Kocaeli University / European Credit Transfer System (ECTS)

Name of Lecturer(s)

Research Assistant Dr. DOĞUKAN DURDAĞ

Learning Outcomes of the Course Unit
Program Competencies-Learning Outcomes Relation

Learning Outcomes of the Course Unit

) Recognize Linear Equation Systems and Matrices
) Explain the Gaussian elimination, homogeneous equation systems, the basic matrices and inverse of the matrix
) Use the diagonal, triangular, symmetric matrices and Marquardt algorithm
) Calculate the determinant of matrix by different methods.
) Recognize Eigenvalues and eigenvectors, two and three dimensions vectors, vectors in coordinate system and vector norm
) Make a proccess on complex numbers and Complex Vector Spaces

Program Competencies-Learning Outcomes Relation

	Program Competencies
	1	2	3	4	5	6	7	8	9
Learning Outcomes
	High	High	High	No relation	High	No relation	No relation	No relation	High
	High	High	High	No relation	High	No relation	No relation	No relation	High
	High	High	High	No relation	High	No relation	No relation	No relation	High
	High	High	High	No relation	High	No relation	No relation	No relation	High
	High	High	High	No relation	High	No relation	No relation	No relation	High
	High	High	High	No relation	High	No relation	No relation	No relation	High

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Numerical Analysis

Course Contents

This course covers;systems of Linear Equations and Matrices and matrix operations, special matrices, elementary row and column operations, inverse matrix, solution of linear systems of equations, vector spaces, vector spaces, subspaces, bases and dimension, coordinates, base exchange, a matrix Range, Linear Transformations , linear transformations, kernel and rank of the linear transformation matrix, linear transformations, space, dual space, similarity, determinants, properties of determinants, determinant of a matrix, inverse matrix, Cramer's rule, eigenvalues and eigenvectors, diagonalization.

Weekly Schedule

1) Systems of Linear Equations
2) Row Echelon Form
3) Matrix Arithmetic
4) Matrix Algebra
5) Elementary Matrices
6) The Determinant of a Matrix, Properties of Determinants
7) Cramer's Rule
8) Mid-Term Exam
9) Vectors
10) Linear Independence
11) Linear Transformations
12) Matrix Representations of Linear Transformations
13) Orthogonal Matrices
14) Orthogonal Matrices
15) Eigenvalues and Eigenvectors
16) Final Exam

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	40%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required

Course Unit Title	Course Unit Code	Type of Course Unit	Level of Course Unit	Year of Study	Semester	ECTS Credits
Application Of Linear Algebras In Geophysics	JFZ339	Elective	Bachelor's degree	3	Fall	2