B_MaA_2 Mathematics A 2

University of Finance and Administration
Summer 2016
Extent and Intensity
2/2. 5 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_2/cAPH: Mon 14:00–14:44 E228, Mon 14:45–15:30 E228, E. Ulrychová
B_MaA_2/pAPH: Mon 12:15–12:59 E228, Mon 13:00–13:45 E228, E. Ulrychová
Prerequisites
B_MaA_1 Mathematics A 1
he requirement for the completion of this course is completion of the course B_Ma_A_1.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Students will get familiar with basics of the theory of functions of more variables and with terms and methods of finding of their extrema. They gain basic knowledge of the theory of indefinite, definite and improper integral. They will get familiar with basics of the theory of infinite series.

At the end of the course students should be able to:
- find extrema of function of two variables (local extrema, constrained extrema, global extrema on a compact set)
- use methods of integration
- decide about the convergence or divergence of numerical series and to find the domain of convergence of the power series
Syllabus
  • 1. Basic topological notions in Euclidean space: open , closed bounded sets, compact set.
  • 2. Function of more variables, domain of the function of two variables and its graph.
  • 3. Partial derivatives of the first and second order.
  • 4. Local extrema of functions of two variables.
  • 5. Constrained extrema: Jacobi’s method, method of Lagrange’s multipliers.
  • 6. Global extrema of the function on a compact set.
  • 7. Definition and basic properties of indefinite integral, integration by parts.
  • 8. Integration by substitution, integration of rational functions.
  • 9. Definite integral and its applications. Improper integral.
  • 10. Numerical series, convergence criteria.
  • 11. Power series, radius and domain of convergence.
  • 12. Expansion of a function in a power series, Taylor’s series and its applications.
Literature
    required literature
  • BUDINSKÝ, Petr and Ivan HAVLÍČEK. Matematika pro vysoké školy ekonomického a technického zaměření. Praha: VŠFS, 2005, 131 pp. ISBN 80-86754-45-6. info
  • BUDINSKÝ, Petr and Ivan HAVLÍČEK. Sbírka příkladů z matematiky pro vysoké školy ekonomického a technického zaměření. Praha: VŠFS, 2005, 121 pp. ISBN 80-86754-52-9. info
    recommended literature
  • BATÍKOVÁ, B. a kol.: Učebnice matematiky pro ekonomické fakulty. Oeconomica, Praha, 2009.
Teaching methods
Lectures and seminars in full-time study; tutorials in part-time study; compulsory seminar participation is 75% in full-time study, compulsory tutorial participation is 50% 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
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: 10 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, Summer 2013, Summer 2014, Summer 2015, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2016, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/summer2016/B_MaA_2