The aim of studying and bibliography

The main aim of study: To acquaint the students with the theory of parameter-dependent integrals

The general information about the module: The module is implemented in the third semester in the form of lectures (30 hours) and exercises (15 hours).

others: Literatura wykorzystywana podczas zajęć zostanie podana po wybraniu tematyki zajęć.

Bibliography required to complete the module

Bibliography used during lectures

1	G.M. Fichtenholz	Rachunek różniczkowy i całkowy, tom 1	PWN Warszawa.	1985
2	G.M. Fichtenholz	Rachunek różniczkowy i całkowy, tom 2	PWN Warszawa.	1985

Bibliography used during classes/laboratories/others

1	B. P. Demidowic,	Zbiór zadań z analizy matematycznej, T.2	Lublin: Naukowa Książka,.	1992
2	W.J. Kaczor, M.T. Nowak	Zadania z analizy matematycznej. Całkowanie, część 3	Wydawnictwo Naukowe PWN, Warszawa.	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: student has mathematical knowledge which allows him/her to understand mathematical terms which are lectured

Basic requirements in category skills: Ability to use fundamental mathematical tools and the knowledge obtained in the first year of the first level studies

Basic requirements in category social competences: A student is prepared to undertake substantiated mathematical operations in order to solve a task and has the ability to extend his/her knowledge independently

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	knows basic concepts and definitions given during the course of lectures	lecture, exercises	test	K_W02++ K_W04++ K_W06+ K_K01+	P6S_KK P6S_WG P6S_WK
02	knows how to check uniform convergence of functions of two variables and improper integral dependent on parameter	lecture, exercises	test	K_W01+ K_W02++ K_W03+ K_W05+ K_U01++ K_K01+	P6S_KK P6S_UK P6S_WG P6S_WK
03	knows how to calculate some integrals using Fubini's theorem and Leibniz integral rule	lecture, exercises	test	K_W03++ K_W04++ K_U01+ K_K01+	P6S_KK P6S_UK 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
3	TK01	Reminder of the necessary information from the courses of analysis.	W01-W02, C01-C02	MEK01
3	TK02	uniform convergence, differentiation and integration of functional series, passing limit under integral, differentiation under the integral sign (Leibniz's rule), Fubini's theorem.	W03-W10, C03-C07	MEK01 MEK02 MEK03
3	TK03	Uniform convergence of improper integral depended on parameter, criterion of convergeces, continuity and differentiation of improper integrals with respect to parameter, Examples of applications. Euler's integrals, the gamma function.	W11-W30, C08-C13	MEK01 MEK02 MEK03
3	TK04	Test based on the materials covered during lectures and exercises.	C14-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. 3)	The preparation for a test: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 6.00 hours/sem.
Class (sem. 3)	The preparation for a Class: 7.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 15.00 hours/sem.
Advice (sem. 3)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Credit (sem. 3)	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
Lecture	A credit for the lectures is based on attendance at the lectures.
Class	A credit for the exercises is based on the result of test and oral answers.
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. Madej	Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations	2024
2	J. Banaś; J. Madej	On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations	2024
3	J. Banaś; J. Ochab; T. Zając	On the smoothness of normed spaces	2024
4	L. Olszowy; T. Zając	On Darbo- and Sadovskii-Type Fixed Point Theorems in Banach Spaces	2024
5	A. Ali; J. Banaś; . Mahfoudhi; B. Saadaoui	(P,Q)–ε-Pseudo Condition Spectrum for 2×2 Matrices. Linear Operator and Application	2023
6	J. Banaś; R. Taktak	Measures of noncompactness in the study of solutions of infinite systems of Volterra-Hammerstein-Stieltjes integral equations	2023
7	J. Banaś; V. Erturk; P. Kumar; A. Manickam; S. Tyagi	A generalized Caputo-type fractional-order neuron model under the electromagnetic field	2023
8	J. Banaś; A. Chlebowicz; M. Taoudi	On solutions of infinite systems of integral equations coordinatewise converging at infinity	2022
9	J. Banaś; R. Nalepa	The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space	2022
10	J. Banaś; R. Nalepa; B. Rzepka	The Study of the Solvability of Infinite Systems of Integral Equations via Measures of Noncompactness	2022
11	S. Dudek; L. Olszowy	Measures of noncompactness in the space of regulated functions on an unbounded interval	2022
12	S. Dudek; L. Olszowy	Remarks on incorrect measure of noncompactness in BC (R+ x R+)	2022
13	J. Banaś; W. Woś	Solvability of an infinite system of integral equations on the real half-axis	2021
14	J. Banaś; A. Chlebowicz; W. Woś	On measures of noncompactness in the space of functions defined on the half-axis with values in a Banach space	2020
15	J. Banaś; B. Krichen; B. Mefteh	Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations	2020
16	J. Banaś; L. Olszowy	Remarks on the space of functions of bounded Wiener-Young variation	2020
17	L. Olszowy; T. Zając	Some inequalities and superposition operator in the space of regulated functions	2020
18	S. Dudek; L. Olszowy	Measures of noncompactness and superposition operator in the space of regulated functions on an unbounded interval	2020
19	J. Banaś; A. Chlebowicz	On solutions of an infinite system of nonlinear integral equations on the real half-axis	2019
20	J. Banaś; B. Rzepka	Ocena efektywności inwestycji	2019
21	J. Banaś; B. Rzepka	Wykłady matematyki finansowej	2019
22	J. Banaś; L. Olszowy	On the equivalence of some concepts in the theory of Banach algebras	2019
23	J. Banaś; M. Krajewska	On solutions of semilinear upper diagonal infinite systems of differential equations	2019
24	J. Banaś; R. Nalepa	A measure of noncompactness in the space of functions with tempered increments on the half-axis and its applications	2019
25	J. Banaś; T. Zając	On a measure of noncompactness in the space of regulated functions and its applications	2019
26	L. Abadias; E. Alvarez; J. Banaś; C. Lizama	Solvability and uniform local attractivity for a Volterra equation of convolution type	2019
27	L. Olszowy	Measures of noncompactness in the space of regulated functions	2019