# MU:MU01022 Analysis in the Complex Domain - Course Information

## MU01022 Analysis in the Complex Domain

**Mathematical Institute in Opava**

Summer 2016

**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 ||**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**- Mathematics (programme MU, B1101)

**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.

- 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.
**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

*recommended literature*- J. Smítal, P. Šindelářová.
**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.

- Enrolment Statistics (Summer 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2016/MU01022