From the PREFACE

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 Schwartz-Sobolev 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.

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 Hertz-Heaviside 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.

Burak POLAT, Ph.D.

Professor of Electromagnetic Theory

Yıldız Technical University

September 2019