Mathematical Principles of Mechanics and Electromagnetism

of Part B.- 5. Classical Theory of Electromagnetism.- Section 30. Classical Laws of Electrostatic Fields.- Section 31. Steady Currents and Magnetic Induction.- Section 32. Time-Dependent Electromagnetic Fields, Maxwell’s Equations.- Section 33. Balance Principles.- Section 34. Electromagnetic Waves.- Section 35. Electromechanical Interactions.- 6. Special Relativistic Theory of Electromagnetism.- Section 36. Newtonian, Galilean, and Ether Space-Times.- Section 37. Minkowskian Space-Time.- Section 38. Lorentz Transformations.- Section 39. Vectors and Tensors in the Minkowskian Space-Time.- Section 40. Maxwell’s Equations in Special Relativistic Form.- Section 41. Lorentz’s Formula and the Balance Principles in Special Relativistic Form.- Section 42. Doppler Effect of Electromagnetic Waves.- 7. General Relativistic Theory of Gravitation.- Section 43. Newton’s Law of Gravitation and the Principle of Equivalence.- Section 44. Minkowskian Manifold.- Section 45. The Stress-Energy-Momentum Tensor in a Material Medium.- Section 46. Einstein’s Field Equations.- Section 47. The Schwarzschild Solution and the Problems of Planetary Orbits and the Deflection of Light.- Section 48. The Action Principle.- Section 49. Action and Coaction.- Section 50. The Nordström-Toupin Ether Relation and the Minkowskian Metric.- 8. General Relativistic Theory of Electromagnetism.- Section 51. Maxwell’s Equations in General Relativistic Form.- Section 52. The Maxwell-Lorentz Ether Relation and the Minkowskian Metric I: Toupin’s Uniqueness Theorem.- Section 53. The Maxwell-Lorentz Ether Relation and the Minkowskian Metric II: Basic Properties and Preliminary Lemmas.- Section 54. The Maxwell-Lorentz Ether Relation and the Minkowskian Metric III: Toupin’s Existence Theorem.- Section 55. The Electromagnetic Action and the Electromagnetic Stress-Energy-Momentum Tensor.- Section 56. Electrogravitational Fields of an Electrically Charged Mass Point.- Selected Reading for Part B.