| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Lınear Algebra | MAT 115 | 1 | 3 + 0 | 3 | 4 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | İngilizce |
| Dersin Seviyesi | Lisans |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Dr.Öğr.Üyesi EMİNE ÇELİK |
| Dersi Verenler | Dr.Öğr.Üyesi EMİNE ÇELİK, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Temel Öğretim |
| 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. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Introduction to systems of linear equations. | |
| 2 | Vector Equations. The Matrix equation Ax=b. Row reduction and echelon forms. | |
| 3 | Gaussian Elimination and Gauss-Jordan Elimination. | |
| 4 | Operations with Matrices. Properties of Matrix operations. | |
| 5 | Theory of linear systems, homogeneous and nonhomogeneous systems, rank. | |
| 6 | The inverse of a matrix. Characterization of invertible matrices. | |
| 7 | The Determinant of a Matrix. Determinants and Elementary operations. Properties of determinants. | |
| 8 | Applications of Determinants, Cramer's rule. | |
| 9 | Vectors, linear independence, bases and transformations. | |
| 10 | The Scalar Product, inner product spaces, orthonormal bases: Gram-Schmidt Process. | |
| 11 | Eigenvalues and eigenvectors. | |
| 12 | The Characteristic function. Cayley-Hamilton Theorem. | |
| 13 | Diagonalization. Similar Matrices. | |
| 14 |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | [1] David C.Lay, Linear Algebra and Its Applications, Pearson, 2003. [2] Ron Larson, Elementary Linear Algebra, Cengage Learning, 2017. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 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. | ||||||
| 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. | X | |||||
| 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. | X | |||||
| 10 | Understanding, practicing of professional and ethical responsibilities, an ability to disseminate this responsibility on society. | X | |||||
| 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 | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Kısa Sınav | 10 |
| 2. Kısa Sınav | 10 |
| 3. Kısa Sınav | 10 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (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 |
| Assignment | 1 | 8 | 8 |
| Final examination | 1 | 10 | 10 |
| Toplam İş Yükü | 106 | ||
| Toplam İş Yükü / 25 (Saat) | 4,24 | ||
| Dersin AKTS Kredisi | 4 | ||