Volume and surface elements in different co-ordinate systems

Volume and surface elements in different co-ordinate systems

This page outlines the value of different volume and surface elements in several different coordinate systems.

Note that in the surface area elements dS, the radius r is not a variable but a constant evaluated at the particular value, hence the absence of the dr differential term.

These elements are computed according to following parametrizations:

Spherical coordinates::{x}=r , sin heta , cosvarphi quad :{y}=r , sin heta , sinvarphi quad , heta in left(0,pi ight),, varphiin left(0,2pi ight) quad :{z}=r , cos heta quad

Cylindrical coordinates:

: x = ho cos varphiquad : y = ho sin varphi quad , varphiin left(0,2pi ight) quad : z = z quad

See also

* Line integral
* Volume integral
* Surface integral
* Spherical coordinates


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