Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics V / 2 / a / i

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- Solution i

Solution

For a continuously differentiable vector field

F

on a neighborhood of the closure of

V

, the divergence theorem states

∭_{V} \nabla \cdot F d V = \iint_{\partial V} F \cdot n d S .

Here

n

is the outward unit normal vector; the right side is the outward flux through the boundary.

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