{"id":764,"date":"2017-11-03T14:49:11","date_gmt":"2017-11-03T12:49:11","guid":{"rendered":"http:\/\/www.math.sk\/mpmnew\/?page_id=764"},"modified":"2024-02-22T13:36:59","modified_gmt":"2024-02-22T11:36:59","slug":"bakalarske-statnice","status":"publish","type":"page","link":"https:\/\/www.math.sk\/mpm\/bakalarske-statnice\/","title":{"rendered":"Bakal\u00e1rske \u0161t\u00e1tnice"},"content":{"rendered":"
\n
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T\u00e9my ot\u00e1zok bakal\u00e1rskych \u0161t\u00e1tnic pre \u0161tudijn\u00fd program Matematicko-po\u010d\u00edta\u010dov\u00e9 modelovanie:<\/h2>\n

1. Line\u00e1rna z\u00e1vislos\u0165 a nez\u00e1vislos\u0165, b\u00e1za, s\u00faradnice v b\u00e1ze, dimenzia<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly<\/a> (od defin\u00edcie 10.5 na strane 131 po koniec strany 147, bez d\u00f4kazov tvrden\u00ed)<\/p>\n

2. Vlastn\u00e9 hodnoty a vlastn\u00e9 vektory lin\u00e1rnej transform\u00e1cie<\/h3>\n

defin\u00edcia a s\u00favislos\u0165 s diagonaliz\u00e1ciou. Charakteristick\u00fd polyn\u00f3m matice. H\u013eadanie vlastn\u00fdch vektorov line\u00e1rneho zobrazenia dan\u00e9ho maticou.
\n\u0161tudijn\u00e9 materi\u00e1ly<\/a> (strany 38 – 50)<\/p>\n

3. N\u00e1vrh programu v jazyku C, funkcie, proced\u00fary a ich parametre, glob\u00e1lne a lok\u00e1lne premenn\u00e9, d\u00e1tov\u00e9 typy<\/h3>\n

\u0161tudijn\u00e1 literat\u00fara: Zuzana Kriv\u00e1: Z\u00e1klady programovania v jazyku C, skript\u00e1 STU, hlavne kapitoly 4, 5, 10, 12.<\/p>\n

4. Dynamicke polia, smern\u00edky, dynamick\u00e1 alok\u00e1cia jednorozmern\u00e9ho a dvojrozmern\u00e9ho po\u013ea<\/h3>\n

\u0161tudijn\u00e1 literat\u00fara: Zuzana Kriv\u00e1: Z\u00e1klady programovania v jazyku C, skript\u00e1 STU, hlavne kapitoly 6, 7, 9.<\/p>\n

5. Objektovo-orientovan\u00e9 programovanie v C++ \u2013 z\u00e1kladn\u00e9 princ\u00edpy<\/h3>\n

Z\u00e1kladn\u00e9 princ\u00edpy objektovo-orientovan\u00e9ho programovania v C++: defin\u00edcia triedy, polia objektov, smern\u00edk na objekt, zapuzdrenie, polymorfizmus a dedi\u010dnos\u0165.
\n\u0161tudijn\u00e9 materi\u00e1ly<\/a><\/p>\n

6. Itera\u010dn\u00e9 met\u00f3dy rie\u0161enia line\u00e1rnych s\u00fastav<\/h3>\n

Pop\u00ed\u0161te sp\u00f4soby rozkladu matice (faktoriz\u00e1cia, splitting). Na jednoduch\u00fdch pr\u00edkladoch vysvetlite Jacobiho, Gauss-Seidelovu a SOR met\u00f3du pre rie\u0161enie s\u00fastav line\u00e1rnych rovn\u00edc (v\u0161eobecn\u00fd alebo maticov\u00fd z\u00e1pis). Zastavovacie kriteria itera\u010dn\u00fdch procesov (podmienky a krit\u00e9ria).
\n\u0161tudijn\u00e9 materi\u00e1ly: predn\u00e1\u0161ky z predmetu Numerick\u00e9 met\u00f3dy line\u00e1rnej algebry<\/p>\n

7. Nehomog\u00e9nna line\u00e1rna oby\u010dajn\u00e1 diferenci\u00e1lna rovnica prv\u00e9ho r\u00e1du a jej rie\u0161enie met\u00f3dou vari\u00e1cie kon\u0161tanty<\/h3>\n

