MU01022 Analysis in the Complex Domain

Mathematical Institute in Opava
Summer 2015
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Miroslav Engliš, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Miroslav Engliš, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU01002 Mathematical Analysis II && ( MU20003 Mathematical Analysis III || MU01003 Mathematical Analysis III ) && MU01921 Anal. in the Complex Domain Ex
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
Students will acquire basic knowledge of complex analysis needed for further study of mathematics, as well as for completing the course of Analysis in the Complex Domain.
Syllabus
  • 1. Complex numbers, analytic functions - algebraic and goniometric form of a complex number; curves and domains in the complex plane; derivatives of functions of complex variable; analytic functions; Cauchy-Riemann equations; exponential and trigonometric functions; logarithm.
    2. Conformal mapping - linear transformations, Moebius transformations, exponential function, logarithm.
    3. Integration in the complex domain - integrals over curves, Cauchy theorem, Cauchy formula.
    4. Power series in the complex domain - Taylor series, Laurent series, singularities and roots.
    5. Integration using residue theorem - residues, residue theorem, evaluation of integrals.
Literature
    recommended literature
  • J. Smítal, P. Šindelářová. Komplexní analýza. MÚ SU, Opava, 2002. info
  • W. Rudin. Analýza v reálném a komplexním oboru. Academia, Praha, 1987. info
  • P. V. O'Neil. Advanced Engineering Mathematics. Wadsworth Publishing Company, Belmont, 1983. info
  • E. Kreyszig. Advanced Engineering Mathematics. Wiley, New York, 1983. info
  • R. V. Churchill, J. W. Brown, R. F. Verhey. Complex Variables and Applications. Mc Graw-Hill, New York, 1976. 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
Requirements for pre-exam credits are set out by the tutorial lecturer. In principle, they should warrant sufficient mastery of the course content.
The same applies to the written part of the exam. The oral part of the exam verifies cognisance of basic concepts of the theory.
The course is also listed under the following terms Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021, Summer 2022.
  • Enrolment Statistics (Summer 2015, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2015/MU01022