Mathematical analysis II.1

General data

Course ID:	1000-113aAM3a
Erasmus code / ISCED:	11.102 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Mathematical analysis II.1
Name in Polish:	Analiza matematyczna II.1 (potok I)
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Main fields of studies for MISMaP:	mathematics physics
Type of course:	obligatory courses
Full description:	Linear and topological structure of Euclidean spaces; transformations, continuity. Calculus in several variables: directional derivative, differentiability, higher-order derivatives, Taylor's formula, the implicit function theorem, local extrema. The concept of measure; outer measure and Caratheodory's theorem. Lebesgue measure; measurable functions, Lebesgue integral. Fubini's theorem, change of variables under the integral. Passing to the limit under integration sign.
Bibliography:	(in Polish) A. Birkholc, Analiza matematyczna: Funkcje wielu zmiennych. W. Kołodziej, Analiza matematyczna G.M. Fichtenholz, Rachunek różniczkowy i całkowy

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