NUMERICAL ANALYSIS

BİL552

Course Code: BİL552
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Master's Degree With Thesis

Year of Study

Semester

ECTS

Name of Lecturer(s)

Learning Outcomes

At the end of this course, the students;

They learn the basic concepts and techniques of numerical analysis.
They can evaluate possible calculation errors.
Learns numerical methods developed for solving mathematical problems.
Solve engineering problems by designing effective algorithms for computer systems.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

None

Course Description

Summary of some topics of mathematical analysis. Taylor's theorem. Error analysis. Error propagation. Numerical solution methods of nonlinear algebraic equations. Numerical solution methods of linear equation systems. Gaussian elimination method. Iterative Newton's method for solving nonlinear systems of equations. Interpolation and approximation with Polynomials. Lagrange and Newton polynomials. Curve fitting using the least squares method. Numerical differentiation and integration.

Course Contents

WEEK	TOPICS
1^st Week	Course introduction, review of some topics from calculus and introduction to numerical analysis
2^nd Week	Installing the R program, introduction to the program and basic operations.
3^rd Week	Error analysis, taylor series.
4^th Week	Solving Nonlinear equations (Bracketing Methods, open methods)
5^th Week	Solving Nonlinear equations (Newton Raphson method)
6^th Week	Solving a System of Linear Equations (The graphical method, Cramer's rule)
7^th Week	Solving a System of Linear Equations (Gauss elimination method)
8^th Week	Midterm exam
9^th Week	Curve fitting
10^th Week	Least Square Regression
11^th Week	Interpolation
12^th Week	Lagrange Interpolation
13^th Week	Numerical Differentiation and Integration
14^th Week	Review

Recommended or Required Reading

1. Chapra, Steven C., Canale Raymond P. (2017). Yazılım ve Programlama Uygulamalarıyla Mühendisler için Sayısal Yöntemler (4. Basımdan çeviri). Literatür Yayıncılık.
2. Bloomfield, V.A. (2014). Usign R for Numerical Analysis in Science and Engineering. A Chapman & Hall Book.
3. Howard, J.P, (2017) Computational Methods for Numerical Analysis with R. A Chapman & Hall Book.
4. Kincaid, D., Cheney, W. (2012). Nümerik Analiz-Bilimsel Hesaplama Matematiği (Üçüncü Baskıdan Çeviri). Gazi Kitabevi.
5. Tezer Sezgin, M., Bozkaya C. (2018). Numerical Analysis. ODTÜ Basım İşbirliği.

Planned Learning Activities and Teaching Methods

Lecture
Questions/Answers
Practice
Problem Solving

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	35
Assignment	2	10
Project	1	15
Total(%)		60
Contribution of In-term Studies to Overall Grade(%)		60
Contribution of Final Examination to Overall Grade(%)		40
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	2	2
Preparation for Quiz
Individual or group work
Preparation for Final exam	1	70	70
Course hours	14	3	42
Preparation for Midterm exam	1	50	50
Laboratory (including preparation)
Final exam	1	2	2
Homework	2	20	40
Presentation (including preperation)	1	40	40
Project	1	45	45
Total Work Load			291
Total Work Load / 30 (h)			9.7
ECTS Credit of the Course			10

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4
K1	X	X	X	X
K2			X
K3	X			X
K4
K5	X
K6	X	X	X
K7
K8				X
K9
K10
K11
K12