The aim of studying and bibliography

The main aim of study: Implementing mathematical methods to describe physical phenomena and chemical processes, technological use of mathematics methods.

The general information about the module: The module is implemented in the first and second semester. In the first semester there are 18 hours of lectures and 27 hours tutorials and in the second semester there are 18 hours of lectures and 18 hours of tutorials. Both in the first and second semester the module ends with an exam.

Bibliography required to complete the module

Bibliography used during lectures

1	M. Gewert, Z. Skoczylas	Analiza matematyczna 1	Oficyna Wydawnicza GiS, Wrocław.	2008
2	G. Decewicz, W. Żakowski	Matematyka cz. 1	WNT, Warszawa.	1995
3	J. Stankiewicz, K. Wilczek	Algebra z geometrią	Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów.	2007
4	D. Bobrowski, J. Mikołajski, J. Morchało	Równania różniczkowe cząstkowe w zastosowaniach	Wydawnictwo Politechniki Poznańskiej, Poznań.	1995

Bibliography used during classes/laboratories/others

1	J. Banaś, S. Wędrychowicz	Zbiór zadań z analizy matematycznej	WNT, Warszawa.	2004
2	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach cz. 1 i cz. 2	PWN, Warszawa.	2004
3	J. Banaś	Podstawy matematyki dla ekonomistów	WNT, Warszawa.	2007
4	B. Gdowski, E. Pluciński	Zadania z rachunku wektorowego i geometrii analitycznej	PWN, Warszawa.	1981

Basic requirements in category knowledge/skills/social competences

Formal requirements: Basic knowledge of mathematics at secondary school level.

Basic requirements in category knowledge:

Basic requirements in category skills:

Basic requirements in category social competences:

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 the basic properties of functions of one real variable and basic elementary functions	lecture, tutorials	test	K_W01++	P6S_WG
02	knows how to calculate the limits of sequences and functions at a simple level of difficulty	lecture, tutorials	test	K_U06++	P6S_UU
03	knows how to calculate the derivatives of functions of one real variable and use the theorems and methods of differential calculus of functions of one real variable to search for local extrema of functions	lecture, tutorials	test, written exam	K_U06++	P6S_UU
04	knows how to integrate the functions of one real variable by parts and by substitution and knows how to calculate integrals of rational functions	lecture, tutorials	test, written exam	K_U06++	P6S_UU
05	knows how to solve ordinary differential equations of the first order with separated variables	lecture, tutorials	test	K_U06++	P6S_UU
06	knows how to calculate the determinants of square matrixes and how to solve Cramer's systems of linear equations	lecture, tutorials	test	K_U06++	P6S_UU
07	knows how to calculate the derivatives of functions of several variables, as well as gradient, divergence, rotation, and knows how to use theorems and methods of differential calculus of functions of several variables to search for local extrema of functions	lecture, tutorials	test, written exam	K_U06++	P6S_UU
08	knows how to calculate power and root of complex numbers	lecture, tutorials	test, written exam	K_U06++	P6S_UU

