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Elementary Differential Geometry

  • Andrew Pressley

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Andrew Pressley
    Pages 1-21
  3. Andrew Pressley
    Pages 23-45
  4. Andrew Pressley
    Pages 47-57
  5. Andrew Pressley
    Pages 59-96
  6. Andrew Pressley
    Pages 97-121
  7. Andrew Pressley
    Pages 123-145
  8. Andrew Pressley
    Pages 147-169
  9. Andrew Pressley
    Pages 171-200
  10. Andrew Pressley
    Pages 201-228
  11. Andrew Pressley
    Pages 229-246
  12. Andrew Pressley
    Pages 247-280
  13. Back Matter
    Pages 281-332

About this book

Introduction

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.

Keywords

Curves and Surfaces Euclidean Geometry Gaussian curvature Geometry Minimal surface curvature differential geometry

Authors and affiliations

  • Andrew Pressley
    • 1
  1. 1.Department of MathematicsKing’s CollegeLondonUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3696-5
  • Copyright Information Springer-Verlag London 2001
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-152-8
  • Online ISBN 978-1-4471-3696-5
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site
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