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Edition: 01

Copyright: 2001

Publisher: Springer-Verlag New York

Published: 2001

International: No

Copyright: 2001

Publisher: Springer-Verlag New York

Published: 2001

International: No

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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, 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.

**Pressley, Andrew : King's College**

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.

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.

Publisher Info

Publisher: Springer-Verlag New York

Published: 2001

International: No

Published: 2001

International: No

**Pressley, Andrew : King's College**

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.