linearization
Sign in to saveIn mathematics, linearization (British English: linearisation) is finding the linear approximation to a 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 systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
Article
12 sectionsContents
- Linearization of a function
- Example
- Linearization of a multivariable function{{anchor|Multivariable functions}}
- Uses of linearization
- Stability analysis
- Microeconomics
- Optimization
- Multiphysics
- See also
- References
- External links
- Linearization tutorials
In mathematics, linearization (British English: linearisation) is finding the linear approximation to a 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 systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
==Linearization of a function== Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function y = f(x) at any x = a based on the value and slope of the function at x = b, given that f(x) is differentiable on [a, b] (or [b, a]) and that a is close to b. In short, linearization approximates the output of a function near x = a.