310-3040/02 – Mathematical modeling of engineering problems (MMIU)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorMgr. Ivona Tomečková, Ph.D.Subject version guarantorMgr. Ivona Tomečková, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesUSP, FEI, HGF, FMTIntended for study typesMaster, Follow-up 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 3+2

Subject aims expressed by acquired skills and competences

Students learn structural approach to mathematical formulation of engineering problems. They shlould know how to analyze given problem, to formulate mathematical task, to choose and correctly use appropriate mathematical method.

Teaching methods

Individual consultations
Project work


The topic offers a complex view on mathematical modeling of physical states and processes with emphasized orientation to the problems described by differential equations. Applications are devoted to the solving of real problems comming out from engineering praxis in regard to prevailing student specialization. The use of mathematical software is assumed,e.g. MATLAB.

Compulsory literature:

Mathematical Modelling (Ed. M.S. Klamkin). SIAM, 1989.

Recommended literature:

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994. Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013

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 25 – 50 points. Theoretical part of the exam is classified by 0 - 20 points.


Other requirements

Elaboration of semestral project


Subject has no prerequisities.


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. First order PDE. Method of characteristics. 7. Application - free and thermal convection. 8. PDE of second order: classification, Fourier method. 9. Fourier method for parabolic and hyperbolic PDE. 10. Multi-dimensional stationary states. 11. Fourier method for elliptic PDE. 12. Boundary problems for multivariate problems. 13. Numerical methods - a brief introduction. 14. Facultative themes.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation: 80 %

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0719A270003) Nanotechnology P English Ostrava 1 Compulsory study plan
2021/2022 (N0719A270003) Nanotechnology P English Ostrava 1 Compulsory study plan
2020/2021 (N0719A270003) Nanotechnology P English Ostrava 1 Compulsory study plan
2019/2020 (N0719A270003) Nanotechnology P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner