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To study a new coordinate system we need to obtain the relevent scale
factors. To this we, as above, analyse how the point
moves when
and
Thus, from Figure 1.15, we see that moves to
, where

(1.30) 
This time the scale factors are (the coefficients of and
) and . The infinitesimal change in area is

(1.31) 
The gradient operator is now

(1.32) 
while

(1.33) 
Note that the dimensions must be correct. has no dimensions.
Finally, for the 2D case considered here,

(1.34) 
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Up: NonCartesian Coordinates
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Prof. Alan Hood
20001106