Section A.6 3d Coordinate Systems
Subsection A.6.1 Cartesian Coordinates
Here is a figure showing the definitions of the three Cartesian coordinates
and here are three figures showing a surface of constant a surface of constant and a surface of constant
Finally here is a figure showing the volume element in cartesian coordinates.
Subsection A.6.2 Cylindrical Coordinates
The cartesian and cylindrical coordinates are related by
Here are three figures showing a surface of constant a surface of constant and a surface of constant
Finally here is a figure showing the volume element in cylindrical coordinates.
Subsection A.6.3 Spherical Coordinates
and here are two more figures giving the side and top views of the previous figure.
The cartesian and spherical coordinates are related by
Here are three figures showing a surface of constant a surface of constant and a surface of constant
Finally, here is a figure showing the volume element in spherical coordinates