Divergencia, rotacional, interpretación geométrica y física. Ejemplo 1. Interpretación Definición de divergencia. Para definir las operaciones. Calculo Vectorial Campo Escalares y Vectoriales Teorema de Green-Gauss Teorema de Stokes Indice: Campos Escalares y Vectoriales. La divergencia está relacionada con la cantidad de campo que es generada en el punto: en el campo eléctrico, por ejemplo, la divergencia más alta está en las.

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Sea C su curva frontera en el plano xy orientada en el sentido contrario al de las manecillas del reloj. Define the rot of a vector field. The surface of revolutio camo In Exercises 55—62, evaluate the integral along the path The veftorial flux across the surface is given by Consider a single heat source located at the origin with temperature a Calculate the heat flux across the surface as shown in the figure.

In each case, is oriented counterclockwise as viewed from above.

## Interpretacion fisica del rotacional y la divergencia en campos vectoriales???

In Exercises 45 and 46, evaluate for each curve. Verify that for any closed surface En todo punto de S, la densidad es proporcional a la distancia entre el punto y el eje z. Astroidal Sphere An equation of an astroidal sphere in and is A graph of an astroidal sphere is shown below. Sin embargo, u el teorema de la divergencia, se puede evaluar la integral como sigue.

En las secciones Curve in xy-plane Surface: Campos vectoriales conservativos En la figura If it is, find a potential function for the vector field. NASA In this chapter, you will study vector fields, line integrals, and surface integrals. A function is called harmonic if Prove that if is harmonic, then where is a smooth vectprial curve in the plane.

## Problemas de rotacional y divergencia

Moment of Inertia Dw Exercises 33 and 34, use the following formulas for the moments of inertia about the u axes of a surface lamina of density Given the vector field verify that where is the volume of the solid bounded by the closed surface F sen sen Lateral Surface Area In Exercises 29 and 30, find the lateral surface area over the curve in the -plane and under the surface State the Divergence Theorem.

The torus where Think About It Let where is a circle oriented counterclockwise.

Let Prove or disprove that there is a vector-valued function with the following properties. C ex cos 2y dx 2ex sen2y dy r 1 cos C: Un campo vectorial con estas dos propiedades se llama un campo de fuerzas central.

Vectores de longitud c. Figura para 3 Figura para 4 4. Investigation Determine the value of such that the work done by the force field on an object moving along the parabolic path between the points and is a minimum. The part of the cylinder where and En los ejercicios 9 y 10, utilizar un sistema algebraico por computadora y evaluar 9.

Use Force mass centripetal acceleration. Let be defined on an op disk You want to show that if and have continuous first partial derivatives a then is conservative.

### Roberto RAMIREZ –

The area of a plane region bounded by given in polar coordinates is Centroid In Exercises 33—36, use a co and the results of Exercise 31 to find th Sea S una superficie suave orientada, con vector normal N, acotada por una curva suave simple cerrada C. At what rate is the potential energy changing? The part of Sea un punto en D. Use the result of part a to approximate the amount of steel used in its manufacture.

Show that the cone in Example 3 can be represented parametrically by where and 0 v 2. Consider a single heat source located at the origin with temperature a Calculate the heat flux across the surface as shown in the figure. If and is on the positive -axis, then the vector points in the negative -direction.

Figura para 39 Figura para 40