oiint
Represents a double surface integral over a closed surface in multivariable calculus and vector analysis.
Overview
Essential for expressing flux integrals and working with vector fields in three-dimensional space, particularly in electromagnetic theory and fluid dynamics.
- Commonly used in Gauss's divergence theorem calculations
- Appears frequently in physics when analyzing closed surfaces
- Found in advanced mathematics for computing flux across boundary surfaces
- Requires the 'amsmath' or 'esint' package for proper rendering
Examples
Surface integral over a closed surface in 3D space, commonly used in physics for Gauss's law.
\oint\!\oint_S \vec{E} \cdot d\vec{S} = \frac{Q}{\epsilon_0}
Double surface integral for calculating the total flux through a closed boundary.
\oiint_{\partial V} \vec{F} \cdot d\vec{S} = \int_V (\nabla \cdot \vec{F})\,dV
Divergence theorem applied to an electromagnetic field.
\oiint_S \vec{B} \cdot d\vec{S} = 0