# Mathematics II

- Credits: 7
- Ending: Examination
- Range: 2P + 2C
- Semester: summer
- Year: 1
- Faculty of Economic Informatics

## Teachers

## Included in study programs

**Teaching results**

Knowledge. Understanding of knowledge of basic principles and knowledge of calculations of definite and improper integrals, numerical and functional series and of linear algebra and their applications in economics,

Skills. Acquired knowledge and skills to be able to apply in the field of discrete and continuous random variable, in the field of discrete and continuous financial cash flows, time series, in solving optimal programming problems and in all areas of finding solutions to economic science problems by quantitative methods.

Competences. Actively expand their mathematical knowledge and skills and use them in other subjects of quantitative focus.

**Indicative content**

1. Definite integral and their calculation. Calculation of area of the region. Economic applications.

2. Improper integral. Methods for calculating improper integrals.

3. Limit of a sequence. Euler's number. Investigation of convergence and divergence of data series.

4. Alternating series. Function series.

5. Power series, radius and interval of convergence. Taylor series and development of elementary functions.

6. Operations with vectors. Linear combination, dependence and independence. Rank the vectors. Dimension and base of linear space.

7. Elementary change of base and its use.

8. EZB. Operations with matrices. Decomposition of the matrix to the product.

9. Calculation of rank of matrix using EZB. Inverse matrix, matrix equations.

10. Economic applications. Determinants of degree n and calculation of them.

11. Solution of system of linear equations by method of EZB.

12. Solution of SLR – by Cramer rule and inverse matrix. Space of solutions. Fundamental system of solutions.

13. The system of linear inequalities. Credit exam.

**Support literature**

Basic literature:

1. FECENKO, Jozef. Nekonečné rady : (číselné, funkcionálne, maticové). 1. vyd. Bratislava : Vydavateľstvo EKONÓM, 2017. online [78 s., 3,67 AH]. ISBN 978-80-225-4387

2. SAKALOVÁ, K. – SIMONKA, Z. – STREŠŇÁKOVÁ, A.: Lineárna algebra pre ekonómov. FHI EU v Bratislave. 1. vydanie. Vydavateľstvo Letra Edu Bratislava 2020. ISBN 978-80-89962-73-3(print). ISBN 978-80-89962-73-0 (online).

Recommended literature:

1. KADEROVÁ, A. KRÁTKA, Z. KRČOVÁ, I., MUCCHA, V., ŠOLTÉSOVÁ T.: Matematika pre Ekonómov. Vydavateľstvo Letra Edu Bratislava 2020. ISBN 978-90-89962-73-4(print). ISBN 978-90-89962-63-1 (online).

2. FECENKO, Jozef – SAKÁLOVÁ, Katarína. Matematika 2. Bratislava : Elita, 1999. 316 s. ISBN 80- 85323-85-0

**Syllabus**

1. Definite integral and their calculation. Calculation of area of the region. Economic applications. 2. Improper integral. Methods for calculating improper integrals. 3. Limit of a sequence. Euler's number. Investigation of convergence and divergence of data series. 4. Alternating series. Function series. 5. Power series, radius and interval of convergence. Taylor series and development of elementary functions. 6. Operations with vectors. Linear combination, dependence and independence. Rank the vectors. Dimension and base of linear space. 7. Elementary change of base and its use. 8. EZB. Operations with matrices. Decomposition of the matrix to the product. 9. Calculation of rank of matrix using EZB. Inverse matrix, matrix equations. 10. Economic applications. Determinants of degree n and calculation of them. 11. Solution of system of linear equations by method of EZB. 12. Solution of SLR – by Cramer rule and inverse matrix. Space of solutions. Fundamental system of solutions. 13. The system of linear inequalities. Credit exam. 1. Definite integral and their calculation. Calculation of area of the region. Economic applications. 2. Improper integral. Methods for calculating improper integrals. 3. Limit of a sequence. Euler's number. Investigation of convergence and divergence of data series. 4. Alternating series. Function series. 5. Power series, radius and interval of convergence. Taylor series and development of elementary functions. 6. Operations with vectors. Linear combination, dependence and independence. Rank the vectors. Dimension and base of linear space. 7. Elementary change of base and its use. 8. EZB. Operations with matrices. Decomposition of the matrix to the product. 9. Calculation of rank of matrix using EZB. Inverse matrix, matrix equations. 10. Economic applications. Determinants of degree n and calculation of them. 11. Solution of system of linear equations by method of EZB. 12. Solution of SLR – by Cramer rule and inverse matrix. Space of solutions. Fundamental system of solutions. 13. The system of linear inequalities. Credit exam.

**Requirements to complete the course**

The semester work and the written test – 30 %

The final written test – 70 %

**Student workload**

Participation in lectures - 30

Participation in exercises - 30

Preparing for exercises - 30

Preparation for course credit - 30

Individual study in preparation for the exam - 62

Total load – 182

**Language whose command is required to complete the course**

slovak

Date of approval: 11.03.2024

Date of the latest change: 15.05.2022