Elements of Classical Electrodynamics and Special Relativity

This book presents the fundamental aspects of classical electrodynamics and special relativity, focusing on the mathematical framework that underpins a coherent theory of electromagnetism. It prioritizes theoretical consistency while summarizing foundational and phenomenological aspects concisely, leaving more detailed discussions to introductory texts. The book provides a set of mathematical tools essential for addressing and solving common problems in the field.

It begins with a review of key mathematical techniques, including vector calculus, Green's theorem, and Dirac delta functions. The discussion then moves to electrostatics, covering Poisson's equation, Green's functions, the method of images, and multipole expansions. Solutions to Laplace's equation are explored in Cartesian, spherical, and cylindrical coordinates, both analytically and numerically. The treatment of electric currents and magnetostatics follows, introducing Ampère's law, the vector potential, and magnetic multipoles.

Maxwell's equations are then derived and applied to wave propagation, energy and momentum conservation, and gauge transformations. The final sections introduce special relativity, covering Lorentz transformations, four-vectors, and the covariant formulation of electrodynamics, concluding with an introduction to relativistic Lagrangian dynamics.

Each chapter includes exercises designed to reinforce students' understanding. This book is intended for advanced undergraduate and graduate students in physics. Readers are expected to have prior knowledge of algebra and electromagnetism.