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Introduction to Complex Analysis

Rolf Nevanlinna and Veikko Paatero
Publisher: 
American Mathematical Society
Publication Date: 
2007
Number of Pages: 
350
Format: 
Hardcover
Edition: 
2
Series: 
AMS/Chelsea
Price: 
49.00
ISBN: 
978-0-8218-4399-4
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Luiz Henrique de Figueiredo
, on
12/5/2007
]

This is a textbook by one of the masters of Complex Analysis. It is a crisp, direct, and surprisingly modern account of the basic material for a first course in Complex Analysis. (It was probably a fresh approach in 1968 when it was published. Now there are several other good books in the same tradition.)

One feature of the book is that it explains the homotopy version of Cauchy's theorem, but homotopy is defined as a finite sequence of elementary deformations, i.e., those that act on a subarc of the path and take place inside a convex subset, such as a small disk. This is not the standard definition of homotopy based on continuous deformations, but it is equivalent to it and seems likely to appeal to intuition and is somewhat easier to deal with technically.

The book does not mention the homological version of Cauchy's theorem (e.g., Dixon's proof, which has become popular in standard references such as Conway's 1978 book.)

In summary, the book remains an excellent reference for a first course in Complex Analysis. It contains over 300 exercises.


Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.

 


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