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, Gram-Schmidt 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 non-homogeneous 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 Gram-Schmidt 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 Face-to-Face
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, Gram-Schmidt 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, McGraw-Hill 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
In-Term Studies
Mid-terms 1 80
Assignments 1 20
In-Term Total 2 100
Contribution of In-Term 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 non-experts 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 off-the-classroom study (Pre-study, practice) 14 5 70
Assignments 1 10 10
Mid-terms 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