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Luigi0210
 one year ago
Stoke's Theorem:
Luigi0210
 one year ago
Stoke's Theorem:

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Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.1Use Stoke's theorem to solve \(\large \int_{C} F~ dr \) where F(x,y,z) =<xz, 2xy, 3xy> and C is the boundary of part of plane 3x+y+z=3 in the first octant.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.4I had trouble understanding Stoke's and I've always wanted to go over it again and learn it a better way...mhm lets see if we can figure this out \[\int\limits_{C} \vec F \cdot d \vec r = \int\limits \int\limits_S curl \vec F \cdot d \vec S\] right

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.1Not sure, I'm a bit confused because of these: http://prntscr.com/7t4ipd

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.4Yes, you should understand the notation and what it means then I think it would be more clear hmm. I'm thinking we can pick any surface S with the boundary C.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.4This would be a nice question to observe haha, I sort of have an idea, but I think @dan815 @ganeshie8 @Empty would be better in teaching this, plus I can learn from them to xD.

dan815
 one year ago
Best ResponseYou've already chosen the best response.3we gotta see those intersections with xz yz and xy plane

dan815
 one year ago
Best ResponseYou've already chosen the best response.3we can see the 3 intersections with the 3 axis by setting x,y=0 y,z=0 x,z=0

dan815
 one year ago
Best ResponseYou've already chosen the best response.3thre u go not integrate over that surface area

dan815
 one year ago
Best ResponseYou've already chosen the best response.3F is a function of x,y so we want to refine our new surface area in terms of x and y too

dan815
 one year ago
Best ResponseYou've already chosen the best response.3i dont remember that exactly, u can work it out though

dan815
 one year ago
Best ResponseYou've already chosen the best response.3there fore ds= fx X fy dxdy

dan815
 one year ago
Best ResponseYou've already chosen the best response.3your domain will be that triangle

dan815
 one year ago
Best ResponseYou've already chosen the best response.3finally note how Gx and Gy vectors are formed

dan815
 one year ago
Best ResponseYou've already chosen the best response.3and finally u can look up a proof for why the determinant of the 2 vectors gives you the area composed by them

dan815
 one year ago
Best ResponseYou've already chosen the best response.3but for starters u can take the formula at face cvalue how u dot v = UV cos theta and U X V = UV sin theta < area

dan815
 one year ago
Best ResponseYou've already chosen the best response.3as V sin theta is the height

dan815
 one year ago
Best ResponseYou've already chosen the best response.3so that would the formula for the area of a parallelogram
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