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Effective for undergraduate and postgraduate students, the single-volume Complex Analysis functions as both a textbook and a reference, depending on the conducted course's structure. The only prerequisites are rudiments of real analysis and linear algebra. Special features include an integrated approach to the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, complex versions of real intermediate value theorem, and exhaustive treatment of contour integration. The book also offers an introduction to the theory of univalent functions on the unit disc, including a brief history of the Bieberbach's conjecture and its solutions.
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V. Karunakaran.: School of Mathematics, Madurai Kamaraj UniversityReview:
V. Karunakaran presents a distinctive introduction to the theory of a single complex variable in the second edition of Complex Analysis. The book has many noteworthy features. It contains, for example, a thorough list of alternate forms of the Cauchy-Riemann equations. Many readers will enjoy the rigorous treatment of Cauchy’s Theorem and Cauchy’s Integral Formula. ... The author clearly makes a consistent effort to highlight the topological aspects of introductory complex analysis as it flows through many of the topics listed above and continues on to the Riemann Mapping Theorem. ... a solid introduction to graduate complex analysis. Its treatment of topology will tie in nicely with other introductory courses. Proofs are complete and many difficult exercises are posed and fully solved. Anyone planning to teach a course in complex analysis should consider listing it as a reference.
―Dov Chelst, MAA Reviews, December 2011
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