MATHEMATICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT3012	Numerical Analysis	Fall	2	2	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Hybrid
Course Coordinator :	Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
Course Lecturer(s):	Dr. UTKU GÜLEN Dr. Öğr. Üyesi ERKUT ARICAN RA ÇİĞDEM ERİŞ Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
Recommended Optional Program Components:	None
Course Objectives:	Numerical Analysis is concerned with the mathematical derivation, description and analysis of obtaining numerical solutions of mathematical problems. We have several objectives for the students. Students should obtain an intuitive and working understanding of some numerical methods for the basic problems of numerical analysis. They should gain some appreciation of the concept of error and of the need to analyze and predict it. Topics cover linear and nonlinear system of equations, interpolation, curve fitting using least-squares method integration, eigenvalue, and singular value decomposition. And also they should develop some experience in the implementation of numerical methods by using MATLAB.

Learning Outcomes

The students who have succeeded in this course;
1. Define errors, big O notation, use Taylor’s theorem
2. Solve nonlinear algebraic equations
3. Solve linear systems and to use iterative methods for linear systems
4. Solve systems of nonlinear algebraic equations
5. Use interpolation methods and polynomial approximation for a given data, piecewise linear interpolation and spline function interpolation;
6. Use least-squares method for curve fitting
7. Calculate maximum eigenvalues and corresponding eigenvectors and to calculate singular value decomposition of a matrix and apply it on image processing
8. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory.

Course Content

The course studies algorithms and computer techniques for solving mathematical problems. They do all computations using MATLAB.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Introduction to Numerical Analysis: kinds of problems we solve. Error analysis, round-off and truncation errors. Taylor Theorem and Taylor series.
2)	Loss of Significance Big O notation
3)	Solution of Nonlinear Equations, i.e. f(x)=0. Bracketing Methods for Locating a Root. Bisection (Method of Bolzano). False-position (Regula-Falsi) Method.
4)	Newton-Raphson Method (Applications from thermodynamics, fluid mechanics, and electronics)
5)	Solution of Linear Systems of Equations. Properties of Vectors and Matrices. Upper-Triangular Linear Systems. Gaussian Elimination and Pivoting.
6)	Triangular Factorization (LU Decomposition)
7)	Iterative Methods for Linear Systems. Jacobi Method. Gauss-Sedidel Method.
8)	Iterative Methods for Linear Systems Gauss-Sedidel Method. Diagonally dominant matrix. Errors is solving linear systems.
9)	System of Nonlinear Equations (Newton’s Method)
10)	Interpolation and Polynomial Approximation. Introduction to Interpolation. Lagrange Approximation.
11)	Newton Interpolation Polynomials. Piecewise Linear Interpolation, Cubic Spline Functions
12)	Curve Fitting (Applications from heat transfer and electrical engineering). Least-Squares Approximation. Linearization of Nonlinear Relationships.
13)	Eigenvalues and Eigenvectors. The power method
14)	Singular Value decomposition. Applications from Image Processing

Sources

Course Notes / Textbooks:

Stephen C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists, 3rd Edition, McGrawHill

References:

• J. Douglas Faires and Richard L. Burden, Numerical Methods, Brooks/Cole Publishing Co., 4th Edition, 2013.
• Applied Numerical Methods Using MATLAB, Won Young Yang, Wenwu Cao, Tae-Sang Chung, John Morris.
• John H. Mathews and Kurtis D. Fink Numerical Methods Using MATLAB, Pearson, 2004. ISBN 0-13-191178-3
• Mustafa Bayram, Nümerik Analiz, Sürat Üniversite Yayınları, 3. Baskı, 2013.
• İrfan Karagöz, Sayısal Analiz ve Mühendislik Uygulamaları, Nobel Yayın Dağıtım, ISBN: 978-605-395-077-6.
• Ömer Akın, Nümerik Analiz, Ankara Üniversitesi Basımevi, 1998, ISBN: 975-482-448-7

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	3	% 10
Homework Assignments	1	% 10
Midterms	1	% 35
Final	1	% 45
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 55
PERCENTAGE OF FINAL WORK		% 45
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	2	28
Laboratory	14	2	28
Study Hours Out of Class	14	2	28
Homework Assignments	1	4	4
Quizzes	3	1	3
Midterms	1	2	2
Final	1	2	2
Total Workload			95

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics	5
2)	To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods,	5
3)	To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials,	4
4)	To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,	4
5)	To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way,	4
6)	To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,	4
7)	To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,	4
8)	To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,	4
9)	By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,	4
10)	To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning,	3
11)	To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school,	3
12)	To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.	3