MAT1041 Linear AlgebraBahçeşehir UniversityDegree Programs ENERGY SYSTEMS ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
ENERGY SYSTEMS ENGINEERING
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT1041 Linear Algebra Spring 3 0 3 6

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Instructor MAHMOUD JAFARI SHAH BELAGHI
Course Lecturer(s): Prof. Dr. SÜREYYA AKYÜZ
Assoc. Prof. HALE GONCE KÖÇKEN
Dr. Öğr. Üyesi DİLRÜBA ÖZMEN ERTEKİN
Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components: None
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.

Learning Outcomes

The students who have succeeded in this course;
1. Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
2. Carry out matrix operations, including inverses and determinants.
3. Demonstrate understanding of the concepts of vector space and subspace.
4. Demonstrate understanding of linear independence, span, and basis.
5. Determine eigenvalues and eigenvectors and solve eigenvalue problems.
6. Apply principles of matrix algebra to linear transformations.

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.

Weekly Detailed Course Contents

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

Evaluation System

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

ECTS / Workload Table

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

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Build up a body of knowledge in mathematics, science and Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. 5
2) Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose. 2
3) Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4) Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively.
5) Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering. 3
6) Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications.
10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions.