B_MaA_1 Mathematics A 1

University of Finance and Administration
Winter 2012
Extent and Intensity
2/2. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Slavomír Burýšek, CSc. (seminar tutor)
RNDr. Eva Ulrychová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Slavomír Burýšek, CSc.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Dagmar Medová, DiS.
Timetable of Seminar Groups
B_MaA_1/cAPH: Wed 12:15–12:59 E305, Wed 13:00–13:45 E305, S. Burýšek
B_MaA_1/pAPH: Wed 10:30–11:14 E305, Wed 11:15–12:00 E305, S. Burýšek
Prerequisites
Secondary mathematics
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
The goals of the course are the following: 1. To gain knowledge about vectors and matrices and their applications to the solution of linear algebraic equations by the Gaussian method, by the inverse matrix and by Cramer`s rule. 2. To gain elemental knowledge from the theory of real functions of one real variable, especially the determination of the domain of continuity, computation of limits and derivatives of elementary functions, using this knowledge to create the graph of a given function. At the end of the course students should be able to: Solve systems of linear algebraic equations by the Gaussian elimination method, by inverse matrix even by Cramer’s rule. Further they should know properties and graphs of basic elementary functions, they should be able to determine the domain of continuity of functions, their first and second derivatives, to compute limits, to determine intervals of monotonicity, intervals of convexity and concavity, to find extreme of functions and to create graphs of given functions. All these knowledge they should be able to apply in others subject of their studies.
Syllabus
  • 1. Logical rules, set`s operations.
  • 2. Vector space, linear dependence and independence of vectors. Scalar product.
  • 3. Matrix and its rank. Basic operations with matrices.
  • 4. Solution of systems of linear agebraic equations by Gaussian elimination method.
  • 5. Matrix algebra. Application of the inverse matrix to the solution of a linear system.
  • 6. Determinants and solution of a linear system by Cramer`s rule.
  • 7. Sequences of real numbers. Computation of the limit of a sequence.
  • 8. Continuity and limits of functions.
  • 9. Derivatives of functions and their properties. Derivatives of higher orders. L`Hospital`s rule.
  • 10. Determination of monotonicity intervals, convexity and concavity intervals and extremes of functions by the first ad second derivatives.
  • 11. Investigation of the course of a function and creating its graph.
  • 12. Taylor`s polynomial and its applications.
Literature
    required literature
  • BUDINSKÝ, P., HAVLÍČEK, I.: Matematika pro vysoké školy ekonomického a technického zaměření. EUPRESS, Praha 2005, ISBN 80-886754-45-6.
  • BUDINSKÝ, P., HAVLÍČEK, I.: Sbírka příkladů z matematiky pro vysoké školy ekonomického a technického zaměření. EUPRESS, Praha 2005, ISBN 80-86754-52-9.
    recommended literature
  • KLŮFA, J.: Učebnice matematiky pro studenty VŠE. Ekopress, Praha 2011, ISBN 978-80-86929-74-3.
Teaching methods
- lectures and seminars in full-time study, - tutorials in part-time study, Minimal required participation is 75% on seminars in full-time study and 50% on tutorials in part-time study. Students with lower than required participation have to fulfill additional study duties.
Assessment methods
The course ends with an exam. The exam is based on active participation on lectures and seminars, in creation and presentation of a final seminar study and on specific written test (5 out of 10 points required) and subsequent verbal exam (answer one of the 15 topic questions correctly is required) to pass the exam.“
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
General note: Bb1.
Information on the extent and intensity of the course: 12 hodin KS/semestr.
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 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (Winter 2012, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/winter2012/B_MaA_1