Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT441 - MATHEMATICS

Code: MAT441 Course Title: MATRICES ALGEBRA I Theoretical+Practice: 4+0 ECTS: 6
Year/Semester of Study 4 / Fall Semester
Level of Course 1st Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEZER SORGUN (ssorgun@nevsehir.edu.tr)
Name of Lecturer(s)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
To define the operations on matrices and apply the methods of it to other discipline.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Can understand matrix operations in advance level. PO-4 Analytically use the interdisciplinary approach at learning process.
Examination
LO-2 Can also apply matrices to other discipline. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education.
Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Matrices and matrix operations, Common linear equations, Square matrices, Determinants, Vectors, Eigenvalues and eigenvectors, Matrix funcitons, Canonical basis,Similarity, Inner products, Norms
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Matrices ,Vectors and dot products, Matrix addition and matrix subtraction, Teaching topic and applications
2 Scalar multiplication and matrix multiplication, Row-echelon form,Elementary row and column operations, Rank Teaching topic and applications
3 Consistency, Matrix notation, Theory of solutions,Simpliflying operations, Gaussian elimination algorthm, Pivoting strategies Teaching topic and applications
4 Diagonals, Elementary matrices, LU decomposition,Simultaneous linear equations, Powers of a matrix Teaching topic and applications
5 The inverse , Simple inverses, Calculating inverses, Simultaneous linear equations, Properties of the inverse Teaching topic and applications
6 Expansion by cofactors, Properties of determinants, Determinants of partitioned matrices,Pivotal condensation, Inversion by determinants Teaching topic and applications
7 Dimension,Linear dependence and independence, Linear combinations,Properties of linearly dependent vectors, Row rank and column rank Teaching topic and applications
8 mid-term exam
9 Characterictic equation, Properties of eigenvalues and eigenvectors, Linearly independent eigenvectors, ,Computational considerations, The Cayley-Hamilton theorem Teaching topic and applications
10 Sequences and series of matrices, Well-defined functions,Computing functions of matrices Teaching topic and applications
11 The function e, Differentiation and integration of matrices, Differential equations, The matrix equation AX+XB=C Teaching topic and applications
12 Generalized eigenvectors,Chains,Canonical basis, The minimum polynomial Teaching topic and applications
13 Similar matrices, Modal matrix, Jordan canonical form, Similarty and Jordan canonical form, Functions of matrices Teaching topic and applications
14 Complex conjugates, The inner product, Properties of inner products Orthogonality, Gram-Schmidt ortogonalization Teaching topic and applications
15 Vector norms, Normalized vectors and distance, Matrix norms, Induced norms, Compatility, Spectral radius Teaching topic and applications
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Matris işlemleri, R.Bronson, Çeviri Editörü: H.H.Hacısalihoğlu, Schaum's outlines,Nobel yayın dağıtım,1989.
Required Course instruments and materials
The lecture books

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 4 14 56
Outside Class
       a) Reading 2 14 28
       b) Search in internet/Library 3 14 42
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 3 7 21
mid-term exam 2 1 2
Own study for final exam 3 7 21
final exam 2 1 2
0
0
Total work load; 172