is somehow more sophisticated in that it uses linear algebra (or some functional analysis) more extensively and covers some concepts from differential geometry such as differential forms and Stokes' formula in terms of differential forms. This extensive use of linear algebra also allows a natural generalization of multivariable calculus to calculus on Banach spaces or topological vector spaces.

Attributes	Values
rdf:type	Thing
rdfs:label	Calculus on Euclidean space (en)
rdfs:comment	In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean space as well as a finite-dimensional real vector space. This calculus is also known as advanced calculus, especially in the United States. It is similar to multivariable calculus but is somehow more sophisticated in that it uses linear algebra (or some functional analysis) more extensively and covers some concepts from differential geometry such as differential forms and Stokes' formula in terms of differential forms. This extensive use of linear algebra also allows a natural generalization of multivariable calculus to calculus on Banach spaces or topological vector spaces. (en)
rdfs:seeAlso	Limit of distributions Function of a real variable
name	Fubini's theorem Chain rule Lagrange multiplier Poincaré lemma Stokes' formula Whitney's embedding theorem Lemma (en) Theorem (en) Corollary (en) Inverse function theorem (en) Mean value inequality (en) The Gauss–Bonnet theorem (en)
dct:subject	Calculus
Wikipage page ID	64965378 (xsd:integer)
Wikipage revision ID	1114780233 (xsd:integer)
Link from a Wikipage to another Wikipage	Product rule Schwartz space Holomorphic function Riemann sum Vector field Integration along fibers Inverse function theorem Matrix exponential General topology Operator norm Symmetric matrix Fundamental solution Fundamental theorem of calculus Gauss–Bonnet theorem Generalized function Multivariable calculus Möbius strip Loop (topology) Stokes' theorem Density on a manifold Fubini's theorem Fundamental lemma of calculus of variations Partition of unity Stationary point Surface integral Cauchy's integral formula Cauchy–Riemann equations Whitney extension theorem Euclidean space Exterior derivative Exterior power Fourier transform Normed space Paracompact space Directional derivative Jacobian matrix Taylor's theorem Calculus Chain rule Lagrange multiplier Symmetry of second derivatives Hessian matrix Homotopy Differentiable function Differential form Differential geometry of surfaces Dirac delta function Distribution (mathematics) Manifold Borel's lemma Continuously differentiable Green’s theorem Measure zero Implicit function theorem Inner product Integration by parts Self-adjoint operator Éditions Hermann Lusin's theorem Characteristic function Weak derivative Tensor-hom adjunction Poincaré lemma Stokes' formula Whitney's embedding theorem Frenet frame Simply connected Atlas (mathematics) Fourier inversion formula Frame field Finite-dimensional real vector space Heaviside function Calculus of functions Manifold-with-boundary Integrable function Closed and exact forms Differentiable structure Nash's embedding theorem Submersion theorem dbr:Invariance_of_differential

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