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Commerce
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COMMERCE 2MA3
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Ambika Badh
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Lecture

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McMaster University

Commerce

COMMERCE 2MA3

Ambika Badh

Spring

Description

Green’s theorem: PdxQdy Q P xdy
C R x y
Stoke’s theorem: F dr F d
C R
Gauss’s Theorem: Fds 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 2dxdy
R
x 2 rcos
y rsin
0 r 2
0 2
2 2 2 2
0 0r sin rcos rdrd
2 2
r sin 44rcos r cos rdrd
0 0
2 2 2
0 0r 44rcos 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 13x 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 PdxQdy PdxQdy.
1

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