DEPARTMENT OF INDUSTRIAL ENGINEERING (ENGLISH)
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Ders Genel Tanıtım Bilgileri

Course Code:

1411121010

Ders İsmi:

Linear Algebra

Ders Yarıyılı:

Spring

Ders Kredileri:

Theoretical	Practical	Credit	ECTS
2	0	2	5

Language of instruction:

Ders Koşulu:

Ders İş Deneyimini Gerektiriyor mu?:

Type of course:

Necessary

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator :

Prof. Dr. Ramazan YAMAN

Course Lecturer(s):

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:

Building the knowledge needed for more advanced math topics

Course Content:

Matrices: Definition of matrix, types of matrices, equality of matrices, sum and difference of matrices, product of a matrix with a scalar, properties of sum of matrices and multiplication of scalars, multiplication of matrices and their properties, transpose of matrix and its properties -Some Special Matrices and matrix applications - Elementary row and column operations in matrices, reduced row (echolon) form of a matrix, rank of matrix, inverse of a square matrix -Determinants: Determinant of a square matrix, Laplace expansion, determinant properties -Sarrus rule, Supplementary matrix, inverse of a matrix with the help of additional matrix calculation, -Linear Equation Systems: Solution of systems of linear equations with the help of equivalent matrices, Systems of linear homogeneous equations, -Cramer's method, Solution with the help of coefficients matrix, -Vectors: Vector definition, sum of vectors, difference, analytical expression of vectors, scalar product of vectors, properties of the scalar product. Vector product and its properties, Mixed product and its properties, Double vector product and its properties, -Vector Spaces: Definition of vector spaces and related theorems. Sub vector space. The concept of stretching and basic theorems. Linear dependence and linear independence of vectors and related theorems, -Base and dimension concept and fundamental theorems. Definition of coordinates and transition matrices and related theorems. -Eigenvalues and Eigenvectors:Calculation of eigenvalues and eigenvectors of a square matrix, -Calculation of inverse and power of a square matrix with the help of Cayley-Hamilton Theorem

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
2 - Skills
Cognitive - Practical
1) Students who successfully complete this course; To be able to perform matrix operations (addition, subtraction, multiplication). Calculate the determinant of a given matrix.
2) Ability to apply many basic techniques of Matrix algebra, such as solving systems of linear equations using the Gauss Method and finding the inverse of an invertible matrix using the Gauss-Jordan Method.
3 - Competences
Communication and Social Competence
Learning Competence
1) To be able to understand the basics of vector algebra such as linear dependence and independence and to comprehend vector spaces and sub-vector spaces.
2) They will have the ability to calculate the inverse and nth power of a square matrix using the Cayley-Hamilton theorem.
Field Specific Competence
Competence to Work Independently and Take Responsibility
1) Finding the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial.

Ders Akış Planı

Week	Subject	Related Preparation
1)	Introduction to Systems of Linear Equations, Gaussian Elimination and Gauss-Jordan Elimination	Textbook
2)	Operations with Matrices, Properties of Matrix Operations	Textbook
3)	The Inverse of a Matrix	Textbook
4)	The Determinant of a Matrix, Evaluation of a Determinant Using Elementary Operations	Textbook
5)	Properties of Determinants	Textbook
6)	Vectors in Rn Vector Spaces Subspaces of Vector Spaces	Textbook
7)	Review for the midterm exam	Textbook
8)	Midterm 1	Textbook
9)	Spanning Sets and Linear Independence Basis and Dimension Rank of a Matrix and Systems of Linear Equations	Textbook
10)	Coordinates and Change of Basis	Textbook
11)	Introduction to Linear Transformations The Kernel and Range of a Linear Transformation	Textbook
12)	Matrices for Linear Transformations Transition Matrices and Similarity Midterm 2 Exam	Textbook
13)	Eigenvalues and Eigenvectors Diagonalization	Textbook
14)	Symmetric Matrices and Orthogonal Diagonalization	Textbook
15)	Review for the final exam	Textbook
16)	Final	Textbook

Sources

Course Notes / Textbooks:	Lineer Cebir ve Çözümlü Problemleri\Linear Algebra and Solving Problems Lineer Cebir Çözümlü Problemleri” ,Doç.Dr.Gürsel Yeşilot
References:	Linear Algebra and Solving Problems\Linear Algebra and Solving Problems Linear Algebra Solved Problems”, Associate Professor Gürsel Yeşilot

