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Greens theorem

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''Greens Theorem'', also known as ''Divergence Theorem'' is an important identity in vector calculus. If <math>u_i</math> is a vector field variable defined over a domain <math>\Omega</math> then Greens Theorem states that
''Greens Theorem'', also known as ''Divergence Theorem'' is an important identity in vector calculus. If <math>u_i</math> is a vector field variable defined over a domain <math>\Omega</math> then Greens Theorem states that
-
<math>
+
:<math>
\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
</math>
</math>
where <math>\partial\Omega</math> represents the boundary of <math>\Omega</math> and <math>n_i</math> is the unit outward normal to <math>\partial\Omega</math>.
where <math>\partial\Omega</math> represents the boundary of <math>\Omega</math> and <math>n_i</math> is the unit outward normal to <math>\partial\Omega</math>.

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.

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