The aim of studying and bibliography

The main aim of study: Familiarising students with chosen issues concerning the theory of absolutely continuous functions, regulated functions and measures of noncompactness.

The general information about the module: The course consists of 30 hours of lectures and 15 hours of exercise..Subiect classes were chosen by students.

Bibliography required to complete the module

Bibliography used during lectures

1	J. Appell, J. Banaś, N. Merentes	Bounded variation and around	de Gruyter, Berlin.	2013
2	S. Łojasiewicz	Wstęp do teorii funkcji rzeczywistych	PWN, Warszawa.	1976
3	J. Banaś, K. Goebel	Measures of noncompactness	Marcel Dekker, New York.	1980
4	J. Banaś, M. Mursaleen	Sequence spaces and measures of noncompactness with applications to differential and integral equations	Springer, New York.	2014

Bibliography used during classes/laboratories/others

1	J. Banaś, S. Wędrychowicz	Zbiór zadań z analizy matematycznej	Wydawnictwo Naukowe PWN.	2020
2	W. J. Kaczor, M. T. Nowak	Zadania z analizy matematycznej	Wydawnictwo Naukowe PWN.	2006

Basic requirements in category knowledge/skills/social competences

Formal requirements: Student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge: Student has mathematical knowledge which allows him/her to understand mathematical terms which are lectured.

Basic requirements in category skills: Student knows, understands and can apply concepts of Calculus and Functional Analysis.

Basic requirements in category social competences: Student has the ability to independent and collaborative learning, is aware of the level of his knowledge and understands the need of self-learning.

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 the basic theorems of issues discussed during classes.	Lecture/Exercises	Test, oral answering during the exercises.	K_W01+++ K_W02++ K_W03++ K_W04++ K_W05+++ K_W07+	P7S_WG P7S_WK
02	Student knows the basic examples illustrating the issues discussed during classes.	Lecture/Exercises	Test, oral answering during the exercises.	K_W01+++ K_K02++	P7S_KK P7S_KO P7S_WG
03	Student is able - in speech and in writing - to present an issue related to the discussed topic.	Lecture/Exercises	Test, oral answering during the exercises.	K_U01++ K_U02++ K_U03++ K_K01++ K_K04++ K_K07++	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UW

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
4	TK01	Absolutely continuous functions, functions of bounded variation and regulated functions.Presentation of selected theorems concerning these functions.	W1-W30, C1-C15	MEK01 MEK02 MEK03
4	TK02	Measures of noncompactness in mertic spaces and in Banach spaces.Examples, properties and different uses of these measures.	W1-W30, C1-C15	MEK01 MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 4)		contact hours: 30.00 hours/sem.
Class (sem. 4)	The preparation for a Class: 7.00 hours/sem.	contact hours: 15.00 hours/sem.
Advice (sem. 4)		The participation in Advice: 1.00 hours/sem.
Credit (sem. 4)	The preparation for a Credit: 5.00 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
Lecture	A credit for the lecture is based on attendance at the lectures.
Class	The credit for the exercises is based on the result of the test and oral answers during the exercises.
The final grade	The final grade is a credit for the exercises.

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: yes

1	J. Banaś; J. Ochab; T. Zając	On the smoothness of normed spaces	2024
2	L. Olszowy; T. Zając	On Darbo- and Sadovskii-Type Fixed Point Theorems in Banach Spaces	2024
3	L. Olszowy; T. Zając	Some inequalities and superposition operator in the space of regulated functions	2020
4	J. Banaś; T. Zając	On a measure of noncompactness in the space of regulated functions and its applications	2019