PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 230	NUMERICAL ANALYSIS	3 + 0	6th Semester	5

COURSE DESCRIPTION

Course Level	Bachelor's Degree
Course Type	Elective
Course Objective	Learning basic methods of numerical analysis in detail, grasping the algorithms needed for implementation of numerical methods on a computer, making contribution to algebraic and analytical methods.
Course Content	Mathematical preliminaries: Taylor’s theorem, order of convergence, difference equations / Computer arithmetic: representations of numbers, absolute and relative error, errors and their sources, significant digits / Solutions of nonlinear equations: Bisection method, Newton’s method, Secant method, Fixed point iteration, Zeros of polynomials / Interpolation: Polinomial interpolation, Divided differences, Equispaced interpolation, Inverse interpolation, Extrapolation, Curve fitting / Solutions of linear systems of equations, Matrix algebra, direct methods, iterative techniques, Numerical integration.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.
Mode of Delivery	Face to Face

COURSE LEARNING OUTCOMES

1	Who has knowledge about general concepts of numerical analysis.
2	Who has knowledge about computer arithmetic and numerical errors.
3	Who learns various methods for the solutions of linear and nonlinear equations.
4	Who learns various iteration methods.
5	Who has knowledges about curve fitting.
6	Who learns numerical integral.
7	Who learns how to use numerical analysis in computer programs.

COURSE'S CONTRIBUTION TO PROGRAM

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	4	56
Mid-terms	1	12	12
Final examination	1	20	20
Total Work Load ECTS Credit of the Course			130 5

COURSE DETAILS

Select Year

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester
MAT 230	NUMERICAL ANALYSIS	3 + 0	1	Turkish	2021-2022 Summer

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. ALİ FİLİZ	alifiliz@pau.edu.tr		MUH A0012 MUH B0130	%

Goals		Learning basic methods of numerical analysis in detail, grasping the algorithms needed for implementation of numerical methods on a computer, making contribution to algebraic and analytical methods.
Content		Mathematical preliminaries: Taylor’s theorem, order of convergence, difference equations / Computer arithmetic: representations of numbers, absolute and relative error, errors and their sources, significant digits / Solutions of nonlinear equations: Bisection method, Newton’s method, Secant method, Fixed point iteration, Zeros of polynomials / Interpolation: Polinomial interpolation, Divided differences, Equispaced interpolation, Inverse interpolation, Extrapolation, Curve fitting / Solutions of linear systems of equations, Matrix algebra, direct methods, iterative techniques, Numerical integration.

Topics

Weeks	Topics
1	Fundamental Definitions and Theorems Machine Numbers Errors Arithmetical Process and Error Accumulation
2	Approximate Calculation of Equations with one Variable Bisection Method Regula Falsi Method
3	Changed Regula Falsi Method Newton-Raphson Method Secant Method
4	Fixed Point Iteration Convergence Rate of Fixed Point Zeros of Polynomial and Muller Method
5	Interpolation Theory Taylor Polynomial Interpolation and Lagrange Polynomial
6	Iterative Interpolation Divided Differences Numerical Derivative
7	Midterm Exam
8	Numerical Integral Matrices and Other Process related to Matrices Linear Equation Systems
9	Gauss’s Elimination Method Gauss-Jordan Method Pivot Application
10	L.U. Decomposition Method Cholesky Method Jacobi Iteration Method
11	Gauss-Seidel Iteration Method Eigenvalue and Eigenvector Force and Iteration Method
12	QR Factorization Method Curve Fitting
13	The Least Squares Method Multivariate Regression
14	Orthogonal Polynomial and The Least Squares Method Curve Fitting by Trigonometrically Functions

Materials

Materials are not specified.

Resources

Resources	Resources Language
1- Numerical Methods for Mathematics, Science, and Engineering, 2nd Edition, John H. Mathews, Prentice Hall International Edition, 1992.	English
2- Numerical Analysis, Brooks/Cole, 7th Edition, Richard L. Burden, J. Douglas Faires, 2001	English

Course Assessment

Assesment Methods	Percentage (%)	Assesment Methods Title
Final Exam	60	Final Exam
Midterm Exam	40	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student