ARCHITECTURE | |||||
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 | Spring | 3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | English |
Type of course: | Non-Departmental Elective |
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) | Using the theoretical/conceptual and practical knowledge acquired for architectural design, design activities and research. | |
2) | Identifying, defining and effectively discussing aesthetic, functional and structural requirements for solving design problems using critical thinking methods. | |
3) | Being aware of the diversity of social patterns and user needs, values and behavioral norms, which are important inputs in the formation of the built environment, at local, regional, national and international scales. | |
4) | Gaining knowledge and skills about architectural design methods that are focused on people and society, sensitive to natural and built environment in the field of architecture. | |
5) | Gaining skills to understand the relationship between architecture and other disciplines, to be able to cooperate, to develop comprehensive projects; to take responsibility in independent studies and group work. | |
6) | Giving importance to the protection of natural and cultural values in the design of the built environment by being aware of the responsibilities in terms of human rights and social interests. | |
7) | Giving importance to sustainability in the solution of design problems and the use of natural and artificial resources by considering the social, cultural and environmental issues of architecture. | |
8) | Being able to convey and communicate all kinds of conceptual and practical thoughts related to the field of architecture by using written, verbal and visual media and information technologies. | |
9) | Gaining the ability to understand and use technical information about building technology such as structural systems, building materials, building service systems, construction systems, life safety. | |
10) | Being aware of legal and ethical responsibilities in design and application processes. |