Ders Bilgileri
Yazdır
Ders Tanımı
Ders  Kodu  Yarıyıl  T+U Saat  Kredi  AKTS 

LINEAR ALGEBRA  MAT 114  2  2 + 0  2  4 
Ön Koşul Dersleri  

Önerilen Seçmeli Dersler 
Dersin Dili  Türkçe 
Dersin Seviyesi  Lisans 
Dersin Türü  ZORUNLU 
Dersin Koordinatörü 
Doç.Dr. MURAT SARDUVAN 
Dersi Verenler 
Doç.Dr. YALÇIN YILMAZ Prof.Dr. ÖMER FARUK GÖZÜKIZIL Prof.Dr. ŞEVKET GÜR Arş.Gör. TUĞBA PETİK Öğr.Gör.Dr. EMİNE ÇELİK 
Dersin Yardımcıları  
Dersin Kategorisi  
Dersin Amacı 
Students learn the concepts and apply the methods related with; the solution of systems of linear equations, matrices and matrix operations, determinant, rank, eigenvalues and eigenvectors, conversions in twodimensional space, vector spaces and the theory of linear operators.

Dersin İçeriği 
Solution of linear equations systems (Cramer, inverse matrix, reducing the normal form), matrix and determinant operations, eigenvalues and eigenvectors of the matrix, linear transformations in linear spaces.

Dersin Öğrenme Çıktıları  Öğretim Yöntemleri  Ölçme Yöntemleri 
1  Make conversions through the transformation matrices in 2 and 3dimensional spaces.  1  2  3  6  15   A  
Öğretim Yöntemleri:  1:Lecture 2:QuestionAnswer 3:Discussion 6:Motivations to Show 15:Problem Solving 
Ölçme Yöntemleri:  A:Testing 
Ders Akışı
Hafta  Konular  ÖnHazırlık 

1  Introduction. Overview of the subjects, history and methods of the linear algebra.  
2  Systems involving two and three variables. Gauss method. Determinants of 2 and 3dimensional matrices.  
3  Geometric interpretation of the two and threedimensional system. Definition of the ndimensional determinant.  
4  Characteristics of the ndimensional determinant and its calculation methods.  
5  Special determinants. Triangular, Wandermond and Tridiagonal shape determinants.  
6  Laplace and AntiLaplace theorems. Cramer’s theorem for the square system.  
7  Matrices, operations on matrices. Inverse matrix and its finding methods.  
8  Transformations of the square system to matrix form and solution with inverse matrix method.  
9  Rank of matrix. Extended matrix. Theorem of KroneckerKapelli for general systems.  
10  ndimensional real and complex vector spaces. Linear independence bases and coordinates.  
11  Linear transformation and its matrix. Transformation of matrix by base change.  
12  Eigenvalues and eigenvectors. HamiltonCayley and Silvester theorems.  
13  Jordan normal form of matrix. Similarity. Similarity condition of diagonal matrix.  
14  Metric, Normed and Euclidean space. Length, angle, quadratic forms, numerical image. 
Kaynaklar 


Ders Notu  1. Aşkın Demirkol, Lecture Notes.  
Ders Kaynakları 
1. David C.Lay, Linear Algebra and Its Applications, Pearson, 2003. 2. Aşkın Demirkol, Mühendisler İçin Lineer Sistemler Lineer Cebir  I , Sakarya Kitabevi, 2011. 3. Aşkın Demirkol, Mühendisler İçin Lineer Sistemler Lineer Cebir  II , Sakarya Kitabevi, 2011. 4. Ömer Faruk Gözükızıl, Lineer Cebir, Değişim Yayınları, İstanbul, 2000. 5.S. Lipschutz, H. Hacısalihoğlu, Ö. Akın, Lineer Cebir Teori ve Problemleri, Nobel Yayın Dağıtım, Ankara, 1991. 
Döküman Paylaşımı 

Dersin Program Çıktılarına Katkısı
No  Program Öğrenme Çıktıları  KatkıDüzeyi  

1  2  3  4  5  
1  Engineering graduates with sufficient knowledge background on science and engineering subjects of their related area, and who are skillful in implementing theoretical and practical knowledge for modelling and solving engineering problems.  X  
2  Engineering graduates with skills in identifying, describing, formulating and solving complex engineering problems, and thus,deciding and implementing appropriate methods for analyzing and modelling.  X  
3  Engineering graduates with skills in designing a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; for this purpose, skills in implementing modern design methods.  X  
4  Engineering graduates with skills in developing, selecting and implementing modern techniques and tools required for engineering applications as well as with skills in using information technologies effectively.  
5  Engineering graduates with skills in designing and conducting experiments, collecting data, analyzing and interpreting the results in order to evaluate engineering problems.  
6  Engineering graduates who are able to work within a one discipline or multidiscipline team,as well as who are able to work individually  
7  Engineering graduates with motivation to lifelong learning and having known significance of continuous education beyond undergraduate studies for science and technology  
8  Engineering graduates with wellstructured responsibilities in profession and ethics  
9  Engineering graduates having knowledge about practices in professional life such as project management, risk management and change management, and who are aware of innovation and sustainable development.  
10  Engineering graduates having knowledge about universal and social effects of engineering applications on health, environment and safety, as well as having awareness for juridical consequences of engineering solutions.  
11  Engineering graduates who are able to effectively communicate orally and officially in Turkish Language as well as who knows at least one foreign language 
Değerlendirme Sistemi
YARIYIL İÇİ ÇALIŞMALARI  SIRA  KATKI YÜZDESİ 

AraSinav  1  70 
KisaSinav  1  10 
KisaSinav  2  10 
Odev  1  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  2  32 
Hours for offtheclassroom study (Prestudy, practice)  16  2  32 
Midterms  1  8  8 
Quiz  2  8  16 
Final examination  1  10  10 
Toplam İş Yükü  98  
Toplam İş Yükü /25(s)  3.92  
Dersin AKTS Kredisi  3.92 