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Differential Geometry (Dover Books on Mathematics) [Paperback]

Erwin Kreyszig , Mathematics
4.4 out of 5 stars  See all reviews (21 customer reviews)

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Book Description

June 1, 1991 0486667219 978-0486667218 1st
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.

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Differential Geometry (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics) + Fourier Series (Dover Books on Mathematics)
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Editorial Reviews

Language Notes

Text: English (translation)
Original Language: German

Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 384 pages
  • Publisher: Dover Publications; 1st edition (June 1, 1991)
  • Language: English
  • ISBN-10: 0486667219
  • ISBN-13: 978-0486667218
  • Product Dimensions: 8.5 x 5.4 x 0.7 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (21 customer reviews)
  • Amazon Best Sellers Rank: #60,100 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
120 of 123 people found the following review helpful
5.0 out of 5 stars Agree -- one of the best; elegant; beautiful March 19, 2004
I had been seeking a book on differential geometry for self-study, as a preface to learning general relativity. A seasoned mathematics friend recommended Kreyszig.
So, I waded in, and patiently made my way through every page of the first six chapters, working the problems along the way, at a pace of a few pages per day. Now that the journey is behind me, I can say that I appreciated this book. It compares favorably to some other texts I had tried reading, with less success.
I realize that the author's approach is an old-style classical one, with a reliance on specific coordinate systems and transformations between coordinate systems. To work the problems requires a fair amount of paper and pencil work. Nonetheless, this approach worked well for me. On those occasions when my reading bogged down, inevitably there was a good reason. If I went back carefully, re-read and pondered, doodled on paper, and tried to visualize what Kreyszig was describing, it always worked! The light would soon go on, usually with a pleasurable sense of discovery.
I went back to re-read certain sections of the book to refresh my memory, and realized how elegant the writing is. Crystal clear, right to the heart, and always trustworthy. Everything follows in a gentle persuasive way; there are no jarring leaps or gaps.
Additionally, I had a nice sense of the different flavor brought to the field by the French geometers who made many of the key advances around the turn of the 19th-20th century.
Finally, the summary of key results and equations at the end is very smart and helpful.
Since finishing Kreysig, I did find it helpful to push on and try to grasp these same ideas from the standpoint of one-forms and the coordinate-free approach to tensors.
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55 of 56 people found the following review helpful
This is the sort of math book that you pick up, get something to drink, sit on the couch and read through as you would read a novel. I dont know if its possible to write a simpler or clearer treatment on differential geomerty. But be warned that it is still only "classical". Tensros are treated as objects that tranform in a certain way, rather than studied as general multilinear functions. However, after reading this book, any book on tensors is a breeeze to go through. Well worth having, especially considering the price.
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51 of 57 people found the following review helpful
5.0 out of 5 stars highly recommended August 1, 2002
Format:Paperback|Verified Purchase
This is a wonderfully well written book. If you have a good background in calculus and analytic geometry, you will have no problems with understanding most of the book. (If you don't, you shouldn't be studying differential geometry anyway.) The last couple of chapters are more difficult. Make sure to do the problems after each chapter; they are very well designed to enhance your understanding, and as a huge bonus, their solutions can be found at the end of the book. Forget about those books with a fancy hard cover and cost ten times as much. Buy this book and enjoy!
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27 of 29 people found the following review helpful
3.0 out of 5 stars Old Fashioned October 19, 2007
I read the first couple chapters, trying to learn differential geometry on my own. The approach that this text uses seems a bit dated. Most of the terminology used isn't frequent in modern math texts. If you're an undergrad and interested in the subject, I found that the Springer book by Andrew Pressley is a much nicer option for self-teaching. It has a modern feel to it, and all the exercises have hints or solutions in the back, so you can check your work, or get help when stuck.
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17 of 17 people found the following review helpful
5.0 out of 5 stars Very nice, useful style May 29, 2000
I really like this book. I checked out Manfredo P. Do Carmo'sfrom the library and bought this one, and I prefer this one just oncontent. The concepts are explained in a very approachable style and in a nice order to give you an understanding of diff. geometry as well as what you might use it for.. This is not a math text for just math in my opinion. This is geared for you to use differential geometry. I thought most of the concepts are explained nicely but it doesn't hurt to read another book to get another point of view. One advantage this book has over a number of others is that every answer to the exercises is in the back of the book with a very nice solution.. If you're interested in the subject I think this book is a great deal.
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16 of 17 people found the following review helpful
5.0 out of 5 stars Excellent, but Challenging, Introduction September 2, 2009
Format:Paperback|Verified Purchase
I strongly recommend this book to anyone looking for an introduction to differential geometry. This book restricts its coverage to curves and surfaces in three dimensional Euclidean space, which is highly appropriate for a first book on the subject. Beyond that, nothing is held back. This book includes a self-contained introduction to tensorial methods in chapter two, and tensors are used heavily in the remainder of the book, which makes this book much more suitable for anyone interested in studying general relativity than a book that tries to limp through the same subject matter using only vector methods.

