Visual Complex Analysis

If only this book had been available when I did my degree! I got a First, and A grades in all the papers, but two of which I had no proper understanding of: Galois Theory, and Complex Analysis. I am still searching for the book which can explain to me what made Galois set off in the direction he did. As for the latter, this work by Needham more than fulfills the comprehension I have been looking for ever since I finished my degree course, 33 years ago! Admittedly it has been a rather leisurely search. Some reviewers complain that it is not very accessible. I think it is plain right at the outset that it is not an attempt at popularising complex analysis. Nor is it intended to be a text book. The author clearly states on several occasions that sometimes he is only offering a geometric insight rather than a rigorous proof. This book is perfect in complementing a typical text on the subject, which may provide the rigour but possibly totally neglect the geometry. None of this is to suggest that the book is sloppy, or inaccurate in any way. The mathematics is not compromised at all. What was a true revelation for me was the magical world that slowly but surely unfolded with each chapter. When I did my degree, all the results of complex calculus were presented in the usual way, with rigorous proofs, which I could reproduce in exams, and knew that those results which gave complex analysis an advantage over real analysis derived from the definition of an analytic function. But I never understood why until now. People like Cauchy and Riemann clearly understood and saw in a way which is brought to life in CVA. Needham refers to Bach and Wagner in his preface. I think it is no exaggeration to say that exploring the magical world of complex analysis as presented here is just as sublime and beautiful as the music of those two giants.

This is not just an excellent book, this book is exceptional. I can actually name just a couple of books of the same quality. This book is in the same division as Feyman's lectures.First of all, it is a very good piece of writing. The book very easy to read (although the content is far from being easy!) and I can compare the reading of this book to reading a good classical literature. Besides that, all of the explanations in the book is very clear and visual.I knew a bit of complex analysis before, but I always felt that I miss some parts and I don't have a whole image of this field in my head. But I was quite prepared. Surprisingly, even those things which I already knew this book presented in a different way, which was very interesting.I strongly recommend this book to everyone (even to those who is confident in his knowledge of Complex Analysis!) and personally I'll follow this author and by his upcoming books.

Everyone is different. I believe that I am a visual thinker and develop understanding faster and better with a visual model or visual interpretation of the maths. This book was written with this approach in mind, so, for me, is one of the best text books on maths that i have read. Many maths text books are dense with maths, formulae, equations etc leaving the insight to the reader to develop on their own. With these other text books, I can plough my way through the maths eventually, but often i am left wondering whether i have fully understood the maths being presented and its implications. I thought this book was different. It was a thoroughly enjoyable book to read and one that i am likely to be referring to again and again.

This is a well known and highly regarded text on Complex Analysis. I wouldn’t buy it if you are an undergraduate student, but if you are already familiar and confident with complex numbers to degree level then you will find this book to be well worth the investment.

Starting easily and stepping up gradually. A graduate textbook overall

Great to visualize difficult concepts, really deepens understanding.

A book whose purpose is to provide the reader with much needed intuition for complex analysis through visual representations of the material. It's the best supplement for any complex analysis books out there because it is mostly useful in understanding what the hell you are actually learning/doing. The only proofs here are the ones that are not lengthy and contribute to the understanding. This book is a gem for everybody who wants to build some intuition on complex analysis but it should not be thought of as a main textbook that can be used for a complex analysis course (either on the pure math side or the applied math side); it works best as a supplement that's there to deepen the reader's understanding.It contains helpful graphs and figures, offers explanations on nearly every concept that it tries to teach the reader and it's full of applications from physics and engineering. It does not shy away from more "abstract" applications like Quantum Mechanics, which is another one of its strong points. Furthermore, most of the applications are carefully chosen so that they contributes mathematically and intuitively.