DEPARTMENT OF ELECTRICAL-ELECTRONICS ENGINEERING
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Ders Genel Tanıtım Bilgileri

Course Code:

MAT 124

Ders İsmi:

Linear Algebra

Ders Yarıyılı:

Spring

Ders Kredileri:

Theoretical	Practical	Credit	ECTS
3	0	3	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 :

Dr.Öğr.Üyesi SELVİ DURMUŞ

Course Lecturer(s):

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:	This course aims study, learn and investigate solutions of linear systems of equations and the underlying theory
Course Content:	Linear systems of equations and their solutions, Matrices and Determinant, Vector spaces, Linear transformations, Eigenvalues and Eigenvectors

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
1) Student will be able to solve systems of linear equations using Gauss and Gauss-Jordan elimination method.
2) Student can perform matrix operations. Student can calculate the inverse of a non-singular matrix using elementary row operations.
3) Student can compute the determinant of a square matrix. Student knows how to apply Cramer's rule.
4) Student knows definition of a vector space, subspace, linear independence of vectors, spanning set, set spanning a space, basis of a finite dimensional vector space. Student knows definition of a linear transformation and its basic properties. Student can compute the matrix representation of a linear transformation according to an ordered basis.
5) Student knows how to compute eigenvalues and eigenvectors of a linear transformation. Student can diagonalize a diagonalizable square matrix.
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Ders Akış Planı

Week	Subject	Related Preparation
1)	Introduction to systems of linear equations, Gauss and Gauss-Jordan Elimination method, Elementary row operations
2)	n-dimensional Euclidean spaces R^n and C^n (real and complex Euclidean spaces), operations defined in these spaces and their properties, Cauchy-Schwarz inequality, projection
3)	Matrices and Matrix operations (Addition, Scalar Multiplication, Matrix Multiplication, Transpose), Properties of Matrix Operations
4)	Invertibility and inverse of a square matrix
5)	Determinant of a square matrix, computation of determinant using elementary row operations
6)	Properties of Determinant and Applications
7)	Review
8)	Midterm
9)	Vector Spaces, Subspace, Spanning Set, Linear Independence
10)	Basis and dimension of a vector space. Rank of a matrix, rank of a system of linear equations.
11)	Linear Transformations
12)	Kernel and image of a linear transformation, "rank + nullity = dimension of domain of linear transformation" theorem, Matrices of Linear Transformations, Basis Change
13)	Eigenvalue and Eigenvector, Diagonalizability of symmetric matrices
14)	Review

Sources

Course Notes / Textbooks:	Seymour Lipschutz, Marc Lipson. Lineer Cebir. (Çeviren: İlker Akkuş)
References:	G. Strang. Linear Algebra and its Applications. R. Larson. Elementary Linear Algebra. S. Leon, L. de Pillis. Linear Algebra with Applications. K. Hoffman, R. Kunze. Linear Algebra. N. Gürsakal, S. Çelik. Makine Öğrenmesi ve Derin Öğrenme İçin R Uygulamalı Doğrusal Cebir. A. Sabuncuoğlu. Çözümlü Lineer Cebir Alıştırmaları.

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları	1	2	3	4	5
Program Outcomes
1) 1-Knowledge by conducting scientific research in the field of engineering reaches broadly and deeply, evaluates and interprets information and applies them. 2-Up-to-date techniques and methods applied in engineering and their has a comprehensive knowledge of constraints. 3-Using limited or incomplete data to obtain information with scientific methods completes and applies; integrates knowledge from different disciplines. 4-To be aware of the new and developing practices of his/her profession, study and learn from them as needed
2) 1-Using limited or incomplete data to obtain information using scientific methods completes and applies; integrates knowledge from different disciplines. 2-Figures engineering problems and develops methods to solve them and applies innovative methods in solutions. 3-Develops new and/or original ideas and methods; develops systems, parts or develops innovative solutions in process design. 4-Designs analytical, modeling and experimental based research and apply; solve the complex situations encountered in this process and Comments.
3) 1-Lead in multi-disciplinary teams, in complex situations develops solution approaches and takes responsibility. 2-Knowledge by conducting scientific research in the field of engineering reaches broadly and deeply, evaluates and interprets information and applies them. 3-Using limited or incomplete data, using scientific methods to obtain information. completes and applies; integrates knowledge from different disciplines. 4-Figures engineering problems and develops methods to solve them and applies innovative methods in solutions. 5-Develops new and/or original ideas and methods; develops systems, parts or develops innovative solutions in process design. 6-Designs analytical, modeling and experimental based research and apply; solve the complex situations encountered in this process and Comments.
4) 1-Aware of new and emerging applications of his/her profession; examines and learns them when necessary. 2-Uses limited or incomplete data and uses scientific methods to obtain information. completes and applies; integrates knowledge from different disciplines. 3-Figures engineering problems and develops methods to solve them. and applies innovative methods in solutions. 4-Develops new and/or original ideas and methods; develops systems, parts or develops innovative solutions in process designs.
5) 1- During the stages of data collection, interpretation, announcement and social, scientific and ethical values in all professional activities observes. 2-Using limited or incomplete data and using scientific methods completes and applies; integrates knowledge from different disciplines. 3-Lead in multidisciplinary teams, in complex situations Develops solution approaches and takes responsibility. 4-To be able to analyze the processes and results of his/her studies in the field or outside the field. systematically and clearly written in national and international settings or verbally transmitted
6) 1-The process and results of his/her work in the field or outside the field systematically and clearly written in national and international settings or verbally. 2-To be able to analyze the social and environmental dimensions of engineering applications. describes. 3-Has knowledge by conducting scientific research in the field of engineering. reaches broadly and deeply, evaluates information, interprets and applies. 4-Uses limited or incomplete data and uses scientific methods to obtain information. completes and applies; integrates the knowledge of different disciplines. 5-Figures engineering problems and develops methods to solve them. and applies innovative methods in solutions. 6-Up-to-date techniques and methods applied in engineering and their have comprehensive knowledge about constraints. 7-Design analytical, modeling and experimental based research and apply; solve the complex situations encountered in this process and Comments.

