Linear Algebra (MATH275) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Linear Algebra MATH275 3. Semester 4 0 0 4 6
Pre-requisite Course(s)
None
Course Language İngilizce
Course Type Service Courses Taken From Other Departments
Course Level Lisans
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Drill and Practice.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives 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.
Course Learning Outcomes 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.
Course Content 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
Other Sources 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

Requirements Number Percentage of Grade
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
Percentage of Final Work 40
Total 100

Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.)
4 An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively.
5 An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies.
6 An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. X
7 An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written, and technical drawings.
8 An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Consciousness on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions. X
12 Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism.

ECTS/Workload Table

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
Total Workload 86