FACULTY OF ENGINEERING
Department of Mechatronics Engineering
MATH 250 | Course Introduction and Application Information
| Course Name |
Linear Algebra for Engineers
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 250
|
Spring
|
3
|
0
|
3
|
6
|
| Prerequisites |
|
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| Course Language |
English
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| Course Type |
Required
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| Course Level |
First Cycle
|
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| Mode of Delivery | - | |||||||||
| Teaching Methods and Techniques of the Course | Problem SolvingQ&ALecture / Presentation | |||||||||
| Course Coordinator | ||||||||||
| Course Lecturer(s) | ||||||||||
| Assistant(s) | ||||||||||
| Course Objectives | The main objective of this course is to establish a basic mathematical background for the students who will receive engineering courses based on linear algebra by providing them with the basic knowledge on linear vector spaces, matrix operations as well as on the methods for solving and analyzing linear systems of algebraic equations. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | The main subjects of the course are the vector and matrix operations, linear independence and dependence of vectors, linear vector spaces and subspaces, dimensions and basis vectors for vector spaces, linear transformations, determinants, eigenvalue and eigenvectors. |
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Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Systems of linear equations, row reduction and echelon forms, vector equations | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, D0avid C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, 1.3 |
| 2 | The matrix equation Ax=b, Solution sets of linear systems, applications of linear systems | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.4, 1.5, 1.6 |
| 3 | Linear Independence, introduction to linear transformations | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.7, 1.8 |
| 4 | The matrix of a linear transformations, linear models in business, science and engineering | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.9, 1.10 |
| 5 | Matrix operations, The inverse of a matrix | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.1, 2.2 |
| 6 | Characterization of invertible matrices, Matrix factorizations | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.3, 2.5 |
| 7 | Midterm | |
| 8 | Introduction to determinants, properties of determinants, | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.1, 3.2, 3.3 |
| 9 | Cramer’s rule, volume, and linear transformations, Vector spaces and subspaces | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.3, 4.1 |
| 10 | Null spaces, column spaces, and linear transformations, Linearly independent sets, bases | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.2, 4.3 |
| 11 | The dimension of a vector space, Rank, Application for Markov chains | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.5, 4.6, 4.9 |
| 12 | Eigenvalues and eigenvectors, The characteristic equation, Diagonalization | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.1, 5.2, 5.3 |
| 13 | Diagonalization, Inner product, length, and orthogonality, orthogonal sets | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.3, 6.1, 6.2 |
| 14 | The Gram-Schmidt process, review | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Section 6.4 |
| 15 | Semester review | |
| 16 | Final exam |
| Course Notes/Textbooks | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). ISBN-13:978-0321982384 |
| Suggested Readings/Materials |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques |
5
|
20
|
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
30
|
| Final Exam |
1
|
50
|
| Total |
| Weighting of Semester Activities on the Final Grade |
6
|
50
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
50
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
5
|
6
|
30
|
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
28
|
28
|
| Final Exam |
1
|
32
|
32
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To have knowledge in Mathematics, science, physics knowledge based on mathematics; mathematics with multiple variables, differential equations, statistics, optimization and linear algebra; to be able to use theoretical and applied knowledge in complex engineering problems |
X | ||||
| 2 | To be able to identify, define, formulate, and solve complex mechatronics engineering problems; to be able to select and apply appropriate analysis and modeling methods for this purpose. |
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| 3 | To be able to design a complex electromechanical system, process, device or product with sensor, actuator, control, hardware, and software to meet specific requirements under realistic constraints and conditions; to be able to apply modern design methods for this purpose. |
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| 4 | To be able to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Mechatronics Engineering applications; to be able to use information technologies effectively. |
X | ||||
| 5 | To be able to design, conduct experiments, collect data, analyze and interpret results for investigating Mechatronics Engineering problems. |
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| 6 | To be able to work effectively in Mechatronics Engineering disciplinary and multidisciplinary teams; to be able to work individually. |
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| 7 | To be able to communicate effectively in Turkish, both in oral and written forms; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions. |
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| 8 | To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions. |
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| 9 | To be aware of ethical behavior, professional and ethical responsibility; information on standards used in engineering applications. |
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| 10 | To have knowledge about industrial practices such as project management, risk management and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development. |
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| 11 | Using a foreign language, he collects information about Mechatronics Engineering and communicates with his colleagues. ("European Language Portfolio Global Scale", Level B1) |
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| 12 | To be able to use the second foreign language at intermediate level. |
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| 13 | To recognize the need for lifelong learning; to be able to access information; to be able to follow developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechatronics Engineering. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
