If is a domain in with boundary with outward unit normal , and and , then we obtain applying the Divergence Theorem to the product ,
These formulas are referred to as Green’s Formulas and express 3d analogs to integration by parts in 1d.
If is a surface in bounded by a closed curve , is a unit normal to , is oriented in a clockwise direction following the positive direction of the normal , and is differentiable, then
which is Stokes’ Theorem.
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