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Mathematical modeling of engineering problems

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Course Unit Code310-3040/01
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
KUC14prof. RNDr. Radek Kučera, Ph.D.
KRC76Mgr. Jiří Krček
SVO19Mgr. Ivona Tomečková, Ph.D.
Summary
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
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
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
Required Reading:
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:
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
Lectures, Individual consultations, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 21