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