Complex Analysis | 
 enlarge | Author: Theodore W. Gamelin
Publisher: Springer
Category: Book
List Price: $54.95
Buy New: $44.00
You Save: $10.95 (20%)
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Rating:  11 reviews
Sales Rank: 389961
Media: Paperback
Edition: Corrected
Pages: 464
Number Of Items: 1
Shipping Weight (lbs): 1.5
Dimensions (in): 9.2 x 6.1 x 1
ISBN: 0387950699
Dewey Decimal Number: 515
EAN: 9780387950693
Publication Date: July 17, 2003
Availability: Usually ships in 1-2 business days
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Product Description
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing Ph.D. qualifying exams in complex analysis.
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| Customer Reviews: Read 6 more reviews...
 Outstanding book: very clear, covers a great deal of material too September 17, 2006
Alexander C. Zorach (New Haven, CT)
6 out of 7 found this review helpful
This is the closest I come to a favourite book on Complex Analysis. It wins on clarity, amount of material covered, and the order in which topics are presented.
Gamelin's writing is very clear and he provides a lot of motivation and discussion; his proofs are easy to follow, and the book has a healthy dose of geometry that clarifies and enriches the subject. In spite of being very easy to read, this book manages to cover a lot of ground, and gets into some more advanced topics. I have not been able to find any book that is as accessible as this book is while also being as comprehensive. Also, this is one of the few books that explores the connections of complex analysis to applied mathematics and pure mathematics equally well.
This book's greatest asset is that it address the differences in background that students inevitably have when approaching the subject of complex analysis. This book covers all the necessary ground thoroughly, but in neat sections which are easy to skip, and it introduces more advanced topics (again in neat sections) very early so that students with a strong background will not be bored. The early introduction to Riemann surfaces is outstanding and greatly enriches the study of the material; the book's final chapter presents the theory rigorously. The two chapters on integration move slowly, but develop the subject in a manner that explores the rich interplay between the theory of analytical functions and the general theory of differentiable functions of two variables.
The exercises are outstanding. They are fairly diverse in difficulty level, and very interesting and informative. They range from simple computations up through interesting tangential theorems.
I think this would make an outstanding text for an undergraduate complex analysis course, and it might make a good text for a graduate course as well. It is also useful for self-study or as a reference. The best part about this book is that it can be used for a first course, and motivated students can plow through the rest of the book, getting into some more advanced and interesting material. After this book one should have no trouble tackling a denser text like the Ahlfors.
A good introduction for any level September 11, 2007
B. (LA, CA, USA)
1 out of 1 found this review helpful
There are plenty of Complex Analysis books to choose from, but I really like this one. The exercises are very interesting and there hints for most of the more complicated ones. I've used this book in both undergraduate and the first year graduate courses, and it's been pretty consistently enjoyed.
Great read!! October 21, 2002
qubit (Los Angeles, CA)
This is a neat textbook on complex analysis. Covers the basic undergraduate curriculum, plus it has some surprisingly refreshing material thrown in towards the end.
The exercises are really helpful and there is a nice variety of problems. The good part is that there are partial hints to problems in the back. With the hints and the answers, one feels that one is heading in the right direction.
I would definitely recommend it.
Here comes Ramblin' Gamelin' July 10, 2001
5 out of 11 found this review helpful
A fantastic book. Quite clear and readable, and really brings out the beauty of the subject. Topics cover standard introductory material, standard not-so-introductory material, and a little bit of the crazy stuff just for fun. I used this book as a companion to Teddy G's course, and it was grreat. Excellent for PHD-level qualifying exams (especially at UCLA).
Interesting Book December 12, 2002
20 out of 22 found this review helpful
Gamelin's book covers an interesting and wide range of topics in a somewhat unorthodox manner. Examples: Riemann surfaces are introduced in the first chapter, whereas winding numbers don't make an appearance until halfway into the book. Cauchy's theorem and its kin are instead developed in the context of piecewise-smooth boundaries of domains (in particular, simple closed curves) and only later generalized to arbitrary closed paths, almost as an afterthought.In general, the author successfully conveys the spirit of the subject, and manages to do so quite efficiently. It's not the most painstakingly rigorous text out there, and the reader is expected to fill in some of the details himself, but the payoff is that a lot of ground is covered without getting bogged down in technicalities. In many books on this subject it can be tough to see the forest for the trees. This one is a pleasant exception. There are a lot of good complex analysis books out there: Conway, Ahlfors, Remmert, Palka, Narasimhan, the second half of big Rudin, and of course Needham's "Visual Complex Analysis." (And many others that are well-regarded but that I have not looked at, such as Lang and Jones/Singerman, as well as the old classics by Hille, Knopp, Cartan, Saks and Zygmund.) Every one of these has its own perspective, and complex analysis is a big, multifaceted subject that is perhaps best studied from multiple points of view. Anyone wanting to learn this subject well will benefit from having several books at hand. Gamelin's contribution to the pantheon is not revolutionary, but it does collect between its pages a wide assortment of topics not generally found in a single text. The reader is whisked from the basics to the Riemann mapping theorem in 300 pages with surprising ease. The ensuing "topics" chapters include a dynamical systems-flavored section on Julia sets and fractals; special functions (gamma, zeta, etc.); the prime number theorem; and an introduction to abstract Riemann surfaces. Overall a fun text. Certainly not the only complex analysis book one should read, but then again the the same can be said of any complex analysis book. My only real complaint is that the selection of exercises is somewhat small in some chapters.
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