Difference between revisions of "Template:Intorient/doc"
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imported>Edokter m (→Examples) |
imported>Tentacles (→Examples: presentation tweaks) |
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| Line 49: | Line 49: | ||
*The work done in a [[thermodynamic cycle]] on an [[indicator diagram]]: {{intorient | *The work done in a [[thermodynamic cycle]] on an [[indicator diagram]]: {{intorient | ||
| − | | preintegral=<math>W=</math> | + | | preintegral = <math>W = </math> |
| symbol = varoint | | symbol = varoint | ||
| intsubscpt = <math>{\scriptstyle \Gamma}</math> | | intsubscpt = <math>{\scriptstyle \Gamma}</math> | ||
| − | | integrand = <math>p{\rm d}V</math> | + | | integrand = <math>p \, {\rm d}V</math> |
}} | }} | ||
<source lang="tex">{{intorient | <source lang="tex">{{intorient | ||
| − | | preintegral=<math>W=</math> | + | | preintegral = <math>W = </math> |
| symbol = varoint | | symbol = varoint | ||
| intsubscpt = <math>{\scriptstyle \Gamma}</math> | | intsubscpt = <math>{\scriptstyle \Gamma}</math> | ||
| − | | integrand = <math>p{\rm d}V</math> | + | | integrand = <math>p \, {\rm d}V</math> |
}}</source> | }}</source> | ||
| Line 65: | Line 65: | ||
| symbol = varoint | | symbol = varoint | ||
| intsubscpt = <math>{\scriptstyle \Gamma}</math> | | intsubscpt = <math>{\scriptstyle \Gamma}</math> | ||
| − | | integrand = <math>\frac{{\rm d}z}{(z+a)^ | + | | integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math> |
}} | }} | ||
<source lang="tex">{{intorient| | <source lang="tex">{{intorient| | ||
| Line 71: | Line 71: | ||
| symbol = varoint | | symbol = varoint | ||
| intsubscpt = <math>{\scriptstyle \Gamma}</math> | | intsubscpt = <math>{\scriptstyle \Gamma}</math> | ||
| − | | integrand = <math>\frac{{\rm d}z}{(z+a)^ | + | | integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math> |
}}</source> | }}</source> | ||
| − | *Line integrals of vector fields: {{intorient| | + | *Line integrals of vector fields: {{intorient|<!-- You have to nest things this way to insure everything stays in one line. --> |
| preintegral = {{intorient| | | preintegral = {{intorient| | ||
| preintegral = | | preintegral = | ||
| symbol = oint | | symbol = oint | ||
| intsubscpt = <math>{\scriptstyle \partial S}</math> | | intsubscpt = <math>{\scriptstyle \partial S}</math> | ||
| − | | integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}=-</math> | + | | integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math> |
}} | }} | ||
| symbol = ointctr | | symbol = ointctr | ||
| intsubscpt = <math>{\scriptstyle \partial S}</math> | | intsubscpt = <math>{\scriptstyle \partial S}</math> | ||
| − | | integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}</math> | + | | integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math> |
}} | }} | ||
| − | <source lang="tex">{{intorient| | + | <source lang="tex">{{intorient|<!-- You have to nest things this way to insure everything stays in one line. --> |
| preintegral = {{intorient| | | preintegral = {{intorient| | ||
| preintegral = | | preintegral = | ||
| symbol = oint | | symbol = oint | ||
| intsubscpt = <math>{\scriptstyle \partial S}</math> | | intsubscpt = <math>{\scriptstyle \partial S}</math> | ||
| − | | integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}=-</math> | + | | integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math> |
}} | }} | ||
|symbol=ointctr | |symbol=ointctr | ||
| intsubscpt = <math>{\scriptstyle \partial S}</math> | | intsubscpt = <math>{\scriptstyle \partial S}</math> | ||
| − | | integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}</math> | + | | integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math> |
}}</source> | }}</source> | ||
| Line 101: | Line 101: | ||
| symbol = oiint | | symbol = oiint | ||
| intsubscpt = <math>{\scriptstyle \Sigma}</math> | | intsubscpt = <math>{\scriptstyle \Sigma}</math> | ||
| − | | integrand = <math>(E+H\wedge T) {\rm d}^2 \Sigma</math> | + | | integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math> |
}} | }} | ||
<source lang="tex">{{Intorient| | <source lang="tex">{{Intorient| | ||
| Line 107: | Line 107: | ||
| symbol = oiiintctr | | symbol = oiiintctr | ||
| intsubscpt = <math>{\scriptstyle \Sigma}</math> | | intsubscpt = <math>{\scriptstyle \Sigma}</math> | ||
| − | | integrand = <math>(E+H\wedge T) {\rm d}^2 \Sigma</math> | + | | integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math> |
}}</source> | }}</source> | ||
| Line 114: | Line 114: | ||
| symbol = varoiiintctr | | symbol = varoiiintctr | ||
| intsubscpt = <math>{\scriptstyle \Omega}</math> | | intsubscpt = <math>{\scriptstyle \Omega}</math> | ||
| − | | integrand = <math>(E+H\wedge T) {\rm d}^4\Omega</math> | + | | integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math> |
}} | }} | ||
<source lang="tex">{{Intorient| | <source lang="tex">{{Intorient| | ||
| Line 120: | Line 120: | ||
| symbol = varoiiintctr | | symbol = varoiiintctr | ||
| intsubscpt = <math>{\scriptstyle \Omega}</math> | | intsubscpt = <math>{\scriptstyle \Omega}</math> | ||
| − | | integrand = <math>(E+H\wedge T) {\rm d}^4 \Omega</math> | + | | integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math> |
}}</source> | }}</source> | ||
Revision as of 01:05, 12 April 2016
| 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 \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: