Course Name Code Semester T+U Hours Credit ECTS
Linear Algebra MAT 114 2 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 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. X
2 Ability to identify formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues, according to the nature of the design.)
4 Ability to devise, select, and use modem techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5 Ability to design and conduct experiments, gather data analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11 Knowledge about the global and social effects of engineering practice on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.
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
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 98
Total Workload / 25 (Hours) 3.92
dersAKTSKredisi 4