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Manifolds, tensor analysis, and applications / R. Abraham, J. E. Marsden, T. Ratiu

Main Author Abraham, Ralph H. Coauthor Marsden, Jerrold E.
Ratiu, Tudor
Country Estados Unidos. Edition 2nd ed Publication New York : Springer, cop. 1988 Description 654 p. : il. ; 24 cm Series Applied mathematical sciences , 75 ISBN 0-387-96790-7 CDU 514.76
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Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca da UMinho no Campus de Azurém
BPG 514.76 - A Available 198645
Monografia Biblioteca Geral da Universidade do Minho
BGUM1 514.76 - A Available 202369
Monografia Biblioteca da UMinho no Campus de Azurém
BPG2 514.76 - A Available 207055
Total holds: 0

Enhanced descriptions from Syndetics:

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.

Table of contents provided by Syndetics

  • Preface
  • Background Notation
  • Chapter 1 Topology
  • Chapter 2 Banach Spaces and Differential Calculus
  • Chapter 3 Manifolds and Vector Bundles
  • Chapter 4 Vector Fields and Dynamical Systems
  • Chapter 5 Tensors
  • Chapter 6 Differential Forms
  • Chapter 7 Integration on Manifolds
  • Chapter 8 Applications
  • References
  • Index
  • Supplementary Chapters
  • S-1 Lie Groups
  • S-2 Introduction to Differential Topology
  • S-3 Topics in Riemannian Geometry

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