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Bachelor's Degree
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Course Structure Diagram with Credits
Linear Algebra (Physics) Course Details
Course Information  

Course Title  Code  Semester  T + P  ECTS 
Linear Algebra (Physics)  MAT287  3  4 + 0  6 
Prerequisites  None 
Language  Turkish 
Level  Bachelor's Degree 
Type  Compulsory 
Coordinator  Assist.Prof. SEYHUN KESİM 
Instructors  Assist.Prof. SEYHUN KESİM 
Goals  To give basic information about linear algebra and matrix theory which is used widely in physics. 
Contents  Elementary Row Operations on Matrices. Matrix Algebra, Special Types of Matrices. Elementary Matrices, Elementary Column Operations and Equivalent Matrices. 2x2 and 3x3 Determinants, nxn Determinants. Further Froperties of Determinants, The Inverse of a Matrix. Definition and Examples of Vector Spaces, Subspaces. Linear Independence, Basis and Dimension. Linear Transformations on Vector Spaces, The Matrix of a Linear Transformation. Change of Basis, The Kernel and Image of a Linear Transformation. Inner Product Spaces. Orthogonal Vectors, GramSchmidt Orthogonalization Procedure. Eigenvalues and Eigenvectors of a Square Matrix, Diagonalization of Square Matrices. Diagonalization of Square Matrices. 
Work Placement(s)  Absent 
Number  Learning Outcomes 
1  He\She solves homogeneous and nonhomogeneous systems of linear equations. He\She does matrix algebra and knows special types of matrices. 
2  He\She computes determinants of square matrices using properties of determinants. He\She decides whether or not a square matrix is invertible and, if inertible, computes its inverse. 
3  He\She knows notions of vector space and subspace with their examples. He\She decides whether or not a subset of a vector space is linearly independent. 
4  He\She determines a generating set and a basis for a vector space and finds its dimension. He\She determines the matrix of a linear transformation with respect to bases of vector spaces. 
5  He\She determines elements, bases and dimensions of the image and the kernel of a linear transformation. He\She determines the rank of a matrix. 
6  He\She knows the definition and examples of inner product. He\She knows inner product spaces (Euclidean and unitary spaces) with their examples. 
7  He\She determines an orthonormal basis for a finite dimensional inner product space by using GramSchmidt orthogonalization procedure. He\She determines whether or not a square matrix is diagonalizable and does some important applications of diagonalizable square matrices. 
Mode of Delivery  FacetoFace 
Planned Learning Activities & Teaching Methods  Lecture, question and answer, discussion, problem solving. 
Assessment Methods  Midterm exam, homework, final exam. 
Course Content  

Week  Topics  Study Materials 
1  Elementary Row Operations on Matrices  Studying on related topics from the course materials 
2  Matrix Algebra, Special Types of Matrices  Studying on related topics from the course materials 
3  Elementary Matrices, Elementary Column Operations and Equivalent Matrices  Studying on related topics from the course materials 
4  2x2 and 3x3 Determinants, nxn Determinants  Studying on related topics from the course materials 
5  Further Froperties of Determinants, The Inverse of a Matrix  Studying on related topics from the course materials 
6  Definition and Examples of Vector Spaces, Subspaces  Studying on related topics from the course materials 
7  Linear Independence, Basis and Dimension  Studying on related topics from the course materials 
8  Midterm Exam  Studying on topics covered in the previous weeks from the course materials and solving various problems 
9  Linear Transformations on Vector Spaces, The Matrix of a Linear Transformation  Studying on related topics from the course materials 
10  Change of Basis, The Kernel and Image of a Linear Transformation  Studying on related topics from the course materials 
11  Inner Product Spaces  Studying on related topics from the course materials 
12  Orthogonal Vectors, GramSchmidt Orthogonalization Procedure  Studying on related topics from the course materials 
13  Eigenvalues and Eigenvectors of a Square Matrix, Diagonalization of Square Matrices  Studying on related topics from the course materials 
14  Diagonalization of Square Matrices  Studying on related topics from the course materials 
15  Final Exam  Studying on topics covered in the previous weeks from the course materials and solving various problems 

