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on 23 November 2006
This book has been the text book for the second year course I have been studying, "Complex Analysis", and I have found Priestley's book to be invaluable. Priestley's style is excellent, and the way she has organised the material is helpful, because she breaks certain topics down into a "basic" and "advanced" track, so you can get the feel for the topic before considering it in more detail.

Priestley also includes many worked examples, which again I found to be very helpful, because by working through the examples myself, I managed to consolidate what I had learned previously.

I would recommend this book to anyone who is an undergraduate studying complex analysis.
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on 7 April 2012
From what I can tell, in an effort to save space or something, the author has omitted more or less half of the steps of proofs and instead chooses to list off a bunch of relevant theorems that one would use in order to justify a step without explaining how they fit together. As a result, it was often unclear how the author gets from one step to the next, and I had to spend time on many of the proofs redoing the proof myself on paper in order for the steps to feel like they had logical flow.
The layout of the text is much too dense, as many equations that should be given their own line are stuffed into the text, with no adjustment for size. In addition, the author has some strange obsession with using negative exponents rather than inserting fractions, possibly as another attempt to save space, which unfortunately renders the equations looking unnaturally long.
Examples are sparse, and rarely illustrated, making a subject that is already tricky to visualize even less visualizable. The exercises vary wildly in difficulty, mainly either being incredibly easy plug-and-chug problems, or incredibly complicated proofs that require multiple pages of justifications. There are also no solutions, hints, or answers to any of the problems. Also, despite being the second edition, there are still plenty of typos in this book.
Overall, this is not a particularly good book if you are a beginner to complex analysis, or trying to teach yourself. It makes a nice reference book or review guide, in that it is extremely concise, and so it is relatively easy to go through and refresh your memory on theorems covered in class.
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on 31 July 2014
As an undergraduate, I was lectured by Dr. Priestley. I have had her book for 28 years. It is super-complex material, and I enjoy reading it as much today as I did when I was first introduced it. I can see the point that less favourable reviews are making, but it's still 5 stars.
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on 20 December 2006
Good things; the "tactical tips" are generally excellent and the material in the book is adequate and reasonably well paced for the 1st to 2nd year undergraduate. Wise choices with regards to topological abstraction are also made and worked in well to the text.

Occasionally important insights in proofs are omitted or worse genuine oversights are made (for instance, on p25 where the proof does not hold for all triplets in Cinfinity), there are also a few comical errors, e.g. p56 where even on the 2nd printing there is a glaring error in the very first definition of complex differentiable!

The author seems to take a dim view of alternative ways of constructing complex analysis which are genuinely quite interesting and worth exploring.

The downside of the book is the routineness of the exercises which are well below exam standard in a lot of places and sometimes is nothing more than a list of dull applications. The silly "Z mistake" things everywhere are also sort of insulting...
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on 26 November 2014
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.
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on 28 December 2012
Suffice to say, I sat through a lecture course on complex analysis. My tutor told me that I "lack basic understanding" at the end of the term.
I bought this book.
Wow! It is so clear and well set out. Explains a lot and also has little side notes about common mistakes, etc.
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on 24 December 2012
Impressed with this text as explains various ideas in complex analysis using many examples. Would (and have) recommend this book to others.
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on 3 July 2011
When I ordered this book, it arrived quickly and was in excellent condition. It explains the points very well (despite the occasional typos), so I am very pleased with the book - I recommend it for anyone studying Complex Analysis.
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on 8 March 2013
An excellent book for a first introduction to Complex Analysis.
It is very well presented and covers all the key material (or at least the stuff in the Cambridge IB 'Complex Analysis' and 'Complex Methods' courses.
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