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## Transformation of the 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 |

Let be a continuous scalar function. A bijective, continuously differentiable transformation of a regular region with

where is the jacobian determinant of the transformation. It describes the local change of the volume element

For a local orthogonal coordinate transformation , i.e. the columns of are orthogonal, the jacobian determinant has the form

The conditions can be formulated weaker, e.g. it suffices to require the bijectivity of and the invertibility of in the interior of . Also if both integrals exist may have some singularities.

**Annotation:**

automatically generated 5/30/2011 |