Main Question or Discussion Point
how vector area of a closed surface is zero?
You should explain the context, as well as your mathematical experience. There are varying ways we can answer your question. The best way to answer your question, if I'm understanding it correctly, goes beyond multivariate calculus. What course is this for?how vector area of a closed surface is zero?
I did say the best way, right? The best way, in my opinion, is via the generalized Stokes' Theorem.Mandelbroth can you explain what you mean by goes goes beyond calculus? That is very much a first year calculus question.
Not the Stokes' Thoerem I'm talking about. :tongue:Stokes' Theorem is a fundamental theorem of calculus. Some might say Stokes' Theorem is the fundamental theorem of calculus. Granted as I said above it involves other mathematics (ie algebra and geometry) and is difficult to show in general or for difficult specific examples. Many calculus books have Stokes' theorem towards the end and/or do little with it. A big problem is that calculus is a hodge podge of random techniques and not a unified subject.