In other words, this:
http://www.math.ucla.edu/~archristian/teaching/32b-w17/week-7.pdf
Is this just a definition because what we really care about is how much the vectors are "pushing" through the surface? Or is it an actual equality?
2026-03-26 03:13:35.1774494815
Why is it that the surface integral of the flux of a vector field is the same as the surface integral of the vector field itself?
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This is just notation: $d\mathbf S = \mathbf n\,dS$. Both sides are computing the flux of $\mathbf F$, i.e., the net amount of $\mathbf F$ pushing outwards across the surface.