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

Ders Genel Tanıtım Bilgileri

Course Code:

MAT1041

Ders İsmi:

Linear Algebra

Ders Yarıyılı:

Fall
Spring

Ders Kredileri:

Theoretical	Practical	Credit	ECTS
3	0	3	6

Language of instruction:

English

Ders Koşulu:

Ders İş Deneyimini Gerektiriyor mu?:

Type of course:

Non-Departmental Elective

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 :

Instructor MAHMOUD JAFARI SHAH BELAGHI

Course Lecturer(s):

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:

To define matrix operations such as addition, multiplication, inversion and to prove some of related properties; To teach to solve a system of linear equations by using matrices; To give the definitions of a vector space, subspace, base and dimension and to prove some of related theorems; To introduce the notion of a linear map and the types of linear maps (such as injective, surjective and bijective); To teach the matrix representation of linear mappings and proving some of related properties; To construct the space of linear mappings and to give its structural properties; To define the transpose of a linear functional and to prove related properties.

Course Content:

Systems of linear equations, matrices; Vector spaces, subspaces, base and dimension, coordinate; Linear mappings, kernel and image subspaces; Matrix representations of linear mappings; Linear functional, transpose of a linear mapping. Eigenvalues and eigenvectors, diagonalization of matrices.

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
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 - Gaussian Elimination and Gauss-Jordan Elimination
2)	- Operations with Matrices - Properties of Matrix Operations
3)	- The Inverse of a Matrix
4)	- The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations
5)	- Properties of Determinants
6)	- Vectors in R^n - Vector Spaces \ review.
7)	- Subspaces of Vector Spaces - Spanning Sets and Linear Independence
8)	- Basis and Dimension
9)	- Rank of a Matrix and Systems of Linear Equations
10)	- Introduction to Linear Transformations
11)	- The Kernel and Range of a Linear Transformation
12)	- Matrices for Linear Transformations - Transition Matrices and Similarity \ review.
13)	- Eigenvalues and Eigenvectors - Diagonalization
14)	- Symmetric Matrices and Orthogonal Diagonalization

Sources

Course Notes / Textbooks:	Elementary Linear Algebra, Howard Anton, Wiley Publishing Co. (2000)
References:	1.Lang, S., "Linear Algebra", Addison-Wesley Publishing Company, (1968). 2.Hoffman, K. M., Kunze R. A., "Linear Algebra", Printice Hall, 2. edition, (1971). 3.Koç, C., "Basic Linear Algebra", Matematik Vakfı, (1995). 4. Lipschutz, S., "Linear Algebra, Schaum’s Outline Series", McGraw-Hill, Inc., (1974). 5.Kolman, B., Hill, D. R., "Introductory Algebra with Applications", Prentice Hall

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları
Program Outcomes
1) Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3) Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4) Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively.
5) Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics.
6) Ability to work effectively within and multi-disciplinary teams; individual study skills.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8) Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology.
9) To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety.
10) Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions.

Ders - Öğrenme Kazanımı İlişkisi

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

	Program Outcomes	Level of Contribution
1)	Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
2)	Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3)	Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4)	Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively.
5)	Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics.
6)	Ability to work effectively within and multi-disciplinary teams; individual study skills.
7)	Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8)	Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology.
9)	To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety.
10)	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11)	Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions.

Öğrenme Etkinliği ve Öğretme Yöntemleri

Ölçme ve Değerlendirme Yöntemleri ve Kriterleri

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 60
Final	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	14	7	98
Midterms	2	2	4
Final	1	2	2
Total Workload			146