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- Taylor's_theorem abstract "In calculus, Taylor's theorem gives an approximation of a k times differentiable function around a given point by a k-th order Taylor polynomial. For analytic functions the Taylor polynomials at a given point are finite order truncations of its Taylor series, which completely determines the function in some neighborhood of the point. The exact content of "Taylor's theorem" is not universally agreed upon. Indeed, there are several versions of it applicable in different situations, and some of them contain explicit estimates on the approximation error of the function by its Taylor polynomial.Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1712. Yet an explicit expression of the error was not provided until much later on by Joseph-Louis Lagrange. An earlier version of the result is already mentioned in 1671 by James Gregory.Taylor's theorem is taught on introductory level calculus courses and it is one of the central elementary tools in mathematical analysis. Within pure mathematics it is the starting point of more advanced asymptotic analysis, and it is commonly used in more applied fields of numerics as well as in mathematical physics. Taylor's theorem also generalizes to multivariate and vector valued functions f : Rn → Rm on any dimensions n and m. This generalization of Taylor's theorem is the basis for the definition of so-called jets which appear in differential geometry and partial differential equations.".
- Taylor's_theorem thumbnail Taylorspolynomialexbig.svg?width=300.
- Taylor's_theorem wikiPageExternalLink 2C02_Taylor.html.
- Taylor's_theorem wikiPageExternalLink numericalmethods.eng.usf.edu.
- Taylor's_theorem wikiPageExternalLink taylor_series.html.
- Taylor's_theorem wikiPageExternalLink TaylorSeries.shtml.
- Taylor's_theorem wikiPageID "51714".
- Taylor's_theorem wikiPageRevisionID "606806976".
- Taylor's_theorem hasPhotoCollection Taylor's_theorem.
- Taylor's_theorem id "Taylor%27s_Theorem/One_Variable".
- Taylor's_theorem title "Proofs for a few forms of the remainder in one-variable case".
- Taylor's_theorem subject Category:Articles_containing_proofs.
- Taylor's_theorem subject Category:Theorems_in_calculus.
- Taylor's_theorem subject Category:Theorems_in_real_analysis.
- Taylor's_theorem type Abstraction100002137.
- Taylor's_theorem type Communication100033020.
- Taylor's_theorem type Message106598915.
- Taylor's_theorem type Proposition106750804.
- Taylor's_theorem type Statement106722453.
- Taylor's_theorem type Theorem106752293.
- Taylor's_theorem type TheoremsInCalculus.
- Taylor's_theorem type TheoremsInRealAnalysis.
- Taylor's_theorem comment "In calculus, Taylor's theorem gives an approximation of a k times differentiable function around a given point by a k-th order Taylor polynomial. For analytic functions the Taylor polynomials at a given point are finite order truncations of its Taylor series, which completely determines the function in some neighborhood of the point. The exact content of "Taylor's theorem" is not universally agreed upon.".
- Taylor's_theorem label "Stelling van Taylor".
- Taylor's_theorem label "Taylor's theorem".
- Taylor's_theorem label "Taylor-Formel".
- Taylor's_theorem label "Teorema de Taylor".
- Taylor's_theorem label "Teorema de Taylor".
- Taylor's_theorem label "Teorema di Taylor".
- Taylor's_theorem label "Théorème de Taylor".
- Taylor's_theorem label "Wzór Taylora".
- Taylor's_theorem label "Теорема Тейлора".
- Taylor's_theorem label "مبرهنة تايلور".
- Taylor's_theorem label "テイラーの定理".
- Taylor's_theorem label "泰勒公式".
- Taylor's_theorem sameAs Taylor-Formel.
- Taylor's_theorem sameAs Teorema_de_Taylor.
- Taylor's_theorem sameAs Théorème_de_Taylor.
- Taylor's_theorem sameAs Teorema_Taylor.
- Taylor's_theorem sameAs Teorema_di_Taylor.
- Taylor's_theorem sameAs テイラーの定理.
- Taylor's_theorem sameAs 테일러_정리.
- Taylor's_theorem sameAs Stelling_van_Taylor.
- Taylor's_theorem sameAs Wzór_Taylora.
- Taylor's_theorem sameAs Teorema_de_Taylor.
- Taylor's_theorem sameAs m.0dmmh.
- Taylor's_theorem sameAs Q1137206.
- Taylor's_theorem sameAs Q1137206.
- Taylor's_theorem sameAs Taylor's_theorem.
- Taylor's_theorem wasDerivedFrom Taylor's_theorem?oldid=606806976.
- Taylor's_theorem depiction Taylorspolynomialexbig.svg.
- Taylor's_theorem isPrimaryTopicOf Taylor's_theorem.
