714-0941/03 – 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 levelpostgraduateRequirementCompulsory
Study languageCzech
Year of introduction2007/2008Year of cancellation2009/2010
Intended for the facultiesUSPIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
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+1

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 and its toolboxes.

Compulsory literature:

Vlček, J.: Mathematical modeling, http://homen.vsb.cz/~vlc20/ Mathematical Modelling (Ed. M.S. Klamkin). SIAM, 1989. Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013

Recommended literature:

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994. Keener, J. P.: Principles of Applied Mathematics. Adison-Wesley Publ. Comp. 1994

Way of continuous check of knowledge in the course of semester

Cvičení - podmínky udělení zápočtu: • maximální omluvená neúčast 20 % • absolvování testu (maximum 20 bodů) Zkouška: Obhajoba semestrální práce ( 0 – 80 bodů )


Other requirements

Elaboration of semestral project to given theme.


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 6. Corectness of mathematical model 7. One-dimensional stationary states 8. Multi-dimensional stationary states. 9. Non-stationary processes - one-dimensional case 10. Initial problems for multivariate problems 11.-13. Facultative themes

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 40 (40) 0
                Project Project 30  0
                Written exam Written test 10  0
        Examination Examination 60 (60) 0
                Written examination Written examination 30  0
                Oral Oral examination 30  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (N3942) Nanotechnology (3942T001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3942) Nanotechnology (3942T001) Nanotechnology P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner