Course detail
Mathematics - Selected Topics II
FSI-T2K Acad. year: 2023/2024 Winter semester
The course familiarises students with fundamentals of the complex variable analysis. It gives information about elementary functions of complex variable, about derivative and the theory of holomorphic functions, conform mapping, and integration of complex variable functions including the theory of residue.
Language of instruction
Czech
Number of ECTS credits
4
Supervisor
Department
Entry knowledge
Knowledge of mathematical analysis at the basic course level
Rules for evaluation and completion of the course
Course-unit credit based on a written test.
Exam has a written and an oral part.
Missed lessons can be compensated via a written test.
Aims
Then aim of the course is to extend students´ knowledge of real variable analysis to complex domain.
Fundamental knowledge of complex functions analysis.
The study programmes with the given course
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Complex numbers, Gauss plain, sets of complex numbers
2. Functions of complex variable, limit, continuity, elementary
functions
3. Series and rows of complex numbers
4. Curves
5. Derivative, holomorphy functions, harmonic functions
6. Series and rows of complex functions, power set
7. Integral of complex function
8. Cauchy's theorem, Cauchy's integral formula
9. Laurent series
10. Isolated singular points of holomorphy functions
11. Residue
12. Using of residue
13. Conformal mapping
Exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
1. Complex numbers, Gauss plain, sets of complex numbers
2. Functions of complex variable, limit, continuity, elementary
functions
3. Series and rows of complex numbers
4. Curves
5. Derivative, holomorphy functions, harmonic functions
6. Series and rows of complex functions, power set
7. Integral of complex function
8. Cauchy's theorem, Cauchy's integral formula
9. Laurent series
10. Isolated singular points of holomorphy functions
11. Integration using residua theory
12. Using of residue
13. Test