Template:Intorient

From Wikipedia, the free encyclopedia
Jump to: navigation, search

\ointclockwise

Template documentation[view] [edit] [history] [purge]

This template is used to include the oriented integrals around closed surfaces (or hypersurfaces in higher dimensions), usually in a mathematical formula. They are additional symbols to the non-oriented integrals \oiint and \oiiint which are not yet rendered on Wikipedia.

Arguments[edit]

  • preintegral the text or formula immediately before the integral
  • symbol the integral symbol,
Select one of... Arrow up, integrals over a closed Arrow down, integrals over a closed
1-surface 2-surface 3-surface 1-surface 2-surface 3-surface
Clockwise
orientation
oint=\oiint oiint=\oiint oiiint=\oiint varoint=\oiint varoiint=\oiint varoiiint=\oiint
Counterclockwise
orientation
ointctr=\oiint oiintctr=\oiint oiiintctr=\oiint varointctr=\oiint varoiintctr=\oiint varoiiintctr=\oiint
The default is \oiint
  • intsubscpt the subscript below the integral
  • integrand the text or formula immediately after the formula

All parameters are optional.

Examples[edit]

{{intorient
| preintegral = <math>W = </math>
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>p \, {\rm d}V</math>
}}
  • In complex analysis for contour integrals: \varointclockwise
{{intorient|
| preintegral = 
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math>
}}
  • Line integrals of vector fields: \ointclockwise \ointctrclockwise
{{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->
| preintegral = {{intorient|
| preintegral =
| symbol = oint
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math>
}}
|symbol=ointctr
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
}}
  • Other examples: \oiintclockwise
{{Intorient|
| preintegral = 
| symbol = oiiintctr
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
}}
\varoiiintctrclockwise
{{Intorient|
| preintegral = 
| symbol = varoiiintctr
| intsubscpt = <math>{\scriptstyle \Omega}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
}}

See also[edit]

Non-oriented boundary integrals over a 2-surface and 3-surface can be implemented respectively by: