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Geometry Applied Differential Geometry by Burke

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  1. Jan 24, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Preface
    [*] Glossary of notation
    [*] Introduction
    [*] Tensor in linear spaces
    [LIST]
    [*] Linear and affine spaces
    [*] Differential calculus
    [*] Tensor algebra
    [*] Alternating products
    [*] Special relativity
    [*] The uses of covariance
    [/LIST]
    [*] Manifolds
    [LIST]
    [*] Manifolds
    [*] Tangent vectors and 1-forms
    [*] Lie bracket
    [*] Tensors on manifolds
    [*] Mappings
    [*] Cotangent bundle
    [*] Tangent bundle
    [*] Vector fields and dynamical systems
    [*] Contact bundles
    [*] The geometry of thermodynamics
    [/LIST]
    [*] Transformations
    [LIST]
    [*] Lie groups
    [*] Lie derivative
    [*] Holonomy
    [*] Contact transformations
    [*] Symmetries
    [/LIST]
    [*] The calculus of differential forms
    [LIST]
    [*] Differential forms
    [*] Exterior calculus
    [*] The * Operator
    [*] Metric Symmetries
    [*] Normal forms
    [*] Index notation
    [*] Twisted differential forms
    [*] Integration
    [*] Cohomology
    [/LIST]
    [*] Applications of the exterior calculus
    [LIST]
    [*] Diffusion equations
    [*] First-order partial differential equations
    [*] Conservation laws
    [*] Calculus of variations
    [*] Constrained variations
    [*] Variations of multiple integrals
    [*] Holonomy and thermodynamics
    [*] Exterior differential systems
    [*] Symmetries and similarity solutions
    [*] Variational principles and conservation laws
    [*] When not to use forms
    [/LIST]
    [*] Classical electrodynamics
    [LIST]
    [*] Electrodynamics and differential forms
    [*] Electrodynamics in spacetime
    [*] Laws of conservation and balance
    [*] Maccroscopic electrodynamics
    [*] Electrodynamics of moving bodies
    [/LIST]
    [*] Dynamics of particles and fields
    [LIST]
    [*] Lagrangian mechanics of conservative systems
    [*] Lagrange's equations for general systems
    [*] Lagrangian field theory
    [*] Hamiltonian systems
    [*] Symplectic geometry
    [*] Hamiltonian optics
    [*] Dynamics of wave packets
    [/LIST]
    [*] Calculus on fiber bundles
    [LIST]
    [*] Connections
    [*] Parallel transport
    [*] Curvature and torsion
    [*] Covariant differentiation
    [*] Metric connections
    [/LIST]
    [*] Gravitations
    [LIST]
    [*] General relativity
    [*] Geodesics
    [*] Geodesic deviation
    [*] Symmetries and conserved quantities
    [*] Schwarzschild orbit problem
    [*] Light deflection
    [*] Gravitational lenses
    [*] Moving frames
    [/LIST]
    [*] Bibliography
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 24, 2013 #2

    dx

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    One of the few differential geometry books that emphasize the importance of twisted tensors.
     
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