| Course Unit Code | 310-3340/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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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 | Summer 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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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| SVO19 | Mgr. Ivona Tomečková, Ph.D. |
| Summary |
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The course offers a unified view of mathematical modeling of physical states and
processes with a focus on tasks described by differential equations. Applications are
devoted to the solving real problems of engineering practice with regard to the prevailing professional focus of students. Students' knowledge of some mathematical software is assumed, for example MatLab, to get the result or its visualization. |
| Learning Outcomes of the Course Unit |
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Students will learn a structural approach to move from meaningful physical assumptions and observed conclusions to mathematical problems known from previous studies and engineering practice.
The acquired knowledge will then be used to analyse of specific tasks via
- a suitable mathematical formulation through differential equations,
- recognizing the appropriate calculation method and the correct calculation of the mathematical issue and
- a final meaningful physical interpretation of the results.
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| Course Contents |
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Principles of mathematical modeling. Model quantities.
Basic relations, local and global balance.
One-dimensional stationary states.
Classification of boundary problems. Corectness of mathematical model.
Non-stationary processes - one-dimensional case. Initial problems.
Method of characteristics for the PDEs of the first order.
Application - free thermal convection.
PDEs of the second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDEs.
Multi-dimensional stationary states.
Fourier method for elliptic PDEs. Boundary problems for multivariate problems.
Facultative themes. |
| Recommended or Required Reading |
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| Required Reading: |
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[1]
William E.: Partial Differential Equation Analysis in Biomedical Engineering - Case Studies with MATLAB, 2013
[2]
Kulakowski, Bohdan T.; Gardner, John F.; Shearer, J. Lowen: Dynamic Modeling and Control of Engineering Systems, 3rd Edition, 2007
[3]
Mathematical Modelling: Classroom Notes in Applied Mathematics (Ed. M.S. Klamkin). SIAM Philadelphia, 3rd printing, 1995. |
vše dosažitelné z internetu:
[1]
Vlček J.: Matematické modelování.
http://mdg.vsb.cz/portal/dr/U18Mod.pdf
[2]
Drábek P., Holubová G.: Parciální diferenciální rovnice
https://mi21.vsb.cz/sites/mi21.vsb.cz/files/unit/parcialni_diferencialni_rovnice.pdf
[3]
Mathematical Modelling: Classroom Notes in Applied Mathematics (Ed. M.S. Klamkin). SIAM Philadelphia, 3rd printing, 1995. |
| Recommended Reading: |
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Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994
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Kuneš, J. - Vavroch, O. - Franta, V.: Základy modelování. SNTL, Praha 1989
|
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, 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 | 30 | 10 |
| Examination | Examination | 70 | 21 |