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by the implicit function theorem

См. также в других словарях:

  • 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 — 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

  • 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

  • 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

  • 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

  • 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

  • Lambert W function — The graph of W(x) for W > −4 and x < 6. The upper branch with W ≥ −1 is the function W0 (principal branch), the lower branch with W ≤ −1 is the function W−1. In mathematics, the Lambert W function, also called the Omega function or product… …   Wikipedia

  • Mean value theorem — For the theorem in harmonic function theory, see Harmonic function#Mean value property. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables …   Wikipedia

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