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 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, definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS Wrocław .	2006
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

Bibliography used during classes/laboratories/others

1

W. Krysicki, L. Włodarski

Analiza matematyczna w zadaniach, część I i II

PWN Warszawa.

2004

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.	2006
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

Basic requirements in category knowledge/skills/social competences

Formal requirements: According to the regulations of PRz.

Basic requirements in category knowledge: Basic knowledge of mathematics on secondary school level

Basic requirements in category skills: Ability to use the fundamental mathematical tools in the area of the secondary school

Basic requirements in category social competences: The 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	can perform basic operations on complex numbers	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
02	knows how to calculate the determinants of square matrixes and how to solve Cramer's systems of linear equations	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
03	knows the basic properties of functions of one real variable and basic elementary functions	lecture, tutorials	written test	K_W01++	P6S_WG
04	knows how to calculate the basic limits of sequences and functions	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
05	can investigate the convergence of simple number series	lecture and tutorials	written test or exam	K_W01++	P6S_WG
06	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 in tasks	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
07	knows how to integrate the functions of one real variable by parts and by substitution, knows how to calculate integrals of basic class of functions	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
08	knows how to calculate the derivatives of functions of several variables and knows how to use theorems and methods of differential calculus of functions of several variables to search for local extrema of functions; knows the basic properties of double integrals, and can be applied in simple tasks; an calculate a triple integral over a normal region at a basic level of difficulty	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
09	knows how to solve first-order differential equations; knows how to solve second-order differential equations	lecture, tutorials	written test or written exam	K_U06++	P6S_UU
10	can calculate the definite integral and improper integral of functions of one variable and use it in tasks	Lecture and tutorial	written test or exam	K_W01+++	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	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, W02, C01, C02	MEK01
1	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.	W03, W04, W05, C03, C04, C05,	MEK02
1	TK03	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.	W06, C06	MEK03
1	TK04	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 of a function. Asymptotes of a function.	W05, W06, W07, C05, C06, C07	MEK04
1	TK05	Study of the convergence of numerical series.	W07, W08, C07, C08	MEK05
1	TK06	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.	W09, W10, W11, W12, C09, C10, C11, C12, C13	MEK06
1	TK07	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.	W14, W15, C14, C15	MEK07
2	TK01	Notion of definite integral, applications of definite integrals, improper integrals.	W01, W02, W03, W04, C01, C02, C03, C04	MEK10
2	TK02	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, linear), ordinary differential equations of second-order reducible to equations of first-order, linear equations.	W05, W06, W07, W08, W09, C05, C06, C07, W08, W09	MEK09
2	TK03	Basic properties of function of several variables: limit and continuity of functions of several variables, partial derivatives, extrema of functions of several variables.	W10, W11, W12, C10, C11, C12	MEK08
2	TK04	Elements of field theory: scalar and vector fields, gradient, divergence, rotation, potential of vector field. Double and triple integrals - basic concepts.	W13, W14, W15, C13, C14, C15	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: 15.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 15.00 hours/sem. Studying the recommended bibliography: 5.00 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: 10.00 hours/sem.
Advice (sem. 1)
Exam (sem. 1)	The preparation for an Exam: 20.00 hours/sem.
Lecture (sem. 2)	The preparation for a test: 15.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 10.00 hours/sem. Studying the recommended bibliography: 5.00 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: 10.00 hours/sem.
Advice (sem. 2)
Exam (sem. 2)	The preparation for an Exam: 25.00 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 to which only those students who have obtained credit for the exercises are admitted.
Class	A credit for the classes is based on the attendance, the results of a test or activities in the classes.
The final grade	Final grade is determined on the basis of the credit from the lecture or on the basis of the credit for the classes.
Lecture	A credit for the lecture is based on the result of the written exam to which only those students who have obtained credit for the exercises are admitted.
Class	A credit for the classes is based on the attendance, the results of a test or activities in the classes.
The final grade	Final grade is determined on the basis of the credit from the lecture or on the basis of the credit for the 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: no