# Linear Algebra (MATH275) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear Algebra MATH275 4 0 0 4 6
Pre-requisite Course(s)
None
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Drill and Practice. This course is designed to enrich the knowledge of engineering students in linear algebra, and to teach them the basics and application of the methods for the solution of linear systems occurring in engineering problems. The students who succeeded in this course; understand the notion of matrix and perform algebraic operations on matrices, find the inverse of a nonsingular matrix, solve linear systems by using echelon form of matrices, determine the existence and uniquness of the solution and determine infinitely many solutions, if any makes sense of vector spaces, subspaces, linear independence, basis and dimensions and rank of a matrix, comprehend and use inner product, Gram-Schmidt process, orthogonal complements, understand and use linear transformation and associated matrices, evaluate determinants and solve linear systems with unique solution via determinant (Cramer’s Rule), understand and find eigenvalues and eigenvectors, determine if a matrix is diagonalizable, and if it is, diagonalize it. Linear equations and matrices, real vector spaces, inner product spaces, linear transformations and matrices, determinants, eigenvalues and eigenvectors.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Systems of Linear Equations, Matrices, Matrix Multiplication, Algebraic Properties of Matrix Operations pp. 1-39
2 Special Types of Matrices and Partitioned Matrices, Echelon Form of a Matrix, Solving Linear Systems pp. 42-49, 86-93, 95-103, 111-113
3 Elementary Matrices; Finding Inverses, Equivalent Matrices pp. 117-124, 126-129
4 Determinants, Properties of Determinants, Cofactor Expansion pp. 141-145, 146-154, 157-163
5 Inverse of a Matrix (via Its Determinant), Other Applications of Determinants (Cramer’s Rule) pp. 165-168, 169-172
6 Vectors in the Plane and In 3-D Space, Vector Spaces, Subspaces pp. 177-186, 188-196, 197-203
7 Span, Linear Independence, Basis and Dimension pp. 209-214, 216-226, 229-241
8 Homogeneous Systems, Coordinates and Isomorphism, Rank of a Matrix pp. 244-250, 253-266, 270-281
9 Inner Product Spaces, Gram-Schmidt Process pp. 290-296, 307-317, 320-329
10 Orthogonal Complements, Linear Transformations and Matrices pp. 332-343, 363-372
11 Kernel and Range of a Linear Transformation pp. 375-387
12 Matrix of a Linear Transformation pp. 389-397
13 Eigenvalues and Eigenvectors pp. 436-449
14 Diagonalization and Similar Matrices, Diagonalization of Symmetric Matrices pp. 453-461, 463-472
15 General Review
16 Final Exam

### Sources

Course Book 1. Elementary Linear Algebra, B. Kolman and D.R. Hill, 9th Edition, Prentice Hall, New Jersey, 2008 2. Linear Algebra, S. H. Friedberg, A. J. Insel, L. E. Spence, Prentice Hall, New Jersey, 1979 3. Basic Linear Algebra, Cemal Koç, Matematik Vakfı Yay., Ankara, 1996

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Adequate knowledge of mathematics, physical sciences and the subjects specific to engineering disciplines; the ability to apply theoretical and practical knowledge of these areas in the solution of complex engineering problems. X
2 The ability to define, formulate, and solve complex engineering problems; the ability to select and apply proper analysis and modeling methods for this purpose.
3 The ability to design a complex system, process, device or product under realistic constraints and conditions in such a way as to meet the specific requirements; the ability to apply modern design methods for this purpose.
4 The ability to select, and use modern techniques and tools needed to analyze and solve complex problems encountered in engineering practices; the ability to use information technologies effectively.
5 The ability to design experiments, conduct experiments, gather data, and analyze and interpret results for investigating complex engineering problems or research areas specific to engineering disciplines.
6 The ability to work efficiently in inter-, intra-, and multi-disciplinary teams; the ability to work individually.
7 (a) Sözlü ve yazılı etkin iletişim kurma becerisi; etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi. (b) En az bir yabancı dil bilgisi; bu yabancı dilde etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi.
8 Recognition of the need for lifelong learning; the ability to access information, follow developments in science and technology, and adapt and excel oneself continuously.
9 Acting in conformity with the ethical principles; professional and ethical responsibility and knowledge of the standards employed in engineering applications.
10 Knowledge of business practices such as project management, risk management, and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development.
11 Knowledge of the global and social effects of engineering practices on health, environment, and safety issues, and knowledge of the contemporary issues in engineering areas; awareness of the possible legal consequences of engineering practices.
12 (a) Knowledge of (i) fluid mechanics, (ii) heat transfer, (iii) manufacturing process, (iv) electronics and control, (v) vehicle components design, (vi) vehicle dynamics, (vii) vehicle propulsion/drive and power systems, (viii) technical laws and regulations in automotive engineering field, and (ix) vehicle verification tests. (b) The ability to merge and apply these knowledge in solving multi-disciplinary automotive problems.
13 The ability to make use of theoretical, experimental, and simulation methods, and computer aided design techniques in automotive engineering field.
14 The ability to work in the field of vehicle design and manufacturing.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 10 10