# 470-4109/04 – Functions of Complex Variable and Integral Transformations (FKP IT)

 Gurantor department Department of Applied Mathematics Credits 6 Subject guarantor doc. RNDr. Marek Lampart, Ph.D. Subject version guarantor doc. RNDr. Marek Lampart, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2015/2016 Year of cancellation Intended for the faculties FEI, FS, USP Intended for study types Follow-up Master
Instruction secured by
LAM05 doc. RNDr. Marek Lampart, Ph.D.
MRO0010 Ing. Martin Mrovec
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Part-time Credit and Examination 10+10

### Subject aims expressed by acquired skills and competences

To give students knowledge of basic concepts of complex functions of complex variable and integral transformations.

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 and integral transformations.

### 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:

Howie J.M., Complex Analysis, Springer-Verlag London, 2003, ISBN 978-1-85233-733-9. Needham T., Visual complex analysis, Oxford University Press, 1997, ISBN 0-19-853446-9.

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

Verification of study: Test of complex variable - max. 10 points. Test of Laplace transform - 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. Fourier transform, fundamental properties. Inverse Fourier transform. Applications. Z-transform, fundamental properties. Inverse Z-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. Practising of Fourier transform and examples. Practising of Z-transform. Solution of difference equation. Projects: Two individual works and their presentation on the theme: Fourier series. Laplace transform.

### Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 40 (40) 20
Test 1. Written test 10  0
Test 2. Written test 10  0
Projekt 1. Project 10  0
Projekt 2. Project 10  0
Examination Examination 60  11
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (N0714A270004) Mechatronics CMS P English Ostrava 1 Compulsory study plan
2020/2021 (N0714A270004) Mechatronics CMS P English Ostrava 1 Compulsory study plan
2019/2020 (N3943) Mechatronics (3906T006) Mechatronic Systems P English Ostrava 1 Compulsory study plan
2019/2020 (N0714A270004) Mechatronics CMS P English Ostrava 1 Compulsory study plan
2018/2019 (N3943) Mechatronics (3906T006) Mechatronic Systems P English Ostrava 1 Compulsory study plan
2017/2018 (N3943) Mechatronics (3906T006) Mechatronic Systems P English Ostrava 1 Compulsory study plan
2016/2017 (N3943) Mechatronics (3906T006) Mechatronic Systems P English Ostrava 1 Compulsory study plan
2015/2016 (N3943) Mechatronics (3906T006) Mechatronic Systems P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

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