Sources  

Textbook  • A. O. Morris, “Linear Algebra an Introduction”, Chapman & Hall, London, 1982. 
Additional Resources  • Seymour Lipschutz, “Theory and Problems of Linear Algebra”, 2nd Ed., Schaum’s Outline Series, McGrawHill Book Company, 1991. (Türkçesi: Prof. Dr. H. Hilmi Hacısalihoğlu, “Schaum Serisinden Lineer Cebir Teori ve Problemleri”, Nobel Yayın Dağıtım, Ankara, 1991). • Ward Cheney and David Kincaid, “Linear Algebra Theory and Applications”, Jones and Bartlett Publishers, 2009. 
Assessment System  Quantity  Percentage 

InTerm Studies  
Midterms  1  80 
Assignments  1  20 
InTerm Total  2  100 
Contribution of InTerm Studies to Overall  40  
Contribution of Final Exam to Overall  60  
Total  100 
Course's Contribution to PLO  

No  Key Learning Outcomes  Level  
1  2  3  4  5  
1  Has textbooks containing current information, application tools and equipment , and advanced theoretical and practical knowledge supported by other resources in a scientific approach.  x  
2  Adapts and transfers the acquired knowledge to secondary education.  x  
3  Uses advanced institutional and practical knowledge acquired in the physics field.  x  
4  Updates the information on daily conditions.  x  
5  Comments on and evaluate the data by using advanced knowledge and skills acquired in the field, identifies and analyzes the current problems of technological developments, and comes up with solutions based on research and evidence.  x  
6  Has the ability to conceptualize the events and facts related with the field; analyze them with scientific methods and techniques.  x  
7  Designs and performs experiments to analyze the problems, collects data, performs analyzes and comment on the results.  x  
8  Carries out an advanced study related to the field independently.  x  
9  Takes on responsibility individually and as a team member in order to solve unpredictable and complex problems encountered in applications related to the field.  x  
10  Plans and manages the activities in a project under his responsibility for development.  x  
11  Plays a role in the process of decision making when faced with problems about different discipline fields.  x  
12  Uses time effectively in the process of inference with the ability of thinking analytically.  x  
13  Evaluates the advanced knowledge and skills acquired in the field with a critical perspective.  x  
14  Determines the learning requirements and leads the learning process.  x  
15  Develops a positive attitude towards lifelong learning.  x  
16  Is aware of the necessity of lifelong learning and develops his Professional knowledge and skills continuously.  x  
17  Informs people and organizations about the topics related to their fields; expresses his ideas and suggestions for solutions to problems in both oral and written form.  x  
18  Shares his ideas and suggestions for solutions to the problems with experts and nonexperts by supporting them with quantitative and qualitative data.  x  
19  Organizes projects and activities for social environment he lives in with an awareness of social responsibility.  x  
20  Follows advances in the field and communicate with colleagues by using a foreign language at least at B1 level of European Language Portfolio.  x  
21  Uses information and communication technology along with software the Human Sciences the field requires at an advanced level.  x  
22  Uses his knowledge of human health and environmental awareness acquired in their fields for society’s ends.  x  
23  Behaves in a way adhering to the social, scientific, cultural and ethical values in the process of data collection, commenting, application, publicizing the results related with the field.  x  
24  Has a sufficient level of awareness about the universality of social rights, social justice, quality management, acting in a suitable way in processes and attendance (Instead of quality culture) the protection of cultural values, protection of the environment and health and security in the professional field.  x 
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION  

Activities  Quantity  Duration (Hour)  Total Work Load (h) 
Course Duration  14  4  56 
Hours for offtheclassroom study (Prestudy, practice)  14  5  70 
Assignments  1  10  10 
Midterms  1  20  20 
Final examination  1  30  30 
Total Work Load (h)  186  
Total Work Load / 30 (h)  6.2  
ECTS Credit of the Course  6 