Mathematics-Online lexicon: Region of Integration

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	Mathematics-Online lexicon:
	Region of Integration

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

overview

$V \subseteq \mathbb{R}^n$ is called an elementary region if - after a suitable orthogonal transformation $x\to x'$ - it is bounded by the graphs of continuous functions:

$\displaystyle V :\; a_j(x'_1,\ldots,x'_{j-1})\le x'_j\le b_j(x'_1,\ldots,x'_{j-1})\,,\quad j=1,\ldots,n \,.$

$\includegraphics[width=0.45\linewidth]{a_intbereiche1}$

$\includegraphics[width=0.5\linewidth]{a_intbereiche2}$

A union of elementary regions that are disjoint except possibly at the boundary is called a regular region. A special case is a polygonal region consisting of simplices.

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see also:

Keyword: Domain of integration
Keyword: Domain

automatically generated 5/30/2011