MMEPKVAA Quantitative Methods A

School of Business Administration in Karvina
Summer 2014
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Radmila Krkošková, Ph.D. (lecturer)
prof. RNDr. Jaroslav Ramík, CSc. (lecturer)
Mgr. Radmila Krkošková, Ph.D. (seminar tutor)
doc. Mgr. Jiří Mazurek, Ph.D. (seminar tutor)
Ing. Elena Mielcová, Ph.D. (seminar tutor)
Ing. Radomír Perzina, Ph.D. (seminar tutor)
prof. RNDr. Jaroslav Ramík, CSc. (seminar tutor)
Ing. Filip Tošenovský, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jaroslav Ramík, CSc.
Department of Informatics and Mathematics – School of Business Administration in Karvina
Prerequisites (in Czech)
K absolvování předmětu nejsou vyžadovány žádné podmínky a předmět může být zapsán nezávisle na jiných předmětech.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
The course Quantitative Methods A makes the participants acquainted with basic knowledge and terms from the area of algebra and mathematics so that the students shall be able to use the introduced constructions and explained thought and numerical procedures in their future autonomous study. Further, they will acquire a variety of numerical skills. This course will be followed by the course Quantitative Methods B.
Syllabus (in Czech)
  • 1. Motivational introduction, history of mathematics
    2. Linear vector spaces
    3. Matrices and matrix algebra
    4. Linear algebraic equations systems
    5. Determinants
    6. Sequences and their limits
    7. Function limit and continuity
    8. Differential calculus of one variable function
    9. Using of differential calculus of one variable function
    10. Indefinite integral
    11. Definite integral
    12. Infinite nonnegative numeric series
    1. Motivational introduction, history of mathematics
    Prehistory of mathematics development, development of mathematics in Greece, fundaments of European mathematics, foundation of scientific centres in the 17 and 18 centuries. Development of mathematics in the 19 and 20 centuries. Calculators, computers and mathematics. Set symbols, propositions and logic operations, set relations and operations. Mapping. Numerical sets.
    2. Linear vector spaces
    Example - arithmetic vector space. Linear combination of vectors, linear dependence and independence of vectors. Linear space basis, attributes of basis, degree of linear space.
    3. Matrices and matrix algebra
    Basic terminology, sum of matrices and multiplications of matrices by constant, linear space of matrices. Transformation to triangular matrix, degree of matrix. Square, rectangular, unit, invertible and singular matrices. Matrix product and its attributes. Inverse matrices. Solving of matrix equations.
    4. Linear algebraic equations systems
    Matrix of the system of equations, extended matrix of the system of equations. Frobeniov theorem and its consequences. Gauss and Jordan method of solving the system of linear equations. Homogenous system of linear equations given as a other example of linear space.
    5. Determinants
    Definition, basic attributes. Cramer theorem. Expansion of determinant. Calculation of inverse matrices.
    6. Sequences and their limits
    Arithmetic and geometric sequence. Definite and indefinite sequence. Bounded and unbounded sequence. Monotonous sequence, limit of sequence. Convergent and divergent sequence. Calculation of sequence limit, attributes of sequence limit.
    7. Function limit and continuity
    Real function of one real variable. Supremum and infimum, bounded, convex and concave function. Invertible and inverse function. Elementary functions. Domain of elementary functions, their attributes and graphs. Continuity of function of one real variable and its attributes. Bolzan and Weierstrass sentence. Limit of function of one variable and its attributes.
    8. Differential calculus of one variable function
    Differentiation of explicit function, geometrical meaning of differentiation, relation of continuity and differentiation. Sentence about differentiation of arithmetic operations and compounded function. Differential, differentiation of higher degree.
    9. Using of differential calculus of one variable function
    L'Hospital rule. Sentences about significance of first and second differentiation for construction of function graph, construction of graph. Taylor polynomial.
    10. Indefinite integral
    Primitive function, integration methods per partes and substitution.
    11. Definite integral
    Rieman definite integral, Newton-Leibniz formula. Calculation of area. Improper integrals, convergence and divergence of improper integral.
    12. Infinite nonnegative numeric series
    Infinite series and their sum, convergence and divergence of series, geometric series. Necessary condition of convergence, reminder of series, series with positive elements, criteria of convergence.
Literature
    required literature
  • SIMON, C.P., BLUME,L. Mathematics for Economists. New York: W.W.Norton and Company, 1994. ISBN 0-393-95733-0. info
    recommended literature
  • GODULOVÁ, M., JANŮ, J., STOKLASOVÁ, R. Matematika A. Učební text. Karviná: OPF SU, 2003. ISBN 7248-206-8. info
  • CHIANG, C.C. Fundamentals Methods of Mathematical Economics. New York: cGraw-Hill, Inc., 2000. ISBN 0-12-417890-1. info
  • POLÁK, J. Středoškolská matematika v úlohách II. Praha. PROMETHEUS, 1999. ISBN 80-7196-166-3. info
  • BRADLEY, T., PATTON, P. Essentials Mathematics hor Economics and Business. West Susex: John Wiley & Sons Ltd, 1998. ISBN 0-471-97511-7. info
  • KOLEKTIV AUTORŮ. Matematická ekonomie 1, 2. text. Ostrava: EF VŠB - TU, 1995. info
  • PISZCZALA, J. Matematika i jej zastosowanie w naukach ekonomicznych. Poznań:Wydawnictwo Akademii Ekonomicznej w Pozna, 1995. ISBN 83-85530-65-7. info
  • REKTORYS, K. a kol. Přehled užité matematiky I, II. Praha. SNTL, 1995. ISBN 80-85849-92-5. info
  • POLÁK, J. Přehled středoškolské matematiky. Praha. PROMETHEUS, 1991. ISBN 80-7196-196-5. info
  • BARTSCH, H. J. Matematické vzorce. Praha: SNTL, 1987. info
Teaching methods
Skills demonstration
Seminar classes
Assessment methods
Written exam
Written test
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Winter 2013.
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