MU20011 Selected Topics in Mathematical Analysis I

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
2/2/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Karel Hasík, Ph.D. (lecturer)
Mgr. Jan Tesarčík, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava
Timetable
Wed 8:05–9:40 20
  • Timetable of Seminar Groups:
MU20011/01: Thu 8:05–9:40 203, J. Tesarčík
Prerequisites (in Czech)
MU20002 Mathematical Analysis II && TYP_STUDIA ( B )
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 main objective of this course is to provide an introduction to the differential calculus of several variables. The curriculum aims at applications.
Syllabus
  • 1. Functions of several variables
    - metric spaces, Euclidean metric on R^n, natural topology on R^n
    - graph of function, contour diagram
    - limit and continuity
    2. The first derivative
    - partial derivatives, directional derivatives
    - mean value theorem
    - total differential
    - derivatives of composite functions
    3. Imlicit function
    - functions defined implicitly by equations
    - derivatives of implicit functions
    4. Higher derivatives
    - higher partial derivatives
    - theorem on equality of mixed partials
    - Taylor formula
    - maxima and minima of function, constrained maxima and minima
    - method of Lagrange multipliers
Literature
    required literature
  • P. Kreml, J. Vlček. Matematika II. VŠB TU-Ostrava. ISBN 978-80-248-1316-5. info
  • S. Lang. Calculus of Several Variables. Springer, 1996. info
  • Z. Došlá, O. Došlý. Diferenciální počet funkcí více proměnných. Masarykova univerzita v Brně, Brno, 1994. ISBN 80-210-2052-0. info
  • J. Škrášek, Z. Tichý. Základy aplikované matematiky II. SNTL Praha, 1986. info
    not specified
  • M. Jůza. Vybrané partie z matematické analýzy. MÚ SU, Opava, 1997. 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
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Requirements for pre-exam credits are active participation in tutorials and reaching at least 60% overall in partial tests. The examination comprises two part - written and oral.
The oral part follows the successful written part and verifies professional knowledge and skills resulting from the course.

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