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 tostudent 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 instructors manual.
* Presents text in a direct mathematical language, avoiding unnecessary abstract style
* Contains planes of domain and image of mappings which are always clearly specified and well-illustrated with figures
* Provides several new integration and summation formulas which may eventually find their way into symbolic softwares
* Includes a large collection of exercises
* Expands entire functions in infinite products into simpler forms than those found in many texts
* Presents fresh information on the dynamics of meromorphic functions to solve transcendental equations found in the applications
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M. Ya. Antimirov graduated from Kirgiz State University in Frunze (Kirgizstan) in theoretical physics. A Candidate in physics and mathematics, he obtained his Ph.D., then became docent in the Department of Applied Mathematics of the Riga Technical University, Latvia. In 1991, he obtained the degree of Doctor of Mathematics and Physics at the Physics Institute of the Academy of Sciences of Latvia, and he was promoted to full professorship of the department where he served as docent. He has published more than 75 research papers.
A.A. Kolyshkin graduated in applied mathematics from the Riga Technical University and obtained his Ph.D. (Candidate in physics and mathematics) from Saint-Petersburg (then Leningrad) State University. For two years, he held a Research Fellowship in the Laboratory of Nondestructive Testing at the Riga Technical University. Since then he has been with the Department of Engineering Mathematics at the Riga Technical University, as assistant, then as senior lecturer, and finally as associate professor. In 1987(1988, he visited the University of Ottawa under the auspices of the Canada(USSR Academic Exchange Program, and he returned again in 1991(1992 as a visiting researcher. He now serves as adjunct professor of mathematics and returns almost every year to Ottawa.
Remi Vaillancourt took several bachelors and masters degrees at the University of Ottawa, Ontario, Canada, and received his Ph.D. at the Courant Institute of Mathematical Sciences at New York University. Then for two years, he held an Office of Naval Research Fellowship at the University of Chicago. He is known for the Yamanugi-Nogi-Vaillancourt pseudodifference operators and the Calderon-Vaillancourt theorem for non-classical pseudodifferential operators. Since 1970 he has been at the University of Ottawa with the department of Mathematics and jointly, since 1974, with the department of Computer Science which has been absorbed in the new School of Information Technology and Engineering. Dr. Vaillancourt is a full professor. He has also served as chairman of the former department in 1972 - 1976; as vice president, present, and past-president of the Canadian Mathematical Society in 1975 - 1981; as chairman of the Canadian National Committee for the International Mathematical Union in 1979 - 1988, and as president and past-president of the Canadian Applied Mathematics Society. He writes reviews for Mathematical Reviews and Zentralblatt fur Mathematik.
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