Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
3MATH211Linear Algebra3+0+03629.07.2024
Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program Civil Engineering
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course The course is standard first year course on linear algebra providing basic definitions, concepts and methods. Discussion and proofs are given in form of algorithms whenever is possible. The objective Concepts of basic operations in Linear algebra: Introduction to Systems of Linear Equations, Gaussian Elimination, Matrices and Matrix Operations. Inverses; Rules of Matrix Arithmetic, Elementary is twofold: to make students ready to see applications of linear algebra on subsequent courses and to enable them to continue their study on more advanced level.
Course Content Systems of linear equations. Matrices. Algebraic properties of matrix operations. Special types of matrices. Echelon form of a matrix. Solving linear systems by Gauss-Jordan reduction. Finding the inverse of a matrix by row reduction. Equivalent matrices. Determinants. Properties of determinants. Cofactor expansion. Inverse of a matrix (via its determinant). Other applications of determinants (Cramers rule). Vectors in the plane and in 3-space. Vector spaces. Subspaces. Span and linear independence. Basis and dimension. Row space. Null space. Nullity and rank of a matrix. Homogeneos systems. Change of basis. Transition matrices. Orthogonalization. Linear transformations. Kernel and range of a linear transformation.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Associate Prof.Dr. Ece Yetkin Çelikel
Name of Lecturers None
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Lectrure Notes
Course Notes Elementary Linear Algebra with Applications, 9 ed. B.Kolman, D.Hill, Person Inc.

Course Category
Mathematics and Basic Sciences %60
Engineering %40

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
Mid-terms 1 % 40
Final examination 1 % 60
Total
2
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 13 4 52
Hours for off-the-c.r.stud 14 7 98
Mid-terms 1 2 2
Final examination 1 2 2
Total Work Load   Number of ECTS Credits 5 154

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 A comprehension of mathematics (algebra, differential, integration …) and fundamentals of science
2 Ability to apply knowledge of mathematics, science and engineering to problems in electronics engineering.
3 Ability to recognize the needs and challenges of our age and to assess the global and social impact of engineering solutions
4 Ability to identify, formulate and solve engineering problems.
5 Ability to effectively communicate knowledge and opinions via written, oral visual means.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction to Systems of Linear Equations
2 Matrices and Matrix Operations, Inverses; Diagonal, Triangular and Symmetric Matrices, Rules of Matrix Arithmetic
3 Gaussian Elimination., Gauss- Jordan reduction, a method for finding inverse of a matrix
4 Solutions of system of linear equations
5 The Determinant Function, Evaluating Determinants by Row Reduction, Properties of the Determinant Function
6 Cofactor Expansion
7 Cramer’s Rule
8 MIDTERM
9 Real Vector Spaces, Subspaces
10 Linear Independence, dependence
11 Spanning set of vector spaces
12 Basis and Dimension Rank and nullity , Orthogonal Bases; Gram-Schmidt Process
13 Eigenvalues and Eigenvectors
14 Diagonalization

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
All 5 5
C1 5 5
C2 5 5
C3 5 5
C4 5 5
C5 5 5

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