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# /sci/ - Science & Math

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Help me out here...what exactly is the difference between these 2 integrals? I'm not asking about the answer, but rather the notation. I've seen this "circle inside an integral" notation a lot, but it's never been explained. Is there actually a difference, or do mathematicians just put that circle there to look "fancy"?

 >> Anonymous Thu Mar 14 22:20:55 2019 No.10468189 File: 39 KB, 880x657, 1535412787471.jpg [View same] [iqdb] [saucenao] [google] [report] >>10468177The circle indicates that the surface fully encloses a volume, i.e, when Gauss's Law for magnetism applies. Top integral always equates to zero. The bottom integral refers to any old surface, doesn't equate to zero in general.
 >> Anonymous Thu Mar 14 22:23:43 2019 No.10468195 File: 53 KB, 520x390, 141794483352.png [View same] [iqdb] [saucenao] [google] [report] >>10468189Ok, that makes sense. Thanks
 >> Anonymous Thu Mar 14 22:26:41 2019 No.10468200 >>10468195yw bby, just please don't use the nasty $\text{d}\mathbf{s}$ when you can write $\text{d}\mathbf{A}$
 >> Anonymous Thu Mar 14 23:02:53 2019 No.10468269 >>10468200I think the ds means its a line integral though? Anyway, the circle means youre integrating along a closed loop.
 >> Anonymous Thu Mar 14 23:08:51 2019 No.10468280 >>10468269The integral is over "S" which I assumed was a surface. In any case, just try to be unambiguous.
 >> Anonymous Thu Mar 14 23:32:30 2019 No.10468325 >>10468280oh yeah you're right, it's over a closed surface. Follow up question (Im not OP): If I integrated the curl of a vector field over a closed surface, will that integral always be zero?
 >> Anonymous Fri Mar 15 00:00:42 2019 No.10468379 >>10468325Yes, that comes from Stoke's theorem. The curl of a vector field integrate over a surface is equal to the circulation of the closed path that bounce the surface. If the surface encloses a volume, that path does not exist.
 >> Anonymous Fri Mar 15 00:05:06 2019 No.10468383 Mew knot surface integral current density dot dee ay
 >> Anonymous Fri Mar 15 00:08:48 2019 No.10468389 Might be helpful to look at their stoke alternative to see kinda what it might imply. This can also be done for gauss if you look at divergenve theorem and it's implications.
 >> Anonymous Fri Mar 15 00:47:09 2019 No.10468463 >>10468177The circle means that you are integrating over a enclosed region. Sort of like a cyclic process in a PV diagram.
 >> Anonymous Fri Mar 15 01:45:41 2019 No.10468537 >>10468177First one's on a loop. Second holds value.
 >> Anonymous Fri Mar 15 01:52:25 2019 No.10468545 the circle means if you cant solve it in less than 10 min you are going to get fucked in your ass
 >> Anonymous Fri Mar 15 01:54:07 2019 No.10468550 >>10468545... no wonder calc turned me gay
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