Calculus On Manifolds by Michael Spivak

Calculus On Manifolds

This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calc...

Details Calculus On Manifolds

TitleCalculus On Manifolds
Release DateJan 22nd, 1971
PublisherWestview Press
GenreScience, Mathematics, Textbooks, Calculus, Reference, Nonfiction

Reviews Calculus On Manifolds

  • Vincent
    Ehhhhh... reading it now it's good. It's a succinct exposition of everything leading up to Stokes-Cartan, basically.But I already know most of the material. When I originally tried reading it without already knowing differential geometry it was totally opaque.So: good for review, bad for self-study.
  • Ayush Bhat
    A timeless classic.
  • Chris
    a good 5th / 10th review of calculus, for people who want that kind of thing.I like his explanation of where π comes from in the normal distribution, but in the same breath Spivak lets us know that he's an asshole.It's mercifully short. Major points for that in a field where nearly everything you could buy explaining the material is a doorstop or wordy/obtuse in some other way. a good 5th / 10th review of calculus, for people who want that kin...
  • K MacDonald
    It's a classic for a reason, but the treatment of manifolds as subsets of Euclidean space is old-fashioned. That's not bad in itself, it's just not what I'm into.
  • Molidere
    Fairly good exposition, shows its age in parts but strong on problem sets. Among the better treatments of the topic for more able students.
  • Dimitri
    This is one the best instructional books for analysis. It was probably the first real math book I ever read and probably what first made me appreciate the difference between calculations and pure mathematics and the power and beauty of the later.The book is extremely well structured and works towards a definite objective: to derive Stoke's theorem on Euclidean spaces and manifolds. It starts from the very basics - linear algebra and topology - an...
  • Pietro
    Good introduction to the topic.Excellent chapters on basic R^n topology and differentiable calculus, including inverse function and implicit function theorems. The notation is non-classical (but standard) and exceedingly clear. Sadly, the proofs are fairly unmotivated, and one has to work hard to do more than just check their validity. Inverse function, for example, is proved in a way that does not generalize to infinite-dimensional spaces, and o...
  • Brian
    I just read this again because another book was obfuscating exterior calculus for me, where it had formerly been clear. It's Spivak's usual clear (and very brief style) which I love. Stokes' Theorem in half a page!
  • Chu Uyen Dinh Diệp
    My bible