Sinopsis
The authors' aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.
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Críticas
From the reviews: "This is a fairly conventional text for a first course in complex analysis. It is an interesting mix of the concrete and the abstract, and of the formulaic and the geometric. It has good exercises ... . It is nominally a graduate text (it is in Springer’s series of Graduate Texts in Mathematics) ... . The book covers all the usual topics for a first course and includes a lot of advanced topics ... ." (Allen Stenger, MathDL, February, 2008) "This book is based on the original courses of Complex Analysis that was delivered by the well-known American specialist and lecturer in Analysis, Professor Lipman Bers. ... the book is written in a clear and easily readable manner. ... this book is useful for all specialists and lecturers in Complex Analysis ... and also all specialists who deal with applications of Complex Analysis. I also recommend this book to beginners who want to study Complex Analysis ... ." (Peter Zabreiko, Zentralblatt MATH, Vol. 1139 (17), 2008)
Reseña del editor
The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.
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