Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon:

Integration with Spherical Coordiantes


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

For the coordinate transformation

$\displaystyle x = r\sin\vartheta\cos\varphi,\quad
y = r\sin\vartheta\sin\varphi,\quad
z = r\cos\vartheta
$

we have

$\displaystyle dx\,dy\,dz =
r^2 \sin\vartheta\,dr\,d\vartheta\,d\varphi
\,.
$

Particulary the integral of a function $ f$ on a sphere $ K: \; 0 \le r \le R$ is given by

$\displaystyle \int\limits_K f = \int\limits_0^{2 \pi}\int\limits_0^{\pi} \int\limits_0^{R} f(r,\vartheta,\varphi)r^2
\sin\vartheta\,dr\,d\vartheta\,d\varphi \,.
$

(Authors: Höllig/Much/Höfert)

see also:


[Annotations] [Examples]

  automatically generated 8/ 4/2008