# Gauss’, Green’s and Stokes’ Theorems

If is a domain in with boundary with outward unit normal , and and , then we obtain applying the Divergence Theorem to the product ,

- .

Further, similarly,

and

- .

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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