Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
VECTORIAL ANALYSIS MAT 260 4 2 + 1 3 5
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHMUT AKYİĞİT Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To learn the use of vectors and previously known as scalar and vector simpler to interpret by comparing the similarities and differences with concepts Dersin İçeriği Basic concepts of metric spaces, Continuity, uniform Continuity, isometri, convergence of sequences, Couchy sequences, complete metric spaces, completion of a metric space, Baire theorems, completely bounded sets, uniform homeomorphism.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She realizes definition of tensor 1 - 2 - 3 - 4 - 14 - A - C - 2 - He/She comparies scalar and vector with tensors 1 - 2 - 3 - 4 - 14 - A - C - 3 - He/She distinguishes types of the tensor 1 - 2 - 3 - 4 - 14 - A - C - 4 - He/She makes operations on tensors 1 - 2 - 3 - 4 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 14:Self Study Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Definition of Vector, Scalar Product, Vector Multiplication, Mixed Product
2 Algebra of Vector Functions
3 Spatial Curves and Tangential Vectors
4 Torsion and Frenet Serret Formulae, Velocity and Acceleration with respect to Polar Coordinates
5 Scalar and Vector Fields, Algebra of Vector Fields
6 Integral Operations on the Scalar and Vector Fields
7 Integrals of Scalar and Vector Fields on the Surface
8 Definition of Tensor and Operations on it
9 Covariant and Contravariant Tensors
10 Mixed Tensors, Polivector and Afinor
11 Contraction Functions
12 Tensor Product of two Tensor Spaces
13 Symmetric Tensors
14 Anti-Symmetric Tensors

#### Kaynaklar

Ders Notu 1.)M.Kemal Sağel, Vektörel Analiz ve Tensör Analize Giriş Cilt I-II-III, A.Ü.F.F. Döner Sermaye İşletmesi Yayınları, 2006.
2) H.Hilmi Hacısalihoğlu, Tensör Geometri, Ankara, 2003
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
Odev 1 10
KisaSinav 2 10
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 8 8
Quiz 2 8 16
Assignment 1 4 4
Final examination 1 10 10
Toplam İş Yükü 134
Toplam İş Yükü /25(s) 5.36
Dersin AKTS Kredisi 5.36
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