151-0502/01 – Mathematics B (MathB)
Gurantor department | Department of Mathematical Methods in Economics | Credits | 4 |
Subject guarantor | Mgr. Marian Genčev, Ph.D. | Subject version guarantor | Mgr. Marian Genčev, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 2 | Semester | summer |
| | Study language | English |
Year of introduction | 1999/2000 | Year of cancellation | 2014/2015 |
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
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:
Way of continuous check of knowledge in the course of semester
active participation on seminars, maximal three unexcused absences, understanding the basic concepts and methods presented at the lecture
E-learning
Other requirements
no further requirements
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Part 1 - Linear Algebra
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* Systems of linear equations - basic concepts, equivalent systems of equations, Gauß elimination, Frobenius Theorem, the solvability of systems of linear equations; analytic geometry in affine spaces A2, A3 and Euclidean spaces E2, E3 - basic affine concepts, line and plane equations; vector spaces with scalar multiplication, norm of general vectors, mutual position of planes, lines and their combinations; the distance of a point from a line or plane in E2 and E3.
Part 2 - Introduction to integral calculus
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* Antiderivative of functions - definitions and basic concepts, rules of integration, integrations by parts.
* Antiderivative of functions - integration by substitution (transformations of integrals), integration of basic rational, irrational and goniometric functions.
* The definite integral, properties of the Riemann integral, Newton-Leibniz' formula, geometric application of Riemann integral (computation of area-largeness).
* The definite integral - definition of improper integral, basic properties.
Part 3 - Introduction to differential calculus of two variables
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* Functions of two variables - basic concepts, the domain of real functions of two real variables and their visualisation; graph of a function and its visualisation.
* Functions of two variables - partial derivatives of first and higher orders; tangent plane, total differential of a function and its basic applications.
* Functions of two variables - local extrema and basic optimization methods (unconstrained optimization).
* Functions of two variables - constrained optimization (elimination of variables, the method of Lagrange multiplier).
Part 4 - Ordinary differential equations (ODE)
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* 1st-order ODE - basic concepts, general solution, particular solution; solving ODE by separation and integration; linear differential equations with non-constant coefficients, variation of constant.
* 2nd-order ODE - 2nd-order linear differential equations with constant coefficients and special RHS, solution estimation.
Part 5 - Ordinary difference equations
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* Introduction to difference calculus - basic concepts, general and particular solution, 1st-order linear difference equation with constant coefficients and special RHS, solution estimation.
* Introduction to difference calculus - 2nd-order linear difference equation with constant coefficients and special RHS, solution estimation.
Part 6 (formally)
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Revision of the previous concepts and their interrelationship.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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