| Course Name | Code | Semester | T+U Hours | Credit | ECTS |
|---|---|---|---|---|---|
| Linear Algebra II | IME 204 | 4 | 3 + 1 | 4 | 5 |
| Precondition Courses | |
| Recommended Optional Courses | |
| Course Language | Turkish |
| Course Level | Bachelor's Degree |
| Course Type | Compulsory |
| Course Coordinator | Prof.Dr. MELEK MASAL |
| Course Lecturers | Prof.Dr. MELEK MASAL, |
| Course Assistants | Assist.Emine Nur BİLGİÇ |
| Course Category | Available Basic Education in the Field |
| Course Objective | To show application fields of mathematics by getting mathematics easier and pleasurable by means of this course which contain basic equipment in mathematics and engineer and most important concepts of mathematical language |
| Course Content | Orthogonal; concepts of orthogonal in R^ n and distance function, Gram-Schmidt operation, othogonal matrix, least squances and aplications. Determinants: determinant and reduction, solutions of linear equations with Cramer Rule. Characteristic equations of matrix, characteristic values and eigen vectors, Diagonalize and matrix operations. |
| # | Course Learning Outcomes | Teaching Methods | Assessment Methods |
|---|---|---|---|
| 1 | Express the definition of orthogonality | Lecture, Drilland Practice, | Testing, |
| 2 | Express the concepts of inner product spaces, euclidean space, unitary space and their properties | Lecture, Drilland Practice, | Testing, |
| 3 | Explain linear transformations and their properties | Lecture, Drilland Practice, | Testing, |
| 4 | Express and apply diagonalisation, characteristic value, characteristic vector, characteristic polynomial, characteristic equations. | Lecture, Drilland Practice, | Testing, |
| 5 | Express and applyTheorem of Cayley-Hamilton and its conclusions. | Lecture, Drilland Practice, | Testing, |
| 6 | Explain orthogonal and unitary transformations with symmetric and hermit transformations | Lecture, Drilland Practice, | Testing, |
| Week | Course Topics | Preliminary Preparation |
|---|---|---|
| 1 | Orthogonal; concepts of orthogonal in R^ n, inner product spaces, euclidean space, unitary space, matrix equaled to inner product | |
| 2 | Schwarz inequality, distance function, orthogonal complement, orthonormal base | |
| 3 | Gram-Schmidt Method, linear transformations and matrixes | |
| 4 | Rank and core of linear transformation | |
| 5 | Matrix of linear transformation, briefly permutations | |
| 6 | Determinants: determinant and reduction, properties of determinant, determinants of elementary matrixes | |
| 7 | Minor, cofactor, determinant expansions, inverse of a matrix | |
| 8 | Solutions of linear equations with Cramer Rule, vector product, mixed scalar product | |
| 9 | Mid – Term Exam | |
| 10 | Diagonalisation, characteristic value, characteristic vector, characteristic polynomial, characteristic equations | |
| 11 | Theorems related diagonalisation, characteristic vectors and exercises | |
| 12 | Theorem of Cayley-Hamilton and its conclusions, applications | |
| 13 | Orthogonal and unitary transformations | |
| 14 | Symmetric and hermit transformations |
| Resources | |
|---|---|
| Course Notes | |
| Course Resources | |
| Order | Program Outcomes | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Have general information about basic concept, theory and applicaitons on mathematics | X | |||||
| 2 | Have ability of mathematical thinking and apply to real life | X | |||||
| 3 | Classify a problem systematically also create comprehensible, understandable and objective solutions | X | |||||
| 4 | Establish relationship among events looked different | X | |||||
| 5 | Get clear and exact ideas about relationships among time, place and numbers | X | |||||
| 6 | Use principles of scientific method on problem solving | X | |||||
| 7 | Have character on explorer, impartial, disinterested, give sound decisions, open mind and believe that spreading information is needed | X | |||||
| 8 | Think creative and critical | X | |||||
| 9 | Improve methods as fast, understandable and practical to faced problems | X | |||||
| 10 | Have information about national and international modern problems | ||||||
| 11 | Get life long learning behaviour | X | |||||
| 12 | Know and apply approach, aim, goal, principle and techniques of teaching program on special field with basic value and principles of Turkish National Education System | ||||||
| 13 | Evaluate development and learning of students, provide to evaluate self-assessment and other students. Use the assessment results to better instruction; share the results with student, parent, administrators and teachers. | ||||||
| 14 | Endeavor for constant development by making self-evaluation. Open the new knowledge and ideas, have a role to develop himself/herself and his/her institution. Have enough knowledge and conscious to protection subjects on society values and environment. | ||||||
| 15 | Interrogator ( get habit to find source of knowledge by asking “Why?” question instead of direct acceptance to given knowledges ) | X | |||||
| Evaluation System | |
|---|---|
| Semester Studies | Contribution Rate |
| 1. Ödev | 10 |
| 1. Ara Sınav | 50 |
| 1. Kısa Sınav | 20 |
| 2. Kısa Sınav | 20 |
| Total | 100 |
| 1. Yıl İçinin Başarıya | 40 |
| 1. Final | 60 |
| Total | 100 |
| ECTS - Workload Activity | Quantity | Time (Hours) | Total Workload (Hours) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 5 | 5 |
| Quiz | 3 | 5 | 15 |
| Final examination | 1 | 5 | 5 |
| Total Workload | 121 | ||
| Total Workload / 25 (Hours) | 4.84 | ||
| dersAKTSKredisi | 5 | ||