Course Name Code Semester T+U Hours Credit ECTS
Linear Algebra MAT 113 1 2 + 0 2 4
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level Bachelor's Degree Course Type Compulsory Course Coordinator Prof.Dr. ÖMER FARUK GÖZÜKIZIL Course Lecturers Dr.Öğr.Üyesi NESLİHAN ÖZSOY, Doç.Dr. MAHMUT AKYİĞİT, Prof.Dr. ÖMER FARUK GÖZÜKIZIL, Prof.Dr. METİN YAMAN, Prof.Dr. YILMAZ UYAROĞLU, Prof.Dr. AŞKIN DEMİRKOL, Prof.Dr. MEHMET ALİ GÜNGÖR, Doç.Dr. GÖKHAN COŞKUN, Dr.Öğr.Üyesi EMRE KİŞİ, Course Assistants Course Category Available Basic Education in the Field Course Objective 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. Course Content 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.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Make conversions through the transformation matrices in 2 and 3-dimensional spaces. Lecture, Question-Answer, Discussion, Motivations to Show, Problem Solving, Testing,
Week Course Topics Preliminary Preparation
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.
Resources
Course Notes 1. Aşkın Demirkol, Lecture Notes.
Course Resources 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.
Order Program Outcomes Level of Contribution
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, X
5 An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research, X
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, X
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.
Evaluation System
Semester Studies Contribution Rate
1. Kısa Sınav 10
2. Kısa Sınav 10
3. Kısa Sınav 10
1. Ara Sınav 70
Total 100
1. Final 50
1. Yıl İçinin Başarıya 50
Total 100