| Course Name: | NUMERICAL ANALYSIS I |
| Course Code: | MATH 375 |
| Type of Course: | Undefined |
| Level of Course: | Undergraduate (First Cycle) |
| Year of Study: | 3 |
| Semester/Trimester: | Fall |
| ECTS Credits: | 5 |
| FU Credits: | 3 |
| Name(s) of Lecturer(s): | Abdullah Said ERDOÐAN A-335 ( aserdogan@fatih.edu.tr )
Allaberen ASHYRALYEV A-322 ( aashyr@fatih.edu.tr ) |
| Course Coordinator: | Abdullah Said ERDOÐAN |
| Objectives of the Course: | Binary Numbers. Error analysis. Solving systems of linear equations: Gaussian Elimination, modification Gaussian Elimination and L-U decomposition. Solutions of nonlinear equations and systems: Bisection, Newton’s, secant and fixed-point iteration methods. Interpolation: Lagrange Approximation, Newton’s Polynomials and Polynomial Approximation. Curve Fitting. Numerical Differentiation. Numerical Integration. Numerical Optimization. Numerical Solutions of the initial value and boundary value problems: Euler’s, Heun’s, Taylor’s, Runge-Kutta Methods. |
| Course Description: | Binary Numbers. Error analysis. Solving systems of linear equations: Gaussian Elimination, modification Gaussian Elimination and L-U decomposition. Solutions of nonlinear equations and systems: Bisection, Newton's, secant and fixed-point iteration methods. Interpolation: Lagrange Approximation, Newton's Polynomials and Polynomial Approximation. Curve Fitting. Numerical Differentiation. Numerical Integration. Numerical Optimization. Numerical Solutions of the initial value and boundary value problems: Euler's, Heun's, Taylor's, Runge-Kutta Methods.
|
| Learning Outcomes: | 1. Students will overcome physical and mechanical problems.
2. Students will analyze numerical methods. |
| Mode of Delivery: | Face-to-Face |
| Prerequisites: | None |
| Co-requisites: | None |
Course Contents:
( Weekly Lecture Plan ) | | Week | Topics | | 1 | Binary Numbers | | 2 | Error analysis | | 3 | Solving equations x=g(x).Bracketing Method, Newton’s, Secant and Fixed-Point Iteration Methods | | 4 | Aitken’s Process and Steffensen’s and Muller’ Methods | | 5 | Iteration for Nonlinear Systems | | 6 | Newton’s Method for Nonlinear Systems | | 7 | Solutions of systems of linear equations. Gaussian Elimination and L-U decomposition | | 8 | Solutions of systems of linear equations. Modification Gaussian Elimination Method | | 9 | Lagrange Polynomials | | 10 | Newton Polynomials and Polynomial Approximation | | 11 | Least-squares line. Curve fitting | | 12 | Numerical Differentiation and Numerical Integration | | 13 | Numerical Optimization | | 14 | Numerical Solutions of the initial value and boundary value problems: Euler’s, Heun’s, Taylor’s Methods, Runge-Kutta Methods |
|
| Recommended Reading: | John H.Mathews, Numerical Methods using Matlab, Prentice-Hall International, 2004 |
| Planned Learning Activities and Teaching Methods: | Lectures |
| Assessment Methods: |
| Method | Quantity |
(%) | | Homework | 1 | 15 | | Midterm Exam(s) | 1 | 35 | | Final Exam | 1 | 50 | |
| Language of Instruction: | English |
| Work Placement(s): | N/A |
syllabus
