# 151-0300/03 – Mathematics A (Mat A)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor prof. RNDr. Dana Šalounová, Ph.D. Subject version guarantor RNDr. Pavel Rucki, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2010/2011 Year of cancellation 2017/2018 Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
CTV0004 RNDr. Eva Čtveráčková
GEN02 Mgr. Marian Genčev, Ph.D.
HAN0001 Mgr. Vít Hanák
HRD0001 Mgr. Zdeněk Hrdina
HRU61 RNDr. Jana Hrubá, Ph.D.
LOR21 Mgr. Kristina Lorencová
MIH22 RNDr. Šárka Michalcová, Ph.D.
SED05 Ing. Bc. Monika Poledníková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
REZ0011 RNDr. Lenka Řezníčková
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 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.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Taught in Czech. 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 real world. This is being done especially by mathematization of the practical 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 investigation of economic models.

### Compulsory literature:

[1] SYDSAETER, K., HAMMOND, P. J. Mathematics for Economics Analysis. Pearson, 2002, ISBN 978-81-7758104-1. [2] HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. The MIT Press, London, 3rd edition, 2011, ISBN 978-0-262-01507-3. [3] TAN, T.S. Single variable calculus: early transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011, ISBN 978-1-4390-4600-5.

### Recommended literature:

[1] LARSON, R. Elementary Linear Algebra. Brooks/Cole Cengage Learning, Belmont, 8th edition, 2016, ISBN 978-1305658004. [2] LUDERER, B., NOLLAU, V., VETTERS, K. Mathematical Formulas for Economists. Springer Verlag, 3rd edition, 2006, ISBN 978-3540469018.

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

Credit requirements: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. Passing the credit test (succes rate - at least 50%) 2. Fulfiling of all task assigned by a teacher 3. Active participation at seminars - at most one absence without leave 4. Familiarity with lecture topics and ability to solve assigned problems The deadline is February 11th, 2018. Credit requirements in case of individual study: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.

### E-learning

Credit requirements: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. Passing the credit test (succes rate - at least 50%) 2. Fulfiling of all tasks assigned by a teacher 3. Active participation at seminars - at most one absence without leave 4. Familiarity with lecture topics and ability to solve assigned problems The deadline is February 11th, 2018. Credit requirements in case of individual study: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Introduction to mathematical logic and set theory. 2. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions, composition of functions. 3. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval. 4. 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. 5. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations.

### Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2017/2018 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2016/2017 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2016/2017 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2016/2017 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2015/2016 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration P Czech Uherské Hradiště 1 Compulsory study plan
2014/2015 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2014/2015 (B6209) Systems Engineering and Informatics P Czech Uherské Hradiště 1 Compulsory study plan
2013/2014 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2013/2014 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2013/2014 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2013/2014 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2011/2012 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6234) Quantitative Methods and Decision Making in Economics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2010/2011 (B6207) Quantitative Methods in Economics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6208R101) Sports Management (02) Sports Management P Czech Uherské Hradiště 1 Compulsory study plan
2010/2011 (B6234) Quantitative Methods and Decision Making in Economics P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner