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Elementary Differential Geometry (Springer Undergraduate Mathematics Series) Paperback – 12 Dec 2000


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Product details

  • Paperback: 332 pages
  • Publisher: Springer; 1st ed. 2001. Corr. 2nd printing edition (12 Dec 2000)
  • Language: English
  • ISBN-10: 1852331526
  • ISBN-13: 978-1852331528
  • Product Dimensions: 17 x 1.8 x 24.4 cm
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Bestsellers Rank: 1,083,927 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

From the reviews: "By the inclusion of 200 exercises with full solutions, this book has become a helpful tool for everyone teaching in its field. Summing up, it is a very good first book on the topic." (Internationale Mathematische Nachrichten, 187, August 2001) "a ]Pressley takes the simplest route with respect to all the technical setup: avoid it all. Instead of covariant derivatives, use derivatives with respect to local coordinates. Use moving frames without mentioning connections. Mention the Christoffel symbols very quickly, but dona (TM)t do very much with them. For the most part, it worksa ]the book does include several versions of the Gauss-Bonnett theorem, allowing the professor to end the course with a bang. All in all, I was quite happy with the book." (MAA Online)

From the Back Cover

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout.

New features of this revised and expanded second edition include:

  • a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
  • Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
  • Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com

Praise for the first edition:

"The text is nicely illustrated, the definitions are well-motivated and the proofs are particularly well-written and student-friendly…this book would make an excellent text for an undergraduate course, but could also well be used for a reading course, or simply read for pleasure."

Australian Mathematical Society Gazette

"Excellent figures supplement a good account, sprinkled with illustrative examples."

Times Higher Education Supplement

--This text refers to an alternate Paperback edition.

Inside This Book (Learn More)
First Sentence
If asked to give an example of a curve, you might give a straight line, say y - 2x = 1 (even though this is not 'curved'!), or a circle, say x2 + y2 = 1, or perhaps a parabola, say y - x2 = 0. Read the first page
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Front Cover | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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Most Helpful Customer Reviews

19 of 20 people found the following review helpful By D. Siska on 4 Nov 2003
Format: Paperback Verified Purchase
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.
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3 of 3 people found the following review helpful By Andrea Bernasconi on 30 Sep 2010
Format: 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 By Yang Chen on 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 By randomlise on 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 By Linda on 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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