Karl Jones: Created page with "In mathematics, an '''implicit equation''' is a binary relation of the form R(x1,..., xn) = 0, where R is a function of several variables (o..."

2016-09-13T20:31:31Z

Created page with "In mathematics, an '''implicit equation''' is a binary relation of the form R(x1,..., xn) = 0, where R is a function of several variables (o..."

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In [[mathematics]], an '''implicit equation''' is a [[binary relation]] of the form R(x1,..., xn) = 0, where R is a function of several [[Variable (mathematics)|variables]] (often a [[polynomial]]).

For example, the implicit equation of the unit circle is x^2 +y^2-1 = 0.

An '''implicit function''' is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments).

Thus, an implicit function for y in the context of the unit circle is defined implicitly by x^2 +[f(x)]^2-1 = 0.

This implicit equation defines f as a function of x only if -1 ≤ x ≤ 1 and one considers only non-negative (or non-positive) values for the values of the function.

The [[implicit function theorem]] provides conditions under which a relation defines an implicit function.

== See also ==

* [[Functional equation]]
* [[Function (mathematics)]]
* [[Level set]]
* [[Contour line]]
* [[Isosurface]]
* [[Marginal rate of substitution]]
* [[Implicit function theorem]]
** [[Logarithmic differentiation]]
** [[Polygonizer]]

== External links ==

* [https://en.wikipedia.org/wiki/Implicit_function Implicit function] @ Wikipedia.org

[[Category:Mathematics]]

Implicit function - Revision history

Karl Jones: Created page with "In mathematics, an '''implicit equation''' is a binary relation of the form R(x1,..., xn) = 0, where R is a function of several variables (o..."