Calculus III
Contents
3 Dimensional space
Partial derivatives
Multiple integrals
Vector Functions
Line integrals
Surface integrals
Vector operators
Applications
© The scientific sentence. 2010
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CYLINDRICAL COORDINATES
1. The basic relationships
The coordinates of a vector  are the
coordinates of its associated point P.
The cartesian coordinates of a
point P are x, y and z.
The relationships btween cartesian coordinates and cylindrical coordinates
for a point P are:
x = s cos φ
y = s sin φ
z = z
x2 = x2 + y2
The folowing figure shows how to transform units vectors:
2. The cross product
 x 
The components of the two vectors are:
= 〈 0, 0, 1 〉
= 〈 - sin φ, cos φ, 0 〉
Then
x =
〈 - cos φ, - sin φ, 0 〉 =
- cos φ - sin φ
x =
- cos φ - sin φ
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