151-0401/04 – Mathematics B (MBKS)
| 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 | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2020/2021 |
| 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
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
Written exam
- max. 100 pts,
- min. 51 pts
E-learning
Other requirements
According to teacher's instructions.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
I. Systems of linear equations and analytic geometry
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- basic concepts,
- Gaussian elimination, Frobenius' theorem,
- Cramer's rule,
- use of systems of linear equations for determining the mutual position of
- two planes in E3,
- two lines in E2 and E3,
- plane and a line in E3
- basic applications in economics
II. Integral calculus
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Indefinite integral
- definition and properties,
- basic integration formulas and rules,
- per partes, substitution,
- integration of rational functions (partial fractions),
- basic applications in economics
Definite integral
- the problem of calculating the area of a region bounded by continuous curves
- definitions a properties of the definite integral,
- Newton-Leibniz' formula,
- basic applications in economics
Generalized and improper integral
- improper integral of the first and second kind,
- Gaussian integral (for information only),
- calculating improper integrals by limits,
- generalized definite integrals (the case of discontinuous functions),
- basic applications in economics and connection with statistics
III. Functions of two real variables
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- definitions of basic concepts,
- domain and its visualization,
- homogeneous functions of order 's',
- partial derivatives and their geometric interpretation
- tangent plane,
- total differential, differentiable functions, approximations of number expressions,
- local extremes,
- constrained local extremes
- method of substitution,
- Lagrange's multiplier,
- basic applications in economics
IV. Ordinary differential equations (ODE)
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- definition of ODE,
- order of ODE,
- solution of ODE (general, particular, singular, extraordinary),
- basic types of first-order ODE's
- separated,
- separable,
- linear first-order DE (variation of constants),
- second-order linear DE with constant coefficients and special right-hand side (undetermined coefficients),
- basic applications in economics
V. Difference calculus and difference equations
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Introduction to difference calculus
- difference of order 'k',
- basic formulas and rules for calculating the differences,
- the sign of the first-order difference as the indicator of the sequence monotonicity,
- the sign of the second-order difference as the indicator of the sequence monotonicity dynamics,
- relation of summation and difference
Ordinary difference equations (ODifE)
- definition of the ODifE
- order of the ODifE
- solution of the ODifE (general, particular)
- first- and second-order ODifE with constant coefficients and special right-hand side (undetermined coefficients)
- basic applications in economics
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction