Introductory Complex Analysis is a scaled-down version of A. I.
Markushevich's masterly three-volume "Theory of Functions of a Complex
Variable." Dr. Richard Silverman, the editor and translator of the
original, has prepared this shorter version expressly to meet the needs
of a one-year graduate or undergraduate course in complex analysis. In
his selection and adaptation of the more elementary topics from the
original larger work, he was guided by a brief course prepared by
Markushevich himself.The book begins with fundamentals, with a definition of complex numbers, their geometric representation, their algebra, powers and roots of complex numbers, set theory as applied to complex analysis, and complex functions and sequences. The notions of proper and improper complex numbers and of infinity are fully and clearly explained, as is stereographic projection. Individual chapters then cover limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations with their circle-preserving property, exponentials and logarithms, complex integrals and the Cauchy theorem , complex series and uniform convergence, power series, Laurent series and singular points, the residue theorem and its implications, harmonic functions (a subject too often slighted in first courses in complex analysis), partial fraction expansions, conformal mapping, and analytic continuation.
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