COURSE UNIT TITLE

: INTERPOLATION AND APPROXIMATION

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6041 INTERPOLATION AND APPROXIMATION ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics
Mathematics

Course Objective

This course aims to investigate interpolation in q-integers, best approximation in L2 , orthogonal polynomials, multivariate interpolation, Bernstein polynomials, B-splines and their generalizations.

Learning Outcomes of the Course Unit

1   to use q-integers for interpolation
2   to use multivariate interpolation
3   to construct several orthogonal polynomials
4   to understand multivariate approximation operators
5   to comprehend generalization in terms of q-analogs

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Properties of q-integers
2 Generating functions Symmetric functions
3 q-differences
4 Divided differences and interpolation at the q-integers
5 Legendre and other orthogonal polynomials
6 Minimax approximation and Remez algorithm
7 Lebesque function
8 Midterm
9 Peano s Theorem
10 Multivariate interpolation on rectangular regions
11 Multivariate interpolation on triangular regions
12 Multivariate Bernstein polynomials
13 Splines at the q-integers
14 Spline approximation operators

Recomended or Required Reading

1. G.M. Phillips, Interpolation and Approximation by polynomials, Springer New York 2002. ISBN: 0-387 00215-4
References
2. M.J.D. Powell, Approximation theory and methods, Cambridge University Press, Cambridge 1981.
3. P.J. Davis, Interpolation and Approximation, Dover 1976
4. E.W. Cheney, Introduction to Approximation Theory, AMS Chelsea Pub. 2ed 2000.
5. 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 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

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)

Prof.Dr.Halil ORUÇ
e-posta:halil.oruc@deu.edu.tr
Tel: 0232 301 85 77

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 4 52
Preparation for midterm exam 1 25 25
Preparation for final exam 1 30 30
Preparing assignments 1 20 20
Preparing presentations 1 25 25
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 197

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155344445444
LO.255334444444
LO.355444444444
LO.455434544444
LO.555444544554

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

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