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.
Non-stationary processes - one-dimensional case. Initial problems.
First order PDE. Method of characteristics.
Application - free and thermal convection.
PDE of second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDE.
Multi-dimensional stationary states.
Fourier method for elliptic PDE.
Boundary problems for multivariate problems.
Numerical methods - a brief introduction.
Facultative themes.