Overview
- Taking a unique approach to the subject, the book allows the reader to see some amazing results of claissical differential geometry using nothing more than basic calculus
- The technical definitions are kept simple and there are many examples
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
Keywords
About this book
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, and with trying to answer them using calculus techniques. 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 while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there.
The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject.
Andrew Pressley is Professor of Mathematics at King’s College London, UK.
The Springer Undergraduate Mathematics Series (SUMS) is a series designed for undergraduates in mathematics and the sciences worldwide. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully worked solutions.
Reviews
From the 1st edition 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)
"…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 don’t do very much with them. For the most part, it works…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)
Authors and Affiliations
About the author
Andrew Pressley is Professor of Mathematics at King’s College London, UK.
Bibliographic Information
Book Title: Elementary Differential Geometry
Authors: Andrew Pressley
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-1-4471-3696-5
Publisher: Springer London
-
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London 2001
eBook ISBN: 978-1-4471-3696-5Published: 11 November 2013
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: IX, 332
Number of Illustrations: 74 b/w illustrations
Topics: Differential Geometry