Differential Geometry of Curves and Surfaces
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Differential Geometry of Curves and Surfaces : Second Edition

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One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
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Product details

  • Paperback | 512 pages
  • 152 x 228 x 27.94mm | 703.07g
  • New York, United States
  • English
  • Revised
  • 2nd Revised edition
  • 0486806995
  • 9780486806990
  • 24,620

Back cover copy

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
Dover revised and updated republication of the edition originally published by Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.
www.doverpublications.com
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Table of contents

PrefaceSome Remarks on Using this Book1. Curves2. Regular Surfaces3. The Geometry of the Gauss Map4. The Intrinsic Geometry of Surfaces5. Global Differential GeometryBibliography and CommentsHints and Answers to Some ExercisesIndex
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About Manfredo P. Do Carmo

Manfredo P. do Carmo is a Brazilian mathematician and authority in the very active field of differential geometry. He is an emeritus researcher at Rio's National Institute for Pure and Applied Mathematics and the author of Differential Forms and Applications.
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