UFDF036 Applications of the Theory of Complex Functions in Physics

Faculty of Philosophy and Science in Opava
Winter 2021
Extent and Intensity
0/0/0. 0 credit(s). Type of Completion: dzk.
Guaranteed by
RNDr. Filip Blaschke, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Introduces basic and advanced parts of theory of functions of complex variable, and its applications in theoretical physics.
Syllabus
  • - Analytické funkce
    - Komplexní derivace
    - Chachyho věta
    - Liouvileův teorém
    - Laurentova řada
    - Singularity a jejich klasifikace
    - Reziduová věta
    - Meromorfní funkce
    - Póly a nuly meromorfní funkce
    - Poissonův kernel
    - Cauchyho-Riemannovy rovnice
    - Harmonické funkce
    - Konformní zobrazení
    - Celé funkce
    - Analytické prodloužení
    - Riemannovy plochy
    - Riemannova sféra
    - Gamma funkce
    - Riemannova zeta funkce
    - Nekonečné produkty
    - Hadamardův faktorizační teorém
    - Mittagův-Lefflerův teorém
    - Picardoy věty
    - Modulární funkce
Literature
    recommended literature
  • Rudin W. Real and Complex Analysis. McGraw-Hill series in higher mathematics, 1970. info
  • Titchmarch E.C. The theory of functions. Oxford University Press, 1932. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attendance at lectures is recommended. It can be substituted by
the self-study of recommended literature and individual consultations.
The course is also listed under the following terms Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Winter 2013, Summer 2014, Winter 2014, Summer 2015, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Winter 2019, Summer 2020, Winter 2020, Summer 2021, Summer 2022.
  • Enrolment Statistics (Winter 2021, recent)
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