NUMERICAL ANALYSIS TECHNIQUES

MAT311

Course Code: MAT311
Semester: Fifth Term (Fall)
Theory+Practice: 3 + 2
ECTS: 5

Course Type

Compulsory Course

Course Level

Bachelor's Degree

Year of Study

Semester

Fifth Term (Fall)

ECTS

Name of Lecturer(s)

Assistant Professor Elmas Burcu Mamak Ekinci

Learning Outcomes

At the end of this course, the students;

Learn the basic concepts and techniques of numerical analysis.
Evaluate the possible calculation errors.
Learn their knowledge about nonlinear equations, numerical solution methods of linear equation systems.
Learn the techniques of interpolation and approximation with polynomials.
Apply the method of curve fitting by least squares method.
Be able to use numerical methods to solve optimization problems.

Mode of Delivery

Face to face

Prerequisites

Yes(MAT151)

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	Introduction to Numerical Analysis
2^nd Week	Mathematical Background
3^rd Week	Introduction to R Programming Language
4^th Week	Error Analysis, The Taylor Series
5^th Week	Roots of Equations
6^th Week	Roots of Equations
7^th Week	Linear Algebraic Equations
8^th Week	Midterm
9^th Week	Linear Algebraic Equations
10^th Week	Curve Fitting-Least Square Regression
11^th Week	Least Square Regression
12^th Week	Interpolation
13^th Week	Lagrange Interpolation
14^th Week	Numerical Differentiation and Integration
15^th Week	Numerical Differentiation and Integration

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
Problem Solving
Practice

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	30
Assignment	2	10
Quiz	3	20
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	1.5	1.5
Preparation for Quiz	3	4	12
Individual or group work
Preparation for Final exam	1	30	30
Course hours	14	5	70
Preparation for Midterm exam	1	25	25
Laboratory (including preparation)
Final exam	1	1.5	1.5
Homework	2	5	10
Quiz	3	0.8	2.4
Total Work Load			152.4
Total Work Load / 30 (h)			5.08
ECTS Credit of the Course			5

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4	LO5	LO6
K1	X	X	X	X	X	X
K2	X		X	X		X
K3	X
K4
K5	X
K6	X
K7
K8
K9
K10
K11