Applied Mathematical Sciences

Manifolds, Tensor Analysis, and Applications

Authors: Abraham, Ralph, Marsden, J.E., Ratiu, Tudor

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About this Textbook

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 meĀ­ 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.

Table of contents (8 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4612-1029-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $134.00
price for USA
  • ISBN 978-0-387-96790-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $134.00
price for USA
  • ISBN 978-1-4612-6990-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Manifolds, Tensor Analysis, and Applications
Authors
Series Title
Applied Mathematical Sciences
Series Volume
75
Copyright
1988
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1029-0
DOI
10.1007/978-1-4612-1029-0
Hardcover ISBN
978-0-387-96790-5
Softcover ISBN
978-1-4612-6990-8
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XI, 656
Additional Information
Originally published by Addison-Wesley Publishing Company, 1983
Topics