151-0300/02 – Mathematics A (Mat A)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits4
Subject guarantorRNDr. Pavel Rucki, Ph.D.Subject version guarantorMgr. Marian Genčev, Ph.D.
Study levelundergraduate or graduate
Study languageGerman
Year of introduction2009/2010Year of cancellation2009/2010
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
GEN02 Mgr. Marian Genčev, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 1+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. [3] 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.

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:

Znalost, vědomost: • Definovat funkci jedné proměnné. • Určit definiční obor a obor hodnot funkce a základní vlastnosti funkce, • Nakreslit grafy elementárních funkcí. • Vypočítat limitu a derivaci funkce. • Zjistit vlastnosti neelementárních funkcí a nakreslit jejich grafy. • Získat jednodušší představu o ekonomických funkcích. • Uspořádat znalosti o vektorech v rovině. • Charakterizovat typy matic. • Vyřešit soustavu lineárních rovnic. Pochopení: • Vyjádřit ekonomické závislosti matematickou funkcí. • Vysvětlit sklon funkce pomocí první derivace. • Spojit matematické pojmy konkávní, konvexní s ekonomickými pojmy degresivní, progresivní. • Zevšeobecnit pojem funkce na závislosti z běžného života. • Přeformulovat ekonomické závislosti pomocí matematických vlastností funkcí. • Zevšeobecnit znalosti o vektorech v rovině na trojrozměrný prostor. Aplikace: • Srovnávat ekonomické a matematické funkce • Objevit nástroj pro popis závislostí a vztahů v ekonomice, ale i v jiných vědách. • Rozvinout zručnost v kreslení grafů funkcí. • Uplatnit znalosti lineární algebry v ekonomických oblastech, např. dopravní úlohy, strukturní modely. • Řešit základní úlohy lineárního programování.

Conditions for subject completion

Full-time form (validity from: 2009/2010 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation Credit  
Mandatory attendence parzicipation:

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