Differential Geometry of Curves and Surfaces (Paperback)

~ Manfredo Do Carmo (Author)

Editorial Reviews

Product Description

This volume covers local as well as global differential geometry of curves and surfaces. *Makes extensive use of elementary linear algebra - with emphasis on basic geometrical facts rather than on machinery or random details. *Stresses the basic ideas of differential geometry - regular surfaces, the Gauss map, covariant derivatives. *Includes a large number of fully-worked examples.

Language Notes

Text: English, Portugese (translation)

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Product Details

• Paperback: 503 pages
• Publisher: Prentice Hall; First edition (February 11, 1976)
• Language: English
• ISBN-10: 0132125897
• ISBN-13: 978-0132125895
• Product Dimensions: 9.1 x 6.1 x 1.3 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 3.9 out of 5 stars  See all reviews (18 customer reviews)
• Amazon.com Sales Rank: #209,625 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

25 of 26 people found the following review helpful:

5.0 out of 5 stars Best DG book out there, April 21, 2005

By	matematik - See all my reviews

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.

36 of 40 people found the following review helpful:

5.0 out of 5 stars There is a reason why it is a classic., April 2, 2005

By	a reader - See all my reviews

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.

8 of 8 people found the following review helpful:

4.0 out of 5 stars Excellent introduction to differential geometry, December 2, 1998

By A Customer

I found this book to be a good introduction to differential geometry for undergraduates. All concepts are clearly and concisely developed and explained well. Also, the details of advanced calculus and analysis required for the book are covered very well in appendices. My only reservation is that the problems can be very difficult at first. For someone interested in really exploring and learning differential geometry, however, this is not a problem.