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Course detail
FSI-SKFAcad. year: 2023/2024
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
Guarantor
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
Recommended reading
Elearning
Classification of course in study plans
Lecture
Teacher / Lecturer
Syllabus
1. Complex numbers, Gauss plane, Riemann sphere2. Functions of complex variable, limit, continuity, elementary functions3. 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 convergence6. Curves, integral of complex function, primitive function, integral path independence7. Cauchy's integral formula, uniqueness theorem8. Taylor and Laurent series9. Singular points of holomorphic functions, residue, residue theorem 10. Integration by means of residue theory 11. Conformal mapping 12. Fourier transform13. Fourier transform aplications
Exercise
1. Complex numbers, Moivre's formula, n-th root2. Functions of complex variable, limit, continuity, elementary functions3. 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 convergence6. Curves, integral of complex function, primitive function, integral path independence7. Cauchy's integral formula, uniqueness theorem8. Taylor and Laurent series9. Singular points of holomorphic functions, residue, residue theorem 10. Integration by means of residue theory 11. Conformal mapping 12. Fourier transform13. Fourier transform aplications