Template:Intorient
Revision as of 03:48, 24 December 2019 by 89.107.6.187 (talk)
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,
- 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>
<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:
<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:
<math>{\scriptstyle \partial S}</math> <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math>
<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:
<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>
}}
-
<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.
| The above documentation is transcluded from Template:Intorient/doc. (edit | history) Editors can experiment in this template's sandbox (create | mirror) and testcases (create) pages. Please add categories to the /doc subpage. Subpages of this template. |