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undergraduate thesis
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Calculus of Variations and its Applications
Una Radojičić (2015)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
Metadata
TitleVarijacijski račun i primjene
AuthorUna Radojičić
Mentor(s)Krešimir Burazin (thesis advisor)
Abstract
U ovome radu ukratko ćemo se upoznati sa osnovama varijacijskog računa. Bavit ćemo se problemom traženja lokalnog minimuma odredenog funkcionala na način da tražimo nužne i dovoljne uvjete postojanja ekstrema tog funkcionala. Također, razmatrat ćemo i problem traženja globalnog minimuma funkcionala. Na kraju rada pokazat ćemo neke od primjena varijacijskog računa u matematici i fizici.
KeywordsEuler-Lagrange equation Beltram's identity Variation of functional Legendre's test Jacobi's test Brachistohorne problem Plato's problem Geodetics on sphere Hamilton's principe
Parallel title (English)Calculus of Variations and its Applications
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Pure Mathematics
Algebra and Calculus Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Mathematical Analysis
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2015-09-30
Parallel abstract (English)
In this paper, we will shortly be introduced to the basics of Calculus of Variations. We will deal with problem of nding a local minima of certain functional in a way to seek the necessary and sucient conditions for the existence of extrema of this functional. Also, we will consider the problem of searching for the global minimum of functional. At the end of the paper we will show some of the applications of Calculus of Variations in mathematics and physics.
Parallel keywords (Croatian)Euler-Lagrangeova jednadžba Beltramov identitet varijacija funkcionala Legendreov test Jacobijev test problem Brachistohorne Platonov problem geodezija na sferi Hamiltonov princip
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:716004