Curl and Divergence

Forum for the GRE subject test in mathematics.
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Joined: Tue Feb 12, 2013 12:12 am

Curl and Divergence

Post by markisus » Sat Mar 09, 2013 4:51 pm

Are Curl and Divergence tested on the mathematics GRE?

Are we expected to know that for R^3:
F is a gradient of g => Curl of F = 0
F is a curl of G => Divergence of F = 0
(and converses inside convex sets)

Greene's Theorem, 3 dimensional Stoke's formula, Divergence theorem?

And of course I would expect no coverage of generalized Stoke's Theorem which requires differential forms.

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Joined: Fri Jan 25, 2013 9:11 pm

Re: Curl and Divergence

Post by IfhhoteCannot » Sat Mar 09, 2013 5:09 pm

I don't think anyone can really answer this, because the Math GRE tests whatever it wants to, and is fairly unpredictable. If you look at some of the previously administered tests, there's usually one or two questions that seem out of NOWHERE. There is a chance they would test something like this, but it's not necessarily worth your time to spend a lot of time studying it because it is unlikely, and it would only be one question.

If you check out the ETS website you can see what they test on, and you will notice it's 50% calc/analysis, 25% algebra, and 25% miscellaneous. It's not very specific, and leaves a lot of room for random stuff.

Personally, I think you should know every detail of calculus like the back of your hand for this test, including this stuff. Depending on when you are taking the test, however, it may not be in your best interest to focus on such details. A solid understand of the basics of linear algebra, for example, is much more important.

Basically: Just know everything about math ever, and you'll do well.

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