Khác biệt giữa các bản “Định lý Green”

(Dịch sơ sơ)
 
 
==Định lý==
Let ''C'' be a positivelymột [[orientationđường (mathematics)|orientedđơn đóng]], [[piecewiseđịnh smoothhướng]], [[simple closed curvedương]] in thetrong [[planemặt (mathematics)|planephẳng]] '''<math> \mathbb{R} </math><sup>2</sup>''', and let ''D'' be themiền regionđược boundedbao byquanh bởi ''C''. IfNếu ''L'' and ''M'' are functionscác ofhàm số với biến (''x'', ''y'') definedđược onđịnh annghĩa trên [[Open setmở|openmiền regionmở]] containingchứa ''D'' and have [[Continuouscác function|continuous]]đạo [[partialhàm derivatives]]riêng phần liên tục trên theređó, thenthì<ref>Mathematical methods for physics and engineering, K.F. Riley, M.P. Hobson, S.J. Bence, Cambridge University Press, 2010, ISBN 978-0-521-86153-3</ref><ref>Vector Analysis (2nd Edition), M.R. Spiegel, S. Lipcshutz, D. Spellman, Schaum’s Outlines, McGraw Hill (USA), 2009, ISBN 978-0-07-161545-7</ref>
 
:<math>\oint_{C} (L\, \mathrm{d}x + M\, \mathrm{d}y) = \iint_{D} \left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)\, \mathrm{d}x\, \mathrm{d}y.</math>
 
For [[Curve orientation|positive orientation]], an arrow pointing in the [[counterclockwise]] direction may be drawn in the small circle in the integral symbol.
 
In physics, Green's theorem is mostly used to solve two-dimensional flow integrals, stating that the sum of fluid outflows at any point inside a volume is equal to the total outflow summed about an enclosing area. In [[Euclidean plane geometry|plane geometry]], and in particular, area [[surveying]], Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.
 
 
 
==Relationship to the Stokes theorem==
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