This book is an outgrowth of my university lectures and certain of my published works on mathematical foundations, principles and applications of classical electromagnetic field theory. The targeted readers range from sophomore students with no background on electromagnetic theory to graduates and researchers of basic sciences and electrical engineering who are specializing on this field.
The structure and design of the book is a reflection of my “personal perspective” on foundations of electromagnetism. By personal perspective I mean to adhere to the worldview that the laws of macroscobic electromagnetism as described by Maxwell’s equations of stationary media are frame indifferent and recognize all frame indifferent axioms, postulates, principles and laws of other disciplines that constitute Newtonian continuum mechanics in Euclidean space. It should be understood that I avoid any contradicting alternative theory for moving bodies (especially Special and General Theories of Relavity) in the context of macroscobic electromagnetism.
This monograph currently comprises 5 parts, while additional ones are also planned in the long term.
Part 1: Mathematical Foundations of Classical Electromagnetism
Part 2: Classical Electromagnetism in Stationary Continuous Media
Part 3: Singularities in Stationary Media
Part 4: Canonical Propagation and Scattering Problems in Stationary Media
Part 5: Hertzian Electrodynamics of Moving Media
Part I focuses on the critical mathematical tools that serve as background material for the contents of the subsequent parts. The choice of the topics and their complexity are arranged according to the requirements of the physical theories that follow.
Part II focuses on the axiomatic foundations, principles and theorems of electromagnetism in stationary media in the space of continuous functions. It involves the discussion of field equations, the laws and postulates that complement the field theory, the constitutive relations in material media, and the principles, theorems, relations which they yield. The style and complexity is especially suited to sophomore students as an introduction to the field.
Electromagnetic field behavior in presence of singularities constitute an established area of study, which is tackled separately in a systematic manner as the subject of Part III using Schwartz-Sobolev theory of distributions.
Various boundary value problems in electromagnetic wave propagation and scattering in stationary media are studied in Part IV.
The axiomatic structure of field theory in moving media from a Hertzian perspective and a group of associated canonical boundary value problems are treated in Part V.
The chapters are self-content with individual page and equation numberings and references while unity holds for all mathematical and physical symbols and abbreviations used in the text.