B_MaA_1 Mathematics A 1

University of Finance and Administration
Winter 2016
Extent and Intensity
2/2. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Eva Ulrychová, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Eva Ulrychová, Ph.D.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Ing. Barbora Ptáčková
Timetable of Seminar Groups
B_MaA_1/cAPH: Tue 10:30–11:14 E227, Tue 11:15–12:00 E227, E. Ulrychová
B_MaA_1/pAPH: Tue 8:45–9:29 E227, Tue 9:30–10:15 E227, E. Ulrychová
B_MaA_1/vAPH: Sat 8. 10. 9:45–11:15 E223, 11:30–13:00 E223, Sat 22. 10. 9:45–11:15 E122, 11:30–13:00 E122, Fri 18. 11. 17:30–19:00 E122, 19:15–20:45 E122, E. Ulrychová
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
Students will get familiar with the basic terms of linear algebra and their mutual relationships, with the basic properties of real sequences and real functions of one real variable, with the basics of the differential calculus and with the notions and procedures used in the investigation of the behaviour of functions.

At the end of the course students should be able to:
- find the solution of a system of linear equations using matrices
- calculate the limit of a a sequence and the limit of a function
- calculate the derivative of a function and use it for finding extrema, monotonicity intervals and convexity and concavity intervals.
Syllabus
  • 1. Vector space, linear dependence and independence of vectors.
  • 2. Matrices - elementary row operations. Rank of the matrix.
  • 3. Solution of systems of linear agebraic equations by Gaussian elimination method.
  • 4. Matrix algebra. Application of the inverse matrix to the solution of a linear system.
  • 5. Determinants and solution of a linear system by Cramer's rule.
  • 6. Sequences of real numbers. Computation of the limit of a sequence.
  • 7. Continuity and limits of functions.
  • 8. Derivatives of functions and their properties. Derivatives of basic functions.
  • 9. Derivatives of composite functions. Derivatives of higher orders. L'Hospital's rule.
  • 10. Determination of monotonicity intervals and extrema of functions (local extrema and global extrema on closed interval). Determination of convexity and concavity intervals.
  • 11. Investigation of the course of a function and creating its graph.
  • 12. Taylor's polynomial and its applications.
Literature
    required literature
  • BUDINSKÝ, Petr a Ivan HAVLÍČEK. Matematika pro vysoké školy ekonomického a technického zaměření. Praha: VŠFS, 2005 (dotisk 2013). 131 s. ISBN 80-86754-45-6.
  • BUDINSKÝ, Petr a Ivan HAVLÍČEK. Sbírka příkladů z matematiky pro vysoké školy ekonomického a technického zaměření. Praha: VŠFS, 2005 (dotisk 2016). 121 s. ISBN 80-86754-52-9.
    recommended literature
  • BATÍKOVÁ, B. a kol.: Učebnice matematiky pro ekonomické fakulty. Oeconomica, Praha, 2009.
  • LÁNSKÝ, Jan and Eva ULRYCHOVÁ. Maticové algoritmy. Praha: Publishing House CURRICULUM, 2015, 138 pp. ISBN 978-80-904948-8-6. info
  • Lánský J., Ulrychová E.: Maticové algoritmy - online catalogue NKP: www.csrggroup.org
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 is completed with a credit and an exam. Passing a written test (min. 60%) is required to award the credit. Prerequisite for taking the exam is the credit. The exam consists of a written part and a verbal part; prerequisite for taking the verbal part of the exam is to pass the written part (min. 50%).
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
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 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2017, Winter 2018.
  • Enrolment Statistics (Winter 2016, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/winter2016/B_MaA_1