the contribution to the outside
must equal sum of contributions inside...
if things cancel inside, will cancel outside.
neighboring points will aid each other?
http://omega.albany.edu:8008/calc3/div-curl-dir/lec5.html
FLUX: going through F dot NORMAL
CIRCULATION: pushing ALONG (F dot TANGENT)
tangent and NORMAL
t: dx/ds (i) + dy/ds (j)
tangent in same direction as path, so x and y's match
normal:
dy/ds (i) - dx/ds (j(
opposite slope: negative inverse. cool.
WHY IS THAT? have a short thing on slope. how the negative inverse.
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what is normal to that?
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form 90 degree angle?
hypotenuses are the SAME. so have.
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if you do the rotation. various ways to see it!
this! so, flip the x and y lengths. AND have to go in the opposite direction (if path going right, tangent going left. if path going up, tangent going down).
so, flip x and y, flip one of the signs.
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not quite tangent... need to invert
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RELATIONSHIP between green's theorem and gauss
flux/area = div
circ/area = curl
div * area = flux (gauss)
curl * area = circulation (green)
http://216.239.33.100/search?q=cache:NXH6eKiTtCUC:planetmath.org/encyclopedia/ProofOfGreensTheorem.html+proof+of+green%27s+theorem&hl=en&ie=UTF-8
