Ders Adı Kodu Yarıyıl T+U Saat Kredi AKTS
Lınear 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 Prof.Dr. ÖMER FARUK GÖZÜKIZIL
Dersi Verenler Doç.Dr. YAŞAR KAHRAMAN, Doç.Dr. NESLİHAN ÖZSOY, Prof.Dr. MAHMUT AKYİĞİT, Prof.Dr. ÖMER FARUK GÖZÜKIZIL, Prof.Dr. METİN YAMAN, Prof.Dr. YILMAZ UYAROĞLU, Prof.Dr. AŞKIN DEMİRKOL, Prof.Dr. REFİK KESKİN, Prof.Dr. MEHMET ALİ GÜNGÖR, Doç.Dr. GÖKHAN COŞKUN, Dr.Öğr.Üyesi EMRE KİŞİ,
Dersin Yardımcıları
Dersin Kategorisi Alanına Uygun Temel Öğretim
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.
# Ders Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 Make conversions through the transformation matrices in 2 and 3-dimensional spaces. Lecture, Question-Answer, Discussion, Motivations to Show, Problem Solving, Testing,
Hafta Ders Konuları Ön Hazırlık
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.
Sıra Program Çıktıları Katkı Düzeyi
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. X
5 Engineering graduates with skills in designing and conducting experiments, collecting data, analyzing and interpreting the results in order to evaluate engineering problems. X
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
Yarıyıl Çalışmaları Katkı Oranı
1. Kısa Sınav 10
2. Kısa Sınav 10
3. Kısa Sınav 10
1. Ara Sınav 70
Toplam 100
1. Final 50
1. Yıl İçinin Başarıya 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 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 (Saat) 3,92
Dersin AKTS Kredisi 4