OPF:INMBAKVA Quantitative Methods - Course Information

INMBAKVA Quantitative Methods

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

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)

Guaranteed by

prof. RNDr. Jaroslav Ramík, CSc.
Department of Informatics and Mathematics – School of Business Administration in Karvina
Contact Person: Mgr. Radmila Krkošková, Ph.D.

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

• Banking (programme OPF, B_HOSPOL)
• Business Economics in Trade and Services (programme OPF, B_EKOMAN)

Course objectives

The course Quantitative Methods 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 Statistics.

Syllabus

• 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

recommended literature
• PRICHET, G. D., SABER, J.C. Mathematics with applications in management and economics. IRWIN, Burr Ridge, Boston, Sydney, 2004. ISBN 0-256-09237-0. info
• ČERNÝ,I., ROKYTA, M. Differential and integral calculus of one real variable. Praha : Karolinum, 1998. ISBN 80-7184-661-9. 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.

Teacher's information

running test, 70% attendance at the seminars, exam test

Activity	Difficulty [h]
Ostatní studijní zátěž	78
Přednáška	26
Seminář	26
Zkouška	40
Summary	170

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