151-0301/04 – Mathematics B (Mat B)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits5
Subject guarantorMgr. Marian Genčev, Ph.D.Subject version guarantorMgr. Marian Genčev, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
CTV0004 RNDr. Eva Čtveráčková
GEN02 Mgr. Marian Genčev, Ph.D.
HRD0001 Mgr. Zdeněk Hrdina
HRU61 RNDr. Jana Hrubá, Ph.D.
KOZ214 Ing. Mgr. Petr Kozel, Ph.D.
LOR21 Mgr. Kristina Lorencová
MIH22 RNDr. Šárka Michalcová, Ph.D.
OND10 Mgr. Ivana Onderková, Ph.D.
SED05 Ing. Bc. Monika Poledníková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
REZ0011 RNDr. Lenka Řezníčková
RUC05 RNDr. Pavel Rucki, Ph.D.
ZAH0001 Marek Zahradníček
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Knowledge, comprehension The student will be able... - to solve the systems of linear equations (including simple parameterized coefficients), to control basic terminology and related applications - to explain the concept of the primitive function and indefinite integral, to control the basic rules, formulas and techniques of integration - to define the definite integral, to compute the definite integral with the help of Newton-Leibniz formula, to outline the proof of Newton-Leibniz formula, to control the related basic geometric and economic applications - to define real functions of two real variables, to find the domain of functions of two variables and its visualization, to give the overview of basic functions of two variables used in economics (mainly constant, linear and Cobb-Douglass function), to explain the concept of homogenous functions of order 's' and to give the connections to economics - to define and to compute the partial derivatives with the help of their definitions and with the help of rules and formulas, to apply the partial derivatives for determining of local extremes (Hessian matrix), to define and interpret local extrema in a correct way, to discuss local extrema by means of their definition (inequality-type conditions, i.e., without the Hessian matrix), to find constrained extremes (method of substitution, Lagrange's multiplier) - to distinguish and to solve the basic types of differential and difference equations of 1st and 2nd order, to state the basic application possibilities in economics - to control the principles of difference calculus in connection with the monotonicity and dynamics of real sequences, to explain the connection between summation and difference, to find closed form of basic sums by means of 1st order difference equations

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The aim of the subject is to get acquainted with the basic knowledge of advanced mathematics, which is necessary for further studies of quantitative methods in economics. The subject’s structure and nature themselves have their importance as they help to develop logical thinking as well as the ability to enunciate thoughts accurately and to give clear argumentation when solving the practical problems. Formal prerequisites: Mathematics A

Compulsory literature:

[1] Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. [2] Tan T.S. Calculus: Multivariable Calculus. Brooks/Cole Cengage Learning, Belmont, 2010. [3] Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011.

Recommended literature:

[1] Stewart J.S. Calculus - Concepts and Contexts. Cengage Learning, 2010. [2] Canuto C., Tabacco A. Mathematical Analysis I. Springer Verlag, 2008. [4] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, 3rd ed., 2007. [5] Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.

Way of continuous check of knowledge in the course of semester

Zápočet (písemná forma) ======================= - max. 40 bodů, - min. 20 bodů. Maximální povolený počet neomluvených absencí na cvičení: jedna. Zkouška (písemná, resp. ústní forma) ==================================== - písemná zkouška -- max. 42 bodů, -- min. 22 bodů; - ústní zkouška -- max. 18 bodů, -- min. 9 bodů.

E-learning

Další požadavky na studenta

According to teacher's requests in accoradnce with official conditions discussed with the department head.

Prerequisities

Subject codeAbbreviationTitleRequirement
151-0300 Mat A Mathematics A Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

(1) Linear algebra ============================== Systems of linear equations - introduction and definitions, solvability, methods of solving, Frobenius theorem, system consistence in case of parameterized coefficients. Analytical geometry in 2- and 3-dimensional Euclidean space - basic concepts, mutual position of plains and/or lines in 2- and 3-dimensional space, the distance between points, lines and planes. Appliacations of systems of linear equations in economics. (2) Indefinite integral - introduction ============================== Indefinite integral of functions of one variable - basic definitions and rules, per-partes technique, substitution, integration of rational functions. Definite integral - basic definitions and properties, Newton-Leibniz formula, principle of its proof, geometric and economic applications. Generalized and improper integral - definitions and basic properties. (3) Functions of two real variables ============================== Basic definitions, domain determination and its graphic representation, homogenous functions of order 's'. Partial functions, partial derivatives, tangent plane and normal line to a surface, partial and total differential. Local extremes (un-/constrained), method of substitution and Lagrange's function. Applications in economics. (4) Ordinary differential equations ============================== Ordinary differential equations (ODE), order of ODE, general, particular and singular solution, basic types of ODE of the 1st and 2nd order (separable, linear), the method of undetermined coefficients. Applications in economics. (5) Differential calculus ============================== Introduction to the calculus of differences - difference of order 'k', the signum of the difference as an indicator of sequence monotonicity. Difference equations - its order and solution, linear difference equations solved by undetermined coefficients. Summation and its connection to difference calculus, closed form of finite sums solved by means of 1st order difference equations. Applications in economics. (6) Final considerations ==============================

Conditions for subject completion

Full-time form (validity from: 2016/2017 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40 (40) 20
                Písemka Written test 40  20
        Examination Examination 60 (60) 31
                Písemná zkouška Written examination 42  22
                Ústní zkouška Oral examination 18  9
Mandatory attendence parzicipation: One unexcused absence in seminars.

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