Course: Functions of Complex Variable

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Course title Functions of Complex Variable
Course code KMD/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)
  • Bittnerová Daniela, RNDr. CSc.
Course content
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.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
Learning outcomes
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
Basic knowledge of real analysis.

Assessment methods and criteria
Combined examination

Credit: Participation on seminars. Working out seminar work.
Recommended literature


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
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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): Professional studies for lower-secondary school teachers. (15) 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): Recreology (15) Category: Physical education and sport - 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: -