MA562 Curvilinear and surface integrals, complex analysis 2

Faculty of Science
Spring 2005
Extent and Intensity
2/0/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Jaromír Šimša, CSc. (lecturer)
Guaranteed by
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Jaromír Šimša, CSc.
Timetable
Fri 18:00–19:50 UM
Prerequisites (in Czech)
M1510 Mathematical Analysis 1 && M2510 Mathematical Analysis 2 && M5520 Mathematical Analysis 4 && M9561 Curv. and surf. integrals
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
The goal of the course is to present the basic concepts and techniques of the calculus of functions whose domains of definitions and co-domains are formed by complex numbers. Differential properties of such functions are extremely different from the analogous properties of "common" functions in the real domain. The resulting theory (called Complex Analysis) is an important area of mathematical research with numerous applications inside Mathematics as well as in Physics. An example will be presented in our course when we apply the residue theorem to compute the values of some definite integrals in the real domain.
Syllabus
  • Functions of complex variables. Complex series. Elementary functions in complex domain. Curvilinear integrals in complex domain. Derivation of complex functions. Holomorphic functions. Cauchy theorem. Isolated singularities and residue theory.
Literature
  • NOVÁK, Vítězslav. Analýza v komplexním oboru. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 103 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2005/MA562