Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon:

Surface Integrals of Scalar Functions

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
Let $ S$ be a surface with regular parametrization $ \sigma: A \longrightarrow \mathbb{R}^3 \ ,\ (t,u) \mapsto \sigma(t,u) .$ Further let $ f$ be a differentiable scalar function defined on an open set containing $ S .$ Then the integral

$\displaystyle \iint\limits_S f \ d\sigma := \iint\limits_A f(\sigma(t,u)) \vert\sigma_t \times \sigma_u \vert \ dt du $

is called the surface integral of $ f$ over $ S .$ The value of the integral does not depend on the parametrization.

If $ f$ represents a density of mass then the integral yields the mass of the surface.

If $ f = 1$ then the integral just gives the area of the surface.

()

see also:

  automatically generated 7/ 5/2005