Course Name  Linear Algebra I 
Code  Semester  Theory (hour/week)  Application/Lab (hour/week)  Local Credits  ECTS 

MATH 105  Fall  2  2  3  6 
Prerequisites  None  
Course Language  English  
Course Type  Required  
Course Level  First Cycle  
Mode of Delivery    
Teaching Methods and Techniques of the Course  
Course Coordinator    
Course Lecturer(s)  
Assistant(s)   
Course Objectives  Linear Algebra I course is a theoretic course which is a base for most of variety of mathematical theories including the subjects such as solutions of linear systems of equations, the concepts of matrices, determinants, vectors in n dimensions and vector spaces. This course starts with the introduction of linear systems, the correspondence with matrices and continues with the solutions of linear systems, determinants of matrices and vector spaces. These fundamental topics will be used and improved in a variety of mathematical courses. 
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, 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 Managment Skills Courses  
Transferable Skill Courses 
Week  Subjects  Required Materials 
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  Vector Equations. Solution Sets of Linear Systems.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.3, 1.5, 
3  Applications of Linear Systems. Linear Independence.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.6, 1.7 
4  Introduction to 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 1.8, 1.10 
5  Matrix Operations. The Inverse of a Matrix. Characterizations 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 
6  Partitioned Matrices. Matrix Factorizations. The Leontief InputOutput Model. Midterm Exam 1.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.4, 2.5, 2.6 
7  Applications to Computer Graphics. Introduction of Determinants. Properties of Determinants  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.7, 3.1, 3.2 
8  Cramer’s Rule. 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 3.3, 4.1 4.2 
9  Linearly Independent Sets; Bases. The Dimension of a vector space. Rank  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.3, 4.5, 4.6 
10  Coordinate Systems. Change of a Basis. Applications to Difference Equations.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.4, 4.7, 4.8 
11  Applications to Markov Chains. Eigenvectors and Eigenvalues. The Characteristic Equation.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.9, 5.1, 5.2 
12  Diagonalization. Inner Product, Length and Orthogonality. Midterm  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 5.3, 6.1 
13  Orthogonal Projections. Orthogonal Sets.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.2, 6.3 
14  The GramSchmidt Process. LeastSquares Problems.  Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.4, 6.5 
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  5  20 
Portfolio  
Homework / Assignments  10  10 
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterm  1  30 
Final Exam  1  40 
Total 
Weighting of Semester Activities on the Final Grade  16  60 
Weighting of EndofSemester Activities on the Final Grade  1  40 
Total 
Semester Activities  Number  Duration (Hours)  Workload 

Course Hours (Including exam week: 16 x total hours)  16  4  64 
Laboratory / Application Hours (Including exam week: 16 x total hours)  16  
Study Hours Out of Class  15  3  
Field Work  
Quizzes / Studio Critiques  2  
Portfolio  
Homework / Assignments  10  1  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms  2  11  
Final Exams  1  20  
Total  161 
#  Program Competencies/Outcomes  * Contribution Level  
1  2  3  4  5  
1  To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics.  X  
2  To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics,  X  
3  To be able to define and analyze problems and to find solutions based on scientific methods,  X  
4  To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,  X  
5  To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,  X  
6  To be able to criticize and renew her/his own models and solutions,  X  
7  To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way,  X  
8  To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge uptodate, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,  X  
9  To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,  
10  To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,  
11  To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,  X  
12  By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,  X  
13  To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,  
14  To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,  X  
15  To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest