| 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 | 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 | ||