Course Name 
Linear Algebra and Differential Equations for Engineers

Code

Semester

Theory
(hour/week) 
Application/Lab
(hour/week) 
Local Credits

ECTS

MATH 250

Fall

3

0

3

6

Prerequisites 


Course Language 
English


Course Type 
Required


Course Level 
First Cycle


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 and/or linear differential equations by providing them with the basic knowledge on linear vector spaces, matrix operations and linear differential equations , as well as on the methods for solving and analyzing linear systems of algebraic and differential equations. 
Course Description 
The students who succeeded in this course;

Course Content  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, solution methods for first order and second order ordinary differential equations and their engineering applications, eigenvalues eigenvectors analysis and diagonalization 

Core Courses 
X

Major Area Courses  
Supportive Courses  
Media and Management Skills Courses  
Transferable Skill Courses 
Week  Subjects  Related Preparation 
1  Systems of linear equations, row reduction and echelon forms.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.1, 1.2 
2  Row reduction and echelon forms, Vector equations, The matrix equation Ax=b.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.2, 1.3, 1.4. 
3  Solution sets of linear systems, Applications of Linear Systems.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.5, 1.6 
4  Linear Independence, Introduction to Linear Transformations.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.7, 1.8 
5  The matrix of a Linear Transformations, Linear Models in Business, Science and Engineering.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.9, 1.10 
6  Matrix Operations, Review for 1. MIDTERM  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.1 
7  The inverse of a matrix, Characterization of invertible matrices, Matrix factorizations,  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.2, 2.3, 2.5 
8  Introduction to determinants, Properties of determinants, Cramer’s rule, volume and linear transformations.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 3.1, 3.2, 3.3 
9  Vector spaces and subspaces, Null Spaces, Column Spaces and Linear Transformations  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.1, 4.2 
10  Linearly Independent Sets, Bases, Application to Markov Chains.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.3, 4.9 
11  Eigenvalues and Eigenvectors, The Characteristic Equation.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 5.1, 5.2 
12  Review for 2. MIDTERM  
13  Inner Product, Length, and Orthogonality, Orthogonal Sets.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.1, 6.2 
14  The GramSchmidt Process, Review.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.3 
15  Review  
16  Review 
Course Notes/Textbooks  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition. 
Suggested Readings/Materials  1)Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 9th Edition. 2)Linear Algebra, Seymour Lipschutz, Shaum’s Outline Series, 2nd Edition. 
Semester Activities  Number  Weigthing 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exams  
Midterm 
2

60

Final Exam 
1

40

Total 
Weighting of Semester Activities on the Final Grade  2 
60 
Weighting of EndofSemester Activities on the Final Grade  1 
40 
Total 
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


Study Hours Out of Class 
16

3


Field Work  
Quizzes / Studio Critiques  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms 
2

22


Final Exam 
1

40


Total 
180

#

Program Competencies/Outcomes 
* Contribution Level


1 
2 
3 
4 
5 

1  To have adequate knowledge in Mathematics, Science, Computer Science and Software Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems. 
X  
2  To be able to identify, define, formulate, and solve complex Software Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose. 
X  
3  To be able to design, implement, verify, validate, document, measure and maintain a complex software system, process, or product under realistic constraints and conditions, in such a way as to meet the requirements; ability to apply modern methods for this purpose. 

4  To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in software engineering applications; to be able to use information technologies effectively. 

5  To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex Software Engineering problems. 
X  
6  To be able to work effectively in Software Engineering disciplinary and multidisciplinary teams; to be able to work individually. 

7  To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to be able to present effectively, to be able to give and receive clear and comprehensible instructions. 

8  To have knowledge about global and social impact of engineering practices and software applications 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 and Software Engineering solutions. 

9  To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications. 

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. 

11  To be able to collect data in the area of Software Engineering, and to be able to communicate with colleagues in a foreign language. 

12  To be able to speak a second foreign language at a medium level of fluency efficiently. 

13  To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Software Engineering. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest