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Complex Analysis, by V. Karunakaran
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This book, an introduction to basic Complex Analysis at the undergraduate and postgraduate levels, features an integrated approach to the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, a detailed discussion on the construction of Riemann surfaces for elementary functions leading to its abstract concept, step-by-step development of the most general form of Cauchy's theorem, complex version of the real intermediate value theorem, exhaustive treatment of contour integration and an introduction to the theory of univalent functions on the unit disc including a brief history of the Bieberbach's conjecture and its solution.
- Sales Rank: #3862217 in Books
- Brand: Brand: Alpha Science Intl Ltd
- Published on: 2005-04
- Original language: English
- Dimensions: 9.50" h x 6.50" w x 1.00" l,
- Binding: Hardcover
- 427 pages
- Used Book in Good Condition
Review
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
About the Author
V. Karunakaran.: School of Mathematics, Madurai Kamaraj University
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