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**A friendly approach to complex analysis.**
*(English)*
Zbl 1318.30002

Hackensack, NJ: World Scientific (ISBN 978-981-4578-98-1/hbk; 978-981-4578-99-8/ebook). xv, 272 p. (2014).

The title shows the direction. This textbook is a really friendly approach to complex analysis in one variable. The authors present the basics in an extended way including a large number of examples and exercises as well as corresponding detailed solutions.

In the preface, the authors provide a number of arguments why to study complex analysis and in Theorem 0.2 they already summarize main parts of the theory. This theorem serves as a kind of agenda. In the first two chapters, emphasis is placed on the geometry of complex numbers and elementary functions and in particular on the geometric interpretation of complex differentiability. In this part, the presentation goes beyond most textbooks and thus makes it in a sense unique. Chapters 3 and 4 contain the classical core of basic complex analysis, namely the Cauchy integral approach and the concept of Taylor and Laurent series including a number of applications. A remarkable feature of the presentation is the fact that the authors avoid the notion of uniform convergence of series. After a short introduction to harmonic functions given in Chapter 5, the textbook closes with an extended part on solutions of the exercises.

This friendly introduction to complex analysis can be really helpful for readers starting to learn in that field and may act as a stimulant for more.

In the preface, the authors provide a number of arguments why to study complex analysis and in Theorem 0.2 they already summarize main parts of the theory. This theorem serves as a kind of agenda. In the first two chapters, emphasis is placed on the geometry of complex numbers and elementary functions and in particular on the geometric interpretation of complex differentiability. In this part, the presentation goes beyond most textbooks and thus makes it in a sense unique. Chapters 3 and 4 contain the classical core of basic complex analysis, namely the Cauchy integral approach and the concept of Taylor and Laurent series including a number of applications. A remarkable feature of the presentation is the fact that the authors avoid the notion of uniform convergence of series. After a short introduction to harmonic functions given in Chapter 5, the textbook closes with an extended part on solutions of the exercises.

This friendly introduction to complex analysis can be really helpful for readers starting to learn in that field and may act as a stimulant for more.

Reviewer: Jürgen Müller (Trier)

### MSC:

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