Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

George Fikioris, Ioannis Tastsoglou, Odysseas N. Bakas
ISBN: 9781627050395 | PDF ISBN: 9781627050401
Copyright © 2013 | 207 Pages | Publication Date: 09/01/2013

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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.

Table of Contents

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

About the Author(s)

George Fikioris, School of Electrical and Computer Engineering, National Technical University of Athens, Greece

Ioannis Tastsoglou, School of Electrical and Computer Engineering, National Technical University of Athens, Greece

Odysseas N. Bakas, School of Electrical and Computer Engineering, National Technical University of Athens, Greece

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