714-0941/05 – Mathematical modeling of engineering problems (MMIU)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 10 |
| Subject guarantor | doc. RNDr. Jaroslav Vlček, CSc. | Subject version guarantor | doc. RNDr. Jaroslav Vlček, CSc. |
| Study level | postgraduate | Requirement | Choice-compulsory |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2013/2014 | Year of cancellation | 2018/2019 |
| Intended for the faculties | FMT, FS, FBI, HGF, FAST, FEI, USP | Intended for study types | Doctoral |
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
Lectures
Individual consultations
Project work
Summary
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
Additional study materials
Way of continuous check of knowledge in the course of semester
It does not specified.
E-learning
Other requirements
Elaboration of semestral 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. 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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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