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**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.

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)

### MSC:

30-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |