• 1. Linear, metric, normed, and unitary spaces. Fixed-point theorems.
• 2. Linear operators, the notion of a functional, special functional spaces
• 3. Differential operators. Initial and boundary problems in differential equations.
• 4. First derivative of a functional, potentials of some boundary problems.
• 5. Second derivative of a functional. Lagrange conditions.
• 6. Convex functionals, strong and weak convergence.
• 7. Classic, minimizing and variational formulation of differential problems
• 8. Primary, dual, and mixed formulation - examples in mechanics of building structures
• 9. Numeric solutions to initial and boundary problems, discretization schemes.
• 10. Numeric solutions to boundary problems. Ritz and Galerkin method.
• 11. Finite-element method, comparison with the method of grids.
• 12. Kačanov method, method of contraction, method of maximal slope.
• 13. Numeric solution of general evolution problems. Full discretization and semi-discretization. Method of straight lines. Rothe method of time discretization.
• 14. An overview of further variational methods: method of boundary elements, method of finite volumes, non-grid approaches. Variational inequalities.

Follows directly particular lectures.

• 1. Linear, metric, normed, and unitary spaces. Fixed-point theorems.
• 2. Linear operators, the notion of a functional, special functional spaces
• 3. Differential operators. Initial and boundary problems in differential equations.
• 4. First derivative of a functional, potentials of some boundary problems.
• 5. Second derivative of a functional. Lagrange conditions.
• 6. Convex functionals, strong and weak convergence.
• 7. Classic, minimizing and variational formulation of differential problems
• 8. Primary, dual, and mixed formulation - examples in mechanics of building structures
• 9. Numeric solutions to initial and boundary problems, discretization schemes.
• 10. Numeric solutions to boundary problems. Ritz and Galerkin method.
• 11. Finite-element method, comparison with the method of grids.
• 12. Kačanov method, method of contraction, method of maximal slope.
• 13. Numeric solution of general evolution problems. Full discretization and semi-discretization. Method of straight lines. Rothe method of time discretization.
• 14. An overview of further variational methods: method of boundary elements, method of finite volumes, non-grid approaches. Variational inequalities.