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9780821869017

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"This textbook provides a profound introduction to the classical theory of functions of one complex variable . . . [T]he present text covers a remarkably broad spectrum between basic and advanced complex analysis, on the one hand, and between purely theoretical and concrete computational aspects on the other hand . . . Every section comes with a long series of related exercises, which differ widely with respect to both their abstraction and their difficulty . . . [T]hese exercises are utmost carefully selected and supplement the main text in a very instructive and efficient manner. Furthermore, the entire text is amply interspersed with illustrating examples, most of which appear as relevant working problems followed by detailed model solutions. All in all, the rich material is presented in a fashion that stands out by its laudable clarity, rigor, functionalism, versatility, and straightforward explanations. The book appears to be tailor-made for both students and instructors, and it certainly bespeaks the author's great teaching experience, expository expertise, enthusiasm for the subject, and sympathy for the needs of students."" - Werner Kleinert, Zentralblatt MATH ""[This] book presents topics in a logical way that allows the reader to build their intuition about the subject. [For] example, the elementary functions are defined in the first chapter. The first chapter then provides the reader with applications of the rectangular and polar coordinate forms of complex numbers and with examples to understand the properties of analytic and meromorphic functions developed in the subsequent chapters. The proofs of the major theorems follow the same logical and intuitive approach. The exercises are thoughtful and yet accessible to anyone with a sound understanding of multivariable calculus. This is an excellent book."" - Peter Trombi, University of Utah"

This textbook provides a profound introduction to the classical theory of functions of one complex variable . . . [T]he present text covers a remarkably broad spectrum between basic and advanced complex analysis, on the one hand, and between purely theoretical and concrete computational aspects on the other hand . . . Every section comes with a long series of related exercises, which differ widely with respect to both their abstraction and their difficulty . . . [T]hese exercises are utmost carefully selected and supplement the main text in a very instructive and efficient manner. Furthermore, the entire text is amply interspersed with illustrating examples, most of which appear as relevant working problems followed by detailed model solutions. All in all, the rich material is presented in a fashion that stands out by its laudable clarity, rigor, functionalism, versatility, and straightforward explanations. The book appears to be tailor-made for both students and instructors, and it certainly bespeaks the author's great teaching experience, expository expertise, enthusiasm for the subject, and sympathy for the needs of students. - Werner Kleinert, Zentralblatt MATH [This] book presents topics in a logical way that allows the reader to build their intuition about the subject. [For] example, the elementary functions are defined in the first chapter. The first chapter then provides the reader with applications of the rectangular and polar coordinate forms of complex numbers and with examples to understand the properties of analytic and meromorphic functions developed in the subsequent chapters. The proofs of the major theorems follow the same logical and intuitive approach. The exercises are thoughtful and yet accessible to anyone with a sound understanding of multivariable calculus. This is an excellent book. - Peter Trombi, University of Utah

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Joseph L. Taylor, University of Utah, Salt Lake City, UT

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