714-0766/03 – Mathematical modeling of engineering problems (MMIU)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits3
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Study languageEnglish
Year of introduction2014/2015Year of cancellation
Intended for the facultiesFMT, USP, HGFIntended for study typesFollow-up Master, Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+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:

Vlček, J.: Mathematical modeling, http://homen.vsb.cz/~vlc20/ 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. 2. State, flow, material and source quantities. 3. Basic relations: balance and constitutive. 4. Local and global balance. 5. Classification of boundary problems. Corectness of mathematical model. 6. One-dimensional stationary states. 7. Multi-dimensional stationary states. 8. PDE of second order: classification, Fourier method. 9. Non-stationary processes - one-dimensional case. 10. First order PDE. Method of characteristics. 11. Initial problems for multivariate problems. 12. Facultative themes

Conditions for subject completion

Full-time form (validity from: 2013/2014 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  51
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava 1 Compulsory study plan
2018/2019 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava 1 Compulsory study plan
2017/2018 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava 1 Compulsory study plan
2015/2016 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner