Numerical Analysis I (MATH521) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Numerical Analysis I	MATH521	Area Elective	3	0	0	3	5

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Elective Courses
Course Level	Ph.D.
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Discussion, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)	Assoc. Prof. Dr. İnci Erhan
Course Assistants
Course Objectives	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.
Course Learning Outcomes	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
Course Content	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
Other Sources	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

Requirements	Number	Percentage of Grade
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
Percentage of Final Work	40
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir					X
2	Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur.				X
3	Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir				X
4	Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir			X
5	Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir.				X
6	Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir					X
7	Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir.				X
8	Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur.					X
9	Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir.	X
10	Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir.				X

ECTS/Workload Table

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
Total Workload			125