both divergence and curl of a vector field have a formal definition, however, we don't use these definitions when we compute the divergence or curl. so can we just derive the computations from the definitions?
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2$\begingroup$ What do you mean with 'we don't use these definitions'?, because I think we do. Or can you give the definitions? $\endgroup$– WarreGCommented Jan 24, 2019 at 10:09
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$\begingroup$ Would Mathematics be a better home for this question? $\endgroup$– Qmechanic ♦Commented Jan 24, 2019 at 10:17
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$\begingroup$ I just want to know how to derive the formula for the curl or divergence from their formal definitions $\endgroup$– gogo okaCommented Jan 24, 2019 at 16:38
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$\begingroup$ For some intuition on the $del$ operator formulas of divergence and curl, take a look at the last portion of this video (the whole thing is excellent): 10:18-13:28 youtu.be/rB83DpBJQsE $\endgroup$– novawarrior77Commented Aug 28, 2020 at 14:25
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