# 151-0560/01 – Basic Mathematics (BasicM)

 Gurantor department Department of Mathematical Methods in Economics Credits 6 Subject guarantor prof. RNDr. Dana Šalounová, Ph.D. Subject version guarantor prof. RNDr. Dana Šalounová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2009/2010 Year of cancellation Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
RUC05 RNDr. Pavel Rucki, Ph.D.
S1A20 prof. RNDr. Dana Šalounová, Ph.D.
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

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. After successful and active graduation of subject • will know: count limit of function, derivate of function, count with matrices, count integral indefinite and definite, • profit: basic knowledge from differential calculus, from linear algebra and from integral calculus, • will be able: use mathematics as instrument for better comprehension of economy.

Lectures
Tutorials

### Summary

1. Functions of one real variable – definition, domain and range, classification, graphs, 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. 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. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations. 5. The indefinite integral – definition and properties, basic integration rules, methods of integration: integration by substitution, integration by parts. 6. The definite integral – definition and properties, the Newton-Leibniz formula.

### Compulsory literature:

Haeussler, E., Paul, R., Wood, R. Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences. Pearson, 2010, ISBN13 9780321643889, ISBN10 0321643887. Doležalová, J. Mathematics I. VŠB-TU Ostrava, 2005, ISBN 80-248-0796-3.

### Recommended literature:

Goldstein, L., Lay, D., Schneider, D. and Asmar, N. Calculus and Its Applications. Pearson, 2010, ISBN: 978-0-3-21571304. Larson, R., Falvo, C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007. Sydsaeter, K., Hammond, P. J. Mathematics for Economics Analysis. Pearson Education Limited, 2008, ISBN 978-0-273-71324-1. Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.

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

Two check tests (35 points total) during the semester. Homeworks, activity in the lessons (5 points total).

### Other requirements

Two check tests (35 points total) during the semester. Homeworks, activity in the lessons (5 points total).

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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. After successful and active graduation of subject • will know: count limit of function, derivate of function, count with matrices, count integral indefinite and definite, • profit: basic knowledge from differential calculus, from linear algebra and from integral calculus, • will be able: use mathematics as instrument for better comprehension of economy.

### Conditions for subject completion

Full-time form (validity from: 2009/2010 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 40  20
Examination Examination 60  31
Mandatory attendence parzicipation:

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2009/2010 (B6208) Economics and Management (6208R174) European Business Studies P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner