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

• Main Authors: Rudolph, Gerd. (Author), Schmidt, Matthias. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2013.
• Series: Theoretical and Mathematical Physics,
• Subjects: Physics.; Topological Groups.; Global analysis.; Global differential geometry.; Mathematical physics.; Mechanics.; Mathematical Methods in Physics.; Global Analysis and Analysis on Manifolds.; Topological Groups, Lie Groups.; Differential Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-94-007-5345-7

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, sym...

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.