Numerical Analysis II (MATH522) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Numerical Analysis II	MATH522	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 graduate level course is designed to give math students the expertise necessary to understand, construct and use computational methods for the numerical solution of certain problems such as root finding, interpolation, approximation and integration. The emphasis is on numerical methods for solving nonlinear equations and systems, interpolation and approximation, numerical differentiation and integration as well as the error analysis 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 nonlinear equations and systems. Choose a numerical integration or differentiation method suitable for the problem under consideration and write an interpolation polynomial 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	Iterative methods for nonlinear equations and nonlinear systems, interpolation and approximation: polynomial trigonometric, spline interpolation; least squares and minimax approximations; numerical differentiation and integration: Newton-Cotes, Gauss, Romberg methods, extrapolation, error analysis.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Iterative methods for nonlinear equation and systems: Newton’s method, Secant Method	K. Atkinson- Sec. 2.1, 2.2 ,2.3 R. Kress- Sec. 6.2
2	Iterative methods for nonlinear equation and systems: Regula Falsi, Zeros of polynomials	K.Atkinson- Sec. 2.9 R. Kress- Sec. 6.3
3	Interpolation: Lagrange and Newton interpolating polynomials	K.Atkinson- Sec. 3.1, 3.2 R. Kress- Sec.8.1
4	Interpolation: Hermite interpolating polynomial, Spline interpolation	K. Atkinson- Sec. 3.6,3.7 R. Kress- Sec. 8.3
5	Interpolation: Fourier series, trigonometric interpolation	K. Atkinson-Sec. 3.8 R. Kress- Sec. 8.2
6	Approximation: Least squres approximation	K. Atkinson- Sec. 4.1,4.3
7	Approximation: Minimax approximation	K. Atkinson- Sec. 4.2
8	Numerical differentiation	K.Atkinson- Sec. 5.7
9	Midterm Exam
10	Numerical differentiation: error analysis	K. Atkinson- Sec. 5.7
11	Numerical integration: Newton-Cotes formulae	K. Atkinson- Sec. 5.2 R. Kress- Sec. 9.1
12	Numerical integration: Gaussian quadrature	K. Atkinson-Sec. 5.3 R. Kress- Sec. 9.3
13	Numerical integration: Romberg integration	R. Kress-Sec. 9.5
14	Numerical integration: Error analysis	K. Atkinson- Sec. 5.4 R. Kress- Sec. 9.2
15	Extrapolation methods: Richardson extrapolation,	Other references
16	Final Exam

Sources

Course Book	1. R. Kress, “Numerical Analysis: v. 181 (Graduate Texts in Mathematics)”, Kindle Edition, Springer, 1998.
	3. K. E. Atkinson, “An Introduction to Numerical Analysis”, 2nd edition, John Wiley and Sons, 1989
Other Sources	4. J. Stoer, R. Bulirsch, “Introduction to Numerical Analysis”, 3rd edition
	5. 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)
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			77