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
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