Course Details

LINEAR ALGEBRA

MATH203

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS Credits
3MATH203LINEAR ALGEBRA3+0+035

Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program ENGINEERING SCIENCES
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course - Providing scientific knowledge and skills in accordance with the features of linear algebra
-Constructing theoretical and conceptual understanding of essential algebra tools like matrices, linear systems, vector spaces and building the competency to explore interactions between them.
- Developing the ability of using the notions and tools of basic linear algebra to recognize and analyze problems deduced from real life/nature and offering solutions to these problems by applying relevant computation and analysis techniques.
Course Content This course provides fundamentals of matrices, linear systems and vector spaces. In this context, matrices and operations on them, solving linear systems by using matices and basics of vector spaces are being taught. By the end of the semester, the students will be able to demonstrate understanding of matrices in every aspect, solve systems of linear equations and analyze vector spaces by means of the concepts basis and dimension.
The course covers the following topics: Matrices, Determinants, Solving Linear Systems, Vector Spaces and Bases, Linear Transformations, Eigen Spaces.
Course Methods and Techniques -
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Zübeyir Çınkır people.agu.edu.tr/zcinkir/ zubeyir.cinkir@agu.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources (Main Text Book): Linear Algebra and Its Applications, 5th Edition (or new edition). Authors: David C. Lay.
Elementary Linear Algebra, 11th Edition. Authors: Howard Anton and Chris Rorres.
Elementary Linear Algebra Authors: Bernard Kolman and David Hill.
Introduction to Linear Algebra Authors: Gilbert Strang.
Shared on One Drive

Course Category
Mathematics and Basic Sciences %100

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Yarıyıl İçi Çalışmalarının Başarı Notunun Katkısı 2 % 50
Quiz/Küçük Sınav 8 % 10
Ödev 8 % 10
Final examination 1 % 30
Total
19
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Ev Ödevi 8 2 16
Kısa Sınav 8 1 8
Yüz Yüze Ders 15 3 45
Ders Dışı Ara Sınav 2 10 20
Derse Devam 15 3 45
Final Sınavı 1 16 16
Total Work Load   Number of ECTS Credits 5 150

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Understand the concept of matrices with all the essential components including operations on matrices, invertibility, rank of a matrix and link them to other course tools.
2 Calculate determinant using row and column operations and solve application problems by using systems of linear equations
3 Establish conceptual understanding of vector spaces and explore the structural properties of them by focusing on the span set, linearly independent vectors, basis and dimension and orthogonal complements and inner products.
4 Understand linear transformations and use them in relevant applications
5 Compute eigenvalues, eigenvectors and eigenspaces of a matrix and use this information to detect diagonalizability.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Allsection numbers are from the main textbook, Linear Algebra and Its Applications, 5th Edition (or new edition). Authors: David C. Lay. 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms - Shared on OneDrive
2 1.3 Vector equations; 1.4 The matrix equation Ax=b; 1.5 Solution sets of linear systems; - Shared on One Drive
3 1.7 Linear independence; 1.8 Introduction to linear transformations; 1.9 The matrix of a linear transformation - Shared on OneDrive
4 2.1 Matrix operations; 2.2 The inverse of a matrix. 2.3 Characterization of invertible matrices; - Shared on OneDrive
5 2.5 Matrix factorization; 2.8 Subspaces of R^n; 2.9 Dimension and rank - Shared on OneDrive
6 3.1 Introduction to determinants; 3.2 Properties of determinants; 3.3 Cramer’s rule, volume, and linear transformations - Shared on OneDrive
7 MIDTERM I 4.1 Vector spaces and subspaces; 4.2 Null space, column space, and linear transformations; 4.3 Linearly independent sets, bases - Shared on OneDrive
8 Fall/Spring Brake - -
9 4.4 Coordinate systems; 4.5 The dimension of a vector space; 4.6 Rank 4.7 Change of bases; - Shared on One Drive
10 5.1 Eigenvectors and eigenvalues; 5.2 The characteristic equation 5.3 Diagonalization - Shared on OneDrive
11 5.3 Diagonalization; 5.4 Eigenvectors and linear transformations; - Shared on OneDrive
12 6.1 Inner product, length, and orthogonality; 6.2 Orthogonal sets 6.3 Orthogonal projections; - Shared on One Drive
13 MIDTERM II 6.4 The Gram-Schmidth process; 6.5 Least-square problems 6.7 Inner product spaces - Shared on One Drive
14 6.7 Inner product spaces - Shared on One Drive
15 Exercises and some Applications - Shared on One Drive


Contribution of Learning Outcomes to Programme Outcomes
C1
C2
C3
C4
C5

Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant


https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=76667&lang=en
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