Talk:Green's theorem

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Notation Question

Not that it really matters, but I usually see (American mathematics texts) Green's thm stated with functions named P and Q, rather than L and M. In fact, the last section of this article employs these letters. Does anyone object to me going through and switching to P and Q? Chip McShoulder (talk) 21:58, 6 February 2010 (UTC)[reply]

Higher maths require being able to go beyond issues of notation.

Green's theorem is supposedly intended to ease evaluation of line integrals. So the traditional way of teaching it boils down to: in order to simply the problem, replace a function by two functions M-N / P-Q. Then evaluate two double integrals.

I am totally dissatisfied with that traditional approach. While it must please mathematicians, it is not intuitive. Would it be so difficult to start with the insight that possessed Mr. Green to come up with something so profound ?

Unfortunately, * teaching * has been replaced by merely * telling *.

http://mathinsight.org/greens_theorem_idea does a far better job * explaining * the concept but is not even listed in the references and other links. Instead a reference is given to Math World, which manages to regurgitate the same hermetic P-Q gospel without bothering with any supporting drawing. — Preceding unsigned comment added by 74.56.95.120 (talk) 15:28, 13 December 2014 (UTC)[reply]

Wikipedia is not a textbook, thus it's not our job to teach it. Wolfram Mathworld also isn't the best resource for learning either - it's more a reference or "handbook" like Wikipedia is.--Jasper Deng (talk) 17:14, 13 December 2014 (UTC)[reply]

Stokes

What about Stokes theorem

Alternative Notation

The alternative notation given doesn't indicate the integral is calculated using the positive orientation of C. It just tells the integral is calculated over a closed curve. To indicate positive orientation, an arrow pointing in the counter-clockwise direction is usually drawn in the circle over the integral symbol.

Notation for counter-clockwise integral symbol

I changed the integral code to use the {{intorient | symbol = ointctr template. But I don't know if there's a specific template for the double-integral, so I can't embed the double integral notation for the right side of the equation (as is shown on the template documentation example). So it's shown on two lines - is there a way to get this on a single line? Jimw338 (talk) 07:17, 12 June 2017 (UTC)[reply]

Type I vs Type II

I don't know what these are and I don't know why there's no links about them. I would expect a hyperlink to another wikipage 132.204.27.207 (talk) 18:27, 13 July 2023 (UTC)[reply]

Proof fails when g1(x) is not constant

If you use parametric equations: x = x, y = g1(x), a ≤ x ≤ b then you should be getting a factor of sqrt(1+(g1'(x))^2) when you evaluate the line integral, because the line integral depends on the magnitude of the tangent vector of the parameterization (see https://en.wikipedia.org/wiki/Line_integral). So, this proof is not correct, though it would still be correct for rectangular regions since then g1(x) is constant and we have a paremeterization by arclength. — Preceding unsigned comment added by 142.244.195.252 (talk) 19:42, 13 December 2024 (UTC)[reply]