Difference between revisions of "Template:Intorient/doc"

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imported>Edokter
imported>Tentacles
(→‎Examples: presentation tweaks)
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*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)^3z^{1/2}}</math>
+
| 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)^3z^{1/2}}</math>
+
| 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|
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| 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

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
orientation
oint=x45px oiint=x45px oiiint=x45px varoint=x45px varoiint=x45px varoiiint=x45px
Counterclockwise
orientation
ointctr=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

{{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: 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: