Course Name 
Linear Algebra and Differential Equations for Engineers

Code

Semester

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

ECTS

MATH 250

Spring

3

0

3

6

Prerequisites 
None


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. 
Learning Outcomes 
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  
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 Models in Business, Science and Engineering, Matrix Operations 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, The inverse of a matrix, Characterization of invertible matrices.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.1, 2.2, 2.3 
7  Review  
8  Matrix factorizations, Introduction to determinants, Properties of determinants.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.5, 3.1 3.2 
9  Cramer’s rule, volume and linear transformations, Vector spaces and subspaces.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 3.3, 4.1 
10  Null Spaces, Column Spaces and Linear Transformations, Linearly Independent Sets, Bases.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.2, 4.3. 
11  Application to Markov Chains, Eigenvalues and Eigenvectors.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.9, 5.1. 
12  The Characteristic Equation, Inner Product, Length, and Orthogonality  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 5.2, 6.1. 
13  Orthogonal Sets, The GramSchmidt Process  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.2, 6.4 
14  Review  
15  Review  
16  Review 
Course Textbooks  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition. 
References  1)Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 9th Edition. 2)Linear Algebra, Seymour Lipschutz, Shaum’s Outline Series, 2nd Edition. 
Semester Requirements  Number  Percentage 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques 
4

20

Homework / Assignments 
8

10

Presentation / Jury  
Project  
Seminar / Workshop  
Portfolios  
Midterms / Oral Exams 
1

30

Final / Oral Exam 
1

40

Total 
Contribution of Semester Work to Final Grade  13 
60 
Contribution of Final Work to Final Grade  1 
40 
Total 
Activities  Number  Duration (Hours)  Workload 

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 
4

3


Homework / Assignments 
8

2


Presentation / Jury  
Project  
Seminar / Workshop  
Portfolios  
Midterms / Oral Exams 
1

22


Final / Oral Exam 
1

34


Total 
180

#

Program Qualifications / Outcomes 
* Level of Contribution


1 
2 
3 
4 
5 

1  To have sufficient background in Mathematics, Basic sciences and Biomedical Engineering areas and the skill to use this theoretical and practical background in the problems of the Biomedical Engineering. 

2  To identify, formulate and solve Biomedical Engineeringrelated problems by using stateoftheart methods, techniques and equipment; to select and apply appropriate analysis and modeling methods for this purpose. 

3  To analyze a complex system, system components or process, and to design with realistic limitations to meet the requirements using modern design techniques; to apply modern design techniques for this purpose. 

4  To choose and use the required modern techniques and tools for analysis and solution of complex problems in Biomedical Engineering applications; to skillfully use information technologies. 

5  To design and do simulation and/or experiment, collect and analyze data and interpret results for studying complex engineering problems or research topics of the discipline. 

6  To efficiently participate in intradisciplinary and multidisciplinary teams; to work independently. 

7  To communicate both in oral and written form in Turkish; to have knowledge of at least one foreign language; to have the skill to write and understand reports, prepare design and production reports, present, give and receive clear instructions. 

8  To recognize the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. 

9  To behave ethically, to be aware of professional and ethical responsibilities; to have knowledge about the standards in Biomedical Engineering applications. 

10  To have information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development. 

11  To have knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Biomedical Engineering solutions. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest