Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
LINEAR ALGEBRA MAT 114 2 2 + 0 2 4
 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 two-dimensional 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 3-dimensional spaces. 1 - 2 - 3 - 6 - 15 - A -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 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 3-dimensional matrices.
3 Geometric interpretation of the two- and three-dimensional system. Definition of the n-dimensional determinant.
4 Characteristics of the n-dimensional determinant and its calculation methods.
5 Special determinants. Triangular, Wandermond and Tridiagonal shape determinants.
6 Laplace and Anti-Laplace 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 Kronecker-Kapelli for general systems.
10 n-dimensional 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. Hamilton-Cayley 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.

#### 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 multi-discipline team,as well as who are able to work individually
7 -Engineering graduates who are able to effectively communicate orally and officially in Turkish Language as well as who knows at least one foreign language
8 -Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology
9 -Engineering graduates with well-structured responsibilities in profession and ethics
10 -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.
11 -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.

#### 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 off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 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
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