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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
APPROXIMATION THEORY MAT 611 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Doktora
Dersin Türü SECMELI
Dersin Koordinatörü Doç.Dr. MUSTAFA ERÖZ
Dersi Verenler
Dersin Yardımcıları
Dersin Kategorisi
Dersin Amacı

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

Dersin İçeriği

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

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - Students will be familiar with the notion of approximation. 1 - 2 - 4 - A - C -
2 - Students will have explained polynomial approximation and interpolation. 1 - 2 - 4 - A - C -
3 - Students will have defined Best-approximation. 1 - 2 - 4 - A - C -
4 - Students will have explained least-squares approximation. 1 - 2 - 4 - A - C -
5 - Students will have explained trigonometric approximation. 1 - 2 - 4 - A - C -
6 - Students will have applied the concepts learned to a system of equations. 1 - 2 - 4 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
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.

Kaynaklar

Ders Notu

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

Ders Kaynakları

[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


Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
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

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 50
Odev 1 50
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
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
Toplam İş Yükü 138
Toplam İş Yükü /25(s) 5.52
Dersin AKTS Kredisi 5.52
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