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geometry > differential geometry > implicit function theorem
mathematical analysis > calculus > multivariable calculus > implicit function theorem

Preferred term

implicit function theorem  

Definition(s)

  • 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 can represent 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.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Implicit_function_theorem)

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