Food 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:

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):

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
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) Has sufficient background in mathematics, science and engineering related fields.
2) Uses the theoretical and practical knowledge in mathematics, science and their fields together for engineering solutions.
3) Identifies, formulates and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques for this purpose.
4) Analyze a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods accordingly.
5) Selects and uses the modern techniques and tools necessary for engineering applications.
6) Design experiments, conduct experiments, collect data, analyze and interpret results.
7) Works individually and in multi-disciplinary teams.
8) Accesses information and conducts resource research for this purpose, uses databases and other information sources.
9) Accesses information and conducts resource research for this purpose, uses databases and other information sources.
10) Accesses information and conducts resource research for this purpose, uses databases and other information sources.
11) Uses the theoretical and practical knowledge in mathematics, science and their fields together for engineering solutions.
12) Identifies, formulates and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques for this purpose.
13) Analyze a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods accordingly.
14) Selects and uses the modern techniques and tools necessary for engineering applications.
15) Works individually and in multi-disciplinary teams
16) Uses information and communication technologies together with computer software required by the field at least Advanced Level of European Computer Skills License.
17) Communicate effectively verbally and in writing; use a foreign language at least at level B1 of the European Language Portfolio.
18) Communicates using technical drawing.
19) Accesses information and conducts resource research for this purpose, uses databases and other information sources.
20) Becomes aware of the universal and social effects of engineering solutions and applications; entrepreneurship and innovation and have knowledge about the problems of the age.
21) Has professional and ethical responsibility.
22) Have awareness of project management, workplace practices, employee health, environmental and occupational safety; the legal consequences of engineering applications.
23) Demonstrates awareness of the universal and social impact of engineering solutions and applications; is aware of entrepreneurship and innovation and has knowledge about the problems of the age.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Has sufficient background in mathematics, science and engineering related fields.	5
2)	Uses the theoretical and practical knowledge in mathematics, science and their fields together for engineering solutions.	5
3)	Identifies, formulates and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques for this purpose.	5
4)	Analyze a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods accordingly.	5
5)	Selects and uses the modern techniques and tools necessary for engineering applications.	5
6)	Design experiments, conduct experiments, collect data, analyze and interpret results.	4
7)	Works individually and in multi-disciplinary teams.	5
8)	Accesses information and conducts resource research for this purpose, uses databases and other information sources.	4
9)	Accesses information and conducts resource research for this purpose, uses databases and other information sources.	4
10)	Accesses information and conducts resource research for this purpose, uses databases and other information sources.	4
11)	Uses the theoretical and practical knowledge in mathematics, science and their fields together for engineering solutions.	5
12)	Identifies, formulates and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques for this purpose.	5
13)	Analyze a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods accordingly.	5
14)	Selects and uses the modern techniques and tools necessary for engineering applications.	5
15)	Works individually and in multi-disciplinary teams	5
16)	Uses information and communication technologies together with computer software required by the field at least Advanced Level of European Computer Skills License.	5
17)	Communicate effectively verbally and in writing; use a foreign language at least at level B1 of the European Language Portfolio.	5
18)	Communicates using technical drawing.
19)	Accesses information and conducts resource research for this purpose, uses databases and other information sources.
20)	Becomes aware of the universal and social effects of engineering solutions and applications; entrepreneurship and innovation and have knowledge about the problems of the age.
21)	Has professional and ethical responsibility.
22)	Have awareness of project management, workplace practices, employee health, environmental and occupational safety; the legal consequences of engineering applications.
23)	Demonstrates awareness of the universal and social impact of engineering solutions and applications; is aware of entrepreneurship and innovation and has knowledge about the problems of the age.

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