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

Course Introduction and Application Information

Course Code:

MATH112

Course Name:

Linear Algebra with Applications

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

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. Üy. FUNDA ÖZDEMİR

Course Lecturer(s):

Assist. Prof. Dr. FUNDA ÖZDEMIR

Course Assistants:

Course Objective and Content

Course Objectives:	To improve abstract thinking skills by equipping students with the fundamental concepts of linear algebra and to gain the ability to use these concepts in solving engineering problems.
Course Content:	Systems of linear equations and their solution sets, linear transformations, matrices and matrix operations, determinants, vector spaces, subspaces, linear independence, dimension, bases, change of basis, eigenvalues and eigenvectors, inner product, orthogonality, singular value decomposition.

Learning Outcomes

The students who have succeeded in this course;
1) Solve a system of linear equations using matrix reduction (elimination).
2) Represent linear transformations as matrices and, conversely, interpret matrices as linear maps; do basic arithmetical operations with matrices and find the inverse of an invertible matrix.
3) Compute determinant of a matrix and comprehends the properties of determinants.
4) Find the dimension and basis of a vector space and its subspaces,analyze some fundamental subspaces.
5) Compute eigenvalues and eigenvectors of a matrix via characteristic equation, identify whether a matrix is diagonalizable or not, learn how to diagonalize the symmetric matrices and to learn singular value decomposition.
6) Knows the concepts of length, distance and orthogonality in inner product spaces, and produce an orthogonal basis for any of its subspaces.

Course Flow Plan

Week	Subject	Related Preparation
1)	Systems of linear equations, row reduction and echelon forms
2)	Vector equations, the matrix equation Ax=b, solution sets of linear systems, linear independence
3)	Introduction to linear transformations;, the matrix of a linear transformation
4)	Matrix operations, the inverse of a matrix, characterization of invertible matrices
5)	Partitioned (block) matrices, LU decomposition
6)	Determinants, properties of determinants, Cramer’s rule, volume
7)	Vector spaces, subspaces, null spaces and column spaces, kernel and range of a linear transformation
8)	Midterm Exam
9)	Linearly independent sets, span, bases, coordinates
10)	Dimension, rank, change of basis
11)	Eigenvalues and eigenvectors, characteristic equation, diagonalization
12)	Inner product spaces, length, distance and orthogonality, orthogonal sets
13)	Orthogonal projections, Gram-Schmidt process and QR decomposition
14)	Diagonalization of symmetric matrices, singular value decomposition

Sources

Course Notes / Textbooks:	Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson.
References:	Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 11th Edition.

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5	6
Program Outcomes
1) Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.	3	3	3	3	3	3
2) Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose.
3) Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4) Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively.
5) Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering.
6) Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications.
10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.	3
2)	Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose.
3)	Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4)	Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively.
5)	Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering.
6)	Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems.
7)	Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8)	Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9)	Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications.
10)	Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11)	Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions.

Assessment & Grading

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

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	2		26
Application	13	0	2		26
Study Hours Out of Class	13	0	2		26
Midterms	1	13	2		15
Final	1	23	2		25
Total Workload					118