Lecture15_Green - Green's Theorem There is an important...

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12 Green’s Theorem ± Most of the functions that engineers deal with satisfy these conditions. ± There is an important relationship between line and double integrals expressed in terms of Green’s theorem in the plane. ± If the functions P(x,y) and Q(x,y) and their derivatives are finite and continuous functions in a region R and on its boundary, the closed curve C, then [] ∫∫ = + R C dxdy y P x Q Qdy Pdx ± The direction of integration along C is such that the region R is always to the left ± The theorem is a special case of two important theorems: Divergence and Stokes Theorems (to be discussed)
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13 Example (P9-12.1) [] ∫∫ = + R C dxdy y P x Q Qdy Pdx Verify Green’s theorem: P = x - y, & Q = xy. C is the triangle: (0,0), (1,0), (1,3) x=1
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This note was uploaded on 05/09/2010 for the course ENGR 233 taught by Professor S.samuelli during the Winter '10 term at Concordia Canada.

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Lecture15_Green - Green's Theorem There is an important...

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