Mathematical modeling of engineering problems

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.