Difference between revisions of "Template:Intorient/doc"
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!Clockwise<br />orientation | !Clockwise<br />orientation | ||
| − | |oint=[[File:OintclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |oint = [[File:OintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiint=[[File:OiintclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |oiint = [[File:OiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiiint=[[File:OiiintclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |oiiint = [[File:OiiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoint=[[File:VarointclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |varoint = [[File:VarointclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiint=[[File:VaroiintclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |varoiint = [[File:VaroiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiiint=[[File:VaroiiintclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |varoiiint = [[File:VaroiiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
|- | |- | ||
!Counterclockwise<br />orientation | !Counterclockwise<br />orientation | ||
| − | |ointctr=[[File:OintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |ointctr = [[File:OintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiintctr=[[File:OiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |oiintctr = [[File:OiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiiintctr=[[File:OiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |oiiintctr = [[File:OiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varointctr=[[File:VarointctrclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |varointctr = [[File:VarointctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiintctr=[[File:VaroiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |varoiintctr = [[File:VaroiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiiintctr=[[File:VaroiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] | + | |varoiiintctr = [[File:VaroiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
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|} | |} | ||
Revision as of 18:26, 8 December 2017
| 40px | This is a documentation subpage for Template:Intorient. It contains usage information, categories and other content that is not part of the original 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 Wikipedia.
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
orientationoint = x45px oiint = x45px oiiint = x45px varoint = x45px varoiint = x45px varoiiint = x45px Counterclockwise
orientationointctr = x45px oiintctr = x45px oiiintctr = x45px varointctr = x45px varoiintctr = x45px varoiiintctr = x45px
- The default is x45px
- intsubscpt the subscript below the integral
- integrand the text or formula immediately after the formula
All parameters are optional.
Examples
- The work done in a thermodynamic cycle on an indicator diagram: <math>W = </math> x44px<math>{\scriptstyle \Gamma}</math> <math>p \, {\rm d}V</math>
{{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: x44px<math>{\scriptstyle \Gamma}</math> <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</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: x44px<math>{\scriptstyle \partial S}</math> <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math> x44px<math>{\scriptstyle \partial S}</math> <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
{{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: x44px<math>{\scriptstyle \Sigma}</math> <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
{{Intorient|
| preintegral =
| symbol = oiiintctr
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
}}
- x44px<math>{\scriptstyle \Omega}</math> <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
{{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.