Complex Variables is an extended course in complex analysis and its applications for engineering students and for those who use complex analysis in their work. In addition to classical results, it includes results recently obtained by the authors. The book is based on many years of experience teaching complex analysis to students in applied mathematics at the University of Ottawa and Riga University and contains material that was tested and revised according to student comments. The authors have combined a rigorous presentation with clarity and many solved examples. The text introduces the theory of functions of one complex variable, and it presents an evaluation of many new integration formulae and the summation of new infinite series by the calculus of residue. The book also includes the Fatou-Julia theory for meromorphic functions for finding selective roots of some transcendental equations as found in the applications. The exercises provided in the text are elementary and aim at the understanding of the theory of analytic functions. Answers to odd-numbered exercises are in the back of the book, answers to even-numbered exercises are provided in an accompanying instructor"s manual.