Definujte line\u00e1rnu ODR, kedy je homog\u00e9nna. Ako sa rie\u0161i homog\u00e9nna ODR, ako funguje met\u00f3da vari\u00e1cie kon\u0161tanty. \u010co je auton\u00f3mna OD rovnica, \u010do je charakteristick\u00e1 rovnica, ako funguje met\u00f3da neur\u010dit\u00fdch koeficientov a met\u00f3da vari\u00e1cie viacer\u00fdch kon\u0161t\u00e1nt.
\n\u0161tudijn\u00e1 literat\u00fara: Igor Bock, Lubom\u00edr Marko: Diferenci\u00e1lne rovnice, Vydavatelstvo STU v Bratislave, prv\u00e9 vydanie 1993, druh\u00e9 vydanie 2000, \u010das\u0165 1.4 Line\u00e1rne homog\u00e9nne diferenci\u00e1lne rovnice 1. r\u00e1du a \u010das\u0165 1.5 Line\u00e1rne nehomog\u00e9nne diferenci\u00e1lne rovnice 1. r\u00e1du.
\n\u0161tudijn\u00e9 materialy<\/a><\/p>\n

8. Met\u00f3da siet\u00ed na rie\u0161enie okrajov\u00fdch \u00faloh pre oby\u010dajn\u00e9 diferenci\u00e1lne rovnice<\/h3>\n

Numerick\u00e9 rie\u0161enie line\u00e1rnej oby\u010dajnej diferenci\u00e1lnej rovnice druh\u00e9ho r\u00e1du s okrajov\u00fdmi podmienkami met\u00f3dou kone\u010dn\u00fdch diferenci\u00ed.
\n\u0161tudijn\u00e9 materi\u00e1ly<\/a><\/p>\n

9. N\u00e1hodn\u00e9 premenn\u00e9 a ich parametre<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly<\/a>
\n\u0161tudijn\u00e1 literat\u00fara: A.Dallosov\u00e1, R.Mesiar: Pravdepodobnos\u0165 a matematick\u00e1 \u0161tatistika, skript\u00e1, ES SV\u0160T Bratislava, 1984<\/p>\n

10. Testy a intervaly spo\u013eahlivosti pre parametre norm\u00e1lneho rozdelenia<\/h3>\n

\u0161tudijn\u00fd materi\u00e1l 1<\/a>,\u00a0\u0161tudijn\u00fd materi\u00e1l 2<\/a>,\u00a0\u0161tudijn\u00fd materi\u00e1l 3<\/a><\/p>\n

11. Korela\u010dn\u00e1 a regresn\u00e1 anal\u00fdza<\/h3>\n

\u0161tudijn\u00fd materi\u00e1l 1<\/a>,\u00a0\u0161tudijn\u00fd materi\u00e1l 2<\/a><\/p>\n

12. Kanonick\u00fd tvar \u00falohy line\u00e1rneho programovania a simplexov\u00fd algoritmus<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly<\/a><\/p>\n

13. Parci\u00e1lne diferenci\u00e1lne rovnice – nestacion\u00e1rneho vedenie tepla v 1D – odvodenie rovnice, okrajov\u00e9 podmienky<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly: predn\u00e1\u0161ky z predmetu Parci\u00e1lne diferenci\u00e1lne rovnice<\/p>\n

14. Parci\u00e1lne diferenci\u00e1lne rovnice – harmonick\u00e9 funkcie a ich z\u00e1kladn\u00e9 vlastnosti<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly: predn\u00e1\u0161ky z predmetu Parci\u00e1lne diferenci\u00e1lne rovnice<\/p>\n

15. Pojem slab\u00e9ho rie\u0161enia okrajov\u00fdch \u00faloh, existencie tak\u00e9hoto rie\u0161enia, Lax-Milgramova veta<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly<\/a><\/p>\n

16.\u00a0 Met\u00f3da kone\u010dn\u00fdch prvkov pre 1D okrajov\u00e9 \u00falohy 2. r\u00e1du<\/h3>\n

Okrajov\u00e1 \u00faloha (1D stacon\u00e1rna rovnica vedenia tepla), diskretiz\u00e1ca v\u00fdpo\u010dtovej oblasti, slab\u00e1 formul\u00e1cia, aproxima\u010dn\u00e9 funkcie na elemente, s\u00fastava rovn\u00edc na elemente, spojenie do glob\u00e1lnej s\u00fastavy rovn\u00edc, vyu\u017eitie okrajov\u00fdch podmienok<\/p>\n

\u0160tudijn\u00e1 literat\u00fara: L. Tomek, K. Mikula: Numerick\u00e9 modelovanie pomocou met\u00f3dy kone\u010dn\u00fdch prvkov<\/a>, 2024, kapitola 4<\/p>\n

