Help finding more info on some theorems [Vector Integrals]

[mishima]

Hi, in Boas Mathematical Methods in the Physical Sciences, Chapter 6 section 11 problem 17 has a list of 7 theorems it calls "Vector Integral Theorems". For example,

$$\int \vec \nabla \times \vec V \ d\tau = \oint \vec n \times \vec V \ d\sigma$$

I understand their derivations from the Divergence and Stoke's theorems, but I was looking for a reference where I could find more information on how these theorems are applied in practical situations of science. Or perhaps they have a more formal name in mathematics I could use to search for more information on my own. Thanks.

 

[Charles Link]

See post 4 of https://www.physicsforums.com/threa...auses-conservative-force.958988/#post-6080947 for a vector integral theorem that leads to Archimedes' principle.

 

[fresh_42]

Here's a small list of theorems about differentiation and integration with their mathematical names:
https://www.physicsforums.com/insights/pantheon-derivatives-part-v/#toggle-id-2
and also a long list of sources.

Stokes theorem and its (many) variations occur all over the place of physics, from electromagnetism to fluid dynamics. It's one of the main tools. And here is an example (problem #4) (+ solution, post #19) of Gauß' divergence theorem: https://www.physicsforums.com/threads/intermediate-math-challenge-august-2018.952511/