|
Function Theory of One Complex Variable: Third Edition (Graduate Studies in Mathematics) | 
 enlarge | Author: Robert E. Greene And Steven G. Krantz
Publisher: American Mathematical Society
Category: Book
List Price: $79.00
Buy New: $77.42
You Save: $1.58 (2%)
New (8) Used (2) from $77.42
Rating:  2 reviews
Sales Rank: 457292
Media: Hardcover
Edition: 3rd
Pages: 504
Number Of Items: 1
Shipping Weight (lbs): 2.4
Dimensions (in): 10.3 x 7.1 x 1.3
ISBN: 0821839624
Dewey Decimal Number: 515.9
EAN: 9780821839621
Publication Date: March 29, 2006
Shipping: Eligible for Super Saver Shipping
Availability: Usually ships in 24 hours
| |
| Similar Items:
|
| Editorial Reviews:
Product Description
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat $H^p$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.
|
| Customer Reviews:
 Very clear prose, explanations, good motivation, an all-around well-written book January 12, 2007
Alexander C. Zorach (New Haven, CT)
4 out of 4 found this review helpful
This book is rather unorthodox in a number of respects, but it has become one of my favourite texts in complex analysis. The authors claim that their motivation for their presentation of the subject is to emphasize the interconnectedness of complex function theory with multivariable calculus, and de-emphasize the connection with topology. While I do not exactly agree with these goals, I think they do an excellent job of acheiving them. My only complaint about the book is that a few proofs in early chapters result in a sea of differential operators that is resolved by a plug-and-chug computation, something I'd always rather avoid.
The level of the book is elementary, especially for a graduate text, and I appreciate the authors for making honest and reasonable claims about the accessibility of their book. This book would probably even work well for someone who has not had a prior course in complex analysis, such as senior undergraduates. Some of the more advanced topics are presented in clearer ways in this book than I have seen elsewhere.
This book has a wealth of exercises, and the difficulty level is somewhat inconsistent. Some of the exercises are outright inane--possibly inappropriate for a graduate-level text, but useful for rote practice. Others are more interesting. I appreciate, however, the inclusion of more elementary exercises: many graduate texts have the problem of not including enough such exercises, which can make it hard for students to master the fundamentals. This book avoids this pitfall.
The best part about this book is the prose. This book is well-written and is a pleasure to read. Theorems and results are well-motivated, and necessary nuances are effectively communicated through the text. The authors do not over-emphasize equations: they use words in a proof when they are clearer.
The book is well-indexed and comprehensive. A student with prior background in Complex analysis might want to read the first chapter to get familiar with the authors' incessant use of differential operators, and then feel free to skip around. I think this book would make an excellent textbook for a course in complex analysis, although the unusual development in the first chapter might annoy some professors.
 Not Bad... May 2, 2007
ikantspel (South Carolina)
1 out of 2 found this review helpful
This book is reasonably accessible to those who may not have had any previous exposure to complex analysis. Many parts of the text are well written and easy to read and I really enjoyed the exposition on harmonic functions. With that being said, however, there are some things that I did not particularly like.
I thought it was strange that the author discusses the Cauchy integral formula for a disk, develops more aspects of the theory, and then later comes back to deal with homotopy theory and topology insofar as integration is concerned. In this aspect, Conway's treatise on the subject is superior, in my opinion.
I also prefer Conway's proof of Mittag-Leffler's theorem which is eloquent and a good application of Runge's Theorem. Additionally, I prefer Conway's proof of the Picard theorems as well (Conway uses Montel-Caratheodory which in and of itself is interesting while Greene and Krantz use the modular function and there are a few choice spots when Krantz is a bit vague).
Finally, some of the proofs and exercises contain errors (most of them minor, some of them not so minor) and a few of the proofs are quite difficult to follow at times while Conway's book seems more readable in these areas. This comment mainly applies to the 2nd edition and it is quite conceivable that the author has remedied these errors in the 3rd edition.
Overall, this book has some value. I believe that this book, coupled with Conway's book is a good combination. There are many things that Greene and Krantz do that I prefer over Conway and vice versa although if I had to compare the two, I would prefer Conway.
|
|
|
| |
