Elementary Differential Geometry, Revised 2nd Edition 2nd Edition by Barrett O’Neill (PDF)

Description

Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces.The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.Over 36,000 copies sold worldwideAccessible, practical yet rigorous approach to a complex topic–also suitable for self-studyExtensive update of appendices on Mathematica and Maple software packagesThorough streamlining of second edition’s numbering systemFuller information on solutions to odd-numbered problemsAdditional exercises and hints guide students in using the latest computer modeling tools

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Perfect introduction to the field of differential geometry. I found this book to be exactly what I needed to build my fundamental knowledge of the subject, especially in terms of computations. Very accessible for undergrads.For a more intuitive companion book, I strongly recommend John McCleary’s “Geometry from a Differentiable Point of View” (which I picked up at Powell’s annex building in Portland, OR). I’ve used both books together and felt that the two books compliment each other very well. (Edit: I say McCleary’s book is more intuitive because he builds up differential geometry from the more classical roots of geometry. You won’t lose any rigour from McCleary’s book, though I feel O’Neill does a better job of explicitly building up the rigour of differential geometry in a more modern context).What O’Neill’s book lacks in set-up and motivation, McCleary’s book more than makes up for. What McCleary’s book lacks in computational methodology and rigour, O’Neill’s book more than makes up for. O’Neill also includes many more exercises for practice than McCleary. Both books have quality exercises, but O’Neill also has sheer quantity working for his text.If you’re feeling passionate about getting into the subject of differential geometry, and modern geometry in general, I cannot highly recommend using both books together enough.

⭐I really liked this book. I read it to review some basic concepts in differential geometry. I found the book very concise (but not too terse) and well organized. It is less advanced than the book by do Carmo and this book has a slightly more computational approach in some sections. However, this is good because of the intended audience. Some books start off right away with manifolds and a chapter full of definitions such as derivations and p-forms and such. I think this book does an excellent job preparing the reader for more advanced books on differential geometry by starting with Euclidean space and exposing the reader to the important ideas that make the emergence of the more abstract idea of manifolds very logical. The reader should find differential geometry and/or introduction to manifolds books by do Carmo, Frankel (more oriented towards physicists/engineers), Loring Tu (less intense than John Lee’s book but more “mathy” than Frankel), etc. very readable after O’Neill.

⭐I like the attention to detail and the numerous examples. The exercises and tips on the use of Mathematica to generate images of curves and surfaces turned what could be a dry subject into something exciting. On the down side, the hyperlinks to prior exercises, lemmas, theorems, etc. often go to the wrong chapter. This is a small price to pay.I am using this product to prepare for the study of general relativity.

⭐Good subject and content, not to difficult to grasp. However, book falls apart quite easily after a couple of readings

⭐This is an excellent introduction to differential geometry. It has numerous exercises with answers in the book which make it appropriate for self study. All that is needed is some familiarity with linear algebra and vector calculus, but even this book is self contained enough that even without exposure to either of those it is still approachable. I think that after working through this book a student will be well prepared to take on a more advanced book like Riemannian Geometry by do Carmo or Differential Geometry by Kuhnel.

⭐Page 1 appears after pg 42. The fact that the page is nearly randomly placed within the book, and that’s only after skimming the first chapter, is appalling. I should not have to pay $80 for a book, and then pages are not even in order.

⭐This book is not like new, but very new. The package is very, very good! Thank you!

⭐I enjoyed this course in college. The book was difficult in areas, but I think it covers the subject area well.

⭐Despite the fact that it’s a hardcover book, the overall quality it’s very bad. Bad paper quality, bad ink quality, very bad images resolutions. I guess Academic Press is about to leave this business of selling books.The book’s contents are O.K.

⭐ok

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