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2008-05-18T19:16:50Z

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Vipul: New page: {{contour}} ==Definition== The '''mousehole contour''' with ''inner radius'' $r$ and ''outer radius'' $R > r$ comprises the following three pieces: * A semicircle ...

2008-05-01T19:19:17Z

New page: {{contour}} ==Definition== The '''mousehole contour''' with ''inner radius'' <math>r</math> and ''outer radius'' <math>R > r</math> comprises the following three pieces: * A semicircle ...

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{{contour}}

==Definition==

The '''mousehole contour''' with ''inner radius'' <math>r</math> and ''outer radius'' <math>R > r</math> comprises the following three pieces:

* A semicircle of radius <math>r</math>, centered at the origin, and in the [[upper half-plane]]
* A semicircle of radius <math>R</math>, centered at the origin, and in the upper half-plane
* Line segments joining the ends of these semicircles: one joining <math>r</math> to <math>R</math>, and one joining <math>-r</math> to <math>-R</math>.

There are more general versions of this; for instance, the [[quadrant mousehole contour]], which comprises two concentric quadrants with joining line segments at the ends.

The mousehole contour is used as a tool in computing integrals of real-valued functions. For this, we let the inner radius tend to zero and the outer radius tend to <math>\infty</math>. {{further|[[mousehole contour integration method]]}}

Mousehole contour - Revision history

Vipul: 1 revision

Vipul: New page: {{contour}} ==Definition== The '''mousehole contour''' with ''inner radius'' r and ''outer radius'' R > r comprises the following three pieces: * A semicircle ...

Vipul: New page: {{contour}} ==Definition== The '''mousehole contour''' with ''inner radius'' $r$ and ''outer radius'' $R > r$ comprises the following three pieces: * A semicircle ...