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 | |
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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 | X | ||||||
2 | X | ||||||
3 | X | ||||||
4 | |||||||
5 | X | ||||||
6 | |||||||
7 | |||||||
8 | |||||||
9 | |||||||
10 | |||||||
11 | |||||||
12 |
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 |