COURSE INTRODUCTION AND APPLICATION INFORMATION


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;
  • will be able to determine if a linear system is consistent and solve the system by Gaussian elimination method
  • will be able to apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix using Gauss-Jordan elimination
  • will be able to apply basic concepts of linear models to various applications
  • will be able to find dimension and basis vectors of linear vector spaces and subspaces
  • will be able to find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial and diagonalize a matrix when this is possible
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

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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 Input-Output 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 Gram-Schmidt Process. Least-Squares 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.

 

EVALUATION SYSTEM

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 End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

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

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
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 up-to-date, 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

 

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