Linear Algebra (MATH275) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Linear Algebra	MATH275	3. Semester	4	0	0	4	6

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Compulsory Departmental Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer, Drill and Practice.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	This course is designed to enrich the knowledge of engineering students in linear algebra, and to teach them the basics and application of the methods for the solution of linear systems occurring in engineering problems.
Course Learning Outcomes	The students who succeeded in this course; understand the notion of matrix and perform algebraic operations on matrices, find the inverse of a nonsingular matrix, solve linear systems by using echelon form of matrices, determine the existence and uniquness of the solution and determine infinitely many solutions, if any makes sense of vector spaces, subspaces, linear independence, basis and dimensions and rank of a matrix, comprehend and use inner product, Gram-Schmidt process, orthogonal complements, understand and use linear transformation and associated matrices, evaluate determinants and solve linear systems with unique solution via determinant (Cramer’s Rule), understand and find eigenvalues and eigenvectors, determine if a matrix is diagonalizable, and if it is, diagonalize it.
Course Content	Linear equations and matrices, real vector spaces, inner product spaces, linear transformations and matrices, determinants, eigenvalues and eigenvectors.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Systems of Linear Equations, Matrices, Matrix Multiplication, Algebraic Properties of Matrix Operations	pp. 1-39
2	Special Types of Matrices and Partitioned Matrices, Echelon Form of a Matrix, Solving Linear Systems	pp. 42-49, 86-93, 95-103, 111-113
3	Elementary Matrices; Finding Inverses, Equivalent Matrices	pp. 117-124, 126-129
4	Determinants, Properties of Determinants, Cofactor Expansion	pp. 141-145, 146-154, 157-163
5	Inverse of a Matrix (via Its Determinant), Other Applications of Determinants (Cramer’s Rule)	pp. 165-168, 169-172
6	Vectors in the Plane and In 3-D Space, Vector Spaces, Subspaces	pp. 177-186, 188-196, 197-203
7	Span, Linear Independence, Basis and Dimension	pp. 209-214, 216-226, 229-241
8	Homogeneous Systems, Coordinates and Isomorphism, Rank of a Matrix	pp. 244-250, 253-266, 270-281
9	Inner Product Spaces, Gram-Schmidt Process	pp. 290-296, 307-317, 320-329
10	Orthogonal Complements, Linear Transformations and Matrices	pp. 332-343, 363-372
11	Kernel and Range of a Linear Transformation	pp. 375-387
12	Matrix of a Linear Transformation	pp. 389-397
13	Eigenvalues and Eigenvectors	pp. 436-449
14	Diagonalization and Similar Matrices, Diagonalization of Symmetric Matrices	pp. 453-461, 463-472
15	General Review
16	Final Exam

Sources

Course Book	1. Elementary Linear Algebra, B. Kolman and D.R. Hill, 9th Edition, Prentice Hall, New Jersey, 2008
Other Sources	2. Linear Algebra, S. H. Friedberg, A. J. Insel, L. E. Spence, Prentice Hall, New Jersey, 1979
	3. Basic Linear Algebra, Cemal Koç, Matematik Vakfı Yay., Ankara, 1996

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	-	-
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	60
Final Exam/Final Jury	1	40
Toplam	3	100

Percentage of Semester Work	60
Percentage of Final Work	40
Total	100

Course Category

Core Courses
Major Area Courses
Supportive Courses	X
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Knowledge of mathematics, natural sciences, engineering fundamentals, computing, and topics specific to the relevant engineering discipline; the ability to use this knowledge in the solution of complex engineering problems.					X
2	The ability to identify, formulate, and analyze complex engineering problems using knowledge of basic sciences, mathematics, and engineering, and considering the UN Sustainable Development Goals relevant to the problem.				X
3	The ability to design creative solutions for complex engineering problems; the ability to design complex systems, processes, devices, or products to meet current and future requirements, considering realistic constraints and conditions.	X
4	The ability to select and use appropriate techniques, resources, and modern engineering and IT tools, including prediction and modeling, for the analysis and solution of complex engineering problems, with an awareness of their limitations.		X
5	The ability to use research methods for the investigation of complex engineering problems, including literature search, designing and conducting experiments, collecting data, and analyzing and interpreting results.		X
6	Knowledge of the effects of engineering practices on society, health and safety, the economy, sustainability, and the environment within the scope of the UN Sustainable Development Goals; awareness of the legal consequences of engineering solutions.
7	Acting in accordance with engineering professional principles, knowledge of ethical responsibility; awareness of acting impartially without discrimination on any grounds and being inclusive of diversity.
8	The ability to work effectively individually and in intra-disciplinary and multi-disciplinary teams (face-to-face, remote, or hybrid) as a team member or leader.
9	"The ability to communicate effectively orally and in writing on technical topics, considering the various differences of the target audience (such as education, language, profession).
10	Knowledge of practices in business life such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
11	The ability to engage in life-long learning, including independent and continuous learning, adapting to new and emerging technologies, and thinking inquisitively regarding technological changes.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	14	4	56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	10	20
Prepration of Final Exams/Final Jury	1	10	10
Total Workload			86