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When the coordinates are increased by
the point
moves by the amount
and, as indicated in Figure 1.16, the infinitessimal volume
element is

(1.35) 
Figure 1.16:
Illustrating how the volume element is related to the
increases in the coordinates by
and
. Notice that the lengths of the sides are ,
and .

The scale factors are 1 (in the direction) (in the
direction) and 1 (in the direction).
So the gradient operator is

(1.36) 
The other important expressions in cylindrical coordinates are
and
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Prof. Alan Hood
20001106