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Manifolds, Tensor Analysis, and Applications

  • Ralph Abraham
  • Jerrold E. Marsden
  • Tudor Ratiu

Part of the Applied Mathematical Sciences book series (AMS, volume 75)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 1-39
  3. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 40-140
  4. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 141-237
  5. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 238-337
  6. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 338-391
  7. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 392-463
  8. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 464-559
  9. Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
    Pages 560-630
  10. Back Matter
    Pages 631-656

About this book

Introduction

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me­ chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Keywords

Derivative Electromagnetism Hodge star operator Implicit function Riemannian geometry calculus compactness exterior derivative manifold

Authors and affiliations

  • Ralph Abraham
    • 1
  • Jerrold E. Marsden
    • 2
  • Tudor Ratiu
    • 1
  1. 1.Department of MathematicsUniversity of California—Santa CruzSanta CruzUSA
  2. 2.Control and Dynamical Systems, 107–81California Institute of TechnologyPasadenaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1029-0
  • Copyright Information Springer-Verlag, New York Inc. 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6990-8
  • Online ISBN 978-1-4612-1029-0
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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