undergraduate thesis
Calculus of Variations

Josip Živković (2016)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za fiziku
Zavod za eksperimentalnu fiziku
Katedra za osnove fizike
Metadata
TitleVarijacijske metode
AuthorJosip Živković
Mentor(s)Zvonko Glumac (thesis advisor)
Abstract
U ovome radu ukratko ćemo se upoznati sa osnovama varijacijskih metoda. Bavit ćemo se problemom traženja lokalnog minimuma određenog funkcionala, na način da tražimo nužne i dovoljne uvjete postojanja ekstrema tog funkcionala. Upoznat ćemo se sa Euler - Lagrangeovom jednadžbom, Hamiltonovim načelom, Sturm-Liouvilleovim operatorom i Rayleigh-Ritzovom metodom. Također, razmatrat ćemo više metoda pronalaženja svojstvenih vrijednosti. Na poslijetku ćemo pokazati kako se varijacijski postupak može proširiti za slučaj više nezavisnih varijabli.
KeywordsEuler-Lagrange equation Brachistohorne problem Hamilton's principe
Parallel title (English)Calculus of Variations
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za fiziku
Lower level organizational unitsZavod za eksperimentalnu fiziku
Katedra za osnove fizike
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Physics
General and Classical Physics
Study programme typeuniversity
Study levelundergraduate
Study programmePhysics
Academic title abbreviationuniv.bacc.phys.
Genreundergraduate thesis
Language Croatian
Defense date2016-09-21
Parallel abstract (English)
In this paper, we will shortly be introduced to the basics of Calculus of Variations. We will deal with problem of finding a local minima of certain functional in a way to seek the necessary and sufficient conditions for the existence of ekstreme of this functional. We will meet with Euler-Lagrange equation, Hamilton's principe, Sturm-Liouvilles operator and Rayleigh-Ritz method. Also, we will consider more methods for finding eigenvalues. In the end, we will show how calculus of variations can be extended to handle more than one independent variable.
Parallel keywords (Croatian)Euler-Lagrangeova jednadžba problem Brachistohorne Hamiltonov princip
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:160:748190
CommitterMirna Šušak Lukačević