# Difference between revisions of "Green's theorem"

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− | <div class="definition"><div class="short_definition">A form of the [[divergence theorem]] applied to a [[vector field]] so chosen as to yield a formula useful in applying the [[Green's function]] method of solution of a [[boundary-value problem]].</div><br/> <div class="paragraph">The most common form of the theorem is <div class="display-formula"><blockquote>[[File:ams2001glos-Ge47.gif|link=|center|ams2001glos-Ge47]]</blockquote></div> where ''dV'' and ''dS'' are elements of the volume ''V'' and closed bounding surface ''S'', respectively; φ and ψ are any twice differential functions with continuous second partial derivatives in ''V''; ''n'' is the outer normal to ''S''; and ∇<sup>2</sup> is the [[Laplacian operator]].</div><br/> </div> | + | <div class="definition"><div class="short_definition">A form of the [[divergence theorem]] applied to a [[vector field]] so chosen as to yield a formula useful in applying the [[Green's function]] method of solution of a [[boundary-value problem|boundary-value problem]].</div><br/> <div class="paragraph">The most common form of the theorem is <div class="display-formula"><blockquote>[[File:ams2001glos-Ge47.gif|link=|center|ams2001glos-Ge47]]</blockquote></div> where ''dV'' and ''dS'' are elements of the volume ''V'' and closed bounding surface ''S'', respectively; φ and ψ are any twice differential functions with continuous second partial derivatives in ''V''; ''n'' is the outer normal to ''S''; and ∇<sup>2</sup> is the [[Laplacian operator]].</div><br/> </div> |

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## Latest revision as of 17:05, 25 April 2012

## Green's theorem

A form of the divergence theorem applied to a vector field so chosen as to yield a formula useful in applying the Green's function method of solution of a boundary-value problem.

The most common form of the theorem is where

*dV*and*dS*are elements of the volume*V*and closed bounding surface*S*, respectively; φ and ψ are any twice differential functions with continuous second partial derivatives in*V*;*n*is the outer normal to*S*; and ∇^{2}is the Laplacian operator.

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