1. Functional and its Euler equation, the simlest problem of calculus of variations. 2. Concrete examples of functionals and related Euler equations. Elementary solutions. 3. Derivation of an elliptic problem for ODE of degree 2, the problems of heat conduction and distribution of polution. 4. Discretization of the elliptic problem for ODE of degree 2 by the standard finite difference method, stability of numerical solutions. 5. Variational (weak) and minimization formulation of the elliptic problem for the elliptic problem for ODE of degree 2. 6. The Ritz and Galerkin methods. 7. Discretization of the elliptic problem for ODE of degree 2 by the finite element method. 8. Discretization of the variational formulation of the elliptic problem for ODE of degree 2 by the finite element method. 9. Discretization of the minimization formulation of the elliptic problem for ODE of degree 2 by the finite element method. 10. Discretization of the variational formulation of the elliptic problem for PDE of degree 2 by the finite element method. 11. Variational formulation and the finite element method for the linear elasticity problem. 12. Navier-Stokes equations and their numerical solution by the particle method. 13. A mathematical model of simultaneous distribution of moisture and heat in porous materials, discretizations.