Universität Wien
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040796 VO Advanced Analysis (2022W)

6.00 ECTS (3.00 SWS), SPL 4 - Wirtschaftswissenschaften
REMOTE
Moodle

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 07.10. 15:00 - 18:15 Digital
  • Friday 14.10. 15:00 - 18:15 Digital
  • Friday 21.10. 15:00 - 18:15 Digital
  • Friday 28.10. 15:00 - 18:15 Digital
  • Friday 04.11. 15:00 - 18:15 Digital
  • Friday 11.11. 15:00 - 18:15 Digital
  • Friday 18.11. 15:00 - 18:15 Digital
  • Friday 25.11. 15:00 - 18:15 Digital
  • Friday 02.12. 15:00 - 18:15 Digital
  • Friday 09.12. 15:00 - 18:15 Digital
  • Friday 16.12. 15:00 - 18:15 Digital
  • Friday 13.01. 15:00 - 18:15 Digital
  • Friday 20.01. 15:00 - 18:15 Digital
  • Friday 27.01. 15:00 - 18:15 Digital
  • Monday 30.01. 11:30 - 13:00 Hörsaal 5 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

Contents:
0. Basics of point set topology
- open, closed and compact subsets of metric spaces
- Heine-Borel theorem
- continuity and uniform continuity
- liminf and limsup
I. Numerical analysis
- basics (floating-point arithmetic,condition numbers, algorithms, error propagation)
- zeros and fixed-points of functions (contraction mappings, fixed-point iterations, Banach fixed-point theorem,
order of convergence, Newton's method, secant method, regula falsi)
- solving linear equations numerically (Jacobi, Gauß-Seidel)
- Cholesky decomposition
- Gershgorin circle theorem
- interpolation
--- polynomials: Lagrange, Neville, Newton, error estimate
--- rational functions
--- Hermite interpolation
--- spline interpolation
- approximation
--- Bernstein polynomials
--- Chebyshev polynomials
- numerical integration (Newton-Cotes formulas, error estimate)
II. Integration by substitution (multiple variables) with applications to statistics, like derivation
of densities of Chi^2-, t-, F-distribution)

Assessment and permitted materials

written exam, 90 min

Minimum requirements and assessment criteria

Let X be the number of points (the maximum is 24) you achieve at the written exam. Then your grade is computed as follows:

X≤ 12: Nicht genügend
12< X≤ 15: Genügend
15< X≤ 18: Befriedigend
18< X≤ 21: Gut
21< X: Sehr gut

Examination topics

See contents above.

Reading list

Skriptum "Materialien zur Höheren Mathematik für Studierende der Statistik" von Immmanuel Bomze.

Association in the course directory

Last modified: Tu 05.09.2023 13:27