310-3340/01 – Mathematical Modelling (MM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorMgr. Ivona Tomečková, Ph.D.Subject version guarantorMgr. Ivona Tomečková, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master, Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+0
Distance Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

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.

Compulsory literature:

[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.

Recommended literature:

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994

Way of continuous check of knowledge in the course of semester

Course-credit: -participation on tutorials is obligatory, 20% of absence can be apologized, -pass the written test (30 points), Point classification: 0-30 points. Exam Semestral thesis classified by 50 points. Theoretical 20 points

E-learning

Other requirements

Individual application project.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Principles of mathematical modeling. Model quantities. 2. Basic relations, local and global balance. 3. One-dimensional stationary states. 4. Classification of boundary problems. Corectness of mathematical model. 5. Non-stationary processes - one-dimensional case. Initial problems. 6. Method of characteristics for the PDEs of the first order. 7. Application - free thermal convection. 8. PDEs of the second order: classification, Fourier method. 9. Fourier method for parabolic and hyperbolic PDEs. 10. Multi-dimensional stationary states. 11. Fourier method for elliptic PDEs. Boundary problems for multivariate problems. 12. Facultative themes.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21 3
Mandatory attendence participation: 50 %

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Optional study plan
2023/2024 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Optional study plan
2023/2024 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Optional study plan
2023/2024 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Optional study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Optional study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Optional study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Optional study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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