From a mathematical point of view, acoustics and electromagnetism exhibit similar phenomena and are tackled with the same kind of technique. Jones's exhaustive study is unique in providing a unified treatment of the two fields, bringing out their common and disparate features and showing how they cross-fertilize one another. The book is designed so that the reader with a familiarity with either Maxwell's Equations or the equation of sound waves in fluid dynamics can follow the developments in both fields without difficulty. This is a comprehensive treatment which will provide a needed reference for researchers in applied mathematics and mathematical physics but also caters to the student, who is taken up to the frontiers of research with the help of appropriate exercises. Engineers with any sort of mathematical competence, particularly electrical engineers and those concerned with communications technology, will need to have access to it.

The book deals with the analysis of oscillations, mechanical and electromagnetic waves, and their use in medicine. Each chapter contains the theoretical basis and the use of relevant phenomena in medical practice. Description of oscillations is important for understanding waves and the nature of magnetic resonance. A chapter on mechanical waves describes the origin and properties of sound, infrasound and ultrasound, their medical applications, and perception of sound by human hearing. A chapter on electromagnetic waves examines their origin, properties, and applications in therapy and diagnostics. Subsequent chapters describe how interference and diffraction lead to applications like optical imaging, holography, virtual reality, and perception of light by human vision. Also addressed is how quantum properties of radiation helped develop the laser scalpel, fluorescence microscopy, spectroscopy, X-rays, and gamma radiation.

It has now been almost ten years since our first book on scattering theory ap peared [32]. At that time we claimed that "in recent years the development of integral equation methods for the direct scattering problem seems to be nearing completion, whereas the use of such an approach to study the inverse scattering problem has progressed to an extent that a 'state of the art' survey appears highly desirable". Since we wrote these words, the inverse scattering problem for acoustic and electromagnetic waves has grown from being a few theoreti cal considerations with limited numerical implementations to a weH developed mathematical theory with tested numerical algorithms. This maturing of the field of inverse scattering theory has been based on the realization that such problems are in general not only nonlinear but also improperly posed in the sense that the solution does not depend continuously on the measured data. This was emphasized in [32] and treated with the ideas and tools available at that time. Now, almost ten years later, these initial ideas have developed to the extent that a monograph summarizing the mathematical basis of the field seems appropriate. This book is oUf attempt to write such a monograph. The inverse scattering problem for acoustic and electromagnetic waves can broadly be divided into two classes, the inverse obstacle problem and the inverse medium problem.

The discrete sources method is an efficient and powerful tool for solving a large class of boundary-value problems in scattering theory. A variety of numerical methods for discrete sources now exist. In this book, the authors unify these formulations in the context of the so-called discrete sources method. Comprehensive presentation of the discrete sources method Original theory - an extension of the conventional null-field method using discrete sources Practical examples that demonstrate the efficiency and flexibility of elaborated methods (scattering by particles with high aspect ratio, rough particles, nonaxisymmetric particles, multiple scattering) List of discrete sources programmes available via the Internet

The book represents an exhaustive study of the scattering properties of acoustically soft and hard bodies and of perfect conductors, presented for 15 geometrically-simple shapes. Such shapes are important in their own right and as a basis for synthesizing the radiation and scattering properties of more complex configurations. Each shape is treated in a separate chapter whose contents are presented in stylized format for easy reference. Emphasis is placed on results in the form of formulae and diagrams. Although no detailed derivation are included, an outline of methods in scattering theory is given in the Introduction. (Author).

The propagation of waves along and across the boundary between two media with different characteristic velocities is much more complicated when the source is on or near the boundary than when it is far away and the incident waves are plane. Examples of waves generated by localized sources near a boundary are the electromagnetic waves from the currents in a dipole on the surface of the earth and the seismic waves from a slip event in a fault in the earth's crust like the San Andreas fault in California. Both involve a type of surface wave that is called a lateral wave in electro magnetics and a head wave in seismology. Since the two are analogous and the latter is more easily visualized, it is conveniently used here to introduce and describe this important type of surface wave using the data of Y. Ben Zion and P. Malin ("San Andreas Fault Zone Head Waves Near Parkfield, CA," Science 251, 1592-1594, 29 March 1991).