1. Formulation of the initial-value problem for ordinary differential equations of degree 1, basic properties, existence and uniqueness of solutions. 2. Basic numerical methods for the initial-value problems and their absolute stability. 3. Introduction to the variational calculus, basic spaces of integrable functions. 4. Classical and variational formulations of elliptic problems for ordinary differential equations of degree 2, basic physical meanings. 5. Standard finite difference method for elliptic problems for ordinary differential equations (ODE) of degree 2 and its stable modifications. 6. Approximation of boundary-value problems for ODE of degree 2 by the finite element method. 7. Classical and variational formulation of elliptic problems for ODE od degree 4 and approximation by the finite element method. 8. Classical and variational formulation of elliptic problems for partial differential equations od degree 2. 9. Finite element method for elliptic problems for partial differential equations od degree 2. 10. Finite volume method. 11. Discretization of non-stationary problems for degree 2 differential equations by the method of lines. 12. Mathematical models of flow. Nonlinear problems and problems with dominating convection. 13. Numerical methods for the models of flow.