Winter Semester 2006/07
Winter Semester 2009/10
Winter Semester 2010/11
Winter Semester 2011/12
Winter Semester 2012/13
Winter Semester 2013/14
Calculus I11006
Course content:
Sets of numbers and their properties. Supremum, infimum. Function of real variable. Elementary functions.
Number sequences and their limits. Bolzano-Weierstrass theorem.
Number series and their properties.
Limits of a function in a point. Darboux property. Weierstrass theorem.
Derivatives of functions and its interpretations. A tangent to a graph of a function. Rolle's Lagrange's and Cauchy's theorems.
The de l'hospital law. Extremum of a function. The formulas of Taylor and Maclaurin.
Partial derivatives. Global and local extremes.
Riemann integral of a function. Methods of counting of integrals. Integration of particular types of functions.
Applications of integrals. Fourier series
Learning outcomes: knowledge of basic theorems concerning sequences, limits, continuity differentiability of functions of one and several variables; knowledge of number and funcion series and integral calculus
(in Polish) Rodzaj przedmiotu
Course coordinators
Term 2013Z: | Term 2009Z: | Term 2010Z: | Term 2012Z: | Term 2011Z: |
Bibliography
a) basic references:
1. A. Birkholc, Analiza matematyczna dla nauczycieli. PWN, Warszawa 1977.
2. G.N. Berman, Zbiór zadań z analizy matematycznej, PWN, Warszawa.
3. B.P. Demidowicz, Zbiór zadań z analizy matematycznej, Naukowa Książka, Lublin 1992 (t. I) i 1993 (t. II i III).
4. K. Kuratowski, Rachunek różniczkowy i całkowy, PWN, Warszawa 1979.
b) supplementary references:
1. G.M. Fichtenholz, Rachunek różniczkowy i całkowy. Tom I i II, PWN, Warszawa 1999.
2. W. Rudin, Podstawy analizy matematycznej, PWN, Warszawa 2000.