• Brno University of Technology - Centre of Sports Activities
  • Research centres

  • Pravděpodobně máte vypnutý JavaScript. Některé funkce portálu nebudou funkční.

Course detail

Mathematics - Selected Topics II

Course unit code: FSI-T2K
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Bachelor's (1st cycle)
Year of study: 3
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
Fundamental knowledge of complex functions analysis.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
Knowledge of mathematical analysis at the basic course level
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
Druckmüller, M., Ženíšek, A.: Funkce komplexní proměnné, PC-Dir Real, Brno 2000 proměnné, PC-Dir Real, Brno 2000
Druckmüller, M., Ženíšek, A.: Funkce komplexní proměnné, PC-Dir Real, Brno 2000
Šulista, M.: Základy analýzy v komplexním oboru, Stát.nakl.techn.lit., Praha 1981
Druckmüller, M., Svoboda, K.: Vybrané statě z matematiky I., skriptum FS VUT Brno, Brno 1986
Šulista, M.: Základy analýzy v komplexním oboru, Stát.nakl.techn.lit., Praha 1981
Druckmüller, M., Svoboda, K.: Vybrané statě z matematiky I., skriptum FS VUT Brno, Brno 1986
Šulista, M.: Analýza v komplexním oboru, Stát.nakl.techn.lit., Praha 1986
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.
Language of instruction:
Czech
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
Then aim of the course is to extend students´knowledge of real variable analysis to complex domain.
Specification of controlled education, way of implementation and compensation for absences:
Missed lessons can be compensated for via a written test.

Type of course unit:

Lecture: 26 hours, optionally
Teacher / Lecturer: prof. RNDr. Miloslav Druckmüller, CSc.
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 set
10. Isolated singular points of holomorphy functions
11. Residua
12. Using of residua
13. Conformal mapping
seminars: 26 hours, compulsory
Teacher / Lecturer: prof. RNDr. Miloslav Druckmüller, CSc.
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 set
10. Isolated singular points of holomorphy functions
11. Integration using residua theory
12. Using of residua
13. Test

The study programmes with the given course