714-0941/04 – Mathematical modeling of engineering problems (MMIU)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelpostgraduateRequirementOptional
YearSemesterwinter + summer
Study languageCzech
Year of introduction2009/2010Year of cancellation2018/2019
Intended for the facultiesFMT, HGF, FEI, USP, FBI, FSIntended 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 Examination 20+0
Part-time Examination 20+0

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



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

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2010/2011 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes P Czech Ostrava Optional study plan
2010/2011 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Optional study plan
2010/2011 (P1701) Physics K Czech Ostrava Optional study plan
2010/2011 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Optional study plan
2010/2011 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes K Czech Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner