# Greens theorem

(Difference between revisions)
 Revision as of 09:06, 12 September 2005 (view source)Praveen (Talk | contribs)← Older edit Latest revision as of 11:40, 12 September 2005 (view source)Jola (Talk | contribs) m (One intermediate revision not shown) Line 1: Line 1: ''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 ''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 - $+ :[itex] \int_\Omega \frac{\partial u_i}{\partial x_i} dV = \oint_{\partial \Omega} u_i n_i dS \int_\Omega \frac{\partial u_i}{\partial x_i} dV = \oint_{\partial \Omega} u_i n_i dS$ [/itex] where $\partial\Omega$ represents the boundary of $\Omega$ and $n_i$ is the unit outward normal to $\partial\Omega$. where $\partial\Omega$ represents the boundary of $\Omega$ and $n_i$ is the unit outward normal to $\partial\Omega$.

## Latest revision as of 11:40, 12 September 2005

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 $\partial\Omega$.