A new book on mathematical principles behind electromagnetics
A new book on mathematical principles behind electromagnetics

The Math Behind Engineering Electromagnetics

A new book by Professor Ramakrishna Janaswamy seeks to bring together the underlying mathematical principles behind electromagnetics

Team Lede

Team Lede

Electromagnetic fields/waves are ubiquitous and play a major role in modern day technology.

They are encountered in wired and wireless communications, radar, consumer electronics, defence electronics, wireless health-monitoring systems, healthcare diagnostic systems, to name a few.

Most undergraduate engineering curricula include a one-semester course in electromagnetic theory comprised of basic topics such as electrostatics, magnetostatics, Maxwell’s equations, plane waves, etc.

In the design of many electromagnetic subsystems, more advanced topics are needed which are typically covered in a one-semester to a two-semester sequence of courses at the graduate level. Several books already exist that selectively treat these advanced topics. Majority of the treatments are focused on the physical operation of the electromagnetic subsystems.

As a result, the underlying mathematical principles are scattered all over and the themes repeat in various geometries. For instance, rectangular waveguide, circular waveguides and spherical structures are all governed by the same underlying mathematical principles, although the coordinate systems are different.

The latest book Engineering Electrodynamics: A Collection of Theorems, Principles and Field Representations, Ramakrishna Janaswamy, Institute of Physics, London: UK, November 2020, unifies the mathematical principles behind engineering electromagnetics and presents the relevant material in the form of definitions, theorems and detailed analytical examples.

As a result, readers would better appreciate the unifying mathematical ideas behind the various geometrical structures and be better prepared to handle new situations. The content of the book is broken up into the following chapters: Maxwell’s equations and potentials; Static fields; Gauge invariance; Causality and dispersion; Uniqueness, energy and momentum; Duality and Babinet’s principle; Electromagnetic reciprocity; Reactance theorems; Geometrical optics and Fermat’s principle; Integral field representations; Induction theorem and optical theorem; Eigenfunctions, Green’s functions and completeness; Electromagnetic degrees of freedom; Radon transform and projection slice theorem; Free-space Green’s function; Asymptotic analysis; Covariant formulation of Maxwell’s equations; Maxwell’s equations in the sense of distributions; and finally Stochastic representation of wave phenomenon.

A handy appendix comprised of complex variable theory, vector analysis, Bessel functions, and associated Legendre functions is included. The material in the book is presented in self-consistent way, while including all the needed background information for advanced topics.

Ramakrishna Janaswamy is a professor in the Department of Electrical & Computer Engineering, University of Massachusetts, Amherst, MA, USA. His teaching and research interests include analytical and computational electromagnetics, deterministic and stochastic radio wave propagation modeling, antenna theory and design, system theory, mathematical physics, and wireless communications.

Ramakrishna Janaswamy, the author
Ramakrishna Janaswamy, the authorPhoto credit: Ben Barnhart

He is a Fellow of IEEE, the recipient of the 1995 RWP King Prize Paper Award of the IEEE Transactions on Antennas & Propagation, and a recipient of the IEEE 3rd Millennium Medal in 2000.

He received the Distinguished Alumni Professional Achievement Award from the National Institute of Technology, Warangal, India in 2017 and the College of Engineering Outstanding Teacher Award from the University of Massachusetts, Amherst in 2014.

He is an elected member of the US National Committee of URSI, Commissions B and F. He served as an Associate Editor of Radio Science, IEEE Transactions on Vehicular Technology, IEEE Transactions on Antennas & Propagation, IET Electronics Letters and serves as an active member of the IEEE Antennas & Propagation Standards Committee.

He is the author of the book Radiowave Propagation and Smart Antennas for Wireless Communications, Kluwer Academic Publishers, November 2000.

During his spare time, he indulges in nature photography, particularly of birds and has captured several species of birds in India.

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