COURSE SYLLABUS

NUMERICAL ANALYSIS

1	Course Title:	NUMERICAL ANALYSIS
2	Course Code:	MAT3044
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	3
6	Semester:	6
7	ECTS Credits Allocated:	5
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. SEZAYİ HIZLIYEL
16	Course Lecturers:	Doç. Dr. Yeşim Sağlam ÖZKAN
17	Contactinformation of the Course Coordinator:	hizliyel@uludag.edu.tr Tel:(0224)2941765 Bursa Uludağ Ünv. Fen Ed. Fakültesi Matematik Bölümü Görükle Yerleşkesi 16059 Bursa-Türkiye
18	Website:
19	Objective of the Course:	The aim of the course is the design and analysis of techniques to give approximate but accurate solutions to hard problems
20	Contribution of the Course to Professional Development	Gain analytical thinking and problem solving skills

Learning Outcomes:

1	understand IEEE standard binary floating point format, machine precision and computer errors;
2	use Newton's method, Newton-Raphson's method, or the secant method to solve the equation f(x)=0 within the given tolerance;
3	use polynomial interpolations, including the Lagrange polynomial, the Hermit polynomial and cubic spline functions, for curve fitting, or data analysis; use, Newton's divided difference or cubic spline algorithms to evaluate the interpolations;;
4	difference formulas to calculate the approximate derivatives of functions and uses Lagrange polynominal approach to estimate errors;
5	external estimation method calculates numerical derivatives;
6	using the method of Romberg, Simson and Gauss calculates the numerical integration and determines the numerical error;
7	Solutions for non-linear systems of equations uses Newton Raphson method and fixed-point iteration;
8	write numerical programs, such as Matlab programs, to solve the above problems;

22	Course Content:

Week	Theoretical	Practical
1	Error varieties, Arithmetic error analysis, some basic mathematical information
2	operators and types (forward, backward, expansion, etc.)
3	Approximate calculation of the roots of equations in one variable (Regula Falsi, Cutting, Newton-Raphson method)
4	Approximate calculation of the roots of equations in one variable (Adjusted Regula Falsi, Corrected Newton Raphson, etc.).
5	Interpolation and Lagrange interpolation polynomials
6	Finite difference calculation, founded on the finite difference backward difference interpolation, advanced notice of Stirling, Everet, and Gaussian interpolasyon
7	General problem-solving
8	Repeating courses and midterm exam
9	Numerical differentiation and error, analytical methods of substitution numerical differential calculus, exterior derivative estimation method
10	Introduction to Numerical integrals, integral calculus with the help of Newton's interpolation (trapezoid, rectangle, etc.).
11	Romberg, Simson and Gauss numerical integral calculation method and the numerical error
12	Newton Raphson method for the solution of non-linear systems of equations
13	Solutions of systems of nonlinear equations with fixed point iteration
14	Matrices and matrix algebra

23	Textbooks, References and/or Other Materials:	1. Prof.Dr. Ömer AKIN, Nümerik Analiz, Ankara Üniversitesi Fen-Fak. Ders Kitapları, 1998, Ankara. 2. Doç.Dr. Mustafa Bayram, Nümerik Analiz, Aktif yayınevi, 2002.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course	Success is evaluated with 1 midterm and 1 YYSS according to the content of the course.
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High