Module MA4410-KP05
Approximation Theory (ApproxKP05)
Duration
1 Semester
Turnus of offer
irregularly
Credit points
5
Course of studies, specific fields and terms:
- Master CLS 2023, optional subject, mathematics
- Bachelor CLS 2023, optional subject, mathematics
- Minor in Teaching Mathematics, Master of Education 2023, optional subject, mathematics
- Minor in Teaching Mathematics, Master of Education 2017, optional subject, mathematics
- Bachelor CLS 2016, optional subject, mathematics
- Master CLS 2016, optional subject, mathematics
Classes and lectures:
- Approximation theory (exercise, 1 SWS)
- Approximation theory (lecture, 2 SWS)
Workload:
- 30 hours work on project
- 10 hours exam preparation
- 45 hours in-classroom work
- 65 hours private studies and exercises
Contents of teaching:
- Fundamentals of functional analysis
- Best approximation
- Linear methods, trigonometric kernels
- Theorems of Jackson and Bernstein
- Moduli of continuity
- Singular integrals
- Theorem of Banach-Steinhaus
- Interpolation methods
- Stability inequalities
Qualification-goals/Competencies:
- practicing mathematical techniques (developing mathematical intuition and its formal justification, training the ability to abstract, reasoning)
- application of basic concepts from functional analysis and the theory of function spaces
- Learning the basic principles of approximation theory
- Understanding the relationship between order of convergence and smoothness
- Knowledge of the basic approximation methods
- application of computer algebra for visualization and better understanding of the methods used
Grading through:
- exercises, project, oral or written exam
Responsible for this module:
Literature:
- P. L. Butzer, R. J. Nessel : Fourier Analysis and Approximation Birkhäuser Verlag 1971
- R. A. Devore, G. G. Lorentz : Constructive Approximation Springer 1993
Language:
- English, except in case of only German-speaking participants
Notes:
Admission requirements for taking the module:- None (The competencies of the modules listed under 'Requires' are needed for this module, but are not a formal prerequisite)
Admission requirements for participation in module examination(s):
- Successful completion of homework assignments as specified at the beginning of the semester
Module exam(s):
- MA4410-L1: Approximation Theory, oral exam, 30 min, 100 % of module grade
Last Updated:
22.02.2022