Mathematical analysis II.1 *
General data
Course ID: | 1000-113aAM3* |
Erasmus code / ISCED: |
11.102
|
Course title: | Mathematical analysis II.1 * |
Name in Polish: | Analiza matematyczna II.1 * |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: | |
ECTS credit allocation (and other scores): |
(not available)
|
Language: | Polish |
Main fields of studies for MISMaP: | mathematics |
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. PWN, Warszawa 2002. B.P. Demidowicz, Zbiór zadań z analizy matematycznej, Naukowa Książka, Lublin 1992 (t. I) i 1993 (t. II i III). G.M. Fichtenholz, Rachunek różniczkowy i całkowy. Tom I--III, PWN, Warszawa 1999 W. Pusz, A. Strasburger, Zbiór zadań z analizy matematycznej Wydział Fizyki UW, Warszawa 1982. W. Rudin, Analiza rzeczywista i zespolona, PWN, Warszawa 1998. R. Sikorski, Rachunek różniczkowy i całkowy, funkcje wielu zmiennych . Bibl. Matem. 28, wyd. IV rozsz., PWN, Warszawa 1977 M. Spivak, Analiza na rozmaitościach, PWN, Warszawa 1977. |
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