COURSE DESCRIPTION

Course code

MAP1156

Kind of studies

common to all departments;

Course title

Mathematical Analysis 2

First name, surname and title of the lecturer/supervisor

Komisja programowa Instytutu Matematyki i Informatyki

First name, surname and title of the team's members

Lecturers of the Institute of Mathematics and Computer Science

Course structure

Form of class Lecture Problems classes Laboratory Project Seminar Number of points
Number of hours/week 2 2 4+3
Course grade based on Examination Test

Prerequisites

Mathematical Analysis 1

Course description

Definite integral. Improper integral. Differential calculus for functions of two or three variables. Double and triple integrals. Number and power series.

Lectures

Contents of particular hours Number of hours
1. Definite integral. Definition, geometric and physics interpretation of definite integral. Fundamental theorem of integral calculus. Integration by parts, change of variable of integration.2
2. Properties of definite integrals. Average value of function. Applications of integral calculus in geometry (area of region, length of arc, volume generated by revolving the region, area of surface generated by revolving the graph) and technique.3
3. Improper integrals of the first kind. Definition. Comparison and quotient convergence tests. Applications of improper integrals in geometry and technique.2
4. Functions of two or more variables. Graphs of functions of two variables.2
5. Partial derivatives. Definition. Geometric interpretation. Higher order partial derivatives. Equality of mixed partial derivatives.2
6. Tangent plane to a surface. Differentials and their applications. Differentiation of composite functions. Directional derivatives. Gradient of function.2
7. Local extreme of function of two variables. First and second derivative tests for locating extreme points. Relative maximum or minimum values of function. Optimization problems in geometry and technique.3
8. Double integrals. Definition, geometric and physics interpretation of double integral. Evaluation of double integrals.2
9. Properties of double integrals. Double integrals in polar coordinates.2
10. Triple integrals. Evaluation of triple integrals. Triple integrals in cylindrical and spherical coordinates.2
11. Applications of double and triple integrals in geometry, physics and technique.2
12. Number series. Convergence and divergence of number series. Geometric series. Tests for convergence of number series. Absolute and conditional convergence. Alternating series test.4
13. Power series. Radius and interval of convergence. Taylor and Maclaurin series. Expansion of functions in power series. 2

Problems classes

Contents of particular hours Number of hours
1. Exercises illustrating the material presented during the lectures.30

Material for self preparation

Basic literature

1. W. Żakowski, W. Kołodziej, Matematyka, Cz. II, WNT, Warszawa 2003.
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 2006.

Additional literature

1. G. M. Fichtenholz, Rachunek różniczkowy i całkowy, T. I-II, PWN, Warszawa 2007.
2. M. Gewert, Z. Skoczylas, Analiza matematyczna 2. Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS, Wrocław 2005.
3. F. Leja, Rachunek różniczkowy i całkowy ze wstępem do równań różniczkowych, PWN, Warszawa 2008.
4. R. Leitner, Zarys matematyki wyższej dla studiów technicznych, Cz. 1-2, WNT, Warszawa 2006.
5. H. i J. Musielakowie, Analiza matematyczna, T. I, 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.
7. W. Stankiewicz, Zadania z matematyki dla wyższych uczelni technicznych, Cz. B, PWN, Warszawa 2003.

Conditions required for a student to pass the course

Positive result of the written test (for problems classes) and of the written exam (for the lecture).