The aim of studying and bibliography

The main aim of study: Strengthening the knowledge needed to pass the final exam.

The general information about the module: This course consists of 30 hours of exercises.

Bibliography required to complete the module

Bibliography used during classes/laboratories/others

1	A. Birkholc	Analiza matematyczna. Funkcje wielu zmiennych	PWN, Warszawa.	2012
2	K. Kuratowski	Rachunek różniczkowy i całkowy. Funkcje jednej zmiennej	PWN, Warszawa.	1975
3	F. Leja	Rachunek różniczkowy i całkowy	PWN, Warszawa.	1975
4	M. Startek	Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej	Oficyna Wydawnicza Politechniki Rzeszowskiej.	2005

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: Knowledge of the maths sections presented during the semesters 1-5

Basic requirements in category skills: Student can apply the acquired knowledge to solve problems.

Basic requirements in category social competences: Ability to comprehensively present mathematical content

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	Is able to prepare a presentation on topics related to the basic branches of mathematics from the course of study.	seminar	oral presentation	K_W03+ K_W04++ K_W06+ K_U01+ K_U12++ K_U16+ K_U23+ K_K07++	P6S_KK P6S_UK P6S_UW P6S_WG P6S_WK
02	is able to apply the main theorems of the basic branches of mathematics from the course of study to to solve tasks.	solving classes	written test	K_W04+++ K_W06+ K_U01++ K_U12+++ K_U16+ K_U23+ K_K01+ K_K07+	P6S_KK P6S_UK P6S_UW P6S_WG P6S_WK

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
6	TK01	Basics of the differential calculus of functions of single variable: computation of the derivative, theorems on the mean value, relationship between the derivative and the monotonicity. Local extrema of functions and their determination, Taylor's formula.	C1-C7	MEK01 MEK02
6	TK02	The indefinite integral. Basic methods of calculating indefinite integrals. Calculation of integrals of rational functions. Definition of the Riemann integral - geometric interpretation. The Newton-Leibniz theorem, Geometrical applications of the definite integral.	C8-C13	MEK01 MEK02
6	TK03	Numerical series. Convergence of a number series. Convergence criteria for numerical series. Absolutely convergent series and conditionally convergent. Power series. Radius and convergence area of ​​the power series. Taylor's series. Expansion of a function into Taylor and Maclaurin series.	C14-C18	MEK01 MEK02
6	TK04	Derivative of a function of several variables. Partial derivatives. Gradient, Extremes of functions of several variables.	C19-C24	MEK01 MEK02
6	TK05	Independence of random events and independence of random variables. Conditional probability and Bayes' theorem. A partition of a sample space and theorem on total probability. The cumulative distribution function of a real-valued random variable. Moments of random variable.	C25-C30	MEK01 MEK02

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Class (sem. 6)	The preparation for a Class: 10.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 3.00 hours/sem.
Advice (sem. 6)		The participation in Advice: 2.00 hours/sem.
Credit (sem. 6)	The preparation for a Credit: 10.00 hours/sem.	The written credit: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Class	A credit is based on the results of test and oral presentation.
The final grade	The final mark is the average of the mark of test and mark of oral presentation.

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: no