Download PDF Complex Analysis: In the Spirit of Lipman Bers: 245 (Graduate Texts in Mathematics)

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Kindle Cloud Reader Read instantly in your browser. Editorial Reviews Review 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 …. The book covers all the usual topics for a first course and includes a lot of advanced topics …. I also recommend this book to beginners who want to study Complex Analysis ….

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This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory.

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The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity. The many ways of formulating the concept of an analytic function are summarized in what is termed the Fundamental Theorem for functions of a complex variable.


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The organization of these conditions into a single unifying theorem with an emphasis on clarity and elegance is a hallmark of Lipman Bers's mathematical style. Here it provides a conceptual framework for results that are highly technical and often computational.

The framework comes from an insight that, once articulated, will drive the subsequent mathematics and lead to new results.

In the second part, the text proceeds to a leisurely exploration of interesting ramifications of the main concepts. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored. Not Enabled. Share your thoughts with other customers. Write a customer review. Showing of 2 reviews.

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Please try again later. Format: Hardcover Verified Purchase. As a tribute to their past master, I must award 5 stars to the book's authors, but something has been nagging at me since I first opened the book; first of all, there is a chapter on the topology of H D , i.

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Bluntly, the book contains less material than Cartan, is much more expensive but less than Ahlfors so why bother with it? On the other side, the authors have taken stock from the some of greatest specialists and writers in the field from a classical point of view which means that their work contains some outstanding mathematics. In the end, it is four stars as a tribute to Bers, Cartan, Ahlfors and Serge Lang who is said to have traded a lot of ideas with Bers while he was writing his own book on complex analysis guess what: from page 37 to 46, Lang begins his chapter on power series with formal power series shades of his french background?

Format: Paperback. This is an excellent first course on complex analysis.


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  5. It develops the subject's beautiful geometric ideas in a very smooth and intuitive way, making learning easier on students. In all, I think this is a great book to have to either study independently the subject, use it for a first course or complementary material, or just as a reference. See both reviews. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about Amazon Giveaway.

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    Complex Analysis - In the Spirit of Lipman Bers | Jane P. Gilman | Springer

    This bookpresents fundamental material that should be part of the education of every practicing mathematician. This material will also be of interest to computer scientists, physicists, and engineers. Complex analysis is also known as function theory. In this text we address the theory of complex-valued functions of a single complex variable.

    This is a prerequisite for the study of many current and rapidlydevelopingareasofmathematics, includingthetheoryofseveral andin? Complex analysis has connections and applications to many other many other subjects in mathematics, and also to other sciences as an area where the classic and the modern techniques meet and bene?

    We will try to illustrate this in the applications we give. Because function theory has been used by generations of practicing mathematicians working in a number of di? We are not wedded to any one viewpoint. Rather we will try to exploit the richness of the subject and explain and interpret standard de?