Ablowitz, Mark J.; Fokas, Athanassios S. Complex variables: introduction and applications. (English) Zbl 0885.30001 Cambridge Texts in Applied Mathematics. Cambridge: Cambridge University Press. xii, 647 p. (1997). This book gives an introduction to the theory of functions of one complex variable and its various applications. It is less rigorous than other introductory books on the subject, but instead emphasizes applications to problems in physics and engineering. In fact it covers some applications of complex function theory not usually found in introductory textbooks. The book consists of two parts. The first part is an introduction to the theory of analytic functions covering the basic things like Cauchy-Riemann equations, Cauchy’s theorem and integral formula, power series, the residue theorem, etc. Some applications like ideal fluid flow are also discussed here, and an introduction to complex differential equations is included. The second part of the book is then devoted to applications of complex function theory. It consists of three chapters on conformal mappings and its applications, asymptotic evaluation of integrals, and Riemann-Hilbert problems. The broad range of applications given makes the book useful for students in engineering and the physical sciences (and for instructors teaching such students, of course). It is not so much intended as a basis for rigorous courses on the subject addressed to mathematics students. Reviewer: W.Bergweiler (Kiel) Cited in 1 ReviewCited in 71 Documents MSC: 30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) Keywords:functions of one complex variable; applications in physics and engineering; introductory textbooks; analytic functions; Cauchy-Riemann equations; Cauchy’s theorem; complex differential equations; conformal mappings; asymptotic evaluation of integrals; Riemann-Hilbert problems PDFBibTeX XMLCite \textit{M. J. Ablowitz} and \textit{A. S. Fokas}, Complex variables: introduction and applications. Cambridge: Cambridge University Press (1997; Zbl 0885.30001)