An Introduction to Manifolds

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Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined i...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Tu, Loring W. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: New York, NY : Springer New York : Imprint: Springer, 2011.
Edition:2nd ed. 2011.
Series:Universitext,
Subjects:
Manifolds (Mathematics).
Global analysis (Mathematics).
Geometry, Differential.
Manifolds and Cell Complexes.
Global Analysis and Analysis on Manifolds.
Differential Geometry.
Online Access:Texto Completo
Table of Contents:
  • Preface to the Second Edition
  • Preface to the First Edition
  • Chapter 1. Euclidean Spaces
  • Chapter 2. Manifolds
  • Chapter 3. The Tangent Space
  • Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms
  • Chapter 6. Integration.-Chapter 7. De Rham Theory
  • Appendices
  • A. Point-Set Topology
  • B. The Inverse Function Theorem on R(N) and Related Results
  • C. Existence of a Partition of Unity in General
  • D. Linear Algebra
  • E. Quaternions and the Symplectic Group
  • Solutions to Selected Exercises
  • Hints and Solutions to Selected End-of-Section Problems
  • List of Symbols
  • References
  • Index.

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