Elementary Differential Geometry Barrett O'neill Pdf 17

I've reviewed a few books online for the MAA. When I learned undergraduate differential geometry with John Terrilla, we used O'Neill and Do Carmo and both are very good indeed. O'Neill is a bit more complete, but be warned - the use of differential forms can be a little unnerving to undergraduates. That being said, there's probably no gentler place to learn about them. I do think it's important to study a modern version of classical DG first (i.e. curves and surfaces in R3, emphazing vector space properties) before going anywhere near forms or manifolds - linear algebra should be automatic for any student learning differential geometry at any level.

If you are looking for text that is good for an undergraduate course in differential geometry, I would suggest Differential Geometry of Curves and Surfaces by Banchoff and Lovett. See -Geometry-Curves-Surfaces-Banchoff/dp/1568814569/ref=sr_1_3?ie=UTF8&qid=1317835776&sr=8-3 . It was published in 2010 so did not show up on this earlier.

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Did someone already mention Geometry of differential forms by Do Carmo?. It is the 2-dimensional version of Riemannian Geometry by the same author. Quite nice since one can see how differential forms work in a riemannian geometry point of view. Here the author works out everything in 2 dimensional manifolds by using definitions that latter on He is going to generalize for high dimensions.

What are the books in Differential Geometry with a good collection of problems? At present I am having John M. Lee's Riemannian Manifolds, Kobayashi & Nomizu's Foundations of Differential Geometry. I particularly like Dieudonne's books in Analysis as well as books like Alexander Kirillov's Functional Analysis. To be precise, the books that have a huge number of exercises. The books I mentioned are definitely not of that category. Can anyone please suggest differential geometry books that gives a lot of exercises?

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