linearization at a point
[ˌlɪnɪəraɪˈzeɪʃən æt ə pɔɪnt]
nounpl: linearizations at points
linearização em um ponto
1. The process of approximating a nonlinear function or system by a linear function or system in the neighborhood of a specific point, typically using the first-order Taylor expansion or Jacobian matrix.
The linearization at a point is obtained by computing the derivative and evaluating it at that point.
A linearização em um ponto é obtida calculando a derivada e avaliando-a naquele ponto.
2. In dynamical systems, the approximation of nonlinear equations near an equilibrium point using linear differential equations for stability analysis.
We used linearization at a point to determine whether the equilibrium is stable or unstable.
Usamos a linearização em um ponto para determinar se o equilíbrio é estável ou instável.
3. The tangent line or tangent plane that best approximates a curve or surface at a given point.
The linearization at a point provides the best linear approximation locally.
A linearização em um ponto fornece a melhor aproximação linear localmente.
This is a specialized mathematical and scientific term used extensively in Brazilian universities and technical institutions, particularly in calculus, differential equations, and control systems courses. The concept is fundamental to both pure and applied mathematics, and the terminology is standardized across academic institutions in Brazil and Portugal.
Related Idioms & Phrases
linearization around a point
linearization near a point
local linear approximation
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