MMEPKVAA Quantitative Methods A

Obchodně podnikatelská fakulta v Karviné
léto 2010
Rozsah
2/2/0. 5 kr. Ukončení: zk.
Vyučující
Mgr. Radmila Krkošková, Ph.D. (přednášející)
prof. RNDr. Jaroslav Ramík, CSc. (přednášející)
Mgr. Šárka Čemerková, Ph.D. (cvičící)
doc. Marie Godulová, CSc. (cvičící)
Mgr. Radmila Krkošková, Ph.D. (cvičící)
Ing. Elena Mielcová, Ph.D. (cvičící)
Ing. Radomír Perzina, Ph.D. (cvičící)
prof. RNDr. Jaroslav Ramík, CSc. (cvičící)
Ing. Filip Tošenovský, Ph.D. (cvičící)
Garance
Mgr. Radmila Krkošková, Ph.D.
Katedra informatiky a matematiky – Obchodně podnikatelská fakulta v Karviné
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
Cíle předmětu
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.
Osnova
  • 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.
Literatura
    povinná literatura
  • SIMON, C.P., BLUME,L. Mathematics for Economists. New York: W.W.Norton and Company, 1994. ISBN 0-393-95733-0. info
    doporučená literatura
  • 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
Vyučovací jazyk
Angličtina
Informace učitele
test, 70% attendance at the seminars, exam test
Další komentáře
Předmět je dovoleno ukončit i mimo zkouškové období.
Předmět je zařazen také v obdobích zima 2007, léto 2008, zima 2008, léto 2009, zima 2009, zima 2010, léto 2011, zima 2011, léto 2012, zima 2012, léto 2013, zima 2013, léto 2014.