Gene see 17

The Setup

D region inDD boundary of D

x y plane ofiented so D ison the left as youmove Tround the bounder

JD susas

iy T

Greenstein If I ix y x 57is smooth on DU OD then

foot.at CEE Fitnaor equivalently

dxted EI FF jet

Examples Cf t L 2g x

Ifoot.atD

z

option 1 do line integralsoption 2 use Green's theorem

c FzTx I d Z

SEE dot i z dA 6

Jdz

2 5 4 F C y 4xty 57o Set.Tr

option 1 do line integral

options use Green s theoremDA 2fy2 Y

C C F C y 4xty5JD C Cz

Cz

GEE TEY 4 1 5

CEE II dA 5 area

5 IT 4 70 T

Cz III for zet ez

F Lt o F Li o

F F Lo 41 7 E F o

3

feat at o

F dot lot

q fSEE oh

E at 4 II Ey HA i

EE Fr

Since JD C C

E die at feet dot

feat at 4 I 3

Useful Facts

D AreaIf

0 OFF I then

SEE oh area g is

Possibilities F Co x

L y o

etc

2 DivergenceFormyGreenistunit outward non al to D

so 7151 7 y

ft a qui

A

A

Taking CF ta then

E rids It E da

Exampled d Cx 312 1 y D I

E ridsµ

F 3 x t eS

y In it x8

J F 3 I 2

I ds 2 area

Z n IT 21T