Multivariate Calculus - Bruce E. Shapiro

Lecture 7
Cylindrical and Spherical
Coordinates
Cylindrical Coordinates
Cylindrical coordinates are polar coordinates with z added to give the distance
of a point above the xy plane. A point P = (x, y, z) is described by the cylindrical
coordinates (r, θ, z) where:
r is the distance, measured in the xy-plane, from the origin to the projection of P
into the xy plane.
θ is the polar angle, measured in the xy-plane, of the projection of P into the
xy-plane.
z is the same is both cylindrical and cartesian coordinates.
Figure 7.1: Cylindrical coordinates (r, θ, z) shown in terms of the usual Cartesian
coordinate frame.
To find (x, y, z ) given (r, θ, z):
x = r cos θ
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