Computer Engineering (English)
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

General course introduction information

Course Code: MATH215
Course Name: Mathematics III
Course Semester: Spring
Course Credits:
Theoretical Practical Credit ECTS
2 2 3 6
Language of instruction: EN
Course Requisites: MATH113 - Mathematics I
Does the Course Require Work Experience?: No
Type of course:
Course Level:
Bachelor TR-NQF-HE:6. Master`s Degree QF-EHEA:First Cycle EQF-LLL:6. Master`s Degree
Mode of Delivery: Face to face
Course Coordinator : Dr.Öğr.Üyesi MESERET TUBA GÜLPINAR
Course Lecturer(s): Prof. Dr. SEZGİN SEZER
Prof. Dr. VASFİ ELDEM
Prof. Dr. HASAN ÖZEKES
Course Assistants:

Course Objective and Content

Course Objectives: The aim of this course to understand basic concepts of linear algebra ( systems of linear equations and their solutions, the operations of the matrix and vector algebra, evaluations of the determinants and inverse matrix, properties of determinants, Cramer’s Rule, vector spaces, subspaces, linear independence, basis, row space, column space, null space, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt process, least squares, orthogonal diagonalization and singular value decomposition) and solve problems about it.

Course Content: This course will investigate systems of linear equations and their solutions, the operations of the matrix and vector algebra, evaluations of the determinants and inverse matrix, properties of determinants, Cramer’s Rule, vector spaces, subspaces, linear independence, basis, row space, column space, null space, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt process, least squares, orthogonal diagonalization and singular value decomposition.

Learning Outcomes

The students who have succeeded in this course;
Learning Outcomes
1 - Knowledge
Theoretical - Conceptual
1) Able to calculate the set of all solutions for systems of linear equations if it exists, by using row echelon or reduced row echelon forms. Calculate the inverse of a square matrix, if it exists, using reduced row echelon form or elementary matrices and characterize invertible matrices.
2) Calculate the determinant of a square matrix. Use Cramers Rule to solve linear systems of equations. Determine the linear dependence or independence of a set of nonzero vectors.
3) Identify vectors spaces and subspaces and linear transformations between vector spaces. Calculate basis for null spaces and images of linear transformations. Calculate the representation of linear transformation under various bases.
4) Able to calculate the eigenvalues and the corresponding eigenvectors in order to diagonalize a square matrix by similarity transformation. Characterize diagonalizable matrices
5) Able to use Gram-Schmidt Process to obtain a set of orthogonal vectors and diagonalize a symmetric matrix using orthogonal matrices. Calculate orthogonal projections onto a given subspace and solve the least squares problems. Calculate Singular Value Decomposition of a given matrix.
2 - Skills
Cognitive - Practical
3 - Competences
Competence to Work Independently and Take Responsibility
Field Specific Competence
Learning Competence
Communication and Social Competence

Lesson Plan

Week Subject Related Preparation
1) Syllabus. Systems of linear equations. Elementary row operations. Gauss-Jordan Elimination Lecture Notes
2) Matrix Algebra Lecture Notes
3) Matrix Algebra Lecture Notes
4) Determinants Lecture Notes
5) Determinants Lecture Notes

Sources

Course Notes / Textbooks: Linear Algebra and Its Applications, 5th Edition
David C. Lay, Stephan R. Lay, Judi J. McDonald
Pearson Education Limited
References: Lecture notes - Ders notları

Course-Program Learning Outcome Relationship

Learning Outcomes

1

2

3

4

5
Program Outcomes
1) Sufficient knowledge in mathematics, science and engineering related to their branches; the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems.
2) The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modeling methods for this purpose.
3) The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. (Realistic constraints and conditions include such issues as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, according to the nature of design.)
4) Ability to develop, select and use modern techniques and tools necessary for engineering applications; ability to use information technologies effectively.
5) Ability to design experiments, conduct experiments, collect data, analyze and interpret results for examination of engineering problems.
6) The ability to work effectively in disciplinary and multidisciplinary teams; individual work skill.
7) Effective communication skills in Turkish oral and written communication; at least one foreign language knowledge.
8) Awareness of the need for lifelong learning; access to knowledge, ability to follow developments in science and technology, and constant self-renewal.
9) Professional and ethical responsibility.
10) Information on project management and practices in business life such as risk management and change management; awareness about entrepreneurship, innovation and sustainable development.
11) Information on the effects of engineering applications on health, environment and safety in the universal and social dimensions and the problems of the times; awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Sufficient knowledge in mathematics, science and engineering related to their branches; the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems.
2) The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modeling methods for this purpose. 1
3) The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. (Realistic constraints and conditions include such issues as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, according to the nature of design.) 4
4) Ability to develop, select and use modern techniques and tools necessary for engineering applications; ability to use information technologies effectively. 2
5) Ability to design experiments, conduct experiments, collect data, analyze and interpret results for examination of engineering problems.
6) The ability to work effectively in disciplinary and multidisciplinary teams; individual work skill. 5
7) Effective communication skills in Turkish oral and written communication; at least one foreign language knowledge.
8) Awareness of the need for lifelong learning; access to knowledge, ability to follow developments in science and technology, and constant self-renewal.
9) Professional and ethical responsibility.
10) Information on project management and practices in business life such as risk management and change management; awareness about entrepreneurship, innovation and sustainable development. 3
11) Information on the effects of engineering applications on health, environment and safety in the universal and social dimensions and the problems of the times; awareness of the legal consequences of engineering solutions.

Learning Activity and Teaching Methods

Lesson
Reading
Homework
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)
Homework

Assessment & Grading

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 5 % 20
Midterms 2 % 40
Final 1 % 40
total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
total % 100

Workload and ECTS Credit Grading

Activities Number of Activities Duration (Hours) Workload
Course Hours 15 4 60
Study Hours Out of Class 15 3 45
Homework Assignments 5 5 25
Midterms 2 10 20
Final 1 15 15
Total Workload 165