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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS EED 1008 LINEAR ALGEBRA COMPULSORY 3 0 0 4

Offered By

Electrical and Electronics Engineering

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR DAMLA GÜRKAN KUNTALP

Offered to

Electrical and Electronics Engineering

Course Objective

To teach the fundamentals and main methods and techniques of linear algebra.

Learning Outcomes of the Course Unit

1   To be able to use and express the fundamental concepts of linear algebra 2   To be able to operate with matrices and vectors 3   To be able to derive the row echelon form, rank of matrices 4   To be able to analyze consistence of the system of linear algebraic equations and find solutions of the systems 5   To be able to reduce quadratic form to sum of squares in principal axes 6   To be able to find eigenvalues and corresponding to them. eigenvectors of matrices 7   To be able to solve linear equation systems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Matrix Algebra: addition, multiplication by scalar, multiplication of matrices, transpose matrix. 2 Elementary row operations, row-echelon matrices; the algorithm of the reduction of a matrix to REM; examples, rank of matrix. 3 System of linear algebraic equations, consistent and inconsistent systems. Gaussian elimination method for solving linear algebraic systems. System with infinite number of solutions, properties of solutions 4 The inverse of a square matrix, main properties of the inverse matrix; procedure of computing the inverse matrices 5 Permutations, even and odd permutations. The determinant of the square matrix, properties. Minor and cofactor of the matrix, expansion of the determinant, Midterm 1 6 Adjoin matrix, properties of adjoin matrix. Cramer s rule for solving the linear algebraic system 7 Vector spaces, axioms of the vector space, examples. Subspaces, spanning sets, span; linear dependence and linear independence of vectors and functions 8 Eigenvalues and eigenvectors of the square matrix, solving eigenvalue-eigenvector problems. Finding eigenspaces 9 Defective and non-defective matrices, similarity of matrices, diagonalizable matrices 10 Inner product, Cauchy-Schwarz inequality; orthogonal and orthonormal sets of vectors, Gram-Schmidt orthogonalization procedure. Basis and dimension of the space 11 Midterm II, The cross product in three dimensional space, norm of the cross product 12 Symmetric matrix: properties, diagonalization by orthogonal matrix 13 Quadratic forms, reduction of the quadratic form to a sum of squares, principal axes 14 Transformations of vector spaces. Structure of linear transformations. Examples of the linear transformations: the rotation and the reflection in two dimensional spaces

Recomended or Required Reading

Ana kaynak: Goode S.W., Differential Equations and Linear Algebra, Prentice Hall, New Jersey, 2002 Chapters 3,4,5,6 Yardımcı kaynaklar: Piziak R. and Odell P.L., Matrix Theory, Baylor University, Texas, 2007 Goldberg J.L., Matrix theory with applications, McGraw-hill, New York, 1992 Referanslar: Diğer ders materyalleri: PDF files of lecture notes of Prof. Dr. Valery Yakhno

Planned Learning Activities and Teaching Methods

Lectures Homeworks Examinations

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE 1 MIDTERM EXAM 1 2 MTE 2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + FIN * 0.50 5 RST RESIT 6 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

Sınavlar

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

damla.kuntalp@deu.edu.tr 02323017166

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 2 28 Preparations before/after weekly lectures 14 2 28 Preparation for midterm exam 2 4 8 Preparation for final exam 1 10 10 Preparation for quiz etc. 2 3 6 Final 1 2 2 Midterm 2 2 4 Quiz etc. 2 1 2 TOTAL WORKLOAD (hours) 88

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 5 4 LO.2 5 5 4 LO.3 5 5 4 LO.4 5 5 4 LO.5 5 5 4 LO.6 5 5 4 LO.7 5 5 4