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Electromagnetic wave theory for boundary-value problems. An advanced course on analytical methods. (English) Zbl 1053.78001
Berlin: Springer (ISBN 3-540-21266-3/hbk). xvi, 314 p. (2004).
According to the preface, this book, based on a graduate course on electromagnetism in Korea is “to present solutions to canonical boundary – value problems”. There are eleven chapters. The first chapter is on Maxwell’s equations. The equations are set out, the boundary conditions are discussed and the potentials of electromagnetic theory are introduced. Interestingly, the author, in order to give a symmetric form to Maxwell’s equations allows the introduction of magnetic charge and current although pointing out that these are fictitious. In the second chapter the ideas of plane waves are discussed. Topics introduced are the intrinsic impedance of a medium, lossy media, polarization. These lead to topics such as TE, TM and TEM waves, and transmission lines and there is, unusually, but very welcome and interesting an analysis of the laser in the form of a gaussian beam. The next two chapters deal respectively with two topics of great importance in this field namely waveguides and resonators. Relevant fields are discussed in rectangular, circular and spherical coordinates. Amongst other topics discussed are quality factor, shielded strip lines and some possible uses of complex variable theory.
The fifth chapter is a short one and introduces propagation in anisotropic media, paying particular attention to crystals, and ferrites including propagation in a ferrite field waveguide. The next chapter is entitled “Electromagnetic Theorems”. Topics discussed include uniqueness, images and the equivalence, duality and reciprocity theorems. At this stage problems such as dipoles and propagation through aperture are discussed. In a sense, these first six chapters form the basis for the rest of the book which discusses more complicated problems.
The seventh chapter is entitled “Wave Scattering” amongst the scatters treated are dielectric, and perfectly conducting spheres and cylinders, including the corresponding electrostatic problems. More complicated problems in transmission discussed are a step in a parallel-plate waveguide, a slit in a conducting plane and the circular aperture. The next chapter on Green’s functions is almost entirely mathematical in character. The Sturm-Liouville equation is discussed, the idea of the delta function is explained and examples of the evaluation of Green’s functions in one, two and three dimensions are given, it being pointed out that more than one method is possible. The ninth chapter is concerned with applications of Green’s functions. This comprises solutions of a number of problems. Amongst topics discussed are radiation from currents in free space and waveguides. Here again it is pointed out that the results can be obtained by more than one method.
The tenth chapter is on Antennas. The radiation from some simple antennas such as conducting wires, loops and apertures is discussed, the importance of the power flow of the radiated field at infinity being indicated. More complicated antennas mentioned are groove-backed, slit array, and coaxial live antennas. Here again, the possibility of more than one approach in some cases is emphasized. The final short chapter has the title “Radiation above Half Space”. The topics discussed here are electric line sources and dipoles.
The text is followed by a list of 18 references and a number of appendices treating of topics such as vector analysis, Bessel functions, the residue theorem of complex analysis, legendre functions, transforms and series. There is an adequate index and there is a list of symbols used at the beginning of the text.
What of the book as a whole? It has clearly been written with a particular course in view. The treatment is clear, and the book reads easily. There are however, I feel, two matters which are unsatisfactory. Firstly, in a number of places, solutions are left in terms of a number of coefficients which are left unsolved e.g. page 179, equations (7.202) and (7.206) are not solved. An approximate solution would give an idea as to how the fields behave. Secondly, there is no mention of the variational methods which were used to great effect by Schwinger and others during the Second World War. The printing is, as one expects with this publisher, is pleasing and the price is not unreasonable for these days. Subject to the remarks above, the book would be useful to those beginning on electromagnetic research or graduate courses.

MSC:
78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
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