Efe Academy Press, İstanbul, 2019
Foundations of Classical Electromagnetism is the first volume of the series Lectures in Electromagnetic Theory. The content of the present
volume is integrated to the following volumes, which are also planned to be
released soon:
Vol.2 Electromagnetic Fields and Waves
Vol.3 Singularities in Classical Electromagnetism
Vol.4 Hertzian Electrodynamics
Vol.5
Electromagnetic Scattering by Moving Bodies
The
present volume is a reflection of my personal outlook on physics centered
around original contributions to mathematical foundations, principles and
applications of classical electromagnetic field theory. It is not designed as a
typical textbook covering all topics in the curriculum with plenty of solved
problems but should rather be considered as a supplementary source for readers ranging from undergraduate
students with little background on electromagnetic theory to graduates and
researchers of Electrical Engineering and Basic Sciences who are specializing
on this field.
The
first part of the present book focuses on axiomatic foundations and principles
of electromagnetic theory from a deductive perspective. It involves discussions
of the postulates and laws that constitute the field theory, along with various
principles, theorems and relations which they reveal.
In
the second part static electric and magnetic fields in stationary media are
studied in the space of continuous functions to be able to appeal to sophomore
students as well. This comes at the cost of a severely restricted analytical
freedom that hinders legitimate derivations of certain relations. However, I
shall compensate for all missing proofs in Volume 3, where discontinuities and
singularities in electromagnetic field theory are treated systematically accompanied
by a thorough review of required topics from Analysis in Lebesgue and
SchwartzSobolev Spaces.
I
also devoted an Appendix to customary approaches and various discussions from
literature along with my commentaries and pedagogical solutions to a number of
issues in the teaching of Vector Calculus. Unity holds for all mathematical and
physical symbols and abbreviations in the series, while MKSA units are adopted as
they are rather focused on engineering applications. Semicolon (;) is used to
distinguish between variables of different units in arguments of functions as
Main contributions of the present volume to literature
can be outlined as follows:

Original approaches to modeling and interpretation of
electromagnetic phenomena

Alternative representations for Maxwell’s Equations
with emphasis on Duality Transformations.

Proper descriptions of work and energy in static
electric and magnetic fields

Proper definitions for Perfect Electric and Magnetic
Conductors

Introduction of Principle of Conservation of Energy
and Power in moving media

New physical concepts and quantities associated with
Duality Principle and Conservation of Energy and Power in moving media
The
structure and design of these volumes are reflections of my worldview that the
laws of macroscopic electromagnetism  as described by Maxwell’s Equations of
stationary media  are frame indifferent
and recognize all frame indifferent (complementary) axioms, postulates,
principles and laws of other disciplines that constitute Newtonian Continuum
Mechanics in Euclidean Space. In the spirit of Natural Philosophy I draw
criticism for the attempts to integrate (contradicting) alternative theories for
moving bodies (especially Special and General Theories of Relativity) into the
areas of study of Electrical Engineering. If a relativistic improvement for
Maxwell’s Equations will ever be required on cosmological scale, then I believe
it is bound to be constructed in a way as to yield the frame indifferent HertzHeaviside
Equations exactly in the nonrelativistic limiting cases.
The volumes themselves are much better suited for
citation purposes since they involve a considerable number of corrections and
advances over my published papers.