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Conceptos clave de Rotacional, Gradiente y Divergencia

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Conceptos clave de Rotacional, Gradiente y Divergencia

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Conceptos clave de cálculo vectorial

Created by

Yuridiana Lopez Arias
Yuridiana Lopez Arias
Mexico

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Conceptos clave de Rotacional, Gradiente y Divergencia
 

Conceptos clave de Rotacional, Gradiente y DivergenciaOnline version

Conceptos clave de cálculo vectorial

by Yuridiana Lopez Arias
1

¿Qué describe el gradiente de un campo escalar?

2

¿Qué operador se usa para calcular la divergencia de un campo vectorial?

3

¿Qué representa el rotacional (curl) de un campo vectorial?

4

Propiedad: El rotacional de un gradiente siempre es cero. ¿Verdadero o falso?

5

Si un campo F tiene divergencia constante, ¿qué indica?

6

¿Qué tipo de objeto es el gradiente de un campo escalar?

7

¿Qué operador da el rotacional de un campo F?

8

¿Qué condición define que un campo sea irrotacional?

9

Ejemplo de un campo escalar

10

La divergencia puede ser aplicado a un campo de velocidades de un fluido. Verdero/Falso.

Explicación

El gradiente señala hacia donde el valor del campo sube más rápidamente.

Divergencia mide la expansión o contracción en un punto; usa ∇·F.

Curl mide la rotación o circulación del campo alrededor de un punto.

Es una propiedad clásica: ∇×(∇f)=0 para cualquier f suave.

Divergencia constante sugiere generación o absorción de flujo en punto.

El gradiente produce un campo vectorial.

∇×F es el rotacional, mide la circulación del campo.

Un campo irrotacional tiene rotacional nulo en cada punto.

Un campo de presiones, se puede expresar como P(x,y,z), donde (x,y,z) indica la ubicación geográfica.

La divergencia se aplica a campos vectoriales y da como resultado un escalar.

 
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