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Need help in proof of 2 very important theorems!

Well, if anyone starts learning electricity and magnetism(or in particular Vol.2 of Feynman lectures, as that is my site of learning), one always gets these 2 important theorems for sure -

\[\displaystyle \text{1. Gauss' Theorem -} \int_{S}{C.n dS} = \int_{V}{\nabla.C dV}\] such that C is any vector, S area, V volume and \(\nabla.C\) is the divergence of C.

\[\displaystyle \text{2. Stokes' Theorem -} \int_{line}{C ds} = \int_{S}{{(\nabla \times C)}_{n} dS}\] such that C is any vector, \(\int_{line}{}\) means line integral, \(\nabla \times C\) is curl of C.

Now, I want proofs of both these strong theorems. Please if anyone can help me in any way, care to do so. Thanks in anticipation!

Note by Kartik Sharma
1 year, 9 months ago

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Do you still need help with it or have you found out a way to solve it yourself ? Azhaghu Roopesh M · 1 year, 9 months ago

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@Azhaghu Roopesh M Still need! That's why I have shared the set! Check out others also! Well, I have one proof with some assumptions but I want a 'proper mathematical proof'! Kartik Sharma · 1 year, 9 months ago

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@Kartik Sharma Good problems should be challenging but not tedious. Unrelated to this thread but just a reminder/word of advice. Jake Lai · 1 year, 9 months ago

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@Jake Lai Oh yeah! That's right. I was thinking of that while sharing them but then I thought there isn't any 'tedious' type of thing in mathematics. If calculations is what you are saying, then you have a calculator, I wouldn't mind. Kartik Sharma · 1 year, 9 months ago

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