Functions of complex variables / Philip Franklin

The book is intended as an elementary text for a first course in complex variables at either the senior or first year graduate level. For students with an adequate background in advanced calculus the present text could be completed in one semester. In the reviewer's opinion this book achieves its objective of being an adequate introduction to the subject both for those whose interest is in the applications as well as those whose interest is primarily mathematical.
The first six chapters are devoted to geometric function theory. The author gives a detailed treatment to the bilinear transformation together with an introduction to the geometry of inversion. The latter topic, though not usually found in an elementary text, gives the student a clearer view of the significant geometric properties of the bilinear transformation. In the remaining four chapters the author develops the usual consequences of the Cauchy Integral Theorem. The large number of drill exercises and exercises intended to extend the text will thoroughly test the student's mastery of the material. Some typographical errors were noted but the reviewer found none that the student could not easily correct. (MathSciNet)

Notes bibliogr. Index