Customer Reviews

Complex Analysis

5 star:		(5)
4 star:		(2)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

This is the book that really made me understand basic complex analysis. It doesn't try to give the most sophisticated or slickest presentation for experts. Instead, it gives a beautiful, concrete, down to earth explanations. The best feature is the applications. D. J. Newman is one of the world's great problem solvers, and this book includes numerous examples of how to use complex analysis to solve problems in surprising ways. Even in the more standard applications, such as summing series, the book gives many unusual examples. It concludes with Newman's proof of the prime number theorem, which is substantially shorter and clearer than many other proofs.

This is a brief text on complex analysis aimed at the traditional junior-senior course. As a text it may be a little too succinct for the average undergraduate. For example, I have no intention of teaching out of it. However, its clarity and presentation is absolutely refreshing. I think it is one of the best books written on complex analysis in the last twenty years. I recommend this book to any student of complex analysis.

In my viewpoint this book is one of the best complex analysis textbooks to date. It is succint and neat, without too many pages and too much content, while every facet of elementary complex analysis theory gets a chapter or two in it. It deals with power series first, then analytic fuctions, then singular pts and residue theorem, then conformal mapping. After these basic topic, it gives some futher theme like harmonic function and Riemann mapping theorem. And the last with some chapters, including a topic on proving prime number theorem, in application of the previous theorem. The pace of this book is very natural, the exercises adequate and well-selected. And in my experience, via this book students usually can handle the most some important topics and get a good structure feeling of this course. Highly recommended.

If you want to learn Complex Analysis, start with Schaum's Outlines. Then when you want to learn the methods and thinking of complex analysis, read this book. It's concise and gets the MAIN POINTS across in a friendly way.

Except for the topological stuff (they simplify things to avoid lengthy tedious discussion) this book is EXCELLENT. I disagree with the reviewers who said this book deals with things in too elementary a way. In fact it gives more general results and the REAL reasons behind complex numbers. Most importantly, it gives you a CONSISTENT FEEL for complex analysis techniques and concepts! For example, whereas most books treat a special case of the Riemann Principle of Removable Singularities where f is bounded. They use slightly tedious estimates of the Laurent coefficients to show that the terms with negative indices are all zero. This book simply shows that if lim (z-w)f(z) = 0 as z->w, then f(z) has a removable singularity, by appealing to the Schwartz Reflection Principle it proved earlier in the book. A more general result and gives a more integrated feeling for the theory.

ALL IN ALL A GREAT RESOURCE. After this, you can read Alfohrs, and then spcialized books on whatever. Lang is okay too but his results are not as general or intuitive as this book, and he uses power series constantly and is good for people who want a different perspective.

This book is disappointing, especially after encountering Newman's "Analytic Number Theory", which is a wonderful book. This book takes the readers on a concise, linear journey through Complex analysis to a few key theorems at the end, but does not do justice to the richness or diversity of the subject. This book will be especially lacking to students studying complex analysis for purposes related to applied mathematics.

The prose in the book is clear, but at times, as early as chapters 2 and 3, the equations are dense for an undergraduate text, with some steps less than obvious. There is a lack of motivation for the direction of development chosen in chapters 4-6, possibly a little of 2, 7, and 8 as well. Results are proven three or more times in cases of increasing generality. While this makes the theorems easy to follow, the redundancy may be confusing for a student studying the material for the first time. The authors do not provide much of a preview of what is to come, as I think authors of an undergraduate text should (and many, such as Gamelin, do).

This book is so small and compact that I question the authors' judgment in leaving out these various explanations--little would be lost and much gained by additional explanations. This makes me wonder what the intended audience is. I think anyone who is able to follow this book without trouble would also have no trouble following a more advanced and comprehensive book. There are a number of more advanced books that are actually much easier to follow. This brings me to my next comment:

This book leaves out a lot of important topics; it is far from comprehensive. There are not very many exercises either, and the exercises are mostly related to the material in simple ways.

For those studying complex analysis for the first time, I would recommend the Gamelin book over this one; its proofs are much easier to follow, it contains much more explanatory prose. It moves slower but it is much more comprehensive and covers more advanced material, and it is better suited to students with diverse interests and different backgrounds. I also recommend the Churchhill text as a straightforward book covering the basics. Advanced students might want to use the classic Ahlfors text.

Frankly, when I first learned complex analysis, I found it to be highly confusing, with the results bizzare and not intuitive even after long arduous proofs. This is probably the book that unlocked that confusion for me. Its slow start from analytic polynomials quickly moved into analytic functions. The link between path integrals and differentiation is nicely done through the means of first proving the rectangular version of the Cauchy integral. All the main results of introductory complex analysis falls naturally from that. Interestingly, the second half of the book then touches upon interesting topics in a very delightful way: conformal mappings, sample series and integrals, the Laplace equations and the Drichilet problems, and lastly non-power series and the Zeta functions.

This book is excelent for a basic Complex Analysis course. It is very well writen, and the examples help you to understand the theorems. The book doesnt have to much solved examples, sometimes you need them.
I recommned to the complex Analysis book writen by Palka.

This is a very good self-contained text book for entry-level studies. Most of the main principles are high-lighted and explained thoroughlly. I strongly recommended if anyone who has any extra money to spend on this book.