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Предметни професор
Термин консултација:

четвртак 10-12

Кабинет: 222
E-mail: aleksandar.ivic@rgf.bg.ac.rs

Диференцијалне једначине и Нумеричка анализа

О предмету

Студијски програм: Геотехника (I семестар -DOS), Рударско инжењерство (I семестар -DOS)

Назив предмета: Диференцијалне једначине и Нумеричка анализа

Предавачи: проф. др Александар Ивић

Статус предмета: Изборни

ЕСПБ бодови: 10

Услов: Завршене основне и мастер студије рударства

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Циљ предмета: Упознавање са теоријом и праксом основних метода у разним областима Диференцијалних једначина и Нумеричке анализе за потребе будућих доктора рударства

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Исход предмета: Оспособљавање студената да користе у инжењерској пракси методе из разних области Математике на нивоу доктора наука

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Садржај предмета:

Теоријска настава
Диференцијалне једначине. Формирање и типови обичних диференцијалних једначина. Егзистенција решења. Поједини типови једначина првог реда. Општа линеарна једначина n-тог реда. Системи обичних диференцијалних једначина. Решавање једначина помоћу редова и преко Лапласове трансформације. Парцијалне диференцијалне једначине, типови и формирање. Неке посебне парцијалне диференцијалне једначине првог и другог реда. Нумеричка анализа. Методе приближног решавања једначина. Приближно решавање обичних диференцијалних једначина и парцијалних диференцијалних једначина. Полиноми и интерполација. Приближно решавање система диференцијалних једначина. Нумеричка интеграција и диференцирање. Сплајнови.

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Практична настава
Израда задатака или семинарског који одговарају материјалу који се ради на предавањима.

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Литература:

  1. I.S. Sokolnikoff and R.M. Redheffer, Mathematics of physics and modern engineering, McGraw Hill, New York etc, 2nd. ed., 1966.
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  2. Miloš Miličić, Nada Miličić, Dragan Stankov, Elementi Numeričke analize, Rudarsko-geološki fakultet u Beogradu, 2003
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  3. D. Kuzmanović, A. Sedmak, I. Obradović, D. Nikolić, Matematička Fizika, RGF, Univerzitet u Beogradu, 2003
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  4. Slobodan Vujić i Aleksandar Ivić, Matematičke metode u rudarstvu i geologijи, RGF, Univerzitet u Beogradu, 1991.
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  5. G.V. Milovanović, Numerička Analiza I deo (1985), II deo (1985), III deo(1988), Naučna Knjiga, Beograd,
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Фонд часова:

Предавања Вежбе Други облици наставе Студијски истраживачки рад
4 0 0 0

Метода извођења наставе: Класична метода преко табле, за неке делове курса постоје скрипта А. Ивића која студенти могу да преузму.

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