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	Service Courses Taken From Other Departments
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	Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems.					X
2	Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4	Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5	Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6	Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7	Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8	Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9	Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10	Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11	Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.

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