Mathematical modeling of engineering problems

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. Corectness of mathematical model.
6. One-dimensional stationary states.
7. Multi-dimensional stationary states.
8. PDE of second order: classification, Fourier method.
9. Non-stationary processes - one-dimensional case.
10. First order PDE. Method of characteristics.
11. Initial problems for multivariate problems.
12. Facultative themes