1. komponenta

Lecture type	Total
Lectures	45

COURSE AIMS AND OBJECTIVES: This course gives an introduction to modern analysis. First the Sobolev spaces on an interval are defined. Developed theory is then applied to theoretical and numerical analysis of boundary value problems for ordinary differential equations, the Sturm-Liouville problem and the obstacle problem. Examples and simulation of real world problems.

COURSE DESCRIPTION AND SYLLABUS:
1. Weak derivative, Sobolev spaces on an interval. Ulaganja prostora Soboljeva.
2. The Poincare inequality, subspaces oft he Sobolev spaces.
3. Hilbert spaces, the theorem of Stampacchia, the Lax-Milgramova lemma.
4. Boundary value problems for ordinary differential , variational equations.
5. Regularity of weak solutions, classical solutions.
6. Finite element method for boundary value problems.
7. Unilateral boundary value problems, variational inequalities.
8. Minimization of quadratic functionals, regularity of solutions of unilateral boundary value problems.
9. Finite element method for unilateral boundary value problems.
10. Compact operators in Hilbertovom spaces.
11. The Sturm-Liouvilleov problem, variational formulation.
12. Finite element method for the Sturm-Liouvilleov problem.

1. Functional analysis, Sobolev spaces and partial differential equations, H. Brezis, Springer, 2011.
2. Introduction to the calculus of variations, 3rd ed., B. Dacorogna, Imperial Collage Press, London, 2015.
3. Calculus of variations, revised English edition, I. M. Gelfand, S. V. Fomin, Prentice-Hall, 1963.
4. Variational calculus and optimal control, J. L. Troutman, Springer-Verlag, 1996.
5. Numerical Analysis and Optimization, G. Allaire, Oxford University Press, Oxford, 2007.
6. Variational analysis in Sobolev and BV spaces, Applications to PDEs and Optimization, H. Attouch, G. Buttazzo, G. Michaille, SIAM, 2006.
7. S. C. Brenner, L. Ridgway ScottThe Mathematical Theory of Finite Element Methods, S. C. Brenner, L. Ridgway Scott, Springer, New York, 1994.
8. Direct methods in the calculus of variations, B. Dacorogna, Springer, 2007.
9. Partial differential equations in action: From modelling to theory, S. Salsa, Springer, 2015.

Izborni modul Optimizacija - Regular study - Applied Mathematics

Izborni modul Optimizacija - Regular study - Applied Mathematics

Izborni modul Optimizacija - Regular study - Applied Mathematics

Izborni modul Optimizacija - Regular study - Applied Mathematics