F5066 Functions of complex variable

Faculty of Science
Autumn 2003
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Dušan Hemzal, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Prerequisites
Fundamentals of analysis of real variables
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
Fundamental course of mathematical analysis for students of physics. Function of a complex variable. Power series of function of a complex variable. Regular and holomorphous functions, Taylor series, Cauchy theorem and Cauchy formula, calculations of integrals. Singularities and their classification, Laurent series. Residue theorem and its consequences, evaluating integrals. Many-valued functions. Conformal mapping. Laplace transformation. Applications - response function of a physical system, Kramers-Kronig dispersion relations.
Syllabus (in Czech)
  • 1.Úvodní pojmy-definice funkce komplexní proměnné, integrál. 2. Holomorfní funkce, Cauchyovy-Riemannovy podmínky 3. Regulární funkce, Taylorova řada. 4. Cauchyova věta a její použití pro výpočet integrálů. 5. Věta o jednoznačnosti, holomorfní prodloužení. 6. Aplikace věty o jednoznačnosti, elementární funkce definované řadam. 7. Fyzikální aplikace Cauchyovy věty (Kramersovy-Kronigovy relace) a věty o jednoznačnosti. 8. Laurentova řada a reziduum. 9. Věta o reziduích a její důsledky. 10. Aplikace věty o reziduích při výpočtu integrálů. 11. Mnohoznačné funkce, prodloužení podél křivek, základní mnohoznačné funkce. 12. Laplaceova transformace. 13. Aplikace Laplaceovy transformace ve fyzice. 14. Konformní zobrazení a fyzikální aplikace.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Spring 2012, Autumn 2011 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2023, Spring 2025.
  • Enrolment Statistics (Autumn 2003, recent)
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