# 151-0502/01 – Mathematics B (MathB)

 Gurantor department Department of Mathematical Methods in Economics Credits 4 Subject guarantor prof. RNDr. Dana Šalounová, 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
Instruction secured by
GEN02 Mgr. Marian Genčev, Ph.D.  MAJ40 PaedDr. Renata Majovská, PhD.
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 1+2

### Subject aims expressed by acquired skills and competences

Knowledge, comprehension The student will be able... - to solve the systems of linear equations, 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 (Darboux construction), to compute the definite integral with the help 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, 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 (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

Lectures
Tutorials

### Summary

The aim of the subject is to get acquainted with the basic knowledge of advanced mathematics (linear algebra, in-/definite integral, functions of two variables, differential and difference equations), 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 practical problems.

### Compulsory literature:

 Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008.  Larson R., Edwards B. Calculus. Brooks/Cole Cengage Learning, Belmont, 2014.  Tan T.S. Calculus: Multivariable Calculus. Brooks/Cole Cengage Learning, Belmont, 2010.  Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011.

### Recommended literature:

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

### 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

no further requirements

### Prerequisities

Subject codeAbbreviationTitleRequirement
151-0500 Math A Mathematics A Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Part 1 - Linear Algebra ========================= * 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 ========================= * 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 ========================= * 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) ========================= * 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 ========================= * 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) ========================= Revision of the previous concepts and their interrelationship.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2014/2015 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 40 (40) 20
Examination Examination 60 (60) 31
Written examination Written examination 50  26
Ústní zkouška Oral examination 10  5
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty 2006/2007 (B6202) Economic Policy and Administration (6202R010) Finance (01) Finance P Czech Ostrava 1 Compulsory study plan
2005/2006 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 2 Compulsory study plan
2004/2005 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 2 Compulsory study plan
2004/2005 (M6208) Business and Management (6201T004) Economics P Czech Ostrava 2 Compulsory study plan
2003/2004 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 2 Compulsory study plan
2003/2004 (B6202) Economic Policy and Administration (6201R004) Economics P Czech Ostrava 2 Compulsory study plan
2003/2004 (B6208) Economics and Management (6201R004) Economics P Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

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