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Differential Geometry (Dover Books on Mathematics) [Paperback]

Erwin Kreyszig
4.0 out of 5 stars  See all reviews (4 customer reviews)
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Book Description

17 Mar 2003 Dover Books on Mathematics
An introductory textbook on the differential geometry of curves and surfaces in 3-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 and solutions. Includes 99 illustrations.

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Differential Geometry (Dover Books on Mathematics) + Vector and Tensor Analysis with Applications (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics)
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Product details

  • Paperback: 384 pages
  • Publisher: Dover Publications Inc.; New edition edition (17 Mar 2003)
  • Language: English
  • ISBN-10: 0486667219
  • ISBN-13: 978-0486667218
  • Product Dimensions: 5.4 x 8.5 x 0.7 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 322,529 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Customer Reviews

4.0 out of 5 stars
4.0 out of 5 stars
Most Helpful Customer Reviews
14 of 14 people found the following review helpful
4.0 out of 5 stars A Classic 28 Jan 1998
By A Customer
Erwin Kreyszig, who was a teacher at various Universities in Germany and Canada, originally published this book as a free translation from the German textbook "Differentialgeometrie" in 1959. It is one of the few English books that are able to cover the material in a mainly geometric fashion thus following the German tradition of classical geometry. Erwin Kreyszig develops advanced geometrical concept without a huge mathematical background; however, this also has the effect the people that are used to a more mathematical approach might have a hard time to get used to the style of the book. In my opinion, this book is clearly a must-have for everybody interested in this area.
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1 of 1 people found the following review helpful
By James
A good book for preliminary differential geometry, although the author limits the scope to 2 and 3 dimension, but it is classic and very good description. Read it before you go to more advanced topics.
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5 of 7 people found the following review helpful
2.0 out of 5 stars A hard read 28 April 1997
By A Customer
This is a very difficult book to read. It's translated from German, and it shows. I would advise against this as a primary text.
It might be cheaper than other books, but unless your in Germany, reading the original german, it's not worth it.
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1 of 2 people found the following review helpful
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 same vein as Coxeter's in treating projective and non-Euclidean geometry.

Kreyszig explains a lot and draws illuminating figures, but there is so much to explain that he cannot avoid skipping a few steps, to be filled by a "participative" reader, i.e. you need a good load of pencils and paper... And the reward is thrilling.

I personally found the last chapter on "Special Curves" the most difficult, where Kreyszig decided to avoid figures, adopted a somewhat cryptic tone, turned to an exclusively analytical treatment, hence giving an unclear exposition of concepts such as characteristics, characteristic points, edge of regression and centre surfaces.

All in all, it's probably the best choice available as far as contents, treatment, form and price.
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Amazon.com: 4.4 out of 5 stars  21 reviews
119 of 122 people found the following review helpful
5.0 out of 5 stars Agree -- one of the best; elegant; beautiful 20 Mar 2004
By Paul J. Papanek - Published on Amazon.com
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. But I'm not sorry I came at the subject this way first.
I do recommend this book, and think that a beginner needs only a moderate amount of stamina and patience here.
A postscript -- the book is also beautiful. I like that in a math book.
54 of 55 people found the following review helpful
5.0 out of 5 stars By far the best intro to classical differential geometry 24 May 2001
By Muraari Vasudevan - Published on Amazon.com
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.
51 of 57 people found the following review helpful
5.0 out of 5 stars highly recommended 1 Aug 2002
By ubuntu - Published on Amazon.com
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!
26 of 28 people found the following review helpful
3.0 out of 5 stars Old Fashioned 19 Oct 2007
By From Detroit - Published on Amazon.com
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.
17 of 17 people found the following review helpful
5.0 out of 5 stars Very nice, useful style 30 May 2000
By J. Carlson - Published on Amazon.com
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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