MATH 250 | Course Introduction and Application Information - Department of Mechanical 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
	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	Weigthing	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	To have adequate knowledge in Mathematics, Mathematics based physics, statistics and linear algebra and Mechanical Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems.		-	-	X	-	-
2	To be able to identify, define, formulate, and solve complex Mechanical Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.		-	-	-	-	-
3	To be able to design a thermal and mechanical system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose.		-	-	-	-	-
4	To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in engineering applications.		-	-	X	-	-
5	To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Mechanical Engineering research topics.		-	-	-	-	-
6	To be able to work efficiently in Mechanical Engineering disciplinary and multi-disciplinary teams; to be able to work individually.		-	-	-	-	-
7	To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions.		-	-	-	-	-
8	To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions.		-	-	-	-	-
9	To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications.		-	-	-	-	-
10	To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.		-	-	-	-	-
11	To be able to collect data in the area of Mechanical Engineering, and to be able to communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechanical Engineering.		-	-	-	-	-

MATH 250 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

NEW GÜZELBAHÇE CAMPUS

GLOBAL CAREER

CONTRIBUTION TO SCIENCE

VALUING PEOPLE

BENEFIT TO SOCIETY