# Mathematics I

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

## Teachers

## Included in study programs

**Teaching results**

A successful graduate of the course will have knowledge of differential and integral calculus, necessary for the study of other economic subjects. After completing the course, students will receive:

Knowledge and understanding

- understanding the basic principle of differential and integral calculus and their simple

applications in economy,

- awareness of the inevitability of the use of quantitative (mathematical) methods in economic

applications.

Skills

- students can solve fundamental problems of differential and integral calculus by using appropriate open-source software systems,

- solve fundamental problems of economic analysis and interpret the results of solutions.

Competence

- actively expand their mathematical knowledge and skills and use them in other subjects of quantitative orientation.

**Indicative content**

.

**Support literature**

1. KADEROVÁ, A. - KRÁTKA, Z. - KRČOVÁ, I. - MUCHA, V. - ŠOLTÉSOVÁ, T. (2020). Matematika pre ekonómov. Bratislava: Letra Edu.

2. KADEROVÁ, A. - MUCHA, V. - ONDREJKOVÁ KRČOVÁ, I. - ŠOLTÉSOVÁ, T. (2016). Matematika pre 1. ročník: učebný text. Bratislava: Vydavateľstvo EKONÓM, online.

3. FECENKO, J. - PINDA, Ľ. (2006). Matematika 1. IURA EDITION. Bratislava.

4. FECENKO, J. - SAKÁLOVÁ, K. (2006). Matematika 2. IURA EDITION. Bratislava.

**Syllabus**

1. Functions of one real variable. Properties of functions. Graphs of functions. 2. Functions of economic analysis, their properties and graphs. 3. Limit of function. Rules for calculating limits. One-sided limits. 4. Continuity of function in point and on the set. Asymptotes. 5. Difference quotient and derivative of function. Its geometric and economic interpretation. Tabular differentiation. Differential of function and its applications. L’Hospital rules. 6. Marginal value. Elasticity of function. Price elasticity of demand. Monotonicity of function. 7. Higher-order derivatives. Convexity and concavity of function. Point of inflection. 8. Local extremes. Economic applications. Graphing functions by characteristic points. 9. 2-dimensional Euclidean space. The function of two variables. Functions of economic analysis. Homogeneous function. 10. Partial function. Partial derivatives. Higher-order partial derivatives. Economic applications of partial derivatives. Marginal value. Partial elasticity. 11. Definition of local extremes. Necessary and sufficient condition for local extreme. Economic applications of local extremes. 12. Bound extremes. Economic applications of bounded extremes. 13. Definition of primitive functions and indefinite integrals. Basic rules of integration and table of standard integrals. Economic application of indefinite integrals.

**Requirements to complete the course**

The semester work - the written test - 30%,

The final written test (theory and examples) - 70%

**Student workload**

Total study load (in hours):

Participation in lectures - 26

Participation in exercises - 26

Preparing for exercise - 26

Preparation for course credit - 26

Exam Preparation (theory) - 26

Exam Preparation (examples) – 52

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