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Textbook

ISBN: 978-605-2308-64-6
First Edition: September 2019

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