Mathematics - Selected Topics II (FSI-T2K)

Academic year 2018/2019
Supervisor: prof. RNDr. Miloslav Druckmüller, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
Then aim of the course is to extend students´knowledge of real variable analysis to complex domain.
Learning outcomes and competences:
Fundamental knowledge of complex functions analysis.
Prerequisites:
Knowledge of mathematical analysis at the basic course level
Course contents:
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 analytic functions, conform mapping, and integration of complex variable functions
including the theory of residua.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Missed lessons can be compensated for via a written test.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture 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 set
10. Isolated singular points of holomorphy functions
11. Residua
12. Using of residua
13. Conformal mapping
    Exercise 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 set
10. Isolated singular points of holomorphy functions
11. Integration using residua theory
12. Using of residua
13. Test
Literature - fundamental:
1. Druckmüller, M., Ženíšek, A.: Funkce komplexní proměnné, PC-Dir Real, Brno 2000
2. Šulista, M.: Základy analýzy v komplexním oboru, Stát.nakl.techn.lit., Praha 1981
3. Druckmüller, M., Svoboda, K.: Vybrané statě z matematiky I., skriptum FS VUT Brno, Brno 1986
Literature - recommended:
1. Druckmüller, M., Ženíšek, A.: Funkce komplexní proměnné, PC-Dir Real, Brno 2000 proměnné, PC-Dir Real, Brno 2000
2. Druckmüller, M., Svoboda, K.: Vybrané statě z matematiky I., skriptum FS VUT Brno, Brno 1986
3. Šulista, M.: Základy analýzy v komplexním oboru, Stát.nakl.techn.lit., Praha 1981
4. Šulista, M.: Analýza v komplexním oboru, Stát.nakl.techn.lit., Praha 1986
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3A-P full-time study B-FIN Physical Engineering and Nanotechnology -- Cr,Ex 4 Compulsory 1 3 W