| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Tensor Geometry I | MAT 621 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Students are assumed to be familiar with Differential Geometry I and Differential Geometry II |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. MEHMET ALİ GÜNGÖR |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | The tensor geometry I course aims to give the fundamental knowledge for the studies of graduate students who study at geometry branch. |
| Dersin İçeriği | Tensors, covariant and contravariant tensors, mixed tensors, tensor product of two tensors, symmetric and anti-symmetric tensors, exterior product and exterior algebra, parallel vector fields, Levi-Civita parallelism, tensors on the Riemannnian manifolds, sectional curvature, Ricci curvature, scalar curvature, Ricci identity. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She knows the fundamental consepts of analysis and algebra of tensor. | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 2 | He/She defines the fundamental calculations related to the parallelism on n- | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 3 | He/She computes the metric, curvatures and connections in the sense of Riemannian | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 4 | He/She computes the Laplacian, sectional curvatures, Ricci curvatures and scalar curvatures. | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Tensors | |
| 2 | Covariant and contravariant tensors | |
| 3 | Mixed tensors | |
| 4 | Tensor product of two tensors | |
| 5 | Symmetric and anti-symmetric tensors | |
| 6 | Exterior product and exterior algebra | |
| 7 | Parallel vector fields | |
| 8 | Levi-Civita parallelism | |
| 9 | Mid term exam | |
| 10 | Tensors on the Riemannnian manifolds | |
| 11 | Sectional curvature | |
| 12 | Ricci curvature | |
| 13 | Scalar curvature | |
| 14 | Ricci identity |
| Kaynaklar | |
|---|---|
| Ders Notu | 1. Hacısalihoğlu H. H. ve Ekmekçi N., Tensör Geometri, Ankara Üni., Fen Fakültesi,2003. |
| Ders Kaynakları | 1. Kobayashi, S., and Nomizu, K., Foundations of differential geometry, Number 15, Volume II, New York, 1969. 2. ONeill B., Elementary Differential Geometry, Academic Press, New York, 1997. 3. D. C. Kay, , Schaums outline of theory and problems, McGraw-Hill, 1988. 4. C. T. J. Dodson, T. Poston, Tensor geometry, Graduate Texts in Mathematics, 130. Springer-Verlag, Berlin, 1991. |
| 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 | 70 |
| 1. Ödev | 30 |
| 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 | 1 | 10 | 10 |
| Final examination | 1 | 25 | 25 |
| Toplam İş Yükü | 146 | ||
| Toplam İş Yükü / 25 (Saat) | 5,84 | ||
| Dersin AKTS Kredisi | 6 | ||