| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Matematik Analizde Seçme Konular | MAT 612 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. METİN BAŞARIR |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | The aim of this course is to give some concepts which are related to graduate level in Mathematics. |
| Dersin İçeriği | The elements of functions theory (Number fields, Topological prelinimanires, convergent sequnces and series, continuous functions) Differential Calculus (Differentiable and holomorf functions) Analiticity and Conformity, Convergence types in functions theory (pointwise convergence, regular convergence, local regular convergence and convergence into compact) Power series (analiticity) Cauchy theory, Laurent and Fourier series, Rezidü Calculus |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 2 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 3 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 4 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 5 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 6 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | The elements of function theory | |
| 2 | Convergent sequences and series | |
| 3 | Differential calculus | |
| 4 | Analiticity and conformity | |
| 5 | Convergence types in funcitons theory | |
| 6 | Power series | |
| 7 | Cauchy theory | |
| 8 | Cauchy integral theory | |
| 9 | Laurent and taylor series | |
| 10 | Mid exam | |
| 11 | Rezidues Calculus | |
| 12 | Cauchy-Riemann-Weierstrass in functions theory | |
| 13 | Open mapping theorem and maksimum principle | |
| 14 | General Review |
| Kaynaklar | |
|---|---|
| Ders Notu | -Theory of Compleks Functions, R. Remmert, Springer-Verlag, London, New York, 1991. |
| Ders Kaynakları | |
| 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. | 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 | 10 |
| 2. Ödev | 10 |
| 1. Kısa Sınav | 20 |
| 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 | 15 | 15 |
| Assignment | 2 | 15 | 30 |
| Final examination | 1 | 18 | 18 |
| Toplam İş Yükü | 159 | ||
| Toplam İş Yükü / 25 (Saat) | 6,36 | ||
| Dersin AKTS Kredisi | 6 | ||