Book description
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 allimportant 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 RiemannLebesgue 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
 Gamma Function and Related Functions
 Power Series
 Analytic Continuation
 Multivalued Functions and Branch Points
 Branches and Principal Values of Multivalued Functions
 Applications to Antennas and Electromagnetics: Nonsolvability
 Supplementary Remarks and Further Reading
 Problems (1/2)
 Problems (2/2)
 References
 Laplace's Method and Watson's Lemma
 Integration by Parts and Asymptotics of Some Fourier Transforms
 Poisson Summation Formula and Applications
 MellinTransform Method for Asymptotic Evaluation of Integrals
 More Applications to Wire Antennas
 Special Functions
 On the Convergence/Divergence of Definite Integrals
 Authors' Biographies
 Index (1/2)
 Index (2/2)
Product information
 Title: Selected Asymptotic Methods with Applications to Electromagnetics and Antennas
 Author(s):
 Release date: September 2013
 Publisher(s): Morgan & Claypool Publishers
 ISBN: 9781627050401
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