151-0400/01 – Mathematics A (MatKomb)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits4
Subject guarantorRNDr. Pavel Rucki, Ph.D.Subject version guarantorRNDr. Jana Hrubá, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2009/2010
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BAU20 RNDr. Danuše Bauerová, Ph.D.
HRU61 RNDr. Jana Hrubá, Ph.D.
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit 8+0

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

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Témata výkladu zpracovaných v podobě multimediálních studijních opor: 1. Lineární algebra – Euklidovský prostor, vektory, lineární závislost a nezávislost vektorů, lineární kombinace vektorů, matice, operace s maticemi, hodnost matice, determinanty, inverzní matice, maticové rovnice, soustavy lineárních rovnic, Gaussova eliminační metoda. 2. Funkce jedné reálné proměnné – definice, definiční obor, obor hodnot, graf funkce, vlastnosti funkcí: funkce monotónní, omezená, sudá, lichá, periodická, prostá, složená, elementární funkce, inverzní funkce, cyklometrické funkce. 3. Limita funkce a posloupnosti – pravidla pro výpočet limit, limita funkce v nevlastním bodě, nevlastní limita, jednostranné limity, spojitost funkce, posloupnosti, limita posloupnosti. 4. Derivace funkce – geometrický a obecný význam derivace, pravidla derivování, derivace vyšších řádů, diferenciál, rovnice tečny a normály, L’Hospitalovo pravidlo. 5. Průběh funkce – extrémy funkce, intervaly monotónnosti, inflexní body, konvexnost, konkávnost, asymptoty grafu funkce, globální extrémy. Offline procvičování (samostatně, bez stálého online připojení k internetu, pod vedením tutora prostřednictvím Průvodce studiem a se soustavným využíváním studijních opor): Offline procvičování obsahově navazuje na témata výkladu. Organizačně je zařazeno do vzdělávání tak, aby byl zajištěn co nejefektivnější dopad na studující, tzn. procvičování prostupuje výkladem dle metodických a didaktických zásad.

Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation Credit 85 (85) 0
        Written exam Written examination 80  40
        Written exam Other task type 5  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2006/2007 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (01) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner