# 151-0340/01 – Mathematics E (Mat E)

 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 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 the function of one variable. • Find the domain and range and basic properties. • Draw graphs of elementary functions. • Compute limits and derivates of functions. • Find the properties of no elementary functions a draw theirs graphs. • Obtain easier imagine about economic functions. • Order knowledge about vectors in the plain. • Identify the types of matrices. • Solve the system of linear equations. Comprehension • Express economic dependences using a mathematical function. • Explain the slope of a function. • Restate the terms “concavity” and “convexity” into the “degressive” and “progressive”. • Generalise the functions on the dependences in the real live. • Express knowledge of vectors to the space. Applications • Relate economic and mathematical functions. • Discover the tools suitable for describing of dependences in economics and other sciences. • Develop the technique of graphs drawing. • Apply knowledge of linear algebra in economics, e.g. traffic problems, structural analysis. • Solve basic problems of linear programming. Analysis • Analyse mathematical principle of some economic terms and properties. • Appraise the trends of economic values.

### Summary

The subject is built on the university level of mathematics. It 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 as well as the ability to enunciate thoughts accurately and to give the correct argumentation when solving the practical problems. This is being done especially by mathematization of the real as well as theoretical economic problems. This subject supplies the students’ education with realms of higher mathematics which is applicable namely to the creation and study of economic models.

### Compulsory literature:

Doležalová, J., Mathematics I. VŠB-TU Ostrava, 2005, ISBN 80-248-0796-3. Sydsaeter, K., Hammond, P. J. Mathematics for Economics Analysis. Prentice Hall, Inc., 1995, ISBN 0-13-583600-X.

### Recommended literature:

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 has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1.Functions of one real variable – definition, domain and range, classification, graph, even and odd functions, monotonic functions (strictly increasing, strictly decreasing). Inverse functions. 2.The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval, sequences, limits of sequences. 3.An introduction to the derivate – slope of a tangent line at a point, derivative, equation of a tangent line and normal line to a curve at a point, techniques of differentiation, higher order derivations, l´Hospital´s rule. 4.Additional applications of derivative – extreme values of a continuous function, intervals of increase and decrease, the second-derivative test for concavity, the second-derivative test for relative extreme, asymptotes. 5.Linear algebra – matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations. 6.Linear algebra – system of linear equations, Gauss elimination method.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 45 (45) 23
Examination Examination 55 (55) 0
Written examination Written examination 45  23
Oral Oral examination 10  5
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy 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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