Elementary Differential Geometry

Elementary Differential Geometry

Paperback Springer Undergraduate Mathematics

By (author) Andrew Pressley

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  • Publisher: Springer London Ltd
  • Format: Paperback | 486 pages
  • Dimensions: 156mm x 234mm x 24mm | 679g
  • Publication date: 1 September 2010
  • Publication City/Country: England
  • ISBN 10: 184882890X
  • ISBN 13: 9781848828902
  • Edition: 2, Revised
  • Edition statement: 2nd ed. 2012
  • Illustrations note: 150 black & white illustrations, biography
  • Sales rank: 147,113

Product description

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

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Author information

Andrew Pressley is Professor of Mathematics at King's College London, UK.

Review quote

From the reviews of the second edition: "Pressley's gives you a very comprehensible and down to earth introduction to differential geometry. ... the book contains lots of examples and fully worked answers to all exercises, which makes it perfect for self-study. ... This book will also appeal to those who want to learn on their own, as every problem has a hint/solution in the back. If you want a very general introduction of Differential Geometry, this is the book to start." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013) "I am very happy to report that the new edition of Pressley's Elementary Differential Geometry is an even better book than the first edition ... . full solutions to all problems given in an appendix. ... Most of the problems are in the book and have solutions in the back. ... The upshot is that this is still an excellent book and still my first choice for an undergraduate introduction to differential geometry." (Fernando Q. Gouvea, The Mathematical Association of America, May, 2010)

Back cover copy

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

Table of contents

Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature of surfaces.- Gaussian, mean and principal curvatures.- Geodesics.- Gauss' Theorema Egregium.- Hyperbolic geometry.- Minimal surfaces.- The Gauss-Bonnet theorem.