Can anyone give me a very brief summary of what vector calculus means? I know this sounds like a "specify what you mean" type question, but I hope it isn't. Let me explain further. I know all the equations, how to find line integrals, what Green's theorem is, etc. but I don't exactly know what they mean (I have an idea but i'm just not as set with it as I am with single/multivariable calculus). When I find an integral with Green's theorem, what am I finding (generally)? What about line integrals (mass if you have a density if I recall correctly)?(adsbygoogle = window.adsbygoogle || []).push({});

Also I have about 5-6 ways of writing what seems to be finding the same thing, ie the integral of F(r(t))*r'(t) = the integral of F*T ds (where * is dot product), etc. Are they just the same thing? Is independence of path just a special case of sorts for finding line integrals in vector fields?

Any help is appreciated

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# Vector Calculus

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