# implicit function

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Related to implicit function: Implicit function theorem

## implicit function

[im′plis·ət ′fəŋk·shən]
(mathematics)
A function defined by an equation ƒ(x,y) = 0, when x is considered as an independent variable and y, called an implicit function of x, as a dependent variable.
References in periodicals archive ?
i](x) can be calculated from each local implicit function defined in {[[OMEGA].
By the implicit function theorem, there exist a function x = g(y) satisfying [phi](g(y),y) = 0, in a neighborhood of [y.
We also show that numerous contrastive conditions of the existing literature enjoy the format of our newly introduced implicit function besides admitting several new and natural contrastive conditions.
as an implicit function X(Y, D) of the array of independent variables (controls) Y and of the array of initial information D.
We prove that the first-order condition is an implicit function [R.
After a chapter on general preliminaries, chapters cover differential calculus of boundary perturbations, the implicit function theorem, bifurcation problems, the transversality theorem, generic perturbation of the boundary, boundary operators for second-order elliptic equations, and the method of rapidly oscillating solutions.
Greer (1992) suggested that investigations with a physical system consisting of a bucket attached to a rotational handle could promote a view of multiplication as an implicit function relationship.
j] (Q,P), then the implicit function [GAMMA] (Q,P) [equivalent to] Q = [[SIGMA].
If the implicit function theorem is applicable, the state equation c(y, u) = 0 defines a function y(.
In the case of an interior solution [2a] defines an implicit function f = f(b, s, m, [Eta]).

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