# Numerical Analysis I (MATH521) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Analysis I MATH521 3 0 0 3 5
Pre-requisite Course(s)
Consent of the department
Course Language English N/A Natural & Applied Sciences Master's Degree Face To Face Lecture, Discussion, Question and Answer, Problem Solving. Assoc. Prof. Dr. İnci Erhan This course is designed to give the expertise necessary to understand, construct and use computational methods for the numerical solution of linear algebra problems. The emphasis is on derivation and analysis of iterative methods for linear algebra problems as well as condition number, convergence, stability of algorithms and the criteria for choosing the best algorithm for the problem under consideration. The students who succeeded in this course; Understand the theoretical and practical aspects of the construction and implementation of the numerical methods Establish the advantages, disadvantages and limitations of the numerical methods and select the algorithms that converge to solutions in the most effective way Construct and apply iterative methods for the approximate solution of linear systems and eigenvalue-eigenvector problems, Estimate/determine the condition number of the linear system and condition the linear system whenever necessary Analyze the error and establish the conditions for convergence related to these methods Implement the methods and/or algorithms as computer code and use them to solve applied problems Discuss the numerical methods and/or algorithms with respect to stability, applicability, reliability, conditioning, accuracy, computational complexity and efficiency Matrix and vector norms, error analysis, solution of linear systems: Gaussian elimination and LU decomposition, condition number, stability analysis and computational complexity; least square problems: singular value decomposition, QR algorithm, stability analysis; matrix eigenvalue problems; iterative methods for solving linear systems: Jacobi, Ga

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Matrix and vector norms Atkinson- Sec. 7.3, Kress- Sec. 3.4
2 Error analysis: Absolute and relative error, floating point, round-off errors Atkinson-Sec.1.2-1.5
3 Solutions of linear systems: Gaussian elimination, pivoting and scaling Atkinson-Sec. 8.1,8.2 Kress-Sec. 2.2
4 LU decomposition Kress-Sec. 2.3,2.4
5 Condition numbers, stability, computational complexity Kress- Sec. 5.1
6 QR factorization: Householder transformation, Gram-Schmidt orthogonalization, Givens rotations Atkinson-Sec. 9.3, 9.5
7 Least square problems: Singular value decomposition Atkinson-Sec. 9.7 Kress-Sec. 5.2
8 Midterm Exam
9 Matrix eigenvalue problems: Estimates for eigenvalues, Jacobi method Atkinson-Sec. 9.1 Kress-Sec. 7.2,7.3
10 QR algorithm, Hessenberg Matrices Kress-Sec. 7.4,7.5
11 Schur factorization, Power method, Atkinson-Sec. 9.2, 9.6
12 Inverse Power method Atkinson-Sec. 9.2, 9.6
13 Iterative methods for linear systems: Jacobi Method Gauss-Seidel Method Kress-Sec. 4.1
14 Relaxation Methods Kress-Sec. 4.2
15 Conjugate gradient type methods Atkinson-Sec. 8.9
16 Final Exam

### Sources

Course Book 1. R. Kress, “Numerical Analysis: v. 181 (Graduate Texts in Mathematics)”, Kindle Edition, Springer, 1998. 2. K. E. Atkinson, “An Introduction to Numerical Analysis”, 2nd edition, John Wiley and Sons, 1989 3. G. H. Golub, C.F. Van Loan, “Matrix Computations”, North Oxford Academic, 1983. 4. R. L. Burden, R.J. Faires, “Numerical Analysis”, 9th edition, Brooks/ Cole, 2011.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area.
2 Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3 Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
4 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary.
5 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study.
6 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
8 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation.
9 Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10