Analysis on Manifolds

by James R. Munkres

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

Genres: Mathematics, Textbooks, Geometry, Nonfiction, Technology, Engineering

380 pages, Paperback

First published January 1, 1991

Reviews

[Santaraksita · Rating 4 out of 5]

It is quite unfortunate that this little gem is not better known. Despite its title, this is really an 'Advanced calculus' text and can be read easily by someone with a semester's worth of analysis (at the level of baby Rudin). Fortunately, Munkres is a very thorough expositor -- his proofs rarely have 't's uncrossed or 'i's undotted -- and that makes his texts ideal for self-study at the undergrad level. The only downside to the book is that the exercises are not challenging.

[Alan · Rating 4 out of 5]

Probablemente hasta antes de entrar al tema de las variedades este era mi nueva recomendación para el tema.

Al llegar a variedades, que es medio libro y el propósito principal, creo que volví a preferir «Calculus on manifolds» —obra la cual es claramente su principal competencia—.

Nadie vence a Spivak en geometría diferencial :l

[Harry · Rating 2 out of 5]

The pedagogical approach of this book is VERY questionable. The typical audience for this text is probably mathematically mature enough to approach general manifolds instead of restricting to euclidean space. That being said, I am grateful to Munkres for taking a distinct approach to manifold theory focused on applications.

I prefer the proof of the Inverse Function Theorem via successive approximation, but the proof by the Contraction Mapping Theorem is fine. Munkres' definition of differential forms on manifolds feels a bit hand-wavy. I would expect a book on multivariable calculus to better emphasize Taylor's Theorem.

Overall, I found Munkres' pacing and level of detail quite satisfactory. Although abundant, the problems are mostly on the easier side.

[Shai S. · Rating 3 out of 5]

For MAT322. The font is funky and the pages are small. I thought the proofs were kinda easy to follow, and the examples were manageable. Lots of reading through the book for this class since I was always behind lectures.

[Turgut · Rating 5 out of 5]

Manifolds ...

[C. Hinsley · Rating 2 out of 5]

This book is so, so dry. Just read Spivak or Shifrin instead.

[Ryan Wans · Rating 5 out of 5]

Started on chapter 4 and moved onwards. Was a great introduction.