- A revised and expanded second edition which presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject.
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- About this Textbook
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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
- About the authors
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Andrew Pressley is Professor of Mathematics at King’s College London, UK.
- Table of contents (13 chapters)
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Curves in the plane and in space
Pages 1-27
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How much does a curve curve?
Pages 29-54
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Global properties of curves
Pages 55-65
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Surfaces in three dimensions
Pages 67-93
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Examples of surfaces
Pages 95-119
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Table of contents (13 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Elementary Differential Geometry
- Authors
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- A.N. Pressley
- Series Title
- Springer Undergraduate Mathematics Series
- Copyright
- 2010
- Publisher
- Springer-Verlag London
- Copyright Holder
- Springer-Verlag London Limited
- eBook ISBN
- 978-1-84882-891-9
- DOI
- 10.1007/978-1-84882-891-9
- Softcover ISBN
- 978-1-84882-890-2
- Series ISSN
- 1615-2085
- Edition Number
- 2
- Number of Pages
- XII, 474
- Number of Illustrations
- 150 b/w illustrations
- Topics
