| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Approxımatıon Theory | MAT 611 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. MUSTAFA ERÖZ |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| 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. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 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, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 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 |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 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 | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 50 |
| 1. Ödev | 50 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (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 (Saat) | 5,52 | ||
| Dersin AKTS Kredisi | 6 | ||