1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
The goal of the course is to introduce students to the basic methods of asymptotic analysis in the theory of ordinary and partial differential equations that depend on a small parameter, with emphasis on the rigorous derivations of lower-dimensional models from continuum mechanics.

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction. Basic results from Lebesgue and Sobolev spaces and functional analysis.
2. Boundary value problems for ordinary differential equations dependent on a small parameter.
3. Boundary value problems for the diffusion equation dependent on a small parameter.
4. Derivation of lower-dimensional models from the equations of linearized elasticity. Formal and rigorous approaches.
5. Boundary layer problems.

1. Partial differential equations, L. C. Evans, AMS, 1998.
2. Mathematical Elasticity, Vol. 2, P. G. Ciarlet, Elsevier, 2000.
3. Mathematical Elasticity, Vol. 1, 2, 3, P. G. Ciarlet, Elsevier, 2000.
4. Perturbation methods, A. H. Nayfeh, Pure Appl. Math. John Wiley & Sons, New York-London-Sydney, 1973.

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics