151-0004/02 – Mathematics for economists (MPE)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 6 |
| Subject guarantor | Mgr. Marian Genčev, Ph.D. | Subject version guarantor | Mgr. Marian Genčev, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2024/2025 | Year of cancellation | |
| Intended for the faculties | EKF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
• Student will master basic techniques of using real matrices, including basic matrix operations and calculating the determinant of a matrix.
• Student will be able to apply matrices as an effective tool for solving systems of linear equations.
• Student will be able to model the dependencies of real quantitative processes using real functions.
• Student will determine the domain of a function and the graph of elementary functions.
• Student will calculate the derivative of a function and apply it to solve optimization problems and investigate properties of real functions.
• Student can extend previous knowledge to real functions of two variables.
• Student will learn techniques for finding local extrema of functions of two variables, contours of a function, and be able to decide on their homogeneity.
• Student will be able to use the basic rules and formulas for calculating indefinite and definite integrals and apply them to calculating the area of plane figures.
• The student will acquire basic applications of mathematics in economics.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
The course extends the high school mathematics knowledge of real functions with the help of mathematical analysis and focuses on the acquisition of mathematical methods in linear algebra including applications of mathematics. One of its goals is to emphasize rational thinking and the ability to process quantitative information about the world around us.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Credit requirements:
1. Passing the credit test (succes rate - at least 50%).
2. Active participation at seminars - at most one unexcused absence.
3. Familiarity with lecture topics and ability to solve assigned problems.
E-learning
MS Teams, lms.vsb.cz
Other requirements
Credit requirements:
1. Passing the credit test (succes rate - at least 50%).
2. Active participation at seminars - at most one unexcused absence.
3. Familiarity with lecture topics and ability to solve assigned problems.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Linear algebra - basic matrix operations, second- and third-order determinants.
2. Matrix invesrsion, specific matrix equations.
3. Systems of linear equations, Gaussian elimination.
4. Function of a single real variable - domain, elementary functions.
5. Graph of a function, inverse functions.
6. Limits of functions.
7. Derivative of a function, geometrical meaning.
8. Higher order derivatives, monotonoic functions, local and global extremes of a function.
9. Convex and concave functions, points of inflection.
10. Function of two real variables - domain, graph, level curves, homogenous functions.
11. Partial derivatives, tangent plane, local extremes, constrained extremes (substitution technique).
12. Integral calculus - basic rules and formulas for indefinite integrals, method of substitution.
13. Areas of regions bounded by continuous curves.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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