Complex Analysis [Paperback]

Ian Stewart (Author), David Tall (Author)

Book Description

Publication Date: April 29, 1983 | ISBN-10: 0521287634 | ISBN-13: 978-0521287630

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.

Editorial Reviews

Book Description

A new approach to complex analysis that attempts to make it less complicated than traditional texts suggest.

Product Details

• Paperback: 304 pages
• Publisher: Cambridge University Press (April 29, 1983)
• Language: English
• ISBN-10: 0521287634
• ISBN-13: 978-0521287630
• Product Dimensions: 8.8 x 6 x 0.9 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 3.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,033,989 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 8 people found the following review helpful:

5.0 out of 5 stars Uses geometry of complex plane well to make reading easy., July 26, 1999

By A Customer

This review is from: Complex Analysis (Paperback)

Great book.

It's written for 2nd year university mathematics students. It covers all the standard topics from complex differentiability through to Cauchy's integral theorem, Taylor and Laurent series and then through to evaluating real, definite integrals and finishes up on Reinmann surfaces. The concepts are developed thoroughly from a very simple starting point. The text places a large emphasis on the geometry of the complex plane meaning that diagrams and graphs are used frequently in examples and proofs making reading miles easier. It starts with a few simple theorems in topology (which assume no prior knowledge of the topic) and use these to give convincing proofs of concepts such as Cauchy's theorem and Merton's theorem later in the book.

The index is quite comprehensive.

7 of 10 people found the following review helpful:

3.0 out of 5 stars Pretty good book, January 21, 1998

By 

L. Mintz (Montreal, Quebec Canada) - See all my reviews
(REAL NAME)   

This review is from: Complex Analysis (Paperback)

Most of the material is well thought out. Though I wish the author would give more concrete examples of the theory. For example in parametrising of paths :|z|<2 i,-i he would not show how to do this. Though the theory would give you an idea. It would be nice if more concrete examples were shown in the text. Other than , there is much interesting material and most of th e exercises are doable without too much real analysis being neeeded/

10 of 17 people found the following review helpful:

2.0 out of 5 stars Horrible introduction to complex analysis, December 7, 2006

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: Complex Analysis (Paperback)

This despicable book provides a narrow-minded and unattractive introduction to complex analysis. The brief chapter 0 on the history of the subject is thoroughly distorted to conform with the way the authors want to approach the subject. So, for instance, since the authors don't want to provide any motivation at any stage they simply make up the fact that none is needed, claiming that complex analysis "seems to have been the direct result of the mathematician's urge to generalize. It was sought deliberately, by analogy with real analysis." The truth is of course that the mathematicians who developed complex analysis mostly did so with concrete problems in mind, and were convinced of the value of the theory by its many excellent applications as well as its inner beauty, neither of which is conveyed by this book. These mathematicians would rather have poked their eyes out than investigate stupid nonsense problems such as the arc length of t+it(sin(pi/t)) (example 6.3.2, very representative). It must surely be one of the most hypocritical moments in textbook history when the authors claim to be ardent geometers, speaking of "the dangers of blind 'formula-crunching' analysis. Complex analysis is a highly geometric subject, and the geometry should not be despised." They do indeed plot t+it(sin(pi/t)) in their boring example 6.3.2, but that's the height of their geometric imagination. Formula-crunching is the only way they ever do anything and the entire presentation is deeply antigeometric. Indeed, the authors have worked hard to make sure that no-one obtains any intuitive understanding of the subject at all by postponing the few geometrically insightful topics that actually are discussed (conformality, harmonic functions, Riemann surfaces) until the very end and then treating them extremely briefly without indicating their importance for a geometric understanding of what complex functions, derivatives and integrals really are---which is what all sensible readers were asking themselves 250 pages earlier.