Author | Thirring, Walter. author |
---|---|
Title | A Course in Mathematical Physics 1 and 2 [electronic resource] : Classical Dynamical Systems and Classical Field Theory / by Walter Thirring |
Imprint | New York, NY : Springer New York, 1992 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0517-0 |
Descript | XX, 261 p. online resource |
1 Introduction -- 1.1 Equations of Motion -- 1.2 The Mathematical Language -- 1.3 The Physical Interpretation -- 2 Analysis on Manifolds -- 2.1 Manifolds -- 2.2 Tangent Spaces -- 2.3 Flows -- 2.4 Tensors -- 2.5 Differentiation -- 2.6 Integrals -- 3 Hamiltonian Systems -- 3.1 Canonical Transformations g -- 3.2 Hamiltonโs Equations -- 3.3 Constants of Motion -- 3.4 The Limit t ? I ยฑ ? -- 3.5 Perturbation Theory: Preliminaries -- 3.6 Perturbation Theory: The Iteration -- 4 Nonrelativistic Motion -- 4.1 Free Particles -- 4.2 The Two-Body Problem -- 4.3 The Problem of Two Centers of Force -- 4.4 The Restricted Three-Body Problem -- 4.5 The N-body Problem -- 5 Relativistic Motion -- 5.1 The Hamiltonian Formulation of the Electrodynamic Equations of Motions -- 5.2 The Constant Field -- 5.3 The Coulomb Field -- 5.4 The Betatron -- 5.5 The Traveling Plane Disturbance -- 5.6 Relativistic Motion in a Gravitational Field -- 5.7 Motion in the Schwarzschild Field -- 5.8 Motion in a Gravitational Plane Wave -- 6 The Structure of Space and Time -- 6.1 The Homogeneous Universe -- 6.2 The Isotropic Universe -- 6.3 Me according to Galileo -- 6.4 Me as Minkowski Space -- 6.5 Me as a Pseudo-Riemannian Space -- 1. Introduction -- 1.1 Physical Aspects of Field Dynamics -- 1.2 The Mathematical Formalism -- 1.3 Maxwellโs and Einsteinโs Equations -- 2. The Electromagnetic Field of a Known Charge Distribution -- 2.1 The Stationary-Action Principle and Conservation Theorems -- 2.2 The General Solution -- 2.3 The Field of a Point Charge -- 2.4 Radiative Reaction -- 3. The Field in the Presence of Conductors -- 3.1 The Superconductor -- 3.2 The Half-Space, the Wave-Guide, and the Resonant Cavity -- 3.3 Diffraction at a Wedge -- 3.4 Diffraction at a Cylinder -- 4. Gravitation -- 4.1 Covariant Differentiation and the Curvature of Space -- 4.2 Gauge Theories and Gravitation -- 4.3 Maximally Symmetric Spaces -- 4.4 Spaces with Maximally Symmetric Submanifolds -- 4.5 The Life and Death of Stars -- 4.6 The Existence of Singularities