I Asymmetry in Stokes' theorem & Gauss' theorem

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Stokes' theorem connects closed line integrals to surface integrals over any surface bounded by the curve, while Gauss' theorem relates closed surface integrals to volume integrals within a unique volume. The discussion highlights the asymmetry between these two theorems, attributing it to the dimensional differences; a closed curve can enclose multiple 2D surfaces, whereas a closed surface typically encloses a unique 3D volume. Some participants argue that this perceived asymmetry may not exist if one considers non-simple surfaces or curves that intersect themselves. The conversation also touches on the implications of topology in understanding these relationships, suggesting that the nature of the surfaces and volumes involved plays a crucial role. Overall, the discussion emphasizes the complexity of applying these theorems in various contexts and the need for precise definitions.
  • #31
PeroK said:
Also, this is the third post on the subject. It was already answered in the threads mentioned in post #12 above. Here, for example, is a good answer to the question:

https://www.physicsforums.com/threa...d-by-the-same-curve-in-stokes-theorem.989709/
@feynman1 You apparently got your answer. If you still have problems, then we may have communication problems, which is not unlikely since we are restricted to verbal only communication.

My suggestion is: Quote the original theorem you have a question to. Famous theorems are sometimes differently phrased. It looks as if you have trouble to understand the conditions of Gauß law. So the more precise you ask, the better the answers will be.
 
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