FACULTY OF ENGINEERING

Department of Industrial 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
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
Course Coordinator
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 The students who succeeded in this course;
  • apply the row operations to find (reduced) row echelon forms of matrices.
  • find the inverse of a matrix.
  • apply basic concepts of linear models to various applications.
  • evaluate the determinants of matrices.
  • investigate the linear independence of vectors.
  • identify vector spaces and their subspaces.
  • compute the eigenvalues of a matrix and corresponding eigenvectors.
  • 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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Systems of linear equations, row reduction and echelon forms David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2
2 Row reduction and echelon forms, vector equations, the matrix equation Ax=b David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.2, 1.3, 1.4.
3 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 1.5, 1.6
4 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
5 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
6 Matrix operations David C.Lay, Stephan R.Lay and Judi J. David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.1, 2.2
7 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
8 Midterm
9 Introduction to determinants, properties of determinants, Cramer’s rule, volume, and linear transformations 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
10 Vector spaces and subspaces, null spaces, column spaces, and linear transformations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.1, 4.2
11 Linearly independent sets, bases application for Markov chains David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.3, 4.9
12 Eigenvalues and eigenvectors, the characteristic equation David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.1, 5.2
13 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 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

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
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

ECTS / WORKLOAD TABLE

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
6
24
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
30
30
Final Exam
1
36
36
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science and Industrial Engineering; to be able to use theoretical and applied information in these areas to model and solve Industrial Engineering problems.

X
2

To be able to identify, formulate and solve complex Industrial Engineering problems by using state-of-the-art methods, techniques and equipment; to be able to select and apply proper analysis and modeling methods for this purpose.

3

To be able to analyze a complex system, process, device or product, and to design with realistic limitations to meet the requirements using modern design techniques.

4

To be able to choose and use the required modern techniques and tools for Industrial Engineering applications; to be able to use information technologies efficiently.

X
5

To be able to design and do simulation and/or experiment, collect and analyze data and interpret the results for investigating Industrial Engineering problems and Industrial Engineering related research areas.

6

To be able to work efficiently in Industrial Engineering disciplinary and multidisciplinary 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 contemporary issues and the global and societal effects of Industrial Engineering practices on health, environment, and safety; to be aware of the legal consequences of Industrial Engineering solutions.

9

To be aware of professional and ethical responsibility; to have knowledge of the standards used in Industrial Engineering practice.

10

To have knowledge about business life practices such as project management, risk management, and change management; to be aware of entrepreneurship and innovation; to have knowledge about sustainable development.

11

To be able to collect data in the area of Industrial Engineering; to be able to communicate with colleagues in a foreign language.

12

To be able to speak a second foreign 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 Industrial Engineering.

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

 


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