Course Name Code Semester T+U Hours Credit ECTS
Approximation Theory MAT 611 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. MUSTAFA ERÖZ
Course Lecturers
Course Assistants
Course Category
Course Objective

What are the main problems of approximation theory? What are approximation methods? To discuss improvement of approximation and error analysis.

Course Content

Functional approximation, Hermite interpolation, Spline interpolation, B-spline theory, best-approximation, least-squares approximation.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will be familiar with the notion of approximation. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
2 Students will have explained polynomial approximation and interpolation. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
3 Students will have defined Best-approximation. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
4 Students will have explained least-squares approximation. Drilland Practice, Lecture, Question-Answer, Testing, Homework,
5 Students will have explained trigonometric approximation. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
6 Students will have applied the concepts learned to a system of equations. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 What is functional approximation?
2 Polynomial interpolation, divided differences, Hermite interpolation.
3 Spline interpolation.
4 B-spline theory and applications.
5 Taylor series.
6 Best-approximation
7 Least-squares approximation.
8 Chebyshev theory.
9 Exam
10 Interpolaiton in higher dimensions.
11 Continuous fractions.
12 Trigonometric interpolation, fast Fourier transformation.
13 Adaptive approximations.
14 Approximation in Lp spaces.
Resources
Course Notes <p>[1] De Boor C, A Practical Guide to Splines</p>
Course Resources

[1] De Boor C, A Practical Guide to Splines

[2] Kincaid D.,Cheney, Numerical Analysis,1991

[3] Theory of approximation of functions of a real varible, Timan A.F., Dover Pub., New York, 1994

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 50
1. Ödev 50
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 1 20 20
Final examination 1 2 2
Total Workload 138
Total Workload / 25 (Hours) 5.52
dersAKTSKredisi 6