The aim of studying and bibliography

The main aim of study: The aim of the course is to familiarize students with the basic concepts of mathematical analysis, such as the notion of the continuity of a function, the derivative, indefinite and definite integrals. Students should understand these concepts and gain practical ability to solve related tasks.

The general information about the module: Content provided during the course include: the continuity of a function, the derivative, indefinite and definite integrals and their applications.

Bibliography required to complete the module

Bibliography used during lectures

1	A.V. Efimov, V.P. Demidović	Higher mathematics: worked examples and problems with elements of theory: for engineering students Part 1: Linear algebra and fundamentals of mathematical analysis	Moscov: "Mir".	1984
2	A.V. Efimov, V.P. Demidović	Higher mathematics: worked examples and problems with elements of theory: for engineering students Part 2: Advanced topics of mathematical analysis	Moscov: "Mir".	1984
3	R.J. Harshbarger, J.J. Reynolds	Calculus with applications	D. C. Heath & Co, Lexington.	1993
4	K. Kuratowski	Rachunek różniczkowy i całkowy. Funkcje jednej zmiennej	PWN, Warszawa.	1975
5	F. Leja	Rachunek różniczkowy i całkowy	PWN, Warszawa.	1975
6	A.V. Manzhirov, A. Polyanin	Handbook of mathematics for engineers and scientists	Boca Raton: Chapman a.Hall/CRC.	2007
7	W. Rudin	Podstawy analizy matematycznej	PWN, Warszawa.	1982
8	L.A. Trivieri	Basic Mathematics	New York: McGraw-Hill, Inc..	1990
9	L.A. Trivieri	Essentail mathematics with applications	New York: Random House, Inc..	1988

Bibliography used during classes/laboratories/others

1	J. Banaś, S. Wędrychowicz	Zbiór zadań z analizy matematycznej	WNT, Warszawa.	2003
2	A.V. Efimov, V.P. Demidović	Higher mathematics: worked examples and problems with elements of theory: for engineering students Part 1: Linear algebra and fundamentals of mathematical analysis	Moscov: "Mir".	1984
3	A.V. Efimov, V.P. Demidović	Higher mathematics: worked examples and problems with elements of theory: for engineering students Part 2: Advanced topics of mathematical analysis	Moscov: "Mir".	1984
4	M. Gewert, Z. Skoczylas	Analiza matematyczna I. Przykłady i zadania	GiS.	dow.
5	R.J. Harshbarger, J.J. Reynolds	Calculus with applications	D. C. Heath & Co, Lexington.	1993
6	L.A. Trivieri	Essentail mathematics with applications	New York: Random House, Inc..	1988

Bibliography to self-study

1	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach. Cz. I	PWN, Warszawa.	dow.
2	M. Gewert, Z. Skoczylas	Analiza matematyczna I. Definicje, twierdzenia, wzory	GiS.	dow.

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 basics of real numbers, functions and their properties, the theory of numerical sequences and limits of functions.

Basic requirements in category skills: Ability to use the basic mathematical apparatus in the field of real numbers, functions and their properties and numerical sequences and limits of functions.

