# 151-0400/05 – Mathematics A (MatKomb)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor RNDr. Pavel Rucki, 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
LoginNameTuitorTeacher giving lectures
HRA30 RNDr. Pavel Hradecký, Ph.D.
HRU61 RNDr. Jana Hrubá, Ph.D.
KUB33 Mgr. Aleš Kubíček
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit 6+8

### 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
Other activities

### Summary

Taught in Czech only. It contains the following topics: 1. Linear algebra – matrices, determinant, rank. 2. Linear algebra – the inverse of the matrix, linear equations. 3. Functions of one real variable – definition, properties, graphs, inverse functions. 4. The limit of function – properties of limits, limits to infinity, one sided limits, definition of continuit, sequences, limits of sequences. 5. An introduction to the derivation – slope of a tangent line at a point, 6. Higher order derivations, l´Hospital´s rule. 7. Additional applications of derivation.

### Compulsory literature:

[1] Hoy, M., Livernois, J., McKenna, Ch., Rees, R., Stengos, T. Mathematics for Economics. The MIT Press, London, 2011. [2] Tan, T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.

### Recommended literature:

[1] Larson, R., Falvo, C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. [2] Luderer, B., Nollau, V., Vetters, K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007. [3] Simon, C.P., Blume, L. Mathematics for Economists. W.W. Norton & Company, New York-London, 2005.

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

Odevzdání korespondenčních úkolů v elektronické podobě (viz LMS MOODLE na EkF VŠB-TUO) a vykonání písemky podle pokynů vyučujícícho. Z maximálního počtu bodů je nutno získat alespoň 50%.

### Other requirements

Credit requirements: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1. Fulfiling of all task assigned by a teacher 2. Familiarity with lecture topics and ability to solve assigned problems

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Témata výkladu zpracovaných v podobě multimediálních studijních opor: 1. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations. 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 differential calculus – 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. Course of a function – local and global extrema, intervals of monotonicity, points of inflection, convexity, concavity, asymptotic lines. Problems are solved offline (individually, under the supervision of a tutor with the aid of supportive materials).

### Conditions for subject completion

Part-time form (validity from: 2012/2013 Summer semester, validity until: 2017/2018 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation Credit 45 (45) 23
Zápočtový test Written test 40  20
Kontrolní úkoly Other task type 5  3
Mandatory attendence parzicipation: ***************************

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2017/2018 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2016/2017 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2014/2015 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2013/2014 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2012/2013 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner