Department of Mechanical Engineering

MATH 250 | Course Introduction and Application Information

Course Name

Linear Algebra for Engineers

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

Prerequisites	MATH 153 To get a grade of at least FD MATH 109 To get a grade of at least FD
Course Language	English
Course Type	Required (Core Course)
Course Level	First Cycle
Mode of Delivery
Teaching Methods and Techniques of the Course	Problem Solving Q&A Lecture / Presentation
National Occupational Classification Code	-
Course Coordinator	Doç. Dr. Sevin Gümgüm
Course Lecturer(s)	Dr. Öğr. Üyesi Neslişah İmamoğlu Karabaş Doç. Dr. Sevin Gümgüm
Assistant(s)	-

Course Objectives

The main objective of this course is to establish a basicmathematical background for the students who will receiveengineering courses based on linear algebra by providingthem with the basic knowledge on linear vector spaces,matrix operations as well as on the methods for solving andanalyzing linear systems of algebraic equations.

Learning Outcomes

The students who succeeded in this course;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	apply the rowoperations to find(reduced) rowechelon forms ofmatrices.	1.1					X
LO2	find the inverse ofa matrix.	1.1					X
LO3	apply basicconcepts of linearmodels to variousapplications.	1.1					X
LO4	evaluate thedeterminants ofmatrices.	1.1					X
LO5	investigate thelinearindependence ofvectors.	1.1					X
LO6	identify vectorspaces and theirsubspaces.	1.1					X
LO7	compute theeigenvalues of amatrix andcorrespondingeigenvectors.	1.1	X
LO8	describe the innerproduct.	1.1					X

Course Description

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

Related Sustainable Development Goals

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

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Systems of linearequations, rowreduction andechelon forms, vectorequations	David C.Lay, StephanR.Lay and Judi J.McDonald, "LinearAlgebra and ItsApplications", 5th ed.(Pearson, 2015).Sections 1.1, 1.2,D0avid C.Lay,Stephan R.Lay andJudi J. McDonald,"Linear Algebra andIts Applications", 5thed.( Pearson, 2015).Sections 1.1, 1.2, 1.3	-
2	The matrix equationAx=b, Solution sets oflinear systems,applications of linearsystems	David C.Lay, StephanR.Lay and Judi J.McDonald, "LinearAlgebra and ItsApplications", 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 transformation and applied modeling of electrical networks, population movement, and infrastructure flows	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 and decomposition learning	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	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	-
9	Midterm Exam		-
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" 5 th ed. (Pearson 2015). ISBN-13:978-0321982384
Suggested Readings/Materials	-

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5	LO6	LO7	LO8
Quizzes / Studio Critiques	4	20	X	X	X	X	X	X	X	X
Midterm	1	30	X	X	X	X	X	X	X	X
Final Exam	1	50	X	X	X	X	X	X	X	X
Total	6	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	3	48
Laboratory / Application Hours	-	-	-
Study Hours Out of Class	14	3	42
Field Work	-	-	-
Quizzes / Studio Critiques	4	5	20
Portfolio	-	-	-
Homework / Assignments	-	-	-
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	30	30
Final Exam	1	40	40
		Total	180

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	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, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics	LO7				LO1 LO2 LO3 LO4 LO5 LO6 LO8
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (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) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
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
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

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