Skabelon:Intorient/doc
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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
[rediger kildetekst]- 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
[rediger kildetekst]- The work done in a thermodynamic cycle on an indicator diagram:
{{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:
{{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:
{{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:
{{Intorient| | preintegral = |symbol=oiiintctr | intsubscpt = <math>{\scriptstyle \Sigma}</math> | integrand = <math>(E+H\wedge T) {\rm d}^2 \Sigma</math> }}
{{Intorient| | preintegral = |symbol=varoiiintctr | intsubscpt = <math>{\scriptstyle \Omega}</math> | integrand = <math>(E+H\wedge T) {\rm d}^4 \Omega</math> }}
See also
[rediger kildetekst]Non-oriented boundary integrals over a 2-surface and 3-surface can be implemented respectively by: