* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 470-4109/01 | |||||
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Number of ECTS Credits Allocated | 6 ECTS credits | |||||

Type of Course Unit * | Compulsory | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | First Year | |||||

Semester when the Course Unit is delivered | Winter Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech | |||||

Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

SIM46 | Mgr. Lenka Přibylová, Ph.D. | |||||

HOR33 | doc. Ing. David Horák, Ph.D. | |||||

LAM05 | prof. RNDr. Marek Lampart, Ph.D. | |||||

KAL0063 | prof. RNDr. René Kalus, Ph.D. | |||||

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. | ||||||

Learning Outcomes of the Course Unit | ||||||

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

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. | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

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 | ||||||

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.: Integrální transformace, 2012, http://mi21.vsb.cz/modul/integralni-transformace Bouchala, J.: Funkce komplexní proměnné, 2012, http://mi21.vsb.cz/modul/funkce-komplexni-promenne | ||||||

Recommended Reading: | ||||||

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 | ||||||

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 | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Tutorials, Project work | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 | |||

Exercises evaluation | Credit | 30 (30) | 15 | |||

Sem. pr. 1 | Project | 8 | 0 | |||

Sem. pr. 2 | Project | 8 | 0 | |||

Test 1 | Written test | 7 | 0 | |||

Test 2 | Written test | 7 | 0 | |||

Examination | Examination | 70 | 21 |