FC220 Vybrané aplikace teorie funkcí komplexní proměnné

Faculty of Science
Spring 2007
Extent and Intensity
2/1. 3 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
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
differential and integral calculus of functions of one and many variables, fundaments of theory of functions of a comlex variable
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Students obtain basic knowledge of advanced parts of the tehory of functjins of a complex variable (multivalued functions, Laplace transformation). They will be able to practically use the theory for solving practical physical problems (response functions, optical characteristics of materials, Kramers-Kronig relations). The first part of the presentation is concentrated to mathematical aspects.
Syllabus
  • 1. Summary of basic properties of singlevalued functions of a complex variable, holomorphous functions. Meromorphous functions, residue theorem. 3. Multivalued functions - analytical prolongation along curves. 4. Basic multivalued functions and their properties. 5. Applications of multivalued functions - critical points of the density of electron states. 6. Laplace transformation (LT). 7. Basic theorems for LT. 8. Applications of LT - solving differential equations. 9. Linear material relations. 10. Optical response. 11. Kramers-Kronig relations and their use in the study of the optical response. 12. Conformal mapping I. 13. Conformal mapping II, applications.
Literature
  • Bude průběžně doporučována.
Assessment methods (in Czech)
Typ výuky: přednáška a cvičení. Závěrečné hodnocení: zápočet (písemka). Průběžné požadavky: Zpracování dvou příkladů nebo důkazů během semestru. Povinnost navštěvovat cvičení.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2007/FC220