# 151-0500/02 – Mathematics A (Math A)

 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 English Year of introduction 2014/2015 Year of cancellation 2017/2018 Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
GEN02 Mgr. Marian Genčev, Ph.D.
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

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 9788177581041 [2] Hoy, M., Livernois, J., McKenna, Ch., Rees, R., Stengos, T. Mathematics for Economics. The MIT Press, London, 2011. [3] 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

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 three absence without leave 4. Familiarity with lecture topics and ability to solve assigned problems 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.

### Other requirements

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 three absence without leave 4. Familiarity with lecture topics and ability to solve assigned problems 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 - statement, proposition, logical connectives, quantifiers, necessary and sufficient conditions, set operations, number sets, intervals. 2. Real sequences – basic concepts, properties, arithmetic and geometric sequence and their application. 3. Real sequences – limit of a sequence, improper limit of a sequence, definition of Euler's number e. 4. Function of a single real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing). 5. Function of a single real variable – inverse functions, elementary functions, graph of a function and its transformation, points of intersection. 6. Function of a single real variable – continuous function, limit of a function at a point, properties of limits, one-sided limits. 7. Function of a single real variable – improper limit of a function, limit of a funciton at infinity, properties of continuous functions. 8. Function of a single real variable – derivative of a function, slope of a tangent line at a point, equation of a tangent line and normal line to a curve at a point, differentiation techniques, higher order derivatives. 9. Function of a single real variable - differential of a function, Rolle's and Lagrange'S Theorem, l'Hospital's Theorem, Taylor and Maclaurin polynomial. 10. Function of a single real variable - monotonoic function, local and global extrema of a function. 11. Function of a single real variable – convex and concave function, inflexion points, asymptotes - horizontal, vertical, oblique. 12. Linear algebra – matrix, matrix operation, rank of a matrix. 13. Linear algebra – determinant of a matrix, properties of determinant, Sarrus' scheme, Laplace's formula, inverse matrix, matrix equations. 14. Linear algebra – vector, vector operation, linearly independent vectors, vector spaces, inner product of vectors, length of a vector.

### Conditions for subject completion

Full-time form (validity from: 2014/2015 Winter semester, validity until: 2017/2018 Summer semester)
Min. number of points
Credit Credit 100 (100) 51
Test 1 Written test 40  20
Test 2 Written test 40  20
Test 3 Written test 20  10
Mandatory attendence parzicipation: *******************************

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2017/2018 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner