COMPUTER ENGINEERING
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Ders Genel Tanıtım Bilgileri

Course Code:

1410121010

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 :

Assoc. Prof. Esengül SALTÜRK

Course Lecturer(s):

Dr.Öğr.Üyesi Recep DURANAY

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:	To introduce students the theory of systems of linear equations and a few methods of solutions.
Course Content:	Vectors and linear combinations Solving linear equations Vector spaces, subspaces Ortogonality Determinants Eigenvalues and eigenvectors

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
2 - Skills
Cognitive - Practical
1) To be able to perform matrix operations (addition, subtraction, multiplication). Calculate the determinant of a given matrix.
2) To be able 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 vector spaces and sub-vector spaces.
2) To be able 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) To be able to find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial.

Ders Akış Planı

Week	Subject	Related Preparation
1)	Vectors and linear combinations. Introduction to matrices.
2)	Linear equations. Elimination. Matrix algebra. Inverse matrix.
3)	Inverse matrix (cont.). LU Decomposition. Permutation matrices.
4)	Vector spaces. Subspaces. Nullspace. Complete solution.
5)	Independence, basis and dimension. The four fundamental subspaces.
6)	The four fundamental subspaces (cont.).
7)	Ortogonality. Review
8)	Midterm 1
9)	Projections. Least squares.
11)	Determinants. Cofactors.
12)	Cramer's Rule. Midterm 2
13)	Eigenvalues. Eigenvectors.
14)	Diagonalization. Application to difference equations.
15)	Application to difference equations (cont.). Symmetric matrices. Positive definite matrices.

Sources

Course Notes / Textbooks:	Textbook: G. Strang, Introduction to Linear Algebra, 5th Edition, Wellesley Cambridge, 2016, ISBN : 978-09802327-7-6.
References:	Textbook: G. Strang, Introduction to Linear Algebra, 5th Edition, Wellesley Cambridge, 2016, ISBN : 978-09802327-7-6.

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları	1	2	3	5	4
Program Outcomes
1) PO 1.1) Sufficient knowledge in mathematics, science and computer engineering
2) PO 1.2) Ability to apply theoretical and applied knowledge in mathematics, science and computer engineering for modeling and solving engineering problems.
3) PO 2.1) Identifying complex engineering problems
4) PO 2.2) Defining complex engineering problems
5) PO 2.3) Formulating complex engineering problems
6) PO 2.4) Ability to solve complex engineering problems
7) PO 2.5) Ability to choose and apply appropriate analysis and modeling methods
8) PO 3.1) Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions.
9) PO 3.2) Ability to apply modern design methods under realistic constraints and conditions for a complex system, process, device or product
10) PO 4.1) Developing modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications
11) PO 4.2) Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications
12) PO 4.3) Ability to use information technologies effectively.
13) PO 5.1) Examination of complex engineering problems or discipline-specific research topics, designing experiments
14) PO 5.2) Examination of complex engineering problems or discipline-specific research topics, experimentation
15) PO 5.3 ) Analysis of complex engineering problems or discipline-specific research topics, data collection
16) PO 5.4) Analyzing the results of complex engineering problems or discipline-specific research topics
17) PO 5.5) Examining and interpreting complex engineering problems or discipline-specific research topics

Ders - Öğrenme Kazanımı İlişkisi

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

	Program Outcomes	Level of Contribution
1)	PO 1.1) Sufficient knowledge in mathematics, science and computer engineering	5
2)	PO 1.2) Ability to apply theoretical and applied knowledge in mathematics, science and computer engineering for modeling and solving engineering problems.	5
3)	PO 2.1) Identifying complex engineering problems	4
4)	PO 2.2) Defining complex engineering problems	4
5)	PO 2.3) Formulating complex engineering problems	4
6)	PO 2.4) Ability to solve complex engineering problems	4
7)	PO 2.5) Ability to choose and apply appropriate analysis and modeling methods
8)	PO 3.1) Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions.
9)	PO 3.2) Ability to apply modern design methods under realistic constraints and conditions for a complex system, process, device or product
10)	PO 4.1) Developing modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications
11)	PO 4.2) Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications
12)	PO 4.3) Ability to use information technologies effectively.
13)	PO 5.1) Examination of complex engineering problems or discipline-specific research topics, designing experiments
14)	PO 5.2) Examination of complex engineering problems or discipline-specific research topics, experimentation
15)	PO 5.3 ) Analysis of complex engineering problems or discipline-specific research topics, data collection
16)	PO 5.4) Analyzing the results of complex engineering problems or discipline-specific research topics
17)	PO 5.5) Examining and interpreting complex engineering problems or discipline-specific research topics

Öğrenme Etkinliği ve Öğretme Yöntemleri

Bireysel çalışma ve ödevi
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	2	28
Study Hours Out of Class	14	8	112
Midterms	2	4	8
Final	1	3	3
Total Workload			151