# ITGS219 : Numerical analysis

### Department

Department of Information Systems

Bachelor in Information Systems

General

03

ITMM122

### Overview

This course is a programming course; students need to implement all discussed topics by any programming language in class per class fashion.This course include these topics: Introduction to error analysis, root finding methods for non-linear equations (interval halving, false position), Newton’s method, definition of interpolation, Newton’s-Gregory interpolation, central interpolation (Gauss forward and backward, Bessel, Stirling), Least square approximation, Spline curves, Numerical differentiation, Numerical integration (Trapezoidal method, Simpson's), Numerical solution of ordinary differential equations (Taylor’s series method), Euler method, Runge-Kutta method.

### Knowledge and understanding

• That the student recognize the errors in the numerical solution and measure the error
• To familiarize the student with series and how to use them in numerical methods
• That the student remember the appropriate formulation of the law for solving a problem and how to formulate the solution in the form of an algorithm
• That the student draws a function curve and knows the limits, periods, and operations that are based on functions

### mental skills

• That the student recognize the errors in the numerical solution and measure the error
• To familiarize the student with series and how to use them in numerical methods
• That the student remember the appropriate formulation of the law for solving a problem and how to formulate the solution in the form of an algorithm
• That the student draws a function curve and knows the limits, periods, and operations that are based on functions

### Practical and professional skills

• The ability to solve mathematical problems in: calculus, integration, differential equations, systems of linear equations, find approximate solutions to nonlinear equations using numerical methods and study their accuracy and the possibility of improvement.
• The ability to write an algorithm for the numerical method to solve a given problem
• The ability to write a program for the numerical method to solve a specific problem
• The student should use ready-made software such as a programming language or Math Lab to solve numerical problems
• Work independently to complete weekly assignments and exercises

### General and transferable skills

• The ability to solve mathematical problems in: calculus, integration, differential equations, systems of linear equations, finding approximate solutions to nonlinear equations using numerical methods and studying their accuracy and the possibility of improving them using ready-made software.
• Solve examples and problems on the topic in question
• The ability to use the computer and the Internet to search for a solution to a specific problem or a similar previous study
• Editorial communication through presentations and assignments on a specific topic assigned to the student.

### Teaching and learning methods

• Lectures
• Tutorials
• Problem-based learning
• Mini-projects

### Methods of assessments

• Written test (midterm) = 25
• Written test (final) = 25
• Scientific activities = 15
• Discussions = 10

### Course contents

• Introduction
• Introduction to error analysis and sources of error
• Measuring Errors - Sources of Error - Binary Representation - Floating Pt Representation
• Propagation of Errors - Taylor Theorem Revisit
• Introduction to Matlab and Solving Equations Vectors, Functions, and Plots in Matlab
• Matlab Programs
• Non linear equations – root finding (interval halving, false position, Bisection Method, Newton’s Method, Secant Method).
• Interpolation (definition of interpolation , Gauss forward and backward)
• Interpolation and Polynomial Approximation
• Lagrange Polynomial , Divided Differences
• Least square approximation
• Numerical differentiation – solution of ordinary differential equations (Taylor's series method, Euler method, runge-kutta method).
• Numerical integration ( trapezoidal method , Simpson's method).
• Linear system (Jacobi Method, Gaussian Elimination,)