| Course Unit Code | 470-8727/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type A |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Third Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| LAM05 | prof. RNDr. Marek Lampart, Ph.D. |
| Summary |
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| 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.. |
| Learning Outcomes of the Course Unit |
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| To give students knowledge of basic concepts of complex functions of complex variable, Laplace transforms and Fourier series. |
| Course Contents |
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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.
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| Recommended or Required Reading |
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| Required Reading: |
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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. |
Galajda, P., Schrötter, Š.: Funkce komplexní proměnné a operátorový počet, Alfa-Bratislava, 1991.
Škrášek, J., Tichý, Z.: Základy aplikované matematiky II, SNTL, Praha, 1986.
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Kozubek, T., Lampart, M.,: Integrální transformace, http://mi21.vsb.cz/modul/integralni-transformace
Bouchala, J.: Funkce komplexní proměnné, http://mi21.vsb.cz/modul/funkce-komplexni-promenne |
| Recommended Reading: |
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Galajda, P., Schrötter, Š.: Funkce komplexní proměnné a operátorový počet, Alfa-Bratislava, 1991.
Škrášek, J., Tichý, Z.: Základy aplikované matematiky II, SNTL, Praha, 1986.
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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. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| 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 |