# 151-0341/01 – Mathematics F (Mat F)

 Gurantor department Department of Mathematical Methods in Economics Credits 6 Subject guarantor PaedDr. Renata Majovská, PhD. Subject version guarantor PaedDr. Renata Majovská, PhD. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2006/2007 Year of cancellation 2009/2010 Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
MAJ40 PaedDr. Renata Majovská, PhD.  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 • Define basic integration rules. • Define indefinite and definite integral. • Relate properties of indefinite and definite integral. • Define the function of two variables. • Find the domain and range. • Describe basic properties. • Compute partial derivates of functions. • Order knowledge about first-ordered differential equations. • Identify the types of differential equations. • Solve differential equations. Comprehension • Select suitable integral methods. • Solve integrals of rational functions by the method of partial fractions. • Solve integrals of some irrational functions and trigonometric functions. • Extend knowledge about economic dependences using a mathematical function. • Generalise the functions on the dependences in the real live. • Express knowledge about equation solving. Applications • Apply integration methods in economics. • Obtain easier imagine about economic functions of utility. • Discover the tools suitable for describing of dynamical models. Analysis • Analyse mathematical principle of some economic terms and properties. • Appraise the trends of economic values.

### Summary

The subject continues fulfilling general methodical and professional goals of mathematics, i.e. to train the rational thinking and the ability to conceive and work with quantitative information concerning the outer world. Students get knowledge of several mathematical techniques which are necessary to understand economic relationships and models.

### Compulsory literature:

Kreml, P., Mathematics II. VŠB-TU Ostrava, 2005, ISBN 80-248-0798-X. Sydsaeter, K., Hammond, P. J. Mathematics for Economics Analysis. Prentice Hall, Inc., 1995, ISBN 0-13-583600-X.

### Recommended literature:

Rosser, M., Basic Mathematics for Economist. Routledger, London, 2003, ISBN 0-203-42263-5. Goldstein, L., Schneider, D. Introduction to Mathematics. Ginn Custom Publishing, 1981, ISBN 0-536-03755-8 Bradley, G. L., Smith, K. J. Calculus. Prentice Hall, Inc., 1995, ISBN 0-13-081055-X.

### Way of continuous check of knowledge in the course of semester

Validation tests using CMS Moodle.

### Prerequisities

Subject codeAbbreviationTitleRequirement
151-0340 Mat E Mathematics E Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. The indefinite integral – definition and properties, basic integration rules, methods of integration: integration by parts, integration by substitution. 2. The indefinite integral – integrals of rational functions, the method of partial fractions, integrals of some irrational functions, integrals of some trigonometric functions. 3. The definite integral – definition and properties, Riemann sums, the Newton-Leibniz formula, application of the definite integral: area between curves, capital stock, improper integral. 4. Functions of two variables – introduction and terminology, domain, range, graph, partial derivatives, higher-order partial derivatives. 5. Equation of a tangent plane and a normal of a surface, extreme of functions of two variables: local extreme, extreme with a condition. 6. Ordinary differential equation – first-order differential equations, introduction and terminology, general solution, particular solution, separable differential equation, homogeneous differential equation. 7. Linear differential equation.

### Conditions for subject completion

Full-time form (validity from: 2006/2007 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 45 (45) 23
Written exam Written test 45  23
Examination Examination 55 (55) 28
Written examination Written examination 45  23
Oral Oral examination 10  5
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty 2009/2010 (B6207) Quantitative Methods in Economics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6207) Quantitative Methods in Economics (6207R015) Managerial and Decision Making Methods in Economics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6207) Quantitative Methods in Economics (6207R015) Managerial and Decision Making Methods in Economics P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6207) Quantitative Methods in Economics (6207R015) Managerial and Decision Making Methods in Economics P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

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