| SOFTWARE ENGINEERING | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT1041 | Linear Algebra | Fall | 3 | 0 | 3 | 6 |
| 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. |
|
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. |
| 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. |
| 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 |
| 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 |
| 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 | |
| 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 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Be able to specify functional and non-functional attributes of software projects, processes and products. | |
| 2) | Be able to design software architecture, components, interfaces and subcomponents of a system for complex engineering problems. | |
| 3) | Be able to develop a complex software system with in terms of code development, verification, testing and debugging. | |
| 4) | Be able to verify software by testing its program behavior through expected results for a complex engineering problem. | 4 |
| 5) | Be able to maintain a complex software system due to working environment changes, new user demands and software errors that occur during operation. | |
| 6) | Be able to monitor and control changes in the complex software system, to integrate the software with other systems, and to plan and manage new releases systematically. | |
| 7) | Be able to identify, evaluate, measure, manage and apply complex software system life cycle processes in software development by working within and interdisciplinary teams. | |
| 8) | Be able to use various tools and methods to collect software requirements, design, develop, test and maintain software under realistic constraints and conditions in complex engineering problems. | 1 |
| 9) | Be able to define basic quality metrics, apply software life cycle processes, measure software quality, identify quality model characteristics, apply standards and be able to use them to analyze, design, develop, verify and test complex software system. | 3 |
| 10) | Be able to gain technical information about other disciplines such as sustainable development that have common boundaries with software engineering such as mathematics, science, computer engineering, industrial engineering, systems engineering, economics, management and be able to create innovative ideas in entrepreneurship activities. | 5 |
| 11) | Be able to grasp software engineering culture and concept of ethics and have the basic information of applying them in the software engineering and learn and successfully apply necessary technical skills through professional life. | |
| 12) | Be able to write active reports using foreign languages and Turkish, understand written reports, prepare design and production reports, make effective presentations, give clear and understandable instructions. | |
| 13) | Be able to have knowledge about the effects of engineering applications on health, environment and security in universal and societal dimensions and the problems of engineering in the era and the legal consequences of engineering solutions. |