In the Cartesian coordinates, a point is described by its coordinates (x,y,z), which, in the vector form, is written as
|
| (74) |
where r is the location vector of the point; 
, 
, and 
are the basis vectors of the Cartesian
coordinates, which are constant, independent of spactial location. The transformation between the
Cartesian coordinates system, (x,y,z), and a general coordinates system, (x1,x2,x3), can be expressed
as
 | (75) |
For example, cylindrical coordinates (R,ϕ,Z) can be considered as a general coordinate systems, which
are defined by r = R cosϕ
+ R sinϕ
+ Z
.
The transformation function in Eq. (75) can be written as
 | (76) |