Template:Oiint/doc

This template is used to include the double closed integral, usually in a mathematical formula. It overcomes a limitation of the TeX rendering which cannot display this symbol without clumsy workarounds.

Arguments

• preintegral the text or formula immediately before the integral
• intsubscpt the subscript below the integral
• integrand the text or formula immediately after the formula

All parameters are optional.

Examples

Two of Maxwell's equations, e.g. the Maxwell–Faraday equation and Ampère's circuital law (with Maxwell's addition).

{{block indent|{{oiint
| preintegral = <math>\oint_C \mathbf{E} \cdot {\rm d} \boldsymbol{\ell} = \frac{\partial }{\partial t} </math>
| intsubscpt = <math>{\scriptstyle S}</math>
| integrand = <math>\mathbf{B} \cdot {\rm d}\mathbf{S}</math>
}}}}

${\oint }_C\mathbf{𝐄}\cdot \mathrm{d}\mathit{\ell }=\frac{\partial }{\partial t}$ \oiint$S$ $\mathbf{𝐁}\cdot \mathrm{d}\mathbf{𝐒}$

{{block indent|{{oiint
| preintegral = <math>\oint_C \mathbf{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 </math>
| intsubscpt = <math>{\scriptstyle S}</math>
| integrand = <math>\left ( \mathbf{J} + \epsilon_0\frac{\partial \mathbf{E}}{\partial t} \right )\! \cdot {\rm d}\mathbf{S}</math>
}}}}

${\oint }_C\mathbf{𝐁}\cdot \mathrm{d}\mathit{\ell }={\mu }_0$ \oiint$S$ $(\mathbf{𝐉}+{ϵ}_0\frac{\partial \mathbf{𝐄}}{\partial t})\cdot \mathrm{d}\mathbf{𝐒}$

Technical details

The \oiint command is not part of AMS-LaTeX, and thus not part of the math support that MediaWiki provides. It is available as a unicode character U+222F ∯ SURFACE INTEGRAL but font support for this character can be lacking. For this reason, the template provides an image variant of the character.

See also

• {{Oiiint}} (to implement triple closed integrals)
• {{Intorient}} (to implement oriented boundary integrals over a 2-surface and 3-surface)