The aim of studying and bibliography

The main aim of study: Knowledge mathematical terminology (elements of higher mathematics).

The general information about the module: Classes in mathematics in English.

Bibliography required to complete the module

Bibliography used during classes/laboratories/others

1	J. Marsden, A. Weinstein	Calculus	Springer-Verlag, New York, Berlin, Heidelberg, Tokyo.	1985
2	A.D. Polyanin, A.V. Manzhirov	Mathematics for engineers and scientists	Chapman & Hall/CRC Taylor & Francis Group, Boca Raton, London, New York.	2007

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 basic mathematical concepts gained during the first degree studies.

Basic requirements in category skills: Having the skills required to pass the subjects offered during the first degree studies.

Basic requirements in category social competences: Ability to extend their 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	obtains knowledge of English terminology used in mathematics (basic mathematical concepts and operations, terminology of analysis, algebra and Euclidean geometry).	classes	control of oral answers	K_W13+ K_K01+ K_K04+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_WK
02	obtains ability to read and comprehend scientific mathematical text written in English.	classes	control of oral answers	K_W13+ K_K06+++	P7S_KK P7S_KR P7S_UK P7S_WK
03	obtains ability to translate a simple mathematical text from Polish to English.	classes	control of oral answers	K_W13+ K_U02++ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UW P7S_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	Elementary functions.	C01-C03	MEK01 MEK02 MEK03
1	TK02	Equalities and inequalities, arithmetic operations, absolute value.	C04-C06	MEK01 MEK02 MEK03
1	TK03	Relations, equivalence relations, ordering relations.	C07-C09	MEK01 MEK02 MEK03
1	TK04	Functions, injection, surjection, bijection. Inverse function.	C10-C12	MEK01 MEK02 MEK03
1	TK05	Euclidean geometry of the plane: angles (acute, obtuse, right), triangle, rectangle, polygon, circle.	C13-C18	MEK01 MEK02 MEK03
1	TK06	Polynomials and algebraic equations.	C19-C21	MEK01 MEK02 MEK03
1	TK07	Matrices and determinants.	C22-C24	MEK01 MEK02 MEK03
1	TK08	Sequences, limit of a sequence.	C25-C27	MEK01 MEK02 MEK03
1	TK09	Consistency condition for a linear system, finding solutions of a system of linear equations.	C28-C30	MEK01 MEK02 MEK03
1	TK10	Limit of a function, asymptotes, continuous functions.	C31-C33	MEK01 MEK02 MEK03
1	TK11	Differential calculus for functions of a single variable, differentiation rules, theorems about differentiable functions, L’Hospital rule.	C34-C36	MEK01 MEK02 MEK03
1	TK12	Higher-order derivatives and differentials, qualitative analysis of functions and construction of graphs.	C37-C39	MEK01 MEK02 MEK03
1	TK13	Integration examples, integration of rational functions, integration of irrational functions.	C40-C42	MEK01 MEK02 MEK03
1	TK14	Ordinary differential equations, first-order differential equations, second-order linear differential equations.	C43-C45	MEK01 MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Class (sem. 1)	The preparation for a Class: 10.00 hours/sem. Others: 10.00 hours/sem.	contact hours: 45.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Credit (sem. 1)	The preparation for a Credit: 10.00 hours/sem.	The oral credit: 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
Class	The final mark is the mean of marks obtained for oral answers.
The final grade	The final mark is the mark for knowledge obtained in classes

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