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Green's Theorem and Parameterized Surfaces - Penn Math

green s Thm,ParameterizedSurfacesMath 240 green sTheoremCalculating areaParameterizedSurfacesNormal vectorsTangent planesGreen s Theorem and Parameterized SurfacesMath 240 Calculus IIIS ummer 2013, Session IITuesday, July 2, 2013 green s Thm,ParameterizedSurfacesMath 240 green sTheoremCalculating areaParameterizedSurfacesNormal vectorsTangent planesAgenda1. green s TheoremCalculating area2. Parameterized SurfacesTangent and normal vectorsTangent planesGreen s Thm,ParameterizedSurfacesMath 240 green sTheoremCalculating areaParameterizedSurfacesNormal vectorsTangent planesGreen s theoremTheoremLetDbe a closed, bounded region inR2whose boundaryC= Dconsists of finitely many simple, thatDis on the left as you traverseC. IfF=Mi+Njis aC1vector field onDthen CM dx+N dy= D( N x M y) : OSOcoll50424 ch06 PEAR591-ColleyJuly 28, 201120 s s TheoremGreen s Theorem relates thevector line integralaround a closed curveCinR2to an appropriatedouble integralover the plane regionDbounded byC.

Using Green’s theorem to calculate area Example We can calculate the area of an ellipse using this method. P1: OSO ... (e.g. S, T) to represent the underlying surfaces. Green’s Thm, Parameterized Surfaces Math 240 Green’s Theorem Calculating area Parameterized Surfaces Normal vectors Tangent planes Parameterized surfaces Examples

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