Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition

by Manfredo P. Do Carmo

Book Overview

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers...

• Format: Paperback
• Language: English
• ISBN: 0486806995
• ISBN13: 9780486806990
• Release Date: December 2016
• Publisher: Dover Publications
• Length: 528 Pages
• Weight: 1.63 lbs.
• Dimensions: 1.1" x 5.9" x 8.9"

Customer Reviews

Best DG book out there

This book is rather expensive, but when compared to the other books available, it is not a waste of your money. It has plenty of exercises, many of them with answer or hints in the back of the book, and its exposition is broad, very clear and concise. It is hard to tell being a math student, but I think anyone with a solid knowledge in multi-variable calculus (Apostol's book would be perfect) or, better yet, who has taken multi-variable analysis course would find this book accessible. One of the advantages of this book is that it is self-contained, so even though it uses, for example, the inverse function theorem (which is something unavoidable for a DG book), it has an appendix on differentiability and continuity which covers this. The exercises range from easy to very hard, but because of the exposition and of the way the exercises are stated (the tougher ones are many times itemized so that they drive you to the answer) it is rare to find a problem that the reader will not be able to solve upon a little thinking. The greatest advantage of this book is its clear and well-written exposition. It has very few errors, mostly typographical. It covers a lot of topics and its notation is extremely simple and suggestive, which, believe me, is of great help in a DG book. In short, if you want or have to learn differential geometry, save your time and get this book. As another reader very intelligently put it, there is a reason why this is a classic.

There is a reason why it is a classic.

Before talking about the book itself, let me tell you that I am a mathematician, and when I took a differential geometry course and used do Carmo's book, I already knew I wanted to be a mathematician. So, is this a book for mathematicians? Well, yes, but not exclusively. It is certainly written from a mathematician's point-of-view, and it assumes some maturity on the part of the reader. For instance, the exercises contain very little in the way of drill, and are used to enhance the theory (as pointed out by another reviewer). It seems to me that the author believes that mature readers can provide their own `drill' exercises. So, you won't find many exercises asking for you to find pricipal curvatures for this or that surface, and that other as well; exercises in this book have a theoretical flavor to them. This, of course, makes for some hard exercises, and I do remember spending a lot of time over them, often working together with other students taking the same course. The upside is that we learned the material, and thoroughly. Also, the author provided plenty, plenty of examples. The figures are very well drawn and really allow you to see what is going on - even though these days, with powerful computer packages like Maple, Mathematica, Matlab, and others, any student can provide his/her own pictures. But just because now we can use computers, I wouldn't say the text shows signs of age. It is jus as clear now in its exposition of topics and concepts as it was many years ago. So, even though there are many good alternatives in the market, if I had to teach a course now on this subject, or even better, if I were a student now taking this subject, I would certainly have this book at the top of my list of possible textbooks.

Pretty good

Excellent introduction in differential geometry. Beginning with simple and concrete cases, goes gradually into more abstracts idea of intrinsic geometry, and end up with totally abstract idea of abstract surfaces and Riemannian Manifolds. Full of motivations and examples but at the same time focus on the anylytic and mathematical aspects. You only need to know basic calculus and linear algebra so as to understand the text. Introductory knowledge in differential equations is preferrable but it is not a must. However, this book cost only about US$25 in Hong Kong.....

excellent

For the reader with a basic knowledge of the definition of tangent space on a manifold (chapter zero) this book is excellent. I find it one of the true masterpieces of pedagogy among the books I've read. It's a clear exposition of differential geometry from the mathematical standpoint. I think it goes well with hirsch's differential topology and it's always good to get a second perspective on Diff.G from the physics point of view, like Weinberg's Gravitation and Cosmology.

Very clear and concise geometry book suitable for coursework

In a differential geometry course of three students, this text was used instead of the one we began the course with. This book was far and away more organized and paid attention to detail much better than most math books.