# 470-8727/02 – Functions of a Complex Variable (FKP AVAT)

 Gurantor department Department of Applied Mathematics Credits 4 Subject guarantor doc. RNDr. Marek Lampart, Ph.D. Subject version guarantor doc. RNDr. Marek Lampart, Ph.D. Study level undergraduate or graduate Requirement Choice-compulsory type B Year 3 Semester winter Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties USP, FS Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KAL0063 prof. RNDr. René Kalus, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

To give students knowledge of basic concepts of complex functions of complex variable, Laplace transforms and Fourier series.

Lectures
Tutorials
Project work

### Summary

Functions of complex variable and integral transformations are one of the basic tools of effective solution of technical problems. The students will get knowledge of basic concepts of functions of complex variable, the theory of power series, Taylor and Laurent series, theory of residua, and Laplace transforms and Fouries series..

### Compulsory literature:

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994. William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0. Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer,1999, ISBN 0-387-98639-1.

### Recommended literature:

Galajda, P., Schrötter, Š.: Funkce komplexní proměnné a operátorový počet, Alfa-Bratislava, 1991. Škrášek, J., Tichý, Z.: Základy aplikované matematiky II, SNTL, Praha, 1986.

### Way of continuous check of knowledge in the course of semester

Verification of study: Test of functions of complex variable I. - max. 10 points. Test of functions of complex variable II. - max. 10 points. Individual project of Laplace transform - max. 10 points. Individual project of Fourier series - max. 10 points. Conditions for credit: Two tests - max. 20 points. Two individual projects - max. 20 points. Maximal number of points from exercises - 40 points. Minimal number of points from exercises - 20 points.

### Other requirements

No additional requirements are imposed on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Lectures: Complex functions and mappings. Complex differentiation, contour integration and deforming the contour. Complex series: power series, Taylor and Laurent series. Residue theorem. Applications. Introduction to Fourier series. Orthogonal systems of functions. Generalized Fourier series. Applications. Introduction to integral transforms. Convolution. Laplace transform, fundamental properties. Inverse Laplace transform. Applications. Exercises: Practising of complex functions, linear and quadratic mappings. Practising of complex differentiation, conformal mappings, contour integration and deforming the contour. Examples of Taylor and Laurent series and applications. Examples of orthogonal systems of functions, Fourier series and applications. Practising of Laplace transform. Solution of differential equation. Projects: Two individual works and their presentation on the theme: Fourier series. Laplace transform.

### Conditions for subject completion

Full-time form (validity from: 2018/2019 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 40 (40) 20
Test no. 1 Written test 10  0
Test no. 2 Written test 10  0
Project no. 1 Project 10  0
Project no. 2 Project 10  0
Examination Examination 60  11
Mandatory attendence parzicipation: Compulsory attendance at seminars.

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B0588A170002) Applied Sciences and Technologies PJ P English Ostrava 3 Choice-compulsory type A study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies PJ P English Ostrava 3 Choice-compulsory type A study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies PJ P English Ostrava 3 Choice-compulsory type A study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner