In addition to being a rewarding branch of mathematics in its own right, the theory of functions of a complex variable underlies a large number of enormously powerful techniques which find their application not only in other branches of mathematics but also in the sciences and in engineering. Chapters 1, 2, and 5 of this book provide concisely but honestly the classical aspects of the theory of functions of a complex variable; the rest of the book is devoted to a detailed account of various techniques and the ideas from which they evolve. Many of the illustrative examples are phrased in terms of the physical contexts in which they might arise; however, we have tried to be consistent in including a mathematical statement of each problem to be discussed.
For the acquisition of skill in the use of these techniques, practice is even more important than instruction. Accordingly, we have inserted many exercises, including some which are essential parts of the text. The reader who fails to carry out a substantial number of these exercises will have missed much of the value of this book.
The individual chapters segregate specific topical items, but many readers will find it profitable to study selected parts of Chaps. 3 to 7 as they encounter the related underlying theory in Chap. 2.
We hope that through our presentation the reader will be able to discern the fascination of complex-function theory, recognize its power, and acquire skill in its use.
