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Commerce (1)
Lecture

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School
McMaster University
Department
Commerce
Course
COMMERCE 2MA3
Professor
Semester
Spring

Description
Green’s theorem: PdxQdy   Q  P xdy C  R x y  Stoke’s theorem: F dr  F d C  R Gauss’s Theorem:   Fds     FdV S D MATLAB: 1. Green’s theorem to perform circulation 2. Triplequad – volume integral Sample Test Problems T2 2012 2) A. Green’s theorem to evaluate: I   x ydx xy dy C 2 2 whereC  x  y  4     I    2  x y  dxdy  R x y     y  x 2dxdy R x  2 rcos y  rsin 0  r  2 0   2 2 2 2 2  0 0r sin  rcos  rdrd 2 2  r sin  44rcos r cos  rdrd 0 0 2 2 2  0 0r 44rcos rdrd 2 2    r 4r 4r cos drd 0 0 5) y dx x dy    x3   y 3 dxdy   R x   y    C   2 2    R3   y dxdy comparison 1 1  3   y 2 dxdy 1 x 1 y 2 2  1 13x  y dydx 7) test 2 2012 c :r t  3cost,2sint ,t [0,2] 1 1  c :r t cost,sint ,t (0,2] 2 2 y x P   2 2 ,Q 2 2 x  y x  y a) Green’s theorem to show I  PdxQdy   PdxQdy. 1
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