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Unformatted text preview: F k = F y x F x y So if ~ F = 0, then W = 0 as we already know Chapter7: Fourier series Divergence theorem in two dimensions Consider a vector eld ~ V = V x i + V y j (Notice here V z = 0) If we take Q = V x and P =V y , then Q x P y = V x x + V y y = div ~ V Consider the outward normal n = idx jdy dx 2 + dy 2 = idx jdy ds , and then Pdx + Qdy =V y dx + V x dy = ( V x i + V y j ) ( idy jdx ) = ~ V nds The by Greens theorem in the plane, Z Z A div ~ V dxdy = Z A ~ V nds Chapter7: Fourier series...
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This note was uploaded on 07/30/2011 for the course PHZ 3113 taught by Professor Staff during the Spring '03 term at University of Central Florida.
 Spring '03
 Staff

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