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19 of 20 people found the following review helpful
4.0 out of 5 stars Very good textbook, clearly aimed at undergraduates., 4 Nov 2003
By 
D. Siska "dsiska" (London,) - See all my reviews
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This review is from: Elementary Differential Geometry (Springer Undergraduate Mathematics Series) (Paperback)
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".
It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.
The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.
What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.
Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.
So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.
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3 of 3 people found the following review helpful
5.0 out of 5 stars Circumference on a surface and Differential Geometry, 30 Sep 2010
By 
Andrea Bernasconi "ABDG" (Balerna Switzerland) - See all my reviews
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This review is from: Elementary Differential Geometry (Springer Undergraduate Mathematics Series) (Paperback)
Inspired by the Feynman Lectures on Physics (II page 42-4), I decided to calculate the circumference of a "circle" on a saddle-shaped surface. Since this problem is related to the mathematics of geodesic, after inspection at Amazon, I decided to buy the book Elementary Differential Geometry by A.N. Pressley. This book is clear, enlightening, attractive and written "physicist-friendly". It accompanies the beginner from the concept of curve to the Gauss-Bonnet theorem connecting surface curvature to surface topology. In particular, I realized that geodesic equations are non-linear and usually difficult or impossible to solve explicitly. I recommend this book.
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0 of 1 people found the following review helpful
5.0 out of 5 stars A book offers good introduction, 19 Dec 2013
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Just as its name, this book is for undergraduate level, so one can easily catch the contents without feel so struggling. There are many graphs for reader to build better understanding, and this is quite helpful if one feel so tricky to the formulas.
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0 of 1 people found the following review helpful
4.0 out of 5 stars Clear and concise., 4 July 2013
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This book explained all the necessary concepts very well, it gives lots of examples and illustrations to help the reader.
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0 of 3 people found the following review helpful
4.0 out of 5 stars Good, if a bit elementary, 17 April 2012
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This is a good book on the subject if you have never encountered differential geometry before and want an easy, slow-paced introduction. My only criticism would be that it is perhaps a bit too slow-paced if you are impatient. The same ground could have been covered, probably just as well, in half as many pages. Still, the author did include "elementary" in the title, and what he advertises is what he delivers.
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