1. Special Relativity. - 1. 1 Coordinatizations of spacetime. - 1. 2 Lorentz coordinatizations. - 1. 3 Minkowski space. - 1. 4 Lorentz transformations. - 1. 5 Orientations. - 1. 6 Spacetime diagrams and the metric tensor. - 1. 7 Proper time and four-velocity. - 1. 8 Mass and relativistic momentum. - Exercises 1. - 2. Mathematical Tools. - 2. 1 Multilinear algebra. - 2. 2 Alternating forms. - 2. 3 Manifolds. - 2. 4 Tangent spaces and vector fields. - 2. 5 Covariant derivatives. - 2. 6 Stokes' Theorem. - 2. 7 The metric tensor. - 2. 8 The covariant divergence. - 2. 9 The equation d ? = ? and ?? = ?. - Exercises 2. - 3. The Electrodynamics of Infinitesimal Charges. - 3. 1 Introduction. - 3. 2 The Lorentz force law. - 3. 3 The electromagnetic field tensor. - 3. 4 The electric and magnetic fields. - 3. 5 The first Maxwell equation. - 3. 6 The second Maxwell equation. - 3. 7 Potentials. - 3. 8 The energy-momentum tensor. - Exercises 3. - 4. The Electrodynamics of Point Charges. - 4. 1 Introduction. - 4. 2 The retarded potentials and fields of a pointparticle. - 4. 3 Radiation reaction and the Lorentz-Dirac equation. - 4. 4 Calculation of the energy-momentum radiated by a point particle. - 4. 5 Summary of the logical structure of electrodynamics. - Exercises 4. - 5. Further Difficulties and Alternate Approaches. - 5. 1 The Cauchy problem for the Maxwell-Lorentz system. - 5. 2 Spherically symmetric solutions of the Maxwell-Lorentz system. - 5. 3 Nonexistence of global solutions of the Maxwell-Lorentz system. - 5. 4 An alternate fluid model. - 5. 5 Peculiar solutions of the Lorentz-Dirac equation. - 5. 6 Evidence for the usual energy-momentum tensor. - 5. 7 Alternate energy-momentum tensors and equations of motion. - Appendix on Units. - Solutions to Exercises. - Appendix 2. - Table of Notations. Language: English