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Elementary Topics in Differential Geometry

  • J. A. Thorpe

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. J. A. Thorpe
    Pages 1-5
  3. J. A. Thorpe
    Pages 6-12
  4. J. A. Thorpe
    Pages 13-15
  5. J. A. Thorpe
    Pages 16-22
  6. J. A. Thorpe
    Pages 23-30
  7. J. A. Thorpe
    Pages 31-37
  8. J. A. Thorpe
    Pages 38-44
  9. J. A. Thorpe
    Pages 45-52
  10. J. A. Thorpe
    Pages 53-61
  11. J. A. Thorpe
    Pages 62-67
  12. J. A. Thorpe
    Pages 68-81
  13. J. A. Thorpe
    Pages 82-94
  14. J. A. Thorpe
    Pages 95-107
  15. J. A. Thorpe
    Pages 108-120
  16. J. A. Thorpe
    Pages 132-138
  17. J. A. Thorpe
    Pages 139-155
  18. J. A. Thorpe
    Pages 156-162
  19. J. A. Thorpe
    Pages 163-176
  20. J. A. Thorpe
    Pages 177-189
  21. J. A. Thorpe
    Pages 190-209
  22. J. A. Thorpe
    Pages 210-219
  23. J. A. Thorpe
    Pages 220-230
  24. J. A. Thorpe
    Pages 231-243
  25. Back Matter
    Pages 245-253

About this book

Introduction

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.

Keywords

Differentialgeometrie Isometrie Minimal surface curvature differential geometry

Authors and affiliations

  • J. A. Thorpe
    • 1
  1. 1.Queens CollegeCity University of New YorkFlushingUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-6153-7
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6155-1
  • Online ISBN 978-1-4612-6153-7
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site