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Table of contents

  1. Front Matter
    Pages i-xiv
  2. Klaus Jänich
    Pages 1-24
  3. Klaus Jänich
    Pages 25-48
  4. Klaus Jänich
    Pages 49-64
  5. Klaus Jänich
    Pages 65-78
  6. Klaus Jänich
    Pages 79-100
  7. Klaus Jänich
    Pages 101-115
  8. Klaus Jänich
    Pages 117-131
  9. Klaus Jänich
    Pages 151-165
  10. Klaus Jänich
    Pages 167-193
  11. Klaus Jänich
    Pages 195-213
  12. Klaus Jänich
    Pages 215-237
  13. Klaus Jänich
    Pages 239-268
  14. Klaus Jänich
    Pages 269-271
  15. Back Matter
    Pages 273-283

About this book

Introduction

Classical vector analysis deals with vector fields; the gradient, divergence, and curl operators; line, surface, and volume integrals; and the integral theorems of Gauss, Stokes, and Green. Modern vector analysis distills these into the Cartan calculus and a general form of Stokes' theorem. This essentially modern text carefully develops vector analysis on manifolds and reinterprets it from the classical viewpoint (and with the classical notation) for three-dimensional Euclidean space, then goes on to introduce de Rham cohomology and Hodge theory. The material is accessible to an undergraduate student with calculus, linear algebra, and some topology as prerequisites. The many figures, exercises with detailed hints, and tests with answers make this book particularly suitable for anyone studying the subject independently.

Keywords

Derivative Vector field calculus differential equation differential geometry manifold

Authors and affiliations

  • Klaus Jänich
    • 1
  1. 1.NWF-I MathematikUniversität RegensburgRegensburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3478-2
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3144-3
  • Online ISBN 978-1-4757-3478-2
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site