Ders - Öğrenme Kazanımı İlişkisi

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

	Program Outcomes	Level of Contribution
1)	1-Knowledge by conducting scientific research in the field of engineering reaches broadly and deeply, evaluates and interprets information and applies them. 2-Up-to-date techniques and methods applied in engineering and their has a comprehensive knowledge of constraints. 3-Using limited or incomplete data to obtain information with scientific methods completes and applies; integrates knowledge from different disciplines. 4-To be aware of the new and developing practices of his/her profession, study and learn from them as needed	4
2)	1-Using limited or incomplete data to obtain information using scientific methods completes and applies; integrates knowledge from different disciplines. 2-Figures engineering problems and develops methods to solve them and applies innovative methods in solutions. 3-Develops new and/or original ideas and methods; develops systems, parts or develops innovative solutions in process design. 4-Designs analytical, modeling and experimental based research and apply; solve the complex situations encountered in this process and Comments.	5
3)	1-Lead in multi-disciplinary teams, in complex situations develops solution approaches and takes responsibility. 2-Knowledge by conducting scientific research in the field of engineering reaches broadly and deeply, evaluates and interprets information and applies them. 3-Using limited or incomplete data, using scientific methods to obtain information. completes and applies; integrates knowledge from different disciplines. 4-Figures engineering problems and develops methods to solve them and applies innovative methods in solutions. 5-Develops new and/or original ideas and methods; develops systems, parts or develops innovative solutions in process design. 6-Designs analytical, modeling and experimental based research and apply; solve the complex situations encountered in this process and Comments.	5
4)	1-Aware of new and emerging applications of his/her profession; examines and learns them when necessary. 2-Uses limited or incomplete data and uses scientific methods to obtain information. completes and applies; integrates knowledge from different disciplines. 3-Figures engineering problems and develops methods to solve them. and applies innovative methods in solutions. 4-Develops new and/or original ideas and methods; develops systems, parts or develops innovative solutions in process designs.	4
5)	1- During the stages of data collection, interpretation, announcement and social, scientific and ethical values in all professional activities observes. 2-Using limited or incomplete data and using scientific methods completes and applies; integrates knowledge from different disciplines. 3-Lead in multidisciplinary teams, in complex situations Develops solution approaches and takes responsibility. 4-To be able to analyze the processes and results of his/her studies in the field or outside the field. systematically and clearly written in national and international settings or verbally transmitted	4
6)	1-The process and results of his/her work in the field or outside the field systematically and clearly written in national and international settings or verbally. 2-To be able to analyze the social and environmental dimensions of engineering applications. describes. 3-Has knowledge by conducting scientific research in the field of engineering. reaches broadly and deeply, evaluates information, interprets and applies. 4-Uses limited or incomplete data and uses scientific methods to obtain information. completes and applies; integrates the knowledge of different disciplines. 5-Figures engineering problems and develops methods to solve them. and applies innovative methods in solutions. 6-Up-to-date techniques and methods applied in engineering and their have comprehensive knowledge about constraints. 7-Design analytical, modeling and experimental based research and apply; solve the complex situations encountered in this process and Comments.	4

Öğrenme Etkinliği ve Öğretme Yöntemleri

Anlatım
Course
Problem Çözme
Soru cevap/ Tartışma

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
Homework Assignments	1	% 10
Midterms	1	% 30
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
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	14	7	98
Midterms	1	2	2
Final	1	2	2
Total Workload			144