B What is this equation called and why is it regarded as beautiful?

[Physics Slayer]

$$\int_S dw = \int_{dS}w$$
Saw a few seniors talking about this equation, I don't know what it is called hence I can't google it, It doesn't look very correct as the RHS integral doesn't have a differential and both the limits look incomplete.
(they looked like they knew what they were talking about)

where can I study this equation and see its beauty?

also it didn't show up when searching for the most elegant/beautiful math equations, so maybe it isn't that significant?

 

[Office_Shredder]

https://en.m.wikipedia.org/wiki/Generalized_Stokes_theorem

This is what you're looking for.

 

[fresh_42]

It is the fundamental theorem of calculus: In order to know what is going on inside a region, it is sufficient to know what's going on at the boundary.

Personal remark: It Seems mathematicians found the holographic principle 328 years prior to physicists (James Gregory 1667 vs. Leonard Susskind 1997), .

 

[ohwilleke]

FWIW, it is less beautiful once you add all the terms, conditions and definitions to it in fine print (smoothness, continuity, domain of permissible values, etc.), like a great sale on a new car with a half a page of fine print attached.

 

[robphy]

Possibly enlightening...
Robert Ghrist's CalcBLUE 4 : Ch. 18 : See 18.1 - 18.5


https://www2.math.upenn.edu/~ghrist/BLUE.html#VOL4