Ders Bilgileri

#### Ders Tanımı

Ders 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
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. MEHMET ALİ GÜNGÖR Dersi Verenler Dersin Yardımcıları Dersin Kategorisi 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.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She knows the fundamental consepts of analysis and algebra of tensor. 1 - 2 - 3 - 8 - 15 - A - C - 2 - He/She defines the fundamental calculations related to the parallelism on n- 1 - 2 - 3 - 8 - 15 - A - C - 3 - He/She computes the metric, curvatures and connections in the sense of Riemannian 1 - 2 - 3 - 8 - 15 - A - C - 4 - He/She computes the Laplacian, sectional curvatures, Ricci curvatures and scalar curvatures. 1 - 2 - 3 - 8 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 8:Group Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
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.

#### 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. 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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
Odev 1 30
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 15 15
Assignment 1 10 10
Final examination 1 25 25
Toplam İş Yükü 146
Toplam İş Yükü /25(s) 5.84
Dersin AKTS Kredisi 5.84
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