Green's Theorem Power Point Notes

Green's Theorem Power Point Notes - applied to every line...

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Slide 1 Calculus III Section 14.4 Green’s Theorem Slide 2 Definitions A curve is simple if it does not cross itself. A region is simply connected if its boundary is one simple closed curve. Examples Slide 3 Green’s Theorem Let R be a simply connected region with a piecewise smooth boundary C, oriented counterclockwise (that is, C is traversed once so that the region R always lies to the left ). If M and N have continuous partial derivatives in an open region containing R, then ∫∫ - = + C R dA y M x N Ndy Mdx
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Slide 4 Example 14.4, #10 Note: Green’s Theorem cannot be
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Unformatted text preview: applied to every line integral. However, when it does apply it can save time. Slide 5 Line Integral for Area If R is a plane region bounded by a piecewise smooth simple closed curve C, oriented counterclockwise, then the area of R is given by ydx xdy A C-= 2 1 Slide 6 Example 14.4, #25 Slide 7 Vector Forms of Greens Theorem ( 29 = - = + R R C dA k F curl dA y M x N dy N dx M dA F div ds N F R C =...
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This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

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Green's Theorem Power Point Notes - applied to every line...

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