Course Unit Code | 310-3040/01 |
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Number of ECTS Credits Allocated | 6 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 | Czech |
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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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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| KRC76 | Mgr. Jiří Krček |
| 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 the mathematical formulation of engineering practice problems.
The acquired knowledge will then be used to analyse of specific tasks via
- mathematical formulation through a system of differential equations,
- recognizing the appropriate calculation method,
- the correct calculation of the mathematical issue and
- a final meaningful interpretation of the results. |
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.
First order PDE. Method of characteristics.
Application - free and thermal convection.
PDE of second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDE.
Multi-dimensional stationary states.
Fourier method for elliptic PDE. Boundary problems for multivariate problems.
Numerical methods - a brief introduction (optional) |
Recommended or Required Reading |
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Required Reading: |
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William E.: Partial Differential Equation Analysis in Biomedical Engineering - Case Studies with MATLAB, 2013
Kulakowski, Bohdan T.; Gardner, John F.; Shearer, J. Lowen: Dynamic Modeling and Control of Engineering Systems, 3rd Edition, 2007
Mathematical Modelling: Classroom Notes in Applied Mathematics (Ed. M.S. Klamkin). SIAM Philadelphia, 3rd printing, 1995. |
Vlček J.: Matematické modelování. http://mdg.vsb.cz/portal/dr/U18Mod.pdf
Drábek P., Holubová G.: Parciální diferenciální rovnice
https://mi21.vsb.cz/sites/mi21.vsb.cz/files/unit/parcialni_diferencialni_rovnice.pdf
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.
Lawson D., Marion G.: An Introduction to Mathematical Modelling,
a course text: https://people.maths.bris.ac.uk/~madjl/course_text.pdf
Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013 |
Kuneš, J. - Vavroch, O. - Franta, V.: Základy modelování. SNTL, Praha 1989.
Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013 |
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 |