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Lecturer(s)
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Course content
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The residue theorem and its consequences, calculations of the values of real integrals over the intervals using resudues. Holomorphic, conformal and analytic functions, complex analytic extension of functions and complete analytic function and its Riemann surface. Integral transforms (Laplace and Fourier transform) and Z-transform. Solution of ordinary differential equations, the Volterra integral equations and difference equations.
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Learning activities and teaching methods
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Group discussion, Students' self-study, Lecture, Practicum
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 50 hours per semester
- Preparation for formative assessments (2-20)
- 30 hours per semester
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| prerequisite |
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| Knowledge |
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| define basic notions of complex analysis from the course Základy komplexní analýzy |
| state basic theorems of complex analysis from the course Základy komplexní analýzy |
| Skills |
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| use single-valued complex functions |
| use and generalize tools and notions from real analysis to the complex framework |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| multi-valued complex functions |
| use of complex analysis in solving the problems from real analysis |
| various complex transforms and their use in solving of differential and difference equations |
| Skills |
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| work with set-valued complex functions |
| apply methods and tools from complex analysis to solve the problems of real analysis |
| apply integral transforms to find a solution of differential and difference equations |
| Competences |
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| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Group discussion |
| Self-study of literature |
| Skills |
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| Lecture |
| Practicum |
| Task-based study method |
| Individual study |
| Competences |
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| Practicum |
| Seminar |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Skills |
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| Combined exam |
| Competences |
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| Combined exam |
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Recommended literature
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Debnath, Lokenath; Bhatta, Dambaru. Integral transforms and their applications. 2nd ed. Boca Raton : Chapman & Hall/CRC, 2007. ISBN 1-58488-575-0.
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Hansen, Eric W. Fourier transforms. Principles and applications. Hoboken, New Jersey, 2014. ISBN 978-1-118-47914-8.
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Polák, Josef. Integrální a diskrétní transformace. 3.,přeprac. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-924-9.
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Schiff, Joel L. The Laplace transform: Theory and applications. New York, 1999. ISBN 0-387-98698-7.
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