As far as I can tell ya (and I can’t really tell, since I’m still reading) Vector Analysis is all about a calculus involving vectors and their various properties (various Products and formulae) that has clear analogues to the regular ol’ Calculus that we all know and love.
I’m still reading up on this topic, and learning all kinds of cool weird results that don’t make sense till you think for a second and go “oh fuck, I see!”
If you wanted to know what books I’m reading to learn more about this topic, the Feynman Lectures on Physics has some good stuff, and this book that’s in front of me rn: “Theoretical Physics” by Georg Joos, 3rd Edition. Good stuff.
Check in later, I’ll have more topics posted and linked to from here.
Catch y’all later!