BPM_MAT0 Mathematics 0

Faculty of Economics and Administration
Autumn 2019

The course is not taught in Autumn 2019

Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Luboš Bauer, CSc. (lecturer)
RNDr. Luboš Bauer, CSc. (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)
remo (seminar tutor)
Mgr. et Mgr. Milan Svoboda (seminar tutor)
Guaranteed by
RNDr. Luboš Bauer, CSc.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 600 student(s).
Current registration and enrolment status: enrolled: 0/600, only registered: 0/600, only registered with preference (fields directly associated with the programme): 0/600
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to introduce the principal mathematical means necessary to solve economic problems and to prepare essential foundations for the subjects Statistics and Economic-Mathematical Methods. In addition to this, the subject contributes to the development of logical thinking. The graduates of the course should understand and be able to use the principles of mathematical logic and the theory of sets, basic terms and methods of linear algebra (especially matrices, determinants and solving systems of equations of the first degree), and differential calculus of functions with a single variable, with emphasis on the characteristics of functions.
Syllabus
  • Lectures: 1. The basics of mathematical logic.
  • 2. The theory of sets.
  • 3. Vector spaces. Linear dependence and independence. Basis and dimension.
  • 4. Matrix, matrix rank, matrix operations.
  • 5. Determinants. Matrix inverse.
  • 6. Systems of linear equations. Cramer's rule, elimination methods, Frobenius theorem. Description of solution sets for homogeneous and inhomogeneous systems.
  • 7. Computation of matrix inverse. Eigenvectors and eigenvalues.
  • 8. Functions with a single variable. Even and odd, periodic and monotonous functions. Inverse function.
  • 9. Elementary functions. Polynomials, rational functions, partial fraction decomposition.
  • 10. Limit of function, continuous function. Limit theorems.
  • 11. Derivatives. Basic theorems of differential calculus.
  • 12. Local and global extremes. Inflex points. Characteristics of function.
  • 13. Taylor's theorem and differential of a function - approximation of a function.
  • Exercises: 1. Revision (mathematical expressions, functions, equations and inequations)
  • 2. The basics of mathematical logic and the theory of sets.
  • 3. Preliminary test. Vector spaces. Linear dependence and independence. Basis and dimension.
  • 4. Matrix, matrix rank, matrix operations.
  • 5. Determinants.
  • 6. Systems of linear equations: Cramer's rule, elimination methods.
  • 7. Inverse matrix. Eigenvectors and eigenvalues.
  • 8. Functions with a single variable. Even and odd, periodic and monotonous functions. Inverse function.
  • 9. Test. Polynomials, rational functions, partial fraction decomposition.
  • 10. Limit of function, continuous function.
  • 11. Derivatives.
  • 12. Local and global extremes. Inflex points. Characteristics of function.
  • 13. Final test
Literature
  • KLŮFA, Jindřich and Jan COUFAL. Matematika pro ekonomy. 1. vyd. Praha: Ekopress, 1997, 405 s. ISBN 8086119009. info
  • KAŇKA, Miloš and Jiří HENZLER. Matematika pro ekonomy. 1. vyd. Praha: Ekopress, 1997, 373 s. ISBN 8086119017. info
Assessment methods
The course consists of lectures and seminars. Credit requirements are: active participation in seminars (at least 10 seminars a semester), passing two tests in the course of semester and the final test.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Information on course enrolment limitations: max. 30 cizích studentů; cvičení pouze pro studenty ESF
  • Permalink: https://is.muni.cz/course/econ/autumn2019/BPM_MAT0