ITGS219 : Numerical analysis

Department

Department of Software Engineering

Academic Program

Bachelor in Software Engineering

Type

General

Credits

Prerequisite

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.

Intended learning outcomes

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,)

Networks Programming (ITSE405)
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Cryptographic Algorithms and Protocols (ITSE306)
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Mobile Operating System (ITSE308)
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Introduction to Networking (ITGS215)
Introduction to Statistics (ITST211)
Object Oriented Programmin (ITGS211)
Introduction to Software Engineering (ITGS213)
Discrete Structures (ITGS217)
Numerical analysis (ITGS219)
Introduction to Databases (ITGS228)
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Foundation of Information Systems (ITGS222)
Introduction to Internet Programming (ITGS226)
Computer Architucture & Organization (ITGS223)
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IT Project Management (ITGS303)
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