151-0006/03 – Applied Mathematics for Economists (AME)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |
| 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 | summer |
| | 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
On completion of this course, students will be able to master the basic techniques specified by the three main themes (see below, points 1-3). They will also be able to discuss freely, but logically correct, selected theoretical units that allow talented individuals to excel. The students will also have an overview of the basic applications of the apparatus discussed in the field of economics.
(1) The students will be introduced to the basics of linear algebra and its applications in economics.
(2) The students will be able to apply the basic rules and formulas for the calculation of integrals, use them to calculate the area of planar regions and to calculate improper integrals and integrals of discontinuous functions. They will be able to discuss the related applications in economics.
(3) The students will be able to find local extrema of functions of two variables without/with constraints, level curves and total differential, decide whether the given function is homogeneous. They will be able to discuss the related applications and give appropriate generalisations for functions of 'n' real variables.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Mathematics is an integral part of the study of economics at universities and also an essential tool for the study of professional subjects. The course Applied Mathematics for Economists complements the basic compulsory course Mathematics for Economists with the most common applications of mathematics in economic practice and thus significantly expands the awareness of the use of integral and differential calculus in statistics, in solving optimisation problems, etc. The basic economic context is the motivating basis for the lectures.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
The following are required for the award of classified credit
1. Successful completion of the credit test (minimum 50% success rate).
2. Active participation in exercises - maximum one unexcused absence.
3. Knowledge of the lecture material and the ability to understand and solve the examples given.
E-learning
MS Teams, lms.vsb.cz
Other requirements
Fulfilment of the prerequisite (completed course Statistics for Economists).
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Functions of one variable - derivative, analysis of the function (revision)
2. Basic operations with matrices, calculation of second and third order determinants.
3. Calculation of inverse matrix using adjoint matrix, solution of selected matrix equations and applications in economics.
4. Systems of linear equations. Gauss elimination, network analysis and other economic applications.
5. Basic rules and formulas for the indefinite integral, substitution method, applications in economics.
6. Integration by the per partes method, integration of selected rational functions, applications in economics.
7. The definite integral, content of plane figures bounded by curves, applications in economics.
8. The definite integral and the length of a plane curve. The mean value of a function. Applications in economics.
9. Definite integrals of discontinuous functions, proper integrals, applications in economics.
10. Real functions of several real variables. Graph, def. domain, contour line, homogeneous functions, applications in economics.
11. Partial and total derivatives. The tangent plane. Applications in economics.
12. Local extremes of functions of two variables without and with coupling (substitution, Lagrange multiplier). Applications in economics.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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