Theory of Functions of a Complex Variable

Code – 230100   Information and computer science; section: Software of computer equipment and automation systems

Qualification (degree) – Master

Description of course modules (sections, subjects):

1. Concept of a limit, continuity, differentiability and analyticity of functions of a complex variable.
2. Cauchy theorem and integral representation of functions of a complex variable.
3. Taylor and Laurent series for functions of a complex variable.
4. Theory of residues for functions of a complex variable.
5. Theory of conformal representation.
6. Application of the theory of functions of a complex variable to mechanics problems.

Syllabus of the course:

Objective of the course: introduction of students to key concepts and results of the theory of functions of a complex variable, application of methods of complex analysis and algorithms based thereon to solution of scientific and application problems.

Tasks of the course

The course is aimed at:

• study of a concept of an analytical function which is fundamental for mathematics and its applications,
• development of a technique for differential and integral calculus for functions of a complex variable,
• study of integral representation for functions of a complex variable,
• study of expansion of functions of a complex variable into Taylor and Laurent series,
• study of the theory of residues for functions of a complex variable,
• study of the theory of conformal representation,
• familiarity with application of methods of complex analysis to problems of natural science and engineering.

The course in included in optional courses of a general scientific cycle attributed to the master’s degree educational standard.

As a result of studying the course a student should:

• know key concepts of differential and integral calculus, theory of expansion into series and theory of residues of functions of a complex variable,
• be able in practice apply results of the theory of functions of a complex variable in mathematical problems,
• have skills of application of methods of complex analysis to problems of natural science and engineering,
• show ability and readiness to solve problems of complex analysis as applied to various subject areas.

Teaching methods:

• lectures,
• laboratory work,
• students’ independent work performed according to the teacher’s task in classrooms and on an extracurricular basis, including use of technical training aids (compulsory),
• tutorials.

Total hours – 108.

Total credits – 3.

Laboratory work – 1/36.

Form of interim assessment – pass/fail exam.