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	Elements of mathematical logic and set theory. Basic properties functions of one real variable, polynomials, Horner's scheme, rational functions and other elementary functions, arc functions.	W01, W02, C01, C02	MEK01
1	TK02	Sequences of numbers: monotonicity and boundedness of sequences, limit of a sequence, theorems about existence of a limit, Napierian base and its applications. Series of numbers: properties of series of numbers, tests for convergence of series, tests for divergence of series. Limit and continuity of function of real variable: definitions of limit, counting properties of limits of functions, notion of continuity, continuous function on the set. Asymptotes of a function.	W02, W03, C02, C03	MEK02
1	TK03	Differential calculus of function of one real variable: notion of derivative of function, derivatives of higher order, derivatives of basic elementary functions, derivative of composite function, De l’Hospital's theorem, mean value theorems, investigation of monotonicity and determination of extrema of functions, convex and concave functions, points of inflexion of graph of function, investigation of the behavior and systematic procedure in graphing of function.	W04, W05, C03, C04	MEK03
1	TK04	Test based on the materials covered during lectures and tutorials.	C05	MEK01 MEK02 MEK03
1	TK05	Integral calculus of function of one real variable: notions of primitive function and indefinite integral, integration by parts and by substitution, integration of rational functions, integration of irrational functions, integration of trigonometric functions. Notion of definite integral, applications of definite integrals, improper integrals.	W06, W07, W08, W09, C06, C07, C08	MEK04
1	TK06	Test based on the materials covered during lectures and tutorials.	C09	MEK03 MEK04
2	TK01	Ordinary differential equations: notions of general solution and particular solution, initial-value problem, ordinary differential equations of first-order (about separable variables, linear, homogeneous respect to x and y, solvable by substitution, linear, Bernoulli's), ordinary differential equations of second-order reducible to equations of first-order.	W01, W02, C01, C02	MEK05
2	TK02	Matrixes: definition, operations on matrixes and its properties, square matrixes, determinant and its properties, inverse matrix, rank of a matrix. Systems of linear equations: Kronecker-Capelli's theorem, Cramer's systems.	W03, W04, C03, C04	MEK06
2	TK03	Test based on the materials covered during lectures and tutorials.	C05	MEK05 MEK06
2	TK04	Elements of calculus of vectors and analytic geometry: vectors, operations on vectors and its properties, scalar product of vectors and its properties, vector product and triple scalar product of vectors, equations of a plane and of a straight line in the space.	W05, W06, C06	MEK06
2	TK05	Basic properties of function of several variables: limit and continuity of functions of several variables, partial derivatives, extrema of functions of several variables. Elements of field theory: scalar and vector fields, gradient, divergence, rotation, potential of vector field.	W06, W07, C07	MEK07
2	TK06	The set of complex numbers: canonical and polar form of a complex number, de Moivre's formula, calculation of power and root of complex numbers.	W08, C08	MEK08
2	TK07	Partial differential equations: initial-value problem, first and second-order linear partial differential equations.	W09	MEK05 MEK07
2	TK08	Test based on the materials covered during lectures and tutorials.	C09	MEK07 MEK08

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: 20.00 hours/sem.	contact hours: 18.00 hours/sem.	complementing/reading through notes: 18.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 15.00 hours/sem. The preparation for a test: 30.00 hours/sem.	contact hours: 18.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 3.00 hours/sem.	The participation in Advice: 3.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 25.00 hours/sem.	The written exam: 2.00 hours/sem.
Lecture (sem. 2)	The preparation for a test: 12.00 hours/sem.	contact hours: 18.00 hours/sem.	complementing/reading through notes: 18.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 36.00 hours/sem. The preparation for a test: 20.00 hours/sem.	contact hours: 18.00 hours/sem.
Advice (sem. 2)	The preparation for Advice: 3.00 hours/sem.	The participation in Advice: 3.00 hours/sem.
Exam (sem. 2)	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	A credit for the lecture is based on attendance at the lectures and the result of the written exam.
Class	A credit for the tutorials is based on the results of at least two tests and oral answers.
The final grade	A credit for the module is based on the credit for the tutorials and on the credit for the lectures. The final grade is the arithmetic mean of a grade (positive) of the tutorials and a grade (positive) of the exam. The final grade is rounded to the nearest mark permitted by the regulations of studies.
Lecture	A credit for the lecture is based on attendance at the lectures and the result of the written exam.
Class	A credit for the tutorials is based on the results of at least two tests and oral answers.
The final grade	A credit for the module is based on the credit for the tutorials and on the credit for the lectures. The final grade is the arithmetic mean of a grade (positive) of the tutorials and a grade (positive) of the exam. The final grade is rounded to the nearest mark permitted by the regulations of studies.

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