基本信息出版社：Springer
页码：332 页
出版日期：2002年09月
ISBN：1852331526
International Standard Book Number：1852331526
条形码：9781852331528
EAN：9781852331528
版本：Corrected
装帧：平装
正文语种：英语
丛书名：Springer Undergraduate Mathematics Series

内容简介 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 them 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 prove an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject.
作者简介

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

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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)

目录
Curves in the Plane and in Space.- How Much Does a Curve Curve?- Global Properties of Curves.- Surfaces in Three Dimensions.- The First Fundamental Form.- Curvature of Surfaces.- Gaussian Curvature and the Gauss Map.- Geodesics.- Minimal Surfaces.- Gauss's Theorema Egregium.- The Gauss-Bonnet Theorem.- Solutions.- Index
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