Universität Wien

040796 VO Advanced Analysis (2024W)

6.00 ECTS (3.00 SWS), SPL 4 - Wirtschaftswissenschaften
Moodle
Fr 13.12. 15:00-18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 04.10. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 11.10. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 18.10. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 25.10. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 08.11. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 15.11. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 22.11. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 29.11. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 06.12. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 10.01. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 17.01. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 24.01. 15:00 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

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 Immanuel Bomze.

Association in the course directory

Last modified: Fr 11.10.2024 13:05