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Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems /

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reductio...

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Main Authors: Rudolph, Gerd. (Author, http://id.loc.gov/vocabulary/relators/aut), Schmidt, Matthias. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2013.
Edition:1st ed. 2013.
Series:Theoretical and Mathematical Physics,
Subjects:
Physics.
Global analysis (Mathematics).
Manifolds (Mathematics).
Mechanics.
Topological groups.
Lie groups.
Differential geometry.
Mathematical Methods in Physics.
Global Analysis and Analysis on Manifolds.
Classical Mechanics.
Topological Groups, Lie Groups.
Differential Geometry.
Online Access:https://doi.org/10.1007/978-94-007-5345-7
Table of Contents:
  • 1 Differentiable manifolds
  •  2 Vector bundles
  •  3 Vector fields
  •  4 Differential forms
  •  5 Lie groups
  •  6 Lie group actions
  •  7 Linear symplectic algebra
  •  8 Symplectic geometry
  •  9 Hamiltonian systems
  •  10 Symmetries
  • 11 Integrability
  • 12 Hamilton-Jacobi theory
  •  References.

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