EAN: 9783031005886

SYNTHESIS LECTURES ON COMPUTATIONAL ELECTROMAGN...

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.

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