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

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Marek Lampart, Ph.D.Subject version guarantorprof. RNDr. Marek Lampart, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesUSP, FEI, FSIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOR33 doc. Ing. David Horák, Ph.D.
KAL0063 prof. RNDr. René Kalus, Ph.D.
LAM05 prof. RNDr. Marek Lampart, Ph.D.
SIM46 Mgr. Lenka Přibylová, Ph.D.
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.

Teaching methods

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:

Needham, Tristan, Visual Complex Analysis, Oxford University Press, 2023, ISBN: 0192868926 Stewart Ian, Complex Analysis, Cambridge, 2018, ISBN: 9781108436793 Shah, Nita H. and K. Naik, Monika. Integral Transforms and Applications, Berlin, Boston: De Gruyter, 2022. https://doi.org/10.1515/9783110792850 Kozubek, T., Lampart, M.: Integral Transforms, 2022, https://homel.vsb.cz/~lam05/Teaching.html Bouchala, J., Lampart, M.: An Introduction to Complex Analysis, 2022, https://homel.vsb.cz/~lam05/Teaching.html

Recommended literature:

Howie J.M., Complex Analysis, Springer-Verlag London, 2003, ISBN 978-1-85233-733-9. Abdon Atangana, Ali Akgul, Integral Transforms and Engineering, Taylor & Francis Ltd, 2023, ISBN-13 9781032416830

Way of continuous check of knowledge in the course of semester

Verification of study: Test of a complex variable no.1 - max. 10 points. Test of a complex variable no.2 - max. 10 points. Individual project on Fourier series - max. 10 points. Conditions for credit: Two tests - max. 20 points. One individual project - max. 10 points. The maximum number of points from exercises is 30 points. The minimum number of points from exercises is 15 points. Final exam (written form).

E-learning

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. Project: One individual project on the topic on Fourier series.

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2021/2022 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
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 3
Mandatory attendence participation: Seminars and lectures attendance is recommended.

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0714A270004) Mechatronics CMS P English Ostrava 1 Compulsory study plan
2023/2024 (N0714A270004) Mechatronics CMS P English Ostrava 1 Compulsory study plan
2023/2024 (N0714A060021) Communication and Information Technology P English Ostrava 1 Compulsory study plan
2022/2023 (N0714A060021) Communication and Information Technology P English Ostrava 1 Compulsory study plan
2022/2023 (N0714A270004) Mechatronics CMS P English Ostrava 1 Compulsory study plan
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

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2022/2023 Winter
2021/2022 Winter
2018/2019 Winter
2017/2018 Winter