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sisvu:description Funkcije više varijabli, Euklidov n-dimenzionalni prostor, neprekidnost i limes funkcije, parcijalne derivacije i diferencijali, derivacija kompozicije funkcija. Taylorov razvoj funkcije dviju varijabli, ekstremi funkcije, teorem o implicitnim funkcijama, transformacije varijabli, Jakobijan. Višestruki integrali, supstitucija varijabli, neke primjene u geometriji i mehanici. Obične diferencijalne jednadžbe, jednadžbe prvog reda, početni problem, separacija varijabli, homogene, egzaktne, linearne, Bernoullijeva i Riccatijeva jednadžba, ovojnice i trajektorije. Jednadžbe višeg reda, harmonijski oscilator, linearne diferencijalne jednadžbe reda n, Wronskian. Sustavi diferencijalnih jednadžbi. Vektorske funkcije, krivulje u prostoru, tangenta i normala na krivulju, zakrivljenost i torzija krivulje, Frenetova baza vektora. Skalarna i vektorska polja, gradijent, divergencija i rotacija, geometrijsko i fizikalno značenje, plohe u prostoru, tangencijalna ravnina i normala na plohu. Masa krivulje i krivuljni integral prve vrste, radnja sile po krivulji i krivuljni integral druge vrste, Greenov teorem, potencijalna polja. Masa plohe i plošni integral prve vrste, tok vektorskog polja i plošni integral druge vrste, Gaussov i Stokesov teorem, primjene. (hr)
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