Riassunto
Mathieu functions are employed in solving a variety of problems in mathematic (al? ) physics. In many cases the configuration involves elliptical coordinates. Of course, the circular geometry is the degenerate case of the elliptical cross section. This volume contains values for, and curves of the angular and radial Mathieu functions and their first derivatives. The latter are often needed in the solution of problems, in particular in solving electromagnetic wave propagation problems. Also included are data on zero crossings of the radial Mathieu functions. These are often needed for determining the cut-off frequencies for propagating modes. Other tables are available for the Mathieu functions, but there is very little data available for derivatives or zero crossings. It is felt that the principal value of this volume is in the multitude of curves included. The analyst dealing with elliptical cases can, by inspection of the curves, find values of the functions and derivatives at the origin, maxima and minima, zero crossings, and qualitative behavior of the plots as a function of several parameters. To the author's knowledge, this is the most extensive presentation of plotted information. It is hoped that the information will be helpful in the solution of practical problems. This book is divided into two sections. Section I deals only with the functions themselves, defining the equations and terminology used and presenting the tabular data and curves. Section II treats the derivatives and the zeros. Again the terminology and equations for the first derivatives are given. The Mathieu functions are named after Emile L. Mathieu (1835-1890), a French mathematician, who in 1868 published an article dealing with vibratory movement of the elliptic membrane. The asteroid 27947 Emilemathieu is named in his honor.
L'autore
Dr. James C. Wiltse received the bachelor's and master's degrees from Rensselaer Polytechnic Institute and the doctorate from Johns Hopkins University, all in electrical engineering. He has had a distinguished engineering career. In the past he served as Director of Research and Technology at Martin Marietta, Orlando, Director of Advanced Technology at Electronic Communications, Inc. and, Associate Director of the Georgia Tech Research Institute. He is the author/co-author of 160 technical publications, including three books and a contributor to 14 other books. His works have been referenced in many publications and hundreds of journal articles. He has given scores presentations at technical conferences and symposia, some of them at international sites. Dr. Wiltse has made numerous significant contributions to the microwave, millimeter-wave, and terahertz (far-infrared) technology areas. He and a colleague were the first to use the phase-correcting Fresnel zone plate at millimeter wavelengths, and the first to use quarter-wave correction. This improves the diffraction efficiency of the zone plate by a factor of 2. He was the inventor of the planar lens, which is flat on both sides, by using two or more dielectrics. He was the first to solve the problem of guided wave propagation on a dielectric rod of elliptical cross-section, and the first to investigate broadband superheterodyne receiver design employing a microwave intermediate frequency. This technique has been widely used by radio astronomers for many years. For most of his career he served on the editorial boards of several journals including as guest editor on several occasions. Dr. Wiltse also was editorial book reviewer for a number of publishers. He is a member of several engineering honorary societies and is listed in Who's Who in America, Who's Who in Science and Engineering, and Who's Who in the World.
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