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Goodreads helps you keep track of books you want to read. Want to Read saving…. Want to Read Currently Reading Read. Other editions. Enlarge cover. Error rating book. Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject.
Prerequisites are kept to an absolute minimum - nothing beyond first courses in linear algebra and multivariable calculus - and the most direct and straightforward approach is used throughout. New features of this revise Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject.
New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around additional exercises, and a full solutions manual for instructors, available via www.
Get A Copy. Paperback , pages. Published February 14th by Springer first published December 12th More Details Other Editions 3. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Elementary Differential Geometry , please sign up. Be the first to ask a question about Elementary Differential Geometry. Lists with This Book.
This book is not yet featured on Listopia. Community Reviews. Showing Average rating 3. Rating details. More filters. Sort order. Dec 26, Robert rated it really liked it Shelves: science. One of the reasons I wanted to learn differential geometry was to better understand the general theory of relativity. I didn't stick with it long enough to really get it, but this book was a great help and it certainly gave me a good solid idea of what the main concepts where.
If I ever decided to circle back to it this book would definitely be my starting point. I really like the style and in fact the entire "Springer Undergraduate Mathematics Series". It's about as gentle as you could find with al One of the reasons I wanted to learn differential geometry was to better understand the general theory of relativity.
It's about as gentle as you could find with all the things you could typically want, plenty of examples, explanations and exercises with a clear emphasis on key concepts and lots of motivation.
Now this came out a while ago so perhaps there is something newer and better, but on the other hand the basics of complex analysis haven't changed, so it should still be good! I've read this book for an undergraduate differential geometry class. It's a good primer for more advanced topics. It mainly covers curves and surfaces, not manifolds in general; this is OK, but many proofs can't be generalized and, worst of all, don't teach you anything except rote computations.
Unless you have a teacher who explains the ideas behind these proofs, I wouldn't suggest this for independent learning, as it would give a bad idea of what differential geometry is about. The exercises v I've read this book for an undergraduate differential geometry class.
The exercises vary from trivial to very hard. Some are uninteresting, but there are hidden gems. After reading this book you'll want to read more general treatments if interested , like Lee's Introduction to Smooth Manifolds or even Spivak's first 2 volumes if you have the time. A similar book is do Carmo's, which is also the classic standard doesn't necessarily mean better Apr 30, Peter Pete Mcloughlin rated it really liked it Shelves: mathematics , good-things.
I had to read this for my differential geometry class at grad school. It was pretty helpful in getting me through the course. For a difficult subject it was pretty clear. I wish it covered a wider array of topics in the subject I could have used the more material to get through my course. Still what it did cover was explained well. All and all a pretty good textbook.
For anyone taking a differential geometry course for the first time, this book is super helpful. It really does make a lot of the concepts easier to understand. The only minus of this book is that it doesn't go into some of the more advanced topics of differential geometry. However, it helped me survive my course so I highly highly recommend it. Yeong-Chyuan rated it really liked it Jun 20, Stockfish rated it it was amazing Mar 17, Paulo Antonio Liboni Filho rated it really liked it Aug 20, Kaiser rated it really liked it Apr 30, Valentine Svensson rated it really liked it Jul 28, Jesse rated it it was amazing Feb 02, Peter rated it really liked it Nov 04, Marianna rated it really liked it Apr 19, Shelley rated it liked it Apr 29, Benjamin Cecchetto rated it it was amazing Mar 26, Widianto Wisnu rated it really liked it Aug 19, Anaelle rated it it was ok Oct 06, Riley Williams rated it it was ok May 28, Jacob Reinhold rated it liked it Aug 27, Kirill rated it it was ok Jan 08, IQ rated it liked it Feb 03, Cemile Kazimova rated it it was ok Feb 27, Ron rated it really liked it Aug 04, Rafid Al-Humaimidi rated it it was amazing Sep 28, Yuri Popov rated it really liked it Apr 04, Deniz Ahmet rated it did not like it Apr 18, Luca Signorelli rated it really liked it Sep 30, Subhajit Das rated it liked it Dec 07, Hadyan Luthfan rated it really liked it May 23, Cameron King rated it it was ok Aug 10, There are no discussion topics on this book yet.
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Elementary Differential Geometry
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Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
It seems that you're in Germany. We have a dedicated site for Germany. Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject.