 implicit function theorem

Math.a theorem that gives conditions under which a function written in implicit form can be written in explicit form.
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Universalium. 2010.
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Universalium. 2010.
Implicit function theorem — In the branch of mathematics called multivariable calculus, the implicit function theorem is a tool which allows relations to be converted to functions. It does this by representing the relation as the graph of a function. There may not be a… … Wikipedia
implicit function theorem — Math. a theorem that gives conditions under which a function written in implicit form can be written in explicit form … Useful english dictionary
Implicit function — In mathematics, an implicit function is a generalization for the concept of a function in which the dependent variable has not been given explicitly in terms of the independent variable. To give a function f explicitly is to provide a… … Wikipedia
Inverse function theorem — In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain. The theorem also gives a formula for the derivative of the… … Wikipedia
Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a … Wikipedia
Nash embedding theorem — The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance,… … Wikipedia
Frobenius theorem (differential topology) — In mathematics, Frobenius theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first order homogeneous linear partial differential equations. In modern geometric terms … Wikipedia
Algebraic function — In mathematics, an algebraic function is informally a function which satisfies a polynomial equation whose coefficients are themselves polynomials. For example, an algebraic function in one variable x is a solution y for an equation: a n(x)y^n+a… … Wikipedia
Multivalued function — This diagram does not represent a true function, because the element 3 in X is associated with two elements, b and c, in Y. In mathematics, a multivalued function (shortly: multifunction, other names: set valued function, set valued map, multi… … Wikipedia
Elementary function — This article discusses the concept of elementary functions in differential algebra. For simple functions see the list of mathematical functions. For the concept of elementary form of an atom see oxidation state. In mathematics, an elementary… … Wikipedia