# Greens theorem

Greens Theorem, also known as Divergence Theorem is an important identity in vector calculus. If $u_i$ is a vector field variable defined over a domain $\Omega$ then Greens Theorem states that
$\int_\Omega \frac{\partial u_i}{\partial x_i} dV = \oint_{\partial \Omega} u_i n_i dS$
where $\partial\Omega$ represents the boundary of $\Omega$ and $n_i$ is the unit outward normal to $\partial\Omega$.