| Course title | Functions of Complex Variable |
|---|---|
| Course code | KMA/FCV-E |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Winter and summer |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | Optional |
| Form of instruction | Face-to-face |
| Work placements | Course does not contain work placement |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Complex numbers - algebraic and modulus/argument form, algebraic operations, modulus, complex conjugate number. 2. Complex functions of a real variable, real functions of a complex variable, complex functions of a complex variable - basic functions. 3. Continuity, limit, derivative in C. Holomorphic functions. Cauchy-Riemann Conditions, Conformal mapping. 4. Standard complex functions. Integrals in C, curvilinear integral. 6. Cauchy´s integral, Cauchy´s Theorem, Cauchy´s Integral Rule. 7. Laurent´s series, properties. 8. Singularities, residues, The Residue Theorem,Integral of rational functions by using residues.
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| Learning activities and teaching methods |
| Monological explanation (lecture, presentation,briefing) |
| Learning outcomes |
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The main goal of this subject is to study properties of functions of complex variables and solve some practical problems.
Basic knowledge of the complex analysis. |
| Prerequisites |
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Basic knowledge of real analysis.
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| Assessment methods and criteria |
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Combined examination
Credit: Participation on seminars. Working out seminar work. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science, Humanities and Education | Study plan (Version): Education in Leisure Time (20) | Category: Pedagogy, teacher training and social care | - | Recommended year of study:-, Recommended semester: - |
| Faculty: Faculty of Science, Humanities and Education | Study plan (Version): Professional studies for lower-secondary school teachers. (18) | Category: Pedagogy, teacher training and social care | - | Recommended year of study:-, Recommended semester: - |
| Faculty: Faculty of Science, Humanities and Education | Study plan (Version): Education in Leisure Time (20) | Category: Pedagogy, teacher training and social care | - | Recommended year of study:-, Recommended semester: - |
| Faculty: Faculty of Science, Humanities and Education | Study plan (Version): Applied Geography (19) | Category: Geography courses | - | Recommended year of study:-, Recommended semester: - |
| Faculty: Faculty of Science, Humanities and Education | Study plan (Version): Professional studies for lower-secondary school teachers. (15) | Category: Pedagogy, teacher training and social care | - | Recommended year of study:-, Recommended semester: - |