MATH 403 | Course Introduction and Application Information - Department of Mathematics

Course Name

Numerical Analysis I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 403	Fall	3	0	3	6

Prerequisites	None
Course Language	English
Course Type	Required
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Problem Solving Q&A Lecture / Presentation
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Araş. Gör. Dr. Ayşe BELER Araş. Gör. Merve KAHRAMAN ARİMAN Araş. Gör. Sıla Selenay KOÇ

Course Objectives

The objective of this course is to introduce numerical methods to solve problems, error analysis and error estimation, and to implement numerical methods by using a computer.

Learning Outcomes

The students who succeeded in this course;

calculate roots of functions using several numerical methods.
write an algorithm about root finding methods.
find interpolation polynomial using Lagrange and Newton’s divided differences methods.
use Chebyshev interpolation and cubic splines for approximating functions.
analyze interpolation error.
use least squares method to solve linear and nonlinear systems of equations.
model problems using least squares method.
solve problems using QR factorization.

Course Description

In this course numerical solutions of nonlinear equations will be discussed. Several interpolation methods will be given. Least squares problems will be solved.

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Fundamentals	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 0
2	Solving equations: The Bisection Method, Fixed-Point Iteration	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 1
3	Limits of Accuracy, Newton’s Method	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 1
4	Root-Finding without Derivatives	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 1
5	Data and Interpolating Functions: Lagrange interpolation	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 3
6	Newton’s divided differences, How many degree d polynomials pass through n points?	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 3
7	Interpolation Error	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 3
8	Midterm Exam
9	Chebyshev Interpolation	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 3
10	Cubic Splines	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 3
11	Least Squares and the Normal Equations	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 4
12	A Survey of Models	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 4
13	QR Factorization	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 4
14	Nonlinear Least Squares	Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 4
15	Semester review
16	Final exam

Course Notes/Textbooks

Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012)

ISBN-13: 978-0-321-78367-7

Suggested Readings/Materials

''Numerical Methods for Engineers and Scientists: An Introduction with Applications using MATLAB'' by Gilat and Subramaniam, Wiley,3rd edition,2013,ISBN-13:978-1118554937

Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004,ISBN-13:978-0130652485

Numerical Analysis by Münevver Tezer, ODTÜ Basım İŞliği, 2018.ISBN-13:9789754293777

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	2	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	1	20	20
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	40	40
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	X	-
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	X	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	-	-	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	-	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	X	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	X	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-