The aim of studying and bibliography

The main aim of study: Providing the fundamental knowledge from the differential and integral calculus. The student will understand mathematical language and basis calculus to formulate and solve some problems in mathematics and physics.

The general information about the module: The course includes properties of linear algebra, fundamental properties of the functions of one and several variables, differential calculus of one and several variables, indefinite and definite integral and applications of differential and integral calculus.

Teaching materials: Materiały w wersji elektronicznej umieszczone na stronie domowej

Bibliography required to complete the module

Bibliography used during lectures

1	M. Gewert, Z. Skoczylas	Analiza matematyczna1, definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław ( biblioteka PRz-31 egz., czytelnia PRz - 3 egz.).	2006
2	J. Stankiewicz, K. Wilczek	Rachunek różniczkowy i całkowy funkcji jednej zmiennej, Teoria, przykłady, zadania	Oficyna Wydawnicza Politechniki Rzeszowskiej ( biblioteka PRz-85 egz., czytelnia PRz - 6 egz.).	2000
3	M. Gewert, Z. Skoczylas	Analiza matematyczna 2, definicje, twierdzenie, wzory ( biblioteka PRz-3 egz., czytelnia PRz - 1 e	Oficyna Wydawnicza GiS, Wrocław.	2006

Bibliography used during classes/laboratories/others

1	M. Gewert, Z. Skoczylas	Analiza matematyczna1, definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław.	2006
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2, definicje, twierdzenie, wzory	Oficyna Wydawnicza GiS, Wrocław.	2006

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: basic knowledge of mathematics at the high school level.

Basic requirements in category skills: Ability to use the fundamental mathematical tools in the area of the secondary school

Basic requirements in category social competences: The student is prepared to undertake objective and justified actions in order to solve the posed exercise

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	Student knows elements of logic and sets theory, the notion of function and its fundamental properties. Understand the notion of limit of function and indeterminate forms. Knows the Euler constant.	lecture, exercices	written exam, test	K_W01++ K_U03+ K_U09+++ K_K01+++	P6S_KO P6S_UO P6S_UU P6S_UW P6S_WG P6S_WK
02	Knows functions of one real variable and elementary functions. Understand the limit of function, divergent functions, continuous functions and its properties.	lecture, exercices	written exam, test	K_W01++ K_U03++	P6S_UO P6S_UW P6S_WG P6S_WK
03	Knows the notion of derivative, determine the derivatives of simple derivatives. Know how to use derivatives to determine the properties of function of one real variable.	lecture, exercices	written exam, test	K_W01+++ K_U03+++	P6S_UO P6S_UW P6S_WG P6S_WK
04	Knows the notion of the indefinite and definite integral. Calculate simple integrals. Apply methods of integration in practical simple exercices.	lecture, exercices	written exam, test	K_W01+++ K_U03+++ K_U09+++	P6S_UO P6S_UU P6S_UW P6S_WG P6S_WK
05	knows the notion of functions of several variables, vector functions and its basic properties. Knows the basic applications in physics.	lecture, exercices	written exam, test	K_W01+++ K_U03+++ K_K01++	P6S_KO P6S_UO P6S_UU 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
1	TK01	The basic problems in logic and set theory.Sequences and notion of limit of function	W01-W08, C01-C08	MEK01
1	TK02	Function of one variable. Composition of functions, injection, invers. Elementary functions. Limits of functions, asymptotes and continuity of functions.	W09-W25, C09-C25	MEK02
1	TK03	Derivative of functions, interpretation, mean-value theorem, extremum of function, Hospital rule. Convextity and concavity of function, investigation and graph, applications in physics.	W26-W36, C26-C36	MEK03
1	TK04	Indefinite and definite integral, the methods of calculations, applications of integrals.	W-37-W50, C37-C50	MEK04
1	TK05	Derivative of vector function. Functions of several variables, partial derivatives, directional derivatives, gradient. Applications.	W51-W60, C51-C60	MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 1)	The preparation for a test: 10.00 hours/sem.	contact hours: 60.00 hours/sem.	complementing/reading through notes: 10.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 40.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 60.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 1)
Exam (sem. 1)	The preparation for an Exam: 20.00 hours/sem.	The written exam: 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
Lecture	Written exam consists of 5 exercices (open). The evaluation: 3.0 for 50 %-60%, 3.5 for 61 %-70%, 4.0 for 71%-80%, 4.5 for 81%-90%, 5.0 for 91%-100%
Class	3 tests. The grading for each test: 3.0 for 50 %-60%, 3.5 for 61 %-70%, 4.0 for 71%-80%, 4.5 for 81%-90%, 5.0 for 91%-100%
The final grade	The average of the gradings of written exams and exercices

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