Through a Surface Defined over an Ellipse - Maple Help

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Flux through a Surface Defined over Interior of an Ellipse

Description

This template computes the flux of a vector field through a surface defined over the interior of an ellipse. The field can be specified in its own coordinate system. The surface parameters can be two of the coordinate variables, or all three coordinates for the surface can be functions of two other parameters. The ellipse is specified by giving its rectangular equation in the coordinates of the parameter space. Thus, if the surface is parametrized as x(u, v), y(u, v), z(u, v), the ellipse supporting the surface is a quadratic equation of the form a u2 &plus; b u v &plus; c v2 &plus; d u &plus; e v &plus; f&equals;0, where b24 ac<0, and the resulting ellipse is real and non-degenerate.

Flux through a Surface Defined over Interior of an Ellipse

For the Vector Field:

 

           

           

           

   

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

Commands Used

VectorCalculus[Flux]

See Also

VectorCalculus[SurfaceInt]