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Manifolds, Tensor Analysis, and Applications : Applied Mathematical Sciences - Ralph Abraham

Manifolds, Tensor Analysis, and Applications

Applied Mathematical Sciences

Hardcover

Published: 13th August 1993
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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.

Preface
Background Notation
Topology
Banach Spaces and Differential Calculus
Manifolds and Vector Bundles
Vector Fields and Dynamical Systems
Tensors
Differential Forms
Integration on Manifolds
Applications
References
Index
Supplementary Chapters
S-1 Lie Groups
S-2 Introduction to Differential Topology
S-3 Topics in Riemannian Geometry
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387967905
ISBN-10: 0387967907
Series: Applied Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 656
Published: 13th August 1993
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.1
Edition Number: 2
Edition Type: Revised