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{{About||the linearization of a partial order|Linear extension|the linearization in concurrent computing|Linearizability}}
In [[mathematics]], '''linearization''' ([[British English]]: '''linearisation''') is finding the [[linear approximation]] to a [[function (mathematics)|function]] at a given point. The linear approximation of a function is the first order [[Taylor expansion]] around the point of interest. In the study of [[dynamical system]]s, linearization is a method for assessing the local [[stability theory|stability]] of an [[equilibrium point]] of a [[system]] of [[nonlinear differential equation]]s or discrete [[dynamical system]]s.<ref>[http://www.scholarpedia.org/article/Siegel_disks/Linearization The linearization problem in complex dimension one dynamical systems at Scholarpedia]</ref> This method is used in fields such as [[engineering]], [[physics]], [[economics]], and [[ecology]].
==Linearization of a function==
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===Microeconomics===
In [[microeconomics]], [[decision rule]]s may be approximated under the state-space approach to linearization.<ref name="statespace">Moffatt, Mike. (2008) [[About.com]] ''[http://economics.about.com/od/economicsglossary/g/statespace.htm State-Space Approach] {{Webarchive|url=https://web.archive.org/web/20160304055023/http://economics.about.com/od/economicsglossary/g/statespace.htm |date=2016-03-04 }}'' Economics Glossary; Terms Beginning with S. Accessed June 19, 2008.</ref> Under this approach, the [[Euler equations (fluid dynamics)#Conservation form|Euler equations]] of the [[utility maximization problem]] are linearized around the stationary steady state.<ref name="statespace"/> A unique solution to the resulting system of dynamic equations then is found.<ref name="statespace"/>
===Optimization===
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* [[Taylor approximation]]
* [[Functional equation (L-function)]]
* [[Quasilinearization]]
==References==
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