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Elementary Differential Geometry


  • Date Published: May 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521721493

£ 47.99

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About the Authors
  • The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss–Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The only prerequisites are one year of undergraduate calculus and linear algebra.

    • Assumes only one year of undergraduate calculus and linear algebra
    • Equips the reader for further study in mathematics as well as other fields such as physics and computer science
    • Over 100 exercises and solutions
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    Reviews & endorsements

    'The book under review presents a detailed and pedagogically excellent study about differential geometry of curves and surfaces by introducing modern concepts and techniques so that it can serve as a transition book between classical differential geometry and contemporary theory of manifolds. the concepts are discussed through historical problems as well as motivating examples and applications. Moreover, constructive examples are given in such a way that the reader can easily develop some understanding for extensions, generalizations and adaptations of classical differential geometry to global differential geometry.' Zentralblatt MATH

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    Product details

    • Date Published: May 2010
    • format: Paperback
    • isbn: 9780521721493
    • length: 330 pages
    • dimensions: 247 x 175 x 16 mm
    • weight: 0.67kg
    • contains: 147 b/w illus. 4 colour illus. 125 exercises
    • availability: Available
  • Table of Contents

    1. Euclidean geometry
    2. Curve theory
    3. Classical surface theory
    4. The inner geometry of surfaces
    5. Geometry and analysis
    6. Geometry and topology
    7. Hints for solutions to (most) exercises
    List of symbols

  • Instructors have used or reviewed this title for the following courses

    • Concepts in Modern Mathematics
    • Differential Geometry
    • Independent study/Modern Geometry
  • Author

    Christian Bär, Universität Potsdam, Germany
    Christian Bär is Professor of Geometry in the Institute for Mathematics at the University of Potsdam, Germany.

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