COURSE UNIT TITLE

: APPROXIMATION THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5018 APPROXIMATION THEORY ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR GÜLTER BUDAKÇI

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

This course aims to present key ideas in general theory in the methods of approximation of real functions, interpolation and approximation with respect to both uniform norm and 2-norm.

Learning Outcomes of the Course Unit

1   to prove Weierstrass approximation theorem
2   to understand key ideas of best approximation in normed spaces
3   to discuss the interpolation problem in the sense of minimising the error
4   to use Bohman-Korovkin s Theorem
5   to solve L2 approximation problems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Modes of convergence and Taylor s Theroem
2 The best approximation
3 Bernstein polynomials Wierstarss approximation Theorem
4 Modulus of continuity
5 Linear positive operators, Bohman-Korovkin theorem
6 Divided differences and interpolation
7 Chebyshev alternation theorem, Haar condition
8 Problems and discussion
9 Fejer sums
10 Uniform convergence of trigonometric polynomials
11 Orthogonal polynomials
12 Convergence of orthogonal expansions
13 The Jackson theorems
14 Müntz theorem

Recomended or Required Reading

1. M.J.D. Powell, Approximation theory and methods, Cambridge University Press, Cambridge 1981.
2. E.W. Cheney, Introduction to Approximation Theory, AMS Chelsea Pub. 2ed 2000.
References:
1. G.M. Phillips, Interpolation and Approximation by polynomials, Springer New York 2002. ISBN: 0-387 00215-4
2. R.A. DeVore and G.G. Lorentz, Constructive Approximation , Springer-Verlag Berlin Heidelberg 1993.
Materials: None

Planned Learning Activities and Teaching Methods

The course consists of lectures, homework and exams

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.30 +ASG * 0.20 +FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.20 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

Midterm, Assignment, Final Exam

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the graduate policy at http://web.fbe.deu.edu.tr

Contact Details for the Lecturer(s)

gulter.budakci@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 3 42
Preparation for final exam 1 35 35
Preparation for midterm exam 1 30 30
Preparing assignments 1 25 25
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 180

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155424435444
LO.255424435444
LO.355544544444
LO.455524544444
LO.555444554554

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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