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| MAT2010 | Linear Algebra-II | 4+0+0 | ECTS:7 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Sultan YAMAK | | Co-Lecturer | PROF. DR. Sultan YAMAK, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide the students with a general knowledge on determinants, eigenvectors, eigenvalues, diagonalization and inner product spaces. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | prove elementary statements concerning the theory of matrices and determinants. | 1,2,3,4,5,7 | 1 | | LO - 2 : | use the Gram-Schmidt process to orthogonalize matrices | 1,3,4,5,6,7,8 | 1 | | LO - 3 : | calculate the invert matrices by determinants | 1,2,3,4,5,7,8 | 1 | | LO - 4 : | write the relationships between A, the rank of A and the linear equation AX =b | 1,2,3,4,5,6,7,8 | 1 | | LO - 5 : | prove elementary facts concerning eigenvalues and eigenvectors | 1,2,3,4,5,6,7,8 | 1 | | LO - 6 : | determine if a matrix is diagonalizable, and if it is, diagonalize it. | 1,2,3,4,5,6,7,8 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Determinants, eigenvectors and eigenvalues, the characteristic polynomials, quadratic forms, the space of inner products, Euclidean and unitary spaces, orthogonal and unitary matrices. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Elementary operations and applications | | | Week 2 | Linear equation systems and solution | | | Week 3 | Determinants
| | | Week 4 | Properties of determinant functions
| | | Week 5 | Applications of Determinants
| | | Week 6 | Eigenvalues and Eigenvectors | | | Week 7 | Diagonal matrices | | | Week 8 | Binary linear transformations | | | Week 9 | Mid-term exam | | | Week 10 | Inner-product spaces | | | Week 11 | Euclidean space | | | Week 12 | Orthogonal bases | | | Week 13 | Orthonormal bases | | | Week 14 | Orthogonal matrices | | | Week 15 | positive-defined matrices | | | Week 16 | End-of-term exam | | | |
| 1 | B. Seymour Lipschutz, M. Lipson , 2001, Theory and problems of LINEAR ALGEBRA Linear Algebra, Schaum's outlıne series. | | | |
| 1 | A. Frank, 1962, Theory and Problems of Matrices, Schaum's outline series. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 10/04/2018 | 2 | 50 | | End-of-term exam | 16 | 31/05/2018 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 165 |
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