This textbook is designed for students of the Specialty 131 "Applied Mechanics", studying the discipline "Higher Mathematics 3. Series. Theory of the Functions of a Complex Variable" in English.
The textbook introduces the concepts of numerical, functional, power and Fourier series; application of series; the theory of the functions of a complex variable, including differentiation and integration technics, Laurent series, the residue theory and its applications; the basic concepts of the Laplace and Fourier transforms and their applications.
Each part contains basic mathematical conceptions, explains new mathematical terms and is provided review questions and exercises, which will allow students to master the skills of solving practical problems. The most important concepts of the theory are explained and illustrated by figures and examples to help clarify the theory and show some applications.
The textbook can be also recommended to students of other specialties, who study Theory of Series and Theory of the Functions of a Complex Variable. The manual can be used to provide full-time, distance or mixed education.