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Godina studija:I
Semestar: Zimski
Nastavnici: Dr.Sc.Nermin Okičić, docent
Saradnici:
as.Samra Pirić
as.Amra Muminović
as.Amra Rekić

Predavanja: 4
Auditorne: 4

Plan i program:

Algebra iskaza. Algebra skupova i algebra prekidača. Relacija, operacija, preslikavanje, algebarske strukture. Grafovi. Polje realnih brojeva. Neki podskupovi skupa realnih brojeva (N, Z, Q, J, interval i segment). Princip potpune i nepotpune matematičke indukcije. Kardinalni broj skupa, prebrojivi i neprebrojivi skupovi. Metrika u skupu realnih brojeva, otvoreni i zatvoreni skupovi. Kompleksni brojevi, definicija, algebarski, trigonometrijski i Eulerov oblik. Operacije u skupu C. Moivreova formula. Korijen kompleksnog broja. Logaritam kompleksnog broja. Elementi linearne algebre: algebra matrica, matrične jednačine, determinante. Sistemi linearnih jednačina, opšta teorija. Linearne forme, rang matrice, Kronecker-Capelliev stav. Polinomi, Bezoutov stav i Hornerova šema. Racionalne funkcije i dekompozicija. Elementi vektorske algebre, vektori, skalari i operacije. Vektorski prostor. Analitička geometrija u prostoru. Prava i ravan. Krive i osnovne površi drugog reda. Realne funkcije jedne promjenljive: ograničene, monotone i periodične funkcije. Nizovi i redovi, osnovni kriteriji konvergencije. Osnovne teoreme o graničnim vrijednostima funkcija. Neprekidnost na segmentu. Diferencijalni račun funkcija jedne promjenljive, pojam izvoda i osnovne teoreme diferencijalnog računa. Pojam diferencijala, izvodi i diferencijali višeg reda. Primjena diferencijalnog računa na ispitivanje funkcija. Konveksne funkcije. Taylorov polinom i Taylorov red. Ekstremi funkcija jedne promjenljive.

Literatura:

1.F.Dedagić: Uvod u višu matematiku, Univerzitet u Tuzli, Tuzla, 1997.
2.D.Mihajlović, R.Janić: Elementi matematičke analize I, Naučna knjiga, Beograd, 1978.
3.S.Kurepa, Matematička analiza I, Tehnička knjiga, Zagreb, 1989.
4.P.Miličić, M.Uščumlić, Zbirka zadataka iz Matematike I i II, Građevinska knjiga, Beograd, 1972.
5.B.Demidovič, Zadaci i riješeni zadaci iz više matematike s primjenom na tehničke nauke, Tehnička knjiga, Zagreb, 1986.

Odsjek: Energetska elektrotehnika,Tehnička informatika,Komunikacije


Nema dodanih datoteka na Vašem kursu

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