Parrott S. Relativistic Electrodynamics and Differential Geometry 1987

Textbook in PDF format

The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry. The intended audience is primarily mathematicians who want a bare-bones account of the foundations of electrodynamics written in language with which they are familiar and secondarily physicists who may be curious how their old friend looks in the new clothes of the differential-geometric viewpoint which in recent years has become an important language and tool for theoretical physics.
Preface
Chapter 1. Special Relativity
Chapter 2. Mathematical Tools
Chapter 3. The Electrodynamics of Infinitesimal Charges
Chapter 4. The Electrodynamics of Point Charges
Chapter 5. Further Difficulties and Alternate Approaches