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Elementary Topics in Differential Geometry

  • Textbook
  • © 1979

Overview

Authors:
  1. J. A. Thorpe

    1. Queens College, City University of New York, Flushing, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Graphs and Level Sets

    • J. A. Thorpe
    Pages 1-5

  3. Vector Fields

    • J. A. Thorpe
    Pages 6-12

  4. The Tangent Space

    • J. A. Thorpe
    Pages 13-15

  5. Surfaces

    • J. A. Thorpe
    Pages 16-22

  6. Vector Fields on Surfaces; Orientation

    • J. A. Thorpe
    Pages 23-30

  7. The Gauss Map

    • J. A. Thorpe
    Pages 31-37

  8. Geodesics

    • J. A. Thorpe
    Pages 38-44

  9. Parallel Transport

    • J. A. Thorpe
    Pages 45-52

  10. The Weingarten Map

    • J. A. Thorpe
    Pages 53-61

  11. Curvature of Plane Curves

    • J. A. Thorpe
    Pages 62-67

  12. Arc Length and Line Integrals

    • J. A. Thorpe
    Pages 68-81

  13. Curvature of Surfaces

    • J. A. Thorpe
    Pages 82-94

  14. Convex Surfaces

    • J. A. Thorpe
    Pages 95-107

  15. Parametrized Surfaces

    • J. A. Thorpe
    Pages 108-120

  16. Local Equivalence of Surfaces and Parametrized Surfaces

    • J. A. Thorpe
    Pages 121-131

  17. Focal Points

    • J. A. Thorpe
    Pages 132-138

  18. Surface Area and Volume

    • J. A. Thorpe
    Pages 139-155

  19. Minimal Surfaces

    • J. A. Thorpe
    Pages 156-162

  20. The Exponential Map

    • J. A. Thorpe
    Pages 163-176
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Keywords

About this book

In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under­ standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.

Authors and Affiliations

  • Queens College, City University of New York, Flushing, USA

    J. A. Thorpe

About the author



Bibliographic Information

  • Book Title: Elementary Topics in Differential Geometry

  • Authors: J. A. Thorpe

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-6153-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1979

  • Hardcover ISBN: 978-0-387-90357-6Published: 16 April 1979

  • Softcover ISBN: 978-1-4612-6155-1Published: 12 October 2011

  • eBook ISBN: 978-1-4612-6153-7Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIV, 256

  • Topics: Differential Geometry

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