Course detail
Complex Variable Functions
FSI-SKF-A Acad. year: 2021/2022 Summer semester
The aim of the course is to make studetns familiar with the fundamentals of complex variable functions. The course focuses on the following areas: complex numbers, elementar functions of complex variable, holomorfous functions, derivative and integral of complex variable functions, meromorphous functions, Taylor and Laurent series, residua, residua theorem and its applications in integral computing, conformous mapping, homography and other examples of usage of conformous mapping, Laplace transform and its basic properties, Dirac and delta functions and its applications in differential equations solution, Fourier transform.
Language of instruction
English
Number of ECTS credits
6
Supervisor
Department
Learning outcomes of the course unit
The course provides students with basic knowledge ands skills necessary for using th ecomplex numbers, integrals and residua, usage of Laplace and Fourier transforms.
Prerequisites
Real variable analysis at the basic course level
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes
Course-unit credit – based on a written test.
Exam has a written and an oral part.
Aims
The aim of the course is to familiarise students with basic properties of complex numbers and complex variable functions.
Specification of controlled education, way of implementation and compensation for absences
Missed lessons can be compensated for via a written test.
The study programmes with the given course
Programme N-MAI-A: Mathematical Engineering, Master's, compulsory
Type of course unit
Lecture
39 hours, optionally
Syllabus
1. Complex numbers, sets of complex numbers
2. Functions of complex variable, limit, continuity, elementary functions
3. Derivative, holomorphy functions, harmonic functions, Cauchy-Riemann equations
4. Harmonic functions, geometric interpertation of derivative
5. Series and rows of complex functions, power sets
6. Integral of complex function
7. Curves
8. Cauchy's theorem, Cauchy's integral formula, Liouville's theorem
9. Theorem about uniqueness of holomorphy functions
10. Isolated singular points of holomorphy functions, Laurent series
11. Residua
12. Conformous mapping
13. Laplace transform
Exercise
26 hours, compulsory
Syllabus
1. Complex numbers, sets of complex numbers
2. Functions of complex variable, limit, continuity, elementary functions
3. Derivative, holomorphy functions, harmonic functions, Cauchy-Riemann equations
4. Harmonic functions, geometric interpertation of derivative
5. Series and rows of complex functions, power sets
6. Integral of complex function
7. Curves
8. Cauchy's theorem, Cauchy's integral formula, Liouville's theorem
9. Theorem about uniqueness of holomorphy functions
10. Isolated singular points of holomorphy functions, Laurent series
11. Residua
12. Conformous mapping
13. Laplace transform