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Lecturer(s)
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Slupská Petra, RNDr. Ph.D.
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Course content
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1) Complex numbers. Construction and algebraic characterization 2) Complex sequences and series. Extended complex plane. Construction and topologic characterization 3) Coplex functions. 4) Power series, the exponential function and complex trigonometric functions. 5) Derivatives in complex plane. Cauchy Riemann Equations 6) Integration in complex plane. Integration on path. The coplex integral. 7) Cauchy Theorem. 8) Taylor a Laurent series. 9) Singularities, residue theore. the index of point with respect to close curve. 10) Application of residual theory. Calculation of real intergral. 11) Laplace transform - definitions, using, properties and application. 12) Fourier transform - definitions, using, properties and application. 13) Z transform - definitions, using, properties and application.
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Learning activities and teaching methods
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Group discussion, Students' self-study, Lecture, Practicum
- Contact hours
- 65 hours per semester
- Preparation for formative assessments (2-20)
- 40 hours per semester
- Preparation for an examination (30-60)
- 50 hours per semester
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| prerequisite |
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| Knowledge |
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| Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1 or KMA/MA1. Other broader knowledge of the apparatus of functional analysis would be an advantage. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: - set up space of complex numbers and extended complex space, derivate basic characteristic these spaces; - deal with complex numbers; - deal with complex functions; - demonstrate knowledge of the definitions and fundamental theorems concerning complex sequences and complex series; - give the definitions and use derivatives and integrals in complex space; - deal with holomorphic (analytic) functions; - demonstrate knowledge of the Cauchy theorem and applications of the Cauchy Theorem; - deal with Laurent Series; - demonstrate knowledge of the definitions and fundamental theorems concerning Fourier, Laplace and Z transform. |
| teaching methods |
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| Lecture |
| Practicum |
| Group discussion |
| Self-study of literature |
| assessment methods |
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| Combined exam |
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Recommended literature
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Mašek, Josef. Sbírka úloh z matematiky : integrální transformace. 1. vyd. Plzeň : ZČU, 1993. ISBN 80-7082-117-5.
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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. Integrální a diskrétní transformace. 3.,přeprac. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-924-9.
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Polák, Josef. Matematická analýza v komplexním oboru II/. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-700-9.
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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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