MATH 250 | Course Introduction and Application Information - Department of Software Engineering

Course Name

Linear Algebra for Engineers

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 250	Fall	3	0	3	6

Prerequisites

	MATH 153 To get a grade of at least FD
or	MATH 109 To get a grade of at least FD

Course Language

English

Course Type

Required

Course Level

First Cycle

Mode of Delivery

-

Teaching Methods and Techniques of the Course

Problem Solving
Q&A
Lecture / Presentation

National Occupation Classification

-

Course Coordinator

Doç. Dr. Sevin GÜMGÜM

Course Lecturer(s)

Assistant(s)

Course Objectives

The main objective of this course is to establish a basic mathematical background for the students who will receive engineering courses based on linear algebra by providing them with the basic knowledge on linear vector spaces, matrix operations as well as on the methods for solving and analyzing linear systems of algebraic equations.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	apply the row operations to find (reduced) row echelon forms of matrices.
2	find the inverse of a matrix.
3	apply basic concepts of linear models to various applications.
4	evaluate the determinants of matrices.
5	investigate the linear independence of vectors.
6	identify vector spaces and their subspaces.
7	compute the eigenvalues of a matrix and corresponding eigenvectors.
8	describe the inner product.

Course Description

The main subjects of the course are the vector and matrix operations, linear independence and dependence of vectors, linear vector spaces and subspaces, dimensions and basis vectors for vector spaces, linear transformations, determinants, eigenvalue and eigenvectors.

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Systems of linear equations, row reduction and echelon forms, vector equations	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, D0avid C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, 1.3
2	The matrix equation Ax=b, Solution sets of linear systems, applications of linear systems	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.4, 1.5, 1.6
3	Linear Independence, introduction to linear transformations	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.7, 1.8
4	The matrix of a linear transformations, linear models in business, science and engineering	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.9, 1.10
5	Matrix operations, The inverse of a matrix	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.1, 2.2
6	Characterization of invertible matrices, Matrix factorizations	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.3, 2.5
7	Introduction to determinants, properties of determinants	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.1, 3.2, 3.3
8	Midterm
9	Cramer’s rule, volume, and linear transformations, Vector spaces and subspaces	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.3, 4.1
10	Null spaces, column spaces, and linear transformations, Linearly independent sets, bases	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.2, 4.3
11	The dimension of a vector space, Rank, Application for Markov chains	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.5, 4.6, 4.9
12	Eigenvalues and eigenvectors, The characteristic equation, Diagonalization	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.1, 5.2, 5.3
13	Diagonalization, Inner product, length, and orthogonality, orthogonal sets	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.3, 6.1, 6.2
14	The Gram-Schmidt process, review	David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Section 6.4
15	Semester review
16	Final exam

Course Notes/Textbooks

David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson,

2015). ISBN-13:978-0321982384

Suggested Readings/Materials

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6	LO 7	LO 8
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	4	20
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	5	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques	4	5	20
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	40	40
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computer computation, and topics specific to related engineering disciplines; the ability to use this knowledge in solving complex engineering problems		-	-	X	-	-
	1	Mathematics	-	-	-	-	-
	2	Science	-	-	-	-	-
	3	Basic engineering	-	-	-	-	-
	4	Computer computation	-	-	-	-	-
	5	Topics specific to related engineering disciplines	-	-	-	-	-
	6	The ability to use this knowledge in solving complex engineering problems	-	-	-	-	-
2	Problem Analysis: The ability to define, formulate, and analyze complex engineering problems by using fundamental science, mathematics, and engineering knowledge, while considering the relevant UN Sustainable Development Goals (SDGs) related to the problem.		-	-	-	-	-
3	Engineering Design: The ability to design creative solutions to complex engineering problems; the ability to design complex systems, processes, devices, or products that meet present and future requirements, considering realistic constraints and conditions.		-	-	-	-	-
	1	The ability to design creative solutions to complex engineering problems	-	-	-	-	-
	2	Considering realistic constraints and conditions in designing complex systems, processes, devices, or products	-	-	-	-	-
	3	The ability to design in a way that meets current and future requirements	-	-	-	-	-
4	Use of Techniques and Tools: The ability to select and use appropriate techniques, resources, and modern engineering and information technology tools, including prediction and modeling, for the analysis and solution of complex engineering problems, while being aware of their limitations		-	-	X	-	-
5	Research and Investigation: The ability to use research methods, including literature review, designing experiments, conducting experiments, collecting data, analyzing and interpreting results, for the investigation of complex engineering problems.		-	-	-	-	-
	1	The ability to use research methods, including literature review	-	-	-	-	-
	2	Designing experiments	-	-	-	-	-
	3	Conducting experiments, collecting data, analyzing and interpreting results, for the investigation of complex engineering problems	-	-	-	-	-
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the scope of the UN Sustainable Development Goals (SDGs); awareness of the legal consequences of engineering solutions		-	-	-	-	-
	1	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the scope of the UN Sustainable Development Goals (SDGs)	-	-	-	-	-
	2	Awareness of the legal consequences of engineering solutions	-	-	-	-	-
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession; knowledge of ethical responsibility; awareness of acting impartially and inclusively, without discrimination in any matter. (FENG101)		-	-	-	-	-
	1	Acting in accordance with the principles of the engineering profession; knowledge of ethical responsibility	-	-	-	-	-
	2	Awareness of acting impartially and inclusively, without discrimination in any matter.	-	-	-	-	-
8	Individual and Team Work: The ability to work effectively as an individual and as a member or leader of both intra-disciplinary and interdisciplinary teams (whether face-to-face, remote, or hybrid).		-	-	-	-	-
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession), particularly in technical matters.		-	-	-	-	-
	1	Verbal (ENGxxx)	-	-	-	-	-
	2	Written effective communication skills. (ENGxxx)	-	-	-	-	-
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.		-	-	-	-	-
	1	Knowledge of business practices such as project management and economic feasibility analysis; (FENG497-FENG498)	-	-	-	-	-
	2	Awareness of entrepreneurship and innovation. (FENG101)	-	-	-	-	-
11	Lifelong Learning: The ability to learn independently and continuously, adapt to new and emerging technologies, and think critically about technological changes.		-	-	-	-	-

MATH 250 | Course Introduction and Application Information

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