Kocaeli University / European Credit Transfer System (ECTS)

Name of Lecturer(s)

Assistant Prof. Dr. Metin AŞCI

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

Learning Outcomes of the Course Unit

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

Program Competencies-Learning Outcomes Relation

Program Competencies

Learning Outcomes

High

No relation

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) Linear Equation Systems and Matrices: Introduction to Linear equation systems
2) Linear Equation Systems and Matrices: Gaussian elimination
3) Linear Equation Systems and Matrix: put it back in; homogeneous equation systems
4) Linear Equation Systems and Matrices: Matrices and matrix operations
5) Linear Equation Systems and Matrix: arithmetic and matrix inversion
6) Linear Equation Systems and Matrices: Basic matrices and finding the inverse matrix, linear equation systems and matrix inversion
7) Linear Equation Systems and Matrix: Diagonal, triangular and symmetric matrices, Marquardt algorithm.
8) Midterm examination/Assessment
9) Determinant: Old specifies the cofactor, Cramer's rule, row reduction of the determinant account
10) Determinants: Determinant function properties of eigenvalues ??and eigenvectors in Two and Three Dimensions Vectors: Coordinate system, vectors, vector norm
11) Determinants: Determinant function properties of eigenvalues ??and eigenvectors in Two and Three Dimensions Vectors: Coordinate system, vectors, vector norm
12) Complex Vector Spaces: Complex numbers, complex numbers, division, complex vector spaces Least Squares Approach: Least squares polynomial fitting with the approach of
13) Two and Three Dimensions Vectors: Cross product, size, transformation vectors, the rotation operator
14) Complex Vector Spaces: Complex numbers, complex numbers, division, complex vector spaces Least Squares Approach: Least squares polynomial fitting with the approach of
15) Complex Vector Spaces: Complex numbers, complex numbers, division, complex vector spaces, least squares approximation, and polynomial least squares approximation registration.
16) Final examination

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Group Study
6) Lab / Workshop
7) Problem Solving
8) Project Based Learning

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	30%
Contribution of Final Examination to Course Grade	70%
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	JFZ324	Elective	Bachelor's degree	3	Fall	2