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Differential Geometry of Curves and Surfaces [Paperback]

Manfredo P. Do Carmo
3.9 out of 5 stars  See all reviews (28 customer reviews)

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Book Description

February 11, 1976 0132125897 978-0132125895 1
This volume covers local as well as global differential geometry of curves and surfaces.

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Differential Geometry of Curves and Surfaces + Riemannian Geometry + A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition
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Editorial Reviews

Language Notes

Text: English, Portugese (translation)

From the Publisher

This volume covers local as well as global differential geometry of curves and surfaces.

Product Details

  • Paperback: 503 pages
  • Publisher: Pearson; 1 edition (February 11, 1976)
  • Language: English
  • ISBN-10: 0132125897
  • ISBN-13: 978-0132125895
  • Product Dimensions: 9.3 x 6.3 x 1 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (28 customer reviews)
  • Amazon Best Sellers Rank: #91,756 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
51 of 53 people found the following review helpful
5.0 out of 5 stars Best DG book out there April 21, 2005
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.
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50 of 54 people found the following review helpful
5.0 out of 5 stars There is a reason why it is a classic. April 2, 2005
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.
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31 of 34 people found the following review helpful
An earlier review said this book has few errors, and even then only typographical ones. Are we talking about the same book? The text is pockmarked - nay, cratered - with scads of dire gaffes. The skeptical empiricist should go to Google and enter these keywords: bjorn carmo errata. The first hit will be a link to a 7-page pdf file a U.C. Berkeley professor and his students created a few years ago which compiles errata they turned up. Seven full pages, and they only covered a third of the text! A sample item in the list: "p. 97, definition of domain: It is not clear whether the boundary is the boundary as a subset of R^3 or the boundary as a subset of S. Either way, we run into trouble..." The Heine-Borel theorem on page 124 is so botched up it's beyond repair, and even the basic definition of what it means for a function to be continuous on a set is faulty (p. 123).

The author claims a student should be able to hack the material with "only the most basic concepts" from linear algebra and multivariable calculus. Largely but not entirely true. For example, you better be up to speed on linear mappings defined by NON-square matrices - something no undergraduate-level linear algebra book in my library discusses (though I only possess a handful). Many of those tidy little results for linear operators from R^n into R^n you might know from Linear Algebra 301 become worthless when one of those n's becomes an m. I don't really fault the author for this, but anyone thinking about acquiring this text should know it is not by any stretch "self-contained" as one previous reviewer stated.

The biggest irritant with this text is the constant abuse of notation.
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16 of 20 people found the following review helpful
5.0 out of 5 stars excellent April 23, 2001
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.
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Most Recent Customer Reviews
5.0 out of 5 stars Great Graphs
It is a surprise to me to see the very helpful graphs in this book (remember that the book was published in 1970s).
Published 2 months ago by ADAM
4.0 out of 5 stars Fairly good
Pretty good differential geometry introduction. Easier to read than Spivaks classics, albeit at a lower level. Read more
Published 3 months ago by dclark
5.0 out of 5 stars Fantastic
Best introduction to differential geometry. It's clear and well motivated. The progression is well-thoughtout and pedagogical (although I would recommend doing the two chapter on... Read more
Published 12 months ago by Olive Greene
3.0 out of 5 stars Good content; terrible printing
The printing quality to price ratio for this book is appalling. If I only graded this on content it might squeak by with 5 stars. Read more
Published 15 months ago by Andrew Duncan
1.0 out of 5 stars No motivation
This book is one of the poor math books I have come across. The major issue I had using this book is that it provides very little motivation. Read more
Published 16 months ago by user17762
3.0 out of 5 stars book cover not too good; otherwise great.
The printing of the cover is not as clear as normal books. Some scratches on corners.
I like it otherwise.
Published 17 months ago by taro
5.0 out of 5 stars Clear
The book uses standard notation, so it is easy to follow. It works primarily in 3 real dimensions rather than Space Time or a more abstract space. Read more
Published on June 30, 2012 by Gordon F. Diss
5.0 out of 5 stars Highly recommend
I really like Do Carmo's style of presentation, I can just imagine what type of lecturer he was. Though there are other books on the subject that are more concise a/o cover more... Read more
Published on October 16, 2010 by mathematician-philosopher
5.0 out of 5 stars A must of its kind
This is an excellent book. Anyone who wants to have a global view on classical differential geometry must have it (and read it!). Read more
Published on April 27, 2010 by I. D. PLATIS
2.0 out of 5 stars Good content, cheaply manufactured
The content is well-presented and instructive. My main gripe with this book is the very low quality paperback edition. Read more
Published on February 21, 2010 by W. Jakob
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