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• Implicit_function_theorem abstract "In multivariable calculus, the implicit function theorem, also known, especially in Italy, as Dini's theorem, is a tool that allows relations to be converted to functions of several real variables. It does this 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 wikiPageID "581005".
• Implicit_function_theorem wikiPageLength "16154".
• Implicit_function_theorem wikiPageOutDegree "38".
• Implicit_function_theorem wikiPageRevisionID "678508896".
• Implicit_function_theorem wikiPageWikiLink Analytic_expression.
• 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_coordinates.
• 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 Constant_rank_theorem.
• Implicit_function_theorem wikiPageWikiLink Continuously_differentiable.
• 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_(mathematics).
• Implicit_function_theorem wikiPageWikiLink Domain_of_a_function.
• Implicit_function_theorem wikiPageWikiLink Fréchet_derivative.
• Implicit_function_theorem wikiPageWikiLink Fréchet_differentiable.
• Implicit_function_theorem wikiPageWikiLink Function_of_several_real_variables.
• Implicit_function_theorem wikiPageWikiLink Functions_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 Iff.
• Implicit_function_theorem wikiPageWikiLink Implicit_function.
• Implicit_function_theorem wikiPageWikiLink Implicit_functions.
• Implicit_function_theorem wikiPageWikiLink Inverse_element.
• Implicit_function_theorem wikiPageWikiLink Inverse_function_theorem.
• Implicit_function_theorem wikiPageWikiLink Invertible.
• 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 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 Polar_coordinates.
• Implicit_function_theorem wikiPageWikiLink Relation_(mathematics).
• Implicit_function_theorem wikiPageWikiLink Ulisse_Dini.
• 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 authorLink "Lev Dmitrievich Kudryavtsev".
• Implicit_function_theorem first "L.D.".
• Implicit_function_theorem first "V.I.".
• Implicit_function_theorem hasPhotoCollection Implicit_function_theorem.
• 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:Reflist.
• Implicit_function_theorem wikiPageUsesTemplate Template:Rp.
• 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 Theorem.
• Implicit_function_theorem comment "In multivariable calculus, the implicit function theorem, also known, especially in Italy, as Dini's theorem, is a tool that allows relations to be converted to functions of several real variables. It does this 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 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 Fungsi_implisit.
• 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 Q848375.
• Implicit_function_theorem sameAs 隐函数定理.
• Implicit_function_theorem wasDerivedFrom Implicit_function_theorem?oldid=678508896.
• Implicit_function_theorem depiction Implicit_circle.svg.

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