| Course Unit Code | 330-0534/02 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First 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 | English |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| FUS76 | doc. Ing. Martin Fusek, Ph.D. |
| LIC098 | Ing. Mgr. Dagmar Ličková, Ph.D. |
| Summary |
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| Successful solution of the problems arising in engineering requires anunderstanding of relevant mathematics. The students will learn about basic tools and their applications for the solution of such problems. |
| Learning Outcomes of the Course Unit |
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| Learning outcomes of the course unit The aim of the course is to extend students' knowledge of practical use of mathematics in their study and subsequent engineering practice. |
| Course Contents |
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1. Numerické řešení nelineárních úloh.
2. Některé okrajové úlohy pro obyčejné diferenciální rovnice 2. stupně.
3. Síťová diskretizace.
4. Zavedení okrajových podmínek.
5. Variační formulace okrajových úloh .
6. Diskretizace založená na variační formulaci.
7. Kolokace, Ritzova metoda, Galerkinova metoda.
8. Metoda konečných prvků.
9. Vlastnosti matic a finitní metody řešení diskretizovaných soustav
10. Variační nerovnice a jejich diskretizace.
11. Numerické řešení variačních nerovnic.
12. Hraniční integrální rovnice
13. Metoda hraničních prvků pro modelovou úlohu.
14. Software |
| Recommended or Required Reading |
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| Required Reading: |
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[1] Crandal R. E.Mathematica for the Sciences, Addison-Wesley Publishing Company,Redwood City 1991, pp. 300, ISBN 0-201-51001-4
[2] K. Rektorys, Variational Methods in Mathematics, Science and Engineering. Reidel, Dordrecht, 1980 |
[1] K.Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky. Academia, Praha 1999. ISBN: 80-200-0714-8
[2] Schmidtmayer J.,Maticový počet a jeho použití v technice, SNTL, Praha 1974, pp.360, ISBN 04-007-74.
[3] Boček, L.: Tenzorový počet, SNTL Praha 1976.
[4] Crandal R. E.Mathematica for the Sciences, Addison-Wesley Publishing Company,Redwood City 1991, pp. 300, ISBN 0-201-51001-4
[5] K. Rektorys, Variational Methods in Mathematics, Science and Engineering. Reidel, Dordrecht, 1980 |
| Recommended Reading: |
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[1] G. Strang, Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986. ISBN-13: 9780961408800
[2] Mannucci M. A., Yanofsky N. S.,Quantum Computing For Computer Scientists,Cambridge University Press, Cambridge 2008, pp. 384., ISBN 978-0-521-87996-5 |
[1] Vlček J., Vektorová a tenzorová analýza, http://mdg.vsb.cz/portal/m4/VTA17.pdf
[2] G. Strang, Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986. ISBN-13: 9780961408800
[3] G. Strang, Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986. ISBN-13: 9780961408800
[4] Mannucci M. A., Yanofsky N. S.,Quantum Computing For Computer Scientists,Cambridge University Press, Cambridge 2008, pp. 384., ISBN 978-0-521-87996-5 |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| 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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| Graded credit | Graded credit | 100 | 51 |