Mechanical 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:

Fall

Course Credits:

Theoretical	Practical	Credit	ECTS
2	2	3	6

Language of instruction:

Course Requisites:

MATH113 - Mathematics I

Does the Course Require Work Experience?:

Type of course:

Compulsory

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):

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
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

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; and 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 to examine engineering problems or discipline-specific research topics.
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; ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8) Awareness of the need for lifelong learning; access to knowledge, ability to follow developments in science and technology, and constant self-renewal.
9) Conform to ethical principles, and standards of professional and ethical responsibility; be informed about the standards used in engineering applications.
10) Awareness of applications in business, such as project management, risk management and change management; awareness of entrepreneurship, and innovation; information about sustainable development.
11) The ability to work effectively in disciplinary and multidisciplinary teams; individual work skill.
12) In order to gain depth at least one, physics knowledge based on chemistry knowledge and mathematics; advanced mathematical knowledge, including multivariable mathematical and differential equations; familiarity with statistics and linear algebra.
13) The ability to work in both thermal and mechanical systems, including the design and implementation of such systems.

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; and the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems.	4
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 to examine engineering problems or discipline-specific research topics.
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; ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8)	Awareness of the need for lifelong learning; access to knowledge, ability to follow developments in science and technology, and constant self-renewal.
9)	Conform to ethical principles, and standards of professional and ethical responsibility; be informed about the standards used in engineering applications.
10)	Awareness of applications in business, such as project management, risk management and change management; awareness of entrepreneurship, and innovation; information about sustainable development.
11)	The ability to work effectively in disciplinary and multidisciplinary teams; individual work skill.
12)	In order to gain depth at least one, physics knowledge based on chemistry knowledge and mathematics; advanced mathematical knowledge, including multivariable mathematical and differential equations; familiarity with statistics and linear algebra.
13)	The ability to work in both thermal and mechanical systems, including the design and implementation of such systems.

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