ABSTRACT
Certain linear two-dimensional elliptic problems turn out to be difficult to solve in a Cartesian coordinate setup. In many such cases, it is advisable to go over to equivalent formulations in terms of complex variables. This chapter provides a brief presentation of the basic rules of manipulation of complex functions and a few essential details about complex functions. It consider the mathematical model of plane deformation of an elastic body as an illustration of the efficiency of the complex variable method in solving linear two-dimensional systems of partial differential equations.
