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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
LINEAR ALGEBRA MAT 113 1 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 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.

Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 To have sufficient foundations on engineering subjects such as science and discrete mathematics, probability/statistics; an ability to use theoretical and applied knowledge of these subjects together for engineering solutions, X
2 An ability to determine, describe, formulate and solve engineering problems; for this purpose, an ability to select and apply proper analytic and modeling methods,al background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations X
3 An ability to select and use modern techniques and tools for engineering applications; an ability to use information technologies efficiently, X
4 An ability to analyze a system, a component or a process and design a system under real limits to meet desired needs; in this direction, an ability to apply modern design methods,
5 An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research,
6 Understanding, awareness of administration, control, development and security/reliability issues about information technologies,
7 An ability to work efficiently in multidisciplinary teams, self confidence to take responsibility,
8 An ability to present himself/herself or a problem with oral/written techniques and have efficient communication skills; know at least one extra language,
9 An awareness about importance of lifelong learning; an ability to update his/her knowledge continuously by means of following advances in science and technology,
10 Understanding, practicing of professional and ethical responsibilities, an ability to disseminate this responsibility on society,
11 An understanding of project management, workplace applications, health issues of laborers, environment and job safety; an awareness about legal consequences of engineering applications,
12 An understanding universal and local effects of engineering solutions; awareness of entrepreneurial and innovation and to have knowledge about contemporary problems.

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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