151-0802/01 – Mathematics B (MB Cžv)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits4
Subject guarantorIng. Orlando Arencibia Montero, Ph.D.Subject version guarantorIng. Orlando Arencibia Montero, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2005/2006Year of cancellation2009/2010
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
BAU20 RNDr. Danuše Bauerová, Ph.D.
FRI02 doc. Ing. Václav Friedrich, Ph.D.
HRU61 RNDr. Jana Hrubá, Ph.D.
MAJ40 PaedDr. Renata Majovská, PhD.
POL95 RNDr. Alena Poloučková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Distance Credit and Examination 1+0
Lifelong Credit and Examination 1+0

Subject aims expressed by acquired skills and competences

Knowledge • Define basic integration rules. • Define indefinite and definite integral. • Relate properties of indefinite and definite integral. • Define the function of two variables. • Find the domain and range. • Describe basic properties. • Compute partial derivates of functions. • Order knowledge about first-ordered differential equations. • Identify the types of differential equations. • Solve differential equations. Comprehension • Select suitable integral methods. • Solve integrals of rational functions by the method of partial fractions. • Solve integrals of some irrational functions and trigonometric functions. • Extend knowledge about economic dependences using a mathematical function. • Generalise the functions on the dependences in the real live. • Express knowledge about equation solving. Applications • Apply integration methods in economics. • Obtain easier imagine about economic functions of utility. • Discover the tools suitable for describing of dynamical models.

Teaching methods

Lectures
Individual consultations
Other activities

Summary

Cílem předmětu je seznámit se se základními pojmy a poznatky z vyšší matematiky a takto poskytnout východisko pro další studium kvantitativních metod v ekonomii. Význam má již samotná povaha a struktura předmětu, která výrazně napomáhá k rozvoji logického myšlení, k přesnému formulování myšlenek a jasné argumentaci při řešení praktických úloh. Předmět je podporován možností studia přes webovské rozhraní v LMS Moodle. Součástí jsou zvukové nahrávky doplňující grafickou prezentaci praktických cvičení.

Compulsory literature:

[1] Pampel Th. Mathematik für Wirtschaftswissenschaftler. Springer Verlag, 2010. [2] Dietz H.M. ECOMath 1 Mathematik für Wirtschaftswissenschaftler. Springer Verlag, 2010. [3] Dietz H.M. ECOMath 2 Mathematik für Wirtschaftswissenschaftler. Springer Verlag, 2010. [4] Dietz H.M. ECOMath 3 Mathematik für Wirtschaftswissenschaftler. Springer Verlag, 2011 (v prodeji během roku 2011). [5] Kohn W., Öztürk R. Mathematik für Ökonomen - Ökonomische Anwendungen der linearen Algebra und Analysis mit Scilab. Springer Verlag, 2009. [6] Stewart J.S. Calculus - Concepts and Contexts. Cengage Learning, 2010.

Recommended literature:

[7] Canuto C., Tabacco A. Mathematical Analysis I. Springer Verlag, 2008. [8] Larson R., Falvo D.C. Elementary Linear Algebra. Houghton Mifflin Harcourt Publishing Company, Boston-New York, 6th edition, 2009. [9] Schmidt K., Trenkler G. Einführung in die moderne Matrix-Algebra (mit Anwendungen in der Statistik), 2-te Auflage, Springer Verlag, 2006.

Way of continuous check of knowledge in the course of semester

písemná zkouška (100 bodů, minimum 51 bodů)

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Neurčitý integrál Definice a vlastnosti, základní vzorce, pravidla integrování, metody integrace: substituční metoda, metoda per partes. Integrace racionální lomené funkce, rozklad na parciální zlomky, integrace některých iracionálních funkcí, integrace některých goniometrických funkcí. Určitý integrál Definice a vlastnosti, Newton-Leibnizova formule, obsah rovinného obrazce, nevlastní integrál. Ekonomické aplikace (akumulace kapitálu) Funkce dvou proměnných Úvod a základní pojmy, definiční obor, obor hodnot, graf, parciální derivace prvního řádu, parciální derivace vyšších řádů. Tečná rovina k ploše, extrémy funkce dvou proměnných: lokální extrémy, vázané extrémy. Obyčejné diferenciální rovnice 1. řádu Úvod a základní pojmy, obecné řešení, partikulární řešení, separovatelná diferenciální rovnice, homogenní diferenciální rovnice. Lineární diferenciální rovnice homogenní a nehomogenní (metoda variace konstanty). Diferenční rovnice Úvod a základní pojmy, obecné řešení, partikulární řešení, lineární diferenční rovnice s konstantními koeficienty a speciální pravou stranou. Ekonomické aplikace.

Conditions for subject completion

Lifelong form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 3
        Examination Examination 100  51 3
        Exercises evaluation Credit 0  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2009/2010 (B6208) Economics and Management (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2009/2010 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2009/2010 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration C Czech Ostrava 1 Compulsory study plan
2009/2010 (B6202) Economic Policy and Administration (6202R040) Regional Development C Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration C Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration C Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration C Czech Ostrava 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 2 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6210R004) European Integration (02) European Integration C Czech Ostrava 2 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2009/2010 Summer