Lectures on Entire Functions
by B. Ya. Levin
Publisher: American Mathematical Society 1996
Number of pages: 265
This monograph aims to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis. The general theory starts with the fundamental results on the growth of entire functions of finite order, their factorization according to the Hadamard theorem, properties of indicator and theorems of Phragmen-Lindelof type.
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The textbook for an introductory course in complex analysis. It covers complex numbers and functions, integration, Cauchy's theorem, harmonic functions, Taylor and Laurent series, poles and residues, argument principle, and more.
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Introduction to some of the basic ideas in complex analysis: complex numbers; foundations of complex analysis; complex differentiation; complex integrals; Cauchy's integral theorem; Cauchy's integral formula; Taylor series; Laurent series; etc.