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.
Synonyms / Sinônimos
linear approximation at a pointfirst-order Taylor approximationtangent line approximationlocal linearization
Antonyms / Antônimos
nonlinear analysisglobal approximation

Regional Variations

General Brazilian
linearização em um ponto
Standard term used in mathematics and engineering textbooks
São Paulo
linearização no ponto
Alternative preposition usage common in academic contexts
Portugal
linearização num ponto
Portuguese European variant using contraction 'num' instead of 'em um'
General Technical
aproximação linear local
More descriptive alternative emphasizing the local nature of approximation

Related Words

Taylor expansionJacobian matrixderivativeequilibrium pointstability analysisnonlinear system

Related Idioms & Phrases

linearization around a point
linearization near a point
local linear approximation
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