integral curve
[ˈɪntɪɡrəl kɜːrv]
nounpl: integral curves
curva integral
1. A curve in the solution space of a differential equation where each point on the curve satisfies the equation, representing a particular solution to the differential equation.
The integral curve of the differential equation dy/dx = 2x passes through the point (0,0).
A curva integral da equação diferencial dy/dx = 2x passa pelo ponto (0,0).
2. In the context of vector fields, a curve whose tangent vector at each point coincides with the vector field at that point.
The integral curve traces the path that a particle would follow if it moved according to the vector field.
A curva integral traça o caminho que uma partícula seguiria se se movesse de acordo com o campo vetorial.
This is a specialized mathematical term used primarily in academic and scientific contexts. It is essential terminology in calculus and differential equations courses taught in both Brazilian and Portuguese universities. The term is universally understood among mathematicians and engineers in both Portuguese-speaking countries and the English-speaking world.
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