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Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
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Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus

4.25  ·  Rating details ·  294 ratings  ·  13 reviews
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 ...more
Paperback, 160 pages
Published January 22nd 1971 by Westview Press (first published 1965)
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Brandon Meredith
Sep 01, 2010 marked it as to-read
Shelves: put-aside
What yo mamma never told you you could do with calculus!
Gylfi
Mjög falleg bók. Lestur minn var engan veginn fullnægjandi enda er hún oft sögð erfiðasta kennslubókin í stærðfræði ætluð grunnnemum en ég naut hennar þó. Kem vonandi aftur að henni eftir ár eða tvö.

(las hana ekki á spænsku, útgáfan sem ég las er ekki á goodreads og kápan á nýju útgáfunni þykir mér svo ljót)
Vincent
Oct 22, 2019 rated it liked it
Shelves: mathematics
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
Dec 06, 2017 rated it it was amazing
A timeless classic.
DJ
Feb 04, 2011 marked it as to-read
Shelves: math
recommended by one of the Columbia theory applicants as a "must-read" in physics/math
Chris
Dec 31, 2018 rated it liked it
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.
...more
K MacDonald
Apr 26, 2019 rated it liked it
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
Jun 30, 2019 rated it really liked it
Shelves: maths, non-fiction, study
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
Jun 15, 2007 rated it it was amazing
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 - and works up to the goal by deriving multi-variate
...more
Pietro
Sep 04, 2007 rated it liked it
Shelves: mathematics
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 one is at a loss to find an alternate proof.

The
...more
Brian
Apr 05, 2010 rated it it was amazing
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
Aug 08, 2016 rated it it was amazing
My bible <3
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Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. He is the author of the five-volume Comprehensive Introduction to Differential Geometry. He received a Ph.D. from Princeton University under the supervision of John Milnor in 1964.

His book Calculus takes a very rigorous and theoretical approach to
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