Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

George Fikioris was born in Boston, MA on December 3, 1962. He received the Diploma of Electrical Engineering from the National Technical University of Athens, Greece (NTUA), in 1986, and the S.M. and Ph.D. degrees in Engineering Sciences from Harvard University in 1987 and 1993, respectively. From 1993 to 1998, he was an electronics engineer with the Air Force Research Laboratory (AFRL), Hanscom AFB, MA. From 1999 to 2002, he was a researcher with the Institute of Communication and Computer Systems at the National Technical University of Athens, Greece (NTUA). In 2002, he joined the faculty of the School of Electrical and Computer Engineering, NTUA, where he is currently an Associate Professor. He is the author or coauthor of 50 papers in technical journals, a list of which can be found in ece.ntua.gr/ images/publications/george-fikioris-publications.pdf Ioannis Tastsoglou was born in Kavala, Greece, in 1986. He received the Telecommunications and Electronics degree from the Hellenic Air Force Academy, Athens, Greece, in July 2007. He is currently a Lieutenant in the Hellenic Air Force. He is concurrently working toward the Ph.D. degree in the School of Electrical and Computer Engineering of the National Techni cal University of Athens. His research interests include electromagnetics, antennas, and applied mathematics

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

Preface.- Introduction: Simple Asymptotic Approximations.- Asymptotic Approximations Defined.- Concepts from Complex Variables.- Laplace's Method and Watson's Lemma.- Integration by Parts and Asymptotics of Some Fourier Transforms.- Poisson Summation Formula and Applications.- Mellin-Transform Method for Asymptotic Evaluation of Integrals.- More Applications to Wire Antennas.- Authors' Biographies.- Index.