17. Met\u00f3da kone\u010dn\u00fdch prvkov a typy elementov pre 2D okrajov\u00e9 \u00falohy 2. r\u00e1du<\/h3>\n

Diferenci\u00e1lna rovnica (2D stacon\u00e1rna izotropn\u00e1 rovnica vedenia tepla), diskretiz\u00e1ca v\u00fdpo\u010dtovej oblasti, slab\u00e1 formul\u00e1cia, typy elementov, s\u00fastava rovn\u00edc na elemente, spojenie do glob\u00e1lnej s\u00fastavy rovn\u00edc (iba z\u00e1kladn\u00e9 my\u0161lienky a princ\u00edpy).<\/p>\n

\u0160tudijn\u00e1 literat\u00fara: L. Tomek, K. Mikula: Numerick\u00e9 modelovanie pomocou met\u00f3dy kone\u010dn\u00fdch prvkov<\/a>, 2024, kapitola 9<\/p>\n

18. Odvodenie Black-Scholesovej parci\u00e1lnej diferenci\u00e1lnej rovnice oce\u0148ovania finan\u010dn\u00fdch deriv\u00e1tov, expira\u010dn\u00e9 a okrajov\u00e9 podmienky pre call a put opcie<\/h3>\n

\u0161tudijn\u00e9 materi\u00e1ly<\/a>
\n\u0161tudijn\u00e1 literat\u00fara: J.Komorn\u00edk, M.Komorn\u00edkov\u00e1, K.Mikula, Modelovanie ekonomick\u00fdch a finan\u010dn\u00fdch procesov, skript\u00e1, Univerzita Komensk\u00e9ho, Bratislava, 1998, 3. kapitola<\/p>\n

19. Z\u00e1kladn\u00e9 princ\u00edpy odvodenia Navier-Stokesov\u00fdch rovn\u00edc pr\u00fadenia kvapal\u00edn a plynov<\/h3>\n

Odvodenie z\u00e1kona zachovania hmotnosti a hybnosti tekutiny v integr\u00e1lnom tvare. Odvodenie diferenci\u00e1lnych rovn\u00edc pomocou transportnej vety a Greenovej vety pre plo\u0161n\u00e9 sily v tvare tenzora nap\u00e4t\u00ed pre Newtonovsk\u00fa tekutinu.
\n\u0161tudijn\u00e1 literat\u00fara: P. Frolkovi\u010d: Pr\u00fadenie kvapal\u00edn a plynov. STU 2013. Kapitoly 8, 10 a 12.<\/p>\n

20. \u010casov\u00e9 rady a ich dekompoz\u00edcia<\/h3>\n

V\u00fdznam \u010dasu v \u0161tatistickom modelovan\u00ed, stochastick\u00fd proces, v\u00fdznam stacionariz\u00e1cie, zlo\u017eky \u010dasov\u00e9ho radu a met\u00f3dy ich modelovania (v klasickom dekompozi\u010dnom pr\u00edstupe, v r\u00e1mci integrovan\u00fdch procesov, exponenci\u00e1lnym vyhladzovan\u00edm). Pr\u00edklady neline\u00e1rnych modelov.
\n\u0161tudijn\u00e9 materi\u00e1ly: predn\u00e1\u0161ky z predmetu Anal\u00fdza \u010dasov\u00fdch radov
\n\u0161tudijn\u00e1 literat\u00fara: Cipra, T. (2008). Finan\u010dn\u00ed ekonometrie (Vol. 30). Ekopress
\nHyndman, R., Athanasopoulos, G. (2018). Forecasting: Principles and Practice (https:\/\/otexts.com\/fpp3\/<\/a>)<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

T\u00e9my ot\u00e1zok bakal\u00e1rskych \u0161t\u00e1tnic pre \u0161tudijn\u00fd program Matematicko-po\u010d\u00edta\u010dov\u00e9 modelovanie: 1. Line\u00e1rna z\u00e1vislos\u0165 a nez\u00e1vislos\u0165, b\u00e1za, s\u00faradnice v b\u00e1ze, dimenzia \u0161tudijn\u00e9 materi\u00e1ly (od defin\u00edcie 10.5 na strane 131 po koniec strany 147, bez d\u00f4kazov tvrden\u00ed) 2. Vlastn\u00e9 hodnoty a vlastn\u00e9 vektory lin\u00e1rnej transform\u00e1cie defin\u00edcia a s\u00favislos\u0165 s diagonaliz\u00e1ciou. Charakteristick\u00fd polyn\u00f3m matice. H\u013eadanie vlastn\u00fdch vektorov line\u00e1rneho zobrazenia […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-764","page","type-page","status-publish","hentry"],"yoast_head":"\nMatematicko-po\u010d\u00edta\u010dov\u00e9 modelovanie<\/title>\n<meta name=\"description\" content=\"Katedra matematiky a deskript\u00edvnej geometrie Stavebnej Fakulty Slovenskej Technickej Univerzity v Bratislave. 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