A notoriously difficult subject, covariant electrodynamics is nonetheless vital for understanding relativistic field theory. John M. Charap's classroom-tested introduction to the mathematical foundations of the topic presents the material in an approachable manner. Charap begins with a historical overview of electrodynamics and a discussion of the preliminary mathematics one needs in order to grasp the advanced and abstract concepts underlying the theory. He walks the reader through Maxwell's four equations, explaining how they were developed and demonstrating how they are applied. From there, Charap moves through the other components of electrodynamics, such as Lorentz transformations, tensors, and charged particle behavior. At each point, he carefully works through the mathematics, applies the concepts to simple physical systems, and provides historical context that makes clear the connections among the theories and the mathematicians responsible for developing them. A concluding chapter reviews the history of electrodynamics and points the way for independent testing of the theory. Thorough, evenly paced, and intuitive, this friendly introduction to high-level covariant electrodynamics is a handy and helpful addition to any physicist's toolkit.

Table of Contents:
Preface 1. Introduction 2. Mathematical Preliminaries 2.1. A Reminder of Vector Calculus 2.2. Special Relativity 2.3. Four-Vectors 2.4. Covariant and Contravariant Vectors 2.5. Tensors 2.6. Time Dilation and the Lorentz-FitzGerald Contraction 2.7. The Four-Velocity 2.8. Energy and Momentum 2.9. Plane Waves 2.10. Exercises for Chapter 2 3. Maxwell's Equations 3.1. Our Starting Point 3.2. The Experimental Background 3.2.1. Coulomb's Law 3.2.2. Absence of Magnetic Monopoles 3.2.3. Ørsted and Ampere 3.2.4. The Law of Biot and Savart 3.2.5. The Displacement Current 3.2.6. Faraday's Law of Induction 3.2.7. The Lorentz Force 3.3. Capacitors and Solenoids 3.3.1. Energy 3.4. Electromagnetic Waves 3.4.1. Polarization 3.4.2. Electromagnetism and Light 3.5. Exercises for Chapter 3 4. Behavior under Lorentz Transformations 4.1. The Charge-Current Density Four-Vector 4.2. The Lorentz Force 4.3. The Potential Four-Vector 4.4. Gauge Transformations 4.5. The Field-Strength Tensor 4.6. The Dual Field-Strength Tensor 4.7. Exercises for Chapter 4 5. Lagrangian and Hamiltonian 5.1. Lagrange's Equations 5.2. The Lagrangian for a Charged Particle 5.3. The Hamiltonian for a Charged Particle 5.4. The Lagrangian for the Electromagnetic Field 5.5. The Hamiltonian for the Electromagnetic Field 5.6. Noether's Theorem 5.7. Exercises for Chapter 5 6. Stress, Energy, and Momentum 6.1. The Canonical Stress Tensor 6.2. The Symmetrical Stress Tensor 6.3. The Conservation Laws with Sources 6.4. The Field as an Ensemble of Oscillators 6.5. Exercises for Chapter 6 7. Motion of a Charged Particle 7.1. Fields from an Unaccelerated Particle 7.2. Motion of a Particle in an External Field 7.2.1. Uniform Static Magnetic Field 7.2.2. Crossed E and B Fields 7.2.3. Nonuniform Static B-Field 7.2.4. Curved Magnetic Field Lines 7.3. Exercises for Chapter 7 8. Fields from Sources 8.1. Introducing the Green's Function 8.2. The Delta Function 8.3. The Green's Function 8.4. The Covariant Form for the Green's Function 8.5. Exercises for Chapter 8 9. Radiation 9.1. Potentials from a Moving Charged Particle 9.2. The Lienard-Wiechert Potentials 9.2.1. Fields from an Unaccelerated Particle 9.2.2. Fields from a Charged Oscillator 9.3. The General Case 9.4. The Multipole Expansion 9.4.1. Electric Dipole Radiation 9.4.2. Magnetic Dipole and Higher-Order Terms 9.5. Motion in a Circle 9.6. Radiation from Linear Accelerators 9.7. Radiation from an Antenna 9.8. Exercises for Chapter 9 10. Media 10.1. Dispersion 10.1.1. Newton on the "Phænomena of Colours" 10.2. Refraction 10.2.1. The Boundary Conditions at the Interface 10.3. Cerenkov Radiation 10.4. Exercises for Chapter 10 11. Scattering 11.1. Scattering from a Small Scatterer 11.2. Many Scatterers 11.3. Scattering from the Sky 11.3.1. The Born Approximation 11.3.2. Rayleigh's Explanation for the Blue Sky 11.4. Critical Opalescence 12. Dispersion 12.1. The Oscillator Model 12.1.1. The High-Frequency Limit 12.1.2. The Drude Model 12.2. Dispersion Relations 12.3. The Optical Theorem Epilogue Index