I have these two queries regarding the fundamental theorems:(adsbygoogle = window.adsbygoogle || []).push({});

1. The fundamental theorem for divergences is given by:

[tex]\int_v (\nabla.\vec v)d\tau = \oint_s \vec v.d\vec a [/tex]

According to this theorem, the integral of the divergence of a vector over a volume is equal to its surface integral(i.e. the bounding surface).

Could someone interpret this geometrically taking the example of a fluid flow?

2. Fundamental theorem for curls:

[tex]\int_s {(\nabla\times \vec v).d\vec a = \oint_p\vec v.d\vec r [/tex]

Here the intergral of a curl over a patch of area is equal to its primeter i.e. value of the function at the boundary.

How is this interpreted geometrically and how is the ambiguity for the direction of the line integral resolved?

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# Questions on the fundamental theorems

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