Difference between revisions of "Template:Intorient/doc"
Jump to navigation
Jump to search
imported>Maschen (links to mathjax pages) |
imported>Maschen (png -> svg) |
||
| Line 5: | Line 5: | ||
==Arguments== | ==Arguments== | ||
| − | * '''mode:''' choose either " | + | * '''mode:''' choose either "svg" (large, 45px width) or "[[mathjax]]" (small, 35px width), depending on which rendering is used. The default is the average of 40px width. |
* '''preintegral''' the text or formula immediately before the integral | * '''preintegral''' the text or formula immediately before the integral | ||
* '''symbol''' the integral symbol, | * '''symbol''' the integral symbol, | ||
| Line 23: | Line 23: | ||
|- | |- | ||
!Clockwise<br />orientation | !Clockwise<br />orientation | ||
| − | |oint=[[File:OintclockwiseLaTeX. | + | |oint=[[File:OintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiint=[[File:OiintclockwiseLaTeX. | + | |oiint=[[File:OiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiiint=[[File:OiiintclockwiseLaTeX. | + | |oiiint=[[File:OiiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoint=[[File:VarointclockwiseLaTeX. | + | |varoint=[[File:VarointclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiint=[[File:VaroiintclockwiseLaTeX. | + | |varoiint=[[File:VaroiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiiint=[[File:VaroiiintclockwiseLaTeX. | + | |varoiiint=[[File:VaroiiintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
|- | |- | ||
!Counterclockwise<br />orientation | !Counterclockwise<br />orientation | ||
| − | |ointctr=[[File:OintctrclockwiseLaTeX. | + | |ointctr=[[File:OintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiintctr=[[File:OiintctrclockwiseLaTeX. | + | |oiintctr=[[File:OiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |oiiintctr=[[File:OiiintctrclockwiseLaTeX. | + | |oiiintctr=[[File:OiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varointctr=[[File:VarointctrclockwiseLaTeX. | + | |varointctr=[[File:VarointctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiintctr=[[File:VaroiintctrclockwiseLaTeX. | + | |varoiintctr=[[File:VaroiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
| − | |varoiiintctr=[[File:VaroiiintctrclockwiseLaTeX. | + | |varoiiintctr=[[File:VaroiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]] |
|- | |- | ||
|} | |} | ||
| − | :The default is [[File:OintclockwiseLaTeX. | + | :The default is [[File:OintclockwiseLaTeX.svg|x45px|alt=\oiint]] |
* '''intsubscpt''' the subscript below the integral | * '''intsubscpt''' the subscript below the integral | ||
Revision as of 16:56, 6 May 2013
| 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
- mode: choose either "svg" (large, 45px width) or "mathjax" (small, 35px width), depending on which rendering is used. The default is the average of 40px width.
- 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)^3z^{1/2}}</math>
{{intorient|
| preintegral =
|symbol=varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>\frac{{\rm d}z}{(z+a)^3z^{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|
| 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: