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Commerce (2)

# 2013-03-15 tut.pdf

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

Description
G , y,z d S  FndS S 1) Textbook surface, S: g(x,y,z) = 0, z = f(x,y) n  g g ds  1 f  f dxdy2 x y 2) Parameterizing surface, S :r  r ,v  ndS  r ur v ds  r ur v 9.13 #29 Find the flux, FndS  S Through the given surface, F  x,2z, y S :cylinder y z 4,in1 octant, foundedby :x 0,x 3,y 0,z 0 Parameterize the cylinder,  r  x, y,z  x, y, 4 y 2   2 S : z  4 y   0  x  3 0  y  2  ndS  r r dxdy  x y r  1,0,0 x r  0,1, y y 2 4 y i j k rxr y 1 0 0 0 1  y 2 4 y y  0, 2 ,1 4 y y  FndS   x,2z, y  0, 2 ,1 dxdy S S 4 y 3 2 y  2     02z  y dydx,z  4 y 0 0 4 y 2   3 23ydydx 0 0 22 y  3 2 3 32318 0 9.14 #11 Use Stoke’s theorem to evaluate Fdr,whereF  x,x y ,z3 2 and C is the boundary of C z  4 4x  y 2 in the plane z = 0. Fdr  F ndS     C S 2 2 z  0 0  44x  y C :4x  y  4 x2 y2  1 12 22 2 S : x  y 1 4 i j k 2 2 F  x y z  0,0,3x y x x y 2 z ndS
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