1437212558

1437212558



partial derivatives (Schwarz theorem).

4. Differential and their applications. Partial derivatives of composite functions. Gradient of a function. Local extrema of functions of two variables, necessary and sufficient conditions. Conditional extreme points of a function of two variables. Global extrema. Applications of extreme problems in geometry and technics.

3

5. Double integrals. Geometrie and physical interpretation. Double integrals over normal regions.Całki podwójne. Properties of double integrals. Double integrals in polar coordinates. Applications of double integrals in geometry and technics.

3

6. Number series. Basic theorems. Geometrie series. Necessary condition for convergence of a series. Tests for convergence of series. Alternating series, Leibniz theorem. Approximations of sums of series.

3

7. Power series. Radius and interval of convergence. Taylor and Maclaurin expansions. Differentiation and integration of power series. Applications to approximate calculation of integrals.

3

8. Topics for choice among 14 - 18 or other subjects proposed by faculties.

6

9. Selected algebraic structures - groups, rings, fields.

2

10. Implicit functions.

2

11. Triple integral. Physical interpretation. Triple integrals over normal regions. Change of variables to cylindrical and spherical coordinates.

2

12. Function series, Fourier series.

2

13. Ordinary differential equations. Equations of separated variables First order linear equations. Second order linear equations with constant coefficients.

4

• Classes


Contents of particular hours

Number of hours

1. Exercises illustrating the materiał presented during the lectures.

18

• Basic literaturę


1.    M. Gewert, Z. Skoczylas, Analiza matematyczna 2. Definicje, twierdzenia, wzory. Oficyna

Wydawnicza GiS, Wrocław 2005._

2.    M. Gewert, Z. Skoczylas, Analiza matematyczna 2. Przykłady i zadania. Oficyna

Wydawnicza GiS, Wrocław 2005._

3.    W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, cz. I-II, PWN, Warszawa

1993._

4.    W. Żakowski, W. Kołodziej, Matematyka, cz. II, WNT, Warszawa 1992._


• Additional literaturę


1.    M.Fichtenholz, Rachunek różniczkowy i całkowy. T. I,II, PWN, Warszawa 1995._

2.    M.Gewert, Z.Skoczylas, Analiza matematyczna 2. Kolokwia i egzaminy. GiS, Wrocław

2003._

3.    F. Leja, Rachunek różniczkowy i całkowy ze wstępem do równań różniczkowych, PWN,

Warszawa 1977._

4.    R. Leitner, Zarys matematyki wyższej dla studiów technicznych, cz.1-2, WNT, Warszawa

1994._

5.    H. i J. Musielakowie, Analiza matematyczna, 1.1, cz. 1-2 oraz t. II, cz. 1, Wydawnictwo

Naukowe UAM, Poznań 1993 oraz 2000._

6.    J. Pietraszko, Matematyka. Teoria, przykłady, zadania, Oficyna Wydawnicza Politechniki

Wrocławskiej, Wrocław 2000._




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