UIINP62 Selected Topics in Mathematical Analysis I

Faculty of Philosophy and Science in Opava
Winter 2023
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petr Vojčák, Ph.D. (lecturer)
RNDr. Jiřina Jahnová, Ph.D. (seminar tutor)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
RNDr. Šárka Vavrečková, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Karel Hasík, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Supplier department: Mathematical Institute in Opava
Timetable
Mon 8:05–9:40 R1
  • Timetable of Seminar Groups:
UIINP62/A: Wed 8:05–9:40 R2, J. Jahnová
Prerequisites
Mathematical Analysis II
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 course is intended to familiarize students with the basics of differential calculus of functions of several variables, taking into account the fact that the student composition requires focusing the subject matter as much as possible towards applications.
Learning outcomes
Students will be able to:
- define terms discussed in the course;
- determine partial derivative, free and bound extremum of simple functions of more variables;
- apply the acquired knowledge to practical examples;
Syllabus
  • 1. The concept of the function of more variables
  • 2. Limit and continuity of functions of two or more variables
  • 3. Partial derivatives
  • 4. Total differential
  • 5. Taylor formula
  • 6. Partial derivative of composite functions
  • 7. Derivative in given direction
  • 8. Implicit functions and their derivatives
  • 9. Free extremum of functions of more variables
  • 10. Constrained extremum of functions of more variables
Literature
    required literature
  • P. Kreml, J. Vlček. Matematika II. VŠB TU-Ostrava. ISBN 978-80-248-1316-5. info
  • KUBEN, J., Š. MAYEROVÁ, P. RAŠKOVÁ, P. ŠARMANOVÁ. Diferenciální počet funkcí více proměnných. VŠB-TU, Ostrava a ZCU, Plzeň.
  • Z. Došlá, O. Došlý. Diferenciální počet funkcí více proměnných. Masarykova univerzita v Brně, Brno, 1994. ISBN 80-210-2052-0. info
    recommended literature
  • M. Jůza. Vybrané partie z matematické analýzy. MÚ SU, Opava, 1997. info
  • Škrášek J., Tichý Z. Základy aplikované matematiky II. SNTL, Praha, 1986. info
  • J. Stewart. Calculus. California, 1983. info
  • V. Jarník. Diferenciální počet I. ČSAV, Praha, 1963. info
  • V. Jarník. Diferenciální počet II. ČSAV, Praha, 1963. info
Teaching methods
Seminars, discussion
Assessment methods
Credit:
Obtaining the credit is conditioned by active participation in seminars (min. 75%), completion of partial tests to the sum of 60%.
Examination:
written and oral.
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2024.
  • Enrolment Statistics (Winter 2023, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2023/UIINP62