Privalov, I. I. Introduction to the theory of functions of a complex variable. Textbook. 13th ed. (Введение в теорию функций комплексного переменного. Учебное пособие.) (Russian) Zbl 0571.30001 Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-MatematicheskoĭLiteratury. 432 p. R. 1.30 (1984). The 13the edition of this renewed textbook proves once again its great value. Although it appears without modification with respect to the 12th edition, let us emphasize that the 9th edition was completely revised by A. I. Markushevich so that it now preserves its clear and intuitive style but with the actual rigour. In a rather concise volume it succeeds to introduce the reader not only into the fundaments of complex analysis: limits and series, differentiability, Cauchy integral theory, power series, isolated singularities, residues, analytic continuation, but also in deep classical problems: theorems of Picard, Weierstraß and Mittag- Leffler, elliptic and theta functions, conformal mappings, univalent functions; moreover some subjects specific to Privalov’s work (behaviour of Cauchy type integral on the boundary, boundary behaviour of analytic functions in the circle) are discussed. Suggestive examples, applications to hydrodynamics and exercises with hints and solutions increase the attraction of the book. Reviewer: C.Andreian Cazacu Cited in 1 ReviewCited in 20 Documents MSC: 30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable PDFBibTeX XML