vector_calculus

# Vector r v vextendsingle vextendsingle vextendsingle

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Unformatted text preview: vector r ∂ v vextendsingle vextendsingle vextendsingle vextendsingle ∂ vector r ∂ u × ∂ vector r ∂ v vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ∂ vector r ∂ u × ∂ vector r ∂ v vextendsingle vextendsingle vextendsingle vextendsingle du dv = parenleftbigg ∂ vector r ∂ u × ∂ vector r ∂ v parenrightbigg du dv = d vector S . Therefore, integraldisplayintegraldisplay S vector F · d vector S = integraldisplayintegraldisplay S vector F · ˆ n dS . This shows us that the interpretation of this integral is that we are integrating the com- ponent of the vector field that is normal to the surface, i.e. the component of the field that is perpendicular to the surface. Also, this is really an integration of a scalar quantity (or scalar field, vector F · ˆ n ) over the surface. Another way of saying this, is that the integral computes the flux of the vector quantity through the surface....
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