Basic requirements in category social competences: 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 can investigate the continuity of the functions and the uniform continuity of the functions	lecture, solving classes	written test (colloquium)	K_W01+ K_W02++ K_W03++ K_W04+ K_U01+ K_U02+ K_U08+ K_U10+++ K_U24+ K_K01+	P6S_KK P6S_UK P6S_UU P6S_UW P6S_WG P6S_WK
02	student knows the foundations of differential calculus and can apply the methods of differential calculus for solving various problems	lecture, solving classes	written test (colloquium)	K_W01+ K_W02+++ K_W03++ K_W04+++ K_W05+++ K_W07+++ K_U01+++ K_U02++ K_U06++ K_U08+++ K_U10++ K_U12+++ K_K01+	P6S_KK P6S_UK P6S_UU P6S_UW P6S_WG P6S_WK
03	student knows the basics of integral calculus and can calculate indefinite integrals of the basic classes of functions	lecture, solving classes	written exam	K_W01+ K_W02+++ K_W03++ K_W04++ K_W05+++ K_W07+++ K_U01++ K_U02++ K_U06++ K_U08++ K_U10++ K_U12++ K_U13+++ K_U14+++ K_K01+	P6S_KK P6S_UK P6S_UU P6S_UW P6S_WG P6S_WK
04	student can use the knowledge of integral calculus for evaluating of simple definite integrals and can apply this knowledge to solve simple geometrical problems	lecture, solving classes	written exam	K_W01+ K_W02++ K_W03++ K_W04++ K_W05+++ K_W07+++ K_U01+++ K_U02+ K_U06++ K_U08+ K_U10+ K_U13+++ K_U14+++ K_K01+	P6S_KK P6S_UK 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
2	TK01	Continuous functions. Heine and Cauchy definitions of the continuity of a function. Uniformly continuous functions. Basic properties of a continuous function on a closed and bounded interval.	W01-W14, C01-C14	MEK01
2	TK02	Derivative of a function. Derivative of a function at a point. Derivatives of higher orders. The mean value theorem. Taylor's formula. Monotone functions. Extrema of functions. Convex functions. Asymptotes of a function. Plotting of graphs. Proving equalities and inequalities.	W15-W30, C15-C30	MEK02
2	TK03	Indefinite integrals. Methods of calculation of indefinite integrals. Calculating of integrals of fundamental classes of functions.	W31-W44, C31-C44	MEK03
2	TK04	Definite Riemann integral. Definition and properties of the definite integral. Geometric interpretation of the definite integral. The fundamental theorem of integral calculus. Improper integrals. Geometric applications of the definite integrals.	W45-W60, C45-C60	MEK04

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 2)		contact hours: 60.00 hours/sem.	complementing/reading through notes: 10.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 20.00 hours/sem. The preparation for a test: 30.00 hours/sem.	contact hours: 60.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 2)	The preparation for Advice: 4.00 hours/sem.	The participation in Advice: 4.00 hours/sem.
Exam (sem. 2)	The preparation for an Exam: 20.00 hours/sem.	The written exam: 2.00 hours/sem. The oral exam: 1.00 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. The obvious exercises and the extra exercises. At least 70% of the obvious exercises must be solved. Only the obvious exercises - 3.0. Exam only after the credit of classes.
Class	Two written tests on the dates agreed with the students. The tests contain the obvious exercises and the extra exercises. At least 70% of the obvious exercises must be solved. Only the obvious exercises - 3.0. To receive credit the student must attend training classes.
The final grade	After the credit of all types of classes the final grade is the average of grade of classes and grade of exam.

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	A. Ali; J. Banaś; . Mahfoudhi; B. Saadaoui	(P,Q)–ε-Pseudo Condition Spectrum for 2×2 Matrices. Linear Operator and Application	2023
5	J. Banaś; R. Taktak	Measures of noncompactness in the study of solutions of infinite systems of Volterra-Hammerstein-Stieltjes integral equations	2023
6	J. Banaś; V. Erturk; P. Kumar; A. Manickam; S. Tyagi	A generalized Caputo-type fractional-order neuron model under the electromagnetic field	2023
7	J. Banaś; A. Chlebowicz; M. Taoudi	On solutions of infinite systems of integral equations coordinatewise converging at infinity	2022
8	J. Banaś; R. Nalepa	The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space	2022
9	J. Banaś; R. Nalepa; B. Rzepka	The Study of the Solvability of Infinite Systems of Integral Equations via Measures of Noncompactness	2022
10	J. Banaś; W. Woś	Solvability of an infinite system of integral equations on the real half-axis	2021
11	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
12	J. Banaś; B. Krichen; B. Mefteh	Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations	2020
13	J. Banaś; L. Olszowy	Remarks on the space of functions of bounded Wiener-Young variation	2020
14	J. Banaś; A. Chlebowicz	On solutions of an infinite system of nonlinear integral equations on the real half-axis	2019
15	J. Banaś; B. Rzepka	Ocena efektywności inwestycji	2019
16	J. Banaś; B. Rzepka	Wykłady matematyki finansowej	2019
17	J. Banaś; L. Olszowy	On the equivalence of some concepts in the theory of Banach algebras	2019
18	J. Banaś; M. Krajewska	On solutions of semilinear upper diagonal infinite systems of differential equations	2019
19	J. Banaś; R. Nalepa	A measure of noncompactness in the space of functions with tempered increments on the half-axis and its applications	2019
20	J. Banaś; T. Zając	On a measure of noncompactness in the space of regulated functions and its applications	2019
21	L. Abadias; E. Alvarez; J. Banaś; C. Lizama	Solvability and uniform local attractivity for a Volterra equation of convolution type	2019