Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
5MATH381NUMERICAL ANALYSIS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course 1. Solve linear and nonlinear system of equations.
2. To use direct and iterative methods to solve Linear Systems.
3. To calculate Eigenvalues and Eigenvectors.
4. To find roots of nonlinear equations
5. To gain experience in the implementation of numerical methods by using a computer.
Course Content Convergence, stability, error analysis and conditioning. Solving systems of linear equations: The LU and Cholosky factorization, pivoting,error analysis in Gaussian elimination. Matrix eigenvalue problem, power method, orthogonal factorizations and least squares problems. Solutions of nonlinear equations. Bisection, Newton s, secant and fixed point iteration methods.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. GAMZE TANOĞLU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.

Course Category

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
Midterm exams 2 % 60
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 44 44
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 72 72
Laboratory 1 0 0
Exams and Exam Preparations 1 72 72
Total Work Load   Number of ECTS Credits 6 188

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 1. To understand the numerical methods for the basic problems of numerical analysis
2 2. Ability to solve Linear Systems and nonlinear systems
3 3. Ability to implement basic numerical methods on computer
4 4. Ability to predict the error that arises in computer implementation


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Error and computer arithmetic “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
2 Direkt metodlarSolution of system of linear equations: Direct methods “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
3 Gauss elimination, pivoting “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
4 Matrix factorizations “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
5 MIDTERM 1
6 Solution of system of linear equations: Iterative methods “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
7 Jacobi, Gauss-Seidel method “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
8 SOR method “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
9 Rootfinding “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
10 MIDTERM 2
11 Newton method “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
12 Eigenvalue problem “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
13 Nonlinear system of equations “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
14 Least squares problem “Elementary Numerical Analysis”, K. Atkinson and W. Han, 3rd Ed., Wiley 2004.
15 Final 1st week
16 Final 2nd week


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4 1 1 2
C2 4 4 4 1 2
C3 4 4
C4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=254273&lang=en