Terminated in academic year 2018/2019
Mathematical modeling of engineering problems
| Type of study | Doctoral |
|---|---|
| Language of instruction | Czech |
| Code | 714-0941/04 |
| Abbreviation | MMIU |
| Course title | Mathematical modeling of engineering problems |
| Credits | 10 |
| Coordinating department | Department of Mathematics and Descriptive Geometry |
| Course coordinator | doc. RNDr. Jaroslav Vlček, CSc. |
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.
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.
E-learning
www.mdg.vsb.cz
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
Mathematical Modelling (Ed. M.S. Klamkin). SIAM, 1989.
Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013
Advised literature
Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994.
Keener, J. P.: Principles of Applied Mathematics. Adison-Wesley Publ. Comp. 1994
Keener, J. P.: Principles of Applied Mathematics. Adison-Wesley Publ. Comp. 1994