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 |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

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 study | Way of compl. | Extent |

Full-time | Credit and Examination | 1+2 |

Knowledge, comprehension
The student will be able to...
- solve the systems of linear equations by using the Gaussian elimination and Cramer's rule,
- control basic terminology and related applications in economics,
- write the systems of linear equations with the help of the matrix notation
- explain the concept of the primitive function and the indefinite integral,
- explain and to control the basic rules, formulas and techniques of integration
- define and to calculate the definite integral with the help of the Newton-Leibniz formula,
- explain the validity of the geometric application (quadrature only),
- present at least one application of the definite integral in economics
- define the real function of two real variables,
- give examples of basic functions of two variables (especially the constant, linear and Cobb-Douglass function),
- give examples of using the functions of two variables in economics,
- find the domain of the functions of two variables and its graphical visualization,
- find the level curves of basic functions of two variables and to know the economic interpretation,
- explain the concept of the homogenous functions of order 's' and to present the geometric and economic interpretation
- define and to calculate the partial derivatives with the help of rules and formulas,
- define the local extremes of functions of two variables,
- interpret the local extremes in economics,
- apply the partial derivatives for determining the existence and the nature of local extremes,
- discuss the existence and nature of local extremes by means of their definition,
- find the constrained extremes (the method of substitution, Lagrange's multiplier)
- recognize the type of a basic ordinary first-order differential equation,
- explain the existence and the solution form of the first- and second-order differential equations,
- solve basic types of first-order differential equations with the help of the direct integration, the constant variation and with the method of undetermined coefficients,
- solve the basic second-order linear differential equations with the constant coefficients and with the special right-hand side by means of the method of undetermined coefficients,
- outline at least one basic interpretation of the first- and second-order differential equations in economics
- control and to explain the basic rules and formulas of the difference calculus,
- explain the connection of the first- and second-order difference sign in connection with monotonicity and its dynamics,
- determine the monotonicity of sequences with the help of the first- and second-order difference,
- know the relationship between the summation and difference,
- define the first- and second-order linear difference equations,
- explain the existence of general first- and second-order linear difference equations with constant coefficients,
- explain the solution form of homogeneous first- and second-order linear difference equations with constant coefficients,
- solve the first- and second-order linear difference equations with constant coefficients and with the special right-hand side,
- find the closed form of basic finite sums with the help of the first-order linear difference equations,
- present basic applications of difference equations in economics

Lectures

Individual consultations

Tutorials

Other activities

Aims of the subject are...
- to get acquainted with further basic concepts of caluclus,
- to develop the logical thinking and argumentation skills,
- to point out the basic application context of mathematics and economics.

Larson R., Falvo C.D.: Elementary Linear Algebra. Houghton Mifflin, Boston, New York (2008)
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. MIT Press, London (2011)

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)

active participation on seminars, maximal three unexcused absences, understanding the basic concepts and methods presented at the lecture

no further requirements

Subject code | Abbreviation | Title | Requirement |
---|---|---|---|

151-0500 | Math A | Mathematics A | Compulsory |

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |

Exercises evaluation | Credit | 40 (40) | 20 |

Other task type | Other task type | 40 | 0 |

Examination | Examination | 60 (60) | 31 |

Written examination | Written examination | 50 | 26 |

Ústní zkouška | Oral examination | 10 | 5 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type 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 |

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