PROBLEMS IN THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLES

The book “Problems on the Theory of Functions of Complex Variables” (TFVC) is intended primarily for students of the Faculties of Mechanics and Mathematics and of the Faculty of Physics and Mathematics of Universities, of the corresponding sections of pedagogical institutes and of polytechnic institutes with an extended mathematics program. The “Problems” also contain cycles that go beyond the framework of the programs. Some of them can serve as a basis for coursework and as material for the work of TFVC seminars. The authors also consider that the “Problems” may be useful for people specializing in the mechanics of continuous media (hydrodynamics, elasticity theory) and in electrotechnology, since they contain a considerable number of problems either devoted to the direct application of the TFVC to these branches or related to questions that represent the mathematical foundations of these branches (conformal transformations, harmonic functions, potentials, Cauchy-type integrals, etc.).

The first of these books has recently been translated into Spanish by the publishing house “Mir” 11, which will undoubtedly make it easier for our readers to use the “Problems”.

All suggestions for solving the problems are given in the main text. The most difficult problems, whose numbers are marked with an asterisk, are provided with solutions that are inserted in the answers.