Introduction to Complex Analysis

A super introduction to a difficult subject. T

This is an original book, not a low price edition.

The existing reviews refer to the 1st edition of this book, which I agree was a difficult read, though still accessible to undergraduates. The new book has been revised substantially to make it more readable, with a much more leisurely introduction and better partitioning of tougher material (which can be omitted by those such as physicists and engineers who require only a working knowledge of the subject). If anything I feel the result is too dumbed down; Priestley is loathe even to make use of such basic tools from real analysis as uniform convergence. Nevertheless, the second half of the book is more adventurous, making the totality a guide for an excellent undergrad class, such as the Oxford one on which the book was based. Beware: there is a large number of typos, which one must hope will be corrected in subsequent printings. Usually it will not be too challenging to circumnavigate these.

This seems to be a complex analysis book for people who already know complex analysis. I took an introductory course in complex analysis that used this book. I would not recommend using this text to learn complex analysis. The text mostly consists of standard explanatory material and proofs. As other reviewers have indicated, examples are scarce (some chapters have none!), and no answers to any (non-proof) exercises are given. And this is the second edition, which is claimed to have expanded on problems and examples (I suspect this claim to be a practical joke by Priestly). Overall, my experience with the second edition wasn't completely horrible, but the lack of answers to problems was a huge barrier to actually learning the material. In summary: if you are learning complex analysis, look for a text with better ratings. If you already know complex analysis and just need a refresher, this could be useful.

I learned complex analysis using the first edition of this book. I had never studied complex analysis before and I found the treatment rigorous but pleasurable. Complex analysis is one of the most beautiful areas of both pure and applied mathematics and learning it is essential for any serious student of mathematics. I can't think of a better place to start than Priestley. If you find this book hard then you probably need to spend more time learning basic analysis of the real line so you can follow the mathematical arguments.

This is a great book for mathematically mature students. Exposition is not crystal clear, but very mellow, if you can follow. This is not the first book to read in complex analysis. Try Bak.

I was recommended this book to get a head start in a notoriously difficult subject. I had muddled my way through real analysis beforehand and, as is typical, found myself eventually becoming more comfortable with the subject after gaining as much familiarity as possible. I was now ready to take on analysis in the complex plane! But, oh dear... I think one star is a little harsh but I have to agree largely with the reviewer who gave this rating. Explanations are curt and the tour through the subject is disjointed to the point that your anticipation of having the pieces come together is never satisfied and you are left wondering how productive the time you have spent reading has been. (This is not a "when am I ever going to use this?" gripe. I am leaning more toward pure mathematics in my degree so applications are not of any great concern to me). You then arrive at the end of the chapter to the exercises, which I consider the REAL (or complex?) learning part. I understand that some texts do not provide you with solutions specifically for the reason that the exercises are there just to engage you in the subject. While this is arguably justified for more advanced texts I would expect a little more guidance in an "introduction", so the lack of solutions to exercises was a great disappointment. On the plus-side, the book is direct in its explanations and concise, so it is a handy reference. Buying this book will give you the structure (albeit a disjointed one) that you would not get from simply looking up theorems on Wikipedia. It may be useful book to have but I am still pleased I bought it used and hence did not pay the full price.

No doubt the best and standard text for complex analysis, based on lecture notes given in Oxford and widely used there as the core text book. Only complaint is that the Kindle version has a number of typographical error.

Good book

A really good course book for a first course in the theory of complex variables. I needed it more for the applications than the proofs (coming from a Physics background) but this seems to cover both clearly and well.