Integrating Vector Fields: Volume vs. Surface

[likephysics]

Homework Statement

$$\int$$ delxA dv = -$$\oint$$ Axds

where A is a vector field
Left hand side is integral over volume. Right hand side is integral over closed surface.

Homework Equations

The Attempt at a Solution

Can't understand what Axds means.

 

[payumooli]

A is the vector field
and dS is the closed surface on which you want to see the flux
x is a multiplication symbol

 

[LCKurtz]

Presumably what you are calling ds (which is usually used for an element of arc length) should be the vector surface element. If the surface is parameterized as

$$\vec R = \vec R(u,v) = \langle x(u,v),y(u,v),z(u,v)\rangle$$

the surface element is

$$d\vec S = \vec R_u \times \vec R_v\, dudv$$