151-0502/02 – Mathematics B (MathB)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |
| Subject guarantor | doc. Mgr. Marian Genčev, Ph.D. | Subject version guarantor | doc. Mgr. Marian Genčev, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2015/2016 | Year of cancellation | |
| Intended for the faculties | EKF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The students will be able to master the basic techniques specified by the three main topics (see below, items 1-3). Also, they will be able to freely, but logically correct, discuss selected theoretical units that will allow talented individuals to excel. The student will also have an overview of basic application possibilities of the discussed apparatus in the field of economics.
(1) The student will be introduced to the basics of linear algebra and its application possibilities in economics.
(2) The student 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 for calculating of improper integrals and integrals of discontinuous functions. The student will be able to discuss the relating application possibilities in economics.
(3) The student will be able to find local extrema of functions of two variables without/with constraints, level curves and total differential, will be able to decide whether the given function is homogeneous. The student will be able to discuss the relating application possibilities and to mention appropriate generalizations for functions of 'n' real variables.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Practical training
Summary
The course is focused on the practical mastery of selected mathematical methods in the field of linear algebra and calculus, which form the basis for further quantitative considerations in related subjects. The student will also be acquainted with the derivation of basic theoretical findings. This enables the development of logical skills, which form the basis for analytical and critical thinking. For better motivation of students, the presentation in lectures is always connected with appropriate economic problems.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Credit
- passing the written credit test (passing score of at least 50%),
- maximum one unexcused absence
Exam
- compulsory written part (passing rate of at least 50%),
- optional oral part
E-learning
LMS, MS Teams, https://www.vsb.cz/e-vyuka/cs/subject/151-0301/04
Other requirements
According to teacher's requests in accoradnce with official conditions.
Conditions for ISP: Optional attendance at seminars, other conditions without modification.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Basic operations with matrices, calculation of 2nd- and 3rd order determinants.
2. Matrix invesrsion, specific matrix equations. Applications in economics.
3. Systems of linear equations. Gaussian elimination, Cramer's rule,network analysis and further applications.
4. Basic rules and formulas for indefinite integrals, method of substitution. Applications in economics.
5. Integration by parts, integration of selected rational functions. Applications in economics.
6. Definite integral. Areas of regions bounded by continuous curves. Applications in economics.
7. Definite integrals of discontinuous functions, improper integrals. Applications in economics.
8. Real functions of more real variables. Graph, domain, level curves, homgeneous functions. Applications in economics.
9. Partial derivatives, total differential. Tangent plane. Applications in economics.
10. Local extrema of functions of two variables. Constrained extrema (substitution, Lagrange's multiplier). Applications in economics.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction