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Elementary Differential Geometry

Elementary Differential Geometry - 01 edition

ISBN13: 978-1852331528

Cover of Elementary Differential Geometry 01 (ISBN 978-1852331528)
ISBN13: 978-1852331528
ISBN10: 1852331526
Cover type:
Edition/Copyright: 01
Publisher: Springer-Verlag New York
Published: 2001
International: No

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Elementary Differential Geometry - 01 edition

ISBN13: 978-1852331528

Andrew Pressley

ISBN13: 978-1852331528
ISBN10: 1852331526
Cover type:
Edition/Copyright: 01
Publisher: Springer-Verlag New York

Published: 2001
International: No
Summary

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.

Author Bio

Pressley, Andrew : King's College

Table of Contents

1. Curves in the Plane and in Space.
2. How much does a Curve Curve?
3. Global Properties of Curves.
4. Surfaces in Three Dimensions.
5. The First Fundamental Form.
6. Curvature of Surfaces.
7. Gaussian Curvature and the Gauss Map.
8. Geodesics.
9. Minimal Surfaces.
10. Gauss's Theorema Egregium.
11. The GaussBonnet Theorem.
Solutions.
Index.

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Cover of Elementary Differential Geometry 2nd edition

Elementary Differential Geometry - 2nd edition

ISBN13: 978-1848828902
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