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Lecturer(s)
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Course content
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Week 1: The space of complex numbers and its extension. Week 2: The representation of complex numbers in the Gauss plane. Curves in the Gauss plane. Week 3: Complex functions of a complex variable. Week 4: Other elementary functions and their basic properties. Week 5: Sequences and series of complex numbers. Week 6: Limits and the continuity of complex functions. Week 7: 1. written test. The derivative of complex functions. Week 8: The derivative of complex functions, holomorphic functions. Week 9: The integration of functions in the complex plane. Week 10: Sequences and series of complex functions. Week 11: Isolated singular points and their classification. Week 12: Calculating residues. Week 13: Residue theorem and its applications.
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Learning activities and teaching methods
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Lecture supplemented with a discussion, Multimedia supported teaching, Seminar classes, Textual studies
- Contact hours
- 26 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Preparation for comprehensive test (10-40)
- 16 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with a high school algebra and trigonometry. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: 1. Use basic and advanced calculations with complex numbers. 2. Define elementary complex functions of a complex variable and describe their basic properties. 3. Work with sequences and series of complex numbers. 4. Use basic differential and integral calculus in a complex domain. 5. Use holomorphic functions. 6. Use basic techniques to calculate curve integrals in a complex domain. 7. Work with Laurent series. 8. Apply Cauchy theorem and its consequences to calculate real integrals. 9. Use correct procedures to solve mathematical problems in the scope of the content of this course. |
| teaching methods |
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| Lecture supplemented with a discussion |
| Multimedia supported teaching |
| Textual studies |
| Seminar classes |
| assessment methods |
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| Test |
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Recommended literature
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Mašek, Josef. Sbírka úloh z vyšší matematiky : funkce komplexní proměnné. 1. vyd. Plzeň : ZČU, 1992. ISBN 80-7082-074-8.
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Polák, Josef. Matematická analýza v komplexním oboru. 2., upr. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-923-0.
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