Editing Linearization (section)

{{Short description|Finding linear approximation of function at given point}}
{{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]].