Question

can someone help me with curl and divergence, and green's theorem?

Answer 1

yes

Answer 2

I can help with curl and divergence at least

Answer 3

my instructor did some examples and when evaluating an integral, and you use green's theorem, the result for curl and divergence should be the same

Answer 4

but when a problem in the book asks you to find the circulation and flux, the answers are different

Answer 5

they are not supposed to be same in general, your professor probably did a special problem

Answer 6

Divergence results in a scalar, curl in a vector. They generally would not be the same.

Answer 7

i think i am confused, he linked circulation and curl together, and flux and divergence together...i guess just for calculation's sake, he was just referring them to each other to help us remember?

Answer 8

yes, curl is about circulation while divergenc is about flux

Answer 9

ok thank you. i get how to do the calculations but wasn't understanding what i was doing exactly. but i do have a very simple problem that i'm not getting the right answer for. i will post...

Answer 10

F=(x-y)i+(y-x)j. C: square bounded by x=0, x=1, y=0, y=1. use green's theorem to find ccw circulation and outward flux

Answer 11

for flux: M=x-y, N=y-x correct?

Answer 12

divergence at a point =

dU/dx + d V/ dy = 1+ 1=2

Answer 13

yes, that's the answer i'm not getting...i get 0

Answer 14

you have to do \[M_x + N_y\]

Answer 15

i like using double integral so it should be double integral (dV/dx-dM/dy) dxdy

Answer 16

oops, (dV/dx-dU/dy). i'm use to using M and N

Answer 17

in order to use the double integral, the form of the original equation has to change to closed loop integral (Vdy-Udx)

Answer 18

so just integrate the divergence of 2 over your region
\[\int_0^1\int_0^1 2 dx dy\]

Answer 19

then you define V and U. and then it's double integral dU/dx+dV/dy)dxdy. sorry i made a mistake earlier.

Answer 20

well my new U and V are:
U=y-x and V=-x+y

Answer 21

dU/dx= -1, dV/dy= 1. dU/dx+dV/dy=0

Answer 22

i follow this form for other problems which work but not for this.

Answer 23

i must be doing something wrong

Answer 24

Since your field is conservative , the green theorem should turn out be zero

Answer 25

so what i've been doing is green's theorem? ahhhhhh ok so to find flux, it's simply Mx+Ny?

Answer 26

or what is the difference??? what is green's theorem used for?

Answer 27

you don't need to do green theorem if the field is conservative, it is always zero

Answer 28

Green theorem is for line integral on closed path of non-conservative field

Answer 29

i thought it's zero for circulation cuz conservative means the terms will cancel out since they're equal. this is the case for flux too?

Answer 30

I don't think so

Answer 31

i will work out some more probs thanks for your help