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a number of issues
1) give the hypotheses. What is the space in which F lives. R^3? 3-d Euclidean
space? Mention that curl turns a vector field into a vector
2) Do not capitalize the entry title. This has to do
w/ encyclopedia organization and autolinking. See users
guide for details.
3) In your formula you do not say what S is. Do not
use unintroduced symbols.
4) Suggestion: give the definition relative to an ortho coord
system; remark that the formula is covariant w.r.t. choice
of coordinate system; give the coord-free definition.
5) The sentence
"Curl is easily computed in an arbitrary
orthogonal coordinate system by using the appropriate scale factors."
is not helpful. Either provide the details, or drop it.
6) The sentence "Physically, the curl gives the tendency of the vector field to
curl about a point."
Again, either elaborate or drop it. As it stands such a
description only mystifies the reader. You are using the word
"curl" to illuminate a concept called "curl". You are not
adding anything useful here. A different choice of words
may convey more useful information. Try invoking an image
of a little ball, whose center is fixed but that is otherwise
free to rotate. As V flows past such a little ball, it
imparts angular momentum to it. This angular momentum vector
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