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4.5
Yes, that headline is somewhat contradictory. Allow me to explain.As an undergraduate math major decades ago, I took the standard multivariable calculus courses, which were somewhat less rigorous treatments culminating in the fundamental theorem for line integrals, Gauss' divergence theorem, and Green's/Stokes' theorems. Then I took the typical real analysis courses, which were a rigorous treatment of analysis on R (with some complex analysis). But, somehow, I ended up never taking any rigorous coursework on multivariable analysis.Since it's been so long, I was wary of trying to wade into Spivak or Rudin, especially without the benefit of a formal course. I tried Vector Calculus by Baxandall and Liebeck, but had some difficulties with some of the notation (possibly Britishisms? not sure) in differential calculus, and was also hoping for a "novice introduction" (if there is such a thing) to differential forms.So, for the reviews that complained that Munkres is too pedantic, that's exactly what I was looking for, and so far, I've been quite pleased. Being a much shorter book, it obviously goes much faster than Baxandall and Liebeck, but I've also appreciated the detail that he puts in to a small space. (I also slightly prefer his writing style over Baxandall/Liebeck.)I'm still working my way through, so I suspect I'll have to slow down significantly once I hit manifolds (something Munkres touches on in the Preface; he says the latter half of the book is more sophisticated). But I am hoping that the detail combined with somewhat more familiar notation will help ease understanding.
