Template:Intorient/doc

Template page

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 OODA WIKI.

Arguments

  • 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 = File:OiintclockwiseLaTeX.svg oiiint = File:OiiintclockwiseLaTeX.svg varoint = File:VarointclockwiseLaTeX.svg varoiint = File:VaroiintclockwiseLaTeX.svg varoiiint = File:VaroiiintclockwiseLaTeX.svg
Counterclockwise
orientation
ointctr = File:OintctrclockwiseLaTeX.svg oiintctr = File:OiintctrclockwiseLaTeX.svg oiiintctr = File:OiiintctrclockwiseLaTeX.svg varointctr = File:VarointctrclockwiseLaTeX.svg varoiintctr = File:VaroiintctrclockwiseLaTeX.svg varoiiintctr = File:VaroiiintctrclockwiseLaTeX.svg
The default is \oiint
  • intsubscpt the subscript below the integral
  • integrand the text or formula immediately after the formula

All parameters are optional.

Examples

{{intorient
| preintegral = <math>W = </math>
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>p \, {\rm d}V</math>
}}
{{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 File:OintctrclockwiseLaTeX.svg
{{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: File:OiintclockwiseLaTeX.svg
{{Intorient|
| preintegral = 
| symbol = oiiintctr
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
}}
File:VaroiiintctrclockwiseLaTeX.svg
{{Intorient|
| preintegral = 
| symbol = varoiiintctr
| intsubscpt = <math>{\scriptstyle \Omega}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
}}

See also

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

These symbols are currently not supported in MediaWiki's Math mode and this feature request is tracked in phab:T182127.