| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Advanced Analysıs II | MAT 006 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | Advanced Analysis I |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Prof.Dr. MUSTAFA ERÖZ |
| Dersi Verenler | Prof.Dr. METİN BAŞARIR, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Temel Öğretim |
| Dersin Amacı | The aim of this course is to give some concepts which are related to Phd level in Mathematics. |
| Dersin İçeriği | Lp spaces, Convergence types, Convergence in Lp spaces, Convergence in Measure spaces, Derivative and Anti-derivative ( Integral of monotone functions, The functions of bounded vibrations, The derivative of anti-derivative, Absolute continuity) |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Lp and L inifinite spaces knowing | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 2 | Convergence types knowing | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 3 | The relations of derivative and integral knowing | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Preliminaries | |
| 2 | Lp spaces | |
| 3 | Some inequalities | |
| 4 | Riesz-Fischer theorem | |
| 5 | L infinite space | |
| 6 | The concept of convergence | |
| 7 | Convergence in Lp | |
| 8 | The convergence in measure spaces | |
| 9 | Mid Exam | |
| 10 | Differential and integral | |
| 11 | Integral of monotone functions | |
| 12 | The functions of bounded vibrations | |
| 13 | The derivations of anti-derivative | |
| 14 | Absolute continuity |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | 1- R.G.Bartle, The elements of real analysis, John Wiley and Sons, New York, 1964. 2- H.L.Royden, Real Analysis, MacMillan, New York, 1968. 3-P.R.Halmos, Measure Theory, Princeton, Springer, 1974. 4- S.K.Barberian, Measure and Integration, MacMillan, New York, 1965. 5- M.Balcı, Reel Analiz, Balcı Yayınları, , Ankara, 2000. |
| 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 | X | |||||
| 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. | X | |||||
| 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 | 60 |
| 1. Ödev | 20 |
| 1. Kısa Sınav | 10 |
| 2. Ara Sınav | 10 |
| 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 |
| Quiz | 1 | 10 | 10 |
| Assignment | 1 | 4 | 4 |
| Final examination | 1 | 25 | 25 |
| Toplam İş Yükü | 155 | ||
| Toplam İş Yükü / 25 (Saat) | 6,2 | ||
| Dersin AKTS Kredisi | 6 | ||