Straightforward in concise, this introductory volume treats the theory rigorously but uses a minimum of sophisticated machinery and assumes no prior knowledge of topology. Priestley presents the major theorems as early as possible, so that those meeting complex analysis for the first time can appreciate the power and elegance of the subject by seeing applications of results, both practical and theoretical. A valuable resource for pure and applied mathematicians, this book is also suitable for graduate students and, as a reference, for engineers.
A concise and well structured introduction to complex analysis with many examples. Some theorems are repeated and unclearly stated such as the deformation theorem which starts for a triangle and is then generalized. Some pictures and proofs are not explained and too many are left to the reader, making some chapters more of an annotated exposition of facts rather than an exploration of the deep insights and uses of the theorems in complex analysis. Overall: not the best introductory textbook, but probably enough for reviewing the main theorems and concisely getting up to speed with the subject.