Course detail
Complex Variable Functions
FSI-SKFAcad. year: 2024/2025
The aim of the course is to make students familiar with the fundamentals of complex variable functions and Fourier transform.
Language of instruction
Number of ECTS credits
Mode of study
Department
Entry knowledge
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
The aim of the course is to familiarise students with elements of complex analysis and with Fourier transform including applications.
The course provides students with basic knowledge and skills necessary for using the ecomplex numbers, integrals and residue, usage of Fourier transforms.
Study aids
Prerequisites and corequisites
Basic literature
Markushevich A.,I., Silverman R., A.:Theory of Functions of a Complex Variable, AMS Publishing, 2005 (EN)
Šulista M.: Základy analýzy v komplexním oboru. SNTL Praha 1981 (CS)
Recommended reading
Elearning
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
1. Complex numbers, Gauss plane, Riemann sphere
2. Functions of complex variable, limit, continuity, elementary functions
3. Derivative, holomorphic functions, harmonic functions, Cauchy-Riemann equations
4. Harmonic functions, geometric interpretation of derivative in complex domain
5. Series and rows of complex functions, power sets, uniform convergence
6. Curves, integral of complex function, primitive function, integral path independence
7. Cauchy's integral formula, uniqueness theorem
8. Taylor and Laurent series
9. Singular points of holomorphic functions, residue, residue theorem
10. Integration by means of residue theory
11. Conformal mapping
12. Fourier transform
13. Fourier transform aplications
Exercise
Teacher / Lecturer
Syllabus
1. Complex numbers, Moivre's formula, n-th root
2. Functions of complex variable, limit, continuity, elementary functions
3. Derivative, holomorphic functions, harmonic functions, Cauchy-Riemann equations
4. Harmonic functions, geometric interpretation of derivative in complex domain
5. Series and rows of complex functions, power sets, uniform convergence
6. Curves, integral of complex function, primitive function, integral path independence
7. Cauchy's integral formula, uniqueness theorem
8. Taylor and Laurent series
9. Singular points of holomorphic functions, residue, residue theorem
10. Integration by means of residue theory
11. Conformal mapping
12. Fourier transform
13. Fourier transform aplications
Elearning