| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | IMO2042013331 | LINEAR ALGEBRA II | Compulsory | 2 | 4 | 6 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| To have enough knowledge and about the concepts of eigen values and eigen vectors, inner product spaces and dual spaces which have important applications on science and engineering. |
| Name of Lecturer(s) |
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| Learning Outcomes |
| 1 | Computes the determinant of a matrix, learns the properties of determinants | | 2 | Finds the eigen values and eigen vectors of a linear map and a matrix, make some applications of diagonalization. | | 3 | Defines inner product space and makes its some applications | | 4 | Learns the concepts of orthogonal and orthonormal bases | | 5 | Explains the concept of dual space, finds the dual bases. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Orthogonality, orthogonalite concept and distance functions in R^n, Gram-Schmidt process, orthogonal matrices, at least squares and their application. Determinants, properties of determinant functions, solution of linear equation system with Cramer rule, characteristic equation and polynomial of a matrix, Eigenvalues and Eigenvectors, diagonaling and matrices operations. |
| Weekly Detailed Course Contents |
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| 1 | Definition of determinant | | | | 2 | Properties and applications of determinants | | | | 3 | Finding inverse of a matrix with the help of adjoint matrix and determinat, Cramer's rule | | | | 4 | Eigenvalues and eigenvectors | | | | 5 | Diagonalization and matrix operations | | | | 6 | Characteristic equation and eigenvalues | | | | 7 | Minimal polynomial | | | | 8 | Midterm exam | | | | 9 | Inner product spaces | | | | 10 | Inner product spaces | | | | 11 | Orthogonal and orthonormal bases | | | | 12 | Solution of least squares | | | | 13 | Linear functionals and dual spaces | | | | 14 | Dual bases | | | | 15 | Second dual space, Transpose of a linear map | | | | 16 | Final exam | | |
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| Recommended or Required Reading |
| 1) Arif Sabuncuoğlu, (2011). Lineer cebir, Nobel Yayın Dağıtım, Ankara.
2) Lipschutz, B. S. and Lipson, M. 2001, Theory and problems of Linear Algebra, Schaum's outline series. |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
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| Workload Calculation |
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| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 3 | 42 |
| Problem Solving | 14 | 3 | 42 |
| Individual Study for Homework Problems | 14 | 3 | 42 |
| Individual Study for Mid term Examination | 1 | 25 | 25 |
| Individual Study for Final Examination | 1 | 25 | 25 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | | 1 | | | | | LO2 | 3 | 1 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | | | 1 | | | | | LO3 | 3 | 1 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | | | 1 | | | | | LO4 | 3 | 1 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | | | 1 | | | | | LO5 | 3 | 1 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | | | 1 | | | |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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