Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than is found in other texts, and the resulting proofs often shed more light on the results than the standard proofs. While the first part is suitable for an introductory course at undergraduate level, the additional topics covered in the second part give the instructor of a gradute course a great deal of flexibility in structuring a more advanced course.
In this new edition of a standard textbook, new exercises have been added, in addition to more material on the Borel theorem, Picard's theorem, and J.D. Newman's proof of the prime number theorem. The treatment of gamma and zeta functions has been expanded and an appendix has been added which includes material not usually included in standard texts. The first part of the book is an introduction to complex analysis, while the second covers many special topics which may be used in an advanced course. Annotation c. Book News, Inc., Portland, OR (booknews.com)