In fact, all of the basic elements that are necessary for the study of general relativity are introduced in this book and in the simplest possible setting.

This book includes exactly 99 figures and a large number of examples which are extremely helpful in understanding the material and as other reviewers have remarked has numerous exercises with full solutions in the back of the book. There is also a collection of formulae at the end which makes for a good review and enhances the book's usefulness as a reference.

The definitions are explicit and the proofs are quite clear. However, the proofs do make references to the theory of differential equations and to results in complex variable theory in a couple of places.

Downsides? While the exposition is excellent, it is a bit terse. Towards the end, there is a lot of flipping back to look at referenced earlier formulas. In addition, small steps are omitted from many derivations. Also, there is a section on the Bergman metric that seemed completely tangential to the rest of the material in the book.

Here's a breakdown of the contents:

Chapter 1 is preliminaries.
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Most Recent Customer Reviews
5.0 out of 5 stars Good book to learn from
The book is readable and informative. I liked the level of data, not overly theoretical, but very understandable. It is a very clear text.
Published 7 months ago by happy joe
5.0 out of 5 stars Thank You !!!
Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature,... Read more
Published 11 months ago by Ed Harris
5.0 out of 5 stars good text on the subject
Differential geometry is concerned with geometric structures on differentiable manifolds, and this book goes into them. Read more
Published 12 months ago by jibber_jabber
5.0 out of 5 stars Beautiful, elegant and comprehensive masterpiece...
I can only agree with all the positive reviewers !

Kreyszig's style in treating such a difficult subject as differential geometry and its associated tensors, is in the... Read more
Published 12 months ago by André Gargoura
5.0 out of 5 stars Surprisingly modern treatment for 1959.
This is a surprisingly modern work when one considers the 1959 publication date. It covers both Riemannian geometry and covariant differentiation, as well as the classical... Read more
Published 12 months ago by Alan U. Kennington
5.0 out of 5 stars GOOD
I wanted to learn differential geometry and I found this book. It is really good as most of the Dover mathematics and physics books are. This is a really good and challenging book.
Published on March 10, 2012 by PersonReviewing
5.0 out of 5 stars a question about 2nd fundamental form mixed tensor
In the book 'differential geometry' by Kreyszig, a result is frequently used
about the principal curvature k1, k2. Read more
Published on May 6, 2009 by F. Liu
5.0 out of 5 stars The best book of Differential Geometry ever written !!!
It is written in a clear cut and concise manner.
It is unlikely that another author will be able to write a better book in Differential Geometry. Read more
Published on February 24, 2008 by Evangelos Lefakis
4.0 out of 5 stars Very well written and informative
If I hadn't seen much worse and somewhat better,

I would have given this five stars.

What it lacks is a good classification of curvature types, a discussion... Read more
Published on May 18, 2007 by Roger Bagula
3.0 out of 5 stars Good book - rather short
It's a good book, but not for an interested reader of popularized science. For the scientist or student it is rather short. Still a good book to have though.
Published on January 16, 2007 by Erik Bijkerk
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