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları	1	2	3	5	4
Program Outcomes
1) Adequate knowledge of mathematics (a), science (b) and industrial engineering (c) (1) and the ability to use this knowledge in complex engineering problems.
2) Ability to work effectively both individually and in interdisciplinary and multidisciplinary teams.
3) Awareness of the necessity of lifelong learning and the ability to access information, to follow developments in science and technology, and to constantly renew oneself.
4) Knowledge of project management, risk management, innovation and change management, entrepreneurship and sustainable development
5) Awareness of the sectors and the ability to prepare a business plan.
6) Professional and ethical responsibility awareness and acting in accordance with ethical principles.
7) Information about the problems of the age in the field of engineering and the effects and legal consequences of engineering practices on health, environment and safety in universal and social dimensions.
8) Information about current engineering practices and standards used in engineering practices.
9) The ability to identify, formulate and solve complex engineering problems, and the ability to select and apply appropriate analysis and modeling methods for this purpose.
10) The ability to design a complex system, process, device or product using modern methods under realistic constraints and conditions and to meet specific requirements.
11) The ability to develop, select and use modern techniques and tools necessary for the solution of engineering problems, and the ability to use information technologies effectively.
12) Ability to design and conduct experiments, collect data, analyze data and interpret results for the study of engineering problems or research issues.
13) Ability to communicate effectively, write reports and make presentations in Turkish and English with oral, written and visual methods.
14) In-depth knowledge of appropriate analytical and experimental methods and computational methods for system integration such as simulation (a), production systems (b) operations research (c) and statistics (d).
15) Skills in designing (a) and improving (b), defining goals and criteria (c), analyzing (d) and developing solutions (e) systems that include people, materials, information, equipment and energy to creatively solve real-life problems

Ders - Öğrenme Kazanımı İlişkisi

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Adequate knowledge of mathematics (a), science (b) and industrial engineering (c) (1) and the ability to use this knowledge in complex engineering problems.	5
2)	Ability to work effectively both individually and in interdisciplinary and multidisciplinary teams.
3)	Awareness of the necessity of lifelong learning and the ability to access information, to follow developments in science and technology, and to constantly renew oneself.
4)	Knowledge of project management, risk management, innovation and change management, entrepreneurship and sustainable development
5)	Awareness of the sectors and the ability to prepare a business plan.
6)	Professional and ethical responsibility awareness and acting in accordance with ethical principles.
7)	Information about the problems of the age in the field of engineering and the effects and legal consequences of engineering practices on health, environment and safety in universal and social dimensions.
8)	Information about current engineering practices and standards used in engineering practices.
9)	The ability to identify, formulate and solve complex engineering problems, and the ability to select and apply appropriate analysis and modeling methods for this purpose.
10)	The ability to design a complex system, process, device or product using modern methods under realistic constraints and conditions and to meet specific requirements.	5
11)	The ability to develop, select and use modern techniques and tools necessary for the solution of engineering problems, and the ability to use information technologies effectively.
12)	Ability to design and conduct experiments, collect data, analyze data and interpret results for the study of engineering problems or research issues.
13)	Ability to communicate effectively, write reports and make presentations in Turkish and English with oral, written and visual methods.
14)	In-depth knowledge of appropriate analytical and experimental methods and computational methods for system integration such as simulation (a), production systems (b) operations research (c) and statistics (d).
15)	Skills in designing (a) and improving (b), defining goals and criteria (c), analyzing (d) and developing solutions (e) systems that include people, materials, information, equipment and energy to creatively solve real-life problems	3

Öğrenme Etkinliği ve Öğretme Yöntemleri

Course
Homework
Problem Çözme

Ölçme ve Değerlendirme Yöntemleri ve Kriterleri

Yazılı Sınav (Açık uçlu sorular, çoktan seçmeli, doğru yanlış, eşleştirme, boşluk doldurma, sıralama)
Homework

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 60
Semester Final Exam	1	% 40
total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
total		% 100

İş Yükü ve AKTS Kredisi Hesaplaması

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	28	4	112
Midterms	2	2	4
Final	1	3	3
Total Workload			161