Product Description

This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.

Product Details

• Amazon Sales Rank: #324906 in Books
• Published on: 1983-03-10
• Original language: English
• Number of items: 1
• Binding: Paperback
• 304 pages

Customer Reviews

A useful introduction to Complex Analysis
I have recently completed a third year undergraduate course in complex analysis and I found this book to be helpful to me in explaining the ideas and concepts of analysis in the complex plane. The book is set out in an easy to follow manner with many worked examples and lots of exercises at the end of each chapter to help consolidate the ideas learnt. I found it complemented my class notes with more in depth explainations. I also found it a good point of reference for exercises set by my tutor.

revealing questions help
Hi,

The way the subjects in the book have been organised shows tight control during its creation. Each explanation is crafted; each of the many questions in the chapters has been carefully selected to point something out to the reader that helps its appreciation. The deeper you read into the books topics the more rarefied the level of mathematics.

The initial chapters are straightforward bridging level. The usage of many helpfully diagrams explains the importance of `power series' using `x' as the independent variable and allows the transition in their relationships using 'Cauchy-Riemann' partial-differential equations. Then usage of trigonometrically based series with 'Z' functions is painlessly introduced and explored and into the calculus using these functions. The role of the complex logarithm is shown by how many times it's reworked to highlight points in the area.

The Calculus with 'Z' variables allows greater depth of Complex functions to be explored and the nature of the requirements in this area is made clearer. I liked especially how the `Cauchy Theorem' was interpreted via the theorem of a triangle, paths in their domains and how this allows homotopy / analytic answers to be made and again slides from Taylor series painlessly into the more applicable `Laurent' series and residues.

The latter parts have greater complexity -excuse the pun- and much more real mathematical reasoning is used to firm the results. I really feel this book is a workshop to sharpen the skills in this area and it's worth every penny I paid for it. This is one of a few books I feel it's worth buying I.M.H.O

Ian Stewart does it again
Its ashame that Stewart no longer lectures and I had an awful lecturer who taught me Complex Analysis, and when I struggled throught the course, this book was my saviour. Somehow Stewart always seem able to explain complicated ideas in simplistic ways so that the ideas stick in the mind.
Also recommend Galois Theory by Stewart if you are doing a course in Galois Theory, equally complicated ideas made simple again.