The aim of studying and bibliography

The main aim of study: Explore the basic messages and methods linear algebra and mathematical analysis. Development of mathematical knowledge and ability to solve basic mathematical and technical problems with the help of mathematical apparatus.

The general information about the module: The module is implemented in the first and second semester. In the first and second semester there are 30 hours of lectures and 30 hours exercises. 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. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS Wrocław .	2008
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS Wrocław .	2006
3	M. Gewert, Z. Skoczylas	Algebra liniowa 1. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław.	2006
4	M. Gewert, Z. Skoczylas	Równania różniczkowe zwyczajne. Teoria, przykłady, zadania	Oficyna Wydawnicza GiS, Wrocław.	2002
5	T. Jurlewicz, Z. Skoczylas	Algebra i geometria analityczna. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS.	2008
6	W. Żakowski, W. Kołodziej	Matematyka, część II	Wydawnictwa Naukowo-Techniczne, Warszawa.	2003
7	A. Sołtysiak	Analiza matematyczna. Część I	Wydawnictwo Naukowe UAM, Poznań.	2009
8	A. Sołtysiak	Analiza matematyczna. Część II	Wydawnictwo Naukowe UAM, Poznań.	2004

Bibliography used during classes/laboratories/others

1	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach, część I i II	PWN Warszawa.	2004
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2008
3	M. Gewert, Z. Skoczylas	Analiza matematyczna 1. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2006
4	M. Gewert, Z. Skoczylas	Równania różniczkowe zwyczajne. Teoria, przykłady, zadania	Oficyna Wydawnicza GiS, Wrocław.	2002
5	M. Gewert, Z. Skoczylas	Algebra liniowa 1. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2001
6	J. Banaś, S. Wędrychowicz	Zbiór zadań z analizy matematycznej	Wydawnictwa Naukowego PWN, Warszawa.	2012
7	T. Jurlewicz, Z. Skoczylas	Algebra i geometria analityczna. Przykłady i zadania	Oficyna Wydawnicza GiS.	2008

Bibliography to self-study

1	M. Gewert, Z. Skoczylas	Analiza matematyczna 1. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2006
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2008
3	M. Gewert, Z. Skoczylas	Algebra liniowa 1. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2006
4	M. Gewert, Z. Skoczylas	Równania różniczkowe zwyczajne. Teoria, przykłady, zadania	Oficyna Wydawnicza GiS, Wrocław.	2002
5	J. Banaś	Podstawy matematyki dla ekonomistów	WNT, Warszawa.	2007
6	T. Jurlewicz, Z. Skoczylas	Algebra i geometria analityczna. Przykłady i zadania	Oficyna Wydawnicza GiS.	2008
7	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach, część I i II	PWN Warszawa.	2004

Basic requirements in category knowledge/skills/social competences

Formal requirements:

Basic requirements in category knowledge: A 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 in the area of secondary school education and the knowledge obtained in the first semester 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 the basic properties of functions of one real variable and basic elementary functions	lecture, exercises	written test	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
02	knows how to calculate the limits of sequences and functions at a simple level of difficulty	lecture, exercises	written test, written exam	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
03	knows how to calculate the derivatives of functions of one real variable	lecture, exercises	written test, written exam	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
04	knows how to integrate the functions of one real variable by parts and by substitution and knows how to calculate simple definite integrals	lecture, exercises	written test, written exam	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
05	can perform basic operations on complex numbers	lecture, exercises	written test, written exam	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
06	knows how to perform operations on matrixes, knows how to calculate determinants of square matrixes and how to solve Cramer’s systems of linear equations	lecture, exercises	written test	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
07	knows how to solve first-order differential equations: separable and linear	lecture, exercises	written test, written exam	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
08	knows how to calcuate scalar, vector and triple scalar product of vectors	lecture, exercises	written test	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG
09	knows how to calculate the partial derivatives of functions of several variables	lecture, exercises	written test, written exam	K_W01++ K_U05++ K_K03+	P6S_KR P6S_UW P6S_WG

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-W04, C01-C04	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.	W05-W10, C05-C10	MEK02
1	TK03	Limit and continuity of functions of real variable: definitions of limit, counting properties of limits of functions, notion of continuity of a function. Asymptotes of a function.	W11-W12, C11-C12	MEK02
1	TK04	Differential calculus of functions 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.	W13-W18, C15-C20	MEK03
1	TK05	Integral calculus of functions 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.	W19-W30, C21-C28	MEK04
1	TK06	Tests based on the materials covered during lectures and exercises.	C13-C14, C29-C30	MEK01 MEK02 MEK03 MEK04
2	TK01	Algebraic structures: group, ring, field. 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.	W01-W03, C01-C03	MEK05
2	TK02	Matrices: definition, operations on matrixes and its properties, square matrices, determinant and its properties, inverse matrix, rank of a matrix. Systems of linear equations: Kronecker-Capelli's theorem, Cramer's systems.	W04-W07, C04-C10	MEK06
2	TK03	Ordinary differential equations: notions of general solution and particular solution, initial-value problem, ordinary differential equations of first-order (separable, homogeneous respect to x and y, linear, Bernoulli's), ordinary differential equations of second-order (reducible to equations of first-order, linear equations).	W08-W14, C11-C16	MEK07
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.	W15-W16, C19-C20	MEK08
2	TK05	Basic properties of function of several variables: limit and continuity of functions of several variables, partial derivatives and directional derivative, extrema of functions of several variables. Elements of field theory: scalar and vector fields, gradient, divergence, rotation, potential of vector field. Double and triple integrals - basic concepts.	W17-W30, C21-C28	MEK09
2	TK06	Tests based on the materials covered during lectures and exercises.	C17-C18, C29-C30	MEK05 MEK06 MEK07 MEK08 MEK09

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: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 15.00 hours/sem. The preparation for a test: 10.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 15.00 hours/sem.
Advice (sem. 1)		The participation in Advice: 5.00 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: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 15.00 hours/sem. The preparation for a test: 10.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 15.00 hours/sem.
Advice (sem. 2)		The participation in Advice: 5.00 hours/sem.
Exam (sem. 2)	The preparation for an Exam: 25.00 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 the result of the written exam. Obtaining a credit for the exercises is a prerequisite for taking a final exam. There is a possibility of exemption from the written exam based on a credit for the exercises.
Class	A credit for the exercises is based on the results of tests and oral answers.
The final grade
Lecture	A credit for the lecture is based on the result of the written exam. Obtaining a credit for the exercises is a prerequisite for taking a final exam. There is a possibility of exemption from the written exam based on a credit for the exercises.
Class	A credit for the exercises is based on the results of tests and oral answers.
The final grade	The final grade is the average grade of a grade (positive) of the exercises and a grade (positive) of the written 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: no