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- Implicit_function_theorem abstract "In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of a function. There may not be a single function whose graph is the entire relation, but there may be such a function on a restriction of the domain of the relation. The implicit function theorem gives a sufficient condition to ensure that there is such a function.The theorem states that if the equation F(x1, ..., xn, y1, ..., ym) = F(x, y) = 0 satisfies some mild conditions on its partial derivatives, then one can in principle (though not necessarily with an analytic expression) express the m variables yi in terms of the n variables xj as yi = fi (x), at least in some disk. Then each of these implicit functions fi (x), implied by F(x, y) = 0, is such that geometrically the locus defined by F(x, y) = 0 will coincide locally (that is in that disk) with the hypersurface given by y = f(x).".
- Implicit_function_theorem thumbnail Implicit_circle.svg?width=300.
- Implicit_function_theorem wikiPageExternalLink v=onepage&q&f=false.
- Implicit_function_theorem wikiPageID "581005".
- Implicit_function_theorem wikiPageLength "16538".
- Implicit_function_theorem wikiPageOutDegree "38".
- Implicit_function_theorem wikiPageRevisionID "707840530".
- Implicit_function_theorem wikiPageWikiLink Analytic_function.
- Implicit_function_theorem wikiPageWikiLink Banach_space.
- Implicit_function_theorem wikiPageWikiLink Binary_relation.
- Implicit_function_theorem wikiPageWikiLink Cartesian_coordinate_system.
- Implicit_function_theorem wikiPageWikiLink Cartesian_product.
- Implicit_function_theorem wikiPageWikiLink Category:Theorems_in_calculus.
- Implicit_function_theorem wikiPageWikiLink Category:Theorems_in_real_analysis.
- Implicit_function_theorem wikiPageWikiLink Closed-form_expression.
- Implicit_function_theorem wikiPageWikiLink Differentiable_function.
- Implicit_function_theorem wikiPageWikiLink Differential_of_a_function.
- Implicit_function_theorem wikiPageWikiLink Disk_(mathematics).
- Implicit_function_theorem wikiPageWikiLink Domain_of_a_function.
- Implicit_function_theorem wikiPageWikiLink Fréchet_derivative.
- Implicit_function_theorem wikiPageWikiLink Function_of_several_real_variables.
- Implicit_function_theorem wikiPageWikiLink Graph_of_a_function.
- Implicit_function_theorem wikiPageWikiLink Identity_matrix.
- Implicit_function_theorem wikiPageWikiLink If_and_only_if.
- Implicit_function_theorem wikiPageWikiLink Implicit_function.
- Implicit_function_theorem wikiPageWikiLink Inverse_element.
- Implicit_function_theorem wikiPageWikiLink Inverse_function_theorem.
- Implicit_function_theorem wikiPageWikiLink Jacobian_matrix_and_determinant.
- Implicit_function_theorem wikiPageWikiLink Level_set.
- Implicit_function_theorem wikiPageWikiLink Local_property.
- Implicit_function_theorem wikiPageWikiLink Locus_(mathematics).
- Implicit_function_theorem wikiPageWikiLink Mathematics.
- Implicit_function_theorem wikiPageWikiLink Multivariable_calculus.
- Implicit_function_theorem wikiPageWikiLink Open_set.
- Implicit_function_theorem wikiPageWikiLink Partial_derivative.
- Implicit_function_theorem wikiPageWikiLink Polar_coordinate_system.
- Implicit_function_theorem wikiPageWikiLink Unit_circle.
- Implicit_function_theorem wikiPageWikiLink File:Implicit_circle.svg.
- Implicit_function_theorem wikiPageWikiLinkText "Implicit function theorem".
- Implicit_function_theorem wikiPageWikiLinkText "functions of real variables".
- Implicit_function_theorem wikiPageWikiLinkText "implicit function theorem".
- Implicit_function_theorem wikiPageWikiLinkText "solvable".
- Implicit_function_theorem first "Lev Dmitrievich".
- Implicit_function_theorem first "V.I.".
- Implicit_function_theorem id "i/i050310".
- Implicit_function_theorem id "i/i050320".
- Implicit_function_theorem last "Danilov".
- Implicit_function_theorem last "Kudryavtsev".
- Implicit_function_theorem title "Implicit function".
- Implicit_function_theorem wikiPageUsesTemplate Template:Cite_book.
- Implicit_function_theorem wikiPageUsesTemplate Template:Cite_journal.
- Implicit_function_theorem wikiPageUsesTemplate Template:Reflist.
- Implicit_function_theorem wikiPageUsesTemplate Template:Springer.
- Implicit_function_theorem subject Category:Theorems_in_calculus.
- Implicit_function_theorem subject Category:Theorems_in_real_analysis.
- Implicit_function_theorem hypernym Tool.
- Implicit_function_theorem type Software.
- Implicit_function_theorem type Redirect.
- Implicit_function_theorem type Theorem.
- Implicit_function_theorem comment "In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of a function. There may not be a single function whose graph is the entire relation, but there may be such a function on a restriction of the domain of the relation.".
- Implicit_function_theorem label "Implicit function theorem".
- Implicit_function_theorem sameAs Q848375.
- Implicit_function_theorem sameAs مبرهنة_الدالة_الضمنية.
- Implicit_function_theorem sameAs Teorema_de_la_funció_implícita.
- Implicit_function_theorem sameAs Satz_von_der_impliziten_Funktion.
- Implicit_function_theorem sameAs Teorema_de_la_función_implícita.
- Implicit_function_theorem sameAs Théorème_des_fonctions_implicites.
- Implicit_function_theorem sameAs Teorema_da_función_implícita.
- Implicit_function_theorem sameAs משפט_הפונקציות_הסתומות.
- Implicit_function_theorem sameAs Implicitfüggvény-tétel.
- Implicit_function_theorem sameAs Fólgið_fall.
- Implicit_function_theorem sameAs Teorema_delle_funzioni_implicite.
- Implicit_function_theorem sameAs Айқындалмаған_функция.
- Implicit_function_theorem sameAs 음함수_정리.
- Implicit_function_theorem sameAs Айкын_эмес_функция.
- Implicit_function_theorem sameAs Извод_на_имплицитна_функција.
- Implicit_function_theorem sameAs Impliciete_functiestelling.
- Implicit_function_theorem sameAs Funkcja_uwikłana.
- Implicit_function_theorem sameAs m.02s4mn.
- Implicit_function_theorem sameAs Теорема_о_неявной_функции.
- Implicit_function_theorem sameAs Tiurema_dâ_funzioni_mplicita.
- Implicit_function_theorem sameAs Implicita_funktionssatsen.
- Implicit_function_theorem sameAs Теорема_про_неявну_функцію.
- Implicit_function_theorem sameAs Q848375.
- Implicit_function_theorem sameAs 隐函数定理.
- Implicit_function_theorem wasDerivedFrom Implicit_function_theorem?oldid=707840530.
- Implicit_function_theorem depiction Implicit_circle.svg.
- Implicit_function_theorem isPrimaryTopicOf Implicit_function_theorem.