MU:MU20011 Selected Topics in MA I - Course Information

MU20011 Selected Topics in Mathematical Analysis I

Extent and Intensity

2/2/0. 7 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Petr Vojčák, Ph.D. (lecturer)

Guaranteed by

doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava

Timetable

Mon 11:25–13:00 R1

• Timetable of Seminar Groups:

MU20011/01: Thu 8:55–10:30 R2, P. Vojčák

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

• Mathematical Methods in Economics (programme MU, Bc-M)
• Mathematical Methods in Risk Management (programme MU, Bc-M)

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.

• Enrolment Statistics (Winter 2022, recent)
  
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