The authors are great writers, who present the topic in a valuable historical context. Nevertheless, this book moves fast -- all the beautiful results that distinguish the "nice" behavior of complex-differentiable functions from the "ugly" ones of differentiable functions of real variables are proved in the first three chapters. It then quickly goes on to discuss more advanced results relating to Fourier analysis (most notably, the Paley-Wiener theorem) and techniques (e.g., the Phragmen-Lindelof principle), followed by some interesting applications of complex analysis to number theory.
For a first undergraduate course in complex analysis for math majors (i.e., a theory course, as opposed to a course primarily concerned with computing contour integrals), coverage of the first four chapters plus a few selected topics (e.g., the Riemann mapping theorem, properties of the Gamma and Zeta functions, etc.) with the harder exercises and easier problems assigned should already make for a fast paced course, despite what the preface of the text claims. A course in real analysis based on Rudin's Principles of Mathematical Analysis should probably be considered a prerequisite. The proofs are written in a way for someone already quite comfortable with rigorous arguments, with the reader expected to be able to supply the routine epsilon-delta manipulations that are left out when the authors feel like they are tedious.
As a warning, many of the exercises are rather difficult, while the problems are quite involved and even the easier ones will take even good students many hours (or even days) of thought while the harder ones may be out of reach unless substantial hints are given by the instructor. No problem or exercise is really a "routine" verification or computation.
That said, the mathematics is beautiful, and I had the good fortune of taking this course from Prof. Yum-Tong Siu, an expert in the field and an inspiring instructor. This was also my mathematical swansong, since I was taking the course in my senior year, and I was headed to grad school in organic chemistry. The work load was a bit high because of this new text, but the course was rewarding.
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The actual content has been ably reviewed already. I will address only the particulars of this printing. This printing is a photocopy of the original, as you can see from the human hair on one of the first pages. The Chinese translation of the preface is titled "Photocopy Preface" according to Google Translate. According to Princeton University Press, this title was licensed for printing in 2006 for distribution solely in China, and they are aware that copies have been distributed outside of China. If none of this bothers you, then... enjoy!
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The actual content has been ably reviewed already. I will address only the particulars of this printing. This printing is a photocopy of the original, as you can see from the human hair on one of the first pages. The Chinese translation of the preface is titled "Photocopy Preface" according to Google Translate. According to Princeton University Press, this title was licensed for printing in 2006 for distribution solely in China, and they are aware that copies have been distributed outside of China. If none of this bothers you, then... enjoy!
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Luigi Orlandi
The ebook does not shows the formula correctly
Reviewed in Italy on May 24, 2023